id	sid	tid	token	lemma	pos
ejpam-3049	1	1	european	european	PROPN
ejpam-3049	1	2	journal	journal	PROPN
ejpam-3049	1	3	of	of	ADP
ejpam-3049	1	4	pure	pure	ADJ
ejpam-3049	1	5	and	and	CCONJ
ejpam-3049	1	6	applied	apply	VERB
ejpam-3049	1	7	mathematics	mathematic	NOUN
ejpam-3049	1	8	vol	vol	NOUN
ejpam-3049	1	9	.	.	PROPN
ejpam-3049	2	1	10	10	NUM
ejpam-3049	2	2	,	,	PUNCT
ejpam-3049	2	3	no	no	INTJ
ejpam-3049	2	4	.	.	NOUN
ejpam-3049	2	5	5	5	NUM
ejpam-3049	2	6	,	,	PUNCT
ejpam-3049	2	7	2017	2017	NUM
ejpam-3049	2	8	,	,	PUNCT
ejpam-3049	2	9	929	929	NUM
ejpam-3049	2	10	-	-	SYM
ejpam-3049	2	11	945	945	NUM
ejpam-3049	2	12	issn	issn	PROPN
ejpam-3049	2	13	1307	1307	NUM
ejpam-3049	2	14	-	-	SYM
ejpam-3049	2	15	5543	5543	NUM
ejpam-3049	2	16	–	–	PUNCT
ejpam-3049	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3049	2	18	published	publish	VERB
ejpam-3049	2	19	by	by	ADP
ejpam-3049	2	20	new	new	PROPN
ejpam-3049	2	21	york	york	PROPN
ejpam-3049	2	22	business	business	PROPN
ejpam-3049	2	23	global	global	ADJ
ejpam-3049	2	24	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	2	25	and	and	CCONJ
ejpam-3049	2	26	fuzzy	fuzzy	ADJ
ejpam-3049	2	27	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	2	28	niovi	niovi	PROPN
ejpam-3049	2	29	kehayopulu	kehayopulu	PROPN
ejpam-3049	2	30	university	university	PROPN
ejpam-3049	2	31	of	of	ADP
ejpam-3049	2	32	athens	athens	PROPN
ejpam-3049	2	33	,	,	PUNCT
ejpam-3049	2	34	department	department	NOUN
ejpam-3049	2	35	of	of	ADP
ejpam-3049	2	36	mathematics	mathematic	NOUN
ejpam-3049	2	37	,	,	PUNCT
ejpam-3049	2	38	15784	15784	NUM
ejpam-3049	2	39	panepistimiopolis	panepistimiopolis	PROPN
ejpam-3049	2	40	,	,	PUNCT
ejpam-3049	2	41	greece	greece	PROPN
ejpam-3049	2	42	abstract	abstract	PROPN
ejpam-3049	2	43	.	.	PUNCT
ejpam-3049	3	1	the	the	DET
ejpam-3049	3	2	aim	aim	NOUN
ejpam-3049	3	3	is	be	AUX
ejpam-3049	3	4	to	to	PART
ejpam-3049	3	5	show	show	VERB
ejpam-3049	3	6	that	that	SCONJ
ejpam-3049	3	7	the	the	DET
ejpam-3049	3	8	theory	theory	NOUN
ejpam-3049	3	9	of	of	ADP
ejpam-3049	3	10	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	3	11	and	and	CCONJ
ejpam-3049	3	12	the	the	DET
ejpam-3049	3	13	theory	theory	NOUN
ejpam-3049	3	14	of	of	ADP
ejpam-3049	3	15	fuzzy	fuzzy	ADJ
ejpam-3049	3	16	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	3	17	are	be	AUX
ejpam-3049	3	18	parallel	parallel	ADJ
ejpam-3049	3	19	to	to	ADP
ejpam-3049	3	20	each	each	DET
ejpam-3049	3	21	other	other	ADJ
ejpam-3049	3	22	,	,	PUNCT
ejpam-3049	3	23	in	in	ADP
ejpam-3049	3	24	the	the	DET
ejpam-3049	3	25	following	follow	VERB
ejpam-3049	3	26	sense	sense	NOUN
ejpam-3049	3	27	:	:	PUNCT
ejpam-3049	3	28	an	an	DET
ejpam-3049	3	29	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	3	30	h	h	NOUN
ejpam-3049	3	31	is	be	AUX
ejpam-3049	3	32	intra	intra	ADJ
ejpam-3049	3	33	-	-	ADJ
ejpam-3049	3	34	regular	regular	ADJ
ejpam-3049	3	35	,	,	PUNCT
ejpam-3049	3	36	for	for	ADP
ejpam-3049	3	37	example	example	NOUN
ejpam-3049	3	38	,	,	PUNCT
ejpam-3049	3	39	if	if	SCONJ
ejpam-3049	3	40	and	and	CCONJ
ejpam-3049	3	41	only	only	ADV
ejpam-3049	3	42	if	if	SCONJ
ejpam-3049	3	43	a∩b	a∩b	PROPN
ejpam-3049	3	44	⊆	⊆	NUM
ejpam-3049	3	45	b∗a	b∗a	PROPN
ejpam-3049	3	46	for	for	ADP
ejpam-3049	3	47	every	every	DET
ejpam-3049	3	48	right	right	ADJ
ejpam-3049	3	49	ideal	ideal	NOUN
ejpam-3049	3	50	a	a	PRON
ejpam-3049	3	51	and	and	CCONJ
ejpam-3049	3	52	every	every	PRON
ejpam-3049	3	53	left	leave	VERB
ejpam-3049	3	54	ideal	ideal	PROPN
ejpam-3049	3	55	b	b	PROPN
ejpam-3049	3	56	of	of	ADP
ejpam-3049	3	57	h.	h.	PROPN
ejpam-3049	3	58	and	and	CCONJ
ejpam-3049	3	59	an	an	DET
ejpam-3049	3	60	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	3	61	h	h	NOUN
ejpam-3049	3	62	is	be	AUX
ejpam-3049	3	63	intra	intra	ADJ
ejpam-3049	3	64	-	-	ADJ
ejpam-3049	3	65	regular	regular	ADJ
ejpam-3049	3	66	if	if	SCONJ
ejpam-3049	3	67	and	and	CCONJ
ejpam-3049	3	68	only	only	ADV
ejpam-3049	3	69	if	if	SCONJ
ejpam-3049	3	70	f	f	PROPN
ejpam-3049	3	71	∧g	∧g	PROPN
ejpam-3049	3	72	�	�	PROPN
ejpam-3049	3	73	g	g	PROPN
ejpam-3049	3	74	◦	◦	NOUN
ejpam-3049	3	75	f	f	NOUN
ejpam-3049	3	76	for	for	ADP
ejpam-3049	3	77	every	every	DET
ejpam-3049	3	78	fuzzy	fuzzy	ADJ
ejpam-3049	3	79	right	right	ADJ
ejpam-3049	3	80	ideal	ideal	NOUN
ejpam-3049	3	81	f	f	PROPN
ejpam-3049	3	82	and	and	CCONJ
ejpam-3049	3	83	every	every	DET
ejpam-3049	3	84	fuzzy	fuzzy	ADJ
ejpam-3049	3	85	left	leave	VERB
ejpam-3049	3	86	ideal	ideal	NOUN
ejpam-3049	3	87	g	g	PROPN
ejpam-3049	3	88	of	of	ADP
ejpam-3049	3	89	h.	h.	PROPN
ejpam-3049	4	1	an	an	DET
ejpam-3049	4	2	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	4	3	h	h	NOUN
ejpam-3049	4	4	is	be	AUX
ejpam-3049	4	5	left	leave	VERB
ejpam-3049	4	6	quasi	quasi	ADJ
ejpam-3049	4	7	-	-	ADJ
ejpam-3049	4	8	regular	regular	ADJ
ejpam-3049	4	9	if	if	SCONJ
ejpam-3049	5	1	and	and	CCONJ
ejpam-3049	5	2	only	only	ADV
ejpam-3049	5	3	if	if	SCONJ
ejpam-3049	5	4	a∩b	a∩b	PROPN
ejpam-3049	5	5	⊆	⊆	NUM
ejpam-3049	5	6	a	a	DET
ejpam-3049	5	7	∗b	∗b	NOUN
ejpam-3049	5	8	for	for	ADP
ejpam-3049	5	9	every	every	DET
ejpam-3049	5	10	ideal	ideal	NOUN
ejpam-3049	5	11	a	a	PRON
ejpam-3049	5	12	and	and	CCONJ
ejpam-3049	5	13	every	every	PRON
ejpam-3049	5	14	nonempty	nonempty	NOUN
ejpam-3049	5	15	subset	subset	VERB
ejpam-3049	5	16	b	b	PROPN
ejpam-3049	5	17	of	of	ADP
ejpam-3049	5	18	h.	h.	PROPN
ejpam-3049	5	19	and	and	CCONJ
ejpam-3049	5	20	an	an	DET
ejpam-3049	5	21	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	5	22	h	h	NOUN
ejpam-3049	5	23	is	be	AUX
ejpam-3049	5	24	left	leave	VERB
ejpam-3049	5	25	quasi	quasi	ADJ
ejpam-3049	5	26	-	-	ADJ
ejpam-3049	5	27	regular	regular	ADJ
ejpam-3049	5	28	if	if	SCONJ
ejpam-3049	6	1	and	and	CCONJ
ejpam-3049	6	2	only	only	ADV
ejpam-3049	6	3	if	if	SCONJ
ejpam-3049	6	4	f	f	PROPN
ejpam-3049	6	5	∧	∧	PROPN
ejpam-3049	6	6	g	g	PROPN
ejpam-3049	6	7	�	�	PROPN
ejpam-3049	6	8	f	f	PROPN
ejpam-3049	6	9	◦	◦	VERB
ejpam-3049	6	10	g	g	NOUN
ejpam-3049	6	11	for	for	ADP
ejpam-3049	6	12	every	every	DET
ejpam-3049	6	13	fuzzy	fuzzy	ADJ
ejpam-3049	6	14	ideal	ideal	NOUN
ejpam-3049	6	15	f	f	PROPN
ejpam-3049	6	16	and	and	CCONJ
ejpam-3049	6	17	every	every	DET
ejpam-3049	6	18	fuzzy	fuzzy	NOUN
ejpam-3049	6	19	subset	subset	VERB
ejpam-3049	6	20	g	g	PROPN
ejpam-3049	6	21	of	of	ADP
ejpam-3049	6	22	h.	h.	PROPN
ejpam-3049	6	23	2010	2010	NUM
ejpam-3049	6	24	mathematics	mathematics	PROPN
ejpam-3049	6	25	subject	subject	NOUN
ejpam-3049	6	26	classifications	classification	NOUN
ejpam-3049	6	27	:	:	PUNCT
ejpam-3049	6	28	ams	am	NOUN
ejpam-3049	6	29	20m99	20m99	NUM
ejpam-3049	6	30	,	,	PUNCT
ejpam-3049	6	31	08a72	08a72	NOUN
ejpam-3049	6	32	key	key	ADJ
ejpam-3049	6	33	words	word	NOUN
ejpam-3049	6	34	and	and	CCONJ
ejpam-3049	6	35	phrases	phrase	NOUN
ejpam-3049	6	36	:	:	PUNCT
ejpam-3049	6	37	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	6	38	,	,	PUNCT
ejpam-3049	6	39	right	right	INTJ
ejpam-3049	6	40	(	(	PUNCT
ejpam-3049	6	41	left	left	ADJ
ejpam-3049	6	42	)	)	PUNCT
ejpam-3049	6	43	ideal	ideal	ADJ
ejpam-3049	6	44	,	,	PUNCT
ejpam-3049	6	45	bi	bi	NOUN
ejpam-3049	6	46	-	-	ADJ
ejpam-3049	6	47	ideal	ideal	ADJ
ejpam-3049	6	48	,	,	PUNCT
ejpam-3049	6	49	fuzzy	fuzzy	ADJ
ejpam-3049	6	50	right	right	INTJ
ejpam-3049	6	51	(	(	PUNCT
ejpam-3049	6	52	left	left	ADJ
ejpam-3049	6	53	)	)	PUNCT
ejpam-3049	6	54	ideal	ideal	ADJ
ejpam-3049	6	55	,	,	PUNCT
ejpam-3049	6	56	fuzzy	fuzzy	ADJ
ejpam-3049	6	57	bi	bi	NOUN
ejpam-3049	6	58	-	-	ADJ
ejpam-3049	6	59	ideal	ideal	ADJ
ejpam-3049	6	60	,	,	PUNCT
ejpam-3049	6	61	regular	regular	ADJ
ejpam-3049	6	62	,	,	PUNCT
ejpam-3049	6	63	intra	intra	ADJ
ejpam-3049	6	64	-	-	ADJ
ejpam-3049	6	65	regular	regular	ADJ
ejpam-3049	6	66	,	,	PUNCT
ejpam-3049	6	67	left	leave	VERB
ejpam-3049	6	68	(	(	PUNCT
ejpam-3049	6	69	right	right	ADJ
ejpam-3049	6	70	)	)	PUNCT
ejpam-3049	6	71	quasi	quasi	ADJ
ejpam-3049	6	72	-	-	ADJ
ejpam-3049	6	73	regular	regular	ADJ
ejpam-3049	6	74	,	,	PUNCT
ejpam-3049	6	75	semisimple	semisimple	NOUN
ejpam-3049	6	76	1	1	NUM
ejpam-3049	6	77	.	.	PUNCT
ejpam-3049	6	78	introduction	introduction	NOUN
ejpam-3049	6	79	and	and	CCONJ
ejpam-3049	6	80	prerequisites	prerequisite	VERB
ejpam-3049	6	81	a	a	DET
ejpam-3049	6	82	semigroup	semigroup	NOUN
ejpam-3049	6	83	(	(	PUNCT
ejpam-3049	6	84	s	s	PROPN
ejpam-3049	6	85	,	,	PUNCT
ejpam-3049	6	86	·	·	PUNCT
ejpam-3049	6	87	)	)	PUNCT
ejpam-3049	6	88	is	be	AUX
ejpam-3049	6	89	called	call	VERB
ejpam-3049	6	90	regular	regular	ADJ
ejpam-3049	6	91	(	(	PUNCT
ejpam-3049	6	92	von	von	PROPN
ejpam-3049	6	93	neumann	neumann	PROPN
ejpam-3049	6	94	regular	regular	PROPN
ejpam-3049	6	95	)	)	PUNCT
ejpam-3049	6	96	if	if	SCONJ
ejpam-3049	6	97	for	for	ADP
ejpam-3049	6	98	every	every	DET
ejpam-3049	6	99	a	a	DET
ejpam-3049	6	100	∈	∈	NOUN
ejpam-3049	6	101	s	s	VERB
ejpam-3049	6	102	there	there	PRON
ejpam-3049	6	103	exists	exist	VERB
ejpam-3049	6	104	x	x	X
ejpam-3049	6	105	∈	∈	NOUN
ejpam-3049	6	106	s	s	VERB
ejpam-3049	6	107	such	such	ADJ
ejpam-3049	6	108	that	that	SCONJ
ejpam-3049	6	109	a	a	DET
ejpam-3049	6	110	=	=	X
ejpam-3049	6	111	axa	axa	NOUN
ejpam-3049	6	112	.	.	PUNCT
ejpam-3049	7	1	this	this	PRON
ejpam-3049	7	2	is	be	AUX
ejpam-3049	7	3	equivalent	equivalent	ADJ
ejpam-3049	7	4	to	to	ADP
ejpam-3049	7	5	saying	say	VERB
ejpam-3049	7	6	that	that	SCONJ
ejpam-3049	7	7	a	a	DET
ejpam-3049	7	8	∈	∈	PROPN
ejpam-3049	7	9	asa	asa	PROPN
ejpam-3049	7	10	for	for	ADP
ejpam-3049	7	11	every	every	DET
ejpam-3049	7	12	a	a	DET
ejpam-3049	7	13	∈	∈	PROPN
ejpam-3049	7	14	s	s	NOUN
ejpam-3049	7	15	or	or	CCONJ
ejpam-3049	7	16	a	a	DET
ejpam-3049	7	17	⊆	⊆	NUM
ejpam-3049	7	18	asa	asa	PROPN
ejpam-3049	7	19	for	for	ADP
ejpam-3049	7	20	every	every	DET
ejpam-3049	7	21	a	a	DET
ejpam-3049	7	22	⊆	⊆	NUM
ejpam-3049	7	23	s.	s.	PROPN
ejpam-3049	7	24	a	a	DET
ejpam-3049	7	25	nonempty	nonempty	NOUN
ejpam-3049	7	26	subset	subset	VERB
ejpam-3049	7	27	a	a	PRON
ejpam-3049	7	28	of	of	ADP
ejpam-3049	7	29	a	a	DET
ejpam-3049	7	30	groupoid	groupoid	NOUN
ejpam-3049	7	31	(	(	PUNCT
ejpam-3049	7	32	s	s	PROPN
ejpam-3049	7	33	,	,	PUNCT
ejpam-3049	7	34	·	·	PUNCT
ejpam-3049	7	35	)	)	PUNCT
ejpam-3049	7	36	is	be	AUX
ejpam-3049	7	37	called	call	VERB
ejpam-3049	7	38	a	a	DET
ejpam-3049	7	39	right	right	NOUN
ejpam-3049	7	40	(	(	PUNCT
ejpam-3049	7	41	resp	resp	NOUN
ejpam-3049	7	42	.	.	PUNCT
ejpam-3049	8	1	left	left	ADJ
ejpam-3049	8	2	)	)	PUNCT
ejpam-3049	8	3	ideal	ideal	NOUN
ejpam-3049	8	4	of	of	ADP
ejpam-3049	8	5	s	s	PRON
ejpam-3049	8	6	if	if	SCONJ
ejpam-3049	8	7	as	as	ADP
ejpam-3049	8	8	⊆	⊆	NUM
ejpam-3049	8	9	a	a	DET
ejpam-3049	8	10	(	(	PUNCT
ejpam-3049	8	11	resp	resp	NOUN
ejpam-3049	8	12	.	.	PUNCT
ejpam-3049	9	1	sa	sa	PROPN
ejpam-3049	9	2	⊆	⊆	NUM
ejpam-3049	9	3	a	a	PRON
ejpam-3049	9	4	)	)	PUNCT
ejpam-3049	9	5	.	.	PUNCT
ejpam-3049	10	1	if	if	SCONJ
ejpam-3049	10	2	a	a	PRON
ejpam-3049	10	3	is	be	AUX
ejpam-3049	10	4	both	both	PRON
ejpam-3049	10	5	a	a	DET
ejpam-3049	10	6	right	right	NOUN
ejpam-3049	10	7	and	and	CCONJ
ejpam-3049	10	8	a	a	DET
ejpam-3049	10	9	left	left	ADJ
ejpam-3049	10	10	ideal	ideal	NOUN
ejpam-3049	10	11	of	of	ADP
ejpam-3049	10	12	s	s	PROPN
ejpam-3049	10	13	,	,	PUNCT
ejpam-3049	10	14	then	then	ADV
ejpam-3049	10	15	it	it	PRON
ejpam-3049	10	16	is	be	AUX
ejpam-3049	10	17	called	call	VERB
ejpam-3049	10	18	an	an	DET
ejpam-3049	10	19	ideal	ideal	NOUN
ejpam-3049	10	20	of	of	ADP
ejpam-3049	10	21	s.	s.	PROPN
ejpam-3049	10	22	a	a	DET
ejpam-3049	10	23	nonempty	nonempty	ADV
ejpam-3049	10	24	subset	subset	VERB
ejpam-3049	10	25	b	b	NOUN
ejpam-3049	10	26	of	of	ADP
ejpam-3049	10	27	a	a	DET
ejpam-3049	10	28	semigroup	semigroup	NOUN
ejpam-3049	10	29	(	(	PUNCT
ejpam-3049	10	30	s	s	PROPN
ejpam-3049	10	31	,	,	PUNCT
ejpam-3049	10	32	·	·	PUNCT
ejpam-3049	10	33	)	)	PUNCT
ejpam-3049	10	34	is	be	AUX
ejpam-3049	10	35	called	call	VERB
ejpam-3049	10	36	a	a	DET
ejpam-3049	10	37	bi	bi	NOUN
ejpam-3049	10	38	-	-	NOUN
ejpam-3049	10	39	ideal	ideal	NOUN
ejpam-3049	10	40	of	of	ADP
ejpam-3049	10	41	s	s	PRON
ejpam-3049	10	42	if	if	SCONJ
ejpam-3049	10	43	bsb	bsb	PROPN
ejpam-3049	10	44	⊆	⊆	NUM
ejpam-3049	10	45	b.	b.	PROPN
ejpam-3049	10	46	it	it	PRON
ejpam-3049	10	47	is	be	AUX
ejpam-3049	10	48	well	well	ADV
ejpam-3049	10	49	known	know	VERB
ejpam-3049	10	50	that	that	SCONJ
ejpam-3049	10	51	a	a	DET
ejpam-3049	10	52	semigroup	semigroup	NOUN
ejpam-3049	10	53	s	s	VERB
ejpam-3049	10	54	is	be	AUX
ejpam-3049	10	55	regular	regular	ADJ
ejpam-3049	10	56	if	if	SCONJ
ejpam-3049	11	1	and	and	CCONJ
ejpam-3049	11	2	only	only	ADV
ejpam-3049	11	3	if	if	SCONJ
ejpam-3049	11	4	for	for	ADP
ejpam-3049	11	5	every	every	DET
ejpam-3049	11	6	right	right	ADJ
ejpam-3049	11	7	ideal	ideal	NOUN
ejpam-3049	11	8	a	a	PRON
ejpam-3049	11	9	and	and	CCONJ
ejpam-3049	11	10	every	every	PRON
ejpam-3049	11	11	left	leave	VERB
ejpam-3049	11	12	ideal	ideal	NOUN
ejpam-3049	12	1	b	b	PROPN
ejpam-3049	13	1	if	if	SCONJ
ejpam-3049	13	2	s	s	VERB
ejpam-3049	13	3	,	,	PUNCT
ejpam-3049	13	4	we	we	PRON
ejpam-3049	13	5	have	have	VERB
ejpam-3049	13	6	a	a	DET
ejpam-3049	13	7	∩	∩	ADJ
ejpam-3049	13	8	b	b	NOUN
ejpam-3049	13	9	=	=	SYM
ejpam-3049	13	10	ab	ab	PROPN
ejpam-3049	13	11	(	(	PUNCT
ejpam-3049	13	12	iséki	iséki	PROPN
ejpam-3049	13	13	[	[	X
ejpam-3049	13	14	2	2	NUM
ejpam-3049	13	15	]	]	PUNCT
ejpam-3049	13	16	)	)	PUNCT
ejpam-3049	13	17	.	.	PUNCT
ejpam-3049	14	1	a	a	DET
ejpam-3049	14	2	semigroup	semigroup	NOUN
ejpam-3049	14	3	(	(	PUNCT
ejpam-3049	14	4	s	s	PROPN
ejpam-3049	14	5	,	,	PUNCT
ejpam-3049	14	6	·	·	PUNCT
ejpam-3049	14	7	)	)	PUNCT
ejpam-3049	14	8	is	be	AUX
ejpam-3049	14	9	called	call	VERB
ejpam-3049	14	10	intra	intra	ADJ
ejpam-3049	14	11	-	-	ADJ
ejpam-3049	14	12	regular	regular	ADJ
ejpam-3049	14	13	[	[	X
ejpam-3049	14	14	1	1	NUM
ejpam-3049	14	15	]	]	X
ejpam-3049	14	16	if	if	SCONJ
ejpam-3049	14	17	for	for	ADP
ejpam-3049	14	18	every	every	DET
ejpam-3049	14	19	a	a	DET
ejpam-3049	14	20	∈	∈	NOUN
ejpam-3049	14	21	s	s	VERB
ejpam-3049	14	22	there	there	PRON
ejpam-3049	14	23	exist	exist	VERB
ejpam-3049	14	24	x	x	NOUN
ejpam-3049	14	25	,	,	PUNCT
ejpam-3049	14	26	y	y	PROPN
ejpam-3049	14	27	∈	∈	PROPN
ejpam-3049	14	28	s	s	VERB
ejpam-3049	14	29	such	such	ADJ
ejpam-3049	14	30	that	that	SCONJ
ejpam-3049	14	31	a	a	DET
ejpam-3049	14	32	=	=	X
ejpam-3049	14	33	xa2y	xa2y	PROPN
ejpam-3049	14	34	.	.	PUNCT
ejpam-3049	15	1	this	this	PRON
ejpam-3049	15	2	is	be	AUX
ejpam-3049	15	3	equivalent	equivalent	ADJ
ejpam-3049	15	4	to	to	ADP
ejpam-3049	15	5	saying	say	VERB
ejpam-3049	15	6	that	that	SCONJ
ejpam-3049	15	7	a	a	DET
ejpam-3049	15	8	∈	∈	PROPN
ejpam-3049	15	9	sa2s	sa2s	NOUN
ejpam-3049	15	10	for	for	ADP
ejpam-3049	15	11	every	every	DET
ejpam-3049	15	12	a	a	DET
ejpam-3049	15	13	∈	∈	PROPN
ejpam-3049	15	14	s	s	NOUN
ejpam-3049	15	15	or	or	CCONJ
ejpam-3049	15	16	a	a	DET
ejpam-3049	15	17	⊆	⊆	NUM
ejpam-3049	15	18	sa2s	sa2s	NOUN
ejpam-3049	15	19	for	for	ADP
ejpam-3049	15	20	every	every	DET
ejpam-3049	15	21	a	a	DET
ejpam-3049	15	22	⊆	⊆	NUM
ejpam-3049	15	23	s.	s.	PROPN
ejpam-3049	15	24	it	it	PRON
ejpam-3049	15	25	is	be	AUX
ejpam-3049	15	26	also	also	ADV
ejpam-3049	15	27	well	well	ADV
ejpam-3049	15	28	known	know	VERB
ejpam-3049	15	29	that	that	SCONJ
ejpam-3049	15	30	a	a	DET
ejpam-3049	15	31	semigroup	semigroup	NOUN
ejpam-3049	15	32	s	s	VERB
ejpam-3049	15	33	is	be	AUX
ejpam-3049	15	34	intra	intra	ADJ
ejpam-3049	15	35	-	-	ADJ
ejpam-3049	15	36	regular	regular	ADJ
ejpam-3049	15	37	if	if	SCONJ
ejpam-3049	15	38	and	and	CCONJ
ejpam-3049	15	39	only	only	ADV
ejpam-3049	15	40	if	if	SCONJ
ejpam-3049	15	41	for	for	ADP
ejpam-3049	15	42	any	any	DET
ejpam-3049	15	43	right	right	ADJ
ejpam-3049	15	44	ideal	ideal	NOUN
ejpam-3049	15	45	a	a	PRON
ejpam-3049	15	46	and	and	CCONJ
ejpam-3049	15	47	any	any	DET
ejpam-3049	15	48	left	left	ADJ
ejpam-3049	15	49	ideal	ideal	NOUN
ejpam-3049	15	50	b	b	PROPN
ejpam-3049	15	51	of	of	ADP
ejpam-3049	15	52	s	s	PROPN
ejpam-3049	15	53	,	,	PUNCT
ejpam-3049	15	54	we	we	PRON
ejpam-3049	15	55	have	have	VERB
ejpam-3049	15	56	a	a	DET
ejpam-3049	15	57	∩	∩	ADJ
ejpam-3049	15	58	b	b	PROPN
ejpam-3049	15	59	⊆	⊆	NUM
ejpam-3049	15	60	ba	ba	PROPN
ejpam-3049	15	61	(	(	PUNCT
ejpam-3049	15	62	lajos	lajos	NOUN
ejpam-3049	15	63	and	and	CCONJ
ejpam-3049	15	64	szász	szász	NUM
ejpam-3049	16	1	[	[	X
ejpam-3049	16	2	9	9	NUM
ejpam-3049	16	3	]	]	PUNCT
ejpam-3049	16	4	)	)	PUNCT
ejpam-3049	16	5	.	.	PUNCT
ejpam-3049	17	1	for	for	ADP
ejpam-3049	17	2	the	the	DET
ejpam-3049	17	3	concepts	concept	NOUN
ejpam-3049	17	4	of	of	ADP
ejpam-3049	17	5	left	left	ADJ
ejpam-3049	17	6	(	(	PUNCT
ejpam-3049	17	7	right	right	ADJ
ejpam-3049	17	8	)	)	PUNCT
ejpam-3049	17	9	quasi	quasi	ADJ
ejpam-3049	17	10	-	-	ADJ
ejpam-3049	17	11	regular	regular	ADJ
ejpam-3049	17	12	and	and	CCONJ
ejpam-3049	17	13	semisimple	semisimple	ADJ
ejpam-3049	17	14	semigroups	semigroup	NOUN
ejpam-3049	17	15	we	we	PRON
ejpam-3049	17	16	refer	refer	VERB
ejpam-3049	17	17	to	to	ADP
ejpam-3049	17	18	[	[	X
ejpam-3049	17	19	11	11	NUM
ejpam-3049	17	20	]	]	SYM
ejpam-3049	17	21	:	:	PUNCT
ejpam-3049	17	22	a	a	DET
ejpam-3049	17	23	semigroup	semigroup	NOUN
ejpam-3049	17	24	s	s	VERB
ejpam-3049	17	25	is	be	AUX
ejpam-3049	17	26	called	call	VERB
ejpam-3049	17	27	left	left	ADJ
ejpam-3049	17	28	(	(	PUNCT
ejpam-3049	17	29	resp	resp	NOUN
ejpam-3049	17	30	.	.	PUNCT
ejpam-3049	18	1	right	right	ADJ
ejpam-3049	18	2	)	)	PUNCT
ejpam-3049	18	3	quasi	quasi	NOUN
ejpam-3049	18	4	-	-	ADJ
ejpam-3049	18	5	regular	regular	ADJ
ejpam-3049	18	6	if	if	SCONJ
ejpam-3049	18	7	for	for	ADP
ejpam-3049	18	8	every	every	DET
ejpam-3049	18	9	a	a	DET
ejpam-3049	18	10	∈	∈	NOUN
ejpam-3049	18	11	s	s	VERB
ejpam-3049	18	12	there	there	PRON
ejpam-3049	18	13	exist	exist	VERB
ejpam-3049	18	14	x	x	NOUN
ejpam-3049	18	15	,	,	PUNCT
ejpam-3049	18	16	y	y	PROPN
ejpam-3049	18	17	∈	∈	PROPN
ejpam-3049	18	18	s	s	VERB
ejpam-3049	18	19	such	such	ADJ
ejpam-3049	18	20	that	that	SCONJ
ejpam-3049	18	21	a	a	DET
ejpam-3049	18	22	=	=	SYM
ejpam-3049	18	23	xaya	xaya	PROPN
ejpam-3049	18	24	(	(	PUNCT
ejpam-3049	18	25	resp	resp	PROPN
ejpam-3049	18	26	.	.	PUNCT
ejpam-3049	19	1	a	a	DET
ejpam-3049	19	2	=	=	SYM
ejpam-3049	19	3	axay	axay	NOUN
ejpam-3049	19	4	)	)	PUNCT
ejpam-3049	19	5	.	.	PUNCT
ejpam-3049	20	1	we	we	PRON
ejpam-3049	20	2	remark	remark	VERB
ejpam-3049	20	3	that	that	SCONJ
ejpam-3049	20	4	a	a	DET
ejpam-3049	20	5	semigroup	semigroup	NOUN
ejpam-3049	20	6	s	s	PART
ejpam-3049	20	7	is	be	AUX
ejpam-3049	20	8	left	leave	VERB
ejpam-3049	20	9	(	(	PUNCT
ejpam-3049	20	10	resp	resp	NOUN
ejpam-3049	20	11	.	.	PUNCT
ejpam-3049	21	1	right	right	ADJ
ejpam-3049	21	2	)	)	PUNCT
ejpam-3049	21	3	quasi	quasi	NOUN
ejpam-3049	21	4	-	-	ADJ
ejpam-3049	21	5	regular	regular	ADJ
ejpam-3049	21	6	if	if	SCONJ
ejpam-3049	21	7	and	and	CCONJ
ejpam-3049	21	8	only	only	ADV
ejpam-3049	21	9	if	if	SCONJ
ejpam-3049	21	10	a	a	DET
ejpam-3049	21	11	∈	∈	PROPN
ejpam-3049	21	12	sasa	sasa	NOUN
ejpam-3049	21	13	(	(	PUNCT
ejpam-3049	21	14	resp	resp	NOUN
ejpam-3049	21	15	.	.	PUNCT
ejpam-3049	22	1	a	a	DET
ejpam-3049	22	2	∈	∈	PROPN
ejpam-3049	22	3	asas	asa	NOUN
ejpam-3049	22	4	)	)	PUNCT
ejpam-3049	22	5	for	for	ADP
ejpam-3049	22	6	every	every	DET
ejpam-3049	22	7	a	a	DET
ejpam-3049	22	8	∈	∈	PROPN
ejpam-3049	22	9	s	s	NOUN
ejpam-3049	22	10	,	,	PUNCT
ejpam-3049	22	11	equivalently	equivalently	ADV
ejpam-3049	22	12	if	if	SCONJ
ejpam-3049	22	13	a	a	DET
ejpam-3049	22	14	⊆	⊆	NUM
ejpam-3049	22	15	sasa	sasa	NOUN
ejpam-3049	22	16	(	(	PUNCT
ejpam-3049	22	17	resp	resp	NOUN
ejpam-3049	22	18	.	.	PUNCT
ejpam-3049	23	1	a	a	DET
ejpam-3049	23	2	⊆	⊆	NUM
ejpam-3049	23	3	asas	asa	NOUN
ejpam-3049	23	4	)	)	PUNCT
ejpam-3049	23	5	for	for	ADP
ejpam-3049	23	6	every	every	DET
ejpam-3049	23	7	a	a	DET
ejpam-3049	23	8	⊆	⊆	NUM
ejpam-3049	23	9	s.	s.	PROPN
ejpam-3049	23	10	a	a	DET
ejpam-3049	23	11	semigroup	semigroup	PROPN
ejpam-3049	23	12	s	s	VERB
ejpam-3049	23	13	is	be	AUX
ejpam-3049	23	14	called	call	VERB
ejpam-3049	23	15	semisimple	semisimple	NOUN
ejpam-3049	23	16	if	if	SCONJ
ejpam-3049	23	17	for	for	SCONJ
ejpam-3049	23	18	every	every	DET
ejpam-3049	23	19	a	a	DET
ejpam-3049	23	20	∈	∈	NOUN
ejpam-3049	23	21	s	s	VERB
ejpam-3049	23	22	there	there	PRON
ejpam-3049	23	23	exist	exist	VERB
ejpam-3049	23	24	x	x	NOUN
ejpam-3049	23	25	,	,	PUNCT
ejpam-3049	23	26	y	y	PROPN
ejpam-3049	23	27	,	,	PUNCT
ejpam-3049	23	28	z	z	PROPN
ejpam-3049	23	29	∈	∈	PROPN
ejpam-3049	23	30	s	s	VERB
ejpam-3049	23	31	such	such	ADJ
ejpam-3049	23	32	that	that	SCONJ
ejpam-3049	23	33	a	a	DET
ejpam-3049	23	34	=	=	SYM
ejpam-3049	23	35	xayaz	xayaz	PROPN
ejpam-3049	23	36	.	.	PUNCT
ejpam-3049	24	1	we	we	PRON
ejpam-3049	24	2	note	note	VERB
ejpam-3049	24	3	that	that	SCONJ
ejpam-3049	24	4	a	a	DET
ejpam-3049	24	5	semigroup	semigroup	NOUN
ejpam-3049	24	6	s	s	PART
ejpam-3049	24	7	is	be	AUX
ejpam-3049	24	8	email	email	NOUN
ejpam-3049	24	9	address	address	NOUN
ejpam-3049	24	10	:	:	PUNCT
ejpam-3049	24	11	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3049	24	12	(	(	PUNCT
ejpam-3049	24	13	n.	n.	PROPN
ejpam-3049	24	14	kehayopulu	kehayopulu	PROPN
ejpam-3049	24	15	)	)	PUNCT
ejpam-3049	24	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3049	25	1	929	929	NUM
ejpam-3049	25	2	c	c	X
ejpam-3049	25	3	©	©	PROPN
ejpam-3049	25	4	2017	2017	NUM
ejpam-3049	25	5	ejpam	ejpam	NOUN
ejpam-3049	25	6	all	all	DET
ejpam-3049	25	7	rights	right	NOUN
ejpam-3049	25	8	reserved	reserve	VERB
ejpam-3049	25	9	.	.	PUNCT
ejpam-3049	26	1	n.	n.	PROPN
ejpam-3049	26	2	kehayopulu	kehayopulu	PROPN
ejpam-3049	26	3	/	/	SYM
ejpam-3049	26	4	eur	eur	PROPN
ejpam-3049	26	5	.	.	PUNCT
ejpam-3049	27	1	j.	j.	PROPN
ejpam-3049	27	2	pure	pure	PROPN
ejpam-3049	27	3	appl	appl	PROPN
ejpam-3049	27	4	.	.	PROPN
ejpam-3049	27	5	math	math	PROPN
ejpam-3049	27	6	,	,	PUNCT
ejpam-3049	27	7	10	10	NUM
ejpam-3049	27	8	(	(	PUNCT
ejpam-3049	27	9	5	5	NUM
ejpam-3049	27	10	)	)	PUNCT
ejpam-3049	27	11	(	(	PUNCT
ejpam-3049	27	12	2017	2017	NUM
ejpam-3049	27	13	)	)	PUNCT
ejpam-3049	27	14	,	,	PUNCT
ejpam-3049	27	15	929	929	NUM
ejpam-3049	27	16	-	-	SYM
ejpam-3049	27	17	945	945	NUM
ejpam-3049	27	18	930	930	NUM
ejpam-3049	27	19	semisimple	semisimple	NOUN
ejpam-3049	27	20	if	if	SCONJ
ejpam-3049	27	21	and	and	CCONJ
ejpam-3049	27	22	only	only	ADV
ejpam-3049	27	23	if	if	SCONJ
ejpam-3049	27	24	a	a	DET
ejpam-3049	27	25	∈	∈	PROPN
ejpam-3049	27	26	sasas	sasas	NOUN
ejpam-3049	27	27	for	for	ADP
ejpam-3049	27	28	every	every	DET
ejpam-3049	27	29	a	a	DET
ejpam-3049	27	30	∈	∈	PROPN
ejpam-3049	27	31	s	s	NOUN
ejpam-3049	27	32	,	,	PUNCT
ejpam-3049	27	33	equivalently	equivalently	ADV
ejpam-3049	27	34	if	if	SCONJ
ejpam-3049	27	35	a	a	DET
ejpam-3049	27	36	⊆	⊆	NUM
ejpam-3049	27	37	sasas	sasas	NOUN
ejpam-3049	27	38	for	for	ADP
ejpam-3049	27	39	every	every	DET
ejpam-3049	27	40	a	a	DET
ejpam-3049	27	41	⊆	⊆	NUM
ejpam-3049	27	42	s.	s.	PROPN
ejpam-3049	27	43	in	in	ADP
ejpam-3049	27	44	the	the	DET
ejpam-3049	27	45	present	present	ADJ
ejpam-3049	27	46	paper	paper	NOUN
ejpam-3049	27	47	we	we	PRON
ejpam-3049	27	48	show	show	VERB
ejpam-3049	27	49	that	that	SCONJ
ejpam-3049	27	50	the	the	DET
ejpam-3049	27	51	theories	theory	NOUN
ejpam-3049	27	52	of	of	ADP
ejpam-3049	27	53	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	27	54	and	and	CCONJ
ejpam-3049	27	55	fuzzy	fuzzy	ADJ
ejpam-3049	27	56	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	27	57	are	be	AUX
ejpam-3049	27	58	parallel	parallel	ADJ
ejpam-3049	27	59	to	to	ADP
ejpam-3049	27	60	each	each	DET
ejpam-3049	27	61	other	other	ADJ
ejpam-3049	27	62	,	,	PUNCT
ejpam-3049	27	63	in	in	ADP
ejpam-3049	27	64	the	the	DET
ejpam-3049	27	65	following	follow	VERB
ejpam-3049	27	66	sense	sense	NOUN
ejpam-3049	27	67	:	:	PUNCT
ejpam-3049	27	68	an	an	DET
ejpam-3049	27	69	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	27	70	h	h	NOUN
ejpam-3049	27	71	is	be	AUX
ejpam-3049	27	72	regular	regular	ADJ
ejpam-3049	27	73	if	if	SCONJ
ejpam-3049	28	1	and	and	CCONJ
ejpam-3049	28	2	only	only	ADV
ejpam-3049	28	3	if	if	SCONJ
ejpam-3049	28	4	a	a	DET
ejpam-3049	28	5	∩	∩	ADJ
ejpam-3049	28	6	b	b	X
ejpam-3049	28	7	=	=	PUNCT
ejpam-3049	28	8	a	a	DET
ejpam-3049	28	9	∗	∗	NOUN
ejpam-3049	28	10	b	b	NOUN
ejpam-3049	28	11	,	,	PUNCT
ejpam-3049	28	12	equivalently	equivalently	ADV
ejpam-3049	28	13	if	if	SCONJ
ejpam-3049	28	14	a	a	DET
ejpam-3049	28	15	∩	∩	NOUN
ejpam-3049	28	16	b	b	NOUN
ejpam-3049	28	17	⊆	⊆	NUM
ejpam-3049	28	18	a	a	DET
ejpam-3049	28	19	∗	∗	NOUN
ejpam-3049	28	20	b	b	NOUN
ejpam-3049	28	21	for	for	ADP
ejpam-3049	28	22	every	every	DET
ejpam-3049	28	23	right	right	ADJ
ejpam-3049	28	24	ideal	ideal	NOUN
ejpam-3049	28	25	a	a	PRON
ejpam-3049	28	26	and	and	CCONJ
ejpam-3049	28	27	every	every	DET
ejpam-3049	28	28	left	leave	VERB
ejpam-3049	28	29	ideal	ideal	PROPN
ejpam-3049	28	30	b	b	PROPN
ejpam-3049	28	31	of	of	ADP
ejpam-3049	28	32	h.	h.	PROPN
ejpam-3049	28	33	on	on	ADP
ejpam-3049	28	34	the	the	DET
ejpam-3049	28	35	other	other	ADJ
ejpam-3049	28	36	hand	hand	NOUN
ejpam-3049	28	37	,	,	PUNCT
ejpam-3049	28	38	an	an	DET
ejpam-3049	28	39	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	28	40	h	h	NOUN
ejpam-3049	28	41	is	be	AUX
ejpam-3049	28	42	regular	regular	ADJ
ejpam-3049	28	43	if	if	SCONJ
ejpam-3049	29	1	and	and	CCONJ
ejpam-3049	29	2	only	only	ADV
ejpam-3049	29	3	if	if	SCONJ
ejpam-3049	29	4	f	f	PROPN
ejpam-3049	29	5	∧	∧	NOUN
ejpam-3049	29	6	g	g	PROPN
ejpam-3049	29	7	=	=	SYM
ejpam-3049	29	8	f	f	PROPN
ejpam-3049	30	1	◦	◦	NOUN
ejpam-3049	30	2	g	g	NOUN
ejpam-3049	30	3	,	,	PUNCT
ejpam-3049	30	4	equivalently	equivalently	ADV
ejpam-3049	30	5	if	if	SCONJ
ejpam-3049	30	6	f	f	PROPN
ejpam-3049	30	7	∧	∧	PROPN
ejpam-3049	30	8	g	g	PROPN
ejpam-3049	30	9	�	�	PROPN
ejpam-3049	30	10	f	f	PROPN
ejpam-3049	30	11	◦	◦	VERB
ejpam-3049	30	12	g	g	NOUN
ejpam-3049	30	13	for	for	ADP
ejpam-3049	30	14	every	every	DET
ejpam-3049	30	15	fuzzy	fuzzy	ADJ
ejpam-3049	30	16	right	right	ADJ
ejpam-3049	30	17	ideal	ideal	NOUN
ejpam-3049	30	18	f	f	PROPN
ejpam-3049	31	1	and	and	CCONJ
ejpam-3049	31	2	every	every	DET
ejpam-3049	31	3	fuzzy	fuzzy	ADJ
ejpam-3049	31	4	left	leave	VERB
ejpam-3049	31	5	ideal	ideal	NOUN
ejpam-3049	31	6	g	g	PROPN
ejpam-3049	31	7	of	of	ADP
ejpam-3049	31	8	h.	h.	PROPN
ejpam-3049	31	9	an	an	DET
ejpam-3049	31	10	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	31	11	h	h	NOUN
ejpam-3049	31	12	is	be	AUX
ejpam-3049	31	13	intra	intra	ADJ
ejpam-3049	31	14	-	-	ADJ
ejpam-3049	31	15	regular	regular	ADJ
ejpam-3049	31	16	if	if	SCONJ
ejpam-3049	31	17	and	and	CCONJ
ejpam-3049	31	18	only	only	ADV
ejpam-3049	31	19	if	if	SCONJ
ejpam-3049	31	20	for	for	ADP
ejpam-3049	31	21	every	every	DET
ejpam-3049	31	22	right	right	ADJ
ejpam-3049	31	23	ideal	ideal	NOUN
ejpam-3049	31	24	a	a	DET
ejpam-3049	31	25	and	and	CCONJ
ejpam-3049	31	26	every	every	PRON
ejpam-3049	31	27	left	leave	VERB
ejpam-3049	31	28	ideal	ideal	PROPN
ejpam-3049	31	29	b	b	PROPN
ejpam-3049	31	30	of	of	ADP
ejpam-3049	31	31	h	h	NOUN
ejpam-3049	31	32	we	we	PRON
ejpam-3049	31	33	have	have	VERB
ejpam-3049	31	34	a	a	DET
ejpam-3049	31	35	∩	∩	ADJ
ejpam-3049	31	36	b	b	NOUN
ejpam-3049	31	37	⊆	⊆	NUM
ejpam-3049	31	38	b	b	PROPN
ejpam-3049	31	39	∗	∗	NOUN
ejpam-3049	31	40	a.	a.	NOUN
ejpam-3049	32	1	an	an	DET
ejpam-3049	32	2	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	32	3	h	h	NOUN
ejpam-3049	32	4	is	be	AUX
ejpam-3049	32	5	intra	intra	ADJ
ejpam-3049	32	6	-	-	ADJ
ejpam-3049	32	7	regular	regular	ADJ
ejpam-3049	32	8	if	if	SCONJ
ejpam-3049	32	9	and	and	CCONJ
ejpam-3049	32	10	only	only	ADV
ejpam-3049	32	11	if	if	SCONJ
ejpam-3049	32	12	for	for	ADP
ejpam-3049	32	13	every	every	DET
ejpam-3049	32	14	fuzzy	fuzzy	ADJ
ejpam-3049	32	15	right	right	ADJ
ejpam-3049	32	16	ideal	ideal	NOUN
ejpam-3049	33	1	f	f	PROPN
ejpam-3049	33	2	and	and	CCONJ
ejpam-3049	33	3	every	every	DET
ejpam-3049	33	4	fuzzy	fuzzy	ADJ
ejpam-3049	33	5	left	leave	VERB
ejpam-3049	33	6	ideal	ideal	NOUN
ejpam-3049	33	7	g	g	PROPN
ejpam-3049	33	8	of	of	ADP
ejpam-3049	33	9	h	h	NOUN
ejpam-3049	33	10	we	we	PRON
ejpam-3049	33	11	have	have	VERB
ejpam-3049	33	12	f	f	PROPN
ejpam-3049	33	13	∧	∧	PROPN
ejpam-3049	33	14	g	g	PROPN
ejpam-3049	33	15	�	�	PROPN
ejpam-3049	33	16	g	g	PROPN
ejpam-3049	33	17	◦	◦	PROPN
ejpam-3049	33	18	f.	f.	PROPN
ejpam-3049	33	19	an	an	DET
ejpam-3049	33	20	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	33	21	h	h	NOUN
ejpam-3049	33	22	is	be	AUX
ejpam-3049	33	23	left	leave	VERB
ejpam-3049	33	24	quasi	quasi	ADJ
ejpam-3049	33	25	-	-	ADJ
ejpam-3049	33	26	regular	regular	ADJ
ejpam-3049	33	27	if	if	SCONJ
ejpam-3049	34	1	and	and	CCONJ
ejpam-3049	34	2	only	only	ADV
ejpam-3049	34	3	if	if	SCONJ
ejpam-3049	34	4	a	a	DET
ejpam-3049	34	5	∩	∩	NOUN
ejpam-3049	34	6	b	b	NOUN
ejpam-3049	34	7	⊆	⊆	NUM
ejpam-3049	34	8	a	a	DET
ejpam-3049	34	9	∗	∗	NOUN
ejpam-3049	34	10	b	b	NOUN
ejpam-3049	34	11	for	for	ADP
ejpam-3049	34	12	every	every	DET
ejpam-3049	34	13	ideal	ideal	NOUN
ejpam-3049	34	14	a	a	PRON
ejpam-3049	34	15	and	and	CCONJ
ejpam-3049	34	16	every	every	DET
ejpam-3049	34	17	bi	bi	ADJ
ejpam-3049	34	18	-	-	ADJ
ejpam-3049	34	19	ideal	ideal	ADJ
ejpam-3049	34	20	b	b	PROPN
ejpam-3049	34	21	of	of	ADP
ejpam-3049	34	22	h	h	NOUN
ejpam-3049	34	23	,	,	PUNCT
ejpam-3049	34	24	equivalently	equivalently	ADV
ejpam-3049	34	25	if	if	SCONJ
ejpam-3049	34	26	a∩b	a∩b	PROPN
ejpam-3049	34	27	⊆	⊆	SYM
ejpam-3049	34	28	a	a	DET
ejpam-3049	34	29	∗b	∗b	NOUN
ejpam-3049	34	30	for	for	ADP
ejpam-3049	34	31	every	every	DET
ejpam-3049	34	32	ideal	ideal	NOUN
ejpam-3049	34	33	a	a	DET
ejpam-3049	34	34	and	and	CCONJ
ejpam-3049	34	35	every	every	PRON
ejpam-3049	34	36	left	leave	VERB
ejpam-3049	34	37	ideal	ideal	PROPN
ejpam-3049	34	38	b	b	PROPN
ejpam-3049	34	39	of	of	ADP
ejpam-3049	34	40	h.	h.	PROPN
ejpam-3049	34	41	an	an	DET
ejpam-3049	34	42	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	34	43	h	h	NOUN
ejpam-3049	34	44	is	be	AUX
ejpam-3049	34	45	left	leave	VERB
ejpam-3049	34	46	quasi	quasi	ADJ
ejpam-3049	34	47	-	-	ADJ
ejpam-3049	34	48	regular	regular	ADJ
ejpam-3049	34	49	if	if	SCONJ
ejpam-3049	34	50	and	and	CCONJ
ejpam-3049	34	51	only	only	ADV
ejpam-3049	34	52	if	if	SCONJ
ejpam-3049	34	53	f	f	PROPN
ejpam-3049	34	54	∧g	∧g	PROPN
ejpam-3049	34	55	�	�	PROPN
ejpam-3049	34	56	f	f	PROPN
ejpam-3049	34	57	◦	◦	NOUN
ejpam-3049	34	58	g	g	NOUN
ejpam-3049	34	59	for	for	ADP
ejpam-3049	34	60	every	every	DET
ejpam-3049	34	61	fuzzy	fuzzy	ADJ
ejpam-3049	34	62	ideal	ideal	NOUN
ejpam-3049	34	63	f	f	PROPN
ejpam-3049	34	64	and	and	CCONJ
ejpam-3049	34	65	every	every	DET
ejpam-3049	34	66	fuzzy	fuzzy	ADJ
ejpam-3049	34	67	bi	bi	ADJ
ejpam-3049	34	68	-	-	ADJ
ejpam-3049	34	69	ideal	ideal	ADJ
ejpam-3049	34	70	g	g	NOUN
ejpam-3049	34	71	of	of	ADP
ejpam-3049	34	72	h	h	NOUN
ejpam-3049	34	73	,	,	PUNCT
ejpam-3049	34	74	equivalently	equivalently	ADV
ejpam-3049	34	75	if	if	SCONJ
ejpam-3049	34	76	f	f	PROPN
ejpam-3049	34	77	∧g	∧g	PROPN
ejpam-3049	34	78	�	�	PROPN
ejpam-3049	34	79	f	f	PROPN
ejpam-3049	34	80	◦	◦	NOUN
ejpam-3049	34	81	g	g	NOUN
ejpam-3049	34	82	for	for	ADP
ejpam-3049	34	83	every	every	DET
ejpam-3049	34	84	fuzzy	fuzzy	ADJ
ejpam-3049	34	85	ideal	ideal	NOUN
ejpam-3049	34	86	f	f	PROPN
ejpam-3049	34	87	and	and	CCONJ
ejpam-3049	34	88	every	every	DET
ejpam-3049	34	89	fuzzy	fuzzy	ADJ
ejpam-3049	34	90	left	leave	VERB
ejpam-3049	34	91	ideal	ideal	NOUN
ejpam-3049	34	92	g	g	PROPN
ejpam-3049	34	93	of	of	ADP
ejpam-3049	34	94	h.	h.	PROPN
ejpam-3049	34	95	an	an	DET
ejpam-3049	34	96	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	34	97	h	h	NOUN
ejpam-3049	34	98	is	be	AUX
ejpam-3049	34	99	left	leave	VERB
ejpam-3049	34	100	quasi	quasi	ADJ
ejpam-3049	34	101	-	-	ADJ
ejpam-3049	34	102	regular	regular	ADJ
ejpam-3049	34	103	if	if	SCONJ
ejpam-3049	35	1	and	and	CCONJ
ejpam-3049	35	2	only	only	ADV
ejpam-3049	35	3	if	if	SCONJ
ejpam-3049	35	4	the	the	DET
ejpam-3049	35	5	left	left	ADJ
ejpam-3049	35	6	ideals	ideal	NOUN
ejpam-3049	35	7	of	of	ADP
ejpam-3049	35	8	h	h	NOUN
ejpam-3049	35	9	are	be	AUX
ejpam-3049	35	10	idempotent	idempotent	ADJ
ejpam-3049	35	11	.	.	PUNCT
ejpam-3049	36	1	and	and	CCONJ
ejpam-3049	36	2	an	an	DET
ejpam-3049	36	3	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	36	4	h	h	NOUN
ejpam-3049	36	5	is	be	AUX
ejpam-3049	36	6	left	leave	VERB
ejpam-3049	36	7	quasi	quasi	ADJ
ejpam-3049	36	8	-	-	ADJ
ejpam-3049	36	9	regular	regular	ADJ
ejpam-3049	36	10	if	if	SCONJ
ejpam-3049	37	1	and	and	CCONJ
ejpam-3049	37	2	only	only	ADV
ejpam-3049	37	3	if	if	SCONJ
ejpam-3049	37	4	the	the	DET
ejpam-3049	37	5	fuzzy	fuzzy	ADJ
ejpam-3049	37	6	left	leave	VERB
ejpam-3049	37	7	ideals	ideal	NOUN
ejpam-3049	37	8	of	of	ADP
ejpam-3049	37	9	h	h	NOUN
ejpam-3049	37	10	are	be	AUX
ejpam-3049	37	11	idempotent	idempotent	ADJ
ejpam-3049	37	12	.	.	PUNCT
ejpam-3049	38	1	an	an	DET
ejpam-3049	38	2	hypersemigroup	hypersemigroup	ADJ
ejpam-3049	38	3	h	h	NOUN
ejpam-3049	38	4	is	be	AUX
ejpam-3049	38	5	semisimple	semisimple	ADJ
ejpam-3049	38	6	if	if	SCONJ
ejpam-3049	38	7	and	and	CCONJ
ejpam-3049	38	8	only	only	ADV
ejpam-3049	38	9	if	if	SCONJ
ejpam-3049	38	10	the	the	DET
ejpam-3049	38	11	ideals	ideal	NOUN
ejpam-3049	38	12	of	of	ADP
ejpam-3049	38	13	h	h	NOUN
ejpam-3049	38	14	are	be	AUX
ejpam-3049	38	15	idempotent	idempotent	ADJ
ejpam-3049	38	16	,	,	PUNCT
ejpam-3049	38	17	equivalently	equivalently	ADV
ejpam-3049	38	18	if	if	SCONJ
ejpam-3049	38	19	a∩b	a∩b	PROPN
ejpam-3049	38	20	=	=	PUNCT
ejpam-3049	38	21	a	a	DET
ejpam-3049	38	22	∗b	∗b	PROPN
ejpam-3049	38	23	for	for	ADP
ejpam-3049	38	24	all	all	DET
ejpam-3049	38	25	ideals	ideal	NOUN
ejpam-3049	38	26	a	a	DET
ejpam-3049	38	27	,	,	PUNCT
ejpam-3049	38	28	b	b	PROPN
ejpam-3049	38	29	of	of	ADP
ejpam-3049	38	30	h.	h.	PROPN
ejpam-3049	38	31	an	an	DET
ejpam-3049	38	32	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	38	33	h	h	NOUN
ejpam-3049	38	34	is	be	AUX
ejpam-3049	38	35	semisimple	semisimple	ADJ
ejpam-3049	38	36	if	if	SCONJ
ejpam-3049	38	37	and	and	CCONJ
ejpam-3049	38	38	only	only	ADV
ejpam-3049	38	39	if	if	SCONJ
ejpam-3049	38	40	the	the	DET
ejpam-3049	38	41	fuzzy	fuzzy	ADJ
ejpam-3049	38	42	ideals	ideal	NOUN
ejpam-3049	38	43	of	of	ADP
ejpam-3049	38	44	h	h	NOUN
ejpam-3049	38	45	are	be	AUX
ejpam-3049	38	46	idempotent	idempotent	ADJ
ejpam-3049	38	47	,	,	PUNCT
ejpam-3049	38	48	equivalently	equivalently	ADV
ejpam-3049	38	49	if	if	SCONJ
ejpam-3049	38	50	for	for	ADP
ejpam-3049	38	51	each	each	DET
ejpam-3049	38	52	fuzzy	fuzzy	ADJ
ejpam-3049	38	53	ideals	ideal	NOUN
ejpam-3049	38	54	f	f	PROPN
ejpam-3049	38	55	and	and	CCONJ
ejpam-3049	38	56	g	g	PROPN
ejpam-3049	38	57	of	of	ADP
ejpam-3049	38	58	h	h	NOUN
ejpam-3049	38	59	we	we	PRON
ejpam-3049	38	60	have	have	VERB
ejpam-3049	38	61	f	f	PROPN
ejpam-3049	38	62	∧	∧	PROPN
ejpam-3049	39	1	g	g	PROPN
ejpam-3049	39	2	=	=	SYM
ejpam-3049	39	3	f	f	PROPN
ejpam-3049	39	4	◦	◦	NOUN
ejpam-3049	39	5	g.	g.	X
ejpam-3049	39	6	our	our	PRON
ejpam-3049	39	7	aim	aim	NOUN
ejpam-3049	39	8	being	be	AUX
ejpam-3049	39	9	to	to	PART
ejpam-3049	39	10	show	show	VERB
ejpam-3049	39	11	that	that	SCONJ
ejpam-3049	39	12	the	the	DET
ejpam-3049	39	13	theories	theory	NOUN
ejpam-3049	39	14	of	of	ADP
ejpam-3049	39	15	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	39	16	and	and	CCONJ
ejpam-3049	39	17	of	of	ADP
ejpam-3049	39	18	fuzzy	fuzzy	ADJ
ejpam-3049	39	19	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	39	20	are	be	AUX
ejpam-3049	39	21	parallel	parallel	ADJ
ejpam-3049	39	22	to	to	ADP
ejpam-3049	39	23	each	each	DET
ejpam-3049	39	24	other	other	ADJ
ejpam-3049	39	25	,	,	PUNCT
ejpam-3049	39	26	we	we	PRON
ejpam-3049	39	27	restrict	restrict	VERB
ejpam-3049	39	28	ourselves	ourselves	PRON
ejpam-3049	39	29	to	to	ADP
ejpam-3049	39	30	an	an	DET
ejpam-3049	39	31	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	39	32	(	(	PUNCT
ejpam-3049	39	33	without	without	ADP
ejpam-3049	39	34	order	order	NOUN
ejpam-3049	39	35	)	)	PUNCT
ejpam-3049	39	36	and	and	CCONJ
ejpam-3049	39	37	further	far	ADV
ejpam-3049	39	38	interesting	interesting	ADJ
ejpam-3049	39	39	information	information	NOUN
ejpam-3049	39	40	related	relate	VERB
ejpam-3049	39	41	to	to	ADP
ejpam-3049	39	42	this	this	DET
ejpam-3049	39	43	parallelism	parallelism	NOUN
ejpam-3049	39	44	will	will	AUX
ejpam-3049	39	45	be	be	AUX
ejpam-3049	39	46	given	give	VERB
ejpam-3049	39	47	in	in	ADP
ejpam-3049	39	48	a	a	DET
ejpam-3049	39	49	forthcoming	forthcoming	ADJ
ejpam-3049	39	50	paper	paper	NOUN
ejpam-3049	39	51	.	.	PUNCT
ejpam-3049	40	1	however	however	ADV
ejpam-3049	40	2	,	,	PUNCT
ejpam-3049	40	3	analogous	analogous	ADJ
ejpam-3049	40	4	results	result	NOUN
ejpam-3049	40	5	with	with	ADP
ejpam-3049	40	6	the	the	DET
ejpam-3049	40	7	results	result	NOUN
ejpam-3049	40	8	given	give	VERB
ejpam-3049	40	9	in	in	ADP
ejpam-3049	40	10	this	this	DET
ejpam-3049	40	11	paper	paper	NOUN
ejpam-3049	40	12	for	for	ADP
ejpam-3049	40	13	ordered	order	VERB
ejpam-3049	40	14	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	40	15	also	also	ADV
ejpam-3049	40	16	hold	hold	VERB
ejpam-3049	40	17	.	.	PUNCT
ejpam-3049	41	1	for	for	ADP
ejpam-3049	41	2	related	related	ADJ
ejpam-3049	41	3	results	result	NOUN
ejpam-3049	41	4	on	on	ADP
ejpam-3049	41	5	ordered	order	VERB
ejpam-3049	41	6	semigroups	semigroup	NOUN
ejpam-3049	41	7	on	on	ADP
ejpam-3049	41	8	which	which	PRON
ejpam-3049	41	9	the	the	DET
ejpam-3049	41	10	present	present	ADJ
ejpam-3049	41	11	article	article	NOUN
ejpam-3049	41	12	is	be	AUX
ejpam-3049	41	13	based	base	VERB
ejpam-3049	41	14	we	we	PRON
ejpam-3049	41	15	refer	refer	VERB
ejpam-3049	41	16	to	to	ADP
ejpam-3049	41	17	[	[	X
ejpam-3049	41	18	3	3	NUM
ejpam-3049	41	19	,	,	PUNCT
ejpam-3049	41	20	7	7	NUM
ejpam-3049	41	21	]	]	PUNCT
ejpam-3049	41	22	.	.	PUNCT
ejpam-3049	42	1	the	the	DET
ejpam-3049	42	2	left	left	ADJ
ejpam-3049	42	3	(	(	PUNCT
ejpam-3049	42	4	right	right	ADJ
ejpam-3049	42	5	)	)	PUNCT
ejpam-3049	42	6	quasi	quasi	ADJ
ejpam-3049	42	7	-	-	ADJ
ejpam-3049	42	8	regular	regular	ADJ
ejpam-3049	42	9	fuzzy	fuzzy	ADJ
ejpam-3049	42	10	ordered	order	VERB
ejpam-3049	42	11	semigroups	semigroup	NOUN
ejpam-3049	42	12	under	under	ADP
ejpam-3049	42	13	the	the	DET
ejpam-3049	42	14	name	name	NOUN
ejpam-3049	42	15	left	leave	VERB
ejpam-3049	42	16	(	(	PUNCT
ejpam-3049	42	17	right	right	ADJ
ejpam-3049	42	18	)	)	PUNCT
ejpam-3049	42	19	weakly	weakly	ADV
ejpam-3049	42	20	regular	regular	ADV
ejpam-3049	42	21	and	and	CCONJ
ejpam-3049	42	22	the	the	DET
ejpam-3049	42	23	semisimple	semisimple	NOUN
ejpam-3049	42	24	ordered	order	VERB
ejpam-3049	42	25	semigroups	semigroup	NOUN
ejpam-3049	42	26	have	have	AUX
ejpam-3049	42	27	been	be	AUX
ejpam-3049	42	28	studied	study	VERB
ejpam-3049	42	29	by	by	ADP
ejpam-3049	42	30	shabir	shabir	PROPN
ejpam-3049	42	31	and	and	CCONJ
ejpam-3049	42	32	khan	khan	PROPN
ejpam-3049	42	33	in	in	ADP
ejpam-3049	42	34	[	[	X
ejpam-3049	42	35	12	12	NUM
ejpam-3049	42	36	,	,	PUNCT
ejpam-3049	42	37	13	13	NUM
ejpam-3049	42	38	]	]	PUNCT
ejpam-3049	42	39	,	,	PUNCT
ejpam-3049	42	40	and	and	CCONJ
ejpam-3049	42	41	by	by	ADP
ejpam-3049	42	42	kehayopulu	kehayopulu	VERB
ejpam-3049	42	43	in	in	ADP
ejpam-3049	42	44	[	[	X
ejpam-3049	42	45	4	4	NUM
ejpam-3049	42	46	]	]	PUNCT
ejpam-3049	42	47	.	.	PUNCT
ejpam-3049	43	1	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	43	2	under	under	ADP
ejpam-3049	43	3	the	the	DET
ejpam-3049	43	4	name	name	NOUN
ejpam-3049	43	5	semihypergroups	semihypergroup	NOUN
ejpam-3049	43	6	have	have	AUX
ejpam-3049	43	7	been	be	AUX
ejpam-3049	43	8	first	first	ADV
ejpam-3049	43	9	systematically	systematically	ADV
ejpam-3049	43	10	studied	study	VERB
ejpam-3049	43	11	in	in	ADP
ejpam-3049	43	12	2011	2011	NUM
ejpam-3049	43	13	by	by	ADP
ejpam-3049	43	14	mahmood	mahmood	PROPN
ejpam-3049	43	15	in	in	ADP
ejpam-3049	43	16	his	his	PRON
ejpam-3049	43	17	phd	phd	NOUN
ejpam-3049	43	18	thesis	thesis	NOUN
ejpam-3049	43	19	[	[	X
ejpam-3049	43	20	10	10	NUM
ejpam-3049	43	21	]	]	PUNCT
ejpam-3049	43	22	.	.	PUNCT
ejpam-3049	44	1	however	however	ADV
ejpam-3049	44	2	a	a	DET
ejpam-3049	44	3	revision	revision	NOUN
ejpam-3049	44	4	in	in	ADP
ejpam-3049	44	5	the	the	DET
ejpam-3049	44	6	notation	notation	NOUN
ejpam-3049	44	7	in	in	ADP
ejpam-3049	44	8	this	this	DET
ejpam-3049	44	9	thesis	thesis	NOUN
ejpam-3049	44	10	is	be	AUX
ejpam-3049	44	11	necessary	necessary	ADJ
ejpam-3049	44	12	.	.	PUNCT
ejpam-3049	45	1	for	for	ADP
ejpam-3049	45	2	the	the	DET
ejpam-3049	45	3	sake	sake	NOUN
ejpam-3049	45	4	of	of	ADP
ejpam-3049	45	5	completeness	completeness	NOUN
ejpam-3049	45	6	,	,	PUNCT
ejpam-3049	45	7	let	let	VERB
ejpam-3049	45	8	us	we	PRON
ejpam-3049	45	9	mention	mention	VERB
ejpam-3049	45	10	some	some	DET
ejpam-3049	45	11	definitions	definition	NOUN
ejpam-3049	45	12	and	and	CCONJ
ejpam-3049	45	13	results	result	NOUN
ejpam-3049	45	14	already	already	ADV
ejpam-3049	45	15	given	give	VERB
ejpam-3049	45	16	in	in	ADP
ejpam-3049	45	17	[	[	X
ejpam-3049	45	18	5	5	NUM
ejpam-3049	45	19	,	,	PUNCT
ejpam-3049	45	20	6	6	NUM
ejpam-3049	45	21	]	]	PUNCT
ejpam-3049	45	22	.	.	PUNCT
ejpam-3049	46	1	an	an	DET
ejpam-3049	46	2	hypergroupoid	hypergroupoid	PROPN
ejpam-3049	46	3	is	be	AUX
ejpam-3049	46	4	a	a	DET
ejpam-3049	46	5	nonempty	nonempty	ADV
ejpam-3049	46	6	set	set	VERB
ejpam-3049	46	7	h	h	NOUN
ejpam-3049	46	8	with	with	ADP
ejpam-3049	46	9	an	an	DET
ejpam-3049	46	10	hyperoperation	hyperoperation	NOUN
ejpam-3049	46	11	◦	◦	NOUN
ejpam-3049	46	12	:	:	PUNCT
ejpam-3049	46	13	h	h	NOUN
ejpam-3049	46	14	×h	×h	PROPN
ejpam-3049	46	15	→	→	SYM
ejpam-3049	46	16	p∗(h	p∗(h	NOUN
ejpam-3049	46	17	)	)	PUNCT
ejpam-3049	46	18	|	|	ADV
ejpam-3049	46	19	(	(	PUNCT
ejpam-3049	46	20	a	a	PRON
ejpam-3049	46	21	,	,	PUNCT
ejpam-3049	46	22	b)→	b)→	VERB
ejpam-3049	46	23	a	a	DET
ejpam-3049	46	24	◦	◦	NOUN
ejpam-3049	46	25	b	b	NOUN
ejpam-3049	46	26	on	on	ADP
ejpam-3049	46	27	h	h	NOUN
ejpam-3049	46	28	and	and	CCONJ
ejpam-3049	46	29	an	an	DET
