id	sid	tid	token	lemma	pos
ejpam-3085	1	1	european	european	PROPN
ejpam-3085	1	2	journal	journal	PROPN
ejpam-3085	1	3	of	of	ADP
ejpam-3085	1	4	pure	pure	ADJ
ejpam-3085	1	5	and	and	CCONJ
ejpam-3085	1	6	applied	apply	VERB
ejpam-3085	1	7	mathematics	mathematic	NOUN
ejpam-3085	1	8	vol	vol	NOUN
ejpam-3085	1	9	.	.	PUNCT
ejpam-3085	2	1	11	11	NUM
ejpam-3085	2	2	,	,	PUNCT
ejpam-3085	2	3	no	no	INTJ
ejpam-3085	2	4	.	.	NOUN
ejpam-3085	2	5	1	1	NUM
ejpam-3085	2	6	,	,	PUNCT
ejpam-3085	2	7	2018	2018	NUM
ejpam-3085	2	8	,	,	PUNCT
ejpam-3085	2	9	10	10	NUM
ejpam-3085	2	10	-	-	SYM
ejpam-3085	2	11	22	22	NUM
ejpam-3085	2	12	issn	issn	PROPN
ejpam-3085	2	13	1307	1307	NUM
ejpam-3085	2	14	-	-	SYM
ejpam-3085	2	15	5543	5543	NUM
ejpam-3085	2	16	–	–	PUNCT
ejpam-3085	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3085	2	18	published	publish	VERB
ejpam-3085	2	19	by	by	ADP
ejpam-3085	2	20	new	new	PROPN
ejpam-3085	2	21	york	york	PROPN
ejpam-3085	2	22	business	business	PROPN
ejpam-3085	2	23	global	global	PROPN
ejpam-3085	2	24	on	on	ADP
ejpam-3085	2	25	ordered	order	VERB
ejpam-3085	2	26	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	2	27	with	with	ADP
ejpam-3085	2	28	idempotent	idempotent	ADJ
ejpam-3085	2	29	ideals	ideal	NOUN
ejpam-3085	2	30	,	,	PUNCT
ejpam-3085	2	31	prime	prime	ADJ
ejpam-3085	2	32	or	or	CCONJ
ejpam-3085	2	33	weakly	weakly	ADJ
ejpam-3085	2	34	prime	prime	ADJ
ejpam-3085	2	35	ideals	ideal	NOUN
ejpam-3085	2	36	niovi	niovi	NOUN
ejpam-3085	2	37	kehayopulu	kehayopulu	VERB
ejpam-3085	2	38	to	to	ADP
ejpam-3085	2	39	the	the	DET
ejpam-3085	2	40	memory	memory	NOUN
ejpam-3085	2	41	of	of	ADP
ejpam-3085	2	42	my	my	PRON
ejpam-3085	2	43	teachers	teacher	NOUN
ejpam-3085	2	44	professor	professor	PROPN
ejpam-3085	2	45	nazım	nazım	NOUN
ejpam-3085	2	46	terzioğlu	terzioğlu	NOUN
ejpam-3085	2	47	and	and	CCONJ
ejpam-3085	2	48	professor	professor	PROPN
ejpam-3085	2	49	suzan	suzan	PROPN
ejpam-3085	2	50	kahramaner	kahramaner	PROPN
ejpam-3085	2	51	abstract	abstract	PROPN
ejpam-3085	2	52	.	.	PUNCT
ejpam-3085	3	1	some	some	DET
ejpam-3085	3	2	well	well	ADV
ejpam-3085	3	3	known	know	VERB
ejpam-3085	3	4	results	result	NOUN
ejpam-3085	3	5	on	on	ADP
ejpam-3085	3	6	ordered	order	VERB
ejpam-3085	3	7	semigroups	semigroup	NOUN
ejpam-3085	3	8	are	be	AUX
ejpam-3085	3	9	examined	examine	VERB
ejpam-3085	3	10	in	in	ADP
ejpam-3085	3	11	case	case	NOUN
ejpam-3085	3	12	of	of	ADP
ejpam-3085	3	13	ordered	order	VERB
ejpam-3085	3	14	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	3	15	.	.	PUNCT
ejpam-3085	4	1	following	follow	VERB
ejpam-3085	4	2	the	the	DET
ejpam-3085	4	3	paper	paper	NOUN
ejpam-3085	4	4	in	in	ADP
ejpam-3085	4	5	semigroup	semigroup	PROPN
ejpam-3085	4	6	forum	forum	PROPN
ejpam-3085	4	7	44	44	NUM
ejpam-3085	4	8	(	(	PUNCT
ejpam-3085	4	9	1992	1992	NUM
ejpam-3085	4	10	)	)	PUNCT
ejpam-3085	4	11	,	,	PUNCT
ejpam-3085	4	12	341–346	341–346	NUM
ejpam-3085	4	13	,	,	PUNCT
ejpam-3085	4	14	we	we	PRON
ejpam-3085	4	15	prove	prove	VERB
ejpam-3085	4	16	the	the	DET
ejpam-3085	4	17	following	following	NOUN
ejpam-3085	4	18	:	:	PUNCT
ejpam-3085	4	19	the	the	DET
ejpam-3085	4	20	ideals	ideal	NOUN
ejpam-3085	4	21	of	of	ADP
ejpam-3085	4	22	an	an	DET
ejpam-3085	4	23	ordered	order	VERB
ejpam-3085	4	24	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	4	25	h	h	PROPN
ejpam-3085	4	26	are	be	AUX
ejpam-3085	4	27	idempotent	idempotent	ADJ
ejpam-3085	5	1	if	if	SCONJ
ejpam-3085	5	2	and	and	CCONJ
ejpam-3085	5	3	only	only	ADV
ejpam-3085	5	4	if	if	SCONJ
ejpam-3085	5	5	for	for	ADP
ejpam-3085	5	6	any	any	DET
ejpam-3085	5	7	two	two	NUM
ejpam-3085	5	8	ideals	ideal	NOUN
ejpam-3085	5	9	a	a	PRON
ejpam-3085	5	10	and	and	CCONJ
ejpam-3085	5	11	b	b	NOUN
ejpam-3085	5	12	of	of	ADP
ejpam-3085	5	13	h	h	NOUN
ejpam-3085	5	14	,	,	PUNCT
ejpam-3085	5	15	we	we	PRON
ejpam-3085	5	16	have	have	VERB
ejpam-3085	5	17	a	a	DET
ejpam-3085	5	18	∩b	∩b	NOUN
ejpam-3085	5	19	=	=	PUNCT
ejpam-3085	5	20	(	(	PUNCT
ejpam-3085	5	21	a	a	DET
ejpam-3085	5	22	∗b	∗b	NOUN
ejpam-3085	5	23	]	]	PUNCT
ejpam-3085	5	24	.	.	PUNCT
ejpam-3085	6	1	let	let	VERB
ejpam-3085	6	2	now	now	ADV
ejpam-3085	6	3	h	h	NOUN
ejpam-3085	6	4	be	be	AUX
ejpam-3085	6	5	an	an	DET
ejpam-3085	6	6	ordered	order	VERB
ejpam-3085	6	7	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	6	8	.	.	PUNCT
ejpam-3085	7	1	then	then	ADV
ejpam-3085	7	2	,	,	PUNCT
ejpam-3085	7	3	the	the	DET
ejpam-3085	7	4	ideals	ideal	NOUN
ejpam-3085	7	5	of	of	ADP
ejpam-3085	7	6	h	h	NOUN
ejpam-3085	7	7	are	be	AUX
ejpam-3085	7	8	idempotent	idempotent	ADJ
ejpam-3085	7	9	if	if	SCONJ
ejpam-3085	8	1	and	and	CCONJ
ejpam-3085	8	2	only	only	ADV
ejpam-3085	8	3	if	if	SCONJ
ejpam-3085	8	4	h	h	NOUN
ejpam-3085	8	5	is	be	AUX
ejpam-3085	8	6	semisimple	semisimple	ADJ
ejpam-3085	8	7	.	.	PUNCT
ejpam-3085	9	1	the	the	DET
ejpam-3085	9	2	ideals	ideal	NOUN
ejpam-3085	9	3	of	of	ADP
ejpam-3085	9	4	h	h	NOUN
ejpam-3085	9	5	are	be	AUX
ejpam-3085	9	6	weakly	weakly	ADV
ejpam-3085	9	7	prime	prime	ADJ
ejpam-3085	9	8	if	if	SCONJ
ejpam-3085	10	1	and	and	CCONJ
ejpam-3085	10	2	only	only	ADV
ejpam-3085	10	3	if	if	SCONJ
ejpam-3085	10	4	they	they	PRON
ejpam-3085	10	5	are	be	AUX
ejpam-3085	10	6	idempotent	idempotent	ADJ
ejpam-3085	10	7	and	and	CCONJ
ejpam-3085	10	8	they	they	PRON
ejpam-3085	10	9	form	form	VERB
ejpam-3085	10	10	a	a	DET
ejpam-3085	10	11	chain	chain	NOUN
ejpam-3085	10	12	.	.	PUNCT
ejpam-3085	11	1	the	the	DET
ejpam-3085	11	2	ideals	ideal	NOUN
ejpam-3085	11	3	of	of	ADP
ejpam-3085	11	4	h	h	NOUN
ejpam-3085	11	5	are	be	AUX
ejpam-3085	11	6	prime	prime	ADJ
ejpam-3085	11	7	if	if	SCONJ
ejpam-3085	12	1	and	and	CCONJ
ejpam-3085	12	2	only	only	ADV
ejpam-3085	12	3	if	if	SCONJ
ejpam-3085	12	4	they	they	PRON
ejpam-3085	12	5	form	form	VERB
ejpam-3085	12	6	a	a	DET
ejpam-3085	12	7	chain	chain	NOUN
ejpam-3085	12	8	and	and	CCONJ
ejpam-3085	12	9	h	h	NOUN
ejpam-3085	12	10	is	be	AUX
ejpam-3085	12	11	intra	intra	ADJ
ejpam-3085	12	12	-	-	ADJ
ejpam-3085	12	13	regular	regular	ADJ
ejpam-3085	12	14	.	.	PUNCT
ejpam-3085	13	1	the	the	DET
ejpam-3085	13	2	paper	paper	NOUN
ejpam-3085	13	3	serves	serve	VERB
ejpam-3085	13	4	as	as	ADP
ejpam-3085	13	5	an	an	DET
ejpam-3085	13	6	example	example	NOUN
ejpam-3085	13	7	to	to	PART
ejpam-3085	13	8	show	show	VERB
ejpam-3085	13	9	how	how	SCONJ
ejpam-3085	13	10	we	we	PRON
ejpam-3085	13	11	pass	pass	VERB
ejpam-3085	13	12	from	from	ADP
ejpam-3085	13	13	ordered	order	VERB
ejpam-3085	13	14	semigroups	semigroup	NOUN
ejpam-3085	13	15	to	to	PART
ejpam-3085	13	16	ordered	order	VERB
ejpam-3085	13	17	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	13	18	.	.	PUNCT
ejpam-3085	14	1	2010	2010	NUM
ejpam-3085	14	2	mathematics	mathematic	NOUN
ejpam-3085	14	3	subject	subject	NOUN
ejpam-3085	14	4	classifications	classification	NOUN
ejpam-3085	14	5	:	:	PUNCT
ejpam-3085	14	6	ams	am	NOUN
ejpam-3085	14	7	06f99	06f99	X
ejpam-3085	14	8	key	key	ADJ
ejpam-3085	14	9	words	word	NOUN
ejpam-3085	14	10	and	and	CCONJ
ejpam-3085	14	11	phrases	phrase	NOUN
ejpam-3085	14	12	:	:	PUNCT
ejpam-3085	14	13	ordered	order	VERB
ejpam-3085	14	14	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	14	15	,	,	PUNCT
ejpam-3085	14	16	ideal	ideal	ADJ
ejpam-3085	14	17	,	,	PUNCT
ejpam-3085	14	18	weakly	weakly	ADJ
ejpam-3085	14	19	prime	prime	ADJ
ejpam-3085	14	20	,	,	PUNCT
ejpam-3085	14	21	prime	prime	ADJ
ejpam-3085	14	22	,	,	PUNCT
ejpam-3085	14	23	idempotent	idempotent	ADJ
ejpam-3085	14	24	,	,	PUNCT
ejpam-3085	14	25	semisimple	semisimple	NOUN
ejpam-3085	14	26	,	,	PUNCT
ejpam-3085	14	27	left	leave	VERB
ejpam-3085	14	28	regular	regular	ADV
ejpam-3085	14	29	,	,	PUNCT
ejpam-3085	14	30	intra	intra	ADJ
ejpam-3085	14	31	-	-	ADJ
ejpam-3085	14	32	regular	regular	ADJ
ejpam-3085	14	33	1	1	NUM
ejpam-3085	14	34	.	.	PUNCT
ejpam-3085	15	1	introduction	introduction	NOUN
ejpam-3085	15	2	and	and	CCONJ
ejpam-3085	15	3	prerequisites	prerequisite	NOUN
ejpam-3085	15	4	in	in	ADP
ejpam-3085	15	5	our	our	PRON
ejpam-3085	15	6	paper	paper	NOUN
ejpam-3085	15	7	in	in	ADP
ejpam-3085	15	8	semigroup	semigroup	PROPN
ejpam-3085	15	9	forum	forum	PROPN
ejpam-3085	15	10	44	44	NUM
ejpam-3085	15	11	(	(	PUNCT
ejpam-3085	15	12	1992	1992	NUM
ejpam-3085	15	13	)	)	PUNCT
ejpam-3085	15	14	341–346	341–346	NUM
ejpam-3085	15	15	[	[	SYM
ejpam-3085	15	16	4	4	X
ejpam-3085	15	17	]	]	PUNCT
ejpam-3085	15	18	we	we	PRON
ejpam-3085	15	19	characterized	characterize	VERB
ejpam-3085	15	20	the	the	DET
ejpam-3085	15	21	ordered	order	VERB
ejpam-3085	15	22	semigroup	semigroup	NOUN
ejpam-3085	15	23	s	s	X
ejpam-3085	15	24	in	in	ADP
ejpam-3085	15	25	which	which	PRON
ejpam-3085	15	26	the	the	DET
ejpam-3085	15	27	ideals	ideal	NOUN
ejpam-3085	15	28	are	be	AUX
ejpam-3085	15	29	idempotent	idempotent	ADJ
ejpam-3085	15	30	in	in	ADP
ejpam-3085	15	31	terms	term	NOUN
ejpam-3085	15	32	of	of	ADP
ejpam-3085	15	33	the	the	DET
ejpam-3085	15	34	ideals	ideal	NOUN
ejpam-3085	15	35	of	of	ADP
ejpam-3085	15	36	s	s	PRON
ejpam-3085	15	37	and	and	CCONJ
ejpam-3085	15	38	we	we	PRON
ejpam-3085	15	39	proved	prove	VERB
ejpam-3085	15	40	that	that	SCONJ
ejpam-3085	15	41	this	this	DET
ejpam-3085	15	42	type	type	NOUN
ejpam-3085	15	43	of	of	ADP
ejpam-3085	15	44	ordered	order	VERB
ejpam-3085	15	45	semigroups	semigroup	NOUN
ejpam-3085	15	46	are	be	AUX
ejpam-3085	15	47	the	the	DET
ejpam-3085	15	48	semisimple	semisimple	NOUN
ejpam-3085	15	49	ordered	order	VERB
ejpam-3085	15	50	semigroups	semigroup	NOUN
ejpam-3085	15	51	.	.	PUNCT
ejpam-3085	16	1	we	we	PRON
ejpam-3085	16	2	also	also	ADV
ejpam-3085	16	3	proved	prove	VERB
ejpam-3085	16	4	that	that	SCONJ
ejpam-3085	16	5	the	the	DET
ejpam-3085	16	6	ideals	ideal	NOUN
ejpam-3085	16	7	of	of	ADP
ejpam-3085	16	8	an	an	DET
ejpam-3085	16	9	ordered	order	VERB
ejpam-3085	16	10	semigroup	semigroup	NOUN
ejpam-3085	16	11	s	s	VERB
ejpam-3085	16	12	are	be	AUX
ejpam-3085	16	13	weakly	weakly	ADV
ejpam-3085	16	14	prime	prime	ADJ
ejpam-3085	16	15	if	if	SCONJ
ejpam-3085	16	16	and	and	CCONJ
ejpam-3085	16	17	only	only	ADV
ejpam-3085	16	18	if	if	SCONJ
ejpam-3085	16	19	they	they	PRON
ejpam-3085	16	20	are	be	AUX
ejpam-3085	16	21	idempotent	idempotent	ADJ
ejpam-3085	16	22	and	and	CCONJ
ejpam-3085	16	23	they	they	PRON
ejpam-3085	16	24	form	form	VERB
ejpam-3085	16	25	a	a	DET
ejpam-3085	16	26	chain	chain	NOUN
ejpam-3085	16	27	.	.	PUNCT
ejpam-3085	17	1	and	and	CCONJ
ejpam-3085	17	2	that	that	SCONJ
ejpam-3085	17	3	the	the	DET
ejpam-3085	17	4	ideals	ideal	NOUN
ejpam-3085	17	5	of	of	ADP
ejpam-3085	17	6	an	an	DET
ejpam-3085	17	7	ordered	order	VERB
ejpam-3085	17	8	semigroup	semigroup	NOUN
ejpam-3085	17	9	s	s	VERB
ejpam-3085	17	10	are	be	AUX
ejpam-3085	17	11	prime	prime	ADJ
ejpam-3085	17	12	if	if	SCONJ
ejpam-3085	18	1	and	and	CCONJ
ejpam-3085	18	2	only	only	ADV
ejpam-3085	18	3	if	if	SCONJ
ejpam-3085	18	4	they	they	PRON
ejpam-3085	18	5	form	form	VERB
ejpam-3085	18	6	a	a	DET
ejpam-3085	18	7	chain	chain	NOUN
ejpam-3085	18	8	and	and	CCONJ
ejpam-3085	18	9	s	s	NOUN
ejpam-3085	18	10	is	be	AUX
ejpam-3085	18	11	intra	intra	ADJ
ejpam-3085	18	12	-	-	ADJ
ejpam-3085	18	13	regular	regular	ADJ
ejpam-3085	18	14	.	.	PUNCT
ejpam-3085	19	1	in	in	ADP
ejpam-3085	19	2	the	the	DET
ejpam-3085	19	3	present	present	ADJ
ejpam-3085	19	4	paper	paper	NOUN
ejpam-3085	19	5	we	we	PRON
ejpam-3085	19	6	show	show	VERB
ejpam-3085	19	7	the	the	DET
ejpam-3085	19	8	way	way	NOUN
ejpam-3085	19	9	we	we	PRON
ejpam-3085	19	10	pass	pass	VERB
ejpam-3085	19	11	from	from	ADP
ejpam-3085	19	12	ordered	order	VERB
ejpam-3085	19	13	semigroups	semigroup	NOUN
ejpam-3085	19	14	to	to	PART
ejpam-3085	19	15	ordered	order	VERB
ejpam-3085	19	16	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	19	17	.	.	PUNCT
ejpam-3085	20	1	for	for	ADP
ejpam-3085	20	2	convenience	convenience	NOUN
ejpam-3085	20	3	,	,	PUNCT
ejpam-3085	20	4	we	we	PRON
ejpam-3085	20	5	will	will	AUX
ejpam-3085	20	6	give	give	VERB
ejpam-3085	20	7	some	some	DET
ejpam-3085	20	8	definitions	definition	NOUN
ejpam-3085	20	9	–	–	PUNCT
ejpam-3085	20	10	notations	notation	NOUN
ejpam-3085	20	11	already	already	ADV
ejpam-3085	20	12	given	give	VERB
ejpam-3085	20	13	in	in	ADP
ejpam-3085	20	14	[	[	X
ejpam-3085	20	15	8–10	8–10	NOUN
ejpam-3085	20	16	]	]	PUNCT
ejpam-3085	20	17	.	.	PUNCT
ejpam-3085	21	1	an	an	DET
ejpam-3085	21	2	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	21	3	is	be	AUX
ejpam-3085	21	4	a	a	DET
ejpam-3085	21	5	nonempty	nonempty	ADV
ejpam-3085	21	6	set	set	VERB
ejpam-3085	21	7	h	h	NOUN
ejpam-3085	21	8	endowed	endow	VERB
ejpam-3085	21	9	with	with	ADP
ejpam-3085	21	10	an	an	DET
ejpam-3085	21	11	hyperoperation	hyperoperation	NOUN
ejpam-3085	21	12	◦	◦	NOUN
ejpam-3085	21	13	:	:	PUNCT
ejpam-3085	21	14	h	h	NOUN
ejpam-3085	21	15	×h	×h	PROPN
ejpam-3085	21	16	→	→	SYM
ejpam-3085	21	17	p∗(h	p∗(h	NOUN
ejpam-3085	21	18	)	)	PUNCT
ejpam-3085	21	19	|	|	ADV
ejpam-3085	21	20	(	(	PUNCT
ejpam-3085	21	21	a	a	PRON
ejpam-3085	21	22	,	,	PUNCT
ejpam-3085	21	23	b)→	b)→	VERB
ejpam-3085	21	24	a	a	DET
ejpam-3085	21	25	◦	◦	NOUN
ejpam-3085	21	26	b	b	NOUN
ejpam-3085	21	27	on	on	ADP
ejpam-3085	21	28	h	h	NOUN
ejpam-3085	21	29	and	and	CCONJ
ejpam-3085	21	30	an	an	DET
ejpam-3085	21	31	operation	operation	NOUN
ejpam-3085	21	32	∗	∗	NOUN
ejpam-3085	21	33	:	:	PUNCT
ejpam-3085	21	34	p∗(h	p∗(h	X
ejpam-3085	21	35	)	)	PUNCT
ejpam-3085	21	36	×	×	PROPN
ejpam-3085	21	37	p∗(h	p∗(h	PROPN
ejpam-3085	21	38	)	)	PUNCT
ejpam-3085	21	39	→	→	SYM
ejpam-3085	21	40	p∗(h	p∗(h	NOUN
ejpam-3085	21	41	)	)	PUNCT
ejpam-3085	22	1	|	|	ADV
ejpam-3085	22	2	(	(	PUNCT
ejpam-3085	22	3	a	a	DET
ejpam-3085	22	4	,	,	PUNCT
ejpam-3085	22	5	b	b	NOUN
ejpam-3085	22	6	)	)	PUNCT
ejpam-3085	22	7	→	→	ADP
ejpam-3085	22	8	a	a	DET
ejpam-3085	22	9	∗	∗	NOUN
ejpam-3085	22	10	b	b	NOUN
ejpam-3085	22	11	on	on	ADP
ejpam-3085	22	12	p∗(h	p∗(h	PROPN
ejpam-3085	22	13	)	)	PUNCT
ejpam-3085	22	14	(	(	PUNCT
ejpam-3085	22	15	induced	induce	VERB
ejpam-3085	22	16	by	by	ADP
ejpam-3085	22	17	the	the	DET
ejpam-3085	22	18	operation	operation	NOUN
ejpam-3085	22	19	of	of	ADP
ejpam-3085	22	20	h	h	NOUN
ejpam-3085	22	21	)	)	PUNCT
ejpam-3085	22	22	such	such	ADJ
ejpam-3085	22	23	that	that	SCONJ
ejpam-3085	22	24	a	a	DET
ejpam-3085	22	25	∗	∗	NOUN
ejpam-3085	22	26	b	b	NOUN
ejpam-3085	22	27	=	=	X
ejpam-3085	22	28	⋃	⋃	PROPN
ejpam-3085	22	29	(	(	PUNCT
ejpam-3085	22	30	a	a	PRON
ejpam-3085	22	31	,	,	PUNCT
ejpam-3085	22	32	b)∈a×b	b)∈a×b	NUM
ejpam-3085	22	33	(	(	PUNCT
ejpam-3085	22	34	a	a	DET
ejpam-3085	22	35	◦	◦	NOUN
ejpam-3085	22	36	b	b	NOUN
ejpam-3085	22	37	)	)	PUNCT
ejpam-3085	22	38	for	for	ADP
ejpam-3085	22	39	every	every	DET
ejpam-3085	22	40	a	a	PROPN
ejpam-3085	22	41	,	,	PUNCT
ejpam-3085	22	42	b	b	PROPN
ejpam-3085	22	43	∈	∈	PROPN
ejpam-3085	22	44	p∗(h	p∗(h	PROPN
ejpam-3085	22	45	)	)	PUNCT
ejpam-3085	22	46	.	.	PUNCT
ejpam-3085	23	1	as	as	SCONJ
ejpam-3085	23	2	the	the	DET
ejpam-3085	23	3	operation	operation	NOUN
ejpam-3085	23	4	“	"	PUNCT
ejpam-3085	23	5	∗	∗	NOUN
ejpam-3085	23	6	”	"	PUNCT
ejpam-3085	23	7	depends	depend	VERB
ejpam-3085	23	8	on	on	ADP
ejpam-3085	23	9	the	the	DET
ejpam-3085	23	10	hyperoperation	hyperoperation	NOUN
ejpam-3085	23	11	“	"	PUNCT
ejpam-3085	23	12	◦	◦	NOUN
ejpam-3085	23	13	”	"	PUNCT
ejpam-3085	23	14	,	,	PUNCT
ejpam-3085	23	15	an	an	DET
ejpam-3085	23	16	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	23	17	h	h	NOUN
ejpam-3085	23	18	is	be	AUX
ejpam-3085	23	19	denoted	denote	VERB
ejpam-3085	23	20	by	by	ADP
ejpam-3085	23	21	(	(	PUNCT
ejpam-3085	23	22	h	h	NOUN
ejpam-3085	23	23	,	,	PUNCT
ejpam-3085	23	24	◦	◦	NOUN
ejpam-3085	23	25	)	)	PUNCT
ejpam-3085	23	26	.	.	PUNCT
ejpam-3085	24	1	clearly	clearly	ADV
ejpam-3085	24	2	,	,	PUNCT
ejpam-3085	24	3	a	a	DET
ejpam-3085	24	4	⊆	⊆	NUM
ejpam-3085	24	5	b	b	NOUN
ejpam-3085	24	6	implies	imply	VERB
ejpam-3085	24	7	a∗c	a∗c	NUM
ejpam-3085	24	8	⊆	⊆	NUM
ejpam-3085	24	9	b	b	SYM
ejpam-3085	24	10	∗c	∗c	PROPN
ejpam-3085	24	11	and	and	CCONJ
ejpam-3085	24	12	c	c	NOUN
ejpam-3085	24	13	∗a	∗a	PROPN
ejpam-3085	24	14	⊆	⊆	NUM
ejpam-3085	24	15	c	c	NOUN
ejpam-3085	24	16	∗b	∗b	PROPN
ejpam-3085	24	17	for	for	ADP
ejpam-3085	24	18	any	any	DET
ejpam-3085	24	19	a	a	DET
ejpam-3085	24	20	,	,	PUNCT
ejpam-3085	24	21	b	b	NOUN
ejpam-3085	24	22	,	,	PUNCT
ejpam-3085	24	23	c	c	PROPN
ejpam-3085	24	24	∈	∈	PROPN
ejpam-3085	24	25	p∗(h	p∗(h	PROPN
ejpam-3085	24	26	)	)	PUNCT
ejpam-3085	24	27	and	and	CCONJ
ejpam-3085	24	28	h	h	NOUN
ejpam-3085	24	29	∗h	∗h	VERB
ejpam-3085	24	30	⊆	⊆	NUM
ejpam-3085	24	31	h.	h.	NOUN
ejpam-3085	24	32	email	email	NOUN
ejpam-3085	24	33	address	address	NOUN
ejpam-3085	24	34	:	:	PUNCT
ejpam-3085	24	35	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3085	24	36	(	(	PUNCT
ejpam-3085	24	37	n.	n.	PROPN
ejpam-3085	24	38	kehayopulu	kehayopulu	PROPN
ejpam-3085	24	39	)	)	PUNCT
ejpam-3085	24	40	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3085	25	1	10	10	NUM
ejpam-3085	25	2	c	c	X
ejpam-3085	25	3	©	©	PROPN
ejpam-3085	25	4	2018	2018	NUM
ejpam-3085	25	5	ejpam	ejpam	VERB
ejpam-3085	25	6	all	all	DET
ejpam-3085	25	7	rights	right	NOUN
ejpam-3085	25	8	reserved	reserve	VERB
ejpam-3085	25	9	.	.	PUNCT
ejpam-3085	26	1	n.	n.	PROPN
ejpam-3085	26	2	kehayopulu	kehayopulu	PROPN
ejpam-3085	26	3	/	/	SYM
ejpam-3085	26	4	eur	eur	PROPN
ejpam-3085	26	5	.	.	PUNCT
ejpam-3085	27	1	j.	j.	PROPN
ejpam-3085	27	2	pure	pure	PROPN
ejpam-3085	27	3	appl	appl	PROPN
ejpam-3085	27	4	.	.	PROPN
ejpam-3085	27	5	math	math	PROPN
ejpam-3085	27	6	,	,	PUNCT
ejpam-3085	27	7	11	11	NUM
ejpam-3085	27	8	(	(	PUNCT
ejpam-3085	27	9	1	1	NUM
ejpam-3085	27	10	)	)	PUNCT
ejpam-3085	27	11	(	(	PUNCT
ejpam-3085	27	12	2018	2018	NUM
ejpam-3085	27	13	)	)	PUNCT
ejpam-3085	27	14	,	,	PUNCT
ejpam-3085	27	15	10	10	NUM
ejpam-3085	27	16	-	-	SYM
ejpam-3085	27	17	22	22	NUM
ejpam-3085	27	18	11	11	NUM
ejpam-3085	27	19	as	as	ADP
ejpam-3085	27	20	in	in	ADP
ejpam-3085	27	21	ordered	order	VERB
ejpam-3085	27	22	semigroups	semigroup	NOUN
ejpam-3085	27	23	,	,	PUNCT
ejpam-3085	27	24	for	for	ADP
ejpam-3085	27	25	a	a	DET
ejpam-3085	27	26	subset	subset	NOUN
ejpam-3085	27	27	a	a	PRON
ejpam-3085	27	28	of	of	ADP
ejpam-3085	27	29	an	an	DET
ejpam-3085	27	30	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	27	31	h	h	NOUN
ejpam-3085	27	32	,	,	PUNCT
ejpam-3085	27	33	we	we	PRON
ejpam-3085	27	34	denote	denote	VERB
ejpam-3085	27	35	by	by	ADP
ejpam-3085	27	36	(	(	PUNCT
ejpam-3085	27	37	a	a	X
ejpam-3085	27	38	]	]	X
ejpam-3085	27	39	the	the	DET
ejpam-3085	27	40	subset	subset	NOUN
ejpam-3085	27	41	of	of	ADP
ejpam-3085	27	42	h	h	NOUN
ejpam-3085	27	43	defined	define	VERB
ejpam-3085	27	44	by	by	ADP
ejpam-3085	27	45	(	(	PUNCT
ejpam-3085	27	46	a	a	X
ejpam-3085	27	47	]	]	X
ejpam-3085	27	48	:	:	PUNCT
ejpam-3085	27	49	=	=	SYM
ejpam-3085	27	50	{	{	PUNCT
ejpam-3085	27	51	t	t	NOUN
ejpam-3085	27	52	∈	∈	PROPN
ejpam-3085	27	53	h	h	NOUN
ejpam-3085	27	54	|	|	ADV
ejpam-3085	27	55	t	t	X
ejpam-3085	27	56	≤	≤	NOUN
ejpam-3085	27	57	a	a	PRON
ejpam-3085	27	58	for	for	ADP
ejpam-3085	27	59	some	some	DET
ejpam-3085	27	60	a	a	DET
ejpam-3085	27	61	∈	∈	PROPN
ejpam-3085	27	62	a	a	PRON
ejpam-3085	27	63	}	}	PUNCT
ejpam-3085	27	64	,	,	PUNCT
ejpam-3085	27	65	and	and	CCONJ
ejpam-3085	27	66	we	we	PRON
ejpam-3085	27	67	have	have	VERB
ejpam-3085	27	68	the	the	DET
ejpam-3085	27	69	following	following	NOUN
ejpam-3085	27	70	:	:	PUNCT
ejpam-3085	27	71	a	a	DET
ejpam-3085	27	72	⊆	⊆	NUM
ejpam-3085	27	73	(	(	PUNCT
ejpam-3085	27	74	a	a	NOUN
ejpam-3085	27	75	]	]	X
ejpam-3085	27	76	;	;	PUNCT
ejpam-3085	28	1	if	if	SCONJ
ejpam-3085	28	2	a	a	DET
ejpam-3085	28	3	⊆	⊆	NUM
ejpam-3085	28	4	b	b	NOUN
ejpam-3085	28	5	,	,	PUNCT
ejpam-3085	28	6	then	then	ADV
ejpam-3085	28	7	(	(	PUNCT
ejpam-3085	28	8	a	a	X
ejpam-3085	28	9	]	]	X
ejpam-3085	28	10	⊆	⊆	NUM
ejpam-3085	28	11	(	(	PUNCT
ejpam-3085	28	12	b	b	NOUN
ejpam-3085	28	13	]	]	X
ejpam-3085	28	14	;	;	PUNCT
ejpam-3085	28	15	(	(	PUNCT
ejpam-3085	28	16	h	h	X
ejpam-3085	28	17	]	]	X
ejpam-3085	28	18	=	=	SYM
ejpam-3085	28	19	h	h	NOUN
ejpam-3085	28	20	;	;	PUNCT
ejpam-3085	28	21	(	(	PUNCT
ejpam-3085	28	22	(	(	PUNCT
ejpam-3085	28	23	a	a	X
ejpam-3085	28	24	]	]	X
ejpam-3085	28	25	]	]	X
ejpam-3085	28	26	=	=	X
ejpam-3085	28	27	(	(	PUNCT
ejpam-3085	28	28	a	a	X
ejpam-3085	28	29	]	]	X
ejpam-3085	28	30	.	.	PUNCT
ejpam-3085	29	1	for	for	ADP
ejpam-3085	29	2	an	an	DET
ejpam-3085	29	3	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	29	4	h	h	NOUN
ejpam-3085	29	5	,	,	PUNCT
ejpam-3085	29	6	the	the	DET
ejpam-3085	29	7	following	follow	VERB
ejpam-3085	29	8	two	two	NUM
ejpam-3085	29	9	properties	property	NOUN
ejpam-3085	29	10	,	,	PUNCT
ejpam-3085	29	11	being	be	AUX
ejpam-3085	29	12	obvious	obvious	ADJ
ejpam-3085	29	13	,	,	PUNCT
ejpam-3085	29	14	play	play	VERB
ejpam-3085	29	15	an	an	DET
ejpam-3085	29	16	essential	essential	ADJ
ejpam-3085	29	17	role	role	NOUN
ejpam-3085	29	18	in	in	ADP
ejpam-3085	29	19	the	the	DET
ejpam-3085	29	20	investigation	investigation	NOUN
ejpam-3085	29	21	:	:	PUNCT
ejpam-3085	29	22	(	(	PUNCT
ejpam-3085	29	23	1	1	X
ejpam-3085	29	24	)	)	PUNCT
ejpam-3085	29	25	if	if	SCONJ
ejpam-3085	29	26	x	x	SYM
ejpam-3085	29	27	∈	∈	PROPN
ejpam-3085	29	28	a	a	DET
ejpam-3085	29	29	∗b	∗b	NOUN
ejpam-3085	29	30	,	,	PUNCT
ejpam-3085	29	31	then	then	ADV
ejpam-3085	29	32	x	x	PART
ejpam-3085	29	33	∈	∈	PROPN
ejpam-3085	29	34	a	a	DET
ejpam-3085	29	35	◦	◦	NOUN
ejpam-3085	29	36	b	b	NOUN
ejpam-3085	29	37	for	for	ADP
ejpam-3085	29	38	some	some	DET
ejpam-3085	29	39	a	a	DET
ejpam-3085	29	40	∈	∈	PROPN
ejpam-3085	29	41	a	a	PRON
ejpam-3085	29	42	,	,	PUNCT
ejpam-3085	29	43	b	b	PROPN
ejpam-3085	29	44	∈	∈	PROPN
ejpam-3085	29	45	b.	b.	PROPN
ejpam-3085	29	46	(	(	PUNCT
ejpam-3085	29	47	2	2	NUM
ejpam-3085	29	48	)	)	PUNCT
ejpam-3085	29	49	if	if	SCONJ
ejpam-3085	29	50	a	a	DET
ejpam-3085	29	51	∈	∈	PROPN
ejpam-3085	29	52	a	a	PRON
ejpam-3085	29	53	and	and	CCONJ
ejpam-3085	29	54	b	b	PROPN
ejpam-3085	29	55	∈	∈	PROPN
ejpam-3085	29	56	b	b	PROPN
ejpam-3085	29	57	,	,	PUNCT
ejpam-3085	29	58	then	then	ADV
ejpam-3085	29	59	a	a	DET
ejpam-3085	29	60	◦	◦	NOUN
ejpam-3085	29	61	b	b	NOUN
ejpam-3085	29	62	⊆	⊆	NUM
ejpam-3085	29	63	a	a	DET
ejpam-3085	29	64	∗b	∗b	NOUN
ejpam-3085	29	65	.	.	PUNCT
ejpam-3085	30	1	if	if	SCONJ
ejpam-3085	30	2	h	h	NOUN
ejpam-3085	30	3	is	be	AUX
ejpam-3085	30	4	an	an	DET
ejpam-3085	30	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	30	6	and	and	CCONJ
ejpam-3085	30	7	ai	ai	VERB
ejpam-3085	30	8	,	,	PUNCT
ejpam-3085	30	9	b	b	PROPN
ejpam-3085	30	10	∈	∈	PROPN
ejpam-3085	30	11	p∗(h	p∗(h	PROPN
ejpam-3085	30	12	)	)	PUNCT
ejpam-3085	30	13	,	,	PUNCT
ejpam-3085	30	14	i	i	PRON
ejpam-3085	30	15	∈	∈	VERB
ejpam-3085	31	1	i	i	PRON
ejpam-3085	31	2	,	,	PUNCT
ejpam-3085	31	3	then	then	ADV
ejpam-3085	31	4	we	we	PRON
ejpam-3085	31	5	have	have	VERB
ejpam-3085	31	6	the	the	DET
ejpam-3085	31	7	following	following	NOUN
ejpam-3085	31	8	:	:	PUNCT
ejpam-3085	31	9	(	(	PUNCT
ejpam-3085	31	10	1	1	X
ejpam-3085	31	11	)	)	PUNCT
ejpam-3085	31	12	(	(	PUNCT
ejpam-3085	31	13	⋃	⋃	ADP
ejpam-3085	31	14	i∈i	i∈i	ADJ
ejpam-3085	31	15	ai	ai	NOUN
ejpam-3085	31	16	)	)	PUNCT
ejpam-3085	31	17	∗b	∗b	NOUN
ejpam-3085	31	18	=	=	SYM
ejpam-3085	31	19	⋃	⋃	PROPN
ejpam-3085	31	20	i∈i	i∈i	ADJ
ejpam-3085	31	21	(	(	PUNCT
ejpam-3085	31	22	ai	ai	PROPN
ejpam-3085	31	23	∗b	∗b	PROPN
ejpam-3085	31	24	)	)	PUNCT
ejpam-3085	31	25	.	.	PUNCT
ejpam-3085	32	1	(	(	PUNCT
ejpam-3085	32	2	2	2	X
ejpam-3085	32	3	)	)	PUNCT
ejpam-3085	32	4	b	b	NOUN
ejpam-3085	32	5	∗	∗	NOUN
ejpam-3085	32	6	(	(	PUNCT
ejpam-3085	32	7	⋃	⋃	PROPN
ejpam-3085	32	8	i∈i	i∈i	ADJ
ejpam-3085	32	9	ai	ai	VERB
ejpam-3085	32	10	)	)	PUNCT
ejpam-3085	33	1	=	=	SYM
ejpam-3085	33	2	⋃	⋃	PROPN
ejpam-3085	33	3	i∈i	i∈i	ADJ
ejpam-3085	33	4	(	(	PUNCT
ejpam-3085	33	5	b	b	NOUN
ejpam-3085	33	6	∗ai	∗ai	PROPN
ejpam-3085	33	7	)	)	PUNCT
ejpam-3085	33	8	.	.	PUNCT
ejpam-3085	34	1	an	an	DET
ejpam-3085	34	2	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	34	3	satisfying	satisfy	VERB
ejpam-3085	34	4	the	the	DET
ejpam-3085	34	5	relation	relation	NOUN
ejpam-3085	34	6	{	{	PUNCT
ejpam-3085	34	7	x}∗	x}∗	PROPN
ejpam-3085	34	8	(	(	PUNCT
ejpam-3085	34	9	y	y	PROPN
ejpam-3085	34	10	◦	◦	PROPN
ejpam-3085	34	11	z	z	NOUN
ejpam-3085	34	12	)	)	PUNCT
ejpam-3085	34	13	=	=	SYM
ejpam-3085	34	14	(	(	PUNCT
ejpam-3085	34	15	x	x	X
ejpam-3085	34	16	◦	◦	NOUN
ejpam-3085	34	17	y)∗{z	y)∗{z	NOUN
ejpam-3085	34	18	}	}	PUNCT
ejpam-3085	34	19	for	for	ADP
ejpam-3085	34	20	any	any	DET
ejpam-3085	34	21	x	x	NOUN
ejpam-3085	34	22	,	,	PUNCT
ejpam-3085	34	23	y	y	PROPN
ejpam-3085	34	24	,	,	PUNCT
ejpam-3085	34	25	z	z	PROPN
ejpam-3085	34	26	∈	∈	PROPN
ejpam-3085	34	27	h	h	NOUN
ejpam-3085	34	28	is	be	AUX
ejpam-3085	34	29	called	call	VERB
ejpam-3085	34	30	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	34	31	.	.	PUNCT
ejpam-3085	35	1	identifying	identify	VERB
ejpam-3085	35	2	the	the	DET
ejpam-3085	35	3	singleton	singleton	NOUN
ejpam-3085	35	4	{	{	PUNCT
ejpam-3085	35	5	x	x	NOUN
ejpam-3085	35	6	}	}	PUNCT
ejpam-3085	35	7	by	by	ADP
ejpam-3085	35	8	the	the	DET
ejpam-3085	35	9	element	element	NOUN
ejpam-3085	35	10	x	x	PUNCT
ejpam-3085	35	11	and	and	CCONJ
ejpam-3085	35	12	the	the	DET
ejpam-3085	35	13	{	{	PUNCT
ejpam-3085	35	14	z	z	NOUN
ejpam-3085	35	15	}	}	PUNCT
ejpam-3085	35	16	by	by	ADP
ejpam-3085	35	17	z	z	NOUN
ejpam-3085	35	18	we	we	PRON
ejpam-3085	35	19	can	can	AUX
ejpam-3085	35	20	write	write	VERB
ejpam-3085	35	21	,	,	PUNCT
ejpam-3085	35	22	for	for	ADP
ejpam-3085	35	23	short	short	ADJ
ejpam-3085	35	24	,	,	PUNCT
ejpam-3085	35	25	x	x	SYM
ejpam-3085	35	26	∗	∗	NOUN
ejpam-3085	35	27	(	(	PUNCT
ejpam-3085	35	28	y	y	PROPN
ejpam-3085	35	29	◦	◦	PROPN
ejpam-3085	35	30	z	z	PROPN
ejpam-3085	35	31	)	)	PUNCT
ejpam-3085	35	32	=	=	SYM
ejpam-3085	36	1	(	(	PUNCT
ejpam-3085	36	2	x	x	SYM
ejpam-3085	36	3	◦	◦	VERB
ejpam-3085	36	4	y	y	NOUN
ejpam-3085	36	5	)	)	PUNCT
ejpam-3085	36	6	∗	∗	NOUN
ejpam-3085	36	7	z.	z.	PROPN
ejpam-3085	36	8	for	for	ADP
ejpam-3085	36	9	every	every	DET
ejpam-3085	36	10	x	x	PROPN
ejpam-3085	36	11	,	,	PUNCT
ejpam-3085	36	12	y	y	PROPN
ejpam-3085	36	13	∈	∈	PROPN
ejpam-3085	36	14	h	h	NOUN
ejpam-3085	36	15	,	,	PUNCT
ejpam-3085	36	16	we	we	PRON
ejpam-3085	36	17	can	can	AUX
ejpam-3085	36	18	easily	easily	ADV
ejpam-3085	36	19	show	show	VERB
ejpam-3085	36	20	that	that	SCONJ
ejpam-3085	36	21	{	{	PUNCT
ejpam-3085	36	22	x	x	NOUN
ejpam-3085	36	23	}	}	PUNCT
ejpam-3085	36	24	∗	∗	NOUN
ejpam-3085	36	25	{	{	PUNCT
ejpam-3085	36	26	y	y	NOUN
ejpam-3085	36	27	}	}	PUNCT
ejpam-3085	36	28	=	=	SYM
ejpam-3085	36	29	x	x	PUNCT
ejpam-3085	36	30	◦	◦	NOUN
ejpam-3085	36	31	y	y	NOUN
ejpam-3085	36	32	,	,	PUNCT
ejpam-3085	36	33	so	so	ADV
ejpam-3085	36	34	instead	instead	ADV
ejpam-3085	36	35	of	of	ADP
ejpam-3085	36	36	writing	write	VERB
ejpam-3085	36	37	{	{	PUNCT
ejpam-3085	36	38	x	x	NOUN
ejpam-3085	36	39	}	}	PUNCT
ejpam-3085	36	40	∗	∗	NOUN
ejpam-3085	36	41	(	(	PUNCT
ejpam-3085	36	42	y	y	PROPN
ejpam-3085	36	43	◦	◦	PROPN
ejpam-3085	36	44	z	z	PROPN
ejpam-3085	36	45	)	)	PUNCT
ejpam-3085	36	46	=	=	SYM
ejpam-3085	36	47	(	(	PUNCT
ejpam-3085	36	48	x	x	SYM
ejpam-3085	36	49	◦	◦	VERB
ejpam-3085	36	50	y	y	NOUN
ejpam-3085	36	51	)	)	PUNCT
ejpam-3085	36	52	∗	∗	NOUN
ejpam-3085	36	53	{	{	PUNCT
ejpam-3085	36	54	z	z	NOUN
ejpam-3085	36	55	}	}	PUNCT
ejpam-3085	36	56	we	we	PRON
ejpam-3085	36	57	can	can	AUX
ejpam-3085	36	58	also	also	ADV
ejpam-3085	36	59	write	write	VERB
ejpam-3085	36	60	{	{	PUNCT
ejpam-3085	36	61	x	x	NOUN
ejpam-3085	36	62	}	}	PUNCT
ejpam-3085	36	63	∗	∗	NOUN
ejpam-3085	36	64	(	(	PUNCT
ejpam-3085	36	65	{	{	PUNCT
ejpam-3085	36	66	y	y	NOUN
ejpam-3085	36	67	}	}	PUNCT
ejpam-3085	36	68	∗	∗	NOUN
ejpam-3085	36	69	{	{	PUNCT
ejpam-3085	36	70	z	z	NOUN
ejpam-3085	36	71	}	}	PUNCT
ejpam-3085	36	72	)	)	PUNCT
ejpam-3085	37	1	=	=	SYM
ejpam-3085	37	2	(	(	PUNCT
ejpam-3085	37	3	{	{	PUNCT
ejpam-3085	37	4	x	x	NOUN
ejpam-3085	37	5	}	}	PUNCT
ejpam-3085	37	6	∗	∗	NOUN
ejpam-3085	37	7	{	{	PUNCT
ejpam-3085	37	8	y	y	NOUN
ejpam-3085	37	9	}	}	PUNCT
ejpam-3085	37	10	)	)	PUNCT
ejpam-3085	37	11	∗	∗	NOUN
ejpam-3085	37	12	{	{	PUNCT
ejpam-3085	37	13	z	z	NOUN
ejpam-3085	37	14	}	}	PUNCT
ejpam-3085	37	15	.	.	PUNCT
ejpam-3085	38	1	if	if	SCONJ
ejpam-3085	38	2	(	(	PUNCT
ejpam-3085	38	3	h	h	NOUN
ejpam-3085	38	4	,	,	PUNCT
ejpam-3085	38	5	◦	◦	NOUN
ejpam-3085	38	6	)	)	PUNCT
ejpam-3085	38	7	is	be	AUX
ejpam-3085	38	8	an	an	DET
ejpam-3085	38	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	38	10	,	,	PUNCT
ejpam-3085	38	11	then	then	ADV
ejpam-3085	38	12	the	the	DET
ejpam-3085	38	13	operation	operation	NOUN
ejpam-3085	38	14	“	"	PUNCT
ejpam-3085	38	15	∗	∗	NOUN
ejpam-3085	38	16	”	"	PUNCT
ejpam-3085	38	17	on	on	ADP
ejpam-3085	38	18	p∗(h	p∗(h	PROPN
ejpam-3085	38	19	)	)	PUNCT
ejpam-3085	38	20	is	be	AUX
ejpam-3085	38	21	associative	associative	ADJ
ejpam-3085	38	22	,	,	PUNCT
ejpam-3085	38	23	that	that	ADV
ejpam-3085	38	24	is	is	ADV
ejpam-3085	38	25	(	(	PUNCT
ejpam-3085	38	26	p∗(h	p∗(h	NOUN
ejpam-3085	38	27	)	)	PUNCT
ejpam-3085	38	28	,	,	PUNCT
ejpam-3085	38	29	∗	∗	NOUN
ejpam-3085	38	30	)	)	PUNCT
ejpam-3085	38	31	is	be	AUX
ejpam-3085	38	32	a	a	DET
ejpam-3085	38	33	semigroup	semigroup	NOUN
ejpam-3085	38	34	.	.	PUNCT
ejpam-3085	39	1	so	so	ADV
ejpam-3085	39	2	in	in	ADP
ejpam-3085	39	3	an	an	DET
ejpam-3085	39	4	expression	expression	NOUN
ejpam-3085	39	5	of	of	ADP
ejpam-3085	39	6	the	the	DET
ejpam-3085	39	7	form	form	NOUN
ejpam-3085	39	8	a1	a1	NOUN
ejpam-3085	39	9	∗	∗	NOUN
ejpam-3085	39	10	a2	a2	PROPN
ejpam-3085	39	11	∗	∗	NOUN
ejpam-3085	39	12	·	·	PUNCT
ejpam-3085	39	13	·	·	PUNCT
ejpam-3085	39	14	·	·	PUNCT
ejpam-3085	39	15	∗	∗	NOUN
ejpam-3085	39	16	an	an	PRON
ejpam-3085	39	17	,	,	PUNCT
ejpam-3085	39	18	where	where	SCONJ
ejpam-3085	39	19	a1	a1	NOUN
ejpam-3085	39	20	,	,	PUNCT
ejpam-3085	39	21	a2	a2	PROPN
ejpam-3085	39	22	,	,	PUNCT
ejpam-3085	39	23	·	·	PUNCT
ejpam-3085	39	24	·	·	PUNCT
ejpam-3085	39	25	·	·	PUNCT
ejpam-3085	39	26	,	,	PUNCT
ejpam-3085	39	27	an	an	PRON
ejpam-3085	39	28	are	be	AUX
ejpam-3085	39	29	nonempty	nonempty	ADJ
ejpam-3085	39	30	subsets	subset	NOUN
ejpam-3085	39	31	of	of	ADP
ejpam-3085	39	32	h	h	NOUN
ejpam-3085	39	33	and	and	CCONJ
ejpam-3085	39	34	n	n	CCONJ
ejpam-3085	39	35	∈	∈	PROPN
ejpam-3085	40	1	n	n	NOUN
ejpam-3085	40	2	=	=	SYM
ejpam-3085	40	3	{	{	PUNCT
ejpam-3085	40	4	1	1	NUM
ejpam-3085	40	5	,	,	PUNCT
ejpam-3085	40	6	2	2	NUM
ejpam-3085	40	7	,	,	PUNCT
ejpam-3085	40	8	·	·	PUNCT
ejpam-3085	40	9	·	·	PUNCT
ejpam-3085	40	10	·	·	PUNCT
ejpam-3085	40	11	,	,	PUNCT
ejpam-3085	40	12	n	n	CCONJ
ejpam-3085	40	13	}	}	PUNCT
ejpam-3085	40	14	(	(	PUNCT
ejpam-3085	40	15	the	the	DET
ejpam-3085	40	16	set	set	NOUN
ejpam-3085	40	17	of	of	ADP
ejpam-3085	40	18	natural	natural	ADJ
ejpam-3085	40	19	numbers	number	NOUN
ejpam-3085	40	20	)	)	PUNCT
ejpam-3085	40	21	,	,	PUNCT
ejpam-3085	40	22	we	we	PRON
ejpam-3085	40	23	can	can	AUX
ejpam-3085	40	24	put	put	VERB
ejpam-3085	40	25	parentheses	parenthesis	NOUN
ejpam-3085	40	26	in	in	ADP
ejpam-3085	40	27	any	any	DET
ejpam-3085	40	28	expression	expression	NOUN
ejpam-3085	40	29	beginning	begin	VERB
ejpam-3085	40	30	with	with	ADP
ejpam-3085	40	31	some	some	DET
ejpam-3085	40	32	ai	ai	NOUN
ejpam-3085	40	33	and	and	CCONJ
ejpam-3085	40	34	ending	end	VERB
ejpam-3085	40	35	in	in	ADP
ejpam-3085	40	36	some	some	DET
ejpam-3085	40	37	aj	aj	PROPN
ejpam-3085	40	38	(	(	PUNCT
ejpam-3085	40	39	i	i	PROPN
ejpam-3085	40	40	,	,	PUNCT
ejpam-3085	40	41	j	j	PROPN
ejpam-3085	40	42	∈	∈	PROPN
ejpam-3085	40	43	n	n	CCONJ
ejpam-3085	40	44	)	)	PUNCT
ejpam-3085	40	45	.	.	PUNCT
ejpam-3085	41	1	if	if	SCONJ
ejpam-3085	41	2	“	"	PUNCT
ejpam-3085	41	3	≤	≤	NUM
ejpam-3085	41	4	”	"	PUNCT
ejpam-3085	41	5	is	be	AUX
ejpam-3085	41	6	an	an	DET
ejpam-3085	41	7	order	order	NOUN
ejpam-3085	41	8	relation	relation	NOUN
ejpam-3085	41	9	on	on	ADP
ejpam-3085	41	10	an	an	DET
ejpam-3085	41	11	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	41	12	h	h	NOUN
ejpam-3085	41	13	,	,	PUNCT
ejpam-3085	41	14	we	we	PRON
ejpam-3085	41	15	denote	denote	VERB
ejpam-3085	41	16	by	by	ADP
ejpam-3085	41	17	“	"	PUNCT
ejpam-3085	41	18	�	�	PROPN
ejpam-3085	41	19	”	"	PUNCT
ejpam-3085	41	20	the	the	DET
ejpam-3085	41	21	relation	relation	NOUN
ejpam-3085	41	22	on	on	ADP
ejpam-3085	41	23	p∗(h	p∗(h	PROPN
ejpam-3085	41	24	)	)	PUNCT
ejpam-3085	41	25	defined	define	VERB
ejpam-3085	41	26	by	by	ADP
ejpam-3085	41	27	�	�	PROPN
ejpam-3085	41	28	:	:	PUNCT
ejpam-3085	41	29	=	=	SYM
ejpam-3085	41	30	{	{	PUNCT
ejpam-3085	41	31	(	(	PUNCT
ejpam-3085	41	32	a	a	DET
ejpam-3085	41	33	,	,	PUNCT
ejpam-3085	41	34	b	b	NOUN
ejpam-3085	41	35	)	)	PUNCT
ejpam-3085	41	36	|	|	ADV
ejpam-3085	41	37	∀	∀	PUNCT
ejpam-3085	41	38	a	a	DET
ejpam-3085	41	39	∈	∈	PROPN
ejpam-3085	41	40	a	a	DET
ejpam-3085	41	41	∃	∃	PROPN
ejpam-3085	41	42	b	b	PROPN
ejpam-3085	41	43	∈	∈	PROPN
ejpam-3085	41	44	b	b	NOUN
ejpam-3085	41	45	such	such	ADJ
ejpam-3085	41	46	that	that	SCONJ
ejpam-3085	41	47	a	a	DET
ejpam-3085	41	48	≤	≤	NUM
ejpam-3085	41	49	b	b	NOUN
ejpam-3085	41	50	}	}	PUNCT
ejpam-3085	41	51	.	.	PUNCT
ejpam-3085	42	1	so	so	ADV
ejpam-3085	42	2	,	,	PUNCT
ejpam-3085	42	3	for	for	ADP
ejpam-3085	42	4	a	a	DET
ejpam-3085	42	5	,	,	PUNCT
ejpam-3085	42	6	b	b	PROPN
ejpam-3085	42	7	∈	∈	PROPN
ejpam-3085	42	8	p∗(h	p∗(h	PROPN
ejpam-3085	42	9	)	)	PUNCT
ejpam-3085	42	10	,	,	PUNCT
ejpam-3085	42	11	we	we	PRON
ejpam-3085	42	12	write	write	VERB
ejpam-3085	42	13	a	a	DET
ejpam-3085	42	14	�	�	PROPN
ejpam-3085	42	15	b	b	PROPN
ejpam-3085	42	16	if	if	SCONJ
ejpam-3085	42	17	for	for	ADP
ejpam-3085	42	18	every	every	DET
ejpam-3085	42	19	a	a	DET
ejpam-3085	42	20	∈	∈	PROPN
ejpam-3085	42	21	a	a	DET
ejpam-3085	42	22	there	there	PRON
ejpam-3085	42	23	exists	exist	VERB
ejpam-3085	42	24	b	b	PROPN
ejpam-3085	42	25	∈	∈	PROPN
ejpam-3085	42	26	b	b	NOUN
ejpam-3085	42	27	such	such	ADJ
ejpam-3085	42	28	that	that	SCONJ
ejpam-3085	42	29	a	a	DET
ejpam-3085	42	30	≤	≤	PROPN
ejpam-3085	42	31	b.	b.	NOUN
ejpam-3085	43	1	this	this	PRON
ejpam-3085	43	2	is	be	AUX
ejpam-3085	43	3	a	a	DET
ejpam-3085	43	4	reflexive	reflexive	ADJ
ejpam-3085	43	5	and	and	CCONJ
ejpam-3085	43	6	transitive	transitive	ADJ
ejpam-3085	43	7	relation	relation	NOUN
ejpam-3085	43	8	on	on	ADP
ejpam-3085	43	9	p∗(h	p∗(h	PROPN
ejpam-3085	43	10	)	)	PUNCT
ejpam-3085	43	11	,	,	PUNCT
ejpam-3085	43	12	that	that	PRON
ejpam-3085	43	13	is	be	AUX
