id	sid	tid	token	lemma	pos
ejpam-3266	1	1	european	european	PROPN
ejpam-3266	1	2	journal	journal	PROPN
ejpam-3266	1	3	of	of	ADP
ejpam-3266	1	4	pure	pure	ADJ
ejpam-3266	1	5	and	and	CCONJ
ejpam-3266	1	6	applied	apply	VERB
ejpam-3266	1	7	mathematics	mathematic	NOUN
ejpam-3266	1	8	vol	vol	NOUN
ejpam-3266	1	9	.	.	PUNCT
ejpam-3266	2	1	11	11	NUM
ejpam-3266	2	2	,	,	PUNCT
ejpam-3266	2	3	no	no	INTJ
ejpam-3266	2	4	.	.	NOUN
ejpam-3266	2	5	2	2	NUM
ejpam-3266	2	6	,	,	PUNCT
ejpam-3266	2	7	2018	2018	NUM
ejpam-3266	2	8	,	,	PUNCT
ejpam-3266	2	9	476	476	NUM
ejpam-3266	2	10	-	-	SYM
ejpam-3266	2	11	492	492	NUM
ejpam-3266	2	12	issn	issn	PROPN
ejpam-3266	2	13	1307	1307	NUM
ejpam-3266	2	14	-	-	SYM
ejpam-3266	2	15	5543	5543	NUM
ejpam-3266	2	16	–	–	PUNCT
ejpam-3266	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3266	2	18	published	publish	VERB
ejpam-3266	2	19	by	by	ADP
ejpam-3266	2	20	new	new	PROPN
ejpam-3266	2	21	york	york	PROPN
ejpam-3266	2	22	business	business	PROPN
ejpam-3266	2	23	global	global	PROPN
ejpam-3266	2	24	on	on	ADP
ejpam-3266	2	25	semilattice	semilattice	NOUN
ejpam-3266	2	26	congruences	congruence	NOUN
ejpam-3266	2	27	on	on	ADP
ejpam-3266	2	28	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	2	29	and	and	CCONJ
ejpam-3266	2	30	on	on	ADP
ejpam-3266	2	31	ordered	order	VERB
ejpam-3266	2	32	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	2	33	niovi	niovi	PROPN
ejpam-3266	2	34	kehayopulu	kehayopulu	ADJ
ejpam-3266	2	35	abstract	abstract	NOUN
ejpam-3266	2	36	.	.	PUNCT
ejpam-3266	3	1	we	we	PRON
ejpam-3266	3	2	prove	prove	VERB
ejpam-3266	3	3	that	that	SCONJ
ejpam-3266	3	4	if	if	SCONJ
ejpam-3266	3	5	h	h	NOUN
ejpam-3266	3	6	is	be	AUX
ejpam-3266	3	7	an	an	DET
ejpam-3266	3	8	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	3	9	(	(	PUNCT
ejpam-3266	3	10	resp	resp	NOUN
ejpam-3266	3	11	.	.	PUNCT
ejpam-3266	4	1	ordered	order	VERB
ejpam-3266	4	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	4	3	)	)	PUNCT
ejpam-3266	4	4	and	and	CCONJ
ejpam-3266	4	5	σ	σ	PROPN
ejpam-3266	4	6	is	be	AUX
ejpam-3266	4	7	a	a	DET
ejpam-3266	4	8	semilattice	semilattice	NOUN
ejpam-3266	4	9	congruence	congruence	NOUN
ejpam-3266	4	10	(	(	PUNCT
ejpam-3266	4	11	resp	resp	NOUN
ejpam-3266	4	12	.	.	PUNCT
ejpam-3266	5	1	complete	complete	ADJ
ejpam-3266	5	2	semilattice	semilattice	NOUN
ejpam-3266	5	3	congruence	congruence	NOUN
ejpam-3266	5	4	)	)	PUNCT
ejpam-3266	5	5	on	on	ADP
ejpam-3266	5	6	h	h	NOUN
ejpam-3266	5	7	,	,	PUNCT
ejpam-3266	5	8	then	then	ADV
ejpam-3266	5	9	there	there	PRON
ejpam-3266	5	10	exists	exist	VERB
ejpam-3266	5	11	a	a	DET
ejpam-3266	5	12	family	family	NOUN
ejpam-3266	5	13	a	a	PRON
ejpam-3266	5	14	of	of	ADP
ejpam-3266	5	15	proper	proper	ADJ
ejpam-3266	5	16	prime	prime	ADJ
ejpam-3266	5	17	ideals	ideal	NOUN
ejpam-3266	5	18	of	of	ADP
ejpam-3266	5	19	h	h	NOUN
ejpam-3266	5	20	such	such	ADJ
ejpam-3266	5	21	that	that	SCONJ
ejpam-3266	5	22	σ	σ	PROPN
ejpam-3266	5	23	is	be	AUX
ejpam-3266	5	24	the	the	DET
ejpam-3266	5	25	intersection	intersection	NOUN
ejpam-3266	5	26	of	of	ADP
ejpam-3266	5	27	the	the	DET
ejpam-3266	5	28	semilattice	semilattice	NOUN
ejpam-3266	5	29	congruences	congruence	VERB
ejpam-3266	5	30	σi	σi	PRON
ejpam-3266	5	31	,	,	PUNCT
ejpam-3266	5	32	i	i	PRON
ejpam-3266	5	33	∈	∈	VERB
ejpam-3266	5	34	a	a	PRON
ejpam-3266	5	35	(	(	PUNCT
ejpam-3266	5	36	σi	σi	NOUN
ejpam-3266	5	37	is	be	AUX
ejpam-3266	5	38	the	the	DET
ejpam-3266	5	39	known	know	VERB
ejpam-3266	5	40	relation	relation	NOUN
ejpam-3266	5	41	defined	define	VERB
ejpam-3266	5	42	by	by	ADP
ejpam-3266	5	43	aσib⇔	aσib⇔	PROPN
ejpam-3266	5	44	a	a	PROPN
ejpam-3266	5	45	,	,	PUNCT
ejpam-3266	5	46	b	b	X
ejpam-3266	5	47	∈	∈	NOUN
ejpam-3266	5	48	i	i	PRON
ejpam-3266	5	49	or	or	CCONJ
ejpam-3266	5	50	a	a	PRON
ejpam-3266	5	51	,	,	PUNCT
ejpam-3266	5	52	b	b	PROPN
ejpam-3266	5	53	/∈	/∈	PUNCT
ejpam-3266	5	54	i	i	PROPN
ejpam-3266	5	55	)	)	PUNCT
ejpam-3266	5	56	.	.	PUNCT
ejpam-3266	6	1	furthermore	furthermore	ADV
ejpam-3266	6	2	,	,	PUNCT
ejpam-3266	6	3	we	we	PRON
ejpam-3266	6	4	study	study	VERB
ejpam-3266	6	5	the	the	DET
ejpam-3266	6	6	relation	relation	NOUN
ejpam-3266	6	7	between	between	ADP
ejpam-3266	6	8	the	the	DET
ejpam-3266	6	9	semilattices	semilattice	NOUN
ejpam-3266	6	10	of	of	ADP
ejpam-3266	6	11	an	an	DET
ejpam-3266	6	12	ordered	order	VERB
ejpam-3266	6	13	semigroup	semigroup	NOUN
ejpam-3266	6	14	and	and	CCONJ
ejpam-3266	6	15	the	the	DET
ejpam-3266	6	16	ordered	order	VERB
ejpam-3266	6	17	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	6	18	derived	derive	VERB
ejpam-3266	6	19	by	by	ADP
ejpam-3266	6	20	the	the	DET
ejpam-3266	6	21	hyperoperations	hyperoperation	NOUN
ejpam-3266	6	22	a	a	DET
ejpam-3266	6	23	◦	◦	NOUN
ejpam-3266	6	24	b	b	NOUN
ejpam-3266	6	25	=	=	SYM
ejpam-3266	6	26	{	{	PUNCT
ejpam-3266	6	27	ab	ab	NOUN
ejpam-3266	6	28	}	}	PUNCT
ejpam-3266	6	29	and	and	CCONJ
ejpam-3266	6	30	a	a	DET
ejpam-3266	6	31	◦	◦	NOUN
ejpam-3266	6	32	b	b	X
ejpam-3266	6	33	:	:	PUNCT
ejpam-3266	6	34	=	=	X
ejpam-3266	6	35	{	{	PUNCT
ejpam-3266	6	36	t	t	NOUN
ejpam-3266	6	37	∈	∈	PROPN
ejpam-3266	6	38	s	s	AUX
ejpam-3266	6	39	|	|	NOUN
ejpam-3266	6	40	t	t	X
ejpam-3266	6	41	≤	≤	PROPN
ejpam-3266	6	42	ab	ab	PROPN
ejpam-3266	6	43	}	}	PUNCT
ejpam-3266	6	44	.	.	PUNCT
ejpam-3266	7	1	we	we	PRON
ejpam-3266	7	2	introduce	introduce	VERB
ejpam-3266	7	3	the	the	DET
ejpam-3266	7	4	concept	concept	NOUN
ejpam-3266	7	5	of	of	ADP
ejpam-3266	7	6	a	a	DET
ejpam-3266	7	7	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	7	8	semilattice	semilattice	NOUN
ejpam-3266	7	9	congruence	congruence	NOUN
ejpam-3266	7	10	as	as	ADP
ejpam-3266	7	11	a	a	DET
ejpam-3266	7	12	semilattice	semilattice	NOUN
ejpam-3266	7	13	congruence	congruence	PROPN
ejpam-3266	7	14	σ	σ	PROPN
ejpam-3266	7	15	for	for	ADP
ejpam-3266	7	16	which	which	PRON
ejpam-3266	7	17	≤⊆	≤⊆	PROPN
ejpam-3266	7	18	σ	σ	PROPN
ejpam-3266	7	19	and	and	CCONJ
ejpam-3266	7	20	we	we	PRON
ejpam-3266	7	21	prove	prove	VERB
ejpam-3266	7	22	,	,	PUNCT
ejpam-3266	7	23	among	among	ADP
ejpam-3266	7	24	others	other	NOUN
ejpam-3266	7	25	,	,	PUNCT
ejpam-3266	7	26	that	that	SCONJ
ejpam-3266	7	27	if	if	SCONJ
ejpam-3266	7	28	(	(	PUNCT
ejpam-3266	7	29	s	s	X
ejpam-3266	7	30	,	,	PUNCT
ejpam-3266	7	31	·	·	PUNCT
ejpam-3266	7	32	,	,	PUNCT
ejpam-3266	7	33	≤	≤	NUM
ejpam-3266	7	34	)	)	PUNCT
ejpam-3266	7	35	is	be	AUX
ejpam-3266	7	36	an	an	DET
ejpam-3266	7	37	ordered	order	VERB
ejpam-3266	7	38	semigroup	semigroup	NOUN
ejpam-3266	7	39	,	,	PUNCT
ejpam-3266	7	40	(	(	PUNCT
ejpam-3266	7	41	s	s	X
ejpam-3266	7	42	,	,	PUNCT
ejpam-3266	7	43	◦	◦	NOUN
ejpam-3266	7	44	,	,	PUNCT
ejpam-3266	7	45	≤	≤	NUM
ejpam-3266	7	46	)	)	PUNCT
ejpam-3266	7	47	the	the	DET
ejpam-3266	7	48	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	7	49	defined	define	VERB
ejpam-3266	7	50	by	by	ADP
ejpam-3266	7	51	t	t	PROPN
ejpam-3266	7	52	∈	∈	PROPN
ejpam-3266	7	53	a	a	DET
ejpam-3266	7	54	◦	◦	NOUN
ejpam-3266	7	55	b	b	NOUN
ejpam-3266	8	1	if	if	SCONJ
ejpam-3266	9	1	and	and	CCONJ
ejpam-3266	9	2	only	only	ADV
ejpam-3266	9	3	if	if	SCONJ
ejpam-3266	9	4	t	t	PROPN
ejpam-3266	9	5	≤	≤	X
ejpam-3266	9	6	ab	ab	PROPN
ejpam-3266	9	7	and	and	CCONJ
ejpam-3266	9	8	σ	σ	PROPN
ejpam-3266	9	9	is	be	AUX
ejpam-3266	9	10	a	a	DET
ejpam-3266	9	11	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	9	12	semilattice	semilattice	NOUN
ejpam-3266	9	13	congruence	congruence	NOUN
ejpam-3266	9	14	on	on	ADP
ejpam-3266	9	15	(	(	PUNCT
ejpam-3266	9	16	s	s	X
ejpam-3266	9	17	,	,	PUNCT
ejpam-3266	9	18	·	·	PUNCT
ejpam-3266	9	19	,	,	PUNCT
ejpam-3266	9	20	≤	≤	NUM
ejpam-3266	9	21	)	)	PUNCT
ejpam-3266	9	22	,	,	PUNCT
ejpam-3266	9	23	then	then	ADV
ejpam-3266	9	24	it	it	PRON
ejpam-3266	9	25	is	be	AUX
ejpam-3266	9	26	a	a	DET
ejpam-3266	9	27	complete	complete	ADJ
ejpam-3266	9	28	semilattice	semilattice	NOUN
ejpam-3266	9	29	congruence	congruence	NOUN
ejpam-3266	9	30	on	on	ADP
ejpam-3266	9	31	(	(	PUNCT
ejpam-3266	9	32	s	s	NOUN
ejpam-3266	9	33	,	,	PUNCT
ejpam-3266	9	34	◦	◦	NOUN
ejpam-3266	9	35	,	,	PUNCT
ejpam-3266	9	36	≤	≤	NUM
ejpam-3266	9	37	)	)	PUNCT
ejpam-3266	9	38	.	.	PUNCT
ejpam-3266	10	1	illustrative	illustrative	ADJ
ejpam-3266	10	2	examples	example	NOUN
ejpam-3266	10	3	are	be	AUX
ejpam-3266	10	4	given	give	VERB
ejpam-3266	10	5	.	.	PUNCT
ejpam-3266	11	1	2010	2010	NUM
ejpam-3266	11	2	mathematics	mathematic	NOUN
ejpam-3266	11	3	subject	subject	NOUN
ejpam-3266	11	4	classifications	classification	NOUN
ejpam-3266	11	5	:	:	PUNCT
ejpam-3266	11	6	06f99	06f99	NUM
ejpam-3266	11	7	,	,	PUNCT
ejpam-3266	11	8	20m99	20m99	NUM
ejpam-3266	11	9	,	,	PUNCT
ejpam-3266	11	10	06f05	06f05	NOUN
ejpam-3266	11	11	key	key	ADJ
ejpam-3266	11	12	words	word	NOUN
ejpam-3266	11	13	and	and	CCONJ
ejpam-3266	11	14	phrases	phrase	NOUN
ejpam-3266	11	15	:	:	PUNCT
ejpam-3266	11	16	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	11	17	,	,	PUNCT
ejpam-3266	11	18	ordered	order	VERB
ejpam-3266	11	19	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	11	20	,	,	PUNCT
ejpam-3266	11	21	semilattice	semilattice	NOUN
ejpam-3266	11	22	congruence	congruence	NOUN
ejpam-3266	11	23	,	,	PUNCT
ejpam-3266	11	24	complete	complete	ADJ
ejpam-3266	11	25	(	(	PUNCT
ejpam-3266	11	26	pseudocomplete	pseudocomplete	NOUN
ejpam-3266	11	27	)	)	PUNCT
ejpam-3266	11	28	semilattice	semilattice	NOUN
ejpam-3266	11	29	congruence	congruence	NOUN
ejpam-3266	11	30	,	,	PUNCT
ejpam-3266	11	31	filter	filter	NOUN
ejpam-3266	11	32	,	,	PUNCT
ejpam-3266	11	33	prime	prime	ADJ
ejpam-3266	11	34	ideal	ideal	NOUN
ejpam-3266	11	35	1	1	NUM
ejpam-3266	11	36	.	.	PUNCT
ejpam-3266	12	1	introduction	introduction	NOUN
ejpam-3266	12	2	filters	filter	NOUN
ejpam-3266	12	3	play	play	VERB
ejpam-3266	12	4	an	an	DET
ejpam-3266	12	5	essential	essential	ADJ
ejpam-3266	12	6	role	role	NOUN
ejpam-3266	12	7	in	in	ADP
ejpam-3266	12	8	studying	study	VERB
ejpam-3266	12	9	the	the	DET
ejpam-3266	12	10	structure	structure	NOUN
ejpam-3266	12	11	of	of	ADP
ejpam-3266	12	12	semigroups	semigroup	NOUN
ejpam-3266	12	13	or	or	CCONJ
ejpam-3266	12	14	ordered	order	VERB
ejpam-3266	12	15	semigroups	semigroup	NOUN
ejpam-3266	12	16	.	.	PUNCT
ejpam-3266	13	1	for	for	ADP
ejpam-3266	13	2	a	a	DET
ejpam-3266	13	3	semigroup	semigroup	NOUN
ejpam-3266	13	4	s	s	PART
ejpam-3266	13	5	–	–	PUNCT
ejpam-3266	13	6	especially	especially	ADV
ejpam-3266	13	7	for	for	ADP
ejpam-3266	13	8	decompositions	decomposition	NOUN
ejpam-3266	13	9	of	of	ADP
ejpam-3266	13	10	a	a	DET
ejpam-3266	13	11	semigroup	semigroup	NOUN
ejpam-3266	13	12	s	s	NOUN
ejpam-3266	13	13	–	–	PUNCT
ejpam-3266	13	14	an	an	DET
ejpam-3266	13	15	important	important	ADJ
ejpam-3266	13	16	role	role	NOUN
ejpam-3266	13	17	is	be	AUX
ejpam-3266	13	18	played	play	VERB
ejpam-3266	13	19	by	by	ADP
ejpam-3266	13	20	the	the	DET
ejpam-3266	13	21	relation	relation	NOUN
ejpam-3266	13	22	n	n	CCONJ
ejpam-3266	13	23	which	which	PRON
ejpam-3266	13	24	is	be	AUX
ejpam-3266	13	25	the	the	DET
ejpam-3266	13	26	least	least	ADJ
ejpam-3266	13	27	semilattice	semilattice	NOUN
ejpam-3266	13	28	congruence	congruence	NOUN
ejpam-3266	13	29	on	on	ADP
ejpam-3266	13	30	s	s	PRON
ejpam-3266	13	31	and	and	CCONJ
ejpam-3266	13	32	leads	lead	VERB
ejpam-3266	13	33	to	to	ADP
ejpam-3266	13	34	several	several	ADJ
ejpam-3266	13	35	important	important	ADJ
ejpam-3266	13	36	results	result	NOUN
ejpam-3266	13	37	concerning	concern	VERB
ejpam-3266	13	38	the	the	DET
ejpam-3266	13	39	structure	structure	NOUN
ejpam-3266	13	40	of	of	ADP
ejpam-3266	13	41	semigroups	semigroup	NOUN
ejpam-3266	13	42	(	(	PUNCT
ejpam-3266	13	43	cf	cf	NOUN
ejpam-3266	13	44	.	.	PUNCT
ejpam-3266	14	1	[	[	X
ejpam-3266	14	2	13	13	NUM
ejpam-3266	14	3	]	]	PUNCT
ejpam-3266	14	4	)	)	PUNCT
ejpam-3266	14	5	.	.	PUNCT
ejpam-3266	15	1	using	use	VERB
ejpam-3266	15	2	our	our	PRON
ejpam-3266	15	3	computer	computer	NOUN
ejpam-3266	15	4	program	program	NOUN
ejpam-3266	15	5	,	,	PUNCT
ejpam-3266	15	6	we	we	PRON
ejpam-3266	15	7	have	have	AUX
ejpam-3266	15	8	proved	prove	VERB
ejpam-3266	15	9	in	in	ADP
ejpam-3266	15	10	[	[	X
ejpam-3266	15	11	11	11	NUM
ejpam-3266	15	12	]	]	PUNCT
ejpam-3266	15	13	that	that	SCONJ
ejpam-3266	15	14	for	for	ADP
ejpam-3266	15	15	an	an	DET
ejpam-3266	15	16	ordered	order	VERB
ejpam-3266	15	17	semigroup	semigroup	PROPN
ejpam-3266	15	18	s	s	PROPN
ejpam-3266	15	19	,	,	PUNCT
ejpam-3266	15	20	n	n	PRON
ejpam-3266	15	21	is	be	AUX
ejpam-3266	15	22	not	not	PART
ejpam-3266	15	23	the	the	DET
ejpam-3266	15	24	least	least	ADJ
ejpam-3266	15	25	semilattice	semilattice	NOUN
ejpam-3266	15	26	congruence	congruence	NOUN
ejpam-3266	15	27	on	on	ADP
ejpam-3266	15	28	s	s	PRON
ejpam-3266	15	29	in	in	ADP
ejpam-3266	15	30	general	general	ADJ
ejpam-3266	15	31	,	,	PUNCT
ejpam-3266	15	32	we	we	PRON
ejpam-3266	15	33	introduced	introduce	VERB
ejpam-3266	15	34	the	the	DET
ejpam-3266	15	35	concept	concept	NOUN
ejpam-3266	15	36	of	of	ADP
ejpam-3266	15	37	the	the	DET
ejpam-3266	15	38	complete	complete	ADJ
ejpam-3266	15	39	semilattice	semilattice	NOUN
ejpam-3266	15	40	congruence	congruence	NOUN
ejpam-3266	15	41	and	and	CCONJ
ejpam-3266	15	42	proved	prove	VERB
ejpam-3266	15	43	that	that	SCONJ
ejpam-3266	15	44	n	n	X
ejpam-3266	15	45	is	be	AUX
ejpam-3266	15	46	the	the	DET
ejpam-3266	15	47	least	least	ADJ
ejpam-3266	15	48	complete	complete	ADJ
ejpam-3266	15	49	semilattice	semilattice	NOUN
ejpam-3266	15	50	congruence	congruence	NOUN
ejpam-3266	15	51	on	on	ADP
ejpam-3266	15	52	s.	s.	PROPN
ejpam-3266	15	53	we	we	PRON
ejpam-3266	15	54	always	always	ADV
ejpam-3266	15	55	use	use	VERB
ejpam-3266	15	56	the	the	DET
ejpam-3266	15	57	terms	term	NOUN
ejpam-3266	15	58	“	"	PUNCT
ejpam-3266	15	59	prime	prime	ADJ
ejpam-3266	15	60	”	"	PUNCT
ejpam-3266	15	61	,	,	PUNCT
ejpam-3266	15	62	“	"	PUNCT
ejpam-3266	15	63	weakly	weakly	ADJ
ejpam-3266	15	64	prime	prime	NOUN
ejpam-3266	15	65	”	"	PUNCT
ejpam-3266	15	66	instead	instead	ADV
ejpam-3266	15	67	of	of	ADP
ejpam-3266	15	68	“	"	PUNCT
ejpam-3266	15	69	completely	completely	ADV
ejpam-3266	15	70	prime	prime	ADJ
ejpam-3266	15	71	”	"	PUNCT
ejpam-3266	15	72	,	,	PUNCT
ejpam-3266	15	73	“	"	PUNCT
ejpam-3266	15	74	prime	prime	ADJ
ejpam-3266	15	75	”	"	PUNCT
ejpam-3266	15	76	considered	consider	VERB
ejpam-3266	15	77	by	by	ADP
ejpam-3266	15	78	petrich	petrich	NOUN
ejpam-3266	15	79	in	in	ADP
ejpam-3266	15	80	[	[	X
ejpam-3266	15	81	13	13	NUM
ejpam-3266	15	82	]	]	PUNCT
ejpam-3266	15	83	.	.	PUNCT
ejpam-3266	16	1	the	the	DET
ejpam-3266	16	2	present	present	ADJ
ejpam-3266	16	3	paper	paper	NOUN
ejpam-3266	16	4	is	be	AUX
ejpam-3266	16	5	based	base	VERB
ejpam-3266	16	6	on	on	ADP
ejpam-3266	16	7	our	our	PRON
ejpam-3266	16	8	papers	paper	NOUN
ejpam-3266	16	9	in	in	ADP
ejpam-3266	16	10	[	[	X
ejpam-3266	16	11	3	3	NUM
ejpam-3266	16	12	,	,	PUNCT
ejpam-3266	16	13	11	11	NUM
ejpam-3266	16	14	]	]	PUNCT
ejpam-3266	16	15	and	and	CCONJ
ejpam-3266	16	16	its	its	PRON
ejpam-3266	16	17	aim	aim	NOUN
ejpam-3266	16	18	is	be	AUX
ejpam-3266	16	19	to	to	PART
ejpam-3266	16	20	show	show	VERB
ejpam-3266	16	21	how	how	SCONJ
ejpam-3266	16	22	we	we	PRON
ejpam-3266	16	23	pass	pass	VERB
ejpam-3266	16	24	from	from	ADP
ejpam-3266	16	25	semigroups	semigroup	NOUN
ejpam-3266	16	26	(	(	PUNCT
ejpam-3266	16	27	ordered	order	VERB
ejpam-3266	16	28	semigroups	semigroup	NOUN
ejpam-3266	16	29	)	)	PUNCT
ejpam-3266	16	30	to	to	ADP
ejpam-3266	16	31	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	16	32	(	(	PUNCT
ejpam-3266	16	33	ordered	order	VERB
ejpam-3266	16	34	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	16	35	)	)	PUNCT
ejpam-3266	16	36	.	.	PUNCT
ejpam-3266	17	1	the	the	DET
ejpam-3266	17	2	main	main	ADJ
ejpam-3266	17	3	result	result	NOUN
ejpam-3266	17	4	is	be	AUX
ejpam-3266	17	5	that	that	SCONJ
ejpam-3266	17	6	if	if	SCONJ
ejpam-3266	17	7	h	h	NOUN
ejpam-3266	17	8	is	be	AUX
ejpam-3266	17	9	an	an	DET
ejpam-3266	17	10	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	17	11	(	(	PUNCT
ejpam-3266	17	12	resp	resp	NOUN
ejpam-3266	17	13	.	.	PUNCT
ejpam-3266	18	1	ordered	order	VERB
ejpam-3266	18	2	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	18	3	)	)	PUNCT
ejpam-3266	18	4	and	and	CCONJ
ejpam-3266	18	5	σ	σ	NOUN
ejpam-3266	18	6	a	a	DET
ejpam-3266	18	7	semilattice	semilattice	NOUN
ejpam-3266	18	8	congruence	congruence	NOUN
ejpam-3266	18	9	(	(	PUNCT
ejpam-3266	18	10	resp	resp	NOUN
ejpam-3266	18	11	.	.	PUNCT
ejpam-3266	19	1	complete	complete	ADJ
ejpam-3266	19	2	semilattice	semilattice	NOUN
ejpam-3266	19	3	congruence	congruence	NOUN
ejpam-3266	19	4	)	)	PUNCT
ejpam-3266	19	5	on	on	ADP
ejpam-3266	19	6	h	h	NOUN
ejpam-3266	19	7	,	,	PUNCT
ejpam-3266	19	8	then	then	ADV
ejpam-3266	19	9	there	there	PRON
ejpam-3266	19	10	exists	exist	VERB
ejpam-3266	19	11	a	a	DET
ejpam-3266	19	12	family	family	NOUN
ejpam-3266	19	13	a	a	PRON
ejpam-3266	19	14	of	of	ADP
ejpam-3266	19	15	proper	proper	ADJ
ejpam-3266	19	16	prime	prime	ADJ
ejpam-3266	19	17	ideals	ideal	NOUN
ejpam-3266	19	18	of	of	ADP
ejpam-3266	19	19	h	h	NOUN
ejpam-3266	19	20	such	such	ADJ
ejpam-3266	19	21	that	that	SCONJ
ejpam-3266	19	22	σ	σ	PROPN
ejpam-3266	19	23	=	=	SYM
ejpam-3266	19	24	⋂	⋂	PROPN
ejpam-3266	19	25	i∈a	i∈a	ADJ
ejpam-3266	19	26	σi	σi	NOUN
ejpam-3266	19	27	,	,	PUNCT
ejpam-3266	19	28	σi	σi	PROPN
ejpam-3266	19	29	is	be	AUX
ejpam-3266	19	30	the	the	DET
ejpam-3266	19	31	relation	relation	NOUN
ejpam-3266	19	32	on	on	ADP
ejpam-3266	19	33	h	h	NOUN
ejpam-3266	19	34	defined	define	VERB
ejpam-3266	19	35	by	by	ADP
ejpam-3266	19	36	aσi	aσi	PROPN
ejpam-3266	19	37	⇔	⇔	PROPN
ejpam-3266	19	38	a	a	PROPN
ejpam-3266	19	39	,	,	PUNCT
ejpam-3266	19	40	b	b	X
ejpam-3266	19	41	∈	∈	PROPN
ejpam-3266	19	42	i	i	PRON
ejpam-3266	19	43	or	or	CCONJ
ejpam-3266	19	44	a	a	DET
ejpam-3266	19	45	,	,	PUNCT
ejpam-3266	19	46	b	b	PROPN
ejpam-3266	19	47	/∈	/∈	NOUN
ejpam-3266	19	48	i.	i.	NOUN
ejpam-3266	19	49	then	then	ADV
ejpam-3266	19	50	email	email	NOUN
ejpam-3266	19	51	address	address	NOUN
ejpam-3266	19	52	:	:	PUNCT
ejpam-3266	19	53	nkehayop@math.uoa.gr	nkehayop@math.uoa.gr	ADV
ejpam-3266	19	54	(	(	PUNCT
ejpam-3266	19	55	n.	n.	PROPN
ejpam-3266	19	56	kehayopulu	kehayopulu	PROPN
ejpam-3266	19	57	)	)	PUNCT
ejpam-3266	19	58	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3266	20	1	476	476	NUM
ejpam-3266	20	2	c	c	X
ejpam-3266	20	3	©	©	PROPN
ejpam-3266	20	4	2018	2018	NUM
ejpam-3266	20	5	ejpam	ejpam	VERB
ejpam-3266	20	6	all	all	DET
ejpam-3266	20	7	rights	right	NOUN
ejpam-3266	20	8	reserved	reserve	VERB
ejpam-3266	20	9	.	.	PUNCT
ejpam-3266	21	1	n.	n.	PROPN
ejpam-3266	21	2	kehayopulu	kehayopulu	PROPN
ejpam-3266	21	3	/	/	SYM
ejpam-3266	21	4	eur	eur	PROPN
ejpam-3266	21	5	.	.	PUNCT
ejpam-3266	22	1	j.	j.	PROPN
ejpam-3266	22	2	pure	pure	PROPN
ejpam-3266	22	3	appl	appl	PROPN
ejpam-3266	22	4	.	.	PROPN
ejpam-3266	22	5	math	math	PROPN
ejpam-3266	22	6	,	,	PUNCT
ejpam-3266	22	7	11	11	NUM
ejpam-3266	22	8	(	(	PUNCT
ejpam-3266	22	9	2	2	NUM
ejpam-3266	22	10	)	)	PUNCT
ejpam-3266	22	11	(	(	PUNCT
ejpam-3266	22	12	2018	2018	NUM
ejpam-3266	22	13	)	)	PUNCT
ejpam-3266	22	14	,	,	PUNCT
ejpam-3266	22	15	476	476	NUM
ejpam-3266	22	16	-	-	SYM
ejpam-3266	22	17	492	492	NUM
ejpam-3266	22	18	477	477	NUM
ejpam-3266	22	19	we	we	PRON
ejpam-3266	22	20	prove	prove	VERB
ejpam-3266	22	21	,	,	PUNCT
ejpam-3266	22	22	among	among	ADP
ejpam-3266	22	23	others	other	NOUN
ejpam-3266	22	24	,	,	PUNCT
ejpam-3266	22	25	that	that	SCONJ
ejpam-3266	22	26	if	if	SCONJ
ejpam-3266	22	27	(	(	PUNCT
ejpam-3266	22	28	s	s	X
ejpam-3266	22	29	,	,	PUNCT
ejpam-3266	22	30	·	·	PUNCT
ejpam-3266	22	31	,	,	PUNCT
ejpam-3266	22	32	≤	≤	NUM
ejpam-3266	22	33	)	)	PUNCT
ejpam-3266	22	34	is	be	AUX
ejpam-3266	22	35	an	an	DET
ejpam-3266	22	36	ordered	ordered	ADJ
ejpam-3266	22	37	groupoid	groupoid	NOUN
ejpam-3266	22	38	,	,	PUNCT
ejpam-3266	22	39	and	and	CCONJ
ejpam-3266	22	40	(	(	PUNCT
ejpam-3266	22	41	s	s	X
ejpam-3266	22	42	,	,	PUNCT
ejpam-3266	22	43	◦	◦	NOUN
ejpam-3266	22	44	,	,	PUNCT
ejpam-3266	22	45	≤	≤	NUM
ejpam-3266	22	46	)	)	PUNCT
ejpam-3266	22	47	the	the	DET
ejpam-3266	22	48	ordered	order	VERB
ejpam-3266	22	49	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	22	50	defined	define	VERB
ejpam-3266	22	51	by	by	ADP
ejpam-3266	22	52	a	a	DET
ejpam-3266	22	53	◦	◦	NOUN
ejpam-3266	22	54	b	b	NOUN
ejpam-3266	22	55	=	=	SYM
ejpam-3266	22	56	{	{	PUNCT
ejpam-3266	22	57	ab	ab	NOUN
ejpam-3266	22	58	}	}	PUNCT
ejpam-3266	22	59	,	,	PUNCT
ejpam-3266	22	60	then	then	ADV
ejpam-3266	22	61	σ	σ	PROPN
ejpam-3266	22	62	is	be	AUX
ejpam-3266	22	63	a	a	DET
ejpam-3266	22	64	semilattice	semilattice	NOUN
ejpam-3266	22	65	(	(	PUNCT
ejpam-3266	22	66	resp	resp	NOUN
ejpam-3266	22	67	.	.	PUNCT
ejpam-3266	23	1	complete	complete	ADJ
ejpam-3266	23	2	semilattice	semilattice	PROPN
ejpam-3266	23	3	)	)	PUNCT
ejpam-3266	23	4	congruence	congruence	NOUN
ejpam-3266	23	5	on	on	ADP
ejpam-3266	23	6	(	(	PUNCT
ejpam-3266	23	7	s	s	X
ejpam-3266	23	8	,	,	PUNCT
ejpam-3266	23	9	·	·	PUNCT
ejpam-3266	23	10	,	,	PUNCT
ejpam-3266	23	11	≤	≤	NUM
ejpam-3266	23	12	)	)	PUNCT
ejpam-3266	24	1	if	if	SCONJ
ejpam-3266	24	2	and	and	CCONJ
ejpam-3266	24	3	only	only	ADV
ejpam-3266	24	4	if	if	SCONJ
ejpam-3266	24	5	it	it	PRON
ejpam-3266	24	6	is	be	AUX
ejpam-3266	24	7	a	a	DET
ejpam-3266	24	8	semilattice	semilattice	NOUN
ejpam-3266	24	9	(	(	PUNCT
ejpam-3266	24	10	resp	resp	NOUN
ejpam-3266	24	11	.	.	PUNCT
ejpam-3266	25	1	complete	complete	ADJ
ejpam-3266	25	2	semilattice	semilattice	PROPN
ejpam-3266	25	3	)	)	PUNCT
ejpam-3266	25	4	congruence	congruence	NOUN
ejpam-3266	25	5	on	on	ADP
ejpam-3266	25	6	(	(	PUNCT
ejpam-3266	25	7	s	s	NOUN
ejpam-3266	25	8	,	,	PUNCT
ejpam-3266	25	9	◦	◦	NOUN
ejpam-3266	25	10	,	,	PUNCT
ejpam-3266	25	11	≤	≤	NUM
ejpam-3266	25	12	)	)	PUNCT
ejpam-3266	25	13	.	.	PUNCT
ejpam-3266	26	1	as	as	ADP
ejpam-3266	26	2	an	an	DET
ejpam-3266	26	3	immediate	immediate	ADJ
ejpam-3266	26	4	consequence	consequence	NOUN
ejpam-3266	26	5	,	,	PUNCT
ejpam-3266	26	6	in	in	ADP
ejpam-3266	26	7	an	an	DET
ejpam-3266	26	8	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	26	9	h	h	NOUN
ejpam-3266	26	10	,	,	PUNCT
ejpam-3266	26	11	the	the	DET
ejpam-3266	26	12	complete	complete	ADJ
ejpam-3266	26	13	semilattice	semilattice	NOUN
ejpam-3266	26	14	congruence	congruence	NOUN
ejpam-3266	26	15	n	n	CCONJ
ejpam-3266	26	16	defined	define	VERB
ejpam-3266	26	17	by	by	ADP
ejpam-3266	26	18	xn	xn	PROPN
ejpam-3266	26	19	y	y	PROPN
ejpam-3266	26	20	⇔	⇔	PROPN
ejpam-3266	26	21	n(x	n(x	PROPN
ejpam-3266	26	22	)	)	PUNCT
ejpam-3266	26	23	=	=	SYM
ejpam-3266	26	24	n(y	n(y	ADJ
ejpam-3266	26	25	)	)	PUNCT
ejpam-3266	26	26	(	(	PUNCT
ejpam-3266	26	27	where	where	SCONJ
ejpam-3266	26	28	n(x	n(x	X
ejpam-3266	26	29	)	)	PUNCT
ejpam-3266	26	30	is	be	AUX
ejpam-3266	26	31	the	the	DET
ejpam-3266	26	32	filter	filter	NOUN
ejpam-3266	26	33	generated	generate	VERB
ejpam-3266	26	34	by	by	ADP
ejpam-3266	26	35	the	the	DET
ejpam-3266	26	36	element	element	NOUN
ejpam-3266	26	37	x	x	PROPN
ejpam-3266	26	38	of	of	ADP
ejpam-3266	26	39	h	h	NOUN
ejpam-3266	26	40	)	)	PUNCT
ejpam-3266	26	41	can	can	AUX
ejpam-3266	26	42	not	not	PART
ejpam-3266	26	43	be	be	AUX
ejpam-3266	26	44	the	the	DET
ejpam-3266	26	45	least	least	ADJ
ejpam-3266	26	46	semilattice	semilattice	NOUN
ejpam-3266	26	47	congruence	congruence	NOUN
ejpam-3266	26	48	on	on	ADP
ejpam-3266	26	49	h	h	NOUN
ejpam-3266	26	50	in	in	ADP
ejpam-3266	26	51	general	general	ADJ
ejpam-3266	26	52	.	.	PUNCT
ejpam-3266	27	1	for	for	ADP
ejpam-3266	27	2	an	an	DET
ejpam-3266	27	3	ordered	order	VERB
ejpam-3266	27	4	groupoid	groupoid	NOUN
ejpam-3266	27	5	(	(	PUNCT
ejpam-3266	27	6	s	s	PROPN
ejpam-3266	27	7	,	,	PUNCT
ejpam-3266	27	8	·	·	PUNCT
ejpam-3266	27	9	,	,	PUNCT
ejpam-3266	27	10	≤	≤	NUM
ejpam-3266	27	11	)	)	PUNCT
ejpam-3266	27	12	we	we	PRON
ejpam-3266	27	13	consider	consider	VERB
ejpam-3266	27	14	the	the	DET
ejpam-3266	27	15	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	27	16	on	on	ADP
ejpam-3266	27	17	s	s	PRON
ejpam-3266	27	18	with	with	ADP
ejpam-3266	27	19	the	the	DET
ejpam-3266	27	20	hyperoperation	hyperoperation	NOUN
ejpam-3266	27	21	defined	define	VERB
ejpam-3266	27	22	by	by	ADP
ejpam-3266	27	23	a	a	DET
ejpam-3266	27	24	◦	◦	NOUN
ejpam-3266	27	25	b	b	X
ejpam-3266	27	26	=	=	NOUN
ejpam-3266	27	27	:	:	PUNCT
ejpam-3266	27	28	{	{	PUNCT
ejpam-3266	27	29	t	t	NOUN
ejpam-3266	27	30	∈	∈	PROPN
ejpam-3266	27	31	s	s	AUX
ejpam-3266	27	32	|	|	NOUN
ejpam-3266	27	33	t	t	X
ejpam-3266	27	34	≤	≤	PROPN
ejpam-3266	27	35	ab	ab	ADP
ejpam-3266	27	36	}	}	PUNCT
ejpam-3266	27	37	and	and	CCONJ
ejpam-3266	27	38	we	we	PRON
ejpam-3266	27	39	prove	prove	VERB
ejpam-3266	27	40	that	that	SCONJ
ejpam-3266	27	41	if	if	SCONJ
ejpam-3266	27	42	σ	σ	PROPN
ejpam-3266	27	43	is	be	AUX
ejpam-3266	27	44	a	a	DET
ejpam-3266	27	45	semilattice	semilattice	NOUN
ejpam-3266	27	46	congruence	congruence	NOUN
ejpam-3266	27	47	on	on	ADP
ejpam-3266	27	48	(	(	PUNCT
ejpam-3266	27	49	s	s	NOUN
ejpam-3266	27	50	,	,	PUNCT
ejpam-3266	27	51	◦	◦	NOUN
ejpam-3266	27	52	,	,	PUNCT
ejpam-3266	27	53	≤	≤	NUM
ejpam-3266	27	54	)	)	PUNCT
ejpam-3266	27	55	,	,	PUNCT
ejpam-3266	27	56	then	then	ADV
ejpam-3266	27	57	it	it	PRON
ejpam-3266	27	58	is	be	AUX
ejpam-3266	27	59	a	a	DET
ejpam-3266	27	60	semilattice	semilattice	NOUN
ejpam-3266	27	61	congruence	congruence	NOUN
ejpam-3266	27	62	on	on	ADP
ejpam-3266	27	63	(	(	PUNCT
ejpam-3266	27	64	s	s	X
ejpam-3266	27	65	,	,	PUNCT
ejpam-3266	27	66	·	·	PUNCT
ejpam-3266	27	67	,	,	PUNCT
ejpam-3266	27	68	≤	≤	NUM
ejpam-3266	27	69	)	)	PUNCT
ejpam-3266	27	70	but	but	CCONJ
ejpam-3266	27	71	the	the	DET
ejpam-3266	27	72	converse	converse	NOUN
ejpam-3266	27	73	statement	statement	NOUN
ejpam-3266	27	74	does	do	AUX
ejpam-3266	27	75	not	not	PART
ejpam-3266	27	76	hold	hold	VERB
ejpam-3266	27	77	in	in	ADP
ejpam-3266	27	78	general	general	ADJ
ejpam-3266	27	79	.	.	PUNCT
ejpam-3266	28	1	in	in	ADP
ejpam-3266	28	2	addition	addition	NOUN
ejpam-3266	28	3	,	,	PUNCT
ejpam-3266	28	4	if	if	SCONJ
ejpam-3266	28	5	σ	σ	PROPN
ejpam-3266	28	6	is	be	AUX
ejpam-3266	28	7	a	a	DET
ejpam-3266	28	8	complete	complete	ADJ
ejpam-3266	28	9	semilattice	semilattice	NOUN
ejpam-3266	28	10	congruence	congruence	NOUN
ejpam-3266	28	11	on	on	ADP
ejpam-3266	28	12	(	(	PUNCT
ejpam-3266	28	13	s	s	NOUN
ejpam-3266	28	14	,	,	PUNCT
ejpam-3266	28	15	◦	◦	NOUN
ejpam-3266	28	16	,	,	PUNCT
ejpam-3266	28	17	≤	≤	NUM
ejpam-3266	28	18	)	)	PUNCT
ejpam-3266	28	19	,	,	PUNCT
ejpam-3266	28	20	then	then	ADV
ejpam-3266	28	21	it	it	PRON
ejpam-3266	28	22	is	be	AUX
ejpam-3266	28	23	a	a	DET
ejpam-3266	28	24	complete	complete	ADJ
ejpam-3266	28	25	semilattice	semilattice	NOUN
ejpam-3266	28	26	congruence	congruence	NOUN
ejpam-3266	28	27	on	on	ADP
ejpam-3266	28	28	(	(	PUNCT
ejpam-3266	28	29	s	s	X
ejpam-3266	28	30	,	,	PUNCT
ejpam-3266	28	31	·	·	PUNCT
ejpam-3266	28	32	,	,	PUNCT
ejpam-3266	28	33	≤	≤	NUM
ejpam-3266	28	34	)	)	PUNCT
ejpam-3266	28	35	.	.	PUNCT
ejpam-3266	29	1	it	it	PRON
ejpam-3266	29	2	is	be	AUX
ejpam-3266	29	3	natural	natural	ADJ
ejpam-3266	29	4	to	to	PART
ejpam-3266	29	5	ask	ask	VERB
ejpam-3266	29	6	if	if	SCONJ
ejpam-3266	29	7	there	there	PRON
ejpam-3266	29	8	are	be	VERB
ejpam-3266	29	9	semilattice	semilattice	NOUN
ejpam-3266	29	10	congruences	congruence	NOUN
ejpam-3266	29	11	on	on	ADP
ejpam-3266	29	12	an	an	DET
ejpam-3266	29	13	ordered	order	VERB
ejpam-3266	29	14	groupoid	groupoid	NOUN
ejpam-3266	29	15	(	(	PUNCT
ejpam-3266	29	16	s	s	PROPN
ejpam-3266	29	17	,	,	PUNCT
ejpam-3266	29	18	·	·	PUNCT
ejpam-3266	29	19	,	,	PUNCT
ejpam-3266	29	20	≤	≤	NUM
ejpam-3266	29	21	)	)	PUNCT
ejpam-3266	29	22	that	that	PRON
ejpam-3266	29	23	are	be	AUX
ejpam-3266	29	24	semilattice	semilattice	NOUN
ejpam-3266	29	25	congruences	congruence	NOUN
ejpam-3266	29	26	on	on	ADP
ejpam-3266	29	27	(	(	PUNCT
ejpam-3266	29	28	s	s	NOUN
ejpam-3266	29	29	,	,	PUNCT
ejpam-3266	29	30	◦	◦	NOUN
ejpam-3266	29	31	,	,	PUNCT
ejpam-3266	29	32	≤	≤	NUM
ejpam-3266	29	33	)	)	PUNCT
ejpam-3266	29	34	as	as	ADV
ejpam-3266	29	35	well	well	ADV
ejpam-3266	29	36	.	.	PUNCT
ejpam-3266	30	1	on	on	ADP