ejpam-3049	46	30	operation	operation	NOUN
ejpam-3049	46	31	∗	∗	NOUN
ejpam-3049	46	32	:	:	PUNCT
ejpam-3049	46	33	p∗(h	p∗(h	X
ejpam-3049	46	34	)	)	PUNCT
ejpam-3049	46	35	×	×	PROPN
ejpam-3049	46	36	p∗(h	p∗(h	PROPN
ejpam-3049	46	37	)	)	PUNCT
ejpam-3049	46	38	→	→	SYM
ejpam-3049	46	39	p∗(h	p∗(h	NOUN
ejpam-3049	46	40	)	)	PUNCT
ejpam-3049	47	1	|	|	ADV
ejpam-3049	47	2	(	(	PUNCT
ejpam-3049	47	3	a	a	DET
ejpam-3049	47	4	,	,	PUNCT
ejpam-3049	47	5	b	b	NOUN
ejpam-3049	47	6	)	)	PUNCT
ejpam-3049	47	7	→	→	ADP
ejpam-3049	47	8	a	a	DET
ejpam-3049	47	9	∗	∗	NOUN
ejpam-3049	47	10	b	b	NOUN
ejpam-3049	47	11	on	on	ADP
ejpam-3049	47	12	p∗(h	p∗(h	PROPN
ejpam-3049	47	13	)	)	PUNCT
ejpam-3049	47	14	(	(	PUNCT
ejpam-3049	47	15	induced	induce	VERB
ejpam-3049	47	16	by	by	ADP
ejpam-3049	47	17	the	the	DET
ejpam-3049	47	18	operation	operation	NOUN
ejpam-3049	47	19	of	of	ADP
ejpam-3049	47	20	h	h	NOUN
ejpam-3049	47	21	)	)	PUNCT
ejpam-3049	47	22	such	such	ADJ
ejpam-3049	47	23	that	that	SCONJ
ejpam-3049	47	24	a	a	DET
ejpam-3049	47	25	∗	∗	NOUN
ejpam-3049	47	26	b	b	NOUN
ejpam-3049	47	27	=	=	X
ejpam-3049	47	28	⋃	⋃	PROPN
ejpam-3049	47	29	(	(	PUNCT
ejpam-3049	47	30	a	a	PRON
ejpam-3049	47	31	,	,	PUNCT
ejpam-3049	47	32	b)∈a×b	b)∈a×b	NUM
ejpam-3049	47	33	(	(	PUNCT
ejpam-3049	47	34	a	a	DET
ejpam-3049	47	35	◦	◦	NOUN
ejpam-3049	47	36	b	b	NOUN
ejpam-3049	47	37	)	)	PUNCT
ejpam-3049	47	38	for	for	ADP
ejpam-3049	47	39	every	every	DET
ejpam-3049	47	40	a	a	PROPN
ejpam-3049	47	41	,	,	PUNCT
ejpam-3049	47	42	b	b	PROPN
ejpam-3049	47	43	∈	∈	PROPN
ejpam-3049	47	44	p∗(h	p∗(h	PROPN
ejpam-3049	47	45	)	)	PUNCT
ejpam-3049	47	46	,	,	PUNCT
ejpam-3049	47	47	p∗(h	p∗(h	PROPN
ejpam-3049	47	48	)	)	PUNCT
ejpam-3049	47	49	being	be	AUX
ejpam-3049	47	50	the	the	DET
ejpam-3049	47	51	set	set	NOUN
ejpam-3049	47	52	of	of	ADP
ejpam-3049	47	53	nonempty	nonempty	ADJ
ejpam-3049	47	54	subsets	subset	NOUN
ejpam-3049	47	55	of	of	ADP
ejpam-3049	47	56	h.	h.	PROPN
ejpam-3049	47	57	as	as	SCONJ
ejpam-3049	47	58	the	the	DET
ejpam-3049	47	59	operation	operation	NOUN
ejpam-3049	47	60	“	"	PUNCT
ejpam-3049	47	61	∗	∗	NOUN
ejpam-3049	47	62	”	"	PUNCT
ejpam-3049	47	63	depends	depend	VERB
ejpam-3049	47	64	on	on	ADP
ejpam-3049	47	65	the	the	DET
ejpam-3049	47	66	hyperoperation	hyperoperation	NOUN
ejpam-3049	47	67	“	"	PUNCT
ejpam-3049	47	68	◦	◦	NOUN
ejpam-3049	47	69	”	"	PUNCT
ejpam-3049	47	70	,	,	PUNCT
ejpam-3049	47	71	an	an	DET
ejpam-3049	47	72	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	47	73	can	can	AUX
ejpam-3049	47	74	be	be	AUX
ejpam-3049	47	75	denoted	denote	VERB
ejpam-3049	47	76	by	by	ADP
ejpam-3049	47	77	(	(	PUNCT
ejpam-3049	47	78	h	h	NOUN
ejpam-3049	47	79	,	,	PUNCT
ejpam-3049	47	80	◦	◦	NOUN
ejpam-3049	47	81	)	)	PUNCT
ejpam-3049	47	82	(	(	PUNCT
ejpam-3049	47	83	instead	instead	ADV
ejpam-3049	47	84	of	of	ADP
ejpam-3049	47	85	(	(	PUNCT
ejpam-3049	47	86	h	h	NOUN
ejpam-3049	47	87	,	,	PUNCT
ejpam-3049	47	88	◦	◦	NOUN
ejpam-3049	47	89	,	,	PUNCT
ejpam-3049	47	90	∗	∗	NOUN
ejpam-3049	47	91	)	)	PUNCT
ejpam-3049	47	92	)	)	PUNCT
ejpam-3049	47	93	.	.	PUNCT
ejpam-3049	48	1	if	if	SCONJ
ejpam-3049	48	2	(	(	PUNCT
ejpam-3049	48	3	h	h	NOUN
ejpam-3049	48	4	,	,	PUNCT
ejpam-3049	48	5	◦	◦	NOUN
ejpam-3049	48	6	)	)	PUNCT
ejpam-3049	48	7	is	be	AUX
ejpam-3049	48	8	an	an	DET
ejpam-3049	48	9	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	48	10	then	then	ADV
ejpam-3049	48	11	,	,	PUNCT
ejpam-3049	48	12	for	for	ADP
ejpam-3049	48	13	every	every	DET
ejpam-3049	48	14	x	x	NOUN
ejpam-3049	48	15	,	,	PUNCT
ejpam-3049	48	16	y	y	PROPN
ejpam-3049	48	17	∈	∈	PROPN
ejpam-3049	48	18	h	h	NOUN
ejpam-3049	48	19	,	,	PUNCT
ejpam-3049	48	20	we	we	PRON
ejpam-3049	48	21	have	have	VERB
ejpam-3049	48	22	{	{	PUNCT
ejpam-3049	48	23	x	x	NOUN
ejpam-3049	48	24	}	}	PUNCT
ejpam-3049	48	25	∗	∗	NOUN
ejpam-3049	48	26	{	{	PUNCT
ejpam-3049	48	27	y	y	NOUN
ejpam-3049	48	28	}	}	PUNCT
ejpam-3049	48	29	=	=	SYM
ejpam-3049	48	30	x	x	PUNCT
ejpam-3049	48	31	◦	◦	NOUN
ejpam-3049	48	32	y.	y.	NOUN
ejpam-3049	49	1	if	if	SCONJ
ejpam-3049	49	2	(	(	PUNCT
ejpam-3049	49	3	h	h	NOUN
ejpam-3049	49	4	,	,	PUNCT
ejpam-3049	49	5	◦	◦	NOUN
ejpam-3049	49	6	)	)	PUNCT
ejpam-3049	49	7	is	be	AUX
ejpam-3049	49	8	an	an	DET
ejpam-3049	49	9	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	49	10	and	and	CCONJ
ejpam-3049	49	11	a	a	DET
ejpam-3049	49	12	,	,	PUNCT
ejpam-3049	49	13	b	b	NOUN
ejpam-3049	49	14	,	,	PUNCT
ejpam-3049	49	15	c	c	PROPN
ejpam-3049	49	16	∈	∈	PROPN
ejpam-3049	49	17	p∗(h	p∗(h	PROPN
ejpam-3049	49	18	)	)	PUNCT
ejpam-3049	49	19	,	,	PUNCT
ejpam-3049	49	20	then	then	ADV
ejpam-3049	49	21	a	a	DET
ejpam-3049	49	22	⊆	⊆	NUM
ejpam-3049	49	23	b	b	NOUN
ejpam-3049	49	24	implies	imply	VERB
ejpam-3049	49	25	a	a	DET
ejpam-3049	49	26	∗	∗	NOUN
ejpam-3049	49	27	c	c	NOUN
ejpam-3049	49	28	⊆	⊆	NUM
ejpam-3049	49	29	b	b	NOUN
ejpam-3049	49	30	∗	∗	NOUN
ejpam-3049	49	31	c	c	NOUN
ejpam-3049	49	32	and	and	CCONJ
ejpam-3049	49	33	c	c	PROPN
ejpam-3049	49	34	∗	∗	NOUN
ejpam-3049	49	35	a	a	DET
ejpam-3049	49	36	⊆	⊆	NUM
ejpam-3049	49	37	c	c	NOUN
ejpam-3049	49	38	∗	∗	X
ejpam-3049	49	39	b.	b.	NOUN
ejpam-3049	49	40	we	we	PRON
ejpam-3049	49	41	also	also	ADV
ejpam-3049	49	42	have	have	VERB
ejpam-3049	49	43	h	h	NOUN
ejpam-3049	49	44	∗h	∗h	NOUN
ejpam-3049	49	45	⊆	⊆	NUM
ejpam-3049	49	46	h.	h.	NOUN
ejpam-3049	50	1	if	if	SCONJ
ejpam-3049	50	2	(	(	PUNCT
ejpam-3049	50	3	h	h	NOUN
ejpam-3049	50	4	,	,	PUNCT
ejpam-3049	50	5	◦	◦	NOUN
ejpam-3049	50	6	)	)	PUNCT
ejpam-3049	50	7	is	be	AUX
ejpam-3049	50	8	an	an	DET
ejpam-3049	50	9	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	50	10	,	,	PUNCT
ejpam-3049	50	11	x	x	SYM
ejpam-3049	50	12	∈	∈	PROPN
ejpam-3049	50	13	h	h	NOUN
ejpam-3049	50	14	and	and	CCONJ
ejpam-3049	50	15	a	a	DET
ejpam-3049	50	16	,	,	PUNCT
ejpam-3049	50	17	b	b	PROPN
ejpam-3049	50	18	∈	∈	PROPN
ejpam-3049	50	19	p∗(h	p∗(h	PROPN
ejpam-3049	50	20	)	)	PUNCT
ejpam-3049	50	21	,	,	PUNCT
ejpam-3049	50	22	then	then	ADV
ejpam-3049	50	23	the	the	DET
ejpam-3049	50	24	following	follow	VERB
ejpam-3049	50	25	two	two	NUM
ejpam-3049	50	26	properties	property	NOUN
ejpam-3049	50	27	,	,	PUNCT
ejpam-3049	50	28	though	though	SCONJ
ejpam-3049	50	29	clear	clear	ADJ
ejpam-3049	50	30	,	,	PUNCT
ejpam-3049	50	31	are	be	AUX
ejpam-3049	50	32	essential	essential	ADJ
ejpam-3049	50	33	to	to	ADP
ejpam-3049	50	34	the	the	DET
ejpam-3049	50	35	investigation	investigation	NOUN
ejpam-3049	50	36	:	:	PUNCT
ejpam-3049	50	37	(	(	PUNCT
ejpam-3049	50	38	1	1	X
ejpam-3049	50	39	)	)	PUNCT
ejpam-3049	50	40	if	if	SCONJ
ejpam-3049	50	41	x	x	SYM
ejpam-3049	50	42	∈	∈	PROPN
ejpam-3049	50	43	a	a	DET
ejpam-3049	50	44	∗b	∗b	NOUN
ejpam-3049	50	45	,	,	PUNCT
ejpam-3049	50	46	then	then	ADV
ejpam-3049	50	47	x	x	PART
ejpam-3049	50	48	∈	∈	PROPN
ejpam-3049	50	49	a	a	DET
ejpam-3049	50	50	◦	◦	NOUN
ejpam-3049	50	51	b	b	NOUN
ejpam-3049	50	52	for	for	ADP
ejpam-3049	50	53	some	some	DET
ejpam-3049	50	54	a	a	DET
ejpam-3049	50	55	∈	∈	PROPN
ejpam-3049	50	56	a	a	PRON
ejpam-3049	50	57	,	,	PUNCT
ejpam-3049	50	58	b	b	PROPN
ejpam-3049	50	59	∈	∈	PROPN
ejpam-3049	50	60	b.	b.	PROPN
ejpam-3049	50	61	n.	n.	PROPN
ejpam-3049	50	62	kehayopulu	kehayopulu	PROPN
ejpam-3049	50	63	/	/	SYM
ejpam-3049	50	64	eur	eur	PROPN
ejpam-3049	50	65	.	.	PUNCT
ejpam-3049	51	1	j.	j.	PROPN
ejpam-3049	51	2	pure	pure	PROPN
ejpam-3049	51	3	appl	appl	PROPN
ejpam-3049	51	4	.	.	PROPN
ejpam-3049	51	5	math	math	PROPN
ejpam-3049	51	6	,	,	PUNCT
ejpam-3049	51	7	10	10	NUM
ejpam-3049	51	8	(	(	PUNCT
ejpam-3049	51	9	5	5	NUM
ejpam-3049	51	10	)	)	PUNCT
ejpam-3049	51	11	(	(	PUNCT
ejpam-3049	51	12	2017	2017	NUM
ejpam-3049	51	13	)	)	PUNCT
ejpam-3049	51	14	,	,	PUNCT
ejpam-3049	51	15	929	929	NUM
ejpam-3049	51	16	-	-	SYM
ejpam-3049	51	17	945	945	NUM
ejpam-3049	51	18	931	931	NUM
ejpam-3049	51	19	(	(	PUNCT
ejpam-3049	51	20	2	2	NUM
ejpam-3049	51	21	)	)	PUNCT
ejpam-3049	51	22	if	if	SCONJ
ejpam-3049	51	23	a	a	DET
ejpam-3049	51	24	∈	∈	PROPN
ejpam-3049	51	25	a	a	PRON
ejpam-3049	51	26	and	and	CCONJ
ejpam-3049	51	27	b	b	PROPN
ejpam-3049	51	28	∈	∈	PROPN
ejpam-3049	51	29	b	b	PROPN
ejpam-3049	51	30	,	,	PUNCT
ejpam-3049	51	31	then	then	ADV
ejpam-3049	51	32	a	a	DET
ejpam-3049	51	33	◦	◦	NOUN
ejpam-3049	51	34	b	b	NOUN
ejpam-3049	51	35	⊆	⊆	NUM
ejpam-3049	51	36	a	a	DET
ejpam-3049	51	37	∗b	∗b	PROPN
ejpam-3049	52	1	[	[	X
ejpam-3049	52	2	5	5	NUM
ejpam-3049	52	3	,	,	PUNCT
ejpam-3049	52	4	6	6	NUM
ejpam-3049	52	5	]	]	PUNCT
ejpam-3049	52	6	.	.	PUNCT
ejpam-3049	53	1	lemma	lemma	PROPN
ejpam-3049	53	2	1.1	1.1	NUM
ejpam-3049	54	1	[	[	X
ejpam-3049	54	2	5	5	NUM
ejpam-3049	54	3	]	]	X
ejpam-3049	54	4	if	if	SCONJ
ejpam-3049	54	5	(	(	PUNCT
ejpam-3049	54	6	h	h	NOUN
ejpam-3049	54	7	,	,	PUNCT
ejpam-3049	54	8	◦	◦	NOUN
ejpam-3049	54	9	)	)	PUNCT
ejpam-3049	54	10	is	be	AUX
ejpam-3049	54	11	an	an	DET
ejpam-3049	54	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	54	13	and	and	CCONJ
ejpam-3049	54	14	ai	ai	VERB
ejpam-3049	54	15	,	,	PUNCT
ejpam-3049	54	16	b	b	PROPN
ejpam-3049	54	17	∈	∈	PROPN
ejpam-3049	54	18	p∗(h	p∗(h	PROPN
ejpam-3049	54	19	)	)	PUNCT
ejpam-3049	54	20	,	,	PUNCT
ejpam-3049	54	21	i	i	PRON
ejpam-3049	54	22	∈	∈	VERB
ejpam-3049	55	1	i	i	PRON
ejpam-3049	55	2	,	,	PUNCT
ejpam-3049	55	3	then	then	ADV
ejpam-3049	55	4	we	we	PRON
ejpam-3049	55	5	have	have	VERB
ejpam-3049	55	6	the	the	DET
ejpam-3049	55	7	following	following	NOUN
ejpam-3049	55	8	:	:	PUNCT
ejpam-3049	55	9	(	(	PUNCT
ejpam-3049	55	10	1	1	X
ejpam-3049	55	11	)	)	PUNCT
ejpam-3049	55	12	(	(	PUNCT
ejpam-3049	55	13	⋃	⋃	ADP
ejpam-3049	55	14	i∈i	i∈i	ADJ
ejpam-3049	55	15	ai	ai	NOUN
ejpam-3049	55	16	)	)	PUNCT
ejpam-3049	55	17	∗b	∗b	NOUN
ejpam-3049	55	18	=	=	SYM
ejpam-3049	55	19	⋃	⋃	PROPN
ejpam-3049	55	20	i∈i	i∈i	ADJ
ejpam-3049	55	21	(	(	PUNCT
ejpam-3049	55	22	ai	ai	PROPN
ejpam-3049	55	23	∗b	∗b	PROPN
ejpam-3049	55	24	)	)	PUNCT
ejpam-3049	55	25	.	.	PUNCT
ejpam-3049	56	1	(	(	PUNCT
ejpam-3049	56	2	2	2	X
ejpam-3049	56	3	)	)	PUNCT
ejpam-3049	56	4	b	b	NOUN
ejpam-3049	56	5	∗	∗	NOUN
ejpam-3049	56	6	(	(	PUNCT
ejpam-3049	56	7	⋃	⋃	PROPN
ejpam-3049	56	8	i∈i	i∈i	ADJ
ejpam-3049	56	9	ai	ai	VERB
ejpam-3049	56	10	)	)	PUNCT
ejpam-3049	57	1	=	=	SYM
ejpam-3049	57	2	⋃	⋃	PROPN
ejpam-3049	57	3	i∈i	i∈i	ADJ
ejpam-3049	57	4	(	(	PUNCT
ejpam-3049	57	5	b	b	NOUN
ejpam-3049	57	6	∗ai	∗ai	PROPN
ejpam-3049	57	7	)	)	PUNCT
ejpam-3049	57	8	.	.	PUNCT
ejpam-3049	58	1	an	an	PRON
ejpam-3049	58	2	hypergroupoid	hypergroupoid	PROPN
ejpam-3049	58	3	(	(	PUNCT
ejpam-3049	58	4	h	h	NOUN
ejpam-3049	58	5	,	,	PUNCT
ejpam-3049	58	6	◦	◦	NOUN
ejpam-3049	58	7	)	)	PUNCT
ejpam-3049	58	8	is	be	AUX
ejpam-3049	58	9	called	call	VERB
ejpam-3049	58	10	hypersemigroup	hypersemigroup	ADV
ejpam-3049	58	11	if	if	SCONJ
ejpam-3049	58	12	(	(	PUNCT
ejpam-3049	58	13	x	x	SYM
ejpam-3049	58	14	◦	◦	VERB
ejpam-3049	58	15	y	y	NOUN
ejpam-3049	58	16	)	)	PUNCT
ejpam-3049	58	17	∗	∗	NOUN
ejpam-3049	58	18	{	{	PUNCT
ejpam-3049	58	19	z	z	NOUN
ejpam-3049	58	20	}	}	PUNCT
ejpam-3049	58	21	=	=	SYM
ejpam-3049	58	22	{	{	PUNCT
ejpam-3049	58	23	x	x	NOUN
ejpam-3049	58	24	}	}	PUNCT
ejpam-3049	58	25	∗	∗	NOUN
ejpam-3049	58	26	(	(	PUNCT
ejpam-3049	58	27	y	y	PROPN
ejpam-3049	58	28	◦	◦	PROPN
ejpam-3049	58	29	z	z	PROPN
ejpam-3049	58	30	)	)	PUNCT
ejpam-3049	58	31	for	for	ADP
ejpam-3049	58	32	every	every	DET
ejpam-3049	58	33	x	x	PROPN
ejpam-3049	58	34	,	,	PUNCT
ejpam-3049	58	35	y	y	PROPN
ejpam-3049	58	36	,	,	PUNCT
ejpam-3049	58	37	z	z	PROPN
ejpam-3049	58	38	∈	∈	PROPN
ejpam-3049	58	39	h.	h.	PROPN
ejpam-3049	58	40	for	for	ADP
ejpam-3049	58	41	short	short	ADJ
ejpam-3049	58	42	,	,	PUNCT
ejpam-3049	58	43	we	we	PRON
ejpam-3049	58	44	can	can	AUX
ejpam-3049	58	45	identify	identify	VERB
ejpam-3049	58	46	the	the	DET
ejpam-3049	58	47	singleton	singleton	NOUN
ejpam-3049	58	48	{	{	PUNCT
ejpam-3049	58	49	x	x	NOUN
ejpam-3049	58	50	}	}	PUNCT
ejpam-3049	58	51	by	by	ADP
ejpam-3049	58	52	the	the	DET
ejpam-3049	58	53	element	element	NOUN
ejpam-3049	58	54	x	x	PUNCT
ejpam-3049	58	55	and	and	CCONJ
ejpam-3049	58	56	the	the	DET
ejpam-3049	58	57	{	{	PUNCT
ejpam-3049	58	58	z	z	NOUN
ejpam-3049	58	59	}	}	PUNCT
ejpam-3049	58	60	by	by	ADP
ejpam-3049	58	61	z	z	NOUN
ejpam-3049	58	62	and	and	CCONJ
ejpam-3049	58	63	define	define	VERB
ejpam-3049	58	64	the	the	DET
ejpam-3049	58	65	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	58	66	as	as	ADP
ejpam-3049	58	67	(	(	PUNCT
ejpam-3049	58	68	x	x	SYM
ejpam-3049	58	69	◦	◦	NOUN
ejpam-3049	58	70	y	y	NOUN
ejpam-3049	58	71	)	)	PUNCT
ejpam-3049	58	72	∗	∗	NOUN
ejpam-3049	58	73	z	z	NOUN
ejpam-3049	59	1	=	=	SYM
ejpam-3049	59	2	x	x	X
ejpam-3049	59	3	∗	∗	NOUN
ejpam-3049	59	4	(	(	PUNCT
ejpam-3049	59	5	y	y	PROPN
ejpam-3049	59	6	◦	◦	PROPN
ejpam-3049	59	7	z	z	PROPN
ejpam-3049	59	8	)	)	PUNCT
ejpam-3049	59	9	.	.	PUNCT
ejpam-3049	60	1	if	if	SCONJ
ejpam-3049	60	2	(	(	PUNCT
ejpam-3049	60	3	h	h	NOUN
ejpam-3049	60	4	,	,	PUNCT
ejpam-3049	60	5	◦	◦	NOUN
ejpam-3049	60	6	)	)	PUNCT
ejpam-3049	60	7	is	be	AUX
ejpam-3049	60	8	an	an	DET
ejpam-3049	60	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	60	10	,	,	PUNCT
ejpam-3049	60	11	then	then	ADV
ejpam-3049	60	12	the	the	DET
ejpam-3049	60	13	operation	operation	NOUN
ejpam-3049	60	14	“	"	PUNCT
ejpam-3049	60	15	∗	∗	NOUN
ejpam-3049	60	16	”	"	PUNCT
ejpam-3049	60	17	on	on	ADP
ejpam-3049	60	18	p∗(h	p∗(h	PROPN
ejpam-3049	60	19	)	)	PUNCT
ejpam-3049	60	20	is	be	AUX
ejpam-3049	60	21	associative	associative	ADJ
ejpam-3049	60	22	so	so	ADV
ejpam-3049	60	23	,	,	PUNCT
ejpam-3049	60	24	for	for	ADP
ejpam-3049	60	25	any	any	DET
ejpam-3049	60	26	subsets	subset	NOUN
ejpam-3049	60	27	a	a	DET
ejpam-3049	60	28	,	,	PUNCT
ejpam-3049	60	29	b	b	NOUN
ejpam-3049	60	30	,	,	PUNCT
ejpam-3049	60	31	c	c	PROPN
ejpam-3049	60	32	∈	∈	PROPN
ejpam-3049	60	33	p∗(h	p∗(h	PROPN
ejpam-3049	60	34	)	)	PUNCT
ejpam-3049	60	35	we	we	PRON
ejpam-3049	60	36	can	can	AUX
ejpam-3049	60	37	write	write	VERB
ejpam-3049	60	38	(	(	PUNCT
ejpam-3049	60	39	a	a	DET
ejpam-3049	60	40	∗b	∗b	NOUN
ejpam-3049	60	41	)	)	PUNCT
ejpam-3049	61	1	∗c	∗c	PROPN
ejpam-3049	61	2	=	=	PUNCT
ejpam-3049	61	3	a	a	DET
ejpam-3049	61	4	∗	∗	NOUN
ejpam-3049	61	5	(	(	PUNCT
ejpam-3049	61	6	b	b	NOUN
ejpam-3049	61	7	∗c	∗c	PROPN
ejpam-3049	61	8	)	)	PUNCT
ejpam-3049	61	9	=	=	PUNCT
ejpam-3049	62	1	a	a	DET
ejpam-3049	62	2	∗b	∗b	PROPN
ejpam-3049	62	3	∗c	∗c	PROPN
ejpam-3049	62	4	and	and	CCONJ
ejpam-3049	62	5	for	for	ADP
ejpam-3049	62	6	any	any	DET
ejpam-3049	62	7	product	product	NOUN
ejpam-3049	62	8	a1	a1	NOUN
ejpam-3049	62	9	∗a2	∗a2	NOUN
ejpam-3049	62	10	∗	∗	NOUN
ejpam-3049	62	11	.....	.....	PUNCT
ejpam-3049	63	1	∗an	∗an	PUNCT
ejpam-3049	63	2	of	of	ADP
ejpam-3049	63	3	elements	element	NOUN
ejpam-3049	63	4	of	of	ADP
ejpam-3049	63	5	p∗(h	p∗(h	NOUN
ejpam-3049	63	6	)	)	PUNCT
ejpam-3049	63	7	we	we	PRON
ejpam-3049	63	8	can	can	AUX
ejpam-3049	63	9	put	put	VERB
ejpam-3049	63	10	parentheses	parenthesis	NOUN
ejpam-3049	63	11	in	in	ADP
ejpam-3049	63	12	any	any	DET
ejpam-3049	63	13	place	place	NOUN
ejpam-3049	63	14	beginning	begin	VERB
ejpam-3049	63	15	with	with	ADP
ejpam-3049	63	16	some	some	DET
ejpam-3049	63	17	ai	ai	NOUN
ejpam-3049	63	18	and	and	CCONJ
ejpam-3049	63	19	ending	end	VERB
ejpam-3049	63	20	in	in	ADP
ejpam-3049	63	21	some	some	DET
ejpam-3049	63	22	aj	aj	PROPN
ejpam-3049	63	23	(	(	PUNCT
ejpam-3049	63	24	1	1	NUM
ejpam-3049	63	25	≤	≤	NUM
ejpam-3049	63	26	i	i	PROPN
ejpam-3049	63	27	,	,	PUNCT
ejpam-3049	63	28	j	j	PROPN
ejpam-3049	63	29	≤	≤	PROPN
ejpam-3049	63	30	n	n	CCONJ
ejpam-3049	63	31	)	)	PUNCT
ejpam-3049	63	32	.	.	PUNCT
ejpam-3049	64	1	following	follow	VERB
ejpam-3049	64	2	the	the	DET
ejpam-3049	64	3	concepts	concept	NOUN
ejpam-3049	64	4	of	of	ADP
ejpam-3049	64	5	right	right	NOUN
ejpam-3049	64	6	and	and	CCONJ
ejpam-3049	64	7	left	leave	VERB
ejpam-3049	64	8	ideals	ideal	NOUN
ejpam-3049	64	9	of	of	ADP
ejpam-3049	64	10	groupoids	groupoid	NOUN
ejpam-3049	64	11	,	,	PUNCT
ejpam-3049	64	12	a	a	DET
ejpam-3049	64	13	nonempty	nonempty	NOUN
ejpam-3049	64	14	subset	subset	VERB
ejpam-3049	64	15	a	a	PRON
ejpam-3049	64	16	of	of	ADP
ejpam-3049	64	17	an	an	DET
ejpam-3049	64	18	hypergroupoid	hypergroupoid	PROPN
ejpam-3049	64	19	(	(	PUNCT
ejpam-3049	64	20	h	h	NOUN
ejpam-3049	64	21	,	,	PUNCT
ejpam-3049	64	22	◦	◦	NOUN
ejpam-3049	64	23	)	)	PUNCT
ejpam-3049	64	24	is	be	AUX
ejpam-3049	64	25	called	call	VERB
ejpam-3049	64	26	a	a	DET
ejpam-3049	64	27	right	right	NOUN
ejpam-3049	64	28	(	(	PUNCT
ejpam-3049	64	29	resp	resp	NOUN
ejpam-3049	64	30	.	.	PUNCT
ejpam-3049	65	1	left	left	ADJ
ejpam-3049	65	2	)	)	PUNCT
ejpam-3049	65	3	ideal	ideal	NOUN
ejpam-3049	65	4	of	of	ADP
ejpam-3049	65	5	h	h	NOUN
ejpam-3049	65	6	if	if	SCONJ
ejpam-3049	65	7	a	a	DET
ejpam-3049	65	8	∗h	∗h	NOUN
ejpam-3049	65	9	⊆	⊆	NUM
ejpam-3049	65	10	a	a	DET
ejpam-3049	65	11	(	(	PUNCT
ejpam-3049	65	12	resp	resp	NOUN
ejpam-3049	65	13	.	.	PUNCT
ejpam-3049	66	1	h	h	PROPN
ejpam-3049	66	2	∗a	∗a	PROPN
ejpam-3049	66	3	⊆	⊆	NUM
ejpam-3049	66	4	a	a	PRON
ejpam-3049	66	5	)	)	PUNCT
ejpam-3049	66	6	.	.	PUNCT
ejpam-3049	67	1	it	it	PRON
ejpam-3049	67	2	is	be	AUX
ejpam-3049	67	3	called	call	VERB
ejpam-3049	67	4	an	an	DET
ejpam-3049	67	5	ideal	ideal	NOUN
ejpam-3049	67	6	of	of	ADP
ejpam-3049	67	7	h	h	NOUN
ejpam-3049	67	8	if	if	SCONJ
ejpam-3049	67	9	it	it	PRON
ejpam-3049	67	10	is	be	AUX
ejpam-3049	67	11	both	both	CCONJ
ejpam-3049	67	12	a	a	DET
ejpam-3049	67	13	right	right	NOUN
ejpam-3049	67	14	and	and	CCONJ
ejpam-3049	67	15	left	leave	VERB
ejpam-3049	67	16	ideal	ideal	NOUN
ejpam-3049	67	17	of	of	ADP
ejpam-3049	67	18	h.	h.	PROPN
ejpam-3049	67	19	for	for	ADP
ejpam-3049	67	20	a	a	DET
ejpam-3049	67	21	subset	subset	NOUN
ejpam-3049	67	22	a	a	PRON
ejpam-3049	67	23	of	of	ADP
ejpam-3049	67	24	h	h	NOUN
ejpam-3049	67	25	,	,	PUNCT
ejpam-3049	67	26	we	we	PRON
ejpam-3049	67	27	denote	denote	VERB
ejpam-3049	67	28	by	by	ADP
ejpam-3049	67	29	r(a	r(a	PROPN
ejpam-3049	67	30	)	)	PUNCT
ejpam-3049	67	31	(	(	PUNCT
ejpam-3049	67	32	resp	resp	NOUN
ejpam-3049	67	33	.	.	PUNCT
ejpam-3049	68	1	l(a	l(a	PROPN
ejpam-3049	68	2	)	)	PUNCT
ejpam-3049	68	3	)	)	PUNCT
ejpam-3049	69	1	the	the	DET
ejpam-3049	69	2	right	right	NOUN
ejpam-3049	69	3	(	(	PUNCT
ejpam-3049	69	4	resp	resp	NOUN
ejpam-3049	69	5	.	.	PUNCT
ejpam-3049	70	1	left	left	ADJ
ejpam-3049	70	2	)	)	PUNCT
ejpam-3049	70	3	ideal	ideal	NOUN
ejpam-3049	70	4	of	of	ADP
ejpam-3049	70	5	h	h	PROPN
ejpam-3049	70	6	generated	generate	VERB
ejpam-3049	70	7	by	by	ADP
ejpam-3049	70	8	a	a	PRON
ejpam-3049	70	9	and	and	CCONJ
ejpam-3049	70	10	by	by	ADP
ejpam-3049	70	11	i(a	i(a	NOUN
ejpam-3049	70	12	)	)	PUNCT
ejpam-3049	70	13	the	the	DET
ejpam-3049	70	14	ideal	ideal	NOUN
ejpam-3049	70	15	of	of	ADP
ejpam-3049	70	16	h	h	PROPN
ejpam-3049	70	17	generated	generate	VERB
ejpam-3049	70	18	by	by	ADP
ejpam-3049	70	19	a.	a.	NOUN
ejpam-3049	70	20	if	if	SCONJ
ejpam-3049	70	21	(	(	PUNCT
ejpam-3049	70	22	h	h	NOUN
ejpam-3049	70	23	,	,	PUNCT
ejpam-3049	70	24	◦	◦	NOUN
ejpam-3049	70	25	)	)	PUNCT
ejpam-3049	70	26	is	be	AUX
ejpam-3049	70	27	an	an	DET
ejpam-3049	70	28	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	70	29	,	,	PUNCT
ejpam-3049	70	30	then	then	ADV
ejpam-3049	70	31	r(a	r(a	PROPN
ejpam-3049	70	32	)	)	PUNCT
ejpam-3049	70	33	=	=	PUNCT
ejpam-3049	70	34	a	a	DET
ejpam-3049	70	35	∪	∪	X
ejpam-3049	70	36	(	(	PUNCT
ejpam-3049	70	37	a	a	DET
ejpam-3049	70	38	∗h	∗h	NOUN
ejpam-3049	70	39	)	)	PUNCT
ejpam-3049	70	40	,	,	PUNCT
ejpam-3049	70	41	l(a	l(a	PROPN
ejpam-3049	70	42	)	)	PUNCT
ejpam-3049	70	43	=	=	PUNCT
ejpam-3049	70	44	a	a	DET
ejpam-3049	70	45	∪	∪	X
ejpam-3049	70	46	(	(	PUNCT
ejpam-3049	70	47	h	h	NOUN
ejpam-3049	70	48	∗a	∗a	ADJ
ejpam-3049	70	49	)	)	PUNCT
ejpam-3049	70	50	and	and	CCONJ
ejpam-3049	70	51	i(a	i(a	NOUN
ejpam-3049	70	52	)	)	PUNCT
ejpam-3049	70	53	=	=	PUNCT
ejpam-3049	70	54	a∪(a∗h)∪(h	a∪(a∗h)∪(h	X
ejpam-3049	71	1	∗a)∪(h	∗a)∪(h	NOUN
ejpam-3049	71	2	∗a∗h	∗a∗h	PROPN
ejpam-3049	71	3	)	)	PUNCT
ejpam-3049	71	4	.	.	PUNCT
ejpam-3049	72	1	for	for	ADP
ejpam-3049	72	2	a	a	DET
ejpam-3049	72	3	=	=	X
ejpam-3049	72	4	{	{	PUNCT
ejpam-3049	72	5	a	a	NOUN
ejpam-3049	72	6	}	}	PUNCT
ejpam-3049	72	7	(	(	PUNCT
ejpam-3049	72	8	a	a	DET
ejpam-3049	72	9	∈	∈	PROPN
ejpam-3049	72	10	h	h	NOUN
ejpam-3049	72	11	)	)	PUNCT
ejpam-3049	72	12	,	,	PUNCT
ejpam-3049	72	13	we	we	PRON
ejpam-3049	72	14	write	write	VERB
ejpam-3049	72	15	r(a	r(a	PROPN
ejpam-3049	72	16	)	)	PUNCT
ejpam-3049	72	17	,	,	PUNCT
ejpam-3049	72	18	l(a	l(a	PROPN
ejpam-3049	72	19	)	)	PUNCT
ejpam-3049	72	20	,	,	PUNCT
ejpam-3049	72	21	i(a	i(a	PROPN
ejpam-3049	72	22	)	)	PUNCT
ejpam-3049	72	23	instead	instead	ADV
ejpam-3049	72	24	of	of	ADP
ejpam-3049	72	25	l({a	l({a	PROPN
ejpam-3049	72	26	}	}	PUNCT
ejpam-3049	72	27	)	)	PUNCT
ejpam-3049	72	28	,	,	PUNCT
ejpam-3049	72	29	r({a	r({a	PROPN
ejpam-3049	72	30	}	}	PUNCT
ejpam-3049	72	31	)	)	PUNCT
ejpam-3049	72	32	,	,	PUNCT
ejpam-3049	72	33	i({a	i({a	PROPN
ejpam-3049	72	34	}	}	PUNCT
ejpam-3049	72	35	)	)	PUNCT
ejpam-3049	72	36	.	.	PUNCT
ejpam-3049	73	1	following	follow	VERB
ejpam-3049	73	2	the	the	DET
ejpam-3049	73	3	concepts	concept	NOUN
ejpam-3049	73	4	of	of	ADP
ejpam-3049	73	5	bi	bi	NOUN
ejpam-3049	73	6	-	-	NOUN
ejpam-3049	73	7	ideals	ideal	NOUN
ejpam-3049	73	8	of	of	ADP
ejpam-3049	73	9	semigroups	semigroup	NOUN
ejpam-3049	73	10	,	,	PUNCT
ejpam-3049	73	11	a	a	DET
ejpam-3049	73	12	nonempty	nonempty	NOUN
ejpam-3049	73	13	subset	subset	VERB
ejpam-3049	73	14	b	b	PROPN
ejpam-3049	73	15	of	of	ADP
ejpam-3049	73	16	an	an	DET
ejpam-3049	73	17	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	73	18	(	(	PUNCT
ejpam-3049	73	19	h	h	NOUN
ejpam-3049	73	20	,	,	PUNCT
ejpam-3049	73	21	◦	◦	NOUN
ejpam-3049	73	22	)	)	PUNCT
ejpam-3049	73	23	is	be	AUX
ejpam-3049	73	24	called	call	VERB
ejpam-3049	73	25	a	a	DET
ejpam-3049	73	26	bi	bi	NOUN
ejpam-3049	73	27	-	-	NOUN
ejpam-3049	73	28	ideal	ideal	NOUN
ejpam-3049	73	29	of	of	ADP
ejpam-3049	73	30	h	h	NOUN
ejpam-3049	73	31	if	if	SCONJ
ejpam-3049	73	32	b	b	PROPN
ejpam-3049	73	33	∗h	∗h	NOUN
ejpam-3049	73	34	∗b	∗b	PROPN
ejpam-3049	73	35	⊆	⊆	NUM
ejpam-3049	73	36	b.	b.	NOUN
ejpam-3049	73	37	following	follow	VERB
ejpam-3049	73	38	the	the	DET
ejpam-3049	73	39	concepts	concept	NOUN
ejpam-3049	73	40	of	of	ADP
ejpam-3049	73	41	regular	regular	ADJ
ejpam-3049	73	42	and	and	CCONJ
ejpam-3049	73	43	intra	intra	ADJ
ejpam-3049	73	44	-	-	ADJ
ejpam-3049	73	45	regular	regular	ADJ
ejpam-3049	73	46	semigroups	semigroup	NOUN
ejpam-3049	73	47	,	,	PUNCT
ejpam-3049	73	48	an	an	DET
ejpam-3049	73	49	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	73	50	(	(	PUNCT
ejpam-3049	73	51	h	h	NOUN
ejpam-3049	73	52	,	,	PUNCT
ejpam-3049	73	53	◦	◦	NOUN
ejpam-3049	73	54	)	)	PUNCT
ejpam-3049	73	55	is	be	AUX
ejpam-3049	73	56	called	call	VERB
ejpam-3049	73	57	regular	regular	ADV
ejpam-3049	73	58	if	if	SCONJ
ejpam-3049	73	59	for	for	ADP
ejpam-3049	73	60	every	every	DET
ejpam-3049	73	61	a	a	DET
ejpam-3049	73	62	∈	∈	PROPN
ejpam-3049	73	63	h	h	NOUN
ejpam-3049	73	64	there	there	PRON
ejpam-3049	73	65	exists	exist	VERB
ejpam-3049	73	66	x	x	X
ejpam-3049	73	67	∈	∈	NOUN
ejpam-3049	73	68	h	h	NOUN
ejpam-3049	73	69	such	such	ADJ
ejpam-3049	73	70	that	that	SCONJ
ejpam-3049	73	71	a	a	DET
ejpam-3049	73	72	∈	∈	NOUN
ejpam-3049	73	73	(	(	PUNCT
ejpam-3049	73	74	a	a	DET
ejpam-3049	73	75	◦	◦	NOUN
ejpam-3049	73	76	x	x	SYM
ejpam-3049	73	77	)	)	PUNCT
ejpam-3049	73	78	∗	∗	NOUN
ejpam-3049	73	79	{	{	PUNCT
ejpam-3049	73	80	a	a	X
ejpam-3049	73	81	}	}	PUNCT
ejpam-3049	73	82	;	;	PUNCT
ejpam-3049	73	83	it	it	PRON
ejpam-3049	73	84	is	be	AUX
ejpam-3049	73	85	called	call	VERB
ejpam-3049	73	86	intra	intra	ADJ
ejpam-3049	73	87	-	-	ADJ
ejpam-3049	73	88	regular	regular	ADJ
ejpam-3049	73	89	if	if	SCONJ
ejpam-3049	73	90	for	for	ADP
ejpam-3049	73	91	every	every	DET
ejpam-3049	73	92	a	a	DET
ejpam-3049	73	93	∈	∈	PROPN
ejpam-3049	73	94	h	h	NOUN
ejpam-3049	73	95	there	there	PRON
ejpam-3049	73	96	exist	exist	VERB
ejpam-3049	73	97	x	x	NOUN
ejpam-3049	73	98	,	,	PUNCT
ejpam-3049	73	99	y	y	PROPN
ejpam-3049	73	100	∈	∈	PROPN
ejpam-3049	73	101	h	h	NOUN
ejpam-3049	73	102	such	such	ADJ
ejpam-3049	73	103	that	that	SCONJ
ejpam-3049	73	104	a	a	DET
ejpam-3049	73	105	∈	∈	NOUN
ejpam-3049	73	106	(	(	PUNCT
ejpam-3049	73	107	x	x	SYM
ejpam-3049	73	108	◦	◦	VERB
ejpam-3049	73	109	a	a	X
ejpam-3049	73	110	)	)	PUNCT
ejpam-3049	73	111	∗	∗	NOUN
ejpam-3049	73	112	(	(	PUNCT
ejpam-3049	73	113	a	a	DET
ejpam-3049	73	114	◦	◦	NOUN
ejpam-3049	73	115	y	y	NOUN
ejpam-3049	73	116	)	)	PUNCT
ejpam-3049	73	117	.	.	PUNCT
ejpam-3049	74	1	lemma	lemma	PROPN
ejpam-3049	74	2	1.2	1.2	NUM
ejpam-3049	74	3	.	.	PUNCT
ejpam-3049	75	1	let	let	AUX
ejpam-3049	75	2	(	(	PUNCT
ejpam-3049	75	3	h	h	NOUN
ejpam-3049	75	4	,	,	PUNCT
ejpam-3049	75	5	◦	◦	NOUN
ejpam-3049	75	6	)	)	PUNCT
ejpam-3049	75	7	be	be	VERB
ejpam-3049	75	8	an	an	DET
ejpam-3049	75	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	75	10	.	.	PUNCT
ejpam-3049	76	1	the	the	DET
ejpam-3049	76	2	following	follow	VERB
ejpam-3049	76	3	are	be	AUX
ejpam-3049	76	4	equivalent	equivalent	ADJ
ejpam-3049	76	5	:	:	PUNCT
ejpam-3049	76	6	(	(	PUNCT
ejpam-3049	76	7	1	1	X
ejpam-3049	76	8	)	)	PUNCT
ejpam-3049	76	9	h	h	NOUN
ejpam-3049	76	10	is	be	AUX
ejpam-3049	76	11	regular	regular	ADJ
ejpam-3049	76	12	.	.	PUNCT
ejpam-3049	77	1	(	(	PUNCT
ejpam-3049	77	2	2	2	X
ejpam-3049	77	3	)	)	PUNCT
ejpam-3049	77	4	a	a	DET
ejpam-3049	77	5	∈	∈	NOUN
ejpam-3049	77	6	{	{	PUNCT
ejpam-3049	77	7	a	a	NOUN
ejpam-3049	77	8	}	}	PUNCT
ejpam-3049	77	9	∗h	∗h	NOUN
ejpam-3049	77	10	∗	∗	NOUN
ejpam-3049	77	11	{	{	PUNCT
ejpam-3049	77	12	a	a	NOUN
ejpam-3049	77	13	}	}	PUNCT
ejpam-3049	77	14	for	for	ADP
ejpam-3049	77	15	every	every	DET
ejpam-3049	77	16	a	a	DET
ejpam-3049	77	17	∈	∈	PROPN
ejpam-3049	77	18	h.	h.	NOUN
ejpam-3049	77	19	(	(	PUNCT
ejpam-3049	77	20	3	3	X
ejpam-3049	77	21	)	)	PUNCT
ejpam-3049	77	22	a	a	DET
ejpam-3049	77	23	⊆	⊆	NUM
ejpam-3049	77	24	a	a	DET
ejpam-3049	77	25	∗h	∗h	NOUN
ejpam-3049	77	26	∗a	∗a	ADJ
ejpam-3049	77	27	for	for	ADP
ejpam-3049	77	28	every	every	DET
ejpam-3049	77	29	a	a	DET
ejpam-3049	77	30	∈	∈	PROPN
ejpam-3049	77	31	p∗(h	p∗(h	PROPN
ejpam-3049	77	32	)	)	PUNCT
ejpam-3049	77	33	.	.	PUNCT
ejpam-3049	78	1	indeed	indeed	ADV
ejpam-3049	78	2	:	:	PUNCT
ejpam-3049	78	3	if	if	SCONJ
ejpam-3049	78	4	h	h	NOUN
ejpam-3049	78	5	is	be	AUX
ejpam-3049	78	6	regular	regular	ADJ
ejpam-3049	78	7	and	and	CCONJ
ejpam-3049	78	8	a	a	DET
ejpam-3049	78	9	∈	∈	PROPN
ejpam-3049	78	10	h	h	NOUN
ejpam-3049	78	11	,	,	PUNCT
ejpam-3049	78	12	then	then	ADV
ejpam-3049	78	13	there	there	PRON
ejpam-3049	78	14	exists	exist	VERB
ejpam-3049	78	15	x	x	X
ejpam-3049	78	16	∈	∈	NOUN
ejpam-3049	78	17	h	h	NOUN
ejpam-3049	78	18	such	such	ADJ
ejpam-3049	78	19	that	that	SCONJ
ejpam-3049	78	20	a	a	DET
ejpam-3049	78	21	∈	∈	NOUN
ejpam-3049	78	22	(	(	PUNCT
ejpam-3049	78	23	a	a	DET
ejpam-3049	78	24	◦	◦	NOUN
ejpam-3049	78	25	x	x	SYM
ejpam-3049	78	26	)	)	PUNCT
ejpam-3049	78	27	∗	∗	NOUN
ejpam-3049	78	28	{	{	PUNCT
ejpam-3049	78	29	a	a	NOUN
ejpam-3049	78	30	}	}	PUNCT
ejpam-3049	78	31	=	=	SYM
ejpam-3049	78	32	{	{	PUNCT
ejpam-3049	78	33	a	a	PRON
ejpam-3049	78	34	}	}	PUNCT
ejpam-3049	78	35	∗	∗	NOUN
ejpam-3049	78	36	{	{	PUNCT
ejpam-3049	78	37	x	x	NOUN
ejpam-3049	78	38	}	}	PUNCT
ejpam-3049	78	39	∗	∗	NOUN
ejpam-3049	78	40	{	{	PUNCT
ejpam-3049	78	41	a	a	PRON
ejpam-3049	78	42	}	}	PUNCT
ejpam-3049	78	43	⊆	⊆	NUM
ejpam-3049	78	44	{	{	PUNCT
ejpam-3049	78	45	a	a	DET
ejpam-3049	78	46	}	}	PUNCT
ejpam-3049	78	47	∗h	∗h	NOUN
ejpam-3049	78	48	∗	∗	NOUN
ejpam-3049	78	49	{	{	PUNCT
ejpam-3049	78	50	a	a	PRON
ejpam-3049	78	51	}	}	PUNCT
ejpam-3049	78	52	.	.	PUNCT
ejpam-3049	79	1	“	"	PUNCT
ejpam-3049	79	2	conversely	conversely	ADV
ejpam-3049	79	3	”	"	PUNCT
ejpam-3049	79	4	,	,	PUNCT
ejpam-3049	79	5	if	if	SCONJ
ejpam-3049	79	6	a	a	DET
ejpam-3049	79	7	⊆	⊆	NUM
ejpam-3049	79	8	a	a	DET
ejpam-3049	79	9	∗h	∗h	NOUN
ejpam-3049	79	10	∗a	∗a	ADJ
ejpam-3049	79	11	for	for	ADP
ejpam-3049	79	12	every	every	DET
ejpam-3049	79	13	a	a	DET
ejpam-3049	79	14	∈	∈	PROPN
ejpam-3049	79	15	p∗(h	p∗(h	PROPN
ejpam-3049	79	16	)	)	PUNCT
ejpam-3049	79	17	and	and	CCONJ
ejpam-3049	79	18	a	a	DET
ejpam-3049	79	19	∈	∈	PROPN
ejpam-3049	79	20	a	a	DET
ejpam-3049	79	21	,	,	PUNCT
ejpam-3049	79	22	then	then	ADV
ejpam-3049	79	23	{	{	PUNCT
ejpam-3049	79	24	a	a	PRON
ejpam-3049	79	25	}	}	PUNCT
ejpam-3049	79	26	⊆	⊆	NUM
ejpam-3049	79	27	(	(	PUNCT
ejpam-3049	79	28	{	{	PUNCT
ejpam-3049	79	29	a	a	DET
ejpam-3049	79	30	}	}	PUNCT
ejpam-3049	79	31	∗h	∗h	NOUN
ejpam-3049	79	32	)	)	PUNCT
ejpam-3049	79	33	∗	∗	NOUN
ejpam-3049	79	34	{	{	PUNCT
ejpam-3049	79	35	a	a	NOUN
ejpam-3049	79	36	}	}	PUNCT
ejpam-3049	79	37	,	,	PUNCT
ejpam-3049	79	38	then	then	ADV
ejpam-3049	79	39	there	there	PRON
ejpam-3049	79	40	exists	exist	VERB
ejpam-3049	79	41	u	u	PROPN
ejpam-3049	79	42	∈	∈	PROPN
ejpam-3049	79	43	{	{	PUNCT
ejpam-3049	79	44	a	a	NOUN
ejpam-3049	79	45	}	}	PUNCT
ejpam-3049	79	46	∗h	∗h	NOUN
ejpam-3049	79	47	such	such	ADJ
ejpam-3049	79	48	that	that	SCONJ
ejpam-3049	79	49	a	a	DET
ejpam-3049	79	50	∈	∈	PROPN
ejpam-3049	79	51	u	u	NOUN
ejpam-3049	79	52	◦	◦	NOUN
ejpam-3049	79	53	a	a	PRON
ejpam-3049	79	54	and	and	CCONJ
ejpam-3049	79	55	h	h	NOUN
ejpam-3049	79	56	∈	∈	PROPN
ejpam-3049	79	57	h	h	NOUN
ejpam-3049	79	58	such	such	ADJ
ejpam-3049	79	59	that	that	SCONJ
ejpam-3049	79	60	u	u	PROPN
ejpam-3049	79	61	∈	∈	PROPN
ejpam-3049	79	62	a	a	DET
ejpam-3049	79	63	◦	◦	NOUN
ejpam-3049	79	64	h.	h.	NOUN
ejpam-3049	79	65	then	then	ADV
ejpam-3049	79	66	we	we	PRON
ejpam-3049	79	67	have	have	VERB
ejpam-3049	79	68	a	a	DET
ejpam-3049	79	69	∈	∈	PROPN
ejpam-3049	79	70	u	u	NOUN
ejpam-3049	79	71	◦	◦	NOUN
ejpam-3049	79	72	a	a	DET
ejpam-3049	79	73	=	=	PUNCT
ejpam-3049	79	74	{	{	PUNCT
ejpam-3049	79	75	u	u	NOUN
ejpam-3049	79	76	}	}	PUNCT
ejpam-3049	79	77	∗	∗	NOUN
ejpam-3049	79	78	{	{	PUNCT
ejpam-3049	79	79	a	a	NOUN
ejpam-3049	79	80	}	}	PUNCT
ejpam-3049	79	81	⊆	⊆	NUM
ejpam-3049	79	82	(	(	PUNCT
ejpam-3049	79	83	a	a	DET
ejpam-3049	79	84	◦	◦	NOUN
ejpam-3049	79	85	h	h	NOUN
ejpam-3049	79	86	)	)	PUNCT
ejpam-3049	79	87	∗	∗	NOUN
ejpam-3049	79	88	{	{	PUNCT
ejpam-3049	79	89	a	a	NOUN
ejpam-3049	79	90	}	}	PUNCT
ejpam-3049	79	91	,	,	PUNCT
ejpam-3049	79	92	where	where	SCONJ
ejpam-3049	79	93	h	h	PROPN
ejpam-3049	79	94	∈	∈	PROPN
ejpam-3049	79	95	h	h	NOUN
ejpam-3049	79	96	,	,	PUNCT
ejpam-3049	79	97	so	so	ADV
ejpam-3049	79	98	h	h	NOUN
ejpam-3049	79	99	is	be	AUX
ejpam-3049	79	100	regular	regular	ADJ
ejpam-3049	79	101	.	.	PUNCT
ejpam-3049	80	1	in	in	ADP
ejpam-3049	80	2	a	a	DET
ejpam-3049	80	3	similar	similar	ADJ
ejpam-3049	80	4	way	way	NOUN
ejpam-3049	80	5	,	,	PUNCT
ejpam-3049	80	6	an	an	DET
ejpam-3049	80	7	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	80	8	h	h	NOUN
ejpam-3049	80	9	is	be	AUX
ejpam-3049	80	10	intra	intra	ADJ
ejpam-3049	80	11	-	-	ADJ
ejpam-3049	80	12	regular	regular	ADJ
ejpam-3049	80	13	if	if	SCONJ
ejpam-3049	80	14	and	and	CCONJ
ejpam-3049	80	15	only	only	ADV
ejpam-3049	80	16	if	if	SCONJ
ejpam-3049	80	17	,	,	PUNCT
ejpam-3049	80	18	for	for	ADP
ejpam-3049	80	19	every	every	DET
ejpam-3049	80	20	a	a	DET
ejpam-3049	80	21	∈	∈	PROPN
ejpam-3049	80	22	h	h	NOUN
ejpam-3049	80	23	,	,	PUNCT
ejpam-3049	80	24	we	we	PRON
ejpam-3049	80	25	have	have	VERB
ejpam-3049	80	26	a	a	DET
ejpam-3049	80	27	∈	∈	PROPN
ejpam-3049	80	28	h	h	NOUN
ejpam-3049	80	29	∗	∗	NOUN
ejpam-3049	80	30	{	{	PUNCT
ejpam-3049	80	31	a	a	DET
ejpam-3049	80	32	}	}	PUNCT
ejpam-3049	80	33	∗	∗	NOUN
ejpam-3049	80	34	{	{	PUNCT
ejpam-3049	80	35	a	a	DET
ejpam-3049	80	36	}	}	PUNCT
ejpam-3049	80	37	∗h	∗h	NOUN
ejpam-3049	80	38	,	,	PUNCT
ejpam-3049	80	39	equivalently	equivalently	ADV
ejpam-3049	80	40	if	if	SCONJ
ejpam-3049	80	41	for	for	ADP
ejpam-3049	80	42	any	any	DET
ejpam-3049	80	43	nonempty	nonempty	NOUN
ejpam-3049	80	44	subset	subset	VERB
ejpam-3049	80	45	a	a	PRON
ejpam-3049	80	46	of	of	ADP
ejpam-3049	80	47	h	h	NOUN
ejpam-3049	80	48	we	we	PRON
ejpam-3049	80	49	have	have	VERB
ejpam-3049	80	50	a	a	DET
ejpam-3049	80	51	⊆	⊆	NUM
ejpam-3049	80	52	h	h	NOUN
ejpam-3049	80	53	∗a	∗a	ADJ
ejpam-3049	80	54	∗a	∗a	ADJ
ejpam-3049	80	55	∗h	∗h	NOUN
ejpam-3049	80	56	.	.	PUNCT
ejpam-3049	81	1	following	follow	VERB
ejpam-3049	81	2	zadeh	zadeh	PROPN
ejpam-3049	81	3	,	,	PUNCT
ejpam-3049	81	4	any	any	DET
ejpam-3049	81	5	mapping	mapping	NOUN
ejpam-3049	81	6	f	f	NOUN
ejpam-3049	81	7	:	:	PUNCT
ejpam-3049	81	8	h	h	NOUN
ejpam-3049	81	9	→	→	PUNCT
ejpam-3049	81	10	[	[	X
ejpam-3049	81	11	0	0	NUM
ejpam-3049	81	12	,	,	PUNCT
ejpam-3049	81	13	1	1	NUM
ejpam-3049	81	14	]	]	PUNCT
ejpam-3049	81	15	of	of	ADP
ejpam-3049	81	16	an	an	DET
ejpam-3049	81	17	hypergroupoid	hypergroupoid	ADJ
ejpam-3049	81	18	h	h	NOUN
ejpam-3049	81	19	into	into	ADP
ejpam-3049	81	20	the	the	DET
ejpam-3049	81	21	closed	closed	ADJ
ejpam-3049	81	22	interval	interval	NOUN
ejpam-3049	81	23	[	[	X
ejpam-3049	81	24	0	0	NUM
ejpam-3049	81	25	,	,	PUNCT
ejpam-3049	81	26	1	1	NUM
ejpam-3049	81	27	]	]	PUNCT
ejpam-3049	81	28	of	of	ADP
ejpam-3049	81	29	real	real	ADJ
ejpam-3049	81	30	numbers	number	NOUN
ejpam-3049	81	31	is	be	AUX
ejpam-3049	81	32	called	call	VERB
ejpam-3049	81	33	a	a	DET
ejpam-3049	81	34	fuzzy	fuzzy	ADJ
ejpam-3049	81	35	subset	subset	NOUN
ejpam-3049	81	36	of	of	ADP
ejpam-3049	81	37	h	h	PROPN
ejpam-3049	81	38	(	(	PUNCT
ejpam-3049	81	39	or	or	CCONJ
ejpam-3049	81	40	a	a	DET
ejpam-3049	81	41	fuzzy	fuzzy	ADJ
ejpam-3049	81	42	set	set	NOUN
ejpam-3049	81	43	in	in	ADP
ejpam-3049	81	44	h	h	NOUN
ejpam-3049	81	45	)	)	PUNCT
ejpam-3049	81	46	and	and	CCONJ
ejpam-3049	81	47	the	the	DET
ejpam-3049	81	48	n.	n.	PROPN
ejpam-3049	81	49	kehayopulu	kehayopulu	PROPN
ejpam-3049	81	50	/	/	SYM
ejpam-3049	81	51	eur	eur	PROPN
ejpam-3049	81	52	.	.	PUNCT
ejpam-3049	82	1	j.	j.	PROPN
ejpam-3049	82	2	pure	pure	PROPN
ejpam-3049	82	3	appl	appl	PROPN
ejpam-3049	82	4	.	.	PROPN
ejpam-3049	82	5	math	math	PROPN
ejpam-3049	82	6	,	,	PUNCT
ejpam-3049	82	7	10	10	NUM
ejpam-3049	82	8	(	(	PUNCT
ejpam-3049	82	9	5	5	NUM
ejpam-3049	82	10	)	)	PUNCT
ejpam-3049	82	11	(	(	PUNCT
ejpam-3049	82	12	2017	2017	NUM
ejpam-3049	82	13	)	)	PUNCT
ejpam-3049	82	14	,	,	PUNCT
ejpam-3049	82	15	929	929	NUM
ejpam-3049	82	16	-	-	SYM
ejpam-3049	82	17	945	945	NUM
ejpam-3049	82	18	932	932	NUM
ejpam-3049	82	19	mapping	mapping	NOUN
ejpam-3049	82	20	fa	fa	INTJ
ejpam-3049	82	21	(	(	PUNCT
ejpam-3049	82	22	the	the	DET
ejpam-3049	82	23	so	so	ADV
ejpam-3049	82	24	called	call	VERB
ejpam-3049	82	25	characteristic	characteristic	ADJ
ejpam-3049	82	26	function	function	NOUN
ejpam-3049	82	27	of	of	ADP
ejpam-3049	82	28	a	a	PRON
ejpam-3049	82	29	)	)	PUNCT
ejpam-3049	82	30	is	be	AUX
ejpam-3049	82	31	the	the	DET
ejpam-3049	82	32	fuzzy	fuzzy	ADJ
ejpam-3049	82	33	subset	subset	NOUN
ejpam-3049	82	34	of	of	ADP
ejpam-3049	82	35	h	h	NOUN
ejpam-3049	82	36	defined	define	VERB
ejpam-3049	82	37	as	as	SCONJ
ejpam-3049	82	38	follows	follow	VERB
ejpam-3049	82	39	:	:	PUNCT
ejpam-3049	82	40	fa	fa	INTJ
ejpam-3049	82	41	:	:	PUNCT
ejpam-3049	82	42	h	h	NOUN
ejpam-3049	82	43	→	→	SYM
ejpam-3049	82	44	{	{	PUNCT
ejpam-3049	82	45	0	0	NUM
ejpam-3049	82	46	,	,	PUNCT
ejpam-3049	82	47	1	1	NUM
ejpam-3049	82	48	}	}	PUNCT
ejpam-3049	82	49	|	|	NOUN
ejpam-3049	82	50	x→	x→	PUNCT
ejpam-3049	82	51	fa(x	fa(x	PROPN
ejpam-3049	82	52	)	)	PUNCT
ejpam-3049	82	53	=	=	PRON
ejpam-3049	82	54	{	{	PUNCT
ejpam-3049	82	55	1	1	NUM
ejpam-3049	82	56	if	if	SCONJ
ejpam-3049	82	57	x	x	PROPN
ejpam-3049	82	58	∈	∈	PROPN
ejpam-3049	82	59	a	a	DET
ejpam-3049	82	60	0	0	NOUN
ejpam-3049	83	1	if	if	SCONJ
ejpam-3049	83	2	x	x	X
ejpam-3049	83	3	/∈	/∈	VERB
ejpam-3049	83	4	a.	a.	NOUN
ejpam-3049	83	5	for	for	ADP
ejpam-3049	83	6	an	an	DET
ejpam-3049	83	7	element	element	NOUN
ejpam-3049	83	8	a	a	PRON
ejpam-3049	83	9	of	of	ADP
ejpam-3049	83	10	h	h	NOUN
ejpam-3049	83	11	,	,	PUNCT
ejpam-3049	83	12	we	we	PRON
ejpam-3049	83	13	denote	denote	VERB
ejpam-3049	83	14	by	by	ADP
ejpam-3049	83	15	aa	aa	PRON
ejpam-3049	83	16	the	the	DET
ejpam-3049	83	17	subset	subset	NOUN
ejpam-3049	83	18	of	of	ADP
ejpam-3049	83	19	h	h	PROPN
ejpam-3049	83	20	×h	×h	AUX
ejpam-3049	83	21	defined	define	VERB
ejpam-3049	83	22	by	by	ADP
ejpam-3049	83	23	aa	aa	NOUN
ejpam-3049	83	24	:	:	PUNCT
ejpam-3049	83	25	=	=	SYM
ejpam-3049	83	26	{	{	PUNCT
ejpam-3049	83	27	(	(	PUNCT
ejpam-3049	83	28	y	y	PROPN
ejpam-3049	83	29	,	,	PUNCT
ejpam-3049	83	30	z	z	NOUN
ejpam-3049	83	31	)	)	PUNCT
ejpam-3049	83	32	∈	∈	PROPN
ejpam-3049	83	33	h	h	NOUN
ejpam-3049	84	1	×h	×h	PROPN
ejpam-3049	85	1	|	|	ADV
ejpam-3049	85	2	a	a	DET
ejpam-3049	85	3	∈	∈	PROPN
ejpam-3049	85	4	y	y	PROPN
ejpam-3049	85	5	◦	◦	NOUN
ejpam-3049	85	6	z	z	PROPN
ejpam-3049	85	7	}	}	PUNCT
ejpam-3049	85	8	.	.	PUNCT
ejpam-3049	86	1	for	for	ADP
ejpam-3049	86	2	two	two	NUM
ejpam-3049	86	3	fuzzy	fuzzy	ADJ
ejpam-3049	86	4	subsets	subset	NOUN
ejpam-3049	86	5	f	f	PROPN
ejpam-3049	86	6	and	and	CCONJ
ejpam-3049	86	7	g	g	PROPN
ejpam-3049	86	8	of	of	ADP
ejpam-3049	86	9	h	h	NOUN
ejpam-3049	86	10	,	,	PUNCT
ejpam-3049	86	11	we	we	PRON
ejpam-3049	86	12	denote	denote	VERB
ejpam-3049	86	13	by	by	ADP
ejpam-3049	86	14	f	f	PROPN
ejpam-3049	86	15	◦	◦	NOUN
ejpam-3049	86	16	g	g	ADP
ejpam-3049	86	17	the	the	DET
ejpam-3049	86	18	fuzzy	fuzzy	ADJ
ejpam-3049	86	19	subset	subset	NOUN
ejpam-3049	86	20	of	of	ADP
ejpam-3049	86	21	h	h	NOUN
ejpam-3049	86	22	defined	define	VERB
ejpam-3049	86	23	as	as	SCONJ
ejpam-3049	86	24	follows	follow	VERB
ejpam-3049	86	25	:	:	PUNCT
ejpam-3049	86	26	f	f	X
ejpam-3049	86	27	◦	◦	NOUN
ejpam-3049	86	28	g	g	NOUN
ejpam-3049	86	29	:	:	PUNCT
ejpam-3049	86	30	h	h	NOUN
ejpam-3049	86	31	→	→	PUNCT
ejpam-3049	87	1	[	[	X
ejpam-3049	87	2	0	0	NUM
ejpam-3049	87	3	,	,	PUNCT
ejpam-3049	87	4	1	1	NUM
ejpam-3049	87	5	]	]	PUNCT
ejpam-3049	87	6	a→	a→	X
ejpam-3049	87	7			PUNCT
ejpam-3049	87	8	∨	∨	X
ejpam-3049	87	9	(	(	PUNCT
ejpam-3049	87	10	y	y	PROPN
ejpam-3049	87	11	,	,	PUNCT
ejpam-3049	87	12	z)∈aa	z)∈aa	PROPN
ejpam-3049	87	13	min{f(y	min{f(y	NUM
ejpam-3049	87	14	)	)	PUNCT
ejpam-3049	87	15	,	,	PUNCT
ejpam-3049	87	16	g(z	g(z	PROPN
ejpam-3049	87	17	)	)	PUNCT
ejpam-3049	87	18	}	}	PUNCT
ejpam-3049	87	19	if	if	SCONJ
ejpam-3049	87	20	aa	aa	NOUN
ejpam-3049	87	21	6=	6=	PUNCT
ejpam-3049	87	22	∅	∅	NOUN
ejpam-3049	87	23	0	0	NUM
ejpam-3049	88	1	if	if	SCONJ
ejpam-3049	88	2	aa	aa	NOUN
ejpam-3049	88	3	=	=	PUNCT
ejpam-3049	88	4	∅.	∅.	NOUN
ejpam-3049	88	5	as	as	ADP
ejpam-3049	88	6	no	no	DET
ejpam-3049	88	7	confusion	confusion	NOUN
ejpam-3049	88	8	is	be	AUX
ejpam-3049	88	9	possible	possible	ADJ
ejpam-3049	88	10	,	,	PUNCT
ejpam-3049	88	11	we	we	PRON
ejpam-3049	88	12	denote	denote	VERB
ejpam-3049	88	13	the	the	DET
ejpam-3049	88	14	operation	operation	NOUN
ejpam-3049	88	15	between	between	ADP
ejpam-3049	88	16	fuzzy	fuzzy	ADJ
ejpam-3049	88	17	subsets	subset	NOUN
ejpam-3049	88	18	of	of	ADP
ejpam-3049	88	19	h	h	NOUN
ejpam-3049	88	20	and	and	CCONJ
ejpam-3049	88	21	the	the	DET
ejpam-3049	88	22	hyperoperation	hyperoperation	NOUN
ejpam-3049	88	23	on	on	ADP
ejpam-3049	88	24	h	h	NOUN
ejpam-3049	88	25	by	by	ADP
ejpam-3049	88	26	the	the	DET
ejpam-3049	88	27	same	same	ADJ
ejpam-3049	88	28	symbol	symbol	NOUN
ejpam-3049	88	29	.	.	PUNCT
ejpam-3049	89	1	denote	denote	VERB
ejpam-3049	89	2	by	by	ADP
ejpam-3049	89	3	f	f	PROPN
ejpam-3049	89	4	(	(	PUNCT
ejpam-3049	89	5	h	h	NOUN
ejpam-3049	89	6	)	)	PUNCT
ejpam-3049	89	7	the	the	DET
ejpam-3049	89	8	set	set	NOUN
ejpam-3049	89	9	of	of	ADP
ejpam-3049	89	10	all	all	DET
ejpam-3049	89	11	fuzzy	fuzzy	ADJ
ejpam-3049	89	12	subsets	subset	NOUN
ejpam-3049	89	13	of	of	ADP
ejpam-3049	89	14	h	h	NOUN
ejpam-3049	89	15	and	and	CCONJ
ejpam-3049	89	16	by	by	ADP
ejpam-3049	89	17	“	"	PUNCT
ejpam-3049	89	18	�	�	PROPN
ejpam-3049	89	19	”	"	PUNCT
ejpam-3049	89	20	the	the	DET
ejpam-3049	89	21	order	order	NOUN
ejpam-3049	89	22	relation	relation	NOUN
ejpam-3049	89	23	on	on	ADP
ejpam-3049	89	24	f	f	PROPN
ejpam-3049	89	25	(	(	PUNCT
ejpam-3049	89	26	h	h	NOUN
ejpam-3049	89	27	)	)	PUNCT
ejpam-3049	89	28	defined	define	VERB
ejpam-3049	89	29	by	by	ADP
ejpam-3049	89	30	f	f	PROPN
ejpam-3049	89	31	�	�	PROPN
ejpam-3049	89	32	g	g	PROPN
ejpam-3049	89	33	⇐	⇐	PROPN
ejpam-3049	89	34	⇒	⇒	PROPN
ejpam-3049	89	35	f(x	f(x	PROPN
ejpam-3049	89	36	)	)	PUNCT
ejpam-3049	89	37	≤	≤	NOUN
ejpam-3049	89	38	g(x	g(x	NOUN
ejpam-3049	89	39	)	)	PUNCT
ejpam-3049	89	40	for	for	ADP
ejpam-3049	89	41	every	every	DET
ejpam-3049	89	42	x	x	PROPN
ejpam-3049	89	43	∈	∈	PROPN
ejpam-3049	89	44	h.	h.	NOUN
ejpam-3049	89	45	for	for	ADP
ejpam-3049	89	46	two	two	NUM
ejpam-3049	89	47	fuzzy	fuzzy	ADJ
ejpam-3049	89	48	subsets	subset	NOUN
ejpam-3049	89	49	f	f	PROPN
ejpam-3049	89	50	and	and	CCONJ
ejpam-3049	89	51	g	g	PROPN
ejpam-3049	89	52	of	of	ADP
ejpam-3049	89	53	an	an	DET
ejpam-3049	89	54	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	89	55	h	h	NOUN
ejpam-3049	89	56	we	we	PRON
ejpam-3049	89	57	denote	denote	VERB
ejpam-3049	89	58	by	by	ADP
ejpam-3049	89	59	f	f	PROPN
ejpam-3049	89	60	∧	∧	PROPN
ejpam-3049	89	61	g	g	PROPN
ejpam-3049	89	62	the	the	DET
ejpam-3049	89	63	fuzzy	fuzzy	ADJ
ejpam-3049	89	64	subset	subset	NOUN
ejpam-3049	89	65	of	of	ADP
ejpam-3049	89	66	h	h	NOUN
ejpam-3049	89	67	defined	define	VERB
ejpam-3049	89	68	as	as	SCONJ
ejpam-3049	89	69	follows	follow	VERB
ejpam-3049	89	70	:	:	PUNCT
ejpam-3049	89	71	f	f	PROPN
ejpam-3049	89	72	∧	∧	PROPN
ejpam-3049	89	73	g	g	PROPN
ejpam-3049	89	74	:	:	PUNCT
ejpam-3049	89	75	h	h	NOUN
ejpam-3049	89	76	→	→	PUNCT
ejpam-3049	90	1	[	[	X
ejpam-3049	90	2	0	0	NUM
ejpam-3049	90	3	,	,	PUNCT
ejpam-3049	90	4	1	1	NUM
ejpam-3049	90	5	]	]	PUNCT
ejpam-3049	90	6	|	|	NOUN
ejpam-3049	90	7	x→	x→	PUNCT
ejpam-3049	91	1	(	(	PUNCT
ejpam-3049	91	2	f	f	PROPN
ejpam-3049	91	3	∧	∧	PROPN
ejpam-3049	91	4	g)(x	g)(x	PROPN
ejpam-3049	91	5	)	)	PUNCT
ejpam-3049	91	6	:	:	PUNCT
ejpam-3049	91	7	=	=	PUNCT
ejpam-3049	91	8	min{f(x	min{f(x	PROPN
ejpam-3049	91	9	)	)	PUNCT
ejpam-3049	91	10	,	,	PUNCT
ejpam-3049	91	11	g(x	g(x	NOUN
ejpam-3049	91	12	)	)	PUNCT
ejpam-3049	91	13	}	}	PUNCT