ejpam-3085	43	14	a	a	DET
ejpam-3085	43	15	preorder	preorder	NOUN
ejpam-3085	43	16	on	on	ADP
ejpam-3085	43	17	p∗(h	p∗(h	PROPN
ejpam-3085	43	18	)	)	PUNCT
ejpam-3085	43	19	.	.	PUNCT
ejpam-3085	44	1	the	the	DET
ejpam-3085	44	2	concept	concept	NOUN
ejpam-3085	44	3	of	of	ADP
ejpam-3085	44	4	the	the	DET
ejpam-3085	44	5	ordered	order	VERB
ejpam-3085	44	6	groupoid	groupoid	NOUN
ejpam-3085	44	7	[	[	X
ejpam-3085	44	8	1	1	NUM
ejpam-3085	44	9	]	]	PUNCT
ejpam-3085	44	10	can	can	AUX
ejpam-3085	44	11	be	be	AUX
ejpam-3085	44	12	naturally	naturally	ADV
ejpam-3085	44	13	transferred	transfer	VERB
ejpam-3085	44	14	to	to	ADP
ejpam-3085	44	15	an	an	DET
ejpam-3085	44	16	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	44	17	as	as	SCONJ
ejpam-3085	44	18	follows	follow	VERB
ejpam-3085	44	19	:	:	PUNCT
ejpam-3085	44	20	an	an	DET
ejpam-3085	44	21	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	44	22	(	(	PUNCT
ejpam-3085	44	23	h	h	NOUN
ejpam-3085	44	24	,	,	PUNCT
ejpam-3085	44	25	◦	◦	NOUN
ejpam-3085	44	26	)	)	PUNCT
ejpam-3085	44	27	is	be	AUX
ejpam-3085	44	28	called	call	VERB
ejpam-3085	44	29	an	an	DET
ejpam-3085	44	30	ordered	order	VERB
ejpam-3085	44	31	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	44	32	if	if	SCONJ
ejpam-3085	44	33	there	there	PRON
ejpam-3085	44	34	is	be	VERB
ejpam-3085	44	35	an	an	DET
ejpam-3085	44	36	order	order	NOUN
ejpam-3085	44	37	relation	relation	NOUN
ejpam-3085	44	38	“	"	PUNCT
ejpam-3085	44	39	≤	≤	NUM
ejpam-3085	44	40	”	"	PUNCT
ejpam-3085	44	41	on	on	ADP
ejpam-3085	44	42	h	h	NOUN
ejpam-3085	44	43	satisfying	satisfy	VERB
ejpam-3085	44	44	the	the	DET
ejpam-3085	44	45	property	property	NOUN
ejpam-3085	44	46	a	a	DET
ejpam-3085	44	47	≤	≤	NUM
ejpam-3085	44	48	b	b	NOUN
ejpam-3085	44	49	implies	imply	VERB
ejpam-3085	44	50	a	a	DET
ejpam-3085	44	51	◦	◦	NOUN
ejpam-3085	44	52	c	c	X
ejpam-3085	44	53	�	�	PROPN
ejpam-3085	44	54	b	b	PROPN
ejpam-3085	44	55	◦	◦	NOUN
ejpam-3085	44	56	c	c	PROPN
ejpam-3085	44	57	and	and	CCONJ
ejpam-3085	44	58	c	c	AUX
ejpam-3085	44	59	◦	◦	VERB
ejpam-3085	44	60	a	a	DET
ejpam-3085	44	61	�	�	PROPN
ejpam-3085	44	62	c	c	PROPN
ejpam-3085	44	63	◦	◦	NOUN
ejpam-3085	44	64	b	b	NOUN
ejpam-3085	44	65	for	for	ADP
ejpam-3085	44	66	every	every	DET
ejpam-3085	44	67	c	c	PROPN
ejpam-3085	44	68	∈	∈	PROPN
ejpam-3085	44	69	h	h	NOUN
ejpam-3085	44	70	(	(	PUNCT
ejpam-3085	44	71	cf	cf	NOUN
ejpam-3085	44	72	.	.	PUNCT
ejpam-3085	45	1	also	also	ADV
ejpam-3085	45	2	[	[	X
ejpam-3085	45	3	11	11	NUM
ejpam-3085	45	4	]	]	PUNCT
ejpam-3085	45	5	)	)	PUNCT
ejpam-3085	45	6	and	and	CCONJ
ejpam-3085	45	7	it	it	PRON
ejpam-3085	45	8	is	be	AUX
ejpam-3085	45	9	denoted	denote	VERB
ejpam-3085	45	10	by	by	ADP
ejpam-3085	45	11	(	(	PUNCT
ejpam-3085	45	12	h	h	NOUN
ejpam-3085	45	13	,	,	PUNCT
ejpam-3085	45	14	◦	◦	NOUN
ejpam-3085	45	15	,	,	PUNCT
ejpam-3085	45	16	≤	≤	NUM
ejpam-3085	45	17	)	)	PUNCT
ejpam-3085	45	18	.	.	PUNCT
ejpam-3085	46	1	the	the	DET
ejpam-3085	46	2	concept	concept	NOUN
ejpam-3085	46	3	of	of	ADP
ejpam-3085	46	4	right	right	ADJ
ejpam-3085	46	5	(	(	PUNCT
ejpam-3085	46	6	left	left	ADJ
ejpam-3085	46	7	)	)	PUNCT
ejpam-3085	46	8	ideals	ideal	NOUN
ejpam-3085	46	9	of	of	ADP
ejpam-3085	46	10	ordered	order	VERB
ejpam-3085	46	11	groupoids	groupoid	NOUN
ejpam-3085	46	12	introduced	introduce	VERB
ejpam-3085	46	13	by	by	ADP
ejpam-3085	46	14	kehayopulu	kehayopulu	VERB
ejpam-3085	46	15	in	in	ADP
ejpam-3085	46	16	[	[	X
ejpam-3085	46	17	2	2	NUM
ejpam-3085	46	18	]	]	PUNCT
ejpam-3085	46	19	,	,	PUNCT
ejpam-3085	46	20	can	can	AUX
ejpam-3085	46	21	be	be	AUX
ejpam-3085	46	22	naturally	naturally	ADV
ejpam-3085	46	23	transferred	transfer	VERB
ejpam-3085	46	24	to	to	ADP
ejpam-3085	46	25	hypergroupoids	hypergroupoid	NOUN
ejpam-3085	46	26	as	as	SCONJ
ejpam-3085	46	27	follows	follow	VERB
ejpam-3085	46	28	:	:	PUNCT
ejpam-3085	46	29	if	if	SCONJ
ejpam-3085	46	30	(	(	PUNCT
ejpam-3085	46	31	h	h	NOUN
ejpam-3085	46	32	,	,	PUNCT
ejpam-3085	46	33	◦	◦	NOUN
ejpam-3085	46	34	,	,	PUNCT
ejpam-3085	46	35	≤	≤	NUM
ejpam-3085	46	36	)	)	PUNCT
ejpam-3085	46	37	is	be	AUX
ejpam-3085	46	38	an	an	DET
ejpam-3085	46	39	ordered	ordered	ADJ
ejpam-3085	46	40	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	46	41	,	,	PUNCT
ejpam-3085	46	42	a	a	DET
ejpam-3085	46	43	nonempty	nonempty	NOUN
ejpam-3085	46	44	subset	subset	VERB
ejpam-3085	46	45	a	a	PRON
ejpam-3085	46	46	of	of	ADP
ejpam-3085	46	47	h	h	NOUN
ejpam-3085	46	48	is	be	AUX
ejpam-3085	46	49	called	call	VERB
ejpam-3085	46	50	a	a	DET
ejpam-3085	46	51	right	right	NOUN
ejpam-3085	46	52	(	(	PUNCT
ejpam-3085	46	53	resp	resp	NOUN
ejpam-3085	46	54	.	.	PUNCT
ejpam-3085	47	1	left	left	ADJ
ejpam-3085	47	2	)	)	PUNCT
ejpam-3085	47	3	ideal	ideal	NOUN
ejpam-3085	47	4	of	of	ADP
ejpam-3085	47	5	h	h	NOUN
ejpam-3085	47	6	if	if	SCONJ
ejpam-3085	47	7	(	(	PUNCT
ejpam-3085	47	8	1	1	X
ejpam-3085	47	9	)	)	PUNCT
ejpam-3085	47	10	a	a	DET
ejpam-3085	47	11	∗	∗	NOUN
ejpam-3085	47	12	h	h	NOUN
ejpam-3085	48	1	⊆	⊆	NUM
ejpam-3085	48	2	a	a	DET
ejpam-3085	48	3	(	(	PUNCT
ejpam-3085	48	4	resp	resp	NOUN
ejpam-3085	48	5	.	.	PUNCT
ejpam-3085	49	1	h	h	PROPN
ejpam-3085	49	2	∗	∗	VERB
ejpam-3085	49	3	a	a	DET
ejpam-3085	49	4	⊆	⊆	NUM
ejpam-3085	49	5	a	a	NOUN
ejpam-3085	49	6	)	)	PUNCT
ejpam-3085	49	7	and	and	CCONJ
ejpam-3085	49	8	(	(	PUNCT
ejpam-3085	49	9	2	2	X
ejpam-3085	49	10	)	)	PUNCT
ejpam-3085	49	11	if	if	SCONJ
ejpam-3085	49	12	a	a	DET
ejpam-3085	49	13	∈	∈	PROPN
ejpam-3085	49	14	a	a	PRON
ejpam-3085	50	1	and	and	CCONJ
ejpam-3085	50	2	h	h	NOUN
ejpam-3085	51	1	3	3	NUM
ejpam-3085	51	2	b	b	NOUN
ejpam-3085	51	3	≤	≤	NUM
ejpam-3085	51	4	a	a	PRON
ejpam-3085	51	5	,	,	PUNCT
ejpam-3085	51	6	then	then	ADV
ejpam-3085	51	7	b	b	X
ejpam-3085	51	8	∈	∈	PROPN
ejpam-3085	51	9	a	a	PRON
ejpam-3085	51	10	,	,	PUNCT
ejpam-3085	51	11	that	that	PRON
ejpam-3085	51	12	is	be	AUX
ejpam-3085	51	13	if	if	SCONJ
ejpam-3085	51	14	(	(	PUNCT
ejpam-3085	51	15	a	a	X
ejpam-3085	51	16	]	]	X
ejpam-3085	51	17	=	=	PUNCT
ejpam-3085	51	18	a.	a.	NOUN
ejpam-3085	51	19	a	a	DET
ejpam-3085	51	20	subset	subset	NOUN
ejpam-3085	51	21	of	of	ADP
ejpam-3085	51	22	h	h	NOUN
ejpam-3085	51	23	which	which	PRON
ejpam-3085	51	24	is	be	AUX
ejpam-3085	51	25	both	both	CCONJ
ejpam-3085	51	26	a	a	DET
ejpam-3085	51	27	right	right	NOUN
ejpam-3085	51	28	and	and	CCONJ
ejpam-3085	51	29	left	leave	VERB
ejpam-3085	51	30	ideal	ideal	NOUN
ejpam-3085	51	31	of	of	ADP
ejpam-3085	51	32	h	h	NOUN
ejpam-3085	51	33	is	be	AUX
ejpam-3085	51	34	called	call	VERB
ejpam-3085	51	35	an	an	DET
ejpam-3085	51	36	ideal	ideal	NOUN
ejpam-3085	51	37	of	of	ADP
ejpam-3085	51	38	h.	h.	PROPN
ejpam-3085	51	39	recall	recall	PROPN
ejpam-3085	51	40	that	that	SCONJ
ejpam-3085	51	41	we	we	PRON
ejpam-3085	51	42	have	have	AUX
ejpam-3085	51	43	a	a	DET
ejpam-3085	51	44	∗h	∗h	NOUN
ejpam-3085	51	45	⊆	⊆	NUM
ejpam-3085	51	46	a	a	DET
ejpam-3085	51	47	(	(	PUNCT
ejpam-3085	51	48	resp	resp	NOUN
ejpam-3085	51	49	.	.	PUNCT
ejpam-3085	52	1	h	h	PROPN
ejpam-3085	52	2	∗	∗	VERB
ejpam-3085	52	3	a	a	DET
ejpam-3085	52	4	⊆	⊆	NUM
ejpam-3085	52	5	a	a	NOUN
ejpam-3085	52	6	)	)	PUNCT
ejpam-3085	52	7	if	if	SCONJ
ejpam-3085	53	1	and	and	CCONJ
ejpam-3085	53	2	only	only	ADV
ejpam-3085	53	3	if	if	SCONJ
ejpam-3085	53	4	a	a	DET
ejpam-3085	53	5	◦	◦	NOUN
ejpam-3085	53	6	h	h	NOUN
ejpam-3085	53	7	⊆	⊆	NUM
ejpam-3085	53	8	a	a	DET
ejpam-3085	53	9	(	(	PUNCT
ejpam-3085	53	10	resp	resp	NOUN
ejpam-3085	53	11	.	.	PUNCT
ejpam-3085	54	1	h	h	PROPN
ejpam-3085	54	2	◦	◦	VERB
ejpam-3085	54	3	a	a	DET
ejpam-3085	54	4	⊆	⊆	NUM
ejpam-3085	54	5	a	a	NOUN
ejpam-3085	54	6	)	)	PUNCT
ejpam-3085	54	7	for	for	ADP
ejpam-3085	54	8	every	every	DET
ejpam-3085	54	9	a	a	DET
ejpam-3085	54	10	∈	∈	PROPN
ejpam-3085	54	11	a	a	PRON
ejpam-3085	55	1	and	and	CCONJ
ejpam-3085	55	2	every	every	DET
ejpam-3085	55	3	h	h	NOUN
ejpam-3085	55	4	∈	∈	PROPN
ejpam-3085	55	5	h.	h.	NOUN
ejpam-3085	55	6	a	a	DET
ejpam-3085	55	7	nonempty	nonempty	NOUN
ejpam-3085	55	8	subset	subset	VERB
ejpam-3085	55	9	a	a	PRON
ejpam-3085	55	10	of	of	ADP
ejpam-3085	55	11	an	an	DET
ejpam-3085	55	12	ordered	order	VERB
ejpam-3085	55	13	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	55	14	h	h	PROPN
ejpam-3085	55	15	is	be	AUX
ejpam-3085	55	16	called	call	VERB
ejpam-3085	55	17	a	a	DET
ejpam-3085	55	18	subgroupoid	subgroupoid	NOUN
ejpam-3085	55	19	of	of	ADP
ejpam-3085	55	20	h	h	NOUN
ejpam-3085	55	21	if	if	SCONJ
ejpam-3085	55	22	a	a	DET
ejpam-3085	55	23	∗	∗	NOUN
ejpam-3085	55	24	a	a	DET
ejpam-3085	55	25	⊆	⊆	NUM
ejpam-3085	55	26	a	a	NOUN
ejpam-3085	55	27	,	,	PUNCT
ejpam-3085	55	28	equivalently	equivalently	ADV
ejpam-3085	55	29	if	if	SCONJ
ejpam-3085	55	30	for	for	ADP
ejpam-3085	55	31	every	every	DET
ejpam-3085	55	32	a	a	PROPN
ejpam-3085	55	33	,	,	PUNCT
ejpam-3085	55	34	b	b	X
ejpam-3085	55	35	∈	∈	PROPN
ejpam-3085	55	36	a	a	PRON
ejpam-3085	55	37	we	we	PRON
ejpam-3085	55	38	have	have	VERB
ejpam-3085	55	39	a	a	DET
ejpam-3085	55	40	◦	◦	NOUN
ejpam-3085	55	41	b	b	NOUN
ejpam-3085	55	42	⊆	⊆	NUM
ejpam-3085	55	43	a.	a.	NOUN
ejpam-3085	55	44	clearly	clearly	ADV
ejpam-3085	55	45	,	,	PUNCT
ejpam-3085	55	46	every	every	DET
ejpam-3085	55	47	right	right	NOUN
ejpam-3085	55	48	(	(	PUNCT
ejpam-3085	55	49	left	left	ADJ
ejpam-3085	55	50	)	)	PUNCT
ejpam-3085	55	51	ideal	ideal	NOUN
ejpam-3085	55	52	of	of	ADP
ejpam-3085	55	53	an	an	DET
ejpam-3085	55	54	ordered	order	VERB
ejpam-3085	55	55	groupoid	groupoid	PROPN
ejpam-3085	55	56	h	h	PROPN
ejpam-3085	55	57	is	be	AUX
ejpam-3085	55	58	a	a	DET
ejpam-3085	55	59	subgroupoid	subgroupoid	NOUN
ejpam-3085	55	60	of	of	ADP
ejpam-3085	55	61	h.	h.	PROPN
ejpam-3085	55	62	n.	n.	PROPN
ejpam-3085	55	63	kehayopulu	kehayopulu	PROPN
ejpam-3085	55	64	/	/	SYM
ejpam-3085	55	65	eur	eur	PROPN
ejpam-3085	55	66	.	.	PUNCT
ejpam-3085	56	1	j.	j.	PROPN
ejpam-3085	56	2	pure	pure	PROPN
ejpam-3085	56	3	appl	appl	PROPN
ejpam-3085	56	4	.	.	PROPN
ejpam-3085	56	5	math	math	PROPN
ejpam-3085	56	6	,	,	PUNCT
ejpam-3085	56	7	11	11	NUM
ejpam-3085	56	8	(	(	PUNCT
ejpam-3085	56	9	1	1	NUM
ejpam-3085	56	10	)	)	PUNCT
ejpam-3085	56	11	(	(	PUNCT
ejpam-3085	56	12	2018	2018	NUM
ejpam-3085	56	13	)	)	PUNCT
ejpam-3085	56	14	,	,	PUNCT
ejpam-3085	56	15	10	10	NUM
ejpam-3085	56	16	-	-	SYM
ejpam-3085	56	17	22	22	NUM
ejpam-3085	56	18	12	12	NUM
ejpam-3085	56	19	2	2	NUM
ejpam-3085	56	20	.	.	PUNCT
ejpam-3085	56	21	main	main	ADJ
ejpam-3085	56	22	results	result	NOUN
ejpam-3085	56	23	proposition	proposition	NOUN
ejpam-3085	56	24	1	1	NUM
ejpam-3085	56	25	.	.	PUNCT
ejpam-3085	57	1	let	let	AUX
ejpam-3085	57	2	(	(	PUNCT
ejpam-3085	57	3	h	h	NOUN
ejpam-3085	57	4	,	,	PUNCT
ejpam-3085	57	5	◦	◦	NOUN
ejpam-3085	57	6	,	,	PUNCT
ejpam-3085	57	7	≤	≤	NUM
ejpam-3085	57	8	)	)	PUNCT
ejpam-3085	57	9	be	be	VERB
ejpam-3085	57	10	an	an	DET
ejpam-3085	57	11	ordered	ordered	ADJ
ejpam-3085	57	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	57	13	,	,	PUNCT
ejpam-3085	57	14	a	a	DET
ejpam-3085	57	15	≤	≤	PROPN
ejpam-3085	57	16	b	b	NOUN
ejpam-3085	57	17	and	and	CCONJ
ejpam-3085	57	18	c	c	PROPN
ejpam-3085	57	19	≤	≤	X
ejpam-3085	57	20	d.	d.	PROPN
ejpam-3085	58	1	then	then	ADV
ejpam-3085	58	2	we	we	PRON
ejpam-3085	58	3	have	have	VERB
ejpam-3085	58	4	a	a	DET
ejpam-3085	58	5	◦	◦	NOUN
ejpam-3085	58	6	c	c	NOUN
ejpam-3085	58	7	�	�	PROPN
ejpam-3085	58	8	b	b	PROPN
ejpam-3085	58	9	◦	◦	VERB
ejpam-3085	58	10	d.	d.	PROPN
ejpam-3085	58	11	proof	proof	NOUN
ejpam-3085	58	12	.	.	PUNCT
ejpam-3085	59	1	since	since	SCONJ
ejpam-3085	59	2	a	a	DET
ejpam-3085	59	3	≤	≤	NUM
ejpam-3085	59	4	b	b	NOUN
ejpam-3085	59	5	and	and	CCONJ
ejpam-3085	59	6	c	c	NOUN
ejpam-3085	59	7	∈	∈	PROPN
ejpam-3085	59	8	h	h	NOUN
ejpam-3085	59	9	,	,	PUNCT
ejpam-3085	59	10	we	we	PRON
ejpam-3085	59	11	have	have	VERB
ejpam-3085	59	12	a	a	DET
ejpam-3085	59	13	◦	◦	NOUN
ejpam-3085	59	14	c	c	NOUN
ejpam-3085	59	15	�	�	PROPN
ejpam-3085	59	16	b	b	PROPN
ejpam-3085	59	17	◦	◦	NOUN
ejpam-3085	59	18	c.	c.	NOUN
ejpam-3085	59	19	since	since	SCONJ
ejpam-3085	59	20	c	c	PROPN
ejpam-3085	59	21	≤	≤	NUM
ejpam-3085	59	22	d	d	PROPN
ejpam-3085	59	23	and	and	CCONJ
ejpam-3085	59	24	b	b	X
ejpam-3085	59	25	∈	∈	PROPN
ejpam-3085	59	26	h	h	NOUN
ejpam-3085	59	27	,	,	PUNCT
ejpam-3085	59	28	we	we	PRON
ejpam-3085	59	29	have	have	VERB
ejpam-3085	59	30	b	b	NUM
ejpam-3085	59	31	◦	◦	NOUN
ejpam-3085	59	32	c	c	PROPN
ejpam-3085	59	33	�	�	PROPN
ejpam-3085	59	34	b	b	PROPN
ejpam-3085	59	35	◦	◦	NOUN
ejpam-3085	59	36	d.	d.	PROPN
ejpam-3085	59	37	since	since	SCONJ
ejpam-3085	59	38	the	the	DET
ejpam-3085	59	39	relation	relation	NOUN
ejpam-3085	59	40	“	"	PUNCT
ejpam-3085	59	41	�	�	PROPN
ejpam-3085	59	42	”	"	PUNCT
ejpam-3085	59	43	is	be	AUX
ejpam-3085	59	44	transitive	transitive	ADJ
ejpam-3085	59	45	on	on	ADP
ejpam-3085	59	46	p∗(h	p∗(h	PROPN
ejpam-3085	59	47	)	)	PUNCT
ejpam-3085	59	48	,	,	PUNCT
ejpam-3085	59	49	we	we	PRON
ejpam-3085	59	50	have	have	VERB
ejpam-3085	59	51	a	a	DET
ejpam-3085	59	52	◦	◦	NOUN
ejpam-3085	59	53	c	c	NOUN
ejpam-3085	59	54	�	�	PROPN
ejpam-3085	59	55	b	b	PROPN
ejpam-3085	59	56	◦	◦	PROPN
ejpam-3085	59	57	d.	d.	PROPN
ejpam-3085	59	58	�	�	PROPN
ejpam-3085	59	59	proposition	proposition	NOUN
ejpam-3085	59	60	2	2	NUM
ejpam-3085	59	61	.	.	PUNCT
ejpam-3085	60	1	let	let	VERB
ejpam-3085	60	2	(	(	PUNCT
ejpam-3085	60	3	h	h	NOUN
ejpam-3085	60	4	,	,	PUNCT
ejpam-3085	60	5	◦	◦	NOUN
ejpam-3085	60	6	,	,	PUNCT
ejpam-3085	60	7	≤	≤	NUM
ejpam-3085	60	8	)	)	PUNCT
ejpam-3085	60	9	be	be	AUX
ejpam-3085	60	10	an	an	DET
ejpam-3085	60	11	ordered	ordered	ADJ
ejpam-3085	60	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	60	13	and	and	CCONJ
ejpam-3085	60	14	a	a	DET
ejpam-3085	60	15	,	,	PUNCT
ejpam-3085	60	16	b	b	NOUN
ejpam-3085	60	17	,	,	PUNCT
ejpam-3085	60	18	c	c	X
ejpam-3085	60	19	nonempty	nonempty	NOUN
ejpam-3085	60	20	subsets	subset	NOUN
ejpam-3085	60	21	of	of	ADP
ejpam-3085	60	22	h	h	NOUN
ejpam-3085	60	23	such	such	ADJ
ejpam-3085	60	24	that	that	SCONJ
ejpam-3085	60	25	a	a	DET
ejpam-3085	60	26	�	�	PROPN
ejpam-3085	60	27	b.	b.	PROPN
ejpam-3085	60	28	then	then	ADV
ejpam-3085	60	29	we	we	PRON
ejpam-3085	60	30	have	have	AUX
ejpam-3085	60	31	a	a	DET
ejpam-3085	60	32	∗	∗	NOUN
ejpam-3085	60	33	c	c	NOUN
ejpam-3085	61	1	⊆	⊆	NUM
ejpam-3085	61	2	(	(	PUNCT
ejpam-3085	61	3	b	b	NOUN
ejpam-3085	61	4	∗	∗	X
ejpam-3085	61	5	c	c	NOUN
ejpam-3085	61	6	]	]	PUNCT
ejpam-3085	61	7	and	and	CCONJ
ejpam-3085	61	8	c	c	PROPN
ejpam-3085	61	9	∗a	∗a	PROPN
ejpam-3085	61	10	⊆	⊆	NUM
ejpam-3085	61	11	(	(	PUNCT
ejpam-3085	61	12	c	c	NOUN
ejpam-3085	61	13	∗b	∗b	PROPN
ejpam-3085	61	14	]	]	PUNCT
ejpam-3085	61	15	.	.	PUNCT
ejpam-3085	62	1	proof	proof	NOUN
ejpam-3085	62	2	.	.	PUNCT
ejpam-3085	63	1	let	let	VERB
ejpam-3085	63	2	x	x	SYM
ejpam-3085	63	3	∈	∈	VERB
ejpam-3085	63	4	a	a	DET
ejpam-3085	63	5	∗	∗	NOUN
ejpam-3085	63	6	c.	c.	NOUN
ejpam-3085	63	7	then	then	ADV
ejpam-3085	63	8	x	x	SYM
ejpam-3085	63	9	∈	∈	PROPN
ejpam-3085	63	10	a	a	DET
ejpam-3085	63	11	◦	◦	NOUN
ejpam-3085	63	12	c	c	NOUN
ejpam-3085	63	13	for	for	ADP
ejpam-3085	63	14	some	some	DET
ejpam-3085	63	15	a	a	DET
ejpam-3085	63	16	∈	∈	PROPN
ejpam-3085	63	17	a	a	PRON
ejpam-3085	63	18	,	,	PUNCT
ejpam-3085	63	19	c	c	PROPN
ejpam-3085	63	20	∈	∈	PROPN
ejpam-3085	63	21	c.	c.	NOUN
ejpam-3085	63	22	since	since	SCONJ
ejpam-3085	63	23	a	a	DET
ejpam-3085	63	24	�	�	PROPN
ejpam-3085	63	25	b	b	PROPN
ejpam-3085	63	26	and	and	CCONJ
ejpam-3085	63	27	a	a	DET
ejpam-3085	63	28	∈	∈	PROPN
ejpam-3085	63	29	a	a	PRON
ejpam-3085	63	30	,	,	PUNCT
ejpam-3085	63	31	there	there	PRON
ejpam-3085	63	32	exists	exist	VERB
ejpam-3085	63	33	b	b	PROPN
ejpam-3085	63	34	∈	∈	PROPN
ejpam-3085	63	35	b	b	NOUN
ejpam-3085	63	36	such	such	ADJ
ejpam-3085	63	37	that	that	SCONJ
ejpam-3085	63	38	a	a	DET
ejpam-3085	63	39	≤	≤	PROPN
ejpam-3085	63	40	b.	b.	NOUN
ejpam-3085	63	41	since	since	SCONJ
ejpam-3085	63	42	a	a	DET
ejpam-3085	63	43	≤	≤	NUM
ejpam-3085	63	44	b	b	NOUN
ejpam-3085	63	45	,	,	PUNCT
ejpam-3085	63	46	we	we	PRON
ejpam-3085	63	47	have	have	VERB
ejpam-3085	63	48	a	a	DET
ejpam-3085	63	49	◦	◦	NOUN
ejpam-3085	63	50	c	c	NOUN
ejpam-3085	63	51	�	�	PROPN
ejpam-3085	63	52	b	b	PROPN
ejpam-3085	63	53	◦	◦	NOUN
ejpam-3085	63	54	c.	c.	NOUN
ejpam-3085	63	55	since	since	SCONJ
ejpam-3085	63	56	x	x	PROPN
ejpam-3085	63	57	∈	∈	PROPN
ejpam-3085	63	58	a	a	DET
ejpam-3085	63	59	◦	◦	NOUN
ejpam-3085	63	60	c	c	X
ejpam-3085	63	61	,	,	PUNCT
ejpam-3085	63	62	there	there	PRON
ejpam-3085	63	63	exists	exist	VERB
ejpam-3085	63	64	y	y	PROPN
ejpam-3085	63	65	∈	∈	PROPN
ejpam-3085	63	66	b	b	PROPN
ejpam-3085	63	67	◦	◦	NOUN
ejpam-3085	63	68	c	c	ADP
ejpam-3085	63	69	such	such	ADJ
ejpam-3085	63	70	that	that	SCONJ
ejpam-3085	63	71	x	x	X
ejpam-3085	63	72	≤	≤	NUM
ejpam-3085	63	73	y.	y.	NOUN
ejpam-3085	63	74	we	we	PRON
ejpam-3085	63	75	have	have	VERB
ejpam-3085	64	1	x	x	NOUN
ejpam-3085	64	2	≤	≤	NUM
ejpam-3085	64	3	y	y	PROPN
ejpam-3085	64	4	∈	∈	PROPN
ejpam-3085	64	5	b	b	PROPN
ejpam-3085	64	6	◦	◦	NOUN
ejpam-3085	64	7	c	c	NOUN
ejpam-3085	64	8	=	=	SYM
ejpam-3085	64	9	{	{	PUNCT
ejpam-3085	64	10	b	b	NOUN
ejpam-3085	64	11	}	}	PUNCT
ejpam-3085	64	12	∗	∗	NOUN
ejpam-3085	64	13	{	{	PUNCT
ejpam-3085	64	14	c	c	NOUN
ejpam-3085	64	15	}	}	PUNCT
ejpam-3085	64	16	⊆	⊆	NUM
ejpam-3085	64	17	b	b	NOUN
ejpam-3085	64	18	∗c	∗c	PROPN
ejpam-3085	64	19	,	,	PUNCT
ejpam-3085	64	20	so	so	ADV
ejpam-3085	64	21	x	x	SYM
ejpam-3085	64	22	∈	∈	PROPN
ejpam-3085	64	23	(	(	PUNCT
ejpam-3085	64	24	b	b	NOUN
ejpam-3085	64	25	∗c	∗c	PROPN
ejpam-3085	64	26	]	]	PUNCT
ejpam-3085	64	27	.	.	PUNCT
ejpam-3085	65	1	similarly	similarly	ADV
ejpam-3085	65	2	c	c	X
ejpam-3085	65	3	∗a	∗a	PROPN
ejpam-3085	65	4	⊆	⊆	NUM
ejpam-3085	65	5	(	(	PUNCT
ejpam-3085	65	6	c	c	NOUN
ejpam-3085	65	7	∗b	∗b	PROPN
ejpam-3085	65	8	]	]	PUNCT
ejpam-3085	65	9	.	.	PUNCT
ejpam-3085	66	1	�	�	PROPN
ejpam-3085	66	2	definition	definition	NOUN
ejpam-3085	66	3	3	3	X
ejpam-3085	66	4	.	.	PUNCT
ejpam-3085	67	1	let	let	VERB
ejpam-3085	67	2	h	h	PRON
ejpam-3085	67	3	be	be	AUX
ejpam-3085	67	4	an	an	DET
ejpam-3085	67	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	67	6	or	or	CCONJ
ejpam-3085	67	7	an	an	DET
ejpam-3085	67	8	ordered	order	VERB
ejpam-3085	67	9	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	67	10	.	.	PUNCT
ejpam-3085	68	1	a	a	DET
ejpam-3085	68	2	nonempty	nonempty	NOUN
ejpam-3085	68	3	subset	subset	VERB
ejpam-3085	68	4	t	t	PROPN
ejpam-3085	68	5	of	of	ADP
ejpam-3085	68	6	h	h	PROPN
ejpam-3085	68	7	is	be	AUX
ejpam-3085	68	8	called	call	VERB
ejpam-3085	68	9	prime	prime	ADJ
ejpam-3085	68	10	(	(	PUNCT
ejpam-3085	68	11	subset	subset	NOUN
ejpam-3085	68	12	)	)	PUNCT
ejpam-3085	68	13	of	of	ADP
ejpam-3085	68	14	h	h	NOUN
ejpam-3085	68	15	if	if	SCONJ
ejpam-3085	68	16	the	the	DET
ejpam-3085	68	17	following	follow	VERB
ejpam-3085	68	18	assertion	assertion	NOUN
ejpam-3085	68	19	is	be	AUX
ejpam-3085	68	20	satisfied	satisfied	ADJ
ejpam-3085	68	21	:	:	PUNCT
ejpam-3085	68	22	if	if	SCONJ
ejpam-3085	68	23	a	a	PRON
ejpam-3085	68	24	,	,	PUNCT
ejpam-3085	68	25	b	b	PROPN
ejpam-3085	68	26	∈	∈	PROPN
ejpam-3085	68	27	p∗(h	p∗(h	PROPN
ejpam-3085	68	28	)	)	PUNCT
ejpam-3085	68	29	such	such	ADJ
ejpam-3085	68	30	that	that	SCONJ
ejpam-3085	68	31	a	a	DET
ejpam-3085	68	32	∗b	∗b	PROPN
ejpam-3085	68	33	⊆	⊆	NUM
ejpam-3085	68	34	t	t	NOUN
ejpam-3085	68	35	,	,	PUNCT
ejpam-3085	68	36	then	then	ADV
ejpam-3085	68	37	a	a	DET
ejpam-3085	68	38	⊆	⊆	NUM
ejpam-3085	68	39	t	t	NOUN
ejpam-3085	68	40	or	or	CCONJ
ejpam-3085	68	41	b	b	NOUN
ejpam-3085	68	42	⊆	⊆	NUM
ejpam-3085	68	43	t.	t.	NOUN
ejpam-3085	68	44	it	it	PRON
ejpam-3085	68	45	is	be	AUX
ejpam-3085	68	46	called	call	VERB
ejpam-3085	68	47	weakly	weakly	ADJ
ejpam-3085	68	48	prime	prime	NOUN
ejpam-3085	68	49	if	if	SCONJ
ejpam-3085	68	50	we	we	PRON
ejpam-3085	68	51	have	have	VERB
ejpam-3085	68	52	the	the	DET
ejpam-3085	68	53	following	following	NOUN
ejpam-3085	68	54	:	:	PUNCT
ejpam-3085	68	55	if	if	SCONJ
ejpam-3085	68	56	a	a	DET
ejpam-3085	68	57	,	,	PUNCT
ejpam-3085	68	58	b	b	NOUN
ejpam-3085	68	59	are	be	AUX
ejpam-3085	68	60	ideals	ideal	NOUN
ejpam-3085	68	61	of	of	ADP
ejpam-3085	68	62	h	h	NOUN
ejpam-3085	68	63	such	such	ADJ
ejpam-3085	68	64	that	that	SCONJ
ejpam-3085	68	65	a	a	DET
ejpam-3085	68	66	∗b	∗b	PROPN
ejpam-3085	68	67	⊆	⊆	NUM
ejpam-3085	68	68	t	t	NOUN
ejpam-3085	68	69	,	,	PUNCT
ejpam-3085	68	70	then	then	ADV
ejpam-3085	68	71	a	a	DET
ejpam-3085	68	72	⊆	⊆	NUM
ejpam-3085	68	73	t	t	NOUN
ejpam-3085	68	74	or	or	CCONJ
ejpam-3085	68	75	b	b	NOUN
ejpam-3085	68	76	⊆	⊆	NUM
ejpam-3085	68	77	t.	t.	NOUN
ejpam-3085	68	78	proposition	proposition	NOUN
ejpam-3085	68	79	4	4	NUM
ejpam-3085	68	80	.	.	PUNCT
ejpam-3085	69	1	let	let	VERB
ejpam-3085	69	2	h	h	PRON
ejpam-3085	69	3	be	be	AUX
ejpam-3085	69	4	an	an	DET
ejpam-3085	69	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	69	6	or	or	CCONJ
ejpam-3085	69	7	an	an	DET
ejpam-3085	69	8	ordered	order	VERB
ejpam-3085	69	9	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	69	10	.	.	PUNCT
ejpam-3085	70	1	a	a	DET
ejpam-3085	70	2	nonempty	nonempty	NOUN
ejpam-3085	70	3	subset	subset	VERB
ejpam-3085	70	4	t	t	PROPN
ejpam-3085	70	5	of	of	ADP
ejpam-3085	70	6	h	h	PROPN
ejpam-3085	70	7	is	be	AUX
ejpam-3085	70	8	a	a	DET
ejpam-3085	70	9	prime	prime	ADJ
ejpam-3085	70	10	subset	subset	NOUN
ejpam-3085	70	11	of	of	ADP
ejpam-3085	70	12	h	h	NOUN
ejpam-3085	70	13	if	if	SCONJ
ejpam-3085	71	1	and	and	CCONJ
ejpam-3085	71	2	only	only	ADV
ejpam-3085	71	3	if	if	SCONJ
ejpam-3085	71	4	a	a	PRON
ejpam-3085	71	5	,	,	PUNCT
ejpam-3085	71	6	b	b	X
ejpam-3085	71	7	∈	∈	ADJ
ejpam-3085	71	8	h	h	NOUN
ejpam-3085	71	9	such	such	ADJ
ejpam-3085	71	10	that	that	SCONJ
ejpam-3085	71	11	a	a	DET
ejpam-3085	71	12	◦	◦	NOUN
ejpam-3085	71	13	b	b	NOUN
ejpam-3085	71	14	⊆	⊆	NUM
ejpam-3085	71	15	t	t	NOUN
ejpam-3085	71	16	implies	imply	VERB
ejpam-3085	71	17	a	a	DET
ejpam-3085	71	18	∈	∈	PROPN
ejpam-3085	71	19	t	t	NOUN
ejpam-3085	71	20	or	or	CCONJ
ejpam-3085	71	21	b	b	NOUN
ejpam-3085	71	22	∈	∈	NOUN
ejpam-3085	71	23	t.	t.	NOUN
ejpam-3085	71	24	proof	proof	NOUN
ejpam-3085	71	25	.	.	PUNCT
ejpam-3085	72	1	=	=	NOUN
ejpam-3085	72	2	⇒.	⇒.	NOUN
ejpam-3085	72	3	let	let	VERB
ejpam-3085	72	4	a	a	DET
ejpam-3085	72	5	,	,	PUNCT
ejpam-3085	72	6	b	b	X
ejpam-3085	72	7	∈	∈	PROPN
ejpam-3085	72	8	h	h	NOUN
ejpam-3085	72	9	,	,	PUNCT
ejpam-3085	72	10	a	a	DET
ejpam-3085	72	11	◦	◦	NOUN
ejpam-3085	72	12	b	b	NOUN
ejpam-3085	72	13	⊆	⊆	NUM
ejpam-3085	72	14	t	t	NOUN
ejpam-3085	72	15	.	.	PUNCT
ejpam-3085	73	1	since	since	SCONJ
ejpam-3085	73	2	{	{	PUNCT
ejpam-3085	73	3	a	a	X
ejpam-3085	73	4	}	}	PUNCT
ejpam-3085	73	5	,	,	PUNCT
ejpam-3085	73	6	{	{	PUNCT
ejpam-3085	73	7	b	b	X
ejpam-3085	73	8	}	}	PUNCT
ejpam-3085	73	9	∈	∈	PROPN
ejpam-3085	73	10	p∗(h	p∗(h	PROPN
ejpam-3085	73	11	)	)	PUNCT
ejpam-3085	73	12	,	,	PUNCT
ejpam-3085	73	13	{	{	PUNCT
ejpam-3085	73	14	a	a	PRON
ejpam-3085	73	15	}	}	PUNCT
ejpam-3085	73	16	∗	∗	NOUN
ejpam-3085	73	17	{	{	PUNCT
ejpam-3085	73	18	b	b	NOUN
ejpam-3085	73	19	}	}	PUNCT
ejpam-3085	73	20	=	=	PUNCT
ejpam-3085	73	21	a	a	DET
ejpam-3085	73	22	◦	◦	NOUN
ejpam-3085	73	23	b	b	NUM
ejpam-3085	73	24	⊆	⊆	NUM
ejpam-3085	73	25	t	t	NOUN
ejpam-3085	73	26	and	and	CCONJ
ejpam-3085	73	27	t	t	PROPN
ejpam-3085	73	28	is	be	AUX
ejpam-3085	73	29	prime	prime	ADJ
ejpam-3085	73	30	,	,	PUNCT
ejpam-3085	73	31	we	we	PRON
ejpam-3085	73	32	have	have	VERB
ejpam-3085	73	33	{	{	PUNCT
ejpam-3085	73	34	a	a	NOUN
ejpam-3085	73	35	}	}	PUNCT
ejpam-3085	73	36	⊆	⊆	NUM
ejpam-3085	73	37	t	t	NOUN
ejpam-3085	73	38	or	or	CCONJ
ejpam-3085	73	39	{	{	PUNCT
ejpam-3085	73	40	b	b	NOUN
ejpam-3085	73	41	}	}	PUNCT
ejpam-3085	73	42	⊆	⊆	NUM
ejpam-3085	73	43	t	t	NOUN
ejpam-3085	73	44	.	.	PUNCT
ejpam-3085	74	1	then	then	ADV
ejpam-3085	74	2	a	a	DET
ejpam-3085	74	3	∈	∈	PROPN
ejpam-3085	74	4	t	t	NOUN
ejpam-3085	74	5	or	or	CCONJ
ejpam-3085	74	6	b	b	PROPN
ejpam-3085	74	7	∈	∈	PROPN
ejpam-3085	74	8	t	t	NOUN
ejpam-3085	74	9	.	.	PUNCT
ejpam-3085	75	1	⇐	⇐	PROPN
ejpam-3085	75	2	=	=	PRON
ejpam-3085	75	3	.	.	PUNCT
ejpam-3085	76	1	let	let	VERB
ejpam-3085	76	2	a	a	DET
ejpam-3085	76	3	,	,	PUNCT
ejpam-3085	76	4	b	b	PROPN
ejpam-3085	76	5	∈	∈	PROPN
ejpam-3085	76	6	p∗(h	p∗(h	PROPN
ejpam-3085	76	7	)	)	PUNCT
ejpam-3085	76	8	such	such	ADJ
ejpam-3085	76	9	that	that	SCONJ
ejpam-3085	76	10	a	a	DET
ejpam-3085	76	11	∗	∗	NOUN
ejpam-3085	76	12	b	b	NOUN
ejpam-3085	76	13	⊆	⊆	NUM
ejpam-3085	76	14	t	t	NOUN
ejpam-3085	76	15	and	and	CCONJ
ejpam-3085	76	16	let	let	VERB
ejpam-3085	76	17	a	a	DET
ejpam-3085	76	18	6⊆	6⊆	PROPN
ejpam-3085	76	19	t	t	PROPN
ejpam-3085	76	20	and	and	CCONJ
ejpam-3085	76	21	b	b	PROPN
ejpam-3085	76	22	∈	∈	PROPN
ejpam-3085	76	23	b.	b.	PROPN
ejpam-3085	76	24	take	take	VERB
ejpam-3085	76	25	an	an	DET
ejpam-3085	76	26	element	element	NOUN
ejpam-3085	76	27	a	a	DET
ejpam-3085	76	28	∈	∈	PROPN
ejpam-3085	76	29	a	a	DET
ejpam-3085	76	30	such	such	ADJ
ejpam-3085	76	31	that	that	SCONJ
ejpam-3085	76	32	a	a	DET
ejpam-3085	76	33	6∈	6∈	NOUN
ejpam-3085	76	34	t	t	NOUN
ejpam-3085	76	35	.	.	PUNCT
ejpam-3085	77	1	since	since	SCONJ
ejpam-3085	77	2	a	a	DET
ejpam-3085	77	3	◦	◦	NOUN
ejpam-3085	77	4	b	b	NOUN
ejpam-3085	77	5	⊆	⊆	NUM
ejpam-3085	77	6	a	a	DET
ejpam-3085	77	7	∗b	∗b	PROPN
ejpam-3085	77	8	⊆	⊆	NUM
ejpam-3085	77	9	t	t	NOUN
ejpam-3085	77	10	,	,	PUNCT
ejpam-3085	77	11	by	by	ADP
ejpam-3085	77	12	hypothesis	hypothesis	NOUN
ejpam-3085	77	13	,	,	PUNCT
ejpam-3085	77	14	we	we	PRON
ejpam-3085	77	15	have	have	VERB
ejpam-3085	77	16	a	a	DET
ejpam-3085	77	17	∈	∈	PROPN
ejpam-3085	77	18	t	t	NOUN
ejpam-3085	77	19	or	or	CCONJ
ejpam-3085	77	20	b	b	PROPN
ejpam-3085	77	21	∈	∈	PROPN
ejpam-3085	77	22	t	t	NOUN
ejpam-3085	77	23	.	.	PUNCT
ejpam-3085	78	1	since	since	SCONJ
ejpam-3085	78	2	a	a	DET
ejpam-3085	78	3	6∈	6∈	PROPN
ejpam-3085	78	4	t	t	NOUN
ejpam-3085	78	5	,	,	PUNCT
ejpam-3085	78	6	we	we	PRON
ejpam-3085	78	7	have	have	VERB
ejpam-3085	78	8	b	b	PROPN
ejpam-3085	78	9	∈	∈	PROPN
ejpam-3085	78	10	t	t	PROPN
ejpam-3085	78	11	.	.	PUNCT
ejpam-3085	79	1	�	�	PROPN
ejpam-3085	79	2	definition	definition	NOUN
ejpam-3085	79	3	5	5	NUM
ejpam-3085	79	4	.	.	PUNCT
ejpam-3085	80	1	let	let	VERB
ejpam-3085	80	2	h	h	PRON
ejpam-3085	80	3	be	be	AUX
ejpam-3085	80	4	an	an	DET
ejpam-3085	80	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	80	6	or	or	CCONJ
ejpam-3085	80	7	an	an	DET
ejpam-3085	80	8	ordered	order	VERB
ejpam-3085	80	9	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	80	10	.	.	PUNCT
ejpam-3085	81	1	a	a	DET
ejpam-3085	81	2	nonempty	nonempty	NOUN
ejpam-3085	81	3	subset	subset	VERB
ejpam-3085	81	4	t	t	PROPN
ejpam-3085	81	5	of	of	ADP
ejpam-3085	81	6	h	h	PROPN
ejpam-3085	81	7	is	be	AUX
ejpam-3085	81	8	called	call	VERB
ejpam-3085	81	9	semiprime	semiprime	NOUN
ejpam-3085	81	10	if	if	SCONJ
ejpam-3085	81	11	for	for	ADP
ejpam-3085	81	12	any	any	DET
ejpam-3085	81	13	a	a	DET
ejpam-3085	81	14	∈	∈	PROPN
ejpam-3085	81	15	p∗(h	p∗(h	NOUN
ejpam-3085	81	16	)	)	PUNCT
ejpam-3085	81	17	such	such	ADJ
ejpam-3085	81	18	that	that	SCONJ
ejpam-3085	81	19	a	a	DET
ejpam-3085	81	20	∗a	∗a	PROPN
ejpam-3085	81	21	⊆	⊆	NUM
ejpam-3085	81	22	t	t	NOUN
ejpam-3085	81	23	,	,	PUNCT
ejpam-3085	81	24	we	we	PRON
ejpam-3085	81	25	have	have	VERB
ejpam-3085	81	26	a	a	DET
ejpam-3085	81	27	⊆	⊆	NUM
ejpam-3085	81	28	t.	t.	NOUN
ejpam-3085	81	29	clearly	clearly	ADV
ejpam-3085	81	30	,	,	PUNCT
ejpam-3085	81	31	the	the	DET
ejpam-3085	81	32	prime	prime	ADJ
ejpam-3085	81	33	subsets	subset	NOUN
ejpam-3085	81	34	are	be	AUX
ejpam-3085	81	35	both	both	PRON
ejpam-3085	81	36	weakly	weakly	ADJ
ejpam-3085	81	37	prime	prime	ADJ
ejpam-3085	81	38	and	and	CCONJ
ejpam-3085	81	39	semiprime	semiprime	NOUN
ejpam-3085	81	40	.	.	PUNCT
ejpam-3085	82	1	proposition	proposition	NOUN
ejpam-3085	82	2	6	6	NUM
ejpam-3085	82	3	.	.	PUNCT
ejpam-3085	83	1	let	let	VERB
ejpam-3085	83	2	h	h	PRON
ejpam-3085	83	3	be	be	AUX
ejpam-3085	83	4	an	an	DET
ejpam-3085	83	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	83	6	or	or	CCONJ
ejpam-3085	83	7	an	an	DET
ejpam-3085	83	8	ordered	order	VERB
ejpam-3085	83	9	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	83	10	.	.	PUNCT
ejpam-3085	84	1	a	a	DET
ejpam-3085	84	2	nonempty	nonempty	NOUN
ejpam-3085	84	3	subset	subset	VERB
ejpam-3085	84	4	t	t	PROPN
ejpam-3085	84	5	of	of	ADP
ejpam-3085	84	6	h	h	PROPN
ejpam-3085	84	7	is	be	AUX
ejpam-3085	84	8	semiprime	semiprime	ADJ
ejpam-3085	84	9	if	if	SCONJ
ejpam-3085	84	10	and	and	CCONJ
ejpam-3085	84	11	only	only	ADV
ejpam-3085	84	12	if	if	SCONJ
ejpam-3085	84	13	for	for	ADP
ejpam-3085	84	14	any	any	DET
ejpam-3085	84	15	a	a	DET
ejpam-3085	84	16	∈	∈	ADJ
ejpam-3085	84	17	h	h	NOUN
ejpam-3085	84	18	such	such	ADJ
ejpam-3085	84	19	that	that	SCONJ
ejpam-3085	84	20	a	a	DET
ejpam-3085	84	21	◦	◦	NOUN
ejpam-3085	84	22	a	a	DET
ejpam-3085	84	23	⊆	⊆	NUM
ejpam-3085	84	24	t	t	NOUN
ejpam-3085	84	25	,	,	PUNCT
ejpam-3085	84	26	we	we	PRON
ejpam-3085	84	27	have	have	VERB
ejpam-3085	84	28	a	a	DET
ejpam-3085	84	29	∈	∈	NOUN
ejpam-3085	84	30	t.	t.	NOUN
ejpam-3085	84	31	proof	proof	NOUN
ejpam-3085	84	32	.	.	PUNCT
ejpam-3085	85	1	=	=	NOUN
ejpam-3085	85	2	⇒.	⇒.	NOUN
ejpam-3085	85	3	let	let	VERB
ejpam-3085	85	4	a	a	DET
ejpam-3085	85	5	∈	∈	ADJ
ejpam-3085	85	6	h	h	NOUN
ejpam-3085	85	7	such	such	ADJ
ejpam-3085	85	8	that	that	SCONJ
ejpam-3085	85	9	a	a	DET
ejpam-3085	85	10	◦	◦	NOUN
ejpam-3085	85	11	a	a	DET
ejpam-3085	85	12	⊆	⊆	NUM
ejpam-3085	85	13	t	t	NOUN
ejpam-3085	85	14	.	.	PUNCT
ejpam-3085	86	1	since	since	SCONJ
ejpam-3085	86	2	{	{	PUNCT
ejpam-3085	86	3	a	a	PRON
ejpam-3085	86	4	}	}	PUNCT
ejpam-3085	86	5	∈	∈	PROPN
ejpam-3085	86	6	p∗(h	p∗(h	PROPN
ejpam-3085	86	7	)	)	PUNCT
ejpam-3085	86	8	and	and	CCONJ
ejpam-3085	86	9	{	{	PUNCT
ejpam-3085	86	10	a}∗{a	a}∗{a	PROPN
ejpam-3085	86	11	}	}	PUNCT
ejpam-3085	86	12	=	=	PUNCT
ejpam-3085	86	13	a	a	DET
ejpam-3085	86	14	◦	◦	NOUN
ejpam-3085	86	15	a	a	DET
ejpam-3085	86	16	⊆	⊆	NUM
ejpam-3085	86	17	t	t	NOUN
ejpam-3085	86	18	,	,	PUNCT
ejpam-3085	86	19	by	by	ADP
ejpam-3085	86	20	hypothesis	hypothesis	NOUN
ejpam-3085	86	21	,	,	PUNCT
ejpam-3085	86	22	we	we	PRON
ejpam-3085	86	23	have	have	VERB
ejpam-3085	86	24	{	{	PUNCT
ejpam-3085	86	25	a	a	DET
ejpam-3085	86	26	}	}	PUNCT
ejpam-3085	86	27	⊆	⊆	NUM
ejpam-3085	86	28	t	t	NOUN
ejpam-3085	86	29	,	,	PUNCT
ejpam-3085	86	30	then	then	ADV
ejpam-3085	86	31	a	a	DET
ejpam-3085	86	32	∈	∈	PROPN
ejpam-3085	86	33	t	t	NOUN
ejpam-3085	86	34	.	.	PUNCT
ejpam-3085	87	1	n.	n.	PROPN
ejpam-3085	87	2	kehayopulu	kehayopulu	PROPN
ejpam-3085	87	3	/	/	SYM
ejpam-3085	87	4	eur	eur	PROPN
ejpam-3085	87	5	.	.	PUNCT
ejpam-3085	88	1	j.	j.	PROPN
ejpam-3085	88	2	pure	pure	PROPN
ejpam-3085	88	3	appl	appl	PROPN
ejpam-3085	88	4	.	.	PROPN
ejpam-3085	88	5	math	math	PROPN
ejpam-3085	88	6	,	,	PUNCT
ejpam-3085	88	7	11	11	NUM
ejpam-3085	88	8	(	(	PUNCT
ejpam-3085	88	9	1	1	NUM
ejpam-3085	88	10	)	)	PUNCT
ejpam-3085	88	11	(	(	PUNCT
ejpam-3085	88	12	2018	2018	NUM
ejpam-3085	88	13	)	)	PUNCT
ejpam-3085	88	14	,	,	PUNCT
ejpam-3085	88	15	10	10	NUM
ejpam-3085	88	16	-	-	SYM
ejpam-3085	88	17	22	22	NUM
ejpam-3085	88	18	13	13	NUM
ejpam-3085	88	19	⇐	⇐	NOUN
ejpam-3085	88	20	=	=	PRON
ejpam-3085	88	21	.	.	PUNCT
ejpam-3085	89	1	let	let	VERB
ejpam-3085	89	2	a	a	DET
ejpam-3085	89	3	∈	∈	PROPN
ejpam-3085	89	4	p∗(h	p∗(h	NOUN
ejpam-3085	89	5	)	)	PUNCT
ejpam-3085	89	6	such	such	ADJ
ejpam-3085	89	7	that	that	SCONJ
ejpam-3085	89	8	a	a	DET
ejpam-3085	89	9	∗	∗	NOUN
ejpam-3085	89	10	a	a	DET
ejpam-3085	89	11	⊆	⊆	NUM
ejpam-3085	89	12	t	t	NOUN
ejpam-3085	89	13	and	and	CCONJ
ejpam-3085	89	14	a	a	DET
ejpam-3085	89	15	∈	∈	NOUN
ejpam-3085	89	16	a.	a.	NOUN
ejpam-3085	89	17	since	since	SCONJ
ejpam-3085	89	18	a	a	DET
ejpam-3085	89	19	◦	◦	NOUN
ejpam-3085	89	20	a	a	DET
ejpam-3085	89	21	⊆	⊆	NUM
ejpam-3085	89	22	a	a	DET
ejpam-3085	89	23	∗	∗	NOUN
ejpam-3085	89	24	a	a	DET
ejpam-3085	89	25	⊆	⊆	NUM
ejpam-3085	89	26	t	t	NOUN
ejpam-3085	89	27	,	,	PUNCT
ejpam-3085	89	28	by	by	ADP
ejpam-3085	89	29	hypothesis	hypothesis	NOUN
ejpam-3085	89	30	,	,	PUNCT
ejpam-3085	89	31	we	we	PRON
ejpam-3085	89	32	have	have	VERB
ejpam-3085	89	33	a	a	DET
ejpam-3085	89	34	∈	∈	PROPN
ejpam-3085	89	35	t	t	NOUN
ejpam-3085	89	36	.	.	PUNCT
ejpam-3085	90	1	thus	thus	ADV
ejpam-3085	90	2	a	a	PRON
ejpam-3085	90	3	is	be	AUX
ejpam-3085	90	4	a	a	DET
ejpam-3085	90	5	subset	subset	NOUN
ejpam-3085	90	6	of	of	ADP
ejpam-3085	90	7	t	t	PROPN
ejpam-3085	90	8	,	,	PUNCT
ejpam-3085	90	9	and	and	CCONJ
ejpam-3085	90	10	t	t	PROPN
ejpam-3085	90	11	is	be	AUX
ejpam-3085	90	12	semiprime	semiprime	NOUN
ejpam-3085	90	13	.	.	PUNCT
ejpam-3085	91	1	�	�	PROPN
ejpam-3085	91	2	proposition	proposition	NOUN
ejpam-3085	91	3	7	7	NUM
ejpam-3085	91	4	.	.	PUNCT
ejpam-3085	92	1	let	let	VERB
ejpam-3085	92	2	(	(	PUNCT
ejpam-3085	92	3	h	h	NOUN
ejpam-3085	92	4	,	,	PUNCT
ejpam-3085	92	5	◦	◦	NOUN
ejpam-3085	92	6	,	,	PUNCT
ejpam-3085	92	7	≤	≤	NUM
ejpam-3085	92	8	)	)	PUNCT
ejpam-3085	92	9	be	be	AUX
ejpam-3085	92	10	an	an	DET
ejpam-3085	92	11	ordered	ordered	ADJ
ejpam-3085	92	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	92	13	.	.	PUNCT
ejpam-3085	93	1	if	if	SCONJ
ejpam-3085	93	2	a	a	PRON
ejpam-3085	93	3	and	and	CCONJ
ejpam-3085	93	4	b	b	NOUN
ejpam-3085	93	5	are	be	AUX
ejpam-3085	93	6	ideals	ideal	NOUN
ejpam-3085	93	7	of	of	ADP
ejpam-3085	93	8	h	h	NOUN
ejpam-3085	93	9	,	,	PUNCT
ejpam-3085	93	10	then	then	ADV
ejpam-3085	93	11	the	the	DET
ejpam-3085	93	12	intersection	intersection	NOUN
ejpam-3085	93	13	a	a	DET
ejpam-3085	93	14	∩b	∩b	NOUN
ejpam-3085	93	15	is	be	AUX
ejpam-3085	93	16	an	an	DET
ejpam-3085	93	17	ideal	ideal	NOUN
ejpam-3085	93	18	of	of	ADP
ejpam-3085	93	19	h	h	NOUN
ejpam-3085	93	20	as	as	ADV
ejpam-3085	93	21	well	well	ADV
ejpam-3085	93	22	.	.	PUNCT
ejpam-3085	94	1	proof	proof	NOUN
ejpam-3085	94	2	.	.	PUNCT
ejpam-3085	95	1	first	first	ADV
ejpam-3085	95	2	of	of	ADP
ejpam-3085	95	3	all	all	PRON
ejpam-3085	95	4	,	,	PUNCT
ejpam-3085	95	5	since	since	SCONJ
ejpam-3085	95	6	a	a	PRON
ejpam-3085	95	7	is	be	AUX
ejpam-3085	95	8	a	a	DET
ejpam-3085	95	9	right	right	ADJ
ejpam-3085	95	10	ideal	ideal	NOUN
ejpam-3085	95	11	and	and	CCONJ
ejpam-3085	95	12	b	b	DET
ejpam-3085	95	13	a	a	DET
ejpam-3085	95	14	left	left	ADJ
ejpam-3085	95	15	ideal	ideal	NOUN
ejpam-3085	95	16	of	of	ADP
ejpam-3085	95	17	h	h	NOUN
ejpam-3085	95	18	,	,	PUNCT
ejpam-3085	95	19	we	we	PRON
ejpam-3085	95	20	have	have	VERB
ejpam-3085	95	21	a	a	DET
ejpam-3085	95	22	∩	∩	ADJ