ejpam-3266	30	2	this	this	DET
ejpam-3266	30	3	purpose	purpose	NOUN
ejpam-3266	30	4	,	,	PUNCT
ejpam-3266	30	5	we	we	PRON
ejpam-3266	30	6	introduce	introduce	VERB
ejpam-3266	30	7	the	the	DET
ejpam-3266	30	8	concept	concept	NOUN
ejpam-3266	30	9	of	of	ADP
ejpam-3266	30	10	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	30	11	semilattice	semilattice	NOUN
ejpam-3266	30	12	congruences	congruence	NOUN
ejpam-3266	30	13	as	as	SCONJ
ejpam-3266	30	14	the	the	DET
ejpam-3266	30	15	semilattice	semilattice	NOUN
ejpam-3266	30	16	congruences	congruence	VERB
ejpam-3266	30	17	σ	σ	NOUN
ejpam-3266	30	18	such	such	ADJ
ejpam-3266	30	19	that	that	SCONJ
ejpam-3266	30	20	≤⊆	≤⊆	PROPN
ejpam-3266	30	21	σ	σ	PROPN
ejpam-3266	30	22	,	,	PUNCT
ejpam-3266	30	23	and	and	CCONJ
ejpam-3266	30	24	we	we	PRON
ejpam-3266	30	25	prove	prove	VERB
ejpam-3266	30	26	that	that	SCONJ
ejpam-3266	30	27	the	the	DET
ejpam-3266	30	28	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	30	29	semilattice	semilattice	NOUN
ejpam-3266	30	30	congruences	congruence	VERB
ejpam-3266	30	31	on	on	ADP
ejpam-3266	30	32	an	an	DET
ejpam-3266	30	33	ordered	order	VERB
ejpam-3266	30	34	groupoid	groupoid	NOUN
ejpam-3266	30	35	(	(	PUNCT
ejpam-3266	30	36	s	s	PROPN
ejpam-3266	30	37	,	,	PUNCT
ejpam-3266	30	38	·	·	PUNCT
ejpam-3266	30	39	,	,	PUNCT
ejpam-3266	30	40	≤	≤	NUM
ejpam-3266	30	41	)	)	PUNCT
ejpam-3266	30	42	are	be	AUX
ejpam-3266	30	43	complete	complete	ADJ
ejpam-3266	30	44	semilattice	semilattice	NOUN
ejpam-3266	30	45	congruences	congruence	NOUN
ejpam-3266	30	46	on	on	ADP
ejpam-3266	30	47	(	(	PUNCT
ejpam-3266	30	48	s	s	NOUN
ejpam-3266	30	49	,	,	PUNCT
ejpam-3266	30	50	◦	◦	NOUN
ejpam-3266	30	51	,	,	PUNCT
ejpam-3266	30	52	≤	≤	NUM
ejpam-3266	30	53	)	)	PUNCT
ejpam-3266	30	54	.	.	PUNCT
ejpam-3266	31	1	we	we	PRON
ejpam-3266	31	2	could	could	AUX
ejpam-3266	31	3	finally	finally	ADV
ejpam-3266	31	4	mention	mention	VERB
ejpam-3266	31	5	the	the	DET
ejpam-3266	31	6	following	following	NOUN
ejpam-3266	31	7	:	:	PUNCT
ejpam-3266	31	8	if	if	SCONJ
ejpam-3266	31	9	(	(	PUNCT
ejpam-3266	31	10	s	s	X
ejpam-3266	31	11	,	,	PUNCT
ejpam-3266	31	12	·	·	PUNCT
ejpam-3266	31	13	)	)	PUNCT
ejpam-3266	31	14	is	be	AUX
ejpam-3266	31	15	a	a	DET
ejpam-3266	31	16	groupoid	groupoid	NOUN
ejpam-3266	31	17	and	and	CCONJ
ejpam-3266	31	18	“	"	PUNCT
ejpam-3266	31	19	◦	◦	NOUN
ejpam-3266	31	20	”	"	PUNCT
ejpam-3266	31	21	the	the	DET
ejpam-3266	31	22	hyperoperation	hyperoperation	NOUN
ejpam-3266	31	23	on	on	ADP
ejpam-3266	31	24	s	s	PRON
ejpam-3266	31	25	defined	define	VERB
ejpam-3266	31	26	by	by	ADP
ejpam-3266	31	27	a	a	DET
ejpam-3266	31	28	◦	◦	NOUN
ejpam-3266	31	29	b	b	X
ejpam-3266	31	30	:	:	PUNCT
ejpam-3266	31	31	=	=	SYM
ejpam-3266	31	32	{	{	PUNCT
ejpam-3266	31	33	ab	ab	NOUN
ejpam-3266	31	34	}	}	PUNCT
ejpam-3266	31	35	,	,	PUNCT
ejpam-3266	31	36	then	then	ADV
ejpam-3266	31	37	f	f	PROPN
ejpam-3266	31	38	is	be	AUX
ejpam-3266	31	39	a	a	DET
ejpam-3266	31	40	filter	filter	NOUN
ejpam-3266	31	41	of	of	ADP
ejpam-3266	31	42	(	(	PUNCT
ejpam-3266	31	43	s	s	X
ejpam-3266	31	44	,	,	PUNCT
ejpam-3266	31	45	·	·	PUNCT
ejpam-3266	31	46	)	)	PUNCT
ejpam-3266	32	1	if	if	SCONJ
ejpam-3266	32	2	and	and	CCONJ
ejpam-3266	32	3	and	and	CCONJ
ejpam-3266	32	4	only	only	ADV
ejpam-3266	32	5	if	if	SCONJ
ejpam-3266	32	6	it	it	PRON
ejpam-3266	32	7	is	be	AUX
ejpam-3266	32	8	a	a	DET
ejpam-3266	32	9	filter	filter	NOUN
ejpam-3266	32	10	of	of	ADP
ejpam-3266	32	11	(	(	PUNCT
ejpam-3266	32	12	s	s	X
ejpam-3266	32	13	,	,	PUNCT
ejpam-3266	32	14	◦	◦	NOUN
ejpam-3266	32	15	)	)	PUNCT
ejpam-3266	32	16	;	;	PUNCT
ejpam-3266	32	17	for	for	ADP
ejpam-3266	32	18	an	an	DET
ejpam-3266	32	19	ordered	order	VERB
ejpam-3266	32	20	groupoid	groupoid	NOUN
ejpam-3266	32	21	(	(	PUNCT
ejpam-3266	32	22	s	s	PROPN
ejpam-3266	32	23	,	,	PUNCT
ejpam-3266	32	24	·	·	PUNCT
ejpam-3266	32	25	,	,	PUNCT
ejpam-3266	32	26	≤	≤	NUM
ejpam-3266	32	27	)	)	PUNCT
ejpam-3266	32	28	with	with	ADP
ejpam-3266	32	29	the	the	DET
ejpam-3266	32	30	same	same	ADJ
ejpam-3266	32	31	hyperoperation	hyperoperation	NOUN
ejpam-3266	32	32	,	,	PUNCT
ejpam-3266	32	33	the	the	DET
ejpam-3266	32	34	filters	filter	NOUN
ejpam-3266	32	35	of	of	ADP
ejpam-3266	32	36	(	(	PUNCT
ejpam-3266	32	37	s	s	X
ejpam-3266	32	38	,	,	PUNCT
ejpam-3266	32	39	·	·	PUNCT
ejpam-3266	32	40	,	,	PUNCT
ejpam-3266	32	41	≤	≤	NUM
ejpam-3266	32	42	)	)	PUNCT
ejpam-3266	32	43	and	and	CCONJ
ejpam-3266	32	44	the	the	DET
ejpam-3266	32	45	filters	filter	NOUN
ejpam-3266	32	46	of	of	ADP
ejpam-3266	32	47	(	(	PUNCT
ejpam-3266	32	48	s	s	X
ejpam-3266	32	49	,	,	PUNCT
ejpam-3266	32	50	◦	◦	NOUN
ejpam-3266	32	51	,	,	PUNCT
ejpam-3266	32	52	≤	≤	NUM
ejpam-3266	32	53	)	)	PUNCT
ejpam-3266	32	54	are	be	AUX
ejpam-3266	32	55	also	also	ADV
ejpam-3266	32	56	the	the	DET
ejpam-3266	32	57	same	same	ADJ
ejpam-3266	32	58	.	.	PUNCT
ejpam-3266	33	1	if	if	SCONJ
ejpam-3266	33	2	(	(	PUNCT
ejpam-3266	33	3	s	s	X
ejpam-3266	33	4	,	,	PUNCT
ejpam-3266	33	5	·	·	PUNCT
ejpam-3266	33	6	,	,	PUNCT
ejpam-3266	33	7	≤	≤	NUM
ejpam-3266	33	8	)	)	PUNCT
ejpam-3266	33	9	is	be	AUX
ejpam-3266	33	10	an	an	DET
ejpam-3266	33	11	ordered	order	VERB
ejpam-3266	33	12	groupoid	groupoid	NOUN
ejpam-3266	33	13	and	and	CCONJ
ejpam-3266	33	14	“	"	PUNCT
ejpam-3266	33	15	◦	◦	NOUN
ejpam-3266	33	16	”	"	PUNCT
ejpam-3266	33	17	the	the	DET
ejpam-3266	33	18	hyperoperation	hyperoperation	NOUN
ejpam-3266	33	19	on	on	ADP
ejpam-3266	33	20	s	s	PRON
ejpam-3266	33	21	defined	define	VERB
ejpam-3266	33	22	by	by	ADP
ejpam-3266	33	23	t	t	PROPN
ejpam-3266	33	24	∈	∈	PROPN
ejpam-3266	33	25	a	a	DET
ejpam-3266	33	26	◦	◦	NOUN
ejpam-3266	33	27	b	b	X
ejpam-3266	33	28	⇔	⇔	PROPN
ejpam-3266	33	29	t	t	PROPN
ejpam-3266	33	30	≤	≤	PROPN
ejpam-3266	33	31	ab	ab	PROPN
ejpam-3266	33	32	,	,	PUNCT
ejpam-3266	33	33	the	the	DET
ejpam-3266	33	34	filters	filter	NOUN
ejpam-3266	33	35	of	of	ADP
ejpam-3266	33	36	(	(	PUNCT
ejpam-3266	33	37	s	s	X
ejpam-3266	33	38	,	,	PUNCT
ejpam-3266	33	39	◦	◦	NOUN
ejpam-3266	33	40	,	,	PUNCT
ejpam-3266	33	41	≤	≤	NUM
ejpam-3266	33	42	)	)	PUNCT
ejpam-3266	33	43	are	be	AUX
ejpam-3266	33	44	also	also	ADV
ejpam-3266	33	45	filters	filter	NOUN
ejpam-3266	33	46	of	of	ADP
ejpam-3266	33	47	(	(	PUNCT
ejpam-3266	33	48	s	s	X
ejpam-3266	33	49	,	,	PUNCT
ejpam-3266	33	50	·	·	PUNCT
ejpam-3266	33	51	,	,	PUNCT
ejpam-3266	33	52	≤	≤	NUM
ejpam-3266	33	53	)	)	PUNCT
ejpam-3266	33	54	but	but	CCONJ
ejpam-3266	33	55	the	the	DET
ejpam-3266	33	56	converse	converse	NOUN
ejpam-3266	33	57	statement	statement	NOUN
ejpam-3266	33	58	does	do	AUX
ejpam-3266	33	59	not	not	PART
ejpam-3266	33	60	hold	hold	VERB
ejpam-3266	33	61	in	in	ADP
ejpam-3266	33	62	general	general	ADJ
ejpam-3266	33	63	.	.	PUNCT
ejpam-3266	34	1	an	an	DET
ejpam-3266	34	2	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	34	3	is	be	AUX
ejpam-3266	34	4	a	a	DET
ejpam-3266	34	5	nonempty	nonempty	ADV
ejpam-3266	34	6	set	set	VERB
ejpam-3266	34	7	h	h	NOUN
ejpam-3266	34	8	with	with	ADP
ejpam-3266	34	9	an	an	DET
ejpam-3266	34	10	hyperoperation	hyperoperation	NOUN
ejpam-3266	34	11	◦	◦	NOUN
ejpam-3266	34	12	:	:	PUNCT
ejpam-3266	34	13	h	h	NOUN
ejpam-3266	34	14	×h	×h	PROPN
ejpam-3266	34	15	→	→	SYM
ejpam-3266	34	16	p∗(h	p∗(h	NOUN
ejpam-3266	34	17	)	)	PUNCT
ejpam-3266	35	1	|	|	ADV
ejpam-3266	35	2	(	(	PUNCT
ejpam-3266	35	3	a	a	PRON
ejpam-3266	35	4	,	,	PUNCT
ejpam-3266	35	5	b)→	b)→	VERB
ejpam-3266	35	6	a	a	DET
ejpam-3266	35	7	◦	◦	NOUN
ejpam-3266	35	8	b	b	NOUN
ejpam-3266	35	9	on	on	ADP
ejpam-3266	35	10	h	h	NOUN
ejpam-3266	35	11	and	and	CCONJ
ejpam-3266	35	12	an	an	DET
ejpam-3266	35	13	operation	operation	NOUN
ejpam-3266	35	14	∗	∗	NOUN
ejpam-3266	35	15	:	:	PUNCT
ejpam-3266	35	16	p∗(h	p∗(h	X
ejpam-3266	35	17	)	)	PUNCT
ejpam-3266	35	18	×	×	PROPN
ejpam-3266	35	19	p∗(h	p∗(h	PROPN
ejpam-3266	35	20	)	)	PUNCT
ejpam-3266	35	21	→	→	SYM
ejpam-3266	35	22	p∗(h	p∗(h	NOUN
ejpam-3266	35	23	)	)	PUNCT
ejpam-3266	36	1	|	|	ADV
ejpam-3266	36	2	(	(	PUNCT
ejpam-3266	36	3	a	a	DET
ejpam-3266	36	4	,	,	PUNCT
ejpam-3266	36	5	b	b	NOUN
ejpam-3266	36	6	)	)	PUNCT
ejpam-3266	36	7	→	→	ADP
ejpam-3266	36	8	a	a	DET
ejpam-3266	36	9	∗	∗	NOUN
ejpam-3266	36	10	b	b	NOUN
ejpam-3266	36	11	on	on	ADP
ejpam-3266	36	12	p∗(h	p∗(h	PROPN
ejpam-3266	36	13	)	)	PUNCT
ejpam-3266	36	14	(	(	PUNCT
ejpam-3266	36	15	induced	induce	VERB
ejpam-3266	36	16	by	by	ADP
ejpam-3266	36	17	the	the	DET
ejpam-3266	36	18	operation	operation	NOUN
ejpam-3266	36	19	of	of	ADP
ejpam-3266	36	20	h	h	NOUN
ejpam-3266	36	21	)	)	PUNCT
ejpam-3266	36	22	such	such	ADJ
ejpam-3266	36	23	that	that	SCONJ
ejpam-3266	36	24	a	a	DET
ejpam-3266	36	25	∗	∗	NOUN
ejpam-3266	36	26	b	b	NOUN
ejpam-3266	36	27	=	=	X
ejpam-3266	36	28	⋃	⋃	PROPN
ejpam-3266	36	29	(	(	PUNCT
ejpam-3266	36	30	a	a	PRON
ejpam-3266	36	31	,	,	PUNCT
ejpam-3266	36	32	b)∈a×b	b)∈a×b	NUM
ejpam-3266	36	33	(	(	PUNCT
ejpam-3266	36	34	a	a	DET
ejpam-3266	36	35	◦	◦	NOUN
ejpam-3266	36	36	b	b	NOUN
ejpam-3266	36	37	)	)	PUNCT
ejpam-3266	36	38	for	for	ADP
ejpam-3266	36	39	every	every	DET
ejpam-3266	36	40	a	a	PROPN
ejpam-3266	36	41	,	,	PUNCT
ejpam-3266	36	42	b	b	PROPN
ejpam-3266	36	43	∈	∈	PROPN
ejpam-3266	36	44	p∗(h	p∗(h	PROPN
ejpam-3266	36	45	)	)	PUNCT
ejpam-3266	36	46	(	(	PUNCT
ejpam-3266	36	47	p∗(h	p∗(h	NOUN
ejpam-3266	36	48	)	)	PUNCT
ejpam-3266	36	49	denotes	denote	VERB
ejpam-3266	36	50	the	the	DET
ejpam-3266	36	51	set	set	NOUN
ejpam-3266	36	52	of	of	ADP
ejpam-3266	36	53	nonempty	nonempty	ADJ
ejpam-3266	36	54	subsets	subset	NOUN
ejpam-3266	36	55	of	of	ADP
ejpam-3266	36	56	h	h	NOUN
ejpam-3266	36	57	)	)	PUNCT
ejpam-3266	36	58	.	.	PUNCT
ejpam-3266	37	1	a	a	DET
ejpam-3266	37	2	nonempty	nonempty	NOUN
ejpam-3266	37	3	subset	subset	VERB
ejpam-3266	37	4	a	a	PRON
ejpam-3266	37	5	of	of	ADP
ejpam-3266	37	6	h	h	NOUN
ejpam-3266	37	7	is	be	AUX
ejpam-3266	37	8	called	call	VERB
ejpam-3266	37	9	a	a	DET
ejpam-3266	37	10	subgroupoid	subgroupoid	NOUN
ejpam-3266	37	11	of	of	ADP
ejpam-3266	37	12	h	h	NOUN
ejpam-3266	37	13	if	if	SCONJ
ejpam-3266	37	14	a	a	DET
ejpam-3266	37	15	∗	∗	NOUN
ejpam-3266	37	16	a	a	DET
ejpam-3266	37	17	⊆	⊆	NUM
ejpam-3266	37	18	a	a	PRON
ejpam-3266	37	19	,	,	PUNCT
ejpam-3266	37	20	equivalently	equivalently	ADV
ejpam-3266	37	21	if	if	SCONJ
ejpam-3266	37	22	,	,	PUNCT
ejpam-3266	37	23	for	for	ADP
ejpam-3266	37	24	any	any	DET
ejpam-3266	37	25	a	a	NOUN
ejpam-3266	37	26	,	,	PUNCT
ejpam-3266	37	27	b	b	PROPN
ejpam-3266	37	28	∈	∈	PROPN
ejpam-3266	37	29	a	a	X
ejpam-3266	37	30	,	,	PUNCT
ejpam-3266	37	31	we	we	PRON
ejpam-3266	37	32	have	have	VERB
ejpam-3266	37	33	a	a	DET
ejpam-3266	37	34	◦	◦	NOUN
ejpam-3266	37	35	b	b	NUM
ejpam-3266	37	36	⊆	⊆	NUM
ejpam-3266	37	37	a.	a.	NOUN
ejpam-3266	38	1	the	the	DET
ejpam-3266	38	2	following	follow	VERB
ejpam-3266	38	3	two	two	NUM
ejpam-3266	38	4	properties	property	NOUN
ejpam-3266	38	5	,	,	PUNCT
ejpam-3266	38	6	though	though	SCONJ
ejpam-3266	38	7	clear	clear	ADJ
ejpam-3266	38	8	,	,	PUNCT
ejpam-3266	38	9	play	play	VERB
ejpam-3266	38	10	an	an	DET
ejpam-3266	38	11	essential	essential	ADJ
ejpam-3266	38	12	role	role	NOUN
ejpam-3266	38	13	in	in	ADP
ejpam-3266	38	14	the	the	DET
ejpam-3266	38	15	theory	theory	NOUN
ejpam-3266	38	16	of	of	ADP
ejpam-3266	38	17	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	38	18	:	:	PUNCT
ejpam-3266	38	19	(	(	PUNCT
ejpam-3266	38	20	1	1	X
ejpam-3266	38	21	)	)	PUNCT
ejpam-3266	38	22	if	if	SCONJ
ejpam-3266	38	23	x	x	SYM
ejpam-3266	38	24	∈	∈	PROPN
ejpam-3266	38	25	a	a	DET
ejpam-3266	38	26	∗b	∗b	NOUN
ejpam-3266	38	27	,	,	PUNCT
ejpam-3266	38	28	then	then	ADV
ejpam-3266	38	29	x	x	PART
ejpam-3266	38	30	∈	∈	PROPN
ejpam-3266	38	31	a	a	DET
ejpam-3266	38	32	◦	◦	NOUN
ejpam-3266	38	33	b	b	NOUN
ejpam-3266	38	34	for	for	ADP
ejpam-3266	38	35	some	some	DET
ejpam-3266	38	36	a	a	DET
ejpam-3266	38	37	∈	∈	PROPN
ejpam-3266	38	38	a	a	PRON
ejpam-3266	38	39	,	,	PUNCT
ejpam-3266	38	40	b	b	PROPN
ejpam-3266	38	41	∈	∈	PROPN
ejpam-3266	38	42	b	b	PROPN
ejpam-3266	38	43	and	and	CCONJ
ejpam-3266	38	44	(	(	PUNCT
ejpam-3266	38	45	2	2	NUM
ejpam-3266	38	46	)	)	PUNCT
ejpam-3266	38	47	if	if	SCONJ
ejpam-3266	38	48	a	a	DET
ejpam-3266	38	49	∈	∈	PROPN
ejpam-3266	38	50	a	a	PRON
ejpam-3266	38	51	and	and	CCONJ
ejpam-3266	38	52	b	b	PROPN
ejpam-3266	38	53	∈	∈	PROPN
ejpam-3266	38	54	b	b	PROPN
ejpam-3266	38	55	,	,	PUNCT
ejpam-3266	38	56	then	then	ADV
ejpam-3266	38	57	a	a	DET
ejpam-3266	38	58	◦	◦	NOUN
ejpam-3266	38	59	b	b	NOUN
ejpam-3266	38	60	⊆	⊆	NUM
ejpam-3266	38	61	a	a	DET
ejpam-3266	38	62	∗b	∗b	NOUN
ejpam-3266	38	63	.	.	PUNCT
ejpam-3266	39	1	moreover	moreover	ADV
ejpam-3266	39	2	,	,	PUNCT
ejpam-3266	39	3	we	we	PRON
ejpam-3266	39	4	have	have	VERB
ejpam-3266	39	5	{	{	PUNCT
ejpam-3266	39	6	x}∗{y	x}∗{y	NOUN
ejpam-3266	39	7	}	}	PUNCT
ejpam-3266	39	8	=	=	SYM
ejpam-3266	39	9	x	x	SYM
ejpam-3266	39	10	◦	◦	NOUN
ejpam-3266	39	11	y	y	NOUN
ejpam-3266	39	12	for	for	ADP
ejpam-3266	39	13	any	any	DET
ejpam-3266	39	14	x	x	NOUN
ejpam-3266	39	15	,	,	PUNCT
ejpam-3266	39	16	y	y	PROPN
ejpam-3266	39	17	∈	∈	PROPN
ejpam-3266	39	18	h.	h.	PROPN
ejpam-3266	40	1	an	an	DET
ejpam-3266	40	2	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	40	3	(	(	PUNCT
ejpam-3266	40	4	h	h	NOUN
ejpam-3266	40	5	,	,	PUNCT
ejpam-3266	40	6	◦	◦	NOUN
ejpam-3266	40	7	,	,	PUNCT
ejpam-3266	40	8	∗	∗	NOUN
ejpam-3266	40	9	)	)	PUNCT
ejpam-3266	40	10	is	be	AUX
ejpam-3266	40	11	called	call	VERB
ejpam-3266	40	12	hypersemigroup	hypersemigroup	ADV
ejpam-3266	40	13	if	if	SCONJ
ejpam-3266	40	14	{	{	PUNCT
ejpam-3266	40	15	x	x	NOUN
ejpam-3266	40	16	}	}	PUNCT
ejpam-3266	40	17	∗	∗	NOUN
ejpam-3266	40	18	(	(	PUNCT
ejpam-3266	40	19	y	y	PROPN
ejpam-3266	40	20	◦	◦	PROPN
ejpam-3266	40	21	z	z	PROPN
ejpam-3266	40	22	)	)	PUNCT
ejpam-3266	40	23	=	=	SYM
ejpam-3266	40	24	(	(	PUNCT
ejpam-3266	40	25	x	x	SYM
ejpam-3266	40	26	◦	◦	VERB
ejpam-3266	40	27	y	y	NOUN
ejpam-3266	40	28	)	)	PUNCT
ejpam-3266	40	29	∗	∗	NOUN
ejpam-3266	40	30	{	{	PUNCT
ejpam-3266	40	31	z	z	NOUN
ejpam-3266	40	32	}	}	PUNCT
ejpam-3266	40	33	for	for	ADP
ejpam-3266	40	34	every	every	DET
ejpam-3266	40	35	x	x	PROPN
ejpam-3266	40	36	,	,	PUNCT
ejpam-3266	40	37	y	y	PROPN
ejpam-3266	40	38	,	,	PUNCT
ejpam-3266	40	39	z	z	PROPN
ejpam-3266	40	40	∈	∈	PROPN
ejpam-3266	40	41	h.	h.	NOUN
ejpam-3266	40	42	2	2	NUM
ejpam-3266	40	43	.	.	PUNCT
ejpam-3266	41	1	some	some	DET
ejpam-3266	41	2	results	result	NOUN
ejpam-3266	41	3	on	on	ADP
ejpam-3266	41	4	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	41	5	if	if	SCONJ
ejpam-3266	41	6	s	s	VERB
ejpam-3266	41	7	is	be	AUX
ejpam-3266	41	8	a	a	DET
ejpam-3266	41	9	groupoid	groupoid	NOUN
ejpam-3266	41	10	or	or	CCONJ
ejpam-3266	41	11	an	an	DET
ejpam-3266	41	12	ordered	ordered	ADJ
ejpam-3266	41	13	groupoid	groupoid	NOUN
ejpam-3266	41	14	,	,	PUNCT
ejpam-3266	41	15	an	an	DET
ejpam-3266	41	16	equivalence	equivalence	NOUN
ejpam-3266	41	17	relation	relation	NOUN
ejpam-3266	41	18	σ	σ	NOUN
ejpam-3266	41	19	on	on	ADP
ejpam-3266	41	20	s	s	PROPN
ejpam-3266	41	21	is	be	AUX
ejpam-3266	41	22	called	call	VERB
ejpam-3266	41	23	right	right	ADJ
ejpam-3266	41	24	(	(	PUNCT
ejpam-3266	41	25	resp	resp	NOUN
ejpam-3266	41	26	.	.	PUNCT
ejpam-3266	42	1	left	leave	VERB
ejpam-3266	42	2	)	)	PUNCT
ejpam-3266	42	3	congruence	congruence	NOUN
ejpam-3266	42	4	on	on	ADP
ejpam-3266	42	5	s	s	PRON
ejpam-3266	42	6	if	if	SCONJ
ejpam-3266	42	7	(	(	PUNCT
ejpam-3266	42	8	a	a	DET
ejpam-3266	42	9	,	,	PUNCT
ejpam-3266	42	10	b	b	NOUN
ejpam-3266	42	11	)	)	PUNCT
ejpam-3266	42	12	∈	∈	PROPN
ejpam-3266	42	13	σ	σ	NOUN
ejpam-3266	42	14	implies	imply	VERB
ejpam-3266	42	15	(	(	PUNCT
ejpam-3266	42	16	ac	ac	PROPN
ejpam-3266	42	17	,	,	PUNCT
ejpam-3266	42	18	bc	bc	PROPN
ejpam-3266	42	19	)	)	PUNCT
ejpam-3266	42	20	∈	∈	PROPN
ejpam-3266	42	21	σ	σ	PROPN
ejpam-3266	42	22	(	(	PUNCT
ejpam-3266	42	23	resp	resp	NOUN
ejpam-3266	42	24	.	.	PUNCT
ejpam-3266	43	1	(	(	PUNCT
ejpam-3266	43	2	ca	ca	NOUN
ejpam-3266	43	3	,	,	PUNCT
ejpam-3266	43	4	cb	cb	PROPN
ejpam-3266	43	5	)	)	PUNCT
ejpam-3266	43	6	∈	∈	PROPN
ejpam-3266	43	7	σ	σ	PROPN
ejpam-3266	43	8	)	)	PUNCT
ejpam-3266	43	9	for	for	ADP
ejpam-3266	43	10	every	every	DET
ejpam-3266	43	11	c	c	PROPN
ejpam-3266	43	12	∈	∈	PROPN
ejpam-3266	43	13	s.	s.	PROPN
ejpam-3266	43	14	it	it	PRON
ejpam-3266	43	15	is	be	AUX
ejpam-3266	43	16	called	call	VERB
ejpam-3266	43	17	a	a	DET
ejpam-3266	43	18	congruence	congruence	NOUN
ejpam-3266	43	19	on	on	ADP
ejpam-3266	43	20	s	s	PRON
ejpam-3266	43	21	if	if	SCONJ
ejpam-3266	43	22	it	it	PRON
ejpam-3266	43	23	is	be	AUX
ejpam-3266	43	24	both	both	CCONJ
ejpam-3266	43	25	a	a	DET
ejpam-3266	43	26	right	right	NOUN
ejpam-3266	43	27	and	and	CCONJ
ejpam-3266	43	28	a	a	DET
ejpam-3266	43	29	left	left	ADJ
ejpam-3266	43	30	congruence	congruence	NOUN
ejpam-3266	43	31	on	on	ADP
ejpam-3266	43	32	s.	s.	PROPN
ejpam-3266	43	33	a	a	DET
ejpam-3266	43	34	congruence	congruence	PROPN
ejpam-3266	43	35	σ	σ	NOUN
ejpam-3266	43	36	on	on	ADP
ejpam-3266	43	37	s	s	PROPN
ejpam-3266	43	38	is	be	AUX
ejpam-3266	43	39	called	call	VERB
ejpam-3266	43	40	semilattice	semilattice	NOUN
ejpam-3266	43	41	congruence	congruence	NOUN
ejpam-3266	43	42	if	if	SCONJ
ejpam-3266	43	43	(	(	PUNCT
ejpam-3266	43	44	a2	a2	PROPN
ejpam-3266	43	45	,	,	PUNCT
ejpam-3266	43	46	a	a	PRON
ejpam-3266	43	47	)	)	PUNCT
ejpam-3266	43	48	∈	∈	PROPN
ejpam-3266	43	49	σ	σ	PROPN
ejpam-3266	43	50	and	and	CCONJ
ejpam-3266	43	51	(	(	PUNCT
ejpam-3266	43	52	ab	ab	PROPN
ejpam-3266	43	53	,	,	PUNCT
ejpam-3266	43	54	ba	ba	PROPN
ejpam-3266	43	55	)	)	PUNCT
ejpam-3266	43	56	∈	∈	PROPN
ejpam-3266	43	57	σ	σ	NOUN
ejpam-3266	43	58	for	for	ADP
ejpam-3266	43	59	any	any	DET
ejpam-3266	43	60	n.	n.	NOUN
ejpam-3266	43	61	kehayopulu	kehayopulu	ADJ
ejpam-3266	43	62	/	/	SYM
ejpam-3266	43	63	eur	eur	PROPN
ejpam-3266	43	64	.	.	PUNCT
ejpam-3266	44	1	j.	j.	PROPN
ejpam-3266	44	2	pure	pure	PROPN
ejpam-3266	44	3	appl	appl	PROPN
ejpam-3266	44	4	.	.	PROPN
ejpam-3266	44	5	math	math	PROPN
ejpam-3266	44	6	,	,	PUNCT
ejpam-3266	44	7	11	11	NUM
ejpam-3266	44	8	(	(	PUNCT
ejpam-3266	44	9	2	2	NUM
ejpam-3266	44	10	)	)	PUNCT
ejpam-3266	44	11	(	(	PUNCT
ejpam-3266	44	12	2018	2018	NUM
ejpam-3266	44	13	)	)	PUNCT
ejpam-3266	44	14	,	,	PUNCT
ejpam-3266	44	15	476	476	NUM
ejpam-3266	44	16	-	-	SYM
ejpam-3266	44	17	492	492	NUM
ejpam-3266	44	18	478	478	NUM
ejpam-3266	44	19	a	a	PRON
ejpam-3266	44	20	,	,	PUNCT
ejpam-3266	44	21	b	b	X
ejpam-3266	44	22	∈	∈	NOUN
ejpam-3266	44	23	s	s	PART
ejpam-3266	44	24	[	[	X
ejpam-3266	44	25	3,13	3,13	NUM
ejpam-3266	44	26	]	]	PUNCT
ejpam-3266	44	27	.	.	PUNCT
ejpam-3266	45	1	these	these	DET
ejpam-3266	45	2	concepts	concept	NOUN
ejpam-3266	45	3	can	can	AUX
ejpam-3266	45	4	be	be	AUX
ejpam-3266	45	5	naturally	naturally	ADV
ejpam-3266	45	6	transferred	transfer	VERB
ejpam-3266	45	7	to	to	ADP
ejpam-3266	45	8	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	45	9	by	by	ADP
ejpam-3266	45	10	replacing	replace	VERB
ejpam-3266	45	11	the	the	DET
ejpam-3266	45	12	multiplication	multiplication	NOUN
ejpam-3266	45	13	“	"	PUNCT
ejpam-3266	45	14	·	·	PUNCT
ejpam-3266	45	15	”	"	PUNCT
ejpam-3266	45	16	of	of	ADP
ejpam-3266	45	17	the	the	DET
ejpam-3266	45	18	groupoid	groupoid	NOUN
ejpam-3266	45	19	by	by	ADP
ejpam-3266	45	20	the	the	DET
ejpam-3266	45	21	hyperoperation	hyperoperation	NOUN
ejpam-3266	45	22	“	"	PUNCT
ejpam-3266	45	23	◦	◦	NOUN
ejpam-3266	45	24	”	"	PUNCT
ejpam-3266	45	25	of	of	ADP
ejpam-3266	45	26	the	the	DET
ejpam-3266	45	27	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	45	28	.	.	PUNCT
ejpam-3266	46	1	but	but	CCONJ
ejpam-3266	46	2	while	while	SCONJ
ejpam-3266	46	3	for	for	ADP
ejpam-3266	46	4	a	a	DET
ejpam-3266	46	5	groupoid	groupoid	PROPN
ejpam-3266	46	6	ac	ac	PROPN
ejpam-3266	46	7	is	be	AUX
ejpam-3266	46	8	an	an	DET
ejpam-3266	46	9	element	element	NOUN
ejpam-3266	46	10	,	,	PUNCT
ejpam-3266	46	11	in	in	ADP
ejpam-3266	46	12	case	case	NOUN
ejpam-3266	46	13	of	of	ADP
ejpam-3266	46	14	an	an	DET
ejpam-3266	46	15	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	46	16	where	where	SCONJ
ejpam-3266	46	17	a	a	DET
ejpam-3266	46	18	◦	◦	NOUN
ejpam-3266	46	19	c	c	NOUN
ejpam-3266	46	20	is	be	AUX
ejpam-3266	46	21	a	a	DET
ejpam-3266	46	22	set	set	NOUN
ejpam-3266	46	23	,	,	PUNCT
ejpam-3266	46	24	we	we	PRON
ejpam-3266	46	25	have	have	VERB
ejpam-3266	46	26	to	to	PART
ejpam-3266	46	27	declare	declare	VERB
ejpam-3266	46	28	what	what	PRON
ejpam-3266	46	29	the	the	DET
ejpam-3266	46	30	(	(	PUNCT
ejpam-3266	46	31	a	a	DET
ejpam-3266	46	32	◦	◦	NOUN
ejpam-3266	46	33	c	c	NOUN
ejpam-3266	46	34	,	,	PUNCT
ejpam-3266	46	35	b	b	X
ejpam-3266	46	36	◦	◦	NOUN
ejpam-3266	46	37	c	c	NOUN
ejpam-3266	46	38	)	)	PUNCT
ejpam-3266	46	39	∈	∈	PROPN
ejpam-3266	46	40	σ	σ	NOUN
ejpam-3266	46	41	means	mean	NOUN
ejpam-3266	46	42	.	.	PUNCT
ejpam-3266	47	1	we	we	PRON
ejpam-3266	47	2	can	can	AUX
ejpam-3266	47	3	define	define	VERB
ejpam-3266	47	4	it	it	PRON
ejpam-3266	47	5	as	as	ADP
ejpam-3266	47	6	“	"	PUNCT
ejpam-3266	47	7	for	for	ADP
ejpam-3266	47	8	every	every	DET
ejpam-3266	47	9	u	u	PROPN
ejpam-3266	47	10	∈	∈	PROPN
ejpam-3266	47	11	a	a	DET
ejpam-3266	47	12	◦	◦	NOUN
ejpam-3266	47	13	c	c	NOUN
ejpam-3266	47	14	and	and	CCONJ
ejpam-3266	47	15	every	every	DET
ejpam-3266	47	16	v	v	ADP
ejpam-3266	47	17	∈	∈	PROPN
ejpam-3266	47	18	b	b	NOUN
ejpam-3266	47	19	◦	◦	NOUN
ejpam-3266	47	20	c	c	NOUN
ejpam-3266	47	21	we	we	PRON
ejpam-3266	47	22	have	have	VERB
ejpam-3266	47	23	(	(	PUNCT
ejpam-3266	47	24	u	u	NOUN
ejpam-3266	47	25	,	,	PUNCT
ejpam-3266	47	26	v	v	NOUN
ejpam-3266	47	27	)	)	PUNCT
ejpam-3266	47	28	∈	∈	PROPN
ejpam-3266	47	29	σ	σ	PROPN
ejpam-3266	47	30	”	"	PUNCT
ejpam-3266	47	31	or	or	CCONJ
ejpam-3266	47	32	“	"	PUNCT
ejpam-3266	47	33	for	for	ADP
ejpam-3266	47	34	every	every	DET
ejpam-3266	47	35	u	u	PROPN
ejpam-3266	47	36	∈	∈	PROPN
ejpam-3266	47	37	a	a	DET
ejpam-3266	47	38	◦	◦	NOUN
ejpam-3266	47	39	c	c	NOUN
ejpam-3266	47	40	there	there	PRON
ejpam-3266	47	41	exists	exist	VERB
ejpam-3266	47	42	v	v	ADP
ejpam-3266	47	43	∈	∈	PROPN
ejpam-3266	47	44	b	b	PROPN
ejpam-3266	47	45	◦	◦	NOUN
ejpam-3266	47	46	c	c	ADP
ejpam-3266	47	47	such	such	ADJ
ejpam-3266	47	48	that	that	PRON
ejpam-3266	47	49	(	(	PUNCT
ejpam-3266	47	50	u	u	NOUN
ejpam-3266	47	51	,	,	PUNCT
ejpam-3266	47	52	v	v	NOUN
ejpam-3266	47	53	)	)	PUNCT
ejpam-3266	47	54	∈	∈	PROPN
ejpam-3266	47	55	σ	σ	PROPN
ejpam-3266	47	56	”	"	PUNCT
ejpam-3266	47	57	and	and	CCONJ
ejpam-3266	47	58	get	get	VERB
ejpam-3266	47	59	two	two	NUM
ejpam-3266	47	60	different	different	ADJ
ejpam-3266	47	61	definitions	definition	NOUN
ejpam-3266	47	62	of	of	ADP
ejpam-3266	47	63	the	the	DET
ejpam-3266	47	64	left	left	ADJ
ejpam-3266	47	65	congruence	congruence	NOUN
ejpam-3266	47	66	,	,	PUNCT
ejpam-3266	47	67	two	two	NUM
ejpam-3266	47	68	different	different	ADJ
ejpam-3266	47	69	definitions	definition	NOUN
ejpam-3266	47	70	for	for	ADP
ejpam-3266	47	71	the	the	DET
ejpam-3266	47	72	right	right	ADJ
ejpam-3266	47	73	congruence	congruence	NOUN
ejpam-3266	47	74	;	;	PUNCT
ejpam-3266	47	75	and	and	CCONJ
ejpam-3266	47	76	so	so	ADV
ejpam-3266	47	77	two	two	NUM
ejpam-3266	47	78	different	different	ADJ
ejpam-3266	47	79	definitions	definition	NOUN
ejpam-3266	47	80	of	of	ADP
ejpam-3266	47	81	a	a	DET
ejpam-3266	47	82	congruence	congruence	NOUN
ejpam-3266	47	83	or	or	CCONJ
ejpam-3266	47	84	a	a	DET
ejpam-3266	47	85	semilattice	semilattice	NOUN
ejpam-3266	47	86	congruence	congruence	NOUN
ejpam-3266	47	87	.	.	PUNCT
ejpam-3266	48	1	although	although	SCONJ
ejpam-3266	48	2	there	there	PRON
ejpam-3266	48	3	is	be	VERB
ejpam-3266	48	4	one	one	NUM
ejpam-3266	48	5	between	between	ADP
ejpam-3266	48	6	them	they	PRON
ejpam-3266	48	7	that	that	PRON
ejpam-3266	48	8	implies	imply	VERB
ejpam-3266	48	9	the	the	DET
ejpam-3266	48	10	other	other	ADJ
ejpam-3266	48	11	(	(	PUNCT
ejpam-3266	48	12	it	it	PRON
ejpam-3266	48	13	can	can	AUX
ejpam-3266	48	14	be	be	AUX
ejpam-3266	48	15	easily	easily	ADV
ejpam-3266	48	16	proved	prove	VERB
ejpam-3266	48	17	)	)	PUNCT
ejpam-3266	48	18	and	and	CCONJ
ejpam-3266	48	19	so	so	ADV
ejpam-3266	48	20	they	they	PRON
ejpam-3266	48	21	could	could	AUX
ejpam-3266	48	22	be	be	AUX
ejpam-3266	48	23	named	name	VERB
ejpam-3266	48	24	differently	differently	ADV
ejpam-3266	48	25	(	(	PUNCT
ejpam-3266	48	26	like	like	ADP
ejpam-3266	48	27	congruence	congruence	NOUN
ejpam-3266	48	28	–	–	PUNCT
ejpam-3266	48	29	weak	weak	ADJ
ejpam-3266	48	30	congruence	congruence	NOUN
ejpam-3266	48	31	;	;	PUNCT
ejpam-3266	48	32	complete	complete	ADJ
ejpam-3266	48	33	congruence	congruence	NOUN
ejpam-3266	48	34	–	–	PUNCT
ejpam-3266	48	35	congruence	congruence	ADJ
ejpam-3266	48	36	;	;	PUNCT
ejpam-3266	48	37	strong	strong	ADJ
ejpam-3266	48	38	congruence	congruence	NOUN
ejpam-3266	48	39	–	–	PUNCT
ejpam-3266	48	40	congruence	congruence	NOUN
ejpam-3266	48	41	,	,	PUNCT
ejpam-3266	48	42	for	for	ADP
ejpam-3266	48	43	example	example	NOUN
ejpam-3266	48	44	)	)	PUNCT
ejpam-3266	48	45	,	,	PUNCT
ejpam-3266	48	46	we	we	PRON
ejpam-3266	48	47	will	will	AUX
ejpam-3266	48	48	define	define	VERB
ejpam-3266	48	49	as	as	ADP
ejpam-3266	48	50	“	"	PUNCT
ejpam-3266	48	51	congruence	congruence	NOUN
ejpam-3266	48	52	”	"	PUNCT
ejpam-3266	48	53	both	both	PRON
ejpam-3266	48	54	of	of	ADP
ejpam-3266	48	55	them	they	PRON
ejpam-3266	48	56	and	and	CCONJ
ejpam-3266	48	57	,	,	PUNCT
ejpam-3266	48	58	according	accord	VERB
ejpam-3266	48	59	to	to	ADP
ejpam-3266	48	60	our	our	PRON
ejpam-3266	48	61	investigation	investigation	NOUN
ejpam-3266	48	62	it	it	PRON
ejpam-3266	48	63	will	will	AUX
ejpam-3266	48	64	be	be	AUX
ejpam-3266	48	65	clear	clear	ADJ
ejpam-3266	48	66	which	which	PRON
ejpam-3266	48	67	of	of	ADP
ejpam-3266	48	68	them	they	PRON
ejpam-3266	48	69	we	we	PRON
ejpam-3266	48	70	use	use	VERB
ejpam-3266	48	71	.	.	PUNCT
ejpam-3266	49	1	this	this	PRON
ejpam-3266	49	2	have	have	AUX
ejpam-3266	49	3	been	be	AUX
ejpam-3266	49	4	said	say	VERB
ejpam-3266	49	5	,	,	PUNCT
ejpam-3266	49	6	we	we	PRON
ejpam-3266	49	7	give	give	VERB
ejpam-3266	49	8	the	the	DET
ejpam-3266	49	9	definitions	definition	NOUN
ejpam-3266	49	10	2.2	2.2	NUM
ejpam-3266	49	11	and	and	CCONJ
ejpam-3266	49	12	2.3	2.3	NUM
ejpam-3266	49	13	below	below	ADV
ejpam-3266	49	14	.	.	PUNCT
ejpam-3266	50	1	we	we	PRON
ejpam-3266	50	2	first	first	ADV
ejpam-3266	50	3	have	have	VERB
ejpam-3266	50	4	to	to	PART
ejpam-3266	50	5	introduce	introduce	VERB
ejpam-3266	50	6	the	the	DET
ejpam-3266	50	7	following	following	ADJ
ejpam-3266	50	8	notation	notation	NOUN
ejpam-3266	50	9	:	:	PUNCT
ejpam-3266	50	10	notation	notation	NOUN
ejpam-3266	50	11	2.1	2.1	NUM
ejpam-3266	50	12	.	.	PUNCT
ejpam-3266	51	1	if	if	SCONJ
ejpam-3266	51	2	h	h	NOUN
ejpam-3266	51	3	is	be	AUX
ejpam-3266	51	4	an	an	DET
ejpam-3266	51	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	51	6	,	,	PUNCT
ejpam-3266	51	7	σ	σ	VERB
ejpam-3266	51	8	an	an	DET
ejpam-3266	51	9	equivalence	equivalence	NOUN
ejpam-3266	51	10	relation	relation	NOUN
ejpam-3266	51	11	on	on	ADP
ejpam-3266	51	12	h	h	NOUN
ejpam-3266	51	13	and	and	CCONJ
ejpam-3266	51	14	a	a	DET
ejpam-3266	51	15	,	,	PUNCT
ejpam-3266	51	16	b	b	PROPN
ejpam-3266	51	17	two	two	NUM
ejpam-3266	51	18	nonempty	nonempty	ADJ
ejpam-3266	51	19	subsets	subset	NOUN
ejpam-3266	51	20	of	of	ADP
ejpam-3266	51	21	h	h	NOUN
ejpam-3266	51	22	,	,	PUNCT
ejpam-3266	51	23	then	then	ADV
ejpam-3266	51	24	we	we	PRON
ejpam-3266	51	25	write	write	VERB
ejpam-3266	51	26	(	(	PUNCT
ejpam-3266	51	27	a	a	PRON
ejpam-3266	51	28	,	,	PUNCT
ejpam-3266	51	29	b	b	NOUN
ejpam-3266	51	30	)	)	PUNCT
ejpam-3266	51	31	∈	∈	PROPN
ejpam-3266	51	32	σ	σ	NOUN
ejpam-3266	51	33	if	if	SCONJ
ejpam-3266	51	34	for	for	ADP
ejpam-3266	51	35	every	every	DET
ejpam-3266	51	36	a	a	DET
ejpam-3266	51	37	∈	∈	PROPN
ejpam-3266	51	38	a	a	PRON
ejpam-3266	51	39	and	and	CCONJ
ejpam-3266	51	40	every	every	DET
ejpam-3266	51	41	b	b	PROPN
ejpam-3266	51	42	∈	∈	PROPN
ejpam-3266	51	43	b	b	NOUN
ejpam-3266	51	44	,	,	PUNCT
ejpam-3266	51	45	we	we	PRON
ejpam-3266	51	46	have	have	VERB
ejpam-3266	51	47	(	(	PUNCT
ejpam-3266	51	48	a	a	DET
ejpam-3266	51	49	,	,	PUNCT
ejpam-3266	51	50	b	b	NOUN