ejpam-3049	91	14	.	.	PUNCT
ejpam-3049	92	1	one	one	PRON
ejpam-3049	92	2	can	can	AUX
ejpam-3049	92	3	easily	easily	ADV
ejpam-3049	92	4	see	see	VERB
ejpam-3049	92	5	that	that	SCONJ
ejpam-3049	92	6	the	the	DET
ejpam-3049	92	7	fuzzy	fuzzy	ADJ
ejpam-3049	92	8	subset	subset	VERB
ejpam-3049	92	9	f	f	PROPN
ejpam-3049	92	10	∧	∧	PROPN
ejpam-3049	92	11	g	g	PROPN
ejpam-3049	92	12	is	be	AUX
ejpam-3049	92	13	the	the	DET
ejpam-3049	92	14	infimum	infimum	NOUN
ejpam-3049	92	15	of	of	ADP
ejpam-3049	92	16	the	the	DET
ejpam-3049	92	17	fuzzy	fuzzy	ADJ
ejpam-3049	92	18	subsets	subset	NOUN
ejpam-3049	92	19	f	f	PROPN
ejpam-3049	92	20	and	and	CCONJ
ejpam-3049	92	21	g	g	NOUN
ejpam-3049	92	22	,	,	PUNCT
ejpam-3049	92	23	and	and	CCONJ
ejpam-3049	92	24	this	this	PRON
ejpam-3049	92	25	is	be	AUX
ejpam-3049	92	26	why	why	SCONJ
ejpam-3049	92	27	we	we	PRON
ejpam-3049	92	28	write	write	VERB
ejpam-3049	92	29	f	f	PROPN
ejpam-3049	92	30	∧	∧	PROPN
ejpam-3049	92	31	g	g	PROPN
ejpam-3049	92	32	=	=	SYM
ejpam-3049	92	33	inf{f	inf{f	NOUN
ejpam-3049	92	34	,	,	PUNCT
ejpam-3049	92	35	g	g	NOUN
ejpam-3049	92	36	}	}	PUNCT
ejpam-3049	92	37	.	.	PUNCT
ejpam-3049	93	1	if	if	SCONJ
ejpam-3049	93	2	f	f	PROPN
ejpam-3049	93	3	is	be	AUX
ejpam-3049	93	4	a	a	DET
ejpam-3049	93	5	fuzzy	fuzzy	ADJ
ejpam-3049	93	6	subset	subset	NOUN
ejpam-3049	93	7	of	of	ADP
ejpam-3049	93	8	h	h	NOUN
ejpam-3049	93	9	,	,	PUNCT
ejpam-3049	93	10	then	then	ADV
ejpam-3049	93	11	f	f	PROPN
ejpam-3049	93	12	∧	∧	PROPN
ejpam-3049	93	13	f	f	PROPN
ejpam-3049	93	14	=	=	SYM
ejpam-3049	93	15	f	f	PROPN
ejpam-3049	93	16	.	.	PUNCT
ejpam-3049	94	1	indeed	indeed	ADV
ejpam-3049	94	2	,	,	PUNCT
ejpam-3049	94	3	if	if	SCONJ
ejpam-3049	94	4	x	x	SYM
ejpam-3049	94	5	∈	∈	PROPN
ejpam-3049	94	6	h	h	NOUN
ejpam-3049	94	7	,	,	PUNCT
ejpam-3049	94	8	then	then	ADV
ejpam-3049	94	9	(	(	PUNCT
ejpam-3049	94	10	f	f	PROPN
ejpam-3049	94	11	∧	∧	PROPN
ejpam-3049	94	12	f)(x	f)(x	PROPN
ejpam-3049	94	13	)	)	PUNCT
ejpam-3049	94	14	:	:	PUNCT
ejpam-3049	94	15	=	=	PUNCT
ejpam-3049	94	16	min{f(x	min{f(x	PROPN
ejpam-3049	94	17	)	)	PUNCT
ejpam-3049	94	18	,	,	PUNCT
ejpam-3049	94	19	f(x	f(x	PROPN
ejpam-3049	94	20	)	)	PUNCT
ejpam-3049	94	21	}	}	PUNCT
ejpam-3049	94	22	=	=	SYM
ejpam-3049	94	23	f(x	f(x	PROPN
ejpam-3049	94	24	)	)	PUNCT
ejpam-3049	94	25	.	.	PUNCT
ejpam-3049	95	1	the	the	DET
ejpam-3049	95	2	concepts	concept	NOUN
ejpam-3049	95	3	of	of	ADP
ejpam-3049	95	4	fuzzy	fuzzy	ADJ
ejpam-3049	95	5	right	right	NOUN
ejpam-3049	95	6	and	and	CCONJ
ejpam-3049	95	7	fuzzy	fuzzy	ADJ
ejpam-3049	95	8	left	leave	VERB
ejpam-3049	95	9	ideal	ideal	NOUN
ejpam-3049	95	10	of	of	ADP
ejpam-3049	95	11	a	a	DET
ejpam-3049	95	12	groupoid	groupoid	NOUN
ejpam-3049	95	13	due	due	ADP
ejpam-3049	95	14	to	to	ADP
ejpam-3049	95	15	kuroki	kuroki	NOUN
ejpam-3049	95	16	[	[	X
ejpam-3049	95	17	8	8	NUM
ejpam-3049	95	18	]	]	PUNCT
ejpam-3049	95	19	can	can	AUX
ejpam-3049	95	20	be	be	AUX
ejpam-3049	95	21	naturally	naturally	ADV
ejpam-3049	95	22	transferred	transfer	VERB
ejpam-3049	95	23	to	to	ADP
ejpam-3049	95	24	hypergroupoids	hypergroupoid	NOUN
ejpam-3049	95	25	as	as	SCONJ
ejpam-3049	95	26	follows	follow	VERB
ejpam-3049	95	27	:	:	PUNCT
ejpam-3049	95	28	a	a	DET
ejpam-3049	95	29	fuzzy	fuzzy	ADJ
ejpam-3049	95	30	subset	subset	NOUN
ejpam-3049	95	31	f	f	PROPN
ejpam-3049	95	32	of	of	ADP
ejpam-3049	95	33	an	an	DET
ejpam-3049	95	34	hypergroupoid	hypergroupoid	PROPN
ejpam-3049	95	35	h	h	NOUN
ejpam-3049	95	36	is	be	AUX
ejpam-3049	95	37	called	call	VERB
ejpam-3049	95	38	a	a	DET
ejpam-3049	95	39	fuzzy	fuzzy	ADJ
ejpam-3049	95	40	right	right	ADJ
ejpam-3049	95	41	ideal	ideal	NOUN
ejpam-3049	95	42	of	of	ADP
ejpam-3049	95	43	h	h	NOUN
ejpam-3049	95	44	if	if	SCONJ
ejpam-3049	95	45	f(x	f(x	PROPN
ejpam-3049	95	46	◦	◦	VERB
ejpam-3049	95	47	y	y	PROPN
ejpam-3049	95	48	)	)	PUNCT
ejpam-3049	95	49	≥	≥	NOUN
ejpam-3049	95	50	f(x	f(x	PROPN
ejpam-3049	95	51	)	)	PUNCT
ejpam-3049	95	52	for	for	ADP
ejpam-3049	95	53	every	every	DET
ejpam-3049	95	54	x	x	PROPN
ejpam-3049	95	55	,	,	PUNCT
ejpam-3049	95	56	y	y	PROPN
ejpam-3049	95	57	∈	∈	PROPN
ejpam-3049	95	58	h	h	NOUN
ejpam-3049	95	59	,	,	PUNCT
ejpam-3049	95	60	in	in	ADP
ejpam-3049	95	61	the	the	DET
ejpam-3049	95	62	sense	sense	NOUN
ejpam-3049	96	1	that	that	SCONJ
ejpam-3049	96	2	if	if	SCONJ
ejpam-3049	96	3	x	x	X
ejpam-3049	96	4	,	,	PUNCT
ejpam-3049	96	5	y	y	PROPN
ejpam-3049	96	6	∈	∈	PROPN
ejpam-3049	96	7	h	h	NOUN
ejpam-3049	96	8	and	and	CCONJ
ejpam-3049	96	9	u	u	NOUN
ejpam-3049	96	10	∈	∈	PROPN
ejpam-3049	96	11	x	x	PUNCT
ejpam-3049	96	12	◦	◦	NOUN
ejpam-3049	96	13	y	y	PROPN
ejpam-3049	96	14	,	,	PUNCT
ejpam-3049	96	15	then	then	ADV
ejpam-3049	96	16	f(u	f(u	PROPN
ejpam-3049	96	17	)	)	PUNCT
ejpam-3049	96	18	≥	≥	NOUN
ejpam-3049	96	19	f(x	f(x	PROPN
ejpam-3049	96	20	)	)	PUNCT
ejpam-3049	96	21	.	.	PUNCT
ejpam-3049	97	1	a	a	DET
ejpam-3049	97	2	fuzzy	fuzzy	ADJ
ejpam-3049	97	3	subset	subset	NOUN
ejpam-3049	97	4	f	f	PROPN
ejpam-3049	97	5	of	of	ADP
ejpam-3049	97	6	an	an	DET
ejpam-3049	97	7	hypergroupoid	hypergroupoid	PROPN
ejpam-3049	97	8	h	h	NOUN
ejpam-3049	97	9	is	be	AUX
ejpam-3049	97	10	called	call	VERB
ejpam-3049	97	11	a	a	DET
ejpam-3049	97	12	fuzzy	fuzzy	ADJ
ejpam-3049	97	13	left	leave	VERB
ejpam-3049	97	14	ideal	ideal	NOUN
ejpam-3049	97	15	of	of	ADP
ejpam-3049	97	16	h	h	NOUN
ejpam-3049	97	17	if	if	SCONJ
ejpam-3049	97	18	f(x	f(x	PROPN
ejpam-3049	97	19	◦	◦	VERB
ejpam-3049	97	20	y	y	PROPN
ejpam-3049	97	21	)	)	PUNCT
ejpam-3049	97	22	≥	≥	NOUN
ejpam-3049	97	23	f(y	f(y	NOUN
ejpam-3049	97	24	)	)	PUNCT
ejpam-3049	97	25	for	for	ADP
ejpam-3049	97	26	every	every	DET
ejpam-3049	97	27	x	x	PROPN
ejpam-3049	97	28	,	,	PUNCT
ejpam-3049	97	29	y	y	PROPN
ejpam-3049	97	30	∈	∈	PROPN
ejpam-3049	97	31	h	h	NOUN
ejpam-3049	97	32	,	,	PUNCT
ejpam-3049	97	33	meaning	mean	VERB
ejpam-3049	97	34	that	that	SCONJ
ejpam-3049	97	35	if	if	SCONJ
ejpam-3049	97	36	x	x	X
ejpam-3049	97	37	,	,	PUNCT
ejpam-3049	97	38	y	y	PROPN
ejpam-3049	97	39	∈	∈	PROPN
ejpam-3049	97	40	h	h	NOUN
ejpam-3049	97	41	and	and	CCONJ
ejpam-3049	97	42	u	u	NOUN
ejpam-3049	97	43	∈	∈	PROPN
ejpam-3049	97	44	x	x	PUNCT
ejpam-3049	97	45	◦	◦	NOUN
ejpam-3049	97	46	y	y	PROPN
ejpam-3049	97	47	,	,	PUNCT
ejpam-3049	97	48	then	then	ADV
ejpam-3049	97	49	f(u	f(u	PROPN
ejpam-3049	97	50	)	)	PUNCT
ejpam-3049	97	51	≥	≥	NOUN
ejpam-3049	97	52	f(y	f(y	NOUN
ejpam-3049	97	53	)	)	PUNCT
ejpam-3049	97	54	.	.	PUNCT
ejpam-3049	98	1	if	if	SCONJ
ejpam-3049	98	2	f	f	PROPN
ejpam-3049	98	3	is	be	AUX
ejpam-3049	98	4	both	both	CCONJ
ejpam-3049	98	5	a	a	DET
ejpam-3049	98	6	fuzzy	fuzzy	ADJ
ejpam-3049	98	7	right	right	NOUN
ejpam-3049	98	8	and	and	CCONJ
ejpam-3049	98	9	a	a	DET
ejpam-3049	98	10	fuzzy	fuzzy	ADJ
ejpam-3049	98	11	left	leave	VERB
ejpam-3049	98	12	ideal	ideal	NOUN
ejpam-3049	98	13	of	of	ADP
ejpam-3049	98	14	h	h	NOUN
ejpam-3049	98	15	,	,	PUNCT
ejpam-3049	98	16	then	then	ADV
ejpam-3049	98	17	it	it	PRON
ejpam-3049	98	18	is	be	AUX
ejpam-3049	98	19	called	call	VERB
ejpam-3049	98	20	a	a	DET
ejpam-3049	98	21	fuzzy	fuzzy	ADJ
ejpam-3049	98	22	ideal	ideal	NOUN
ejpam-3049	98	23	of	of	ADP
ejpam-3049	98	24	h.	h.	PROPN
ejpam-3049	98	25	a	a	DET
ejpam-3049	98	26	fuzzy	fuzzy	ADJ
ejpam-3049	98	27	subset	subset	NOUN
ejpam-3049	98	28	f	f	PROPN
ejpam-3049	98	29	of	of	ADP
ejpam-3049	98	30	an	an	DET
ejpam-3049	98	31	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	98	32	h	h	NOUN
ejpam-3049	98	33	is	be	AUX
ejpam-3049	98	34	called	call	VERB
ejpam-3049	98	35	a	a	DET
ejpam-3049	98	36	fuzzy	fuzzy	ADJ
ejpam-3049	98	37	bi	bi	NOUN
ejpam-3049	98	38	-	-	NOUN
ejpam-3049	98	39	ideal	ideal	NOUN
ejpam-3049	98	40	of	of	ADP
ejpam-3049	98	41	h	h	NOUN
ejpam-3049	98	42	if	if	SCONJ
ejpam-3049	98	43	f	f	PROPN
ejpam-3049	98	44	(	(	PUNCT
ejpam-3049	98	45	(	(	PUNCT
ejpam-3049	98	46	x	x	SYM
ejpam-3049	98	47	◦	◦	VERB
ejpam-3049	98	48	y	y	NOUN
ejpam-3049	98	49	)	)	PUNCT
ejpam-3049	98	50	∗	∗	NOUN
ejpam-3049	98	51	{	{	PUNCT
ejpam-3049	98	52	z	z	NOUN
ejpam-3049	98	53	}	}	PUNCT
ejpam-3049	98	54	)	)	PUNCT
ejpam-3049	98	55	≥	≥	NOUN
ejpam-3049	98	56	min{f(x	min{f(x	NOUN
ejpam-3049	98	57	)	)	PUNCT
ejpam-3049	98	58	,	,	PUNCT
ejpam-3049	98	59	f(z	f(z	PROPN
ejpam-3049	98	60	)	)	PUNCT
ejpam-3049	98	61	}	}	PUNCT
ejpam-3049	98	62	for	for	ADP
ejpam-3049	98	63	every	every	DET
ejpam-3049	98	64	x	x	PROPN
ejpam-3049	98	65	,	,	PUNCT
ejpam-3049	98	66	y	y	PROPN
ejpam-3049	98	67	,	,	PUNCT
ejpam-3049	98	68	z	z	PROPN
ejpam-3049	98	69	∈	∈	PROPN
ejpam-3049	98	70	h	h	NOUN
ejpam-3049	98	71	,	,	PUNCT
ejpam-3049	98	72	in	in	ADP
ejpam-3049	98	73	the	the	DET
ejpam-3049	98	74	sense	sense	NOUN
ejpam-3049	98	75	that	that	SCONJ
ejpam-3049	98	76	if	if	SCONJ
ejpam-3049	98	77	x	x	X
ejpam-3049	98	78	,	,	PUNCT
ejpam-3049	98	79	y	y	PROPN
ejpam-3049	98	80	,	,	PUNCT
ejpam-3049	98	81	z	z	PROPN
ejpam-3049	98	82	∈	∈	PROPN
ejpam-3049	98	83	h	h	NOUN
ejpam-3049	98	84	and	and	CCONJ
ejpam-3049	98	85	u	u	PROPN
ejpam-3049	98	86	∈	∈	PROPN
ejpam-3049	98	87	(	(	PUNCT
ejpam-3049	98	88	x	x	SYM
ejpam-3049	98	89	◦	◦	VERB
ejpam-3049	98	90	y	y	NOUN
ejpam-3049	98	91	)	)	PUNCT
ejpam-3049	98	92	∗	∗	NOUN
ejpam-3049	98	93	{	{	PUNCT
ejpam-3049	98	94	z	z	NOUN
ejpam-3049	98	95	}	}	PUNCT
ejpam-3049	98	96	,	,	PUNCT
ejpam-3049	98	97	then	then	ADV
ejpam-3049	98	98	f(u	f(u	PROPN
ejpam-3049	98	99	)	)	PUNCT
ejpam-3049	98	100	≥	≥	NOUN
ejpam-3049	98	101	min{f(x	min{f(x	NOUN
ejpam-3049	98	102	)	)	PUNCT
ejpam-3049	98	103	,	,	PUNCT
ejpam-3049	98	104	f(z	f(z	PROPN
ejpam-3049	98	105	)	)	PUNCT
ejpam-3049	98	106	}	}	PUNCT
ejpam-3049	98	107	.	.	PUNCT
ejpam-3049	99	1	exactly	exactly	ADV
ejpam-3049	99	2	as	as	ADP
ejpam-3049	99	3	in	in	ADP
ejpam-3049	99	4	groupoids	groupoid	NOUN
ejpam-3049	99	5	–	–	PUNCT
ejpam-3049	99	6	semigroups	semigroup	NOUN
ejpam-3049	99	7	,	,	PUNCT
ejpam-3049	99	8	the	the	DET
ejpam-3049	99	9	following	follow	VERB
ejpam-3049	99	10	hold	hold	NOUN
ejpam-3049	99	11	:	:	PUNCT
ejpam-3049	99	12	n.	n.	PROPN
ejpam-3049	99	13	kehayopulu	kehayopulu	PROPN
ejpam-3049	99	14	/	/	SYM
ejpam-3049	99	15	eur	eur	PROPN
ejpam-3049	99	16	.	.	PUNCT
ejpam-3049	100	1	j.	j.	PROPN
ejpam-3049	100	2	pure	pure	PROPN
ejpam-3049	100	3	appl	appl	PROPN
ejpam-3049	100	4	.	.	PROPN
ejpam-3049	100	5	math	math	PROPN
ejpam-3049	100	6	,	,	PUNCT
ejpam-3049	100	7	10	10	NUM
ejpam-3049	100	8	(	(	PUNCT
ejpam-3049	100	9	5	5	NUM
ejpam-3049	100	10	)	)	PUNCT
ejpam-3049	100	11	(	(	PUNCT
ejpam-3049	100	12	2017	2017	NUM
ejpam-3049	100	13	)	)	PUNCT
ejpam-3049	100	14	,	,	PUNCT
ejpam-3049	100	15	929	929	NUM
ejpam-3049	100	16	-	-	SYM
ejpam-3049	100	17	945	945	NUM
ejpam-3049	100	18	933	933	NUM
ejpam-3049	100	19	(	(	PUNCT
ejpam-3049	100	20	1	1	NUM
ejpam-3049	100	21	)	)	PUNCT
ejpam-3049	100	22	if	if	SCONJ
ejpam-3049	100	23	h	h	NOUN
ejpam-3049	100	24	is	be	AUX
ejpam-3049	100	25	an	an	DET
ejpam-3049	100	26	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	100	27	,	,	PUNCT
ejpam-3049	100	28	then	then	ADV
ejpam-3049	100	29	a	a	PRON
ejpam-3049	100	30	is	be	AUX
ejpam-3049	100	31	a	a	DET
ejpam-3049	100	32	right	right	ADJ
ejpam-3049	100	33	(	(	PUNCT
ejpam-3049	100	34	resp	resp	NOUN
ejpam-3049	100	35	.	.	PUNCT
ejpam-3049	101	1	left	left	ADJ
ejpam-3049	101	2	)	)	PUNCT
ejpam-3049	101	3	ideal	ideal	NOUN
ejpam-3049	101	4	of	of	ADP
ejpam-3049	101	5	h	h	NOUN
ejpam-3049	101	6	if	if	SCONJ
ejpam-3049	102	1	and	and	CCONJ
ejpam-3049	102	2	only	only	ADV
ejpam-3049	102	3	if	if	SCONJ
ejpam-3049	102	4	the	the	DET
ejpam-3049	102	5	characteristic	characteristic	ADJ
ejpam-3049	102	6	function	function	NOUN
ejpam-3049	102	7	fa	fa	PROPN
ejpam-3049	102	8	is	be	AUX
ejpam-3049	102	9	a	a	DET
ejpam-3049	102	10	fuzzy	fuzzy	ADJ
ejpam-3049	102	11	right	right	NOUN
ejpam-3049	102	12	(	(	PUNCT
ejpam-3049	102	13	resp	resp	NOUN
ejpam-3049	102	14	.	.	PUNCT
ejpam-3049	103	1	fuzzy	fuzzy	ADJ
ejpam-3049	103	2	left	left	ADJ
ejpam-3049	103	3	)	)	PUNCT
ejpam-3049	103	4	ideal	ideal	NOUN
ejpam-3049	103	5	of	of	ADP
ejpam-3049	103	6	h.	h.	PROPN
ejpam-3049	103	7	(	(	PUNCT
ejpam-3049	103	8	2	2	NUM
ejpam-3049	103	9	)	)	PUNCT
ejpam-3049	103	10	if	if	SCONJ
ejpam-3049	103	11	h	h	NOUN
ejpam-3049	103	12	is	be	AUX
ejpam-3049	103	13	an	an	DET
ejpam-3049	103	14	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	103	15	,	,	PUNCT
ejpam-3049	103	16	then	then	ADV
ejpam-3049	103	17	a	a	PRON
ejpam-3049	103	18	is	be	AUX
ejpam-3049	103	19	a	a	DET
ejpam-3049	103	20	bi	bi	NOUN
ejpam-3049	103	21	-	-	NOUN
ejpam-3049	103	22	ideal	ideal	NOUN
ejpam-3049	103	23	of	of	ADP
ejpam-3049	103	24	h	h	NOUN
ejpam-3049	103	25	if	if	SCONJ
ejpam-3049	104	1	and	and	CCONJ
ejpam-3049	104	2	only	only	ADV
ejpam-3049	104	3	if	if	SCONJ
ejpam-3049	104	4	fa	fa	PROPN
ejpam-3049	104	5	is	be	AUX
ejpam-3049	104	6	a	a	DET
ejpam-3049	104	7	fuzzy	fuzzy	ADJ
ejpam-3049	104	8	bi	bi	NOUN
ejpam-3049	104	9	-	-	NOUN
ejpam-3049	104	10	ideal	ideal	NOUN
ejpam-3049	104	11	of	of	ADP
ejpam-3049	104	12	h.	h.	PROPN
ejpam-3049	104	13	2	2	NUM
ejpam-3049	104	14	.	.	PUNCT
ejpam-3049	104	15	main	main	ADJ
ejpam-3049	104	16	results	result	NOUN
ejpam-3049	104	17	theorem	theorem	VERB
ejpam-3049	104	18	2.1	2.1	NUM
ejpam-3049	104	19	.	.	PUNCT
ejpam-3049	105	1	let	let	AUX
ejpam-3049	105	2	(	(	PUNCT
ejpam-3049	105	3	h	h	NOUN
ejpam-3049	105	4	,	,	PUNCT
ejpam-3049	105	5	◦	◦	NOUN
ejpam-3049	105	6	)	)	PUNCT
ejpam-3049	105	7	be	be	VERB
ejpam-3049	105	8	an	an	DET
ejpam-3049	105	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	105	10	.	.	PUNCT
ejpam-3049	106	1	the	the	DET
ejpam-3049	106	2	following	follow	VERB
ejpam-3049	106	3	are	be	AUX
ejpam-3049	106	4	equivalent	equivalent	ADJ
ejpam-3049	106	5	:	:	PUNCT
ejpam-3049	106	6	(	(	PUNCT
ejpam-3049	106	7	1	1	X
ejpam-3049	106	8	)	)	PUNCT
ejpam-3049	106	9	h	h	NOUN
ejpam-3049	106	10	is	be	AUX
ejpam-3049	106	11	regular	regular	ADJ
ejpam-3049	106	12	.	.	PUNCT
ejpam-3049	107	1	(	(	PUNCT
ejpam-3049	107	2	2	2	X
ejpam-3049	107	3	)	)	PUNCT
ejpam-3049	107	4	a	a	DET
ejpam-3049	107	5	∩b	∩b	NOUN
ejpam-3049	107	6	=	=	PUNCT
ejpam-3049	107	7	a	a	DET
ejpam-3049	107	8	∗b	∗b	PROPN
ejpam-3049	107	9	for	for	ADP
ejpam-3049	107	10	every	every	DET
ejpam-3049	107	11	right	right	ADJ
ejpam-3049	107	12	ideal	ideal	NOUN
ejpam-3049	107	13	a	a	PRON
ejpam-3049	107	14	and	and	CCONJ
ejpam-3049	107	15	every	every	DET
ejpam-3049	107	16	left	leave	VERB
ejpam-3049	107	17	ideal	ideal	PROPN
ejpam-3049	107	18	b	b	PROPN
ejpam-3049	107	19	of	of	ADP
ejpam-3049	107	20	h.	h.	PROPN
ejpam-3049	107	21	(	(	PUNCT
ejpam-3049	107	22	3	3	X
ejpam-3049	107	23	)	)	PUNCT
ejpam-3049	107	24	a	a	DET
ejpam-3049	107	25	∩b	∩b	NOUN
ejpam-3049	107	26	⊆	⊆	NUM
ejpam-3049	107	27	a	a	DET
ejpam-3049	107	28	∗b	∗b	NOUN
ejpam-3049	107	29	for	for	ADP
ejpam-3049	107	30	every	every	DET
ejpam-3049	107	31	right	right	ADJ
ejpam-3049	107	32	ideal	ideal	NOUN
ejpam-3049	107	33	a	a	PRON
ejpam-3049	107	34	and	and	CCONJ
ejpam-3049	107	35	every	every	DET
ejpam-3049	107	36	left	leave	VERB
ejpam-3049	107	37	ideal	ideal	PROPN
ejpam-3049	107	38	b	b	PROPN
ejpam-3049	107	39	of	of	ADP
ejpam-3049	107	40	h.	h.	PROPN
ejpam-3049	107	41	(	(	PUNCT
ejpam-3049	107	42	4	4	NUM
ejpam-3049	107	43	)	)	PUNCT
ejpam-3049	107	44	r(a	r(a	ADJ
ejpam-3049	107	45	)	)	PUNCT
ejpam-3049	107	46	∩	∩	NOUN
ejpam-3049	107	47	l(a	l(a	PROPN
ejpam-3049	107	48	)	)	PUNCT
ejpam-3049	107	49	⊆	⊆	NUM
ejpam-3049	107	50	r(a	r(a	NUM
ejpam-3049	107	51	)	)	PUNCT
ejpam-3049	107	52	∗	∗	NOUN
ejpam-3049	107	53	l(a	l(a	PROPN
ejpam-3049	107	54	)	)	PUNCT
ejpam-3049	107	55	for	for	ADP
ejpam-3049	107	56	every	every	DET
ejpam-3049	107	57	a	a	DET
ejpam-3049	107	58	∈	∈	PROPN
ejpam-3049	107	59	p∗(h	p∗(h	PROPN
ejpam-3049	107	60	)	)	PUNCT
ejpam-3049	107	61	.	.	PUNCT
ejpam-3049	108	1	(	(	PUNCT
ejpam-3049	108	2	5	5	X
ejpam-3049	108	3	)	)	PUNCT
ejpam-3049	108	4	r(a	r(a	ADJ
ejpam-3049	108	5	)	)	PUNCT
ejpam-3049	108	6	∩	∩	NOUN
ejpam-3049	108	7	l(a	l(a	PROPN
ejpam-3049	108	8	)	)	PUNCT
ejpam-3049	108	9	⊆	⊆	NUM
ejpam-3049	108	10	r(a	r(a	NUM
ejpam-3049	108	11	)	)	PUNCT
ejpam-3049	108	12	∗	∗	NOUN
ejpam-3049	108	13	l(a	l(a	PROPN
ejpam-3049	108	14	)	)	PUNCT
ejpam-3049	108	15	for	for	ADP
ejpam-3049	108	16	every	every	DET
ejpam-3049	108	17	a	a	DET
ejpam-3049	108	18	∈	∈	PROPN
ejpam-3049	108	19	h.	h.	NOUN
ejpam-3049	108	20	proof	proof	NOUN
ejpam-3049	108	21	.	.	PUNCT
ejpam-3049	109	1	(	(	PUNCT
ejpam-3049	109	2	1	1	X
ejpam-3049	109	3	)	)	PUNCT
ejpam-3049	109	4	=	=	NOUN
ejpam-3049	109	5	⇒	⇒	NOUN
ejpam-3049	109	6	(	(	PUNCT
ejpam-3049	109	7	2	2	NUM
ejpam-3049	109	8	)	)	PUNCT
ejpam-3049	109	9	.	.	PUNCT
ejpam-3049	110	1	let	let	VERB
ejpam-3049	110	2	a	a	PRON
ejpam-3049	110	3	be	be	AUX
ejpam-3049	110	4	a	a	DET
ejpam-3049	110	5	right	right	ADJ
ejpam-3049	110	6	ideal	ideal	NOUN
ejpam-3049	110	7	and	and	CCONJ
ejpam-3049	110	8	b	b	DET
ejpam-3049	110	9	a	a	DET
ejpam-3049	110	10	left	left	ADJ
ejpam-3049	110	11	ideal	ideal	NOUN
ejpam-3049	110	12	of	of	ADP
ejpam-3049	110	13	h.	h.	PROPN
ejpam-3049	110	14	the	the	DET
ejpam-3049	110	15	set	set	NOUN
ejpam-3049	110	16	a	a	DET
ejpam-3049	110	17	∩	∩	ADJ
ejpam-3049	110	18	b	b	NOUN
ejpam-3049	110	19	is	be	AUX
ejpam-3049	110	20	a	a	DET
ejpam-3049	110	21	nonempty	nonempty	ADJ
ejpam-3049	110	22	subset	subset	NOUN
ejpam-3049	110	23	of	of	ADP
ejpam-3049	110	24	h.	h.	PROPN
ejpam-3049	110	25	indeed	indeed	ADV
ejpam-3049	110	26	:	:	PUNCT
ejpam-3049	110	27	take	take	VERB
ejpam-3049	110	28	an	an	DET
ejpam-3049	110	29	element	element	NOUN
ejpam-3049	110	30	a	a	DET
ejpam-3049	110	31	∈	∈	PROPN
ejpam-3049	110	32	a	a	PRON
ejpam-3049	110	33	and	and	CCONJ
ejpam-3049	110	34	an	an	DET
ejpam-3049	110	35	element	element	NOUN
ejpam-3049	110	36	b	b	PROPN
ejpam-3049	110	37	∈	∈	PROPN
ejpam-3049	110	38	b	b	PROPN
ejpam-3049	110	39	(	(	PUNCT
ejpam-3049	110	40	a	a	PRON
ejpam-3049	110	41	,	,	PUNCT
ejpam-3049	110	42	b	b	NOUN
ejpam-3049	110	43	6=	6=	NUM
ejpam-3049	110	44	∅	∅	NOUN
ejpam-3049	110	45	)	)	PUNCT
ejpam-3049	110	46	.	.	PUNCT
ejpam-3049	111	1	then	then	ADV
ejpam-3049	111	2	a	a	DET
ejpam-3049	111	3	◦	◦	NOUN
ejpam-3049	111	4	b	b	NOUN
ejpam-3049	111	5	⊆	⊆	NUM
ejpam-3049	111	6	a	a	DET
ejpam-3049	111	7	∗h	∗h	NOUN
ejpam-3049	111	8	⊆	⊆	NUM
ejpam-3049	111	9	a	a	PRON
ejpam-3049	111	10	and	and	CCONJ
ejpam-3049	111	11	a	a	DET
ejpam-3049	111	12	◦	◦	NOUN
ejpam-3049	111	13	b	b	NOUN
ejpam-3049	112	1	⊆	⊆	NUM
ejpam-3049	112	2	h	h	NOUN
ejpam-3049	112	3	∗b	∗b	PROPN
ejpam-3049	112	4	⊆	⊆	NUM
ejpam-3049	112	5	b	b	NOUN
ejpam-3049	112	6	,	,	PUNCT
ejpam-3049	112	7	so	so	SCONJ
ejpam-3049	112	8	a	a	DET
ejpam-3049	112	9	◦	◦	NOUN
ejpam-3049	112	10	b	b	NOUN
ejpam-3049	112	11	⊆	⊆	NUM
ejpam-3049	112	12	a∩b	a∩b	PROPN
ejpam-3049	112	13	.	.	PUNCT
ejpam-3049	113	1	since	since	SCONJ
ejpam-3049	113	2	a	a	DET
ejpam-3049	113	3	◦	◦	NOUN
ejpam-3049	113	4	b	b	SYM
ejpam-3049	113	5	6=	6=	NUM
ejpam-3049	113	6	∅	∅	NOUN
ejpam-3049	113	7	,	,	PUNCT
ejpam-3049	113	8	we	we	PRON
ejpam-3049	113	9	have	have	VERB
ejpam-3049	113	10	a	a	DET
ejpam-3049	113	11	∩b	∩b	NOUN
ejpam-3049	113	12	6=	6=	ADP
ejpam-3049	113	13	∅.	∅.	NOUN
ejpam-3049	113	14	since	since	SCONJ
ejpam-3049	113	15	h	h	NOUN
ejpam-3049	113	16	is	be	AUX
ejpam-3049	113	17	regular	regular	ADJ
ejpam-3049	113	18	and	and	CCONJ
ejpam-3049	113	19	a	a	DET
ejpam-3049	113	20	∩b	∩b	NOUN
ejpam-3049	113	21	∈	∈	PROPN
ejpam-3049	113	22	p∗(h	p∗(h	PROPN
ejpam-3049	113	23	)	)	PUNCT
ejpam-3049	113	24	,	,	PUNCT
ejpam-3049	113	25	we	we	PRON
ejpam-3049	113	26	have	have	VERB
ejpam-3049	113	27	a	a	DET
ejpam-3049	113	28	∩b	∩b	NOUN
ejpam-3049	113	29	⊆	⊆	NUM
ejpam-3049	113	30	(	(	PUNCT
ejpam-3049	113	31	a	a	DET
ejpam-3049	113	32	∩b	∩b	NOUN
ejpam-3049	113	33	)	)	PUNCT
ejpam-3049	113	34	∗h	∗h	NOUN
ejpam-3049	113	35	∗	∗	NOUN
ejpam-3049	113	36	(	(	PUNCT
ejpam-3049	113	37	a	a	DET
ejpam-3049	113	38	∩b	∩b	NOUN
ejpam-3049	113	39	)	)	PUNCT
ejpam-3049	113	40	⊆	⊆	NUM
ejpam-3049	113	41	a	a	DET
ejpam-3049	113	42	∗h	∗h	NOUN
ejpam-3049	113	43	∗b	∗b	NOUN
ejpam-3049	113	44	=	=	SYM
ejpam-3049	113	45	(	(	PUNCT
ejpam-3049	113	46	a	a	DET
ejpam-3049	113	47	∗h	∗h	NOUN
ejpam-3049	113	48	)	)	PUNCT
ejpam-3049	113	49	∗b	∗b	PROPN
ejpam-3049	113	50	⊆	⊆	SYM
ejpam-3049	113	51	a	a	DET
ejpam-3049	113	52	∗b	∗b	PROPN
ejpam-3049	113	53	⊆	⊆	X
ejpam-3049	113	54	(	(	PUNCT
ejpam-3049	113	55	a	a	DET
ejpam-3049	113	56	∗h	∗h	NOUN
ejpam-3049	113	57	)	)	PUNCT
ejpam-3049	113	58	∩	∩	NOUN
ejpam-3049	113	59	(	(	PUNCT
ejpam-3049	113	60	h	h	NOUN
ejpam-3049	113	61	∗b	∗b	PROPN
ejpam-3049	113	62	)	)	PUNCT
ejpam-3049	113	63	⊆	⊆	NUM
ejpam-3049	113	64	a	a	DET
ejpam-3049	113	65	∩b	∩b	NOUN
ejpam-3049	113	66	.	.	PUNCT
ejpam-3049	114	1	thus	thus	ADV
ejpam-3049	114	2	we	we	PRON
ejpam-3049	114	3	have	have	VERB
ejpam-3049	114	4	a	a	DET
ejpam-3049	114	5	∩b	∩b	NOUN
ejpam-3049	114	6	=	=	PUNCT
ejpam-3049	114	7	a	a	DET
ejpam-3049	114	8	∗b	∗b	NOUN
ejpam-3049	114	9	.	.	PUNCT
ejpam-3049	115	1	the	the	DET
ejpam-3049	115	2	implications	implication	NOUN
ejpam-3049	115	3	(	(	PUNCT
ejpam-3049	115	4	2)⇒	2)⇒	NUM
ejpam-3049	115	5	(	(	PUNCT
ejpam-3049	115	6	3)⇒	3)⇒	NUM
ejpam-3049	115	7	(	(	PUNCT
ejpam-3049	115	8	4)⇒	4)⇒	NUM
ejpam-3049	115	9	(	(	PUNCT
ejpam-3049	115	10	5	5	NUM
ejpam-3049	115	11	)	)	PUNCT
ejpam-3049	115	12	are	be	AUX
ejpam-3049	115	13	obvious	obvious	ADJ
ejpam-3049	115	14	.	.	PUNCT
ejpam-3049	116	1	(	(	PUNCT
ejpam-3049	116	2	5	5	X
ejpam-3049	116	3	)	)	PUNCT
ejpam-3049	116	4	=	=	NOUN
ejpam-3049	116	5	⇒	⇒	NOUN
ejpam-3049	116	6	(	(	PUNCT
ejpam-3049	116	7	1	1	NUM
ejpam-3049	116	8	)	)	PUNCT
ejpam-3049	116	9	.	.	PUNCT
ejpam-3049	117	1	let	let	VERB
ejpam-3049	117	2	a	a	DET
ejpam-3049	117	3	∈	∈	PROPN
ejpam-3049	117	4	h.	h.	NOUN
ejpam-3049	117	5	since	since	SCONJ
ejpam-3049	117	6	r(a	r(a	PROPN
ejpam-3049	117	7	)	)	PUNCT
ejpam-3049	117	8	is	be	AUX
ejpam-3049	117	9	a	a	DET
ejpam-3049	117	10	right	right	ADJ
ejpam-3049	117	11	ideal	ideal	NOUN
ejpam-3049	117	12	of	of	ADP
ejpam-3049	117	13	h	h	NOUN
ejpam-3049	117	14	and	and	CCONJ
ejpam-3049	117	15	l(a	l(a	PROPN
ejpam-3049	117	16	)	)	PUNCT
ejpam-3049	117	17	is	be	AUX
ejpam-3049	117	18	a	a	DET
ejpam-3049	117	19	left	left	ADJ
ejpam-3049	117	20	ideal	ideal	NOUN
ejpam-3049	117	21	of	of	ADP
ejpam-3049	117	22	h	h	NOUN
ejpam-3049	117	23	,	,	PUNCT
ejpam-3049	117	24	by	by	ADP
ejpam-3049	117	25	hypothesis	hypothesis	NOUN
ejpam-3049	117	26	,	,	PUNCT
ejpam-3049	117	27	we	we	PRON
ejpam-3049	117	28	have	have	VERB
ejpam-3049	117	29	a	a	DET
ejpam-3049	117	30	∈	∈	PROPN
ejpam-3049	117	31	r(a	r(a	NUM
ejpam-3049	117	32	)	)	PUNCT
ejpam-3049	117	33	∩	∩	NOUN
ejpam-3049	117	34	l(a	l(a	PROPN
ejpam-3049	117	35	)	)	PUNCT
ejpam-3049	117	36	⊆	⊆	NUM
ejpam-3049	117	37	r(a	r(a	NUM
ejpam-3049	117	38	)	)	PUNCT
ejpam-3049	117	39	∗	∗	NOUN
ejpam-3049	117	40	l(a	l(a	PROPN
ejpam-3049	117	41	)	)	PUNCT
ejpam-3049	118	1	=	=	PRON
ejpam-3049	118	2	(	(	PUNCT
ejpam-3049	118	3	{	{	PUNCT
ejpam-3049	118	4	a	a	DET
ejpam-3049	118	5	}	}	PUNCT
ejpam-3049	118	6	∪	∪	X
ejpam-3049	118	7	(	(	PUNCT
ejpam-3049	118	8	{	{	PUNCT
ejpam-3049	118	9	a	a	DET
ejpam-3049	118	10	}	}	PUNCT
ejpam-3049	118	11	∗h	∗h	NOUN
ejpam-3049	118	12	)	)	PUNCT
ejpam-3049	118	13	)	)	PUNCT
ejpam-3049	118	14	∗	∗	NOUN
ejpam-3049	118	15	(	(	PUNCT
ejpam-3049	118	16	{	{	PUNCT
ejpam-3049	118	17	a	a	DET
ejpam-3049	118	18	}	}	PUNCT
ejpam-3049	118	19	∪	∪	NOUN
ejpam-3049	118	20	(	(	PUNCT
ejpam-3049	118	21	h	h	NOUN
ejpam-3049	118	22	∗	∗	NOUN
ejpam-3049	118	23	{	{	PUNCT
ejpam-3049	118	24	a	a	NOUN
ejpam-3049	118	25	}	}	PUNCT
ejpam-3049	118	26	)	)	PUNCT
ejpam-3049	118	27	)	)	PUNCT
ejpam-3049	119	1	=	=	PRON
ejpam-3049	119	2	(	(	PUNCT
ejpam-3049	119	3	a	a	DET
ejpam-3049	119	4	◦	◦	NOUN
ejpam-3049	119	5	a	a	X
ejpam-3049	119	6	)	)	PUNCT
ejpam-3049	119	7	∪	∪	NOUN
ejpam-3049	119	8	(	(	PUNCT
ejpam-3049	119	9	{	{	PUNCT
ejpam-3049	119	10	a	a	DET
ejpam-3049	119	11	}	}	PUNCT
ejpam-3049	119	12	∗h	∗h	NOUN
ejpam-3049	119	13	∗	∗	NOUN
ejpam-3049	119	14	{	{	PUNCT
ejpam-3049	119	15	a	a	NOUN
ejpam-3049	119	16	}	}	PUNCT
ejpam-3049	119	17	)	)	PUNCT
ejpam-3049	119	18	∪	∪	NOUN
ejpam-3049	119	19	(	(	PUNCT
ejpam-3049	119	20	{	{	PUNCT
ejpam-3049	119	21	a	a	PRON
ejpam-3049	119	22	}	}	PUNCT
ejpam-3049	119	23	∗h	∗h	NOUN
ejpam-3049	119	24	∗h	∗h	NOUN
ejpam-3049	119	25	∗	∗	NOUN
ejpam-3049	119	26	{	{	PUNCT
ejpam-3049	119	27	a	a	NOUN
ejpam-3049	119	28	}	}	PUNCT
ejpam-3049	119	29	)	)	PUNCT
ejpam-3049	119	30	(	(	PUNCT
ejpam-3049	119	31	by	by	ADP
ejpam-3049	119	32	lemma	lemma	PROPN
ejpam-3049	119	33	1.1	1.1	NUM
ejpam-3049	119	34	)	)	PUNCT
ejpam-3049	119	35	=	=	NOUN
ejpam-3049	119	36	(	(	PUNCT
ejpam-3049	119	37	a	a	DET
ejpam-3049	119	38	◦	◦	NOUN
ejpam-3049	119	39	a	a	X
ejpam-3049	119	40	)	)	PUNCT
ejpam-3049	119	41	∪	∪	NOUN
ejpam-3049	119	42	(	(	PUNCT
ejpam-3049	119	43	{	{	PUNCT
ejpam-3049	119	44	a	a	DET
ejpam-3049	119	45	}	}	PUNCT
ejpam-3049	119	46	∗h	∗h	NOUN
ejpam-3049	119	47	∗	∗	NOUN
ejpam-3049	119	48	{	{	PUNCT
ejpam-3049	119	49	a	a	NOUN
ejpam-3049	119	50	}	}	PUNCT
ejpam-3049	119	51	)	)	PUNCT
ejpam-3049	119	52	.	.	PUNCT
ejpam-3049	120	1	we	we	PRON
ejpam-3049	120	2	have	have	VERB
ejpam-3049	120	3	a	a	DET
ejpam-3049	120	4	∈	∈	PROPN
ejpam-3049	120	5	a	a	DET
ejpam-3049	120	6	◦	◦	NOUN
ejpam-3049	120	7	a	a	X
ejpam-3049	120	8	,	,	PUNCT
ejpam-3049	120	9	so	so	SCONJ
ejpam-3049	120	10	a	a	DET
ejpam-3049	120	11	∈	∈	NOUN
ejpam-3049	120	12	(	(	PUNCT
ejpam-3049	120	13	a	a	DET
ejpam-3049	120	14	◦	◦	NOUN
ejpam-3049	120	15	a	a	X
ejpam-3049	120	16	)	)	PUNCT
ejpam-3049	120	17	∗	∗	NOUN
ejpam-3049	120	18	{	{	PUNCT
ejpam-3049	120	19	a	a	NOUN
ejpam-3049	120	20	}	}	PUNCT
ejpam-3049	120	21	or	or	CCONJ
ejpam-3049	120	22	a	a	DET
ejpam-3049	120	23	∈	∈	NOUN
ejpam-3049	120	24	{	{	PUNCT
ejpam-3049	120	25	a	a	NOUN
ejpam-3049	120	26	}	}	PUNCT
ejpam-3049	120	27	∗h	∗h	NOUN
ejpam-3049	120	28	∗	∗	NOUN
ejpam-3049	120	29	{	{	PUNCT
ejpam-3049	120	30	a	a	NOUN
ejpam-3049	120	31	}	}	PUNCT
ejpam-3049	120	32	.	.	PUNCT
ejpam-3049	121	1	in	in	ADP
ejpam-3049	121	2	each	each	DET
ejpam-3049	121	3	case	case	NOUN
ejpam-3049	121	4	,	,	PUNCT
ejpam-3049	121	5	h	h	NOUN
ejpam-3049	121	6	is	be	AUX
ejpam-3049	121	7	regular	regular	ADJ
ejpam-3049	121	8	.	.	PUNCT
ejpam-3049	122	1	�	�	PROPN
ejpam-3049	122	2	proposition	proposition	NOUN
ejpam-3049	122	3	2.2	2.2	NUM
ejpam-3049	122	4	.	.	PUNCT
ejpam-3049	123	1	let	let	AUX
ejpam-3049	123	2	(	(	PUNCT
ejpam-3049	123	3	h	h	NOUN
ejpam-3049	123	4	,	,	PUNCT
ejpam-3049	123	5	◦	◦	NOUN
ejpam-3049	123	6	)	)	PUNCT
ejpam-3049	123	7	be	be	VERB
ejpam-3049	123	8	an	an	DET
ejpam-3049	123	9	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	123	10	,	,	PUNCT
ejpam-3049	123	11	f	f	PROPN
ejpam-3049	123	12	a	a	DET
ejpam-3049	123	13	fuzzy	fuzzy	ADJ
ejpam-3049	123	14	right	right	ADJ
ejpam-3049	123	15	ideal	ideal	NOUN
ejpam-3049	123	16	and	and	CCONJ
ejpam-3049	123	17	g	g	ADP
ejpam-3049	123	18	a	a	DET
ejpam-3049	123	19	fuzzy	fuzzy	ADJ
ejpam-3049	123	20	left	leave	VERB
ejpam-3049	123	21	ideal	ideal	NOUN
ejpam-3049	123	22	of	of	ADP
ejpam-3049	123	23	h.	h.	PROPN
ejpam-3049	124	1	then	then	ADV
ejpam-3049	124	2	we	we	PRON
ejpam-3049	124	3	have	have	VERB
ejpam-3049	124	4	f	f	NUM
ejpam-3049	124	5	◦	◦	NOUN
ejpam-3049	124	6	g	g	PROPN
ejpam-3049	124	7	�	�	PROPN
ejpam-3049	124	8	f	f	PROPN
ejpam-3049	124	9	∧	∧	PROPN
ejpam-3049	124	10	g.	g.	PROPN
ejpam-3049	124	11	proof	proof	NOUN
ejpam-3049	124	12	.	.	PUNCT
ejpam-3049	125	1	let	let	VERB
ejpam-3049	125	2	a	a	DET
ejpam-3049	125	3	∈	∈	PROPN
ejpam-3049	125	4	h.	h.	NOUN
ejpam-3049	126	1	then	then	ADV
ejpam-3049	126	2	(	(	PUNCT
ejpam-3049	126	3	f	f	X
ejpam-3049	126	4	◦	◦	PROPN
ejpam-3049	126	5	g)(a	g)(a	PROPN
ejpam-3049	126	6	)	)	PUNCT
ejpam-3049	126	7	≤	≤	NOUN
ejpam-3049	126	8	(	(	PUNCT
ejpam-3049	126	9	f	f	PROPN
ejpam-3049	126	10	∧	∧	PROPN
ejpam-3049	126	11	g)(a	g)(a	PROPN
ejpam-3049	126	12	)	)	PUNCT
ejpam-3049	126	13	.	.	PUNCT
ejpam-3049	127	1	in	in	ADP
ejpam-3049	127	2	fact	fact	NOUN
ejpam-3049	127	3	:	:	PUNCT
ejpam-3049	127	4	if	if	SCONJ
ejpam-3049	127	5	aa	aa	NOUN
ejpam-3049	127	6	=	=	NOUN
ejpam-3049	127	7	∅	∅	NOUN
ejpam-3049	127	8	,	,	PUNCT
ejpam-3049	127	9	then	then	ADV
ejpam-3049	127	10	(	(	PUNCT
ejpam-3049	127	11	f	f	X
ejpam-3049	127	12	◦	◦	NOUN
ejpam-3049	127	13	g)(a	g)(a	PROPN
ejpam-3049	127	14	)	)	PUNCT
ejpam-3049	127	15	:	:	PUNCT
ejpam-3049	127	16	=	=	SYM
ejpam-3049	127	17	0	0	X
ejpam-3049	127	18	.	.	PUNCT
ejpam-3049	128	1	since	since	SCONJ
ejpam-3049	128	2	a	a	DET
ejpam-3049	128	3	∈	∈	PROPN
ejpam-3049	128	4	h	h	NOUN
ejpam-3049	128	5	and	and	CCONJ
ejpam-3049	128	6	f	f	PROPN
ejpam-3049	128	7	∧	∧	PROPN
ejpam-3049	128	8	g	g	PROPN
ejpam-3049	128	9	is	be	AUX
ejpam-3049	128	10	a	a	DET
ejpam-3049	128	11	fuzzy	fuzzy	ADJ
ejpam-3049	128	12	subset	subset	NOUN
ejpam-3049	128	13	of	of	ADP
ejpam-3049	128	14	h	h	NOUN
ejpam-3049	128	15	,	,	PUNCT
ejpam-3049	128	16	we	we	PRON
ejpam-3049	128	17	have	have	VERB
ejpam-3049	128	18	(	(	PUNCT
ejpam-3049	128	19	f	f	PROPN
ejpam-3049	128	20	∧	∧	PROPN
ejpam-3049	128	21	g)(a	g)(a	PROPN
ejpam-3049	128	22	)	)	PUNCT
ejpam-3049	128	23	≥	≥	NOUN
ejpam-3049	128	24	0	0	NUM
ejpam-3049	128	25	,	,	PUNCT
ejpam-3049	128	26	thus	thus	ADV
ejpam-3049	128	27	we	we	PRON
ejpam-3049	128	28	have	have	VERB
ejpam-3049	128	29	(	(	PUNCT
ejpam-3049	128	30	f	f	X
ejpam-3049	128	31	◦	◦	PROPN
ejpam-3049	128	32	g)(a	g)(a	PROPN
ejpam-3049	128	33	)	)	PUNCT
ejpam-3049	128	34	≤	≤	NOUN
ejpam-3049	128	35	(	(	PUNCT
ejpam-3049	128	36	f	f	PROPN
ejpam-3049	128	37	∧	∧	PROPN
ejpam-3049	128	38	g)(a	g)(a	PROPN
ejpam-3049	128	39	)	)	PUNCT
ejpam-3049	128	40	.	.	PUNCT
ejpam-3049	129	1	let	let	VERB
ejpam-3049	129	2	now	now	ADV
ejpam-3049	129	3	aa	aa	VERB
ejpam-3049	129	4	6=	6=	ADP
ejpam-3049	129	5	∅.	∅.	VERB
ejpam-3049	129	6	then	then	ADV
ejpam-3049	129	7	(	(	PUNCT
ejpam-3049	129	8	f	f	X
ejpam-3049	129	9	◦	◦	NOUN
ejpam-3049	129	10	g)(a	g)(a	PROPN
ejpam-3049	129	11	)	)	PUNCT
ejpam-3049	129	12	:	:	PUNCT
ejpam-3049	130	1	=	=	SYM
ejpam-3049	130	2	∨	∨	X
ejpam-3049	130	3	(	(	PUNCT
ejpam-3049	130	4	x	x	X
ejpam-3049	130	5	,	,	PUNCT
ejpam-3049	130	6	y)∈aa	y)∈aa	PROPN
ejpam-3049	130	7	min{f(x	min{f(x	PROPN
ejpam-3049	130	8	)	)	PUNCT
ejpam-3049	130	9	,	,	PUNCT
ejpam-3049	130	10	g(y	g(y	PROPN
ejpam-3049	130	11	)	)	PUNCT
ejpam-3049	130	12	}	}	PUNCT
ejpam-3049	130	13	(	(	PUNCT
ejpam-3049	130	14	∗	∗	NOUN
ejpam-3049	130	15	)	)	PUNCT
ejpam-3049	130	16	n.	n.	NOUN
ejpam-3049	130	17	kehayopulu	kehayopulu	PROPN
ejpam-3049	130	18	/	/	SYM
ejpam-3049	130	19	eur	eur	PROPN
ejpam-3049	130	20	.	.	PUNCT
ejpam-3049	131	1	j.	j.	PROPN
ejpam-3049	131	2	pure	pure	PROPN
ejpam-3049	131	3	appl	appl	PROPN
ejpam-3049	131	4	.	.	PROPN
ejpam-3049	131	5	math	math	PROPN
ejpam-3049	131	6	,	,	PUNCT
ejpam-3049	131	7	10	10	NUM
ejpam-3049	131	8	(	(	PUNCT
ejpam-3049	131	9	5	5	NUM
ejpam-3049	131	10	)	)	PUNCT
ejpam-3049	131	11	(	(	PUNCT
ejpam-3049	131	12	2017	2017	NUM
ejpam-3049	131	13	)	)	PUNCT
ejpam-3049	131	14	,	,	PUNCT
ejpam-3049	131	15	929	929	NUM
ejpam-3049	131	16	-	-	SYM
ejpam-3049	131	17	945	945	NUM
ejpam-3049	131	18	934	934	NUM
ejpam-3049	131	19	we	we	PRON
ejpam-3049	131	20	have	have	VERB
ejpam-3049	131	21	min{f(x	min{f(x	NOUN
ejpam-3049	131	22	)	)	PUNCT
ejpam-3049	131	23	,	,	PUNCT
ejpam-3049	131	24	g(y	g(y	NOUN
ejpam-3049	131	25	)	)	PUNCT
ejpam-3049	131	26	}	}	PUNCT
ejpam-3049	131	27	≤	≤	NOUN
ejpam-3049	131	28	(	(	PUNCT
ejpam-3049	131	29	f	f	PROPN
ejpam-3049	131	30	∧	∧	PROPN
ejpam-3049	131	31	g)(a	g)(a	PROPN
ejpam-3049	131	32	)	)	PUNCT
ejpam-3049	131	33	for	for	ADP
ejpam-3049	131	34	every	every	DET
ejpam-3049	131	35	(	(	PUNCT
ejpam-3049	131	36	x	x	NOUN
ejpam-3049	131	37	,	,	PUNCT
ejpam-3049	131	38	y	y	NOUN
ejpam-3049	131	39	)	)	PUNCT
ejpam-3049	131	40	∈	∈	PROPN
ejpam-3049	131	41	aa	aa	NOUN
ejpam-3049	131	42	(	(	PUNCT
ejpam-3049	131	43	∗∗	∗∗	NOUN
ejpam-3049	131	44	)	)	PUNCT
ejpam-3049	131	45	indeed	indeed	ADV
ejpam-3049	131	46	:	:	PUNCT
ejpam-3049	131	47	let	let	VERB
ejpam-3049	131	48	(	(	PUNCT
ejpam-3049	131	49	x	x	NOUN
ejpam-3049	131	50	,	,	PUNCT
ejpam-3049	131	51	y	y	NOUN
ejpam-3049	131	52	)	)	PUNCT
ejpam-3049	131	53	∈	∈	PROPN
ejpam-3049	131	54	aa	aa	NOUN
ejpam-3049	131	55	.	.	PUNCT
ejpam-3049	132	1	then	then	ADV
ejpam-3049	132	2	a	a	DET
ejpam-3049	132	3	∈	∈	PROPN
ejpam-3049	132	4	x	x	PUNCT
ejpam-3049	132	5	◦	◦	NOUN
ejpam-3049	132	6	y.	y.	NOUN
ejpam-3049	132	7	since	since	SCONJ
ejpam-3049	132	8	f	f	PROPN
ejpam-3049	132	9	is	be	AUX
ejpam-3049	132	10	a	a	DET
ejpam-3049	132	11	fuzzy	fuzzy	ADJ
ejpam-3049	132	12	right	right	ADJ
ejpam-3049	132	13	ideal	ideal	NOUN
ejpam-3049	132	14	of	of	ADP
ejpam-3049	132	15	h	h	NOUN
ejpam-3049	132	16	,	,	PUNCT
ejpam-3049	132	17	we	we	PRON
ejpam-3049	132	18	have	have	VERB
ejpam-3049	132	19	f(x	f(x	PROPN
ejpam-3049	132	20	◦	◦	PROPN
ejpam-3049	132	21	y	y	PROPN
ejpam-3049	132	22	)	)	PUNCT
ejpam-3049	132	23	≥	≥	NOUN
ejpam-3049	132	24	f(x	f(x	PROPN
ejpam-3049	132	25	)	)	PUNCT
ejpam-3049	132	26	,	,	PUNCT
ejpam-3049	132	27	then	then	ADV
ejpam-3049	132	28	we	we	PRON
ejpam-3049	132	29	have	have	VERB
ejpam-3049	132	30	f(a	f(a	PROPN
ejpam-3049	132	31	)	)	PUNCT
ejpam-3049	132	32	≥	≥	NOUN
ejpam-3049	132	33	f(x	f(x	PROPN
ejpam-3049	132	34	)	)	PUNCT
ejpam-3049	132	35	.	.	PUNCT
ejpam-3049	133	1	since	since	SCONJ
ejpam-3049	133	2	g	g	PROPN
ejpam-3049	133	3	is	be	AUX
ejpam-3049	133	4	a	a	DET
ejpam-3049	133	5	fuzzy	fuzzy	ADJ
ejpam-3049	133	6	left	leave	VERB
ejpam-3049	133	7	ideal	ideal	NOUN
ejpam-3049	133	8	of	of	ADP
ejpam-3049	133	9	h	h	NOUN
ejpam-3049	133	10	,	,	PUNCT
ejpam-3049	133	11	we	we	PRON
ejpam-3049	133	12	have	have	VERB
ejpam-3049	133	13	g(x	g(x	NOUN
ejpam-3049	133	14	◦	◦	NOUN
ejpam-3049	133	15	y	y	NOUN
ejpam-3049	133	16	)	)	PUNCT
ejpam-3049	133	17	≥	≥	NOUN
ejpam-3049	133	18	g(y	g(y	NOUN
ejpam-3049	133	19	)	)	PUNCT
ejpam-3049	133	20	,	,	PUNCT
ejpam-3049	133	21	then	then	ADV
ejpam-3049	133	22	g(a	g(a	PROPN
ejpam-3049	133	23	)	)	PUNCT
ejpam-3049	133	24	≥	≥	NOUN
ejpam-3049	133	25	g(y	g(y	NOUN
ejpam-3049	133	26	)	)	PUNCT
ejpam-3049	133	27	,	,	PUNCT
ejpam-3049	133	28	so	so	CCONJ
ejpam-3049	133	29	(	(	PUNCT
ejpam-3049	133	30	f	f	PROPN
ejpam-3049	133	31	∧	∧	PROPN
ejpam-3049	133	32	g)(a	g)(a	PROPN
ejpam-3049	133	33	)	)	PUNCT
ejpam-3049	133	34	:	:	PUNCT
ejpam-3049	133	35	=	=	SYM
ejpam-3049	133	36	min{f(a	min{f(a	PROPN
ejpam-3049	133	37	)	)	PUNCT
ejpam-3049	133	38	,	,	PUNCT
ejpam-3049	133	39	g(a	g(a	PROPN
ejpam-3049	133	40	)	)	PUNCT
ejpam-3049	133	41	}	}	PUNCT
ejpam-3049	133	42	≥	≥	NUM
ejpam-3049	133	43	min{f(x	min{f(x	NOUN
ejpam-3049	133	44	)	)	PUNCT
ejpam-3049	133	45	,	,	PUNCT
ejpam-3049	133	46	g(y	g(y	PROPN
ejpam-3049	133	47	)	)	PUNCT
ejpam-3049	133	48	}	}	PUNCT
ejpam-3049	133	49	,	,	PUNCT
ejpam-3049	133	50	and	and	CCONJ
ejpam-3049	133	51	condition	condition	NOUN
ejpam-3049	133	52	(	(	PUNCT
ejpam-3049	133	53	∗∗	∗∗	NOUN
ejpam-3049	133	54	)	)	PUNCT
ejpam-3049	133	55	is	be	AUX
ejpam-3049	133	56	satisfied	satisfied	ADJ
ejpam-3049	133	57	.	.	PUNCT
ejpam-3049	134	1	by	by	ADP
ejpam-3049	134	2	(	(	PUNCT
ejpam-3049	134	3	∗∗	∗∗	PROPN
ejpam-3049	134	4	)	)	PUNCT
ejpam-3049	134	5	,	,	PUNCT
ejpam-3049	134	6	we	we	PRON
ejpam-3049	134	7	have∨	have∨	VERB
ejpam-3049	134	8	(	(	PUNCT
ejpam-3049	134	9	x	x	X
ejpam-3049	134	10	,	,	PUNCT
ejpam-3049	134	11	y)∈aa	y)∈aa	PROPN
ejpam-3049	134	12	min{f(x	min{f(x	PROPN
ejpam-3049	134	13	)	)	PUNCT
ejpam-3049	134	14	,	,	PUNCT
ejpam-3049	134	15	g(y	g(y	PROPN
ejpam-3049	134	16	)	)	PUNCT
ejpam-3049	134	17	}	}	PUNCT
ejpam-3049	134	18	≤	≤	NOUN
ejpam-3049	134	19	(	(	PUNCT
ejpam-3049	134	20	f	f	PROPN
ejpam-3049	134	21	∧	∧	PROPN
ejpam-3049	134	22	g)(a	g)(a	PROPN
ejpam-3049	134	23	)	)	PUNCT
ejpam-3049	134	24	.	.	PUNCT
ejpam-3049	135	1	then	then	ADV
ejpam-3049	135	2	,	,	PUNCT
ejpam-3049	135	3	by	by	ADP
ejpam-3049	135	4	(	(	PUNCT
ejpam-3049	135	5	∗	∗	NOUN
ejpam-3049	135	6	)	)	PUNCT
ejpam-3049	135	7	,	,	PUNCT
ejpam-3049	135	8	(	(	PUNCT
ejpam-3049	135	9	f	f	X
ejpam-3049	135	10	◦	◦	PROPN
ejpam-3049	135	11	g)(a	g)(a	PROPN
ejpam-3049	135	12	)	)	PUNCT
ejpam-3049	135	13	≤	≤	NOUN
ejpam-3049	135	14	(	(	PUNCT
ejpam-3049	135	15	f	f	PROPN
ejpam-3049	135	16	∧	∧	PROPN
ejpam-3049	135	17	g)(a	g)(a	PROPN
ejpam-3049	135	18	)	)	PUNCT
ejpam-3049	135	19	.	.	PUNCT
ejpam-3049	136	1	�	�	PROPN
ejpam-3049	136	2	proposition	proposition	NOUN
ejpam-3049	136	3	2.3	2.3	NUM
ejpam-3049	136	4	.	.	PUNCT
ejpam-3049	137	1	let	let	AUX
ejpam-3049	137	2	(	(	PUNCT
ejpam-3049	137	3	h	h	NOUN
ejpam-3049	137	4	,	,	PUNCT
ejpam-3049	137	5	◦	◦	NOUN
ejpam-3049	137	6	)	)	PUNCT
ejpam-3049	137	7	be	be	VERB
ejpam-3049	137	8	a	a	DET
ejpam-3049	137	9	regular	regular	ADJ
ejpam-3049	137	10	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	137	11	,	,	PUNCT
ejpam-3049	137	12	f	f	PROPN
ejpam-3049	137	13	a	a	DET
ejpam-3049	137	14	fuzzy	fuzzy	ADJ
ejpam-3049	137	15	right	right	ADJ
ejpam-3049	137	16	ideal	ideal	NOUN
ejpam-3049	137	17	of	of	ADP
ejpam-3049	137	18	h	h	NOUN
ejpam-3049	137	19	and	and	CCONJ
ejpam-3049	137	20	g	g	ADP
ejpam-3049	137	21	a	a	DET
ejpam-3049	137	22	fuzzy	fuzzy	ADJ
ejpam-3049	137	23	subset	subset	NOUN
ejpam-3049	137	24	of	of	ADP
ejpam-3049	137	25	h.	h.	PROPN
ejpam-3049	137	26	then	then	ADV
ejpam-3049	137	27	we	we	PRON
ejpam-3049	137	28	have	have	VERB
ejpam-3049	137	29	f	f	PROPN
ejpam-3049	137	30	∧	∧	PROPN
ejpam-3049	137	31	g	g	PROPN
ejpam-3049	137	32	�	�	PROPN
ejpam-3049	137	33	f	f	PROPN
ejpam-3049	137	34	◦	◦	NOUN
ejpam-3049	137	35	g.	g.	NOUN
ejpam-3049	137	36	proof	proof	NOUN
ejpam-3049	137	37	.	.	PUNCT
ejpam-3049	138	1	let	let	VERB
ejpam-3049	138	2	a	a	DET
ejpam-3049	138	3	∈	∈	PROPN
ejpam-3049	138	4	h.	h.	NOUN
ejpam-3049	138	5	since	since	SCONJ
ejpam-3049	138	6	h	h	PROPN
ejpam-3049	138	7	is	be	AUX
ejpam-3049	138	8	regular	regular	ADJ
ejpam-3049	138	9	,	,	PUNCT
ejpam-3049	138	10	there	there	PRON
ejpam-3049	138	11	exists	exist	VERB
ejpam-3049	138	12	x	x	X
ejpam-3049	138	13	∈	∈	NOUN
ejpam-3049	138	14	h	h	NOUN
ejpam-3049	138	15	such	such	ADJ
ejpam-3049	138	16	that	that	SCONJ
ejpam-3049	138	17	a	a	DET
ejpam-3049	138	18	∈	∈	NOUN
ejpam-3049	138	19	(	(	PUNCT
ejpam-3049	138	20	a	a	DET
ejpam-3049	138	21	◦	◦	NOUN
ejpam-3049	138	22	x	x	NOUN
ejpam-3049	138	23	)	)	PUNCT
ejpam-3049	138	24	∗	∗	NOUN
ejpam-3049	138	25	{	{	PUNCT
ejpam-3049	138	26	a	a	NOUN
ejpam-3049	138	27	}	}	PUNCT
ejpam-3049	138	28	.	.	PUNCT
ejpam-3049	139	1	then	then	ADV
ejpam-3049	139	2	a	a	DET
ejpam-3049	139	3	∈	∈	PROPN
ejpam-3049	139	4	u	u	NOUN
ejpam-3049	139	5	◦	◦	NOUN
ejpam-3049	139	6	a	a	PRON
ejpam-3049	139	7	for	for	ADP
ejpam-3049	139	8	some	some	DET
ejpam-3049	139	9	u	u	NOUN
ejpam-3049	139	10	∈	∈	PROPN
ejpam-3049	139	11	a	a	DET
ejpam-3049	139	12	◦	◦	NOUN
ejpam-3049	139	13	x.	x.	NOUN
ejpam-3049	139	14	since	since	SCONJ
ejpam-3049	139	15	a	a	DET
ejpam-3049	139	16	∈	∈	PROPN
ejpam-3049	139	17	u	u	NOUN
ejpam-3049	139	18	◦	◦	NOUN
ejpam-3049	139	19	a	a	X
ejpam-3049	139	20	,	,	PUNCT
ejpam-3049	139	21	we	we	PRON
ejpam-3049	139	22	have	have	VERB
ejpam-3049	139	23	(	(	PUNCT
ejpam-3049	139	24	u	u	NOUN
ejpam-3049	139	25	,	,	PUNCT
ejpam-3049	139	26	a	a	PRON
ejpam-3049	139	27	)	)	PUNCT
ejpam-3049	139	28	∈	∈	NOUN
ejpam-3049	139	29	aa	aa	NOUN
ejpam-3049	139	30	,	,	PUNCT
ejpam-3049	139	31	then	then	ADV
ejpam-3049	139	32	(	(	PUNCT
ejpam-3049	139	33	f	f	X
ejpam-3049	139	34	◦	◦	NOUN
ejpam-3049	139	35	g)(a	g)(a	PROPN
ejpam-3049	139	36	)	)	PUNCT
ejpam-3049	139	37	:	:	PUNCT
ejpam-3049	140	1	=	=	SYM
ejpam-3049	140	2	∨	∨	X
ejpam-3049	140	3	(	(	PUNCT
ejpam-3049	140	4	y	y	PROPN
ejpam-3049	140	5	,	,	PUNCT
ejpam-3049	140	6	z)∈aa	z)∈aa	PROPN
ejpam-3049	140	7	min{f(y	min{f(y	NUM
ejpam-3049	140	8	)	)	PUNCT
ejpam-3049	140	9	,	,	PUNCT
ejpam-3049	140	10	g(z	g(z	PROPN
ejpam-3049	140	11	)	)	PUNCT
ejpam-3049	140	12	}	}	PUNCT
ejpam-3049	140	13	≥	≥	NOUN
ejpam-3049	140	14	min{f(u	min{f(u	PROPN
ejpam-3049	140	15	)	)	PUNCT
ejpam-3049	140	16	,	,	PUNCT
ejpam-3049	140	17	g(a	g(a	PROPN
ejpam-3049	140	18	)	)	PUNCT
ejpam-3049	140	19	}	}	PUNCT
ejpam-3049	140	20	.	.	PUNCT
ejpam-3049	141	1	since	since	SCONJ
ejpam-3049	141	2	f	f	PROPN
ejpam-3049	141	3	is	be	AUX
ejpam-3049	141	4	a	a	DET
ejpam-3049	141	5	fuzzy	fuzzy	ADJ
ejpam-3049	141	6	right	right	ADJ
ejpam-3049	141	7	ideal	ideal	NOUN
ejpam-3049	141	8	of	of	ADP
ejpam-3049	141	9	h	h	NOUN
ejpam-3049	141	10	,	,	PUNCT
ejpam-3049	141	11	we	we	PRON
ejpam-3049	141	12	have	have	VERB
ejpam-3049	141	13	f(a	f(a	NOUN
ejpam-3049	141	14	◦	◦	NOUN
ejpam-3049	141	15	x	x	SYM
ejpam-3049	141	16	)	)	PUNCT
ejpam-3049	141	17	≥	≥	NOUN
ejpam-3049	141	18	f(a	f(a	NOUN
ejpam-3049	141	19	)	)	PUNCT
ejpam-3049	141	20	.	.	PUNCT
ejpam-3049	142	1	since	since	SCONJ
ejpam-3049	142	2	u	u	PROPN
ejpam-3049	142	3	∈	∈	PROPN
ejpam-3049	142	4	a	a	DET
ejpam-3049	142	5	◦	◦	NOUN
ejpam-3049	142	6	x	x	SYM
ejpam-3049	142	7	,	,	PUNCT
ejpam-3049	142	8	we	we	PRON
ejpam-3049	142	9	have	have	VERB
ejpam-3049	142	10	f(u	f(u	PROPN
ejpam-3049	142	11	)	)	PUNCT
ejpam-3049	142	12	≥	≥	NOUN
ejpam-3049	142	13	f(a	f(a	NOUN
ejpam-3049	142	14	)	)	PUNCT
ejpam-3049	142	15	.	.	PUNCT
ejpam-3049	143	1	then	then	ADV
ejpam-3049	143	2	we	we	PRON
ejpam-3049	143	3	have	have	VERB
ejpam-3049	143	4	(	(	PUNCT
ejpam-3049	143	5	f	f	X
ejpam-3049	143	6	◦	◦	PROPN
ejpam-3049	143	7	g)(a	g)(a	PROPN
ejpam-3049	143	8	)	)	PUNCT
ejpam-3049	143	9	≥	≥	NOUN
ejpam-3049	143	10	min{f(u	min{f(u	PROPN
ejpam-3049	143	11	)	)	PUNCT
ejpam-3049	143	12	,	,	PUNCT
ejpam-3049	143	13	g(a	g(a	PROPN
ejpam-3049	143	14	)	)	PUNCT
ejpam-3049	143	15	}	}	PUNCT
ejpam-3049	143	16	≥	≥	NOUN
ejpam-3049	143	17	min{f(a	min{f(a	PRON
ejpam-3049	143	18	)	)	PUNCT
ejpam-3049	143	19	,	,	PUNCT
ejpam-3049	143	20	g(a	g(a	PROPN
ejpam-3049	143	21	)	)	PUNCT
ejpam-3049	143	22	}	}	PUNCT
ejpam-3049	143	23	:	:	PUNCT
ejpam-3049	143	24	=	=	SYM
ejpam-3049	143	25	(	(	PUNCT
ejpam-3049	143	26	f	f	PROPN
ejpam-3049	143	27	∧	∧	PROPN
ejpam-3049	143	28	g)(a	g)(a	PROPN
ejpam-3049	143	29	)	)	PUNCT
ejpam-3049	143	30	,	,	PUNCT
ejpam-3049	143	31	so	so	SCONJ
ejpam-3049	143	32	f	f	PROPN
ejpam-3049	143	33	∧	∧	PROPN
ejpam-3049	143	34	g	g	PROPN
ejpam-3049	143	35	�	�	PROPN