ejpam-3085	95	23	b	b	NOUN
ejpam-3085	95	24	6=	6=	NUM
ejpam-3085	95	25	∅.	∅.	X
ejpam-3085	95	26	indeed	indeed	ADV
ejpam-3085	95	27	:	:	PUNCT
ejpam-3085	95	28	take	take	VERB
ejpam-3085	95	29	an	an	DET
ejpam-3085	95	30	element	element	NOUN
ejpam-3085	95	31	a	a	DET
ejpam-3085	95	32	∈	∈	PROPN
ejpam-3085	95	33	a	a	PRON
ejpam-3085	95	34	and	and	CCONJ
ejpam-3085	95	35	an	an	DET
ejpam-3085	95	36	element	element	NOUN
ejpam-3085	95	37	b	b	PROPN
ejpam-3085	95	38	∈	∈	PROPN
ejpam-3085	95	39	b	b	PROPN
ejpam-3085	95	40	(	(	PUNCT
ejpam-3085	95	41	a	a	PRON
ejpam-3085	95	42	,	,	PUNCT
ejpam-3085	95	43	b	b	NOUN
ejpam-3085	95	44	6=	6=	NUM
ejpam-3085	95	45	∅	∅	NOUN
ejpam-3085	95	46	)	)	PUNCT
ejpam-3085	95	47	.	.	PUNCT
ejpam-3085	96	1	then	then	ADV
ejpam-3085	96	2	a	a	DET
ejpam-3085	96	3	◦	◦	NOUN
ejpam-3085	96	4	b	b	NUM
ejpam-3085	96	5	⊆	⊆	NUM
ejpam-3085	96	6	a∗h	a∗h	NUM
ejpam-3085	96	7	⊆	⊆	NUM
ejpam-3085	96	8	a	a	PRON
ejpam-3085	96	9	and	and	CCONJ
ejpam-3085	96	10	a	a	DET
ejpam-3085	96	11	◦	◦	NOUN
ejpam-3085	96	12	b	b	NOUN
ejpam-3085	96	13	⊆	⊆	NUM
ejpam-3085	96	14	b	b	NOUN
ejpam-3085	96	15	∗h	∗h	VERB
ejpam-3085	96	16	⊆	⊆	NUM
ejpam-3085	96	17	b	b	NOUN
ejpam-3085	96	18	,	,	PUNCT
ejpam-3085	96	19	so	so	SCONJ
ejpam-3085	96	20	a	a	DET
ejpam-3085	96	21	◦	◦	NOUN
ejpam-3085	96	22	b	b	NOUN
ejpam-3085	96	23	⊆	⊆	NUM
ejpam-3085	96	24	a	a	DET
ejpam-3085	96	25	∩	∩	ADJ
ejpam-3085	96	26	b.	b.	NOUN
ejpam-3085	96	27	as	as	ADP
ejpam-3085	96	28	a	a	DET
ejpam-3085	96	29	◦	◦	NOUN
ejpam-3085	96	30	b	b	NOUN
ejpam-3085	96	31	is	be	AUX
ejpam-3085	96	32	a	a	DET
ejpam-3085	96	33	nonempty	nonempty	ADJ
ejpam-3085	96	34	set	set	NOUN
ejpam-3085	96	35	,	,	PUNCT
ejpam-3085	96	36	the	the	DET
ejpam-3085	96	37	set	set	NOUN
ejpam-3085	96	38	a	a	DET
ejpam-3085	96	39	∩	∩	ADJ
ejpam-3085	96	40	b	b	NOUN
ejpam-3085	96	41	is	be	AUX
ejpam-3085	96	42	a	a	DET
ejpam-3085	96	43	nonempty	nonempty	ADJ
ejpam-3085	96	44	subset	subset	NOUN
ejpam-3085	96	45	of	of	ADP
ejpam-3085	96	46	h.	h.	PROPN
ejpam-3085	96	47	in	in	ADP
ejpam-3085	96	48	addition	addition	NOUN
ejpam-3085	96	49	,	,	PUNCT
ejpam-3085	96	50	(	(	PUNCT
ejpam-3085	96	51	a∩b)∗h	a∩b)∗h	PROPN
ejpam-3085	96	52	⊆	⊆	NUM
ejpam-3085	96	53	a∗h	a∗h	NUM
ejpam-3085	96	54	⊆	⊆	NUM
ejpam-3085	96	55	a	a	PRON
ejpam-3085	96	56	and	and	CCONJ
ejpam-3085	96	57	(	(	PUNCT
ejpam-3085	96	58	a∩b)∗h	a∩b)∗h	VERB
ejpam-3085	97	1	⊆	⊆	NUM
ejpam-3085	97	2	b∗h	b∗h	NUM
ejpam-3085	97	3	⊆	⊆	NUM
ejpam-3085	97	4	b	b	NOUN
ejpam-3085	97	5	,	,	PUNCT
ejpam-3085	97	6	thus	thus	ADV
ejpam-3085	97	7	(	(	PUNCT
ejpam-3085	97	8	a	a	DET
ejpam-3085	97	9	∩	∩	ADJ
ejpam-3085	97	10	b	b	X
ejpam-3085	97	11	)	)	PUNCT
ejpam-3085	97	12	∗h	∗h	VERB
ejpam-3085	97	13	⊆	⊆	NUM
ejpam-3085	97	14	a	a	DET
ejpam-3085	97	15	∩	∩	ADJ
ejpam-3085	97	16	b.	b.	NOUN
ejpam-3085	98	1	if	if	SCONJ
ejpam-3085	98	2	now	now	ADV
ejpam-3085	98	3	x	x	X
ejpam-3085	98	4	∈	∈	PROPN
ejpam-3085	98	5	a	a	DET
ejpam-3085	98	6	∩	∩	ADJ
ejpam-3085	98	7	b	b	NOUN
ejpam-3085	98	8	and	and	CCONJ
ejpam-3085	98	9	h	h	NOUN
ejpam-3085	98	10	3	3	NUM
ejpam-3085	98	11	y	y	NOUN
ejpam-3085	98	12	≤	≤	NUM
ejpam-3085	98	13	x	x	PUNCT
ejpam-3085	98	14	then	then	ADV
ejpam-3085	98	15	,	,	PUNCT
ejpam-3085	98	16	since	since	SCONJ
ejpam-3085	98	17	y	y	PROPN
ejpam-3085	98	18	≤	≤	NUM
ejpam-3085	98	19	x	x	PUNCT
ejpam-3085	98	20	∈	∈	PROPN
ejpam-3085	98	21	a	a	PRON
ejpam-3085	98	22	we	we	PRON
ejpam-3085	98	23	have	have	VERB
ejpam-3085	98	24	y	y	PROPN
ejpam-3085	98	25	∈	∈	PROPN
ejpam-3085	98	26	a	a	PRON
ejpam-3085	98	27	and	and	CCONJ
ejpam-3085	98	28	,	,	PUNCT
ejpam-3085	98	29	since	since	SCONJ
ejpam-3085	98	30	y	y	PROPN
ejpam-3085	98	31	≤	≤	NUM
ejpam-3085	98	32	x	x	PUNCT
ejpam-3085	98	33	∈	∈	PROPN
ejpam-3085	98	34	b	b	NOUN
ejpam-3085	98	35	we	we	PRON
ejpam-3085	98	36	have	have	VERB
ejpam-3085	98	37	y	y	PROPN
ejpam-3085	98	38	∈	∈	PROPN
ejpam-3085	98	39	b	b	PROPN
ejpam-3085	98	40	,	,	PUNCT
ejpam-3085	98	41	so	so	ADV
ejpam-3085	98	42	y	y	PROPN
ejpam-3085	98	43	∈	∈	PROPN
ejpam-3085	98	44	a	a	DET
ejpam-3085	98	45	∩	∩	ADJ
ejpam-3085	98	46	b.	b.	NOUN
ejpam-3085	98	47	thus	thus	ADV
ejpam-3085	98	48	a	a	DET
ejpam-3085	98	49	∩	∩	ADJ
ejpam-3085	98	50	b	b	NOUN
ejpam-3085	98	51	is	be	AUX
ejpam-3085	98	52	a	a	DET
ejpam-3085	98	53	right	right	ADJ
ejpam-3085	98	54	ideal	ideal	NOUN
ejpam-3085	98	55	of	of	ADP
ejpam-3085	98	56	h.	h.	PROPN
ejpam-3085	98	57	similarly	similarly	ADV
ejpam-3085	98	58	,	,	PUNCT
ejpam-3085	98	59	a	a	DET
ejpam-3085	98	60	∩b	∩b	NOUN
ejpam-3085	98	61	is	be	AUX
ejpam-3085	98	62	a	a	DET
ejpam-3085	98	63	left	left	ADJ
ejpam-3085	98	64	ideal	ideal	NOUN
ejpam-3085	98	65	of	of	ADP
ejpam-3085	98	66	h	h	NOUN
ejpam-3085	98	67	and	and	CCONJ
ejpam-3085	98	68	so	so	ADV
ejpam-3085	98	69	it	it	PRON
ejpam-3085	98	70	is	be	AUX
ejpam-3085	98	71	an	an	DET
ejpam-3085	98	72	ideal	ideal	NOUN
ejpam-3085	98	73	of	of	ADP
ejpam-3085	98	74	h.	h.	PROPN
ejpam-3085	98	75	�	�	PROPN
ejpam-3085	98	76	definition	definition	NOUN
ejpam-3085	98	77	8	8	NUM
ejpam-3085	98	78	.	.	PUNCT
ejpam-3085	99	1	a	a	DET
ejpam-3085	99	2	nonempty	nonempty	NOUN
ejpam-3085	99	3	subset	subset	VERB
ejpam-3085	99	4	a	a	PRON
ejpam-3085	99	5	of	of	ADP
ejpam-3085	99	6	an	an	DET
ejpam-3085	99	7	ordered	order	VERB
ejpam-3085	99	8	hypergroupoid	hypergroupoid	PROPN
ejpam-3085	99	9	(	(	PUNCT
ejpam-3085	99	10	h	h	NOUN
ejpam-3085	99	11	,	,	PUNCT
ejpam-3085	99	12	◦	◦	NOUN
ejpam-3085	99	13	,	,	PUNCT
ejpam-3085	99	14	≤	≤	NUM
ejpam-3085	99	15	)	)	PUNCT
ejpam-3085	99	16	is	be	AUX
ejpam-3085	99	17	called	call	VERB
ejpam-3085	99	18	idempotent	idempotent	ADJ
ejpam-3085	99	19	if	if	SCONJ
ejpam-3085	99	20	a	a	PRON
ejpam-3085	99	21	=	=	X
ejpam-3085	99	22	(	(	PUNCT
ejpam-3085	99	23	a	a	DET
ejpam-3085	99	24	∗a	∗a	PROPN
ejpam-3085	99	25	]	]	PUNCT
ejpam-3085	99	26	.	.	PUNCT
ejpam-3085	100	1	theorem	theorem	NOUN
ejpam-3085	100	2	9	9	NUM
ejpam-3085	100	3	.	.	PUNCT
ejpam-3085	101	1	let	let	VERB
ejpam-3085	101	2	(	(	PUNCT
ejpam-3085	101	3	h	h	NOUN
ejpam-3085	101	4	,	,	PUNCT
ejpam-3085	101	5	◦	◦	NOUN
ejpam-3085	101	6	,	,	PUNCT
ejpam-3085	101	7	≤	≤	NUM
ejpam-3085	101	8	)	)	PUNCT
ejpam-3085	101	9	be	be	AUX
ejpam-3085	101	10	an	an	DET
ejpam-3085	101	11	ordered	ordered	ADJ
ejpam-3085	101	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	101	13	.	.	PUNCT
ejpam-3085	102	1	the	the	DET
ejpam-3085	102	2	ideals	ideal	NOUN
ejpam-3085	102	3	of	of	ADP
ejpam-3085	102	4	h	h	NOUN
ejpam-3085	102	5	are	be	AUX
ejpam-3085	102	6	idempotent	idempotent	ADJ
ejpam-3085	102	7	if	if	SCONJ
ejpam-3085	102	8	and	and	CCONJ
ejpam-3085	102	9	only	only	ADV
ejpam-3085	102	10	if	if	SCONJ
ejpam-3085	102	11	for	for	ADP
ejpam-3085	102	12	any	any	DET
ejpam-3085	102	13	two	two	NUM
ejpam-3085	102	14	ideals	ideal	NOUN
ejpam-3085	102	15	a	a	PRON
ejpam-3085	102	16	and	and	CCONJ
ejpam-3085	102	17	b	b	NOUN
ejpam-3085	102	18	of	of	ADP
ejpam-3085	102	19	h	h	NOUN
ejpam-3085	102	20	,	,	PUNCT
ejpam-3085	102	21	we	we	PRON
ejpam-3085	102	22	have	have	VERB
ejpam-3085	102	23	a	a	DET
ejpam-3085	102	24	∩b	∩b	NOUN
ejpam-3085	102	25	=	=	PUNCT
ejpam-3085	102	26	(	(	PUNCT
ejpam-3085	102	27	a	a	DET
ejpam-3085	102	28	∗b	∗b	NOUN
ejpam-3085	102	29	]	]	PUNCT
ejpam-3085	102	30	.	.	PUNCT
ejpam-3085	103	1	proof	proof	NOUN
ejpam-3085	103	2	.	.	PUNCT
ejpam-3085	104	1	=	=	NOUN
ejpam-3085	104	2	⇒.	⇒.	NOUN
ejpam-3085	104	3	let	let	VERB
ejpam-3085	104	4	a	a	DET
ejpam-3085	104	5	,	,	PUNCT
ejpam-3085	104	6	b	b	NOUN
ejpam-3085	104	7	be	be	AUX
ejpam-3085	104	8	ideals	ideal	NOUN
ejpam-3085	104	9	of	of	ADP
ejpam-3085	104	10	h.	h.	NOUN
ejpam-3085	104	11	by	by	ADP
ejpam-3085	104	12	proposition	proposition	NOUN
ejpam-3085	104	13	7	7	NUM
ejpam-3085	104	14	,	,	PUNCT
ejpam-3085	104	15	a	a	DET
ejpam-3085	104	16	∩	∩	ADJ
ejpam-3085	104	17	b	b	NOUN
ejpam-3085	104	18	is	be	AUX
ejpam-3085	104	19	an	an	DET
ejpam-3085	104	20	ideal	ideal	NOUN
ejpam-3085	104	21	of	of	ADP
ejpam-3085	104	22	h.	h.	NOUN
ejpam-3085	104	23	by	by	ADP
ejpam-3085	104	24	hypothesis	hypothesis	NOUN
ejpam-3085	104	25	,	,	PUNCT
ejpam-3085	104	26	we	we	PRON
ejpam-3085	104	27	have	have	VERB
ejpam-3085	104	28	a	a	DET
ejpam-3085	104	29	∩b	∩b	NOUN
ejpam-3085	104	30	=	=	SYM
ejpam-3085	104	31	(	(	PUNCT
ejpam-3085	104	32	(	(	PUNCT
ejpam-3085	104	33	a	a	DET
ejpam-3085	104	34	∩b	∩b	NOUN
ejpam-3085	104	35	)	)	PUNCT
ejpam-3085	104	36	∗	∗	NOUN
ejpam-3085	104	37	(	(	PUNCT
ejpam-3085	104	38	a	a	DET
ejpam-3085	104	39	∩b	∩b	NOUN
ejpam-3085	104	40	)	)	PUNCT
ejpam-3085	104	41	]	]	PUNCT
ejpam-3085	105	1	⊆	⊆	X
ejpam-3085	105	2	(	(	PUNCT
ejpam-3085	105	3	a	a	DET
ejpam-3085	105	4	∗b	∗b	NOUN
ejpam-3085	105	5	]	]	X
ejpam-3085	105	6	⊆	⊆	NUM
ejpam-3085	105	7	(	(	PUNCT
ejpam-3085	105	8	a	a	DET
ejpam-3085	105	9	∗h	∗h	NOUN
ejpam-3085	105	10	]	]	X
ejpam-3085	105	11	∩	∩	NOUN
ejpam-3085	105	12	(	(	PUNCT
ejpam-3085	105	13	h	h	NOUN
ejpam-3085	105	14	∗b	∗b	X
ejpam-3085	105	15	]	]	X
ejpam-3085	105	16	⊆	⊆	NUM
ejpam-3085	105	17	(	(	PUNCT
ejpam-3085	105	18	a	a	PRON
ejpam-3085	105	19	]	]	X
ejpam-3085	105	20	∩	∩	NOUN
ejpam-3085	105	21	(	(	PUNCT
ejpam-3085	105	22	b	b	X
ejpam-3085	105	23	]	]	X
ejpam-3085	105	24	=	=	PUNCT
ejpam-3085	105	25	a	a	DET
ejpam-3085	105	26	∩b	∩b	NOUN
ejpam-3085	105	27	.	.	PUNCT
ejpam-3085	106	1	thus	thus	ADV
ejpam-3085	106	2	we	we	PRON
ejpam-3085	106	3	have	have	VERB
ejpam-3085	106	4	a	a	DET
ejpam-3085	106	5	∩b	∩b	NOUN
ejpam-3085	106	6	=	=	PUNCT
ejpam-3085	106	7	(	(	PUNCT
ejpam-3085	106	8	a	a	DET
ejpam-3085	106	9	∗b	∗b	NOUN
ejpam-3085	106	10	]	]	X
ejpam-3085	106	11	.	.	PUNCT
ejpam-3085	107	1	⇐	⇐	PROPN
ejpam-3085	107	2	=	=	PRON
ejpam-3085	107	3	.	.	PUNCT
ejpam-3085	108	1	let	let	VERB
ejpam-3085	108	2	a	a	PRON
ejpam-3085	108	3	be	be	AUX
ejpam-3085	108	4	an	an	DET
ejpam-3085	108	5	ideal	ideal	NOUN
ejpam-3085	108	6	of	of	ADP
ejpam-3085	108	7	h.	h.	NOUN
ejpam-3085	108	8	by	by	ADP
ejpam-3085	108	9	hypothesis	hypothesis	NOUN
ejpam-3085	108	10	,	,	PUNCT
ejpam-3085	108	11	we	we	PRON
ejpam-3085	108	12	have	have	VERB
ejpam-3085	108	13	a	a	DET
ejpam-3085	108	14	=	=	PUNCT
ejpam-3085	108	15	a	a	DET
ejpam-3085	108	16	∩	∩	NOUN
ejpam-3085	108	17	a	a	X
ejpam-3085	108	18	=	=	X
ejpam-3085	108	19	(	(	PUNCT
ejpam-3085	108	20	a	a	DET
ejpam-3085	108	21	∗	∗	NOUN
ejpam-3085	108	22	a	a	X
ejpam-3085	108	23	]	]	X
ejpam-3085	108	24	,	,	PUNCT
ejpam-3085	108	25	so	so	CCONJ
ejpam-3085	108	26	a	a	PRON
ejpam-3085	108	27	is	be	AUX
ejpam-3085	108	28	idempotent	idempotent	ADJ
ejpam-3085	108	29	.	.	PUNCT
ejpam-3085	109	1	�	�	PROPN
ejpam-3085	109	2	proposition	proposition	NOUN
ejpam-3085	109	3	10	10	NUM
ejpam-3085	109	4	.	.	PUNCT
ejpam-3085	110	1	[	[	X
ejpam-3085	110	2	10	10	NUM
ejpam-3085	110	3	;	;	PUNCT
ejpam-3085	110	4	lemma	lemma	PROPN
ejpam-3085	110	5	2.8	2.8	NUM
ejpam-3085	110	6	]	]	PUNCT
ejpam-3085	110	7	let	let	VERB
ejpam-3085	110	8	(	(	PUNCT
ejpam-3085	110	9	h	h	NOUN
ejpam-3085	110	10	,	,	PUNCT
ejpam-3085	110	11	◦	◦	NOUN
ejpam-3085	110	12	,	,	PUNCT
ejpam-3085	110	13	≤	≤	NUM
ejpam-3085	110	14	)	)	PUNCT
ejpam-3085	110	15	be	be	VERB
ejpam-3085	110	16	an	an	DET
ejpam-3085	110	17	ordered	ordered	ADJ
ejpam-3085	110	18	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	110	19	and	and	CCONJ
ejpam-3085	110	20	a	a	DET
ejpam-3085	110	21	,	,	PUNCT
ejpam-3085	110	22	b	b	PROPN
ejpam-3085	110	23	∈	∈	PROPN
ejpam-3085	110	24	p∗(h	p∗(h	PROPN
ejpam-3085	110	25	)	)	PUNCT
ejpam-3085	110	26	.	.	PUNCT
ejpam-3085	111	1	then	then	ADV
ejpam-3085	111	2	we	we	PRON
ejpam-3085	111	3	have	have	VERB
ejpam-3085	111	4	(	(	PUNCT
ejpam-3085	111	5	a	a	PRON
ejpam-3085	111	6	]	]	X
ejpam-3085	111	7	∗	∗	NOUN
ejpam-3085	111	8	(	(	PUNCT
ejpam-3085	111	9	b	b	X
ejpam-3085	111	10	]	]	X
ejpam-3085	111	11	⊆	⊆	NUM
ejpam-3085	111	12	(	(	PUNCT
ejpam-3085	111	13	a	a	DET
ejpam-3085	111	14	∗b	∗b	NOUN
ejpam-3085	111	15	]	]	PUNCT
ejpam-3085	111	16	.	.	PUNCT
ejpam-3085	112	1	proposition	proposition	NOUN
ejpam-3085	112	2	11	11	NUM
ejpam-3085	112	3	.	.	PUNCT
ejpam-3085	113	1	let	let	AUX
ejpam-3085	113	2	(	(	PUNCT
ejpam-3085	113	3	h	h	NOUN
ejpam-3085	113	4	,	,	PUNCT
ejpam-3085	113	5	◦	◦	NOUN
ejpam-3085	113	6	,	,	PUNCT
ejpam-3085	113	7	≤	≤	NUM
ejpam-3085	113	8	)	)	PUNCT
ejpam-3085	113	9	be	be	VERB
ejpam-3085	113	10	an	an	DET
ejpam-3085	113	11	ordered	ordered	ADJ
ejpam-3085	113	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3085	113	13	and	and	CCONJ
ejpam-3085	113	14	a	a	DET
ejpam-3085	113	15	,	,	PUNCT
ejpam-3085	113	16	b	b	PROPN
ejpam-3085	113	17	∈	∈	PROPN
ejpam-3085	113	18	p∗(h	p∗(h	PROPN
ejpam-3085	113	19	)	)	PUNCT
ejpam-3085	113	20	.	.	PUNCT
ejpam-3085	114	1	then	then	ADV
ejpam-3085	114	2	we	we	PRON
ejpam-3085	114	3	have	have	VERB
ejpam-3085	114	4	(	(	PUNCT
ejpam-3085	114	5	a	a	DET
ejpam-3085	114	6	∗b	∗b	NOUN
ejpam-3085	114	7	]	]	X
ejpam-3085	114	8	=	=	SYM
ejpam-3085	114	9	(	(	PUNCT
ejpam-3085	114	10	(	(	PUNCT
ejpam-3085	114	11	a	a	PRON
ejpam-3085	114	12	]	]	X
ejpam-3085	114	13	∗	∗	NOUN
ejpam-3085	114	14	(	(	PUNCT
ejpam-3085	114	15	b	b	NOUN
ejpam-3085	114	16	]	]	X
ejpam-3085	114	17	]	]	PUNCT
ejpam-3085	115	1	=	=	PUNCT
ejpam-3085	115	2	(	(	PUNCT
ejpam-3085	115	3	(	(	PUNCT
ejpam-3085	115	4	a	a	PRON
ejpam-3085	115	5	]	]	X
ejpam-3085	115	6	∗b	∗b	X
ejpam-3085	115	7	]	]	X
ejpam-3085	115	8	=	=	PUNCT
ejpam-3085	115	9	(	(	PUNCT
ejpam-3085	115	10	a	a	DET
ejpam-3085	115	11	∗	∗	NOUN
ejpam-3085	115	12	(	(	PUNCT
ejpam-3085	115	13	b	b	NOUN
ejpam-3085	115	14	]	]	X
ejpam-3085	115	15	]	]	PUNCT
ejpam-3085	115	16	.	.	PUNCT
ejpam-3085	116	1	proof	proof	NOUN
ejpam-3085	116	2	.	.	PUNCT
ejpam-3085	117	1	let	let	VERB
ejpam-3085	117	2	us	we	PRON
ejpam-3085	117	3	prove	prove	VERB
ejpam-3085	117	4	the	the	DET
ejpam-3085	117	5	equality	equality	NOUN
ejpam-3085	117	6	(	(	PUNCT
ejpam-3085	117	7	(	(	PUNCT
ejpam-3085	117	8	a	a	PRON
ejpam-3085	117	9	]	]	X
ejpam-3085	117	10	∗	∗	NOUN
ejpam-3085	117	11	(	(	PUNCT
ejpam-3085	117	12	b	b	NOUN
ejpam-3085	117	13	]	]	X
ejpam-3085	117	14	]	]	PUNCT
ejpam-3085	118	1	=	=	PUNCT
ejpam-3085	118	2	(	(	PUNCT
ejpam-3085	118	3	(	(	PUNCT
ejpam-3085	118	4	a	a	PRON
ejpam-3085	118	5	]	]	X
ejpam-3085	118	6	∗b	∗b	NOUN
ejpam-3085	118	7	]	]	X
ejpam-3085	118	8	.	.	PUNCT
ejpam-3085	119	1	the	the	DET
ejpam-3085	119	2	rest	rest	NOUN
ejpam-3085	119	3	of	of	ADP
ejpam-3085	119	4	the	the	DET
ejpam-3085	119	5	proposition	proposition	NOUN
ejpam-3085	119	6	can	can	AUX
ejpam-3085	119	7	be	be	AUX
ejpam-3085	119	8	proved	prove	VERB
ejpam-3085	119	9	in	in	ADP
ejpam-3085	119	10	a	a	DET
ejpam-3085	119	11	similar	similar	ADJ
ejpam-3085	119	12	way	way	NOUN
ejpam-3085	119	13	.	.	PUNCT
ejpam-3085	120	1	first	first	ADV
ejpam-3085	120	2	of	of	ADP
ejpam-3085	120	3	all	all	PRON
ejpam-3085	120	4	,	,	PUNCT
ejpam-3085	120	5	the	the	DET
ejpam-3085	120	6	sets	set	NOUN
ejpam-3085	120	7	(	(	PUNCT
ejpam-3085	120	8	a	a	X
ejpam-3085	120	9	]	]	X
ejpam-3085	120	10	and	and	CCONJ
ejpam-3085	120	11	(	(	PUNCT
ejpam-3085	120	12	b	b	X
ejpam-3085	120	13	]	]	X
ejpam-3085	120	14	are	be	AUX
ejpam-3085	120	15	nonempty	nonempty	ADJ
ejpam-3085	120	16	subsets	subset	NOUN
ejpam-3085	120	17	of	of	ADP
ejpam-3085	120	18	h	h	NOUN
ejpam-3085	120	19	as	as	ADP
ejpam-3085	120	20	a	a	DET
ejpam-3085	120	21	and	and	CCONJ
ejpam-3085	120	22	b	b	NOUN
ejpam-3085	120	23	are	be	AUX
ejpam-3085	120	24	so	so	ADV
ejpam-3085	120	25	.	.	PUNCT
ejpam-3085	121	1	since	since	SCONJ
ejpam-3085	121	2	b	b	PROPN
ejpam-3085	121	3	⊆	⊆	NUM
ejpam-3085	121	4	(	(	PUNCT
ejpam-3085	121	5	b	b	NOUN
ejpam-3085	121	6	]	]	X
ejpam-3085	121	7	,	,	PUNCT
ejpam-3085	121	8	we	we	PRON
ejpam-3085	121	9	have	have	VERB
ejpam-3085	121	10	(	(	PUNCT
ejpam-3085	121	11	a]∗b	a]∗b	NOUN
ejpam-3085	121	12	⊆	⊆	NUM
ejpam-3085	121	13	(	(	PUNCT
ejpam-3085	121	14	a]∗	a]∗	PROPN
ejpam-3085	121	15	(	(	PUNCT
ejpam-3085	121	16	b	b	NOUN
ejpam-3085	121	17	]	]	X
ejpam-3085	121	18	,	,	PUNCT
ejpam-3085	121	19	then	then	ADV
ejpam-3085	121	20	(	(	PUNCT
ejpam-3085	121	21	(	(	PUNCT
ejpam-3085	121	22	a]∗b	a]∗b	INTJ
ejpam-3085	121	23	]	]	PUNCT
ejpam-3085	121	24	⊆	⊆	NUM
ejpam-3085	121	25	(	(	PUNCT
ejpam-3085	121	26	(	(	PUNCT
ejpam-3085	121	27	a]∗	a]∗	PROPN
ejpam-3085	121	28	(	(	PUNCT
ejpam-3085	121	29	b	b	NOUN
ejpam-3085	121	30	]	]	X
ejpam-3085	121	31	]	]	PUNCT
ejpam-3085	121	32	.	.	PUNCT
ejpam-3085	122	1	let	let	VERB
ejpam-3085	122	2	now	now	ADV
ejpam-3085	122	3	t	t	X
ejpam-3085	122	4	∈	∈	PROPN
ejpam-3085	122	5	(	(	PUNCT
ejpam-3085	122	6	(	(	PUNCT
ejpam-3085	122	7	a	a	PRON
ejpam-3085	122	8	]	]	X
ejpam-3085	122	9	∗	∗	NOUN
ejpam-3085	122	10	(	(	PUNCT
ejpam-3085	122	11	b	b	NOUN
ejpam-3085	122	12	]	]	X
ejpam-3085	122	13	]	]	PUNCT
ejpam-3085	122	14	.	.	PUNCT
ejpam-3085	123	1	then	then	ADV
ejpam-3085	123	2	t	t	X
ejpam-3085	123	3	≤	≤	NUM
ejpam-3085	123	4	u	u	NOUN
ejpam-3085	123	5	for	for	ADP
ejpam-3085	123	6	some	some	DET
ejpam-3085	123	7	u	u	NOUN
ejpam-3085	123	8	∈	∈	PROPN
ejpam-3085	123	9	(	(	PUNCT
ejpam-3085	123	10	a	a	PRON
ejpam-3085	123	11	]	]	X
ejpam-3085	123	12	∗	∗	NOUN
ejpam-3085	123	13	(	(	PUNCT
ejpam-3085	123	14	b	b	NOUN
ejpam-3085	123	15	]	]	X
ejpam-3085	123	16	.	.	PUNCT
ejpam-3085	124	1	we	we	PRON
ejpam-3085	124	2	have	have	VERB
ejpam-3085	124	3	u	u	NOUN
ejpam-3085	124	4	∈	∈	NOUN
ejpam-3085	124	5	x	x	PUNCT
ejpam-3085	124	6	◦	◦	NOUN
ejpam-3085	124	7	y	y	NOUN
ejpam-3085	124	8	for	for	ADP
ejpam-3085	124	9	some	some	DET
ejpam-3085	124	10	x	x	SYM
ejpam-3085	124	11	∈	∈	PROPN
ejpam-3085	124	12	(	(	PUNCT
ejpam-3085	124	13	a	a	X
ejpam-3085	124	14	]	]	X
ejpam-3085	124	15	,	,	PUNCT
ejpam-3085	124	16	y	y	PROPN
ejpam-3085	124	17	∈	∈	PROPN
ejpam-3085	124	18	(	(	PUNCT
ejpam-3085	124	19	b	b	NOUN
ejpam-3085	124	20	]	]	X
ejpam-3085	124	21	.	.	PUNCT
ejpam-3085	125	1	then	then	ADV
ejpam-3085	125	2	x	x	X
ejpam-3085	125	3	≤	≤	ADV
ejpam-3085	125	4	a	a	PRON
ejpam-3085	125	5	for	for	ADP
ejpam-3085	125	6	some	some	DET
ejpam-3085	125	7	a	a	DET
ejpam-3085	125	8	∈	∈	PROPN
ejpam-3085	125	9	a	a	PRON
ejpam-3085	125	10	and	and	CCONJ
ejpam-3085	125	11	y	y	PROPN
ejpam-3085	125	12	≤	≤	PROPN
ejpam-3085	125	13	b	b	NOUN
ejpam-3085	125	14	for	for	ADP
ejpam-3085	125	15	some	some	DET
ejpam-3085	125	16	b	b	PROPN
ejpam-3085	125	17	∈	∈	PROPN
ejpam-3085	125	18	b.	b.	PROPN
ejpam-3085	125	19	by	by	ADP
ejpam-3085	125	20	proposition	proposition	NOUN
ejpam-3085	125	21	1	1	NUM
ejpam-3085	125	22	,	,	PUNCT
ejpam-3085	125	23	we	we	PRON
ejpam-3085	125	24	have	have	VERB
ejpam-3085	125	25	x	x	PART
ejpam-3085	125	26	◦	◦	VERB
ejpam-3085	125	27	y	y	PROPN
ejpam-3085	125	28	�	�	PROPN
ejpam-3085	125	29	a	a	DET
ejpam-3085	125	30	◦	◦	NOUN
ejpam-3085	125	31	b.	b.	NOUN
ejpam-3085	125	32	since	since	SCONJ
ejpam-3085	125	33	u	u	PROPN
ejpam-3085	125	34	∈	∈	PROPN
ejpam-3085	125	35	x	x	PUNCT
ejpam-3085	125	36	◦	◦	NOUN
ejpam-3085	125	37	y	y	NUM
ejpam-3085	125	38	,	,	PUNCT
ejpam-3085	125	39	we	we	PRON
ejpam-3085	125	40	have	have	VERB
ejpam-3085	125	41	u	u	NOUN
ejpam-3085	125	42	≤	≤	ADJ
ejpam-3085	125	43	v	v	NOUN
ejpam-3085	125	44	for	for	ADP
ejpam-3085	125	45	some	some	DET
ejpam-3085	125	46	v	v	ADP
ejpam-3085	125	47	∈	∈	PROPN
ejpam-3085	125	48	a	a	DET
ejpam-3085	125	49	◦	◦	NOUN
ejpam-3085	125	50	b.	b.	NOUN
ejpam-3085	126	1	then	then	ADV
ejpam-3085	126	2	we	we	PRON
ejpam-3085	126	3	have	have	VERB
ejpam-3085	126	4	t	t	NOUN
ejpam-3085	126	5	≤	≤	NUM
ejpam-3085	126	6	v	v	ADP
ejpam-3085	126	7	∈	∈	PROPN
ejpam-3085	126	8	a	a	DET
ejpam-3085	126	9	◦	◦	NOUN
ejpam-3085	126	10	b	b	NOUN
ejpam-3085	126	11	,	,	PUNCT
ejpam-3085	126	12	then	then	ADV
ejpam-3085	126	13	t	t	PROPN
ejpam-3085	126	14	∈	∈	PROPN
ejpam-3085	126	15	(	(	PUNCT
ejpam-3085	126	16	a	a	DET
ejpam-3085	126	17	◦	◦	NOUN
ejpam-3085	126	18	b	b	AUX
ejpam-3085	126	19	]	]	X
ejpam-3085	126	20	⊆	⊆	NUM
ejpam-3085	126	21	(	(	PUNCT
ejpam-3085	126	22	a	a	DET
ejpam-3085	126	23	∗b	∗b	NOUN
ejpam-3085	126	24	]	]	X
ejpam-3085	126	25	⊆	⊆	NUM
ejpam-3085	126	26	(	(	PUNCT
ejpam-3085	126	27	(	(	PUNCT
ejpam-3085	126	28	a	a	PRON
ejpam-3085	126	29	]	]	X
ejpam-3085	126	30	∗b	∗b	NOUN
ejpam-3085	126	31	]	]	PUNCT
ejpam-3085	126	32	.	.	PUNCT
ejpam-3085	127	1	�	�	PROPN
ejpam-3085	127	2	n.	n.	PROPN
ejpam-3085	127	3	kehayopulu	kehayopulu	PROPN
ejpam-3085	127	4	/	/	SYM
ejpam-3085	127	5	eur	eur	PROPN
ejpam-3085	127	6	.	.	PUNCT
ejpam-3085	128	1	j.	j.	PROPN
ejpam-3085	128	2	pure	pure	PROPN
ejpam-3085	128	3	appl	appl	PROPN
ejpam-3085	128	4	.	.	PROPN
ejpam-3085	128	5	math	math	PROPN
ejpam-3085	128	6	,	,	PUNCT
ejpam-3085	128	7	11	11	NUM
ejpam-3085	128	8	(	(	PUNCT
ejpam-3085	128	9	1	1	NUM
ejpam-3085	128	10	)	)	PUNCT
ejpam-3085	128	11	(	(	PUNCT
ejpam-3085	128	12	2018	2018	NUM
ejpam-3085	128	13	)	)	PUNCT
ejpam-3085	128	14	,	,	PUNCT
ejpam-3085	128	15	10	10	NUM
ejpam-3085	128	16	-	-	SYM
ejpam-3085	128	17	22	22	NUM
ejpam-3085	128	18	14	14	NUM
ejpam-3085	128	19	proposition	proposition	NOUN
ejpam-3085	128	20	12	12	NUM
ejpam-3085	128	21	.	.	PUNCT
ejpam-3085	129	1	let	let	AUX
ejpam-3085	129	2	(	(	PUNCT
ejpam-3085	129	3	h	h	NOUN
ejpam-3085	129	4	,	,	PUNCT
ejpam-3085	129	5	◦	◦	NOUN
ejpam-3085	129	6	,	,	PUNCT
ejpam-3085	129	7	≤	≤	NUM
ejpam-3085	129	8	)	)	PUNCT
ejpam-3085	129	9	be	be	VERB
ejpam-3085	129	10	an	an	DET
ejpam-3085	129	11	ordered	order	VERB
ejpam-3085	129	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	129	13	and	and	CCONJ
ejpam-3085	129	14	a	a	DET
ejpam-3085	129	15	,	,	PUNCT
ejpam-3085	129	16	b	b	NOUN
ejpam-3085	129	17	,	,	PUNCT
ejpam-3085	129	18	c	c	X
ejpam-3085	129	19	nonempty	nonempty	NOUN
ejpam-3085	129	20	subsets	subset	NOUN
ejpam-3085	129	21	of	of	ADP
ejpam-3085	129	22	h.	h.	PROPN
ejpam-3085	129	23	then	then	ADV
ejpam-3085	129	24	we	we	PRON
ejpam-3085	129	25	have	have	VERB
ejpam-3085	129	26	(	(	PUNCT
ejpam-3085	129	27	a	a	DET
ejpam-3085	129	28	∗	∗	NOUN
ejpam-3085	129	29	(	(	PUNCT
ejpam-3085	129	30	b	b	NOUN
ejpam-3085	129	31	]	]	PUNCT
ejpam-3085	129	32	∗	∗	X
ejpam-3085	129	33	c	c	NOUN
ejpam-3085	129	34	]	]	X
ejpam-3085	130	1	=	=	SYM
ejpam-3085	130	2	(	(	PUNCT
ejpam-3085	130	3	a	a	DET
ejpam-3085	130	4	∗b	∗b	PROPN
ejpam-3085	130	5	∗	∗	NOUN
ejpam-3085	130	6	c	c	NOUN
ejpam-3085	130	7	]	]	PUNCT
ejpam-3085	130	8	.	.	PUNCT
ejpam-3085	131	1	proof	proof	NOUN
ejpam-3085	131	2	.	.	PUNCT
ejpam-3085	132	1	by	by	ADP
ejpam-3085	132	2	proposition	proposition	NOUN
ejpam-3085	132	3	11	11	NUM
ejpam-3085	132	4	,	,	PUNCT
ejpam-3085	132	5	we	we	PRON
ejpam-3085	132	6	have	have	VERB
ejpam-3085	132	7	(	(	PUNCT
ejpam-3085	132	8	a	a	DET
ejpam-3085	132	9	∗	∗	NOUN
ejpam-3085	132	10	(	(	PUNCT
ejpam-3085	132	11	b	b	NOUN
ejpam-3085	132	12	]	]	PUNCT
ejpam-3085	132	13	∗	∗	X
ejpam-3085	132	14	c	c	NOUN
ejpam-3085	132	15	]	]	X
ejpam-3085	133	1	=	=	PUNCT
ejpam-3085	133	2	(	(	PUNCT
ejpam-3085	133	3	(	(	PUNCT
ejpam-3085	133	4	a	a	DET
ejpam-3085	133	5	∗	∗	NOUN
ejpam-3085	133	6	(	(	PUNCT
ejpam-3085	133	7	b	b	NOUN
ejpam-3085	133	8	]	]	PUNCT
ejpam-3085	133	9	)	)	PUNCT
ejpam-3085	133	10	∗	∗	NOUN
ejpam-3085	133	11	c	c	NOUN
ejpam-3085	133	12	]	]	X
ejpam-3085	133	13	=	=	PUNCT
ejpam-3085	133	14	(	(	PUNCT
ejpam-3085	133	15	(	(	PUNCT
ejpam-3085	133	16	a	a	DET
ejpam-3085	133	17	∗b	∗b	NOUN
ejpam-3085	133	18	]	]	X
ejpam-3085	133	19	∗	∗	NOUN
ejpam-3085	133	20	c	c	NOUN
ejpam-3085	133	21	]	]	X
ejpam-3085	134	1	=	=	PUNCT
ejpam-3085	134	2	(	(	PUNCT
ejpam-3085	134	3	(	(	PUNCT
ejpam-3085	134	4	a	a	DET
ejpam-3085	134	5	∗b	∗b	NOUN
ejpam-3085	134	6	)	)	PUNCT
ejpam-3085	134	7	∗	∗	NOUN
ejpam-3085	134	8	c	c	NOUN
ejpam-3085	134	9	]	]	X
ejpam-3085	135	1	=	=	SYM
ejpam-3085	135	2	(	(	PUNCT
ejpam-3085	135	3	a	a	DET
ejpam-3085	135	4	∗b	∗b	PROPN
ejpam-3085	135	5	∗	∗	NOUN
ejpam-3085	135	6	c	c	NOUN
ejpam-3085	135	7	]	]	PUNCT
ejpam-3085	135	8	.	.	PUNCT
ejpam-3085	136	1	an	an	DET
ejpam-3085	136	2	independent	independent	ADJ
ejpam-3085	136	3	proof	proof	NOUN
ejpam-3085	136	4	is	be	AUX
ejpam-3085	136	5	as	as	SCONJ
ejpam-3085	136	6	follows	follow	VERB
ejpam-3085	136	7	:	:	PUNCT
ejpam-3085	136	8	let	let	VERB
ejpam-3085	136	9	t	t	PROPN
ejpam-3085	136	10	∈	∈	PROPN
ejpam-3085	136	11	(	(	PUNCT
ejpam-3085	136	12	a	a	DET
ejpam-3085	136	13	∗	∗	NOUN
ejpam-3085	136	14	(	(	PUNCT
ejpam-3085	136	15	b	b	NOUN
ejpam-3085	136	16	]	]	PUNCT
ejpam-3085	136	17	∗	∗	NOUN
ejpam-3085	136	18	c	c	NOUN
ejpam-3085	136	19	]	]	PUNCT
ejpam-3085	136	20	.	.	PUNCT
ejpam-3085	137	1	then	then	ADV
ejpam-3085	137	2	t	t	X
ejpam-3085	137	3	≤	≤	NUM
ejpam-3085	137	4	x	x	PUNCT
ejpam-3085	137	5	for	for	ADP
ejpam-3085	137	6	some	some	DET
ejpam-3085	137	7	x	x	SYM
ejpam-3085	137	8	∈	∈	PROPN
ejpam-3085	137	9	a	a	DET
ejpam-3085	137	10	∗	∗	NOUN
ejpam-3085	137	11	(	(	PUNCT
ejpam-3085	137	12	b	b	NOUN
ejpam-3085	137	13	]	]	PUNCT
ejpam-3085	137	14	∗	∗	X
ejpam-3085	137	15	c	c	NOUN
ejpam-3085	137	16	,	,	PUNCT
ejpam-3085	137	17	x	x	PUNCT
ejpam-3085	137	18	∈	∈	PROPN
ejpam-3085	137	19	y	y	PROPN
ejpam-3085	137	20	◦	◦	NOUN
ejpam-3085	137	21	z	z	NOUN
ejpam-3085	137	22	for	for	ADP
ejpam-3085	137	23	some	some	DET
ejpam-3085	137	24	y	y	PROPN
ejpam-3085	137	25	∈	∈	PROPN
ejpam-3085	137	26	a	a	DET
ejpam-3085	137	27	∗	∗	NOUN
ejpam-3085	137	28	(	(	PUNCT
ejpam-3085	137	29	b	b	NOUN
ejpam-3085	137	30	]	]	X
ejpam-3085	137	31	,	,	PUNCT
ejpam-3085	137	32	z	z	PROPN
ejpam-3085	137	33	∈	∈	PROPN
ejpam-3085	137	34	c	c	X
ejpam-3085	137	35	,	,	PUNCT
ejpam-3085	137	36	y	y	PROPN
ejpam-3085	137	37	∈	∈	PROPN
ejpam-3085	137	38	u	u	NOUN
ejpam-3085	137	39	◦	◦	NOUN
ejpam-3085	137	40	v	v	NOUN
ejpam-3085	137	41	for	for	ADP
ejpam-3085	137	42	some	some	DET
ejpam-3085	137	43	u	u	NOUN
ejpam-3085	137	44	∈	∈	PROPN
ejpam-3085	137	45	a	a	PRON
ejpam-3085	137	46	,	,	PUNCT
ejpam-3085	137	47	v	v	NOUN
ejpam-3085	137	48	∈	∈	PROPN
ejpam-3085	137	49	(	(	PUNCT
ejpam-3085	137	50	b	b	NOUN
ejpam-3085	137	51	]	]	PUNCT
ejpam-3085	137	52	and	and	CCONJ
ejpam-3085	137	53	v	v	ADP
ejpam-3085	137	54	≤	≤	NUM
ejpam-3085	137	55	b	b	NOUN
ejpam-3085	137	56	for	for	ADP
ejpam-3085	137	57	some	some	DET
ejpam-3085	137	58	b	b	PROPN
ejpam-3085	137	59	∈	∈	PROPN
ejpam-3085	137	60	b.	b.	PROPN
ejpam-3085	137	61	then	then	ADV
ejpam-3085	137	62	we	we	PRON
ejpam-3085	137	63	have	have	VERB
ejpam-3085	137	64	t	t	NOUN
ejpam-3085	137	65	≤	≤	NUM
ejpam-3085	137	66	x	x	PUNCT
ejpam-3085	137	67	∈	∈	PROPN
ejpam-3085	137	68	y	y	PROPN
ejpam-3085	137	69	◦	◦	NOUN
ejpam-3085	137	70	z	z	NOUN
ejpam-3085	138	1	=	=	SYM
ejpam-3085	138	2	{	{	PUNCT
ejpam-3085	138	3	y	y	NOUN
ejpam-3085	138	4	}	}	PUNCT
ejpam-3085	138	5	∗	∗	NOUN
ejpam-3085	138	6	{	{	PUNCT
ejpam-3085	138	7	z	z	NOUN
ejpam-3085	138	8	}	}	PUNCT
ejpam-3085	138	9	⊆	⊆	NUM
ejpam-3085	138	10	(	(	PUNCT
ejpam-3085	138	11	u	u	NOUN
ejpam-3085	138	12	◦	◦	NOUN
ejpam-3085	138	13	v	v	NOUN
ejpam-3085	138	14	)	)	PUNCT
ejpam-3085	138	15	∗	∗	NOUN
ejpam-3085	138	16	{	{	PUNCT
ejpam-3085	138	17	z	z	NOUN
ejpam-3085	138	18	}	}	PUNCT
ejpam-3085	138	19	.	.	PUNCT
ejpam-3085	139	1	since	since	SCONJ
ejpam-3085	139	2	v	v	NOUN
ejpam-3085	139	3	≤	≤	NUM
ejpam-3085	139	4	b	b	NOUN
ejpam-3085	139	5	,	,	PUNCT
ejpam-3085	139	6	by	by	ADP
ejpam-3085	139	7	proposition	proposition	NOUN
ejpam-3085	139	8	1	1	NUM
ejpam-3085	139	9	,	,	PUNCT
ejpam-3085	139	10	we	we	PRON
ejpam-3085	139	11	have	have	VERB
ejpam-3085	139	12	u	u	NOUN
ejpam-3085	139	13	◦	◦	NOUN
ejpam-3085	139	14	v	v	NUM
ejpam-3085	139	15	�	�	PROPN
ejpam-3085	139	16	u	u	PROPN
ejpam-3085	139	17	◦	◦	PROPN
ejpam-3085	139	18	b.	b.	NOUN
ejpam-3085	139	19	then	then	ADV
ejpam-3085	139	20	,	,	PUNCT
ejpam-3085	139	21	by	by	ADP
ejpam-3085	139	22	proposition	proposition	NOUN
ejpam-3085	139	23	2	2	NUM
ejpam-3085	139	24	,	,	PUNCT
ejpam-3085	139	25	we	we	PRON
ejpam-3085	139	26	have	have	VERB
ejpam-3085	139	27	(	(	PUNCT
ejpam-3085	139	28	u	u	NOUN
ejpam-3085	139	29	◦	◦	NOUN
ejpam-3085	139	30	v	v	NOUN
ejpam-3085	139	31	)	)	PUNCT
ejpam-3085	139	32	∗	∗	NOUN
ejpam-3085	139	33	{	{	PUNCT
ejpam-3085	139	34	z	z	NOUN
ejpam-3085	139	35	}	}	PUNCT
ejpam-3085	139	36	⊆	⊆	NUM
ejpam-3085	139	37	(	(	PUNCT
ejpam-3085	139	38	(	(	PUNCT
ejpam-3085	139	39	u	u	NOUN
ejpam-3085	139	40	◦	◦	NOUN
ejpam-3085	139	41	b	b	NUM
ejpam-3085	139	42	)	)	PUNCT
ejpam-3085	139	43	∗	∗	NOUN
ejpam-3085	139	44	{	{	PUNCT
ejpam-3085	139	45	z	z	NOUN
ejpam-3085	139	46	}	}	PUNCT
ejpam-3085	139	47	]	]	PUNCT
ejpam-3085	139	48	.	.	PUNCT
ejpam-3085	140	1	hence	hence	ADV
ejpam-3085	140	2	we	we	PRON
ejpam-3085	140	3	obtain	obtain	VERB
ejpam-3085	140	4	t	t	NOUN
ejpam-3085	140	5	≤	≤	NUM
ejpam-3085	140	6	x	x	PUNCT
ejpam-3085	140	7	∈	∈	PROPN
ejpam-3085	140	8	(	(	PUNCT
ejpam-3085	140	9	(	(	PUNCT
ejpam-3085	140	10	u	u	NOUN
ejpam-3085	140	11	◦	◦	NOUN
ejpam-3085	140	12	b	b	NUM
ejpam-3085	140	13	)	)	PUNCT
ejpam-3085	140	14	∗	∗	NOUN
ejpam-3085	140	15	{	{	PUNCT
ejpam-3085	140	16	z	z	NOUN
ejpam-3085	140	17	}	}	PUNCT
ejpam-3085	140	18	]	]	PUNCT
ejpam-3085	140	19	=	=	PUNCT
ejpam-3085	140	20	(	(	PUNCT
ejpam-3085	140	21	{	{	PUNCT
ejpam-3085	140	22	u	u	NOUN
ejpam-3085	140	23	}	}	PUNCT
ejpam-3085	140	24	∗	∗	NOUN
ejpam-3085	140	25	{	{	PUNCT
ejpam-3085	140	26	b	b	NOUN
ejpam-3085	140	27	}	}	PUNCT
ejpam-3085	140	28	∗	∗	NOUN
ejpam-3085	140	29	{	{	PUNCT
ejpam-3085	140	30	z	z	NOUN
ejpam-3085	140	31	}	}	PUNCT
ejpam-3085	140	32	]	]	PUNCT
ejpam-3085	141	1	⊆	⊆	X
ejpam-3085	141	2	(	(	PUNCT
ejpam-3085	141	3	a	a	DET
ejpam-3085	141	4	∗b	∗b	PROPN
ejpam-3085	141	5	∗	∗	NOUN
ejpam-3085	141	6	c	c	NOUN
ejpam-3085	141	7	]	]	PUNCT
ejpam-3085	141	8	,	,	PUNCT
ejpam-3085	141	9	and	and	CCONJ
ejpam-3085	141	10	then	then	ADV
ejpam-3085	141	11	t	t	PROPN
ejpam-3085	141	12	∈	∈	PROPN
ejpam-3085	141	13	(	(	PUNCT
ejpam-3085	141	14	(	(	PUNCT
ejpam-3085	141	15	a	a	DET
ejpam-3085	141	16	∗	∗	NOUN
ejpam-3085	141	17	b	b	NOUN
ejpam-3085	141	18	∗	∗	NOUN
ejpam-3085	141	19	c	c	NOUN
ejpam-3085	141	20	]	]	X
ejpam-3085	141	21	]	]	PUNCT
ejpam-3085	142	1	=	=	X
ejpam-3085	142	2	(	(	PUNCT
ejpam-3085	142	3	a	a	DET
ejpam-3085	142	4	∗	∗	NOUN
ejpam-3085	142	5	b	b	NOUN
ejpam-3085	142	6	∗	∗	NOUN
ejpam-3085	142	7	c	c	NOUN
ejpam-3085	142	8	]	]	X
ejpam-3085	142	9	,	,	PUNCT
ejpam-3085	142	10	so	so	CCONJ
ejpam-3085	142	11	(	(	PUNCT
ejpam-3085	142	12	a	a	DET
ejpam-3085	142	13	∗	∗	NOUN
ejpam-3085	142	14	(	(	PUNCT
ejpam-3085	142	15	b	b	NOUN
ejpam-3085	142	16	]	]	PUNCT
ejpam-3085	142	17	∗	∗	X
ejpam-3085	142	18	c	c	NOUN
ejpam-3085	142	19	]	]	X
ejpam-3085	143	1	⊆	⊆	X
ejpam-3085	143	2	(	(	PUNCT
ejpam-3085	143	3	a	a	DET
ejpam-3085	143	4	∗	∗	NOUN
ejpam-3085	143	5	b	b	NOUN
ejpam-3085	143	6	∗	∗	NOUN
ejpam-3085	143	7	c	c	NOUN
ejpam-3085	143	8	]	]	PUNCT
ejpam-3085	143	9	.	.	PUNCT
ejpam-3085	144	1	on	on	ADP
ejpam-3085	144	2	the	the	DET
ejpam-3085	144	3	other	other	ADJ
ejpam-3085	144	4	hand	hand	NOUN
ejpam-3085	144	5	,	,	PUNCT
ejpam-3085	144	6	since	since	SCONJ
ejpam-3085	144	7	b	b	NOUN
ejpam-3085	144	8	⊆	⊆	NUM
ejpam-3085	144	9	(	(	PUNCT
ejpam-3085	144	10	b	b	NOUN
ejpam-3085	144	11	]	]	X
ejpam-3085	144	12	,	,	PUNCT
ejpam-3085	144	13	we	we	PRON
ejpam-3085	144	14	have	have	VERB
ejpam-3085	144	15	(	(	PUNCT
ejpam-3085	144	16	a	a	DET
ejpam-3085	144	17	∗b	∗b	PROPN
ejpam-3085	144	18	∗	∗	NOUN
ejpam-3085	144	19	c	c	NOUN
ejpam-3085	144	20	]	]	X
ejpam-3085	144	21	⊆	⊆	NUM
ejpam-3085	144	22	(	(	PUNCT
ejpam-3085	144	23	a	a	DET
ejpam-3085	144	24	∗	∗	NOUN
ejpam-3085	144	25	(	(	PUNCT
ejpam-3085	144	26	b	b	NOUN
ejpam-3085	144	27	]	]	PUNCT
ejpam-3085	144	28	∗	∗	NOUN
ejpam-3085	144	29	c	c	NOUN
ejpam-3085	144	30	]	]	PUNCT
ejpam-3085	144	31	.	.	PUNCT
ejpam-3085	145	1	�	�	PROPN
ejpam-3085	145	2	let	let	VERB
ejpam-3085	145	3	h	h	NOUN
ejpam-3085	145	4	be	be	AUX
ejpam-3085	145	5	an	an	DET
ejpam-3085	145	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	145	7	.	.	PUNCT
ejpam-3085	146	1	for	for	ADP
ejpam-3085	146	2	a	a	DET
ejpam-3085	146	3	nonempty	nonempty	NOUN
ejpam-3085	146	4	subset	subset	VERB
ejpam-3085	146	5	a	a	PRON
ejpam-3085	146	6	of	of	ADP
ejpam-3085	146	7	h	h	NOUN
ejpam-3085	146	8	we	we	PRON
ejpam-3085	146	9	denote	denote	VERB
ejpam-3085	146	10	by	by	ADP
ejpam-3085	146	11	i(a	i(a	PROPN
ejpam-3085	146	12	)	)	PUNCT
ejpam-3085	146	13	the	the	DET
ejpam-3085	146	14	ideal	ideal	NOUN
ejpam-3085	146	15	of	of	ADP
ejpam-3085	146	16	h	h	PROPN
ejpam-3085	146	17	generated	generate	VERB
ejpam-3085	146	18	by	by	ADP
ejpam-3085	146	19	a.	a.	NOUN
ejpam-3085	146	20	for	for	ADP
ejpam-3085	146	21	a	a	DET
ejpam-3085	146	22	=	=	X
ejpam-3085	146	23	{	{	PUNCT
ejpam-3085	146	24	a	a	NOUN
ejpam-3085	146	25	}	}	PUNCT
ejpam-3085	146	26	(	(	PUNCT
ejpam-3085	146	27	a	a	DET
ejpam-3085	146	28	∈	∈	PROPN
ejpam-3085	146	29	h	h	NOUN
ejpam-3085	146	30	)	)	PUNCT
ejpam-3085	146	31	,	,	PUNCT
ejpam-3085	146	32	we	we	PRON
ejpam-3085	146	33	write	write	VERB
ejpam-3085	146	34	i(a	i(a	PROPN
ejpam-3085	146	35	)	)	PUNCT
ejpam-3085	146	36	instead	instead	ADV
ejpam-3085	146	37	of	of	ADP
ejpam-3085	146	38	i({a	i({a	PROPN
ejpam-3085	146	39	}	}	PUNCT
ejpam-3085	146	40	)	)	PUNCT
ejpam-3085	146	41	.	.	PUNCT
ejpam-3085	147	1	proposition	proposition	NOUN
ejpam-3085	147	2	13	13	NUM
ejpam-3085	147	3	.	.	PUNCT
ejpam-3085	148	1	let	let	AUX
ejpam-3085	148	2	(	(	PUNCT
ejpam-3085	148	3	h	h	NOUN
ejpam-3085	148	4	,	,	PUNCT
ejpam-3085	148	5	◦	◦	NOUN
ejpam-3085	148	6	,	,	PUNCT
ejpam-3085	148	7	≤	≤	NUM
ejpam-3085	148	8	)	)	PUNCT
ejpam-3085	148	9	be	be	VERB
ejpam-3085	148	10	an	an	DET
ejpam-3085	148	11	ordered	order	VERB
ejpam-3085	148	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	148	13	and	and	CCONJ
ejpam-3085	148	14	a	a	DET
ejpam-3085	148	15	a	a	DET
ejpam-3085	148	16	nonempty	nonempty	ADJ
ejpam-3085	148	17	subset	subset	NOUN
ejpam-3085	148	18	of	of	ADP
ejpam-3085	148	19	h.	h.	PROPN
ejpam-3085	148	20	then	then	ADV
ejpam-3085	148	21	we	we	PRON
ejpam-3085	148	22	have	have	VERB
ejpam-3085	148	23	i(a	i(a	PROPN
ejpam-3085	148	24	)	)	PUNCT
ejpam-3085	149	1	=	=	PRON
ejpam-3085	149	2	(	(	PUNCT
ejpam-3085	149	3	a	a	DET
ejpam-3085	149	4	∪	∪	X
ejpam-3085	149	5	(	(	PUNCT
ejpam-3085	149	6	h	h	NOUN
ejpam-3085	149	7	∗a	∗a	ADJ
ejpam-3085	149	8	)	)	PUNCT
ejpam-3085	149	9	∪	∪	NOUN
ejpam-3085	149	10	(	(	PUNCT
ejpam-3085	149	11	a	a	DET
ejpam-3085	149	12	∗h	∗h	NOUN
ejpam-3085	149	13	)	)	PUNCT
ejpam-3085	149	14	∪	∪	NOUN
ejpam-3085	149	15	(	(	PUNCT
ejpam-3085	149	16	h	h	NOUN
ejpam-3085	149	17	∗a	∗a	ADJ
ejpam-3085	149	18	∗h	∗h	NOUN
ejpam-3085	149	19	)	)	PUNCT
ejpam-3085	149	20	]	]	PUNCT
ejpam-3085	149	21	.	.	PUNCT
ejpam-3085	150	1	proof	proof	NOUN
ejpam-3085	150	2	.	.	PUNCT
ejpam-3085	151	1	we	we	PRON
ejpam-3085	151	2	set	set	VERB
ejpam-3085	151	3	t	t	NOUN
ejpam-3085	151	4	:	:	PUNCT
ejpam-3085	151	5	=	=	SYM