ejpam-3266	51	51	)	)	PUNCT
ejpam-3266	51	52	∈	∈	PROPN
ejpam-3266	51	53	σ	σ	PROPN
ejpam-3266	51	54	.	.	PUNCT
ejpam-3266	52	1	we	we	PRON
ejpam-3266	52	2	write	write	VERB
ejpam-3266	52	3	(	(	PUNCT
ejpam-3266	52	4	a	a	DET
ejpam-3266	52	5	,	,	PUNCT
ejpam-3266	52	6	b	b	NOUN
ejpam-3266	52	7	)	)	PUNCT
ejpam-3266	52	8	instead	instead	ADV
ejpam-3266	52	9	of	of	ADP
ejpam-3266	52	10	(	(	PUNCT
ejpam-3266	52	11	a	a	PRON
ejpam-3266	52	12	,	,	PUNCT
ejpam-3266	52	13	{	{	PUNCT
ejpam-3266	52	14	b	b	NOUN
ejpam-3266	52	15	}	}	PUNCT
ejpam-3266	52	16	)	)	PUNCT
ejpam-3266	52	17	and	and	CCONJ
ejpam-3266	52	18	(	(	PUNCT
ejpam-3266	52	19	a	a	DET
ejpam-3266	52	20	,	,	PUNCT
ejpam-3266	52	21	b	b	NOUN
ejpam-3266	52	22	)	)	PUNCT
ejpam-3266	52	23	instead	instead	ADV
ejpam-3266	52	24	of	of	ADP
ejpam-3266	52	25	(	(	PUNCT
ejpam-3266	52	26	{	{	PUNCT
ejpam-3266	52	27	a	a	NOUN
ejpam-3266	52	28	}	}	PUNCT
ejpam-3266	52	29	,	,	PUNCT
ejpam-3266	52	30	b	b	NOUN
ejpam-3266	52	31	)	)	PUNCT
ejpam-3266	52	32	.	.	PUNCT
ejpam-3266	53	1	so	so	ADV
ejpam-3266	53	2	(	(	PUNCT
ejpam-3266	53	3	a	a	DET
ejpam-3266	53	4	,	,	PUNCT
ejpam-3266	53	5	b	b	NOUN
ejpam-3266	53	6	)	)	PUNCT
ejpam-3266	53	7	means	mean	VERB
ejpam-3266	53	8	that	that	SCONJ
ejpam-3266	53	9	,	,	PUNCT
ejpam-3266	53	10	for	for	ADP
ejpam-3266	53	11	every	every	DET
ejpam-3266	53	12	a	a	DET
ejpam-3266	53	13	∈	∈	PROPN
ejpam-3266	53	14	a	a	X
ejpam-3266	53	15	,	,	PUNCT
ejpam-3266	53	16	we	we	PRON
ejpam-3266	53	17	have	have	VERB
ejpam-3266	53	18	(	(	PUNCT
ejpam-3266	53	19	a	a	DET
ejpam-3266	53	20	,	,	PUNCT
ejpam-3266	53	21	b	b	NOUN
ejpam-3266	53	22	)	)	PUNCT
ejpam-3266	53	23	∈	∈	PROPN
ejpam-3266	53	24	σ	σ	PROPN
ejpam-3266	53	25	.	.	PUNCT
ejpam-3266	54	1	if	if	SCONJ
ejpam-3266	54	2	it	it	PRON
ejpam-3266	54	3	is	be	AUX
ejpam-3266	54	4	convenient	convenient	ADJ
ejpam-3266	54	5	we	we	PRON
ejpam-3266	54	6	write	write	VERB
ejpam-3266	54	7	,	,	PUNCT
ejpam-3266	54	8	for	for	ADP
ejpam-3266	54	9	short	short	ADJ
ejpam-3266	54	10	,	,	PUNCT
ejpam-3266	54	11	a	a	DET
ejpam-3266	54	12	∗	∗	NOUN
ejpam-3266	54	13	c	c	NOUN
ejpam-3266	54	14	instead	instead	ADV
ejpam-3266	54	15	of	of	ADP
ejpam-3266	54	16	a	a	DET
ejpam-3266	54	17	∗	∗	NOUN
ejpam-3266	54	18	{	{	PUNCT
ejpam-3266	54	19	c	c	NOUN
ejpam-3266	54	20	}	}	PUNCT
ejpam-3266	54	21	(	(	PUNCT
ejpam-3266	54	22	a	a	DET
ejpam-3266	54	23	⊆	⊆	NUM
ejpam-3266	54	24	h	h	NOUN
ejpam-3266	54	25	,	,	PUNCT
ejpam-3266	54	26	c	c	PROPN
ejpam-3266	54	27	∈	∈	PROPN
ejpam-3266	54	28	h	h	NOUN
ejpam-3266	54	29	)	)	PUNCT
ejpam-3266	54	30	.	.	PUNCT
ejpam-3266	55	1	definition	definition	NOUN
ejpam-3266	55	2	2.2	2.2	NUM
ejpam-3266	55	3	.	.	PUNCT
ejpam-3266	56	1	let	let	VERB
ejpam-3266	56	2	h	h	PRON
ejpam-3266	56	3	be	be	AUX
ejpam-3266	56	4	an	an	DET
ejpam-3266	56	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	56	6	.	.	PUNCT
ejpam-3266	57	1	an	an	DET
ejpam-3266	57	2	equivalence	equivalence	NOUN
ejpam-3266	57	3	relation	relation	NOUN
ejpam-3266	57	4	σ	σ	NOUN
ejpam-3266	57	5	on	on	ADP
ejpam-3266	57	6	h	h	NOUN
ejpam-3266	57	7	is	be	AUX
ejpam-3266	57	8	called	call	VERB
ejpam-3266	57	9	right	right	ADJ
ejpam-3266	57	10	congruence	congruence	NOUN
ejpam-3266	57	11	if	if	SCONJ
ejpam-3266	57	12	(	(	PUNCT
ejpam-3266	57	13	a	a	DET
ejpam-3266	57	14	,	,	PUNCT
ejpam-3266	57	15	b	b	NOUN
ejpam-3266	57	16	)	)	PUNCT
ejpam-3266	57	17	∈	∈	PROPN
ejpam-3266	57	18	σ	σ	NOUN
ejpam-3266	57	19	implies	imply	VERB
ejpam-3266	57	20	(	(	PUNCT
ejpam-3266	57	21	a	a	DET
ejpam-3266	57	22	◦	◦	NOUN
ejpam-3266	57	23	c	c	NOUN
ejpam-3266	57	24	,	,	PUNCT
ejpam-3266	57	25	b	b	X
ejpam-3266	57	26	◦	◦	NOUN
ejpam-3266	57	27	c	c	NOUN
ejpam-3266	57	28	)	)	PUNCT
ejpam-3266	57	29	∈	∈	PROPN
ejpam-3266	57	30	σ	σ	NOUN
ejpam-3266	57	31	for	for	ADP
ejpam-3266	57	32	every	every	DET
ejpam-3266	57	33	c	c	PROPN
ejpam-3266	57	34	∈	∈	PROPN
ejpam-3266	57	35	h.	h.	NOUN
ejpam-3266	58	1	it	it	PRON
ejpam-3266	58	2	is	be	AUX
ejpam-3266	58	3	called	call	VERB
ejpam-3266	58	4	left	leave	VERB
ejpam-3266	58	5	congruence	congruence	NOUN
ejpam-3266	58	6	if	if	SCONJ
ejpam-3266	58	7	(	(	PUNCT
ejpam-3266	58	8	a	a	DET
ejpam-3266	58	9	,	,	PUNCT
ejpam-3266	58	10	b	b	NOUN
ejpam-3266	58	11	)	)	PUNCT
ejpam-3266	58	12	∈	∈	PROPN
ejpam-3266	58	13	σ	σ	NOUN
ejpam-3266	58	14	implies	imply	VERB
ejpam-3266	58	15	(	(	PUNCT
ejpam-3266	58	16	c	c	X
ejpam-3266	58	17	◦	◦	NOUN
ejpam-3266	58	18	a	a	PRON
ejpam-3266	58	19	,	,	PUNCT
ejpam-3266	58	20	c	c	PROPN
ejpam-3266	58	21	◦	◦	NOUN
ejpam-3266	58	22	b	b	X
ejpam-3266	58	23	)	)	PUNCT
ejpam-3266	58	24	∈	∈	PROPN
ejpam-3266	58	25	σ	σ	NOUN
ejpam-3266	58	26	for	for	ADP
ejpam-3266	58	27	every	every	DET
ejpam-3266	58	28	c	c	PROPN
ejpam-3266	58	29	∈	∈	PROPN
ejpam-3266	58	30	h.	h.	NOUN
ejpam-3266	58	31	by	by	ADP
ejpam-3266	58	32	a	a	DET
ejpam-3266	58	33	congruence	congruence	NOUN
ejpam-3266	58	34	on	on	ADP
ejpam-3266	58	35	h	h	NOUN
ejpam-3266	58	36	we	we	PRON
ejpam-3266	58	37	mean	mean	VERB
ejpam-3266	58	38	a	a	DET
ejpam-3266	58	39	relation	relation	NOUN
ejpam-3266	58	40	on	on	ADP
ejpam-3266	58	41	h	h	NOUN
ejpam-3266	58	42	which	which	PRON
ejpam-3266	58	43	is	be	AUX
ejpam-3266	58	44	both	both	CCONJ
ejpam-3266	58	45	a	a	DET
ejpam-3266	58	46	right	right	NOUN
ejpam-3266	58	47	and	and	CCONJ
ejpam-3266	58	48	a	a	DET
ejpam-3266	58	49	left	left	ADJ
ejpam-3266	58	50	congruence	congruence	NOUN
ejpam-3266	58	51	on	on	ADP
ejpam-3266	58	52	h.	h.	PROPN
ejpam-3266	58	53	definition	definition	NOUN
ejpam-3266	58	54	2.3	2.3	NUM
ejpam-3266	58	55	.	.	PUNCT
ejpam-3266	59	1	let	let	VERB
ejpam-3266	59	2	h	h	PRON
ejpam-3266	59	3	be	be	AUX
ejpam-3266	59	4	an	an	DET
ejpam-3266	59	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	59	6	.	.	PUNCT
ejpam-3266	60	1	a	a	DET
ejpam-3266	60	2	congruence	congruence	NOUN
ejpam-3266	60	3	σ	σ	NOUN
ejpam-3266	60	4	on	on	ADP
ejpam-3266	60	5	h	h	NOUN
ejpam-3266	60	6	is	be	AUX
ejpam-3266	60	7	called	call	VERB
ejpam-3266	60	8	semilattice	semilattice	NOUN
ejpam-3266	60	9	congruence	congruence	NOUN
ejpam-3266	60	10	if	if	SCONJ
ejpam-3266	60	11	,	,	PUNCT
ejpam-3266	60	12	for	for	ADP
ejpam-3266	60	13	any	any	DET
ejpam-3266	60	14	a	a	NOUN
ejpam-3266	60	15	,	,	PUNCT
ejpam-3266	60	16	b	b	X
ejpam-3266	60	17	∈	∈	PROPN
ejpam-3266	60	18	h	h	NOUN
ejpam-3266	60	19	,	,	PUNCT
ejpam-3266	60	20	we	we	PRON
ejpam-3266	60	21	have	have	VERB
ejpam-3266	60	22	(	(	PUNCT
ejpam-3266	60	23	a	a	DET
ejpam-3266	60	24	◦	◦	NOUN
ejpam-3266	60	25	a	a	DET
ejpam-3266	60	26	,	,	PUNCT
ejpam-3266	60	27	a	a	PRON
ejpam-3266	60	28	)	)	PUNCT
ejpam-3266	60	29	∈	∈	PROPN
ejpam-3266	60	30	σ	σ	PROPN
ejpam-3266	60	31	and	and	CCONJ
ejpam-3266	60	32	(	(	PUNCT
ejpam-3266	60	33	a	a	DET
ejpam-3266	60	34	◦	◦	NOUN
ejpam-3266	60	35	b	b	NUM
ejpam-3266	60	36	,	,	PUNCT
ejpam-3266	60	37	b	b	X
ejpam-3266	60	38	◦	◦	NOUN
ejpam-3266	60	39	a	a	X
ejpam-3266	60	40	)	)	PUNCT
ejpam-3266	60	41	∈	∈	PROPN
ejpam-3266	60	42	σ	σ	PROPN
ejpam-3266	60	43	.	.	PUNCT
ejpam-3266	61	1	if	if	SCONJ
ejpam-3266	61	2	(	(	PUNCT
ejpam-3266	61	3	s	s	X
ejpam-3266	61	4	,	,	PUNCT
ejpam-3266	61	5	·	·	PUNCT
ejpam-3266	61	6	)	)	PUNCT
ejpam-3266	61	7	is	be	AUX
ejpam-3266	61	8	a	a	DET
ejpam-3266	61	9	groupoid	groupoid	NOUN
ejpam-3266	61	10	,	,	PUNCT
ejpam-3266	61	11	a	a	DET
ejpam-3266	61	12	nonempty	nonempty	NOUN
ejpam-3266	61	13	subset	subset	VERB
ejpam-3266	61	14	f	f	PROPN
ejpam-3266	61	15	of	of	ADP
ejpam-3266	61	16	s	s	PROPN
ejpam-3266	61	17	is	be	AUX
ejpam-3266	61	18	called	call	VERB
ejpam-3266	61	19	a	a	DET
ejpam-3266	61	20	filter	filter	NOUN
ejpam-3266	61	21	of	of	ADP
ejpam-3266	61	22	s	s	NOUN
ejpam-3266	61	23	[	[	X
ejpam-3266	61	24	13	13	NUM
ejpam-3266	61	25	]	]	PUNCT
ejpam-3266	61	26	if	if	SCONJ
ejpam-3266	61	27	the	the	DET
ejpam-3266	61	28	following	follow	VERB
ejpam-3266	61	29	assertions	assertion	NOUN
ejpam-3266	61	30	are	be	AUX
ejpam-3266	61	31	satisfied	satisfied	ADJ
ejpam-3266	61	32	:	:	PUNCT
ejpam-3266	61	33	(	(	PUNCT
ejpam-3266	61	34	1	1	X
ejpam-3266	61	35	)	)	PUNCT
ejpam-3266	61	36	if	if	SCONJ
ejpam-3266	61	37	a	a	PRON
ejpam-3266	61	38	,	,	PUNCT
ejpam-3266	61	39	b	b	PROPN
ejpam-3266	61	40	∈	∈	PROPN
ejpam-3266	61	41	f	f	X
ejpam-3266	61	42	,	,	PUNCT
ejpam-3266	61	43	then	then	ADV
ejpam-3266	61	44	ab	ab	PROPN
ejpam-3266	61	45	∈	∈	PROPN
ejpam-3266	61	46	f	f	PROPN
ejpam-3266	61	47	and	and	CCONJ
ejpam-3266	61	48	(	(	PUNCT
ejpam-3266	61	49	2	2	X
ejpam-3266	61	50	)	)	PUNCT
ejpam-3266	61	51	if	if	SCONJ
ejpam-3266	61	52	a	a	PRON
ejpam-3266	61	53	,	,	PUNCT
ejpam-3266	61	54	b	b	X
ejpam-3266	61	55	∈	∈	NOUN
ejpam-3266	61	56	s	s	VERB
ejpam-3266	61	57	such	such	ADJ
ejpam-3266	61	58	that	that	SCONJ
ejpam-3266	61	59	ab	ab	PROPN
ejpam-3266	61	60	∈	∈	PROPN
ejpam-3266	61	61	f	f	PROPN
ejpam-3266	61	62	,	,	PUNCT
ejpam-3266	61	63	then	then	ADV
ejpam-3266	61	64	a	a	DET
ejpam-3266	61	65	∈	∈	PROPN
ejpam-3266	61	66	f	f	X
ejpam-3266	61	67	and	and	CCONJ
ejpam-3266	61	68	b	b	PROPN
ejpam-3266	61	69	∈	∈	PROPN
ejpam-3266	61	70	f	f	X
ejpam-3266	61	71	;	;	PUNCT
ejpam-3266	61	72	in	in	ADP
ejpam-3266	61	73	other	other	ADJ
ejpam-3266	61	74	words	word	NOUN
ejpam-3266	61	75	,	,	PUNCT
ejpam-3266	61	76	if	if	SCONJ
ejpam-3266	61	77	it	it	PRON
ejpam-3266	61	78	is	be	AUX
ejpam-3266	61	79	a	a	DET
ejpam-3266	61	80	subgroupoid	subgroupoid	NOUN
ejpam-3266	61	81	of	of	ADP
ejpam-3266	61	82	s	s	AUX
ejpam-3266	61	83	satisfying	satisfy	VERB
ejpam-3266	61	84	the	the	DET
ejpam-3266	61	85	property	property	NOUN
ejpam-3266	61	86	(	(	PUNCT
ejpam-3266	61	87	2	2	NUM
ejpam-3266	61	88	)	)	PUNCT
ejpam-3266	61	89	.	.	PUNCT
ejpam-3266	62	1	a	a	DET
ejpam-3266	62	2	nonempty	nonempty	NOUN
ejpam-3266	62	3	subset	subset	VERB
ejpam-3266	62	4	a	a	PRON
ejpam-3266	62	5	of	of	ADP
ejpam-3266	62	6	s	s	PRON
ejpam-3266	62	7	is	be	AUX
ejpam-3266	62	8	called	call	VERB
ejpam-3266	62	9	an	an	DET
ejpam-3266	62	10	ideal	ideal	NOUN
ejpam-3266	62	11	of	of	ADP
ejpam-3266	62	12	s	s	NOUN
ejpam-3266	62	13	[	[	X
ejpam-3266	62	14	13	13	NUM
ejpam-3266	62	15	]	]	PUNCT
ejpam-3266	62	16	if	if	SCONJ
ejpam-3266	62	17	as	as	ADP
ejpam-3266	62	18	⊆	⊆	X
ejpam-3266	62	19	a	a	PRON
ejpam-3266	62	20	and	and	CCONJ
ejpam-3266	62	21	sa	sa	ADP
ejpam-3266	62	22	⊆	⊆	NUM
ejpam-3266	62	23	a	a	PRON
ejpam-3266	62	24	,	,	PUNCT
ejpam-3266	62	25	that	that	PRON
ejpam-3266	62	26	is	be	AUX
ejpam-3266	62	27	if	if	SCONJ
ejpam-3266	62	28	a	a	DET
ejpam-3266	62	29	∈	∈	PROPN
ejpam-3266	62	30	a	a	DET
ejpam-3266	62	31	and	and	CCONJ
ejpam-3266	62	32	s	s	PROPN
ejpam-3266	62	33	∈	∈	NOUN
ejpam-3266	62	34	s	s	PART
ejpam-3266	62	35	implies	imply	VERB
ejpam-3266	62	36	as	as	ADP
ejpam-3266	62	37	∈	∈	PROPN
ejpam-3266	62	38	a	a	PRON
ejpam-3266	62	39	and	and	CCONJ
ejpam-3266	62	40	sa	sa	ADP
ejpam-3266	62	41	∈	∈	PROPN
ejpam-3266	62	42	a.	a.	NOUN
ejpam-3266	63	1	if	if	SCONJ
ejpam-3266	63	2	(	(	PUNCT
ejpam-3266	63	3	s	s	X
ejpam-3266	63	4	,	,	PUNCT
ejpam-3266	63	5	·	·	PUNCT
ejpam-3266	63	6	,	,	PUNCT
ejpam-3266	63	7	≤	≤	NUM
ejpam-3266	63	8	)	)	PUNCT
ejpam-3266	63	9	is	be	AUX
ejpam-3266	63	10	an	an	DET
ejpam-3266	63	11	ordered	ordered	ADJ
ejpam-3266	63	12	groupoid	groupoid	NOUN
ejpam-3266	63	13	,	,	PUNCT
ejpam-3266	63	14	a	a	DET
ejpam-3266	63	15	subset	subset	NOUN
ejpam-3266	63	16	f	f	NOUN
ejpam-3266	63	17	of	of	ADP
ejpam-3266	63	18	s	s	PROPN
ejpam-3266	63	19	is	be	AUX
ejpam-3266	63	20	called	call	VERB
ejpam-3266	63	21	a	a	DET
ejpam-3266	63	22	filter	filter	NOUN
ejpam-3266	63	23	of	of	ADP
ejpam-3266	63	24	s	s	PRON
ejpam-3266	63	25	if	if	SCONJ
ejpam-3266	63	26	it	it	PRON
ejpam-3266	63	27	is	be	AUX
ejpam-3266	63	28	a	a	DET
ejpam-3266	63	29	filter	filter	NOUN
ejpam-3266	63	30	of	of	ADP
ejpam-3266	63	31	(	(	PUNCT
ejpam-3266	63	32	s	s	X
ejpam-3266	63	33	,	,	PUNCT
ejpam-3266	63	34	·	·	PUNCT
ejpam-3266	63	35	)	)	PUNCT
ejpam-3266	63	36	and	and	CCONJ
ejpam-3266	63	37	,	,	PUNCT
ejpam-3266	63	38	in	in	ADP
ejpam-3266	63	39	addition	addition	NOUN
ejpam-3266	63	40	if	if	SCONJ
ejpam-3266	63	41	a	a	DET
ejpam-3266	63	42	∈	∈	PROPN
ejpam-3266	63	43	f	f	X
ejpam-3266	63	44	and	and	CCONJ
ejpam-3266	63	45	s	s	PROPN
ejpam-3266	63	46	∈	∈	PROPN
ejpam-3266	63	47	b	b	PROPN
ejpam-3266	63	48	≥	≥	PRON
ejpam-3266	63	49	a	a	DET
ejpam-3266	63	50	implies	implie	NOUN
ejpam-3266	63	51	b	b	X
ejpam-3266	63	52	∈	∈	X
ejpam-3266	63	53	f	f	X
ejpam-3266	64	1	[	[	X
ejpam-3266	64	2	1	1	NUM
ejpam-3266	64	3	]	]	PUNCT
ejpam-3266	64	4	;	;	PUNCT
ejpam-3266	64	5	it	it	PRON
ejpam-3266	64	6	is	be	AUX
ejpam-3266	64	7	called	call	VERB
ejpam-3266	64	8	an	an	DET
ejpam-3266	64	9	ideal	ideal	NOUN
ejpam-3266	64	10	of	of	ADP
ejpam-3266	64	11	(	(	PUNCT
ejpam-3266	64	12	s	s	PROPN
ejpam-3266	64	13	,	,	PUNCT
ejpam-3266	64	14	·	·	PUNCT
ejpam-3266	64	15	,	,	PUNCT
ejpam-3266	64	16	≤	≤	NUM
ejpam-3266	64	17	)	)	PUNCT
ejpam-3266	64	18	if	if	SCONJ
ejpam-3266	64	19	it	it	PRON
ejpam-3266	64	20	is	be	AUX
ejpam-3266	64	21	an	an	DET
ejpam-3266	64	22	ideal	ideal	NOUN
ejpam-3266	64	23	of	of	ADP
ejpam-3266	64	24	(	(	PUNCT
ejpam-3266	64	25	s	s	X
ejpam-3266	64	26	,	,	PUNCT
ejpam-3266	64	27	·	·	PUNCT
ejpam-3266	64	28	)	)	PUNCT
ejpam-3266	64	29	and	and	CCONJ
ejpam-3266	64	30	,	,	PUNCT
ejpam-3266	64	31	in	in	ADP
ejpam-3266	64	32	addition	addition	NOUN
ejpam-3266	64	33	if	if	SCONJ
ejpam-3266	64	34	a	a	DET
ejpam-3266	64	35	∈	∈	PROPN
ejpam-3266	64	36	a	a	PRON
ejpam-3266	64	37	and	and	CCONJ
ejpam-3266	64	38	s	s	PROPN
ejpam-3266	64	39	3	3	NUM
ejpam-3266	64	40	b	b	NOUN
ejpam-3266	64	41	≤	≤	NOUN
ejpam-3266	64	42	a	a	DET
ejpam-3266	64	43	implies	implie	NOUN
ejpam-3266	64	44	b	b	X
ejpam-3266	64	45	∈	∈	PROPN
ejpam-3266	65	1	a	a	PRON
ejpam-3266	66	1	[	[	X
ejpam-3266	66	2	2	2	NUM
ejpam-3266	66	3	]	]	PUNCT
ejpam-3266	66	4	.	.	PUNCT
ejpam-3266	67	1	a	a	DET
ejpam-3266	67	2	subset	subset	NOUN
ejpam-3266	67	3	t	t	NOUN
ejpam-3266	67	4	of	of	ADP
ejpam-3266	67	5	a	a	DET
ejpam-3266	67	6	groupoid	groupoid	NOUN
ejpam-3266	67	7	(	(	PUNCT
ejpam-3266	67	8	or	or	CCONJ
ejpam-3266	67	9	ordered	order	VERB
ejpam-3266	67	10	groupoid	groupoid	PROPN
ejpam-3266	67	11	)	)	PUNCT
ejpam-3266	67	12	s	s	VERB
ejpam-3266	67	13	is	be	AUX
ejpam-3266	67	14	said	say	VERB
ejpam-3266	67	15	to	to	PART
ejpam-3266	67	16	be	be	AUX
ejpam-3266	67	17	prime	prime	ADJ
ejpam-3266	67	18	[	[	X
ejpam-3266	67	19	3,13	3,13	X
ejpam-3266	67	20	]	]	X
ejpam-3266	67	21	if	if	SCONJ
ejpam-3266	67	22	a	a	PRON
ejpam-3266	67	23	,	,	PUNCT
ejpam-3266	67	24	b	b	X
ejpam-3266	67	25	∈	∈	NOUN
ejpam-3266	67	26	s	s	VERB
ejpam-3266	67	27	such	such	ADJ
ejpam-3266	67	28	that	that	SCONJ
ejpam-3266	67	29	ab	ab	PROPN
ejpam-3266	67	30	∈	∈	PROPN
ejpam-3266	67	31	t	t	PROPN
ejpam-3266	67	32	implies	imply	VERB
ejpam-3266	67	33	a	a	DET
ejpam-3266	67	34	∈	∈	PROPN
ejpam-3266	67	35	t	t	NOUN
ejpam-3266	67	36	or	or	CCONJ
ejpam-3266	67	37	b	b	PROPN
ejpam-3266	67	38	∈	∈	PROPN
ejpam-3266	67	39	t	t	NOUN
ejpam-3266	67	40	.	.	PUNCT
ejpam-3266	68	1	it	it	PRON
ejpam-3266	68	2	is	be	AUX
ejpam-3266	68	3	well	well	ADV
ejpam-3266	68	4	known	know	VERB
ejpam-3266	68	5	that	that	SCONJ
ejpam-3266	68	6	a	a	DET
ejpam-3266	68	7	nonempty	nonempty	NOUN
ejpam-3266	68	8	subset	subset	VERB
ejpam-3266	68	9	f	f	PROPN
ejpam-3266	68	10	of	of	ADP
ejpam-3266	68	11	a	a	DET
ejpam-3266	68	12	groupoid	groupoid	NOUN
ejpam-3266	68	13	(	(	PUNCT
ejpam-3266	68	14	or	or	CCONJ
ejpam-3266	68	15	an	an	DET
ejpam-3266	68	16	ordered	order	VERB
ejpam-3266	68	17	groupoid	groupoid	NOUN
ejpam-3266	68	18	)	)	PUNCT
ejpam-3266	68	19	s	s	VERB
ejpam-3266	68	20	is	be	AUX
ejpam-3266	68	21	a	a	DET
ejpam-3266	68	22	filter	filter	NOUN
ejpam-3266	68	23	of	of	ADP
ejpam-3266	68	24	s	s	PRON
ejpam-3266	68	25	if	if	SCONJ
ejpam-3266	68	26	and	and	CCONJ
ejpam-3266	68	27	only	only	ADV
ejpam-3266	68	28	if	if	SCONJ
ejpam-3266	68	29	the	the	DET
ejpam-3266	68	30	complement	complement	NOUN
ejpam-3266	68	31	of	of	ADP
ejpam-3266	68	32	f	f	PROPN
ejpam-3266	68	33	to	to	PART
ejpam-3266	68	34	s	s	PRON
ejpam-3266	68	35	is	be	AUX
ejpam-3266	68	36	either	either	CCONJ
ejpam-3266	68	37	empty	empty	ADJ
ejpam-3266	68	38	or	or	CCONJ
ejpam-3266	68	39	a	a	DET
ejpam-3266	68	40	prime	prime	ADJ
ejpam-3266	68	41	ideal	ideal	NOUN
ejpam-3266	68	42	of	of	ADP
ejpam-3266	68	43	s	s	PRON
ejpam-3266	68	44	[	[	X
ejpam-3266	68	45	3,13	3,13	NUM
ejpam-3266	68	46	]	]	PUNCT
ejpam-3266	68	47	and	and	CCONJ
ejpam-3266	68	48	,	,	PUNCT
ejpam-3266	68	49	when	when	SCONJ
ejpam-3266	68	50	we	we	PRON
ejpam-3266	68	51	pass	pass	VERB
ejpam-3266	68	52	from	from	ADP
ejpam-3266	68	53	groupoids	groupoid	NOUN
ejpam-3266	68	54	to	to	PART
ejpam-3266	68	55	hypergroupoids	hypergroupoids	VERB
ejpam-3266	68	56	the	the	DET
ejpam-3266	68	57	corresponding	corresponding	ADJ
ejpam-3266	68	58	result	result	NOUN
ejpam-3266	68	59	should	should	AUX
ejpam-3266	68	60	be	be	AUX
ejpam-3266	68	61	satisfied	satisfied	ADJ
ejpam-3266	68	62	.	.	PUNCT
ejpam-3266	69	1	to	to	PART
ejpam-3266	69	2	manage	manage	VERB
ejpam-3266	69	3	it	it	PRON
ejpam-3266	69	4	,	,	PUNCT
ejpam-3266	69	5	a	a	DET
ejpam-3266	69	6	new	new	ADJ
ejpam-3266	69	7	condition	condition	NOUN
ejpam-3266	69	8	should	should	AUX
ejpam-3266	69	9	be	be	AUX
ejpam-3266	69	10	added	add	VERB
ejpam-3266	69	11	to	to	ADP
ejpam-3266	69	12	the	the	DET
ejpam-3266	69	13	corresponding	corresponding	ADJ
ejpam-3266	69	14	conditions	condition	NOUN
ejpam-3266	69	15	of	of	ADP
ejpam-3266	69	16	the	the	DET
ejpam-3266	69	17	filter	filter	NOUN
ejpam-3266	69	18	and	and	CCONJ
ejpam-3266	69	19	of	of	ADP
ejpam-3266	69	20	prime	prime	ADJ
ejpam-3266	69	21	ideals	ideal	NOUN
ejpam-3266	69	22	of	of	ADP
ejpam-3266	69	23	groupoids	groupoid	NOUN
ejpam-3266	69	24	we	we	PRON
ejpam-3266	69	25	already	already	ADV
ejpam-3266	69	26	have	have	VERB
ejpam-3266	69	27	.	.	PUNCT
ejpam-3266	70	1	and	and	CCONJ
ejpam-3266	70	2	the	the	DET
ejpam-3266	70	3	concept	concept	NOUN
ejpam-3266	70	4	n.	n.	PROPN
ejpam-3266	70	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	70	6	/	/	SYM
ejpam-3266	70	7	eur	eur	PROPN
ejpam-3266	70	8	.	.	PUNCT
ejpam-3266	71	1	j.	j.	PROPN
ejpam-3266	71	2	pure	pure	PROPN
ejpam-3266	71	3	appl	appl	PROPN
ejpam-3266	71	4	.	.	PROPN
ejpam-3266	71	5	math	math	PROPN
ejpam-3266	71	6	,	,	PUNCT
ejpam-3266	71	7	11	11	NUM
ejpam-3266	71	8	(	(	PUNCT
ejpam-3266	71	9	2	2	NUM
ejpam-3266	71	10	)	)	PUNCT
ejpam-3266	71	11	(	(	PUNCT
ejpam-3266	71	12	2018	2018	NUM
ejpam-3266	71	13	)	)	PUNCT
ejpam-3266	71	14	,	,	PUNCT
ejpam-3266	71	15	476	476	NUM
ejpam-3266	71	16	-	-	SYM
ejpam-3266	71	17	492	492	NUM
ejpam-3266	71	18	479	479	NUM
ejpam-3266	71	19	of	of	ADP
ejpam-3266	71	20	the	the	DET
ejpam-3266	71	21	filter	filter	NOUN
ejpam-3266	71	22	of	of	ADP
ejpam-3266	71	23	groupoids	groupoid	NOUN
ejpam-3266	71	24	can	can	AUX
ejpam-3266	71	25	be	be	AUX
ejpam-3266	71	26	naturally	naturally	ADV
ejpam-3266	71	27	transferred	transfer	VERB
ejpam-3266	71	28	to	to	ADP
ejpam-3266	71	29	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	71	30	in	in	ADP
ejpam-3266	71	31	the	the	DET
ejpam-3266	71	32	definition	definition	NOUN
ejpam-3266	71	33	below	below	ADV
ejpam-3266	71	34	;	;	PUNCT
ejpam-3266	71	35	the	the	DET
ejpam-3266	71	36	prime	prime	ADJ
ejpam-3266	71	37	subsets	subset	NOUN
ejpam-3266	71	38	can	can	AUX
ejpam-3266	71	39	be	be	AUX
ejpam-3266	71	40	defined	define	VERB
ejpam-3266	71	41	in	in	ADP
ejpam-3266	71	42	a	a	DET
ejpam-3266	71	43	similar	similar	ADJ
ejpam-3266	71	44	way	way	NOUN
ejpam-3266	71	45	–	–	PUNCT
ejpam-3266	71	46	adding	add	VERB
ejpam-3266	71	47	a	a	DET
ejpam-3266	71	48	new	new	ADJ
ejpam-3266	71	49	condition	condition	NOUN
ejpam-3266	71	50	.	.	PUNCT
ejpam-3266	72	1	definition	definition	NOUN
ejpam-3266	72	2	2.4	2.4	NUM
ejpam-3266	72	3	.	.	PUNCT
ejpam-3266	73	1	(	(	PUNCT
ejpam-3266	73	2	cf	cf	NOUN
ejpam-3266	73	3	.	.	PUNCT
ejpam-3266	74	1	also	also	ADV
ejpam-3266	74	2	[	[	X
ejpam-3266	74	3	7	7	NUM
ejpam-3266	74	4	]	]	PUNCT
ejpam-3266	74	5	)	)	PUNCT
ejpam-3266	74	6	let	let	VERB
ejpam-3266	74	7	h	h	NOUN
ejpam-3266	74	8	be	be	AUX
ejpam-3266	74	9	an	an	DET
ejpam-3266	74	10	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	74	11	.	.	PUNCT
ejpam-3266	75	1	a	a	DET
ejpam-3266	75	2	nonempty	nonempty	NOUN
ejpam-3266	75	3	subset	subset	VERB
ejpam-3266	75	4	f	f	PROPN
ejpam-3266	75	5	of	of	ADP
ejpam-3266	75	6	h	h	PROPN
ejpam-3266	75	7	is	be	AUX
ejpam-3266	75	8	called	call	VERB
ejpam-3266	75	9	a	a	DET
ejpam-3266	75	10	filter	filter	NOUN
ejpam-3266	75	11	of	of	ADP
ejpam-3266	75	12	h	h	NOUN
ejpam-3266	75	13	if	if	SCONJ
ejpam-3266	75	14	the	the	DET
ejpam-3266	75	15	following	follow	VERB
ejpam-3266	75	16	assertions	assertion	NOUN
ejpam-3266	75	17	are	be	AUX
ejpam-3266	75	18	satisfied	satisfied	ADJ
ejpam-3266	75	19	:	:	PUNCT
ejpam-3266	75	20	(	(	PUNCT
ejpam-3266	75	21	1	1	X
ejpam-3266	75	22	)	)	PUNCT
ejpam-3266	75	23	if	if	SCONJ
ejpam-3266	75	24	x	x	X
ejpam-3266	75	25	,	,	PUNCT
ejpam-3266	75	26	y	y	PROPN
ejpam-3266	75	27	∈	∈	PROPN
ejpam-3266	75	28	f	f	PROPN
ejpam-3266	75	29	,	,	PUNCT
ejpam-3266	75	30	then	then	ADV
ejpam-3266	75	31	x	x	PART
ejpam-3266	75	32	◦	◦	NOUN
ejpam-3266	75	33	y	y	PROPN
ejpam-3266	75	34	⊆	⊆	NUM
ejpam-3266	75	35	f	f	NOUN
ejpam-3266	75	36	;	;	PUNCT
ejpam-3266	75	37	(	(	PUNCT
ejpam-3266	75	38	2	2	X
ejpam-3266	75	39	)	)	PUNCT
ejpam-3266	75	40	if	if	SCONJ
ejpam-3266	75	41	x	x	X
ejpam-3266	75	42	,	,	PUNCT
ejpam-3266	75	43	y	y	PROPN
ejpam-3266	75	44	∈	∈	PROPN
ejpam-3266	75	45	h	h	NOUN
ejpam-3266	75	46	such	such	ADJ
ejpam-3266	75	47	that	that	SCONJ
ejpam-3266	75	48	x	x	X
ejpam-3266	75	49	◦	◦	NOUN
ejpam-3266	75	50	y	y	PROPN
ejpam-3266	75	51	⊆	⊆	NUM
ejpam-3266	75	52	f	f	PROPN
ejpam-3266	75	53	,	,	PUNCT
ejpam-3266	75	54	then	then	ADV
ejpam-3266	75	55	x	x	SYM
ejpam-3266	75	56	∈	∈	PROPN
ejpam-3266	75	57	f	f	PROPN
ejpam-3266	75	58	and	and	CCONJ
ejpam-3266	75	59	y	y	PROPN
ejpam-3266	75	60	∈	∈	PROPN
ejpam-3266	75	61	f	f	X
ejpam-3266	75	62	;	;	PUNCT
ejpam-3266	75	63	and	and	CCONJ
ejpam-3266	75	64	(	(	PUNCT
ejpam-3266	75	65	3	3	X
ejpam-3266	75	66	)	)	PUNCT
ejpam-3266	75	67	for	for	ADP
ejpam-3266	75	68	any	any	DET
ejpam-3266	75	69	x	x	NOUN
ejpam-3266	75	70	,	,	PUNCT
ejpam-3266	75	71	y	y	PROPN
ejpam-3266	75	72	∈	∈	PROPN
ejpam-3266	75	73	h	h	NOUN
ejpam-3266	75	74	,	,	PUNCT
ejpam-3266	75	75	we	we	PRON
ejpam-3266	75	76	have	have	AUX
ejpam-3266	75	77	x	x	PART
ejpam-3266	75	78	◦	◦	VERB
ejpam-3266	75	79	y	y	PROPN
ejpam-3266	75	80	⊆	⊆	NUM
ejpam-3266	75	81	f	f	PROPN
ejpam-3266	75	82	or	or	CCONJ
ejpam-3266	75	83	(	(	PUNCT
ejpam-3266	75	84	x	x	PART
ejpam-3266	75	85	◦	◦	VERB
ejpam-3266	75	86	y	y	NOUN
ejpam-3266	75	87	)	)	PUNCT
ejpam-3266	75	88	∩	∩	NOUN
ejpam-3266	75	89	f	f	X
ejpam-3266	75	90	=	=	PUNCT
ejpam-3266	75	91	∅.	∅.	NOUN
ejpam-3266	75	92	that	that	PRON
ejpam-3266	75	93	is	be	AUX
ejpam-3266	75	94	,	,	PUNCT
ejpam-3266	75	95	a	a	DET
ejpam-3266	75	96	filter	filter	NOUN
ejpam-3266	75	97	of	of	ADP
ejpam-3266	75	98	h	h	NOUN
ejpam-3266	75	99	is	be	AUX
ejpam-3266	75	100	a	a	DET
ejpam-3266	75	101	subgroupoid	subgroupoid	NOUN
ejpam-3266	75	102	of	of	ADP
ejpam-3266	75	103	h	h	NOUN
ejpam-3266	75	104	satisfying	satisfy	VERB
ejpam-3266	75	105	the	the	DET
ejpam-3266	75	106	relations	relation	NOUN
ejpam-3266	75	107	(	(	PUNCT
ejpam-3266	75	108	2	2	NUM
ejpam-3266	75	109	)	)	PUNCT
ejpam-3266	75	110	and	and	CCONJ
ejpam-3266	75	111	(	(	PUNCT
ejpam-3266	75	112	3	3	NUM
ejpam-3266	75	113	)	)	PUNCT
ejpam-3266	75	114	.	.	PUNCT
ejpam-3266	76	1	definition	definition	NOUN
ejpam-3266	76	2	2.5	2.5	NUM
ejpam-3266	76	3	.	.	PUNCT
ejpam-3266	77	1	let	let	VERB
ejpam-3266	77	2	h	h	PRON
ejpam-3266	77	3	be	be	AUX
ejpam-3266	77	4	an	an	DET
ejpam-3266	77	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	77	6	.	.	PUNCT
ejpam-3266	78	1	a	a	DET
ejpam-3266	78	2	nonempty	nonempty	NOUN
ejpam-3266	78	3	subset	subset	VERB
ejpam-3266	78	4	t	t	PROPN
ejpam-3266	78	5	of	of	ADP
ejpam-3266	78	6	h	h	PROPN
ejpam-3266	78	7	is	be	AUX
ejpam-3266	78	8	called	call	VERB
ejpam-3266	78	9	a	a	DET
ejpam-3266	78	10	prime	prime	ADJ
ejpam-3266	78	11	subset	subset	NOUN
ejpam-3266	78	12	of	of	ADP
ejpam-3266	78	13	h	h	NOUN
ejpam-3266	78	14	if	if	SCONJ
ejpam-3266	78	15	the	the	DET
ejpam-3266	78	16	following	follow	VERB
ejpam-3266	78	17	assertions	assertion	NOUN
ejpam-3266	78	18	are	be	AUX
ejpam-3266	78	19	satisfied	satisfied	ADJ
ejpam-3266	78	20	:	:	PUNCT
ejpam-3266	78	21	(	(	PUNCT
ejpam-3266	78	22	1	1	X
ejpam-3266	78	23	)	)	PUNCT
ejpam-3266	78	24	if	if	SCONJ
ejpam-3266	78	25	a	a	PRON
ejpam-3266	78	26	,	,	PUNCT
ejpam-3266	78	27	b	b	X
ejpam-3266	78	28	∈	∈	ADJ
ejpam-3266	78	29	h	h	NOUN
ejpam-3266	78	30	such	such	ADJ
ejpam-3266	78	31	that	that	SCONJ
ejpam-3266	78	32	a	a	DET
ejpam-3266	78	33	◦	◦	NOUN
ejpam-3266	78	34	b	b	NUM
ejpam-3266	78	35	⊆	⊆	NUM
ejpam-3266	78	36	t	t	NOUN
ejpam-3266	78	37	,	,	PUNCT
ejpam-3266	78	38	then	then	ADV
ejpam-3266	78	39	a	a	DET
ejpam-3266	78	40	∈	∈	PROPN
ejpam-3266	78	41	t	t	NOUN
ejpam-3266	78	42	or	or	CCONJ
ejpam-3266	78	43	b	b	PROPN
ejpam-3266	78	44	∈	∈	PROPN
ejpam-3266	78	45	t	t	PROPN
ejpam-3266	78	46	and	and	CCONJ
ejpam-3266	78	47	(	(	PUNCT
ejpam-3266	78	48	2	2	NUM
ejpam-3266	78	49	)	)	PUNCT
ejpam-3266	78	50	for	for	ADP
ejpam-3266	78	51	every	every	DET
ejpam-3266	78	52	a	a	PROPN
ejpam-3266	78	53	,	,	PUNCT
ejpam-3266	78	54	b	b	X
ejpam-3266	78	55	∈	∈	PROPN
ejpam-3266	78	56	h	h	NOUN
ejpam-3266	78	57	,	,	PUNCT
ejpam-3266	78	58	we	we	PRON
ejpam-3266	78	59	have	have	VERB
ejpam-3266	78	60	a	a	DET
ejpam-3266	78	61	◦	◦	NOUN
ejpam-3266	78	62	b	b	NUM
ejpam-3266	78	63	⊆	⊆	NUM
ejpam-3266	78	64	t	t	NOUN
ejpam-3266	78	65	or	or	CCONJ
ejpam-3266	78	66	(	(	PUNCT
ejpam-3266	78	67	a	a	DET
ejpam-3266	78	68	◦	◦	NOUN
ejpam-3266	78	69	b	b	NOUN
ejpam-3266	78	70	)	)	PUNCT
ejpam-3266	78	71	∩	∩	NOUN
ejpam-3266	78	72	t	t	NOUN
ejpam-3266	78	73	=	=	PUNCT
ejpam-3266	78	74	∅.	∅.	NOUN
ejpam-3266	78	75	as	as	SCONJ
ejpam-3266	78	76	we	we	PRON
ejpam-3266	78	77	see	see	VERB
ejpam-3266	78	78	,	,	PUNCT
ejpam-3266	78	79	we	we	PRON
ejpam-3266	78	80	keep	keep	VERB
ejpam-3266	78	81	the	the	DET
ejpam-3266	78	82	definitions	definition	NOUN
ejpam-3266	78	83	of	of	ADP
ejpam-3266	78	84	filters	filter	NOUN
ejpam-3266	78	85	and	and	CCONJ
ejpam-3266	78	86	prime	prime	ADJ
ejpam-3266	78	87	subsets	subset	NOUN
ejpam-3266	78	88	of	of	ADP
ejpam-3266	78	89	groupoids	groupoid	NOUN
ejpam-3266	78	90	in	in	ADP
ejpam-3266	78	91	which	which	PRON
ejpam-3266	78	92	we	we	PRON
ejpam-3266	78	93	add	add	VERB
ejpam-3266	78	94	condition	condition	NOUN
ejpam-3266	78	95	(	(	PUNCT
ejpam-3266	78	96	3	3	NUM
ejpam-3266	78	97	)	)	PUNCT
ejpam-3266	78	98	in	in	ADP
ejpam-3266	78	99	case	case	NOUN
ejpam-3266	78	100	of	of	ADP
ejpam-3266	78	101	filters	filter	NOUN
ejpam-3266	78	102	and	and	CCONJ
ejpam-3266	78	103	condition	condition	NOUN
ejpam-3266	78	104	(	(	PUNCT
ejpam-3266	78	105	2	2	NUM
ejpam-3266	78	106	)	)	PUNCT
ejpam-3266	78	107	in	in	ADP
ejpam-3266	78	108	case	case	NOUN
ejpam-3266	78	109	of	of	ADP
ejpam-3266	78	110	prime	prime	ADJ
ejpam-3266	78	111	subsets	subset	NOUN
ejpam-3266	78	112	.	.	PUNCT
ejpam-3266	79	1	if	if	SCONJ
ejpam-3266	79	2	a	a	DET
ejpam-3266	79	3	subset	subset	NOUN
ejpam-3266	79	4	t	t	NOUN
ejpam-3266	79	5	of	of	ADP
ejpam-3266	79	6	an	an	DET
ejpam-3266	79	7	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	79	8	satisfies	satisfie	NOUN
ejpam-3266	79	9	only	only	ADV
ejpam-3266	79	10	the	the	DET
ejpam-3266	79	11	condition	condition	NOUN
ejpam-3266	79	12	(	(	PUNCT
ejpam-3266	79	13	2	2	NUM
ejpam-3266	79	14	)	)	PUNCT
ejpam-3266	79	15	of	of	ADP
ejpam-3266	79	16	definition	definition	NOUN
ejpam-3266	79	17	2.5	2.5	NUM
ejpam-3266	79	18	,	,	PUNCT
ejpam-3266	79	19	then	then	ADV
ejpam-3266	79	20	we	we	PRON
ejpam-3266	79	21	call	call	VERB
ejpam-3266	79	22	it	it	PRON
ejpam-3266	79	23	half	half	ADJ
ejpam-3266	79	24	prime	prime	NOUN
ejpam-3266	79	25	subset	subset	NOUN
ejpam-3266	79	26	of	of	ADP
ejpam-3266	79	27	h.	h.	PROPN
ejpam-3266	79	28	remark	remark	PROPN
ejpam-3266	79	29	2.6	2.6	NUM
ejpam-3266	79	30	.	.	PUNCT
ejpam-3266	80	1	if	if	SCONJ
ejpam-3266	80	2	h	h	NOUN
ejpam-3266	80	3	is	be	AUX
ejpam-3266	80	4	an	an	DET