ejpam-3049	143	36	f	f	PROPN
ejpam-3049	143	37	◦	◦	NOUN
ejpam-3049	143	38	g	g	NOUN
ejpam-3049	143	39	and	and	CCONJ
ejpam-3049	143	40	the	the	DET
ejpam-3049	143	41	proof	proof	NOUN
ejpam-3049	143	42	is	be	AUX
ejpam-3049	143	43	complete	complete	ADJ
ejpam-3049	143	44	.	.	PUNCT
ejpam-3049	144	1	�	�	PROPN
ejpam-3049	144	2	theorem	theorem	VERB
ejpam-3049	144	3	2.4	2.4	NUM
ejpam-3049	144	4	.	.	PUNCT
ejpam-3049	145	1	let	let	AUX
ejpam-3049	145	2	(	(	PUNCT
ejpam-3049	145	3	h	h	NOUN
ejpam-3049	145	4	,	,	PUNCT
ejpam-3049	145	5	◦	◦	NOUN
ejpam-3049	145	6	)	)	PUNCT
ejpam-3049	145	7	be	be	VERB
ejpam-3049	145	8	an	an	DET
ejpam-3049	145	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	145	10	.	.	PUNCT
ejpam-3049	146	1	the	the	DET
ejpam-3049	146	2	following	follow	VERB
ejpam-3049	146	3	are	be	AUX
ejpam-3049	146	4	equivalent	equivalent	ADJ
ejpam-3049	146	5	:	:	PUNCT
ejpam-3049	146	6	(	(	PUNCT
ejpam-3049	146	7	1	1	X
ejpam-3049	146	8	)	)	PUNCT
ejpam-3049	146	9	h	h	NOUN
ejpam-3049	146	10	is	be	AUX
ejpam-3049	146	11	regular	regular	ADJ
ejpam-3049	146	12	.	.	PUNCT
ejpam-3049	147	1	(	(	PUNCT
ejpam-3049	147	2	2	2	X
ejpam-3049	147	3	)	)	PUNCT
ejpam-3049	147	4	f	f	NOUN
ejpam-3049	148	1	∧	∧	NOUN
ejpam-3049	148	2	g	g	PROPN
ejpam-3049	148	3	=	=	SYM
ejpam-3049	148	4	f	f	PROPN
ejpam-3049	148	5	◦	◦	NOUN
ejpam-3049	148	6	g	g	NOUN
ejpam-3049	148	7	for	for	ADP
ejpam-3049	148	8	every	every	DET
ejpam-3049	148	9	fuzzy	fuzzy	ADJ
ejpam-3049	148	10	right	right	ADJ
ejpam-3049	148	11	ideal	ideal	NOUN
ejpam-3049	149	1	f	f	PROPN
ejpam-3049	149	2	and	and	CCONJ
ejpam-3049	149	3	every	every	DET
ejpam-3049	149	4	fuzzy	fuzzy	ADJ
ejpam-3049	149	5	left	leave	VERB
ejpam-3049	149	6	ideal	ideal	NOUN
ejpam-3049	149	7	g	g	PROPN
ejpam-3049	149	8	of	of	ADP
ejpam-3049	149	9	h.	h.	PROPN
ejpam-3049	149	10	(	(	PUNCT
ejpam-3049	149	11	3	3	NUM
ejpam-3049	149	12	)	)	PUNCT
ejpam-3049	149	13	f	f	NOUN
ejpam-3049	150	1	∧	∧	PROPN
ejpam-3049	150	2	g	g	PROPN
ejpam-3049	150	3	�	�	PROPN
ejpam-3049	150	4	f	f	PROPN
ejpam-3049	150	5	◦	◦	VERB
ejpam-3049	150	6	g	g	NOUN
ejpam-3049	150	7	for	for	ADP
ejpam-3049	150	8	every	every	DET
ejpam-3049	150	9	fuzzy	fuzzy	ADJ
ejpam-3049	150	10	right	right	ADJ
ejpam-3049	150	11	ideal	ideal	NOUN
ejpam-3049	150	12	f	f	PROPN
ejpam-3049	150	13	and	and	CCONJ
ejpam-3049	150	14	every	every	DET
ejpam-3049	150	15	fuzzy	fuzzy	ADJ
ejpam-3049	150	16	left	leave	VERB
ejpam-3049	150	17	ideal	ideal	NOUN
ejpam-3049	150	18	g	g	PROPN
ejpam-3049	150	19	of	of	ADP
ejpam-3049	150	20	h.	h.	PROPN
ejpam-3049	150	21	proof	proof	NOUN
ejpam-3049	150	22	.	.	PUNCT
ejpam-3049	151	1	(	(	PUNCT
ejpam-3049	151	2	1	1	X
ejpam-3049	151	3	)	)	PUNCT
ejpam-3049	151	4	=	=	NOUN
ejpam-3049	151	5	⇒	⇒	NOUN
ejpam-3049	151	6	(	(	PUNCT
ejpam-3049	151	7	2	2	NUM
ejpam-3049	151	8	)	)	PUNCT
ejpam-3049	151	9	.	.	PUNCT
ejpam-3049	152	1	let	let	VERB
ejpam-3049	152	2	f	f	PRON
ejpam-3049	152	3	be	be	AUX
ejpam-3049	152	4	a	a	DET
ejpam-3049	152	5	fuzzy	fuzzy	ADJ
ejpam-3049	152	6	right	right	ADJ
ejpam-3049	152	7	ideal	ideal	NOUN
ejpam-3049	152	8	and	and	CCONJ
ejpam-3049	152	9	g	g	ADP
ejpam-3049	152	10	a	a	DET
ejpam-3049	152	11	fuzzy	fuzzy	ADJ
ejpam-3049	152	12	left	leave	VERB
ejpam-3049	152	13	ideal	ideal	NOUN
ejpam-3049	152	14	of	of	ADP
ejpam-3049	152	15	h.	h.	NOUN
ejpam-3049	152	16	by	by	ADP
ejpam-3049	152	17	proposition	proposition	NOUN
ejpam-3049	152	18	2.2	2.2	NUM
ejpam-3049	152	19	,	,	PUNCT
ejpam-3049	152	20	we	we	PRON
ejpam-3049	152	21	have	have	VERB
ejpam-3049	152	22	f	f	NUM
ejpam-3049	152	23	◦	◦	NOUN
ejpam-3049	152	24	g	g	PROPN
ejpam-3049	152	25	�	�	PROPN
ejpam-3049	152	26	f	f	PROPN
ejpam-3049	152	27	∧	∧	PROPN
ejpam-3049	152	28	g.	g.	NOUN
ejpam-3049	152	29	by	by	ADP
ejpam-3049	152	30	proposition	proposition	NOUN
ejpam-3049	152	31	2.3	2.3	NUM
ejpam-3049	152	32	,	,	PUNCT
ejpam-3049	152	33	we	we	PRON
ejpam-3049	152	34	have	have	VERB
ejpam-3049	152	35	f	f	PROPN
ejpam-3049	152	36	∧	∧	PROPN
ejpam-3049	152	37	g	g	PROPN
ejpam-3049	152	38	�	�	PROPN
ejpam-3049	152	39	f	f	PROPN
ejpam-3049	152	40	◦	◦	VERB
ejpam-3049	152	41	g	g	PROPN
ejpam-3049	152	42	,	,	PUNCT
ejpam-3049	152	43	and	and	CCONJ
ejpam-3049	152	44	(	(	PUNCT
ejpam-3049	152	45	2	2	X
ejpam-3049	152	46	)	)	PUNCT
ejpam-3049	152	47	is	be	AUX
ejpam-3049	152	48	satisfied	satisfied	ADJ
ejpam-3049	152	49	.	.	PUNCT
ejpam-3049	153	1	the	the	DET
ejpam-3049	153	2	implication	implication	NOUN
ejpam-3049	153	3	(	(	PUNCT
ejpam-3049	153	4	2)⇒	2)⇒	NUM
ejpam-3049	153	5	(	(	PUNCT
ejpam-3049	153	6	3	3	NUM
ejpam-3049	153	7	)	)	PUNCT
ejpam-3049	153	8	is	be	AUX
ejpam-3049	153	9	obvious	obvious	ADJ
ejpam-3049	153	10	.	.	PUNCT
ejpam-3049	154	1	(	(	PUNCT
ejpam-3049	154	2	3	3	X
ejpam-3049	154	3	)	)	PUNCT
ejpam-3049	154	4	=	=	NOUN
ejpam-3049	154	5	⇒	⇒	NOUN
ejpam-3049	154	6	(	(	PUNCT
ejpam-3049	154	7	1	1	NUM
ejpam-3049	154	8	)	)	PUNCT
ejpam-3049	154	9	.	.	PUNCT
ejpam-3049	155	1	by	by	ADP
ejpam-3049	155	2	theorem	theorem	NOUN
ejpam-3049	155	3	2.1	2.1	NUM
ejpam-3049	155	4	,	,	PUNCT
ejpam-3049	155	5	it	it	PRON
ejpam-3049	155	6	is	be	AUX
ejpam-3049	155	7	enough	enough	ADJ
ejpam-3049	155	8	to	to	PART
ejpam-3049	155	9	prove	prove	VERB
ejpam-3049	155	10	that	that	SCONJ
ejpam-3049	155	11	r(a	r(a	NOUN
ejpam-3049	155	12	)	)	PUNCT
ejpam-3049	155	13	∩	∩	NOUN
ejpam-3049	155	14	l(a	l(a	PROPN
ejpam-3049	155	15	)	)	PUNCT
ejpam-3049	155	16	⊆	⊆	NUM
ejpam-3049	155	17	r(a	r(a	NUM
ejpam-3049	155	18	)	)	PUNCT
ejpam-3049	155	19	∗	∗	NOUN
ejpam-3049	155	20	l(a	l(a	PROPN
ejpam-3049	155	21	)	)	PUNCT
ejpam-3049	155	22	for	for	ADP
ejpam-3049	155	23	every	every	DET
ejpam-3049	155	24	a	a	DET
ejpam-3049	155	25	∈	∈	PROPN
ejpam-3049	155	26	h.	h.	NOUN
ejpam-3049	156	1	so	so	ADV
ejpam-3049	156	2	,	,	PUNCT
ejpam-3049	156	3	let	let	VERB
ejpam-3049	156	4	a	a	DET
ejpam-3049	156	5	∈	∈	PROPN
ejpam-3049	156	6	h	h	NOUN
ejpam-3049	156	7	and	and	CCONJ
ejpam-3049	156	8	b	b	X
ejpam-3049	156	9	∈	∈	PROPN
ejpam-3049	156	10	r(a	r(a	PROPN
ejpam-3049	156	11	)	)	PUNCT
ejpam-3049	156	12	∩	∩	NOUN
ejpam-3049	156	13	l(a	l(a	PROPN
ejpam-3049	156	14	)	)	PUNCT
ejpam-3049	156	15	.	.	PUNCT
ejpam-3049	157	1	since	since	SCONJ
ejpam-3049	157	2	r(a	r(a	PROPN
ejpam-3049	157	3	)	)	PUNCT
ejpam-3049	157	4	is	be	AUX
ejpam-3049	157	5	a	a	DET
ejpam-3049	157	6	right	right	ADJ
ejpam-3049	157	7	ideal	ideal	NOUN
ejpam-3049	157	8	of	of	ADP
ejpam-3049	157	9	h	h	NOUN
ejpam-3049	157	10	,	,	PUNCT
ejpam-3049	157	11	the	the	DET
ejpam-3049	157	12	characteristic	characteristic	ADJ
ejpam-3049	157	13	function	function	NOUN
ejpam-3049	157	14	fr(a	fr(a	VERB
ejpam-3049	157	15	)	)	PUNCT
ejpam-3049	157	16	is	be	AUX
ejpam-3049	157	17	a	a	DET
ejpam-3049	157	18	fuzzy	fuzzy	ADJ
ejpam-3049	157	19	right	right	ADJ
ejpam-3049	157	20	ideal	ideal	NOUN
ejpam-3049	157	21	of	of	ADP
ejpam-3049	157	22	h	h	NOUN
ejpam-3049	157	23	and	and	CCONJ
ejpam-3049	157	24	,	,	PUNCT
ejpam-3049	157	25	since	since	SCONJ
ejpam-3049	157	26	l(a	l(a	PROPN
ejpam-3049	157	27	)	)	PUNCT
ejpam-3049	157	28	is	be	AUX
ejpam-3049	157	29	a	a	DET
ejpam-3049	157	30	left	left	ADJ
ejpam-3049	157	31	ideal	ideal	NOUN
ejpam-3049	157	32	of	of	ADP
ejpam-3049	157	33	h	h	NOUN
ejpam-3049	157	34	,	,	PUNCT
ejpam-3049	157	35	fl(a	fl(a	NUM
ejpam-3049	157	36	)	)	PUNCT
ejpam-3049	157	37	is	be	AUX
ejpam-3049	157	38	a	a	DET
ejpam-3049	157	39	fuzzy	fuzzy	ADJ
ejpam-3049	157	40	left	leave	VERB
ejpam-3049	157	41	ideal	ideal	NOUN
ejpam-3049	157	42	of	of	ADP
ejpam-3049	157	43	h.	h.	PROPN
ejpam-3049	157	44	by	by	ADP
ejpam-3049	157	45	hypothesis	hypothesis	NOUN
ejpam-3049	157	46	,	,	PUNCT
ejpam-3049	157	47	we	we	PRON
ejpam-3049	157	48	have	have	AUX
ejpam-3049	157	49	fr(a	fr(a	VERB
ejpam-3049	157	50	)	)	PUNCT
ejpam-3049	158	1	∧	∧	NOUN
ejpam-3049	158	2	fl(a	fl(a	NUM
ejpam-3049	158	3	)	)	PUNCT
ejpam-3049	158	4	�	�	PROPN
ejpam-3049	158	5	fl(a	fl(a	NUM
ejpam-3049	158	6	)	)	PUNCT
ejpam-3049	158	7	◦	◦	NOUN
ejpam-3049	158	8	fr(a	fr(a	PUNCT
ejpam-3049	158	9	)	)	PUNCT
ejpam-3049	158	10	,	,	PUNCT
ejpam-3049	158	11	then	then	ADV
ejpam-3049	158	12	(	(	PUNCT
ejpam-3049	158	13	fr(a	fr(a	ADV
ejpam-3049	158	14	)	)	PUNCT
ejpam-3049	158	15	∧	∧	NOUN
ejpam-3049	158	16	fl(a	fl(a	X
ejpam-3049	158	17	)	)	PUNCT
ejpam-3049	158	18	)	)	PUNCT
ejpam-3049	159	1	(	(	PUNCT
ejpam-3049	159	2	b	b	X
ejpam-3049	159	3	)	)	PUNCT
ejpam-3049	159	4	≤	≤	NOUN
ejpam-3049	159	5	(	(	PUNCT
ejpam-3049	159	6	fr(a	fr(a	NUM
ejpam-3049	159	7	)	)	PUNCT
ejpam-3049	159	8	◦	◦	NOUN
ejpam-3049	159	9	fl(a	fl(a	NUM
ejpam-3049	159	10	)	)	PUNCT
ejpam-3049	159	11	)	)	PUNCT
ejpam-3049	160	1	(	(	PUNCT
ejpam-3049	160	2	b	b	NOUN
ejpam-3049	160	3	)	)	PUNCT
ejpam-3049	160	4	.	.	PUNCT
ejpam-3049	161	1	n.	n.	PROPN
ejpam-3049	161	2	kehayopulu	kehayopulu	PROPN
ejpam-3049	161	3	/	/	SYM
ejpam-3049	161	4	eur	eur	PROPN
ejpam-3049	161	5	.	.	PUNCT
ejpam-3049	162	1	j.	j.	PROPN
ejpam-3049	162	2	pure	pure	PROPN
ejpam-3049	162	3	appl	appl	PROPN
ejpam-3049	162	4	.	.	PROPN
ejpam-3049	162	5	math	math	PROPN
ejpam-3049	162	6	,	,	PUNCT
ejpam-3049	162	7	10	10	NUM
ejpam-3049	162	8	(	(	PUNCT
ejpam-3049	162	9	5	5	NUM
ejpam-3049	162	10	)	)	PUNCT
ejpam-3049	162	11	(	(	PUNCT
ejpam-3049	162	12	2017	2017	NUM
ejpam-3049	162	13	)	)	PUNCT
ejpam-3049	162	14	,	,	PUNCT
ejpam-3049	162	15	929	929	NUM
ejpam-3049	162	16	-	-	SYM
ejpam-3049	162	17	945	945	NUM
ejpam-3049	162	18	935	935	NUM
ejpam-3049	162	19	thus	thus	ADV
ejpam-3049	162	20	min{fr(a)(b	min{fr(a)(b	ADJ
ejpam-3049	162	21	)	)	PUNCT
ejpam-3049	162	22	,	,	PUNCT
ejpam-3049	162	23	fl(a)(b	fl(a)(b	NOUN
ejpam-3049	162	24	)	)	PUNCT
ejpam-3049	162	25	}	}	PUNCT
ejpam-3049	162	26	≤	≤	NOUN
ejpam-3049	162	27	(	(	PUNCT
ejpam-3049	162	28	fr(a	fr(a	X
ejpam-3049	162	29	)	)	PUNCT
ejpam-3049	162	30	◦	◦	NOUN
ejpam-3049	162	31	fl(a	fl(a	NUM
ejpam-3049	162	32	)	)	PUNCT
ejpam-3049	162	33	)	)	PUNCT
ejpam-3049	163	1	(	(	PUNCT
ejpam-3049	163	2	b	b	NOUN
ejpam-3049	163	3	)	)	PUNCT
ejpam-3049	163	4	.	.	PUNCT
ejpam-3049	164	1	since	since	SCONJ
ejpam-3049	164	2	b	b	PROPN
ejpam-3049	164	3	∈	∈	PROPN
ejpam-3049	164	4	r(a	r(a	PROPN
ejpam-3049	164	5	)	)	PUNCT
ejpam-3049	164	6	and	and	CCONJ
ejpam-3049	164	7	b	b	PROPN
ejpam-3049	164	8	∈	∈	PROPN
ejpam-3049	164	9	l(a	l(a	PROPN
ejpam-3049	164	10	)	)	PUNCT
ejpam-3049	164	11	,	,	PUNCT
ejpam-3049	164	12	we	we	PRON
ejpam-3049	164	13	have	have	VERB
ejpam-3049	164	14	fr(a)(b	fr(a)(b	NOUN
ejpam-3049	164	15	)	)	PUNCT
ejpam-3049	165	1	=	=	SYM
ejpam-3049	165	2	fl(a)(b	fl(a)(b	NOUN
ejpam-3049	165	3	)	)	PUNCT
ejpam-3049	165	4	=	=	SYM
ejpam-3049	165	5	1	1	NUM
ejpam-3049	165	6	,	,	PUNCT
ejpam-3049	165	7	and	and	CCONJ
ejpam-3049	165	8	so	so	ADV
ejpam-3049	165	9	1	1	NUM
ejpam-3049	165	10	≤	≤	NOUN
ejpam-3049	165	11	(	(	PUNCT
ejpam-3049	165	12	fr(a	fr(a	X
ejpam-3049	165	13	)	)	PUNCT
ejpam-3049	165	14	◦	◦	NOUN
ejpam-3049	165	15	fl(a	fl(a	NUM
ejpam-3049	165	16	)	)	PUNCT
ejpam-3049	165	17	)	)	PUNCT
ejpam-3049	166	1	(	(	PUNCT
ejpam-3049	166	2	b	b	NOUN
ejpam-3049	166	3	)	)	PUNCT
ejpam-3049	166	4	.	.	PUNCT
ejpam-3049	167	1	if	if	SCONJ
ejpam-3049	167	2	ab	ab	PROPN
ejpam-3049	167	3	=	=	NOUN
ejpam-3049	167	4	∅	∅	NOUN
ejpam-3049	167	5	,	,	PUNCT
ejpam-3049	167	6	then	then	ADV
ejpam-3049	167	7	(	(	PUNCT
ejpam-3049	167	8	fr(a	fr(a	X
ejpam-3049	167	9	)	)	PUNCT
ejpam-3049	167	10	◦	◦	NOUN
ejpam-3049	167	11	fl(a	fl(a	NUM
ejpam-3049	167	12	)	)	PUNCT
ejpam-3049	167	13	)	)	PUNCT
ejpam-3049	168	1	(	(	PUNCT
ejpam-3049	168	2	b	b	X
ejpam-3049	168	3	)	)	PUNCT
ejpam-3049	168	4	=	=	SYM
ejpam-3049	168	5	0	0	NUM
ejpam-3049	168	6	which	which	PRON
ejpam-3049	168	7	is	be	AUX
ejpam-3049	168	8	impossible	impossible	ADJ
ejpam-3049	168	9	.	.	PUNCT
ejpam-3049	169	1	thus	thus	ADV
ejpam-3049	169	2	we	we	PRON
ejpam-3049	169	3	have	have	VERB
ejpam-3049	169	4	ab	ab	PROPN
ejpam-3049	169	5	6=	6=	NOUN
ejpam-3049	169	6	∅	∅	NOUN
ejpam-3049	169	7	and	and	CCONJ
ejpam-3049	169	8	(	(	PUNCT
ejpam-3049	169	9	fr(a	fr(a	X
ejpam-3049	169	10	)	)	PUNCT
ejpam-3049	169	11	◦	◦	NOUN
ejpam-3049	169	12	fl(a	fl(a	NUM
ejpam-3049	169	13	)	)	PUNCT
ejpam-3049	169	14	)	)	PUNCT
ejpam-3049	170	1	(	(	PUNCT
ejpam-3049	170	2	b	b	X
ejpam-3049	170	3	)	)	PUNCT
ejpam-3049	170	4	=	=	SYM
ejpam-3049	170	5	∨	∨	X
ejpam-3049	170	6	(	(	PUNCT
ejpam-3049	170	7	y	y	PROPN
ejpam-3049	170	8	,	,	PUNCT
ejpam-3049	170	9	z)∈ab	z)∈ab	PROPN
ejpam-3049	170	10	min{fr(a)(y	min{fr(a)(y	NOUN
ejpam-3049	170	11	)	)	PUNCT
ejpam-3049	170	12	,	,	PUNCT
ejpam-3049	170	13	fl(a)(z	fl(a)(z	PROPN
ejpam-3049	170	14	)	)	PUNCT
ejpam-3049	170	15	}	}	PUNCT
ejpam-3049	170	16	.	.	PUNCT
ejpam-3049	171	1	then	then	ADV
ejpam-3049	171	2	there	there	PRON
ejpam-3049	171	3	exists	exist	VERB
ejpam-3049	171	4	(	(	PUNCT
ejpam-3049	171	5	y	y	NOUN
ejpam-3049	171	6	,	,	PUNCT
ejpam-3049	171	7	z	z	NOUN
ejpam-3049	171	8	)	)	PUNCT
ejpam-3049	171	9	∈	∈	PROPN
ejpam-3049	171	10	ab	ab	PROPN
ejpam-3049	171	11	such	such	ADJ
ejpam-3049	171	12	that	that	SCONJ
ejpam-3049	171	13	y	y	PROPN
ejpam-3049	171	14	∈	∈	PROPN
ejpam-3049	171	15	r(a	r(a	PROPN
ejpam-3049	171	16	)	)	PUNCT
ejpam-3049	171	17	and	and	CCONJ
ejpam-3049	171	18	z	z	PROPN
ejpam-3049	171	19	∈	∈	PROPN
ejpam-3049	171	20	l(a	l(a	PROPN
ejpam-3049	171	21	)	)	PUNCT
ejpam-3049	171	22	(	(	PUNCT
ejpam-3049	171	23	∗	∗	NOUN
ejpam-3049	171	24	)	)	PUNCT
ejpam-3049	171	25	indeed	indeed	ADV
ejpam-3049	171	26	:	:	PUNCT
ejpam-3049	171	27	suppose	suppose	VERB
ejpam-3049	171	28	there	there	PRON
ejpam-3049	171	29	is	be	VERB
ejpam-3049	171	30	no	no	DET
ejpam-3049	171	31	(	(	PUNCT
ejpam-3049	171	32	y	y	NOUN
ejpam-3049	171	33	,	,	PUNCT
ejpam-3049	171	34	z	z	NOUN
ejpam-3049	171	35	)	)	PUNCT
ejpam-3049	171	36	∈	∈	PROPN
ejpam-3049	171	37	ab	ab	PROPN
ejpam-3049	171	38	such	such	ADJ
ejpam-3049	171	39	that	that	SCONJ
ejpam-3049	171	40	y	y	PROPN
ejpam-3049	171	41	∈	∈	PROPN
ejpam-3049	171	42	r(a	r(a	PROPN
ejpam-3049	171	43	)	)	PUNCT
ejpam-3049	171	44	and	and	CCONJ
ejpam-3049	171	45	z	z	PROPN
ejpam-3049	171	46	∈	∈	PROPN
ejpam-3049	171	47	l(a	l(a	PROPN
ejpam-3049	171	48	)	)	PUNCT
ejpam-3049	171	49	.	.	PUNCT
ejpam-3049	172	1	then	then	ADV
ejpam-3049	172	2	,	,	PUNCT
ejpam-3049	172	3	for	for	ADP
ejpam-3049	172	4	each	each	DET
ejpam-3049	172	5	(	(	PUNCT
ejpam-3049	172	6	y	y	PROPN
ejpam-3049	172	7	,	,	PUNCT
ejpam-3049	172	8	z	z	NOUN
ejpam-3049	172	9	)	)	PUNCT
ejpam-3049	172	10	∈	∈	PROPN
ejpam-3049	172	11	ab	ab	PROPN
ejpam-3049	172	12	,	,	PUNCT
ejpam-3049	172	13	we	we	PRON
ejpam-3049	172	14	have	have	VERB
ejpam-3049	172	15	y	y	PROPN
ejpam-3049	172	16	/∈	/∈	PUNCT
ejpam-3049	173	1	r(a	r(a	ADJ
ejpam-3049	173	2	)	)	PUNCT
ejpam-3049	173	3	or	or	CCONJ
ejpam-3049	173	4	z	z	NOUN
ejpam-3049	173	5	/∈	/∈	PUNCT
ejpam-3049	174	1	l(a	l(a	PROPN
ejpam-3049	174	2	)	)	PUNCT
ejpam-3049	174	3	.	.	PUNCT
ejpam-3049	175	1	then	then	ADV
ejpam-3049	175	2	,	,	PUNCT
ejpam-3049	175	3	for	for	ADP
ejpam-3049	175	4	each	each	DET
ejpam-3049	175	5	(	(	PUNCT
ejpam-3049	175	6	y	y	PROPN
ejpam-3049	175	7	,	,	PUNCT
ejpam-3049	175	8	z	z	NOUN
ejpam-3049	175	9	)	)	PUNCT
ejpam-3049	175	10	∈	∈	PROPN
ejpam-3049	175	11	ab	ab	PROPN
ejpam-3049	175	12	,	,	PUNCT
ejpam-3049	175	13	we	we	PRON
ejpam-3049	175	14	have	have	AUX
ejpam-3049	175	15	fr(a)(y	fr(a)(y	NUM
ejpam-3049	175	16	)	)	PUNCT
ejpam-3049	176	1	=	=	SYM
ejpam-3049	176	2	0	0	NUM
ejpam-3049	176	3	or	or	CCONJ
ejpam-3049	176	4	fl(a)(z	fl(a)(z	PROPN
ejpam-3049	176	5	)	)	PUNCT
ejpam-3049	177	1	=	=	SYM
ejpam-3049	177	2	0	0	X
ejpam-3049	177	3	.	.	PUNCT
ejpam-3049	178	1	then	then	ADV
ejpam-3049	178	2	min{fr(a)(y	min{fr(a)(y	NOUN
ejpam-3049	178	3	)	)	PUNCT
ejpam-3049	178	4	,	,	PUNCT
ejpam-3049	178	5	fr(a)(z	fr(a)(z	NUM
ejpam-3049	178	6	)	)	PUNCT
ejpam-3049	178	7	}	}	PUNCT
ejpam-3049	179	1	=	=	SYM
ejpam-3049	179	2	0	0	NUM
ejpam-3049	179	3	for	for	ADP
ejpam-3049	179	4	every	every	DET
ejpam-3049	179	5	(	(	PUNCT
ejpam-3049	179	6	y	y	PROPN
ejpam-3049	179	7	,	,	PUNCT
ejpam-3049	179	8	z	z	NOUN
ejpam-3049	179	9	)	)	PUNCT
ejpam-3049	179	10	∈	∈	PROPN
ejpam-3049	180	1	ab	ab	PROPN
ejpam-3049	180	2	.	.	PUNCT
ejpam-3049	181	1	then∨	then∨	PROPN
ejpam-3049	181	2	(	(	PUNCT
ejpam-3049	181	3	y	y	PROPN
ejpam-3049	181	4	,	,	PUNCT
ejpam-3049	181	5	z)∈ab	z)∈ab	PROPN
ejpam-3049	181	6	min{fr(a)(y	min{fr(a)(y	NOUN
ejpam-3049	181	7	)	)	PUNCT
ejpam-3049	181	8	,	,	PUNCT
ejpam-3049	181	9	fl(a)(z	fl(a)(z	PROPN
ejpam-3049	181	10	)	)	PUNCT
ejpam-3049	181	11	}	}	PUNCT
ejpam-3049	181	12	=	=	SYM
ejpam-3049	181	13	0	0	NUM
ejpam-3049	181	14	,	,	PUNCT
ejpam-3049	181	15	so	so	ADV
ejpam-3049	181	16	(	(	PUNCT
ejpam-3049	181	17	fr(a	fr(a	X
ejpam-3049	181	18	)	)	PUNCT
ejpam-3049	181	19	◦	◦	NOUN
ejpam-3049	181	20	fl(a	fl(a	NUM
ejpam-3049	181	21	)	)	PUNCT
ejpam-3049	181	22	)	)	PUNCT
ejpam-3049	182	1	(	(	PUNCT
ejpam-3049	182	2	b	b	X
ejpam-3049	182	3	)	)	PUNCT
ejpam-3049	182	4	=	=	SYM
ejpam-3049	182	5	0	0	NUM
ejpam-3049	182	6	which	which	PRON
ejpam-3049	182	7	is	be	AUX
ejpam-3049	182	8	no	no	DET
ejpam-3049	182	9	possible	possible	ADJ
ejpam-3049	182	10	.	.	PUNCT
ejpam-3049	183	1	by	by	ADP
ejpam-3049	183	2	(	(	PUNCT
ejpam-3049	183	3	∗	∗	NOUN
ejpam-3049	183	4	)	)	PUNCT
ejpam-3049	183	5	,	,	PUNCT
ejpam-3049	183	6	we	we	PRON
ejpam-3049	183	7	have	have	VERB
ejpam-3049	183	8	b	b	NUM
ejpam-3049	183	9	∈	∈	PROPN
ejpam-3049	183	10	y	y	PROPN
ejpam-3049	183	11	◦	◦	NOUN
ejpam-3049	183	12	z	z	NOUN
ejpam-3049	183	13	⊆	⊆	NUM
ejpam-3049	183	14	r(a	r(a	NUM
ejpam-3049	183	15	)	)	PUNCT
ejpam-3049	183	16	∗	∗	NOUN
ejpam-3049	183	17	l(a	l(a	PROPN
ejpam-3049	183	18	)	)	PUNCT
ejpam-3049	183	19	,	,	PUNCT
ejpam-3049	183	20	and	and	CCONJ
ejpam-3049	183	21	the	the	DET
ejpam-3049	183	22	proof	proof	NOUN
ejpam-3049	183	23	is	be	AUX
ejpam-3049	183	24	complete	complete	ADJ
ejpam-3049	183	25	.	.	PUNCT
ejpam-3049	184	1	�	�	PROPN
ejpam-3049	184	2	theorem	theorem	VERB
ejpam-3049	184	3	2.5	2.5	NUM
ejpam-3049	184	4	.	.	PUNCT
ejpam-3049	185	1	(	(	PUNCT
ejpam-3049	185	2	cf	cf	NOUN
ejpam-3049	185	3	.	.	PUNCT
ejpam-3049	186	1	also	also	ADV
ejpam-3049	186	2	[	[	X
ejpam-3049	186	3	10	10	NUM
ejpam-3049	186	4	]	]	PUNCT
ejpam-3049	186	5	)	)	PUNCT
ejpam-3049	186	6	let	let	VERB
ejpam-3049	186	7	(	(	PUNCT
ejpam-3049	186	8	h	h	NOUN
ejpam-3049	186	9	,	,	PUNCT
ejpam-3049	186	10	◦	◦	NOUN
ejpam-3049	186	11	)	)	PUNCT
ejpam-3049	186	12	be	be	VERB
ejpam-3049	186	13	an	an	DET
ejpam-3049	186	14	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	186	15	.	.	PUNCT
ejpam-3049	187	1	the	the	DET
ejpam-3049	187	2	following	follow	VERB
ejpam-3049	187	3	are	be	AUX
ejpam-3049	187	4	equivalent	equivalent	ADJ
ejpam-3049	187	5	:	:	PUNCT
ejpam-3049	187	6	(	(	PUNCT
ejpam-3049	187	7	1	1	X
ejpam-3049	187	8	)	)	PUNCT
ejpam-3049	187	9	h	h	NOUN
ejpam-3049	187	10	is	be	AUX
ejpam-3049	187	11	intra	intra	ADJ
ejpam-3049	187	12	-	-	ADJ
ejpam-3049	187	13	regular	regular	ADJ
ejpam-3049	187	14	.	.	PUNCT
ejpam-3049	188	1	(	(	PUNCT
ejpam-3049	188	2	2	2	X
ejpam-3049	188	3	)	)	PUNCT
ejpam-3049	188	4	a	a	DET
ejpam-3049	188	5	∩b	∩b	NOUN
ejpam-3049	188	6	⊆	⊆	NUM
ejpam-3049	188	7	b	b	NOUN
ejpam-3049	188	8	∗a	∗a	ADJ
ejpam-3049	188	9	for	for	ADP
ejpam-3049	188	10	every	every	DET
ejpam-3049	188	11	right	right	ADJ
ejpam-3049	188	12	ideal	ideal	NOUN
ejpam-3049	188	13	a	a	PRON
ejpam-3049	188	14	and	and	CCONJ
ejpam-3049	188	15	every	every	DET
ejpam-3049	188	16	left	leave	VERB
ejpam-3049	188	17	ideal	ideal	PROPN
ejpam-3049	188	18	b	b	PROPN
ejpam-3049	188	19	of	of	ADP
ejpam-3049	188	20	h.	h.	PROPN
ejpam-3049	188	21	(	(	PUNCT
ejpam-3049	188	22	3	3	NUM
ejpam-3049	188	23	)	)	PUNCT
ejpam-3049	188	24	r(a	r(a	ADJ
ejpam-3049	188	25	)	)	PUNCT
ejpam-3049	188	26	∩	∩	NOUN
ejpam-3049	188	27	l(a	l(a	PROPN
ejpam-3049	188	28	)	)	PUNCT
ejpam-3049	188	29	⊆	⊆	NUM
ejpam-3049	188	30	l(a	l(a	PROPN
ejpam-3049	188	31	)	)	PUNCT
ejpam-3049	188	32	∗r(a	∗r(a	NOUN
ejpam-3049	188	33	)	)	PUNCT
ejpam-3049	188	34	for	for	ADP
ejpam-3049	188	35	every	every	DET
ejpam-3049	188	36	a	a	DET
ejpam-3049	188	37	∈	∈	PROPN
ejpam-3049	188	38	p∗(h	p∗(h	PROPN
ejpam-3049	188	39	)	)	PUNCT
ejpam-3049	188	40	.	.	PUNCT
ejpam-3049	189	1	(	(	PUNCT
ejpam-3049	189	2	4	4	X
ejpam-3049	189	3	)	)	PUNCT
ejpam-3049	189	4	r(a	r(a	ADJ
ejpam-3049	189	5	)	)	PUNCT
ejpam-3049	189	6	∩	∩	NOUN
ejpam-3049	189	7	l(a	l(a	PROPN
ejpam-3049	189	8	)	)	PUNCT
ejpam-3049	189	9	⊆	⊆	NUM
ejpam-3049	189	10	l(a	l(a	PROPN
ejpam-3049	189	11	)	)	PUNCT
ejpam-3049	189	12	∗r(a	∗r(a	NOUN
ejpam-3049	189	13	)	)	PUNCT
ejpam-3049	189	14	for	for	SCONJ
ejpam-3049	189	15	every	every	DET
ejpam-3049	189	16	a	a	DET
ejpam-3049	189	17	∈	∈	PROPN
ejpam-3049	189	18	h.	h.	NOUN
ejpam-3049	189	19	theorem	theorem	VERB
ejpam-3049	189	20	2.6	2.6	NUM
ejpam-3049	189	21	.	.	PUNCT
ejpam-3049	190	1	an	an	DET
ejpam-3049	190	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	190	3	(	(	PUNCT
ejpam-3049	190	4	h	h	NOUN
ejpam-3049	190	5	,	,	PUNCT
ejpam-3049	190	6	◦	◦	NOUN
ejpam-3049	190	7	)	)	PUNCT
ejpam-3049	190	8	is	be	AUX
ejpam-3049	190	9	intra	intra	ADJ
ejpam-3049	190	10	-	-	ADJ
ejpam-3049	190	11	regular	regular	ADJ
ejpam-3049	190	12	if	if	SCONJ
ejpam-3049	190	13	and	and	CCONJ
ejpam-3049	190	14	only	only	ADV
ejpam-3049	190	15	if	if	SCONJ
ejpam-3049	190	16	,	,	PUNCT
ejpam-3049	190	17	for	for	ADP
ejpam-3049	190	18	every	every	DET
ejpam-3049	190	19	fuzzy	fuzzy	ADJ
ejpam-3049	190	20	right	right	ADJ
ejpam-3049	190	21	ideal	ideal	NOUN
ejpam-3049	191	1	f	f	PROPN
ejpam-3049	191	2	and	and	CCONJ
ejpam-3049	191	3	every	every	DET
ejpam-3049	191	4	fuzzy	fuzzy	ADJ
ejpam-3049	191	5	left	leave	VERB
ejpam-3049	191	6	ideal	ideal	NOUN
ejpam-3049	191	7	g	g	PROPN
ejpam-3049	191	8	of	of	ADP
ejpam-3049	191	9	h	h	NOUN
ejpam-3049	191	10	,	,	PUNCT
ejpam-3049	191	11	we	we	PRON
ejpam-3049	191	12	have	have	VERB
ejpam-3049	191	13	f	f	PROPN
ejpam-3049	191	14	∧	∧	PROPN
ejpam-3049	191	15	g	g	PROPN
ejpam-3049	191	16	�	�	PROPN
ejpam-3049	191	17	g	g	PROPN
ejpam-3049	191	18	◦	◦	PROPN
ejpam-3049	191	19	f.	f.	PROPN
ejpam-3049	191	20	proof	proof	NOUN
ejpam-3049	191	21	.	.	PUNCT
ejpam-3049	192	1	=	=	NOUN
ejpam-3049	192	2	⇒.	⇒.	NOUN
ejpam-3049	192	3	let	let	VERB
ejpam-3049	192	4	a	a	DET
ejpam-3049	192	5	∈	∈	PROPN
ejpam-3049	192	6	h.	h.	NOUN
ejpam-3049	192	7	since	since	SCONJ
ejpam-3049	192	8	h	h	PROPN
ejpam-3049	192	9	is	be	AUX
ejpam-3049	192	10	intra	intra	ADJ
ejpam-3049	192	11	-	-	ADJ
ejpam-3049	192	12	regular	regular	ADJ
ejpam-3049	192	13	,	,	PUNCT
ejpam-3049	192	14	there	there	PRON
ejpam-3049	192	15	exist	exist	VERB
ejpam-3049	192	16	x	x	NOUN
ejpam-3049	192	17	,	,	PUNCT
ejpam-3049	192	18	y	y	PROPN
ejpam-3049	192	19	∈	∈	PROPN
ejpam-3049	192	20	h	h	NOUN
ejpam-3049	192	21	such	such	ADJ
ejpam-3049	192	22	that	that	SCONJ
ejpam-3049	192	23	a	a	DET
ejpam-3049	192	24	∈	∈	NOUN
ejpam-3049	192	25	(	(	PUNCT
ejpam-3049	192	26	x	x	SYM
ejpam-3049	192	27	◦	◦	VERB
ejpam-3049	192	28	a	a	X
ejpam-3049	192	29	)	)	PUNCT
ejpam-3049	192	30	∗	∗	NOUN
ejpam-3049	192	31	(	(	PUNCT
ejpam-3049	192	32	a	a	DET
ejpam-3049	192	33	◦	◦	NOUN
ejpam-3049	192	34	y	y	NOUN
ejpam-3049	192	35	)	)	PUNCT
ejpam-3049	192	36	.	.	PUNCT
ejpam-3049	193	1	then	then	ADV
ejpam-3049	193	2	a	a	DET
ejpam-3049	193	3	∈	∈	PROPN
ejpam-3049	193	4	u	u	NOUN
ejpam-3049	193	5	◦	◦	NOUN
ejpam-3049	193	6	v	v	NOUN
ejpam-3049	193	7	for	for	ADP
ejpam-3049	193	8	some	some	DET
ejpam-3049	193	9	u	u	NOUN
ejpam-3049	193	10	∈	∈	PROPN
ejpam-3049	193	11	x	x	PUNCT
ejpam-3049	193	12	◦	◦	NOUN
ejpam-3049	193	13	a	a	PRON
ejpam-3049	193	14	,	,	PUNCT
ejpam-3049	193	15	v	v	NOUN
ejpam-3049	193	16	∈	∈	NOUN
ejpam-3049	193	17	a	a	DET
ejpam-3049	193	18	◦	◦	NOUN
ejpam-3049	193	19	y.	y.	NOUN
ejpam-3049	193	20	since	since	SCONJ
ejpam-3049	193	21	a	a	DET
ejpam-3049	193	22	∈	∈	PROPN
ejpam-3049	193	23	u	u	NOUN
ejpam-3049	193	24	◦	◦	NOUN
ejpam-3049	193	25	v	v	NUM
ejpam-3049	193	26	,	,	PUNCT
ejpam-3049	193	27	we	we	PRON
ejpam-3049	193	28	have	have	VERB
ejpam-3049	193	29	(	(	PUNCT
ejpam-3049	193	30	u	u	NOUN
ejpam-3049	193	31	,	,	PUNCT
ejpam-3049	193	32	v	v	NOUN
ejpam-3049	193	33	)	)	PUNCT
ejpam-3049	193	34	∈	∈	NOUN
ejpam-3049	193	35	aa	aa	NOUN
ejpam-3049	193	36	,	,	PUNCT
ejpam-3049	193	37	then	then	ADV
ejpam-3049	193	38	we	we	PRON
ejpam-3049	193	39	have	have	VERB
ejpam-3049	193	40	(	(	PUNCT
ejpam-3049	193	41	g	g	NOUN
ejpam-3049	193	42	◦	◦	NOUN
ejpam-3049	193	43	f)(a	f)(a	NUM
ejpam-3049	193	44	)	)	PUNCT
ejpam-3049	193	45	:	:	PUNCT
ejpam-3049	194	1	=	=	SYM
ejpam-3049	194	2	∨	∨	X
ejpam-3049	194	3	(	(	PUNCT
ejpam-3049	194	4	h	h	NOUN
ejpam-3049	194	5	,	,	PUNCT
ejpam-3049	194	6	k)∈aa	k)∈aa	PROPN
ejpam-3049	194	7	min{g(h	min{g(h	PROPN
ejpam-3049	194	8	)	)	PUNCT
ejpam-3049	194	9	,	,	PUNCT
ejpam-3049	194	10	f(k	f(k	VERB
ejpam-3049	194	11	)	)	PUNCT
ejpam-3049	194	12	}	}	PUNCT
ejpam-3049	194	13	≥	≥	NOUN
ejpam-3049	194	14	min{g(u	min{g(u	NOUN
ejpam-3049	194	15	)	)	PUNCT
ejpam-3049	194	16	,	,	PUNCT
ejpam-3049	194	17	f(v	f(v	NOUN
ejpam-3049	194	18	)	)	PUNCT
ejpam-3049	194	19	}	}	PUNCT
ejpam-3049	194	20	.	.	PUNCT
ejpam-3049	195	1	since	since	SCONJ
ejpam-3049	195	2	g	g	PROPN
ejpam-3049	195	3	is	be	AUX
ejpam-3049	195	4	a	a	DET
ejpam-3049	195	5	fuzzy	fuzzy	ADJ
ejpam-3049	195	6	left	leave	VERB
ejpam-3049	195	7	ideal	ideal	NOUN
ejpam-3049	195	8	of	of	ADP
ejpam-3049	195	9	h	h	NOUN
ejpam-3049	195	10	,	,	PUNCT
ejpam-3049	195	11	we	we	PRON
ejpam-3049	195	12	have	have	VERB
ejpam-3049	195	13	g(x	g(x	NOUN
ejpam-3049	195	14	◦	◦	NOUN
ejpam-3049	195	15	a	a	DET
ejpam-3049	195	16	)	)	PUNCT
ejpam-3049	195	17	≥	≥	NOUN
ejpam-3049	195	18	g(a	g(a	PROPN
ejpam-3049	195	19	)	)	PUNCT
ejpam-3049	195	20	.	.	PUNCT
ejpam-3049	196	1	since	since	SCONJ
ejpam-3049	196	2	u	u	NOUN
ejpam-3049	196	3	∈	∈	PROPN
ejpam-3049	196	4	x	x	PUNCT
ejpam-3049	196	5	◦	◦	NOUN
ejpam-3049	196	6	a	a	X
ejpam-3049	196	7	,	,	PUNCT
ejpam-3049	196	8	we	we	PRON
ejpam-3049	196	9	get	get	VERB
ejpam-3049	196	10	g(u	g(u	PROPN
ejpam-3049	196	11	)	)	PUNCT
ejpam-3049	196	12	≥	≥	NOUN
ejpam-3049	196	13	g(a	g(a	PROPN
ejpam-3049	196	14	)	)	PUNCT
ejpam-3049	196	15	.	.	PUNCT
ejpam-3049	197	1	since	since	SCONJ
ejpam-3049	197	2	f	f	PROPN
ejpam-3049	197	3	is	be	AUX
ejpam-3049	197	4	a	a	DET
ejpam-3049	197	5	fuzzy	fuzzy	ADJ
ejpam-3049	197	6	right	right	ADJ
ejpam-3049	197	7	ideal	ideal	NOUN
ejpam-3049	197	8	of	of	ADP
ejpam-3049	197	9	h	h	NOUN
ejpam-3049	197	10	,	,	PUNCT
ejpam-3049	197	11	we	we	PRON
ejpam-3049	197	12	have	have	VERB
ejpam-3049	197	13	f(a	f(a	NOUN
ejpam-3049	197	14	◦	◦	NOUN
ejpam-3049	197	15	y	y	PROPN
ejpam-3049	197	16	)	)	PUNCT
ejpam-3049	197	17	≥	≥	NOUN
ejpam-3049	197	18	f(a	f(a	NOUN
ejpam-3049	197	19	)	)	PUNCT
ejpam-3049	197	20	.	.	PUNCT
ejpam-3049	198	1	since	since	SCONJ
ejpam-3049	198	2	v	v	NUM
ejpam-3049	198	3	∈	∈	PROPN
ejpam-3049	198	4	a	a	DET
ejpam-3049	198	5	◦	◦	NOUN
ejpam-3049	198	6	y	y	PROPN
ejpam-3049	198	7	,	,	PUNCT
ejpam-3049	198	8	we	we	PRON
ejpam-3049	198	9	have	have	VERB
ejpam-3049	198	10	f(v	f(v	NOUN
ejpam-3049	198	11	)	)	PUNCT
ejpam-3049	198	12	≥	≥	NOUN
ejpam-3049	198	13	f(a	f(a	NOUN
ejpam-3049	198	14	)	)	PUNCT
ejpam-3049	198	15	.	.	PUNCT
ejpam-3049	199	1	thus	thus	ADV
ejpam-3049	199	2	we	we	PRON
ejpam-3049	199	3	have	have	VERB
ejpam-3049	199	4	(	(	PUNCT
ejpam-3049	199	5	g	g	NOUN
ejpam-3049	199	6	◦	◦	NOUN
ejpam-3049	199	7	f)(a	f)(a	NOUN
ejpam-3049	199	8	)	)	PUNCT
ejpam-3049	199	9	≥	≥	NOUN
ejpam-3049	199	10	min{g(u	min{g(u	PROPN
ejpam-3049	199	11	)	)	PUNCT
ejpam-3049	199	12	,	,	PUNCT
ejpam-3049	199	13	f(v	f(v	NOUN
ejpam-3049	199	14	)	)	PUNCT
ejpam-3049	199	15	}	}	PUNCT
ejpam-3049	199	16	≥	≥	PROPN
ejpam-3049	199	17	min{g(a	min{g(a	PROPN
ejpam-3049	199	18	)	)	PUNCT
ejpam-3049	199	19	,	,	PUNCT
ejpam-3049	199	20	f(a	f(a	NOUN
ejpam-3049	199	21	)	)	PUNCT
ejpam-3049	199	22	}	}	PUNCT
ejpam-3049	200	1	=	=	SYM
ejpam-3049	201	1	(	(	PUNCT
ejpam-3049	201	2	f	f	PROPN
ejpam-3049	201	3	∧	∧	PROPN
ejpam-3049	201	4	g)(a	g)(a	PROPN
ejpam-3049	201	5	)	)	PUNCT
ejpam-3049	201	6	,	,	PUNCT
ejpam-3049	201	7	n.	n.	PROPN
ejpam-3049	201	8	kehayopulu	kehayopulu	PROPN
ejpam-3049	201	9	/	/	SYM
ejpam-3049	201	10	eur	eur	PROPN
ejpam-3049	201	11	.	.	PUNCT
ejpam-3049	202	1	j.	j.	PROPN
ejpam-3049	202	2	pure	pure	PROPN
ejpam-3049	202	3	appl	appl	PROPN
ejpam-3049	202	4	.	.	PROPN
ejpam-3049	202	5	math	math	PROPN
ejpam-3049	202	6	,	,	PUNCT
ejpam-3049	202	7	10	10	NUM
ejpam-3049	202	8	(	(	PUNCT
ejpam-3049	202	9	5	5	NUM
ejpam-3049	202	10	)	)	PUNCT
ejpam-3049	202	11	(	(	PUNCT
ejpam-3049	202	12	2017	2017	NUM
ejpam-3049	202	13	)	)	PUNCT
ejpam-3049	202	14	,	,	PUNCT
ejpam-3049	202	15	929	929	NUM
ejpam-3049	202	16	-	-	SYM
ejpam-3049	202	17	945	945	NUM
ejpam-3049	202	18	936	936	NUM
ejpam-3049	202	19	thus	thus	ADV
ejpam-3049	202	20	f	f	PROPN
ejpam-3049	202	21	∧	∧	PROPN
ejpam-3049	202	22	g	g	PROPN
ejpam-3049	202	23	�	�	PROPN
ejpam-3049	202	24	g	g	PROPN
ejpam-3049	202	25	◦	◦	NOUN
ejpam-3049	202	26	f	f	X
ejpam-3049	202	27	.	.	PUNCT
ejpam-3049	203	1	⇐	⇐	PROPN
ejpam-3049	203	2	=	=	NOUN
ejpam-3049	203	3	.	.	PUNCT
ejpam-3049	203	4	by	by	ADP
ejpam-3049	203	5	theorem	theorem	NOUN
ejpam-3049	203	6	2.5	2.5	NUM
ejpam-3049	203	7	,	,	PUNCT
ejpam-3049	203	8	it	it	PRON
ejpam-3049	203	9	is	be	AUX
ejpam-3049	203	10	enough	enough	ADJ
ejpam-3049	203	11	to	to	PART
ejpam-3049	203	12	prove	prove	VERB
ejpam-3049	203	13	that	that	SCONJ
ejpam-3049	203	14	r(a	r(a	NOUN
ejpam-3049	203	15	)	)	PUNCT
ejpam-3049	203	16	∩	∩	NOUN
ejpam-3049	203	17	l(a	l(a	PROPN
ejpam-3049	203	18	)	)	PUNCT
ejpam-3049	203	19	⊆	⊆	NUM
ejpam-3049	203	20	l(a	l(a	PROPN
ejpam-3049	203	21	)	)	PUNCT
ejpam-3049	203	22	∗	∗	NOUN
ejpam-3049	203	23	r(a	r(a	NUM
ejpam-3049	203	24	)	)	PUNCT
ejpam-3049	203	25	for	for	ADP
ejpam-3049	203	26	every	every	DET
ejpam-3049	203	27	a	a	DET
ejpam-3049	203	28	∈	∈	PROPN
ejpam-3049	203	29	h.	h.	NOUN
ejpam-3049	203	30	let	let	VERB
ejpam-3049	203	31	now	now	ADV
ejpam-3049	203	32	a	a	DET
ejpam-3049	203	33	∈	∈	ADJ
ejpam-3049	203	34	h	h	NOUN
ejpam-3049	203	35	and	and	CCONJ
ejpam-3049	203	36	b	b	X
ejpam-3049	203	37	∈	∈	PROPN
ejpam-3049	203	38	r(a	r(a	PROPN
ejpam-3049	203	39	)	)	PUNCT
ejpam-3049	203	40	∩	∩	NOUN
ejpam-3049	203	41	l(a	l(a	PROPN
ejpam-3049	203	42	)	)	PUNCT
ejpam-3049	203	43	.	.	PUNCT
ejpam-3049	204	1	as	as	ADP
ejpam-3049	204	2	fr(a	fr(a	ADV
ejpam-3049	204	3	)	)	PUNCT
ejpam-3049	204	4	is	be	AUX
ejpam-3049	204	5	a	a	DET
ejpam-3049	204	6	fuzzy	fuzzy	ADJ
ejpam-3049	204	7	right	right	ADJ
ejpam-3049	204	8	ideal	ideal	NOUN
ejpam-3049	204	9	and	and	CCONJ
ejpam-3049	204	10	fl(a	fl(a	NUM
ejpam-3049	204	11	)	)	PUNCT
ejpam-3049	204	12	is	be	AUX
ejpam-3049	204	13	a	a	DET
ejpam-3049	204	14	fuzzy	fuzzy	ADJ
ejpam-3049	204	15	left	leave	VERB
ejpam-3049	204	16	ideal	ideal	NOUN
ejpam-3049	204	17	of	of	ADP
ejpam-3049	204	18	h	h	NOUN
ejpam-3049	204	19	,	,	PUNCT
ejpam-3049	204	20	by	by	ADP
ejpam-3049	204	21	hypothesis	hypothesis	NOUN
ejpam-3049	204	22	,	,	PUNCT
ejpam-3049	204	23	we	we	PRON
ejpam-3049	204	24	have	have	VERB
ejpam-3049	204	25	(	(	PUNCT
ejpam-3049	204	26	fr(a	fr(a	ADV
ejpam-3049	204	27	)	)	PUNCT
ejpam-3049	204	28	∧	∧	NOUN
ejpam-3049	204	29	fl(a	fl(a	X
ejpam-3049	204	30	)	)	PUNCT
ejpam-3049	204	31	)	)	PUNCT
ejpam-3049	205	1	(	(	PUNCT
ejpam-3049	205	2	b	b	X
ejpam-3049	205	3	)	)	PUNCT
ejpam-3049	205	4	≤	≤	NOUN
ejpam-3049	205	5	(	(	PUNCT
ejpam-3049	205	6	fl(a	fl(a	NUM
ejpam-3049	205	7	)	)	PUNCT
ejpam-3049	205	8	◦	◦	NOUN
ejpam-3049	205	9	fr(a	fr(a	VERB
ejpam-3049	205	10	)	)	PUNCT
ejpam-3049	205	11	)	)	PUNCT
ejpam-3049	206	1	(	(	PUNCT
ejpam-3049	206	2	b	b	NOUN
ejpam-3049	206	3	)	)	PUNCT
ejpam-3049	206	4	.	.	PUNCT
ejpam-3049	207	1	thus	thus	ADV
ejpam-3049	207	2	min{fr(a)(b	min{fr(a)(b	ADJ
ejpam-3049	207	3	)	)	PUNCT
ejpam-3049	207	4	,	,	PUNCT
ejpam-3049	207	5	fl(a)(b	fl(a)(b	NOUN
ejpam-3049	207	6	)	)	PUNCT
ejpam-3049	207	7	}	}	PUNCT
ejpam-3049	207	8	≤	≤	NOUN
ejpam-3049	207	9	(	(	PUNCT
ejpam-3049	207	10	fl(a	fl(a	NUM
ejpam-3049	207	11	)	)	PUNCT
ejpam-3049	207	12	◦	◦	NOUN
ejpam-3049	207	13	fr(a	fr(a	VERB
ejpam-3049	207	14	)	)	PUNCT
ejpam-3049	207	15	)	)	PUNCT
ejpam-3049	208	1	(	(	PUNCT
ejpam-3049	208	2	b	b	NOUN
ejpam-3049	208	3	)	)	PUNCT
ejpam-3049	208	4	.	.	PUNCT
ejpam-3049	209	1	since	since	SCONJ
ejpam-3049	209	2	b	b	PROPN
ejpam-3049	209	3	∈	∈	PROPN
ejpam-3049	209	4	r(a	r(a	PROPN
ejpam-3049	209	5	)	)	PUNCT
ejpam-3049	209	6	and	and	CCONJ
ejpam-3049	209	7	b	b	PROPN
ejpam-3049	209	8	∈	∈	PROPN
ejpam-3049	209	9	l(a	l(a	PROPN
ejpam-3049	209	10	)	)	PUNCT
ejpam-3049	209	11	,	,	PUNCT
ejpam-3049	209	12	we	we	PRON
ejpam-3049	209	13	have	have	VERB
ejpam-3049	209	14	fr(a)(b	fr(a)(b	NOUN
ejpam-3049	209	15	)	)	PUNCT
ejpam-3049	210	1	=	=	SYM
ejpam-3049	210	2	fl(a)(b	fl(a)(b	NOUN
ejpam-3049	210	3	)	)	PUNCT
ejpam-3049	210	4	=	=	SYM
ejpam-3049	210	5	1	1	NUM
ejpam-3049	210	6	,	,	PUNCT
ejpam-3049	210	7	and	and	CCONJ
ejpam-3049	210	8	so	so	ADV
ejpam-3049	210	9	1	1	NUM
ejpam-3049	210	10	≤	≤	NOUN
ejpam-3049	210	11	(	(	PUNCT
ejpam-3049	210	12	fl(a	fl(a	NUM
ejpam-3049	210	13	)	)	PUNCT
ejpam-3049	210	14	◦	◦	NOUN
ejpam-3049	210	15	fr(a	fr(a	VERB
ejpam-3049	210	16	)	)	PUNCT
ejpam-3049	210	17	)	)	PUNCT
ejpam-3049	211	1	(	(	PUNCT
ejpam-3049	211	2	b	b	NOUN
ejpam-3049	211	3	)	)	PUNCT
ejpam-3049	211	4	.	.	PUNCT
ejpam-3049	212	1	if	if	SCONJ
ejpam-3049	212	2	ab	ab	PROPN
ejpam-3049	212	3	=	=	NOUN
ejpam-3049	212	4	∅	∅	NOUN
ejpam-3049	212	5	,	,	PUNCT
ejpam-3049	212	6	then	then	ADV
ejpam-3049	212	7	(	(	PUNCT
ejpam-3049	212	8	fl(a	fl(a	NUM
ejpam-3049	212	9	)	)	PUNCT
ejpam-3049	212	10	◦	◦	NOUN
ejpam-3049	212	11	fr(a	fr(a	VERB
ejpam-3049	212	12	)	)	PUNCT
ejpam-3049	212	13	)	)	PUNCT
ejpam-3049	213	1	(	(	PUNCT
ejpam-3049	213	2	b	b	X
ejpam-3049	213	3	)	)	PUNCT
ejpam-3049	213	4	=	=	SYM
ejpam-3049	213	5	0	0	NUM
ejpam-3049	213	6	which	which	PRON
ejpam-3049	213	7	is	be	AUX
ejpam-3049	213	8	impossible	impossible	ADJ
ejpam-3049	213	9	.	.	PUNCT
ejpam-3049	214	1	then	then	ADV
ejpam-3049	214	2	we	we	PRON
ejpam-3049	214	3	have	have	VERB
ejpam-3049	214	4	ab	ab	PROPN
ejpam-3049	214	5	6=	6=	NOUN
ejpam-3049	214	6	∅	∅	NOUN
ejpam-3049	214	7	and	and	CCONJ
ejpam-3049	214	8	then	then	ADV
ejpam-3049	214	9	(	(	PUNCT
ejpam-3049	214	10	fl(a	fl(a	NUM
ejpam-3049	214	11	)	)	PUNCT
ejpam-3049	214	12	◦	◦	NOUN
ejpam-3049	214	13	fr(a	fr(a	VERB
ejpam-3049	214	14	)	)	PUNCT
ejpam-3049	214	15	)	)	PUNCT
ejpam-3049	215	1	(	(	PUNCT
ejpam-3049	215	2	b	b	X
ejpam-3049	215	3	)	)	PUNCT
ejpam-3049	215	4	=	=	SYM
ejpam-3049	215	5	∨	∨	X
ejpam-3049	215	6	(	(	PUNCT
ejpam-3049	215	7	y	y	NOUN
ejpam-3049	215	8	,	,	PUNCT
ejpam-3049	215	9	z)∈ab	z)∈ab	PROPN
ejpam-3049	215	10	min{fl(a)(y	min{fl(a)(y	NOUN
ejpam-3049	215	11	)	)	PUNCT
ejpam-3049	215	12	,	,	PUNCT
ejpam-3049	215	13	fr(a)(z	fr(a)(z	NUM
ejpam-3049	215	14	)	)	PUNCT
ejpam-3049	215	15	}	}	PUNCT
ejpam-3049	215	16	.	.	PUNCT
ejpam-3049	216	1	then	then	ADV
ejpam-3049	216	2	there	there	PRON
ejpam-3049	216	3	exists	exist	VERB
ejpam-3049	216	4	(	(	PUNCT
ejpam-3049	216	5	y	y	NOUN
ejpam-3049	216	6	,	,	PUNCT
ejpam-3049	216	7	z	z	NOUN
ejpam-3049	216	8	)	)	PUNCT
ejpam-3049	216	9	∈	∈	PROPN
ejpam-3049	216	10	ab	ab	PROPN
ejpam-3049	216	11	such	such	ADJ
ejpam-3049	216	12	that	that	SCONJ
ejpam-3049	216	13	y	y	PROPN
ejpam-3049	216	14	∈	∈	PROPN
ejpam-3049	216	15	l(a	l(a	PROPN
ejpam-3049	216	16	)	)	PUNCT
ejpam-3049	216	17	and	and	CCONJ
ejpam-3049	216	18	z	z	NOUN
ejpam-3049	216	19	∈	∈	PROPN
ejpam-3049	216	20	r(a	r(a	PROPN
ejpam-3049	216	21	)	)	PUNCT
ejpam-3049	216	22	.	.	PUNCT
ejpam-3049	217	1	then	then	ADV
ejpam-3049	217	2	we	we	PRON
ejpam-3049	217	3	get	get	VERB
ejpam-3049	217	4	b	b	NOUN
ejpam-3049	217	5	∈	∈	PROPN
ejpam-3049	217	6	y	y	PROPN
ejpam-3049	217	7	◦	◦	NOUN
ejpam-3049	217	8	z	z	NOUN
ejpam-3049	217	9	⊆	⊆	NUM
ejpam-3049	217	10	l(a	l(a	PROPN
ejpam-3049	217	11	)	)	PUNCT
ejpam-3049	217	12	∗r(a	∗r(a	NOUN
ejpam-3049	217	13	)	)	PUNCT
ejpam-3049	217	14	.	.	PUNCT
ejpam-3049	218	1	�	�	PROPN
ejpam-3049	218	2	the	the	DET
ejpam-3049	218	3	concept	concept	NOUN
ejpam-3049	218	4	of	of	ADP
ejpam-3049	218	5	left	left	ADJ
ejpam-3049	218	6	quasi	quasi	ADJ
ejpam-3049	218	7	-	-	ADJ
ejpam-3049	218	8	regular	regular	ADJ
ejpam-3049	218	9	semigroups	semigroup	NOUN
ejpam-3049	218	10	can	can	AUX
ejpam-3049	218	11	be	be	AUX
ejpam-3049	218	12	naturally	naturally	ADV
ejpam-3049	218	13	transferred	transfer	VERB
ejpam-3049	218	14	to	to	ADP
ejpam-3049	218	15	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	218	16	in	in	ADP
ejpam-3049	218	17	the	the	DET
ejpam-3049	218	18	definition	definition	NOUN
ejpam-3049	218	19	below	below	ADV
ejpam-3049	218	20	.	.	PUNCT
ejpam-3049	219	1	definition	definition	NOUN
ejpam-3049	219	2	2.7	2.7	NUM
ejpam-3049	219	3	.	.	PUNCT
ejpam-3049	220	1	an	an	DET
ejpam-3049	220	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	220	3	(	(	PUNCT
ejpam-3049	220	4	h	h	NOUN
ejpam-3049	220	5	,	,	PUNCT
ejpam-3049	220	6	◦	◦	NOUN
ejpam-3049	220	7	)	)	PUNCT
ejpam-3049	220	8	is	be	AUX
ejpam-3049	220	9	called	call	VERB
ejpam-3049	220	10	left	leave	VERB
ejpam-3049	220	11	quasi	quasi	NOUN
ejpam-3049	220	12	-	-	ADJ
ejpam-3049	220	13	regular	regular	ADJ
ejpam-3049	220	14	if	if	SCONJ
ejpam-3049	220	15	for	for	ADP
ejpam-3049	220	16	every	every	DET
ejpam-3049	220	17	a	a	DET
ejpam-3049	220	18	∈	∈	PROPN
ejpam-3049	220	19	h	h	NOUN
ejpam-3049	220	20	there	there	PRON
ejpam-3049	220	21	exist	exist	VERB
ejpam-3049	220	22	x	x	NOUN
ejpam-3049	220	23	,	,	PUNCT
ejpam-3049	220	24	y	y	PROPN
ejpam-3049	220	25	∈	∈	PROPN
ejpam-3049	220	26	h	h	NOUN
ejpam-3049	220	27	such	such	ADJ
ejpam-3049	220	28	that	that	SCONJ
ejpam-3049	220	29	a	a	DET
ejpam-3049	220	30	∈	∈	NOUN
ejpam-3049	220	31	(	(	PUNCT
ejpam-3049	220	32	x	x	SYM
ejpam-3049	220	33	◦	◦	VERB
ejpam-3049	220	34	a	a	X
ejpam-3049	220	35	)	)	PUNCT
ejpam-3049	220	36	∗	∗	NOUN
ejpam-3049	220	37	(	(	PUNCT
ejpam-3049	220	38	y	y	PROPN
ejpam-3049	220	39	◦	◦	VERB
ejpam-3049	220	40	a	a	PRON
ejpam-3049	220	41	)	)	PUNCT
ejpam-3049	220	42	.	.	PUNCT
ejpam-3049	221	1	proposition	proposition	NOUN
ejpam-3049	221	2	2.8	2.8	NUM
ejpam-3049	221	3	.	.	PUNCT
ejpam-3049	222	1	let	let	AUX
ejpam-3049	222	2	(	(	PUNCT
ejpam-3049	222	3	h	h	NOUN
ejpam-3049	222	4	,	,	PUNCT
ejpam-3049	222	5	◦	◦	NOUN
ejpam-3049	222	6	)	)	PUNCT
ejpam-3049	222	7	be	be	VERB
ejpam-3049	222	8	an	an	DET
ejpam-3049	222	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	222	10	.	.	PUNCT
ejpam-3049	223	1	the	the	DET
ejpam-3049	223	2	following	follow	VERB
ejpam-3049	223	3	are	be	AUX
ejpam-3049	223	4	equivalent	equivalent	ADJ
ejpam-3049	223	5	:	:	PUNCT
ejpam-3049	223	6	(	(	PUNCT
ejpam-3049	223	7	1	1	X
ejpam-3049	223	8	)	)	PUNCT
ejpam-3049	223	9	h	h	NOUN
ejpam-3049	223	10	is	be	AUX
ejpam-3049	223	11	left	leave	VERB
ejpam-3049	223	12	quasi	quasi	ADJ
ejpam-3049	223	13	-	-	ADJ
ejpam-3049	223	14	regular	regular	ADJ
ejpam-3049	223	15	.	.	PUNCT
ejpam-3049	224	1	(	(	PUNCT
ejpam-3049	224	2	2	2	X
ejpam-3049	224	3	)	)	PUNCT
ejpam-3049	224	4	a	a	DET
ejpam-3049	224	5	∈	∈	PROPN
ejpam-3049	224	6	h	h	NOUN
ejpam-3049	224	7	∗	∗	NOUN
ejpam-3049	224	8	{	{	PUNCT
ejpam-3049	224	9	a	a	DET
ejpam-3049	224	10	}	}	PUNCT
ejpam-3049	224	11	∗h	∗h	NOUN
ejpam-3049	224	12	∗	∗	NOUN
ejpam-3049	224	13	{	{	PUNCT
ejpam-3049	224	14	a	a	NOUN
ejpam-3049	224	15	}	}	PUNCT
ejpam-3049	224	16	for	for	ADP
ejpam-3049	224	17	every	every	DET
ejpam-3049	224	18	a	a	DET
ejpam-3049	224	19	∈	∈	PROPN
ejpam-3049	224	20	h.	h.	NOUN
ejpam-3049	224	21	(	(	PUNCT
ejpam-3049	224	22	3	3	X
ejpam-3049	224	23	)	)	PUNCT
ejpam-3049	224	24	a	a	DET
ejpam-3049	224	25	⊆	⊆	NUM
ejpam-3049	224	26	h	h	NOUN
ejpam-3049	224	27	∗a	∗a	ADJ
ejpam-3049	224	28	∗h	∗h	NOUN
ejpam-3049	224	29	∗a	∗a	ADJ
ejpam-3049	224	30	for	for	ADP
ejpam-3049	224	31	every	every	DET
ejpam-3049	224	32	a	a	DET
ejpam-3049	224	33	∈	∈	PROPN
ejpam-3049	224	34	p∗(h	p∗(h	PROPN
ejpam-3049	224	35	)	)	PUNCT
ejpam-3049	224	36	.	.	PUNCT
ejpam-3049	225	1	theorem	theorem	VERB
ejpam-3049	225	2	2.9	2.9	NUM
ejpam-3049	225	3	.	.	PUNCT
ejpam-3049	226	1	let	let	AUX
ejpam-3049	226	2	(	(	PUNCT
ejpam-3049	226	3	h	h	NOUN
ejpam-3049	226	4	,	,	PUNCT
ejpam-3049	226	5	◦	◦	NOUN
ejpam-3049	226	6	)	)	PUNCT
ejpam-3049	226	7	be	be	VERB
ejpam-3049	226	8	an	an	DET
ejpam-3049	226	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	226	10	.	.	PUNCT
ejpam-3049	227	1	the	the	DET
ejpam-3049	227	2	following	follow	VERB
ejpam-3049	227	3	are	be	AUX
ejpam-3049	227	4	equivalent	equivalent	ADJ
ejpam-3049	227	5	:	:	PUNCT
ejpam-3049	227	6	(	(	PUNCT
ejpam-3049	227	7	1	1	X
ejpam-3049	227	8	)	)	PUNCT
ejpam-3049	227	9	h	h	NOUN
ejpam-3049	227	10	is	be	AUX
ejpam-3049	227	11	left	leave	VERB
ejpam-3049	227	12	quasi	quasi	ADJ
ejpam-3049	227	13	-	-	ADJ
ejpam-3049	227	14	regular	regular	ADJ
ejpam-3049	227	15	.	.	PUNCT
ejpam-3049	228	1	(	(	PUNCT
ejpam-3049	228	2	2	2	X
ejpam-3049	228	3	)	)	PUNCT
ejpam-3049	228	4	a	a	DET
ejpam-3049	228	5	∩b	∩b	NOUN
ejpam-3049	228	6	⊆	⊆	NUM
ejpam-3049	228	7	a	a	DET
ejpam-3049	228	8	∗b	∗b	NOUN
ejpam-3049	228	9	for	for	ADP
ejpam-3049	228	10	every	every	DET
ejpam-3049	228	11	ideal	ideal	NOUN
ejpam-3049	228	12	a	a	PRON
ejpam-3049	229	1	and	and	CCONJ
ejpam-3049	229	2	every	every	DET
ejpam-3049	229	3	nonempty	nonempty	NOUN
ejpam-3049	229	4	subset	subset	VERB
ejpam-3049	229	5	b	b	PROPN
ejpam-3049	229	6	of	of	ADP
ejpam-3049	229	7	h.	h.	PROPN
ejpam-3049	229	8	(	(	PUNCT
ejpam-3049	229	9	3	3	X
ejpam-3049	229	10	)	)	PUNCT
ejpam-3049	229	11	a	a	DET
ejpam-3049	229	12	∩b	∩b	NOUN
ejpam-3049	229	13	⊆	⊆	NUM
ejpam-3049	229	14	a	a	DET
ejpam-3049	229	15	∗b	∗b	NOUN
ejpam-3049	229	16	for	for	ADP
ejpam-3049	229	17	every	every	DET
ejpam-3049	229	18	ideal	ideal	NOUN
ejpam-3049	229	19	a	a	PRON
ejpam-3049	229	20	and	and	CCONJ
ejpam-3049	229	21	every	every	DET
ejpam-3049	229	22	bi	bi	ADJ
ejpam-3049	229	23	-	-	ADJ
ejpam-3049	229	24	ideal	ideal	ADJ
ejpam-3049	229	25	b	b	PROPN
ejpam-3049	229	26	of	of	ADP
ejpam-3049	229	27	h.	h.	PROPN
ejpam-3049	229	28	(	(	PUNCT
ejpam-3049	229	29	4	4	NUM
ejpam-3049	229	30	)	)	PUNCT
ejpam-3049	229	31	a	a	DET
ejpam-3049	229	32	∩b	∩b	NOUN
ejpam-3049	229	33	⊆	⊆	NUM
ejpam-3049	229	34	a	a	DET