ejpam-3085	151	6	(	(	PUNCT
ejpam-3085	151	7	a	a	DET
ejpam-3085	151	8	∪	∪	X
ejpam-3085	151	9	(	(	PUNCT
ejpam-3085	151	10	h	h	NOUN
ejpam-3085	151	11	∗	∗	NOUN
ejpam-3085	151	12	a	a	NOUN
ejpam-3085	151	13	)	)	PUNCT
ejpam-3085	151	14	∪	∪	NOUN
ejpam-3085	151	15	(	(	PUNCT
ejpam-3085	151	16	a	a	DET
ejpam-3085	151	17	∗	∗	NOUN
ejpam-3085	151	18	h	h	NOUN
ejpam-3085	151	19	)	)	PUNCT
ejpam-3085	151	20	∪	∪	NOUN
ejpam-3085	151	21	(	(	PUNCT
ejpam-3085	151	22	h	h	NOUN
ejpam-3085	151	23	∗	∗	VERB
ejpam-3085	151	24	a	a	DET
ejpam-3085	151	25	∗	∗	NOUN
ejpam-3085	151	26	h	h	NOUN
ejpam-3085	151	27	)	)	PUNCT
ejpam-3085	151	28	]	]	PUNCT
ejpam-3085	151	29	.	.	PUNCT
ejpam-3085	152	1	the	the	DET
ejpam-3085	152	2	set	set	PROPN
ejpam-3085	152	3	t	t	PROPN
ejpam-3085	152	4	is	be	AUX
ejpam-3085	152	5	a	a	DET
ejpam-3085	152	6	nonempty	nonempty	ADJ
ejpam-3085	152	7	subset	subset	NOUN
ejpam-3085	152	8	of	of	ADP
ejpam-3085	152	9	h	h	NOUN
ejpam-3085	152	10	containing	contain	VERB
ejpam-3085	152	11	a.	a.	NOUN
ejpam-3085	152	12	moreover	moreover	ADV
ejpam-3085	152	13	,	,	PUNCT
ejpam-3085	152	14	t	t	PROPN
ejpam-3085	152	15	is	be	AUX
ejpam-3085	152	16	an	an	DET
ejpam-3085	152	17	ideal	ideal	NOUN
ejpam-3085	152	18	of	of	ADP
ejpam-3085	152	19	h.	h.	NOUN
ejpam-3085	152	20	in	in	ADP
ejpam-3085	152	21	fact	fact	NOUN
ejpam-3085	152	22	:	:	PUNCT
ejpam-3085	152	23	t	t	NOUN
ejpam-3085	152	24	∗h	∗h	NOUN
ejpam-3085	152	25	=	=	SYM
ejpam-3085	152	26	(	(	PUNCT
ejpam-3085	152	27	a	a	DET
ejpam-3085	152	28	∪	∪	X
ejpam-3085	152	29	(	(	PUNCT
ejpam-3085	152	30	h	h	NOUN
ejpam-3085	152	31	∗a	∗a	ADJ
ejpam-3085	152	32	)	)	PUNCT
ejpam-3085	152	33	∪	∪	NOUN
ejpam-3085	152	34	(	(	PUNCT
ejpam-3085	152	35	a	a	DET
ejpam-3085	152	36	∗h	∗h	NOUN
ejpam-3085	152	37	)	)	PUNCT
ejpam-3085	152	38	∪	∪	NOUN
ejpam-3085	152	39	(	(	PUNCT
ejpam-3085	152	40	h	h	NOUN
ejpam-3085	152	41	∗a	∗a	ADJ
ejpam-3085	152	42	∗h	∗h	NOUN
ejpam-3085	152	43	)	)	PUNCT
ejpam-3085	152	44	]	]	PUNCT
ejpam-3085	152	45	∗h	∗h	NOUN
ejpam-3085	152	46	=	=	SYM
ejpam-3085	152	47	(	(	PUNCT
ejpam-3085	152	48	a	a	DET
ejpam-3085	152	49	∪	∪	X
ejpam-3085	152	50	(	(	PUNCT
ejpam-3085	152	51	h	h	NOUN
ejpam-3085	152	52	∗a	∗a	ADJ
ejpam-3085	152	53	)	)	PUNCT
ejpam-3085	152	54	∪	∪	NOUN
ejpam-3085	152	55	(	(	PUNCT
ejpam-3085	152	56	a	a	DET
ejpam-3085	152	57	∗h	∗h	NOUN
ejpam-3085	152	58	)	)	PUNCT
ejpam-3085	152	59	∪	∪	NOUN
ejpam-3085	152	60	(	(	PUNCT
ejpam-3085	152	61	h	h	NOUN
ejpam-3085	152	62	∗a	∗a	ADJ
ejpam-3085	152	63	∗h	∗h	NOUN
ejpam-3085	152	64	)	)	PUNCT
ejpam-3085	152	65	]	]	PUNCT
ejpam-3085	153	1	∗	∗	NOUN
ejpam-3085	153	2	(	(	PUNCT
ejpam-3085	153	3	h	h	X
ejpam-3085	153	4	]	]	X
ejpam-3085	153	5	⊆	⊆	NUM
ejpam-3085	153	6	(	(	PUNCT
ejpam-3085	153	7	(	(	PUNCT
ejpam-3085	153	8	a	a	DET
ejpam-3085	153	9	∪	∪	X
ejpam-3085	153	10	(	(	PUNCT
ejpam-3085	153	11	h	h	NOUN
ejpam-3085	153	12	∗a	∗a	ADJ
ejpam-3085	153	13	)	)	PUNCT
ejpam-3085	153	14	∪	∪	NOUN
ejpam-3085	153	15	(	(	PUNCT
ejpam-3085	153	16	a	a	DET
ejpam-3085	153	17	∗h	∗h	NOUN
ejpam-3085	153	18	)	)	PUNCT
ejpam-3085	153	19	∪	∪	NOUN
ejpam-3085	153	20	(	(	PUNCT
ejpam-3085	153	21	h	h	NOUN
ejpam-3085	153	22	∗a	∗a	ADJ
ejpam-3085	153	23	∗h	∗h	NOUN
ejpam-3085	153	24	)	)	PUNCT
ejpam-3085	153	25	)	)	PUNCT
ejpam-3085	153	26	∗h	∗h	NOUN
ejpam-3085	153	27	]	]	PUNCT
ejpam-3085	153	28	(	(	PUNCT
ejpam-3085	153	29	by	by	ADP
ejpam-3085	153	30	proposition	proposition	NOUN
ejpam-3085	153	31	10	10	NUM
ejpam-3085	153	32	)	)	PUNCT
ejpam-3085	153	33	=	=	PRON
ejpam-3085	153	34	(	(	PUNCT
ejpam-3085	153	35	(	(	PUNCT
ejpam-3085	153	36	a	a	DET
ejpam-3085	153	37	∗h	∗h	NOUN
ejpam-3085	153	38	)	)	PUNCT
ejpam-3085	153	39	∪	∪	NOUN
ejpam-3085	153	40	(	(	PUNCT
ejpam-3085	153	41	h	h	NOUN
ejpam-3085	153	42	∗a	∗a	ADJ
ejpam-3085	153	43	∗h	∗h	NOUN
ejpam-3085	153	44	)	)	PUNCT
ejpam-3085	153	45	∪	∪	NOUN
ejpam-3085	153	46	(	(	PUNCT
ejpam-3085	153	47	a	a	DET
ejpam-3085	153	48	∗h	∗h	NOUN
ejpam-3085	153	49	∗h	∗h	NOUN
ejpam-3085	153	50	)	)	PUNCT
ejpam-3085	153	51	∪	∪	NOUN
ejpam-3085	153	52	(	(	PUNCT
ejpam-3085	153	53	h	h	NOUN
ejpam-3085	153	54	∗a	∗a	ADJ
ejpam-3085	153	55	∗h	∗h	NOUN
ejpam-3085	153	56	∗h	∗h	NOUN
ejpam-3085	153	57	)	)	PUNCT
ejpam-3085	153	58	]	]	PUNCT
ejpam-3085	154	1	n.	n.	PROPN
ejpam-3085	155	1	kehayopulu	kehayopulu	PROPN
ejpam-3085	155	2	/	/	SYM
ejpam-3085	155	3	eur	eur	PROPN
ejpam-3085	155	4	.	.	PUNCT
ejpam-3085	156	1	j.	j.	PROPN
ejpam-3085	156	2	pure	pure	PROPN
ejpam-3085	156	3	appl	appl	PROPN
ejpam-3085	156	4	.	.	PROPN
ejpam-3085	156	5	math	math	PROPN
ejpam-3085	156	6	,	,	PUNCT
ejpam-3085	156	7	11	11	NUM
ejpam-3085	156	8	(	(	PUNCT
ejpam-3085	156	9	1	1	NUM
ejpam-3085	156	10	)	)	PUNCT
ejpam-3085	156	11	(	(	PUNCT
ejpam-3085	156	12	2018	2018	NUM
ejpam-3085	156	13	)	)	PUNCT
ejpam-3085	156	14	,	,	PUNCT
ejpam-3085	156	15	10	10	NUM
ejpam-3085	156	16	-	-	SYM
ejpam-3085	156	17	22	22	NUM
ejpam-3085	156	18	15	15	NUM
ejpam-3085	156	19	=	=	SYM
ejpam-3085	156	20	(	(	PUNCT
ejpam-3085	156	21	(	(	PUNCT
ejpam-3085	156	22	a	a	DET
ejpam-3085	156	23	∗h	∗h	NOUN
ejpam-3085	156	24	)	)	PUNCT
ejpam-3085	156	25	∪	∪	NOUN
ejpam-3085	156	26	(	(	PUNCT
ejpam-3085	156	27	h	h	NOUN
ejpam-3085	156	28	∗a	∗a	ADJ
ejpam-3085	156	29	∗h	∗h	NOUN
ejpam-3085	156	30	)	)	PUNCT
ejpam-3085	156	31	]	]	PUNCT
ejpam-3085	157	1	⊆	⊆	NUM
ejpam-3085	157	2	t	t	NOUN
ejpam-3085	157	3	;	;	PUNCT
ejpam-3085	157	4	also	also	ADV
ejpam-3085	157	5	(	(	PUNCT
ejpam-3085	157	6	t	t	X
ejpam-3085	157	7	]	]	PUNCT
ejpam-3085	157	8	=	=	SYM
ejpam-3085	157	9	t	t	PROPN
ejpam-3085	157	10	.	.	PUNCT
ejpam-3085	158	1	similarly	similarly	ADV
ejpam-3085	158	2	t	t	PROPN
ejpam-3085	158	3	is	be	AUX
ejpam-3085	158	4	a	a	DET
ejpam-3085	158	5	left	left	ADJ
ejpam-3085	158	6	ideal	ideal	NOUN
ejpam-3085	158	7	of	of	ADP
ejpam-3085	158	8	h.	h.	PROPN
ejpam-3085	158	9	let	let	VERB
ejpam-3085	158	10	now	now	ADV
ejpam-3085	158	11	k	k	ADV
ejpam-3085	158	12	be	be	AUX
ejpam-3085	158	13	an	an	DET
ejpam-3085	158	14	ideal	ideal	NOUN
ejpam-3085	158	15	of	of	ADP
ejpam-3085	158	16	h	h	NOUN
ejpam-3085	158	17	such	such	ADJ
ejpam-3085	158	18	that	that	SCONJ
ejpam-3085	158	19	k	k	PROPN
ejpam-3085	158	20	⊇	⊇	PROPN
ejpam-3085	158	21	a.	a.	NOUN
ejpam-3085	158	22	then	then	ADV
ejpam-3085	158	23	t	t	PROPN
ejpam-3085	158	24	⊆	⊆	NUM
ejpam-3085	158	25	k.	k.	PROPN
ejpam-3085	158	26	indeed	indeed	ADV
ejpam-3085	158	27	,	,	PUNCT
ejpam-3085	158	28	we	we	PRON
ejpam-3085	158	29	have	have	VERB
ejpam-3085	158	30	t	t	NOUN
ejpam-3085	158	31	=	=	PUNCT
ejpam-3085	158	32	(	(	PUNCT
ejpam-3085	158	33	a	a	DET
ejpam-3085	158	34	∪	∪	X
ejpam-3085	158	35	(	(	PUNCT
ejpam-3085	158	36	h	h	NOUN
ejpam-3085	158	37	∗a	∗a	ADJ
ejpam-3085	158	38	)	)	PUNCT
ejpam-3085	158	39	∪	∪	NOUN
ejpam-3085	158	40	(	(	PUNCT
ejpam-3085	158	41	a	a	DET
ejpam-3085	158	42	∗h	∗h	NOUN
ejpam-3085	158	43	)	)	PUNCT
ejpam-3085	158	44	∪	∪	NOUN
ejpam-3085	158	45	(	(	PUNCT
ejpam-3085	158	46	h	h	NOUN
ejpam-3085	158	47	∗a	∗a	ADJ
ejpam-3085	158	48	∗h	∗h	NOUN
ejpam-3085	158	49	)	)	PUNCT
ejpam-3085	158	50	]	]	PUNCT
ejpam-3085	159	1	⊆	⊆	X
ejpam-3085	159	2	(	(	PUNCT
ejpam-3085	159	3	k	k	X
ejpam-3085	159	4	∪	∪	X
ejpam-3085	159	5	(	(	PUNCT
ejpam-3085	159	6	h	h	NOUN
ejpam-3085	159	7	∗k	∗k	NOUN
ejpam-3085	159	8	)	)	PUNCT
ejpam-3085	159	9	∪	∪	NOUN
ejpam-3085	159	10	(	(	PUNCT
ejpam-3085	159	11	k	k	NOUN
ejpam-3085	159	12	∗h	∗h	NOUN
ejpam-3085	159	13	)	)	PUNCT
ejpam-3085	159	14	∪	∪	NOUN
ejpam-3085	159	15	(	(	PUNCT
ejpam-3085	159	16	h	h	NOUN
ejpam-3085	159	17	∗k	∗k	NOUN
ejpam-3085	159	18	∗h	∗h	NOUN
ejpam-3085	159	19	)	)	PUNCT
ejpam-3085	159	20	]	]	PUNCT
ejpam-3085	160	1	=	=	PUNCT
ejpam-3085	160	2	(	(	PUNCT
ejpam-3085	160	3	k	k	X
ejpam-3085	160	4	]	]	X
ejpam-3085	160	5	=	=	PUNCT
ejpam-3085	160	6	k.	k.	PROPN
ejpam-3085	160	7	�	�	PROPN
ejpam-3085	160	8	proposition	proposition	PROPN
ejpam-3085	160	9	14	14	NUM
ejpam-3085	160	10	.	.	PUNCT
ejpam-3085	161	1	let	let	AUX
ejpam-3085	161	2	(	(	PUNCT
ejpam-3085	161	3	h	h	NOUN
ejpam-3085	161	4	,	,	PUNCT
ejpam-3085	161	5	◦	◦	NOUN
ejpam-3085	161	6	,	,	PUNCT
ejpam-3085	161	7	≤	≤	NUM
ejpam-3085	161	8	)	)	PUNCT
ejpam-3085	161	9	be	be	VERB
ejpam-3085	161	10	an	an	DET
ejpam-3085	161	11	ordered	order	VERB
ejpam-3085	161	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	161	13	.	.	PUNCT
ejpam-3085	162	1	if	if	SCONJ
ejpam-3085	162	2	a	a	PRON
ejpam-3085	162	3	is	be	AUX
ejpam-3085	162	4	a	a	DET
ejpam-3085	162	5	left	left	ADJ
ejpam-3085	162	6	ideal	ideal	NOUN
ejpam-3085	162	7	and	and	CCONJ
ejpam-3085	162	8	b	b	NOUN
ejpam-3085	162	9	is	be	AUX
ejpam-3085	162	10	a	a	DET
ejpam-3085	162	11	right	right	ADJ
ejpam-3085	162	12	ideal	ideal	NOUN
ejpam-3085	162	13	of	of	ADP
ejpam-3085	162	14	h	h	NOUN
ejpam-3085	162	15	,	,	PUNCT
ejpam-3085	162	16	then	then	ADV
ejpam-3085	162	17	the	the	DET
ejpam-3085	162	18	set	set	NOUN
ejpam-3085	162	19	(	(	PUNCT
ejpam-3085	162	20	a	a	DET
ejpam-3085	162	21	∗b	∗b	NOUN
ejpam-3085	162	22	]	]	PUNCT
ejpam-3085	162	23	is	be	AUX
ejpam-3085	162	24	an	an	DET
ejpam-3085	162	25	ideal	ideal	NOUN
ejpam-3085	162	26	of	of	ADP
ejpam-3085	162	27	h.	h.	NOUN
ejpam-3085	162	28	proof	proof	NOUN
ejpam-3085	162	29	.	.	PUNCT
ejpam-3085	163	1	since	since	SCONJ
ejpam-3085	163	2	a	a	PRON
ejpam-3085	163	3	and	and	CCONJ
ejpam-3085	163	4	b	b	NOUN
ejpam-3085	163	5	are	be	AUX
ejpam-3085	163	6	nonempty	nonempty	ADJ
ejpam-3085	163	7	subsets	subset	NOUN
ejpam-3085	163	8	of	of	ADP
ejpam-3085	163	9	h	h	NOUN
ejpam-3085	163	10	,	,	PUNCT
ejpam-3085	163	11	the	the	DET
ejpam-3085	163	12	set	set	NOUN
ejpam-3085	163	13	a∗b	a∗b	NUM
ejpam-3085	163	14	is	be	AUX
ejpam-3085	163	15	also	also	ADV
ejpam-3085	163	16	a	a	DET
ejpam-3085	163	17	nonempty	nonempty	ADJ
ejpam-3085	163	18	subset	subset	NOUN
ejpam-3085	163	19	of	of	ADP
ejpam-3085	163	20	h	h	NOUN
ejpam-3085	163	21	and	and	CCONJ
ejpam-3085	163	22	so	so	ADV
ejpam-3085	163	23	is	be	AUX
ejpam-3085	163	24	(	(	PUNCT
ejpam-3085	163	25	a	a	DET
ejpam-3085	163	26	∗b	∗b	NOUN
ejpam-3085	163	27	]	]	PUNCT
ejpam-3085	163	28	.	.	PUNCT
ejpam-3085	164	1	in	in	ADP
ejpam-3085	164	2	addition	addition	NOUN
ejpam-3085	164	3	,	,	PUNCT
ejpam-3085	164	4	h	h	NOUN
ejpam-3085	164	5	∗	∗	NOUN
ejpam-3085	164	6	(	(	PUNCT
ejpam-3085	164	7	a	a	DET
ejpam-3085	164	8	∗b	∗b	NOUN
ejpam-3085	164	9	]	]	X
ejpam-3085	164	10	=	=	SYM
ejpam-3085	164	11	(	(	PUNCT
ejpam-3085	164	12	h	h	X
ejpam-3085	164	13	]	]	X
ejpam-3085	164	14	∗	∗	NOUN
ejpam-3085	164	15	(	(	PUNCT
ejpam-3085	164	16	a	a	DET
ejpam-3085	164	17	∗b	∗b	NOUN
ejpam-3085	164	18	]	]	X
ejpam-3085	164	19	⊆	⊆	NUM
ejpam-3085	164	20	(	(	PUNCT
ejpam-3085	164	21	h	h	NOUN
ejpam-3085	164	22	∗	∗	NOUN
ejpam-3085	164	23	(	(	PUNCT
ejpam-3085	164	24	a	a	DET
ejpam-3085	164	25	∗b	∗b	NOUN
ejpam-3085	164	26	)	)	PUNCT
ejpam-3085	164	27	]	]	PUNCT
ejpam-3085	164	28	(	(	PUNCT
ejpam-3085	164	29	by	by	ADP
ejpam-3085	164	30	proposition	proposition	NOUN
ejpam-3085	164	31	10	10	NUM
ejpam-3085	164	32	)	)	PUNCT
ejpam-3085	164	33	=	=	PRON
ejpam-3085	164	34	(	(	PUNCT
ejpam-3085	164	35	(	(	PUNCT
ejpam-3085	164	36	h	h	NOUN
ejpam-3085	164	37	∗a	∗a	ADJ
ejpam-3085	164	38	)	)	PUNCT
ejpam-3085	164	39	∗b	∗b	NOUN
ejpam-3085	164	40	]	]	PUNCT
ejpam-3085	165	1	⊆	⊆	X
ejpam-3085	165	2	(	(	PUNCT
ejpam-3085	165	3	a	a	DET
ejpam-3085	165	4	∗b	∗b	NOUN
ejpam-3085	165	5	]	]	PUNCT
ejpam-3085	165	6	,	,	PUNCT
ejpam-3085	165	7	similarly	similarly	ADV
ejpam-3085	165	8	(	(	PUNCT
ejpam-3085	165	9	a	a	DET
ejpam-3085	165	10	∗b	∗b	NOUN
ejpam-3085	165	11	]	]	X
ejpam-3085	165	12	∗h	∗h	NOUN
ejpam-3085	165	13	⊆	⊆	NUM
ejpam-3085	165	14	(	(	PUNCT
ejpam-3085	165	15	a	a	DET
ejpam-3085	165	16	∗b	∗b	NOUN
ejpam-3085	165	17	]	]	PUNCT
ejpam-3085	165	18	.	.	PUNCT
ejpam-3085	166	1	let	let	VERB
ejpam-3085	166	2	now	now	ADV
ejpam-3085	166	3	x	x	X
ejpam-3085	166	4	∈	∈	PROPN
ejpam-3085	166	5	(	(	PUNCT
ejpam-3085	166	6	a	a	DET
ejpam-3085	166	7	∗b	∗b	NOUN
ejpam-3085	166	8	]	]	PUNCT
ejpam-3085	166	9	and	and	CCONJ
ejpam-3085	166	10	h	h	NOUN
ejpam-3085	166	11	3	3	NUM
ejpam-3085	166	12	y	y	PROPN
ejpam-3085	166	13	≤	≤	NUM
ejpam-3085	166	14	x.	x.	NOUN
ejpam-3085	167	1	we	we	PRON
ejpam-3085	167	2	have	have	VERB
ejpam-3085	167	3	x	x	NOUN
ejpam-3085	167	4	≤	≤	NUM
ejpam-3085	167	5	u	u	NOUN
ejpam-3085	167	6	for	for	ADP
ejpam-3085	167	7	some	some	DET
ejpam-3085	167	8	u	u	NOUN
ejpam-3085	167	9	∈	∈	PROPN
ejpam-3085	167	10	a	a	DET
ejpam-3085	167	11	∗b	∗b	NOUN
ejpam-3085	167	12	.	.	PUNCT
ejpam-3085	168	1	since	since	SCONJ
ejpam-3085	168	2	h	h	PROPN
ejpam-3085	168	3	3	3	NUM
ejpam-3085	168	4	y	y	PROPN
ejpam-3085	168	5	≤	≤	NUM
ejpam-3085	168	6	u	u	NOUN
ejpam-3085	168	7	∈	∈	PROPN
ejpam-3085	168	8	a	a	DET
ejpam-3085	168	9	∗b	∗b	NOUN
ejpam-3085	168	10	,	,	PUNCT
ejpam-3085	168	11	we	we	PRON
ejpam-3085	168	12	have	have	VERB
ejpam-3085	168	13	y	y	PROPN
ejpam-3085	168	14	∈	∈	PROPN
ejpam-3085	168	15	(	(	PUNCT
ejpam-3085	168	16	a	a	DET
ejpam-3085	168	17	∗b	∗b	NOUN
ejpam-3085	168	18	]	]	PUNCT
ejpam-3085	168	19	.	.	PUNCT
ejpam-3085	169	1	thus	thus	ADV
ejpam-3085	169	2	(	(	PUNCT
ejpam-3085	169	3	a	a	DET
ejpam-3085	169	4	∗b	∗b	NOUN
ejpam-3085	169	5	]	]	PUNCT
ejpam-3085	169	6	is	be	AUX
ejpam-3085	169	7	an	an	DET
ejpam-3085	169	8	ideal	ideal	NOUN
ejpam-3085	169	9	of	of	ADP
ejpam-3085	169	10	h.	h.	PROPN
ejpam-3085	169	11	�	�	PROPN
ejpam-3085	169	12	corollary	corollary	PROPN
ejpam-3085	169	13	15	15	NUM
ejpam-3085	169	14	.	.	PUNCT
ejpam-3085	170	1	if	if	SCONJ
ejpam-3085	170	2	h	h	NOUN
ejpam-3085	170	3	is	be	AUX
ejpam-3085	170	4	an	an	DET
ejpam-3085	170	5	ordered	order	VERB
ejpam-3085	170	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	170	7	and	and	CCONJ
ejpam-3085	170	8	a	a	PRON
ejpam-3085	170	9	,	,	PUNCT
ejpam-3085	170	10	b	b	PROPN
ejpam-3085	170	11	ideals	ideal	NOUN
ejpam-3085	170	12	of	of	ADP
ejpam-3085	170	13	h	h	NOUN
ejpam-3085	170	14	,	,	PUNCT
ejpam-3085	170	15	then	then	ADV
ejpam-3085	170	16	the	the	DET
ejpam-3085	170	17	set	set	NOUN
ejpam-3085	170	18	(	(	PUNCT
ejpam-3085	170	19	a	a	DET
ejpam-3085	170	20	∗b	∗b	NOUN
ejpam-3085	170	21	]	]	PUNCT
ejpam-3085	170	22	is	be	AUX
ejpam-3085	170	23	an	an	DET
ejpam-3085	170	24	ideal	ideal	NOUN
ejpam-3085	170	25	of	of	ADP
ejpam-3085	170	26	h.	h.	PROPN
ejpam-3085	170	27	this	this	PRON
ejpam-3085	170	28	is	be	AUX
ejpam-3085	170	29	the	the	DET
ejpam-3085	170	30	concept	concept	NOUN
ejpam-3085	170	31	of	of	ADP
ejpam-3085	170	32	semisimple	semisimple	NOUN
ejpam-3085	170	33	ordered	order	VERB
ejpam-3085	170	34	semigroups	semigroup	NOUN
ejpam-3085	170	35	introduced	introduce	VERB
ejpam-3085	170	36	by	by	ADP
ejpam-3085	170	37	kehayopulu	kehayopulu	VERB
ejpam-3085	170	38	in	in	ADP
ejpam-3085	170	39	[	[	X
ejpam-3085	170	40	7	7	NUM
ejpam-3085	170	41	]	]	X
ejpam-3085	170	42	:	:	PUNCT
ejpam-3085	170	43	an	an	DET
ejpam-3085	170	44	ordered	order	VERB
ejpam-3085	170	45	semigroup	semigroup	NOUN
ejpam-3085	170	46	(	(	PUNCT
ejpam-3085	170	47	s	s	PROPN
ejpam-3085	170	48	,	,	PUNCT
ejpam-3085	170	49	·	·	PUNCT
ejpam-3085	170	50	,	,	PUNCT
ejpam-3085	170	51	≤	≤	NUM
ejpam-3085	170	52	)	)	PUNCT
ejpam-3085	170	53	is	be	AUX
ejpam-3085	170	54	called	call	VERB
ejpam-3085	170	55	semisimple	semisimple	NOUN
ejpam-3085	170	56	if	if	SCONJ
ejpam-3085	170	57	for	for	SCONJ
ejpam-3085	170	58	every	every	DET
ejpam-3085	170	59	a	a	DET
ejpam-3085	170	60	∈	∈	NOUN
ejpam-3085	170	61	s	s	VERB
ejpam-3085	170	62	there	there	PRON
ejpam-3085	170	63	exist	exist	VERB
ejpam-3085	170	64	x	x	NOUN
ejpam-3085	170	65	,	,	PUNCT
ejpam-3085	170	66	y	y	PROPN
ejpam-3085	170	67	,	,	PUNCT
ejpam-3085	170	68	z	z	PROPN
ejpam-3085	170	69	∈	∈	PROPN
ejpam-3085	170	70	s	s	VERB
ejpam-3085	170	71	such	such	ADJ
ejpam-3085	170	72	that	that	SCONJ
ejpam-3085	170	73	a	a	DET
ejpam-3085	170	74	≤	≤	PROPN
ejpam-3085	170	75	xayaz	xayaz	ADJ
ejpam-3085	170	76	.	.	PUNCT
ejpam-3085	171	1	this	this	PRON
ejpam-3085	171	2	is	be	AUX
ejpam-3085	171	3	equivalent	equivalent	ADJ
ejpam-3085	171	4	to	to	ADP
ejpam-3085	171	5	saying	say	VERB
ejpam-3085	171	6	that	that	SCONJ
ejpam-3085	171	7	a	a	DET
ejpam-3085	171	8	∈	∈	PROPN
ejpam-3085	171	9	(	(	PUNCT
ejpam-3085	171	10	sasas	sasa	NOUN
ejpam-3085	171	11	]	]	PUNCT
ejpam-3085	171	12	for	for	ADP
ejpam-3085	171	13	every	every	DET
ejpam-3085	171	14	a	a	DET
ejpam-3085	171	15	∈	∈	PROPN
ejpam-3085	171	16	s	s	NOUN
ejpam-3085	171	17	or	or	CCONJ
ejpam-3085	171	18	a	a	DET
ejpam-3085	171	19	⊆	⊆	NUM
ejpam-3085	171	20	(	(	PUNCT
ejpam-3085	171	21	sasas	sasa	NOUN
ejpam-3085	171	22	]	]	PUNCT
ejpam-3085	171	23	for	for	ADP
ejpam-3085	171	24	any	any	DET
ejpam-3085	171	25	a	a	DET
ejpam-3085	171	26	⊆	⊆	NUM
ejpam-3085	171	27	s.	s.	NOUN
ejpam-3085	171	28	this	this	DET
ejpam-3085	171	29	concept	concept	NOUN
ejpam-3085	171	30	can	can	AUX
ejpam-3085	171	31	be	be	AUX
ejpam-3085	171	32	naturally	naturally	ADV
ejpam-3085	171	33	transferred	transfer	VERB
ejpam-3085	171	34	to	to	ADP
ejpam-3085	171	35	ordered	order	VERB
ejpam-3085	171	36	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	171	37	by	by	ADP
ejpam-3085	171	38	the	the	DET
ejpam-3085	171	39	following	follow	VERB
ejpam-3085	171	40	definition	definition	NOUN
ejpam-3085	171	41	.	.	PUNCT
ejpam-3085	172	1	definition	definition	NOUN
ejpam-3085	172	2	16	16	NUM
ejpam-3085	172	3	.	.	PUNCT
ejpam-3085	173	1	an	an	DET
ejpam-3085	173	2	ordered	order	VERB
ejpam-3085	173	3	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	173	4	(	(	PUNCT
ejpam-3085	173	5	h	h	NOUN
ejpam-3085	173	6	,	,	PUNCT
ejpam-3085	173	7	◦	◦	NOUN
ejpam-3085	173	8	,	,	PUNCT
ejpam-3085	173	9	≤	≤	NUM
ejpam-3085	173	10	)	)	PUNCT
ejpam-3085	173	11	is	be	AUX
ejpam-3085	173	12	called	call	VERB
ejpam-3085	173	13	semisimple	semisimple	NOUN
ejpam-3085	173	14	if	if	SCONJ
ejpam-3085	173	15	for	for	ADP
ejpam-3085	173	16	every	every	DET
ejpam-3085	173	17	a	a	DET
ejpam-3085	173	18	∈	∈	PROPN
ejpam-3085	173	19	h	h	NOUN
ejpam-3085	173	20	there	there	PRON
ejpam-3085	173	21	exist	exist	VERB
ejpam-3085	173	22	x	x	NOUN
ejpam-3085	173	23	,	,	PUNCT
ejpam-3085	173	24	y	y	PROPN
ejpam-3085	173	25	,	,	PUNCT
ejpam-3085	173	26	z	z	PROPN
ejpam-3085	173	27	∈	∈	PROPN
ejpam-3085	173	28	h	h	NOUN
ejpam-3085	173	29	such	such	ADJ
ejpam-3085	173	30	that	that	SCONJ
ejpam-3085	173	31	{	{	PUNCT
ejpam-3085	173	32	a	a	DET
ejpam-3085	173	33	}	}	PUNCT
ejpam-3085	173	34	�	�	PROPN
ejpam-3085	173	35	(	(	PUNCT
ejpam-3085	173	36	x	x	SYM
ejpam-3085	173	37	◦	◦	VERB
ejpam-3085	173	38	a	a	X
ejpam-3085	173	39	)	)	PUNCT
ejpam-3085	173	40	∗	∗	NOUN
ejpam-3085	173	41	(	(	PUNCT
ejpam-3085	173	42	y	y	NOUN
ejpam-3085	173	43	◦	◦	VERB
ejpam-3085	173	44	a	a	X
ejpam-3085	173	45	)	)	PUNCT
ejpam-3085	173	46	∗	∗	NOUN
ejpam-3085	173	47	{	{	PUNCT
ejpam-3085	173	48	z	z	NOUN
ejpam-3085	173	49	}	}	PUNCT
ejpam-3085	173	50	.	.	PUNCT
ejpam-3085	174	1	that	that	PRON
ejpam-3085	174	2	is	be	AUX
ejpam-3085	174	3	,	,	PUNCT
ejpam-3085	174	4	for	for	ADP
ejpam-3085	174	5	every	every	DET
ejpam-3085	174	6	a	a	DET
ejpam-3085	174	7	∈	∈	PROPN
ejpam-3085	174	8	h	h	NOUN
ejpam-3085	174	9	there	there	PRON
ejpam-3085	174	10	exist	exist	VERB
ejpam-3085	174	11	x	x	NOUN
ejpam-3085	174	12	,	,	PUNCT
ejpam-3085	174	13	y	y	PROPN
ejpam-3085	174	14	,	,	PUNCT
ejpam-3085	174	15	z	z	PROPN
ejpam-3085	174	16	,	,	PUNCT
ejpam-3085	174	17	t	t	PROPN
ejpam-3085	174	18	∈	∈	PROPN
ejpam-3085	174	19	h	h	NOUN
ejpam-3085	174	20	such	such	ADJ
ejpam-3085	174	21	that	that	SCONJ
ejpam-3085	174	22	t	t	PROPN
ejpam-3085	174	23	∈	∈	PROPN
ejpam-3085	174	24	(	(	PUNCT
ejpam-3085	174	25	x	x	SYM
ejpam-3085	174	26	◦	◦	VERB
ejpam-3085	174	27	a	a	X
ejpam-3085	174	28	)	)	PUNCT
ejpam-3085	174	29	∗	∗	NOUN
ejpam-3085	174	30	(	(	PUNCT
ejpam-3085	174	31	y	y	NOUN
ejpam-3085	174	32	◦	◦	VERB
ejpam-3085	174	33	a	a	X
ejpam-3085	174	34	)	)	PUNCT
ejpam-3085	174	35	∗	∗	NOUN
ejpam-3085	174	36	{	{	PUNCT
ejpam-3085	174	37	z	z	NOUN
ejpam-3085	174	38	}	}	PUNCT
ejpam-3085	174	39	and	and	CCONJ
ejpam-3085	174	40	a	a	DET
ejpam-3085	174	41	≤	≤	ADJ
ejpam-3085	174	42	t.	t.	NOUN
ejpam-3085	174	43	clearly	clearly	ADV
ejpam-3085	174	44	,	,	PUNCT
ejpam-3085	174	45	(	(	PUNCT
ejpam-3085	174	46	x	x	X
ejpam-3085	174	47	◦	◦	VERB
ejpam-3085	174	48	a	a	X
ejpam-3085	174	49	)	)	PUNCT
ejpam-3085	174	50	∗	∗	NOUN
ejpam-3085	174	51	(	(	PUNCT
ejpam-3085	174	52	y	y	NOUN
ejpam-3085	174	53	◦	◦	VERB
ejpam-3085	174	54	a	a	X
ejpam-3085	174	55	)	)	PUNCT
ejpam-3085	174	56	∗	∗	NOUN
ejpam-3085	174	57	{	{	PUNCT
ejpam-3085	174	58	z	z	NOUN
ejpam-3085	174	59	}	}	PUNCT
ejpam-3085	174	60	=	=	SYM
ejpam-3085	174	61	{	{	PUNCT
ejpam-3085	174	62	x	x	NOUN
ejpam-3085	174	63	}	}	PUNCT
ejpam-3085	174	64	∗	∗	NOUN
ejpam-3085	174	65	(	(	PUNCT
ejpam-3085	174	66	a	a	DET
ejpam-3085	174	67	◦	◦	NOUN
ejpam-3085	174	68	y	y	NOUN
ejpam-3085	174	69	)	)	PUNCT
ejpam-3085	174	70	∗	∗	NOUN
ejpam-3085	174	71	(	(	PUNCT
ejpam-3085	174	72	a	a	DET
ejpam-3085	174	73	◦	◦	NOUN
ejpam-3085	174	74	z	z	NOUN
ejpam-3085	174	75	)	)	PUNCT
ejpam-3085	174	76	=	=	SYM
ejpam-3085	175	1	(	(	PUNCT
ejpam-3085	175	2	x	x	SYM
ejpam-3085	175	3	◦	◦	VERB
ejpam-3085	175	4	a	a	X
ejpam-3085	175	5	)	)	PUNCT
ejpam-3085	175	6	∗	∗	NOUN
ejpam-3085	175	7	{	{	PUNCT
ejpam-3085	175	8	y	y	NOUN
ejpam-3085	175	9	}	}	PUNCT
ejpam-3085	175	10	∗	∗	NOUN
ejpam-3085	175	11	(	(	PUNCT
ejpam-3085	175	12	a	a	DET
ejpam-3085	175	13	◦	◦	NOUN
ejpam-3085	175	14	z	z	NOUN
ejpam-3085	175	15	)	)	PUNCT
ejpam-3085	175	16	=	=	PRON
ejpam-3085	175	17	{	{	PUNCT
ejpam-3085	175	18	x	x	NOUN
ejpam-3085	175	19	}	}	PUNCT
ejpam-3085	175	20	∗	∗	NOUN
ejpam-3085	175	21	{	{	PUNCT
ejpam-3085	175	22	a	a	PRON
ejpam-3085	175	23	}	}	PUNCT
ejpam-3085	175	24	∗	∗	NOUN
ejpam-3085	175	25	{	{	PUNCT
ejpam-3085	175	26	y	y	NOUN
ejpam-3085	175	27	}	}	PUNCT
ejpam-3085	175	28	∗	∗	NOUN
ejpam-3085	175	29	{	{	PUNCT
ejpam-3085	175	30	a	a	DET
ejpam-3085	175	31	}	}	PUNCT
ejpam-3085	175	32	∗	∗	NOUN
ejpam-3085	175	33	{	{	PUNCT
ejpam-3085	175	34	z	z	NOUN
ejpam-3085	175	35	}	}	PUNCT
ejpam-3085	175	36	.	.	PUNCT
ejpam-3085	176	1	proposition	proposition	NOUN
ejpam-3085	176	2	17	17	NUM
ejpam-3085	176	3	.	.	PUNCT
ejpam-3085	177	1	let	let	AUX
ejpam-3085	177	2	(	(	PUNCT
ejpam-3085	177	3	h	h	NOUN
ejpam-3085	177	4	,	,	PUNCT
ejpam-3085	177	5	◦	◦	NOUN
ejpam-3085	177	6	,	,	PUNCT
ejpam-3085	177	7	≤	≤	NUM
ejpam-3085	177	8	)	)	PUNCT
ejpam-3085	177	9	be	be	VERB
ejpam-3085	177	10	an	an	DET
ejpam-3085	177	11	ordered	order	VERB
ejpam-3085	177	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	177	13	.	.	PUNCT
ejpam-3085	178	1	the	the	DET
ejpam-3085	178	2	following	follow	VERB
ejpam-3085	178	3	are	be	AUX
ejpam-3085	178	4	equivalent	equivalent	ADJ
ejpam-3085	178	5	:	:	PUNCT
ejpam-3085	178	6	(	(	PUNCT
ejpam-3085	178	7	1	1	X
ejpam-3085	178	8	)	)	PUNCT
ejpam-3085	178	9	h	h	NOUN
ejpam-3085	178	10	is	be	AUX
ejpam-3085	178	11	semisimple	semisimple	ADJ
ejpam-3085	178	12	.	.	PUNCT
ejpam-3085	179	1	(	(	PUNCT
ejpam-3085	179	2	2	2	X
ejpam-3085	179	3	)	)	PUNCT
ejpam-3085	179	4	a	a	DET
ejpam-3085	179	5	∈	∈	NOUN
ejpam-3085	179	6	(	(	PUNCT
ejpam-3085	179	7	h	h	NOUN
ejpam-3085	179	8	∗	∗	NOUN
ejpam-3085	179	9	{	{	PUNCT
ejpam-3085	179	10	a	a	DET
ejpam-3085	179	11	}	}	PUNCT
ejpam-3085	179	12	∗h	∗h	NOUN
ejpam-3085	179	13	∗	∗	NOUN
ejpam-3085	179	14	{	{	PUNCT
ejpam-3085	179	15	a	a	DET
ejpam-3085	179	16	}	}	PUNCT
ejpam-3085	179	17	∗h	∗h	NOUN
ejpam-3085	179	18	]	]	PUNCT
ejpam-3085	179	19	for	for	ADP
ejpam-3085	179	20	every	every	DET
ejpam-3085	179	21	a	a	DET
ejpam-3085	179	22	∈	∈	PROPN
ejpam-3085	179	23	h.	h.	NOUN
ejpam-3085	179	24	(	(	PUNCT
ejpam-3085	179	25	3	3	X
ejpam-3085	179	26	)	)	PUNCT
ejpam-3085	179	27	a	a	DET
ejpam-3085	179	28	⊆	⊆	NUM
ejpam-3085	179	29	(	(	PUNCT
ejpam-3085	179	30	h	h	NOUN
ejpam-3085	179	31	∗a	∗a	ADJ
ejpam-3085	179	32	∗h	∗h	NOUN
ejpam-3085	179	33	∗a	∗a	ADJ
ejpam-3085	179	34	∗h	∗h	NOUN
ejpam-3085	179	35	]	]	PUNCT
ejpam-3085	179	36	for	for	ADP
ejpam-3085	179	37	every	every	DET
ejpam-3085	179	38	nonempty	nonempty	NOUN
ejpam-3085	179	39	subset	subset	VERB
ejpam-3085	179	40	a	a	PRON
ejpam-3085	179	41	of	of	ADP
ejpam-3085	179	42	h.	h.	PROPN
ejpam-3085	179	43	n.	n.	PROPN
ejpam-3085	179	44	kehayopulu	kehayopulu	PROPN
ejpam-3085	179	45	/	/	SYM
ejpam-3085	179	46	eur	eur	PROPN
ejpam-3085	179	47	.	.	PUNCT
ejpam-3085	180	1	j.	j.	PROPN
ejpam-3085	180	2	pure	pure	PROPN
ejpam-3085	180	3	appl	appl	PROPN
ejpam-3085	180	4	.	.	PROPN
ejpam-3085	180	5	math	math	PROPN
ejpam-3085	180	6	,	,	PUNCT
ejpam-3085	180	7	11	11	NUM
ejpam-3085	180	8	(	(	PUNCT
ejpam-3085	180	9	1	1	NUM
ejpam-3085	180	10	)	)	PUNCT
ejpam-3085	180	11	(	(	PUNCT
ejpam-3085	180	12	2018	2018	NUM
ejpam-3085	180	13	)	)	PUNCT
ejpam-3085	180	14	,	,	PUNCT
ejpam-3085	180	15	10	10	NUM
ejpam-3085	180	16	-	-	SYM
ejpam-3085	180	17	22	22	NUM
ejpam-3085	180	18	16	16	NUM
ejpam-3085	180	19	proof	proof	NOUN
ejpam-3085	180	20	.	.	PUNCT
ejpam-3085	181	1	(	(	PUNCT
ejpam-3085	181	2	1	1	X
ejpam-3085	181	3	)	)	PUNCT
ejpam-3085	181	4	=	=	NOUN
ejpam-3085	181	5	⇒	⇒	NOUN
ejpam-3085	181	6	(	(	PUNCT
ejpam-3085	181	7	2	2	NUM
ejpam-3085	181	8	)	)	PUNCT
ejpam-3085	181	9	.	.	PUNCT
ejpam-3085	182	1	let	let	VERB
ejpam-3085	182	2	a	a	DET
ejpam-3085	182	3	∈	∈	PROPN
ejpam-3085	182	4	h.	h.	NOUN
ejpam-3085	182	5	since	since	SCONJ
ejpam-3085	182	6	h	h	PROPN
ejpam-3085	182	7	is	be	AUX
ejpam-3085	182	8	semisimple	semisimple	ADJ
ejpam-3085	182	9	,	,	PUNCT
ejpam-3085	182	10	there	there	PRON
ejpam-3085	182	11	exist	exist	VERB
ejpam-3085	182	12	x	x	NOUN
ejpam-3085	182	13	,	,	PUNCT
ejpam-3085	182	14	y	y	PROPN
ejpam-3085	182	15	,	,	PUNCT
ejpam-3085	182	16	z	z	PROPN
ejpam-3085	182	17	,	,	PUNCT
ejpam-3085	182	18	t	t	PROPN
ejpam-3085	182	19	∈	∈	PROPN
ejpam-3085	182	20	h	h	NOUN
ejpam-3085	182	21	such	such	ADJ
ejpam-3085	182	22	that	that	SCONJ
ejpam-3085	182	23	a	a	DET
ejpam-3085	182	24	≤	≤	PROPN
ejpam-3085	182	25	t	t	X
ejpam-3085	182	26	∈	∈	PROPN
ejpam-3085	182	27	{	{	PUNCT
ejpam-3085	182	28	x}∗{a}∗{y}∗{a}∗{z	x}∗{a}∗{y}∗{a}∗{z	PROPN
ejpam-3085	182	29	}	}	PUNCT
ejpam-3085	182	30	⊆	⊆	NUM
ejpam-3085	182	31	h∗{a}∗h∗{a}∗h	h∗{a}∗h∗{a}∗h	NOUN
ejpam-3085	182	32	,	,	PUNCT
ejpam-3085	182	33	so	so	SCONJ
ejpam-3085	182	34	we	we	PRON
ejpam-3085	182	35	have	have	AUX
ejpam-3085	182	36	a	a	DET
ejpam-3085	182	37	∈	∈	PROPN
ejpam-3085	182	38	(	(	PUNCT
ejpam-3085	182	39	h∗{a}∗h∗{a}∗h	h∗{a}∗h∗{a}∗h	PROPN
ejpam-3085	182	40	]	]	PUNCT
ejpam-3085	182	41	.	.	PUNCT
ejpam-3085	183	1	(	(	PUNCT
ejpam-3085	183	2	2	2	X
ejpam-3085	183	3	)	)	PUNCT
ejpam-3085	183	4	=	=	NOUN
ejpam-3085	183	5	⇒	⇒	NOUN
ejpam-3085	183	6	(	(	PUNCT
ejpam-3085	183	7	3	3	NUM
ejpam-3085	183	8	)	)	PUNCT
ejpam-3085	183	9	.	.	PUNCT
ejpam-3085	184	1	let	let	VERB
ejpam-3085	184	2	a	a	DET
ejpam-3085	184	3	∈	∈	PROPN
ejpam-3085	184	4	p∗(h	p∗(h	PROPN
ejpam-3085	184	5	)	)	PUNCT
ejpam-3085	184	6	and	and	CCONJ
ejpam-3085	184	7	a	a	DET
ejpam-3085	184	8	∈	∈	NOUN
ejpam-3085	184	9	a.	a.	NOUN
ejpam-3085	184	10	by	by	ADP
ejpam-3085	184	11	(	(	PUNCT
ejpam-3085	184	12	2	2	NUM
ejpam-3085	184	13	)	)	PUNCT
ejpam-3085	184	14	,	,	PUNCT
ejpam-3085	184	15	we	we	PRON
ejpam-3085	184	16	have	have	VERB
ejpam-3085	184	17	a	a	DET
ejpam-3085	184	18	∈	∈	NOUN
ejpam-3085	184	19	(	(	PUNCT
ejpam-3085	184	20	h	h	NOUN
ejpam-3085	184	21	∗	∗	NOUN
ejpam-3085	184	22	{	{	PUNCT
ejpam-3085	184	23	a	a	DET
ejpam-3085	184	24	}	}	PUNCT
ejpam-3085	184	25	∗h	∗h	NOUN
ejpam-3085	184	26	∗	∗	NOUN
ejpam-3085	184	27	{	{	PUNCT
ejpam-3085	184	28	a	a	DET
ejpam-3085	184	29	}	}	PUNCT
ejpam-3085	184	30	∗h	∗h	NOUN
ejpam-3085	184	31	]	]	X
ejpam-3085	184	32	⊆	⊆	NUM
ejpam-3085	184	33	(	(	PUNCT
ejpam-3085	184	34	h	h	NOUN
ejpam-3085	184	35	∗a	∗a	ADJ
ejpam-3085	184	36	∗h	∗h	NOUN
ejpam-3085	184	37	∗a	∗a	ADJ
ejpam-3085	184	38	∗h	∗h	NOUN
ejpam-3085	184	39	]	]	PUNCT
ejpam-3085	184	40	.	.	PUNCT
ejpam-3085	185	1	(	(	PUNCT
ejpam-3085	185	2	3	3	X
ejpam-3085	185	3	)	)	PUNCT
ejpam-3085	185	4	=	=	NOUN
ejpam-3085	185	5	⇒	⇒	NOUN
ejpam-3085	185	6	(	(	PUNCT
ejpam-3085	185	7	1	1	NUM
ejpam-3085	185	8	)	)	PUNCT
ejpam-3085	185	9	.	.	PUNCT
ejpam-3085	186	1	let	let	VERB
ejpam-3085	186	2	a	a	DET
ejpam-3085	186	3	∈	∈	PROPN
ejpam-3085	186	4	h.	h.	NOUN
ejpam-3085	186	5	by	by	ADP
ejpam-3085	186	6	(	(	PUNCT
ejpam-3085	186	7	3	3	NUM
ejpam-3085	186	8	)	)	PUNCT
ejpam-3085	186	9	,	,	PUNCT
ejpam-3085	186	10	we	we	PRON
ejpam-3085	186	11	have	have	VERB
ejpam-3085	186	12	a	a	DET
ejpam-3085	186	13	∈	∈	NOUN
ejpam-3085	186	14	{	{	PUNCT
ejpam-3085	186	15	a	a	NOUN
ejpam-3085	186	16	}	}	PUNCT
ejpam-3085	186	17	⊆	⊆	NUM
ejpam-3085	186	18	(	(	PUNCT
ejpam-3085	186	19	h	h	NOUN
ejpam-3085	186	20	∗{a}∗h	∗{a}∗h	PROPN
ejpam-3085	186	21	∗{a}∗h	∗{a}∗h	PROPN
ejpam-3085	186	22	]	]	PUNCT
ejpam-3085	186	23	.	.	PUNCT
ejpam-3085	187	1	then	then	ADV
ejpam-3085	187	2	a	a	DET
ejpam-3085	187	3	≤	≤	ADJ
ejpam-3085	187	4	t	t	NOUN
ejpam-3085	187	5	for	for	ADP
ejpam-3085	187	6	some	some	DET
ejpam-3085	187	7	t	t	NOUN
ejpam-3085	187	8	∈	∈	PROPN
ejpam-3085	187	9	(	(	PUNCT
ejpam-3085	187	10	h	h	NOUN
ejpam-3085	187	11	∗	∗	NOUN
ejpam-3085	187	12	{	{	PUNCT
ejpam-3085	187	13	a	a	DET
ejpam-3085	187	14	}	}	PUNCT
ejpam-3085	187	15	∗h	∗h	NOUN
ejpam-3085	187	16	)	)	PUNCT
ejpam-3085	187	17	∗	∗	NOUN
ejpam-3085	187	18	{	{	PUNCT
ejpam-3085	187	19	a	a	DET
ejpam-3085	187	20	}	}	PUNCT
ejpam-3085	187	21	∗h	∗h	NOUN
ejpam-3085	187	22	,	,	PUNCT
ejpam-3085	188	1	t	t	PROPN
ejpam-3085	188	2	∈	∈	PROPN
ejpam-3085	188	3	u	u	PROPN
ejpam-3085	188	4	◦	◦	NOUN
ejpam-3085	188	5	v	v	NOUN
ejpam-3085	188	6	for	for	ADP
ejpam-3085	188	7	some	some	DET
ejpam-3085	188	8	u	u	NOUN
ejpam-3085	188	9	∈	∈	PROPN
ejpam-3085	188	10	h	h	NOUN
ejpam-3085	188	11	∗	∗	NOUN
ejpam-3085	188	12	{	{	PUNCT
ejpam-3085	188	13	a	a	DET
ejpam-3085	188	14	}	}	PUNCT
ejpam-3085	188	15	∗h	∗h	NOUN
ejpam-3085	188	16	,	,	PUNCT
ejpam-3085	188	17	v	v	NOUN
ejpam-3085	188	18	∈	∈	PROPN
ejpam-3085	188	19	{	{	PUNCT
ejpam-3085	188	20	a	a	NOUN
ejpam-3085	188	21	}	}	PUNCT
ejpam-3085	188	22	∗h	∗h	NOUN
ejpam-3085	188	23	,	,	PUNCT
ejpam-3085	188	24	u	u	NOUN
ejpam-3085	188	25	∈	∈	PROPN
ejpam-3085	188	26	w	w	PROPN
ejpam-3085	188	27	◦	◦	NOUN
ejpam-3085	188	28	y	y	PROPN
ejpam-3085	188	29	for	for	ADP
ejpam-3085	188	30	some	some	DET
ejpam-3085	188	31	w	w	PROPN
ejpam-3085	188	32	∈	∈	PROPN
ejpam-3085	188	33	h	h	NOUN
ejpam-3085	188	34	∗	∗	NOUN
ejpam-3085	188	35	{	{	PUNCT
ejpam-3085	188	36	a	a	NOUN
ejpam-3085	188	37	}	}	PUNCT
ejpam-3085	188	38	,	,	PUNCT
ejpam-3085	188	39	y	y	PROPN
ejpam-3085	188	40	∈	∈	PROPN
ejpam-3085	188	41	h	h	NOUN
ejpam-3085	188	42	,	,	PUNCT
ejpam-3085	188	43	w	w	PROPN
ejpam-3085	188	44	∈	∈	PROPN
ejpam-3085	188	45	x	x	PUNCT
ejpam-3085	188	46	◦	◦	VERB
ejpam-3085	188	47	a	a	PRON
ejpam-3085	188	48	for	for	ADP
ejpam-3085	188	49	some	some	DET
ejpam-3085	188	50	x	x	SYM
ejpam-3085	188	51	∈	∈	PROPN
ejpam-3085	188	52	h	h	NOUN
ejpam-3085	188	53	and	and	CCONJ
ejpam-3085	188	54	v	v	ADP
ejpam-3085	188	55	∈	∈	PROPN
ejpam-3085	188	56	a	a	DET
ejpam-3085	188	57	◦	◦	NOUN
ejpam-3085	188	58	z	z	NOUN
ejpam-3085	188	59	for	for	ADP
ejpam-3085	188	60	some	some	DET
ejpam-3085	188	61	z	z	PROPN
ejpam-3085	188	62	∈	∈	PROPN
ejpam-3085	188	63	h.	h.	NOUN
ejpam-3085	188	64	thus	thus	ADV
ejpam-3085	188	65	we	we	PRON
ejpam-3085	188	66	have	have	VERB
ejpam-3085	188	67	t	t	PROPN
ejpam-3085	188	68	∈	∈	PROPN
ejpam-3085	188	69	u	u	NOUN
ejpam-3085	188	70	◦	◦	NOUN
ejpam-3085	188	71	v	v	NOUN
ejpam-3085	188	72	=	=	PUNCT
ejpam-3085	188	73	{	{	PUNCT
ejpam-3085	188	74	u	u	NOUN
ejpam-3085	188	75	}	}	PUNCT
ejpam-3085	188	76	∗	∗	NOUN
ejpam-3085	188	77	{	{	PUNCT
ejpam-3085	188	78	v	v	NOUN
ejpam-3085	188	79	}	}	PUNCT
ejpam-3085	188	80	⊆	⊆	NUM
ejpam-3085	188	81	(	(	PUNCT
ejpam-3085	188	82	w	w	NOUN
ejpam-3085	188	83	◦	◦	NOUN
ejpam-3085	188	84	y	y	PROPN
ejpam-3085	188	85	)	)	PUNCT
ejpam-3085	188	86	∗	∗	NOUN
ejpam-3085	188	87	{	{	PUNCT
ejpam-3085	188	88	v	v	NOUN
ejpam-3085	188	89	}	}	PUNCT
ejpam-3085	188	90	=	=	PUNCT
ejpam-3085	188	91	{	{	PUNCT
ejpam-3085	188	92	w	w	NOUN
ejpam-3085	188	93	}	}	PUNCT
ejpam-3085	188	94	∗	∗	NOUN
ejpam-3085	188	95	{	{	PUNCT
ejpam-3085	188	96	y	y	NOUN
ejpam-3085	188	97	}	}	PUNCT
ejpam-3085	188	98	∗	∗	NOUN
ejpam-3085	188	99	{	{	PUNCT
ejpam-3085	188	100	v	v	NOUN
ejpam-3085	188	101	}	}	PUNCT
ejpam-3085	188	102	⊆	⊆	NUM
ejpam-3085	188	103	(	(	PUNCT
ejpam-3085	188	104	x	x	SYM
ejpam-3085	188	105	◦	◦	VERB
ejpam-3085	188	106	a	a	X
ejpam-3085	188	107	)	)	PUNCT
ejpam-3085	188	108	∗	∗	NOUN
ejpam-3085	188	109	{	{	PUNCT
ejpam-3085	188	110	y	y	NOUN
ejpam-3085	188	111	}	}	PUNCT
ejpam-3085	188	112	∗	∗	NOUN
ejpam-3085	188	113	(	(	PUNCT
ejpam-3085	188	114	a	a	DET
ejpam-3085	188	115	◦	◦	NOUN
ejpam-3085	188	116	z	z	NOUN
ejpam-3085	188	117	)	)	PUNCT
ejpam-3085	188	118	,	,	PUNCT
ejpam-3085	188	119	where	where	SCONJ
ejpam-3085	188	120	x	x	X
ejpam-3085	188	121	,	,	PUNCT
ejpam-3085	188	122	y	y	PROPN
ejpam-3085	188	123	,	,	PUNCT
ejpam-3085	188	124	z	z	PROPN
ejpam-3085	188	125	∈	∈	PROPN
ejpam-3085	188	126	h	h	NOUN
ejpam-3085	188	127	and	and	CCONJ
ejpam-3085	188	128	a	a	DET
ejpam-3085	188	129	≤	≤	NUM
ejpam-3085	188	130	t	t	NOUN
ejpam-3085	188	131	,	,	PUNCT
ejpam-3085	188	132	so	so	ADV
ejpam-3085	188	133	h	h	NOUN
ejpam-3085	188	134	is	be	AUX
ejpam-3085	188	135	semisimple	semisimple	ADJ
ejpam-3085	188	136	.	.	PUNCT
ejpam-3085	189	1	�	�	PROPN
ejpam-3085	189	2	theorem	theorem	VERB
ejpam-3085	189	3	18	18	NUM
ejpam-3085	189	4	.	.	PUNCT
ejpam-3085	190	1	an	an	DET
ejpam-3085	190	2	ordered	order	VERB
ejpam-3085	190	3	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	190	4	(	(	PUNCT
ejpam-3085	190	5	h	h	NOUN
ejpam-3085	190	6	,	,	PUNCT
ejpam-3085	190	7	◦	◦	NOUN
ejpam-3085	190	8	,	,	PUNCT
ejpam-3085	190	9	≤	≤	NUM
ejpam-3085	190	10	)	)	PUNCT
ejpam-3085	190	11	is	be	AUX
ejpam-3085	190	12	semisimple	semisimple	ADJ
ejpam-3085	190	13	if	if	SCONJ
ejpam-3085	190	14	and	and	CCONJ
ejpam-3085	190	15	only	only	ADV
ejpam-3085	190	16	if	if	SCONJ
ejpam-3085	190	17	the	the	DET
ejpam-3085	190	18	ideals	ideal	NOUN
ejpam-3085	190	19	of	of	ADP
ejpam-3085	190	20	h	h	NOUN
ejpam-3085	190	21	are	be	AUX
ejpam-3085	190	22	idempotent	idempotent	ADJ
ejpam-3085	190	23	.	.	PUNCT
ejpam-3085	191	1	proof	proof	NOUN
ejpam-3085	191	2	.	.	PUNCT
ejpam-3085	192	1	=	=	NOUN
ejpam-3085	192	2	⇒.	⇒.	NOUN
ejpam-3085	192	3	let	let	VERB
ejpam-3085	192	4	a	a	PRON
ejpam-3085	192	5	be	be	AUX
ejpam-3085	192	6	an	an	DET
ejpam-3085	192	7	ideal	ideal	NOUN
ejpam-3085	192	8	of	of	ADP
ejpam-3085	192	9	h.	h.	NOUN
ejpam-3085	192	10	if	if	SCONJ