ejpam-3266	80	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	80	6	,	,	PUNCT
ejpam-3266	80	7	i	i	PRON
ejpam-3266	80	8	a	a	DET
ejpam-3266	80	9	half	half	ADJ
ejpam-3266	80	10	prime	prime	NOUN
ejpam-3266	80	11	subset	subset	NOUN
ejpam-3266	80	12	of	of	ADP
ejpam-3266	80	13	h	h	NOUN
ejpam-3266	80	14	and	and	CCONJ
ejpam-3266	80	15	a	a	PRON
ejpam-3266	80	16	,	,	PUNCT
ejpam-3266	80	17	c	c	NOUN
ejpam-3266	80	18	/∈	/∈	PUNCT
ejpam-3266	81	1	i	i	PRON
ejpam-3266	81	2	,	,	PUNCT
ejpam-3266	81	3	then	then	ADV
ejpam-3266	81	4	a	a	DET
ejpam-3266	81	5	◦	◦	NOUN
ejpam-3266	81	6	c	c	NOUN
ejpam-3266	81	7	*	*	PUNCT
ejpam-3266	81	8	i.	i.	NOUN
ejpam-3266	82	1	so	so	ADV
ejpam-3266	82	2	a	a	PRON
ejpam-3266	82	3	/∈	/∈	PUNCT
ejpam-3266	83	1	i	i	PRON
ejpam-3266	83	2	implies	imply	VERB
ejpam-3266	83	3	a	a	DET
ejpam-3266	83	4	◦	◦	NOUN
ejpam-3266	83	5	a	a	DET
ejpam-3266	83	6	*	*	X
ejpam-3266	83	7	i.	i.	NOUN
ejpam-3266	83	8	as	as	ADP
ejpam-3266	83	9	in	in	ADP
ejpam-3266	83	10	groupoids	groupoid	NOUN
ejpam-3266	83	11	,	,	PUNCT
ejpam-3266	83	12	for	for	ADP
ejpam-3266	83	13	an	an	DET
ejpam-3266	83	14	element	element	NOUN
ejpam-3266	83	15	x	x	PUNCT
ejpam-3266	83	16	of	of	ADP
ejpam-3266	83	17	h	h	NOUN
ejpam-3266	83	18	,	,	PUNCT
ejpam-3266	83	19	we	we	PRON
ejpam-3266	83	20	denote	denote	VERB
ejpam-3266	83	21	by	by	ADP
ejpam-3266	83	22	n(x	n(x	NOUN
ejpam-3266	83	23	)	)	PUNCT
ejpam-3266	83	24	the	the	DET
ejpam-3266	83	25	filter	filter	NOUN
ejpam-3266	83	26	of	of	ADP
ejpam-3266	83	27	h	h	NOUN
ejpam-3266	83	28	generated	generate	VERB
ejpam-3266	83	29	by	by	ADP
ejpam-3266	83	30	x	x	X
ejpam-3266	83	31	,	,	PUNCT
ejpam-3266	83	32	and	and	CCONJ
ejpam-3266	83	33	by	by	ADP
ejpam-3266	83	34	n	n	CCONJ
ejpam-3266	83	35	the	the	DET
ejpam-3266	83	36	equivalence	equivalence	NOUN
ejpam-3266	83	37	relation	relation	NOUN
ejpam-3266	83	38	on	on	ADP
ejpam-3266	83	39	h	h	NOUN
ejpam-3266	83	40	defined	define	VERB
ejpam-3266	83	41	by	by	ADP
ejpam-3266	83	42	n	n	PROPN
ejpam-3266	83	43	:	:	PUNCT
ejpam-3266	84	1	=	=	SYM
ejpam-3266	84	2	{	{	PUNCT
ejpam-3266	84	3	(	(	PUNCT
ejpam-3266	84	4	x	x	NOUN
ejpam-3266	84	5	,	,	PUNCT
ejpam-3266	84	6	y	y	NOUN
ejpam-3266	84	7	)	)	PUNCT
ejpam-3266	84	8	∈	∈	PROPN
ejpam-3266	84	9	h	h	NOUN
ejpam-3266	84	10	×h	×h	X
ejpam-3266	84	11	|	|	ADV
ejpam-3266	84	12	n(x	n(x	ADJ
ejpam-3266	84	13	)	)	PUNCT
ejpam-3266	84	14	=	=	SYM
ejpam-3266	84	15	n(y	n(y	PROPN
ejpam-3266	84	16	)	)	PUNCT
ejpam-3266	84	17	}	}	PUNCT
ejpam-3266	84	18	.	.	PUNCT
ejpam-3266	85	1	using	use	VERB
ejpam-3266	85	2	the	the	DET
ejpam-3266	85	3	definitions	definition	NOUN
ejpam-3266	85	4	2.4	2.4	NUM
ejpam-3266	85	5	and	and	CCONJ
ejpam-3266	85	6	2.5	2.5	NUM
ejpam-3266	85	7	,	,	PUNCT
ejpam-3266	85	8	with	with	ADP
ejpam-3266	85	9	the	the	DET
ejpam-3266	85	10	usual	usual	ADJ
ejpam-3266	85	11	changes	change	NOUN
ejpam-3266	85	12	we	we	PRON
ejpam-3266	85	13	pass	pass	VERB
ejpam-3266	85	14	from	from	ADP
ejpam-3266	85	15	groupoids	groupoid	NOUN
ejpam-3266	85	16	to	to	ADP
ejpam-3266	85	17	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	85	18	.	.	PUNCT
ejpam-3266	86	1	in	in	ADP
ejpam-3266	86	2	an	an	DET
ejpam-3266	86	3	ordered	order	VERB
ejpam-3266	86	4	semigroup	semigroup	NOUN
ejpam-3266	86	5	s	s	PROPN
ejpam-3266	86	6	,	,	PUNCT
ejpam-3266	86	7	the	the	DET
ejpam-3266	86	8	relation	relation	NOUN
ejpam-3266	86	9	n	n	PART
ejpam-3266	86	10	is	be	AUX
ejpam-3266	86	11	a	a	DET
ejpam-3266	86	12	semilattice	semilattice	NOUN
ejpam-3266	86	13	congruence	congruence	NOUN
ejpam-3266	86	14	on	on	ADP
ejpam-3266	86	15	s	s	PRON
ejpam-3266	86	16	[	[	X
ejpam-3266	86	17	3	3	NUM
ejpam-3266	86	18	]	]	PUNCT
ejpam-3266	86	19	,	,	PUNCT
ejpam-3266	86	20	and	and	CCONJ
ejpam-3266	86	21	the	the	DET
ejpam-3266	86	22	same	same	ADJ
ejpam-3266	86	23	holds	hold	VERB
ejpam-3266	86	24	for	for	ADP
ejpam-3266	86	25	groupoids	groupoid	NOUN
ejpam-3266	86	26	as	as	ADV
ejpam-3266	86	27	well	well	ADV
ejpam-3266	86	28	.	.	PUNCT
ejpam-3266	87	1	by	by	ADP
ejpam-3266	87	2	a	a	DET
ejpam-3266	87	3	modification	modification	NOUN
ejpam-3266	87	4	of	of	ADP
ejpam-3266	87	5	that	that	DET
ejpam-3266	87	6	proof	proof	NOUN
ejpam-3266	87	7	,	,	PUNCT
ejpam-3266	87	8	we	we	PRON
ejpam-3266	87	9	have	have	VERB
ejpam-3266	87	10	the	the	DET
ejpam-3266	87	11	following	follow	VERB
ejpam-3266	87	12	proposition	proposition	NOUN
ejpam-3266	87	13	;	;	PUNCT
ejpam-3266	87	14	for	for	ADP
ejpam-3266	87	15	the	the	DET
ejpam-3266	87	16	sake	sake	NOUN
ejpam-3266	87	17	of	of	ADP
ejpam-3266	87	18	completeness	completeness	NOUN
ejpam-3266	87	19	we	we	PRON
ejpam-3266	87	20	will	will	AUX
ejpam-3266	87	21	give	give	VERB
ejpam-3266	87	22	its	its	PRON
ejpam-3266	87	23	proof	proof	NOUN
ejpam-3266	87	24	.	.	PUNCT
ejpam-3266	88	1	proposition	proposition	NOUN
ejpam-3266	88	2	2.7	2.7	NUM
ejpam-3266	88	3	.	.	PUNCT
ejpam-3266	89	1	(	(	PUNCT
ejpam-3266	89	2	see	see	VERB
ejpam-3266	89	3	also	also	ADV
ejpam-3266	89	4	[	[	X
ejpam-3266	89	5	3	3	NUM
ejpam-3266	89	6	;	;	PUNCT
ejpam-3266	89	7	the	the	DET
ejpam-3266	89	8	proposition	proposition	NOUN
ejpam-3266	89	9	]	]	PUNCT
ejpam-3266	89	10	)	)	PUNCT
ejpam-3266	89	11	if	if	SCONJ
ejpam-3266	89	12	h	h	NOUN
ejpam-3266	89	13	is	be	AUX
ejpam-3266	89	14	an	an	DET
ejpam-3266	89	15	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	89	16	,	,	PUNCT
ejpam-3266	89	17	then	then	ADV
ejpam-3266	89	18	the	the	DET
ejpam-3266	89	19	equivalence	equivalence	NOUN
ejpam-3266	89	20	relation	relation	NOUN
ejpam-3266	89	21	n	n	PART
ejpam-3266	89	22	is	be	AUX
ejpam-3266	89	23	a	a	DET
ejpam-3266	89	24	semilattice	semilattice	NOUN
ejpam-3266	89	25	congruence	congruence	NOUN
ejpam-3266	89	26	on	on	ADP
ejpam-3266	89	27	h.	h.	PROPN
ejpam-3266	89	28	proof	proof	NOUN
ejpam-3266	89	29	.	.	PUNCT
ejpam-3266	90	1	let	let	VERB
ejpam-3266	90	2	(	(	PUNCT
ejpam-3266	90	3	x	x	NOUN
ejpam-3266	90	4	,	,	PUNCT
ejpam-3266	90	5	y	y	NOUN
ejpam-3266	90	6	)	)	PUNCT
ejpam-3266	90	7	∈	∈	PROPN
ejpam-3266	90	8	n	n	NOUN
ejpam-3266	90	9	and	and	CCONJ
ejpam-3266	90	10	z	z	PROPN
ejpam-3266	90	11	∈	∈	PROPN
ejpam-3266	90	12	h.	h.	NOUN
ejpam-3266	91	1	then	then	ADV
ejpam-3266	91	2	(	(	PUNCT
ejpam-3266	91	3	z	z	NOUN
ejpam-3266	91	4	◦	◦	NOUN
ejpam-3266	91	5	x	x	NOUN
ejpam-3266	91	6	,	,	PUNCT
ejpam-3266	91	7	z	z	NOUN
ejpam-3266	91	8	◦	◦	NOUN
ejpam-3266	91	9	y	y	NOUN
ejpam-3266	91	10	)	)	PUNCT
ejpam-3266	91	11	∈	∈	PROPN
ejpam-3266	91	12	n	n	NOUN
ejpam-3266	91	13	.	.	PUNCT
ejpam-3266	92	1	in	in	ADP
ejpam-3266	92	2	fact	fact	NOUN
ejpam-3266	92	3	:	:	PUNCT
ejpam-3266	92	4	let	let	VERB
ejpam-3266	92	5	u	u	PRON
ejpam-3266	92	6	∈	∈	PROPN
ejpam-3266	92	7	z	z	NOUN
ejpam-3266	92	8	◦	◦	NOUN
ejpam-3266	92	9	x	x	X
ejpam-3266	92	10	and	and	CCONJ
ejpam-3266	92	11	v	v	ADP
ejpam-3266	92	12	∈	∈	PROPN
ejpam-3266	92	13	z	z	NOUN
ejpam-3266	92	14	◦	◦	NOUN
ejpam-3266	92	15	y.	y.	NOUN
ejpam-3266	92	16	then	then	ADV
ejpam-3266	92	17	(	(	PUNCT
ejpam-3266	92	18	u	u	NOUN
ejpam-3266	92	19	,	,	PUNCT
ejpam-3266	92	20	v	v	NOUN
ejpam-3266	92	21	)	)	PUNCT
ejpam-3266	92	22	∈	∈	PROPN
ejpam-3266	92	23	n	n	X
ejpam-3266	92	24	.	.	PUNCT
ejpam-3266	93	1	indeed	indeed	ADV
ejpam-3266	93	2	:	:	PUNCT
ejpam-3266	93	3	since	since	SCONJ
ejpam-3266	93	4	u	u	PROPN
ejpam-3266	93	5	∈	∈	PROPN
ejpam-3266	93	6	n(u	n(u	PROPN
ejpam-3266	93	7	)	)	PUNCT
ejpam-3266	93	8	and	and	CCONJ
ejpam-3266	93	9	u	u	PROPN
ejpam-3266	93	10	∈	∈	PROPN
ejpam-3266	93	11	z	z	PROPN
ejpam-3266	93	12	◦	◦	NOUN
ejpam-3266	93	13	x	x	SYM
ejpam-3266	93	14	,	,	PUNCT
ejpam-3266	93	15	we	we	PRON
ejpam-3266	93	16	have	have	VERB
ejpam-3266	93	17	(	(	PUNCT
ejpam-3266	93	18	z	z	NOUN
ejpam-3266	93	19	◦	◦	NOUN
ejpam-3266	93	20	x	x	NOUN
ejpam-3266	93	21	)	)	PUNCT
ejpam-3266	93	22	∩	∩	PROPN
ejpam-3266	93	23	n(u	n(u	PROPN
ejpam-3266	93	24	)	)	PUNCT
ejpam-3266	93	25	6=	6=	ADP
ejpam-3266	94	1	∅.	∅.	ADP
ejpam-3266	94	2	since	since	SCONJ
ejpam-3266	94	3	n(u	n(u	PROPN
ejpam-3266	94	4	)	)	PUNCT
ejpam-3266	94	5	is	be	AUX
ejpam-3266	94	6	a	a	DET
ejpam-3266	94	7	filter	filter	NOUN
ejpam-3266	94	8	of	of	ADP
ejpam-3266	94	9	h	h	NOUN
ejpam-3266	94	10	,	,	PUNCT
ejpam-3266	94	11	we	we	PRON
ejpam-3266	94	12	have	have	VERB
ejpam-3266	94	13	z	z	NOUN
ejpam-3266	94	14	◦	◦	NOUN
ejpam-3266	94	15	x	x	SYM
ejpam-3266	94	16	⊆	⊆	NUM
ejpam-3266	94	17	n(u	n(u	NUM
ejpam-3266	94	18	)	)	PUNCT
ejpam-3266	94	19	,	,	PUNCT
ejpam-3266	94	20	and	and	CCONJ
ejpam-3266	94	21	z	z	X
ejpam-3266	94	22	,	,	PUNCT
ejpam-3266	94	23	x	x	PROPN
ejpam-3266	94	24	∈	∈	PROPN
ejpam-3266	94	25	n(u	n(u	PROPN
ejpam-3266	94	26	)	)	PUNCT
ejpam-3266	94	27	.	.	PUNCT
ejpam-3266	95	1	since	since	SCONJ
ejpam-3266	95	2	x	x	PROPN
ejpam-3266	95	3	∈	∈	PROPN
ejpam-3266	95	4	n(u	n(u	PROPN
ejpam-3266	95	5	)	)	PUNCT
ejpam-3266	95	6	,	,	PUNCT
ejpam-3266	95	7	we	we	PRON
ejpam-3266	95	8	have	have	VERB
ejpam-3266	95	9	n(x	n(x	NOUN
ejpam-3266	95	10	)	)	PUNCT
ejpam-3266	95	11	⊆	⊆	NUM
ejpam-3266	95	12	n(u	n(u	PROPN
ejpam-3266	95	13	)	)	PUNCT
ejpam-3266	95	14	,	,	PUNCT
ejpam-3266	95	15	then	then	ADV
ejpam-3266	95	16	y	y	PROPN
ejpam-3266	95	17	∈	∈	PROPN
ejpam-3266	95	18	n(u	n(u	PROPN
ejpam-3266	95	19	)	)	PUNCT
ejpam-3266	95	20	.	.	PUNCT
ejpam-3266	96	1	since	since	SCONJ
ejpam-3266	96	2	z	z	PROPN
ejpam-3266	96	3	,	,	PUNCT
ejpam-3266	96	4	y	y	PROPN
ejpam-3266	96	5	∈	∈	PROPN
ejpam-3266	96	6	n(u	n(u	PROPN
ejpam-3266	96	7	)	)	PUNCT
ejpam-3266	96	8	,	,	PUNCT
ejpam-3266	96	9	we	we	PRON
ejpam-3266	96	10	have	have	VERB
ejpam-3266	96	11	z	z	AUX
ejpam-3266	96	12	◦	◦	VERB
ejpam-3266	96	13	y	y	PROPN
ejpam-3266	96	14	⊆	⊆	NUM
ejpam-3266	96	15	n(u	n(u	PROPN
ejpam-3266	96	16	)	)	PUNCT
ejpam-3266	96	17	,	,	PUNCT
ejpam-3266	96	18	then	then	ADV
ejpam-3266	96	19	v	v	ADP
ejpam-3266	96	20	∈	∈	PROPN
ejpam-3266	96	21	n(u	n(u	PROPN
ejpam-3266	96	22	)	)	PUNCT
ejpam-3266	96	23	,	,	PUNCT
ejpam-3266	96	24	and	and	CCONJ
ejpam-3266	96	25	n(v	n(v	PROPN
ejpam-3266	96	26	)	)	PUNCT
ejpam-3266	96	27	⊆	⊆	NUM
ejpam-3266	96	28	n(u	n(u	PROPN
ejpam-3266	96	29	)	)	PUNCT
ejpam-3266	96	30	.	.	PUNCT
ejpam-3266	97	1	by	by	ADP
ejpam-3266	97	2	symmetry	symmetry	NOUN
ejpam-3266	97	3	,	,	PUNCT
ejpam-3266	97	4	we	we	PRON
ejpam-3266	97	5	get	get	VERB
ejpam-3266	97	6	n(u	n(u	PROPN
ejpam-3266	97	7	)	)	PUNCT
ejpam-3266	97	8	⊆	⊆	NUM
ejpam-3266	97	9	n(v	n(v	NOUN
ejpam-3266	97	10	)	)	PUNCT
ejpam-3266	97	11	,	,	PUNCT
ejpam-3266	97	12	so	so	SCONJ
ejpam-3266	97	13	we	we	PRON
ejpam-3266	97	14	have	have	VERB
ejpam-3266	97	15	n(u	n(u	PROPN
ejpam-3266	97	16	)	)	PUNCT
ejpam-3266	98	1	=	=	SYM
ejpam-3266	98	2	n(v	n(v	PROPN
ejpam-3266	98	3	)	)	PUNCT
ejpam-3266	98	4	,	,	PUNCT
ejpam-3266	98	5	and	and	CCONJ
ejpam-3266	98	6	(	(	PUNCT
ejpam-3266	98	7	u	u	NOUN
ejpam-3266	98	8	,	,	PUNCT
ejpam-3266	98	9	v	v	NOUN
ejpam-3266	98	10	)	)	PUNCT
ejpam-3266	98	11	∈	∈	PROPN
ejpam-3266	98	12	n	n	NOUN
ejpam-3266	98	13	.	.	PUNCT
ejpam-3266	99	1	thus	thus	ADV
ejpam-3266	99	2	n	n	PRON
ejpam-3266	99	3	is	be	AUX
ejpam-3266	99	4	a	a	DET
ejpam-3266	99	5	left	left	ADJ
ejpam-3266	99	6	congruence	congruence	NOUN
ejpam-3266	99	7	on	on	ADP
ejpam-3266	99	8	h.	h.	PROPN
ejpam-3266	99	9	in	in	ADP
ejpam-3266	99	10	a	a	DET
ejpam-3266	99	11	similar	similar	ADJ
ejpam-3266	99	12	way	way	NOUN
ejpam-3266	99	13	we	we	PRON
ejpam-3266	99	14	prove	prove	VERB
ejpam-3266	99	15	that	that	SCONJ
ejpam-3266	99	16	n	n	PRON
ejpam-3266	99	17	is	be	AUX
ejpam-3266	99	18	a	a	DET
ejpam-3266	99	19	right	right	ADJ
ejpam-3266	99	20	congruence	congruence	NOUN
ejpam-3266	99	21	on	on	ADP
ejpam-3266	99	22	h	h	NOUN
ejpam-3266	99	23	,	,	PUNCT
ejpam-3266	99	24	so	so	ADV
ejpam-3266	99	25	n	n	PRON
ejpam-3266	99	26	is	be	AUX
ejpam-3266	99	27	a	a	DET
ejpam-3266	99	28	congruence	congruence	NOUN
ejpam-3266	99	29	on	on	ADP
ejpam-3266	99	30	h.	h.	PROPN
ejpam-3266	99	31	let	let	VERB
ejpam-3266	99	32	x	x	SYM
ejpam-3266	99	33	∈	∈	PROPN
ejpam-3266	99	34	h.	h.	NOUN
ejpam-3266	100	1	then	then	ADV
ejpam-3266	100	2	(	(	PUNCT
ejpam-3266	100	3	x	x	PUNCT
ejpam-3266	100	4	◦	◦	NOUN
ejpam-3266	100	5	x	x	SYM
ejpam-3266	100	6	,	,	PUNCT
ejpam-3266	100	7	x	x	X
ejpam-3266	100	8	)	)	PUNCT
ejpam-3266	100	9	∈	∈	PROPN
ejpam-3266	100	10	n	n	NOUN
ejpam-3266	100	11	.	.	PUNCT
ejpam-3266	101	1	in	in	ADP
ejpam-3266	101	2	fact	fact	NOUN
ejpam-3266	101	3	:	:	PUNCT
ejpam-3266	101	4	let	let	VERB
ejpam-3266	101	5	u	u	PRON
ejpam-3266	101	6	∈	∈	PROPN
ejpam-3266	101	7	x	x	PUNCT
ejpam-3266	101	8	◦	◦	NOUN
ejpam-3266	101	9	x.	x.	NOUN
ejpam-3266	101	10	then	then	ADV
ejpam-3266	101	11	(	(	PUNCT
ejpam-3266	101	12	u	u	NOUN
ejpam-3266	101	13	,	,	PUNCT
ejpam-3266	101	14	x	x	NOUN
ejpam-3266	101	15	)	)	PUNCT
ejpam-3266	101	16	∈	∈	PROPN
ejpam-3266	101	17	n	n	X
ejpam-3266	101	18	.	.	PUNCT
ejpam-3266	102	1	indeed	indeed	ADV
ejpam-3266	102	2	:	:	PUNCT
ejpam-3266	102	3	since	since	SCONJ
ejpam-3266	102	4	u	u	PROPN
ejpam-3266	102	5	∈	∈	PROPN
ejpam-3266	102	6	n(u	n(u	PROPN
ejpam-3266	102	7	)	)	PUNCT
ejpam-3266	102	8	,	,	PUNCT
ejpam-3266	102	9	we	we	PRON
ejpam-3266	102	10	have	have	VERB
ejpam-3266	102	11	(	(	PUNCT
ejpam-3266	102	12	x	x	PART
ejpam-3266	102	13	◦	◦	NOUN
ejpam-3266	102	14	x	x	NOUN
ejpam-3266	102	15	)	)	PUNCT
ejpam-3266	102	16	∩	∩	PROPN
ejpam-3266	102	17	n(u	n(u	PROPN
ejpam-3266	102	18	)	)	PUNCT
ejpam-3266	102	19	6=	6=	ADP
ejpam-3266	103	1	∅.	∅.	ADP
ejpam-3266	103	2	since	since	SCONJ
ejpam-3266	103	3	n(u	n(u	PROPN
ejpam-3266	103	4	)	)	PUNCT
ejpam-3266	103	5	is	be	AUX
ejpam-3266	103	6	a	a	DET
ejpam-3266	103	7	filter	filter	NOUN
ejpam-3266	103	8	of	of	ADP
ejpam-3266	103	9	h	h	NOUN
ejpam-3266	103	10	,	,	PUNCT
ejpam-3266	103	11	we	we	PRON
ejpam-3266	103	12	have	have	VERB
ejpam-3266	103	13	x	x	PART
ejpam-3266	103	14	◦	◦	NOUN
ejpam-3266	103	15	x	x	SYM
ejpam-3266	103	16	⊆	⊆	NUM
ejpam-3266	103	17	n(u	n(u	PROPN
ejpam-3266	103	18	)	)	PUNCT
ejpam-3266	103	19	,	,	PUNCT
ejpam-3266	103	20	then	then	ADV
ejpam-3266	103	21	x	x	SYM
ejpam-3266	103	22	∈	∈	PROPN
ejpam-3266	103	23	n(u	n(u	PROPN
ejpam-3266	103	24	)	)	PUNCT
ejpam-3266	103	25	,	,	PUNCT
ejpam-3266	103	26	and	and	CCONJ
ejpam-3266	103	27	n(x	n(x	NOUN
ejpam-3266	103	28	)	)	PUNCT
ejpam-3266	103	29	⊆	⊆	NUM
ejpam-3266	103	30	n(u	n(u	PROPN
ejpam-3266	103	31	)	)	PUNCT
ejpam-3266	103	32	.	.	PUNCT
ejpam-3266	104	1	on	on	ADP
ejpam-3266	104	2	the	the	DET
ejpam-3266	104	3	other	other	ADJ
ejpam-3266	104	4	hand	hand	NOUN
ejpam-3266	104	5	,	,	PUNCT
ejpam-3266	104	6	since	since	SCONJ
ejpam-3266	104	7	x	x	PROPN
ejpam-3266	104	8	∈	∈	PROPN
ejpam-3266	104	9	n(x	n(x	PROPN
ejpam-3266	104	10	)	)	PUNCT
ejpam-3266	104	11	and	and	CCONJ
ejpam-3266	104	12	n(x	n(x	NOUN
ejpam-3266	104	13	)	)	PUNCT
ejpam-3266	104	14	is	be	AUX
ejpam-3266	104	15	a	a	DET
ejpam-3266	104	16	filter	filter	NOUN
ejpam-3266	104	17	of	of	ADP
ejpam-3266	104	18	h	h	NOUN
ejpam-3266	104	19	,	,	PUNCT
ejpam-3266	104	20	we	we	PRON
ejpam-3266	104	21	have	have	VERB
ejpam-3266	104	22	x	x	PART
ejpam-3266	104	23	◦	◦	VERB
ejpam-3266	104	24	x	x	SYM
ejpam-3266	104	25	⊆	⊆	NUM
ejpam-3266	104	26	n(x	n(x	NOUN
ejpam-3266	104	27	)	)	PUNCT
ejpam-3266	104	28	.	.	PUNCT
ejpam-3266	105	1	then	then	ADV
ejpam-3266	105	2	u	u	X
ejpam-3266	105	3	∈	∈	PROPN
ejpam-3266	105	4	n(x	n(x	PROPN
ejpam-3266	105	5	)	)	PUNCT
ejpam-3266	105	6	,	,	PUNCT
ejpam-3266	105	7	so	so	SCONJ
ejpam-3266	105	8	n(u	n(u	PROPN
ejpam-3266	105	9	)	)	PUNCT
ejpam-3266	105	10	⊆	⊆	NUM
ejpam-3266	105	11	n(x	n(x	NOUN
ejpam-3266	105	12	)	)	PUNCT
ejpam-3266	105	13	.	.	PUNCT
ejpam-3266	106	1	thus	thus	ADV
ejpam-3266	106	2	we	we	PRON
ejpam-3266	106	3	have	have	VERB
ejpam-3266	106	4	n(u	n(u	PROPN
ejpam-3266	106	5	)	)	PUNCT
ejpam-3266	106	6	=	=	SYM
ejpam-3266	106	7	n(x	n(x	PROPN
ejpam-3266	106	8	)	)	PUNCT
ejpam-3266	106	9	,	,	PUNCT
ejpam-3266	106	10	and	and	CCONJ
ejpam-3266	106	11	(	(	PUNCT
ejpam-3266	106	12	u	u	NOUN
ejpam-3266	106	13	,	,	PUNCT
ejpam-3266	106	14	x	x	NOUN
ejpam-3266	106	15	)	)	PUNCT
ejpam-3266	106	16	∈	∈	PROPN
ejpam-3266	106	17	n	n	ADV
ejpam-3266	106	18	.	.	PUNCT
ejpam-3266	107	1	let	let	VERB
ejpam-3266	107	2	x	x	PRON
ejpam-3266	107	3	,	,	PUNCT
ejpam-3266	107	4	y	y	PROPN
ejpam-3266	107	5	∈	∈	PROPN
ejpam-3266	107	6	h.	h.	NOUN
ejpam-3266	108	1	then	then	ADV
ejpam-3266	108	2	(	(	PUNCT
ejpam-3266	108	3	x	x	X
ejpam-3266	108	4	◦	◦	VERB
ejpam-3266	108	5	y	y	PROPN
ejpam-3266	108	6	,	,	PUNCT
ejpam-3266	108	7	y	y	PROPN
ejpam-3266	108	8	◦	◦	NOUN
ejpam-3266	108	9	x	x	NOUN
ejpam-3266	108	10	)	)	PUNCT
ejpam-3266	108	11	∈	∈	PROPN
ejpam-3266	108	12	n	n	NOUN
ejpam-3266	108	13	.	.	PUNCT
ejpam-3266	109	1	in	in	ADP
ejpam-3266	109	2	fact	fact	NOUN
ejpam-3266	109	3	:	:	PUNCT
ejpam-3266	109	4	let	let	VERB
ejpam-3266	109	5	u	u	PRON
ejpam-3266	109	6	∈	∈	PROPN
ejpam-3266	109	7	x	x	INTJ
ejpam-3266	109	8	◦	◦	NOUN
ejpam-3266	109	9	y	y	PROPN
ejpam-3266	109	10	and	and	CCONJ
ejpam-3266	109	11	v	v	ADP
ejpam-3266	109	12	∈	∈	PROPN
ejpam-3266	109	13	y	y	PROPN
ejpam-3266	109	14	◦	◦	NOUN
ejpam-3266	109	15	x.	x.	PROPN
ejpam-3266	109	16	n.	n.	PROPN
ejpam-3266	109	17	kehayopulu	kehayopulu	PROPN
ejpam-3266	109	18	/	/	SYM
ejpam-3266	109	19	eur	eur	PROPN
ejpam-3266	109	20	.	.	PUNCT
ejpam-3266	110	1	j.	j.	PROPN
ejpam-3266	110	2	pure	pure	PROPN
ejpam-3266	110	3	appl	appl	PROPN
ejpam-3266	110	4	.	.	PROPN
ejpam-3266	110	5	math	math	PROPN
ejpam-3266	110	6	,	,	PUNCT
ejpam-3266	110	7	11	11	NUM
ejpam-3266	110	8	(	(	PUNCT
ejpam-3266	110	9	2	2	NUM
ejpam-3266	110	10	)	)	PUNCT
ejpam-3266	110	11	(	(	PUNCT
ejpam-3266	110	12	2018	2018	NUM
ejpam-3266	110	13	)	)	PUNCT
ejpam-3266	110	14	,	,	PUNCT
ejpam-3266	110	15	476	476	NUM
ejpam-3266	110	16	-	-	SYM
ejpam-3266	110	17	492	492	NUM
ejpam-3266	110	18	480	480	NUM
ejpam-3266	110	19	then	then	ADV
ejpam-3266	110	20	(	(	PUNCT
ejpam-3266	110	21	u	u	NOUN
ejpam-3266	110	22	,	,	PUNCT
ejpam-3266	110	23	v	v	NOUN
ejpam-3266	110	24	)	)	PUNCT
ejpam-3266	110	25	∈	∈	PROPN
ejpam-3266	110	26	n	n	X
ejpam-3266	110	27	.	.	PUNCT
ejpam-3266	111	1	indeed	indeed	ADV
ejpam-3266	111	2	:	:	PUNCT
ejpam-3266	111	3	since	since	SCONJ
ejpam-3266	111	4	u	u	PROPN
ejpam-3266	111	5	∈	∈	PROPN
ejpam-3266	111	6	n(u	n(u	PROPN
ejpam-3266	111	7	)	)	PUNCT
ejpam-3266	111	8	,	,	PUNCT
ejpam-3266	111	9	we	we	PRON
ejpam-3266	111	10	have	have	VERB
ejpam-3266	111	11	(	(	PUNCT
ejpam-3266	111	12	x	x	PART
ejpam-3266	111	13	◦	◦	NOUN
ejpam-3266	111	14	y)∩n(u	y)∩n(u	NOUN
ejpam-3266	111	15	)	)	PUNCT
ejpam-3266	112	1	6=	6=	ADP
ejpam-3266	112	2	∅	∅	NOUN
ejpam-3266	112	3	,	,	PUNCT
ejpam-3266	112	4	then	then	ADV
ejpam-3266	112	5	x	x	PART
ejpam-3266	112	6	◦	◦	NOUN
ejpam-3266	112	7	y	y	PROPN
ejpam-3266	112	8	⊆	⊆	NUM
ejpam-3266	112	9	n(u	n(u	PROPN
ejpam-3266	112	10	)	)	PUNCT
ejpam-3266	112	11	,	,	PUNCT
ejpam-3266	112	12	x	x	X
ejpam-3266	112	13	,	,	PUNCT
ejpam-3266	112	14	y	y	PROPN
ejpam-3266	112	15	∈	∈	PROPN
ejpam-3266	112	16	n(u	n(u	PROPN
ejpam-3266	112	17	)	)	PUNCT
ejpam-3266	112	18	,	,	PUNCT
ejpam-3266	112	19	and	and	CCONJ
ejpam-3266	112	20	y	y	PROPN
ejpam-3266	112	21	◦	◦	NOUN
ejpam-3266	112	22	x	x	SYM
ejpam-3266	112	23	⊆	⊆	NUM
ejpam-3266	112	24	n(u	n(u	NUM
ejpam-3266	112	25	)	)	PUNCT
ejpam-3266	112	26	.	.	PUNCT
ejpam-3266	113	1	then	then	ADV
ejpam-3266	113	2	v	v	X
ejpam-3266	113	3	∈	∈	PROPN
ejpam-3266	113	4	n(u	n(u	PROPN
ejpam-3266	113	5	)	)	PUNCT
ejpam-3266	113	6	,	,	PUNCT
ejpam-3266	113	7	and	and	CCONJ
ejpam-3266	113	8	n(v	n(v	PROPN
ejpam-3266	113	9	)	)	PUNCT
ejpam-3266	113	10	⊆	⊆	NUM
ejpam-3266	113	11	n(u	n(u	PROPN
ejpam-3266	113	12	)	)	PUNCT
ejpam-3266	113	13	.	.	PUNCT
ejpam-3266	114	1	by	by	ADP
ejpam-3266	114	2	symmetry	symmetry	NOUN
ejpam-3266	114	3	,	,	PUNCT
ejpam-3266	114	4	we	we	PRON
ejpam-3266	114	5	get	get	VERB
ejpam-3266	114	6	n(u	n(u	PROPN
ejpam-3266	114	7	)	)	PUNCT
ejpam-3266	114	8	⊆	⊆	NUM
ejpam-3266	114	9	n(v	n(v	PROPN
ejpam-3266	114	10	)	)	PUNCT
ejpam-3266	114	11	,	,	PUNCT
ejpam-3266	114	12	then	then	ADV
ejpam-3266	114	13	n(u	n(u	PROPN
ejpam-3266	114	14	)	)	PUNCT
ejpam-3266	114	15	=	=	SYM
ejpam-3266	115	1	n(v	n(v	PROPN
ejpam-3266	115	2	)	)	PUNCT
ejpam-3266	115	3	,	,	PUNCT
ejpam-3266	115	4	and	and	CCONJ
ejpam-3266	115	5	(	(	PUNCT
ejpam-3266	115	6	u	u	NOUN
ejpam-3266	115	7	,	,	PUNCT
ejpam-3266	115	8	v	v	NOUN
ejpam-3266	115	9	)	)	PUNCT
ejpam-3266	115	10	∈	∈	PROPN
ejpam-3266	115	11	n	n	X
ejpam-3266	115	12	.	.	PUNCT
ejpam-3266	116	1	�	�	PROPN
ejpam-3266	116	2	notation	notation	PROPN
ejpam-3266	116	3	2.8	2.8	NUM
ejpam-3266	116	4	.	.	PUNCT
ejpam-3266	117	1	for	for	ADP
ejpam-3266	117	2	a	a	DET
ejpam-3266	117	3	subset	subset	NOUN
ejpam-3266	117	4	i	i	PRON
ejpam-3266	117	5	of	of	ADP
ejpam-3266	117	6	h	h	NOUN
ejpam-3266	117	7	,	,	PUNCT
ejpam-3266	117	8	we	we	PRON
ejpam-3266	117	9	denote	denote	VERB
ejpam-3266	117	10	by	by	ADP
ejpam-3266	117	11	σi	σi	PRON
ejpam-3266	117	12	the	the	DET
ejpam-3266	117	13	equivalence	equivalence	NOUN
ejpam-3266	117	14	relation	relation	NOUN
ejpam-3266	117	15	on	on	ADP
ejpam-3266	117	16	h	h	NOUN
ejpam-3266	117	17	defined	define	VERB
ejpam-3266	117	18	by	by	ADP
ejpam-3266	117	19	:	:	PUNCT
ejpam-3266	117	20	σi	σi	NOUN
ejpam-3266	117	21	:	:	PUNCT
ejpam-3266	117	22	=	=	SYM
ejpam-3266	117	23	{	{	PUNCT
ejpam-3266	117	24	(	(	PUNCT
ejpam-3266	117	25	a	a	PRON
ejpam-3266	117	26	,	,	PUNCT
ejpam-3266	117	27	b	b	NOUN
ejpam-3266	117	28	)	)	PUNCT
ejpam-3266	117	29	∈	∈	NOUN
ejpam-3266	117	30	h	h	NOUN
ejpam-3266	118	1	×h	×h	PROPN
ejpam-3266	119	1	|	|	ADV
ejpam-3266	119	2	a	a	PRON
ejpam-3266	119	3	,	,	PUNCT
ejpam-3266	119	4	b	b	X
ejpam-3266	119	5	∈	∈	NOUN
ejpam-3266	119	6	i	i	PRON
ejpam-3266	119	7	or	or	CCONJ
ejpam-3266	119	8	a	a	PRON
ejpam-3266	119	9	,	,	PUNCT
ejpam-3266	119	10	b	b	NOUN
ejpam-3266	119	11	/∈	/∈	PUNCT
ejpam-3266	119	12	i	i	PRON
ejpam-3266	119	13	}	}	PUNCT
ejpam-3266	119	14	(	(	PUNCT
ejpam-3266	119	15	i.e.	i.e.	X
ejpam-3266	119	16	a	a	X
ejpam-3266	119	17	,	,	PUNCT
ejpam-3266	119	18	b	b	NOUN
ejpam-3266	119	19	both	both	PRON
ejpam-3266	119	20	belong	belong	VERB
ejpam-3266	119	21	to	to	ADP
ejpam-3266	119	22	i	i	PRON
ejpam-3266	119	23	or	or	CCONJ
ejpam-3266	119	24	a	a	DET
ejpam-3266	119	25	,	,	PUNCT
ejpam-3266	119	26	b	b	NOUN
ejpam-3266	119	27	both	both	PRON
ejpam-3266	119	28	do	do	AUX
ejpam-3266	119	29	not	not	PART
ejpam-3266	119	30	belong	belong	VERB
ejpam-3266	119	31	to	to	ADP
ejpam-3266	119	32	i	i	PROPN
ejpam-3266	119	33	)	)	PUNCT
ejpam-3266	119	34	.	.	PUNCT
ejpam-3266	120	1	if	if	SCONJ
ejpam-3266	120	2	s	s	NOUN
ejpam-3266	120	3	is	be	AUX
ejpam-3266	120	4	a	a	DET
ejpam-3266	120	5	semigroup	semigroup	NOUN
ejpam-3266	120	6	or	or	CCONJ
ejpam-3266	120	7	an	an	DET
ejpam-3266	120	8	ordered	order	VERB
ejpam-3266	120	9	semigroup	semigroup	NOUN
ejpam-3266	120	10	and	and	CCONJ
ejpam-3266	120	11	i	i	PRON
ejpam-3266	120	12	a	a	DET
ejpam-3266	120	13	prime	prime	ADJ
ejpam-3266	120	14	ideal	ideal	NOUN
ejpam-3266	120	15	of	of	ADP
ejpam-3266	120	16	s	s	PROPN
ejpam-3266	120	17	,	,	PUNCT
ejpam-3266	120	18	then	then	ADV
ejpam-3266	120	19	the	the	DET
ejpam-3266	120	20	relation	relation	NOUN
ejpam-3266	120	21	σi	σi	NOUN
ejpam-3266	120	22	is	be	AUX
ejpam-3266	120	23	a	a	DET
ejpam-3266	120	24	semilattice	semilattice	NOUN
ejpam-3266	120	25	congruence	congruence	NOUN
ejpam-3266	120	26	on	on	ADP
ejpam-3266	120	27	s	s	PRON
ejpam-3266	120	28	[	[	X
ejpam-3266	120	29	3,13	3,13	NUM
ejpam-3266	120	30	]	]	X
ejpam-3266	120	31	(	(	PUNCT
ejpam-3266	120	32	and	and	CCONJ
ejpam-3266	120	33	the	the	DET
ejpam-3266	120	34	same	same	ADJ
ejpam-3266	120	35	holds	hold	VERB
ejpam-3266	120	36	if	if	SCONJ
ejpam-3266	120	37	we	we	PRON
ejpam-3266	120	38	replace	replace	VERB
ejpam-3266	120	39	the	the	DET
ejpam-3266	120	40	work	work	NOUN
ejpam-3266	120	41	“	"	PUNCT
ejpam-3266	120	42	semigroup	semigroup	NOUN
ejpam-3266	120	43	”	"	PUNCT
ejpam-3266	120	44	by	by	ADP
ejpam-3266	120	45	“	"	PUNCT
ejpam-3266	120	46	groupoid	groupoid	PROPN
ejpam-3266	120	47	”	"	PUNCT
ejpam-3266	120	48	)	)	PUNCT
ejpam-3266	120	49	.	.	PUNCT
ejpam-3266	121	1	recall	recall	VERB
ejpam-3266	121	2	that	that	PRON
ejpam-3266	121	3	for	for	ADP
ejpam-3266	121	4	ordered	order	VERB
ejpam-3266	121	5	groupoids	groupoid	NOUN
ejpam-3266	121	6	the	the	DET
ejpam-3266	121	7	semilattice	semilattice	NOUN
ejpam-3266	121	8	congruences	congruence	NOUN
ejpam-3266	121	9	are	be	AUX
ejpam-3266	121	10	defined	define	VERB
ejpam-3266	121	11	exactly	exactly	ADV
ejpam-3266	121	12	as	as	ADP
ejpam-3266	121	13	in	in	ADP
ejpam-3266	121	14	groupoids	groupoid	NOUN
ejpam-3266	121	15	.	.	PUNCT
ejpam-3266	122	1	in	in	ADP
ejpam-3266	122	2	an	an	DET
ejpam-3266	122	3	attempt	attempt	NOUN
ejpam-3266	122	4	to	to	PART
ejpam-3266	122	5	show	show	VERB
ejpam-3266	122	6	the	the	DET
ejpam-3266	122	7	way	way	NOUN
ejpam-3266	122	8	we	we	PRON
ejpam-3266	122	9	pass	pass	VERB
ejpam-3266	122	10	from	from	ADP
ejpam-3266	122	11	semigroups	semigroup	NOUN
ejpam-3266	122	12	to	to	ADP
ejpam-3266	122	13	γ	γ	NOUN
ejpam-3266	122	14	-	-	PUNCT
ejpam-3266	122	15	semigroups	semigroup	NOUN
ejpam-3266	122	16	,	,	PUNCT
ejpam-3266	122	17	we	we	PRON
ejpam-3266	122	18	transferred	transfer	VERB
ejpam-3266	122	19	this	this	DET
ejpam-3266	122	20	result	result	NOUN
ejpam-3266	122	21	to	to	ADP
ejpam-3266	122	22	γ	γ	NOUN
ejpam-3266	122	23	-	-	PUNCT
ejpam-3266	122	24	semigroups	semigroup	NOUN
ejpam-3266	122	25	in	in	ADP
ejpam-3266	122	26	[	[	X
ejpam-3266	122	27	5	5	NUM
ejpam-3266	122	28	]	]	PUNCT
ejpam-3266	122	29	.	.	PUNCT
ejpam-3266	123	1	here	here	ADV
ejpam-3266	123	2	we	we	PRON
ejpam-3266	123	3	do	do	VERB
ejpam-3266	123	4	the	the	DET
ejpam-3266	123	5	same	same	ADJ
ejpam-3266	123	6	for	for	ADP
ejpam-3266	123	7	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	123	8	using	use	VERB
ejpam-3266	123	9	the	the	DET
ejpam-3266	123	10	following	follow	VERB
ejpam-3266	123	11	proposition	proposition	NOUN
ejpam-3266	123	12	.	.	PUNCT
ejpam-3266	124	1	proposition	proposition	NOUN
ejpam-3266	124	2	2.9	2.9	NUM
ejpam-3266	124	3	.	.	PUNCT
ejpam-3266	125	1	let	let	VERB
ejpam-3266	125	2	h	h	PRON
ejpam-3266	125	3	be	be	AUX
ejpam-3266	125	4	an	an	DET
ejpam-3266	125	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	125	6	,	,	PUNCT
ejpam-3266	125	7	a	a	DET
ejpam-3266	125	8	,	,	PUNCT
ejpam-3266	125	9	b	b	NOUN
ejpam-3266	125	10	,	,	PUNCT
ejpam-3266	125	11	c	c	PROPN
ejpam-3266	125	12	∈	∈	PROPN
ejpam-3266	125	13	h	h	NOUN
ejpam-3266	125	14	and	and	CCONJ
ejpam-3266	125	15	i	i	PRON
ejpam-3266	125	16	⊆	⊆	NUM
ejpam-3266	125	17	h.	h.	NOUN
ejpam-3266	126	1	then	then	ADV
ejpam-3266	126	2	we	we	PRON
ejpam-3266	126	3	have	have	VERB
ejpam-3266	126	4	the	the	DET
ejpam-3266	126	5	following	following	NOUN
ejpam-3266	126	6	:	:	PUNCT
ejpam-3266	126	7	(	(	PUNCT
ejpam-3266	126	8	1	1	X
ejpam-3266	126	9	)	)	PUNCT
ejpam-3266	126	10	if	if	SCONJ
ejpam-3266	126	11	a	a	DET
ejpam-3266	126	12	◦	◦	NOUN
ejpam-3266	126	13	c	c	NOUN
ejpam-3266	126	14	,	,	PUNCT
ejpam-3266	126	15	b	b	NOUN
ejpam-3266	127	1	◦	◦	NOUN
ejpam-3266	127	2	c	c	NOUN
ejpam-3266	127	3	⊆	⊆	NUM
ejpam-3266	127	4	i	i	PRON
ejpam-3266	127	5	,	,	PUNCT
ejpam-3266	127	6	then	then	ADV
ejpam-3266	127	7	(	(	PUNCT
ejpam-3266	127	8	a	a	DET
ejpam-3266	127	9	◦	◦	NOUN
ejpam-3266	127	10	c	c	NOUN
ejpam-3266	127	11	,	,	PUNCT
ejpam-3266	127	12	b	b	X
ejpam-3266	127	13	◦	◦	NOUN
ejpam-3266	127	14	c	c	NOUN
ejpam-3266	127	15	)	)	PUNCT
ejpam-3266	127	16	∈	∈	PROPN
ejpam-3266	128	1	σi	σi	X
ejpam-3266	128	2	.	.	PUNCT
ejpam-3266	128	3	suppose	suppose	VERB
ejpam-3266	128	4	now	now	ADV
ejpam-3266	128	5	that	that	SCONJ
ejpam-3266	128	6	,	,	PUNCT
ejpam-3266	128	7	for	for	ADP
ejpam-3266	128	8	every	every	DET
ejpam-3266	128	9	a	a	PROPN
ejpam-3266	128	10	,	,	PUNCT
ejpam-3266	128	11	b	b	X
ejpam-3266	128	12	∈	∈	PROPN
ejpam-3266	128	13	h	h	NOUN
ejpam-3266	128	14	,	,	PUNCT
ejpam-3266	128	15	we	we	PRON
ejpam-3266	128	16	have	have	VERB
ejpam-3266	128	17	a	a	DET
ejpam-3266	128	18	◦	◦	NOUN
ejpam-3266	128	19	b	b	NOUN
ejpam-3266	128	20	⊆	⊆	NUM
ejpam-3266	128	21	i	i	PRON
ejpam-3266	128	22	or	or	CCONJ
ejpam-3266	128	23	(	(	PUNCT
ejpam-3266	128	24	a	a	DET
ejpam-3266	128	25	◦	◦	NOUN
ejpam-3266	128	26	b	b	NOUN
ejpam-3266	128	27	)	)	PUNCT
ejpam-3266	128	28	∩	∩	NOUN
ejpam-3266	128	29	i	i	NOUN
ejpam-3266	128	30	=	=	NOUN