ejpam-3049	229	35	∗b	∗b	NOUN
ejpam-3049	229	36	for	for	ADP
ejpam-3049	229	37	every	every	DET
ejpam-3049	229	38	ideal	ideal	NOUN
ejpam-3049	229	39	a	a	DET
ejpam-3049	229	40	and	and	CCONJ
ejpam-3049	229	41	every	every	PRON
ejpam-3049	229	42	left	leave	VERB
ejpam-3049	229	43	ideal	ideal	PROPN
ejpam-3049	229	44	b	b	PROPN
ejpam-3049	229	45	of	of	ADP
ejpam-3049	229	46	h.	h.	PROPN
ejpam-3049	229	47	(	(	PUNCT
ejpam-3049	229	48	5	5	NUM
ejpam-3049	229	49	)	)	PUNCT
ejpam-3049	229	50	i(a	i(a	PROPN
ejpam-3049	229	51	)	)	PUNCT
ejpam-3049	229	52	∩	∩	NOUN
ejpam-3049	229	53	l(a	l(a	PROPN
ejpam-3049	229	54	)	)	PUNCT
ejpam-3049	229	55	⊆	⊆	NUM
ejpam-3049	229	56	i(a	i(a	PROPN
ejpam-3049	229	57	)	)	PUNCT
ejpam-3049	229	58	∗	∗	NOUN
ejpam-3049	229	59	l(a	l(a	PROPN
ejpam-3049	229	60	)	)	PUNCT
ejpam-3049	229	61	for	for	ADP
ejpam-3049	229	62	every	every	DET
ejpam-3049	229	63	a	a	DET
ejpam-3049	229	64	∈	∈	PROPN
ejpam-3049	229	65	p∗(h	p∗(h	PROPN
ejpam-3049	229	66	)	)	PUNCT
ejpam-3049	229	67	.	.	PUNCT
ejpam-3049	230	1	(	(	PUNCT
ejpam-3049	230	2	6	6	NUM
ejpam-3049	230	3	)	)	PUNCT
ejpam-3049	230	4	i(a	i(a	PROPN
ejpam-3049	230	5	)	)	PUNCT
ejpam-3049	230	6	∩	∩	NOUN
ejpam-3049	230	7	l(a	l(a	PROPN
ejpam-3049	230	8	)	)	PUNCT
ejpam-3049	230	9	⊆	⊆	NUM
ejpam-3049	230	10	i(a	i(a	PROPN
ejpam-3049	230	11	)	)	PUNCT
ejpam-3049	230	12	∗	∗	NOUN
ejpam-3049	230	13	l(a	l(a	PROPN
ejpam-3049	230	14	)	)	PUNCT
ejpam-3049	230	15	for	for	ADP
ejpam-3049	230	16	every	every	DET
ejpam-3049	230	17	a	a	DET
ejpam-3049	230	18	∈	∈	PROPN
ejpam-3049	230	19	h.	h.	PROPN
ejpam-3049	230	20	n.	n.	PROPN
ejpam-3049	230	21	kehayopulu	kehayopulu	PROPN
ejpam-3049	230	22	/	/	SYM
ejpam-3049	230	23	eur	eur	PROPN
ejpam-3049	230	24	.	.	PUNCT
ejpam-3049	231	1	j.	j.	PROPN
ejpam-3049	231	2	pure	pure	PROPN
ejpam-3049	231	3	appl	appl	PROPN
ejpam-3049	231	4	.	.	PROPN
ejpam-3049	231	5	math	math	PROPN
ejpam-3049	231	6	,	,	PUNCT
ejpam-3049	231	7	10	10	NUM
ejpam-3049	231	8	(	(	PUNCT
ejpam-3049	231	9	5	5	NUM
ejpam-3049	231	10	)	)	PUNCT
ejpam-3049	231	11	(	(	PUNCT
ejpam-3049	231	12	2017	2017	NUM
ejpam-3049	231	13	)	)	PUNCT
ejpam-3049	231	14	,	,	PUNCT
ejpam-3049	231	15	929	929	NUM
ejpam-3049	231	16	-	-	SYM
ejpam-3049	231	17	945	945	NUM
ejpam-3049	231	18	937	937	NUM
ejpam-3049	231	19	proof	proof	NOUN
ejpam-3049	231	20	.	.	PUNCT
ejpam-3049	232	1	(	(	PUNCT
ejpam-3049	232	2	1	1	X
ejpam-3049	232	3	)	)	PUNCT
ejpam-3049	232	4	=	=	NOUN
ejpam-3049	232	5	⇒	⇒	NOUN
ejpam-3049	232	6	(	(	PUNCT
ejpam-3049	232	7	2	2	NUM
ejpam-3049	232	8	)	)	PUNCT
ejpam-3049	232	9	.	.	PUNCT
ejpam-3049	233	1	let	let	VERB
ejpam-3049	233	2	a	a	PRON
ejpam-3049	233	3	be	be	AUX
ejpam-3049	233	4	an	an	DET
ejpam-3049	233	5	ideal	ideal	NOUN
ejpam-3049	233	6	,	,	PUNCT
ejpam-3049	233	7	b	b	X
ejpam-3049	233	8	a	a	DET
ejpam-3049	233	9	nonempty	nonempty	NOUN
ejpam-3049	233	10	subset	subset	NOUN
ejpam-3049	233	11	of	of	ADP
ejpam-3049	233	12	h	h	NOUN
ejpam-3049	233	13	and	and	CCONJ
ejpam-3049	233	14	a	a	DET
ejpam-3049	233	15	∈	∈	PROPN
ejpam-3049	233	16	a	a	DET
ejpam-3049	233	17	∩	∩	X
ejpam-3049	233	18	b.	b.	NOUN
ejpam-3049	233	19	since	since	SCONJ
ejpam-3049	233	20	a	a	DET
ejpam-3049	233	21	∈	∈	PROPN
ejpam-3049	233	22	h	h	NOUN
ejpam-3049	233	23	and	and	CCONJ
ejpam-3049	233	24	h	h	NOUN
ejpam-3049	233	25	is	be	AUX
ejpam-3049	233	26	left	leave	VERB
ejpam-3049	233	27	quasi	quasi	ADJ
ejpam-3049	233	28	-	-	ADJ
ejpam-3049	233	29	regular	regular	ADJ
ejpam-3049	233	30	,	,	PUNCT
ejpam-3049	233	31	by	by	ADP
ejpam-3049	233	32	proposition	proposition	NOUN
ejpam-3049	233	33	2.8	2.8	NUM
ejpam-3049	233	34	(	(	PUNCT
ejpam-3049	233	35	1)⇒	1)⇒	NUM
ejpam-3049	233	36	(	(	PUNCT
ejpam-3049	233	37	2	2	NUM
ejpam-3049	233	38	)	)	PUNCT
ejpam-3049	233	39	,	,	PUNCT
ejpam-3049	233	40	we	we	PRON
ejpam-3049	233	41	have	have	VERB
ejpam-3049	233	42	a	a	DET
ejpam-3049	233	43	∈	∈	PROPN
ejpam-3049	233	44	h	h	NOUN
ejpam-3049	233	45	∗	∗	NOUN
ejpam-3049	233	46	{	{	PUNCT
ejpam-3049	233	47	a	a	DET
ejpam-3049	233	48	}	}	PUNCT
ejpam-3049	233	49	∗h	∗h	NOUN
ejpam-3049	233	50	∗	∗	NOUN
ejpam-3049	233	51	{	{	PUNCT
ejpam-3049	233	52	a	a	NOUN
ejpam-3049	233	53	}	}	PUNCT
ejpam-3049	233	54	=	=	SYM
ejpam-3049	233	55	(	(	PUNCT
ejpam-3049	233	56	h	h	NOUN
ejpam-3049	233	57	∗	∗	NOUN
ejpam-3049	233	58	{	{	PUNCT
ejpam-3049	233	59	a	a	DET
ejpam-3049	233	60	}	}	PUNCT
ejpam-3049	233	61	∗h	∗h	NOUN
ejpam-3049	233	62	)	)	PUNCT
ejpam-3049	233	63	∗	∗	NOUN
ejpam-3049	233	64	{	{	PUNCT
ejpam-3049	233	65	a	a	NOUN
ejpam-3049	233	66	}	}	PUNCT
ejpam-3049	233	67	⊆	⊆	NUM
ejpam-3049	233	68	(	(	PUNCT
ejpam-3049	233	69	h	h	NOUN
ejpam-3049	233	70	∗a	∗a	ADJ
ejpam-3049	233	71	∗h	∗h	NOUN
ejpam-3049	233	72	)	)	PUNCT
ejpam-3049	233	73	∗b	∗b	NOUN
ejpam-3049	233	74	.	.	PUNCT
ejpam-3049	234	1	we	we	PRON
ejpam-3049	234	2	have	have	VERB
ejpam-3049	234	3	h	h	NOUN
ejpam-3049	234	4	∗a∗h	∗a∗h	PROPN
ejpam-3049	235	1	=	=	PUNCT
ejpam-3049	235	2	(	(	PUNCT
ejpam-3049	235	3	h	h	NOUN
ejpam-3049	235	4	∗a)∗h	∗a)∗h	PROPN
ejpam-3049	235	5	⊆	⊆	NUM
ejpam-3049	235	6	a∗h	a∗h	NOUN
ejpam-3049	235	7	since	since	SCONJ
ejpam-3049	235	8	a	a	PRON
ejpam-3049	235	9	is	be	AUX
ejpam-3049	235	10	a	a	DET
ejpam-3049	235	11	left	left	ADJ
ejpam-3049	235	12	ideal	ideal	NOUN
ejpam-3049	235	13	of	of	ADP
ejpam-3049	235	14	h	h	NOUN
ejpam-3049	235	15	and	and	CCONJ
ejpam-3049	235	16	a∗h	a∗h	NOUN
ejpam-3049	235	17	⊆	⊆	NUM
ejpam-3049	235	18	a	a	PRON
ejpam-3049	235	19	since	since	SCONJ
ejpam-3049	235	20	a	a	PRON
ejpam-3049	235	21	is	be	AUX
ejpam-3049	235	22	a	a	DET
ejpam-3049	235	23	right	right	ADJ
ejpam-3049	235	24	ideal	ideal	NOUN
ejpam-3049	235	25	of	of	ADP
ejpam-3049	235	26	h.	h.	NOUN
ejpam-3049	235	27	thus	thus	ADV
ejpam-3049	235	28	we	we	PRON
ejpam-3049	235	29	have	have	VERB
ejpam-3049	235	30	h	h	NOUN
ejpam-3049	235	31	∗a	∗a	ADJ
ejpam-3049	235	32	∗h	∗h	NOUN
ejpam-3049	235	33	⊆	⊆	NUM
ejpam-3049	235	34	a.	a.	NOUN
ejpam-3049	235	35	then	then	ADV
ejpam-3049	235	36	a	a	DET
ejpam-3049	235	37	∈	∈	PROPN
ejpam-3049	235	38	(	(	PUNCT
ejpam-3049	235	39	h	h	NOUN
ejpam-3049	235	40	∗a	∗a	ADJ
ejpam-3049	235	41	∗h	∗h	NOUN
ejpam-3049	235	42	)	)	PUNCT
ejpam-3049	235	43	∗b	∗b	PROPN
ejpam-3049	235	44	⊆	⊆	SYM
ejpam-3049	235	45	a	a	DET
ejpam-3049	235	46	∗b	∗b	NOUN
ejpam-3049	235	47	.	.	PUNCT
ejpam-3049	236	1	the	the	DET
ejpam-3049	236	2	implications	implication	NOUN
ejpam-3049	236	3	(	(	PUNCT
ejpam-3049	236	4	2)⇒	2)⇒	NUM
ejpam-3049	236	5	(	(	PUNCT
ejpam-3049	236	6	3	3	NUM
ejpam-3049	236	7	)	)	PUNCT
ejpam-3049	236	8	and	and	CCONJ
ejpam-3049	236	9	(	(	PUNCT
ejpam-3049	236	10	4)⇒	4)⇒	X
ejpam-3049	236	11	(	(	PUNCT
ejpam-3049	236	12	5)⇒	5)⇒	NUM
ejpam-3049	236	13	(	(	PUNCT
ejpam-3049	236	14	6	6	NUM
ejpam-3049	236	15	)	)	PUNCT
ejpam-3049	236	16	are	be	AUX
ejpam-3049	236	17	obvious	obvious	ADJ
ejpam-3049	236	18	,	,	PUNCT
ejpam-3049	236	19	and	and	CCONJ
ejpam-3049	236	20	(	(	PUNCT
ejpam-3049	236	21	3)⇒	3)⇒	NUM
ejpam-3049	236	22	(	(	PUNCT
ejpam-3049	236	23	4	4	NUM
ejpam-3049	236	24	)	)	PUNCT
ejpam-3049	236	25	since	since	SCONJ
ejpam-3049	236	26	the	the	DET
ejpam-3049	236	27	left	left	ADJ
ejpam-3049	236	28	ideals	ideal	NOUN
ejpam-3049	236	29	of	of	ADP
ejpam-3049	236	30	h	h	NOUN
ejpam-3049	236	31	are	be	AUX
ejpam-3049	236	32	bi	bi	ADJ
ejpam-3049	236	33	-	-	NOUN
ejpam-3049	236	34	ideals	ideal	NOUN
ejpam-3049	236	35	of	of	ADP
ejpam-3049	236	36	h	h	NOUN
ejpam-3049	236	37	as	as	ADV
ejpam-3049	236	38	well	well	ADV
ejpam-3049	236	39	.	.	PUNCT
ejpam-3049	237	1	(	(	PUNCT
ejpam-3049	237	2	6	6	NUM
ejpam-3049	237	3	)	)	PUNCT
ejpam-3049	237	4	=	=	NOUN
ejpam-3049	237	5	⇒	⇒	NOUN
ejpam-3049	237	6	(	(	PUNCT
ejpam-3049	237	7	1	1	NUM
ejpam-3049	237	8	)	)	PUNCT
ejpam-3049	237	9	.	.	PUNCT
ejpam-3049	238	1	let	let	VERB
ejpam-3049	238	2	a	a	DET
ejpam-3049	238	3	∈	∈	PROPN
ejpam-3049	238	4	h.	h.	NOUN
ejpam-3049	238	5	by	by	ADP
ejpam-3049	238	6	hypothesis	hypothesis	NOUN
ejpam-3049	238	7	,	,	PUNCT
ejpam-3049	238	8	we	we	PRON
ejpam-3049	238	9	have	have	VERB
ejpam-3049	238	10	a	a	DET
ejpam-3049	238	11	∈	∈	PROPN
ejpam-3049	238	12	i(a	i(a	PROPN
ejpam-3049	238	13	)	)	PUNCT
ejpam-3049	238	14	∩	∩	NOUN
ejpam-3049	238	15	l(a	l(a	PROPN
ejpam-3049	238	16	)	)	PUNCT
ejpam-3049	238	17	⊆	⊆	NUM
ejpam-3049	238	18	i(a	i(a	PROPN
ejpam-3049	238	19	)	)	PUNCT
ejpam-3049	238	20	∗	∗	NOUN
ejpam-3049	238	21	l(a	l(a	PROPN
ejpam-3049	238	22	)	)	PUNCT
ejpam-3049	238	23	=	=	PRON
ejpam-3049	238	24	(	(	PUNCT
ejpam-3049	238	25	{	{	PUNCT
ejpam-3049	238	26	a	a	DET
ejpam-3049	238	27	}	}	PUNCT
ejpam-3049	238	28	∪	∪	NOUN
ejpam-3049	238	29	(	(	PUNCT
ejpam-3049	238	30	h	h	NOUN
ejpam-3049	238	31	∗	∗	NOUN
ejpam-3049	238	32	{	{	PUNCT
ejpam-3049	238	33	a	a	NOUN
ejpam-3049	238	34	}	}	PUNCT
ejpam-3049	238	35	)	)	PUNCT
ejpam-3049	238	36	∪	∪	NOUN
ejpam-3049	238	37	(	(	PUNCT
ejpam-3049	238	38	{	{	PUNCT
ejpam-3049	238	39	a	a	DET
ejpam-3049	238	40	}	}	PUNCT
ejpam-3049	238	41	∗h	∗h	NOUN
ejpam-3049	238	42	)	)	PUNCT
ejpam-3049	238	43	∪	∪	NOUN
ejpam-3049	239	1	(	(	PUNCT
ejpam-3049	239	2	h	h	NOUN
ejpam-3049	239	3	∗	∗	NOUN
ejpam-3049	239	4	{	{	PUNCT
ejpam-3049	239	5	a	a	DET
ejpam-3049	239	6	}	}	PUNCT
ejpam-3049	239	7	∗h	∗h	NOUN
ejpam-3049	239	8	)	)	PUNCT
ejpam-3049	239	9	)	)	PUNCT
ejpam-3049	239	10	∗	∗	NOUN
ejpam-3049	239	11	(	(	PUNCT
ejpam-3049	239	12	{	{	PUNCT
ejpam-3049	239	13	a	a	DET
ejpam-3049	239	14	}	}	PUNCT
ejpam-3049	239	15	∪	∪	NOUN
ejpam-3049	239	16	(	(	PUNCT
ejpam-3049	239	17	h	h	NOUN
ejpam-3049	239	18	∗	∗	NOUN
ejpam-3049	239	19	{	{	PUNCT
ejpam-3049	239	20	a	a	NOUN
ejpam-3049	239	21	}	}	PUNCT
ejpam-3049	239	22	)	)	PUNCT
ejpam-3049	239	23	)	)	PUNCT
ejpam-3049	240	1	=	=	PRON
ejpam-3049	240	2	(	(	PUNCT
ejpam-3049	240	3	{	{	PUNCT
ejpam-3049	240	4	a	a	PRON
ejpam-3049	240	5	}	}	PUNCT
ejpam-3049	240	6	∗	∗	NOUN
ejpam-3049	240	7	{	{	PUNCT
ejpam-3049	240	8	a	a	NOUN
ejpam-3049	240	9	}	}	PUNCT
ejpam-3049	240	10	)	)	PUNCT
ejpam-3049	240	11	∪	∪	NOUN
ejpam-3049	240	12	(	(	PUNCT
ejpam-3049	240	13	h	h	NOUN
ejpam-3049	240	14	∗	∗	NOUN
ejpam-3049	240	15	{	{	PUNCT
ejpam-3049	240	16	a	a	DET
ejpam-3049	240	17	}	}	PUNCT
ejpam-3049	240	18	∗	∗	NOUN
ejpam-3049	240	19	{	{	PUNCT
ejpam-3049	240	20	a	a	NOUN
ejpam-3049	240	21	}	}	PUNCT
ejpam-3049	240	22	)	)	PUNCT
ejpam-3049	240	23	∪	∪	NOUN
ejpam-3049	240	24	(	(	PUNCT
ejpam-3049	240	25	{	{	PUNCT
ejpam-3049	240	26	a	a	PRON
ejpam-3049	240	27	}	}	PUNCT
ejpam-3049	240	28	∗h	∗h	NOUN
ejpam-3049	240	29	∗	∗	NOUN
ejpam-3049	240	30	{	{	PUNCT
ejpam-3049	240	31	a	a	NOUN
ejpam-3049	240	32	}	}	PUNCT
ejpam-3049	240	33	)	)	PUNCT
ejpam-3049	240	34	∪	∪	NOUN
ejpam-3049	240	35	(	(	PUNCT
ejpam-3049	240	36	h	h	NOUN
ejpam-3049	240	37	∗	∗	NOUN
ejpam-3049	240	38	{	{	PUNCT
ejpam-3049	240	39	a	a	DET
ejpam-3049	240	40	}	}	PUNCT
ejpam-3049	240	41	∗h	∗h	NOUN
ejpam-3049	240	42	∗	∗	NOUN
ejpam-3049	240	43	{	{	PUNCT
ejpam-3049	240	44	a	a	NOUN
ejpam-3049	240	45	}	}	PUNCT
ejpam-3049	240	46	)	)	PUNCT
ejpam-3049	240	47	.	.	PUNCT
ejpam-3049	241	1	if	if	SCONJ
ejpam-3049	241	2	a	a	DET
ejpam-3049	241	3	∈	∈	PROPN
ejpam-3049	241	4	{	{	PUNCT
ejpam-3049	241	5	a	a	NOUN
ejpam-3049	241	6	}	}	PUNCT
ejpam-3049	241	7	∗	∗	NOUN
ejpam-3049	241	8	{	{	PUNCT
ejpam-3049	241	9	a	a	NOUN
ejpam-3049	241	10	}	}	PUNCT
ejpam-3049	241	11	,	,	PUNCT
ejpam-3049	241	12	then	then	ADV
ejpam-3049	241	13	a	a	DET
ejpam-3049	241	14	∈	∈	NOUN
ejpam-3049	241	15	{	{	PUNCT
ejpam-3049	241	16	a	a	NOUN
ejpam-3049	241	17	}	}	PUNCT
ejpam-3049	241	18	⊆	⊆	NUM
ejpam-3049	241	19	{	{	PUNCT
ejpam-3049	241	20	a	a	PRON
ejpam-3049	241	21	}	}	PUNCT
ejpam-3049	241	22	∗	∗	NOUN
ejpam-3049	241	23	{	{	PUNCT
ejpam-3049	241	24	a	a	NOUN
ejpam-3049	241	25	}	}	PUNCT
ejpam-3049	241	26	⊆	⊆	NUM
ejpam-3049	241	27	(	(	PUNCT
ejpam-3049	241	28	{	{	PUNCT
ejpam-3049	241	29	a	a	PRON
ejpam-3049	241	30	}	}	PUNCT
ejpam-3049	241	31	∗	∗	NOUN
ejpam-3049	241	32	{	{	PUNCT
ejpam-3049	241	33	a	a	NOUN
ejpam-3049	241	34	}	}	PUNCT
ejpam-3049	241	35	)	)	PUNCT
ejpam-3049	241	36	∗	∗	NOUN
ejpam-3049	241	37	(	(	PUNCT
ejpam-3049	241	38	{	{	PUNCT
ejpam-3049	241	39	a	a	PRON
ejpam-3049	241	40	}	}	PUNCT
ejpam-3049	241	41	∗	∗	NOUN
ejpam-3049	241	42	{	{	PUNCT
ejpam-3049	241	43	a	a	NOUN
ejpam-3049	241	44	}	}	PUNCT
ejpam-3049	241	45	)	)	PUNCT
ejpam-3049	241	46	⊆	⊆	NUM
ejpam-3049	241	47	h	h	NOUN
ejpam-3049	241	48	∗	∗	NOUN
ejpam-3049	241	49	{	{	PUNCT
ejpam-3049	241	50	a	a	DET
ejpam-3049	241	51	}	}	PUNCT
ejpam-3049	241	52	∗h	∗h	NOUN
ejpam-3049	241	53	∗	∗	NOUN
ejpam-3049	241	54	{	{	PUNCT
ejpam-3049	241	55	a	a	NOUN
ejpam-3049	241	56	}	}	PUNCT
ejpam-3049	241	57	.	.	PUNCT
ejpam-3049	242	1	if	if	SCONJ
ejpam-3049	242	2	a	a	DET
ejpam-3049	242	3	∈	∈	PROPN
ejpam-3049	242	4	h	h	NOUN
ejpam-3049	242	5	∗	∗	NOUN
ejpam-3049	242	6	{	{	PUNCT
ejpam-3049	242	7	a	a	DET
ejpam-3049	242	8	}	}	PUNCT
ejpam-3049	242	9	∗	∗	NOUN
ejpam-3049	242	10	{	{	PUNCT
ejpam-3049	242	11	a	a	NOUN
ejpam-3049	242	12	}	}	PUNCT
ejpam-3049	242	13	,	,	PUNCT
ejpam-3049	242	14	then	then	ADV
ejpam-3049	242	15	a	a	DET
ejpam-3049	242	16	∈	∈	NOUN
ejpam-3049	242	17	{	{	PUNCT
ejpam-3049	242	18	a	a	NOUN
ejpam-3049	242	19	}	}	PUNCT
ejpam-3049	242	20	⊆	⊆	NUM
ejpam-3049	242	21	h	h	NOUN
ejpam-3049	242	22	∗	∗	NOUN
ejpam-3049	242	23	{	{	PUNCT
ejpam-3049	242	24	a	a	DET
ejpam-3049	242	25	}	}	PUNCT
ejpam-3049	242	26	∗	∗	NOUN
ejpam-3049	242	27	(	(	PUNCT
ejpam-3049	242	28	h	h	NOUN
ejpam-3049	242	29	∗	∗	NOUN
ejpam-3049	242	30	{	{	PUNCT
ejpam-3049	242	31	a	a	DET
ejpam-3049	242	32	}	}	PUNCT
ejpam-3049	242	33	∗	∗	NOUN
ejpam-3049	242	34	{	{	PUNCT
ejpam-3049	242	35	a	a	NOUN
ejpam-3049	242	36	}	}	PUNCT
ejpam-3049	242	37	)	)	PUNCT
ejpam-3049	242	38	⊆	⊆	NUM
ejpam-3049	242	39	h	h	NOUN
ejpam-3049	242	40	∗	∗	NOUN
ejpam-3049	242	41	{	{	PUNCT
ejpam-3049	242	42	a	a	DET
ejpam-3049	242	43	}	}	PUNCT
ejpam-3049	242	44	∗	∗	NOUN
ejpam-3049	242	45	(	(	PUNCT
ejpam-3049	242	46	h	h	NOUN
ejpam-3049	242	47	∗h	∗h	NOUN
ejpam-3049	242	48	)	)	PUNCT
ejpam-3049	242	49	∗	∗	NOUN
ejpam-3049	242	50	{	{	PUNCT
ejpam-3049	242	51	a	a	PRON
ejpam-3049	242	52	}	}	PUNCT
ejpam-3049	242	53	⊆	⊆	NUM
ejpam-3049	242	54	h	h	NOUN
ejpam-3049	242	55	∗	∗	NOUN
ejpam-3049	242	56	{	{	PUNCT
ejpam-3049	242	57	a	a	DET
ejpam-3049	242	58	}	}	PUNCT
ejpam-3049	242	59	∗h	∗h	NOUN
ejpam-3049	242	60	∗	∗	NOUN
ejpam-3049	242	61	{	{	PUNCT
ejpam-3049	242	62	a	a	NOUN
ejpam-3049	242	63	}	}	PUNCT
ejpam-3049	242	64	.	.	PUNCT
ejpam-3049	243	1	if	if	SCONJ
ejpam-3049	243	2	a	a	DET
ejpam-3049	243	3	∈	∈	PROPN
ejpam-3049	243	4	{	{	PUNCT
ejpam-3049	243	5	a	a	NOUN
ejpam-3049	243	6	}	}	PUNCT
ejpam-3049	243	7	∗h	∗h	NOUN
ejpam-3049	243	8	∗	∗	NOUN
ejpam-3049	243	9	{	{	PUNCT
ejpam-3049	243	10	a	a	NOUN
ejpam-3049	243	11	}	}	PUNCT
ejpam-3049	243	12	,	,	PUNCT
ejpam-3049	243	13	then	then	ADV
ejpam-3049	243	14	{	{	PUNCT
ejpam-3049	243	15	a	a	PRON
ejpam-3049	243	16	}	}	PUNCT
ejpam-3049	243	17	⊆	⊆	NUM
ejpam-3049	243	18	{	{	PUNCT
ejpam-3049	243	19	a	a	DET
ejpam-3049	243	20	}	}	PUNCT
ejpam-3049	243	21	∗h	∗h	NOUN
ejpam-3049	243	22	∗	∗	NOUN
ejpam-3049	243	23	(	(	PUNCT
ejpam-3049	243	24	{	{	PUNCT
ejpam-3049	243	25	a	a	PRON
ejpam-3049	243	26	}	}	PUNCT
ejpam-3049	243	27	∗h	∗h	NOUN
ejpam-3049	243	28	∗	∗	NOUN
ejpam-3049	243	29	{	{	PUNCT
ejpam-3049	243	30	a	a	NOUN
ejpam-3049	243	31	}	}	PUNCT
ejpam-3049	243	32	)	)	PUNCT
ejpam-3049	243	33	⊆	⊆	X
ejpam-3049	243	34	(	(	PUNCT
ejpam-3049	243	35	h	h	NOUN
ejpam-3049	243	36	∗h	∗h	NOUN
ejpam-3049	243	37	)	)	PUNCT
ejpam-3049	243	38	∗	∗	NOUN
ejpam-3049	243	39	(	(	PUNCT
ejpam-3049	243	40	{	{	PUNCT
ejpam-3049	243	41	a	a	PRON
ejpam-3049	243	42	}	}	PUNCT
ejpam-3049	243	43	∗h	∗h	NOUN
ejpam-3049	243	44	∗	∗	NOUN
ejpam-3049	243	45	{	{	PUNCT
ejpam-3049	243	46	a	a	NOUN
ejpam-3049	243	47	}	}	PUNCT
ejpam-3049	243	48	)	)	PUNCT
ejpam-3049	243	49	⊆	⊆	NUM
ejpam-3049	243	50	h	h	NOUN
ejpam-3049	243	51	∗	∗	NOUN
ejpam-3049	243	52	{	{	PUNCT
ejpam-3049	243	53	a	a	DET
ejpam-3049	243	54	}	}	PUNCT
ejpam-3049	243	55	∗h	∗h	NOUN
ejpam-3049	243	56	∗	∗	NOUN
ejpam-3049	243	57	{	{	PUNCT
ejpam-3049	243	58	a	a	NOUN
ejpam-3049	243	59	}	}	PUNCT
ejpam-3049	243	60	.	.	PUNCT
ejpam-3049	244	1	in	in	ADP
ejpam-3049	244	2	each	each	DET
ejpam-3049	244	3	case	case	NOUN
ejpam-3049	244	4	,	,	PUNCT
ejpam-3049	244	5	a	a	DET
ejpam-3049	244	6	∈	∈	PROPN
ejpam-3049	244	7	h	h	NOUN
ejpam-3049	244	8	∗	∗	NOUN
ejpam-3049	244	9	{	{	PUNCT
ejpam-3049	244	10	a	a	PRON
ejpam-3049	244	11	}	}	PUNCT
ejpam-3049	244	12	∗h	∗h	NOUN
ejpam-3049	244	13	∗	∗	NOUN
ejpam-3049	244	14	{	{	PUNCT
ejpam-3049	244	15	a	a	NOUN
ejpam-3049	244	16	}	}	PUNCT
ejpam-3049	244	17	,	,	PUNCT
ejpam-3049	244	18	so	so	CCONJ
ejpam-3049	244	19	h	h	NOUN
ejpam-3049	244	20	is	be	AUX
ejpam-3049	244	21	left	leave	VERB
ejpam-3049	244	22	quasi	quasi	ADJ
ejpam-3049	244	23	-	-	ADJ
ejpam-3049	244	24	regular	regular	ADJ
ejpam-3049	244	25	.	.	PUNCT
ejpam-3049	245	1	�	�	PROPN
ejpam-3049	245	2	theorem	theorem	VERB
ejpam-3049	245	3	2.10	2.10	NUM
ejpam-3049	245	4	.	.	PUNCT
ejpam-3049	246	1	an	an	DET
ejpam-3049	246	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	246	3	(	(	PUNCT
ejpam-3049	246	4	h	h	NOUN
ejpam-3049	246	5	,	,	PUNCT
ejpam-3049	246	6	◦	◦	NOUN
ejpam-3049	246	7	)	)	PUNCT
ejpam-3049	246	8	is	be	AUX
ejpam-3049	246	9	left	leave	VERB
ejpam-3049	246	10	quasi	quasi	ADJ
ejpam-3049	246	11	-	-	ADJ
ejpam-3049	246	12	regular	regular	ADJ
ejpam-3049	246	13	if	if	SCONJ
ejpam-3049	247	1	and	and	CCONJ
ejpam-3049	247	2	only	only	ADV
ejpam-3049	247	3	if	if	SCONJ
ejpam-3049	247	4	,	,	PUNCT
ejpam-3049	247	5	for	for	ADP
ejpam-3049	247	6	any	any	DET
ejpam-3049	247	7	left	left	ADJ
ejpam-3049	247	8	ideals	ideal	NOUN
ejpam-3049	247	9	a	a	PRON
ejpam-3049	247	10	and	and	CCONJ
ejpam-3049	247	11	b	b	NOUN
ejpam-3049	247	12	of	of	ADP
ejpam-3049	247	13	h	h	NOUN
ejpam-3049	247	14	,	,	PUNCT
ejpam-3049	247	15	we	we	PRON
ejpam-3049	247	16	have	have	VERB
ejpam-3049	247	17	a	a	DET
ejpam-3049	247	18	∩b	∩b	NOUN
ejpam-3049	247	19	⊆	⊆	NUM
ejpam-3049	247	20	a	a	DET
ejpam-3049	247	21	∗b	∗b	NOUN
ejpam-3049	247	22	.	.	PUNCT
ejpam-3049	248	1	proof	proof	NOUN
ejpam-3049	248	2	.	.	PUNCT
ejpam-3049	249	1	=	=	NOUN
ejpam-3049	249	2	⇒.	⇒.	NOUN
ejpam-3049	249	3	let	let	VERB
ejpam-3049	249	4	a	a	DET
ejpam-3049	249	5	,	,	PUNCT
ejpam-3049	249	6	b	b	PROPN
ejpam-3049	249	7	be	be	AUX
ejpam-3049	249	8	left	leave	VERB
ejpam-3049	249	9	ideals	ideal	NOUN
ejpam-3049	249	10	of	of	ADP
ejpam-3049	249	11	h	h	NOUN
ejpam-3049	249	12	and	and	CCONJ
ejpam-3049	249	13	a	a	DET
ejpam-3049	249	14	∈	∈	PROPN
ejpam-3049	249	15	a	a	DET
ejpam-3049	249	16	∩	∩	X
ejpam-3049	249	17	b.	b.	NOUN
ejpam-3049	249	18	since	since	SCONJ
ejpam-3049	249	19	h	h	PROPN
ejpam-3049	249	20	is	be	AUX
ejpam-3049	249	21	left	leave	VERB
ejpam-3049	249	22	quasi	quasi	ADJ
ejpam-3049	249	23	-	-	ADJ
ejpam-3049	249	24	regular	regular	ADJ
ejpam-3049	249	25	,	,	PUNCT
ejpam-3049	249	26	there	there	PRON
ejpam-3049	249	27	exist	exist	VERB
ejpam-3049	249	28	x	x	NOUN
ejpam-3049	249	29	,	,	PUNCT
ejpam-3049	249	30	y	y	PROPN
ejpam-3049	249	31	∈	∈	PROPN
ejpam-3049	249	32	h	h	NOUN
ejpam-3049	249	33	such	such	ADJ
ejpam-3049	249	34	that	that	SCONJ
ejpam-3049	249	35	a	a	DET
ejpam-3049	249	36	∈	∈	NOUN
ejpam-3049	249	37	(	(	PUNCT
ejpam-3049	249	38	x	x	SYM
ejpam-3049	249	39	◦	◦	VERB
ejpam-3049	249	40	a	a	X
ejpam-3049	249	41	)	)	PUNCT
ejpam-3049	249	42	∗	∗	NOUN
ejpam-3049	249	43	(	(	PUNCT
ejpam-3049	249	44	y	y	NOUN
ejpam-3049	249	45	◦	◦	VERB
ejpam-3049	249	46	a	a	X
ejpam-3049	249	47	)	)	PUNCT
ejpam-3049	249	48	=	=	SYM
ejpam-3049	249	49	{	{	PUNCT
ejpam-3049	249	50	x	x	NOUN
ejpam-3049	249	51	}	}	PUNCT
ejpam-3049	249	52	∗	∗	NOUN
ejpam-3049	249	53	{	{	PUNCT
ejpam-3049	249	54	a	a	PRON
ejpam-3049	249	55	}	}	PUNCT
ejpam-3049	249	56	∗	∗	NOUN
ejpam-3049	249	57	{	{	PUNCT
ejpam-3049	249	58	y	y	NOUN
ejpam-3049	249	59	}	}	PUNCT
ejpam-3049	249	60	∗	∗	NOUN
ejpam-3049	249	61	{	{	PUNCT
ejpam-3049	249	62	a	a	PRON
ejpam-3049	249	63	}	}	PUNCT
ejpam-3049	249	64	⊆	⊆	NUM
ejpam-3049	249	65	(	(	PUNCT
ejpam-3049	249	66	h	h	NOUN
ejpam-3049	249	67	∗a	∗a	ADJ
ejpam-3049	249	68	)	)	PUNCT
ejpam-3049	249	69	∗	∗	NOUN
ejpam-3049	249	70	(	(	PUNCT
ejpam-3049	249	71	h	h	NOUN
ejpam-3049	249	72	∗b	∗b	PROPN
ejpam-3049	249	73	)	)	PUNCT
ejpam-3049	249	74	⊆	⊆	NUM
ejpam-3049	249	75	a	a	DET
ejpam-3049	249	76	∗b	∗b	PROPN
ejpam-3049	249	77	.	.	PUNCT
ejpam-3049	250	1	⇐	⇐	PROPN
ejpam-3049	250	2	=	=	PRON
ejpam-3049	250	3	.	.	PUNCT
ejpam-3049	250	4	let	let	VERB
ejpam-3049	250	5	a	a	DET
ejpam-3049	250	6	∈	∈	PROPN
ejpam-3049	250	7	p∗(h	p∗(h	PROPN
ejpam-3049	250	8	)	)	PUNCT
ejpam-3049	250	9	.	.	PUNCT
ejpam-3049	251	1	then	then	ADV
ejpam-3049	251	2	a	a	DET
ejpam-3049	251	3	⊆	⊆	NUM
ejpam-3049	251	4	h	h	NOUN
ejpam-3049	251	5	∗a	∗a	ADJ
ejpam-3049	251	6	∗h	∗h	NOUN
ejpam-3049	251	7	∗a	∗a	ADJ
ejpam-3049	251	8	.	.	PUNCT
ejpam-3049	252	1	in	in	ADP
ejpam-3049	252	2	fact	fact	NOUN
ejpam-3049	252	3	,	,	PUNCT
ejpam-3049	252	4	by	by	ADP
ejpam-3049	252	5	hypothesis	hypothesis	NOUN
ejpam-3049	252	6	,	,	PUNCT
ejpam-3049	252	7	we	we	PRON
ejpam-3049	252	8	have	have	VERB
ejpam-3049	252	9	a	a	DET
ejpam-3049	252	10	⊆	⊆	NUM
ejpam-3049	252	11	l(a	l(a	X
ejpam-3049	252	12	)	)	PUNCT
ejpam-3049	252	13	=	=	SYM
ejpam-3049	252	14	l(a	l(a	PROPN
ejpam-3049	252	15	)	)	PUNCT
ejpam-3049	252	16	∩	∩	NOUN
ejpam-3049	252	17	l(a	l(a	PROPN
ejpam-3049	252	18	)	)	PUNCT
ejpam-3049	252	19	⊆	⊆	NUM
ejpam-3049	252	20	l(a	l(a	PROPN
ejpam-3049	252	21	)	)	PUNCT
ejpam-3049	252	22	∗	∗	NOUN
ejpam-3049	252	23	l(a	l(a	PROPN
ejpam-3049	252	24	)	)	PUNCT
ejpam-3049	252	25	=	=	PRON
ejpam-3049	253	1	(	(	PUNCT
ejpam-3049	253	2	a	a	DET
ejpam-3049	253	3	∪	∪	X
ejpam-3049	253	4	(	(	PUNCT
ejpam-3049	253	5	h	h	NOUN
ejpam-3049	253	6	∗a	∗a	ADJ
ejpam-3049	253	7	)	)	PUNCT
ejpam-3049	253	8	)	)	PUNCT
ejpam-3049	253	9	∗	∗	NOUN
ejpam-3049	253	10	(	(	PUNCT
ejpam-3049	253	11	a	a	DET
ejpam-3049	253	12	∪	∪	X
ejpam-3049	253	13	(	(	PUNCT
ejpam-3049	253	14	h	h	NOUN
ejpam-3049	253	15	∗a	∗a	ADJ
ejpam-3049	253	16	)	)	PUNCT
ejpam-3049	253	17	)	)	PUNCT
ejpam-3049	253	18	n.	n.	NOUN
ejpam-3049	253	19	kehayopulu	kehayopulu	PROPN
ejpam-3049	253	20	/	/	SYM
ejpam-3049	253	21	eur	eur	PROPN
ejpam-3049	253	22	.	.	PUNCT
ejpam-3049	254	1	j.	j.	PROPN
ejpam-3049	254	2	pure	pure	PROPN
ejpam-3049	254	3	appl	appl	PROPN
ejpam-3049	254	4	.	.	PROPN
ejpam-3049	254	5	math	math	PROPN
ejpam-3049	254	6	,	,	PUNCT
ejpam-3049	254	7	10	10	NUM
ejpam-3049	254	8	(	(	PUNCT
ejpam-3049	254	9	5	5	NUM
ejpam-3049	254	10	)	)	PUNCT
ejpam-3049	254	11	(	(	PUNCT
ejpam-3049	254	12	2017	2017	NUM
ejpam-3049	254	13	)	)	PUNCT
ejpam-3049	254	14	,	,	PUNCT
ejpam-3049	254	15	929	929	NUM
ejpam-3049	254	16	-	-	SYM
ejpam-3049	254	17	945	945	NUM
ejpam-3049	254	18	938	938	NUM
ejpam-3049	254	19	=	=	SYM
ejpam-3049	254	20	(	(	PUNCT
ejpam-3049	254	21	a	a	DET
ejpam-3049	254	22	∗a	∗a	ADJ
ejpam-3049	254	23	)	)	PUNCT
ejpam-3049	254	24	∪	∪	NOUN
ejpam-3049	254	25	(	(	PUNCT
ejpam-3049	254	26	h	h	NOUN
ejpam-3049	254	27	∗a	∗a	ADJ
ejpam-3049	254	28	∗a	∗a	ADJ
ejpam-3049	254	29	)	)	PUNCT
ejpam-3049	254	30	∪	∪	NOUN
ejpam-3049	254	31	(	(	PUNCT
ejpam-3049	254	32	a	a	DET
ejpam-3049	254	33	∗h	∗h	NOUN
ejpam-3049	254	34	∗a	∗a	ADJ
ejpam-3049	254	35	)	)	PUNCT
ejpam-3049	254	36	∪	∪	NOUN
ejpam-3049	254	37	(	(	PUNCT
ejpam-3049	254	38	h	h	NOUN
ejpam-3049	254	39	∗a	∗a	ADJ
ejpam-3049	254	40	∗h	∗h	NOUN
ejpam-3049	254	41	∗a	∗a	ADJ
ejpam-3049	254	42	)	)	PUNCT
ejpam-3049	254	43	.	.	PUNCT
ejpam-3049	255	1	then	then	ADV
ejpam-3049	255	2	we	we	PRON
ejpam-3049	255	3	have	have	VERB
ejpam-3049	255	4	a	a	DET
ejpam-3049	255	5	∗a	∗a	ADJ
ejpam-3049	255	6	⊆	⊆	NUM
ejpam-3049	255	7	(	(	PUNCT
ejpam-3049	255	8	a	a	DET
ejpam-3049	255	9	∗a	∗a	ADJ
ejpam-3049	255	10	∗a	∗a	NOUN
ejpam-3049	255	11	)	)	PUNCT
ejpam-3049	255	12	∪	∪	NOUN
ejpam-3049	255	13	(	(	PUNCT
ejpam-3049	255	14	a	a	DET
ejpam-3049	255	15	∗h	∗h	NOUN
ejpam-3049	255	16	∗a	∗a	ADJ
ejpam-3049	255	17	∗a	∗a	ADJ
ejpam-3049	255	18	)	)	PUNCT
ejpam-3049	255	19	∪	∪	NOUN
ejpam-3049	255	20	(	(	PUNCT
ejpam-3049	255	21	a	a	DET
ejpam-3049	255	22	∗a	∗a	ADJ
ejpam-3049	255	23	∗h	∗h	NOUN
ejpam-3049	255	24	∗a	∗a	ADJ
ejpam-3049	255	25	)	)	PUNCT
ejpam-3049	255	26	∪	∪	NOUN
ejpam-3049	255	27	(	(	PUNCT
ejpam-3049	255	28	a	a	DET
ejpam-3049	255	29	∗h	∗h	NOUN
ejpam-3049	255	30	∗a	∗a	ADJ
ejpam-3049	255	31	∗h	∗h	NOUN
ejpam-3049	255	32	∗a	∗a	ADJ
ejpam-3049	255	33	)	)	PUNCT
ejpam-3049	255	34	⊆	⊆	NUM
ejpam-3049	255	35	a	a	DET
ejpam-3049	255	36	∗h	∗h	NOUN
ejpam-3049	255	37	∗a	∗a	ADJ
ejpam-3049	255	38	,	,	PUNCT
ejpam-3049	255	39	from	from	ADP
ejpam-3049	255	40	which	which	PRON
ejpam-3049	255	41	h	h	NOUN
ejpam-3049	255	42	∗a	∗a	ADJ
ejpam-3049	255	43	∗a	∗a	ADJ
ejpam-3049	255	44	⊆	⊆	NUM
ejpam-3049	255	45	h	h	NOUN
ejpam-3049	255	46	∗a	∗a	ADJ
ejpam-3049	255	47	∗h	∗h	NOUN
ejpam-3049	255	48	∗a	∗a	ADJ
ejpam-3049	255	49	.	.	PUNCT
ejpam-3049	256	1	thus	thus	ADV
ejpam-3049	256	2	we	we	PRON
ejpam-3049	256	3	obtain	obtain	VERB
ejpam-3049	256	4	a	a	DET
ejpam-3049	256	5	⊆	⊆	NUM
ejpam-3049	256	6	(	(	PUNCT
ejpam-3049	256	7	a	a	DET
ejpam-3049	256	8	∗h	∗h	NOUN
ejpam-3049	256	9	∗a	∗a	ADJ
ejpam-3049	256	10	)	)	PUNCT
ejpam-3049	256	11	∪	∪	NOUN
ejpam-3049	256	12	(	(	PUNCT
ejpam-3049	256	13	h	h	NOUN
ejpam-3049	256	14	∗a	∗a	ADJ
ejpam-3049	256	15	∗h	∗h	NOUN
ejpam-3049	256	16	∗a	∗a	ADJ
ejpam-3049	256	17	)	)	PUNCT
ejpam-3049	256	18	,	,	PUNCT
ejpam-3049	256	19	then	then	ADV
ejpam-3049	256	20	we	we	PRON
ejpam-3049	256	21	get	get	VERB
ejpam-3049	256	22	a	a	DET
ejpam-3049	256	23	∗h	∗h	NOUN
ejpam-3049	256	24	∗a	∗a	ADJ
ejpam-3049	256	25	⊆	⊆	NUM
ejpam-3049	256	26	(	(	PUNCT
ejpam-3049	256	27	a	a	DET
ejpam-3049	256	28	∗h	∗h	NOUN
ejpam-3049	256	29	∗a	∗a	ADJ
ejpam-3049	256	30	∗h	∗h	NOUN
ejpam-3049	256	31	∗a	∗a	ADJ
ejpam-3049	256	32	)	)	PUNCT
ejpam-3049	256	33	∪	∪	NOUN
ejpam-3049	256	34	(	(	PUNCT
ejpam-3049	256	35	h	h	NOUN
ejpam-3049	256	36	∗a	∗a	ADJ
ejpam-3049	256	37	∗h	∗h	NOUN
ejpam-3049	256	38	∗a	∗a	ADJ
ejpam-3049	256	39	∗h	∗h	NOUN
ejpam-3049	256	40	∗a	∗a	ADJ
ejpam-3049	256	41	)	)	PUNCT
ejpam-3049	256	42	⊆	⊆	NUM
ejpam-3049	256	43	h	h	NOUN
ejpam-3049	256	44	∗a	∗a	ADJ
ejpam-3049	256	45	∗h	∗h	NOUN
ejpam-3049	256	46	∗a	∗a	ADJ
ejpam-3049	256	47	,	,	PUNCT
ejpam-3049	256	48	so	so	SCONJ
ejpam-3049	256	49	a	a	DET
ejpam-3049	256	50	⊆	⊆	NUM
ejpam-3049	256	51	h	h	NOUN
ejpam-3049	256	52	∗a	∗a	ADJ
ejpam-3049	256	53	∗h	∗h	NOUN
ejpam-3049	256	54	∗a	∗a	ADJ
ejpam-3049	256	55	,	,	PUNCT
ejpam-3049	256	56	and	and	CCONJ
ejpam-3049	256	57	h	h	NOUN
ejpam-3049	256	58	is	be	AUX
ejpam-3049	256	59	left	leave	VERB
ejpam-3049	256	60	quasi	quasi	ADJ
ejpam-3049	256	61	-	-	ADJ
ejpam-3049	256	62	regular	regular	ADJ
ejpam-3049	256	63	.	.	PUNCT
ejpam-3049	257	1	�	�	PROPN
ejpam-3049	258	1	a	a	DET
ejpam-3049	258	2	subset	subset	NOUN
ejpam-3049	258	3	a	a	PRON
ejpam-3049	258	4	of	of	ADP
ejpam-3049	258	5	an	an	DET
ejpam-3049	258	6	hypergroupoid	hypergroupoid	PROPN
ejpam-3049	258	7	(	(	PUNCT
ejpam-3049	258	8	h	h	NOUN
ejpam-3049	258	9	,	,	PUNCT
ejpam-3049	258	10	◦	◦	NOUN
ejpam-3049	258	11	)	)	PUNCT
ejpam-3049	258	12	is	be	AUX
ejpam-3049	258	13	called	call	VERB
ejpam-3049	258	14	idempotent	idempotent	ADJ
ejpam-3049	258	15	if	if	SCONJ
ejpam-3049	258	16	a	a	DET
ejpam-3049	258	17	∗a	∗a	ADJ
ejpam-3049	258	18	=	=	SYM
ejpam-3049	258	19	a.	a.	NOUN
ejpam-3049	258	20	theorem	theorem	NOUN
ejpam-3049	258	21	2.11	2.11	NUM
ejpam-3049	258	22	.	.	PUNCT
ejpam-3049	259	1	an	an	DET
ejpam-3049	259	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	259	3	(	(	PUNCT
ejpam-3049	259	4	h	h	NOUN
ejpam-3049	259	5	,	,	PUNCT
ejpam-3049	259	6	◦	◦	NOUN
ejpam-3049	259	7	)	)	PUNCT
ejpam-3049	259	8	is	be	AUX
ejpam-3049	259	9	left	leave	VERB
ejpam-3049	259	10	quasi	quasi	ADJ
ejpam-3049	259	11	-	-	ADJ
ejpam-3049	259	12	regular	regular	ADJ
ejpam-3049	259	13	if	if	SCONJ
ejpam-3049	260	1	and	and	CCONJ
ejpam-3049	260	2	only	only	ADV
ejpam-3049	260	3	if	if	SCONJ
ejpam-3049	260	4	the	the	DET
ejpam-3049	260	5	left	left	ADJ
ejpam-3049	260	6	ideals	ideal	NOUN
ejpam-3049	260	7	of	of	ADP
ejpam-3049	260	8	h	h	NOUN
ejpam-3049	260	9	are	be	AUX
ejpam-3049	260	10	idempotent	idempotent	ADJ
ejpam-3049	260	11	.	.	PUNCT
ejpam-3049	261	1	proof	proof	NOUN
ejpam-3049	261	2	.	.	PUNCT
ejpam-3049	262	1	=	=	NOUN
ejpam-3049	262	2	⇒.	⇒.	NOUN
ejpam-3049	262	3	if	if	SCONJ
ejpam-3049	262	4	l	l	NOUN
ejpam-3049	262	5	is	be	AUX
ejpam-3049	262	6	a	a	DET
ejpam-3049	262	7	left	left	ADJ
ejpam-3049	262	8	ideal	ideal	NOUN
ejpam-3049	262	9	of	of	ADP
ejpam-3049	262	10	h	h	NOUN
ejpam-3049	262	11	then	then	ADV
ejpam-3049	262	12	,	,	PUNCT
ejpam-3049	262	13	by	by	ADP
ejpam-3049	262	14	theorem	theorem	NOUN
ejpam-3049	262	15	2.10	2.10	NUM
ejpam-3049	262	16	,	,	PUNCT
ejpam-3049	262	17	we	we	PRON
ejpam-3049	262	18	have	have	VERB
ejpam-3049	262	19	l	l	NOUN
ejpam-3049	262	20	⊆	⊆	NUM
ejpam-3049	262	21	l∗l	l∗l	SYM
ejpam-3049	262	22	⊆	⊆	NUM
ejpam-3049	262	23	h	h	NOUN
ejpam-3049	262	24	∗l	∗l	NOUN
ejpam-3049	262	25	⊆	⊆	NUM
ejpam-3049	262	26	l	l	NOUN
ejpam-3049	262	27	,	,	PUNCT
ejpam-3049	262	28	so	so	SCONJ
ejpam-3049	262	29	l	l	NOUN
ejpam-3049	262	30	∗	∗	NOUN
ejpam-3049	262	31	l	l	NOUN
ejpam-3049	262	32	=	=	PUNCT
ejpam-3049	262	33	l.	l.	X
ejpam-3049	262	34	⇐	⇐	PROPN
ejpam-3049	262	35	=	=	PROPN
ejpam-3049	262	36	.	.	PUNCT
ejpam-3049	262	37	by	by	ADP
ejpam-3049	262	38	theorem	theorem	NOUN
ejpam-3049	262	39	2.9	2.9	NUM
ejpam-3049	262	40	,	,	PUNCT
ejpam-3049	262	41	it	it	PRON
ejpam-3049	262	42	is	be	AUX
ejpam-3049	262	43	enough	enough	ADJ
ejpam-3049	262	44	to	to	PART
ejpam-3049	262	45	prove	prove	VERB
ejpam-3049	262	46	that	that	SCONJ
ejpam-3049	262	47	for	for	ADP
ejpam-3049	262	48	every	every	DET
ejpam-3049	262	49	ideal	ideal	NOUN
ejpam-3049	262	50	a	a	DET
ejpam-3049	262	51	and	and	CCONJ
ejpam-3049	262	52	every	every	PRON
ejpam-3049	262	53	left	leave	VERB
ejpam-3049	262	54	ideal	ideal	PROPN
ejpam-3049	262	55	b	b	PROPN
ejpam-3049	262	56	of	of	ADP
ejpam-3049	262	57	h	h	NOUN
ejpam-3049	262	58	,	,	PUNCT
ejpam-3049	262	59	we	we	PRON
ejpam-3049	262	60	have	have	VERB
ejpam-3049	262	61	a	a	DET
ejpam-3049	262	62	∩	∩	ADJ
ejpam-3049	262	63	b	b	ADP
ejpam-3049	262	64	⊆	⊆	SYM
ejpam-3049	262	65	a	a	DET
ejpam-3049	262	66	∗	∗	X
ejpam-3049	262	67	b.	b.	NOUN
ejpam-3049	262	68	let	let	VERB
ejpam-3049	262	69	now	now	ADV
ejpam-3049	262	70	a	a	DET
ejpam-3049	262	71	be	be	AUX
ejpam-3049	262	72	an	an	DET
ejpam-3049	262	73	ideal	ideal	NOUN
ejpam-3049	262	74	and	and	CCONJ
ejpam-3049	262	75	b	b	DET
ejpam-3049	262	76	a	a	DET
ejpam-3049	262	77	left	left	ADJ
ejpam-3049	262	78	ideal	ideal	NOUN
ejpam-3049	262	79	of	of	ADP
ejpam-3049	262	80	h.	h.	PROPN
ejpam-3049	262	81	the	the	DET
ejpam-3049	262	82	set	set	NOUN
ejpam-3049	262	83	a∩b	a∩b	PROPN
ejpam-3049	262	84	is	be	AUX
ejpam-3049	262	85	a	a	DET
ejpam-3049	262	86	nonempty	nonempty	ADJ
ejpam-3049	262	87	subset	subset	NOUN
ejpam-3049	262	88	of	of	ADP
ejpam-3049	262	89	h	h	NOUN
ejpam-3049	262	90	and	and	CCONJ
ejpam-3049	262	91	h	h	PROPN
ejpam-3049	262	92	∗	∗	NOUN
ejpam-3049	262	93	(	(	PUNCT
ejpam-3049	262	94	a∩b	a∩b	PROPN
ejpam-3049	262	95	)	)	PUNCT
ejpam-3049	263	1	⊆	⊆	NUM
ejpam-3049	263	2	(	(	PUNCT
ejpam-3049	263	3	h	h	NOUN
ejpam-3049	263	4	∗a)∩	∗a)∩	PROPN
ejpam-3049	263	5	(	(	PUNCT
ejpam-3049	263	6	h	h	NOUN
ejpam-3049	263	7	∗b	∗b	PROPN
ejpam-3049	263	8	)	)	PUNCT
ejpam-3049	263	9	⊆	⊆	NUM
ejpam-3049	263	10	a∩b	a∩b	PROPN
ejpam-3049	263	11	,	,	PUNCT
ejpam-3049	263	12	so	so	ADV
ejpam-3049	263	13	the	the	DET
ejpam-3049	263	14	set	set	NOUN
ejpam-3049	263	15	a∩b	a∩b	PROPN
ejpam-3049	263	16	is	be	AUX
ejpam-3049	263	17	a	a	DET
ejpam-3049	263	18	left	left	ADJ
ejpam-3049	263	19	ideal	ideal	NOUN
ejpam-3049	263	20	of	of	ADP
ejpam-3049	263	21	h.	h.	PROPN
ejpam-3049	263	22	by	by	ADP
ejpam-3049	263	23	hypothesis	hypothesis	NOUN
ejpam-3049	263	24	,	,	PUNCT
ejpam-3049	263	25	we	we	PRON
ejpam-3049	263	26	have	have	VERB
ejpam-3049	263	27	a∩b	a∩b	NOUN
ejpam-3049	263	28	=	=	SYM
ejpam-3049	263	29	(	(	PUNCT
ejpam-3049	263	30	a∩b	a∩b	PROPN
ejpam-3049	263	31	)	)	PUNCT
ejpam-3049	263	32	∗	∗	NOUN
ejpam-3049	263	33	(	(	PUNCT
ejpam-3049	263	34	a∩b	a∩b	PROPN
ejpam-3049	263	35	)	)	PUNCT
ejpam-3049	264	1	⊆	⊆	NUM
ejpam-3049	264	2	a	a	DET
ejpam-3049	264	3	∗b	∗b	PROPN
ejpam-3049	264	4	.	.	PUNCT
ejpam-3049	265	1	�	�	PROPN
ejpam-3049	265	2	theorem	theorem	VERB
ejpam-3049	265	3	2.12	2.12	NUM
ejpam-3049	265	4	.	.	PUNCT
ejpam-3049	266	1	let	let	AUX
ejpam-3049	266	2	(	(	PUNCT
ejpam-3049	266	3	h	h	NOUN
ejpam-3049	266	4	,	,	PUNCT
ejpam-3049	266	5	◦	◦	NOUN
ejpam-3049	266	6	)	)	PUNCT
ejpam-3049	266	7	be	be	VERB
ejpam-3049	266	8	an	an	DET
ejpam-3049	266	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	266	10	.	.	PUNCT
ejpam-3049	267	1	the	the	DET
ejpam-3049	267	2	following	follow	VERB
ejpam-3049	267	3	are	be	AUX
ejpam-3049	267	4	equivalent	equivalent	ADJ
ejpam-3049	267	5	:	:	PUNCT
ejpam-3049	267	6	(	(	PUNCT
ejpam-3049	267	7	1	1	X
ejpam-3049	267	8	)	)	PUNCT
ejpam-3049	267	9	h	h	NOUN
ejpam-3049	267	10	is	be	AUX
ejpam-3049	267	11	left	leave	VERB
ejpam-3049	267	12	quasi	quasi	ADJ
ejpam-3049	267	13	-	-	ADJ
ejpam-3049	267	14	regular	regular	ADJ
ejpam-3049	267	15	.	.	PUNCT
ejpam-3049	268	1	(	(	PUNCT
ejpam-3049	268	2	2	2	X
ejpam-3049	268	3	)	)	PUNCT
ejpam-3049	268	4	f	f	NOUN
ejpam-3049	268	5	∧	∧	PROPN
ejpam-3049	268	6	g	g	PROPN
ejpam-3049	268	7	�	�	PROPN
ejpam-3049	268	8	f	f	PROPN
ejpam-3049	268	9	◦	◦	VERB
ejpam-3049	268	10	g	g	NOUN
ejpam-3049	268	11	for	for	ADP
ejpam-3049	268	12	every	every	DET
ejpam-3049	268	13	fuzzy	fuzzy	ADJ
ejpam-3049	268	14	ideal	ideal	NOUN
ejpam-3049	268	15	f	f	PROPN
ejpam-3049	268	16	and	and	CCONJ
ejpam-3049	268	17	every	every	DET
ejpam-3049	268	18	fuzzy	fuzzy	NOUN
ejpam-3049	268	19	subset	subset	VERB
ejpam-3049	268	20	g	g	PROPN
ejpam-3049	268	21	of	of	ADP
ejpam-3049	268	22	h.	h.	PROPN
ejpam-3049	268	23	(	(	PUNCT
ejpam-3049	268	24	3	3	NUM
ejpam-3049	268	25	)	)	PUNCT
ejpam-3049	268	26	f	f	NOUN
ejpam-3049	269	1	∧	∧	PROPN
ejpam-3049	269	2	g	g	PROPN
ejpam-3049	269	3	�	�	PROPN
ejpam-3049	269	4	f	f	PROPN
ejpam-3049	269	5	◦	◦	VERB
ejpam-3049	269	6	g	g	NOUN
ejpam-3049	269	7	for	for	ADP
ejpam-3049	269	8	every	every	DET
ejpam-3049	269	9	fuzzy	fuzzy	ADJ
ejpam-3049	269	10	ideal	ideal	NOUN
ejpam-3049	269	11	f	f	PROPN
ejpam-3049	269	12	and	and	CCONJ
ejpam-3049	269	13	every	every	DET
ejpam-3049	269	14	fuzzy	fuzzy	ADJ
ejpam-3049	269	15	bi	bi	ADJ
ejpam-3049	269	16	-	-	ADJ
ejpam-3049	269	17	ideal	ideal	ADJ
ejpam-3049	269	18	g	g	NOUN
ejpam-3049	269	19	of	of	ADP
ejpam-3049	269	20	h.	h.	PROPN
ejpam-3049	269	21	(	(	PUNCT
ejpam-3049	269	22	4	4	NUM
ejpam-3049	269	23	)	)	PUNCT
ejpam-3049	269	24	f	f	NOUN
ejpam-3049	270	1	∧	∧	PROPN
ejpam-3049	270	2	g	g	PROPN
ejpam-3049	270	3	�	�	PROPN
ejpam-3049	270	4	f	f	PROPN
ejpam-3049	270	5	◦	◦	VERB
ejpam-3049	270	6	g	g	NOUN
ejpam-3049	270	7	for	for	ADP
ejpam-3049	270	8	every	every	DET
ejpam-3049	270	9	fuzzy	fuzzy	ADJ
ejpam-3049	270	10	ideal	ideal	NOUN
ejpam-3049	270	11	f	f	PROPN
ejpam-3049	270	12	and	and	CCONJ
ejpam-3049	270	13	every	every	DET
ejpam-3049	270	14	fuzzy	fuzzy	ADJ
ejpam-3049	270	15	left	leave	VERB
ejpam-3049	270	16	ideal	ideal	NOUN
ejpam-3049	270	17	g	g	PROPN
ejpam-3049	270	18	of	of	ADP
ejpam-3049	270	19	h.	h.	PROPN
ejpam-3049	270	20	proof	proof	NOUN
ejpam-3049	270	21	.	.	PUNCT
ejpam-3049	271	1	(	(	PUNCT
ejpam-3049	271	2	1	1	X
ejpam-3049	271	3	)	)	PUNCT
ejpam-3049	271	4	=	=	NOUN
ejpam-3049	271	5	⇒	⇒	NOUN
ejpam-3049	271	6	(	(	PUNCT
ejpam-3049	271	7	2	2	NUM
ejpam-3049	271	8	)	)	PUNCT
ejpam-3049	271	9	.	.	PUNCT
ejpam-3049	272	1	let	let	VERB
ejpam-3049	272	2	f	f	PRON
ejpam-3049	272	3	be	be	AUX
ejpam-3049	272	4	a	a	DET
ejpam-3049	272	5	fuzzy	fuzzy	ADJ
ejpam-3049	272	6	ideal	ideal	NOUN
ejpam-3049	272	7	,	,	PUNCT
ejpam-3049	272	8	g	g	PROPN
ejpam-3049	272	9	a	a	DET
ejpam-3049	272	10	fuzzy	fuzzy	ADJ
ejpam-3049	272	11	subset	subset	NOUN
ejpam-3049	272	12	of	of	ADP
ejpam-3049	272	13	h	h	NOUN
ejpam-3049	272	14	and	and	CCONJ
ejpam-3049	272	15	a	a	DET
ejpam-3049	272	16	∈	∈	PROPN
ejpam-3049	272	17	h.	h.	NOUN
ejpam-3049	272	18	since	since	SCONJ
ejpam-3049	272	19	h	h	PROPN
ejpam-3049	272	20	is	be	AUX
ejpam-3049	272	21	left	leave	VERB
ejpam-3049	272	22	quasi	quasi	ADJ
ejpam-3049	272	23	-	-	ADJ
ejpam-3049	272	24	regular	regular	ADJ
ejpam-3049	272	25	,	,	PUNCT
ejpam-3049	272	26	there	there	PRON
ejpam-3049	272	27	exist	exist	VERB
ejpam-3049	272	28	x	x	NOUN
ejpam-3049	272	29	,	,	PUNCT
ejpam-3049	272	30	y	y	PROPN
ejpam-3049	272	31	∈	∈	PROPN
ejpam-3049	272	32	h	h	NOUN
ejpam-3049	272	33	such	such	ADJ
ejpam-3049	272	34	that	that	SCONJ
ejpam-3049	272	35	a	a	DET
ejpam-3049	272	36	∈	∈	NOUN
ejpam-3049	272	37	(	(	PUNCT
ejpam-3049	272	38	(	(	PUNCT
ejpam-3049	272	39	x	x	SYM
ejpam-3049	272	40	◦	◦	VERB
ejpam-3049	272	41	a	a	X
ejpam-3049	272	42	)	)	PUNCT
ejpam-3049	272	43	∗	∗	NOUN
ejpam-3049	272	44	{	{	PUNCT
ejpam-3049	272	45	y	y	NOUN
ejpam-3049	272	46	}	}	PUNCT
ejpam-3049	272	47	)	)	PUNCT
ejpam-3049	272	48	∗	∗	NOUN
ejpam-3049	272	49	{	{	PUNCT
ejpam-3049	272	50	a	a	NOUN
ejpam-3049	272	51	}	}	PUNCT
ejpam-3049	272	52	.	.	PUNCT
ejpam-3049	273	1	then	then	ADV
ejpam-3049	273	2	a	a	DET
ejpam-3049	273	3	∈	∈	PROPN
ejpam-3049	273	4	u	u	NOUN
ejpam-3049	273	5	◦	◦	NOUN
ejpam-3049	273	6	a	a	PRON
ejpam-3049	273	7	for	for	ADP
ejpam-3049	273	8	some	some	DET
ejpam-3049	273	9	u	u	NOUN
ejpam-3049	273	10	∈	∈	PROPN
ejpam-3049	273	11	(	(	PUNCT
ejpam-3049	273	12	x	x	SYM
ejpam-3049	273	13	◦	◦	VERB
ejpam-3049	273	14	a	a	X
ejpam-3049	273	15	)	)	PUNCT
ejpam-3049	273	16	∗	∗	NOUN
ejpam-3049	273	17	{	{	PUNCT
ejpam-3049	273	18	y	y	NOUN
ejpam-3049	273	19	}	}	PUNCT
ejpam-3049	273	20	.	.	PUNCT
ejpam-3049	274	1	in	in	ADP
ejpam-3049	274	2	addition	addition	NOUN
ejpam-3049	274	3	,	,	PUNCT
ejpam-3049	274	4	u	u	PROPN
ejpam-3049	274	5	∈	∈	PROPN
ejpam-3049	274	6	v	v	ADP
ejpam-3049	274	7	◦	◦	NOUN
ejpam-3049	274	8	y	y	NOUN
ejpam-3049	274	9	for	for	ADP
ejpam-3049	274	10	some	some	DET
ejpam-3049	274	11	v	v	NOUN
ejpam-3049	274	12	∈	∈	NOUN
ejpam-3049	274	13	x	x	PUNCT
ejpam-3049	274	14	◦	◦	NOUN
ejpam-3049	274	15	a.	a.	NOUN
ejpam-3049	274	16	on	on	ADP
ejpam-3049	274	17	the	the	DET
ejpam-3049	274	18	other	other	ADJ
ejpam-3049	274	19	hand	hand	NOUN
ejpam-3049	274	20	,	,	PUNCT
ejpam-3049	274	21	since	since	SCONJ
ejpam-3049	274	22	(	(	PUNCT
ejpam-3049	274	23	u	u	NOUN
ejpam-3049	274	24	,	,	PUNCT
ejpam-3049	274	25	a	a	PRON
ejpam-3049	274	26	)	)	PUNCT
ejpam-3049	274	27	∈	∈	NOUN
ejpam-3049	274	28	aa	aa	NOUN
ejpam-3049	274	29	,	,	PUNCT
ejpam-3049	274	30	we	we	PRON
ejpam-3049	274	31	have	have	VERB
ejpam-3049	274	32	(	(	PUNCT
ejpam-3049	274	33	f	f	X
ejpam-3049	274	34	◦	◦	NOUN
ejpam-3049	274	35	g)(a	g)(a	PROPN
ejpam-3049	274	36	)	)	PUNCT
ejpam-3049	274	37	:	:	PUNCT
ejpam-3049	275	1	=	=	SYM
ejpam-3049	275	2	∨	∨	X
ejpam-3049	275	3	(	(	PUNCT
ejpam-3049	275	4	h	h	NOUN
ejpam-3049	275	5	,	,	PUNCT
ejpam-3049	275	6	k)∈aa	k)∈aa	PROPN
ejpam-3049	275	7	min{f(h	min{f(h	PROPN
ejpam-3049	275	8	)	)	PUNCT
ejpam-3049	275	9	,	,	PUNCT
ejpam-3049	275	10	g(k	g(k	NOUN
ejpam-3049	275	11	)	)	PUNCT
ejpam-3049	275	12	}	}	PUNCT
ejpam-3049	275	13	≥	≥	NOUN
ejpam-3049	275	14	min{f(u	min{f(u	PROPN
ejpam-3049	275	15	)	)	PUNCT
ejpam-3049	275	16	,	,	PUNCT
ejpam-3049	275	17	g(a	g(a	PROPN
ejpam-3049	275	18	)	)	PUNCT
ejpam-3049	275	19	}	}	PUNCT
ejpam-3049	275	20	.	.	PUNCT
ejpam-3049	276	1	n.	n.	PROPN
ejpam-3049	276	2	kehayopulu	kehayopulu	PROPN
ejpam-3049	276	3	/	/	SYM
ejpam-3049	276	4	eur	eur	PROPN
ejpam-3049	276	5	.	.	PUNCT
ejpam-3049	277	1	j.	j.	PROPN
ejpam-3049	277	2	pure	pure	PROPN
ejpam-3049	277	3	appl	appl	PROPN
ejpam-3049	277	4	.	.	PROPN
ejpam-3049	277	5	math	math	PROPN
ejpam-3049	277	6	,	,	PUNCT
ejpam-3049	277	7	10	10	NUM
ejpam-3049	277	8	(	(	PUNCT
ejpam-3049	277	9	5	5	NUM
ejpam-3049	277	10	)	)	PUNCT
ejpam-3049	277	11	(	(	PUNCT
ejpam-3049	277	12	2017	2017	NUM
ejpam-3049	277	13	)	)	PUNCT
ejpam-3049	277	14	,	,	PUNCT
ejpam-3049	277	15	929	929	NUM
ejpam-3049	277	16	-	-	SYM
ejpam-3049	277	17	945	945	NUM
ejpam-3049	277	18	939	939	NUM
ejpam-3049	277	19	since	since	SCONJ
ejpam-3049	277	20	f	f	PROPN
ejpam-3049	277	21	is	be	AUX
ejpam-3049	277	22	a	a	DET
ejpam-3049	277	23	fuzzy	fuzzy	ADJ
ejpam-3049	277	24	right	right	ADJ
ejpam-3049	277	25	ideal	ideal	NOUN
ejpam-3049	277	26	of	of	ADP
ejpam-3049	277	27	h	h	NOUN
ejpam-3049	277	28	,	,	PUNCT
ejpam-3049	277	29	we	we	PRON
ejpam-3049	277	30	have	have	AUX
ejpam-3049	277	31	f(v	f(v	NOUN
ejpam-3049	277	32	◦	◦	VERB
ejpam-3049	277	33	y	y	NOUN
ejpam-3049	277	34	)	)	PUNCT
ejpam-3049	277	35	≥	≥	NOUN
ejpam-3049	277	36	f(v	f(v	NOUN
ejpam-3049	277	37	)	)	PUNCT
ejpam-3049	277	38	and	and	CCONJ
ejpam-3049	277	39	since	since	SCONJ
ejpam-3049	277	40	u	u	PROPN
ejpam-3049	277	41	∈	∈	PROPN
ejpam-3049	277	42	v	v	ADP
ejpam-3049	277	43	◦	◦	NOUN
ejpam-3049	277	44	y	y	NOUN
ejpam-3049	277	45	,	,	PUNCT
ejpam-3049	277	46	we	we	PRON
ejpam-3049	277	47	have	have	VERB
ejpam-3049	277	48	f(u	f(u	PROPN
ejpam-3049	277	49	)	)	PUNCT
ejpam-3049	277	50	≥	≥	NOUN
ejpam-3049	277	51	f(v	f(v	NOUN
ejpam-3049	277	52	)	)	PUNCT
ejpam-3049	277	53	.	.	PUNCT
ejpam-3049	278	1	since	since	SCONJ
ejpam-3049	278	2	f	f	PROPN
ejpam-3049	278	3	is	be	AUX
ejpam-3049	278	4	a	a	DET
ejpam-3049	278	5	fuzzy	fuzzy	ADJ
ejpam-3049	278	6	left	leave	VERB
ejpam-3049	278	7	ideal	ideal	NOUN
ejpam-3049	278	8	of	of	ADP
ejpam-3049	278	9	h	h	NOUN
ejpam-3049	278	10	,	,	PUNCT
ejpam-3049	278	11	we	we	PRON
ejpam-3049	278	12	have	have	VERB
ejpam-3049	278	13	f(x	f(x	PROPN
ejpam-3049	278	14	◦	◦	NOUN
ejpam-3049	278	15	a	a	DET
ejpam-3049	278	16	)	)	PUNCT
ejpam-3049	278	17	≥	≥	NOUN
ejpam-3049	278	18	f(a	f(a	NOUN
ejpam-3049	278	19	)	)	PUNCT
ejpam-3049	278	20	and	and	CCONJ
ejpam-3049	278	21	since	since	SCONJ
ejpam-3049	278	22	v	v	NUM
ejpam-3049	278	23	∈	∈	NOUN
ejpam-3049	278	24	x	x	NOUN
ejpam-3049	278	25	◦	◦	NOUN
ejpam-3049	278	26	a	a	X
ejpam-3049	278	27	,	,	PUNCT
ejpam-3049	278	28	we	we	PRON
ejpam-3049	278	29	have	have	VERB
ejpam-3049	278	30	f(v	f(v	NOUN
ejpam-3049	278	31	)	)	PUNCT
ejpam-3049	278	32	≥	≥	NOUN