ejpam-3085	192	11	x	x	SYM
ejpam-3085	192	12	∈	∈	PROPN
ejpam-3085	192	13	a	a	PRON
ejpam-3085	192	14	then	then	ADV
ejpam-3085	192	15	,	,	PUNCT
ejpam-3085	192	16	since	since	SCONJ
ejpam-3085	192	17	h	h	NOUN
ejpam-3085	192	18	is	be	AUX
ejpam-3085	192	19	semisimple	semisimple	ADJ
ejpam-3085	192	20	,	,	PUNCT
ejpam-3085	192	21	we	we	PRON
ejpam-3085	192	22	have	have	VERB
ejpam-3085	192	23	x	x	SYM
ejpam-3085	192	24	∈	∈	PROPN
ejpam-3085	192	25	(	(	PUNCT
ejpam-3085	192	26	h	h	NOUN
ejpam-3085	192	27	∗	∗	NOUN
ejpam-3085	192	28	{	{	PUNCT
ejpam-3085	192	29	x	x	NOUN
ejpam-3085	192	30	}	}	PUNCT
ejpam-3085	192	31	∗h	∗h	NOUN
ejpam-3085	192	32	∗	∗	NOUN
ejpam-3085	192	33	{	{	PUNCT
ejpam-3085	192	34	x	x	NOUN
ejpam-3085	192	35	}	}	PUNCT
ejpam-3085	192	36	∗h	∗h	NOUN
ejpam-3085	192	37	]	]	PUNCT
ejpam-3085	192	38	.	.	PUNCT
ejpam-3085	193	1	then	then	ADV
ejpam-3085	193	2	x	x	X
ejpam-3085	193	3	≤	≤	PROPN
ejpam-3085	193	4	t	t	NOUN
ejpam-3085	193	5	for	for	ADP
ejpam-3085	193	6	some	some	DET
ejpam-3085	193	7	t	t	NOUN
ejpam-3085	193	8	∈	∈	PROPN
ejpam-3085	193	9	(	(	PUNCT
ejpam-3085	193	10	h	h	NOUN
ejpam-3085	193	11	∗	∗	NOUN
ejpam-3085	193	12	{	{	PUNCT
ejpam-3085	193	13	x	x	NOUN
ejpam-3085	193	14	}	}	PUNCT
ejpam-3085	193	15	∗h	∗h	NOUN
ejpam-3085	193	16	)	)	PUNCT
ejpam-3085	193	17	∗	∗	NOUN
ejpam-3085	193	18	(	(	PUNCT
ejpam-3085	193	19	{	{	PUNCT
ejpam-3085	193	20	x	x	NOUN
ejpam-3085	193	21	}	}	PUNCT
ejpam-3085	193	22	∗h	∗h	NOUN
ejpam-3085	193	23	)	)	PUNCT
ejpam-3085	193	24	.	.	PUNCT
ejpam-3085	194	1	then	then	ADV
ejpam-3085	194	2	t	t	PROPN
ejpam-3085	194	3	∈	∈	PROPN
ejpam-3085	194	4	a	a	DET
ejpam-3085	194	5	◦	◦	NOUN
ejpam-3085	194	6	b	b	NOUN
ejpam-3085	194	7	for	for	ADP
ejpam-3085	194	8	some	some	PRON
ejpam-3085	194	9	a	a	DET
ejpam-3085	194	10	∈	∈	PROPN
ejpam-3085	194	11	h	h	NOUN
ejpam-3085	194	12	∗	∗	NOUN
ejpam-3085	194	13	{	{	PUNCT
ejpam-3085	194	14	x	x	NOUN
ejpam-3085	194	15	}	}	PUNCT
ejpam-3085	194	16	∗h	∗h	NOUN
ejpam-3085	194	17	,	,	PUNCT
ejpam-3085	194	18	b	b	X
ejpam-3085	194	19	∈	∈	PROPN
ejpam-3085	194	20	{	{	PUNCT
ejpam-3085	194	21	x	x	NOUN
ejpam-3085	194	22	}	}	PUNCT
ejpam-3085	194	23	∗h	∗h	NOUN
ejpam-3085	194	24	.	.	PUNCT
ejpam-3085	195	1	since	since	SCONJ
ejpam-3085	195	2	a	a	DET
ejpam-3085	195	3	∈	∈	PROPN
ejpam-3085	195	4	h	h	NOUN
ejpam-3085	195	5	∗	∗	NOUN
ejpam-3085	195	6	{	{	PUNCT
ejpam-3085	195	7	x	x	NOUN
ejpam-3085	195	8	}	}	PUNCT
ejpam-3085	195	9	∗h	∗h	NOUN
ejpam-3085	195	10	⊆	⊆	NUM
ejpam-3085	195	11	(	(	PUNCT
ejpam-3085	195	12	h	h	NOUN
ejpam-3085	195	13	∗a	∗a	ADJ
ejpam-3085	195	14	)	)	PUNCT
ejpam-3085	195	15	∗h	∗h	VERB
ejpam-3085	195	16	⊆	⊆	NUM
ejpam-3085	195	17	a	a	DET
ejpam-3085	195	18	∗h	∗h	NOUN
ejpam-3085	195	19	⊆	⊆	NUM
ejpam-3085	195	20	a	a	PRON
ejpam-3085	195	21	and	and	CCONJ
ejpam-3085	195	22	b	b	NOUN
ejpam-3085	195	23	∈	∈	NOUN
ejpam-3085	195	24	{	{	PUNCT
ejpam-3085	195	25	x	x	NOUN
ejpam-3085	195	26	}	}	PUNCT
ejpam-3085	195	27	∗h	∗h	VERB
ejpam-3085	195	28	⊆	⊆	NUM
ejpam-3085	195	29	a	a	DET
ejpam-3085	195	30	∗h	∗h	NOUN
ejpam-3085	195	31	⊆	⊆	NUM
ejpam-3085	195	32	a	a	PRON
ejpam-3085	195	33	,	,	PUNCT
ejpam-3085	195	34	we	we	PRON
ejpam-3085	195	35	have	have	VERB
ejpam-3085	195	36	a	a	DET
ejpam-3085	195	37	◦	◦	NOUN
ejpam-3085	195	38	b	b	NOUN
ejpam-3085	195	39	⊆	⊆	NUM
ejpam-3085	195	40	a	a	DET
ejpam-3085	195	41	∗a	∗a	NOUN
ejpam-3085	195	42	.	.	PUNCT
ejpam-3085	196	1	since	since	SCONJ
ejpam-3085	196	2	x	x	PROPN
ejpam-3085	196	3	≤	≤	X
ejpam-3085	196	4	t	t	NOUN
ejpam-3085	196	5	∈	∈	PROPN
ejpam-3085	196	6	a	a	DET
ejpam-3085	196	7	∗a	∗a	PROPN
ejpam-3085	196	8	,	,	PUNCT
ejpam-3085	196	9	we	we	PRON
ejpam-3085	196	10	have	have	VERB
ejpam-3085	196	11	x	x	PART
ejpam-3085	196	12	∈	∈	PROPN
ejpam-3085	196	13	(	(	PUNCT
ejpam-3085	196	14	a	a	DET
ejpam-3085	196	15	∗a	∗a	PROPN
ejpam-3085	196	16	]	]	PUNCT
ejpam-3085	196	17	.	.	PUNCT
ejpam-3085	197	1	let	let	VERB
ejpam-3085	197	2	now	now	ADV
ejpam-3085	197	3	x	x	X
ejpam-3085	197	4	∈	∈	PROPN
ejpam-3085	197	5	(	(	PUNCT
ejpam-3085	197	6	a	a	DET
ejpam-3085	197	7	∗a	∗a	PROPN
ejpam-3085	197	8	]	]	PUNCT
ejpam-3085	197	9	.	.	PUNCT
ejpam-3085	198	1	then	then	ADV
ejpam-3085	198	2	x	x	SYM
ejpam-3085	198	3	≤	≤	PROPN
ejpam-3085	198	4	t	t	NOUN
ejpam-3085	198	5	for	for	ADP
ejpam-3085	198	6	some	some	DET
ejpam-3085	198	7	t	t	NOUN
ejpam-3085	198	8	∈	∈	PROPN
ejpam-3085	198	9	a	a	DET
ejpam-3085	198	10	∗	∗	NOUN
ejpam-3085	198	11	a.	a.	NOUN
ejpam-3085	198	12	since	since	SCONJ
ejpam-3085	198	13	t	t	PROPN
ejpam-3085	198	14	∈	∈	PROPN
ejpam-3085	199	1	a	a	DET
ejpam-3085	199	2	∗	∗	NOUN
ejpam-3085	199	3	a	a	X
ejpam-3085	199	4	,	,	PUNCT
ejpam-3085	199	5	we	we	PRON
ejpam-3085	199	6	have	have	VERB
ejpam-3085	199	7	t	t	PROPN
ejpam-3085	199	8	∈	∈	PROPN
ejpam-3085	199	9	a	a	DET
ejpam-3085	199	10	◦	◦	NOUN
ejpam-3085	199	11	b	b	NOUN
ejpam-3085	199	12	for	for	ADP
ejpam-3085	199	13	some	some	DET
ejpam-3085	199	14	a	a	PRON
ejpam-3085	199	15	,	,	PUNCT
ejpam-3085	199	16	b	b	X
ejpam-3085	199	17	∈	∈	PROPN
ejpam-3085	199	18	a.	a.	NOUN
ejpam-3085	199	19	since	since	SCONJ
ejpam-3085	199	20	a	a	DET
ejpam-3085	199	21	,	,	PUNCT
ejpam-3085	199	22	b	b	PROPN
ejpam-3085	199	23	∈	∈	PROPN
ejpam-3085	199	24	a	a	PRON
ejpam-3085	199	25	and	and	CCONJ
ejpam-3085	199	26	a	a	PRON
ejpam-3085	199	27	is	be	AUX
ejpam-3085	199	28	a	a	DET
ejpam-3085	199	29	subsemigroup	subsemigroup	NOUN
ejpam-3085	199	30	of	of	ADP
ejpam-3085	199	31	h	h	NOUN
ejpam-3085	199	32	,	,	PUNCT
ejpam-3085	199	33	we	we	PRON
ejpam-3085	199	34	have	have	VERB
ejpam-3085	199	35	a	a	DET
ejpam-3085	199	36	◦	◦	NOUN
ejpam-3085	199	37	b	b	NUM
ejpam-3085	199	38	⊆	⊆	NUM
ejpam-3085	199	39	a	a	DET
ejpam-3085	199	40	∗	∗	NOUN
ejpam-3085	199	41	a	a	DET
ejpam-3085	199	42	⊆	⊆	NUM
ejpam-3085	199	43	a.	a.	NOUN
ejpam-3085	199	44	since	since	SCONJ
ejpam-3085	199	45	x	x	PROPN
ejpam-3085	199	46	≤	≤	X
ejpam-3085	199	47	t	t	NOUN
ejpam-3085	199	48	∈	∈	PROPN
ejpam-3085	199	49	a	a	PRON
ejpam-3085	199	50	and	and	CCONJ
ejpam-3085	199	51	a	a	PRON
ejpam-3085	199	52	is	be	AUX
ejpam-3085	199	53	an	an	DET
ejpam-3085	199	54	ideal	ideal	NOUN
ejpam-3085	199	55	of	of	ADP
ejpam-3085	199	56	h	h	NOUN
ejpam-3085	199	57	,	,	PUNCT
ejpam-3085	199	58	we	we	PRON
ejpam-3085	199	59	have	have	VERB
ejpam-3085	199	60	x	x	PART
ejpam-3085	199	61	∈	∈	VERB
ejpam-3085	199	62	a.	a.	NOUN
ejpam-3085	199	63	thus	thus	ADV
ejpam-3085	199	64	the	the	DET
ejpam-3085	199	65	ideals	ideal	NOUN
ejpam-3085	199	66	of	of	ADP
ejpam-3085	199	67	h	h	NOUN
ejpam-3085	199	68	are	be	AUX
ejpam-3085	199	69	idempotent	idempotent	ADJ
ejpam-3085	199	70	.	.	PUNCT
ejpam-3085	200	1	⇐	⇐	PROPN
ejpam-3085	200	2	=	=	PRON
ejpam-3085	200	3	.	.	PUNCT
ejpam-3085	201	1	let	let	VERB
ejpam-3085	201	2	a	a	DET
ejpam-3085	201	3	∈	∈	PROPN
ejpam-3085	201	4	h.	h.	NOUN
ejpam-3085	201	5	by	by	ADP
ejpam-3085	201	6	hypothesis	hypothesis	NOUN
ejpam-3085	201	7	,	,	PUNCT
ejpam-3085	201	8	we	we	PRON
ejpam-3085	201	9	have	have	AUX
ejpam-3085	201	10	i(a	i(a	PROPN
ejpam-3085	201	11	)	)	PUNCT
ejpam-3085	202	1	=	=	PRON
ejpam-3085	202	2	(	(	PUNCT
ejpam-3085	202	3	i(a	i(a	PROPN
ejpam-3085	202	4	)	)	PUNCT
ejpam-3085	202	5	∗	∗	NOUN
ejpam-3085	202	6	i(a	i(a	PROPN
ejpam-3085	202	7	)	)	PUNCT
ejpam-3085	202	8	]	]	PUNCT
ejpam-3085	202	9	.	.	PUNCT
ejpam-3085	203	1	in	in	ADP
ejpam-3085	203	2	the	the	DET
ejpam-3085	203	3	implication	implication	NOUN
ejpam-3085	203	4	(	(	PUNCT
ejpam-3085	203	5	4	4	X
ejpam-3085	203	6	)	)	PUNCT
ejpam-3085	203	7	⇒	⇒	NOUN
ejpam-3085	203	8	(	(	PUNCT
ejpam-3085	203	9	5	5	NUM
ejpam-3085	203	10	)	)	PUNCT
ejpam-3085	203	11	of	of	ADP
ejpam-3085	203	12	lemma	lemma	PROPN
ejpam-3085	203	13	2	2	NUM
ejpam-3085	203	14	in	in	ADP
ejpam-3085	203	15	[	[	X
ejpam-3085	203	16	4	4	NUM
ejpam-3085	203	17	]	]	PUNCT
ejpam-3085	203	18	,	,	PUNCT
ejpam-3085	203	19	we	we	PRON
ejpam-3085	203	20	replace	replace	VERB
ejpam-3085	203	21	the	the	DET
ejpam-3085	203	22	multiplication	multiplication	NOUN
ejpam-3085	203	23	“	"	PUNCT
ejpam-3085	203	24	·	·	PUNCT
ejpam-3085	203	25	”	"	PUNCT
ejpam-3085	203	26	by	by	ADP
ejpam-3085	203	27	“	"	PUNCT
ejpam-3085	203	28	∗	∗	NOUN
ejpam-3085	203	29	”	"	PUNCT
ejpam-3085	203	30	,	,	PUNCT
ejpam-3085	203	31	the	the	DET
ejpam-3085	203	32	proof	proof	NOUN
ejpam-3085	203	33	follows	follow	VERB
ejpam-3085	203	34	.	.	PUNCT
ejpam-3085	204	1	�	�	PROPN
ejpam-3085	204	2	theorem	theorem	VERB
ejpam-3085	204	3	19	19	NUM
ejpam-3085	204	4	.	.	PUNCT
ejpam-3085	205	1	let	let	AUX
ejpam-3085	205	2	(	(	PUNCT
ejpam-3085	205	3	h	h	NOUN
ejpam-3085	205	4	,	,	PUNCT
ejpam-3085	205	5	◦	◦	NOUN
ejpam-3085	205	6	,	,	PUNCT
ejpam-3085	205	7	≤	≤	NUM
ejpam-3085	205	8	)	)	PUNCT
ejpam-3085	205	9	be	be	VERB
ejpam-3085	205	10	an	an	DET
ejpam-3085	205	11	ordered	order	VERB
ejpam-3085	205	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	205	13	.	.	PUNCT
ejpam-3085	206	1	the	the	DET
ejpam-3085	206	2	ideals	ideal	NOUN
ejpam-3085	206	3	of	of	ADP
ejpam-3085	206	4	h	h	NOUN
ejpam-3085	206	5	are	be	AUX
ejpam-3085	206	6	weakly	weakly	ADV
ejpam-3085	206	7	prime	prime	ADJ
ejpam-3085	206	8	if	if	SCONJ
ejpam-3085	207	1	and	and	CCONJ
ejpam-3085	207	2	only	only	ADV
ejpam-3085	207	3	if	if	SCONJ
ejpam-3085	207	4	they	they	PRON
ejpam-3085	207	5	are	be	AUX
ejpam-3085	207	6	idempotent	idempotent	ADJ
ejpam-3085	207	7	and	and	CCONJ
ejpam-3085	207	8	they	they	PRON
ejpam-3085	207	9	form	form	VERB
ejpam-3085	207	10	a	a	DET
ejpam-3085	207	11	chain	chain	NOUN
ejpam-3085	207	12	.	.	PUNCT
ejpam-3085	208	1	proof	proof	NOUN
ejpam-3085	208	2	.	.	PUNCT
ejpam-3085	209	1	=	=	NOUN
ejpam-3085	209	2	⇒.	⇒.	NOUN
ejpam-3085	209	3	let	let	VERB
ejpam-3085	209	4	a	a	PRON
ejpam-3085	209	5	be	be	AUX
ejpam-3085	209	6	an	an	DET
ejpam-3085	209	7	ideal	ideal	NOUN
ejpam-3085	209	8	of	of	ADP
ejpam-3085	209	9	h.	h.	PROPN
ejpam-3085	209	10	then	then	ADV
ejpam-3085	209	11	a	a	PRON
ejpam-3085	209	12	=	=	X
ejpam-3085	209	13	(	(	PUNCT
ejpam-3085	209	14	a	a	DET
ejpam-3085	209	15	∗	∗	NOUN
ejpam-3085	209	16	a	a	X
ejpam-3085	209	17	]	]	X
ejpam-3085	209	18	.	.	PUNCT
ejpam-3085	210	1	indeed	indeed	ADV
ejpam-3085	210	2	:	:	PUNCT
ejpam-3085	210	3	by	by	ADP
ejpam-3085	210	4	corollary	corollary	ADJ
ejpam-3085	210	5	15	15	NUM
ejpam-3085	210	6	,	,	PUNCT
ejpam-3085	210	7	the	the	DET
ejpam-3085	210	8	set	set	NOUN
ejpam-3085	210	9	(	(	PUNCT
ejpam-3085	210	10	a	a	DET
ejpam-3085	210	11	∗	∗	NOUN
ejpam-3085	210	12	a	a	X
ejpam-3085	210	13	]	]	X
ejpam-3085	210	14	is	be	AUX
ejpam-3085	210	15	an	an	DET
ejpam-3085	210	16	ideal	ideal	NOUN
ejpam-3085	210	17	of	of	ADP
ejpam-3085	210	18	h.	h.	PROPN
ejpam-3085	210	19	since	since	SCONJ
ejpam-3085	210	20	a	a	DET
ejpam-3085	210	21	∗	∗	NOUN
ejpam-3085	210	22	a	a	DET
ejpam-3085	210	23	⊆	⊆	NUM
ejpam-3085	210	24	(	(	PUNCT
ejpam-3085	210	25	a	a	DET
ejpam-3085	210	26	∗	∗	NOUN
ejpam-3085	210	27	a	a	X
ejpam-3085	210	28	]	]	X
ejpam-3085	210	29	and	and	CCONJ
ejpam-3085	210	30	(	(	PUNCT
ejpam-3085	210	31	a	a	DET
ejpam-3085	210	32	∗	∗	NOUN
ejpam-3085	210	33	a	a	X
ejpam-3085	210	34	]	]	X
ejpam-3085	210	35	is	be	AUX
ejpam-3085	210	36	weakly	weakly	ADV
ejpam-3085	210	37	prime	prime	ADJ
ejpam-3085	210	38	,	,	PUNCT
ejpam-3085	210	39	we	we	PRON
ejpam-3085	210	40	have	have	VERB
ejpam-3085	210	41	a	a	DET
ejpam-3085	210	42	⊆	⊆	NUM
ejpam-3085	210	43	(	(	PUNCT
ejpam-3085	210	44	a	a	DET
ejpam-3085	210	45	∗	∗	NOUN
ejpam-3085	210	46	a	a	X
ejpam-3085	210	47	]	]	X
ejpam-3085	210	48	⊆	⊆	NUM
ejpam-3085	210	49	(	(	PUNCT
ejpam-3085	210	50	a	a	DET
ejpam-3085	210	51	∗	∗	NOUN
ejpam-3085	210	52	h	h	NOUN
ejpam-3085	210	53	]	]	X
ejpam-3085	210	54	⊆	⊆	NUM
ejpam-3085	210	55	(	(	PUNCT
ejpam-3085	210	56	a	a	X
ejpam-3085	210	57	]	]	X
ejpam-3085	210	58	=	=	SYM
ejpam-3085	210	59	a	a	NOUN
ejpam-3085	210	60	,	,	PUNCT
ejpam-3085	210	61	so	so	SCONJ
ejpam-3085	210	62	a	a	PRON
ejpam-3085	210	63	=	=	X
ejpam-3085	210	64	(	(	PUNCT
ejpam-3085	210	65	a	a	DET
ejpam-3085	210	66	∗	∗	NOUN
ejpam-3085	210	67	a	a	X
ejpam-3085	210	68	]	]	X
ejpam-3085	210	69	.	.	PUNCT
ejpam-3085	211	1	let	let	VERB
ejpam-3085	211	2	now	now	ADV
ejpam-3085	211	3	a	a	PRON
ejpam-3085	211	4	,	,	PUNCT
ejpam-3085	211	5	b	b	NOUN
ejpam-3085	211	6	be	be	AUX
ejpam-3085	211	7	ideals	ideal	NOUN
ejpam-3085	211	8	of	of	ADP
ejpam-3085	211	9	h.	h.	PROPN
ejpam-3085	211	10	then	then	ADV
ejpam-3085	211	11	a	a	DET
ejpam-3085	211	12	⊆	⊆	NUM
ejpam-3085	211	13	b	b	NOUN
ejpam-3085	211	14	or	or	CCONJ
ejpam-3085	211	15	b	b	NOUN
ejpam-3085	211	16	⊆	⊆	NUM
ejpam-3085	211	17	a.	a.	NOUN
ejpam-3085	211	18	indeed	indeed	ADV
ejpam-3085	211	19	:	:	PUNCT
ejpam-3085	211	20	by	by	ADP
ejpam-3085	211	21	corollary	corollary	ADJ
ejpam-3085	211	22	15	15	NUM
ejpam-3085	211	23	,	,	PUNCT
ejpam-3085	211	24	the	the	DET
ejpam-3085	211	25	set	set	NOUN
ejpam-3085	211	26	(	(	PUNCT
ejpam-3085	211	27	a	a	DET
ejpam-3085	211	28	∗	∗	NOUN
ejpam-3085	211	29	b	b	NOUN
ejpam-3085	211	30	]	]	X
ejpam-3085	211	31	is	be	AUX
ejpam-3085	211	32	an	an	DET
ejpam-3085	211	33	ideal	ideal	NOUN
ejpam-3085	211	34	of	of	ADP
ejpam-3085	211	35	h.	h.	PROPN
ejpam-3085	211	36	since	since	SCONJ
ejpam-3085	211	37	a	a	DET
ejpam-3085	211	38	∗b	∗b	PROPN
ejpam-3085	211	39	⊆	⊆	X
ejpam-3085	211	40	(	(	PUNCT
ejpam-3085	211	41	a	a	DET
ejpam-3085	211	42	∗b	∗b	NOUN
ejpam-3085	211	43	]	]	X
ejpam-3085	211	44	and	and	CCONJ
ejpam-3085	211	45	(	(	PUNCT
ejpam-3085	211	46	a	a	DET
ejpam-3085	211	47	∗b	∗b	NOUN
ejpam-3085	211	48	]	]	PUNCT
ejpam-3085	211	49	is	be	AUX
ejpam-3085	211	50	weakly	weakly	ADV
ejpam-3085	211	51	prime	prime	ADJ
ejpam-3085	211	52	,	,	PUNCT
ejpam-3085	211	53	we	we	PRON
ejpam-3085	211	54	have	have	VERB
ejpam-3085	211	55	a	a	DET
ejpam-3085	211	56	⊆	⊆	NUM
ejpam-3085	211	57	(	(	PUNCT
ejpam-3085	211	58	a	a	DET
ejpam-3085	211	59	∗b	∗b	NOUN
ejpam-3085	211	60	]	]	X
ejpam-3085	211	61	⊆	⊆	NUM
ejpam-3085	211	62	(	(	PUNCT
ejpam-3085	211	63	h	h	NOUN
ejpam-3085	211	64	∗b	∗b	PROPN
ejpam-3085	211	65	]	]	X
ejpam-3085	212	1	⊆	⊆	NUM
ejpam-3085	212	2	(	(	PUNCT
ejpam-3085	212	3	b	b	NOUN
ejpam-3085	212	4	]	]	X
ejpam-3085	212	5	=	=	SYM
ejpam-3085	212	6	b	b	PROPN
ejpam-3085	212	7	or	or	CCONJ
ejpam-3085	212	8	b	b	NOUN
ejpam-3085	212	9	⊆	⊆	NUM
ejpam-3085	212	10	(	(	PUNCT
ejpam-3085	212	11	a	a	DET
ejpam-3085	212	12	∗b	∗b	NOUN
ejpam-3085	212	13	]	]	X
ejpam-3085	212	14	⊆	⊆	NUM
ejpam-3085	212	15	(	(	PUNCT
ejpam-3085	212	16	a	a	DET
ejpam-3085	212	17	∗h	∗h	NOUN
ejpam-3085	212	18	]	]	X
ejpam-3085	212	19	⊆	⊆	NUM
ejpam-3085	212	20	(	(	PUNCT
ejpam-3085	212	21	a	a	X
ejpam-3085	212	22	]	]	X
ejpam-3085	212	23	=	=	PUNCT
ejpam-3085	212	24	a.	a.	NOUN
ejpam-3085	212	25	⇐	⇐	NOUN
ejpam-3085	212	26	=	=	PRON
ejpam-3085	212	27	.	.	PUNCT
ejpam-3085	213	1	let	let	VERB
ejpam-3085	213	2	t	t	NOUN
ejpam-3085	213	3	be	be	AUX
ejpam-3085	213	4	an	an	DET
ejpam-3085	213	5	ideal	ideal	NOUN
ejpam-3085	213	6	of	of	ADP
ejpam-3085	213	7	h	h	NOUN
ejpam-3085	213	8	and	and	CCONJ
ejpam-3085	214	1	a	a	DET
ejpam-3085	214	2	,	,	PUNCT
ejpam-3085	214	3	b	b	PROPN
ejpam-3085	214	4	ideals	ideal	NOUN
ejpam-3085	214	5	of	of	ADP
ejpam-3085	214	6	h	h	NOUN
ejpam-3085	214	7	such	such	ADJ
ejpam-3085	214	8	that	that	SCONJ
ejpam-3085	214	9	a	a	DET
ejpam-3085	214	10	∗	∗	NOUN
ejpam-3085	214	11	b	b	NOUN
ejpam-3085	214	12	⊆	⊆	NUM
ejpam-3085	214	13	t	t	NOUN
ejpam-3085	214	14	.	.	PUNCT
ejpam-3085	215	1	since	since	SCONJ
ejpam-3085	215	2	the	the	DET
ejpam-3085	215	3	ideals	ideal	NOUN
ejpam-3085	215	4	of	of	ADP
ejpam-3085	215	5	h	h	NOUN
ejpam-3085	215	6	are	be	AUX
ejpam-3085	215	7	idempotent	idempotent	ADJ
ejpam-3085	215	8	,	,	PUNCT
ejpam-3085	215	9	by	by	ADP
ejpam-3085	215	10	theorem	theorem	NOUN
ejpam-3085	215	11	9	9	NUM
ejpam-3085	215	12	,	,	PUNCT
ejpam-3085	215	13	we	we	PRON
ejpam-3085	215	14	have	have	VERB
ejpam-3085	215	15	a	a	DET
ejpam-3085	215	16	∩	∩	ADJ
ejpam-3085	215	17	b	b	NOUN
ejpam-3085	215	18	=	=	SYM
ejpam-3085	215	19	(	(	PUNCT
ejpam-3085	215	20	a	a	DET
ejpam-3085	215	21	∗	∗	NOUN
ejpam-3085	215	22	b	b	NOUN
ejpam-3085	215	23	]	]	PUNCT
ejpam-3085	215	24	.	.	PUNCT
ejpam-3085	216	1	by	by	ADP
ejpam-3085	216	2	hypothesis	hypothesis	NOUN
ejpam-3085	216	3	,	,	PUNCT
ejpam-3085	216	4	we	we	PRON
ejpam-3085	216	5	have	have	VERB
ejpam-3085	216	6	a	a	DET
ejpam-3085	216	7	⊆	⊆	NUM
ejpam-3085	216	8	b	b	NOUN
ejpam-3085	216	9	or	or	CCONJ
ejpam-3085	216	10	b	b	NOUN
ejpam-3085	216	11	⊆	⊆	NUM
ejpam-3085	216	12	a.	a.	NOUN
ejpam-3085	216	13	if	if	SCONJ
ejpam-3085	216	14	a	a	DET
ejpam-3085	216	15	⊆	⊆	NUM
ejpam-3085	216	16	b	b	NOUN
ejpam-3085	216	17	,	,	PUNCT
ejpam-3085	216	18	then	then	ADV
ejpam-3085	216	19	we	we	PRON
ejpam-3085	216	20	have	have	VERB
ejpam-3085	216	21	a	a	DET
ejpam-3085	216	22	=	=	X
ejpam-3085	216	23	a∩b	a∩b	X
ejpam-3085	216	24	=	=	PUNCT
ejpam-3085	216	25	(	(	PUNCT
ejpam-3085	216	26	a∗b	a∗b	PROPN
ejpam-3085	216	27	]	]	X
ejpam-3085	216	28	⊆	⊆	NUM
ejpam-3085	216	29	(	(	PUNCT
ejpam-3085	216	30	t	t	NOUN
ejpam-3085	216	31	]	]	PUNCT
ejpam-3085	217	1	=	=	PUNCT
ejpam-3085	217	2	t.	t.	NOUN
ejpam-3085	217	3	if	if	SCONJ
ejpam-3085	217	4	b	b	PROPN
ejpam-3085	217	5	⊆	⊆	SYM
ejpam-3085	217	6	a	a	PRON
ejpam-3085	217	7	,	,	PUNCT
ejpam-3085	217	8	then	then	ADV
ejpam-3085	217	9	b	b	X
ejpam-3085	217	10	=	=	PUNCT
ejpam-3085	217	11	a	a	DET
ejpam-3085	217	12	∩b	∩b	NOUN
ejpam-3085	217	13	=	=	PUNCT
ejpam-3085	217	14	(	(	PUNCT
ejpam-3085	217	15	a	a	DET
ejpam-3085	217	16	∗b	∗b	NOUN
ejpam-3085	217	17	]	]	X
ejpam-3085	217	18	⊆	⊆	NUM
ejpam-3085	217	19	t	t	NOUN
ejpam-3085	217	20	,	,	PUNCT
ejpam-3085	217	21	so	so	ADV
ejpam-3085	217	22	t	t	PROPN
ejpam-3085	217	23	is	be	AUX
ejpam-3085	217	24	weakly	weakly	ADV
ejpam-3085	217	25	prime	prime	ADJ
ejpam-3085	217	26	.	.	PUNCT
ejpam-3085	218	1	�	�	PROPN
ejpam-3085	218	2	n.	n.	PROPN
ejpam-3085	218	3	kehayopulu	kehayopulu	PROPN
ejpam-3085	218	4	/	/	SYM
ejpam-3085	218	5	eur	eur	PROPN
ejpam-3085	218	6	.	.	PUNCT
ejpam-3085	219	1	j.	j.	PROPN
ejpam-3085	219	2	pure	pure	PROPN
ejpam-3085	219	3	appl	appl	PROPN
ejpam-3085	219	4	.	.	PROPN
ejpam-3085	219	5	math	math	PROPN
ejpam-3085	219	6	,	,	PUNCT
ejpam-3085	219	7	11	11	NUM
ejpam-3085	219	8	(	(	PUNCT
ejpam-3085	219	9	1	1	NUM
ejpam-3085	219	10	)	)	PUNCT
ejpam-3085	219	11	(	(	PUNCT
ejpam-3085	219	12	2018	2018	NUM
ejpam-3085	219	13	)	)	PUNCT
ejpam-3085	219	14	,	,	PUNCT
ejpam-3085	219	15	10	10	NUM
ejpam-3085	219	16	-	-	SYM
ejpam-3085	219	17	22	22	NUM
ejpam-3085	219	18	17	17	NUM
ejpam-3085	219	19	this	this	PRON
ejpam-3085	219	20	is	be	AUX
ejpam-3085	219	21	the	the	DET
ejpam-3085	219	22	notion	notion	NOUN
ejpam-3085	219	23	of	of	ADP
ejpam-3085	219	24	an	an	DET
ejpam-3085	219	25	intra	intra	ADJ
ejpam-3085	219	26	-	-	ADJ
ejpam-3085	219	27	regular	regular	ADJ
ejpam-3085	219	28	ordered	order	VERB
ejpam-3085	219	29	semigroup	semigroup	NOUN
ejpam-3085	219	30	introduced	introduce	VERB
ejpam-3085	219	31	by	by	ADP
ejpam-3085	219	32	kehayopulu	kehayopulu	VERB
ejpam-3085	219	33	in	in	ADP
ejpam-3085	219	34	[	[	X
ejpam-3085	219	35	5	5	NUM
ejpam-3085	219	36	]	]	PUNCT
ejpam-3085	219	37	:	:	PUNCT
ejpam-3085	219	38	an	an	DET
ejpam-3085	219	39	ordered	order	VERB
ejpam-3085	219	40	semigroup	semigroup	NOUN
ejpam-3085	219	41	(	(	PUNCT
ejpam-3085	219	42	s	s	PROPN
ejpam-3085	219	43	,	,	PUNCT
ejpam-3085	219	44	·	·	PUNCT
ejpam-3085	219	45	,	,	PUNCT
ejpam-3085	219	46	≤	≤	NUM
ejpam-3085	219	47	)	)	PUNCT
ejpam-3085	219	48	is	be	AUX
ejpam-3085	219	49	called	call	VERB
ejpam-3085	219	50	intra	intra	ADJ
ejpam-3085	219	51	-	-	ADJ
ejpam-3085	219	52	regular	regular	ADJ
ejpam-3085	219	53	if	if	SCONJ
ejpam-3085	219	54	for	for	SCONJ
ejpam-3085	219	55	every	every	DET
ejpam-3085	219	56	a	a	DET
ejpam-3085	219	57	∈	∈	NOUN
ejpam-3085	219	58	s	s	VERB
ejpam-3085	219	59	there	there	PRON
ejpam-3085	219	60	exist	exist	VERB
ejpam-3085	219	61	x	x	NOUN
ejpam-3085	219	62	,	,	PUNCT
ejpam-3085	219	63	y	y	PROPN
ejpam-3085	219	64	∈	∈	PROPN
ejpam-3085	219	65	s	s	VERB
ejpam-3085	219	66	such	such	ADJ
ejpam-3085	219	67	that	that	SCONJ
ejpam-3085	219	68	a	a	DET
ejpam-3085	219	69	≤	≤	NOUN
ejpam-3085	219	70	xa2y	xa2y	ADV
ejpam-3085	219	71	,	,	PUNCT
ejpam-3085	219	72	that	that	PRON
ejpam-3085	219	73	is	be	AUX
ejpam-3085	219	74	if	if	SCONJ
ejpam-3085	219	75	a	a	DET
ejpam-3085	219	76	∈	∈	PROPN
ejpam-3085	219	77	(	(	PUNCT
ejpam-3085	219	78	sa2s	sa2s	NOUN
ejpam-3085	219	79	]	]	PUNCT
ejpam-3085	219	80	for	for	ADP
ejpam-3085	219	81	every	every	DET
ejpam-3085	219	82	a	a	DET
ejpam-3085	219	83	∈	∈	PROPN
ejpam-3085	219	84	s	s	NOUN
ejpam-3085	219	85	,	,	PUNCT
ejpam-3085	219	86	equivalently	equivalently	ADV
ejpam-3085	219	87	if	if	SCONJ
ejpam-3085	219	88	a	a	DET
ejpam-3085	219	89	⊆	⊆	NUM
ejpam-3085	219	90	(	(	PUNCT
ejpam-3085	219	91	sa2s	sa2s	NOUN
ejpam-3085	219	92	]	]	PUNCT
ejpam-3085	219	93	for	for	ADP
ejpam-3085	219	94	every	every	DET
ejpam-3085	219	95	a	a	DET
ejpam-3085	219	96	⊆	⊆	NUM
ejpam-3085	219	97	s.	s.	NOUN
ejpam-3085	219	98	this	this	DET
ejpam-3085	219	99	concept	concept	NOUN
ejpam-3085	219	100	can	can	AUX
ejpam-3085	219	101	be	be	AUX
ejpam-3085	219	102	naturally	naturally	ADV
ejpam-3085	219	103	transferred	transfer	VERB
ejpam-3085	219	104	to	to	ADP
ejpam-3085	219	105	ordered	order	VERB
ejpam-3085	219	106	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	219	107	in	in	ADP
ejpam-3085	219	108	the	the	DET
ejpam-3085	219	109	following	follow	VERB
ejpam-3085	219	110	definition	definition	NOUN
ejpam-3085	219	111	.	.	PUNCT
ejpam-3085	220	1	definition	definition	NOUN
ejpam-3085	220	2	20	20	NUM
ejpam-3085	220	3	.	.	PUNCT
ejpam-3085	221	1	an	an	DET
ejpam-3085	221	2	ordered	order	VERB
ejpam-3085	221	3	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	221	4	(	(	PUNCT
ejpam-3085	221	5	h	h	NOUN
ejpam-3085	221	6	,	,	PUNCT
ejpam-3085	221	7	◦	◦	NOUN
ejpam-3085	221	8	,	,	PUNCT
ejpam-3085	221	9	≤	≤	NUM
ejpam-3085	221	10	)	)	PUNCT
ejpam-3085	221	11	is	be	AUX
ejpam-3085	221	12	called	call	VERB
ejpam-3085	221	13	intra	intra	ADJ
ejpam-3085	221	14	-	-	ADJ
ejpam-3085	221	15	regular	regular	ADJ
ejpam-3085	221	16	if	if	SCONJ
ejpam-3085	221	17	for	for	ADP
ejpam-3085	221	18	every	every	DET
ejpam-3085	221	19	a	a	DET
ejpam-3085	221	20	∈	∈	PROPN
ejpam-3085	221	21	h	h	NOUN
ejpam-3085	221	22	there	there	PRON
ejpam-3085	221	23	exist	exist	VERB
ejpam-3085	221	24	x	x	NOUN
ejpam-3085	221	25	,	,	PUNCT
ejpam-3085	221	26	y	y	PROPN
ejpam-3085	221	27	∈	∈	PROPN
ejpam-3085	221	28	h	h	NOUN
ejpam-3085	221	29	such	such	ADJ
ejpam-3085	221	30	that	that	SCONJ
ejpam-3085	221	31	{	{	PUNCT
ejpam-3085	221	32	a	a	DET
ejpam-3085	221	33	}	}	PUNCT
ejpam-3085	221	34	�	�	PROPN
ejpam-3085	221	35	(	(	PUNCT
ejpam-3085	221	36	x	x	SYM
ejpam-3085	221	37	◦	◦	VERB
ejpam-3085	221	38	a	a	X
ejpam-3085	221	39	)	)	PUNCT
ejpam-3085	221	40	∗	∗	NOUN
ejpam-3085	221	41	(	(	PUNCT
ejpam-3085	221	42	a	a	DET
ejpam-3085	221	43	◦	◦	NOUN
ejpam-3085	221	44	y	y	PROPN
ejpam-3085	221	45	)	)	PUNCT
ejpam-3085	221	46	,	,	PUNCT
ejpam-3085	221	47	that	that	ADV
ejpam-3085	221	48	is	is	ADV
ejpam-3085	221	49	,	,	PUNCT
ejpam-3085	221	50	for	for	ADP
ejpam-3085	221	51	every	every	DET
ejpam-3085	221	52	a	a	DET
ejpam-3085	221	53	∈	∈	PROPN
ejpam-3085	221	54	h	h	NOUN
ejpam-3085	221	55	there	there	PRON
ejpam-3085	221	56	exist	exist	VERB
ejpam-3085	221	57	x	x	NOUN
ejpam-3085	221	58	,	,	PUNCT
ejpam-3085	221	59	y	y	PROPN
ejpam-3085	221	60	,	,	PUNCT
ejpam-3085	221	61	t	t	PROPN
ejpam-3085	221	62	∈	∈	PROPN
ejpam-3085	221	63	h	h	NOUN
ejpam-3085	221	64	such	such	ADJ
ejpam-3085	221	65	that	that	SCONJ
ejpam-3085	221	66	t	t	PROPN
ejpam-3085	221	67	∈	∈	PROPN
ejpam-3085	221	68	(	(	PUNCT
ejpam-3085	221	69	x	x	SYM
ejpam-3085	221	70	◦	◦	VERB
ejpam-3085	221	71	a	a	X
ejpam-3085	221	72	)	)	PUNCT
ejpam-3085	221	73	∗	∗	NOUN
ejpam-3085	221	74	(	(	PUNCT
ejpam-3085	221	75	a	a	DET
ejpam-3085	221	76	◦	◦	NOUN
ejpam-3085	221	77	y	y	NOUN
ejpam-3085	221	78	)	)	PUNCT
ejpam-3085	221	79	and	and	CCONJ
ejpam-3085	221	80	a	a	DET
ejpam-3085	221	81	≤	≤	ADJ
ejpam-3085	221	82	t.	t.	NOUN
ejpam-3085	221	83	instead	instead	ADV
ejpam-3085	221	84	of	of	ADP
ejpam-3085	221	85	writing	write	VERB
ejpam-3085	221	86	(	(	PUNCT
ejpam-3085	221	87	x	x	SYM
ejpam-3085	221	88	◦	◦	VERB
ejpam-3085	221	89	a	a	X
ejpam-3085	221	90	)	)	PUNCT
ejpam-3085	221	91	∗	∗	NOUN
ejpam-3085	221	92	(	(	PUNCT
ejpam-3085	221	93	a	a	DET
ejpam-3085	221	94	◦	◦	NOUN
ejpam-3085	221	95	y	y	PROPN
ejpam-3085	221	96	)	)	PUNCT
ejpam-3085	221	97	,	,	PUNCT
ejpam-3085	221	98	we	we	PRON
ejpam-3085	221	99	can	can	AUX
ejpam-3085	221	100	clearly	clearly	ADV
ejpam-3085	221	101	write	write	VERB
ejpam-3085	221	102	{	{	PUNCT
ejpam-3085	221	103	x	x	NOUN
ejpam-3085	221	104	}	}	PUNCT
ejpam-3085	221	105	∗	∗	NOUN
ejpam-3085	221	106	(	(	PUNCT
ejpam-3085	221	107	a	a	DET
ejpam-3085	221	108	◦	◦	NOUN
ejpam-3085	221	109	a	a	X
ejpam-3085	221	110	)	)	PUNCT
ejpam-3085	221	111	∗	∗	NOUN
ejpam-3085	221	112	{	{	PUNCT
ejpam-3085	221	113	y	y	NOUN
ejpam-3085	221	114	}	}	PUNCT
ejpam-3085	221	115	or	or	CCONJ
ejpam-3085	221	116	{	{	PUNCT
ejpam-3085	221	117	x	x	NOUN
ejpam-3085	221	118	}	}	PUNCT
ejpam-3085	221	119	∗	∗	NOUN
ejpam-3085	221	120	{	{	PUNCT
ejpam-3085	221	121	a	a	DET
ejpam-3085	221	122	}	}	PUNCT
ejpam-3085	221	123	∗	∗	NOUN
ejpam-3085	221	124	{	{	PUNCT
ejpam-3085	221	125	a	a	DET
ejpam-3085	221	126	}	}	PUNCT
ejpam-3085	221	127	∗	∗	NOUN
ejpam-3085	221	128	{	{	PUNCT
ejpam-3085	221	129	y	y	NOUN
ejpam-3085	221	130	}	}	PUNCT
ejpam-3085	221	131	.	.	PUNCT
ejpam-3085	222	1	in	in	ADP
ejpam-3085	222	2	a	a	DET
ejpam-3085	222	3	similar	similar	ADJ
ejpam-3085	222	4	way	way	NOUN
ejpam-3085	222	5	as	as	ADP
ejpam-3085	222	6	in	in	ADP
ejpam-3085	222	7	proposition	proposition	NOUN
ejpam-3085	222	8	17	17	NUM
ejpam-3085	222	9	we	we	PRON
ejpam-3085	222	10	can	can	AUX
ejpam-3085	222	11	prove	prove	VERB
ejpam-3085	222	12	the	the	DET
ejpam-3085	222	13	following	follow	VERB
ejpam-3085	222	14	proposition	proposition	NOUN
ejpam-3085	222	15	.	.	PUNCT
ejpam-3085	223	1	proposition	proposition	NOUN
ejpam-3085	223	2	21	21	NUM
ejpam-3085	223	3	.	.	PUNCT
ejpam-3085	224	1	let	let	AUX
ejpam-3085	224	2	(	(	PUNCT
ejpam-3085	224	3	h	h	NOUN
ejpam-3085	224	4	,	,	PUNCT
ejpam-3085	224	5	◦	◦	NOUN
ejpam-3085	224	6	,	,	PUNCT
ejpam-3085	224	7	≤	≤	NUM
ejpam-3085	224	8	)	)	PUNCT
ejpam-3085	224	9	be	be	VERB
ejpam-3085	224	10	an	an	DET
ejpam-3085	224	11	ordered	order	VERB
ejpam-3085	224	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	224	13	.	.	PUNCT
ejpam-3085	225	1	the	the	DET
ejpam-3085	225	2	following	follow	VERB
ejpam-3085	225	3	are	be	AUX
ejpam-3085	225	4	equivalent	equivalent	ADJ
ejpam-3085	225	5	:	:	PUNCT
ejpam-3085	225	6	(	(	PUNCT
ejpam-3085	225	7	1	1	X
ejpam-3085	225	8	)	)	PUNCT
ejpam-3085	225	9	h	h	NOUN
ejpam-3085	225	10	is	be	AUX
ejpam-3085	225	11	intra	intra	ADJ
ejpam-3085	225	12	-	-	ADJ
ejpam-3085	225	13	regular	regular	ADJ
ejpam-3085	225	14	.	.	PUNCT
ejpam-3085	226	1	(	(	PUNCT
ejpam-3085	226	2	2	2	X
ejpam-3085	226	3	)	)	PUNCT
ejpam-3085	226	4	a	a	DET
ejpam-3085	226	5	∈	∈	NOUN
ejpam-3085	226	6	(	(	PUNCT
ejpam-3085	226	7	h	h	NOUN
ejpam-3085	226	8	∗	∗	NOUN
ejpam-3085	226	9	{	{	PUNCT
ejpam-3085	226	10	a	a	PRON
ejpam-3085	226	11	}	}	PUNCT
ejpam-3085	226	12	∗	∗	NOUN
ejpam-3085	226	13	{	{	PUNCT
ejpam-3085	226	14	a	a	DET
ejpam-3085	226	15	}	}	PUNCT
ejpam-3085	226	16	∗h	∗h	NOUN
ejpam-3085	226	17	]	]	PUNCT
ejpam-3085	226	18	for	for	ADP
ejpam-3085	226	19	every	every	DET
ejpam-3085	226	20	a	a	DET
ejpam-3085	226	21	∈	∈	PROPN
ejpam-3085	226	22	h.	h.	NOUN
ejpam-3085	226	23	(	(	PUNCT
ejpam-3085	226	24	3	3	X
ejpam-3085	226	25	)	)	PUNCT
ejpam-3085	226	26	a	a	DET
ejpam-3085	226	27	⊆	⊆	NUM
ejpam-3085	226	28	(	(	PUNCT
ejpam-3085	226	29	h	h	NOUN
ejpam-3085	226	30	∗a	∗a	ADJ
ejpam-3085	226	31	∗a	∗a	ADJ
ejpam-3085	226	32	∗h	∗h	NOUN
ejpam-3085	226	33	]	]	PUNCT
ejpam-3085	226	34	for	for	ADP
ejpam-3085	226	35	every	every	DET
ejpam-3085	226	36	nonempty	nonempty	NOUN
ejpam-3085	226	37	subset	subset	VERB
ejpam-3085	226	38	a	a	PRON
ejpam-3085	226	39	of	of	ADP
ejpam-3085	226	40	h.	h.	NOUN
ejpam-3085	226	41	proposition	proposition	NOUN
ejpam-3085	226	42	22	22	NUM
ejpam-3085	226	43	.	.	PUNCT
ejpam-3085	227	1	if	if	SCONJ
ejpam-3085	227	2	(	(	PUNCT
ejpam-3085	227	3	h	h	NOUN
ejpam-3085	227	4	,	,	PUNCT
ejpam-3085	227	5	◦	◦	NOUN
ejpam-3085	227	6	,	,	PUNCT
ejpam-3085	227	7	≤	≤	NUM
ejpam-3085	227	8	)	)	PUNCT
ejpam-3085	227	9	is	be	AUX
ejpam-3085	227	10	an	an	DET
ejpam-3085	227	11	ordered	order	VERB
ejpam-3085	227	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	227	13	then	then	ADV
ejpam-3085	227	14	,	,	PUNCT
ejpam-3085	227	15	for	for	SCONJ
ejpam-3085	227	16	every	every	DET
ejpam-3085	227	17	nonempty	nonempty	NOUN
ejpam-3085	227	18	subset	subset	VERB
ejpam-3085	227	19	a	a	PRON
ejpam-3085	227	20	of	of	ADP
ejpam-3085	227	21	h	h	NOUN
ejpam-3085	227	22	,	,	PUNCT
ejpam-3085	227	23	the	the	DET
ejpam-3085	227	24	set	set	NOUN
ejpam-3085	227	25	(	(	PUNCT
ejpam-3085	227	26	h	h	NOUN
ejpam-3085	227	27	∗a	∗a	ADJ
ejpam-3085	227	28	∗h	∗h	NOUN
ejpam-3085	227	29	]	]	PUNCT
ejpam-3085	227	30	is	be	AUX
ejpam-3085	227	31	an	an	DET
ejpam-3085	227	32	ideal	ideal	NOUN
ejpam-3085	227	33	of	of	ADP
ejpam-3085	227	34	h.	h.	NOUN
ejpam-3085	227	35	proof	proof	NOUN
ejpam-3085	227	36	.	.	PUNCT
ejpam-3085	228	1	the	the	DET
ejpam-3085	228	2	set	set	NOUN
ejpam-3085	228	3	(	(	PUNCT
ejpam-3085	228	4	h	h	NOUN
ejpam-3085	228	5	∗a	∗a	ADJ
ejpam-3085	228	6	∗h	∗h	NOUN
ejpam-3085	228	7	]	]	PUNCT
ejpam-3085	228	8	is	be	AUX
ejpam-3085	228	9	a	a	DET
ejpam-3085	228	10	nonempty	nonempty	ADJ
ejpam-3085	228	11	subset	subset	NOUN
ejpam-3085	228	12	of	of	ADP
ejpam-3085	228	13	h	h	NOUN
ejpam-3085	228	14	,	,	PUNCT
ejpam-3085	228	15	and	and	CCONJ
ejpam-3085	228	16	we	we	PRON
ejpam-3085	228	17	have	have	VERB
ejpam-3085	228	18	(	(	PUNCT
ejpam-3085	228	19	h	h	NOUN
ejpam-3085	228	20	∗a	∗a	ADJ
ejpam-3085	228	21	∗h	∗h	NOUN
ejpam-3085	228	22	]	]	PUNCT
ejpam-3085	228	23	∗h	∗h	NOUN
ejpam-3085	228	24	=	=	SYM
ejpam-3085	228	25	(	(	PUNCT
ejpam-3085	229	1	h	h	NOUN
ejpam-3085	229	2	∗a	∗a	ADJ
ejpam-3085	229	3	∗h	∗h	NOUN
ejpam-3085	229	4	]	]	PUNCT
ejpam-3085	229	5	∗	∗	NOUN
ejpam-3085	229	6	(	(	PUNCT
ejpam-3085	229	7	h	h	X
ejpam-3085	229	8	]	]	X
ejpam-3085	229	9	⊆	⊆	NUM
ejpam-3085	229	10	(	(	PUNCT
ejpam-3085	229	11	(	(	PUNCT
ejpam-3085	229	12	h	h	NOUN
ejpam-3085	229	13	∗a	∗a	ADJ
ejpam-3085	229	14	∗h	∗h	NOUN
ejpam-3085	229	15	)	)	PUNCT
ejpam-3085	229	16	∗h	∗h	NOUN
ejpam-3085	229	17	]	]	PUNCT
ejpam-3085	229	18	(	(	PUNCT
ejpam-3085	229	19	by	by	ADP
ejpam-3085	229	20	proposition	proposition	NOUN
ejpam-3085	229	21	10	10	NUM
ejpam-3085	229	22	)	)	PUNCT
ejpam-3085	229	23	=	=	SYM
ejpam-3085	230	1	(	(	PUNCT
ejpam-3085	230	2	h	h	NOUN
ejpam-3085	230	3	∗a	∗a	ADJ
ejpam-3085	230	4	∗	∗	NOUN
ejpam-3085	230	5	(	(	PUNCT
ejpam-3085	230	6	h	h	NOUN
ejpam-3085	230	7	∗h	∗h	NOUN
ejpam-3085	230	8	)	)	PUNCT
ejpam-3085	230	9	]	]	PUNCT
ejpam-3085	231	1	=	=	PUNCT
ejpam-3085	231	2	(	(	PUNCT
ejpam-3085	231	3	h	h	NOUN
ejpam-3085	231	4	∗a	∗a	ADJ
ejpam-3085	231	5	∗h	∗h	NOUN
ejpam-3085	231	6	]	]	PUNCT
ejpam-3085	231	7	.	.	PUNCT
ejpam-3085	232	1	similarly	similarly	ADV
ejpam-3085	232	2	,	,	PUNCT
ejpam-3085	232	3	h	h	NOUN
ejpam-3085	232	4	∗	∗	NOUN
ejpam-3085	232	5	(	(	PUNCT
ejpam-3085	232	6	h	h	NOUN
ejpam-3085	232	7	∗	∗	VERB
ejpam-3085	232	8	a	a	DET
ejpam-3085	232	9	∗h	∗h	NOUN
ejpam-3085	232	10	]	]	X
ejpam-3085	232	11	⊆	⊆	NUM
ejpam-3085	232	12	(	(	PUNCT
ejpam-3085	232	13	h	h	NOUN
ejpam-3085	232	14	∗	∗	VERB
ejpam-3085	232	15	a	a	DET
ejpam-3085	232	16	∗h	∗h	NOUN
ejpam-3085	232	17	]	]	PUNCT
ejpam-3085	232	18	,	,	PUNCT
ejpam-3085	232	19	we	we	PRON
ejpam-3085	232	20	also	also	ADV
ejpam-3085	232	21	have	have	VERB
ejpam-3085	232	22	(	(	PUNCT
ejpam-3085	232	23	(	(	PUNCT
ejpam-3085	232	24	h	h	NOUN
ejpam-3085	232	25	∗	∗	VERB
ejpam-3085	232	26	a	a	DET
ejpam-3085	232	27	∗h	∗h	NOUN
ejpam-3085	232	28	]	]	PUNCT
ejpam-3085	232	29	]	]	PUNCT
ejpam-3085	233	1	=	=	SYM
ejpam-3085	233	2	(	(	PUNCT
ejpam-3085	233	3	h	h	NOUN
ejpam-3085	233	4	∗	∗	VERB
ejpam-3085	233	5	a	a	DET
ejpam-3085	233	6	∗h	∗h	NOUN
ejpam-3085	233	7	]	]	PUNCT
ejpam-3085	233	8	(	(	PUNCT
ejpam-3085	233	9	as	as	ADP
ejpam-3085	233	10	(	(	PUNCT
ejpam-3085	233	11	(	(	PUNCT
ejpam-3085	233	12	x	x	X
ejpam-3085	233	13	]	]	X
ejpam-3085	233	14	]	]	X
ejpam-3085	233	15	=	=	SYM
ejpam-3085	233	16	(	(	PUNCT
ejpam-3085	233	17	x	x	X
ejpam-3085	233	18	]	]	X
ejpam-3085	233	19	holds	hold	VERB
ejpam-3085	233	20	for	for	ADP
ejpam-3085	233	21	any	any	DET
ejpam-3085	233	22	subset	subset	NOUN
ejpam-3085	233	23	x	x	PUNCT
ejpam-3085	233	24	of	of	ADP
ejpam-3085	233	25	h	h	NOUN
ejpam-3085	233	26	)	)	PUNCT
ejpam-3085	233	27	.	.	PUNCT
ejpam-3085	234	1	theorem	theorem	VERB
ejpam-3085	234	2	23	23	NUM
ejpam-3085	234	3	.	.	PUNCT
ejpam-3085	235	1	let	let	VERB
ejpam-3085	235	2	h	h	PRON
ejpam-3085	235	3	be	be	AUX
ejpam-3085	235	4	an	an	DET
ejpam-3085	235	5	ordered	order	VERB
ejpam-3085	235	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	235	7	.	.	PUNCT
ejpam-3085	236	1	if	if	SCONJ
ejpam-3085	236	2	the	the	DET
ejpam-3085	236	3	ideals	ideal	NOUN
ejpam-3085	236	4	of	of	ADP
ejpam-3085	236	5	h	h	NOUN
ejpam-3085	236	6	are	be	AUX
ejpam-3085	236	7	weakly	weakly	ADV
ejpam-3085	236	8	prime	prime	ADJ
ejpam-3085	236	9	and	and	CCONJ
ejpam-3085	236	10	semiprime	semiprime	NOUN
ejpam-3085	236	11	,	,	PUNCT
ejpam-3085	236	12	then	then	ADV
ejpam-3085	236	13	they	they	PRON
ejpam-3085	236	14	form	form	VERB
ejpam-3085	236	15	a	a	DET
ejpam-3085	236	16	chain	chain	NOUN
ejpam-3085	236	17	and	and	CCONJ
ejpam-3085	236	18	h	h	NOUN
ejpam-3085	236	19	is	be	AUX
ejpam-3085	236	20	intra	intra	ADJ
ejpam-3085	236	21	-	-	ADJ
ejpam-3085	236	22	regular	regular	ADJ
ejpam-3085	236	23	.	.	PUNCT
ejpam-3085	237	1	“	"	PUNCT
ejpam-3085	237	2	conversely	conversely	ADV
ejpam-3085	237	3	”	"	PUNCT
ejpam-3085	237	4	,	,	PUNCT
ejpam-3085	237	5	if	if	SCONJ
ejpam-3085	237	6	the	the	DET
ejpam-3085	237	7	ideals	ideal	NOUN
ejpam-3085	237	8	of	of	ADP
ejpam-3085	237	9	h	h	NOUN
ejpam-3085	237	10	form	form	VERB
ejpam-3085	237	11	a	a	DET
ejpam-3085	237	12	chain	chain	NOUN
ejpam-3085	237	13	and	and	CCONJ
ejpam-3085	237	14	h	h	NOUN
ejpam-3085	237	15	is	be	AUX
ejpam-3085	237	16	intra	intra	ADJ
ejpam-3085	237	17	-	-	ADJ
ejpam-3085	237	18	regular	regular	ADJ
ejpam-3085	237	19	,	,	PUNCT
ejpam-3085	237	20	then	then	ADV
ejpam-3085	237	21	the	the	DET
ejpam-3085	237	22	ideals	ideal	NOUN