ejpam-3266	128	31	∅	∅	NOUN
ejpam-3266	128	32	(	(	PUNCT
ejpam-3266	128	33	∗	∗	NOUN
ejpam-3266	128	34	)	)	PUNCT
ejpam-3266	128	35	then	then	ADV
ejpam-3266	128	36	the	the	DET
ejpam-3266	128	37	following	follow	VERB
ejpam-3266	128	38	two	two	NUM
ejpam-3266	128	39	conditions	condition	NOUN
ejpam-3266	128	40	are	be	AUX
ejpam-3266	128	41	satisfied	satisfied	ADJ
ejpam-3266	128	42	:	:	PUNCT
ejpam-3266	128	43	(	(	PUNCT
ejpam-3266	128	44	2	2	X
ejpam-3266	128	45	)	)	PUNCT
ejpam-3266	128	46	if	if	SCONJ
ejpam-3266	128	47	a	a	DET
ejpam-3266	128	48	◦	◦	NOUN
ejpam-3266	128	49	c	c	NOUN
ejpam-3266	128	50	,	,	PUNCT
ejpam-3266	128	51	b	b	X
ejpam-3266	129	1	◦	◦	NOUN
ejpam-3266	129	2	c	c	NOUN
ejpam-3266	130	1	*	*	PUNCT
ejpam-3266	130	2	i	i	PRON
ejpam-3266	130	3	,	,	PUNCT
ejpam-3266	130	4	then	then	ADV
ejpam-3266	130	5	(	(	PUNCT
ejpam-3266	130	6	a	a	DET
ejpam-3266	130	7	◦	◦	NOUN
ejpam-3266	130	8	c	c	NOUN
ejpam-3266	130	9	,	,	PUNCT
ejpam-3266	130	10	b	b	X
ejpam-3266	130	11	◦	◦	NOUN
ejpam-3266	130	12	c	c	NOUN
ejpam-3266	130	13	)	)	PUNCT
ejpam-3266	130	14	∈	∈	PROPN
ejpam-3266	131	1	σi	σi	X
ejpam-3266	131	2	.	.	PUNCT
ejpam-3266	132	1	(	(	PUNCT
ejpam-3266	132	2	3	3	X
ejpam-3266	132	3	)	)	PUNCT
ejpam-3266	132	4	if	if	SCONJ
ejpam-3266	132	5	a	a	PRON
ejpam-3266	132	6	/∈	/∈	INTJ
ejpam-3266	133	1	i	i	PRON
ejpam-3266	133	2	and	and	CCONJ
ejpam-3266	133	3	a	a	DET
ejpam-3266	133	4	◦	◦	NOUN
ejpam-3266	133	5	a	a	PRON
ejpam-3266	134	1	*	*	PUNCT
ejpam-3266	134	2	i	i	INTJ
ejpam-3266	134	3	,	,	PUNCT
ejpam-3266	134	4	then	then	ADV
ejpam-3266	134	5	(	(	PUNCT
ejpam-3266	134	6	a	a	X
ejpam-3266	134	7	,	,	PUNCT
ejpam-3266	134	8	a	a	DET
ejpam-3266	134	9	◦	◦	NOUN
ejpam-3266	134	10	a	a	X
ejpam-3266	134	11	)	)	PUNCT
ejpam-3266	134	12	∈	∈	PROPN
ejpam-3266	134	13	σi	σi	NOUN
ejpam-3266	134	14	.	.	PUNCT
ejpam-3266	135	1	proof	proof	NOUN
ejpam-3266	135	2	.	.	PUNCT
ejpam-3266	136	1	(	(	PUNCT
ejpam-3266	136	2	1	1	X
ejpam-3266	136	3	)	)	PUNCT
ejpam-3266	136	4	let	let	VERB
ejpam-3266	136	5	a	a	DET
ejpam-3266	136	6	◦	◦	NOUN
ejpam-3266	136	7	c	c	NOUN
ejpam-3266	136	8	,	,	PUNCT
ejpam-3266	136	9	b	b	NOUN
ejpam-3266	136	10	◦	◦	NOUN
ejpam-3266	136	11	c	c	NOUN
ejpam-3266	136	12	⊆	⊆	NUM
ejpam-3266	136	13	i	i	PRON
ejpam-3266	136	14	,	,	PUNCT
ejpam-3266	136	15	u	u	PROPN
ejpam-3266	136	16	∈	∈	PROPN
ejpam-3266	136	17	a	a	DET
ejpam-3266	136	18	◦	◦	NOUN
ejpam-3266	136	19	c	c	NOUN
ejpam-3266	136	20	and	and	CCONJ
ejpam-3266	136	21	v	v	ADP
ejpam-3266	136	22	∈	∈	PROPN
ejpam-3266	136	23	b	b	PROPN
ejpam-3266	136	24	◦	◦	NOUN
ejpam-3266	136	25	c.	c.	NOUN
ejpam-3266	136	26	then	then	ADV
ejpam-3266	136	27	u	u	PROPN
ejpam-3266	136	28	,	,	PUNCT
ejpam-3266	136	29	v	v	NOUN
ejpam-3266	136	30	∈	∈	X
ejpam-3266	137	1	i	i	PRON
ejpam-3266	137	2	,	,	PUNCT
ejpam-3266	137	3	so	so	CCONJ
ejpam-3266	137	4	(	(	PUNCT
ejpam-3266	137	5	u	u	NOUN
ejpam-3266	137	6	,	,	PUNCT
ejpam-3266	137	7	v	v	NOUN
ejpam-3266	137	8	)	)	PUNCT
ejpam-3266	137	9	∈	∈	PROPN
ejpam-3266	137	10	σi	σi	X
ejpam-3266	137	11	.	.	PUNCT
ejpam-3266	138	1	(	(	PUNCT
ejpam-3266	138	2	2	2	X
ejpam-3266	138	3	)	)	PUNCT
ejpam-3266	138	4	let	let	VERB
ejpam-3266	138	5	a	a	DET
ejpam-3266	138	6	◦	◦	NOUN
ejpam-3266	138	7	c	c	NOUN
ejpam-3266	138	8	,	,	PUNCT
ejpam-3266	138	9	b	b	X
ejpam-3266	139	1	◦	◦	NOUN
ejpam-3266	139	2	c	c	NOUN
ejpam-3266	140	1	*	*	PUNCT
ejpam-3266	140	2	i	i	INTJ
ejpam-3266	140	3	,	,	PUNCT
ejpam-3266	140	4	u	u	PROPN
ejpam-3266	140	5	∈	∈	PROPN
ejpam-3266	140	6	a	a	DET
ejpam-3266	140	7	◦	◦	NOUN
ejpam-3266	140	8	c	c	NOUN
ejpam-3266	140	9	and	and	CCONJ
ejpam-3266	140	10	v	v	ADP
ejpam-3266	140	11	∈	∈	PROPN
ejpam-3266	140	12	b	b	PROPN
ejpam-3266	140	13	◦	◦	NOUN
ejpam-3266	140	14	c.	c.	NOUN
ejpam-3266	140	15	if	if	SCONJ
ejpam-3266	140	16	u	u	PROPN
ejpam-3266	140	17	,	,	PUNCT
ejpam-3266	140	18	v	v	ADP
ejpam-3266	140	19	∈	∈	X
ejpam-3266	141	1	i	i	PRON
ejpam-3266	141	2	,	,	PUNCT
ejpam-3266	141	3	then	then	ADV
ejpam-3266	141	4	(	(	PUNCT
ejpam-3266	141	5	u	u	NOUN
ejpam-3266	141	6	,	,	PUNCT
ejpam-3266	141	7	v	v	NOUN
ejpam-3266	141	8	)	)	PUNCT
ejpam-3266	141	9	∈	∈	PROPN
ejpam-3266	141	10	σi	σi	INTJ
ejpam-3266	141	11	.	.	PUNCT
ejpam-3266	142	1	if	if	SCONJ
ejpam-3266	142	2	u	u	PROPN
ejpam-3266	142	3	/∈	/∈	VERB
ejpam-3266	143	1	i	i	PRON
ejpam-3266	143	2	,	,	PUNCT
ejpam-3266	143	3	then	then	ADV
ejpam-3266	143	4	v	v	X
ejpam-3266	143	5	/∈	/∈	PROPN
ejpam-3266	143	6	i.	i.	PROPN
ejpam-3266	144	1	indeed	indeed	ADV
ejpam-3266	144	2	,	,	PUNCT
ejpam-3266	144	3	if	if	SCONJ
ejpam-3266	144	4	v	v	ADP
ejpam-3266	144	5	∈	∈	NOUN
ejpam-3266	145	1	i	i	PRON
ejpam-3266	145	2	,	,	PUNCT
ejpam-3266	145	3	then	then	ADV
ejpam-3266	145	4	v	v	X
ejpam-3266	145	5	∈	∈	PROPN
ejpam-3266	145	6	(	(	PUNCT
ejpam-3266	145	7	b	b	X
ejpam-3266	145	8	◦	◦	NOUN
ejpam-3266	145	9	c	c	NOUN
ejpam-3266	145	10	)	)	PUNCT
ejpam-3266	145	11	∩	∩	PROPN
ejpam-3266	145	12	i.	i.	NOUN
ejpam-3266	145	13	since	since	SCONJ
ejpam-3266	145	14	(	(	PUNCT
ejpam-3266	145	15	b	b	X
ejpam-3266	145	16	◦	◦	NOUN
ejpam-3266	145	17	c	c	NOUN
ejpam-3266	145	18	)	)	PUNCT
ejpam-3266	145	19	∩	∩	NOUN
ejpam-3266	145	20	i	i	PROPN
ejpam-3266	145	21	6=	6=	NOUN
ejpam-3266	145	22	∅	∅	NOUN
ejpam-3266	145	23	,	,	PUNCT
ejpam-3266	145	24	by	by	ADP
ejpam-3266	145	25	(	(	PUNCT
ejpam-3266	145	26	∗	∗	NOUN
ejpam-3266	145	27	)	)	PUNCT
ejpam-3266	145	28	,	,	PUNCT
ejpam-3266	145	29	we	we	PRON
ejpam-3266	145	30	have	have	VERB
ejpam-3266	145	31	b	b	NUM
ejpam-3266	145	32	◦	◦	NOUN
ejpam-3266	145	33	c	c	NOUN
ejpam-3266	145	34	⊆	⊆	NUM
ejpam-3266	145	35	i	i	PRON
ejpam-3266	145	36	which	which	PRON
ejpam-3266	145	37	is	be	AUX
ejpam-3266	145	38	impossible	impossible	ADJ
ejpam-3266	145	39	.	.	PUNCT
ejpam-3266	146	1	so	so	ADV
ejpam-3266	146	2	u	u	NOUN
ejpam-3266	146	3	,	,	PUNCT
ejpam-3266	146	4	v	v	NOUN
ejpam-3266	146	5	/∈	/∈	PUNCT
ejpam-3266	147	1	i	i	PRON
ejpam-3266	147	2	,	,	PUNCT
ejpam-3266	147	3	and	and	CCONJ
ejpam-3266	147	4	(	(	PUNCT
ejpam-3266	147	5	u	u	NOUN
ejpam-3266	147	6	,	,	PUNCT
ejpam-3266	147	7	v	v	NOUN
ejpam-3266	147	8	)	)	PUNCT
ejpam-3266	147	9	∈	∈	PROPN
ejpam-3266	147	10	σi	σi	INTJ
ejpam-3266	147	11	.	.	PUNCT
ejpam-3266	148	1	if	if	SCONJ
ejpam-3266	148	2	v	v	NUM
ejpam-3266	148	3	/∈	/∈	PUNCT
ejpam-3266	149	1	i	i	PRON
ejpam-3266	149	2	,	,	PUNCT
ejpam-3266	149	3	in	in	ADP
ejpam-3266	149	4	a	a	DET
ejpam-3266	149	5	similar	similar	ADJ
ejpam-3266	149	6	way	way	NOUN
ejpam-3266	149	7	we	we	PRON
ejpam-3266	149	8	get	get	VERB
ejpam-3266	149	9	u	u	NOUN
ejpam-3266	149	10	/∈	/∈	PUNCT
ejpam-3266	150	1	i	i	PRON
ejpam-3266	150	2	,	,	PUNCT
ejpam-3266	150	3	so	so	ADV
ejpam-3266	150	4	again	again	ADV
ejpam-3266	150	5	(	(	PUNCT
ejpam-3266	150	6	u	u	NOUN
ejpam-3266	150	7	,	,	PUNCT
ejpam-3266	150	8	v	v	NOUN
ejpam-3266	150	9	)	)	PUNCT
ejpam-3266	150	10	∈	∈	PROPN
ejpam-3266	151	1	σi	σi	X
ejpam-3266	151	2	.	.	PUNCT
ejpam-3266	152	1	(	(	PUNCT
ejpam-3266	152	2	3	3	X
ejpam-3266	152	3	)	)	PUNCT
ejpam-3266	152	4	let	let	VERB
ejpam-3266	152	5	a	a	PRON
ejpam-3266	152	6	/∈	/∈	PUNCT
ejpam-3266	153	1	i	i	PRON
ejpam-3266	153	2	,	,	PUNCT
ejpam-3266	153	3	a	a	DET
ejpam-3266	153	4	◦	◦	NOUN
ejpam-3266	153	5	a	a	PRON
ejpam-3266	153	6	*	*	PUNCT
ejpam-3266	154	1	i	i	PRON
ejpam-3266	154	2	and	and	CCONJ
ejpam-3266	154	3	u	u	PROPN
ejpam-3266	154	4	∈	∈	PROPN
ejpam-3266	154	5	a	a	DET
ejpam-3266	154	6	◦	◦	NOUN
ejpam-3266	154	7	a.	a.	NOUN
ejpam-3266	155	1	if	if	SCONJ
ejpam-3266	155	2	u	u	PROPN
ejpam-3266	155	3	∈	∈	PROPN
ejpam-3266	155	4	i	i	PRON
ejpam-3266	155	5	,	,	PUNCT
ejpam-3266	155	6	then	then	ADV
ejpam-3266	155	7	(	(	PUNCT
ejpam-3266	155	8	a	a	DET
ejpam-3266	155	9	◦	◦	NOUN
ejpam-3266	155	10	a	a	X
ejpam-3266	155	11	)	)	PUNCT
ejpam-3266	155	12	∩	∩	NOUN
ejpam-3266	155	13	i	i	PROPN
ejpam-3266	155	14	6=	6=	NOUN
ejpam-3266	155	15	∅	∅	NOUN
ejpam-3266	155	16	and	and	CCONJ
ejpam-3266	155	17	,	,	PUNCT
ejpam-3266	155	18	by	by	ADP
ejpam-3266	155	19	(	(	PUNCT
ejpam-3266	155	20	∗	∗	NOUN
ejpam-3266	155	21	)	)	PUNCT
ejpam-3266	155	22	,	,	PUNCT
ejpam-3266	155	23	a	a	DET
ejpam-3266	155	24	◦	◦	NOUN
ejpam-3266	155	25	a	a	DET
ejpam-3266	155	26	⊆	⊆	NUM
ejpam-3266	155	27	i	i	PRON
ejpam-3266	155	28	which	which	PRON
ejpam-3266	155	29	is	be	AUX
ejpam-3266	155	30	impossible	impossible	ADJ
ejpam-3266	156	1	.	.	PUNCT
ejpam-3266	157	1	thus	thus	ADV
ejpam-3266	157	2	we	we	PRON
ejpam-3266	157	3	have	have	VERB
ejpam-3266	157	4	u	u	PROPN
ejpam-3266	157	5	6∈	6∈	PROPN
ejpam-3266	157	6	i.	i.	NOUN
ejpam-3266	157	7	since	since	SCONJ
ejpam-3266	157	8	a	a	DET
ejpam-3266	157	9	,	,	PUNCT
ejpam-3266	157	10	u	u	NOUN
ejpam-3266	157	11	/∈	/∈	PUNCT
ejpam-3266	158	1	i	i	PRON
ejpam-3266	158	2	,	,	PUNCT
ejpam-3266	158	3	we	we	PRON
ejpam-3266	158	4	have	have	VERB
ejpam-3266	158	5	(	(	PUNCT
ejpam-3266	158	6	a	a	PRON
ejpam-3266	158	7	,	,	PUNCT
ejpam-3266	158	8	u	u	NOUN
ejpam-3266	158	9	)	)	PUNCT
ejpam-3266	158	10	∈	∈	PROPN
ejpam-3266	159	1	σi	σi	X
ejpam-3266	159	2	.	.	PUNCT
ejpam-3266	160	1	�	�	PROPN
ejpam-3266	160	2	if	if	SCONJ
ejpam-3266	160	3	h	h	NOUN
ejpam-3266	160	4	is	be	AUX
ejpam-3266	160	5	an	an	DET
ejpam-3266	160	6	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	160	7	,	,	PUNCT
ejpam-3266	160	8	a	a	DET
ejpam-3266	160	9	nonempty	nonempty	NOUN
ejpam-3266	160	10	subset	subset	VERB
ejpam-3266	160	11	a	a	PRON
ejpam-3266	160	12	of	of	ADP
ejpam-3266	160	13	h	h	NOUN
ejpam-3266	160	14	is	be	AUX
ejpam-3266	160	15	called	call	VERB
ejpam-3266	160	16	an	an	DET
ejpam-3266	160	17	ideal	ideal	NOUN
ejpam-3266	160	18	of	of	ADP
ejpam-3266	160	19	h	h	NOUN
ejpam-3266	160	20	if	if	SCONJ
ejpam-3266	160	21	a∗h	a∗h	PROPN
ejpam-3266	160	22	⊆	⊆	NUM
ejpam-3266	160	23	a	a	PRON
ejpam-3266	160	24	and	and	CCONJ
ejpam-3266	160	25	h	h	NOUN
ejpam-3266	160	26	∗	∗	NOUN
ejpam-3266	160	27	a	a	DET
ejpam-3266	160	28	⊆	⊆	NUM
ejpam-3266	160	29	a	a	NOUN
ejpam-3266	160	30	,	,	PUNCT
ejpam-3266	160	31	equivalently	equivalently	ADV
ejpam-3266	160	32	if	if	SCONJ
ejpam-3266	160	33	a	a	DET
ejpam-3266	160	34	∈	∈	PROPN
ejpam-3266	160	35	a	a	PRON
ejpam-3266	160	36	and	and	CCONJ
ejpam-3266	160	37	h	h	NOUN
ejpam-3266	160	38	∈	∈	PROPN
ejpam-3266	160	39	h	h	NOUN
ejpam-3266	160	40	,	,	PUNCT
ejpam-3266	160	41	then	then	ADV
ejpam-3266	160	42	a	a	DET
ejpam-3266	160	43	◦	◦	NOUN
ejpam-3266	160	44	h	h	NOUN
ejpam-3266	160	45	⊆	⊆	NUM
ejpam-3266	160	46	a	a	PRON
ejpam-3266	160	47	and	and	CCONJ
ejpam-3266	160	48	h	h	NOUN
ejpam-3266	160	49	◦	◦	VERB
ejpam-3266	160	50	a	a	DET
ejpam-3266	160	51	⊆	⊆	NUM
ejpam-3266	160	52	a	a	PRON
ejpam-3266	160	53	[	[	X
ejpam-3266	160	54	8	8	NUM
ejpam-3266	160	55	]	]	PUNCT
ejpam-3266	160	56	.	.	PUNCT
ejpam-3266	161	1	by	by	ADP
ejpam-3266	161	2	a	a	DET
ejpam-3266	161	3	prime	prime	ADJ
ejpam-3266	161	4	ideal	ideal	NOUN
ejpam-3266	161	5	of	of	ADP
ejpam-3266	161	6	h	h	NOUN
ejpam-3266	161	7	we	we	PRON
ejpam-3266	161	8	clearly	clearly	ADV
ejpam-3266	161	9	mean	mean	VERB
ejpam-3266	161	10	an	an	DET
ejpam-3266	161	11	ideal	ideal	NOUN
ejpam-3266	161	12	of	of	ADP
ejpam-3266	161	13	h	h	PRON
ejpam-3266	161	14	which	which	PRON
ejpam-3266	161	15	is	be	AUX
ejpam-3266	161	16	at	at	ADP
ejpam-3266	161	17	the	the	DET
ejpam-3266	161	18	same	same	ADJ
ejpam-3266	161	19	time	time	NOUN
ejpam-3266	161	20	a	a	DET
ejpam-3266	161	21	prime	prime	ADJ
ejpam-3266	161	22	subset	subset	NOUN
ejpam-3266	161	23	of	of	ADP
ejpam-3266	161	24	h.	h.	PROPN
ejpam-3266	161	25	corollary	corollary	PROPN
ejpam-3266	161	26	2.10	2.10	NUM
ejpam-3266	161	27	.	.	PUNCT
ejpam-3266	162	1	(	(	PUNCT
ejpam-3266	162	2	cf	cf	NOUN
ejpam-3266	162	3	.	.	PUNCT
ejpam-3266	163	1	also	also	ADV
ejpam-3266	163	2	[	[	X
ejpam-3266	163	3	3	3	X
ejpam-3266	163	4	]	]	PUNCT
ejpam-3266	163	5	and	and	CCONJ
ejpam-3266	163	6	[	[	X
ejpam-3266	163	7	5	5	NUM
ejpam-3266	163	8	;	;	PUNCT
ejpam-3266	163	9	proposition	proposition	NOUN
ejpam-3266	163	10	2.2	2.2	NUM
ejpam-3266	163	11	]	]	PUNCT
ejpam-3266	163	12	)	)	PUNCT
ejpam-3266	163	13	let	let	VERB
ejpam-3266	163	14	h	h	NOUN
ejpam-3266	163	15	be	be	AUX
ejpam-3266	163	16	an	an	DET
ejpam-3266	163	17	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	163	18	and	and	CCONJ
ejpam-3266	163	19	i	i	PRON
ejpam-3266	163	20	a	a	DET
ejpam-3266	163	21	prime	prime	ADJ
ejpam-3266	163	22	ideal	ideal	NOUN
ejpam-3266	163	23	of	of	ADP
ejpam-3266	163	24	h.	h.	PROPN
ejpam-3266	163	25	then	then	ADV
ejpam-3266	163	26	the	the	DET
ejpam-3266	163	27	equivalence	equivalence	NOUN
ejpam-3266	163	28	relation	relation	NOUN
ejpam-3266	163	29	σi	σi	NOUN
ejpam-3266	163	30	is	be	AUX
ejpam-3266	163	31	a	a	DET
ejpam-3266	163	32	semilattice	semilattice	NOUN
ejpam-3266	163	33	congruence	congruence	NOUN
ejpam-3266	163	34	on	on	ADP
ejpam-3266	163	35	h.	h.	PROPN
ejpam-3266	163	36	proof	proof	NOUN
ejpam-3266	163	37	.	.	PUNCT
ejpam-3266	164	1	let	let	VERB
ejpam-3266	164	2	(	(	PUNCT
ejpam-3266	164	3	a	a	PRON
ejpam-3266	164	4	,	,	PUNCT
ejpam-3266	164	5	b	b	NOUN
ejpam-3266	164	6	)	)	PUNCT
ejpam-3266	164	7	∈	∈	PROPN
ejpam-3266	165	1	σi	σi	NOUN
ejpam-3266	166	1	and	and	CCONJ
ejpam-3266	166	2	c	c	PROPN
ejpam-3266	166	3	∈	∈	PROPN
ejpam-3266	166	4	h.	h.	NOUN
ejpam-3266	166	5	then	then	ADV
ejpam-3266	166	6	(	(	PUNCT
ejpam-3266	166	7	a	a	DET
ejpam-3266	166	8	◦	◦	NOUN
ejpam-3266	166	9	c	c	NOUN
ejpam-3266	166	10	,	,	PUNCT
ejpam-3266	166	11	b	b	X
ejpam-3266	166	12	◦	◦	NOUN
ejpam-3266	166	13	c	c	NOUN
ejpam-3266	166	14	)	)	PUNCT
ejpam-3266	166	15	∈	∈	PROPN
ejpam-3266	166	16	σi	σi	X
ejpam-3266	166	17	.	.	PUNCT
ejpam-3266	167	1	in	in	ADP
ejpam-3266	167	2	fact	fact	NOUN
ejpam-3266	167	3	:	:	PUNCT
ejpam-3266	167	4	since	since	SCONJ
ejpam-3266	167	5	(	(	PUNCT
ejpam-3266	167	6	a	a	PRON
ejpam-3266	167	7	,	,	PUNCT
ejpam-3266	167	8	b	b	NOUN
ejpam-3266	167	9	)	)	PUNCT
ejpam-3266	167	10	∈	∈	PROPN
ejpam-3266	167	11	σi	σi	INTJ
ejpam-3266	167	12	,	,	PUNCT
ejpam-3266	167	13	we	we	PRON
ejpam-3266	167	14	have	have	VERB
ejpam-3266	167	15	a	a	DET
ejpam-3266	167	16	,	,	PUNCT
ejpam-3266	167	17	b	b	X
ejpam-3266	167	18	∈	∈	NOUN
ejpam-3266	167	19	i	i	PRON
ejpam-3266	167	20	or	or	CCONJ
ejpam-3266	167	21	a	a	DET
ejpam-3266	167	22	,	,	PUNCT
ejpam-3266	167	23	b	b	PROPN
ejpam-3266	167	24	/∈	/∈	PROPN
ejpam-3266	167	25	i.	i.	PROPN
ejpam-3266	167	26	let	let	VERB
ejpam-3266	167	27	a	a	DET
ejpam-3266	167	28	,	,	PUNCT
ejpam-3266	167	29	b	b	PROPN
ejpam-3266	167	30	∈	∈	PROPN
ejpam-3266	167	31	i.	i.	NOUN
ejpam-3266	167	32	since	since	SCONJ
ejpam-3266	167	33	i	i	PRON
ejpam-3266	167	34	is	be	AUX
ejpam-3266	167	35	an	an	DET
ejpam-3266	167	36	ideal	ideal	NOUN
ejpam-3266	167	37	of	of	ADP
ejpam-3266	167	38	h	h	NOUN
ejpam-3266	167	39	,	,	PUNCT
ejpam-3266	167	40	we	we	PRON
ejpam-3266	167	41	have	have	VERB
ejpam-3266	167	42	a	a	DET
ejpam-3266	167	43	◦	◦	NOUN
ejpam-3266	167	44	c	c	NOUN
ejpam-3266	167	45	,	,	PUNCT
ejpam-3266	167	46	b	b	X
ejpam-3266	168	1	◦	◦	NOUN
ejpam-3266	168	2	c	c	NOUN
ejpam-3266	168	3	⊆	⊆	NUM
ejpam-3266	168	4	i.	i.	NOUN
ejpam-3266	168	5	then	then	ADV
ejpam-3266	168	6	,	,	PUNCT
ejpam-3266	168	7	by	by	ADP
ejpam-3266	168	8	proposition	proposition	NOUN
ejpam-3266	168	9	2.9(1	2.9(1	NUM
ejpam-3266	168	10	)	)	PUNCT
ejpam-3266	168	11	,	,	PUNCT
ejpam-3266	168	12	we	we	PRON
ejpam-3266	168	13	have	have	VERB
ejpam-3266	168	14	(	(	PUNCT
ejpam-3266	168	15	a	a	DET
ejpam-3266	168	16	◦	◦	NOUN
ejpam-3266	168	17	c	c	NOUN
ejpam-3266	168	18	,	,	PUNCT
ejpam-3266	168	19	b	b	X
ejpam-3266	168	20	◦	◦	NOUN
ejpam-3266	168	21	c	c	NOUN
ejpam-3266	168	22	)	)	PUNCT
ejpam-3266	168	23	∈	∈	PROPN
ejpam-3266	169	1	σi	σi	X
ejpam-3266	169	2	.	.	PUNCT
ejpam-3266	170	1	let	let	VERB
ejpam-3266	170	2	a	a	DET
ejpam-3266	170	3	,	,	PUNCT
ejpam-3266	170	4	b	b	PROPN
ejpam-3266	170	5	/∈	/∈	PUNCT
ejpam-3266	170	6	i.	i.	NOUN
ejpam-3266	171	1	if	if	SCONJ
ejpam-3266	171	2	c	c	PROPN
ejpam-3266	171	3	∈	∈	PROPN
ejpam-3266	171	4	i	i	PRON
ejpam-3266	171	5	then	then	ADV
ejpam-3266	171	6	,	,	PUNCT
ejpam-3266	171	7	since	since	SCONJ
ejpam-3266	171	8	i	i	PRON
ejpam-3266	171	9	is	be	AUX
ejpam-3266	171	10	an	an	DET
ejpam-3266	171	11	ideal	ideal	NOUN
ejpam-3266	171	12	of	of	ADP
ejpam-3266	171	13	h	h	NOUN
ejpam-3266	171	14	,	,	PUNCT
ejpam-3266	171	15	we	we	PRON
ejpam-3266	171	16	have	have	VERB
ejpam-3266	171	17	a	a	DET
ejpam-3266	171	18	◦	◦	NOUN
ejpam-3266	171	19	c	c	NOUN
ejpam-3266	171	20	,	,	PUNCT
ejpam-3266	171	21	b	b	NOUN
ejpam-3266	172	1	◦	◦	NOUN
ejpam-3266	172	2	c	c	NOUN
ejpam-3266	172	3	⊆	⊆	NUM
ejpam-3266	172	4	i	i	PRON
ejpam-3266	172	5	,	,	PUNCT
ejpam-3266	172	6	then	then	ADV
ejpam-3266	172	7	(	(	PUNCT
ejpam-3266	172	8	a	a	DET
ejpam-3266	172	9	◦	◦	NOUN
ejpam-3266	172	10	c	c	NOUN
ejpam-3266	172	11	,	,	PUNCT
ejpam-3266	172	12	b	b	X
ejpam-3266	172	13	◦	◦	NOUN
ejpam-3266	172	14	c	c	NOUN
ejpam-3266	172	15	)	)	PUNCT
ejpam-3266	172	16	∈	∈	PROPN
ejpam-3266	173	1	σi	σi	X
ejpam-3266	173	2	.	.	PUNCT
ejpam-3266	174	1	let	let	VERB
ejpam-3266	174	2	c	c	NOUN
ejpam-3266	174	3	/∈	/∈	PUNCT
ejpam-3266	174	4	i.	i.	PROPN
ejpam-3266	174	5	since	since	SCONJ
ejpam-3266	174	6	a	a	DET
ejpam-3266	174	7	,	,	PUNCT
ejpam-3266	174	8	b	b	NOUN
ejpam-3266	174	9	,	,	PUNCT
ejpam-3266	174	10	c	c	NOUN
ejpam-3266	174	11	/∈	/∈	PUNCT
ejpam-3266	175	1	i	i	PRON
ejpam-3266	175	2	,	,	PUNCT
ejpam-3266	175	3	by	by	ADP
ejpam-3266	175	4	remark	remark	NOUN
ejpam-3266	175	5	2.6	2.6	NUM
ejpam-3266	175	6	,	,	PUNCT
ejpam-3266	175	7	we	we	PRON
ejpam-3266	175	8	have	have	VERB
ejpam-3266	175	9	a	a	DET
ejpam-3266	175	10	◦	◦	NOUN
ejpam-3266	175	11	c	c	NOUN
ejpam-3266	175	12	,	,	PUNCT
ejpam-3266	175	13	b	b	X
ejpam-3266	176	1	◦	◦	NOUN
ejpam-3266	176	2	c	c	NOUN
ejpam-3266	176	3	*	*	PUNCT
ejpam-3266	176	4	i.	i.	NOUN
ejpam-3266	176	5	then	then	ADV
ejpam-3266	176	6	,	,	PUNCT
ejpam-3266	176	7	by	by	ADP
ejpam-3266	176	8	proposition	proposition	NOUN
ejpam-3266	176	9	2.9(2	2.9(2	NUM
ejpam-3266	176	10	)	)	PUNCT
ejpam-3266	176	11	,	,	PUNCT
ejpam-3266	176	12	we	we	PRON
ejpam-3266	176	13	have	have	VERB
ejpam-3266	176	14	(	(	PUNCT
ejpam-3266	177	1	a	a	DET
ejpam-3266	177	2	◦	◦	NOUN
ejpam-3266	177	3	c	c	NOUN
ejpam-3266	177	4	,	,	PUNCT
ejpam-3266	177	5	b	b	X
ejpam-3266	177	6	◦	◦	NOUN
ejpam-3266	177	7	c	c	NOUN
ejpam-3266	177	8	)	)	PUNCT
ejpam-3266	177	9	∈	∈	PROPN
ejpam-3266	177	10	σi	σi	NOUN
ejpam-3266	177	11	.	.	PUNCT
ejpam-3266	178	1	thus	thus	ADV
ejpam-3266	178	2	σi	σi	PRON
ejpam-3266	178	3	is	be	AUX
ejpam-3266	178	4	a	a	DET
ejpam-3266	178	5	right	right	ADJ
ejpam-3266	178	6	congruence	congruence	NOUN
ejpam-3266	178	7	on	on	ADP
ejpam-3266	178	8	h.	h.	PROPN
ejpam-3266	178	9	in	in	ADP
ejpam-3266	178	10	a	a	DET
ejpam-3266	178	11	similar	similar	ADJ
ejpam-3266	178	12	way	way	NOUN
ejpam-3266	178	13	we	we	PRON
ejpam-3266	178	14	can	can	AUX
ejpam-3266	178	15	prove	prove	VERB
ejpam-3266	178	16	that	that	SCONJ
ejpam-3266	178	17	σi	σi	PRON
ejpam-3266	178	18	is	be	AUX
ejpam-3266	178	19	a	a	DET
ejpam-3266	178	20	left	left	ADJ
ejpam-3266	178	21	congruence	congruence	NOUN
ejpam-3266	178	22	on	on	ADP
ejpam-3266	178	23	h	h	NOUN
ejpam-3266	179	1	and	and	CCONJ
ejpam-3266	179	2	so	so	ADV
ejpam-3266	179	3	it	it	PRON
ejpam-3266	179	4	is	be	AUX
ejpam-3266	179	5	a	a	DET
ejpam-3266	179	6	congruence	congruence	NOUN
ejpam-3266	179	7	on	on	ADP
ejpam-3266	179	8	h.	h.	PROPN
ejpam-3266	179	9	let	let	VERB
ejpam-3266	179	10	a	a	DET
ejpam-3266	179	11	∈	∈	PROPN
ejpam-3266	179	12	h.	h.	NOUN
ejpam-3266	179	13	then	then	ADV
ejpam-3266	179	14	n.	n.	PROPN
ejpam-3266	179	15	kehayopulu	kehayopulu	PROPN
ejpam-3266	179	16	/	/	SYM
ejpam-3266	179	17	eur	eur	PROPN
ejpam-3266	179	18	.	.	PUNCT
ejpam-3266	180	1	j.	j.	PROPN
ejpam-3266	180	2	pure	pure	PROPN
ejpam-3266	180	3	appl	appl	PROPN
ejpam-3266	180	4	.	.	PROPN
ejpam-3266	180	5	math	math	PROPN
ejpam-3266	180	6	,	,	PUNCT
ejpam-3266	180	7	11	11	NUM
ejpam-3266	180	8	(	(	PUNCT
ejpam-3266	180	9	2	2	NUM
ejpam-3266	180	10	)	)	PUNCT
ejpam-3266	180	11	(	(	PUNCT
ejpam-3266	180	12	2018	2018	NUM
ejpam-3266	180	13	)	)	PUNCT
ejpam-3266	180	14	,	,	PUNCT
ejpam-3266	180	15	476	476	NUM
ejpam-3266	180	16	-	-	SYM
ejpam-3266	180	17	492	492	NUM
ejpam-3266	180	18	481	481	NUM
ejpam-3266	180	19	(	(	PUNCT
ejpam-3266	180	20	a	a	DET
ejpam-3266	180	21	◦	◦	NOUN
ejpam-3266	180	22	a	a	PRON
ejpam-3266	180	23	,	,	PUNCT
ejpam-3266	180	24	a	a	PRON
ejpam-3266	180	25	)	)	PUNCT
ejpam-3266	180	26	∈	∈	PROPN
ejpam-3266	181	1	σi	σi	X
ejpam-3266	181	2	.	.	PUNCT
ejpam-3266	182	1	in	in	ADP
ejpam-3266	182	2	fact	fact	NOUN
ejpam-3266	182	3	:	:	PUNCT
ejpam-3266	182	4	let	let	VERB
ejpam-3266	182	5	u	u	PRON
ejpam-3266	182	6	∈	∈	PROPN
ejpam-3266	182	7	a	a	DET
ejpam-3266	182	8	◦	◦	NOUN
ejpam-3266	182	9	a.	a.	NOUN
ejpam-3266	182	10	if	if	SCONJ
ejpam-3266	182	11	a	a	DET
ejpam-3266	182	12	∈	∈	NOUN
ejpam-3266	183	1	i	i	PRON
ejpam-3266	183	2	then	then	ADV
ejpam-3266	183	3	,	,	PUNCT
ejpam-3266	183	4	since	since	SCONJ
ejpam-3266	183	5	i	i	PRON
ejpam-3266	183	6	is	be	AUX
ejpam-3266	183	7	an	an	DET
ejpam-3266	183	8	ideal	ideal	NOUN
ejpam-3266	183	9	of	of	ADP
ejpam-3266	183	10	h	h	NOUN
ejpam-3266	183	11	,	,	PUNCT
ejpam-3266	183	12	we	we	PRON
ejpam-3266	183	13	have	have	VERB
ejpam-3266	183	14	a	a	DET
ejpam-3266	183	15	◦	◦	NOUN
ejpam-3266	183	16	a	a	DET
ejpam-3266	183	17	⊆	⊆	NUM
ejpam-3266	183	18	i	i	NOUN
ejpam-3266	183	19	,	,	PUNCT
ejpam-3266	183	20	then	then	ADV
ejpam-3266	183	21	u	u	PROPN
ejpam-3266	183	22	∈	∈	PROPN
ejpam-3266	183	23	i	i	PRON
ejpam-3266	183	24	;	;	PUNCT
ejpam-3266	183	25	since	since	SCONJ
ejpam-3266	183	26	u	u	NOUN
ejpam-3266	183	27	,	,	PUNCT
ejpam-3266	183	28	a	a	DET
ejpam-3266	183	29	∈	∈	NOUN
ejpam-3266	184	1	i	i	PRON
ejpam-3266	184	2	,	,	PUNCT
ejpam-3266	184	3	we	we	PRON
ejpam-3266	184	4	have	have	VERB
ejpam-3266	184	5	(	(	PUNCT
ejpam-3266	184	6	u	u	NOUN
ejpam-3266	184	7	,	,	PUNCT
ejpam-3266	184	8	a	a	PRON
ejpam-3266	184	9	)	)	PUNCT
ejpam-3266	184	10	∈	∈	PROPN
ejpam-3266	184	11	σi	σi	INTJ
ejpam-3266	184	12	.	.	PUNCT
ejpam-3266	185	1	if	if	SCONJ
ejpam-3266	185	2	a	a	PRON
ejpam-3266	185	3	/∈	/∈	PUNCT
ejpam-3266	186	1	i	i	PRON
ejpam-3266	186	2	,	,	PUNCT
ejpam-3266	186	3	then	then	ADV
ejpam-3266	186	4	a	a	DET
ejpam-3266	186	5	◦	◦	NOUN
ejpam-3266	186	6	a	a	DET
ejpam-3266	186	7	*	*	PUNCT
ejpam-3266	186	8	i.	i.	NOUN
ejpam-3266	186	9	then	then	ADV
ejpam-3266	186	10	,	,	PUNCT
ejpam-3266	186	11	by	by	ADP
ejpam-3266	186	12	proposition	proposition	NOUN
ejpam-3266	186	13	2.9(3	2.9(3	NUM
ejpam-3266	186	14	)	)	PUNCT
ejpam-3266	186	15	,	,	PUNCT
ejpam-3266	186	16	we	we	PRON
ejpam-3266	186	17	have	have	VERB
ejpam-3266	186	18	(	(	PUNCT
ejpam-3266	186	19	a	a	DET
ejpam-3266	186	20	,	,	PUNCT
ejpam-3266	186	21	a	a	DET
ejpam-3266	186	22	◦	◦	NOUN
ejpam-3266	186	23	a	a	X
ejpam-3266	186	24	)	)	PUNCT
ejpam-3266	186	25	∈	∈	PROPN
ejpam-3266	187	1	σi	σi	X
ejpam-3266	187	2	.	.	PUNCT
ejpam-3266	188	1	let	let	VERB
ejpam-3266	188	2	a	a	DET
ejpam-3266	188	3	,	,	PUNCT
ejpam-3266	188	4	b	b	PROPN
ejpam-3266	188	5	∈	∈	PROPN
ejpam-3266	188	6	h.	h.	NOUN
ejpam-3266	188	7	then	then	ADV
ejpam-3266	188	8	(	(	PUNCT
ejpam-3266	188	9	a	a	DET
ejpam-3266	188	10	◦	◦	NOUN
ejpam-3266	188	11	b	b	NUM
ejpam-3266	188	12	,	,	PUNCT
ejpam-3266	188	13	b	b	X
ejpam-3266	189	1	◦	◦	NOUN
ejpam-3266	189	2	a	a	X
ejpam-3266	189	3	)	)	PUNCT
ejpam-3266	189	4	∈	∈	PROPN
ejpam-3266	190	1	σi	σi	NOUN
ejpam-3266	190	2	.	.	PUNCT
ejpam-3266	191	1	indeed	indeed	ADV
ejpam-3266	191	2	:	:	PUNCT
ejpam-3266	191	3	if	if	SCONJ
ejpam-3266	191	4	a	a	DET
ejpam-3266	191	5	◦	◦	NOUN
ejpam-3266	191	6	b	b	NOUN
ejpam-3266	191	7	⊆	⊆	NUM
ejpam-3266	192	1	i	i	PRON
ejpam-3266	192	2	then	then	ADV
ejpam-3266	192	3	,	,	PUNCT
ejpam-3266	192	4	since	since	SCONJ
ejpam-3266	192	5	i	i	PRON
ejpam-3266	192	6	is	be	AUX
ejpam-3266	192	7	a	a	DET
ejpam-3266	192	8	prime	prime	ADJ
ejpam-3266	192	9	ideal	ideal	NOUN
ejpam-3266	192	10	of	of	ADP
ejpam-3266	192	11	h	h	NOUN
ejpam-3266	192	12	,	,	PUNCT
ejpam-3266	192	13	we	we	PRON
ejpam-3266	192	14	have	have	VERB
ejpam-3266	192	15	a	a	DET
ejpam-3266	192	16	∈	∈	ADJ
ejpam-3266	192	17	i	i	PRON
ejpam-3266	192	18	or	or	CCONJ
ejpam-3266	192	19	b	b	PROPN
ejpam-3266	192	20	∈	∈	PROPN
ejpam-3266	192	21	i.	i.	NOUN
ejpam-3266	192	22	since	since	SCONJ
ejpam-3266	192	23	i	i	PRON
ejpam-3266	192	24	is	be	AUX
ejpam-3266	192	25	an	an	DET
ejpam-3266	192	26	ideal	ideal	NOUN
ejpam-3266	192	27	of	of	ADP
ejpam-3266	192	28	h	h	NOUN
ejpam-3266	192	29	,	,	PUNCT
ejpam-3266	192	30	we	we	PRON
ejpam-3266	192	31	have	have	VERB
ejpam-3266	192	32	b	b	X
ejpam-3266	192	33	◦	◦	VERB
ejpam-3266	192	34	a	a	DET
ejpam-3266	192	35	⊆	⊆	NUM
ejpam-3266	192	36	i.	i.	NOUN
ejpam-3266	192	37	since	since	SCONJ
ejpam-3266	192	38	a	a	DET
ejpam-3266	192	39	◦	◦	NOUN
ejpam-3266	192	40	b	b	NUM
ejpam-3266	192	41	,	,	PUNCT
ejpam-3266	192	42	b	b	X
ejpam-3266	192	43	◦	◦	NOUN
ejpam-3266	192	44	a	a	DET
ejpam-3266	192	45	⊆	⊆	NUM
ejpam-3266	192	46	i	i	PROPN
ejpam-3266	192	47	,	,	PUNCT
ejpam-3266	192	48	by	by	ADP
ejpam-3266	192	49	lemma	lemma	PROPN
ejpam-3266	192	50	2.9(1	2.9(1	NUM
ejpam-3266	192	51	)	)	PUNCT
ejpam-3266	192	52	,	,	PUNCT
ejpam-3266	192	53	we	we	PRON
ejpam-3266	192	54	have	have	VERB
ejpam-3266	192	55	(	(	PUNCT
ejpam-3266	192	56	a	a	DET
ejpam-3266	192	57	◦	◦	NOUN
ejpam-3266	192	58	b	b	NUM
ejpam-3266	192	59	,	,	PUNCT
ejpam-3266	192	60	b	b	X
ejpam-3266	192	61	◦	◦	NOUN
ejpam-3266	192	62	a	a	X
ejpam-3266	192	63	)	)	PUNCT
ejpam-3266	192	64	∈	∈	PROPN
ejpam-3266	193	1	σi	σi	INTJ
ejpam-3266	193	2	.	.	PUNCT
ejpam-3266	194	1	if	if	SCONJ
ejpam-3266	194	2	a	a	DET
ejpam-3266	194	3	◦	◦	NOUN
ejpam-3266	194	4	b	b	X
ejpam-3266	194	5	*	*	PUNCT
ejpam-3266	195	1	i	i	PRON
ejpam-3266	195	2	then	then	ADV
ejpam-3266	195	3	b	b	X
ejpam-3266	195	4	◦	◦	NOUN
ejpam-3266	195	5	a	a	DET
ejpam-3266	195	6	*	*	PUNCT
ejpam-3266	195	7	i.	i.	NOUN
ejpam-3266	195	8	this	this	PRON
ejpam-3266	195	9	is	be	AUX
ejpam-3266	195	10	because	because	SCONJ
ejpam-3266	195	11	if	if	SCONJ
ejpam-3266	195	12	b	b	X
ejpam-3266	195	13	◦	◦	NOUN
ejpam-3266	195	14	a	a	PROPN
ejpam-3266	195	15	*	*	PUNCT
ejpam-3266	196	1	i	i	PRON
ejpam-3266	196	2	then	then	ADV
ejpam-3266	196	3	,	,	PUNCT
ejpam-3266	196	4	since	since	SCONJ
ejpam-3266	196	5	i	i	PRON
ejpam-3266	196	6	is	be	AUX
ejpam-3266	196	7	a	a	DET
ejpam-3266	196	8	prime	prime	ADJ
ejpam-3266	196	9	ideal	ideal	NOUN
ejpam-3266	196	10	of	of	ADP
ejpam-3266	196	11	h	h	NOUN
ejpam-3266	196	12	,	,	PUNCT
ejpam-3266	196	13	we	we	PRON
ejpam-3266	196	14	have	have	VERB
ejpam-3266	196	15	b	b	NUM
ejpam-3266	196	16	∈	∈	ADJ
ejpam-3266	196	17	i	i	PRON
ejpam-3266	196	18	or	or	CCONJ
ejpam-3266	196	19	a	a	DET
ejpam-3266	196	20	∈	∈	NOUN
ejpam-3266	196	21	i	i	PRON
ejpam-3266	196	22	and	and	CCONJ
ejpam-3266	196	23	,	,	PUNCT
ejpam-3266	196	24	since	since	SCONJ
ejpam-3266	196	25	i	i	PRON
ejpam-3266	196	26	is	be	AUX
ejpam-3266	196	27	an	an	DET
ejpam-3266	196	28	ideal	ideal	NOUN
ejpam-3266	196	29	of	of	ADP
ejpam-3266	196	30	h	h	NOUN
ejpam-3266	196	31	,	,	PUNCT
ejpam-3266	196	32	we	we	PRON
ejpam-3266	196	33	have	have	VERB
ejpam-3266	196	34	a	a	DET
ejpam-3266	196	35	◦	◦	NOUN
ejpam-3266	196	36	b	b	NUM
ejpam-3266	196	37	⊆	⊆	NUM
ejpam-3266	196	38	i	i	PRON
ejpam-3266	196	39	which	which	PRON
ejpam-3266	196	40	is	be	AUX
ejpam-3266	196	41	impossible	impossible	ADJ
ejpam-3266	196	42	.	.	PUNCT
ejpam-3266	197	1	since	since	SCONJ
ejpam-3266	197	2	a	a	DET
ejpam-3266	197	3	◦	◦	NOUN
ejpam-3266	197	4	b	b	NUM
ejpam-3266	197	5	,	,	PUNCT
ejpam-3266	197	6	b	b	X
ejpam-3266	197	7	◦	◦	NOUN
ejpam-3266	197	8	a	a	PROPN
ejpam-3266	197	9	*	*	PUNCT
ejpam-3266	197	10	i	i	NOUN
ejpam-3266	197	11	,	,	PUNCT
ejpam-3266	197	12	by	by	ADP
ejpam-3266	197	13	proposition	proposition	NOUN
ejpam-3266	197	14	2.9(2	2.9(2	NUM
ejpam-3266	197	15	)	)	PUNCT
ejpam-3266	197	16	,	,	PUNCT
ejpam-3266	197	17	we	we	PRON
ejpam-3266	197	18	have	have	VERB
ejpam-3266	197	19	(	(	PUNCT
ejpam-3266	197	20	a	a	DET
ejpam-3266	197	21	◦	◦	NOUN
ejpam-3266	197	22	b	b	NUM
ejpam-3266	197	23	,	,	PUNCT
ejpam-3266	197	24	b	b	X
ejpam-3266	197	25	◦	◦	NOUN
ejpam-3266	197	26	a	a	X
ejpam-3266	197	27	)	)	PUNCT
ejpam-3266	197	28	∈	∈	PROPN
ejpam-3266	198	1	σi	σi	X
ejpam-3266	198	2	.	.	PUNCT
ejpam-3266	199	1	�	�	PROPN
ejpam-3266	199	2	we	we	PRON