ejpam-3049	278	33	f(a	f(a	NOUN
ejpam-3049	278	34	)	)	PUNCT
ejpam-3049	278	35	.	.	PUNCT
ejpam-3049	279	1	thus	thus	ADV
ejpam-3049	279	2	we	we	PRON
ejpam-3049	279	3	have	have	VERB
ejpam-3049	279	4	f(u	f(u	PROPN
ejpam-3049	279	5	)	)	PUNCT
ejpam-3049	279	6	≥	≥	NOUN
ejpam-3049	279	7	f(a	f(a	NOUN
ejpam-3049	279	8	)	)	PUNCT
ejpam-3049	279	9	,	,	PUNCT
ejpam-3049	279	10	and	and	CCONJ
ejpam-3049	279	11	(	(	PUNCT
ejpam-3049	279	12	f	f	X
ejpam-3049	279	13	◦	◦	PROPN
ejpam-3049	279	14	g)(a	g)(a	PROPN
ejpam-3049	279	15	)	)	PUNCT
ejpam-3049	279	16	≥	≥	NOUN
ejpam-3049	279	17	min{f(a	min{f(a	PROPN
ejpam-3049	279	18	)	)	PUNCT
ejpam-3049	279	19	,	,	PUNCT
ejpam-3049	279	20	g(a	g(a	PROPN
ejpam-3049	279	21	)	)	PUNCT
ejpam-3049	279	22	}	}	PUNCT
ejpam-3049	279	23	=	=	SYM
ejpam-3049	280	1	(	(	PUNCT
ejpam-3049	280	2	f	f	PROPN
ejpam-3049	280	3	∧	∧	PROPN
ejpam-3049	280	4	g)(a	g)(a	PROPN
ejpam-3049	280	5	)	)	PUNCT
ejpam-3049	280	6	,	,	PUNCT
ejpam-3049	280	7	so	so	SCONJ
ejpam-3049	280	8	f	f	PROPN
ejpam-3049	280	9	∧	∧	PROPN
ejpam-3049	280	10	g	g	PROPN
ejpam-3049	280	11	�	�	PROPN
ejpam-3049	280	12	f	f	PROPN
ejpam-3049	281	1	◦	◦	NOUN
ejpam-3049	281	2	g.	g.	PROPN
ejpam-3049	281	3	the	the	DET
ejpam-3049	281	4	implication	implication	NOUN
ejpam-3049	281	5	(	(	PUNCT
ejpam-3049	281	6	2	2	X
ejpam-3049	281	7	)	)	PUNCT
ejpam-3049	281	8	⇒	⇒	NOUN
ejpam-3049	281	9	(	(	PUNCT
ejpam-3049	281	10	3	3	X
ejpam-3049	281	11	)	)	PUNCT
ejpam-3049	281	12	is	be	AUX
ejpam-3049	281	13	obvious	obvious	ADJ
ejpam-3049	281	14	and	and	CCONJ
ejpam-3049	281	15	(	(	PUNCT
ejpam-3049	281	16	3	3	X
ejpam-3049	281	17	)	)	PUNCT
ejpam-3049	281	18	⇒	⇒	NOUN
ejpam-3049	281	19	(	(	PUNCT
ejpam-3049	281	20	4	4	NUM
ejpam-3049	281	21	)	)	PUNCT
ejpam-3049	281	22	since	since	SCONJ
ejpam-3049	281	23	every	every	DET
ejpam-3049	281	24	fuzzy	fuzzy	ADJ
ejpam-3049	281	25	left	leave	VERB
ejpam-3049	281	26	ideal	ideal	NOUN
ejpam-3049	281	27	is	be	AUX
ejpam-3049	281	28	a	a	DET
ejpam-3049	281	29	fuzzy	fuzzy	ADJ
ejpam-3049	281	30	bi	bi	NOUN
ejpam-3049	281	31	-	-	NOUN
ejpam-3049	281	32	ideal	ideal	NOUN
ejpam-3049	281	33	of	of	ADP
ejpam-3049	281	34	h.	h.	PROPN
ejpam-3049	281	35	(	(	PUNCT
ejpam-3049	281	36	4	4	NUM
ejpam-3049	281	37	)	)	PUNCT
ejpam-3049	282	1	=	=	NOUN
ejpam-3049	282	2	⇒	⇒	NOUN
ejpam-3049	282	3	(	(	PUNCT
ejpam-3049	282	4	1	1	NUM
ejpam-3049	282	5	)	)	PUNCT
ejpam-3049	282	6	.	.	PUNCT
ejpam-3049	283	1	by	by	ADP
ejpam-3049	283	2	theorem	theorem	NOUN
ejpam-3049	283	3	2.9	2.9	NUM
ejpam-3049	283	4	,	,	PUNCT
ejpam-3049	283	5	it	it	PRON
ejpam-3049	283	6	is	be	AUX
ejpam-3049	283	7	enough	enough	ADJ
ejpam-3049	283	8	to	to	PART
ejpam-3049	283	9	prove	prove	VERB
ejpam-3049	283	10	that	that	SCONJ
ejpam-3049	283	11	i(a	i(a	PROPN
ejpam-3049	283	12	)	)	PUNCT
ejpam-3049	283	13	∩	∩	NOUN
ejpam-3049	283	14	l(a	l(a	PROPN
ejpam-3049	283	15	)	)	PUNCT
ejpam-3049	283	16	⊆	⊆	NUM
ejpam-3049	283	17	i(a	i(a	PROPN
ejpam-3049	283	18	)	)	PUNCT
ejpam-3049	283	19	∗	∗	NOUN
ejpam-3049	283	20	l(a	l(a	PROPN
ejpam-3049	283	21	)	)	PUNCT
ejpam-3049	283	22	for	for	SCONJ
ejpam-3049	283	23	every	every	DET
ejpam-3049	283	24	a	a	DET
ejpam-3049	283	25	∈	∈	PROPN
ejpam-3049	283	26	h.	h.	NOUN
ejpam-3049	283	27	let	let	VERB
ejpam-3049	283	28	now	now	ADV
ejpam-3049	283	29	a	a	DET
ejpam-3049	283	30	∈	∈	ADJ
ejpam-3049	283	31	h	h	NOUN
ejpam-3049	283	32	and	and	CCONJ
ejpam-3049	283	33	b	b	PROPN
ejpam-3049	283	34	∈	∈	PROPN
ejpam-3049	283	35	i(a	i(a	PROPN
ejpam-3049	283	36	)	)	PUNCT
ejpam-3049	283	37	∩	∩	NOUN
ejpam-3049	283	38	l(a	l(a	PROPN
ejpam-3049	283	39	)	)	PUNCT
ejpam-3049	283	40	.	.	PUNCT
ejpam-3049	284	1	since	since	SCONJ
ejpam-3049	284	2	i(a	i(a	PROPN
ejpam-3049	284	3	)	)	PUNCT
ejpam-3049	284	4	is	be	AUX
ejpam-3049	284	5	an	an	DET
ejpam-3049	284	6	ideal	ideal	NOUN
ejpam-3049	284	7	of	of	ADP
ejpam-3049	284	8	h	h	NOUN
ejpam-3049	284	9	,	,	PUNCT
ejpam-3049	284	10	the	the	DET
ejpam-3049	284	11	characteristic	characteristic	ADJ
ejpam-3049	284	12	function	function	NOUN
ejpam-3049	284	13	fi(a	fi(a	PROPN
ejpam-3049	284	14	)	)	PUNCT
ejpam-3049	284	15	is	be	AUX
ejpam-3049	284	16	a	a	DET
ejpam-3049	284	17	fuzzy	fuzzy	ADJ
ejpam-3049	284	18	ideal	ideal	NOUN
ejpam-3049	284	19	of	of	ADP
ejpam-3049	284	20	h	h	NOUN
ejpam-3049	284	21	and	and	CCONJ
ejpam-3049	284	22	since	since	SCONJ
ejpam-3049	284	23	l(a	l(a	PROPN
ejpam-3049	284	24	)	)	PUNCT
ejpam-3049	284	25	is	be	AUX
ejpam-3049	284	26	a	a	DET
ejpam-3049	284	27	left	left	ADJ
ejpam-3049	284	28	ideal	ideal	NOUN
ejpam-3049	284	29	of	of	ADP
ejpam-3049	284	30	h	h	NOUN
ejpam-3049	284	31	,	,	PUNCT
ejpam-3049	284	32	fl(a	fl(a	NUM
ejpam-3049	284	33	)	)	PUNCT
ejpam-3049	284	34	is	be	AUX
ejpam-3049	284	35	a	a	DET
ejpam-3049	284	36	fuzzy	fuzzy	ADJ
ejpam-3049	284	37	left	leave	VERB
ejpam-3049	284	38	ideal	ideal	NOUN
ejpam-3049	284	39	of	of	ADP
ejpam-3049	284	40	h.	h.	PROPN
ejpam-3049	284	41	by	by	ADP
ejpam-3049	284	42	hypothesis	hypothesis	NOUN
ejpam-3049	284	43	,	,	PUNCT
ejpam-3049	284	44	we	we	PRON
ejpam-3049	284	45	have	have	VERB
ejpam-3049	284	46	fi(a	fi(a	NOUN
ejpam-3049	284	47	)	)	PUNCT
ejpam-3049	284	48	∧	∧	NOUN
ejpam-3049	284	49	fl(a	fl(a	NOUN
ejpam-3049	284	50	)	)	PUNCT
ejpam-3049	284	51	�	�	PROPN
ejpam-3049	284	52	fi(a	fi(a	PROPN
ejpam-3049	284	53	)	)	PUNCT
ejpam-3049	284	54	◦	◦	NOUN
ejpam-3049	284	55	fl(a	fl(a	NUM
ejpam-3049	284	56	)	)	PUNCT
ejpam-3049	284	57	,	,	PUNCT
ejpam-3049	284	58	and	and	CCONJ
ejpam-3049	284	59	so	so	ADV
ejpam-3049	284	60	(	(	PUNCT
ejpam-3049	284	61	fi(a	fi(a	X
ejpam-3049	284	62	)	)	PUNCT
ejpam-3049	284	63	∧	∧	NOUN
ejpam-3049	284	64	fl(a	fl(a	X
ejpam-3049	284	65	)	)	PUNCT
ejpam-3049	284	66	)	)	PUNCT
ejpam-3049	285	1	(	(	PUNCT
ejpam-3049	285	2	b	b	X
ejpam-3049	285	3	)	)	PUNCT
ejpam-3049	285	4	≤	≤	NOUN
ejpam-3049	285	5	(	(	PUNCT
ejpam-3049	285	6	fi(a	fi(a	X
ejpam-3049	285	7	)	)	PUNCT
ejpam-3049	285	8	◦	◦	NOUN
ejpam-3049	285	9	fl(a	fl(a	NUM
ejpam-3049	285	10	)	)	PUNCT
ejpam-3049	285	11	)	)	PUNCT
ejpam-3049	286	1	(	(	PUNCT
ejpam-3049	286	2	b	b	X
ejpam-3049	286	3	)	)	PUNCT
ejpam-3049	286	4	,	,	PUNCT
ejpam-3049	286	5	that	that	PRON
ejpam-3049	286	6	is	be	AUX
ejpam-3049	286	7	min{fi(a)(b	min{fi(a)(b	ADJ
ejpam-3049	286	8	)	)	PUNCT
ejpam-3049	286	9	,	,	PUNCT
ejpam-3049	286	10	fl(a)(b	fl(a)(b	NOUN
ejpam-3049	286	11	)	)	PUNCT
ejpam-3049	286	12	}	}	PUNCT
ejpam-3049	286	13	≤	≤	NUM
ejpam-3049	286	14	(	(	PUNCT
ejpam-3049	286	15	fi(a	fi(a	X
ejpam-3049	286	16	)	)	PUNCT
ejpam-3049	286	17	◦	◦	NOUN
ejpam-3049	286	18	fl(a	fl(a	NUM
ejpam-3049	286	19	)	)	PUNCT
ejpam-3049	286	20	)	)	PUNCT
ejpam-3049	287	1	(	(	PUNCT
ejpam-3049	287	2	b	b	NOUN
ejpam-3049	287	3	)	)	PUNCT
ejpam-3049	287	4	.	.	PUNCT
ejpam-3049	288	1	since	since	SCONJ
ejpam-3049	288	2	b	b	PROPN
ejpam-3049	288	3	∈	∈	PROPN
ejpam-3049	288	4	i(a	i(a	PROPN
ejpam-3049	288	5	)	)	PUNCT
ejpam-3049	288	6	,	,	PUNCT
ejpam-3049	288	7	we	we	PRON
ejpam-3049	288	8	have	have	VERB
ejpam-3049	288	9	fi(b)(b	fi(b)(b	VERB
ejpam-3049	288	10	)	)	PUNCT
ejpam-3049	288	11	=	=	SYM
ejpam-3049	288	12	1	1	NUM
ejpam-3049	288	13	and	and	CCONJ
ejpam-3049	288	14	since	since	SCONJ
ejpam-3049	288	15	b	b	PROPN
ejpam-3049	288	16	∈	∈	PROPN
ejpam-3049	288	17	l(a	l(a	PROPN
ejpam-3049	288	18	)	)	PUNCT
ejpam-3049	288	19	,	,	PUNCT
ejpam-3049	288	20	we	we	PRON
ejpam-3049	288	21	have	have	VERB
ejpam-3049	288	22	fl(b)(b	fl(b)(b	NUM
ejpam-3049	288	23	)	)	PUNCT
ejpam-3049	289	1	=	=	SYM
ejpam-3049	289	2	1	1	NUM
ejpam-3049	289	3	,	,	PUNCT
ejpam-3049	289	4	so	so	ADV
ejpam-3049	289	5	min{fi(a)(b	min{fi(a)(b	ADJ
ejpam-3049	289	6	)	)	PUNCT
ejpam-3049	289	7	,	,	PUNCT
ejpam-3049	289	8	fl(a)(b	fl(a)(b	NOUN
ejpam-3049	289	9	)	)	PUNCT
ejpam-3049	289	10	}	}	PUNCT
ejpam-3049	289	11	=	=	SYM
ejpam-3049	289	12	1	1	NUM
ejpam-3049	289	13	,	,	PUNCT
ejpam-3049	289	14	and	and	CCONJ
ejpam-3049	289	15	so	so	ADV
ejpam-3049	289	16	1	1	NUM
ejpam-3049	289	17	≤	≤	NUM
ejpam-3049	289	18	(	(	PUNCT
ejpam-3049	289	19	fi(a)	fi(a)	PROPN
ejpam-3049	289	20	◦	◦	NOUN
ejpam-3049	289	21	fl(a	fl(a	NUM
ejpam-3049	289	22	)	)	PUNCT
ejpam-3049	289	23	)	)	PUNCT
ejpam-3049	290	1	(	(	PUNCT
ejpam-3049	290	2	b	b	NOUN
ejpam-3049	290	3	)	)	PUNCT
ejpam-3049	290	4	.	.	PUNCT
ejpam-3049	291	1	if	if	SCONJ
ejpam-3049	291	2	ab	ab	PROPN
ejpam-3049	291	3	=	=	NOUN
ejpam-3049	291	4	∅	∅	NOUN
ejpam-3049	291	5	,	,	PUNCT
ejpam-3049	291	6	then	then	ADV
ejpam-3049	291	7	(	(	PUNCT
ejpam-3049	291	8	fi(a)	fi(a)	PROPN
ejpam-3049	291	9	◦	◦	NOUN
ejpam-3049	291	10	fl(a	fl(a	NUM
ejpam-3049	291	11	)	)	PUNCT
ejpam-3049	291	12	)	)	PUNCT
ejpam-3049	292	1	(	(	PUNCT
ejpam-3049	292	2	b	b	X
ejpam-3049	292	3	)	)	PUNCT
ejpam-3049	292	4	=	=	SYM
ejpam-3049	292	5	0	0	NUM
ejpam-3049	292	6	which	which	PRON
ejpam-3049	292	7	is	be	AUX
ejpam-3049	292	8	impossible	impossible	ADJ
ejpam-3049	292	9	.	.	PUNCT
ejpam-3049	293	1	thus	thus	ADV
ejpam-3049	293	2	we	we	PRON
ejpam-3049	293	3	have	have	VERB
ejpam-3049	293	4	ab	ab	PROPN
ejpam-3049	293	5	6=	6=	ADP
ejpam-3049	293	6	∅.	∅.	ADP
ejpam-3049	293	7	then	then	ADV
ejpam-3049	293	8	(	(	PUNCT
ejpam-3049	293	9	fi(a	fi(a	X
ejpam-3049	293	10	)	)	PUNCT
ejpam-3049	293	11	◦	◦	NOUN
ejpam-3049	293	12	fl(a	fl(a	NUM
ejpam-3049	293	13	)	)	PUNCT
ejpam-3049	293	14	)	)	PUNCT
ejpam-3049	294	1	(	(	PUNCT
ejpam-3049	294	2	b	b	X
ejpam-3049	294	3	)	)	PUNCT
ejpam-3049	294	4	=	=	SYM
ejpam-3049	294	5	∨	∨	X
ejpam-3049	294	6	(	(	PUNCT
ejpam-3049	294	7	y	y	PROPN
ejpam-3049	294	8	,	,	PUNCT
ejpam-3049	294	9	z)∈ab	z)∈ab	PROPN
ejpam-3049	294	10	min{fi(a)(y	min{fi(a)(y	PROPN
ejpam-3049	294	11	)	)	PUNCT
ejpam-3049	294	12	,	,	PUNCT
ejpam-3049	294	13	fl(a)(z	fl(a)(z	PROPN
ejpam-3049	294	14	)	)	PUNCT
ejpam-3049	294	15	}	}	PUNCT
ejpam-3049	294	16	.	.	PUNCT
ejpam-3049	295	1	then	then	ADV
ejpam-3049	295	2	there	there	PRON
ejpam-3049	295	3	exists	exist	VERB
ejpam-3049	295	4	(	(	PUNCT
ejpam-3049	295	5	y	y	NOUN
ejpam-3049	295	6	,	,	PUNCT
ejpam-3049	295	7	z	z	NOUN
ejpam-3049	295	8	)	)	PUNCT
ejpam-3049	295	9	∈	∈	PROPN
ejpam-3049	295	10	ab	ab	PROPN
ejpam-3049	295	11	such	such	ADJ
ejpam-3049	295	12	that	that	SCONJ
ejpam-3049	295	13	y	y	PROPN
ejpam-3049	295	14	∈	∈	PROPN
ejpam-3049	295	15	i(a	i(a	PROPN
ejpam-3049	295	16	)	)	PUNCT
ejpam-3049	295	17	and	and	CCONJ
ejpam-3049	295	18	z	z	PROPN
ejpam-3049	295	19	∈	∈	PROPN
ejpam-3049	295	20	l(a	l(a	PROPN
ejpam-3049	295	21	)	)	PUNCT
ejpam-3049	295	22	(	(	PUNCT
ejpam-3049	295	23	∗	∗	NOUN
ejpam-3049	295	24	)	)	PUNCT
ejpam-3049	295	25	indeed	indeed	ADV
ejpam-3049	295	26	:	:	PUNCT
ejpam-3049	295	27	suppose	suppose	VERB
ejpam-3049	295	28	there	there	PRON
ejpam-3049	295	29	is	be	VERB
ejpam-3049	295	30	no	no	DET
ejpam-3049	295	31	(	(	PUNCT
ejpam-3049	295	32	y	y	NOUN
ejpam-3049	295	33	,	,	PUNCT
ejpam-3049	295	34	z	z	NOUN
ejpam-3049	295	35	)	)	PUNCT
ejpam-3049	295	36	∈	∈	PROPN
ejpam-3049	295	37	ab	ab	PROPN
ejpam-3049	295	38	such	such	ADJ
ejpam-3049	295	39	that	that	AUX
ejpam-3049	295	40	y	y	PROPN
ejpam-3049	295	41	∈	∈	PROPN
ejpam-3049	295	42	i(a	i(a	PROPN
ejpam-3049	295	43	)	)	PUNCT
ejpam-3049	295	44	and	and	CCONJ
ejpam-3049	295	45	z	z	PROPN
ejpam-3049	295	46	∈	∈	PROPN
ejpam-3049	295	47	l(a	l(a	PROPN
ejpam-3049	295	48	)	)	PUNCT
ejpam-3049	295	49	.	.	PUNCT
ejpam-3049	296	1	then	then	ADV
ejpam-3049	296	2	,	,	PUNCT
ejpam-3049	296	3	for	for	ADP
ejpam-3049	296	4	every	every	DET
ejpam-3049	296	5	(	(	PUNCT
ejpam-3049	296	6	y	y	PROPN
ejpam-3049	296	7	,	,	PUNCT
ejpam-3049	296	8	z	z	NOUN
ejpam-3049	296	9	)	)	PUNCT
ejpam-3049	296	10	∈	∈	PROPN
ejpam-3049	296	11	ab	ab	NOUN
ejpam-3049	296	12	we	we	PRON
ejpam-3049	296	13	have	have	VERB
ejpam-3049	296	14	y	y	PROPN
ejpam-3049	296	15	/∈	/∈	PUNCT
ejpam-3049	296	16	i(a	i(a	PROPN
ejpam-3049	296	17	)	)	PUNCT
ejpam-3049	296	18	or	or	CCONJ
ejpam-3049	296	19	z	z	NOUN
ejpam-3049	296	20	/∈	/∈	PUNCT
ejpam-3049	297	1	l(a	l(a	PROPN
ejpam-3049	297	2	)	)	PUNCT
ejpam-3049	297	3	.	.	PUNCT
ejpam-3049	298	1	then	then	ADV
ejpam-3049	298	2	,	,	PUNCT
ejpam-3049	298	3	for	for	ADP
ejpam-3049	298	4	each	each	DET
ejpam-3049	298	5	(	(	PUNCT
ejpam-3049	298	6	y	y	PROPN
ejpam-3049	298	7	,	,	PUNCT
ejpam-3049	298	8	z	z	NOUN
ejpam-3049	298	9	)	)	PUNCT
ejpam-3049	298	10	∈	∈	PROPN
ejpam-3049	298	11	ab	ab	NOUN
ejpam-3049	298	12	we	we	PRON
ejpam-3049	298	13	have	have	VERB
ejpam-3049	298	14	fi(a)(y	fi(a)(y	PUNCT
ejpam-3049	298	15	)	)	PUNCT
ejpam-3049	299	1	=	=	SYM
ejpam-3049	299	2	0	0	NUM
ejpam-3049	299	3	or	or	CCONJ
ejpam-3049	299	4	fl(a)(z	fl(a)(z	PROPN
ejpam-3049	299	5	)	)	PUNCT
ejpam-3049	300	1	=	=	SYM
ejpam-3049	300	2	0	0	NUM
ejpam-3049	300	3	,	,	PUNCT
ejpam-3049	300	4	so	so	ADV
ejpam-3049	300	5	for	for	ADP
ejpam-3049	300	6	each	each	DET
ejpam-3049	300	7	(	(	PUNCT
ejpam-3049	300	8	y	y	PROPN
ejpam-3049	300	9	,	,	PUNCT
ejpam-3049	300	10	z	z	NOUN
ejpam-3049	300	11	)	)	PUNCT
ejpam-3049	300	12	∈	∈	PROPN
ejpam-3049	300	13	ab	ab	PROPN
ejpam-3049	300	14	,	,	PUNCT
ejpam-3049	300	15	we	we	PRON
ejpam-3049	300	16	have	have	VERB
ejpam-3049	300	17	min{fi(a)(y	min{fi(a)(y	NOUN
ejpam-3049	300	18	)	)	PUNCT
ejpam-3049	300	19	,	,	PUNCT
ejpam-3049	300	20	fl(a)(z	fl(a)(z	PROPN
ejpam-3049	300	21	)	)	PUNCT
ejpam-3049	300	22	}	}	PUNCT
ejpam-3049	301	1	=	=	SYM
ejpam-3049	301	2	0	0	NUM
ejpam-3049	301	3	,	,	PUNCT
ejpam-3049	301	4	then	then	ADV
ejpam-3049	301	5	(	(	PUNCT
ejpam-3049	301	6	fi(a	fi(a	X
ejpam-3049	301	7	)	)	PUNCT
ejpam-3049	301	8	◦	◦	NOUN
ejpam-3049	301	9	fl(a	fl(a	NUM
ejpam-3049	301	10	)	)	PUNCT
ejpam-3049	301	11	)	)	PUNCT
ejpam-3049	302	1	(	(	PUNCT
ejpam-3049	302	2	b	b	X
ejpam-3049	302	3	)	)	PUNCT
ejpam-3049	302	4	=	=	SYM
ejpam-3049	302	5	0	0	NUM
ejpam-3049	302	6	which	which	PRON
ejpam-3049	302	7	is	be	AUX
ejpam-3049	302	8	no	no	DET
ejpam-3049	302	9	possible	possible	ADJ
ejpam-3049	302	10	.	.	PUNCT
ejpam-3049	303	1	by	by	ADP
ejpam-3049	303	2	(	(	PUNCT
ejpam-3049	303	3	∗	∗	NOUN
ejpam-3049	303	4	)	)	PUNCT
ejpam-3049	303	5	,	,	PUNCT
ejpam-3049	303	6	we	we	PRON
ejpam-3049	303	7	have	have	VERB
ejpam-3049	303	8	b	b	NUM
ejpam-3049	303	9	∈	∈	PROPN
ejpam-3049	303	10	y	y	PROPN
ejpam-3049	303	11	◦	◦	NOUN
ejpam-3049	303	12	z	z	NOUN
ejpam-3049	303	13	⊆	⊆	NUM
ejpam-3049	303	14	i(a	i(a	PROPN
ejpam-3049	303	15	)	)	PUNCT
ejpam-3049	303	16	∗	∗	NOUN
ejpam-3049	303	17	l(a	l(a	PROPN
ejpam-3049	303	18	)	)	PUNCT
ejpam-3049	303	19	,	,	PUNCT
ejpam-3049	303	20	and	and	CCONJ
ejpam-3049	303	21	the	the	DET
ejpam-3049	303	22	proof	proof	NOUN
ejpam-3049	303	23	is	be	AUX
ejpam-3049	303	24	complete	complete	ADJ
ejpam-3049	303	25	.	.	PUNCT
ejpam-3049	304	1	�	�	PROPN
ejpam-3049	304	2	theorem	theorem	VERB
ejpam-3049	304	3	2.13	2.13	NUM
ejpam-3049	304	4	.	.	PUNCT
ejpam-3049	305	1	an	an	DET
ejpam-3049	305	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	305	3	(	(	PUNCT
ejpam-3049	305	4	h	h	NOUN
ejpam-3049	305	5	,	,	PUNCT
ejpam-3049	305	6	◦	◦	NOUN
ejpam-3049	305	7	)	)	PUNCT
ejpam-3049	305	8	is	be	AUX
ejpam-3049	305	9	left	leave	VERB
ejpam-3049	305	10	quasi	quasi	ADJ
ejpam-3049	305	11	-	-	ADJ
ejpam-3049	305	12	regular	regular	ADJ
ejpam-3049	305	13	if	if	SCONJ
ejpam-3049	306	1	and	and	CCONJ
ejpam-3049	306	2	only	only	ADV
ejpam-3049	306	3	if	if	SCONJ
ejpam-3049	306	4	for	for	ADP
ejpam-3049	306	5	any	any	DET
ejpam-3049	306	6	fuzzy	fuzzy	ADJ
ejpam-3049	306	7	left	leave	VERB
ejpam-3049	306	8	ideals	ideal	NOUN
ejpam-3049	306	9	f	f	PROPN
ejpam-3049	306	10	and	and	CCONJ
ejpam-3049	306	11	g	g	PROPN
ejpam-3049	306	12	of	of	ADP
ejpam-3049	306	13	h	h	NOUN
ejpam-3049	306	14	,	,	PUNCT
ejpam-3049	306	15	we	we	PRON
ejpam-3049	306	16	have	have	VERB
ejpam-3049	306	17	f	f	PROPN
ejpam-3049	306	18	∧	∧	PROPN
ejpam-3049	306	19	g	g	PROPN
ejpam-3049	306	20	�	�	PROPN
ejpam-3049	306	21	f	f	PROPN
ejpam-3049	306	22	◦	◦	NOUN
ejpam-3049	306	23	g.	g.	NOUN
ejpam-3049	306	24	proof	proof	NOUN
ejpam-3049	306	25	.	.	PUNCT
ejpam-3049	307	1	=	=	NOUN
ejpam-3049	307	2	⇒.	⇒.	NOUN
ejpam-3049	307	3	let	let	VERB
ejpam-3049	307	4	f	f	PROPN
ejpam-3049	307	5	and	and	CCONJ
ejpam-3049	307	6	g	g	PROPN
ejpam-3049	307	7	be	be	VERB
ejpam-3049	307	8	fuzzy	fuzzy	ADJ
ejpam-3049	307	9	left	leave	VERB
ejpam-3049	307	10	ideals	ideal	NOUN
ejpam-3049	307	11	of	of	ADP
ejpam-3049	307	12	h	h	NOUN
ejpam-3049	307	13	and	and	CCONJ
ejpam-3049	307	14	a	a	DET
ejpam-3049	307	15	∈	∈	PROPN
ejpam-3049	307	16	h.	h.	NOUN
ejpam-3049	308	1	then	then	ADV
ejpam-3049	308	2	(	(	PUNCT
ejpam-3049	308	3	f	f	X
ejpam-3049	308	4	∧g)(a	∧g)(a	ADV
ejpam-3049	308	5	)	)	PUNCT
ejpam-3049	308	6	≤	≤	NOUN
ejpam-3049	308	7	(	(	PUNCT
ejpam-3049	308	8	f	f	NOUN
ejpam-3049	308	9	◦	◦	NOUN
ejpam-3049	308	10	g)(a	g)(a	NOUN
ejpam-3049	308	11	)	)	PUNCT
ejpam-3049	308	12	.	.	PUNCT
ejpam-3049	309	1	indeed	indeed	ADV
ejpam-3049	309	2	:	:	PUNCT
ejpam-3049	309	3	by	by	ADP
ejpam-3049	309	4	hypothesis	hypothesis	NOUN
ejpam-3049	309	5	,	,	PUNCT
ejpam-3049	309	6	we	we	PRON
ejpam-3049	309	7	have	have	VERB
ejpam-3049	309	8	a	a	DET
ejpam-3049	309	9	∈	∈	NOUN
ejpam-3049	309	10	(	(	PUNCT
ejpam-3049	309	11	x	x	NOUN
ejpam-3049	309	12	◦	◦	NOUN
ejpam-3049	309	13	a)∗	a)∗	PROPN
ejpam-3049	309	14	(	(	PUNCT
ejpam-3049	309	15	y	y	PROPN
ejpam-3049	309	16	◦	◦	NOUN
ejpam-3049	309	17	a	a	NOUN
ejpam-3049	309	18	)	)	PUNCT
ejpam-3049	309	19	,	,	PUNCT
ejpam-3049	309	20	so	so	ADV
ejpam-3049	309	21	we	we	PRON
ejpam-3049	309	22	have	have	VERB
ejpam-3049	309	23	a	a	DET
ejpam-3049	309	24	∈	∈	PROPN
ejpam-3049	309	25	u	u	NOUN
ejpam-3049	309	26	◦	◦	NOUN
ejpam-3049	309	27	v	v	NOUN
ejpam-3049	309	28	for	for	ADP
ejpam-3049	309	29	some	some	DET
ejpam-3049	309	30	u	u	NOUN
ejpam-3049	309	31	∈	∈	PROPN
ejpam-3049	309	32	x	x	NOUN
ejpam-3049	309	33	◦	◦	NOUN
ejpam-3049	309	34	a	a	PRON
ejpam-3049	309	35	,	,	PUNCT
ejpam-3049	309	36	v	v	NOUN
ejpam-3049	309	37	∈	∈	PROPN
ejpam-3049	309	38	y	y	PROPN
ejpam-3049	309	39	◦	◦	NOUN
ejpam-3049	309	40	a.	a.	NOUN
ejpam-3049	309	41	since	since	SCONJ
ejpam-3049	309	42	(	(	PUNCT
ejpam-3049	309	43	u	u	NOUN
ejpam-3049	309	44	,	,	PUNCT
ejpam-3049	309	45	v	v	NOUN
ejpam-3049	309	46	)	)	PUNCT
ejpam-3049	309	47	∈	∈	NOUN
ejpam-3049	309	48	aa	aa	NOUN
ejpam-3049	309	49	,	,	PUNCT
ejpam-3049	309	50	we	we	PRON
ejpam-3049	309	51	have	have	VERB
ejpam-3049	309	52	(	(	PUNCT
ejpam-3049	309	53	f	f	X
ejpam-3049	309	54	◦	◦	NOUN
ejpam-3049	309	55	g)(a	g)(a	PROPN
ejpam-3049	309	56	)	)	PUNCT
ejpam-3049	310	1	=	=	SYM
ejpam-3049	310	2	∨	∨	NOUN
ejpam-3049	310	3	(	(	PUNCT
ejpam-3049	310	4	h	h	NOUN
ejpam-3049	310	5	,	,	PUNCT
ejpam-3049	310	6	k)∈aa	k)∈aa	PROPN
ejpam-3049	310	7	min{f(h	min{f(h	PROPN
ejpam-3049	310	8	)	)	PUNCT
ejpam-3049	310	9	,	,	PUNCT
ejpam-3049	310	10	g(k	g(k	NOUN
ejpam-3049	310	11	)	)	PUNCT
ejpam-3049	310	12	}	}	PUNCT
ejpam-3049	310	13	≥	≥	NOUN
ejpam-3049	310	14	min{f(u	min{f(u	PROPN
ejpam-3049	310	15	)	)	PUNCT
ejpam-3049	310	16	,	,	PUNCT
ejpam-3049	310	17	g(v	g(v	PROPN
ejpam-3049	310	18	)	)	PUNCT
ejpam-3049	310	19	}	}	PUNCT
ejpam-3049	310	20	.	.	PUNCT
ejpam-3049	311	1	since	since	SCONJ
ejpam-3049	311	2	f	f	PROPN
ejpam-3049	311	3	is	be	AUX
ejpam-3049	311	4	a	a	DET
ejpam-3049	311	5	fuzzy	fuzzy	ADJ
ejpam-3049	311	6	left	leave	VERB
ejpam-3049	311	7	ideal	ideal	NOUN
ejpam-3049	311	8	of	of	ADP
ejpam-3049	311	9	h	h	NOUN
ejpam-3049	311	10	,	,	PUNCT
ejpam-3049	311	11	we	we	PRON
ejpam-3049	311	12	have	have	VERB
ejpam-3049	311	13	f(x	f(x	PROPN
ejpam-3049	311	14	◦	◦	VERB
ejpam-3049	311	15	a	a	DET
ejpam-3049	311	16	)	)	PUNCT
ejpam-3049	311	17	≥	≥	NOUN
ejpam-3049	311	18	f(a	f(a	NOUN
ejpam-3049	311	19	)	)	PUNCT
ejpam-3049	311	20	and	and	CCONJ
ejpam-3049	311	21	since	since	SCONJ
ejpam-3049	311	22	u	u	PROPN
ejpam-3049	311	23	∈	∈	PROPN
ejpam-3049	311	24	x	x	PUNCT
ejpam-3049	311	25	◦	◦	NOUN
ejpam-3049	311	26	a	a	X
ejpam-3049	311	27	,	,	PUNCT
ejpam-3049	311	28	we	we	PRON
ejpam-3049	311	29	have	have	VERB
ejpam-3049	311	30	f(u	f(u	PROPN
ejpam-3049	311	31	)	)	PUNCT
ejpam-3049	311	32	≥	≥	NOUN
ejpam-3049	311	33	f(a	f(a	NOUN
ejpam-3049	311	34	)	)	PUNCT
ejpam-3049	311	35	.	.	PUNCT
ejpam-3049	312	1	since	since	SCONJ
ejpam-3049	312	2	g	g	PROPN
ejpam-3049	312	3	is	be	AUX
ejpam-3049	312	4	a	a	DET
ejpam-3049	312	5	fuzzy	fuzzy	ADJ
ejpam-3049	312	6	left	leave	VERB
ejpam-3049	312	7	ideal	ideal	NOUN
ejpam-3049	312	8	of	of	ADP
ejpam-3049	312	9	h	h	NOUN
ejpam-3049	312	10	,	,	PUNCT
ejpam-3049	312	11	we	we	PRON
ejpam-3049	312	12	have	have	VERB
ejpam-3049	312	13	g(y	g(y	NOUN
ejpam-3049	312	14	◦	◦	NOUN
ejpam-3049	312	15	a	a	DET
ejpam-3049	312	16	)	)	PUNCT
ejpam-3049	312	17	≥	≥	NOUN
ejpam-3049	312	18	g(a	g(a	PROPN
ejpam-3049	312	19	)	)	PUNCT
ejpam-3049	312	20	and	and	CCONJ
ejpam-3049	312	21	since	since	SCONJ
ejpam-3049	312	22	v	v	NUM
ejpam-3049	312	23	∈	∈	PROPN
ejpam-3049	312	24	y	y	PROPN
ejpam-3049	312	25	◦	◦	NOUN
ejpam-3049	312	26	a	a	X
ejpam-3049	312	27	,	,	PUNCT
ejpam-3049	312	28	we	we	PRON
ejpam-3049	312	29	have	have	VERB
ejpam-3049	312	30	g(v	g(v	NOUN
ejpam-3049	312	31	)	)	PUNCT
ejpam-3049	312	32	≥	≥	NOUN
ejpam-3049	312	33	g(a	g(a	PROPN
ejpam-3049	312	34	)	)	PUNCT
ejpam-3049	312	35	.	.	PUNCT
ejpam-3049	313	1	hence	hence	ADV
ejpam-3049	313	2	we	we	PRON
ejpam-3049	313	3	obtain	obtain	VERB
ejpam-3049	313	4	(	(	PUNCT
ejpam-3049	313	5	f	f	X
ejpam-3049	313	6	◦	◦	PROPN
ejpam-3049	313	7	g)(a	g)(a	PROPN
ejpam-3049	313	8	)	)	PUNCT
ejpam-3049	313	9	≥	≥	NOUN
ejpam-3049	313	10	min{f(a	min{f(a	PROPN
ejpam-3049	313	11	)	)	PUNCT
ejpam-3049	313	12	,	,	PUNCT
ejpam-3049	313	13	g(a	g(a	PROPN
ejpam-3049	313	14	)	)	PUNCT
ejpam-3049	313	15	}	}	PUNCT
ejpam-3049	313	16	=	=	SYM
ejpam-3049	314	1	(	(	PUNCT
ejpam-3049	314	2	f	f	PROPN
ejpam-3049	314	3	∧	∧	PROPN
ejpam-3049	314	4	g)(a	g)(a	PROPN
ejpam-3049	314	5	)	)	PUNCT
ejpam-3049	314	6	.	.	PUNCT
ejpam-3049	315	1	n.	n.	PROPN
ejpam-3049	315	2	kehayopulu	kehayopulu	PROPN
ejpam-3049	315	3	/	/	SYM
ejpam-3049	315	4	eur	eur	PROPN
ejpam-3049	315	5	.	.	PUNCT
ejpam-3049	316	1	j.	j.	PROPN
ejpam-3049	316	2	pure	pure	PROPN
ejpam-3049	316	3	appl	appl	PROPN
ejpam-3049	316	4	.	.	PROPN
ejpam-3049	316	5	math	math	PROPN
ejpam-3049	316	6	,	,	PUNCT
ejpam-3049	316	7	10	10	NUM
ejpam-3049	316	8	(	(	PUNCT
ejpam-3049	316	9	5	5	NUM
ejpam-3049	316	10	)	)	PUNCT
ejpam-3049	316	11	(	(	PUNCT
ejpam-3049	316	12	2017	2017	NUM
ejpam-3049	316	13	)	)	PUNCT
ejpam-3049	316	14	,	,	PUNCT
ejpam-3049	316	15	929	929	NUM
ejpam-3049	316	16	-	-	SYM
ejpam-3049	316	17	945	945	NUM
ejpam-3049	316	18	940	940	NUM
ejpam-3049	316	19	⇐	⇐	NOUN
ejpam-3049	316	20	=	=	NOUN
ejpam-3049	316	21	.	.	PUNCT
ejpam-3049	316	22	by	by	ADP
ejpam-3049	316	23	theorem	theorem	NOUN
ejpam-3049	316	24	2.11	2.11	NUM
ejpam-3049	316	25	,	,	PUNCT
ejpam-3049	316	26	it	it	PRON
ejpam-3049	316	27	is	be	AUX
ejpam-3049	316	28	enough	enough	ADJ
ejpam-3049	316	29	to	to	PART
ejpam-3049	316	30	prove	prove	VERB
ejpam-3049	316	31	that	that	SCONJ
ejpam-3049	316	32	the	the	DET
ejpam-3049	316	33	left	left	ADJ
ejpam-3049	316	34	ideals	ideal	NOUN
ejpam-3049	316	35	of	of	ADP
ejpam-3049	316	36	h	h	NOUN
ejpam-3049	316	37	are	be	AUX
ejpam-3049	316	38	idempotent	idempotent	ADJ
ejpam-3049	316	39	.	.	PUNCT
ejpam-3049	317	1	let	let	VERB
ejpam-3049	317	2	now	now	ADV
ejpam-3049	317	3	a	a	DET
ejpam-3049	317	4	be	be	AUX
ejpam-3049	317	5	a	a	DET
ejpam-3049	317	6	left	left	ADJ
ejpam-3049	317	7	ideal	ideal	NOUN
ejpam-3049	317	8	of	of	ADP
ejpam-3049	317	9	h	h	NOUN
ejpam-3049	317	10	and	and	CCONJ
ejpam-3049	317	11	a	a	DET
ejpam-3049	317	12	∈	∈	NOUN
ejpam-3049	317	13	a.	a.	NOUN
ejpam-3049	317	14	since	since	SCONJ
ejpam-3049	317	15	fa	fa	PROPN
ejpam-3049	317	16	is	be	AUX
ejpam-3049	317	17	a	a	DET
ejpam-3049	317	18	fuzzy	fuzzy	ADJ
ejpam-3049	317	19	left	leave	VERB
ejpam-3049	317	20	ideal	ideal	NOUN
ejpam-3049	317	21	of	of	ADP
ejpam-3049	317	22	h	h	NOUN
ejpam-3049	317	23	,	,	PUNCT
ejpam-3049	317	24	by	by	ADP
ejpam-3049	317	25	hypothesis	hypothesis	NOUN
ejpam-3049	317	26	,	,	PUNCT
ejpam-3049	317	27	we	we	PRON
ejpam-3049	317	28	have	have	VERB
ejpam-3049	317	29	fa	fa	NOUN
ejpam-3049	317	30	=	=	SYM
ejpam-3049	317	31	fa	fa	PROPN
ejpam-3049	317	32	∧	∧	PROPN
ejpam-3049	317	33	fa	fa	X
ejpam-3049	317	34	�	�	PROPN
ejpam-3049	317	35	fa	fa	PROPN
ejpam-3049	317	36	◦	◦	NOUN
ejpam-3049	317	37	fa	fa	PROPN
ejpam-3049	317	38	.	.	PUNCT
ejpam-3049	318	1	then	then	ADV
ejpam-3049	318	2	1	1	NUM
ejpam-3049	318	3	=	=	SYM
ejpam-3049	318	4	fa(a	fa(a	NOUN
ejpam-3049	318	5	)	)	PUNCT
ejpam-3049	318	6	≤	≤	NUM
ejpam-3049	318	7	fa	fa	NOUN
ejpam-3049	318	8	◦	◦	NOUN
ejpam-3049	318	9	fa)(a	fa)(a	PROPN
ejpam-3049	318	10	)	)	PUNCT
ejpam-3049	318	11	.	.	PUNCT
ejpam-3049	319	1	if	if	SCONJ
ejpam-3049	319	2	aa	aa	NOUN
ejpam-3049	319	3	=	=	NOUN
ejpam-3049	319	4	∅	∅	NOUN
ejpam-3049	319	5	,	,	PUNCT
ejpam-3049	319	6	then	then	ADV
ejpam-3049	319	7	(	(	PUNCT
ejpam-3049	319	8	fa	fa	INTJ
ejpam-3049	319	9	◦	◦	VERB
ejpam-3049	319	10	fa)(a	fa)(a	NOUN
ejpam-3049	319	11	)	)	PUNCT
ejpam-3049	319	12	=	=	SYM
ejpam-3049	319	13	0	0	NUM
ejpam-3049	319	14	which	which	PRON
ejpam-3049	319	15	is	be	AUX
ejpam-3049	319	16	impossible	impossible	ADJ
ejpam-3049	319	17	.	.	PUNCT
ejpam-3049	320	1	thus	thus	ADV
ejpam-3049	320	2	we	we	PRON
ejpam-3049	320	3	have	have	VERB
ejpam-3049	320	4	aa	aa	NOUN
ejpam-3049	320	5	6=	6=	NOUN
ejpam-3049	320	6	∅	∅	NOUN
ejpam-3049	320	7	and	and	CCONJ
ejpam-3049	320	8	(	(	PUNCT
ejpam-3049	320	9	fa	fa	INTJ
ejpam-3049	320	10	◦	◦	VERB
ejpam-3049	320	11	fa)(a	fa)(a	PROPN
ejpam-3049	320	12	)	)	PUNCT
ejpam-3049	320	13	:	:	PUNCT
ejpam-3049	321	1	=	=	SYM
ejpam-3049	321	2	∨	∨	X
ejpam-3049	321	3	(	(	PUNCT
ejpam-3049	321	4	h	h	PROPN
ejpam-3049	321	5	,	,	PUNCT
ejpam-3049	321	6	k)∈aa	k)∈aa	PROPN
ejpam-3049	321	7	min{fa(h	min{fa(h	PROPN
ejpam-3049	321	8	)	)	PUNCT
ejpam-3049	321	9	,	,	PUNCT
ejpam-3049	321	10	fa(k	fa(k	PUNCT
ejpam-3049	321	11	)	)	PUNCT
ejpam-3049	321	12	}	}	PUNCT
ejpam-3049	321	13	.	.	PUNCT
ejpam-3049	322	1	then	then	ADV
ejpam-3049	322	2	there	there	PRON
ejpam-3049	322	3	exists	exist	VERB
ejpam-3049	322	4	(	(	PUNCT
ejpam-3049	322	5	y	y	NOUN
ejpam-3049	322	6	,	,	PUNCT
ejpam-3049	322	7	z	z	NOUN
ejpam-3049	322	8	)	)	PUNCT
ejpam-3049	322	9	∈	∈	PROPN
ejpam-3049	322	10	aa	aa	NOUN
ejpam-3049	322	11	such	such	ADJ
ejpam-3049	322	12	that	that	SCONJ
ejpam-3049	322	13	y	y	PROPN
ejpam-3049	322	14	∈	∈	PROPN
ejpam-3049	322	15	a	a	PRON
ejpam-3049	322	16	and	and	CCONJ
ejpam-3049	322	17	z	z	PROPN
ejpam-3049	322	18	∈	∈	PROPN
ejpam-3049	322	19	a.	a.	NOUN
ejpam-3049	323	1	then	then	ADV
ejpam-3049	323	2	we	we	PRON
ejpam-3049	323	3	have	have	VERB
ejpam-3049	323	4	a	a	DET
ejpam-3049	323	5	∈	∈	PROPN
ejpam-3049	323	6	y	y	PROPN
ejpam-3049	323	7	◦	◦	NOUN
ejpam-3049	323	8	z	z	NOUN
ejpam-3049	323	9	⊆	⊆	NUM
ejpam-3049	323	10	a∗a	a∗a	NUM
ejpam-3049	323	11	,	,	PUNCT
ejpam-3049	323	12	so	so	SCONJ
ejpam-3049	323	13	a	a	DET
ejpam-3049	323	14	⊆	⊆	NUM
ejpam-3049	323	15	a	a	DET
ejpam-3049	323	16	∗a	∗a	ADJ
ejpam-3049	323	17	⊆	⊆	NUM
ejpam-3049	323	18	h	h	NOUN
ejpam-3049	323	19	∗a	∗a	ADJ
ejpam-3049	323	20	⊆	⊆	PROPN
ejpam-3049	323	21	a	a	PRON
ejpam-3049	323	22	,	,	PUNCT
ejpam-3049	323	23	thus	thus	ADV
ejpam-3049	323	24	a	a	DET
ejpam-3049	323	25	∗a	∗a	ADJ
ejpam-3049	323	26	=	=	SYM
ejpam-3049	323	27	a	a	NOUN
ejpam-3049	323	28	,	,	PUNCT
ejpam-3049	323	29	and	and	CCONJ
ejpam-3049	323	30	a	a	PRON
ejpam-3049	323	31	is	be	AUX
ejpam-3049	323	32	idempotent	idempotent	ADJ
ejpam-3049	323	33	.	.	PUNCT
ejpam-3049	324	1	�	�	PROPN
ejpam-3049	324	2	theorem	theorem	VERB
ejpam-3049	324	3	2.14	2.14	NUM
ejpam-3049	324	4	.	.	PUNCT
ejpam-3049	325	1	an	an	DET
ejpam-3049	325	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	325	3	(	(	PUNCT
ejpam-3049	325	4	h	h	NOUN
ejpam-3049	325	5	,	,	PUNCT
ejpam-3049	325	6	◦	◦	NOUN
ejpam-3049	325	7	)	)	PUNCT
ejpam-3049	325	8	is	be	AUX
ejpam-3049	325	9	left	leave	VERB
ejpam-3049	325	10	quasi	quasi	ADJ
ejpam-3049	325	11	-	-	ADJ
ejpam-3049	325	12	regular	regular	ADJ
ejpam-3049	325	13	if	if	SCONJ
ejpam-3049	326	1	and	and	CCONJ
ejpam-3049	326	2	only	only	ADV
ejpam-3049	326	3	if	if	SCONJ
ejpam-3049	326	4	the	the	DET
ejpam-3049	326	5	fuzzy	fuzzy	ADJ
ejpam-3049	326	6	left	leave	VERB
ejpam-3049	326	7	ideals	ideal	NOUN
ejpam-3049	326	8	of	of	ADP
ejpam-3049	326	9	h	h	NOUN
ejpam-3049	326	10	are	be	AUX
ejpam-3049	326	11	idempotent	idempotent	ADJ
ejpam-3049	326	12	.	.	PUNCT
ejpam-3049	327	1	proof	proof	NOUN
ejpam-3049	327	2	.	.	PUNCT
ejpam-3049	328	1	=	=	NOUN
ejpam-3049	328	2	⇒.	⇒.	NOUN
ejpam-3049	328	3	let	let	VERB
ejpam-3049	328	4	f	f	PRON
ejpam-3049	328	5	be	be	AUX
ejpam-3049	328	6	a	a	DET
ejpam-3049	328	7	fuzzy	fuzzy	ADJ
ejpam-3049	328	8	left	leave	VERB
ejpam-3049	328	9	ideal	ideal	NOUN
ejpam-3049	328	10	of	of	ADP
ejpam-3049	328	11	h	h	NOUN
ejpam-3049	328	12	and	and	CCONJ
ejpam-3049	328	13	a	a	DET
ejpam-3049	328	14	∈	∈	PROPN
ejpam-3049	328	15	h.	h.	NOUN
ejpam-3049	328	16	then	then	ADV
ejpam-3049	328	17	(	(	PUNCT
ejpam-3049	328	18	f	f	X
ejpam-3049	328	19	◦	◦	NOUN
ejpam-3049	328	20	f)(a	f)(a	NOUN
ejpam-3049	328	21	)	)	PUNCT
ejpam-3049	328	22	≤	≤	NUM
ejpam-3049	328	23	f(a	f(a	NOUN
ejpam-3049	328	24	)	)	PUNCT
ejpam-3049	328	25	.	.	PUNCT
ejpam-3049	329	1	in	in	ADP
ejpam-3049	329	2	fact	fact	NOUN
ejpam-3049	329	3	,	,	PUNCT
ejpam-3049	329	4	if	if	SCONJ
ejpam-3049	329	5	aa	aa	NOUN
ejpam-3049	329	6	=	=	NOUN
ejpam-3049	329	7	∅	∅	NOUN
ejpam-3049	329	8	,	,	PUNCT
ejpam-3049	329	9	then	then	ADV
ejpam-3049	329	10	(	(	PUNCT
ejpam-3049	329	11	f	f	X
ejpam-3049	329	12	◦	◦	NOUN
ejpam-3049	329	13	f)(a	f)(a	NUM
ejpam-3049	329	14	)	)	PUNCT
ejpam-3049	329	15	=	=	SYM
ejpam-3049	329	16	0	0	NUM
ejpam-3049	329	17	≤	≤	NUM
ejpam-3049	329	18	f(a	f(a	NOUN
ejpam-3049	329	19	)	)	PUNCT
ejpam-3049	329	20	.	.	PUNCT
ejpam-3049	330	1	let	let	VERB
ejpam-3049	330	2	aa	aa	PROPN
ejpam-3049	330	3	6=	6=	ADP
ejpam-3049	330	4	∅.	∅.	VERB
ejpam-3049	330	5	then	then	ADV
ejpam-3049	330	6	(	(	PUNCT
ejpam-3049	330	7	f	f	X
ejpam-3049	330	8	◦	◦	NOUN
ejpam-3049	330	9	f)(a	f)(a	NUM
ejpam-3049	330	10	)	)	PUNCT
ejpam-3049	330	11	=	=	SYM
ejpam-3049	331	1	∨	∨	X
ejpam-3049	331	2	(	(	PUNCT
ejpam-3049	331	3	x	x	X
ejpam-3049	331	4	,	,	PUNCT
ejpam-3049	331	5	y)∈aa	y)∈aa	PROPN
ejpam-3049	331	6	min{f(x	min{f(x	PROPN
ejpam-3049	331	7	)	)	PUNCT
ejpam-3049	331	8	,	,	PUNCT
ejpam-3049	331	9	f(y	f(y	NOUN
ejpam-3049	331	10	)	)	PUNCT
ejpam-3049	331	11	}	}	PUNCT
ejpam-3049	331	12	.	.	PUNCT
ejpam-3049	332	1	on	on	ADP
ejpam-3049	332	2	the	the	DET
ejpam-3049	332	3	other	other	ADJ
ejpam-3049	332	4	hand	hand	NOUN
ejpam-3049	332	5	,	,	PUNCT
ejpam-3049	332	6	min{f(x	min{f(x	PROPN
ejpam-3049	332	7	)	)	PUNCT
ejpam-3049	332	8	,	,	PUNCT
ejpam-3049	332	9	f(y	f(y	NOUN
ejpam-3049	332	10	)	)	PUNCT
ejpam-3049	332	11	}	}	PUNCT
ejpam-3049	332	12	≤	≤	NUM
ejpam-3049	332	13	f(a	f(a	NOUN
ejpam-3049	332	14	)	)	PUNCT
ejpam-3049	332	15	for	for	ADP
ejpam-3049	332	16	every	every	DET
ejpam-3049	332	17	(	(	PUNCT
ejpam-3049	332	18	x	x	NOUN
ejpam-3049	332	19	,	,	PUNCT
ejpam-3049	332	20	y	y	NOUN
ejpam-3049	332	21	)	)	PUNCT
ejpam-3049	332	22	∈	∈	PROPN
ejpam-3049	332	23	aa	aa	NOUN
ejpam-3049	332	24	.	.	PUNCT
ejpam-3049	333	1	indeed	indeed	ADV
ejpam-3049	333	2	:	:	PUNCT
ejpam-3049	333	3	let	let	VERB
ejpam-3049	333	4	(	(	PUNCT
ejpam-3049	333	5	x	x	NOUN
ejpam-3049	333	6	,	,	PUNCT
ejpam-3049	333	7	y	y	NOUN
ejpam-3049	333	8	)	)	PUNCT
ejpam-3049	333	9	∈	∈	PROPN
ejpam-3049	333	10	aa	aa	NOUN
ejpam-3049	333	11	.	.	PUNCT
ejpam-3049	334	1	since	since	SCONJ
ejpam-3049	334	2	f	f	PROPN
ejpam-3049	334	3	is	be	AUX
ejpam-3049	334	4	a	a	DET
ejpam-3049	334	5	fuzzy	fuzzy	ADJ
ejpam-3049	334	6	left	leave	VERB
ejpam-3049	334	7	ideal	ideal	NOUN
ejpam-3049	334	8	of	of	ADP
ejpam-3049	334	9	h	h	NOUN
ejpam-3049	334	10	we	we	PRON
ejpam-3049	334	11	have	have	VERB
ejpam-3049	334	12	f(x	f(x	PROPN
ejpam-3049	334	13	◦	◦	PROPN
ejpam-3049	334	14	y	y	PROPN
ejpam-3049	334	15	)	)	PUNCT
ejpam-3049	334	16	≥	≥	NOUN
ejpam-3049	334	17	f(y	f(y	NOUN
ejpam-3049	334	18	)	)	PUNCT
ejpam-3049	334	19	,	,	PUNCT
ejpam-3049	334	20	and	and	CCONJ
ejpam-3049	334	21	since	since	SCONJ
ejpam-3049	334	22	a	a	DET
ejpam-3049	334	23	∈	∈	NOUN
ejpam-3049	334	24	x	x	PUNCT
ejpam-3049	334	25	◦	◦	NOUN
ejpam-3049	334	26	y	y	NUM
ejpam-3049	334	27	,	,	PUNCT
ejpam-3049	334	28	we	we	PRON
ejpam-3049	334	29	have	have	VERB
ejpam-3049	334	30	f(a	f(a	PROPN
ejpam-3049	334	31	)	)	PUNCT
ejpam-3049	334	32	≥	≥	NOUN
ejpam-3049	334	33	f(y	f(y	NOUN
ejpam-3049	334	34	)	)	PUNCT
ejpam-3049	334	35	≥	≥	NOUN
ejpam-3049	334	36	min{f(x	min{f(x	NOUN
ejpam-3049	334	37	)	)	PUNCT
ejpam-3049	334	38	,	,	PUNCT
ejpam-3049	334	39	f(y	f(y	NOUN
ejpam-3049	334	40	)	)	PUNCT
ejpam-3049	334	41	}	}	PUNCT
ejpam-3049	334	42	.	.	PUNCT
ejpam-3049	335	1	thus	thus	ADV
ejpam-3049	335	2	we	we	PRON
ejpam-3049	335	3	get	get	VERB
ejpam-3049	335	4	(	(	PUNCT
ejpam-3049	335	5	f	f	X
ejpam-3049	335	6	◦	◦	NOUN
ejpam-3049	335	7	f)(a	f)(a	NOUN
ejpam-3049	335	8	)	)	PUNCT
ejpam-3049	335	9	≤	≤	NUM
ejpam-3049	335	10	f(a	f(a	NOUN
ejpam-3049	335	11	)	)	PUNCT
ejpam-3049	335	12	.	.	PUNCT
ejpam-3049	336	1	moreover	moreover	ADV
ejpam-3049	336	2	f	f	PROPN
ejpam-3049	336	3	�	�	PROPN
ejpam-3049	336	4	f	f	PROPN
ejpam-3049	336	5	◦	◦	NOUN
ejpam-3049	336	6	f	f	X
ejpam-3049	336	7	.	.	PUNCT
ejpam-3049	337	1	indeed	indeed	ADV
ejpam-3049	337	2	:	:	PUNCT
ejpam-3049	337	3	let	let	VERB
ejpam-3049	337	4	a	a	DET
ejpam-3049	337	5	∈	∈	PROPN
ejpam-3049	337	6	h.	h.	NOUN
ejpam-3049	337	7	since	since	SCONJ
ejpam-3049	337	8	h	h	PROPN
ejpam-3049	337	9	is	be	AUX
ejpam-3049	337	10	left	leave	VERB
ejpam-3049	337	11	quasi	quasi	ADJ
ejpam-3049	337	12	-	-	ADJ
ejpam-3049	337	13	regular	regular	ADJ
ejpam-3049	337	14	,	,	PUNCT
ejpam-3049	337	15	there	there	PRON
ejpam-3049	337	16	exist	exist	VERB
ejpam-3049	337	17	x	x	NOUN
ejpam-3049	337	18	,	,	PUNCT
ejpam-3049	337	19	y	y	PROPN
ejpam-3049	337	20	∈	∈	PROPN
ejpam-3049	337	21	h	h	NOUN
ejpam-3049	337	22	such	such	ADJ
ejpam-3049	337	23	that	that	SCONJ
ejpam-3049	337	24	a	a	DET
ejpam-3049	337	25	∈	∈	PROPN
ejpam-3049	337	26	(	(	PUNCT
ejpam-3049	337	27	x	x	NOUN
ejpam-3049	337	28	◦	◦	NOUN
ejpam-3049	337	29	a)∗(y	a)∗(y	NOUN
ejpam-3049	337	30	◦	◦	NOUN
ejpam-3049	337	31	a	a	PRON
ejpam-3049	337	32	)	)	PUNCT
ejpam-3049	337	33	.	.	PUNCT
ejpam-3049	338	1	then	then	ADV
ejpam-3049	338	2	a	a	DET
ejpam-3049	338	3	∈	∈	PROPN
ejpam-3049	338	4	u	u	NOUN
ejpam-3049	338	5	◦	◦	NOUN
ejpam-3049	338	6	v	v	NOUN
ejpam-3049	338	7	for	for	ADP
ejpam-3049	338	8	some	some	DET
ejpam-3049	338	9	u	u	NOUN
ejpam-3049	338	10	∈	∈	PROPN
ejpam-3049	338	11	x	x	NOUN
ejpam-3049	338	12	◦	◦	NOUN
ejpam-3049	338	13	a	a	PRON
ejpam-3049	338	14	,	,	PUNCT
ejpam-3049	338	15	v	v	PROPN
ejpam-3049	338	16	∈	∈	PROPN
ejpam-3049	338	17	y	y	PROPN
ejpam-3049	338	18	◦	◦	NOUN
ejpam-3049	338	19	a.	a.	NOUN
ejpam-3049	338	20	since	since	SCONJ
ejpam-3049	338	21	(	(	PUNCT
ejpam-3049	338	22	u	u	NOUN
ejpam-3049	338	23	,	,	PUNCT
ejpam-3049	338	24	v	v	NOUN
ejpam-3049	338	25	)	)	PUNCT
ejpam-3049	338	26	∈	∈	NOUN
ejpam-3049	338	27	aa	aa	NOUN
ejpam-3049	338	28	,	,	PUNCT
ejpam-3049	338	29	we	we	PRON
ejpam-3049	338	30	have	have	VERB
ejpam-3049	338	31	(	(	PUNCT
ejpam-3049	338	32	f	f	X
ejpam-3049	338	33	◦	◦	NOUN
ejpam-3049	338	34	f)(a	f)(a	NUM
ejpam-3049	338	35	)	)	PUNCT
ejpam-3049	338	36	:	:	PUNCT
ejpam-3049	339	1	=	=	SYM
ejpam-3049	339	2	∨	∨	X
ejpam-3049	339	3	(	(	PUNCT
ejpam-3049	339	4	h	h	NOUN
ejpam-3049	339	5	,	,	PUNCT
ejpam-3049	339	6	k)∈aa	k)∈aa	PROPN
ejpam-3049	339	7	min{f(h	min{f(h	PROPN
ejpam-3049	339	8	)	)	PUNCT
ejpam-3049	339	9	,	,	PUNCT
ejpam-3049	339	10	f(k	f(k	VERB
ejpam-3049	339	11	)	)	PUNCT
ejpam-3049	339	12	}	}	PUNCT
ejpam-3049	339	13	≥	≥	NOUN
ejpam-3049	339	14	min{f(u	min{f(u	PROPN
ejpam-3049	339	15	)	)	PUNCT
ejpam-3049	339	16	,	,	PUNCT
ejpam-3049	339	17	f(v	f(v	NOUN
ejpam-3049	339	18	)	)	PUNCT
ejpam-3049	339	19	}	}	PUNCT
ejpam-3049	339	20	.	.	PUNCT
ejpam-3049	340	1	since	since	SCONJ
ejpam-3049	340	2	f	f	PROPN
ejpam-3049	340	3	is	be	AUX
ejpam-3049	340	4	a	a	DET
ejpam-3049	340	5	fuzzy	fuzzy	ADJ
ejpam-3049	340	6	left	leave	VERB
ejpam-3049	340	7	ideal	ideal	NOUN
ejpam-3049	340	8	of	of	ADP
ejpam-3049	340	9	h	h	NOUN
ejpam-3049	340	10	,	,	PUNCT
ejpam-3049	340	11	we	we	PRON
ejpam-3049	340	12	have	have	VERB
ejpam-3049	340	13	f(x	f(x	PROPN
ejpam-3049	340	14	◦	◦	VERB
ejpam-3049	340	15	a	a	DET
ejpam-3049	340	16	)	)	PUNCT
ejpam-3049	340	17	≥	≥	NOUN
ejpam-3049	340	18	f(a	f(a	NOUN
ejpam-3049	340	19	)	)	PUNCT
ejpam-3049	340	20	and	and	CCONJ
ejpam-3049	340	21	since	since	SCONJ
ejpam-3049	340	22	u	u	PROPN
ejpam-3049	340	23	∈	∈	PROPN
ejpam-3049	340	24	x	x	PUNCT
ejpam-3049	340	25	◦	◦	NOUN
ejpam-3049	340	26	a	a	X
ejpam-3049	340	27	,	,	PUNCT
ejpam-3049	340	28	we	we	PRON
ejpam-3049	340	29	get	get	VERB
ejpam-3049	340	30	f(u	f(u	PROPN
ejpam-3049	340	31	)	)	PUNCT
ejpam-3049	340	32	≥	≥	NOUN
ejpam-3049	340	33	f(a	f(a	NOUN
ejpam-3049	340	34	)	)	PUNCT
ejpam-3049	340	35	.	.	PUNCT
ejpam-3049	341	1	again	again	ADV
ejpam-3049	341	2	since	since	SCONJ
ejpam-3049	341	3	f	f	PROPN
ejpam-3049	341	4	is	be	AUX
ejpam-3049	341	5	a	a	DET
ejpam-3049	341	6	fuzzy	fuzzy	ADJ
ejpam-3049	341	7	left	leave	VERB
ejpam-3049	341	8	ideal	ideal	NOUN
ejpam-3049	341	9	of	of	ADP
ejpam-3049	341	10	h	h	NOUN
ejpam-3049	341	11	,	,	PUNCT
ejpam-3049	341	12	we	we	PRON
ejpam-3049	341	13	have	have	VERB
ejpam-3049	341	14	f(y	f(y	NOUN
ejpam-3049	341	15	◦	◦	NOUN
ejpam-3049	341	16	a	a	DET
ejpam-3049	341	17	)	)	PUNCT
ejpam-3049	341	18	≥	≥	NOUN
ejpam-3049	341	19	f(a	f(a	NOUN
ejpam-3049	341	20	)	)	PUNCT
ejpam-3049	341	21	and	and	CCONJ
ejpam-3049	341	22	since	since	SCONJ
ejpam-3049	341	23	v	v	NUM
ejpam-3049	341	24	∈	∈	PROPN
ejpam-3049	341	25	y	y	PROPN
ejpam-3049	341	26	◦	◦	NOUN
ejpam-3049	341	27	a	a	X
ejpam-3049	341	28	,	,	PUNCT
ejpam-3049	341	29	we	we	PRON
ejpam-3049	341	30	get	get	VERB
ejpam-3049	341	31	f(v	f(v	NOUN
ejpam-3049	341	32	)	)	PUNCT
ejpam-3049	341	33	≥	≥	NOUN
ejpam-3049	341	34	f(a	f(a	NOUN
ejpam-3049	341	35	)	)	PUNCT
ejpam-3049	341	36	.	.	PUNCT
ejpam-3049	342	1	thus	thus	ADV
ejpam-3049	342	2	we	we	PRON
ejpam-3049	342	3	have	have	VERB
ejpam-3049	342	4	(	(	PUNCT
ejpam-3049	342	5	f	f	X
ejpam-3049	342	6	◦	◦	NOUN
ejpam-3049	342	7	f)(a	f)(a	NOUN
ejpam-3049	342	8	)	)	PUNCT
ejpam-3049	342	9	≥	≥	NOUN
ejpam-3049	342	10	min{f(a	min{f(a	PROPN
ejpam-3049	342	11	)	)	PUNCT
ejpam-3049	342	12	,	,	PUNCT
ejpam-3049	342	13	f(a	f(a	NOUN
ejpam-3049	342	14	)	)	PUNCT
ejpam-3049	342	15	}	}	PUNCT
ejpam-3049	342	16	=	=	SYM
ejpam-3049	342	17	f(a	f(a	NOUN
ejpam-3049	342	18	)	)	PUNCT
ejpam-3049	342	19	,	,	PUNCT
ejpam-3049	342	20	so	so	CCONJ
ejpam-3049	342	21	f	f	PROPN
ejpam-3049	342	22	�	�	PROPN
ejpam-3049	342	23	f	f	PROPN
ejpam-3049	342	24	◦	◦	NOUN
ejpam-3049	342	25	f	f	X
ejpam-3049	342	26	,	,	PUNCT
ejpam-3049	342	27	and	and	CCONJ
ejpam-3049	342	28	f	f	PROPN
ejpam-3049	342	29	is	be	AUX
ejpam-3049	342	30	idempotent	idempotent	ADJ
ejpam-3049	342	31	.	.	PUNCT
ejpam-3049	343	1	⇐	⇐	PROPN
ejpam-3049	343	2	=	=	NOUN
ejpam-3049	343	3	.	.	PUNCT
ejpam-3049	343	4	by	by	ADP
ejpam-3049	343	5	theorem	theorem	NOUN
ejpam-3049	343	6	2.11	2.11	NUM
ejpam-3049	343	7	,	,	PUNCT
ejpam-3049	343	8	it	it	PRON
ejpam-3049	343	9	is	be	AUX
ejpam-3049	343	10	enough	enough	ADJ
ejpam-3049	343	11	to	to	PART
ejpam-3049	343	12	prove	prove	VERB
ejpam-3049	343	13	that	that	SCONJ
ejpam-3049	343	14	the	the	DET
ejpam-3049	343	15	left	left	ADJ
ejpam-3049	343	16	ideals	ideal	NOUN
ejpam-3049	343	17	of	of	ADP
ejpam-3049	343	18	h	h	NOUN
ejpam-3049	343	19	are	be	AUX
ejpam-3049	343	20	idempotent	idempotent	ADJ
ejpam-3049	343	21	.	.	PUNCT
ejpam-3049	344	1	let	let	VERB
ejpam-3049	344	2	now	now	ADV
ejpam-3049	344	3	a	a	DET
ejpam-3049	344	4	be	be	AUX
ejpam-3049	344	5	a	a	DET
ejpam-3049	344	6	left	left	ADJ
ejpam-3049	344	7	ideal	ideal	NOUN
ejpam-3049	344	8	of	of	ADP
ejpam-3049	344	9	h	h	NOUN
ejpam-3049	344	10	and	and	CCONJ
ejpam-3049	344	11	a	a	DET
ejpam-3049	344	12	∈	∈	NOUN
ejpam-3049	344	13	a.	a.	NOUN
ejpam-3049	344	14	since	since	SCONJ
ejpam-3049	344	15	fa	fa	PROPN
ejpam-3049	344	16	is	be	AUX
ejpam-3049	344	17	a	a	DET
ejpam-3049	344	18	fuzzy	fuzzy	ADJ
ejpam-3049	344	19	left	leave	VERB
ejpam-3049	344	20	ideal	ideal	NOUN
ejpam-3049	344	21	of	of	ADP
ejpam-3049	344	22	h	h	NOUN
ejpam-3049	344	23	,	,	PUNCT
ejpam-3049	344	24	by	by	ADP
ejpam-3049	344	25	hypothesis	hypothesis	NOUN
ejpam-3049	344	26	,	,	PUNCT
ejpam-3049	344	27	we	we	PRON
ejpam-3049	344	28	have	have	VERB
ejpam-3049	344	29	fa	fa	NOUN
ejpam-3049	344	30	=	=	SYM
ejpam-3049	344	31	fa	fa	PROPN
ejpam-3049	344	32	◦	◦	NOUN
ejpam-3049	344	33	fa	fa	NOUN
ejpam-3049	344	34	,	,	PUNCT
ejpam-3049	344	35	thus	thus	ADV
ejpam-3049	344	36	1	1	NUM
ejpam-3049	344	37	=	=	SYM
ejpam-3049	344	38	fa(a	fa(a	NOUN
ejpam-3049	344	39	)	)	PUNCT
ejpam-3049	345	1	=	=	PRON
ejpam-3049	345	2	(	(	PUNCT
ejpam-3049	345	3	fa	fa	INTJ
ejpam-3049	345	4	◦	◦	VERB
ejpam-3049	345	5	fa)(a	fa)(a	PROPN
ejpam-3049	345	6	)	)	PUNCT
ejpam-3049	345	7	.	.	PUNCT
ejpam-3049	346	1	then	then	ADV
ejpam-3049	346	2	1	1	NUM
ejpam-3049	346	3	≤	≤	NUM
ejpam-3049	346	4	(	(	PUNCT
ejpam-3049	346	5	fa	fa	INTJ
ejpam-3049	346	6	◦	◦	NOUN
ejpam-3049	346	7	fa)(a	fa)(a	PROPN
ejpam-3049	346	8	)	)	PUNCT
ejpam-3049	346	9	and	and	CCONJ
ejpam-3049	346	10	for	for	ADP
ejpam-3049	346	11	the	the	DET
ejpam-3049	346	12	rest	rest	NOUN
ejpam-3049	346	13	of	of	ADP
ejpam-3049	346	14	the	the	DET
ejpam-3049	346	15	proof	proof	NOUN
ejpam-3049	346	16	we	we	PRON
ejpam-3049	346	17	refer	refer	VERB
ejpam-3049	346	18	to	to	ADP
ejpam-3049	346	19	the	the	DET
ejpam-3049	346	20	proof	proof	NOUN
ejpam-3049	346	21	of	of	ADP
ejpam-3049	346	22	the	the	DET
ejpam-3049	346	23	⇐	⇐	ADJ
ejpam-3049	346	24	-part	-part	NOUN
ejpam-3049	346	25	of	of	ADP
ejpam-3049	346	26	the	the	DET
ejpam-3049	346	27	previous	previous	ADJ
ejpam-3049	346	28	theorem	theorem	PROPN
ejpam-3049	346	29	.	.	PUNCT
ejpam-3049	346	30	�	�	PROPN
ejpam-3049	346	31	the	the	DET
ejpam-3049	346	32	concept	concept	NOUN
ejpam-3049	346	33	of	of	ADP
ejpam-3049	346	34	right	right	ADJ
ejpam-3049	346	35	quasi	quasi	ADJ
ejpam-3049	346	36	-	-	ADJ
ejpam-3049	346	37	regular	regular	ADJ