ejpam-3085	237	23	of	of	ADP
ejpam-3085	237	24	h	h	NOUN
ejpam-3085	237	25	are	be	AUX
ejpam-3085	237	26	prime	prime	ADJ
ejpam-3085	237	27	.	.	PUNCT
ejpam-3085	238	1	proof	proof	NOUN
ejpam-3085	238	2	.	.	PUNCT
ejpam-3085	239	1	suppose	suppose	VERB
ejpam-3085	239	2	the	the	DET
ejpam-3085	239	3	ideals	ideal	NOUN
ejpam-3085	239	4	of	of	ADP
ejpam-3085	239	5	h	h	NOUN
ejpam-3085	239	6	are	be	AUX
ejpam-3085	239	7	weakly	weakly	ADV
ejpam-3085	239	8	prime	prime	ADJ
ejpam-3085	239	9	and	and	CCONJ
ejpam-3085	239	10	semiprime	semiprime	NOUN
ejpam-3085	239	11	.	.	PUNCT
ejpam-3085	240	1	since	since	SCONJ
ejpam-3085	240	2	they	they	PRON
ejpam-3085	240	3	are	be	AUX
ejpam-3085	240	4	weakly	weakly	ADV
ejpam-3085	240	5	prime	prime	ADJ
ejpam-3085	240	6	,	,	PUNCT
ejpam-3085	240	7	by	by	ADP
ejpam-3085	240	8	theorem	theorem	NOUN
ejpam-3085	240	9	19	19	NUM
ejpam-3085	240	10	,	,	PUNCT
ejpam-3085	240	11	they	they	PRON
ejpam-3085	240	12	form	form	VERB
ejpam-3085	240	13	a	a	DET
ejpam-3085	240	14	chain	chain	NOUN
ejpam-3085	240	15	.	.	PUNCT
ejpam-3085	241	1	let	let	VERB
ejpam-3085	241	2	now	now	ADV
ejpam-3085	241	3	a	a	DET
ejpam-3085	241	4	∈	∈	PROPN
ejpam-3085	241	5	h.	h.	NOUN
ejpam-3085	241	6	we	we	PRON
ejpam-3085	241	7	have	have	VERB
ejpam-3085	241	8	(	(	PUNCT
ejpam-3085	241	9	{	{	PUNCT
ejpam-3085	241	10	a	a	PRON
ejpam-3085	241	11	}	}	PUNCT
ejpam-3085	241	12	∗	∗	NOUN
ejpam-3085	241	13	{	{	PUNCT
ejpam-3085	241	14	a	a	NOUN
ejpam-3085	241	15	}	}	PUNCT
ejpam-3085	241	16	)	)	PUNCT
ejpam-3085	241	17	∗	∗	NOUN
ejpam-3085	241	18	(	(	PUNCT
ejpam-3085	241	19	{	{	PUNCT
ejpam-3085	241	20	a	a	PRON
ejpam-3085	241	21	}	}	PUNCT
ejpam-3085	241	22	∗	∗	NOUN
ejpam-3085	241	23	{	{	PUNCT
ejpam-3085	241	24	a	a	NOUN
ejpam-3085	241	25	}	}	PUNCT
ejpam-3085	241	26	)	)	PUNCT
ejpam-3085	241	27	⊆	⊆	NUM
ejpam-3085	241	28	(	(	PUNCT
ejpam-3085	241	29	h	h	NOUN
ejpam-3085	241	30	∗	∗	NOUN
ejpam-3085	241	31	{	{	PUNCT
ejpam-3085	241	32	a	a	DET
ejpam-3085	241	33	}	}	PUNCT
ejpam-3085	241	34	∗	∗	NOUN
ejpam-3085	241	35	{	{	PUNCT
ejpam-3085	241	36	a	a	DET
ejpam-3085	241	37	}	}	PUNCT
ejpam-3085	241	38	∗h	∗h	NOUN
ejpam-3085	241	39	]	]	PUNCT
ejpam-3085	241	40	,	,	PUNCT
ejpam-3085	241	41	where	where	SCONJ
ejpam-3085	241	42	(	(	PUNCT
ejpam-3085	241	43	h	h	NOUN
ejpam-3085	241	44	∗	∗	NOUN
ejpam-3085	241	45	{	{	PUNCT
ejpam-3085	241	46	a	a	PRON
ejpam-3085	241	47	}	}	PUNCT
ejpam-3085	241	48	∗	∗	NOUN
ejpam-3085	241	49	{	{	PUNCT
ejpam-3085	241	50	a	a	DET
ejpam-3085	241	51	}	}	PUNCT
ejpam-3085	241	52	∗h	∗h	NOUN
ejpam-3085	241	53	]	]	PUNCT
ejpam-3085	241	54	is	be	AUX
ejpam-3085	241	55	an	an	DET
ejpam-3085	241	56	ideal	ideal	NOUN
ejpam-3085	241	57	of	of	ADP
ejpam-3085	241	58	h.	h.	PROPN
ejpam-3085	241	59	since	since	SCONJ
ejpam-3085	241	60	the	the	DET
ejpam-3085	241	61	ideals	ideal	NOUN
ejpam-3085	241	62	of	of	ADP
ejpam-3085	241	63	h	h	NOUN
ejpam-3085	241	64	are	be	AUX
ejpam-3085	241	65	semiprime	semiprime	ADJ
ejpam-3085	241	66	,	,	PUNCT
ejpam-3085	241	67	we	we	PRON
ejpam-3085	241	68	have	have	VERB
ejpam-3085	241	69	{	{	PUNCT
ejpam-3085	241	70	a	a	DET
ejpam-3085	241	71	}	}	PUNCT
ejpam-3085	241	72	∗	∗	NOUN
ejpam-3085	241	73	{	{	PUNCT
ejpam-3085	241	74	a	a	PRON
ejpam-3085	241	75	}	}	PUNCT
ejpam-3085	241	76	⊆	⊆	NUM
ejpam-3085	241	77	(	(	PUNCT
ejpam-3085	241	78	h	h	NOUN
ejpam-3085	241	79	∗	∗	NOUN
ejpam-3085	241	80	{	{	PUNCT
ejpam-3085	241	81	a	a	DET
ejpam-3085	241	82	}	}	PUNCT
ejpam-3085	241	83	∗	∗	NOUN
ejpam-3085	241	84	{	{	PUNCT
ejpam-3085	241	85	a	a	DET
ejpam-3085	241	86	}	}	PUNCT
ejpam-3085	241	87	∗h	∗h	NOUN
ejpam-3085	241	88	]	]	PUNCT
ejpam-3085	241	89	,	,	PUNCT
ejpam-3085	241	90	and	and	CCONJ
ejpam-3085	241	91	a	a	DET
ejpam-3085	241	92	∈	∈	NOUN
ejpam-3085	241	93	{	{	PUNCT
ejpam-3085	241	94	a	a	NOUN
ejpam-3085	241	95	}	}	PUNCT
ejpam-3085	241	96	⊆	⊆	NUM
ejpam-3085	241	97	(	(	PUNCT
ejpam-3085	241	98	h	h	NOUN
ejpam-3085	241	99	∗	∗	NOUN
ejpam-3085	241	100	{	{	PUNCT
ejpam-3085	241	101	a	a	DET
ejpam-3085	241	102	}	}	PUNCT
ejpam-3085	241	103	∗	∗	NOUN
ejpam-3085	241	104	{	{	PUNCT
ejpam-3085	241	105	a	a	DET
ejpam-3085	241	106	}	}	PUNCT
ejpam-3085	241	107	∗h	∗h	NOUN
ejpam-3085	241	108	]	]	PUNCT
ejpam-3085	241	109	,	,	PUNCT
ejpam-3085	241	110	so	so	CCONJ
ejpam-3085	241	111	h	h	NOUN
ejpam-3085	241	112	is	be	AUX
ejpam-3085	241	113	intra	intra	ADJ
ejpam-3085	241	114	-	-	ADJ
ejpam-3085	241	115	regular	regular	ADJ
ejpam-3085	241	116	.	.	PUNCT
ejpam-3085	242	1	for	for	ADP
ejpam-3085	242	2	the	the	DET
ejpam-3085	242	3	converse	converse	NOUN
ejpam-3085	242	4	statement	statement	NOUN
ejpam-3085	242	5	,	,	PUNCT
ejpam-3085	242	6	suppose	suppose	VERB
ejpam-3085	242	7	the	the	DET
ejpam-3085	242	8	ideals	ideal	NOUN
ejpam-3085	242	9	of	of	ADP
ejpam-3085	242	10	h	h	NOUN
ejpam-3085	242	11	form	form	VERB
ejpam-3085	242	12	a	a	DET
ejpam-3085	242	13	chain	chain	NOUN
ejpam-3085	242	14	and	and	CCONJ
ejpam-3085	242	15	h	h	NOUN
ejpam-3085	242	16	is	be	AUX
ejpam-3085	242	17	intraregular	intraregular	ADJ
ejpam-3085	242	18	.	.	PUNCT
ejpam-3085	243	1	since	since	SCONJ
ejpam-3085	243	2	h	h	PROPN
ejpam-3085	243	3	is	be	AUX
ejpam-3085	243	4	intra	intra	ADJ
ejpam-3085	243	5	-	-	ADJ
ejpam-3085	243	6	regular	regular	ADJ
ejpam-3085	243	7	,	,	PUNCT
ejpam-3085	243	8	the	the	DET
ejpam-3085	243	9	ideals	ideal	NOUN
ejpam-3085	243	10	of	of	ADP
ejpam-3085	243	11	h	h	NOUN
ejpam-3085	243	12	are	be	AUX
ejpam-3085	243	13	semiprime	semiprime	ADJ
ejpam-3085	243	14	.	.	PUNCT
ejpam-3085	244	1	in	in	ADP
ejpam-3085	244	2	fact	fact	NOUN
ejpam-3085	244	3	:	:	PUNCT
ejpam-3085	244	4	let	let	VERB
ejpam-3085	244	5	t	t	NOUN
ejpam-3085	244	6	be	be	AUX
ejpam-3085	244	7	an	an	DET
ejpam-3085	244	8	ideal	ideal	ADJ
ejpam-3085	244	9	n.	n.	NOUN
ejpam-3085	244	10	kehayopulu	kehayopulu	PROPN
ejpam-3085	244	11	/	/	SYM
ejpam-3085	244	12	eur	eur	PROPN
ejpam-3085	244	13	.	.	PUNCT
ejpam-3085	245	1	j.	j.	PROPN
ejpam-3085	245	2	pure	pure	PROPN
ejpam-3085	245	3	appl	appl	PROPN
ejpam-3085	245	4	.	.	PROPN
ejpam-3085	245	5	math	math	PROPN
ejpam-3085	245	6	,	,	PUNCT
ejpam-3085	245	7	11	11	NUM
ejpam-3085	245	8	(	(	PUNCT
ejpam-3085	245	9	1	1	NUM
ejpam-3085	245	10	)	)	PUNCT
ejpam-3085	245	11	(	(	PUNCT
ejpam-3085	245	12	2018	2018	NUM
ejpam-3085	245	13	)	)	PUNCT
ejpam-3085	245	14	,	,	PUNCT
ejpam-3085	245	15	10	10	NUM
ejpam-3085	245	16	-	-	SYM
ejpam-3085	245	17	22	22	NUM
ejpam-3085	245	18	18	18	NUM
ejpam-3085	245	19	of	of	ADP
ejpam-3085	245	20	h	h	NOUN
ejpam-3085	245	21	and	and	CCONJ
ejpam-3085	245	22	a	a	DET
ejpam-3085	245	23	∈	∈	NOUN
ejpam-3085	245	24	h	h	NOUN
ejpam-3085	245	25	such	such	ADJ
ejpam-3085	245	26	that	that	SCONJ
ejpam-3085	245	27	a	a	DET
ejpam-3085	245	28	◦	◦	NOUN
ejpam-3085	245	29	a	a	DET
ejpam-3085	245	30	⊆	⊆	NUM
ejpam-3085	245	31	t	t	NOUN
ejpam-3085	245	32	.	.	PUNCT
ejpam-3085	246	1	then	then	ADV
ejpam-3085	246	2	a	a	DET
ejpam-3085	246	3	∈	∈	PROPN
ejpam-3085	246	4	(	(	PUNCT
ejpam-3085	246	5	h	h	NOUN
ejpam-3085	246	6	∗	∗	NOUN
ejpam-3085	246	7	{	{	PUNCT
ejpam-3085	246	8	a	a	DET
ejpam-3085	246	9	}	}	PUNCT
ejpam-3085	246	10	∗	∗	NOUN
ejpam-3085	246	11	{	{	PUNCT
ejpam-3085	246	12	a	a	DET
ejpam-3085	246	13	}	}	PUNCT
ejpam-3085	246	14	∗h	∗h	NOUN
ejpam-3085	246	15	]	]	PUNCT
ejpam-3085	246	16	=	=	SYM
ejpam-3085	246	17	(	(	PUNCT
ejpam-3085	246	18	h	h	NOUN
ejpam-3085	246	19	∗	∗	NOUN
ejpam-3085	246	20	(	(	PUNCT
ejpam-3085	246	21	a	a	DET
ejpam-3085	246	22	◦	◦	NOUN
ejpam-3085	246	23	a	a	X
ejpam-3085	246	24	)	)	PUNCT
ejpam-3085	246	25	∗h	∗h	NOUN
ejpam-3085	246	26	]	]	PUNCT
ejpam-3085	246	27	⊆	⊆	NUM
ejpam-3085	246	28	(	(	PUNCT
ejpam-3085	246	29	h	h	NOUN
ejpam-3085	246	30	∗	∗	PROPN
ejpam-3085	246	31	t	t	PROPN
ejpam-3085	246	32	∗h	∗h	VERB
ejpam-3085	246	33	]	]	X
ejpam-3085	246	34	⊆	⊆	NUM
ejpam-3085	246	35	(	(	PUNCT
ejpam-3085	246	36	t	t	NOUN
ejpam-3085	246	37	]	]	PUNCT
ejpam-3085	246	38	=	=	SYM
ejpam-3085	246	39	t	t	PROPN
ejpam-3085	246	40	,	,	PUNCT
ejpam-3085	246	41	then	then	ADV
ejpam-3085	246	42	a	a	DET
ejpam-3085	246	43	∈	∈	PROPN
ejpam-3085	246	44	t	t	NOUN
ejpam-3085	246	45	,	,	PUNCT
ejpam-3085	246	46	and	and	CCONJ
ejpam-3085	246	47	t	t	PROPN
ejpam-3085	246	48	is	be	AUX
ejpam-3085	246	49	semiprime	semiprime	NOUN
ejpam-3085	246	50	.	.	PUNCT
ejpam-3085	247	1	since	since	SCONJ
ejpam-3085	247	2	the	the	DET
ejpam-3085	247	3	ideals	ideal	NOUN
ejpam-3085	247	4	of	of	ADP
ejpam-3085	247	5	h	h	NOUN
ejpam-3085	247	6	are	be	AUX
ejpam-3085	247	7	semiprime	semiprime	NOUN
ejpam-3085	247	8	,	,	PUNCT
ejpam-3085	247	9	the	the	DET
ejpam-3085	247	10	following	follow	VERB
ejpam-3085	247	11	two	two	NUM
ejpam-3085	247	12	assertions	assertion	NOUN
ejpam-3085	247	13	are	be	AUX
ejpam-3085	247	14	satisfied	satisfied	ADJ
ejpam-3085	247	15	:	:	PUNCT
ejpam-3085	247	16	(	(	PUNCT
ejpam-3085	247	17	1	1	X
ejpam-3085	247	18	)	)	PUNCT
ejpam-3085	247	19	i(a	i(a	PROPN
ejpam-3085	247	20	)	)	PUNCT
ejpam-3085	247	21	=	=	PRON
ejpam-3085	248	1	(	(	PUNCT
ejpam-3085	248	2	h	h	NOUN
ejpam-3085	248	3	∗a	∗a	ADJ
ejpam-3085	248	4	∗h	∗h	NOUN
ejpam-3085	248	5	]	]	PUNCT
ejpam-3085	248	6	for	for	ADP
ejpam-3085	248	7	every	every	DET
ejpam-3085	248	8	a	a	DET
ejpam-3085	248	9	∈	∈	PROPN
ejpam-3085	248	10	p∗(h	p∗(h	PROPN
ejpam-3085	248	11	)	)	PUNCT
ejpam-3085	248	12	.	.	PUNCT
ejpam-3085	249	1	in	in	ADP
ejpam-3085	249	2	fact	fact	NOUN
ejpam-3085	249	3	:	:	PUNCT
ejpam-3085	249	4	we	we	PRON
ejpam-3085	249	5	have	have	VERB
ejpam-3085	249	6	(	(	PUNCT
ejpam-3085	249	7	a∗a)∗(a∗a	a∗a)∗(a∗a	NOUN
ejpam-3085	249	8	)	)	PUNCT
ejpam-3085	250	1	⊆	⊆	NUM
ejpam-3085	250	2	(	(	PUNCT
ejpam-3085	250	3	h	h	NOUN
ejpam-3085	250	4	∗a∗h	∗a∗h	PROPN
ejpam-3085	250	5	]	]	X
ejpam-3085	250	6	,	,	PUNCT
ejpam-3085	250	7	where	where	SCONJ
ejpam-3085	250	8	(	(	PUNCT
ejpam-3085	250	9	h	h	NOUN
ejpam-3085	250	10	∗a∗h	∗a∗h	PROPN
ejpam-3085	250	11	]	]	X
ejpam-3085	250	12	is	be	AUX
ejpam-3085	250	13	an	an	DET
ejpam-3085	250	14	ideal	ideal	NOUN
ejpam-3085	250	15	of	of	ADP
ejpam-3085	250	16	h.	h.	PROPN
ejpam-3085	250	17	since	since	SCONJ
ejpam-3085	250	18	(	(	PUNCT
ejpam-3085	250	19	h	h	NOUN
ejpam-3085	250	20	∗a∗h	∗a∗h	PROPN
ejpam-3085	250	21	]	]	X
ejpam-3085	250	22	is	be	AUX
ejpam-3085	250	23	semiprime	semiprime	NOUN
ejpam-3085	250	24	,	,	PUNCT
ejpam-3085	250	25	we	we	PRON
ejpam-3085	250	26	have	have	VERB
ejpam-3085	250	27	a	a	DET
ejpam-3085	250	28	∗a	∗a	ADJ
ejpam-3085	250	29	⊆	⊆	NUM
ejpam-3085	250	30	(	(	PUNCT
ejpam-3085	250	31	h	h	NOUN
ejpam-3085	250	32	∗a	∗a	ADJ
ejpam-3085	250	33	∗h	∗h	NOUN
ejpam-3085	250	34	]	]	PUNCT
ejpam-3085	250	35	,	,	PUNCT
ejpam-3085	250	36	and	and	CCONJ
ejpam-3085	250	37	a	a	DET
ejpam-3085	250	38	⊆	⊆	NUM
ejpam-3085	250	39	(	(	PUNCT
ejpam-3085	250	40	h	h	NOUN
ejpam-3085	250	41	∗a	∗a	ADJ
ejpam-3085	250	42	∗h	∗h	NOUN
ejpam-3085	250	43	]	]	PUNCT
ejpam-3085	250	44	,	,	PUNCT
ejpam-3085	250	45	so	so	ADV
ejpam-3085	250	46	i(a	i(a	PROPN
ejpam-3085	250	47	)	)	PUNCT
ejpam-3085	250	48	⊆	⊆	NUM
ejpam-3085	250	49	(	(	PUNCT
ejpam-3085	250	50	h	h	NOUN
ejpam-3085	250	51	∗a	∗a	ADJ
ejpam-3085	250	52	∗h	∗h	NOUN
ejpam-3085	250	53	]	]	PUNCT
ejpam-3085	250	54	.	.	PUNCT
ejpam-3085	251	1	on	on	ADP
ejpam-3085	251	2	the	the	DET
ejpam-3085	251	3	other	other	ADJ
ejpam-3085	251	4	hand	hand	NOUN
ejpam-3085	251	5	,	,	PUNCT
ejpam-3085	251	6	(	(	PUNCT
ejpam-3085	251	7	h	h	NOUN
ejpam-3085	251	8	∗a	∗a	ADJ
ejpam-3085	251	9	∗h	∗h	NOUN
ejpam-3085	251	10	]	]	X
ejpam-3085	251	11	⊆	⊆	NUM
ejpam-3085	251	12	(	(	PUNCT
ejpam-3085	251	13	a	a	DET
ejpam-3085	251	14	∪	∪	X
ejpam-3085	251	15	(	(	PUNCT
ejpam-3085	251	16	h	h	NOUN
ejpam-3085	251	17	∗a	∗a	ADJ
ejpam-3085	251	18	)	)	PUNCT
ejpam-3085	251	19	∪	∪	NOUN
ejpam-3085	251	20	(	(	PUNCT
ejpam-3085	251	21	a	a	DET
ejpam-3085	251	22	∗h	∗h	NOUN
ejpam-3085	251	23	)	)	PUNCT
ejpam-3085	251	24	∪	∪	NOUN
ejpam-3085	251	25	(	(	PUNCT
ejpam-3085	251	26	h	h	NOUN
ejpam-3085	251	27	∗a	∗a	ADJ
ejpam-3085	251	28	∗h	∗h	NOUN
ejpam-3085	251	29	)	)	PUNCT
ejpam-3085	251	30	]	]	PUNCT
ejpam-3085	252	1	=	=	SYM
ejpam-3085	252	2	i(a	i(a	PROPN
ejpam-3085	252	3	)	)	PUNCT
ejpam-3085	252	4	,	,	PUNCT
ejpam-3085	252	5	and	and	CCONJ
ejpam-3085	252	6	condition	condition	NOUN
ejpam-3085	252	7	(	(	PUNCT
ejpam-3085	252	8	1	1	X
ejpam-3085	252	9	)	)	PUNCT
ejpam-3085	252	10	holds	hold	VERB
ejpam-3085	252	11	.	.	PUNCT
ejpam-3085	253	1	(	(	PUNCT
ejpam-3085	253	2	2	2	X
ejpam-3085	253	3	)	)	PUNCT
ejpam-3085	253	4	i(x	i(x	NOUN
ejpam-3085	253	5	◦	◦	NOUN
ejpam-3085	253	6	y	y	NOUN
ejpam-3085	253	7	)	)	PUNCT
ejpam-3085	253	8	=	=	SYM
ejpam-3085	253	9	i(x	i(x	NOUN
ejpam-3085	253	10	)	)	PUNCT
ejpam-3085	253	11	∩	∩	NOUN
ejpam-3085	253	12	i(y	i(y	NOUN
ejpam-3085	253	13	)	)	PUNCT
ejpam-3085	253	14	for	for	ADP
ejpam-3085	253	15	every	every	DET
ejpam-3085	253	16	x	x	PROPN
ejpam-3085	253	17	,	,	PUNCT
ejpam-3085	253	18	y	y	PROPN
ejpam-3085	253	19	∈	∈	PROPN
ejpam-3085	253	20	h.	h.	PROPN
ejpam-3085	254	1	in	in	ADP
ejpam-3085	254	2	fact	fact	NOUN
ejpam-3085	254	3	:	:	PUNCT
ejpam-3085	254	4	let	let	VERB
ejpam-3085	254	5	x	x	PRON
ejpam-3085	254	6	,	,	PUNCT
ejpam-3085	254	7	y	y	PROPN
ejpam-3085	254	8	∈	∈	PROPN
ejpam-3085	254	9	h.	h.	PROPN
ejpam-3085	254	10	since	since	SCONJ
ejpam-3085	254	11	x	x	SYM
ejpam-3085	254	12	◦	◦	VERB
ejpam-3085	254	13	y	y	PROPN
ejpam-3085	254	14	⊆	⊆	NUM
ejpam-3085	254	15	i(x	i(x	NOUN
ejpam-3085	254	16	)	)	PUNCT
ejpam-3085	254	17	∗	∗	NOUN
ejpam-3085	254	18	h	h	NOUN
ejpam-3085	254	19	⊆	⊆	NUM
ejpam-3085	254	20	i(x	i(x	NOUN
ejpam-3085	254	21	)	)	PUNCT
ejpam-3085	254	22	,	,	PUNCT
ejpam-3085	254	23	we	we	PRON
ejpam-3085	254	24	have	have	VERB
ejpam-3085	254	25	i(x	i(x	PROPN
ejpam-3085	254	26	◦	◦	NOUN
ejpam-3085	254	27	y	y	NOUN
ejpam-3085	254	28	)	)	PUNCT
ejpam-3085	254	29	⊆	⊆	NUM
ejpam-3085	254	30	i(x	i(x	NOUN
ejpam-3085	254	31	)	)	PUNCT
ejpam-3085	254	32	.	.	PUNCT
ejpam-3085	255	1	since	since	SCONJ
ejpam-3085	255	2	x	x	INTJ
ejpam-3085	255	3	◦	◦	VERB
ejpam-3085	255	4	y	y	PROPN
ejpam-3085	255	5	⊆	⊆	NUM
ejpam-3085	255	6	h	h	PROPN
ejpam-3085	255	7	∗	∗	NOUN
ejpam-3085	255	8	i(y	i(y	NOUN
ejpam-3085	255	9	)	)	PUNCT
ejpam-3085	255	10	⊆	⊆	NUM
ejpam-3085	255	11	i(y	i(y	NOUN
ejpam-3085	255	12	)	)	PUNCT
ejpam-3085	255	13	,	,	PUNCT
ejpam-3085	255	14	we	we	PRON
ejpam-3085	255	15	have	have	VERB
ejpam-3085	255	16	i(x	i(x	PROPN
ejpam-3085	255	17	◦	◦	NOUN
ejpam-3085	255	18	y	y	NOUN
ejpam-3085	255	19	)	)	PUNCT
ejpam-3085	255	20	⊆	⊆	NUM
ejpam-3085	255	21	i(y	i(y	NOUN
ejpam-3085	255	22	)	)	PUNCT
ejpam-3085	255	23	.	.	PUNCT
ejpam-3085	256	1	thus	thus	ADV
ejpam-3085	256	2	we	we	PRON
ejpam-3085	256	3	get	get	VERB
ejpam-3085	256	4	i(x	i(x	PROPN
ejpam-3085	256	5	◦	◦	NOUN
ejpam-3085	256	6	y	y	NOUN
ejpam-3085	256	7	)	)	PUNCT
ejpam-3085	256	8	⊆	⊆	NUM
ejpam-3085	256	9	i(x	i(x	NOUN
ejpam-3085	256	10	)	)	PUNCT
ejpam-3085	256	11	∩	∩	NOUN
ejpam-3085	256	12	i(y	i(y	NOUN
ejpam-3085	256	13	)	)	PUNCT
ejpam-3085	256	14	.	.	PUNCT
ejpam-3085	257	1	let	let	VERB
ejpam-3085	257	2	now	now	ADV
ejpam-3085	257	3	t	t	NOUN
ejpam-3085	257	4	∈	∈	PROPN
ejpam-3085	257	5	i(x	i(x	PROPN
ejpam-3085	257	6	)	)	PUNCT
ejpam-3085	257	7	∩	∩	NOUN
ejpam-3085	257	8	i(y	i(y	NOUN
ejpam-3085	257	9	)	)	PUNCT
ejpam-3085	257	10	.	.	PUNCT
ejpam-3085	258	1	by	by	ADP
ejpam-3085	258	2	(	(	PUNCT
ejpam-3085	258	3	1	1	NUM
ejpam-3085	258	4	)	)	PUNCT
ejpam-3085	258	5	,	,	PUNCT
ejpam-3085	258	6	we	we	PRON
ejpam-3085	258	7	have	have	VERB
ejpam-3085	258	8	t	t	PROPN
ejpam-3085	258	9	∈	∈	PROPN
ejpam-3085	258	10	(	(	PUNCT
ejpam-3085	258	11	h	h	NOUN
ejpam-3085	258	12	∗{x}∗h	∗{x}∗h	PROPN
ejpam-3085	258	13	]	]	PUNCT
ejpam-3085	258	14	and	and	CCONJ
ejpam-3085	258	15	t	t	PROPN
ejpam-3085	258	16	∈	∈	PROPN
ejpam-3085	258	17	(	(	PUNCT
ejpam-3085	258	18	h	h	NOUN
ejpam-3085	258	19	∗{y}∗h	∗{y}∗h	PROPN
ejpam-3085	258	20	]	]	PUNCT
ejpam-3085	258	21	.	.	PUNCT
ejpam-3085	259	1	then	then	ADV
ejpam-3085	259	2	we	we	PRON
ejpam-3085	259	3	have	have	VERB
ejpam-3085	259	4	t	t	NOUN
ejpam-3085	259	5	≤	≤	NUM
ejpam-3085	259	6	u	u	NOUN
ejpam-3085	259	7	for	for	ADP
ejpam-3085	259	8	some	some	DET
ejpam-3085	259	9	u	u	NOUN
ejpam-3085	259	10	∈	∈	PROPN
ejpam-3085	259	11	h	h	NOUN
ejpam-3085	259	12	∗{x}∗h	∗{x}∗h	PROPN
ejpam-3085	260	1	and	and	CCONJ
ejpam-3085	260	2	t	t	PROPN
ejpam-3085	260	3	≤	≤	NUM
ejpam-3085	260	4	v	v	NOUN
ejpam-3085	260	5	for	for	ADP
ejpam-3085	260	6	some	some	DET
ejpam-3085	260	7	v	v	NOUN
ejpam-3085	260	8	∈	∈	PROPN
ejpam-3085	260	9	h	h	NOUN
ejpam-3085	260	10	∗	∗	NOUN
ejpam-3085	260	11	{	{	PUNCT
ejpam-3085	260	12	y	y	NOUN
ejpam-3085	260	13	}	}	PUNCT
ejpam-3085	260	14	∗h	∗h	NOUN
ejpam-3085	260	15	.	.	PUNCT
ejpam-3085	261	1	since	since	SCONJ
ejpam-3085	261	2	u	u	NOUN
ejpam-3085	261	3	∈	∈	PROPN
ejpam-3085	261	4	(	(	PUNCT
ejpam-3085	261	5	h	h	NOUN
ejpam-3085	261	6	∗	∗	NOUN
ejpam-3085	261	7	{	{	PUNCT
ejpam-3085	261	8	x	x	NOUN
ejpam-3085	261	9	}	}	PUNCT
ejpam-3085	261	10	)	)	PUNCT
ejpam-3085	261	11	∗h	∗h	NOUN
ejpam-3085	261	12	,	,	PUNCT
ejpam-3085	261	13	we	we	PRON
ejpam-3085	261	14	have	have	VERB
ejpam-3085	261	15	u	u	NOUN
ejpam-3085	261	16	∈	∈	PROPN
ejpam-3085	261	17	v	v	ADP
ejpam-3085	261	18	◦	◦	NOUN
ejpam-3085	261	19	b	b	NOUN
ejpam-3085	261	20	for	for	ADP
ejpam-3085	261	21	some	some	DET
ejpam-3085	261	22	v	v	NOUN
ejpam-3085	261	23	∈	∈	PROPN
ejpam-3085	261	24	h	h	NOUN
ejpam-3085	261	25	∗	∗	NOUN
ejpam-3085	261	26	{	{	PUNCT
ejpam-3085	261	27	x	x	NOUN
ejpam-3085	261	28	}	}	PUNCT
ejpam-3085	261	29	,	,	PUNCT
ejpam-3085	261	30	b	b	X
ejpam-3085	261	31	∈	∈	PROPN
ejpam-3085	261	32	h.	h.	NOUN
ejpam-3085	261	33	since	since	SCONJ
ejpam-3085	261	34	v	v	NUM
ejpam-3085	261	35	∈	∈	PROPN
ejpam-3085	261	36	h	h	NOUN
ejpam-3085	261	37	∗	∗	NOUN
ejpam-3085	261	38	{	{	PUNCT
ejpam-3085	261	39	x	x	NOUN
ejpam-3085	261	40	}	}	PUNCT
ejpam-3085	261	41	,	,	PUNCT
ejpam-3085	261	42	we	we	PRON
ejpam-3085	261	43	have	have	VERB
ejpam-3085	261	44	v	v	NUM
ejpam-3085	261	45	∈	∈	PROPN
ejpam-3085	261	46	a	a	DET
ejpam-3085	261	47	◦	◦	NOUN
ejpam-3085	261	48	x	x	PUNCT
ejpam-3085	261	49	for	for	ADP
ejpam-3085	261	50	some	some	DET
ejpam-3085	261	51	a	a	DET
ejpam-3085	261	52	∈	∈	PROPN
ejpam-3085	261	53	h.	h.	NOUN
ejpam-3085	261	54	then	then	ADV
ejpam-3085	261	55	we	we	PRON
ejpam-3085	261	56	have	have	VERB
ejpam-3085	261	57	u	u	NOUN
ejpam-3085	261	58	∈	∈	PROPN
ejpam-3085	261	59	v	v	ADP
ejpam-3085	261	60	◦	◦	NOUN
ejpam-3085	261	61	b	b	NOUN
ejpam-3085	261	62	=	=	SYM
ejpam-3085	261	63	{	{	PUNCT
ejpam-3085	261	64	v	v	NOUN
ejpam-3085	261	65	}	}	PUNCT
ejpam-3085	261	66	∗	∗	NOUN
ejpam-3085	261	67	{	{	PUNCT
ejpam-3085	261	68	b	b	NOUN
ejpam-3085	261	69	}	}	PUNCT
ejpam-3085	261	70	⊆	⊆	NUM
ejpam-3085	261	71	(	(	PUNCT
ejpam-3085	261	72	a	a	DET
ejpam-3085	261	73	◦	◦	NOUN
ejpam-3085	261	74	x	x	SYM
ejpam-3085	261	75	)	)	PUNCT
ejpam-3085	261	76	∗	∗	NOUN
ejpam-3085	261	77	{	{	PUNCT
ejpam-3085	261	78	b	b	NOUN
ejpam-3085	261	79	}	}	PUNCT
ejpam-3085	261	80	=	=	SYM
ejpam-3085	261	81	{	{	PUNCT
ejpam-3085	261	82	a	a	PRON
ejpam-3085	261	83	}	}	PUNCT
ejpam-3085	261	84	∗	∗	NOUN
ejpam-3085	261	85	{	{	PUNCT
ejpam-3085	261	86	x	x	NOUN
ejpam-3085	261	87	}	}	PUNCT
ejpam-3085	261	88	∗	∗	NOUN
ejpam-3085	261	89	{	{	PUNCT
ejpam-3085	261	90	b	b	NOUN
ejpam-3085	261	91	}	}	PUNCT
ejpam-3085	261	92	,	,	PUNCT
ejpam-3085	261	93	where	where	SCONJ
ejpam-3085	261	94	a	a	DET
ejpam-3085	261	95	,	,	PUNCT
ejpam-3085	261	96	b	b	PROPN
ejpam-3085	261	97	∈	∈	PROPN
ejpam-3085	261	98	h.	h.	NOUN
ejpam-3085	261	99	similarly	similarly	ADV
ejpam-3085	261	100	,	,	PUNCT
ejpam-3085	261	101	since	since	SCONJ
ejpam-3085	261	102	v	v	NUM
ejpam-3085	261	103	∈	∈	PROPN
ejpam-3085	261	104	h	h	NOUN
ejpam-3085	261	105	∗	∗	NOUN
ejpam-3085	261	106	{	{	PUNCT
ejpam-3085	261	107	y	y	NOUN
ejpam-3085	261	108	}	}	PUNCT
ejpam-3085	261	109	∗h	∗h	NOUN
ejpam-3085	261	110	,	,	PUNCT
ejpam-3085	261	111	we	we	PRON
ejpam-3085	261	112	have	have	VERB
ejpam-3085	261	113	v	v	NUM
ejpam-3085	261	114	∈	∈	NOUN
ejpam-3085	261	115	{	{	PUNCT
ejpam-3085	261	116	c	c	NOUN
ejpam-3085	261	117	}	}	PUNCT
ejpam-3085	261	118	∗	∗	NOUN
ejpam-3085	261	119	{	{	PUNCT
ejpam-3085	261	120	y	y	NOUN
ejpam-3085	261	121	}	}	PUNCT
ejpam-3085	261	122	∗	∗	NOUN
ejpam-3085	261	123	{	{	PUNCT
ejpam-3085	261	124	d	d	NOUN
ejpam-3085	261	125	}	}	PUNCT
ejpam-3085	261	126	for	for	ADP
ejpam-3085	261	127	some	some	DET
ejpam-3085	261	128	c	c	NOUN
ejpam-3085	261	129	,	,	PUNCT
ejpam-3085	261	130	d	d	PROPN
ejpam-3085	261	131	∈	∈	PROPN
ejpam-3085	261	132	h.	h.	NOUN
ejpam-3085	261	133	hence	hence	ADV
ejpam-3085	261	134	we	we	PRON
ejpam-3085	261	135	obtain	obtain	VERB
ejpam-3085	261	136	t	t	NOUN
ejpam-3085	261	137	≤	≤	NUM
ejpam-3085	261	138	u	u	NOUN
ejpam-3085	261	139	,	,	PUNCT
ejpam-3085	261	140	where	where	SCONJ
ejpam-3085	261	141	u	u	PROPN
ejpam-3085	261	142	∈	∈	PROPN
ejpam-3085	261	143	{	{	PUNCT
ejpam-3085	261	144	a	a	NOUN
ejpam-3085	261	145	}	}	PUNCT
ejpam-3085	261	146	∗	∗	NOUN
ejpam-3085	261	147	{	{	PUNCT
ejpam-3085	261	148	x	x	NOUN
ejpam-3085	261	149	}	}	PUNCT
ejpam-3085	261	150	∗	∗	NOUN
ejpam-3085	261	151	{	{	PUNCT
ejpam-3085	261	152	b	b	NOUN
ejpam-3085	261	153	}	}	PUNCT
ejpam-3085	261	154	for	for	ADP
ejpam-3085	261	155	some	some	DET
ejpam-3085	261	156	a	a	PRON
ejpam-3085	261	157	,	,	PUNCT
ejpam-3085	261	158	b	b	X
ejpam-3085	261	159	∈	∈	PROPN
ejpam-3085	261	160	h	h	NOUN
ejpam-3085	261	161	and	and	CCONJ
ejpam-3085	261	162	t	t	X
ejpam-3085	261	163	≤	≤	NUM
ejpam-3085	261	164	v	v	NOUN
ejpam-3085	261	165	,	,	PUNCT
ejpam-3085	261	166	where	where	SCONJ
ejpam-3085	261	167	v	v	X
ejpam-3085	261	168	∈	∈	PROPN
ejpam-3085	261	169	{	{	PUNCT
ejpam-3085	261	170	c	c	NOUN
ejpam-3085	261	171	}	}	PUNCT
ejpam-3085	261	172	∗	∗	NOUN
ejpam-3085	261	173	{	{	PUNCT
ejpam-3085	261	174	y	y	NOUN
ejpam-3085	261	175	}	}	PUNCT
ejpam-3085	261	176	∗	∗	NOUN
ejpam-3085	261	177	{	{	PUNCT
ejpam-3085	261	178	d	d	NOUN
ejpam-3085	261	179	}	}	PUNCT
ejpam-3085	261	180	for	for	ADP
ejpam-3085	261	181	some	some	DET
ejpam-3085	261	182	c	c	NOUN
ejpam-3085	261	183	,	,	PUNCT
ejpam-3085	261	184	d	d	PROPN
ejpam-3085	261	185	∈	∈	PROPN
ejpam-3085	261	186	h.	h.	NOUN
ejpam-3085	261	187	then	then	ADV
ejpam-3085	261	188	,	,	PUNCT
ejpam-3085	261	189	by	by	ADP
ejpam-3085	261	190	proposition	proposition	NOUN
ejpam-3085	261	191	1	1	NUM
ejpam-3085	261	192	,	,	PUNCT
ejpam-3085	261	193	we	we	PRON
ejpam-3085	261	194	have	have	VERB
ejpam-3085	261	195	t	t	NOUN
ejpam-3085	261	196	◦	◦	NOUN
ejpam-3085	261	197	t	t	PROPN
ejpam-3085	261	198	�	�	PROPN
ejpam-3085	261	199	v	v	ADP
ejpam-3085	261	200	◦	◦	NOUN
ejpam-3085	261	201	u	u	NOUN
ejpam-3085	261	202	=	=	NOUN
ejpam-3085	261	203	{	{	PUNCT
ejpam-3085	261	204	v	v	NOUN
ejpam-3085	261	205	}	}	PUNCT
ejpam-3085	261	206	∗	∗	NOUN
ejpam-3085	261	207	{	{	PUNCT
ejpam-3085	261	208	u	u	NOUN
ejpam-3085	261	209	}	}	PUNCT
ejpam-3085	261	210	⊆	⊆	NUM
ejpam-3085	261	211	{	{	PUNCT
ejpam-3085	261	212	c	c	NOUN
ejpam-3085	261	213	}	}	PUNCT
ejpam-3085	261	214	∗	∗	NOUN
ejpam-3085	261	215	(	(	PUNCT
ejpam-3085	261	216	{	{	PUNCT
ejpam-3085	261	217	y	y	NOUN
ejpam-3085	261	218	}	}	PUNCT
ejpam-3085	261	219	∗	∗	NOUN
ejpam-3085	261	220	{	{	PUNCT
ejpam-3085	261	221	d	d	NOUN
ejpam-3085	261	222	}	}	PUNCT
ejpam-3085	261	223	∗	∗	NOUN
ejpam-3085	261	224	{	{	PUNCT
ejpam-3085	261	225	a	a	PRON
ejpam-3085	261	226	}	}	PUNCT
ejpam-3085	261	227	∗	∗	NOUN
ejpam-3085	261	228	{	{	PUNCT
ejpam-3085	261	229	x	x	NOUN
ejpam-3085	261	230	}	}	PUNCT
ejpam-3085	261	231	)	)	PUNCT
ejpam-3085	261	232	∗	∗	NOUN
ejpam-3085	261	233	{	{	PUNCT
ejpam-3085	261	234	b	b	NOUN
ejpam-3085	261	235	}	}	PUNCT
ejpam-3085	261	236	.	.	PUNCT
ejpam-3085	262	1	on	on	ADP
ejpam-3085	262	2	the	the	DET
ejpam-3085	262	3	other	other	ADJ
ejpam-3085	262	4	hand	hand	NOUN
ejpam-3085	262	5	,	,	PUNCT
ejpam-3085	262	6	{	{	PUNCT
ejpam-3085	262	7	y	y	NOUN
ejpam-3085	262	8	}	}	PUNCT
ejpam-3085	262	9	∗	∗	NOUN
ejpam-3085	262	10	{	{	PUNCT
ejpam-3085	262	11	d	d	NOUN
ejpam-3085	262	12	}	}	PUNCT
ejpam-3085	262	13	∗	∗	NOUN
ejpam-3085	262	14	{	{	PUNCT
ejpam-3085	262	15	a	a	DET
ejpam-3085	262	16	}	}	PUNCT
ejpam-3085	262	17	∗	∗	NOUN
ejpam-3085	262	18	{	{	PUNCT
ejpam-3085	262	19	x	x	NOUN
ejpam-3085	262	20	}	}	PUNCT
ejpam-3085	262	21	⊆	⊆	NUM
ejpam-3085	262	22	i(x	i(x	PROPN
ejpam-3085	262	23	◦	◦	NOUN
ejpam-3085	262	24	y	y	NOUN
ejpam-3085	262	25	)	)	PUNCT
ejpam-3085	262	26	.	.	PUNCT
ejpam-3085	263	1	indeed	indeed	ADV
ejpam-3085	263	2	,	,	PUNCT
ejpam-3085	263	3	we	we	PRON
ejpam-3085	263	4	have	have	VERB
ejpam-3085	263	5	(	(	PUNCT
ejpam-3085	263	6	{	{	PUNCT
ejpam-3085	263	7	y	y	NOUN
ejpam-3085	263	8	}	}	PUNCT
ejpam-3085	263	9	∗	∗	NOUN
ejpam-3085	263	10	{	{	PUNCT
ejpam-3085	263	11	d	d	NOUN
ejpam-3085	263	12	}	}	PUNCT
ejpam-3085	263	13	∗	∗	NOUN
ejpam-3085	263	14	{	{	PUNCT
ejpam-3085	263	15	a	a	DET
ejpam-3085	263	16	}	}	PUNCT
ejpam-3085	263	17	∗	∗	NOUN
ejpam-3085	263	18	{	{	PUNCT
ejpam-3085	263	19	x	x	NOUN
ejpam-3085	263	20	}	}	PUNCT
ejpam-3085	263	21	)	)	PUNCT
ejpam-3085	263	22	∗	∗	NOUN
ejpam-3085	263	23	(	(	PUNCT
ejpam-3085	263	24	{	{	PUNCT
ejpam-3085	263	25	y	y	NOUN
ejpam-3085	263	26	}	}	PUNCT
ejpam-3085	263	27	∗	∗	NOUN
ejpam-3085	263	28	{	{	PUNCT
ejpam-3085	263	29	d	d	NOUN
ejpam-3085	263	30	}	}	PUNCT
ejpam-3085	263	31	∗	∗	NOUN
ejpam-3085	263	32	{	{	PUNCT
ejpam-3085	263	33	a	a	DET
ejpam-3085	263	34	}	}	PUNCT
ejpam-3085	263	35	∗	∗	NOUN
ejpam-3085	263	36	{	{	PUNCT
ejpam-3085	263	37	x	x	NOUN
ejpam-3085	263	38	}	}	PUNCT
ejpam-3085	263	39	)	)	PUNCT
ejpam-3085	263	40	⊆	⊆	NUM
ejpam-3085	263	41	h	h	NOUN
ejpam-3085	263	42	∗	∗	NOUN
ejpam-3085	263	43	{	{	PUNCT
ejpam-3085	263	44	x	x	NOUN
ejpam-3085	263	45	}	}	PUNCT
ejpam-3085	263	46	∗	∗	NOUN
ejpam-3085	263	47	{	{	PUNCT
ejpam-3085	263	48	y	y	NOUN
ejpam-3085	263	49	}	}	PUNCT
ejpam-3085	263	50	∗h	∗h	VERB
ejpam-3085	263	51	⊆	⊆	NUM
ejpam-3085	263	52	(	(	PUNCT
ejpam-3085	263	53	h	h	NOUN
ejpam-3085	263	54	∗	∗	NOUN
ejpam-3085	263	55	(	(	PUNCT
ejpam-3085	263	56	x	x	SYM
ejpam-3085	263	57	◦	◦	VERB
ejpam-3085	263	58	y	y	NOUN
ejpam-3085	263	59	)	)	PUNCT
ejpam-3085	263	60	∗h	∗h	VERB
ejpam-3085	263	61	]	]	PUNCT
ejpam-3085	263	62	=	=	PUNCT
ejpam-3085	264	1	i(x	i(x	PROPN
ejpam-3085	265	1	◦	◦	NOUN
ejpam-3085	265	2	y	y	NOUN
ejpam-3085	265	3	)	)	PUNCT
ejpam-3085	265	4	(	(	PUNCT
ejpam-3085	265	5	by	by	ADP
ejpam-3085	265	6	(	(	PUNCT
ejpam-3085	265	7	1	1	NUM
ejpam-3085	265	8	)	)	PUNCT
ejpam-3085	265	9	)	)	PUNCT
ejpam-3085	265	10	.	.	PUNCT
ejpam-3085	266	1	n.	n.	PROPN
ejpam-3085	266	2	kehayopulu	kehayopulu	PROPN
ejpam-3085	266	3	/	/	SYM
ejpam-3085	266	4	eur	eur	PROPN
ejpam-3085	266	5	.	.	PUNCT
ejpam-3085	267	1	j.	j.	PROPN
ejpam-3085	267	2	pure	pure	PROPN
ejpam-3085	267	3	appl	appl	PROPN
ejpam-3085	267	4	.	.	PROPN
ejpam-3085	267	5	math	math	PROPN
ejpam-3085	267	6	,	,	PUNCT
ejpam-3085	267	7	11	11	NUM
ejpam-3085	267	8	(	(	PUNCT
ejpam-3085	267	9	1	1	NUM
ejpam-3085	267	10	)	)	PUNCT
ejpam-3085	267	11	(	(	PUNCT
ejpam-3085	267	12	2018	2018	NUM
ejpam-3085	267	13	)	)	PUNCT
ejpam-3085	267	14	,	,	PUNCT
ejpam-3085	267	15	10	10	NUM
ejpam-3085	267	16	-	-	SYM
ejpam-3085	267	17	22	22	NUM
ejpam-3085	267	18	19	19	NUM
ejpam-3085	267	19	since	since	SCONJ
ejpam-3085	267	20	i(x	i(x	PROPN
ejpam-3085	267	21	◦	◦	PROPN
ejpam-3085	267	22	y	y	NOUN
ejpam-3085	267	23	)	)	PUNCT
ejpam-3085	267	24	is	be	AUX
ejpam-3085	267	25	semiprime	semiprime	NOUN
ejpam-3085	267	26	,	,	PUNCT
ejpam-3085	267	27	we	we	PRON
ejpam-3085	267	28	have	have	VERB
ejpam-3085	267	29	(	(	PUNCT
ejpam-3085	267	30	{	{	PUNCT
ejpam-3085	267	31	y	y	NOUN
ejpam-3085	267	32	}	}	PUNCT
ejpam-3085	267	33	∗	∗	NOUN
ejpam-3085	267	34	{	{	PUNCT
ejpam-3085	267	35	d	d	NOUN
ejpam-3085	267	36	}	}	PUNCT
ejpam-3085	267	37	∗	∗	NOUN
ejpam-3085	267	38	{	{	PUNCT
ejpam-3085	267	39	a	a	DET
ejpam-3085	267	40	}	}	PUNCT
ejpam-3085	267	41	∗	∗	NOUN
ejpam-3085	267	42	{	{	PUNCT
ejpam-3085	267	43	x	x	NOUN
ejpam-3085	267	44	}	}	PUNCT
ejpam-3085	267	45	)	)	PUNCT
ejpam-3085	267	46	⊆	⊆	NUM
ejpam-3085	267	47	i(x	i(x	PROPN
ejpam-3085	267	48	◦	◦	NOUN
ejpam-3085	267	49	y	y	NOUN
ejpam-3085	267	50	)	)	PUNCT
ejpam-3085	267	51	.	.	PUNCT
ejpam-3085	268	1	since	since	SCONJ
ejpam-3085	268	2	i(x	i(x	PROPN
ejpam-3085	268	3	◦	◦	PROPN
ejpam-3085	268	4	y	y	NOUN
ejpam-3085	268	5	)	)	PUNCT
ejpam-3085	268	6	is	be	AUX
ejpam-3085	268	7	an	an	DET
ejpam-3085	268	8	ideal	ideal	NOUN
ejpam-3085	268	9	of	of	ADP
ejpam-3085	268	10	h	h	NOUN
ejpam-3085	268	11	,	,	PUNCT
ejpam-3085	268	12	we	we	PRON
ejpam-3085	268	13	have	have	VERB
ejpam-3085	268	14	{	{	PUNCT
ejpam-3085	268	15	c	c	NOUN
ejpam-3085	268	16	}	}	PUNCT
ejpam-3085	268	17	∗	∗	NOUN
ejpam-3085	268	18	(	(	PUNCT
ejpam-3085	268	19	{	{	PUNCT
ejpam-3085	268	20	y	y	NOUN
ejpam-3085	268	21	}	}	PUNCT
ejpam-3085	268	22	∗	∗	NOUN
ejpam-3085	268	23	{	{	PUNCT
ejpam-3085	268	24	d	d	NOUN
ejpam-3085	268	25	}	}	PUNCT
ejpam-3085	268	26	∗	∗	NOUN
ejpam-3085	268	27	{	{	PUNCT
ejpam-3085	268	28	a	a	PRON
ejpam-3085	268	29	}	}	PUNCT
ejpam-3085	268	30	∗	∗	NOUN
ejpam-3085	268	31	{	{	PUNCT
ejpam-3085	268	32	x	x	NOUN
ejpam-3085	268	33	}	}	PUNCT
ejpam-3085	268	34	)	)	PUNCT
ejpam-3085	268	35	∗	∗	NOUN
ejpam-3085	268	36	{	{	PUNCT
ejpam-3085	268	37	b	b	NOUN
ejpam-3085	268	38	}	}	PUNCT
ejpam-3085	268	39	⊆	⊆	NUM
ejpam-3085	268	40	h	h	NOUN
ejpam-3085	268	41	∗	∗	NOUN
ejpam-3085	268	42	i(x	i(x	PROPN
ejpam-3085	269	1	◦	◦	NOUN
ejpam-3085	269	2	y	y	NOUN
ejpam-3085	269	3	)	)	PUNCT
ejpam-3085	269	4	∗h	∗h	VERB
ejpam-3085	269	5	⊆	⊆	NUM
ejpam-3085	269	6	i(x	i(x	NOUN
ejpam-3085	269	7	◦	◦	NOUN
ejpam-3085	269	8	y	y	NOUN
ejpam-3085	269	9	)	)	PUNCT
ejpam-3085	269	10	.	.	PUNCT
ejpam-3085	270	1	then	then	ADV
ejpam-3085	270	2	t	t	PROPN
ejpam-3085	270	3	◦	◦	PROPN
ejpam-3085	270	4	t	t	PROPN
ejpam-3085	270	5	�	�	PROPN
ejpam-3085	270	6	v	v	ADP
ejpam-3085	270	7	◦	◦	NOUN
ejpam-3085	270	8	u	u	NOUN
ejpam-3085	270	9	⊆	⊆	NUM
ejpam-3085	270	10	i(x	i(x	PROPN
ejpam-3085	270	11	◦	◦	NOUN
ejpam-3085	270	12	y	y	NOUN
ejpam-3085	270	13	)	)	PUNCT
ejpam-3085	270	14	.	.	PUNCT
ejpam-3085	271	1	again	again	ADV
ejpam-3085	271	2	since	since	SCONJ
ejpam-3085	271	3	i(x	i(x	PROPN
ejpam-3085	271	4	◦	◦	NOUN
ejpam-3085	271	5	y	y	NOUN
ejpam-3085	271	6	)	)	PUNCT
ejpam-3085	271	7	is	be	AUX
ejpam-3085	271	8	semiprime	semiprime	NOUN
ejpam-3085	271	9	,	,	PUNCT
ejpam-3085	271	10	we	we	PRON
ejpam-3085	271	11	have	have	VERB
ejpam-3085	271	12	t	t	PROPN
ejpam-3085	271	13	∈	∈	PROPN
ejpam-3085	271	14	i(x	i(x	PROPN
ejpam-3085	271	15	◦	◦	PROPN
ejpam-3085	271	16	y	y	NOUN
ejpam-3085	271	17	)	)	PUNCT
ejpam-3085	271	18	,	,	PUNCT
ejpam-3085	271	19	and	and	CCONJ
ejpam-3085	271	20	condition	condition	NOUN
ejpam-3085	271	21	(	(	PUNCT
ejpam-3085	271	22	2	2	NUM
ejpam-3085	271	23	)	)	PUNCT
ejpam-3085	271	24	holds	hold	VERB
ejpam-3085	271	25	.	.	PUNCT
ejpam-3085	272	1	we	we	PRON
ejpam-3085	272	2	are	be	AUX
ejpam-3085	272	3	ready	ready	ADJ
ejpam-3085	272	4	now	now	ADV
ejpam-3085	272	5	to	to	PART
ejpam-3085	272	6	prove	prove	VERB
ejpam-3085	272	7	that	that	SCONJ
ejpam-3085	272	8	the	the	DET
ejpam-3085	272	9	ideals	ideal	NOUN
ejpam-3085	272	10	of	of	ADP
ejpam-3085	272	11	h	h	NOUN
ejpam-3085	272	12	are	be	AUX
ejpam-3085	272	13	prime	prime	ADJ
ejpam-3085	272	14	.	.	PUNCT
ejpam-3085	273	1	for	for	ADP
ejpam-3085	273	2	this	this	DET
ejpam-3085	273	3	purpose	purpose	NOUN
ejpam-3085	273	4	,	,	PUNCT
ejpam-3085	273	5	suppose	suppose	VERB
ejpam-3085	273	6	t	t	NOUN
ejpam-3085	273	7	is	be	AUX
ejpam-3085	273	8	an	an	DET
ejpam-3085	273	9	ideal	ideal	NOUN
ejpam-3085	273	10	of	of	ADP
ejpam-3085	273	11	h	h	NOUN
ejpam-3085	273	12	and	and	CCONJ
ejpam-3085	273	13	a	a	DET
ejpam-3085	273	14	,	,	PUNCT
ejpam-3085	273	15	b	b	X
ejpam-3085	273	16	∈	∈	ADJ
ejpam-3085	273	17	h	h	NOUN
ejpam-3085	273	18	such	such	ADJ
ejpam-3085	273	19	that	that	SCONJ
ejpam-3085	273	20	a	a	DET
ejpam-3085	273	21	◦	◦	NOUN
ejpam-3085	273	22	b	b	NUM
ejpam-3085	273	23	⊆	⊆	NUM
ejpam-3085	273	24	t	t	NOUN
ejpam-3085	273	25	.	.	PUNCT
ejpam-3085	274	1	since	since	SCONJ
ejpam-3085	274	2	the	the	DET
ejpam-3085	274	3	ideals	ideal	NOUN
ejpam-3085	274	4	of	of	ADP
ejpam-3085	274	5	h	h	NOUN
ejpam-3085	274	6	form	form	VERB
ejpam-3085	274	7	a	a	DET
ejpam-3085	274	8	chain	chain	NOUN
ejpam-3085	274	9	,	,	PUNCT
ejpam-3085	274	10	we	we	PRON
ejpam-3085	274	11	have	have	VERB
ejpam-3085	274	12	i(a	i(a	PROPN
ejpam-3085	274	13	)	)	PUNCT
ejpam-3085	274	14	⊆	⊆	NUM
ejpam-3085	274	15	i(b	i(b	NOUN
ejpam-3085	274	16	)	)	PUNCT
ejpam-3085	274	17	or	or	CCONJ
ejpam-3085	274	18	i(b	i(b	PROPN
ejpam-3085	274	19	)	)	PUNCT
ejpam-3085	274	20	⊆	⊆	NUM
ejpam-3085	274	21	i(a	i(a	NOUN
ejpam-3085	274	22	)	)	PUNCT
ejpam-3085	274	23	.	.	PUNCT
ejpam-3085	275	1	if	if	SCONJ
ejpam-3085	275	2	i(a	i(a	NOUN
ejpam-3085	275	3	)	)	PUNCT
ejpam-3085	275	4	⊆	⊆	NUM
ejpam-3085	275	5	i(b	i(b	NOUN
ejpam-3085	275	6	)	)	PUNCT
ejpam-3085	275	7	then	then	ADV
ejpam-3085	275	8	,	,	PUNCT
ejpam-3085	275	9	by	by	ADP
ejpam-3085	275	10	(	(	PUNCT
ejpam-3085	275	11	2	2	NUM
ejpam-3085	275	12	)	)	PUNCT
ejpam-3085	275	13	,	,	PUNCT
ejpam-3085	275	14	we	we	PRON
ejpam-3085	275	15	have	have	VERB
ejpam-3085	275	16	a	a	DET
ejpam-3085	275	17	∈	∈	PROPN
ejpam-3085	275	18	i(a	i(a	PROPN
ejpam-3085	275	19	)	)	PUNCT
ejpam-3085	275	20	=	=	SYM
ejpam-3085	275	21	i(a	i(a	PROPN
ejpam-3085	275	22	)	)	PUNCT
ejpam-3085	275	23	∩	∩	NOUN
ejpam-3085	275	24	i(b	i(b	NOUN
ejpam-3085	275	25	)	)	PUNCT
ejpam-3085	275	26	=	=	SYM
ejpam-3085	276	1	i(a	i(a	PROPN
ejpam-3085	276	2	◦	◦	NOUN
ejpam-3085	276	3	b	b	NUM
ejpam-3085	276	4	)	)	PUNCT
ejpam-3085	276	5	⊆	⊆	NUM
ejpam-3085	276	6	i(t	i(t	NOUN
ejpam-3085	276	7	)	)	PUNCT
ejpam-3085	277	1	=	=	SYM
ejpam-3085	277	2	t	t	PROPN
ejpam-3085	277	3	,	,	PUNCT
ejpam-3085	277	4	so	so	SCONJ
ejpam-3085	277	5	a	a	DET
ejpam-3085	277	6	∈	∈	PROPN
ejpam-3085	277	7	t	t	NOUN
ejpam-3085	277	8	.	.	PUNCT
ejpam-3085	278	1	if	if	SCONJ
ejpam-3085	278	2	i(b	i(b	PROPN
ejpam-3085	278	3	)	)	PUNCT
ejpam-3085	278	4	⊆	⊆	NUM
ejpam-3085	278	5	i(a	i(a	NOUN
ejpam-3085	278	6	)	)	PUNCT
ejpam-3085	278	7	,	,	PUNCT
ejpam-3085	278	8	again	again	ADV
ejpam-3085	278	9	by	by	ADP
ejpam-3085	278	10	(	(	PUNCT
ejpam-3085	278	11	2	2	NUM
ejpam-3085	278	12	)	)	PUNCT
ejpam-3085	278	13	,	,	PUNCT
ejpam-3085	278	14	we	we	PRON
ejpam-3085	278	15	have	have	VERB
ejpam-3085	278	16	b	b	PROPN
ejpam-3085	278	17	∈	∈	PROPN
ejpam-3085	278	18	i(b	i(b	PROPN
ejpam-3085	278	19	)	)	PUNCT
ejpam-3085	278	20	=	=	SYM
ejpam-3085	278	21	i(a	i(a	PROPN
ejpam-3085	278	22	)	)	PUNCT
ejpam-3085	278	23	∩	∩	NOUN
ejpam-3085	278	24	i(b	i(b	NOUN