ejpam-3266	199	3	have	have	VERB
ejpam-3266	199	4	the	the	DET
ejpam-3266	199	5	following	following	NOUN
ejpam-3266	199	6	:	:	PUNCT
ejpam-3266	199	7	(	(	PUNCT
ejpam-3266	199	8	1	1	X
ejpam-3266	199	9	)	)	PUNCT
ejpam-3266	200	1	if	if	SCONJ
ejpam-3266	200	2	(	(	PUNCT
ejpam-3266	200	3	x	x	NOUN
ejpam-3266	200	4	,	,	PUNCT
ejpam-3266	200	5	a	a	PRON
ejpam-3266	200	6	)	)	PUNCT
ejpam-3266	200	7	∈	∈	PROPN
ejpam-3266	200	8	σ	σ	NOUN
ejpam-3266	200	9	and	and	CCONJ
ejpam-3266	200	10	∅	∅	NOUN
ejpam-3266	200	11	6=	6=	ADP
ejpam-3266	200	12	b	b	ADP
ejpam-3266	200	13	⊆	⊆	NUM
ejpam-3266	200	14	a	a	PRON
ejpam-3266	200	15	,	,	PUNCT
ejpam-3266	200	16	then	then	ADV
ejpam-3266	200	17	(	(	PUNCT
ejpam-3266	200	18	x	x	NOUN
ejpam-3266	200	19	,	,	PUNCT
ejpam-3266	200	20	b	b	NOUN
ejpam-3266	200	21	)	)	PUNCT
ejpam-3266	200	22	∈	∈	PROPN
ejpam-3266	200	23	σ	σ	PROPN
ejpam-3266	200	24	;	;	PUNCT
ejpam-3266	200	25	(	(	PUNCT
ejpam-3266	200	26	2	2	X
ejpam-3266	200	27	)	)	PUNCT
ejpam-3266	200	28	if	if	SCONJ
ejpam-3266	200	29	(	(	PUNCT
ejpam-3266	200	30	a	a	DET
ejpam-3266	200	31	,	,	PUNCT
ejpam-3266	200	32	b	b	NOUN
ejpam-3266	200	33	)	)	PUNCT
ejpam-3266	200	34	∈	∈	PROPN
ejpam-3266	200	35	σ	σ	PROPN
ejpam-3266	200	36	,	,	PUNCT
ejpam-3266	200	37	then	then	ADV
ejpam-3266	200	38	(	(	PUNCT
ejpam-3266	200	39	b	b	X
ejpam-3266	200	40	,	,	PUNCT
ejpam-3266	200	41	a	a	PRON
ejpam-3266	200	42	)	)	PUNCT
ejpam-3266	200	43	∈	∈	PROPN
ejpam-3266	200	44	σ	σ	PROPN
ejpam-3266	200	45	;	;	PUNCT
ejpam-3266	200	46	(	(	PUNCT
ejpam-3266	200	47	3	3	X
ejpam-3266	200	48	)	)	PUNCT
ejpam-3266	200	49	if	if	SCONJ
ejpam-3266	200	50	(	(	PUNCT
ejpam-3266	200	51	a	a	DET
ejpam-3266	200	52	,	,	PUNCT
ejpam-3266	200	53	b	b	NOUN
ejpam-3266	200	54	)	)	PUNCT
ejpam-3266	200	55	∈	∈	PROPN
ejpam-3266	200	56	σ	σ	PROPN
ejpam-3266	200	57	,	,	PUNCT
ejpam-3266	200	58	(	(	PUNCT
ejpam-3266	200	59	b	b	X
ejpam-3266	200	60	,	,	PUNCT
ejpam-3266	200	61	c	c	NOUN
ejpam-3266	200	62	)	)	PUNCT
ejpam-3266	200	63	∈	∈	PROPN
ejpam-3266	200	64	σ	σ	PROPN
ejpam-3266	200	65	and	and	CCONJ
ejpam-3266	200	66	b	b	PROPN
ejpam-3266	200	67	6=	6=	NUM
ejpam-3266	200	68	∅	∅	NOUN
ejpam-3266	200	69	,	,	PUNCT
ejpam-3266	200	70	then	then	ADV
ejpam-3266	200	71	(	(	PUNCT
ejpam-3266	200	72	a	a	PRON
ejpam-3266	200	73	,	,	PUNCT
ejpam-3266	200	74	c	c	NOUN
ejpam-3266	200	75	)	)	PUNCT
ejpam-3266	200	76	∈	∈	PROPN
ejpam-3266	200	77	σ	σ	PROPN
ejpam-3266	200	78	;	;	PUNCT
ejpam-3266	200	79	indeed	indeed	ADV
ejpam-3266	200	80	,	,	PUNCT
ejpam-3266	200	81	let	let	VERB
ejpam-3266	200	82	a	a	DET
ejpam-3266	200	83	∈	∈	PROPN
ejpam-3266	200	84	a	a	X
ejpam-3266	200	85	,	,	PUNCT
ejpam-3266	200	86	c	c	PROPN
ejpam-3266	200	87	∈	∈	PROPN
ejpam-3266	200	88	c.	c.	NOUN
ejpam-3266	200	89	take	take	VERB
ejpam-3266	200	90	an	an	DET
ejpam-3266	200	91	element	element	NOUN
ejpam-3266	200	92	b	b	PROPN
ejpam-3266	200	93	∈	∈	PROPN
ejpam-3266	200	94	b	b	PROPN
ejpam-3266	200	95	(	(	PUNCT
ejpam-3266	200	96	b	b	PROPN
ejpam-3266	200	97	6=	6=	NUM
ejpam-3266	200	98	∅	∅	NOUN
ejpam-3266	200	99	)	)	PUNCT
ejpam-3266	200	100	.	.	PUNCT
ejpam-3266	201	1	since	since	SCONJ
ejpam-3266	201	2	(	(	PUNCT
ejpam-3266	201	3	a	a	PRON
ejpam-3266	201	4	,	,	PUNCT
ejpam-3266	201	5	b	b	NOUN
ejpam-3266	201	6	)	)	PUNCT
ejpam-3266	201	7	∈	∈	PROPN
ejpam-3266	201	8	σ	σ	PROPN
ejpam-3266	201	9	and	and	CCONJ
ejpam-3266	201	10	(	(	PUNCT
ejpam-3266	201	11	b	b	NOUN
ejpam-3266	201	12	,	,	PUNCT
ejpam-3266	201	13	c	c	NOUN
ejpam-3266	201	14	)	)	PUNCT
ejpam-3266	201	15	∈	∈	PROPN
ejpam-3266	201	16	σ	σ	PROPN
ejpam-3266	201	17	,	,	PUNCT
ejpam-3266	201	18	we	we	PRON
ejpam-3266	201	19	have	have	VERB
ejpam-3266	201	20	(	(	PUNCT
ejpam-3266	201	21	a	a	DET
ejpam-3266	201	22	,	,	PUNCT
ejpam-3266	201	23	c	c	NOUN
ejpam-3266	201	24	)	)	PUNCT
ejpam-3266	201	25	∈	∈	PROPN
ejpam-3266	201	26	σ	σ	PROPN
ejpam-3266	201	27	.	.	PUNCT
ejpam-3266	201	28	proposition	proposition	NOUN
ejpam-3266	201	29	2.11	2.11	NUM
ejpam-3266	201	30	.	.	PUNCT
ejpam-3266	202	1	let	let	VERB
ejpam-3266	202	2	h	h	PRON
ejpam-3266	202	3	be	be	AUX
ejpam-3266	202	4	an	an	DET
ejpam-3266	202	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	202	6	,	,	PUNCT
ejpam-3266	202	7	σ	σ	VERB
ejpam-3266	202	8	a	a	DET
ejpam-3266	202	9	congruence	congruence	NOUN
ejpam-3266	202	10	on	on	ADP
ejpam-3266	202	11	h	h	NOUN
ejpam-3266	202	12	and	and	CCONJ
ejpam-3266	202	13	a	a	DET
ejpam-3266	202	14	,	,	PUNCT
ejpam-3266	202	15	b	b	NOUN
ejpam-3266	202	16	,	,	PUNCT
ejpam-3266	202	17	c	c	X
ejpam-3266	202	18	,	,	PUNCT
ejpam-3266	202	19	d	d	X
ejpam-3266	202	20	nonempty	nonempty	VERB
ejpam-3266	202	21	subsets	subset	NOUN
ejpam-3266	202	22	of	of	ADP
ejpam-3266	202	23	h.	h.	PROPN
ejpam-3266	203	1	if	if	SCONJ
ejpam-3266	203	2	(	(	PUNCT
ejpam-3266	203	3	a	a	DET
ejpam-3266	203	4	,	,	PUNCT
ejpam-3266	203	5	b	b	NOUN
ejpam-3266	203	6	)	)	PUNCT
ejpam-3266	203	7	∈	∈	PROPN
ejpam-3266	203	8	σ	σ	PROPN
ejpam-3266	203	9	and	and	CCONJ
ejpam-3266	203	10	(	(	PUNCT
ejpam-3266	203	11	c	c	X
ejpam-3266	203	12	,	,	PUNCT
ejpam-3266	203	13	d	d	NOUN
ejpam-3266	203	14	)	)	PUNCT
ejpam-3266	203	15	∈	∈	PROPN
ejpam-3266	203	16	σ	σ	PROPN
ejpam-3266	203	17	,	,	PUNCT
ejpam-3266	203	18	then	then	ADV
ejpam-3266	203	19	(	(	PUNCT
ejpam-3266	203	20	a	a	DET
ejpam-3266	203	21	∗	∗	NOUN
ejpam-3266	203	22	c	c	NOUN
ejpam-3266	203	23	,	,	PUNCT
ejpam-3266	203	24	b	b	NOUN
ejpam-3266	203	25	∗	∗	X
ejpam-3266	203	26	d	d	NOUN
ejpam-3266	203	27	)	)	PUNCT
ejpam-3266	203	28	∈	∈	PROPN
ejpam-3266	203	29	σ	σ	PROPN
ejpam-3266	203	30	and	and	CCONJ
ejpam-3266	203	31	(	(	PUNCT
ejpam-3266	203	32	c	c	NOUN
ejpam-3266	203	33	∗a	∗a	PROPN
ejpam-3266	203	34	,	,	PUNCT
ejpam-3266	203	35	d	d	PROPN
ejpam-3266	203	36	∗b	∗b	PROPN
ejpam-3266	203	37	)	)	PUNCT
ejpam-3266	203	38	∈	∈	PROPN
ejpam-3266	203	39	σ	σ	PROPN
ejpam-3266	203	40	.	.	PUNCT
ejpam-3266	203	41	proof	proof	NOUN
ejpam-3266	203	42	.	.	PUNCT
ejpam-3266	204	1	let	let	VERB
ejpam-3266	204	2	(	(	PUNCT
ejpam-3266	204	3	a	a	DET
ejpam-3266	204	4	,	,	PUNCT
ejpam-3266	204	5	b	b	NOUN
ejpam-3266	204	6	)	)	PUNCT
ejpam-3266	204	7	∈	∈	PROPN
ejpam-3266	204	8	σ	σ	PROPN
ejpam-3266	204	9	,	,	PUNCT
ejpam-3266	204	10	u	u	PROPN
ejpam-3266	204	11	∈	∈	PROPN
ejpam-3266	204	12	a	a	DET
ejpam-3266	204	13	∗	∗	NOUN
ejpam-3266	204	14	c	c	NOUN
ejpam-3266	205	1	and	and	CCONJ
ejpam-3266	205	2	v	v	ADP
ejpam-3266	205	3	∈	∈	PROPN
ejpam-3266	205	4	b	b	PROPN
ejpam-3266	205	5	∗	∗	X
ejpam-3266	205	6	d.	d.	NOUN
ejpam-3266	205	7	we	we	PRON
ejpam-3266	205	8	have	have	VERB
ejpam-3266	205	9	u	u	NOUN
ejpam-3266	205	10	∈	∈	PROPN
ejpam-3266	205	11	a	a	DET
ejpam-3266	205	12	◦	◦	NOUN
ejpam-3266	205	13	c	c	NOUN
ejpam-3266	205	14	for	for	ADP
ejpam-3266	205	15	some	some	DET
ejpam-3266	205	16	a	a	DET
ejpam-3266	205	17	∈	∈	PROPN
ejpam-3266	205	18	a	a	PRON
ejpam-3266	205	19	,	,	PUNCT
ejpam-3266	205	20	c	c	PROPN
ejpam-3266	205	21	∈	∈	PROPN
ejpam-3266	205	22	c	c	NOUN
ejpam-3266	205	23	and	and	CCONJ
ejpam-3266	205	24	v	v	ADP
ejpam-3266	205	25	∈	∈	PROPN
ejpam-3266	205	26	b	b	NOUN
ejpam-3266	205	27	◦	◦	NOUN
ejpam-3266	205	28	d	d	NOUN
ejpam-3266	205	29	for	for	ADP
ejpam-3266	205	30	some	some	DET
ejpam-3266	205	31	b	b	PROPN
ejpam-3266	205	32	∈	∈	PROPN
ejpam-3266	205	33	b	b	PROPN
ejpam-3266	205	34	,	,	PUNCT
ejpam-3266	205	35	d	d	PROPN
ejpam-3266	205	36	∈	∈	PROPN
ejpam-3266	205	37	d.	d.	PROPN
ejpam-3266	205	38	since	since	SCONJ
ejpam-3266	205	39	a	a	DET
ejpam-3266	205	40	∈	∈	PROPN
ejpam-3266	205	41	a	a	PRON
ejpam-3266	205	42	,	,	PUNCT
ejpam-3266	205	43	b	b	PROPN
ejpam-3266	205	44	∈	∈	PROPN
ejpam-3266	205	45	b	b	PROPN
ejpam-3266	205	46	and	and	CCONJ
ejpam-3266	205	47	(	(	PUNCT
ejpam-3266	205	48	a	a	DET
ejpam-3266	205	49	,	,	PUNCT
ejpam-3266	205	50	b	b	NOUN
ejpam-3266	205	51	)	)	PUNCT
ejpam-3266	205	52	∈	∈	PROPN
ejpam-3266	205	53	σ	σ	PROPN
ejpam-3266	205	54	,	,	PUNCT
ejpam-3266	205	55	we	we	PRON
ejpam-3266	205	56	have	have	VERB
ejpam-3266	205	57	(	(	PUNCT
ejpam-3266	205	58	a	a	DET
ejpam-3266	205	59	,	,	PUNCT
ejpam-3266	205	60	b	b	NOUN
ejpam-3266	205	61	)	)	PUNCT
ejpam-3266	205	62	∈	∈	PROPN
ejpam-3266	205	63	σ	σ	NOUN
ejpam-3266	205	64	and	and	CCONJ
ejpam-3266	205	65	,	,	PUNCT
ejpam-3266	205	66	since	since	SCONJ
ejpam-3266	205	67	σ	σ	PROPN
ejpam-3266	205	68	is	be	AUX
ejpam-3266	205	69	a	a	DET
ejpam-3266	205	70	right	right	ADJ
ejpam-3266	205	71	congruence	congruence	NOUN
ejpam-3266	205	72	on	on	ADP
ejpam-3266	205	73	h	h	NOUN
ejpam-3266	205	74	,	,	PUNCT
ejpam-3266	205	75	we	we	PRON
ejpam-3266	205	76	have	have	VERB
ejpam-3266	205	77	(	(	PUNCT
ejpam-3266	206	1	a	a	DET
ejpam-3266	206	2	◦	◦	NOUN
ejpam-3266	206	3	c	c	NOUN
ejpam-3266	206	4	,	,	PUNCT
ejpam-3266	206	5	b	b	X
ejpam-3266	206	6	◦	◦	NOUN
ejpam-3266	206	7	c	c	NOUN
ejpam-3266	206	8	)	)	PUNCT
ejpam-3266	206	9	∈	∈	PROPN
ejpam-3266	206	10	σ	σ	PROPN
ejpam-3266	206	11	.	.	PUNCT
ejpam-3266	207	1	since	since	SCONJ
ejpam-3266	207	2	(	(	PUNCT
ejpam-3266	207	3	c	c	X
ejpam-3266	207	4	,	,	PUNCT
ejpam-3266	207	5	d	d	NOUN
ejpam-3266	207	6	)	)	PUNCT
ejpam-3266	207	7	∈	∈	PROPN
ejpam-3266	207	8	σ	σ	PROPN
ejpam-3266	207	9	,	,	PUNCT
ejpam-3266	207	10	c	c	PROPN
ejpam-3266	207	11	∈	∈	PROPN
ejpam-3266	207	12	c	c	PROPN
ejpam-3266	207	13	and	and	CCONJ
ejpam-3266	207	14	d	d	PROPN
ejpam-3266	207	15	∈	∈	PROPN
ejpam-3266	207	16	d	d	X
ejpam-3266	207	17	,	,	PUNCT
ejpam-3266	207	18	we	we	PRON
ejpam-3266	207	19	have	have	VERB
ejpam-3266	207	20	(	(	PUNCT
ejpam-3266	207	21	c	c	X
ejpam-3266	207	22	,	,	PUNCT
ejpam-3266	207	23	d	d	NOUN
ejpam-3266	207	24	)	)	PUNCT
ejpam-3266	207	25	∈	∈	PROPN
ejpam-3266	207	26	σ	σ	NOUN
ejpam-3266	207	27	and	and	CCONJ
ejpam-3266	207	28	,	,	PUNCT
ejpam-3266	207	29	since	since	SCONJ
ejpam-3266	207	30	σ	σ	PROPN
ejpam-3266	207	31	is	be	AUX
ejpam-3266	207	32	a	a	DET
ejpam-3266	207	33	left	left	ADJ
ejpam-3266	207	34	congruence	congruence	NOUN
ejpam-3266	207	35	on	on	ADP
ejpam-3266	207	36	h	h	NOUN
ejpam-3266	207	37	,	,	PUNCT
ejpam-3266	207	38	we	we	PRON
ejpam-3266	207	39	have	have	VERB
ejpam-3266	207	40	(	(	PUNCT
ejpam-3266	207	41	b	b	X
ejpam-3266	207	42	◦	◦	NOUN
ejpam-3266	207	43	c	c	NOUN
ejpam-3266	207	44	,	,	PUNCT
ejpam-3266	207	45	b	b	X
ejpam-3266	207	46	◦	◦	NOUN
ejpam-3266	207	47	d	d	NOUN
ejpam-3266	207	48	)	)	PUNCT
ejpam-3266	207	49	∈	∈	PROPN
ejpam-3266	207	50	σ	σ	PROPN
ejpam-3266	207	51	.	.	PUNCT
ejpam-3266	208	1	by	by	ADP
ejpam-3266	208	2	the	the	DET
ejpam-3266	208	3	transitivity	transitivity	NOUN
ejpam-3266	208	4	relation	relation	NOUN
ejpam-3266	208	5	,	,	PUNCT
ejpam-3266	208	6	we	we	PRON
ejpam-3266	208	7	have	have	VERB
ejpam-3266	208	8	(	(	PUNCT
ejpam-3266	208	9	a	a	DET
ejpam-3266	208	10	◦	◦	NOUN
ejpam-3266	208	11	c	c	NOUN
ejpam-3266	208	12	,	,	PUNCT
ejpam-3266	208	13	b	b	X
ejpam-3266	208	14	◦	◦	NOUN
ejpam-3266	208	15	d	d	NOUN
ejpam-3266	208	16	)	)	PUNCT
ejpam-3266	208	17	∈	∈	PROPN
ejpam-3266	208	18	σ	σ	PROPN
ejpam-3266	208	19	.	.	PUNCT
ejpam-3266	209	1	since	since	SCONJ
ejpam-3266	209	2	u	u	PROPN
ejpam-3266	209	3	∈	∈	PROPN
ejpam-3266	209	4	a	a	DET
ejpam-3266	209	5	◦	◦	NOUN
ejpam-3266	209	6	c	c	NOUN
ejpam-3266	209	7	and	and	CCONJ
ejpam-3266	209	8	v	v	ADP
ejpam-3266	209	9	∈	∈	PROPN
ejpam-3266	209	10	b	b	PROPN
ejpam-3266	209	11	◦	◦	NOUN
ejpam-3266	209	12	d	d	PROPN
ejpam-3266	209	13	,	,	PUNCT
ejpam-3266	209	14	we	we	PRON
ejpam-3266	209	15	have	have	VERB
ejpam-3266	209	16	(	(	PUNCT
ejpam-3266	209	17	u	u	NOUN
ejpam-3266	209	18	,	,	PUNCT
ejpam-3266	209	19	v	v	NOUN
ejpam-3266	209	20	)	)	PUNCT
ejpam-3266	209	21	∈	∈	PROPN
ejpam-3266	209	22	σ	σ	PROPN
ejpam-3266	209	23	.	.	PUNCT
ejpam-3266	210	1	similarly	similarly	ADV
ejpam-3266	210	2	we	we	PRON
ejpam-3266	210	3	get	get	VERB
ejpam-3266	210	4	(	(	PUNCT
ejpam-3266	210	5	c	c	NOUN
ejpam-3266	210	6	∗a	∗a	PROPN
ejpam-3266	210	7	,	,	PUNCT
ejpam-3266	210	8	d	d	PROPN
ejpam-3266	210	9	∗b	∗b	PROPN
ejpam-3266	210	10	)	)	PUNCT
ejpam-3266	210	11	∈	∈	PROPN
ejpam-3266	210	12	σ	σ	PROPN
ejpam-3266	210	13	.	.	PUNCT
ejpam-3266	210	14	�	�	PROPN
ejpam-3266	210	15	lemma	lemma	PROPN
ejpam-3266	210	16	2.12	2.12	NUM
ejpam-3266	210	17	.	.	PUNCT
ejpam-3266	211	1	let	let	VERB
ejpam-3266	211	2	h	h	PRON
ejpam-3266	211	3	be	be	AUX
ejpam-3266	211	4	an	an	DET
ejpam-3266	211	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	211	6	,	,	PUNCT
ejpam-3266	211	7	a	a	DET
ejpam-3266	211	8	,	,	PUNCT
ejpam-3266	211	9	b	b	NOUN
ejpam-3266	211	10	nonempty	nonempty	ADJ
ejpam-3266	211	11	subsets	subset	NOUN
ejpam-3266	211	12	of	of	ADP
ejpam-3266	211	13	h	h	NOUN
ejpam-3266	211	14	and	and	CCONJ
ejpam-3266	211	15	c	c	PROPN
ejpam-3266	211	16	∈	∈	PROPN
ejpam-3266	211	17	h.	h.	PROPN
ejpam-3266	212	1	if	if	SCONJ
ejpam-3266	212	2	σ	σ	PROPN
ejpam-3266	212	3	a	a	DET
ejpam-3266	212	4	right	right	ADJ
ejpam-3266	212	5	congruence	congruence	NOUN
ejpam-3266	212	6	on	on	ADP
ejpam-3266	212	7	h	h	PROPN
ejpam-3266	212	8	and	and	CCONJ
ejpam-3266	212	9	(	(	PUNCT
ejpam-3266	212	10	a	a	PRON
ejpam-3266	212	11	,	,	PUNCT
ejpam-3266	212	12	b	b	NOUN
ejpam-3266	212	13	)	)	PUNCT
ejpam-3266	212	14	∈	∈	PROPN
ejpam-3266	212	15	σ	σ	PROPN
ejpam-3266	212	16	,	,	PUNCT
ejpam-3266	212	17	then	then	ADV
ejpam-3266	212	18	(	(	PUNCT
ejpam-3266	212	19	a	a	DET
ejpam-3266	212	20	∗	∗	NOUN
ejpam-3266	212	21	c	c	NOUN
ejpam-3266	212	22	,	,	PUNCT
ejpam-3266	212	23	b	b	NOUN
ejpam-3266	212	24	∗	∗	NOUN
ejpam-3266	212	25	c	c	NOUN
ejpam-3266	212	26	)	)	PUNCT
ejpam-3266	212	27	∈	∈	PROPN
ejpam-3266	212	28	σ	σ	PROPN
ejpam-3266	212	29	.	.	PUNCT
ejpam-3266	212	30	proof	proof	NOUN
ejpam-3266	212	31	.	.	PUNCT
ejpam-3266	213	1	since	since	SCONJ
ejpam-3266	213	2	c	c	PROPN
ejpam-3266	213	3	∈	∈	PROPN
ejpam-3266	213	4	h	h	NOUN
ejpam-3266	213	5	and	and	CCONJ
ejpam-3266	213	6	σ	σ	PROPN
ejpam-3266	213	7	is	be	AUX
ejpam-3266	213	8	a	a	DET
ejpam-3266	213	9	reflexive	reflexive	ADJ
ejpam-3266	213	10	relation	relation	NOUN
ejpam-3266	213	11	on	on	ADP
ejpam-3266	213	12	h	h	NOUN
ejpam-3266	213	13	,	,	PUNCT
ejpam-3266	213	14	we	we	PRON
ejpam-3266	213	15	have	have	VERB
ejpam-3266	213	16	(	(	PUNCT
ejpam-3266	213	17	{	{	PUNCT
ejpam-3266	213	18	c	c	NOUN
ejpam-3266	213	19	}	}	PUNCT
ejpam-3266	213	20	,	,	PUNCT
ejpam-3266	213	21	{	{	PUNCT
ejpam-3266	213	22	c	c	NOUN
ejpam-3266	213	23	}	}	PUNCT
ejpam-3266	213	24	)	)	PUNCT
ejpam-3266	214	1	∈	∈	PROPN
ejpam-3266	214	2	σ	σ	PROPN
ejpam-3266	214	3	.	.	PUNCT
ejpam-3266	215	1	since	since	SCONJ
ejpam-3266	215	2	(	(	PUNCT
ejpam-3266	215	3	a	a	DET
ejpam-3266	215	4	,	,	PUNCT
ejpam-3266	215	5	b	b	NOUN
ejpam-3266	215	6	)	)	PUNCT
ejpam-3266	215	7	∈	∈	PROPN
ejpam-3266	215	8	σ	σ	PROPN
ejpam-3266	215	9	and	and	CCONJ
ejpam-3266	215	10	(	(	PUNCT
ejpam-3266	215	11	{	{	PUNCT
ejpam-3266	215	12	c	c	NOUN
ejpam-3266	215	13	}	}	PUNCT
ejpam-3266	215	14	,	,	PUNCT
ejpam-3266	215	15	{	{	PUNCT
ejpam-3266	215	16	c	c	NOUN
ejpam-3266	215	17	}	}	PUNCT
ejpam-3266	215	18	)	)	PUNCT
ejpam-3266	215	19	∈	∈	PROPN
ejpam-3266	215	20	σ	σ	PROPN
ejpam-3266	215	21	,	,	PUNCT
ejpam-3266	215	22	by	by	ADP
ejpam-3266	215	23	proposition	proposition	NOUN
ejpam-3266	215	24	2.11	2.11	NUM
ejpam-3266	215	25	,	,	PUNCT
ejpam-3266	215	26	we	we	PRON
ejpam-3266	215	27	have	have	VERB
ejpam-3266	215	28	(	(	PUNCT
ejpam-3266	215	29	a	a	DET
ejpam-3266	215	30	∗	∗	NOUN
ejpam-3266	215	31	c	c	NOUN
ejpam-3266	215	32	,	,	PUNCT
ejpam-3266	215	33	b	b	NOUN
ejpam-3266	215	34	∗	∗	NOUN
ejpam-3266	215	35	c	c	NOUN
ejpam-3266	215	36	)	)	PUNCT
ejpam-3266	215	37	∈	∈	PROPN
ejpam-3266	215	38	σ	σ	PROPN
ejpam-3266	215	39	.	.	PUNCT
ejpam-3266	216	1	an	an	DET
ejpam-3266	216	2	independent	independent	ADJ
ejpam-3266	216	3	proof	proof	NOUN
ejpam-3266	216	4	is	be	AUX
ejpam-3266	216	5	the	the	DET
ejpam-3266	216	6	following	following	NOUN
ejpam-3266	216	7	:	:	PUNCT
ejpam-3266	216	8	let	let	VERB
ejpam-3266	216	9	u	u	PRON
ejpam-3266	216	10	∈	∈	PROPN
ejpam-3266	216	11	a	a	DET
ejpam-3266	216	12	∗	∗	NOUN
ejpam-3266	216	13	c	c	NOUN
ejpam-3266	216	14	and	and	CCONJ
ejpam-3266	216	15	v	v	ADP
ejpam-3266	216	16	∈	∈	PROPN
ejpam-3266	216	17	b	b	PROPN
ejpam-3266	216	18	∗	∗	X
ejpam-3266	216	19	c.	c.	NOUN
ejpam-3266	216	20	then	then	ADV
ejpam-3266	216	21	u	u	PROPN
ejpam-3266	216	22	∈	∈	PROPN
ejpam-3266	216	23	a	a	DET
ejpam-3266	216	24	◦	◦	NOUN
ejpam-3266	216	25	c	c	NOUN
ejpam-3266	216	26	for	for	ADP
ejpam-3266	216	27	some	some	DET
ejpam-3266	216	28	a	a	DET
ejpam-3266	216	29	∈	∈	PROPN
ejpam-3266	216	30	a	a	DET
ejpam-3266	216	31	and	and	CCONJ
ejpam-3266	216	32	v	v	ADP
ejpam-3266	216	33	∈	∈	PROPN
ejpam-3266	216	34	b	b	PROPN
ejpam-3266	216	35	◦	◦	NOUN
ejpam-3266	216	36	c	c	NOUN
ejpam-3266	216	37	for	for	ADP
ejpam-3266	216	38	some	some	DET
ejpam-3266	216	39	b	b	PROPN
ejpam-3266	216	40	∈	∈	PROPN
ejpam-3266	216	41	b.	b.	PROPN
ejpam-3266	216	42	since	since	SCONJ
ejpam-3266	216	43	a	a	DET
ejpam-3266	216	44	∈	∈	PROPN
ejpam-3266	216	45	a	a	PRON
ejpam-3266	216	46	,	,	PUNCT
ejpam-3266	216	47	b	b	PROPN
ejpam-3266	216	48	∈	∈	PROPN
ejpam-3266	216	49	b	b	PROPN
ejpam-3266	216	50	and	and	CCONJ
ejpam-3266	216	51	(	(	PUNCT
ejpam-3266	216	52	a	a	DET
ejpam-3266	216	53	,	,	PUNCT
ejpam-3266	216	54	b	b	NOUN
ejpam-3266	216	55	)	)	PUNCT
ejpam-3266	216	56	∈	∈	PROPN
ejpam-3266	216	57	σ	σ	PROPN
ejpam-3266	216	58	,	,	PUNCT
ejpam-3266	216	59	we	we	PRON
ejpam-3266	216	60	have	have	VERB
ejpam-3266	216	61	(	(	PUNCT
ejpam-3266	216	62	a	a	DET
ejpam-3266	216	63	,	,	PUNCT
ejpam-3266	216	64	b	b	NOUN
ejpam-3266	216	65	)	)	PUNCT
ejpam-3266	216	66	∈	∈	PROPN
ejpam-3266	216	67	σ	σ	PROPN
ejpam-3266	216	68	.	.	PROPN
ejpam-3266	217	1	since	since	SCONJ
ejpam-3266	217	2	σ	σ	PROPN
ejpam-3266	217	3	is	be	AUX
ejpam-3266	217	4	a	a	DET
ejpam-3266	217	5	right	right	ADJ
ejpam-3266	217	6	congruence	congruence	NOUN
ejpam-3266	217	7	on	on	ADP
ejpam-3266	217	8	h	h	NOUN
ejpam-3266	217	9	,	,	PUNCT
ejpam-3266	217	10	we	we	PRON
ejpam-3266	217	11	have	have	VERB
ejpam-3266	217	12	(	(	PUNCT
ejpam-3266	217	13	a	a	DET
ejpam-3266	217	14	◦	◦	NOUN
ejpam-3266	217	15	c	c	NOUN
ejpam-3266	217	16	,	,	PUNCT
ejpam-3266	217	17	b	b	X
ejpam-3266	217	18	◦	◦	NOUN
ejpam-3266	217	19	c	c	NOUN
ejpam-3266	217	20	)	)	PUNCT
ejpam-3266	217	21	∈	∈	PROPN
ejpam-3266	217	22	σ	σ	PROPN
ejpam-3266	217	23	.	.	PUNCT
ejpam-3266	218	1	since	since	SCONJ
ejpam-3266	218	2	u	u	PROPN
ejpam-3266	218	3	∈	∈	PROPN
ejpam-3266	218	4	a	a	DET
ejpam-3266	218	5	◦	◦	NOUN
ejpam-3266	218	6	c	c	NOUN
ejpam-3266	218	7	and	and	CCONJ
ejpam-3266	218	8	v	v	ADP
ejpam-3266	218	9	∈	∈	PROPN
ejpam-3266	218	10	b	b	PROPN
ejpam-3266	218	11	◦	◦	NOUN
ejpam-3266	218	12	c	c	X
ejpam-3266	218	13	,	,	PUNCT
ejpam-3266	218	14	we	we	PRON
ejpam-3266	218	15	get	get	VERB
ejpam-3266	218	16	(	(	PUNCT
ejpam-3266	218	17	u	u	NOUN
ejpam-3266	218	18	,	,	PUNCT
ejpam-3266	218	19	v	v	NOUN
ejpam-3266	218	20	)	)	PUNCT
ejpam-3266	218	21	∈	∈	PROPN
ejpam-3266	218	22	σ	σ	NOUN
ejpam-3266	218	23	and	and	CCONJ
ejpam-3266	218	24	so	so	ADV
ejpam-3266	218	25	(	(	PUNCT
ejpam-3266	218	26	a	a	DET
ejpam-3266	218	27	∗	∗	NOUN
ejpam-3266	218	28	c	c	NOUN
ejpam-3266	218	29	,	,	PUNCT
ejpam-3266	218	30	b	b	NOUN
ejpam-3266	218	31	∗	∗	NOUN
ejpam-3266	218	32	c	c	NOUN
ejpam-3266	218	33	)	)	PUNCT
ejpam-3266	218	34	∈	∈	PROPN
ejpam-3266	218	35	σ	σ	PROPN
ejpam-3266	218	36	.	.	PUNCT
ejpam-3266	218	37	�	�	PROPN
ejpam-3266	218	38	in	in	ADP
ejpam-3266	218	39	a	a	DET
ejpam-3266	218	40	similar	similar	ADJ
ejpam-3266	218	41	way	way	NOUN
ejpam-3266	218	42	we	we	PRON
ejpam-3266	218	43	have	have	VERB
ejpam-3266	218	44	the	the	DET
ejpam-3266	218	45	following	follow	VERB
ejpam-3266	218	46	lemma	lemma	PROPN
ejpam-3266	218	47	.	.	PUNCT
ejpam-3266	219	1	lemma	lemma	PROPN
ejpam-3266	219	2	2.13	2.13	NUM
ejpam-3266	219	3	.	.	PUNCT
ejpam-3266	220	1	let	let	VERB
ejpam-3266	220	2	h	h	PRON
ejpam-3266	220	3	be	be	AUX
ejpam-3266	220	4	an	an	DET
ejpam-3266	220	5	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	220	6	,	,	PUNCT
ejpam-3266	220	7	a	a	DET
ejpam-3266	220	8	,	,	PUNCT
ejpam-3266	220	9	b	b	NOUN
ejpam-3266	220	10	nonempty	nonempty	ADJ
ejpam-3266	220	11	subsets	subset	NOUN
ejpam-3266	220	12	of	of	ADP
ejpam-3266	220	13	h	h	NOUN
ejpam-3266	220	14	and	and	CCONJ
ejpam-3266	220	15	c	c	PROPN
ejpam-3266	220	16	∈	∈	PROPN
ejpam-3266	220	17	h.	h.	PROPN
ejpam-3266	221	1	if	if	SCONJ
ejpam-3266	221	2	σ	σ	PROPN
ejpam-3266	221	3	a	a	DET
ejpam-3266	221	4	left	left	ADJ
ejpam-3266	221	5	congruence	congruence	NOUN
ejpam-3266	221	6	on	on	ADP
ejpam-3266	221	7	h	h	PROPN
ejpam-3266	221	8	and	and	CCONJ
ejpam-3266	221	9	(	(	PUNCT
ejpam-3266	221	10	a	a	PRON
ejpam-3266	221	11	,	,	PUNCT
ejpam-3266	221	12	b	b	NOUN
ejpam-3266	221	13	)	)	PUNCT
ejpam-3266	221	14	∈	∈	PROPN
ejpam-3266	221	15	σ	σ	PROPN
ejpam-3266	221	16	,	,	PUNCT
ejpam-3266	221	17	then	then	ADV
ejpam-3266	221	18	(	(	PUNCT
ejpam-3266	221	19	c	c	NOUN
ejpam-3266	221	20	∗a	∗a	PROPN
ejpam-3266	221	21	,	,	PUNCT
ejpam-3266	221	22	c	c	NOUN
ejpam-3266	221	23	∗b	∗b	NOUN
ejpam-3266	221	24	)	)	PUNCT
ejpam-3266	221	25	∈	∈	PROPN
ejpam-3266	221	26	σ	σ	PROPN
ejpam-3266	221	27	.	.	PUNCT
ejpam-3266	222	1	as	as	ADP
ejpam-3266	222	2	in	in	ADP
ejpam-3266	222	3	groupoids	groupoid	NOUN
ejpam-3266	222	4	,	,	PUNCT
ejpam-3266	222	5	the	the	DET
ejpam-3266	222	6	following	follow	VERB
ejpam-3266	222	7	proposition	proposition	NOUN
ejpam-3266	222	8	holds	hold	VERB
ejpam-3266	222	9	and	and	CCONJ
ejpam-3266	222	10	one	one	PRON
ejpam-3266	222	11	can	can	AUX
ejpam-3266	222	12	prove	prove	VERB
ejpam-3266	222	13	it	it	PRON
ejpam-3266	222	14	as	as	ADP
ejpam-3266	222	15	a	a	DET
ejpam-3266	222	16	modification	modification	NOUN
ejpam-3266	222	17	of	of	ADP
ejpam-3266	222	18	the	the	DET
ejpam-3266	222	19	proof	proof	NOUN
ejpam-3266	222	20	of	of	ADP
ejpam-3266	222	21	the	the	DET
ejpam-3266	222	22	corresponding	corresponding	ADJ
ejpam-3266	222	23	result	result	NOUN
ejpam-3266	222	24	in	in	ADP
ejpam-3266	222	25	[	[	X
ejpam-3266	222	26	3	3	NUM
ejpam-3266	222	27	]	]	PUNCT
ejpam-3266	222	28	.	.	PUNCT
ejpam-3266	223	1	proposition	proposition	NOUN
ejpam-3266	223	2	2.14	2.14	NUM
ejpam-3266	223	3	.	.	PUNCT
ejpam-3266	224	1	(	(	PUNCT
ejpam-3266	224	2	cf	cf	NOUN
ejpam-3266	224	3	.	.	PUNCT
ejpam-3266	225	1	also	also	ADV
ejpam-3266	225	2	[	[	X
ejpam-3266	225	3	3	3	NUM
ejpam-3266	225	4	;	;	PUNCT
ejpam-3266	225	5	the	the	DET
ejpam-3266	225	6	lemma	lemma	PROPN
ejpam-3266	225	7	]	]	X
ejpam-3266	225	8	)	)	PUNCT
ejpam-3266	225	9	let	let	VERB
ejpam-3266	225	10	h	h	NOUN
ejpam-3266	225	11	be	be	AUX
ejpam-3266	225	12	an	an	DET
ejpam-3266	225	13	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	225	14	.	.	PUNCT
ejpam-3266	226	1	if	if	SCONJ
ejpam-3266	226	2	h	h	NOUN
ejpam-3266	226	3	is	be	AUX
ejpam-3266	226	4	a	a	DET
ejpam-3266	226	5	filter	filter	NOUN
ejpam-3266	226	6	of	of	ADP
ejpam-3266	226	7	h	h	NOUN
ejpam-3266	226	8	,	,	PUNCT
ejpam-3266	226	9	then	then	ADV
ejpam-3266	226	10	the	the	DET
ejpam-3266	226	11	property	property	NOUN
ejpam-3266	226	12	(	(	PUNCT
ejpam-3266	226	13	∗	∗	NOUN
ejpam-3266	226	14	)	)	PUNCT
ejpam-3266	226	15	is	be	AUX
ejpam-3266	226	16	satisfied	satisfied	ADJ
ejpam-3266	226	17	:	:	PUNCT
ejpam-3266	226	18	n.	n.	PROPN
ejpam-3266	226	19	kehayopulu	kehayopulu	PROPN
ejpam-3266	226	20	/	/	SYM
ejpam-3266	226	21	eur	eur	PROPN
ejpam-3266	226	22	.	.	PUNCT
ejpam-3266	227	1	j.	j.	PROPN
ejpam-3266	227	2	pure	pure	PROPN
ejpam-3266	227	3	appl	appl	PROPN
ejpam-3266	227	4	.	.	PROPN
ejpam-3266	227	5	math	math	PROPN
ejpam-3266	227	6	,	,	PUNCT
ejpam-3266	227	7	11	11	NUM
ejpam-3266	227	8	(	(	PUNCT
ejpam-3266	227	9	2	2	NUM
ejpam-3266	227	10	)	)	PUNCT
ejpam-3266	227	11	(	(	PUNCT
ejpam-3266	227	12	2018	2018	NUM
ejpam-3266	227	13	)	)	PUNCT
ejpam-3266	227	14	,	,	PUNCT
ejpam-3266	227	15	476	476	NUM
ejpam-3266	227	16	-	-	SYM
ejpam-3266	227	17	492	492	NUM
ejpam-3266	227	18	482	482	NUM
ejpam-3266	227	19	(	(	PUNCT
ejpam-3266	227	20	∗	∗	NOUN
ejpam-3266	227	21	)	)	PUNCT
ejpam-3266	227	22	either	either	CCONJ
ejpam-3266	227	23	h\f	h\f	NOUN
ejpam-3266	227	24	=	=	SYM
ejpam-3266	227	25	∅	∅	NOUN
ejpam-3266	227	26	or	or	CCONJ
ejpam-3266	227	27	h\f	h\f	NOUN
ejpam-3266	227	28	is	be	AUX
ejpam-3266	227	29	a	a	DET
ejpam-3266	227	30	prime	prime	ADJ
ejpam-3266	227	31	ideal	ideal	NOUN
ejpam-3266	227	32	of	of	ADP
ejpam-3266	227	33	h.	h.	PROPN
ejpam-3266	227	34	in	in	ADP
ejpam-3266	227	35	particular	particular	ADJ
ejpam-3266	227	36	,	,	PUNCT
ejpam-3266	227	37	any	any	DET
ejpam-3266	227	38	nonempty	nonempty	NOUN
ejpam-3266	227	39	subset	subset	VERB
ejpam-3266	227	40	f	f	PROPN
ejpam-3266	227	41	of	of	ADP
ejpam-3266	227	42	h	h	NOUN
ejpam-3266	227	43	satisfying	satisfying	ADJ
ejpam-3266	227	44	(	(	PUNCT
ejpam-3266	227	45	∗	∗	NOUN
ejpam-3266	227	46	)	)	PUNCT
ejpam-3266	227	47	is	be	AUX
ejpam-3266	227	48	a	a	DET
ejpam-3266	227	49	filter	filter	NOUN
ejpam-3266	227	50	of	of	ADP
ejpam-3266	227	51	h.	h.	PROPN
ejpam-3266	227	52	an	an	DET
ejpam-3266	227	53	ideal	ideal	NOUN
ejpam-3266	227	54	i	i	PRON
ejpam-3266	227	55	of	of	ADP
ejpam-3266	227	56	h	h	NOUN
ejpam-3266	227	57	is	be	AUX
ejpam-3266	227	58	called	call	VERB
ejpam-3266	227	59	proper	proper	ADJ
ejpam-3266	227	60	if	if	SCONJ
ejpam-3266	227	61	i	i	PROPN
ejpam-3266	227	62	6=	6=	PROPN
ejpam-3266	227	63	h.	h.	PROPN
ejpam-3266	227	64	3	3	NUM
ejpam-3266	227	65	.	.	X
ejpam-3266	227	66	main	main	ADJ
ejpam-3266	227	67	result	result	NOUN
ejpam-3266	227	68	theorem	theorem	VERB
ejpam-3266	227	69	3.1	3.1	NUM
ejpam-3266	227	70	.	.	PUNCT
ejpam-3266	228	1	let	let	VERB
ejpam-3266	228	2	h	h	PRON
ejpam-3266	228	3	be	be	AUX
ejpam-3266	228	4	an	an	DET
ejpam-3266	228	5	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	228	6	and	and	CCONJ
ejpam-3266	228	7	σ	σ	PROPN
ejpam-3266	228	8	be	be	VERB
ejpam-3266	228	9	a	a	DET
ejpam-3266	228	10	semilattice	semilattice	NOUN
ejpam-3266	228	11	congruence	congruence	NOUN
ejpam-3266	228	12	on	on	ADP
ejpam-3266	228	13	h.	h.	PROPN
ejpam-3266	228	14	then	then	ADV
ejpam-3266	228	15	there	there	PRON
ejpam-3266	228	16	exists	exist	VERB
ejpam-3266	228	17	a	a	DET
ejpam-3266	228	18	family	family	NOUN
ejpam-3266	228	19	a	a	PRON
ejpam-3266	228	20	of	of	ADP
ejpam-3266	228	21	proper	proper	ADJ
ejpam-3266	228	22	prime	prime	ADJ
ejpam-3266	228	23	ideals	ideal	NOUN
ejpam-3266	228	24	of	of	ADP
ejpam-3266	228	25	h	h	NOUN
ejpam-3266	228	26	such	such	ADJ
ejpam-3266	228	27	that	that	SCONJ
ejpam-3266	228	28	σ	σ	PROPN
ejpam-3266	228	29	=	=	SYM
ejpam-3266	228	30	⋂	⋂	PROPN
ejpam-3266	228	31	i∈a	i∈a	VERB
ejpam-3266	228	32	σi	σi	NOUN
ejpam-3266	228	33	.	.	PUNCT
ejpam-3266	229	1	proof	proof	NOUN
ejpam-3266	229	2	.	.	PUNCT
ejpam-3266	230	1	let	let	VERB
ejpam-3266	230	2	x	x	SYM
ejpam-3266	230	3	∈	∈	PROPN
ejpam-3266	230	4	h.	h.	NOUN
ejpam-3266	230	5	we	we	PRON
ejpam-3266	230	6	consider	consider	VERB
ejpam-3266	230	7	the	the	DET
ejpam-3266	230	8	set	set	ADJ
ejpam-3266	230	9	ax	ax	NOUN
ejpam-3266	230	10	:	:	PUNCT
ejpam-3266	230	11	=	=	SYM
ejpam-3266	230	12	{	{	PUNCT
ejpam-3266	230	13	y	y	PROPN
ejpam-3266	230	14	∈	∈	PROPN
ejpam-3266	230	15	h	h	NOUN
ejpam-3266	231	1	|	|	ADV
ejpam-3266	231	2	(	(	PUNCT
ejpam-3266	231	3	x	x	X
ejpam-3266	231	4	,	,	PUNCT
ejpam-3266	231	5	x	x	PUNCT
ejpam-3266	231	6	◦	◦	NOUN
ejpam-3266	231	7	y	y	NOUN
ejpam-3266	231	8	)	)	PUNCT
ejpam-3266	231	9	∈	∈	PROPN
ejpam-3266	231	10	σ	σ	PROPN
ejpam-3266	231	11	}	}	PUNCT
ejpam-3266	231	12	.	.	PUNCT
ejpam-3266	232	1	the	the	DET
ejpam-3266	232	2	set	set	NOUN
ejpam-3266	232	3	ax	ax	NOUN
ejpam-3266	232	4	is	be	AUX
ejpam-3266	232	5	a	a	DET
ejpam-3266	232	6	filter	filter	NOUN
ejpam-3266	232	7	of	of	ADP
ejpam-3266	232	8	h.	h.	PROPN
ejpam-3266	232	9	indeed	indeed	ADV
ejpam-3266	232	10	:	:	PUNCT
ejpam-3266	232	11	since	since	SCONJ
ejpam-3266	232	12	x	x	SYM
ejpam-3266	232	13	∈	∈	PROPN
ejpam-3266	232	14	h	h	NOUN
ejpam-3266	232	15	and	and	CCONJ
ejpam-3266	232	16	σ	σ	PROPN
ejpam-3266	232	17	is	be	AUX
ejpam-3266	232	18	a	a	DET
ejpam-3266	232	19	semilattice	semilattice	NOUN
ejpam-3266	232	20	congruence	congruence	NOUN
ejpam-3266	232	21	on	on	ADP
ejpam-3266	232	22	h	h	NOUN
ejpam-3266	232	23	,	,	PUNCT
ejpam-3266	232	24	we	we	PRON
ejpam-3266	232	25	have	have	VERB
ejpam-3266	232	26	(	(	PUNCT