ejpam-3049	346	38	semigroups	semigroup	NOUN
ejpam-3049	346	39	is	be	AUX
ejpam-3049	346	40	naturally	naturally	ADV
ejpam-3049	346	41	transferred	transfer	VERB
ejpam-3049	346	42	to	to	ADP
ejpam-3049	346	43	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	346	44	in	in	ADP
ejpam-3049	346	45	the	the	DET
ejpam-3049	346	46	following	follow	VERB
ejpam-3049	346	47	definition	definition	NOUN
ejpam-3049	346	48	.	.	PUNCT
ejpam-3049	347	1	definition	definition	NOUN
ejpam-3049	347	2	2.15	2.15	NUM
ejpam-3049	347	3	.	.	PUNCT
ejpam-3049	348	1	an	an	DET
ejpam-3049	348	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	348	3	(	(	PUNCT
ejpam-3049	348	4	h	h	NOUN
ejpam-3049	348	5	,	,	PUNCT
ejpam-3049	348	6	◦	◦	NOUN
ejpam-3049	348	7	)	)	PUNCT
ejpam-3049	348	8	is	be	AUX
ejpam-3049	348	9	called	call	VERB
ejpam-3049	348	10	right	right	ADV
ejpam-3049	348	11	quasi	quasi	ADJ
ejpam-3049	348	12	-	-	ADJ
ejpam-3049	348	13	regular	regular	ADJ
ejpam-3049	348	14	if	if	SCONJ
ejpam-3049	348	15	for	for	ADP
ejpam-3049	348	16	every	every	DET
ejpam-3049	348	17	a	a	DET
ejpam-3049	348	18	∈	∈	PROPN
ejpam-3049	348	19	h	h	NOUN
ejpam-3049	348	20	there	there	PRON
ejpam-3049	348	21	exist	exist	VERB
ejpam-3049	348	22	x	x	NOUN
ejpam-3049	348	23	,	,	PUNCT
ejpam-3049	348	24	y	y	PROPN
ejpam-3049	348	25	∈	∈	PROPN
ejpam-3049	348	26	h	h	NOUN
ejpam-3049	348	27	such	such	ADJ
ejpam-3049	348	28	that	that	SCONJ
ejpam-3049	348	29	a	a	DET
ejpam-3049	348	30	∈	∈	NOUN
ejpam-3049	348	31	(	(	PUNCT
ejpam-3049	348	32	a	a	DET
ejpam-3049	348	33	◦	◦	NOUN
ejpam-3049	348	34	x	x	SYM
ejpam-3049	348	35	)	)	PUNCT
ejpam-3049	348	36	∗	∗	NOUN
ejpam-3049	348	37	(	(	PUNCT
ejpam-3049	348	38	a	a	DET
ejpam-3049	348	39	◦	◦	NOUN
ejpam-3049	348	40	y	y	NOUN
ejpam-3049	348	41	)	)	PUNCT
ejpam-3049	348	42	.	.	PUNCT
ejpam-3049	349	1	proposition	proposition	NOUN
ejpam-3049	349	2	2.16	2.16	NUM
ejpam-3049	349	3	.	.	PUNCT
ejpam-3049	350	1	let	let	AUX
ejpam-3049	350	2	(	(	PUNCT
ejpam-3049	350	3	h	h	NOUN
ejpam-3049	350	4	,	,	PUNCT
ejpam-3049	350	5	◦	◦	NOUN
ejpam-3049	350	6	)	)	PUNCT
ejpam-3049	350	7	be	be	VERB
ejpam-3049	350	8	an	an	DET
ejpam-3049	350	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	350	10	.	.	PUNCT
ejpam-3049	351	1	the	the	DET
ejpam-3049	351	2	following	follow	VERB
ejpam-3049	351	3	are	be	AUX
ejpam-3049	351	4	equivalent	equivalent	ADJ
ejpam-3049	351	5	:	:	PUNCT
ejpam-3049	351	6	n.	n.	PROPN
ejpam-3049	351	7	kehayopulu	kehayopulu	PROPN
ejpam-3049	351	8	/	/	SYM
ejpam-3049	351	9	eur	eur	PROPN
ejpam-3049	351	10	.	.	PUNCT
ejpam-3049	352	1	j.	j.	PROPN
ejpam-3049	352	2	pure	pure	PROPN
ejpam-3049	352	3	appl	appl	PROPN
ejpam-3049	352	4	.	.	PROPN
ejpam-3049	352	5	math	math	PROPN
ejpam-3049	352	6	,	,	PUNCT
ejpam-3049	352	7	10	10	NUM
ejpam-3049	352	8	(	(	PUNCT
ejpam-3049	352	9	5	5	NUM
ejpam-3049	352	10	)	)	PUNCT
ejpam-3049	352	11	(	(	PUNCT
ejpam-3049	352	12	2017	2017	NUM
ejpam-3049	352	13	)	)	PUNCT
ejpam-3049	352	14	,	,	PUNCT
ejpam-3049	352	15	929	929	NUM
ejpam-3049	352	16	-	-	SYM
ejpam-3049	352	17	945	945	NUM
ejpam-3049	352	18	941	941	NUM
ejpam-3049	352	19	(	(	PUNCT
ejpam-3049	352	20	1	1	NUM
ejpam-3049	352	21	)	)	PUNCT
ejpam-3049	352	22	h	h	NOUN
ejpam-3049	352	23	is	be	AUX
ejpam-3049	352	24	right	right	ADJ
ejpam-3049	352	25	quasi	quasi	ADJ
ejpam-3049	352	26	-	-	ADJ
ejpam-3049	352	27	regular	regular	ADJ
ejpam-3049	352	28	.	.	PUNCT
ejpam-3049	353	1	(	(	PUNCT
ejpam-3049	353	2	2	2	X
ejpam-3049	353	3	)	)	PUNCT
ejpam-3049	353	4	a	a	DET
ejpam-3049	353	5	∈	∈	NOUN
ejpam-3049	353	6	{	{	PUNCT
ejpam-3049	353	7	a	a	NOUN
ejpam-3049	353	8	}	}	PUNCT
ejpam-3049	353	9	∗h	∗h	NOUN
ejpam-3049	353	10	∗	∗	NOUN
ejpam-3049	353	11	{	{	PUNCT
ejpam-3049	353	12	a	a	DET
ejpam-3049	353	13	}	}	PUNCT
ejpam-3049	353	14	∗h	∗h	NOUN
ejpam-3049	353	15	for	for	ADP
ejpam-3049	353	16	every	every	DET
ejpam-3049	353	17	a	a	DET
ejpam-3049	353	18	∈	∈	PROPN
ejpam-3049	353	19	h.	h.	NOUN
ejpam-3049	353	20	(	(	PUNCT
ejpam-3049	353	21	3	3	X
ejpam-3049	353	22	)	)	PUNCT
ejpam-3049	353	23	a	a	DET
ejpam-3049	353	24	⊆	⊆	NUM
ejpam-3049	353	25	a	a	DET
ejpam-3049	353	26	∗h	∗h	NOUN
ejpam-3049	353	27	∗a	∗a	ADJ
ejpam-3049	353	28	∗h	∗h	NOUN
ejpam-3049	353	29	for	for	ADP
ejpam-3049	353	30	every	every	DET
ejpam-3049	353	31	a	a	DET
ejpam-3049	353	32	∈	∈	PROPN
ejpam-3049	353	33	p∗(h	p∗(h	PROPN
ejpam-3049	353	34	)	)	PUNCT
ejpam-3049	353	35	.	.	PUNCT
ejpam-3049	354	1	the	the	DET
ejpam-3049	354	2	right	right	ADJ
ejpam-3049	354	3	analogues	analogue	NOUN
ejpam-3049	354	4	of	of	ADP
ejpam-3049	354	5	theorems	theorem	NOUN
ejpam-3049	354	6	2.9–2.14	2.9–2.14	PRON
ejpam-3049	354	7	also	also	ADV
ejpam-3049	354	8	hold	hold	VERB
ejpam-3049	354	9	and	and	CCONJ
ejpam-3049	354	10	we	we	PRON
ejpam-3049	354	11	have	have	VERB
ejpam-3049	354	12	the	the	DET
ejpam-3049	354	13	following	following	NOUN
ejpam-3049	354	14	:	:	PUNCT
ejpam-3049	354	15	theorem	theorem	VERB
ejpam-3049	354	16	2.17	2.17	NUM
ejpam-3049	354	17	.	.	PUNCT
ejpam-3049	355	1	let	let	AUX
ejpam-3049	355	2	(	(	PUNCT
ejpam-3049	355	3	h	h	NOUN
ejpam-3049	355	4	,	,	PUNCT
ejpam-3049	355	5	◦	◦	NOUN
ejpam-3049	355	6	)	)	PUNCT
ejpam-3049	355	7	be	be	VERB
ejpam-3049	355	8	an	an	DET
ejpam-3049	355	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	355	10	.	.	PUNCT
ejpam-3049	356	1	the	the	DET
ejpam-3049	356	2	following	follow	VERB
ejpam-3049	356	3	are	be	AUX
ejpam-3049	356	4	equivalent	equivalent	ADJ
ejpam-3049	356	5	:	:	PUNCT
ejpam-3049	356	6	(	(	PUNCT
ejpam-3049	356	7	1	1	X
ejpam-3049	356	8	)	)	PUNCT
ejpam-3049	356	9	h	h	NOUN
ejpam-3049	356	10	is	be	AUX
ejpam-3049	356	11	right	right	ADJ
ejpam-3049	356	12	quasi	quasi	ADJ
ejpam-3049	356	13	-	-	ADJ
ejpam-3049	356	14	regular	regular	ADJ
ejpam-3049	356	15	.	.	PUNCT
ejpam-3049	357	1	(	(	PUNCT
ejpam-3049	357	2	2	2	X
ejpam-3049	357	3	)	)	PUNCT
ejpam-3049	357	4	a	a	DET
ejpam-3049	357	5	∩b	∩b	NOUN
ejpam-3049	357	6	⊆	⊆	NUM
ejpam-3049	357	7	a	a	DET
ejpam-3049	357	8	∗b	∗b	NOUN
ejpam-3049	357	9	for	for	ADP
ejpam-3049	357	10	every	every	DET
ejpam-3049	357	11	nonempty	nonempty	NOUN
ejpam-3049	357	12	subset	subset	VERB
ejpam-3049	357	13	a	a	DET
ejpam-3049	357	14	and	and	CCONJ
ejpam-3049	357	15	every	every	DET
ejpam-3049	357	16	ideal	ideal	ADJ
ejpam-3049	357	17	b	b	PROPN
ejpam-3049	357	18	of	of	ADP
ejpam-3049	357	19	h.	h.	PROPN
ejpam-3049	357	20	(	(	PUNCT
ejpam-3049	357	21	3	3	X
ejpam-3049	357	22	)	)	PUNCT
ejpam-3049	357	23	a	a	DET
ejpam-3049	357	24	∩b	∩b	NOUN
ejpam-3049	357	25	⊆	⊆	NUM
ejpam-3049	357	26	a	a	DET
ejpam-3049	357	27	∗b	∗b	NOUN
ejpam-3049	357	28	for	for	ADP
ejpam-3049	357	29	every	every	DET
ejpam-3049	357	30	bi	bi	NOUN
ejpam-3049	357	31	-	-	NOUN
ejpam-3049	357	32	ideal	ideal	ADJ
ejpam-3049	357	33	a	a	PRON
ejpam-3049	358	1	and	and	CCONJ
ejpam-3049	358	2	every	every	DET
ejpam-3049	358	3	ideal	ideal	ADJ
ejpam-3049	358	4	b	b	PROPN
ejpam-3049	358	5	of	of	ADP
ejpam-3049	358	6	h.	h.	PROPN
ejpam-3049	358	7	(	(	PUNCT
ejpam-3049	358	8	4	4	NUM
ejpam-3049	358	9	)	)	PUNCT
ejpam-3049	358	10	a	a	DET
ejpam-3049	358	11	∩b	∩b	NOUN
ejpam-3049	358	12	⊆	⊆	NUM
ejpam-3049	358	13	a	a	DET
ejpam-3049	358	14	∗b	∗b	NOUN
ejpam-3049	358	15	for	for	ADP
ejpam-3049	358	16	every	every	DET
ejpam-3049	358	17	right	right	ADJ
ejpam-3049	358	18	ideal	ideal	NOUN
ejpam-3049	358	19	a	a	PRON
ejpam-3049	358	20	and	and	CCONJ
ejpam-3049	358	21	every	every	DET
ejpam-3049	358	22	ideal	ideal	ADJ
ejpam-3049	358	23	b	b	PROPN
ejpam-3049	358	24	of	of	ADP
ejpam-3049	358	25	h.	h.	PROPN
ejpam-3049	358	26	(	(	PUNCT
ejpam-3049	358	27	5	5	NUM
ejpam-3049	358	28	)	)	PUNCT
ejpam-3049	358	29	r(a	r(a	ADJ
ejpam-3049	358	30	)	)	PUNCT
ejpam-3049	358	31	∩	∩	NOUN
ejpam-3049	358	32	i(a	i(a	PROPN
ejpam-3049	358	33	)	)	PUNCT
ejpam-3049	358	34	⊆	⊆	NUM
ejpam-3049	358	35	r(a	r(a	NUM
ejpam-3049	358	36	)	)	PUNCT
ejpam-3049	358	37	∗	∗	PROPN
ejpam-3049	358	38	i(a	i(a	PROPN
ejpam-3049	358	39	)	)	PUNCT
ejpam-3049	358	40	for	for	ADP
ejpam-3049	358	41	every	every	DET
ejpam-3049	358	42	a	a	DET
ejpam-3049	358	43	∈	∈	PROPN
ejpam-3049	358	44	p∗(h	p∗(h	PROPN
ejpam-3049	358	45	)	)	PUNCT
ejpam-3049	358	46	.	.	PUNCT
ejpam-3049	359	1	(	(	PUNCT
ejpam-3049	359	2	6	6	NUM
ejpam-3049	359	3	)	)	PUNCT
ejpam-3049	359	4	r(a	r(a	ADJ
ejpam-3049	359	5	)	)	PUNCT
ejpam-3049	359	6	∩	∩	NOUN
ejpam-3049	359	7	i(a	i(a	PROPN
ejpam-3049	359	8	)	)	PUNCT
ejpam-3049	359	9	⊆	⊆	NUM
ejpam-3049	359	10	r(a	r(a	NUM
ejpam-3049	359	11	)	)	PUNCT
ejpam-3049	359	12	∗	∗	PROPN
ejpam-3049	359	13	i(a	i(a	PROPN
ejpam-3049	359	14	)	)	PUNCT
ejpam-3049	359	15	for	for	ADP
ejpam-3049	359	16	every	every	DET
ejpam-3049	359	17	a	a	DET
ejpam-3049	359	18	∈	∈	PROPN
ejpam-3049	359	19	h.	h.	NOUN
ejpam-3049	359	20	let	let	VERB
ejpam-3049	359	21	us	we	PRON
ejpam-3049	359	22	prove	prove	VERB
ejpam-3049	359	23	the	the	DET
ejpam-3049	359	24	implication	implication	NOUN
ejpam-3049	359	25	(	(	PUNCT
ejpam-3049	359	26	1)⇒	1)⇒	NUM
ejpam-3049	359	27	(	(	PUNCT
ejpam-3049	359	28	2	2	NUM
ejpam-3049	359	29	):	):	PUNCT
ejpam-3049	359	30	let	let	VERB
ejpam-3049	359	31	a	a	PRON
ejpam-3049	359	32	be	be	AUX
ejpam-3049	359	33	a	a	DET
ejpam-3049	359	34	nonempty	nonempty	ADJ
ejpam-3049	359	35	subset	subset	NOUN
ejpam-3049	359	36	of	of	ADP
ejpam-3049	359	37	h	h	NOUN
ejpam-3049	359	38	,	,	PUNCT
ejpam-3049	359	39	b	b	PROPN
ejpam-3049	359	40	an	an	DET
ejpam-3049	359	41	ideal	ideal	NOUN
ejpam-3049	359	42	of	of	ADP
ejpam-3049	359	43	h	h	NOUN
ejpam-3049	359	44	and	and	CCONJ
ejpam-3049	359	45	a	a	DET
ejpam-3049	359	46	∈	∈	PROPN
ejpam-3049	359	47	a	a	DET
ejpam-3049	359	48	∩b	∩b	NOUN
ejpam-3049	359	49	.	.	PUNCT
ejpam-3049	360	1	since	since	SCONJ
ejpam-3049	360	2	h	h	NOUN
ejpam-3049	360	3	is	be	AUX
ejpam-3049	360	4	right	right	ADJ
ejpam-3049	360	5	quasi	quasi	ADJ
ejpam-3049	360	6	-	-	ADJ
ejpam-3049	360	7	regular	regular	ADJ
ejpam-3049	360	8	,	,	PUNCT
ejpam-3049	360	9	we	we	PRON
ejpam-3049	360	10	have	have	VERB
ejpam-3049	360	11	a	a	DET
ejpam-3049	360	12	∈	∈	NOUN
ejpam-3049	360	13	{	{	PUNCT
ejpam-3049	360	14	a	a	NOUN
ejpam-3049	360	15	}	}	PUNCT
ejpam-3049	360	16	∗h	∗h	NOUN
ejpam-3049	360	17	∗	∗	NOUN
ejpam-3049	360	18	{	{	PUNCT
ejpam-3049	360	19	a	a	DET
ejpam-3049	360	20	}	}	PUNCT
ejpam-3049	360	21	∗h	∗h	NOUN
ejpam-3049	360	22	⊆	⊆	NUM
ejpam-3049	360	23	a	a	DET
ejpam-3049	360	24	∗	∗	NOUN
ejpam-3049	360	25	(	(	PUNCT
ejpam-3049	360	26	h	h	NOUN
ejpam-3049	360	27	∗b	∗b	PROPN
ejpam-3049	360	28	∗h	∗h	NOUN
ejpam-3049	360	29	)	)	PUNCT
ejpam-3049	360	30	⊆	⊆	NUM
ejpam-3049	360	31	a	a	DET
ejpam-3049	360	32	∗b	∗b	PROPN
ejpam-3049	360	33	.	.	PUNCT
ejpam-3049	361	1	�	�	PROPN
ejpam-3049	361	2	theorem	theorem	VERB
ejpam-3049	361	3	2.18	2.18	NUM
ejpam-3049	361	4	.	.	PUNCT
ejpam-3049	362	1	an	an	DET
ejpam-3049	362	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	362	3	(	(	PUNCT
ejpam-3049	362	4	h	h	NOUN
ejpam-3049	362	5	,	,	PUNCT
ejpam-3049	362	6	◦	◦	NOUN
ejpam-3049	362	7	)	)	PUNCT
ejpam-3049	362	8	is	be	AUX
ejpam-3049	362	9	right	right	ADJ
ejpam-3049	362	10	quasi	quasi	ADJ
ejpam-3049	362	11	-	-	ADJ
ejpam-3049	362	12	regular	regular	ADJ
ejpam-3049	362	13	if	if	SCONJ
ejpam-3049	362	14	and	and	CCONJ
ejpam-3049	362	15	only	only	ADV
ejpam-3049	362	16	if	if	SCONJ
ejpam-3049	362	17	,	,	PUNCT
ejpam-3049	362	18	for	for	ADP
ejpam-3049	362	19	any	any	DET
ejpam-3049	362	20	right	right	ADJ
ejpam-3049	362	21	ideals	ideal	NOUN
ejpam-3049	362	22	a	a	PRON
ejpam-3049	362	23	and	and	CCONJ
ejpam-3049	362	24	b	b	NOUN
ejpam-3049	362	25	of	of	ADP
ejpam-3049	362	26	h	h	NOUN
ejpam-3049	362	27	,	,	PUNCT
ejpam-3049	362	28	we	we	PRON
ejpam-3049	362	29	have	have	VERB
ejpam-3049	362	30	a	a	DET
ejpam-3049	362	31	∩b	∩b	NOUN
ejpam-3049	362	32	⊆	⊆	NUM
ejpam-3049	362	33	a	a	DET
ejpam-3049	362	34	∗b	∗b	PROPN
ejpam-3049	362	35	.	.	PUNCT
ejpam-3049	363	1	theorem	theorem	VERB
ejpam-3049	363	2	2.19	2.19	NUM
ejpam-3049	363	3	.	.	PUNCT
ejpam-3049	364	1	an	an	DET
ejpam-3049	364	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	364	3	(	(	PUNCT
ejpam-3049	364	4	h	h	NOUN
ejpam-3049	364	5	,	,	PUNCT
ejpam-3049	364	6	◦	◦	NOUN
ejpam-3049	364	7	)	)	PUNCT
ejpam-3049	364	8	is	be	AUX
ejpam-3049	364	9	right	right	ADJ
ejpam-3049	364	10	quasi	quasi	ADJ
ejpam-3049	364	11	-	-	ADJ
ejpam-3049	364	12	regular	regular	ADJ
ejpam-3049	364	13	if	if	SCONJ
ejpam-3049	364	14	and	and	CCONJ
ejpam-3049	364	15	only	only	ADV
ejpam-3049	364	16	if	if	SCONJ
ejpam-3049	364	17	the	the	DET
ejpam-3049	364	18	right	right	ADJ
ejpam-3049	364	19	ideals	ideal	NOUN
ejpam-3049	364	20	of	of	ADP
ejpam-3049	364	21	h	h	NOUN
ejpam-3049	364	22	are	be	AUX
ejpam-3049	364	23	idempotent	idempotent	ADJ
ejpam-3049	364	24	.	.	PUNCT
ejpam-3049	365	1	theorem	theorem	VERB
ejpam-3049	365	2	2.20	2.20	NUM
ejpam-3049	365	3	.	.	PUNCT
ejpam-3049	366	1	let	let	AUX
ejpam-3049	366	2	(	(	PUNCT
ejpam-3049	366	3	h	h	NOUN
ejpam-3049	366	4	,	,	PUNCT
ejpam-3049	366	5	◦	◦	NOUN
ejpam-3049	366	6	)	)	PUNCT
ejpam-3049	366	7	be	be	VERB
ejpam-3049	366	8	an	an	DET
ejpam-3049	366	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	366	10	.	.	PUNCT
ejpam-3049	367	1	the	the	DET
ejpam-3049	367	2	following	follow	VERB
ejpam-3049	367	3	are	be	AUX
ejpam-3049	367	4	equivalent	equivalent	ADJ
ejpam-3049	367	5	:	:	PUNCT
ejpam-3049	367	6	(	(	PUNCT
ejpam-3049	367	7	1	1	X
ejpam-3049	367	8	)	)	PUNCT
ejpam-3049	367	9	h	h	NOUN
ejpam-3049	367	10	is	be	AUX
ejpam-3049	367	11	right	right	ADJ
ejpam-3049	367	12	quasi	quasi	ADJ
ejpam-3049	367	13	-	-	ADJ
ejpam-3049	367	14	regular	regular	ADJ
ejpam-3049	367	15	.	.	PUNCT
ejpam-3049	368	1	(	(	PUNCT
ejpam-3049	368	2	2	2	X
ejpam-3049	368	3	)	)	PUNCT
ejpam-3049	368	4	f	f	NOUN
ejpam-3049	368	5	∧	∧	PROPN
ejpam-3049	368	6	g	g	PROPN
ejpam-3049	368	7	�	�	PROPN
ejpam-3049	368	8	f	f	PROPN
ejpam-3049	368	9	◦	◦	VERB
ejpam-3049	368	10	g	g	NOUN
ejpam-3049	368	11	for	for	ADP
ejpam-3049	368	12	every	every	DET
ejpam-3049	368	13	fuzzy	fuzzy	ADJ
ejpam-3049	368	14	subset	subset	NOUN
ejpam-3049	368	15	f	f	NOUN
ejpam-3049	368	16	and	and	CCONJ
ejpam-3049	368	17	every	every	DET
ejpam-3049	368	18	fuzzy	fuzzy	ADJ
ejpam-3049	368	19	ideal	ideal	NOUN
ejpam-3049	368	20	g	g	PROPN
ejpam-3049	368	21	of	of	ADP
ejpam-3049	368	22	h.	h.	PROPN
ejpam-3049	368	23	(	(	PUNCT
ejpam-3049	368	24	3	3	NUM
ejpam-3049	368	25	)	)	PUNCT
ejpam-3049	368	26	f	f	NOUN
ejpam-3049	369	1	∧	∧	PROPN
ejpam-3049	369	2	g	g	PROPN
ejpam-3049	369	3	�	�	PROPN
ejpam-3049	369	4	f	f	PROPN
ejpam-3049	369	5	◦	◦	VERB
ejpam-3049	369	6	g	g	NOUN
ejpam-3049	369	7	for	for	ADP
ejpam-3049	369	8	every	every	DET
ejpam-3049	369	9	fuzzy	fuzzy	ADJ
ejpam-3049	369	10	bi	bi	ADJ
ejpam-3049	369	11	-	-	ADJ
ejpam-3049	369	12	ideal	ideal	ADJ
ejpam-3049	369	13	f	f	NOUN
ejpam-3049	369	14	and	and	CCONJ
ejpam-3049	369	15	every	every	DET
ejpam-3049	369	16	fuzzy	fuzzy	ADJ
ejpam-3049	369	17	ideal	ideal	NOUN
ejpam-3049	369	18	g	g	PROPN
ejpam-3049	369	19	of	of	ADP
ejpam-3049	369	20	h.	h.	PROPN
ejpam-3049	369	21	(	(	PUNCT
ejpam-3049	369	22	4	4	NUM
ejpam-3049	369	23	)	)	PUNCT
ejpam-3049	369	24	f	f	NOUN
ejpam-3049	370	1	∧	∧	PROPN
ejpam-3049	370	2	g	g	PROPN
ejpam-3049	370	3	�	�	PROPN
ejpam-3049	370	4	f	f	PROPN
ejpam-3049	370	5	◦	◦	VERB
ejpam-3049	370	6	g	g	NOUN
ejpam-3049	370	7	for	for	ADP
ejpam-3049	370	8	every	every	DET
ejpam-3049	370	9	fuzzy	fuzzy	ADJ
ejpam-3049	370	10	right	right	ADJ
ejpam-3049	370	11	ideal	ideal	NOUN
ejpam-3049	370	12	f	f	PROPN
ejpam-3049	370	13	and	and	CCONJ
ejpam-3049	370	14	every	every	DET
ejpam-3049	370	15	fuzzy	fuzzy	ADJ
ejpam-3049	370	16	ideal	ideal	NOUN
ejpam-3049	370	17	g	g	PROPN
ejpam-3049	370	18	of	of	ADP
ejpam-3049	370	19	h.	h.	PROPN
ejpam-3049	370	20	theorem	theorem	VERB
ejpam-3049	370	21	2.21	2.21	NUM
ejpam-3049	370	22	.	.	PUNCT
ejpam-3049	371	1	an	an	DET
ejpam-3049	371	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	371	3	(	(	PUNCT
ejpam-3049	371	4	h	h	NOUN
ejpam-3049	371	5	,	,	PUNCT
ejpam-3049	371	6	◦	◦	NOUN
ejpam-3049	371	7	)	)	PUNCT
ejpam-3049	371	8	is	be	AUX
ejpam-3049	371	9	right	right	ADJ
ejpam-3049	371	10	quasi	quasi	ADJ
ejpam-3049	371	11	-	-	ADJ
ejpam-3049	371	12	regular	regular	ADJ
ejpam-3049	371	13	if	if	SCONJ
ejpam-3049	371	14	and	and	CCONJ
ejpam-3049	371	15	only	only	ADV
ejpam-3049	371	16	if	if	SCONJ
ejpam-3049	371	17	for	for	ADP
ejpam-3049	371	18	any	any	DET
ejpam-3049	371	19	fuzzy	fuzzy	ADJ
ejpam-3049	371	20	right	right	ADJ
ejpam-3049	371	21	ideals	ideal	NOUN
ejpam-3049	371	22	f	f	PROPN
ejpam-3049	371	23	and	and	CCONJ
ejpam-3049	371	24	g	g	PROPN
ejpam-3049	371	25	of	of	ADP
ejpam-3049	371	26	h	h	NOUN
ejpam-3049	371	27	,	,	PUNCT
ejpam-3049	371	28	we	we	PRON
ejpam-3049	371	29	have	have	VERB
ejpam-3049	371	30	f	f	PROPN
ejpam-3049	371	31	∧	∧	PROPN
ejpam-3049	371	32	g	g	PROPN
ejpam-3049	371	33	�	�	PROPN
ejpam-3049	371	34	f	f	PROPN
ejpam-3049	372	1	◦	◦	NOUN
ejpam-3049	372	2	g.	g.	PROPN
ejpam-3049	372	3	a	a	DET
ejpam-3049	372	4	fuzzy	fuzzy	ADJ
ejpam-3049	372	5	subset	subset	NOUN
ejpam-3049	372	6	f	f	PROPN
ejpam-3049	372	7	of	of	ADP
ejpam-3049	372	8	an	an	DET
ejpam-3049	372	9	hypergroupoid	hypergroupoid	NOUN
ejpam-3049	372	10	is	be	AUX
ejpam-3049	372	11	called	call	VERB
ejpam-3049	372	12	idempotent	idempotent	ADJ
ejpam-3049	372	13	if	if	SCONJ
ejpam-3049	372	14	f	f	PROPN
ejpam-3049	372	15	◦	◦	NOUN
ejpam-3049	372	16	f	f	X
ejpam-3049	372	17	=	=	SYM
ejpam-3049	372	18	f	f	PROPN
ejpam-3049	372	19	.	.	PUNCT
ejpam-3049	373	1	theorem	theorem	VERB
ejpam-3049	373	2	2.22	2.22	NUM
ejpam-3049	373	3	.	.	PUNCT
ejpam-3049	374	1	an	an	DET
ejpam-3049	374	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	374	3	(	(	PUNCT
ejpam-3049	374	4	h	h	NOUN
ejpam-3049	374	5	,	,	PUNCT
ejpam-3049	374	6	◦	◦	NOUN
ejpam-3049	374	7	)	)	PUNCT
ejpam-3049	374	8	is	be	AUX
ejpam-3049	374	9	right	right	ADJ
ejpam-3049	374	10	quasi	quasi	ADJ
ejpam-3049	374	11	-	-	ADJ
ejpam-3049	374	12	regular	regular	ADJ
ejpam-3049	374	13	if	if	SCONJ
ejpam-3049	374	14	and	and	CCONJ
ejpam-3049	374	15	only	only	ADV
ejpam-3049	374	16	if	if	SCONJ
ejpam-3049	374	17	the	the	DET
ejpam-3049	374	18	fuzzy	fuzzy	ADJ
ejpam-3049	374	19	right	right	ADJ
ejpam-3049	374	20	ideals	ideal	NOUN
ejpam-3049	374	21	of	of	ADP
ejpam-3049	374	22	h	h	NOUN
ejpam-3049	374	23	are	be	AUX
ejpam-3049	374	24	idempotent	idempotent	ADJ
ejpam-3049	374	25	.	.	PUNCT
ejpam-3049	375	1	n.	n.	PROPN
ejpam-3049	375	2	kehayopulu	kehayopulu	PROPN
ejpam-3049	375	3	/	/	SYM
ejpam-3049	375	4	eur	eur	PROPN
ejpam-3049	375	5	.	.	PUNCT
ejpam-3049	376	1	j.	j.	PROPN
ejpam-3049	376	2	pure	pure	PROPN
ejpam-3049	376	3	appl	appl	PROPN
ejpam-3049	376	4	.	.	PROPN
ejpam-3049	376	5	math	math	PROPN
ejpam-3049	376	6	,	,	PUNCT
ejpam-3049	376	7	10	10	NUM
ejpam-3049	376	8	(	(	PUNCT
ejpam-3049	376	9	5	5	NUM
ejpam-3049	376	10	)	)	PUNCT
ejpam-3049	376	11	(	(	PUNCT
ejpam-3049	376	12	2017	2017	NUM
ejpam-3049	376	13	)	)	PUNCT
ejpam-3049	376	14	,	,	PUNCT
ejpam-3049	376	15	929	929	NUM
ejpam-3049	376	16	-	-	SYM
ejpam-3049	376	17	945	945	NUM
ejpam-3049	376	18	942	942	NUM
ejpam-3049	376	19	the	the	DET
ejpam-3049	376	20	concept	concept	NOUN
ejpam-3049	376	21	of	of	ADP
ejpam-3049	376	22	semisimple	semisimple	NOUN
ejpam-3049	376	23	semigroups	semigroup	NOUN
ejpam-3049	376	24	can	can	AUX
ejpam-3049	376	25	be	be	AUX
ejpam-3049	376	26	naturally	naturally	ADV
ejpam-3049	376	27	transferred	transfer	VERB
ejpam-3049	376	28	to	to	ADP
ejpam-3049	376	29	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	376	30	as	as	SCONJ
ejpam-3049	376	31	follows	follow	VERB
ejpam-3049	376	32	:	:	PUNCT
ejpam-3049	376	33	definition	definition	NOUN
ejpam-3049	376	34	2.23	2.23	NUM
ejpam-3049	376	35	.	.	PUNCT
ejpam-3049	377	1	an	an	DET
ejpam-3049	377	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	377	3	(	(	PUNCT
ejpam-3049	377	4	h	h	NOUN
ejpam-3049	377	5	,	,	PUNCT
ejpam-3049	377	6	◦	◦	NOUN
ejpam-3049	377	7	)	)	PUNCT
ejpam-3049	377	8	is	be	AUX
ejpam-3049	377	9	called	call	VERB
ejpam-3049	377	10	semisimple	semisimple	NOUN
ejpam-3049	377	11	if	if	SCONJ
ejpam-3049	377	12	for	for	ADP
ejpam-3049	377	13	every	every	DET
ejpam-3049	377	14	a	a	DET
ejpam-3049	377	15	∈	∈	PROPN
ejpam-3049	377	16	h	h	NOUN
ejpam-3049	377	17	there	there	PRON
ejpam-3049	377	18	exist	exist	VERB
ejpam-3049	377	19	x	x	NOUN
ejpam-3049	377	20	,	,	PUNCT
ejpam-3049	377	21	y	y	PROPN
ejpam-3049	377	22	,	,	PUNCT
ejpam-3049	377	23	z	z	PROPN
ejpam-3049	377	24	∈	∈	PROPN
ejpam-3049	377	25	h	h	NOUN
ejpam-3049	377	26	such	such	ADJ
ejpam-3049	377	27	that	that	SCONJ
ejpam-3049	377	28	a	a	DET
ejpam-3049	377	29	∈	∈	NOUN
ejpam-3049	377	30	(	(	PUNCT
ejpam-3049	377	31	x	x	SYM
ejpam-3049	377	32	◦	◦	VERB
ejpam-3049	377	33	a	a	X
ejpam-3049	377	34	)	)	PUNCT
ejpam-3049	377	35	∗	∗	NOUN
ejpam-3049	377	36	(	(	PUNCT
ejpam-3049	377	37	y	y	NOUN
ejpam-3049	377	38	◦	◦	VERB
ejpam-3049	377	39	a	a	X
ejpam-3049	377	40	)	)	PUNCT
ejpam-3049	377	41	∗	∗	NOUN
ejpam-3049	377	42	{	{	PUNCT
ejpam-3049	377	43	z	z	NOUN
ejpam-3049	377	44	}	}	PUNCT
ejpam-3049	377	45	.	.	PUNCT
ejpam-3049	378	1	proposition	proposition	NOUN
ejpam-3049	378	2	2.24	2.24	NUM
ejpam-3049	378	3	.	.	PUNCT
ejpam-3049	379	1	let	let	AUX
ejpam-3049	379	2	(	(	PUNCT
ejpam-3049	379	3	h	h	NOUN
ejpam-3049	379	4	,	,	PUNCT
ejpam-3049	379	5	◦	◦	NOUN
ejpam-3049	379	6	)	)	PUNCT
ejpam-3049	379	7	be	be	VERB
ejpam-3049	379	8	an	an	DET
ejpam-3049	379	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	379	10	.	.	PUNCT
ejpam-3049	380	1	the	the	DET
ejpam-3049	380	2	following	follow	VERB
ejpam-3049	380	3	are	be	AUX
ejpam-3049	380	4	equivalent	equivalent	ADJ
ejpam-3049	380	5	:	:	PUNCT
ejpam-3049	380	6	(	(	PUNCT
ejpam-3049	380	7	1	1	X
ejpam-3049	380	8	)	)	PUNCT
ejpam-3049	380	9	h	h	NOUN
ejpam-3049	380	10	is	be	AUX
ejpam-3049	380	11	semisimple	semisimple	ADJ
ejpam-3049	380	12	.	.	PUNCT
ejpam-3049	381	1	(	(	PUNCT
ejpam-3049	381	2	2	2	X
ejpam-3049	381	3	)	)	PUNCT
ejpam-3049	381	4	a	a	DET
ejpam-3049	381	5	∈	∈	PROPN
ejpam-3049	381	6	h	h	NOUN
ejpam-3049	381	7	∗	∗	NOUN
ejpam-3049	381	8	{	{	PUNCT
ejpam-3049	381	9	a	a	DET
ejpam-3049	381	10	}	}	PUNCT
ejpam-3049	381	11	∗h	∗h	NOUN
ejpam-3049	381	12	∗	∗	NOUN
ejpam-3049	381	13	{	{	PUNCT
ejpam-3049	381	14	a	a	DET
ejpam-3049	381	15	}	}	PUNCT
ejpam-3049	381	16	∗h	∗h	NOUN
ejpam-3049	381	17	for	for	ADP
ejpam-3049	381	18	every	every	DET
ejpam-3049	381	19	a	a	DET
ejpam-3049	381	20	∈	∈	PROPN
ejpam-3049	381	21	h.	h.	NOUN
ejpam-3049	381	22	(	(	PUNCT
ejpam-3049	381	23	3	3	X
ejpam-3049	381	24	)	)	PUNCT
ejpam-3049	381	25	a	a	DET
ejpam-3049	381	26	⊆	⊆	NUM
ejpam-3049	381	27	h	h	NOUN
ejpam-3049	381	28	∗a	∗a	ADJ
ejpam-3049	381	29	∗h	∗h	NOUN
ejpam-3049	381	30	∗a	∗a	ADJ
ejpam-3049	381	31	∗h	∗h	NOUN
ejpam-3049	381	32	for	for	ADP
ejpam-3049	381	33	every	every	DET
ejpam-3049	381	34	a	a	DET
ejpam-3049	381	35	∈	∈	PROPN
ejpam-3049	381	36	p∗(h	p∗(h	PROPN
ejpam-3049	381	37	)	)	PUNCT
ejpam-3049	381	38	.	.	PUNCT
ejpam-3049	382	1	let	let	VERB
ejpam-3049	382	2	us	we	PRON
ejpam-3049	382	3	prove	prove	VERB
ejpam-3049	382	4	the	the	DET
ejpam-3049	382	5	implication	implication	NOUN
ejpam-3049	382	6	(	(	PUNCT
ejpam-3049	382	7	3)⇒	3)⇒	NUM
ejpam-3049	382	8	(	(	PUNCT
ejpam-3049	382	9	1	1	NUM
ejpam-3049	382	10	):	):	PUNCT
ejpam-3049	382	11	let	let	VERB
ejpam-3049	382	12	a	a	DET
ejpam-3049	382	13	∈	∈	PROPN
ejpam-3049	382	14	h.	h.	NOUN
ejpam-3049	382	15	by	by	ADP
ejpam-3049	382	16	(	(	PUNCT
ejpam-3049	382	17	3	3	NUM
ejpam-3049	382	18	)	)	PUNCT
ejpam-3049	382	19	,	,	PUNCT
ejpam-3049	382	20	we	we	PRON
ejpam-3049	382	21	have	have	VERB
ejpam-3049	382	22	{	{	PUNCT
ejpam-3049	382	23	a	a	PRON
ejpam-3049	382	24	}	}	PUNCT
ejpam-3049	382	25	⊆	⊆	NUM
ejpam-3049	382	26	(	(	PUNCT
ejpam-3049	382	27	(	(	PUNCT
ejpam-3049	382	28	h	h	NOUN
ejpam-3049	382	29	∗	∗	NOUN
ejpam-3049	382	30	{	{	PUNCT
ejpam-3049	382	31	a	a	NOUN
ejpam-3049	382	32	}	}	PUNCT
ejpam-3049	382	33	)	)	PUNCT
ejpam-3049	382	34	∗	∗	NOUN
ejpam-3049	382	35	(	(	PUNCT
ejpam-3049	382	36	h	h	NOUN
ejpam-3049	382	37	∗	∗	NOUN
ejpam-3049	382	38	{	{	PUNCT
ejpam-3049	382	39	a	a	NOUN
ejpam-3049	382	40	}	}	PUNCT
ejpam-3049	382	41	)	)	PUNCT
ejpam-3049	382	42	)	)	PUNCT
ejpam-3049	383	1	∗h	∗h	NOUN
ejpam-3049	383	2	.	.	PUNCT
ejpam-3049	384	1	then	then	ADV
ejpam-3049	384	2	a	a	DET
ejpam-3049	384	3	∈	∈	PROPN
ejpam-3049	384	4	x	x	PUNCT
ejpam-3049	384	5	◦	◦	NOUN
ejpam-3049	384	6	z	z	NOUN
ejpam-3049	384	7	for	for	ADP
ejpam-3049	384	8	some	some	DET
ejpam-3049	384	9	x	x	SYM
ejpam-3049	384	10	∈	∈	PROPN
ejpam-3049	384	11	(	(	PUNCT
ejpam-3049	384	12	h	h	NOUN
ejpam-3049	384	13	∗	∗	NOUN
ejpam-3049	384	14	{	{	PUNCT
ejpam-3049	384	15	a	a	NOUN
ejpam-3049	384	16	}	}	PUNCT
ejpam-3049	384	17	)	)	PUNCT
ejpam-3049	384	18	∗	∗	NOUN
ejpam-3049	384	19	(	(	PUNCT
ejpam-3049	384	20	h	h	NOUN
ejpam-3049	384	21	∗	∗	NOUN
ejpam-3049	384	22	{	{	PUNCT
ejpam-3049	384	23	a	a	NOUN
ejpam-3049	384	24	}	}	PUNCT
ejpam-3049	384	25	)	)	PUNCT
ejpam-3049	384	26	,	,	PUNCT
ejpam-3049	384	27	z	z	PROPN
ejpam-3049	384	28	∈	∈	PROPN
ejpam-3049	384	29	h.	h.	NOUN
ejpam-3049	385	1	then	then	ADV
ejpam-3049	385	2	x	x	SYM
ejpam-3049	385	3	∈	∈	PROPN
ejpam-3049	385	4	u	u	NOUN
ejpam-3049	385	5	◦	◦	NOUN
ejpam-3049	385	6	v	v	NOUN
ejpam-3049	385	7	for	for	ADP
ejpam-3049	385	8	some	some	DET
ejpam-3049	385	9	u	u	NOUN
ejpam-3049	385	10	,	,	PUNCT
ejpam-3049	385	11	v	v	PROPN
ejpam-3049	385	12	∈	∈	PROPN
ejpam-3049	385	13	h	h	NOUN
ejpam-3049	385	14	∗	∗	NOUN
ejpam-3049	385	15	{	{	PUNCT
ejpam-3049	385	16	a	a	NOUN
ejpam-3049	385	17	}	}	PUNCT
ejpam-3049	385	18	,	,	PUNCT
ejpam-3049	385	19	u	u	PROPN
ejpam-3049	385	20	∈	∈	PROPN
ejpam-3049	385	21	x	x	PUNCT
ejpam-3049	385	22	◦	◦	VERB
ejpam-3049	385	23	a	a	PRON
ejpam-3049	385	24	for	for	ADP
ejpam-3049	385	25	some	some	DET
ejpam-3049	385	26	x	x	SYM
ejpam-3049	385	27	∈	∈	PROPN
ejpam-3049	385	28	h	h	NOUN
ejpam-3049	385	29	and	and	CCONJ
ejpam-3049	385	30	v	v	ADP
ejpam-3049	385	31	∈	∈	PROPN
ejpam-3049	385	32	y	y	PROPN
ejpam-3049	385	33	◦	◦	VERB
ejpam-3049	385	34	a	a	PRON
ejpam-3049	385	35	for	for	ADP
ejpam-3049	385	36	some	some	DET
ejpam-3049	385	37	y	y	PROPN
ejpam-3049	385	38	∈	∈	PROPN
ejpam-3049	385	39	h.	h.	NOUN
ejpam-3049	385	40	then	then	ADV
ejpam-3049	385	41	a	a	DET
ejpam-3049	385	42	∈	∈	PROPN
ejpam-3049	385	43	x	x	PUNCT
ejpam-3049	385	44	◦	◦	NOUN
ejpam-3049	385	45	z	z	NUM
ejpam-3049	386	1	,	,	PUNCT
ejpam-3049	386	2	x	x	SYM
ejpam-3049	386	3	∈	∈	NOUN
ejpam-3049	386	4	u	u	NOUN
ejpam-3049	386	5	◦	◦	NOUN
ejpam-3049	386	6	v	v	NOUN
ejpam-3049	386	7	,	,	PUNCT
ejpam-3049	386	8	u	u	NOUN
ejpam-3049	386	9	∈	∈	PROPN
ejpam-3049	386	10	x	x	PUNCT
ejpam-3049	386	11	◦	◦	NOUN
ejpam-3049	386	12	a	a	PRON
ejpam-3049	386	13	,	,	PUNCT
ejpam-3049	386	14	v	v	NOUN
ejpam-3049	386	15	∈	∈	PROPN
ejpam-3049	386	16	y	y	PROPN
ejpam-3049	386	17	◦	◦	NOUN
ejpam-3049	386	18	a	a	PRON
ejpam-3049	386	19	,	,	PUNCT
ejpam-3049	386	20	z	z	PROPN
ejpam-3049	386	21	∈	∈	PROPN
ejpam-3049	386	22	h.	h.	NOUN
ejpam-3049	386	23	thus	thus	ADV
ejpam-3049	386	24	we	we	PRON
ejpam-3049	386	25	have	have	VERB
ejpam-3049	386	26	a	a	DET
ejpam-3049	386	27	∈	∈	NOUN
ejpam-3049	386	28	x	x	SYM
ejpam-3049	386	29	◦	◦	NOUN
ejpam-3049	386	30	z	z	NOUN
ejpam-3049	386	31	=	=	SYM
ejpam-3049	386	32	{	{	PUNCT
ejpam-3049	386	33	x	x	NOUN
ejpam-3049	386	34	}	}	PUNCT
ejpam-3049	386	35	∗	∗	NOUN
ejpam-3049	386	36	{	{	PUNCT
ejpam-3049	386	37	z	z	NOUN
ejpam-3049	386	38	}	}	PUNCT
ejpam-3049	386	39	⊆	⊆	NUM
ejpam-3049	386	40	(	(	PUNCT
ejpam-3049	386	41	u	u	NOUN
ejpam-3049	386	42	◦	◦	NOUN
ejpam-3049	386	43	v	v	NOUN
ejpam-3049	386	44	)	)	PUNCT
ejpam-3049	386	45	∗	∗	NOUN
ejpam-3049	386	46	{	{	PUNCT
ejpam-3049	386	47	z	z	NOUN
ejpam-3049	386	48	}	}	PUNCT
ejpam-3049	386	49	=	=	SYM
ejpam-3049	386	50	{	{	PUNCT
ejpam-3049	386	51	u	u	NOUN
ejpam-3049	386	52	}	}	PUNCT
ejpam-3049	386	53	∗	∗	NOUN
ejpam-3049	386	54	{	{	PUNCT
ejpam-3049	386	55	v	v	NOUN
ejpam-3049	386	56	}	}	PUNCT
ejpam-3049	386	57	∗	∗	NOUN
ejpam-3049	386	58	{	{	PUNCT
ejpam-3049	386	59	z	z	NOUN
ejpam-3049	386	60	}	}	PUNCT
ejpam-3049	386	61	⊆	⊆	NUM
ejpam-3049	386	62	(	(	PUNCT
ejpam-3049	386	63	x	x	SYM
ejpam-3049	386	64	◦	◦	VERB
ejpam-3049	386	65	a	a	X
ejpam-3049	386	66	)	)	PUNCT
ejpam-3049	386	67	∗	∗	NOUN
ejpam-3049	386	68	(	(	PUNCT
ejpam-3049	386	69	y	y	NOUN
ejpam-3049	386	70	◦	◦	VERB
ejpam-3049	386	71	a	a	X
ejpam-3049	386	72	)	)	PUNCT
ejpam-3049	386	73	∗	∗	NOUN
ejpam-3049	386	74	{	{	PUNCT
ejpam-3049	386	75	z	z	NOUN
ejpam-3049	386	76	}	}	PUNCT
ejpam-3049	386	77	.	.	PUNCT
ejpam-3049	387	1	since	since	SCONJ
ejpam-3049	387	2	x	x	X
ejpam-3049	387	3	,	,	PUNCT
ejpam-3049	387	4	y	y	PROPN
ejpam-3049	387	5	,	,	PUNCT
ejpam-3049	387	6	z	z	PROPN
ejpam-3049	387	7	∈	∈	PROPN
ejpam-3049	387	8	h	h	NOUN
ejpam-3049	387	9	and	and	CCONJ
ejpam-3049	387	10	a	a	DET
ejpam-3049	387	11	∈	∈	NOUN
ejpam-3049	387	12	(	(	PUNCT
ejpam-3049	387	13	x	x	SYM
ejpam-3049	387	14	◦	◦	VERB
ejpam-3049	387	15	a	a	X
ejpam-3049	387	16	)	)	PUNCT
ejpam-3049	387	17	∗	∗	NOUN
ejpam-3049	387	18	(	(	PUNCT
ejpam-3049	387	19	y	y	NOUN
ejpam-3049	387	20	◦	◦	VERB
ejpam-3049	387	21	a	a	X
ejpam-3049	387	22	)	)	PUNCT
ejpam-3049	387	23	∗	∗	NOUN
ejpam-3049	387	24	{	{	PUNCT
ejpam-3049	387	25	z	z	NOUN
ejpam-3049	387	26	}	}	PUNCT
ejpam-3049	387	27	,	,	PUNCT
ejpam-3049	387	28	h	h	NOUN
ejpam-3049	387	29	is	be	AUX
ejpam-3049	387	30	semisimple	semisimple	ADJ
ejpam-3049	387	31	and	and	CCONJ
ejpam-3049	387	32	condition	condition	NOUN
ejpam-3049	387	33	(	(	PUNCT
ejpam-3049	387	34	1	1	X
ejpam-3049	387	35	)	)	PUNCT
ejpam-3049	387	36	is	be	AUX
ejpam-3049	387	37	satisfied	satisfied	ADJ
ejpam-3049	387	38	.	.	PUNCT
ejpam-3049	388	1	�	�	PROPN
ejpam-3049	388	2	theorem	theorem	VERB
ejpam-3049	388	3	2.25	2.25	NUM
ejpam-3049	388	4	.	.	PUNCT
ejpam-3049	389	1	let	let	AUX
ejpam-3049	389	2	(	(	PUNCT
ejpam-3049	389	3	h	h	NOUN
ejpam-3049	389	4	,	,	PUNCT
ejpam-3049	389	5	◦	◦	NOUN
ejpam-3049	389	6	)	)	PUNCT
ejpam-3049	389	7	be	be	VERB
ejpam-3049	389	8	an	an	DET
ejpam-3049	389	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	389	10	.	.	PUNCT
ejpam-3049	390	1	the	the	DET
ejpam-3049	390	2	following	follow	VERB
ejpam-3049	390	3	are	be	AUX
ejpam-3049	390	4	equivalent	equivalent	ADJ
ejpam-3049	390	5	:	:	PUNCT
ejpam-3049	390	6	(	(	PUNCT
ejpam-3049	390	7	1	1	X
ejpam-3049	390	8	)	)	PUNCT
ejpam-3049	390	9	h	h	NOUN
ejpam-3049	390	10	is	be	AUX
ejpam-3049	390	11	semisimple	semisimple	ADJ
ejpam-3049	390	12	.	.	PUNCT
ejpam-3049	391	1	(	(	PUNCT
ejpam-3049	391	2	2	2	X
ejpam-3049	391	3	)	)	PUNCT
ejpam-3049	391	4	the	the	DET
ejpam-3049	391	5	ideals	ideal	NOUN
ejpam-3049	391	6	of	of	ADP
ejpam-3049	391	7	h	h	NOUN
ejpam-3049	391	8	are	be	AUX
ejpam-3049	391	9	idempotent	idempotent	ADJ
ejpam-3049	391	10	.	.	PUNCT
ejpam-3049	392	1	(	(	PUNCT
ejpam-3049	392	2	3	3	X
ejpam-3049	392	3	)	)	PUNCT
ejpam-3049	392	4	a	a	DET
ejpam-3049	392	5	∩b	∩b	NOUN
ejpam-3049	392	6	=	=	PUNCT
ejpam-3049	392	7	a	a	DET
ejpam-3049	392	8	∗b	∗b	PROPN
ejpam-3049	392	9	for	for	ADP
ejpam-3049	392	10	all	all	DET
ejpam-3049	392	11	ideals	ideal	NOUN
ejpam-3049	392	12	a	a	DET
ejpam-3049	392	13	,	,	PUNCT
ejpam-3049	392	14	b	b	PROPN
ejpam-3049	392	15	of	of	ADP
ejpam-3049	392	16	h.	h.	PROPN
ejpam-3049	392	17	(	(	PUNCT
ejpam-3049	392	18	4	4	NUM
ejpam-3049	392	19	)	)	PUNCT
ejpam-3049	392	20	i(a	i(a	PROPN
ejpam-3049	392	21	)	)	PUNCT
ejpam-3049	392	22	=	=	SYM
ejpam-3049	392	23	i(a	i(a	PROPN
ejpam-3049	392	24	)	)	PUNCT
ejpam-3049	392	25	∗	∗	PROPN
ejpam-3049	392	26	i(a	i(a	PROPN
ejpam-3049	392	27	)	)	PUNCT
ejpam-3049	392	28	for	for	ADP
ejpam-3049	392	29	every	every	DET
ejpam-3049	392	30	a	a	DET
ejpam-3049	392	31	∈	∈	PROPN
ejpam-3049	392	32	p∗(h	p∗(h	PROPN
ejpam-3049	392	33	)	)	PUNCT
ejpam-3049	392	34	.	.	PUNCT
ejpam-3049	393	1	(	(	PUNCT
ejpam-3049	393	2	5	5	X
ejpam-3049	393	3	)	)	PUNCT
ejpam-3049	393	4	i(a	i(a	PROPN
ejpam-3049	393	5	)	)	PUNCT
ejpam-3049	393	6	=	=	SYM
ejpam-3049	393	7	i(a	i(a	PROPN
ejpam-3049	393	8	)	)	PUNCT
ejpam-3049	393	9	∗	∗	PROPN
ejpam-3049	393	10	i(a	i(a	PROPN
ejpam-3049	393	11	)	)	PUNCT
ejpam-3049	393	12	for	for	ADP
ejpam-3049	393	13	every	every	DET
ejpam-3049	393	14	a	a	DET
ejpam-3049	393	15	∈	∈	PROPN
ejpam-3049	393	16	h.	h.	NOUN
ejpam-3049	393	17	proof	proof	NOUN
ejpam-3049	393	18	.	.	PUNCT
ejpam-3049	394	1	(	(	PUNCT
ejpam-3049	394	2	1	1	X
ejpam-3049	394	3	)	)	PUNCT
ejpam-3049	394	4	=	=	NOUN
ejpam-3049	394	5	⇒	⇒	NOUN
ejpam-3049	394	6	(	(	PUNCT
ejpam-3049	394	7	2	2	NUM
ejpam-3049	394	8	)	)	PUNCT
ejpam-3049	394	9	.	.	PUNCT
ejpam-3049	395	1	let	let	VERB
ejpam-3049	395	2	a	a	PRON
ejpam-3049	395	3	be	be	AUX
ejpam-3049	395	4	an	an	DET
ejpam-3049	395	5	ideal	ideal	NOUN
ejpam-3049	395	6	of	of	ADP
ejpam-3049	395	7	h.	h.	PROPN
ejpam-3049	395	8	since	since	SCONJ
ejpam-3049	395	9	a	a	DET
ejpam-3049	395	10	∈	∈	PROPN
ejpam-3049	395	11	p∗(h	p∗(h	PROPN
ejpam-3049	395	12	)	)	PUNCT
ejpam-3049	395	13	and	and	CCONJ
ejpam-3049	395	14	h	h	NOUN
ejpam-3049	395	15	is	be	AUX
ejpam-3049	395	16	semisimple	semisimple	ADJ
ejpam-3049	395	17	,	,	PUNCT
ejpam-3049	395	18	by	by	ADP
ejpam-3049	395	19	proposition	proposition	NOUN
ejpam-3049	395	20	2.24	2.24	NUM
ejpam-3049	395	21	,	,	PUNCT
ejpam-3049	395	22	we	we	PRON
ejpam-3049	395	23	have	have	VERB
ejpam-3049	395	24	a	a	DET
ejpam-3049	395	25	⊆	⊆	NUM
ejpam-3049	395	26	(	(	PUNCT
ejpam-3049	395	27	h	h	NOUN
ejpam-3049	395	28	∗a	∗a	ADJ
ejpam-3049	395	29	)	)	PUNCT
ejpam-3049	395	30	∗h	∗h	NOUN
ejpam-3049	395	31	∗	∗	NOUN
ejpam-3049	395	32	(	(	PUNCT
ejpam-3049	395	33	a	a	DET
ejpam-3049	395	34	∗h	∗h	NOUN
ejpam-3049	395	35	)	)	PUNCT
ejpam-3049	395	36	⊆	⊆	NUM
ejpam-3049	395	37	a	a	DET
ejpam-3049	395	38	∗h	∗h	NOUN
ejpam-3049	395	39	∗a	∗a	ADJ
ejpam-3049	395	40	=	=	PUNCT
ejpam-3049	395	41	(	(	PUNCT
ejpam-3049	395	42	a	a	DET
ejpam-3049	395	43	∗h	∗h	NOUN
ejpam-3049	395	44	)	)	PUNCT
ejpam-3049	395	45	∗a	∗a	PROPN
ejpam-3049	395	46	⊆	⊆	NUM
ejpam-3049	395	47	a	a	DET
ejpam-3049	395	48	∗a	∗a	ADJ
ejpam-3049	395	49	⊆	⊆	NUM
ejpam-3049	395	50	a	a	DET
ejpam-3049	395	51	∗h	∗h	NOUN
ejpam-3049	395	52	⊆	⊆	NUM
ejpam-3049	395	53	a	a	DET
ejpam-3049	395	54	,	,	PUNCT
ejpam-3049	395	55	n.	n.	PROPN
ejpam-3049	395	56	kehayopulu	kehayopulu	PROPN
ejpam-3049	395	57	/	/	SYM
ejpam-3049	395	58	eur	eur	PROPN
ejpam-3049	395	59	.	.	PUNCT
ejpam-3049	396	1	j.	j.	PROPN
ejpam-3049	396	2	pure	pure	PROPN
ejpam-3049	396	3	appl	appl	PROPN
ejpam-3049	396	4	.	.	PROPN
ejpam-3049	396	5	math	math	PROPN
ejpam-3049	396	6	,	,	PUNCT
ejpam-3049	396	7	10	10	NUM
ejpam-3049	396	8	(	(	PUNCT
ejpam-3049	396	9	5	5	NUM
ejpam-3049	396	10	)	)	PUNCT
ejpam-3049	396	11	(	(	PUNCT
ejpam-3049	396	12	2017	2017	NUM
ejpam-3049	396	13	)	)	PUNCT
ejpam-3049	396	14	,	,	PUNCT
ejpam-3049	396	15	929	929	NUM
ejpam-3049	396	16	-	-	SYM
ejpam-3049	396	17	945	945	NUM
ejpam-3049	396	18	943	943	NUM
ejpam-3049	396	19	so	so	SCONJ
ejpam-3049	396	20	a	a	DET
ejpam-3049	396	21	∗a	∗a	PROPN
ejpam-3049	396	22	=	=	SYM
ejpam-3049	396	23	a	a	NOUN
ejpam-3049	396	24	,	,	PUNCT
ejpam-3049	396	25	and	and	CCONJ
ejpam-3049	396	26	a	a	PRON
ejpam-3049	396	27	is	be	AUX
ejpam-3049	396	28	idempotent	idempotent	ADJ
ejpam-3049	396	29	.	.	PUNCT
ejpam-3049	397	1	(	(	PUNCT
ejpam-3049	397	2	2	2	X
ejpam-3049	397	3	)	)	PUNCT
ejpam-3049	397	4	=	=	NOUN
ejpam-3049	397	5	⇒	⇒	NOUN
ejpam-3049	397	6	(	(	PUNCT
ejpam-3049	397	7	3	3	NUM
ejpam-3049	397	8	)	)	PUNCT
ejpam-3049	397	9	.	.	PUNCT
ejpam-3049	398	1	let	let	VERB
ejpam-3049	398	2	a	a	DET
ejpam-3049	398	3	,	,	PUNCT
ejpam-3049	398	4	b	b	NOUN
ejpam-3049	398	5	be	be	AUX
ejpam-3049	398	6	ideals	ideal	NOUN
ejpam-3049	398	7	of	of	ADP
ejpam-3049	398	8	h.	h.	PROPN
ejpam-3049	398	9	then	then	ADV
ejpam-3049	398	10	a	a	DET
ejpam-3049	398	11	∗b	∗b	PROPN
ejpam-3049	398	12	⊆	⊆	SYM
ejpam-3049	398	13	a	a	DET
ejpam-3049	398	14	∗h	∗h	NOUN
ejpam-3049	398	15	⊆	⊆	NUM
ejpam-3049	398	16	a	a	PRON
ejpam-3049	398	17	and	and	CCONJ
ejpam-3049	398	18	a	a	DET
ejpam-3049	398	19	∗b	∗b	PROPN
ejpam-3049	398	20	⊆	⊆	NUM
ejpam-3049	398	21	h	h	NOUN
ejpam-3049	398	22	∗b	∗b	PROPN
ejpam-3049	398	23	⊆	⊆	NUM
ejpam-3049	398	24	b	b	NOUN
ejpam-3049	398	25	,	,	PUNCT
ejpam-3049	398	26	so	so	SCONJ
ejpam-3049	398	27	a	a	DET
ejpam-3049	398	28	∗b	∗b	PROPN
ejpam-3049	398	29	⊆	⊆	NUM
ejpam-3049	398	30	a∩b	a∩b	PROPN
ejpam-3049	398	31	.	.	PUNCT
ejpam-3049	399	1	on	on	ADP
ejpam-3049	399	2	the	the	DET
ejpam-3049	399	3	other	other	ADJ
ejpam-3049	399	4	hand	hand	NOUN
ejpam-3049	399	5	,	,	PUNCT
ejpam-3049	399	6	a∩b	a∩b	PROPN
ejpam-3049	399	7	is	be	AUX
ejpam-3049	399	8	an	an	DET
ejpam-3049	399	9	ideal	ideal	NOUN
ejpam-3049	399	10	of	of	ADP
ejpam-3049	399	11	h	h	NOUN
ejpam-3049	399	12	and	and	CCONJ
ejpam-3049	399	13	,	,	PUNCT
ejpam-3049	399	14	by	by	ADP
ejpam-3049	399	15	hypothesis	hypothesis	NOUN
ejpam-3049	399	16	,	,	PUNCT
ejpam-3049	399	17	we	we	PRON
ejpam-3049	399	18	have	have	VERB
ejpam-3049	399	19	a	a	DET
ejpam-3049	399	20	∩b	∩b	NOUN
ejpam-3049	399	21	=	=	PUNCT
ejpam-3049	399	22	(	(	PUNCT
ejpam-3049	399	23	a	a	DET
ejpam-3049	399	24	∩b	∩b	NOUN
ejpam-3049	399	25	)	)	PUNCT
ejpam-3049	399	26	∗	∗	NOUN
ejpam-3049	399	27	(	(	PUNCT
ejpam-3049	399	28	a	a	DET
ejpam-3049	399	29	∩b	∩b	NOUN
ejpam-3049	399	30	)	)	PUNCT
ejpam-3049	399	31	⊆	⊆	NUM
ejpam-3049	399	32	a	a	DET
ejpam-3049	399	33	∗b	∗b	NOUN
ejpam-3049	399	34	.	.	PUNCT
ejpam-3049	400	1	thus	thus	ADV
ejpam-3049	400	2	we	we	PRON
ejpam-3049	400	3	have	have	VERB
ejpam-3049	400	4	a	a	DET
ejpam-3049	400	5	∩b	∩b	NOUN
ejpam-3049	400	6	=	=	PUNCT
ejpam-3049	400	7	a	a	DET
ejpam-3049	400	8	∗b	∗b	NOUN
ejpam-3049	400	9	.	.	PUNCT
ejpam-3049	401	1	the	the	DET
ejpam-3049	401	2	implications	implication	NOUN
ejpam-3049	401	3	(	(	PUNCT
ejpam-3049	401	4	3)⇒	3)⇒	NUM
ejpam-3049	401	5	(	(	PUNCT
ejpam-3049	401	6	4	4	NUM
ejpam-3049	401	7	)	)	PUNCT
ejpam-3049	401	8	and	and	CCONJ
ejpam-3049	401	9	(	(	PUNCT
ejpam-3049	401	10	4)⇒	4)⇒	X
ejpam-3049	401	11	(	(	PUNCT
ejpam-3049	401	12	5	5	NUM
ejpam-3049	401	13	)	)	PUNCT
ejpam-3049	401	14	are	be	AUX
ejpam-3049	401	15	obvious	obvious	ADJ
ejpam-3049	401	16	.	.	PUNCT
ejpam-3049	402	1	(	(	PUNCT
ejpam-3049	402	2	5	5	X
ejpam-3049	402	3	)	)	PUNCT
ejpam-3049	402	4	=	=	NOUN
ejpam-3049	402	5	⇒	⇒	NOUN
ejpam-3049	402	6	(	(	PUNCT
ejpam-3049	402	7	1	1	NUM
ejpam-3049	402	8	)	)	PUNCT
ejpam-3049	402	9	.	.	PUNCT
ejpam-3049	403	1	exactly	exactly	ADV
ejpam-3049	403	2	as	as	ADP
ejpam-3049	403	3	in	in	ADP
ejpam-3049	403	4	the	the	DET
ejpam-3049	403	5	lemma	lemma	PROPN
ejpam-3049	403	6	2	2	NUM
ejpam-3049	403	7	in	in	ADP
ejpam-3049	403	8	[	[	X
ejpam-3049	403	9	3	3	NUM
ejpam-3049	403	10	]	]	PUNCT
ejpam-3049	403	11	,	,	PUNCT
ejpam-3049	403	12	we	we	PRON
ejpam-3049	403	13	prove	prove	VERB
ejpam-3049	403	14	that	that	SCONJ
ejpam-3049	403	15	i(a	i(a	PROPN
ejpam-3049	403	16	)	)	PUNCT
ejpam-3049	403	17	=	=	SYM
ejpam-3049	403	18	i(a	i(a	PROPN
ejpam-3049	403	19	)	)	PUNCT
ejpam-3049	403	20	∗	∗	PROPN
ejpam-3049	403	21	i(a	i(a	PROPN
ejpam-3049	403	22	)	)	PUNCT
ejpam-3049	403	23	∗	∗	PROPN
ejpam-3049	403	24	i(a	i(a	PROPN
ejpam-3049	403	25	)	)	PUNCT
ejpam-3049	403	26	∗	∗	PROPN
ejpam-3049	403	27	i(a	i(a	PROPN
ejpam-3049	403	28	)	)	PUNCT
ejpam-3049	403	29	∗	∗	PROPN
ejpam-3049	403	30	i(a	i(a	PROPN
ejpam-3049	403	31	)	)	PUNCT
ejpam-3049	403	32	and	and	CCONJ
ejpam-3049	403	33	that	that	DET
ejpam-3049	403	34	i(a	i(a	PROPN
ejpam-3049	403	35	)	)	PUNCT
ejpam-3049	403	36	∗	∗	PROPN
ejpam-3049	403	37	i(a	i(a	PROPN
ejpam-3049	403	38	)	)	PUNCT
ejpam-3049	403	39	∗	∗	PROPN
ejpam-3049	403	40	i(a	i(a	PROPN
ejpam-3049	403	41	)	)	PUNCT
ejpam-3049	403	42	∗	∗	PROPN
ejpam-3049	403	43	i(a	i(a	PROPN
ejpam-3049	403	44	)	)	PUNCT
ejpam-3049	403	45	∗	∗	PROPN
ejpam-3049	403	46	i(a	i(a	PROPN
ejpam-3049	403	47	)	)	PUNCT
ejpam-3049	403	48	⊆	⊆	NUM
ejpam-3049	403	49	h	h	NOUN
ejpam-3049	403	50	∗	∗	NOUN
ejpam-3049	403	51	{	{	PUNCT
ejpam-3049	403	52	a	a	DET
ejpam-3049	403	53	}	}	PUNCT
ejpam-3049	403	54	∗h	∗h	NOUN
ejpam-3049	403	55	∗	∗	NOUN
ejpam-3049	403	56	{	{	PUNCT
ejpam-3049	403	57	a	a	DET
ejpam-3049	403	58	}	}	PUNCT
ejpam-3049	403	59	∗h	∗h	NOUN
ejpam-3049	403	60	.	.	PUNCT
ejpam-3049	404	1	then	then	ADV
ejpam-3049	404	2	we	we	PRON
ejpam-3049	404	3	get	get	VERB
ejpam-3049	404	4	a	a	DET
ejpam-3049	404	5	∈	∈	NOUN
ejpam-3049	404	6	h	h	NOUN
ejpam-3049	404	7	∗	∗	NOUN
ejpam-3049	404	8	{	{	PUNCT
ejpam-3049	404	9	a	a	DET
ejpam-3049	404	10	}	}	PUNCT
ejpam-3049	404	11	∗h	∗h	NOUN
ejpam-3049	404	12	∗	∗	NOUN
ejpam-3049	404	13	{	{	PUNCT
ejpam-3049	404	14	a	a	DET
ejpam-3049	404	15	}	}	PUNCT
ejpam-3049	404	16	∗h	∗h	NOUN
ejpam-3049	404	17	,	,	PUNCT
ejpam-3049	404	18	and	and	CCONJ
ejpam-3049	404	19	h	h	NOUN
ejpam-3049	404	20	is	be	AUX
ejpam-3049	404	21	semisimple	semisimple	ADJ
ejpam-3049	404	22	.	.	PUNCT
ejpam-3049	405	1	�	�	PROPN
ejpam-3049	405	2	proposition	proposition	PROPN
ejpam-3049	405	3	2.26	2.26	NUM
ejpam-3049	405	4	.	.	PUNCT
ejpam-3049	406	1	let	let	VERB
ejpam-3049	406	2	(	(	PUNCT
ejpam-3049	406	3	h	h	NOUN
ejpam-3049	406	4	,	,	PUNCT
ejpam-3049	406	5	◦	◦	NOUN
ejpam-3049	406	6	)	)	PUNCT
ejpam-3049	406	7	be	be	VERB
ejpam-3049	406	8	an	an	DET
ejpam-3049	406	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	406	10	.	.	PUNCT
ejpam-3049	407	1	then	then	ADV
ejpam-3049	407	2	we	we	PRON
ejpam-3049	407	3	have	have	VERB
ejpam-3049	407	4	the	the	DET
ejpam-3049	407	5	following	following	NOUN
ejpam-3049	407	6	:	:	PUNCT
ejpam-3049	407	7	(	(	PUNCT
ejpam-3049	407	8	1	1	X
ejpam-3049	407	9	)	)	PUNCT
ejpam-3049	407	10	if	if	SCONJ
ejpam-3049	407	11	h	h	NOUN
ejpam-3049	407	12	is	be	AUX
ejpam-3049	407	13	regular	regular	ADJ
ejpam-3049	407	14	,	,	PUNCT
ejpam-3049	407	15	then	then	ADV
ejpam-3049	407	16	it	it	PRON
ejpam-3049	407	17	is	be	AUX
ejpam-3049	407	18	left	leave	VERB
ejpam-3049	407	19	and	and	CCONJ
ejpam-3049	407	20	right	right	ADJ
ejpam-3049	407	21	quasi	quasi	NOUN
ejpam-3049	407	22	-	-	ADJ
ejpam-3049	407	23	regular	regular	ADJ
ejpam-3049	407	24	.	.	PUNCT
ejpam-3049	408	1	(	(	PUNCT
ejpam-3049	408	2	2	2	X
ejpam-3049	408	3	)	)	PUNCT
ejpam-3049	408	4	if	if	SCONJ
ejpam-3049	408	5	h	h	NOUN
ejpam-3049	408	6	is	be	AUX
ejpam-3049	408	7	left	leave	VERB