ejpam-3085	278	25	)	)	PUNCT
ejpam-3085	278	26	=	=	SYM
ejpam-3085	279	1	i(a	i(a	PROPN
ejpam-3085	279	2	◦	◦	NOUN
ejpam-3085	279	3	b	b	NUM
ejpam-3085	279	4	)	)	PUNCT
ejpam-3085	279	5	⊆	⊆	NUM
ejpam-3085	279	6	t	t	NOUN
ejpam-3085	279	7	,	,	PUNCT
ejpam-3085	279	8	so	so	PROPN
ejpam-3085	279	9	b	b	PROPN
ejpam-3085	279	10	∈	∈	PROPN
ejpam-3085	279	11	t	t	NOUN
ejpam-3085	279	12	,	,	PUNCT
ejpam-3085	279	13	thus	thus	ADV
ejpam-3085	279	14	t	t	PROPN
ejpam-3085	279	15	is	be	AUX
ejpam-3085	279	16	prime	prime	ADJ
ejpam-3085	279	17	.	.	PUNCT
ejpam-3085	280	1	�	�	PROPN
ejpam-3085	280	2	corollary	corollary	PROPN
ejpam-3085	280	3	24	24	NUM
ejpam-3085	280	4	.	.	PUNCT
ejpam-3085	281	1	let	let	VERB
ejpam-3085	281	2	h	h	PRON
ejpam-3085	281	3	be	be	AUX
ejpam-3085	281	4	an	an	DET
ejpam-3085	281	5	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	281	6	.	.	PUNCT
ejpam-3085	282	1	the	the	DET
ejpam-3085	282	2	following	follow	VERB
ejpam-3085	282	3	are	be	AUX
ejpam-3085	282	4	equivalent	equivalent	ADJ
ejpam-3085	282	5	:	:	PUNCT
ejpam-3085	282	6	(	(	PUNCT
ejpam-3085	282	7	1	1	X
ejpam-3085	282	8	)	)	PUNCT
ejpam-3085	282	9	the	the	DET
ejpam-3085	282	10	ideals	ideal	NOUN
ejpam-3085	282	11	of	of	ADP
ejpam-3085	282	12	h	h	NOUN
ejpam-3085	282	13	are	be	AUX
ejpam-3085	282	14	prime	prime	ADJ
ejpam-3085	282	15	.	.	PUNCT
ejpam-3085	283	1	(	(	PUNCT
ejpam-3085	283	2	2	2	X
ejpam-3085	283	3	)	)	PUNCT
ejpam-3085	283	4	the	the	DET
ejpam-3085	283	5	ideals	ideal	NOUN
ejpam-3085	283	6	of	of	ADP
ejpam-3085	283	7	h	h	NOUN
ejpam-3085	283	8	are	be	AUX
ejpam-3085	283	9	weakly	weakly	ADV
ejpam-3085	283	10	prime	prime	ADJ
ejpam-3085	283	11	and	and	CCONJ
ejpam-3085	283	12	semiprime	semiprime	NOUN
ejpam-3085	283	13	.	.	PUNCT
ejpam-3085	284	1	(	(	PUNCT
ejpam-3085	284	2	3	3	X
ejpam-3085	284	3	)	)	PUNCT
ejpam-3085	284	4	the	the	DET
ejpam-3085	284	5	ideals	ideal	NOUN
ejpam-3085	284	6	of	of	ADP
ejpam-3085	284	7	h	h	NOUN
ejpam-3085	284	8	form	form	VERB
ejpam-3085	284	9	a	a	DET
ejpam-3085	284	10	chain	chain	NOUN
ejpam-3085	284	11	and	and	CCONJ
ejpam-3085	284	12	h	h	NOUN
ejpam-3085	284	13	is	be	AUX
ejpam-3085	284	14	intra	intra	ADJ
ejpam-3085	284	15	-	-	ADJ
ejpam-3085	284	16	regular	regular	ADJ
ejpam-3085	284	17	.	.	PUNCT
ejpam-3085	285	1	remark	remark	PROPN
ejpam-3085	285	2	25	25	NUM
ejpam-3085	285	3	.	.	PUNCT
ejpam-3085	286	1	here	here	ADV
ejpam-3085	286	2	we	we	PRON
ejpam-3085	286	3	give	give	VERB
ejpam-3085	286	4	some	some	DET
ejpam-3085	286	5	examples	example	NOUN
ejpam-3085	286	6	of	of	ADP
ejpam-3085	286	7	ordered	order	VERB
ejpam-3085	286	8	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	286	9	in	in	ADP
ejpam-3085	286	10	which	which	PRON
ejpam-3085	286	11	the	the	DET
ejpam-3085	286	12	ideals	ideal	NOUN
ejpam-3085	286	13	are	be	AUX
ejpam-3085	286	14	idempotent	idempotent	ADJ
ejpam-3085	286	15	.	.	PUNCT
ejpam-3085	287	1	following	follow	VERB
ejpam-3085	287	2	the	the	DET
ejpam-3085	287	3	concept	concept	NOUN
ejpam-3085	287	4	of	of	ADP
ejpam-3085	287	5	regular	regular	ADJ
ejpam-3085	287	6	ordered	order	VERB
ejpam-3085	287	7	semigroups	semigroup	NOUN
ejpam-3085	287	8	introduced	introduce	VERB
ejpam-3085	287	9	by	by	ADP
ejpam-3085	287	10	kehayopulu	kehayopulu	VERB
ejpam-3085	287	11	in	in	ADP
ejpam-3085	287	12	[	[	X
ejpam-3085	287	13	3	3	NUM
ejpam-3085	287	14	]	]	PUNCT
ejpam-3085	287	15	,	,	PUNCT
ejpam-3085	287	16	an	an	DET
ejpam-3085	287	17	ordered	order	VERB
ejpam-3085	287	18	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	287	19	(	(	PUNCT
ejpam-3085	287	20	h	h	NOUN
ejpam-3085	287	21	,	,	PUNCT
ejpam-3085	287	22	◦	◦	NOUN
ejpam-3085	287	23	,	,	PUNCT
ejpam-3085	287	24	≤	≤	NUM
ejpam-3085	287	25	)	)	PUNCT
ejpam-3085	287	26	is	be	AUX
ejpam-3085	287	27	said	say	VERB
ejpam-3085	287	28	to	to	PART
ejpam-3085	287	29	be	be	AUX
ejpam-3085	287	30	regular	regular	ADJ
ejpam-3085	287	31	if	if	SCONJ
ejpam-3085	287	32	for	for	ADP
ejpam-3085	287	33	every	every	DET
ejpam-3085	287	34	a	a	DET
ejpam-3085	287	35	∈	∈	PROPN
ejpam-3085	287	36	h	h	NOUN
ejpam-3085	287	37	there	there	PRON
ejpam-3085	287	38	exists	exist	VERB
ejpam-3085	287	39	x	x	X
ejpam-3085	287	40	∈	∈	NOUN
ejpam-3085	287	41	h	h	NOUN
ejpam-3085	287	42	such	such	ADJ
ejpam-3085	287	43	that	that	SCONJ
ejpam-3085	287	44	{	{	PUNCT
ejpam-3085	287	45	a	a	DET
ejpam-3085	287	46	}	}	PUNCT
ejpam-3085	287	47	�	�	PROPN
ejpam-3085	287	48	(	(	PUNCT
ejpam-3085	287	49	a	a	DET
ejpam-3085	287	50	◦	◦	NOUN
ejpam-3085	287	51	x	x	SYM
ejpam-3085	287	52	)	)	PUNCT
ejpam-3085	287	53	∗	∗	NOUN
ejpam-3085	287	54	{	{	PUNCT
ejpam-3085	287	55	a}(=	a}(=	NOUN
ejpam-3085	287	56	{	{	PUNCT
ejpam-3085	287	57	a	a	NOUN
ejpam-3085	287	58	}	}	PUNCT
ejpam-3085	287	59	∗	∗	NOUN
ejpam-3085	287	60	(	(	PUNCT
ejpam-3085	287	61	x	x	SYM
ejpam-3085	287	62	◦	◦	VERB
ejpam-3085	287	63	a	a	X
ejpam-3085	287	64	)	)	PUNCT
ejpam-3085	287	65	=	=	PRON
ejpam-3085	287	66	{	{	PUNCT
ejpam-3085	287	67	a	a	PRON
ejpam-3085	287	68	}	}	PUNCT
ejpam-3085	287	69	∗	∗	NOUN
ejpam-3085	287	70	{	{	PUNCT
ejpam-3085	287	71	x	x	NOUN
ejpam-3085	287	72	}	}	PUNCT
ejpam-3085	287	73	∗	∗	NOUN
ejpam-3085	287	74	{	{	PUNCT
ejpam-3085	287	75	a	a	NOUN
ejpam-3085	287	76	}	}	PUNCT
ejpam-3085	287	77	)	)	PUNCT
ejpam-3085	287	78	.	.	PUNCT
ejpam-3085	288	1	that	that	PRON
ejpam-3085	288	2	is	be	AUX
ejpam-3085	288	3	,	,	PUNCT
ejpam-3085	288	4	for	for	ADP
ejpam-3085	288	5	every	every	DET
ejpam-3085	288	6	a	a	DET
ejpam-3085	288	7	∈	∈	PROPN
ejpam-3085	288	8	h	h	NOUN
ejpam-3085	288	9	there	there	PRON
ejpam-3085	288	10	exist	exist	VERB
ejpam-3085	288	11	x	x	NOUN
ejpam-3085	288	12	,	,	PUNCT
ejpam-3085	288	13	t	t	PROPN
ejpam-3085	288	14	∈	∈	PROPN
ejpam-3085	288	15	h	h	NOUN
ejpam-3085	288	16	such	such	ADJ
ejpam-3085	288	17	that	that	SCONJ
ejpam-3085	288	18	t	t	PROPN
ejpam-3085	288	19	∈	∈	PROPN
ejpam-3085	288	20	(	(	PUNCT
ejpam-3085	288	21	a	a	DET
ejpam-3085	288	22	◦	◦	NOUN
ejpam-3085	288	23	x	x	SYM
ejpam-3085	288	24	)	)	PUNCT
ejpam-3085	288	25	∗	∗	NOUN
ejpam-3085	288	26	{	{	PUNCT
ejpam-3085	288	27	a	a	NOUN
ejpam-3085	288	28	}	}	PUNCT
ejpam-3085	288	29	and	and	CCONJ
ejpam-3085	288	30	a	a	DET
ejpam-3085	288	31	≤	≤	ADJ
ejpam-3085	288	32	t.	t.	NOUN
ejpam-3085	288	33	this	this	PRON
ejpam-3085	288	34	is	be	AUX
ejpam-3085	288	35	equivalent	equivalent	ADJ
ejpam-3085	288	36	to	to	ADP
ejpam-3085	288	37	saying	say	VERB
ejpam-3085	288	38	that	that	SCONJ
ejpam-3085	288	39	a	a	DET
ejpam-3085	288	40	∈	∈	PROPN
ejpam-3085	288	41	(	(	PUNCT
ejpam-3085	288	42	{	{	PUNCT
ejpam-3085	288	43	a	a	PRON
ejpam-3085	288	44	}	}	PUNCT
ejpam-3085	288	45	∗h	∗h	NOUN
ejpam-3085	288	46	∗	∗	NOUN
ejpam-3085	288	47	{	{	PUNCT
ejpam-3085	288	48	a	a	NOUN
ejpam-3085	288	49	}	}	PUNCT
ejpam-3085	288	50	]	]	PUNCT
ejpam-3085	288	51	for	for	SCONJ
ejpam-3085	288	52	every	every	DET
ejpam-3085	288	53	a	a	DET
ejpam-3085	288	54	∈	∈	PROPN
ejpam-3085	288	55	h	h	NOUN
ejpam-3085	288	56	or	or	CCONJ
ejpam-3085	288	57	a	a	DET
ejpam-3085	288	58	⊆	⊆	NUM
ejpam-3085	288	59	(	(	PUNCT
ejpam-3085	288	60	a	a	DET
ejpam-3085	288	61	∗h	∗h	NOUN
ejpam-3085	288	62	∗a	∗a	ADJ
ejpam-3085	288	63	]	]	PUNCT
ejpam-3085	288	64	for	for	ADP
ejpam-3085	288	65	every	every	DET
ejpam-3085	288	66	a	a	DET
ejpam-3085	288	67	∈	∈	PROPN
ejpam-3085	288	68	p∗(h	p∗(h	PROPN
ejpam-3085	288	69	)	)	PUNCT
ejpam-3085	288	70	.	.	PUNCT
ejpam-3085	289	1	if	if	SCONJ
ejpam-3085	289	2	h	h	NOUN
ejpam-3085	289	3	is	be	AUX
ejpam-3085	289	4	a	a	DET
ejpam-3085	289	5	regular	regular	ADJ
ejpam-3085	289	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	289	7	,	,	PUNCT
ejpam-3085	289	8	then	then	ADV
ejpam-3085	289	9	the	the	DET
ejpam-3085	289	10	right	right	ADJ
ejpam-3085	289	11	ideals	ideal	NOUN
ejpam-3085	289	12	and	and	CCONJ
ejpam-3085	289	13	the	the	DET
ejpam-3085	289	14	left	left	ADJ
ejpam-3085	289	15	ideals	ideal	NOUN
ejpam-3085	289	16	of	of	ADP
ejpam-3085	289	17	h	h	NOUN
ejpam-3085	289	18	are	be	AUX
ejpam-3085	289	19	idempotent	idempotent	ADJ
ejpam-3085	289	20	.	.	PUNCT
ejpam-3085	290	1	in	in	ADP
ejpam-3085	290	2	fact	fact	NOUN
ejpam-3085	290	3	,	,	PUNCT
ejpam-3085	290	4	let	let	VERB
ejpam-3085	290	5	a	a	PRON
ejpam-3085	290	6	be	be	AUX
ejpam-3085	290	7	a	a	DET
ejpam-3085	290	8	right	right	ADJ
ejpam-3085	290	9	ideal	ideal	NOUN
ejpam-3085	290	10	of	of	ADP
ejpam-3085	290	11	h.	h.	PROPN
ejpam-3085	290	12	since	since	SCONJ
ejpam-3085	290	13	h	h	PROPN
ejpam-3085	290	14	is	be	AUX
ejpam-3085	290	15	regular	regular	ADJ
ejpam-3085	290	16	,	,	PUNCT
ejpam-3085	290	17	we	we	PRON
ejpam-3085	290	18	have	have	VERB
ejpam-3085	290	19	a	a	DET
ejpam-3085	290	20	⊆	⊆	NUM
ejpam-3085	290	21	(	(	PUNCT
ejpam-3085	290	22	(	(	PUNCT
ejpam-3085	290	23	a	a	DET
ejpam-3085	290	24	∗h	∗h	NOUN
ejpam-3085	290	25	)	)	PUNCT
ejpam-3085	290	26	∗a	∗a	ADJ
ejpam-3085	290	27	]	]	PUNCT
ejpam-3085	291	1	⊆	⊆	NUM
ejpam-3085	291	2	(	(	PUNCT
ejpam-3085	291	3	a	a	DET
ejpam-3085	291	4	∗a	∗a	PROPN
ejpam-3085	291	5	]	]	X
ejpam-3085	291	6	⊆	⊆	NUM
ejpam-3085	291	7	(	(	PUNCT
ejpam-3085	291	8	a	a	DET
ejpam-3085	291	9	∗h	∗h	NOUN
ejpam-3085	291	10	]	]	X
ejpam-3085	291	11	⊆	⊆	NUM
ejpam-3085	291	12	a	a	PRON
ejpam-3085	291	13	,	,	PUNCT
ejpam-3085	291	14	so	so	CCONJ
ejpam-3085	291	15	(	(	PUNCT
ejpam-3085	291	16	a	a	DET
ejpam-3085	291	17	∗a	∗a	NOUN
ejpam-3085	291	18	]	]	X
ejpam-3085	291	19	=	=	PUNCT
ejpam-3085	291	20	a.	a.	NOUN
ejpam-3085	291	21	if	if	SCONJ
ejpam-3085	291	22	a	a	PRON
ejpam-3085	291	23	is	be	AUX
ejpam-3085	291	24	a	a	DET
ejpam-3085	291	25	left	left	ADJ
ejpam-3085	291	26	ideal	ideal	NOUN
ejpam-3085	291	27	of	of	ADP
ejpam-3085	291	28	h	h	NOUN
ejpam-3085	291	29	,	,	PUNCT
ejpam-3085	291	30	then	then	ADV
ejpam-3085	291	31	we	we	PRON
ejpam-3085	291	32	have	have	VERB
ejpam-3085	291	33	a	a	DET
ejpam-3085	291	34	⊆	⊆	NUM
ejpam-3085	291	35	(	(	PUNCT
ejpam-3085	291	36	a	a	DET
ejpam-3085	291	37	∗	∗	NOUN
ejpam-3085	291	38	(	(	PUNCT
ejpam-3085	291	39	h	h	NOUN
ejpam-3085	291	40	∗	∗	NOUN
ejpam-3085	291	41	a	a	NOUN
ejpam-3085	291	42	)	)	PUNCT
ejpam-3085	291	43	]	]	PUNCT
ejpam-3085	292	1	⊆	⊆	X
ejpam-3085	292	2	(	(	PUNCT
ejpam-3085	292	3	a	a	DET
ejpam-3085	292	4	∗	∗	NOUN
ejpam-3085	292	5	a	a	X
ejpam-3085	292	6	]	]	X
ejpam-3085	292	7	⊆	⊆	NUM
ejpam-3085	292	8	(	(	PUNCT
ejpam-3085	292	9	h	h	NOUN
ejpam-3085	292	10	∗	∗	NOUN
ejpam-3085	292	11	a	a	X
ejpam-3085	292	12	]	]	X
ejpam-3085	292	13	⊆	⊆	NUM
ejpam-3085	292	14	a	a	PRON
ejpam-3085	292	15	,	,	PUNCT
ejpam-3085	292	16	thus	thus	ADV
ejpam-3085	292	17	(	(	PUNCT
ejpam-3085	292	18	a	a	DET
ejpam-3085	292	19	∗	∗	NOUN
ejpam-3085	292	20	a	a	X
ejpam-3085	292	21	]	]	X
ejpam-3085	292	22	=	=	PUNCT
ejpam-3085	292	23	a.	a.	NOUN
ejpam-3085	292	24	again	again	ADV
ejpam-3085	292	25	following	follow	VERB
ejpam-3085	292	26	the	the	DET
ejpam-3085	292	27	corresponding	corresponding	ADJ
ejpam-3085	292	28	notions	notion	NOUN
ejpam-3085	292	29	of	of	ADP
ejpam-3085	292	30	ordered	order	VERB
ejpam-3085	292	31	semigroups	semigroup	NOUN
ejpam-3085	292	32	,	,	PUNCT
ejpam-3085	292	33	an	an	DET
ejpam-3085	292	34	ordered	order	VERB
ejpam-3085	292	35	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	292	36	h	h	NOUN
ejpam-3085	292	37	is	be	AUX
ejpam-3085	292	38	called	call	VERB
ejpam-3085	292	39	left	leave	VERB
ejpam-3085	292	40	regular	regular	ADV
ejpam-3085	292	41	[	[	X
ejpam-3085	292	42	10	10	NUM
ejpam-3085	292	43	]	]	X
ejpam-3085	292	44	if	if	SCONJ
ejpam-3085	292	45	for	for	ADP
ejpam-3085	292	46	every	every	DET
ejpam-3085	292	47	a	a	DET
ejpam-3085	292	48	∈	∈	PROPN
ejpam-3085	292	49	h	h	NOUN
ejpam-3085	292	50	there	there	PRON
ejpam-3085	292	51	exists	exist	VERB
ejpam-3085	292	52	x	x	X
ejpam-3085	292	53	∈	∈	NOUN
ejpam-3085	292	54	h	h	NOUN
ejpam-3085	292	55	such	such	ADJ
ejpam-3085	292	56	that	that	SCONJ
ejpam-3085	292	57	{	{	PUNCT
ejpam-3085	292	58	a	a	PRON
ejpam-3085	292	59	}	}	PUNCT
ejpam-3085	292	60	�	�	PROPN
ejpam-3085	292	61	{	{	PUNCT
ejpam-3085	292	62	x	x	NOUN
ejpam-3085	292	63	}	}	PUNCT
ejpam-3085	292	64	∗	∗	NOUN
ejpam-3085	292	65	(	(	PUNCT
ejpam-3085	292	66	a	a	DET
ejpam-3085	292	67	◦	◦	NOUN
ejpam-3085	292	68	a)(=	a)(=	NOUN
ejpam-3085	292	69	(	(	PUNCT
ejpam-3085	292	70	x	x	SYM
ejpam-3085	292	71	◦	◦	VERB
ejpam-3085	292	72	a	a	X
ejpam-3085	292	73	)	)	PUNCT
ejpam-3085	292	74	∗	∗	NOUN
ejpam-3085	292	75	{	{	PUNCT
ejpam-3085	292	76	a	a	NOUN
ejpam-3085	292	77	}	}	PUNCT
ejpam-3085	292	78	=	=	SYM
ejpam-3085	292	79	{	{	PUNCT
ejpam-3085	292	80	x	x	NOUN
ejpam-3085	292	81	}	}	PUNCT
ejpam-3085	292	82	∗	∗	NOUN
ejpam-3085	292	83	{	{	PUNCT
ejpam-3085	292	84	a	a	DET
ejpam-3085	292	85	}	}	PUNCT
ejpam-3085	292	86	∗	∗	NOUN
ejpam-3085	292	87	{	{	PUNCT
ejpam-3085	292	88	a	a	NOUN
ejpam-3085	292	89	}	}	PUNCT
ejpam-3085	292	90	)	)	PUNCT
ejpam-3085	292	91	.	.	PUNCT
ejpam-3085	293	1	that	that	PRON
ejpam-3085	293	2	is	be	AUX
ejpam-3085	293	3	,	,	PUNCT
ejpam-3085	293	4	for	for	ADP
ejpam-3085	293	5	every	every	DET
ejpam-3085	293	6	a	a	DET
ejpam-3085	293	7	∈	∈	PROPN
ejpam-3085	293	8	h	h	NOUN
ejpam-3085	293	9	there	there	PRON
ejpam-3085	293	10	exist	exist	VERB
ejpam-3085	293	11	x	x	NOUN
ejpam-3085	293	12	,	,	PUNCT
ejpam-3085	293	13	t	t	PROPN
ejpam-3085	293	14	∈	∈	PROPN
ejpam-3085	293	15	h	h	NOUN
ejpam-3085	293	16	such	such	ADJ
ejpam-3085	293	17	that	that	SCONJ
ejpam-3085	293	18	t	t	PROPN
ejpam-3085	293	19	∈	∈	PROPN
ejpam-3085	293	20	{	{	PUNCT
ejpam-3085	293	21	x	x	NOUN
ejpam-3085	293	22	}	}	PUNCT
ejpam-3085	293	23	∗	∗	NOUN
ejpam-3085	293	24	(	(	PUNCT
ejpam-3085	293	25	a	a	DET
ejpam-3085	293	26	◦	◦	NOUN
ejpam-3085	293	27	a	a	X
ejpam-3085	293	28	)	)	PUNCT
ejpam-3085	293	29	and	and	CCONJ
ejpam-3085	293	30	a	a	DET
ejpam-3085	293	31	≤	≤	ADJ
ejpam-3085	293	32	t.	t.	NOUN
ejpam-3085	293	33	this	this	PRON
ejpam-3085	293	34	is	be	AUX
ejpam-3085	293	35	equivalent	equivalent	ADJ
ejpam-3085	293	36	to	to	ADP
ejpam-3085	293	37	saying	say	VERB
ejpam-3085	293	38	that	that	SCONJ
ejpam-3085	293	39	a	a	DET
ejpam-3085	293	40	∈	∈	NOUN
ejpam-3085	293	41	(	(	PUNCT
ejpam-3085	293	42	h	h	NOUN
ejpam-3085	293	43	∗	∗	NOUN
ejpam-3085	293	44	{	{	PUNCT
ejpam-3085	293	45	a	a	DET
ejpam-3085	293	46	}	}	PUNCT
ejpam-3085	293	47	∗	∗	NOUN
ejpam-3085	293	48	{	{	PUNCT
ejpam-3085	293	49	a	a	NOUN
ejpam-3085	293	50	}	}	PUNCT
ejpam-3085	293	51	]	]	PUNCT
ejpam-3085	293	52	for	for	ADP
ejpam-3085	293	53	every	every	DET
ejpam-3085	293	54	a	a	DET
ejpam-3085	293	55	∈	∈	PROPN
ejpam-3085	293	56	h	h	NOUN
ejpam-3085	293	57	or	or	CCONJ
ejpam-3085	293	58	a	a	DET
ejpam-3085	293	59	⊆	⊆	NUM
ejpam-3085	293	60	(	(	PUNCT
ejpam-3085	293	61	h	h	NOUN
ejpam-3085	293	62	∗a	∗a	PROPN
ejpam-3085	293	63	∗a	∗a	PROPN
ejpam-3085	293	64	]	]	PUNCT
ejpam-3085	293	65	for	for	ADP
ejpam-3085	293	66	every	every	DET
ejpam-3085	293	67	a	a	DET
ejpam-3085	293	68	∈	∈	PROPN
ejpam-3085	293	69	p∗(h	p∗(h	PROPN
ejpam-3085	293	70	)	)	PUNCT
ejpam-3085	293	71	.	.	PUNCT
ejpam-3085	294	1	the	the	DET
ejpam-3085	294	2	left	left	ADJ
ejpam-3085	294	3	regular	regular	ADJ
ejpam-3085	294	4	ordered	order	VERB
ejpam-3085	294	5	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	294	6	are	be	AUX
ejpam-3085	294	7	intra	intra	ADJ
ejpam-3085	294	8	-	-	ADJ
ejpam-3085	294	9	regular	regular	ADJ
ejpam-3085	294	10	.	.	PUNCT
ejpam-3085	295	1	indeed	indeed	ADV
ejpam-3085	295	2	,	,	PUNCT
ejpam-3085	295	3	let	let	VERB
ejpam-3085	295	4	a	a	DET
ejpam-3085	295	5	∈	∈	PROPN
ejpam-3085	295	6	p∗(h	p∗(h	PROPN
ejpam-3085	295	7	)	)	PUNCT
ejpam-3085	295	8	.	.	PUNCT
ejpam-3085	296	1	then	then	ADV
ejpam-3085	296	2	we	we	PRON
ejpam-3085	296	3	have	have	VERB
ejpam-3085	296	4	a	a	DET
ejpam-3085	296	5	⊆	⊆	NUM
ejpam-3085	296	6	(	(	PUNCT
ejpam-3085	296	7	h	h	NOUN
ejpam-3085	296	8	∗a	∗a	PROPN
ejpam-3085	296	9	∗a	∗a	PROPN
ejpam-3085	296	10	]	]	X
ejpam-3085	296	11	⊆	⊆	NUM
ejpam-3085	296	12	(	(	PUNCT
ejpam-3085	296	13	h	h	NOUN
ejpam-3085	296	14	∗	∗	NOUN
ejpam-3085	296	15	(	(	PUNCT
ejpam-3085	296	16	h	h	NOUN
ejpam-3085	296	17	∗a	∗a	ADJ
ejpam-3085	296	18	∗a	∗a	ADJ
ejpam-3085	296	19	]	]	PUNCT
ejpam-3085	296	20	∗a	∗a	PROPN
ejpam-3085	296	21	]	]	PUNCT
ejpam-3085	296	22	=	=	SYM
ejpam-3085	296	23	(	(	PUNCT
ejpam-3085	296	24	h	h	NOUN
ejpam-3085	296	25	∗	∗	NOUN
ejpam-3085	296	26	(	(	PUNCT
ejpam-3085	296	27	h	h	NOUN
ejpam-3085	296	28	∗a	∗a	ADJ
ejpam-3085	296	29	∗a	∗a	ADJ
ejpam-3085	296	30	)	)	PUNCT
ejpam-3085	296	31	∗a	∗a	ADJ
ejpam-3085	296	32	]	]	PUNCT
ejpam-3085	296	33	(	(	PUNCT
ejpam-3085	296	34	by	by	ADP
ejpam-3085	296	35	proposition	proposition	NOUN
ejpam-3085	296	36	12	12	NUM
ejpam-3085	296	37	)	)	PUNCT
ejpam-3085	296	38	=	=	PRON
ejpam-3085	296	39	(	(	PUNCT
ejpam-3085	296	40	(	(	PUNCT
ejpam-3085	296	41	h	h	NOUN
ejpam-3085	296	42	∗h	∗h	NOUN
ejpam-3085	296	43	)	)	PUNCT
ejpam-3085	296	44	∗a	∗a	ADJ
ejpam-3085	296	45	∗a	∗a	ADJ
ejpam-3085	296	46	∗a	∗a	PROPN
ejpam-3085	296	47	]	]	PUNCT
ejpam-3085	296	48	n.	n.	PROPN
ejpam-3085	296	49	kehayopulu	kehayopulu	PROPN
ejpam-3085	296	50	/	/	SYM
ejpam-3085	296	51	eur	eur	PROPN
ejpam-3085	296	52	.	.	PUNCT
ejpam-3085	297	1	j.	j.	PROPN
ejpam-3085	297	2	pure	pure	PROPN
ejpam-3085	297	3	appl	appl	PROPN
ejpam-3085	297	4	.	.	PROPN
ejpam-3085	297	5	math	math	PROPN
ejpam-3085	297	6	,	,	PUNCT
ejpam-3085	297	7	11	11	NUM
ejpam-3085	297	8	(	(	PUNCT
ejpam-3085	297	9	1	1	NUM
ejpam-3085	297	10	)	)	PUNCT
ejpam-3085	297	11	(	(	PUNCT
ejpam-3085	297	12	2018	2018	NUM
ejpam-3085	297	13	)	)	PUNCT
ejpam-3085	297	14	,	,	PUNCT
ejpam-3085	297	15	10	10	NUM
ejpam-3085	297	16	-	-	SYM
ejpam-3085	297	17	22	22	NUM
ejpam-3085	297	18	20	20	NUM
ejpam-3085	297	19	⊆	⊆	NUM
ejpam-3085	297	20	(	(	PUNCT
ejpam-3085	297	21	h	h	NOUN
ejpam-3085	297	22	∗a	∗a	ADJ
ejpam-3085	297	23	∗a	∗a	ADJ
ejpam-3085	297	24	∗h	∗h	NOUN
ejpam-3085	297	25	]	]	PUNCT
ejpam-3085	297	26	,	,	PUNCT
ejpam-3085	297	27	so	so	CCONJ
ejpam-3085	297	28	h	h	NOUN
ejpam-3085	297	29	is	be	AUX
ejpam-3085	297	30	intra	intra	ADJ
ejpam-3085	297	31	-	-	ADJ
ejpam-3085	297	32	regular	regular	ADJ
ejpam-3085	297	33	.	.	PUNCT
ejpam-3085	298	1	in	in	ADP
ejpam-3085	298	2	intra	intra	ADJ
ejpam-3085	298	3	-	-	ADJ
ejpam-3085	298	4	regular	regular	ADJ
ejpam-3085	298	5	ordered	order	VERB
ejpam-3085	298	6	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	298	7	the	the	DET
ejpam-3085	298	8	ideals	ideal	NOUN
ejpam-3085	298	9	are	be	AUX
ejpam-3085	298	10	idempotent	idempotent	ADJ
ejpam-3085	298	11	.	.	PUNCT
ejpam-3085	299	1	in	in	ADP
ejpam-3085	299	2	fact	fact	NOUN
ejpam-3085	299	3	:	:	PUNCT
ejpam-3085	299	4	let	let	VERB
ejpam-3085	299	5	h	h	NOUN
ejpam-3085	299	6	be	be	AUX
ejpam-3085	299	7	an	an	DET
ejpam-3085	299	8	intra	intra	ADJ
ejpam-3085	299	9	-	-	ADJ
ejpam-3085	299	10	regular	regular	ADJ
ejpam-3085	299	11	ordered	order	VERB
ejpam-3085	299	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	299	13	and	and	CCONJ
ejpam-3085	299	14	a	a	DET
ejpam-3085	299	15	an	an	DET
ejpam-3085	299	16	ideal	ideal	NOUN
ejpam-3085	299	17	of	of	ADP
ejpam-3085	299	18	h.	h.	PROPN
ejpam-3085	299	19	since	since	SCONJ
ejpam-3085	299	20	a	a	DET
ejpam-3085	299	21	⊆	⊆	NUM
ejpam-3085	299	22	(	(	PUNCT
ejpam-3085	299	23	h	h	NOUN
ejpam-3085	299	24	∗a	∗a	ADJ
ejpam-3085	299	25	∗a	∗a	ADJ
ejpam-3085	299	26	∗h	∗h	NOUN
ejpam-3085	299	27	]	]	PUNCT
ejpam-3085	299	28	,	,	PUNCT
ejpam-3085	299	29	we	we	PRON
ejpam-3085	299	30	have	have	VERB
ejpam-3085	299	31	(	(	PUNCT
ejpam-3085	299	32	a	a	DET
ejpam-3085	299	33	∗a	∗a	PROPN
ejpam-3085	299	34	]	]	X
ejpam-3085	299	35	⊆	⊆	NUM
ejpam-3085	299	36	(	(	PUNCT
ejpam-3085	299	37	(	(	PUNCT
ejpam-3085	299	38	h	h	NOUN
ejpam-3085	299	39	∗a	∗a	ADJ
ejpam-3085	299	40	∗a	∗a	ADJ
ejpam-3085	299	41	∗h	∗h	NOUN
ejpam-3085	299	42	]	]	PUNCT
ejpam-3085	299	43	∗a	∗a	ADJ
ejpam-3085	299	44	]	]	PUNCT
ejpam-3085	299	45	=	=	PUNCT
ejpam-3085	299	46	(	(	PUNCT
ejpam-3085	299	47	(	(	PUNCT
ejpam-3085	299	48	h	h	NOUN
ejpam-3085	299	49	∗a	∗a	ADJ
ejpam-3085	299	50	∗a	∗a	ADJ
ejpam-3085	299	51	∗h	∗h	NOUN
ejpam-3085	299	52	)	)	PUNCT
ejpam-3085	299	53	∗a	∗a	ADJ
ejpam-3085	299	54	]	]	PUNCT
ejpam-3085	299	55	(	(	PUNCT
ejpam-3085	299	56	by	by	ADP
ejpam-3085	299	57	proposition	proposition	NOUN
ejpam-3085	299	58	11	11	NUM
ejpam-3085	299	59	)	)	PUNCT
ejpam-3085	299	60	⊆	⊆	NUM
ejpam-3085	299	61	(	(	PUNCT
ejpam-3085	299	62	h	h	NOUN
ejpam-3085	299	63	∗a	∗a	ADJ
ejpam-3085	299	64	]	]	X
ejpam-3085	300	1	⊆	⊆	NUM
ejpam-3085	300	2	(	(	PUNCT
ejpam-3085	300	3	a	a	X
ejpam-3085	300	4	]	]	X
ejpam-3085	300	5	=	=	PUNCT
ejpam-3085	300	6	a	a	PRON
ejpam-3085	300	7	⊆	⊆	NUM
ejpam-3085	300	8	(	(	PUNCT
ejpam-3085	300	9	(	(	PUNCT
ejpam-3085	300	10	h	h	NOUN
ejpam-3085	300	11	∗a	∗a	ADJ
ejpam-3085	300	12	)	)	PUNCT
ejpam-3085	300	13	∗	∗	NOUN
ejpam-3085	300	14	(	(	PUNCT
ejpam-3085	300	15	a	a	DET
ejpam-3085	300	16	∗h	∗h	NOUN
ejpam-3085	300	17	)	)	PUNCT
ejpam-3085	300	18	]	]	PUNCT
ejpam-3085	301	1	⊆	⊆	X
ejpam-3085	301	2	(	(	PUNCT
ejpam-3085	301	3	a	a	DET
ejpam-3085	301	4	∗a	∗a	PROPN
ejpam-3085	301	5	]	]	PUNCT
ejpam-3085	301	6	,	,	PUNCT
ejpam-3085	301	7	then	then	ADV
ejpam-3085	301	8	(	(	PUNCT
ejpam-3085	301	9	a	a	DET
ejpam-3085	301	10	∗	∗	NOUN
ejpam-3085	301	11	a	a	X
ejpam-3085	301	12	]	]	X
ejpam-3085	301	13	=	=	SYM
ejpam-3085	301	14	a	a	NOUN
ejpam-3085	301	15	,	,	PUNCT
ejpam-3085	301	16	and	and	CCONJ
ejpam-3085	301	17	a	a	PRON
ejpam-3085	301	18	is	be	AUX
ejpam-3085	301	19	idempotent	idempotent	ADJ
ejpam-3085	301	20	.	.	PUNCT
ejpam-3085	302	1	an	an	DET
ejpam-3085	302	2	ordered	order	VERB
ejpam-3085	302	3	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	302	4	h	h	NOUN
ejpam-3085	302	5	is	be	AUX
ejpam-3085	302	6	said	say	VERB
ejpam-3085	302	7	to	to	PART
ejpam-3085	302	8	be	be	AUX
ejpam-3085	302	9	right	right	ADV
ejpam-3085	302	10	regular	regular	ADV
ejpam-3085	302	11	[	[	X
ejpam-3085	302	12	10	10	NUM
ejpam-3085	302	13	]	]	X
ejpam-3085	302	14	if	if	SCONJ
ejpam-3085	302	15	for	for	ADP
ejpam-3085	302	16	every	every	DET
ejpam-3085	302	17	a	a	DET
ejpam-3085	302	18	∈	∈	PROPN
ejpam-3085	302	19	h	h	NOUN
ejpam-3085	302	20	there	there	PRON
ejpam-3085	302	21	exists	exist	VERB
ejpam-3085	302	22	x	x	X
ejpam-3085	302	23	∈	∈	NOUN
ejpam-3085	302	24	h	h	NOUN
ejpam-3085	302	25	such	such	ADJ
ejpam-3085	302	26	that	that	SCONJ
ejpam-3085	302	27	{	{	PUNCT
ejpam-3085	302	28	a	a	DET
ejpam-3085	302	29	}	}	PUNCT
ejpam-3085	302	30	�	�	PROPN
ejpam-3085	302	31	(	(	PUNCT
ejpam-3085	302	32	a	a	DET
ejpam-3085	302	33	◦	◦	NOUN
ejpam-3085	302	34	a	a	X
ejpam-3085	302	35	)	)	PUNCT
ejpam-3085	302	36	∗	∗	NOUN
ejpam-3085	302	37	{	{	PUNCT
ejpam-3085	302	38	x}(=	x}(=	PROPN
ejpam-3085	302	39	{	{	PUNCT
ejpam-3085	302	40	a	a	DET
ejpam-3085	302	41	}	}	PUNCT
ejpam-3085	302	42	∗	∗	NOUN
ejpam-3085	302	43	(	(	PUNCT
ejpam-3085	302	44	a	a	DET
ejpam-3085	302	45	◦	◦	NOUN
ejpam-3085	302	46	x	x	NOUN
ejpam-3085	302	47	)	)	PUNCT
ejpam-3085	302	48	=	=	PRON
ejpam-3085	302	49	{	{	PUNCT
ejpam-3085	302	50	a	a	PRON
ejpam-3085	302	51	}	}	PUNCT
ejpam-3085	302	52	∗	∗	NOUN
ejpam-3085	302	53	{	{	PUNCT
ejpam-3085	302	54	a	a	DET
ejpam-3085	302	55	}	}	PUNCT
ejpam-3085	302	56	∗	∗	NOUN
ejpam-3085	302	57	{	{	PUNCT
ejpam-3085	302	58	x	x	NOUN
ejpam-3085	302	59	}	}	PUNCT
ejpam-3085	302	60	)	)	PUNCT
ejpam-3085	302	61	.	.	PUNCT
ejpam-3085	303	1	this	this	PRON
ejpam-3085	303	2	is	be	AUX
ejpam-3085	303	3	equivalent	equivalent	ADJ
ejpam-3085	303	4	to	to	ADP
ejpam-3085	303	5	saying	say	VERB
ejpam-3085	303	6	that	that	SCONJ
ejpam-3085	303	7	a	a	DET
ejpam-3085	303	8	∈	∈	PROPN
ejpam-3085	303	9	(	(	PUNCT
ejpam-3085	303	10	{	{	PUNCT
ejpam-3085	303	11	a	a	PRON
ejpam-3085	303	12	}	}	PUNCT
ejpam-3085	303	13	∗	∗	NOUN
ejpam-3085	303	14	{	{	PUNCT
ejpam-3085	303	15	a	a	DET
ejpam-3085	303	16	}	}	PUNCT
ejpam-3085	303	17	∗	∗	NOUN
ejpam-3085	303	18	h	h	NOUN
ejpam-3085	303	19	]	]	X
ejpam-3085	303	20	for	for	ADP
ejpam-3085	303	21	every	every	DET
ejpam-3085	303	22	a	a	DET
ejpam-3085	303	23	∈	∈	PROPN
ejpam-3085	303	24	h	h	NOUN
ejpam-3085	303	25	or	or	CCONJ
ejpam-3085	303	26	a	a	DET
ejpam-3085	303	27	⊆	⊆	NUM
ejpam-3085	303	28	(	(	PUNCT
ejpam-3085	303	29	a	a	DET
ejpam-3085	303	30	∗	∗	NOUN
ejpam-3085	303	31	a	a	DET
ejpam-3085	303	32	∗	∗	NOUN
ejpam-3085	303	33	h	h	NOUN
ejpam-3085	303	34	]	]	X
ejpam-3085	303	35	for	for	ADP
ejpam-3085	303	36	every	every	DET
ejpam-3085	303	37	a	a	DET
ejpam-3085	303	38	∈	∈	PROPN
ejpam-3085	303	39	p∗(h	p∗(h	PROPN
ejpam-3085	303	40	)	)	PUNCT
ejpam-3085	303	41	.	.	PUNCT
ejpam-3085	304	1	the	the	DET
ejpam-3085	304	2	right	right	ADJ
ejpam-3085	304	3	regular	regular	ADJ
ejpam-3085	304	4	ordered	order	VERB
ejpam-3085	304	5	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	304	6	are	be	AUX
ejpam-3085	304	7	also	also	ADV
ejpam-3085	304	8	intra	intra	ADJ
ejpam-3085	304	9	-	-	ADJ
ejpam-3085	304	10	regular	regular	ADJ
ejpam-3085	304	11	.	.	PUNCT
ejpam-3085	305	1	thus	thus	ADV
ejpam-3085	305	2	,	,	PUNCT
ejpam-3085	305	3	in	in	ADP
ejpam-3085	305	4	left	left	ADJ
ejpam-3085	305	5	regular	regular	ADJ
ejpam-3085	305	6	,	,	PUNCT
ejpam-3085	305	7	right	right	ADV
ejpam-3085	305	8	regular	regular	ADJ
ejpam-3085	305	9	or	or	CCONJ
ejpam-3085	305	10	intra	intra	ADJ
ejpam-3085	305	11	-	-	ADJ
ejpam-3085	305	12	regular	regular	ADJ
ejpam-3085	305	13	ordered	order	VERB
ejpam-3085	305	14	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	305	15	the	the	DET
ejpam-3085	305	16	ideals	ideal	NOUN
ejpam-3085	305	17	are	be	AUX
ejpam-3085	305	18	idempotent	idempotent	ADJ
ejpam-3085	305	19	.	.	PUNCT
ejpam-3085	306	1	�	�	PROPN
ejpam-3085	306	2	it	it	PRON
ejpam-3085	306	3	might	might	AUX
ejpam-3085	306	4	be	be	AUX
ejpam-3085	306	5	finally	finally	ADV
ejpam-3085	306	6	mentioned	mention	VERB
ejpam-3085	306	7	that	that	SCONJ
ejpam-3085	306	8	in	in	ADP
ejpam-3085	306	9	commutative	commutative	ADJ
ejpam-3085	306	10	ordered	order	VERB
ejpam-3085	306	11	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	306	12	the	the	DET
ejpam-3085	306	13	prime	prime	ADJ
ejpam-3085	306	14	and	and	CCONJ
ejpam-3085	306	15	weakly	weakly	ADJ
ejpam-3085	306	16	prime	prime	ADJ
ejpam-3085	306	17	ideals	ideal	NOUN
ejpam-3085	306	18	coincide	coincide	VERB
ejpam-3085	306	19	–	–	PUNCT
ejpam-3085	306	20	the	the	DET
ejpam-3085	306	21	proof	proof	NOUN
ejpam-3085	306	22	is	be	AUX
ejpam-3085	306	23	the	the	DET
ejpam-3085	306	24	same	same	ADJ
ejpam-3085	306	25	with	with	ADP
ejpam-3085	306	26	the	the	DET
ejpam-3085	306	27	proof	proof	NOUN
ejpam-3085	306	28	of	of	ADP
ejpam-3085	306	29	the	the	DET
ejpam-3085	306	30	proposition	proposition	NOUN
ejpam-3085	306	31	in	in	ADP
ejpam-3085	306	32	[	[	X
ejpam-3085	306	33	4	4	NUM
ejpam-3085	306	34	]	]	PUNCT
ejpam-3085	306	35	,	,	PUNCT
ejpam-3085	306	36	we	we	PRON
ejpam-3085	306	37	just	just	ADV
ejpam-3085	306	38	have	have	VERB
ejpam-3085	306	39	to	to	PART
ejpam-3085	306	40	replace	replace	VERB
ejpam-3085	306	41	the	the	DET
ejpam-3085	306	42	operation	operation	NOUN
ejpam-3085	306	43	“	"	PUNCT
ejpam-3085	306	44	·	·	PUNCT
ejpam-3085	306	45	”	"	PUNCT
ejpam-3085	306	46	of	of	ADP
ejpam-3085	306	47	the	the	DET
ejpam-3085	306	48	semigroup	semigroup	NOUN
ejpam-3085	306	49	by	by	ADP
ejpam-3085	306	50	the	the	DET
ejpam-3085	306	51	hyperoperation	hyperoperation	NOUN
ejpam-3085	306	52	“	"	PUNCT
ejpam-3085	306	53	◦	◦	NOUN
ejpam-3085	306	54	”	"	PUNCT
ejpam-3085	306	55	of	of	ADP
ejpam-3085	306	56	the	the	DET
ejpam-3085	306	57	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	306	58	.	.	PUNCT
ejpam-3085	307	1	we	we	PRON
ejpam-3085	307	2	apply	apply	VERB
ejpam-3085	307	3	the	the	DET
ejpam-3085	307	4	theorems	theorem	NOUN
ejpam-3085	307	5	of	of	ADP
ejpam-3085	307	6	the	the	DET
ejpam-3085	307	7	paper	paper	NOUN
ejpam-3085	307	8	to	to	ADP
ejpam-3085	307	9	the	the	DET
ejpam-3085	307	10	following	follow	VERB
ejpam-3085	307	11	two	two	NUM
ejpam-3085	307	12	examples	example	NOUN
ejpam-3085	307	13	.	.	PUNCT
ejpam-3085	308	1	example	example	NOUN
ejpam-3085	308	2	a.	a.	NOUN
ejpam-3085	308	3	we	we	PRON
ejpam-3085	308	4	consider	consider	VERB
ejpam-3085	308	5	the	the	DET
ejpam-3085	308	6	ordered	order	VERB
ejpam-3085	308	7	hypersemigroup	hypersemigroup	ADJ
ejpam-3085	308	8	h	h	NOUN
ejpam-3085	308	9	:	:	PUNCT
ejpam-3085	308	10	=	=	X
ejpam-3085	308	11	{	{	PUNCT
ejpam-3085	308	12	a	a	PRON
ejpam-3085	308	13	,	,	PUNCT
ejpam-3085	308	14	b	b	NOUN
ejpam-3085	308	15	,	,	PUNCT
ejpam-3085	308	16	c	c	NOUN
ejpam-3085	308	17	,	,	PUNCT
ejpam-3085	308	18	d	d	NOUN
ejpam-3085	308	19	,	,	PUNCT
ejpam-3085	308	20	f	f	NOUN
ejpam-3085	308	21	}	}	PUNCT
ejpam-3085	308	22	defined	define	VERB
ejpam-3085	308	23	by	by	ADP
ejpam-3085	308	24	the	the	DET
ejpam-3085	308	25	hyperoperation	hyperoperation	NOUN
ejpam-3085	308	26	given	give	VERB
ejpam-3085	308	27	in	in	ADP
ejpam-3085	308	28	the	the	DET
ejpam-3085	308	29	table	table	NOUN
ejpam-3085	308	30	below	below	ADV
ejpam-3085	308	31	and	and	CCONJ
ejpam-3085	308	32	the	the	DET
ejpam-3085	308	33	order	order	NOUN
ejpam-3085	308	34	below	below	ADV
ejpam-3085	308	35	.	.	PUNCT
ejpam-3085	309	1	◦	◦	VERB
ejpam-3085	309	2	a	a	DET
ejpam-3085	309	3	b	b	NOUN
ejpam-3085	309	4	c	c	NOUN
ejpam-3085	309	5	d	d	X
ejpam-3085	309	6	f	f	PROPN
ejpam-3085	309	7	a	a	DET
ejpam-3085	309	8	{	{	PUNCT
ejpam-3085	309	9	a	a	NOUN
ejpam-3085	309	10	}	}	PUNCT
ejpam-3085	309	11	{	{	PUNCT
ejpam-3085	309	12	a	a	NOUN
ejpam-3085	309	13	}	}	PUNCT
ejpam-3085	309	14	{	{	PUNCT
ejpam-3085	309	15	a	a	NOUN
ejpam-3085	309	16	}	}	PUNCT
ejpam-3085	309	17	{	{	PUNCT
ejpam-3085	309	18	a	a	NOUN
ejpam-3085	309	19	}	}	PUNCT
ejpam-3085	309	20	{	{	PUNCT
ejpam-3085	309	21	a	a	PRON
ejpam-3085	309	22	}	}	PUNCT
ejpam-3085	309	23	b	b	PROPN
ejpam-3085	309	24	{	{	PUNCT
ejpam-3085	309	25	a	a	NOUN
ejpam-3085	309	26	}	}	PUNCT
ejpam-3085	309	27	{	{	PUNCT
ejpam-3085	309	28	a	a	DET
ejpam-3085	309	29	,	,	PUNCT
ejpam-3085	309	30	b	b	NOUN
ejpam-3085	309	31	}	}	PUNCT
ejpam-3085	309	32	{	{	PUNCT
ejpam-3085	309	33	a	a	PRON
ejpam-3085	309	34	,	,	PUNCT
ejpam-3085	309	35	b	b	NOUN
ejpam-3085	309	36	,	,	PUNCT
ejpam-3085	309	37	c	c	X
ejpam-3085	309	38	,	,	PUNCT
ejpam-3085	309	39	f	f	NOUN
ejpam-3085	309	40	}	}	PUNCT
ejpam-3085	309	41	{	{	PUNCT
ejpam-3085	309	42	a	a	DET
ejpam-3085	309	43	,	,	PUNCT
ejpam-3085	309	44	b	b	NOUN
ejpam-3085	309	45	}	}	PUNCT
ejpam-3085	309	46	{	{	PUNCT
ejpam-3085	309	47	a	a	PRON
ejpam-3085	309	48	,	,	PUNCT
ejpam-3085	309	49	b	b	NOUN
ejpam-3085	309	50	,	,	PUNCT
ejpam-3085	309	51	c	c	NOUN
ejpam-3085	309	52	,	,	PUNCT
ejpam-3085	309	53	f	f	X
ejpam-3085	309	54	}	}	PUNCT
ejpam-3085	309	55	c	c	NOUN
ejpam-3085	309	56	{	{	PUNCT
ejpam-3085	309	57	a	a	NOUN
ejpam-3085	309	58	}	}	PUNCT
ejpam-3085	309	59	{	{	PUNCT
ejpam-3085	309	60	a	a	DET
ejpam-3085	309	61	,	,	PUNCT
ejpam-3085	309	62	b	b	NOUN
ejpam-3085	309	63	}	}	PUNCT
ejpam-3085	309	64	{	{	PUNCT
ejpam-3085	309	65	c	c	NOUN
ejpam-3085	309	66	}	}	PUNCT
ejpam-3085	309	67	{	{	PUNCT
ejpam-3085	309	68	a	a	PRON
ejpam-3085	309	69	,	,	PUNCT
ejpam-3085	309	70	b	b	NOUN
ejpam-3085	309	71	,	,	PUNCT
ejpam-3085	309	72	c	c	X
ejpam-3085	309	73	,	,	PUNCT
ejpam-3085	309	74	f	f	NOUN
ejpam-3085	309	75	}	}	PUNCT
ejpam-3085	309	76	{	{	PUNCT
ejpam-3085	309	77	a	a	PRON
ejpam-3085	309	78	,	,	PUNCT
ejpam-3085	309	79	b	b	NOUN
ejpam-3085	309	80	,	,	PUNCT
ejpam-3085	309	81	c	c	X
ejpam-3085	309	82	,	,	PUNCT
ejpam-3085	309	83	f	f	X
ejpam-3085	309	84	}	}	PUNCT
ejpam-3085	309	85	d	d	PROPN
ejpam-3085	309	86	{	{	PUNCT
ejpam-3085	309	87	a	a	NOUN
ejpam-3085	309	88	}	}	PUNCT
ejpam-3085	309	89	{	{	PUNCT
ejpam-3085	309	90	a	a	DET
ejpam-3085	309	91	,	,	PUNCT
ejpam-3085	309	92	b	b	NOUN
ejpam-3085	309	93	}	}	PUNCT
ejpam-3085	309	94	{	{	PUNCT
ejpam-3085	309	95	a	a	PRON
ejpam-3085	309	96	,	,	PUNCT
ejpam-3085	309	97	b	b	NOUN
ejpam-3085	309	98	,	,	PUNCT
ejpam-3085	309	99	c	c	X
ejpam-3085	309	100	,	,	PUNCT
ejpam-3085	309	101	f	f	NOUN
ejpam-3085	309	102	}	}	PUNCT
ejpam-3085	309	103	{	{	PUNCT
ejpam-3085	309	104	a	a	PRON
ejpam-3085	309	105	,	,	PUNCT
ejpam-3085	309	106	d	d	NOUN
ejpam-3085	309	107	}	}	PUNCT
ejpam-3085	309	108	{	{	PUNCT
ejpam-3085	309	109	a	a	PRON
ejpam-3085	309	110	,	,	PUNCT
ejpam-3085	309	111	b	b	NOUN
ejpam-3085	309	112	,	,	PUNCT
ejpam-3085	309	113	c	c	NOUN
ejpam-3085	309	114	,	,	PUNCT
ejpam-3085	309	115	f	f	X
ejpam-3085	309	116	}	}	PUNCT
ejpam-3085	309	117	f	f	PROPN
ejpam-3085	309	118	{	{	PUNCT
ejpam-3085	309	119	a	a	PROPN
ejpam-3085	309	120	}	}	PUNCT
ejpam-3085	309	121	{	{	PUNCT
ejpam-3085	309	122	a	a	DET
ejpam-3085	309	123	,	,	PUNCT
ejpam-3085	309	124	b	b	NOUN
ejpam-3085	309	125	}	}	PUNCT
ejpam-3085	309	126	{	{	PUNCT
ejpam-3085	309	127	a	a	PRON
ejpam-3085	309	128	,	,	PUNCT
ejpam-3085	309	129	b	b	NOUN
ejpam-3085	309	130	,	,	PUNCT
ejpam-3085	309	131	c	c	X
ejpam-3085	309	132	,	,	PUNCT
ejpam-3085	309	133	f	f	NOUN
ejpam-3085	309	134	}	}	PUNCT
ejpam-3085	309	135	{	{	PUNCT
ejpam-3085	309	136	a	a	PRON
ejpam-3085	309	137	,	,	PUNCT
ejpam-3085	309	138	b	b	NOUN
ejpam-3085	309	139	,	,	PUNCT
ejpam-3085	309	140	c	c	X
ejpam-3085	309	141	,	,	PUNCT
ejpam-3085	309	142	f	f	NOUN
ejpam-3085	309	143	}	}	PUNCT
ejpam-3085	309	144	{	{	PUNCT
ejpam-3085	309	145	a	a	PRON
ejpam-3085	309	146	,	,	PUNCT
ejpam-3085	309	147	b	b	NOUN
ejpam-3085	309	148	,	,	PUNCT
ejpam-3085	309	149	c	c	X
ejpam-3085	309	150	,	,	PUNCT
ejpam-3085	309	151	f	f	X
ejpam-3085	309	152	}	}	PUNCT
ejpam-3085	309	153	≤:=	≤:=	PROPN
ejpam-3085	309	154	{	{	PUNCT
ejpam-3085	309	155	(	(	PUNCT
ejpam-3085	309	156	a	a	DET
ejpam-3085	309	157	,	,	PUNCT
ejpam-3085	309	158	a	a	NOUN
ejpam-3085	309	159	)	)	PUNCT
ejpam-3085	309	160	,	,	PUNCT
ejpam-3085	309	161	(	(	PUNCT
ejpam-3085	309	162	a	a	DET
ejpam-3085	309	163	,	,	PUNCT
ejpam-3085	309	164	b	b	NOUN
ejpam-3085	309	165	)	)	PUNCT
ejpam-3085	309	166	,	,	PUNCT
ejpam-3085	309	167	(	(	PUNCT
ejpam-3085	309	168	a	a	DET
ejpam-3085	309	169	,	,	PUNCT
ejpam-3085	309	170	d	d	NOUN
ejpam-3085	309	171	)	)	PUNCT
ejpam-3085	309	172	,	,	PUNCT
ejpam-3085	309	173	(	(	PUNCT
ejpam-3085	309	174	a	a	X
ejpam-3085	309	175	,	,	PUNCT
ejpam-3085	309	176	f	f	NOUN
ejpam-3085	309	177	)	)	PUNCT
ejpam-3085	309	178	,	,	PUNCT
ejpam-3085	309	179	(	(	PUNCT
ejpam-3085	309	180	b	b	X
ejpam-3085	309	181	,	,	PUNCT
ejpam-3085	309	182	b	b	NOUN
ejpam-3085	309	183	)	)	PUNCT
ejpam-3085	309	184	,	,	PUNCT
ejpam-3085	309	185	(	(	PUNCT
ejpam-3085	309	186	b	b	X
ejpam-3085	309	187	,	,	PUNCT
ejpam-3085	309	188	f	f	PROPN
ejpam-3085	309	189	)	)	PUNCT
ejpam-3085	309	190	,	,	PUNCT
ejpam-3085	309	191	(	(	PUNCT
ejpam-3085	309	192	c	c	X
ejpam-3085	309	193	,	,	PUNCT