ejpam-3266	232	27	x	x	X
ejpam-3266	232	28	,	,	PUNCT
ejpam-3266	232	29	x	x	PART
ejpam-3266	232	30	◦	◦	NOUN
ejpam-3266	232	31	x	x	SYM
ejpam-3266	232	32	)	)	PUNCT
ejpam-3266	232	33	∈	∈	PROPN
ejpam-3266	232	34	σ	σ	PROPN
ejpam-3266	232	35	,	,	PUNCT
ejpam-3266	232	36	thus	thus	ADV
ejpam-3266	232	37	x	x	X
ejpam-3266	232	38	∈	∈	NOUN
ejpam-3266	232	39	ax	ax	NOUN
ejpam-3266	232	40	and	and	CCONJ
ejpam-3266	232	41	ax	ax	NOUN
ejpam-3266	232	42	is	be	AUX
ejpam-3266	232	43	a	a	DET
ejpam-3266	232	44	nonempty	nonempty	ADJ
ejpam-3266	232	45	subset	subset	NOUN
ejpam-3266	232	46	of	of	ADP
ejpam-3266	232	47	h.	h.	PROPN
ejpam-3266	232	48	let	let	VERB
ejpam-3266	232	49	y	y	PRON
ejpam-3266	232	50	,	,	PUNCT
ejpam-3266	232	51	z	z	NOUN
ejpam-3266	232	52	∈	∈	PROPN
ejpam-3266	232	53	ax	ax	NOUN
ejpam-3266	232	54	.	.	PUNCT
ejpam-3266	233	1	then	then	ADV
ejpam-3266	233	2	y	y	PROPN
ejpam-3266	233	3	◦	◦	NOUN
ejpam-3266	233	4	z	z	NOUN
ejpam-3266	233	5	⊆	⊆	NUM
ejpam-3266	233	6	ax	ax	NOUN
ejpam-3266	233	7	.	.	PUNCT
ejpam-3266	234	1	in	in	ADP
ejpam-3266	234	2	fact	fact	NOUN
ejpam-3266	234	3	:	:	PUNCT
ejpam-3266	234	4	let	let	VERB
ejpam-3266	234	5	u	u	PRON
ejpam-3266	234	6	∈	∈	PROPN
ejpam-3266	234	7	y	y	PROPN
ejpam-3266	234	8	◦	◦	NOUN
ejpam-3266	234	9	z.	z.	PROPN
ejpam-3266	235	1	then	then	ADV
ejpam-3266	235	2	u	u	PROPN
ejpam-3266	235	3	∈	∈	NOUN
ejpam-3266	235	4	ax	ax	NOUN
ejpam-3266	235	5	,	,	PUNCT
ejpam-3266	235	6	that	that	ADV
ejpam-3266	235	7	is	is	ADV
ejpam-3266	235	8	(	(	PUNCT
ejpam-3266	235	9	x	x	X
ejpam-3266	235	10	,	,	PUNCT
ejpam-3266	235	11	x	x	PUNCT
ejpam-3266	235	12	◦	◦	NOUN
ejpam-3266	235	13	u	u	NOUN
ejpam-3266	235	14	)	)	PUNCT
ejpam-3266	235	15	∈	∈	PROPN
ejpam-3266	235	16	σ	σ	PROPN
ejpam-3266	235	17	.	.	PUNCT
ejpam-3266	236	1	indeed	indeed	ADV
ejpam-3266	236	2	:	:	PUNCT
ejpam-3266	236	3	let	let	VERB
ejpam-3266	236	4	v	v	NUM
ejpam-3266	236	5	∈	∈	PROPN
ejpam-3266	236	6	x	x	PUNCT
ejpam-3266	236	7	◦	◦	NOUN
ejpam-3266	236	8	u.	u.	NOUN
ejpam-3266	236	9	since	since	SCONJ
ejpam-3266	236	10	y	y	PROPN
ejpam-3266	236	11	∈	∈	PROPN
ejpam-3266	236	12	ax	ax	NOUN
ejpam-3266	236	13	,	,	PUNCT
ejpam-3266	236	14	we	we	PRON
ejpam-3266	236	15	have	have	VERB
ejpam-3266	236	16	(	(	PUNCT
ejpam-3266	236	17	x	x	X
ejpam-3266	236	18	,	,	PUNCT
ejpam-3266	236	19	x	x	PUNCT
ejpam-3266	236	20	◦	◦	NOUN
ejpam-3266	236	21	y	y	NOUN
ejpam-3266	236	22	)	)	PUNCT
ejpam-3266	236	23	∈	∈	PROPN
ejpam-3266	236	24	σ	σ	PROPN
ejpam-3266	236	25	.	.	PUNCT
ejpam-3266	237	1	then	then	ADV
ejpam-3266	237	2	,	,	PUNCT
ejpam-3266	237	3	by	by	ADP
ejpam-3266	237	4	lemma	lemma	PROPN
ejpam-3266	237	5	2.12	2.12	NUM
ejpam-3266	237	6	,	,	PUNCT
ejpam-3266	237	7	we	we	PRON
ejpam-3266	237	8	have	have	VERB
ejpam-3266	237	9	(	(	PUNCT
ejpam-3266	237	10	x	x	SYM
ejpam-3266	237	11	◦	◦	NOUN
ejpam-3266	237	12	z	z	NUM
ejpam-3266	237	13	,	,	PUNCT
ejpam-3266	237	14	(	(	PUNCT
ejpam-3266	237	15	x	x	SYM
ejpam-3266	237	16	◦	◦	VERB
ejpam-3266	237	17	y	y	NOUN
ejpam-3266	237	18	)	)	PUNCT
ejpam-3266	237	19	∗	∗	NOUN
ejpam-3266	237	20	{	{	PUNCT
ejpam-3266	237	21	z	z	NOUN
ejpam-3266	237	22	}	}	PUNCT
ejpam-3266	237	23	)	)	PUNCT
ejpam-3266	238	1	∈	∈	PROPN
ejpam-3266	238	2	σ	σ	PROPN
ejpam-3266	238	3	.	.	PUNCT
ejpam-3266	239	1	since	since	SCONJ
ejpam-3266	239	2	z	z	PROPN
ejpam-3266	239	3	∈	∈	PROPN
ejpam-3266	239	4	ax	ax	NOUN
ejpam-3266	239	5	,	,	PUNCT
ejpam-3266	239	6	we	we	PRON
ejpam-3266	239	7	have	have	VERB
ejpam-3266	239	8	(	(	PUNCT
ejpam-3266	239	9	x	x	X
ejpam-3266	239	10	,	,	PUNCT
ejpam-3266	239	11	x	x	PART
ejpam-3266	239	12	◦	◦	NOUN
ejpam-3266	239	13	z	z	NOUN
ejpam-3266	239	14	)	)	PUNCT
ejpam-3266	239	15	∈	∈	PROPN
ejpam-3266	239	16	σ	σ	NOUN
ejpam-3266	239	17	and	and	CCONJ
ejpam-3266	239	18	,	,	PUNCT
ejpam-3266	239	19	by	by	ADP
ejpam-3266	239	20	the	the	DET
ejpam-3266	239	21	transitivity	transitivity	NOUN
ejpam-3266	239	22	relation	relation	NOUN
ejpam-3266	239	23	,	,	PUNCT
ejpam-3266	239	24	we	we	PRON
ejpam-3266	239	25	have	have	VERB
ejpam-3266	239	26	(	(	PUNCT
ejpam-3266	239	27	x	x	X
ejpam-3266	239	28	,	,	PUNCT
ejpam-3266	239	29	{	{	PUNCT
ejpam-3266	239	30	x	x	NOUN
ejpam-3266	239	31	}	}	PUNCT
ejpam-3266	239	32	∗	∗	NOUN
ejpam-3266	239	33	(	(	PUNCT
ejpam-3266	239	34	y	y	PROPN
ejpam-3266	239	35	◦	◦	PROPN
ejpam-3266	239	36	z	z	PROPN
ejpam-3266	239	37	)	)	PUNCT
ejpam-3266	239	38	)	)	PUNCT
ejpam-3266	240	1	∈	∈	PROPN
ejpam-3266	240	2	σ	σ	PROPN
ejpam-3266	240	3	.	.	PUNCT
ejpam-3266	241	1	since	since	SCONJ
ejpam-3266	241	2	v	v	NUM
ejpam-3266	241	3	∈	∈	NOUN
ejpam-3266	241	4	x	x	PUNCT
ejpam-3266	241	5	◦	◦	NOUN
ejpam-3266	241	6	u	u	NOUN
ejpam-3266	241	7	⊆	⊆	NUM
ejpam-3266	241	8	{	{	PUNCT
ejpam-3266	241	9	x	x	NOUN
ejpam-3266	241	10	}	}	PUNCT
ejpam-3266	241	11	∗	∗	NOUN
ejpam-3266	241	12	(	(	PUNCT
ejpam-3266	241	13	y	y	PROPN
ejpam-3266	241	14	◦	◦	PROPN
ejpam-3266	241	15	z	z	PROPN
ejpam-3266	241	16	)	)	PUNCT
ejpam-3266	241	17	,	,	PUNCT
ejpam-3266	241	18	we	we	PRON
ejpam-3266	241	19	have	have	VERB
ejpam-3266	241	20	(	(	PUNCT
ejpam-3266	241	21	x	x	NOUN
ejpam-3266	241	22	,	,	PUNCT
ejpam-3266	241	23	v	v	NOUN
ejpam-3266	241	24	)	)	PUNCT
ejpam-3266	241	25	∈	∈	PROPN
ejpam-3266	241	26	σ	σ	PROPN
ejpam-3266	241	27	.	.	PUNCT
ejpam-3266	242	1	let	let	VERB
ejpam-3266	242	2	y	y	NOUN
ejpam-3266	242	3	,	,	PUNCT
ejpam-3266	242	4	z	z	PROPN
ejpam-3266	242	5	∈	∈	PROPN
ejpam-3266	242	6	h	h	NOUN
ejpam-3266	243	1	such	such	ADJ
ejpam-3266	243	2	that	that	SCONJ
ejpam-3266	243	3	y	y	PROPN
ejpam-3266	243	4	◦	◦	NOUN
ejpam-3266	243	5	z	z	NOUN
ejpam-3266	243	6	⊆	⊆	NUM
ejpam-3266	243	7	ax	ax	NOUN
ejpam-3266	243	8	.	.	PUNCT
ejpam-3266	244	1	then	then	ADV
ejpam-3266	244	2	y	y	PROPN
ejpam-3266	244	3	∈	∈	PROPN
ejpam-3266	244	4	ax	ax	NOUN
ejpam-3266	244	5	and	and	CCONJ
ejpam-3266	244	6	z	z	NOUN
ejpam-3266	244	7	∈	∈	PROPN
ejpam-3266	244	8	ax	ax	NOUN
ejpam-3266	244	9	.	.	PUNCT
ejpam-3266	245	1	in	in	ADP
ejpam-3266	245	2	fact	fact	NOUN
ejpam-3266	245	3	:	:	PUNCT
ejpam-3266	245	4	since	since	SCONJ
ejpam-3266	245	5	y	y	PROPN
ejpam-3266	245	6	◦	◦	VERB
ejpam-3266	245	7	z	z	NOUN
ejpam-3266	245	8	⊆	⊆	NUM
ejpam-3266	245	9	ax	ax	NOUN
ejpam-3266	245	10	,	,	PUNCT
ejpam-3266	245	11	we	we	PRON
ejpam-3266	245	12	have	have	VERB
ejpam-3266	245	13	(	(	PUNCT
ejpam-3266	245	14	x	x	X
ejpam-3266	245	15	,	,	PUNCT
ejpam-3266	245	16	{	{	PUNCT
ejpam-3266	245	17	x	x	NOUN
ejpam-3266	245	18	}	}	PUNCT
ejpam-3266	245	19	∗	∗	NOUN
ejpam-3266	245	20	(	(	PUNCT
ejpam-3266	245	21	y	y	PROPN
ejpam-3266	245	22	◦	◦	PROPN
ejpam-3266	245	23	z	z	PROPN
ejpam-3266	245	24	)	)	PUNCT
ejpam-3266	245	25	)	)	PUNCT
ejpam-3266	246	1	∈	∈	PROPN
ejpam-3266	246	2	σ	σ	NOUN
ejpam-3266	246	3	(	(	PUNCT
ejpam-3266	246	4	1	1	NUM
ejpam-3266	246	5	)	)	PUNCT
ejpam-3266	246	6	indeed	indeed	ADV
ejpam-3266	246	7	:	:	PUNCT
ejpam-3266	246	8	if	if	SCONJ
ejpam-3266	246	9	u	u	PROPN
ejpam-3266	246	10	∈	∈	PROPN
ejpam-3266	246	11	{	{	PUNCT
ejpam-3266	246	12	x	x	NOUN
ejpam-3266	246	13	}	}	PUNCT
ejpam-3266	246	14	∗	∗	NOUN
ejpam-3266	246	15	(	(	PUNCT
ejpam-3266	246	16	y	y	PROPN
ejpam-3266	246	17	◦	◦	PROPN
ejpam-3266	246	18	z	z	PROPN
ejpam-3266	246	19	)	)	PUNCT
ejpam-3266	246	20	,	,	PUNCT
ejpam-3266	246	21	then	then	ADV
ejpam-3266	246	22	u	u	PROPN
ejpam-3266	246	23	∈	∈	PROPN
ejpam-3266	246	24	x	x	PUNCT
ejpam-3266	246	25	◦	◦	NOUN
ejpam-3266	246	26	t	t	NOUN
ejpam-3266	246	27	for	for	ADP
ejpam-3266	246	28	some	some	DET
ejpam-3266	246	29	t	t	NOUN
ejpam-3266	246	30	∈	∈	PROPN
ejpam-3266	246	31	y	y	PROPN
ejpam-3266	246	32	◦	◦	NOUN
ejpam-3266	246	33	z	z	NOUN
ejpam-3266	246	34	⊆	⊆	NUM
ejpam-3266	246	35	ax	ax	NOUN
ejpam-3266	246	36	.	.	PUNCT
ejpam-3266	247	1	since	since	SCONJ
ejpam-3266	247	2	t	t	PROPN
ejpam-3266	247	3	∈	∈	PROPN
ejpam-3266	247	4	ax	ax	NOUN
ejpam-3266	247	5	,	,	PUNCT
ejpam-3266	247	6	we	we	PRON
ejpam-3266	247	7	have	have	VERB
ejpam-3266	247	8	(	(	PUNCT
ejpam-3266	247	9	x	x	X
ejpam-3266	247	10	,	,	PUNCT
ejpam-3266	247	11	x	x	PUNCT
ejpam-3266	247	12	◦	◦	NOUN
ejpam-3266	247	13	t	t	PROPN
ejpam-3266	247	14	)	)	PUNCT
ejpam-3266	247	15	∈	∈	PROPN
ejpam-3266	247	16	σ	σ	PROPN
ejpam-3266	247	17	.	.	PUNCT
ejpam-3266	248	1	then	then	ADV
ejpam-3266	248	2	,	,	PUNCT
ejpam-3266	248	3	since	since	SCONJ
ejpam-3266	248	4	u	u	PROPN
ejpam-3266	248	5	∈	∈	PROPN
ejpam-3266	248	6	x	x	PUNCT
ejpam-3266	248	7	◦	◦	NOUN
ejpam-3266	248	8	t	t	PROPN
ejpam-3266	248	9	,	,	PUNCT
ejpam-3266	248	10	we	we	PRON
ejpam-3266	248	11	obtain	obtain	VERB
ejpam-3266	248	12	(	(	PUNCT
ejpam-3266	248	13	x	x	NOUN
ejpam-3266	248	14	,	,	PUNCT
ejpam-3266	248	15	u	u	NOUN
ejpam-3266	248	16	)	)	PUNCT
ejpam-3266	248	17	∈	∈	PROPN
ejpam-3266	248	18	σ	σ	PROPN
ejpam-3266	248	19	,	,	PUNCT
ejpam-3266	248	20	so	so	ADV
ejpam-3266	248	21	property	property	NOUN
ejpam-3266	248	22	(	(	PUNCT
ejpam-3266	248	23	1	1	X
ejpam-3266	248	24	)	)	PUNCT
ejpam-3266	248	25	is	be	AUX
ejpam-3266	248	26	satisfied	satisfied	ADJ
ejpam-3266	248	27	.	.	PUNCT
ejpam-3266	249	1	by	by	ADP
ejpam-3266	249	2	(	(	PUNCT
ejpam-3266	249	3	1	1	NUM
ejpam-3266	249	4	)	)	PUNCT
ejpam-3266	249	5	and	and	CCONJ
ejpam-3266	249	6	lemma	lemma	PROPN
ejpam-3266	249	7	2.12	2.12	NUM
ejpam-3266	249	8	,	,	PUNCT
ejpam-3266	249	9	we	we	PRON
ejpam-3266	249	10	have	have	VERB
ejpam-3266	249	11	(	(	PUNCT
ejpam-3266	249	12	x	x	SYM
ejpam-3266	249	13	◦	◦	NOUN
ejpam-3266	249	14	z	z	NUM
ejpam-3266	249	15	,	,	PUNCT
ejpam-3266	249	16	{	{	PUNCT
ejpam-3266	249	17	x	x	NOUN
ejpam-3266	249	18	}	}	PUNCT
ejpam-3266	249	19	∗	∗	NOUN
ejpam-3266	249	20	(	(	PUNCT
ejpam-3266	249	21	y	y	PROPN
ejpam-3266	249	22	◦	◦	PROPN
ejpam-3266	249	23	z	z	PROPN
ejpam-3266	249	24	)	)	PUNCT
ejpam-3266	249	25	∗	∗	NOUN
ejpam-3266	249	26	{	{	PUNCT
ejpam-3266	249	27	z	z	NOUN
ejpam-3266	249	28	}	}	PUNCT
ejpam-3266	249	29	)	)	PUNCT
ejpam-3266	250	1	∈	∈	PROPN
ejpam-3266	250	2	σ	σ	NOUN
ejpam-3266	250	3	(	(	PUNCT
ejpam-3266	250	4	2	2	NUM
ejpam-3266	250	5	)	)	PUNCT
ejpam-3266	250	6	on	on	ADP
ejpam-3266	250	7	the	the	DET
ejpam-3266	250	8	other	other	ADJ
ejpam-3266	250	9	hand	hand	NOUN
ejpam-3266	250	10	,	,	PUNCT
ejpam-3266	250	11	since	since	SCONJ
ejpam-3266	250	12	(	(	PUNCT
ejpam-3266	250	13	z	z	NOUN
ejpam-3266	250	14	,	,	PUNCT
ejpam-3266	250	15	z	z	NOUN
ejpam-3266	250	16	◦	◦	NOUN
ejpam-3266	250	17	z	z	NOUN
ejpam-3266	250	18	)	)	PUNCT
ejpam-3266	250	19	∈	∈	PROPN
ejpam-3266	250	20	σ	σ	PROPN
ejpam-3266	250	21	,	,	PUNCT
ejpam-3266	250	22	we	we	PRON
ejpam-3266	250	23	have	have	VERB
ejpam-3266	250	24	(	(	PUNCT
ejpam-3266	250	25	(	(	PUNCT
ejpam-3266	250	26	x	x	SYM
ejpam-3266	250	27	◦	◦	VERB
ejpam-3266	250	28	y	y	NOUN
ejpam-3266	250	29	)	)	PUNCT
ejpam-3266	250	30	∗	∗	NOUN
ejpam-3266	250	31	{	{	PUNCT
ejpam-3266	250	32	z	z	NOUN
ejpam-3266	250	33	}	}	PUNCT
ejpam-3266	250	34	,	,	PUNCT
ejpam-3266	250	35	(	(	PUNCT
ejpam-3266	250	36	x	x	SYM
ejpam-3266	250	37	◦	◦	VERB
ejpam-3266	250	38	y	y	NOUN
ejpam-3266	250	39	)	)	PUNCT
ejpam-3266	250	40	∗	∗	NOUN
ejpam-3266	250	41	(	(	PUNCT
ejpam-3266	250	42	z	z	NOUN
ejpam-3266	250	43	◦	◦	NOUN
ejpam-3266	250	44	z	z	NOUN
ejpam-3266	250	45	)	)	PUNCT
ejpam-3266	250	46	)	)	PUNCT
ejpam-3266	251	1	∈	∈	PROPN
ejpam-3266	251	2	σ	σ	NOUN
ejpam-3266	251	3	(	(	PUNCT
ejpam-3266	251	4	3	3	NUM
ejpam-3266	251	5	)	)	PUNCT
ejpam-3266	251	6	in	in	ADP
ejpam-3266	251	7	fact	fact	NOUN
ejpam-3266	251	8	:	:	PUNCT
ejpam-3266	251	9	since	since	SCONJ
ejpam-3266	251	10	(	(	PUNCT
ejpam-3266	251	11	z	z	NOUN
ejpam-3266	251	12	,	,	PUNCT
ejpam-3266	251	13	z	z	NOUN
ejpam-3266	251	14	◦	◦	NOUN
ejpam-3266	251	15	z	z	NOUN
ejpam-3266	251	16	)	)	PUNCT
ejpam-3266	251	17	∈	∈	PROPN
ejpam-3266	251	18	σ	σ	PROPN
ejpam-3266	251	19	,	,	PUNCT
ejpam-3266	251	20	by	by	ADP
ejpam-3266	251	21	lemma	lemma	PROPN
ejpam-3266	251	22	2.13	2.13	NUM
ejpam-3266	251	23	,	,	PUNCT
ejpam-3266	251	24	we	we	PRON
ejpam-3266	251	25	have	have	VERB
ejpam-3266	251	26	(	(	PUNCT
ejpam-3266	251	27	y	y	PROPN
ejpam-3266	251	28	◦	◦	PROPN
ejpam-3266	251	29	z	z	PROPN
ejpam-3266	251	30	,	,	PUNCT
ejpam-3266	251	31	{	{	PUNCT
ejpam-3266	251	32	y	y	NOUN
ejpam-3266	251	33	}	}	PUNCT
ejpam-3266	251	34	∗	∗	NOUN
ejpam-3266	251	35	(	(	PUNCT
ejpam-3266	251	36	z	z	NOUN
ejpam-3266	251	37	◦	◦	NOUN
ejpam-3266	251	38	z	z	NOUN
ejpam-3266	251	39	)	)	PUNCT
ejpam-3266	252	1	∈	∈	PROPN
ejpam-3266	252	2	σ	σ	PROPN
ejpam-3266	252	3	;	;	PUNCT
ejpam-3266	252	4	again	again	ADV
ejpam-3266	252	5	by	by	ADP
ejpam-3266	252	6	lemma	lemma	PROPN
ejpam-3266	252	7	2.13	2.13	NUM
ejpam-3266	252	8	,	,	PUNCT
ejpam-3266	252	9	we	we	PRON
ejpam-3266	252	10	have	have	AUX
ejpam-3266	252	11	(	(	PUNCT
ejpam-3266	252	12	{	{	PUNCT
ejpam-3266	252	13	x	x	NOUN
ejpam-3266	252	14	}	}	PUNCT
ejpam-3266	252	15	∗	∗	NOUN
ejpam-3266	252	16	(	(	PUNCT
ejpam-3266	252	17	y	y	PROPN
ejpam-3266	252	18	◦	◦	PROPN
ejpam-3266	252	19	z	z	PROPN
ejpam-3266	252	20	)	)	PUNCT
ejpam-3266	252	21	,	,	PUNCT
ejpam-3266	252	22	(	(	PUNCT
ejpam-3266	252	23	x	x	X
ejpam-3266	252	24	◦	◦	VERB
ejpam-3266	252	25	y	y	NOUN
ejpam-3266	252	26	)	)	PUNCT
ejpam-3266	252	27	∗	∗	NOUN
ejpam-3266	252	28	(	(	PUNCT
ejpam-3266	252	29	z	z	NOUN
ejpam-3266	252	30	◦	◦	NOUN
ejpam-3266	252	31	z	z	NOUN
ejpam-3266	252	32	)	)	PUNCT
ejpam-3266	252	33	)	)	PUNCT
ejpam-3266	253	1	∈	∈	PROPN
ejpam-3266	253	2	σ	σ	NOUN
ejpam-3266	253	3	and	and	CCONJ
ejpam-3266	253	4	(	(	PUNCT
ejpam-3266	253	5	3	3	X
ejpam-3266	253	6	)	)	PUNCT
ejpam-3266	253	7	holds	hold	NOUN
ejpam-3266	253	8	.	.	PUNCT
ejpam-3266	254	1	by	by	ADP
ejpam-3266	254	2	(	(	PUNCT
ejpam-3266	254	3	1),(2	1),(2	PROPN
ejpam-3266	254	4	)	)	PUNCT
ejpam-3266	254	5	and	and	CCONJ
ejpam-3266	254	6	(	(	PUNCT
ejpam-3266	254	7	3	3	NUM
ejpam-3266	254	8	)	)	PUNCT
ejpam-3266	254	9	,	,	PUNCT
ejpam-3266	254	10	we	we	PRON
ejpam-3266	254	11	obtain	obtain	VERB
ejpam-3266	254	12	(	(	PUNCT
ejpam-3266	254	13	x	x	NOUN
ejpam-3266	254	14	,	,	PUNCT
ejpam-3266	254	15	x	x	SYM
ejpam-3266	254	16	◦	◦	NOUN
ejpam-3266	254	17	z	z	NOUN
ejpam-3266	254	18	)	)	PUNCT
ejpam-3266	254	19	∈	∈	PROPN
ejpam-3266	254	20	σ	σ	PROPN
ejpam-3266	254	21	,	,	PUNCT
ejpam-3266	254	22	and	and	CCONJ
ejpam-3266	254	23	so	so	ADV
ejpam-3266	254	24	z	z	NOUN
ejpam-3266	254	25	∈	∈	PROPN
ejpam-3266	254	26	ax	ax	NOUN
ejpam-3266	254	27	.	.	PUNCT
ejpam-3266	255	1	it	it	PRON
ejpam-3266	255	2	remains	remain	VERB
ejpam-3266	255	3	to	to	PART
ejpam-3266	255	4	prove	prove	VERB
ejpam-3266	255	5	that	that	SCONJ
ejpam-3266	255	6	y	y	PROPN
ejpam-3266	255	7	∈	∈	PROPN
ejpam-3266	255	8	ax	ax	NOUN
ejpam-3266	255	9	.	.	PUNCT
ejpam-3266	256	1	since	since	SCONJ
ejpam-3266	256	2	z	z	PROPN
ejpam-3266	256	3	∈	∈	PROPN
ejpam-3266	256	4	ax	ax	NOUN
ejpam-3266	256	5	,	,	PUNCT
ejpam-3266	256	6	we	we	PRON
ejpam-3266	256	7	have	have	VERB
ejpam-3266	256	8	(	(	PUNCT
ejpam-3266	256	9	x	x	X
ejpam-3266	256	10	,	,	PUNCT
ejpam-3266	256	11	x	x	PART
ejpam-3266	256	12	◦	◦	NOUN
ejpam-3266	256	13	z	z	NOUN
ejpam-3266	256	14	)	)	PUNCT
ejpam-3266	256	15	∈	∈	PROPN
ejpam-3266	256	16	σ	σ	PROPN
ejpam-3266	256	17	.	.	PUNCT
ejpam-3266	257	1	by	by	ADP
ejpam-3266	257	2	lemma	lemma	PROPN
ejpam-3266	257	3	2.12	2.12	NUM
ejpam-3266	257	4	,	,	PUNCT
ejpam-3266	257	5	we	we	PRON
ejpam-3266	257	6	have	have	AUX
ejpam-3266	257	7	(	(	PUNCT
ejpam-3266	257	8	x	x	SYM
ejpam-3266	257	9	◦	◦	VERB
ejpam-3266	257	10	y	y	PROPN
ejpam-3266	257	11	,	,	PUNCT
ejpam-3266	257	12	(	(	PUNCT
ejpam-3266	257	13	x	x	PUNCT
ejpam-3266	257	14	◦	◦	NOUN
ejpam-3266	257	15	z	z	NOUN
ejpam-3266	257	16	)	)	PUNCT
ejpam-3266	257	17	∗	∗	NOUN
ejpam-3266	257	18	{	{	PUNCT
ejpam-3266	257	19	y	y	NOUN
ejpam-3266	257	20	}	}	PUNCT
ejpam-3266	257	21	)	)	PUNCT
ejpam-3266	258	1	∈	∈	PROPN
ejpam-3266	258	2	σ	σ	PROPN
ejpam-3266	258	3	.	.	PUNCT
ejpam-3266	259	1	since	since	SCONJ
ejpam-3266	259	2	(	(	PUNCT
ejpam-3266	259	3	y	y	PROPN
ejpam-3266	259	4	◦	◦	PROPN
ejpam-3266	259	5	z	z	PROPN
ejpam-3266	259	6	,	,	PUNCT
ejpam-3266	259	7	z	z	NOUN
ejpam-3266	259	8	◦	◦	NOUN
ejpam-3266	259	9	y	y	NOUN
ejpam-3266	259	10	)	)	PUNCT
ejpam-3266	259	11	∈	∈	PROPN
ejpam-3266	259	12	σ	σ	PROPN
ejpam-3266	259	13	,	,	PUNCT
ejpam-3266	259	14	by	by	ADP
ejpam-3266	259	15	lemma	lemma	PROPN
ejpam-3266	259	16	2.13	2.13	NUM
ejpam-3266	259	17	,	,	PUNCT
ejpam-3266	259	18	we	we	PRON
ejpam-3266	259	19	have	have	VERB
ejpam-3266	259	20	(	(	PUNCT
ejpam-3266	259	21	{	{	PUNCT
ejpam-3266	259	22	x	x	NOUN
ejpam-3266	259	23	}	}	PUNCT
ejpam-3266	259	24	∗	∗	NOUN
ejpam-3266	259	25	(	(	PUNCT
ejpam-3266	259	26	y	y	PROPN
ejpam-3266	259	27	◦	◦	PROPN
ejpam-3266	259	28	z	z	PROPN
ejpam-3266	259	29	)	)	PUNCT
ejpam-3266	259	30	,	,	PUNCT
ejpam-3266	259	31	{	{	PUNCT
ejpam-3266	259	32	x	x	NOUN
ejpam-3266	259	33	}	}	PUNCT
ejpam-3266	259	34	∗	∗	NOUN
ejpam-3266	259	35	(	(	PUNCT
ejpam-3266	259	36	z	z	NOUN
ejpam-3266	259	37	◦	◦	NOUN
ejpam-3266	259	38	y	y	NOUN
ejpam-3266	259	39	)	)	PUNCT
ejpam-3266	259	40	)	)	PUNCT
ejpam-3266	260	1	∈	∈	PROPN
ejpam-3266	260	2	σ	σ	PROPN
ejpam-3266	260	3	.	.	PUNCT
ejpam-3266	261	1	then	then	ADV
ejpam-3266	261	2	,	,	PUNCT
ejpam-3266	261	3	by	by	ADP
ejpam-3266	261	4	(	(	PUNCT
ejpam-3266	261	5	1	1	NUM
ejpam-3266	261	6	)	)	PUNCT
ejpam-3266	261	7	,	,	PUNCT
ejpam-3266	261	8	we	we	PRON
ejpam-3266	261	9	get	get	VERB
ejpam-3266	261	10	(	(	PUNCT
ejpam-3266	261	11	x	x	NOUN
ejpam-3266	261	12	,	,	PUNCT
ejpam-3266	261	13	x	x	PUNCT
ejpam-3266	261	14	◦	◦	NOUN
ejpam-3266	261	15	y	y	NOUN
ejpam-3266	261	16	)	)	PUNCT
ejpam-3266	261	17	∈	∈	PROPN
ejpam-3266	261	18	σ	σ	PROPN
ejpam-3266	261	19	,	,	PUNCT
ejpam-3266	261	20	and	and	CCONJ
ejpam-3266	261	21	so	so	ADV
ejpam-3266	261	22	y	y	PROPN
ejpam-3266	261	23	∈	∈	PROPN
ejpam-3266	261	24	ax	ax	NOUN
ejpam-3266	261	25	.	.	PUNCT
ejpam-3266	262	1	let	let	VERB
ejpam-3266	262	2	y	y	NOUN
ejpam-3266	262	3	,	,	PUNCT
ejpam-3266	262	4	z	z	PROPN
ejpam-3266	262	5	∈	∈	PROPN
ejpam-3266	262	6	h.	h.	NOUN
ejpam-3266	263	1	then	then	ADV
ejpam-3266	263	2	y	y	PROPN
ejpam-3266	263	3	◦	◦	NOUN
ejpam-3266	263	4	z	z	NOUN
ejpam-3266	263	5	⊆	⊆	NUM
ejpam-3266	263	6	ax	ax	NOUN
ejpam-3266	263	7	or	or	CCONJ
ejpam-3266	263	8	(	(	PUNCT
ejpam-3266	263	9	y	y	PROPN
ejpam-3266	263	10	◦	◦	PROPN
ejpam-3266	263	11	z	z	PROPN
ejpam-3266	263	12	)	)	PUNCT
ejpam-3266	263	13	∩ax	∩ax	VERB
ejpam-3266	263	14	=	=	PUNCT
ejpam-3266	263	15	∅.	∅.	NOUN
ejpam-3266	263	16	in	in	ADP
ejpam-3266	263	17	fact	fact	NOUN
ejpam-3266	263	18	:	:	PUNCT
ejpam-3266	263	19	let	let	VERB
ejpam-3266	263	20	y	y	PRON
ejpam-3266	263	21	◦	◦	VERB
ejpam-3266	263	22	z	z	NOUN
ejpam-3266	263	23	*	*	PUNCT
ejpam-3266	263	24	ax	ax	NOUN
ejpam-3266	264	1	and	and	CCONJ
ejpam-3266	264	2	(	(	PUNCT
ejpam-3266	264	3	y	y	PROPN
ejpam-3266	264	4	◦	◦	NOUN
ejpam-3266	264	5	z)∩ax	z)∩ax	X
ejpam-3266	264	6	6=	6=	ADP
ejpam-3266	264	7	∅.	∅.	AUX
ejpam-3266	264	8	let	let	VERB
ejpam-3266	264	9	u	u	PRON
ejpam-3266	264	10	∈	∈	PROPN
ejpam-3266	264	11	y	y	PROPN
ejpam-3266	264	12	◦	◦	NOUN
ejpam-3266	264	13	z	z	NOUN
ejpam-3266	264	14	such	such	ADJ
ejpam-3266	264	15	that	that	DET
ejpam-3266	264	16	u	u	PROPN
ejpam-3266	264	17	/∈	/∈	NOUN
ejpam-3266	265	1	ax	ax	NOUN
ejpam-3266	265	2	,	,	PUNCT
ejpam-3266	265	3	v	v	NOUN
ejpam-3266	265	4	∈	∈	PROPN
ejpam-3266	265	5	y	y	PROPN
ejpam-3266	265	6	◦	◦	NOUN
ejpam-3266	265	7	z	z	PROPN
ejpam-3266	265	8	and	and	CCONJ
ejpam-3266	265	9	v	v	ADP
ejpam-3266	265	10	∈	∈	PROPN
ejpam-3266	265	11	ax	ax	NOUN
ejpam-3266	265	12	.	.	PUNCT
ejpam-3266	266	1	then	then	ADV
ejpam-3266	266	2	we	we	PRON
ejpam-3266	266	3	have	have	VERB
ejpam-3266	266	4	u	u	NOUN
ejpam-3266	266	5	∈	∈	PROPN
ejpam-3266	266	6	y	y	PROPN
ejpam-3266	266	7	◦	◦	PROPN
ejpam-3266	266	8	z	z	PROPN
ejpam-3266	266	9	,	,	PUNCT
ejpam-3266	266	10	(	(	PUNCT
ejpam-3266	266	11	x	x	X
ejpam-3266	266	12	,	,	PUNCT
ejpam-3266	266	13	x	x	PUNCT
ejpam-3266	266	14	◦	◦	NOUN
ejpam-3266	266	15	u	u	NOUN
ejpam-3266	266	16	)	)	PUNCT
ejpam-3266	266	17	/∈	/∈	PUNCT
ejpam-3266	267	1	σ	σ	NOUN
ejpam-3266	267	2	,	,	PUNCT
ejpam-3266	267	3	v	v	NOUN
ejpam-3266	267	4	∈	∈	PROPN
ejpam-3266	267	5	y	y	PROPN
ejpam-3266	267	6	◦	◦	PROPN
ejpam-3266	267	7	z	z	PROPN
ejpam-3266	267	8	,	,	PUNCT
ejpam-3266	267	9	(	(	PUNCT
ejpam-3266	267	10	x	x	X
ejpam-3266	267	11	,	,	PUNCT
ejpam-3266	267	12	x	x	PUNCT
ejpam-3266	267	13	◦	◦	NOUN
ejpam-3266	267	14	v	v	NOUN
ejpam-3266	267	15	)	)	PUNCT
ejpam-3266	267	16	∈	∈	PROPN
ejpam-3266	267	17	σ	σ	PROPN
ejpam-3266	267	18	.	.	PUNCT
ejpam-3266	267	19	n.	n.	PROPN
ejpam-3266	267	20	kehayopulu	kehayopulu	PROPN
ejpam-3266	267	21	/	/	SYM
ejpam-3266	267	22	eur	eur	PROPN
ejpam-3266	267	23	.	.	PUNCT
ejpam-3266	268	1	j.	j.	PROPN
ejpam-3266	268	2	pure	pure	PROPN
ejpam-3266	268	3	appl	appl	PROPN
ejpam-3266	268	4	.	.	PROPN
ejpam-3266	268	5	math	math	PROPN
ejpam-3266	268	6	,	,	PUNCT
ejpam-3266	268	7	11	11	NUM
ejpam-3266	268	8	(	(	PUNCT
ejpam-3266	268	9	2	2	NUM
ejpam-3266	268	10	)	)	PUNCT
ejpam-3266	268	11	(	(	PUNCT
ejpam-3266	268	12	2018	2018	NUM
ejpam-3266	268	13	)	)	PUNCT
ejpam-3266	268	14	,	,	PUNCT
ejpam-3266	268	15	476	476	NUM
ejpam-3266	268	16	-	-	SYM
ejpam-3266	268	17	492	492	NUM
ejpam-3266	268	18	483	483	NUM
ejpam-3266	268	19	on	on	ADP
ejpam-3266	268	20	the	the	DET
ejpam-3266	268	21	other	other	ADJ
ejpam-3266	268	22	hand	hand	NOUN
ejpam-3266	268	23	,	,	PUNCT
ejpam-3266	268	24	(	(	PUNCT
ejpam-3266	268	25	x	x	X
ejpam-3266	268	26	,	,	PUNCT
ejpam-3266	268	27	x	x	PUNCT
ejpam-3266	268	28	◦	◦	NOUN
ejpam-3266	268	29	v	v	NOUN
ejpam-3266	268	30	)	)	PUNCT
ejpam-3266	268	31	∈	∈	PROPN
ejpam-3266	268	32	σ	σ	NOUN
ejpam-3266	268	33	and	and	CCONJ
ejpam-3266	268	34	v	v	ADP
ejpam-3266	268	35	∈	∈	PROPN
ejpam-3266	268	36	y	y	PROPN
ejpam-3266	268	37	◦	◦	NOUN
ejpam-3266	268	38	z	z	NOUN
ejpam-3266	268	39	implies	imply	VERB
ejpam-3266	268	40	(	(	PUNCT
ejpam-3266	268	41	x	x	X
ejpam-3266	268	42	,	,	PUNCT
ejpam-3266	268	43	{	{	PUNCT
ejpam-3266	268	44	x	x	NOUN
ejpam-3266	268	45	}	}	PUNCT
ejpam-3266	268	46	∗	∗	NOUN
ejpam-3266	268	47	(	(	PUNCT
ejpam-3266	268	48	y	y	PROPN
ejpam-3266	268	49	◦	◦	PROPN
ejpam-3266	268	50	z	z	PROPN
ejpam-3266	268	51	)	)	PUNCT
ejpam-3266	268	52	)	)	PUNCT
ejpam-3266	269	1	∈	∈	PROPN
ejpam-3266	269	2	σ	σ	PROPN
ejpam-3266	269	3	.	.	PUNCT
ejpam-3266	270	1	indeed	indeed	ADV
ejpam-3266	270	2	:	:	PUNCT
ejpam-3266	270	3	let	let	VERB
ejpam-3266	270	4	a	a	DET
ejpam-3266	270	5	∈	∈	PROPN
ejpam-3266	270	6	{	{	PUNCT
ejpam-3266	270	7	x	x	NOUN
ejpam-3266	270	8	}	}	PUNCT
ejpam-3266	270	9	∗	∗	NOUN
ejpam-3266	270	10	(	(	PUNCT
ejpam-3266	270	11	y	y	PROPN
ejpam-3266	270	12	◦	◦	PROPN
ejpam-3266	270	13	z	z	PROPN
ejpam-3266	270	14	)	)	PUNCT
ejpam-3266	270	15	.	.	PUNCT
ejpam-3266	271	1	then	then	ADV
ejpam-3266	271	2	a	a	DET
ejpam-3266	271	3	∈	∈	PROPN
ejpam-3266	271	4	x	x	PUNCT
ejpam-3266	271	5	◦	◦	NOUN
ejpam-3266	271	6	d	d	NOUN
ejpam-3266	271	7	for	for	ADP
ejpam-3266	271	8	some	some	DET
ejpam-3266	271	9	d	d	PROPN
ejpam-3266	271	10	∈	∈	PROPN
ejpam-3266	271	11	y	y	PROPN
ejpam-3266	271	12	◦	◦	NOUN
ejpam-3266	271	13	z.	z.	PROPN
ejpam-3266	271	14	since	since	SCONJ
ejpam-3266	271	15	(	(	PUNCT
ejpam-3266	271	16	y	y	PROPN
ejpam-3266	271	17	◦	◦	PROPN
ejpam-3266	271	18	z	z	PROPN
ejpam-3266	271	19	,	,	PUNCT
ejpam-3266	271	20	y	y	PROPN
ejpam-3266	271	21	◦	◦	PROPN
ejpam-3266	271	22	z	z	PROPN
ejpam-3266	271	23	)	)	PUNCT
ejpam-3266	271	24	∈	∈	PROPN
ejpam-3266	271	25	σ	σ	PROPN
ejpam-3266	271	26	,	,	PUNCT
ejpam-3266	271	27	v	v	PROPN
ejpam-3266	271	28	∈	∈	PROPN
ejpam-3266	271	29	y	y	PROPN
ejpam-3266	271	30	◦	◦	NOUN
ejpam-3266	271	31	z	z	PROPN
ejpam-3266	271	32	and	and	CCONJ
ejpam-3266	271	33	d	d	PROPN
ejpam-3266	271	34	∈	∈	PROPN
ejpam-3266	271	35	y	y	PROPN
ejpam-3266	271	36	◦	◦	PROPN
ejpam-3266	272	1	z	z	X
ejpam-3266	272	2	,	,	PUNCT
ejpam-3266	272	3	we	we	PRON
ejpam-3266	272	4	have	have	VERB
ejpam-3266	272	5	(	(	PUNCT
ejpam-3266	272	6	v	v	NOUN
ejpam-3266	272	7	,	,	PUNCT
ejpam-3266	272	8	d	d	NOUN
ejpam-3266	272	9	)	)	PUNCT
ejpam-3266	272	10	∈	∈	PROPN
ejpam-3266	272	11	σ	σ	PROPN
ejpam-3266	272	12	,	,	PUNCT
ejpam-3266	272	13	then	then	ADV
ejpam-3266	272	14	(	(	PUNCT
ejpam-3266	272	15	x	x	X
ejpam-3266	272	16	◦	◦	NOUN
ejpam-3266	272	17	v	v	NOUN
ejpam-3266	272	18	,	,	PUNCT
ejpam-3266	272	19	x	x	PUNCT
ejpam-3266	272	20	◦	◦	NOUN
ejpam-3266	272	21	d	d	NOUN
ejpam-3266	272	22	)	)	PUNCT
ejpam-3266	272	23	∈	∈	PROPN
ejpam-3266	272	24	σ	σ	PROPN
ejpam-3266	272	25	.	.	PUNCT
ejpam-3266	273	1	since	since	SCONJ
ejpam-3266	273	2	(	(	PUNCT
ejpam-3266	273	3	x	x	X
ejpam-3266	273	4	,	,	PUNCT
ejpam-3266	273	5	x	x	PUNCT
ejpam-3266	273	6	◦	◦	NOUN
ejpam-3266	273	7	v	v	NOUN
ejpam-3266	273	8	)	)	PUNCT
ejpam-3266	273	9	∈	∈	PROPN
ejpam-3266	273	10	σ	σ	PROPN
ejpam-3266	273	11	and	and	CCONJ
ejpam-3266	273	12	(	(	PUNCT
ejpam-3266	273	13	x	x	PART
ejpam-3266	273	14	◦	◦	NOUN
ejpam-3266	273	15	v	v	NOUN
ejpam-3266	273	16	,	,	PUNCT
ejpam-3266	273	17	x	x	PUNCT
ejpam-3266	273	18	◦	◦	NOUN
ejpam-3266	273	19	d	d	NOUN
ejpam-3266	273	20	)	)	PUNCT
ejpam-3266	273	21	∈	∈	PROPN
ejpam-3266	273	22	σ	σ	PROPN
ejpam-3266	273	23	,	,	PUNCT
ejpam-3266	273	24	we	we	PRON
ejpam-3266	273	25	have	have	VERB
ejpam-3266	273	26	(	(	PUNCT
ejpam-3266	273	27	x	x	X
ejpam-3266	273	28	,	,	PUNCT
ejpam-3266	273	29	x	x	PUNCT
ejpam-3266	273	30	◦	◦	NOUN
ejpam-3266	273	31	d	d	NOUN
ejpam-3266	273	32	)	)	PUNCT
ejpam-3266	273	33	∈	∈	PROPN
ejpam-3266	273	34	σ	σ	PROPN
ejpam-3266	273	35	.	.	PUNCT
ejpam-3266	274	1	since	since	SCONJ
ejpam-3266	274	2	a	a	DET
ejpam-3266	274	3	∈	∈	PROPN
ejpam-3266	274	4	x	x	PUNCT
ejpam-3266	274	5	◦	◦	NOUN
ejpam-3266	274	6	d	d	NOUN
ejpam-3266	274	7	,	,	PUNCT
ejpam-3266	274	8	we	we	PRON
ejpam-3266	274	9	have	have	VERB
ejpam-3266	274	10	(	(	PUNCT
ejpam-3266	274	11	x	x	NOUN
ejpam-3266	274	12	,	,	PUNCT
ejpam-3266	274	13	a	a	PRON
ejpam-3266	274	14	)	)	PUNCT
ejpam-3266	274	15	∈	∈	PROPN
ejpam-3266	274	16	σ	σ	PROPN
ejpam-3266	274	17	.	.	PUNCT
ejpam-3266	275	1	we	we	PRON
ejpam-3266	275	2	have	have	VERB
ejpam-3266	275	3	x	x	PART
ejpam-3266	275	4	◦	◦	VERB
ejpam-3266	275	5	u	u	NOUN
ejpam-3266	275	6	⊆	⊆	NUM
ejpam-3266	275	7	{	{	PUNCT
ejpam-3266	275	8	x	x	NOUN
ejpam-3266	275	9	}	}	PUNCT
ejpam-3266	275	10	∗	∗	NOUN
ejpam-3266	275	11	(	(	PUNCT
ejpam-3266	275	12	y	y	PROPN
ejpam-3266	275	13	◦	◦	PROPN
ejpam-3266	275	14	z	z	PROPN
ejpam-3266	275	15	)	)	PUNCT
ejpam-3266	275	16	and	and	CCONJ
ejpam-3266	275	17	(	(	PUNCT
ejpam-3266	275	18	x	x	X
ejpam-3266	275	19	,	,	PUNCT
ejpam-3266	275	20	{	{	PUNCT
ejpam-3266	275	21	x	x	NOUN
ejpam-3266	275	22	}	}	PUNCT
ejpam-3266	275	23	∗	∗	NOUN
ejpam-3266	275	24	(	(	PUNCT
ejpam-3266	275	25	y	y	PROPN
ejpam-3266	275	26	◦	◦	PROPN
ejpam-3266	275	27	z	z	PROPN
ejpam-3266	275	28	)	)	PUNCT
ejpam-3266	275	29	)	)	PUNCT
ejpam-3266	276	1	∈	∈	PROPN
ejpam-3266	276	2	σ	σ	PROPN
ejpam-3266	276	3	,	,	PUNCT
ejpam-3266	276	4	thus	thus	ADV
ejpam-3266	276	5	we	we	PRON
ejpam-3266	276	6	have	have	VERB
ejpam-3266	276	7	(	(	PUNCT
ejpam-3266	276	8	x	x	X
ejpam-3266	276	9	,	,	PUNCT
ejpam-3266	276	10	x	x	PUNCT
ejpam-3266	276	11	◦	◦	NOUN
ejpam-3266	276	12	u	u	NOUN
ejpam-3266	276	13	)	)	PUNCT
ejpam-3266	276	14	∈	∈	PROPN
ejpam-3266	276	15	σ	σ	NOUN
ejpam-3266	276	16	which	which	PRON
ejpam-3266	276	17	is	be	AUX
ejpam-3266	276	18	impossible	impossible	ADJ
ejpam-3266	276	19	.	.	PUNCT
ejpam-3266	277	1	since	since	SCONJ
ejpam-3266	277	2	ax	ax	NOUN
ejpam-3266	277	3	is	be	AUX
ejpam-3266	277	4	a	a	DET
ejpam-3266	277	5	filter	filter	NOUN
ejpam-3266	277	6	of	of	ADP
ejpam-3266	277	7	h	h	NOUN
ejpam-3266	277	8	,	,	PUNCT
ejpam-3266	277	9	by	by	ADP
ejpam-3266	277	10	proposition	proposition	NOUN
ejpam-3266	277	11	2.14	2.14	NUM
ejpam-3266	277	12	,	,	PUNCT
ejpam-3266	277	13	we	we	PRON
ejpam-3266	277	14	have	have	VERB
ejpam-3266	277	15	h\ax	h\ax	NOUN
ejpam-3266	277	16	=	=	SYM
ejpam-3266	277	17	∅	∅	NOUN
ejpam-3266	277	18	or	or	CCONJ
ejpam-3266	277	19	h\ax	h\ax	PROPN
ejpam-3266	277	20	is	be	AUX
ejpam-3266	277	21	a	a	DET
ejpam-3266	277	22	prime	prime	ADJ
ejpam-3266	277	23	ideal	ideal	NOUN
ejpam-3266	277	24	of	of	ADP
ejpam-3266	277	25	h.	h.	PROPN
ejpam-3266	278	1	then	then	ADV
ejpam-3266	278	2	h\ax	h\ax	PROPN
ejpam-3266	278	3	=	=	PUNCT
ejpam-3266	278	4	∅	∅	NOUN
ejpam-3266	278	5	or	or	CCONJ
ejpam-3266	278	6	h\ax	h\ax	PROPN
ejpam-3266	278	7	is	be	AUX