ejpam-3049	408	8	(	(	PUNCT
ejpam-3049	408	9	or	or	CCONJ
ejpam-3049	408	10	right	right	ADJ
ejpam-3049	408	11	)	)	PUNCT
ejpam-3049	408	12	quasi	quasi	ADJ
ejpam-3049	408	13	-	-	ADJ
ejpam-3049	408	14	regular	regular	ADJ
ejpam-3049	408	15	,	,	PUNCT
ejpam-3049	408	16	then	then	ADV
ejpam-3049	408	17	it	it	PRON
ejpam-3049	408	18	is	be	AUX
ejpam-3049	408	19	semisimple	semisimple	ADJ
ejpam-3049	408	20	.	.	PUNCT
ejpam-3049	409	1	(	(	PUNCT
ejpam-3049	409	2	3	3	X
ejpam-3049	409	3	)	)	PUNCT
ejpam-3049	409	4	if	if	SCONJ
ejpam-3049	409	5	h	h	NOUN
ejpam-3049	409	6	is	be	AUX
ejpam-3049	409	7	intra	intra	ADJ
ejpam-3049	409	8	-	-	ADJ
ejpam-3049	409	9	regular	regular	ADJ
ejpam-3049	409	10	,	,	PUNCT
ejpam-3049	409	11	then	then	ADV
ejpam-3049	409	12	it	it	PRON
ejpam-3049	409	13	is	be	AUX
ejpam-3049	409	14	semisimple	semisimple	ADJ
ejpam-3049	409	15	.	.	PUNCT
ejpam-3049	410	1	proof	proof	NOUN
ejpam-3049	410	2	.	.	PUNCT
ejpam-3049	411	1	(	(	PUNCT
ejpam-3049	411	2	1	1	X
ejpam-3049	411	3	)	)	PUNCT
ejpam-3049	411	4	let	let	VERB
ejpam-3049	411	5	h	h	NOUN
ejpam-3049	411	6	be	be	AUX
ejpam-3049	411	7	regular	regular	ADJ
ejpam-3049	411	8	and	and	CCONJ
ejpam-3049	411	9	a	a	DET
ejpam-3049	411	10	∈	∈	PROPN
ejpam-3049	411	11	p∗(h	p∗(h	PROPN
ejpam-3049	411	12	)	)	PUNCT
ejpam-3049	411	13	.	.	PUNCT
ejpam-3049	412	1	then	then	ADV
ejpam-3049	412	2	we	we	PRON
ejpam-3049	412	3	have	have	VERB
ejpam-3049	412	4	a	a	DET
ejpam-3049	412	5	⊆	⊆	NUM
ejpam-3049	412	6	a	a	DET
ejpam-3049	412	7	∗h	∗h	NOUN
ejpam-3049	412	8	∗a	∗a	ADJ
ejpam-3049	412	9	⊆	⊆	NUM
ejpam-3049	412	10	a	a	DET
ejpam-3049	412	11	∗h	∗h	NOUN
ejpam-3049	412	12	∗	∗	NOUN
ejpam-3049	412	13	(	(	PUNCT
ejpam-3049	412	14	a	a	DET
ejpam-3049	412	15	∗h	∗h	NOUN
ejpam-3049	412	16	∗a	∗a	ADJ
ejpam-3049	412	17	)	)	PUNCT
ejpam-3049	412	18	⊆	⊆	NUM
ejpam-3049	412	19	(	(	PUNCT
ejpam-3049	412	20	h	h	NOUN
ejpam-3049	412	21	∗h	∗h	NOUN
ejpam-3049	412	22	)	)	PUNCT
ejpam-3049	412	23	∗	∗	NOUN
ejpam-3049	412	24	(	(	PUNCT
ejpam-3049	412	25	a	a	DET
ejpam-3049	412	26	∗h	∗h	NOUN
ejpam-3049	412	27	∗a	∗a	ADJ
ejpam-3049	412	28	)	)	PUNCT
ejpam-3049	412	29	⊆	⊆	NUM
ejpam-3049	412	30	h	h	NOUN
ejpam-3049	412	31	∗a	∗a	ADJ
ejpam-3049	412	32	∗h	∗h	NOUN
ejpam-3049	412	33	∗a	∗a	ADJ
ejpam-3049	412	34	,	,	PUNCT
ejpam-3049	412	35	so	so	SCONJ
ejpam-3049	412	36	h	h	NOUN
ejpam-3049	412	37	is	be	AUX
ejpam-3049	412	38	left	leave	VERB
ejpam-3049	412	39	quasi	quasi	ADJ
ejpam-3049	412	40	-	-	ADJ
ejpam-3049	412	41	regular	regular	ADJ
ejpam-3049	412	42	.	.	PUNCT
ejpam-3049	413	1	similarly	similarly	ADV
ejpam-3049	413	2	h	h	PROPN
ejpam-3049	413	3	is	be	AUX
ejpam-3049	413	4	right	right	ADJ
ejpam-3049	413	5	quasi	quasi	ADJ
ejpam-3049	413	6	-	-	ADJ
ejpam-3049	413	7	regular	regular	ADJ
ejpam-3049	413	8	.	.	PUNCT
ejpam-3049	414	1	(	(	PUNCT
ejpam-3049	414	2	2	2	X
ejpam-3049	414	3	)	)	PUNCT
ejpam-3049	414	4	let	let	VERB
ejpam-3049	414	5	h	h	NOUN
ejpam-3049	414	6	be	be	AUX
ejpam-3049	414	7	left	leave	VERB
ejpam-3049	414	8	quasi	quasi	ADJ
ejpam-3049	414	9	-	-	ADJ
ejpam-3049	414	10	regular	regular	ADJ
ejpam-3049	414	11	and	and	CCONJ
ejpam-3049	414	12	a	a	DET
ejpam-3049	414	13	∈	∈	PROPN
ejpam-3049	414	14	p∗(h	p∗(h	PROPN
ejpam-3049	414	15	)	)	PUNCT
ejpam-3049	414	16	.	.	PUNCT
ejpam-3049	415	1	then	then	ADV
ejpam-3049	415	2	we	we	PRON
ejpam-3049	415	3	have	have	VERB
ejpam-3049	415	4	a	a	DET
ejpam-3049	415	5	⊆	⊆	NUM
ejpam-3049	415	6	h	h	NOUN
ejpam-3049	415	7	∗a	∗a	ADJ
ejpam-3049	415	8	∗h	∗h	NOUN
ejpam-3049	415	9	∗a	∗a	ADJ
ejpam-3049	415	10	⊆	⊆	NUM
ejpam-3049	415	11	h	h	NOUN
ejpam-3049	415	12	∗	∗	NOUN
ejpam-3049	415	13	(	(	PUNCT
ejpam-3049	415	14	h	h	NOUN
ejpam-3049	415	15	∗a	∗a	ADJ
ejpam-3049	415	16	∗h	∗h	NOUN
ejpam-3049	415	17	∗a	∗a	ADJ
ejpam-3049	415	18	)	)	PUNCT
ejpam-3049	415	19	∗	∗	NOUN
ejpam-3049	415	20	(	(	PUNCT
ejpam-3049	415	21	h	h	NOUN
ejpam-3049	415	22	∗a	∗a	ADJ
ejpam-3049	415	23	)	)	PUNCT
ejpam-3049	415	24	=	=	PUNCT
ejpam-3049	415	25	(	(	PUNCT
ejpam-3049	415	26	h	h	NOUN
ejpam-3049	415	27	∗h	∗h	NOUN
ejpam-3049	415	28	)	)	PUNCT
ejpam-3049	415	29	∗	∗	NOUN
ejpam-3049	415	30	(	(	PUNCT
ejpam-3049	415	31	a	a	DET
ejpam-3049	415	32	∗h	∗h	NOUN
ejpam-3049	415	33	∗a	∗a	ADJ
ejpam-3049	415	34	)	)	PUNCT
ejpam-3049	415	35	∗	∗	NOUN
ejpam-3049	415	36	(	(	PUNCT
ejpam-3049	415	37	h	h	NOUN
ejpam-3049	415	38	∗a	∗a	ADJ
ejpam-3049	415	39	)	)	PUNCT
ejpam-3049	415	40	⊆	⊆	NUM
ejpam-3049	415	41	(	(	PUNCT
ejpam-3049	415	42	h	h	NOUN
ejpam-3049	415	43	∗h	∗h	NOUN
ejpam-3049	415	44	)	)	PUNCT
ejpam-3049	415	45	∗	∗	NOUN
ejpam-3049	415	46	(	(	PUNCT
ejpam-3049	415	47	a	a	DET
ejpam-3049	415	48	∗h	∗h	NOUN
ejpam-3049	415	49	∗a	∗a	ADJ
ejpam-3049	415	50	)	)	PUNCT
ejpam-3049	415	51	∗	∗	NOUN
ejpam-3049	415	52	(	(	PUNCT
ejpam-3049	415	53	h	h	NOUN
ejpam-3049	415	54	∗h	∗h	NOUN
ejpam-3049	415	55	)	)	PUNCT
ejpam-3049	415	56	⊆	⊆	NUM
ejpam-3049	415	57	h	h	NOUN
ejpam-3049	415	58	∗a	∗a	ADJ
ejpam-3049	415	59	∗h	∗h	NOUN
ejpam-3049	415	60	∗a	∗a	ADJ
ejpam-3049	415	61	∗h	∗h	NOUN
ejpam-3049	415	62	,	,	PUNCT
ejpam-3049	415	63	thus	thus	ADV
ejpam-3049	415	64	h	h	NOUN
ejpam-3049	415	65	is	be	AUX
ejpam-3049	415	66	semisimple	semisimple	ADJ
ejpam-3049	415	67	.	.	PUNCT
ejpam-3049	416	1	if	if	SCONJ
ejpam-3049	416	2	h	h	NOUN
ejpam-3049	416	3	is	be	AUX
ejpam-3049	416	4	right	right	ADJ
ejpam-3049	416	5	quasi	quasi	ADJ
ejpam-3049	416	6	-	-	ADJ
ejpam-3049	416	7	regular	regular	ADJ
ejpam-3049	416	8	,	,	PUNCT
ejpam-3049	416	9	the	the	DET
ejpam-3049	416	10	proof	proof	NOUN
ejpam-3049	416	11	is	be	AUX
ejpam-3049	416	12	analogous	analogous	ADJ
ejpam-3049	416	13	.	.	PUNCT
ejpam-3049	417	1	(	(	PUNCT
ejpam-3049	417	2	3	3	X
ejpam-3049	417	3	)	)	PUNCT
ejpam-3049	417	4	let	let	VERB
ejpam-3049	417	5	h	h	NOUN
ejpam-3049	417	6	be	be	AUX
ejpam-3049	417	7	intra	intra	ADJ
ejpam-3049	417	8	-	-	ADJ
ejpam-3049	417	9	regular	regular	ADJ
ejpam-3049	417	10	and	and	CCONJ
ejpam-3049	417	11	a	a	DET
ejpam-3049	417	12	a	a	DET
ejpam-3049	417	13	nonempty	nonempty	ADJ
ejpam-3049	417	14	subset	subset	NOUN
ejpam-3049	417	15	of	of	ADP
ejpam-3049	417	16	h.	h.	PROPN
ejpam-3049	417	17	then	then	ADV
ejpam-3049	417	18	we	we	PRON
ejpam-3049	417	19	have	have	VERB
ejpam-3049	417	20	a	a	DET
ejpam-3049	417	21	⊆	⊆	NUM
ejpam-3049	417	22	h	h	NOUN
ejpam-3049	417	23	∗a	∗a	ADJ
ejpam-3049	417	24	∗a	∗a	ADJ
ejpam-3049	417	25	∗h	∗h	VERB
ejpam-3049	417	26	⊆	⊆	NUM
ejpam-3049	417	27	h	h	NOUN
ejpam-3049	417	28	∗	∗	NOUN
ejpam-3049	417	29	(	(	PUNCT
ejpam-3049	417	30	h	h	NOUN
ejpam-3049	417	31	∗a	∗a	ADJ
ejpam-3049	417	32	∗a	∗a	ADJ
ejpam-3049	417	33	∗h	∗h	NOUN
ejpam-3049	417	34	)	)	PUNCT
ejpam-3049	417	35	∗a	∗a	ADJ
ejpam-3049	417	36	∗h	∗h	NOUN
ejpam-3049	417	37	=	=	SYM
ejpam-3049	417	38	(	(	PUNCT
ejpam-3049	417	39	h	h	NOUN
ejpam-3049	417	40	∗h	∗h	NOUN
ejpam-3049	417	41	)	)	PUNCT
ejpam-3049	417	42	∗a	∗a	ADJ
ejpam-3049	417	43	∗	∗	NOUN
ejpam-3049	417	44	(	(	PUNCT
ejpam-3049	417	45	a	a	DET
ejpam-3049	417	46	∗h	∗h	NOUN
ejpam-3049	417	47	)	)	PUNCT
ejpam-3049	417	48	∗a	∗a	ADJ
ejpam-3049	417	49	∗h	∗h	NOUN
ejpam-3049	417	50	⊆	⊆	NUM
ejpam-3049	417	51	(	(	PUNCT
ejpam-3049	417	52	h	h	NOUN
ejpam-3049	417	53	∗h	∗h	NOUN
ejpam-3049	417	54	)	)	PUNCT
ejpam-3049	417	55	∗a	∗a	ADJ
ejpam-3049	417	56	∗	∗	NOUN
ejpam-3049	417	57	(	(	PUNCT
ejpam-3049	417	58	h	h	NOUN
ejpam-3049	417	59	∗h	∗h	NOUN
ejpam-3049	417	60	)	)	PUNCT
ejpam-3049	418	1	∗a	∗a	ADJ
ejpam-3049	418	2	∗h	∗h	NOUN
ejpam-3049	418	3	⊆	⊆	NUM
ejpam-3049	418	4	h	h	NOUN
ejpam-3049	418	5	∗a	∗a	ADJ
ejpam-3049	418	6	∗h	∗h	NOUN
ejpam-3049	418	7	∗a	∗a	ADJ
ejpam-3049	418	8	∗h	∗h	NOUN
ejpam-3049	418	9	,	,	PUNCT
ejpam-3049	418	10	and	and	CCONJ
ejpam-3049	418	11	h	h	NOUN
ejpam-3049	418	12	is	be	AUX
ejpam-3049	418	13	semisimple	semisimple	ADJ
ejpam-3049	418	14	.	.	PUNCT
ejpam-3049	419	1	�	�	PROPN
ejpam-3049	419	2	theorem	theorem	VERB
ejpam-3049	419	3	2.27	2.27	NUM
ejpam-3049	419	4	.	.	PUNCT
ejpam-3049	420	1	let	let	VERB
ejpam-3049	420	2	h	h	PRON
ejpam-3049	420	3	be	be	AUX
ejpam-3049	420	4	an	an	DET
ejpam-3049	420	5	hypersemigroup	hypersemigroup	NOUN
ejpam-3049	420	6	.	.	PUNCT
ejpam-3049	421	1	the	the	DET
ejpam-3049	421	2	following	follow	VERB
ejpam-3049	421	3	are	be	AUX
ejpam-3049	421	4	equivalent	equivalent	ADJ
ejpam-3049	421	5	:	:	PUNCT
ejpam-3049	421	6	n.	n.	PROPN
ejpam-3049	421	7	kehayopulu	kehayopulu	PROPN
ejpam-3049	421	8	/	/	SYM
ejpam-3049	421	9	eur	eur	PROPN
ejpam-3049	421	10	.	.	PUNCT
ejpam-3049	422	1	j.	j.	PROPN
ejpam-3049	422	2	pure	pure	PROPN
ejpam-3049	422	3	appl	appl	PROPN
ejpam-3049	422	4	.	.	PROPN
ejpam-3049	422	5	math	math	PROPN
ejpam-3049	422	6	,	,	PUNCT
ejpam-3049	422	7	10	10	NUM
ejpam-3049	422	8	(	(	PUNCT
ejpam-3049	422	9	5	5	NUM
ejpam-3049	422	10	)	)	PUNCT
ejpam-3049	422	11	(	(	PUNCT
ejpam-3049	422	12	2017	2017	NUM
ejpam-3049	422	13	)	)	PUNCT
ejpam-3049	422	14	,	,	PUNCT
ejpam-3049	422	15	929	929	NUM
ejpam-3049	422	16	-	-	SYM
ejpam-3049	422	17	945	945	NUM
ejpam-3049	422	18	944	944	NUM
ejpam-3049	422	19	(	(	PUNCT
ejpam-3049	422	20	1	1	NUM
ejpam-3049	422	21	)	)	PUNCT
ejpam-3049	422	22	h	h	NOUN
ejpam-3049	422	23	is	be	AUX
ejpam-3049	422	24	semisimple	semisimple	ADJ
ejpam-3049	422	25	.	.	PUNCT
ejpam-3049	423	1	(	(	PUNCT
ejpam-3049	423	2	2	2	X
ejpam-3049	423	3	)	)	PUNCT
ejpam-3049	423	4	for	for	ADP
ejpam-3049	423	5	every	every	DET
ejpam-3049	423	6	fuzzy	fuzzy	ADJ
ejpam-3049	423	7	ideals	ideal	NOUN
ejpam-3049	423	8	f	f	PROPN
ejpam-3049	423	9	and	and	CCONJ
ejpam-3049	423	10	g	g	PROPN
ejpam-3049	423	11	of	of	ADP
ejpam-3049	423	12	h	h	NOUN
ejpam-3049	423	13	,	,	PUNCT
ejpam-3049	423	14	we	we	PRON
ejpam-3049	423	15	have	have	VERB
ejpam-3049	423	16	f	f	PROPN
ejpam-3049	423	17	∧	∧	PROPN
ejpam-3049	423	18	g	g	PROPN
ejpam-3049	423	19	=	=	SYM
ejpam-3049	423	20	f	f	PROPN
ejpam-3049	423	21	◦	◦	NOUN
ejpam-3049	423	22	g.	g.	PROPN
ejpam-3049	423	23	(	(	PUNCT
ejpam-3049	423	24	3	3	X
ejpam-3049	423	25	)	)	PUNCT
ejpam-3049	423	26	for	for	ADP
ejpam-3049	423	27	every	every	DET
ejpam-3049	423	28	fuzzy	fuzzy	ADJ
ejpam-3049	423	29	ideal	ideal	NOUN
ejpam-3049	423	30	f	f	PROPN
ejpam-3049	423	31	of	of	ADP
ejpam-3049	423	32	h	h	NOUN
ejpam-3049	423	33	,	,	PUNCT
ejpam-3049	423	34	we	we	PRON
ejpam-3049	423	35	have	have	VERB
ejpam-3049	423	36	f	f	NOUN
ejpam-3049	423	37	=	=	SYM
ejpam-3049	423	38	f	f	PROPN
ejpam-3049	423	39	◦	◦	NOUN
ejpam-3049	423	40	f	f	X
ejpam-3049	423	41	.	.	PUNCT
ejpam-3049	424	1	proof	proof	NOUN
ejpam-3049	424	2	.	.	PUNCT
ejpam-3049	425	1	(	(	PUNCT
ejpam-3049	425	2	1	1	X
ejpam-3049	425	3	)	)	PUNCT
ejpam-3049	425	4	=	=	NOUN
ejpam-3049	425	5	⇒	⇒	NOUN
ejpam-3049	425	6	(	(	PUNCT
ejpam-3049	425	7	2	2	NUM
ejpam-3049	425	8	)	)	PUNCT
ejpam-3049	425	9	.	.	PUNCT
ejpam-3049	426	1	let	let	VERB
ejpam-3049	426	2	f	f	PROPN
ejpam-3049	426	3	and	and	CCONJ
ejpam-3049	426	4	g	g	PROPN
ejpam-3049	426	5	be	be	VERB
ejpam-3049	426	6	fuzzy	fuzzy	ADJ
ejpam-3049	426	7	ideals	ideal	NOUN
ejpam-3049	426	8	of	of	ADP
ejpam-3049	426	9	h.	h.	PROPN
ejpam-3049	426	10	since	since	SCONJ
ejpam-3049	426	11	f	f	PROPN
ejpam-3049	426	12	is	be	AUX
ejpam-3049	426	13	a	a	DET
ejpam-3049	426	14	fuzzy	fuzzy	ADJ
ejpam-3049	426	15	right	right	ADJ
ejpam-3049	426	16	ideal	ideal	NOUN
ejpam-3049	426	17	and	and	CCONJ
ejpam-3049	426	18	g	g	PROPN
ejpam-3049	426	19	is	be	AUX
ejpam-3049	426	20	a	a	DET
ejpam-3049	426	21	fuzzy	fuzzy	ADJ
ejpam-3049	426	22	left	leave	VERB
ejpam-3049	426	23	ideal	ideal	NOUN
ejpam-3049	426	24	of	of	ADP
ejpam-3049	426	25	h	h	NOUN
ejpam-3049	426	26	,	,	PUNCT
ejpam-3049	426	27	by	by	ADP
ejpam-3049	426	28	proposition	proposition	NOUN
ejpam-3049	426	29	2.2	2.2	NUM
ejpam-3049	426	30	,	,	PUNCT
ejpam-3049	426	31	we	we	PRON
ejpam-3049	426	32	have	have	VERB
ejpam-3049	426	33	f	f	NUM
ejpam-3049	426	34	◦	◦	NOUN
ejpam-3049	426	35	g	g	PROPN
ejpam-3049	426	36	�	�	PROPN
ejpam-3049	426	37	f	f	PROPN
ejpam-3049	426	38	∧	∧	PROPN
ejpam-3049	426	39	g.	g.	PROPN
ejpam-3049	426	40	let	let	VERB
ejpam-3049	426	41	now	now	ADV
ejpam-3049	426	42	a	a	DET
ejpam-3049	426	43	∈	∈	PROPN
ejpam-3049	426	44	h.	h.	NOUN
ejpam-3049	427	1	then	then	ADV
ejpam-3049	427	2	(	(	PUNCT
ejpam-3049	427	3	f	f	PROPN
ejpam-3049	427	4	∧	∧	PROPN
ejpam-3049	427	5	g)(a	g)(a	PROPN
ejpam-3049	427	6	)	)	PUNCT
ejpam-3049	427	7	≤	≤	NOUN
ejpam-3049	427	8	(	(	PUNCT
ejpam-3049	427	9	f	f	X
ejpam-3049	427	10	◦	◦	NOUN
ejpam-3049	427	11	g)(a	g)(a	PROPN
ejpam-3049	427	12	)	)	PUNCT
ejpam-3049	427	13	.	.	PUNCT
ejpam-3049	428	1	in	in	ADP
ejpam-3049	428	2	fact	fact	NOUN
ejpam-3049	428	3	:	:	PUNCT
ejpam-3049	428	4	since	since	SCONJ
ejpam-3049	428	5	h	h	NOUN
ejpam-3049	428	6	is	be	AUX
ejpam-3049	428	7	semisimple	semisimple	ADJ
ejpam-3049	428	8	,	,	PUNCT
ejpam-3049	428	9	there	there	PRON
ejpam-3049	428	10	exist	exist	VERB
ejpam-3049	428	11	x	x	NOUN
ejpam-3049	428	12	,	,	PUNCT
ejpam-3049	428	13	y	y	PROPN
ejpam-3049	428	14	,	,	PUNCT
ejpam-3049	428	15	z	z	PROPN
ejpam-3049	428	16	∈	∈	PROPN
ejpam-3049	428	17	h	h	NOUN
ejpam-3049	428	18	such	such	ADJ
ejpam-3049	428	19	that	that	SCONJ
ejpam-3049	428	20	a	a	DET
ejpam-3049	428	21	∈	∈	NOUN
ejpam-3049	428	22	(	(	PUNCT
ejpam-3049	428	23	x	x	SYM
ejpam-3049	428	24	◦	◦	VERB
ejpam-3049	428	25	a	a	X
ejpam-3049	428	26	)	)	PUNCT
ejpam-3049	428	27	∗	∗	NOUN
ejpam-3049	428	28	(	(	PUNCT
ejpam-3049	428	29	y	y	NOUN
ejpam-3049	428	30	◦	◦	VERB
ejpam-3049	428	31	a	a	X
ejpam-3049	428	32	)	)	PUNCT
ejpam-3049	428	33	∗	∗	NOUN
ejpam-3049	428	34	{	{	PUNCT
ejpam-3049	428	35	z	z	NOUN
ejpam-3049	428	36	}	}	PUNCT
ejpam-3049	428	37	.	.	PUNCT
ejpam-3049	429	1	then	then	ADV
ejpam-3049	429	2	there	there	PRON
ejpam-3049	429	3	exist	exist	VERB
ejpam-3049	429	4	u	u	NOUN
ejpam-3049	429	5	∈	∈	PROPN
ejpam-3049	429	6	x	x	PUNCT
ejpam-3049	429	7	◦	◦	VERB
ejpam-3049	429	8	a	a	PRON
ejpam-3049	429	9	and	and	CCONJ
ejpam-3049	429	10	v	v	ADP
ejpam-3049	429	11	∈	∈	PROPN
ejpam-3049	429	12	(	(	PUNCT
ejpam-3049	429	13	y	y	NOUN
ejpam-3049	429	14	◦	◦	VERB
ejpam-3049	429	15	a	a	X
ejpam-3049	429	16	)	)	PUNCT
ejpam-3049	429	17	∗	∗	NOUN
ejpam-3049	429	18	{	{	PUNCT
ejpam-3049	429	19	z	z	NOUN
ejpam-3049	429	20	}	}	PUNCT
ejpam-3049	429	21	such	such	ADJ
ejpam-3049	429	22	that	that	SCONJ
ejpam-3049	429	23	a	a	DET
ejpam-3049	429	24	∈	∈	PROPN
ejpam-3049	429	25	u	u	NOUN
ejpam-3049	429	26	◦	◦	NOUN
ejpam-3049	429	27	v.	v.	ADV
ejpam-3049	429	28	since	since	SCONJ
ejpam-3049	429	29	v	v	NUM
ejpam-3049	429	30	∈	∈	NOUN
ejpam-3049	429	31	(	(	PUNCT
ejpam-3049	429	32	y	y	NOUN
ejpam-3049	429	33	◦	◦	VERB
ejpam-3049	429	34	a	a	X
ejpam-3049	429	35	)	)	PUNCT
ejpam-3049	429	36	∗	∗	NOUN
ejpam-3049	429	37	{	{	PUNCT
ejpam-3049	429	38	z	z	NOUN
ejpam-3049	429	39	}	}	PUNCT
ejpam-3049	429	40	,	,	PUNCT
ejpam-3049	429	41	there	there	PRON
ejpam-3049	429	42	exists	exist	VERB
ejpam-3049	429	43	w	w	PROPN
ejpam-3049	429	44	∈	∈	PROPN
ejpam-3049	429	45	y	y	PROPN
ejpam-3049	429	46	◦	◦	VERB
ejpam-3049	429	47	a	a	DET
ejpam-3049	429	48	such	such	ADJ
ejpam-3049	430	1	that	that	DET
ejpam-3049	430	2	v	v	NUM
ejpam-3049	430	3	∈	∈	PROPN
ejpam-3049	430	4	w	w	PROPN
ejpam-3049	430	5	◦	◦	NOUN
ejpam-3049	430	6	z.	z.	X
ejpam-3049	430	7	thus	thus	ADV
ejpam-3049	430	8	we	we	PRON
ejpam-3049	430	9	have	have	VERB
ejpam-3049	430	10	u	u	NOUN
ejpam-3049	430	11	∈	∈	NOUN
ejpam-3049	430	12	x	x	PUNCT
ejpam-3049	430	13	◦	◦	NOUN
ejpam-3049	430	14	a	a	PRON
ejpam-3049	430	15	,	,	PUNCT
ejpam-3049	430	16	a	a	DET
ejpam-3049	430	17	∈	∈	X
ejpam-3049	430	18	u	u	NOUN
ejpam-3049	430	19	◦	◦	NOUN
ejpam-3049	430	20	v	v	ADP
ejpam-3049	430	21	,	,	PUNCT
ejpam-3049	430	22	w	w	PROPN
ejpam-3049	430	23	∈	∈	PROPN
ejpam-3049	430	24	y	y	PROPN
ejpam-3049	430	25	◦	◦	NOUN
ejpam-3049	430	26	a	a	PRON
ejpam-3049	430	27	and	and	CCONJ
ejpam-3049	430	28	v	v	ADP
ejpam-3049	430	29	∈	∈	PROPN
ejpam-3049	430	30	w	w	PROPN
ejpam-3049	430	31	◦	◦	NOUN
ejpam-3049	430	32	z.	z.	PROPN
ejpam-3049	430	33	since	since	SCONJ
ejpam-3049	430	34	a	a	DET
ejpam-3049	430	35	∈	∈	PROPN
ejpam-3049	430	36	u	u	NOUN
ejpam-3049	430	37	◦	◦	NOUN
ejpam-3049	430	38	v	v	NUM
ejpam-3049	430	39	,	,	PUNCT
ejpam-3049	430	40	we	we	PRON
ejpam-3049	430	41	have	have	VERB
ejpam-3049	430	42	(	(	PUNCT
ejpam-3049	430	43	u	u	NOUN
ejpam-3049	430	44	,	,	PUNCT
ejpam-3049	430	45	v	v	NOUN
ejpam-3049	430	46	)	)	PUNCT
ejpam-3049	430	47	∈	∈	NOUN
ejpam-3049	430	48	aa	aa	NOUN
ejpam-3049	430	49	.	.	PUNCT
ejpam-3049	431	1	since	since	SCONJ
ejpam-3049	431	2	(	(	PUNCT
ejpam-3049	431	3	u	u	NOUN
ejpam-3049	431	4	,	,	PUNCT
ejpam-3049	431	5	v	v	NOUN
ejpam-3049	431	6	)	)	PUNCT
ejpam-3049	431	7	∈	∈	NOUN
ejpam-3049	431	8	aa	aa	NOUN
ejpam-3049	431	9	,	,	PUNCT
ejpam-3049	431	10	we	we	PRON
ejpam-3049	431	11	have	have	VERB
ejpam-3049	431	12	(	(	PUNCT
ejpam-3049	431	13	f	f	X
ejpam-3049	431	14	◦	◦	NOUN
ejpam-3049	431	15	g)(a	g)(a	PROPN
ejpam-3049	431	16	)	)	PUNCT
ejpam-3049	431	17	:	:	PUNCT
ejpam-3049	432	1	=	=	SYM
ejpam-3049	432	2	∨	∨	X
ejpam-3049	432	3	(	(	PUNCT
ejpam-3049	432	4	h	h	NOUN
ejpam-3049	432	5	,	,	PUNCT
ejpam-3049	432	6	k)∈aa	k)∈aa	PROPN
ejpam-3049	432	7	min{f(h	min{f(h	PROPN
ejpam-3049	432	8	)	)	PUNCT
ejpam-3049	432	9	,	,	PUNCT
ejpam-3049	432	10	g(k	g(k	NOUN
ejpam-3049	432	11	)	)	PUNCT
ejpam-3049	432	12	}	}	PUNCT
ejpam-3049	432	13	≥	≥	NOUN
ejpam-3049	432	14	min{f(u	min{f(u	PROPN
ejpam-3049	432	15	)	)	PUNCT
ejpam-3049	432	16	,	,	PUNCT
ejpam-3049	432	17	g(v	g(v	PROPN
ejpam-3049	432	18	)	)	PUNCT
ejpam-3049	432	19	}	}	PUNCT
ejpam-3049	432	20	.	.	PUNCT
ejpam-3049	433	1	since	since	SCONJ
ejpam-3049	433	2	f	f	PROPN
ejpam-3049	433	3	is	be	AUX
ejpam-3049	433	4	a	a	DET
ejpam-3049	433	5	fuzzy	fuzzy	ADJ
ejpam-3049	433	6	left	leave	VERB
ejpam-3049	433	7	ideal	ideal	NOUN
ejpam-3049	433	8	of	of	ADP
ejpam-3049	433	9	h	h	NOUN
ejpam-3049	433	10	,	,	PUNCT
ejpam-3049	433	11	we	we	PRON
ejpam-3049	433	12	have	have	VERB
ejpam-3049	433	13	f(x	f(x	PROPN
ejpam-3049	433	14	◦	◦	VERB
ejpam-3049	433	15	a	a	DET
ejpam-3049	433	16	)	)	PUNCT
ejpam-3049	433	17	≥	≥	NOUN
ejpam-3049	433	18	f(a	f(a	NOUN
ejpam-3049	433	19	)	)	PUNCT
ejpam-3049	433	20	and	and	CCONJ
ejpam-3049	433	21	since	since	SCONJ
ejpam-3049	433	22	u	u	PROPN
ejpam-3049	433	23	∈	∈	PROPN
ejpam-3049	433	24	x	x	PUNCT
ejpam-3049	433	25	◦	◦	NOUN
ejpam-3049	433	26	a	a	X
ejpam-3049	433	27	,	,	PUNCT
ejpam-3049	433	28	we	we	PRON
ejpam-3049	433	29	have	have	VERB
ejpam-3049	433	30	f(u	f(u	PROPN
ejpam-3049	433	31	)	)	PUNCT
ejpam-3049	433	32	≥	≥	NOUN
ejpam-3049	433	33	f(a	f(a	NOUN
ejpam-3049	433	34	)	)	PUNCT
ejpam-3049	433	35	.	.	PUNCT
ejpam-3049	434	1	since	since	SCONJ
ejpam-3049	434	2	g	g	PROPN
ejpam-3049	434	3	is	be	AUX
ejpam-3049	434	4	a	a	DET
ejpam-3049	434	5	fuzzy	fuzzy	ADJ
ejpam-3049	434	6	right	right	ADJ
ejpam-3049	434	7	ideal	ideal	NOUN
ejpam-3049	434	8	of	of	ADP
ejpam-3049	434	9	h	h	NOUN
ejpam-3049	434	10	,	,	PUNCT
ejpam-3049	434	11	we	we	PRON
ejpam-3049	434	12	have	have	VERB
ejpam-3049	434	13	g(w	g(w	ADJ
ejpam-3049	434	14	◦	◦	PROPN
ejpam-3049	434	15	z	z	NOUN
ejpam-3049	434	16	)	)	PUNCT
ejpam-3049	434	17	≥	≥	NOUN
ejpam-3049	434	18	g(w	g(w	PROPN
ejpam-3049	434	19	)	)	PUNCT
ejpam-3049	434	20	and	and	CCONJ
ejpam-3049	434	21	since	since	SCONJ
ejpam-3049	434	22	v	v	NUM
ejpam-3049	434	23	∈	∈	PROPN
ejpam-3049	434	24	w	w	PROPN
ejpam-3049	434	25	◦	◦	NOUN
ejpam-3049	434	26	z	z	X
ejpam-3049	434	27	,	,	PUNCT
ejpam-3049	434	28	we	we	PRON
ejpam-3049	434	29	have	have	VERB
ejpam-3049	434	30	g(v	g(v	NOUN
ejpam-3049	434	31	)	)	PUNCT
ejpam-3049	434	32	≥	≥	NOUN
ejpam-3049	434	33	g(w	g(w	PROPN
ejpam-3049	434	34	)	)	PUNCT
ejpam-3049	434	35	.	.	PUNCT
ejpam-3049	435	1	since	since	SCONJ
ejpam-3049	435	2	g	g	PROPN
ejpam-3049	435	3	is	be	AUX
ejpam-3049	435	4	a	a	DET
ejpam-3049	435	5	fuzzy	fuzzy	ADJ
ejpam-3049	435	6	left	leave	VERB
ejpam-3049	435	7	ideal	ideal	NOUN
ejpam-3049	435	8	of	of	ADP
ejpam-3049	435	9	h	h	NOUN
ejpam-3049	435	10	,	,	PUNCT
ejpam-3049	435	11	we	we	PRON
ejpam-3049	435	12	have	have	VERB
ejpam-3049	435	13	g(y	g(y	NOUN
ejpam-3049	435	14	◦	◦	NOUN
ejpam-3049	435	15	a	a	DET
ejpam-3049	435	16	)	)	PUNCT
ejpam-3049	435	17	≥	≥	NOUN
ejpam-3049	435	18	g(a	g(a	PROPN
ejpam-3049	435	19	)	)	PUNCT
ejpam-3049	435	20	and	and	CCONJ
ejpam-3049	435	21	since	since	SCONJ
ejpam-3049	435	22	w	w	PROPN
ejpam-3049	435	23	∈	∈	PROPN
ejpam-3049	435	24	y	y	PROPN
ejpam-3049	435	25	◦	◦	NOUN
ejpam-3049	435	26	a	a	X
ejpam-3049	435	27	,	,	PUNCT
ejpam-3049	435	28	we	we	PRON
ejpam-3049	435	29	have	have	VERB
ejpam-3049	435	30	g(w	g(w	ADJ
ejpam-3049	435	31	)	)	PUNCT
ejpam-3049	435	32	≥	≥	NOUN
ejpam-3049	435	33	g(a	g(a	PROPN
ejpam-3049	435	34	)	)	PUNCT
ejpam-3049	435	35	.	.	PUNCT
ejpam-3049	436	1	thus	thus	ADV
ejpam-3049	436	2	we	we	PRON
ejpam-3049	436	3	get	get	VERB
ejpam-3049	436	4	g(v	g(v	NOUN
ejpam-3049	436	5	)	)	PUNCT
ejpam-3049	436	6	≥	≥	NOUN
ejpam-3049	436	7	g(a	g(a	PROPN
ejpam-3049	436	8	)	)	PUNCT
ejpam-3049	436	9	.	.	PUNCT
ejpam-3049	437	1	hence	hence	ADV
ejpam-3049	437	2	we	we	PRON
ejpam-3049	437	3	obtain	obtain	VERB
ejpam-3049	437	4	(	(	PUNCT
ejpam-3049	437	5	f	f	X
ejpam-3049	437	6	◦	◦	PROPN
ejpam-3049	437	7	g)(a	g)(a	PROPN
ejpam-3049	437	8	)	)	PUNCT
ejpam-3049	437	9	≥	≥	NOUN
ejpam-3049	437	10	min{f(a	min{f(a	PROPN
ejpam-3049	437	11	)	)	PUNCT
ejpam-3049	437	12	,	,	PUNCT
ejpam-3049	437	13	g(a	g(a	PROPN
ejpam-3049	437	14	)	)	PUNCT
ejpam-3049	437	15	}	}	PUNCT
ejpam-3049	437	16	=	=	SYM
ejpam-3049	438	1	(	(	PUNCT
ejpam-3049	438	2	f	f	PROPN
ejpam-3049	438	3	∧	∧	PROPN
ejpam-3049	438	4	g)(a	g)(a	PROPN
ejpam-3049	438	5	)	)	PUNCT
ejpam-3049	438	6	,	,	PUNCT
ejpam-3049	438	7	so	so	SCONJ
ejpam-3049	438	8	f	f	PROPN
ejpam-3049	438	9	∧	∧	PROPN
ejpam-3049	438	10	g	g	PROPN
ejpam-3049	438	11	�	�	PROPN
ejpam-3049	438	12	f	f	PROPN
ejpam-3049	439	1	◦	◦	NOUN
ejpam-3049	439	2	g.	g.	PROPN
ejpam-3049	439	3	the	the	DET
ejpam-3049	439	4	implication	implication	NOUN
ejpam-3049	439	5	(	(	PUNCT
ejpam-3049	439	6	2)⇒	2)⇒	NUM
ejpam-3049	439	7	(	(	PUNCT
ejpam-3049	439	8	3	3	NUM
ejpam-3049	439	9	)	)	PUNCT
ejpam-3049	439	10	is	be	AUX
ejpam-3049	439	11	obvious	obvious	ADJ
ejpam-3049	439	12	.	.	PUNCT
ejpam-3049	440	1	(	(	PUNCT
ejpam-3049	440	2	3	3	X
ejpam-3049	440	3	)	)	PUNCT
ejpam-3049	440	4	=	=	NOUN
ejpam-3049	440	5	⇒	⇒	NOUN
ejpam-3049	440	6	(	(	PUNCT
ejpam-3049	440	7	1	1	NUM
ejpam-3049	440	8	)	)	PUNCT
ejpam-3049	440	9	.	.	PUNCT
ejpam-3049	441	1	let	let	VERB
ejpam-3049	441	2	a	a	DET
ejpam-3049	441	3	∈	∈	PROPN
ejpam-3049	441	4	h.	h.	NOUN
ejpam-3049	441	5	we	we	PRON
ejpam-3049	441	6	prove	prove	VERB
ejpam-3049	441	7	that	that	SCONJ
ejpam-3049	441	8	i(a	i(a	PROPN
ejpam-3049	441	9	)	)	PUNCT
ejpam-3049	441	10	⊆	⊆	NUM
ejpam-3049	441	11	i(a	i(a	PROPN
ejpam-3049	441	12	)	)	PUNCT
ejpam-3049	441	13	∗	∗	NOUN
ejpam-3049	441	14	i(a	i(a	PROPN
ejpam-3049	441	15	)	)	PUNCT
ejpam-3049	441	16	.	.	PUNCT
ejpam-3049	442	1	then	then	ADV
ejpam-3049	442	2	,	,	PUNCT
ejpam-3049	442	3	since	since	SCONJ
ejpam-3049	442	4	i(a	i(a	PROPN
ejpam-3049	442	5	)	)	PUNCT
ejpam-3049	442	6	is	be	AUX
ejpam-3049	442	7	an	an	DET
ejpam-3049	442	8	ideal	ideal	NOUN
ejpam-3049	442	9	of	of	ADP
ejpam-3049	442	10	h	h	NOUN
ejpam-3049	442	11	,	,	PUNCT
ejpam-3049	442	12	we	we	PRON
ejpam-3049	442	13	have	have	VERB
ejpam-3049	442	14	i(a	i(a	PROPN
ejpam-3049	442	15	)	)	PUNCT
ejpam-3049	442	16	=	=	SYM
ejpam-3049	442	17	i(a	i(a	PROPN
ejpam-3049	442	18	)	)	PUNCT
ejpam-3049	442	19	∗	∗	PROPN
ejpam-3049	442	20	i(a	i(a	PROPN
ejpam-3049	442	21	)	)	PUNCT
ejpam-3049	442	22	and	and	CCONJ
ejpam-3049	442	23	,	,	PUNCT
ejpam-3049	442	24	by	by	ADP
ejpam-3049	442	25	theorem	theorem	NOUN
ejpam-3049	442	26	2.25	2.25	NUM
ejpam-3049	442	27	,	,	PUNCT
ejpam-3049	442	28	h	h	NOUN
ejpam-3049	442	29	is	be	AUX
ejpam-3049	442	30	semisimple	semisimple	ADJ
ejpam-3049	442	31	.	.	PUNCT
ejpam-3049	443	1	let	let	VERB
ejpam-3049	443	2	now	now	ADV
ejpam-3049	443	3	b	b	X
ejpam-3049	443	4	∈	∈	PROPN
ejpam-3049	443	5	i(a	i(a	PROPN
ejpam-3049	443	6	)	)	PUNCT
ejpam-3049	443	7	.	.	PUNCT
ejpam-3049	444	1	then	then	ADV
ejpam-3049	444	2	b	b	X
ejpam-3049	444	3	∈	∈	PROPN
ejpam-3049	444	4	i(a	i(a	PROPN
ejpam-3049	444	5	)	)	PUNCT
ejpam-3049	444	6	∗	∗	PROPN
ejpam-3049	444	7	i(a	i(a	PROPN
ejpam-3049	444	8	)	)	PUNCT
ejpam-3049	444	9	.	.	PUNCT
ejpam-3049	445	1	in	in	ADP
ejpam-3049	445	2	fact	fact	NOUN
ejpam-3049	445	3	:	:	PUNCT
ejpam-3049	445	4	since	since	SCONJ
ejpam-3049	445	5	i(a	i(a	PROPN
ejpam-3049	445	6	)	)	PUNCT
ejpam-3049	445	7	is	be	AUX
ejpam-3049	445	8	an	an	DET
ejpam-3049	445	9	ideal	ideal	NOUN
ejpam-3049	445	10	of	of	ADP
ejpam-3049	445	11	h	h	NOUN
ejpam-3049	445	12	,	,	PUNCT
ejpam-3049	445	13	the	the	DET
ejpam-3049	445	14	characteristic	characteristic	ADJ
ejpam-3049	445	15	function	function	NOUN
ejpam-3049	445	16	fi(a	fi(a	PROPN
ejpam-3049	445	17	)	)	PUNCT
ejpam-3049	445	18	is	be	AUX
ejpam-3049	445	19	a	a	DET
ejpam-3049	445	20	fuzzy	fuzzy	ADJ
ejpam-3049	445	21	ideal	ideal	NOUN
ejpam-3049	445	22	of	of	ADP
ejpam-3049	445	23	h.	h.	NOUN
ejpam-3049	445	24	by	by	ADP
ejpam-3049	445	25	hypothesis	hypothesis	NOUN
ejpam-3049	445	26	,	,	PUNCT
ejpam-3049	445	27	we	we	PRON
ejpam-3049	445	28	have	have	VERB
ejpam-3049	445	29	fi(a	fi(a	NUM
ejpam-3049	445	30	)	)	PUNCT
ejpam-3049	445	31	=	=	SYM
ejpam-3049	445	32	fi(a	fi(a	X
ejpam-3049	445	33	)	)	PUNCT
ejpam-3049	445	34	◦	◦	NOUN
ejpam-3049	445	35	fi(a	fi(a	NUM
ejpam-3049	445	36	)	)	PUNCT
ejpam-3049	445	37	,	,	PUNCT
ejpam-3049	445	38	then	then	ADV
ejpam-3049	445	39	fi(a)(b	fi(a)(b	NUM
ejpam-3049	445	40	)	)	PUNCT
ejpam-3049	446	1	=	=	PRON
ejpam-3049	446	2	(	(	PUNCT
ejpam-3049	446	3	fi(a)	fi(a)	PROPN
ejpam-3049	446	4	◦	◦	NOUN
ejpam-3049	446	5	fi(a	fi(a	NUM
ejpam-3049	446	6	)	)	PUNCT
ejpam-3049	446	7	)	)	PUNCT
ejpam-3049	447	1	(	(	PUNCT
ejpam-3049	447	2	b	b	NOUN
ejpam-3049	447	3	)	)	PUNCT
ejpam-3049	447	4	.	.	PUNCT
ejpam-3049	448	1	since	since	SCONJ
ejpam-3049	448	2	b	b	PROPN
ejpam-3049	448	3	∈	∈	PROPN
ejpam-3049	448	4	i(a	i(a	PROPN
ejpam-3049	448	5	)	)	PUNCT
ejpam-3049	448	6	,	,	PUNCT
ejpam-3049	448	7	we	we	PRON
ejpam-3049	448	8	have	have	VERB
ejpam-3049	448	9	fi(a)(b	fi(a)(b	VERB
ejpam-3049	448	10	)	)	PUNCT
ejpam-3049	448	11	=	=	SYM
ejpam-3049	448	12	1	1	NUM
ejpam-3049	448	13	,	,	PUNCT
ejpam-3049	448	14	then	then	ADV
ejpam-3049	448	15	1	1	X
ejpam-3049	448	16	=	=	SYM
ejpam-3049	448	17	(	(	PUNCT
ejpam-3049	448	18	fi(a)	fi(a)	PROPN
ejpam-3049	448	19	◦	◦	NOUN
ejpam-3049	448	20	fi(a	fi(a	NUM
ejpam-3049	448	21	)	)	PUNCT
ejpam-3049	448	22	)	)	PUNCT
ejpam-3049	449	1	(	(	PUNCT
ejpam-3049	449	2	b	b	NOUN
ejpam-3049	449	3	)	)	PUNCT
ejpam-3049	449	4	.	.	PUNCT
ejpam-3049	450	1	if	if	SCONJ
ejpam-3049	450	2	ab	ab	PROPN
ejpam-3049	450	3	=	=	NOUN
ejpam-3049	450	4	∅	∅	NOUN
ejpam-3049	450	5	,	,	PUNCT
ejpam-3049	450	6	then	then	ADV
ejpam-3049	450	7	(	(	PUNCT
ejpam-3049	450	8	fi(a	fi(a	X
ejpam-3049	450	9	)	)	PUNCT
ejpam-3049	450	10	◦	◦	NOUN
ejpam-3049	450	11	fi(a	fi(a	NUM
ejpam-3049	450	12	)	)	PUNCT
ejpam-3049	450	13	)	)	PUNCT
ejpam-3049	451	1	(	(	PUNCT
ejpam-3049	451	2	b	b	X
ejpam-3049	451	3	)	)	PUNCT
ejpam-3049	451	4	=	=	SYM
ejpam-3049	451	5	0	0	NUM
ejpam-3049	451	6	which	which	PRON
ejpam-3049	451	7	is	be	AUX
ejpam-3049	451	8	impossible	impossible	ADJ
ejpam-3049	451	9	.	.	PUNCT
ejpam-3049	452	1	thus	thus	ADV
ejpam-3049	452	2	we	we	PRON
ejpam-3049	452	3	have	have	VERB
ejpam-3049	452	4	ab	ab	PROPN
ejpam-3049	452	5	6=	6=	NOUN
ejpam-3049	452	6	∅	∅	NOUN
ejpam-3049	452	7	and	and	CCONJ
ejpam-3049	452	8	(	(	PUNCT
ejpam-3049	452	9	fi(a	fi(a	X
ejpam-3049	452	10	)	)	PUNCT
ejpam-3049	452	11	◦	◦	NOUN
ejpam-3049	452	12	fi(a	fi(a	NUM
ejpam-3049	452	13	)	)	PUNCT
ejpam-3049	452	14	)	)	PUNCT
ejpam-3049	453	1	(	(	PUNCT
ejpam-3049	453	2	b	b	X
ejpam-3049	453	3	)	)	PUNCT
ejpam-3049	453	4	=	=	SYM
ejpam-3049	453	5	∨	∨	X
ejpam-3049	453	6	(	(	PUNCT
ejpam-3049	453	7	y	y	PROPN
ejpam-3049	453	8	,	,	PUNCT
ejpam-3049	453	9	z)∈ab	z)∈ab	PROPN
ejpam-3049	453	10	min{fi(a)(y	min{fi(a)(y	PROPN
ejpam-3049	453	11	)	)	PUNCT
ejpam-3049	453	12	,	,	PUNCT
ejpam-3049	453	13	fi(a)(z	fi(a)(z	NUM
ejpam-3049	453	14	)	)	PUNCT
ejpam-3049	453	15	}	}	PUNCT
ejpam-3049	453	16	.	.	PUNCT
ejpam-3049	454	1	then	then	ADV
ejpam-3049	454	2	there	there	PRON
ejpam-3049	454	3	exists	exist	VERB
ejpam-3049	454	4	(	(	PUNCT
ejpam-3049	454	5	y	y	NOUN
ejpam-3049	454	6	,	,	PUNCT
ejpam-3049	454	7	z	z	NOUN
ejpam-3049	454	8	)	)	PUNCT
ejpam-3049	454	9	∈	∈	PROPN
ejpam-3049	454	10	ab	ab	PROPN
ejpam-3049	454	11	such	such	ADJ
ejpam-3049	454	12	that	that	AUX
ejpam-3049	454	13	y	y	PROPN
ejpam-3049	454	14	∈	∈	PROPN
ejpam-3049	454	15	i(a	i(a	PROPN
ejpam-3049	454	16	)	)	PUNCT
ejpam-3049	454	17	and	and	CCONJ
ejpam-3049	454	18	z	z	NOUN
ejpam-3049	454	19	∈	∈	PROPN
ejpam-3049	454	20	i(a	i(a	PROPN
ejpam-3049	454	21	)	)	PUNCT
ejpam-3049	454	22	(	(	PUNCT
ejpam-3049	454	23	otherwise	otherwise	ADV
ejpam-3049	454	24	,	,	PUNCT
ejpam-3049	454	25	(	(	PUNCT
ejpam-3049	454	26	fi(a	fi(a	X
ejpam-3049	454	27	)	)	PUNCT
ejpam-3049	454	28	◦	◦	NOUN
ejpam-3049	454	29	fi(a	fi(a	NUM
ejpam-3049	454	30	)	)	PUNCT
ejpam-3049	454	31	)	)	PUNCT
ejpam-3049	455	1	(	(	PUNCT
ejpam-3049	455	2	b	b	X
ejpam-3049	455	3	)	)	PUNCT
ejpam-3049	455	4	=	=	SYM
ejpam-3049	455	5	0	0	NUM
ejpam-3049	455	6	which	which	PRON
ejpam-3049	455	7	is	be	AUX
ejpam-3049	455	8	impossible	impossible	ADJ
ejpam-3049	455	9	)	)	PUNCT
ejpam-3049	455	10	.	.	PUNCT
ejpam-3049	456	1	therefore	therefore	ADV
ejpam-3049	456	2	,	,	PUNCT
ejpam-3049	456	3	we	we	PRON
ejpam-3049	456	4	have	have	VERB
ejpam-3049	456	5	b	b	NUM
ejpam-3049	456	6	∈	∈	PROPN
ejpam-3049	456	7	y	y	PROPN
ejpam-3049	456	8	◦	◦	NOUN
ejpam-3049	456	9	z	z	NOUN
ejpam-3049	456	10	⊆	⊆	NUM
ejpam-3049	456	11	i(a	i(a	PROPN
ejpam-3049	456	12	)	)	PUNCT
ejpam-3049	456	13	∗	∗	PROPN
ejpam-3049	456	14	i(a	i(a	PROPN
ejpam-3049	456	15	)	)	PUNCT
ejpam-3049	456	16	,	,	PUNCT
ejpam-3049	456	17	and	and	CCONJ
ejpam-3049	456	18	then	then	ADV
ejpam-3049	456	19	b	b	PROPN
ejpam-3049	456	20	∈	∈	PROPN
ejpam-3049	456	21	i(a	i(a	PROPN
ejpam-3049	456	22	)	)	PUNCT
ejpam-3049	456	23	∗	∗	PROPN
ejpam-3049	456	24	i(a	i(a	PROPN
ejpam-3049	456	25	)	)	PUNCT
ejpam-3049	456	26	.	.	PUNCT
ejpam-3049	457	1	�	�	PROPN
ejpam-3049	457	2	with	with	ADP
ejpam-3049	457	3	my	my	PRON
ejpam-3049	457	4	best	good	ADJ
ejpam-3049	457	5	thanks	thank	NOUN
ejpam-3049	457	6	to	to	ADP
ejpam-3049	457	7	the	the	DET
ejpam-3049	457	8	referee	referee	NOUN
ejpam-3049	457	9	for	for	ADP
ejpam-3049	457	10	reading	read	VERB
ejpam-3049	457	11	the	the	DET
ejpam-3049	457	12	paper	paper	NOUN
ejpam-3049	457	13	carefully	carefully	ADV
ejpam-3049	457	14	(	(	PUNCT
ejpam-3049	457	15	recently	recently	ADV
ejpam-3049	457	16	not	not	PART
ejpam-3049	457	17	very	very	ADV
ejpam-3049	457	18	usual	usual	ADJ
ejpam-3049	457	19	)	)	PUNCT
ejpam-3049	457	20	and	and	CCONJ
ejpam-3049	457	21	his	his	PRON
ejpam-3049	457	22	prompt	prompt	ADJ
ejpam-3049	457	23	reply	reply	NOUN
ejpam-3049	457	24	.	.	PUNCT
ejpam-3049	458	1	references	reference	NOUN
ejpam-3049	458	2	945	945	NUM
ejpam-3049	458	3	references	reference	NOUN
ejpam-3049	458	4	[	[	X
ejpam-3049	458	5	1	1	NUM
ejpam-3049	458	6	]	]	PUNCT
ejpam-3049	458	7	a	a	DET
ejpam-3049	458	8	h	h	NOUN
ejpam-3049	458	9	clifford	clifford	PROPN
ejpam-3049	458	10	,	,	PUNCT
ejpam-3049	458	11	g	g	PROPN
ejpam-3049	458	12	b	b	PROPN
ejpam-3049	458	13	preston	preston	PROPN
ejpam-3049	458	14	.	.	PUNCT
ejpam-3049	459	1	the	the	DET
ejpam-3049	459	2	algebraic	algebraic	PROPN
ejpam-3049	459	3	theory	theory	NOUN
ejpam-3049	459	4	of	of	ADP
ejpam-3049	459	5	semigroups	semigroup	NOUN
ejpam-3049	459	6	.	.	PUNCT
ejpam-3049	460	1	amer	amer	PROPN
ejpam-3049	460	2	.	.	PUNCT
ejpam-3049	460	3	math	math	PROPN
ejpam-3049	460	4	.	.	PUNCT
ejpam-3049	461	1	soc	soc	PROPN
ejpam-3049	461	2	.	.	PUNCT
ejpam-3049	461	3	,	,	PUNCT
ejpam-3049	461	4	math	math	NOUN
ejpam-3049	461	5	.	.	PUNCT
ejpam-3049	462	1	surveys	survey	NOUN
ejpam-3049	462	2	7	7	NUM
ejpam-3049	462	3	,	,	PUNCT
ejpam-3049	462	4	providence	providence	NOUN
ejpam-3049	462	5	,	,	PUNCT
ejpam-3049	462	6	rhode	rhode	NOUN
ejpam-3049	462	7	island	island	NOUN
ejpam-3049	462	8	1961	1961	NUM
ejpam-3049	462	9	.	.	PUNCT
ejpam-3049	463	1	xv+224	xv+224	PROPN
ejpam-3049	464	1	pp	pp	ADV
ejpam-3049	464	2	.	.	PUNCT
ejpam-3049	465	1	[	[	X
ejpam-3049	465	2	2	2	NUM
ejpam-3049	465	3	]	]	X
ejpam-3049	465	4	k	k	PROPN
ejpam-3049	465	5	iséki	iséki	PROPN
ejpam-3049	465	6	.	.	PUNCT
ejpam-3049	466	1	a	a	DET
ejpam-3049	466	2	characterization	characterization	NOUN
ejpam-3049	466	3	of	of	ADP
ejpam-3049	466	4	regular	regular	ADJ
ejpam-3049	466	5	semi	semi	NOUN
ejpam-3049	466	6	-	-	NOUN
ejpam-3049	466	7	group	group	NOUN
ejpam-3049	466	8	.	.	PUNCT
ejpam-3049	467	1	proc	proc	PROPN
ejpam-3049	467	2	.	.	PUNCT
ejpam-3049	468	1	japan	japan	PROPN
ejpam-3049	468	2	acad	acad	PROPN
ejpam-3049	468	3	.	.	PUNCT
ejpam-3049	469	1	32:676–677	32:676–677	NUM
ejpam-3049	469	2	,	,	PUNCT
ejpam-3049	469	3	1956	1956	NUM
ejpam-3049	469	4	.	.	PUNCT
ejpam-3049	470	1	[	[	X
ejpam-3049	470	2	3	3	X
ejpam-3049	470	3	]	]	PUNCT
ejpam-3049	470	4	n	n	PRON
ejpam-3049	470	5	kehayopulu	kehayopulu	VERB
ejpam-3049	470	6	.	.	PUNCT
ejpam-3049	471	1	on	on	ADP
ejpam-3049	471	2	prime	prime	ADJ
ejpam-3049	471	3	,	,	PUNCT
ejpam-3049	471	4	weakly	weakly	ADJ
ejpam-3049	471	5	prime	prime	ADJ
ejpam-3049	471	6	ideals	ideal	NOUN
ejpam-3049	471	7	in	in	ADP
ejpam-3049	471	8	ordered	order	VERB
ejpam-3049	471	9	semigroups	semigroup	NOUN
ejpam-3049	471	10	.	.	PUNCT
ejpam-3049	472	1	semigroup	semigroup	PROPN
ejpam-3049	472	2	forum	forum	PROPN
ejpam-3049	472	3	44(3):341–346	44(3):341–346	PROPN
ejpam-3049	472	4	,	,	PUNCT
ejpam-3049	472	5	1992	1992	NUM
ejpam-3049	472	6	.	.	PUNCT
ejpam-3049	473	1	[	[	X
ejpam-3049	473	2	4	4	X
ejpam-3049	473	3	]	]	PUNCT
ejpam-3049	473	4	n	n	PRON
ejpam-3049	473	5	kehayopulu	kehayopulu	ADJ
ejpam-3049	473	6	.	.	PUNCT
ejpam-3049	474	1	characterization	characterization	NOUN
ejpam-3049	474	2	of	of	ADP
ejpam-3049	474	3	left	left	ADJ
ejpam-3049	474	4	quasi	quasi	ADJ
ejpam-3049	474	5	-	-	ADJ
ejpam-3049	474	6	regular	regular	ADJ
ejpam-3049	474	7	and	and	CCONJ
ejpam-3049	474	8	semisimple	semisimple	NOUN
ejpam-3049	474	9	ordered	order	VERB
ejpam-3049	474	10	semigroups	semigroup	NOUN
ejpam-3049	474	11	in	in	ADP
ejpam-3049	474	12	terms	term	NOUN
ejpam-3049	474	13	of	of	ADP
ejpam-3049	474	14	fuzzy	fuzzy	ADJ
ejpam-3049	474	15	sets	set	NOUN
ejpam-3049	474	16	.	.	PUNCT
ejpam-3049	475	1	int	int	NOUN
ejpam-3049	475	2	.	.	PUNCT
ejpam-3049	476	1	j.	j.	PROPN
ejpam-3049	476	2	algebra	algebra	PROPN
ejpam-3049	476	3	6(13–16):747–755	6(13–16):747–755	NUM
ejpam-3049	476	4	,	,	PUNCT
ejpam-3049	476	5	2012	2012	NUM
ejpam-3049	476	6	.	.	PUNCT
ejpam-3049	477	1	[	[	X
ejpam-3049	477	2	5	5	NUM
ejpam-3049	477	3	]	]	PUNCT
ejpam-3049	477	4	n	n	CCONJ
ejpam-3049	477	5	kehayopulu	kehayopulu	VERB
ejpam-3049	477	6	.	.	PUNCT
ejpam-3049	478	1	on	on	ADP
ejpam-3049	478	2	hypersemigroups	hypersemigroup	NOUN
ejpam-3049	478	3	.	.	PUNCT
ejpam-3049	479	1	pure	pure	ADJ
ejpam-3049	479	2	math	math	NOUN
ejpam-3049	479	3	.	.	PUNCT
ejpam-3049	480	1	appl	appl	PROPN
ejpam-3049	480	2	.	.	PUNCT
ejpam-3049	481	1	(	(	PUNCT
ejpam-3049	481	2	pu.m.a	pu.m.a	PROPN
ejpam-3049	481	3	.	.	PUNCT
ejpam-3049	481	4	)	)	PUNCT
ejpam-3049	482	1	25(2):151–156	25(2):151–156	PROPN
ejpam-3049	482	2	,	,	PUNCT
ejpam-3049	482	3	2015	2015	NUM
ejpam-3049	482	4	.	.	PUNCT
ejpam-3049	483	1	[	[	X
ejpam-3049	483	2	6	6	NUM
ejpam-3049	483	3	]	]	PUNCT
ejpam-3049	483	4	n	n	PRON
ejpam-3049	483	5	kehayopulu	kehayopulu	VERB
ejpam-3049	483	6	.	.	PUNCT
ejpam-3049	484	1	on	on	ADP
ejpam-3049	484	2	fuzzy	fuzzy	ADJ
ejpam-3049	484	3	prime	prime	ADJ
ejpam-3049	484	4	and	and	CCONJ
ejpam-3049	484	5	fuzzy	fuzzy	ADJ
ejpam-3049	484	6	semiprime	semiprime	NOUN
ejpam-3049	484	7	ideals	ideal	NOUN
ejpam-3049	484	8	of	of	ADP
ejpam-3049	484	9	≤–hypergroupoids	≤–hypergroupoids	PROPN
ejpam-3049	484	10	.	.	PUNCT
ejpam-3049	485	1	j.	j.	PROPN
ejpam-3049	485	2	hyperstruct	hyperstruct	PROPN
ejpam-3049	485	3	.	.	PUNCT
ejpam-3049	486	1	5(2):108–114	5(2):108–114	NUM
ejpam-3049	486	2	,	,	PUNCT
ejpam-3049	486	3	2016	2016	NUM
ejpam-3049	486	4	.	.	PUNCT
ejpam-3049	487	1	[	[	X
ejpam-3049	487	2	7	7	X
ejpam-3049	487	3	]	]	PUNCT
ejpam-3049	487	4	n	n	CCONJ
ejpam-3049	487	5	kehayopulu	kehayopulu	VERB
ejpam-3049	487	6	,	,	PUNCT
ejpam-3049	487	7	m	m	PROPN
ejpam-3049	487	8	tsingelis	tsingeli	NOUN
ejpam-3049	487	9	.	.	PUNCT
ejpam-3049	488	1	regular	regular	ADJ
ejpam-3049	488	2	ordered	order	VERB
ejpam-3049	488	3	semigroups	semigroup	NOUN
ejpam-3049	488	4	in	in	ADP
ejpam-3049	488	5	terms	term	NOUN
ejpam-3049	488	6	of	of	ADP
ejpam-3049	488	7	fuzzy	fuzzy	ADJ
ejpam-3049	488	8	subsets	subset	NOUN
ejpam-3049	488	9	.	.	PUNCT
ejpam-3049	489	1	inform	inform	NOUN
ejpam-3049	489	2	.	.	PUNCT
ejpam-3049	490	1	sci	sci	PROPN
ejpam-3049	490	2	.	.	PROPN
ejpam-3049	490	3	176(24):3675–3693	176(24):3675–3693	NUM
ejpam-3049	490	4	,	,	PUNCT
ejpam-3049	490	5	2006	2006	NUM
ejpam-3049	490	6	.	.	PUNCT
ejpam-3049	491	1	[	[	X
ejpam-3049	491	2	8	8	NUM
ejpam-3049	491	3	]	]	PUNCT
ejpam-3049	491	4	n	n	PRON
ejpam-3049	491	5	kuroki	kuroki	NOUN
ejpam-3049	491	6	.	.	PUNCT
ejpam-3049	492	1	fuzzy	fuzzy	ADJ
ejpam-3049	492	2	semiprime	semiprime	NOUN
ejpam-3049	492	3	ideals	ideal	NOUN
ejpam-3049	492	4	in	in	ADP
ejpam-3049	492	5	semigroups	semigroup	NOUN
ejpam-3049	492	6	.	.	PUNCT
ejpam-3049	493	1	fuzzy	fuzzy	ADJ
ejpam-3049	493	2	sets	set	NOUN
ejpam-3049	493	3	and	and	CCONJ
ejpam-3049	493	4	systems	system	NOUN
ejpam-3049	493	5	8(1):71–79	8(1):71–79	NUM
ejpam-3049	493	6	,	,	PUNCT
ejpam-3049	493	7	1982	1982	NUM
ejpam-3049	493	8	.	.	PUNCT
ejpam-3049	494	1	[	[	X
ejpam-3049	494	2	9	9	NUM
ejpam-3049	494	3	]	]	SYM
ejpam-3049	494	4	s	s	PART
ejpam-3049	494	5	lajos	lajos	NOUN
ejpam-3049	494	6	,	,	PUNCT
ejpam-3049	494	7	g	g	PROPN
ejpam-3049	494	8	szász	szász	NUM
ejpam-3049	494	9	.	.	PUNCT
ejpam-3049	495	1	on	on	ADP
ejpam-3049	495	2	characterizations	characterization	NOUN
ejpam-3049	495	3	of	of	ADP
ejpam-3049	495	4	certain	certain	ADJ
ejpam-3049	495	5	classes	class	NOUN
ejpam-3049	495	6	of	of	ADP
ejpam-3049	495	7	semigroups	semigroup	NOUN
ejpam-3049	495	8	.	.	PUNCT
ejpam-3049	496	1	publ	publ	PROPN
ejpam-3049	496	2	.	.	PUNCT
ejpam-3049	497	1	math	math	NOUN
ejpam-3049	497	2	.	.	PUNCT
ejpam-3049	498	1	debrecen	debrecen	PROPN
ejpam-3049	498	2	25(3–4):225–227	25(3–4):225–227	PROPN
ejpam-3049	498	3	,	,	PUNCT
ejpam-3049	498	4	1978	1978	NUM
ejpam-3049	498	5	.	.	PUNCT
ejpam-3049	499	1	[	[	X
ejpam-3049	499	2	10	10	NUM
ejpam-3049	499	3	]	]	PUNCT
ejpam-3049	499	4	t	t	PROPN
ejpam-3049	499	5	mahmood	mahmood	PROPN
ejpam-3049	499	6	.	.	PUNCT
ejpam-3049	500	1	some	some	DET
ejpam-3049	500	2	contributions	contribution	NOUN
ejpam-3049	500	3	to	to	ADP
ejpam-3049	500	4	semihypergroups	semihypergroup	NOUN
ejpam-3049	500	5	.	.	PUNCT
ejpam-3049	501	1	phd	phd	NOUN
ejpam-3049	501	2	thesis	thesis	PROPN
ejpam-3049	501	3	,	,	PUNCT
ejpam-3049	501	4	department	department	NOUN
ejpam-3049	501	5	of	of	ADP
ejpam-3049	501	6	mathematics	mathematic	NOUN
ejpam-3049	501	7	,	,	PUNCT
ejpam-3049	501	8	quaid	quaid	PROPN
ejpam-3049	501	9	-	-	PUNCT
ejpam-3049	501	10	i	i	PROPN
ejpam-3049	501	11	-	-	PUNCT
ejpam-3049	501	12	azam	azam	PROPN
ejpam-3049	501	13	university	university	PROPN
ejpam-3049	501	14	,	,	PUNCT
ejpam-3049	501	15	islamabad	islamabad	PROPN
ejpam-3049	501	16	,	,	PUNCT
ejpam-3049	501	17	pakistan	pakistan	PROPN
ejpam-3049	501	18	2011	2011	NUM
ejpam-3049	501	19	.	.	PUNCT
ejpam-3049	502	1	[	[	X
ejpam-3049	502	2	11	11	NUM
ejpam-3049	502	3	]	]	X
ejpam-3049	502	4	m	m	VERB
ejpam-3049	502	5	mitrović.	mitrović.	ADJ
ejpam-3049	502	6	semilattices	semilattice	NOUN
ejpam-3049	502	7	of	of	ADP
ejpam-3049	502	8	archimedean	archimedean	ADJ
ejpam-3049	502	9	semigroups	semigroup	NOUN
ejpam-3049	502	10	.	.	PUNCT
ejpam-3049	503	1	university	university	NOUN
ejpam-3049	503	2	of	of	ADP
ejpam-3049	503	3	nis	nis	PROPN
ejpam-3049	503	4	,	,	PUNCT
ejpam-3049	503	5	faculty	faculty	NOUN
ejpam-3049	503	6	of	of	ADP
ejpam-3049	503	7	mechanical	mechanical	ADJ
ejpam-3049	503	8	engineering	engineering	NOUN
ejpam-3049	503	9	,	,	PUNCT
ejpam-3049	503	10	nis	nis	PROPN
ejpam-3049	503	11	2003	2003	NUM
ejpam-3049	503	12	.	.	PUNCT
ejpam-3049	504	1	xiv+160	xiv+160	PROPN
ejpam-3049	504	2	pp	pp	PROPN
ejpam-3049	504	3	.	.	PUNCT
ejpam-3049	505	1	[	[	X
ejpam-3049	505	2	12	12	NUM
ejpam-3049	505	3	]	]	X
ejpam-3049	505	4	m	m	NOUN
ejpam-3049	505	5	shabir	shabir	PROPN
ejpam-3049	505	6	,	,	PUNCT
ejpam-3049	505	7	a	a	DET
ejpam-3049	505	8	khan	khan	PROPN
ejpam-3049	505	9	.	.	PUNCT
ejpam-3049	505	10	characterizations	characterization	NOUN
ejpam-3049	505	11	of	of	ADP
ejpam-3049	505	12	ordered	order	VERB
ejpam-3049	505	13	semigroups	semigroup	NOUN
ejpam-3049	505	14	by	by	ADP
ejpam-3049	505	15	the	the	DET
ejpam-3049	505	16	properties	property	NOUN
ejpam-3049	505	17	of	of	ADP
ejpam-3049	505	18	their	their	PRON
ejpam-3049	505	19	fuzzy	fuzzy	ADJ
ejpam-3049	505	20	ideals	ideal	NOUN
ejpam-3049	505	21	.	.	PUNCT
ejpam-3049	506	1	comput	comput	NOUN
ejpam-3049	506	2	.	.	PUNCT
ejpam-3049	507	1	math	math	NOUN
ejpam-3049	507	2	.	.	PUNCT
ejpam-3049	508	1	appl	appl	PROPN
ejpam-3049	508	2	.	.	PUNCT
ejpam-3049	509	1	59(1):539–549	59(1):539–549	NOUN
ejpam-3049	509	2	,	,	PUNCT
ejpam-3049	509	3	2010	2010	NUM
ejpam-3049	509	4	.	.	PUNCT
ejpam-3049	510	1	[	[	X
ejpam-3049	510	2	13	13	NUM
ejpam-3049	510	3	]	]	SYM
ejpam-3049	510	4	m	m	NOUN
ejpam-3049	510	5	shabir	shabir	PROPN
ejpam-3049	510	6	,	,	PUNCT
ejpam-3049	510	7	a	a	DET
ejpam-3049	510	8	khan	khan	PROPN
ejpam-3049	510	9	.	.	PUNCT
ejpam-3049	511	1	on	on	ADP
ejpam-3049	511	2	fuzzy	fuzzy	ADJ
ejpam-3049	511	3	ordered	order	VERB
ejpam-3049	511	4	semigroups	semigroup	NOUN
ejpam-3049	511	5	.	.	PUNCT
ejpam-3049	512	1	inform	inform	NOUN
ejpam-3049	512	2	.	.	PUNCT
ejpam-3049	513	1	sci	sci	PROPN
ejpam-3049	513	2	.	.	PROPN
ejpam-3049	513	3	274:236–248	274:236–248	NUM
ejpam-3049	513	4	,	,	PUNCT
ejpam-3049	513	5	2014	2014	NUM
ejpam-3049	513	6	.	.	PUNCT