ejpam-3085	309	194	c	c	NOUN
ejpam-3085	309	195	)	)	PUNCT
ejpam-3085	309	196	,	,	PUNCT
ejpam-3085	309	197	(	(	PUNCT
ejpam-3085	309	198	c	c	X
ejpam-3085	309	199	,	,	PUNCT
ejpam-3085	309	200	f	f	NOUN
ejpam-3085	309	201	)	)	PUNCT
ejpam-3085	309	202	,	,	PUNCT
ejpam-3085	309	203	(	(	PUNCT
ejpam-3085	309	204	d	d	X
ejpam-3085	309	205	,	,	PUNCT
ejpam-3085	309	206	d	d	NOUN
ejpam-3085	309	207	)	)	PUNCT
ejpam-3085	309	208	,	,	PUNCT
ejpam-3085	309	209	(	(	PUNCT
ejpam-3085	309	210	f	f	X
ejpam-3085	309	211	,	,	PUNCT
ejpam-3085	309	212	f	f	NOUN
ejpam-3085	309	213	)	)	PUNCT
ejpam-3085	309	214	}	}	PUNCT
ejpam-3085	309	215	.	.	PUNCT
ejpam-3085	310	1	we	we	PRON
ejpam-3085	310	2	give	give	VERB
ejpam-3085	310	3	the	the	DET
ejpam-3085	310	4	covering	covering	NOUN
ejpam-3085	310	5	relation	relation	NOUN
ejpam-3085	310	6	and	and	CCONJ
ejpam-3085	310	7	the	the	DET
ejpam-3085	310	8	figure	figure	NOUN
ejpam-3085	310	9	of	of	ADP
ejpam-3085	310	10	h.	h.	PROPN
ejpam-3085	310	11	≺=	≺=	X
ejpam-3085	310	12	{	{	PUNCT
ejpam-3085	310	13	(	(	PUNCT
ejpam-3085	310	14	a	a	DET
ejpam-3085	310	15	,	,	PUNCT
ejpam-3085	310	16	b	b	NOUN
ejpam-3085	310	17	)	)	PUNCT
ejpam-3085	310	18	,	,	PUNCT
ejpam-3085	310	19	(	(	PUNCT
ejpam-3085	310	20	a	a	DET
ejpam-3085	310	21	,	,	PUNCT
ejpam-3085	310	22	d	d	NOUN
ejpam-3085	310	23	)	)	PUNCT
ejpam-3085	310	24	,	,	PUNCT
ejpam-3085	310	25	(	(	PUNCT
ejpam-3085	310	26	b	b	X
ejpam-3085	310	27	,	,	PUNCT
ejpam-3085	310	28	f	f	PROPN
ejpam-3085	310	29	)	)	PUNCT
ejpam-3085	310	30	,	,	PUNCT
ejpam-3085	310	31	(	(	PUNCT
ejpam-3085	310	32	c	c	X
ejpam-3085	310	33	,	,	PUNCT
ejpam-3085	310	34	f	f	NOUN
ejpam-3085	310	35	)	)	PUNCT
ejpam-3085	310	36	}	}	PUNCT
ejpam-3085	310	37	.	.	PUNCT
ejpam-3085	311	1	f	f	PROPN
ejpam-3085	311	2	c	c	PROPN
ejpam-3085	311	3	b	b	PROPN
ejpam-3085	311	4	a	a	DET
ejpam-3085	311	5	d	d	X
ejpam-3085	311	6	n.	n.	NOUN
ejpam-3085	311	7	kehayopulu	kehayopulu	PROPN
ejpam-3085	311	8	/	/	SYM
ejpam-3085	311	9	eur	eur	PROPN
ejpam-3085	311	10	.	.	PUNCT
ejpam-3085	312	1	j.	j.	PROPN
ejpam-3085	312	2	pure	pure	PROPN
ejpam-3085	312	3	appl	appl	PROPN
ejpam-3085	312	4	.	.	PROPN
ejpam-3085	312	5	math	math	PROPN
ejpam-3085	312	6	,	,	PUNCT
ejpam-3085	312	7	11	11	NUM
ejpam-3085	312	8	(	(	PUNCT
ejpam-3085	312	9	1	1	NUM
ejpam-3085	312	10	)	)	PUNCT
ejpam-3085	312	11	(	(	PUNCT
ejpam-3085	312	12	2018	2018	NUM
ejpam-3085	312	13	)	)	PUNCT
ejpam-3085	312	14	,	,	PUNCT
ejpam-3085	312	15	10	10	NUM
ejpam-3085	312	16	-	-	SYM
ejpam-3085	312	17	22	22	NUM
ejpam-3085	312	18	21	21	NUM
ejpam-3085	312	19	this	this	PRON
ejpam-3085	312	20	is	be	AUX
ejpam-3085	312	21	intra	intra	ADJ
ejpam-3085	312	22	-	-	ADJ
ejpam-3085	312	23	regular	regular	ADJ
ejpam-3085	312	24	and	and	CCONJ
ejpam-3085	312	25	the	the	DET
ejpam-3085	312	26	ideals	ideal	NOUN
ejpam-3085	312	27	of	of	ADP
ejpam-3085	312	28	h	h	NOUN
ejpam-3085	312	29	are	be	AUX
ejpam-3085	312	30	the	the	DET
ejpam-3085	312	31	sets	set	NOUN
ejpam-3085	312	32	{	{	PUNCT
ejpam-3085	312	33	a	a	X
ejpam-3085	312	34	}	}	PUNCT
ejpam-3085	312	35	,	,	PUNCT
ejpam-3085	312	36	{	{	PUNCT
ejpam-3085	312	37	a	a	PRON
ejpam-3085	312	38	,	,	PUNCT
ejpam-3085	312	39	b	b	NOUN
ejpam-3085	312	40	,	,	PUNCT
ejpam-3085	312	41	c	c	NOUN
ejpam-3085	312	42	,	,	PUNCT
ejpam-3085	312	43	f	f	NOUN
ejpam-3085	312	44	}	}	PUNCT
ejpam-3085	312	45	and	and	CCONJ
ejpam-3085	312	46	h	h	NOUN
ejpam-3085	312	47	(	(	PUNCT
ejpam-3085	312	48	one	one	PRON
ejpam-3085	312	49	can	can	AUX
ejpam-3085	312	50	check	check	VERB
ejpam-3085	312	51	it	it	PRON
ejpam-3085	312	52	)	)	PUNCT
ejpam-3085	312	53	which	which	PRON
ejpam-3085	312	54	clearly	clearly	ADV
ejpam-3085	312	55	form	form	VERB
ejpam-3085	312	56	a	a	DET
ejpam-3085	312	57	chain	chain	NOUN
ejpam-3085	312	58	.	.	PUNCT
ejpam-3085	313	1	looking	look	VERB
ejpam-3085	313	2	at	at	ADP
ejpam-3085	313	3	the	the	DET
ejpam-3085	313	4	table	table	NOUN
ejpam-3085	313	5	,	,	PUNCT
ejpam-3085	313	6	we	we	PRON
ejpam-3085	313	7	immediately	immediately	ADV
ejpam-3085	313	8	see	see	VERB
ejpam-3085	313	9	that	that	SCONJ
ejpam-3085	313	10	the	the	DET
ejpam-3085	313	11	ideals	ideal	NOUN
ejpam-3085	313	12	of	of	ADP
ejpam-3085	313	13	h	h	NOUN
ejpam-3085	313	14	are	be	AUX
ejpam-3085	313	15	prime	prime	ADJ
ejpam-3085	313	16	(	(	PUNCT
ejpam-3085	313	17	that	that	PRON
ejpam-3085	313	18	is	be	AUX
ejpam-3085	313	19	,	,	PUNCT
ejpam-3085	313	20	x	x	PRON
ejpam-3085	313	21	,	,	PUNCT
ejpam-3085	313	22	y	y	PROPN
ejpam-3085	313	23	∈	∈	PROPN
ejpam-3085	313	24	h	h	NOUN
ejpam-3085	313	25	,	,	PUNCT
ejpam-3085	313	26	x	x	VERB
ejpam-3085	313	27	◦	◦	VERB
ejpam-3085	313	28	y	y	NUM
ejpam-3085	313	29	⊆	⊆	NUM
ejpam-3085	313	30	{	{	PUNCT
ejpam-3085	313	31	a	a	PRON
ejpam-3085	313	32	}	}	PUNCT
ejpam-3085	313	33	implies	imply	VERB
ejpam-3085	313	34	x	x	AUX
ejpam-3085	313	35	∈	∈	PROPN
ejpam-3085	313	36	{	{	PUNCT
ejpam-3085	313	37	a	a	NOUN
ejpam-3085	313	38	}	}	PUNCT
ejpam-3085	313	39	or	or	CCONJ
ejpam-3085	313	40	y	y	PROPN
ejpam-3085	313	41	∈	∈	PROPN
ejpam-3085	313	42	{	{	PUNCT
ejpam-3085	313	43	a	a	NOUN
ejpam-3085	313	44	}	}	PUNCT
ejpam-3085	313	45	;	;	PUNCT
ejpam-3085	313	46	x	x	X
ejpam-3085	313	47	,	,	PUNCT
ejpam-3085	313	48	y	y	PROPN
ejpam-3085	313	49	∈	∈	PROPN
ejpam-3085	313	50	h	h	NOUN
ejpam-3085	313	51	,	,	PUNCT
ejpam-3085	313	52	x	x	VERB
ejpam-3085	313	53	◦	◦	VERB
ejpam-3085	313	54	y	y	PROPN
ejpam-3085	313	55	⊆	⊆	NUM
ejpam-3085	313	56	{	{	PUNCT
ejpam-3085	313	57	a	a	PRON
ejpam-3085	313	58	,	,	PUNCT
ejpam-3085	313	59	b	b	NOUN
ejpam-3085	313	60	,	,	PUNCT
ejpam-3085	313	61	c	c	NOUN
ejpam-3085	313	62	,	,	PUNCT
ejpam-3085	313	63	f	f	X
ejpam-3085	313	64	}	}	PUNCT
ejpam-3085	313	65	implies	imply	VERB
ejpam-3085	313	66	x	x	SYM
ejpam-3085	313	67	∈	∈	PROPN
ejpam-3085	313	68	{	{	PUNCT
ejpam-3085	313	69	a	a	PROPN
ejpam-3085	313	70	,	,	PUNCT
ejpam-3085	313	71	b	b	NOUN
ejpam-3085	313	72	,	,	PUNCT
ejpam-3085	313	73	c	c	X
ejpam-3085	313	74	,	,	PUNCT
ejpam-3085	313	75	f	f	NOUN
ejpam-3085	313	76	}	}	PUNCT
ejpam-3085	313	77	or	or	CCONJ
ejpam-3085	313	78	y	y	PROPN
ejpam-3085	313	79	∈	∈	PROPN
ejpam-3085	313	80	{	{	PUNCT
ejpam-3085	313	81	a	a	PROPN
ejpam-3085	313	82	,	,	PUNCT
ejpam-3085	313	83	b	b	NOUN
ejpam-3085	313	84	,	,	PUNCT
ejpam-3085	313	85	c	c	X
ejpam-3085	313	86	,	,	PUNCT
ejpam-3085	313	87	f	f	NOUN
ejpam-3085	313	88	}	}	PUNCT
ejpam-3085	313	89	)	)	PUNCT
ejpam-3085	313	90	,	,	PUNCT
ejpam-3085	313	91	which	which	PRON
ejpam-3085	313	92	is	be	AUX
ejpam-3085	313	93	also	also	ADV
ejpam-3085	313	94	a	a	DET
ejpam-3085	313	95	consequence	consequence	NOUN
ejpam-3085	313	96	of	of	ADP
ejpam-3085	313	97	theorem	theorem	ADJ
ejpam-3085	313	98	23	23	NUM
ejpam-3085	313	99	.	.	PUNCT
ejpam-3085	314	1	example	example	NOUN
ejpam-3085	314	2	b.	b.	PROPN
ejpam-3085	315	1	we	we	PRON
ejpam-3085	315	2	consider	consider	VERB
ejpam-3085	315	3	the	the	DET
ejpam-3085	315	4	ordered	order	VERB
ejpam-3085	315	5	hypersemigroup	hypersemigroup	ADJ
ejpam-3085	315	6	h	h	NOUN
ejpam-3085	315	7	:	:	PUNCT
ejpam-3085	315	8	=	=	X
ejpam-3085	315	9	{	{	PUNCT
ejpam-3085	315	10	a	a	PRON
ejpam-3085	315	11	,	,	PUNCT
ejpam-3085	315	12	b	b	NOUN
ejpam-3085	315	13	,	,	PUNCT
ejpam-3085	315	14	c	c	NOUN
ejpam-3085	315	15	,	,	PUNCT
ejpam-3085	315	16	d	d	NOUN
ejpam-3085	315	17	,	,	PUNCT
ejpam-3085	315	18	f	f	NOUN
ejpam-3085	315	19	}	}	PUNCT
ejpam-3085	315	20	defined	define	VERB
ejpam-3085	315	21	by	by	ADP
ejpam-3085	315	22	the	the	DET
ejpam-3085	315	23	hyperoperation	hyperoperation	NOUN
ejpam-3085	315	24	and	and	CCONJ
ejpam-3085	315	25	the	the	DET
ejpam-3085	315	26	figure	figure	NOUN
ejpam-3085	315	27	below	below	ADV
ejpam-3085	315	28	:	:	PUNCT
ejpam-3085	315	29	◦	◦	VERB
ejpam-3085	315	30	a	a	DET
ejpam-3085	315	31	b	b	NOUN
ejpam-3085	315	32	c	c	NOUN
ejpam-3085	315	33	d	d	X
ejpam-3085	315	34	f	f	PROPN
ejpam-3085	315	35	a	a	DET
ejpam-3085	315	36	{	{	PUNCT
ejpam-3085	315	37	b	b	PROPN
ejpam-3085	315	38	,	,	PUNCT
ejpam-3085	315	39	c	c	NOUN
ejpam-3085	315	40	}	}	PUNCT
ejpam-3085	315	41	{	{	PUNCT
ejpam-3085	315	42	a	a	NOUN
ejpam-3085	315	43	}	}	PUNCT
ejpam-3085	315	44	{	{	PUNCT
ejpam-3085	315	45	a	a	NOUN
ejpam-3085	315	46	}	}	PUNCT
ejpam-3085	315	47	{	{	PUNCT
ejpam-3085	315	48	a	a	NOUN
ejpam-3085	315	49	}	}	PUNCT
ejpam-3085	315	50	{	{	PUNCT
ejpam-3085	315	51	a	a	DET
ejpam-3085	315	52	}	}	PUNCT
ejpam-3085	315	53	b	b	PROPN
ejpam-3085	315	54	{	{	PUNCT
ejpam-3085	315	55	a	a	NOUN
ejpam-3085	315	56	}	}	PUNCT
ejpam-3085	315	57	{	{	PUNCT
ejpam-3085	315	58	b	b	NOUN
ejpam-3085	315	59	,	,	PUNCT
ejpam-3085	315	60	c	c	NOUN
ejpam-3085	315	61	}	}	PUNCT
ejpam-3085	315	62	{	{	PUNCT
ejpam-3085	315	63	b	b	NOUN
ejpam-3085	315	64	,	,	PUNCT
ejpam-3085	315	65	c	c	NOUN
ejpam-3085	315	66	}	}	PUNCT
ejpam-3085	315	67	{	{	PUNCT
ejpam-3085	315	68	b	b	NOUN
ejpam-3085	315	69	,	,	PUNCT
ejpam-3085	315	70	c	c	NOUN
ejpam-3085	315	71	}	}	PUNCT
ejpam-3085	315	72	{	{	PUNCT
ejpam-3085	315	73	b	b	NOUN
ejpam-3085	315	74	,	,	PUNCT
ejpam-3085	315	75	c	c	NOUN
ejpam-3085	315	76	}	}	PUNCT
ejpam-3085	315	77	c	c	NOUN
ejpam-3085	315	78	{	{	PUNCT
ejpam-3085	315	79	a	a	NOUN
ejpam-3085	315	80	}	}	PUNCT
ejpam-3085	315	81	{	{	PUNCT
ejpam-3085	315	82	b	b	NOUN
ejpam-3085	315	83	,	,	PUNCT
ejpam-3085	315	84	c	c	NOUN
ejpam-3085	315	85	}	}	PUNCT
ejpam-3085	315	86	{	{	PUNCT
ejpam-3085	315	87	b	b	NOUN
ejpam-3085	315	88	,	,	PUNCT
ejpam-3085	315	89	c	c	NOUN
ejpam-3085	315	90	}	}	PUNCT
ejpam-3085	315	91	{	{	PUNCT
ejpam-3085	315	92	b	b	NOUN
ejpam-3085	315	93	,	,	PUNCT
ejpam-3085	315	94	c	c	NOUN
ejpam-3085	315	95	}	}	PUNCT
ejpam-3085	315	96	{	{	PUNCT
ejpam-3085	315	97	b	b	NOUN
ejpam-3085	315	98	,	,	PUNCT
ejpam-3085	315	99	c	c	NOUN
ejpam-3085	315	100	}	}	PUNCT
ejpam-3085	315	101	d	d	NOUN
ejpam-3085	315	102	{	{	PUNCT
ejpam-3085	315	103	a	a	NOUN
ejpam-3085	315	104	}	}	PUNCT
ejpam-3085	315	105	{	{	PUNCT
ejpam-3085	315	106	b	b	NOUN
ejpam-3085	315	107	,	,	PUNCT
ejpam-3085	315	108	c	c	NOUN
ejpam-3085	315	109	}	}	PUNCT
ejpam-3085	315	110	{	{	PUNCT
ejpam-3085	315	111	b	b	NOUN
ejpam-3085	315	112	,	,	PUNCT
ejpam-3085	315	113	d	d	NOUN
ejpam-3085	315	114	}	}	PUNCT
ejpam-3085	315	115	{	{	PUNCT
ejpam-3085	315	116	d	d	NOUN
ejpam-3085	315	117	,	,	PUNCT
ejpam-3085	315	118	f	f	NOUN
ejpam-3085	315	119	}	}	PUNCT
ejpam-3085	315	120	{	{	PUNCT
ejpam-3085	315	121	d	d	NOUN
ejpam-3085	315	122	,	,	PUNCT
ejpam-3085	315	123	f	f	X
ejpam-3085	315	124	}	}	PUNCT
ejpam-3085	315	125	f	f	PROPN
ejpam-3085	315	126	{	{	PUNCT
ejpam-3085	315	127	a	a	PROPN
ejpam-3085	315	128	}	}	PUNCT
ejpam-3085	315	129	{	{	PUNCT
ejpam-3085	315	130	b	b	NOUN
ejpam-3085	315	131	,	,	PUNCT
ejpam-3085	315	132	c	c	NOUN
ejpam-3085	315	133	}	}	PUNCT
ejpam-3085	315	134	{	{	PUNCT
ejpam-3085	315	135	c	c	NOUN
ejpam-3085	315	136	}	}	PUNCT
ejpam-3085	315	137	{	{	PUNCT
ejpam-3085	315	138	d	d	NOUN
ejpam-3085	315	139	,	,	PUNCT
ejpam-3085	315	140	f	f	NOUN
ejpam-3085	315	141	}	}	PUNCT
ejpam-3085	315	142	{	{	PUNCT
ejpam-3085	315	143	f	f	X
ejpam-3085	315	144	}	}	PUNCT
ejpam-3085	315	145	c	c	PROPN
ejpam-3085	316	1	f	f	PROPN
ejpam-3085	316	2	b	b	PROPN
ejpam-3085	316	3	d	d	X
ejpam-3085	316	4	a	a	DET
ejpam-3085	316	5	one	one	NOUN
ejpam-3085	316	6	can	can	AUX
ejpam-3085	316	7	check	check	VERB
ejpam-3085	316	8	that	that	SCONJ
ejpam-3085	316	9	the	the	DET
ejpam-3085	316	10	ideals	ideal	NOUN
ejpam-3085	316	11	of	of	ADP
ejpam-3085	316	12	h	h	NOUN
ejpam-3085	316	13	are	be	AUX
ejpam-3085	316	14	the	the	DET
ejpam-3085	316	15	sets	set	NOUN
ejpam-3085	316	16	{	{	PUNCT
ejpam-3085	316	17	a	a	DET
ejpam-3085	316	18	,	,	PUNCT
ejpam-3085	316	19	b	b	NOUN
ejpam-3085	316	20	,	,	PUNCT
ejpam-3085	316	21	c	c	NOUN
ejpam-3085	316	22	}	}	PUNCT
ejpam-3085	316	23	and	and	CCONJ
ejpam-3085	316	24	h	h	NOUN
ejpam-3085	316	25	and	and	CCONJ
ejpam-3085	316	26	that	that	SCONJ
ejpam-3085	316	27	both	both	PRON
ejpam-3085	316	28	are	be	AUX
ejpam-3085	316	29	idempotent	idempotent	ADJ
ejpam-3085	316	30	.	.	PUNCT
ejpam-3085	317	1	one	one	PRON
ejpam-3085	317	2	can	can	AUX
ejpam-3085	317	3	check	check	VERB
ejpam-3085	317	4	that	that	PRON
ejpam-3085	317	5	for	for	ADP
ejpam-3085	317	6	any	any	DET
ejpam-3085	317	7	ideals	ideal	NOUN
ejpam-3085	317	8	a	a	DET
ejpam-3085	317	9	,	,	PUNCT
ejpam-3085	317	10	b	b	PROPN
ejpam-3085	317	11	of	of	ADP
ejpam-3085	317	12	h	h	NOUN
ejpam-3085	317	13	,	,	PUNCT
ejpam-3085	317	14	we	we	PRON
ejpam-3085	317	15	have	have	VERB
ejpam-3085	317	16	a	a	DET
ejpam-3085	317	17	∩	∩	ADJ
ejpam-3085	317	18	b	b	NOUN
ejpam-3085	317	19	=	=	SYM
ejpam-3085	317	20	(	(	PUNCT
ejpam-3085	317	21	a	a	DET
ejpam-3085	317	22	∗	∗	NOUN
ejpam-3085	317	23	b	b	NOUN
ejpam-3085	317	24	]	]	X
ejpam-3085	317	25	,	,	PUNCT
ejpam-3085	317	26	which	which	PRON
ejpam-3085	317	27	is	be	AUX
ejpam-3085	317	28	also	also	ADV
ejpam-3085	317	29	a	a	DET
ejpam-3085	317	30	consequence	consequence	NOUN
ejpam-3085	317	31	of	of	ADP
ejpam-3085	317	32	theorem	theorem	NOUN
ejpam-3085	317	33	9	9	NUM
ejpam-3085	317	34	.	.	PUNCT
ejpam-3085	318	1	one	one	PRON
ejpam-3085	318	2	can	can	AUX
ejpam-3085	318	3	check	check	VERB
ejpam-3085	318	4	that	that	PRON
ejpam-3085	318	5	h	h	NOUN
ejpam-3085	318	6	is	be	AUX
ejpam-3085	318	7	semisimple	semisimple	NOUN
ejpam-3085	318	8	,	,	PUNCT
ejpam-3085	318	9	which	which	PRON
ejpam-3085	318	10	is	be	AUX
ejpam-3085	318	11	also	also	ADV
ejpam-3085	318	12	a	a	DET
ejpam-3085	318	13	consequence	consequence	NOUN
ejpam-3085	318	14	of	of	ADP
ejpam-3085	318	15	theorem	theorem	NOUN
ejpam-3085	318	16	18	18	NUM
ejpam-3085	318	17	.	.	PUNCT
ejpam-3085	319	1	it	it	PRON
ejpam-3085	319	2	is	be	AUX
ejpam-3085	319	3	obvious	obvious	ADJ
ejpam-3085	319	4	that	that	SCONJ
ejpam-3085	319	5	the	the	DET
ejpam-3085	319	6	ideals	ideal	NOUN
ejpam-3085	319	7	of	of	ADP
ejpam-3085	319	8	h	h	NOUN
ejpam-3085	319	9	form	form	VERB
ejpam-3085	319	10	a	a	DET
ejpam-3085	319	11	chain	chain	NOUN
ejpam-3085	319	12	.	.	PUNCT
ejpam-3085	320	1	so	so	ADV
ejpam-3085	320	2	,	,	PUNCT
ejpam-3085	320	3	by	by	ADP
ejpam-3085	320	4	theorem	theorem	NOUN
ejpam-3085	320	5	19	19	NUM
ejpam-3085	320	6	,	,	PUNCT
ejpam-3085	320	7	the	the	DET
ejpam-3085	320	8	ideals	ideal	NOUN
ejpam-3085	320	9	of	of	ADP
ejpam-3085	320	10	h	h	NOUN
ejpam-3085	320	11	are	be	AUX
ejpam-3085	320	12	weakly	weakly	ADV
ejpam-3085	320	13	prime	prime	ADJ
ejpam-3085	320	14	;	;	PUNCT
ejpam-3085	320	15	its	its	PRON
ejpam-3085	320	16	independent	independent	ADJ
ejpam-3085	320	17	proof	proof	NOUN
ejpam-3085	320	18	is	be	AUX
ejpam-3085	320	19	the	the	DET
ejpam-3085	320	20	following	following	NOUN
ejpam-3085	320	21	:	:	PUNCT
ejpam-3085	320	22	let	let	VERB
ejpam-3085	320	23	a	a	DET
ejpam-3085	320	24	,	,	PUNCT
ejpam-3085	320	25	b	b	NOUN
ejpam-3085	320	26	be	be	AUX
ejpam-3085	320	27	ideals	ideal	NOUN
ejpam-3085	320	28	of	of	ADP
ejpam-3085	320	29	h	h	NOUN
ejpam-3085	320	30	such	such	ADJ
ejpam-3085	320	31	that	that	SCONJ
ejpam-3085	320	32	a	a	DET
ejpam-3085	320	33	∗	∗	NOUN
ejpam-3085	320	34	b	b	NOUN
ejpam-3085	320	35	⊆	⊆	NUM
ejpam-3085	320	36	{	{	PUNCT
ejpam-3085	320	37	a	a	PRON
ejpam-3085	320	38	,	,	PUNCT
ejpam-3085	320	39	b	b	NOUN
ejpam-3085	320	40	,	,	PUNCT
ejpam-3085	320	41	c	c	NOUN
ejpam-3085	320	42	}	}	PUNCT
ejpam-3085	320	43	.	.	PUNCT
ejpam-3085	321	1	we	we	PRON
ejpam-3085	321	2	have	have	VERB
ejpam-3085	321	3	a	a	DET
ejpam-3085	321	4	=	=	X
ejpam-3085	321	5	{	{	PUNCT
ejpam-3085	321	6	a	a	PROPN
ejpam-3085	321	7	,	,	PUNCT
ejpam-3085	321	8	b	b	NOUN
ejpam-3085	321	9	,	,	PUNCT
ejpam-3085	321	10	c	c	NOUN
ejpam-3085	321	11	}	}	PUNCT
ejpam-3085	321	12	or	or	CCONJ
ejpam-3085	321	13	a	a	DET
ejpam-3085	321	14	=	=	NOUN
ejpam-3085	321	15	h	h	NOUN
ejpam-3085	321	16	and	and	CCONJ
ejpam-3085	321	17	b	b	X
ejpam-3085	321	18	=	=	NOUN
ejpam-3085	321	19	{	{	PUNCT
ejpam-3085	321	20	a	a	PRON
ejpam-3085	321	21	,	,	PUNCT
ejpam-3085	321	22	b	b	NOUN
ejpam-3085	321	23	,	,	PUNCT
ejpam-3085	321	24	c	c	NOUN
ejpam-3085	321	25	}	}	PUNCT
ejpam-3085	321	26	or	or	CCONJ
ejpam-3085	321	27	b	b	X
ejpam-3085	321	28	=	=	SYM
ejpam-3085	321	29	h.	h.	PROPN
ejpam-3085	321	30	for	for	ADP
ejpam-3085	321	31	a	a	DET
ejpam-3085	321	32	=	=	SYM
ejpam-3085	321	33	b	b	NOUN
ejpam-3085	321	34	=	=	PUNCT
ejpam-3085	321	35	{	{	PUNCT
ejpam-3085	321	36	a	a	PRON
ejpam-3085	321	37	,	,	PUNCT
ejpam-3085	321	38	b	b	NOUN
ejpam-3085	321	39	,	,	PUNCT
ejpam-3085	321	40	c	c	NOUN
ejpam-3085	321	41	}	}	PUNCT
ejpam-3085	321	42	,	,	PUNCT
ejpam-3085	321	43	the	the	DET
ejpam-3085	321	44	assumption	assumption	NOUN
ejpam-3085	321	45	is	be	AUX
ejpam-3085	321	46	obvious	obvious	ADJ
ejpam-3085	321	47	.	.	PUNCT
ejpam-3085	322	1	if	if	SCONJ
ejpam-3085	322	2	a	a	PRON
ejpam-3085	322	3	=	=	X
ejpam-3085	322	4	{	{	PUNCT
ejpam-3085	322	5	a	a	PROPN
ejpam-3085	322	6	,	,	PUNCT
ejpam-3085	322	7	b	b	NOUN
ejpam-3085	322	8	,	,	PUNCT
ejpam-3085	322	9	c	c	NOUN
ejpam-3085	322	10	}	}	PUNCT
ejpam-3085	322	11	and	and	CCONJ
ejpam-3085	322	12	b	b	X
ejpam-3085	322	13	=	=	SYM
ejpam-3085	322	14	h	h	PROPN
ejpam-3085	322	15	,	,	PUNCT
ejpam-3085	322	16	then	then	ADV
ejpam-3085	322	17	a	a	DET
ejpam-3085	322	18	∗	∗	NOUN
ejpam-3085	322	19	b	b	NOUN
ejpam-3085	322	20	=	=	PUNCT
ejpam-3085	322	21	⋃	⋃	PROPN
ejpam-3085	322	22	x∈{a	x∈{a	NOUN
ejpam-3085	322	23	,	,	PUNCT
ejpam-3085	322	24	b	b	NOUN
ejpam-3085	322	25	,	,	PUNCT
ejpam-3085	322	26	c	c	NOUN
ejpam-3085	322	27	}	}	PUNCT
ejpam-3085	322	28	y∈{a	y∈{a	NOUN
ejpam-3085	322	29	,	,	PUNCT
ejpam-3085	322	30	b	b	NOUN
ejpam-3085	322	31	,	,	PUNCT
ejpam-3085	322	32	c	c	X
ejpam-3085	322	33	,	,	PUNCT
ejpam-3085	322	34	d	d	NOUN
ejpam-3085	322	35	,	,	PUNCT
ejpam-3085	322	36	f	f	NOUN
ejpam-3085	322	37	}	}	PUNCT
ejpam-3085	322	38	x	x	VERB
ejpam-3085	322	39	◦	◦	NOUN
ejpam-3085	322	40	y	y	NOUN
ejpam-3085	322	41	=	=	PUNCT
ejpam-3085	322	42	{	{	PUNCT
ejpam-3085	322	43	a	a	DET
ejpam-3085	322	44	,	,	PUNCT
ejpam-3085	322	45	b	b	NOUN
ejpam-3085	322	46	,	,	PUNCT
ejpam-3085	322	47	c	c	NOUN
ejpam-3085	322	48	}	}	PUNCT
ejpam-3085	322	49	,	,	PUNCT
ejpam-3085	322	50	again	again	ADV
ejpam-3085	322	51	the	the	DET
ejpam-3085	322	52	assumption	assumption	NOUN
ejpam-3085	322	53	is	be	AUX
ejpam-3085	322	54	obvious	obvious	ADJ
ejpam-3085	322	55	.	.	PUNCT
ejpam-3085	323	1	if	if	SCONJ
ejpam-3085	323	2	a	a	DET
ejpam-3085	323	3	=	=	NOUN
ejpam-3085	323	4	h	h	NOUN
ejpam-3085	323	5	and	and	CCONJ
ejpam-3085	323	6	b	b	X
ejpam-3085	323	7	=	=	NOUN
ejpam-3085	323	8	{	{	PUNCT
ejpam-3085	323	9	a	a	PRON
ejpam-3085	323	10	,	,	PUNCT
ejpam-3085	323	11	b	b	NOUN
ejpam-3085	323	12	,	,	PUNCT
ejpam-3085	323	13	c	c	NOUN
ejpam-3085	323	14	}	}	PUNCT
ejpam-3085	323	15	,	,	PUNCT
ejpam-3085	323	16	then	then	ADV
ejpam-3085	323	17	a	a	DET
ejpam-3085	323	18	∗	∗	NOUN
ejpam-3085	323	19	b	b	NOUN
ejpam-3085	323	20	=	=	PRON
ejpam-3085	323	21	{	{	PUNCT
ejpam-3085	323	22	a	a	PRON
ejpam-3085	323	23	,	,	PUNCT
ejpam-3085	323	24	b	b	NOUN
ejpam-3085	323	25	,	,	PUNCT
ejpam-3085	323	26	c	c	NOUN
ejpam-3085	323	27	,	,	PUNCT
ejpam-3085	323	28	d	d	NOUN
ejpam-3085	323	29	}	}	PUNCT
ejpam-3085	323	30	*	*	PUNCT
ejpam-3085	323	31	{	{	PUNCT
ejpam-3085	323	32	a	a	DET
ejpam-3085	323	33	,	,	PUNCT
ejpam-3085	323	34	b	b	NOUN
ejpam-3085	323	35	,	,	PUNCT
ejpam-3085	323	36	c	c	NOUN
ejpam-3085	323	37	}	}	PUNCT
ejpam-3085	323	38	,	,	PUNCT
ejpam-3085	323	39	the	the	DET
ejpam-3085	323	40	case	case	NOUN
ejpam-3085	323	41	is	be	AUX
ejpam-3085	323	42	impossible	impossible	ADJ
ejpam-3085	323	43	.	.	PUNCT
ejpam-3085	324	1	the	the	DET
ejpam-3085	324	2	case	case	NOUN
ejpam-3085	324	3	a	a	DET
ejpam-3085	324	4	=	=	SYM
ejpam-3085	324	5	b	b	NOUN
ejpam-3085	324	6	=	=	NOUN
ejpam-3085	324	7	h	h	NOUN
ejpam-3085	324	8	is	be	AUX
ejpam-3085	324	9	also	also	ADV
ejpam-3085	324	10	impossible	impossible	ADJ
ejpam-3085	324	11	as	as	SCONJ
ejpam-3085	324	12	h	h	NOUN
ejpam-3085	324	13	∗h	∗h	NOUN
ejpam-3085	324	14	=	=	SYM
ejpam-3085	324	15	h.	h.	PROPN
ejpam-3085	324	16	moreover	moreover	ADV
ejpam-3085	324	17	,	,	PUNCT
ejpam-3085	324	18	this	this	PRON
ejpam-3085	324	19	is	be	AUX
ejpam-3085	324	20	an	an	DET
ejpam-3085	324	21	intra	intra	ADJ
ejpam-3085	324	22	-	-	ADJ
ejpam-3085	324	23	regular	regular	ADJ
ejpam-3085	324	24	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	324	25	.	.	PUNCT
ejpam-3085	325	1	since	since	SCONJ
ejpam-3085	325	2	the	the	DET
ejpam-3085	325	3	ideals	ideal	NOUN
ejpam-3085	325	4	of	of	ADP
ejpam-3085	325	5	h	h	NOUN
ejpam-3085	325	6	form	form	VERB
ejpam-3085	325	7	a	a	DET
ejpam-3085	325	8	chain	chain	NOUN
ejpam-3085	325	9	and	and	CCONJ
ejpam-3085	325	10	h	h	NOUN
ejpam-3085	325	11	is	be	AUX
ejpam-3085	325	12	intra	intra	ADJ
ejpam-3085	325	13	-	-	ADJ
ejpam-3085	325	14	regular	regular	ADJ
ejpam-3085	325	15	,	,	PUNCT
ejpam-3085	325	16	by	by	ADP
ejpam-3085	325	17	theorem	theorem	NOUN
ejpam-3085	325	18	23	23	NUM
ejpam-3085	325	19	,	,	PUNCT
ejpam-3085	325	20	the	the	DET
ejpam-3085	325	21	ideals	ideal	NOUN
ejpam-3085	325	22	of	of	ADP
ejpam-3085	325	23	h	h	NOUN
ejpam-3085	325	24	are	be	AUX
ejpam-3085	325	25	prime	prime	ADJ
ejpam-3085	325	26	(	(	PUNCT
ejpam-3085	325	27	one	one	PRON
ejpam-3085	325	28	can	can	AUX
ejpam-3085	325	29	also	also	ADV
ejpam-3085	325	30	check	check	VERB
ejpam-3085	325	31	it	it	PRON
ejpam-3085	325	32	independently	independently	ADV
ejpam-3085	325	33	)	)	PUNCT
ejpam-3085	325	34	.	.	PUNCT
ejpam-3085	326	1	�	�	PROPN
ejpam-3085	327	1	the	the	DET
ejpam-3085	327	2	example	example	NOUN
ejpam-3085	327	3	a	a	PRON
ejpam-3085	327	4	has	have	AUX
ejpam-3085	327	5	been	be	AUX
ejpam-3085	327	6	constructed	construct	VERB
ejpam-3085	327	7	using	use	VERB
ejpam-3085	327	8	the	the	DET
ejpam-3085	327	9	example	example	NOUN
ejpam-3085	327	10	6	6	NUM
ejpam-3085	327	11	in	in	ADP
ejpam-3085	327	12	[	[	X
ejpam-3085	327	13	6	6	NUM
ejpam-3085	327	14	]	]	PUNCT
ejpam-3085	327	15	and	and	CCONJ
ejpam-3085	327	16	the	the	DET
ejpam-3085	327	17	example	example	NOUN
ejpam-3085	327	18	b	b	ADP
ejpam-3085	327	19	using	use	VERB
ejpam-3085	327	20	the	the	DET
ejpam-3085	327	21	example	example	NOUN
ejpam-3085	327	22	1	1	NUM
ejpam-3085	327	23	in	in	ADP
ejpam-3085	327	24	[	[	X
ejpam-3085	327	25	5	5	NUM
ejpam-3085	327	26	]	]	PUNCT
ejpam-3085	327	27	.	.	PUNCT
ejpam-3085	328	1	note	note	VERB
ejpam-3085	328	2	that	that	SCONJ
ejpam-3085	328	3	we	we	PRON
ejpam-3085	328	4	never	never	ADV
ejpam-3085	328	5	work	work	VERB
ejpam-3085	328	6	directly	directly	ADV
ejpam-3085	328	7	on	on	ADP
ejpam-3085	328	8	an	an	DET
ejpam-3085	328	9	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	328	10	(	(	PUNCT
ejpam-3085	328	11	ordered	order	VERB
ejpam-3085	328	12	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	328	13	)	)	PUNCT
ejpam-3085	328	14	.	.	PUNCT
ejpam-3085	329	1	if	if	SCONJ
ejpam-3085	329	2	we	we	PRON
ejpam-3085	329	3	want	want	VERB
ejpam-3085	329	4	to	to	PART
ejpam-3085	329	5	obtain	obtain	VERB
ejpam-3085	329	6	a	a	DET
ejpam-3085	329	7	result	result	NOUN
ejpam-3085	329	8	on	on	ADP
ejpam-3085	329	9	an	an	DET
ejpam-3085	329	10	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	329	11	(	(	PUNCT
ejpam-3085	329	12	ordered	order	VERB
ejpam-3085	329	13	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	329	14	)	)	PUNCT
ejpam-3085	329	15	,	,	PUNCT
ejpam-3085	329	16	then	then	ADV
ejpam-3085	329	17	we	we	PRON
ejpam-3085	329	18	have	have	VERB
ejpam-3085	329	19	to	to	PART
ejpam-3085	329	20	prove	prove	VERB
ejpam-3085	329	21	it	it	PRON
ejpam-3085	329	22	first	first	ADV
ejpam-3085	329	23	for	for	ADP
ejpam-3085	329	24	a	a	DET
ejpam-3085	329	25	semigroup	semigroup	NOUN
ejpam-3085	329	26	(	(	PUNCT
ejpam-3085	329	27	ordered	order	VERB
ejpam-3085	329	28	semigroup	semigroup	NOUN
ejpam-3085	329	29	)	)	PUNCT
ejpam-3085	329	30	and	and	CCONJ
ejpam-3085	329	31	transfer	transfer	VERB
ejpam-3085	329	32	its	its	PRON
ejpam-3085	329	33	proof	proof	NOUN
ejpam-3085	329	34	to	to	ADP
ejpam-3085	329	35	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	329	36	(	(	PUNCT
ejpam-3085	329	37	ordered	order	VERB
ejpam-3085	329	38	hypersemigroup	hypersemigroup	NOUN
ejpam-3085	329	39	)	)	PUNCT
ejpam-3085	329	40	.	.	PUNCT
ejpam-3085	330	1	an	an	DET
ejpam-3085	330	2	interesting	interesting	ADJ
ejpam-3085	330	3	information	information	NOUN
ejpam-3085	330	4	concerning	concern	VERB
ejpam-3085	330	5	the	the	DET
ejpam-3085	330	6	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	330	7	(	(	PUNCT
ejpam-3085	330	8	without	without	ADP
ejpam-3085	330	9	order	order	NOUN
ejpam-3085	330	10	)	)	PUNCT
ejpam-3085	330	11	will	will	AUX
ejpam-3085	330	12	be	be	AUX
ejpam-3085	330	13	given	give	VERB
ejpam-3085	330	14	in	in	ADP
ejpam-3085	330	15	a	a	DET
ejpam-3085	330	16	forthcoming	forthcoming	ADJ
ejpam-3085	330	17	paper	paper	NOUN
ejpam-3085	330	18	.	.	PUNCT
ejpam-3085	331	1	references	reference	NOUN
ejpam-3085	331	2	22	22	NUM
ejpam-3085	331	3	references	reference	NOUN
ejpam-3085	331	4	[	[	X
ejpam-3085	331	5	1	1	NUM
ejpam-3085	331	6	]	]	PUNCT
ejpam-3085	331	7	g.	g.	NOUN
ejpam-3085	331	8	birkhoff	birkhoff	PROPN
ejpam-3085	331	9	.	.	PUNCT
ejpam-3085	332	1	lattice	lattice	PROPN
ejpam-3085	332	2	theory	theory	PROPN
ejpam-3085	332	3	.	.	PUNCT
ejpam-3085	333	1	amer	amer	PROPN
ejpam-3085	333	2	.	.	PUNCT
ejpam-3085	333	3	math	math	PROPN
ejpam-3085	333	4	.	.	PUNCT
ejpam-3085	334	1	soc	soc	PROPN
ejpam-3085	334	2	.	.	PUNCT
ejpam-3085	335	1	colloq	colloq	PROPN
ejpam-3085	335	2	.	.	PUNCT
ejpam-3085	336	1	publ	publ	PROPN
ejpam-3085	336	2	.	.	PUNCT
ejpam-3085	337	1	vol	vol	NOUN
ejpam-3085	337	2	.	.	PUNCT
ejpam-3085	338	1	xxv	xxv	PROPN
ejpam-3085	338	2	.	.	PUNCT
ejpam-3085	339	1	amer	amer	PROPN
ejpam-3085	339	2	.	.	PUNCT
ejpam-3085	339	3	math	math	PROPN
ejpam-3085	339	4	.	.	PUNCT
ejpam-3085	340	1	soc	soc	PROPN
ejpam-3085	340	2	.	.	PUNCT
ejpam-3085	340	3	,	,	PUNCT
ejpam-3085	340	4	providence	providence	NOUN
ejpam-3085	340	5	,	,	PUNCT
ejpam-3085	340	6	r.i	r.i	PROPN
ejpam-3085	340	7	.	.	PROPN
ejpam-3085	340	8	1967	1967	NUM
ejpam-3085	340	9	vi+418	vi+418	NOUN
ejpam-3085	340	10	pp	pp	ADV
ejpam-3085	340	11	.	.	PUNCT
ejpam-3085	341	1	[	[	X
ejpam-3085	341	2	2	2	X
ejpam-3085	341	3	]	]	PUNCT
ejpam-3085	341	4	n.	n.	NOUN
ejpam-3085	341	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	341	6	.	.	PUNCT
ejpam-3085	342	1	remark	remark	PROPN
ejpam-3085	342	2	on	on	ADP
ejpam-3085	342	3	ordered	order	VERB
ejpam-3085	342	4	semigroups	semigroup	NOUN
ejpam-3085	342	5	.	.	PUNCT
ejpam-3085	343	1	math	math	NOUN
ejpam-3085	343	2	.	.	PUNCT
ejpam-3085	344	1	japon	japon	PROPN
ejpam-3085	344	2	.	.	PUNCT
ejpam-3085	345	1	35(6):1061–1063	35(6):1061–1063	NUM
ejpam-3085	345	2	,	,	PUNCT
ejpam-3085	345	3	1990	1990	NUM
ejpam-3085	345	4	.	.	PUNCT
ejpam-3085	346	1	[	[	X
ejpam-3085	346	2	3	3	X
ejpam-3085	346	3	]	]	X
ejpam-3085	346	4	n.	n.	NOUN
ejpam-3085	346	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	346	6	.	.	PUNCT
ejpam-3085	347	1	on	on	ADP
ejpam-3085	347	2	regular	regular	ADJ
ejpam-3085	347	3	duo	duo	NOUN
ejpam-3085	347	4	ordered	order	VERB
ejpam-3085	347	5	semigroups	semigroup	NOUN
ejpam-3085	347	6	.	.	PUNCT
ejpam-3085	347	7	math	math	NOUN
ejpam-3085	347	8	.	.	PUNCT
ejpam-3085	348	1	japon	japon	PROPN
ejpam-3085	348	2	.	.	PUNCT
ejpam-3085	349	1	37(3):535–540	37(3):535–540	NUM
ejpam-3085	349	2	,	,	PUNCT
ejpam-3085	349	3	1992	1992	NUM
ejpam-3085	349	4	.	.	PUNCT
ejpam-3085	350	1	[	[	X
ejpam-3085	350	2	4	4	X
ejpam-3085	350	3	]	]	X
ejpam-3085	350	4	n.	n.	NOUN
ejpam-3085	350	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	350	6	.	.	PUNCT
ejpam-3085	351	1	on	on	ADP
ejpam-3085	351	2	prime	prime	ADJ
ejpam-3085	351	3	,	,	PUNCT
ejpam-3085	351	4	weakly	weakly	ADJ
ejpam-3085	351	5	prime	prime	ADJ
ejpam-3085	351	6	ideals	ideal	NOUN
ejpam-3085	351	7	in	in	ADP
ejpam-3085	351	8	ordered	order	VERB
ejpam-3085	351	9	semigroups	semigroup	NOUN
ejpam-3085	351	10	.	.	PUNCT
ejpam-3085	352	1	semigroup	semigroup	PROPN
ejpam-3085	352	2	forum	forum	PROPN
ejpam-3085	352	3	44(3):341–346	44(3):341–346	PROPN
ejpam-3085	352	4	,	,	PUNCT
ejpam-3085	352	5	1992	1992	NUM
ejpam-3085	352	6	.	.	PUNCT
ejpam-3085	353	1	[	[	X
ejpam-3085	353	2	5	5	NUM
ejpam-3085	353	3	]	]	PUNCT
ejpam-3085	353	4	n.	n.	NOUN
ejpam-3085	353	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	353	6	.	.	PUNCT
ejpam-3085	354	1	on	on	ADP
ejpam-3085	354	2	intra	intra	ADJ
ejpam-3085	354	3	-	-	ADJ
ejpam-3085	354	4	regular	regular	ADJ
ejpam-3085	354	5	ordered	order	VERB
ejpam-3085	354	6	semigroups	semigroup	NOUN
ejpam-3085	354	7	.	.	PUNCT
ejpam-3085	355	1	semigroup	semigroup	PROPN
ejpam-3085	355	2	forum	forum	PROPN
ejpam-3085	355	3	46(3):271	46(3):271	NOUN
ejpam-3085	355	4	–	–	PUNCT
ejpam-3085	355	5	278	278	NUM
ejpam-3085	355	6	,	,	PUNCT
ejpam-3085	355	7	1993	1993	NUM
ejpam-3085	355	8	.	.	PUNCT
ejpam-3085	356	1	[	[	X
ejpam-3085	356	2	6	6	NUM
ejpam-3085	356	3	]	]	X
ejpam-3085	356	4	n.	n.	NOUN
ejpam-3085	356	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	356	6	.	.	PUNCT
ejpam-3085	357	1	on	on	ADP
ejpam-3085	357	2	regular	regular	ADJ
ejpam-3085	357	3	,	,	PUNCT
ejpam-3085	357	4	intra	intra	ADJ
ejpam-3085	357	5	-	-	ADJ
ejpam-3085	357	6	regular	regular	ADJ
ejpam-3085	357	7	ordered	order	VERB
ejpam-3085	357	8	semigroups	semigroup	NOUN
ejpam-3085	357	9	.	.	PUNCT
ejpam-3085	358	1	pure	pure	ADJ
ejpam-3085	358	2	math	math	NOUN
ejpam-3085	358	3	.	.	PUNCT
ejpam-3085	359	1	appl	appl	PROPN
ejpam-3085	359	2	.	.	PUNCT
ejpam-3085	360	1	4(4):447–461	4(4):447–461	NUM
ejpam-3085	360	2	,	,	PUNCT
ejpam-3085	360	3	1993	1993	NUM
ejpam-3085	360	4	.	.	PUNCT
ejpam-3085	361	1	[	[	X
ejpam-3085	361	2	7	7	X
ejpam-3085	361	3	]	]	X
ejpam-3085	361	4	n.	n.	NOUN
ejpam-3085	361	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	361	6	.	.	PUNCT
ejpam-3085	362	1	characterization	characterization	NOUN
ejpam-3085	362	2	of	of	ADP
ejpam-3085	362	3	left	left	ADJ
ejpam-3085	362	4	quasi	quasi	ADJ
ejpam-3085	362	5	-	-	ADJ
ejpam-3085	362	6	regular	regular	ADJ
ejpam-3085	362	7	and	and	CCONJ
ejpam-3085	362	8	semisimple	semisimple	NOUN
ejpam-3085	362	9	ordered	order	VERB
ejpam-3085	362	10	semigroups	semigroup	NOUN
ejpam-3085	362	11	in	in	ADP
ejpam-3085	362	12	terms	term	NOUN
ejpam-3085	362	13	of	of	ADP
ejpam-3085	362	14	fuzzy	fuzzy	ADJ
ejpam-3085	362	15	sets	set	NOUN
ejpam-3085	362	16	.	.	PUNCT
ejpam-3085	363	1	int	int	NOUN
ejpam-3085	363	2	.	.	PUNCT
ejpam-3085	364	1	j.	j.	PROPN
ejpam-3085	364	2	algebra	algebra	PROPN
ejpam-3085	364	3	6(15):747–755	6(15):747–755	NUM
ejpam-3085	364	4	,	,	PUNCT
ejpam-3085	364	5	2012	2012	NUM
ejpam-3085	364	6	.	.	PUNCT
ejpam-3085	365	1	[	[	X
ejpam-3085	365	2	8	8	NUM
ejpam-3085	365	3	]	]	X
ejpam-3085	365	4	n.	n.	NOUN
ejpam-3085	365	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	365	6	.	.	PUNCT
ejpam-3085	366	1	on	on	ADP
ejpam-3085	366	2	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	366	3	.	.	PUNCT
ejpam-3085	367	1	pure	pure	ADJ
ejpam-3085	367	2	math	math	NOUN
ejpam-3085	367	3	.	.	PUNCT
ejpam-3085	368	1	appl	appl	PROPN
ejpam-3085	368	2	.	.	PUNCT
ejpam-3085	369	1	(	(	PUNCT
ejpam-3085	369	2	pu.m.a	pu.m.a	PROPN
ejpam-3085	369	3	.	.	PUNCT
ejpam-3085	369	4	)	)	PUNCT
ejpam-3085	370	1	25(2):151–156	25(2):151–156	PROPN
ejpam-3085	370	2	,	,	PUNCT
ejpam-3085	370	3	2015	2015	NUM
ejpam-3085	370	4	.	.	PUNCT
ejpam-3085	371	1	[	[	X
ejpam-3085	371	2	9	9	NUM
ejpam-3085	371	3	]	]	X
ejpam-3085	371	4	n.	n.	NOUN
ejpam-3085	371	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	371	6	.	.	PUNCT
ejpam-3085	372	1	on	on	ADP
ejpam-3085	372	2	fuzzy	fuzzy	ADJ
ejpam-3085	372	3	prime	prime	ADJ
ejpam-3085	372	4	and	and	CCONJ
ejpam-3085	372	5	fuzzy	fuzzy	ADJ
ejpam-3085	372	6	semiprime	semiprime	NOUN
ejpam-3085	372	7	ideals	ideal	NOUN
ejpam-3085	372	8	in	in	ADP
ejpam-3085	372	9	≤–hypersemigroups	≤–hypersemigroup	NOUN
ejpam-3085	372	10	.	.	PUNCT
ejpam-3085	373	1	j.	j.	PROPN
ejpam-3085	373	2	hyperstruct	hyperstruct	PROPN
ejpam-3085	373	3	.	.	PUNCT
ejpam-3085	374	1	5(2):108–114	5(2):108–114	NUM
ejpam-3085	374	2	,	,	PUNCT
ejpam-3085	374	3	2016	2016	NUM
ejpam-3085	374	4	.	.	PUNCT
ejpam-3085	375	1	[	[	X
ejpam-3085	375	2	10	10	NUM
ejpam-3085	375	3	]	]	X
ejpam-3085	375	4	n.	n.	NOUN
ejpam-3085	375	5	kehayopulu	kehayopulu	PROPN
ejpam-3085	375	6	.	.	PUNCT
ejpam-3085	376	1	left	leave	VERB
ejpam-3085	376	2	regular	regular	ADJ
ejpam-3085	376	3	and	and	CCONJ
ejpam-3085	376	4	intra	intra	ADJ
ejpam-3085	376	5	-	-	ADJ
ejpam-3085	376	6	regular	regular	ADJ
ejpam-3085	376	7	ordered	order	VERB
ejpam-3085	376	8	hypersemigroups	hypersemigroup	NOUN
ejpam-3085	376	9	in	in	ADP
ejpam-3085	376	10	terms	term	NOUN
ejpam-3085	376	11	of	of	ADP
ejpam-3085	376	12	semiprime	semiprime	NOUN
ejpam-3085	376	13	and	and	CCONJ
ejpam-3085	376	14	fuzzy	fuzzy	ADJ
ejpam-3085	376	15	semiprime	semiprime	NOUN
ejpam-3085	376	16	subsets	subset	NOUN
ejpam-3085	376	17	.	.	PUNCT
ejpam-3085	377	1	sci	sci	PROPN
ejpam-3085	377	2	.	.	PROPN
ejpam-3085	377	3	math	math	PROPN
ejpam-3085	377	4	.	.	PUNCT
ejpam-3085	378	1	jpn	jpn	PROPN
ejpam-3085	378	2	.	.	PUNCT
ejpam-3085	379	1	80(3):295–305	80(3):295–305	PROPN
ejpam-3085	379	2	,	,	PUNCT
ejpam-3085	379	3	2017	2017	NUM
ejpam-3085	379	4	.	.	PUNCT
ejpam-3085	380	1	[	[	X
ejpam-3085	380	2	11	11	NUM
ejpam-3085	380	3	]	]	X
ejpam-3085	380	4	b.	b.	PROPN
ejpam-3085	380	5	pibaljommee	pibaljommee	PROPN
ejpam-3085	380	6	,	,	PUNCT
ejpam-3085	380	7	b.	b.	PROPN
ejpam-3085	380	8	davvaz	davvaz	PROPN
ejpam-3085	380	9	.	.	PUNCT
ejpam-3085	381	1	characterizations	characterization	NOUN
ejpam-3085	381	2	of	of	ADP
ejpam-3085	381	3	(	(	PUNCT
ejpam-3085	381	4	fuzzy	fuzzy	ADJ
ejpam-3085	381	5	)	)	PUNCT
ejpam-3085	381	6	bi	bi	NOUN
ejpam-3085	381	7	-	-	NOUN
ejpam-3085	381	8	hyperideals	hyperideal	NOUN
ejpam-3085	381	9	in	in	ADP
ejpam-3085	381	10	ordered	order	VERB
ejpam-3085	381	11	semihypergroups	semihypergroup	NOUN
ejpam-3085	381	12	.	.	PUNCT
ejpam-3085	382	1	j.	j.	PROPN
ejpam-3085	382	2	intell	intell	PROPN
ejpam-3085	382	3	.	.	PUNCT
ejpam-3085	383	1	fuzzy	fuzzy	ADJ
ejpam-3085	383	2	systems	system	NOUN
ejpam-3085	383	3	28(5):2141–2148	28(5):2141–2148	NUM
ejpam-3085	383	4	,	,	PUNCT
ejpam-3085	383	5	2015	2015	NUM
ejpam-3085	383	6	.	.	PUNCT
ejpam-3085	384	1	article	article	NOUN
ejpam-3085	384	2	submission	submission	NOUN
ejpam-3085	384	3	date	date	NOUN
ejpam-3085	384	4	:	:	PUNCT
ejpam-3085	384	5	o7	o7	PROPN
ejpam-3085	384	6	june	june	PROPN
ejpam-3085	384	7	2017	2017	NUM
ejpam-3085	384	8	.	.	PUNCT