ejpam-3266	278	8	a	a	DET
ejpam-3266	278	9	proper	proper	ADJ
ejpam-3266	278	10	prime	prime	ADJ
ejpam-3266	278	11	ideal	ideal	NOUN
ejpam-3266	278	12	of	of	ADP
ejpam-3266	278	13	h	h	NOUN
ejpam-3266	278	14	(	(	PUNCT
ejpam-3266	278	15	indeed	indeed	ADV
ejpam-3266	278	16	,	,	PUNCT
ejpam-3266	278	17	if	if	SCONJ
ejpam-3266	278	18	h\ax	h\ax	PROPN
ejpam-3266	278	19	=	=	PUNCT
ejpam-3266	279	1	h	h	NOUN
ejpam-3266	279	2	then	then	ADV
ejpam-3266	279	3	,	,	PUNCT
ejpam-3266	279	4	since	since	SCONJ
ejpam-3266	279	5	ax	ax	NOUN
ejpam-3266	279	6	⊆	⊆	NUM
ejpam-3266	279	7	h	h	NOUN
ejpam-3266	279	8	,	,	PUNCT
ejpam-3266	279	9	we	we	PRON
ejpam-3266	279	10	have	have	VERB
ejpam-3266	279	11	ax	ax	NOUN
ejpam-3266	279	12	=	=	NOUN
ejpam-3266	279	13	∅	∅	NOUN
ejpam-3266	279	14	which	which	PRON
ejpam-3266	279	15	is	be	AUX
ejpam-3266	279	16	not	not	PART
ejpam-3266	279	17	possible	possible	ADJ
ejpam-3266	279	18	)	)	PUNCT
ejpam-3266	279	19	.	.	PUNCT
ejpam-3266	280	1	we	we	PRON
ejpam-3266	280	2	consider	consider	VERB
ejpam-3266	280	3	the	the	DET
ejpam-3266	280	4	set	set	NOUN
ejpam-3266	280	5	{	{	PUNCT
ejpam-3266	280	6	h\az	h\az	PROPN
ejpam-3266	280	7	|	|	NOUN
ejpam-3266	280	8	z	z	PROPN
ejpam-3266	280	9	∈	∈	PROPN
ejpam-3266	280	10	h	h	NOUN
ejpam-3266	280	11	,	,	PUNCT
ejpam-3266	280	12	h\az	h\az	ADJ
ejpam-3266	280	13	proper	proper	ADJ
ejpam-3266	280	14	prime	prime	ADJ
ejpam-3266	280	15	ideal	ideal	NOUN
ejpam-3266	280	16	of	of	ADP
ejpam-3266	280	17	h	h	NOUN
ejpam-3266	280	18	}	}	PUNCT
ejpam-3266	280	19	.	.	PUNCT
ejpam-3266	281	1	we	we	PRON
ejpam-3266	281	2	have	have	VERB
ejpam-3266	281	3	σ	σ	NOUN
ejpam-3266	281	4	=	=	SYM
ejpam-3266	281	5	⋂	⋂	PROPN
ejpam-3266	281	6	z∈h	z∈h	NOUN
ejpam-3266	281	7	σh\az	σh\az	PROPN
ejpam-3266	281	8	.	.	PUNCT
ejpam-3266	282	1	in	in	ADP
ejpam-3266	282	2	fact	fact	NOUN
ejpam-3266	282	3	:	:	PUNCT
ejpam-3266	282	4	let	let	VERB
ejpam-3266	282	5	(	(	PUNCT
ejpam-3266	282	6	x	x	NOUN
ejpam-3266	282	7	,	,	PUNCT
ejpam-3266	282	8	y	y	NOUN
ejpam-3266	282	9	)	)	PUNCT
ejpam-3266	282	10	∈	∈	PROPN
ejpam-3266	282	11	σ	σ	PROPN
ejpam-3266	282	12	and	and	CCONJ
ejpam-3266	282	13	z	z	PROPN
ejpam-3266	282	14	∈	∈	PROPN
ejpam-3266	282	15	h.	h.	NOUN
ejpam-3266	283	1	then	then	ADV
ejpam-3266	283	2	(	(	PUNCT
ejpam-3266	283	3	x	x	X
ejpam-3266	283	4	,	,	PUNCT
ejpam-3266	283	5	y	y	NOUN
ejpam-3266	283	6	)	)	PUNCT
ejpam-3266	283	7	∈	∈	PROPN
ejpam-3266	283	8	σh\az	σh\az	PROPN
ejpam-3266	283	9	.	.	PUNCT
ejpam-3266	284	1	indeed	indeed	ADV
ejpam-3266	284	2	:	:	PUNCT
ejpam-3266	284	3	since	since	SCONJ
ejpam-3266	284	4	x	x	PROPN
ejpam-3266	284	5	∈	∈	PROPN
ejpam-3266	284	6	h	h	NOUN
ejpam-3266	284	7	,	,	PUNCT
ejpam-3266	284	8	we	we	PRON
ejpam-3266	284	9	have	have	VERB
ejpam-3266	284	10	x	x	PROPN
ejpam-3266	284	11	∈	∈	PROPN
ejpam-3266	284	12	h\az	h\az	NOUN
ejpam-3266	284	13	or	or	CCONJ
ejpam-3266	284	14	x	x	PROPN
ejpam-3266	284	15	/∈	/∈	PUNCT
ejpam-3266	285	1	h\az	h\az	PROPN
ejpam-3266	285	2	.	.	PUNCT
ejpam-3266	286	1	(	(	PUNCT
ejpam-3266	286	2	a	a	X
ejpam-3266	286	3	)	)	PUNCT
ejpam-3266	286	4	if	if	SCONJ
ejpam-3266	286	5	x	x	PROPN
ejpam-3266	286	6	/∈	/∈	PUNCT
ejpam-3266	287	1	h\az	h\az	PROPN
ejpam-3266	287	2	,	,	PUNCT
ejpam-3266	287	3	then	then	ADV
ejpam-3266	287	4	x	x	SYM
ejpam-3266	287	5	∈	∈	PROPN
ejpam-3266	287	6	az	az	PROPN
ejpam-3266	287	7	,	,	PUNCT
ejpam-3266	287	8	so	so	CCONJ
ejpam-3266	287	9	(	(	PUNCT
ejpam-3266	287	10	z	z	NOUN
ejpam-3266	287	11	,	,	PUNCT
ejpam-3266	287	12	z	z	PROPN
ejpam-3266	287	13	◦	◦	NOUN
ejpam-3266	287	14	x	x	NOUN
ejpam-3266	287	15	)	)	PUNCT
ejpam-3266	287	16	∈	∈	PROPN
ejpam-3266	287	17	σ	σ	PROPN
ejpam-3266	287	18	.	.	PUNCT
ejpam-3266	288	1	since	since	SCONJ
ejpam-3266	288	2	(	(	PUNCT
ejpam-3266	288	3	x	x	NOUN
ejpam-3266	288	4	,	,	PUNCT
ejpam-3266	288	5	y	y	NOUN
ejpam-3266	288	6	)	)	PUNCT
ejpam-3266	288	7	∈	∈	PROPN
ejpam-3266	288	8	σ	σ	PROPN
ejpam-3266	288	9	,	,	PUNCT
ejpam-3266	288	10	we	we	PRON
ejpam-3266	288	11	have	have	VERB
ejpam-3266	288	12	(	(	PUNCT
ejpam-3266	288	13	z	z	NOUN
ejpam-3266	288	14	◦	◦	NOUN
ejpam-3266	288	15	x	x	NOUN
ejpam-3266	288	16	,	,	PUNCT
ejpam-3266	288	17	z	z	PROPN
ejpam-3266	288	18	◦	◦	NOUN
ejpam-3266	288	19	y	y	NOUN
ejpam-3266	288	20	)	)	PUNCT
ejpam-3266	288	21	∈	∈	PROPN
ejpam-3266	288	22	σ	σ	PROPN
ejpam-3266	288	23	.	.	PUNCT
ejpam-3266	289	1	then	then	ADV
ejpam-3266	289	2	(	(	PUNCT
ejpam-3266	289	3	z	z	NOUN
ejpam-3266	289	4	,	,	PUNCT
ejpam-3266	289	5	z	z	NOUN
ejpam-3266	289	6	◦	◦	NOUN
ejpam-3266	289	7	y	y	NOUN
ejpam-3266	289	8	)	)	PUNCT
ejpam-3266	289	9	∈	∈	PROPN
ejpam-3266	289	10	σ	σ	PROPN
ejpam-3266	289	11	,	,	PUNCT
ejpam-3266	289	12	and	and	CCONJ
ejpam-3266	289	13	y	y	PROPN
ejpam-3266	289	14	∈	∈	PROPN
ejpam-3266	289	15	az	az	PROPN
ejpam-3266	289	16	,	,	PUNCT
ejpam-3266	289	17	so	so	ADV
ejpam-3266	289	18	y	y	PROPN
ejpam-3266	289	19	/∈	/∈	PUNCT
ejpam-3266	290	1	h\az	h\az	PROPN
ejpam-3266	290	2	.	.	PUNCT
ejpam-3266	291	1	(	(	PUNCT
ejpam-3266	291	2	b	b	X
ejpam-3266	291	3	)	)	PUNCT
ejpam-3266	291	4	let	let	VERB
ejpam-3266	291	5	x	x	PUNCT
ejpam-3266	291	6	∈	∈	PROPN
ejpam-3266	291	7	h\az	h\az	PROPN
ejpam-3266	291	8	.	.	PUNCT
ejpam-3266	292	1	if	if	SCONJ
ejpam-3266	292	2	y	y	PROPN
ejpam-3266	292	3	/∈	/∈	PUNCT
ejpam-3266	293	1	h\az	h\az	PROPN
ejpam-3266	293	2	,	,	PUNCT
ejpam-3266	293	3	then	then	ADV
ejpam-3266	293	4	in	in	ADP
ejpam-3266	293	5	a	a	DET
ejpam-3266	293	6	similar	similar	ADJ
ejpam-3266	293	7	way	way	NOUN
ejpam-3266	293	8	as	as	ADP
ejpam-3266	293	9	in	in	ADP
ejpam-3266	293	10	(	(	PUNCT
ejpam-3266	293	11	a	a	X
ejpam-3266	293	12	)	)	PUNCT
ejpam-3266	293	13	,	,	PUNCT
ejpam-3266	293	14	we	we	PRON
ejpam-3266	293	15	prove	prove	VERB
ejpam-3266	293	16	that	that	SCONJ
ejpam-3266	293	17	x	x	SYM
ejpam-3266	293	18	/∈	/∈	PUNCT
ejpam-3266	294	1	h\az	h\az	NOUN
ejpam-3266	294	2	which	which	PRON
ejpam-3266	294	3	is	be	AUX
ejpam-3266	294	4	impossible	impossible	ADJ
ejpam-3266	294	5	.	.	PUNCT
ejpam-3266	295	1	thus	thus	ADV
ejpam-3266	295	2	we	we	PRON
ejpam-3266	295	3	have	have	VERB
ejpam-3266	295	4	y	y	PROPN
ejpam-3266	295	5	∈	∈	PROPN
ejpam-3266	295	6	h\az	h\az	PROPN
ejpam-3266	295	7	.	.	PUNCT
ejpam-3266	296	1	since	since	SCONJ
ejpam-3266	296	2	both	both	CCONJ
ejpam-3266	296	3	x	x	SYM
ejpam-3266	296	4	and	and	CCONJ
ejpam-3266	296	5	y	y	PROPN
ejpam-3266	296	6	belong	belong	VERB
ejpam-3266	296	7	toh\az	toh\az	NOUN
ejpam-3266	296	8	or	or	CCONJ
ejpam-3266	296	9	both	both	PRON
ejpam-3266	296	10	do	do	AUX
ejpam-3266	296	11	not	not	PART
ejpam-3266	296	12	belong	belong	VERB
ejpam-3266	296	13	toh\az	toh\az	ADP
ejpam-3266	296	14	,	,	PUNCT
ejpam-3266	296	15	we	we	PRON
ejpam-3266	296	16	have	have	VERB
ejpam-3266	296	17	(	(	PUNCT
ejpam-3266	296	18	x	x	NOUN
ejpam-3266	296	19	,	,	PUNCT
ejpam-3266	296	20	y	y	NOUN
ejpam-3266	296	21	)	)	PUNCT
ejpam-3266	296	22	∈	∈	PROPN
ejpam-3266	296	23	σh\az	σh\az	PROPN
ejpam-3266	296	24	.	.	PUNCT
ejpam-3266	297	1	let	let	VERB
ejpam-3266	297	2	now	now	ADV
ejpam-3266	297	3	(	(	PUNCT
ejpam-3266	297	4	x	x	NOUN
ejpam-3266	297	5	,	,	PUNCT
ejpam-3266	297	6	y	y	NOUN
ejpam-3266	297	7	)	)	PUNCT
ejpam-3266	297	8	∈	∈	PROPN
ejpam-3266	297	9	σh\az	σh\az	PROPN
ejpam-3266	297	10	for	for	ADP
ejpam-3266	297	11	every	every	DET
ejpam-3266	297	12	z	z	PROPN
ejpam-3266	297	13	∈	∈	PROPN
ejpam-3266	297	14	h.	h.	NOUN
ejpam-3266	298	1	then	then	ADV
ejpam-3266	298	2	(	(	PUNCT
ejpam-3266	298	3	x	x	X
ejpam-3266	298	4	,	,	PUNCT
ejpam-3266	298	5	y	y	NOUN
ejpam-3266	298	6	)	)	PUNCT
ejpam-3266	298	7	∈	∈	PROPN
ejpam-3266	298	8	σ	σ	PROPN
ejpam-3266	298	9	.	.	PUNCT
ejpam-3266	299	1	indeed	indeed	ADV
ejpam-3266	299	2	:	:	PUNCT
ejpam-3266	299	3	since	since	SCONJ
ejpam-3266	299	4	x	x	PROPN
ejpam-3266	299	5	∈	∈	PROPN
ejpam-3266	299	6	ax	ax	NOUN
ejpam-3266	299	7	,	,	PUNCT
ejpam-3266	299	8	we	we	PRON
ejpam-3266	299	9	have	have	VERB
ejpam-3266	299	10	x	x	PART
ejpam-3266	299	11	/∈	/∈	PUNCT
ejpam-3266	300	1	h\ax	h\ax	PROPN
ejpam-3266	300	2	and	and	CCONJ
ejpam-3266	300	3	,	,	PUNCT
ejpam-3266	300	4	since	since	SCONJ
ejpam-3266	300	5	(	(	PUNCT
ejpam-3266	300	6	x	x	NOUN
ejpam-3266	300	7	,	,	PUNCT
ejpam-3266	300	8	y	y	NOUN
ejpam-3266	300	9	)	)	PUNCT
ejpam-3266	300	10	∈	∈	PROPN
ejpam-3266	301	1	σh\ax	σh\ax	PROPN
ejpam-3266	301	2	,	,	PUNCT
ejpam-3266	301	3	we	we	PRON
ejpam-3266	301	4	have	have	VERB
ejpam-3266	301	5	y	y	PROPN
ejpam-3266	301	6	/∈	/∈	PUNCT
ejpam-3266	302	1	h\ax	h\ax	ADV
ejpam-3266	302	2	,	,	PUNCT
ejpam-3266	302	3	so	so	ADV
ejpam-3266	302	4	y	y	PROPN
ejpam-3266	302	5	∈	∈	PROPN
ejpam-3266	302	6	ax	ax	NOUN
ejpam-3266	302	7	,	,	PUNCT
ejpam-3266	302	8	that	that	ADV
ejpam-3266	302	9	is	is	ADV
ejpam-3266	302	10	(	(	PUNCT
ejpam-3266	302	11	x	x	X
ejpam-3266	302	12	,	,	PUNCT
ejpam-3266	302	13	x	x	PUNCT
ejpam-3266	302	14	◦	◦	NOUN
ejpam-3266	302	15	y	y	NOUN
ejpam-3266	302	16	)	)	PUNCT
ejpam-3266	302	17	∈	∈	PROPN
ejpam-3266	302	18	σ	σ	PROPN
ejpam-3266	302	19	.	.	PUNCT
ejpam-3266	303	1	since	since	SCONJ
ejpam-3266	303	2	y	y	PROPN
ejpam-3266	303	3	∈	∈	PROPN
ejpam-3266	303	4	ay	ay	PROPN
ejpam-3266	303	5	,	,	PUNCT
ejpam-3266	303	6	we	we	PRON
ejpam-3266	303	7	have	have	VERB
ejpam-3266	303	8	y	y	PROPN
ejpam-3266	303	9	/∈	/∈	PUNCT
ejpam-3266	304	1	h\ay	h\ay	PROPN
ejpam-3266	304	2	,	,	PUNCT
ejpam-3266	304	3	then	then	ADV
ejpam-3266	304	4	x	x	X
ejpam-3266	304	5	/∈	/∈	PUNCT
ejpam-3266	304	6	h\ay	h\ay	PROPN
ejpam-3266	304	7	,	,	PUNCT
ejpam-3266	304	8	so	so	ADV
ejpam-3266	304	9	x	x	SYM
ejpam-3266	304	10	∈	∈	PROPN
ejpam-3266	304	11	ay	ay	NOUN
ejpam-3266	304	12	,	,	PUNCT
ejpam-3266	304	13	thus	thus	ADV
ejpam-3266	304	14	(	(	PUNCT
ejpam-3266	304	15	y	y	NOUN
ejpam-3266	304	16	,	,	PUNCT
ejpam-3266	304	17	y	y	PROPN
ejpam-3266	304	18	◦	◦	NOUN
ejpam-3266	304	19	x	x	SYM
ejpam-3266	304	20	)	)	PUNCT
ejpam-3266	304	21	∈	∈	PROPN
ejpam-3266	304	22	σ	σ	PROPN
ejpam-3266	304	23	.	.	PROPN
ejpam-3266	305	1	since	since	SCONJ
ejpam-3266	305	2	σ	σ	PROPN
ejpam-3266	305	3	is	be	AUX
ejpam-3266	305	4	a	a	DET
ejpam-3266	305	5	semilattice	semilattice	NOUN
ejpam-3266	305	6	congruence	congruence	NOUN
ejpam-3266	305	7	on	on	ADP
ejpam-3266	305	8	h	h	NOUN
ejpam-3266	305	9	,	,	PUNCT
ejpam-3266	305	10	we	we	PRON
ejpam-3266	305	11	have	have	VERB
ejpam-3266	305	12	(	(	PUNCT
ejpam-3266	305	13	x	x	SYM
ejpam-3266	305	14	◦	◦	VERB
ejpam-3266	305	15	y	y	PROPN
ejpam-3266	305	16	,	,	PUNCT
ejpam-3266	305	17	y	y	PROPN
ejpam-3266	305	18	◦	◦	NOUN
ejpam-3266	305	19	x	x	SYM
ejpam-3266	305	20	)	)	PUNCT
ejpam-3266	305	21	∈	∈	PROPN
ejpam-3266	305	22	σ	σ	PROPN
ejpam-3266	305	23	.	.	PUNCT
ejpam-3266	306	1	since	since	SCONJ
ejpam-3266	306	2	(	(	PUNCT
ejpam-3266	306	3	x	x	X
ejpam-3266	306	4	,	,	PUNCT
ejpam-3266	306	5	x	x	PUNCT
ejpam-3266	306	6	◦	◦	NOUN
ejpam-3266	306	7	y	y	NOUN
ejpam-3266	306	8	)	)	PUNCT
ejpam-3266	306	9	∈	∈	PROPN
ejpam-3266	306	10	σ	σ	PROPN
ejpam-3266	306	11	,	,	PUNCT
ejpam-3266	306	12	(	(	PUNCT
ejpam-3266	306	13	x	x	SYM
ejpam-3266	306	14	◦	◦	VERB
ejpam-3266	306	15	y	y	PROPN
ejpam-3266	306	16	,	,	PUNCT
ejpam-3266	306	17	y	y	PROPN
ejpam-3266	306	18	◦	◦	NOUN
ejpam-3266	306	19	x	x	X
ejpam-3266	306	20	)	)	PUNCT
ejpam-3266	306	21	∈	∈	PROPN
ejpam-3266	306	22	σ	σ	PROPN
ejpam-3266	306	23	and	and	CCONJ
ejpam-3266	306	24	(	(	PUNCT
ejpam-3266	306	25	y	y	PROPN
ejpam-3266	306	26	◦	◦	PROPN
ejpam-3266	306	27	x	x	SYM
ejpam-3266	306	28	,	,	PUNCT
ejpam-3266	306	29	y	y	NOUN
ejpam-3266	306	30	)	)	PUNCT
ejpam-3266	306	31	∈	∈	PROPN
ejpam-3266	306	32	σ	σ	PROPN
ejpam-3266	306	33	,	,	PUNCT
ejpam-3266	306	34	we	we	PRON
ejpam-3266	306	35	have	have	VERB
ejpam-3266	306	36	(	(	PUNCT
ejpam-3266	306	37	x	x	NOUN
ejpam-3266	306	38	,	,	PUNCT
ejpam-3266	306	39	y	y	NOUN
ejpam-3266	306	40	)	)	PUNCT
ejpam-3266	306	41	∈	∈	PROPN
ejpam-3266	306	42	σ	σ	PROPN
ejpam-3266	306	43	.	.	PUNCT
ejpam-3266	306	44	�	�	PROPN
ejpam-3266	307	1	the	the	DET
ejpam-3266	307	2	following	follow	VERB
ejpam-3266	307	3	proposition	proposition	NOUN
ejpam-3266	307	4	holds	hold	VERB
ejpam-3266	307	5	for	for	ADP
ejpam-3266	307	6	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	307	7	and	and	CCONJ
ejpam-3266	307	8	its	its	PRON
ejpam-3266	307	9	proof	proof	NOUN
ejpam-3266	307	10	is	be	AUX
ejpam-3266	307	11	exactly	exactly	ADV
ejpam-3266	307	12	the	the	DET
ejpam-3266	307	13	same	same	ADJ
ejpam-3266	307	14	as	as	ADP
ejpam-3266	307	15	the	the	DET
ejpam-3266	307	16	proof	proof	NOUN
ejpam-3266	307	17	of	of	ADP
ejpam-3266	307	18	the	the	DET
ejpam-3266	307	19	corresponding	corresponding	ADJ
ejpam-3266	307	20	result	result	NOUN
ejpam-3266	307	21	in	in	ADP
ejpam-3266	307	22	[	[	X
ejpam-3266	307	23	3	3	X
ejpam-3266	307	24	]	]	PUNCT
ejpam-3266	307	25	(	(	PUNCT
ejpam-3266	307	26	no	no	DET
ejpam-3266	307	27	change	change	NOUN
ejpam-3266	307	28	is	be	AUX
ejpam-3266	307	29	needed	need	VERB
ejpam-3266	307	30	)	)	PUNCT
ejpam-3266	307	31	.	.	PUNCT
ejpam-3266	308	1	proposition	proposition	NOUN
ejpam-3266	308	2	3.2	3.2	NUM
ejpam-3266	308	3	.	.	PUNCT
ejpam-3266	309	1	(	(	PUNCT
ejpam-3266	309	2	cf	cf	NOUN
ejpam-3266	309	3	.	.	PUNCT
ejpam-3266	310	1	also	also	ADV
ejpam-3266	310	2	[	[	X
ejpam-3266	310	3	3	3	NUM
ejpam-3266	310	4	;	;	PUNCT
ejpam-3266	310	5	the	the	DET
ejpam-3266	310	6	proposition	proposition	NOUN
ejpam-3266	310	7	]	]	PUNCT
ejpam-3266	310	8	)	)	PUNCT
ejpam-3266	310	9	let	let	VERB
ejpam-3266	310	10	h	h	NOUN
ejpam-3266	310	11	be	be	AUX
ejpam-3266	310	12	an	an	DET
ejpam-3266	310	13	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	310	14	and	and	CCONJ
ejpam-3266	310	15	i(h	i(h	NOUN
ejpam-3266	310	16	)	)	PUNCT
ejpam-3266	310	17	the	the	DET
ejpam-3266	310	18	set	set	NOUN
ejpam-3266	310	19	of	of	ADP
ejpam-3266	310	20	prime	prime	ADJ
ejpam-3266	310	21	ideals	ideal	NOUN
ejpam-3266	310	22	of	of	ADP
ejpam-3266	310	23	h.	h.	PROPN
ejpam-3266	310	24	then	then	ADV
ejpam-3266	310	25	we	we	PRON
ejpam-3266	310	26	have	have	VERB
ejpam-3266	310	27	n	n	NOUN
ejpam-3266	310	28	=	=	SYM
ejpam-3266	310	29	⋂	⋂	PROPN
ejpam-3266	310	30	i∈i(h	i∈i(h	NOUN
ejpam-3266	310	31	)	)	PUNCT
ejpam-3266	310	32	σi	σi	X
ejpam-3266	310	33	.	.	PUNCT
ejpam-3266	311	1	corollary	corollary	ADJ
ejpam-3266	311	2	3.3	3.3	NUM
ejpam-3266	311	3	.	.	PUNCT
ejpam-3266	312	1	if	if	SCONJ
ejpam-3266	312	2	h	h	NOUN
ejpam-3266	312	3	is	be	AUX
ejpam-3266	312	4	an	an	DET
ejpam-3266	312	5	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	312	6	,	,	PUNCT
ejpam-3266	312	7	then	then	ADV
ejpam-3266	312	8	the	the	DET
ejpam-3266	312	9	relation	relation	NOUN
ejpam-3266	312	10	n	n	PRON
ejpam-3266	312	11	is	be	AUX
ejpam-3266	312	12	the	the	DET
ejpam-3266	312	13	least	least	ADJ
ejpam-3266	312	14	semilattice	semilattice	NOUN
ejpam-3266	312	15	congruence	congruence	NOUN
ejpam-3266	312	16	on	on	ADP
ejpam-3266	312	17	h.	h.	PROPN
ejpam-3266	312	18	proof	proof	NOUN
ejpam-3266	312	19	.	.	PUNCT
ejpam-3266	313	1	let	let	VERB
ejpam-3266	313	2	σ	σ	NOUN
ejpam-3266	313	3	be	be	AUX
ejpam-3266	313	4	a	a	DET
ejpam-3266	313	5	semilattice	semilattice	NOUN
ejpam-3266	313	6	congruence	congruence	NOUN
ejpam-3266	313	7	on	on	ADP
ejpam-3266	313	8	h.	h.	PROPN
ejpam-3266	313	9	then	then	ADV
ejpam-3266	313	10	n	n	PROPN
ejpam-3266	313	11	⊆	⊆	NUM
ejpam-3266	313	12	σ	σ	NOUN
ejpam-3266	313	13	.	.	PUNCT
ejpam-3266	314	1	in	in	ADP
ejpam-3266	314	2	fact	fact	NOUN
ejpam-3266	314	3	:	:	PUNCT
ejpam-3266	314	4	by	by	ADP
ejpam-3266	314	5	theorem	theorem	NOUN
ejpam-3266	314	6	3.1	3.1	NUM
ejpam-3266	314	7	,	,	PUNCT
ejpam-3266	314	8	there	there	PRON
ejpam-3266	314	9	exists	exist	VERB
ejpam-3266	314	10	a	a	DET
ejpam-3266	314	11	family	family	NOUN
ejpam-3266	314	12	a	a	PRON
ejpam-3266	314	13	of	of	ADP
ejpam-3266	314	14	proper	proper	ADJ
ejpam-3266	314	15	prime	prime	ADJ
ejpam-3266	314	16	ideals	ideal	NOUN
ejpam-3266	314	17	of	of	ADP
ejpam-3266	314	18	h	h	NOUN
ejpam-3266	314	19	such	such	ADJ
ejpam-3266	314	20	that	that	SCONJ
ejpam-3266	314	21	σ	σ	PROPN
ejpam-3266	314	22	=	=	SYM
ejpam-3266	314	23	⋂	⋂	PROPN
ejpam-3266	314	24	i∈a	i∈a	VERB
ejpam-3266	314	25	σi	σi	NOUN
ejpam-3266	314	26	.	.	PUNCT
ejpam-3266	315	1	by	by	ADP
ejpam-3266	315	2	proposition	proposition	NOUN
ejpam-3266	315	3	3.2	3.2	NUM
ejpam-3266	315	4	,	,	PUNCT
ejpam-3266	315	5	n	n	PROPN
ejpam-3266	315	6	=	=	SYM
ejpam-3266	315	7	⋂	⋂	PROPN
ejpam-3266	315	8	i∈i(h	i∈i(h	NOUN
ejpam-3266	315	9	)	)	PUNCT
ejpam-3266	315	10	σi	σi	INTJ
ejpam-3266	315	11	,	,	PUNCT
ejpam-3266	315	12	where	where	SCONJ
ejpam-3266	315	13	i(h	i(h	NOUN
ejpam-3266	315	14	)	)	PUNCT
ejpam-3266	315	15	is	be	AUX
ejpam-3266	315	16	the	the	DET
ejpam-3266	315	17	set	set	NOUN
ejpam-3266	315	18	of	of	ADP
ejpam-3266	315	19	prime	prime	ADJ
ejpam-3266	315	20	ideals	ideal	NOUN
ejpam-3266	315	21	of	of	ADP
ejpam-3266	315	22	h.	h.	PROPN
ejpam-3266	315	23	on	on	ADP
ejpam-3266	315	24	the	the	DET
ejpam-3266	315	25	other	other	ADJ
ejpam-3266	315	26	hand	hand	NOUN
ejpam-3266	315	27	,	,	PUNCT
ejpam-3266	315	28	n.	n.	PROPN
ejpam-3266	315	29	kehayopulu	kehayopulu	PROPN
ejpam-3266	315	30	/	/	SYM
ejpam-3266	315	31	eur	eur	PROPN
ejpam-3266	315	32	.	.	PUNCT
ejpam-3266	316	1	j.	j.	PROPN
ejpam-3266	316	2	pure	pure	PROPN
ejpam-3266	316	3	appl	appl	PROPN
ejpam-3266	316	4	.	.	PROPN
ejpam-3266	316	5	math	math	PROPN
ejpam-3266	316	6	,	,	PUNCT
ejpam-3266	316	7	11	11	NUM
ejpam-3266	316	8	(	(	PUNCT
ejpam-3266	316	9	2	2	NUM
ejpam-3266	316	10	)	)	PUNCT
ejpam-3266	316	11	(	(	PUNCT
ejpam-3266	316	12	2018	2018	NUM
ejpam-3266	316	13	)	)	PUNCT
ejpam-3266	316	14	,	,	PUNCT
ejpam-3266	316	15	476	476	NUM
ejpam-3266	316	16	-	-	SYM
ejpam-3266	316	17	492	492	NUM
ejpam-3266	316	18	484⋂	484⋂	NOUN
ejpam-3266	316	19	i∈a	i∈a	VERB
ejpam-3266	316	20	σi	σi	PROPN
ejpam-3266	317	1	⊇	⊇	PROPN
ejpam-3266	317	2	⋂	⋂	PROPN
ejpam-3266	317	3	i∈i(h	i∈i(h	PROPN
ejpam-3266	317	4	)	)	PUNCT
ejpam-3266	317	5	σi	σi	NOUN
ejpam-3266	317	6	.	.	PUNCT
ejpam-3266	318	1	indeed	indeed	ADV
ejpam-3266	318	2	,	,	PUNCT
ejpam-3266	318	3	if	if	SCONJ
ejpam-3266	318	4	(	(	PUNCT
ejpam-3266	318	5	x	x	NOUN
ejpam-3266	318	6	,	,	PUNCT
ejpam-3266	318	7	y	y	NOUN
ejpam-3266	318	8	)	)	PUNCT
ejpam-3266	318	9	∈	∈	PROPN
ejpam-3266	318	10	σi	σi	NOUN
ejpam-3266	318	11	for	for	ADP
ejpam-3266	318	12	every	every	DET
ejpam-3266	318	13	prime	prime	ADJ
ejpam-3266	318	14	ideal	ideal	NOUN
ejpam-3266	318	15	of	of	ADP
ejpam-3266	318	16	h	h	NOUN
ejpam-3266	318	17	,	,	PUNCT
ejpam-3266	318	18	then	then	ADV
ejpam-3266	318	19	clearly	clearly	ADV
ejpam-3266	318	20	(	(	PUNCT
ejpam-3266	318	21	x	x	NOUN
ejpam-3266	318	22	,	,	PUNCT
ejpam-3266	318	23	y	y	NOUN
ejpam-3266	318	24	)	)	PUNCT
ejpam-3266	318	25	∈	∈	PROPN
ejpam-3266	318	26	σi	σi	NOUN
ejpam-3266	318	27	for	for	ADP
ejpam-3266	318	28	every	every	DET
ejpam-3266	318	29	proper	proper	ADJ
ejpam-3266	318	30	prime	prime	ADJ
ejpam-3266	318	31	ideal	ideal	NOUN
ejpam-3266	318	32	of	of	ADP
ejpam-3266	318	33	h	h	NOUN
ejpam-3266	318	34	,	,	PUNCT
ejpam-3266	318	35	and	and	CCONJ
ejpam-3266	318	36	so	so	ADV
ejpam-3266	318	37	for	for	ADP
ejpam-3266	318	38	the	the	DET
ejpam-3266	318	39	elements	element	NOUN
ejpam-3266	318	40	of	of	ADP
ejpam-3266	318	41	a	a	PRON
ejpam-3266	318	42	as	as	ADV
ejpam-3266	318	43	well	well	ADV
ejpam-3266	318	44	.	.	PUNCT
ejpam-3266	319	1	hence	hence	ADV
ejpam-3266	319	2	we	we	PRON
ejpam-3266	319	3	obtain	obtain	VERB
ejpam-3266	319	4	n	n	PRON
ejpam-3266	319	5	⊆	⊆	PROPN
ejpam-3266	319	6	σ	σ	PROPN
ejpam-3266	319	7	.	.	PUNCT
ejpam-3266	319	8	�	�	PROPN
ejpam-3266	319	9	proposition	proposition	NOUN
ejpam-3266	319	10	3.4	3.4	NUM
ejpam-3266	319	11	.	.	PUNCT
ejpam-3266	320	1	let	let	AUX
ejpam-3266	320	2	(	(	PUNCT
ejpam-3266	320	3	s	s	X
ejpam-3266	320	4	,	,	PUNCT
ejpam-3266	320	5	·	·	PUNCT
ejpam-3266	320	6	)	)	PUNCT
ejpam-3266	320	7	be	be	AUX
ejpam-3266	320	8	a	a	DET
ejpam-3266	320	9	groupoid	groupoid	NOUN
ejpam-3266	320	10	and	and	CCONJ
ejpam-3266	320	11	“	"	PUNCT
ejpam-3266	320	12	◦	◦	NOUN
ejpam-3266	320	13	”	"	PUNCT
ejpam-3266	320	14	the	the	DET
ejpam-3266	320	15	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	320	16	with	with	ADP
ejpam-3266	320	17	the	the	DET
ejpam-3266	320	18	hyperoperation	hyperoperation	NOUN
ejpam-3266	320	19	“	"	PUNCT
ejpam-3266	320	20	◦	◦	NOUN
ejpam-3266	320	21	”	"	PUNCT
ejpam-3266	320	22	defined	define	VERB
ejpam-3266	320	23	by	by	ADP
ejpam-3266	320	24	◦	◦	NOUN
ejpam-3266	320	25	:	:	PUNCT
ejpam-3266	320	26	s	s	VERB
ejpam-3266	320	27	×	×	PROPN
ejpam-3266	320	28	s	s	X
ejpam-3266	320	29	→	→	SYM
ejpam-3266	320	30	p∗(s	p∗(s	NOUN
ejpam-3266	320	31	)	)	PUNCT
ejpam-3266	320	32	|	|	NOUN
ejpam-3266	320	33	(	(	PUNCT
ejpam-3266	320	34	a	a	PRON
ejpam-3266	320	35	,	,	PUNCT
ejpam-3266	320	36	b)→	b)→	VERB
ejpam-3266	320	37	a	a	DET
ejpam-3266	320	38	◦	◦	NOUN
ejpam-3266	320	39	b	b	NOUN
ejpam-3266	320	40	:	:	PUNCT
ejpam-3266	320	41	=	=	SYM
ejpam-3266	320	42	{	{	PUNCT
ejpam-3266	320	43	ab	ab	NOUN
ejpam-3266	320	44	}	}	PUNCT
ejpam-3266	320	45	.	.	PUNCT
ejpam-3266	321	1	then	then	ADV
ejpam-3266	321	2	f	f	PROPN
ejpam-3266	321	3	is	be	AUX
ejpam-3266	321	4	a	a	DET
ejpam-3266	321	5	filter	filter	NOUN
ejpam-3266	321	6	of	of	ADP
ejpam-3266	321	7	(	(	PUNCT
ejpam-3266	321	8	s	s	X
ejpam-3266	321	9	,	,	PUNCT
ejpam-3266	321	10	·	·	PUNCT
ejpam-3266	321	11	)	)	PUNCT
ejpam-3266	321	12	if	if	SCONJ
ejpam-3266	321	13	and	and	CCONJ
ejpam-3266	321	14	only	only	ADV
ejpam-3266	321	15	if	if	SCONJ
ejpam-3266	321	16	it	it	PRON
ejpam-3266	321	17	is	be	AUX
ejpam-3266	321	18	a	a	DET
ejpam-3266	321	19	filter	filter	NOUN
ejpam-3266	321	20	of	of	ADP
ejpam-3266	321	21	(	(	PUNCT
ejpam-3266	321	22	s	s	NOUN
ejpam-3266	321	23	,	,	PUNCT
ejpam-3266	321	24	◦	◦	NOUN
ejpam-3266	321	25	)	)	PUNCT
ejpam-3266	321	26	.	.	PUNCT
ejpam-3266	322	1	proof	proof	NOUN
ejpam-3266	322	2	.	.	PUNCT
ejpam-3266	323	1	=	=	NOUN
ejpam-3266	323	2	⇒.	⇒.	NOUN
ejpam-3266	323	3	let	let	VERB
ejpam-3266	323	4	f	f	PRON
ejpam-3266	323	5	be	be	AUX
ejpam-3266	323	6	a	a	DET
ejpam-3266	323	7	filter	filter	NOUN
ejpam-3266	323	8	of	of	ADP
ejpam-3266	323	9	(	(	PUNCT
ejpam-3266	323	10	s	s	X
ejpam-3266	323	11	,	,	PUNCT
ejpam-3266	323	12	·	·	PUNCT
ejpam-3266	323	13	)	)	PUNCT
ejpam-3266	323	14	.	.	PUNCT
ejpam-3266	324	1	if	if	SCONJ
ejpam-3266	324	2	a	a	PRON
ejpam-3266	324	3	,	,	PUNCT
ejpam-3266	324	4	b	b	PROPN
ejpam-3266	324	5	∈	∈	PROPN
ejpam-3266	324	6	f	f	PROPN
ejpam-3266	324	7	and	and	CCONJ
ejpam-3266	324	8	x	x	PROPN
ejpam-3266	324	9	∈	∈	PROPN
ejpam-3266	324	10	a	a	DET
ejpam-3266	324	11	◦	◦	NOUN
ejpam-3266	324	12	b	b	NOUN
ejpam-3266	324	13	,	,	PUNCT
ejpam-3266	324	14	then	then	ADV
ejpam-3266	324	15	x	x	X
ejpam-3266	324	16	=	=	PUNCT
ejpam-3266	324	17	ab	ab	PROPN
ejpam-3266	324	18	∈	∈	PROPN
ejpam-3266	324	19	f	f	PROPN
ejpam-3266	324	20	and	and	CCONJ
ejpam-3266	324	21	so	so	ADV
ejpam-3266	324	22	a	a	DET
ejpam-3266	324	23	◦	◦	NOUN
ejpam-3266	324	24	b	b	NOUN
ejpam-3266	324	25	⊆	⊆	NUM
ejpam-3266	324	26	f	f	NOUN
ejpam-3266	324	27	.	.	PUNCT
ejpam-3266	325	1	if	if	SCONJ
ejpam-3266	325	2	a	a	PRON
ejpam-3266	325	3	,	,	PUNCT
ejpam-3266	325	4	b	b	X
ejpam-3266	325	5	∈	∈	NOUN
ejpam-3266	325	6	s	s	VERB
ejpam-3266	325	7	such	such	ADJ
ejpam-3266	325	8	that	that	SCONJ
ejpam-3266	325	9	a	a	DET
ejpam-3266	325	10	◦	◦	NOUN
ejpam-3266	325	11	b	b	NOUN
ejpam-3266	325	12	⊆	⊆	NUM
ejpam-3266	325	13	f	f	NOUN
ejpam-3266	325	14	,	,	PUNCT
ejpam-3266	325	15	then	then	ADV
ejpam-3266	325	16	ab	ab	PROPN
ejpam-3266	325	17	∈	∈	PROPN
ejpam-3266	325	18	a	a	DET
ejpam-3266	325	19	◦	◦	NOUN
ejpam-3266	325	20	b	b	NOUN
ejpam-3266	325	21	⊆	⊆	NUM
ejpam-3266	325	22	f	f	NOUN
ejpam-3266	325	23	,	,	PUNCT
ejpam-3266	325	24	ab	ab	PROPN
ejpam-3266	325	25	∈	∈	PROPN
ejpam-3266	325	26	f	f	PROPN
ejpam-3266	325	27	and	and	CCONJ
ejpam-3266	325	28	so	so	ADV
ejpam-3266	325	29	a	a	DET
ejpam-3266	325	30	∈	∈	PROPN
ejpam-3266	325	31	f	f	PROPN
ejpam-3266	325	32	and	and	CCONJ
ejpam-3266	325	33	b	b	PROPN
ejpam-3266	325	34	∈	∈	PROPN
ejpam-3266	326	1	f	f	X
ejpam-3266	326	2	.	.	PUNCT
ejpam-3266	327	1	let	let	VERB
ejpam-3266	327	2	(	(	PUNCT
ejpam-3266	327	3	a	a	DET
ejpam-3266	327	4	◦	◦	NOUN
ejpam-3266	327	5	b	b	NOUN
ejpam-3266	327	6	)	)	PUNCT
ejpam-3266	327	7	∩	∩	ADJ
ejpam-3266	327	8	f	f	PROPN
ejpam-3266	327	9	6=	6=	PROPN
ejpam-3266	327	10	∅	∅	NOUN
ejpam-3266	327	11	,	,	PUNCT
ejpam-3266	327	12	u	u	NOUN
ejpam-3266	327	13	∈	∈	PROPN
ejpam-3266	327	14	a	a	DET
ejpam-3266	327	15	◦	◦	NOUN
ejpam-3266	327	16	b	b	NOUN
ejpam-3266	327	17	and	and	CCONJ
ejpam-3266	327	18	u	u	PROPN
ejpam-3266	327	19	∈	∈	PROPN
ejpam-3266	327	20	f	f	X
ejpam-3266	327	21	.	.	PUNCT
ejpam-3266	328	1	then	then	ADV
ejpam-3266	328	2	u	u	X
ejpam-3266	328	3	=	=	PROPN
ejpam-3266	328	4	ab	ab	PROPN
ejpam-3266	328	5	and	and	CCONJ
ejpam-3266	328	6	u	u	PROPN
ejpam-3266	328	7	∈	∈	PROPN
ejpam-3266	328	8	f	f	PROPN
ejpam-3266	328	9	,	,	PUNCT
ejpam-3266	328	10	then	then	ADV
ejpam-3266	328	11	ab	ab	PROPN
ejpam-3266	328	12	∈	∈	PROPN
ejpam-3266	328	13	f	f	PROPN
ejpam-3266	328	14	,	,	PUNCT
ejpam-3266	328	15	then	then	ADV
ejpam-3266	328	16	a	a	DET
ejpam-3266	328	17	◦	◦	NOUN
ejpam-3266	328	18	b	b	NOUN
ejpam-3266	328	19	=	=	SYM
ejpam-3266	328	20	{	{	PUNCT
ejpam-3266	328	21	ab	ab	PROPN
ejpam-3266	328	22	}	}	PUNCT
ejpam-3266	328	23	⊆	⊆	NUM
ejpam-3266	328	24	f	f	NOUN
ejpam-3266	328	25	and	and	CCONJ
ejpam-3266	328	26	so	so	ADV
ejpam-3266	328	27	a	a	DET
ejpam-3266	328	28	◦	◦	NOUN
ejpam-3266	328	29	b	b	NOUN
ejpam-3266	328	30	⊆	⊆	NUM
ejpam-3266	328	31	f	f	NOUN
ejpam-3266	328	32	.	.	PUNCT
ejpam-3266	329	1	⇐	⇐	PROPN
ejpam-3266	329	2	=	=	PRON
ejpam-3266	329	3	.	.	PUNCT
ejpam-3266	330	1	let	let	VERB
ejpam-3266	330	2	f	f	PRON
ejpam-3266	330	3	be	be	AUX
ejpam-3266	330	4	a	a	DET
ejpam-3266	330	5	filter	filter	NOUN
ejpam-3266	330	6	of	of	ADP
ejpam-3266	330	7	(	(	PUNCT
ejpam-3266	330	8	s	s	NOUN
ejpam-3266	330	9	,	,	PUNCT
ejpam-3266	330	10	◦	◦	NOUN
ejpam-3266	330	11	)	)	PUNCT
ejpam-3266	330	12	.	.	PUNCT
ejpam-3266	331	1	if	if	SCONJ
ejpam-3266	331	2	a	a	PRON
ejpam-3266	331	3	,	,	PUNCT
ejpam-3266	331	4	b	b	PROPN
ejpam-3266	331	5	∈	∈	PROPN
ejpam-3266	331	6	f	f	X
ejpam-3266	331	7	,	,	PUNCT
ejpam-3266	331	8	then	then	ADV
ejpam-3266	331	9	{	{	PUNCT
ejpam-3266	331	10	ab	ab	NOUN
ejpam-3266	331	11	}	}	PUNCT
ejpam-3266	331	12	=	=	PUNCT
ejpam-3266	331	13	a	a	DET
ejpam-3266	331	14	◦	◦	NOUN
ejpam-3266	331	15	b	b	NOUN
ejpam-3266	331	16	⊆	⊆	NUM
ejpam-3266	331	17	f	f	NOUN
ejpam-3266	331	18	,	,	PUNCT
ejpam-3266	331	19	thus	thus	ADV
ejpam-3266	331	20	ab	ab	PROPN
ejpam-3266	331	21	∈	∈	PROPN
ejpam-3266	331	22	f	f	X
ejpam-3266	331	23	.	.	PUNCT
ejpam-3266	332	1	if	if	SCONJ
ejpam-3266	332	2	a	a	PRON
ejpam-3266	332	3	,	,	PUNCT
ejpam-3266	332	4	b	b	X
ejpam-3266	332	5	∈	∈	NOUN
ejpam-3266	332	6	s	s	VERB
ejpam-3266	332	7	such	such	ADJ
ejpam-3266	332	8	that	that	SCONJ
ejpam-3266	332	9	ab	ab	PROPN
ejpam-3266	332	10	∈	∈	PROPN
ejpam-3266	332	11	f	f	PROPN
ejpam-3266	332	12	,	,	PUNCT
ejpam-3266	332	13	then	then	ADV
ejpam-3266	332	14	a	a	DET
ejpam-3266	332	15	◦	◦	NOUN
ejpam-3266	332	16	b	b	NOUN
ejpam-3266	332	17	=	=	SYM
ejpam-3266	332	18	{	{	PUNCT
ejpam-3266	332	19	ab	ab	PROPN
ejpam-3266	332	20	}	}	PUNCT
ejpam-3266	332	21	⊆	⊆	NUM
ejpam-3266	332	22	f	f	NOUN
ejpam-3266	332	23	,	,	PUNCT
ejpam-3266	332	24	so	so	ADV
ejpam-3266	332	25	a	a	DET
ejpam-3266	332	26	◦	◦	NOUN
ejpam-3266	332	27	b	b	NOUN
ejpam-3266	332	28	⊆	⊆	NUM
ejpam-3266	332	29	f	f	NOUN
ejpam-3266	332	30	,	,	PUNCT
ejpam-3266	332	31	then	then	ADV
ejpam-3266	332	32	a	a	DET
ejpam-3266	332	33	∈	∈	PROPN
ejpam-3266	332	34	f	f	X
ejpam-3266	332	35	and	and	CCONJ
ejpam-3266	332	36	b	b	PROPN
ejpam-3266	332	37	∈	∈	PROPN
ejpam-3266	332	38	f	f	NOUN
ejpam-3266	333	1	and	and	CCONJ
ejpam-3266	333	2	so	so	ADV
ejpam-3266	333	3	f	f	PROPN
ejpam-3266	333	4	is	be	AUX
ejpam-3266	333	5	a	a	DET
ejpam-3266	333	6	filter	filter	NOUN
ejpam-3266	333	7	of	of	ADP
ejpam-3266	333	8	(	(	PUNCT
ejpam-3266	333	9	s	s	X
ejpam-3266	333	10	,	,	PUNCT
ejpam-3266	333	11	·	·	PUNCT
ejpam-3266	333	12	)	)	PUNCT
ejpam-3266	333	13	.	.	PUNCT
ejpam-3266	334	1	�	�	PROPN
ejpam-3266	334	2	4	4	NUM
ejpam-3266	334	3	.	.	PUNCT
ejpam-3266	334	4	complete	complete	ADJ
ejpam-3266	334	5	semilattice	semilattice	NOUN
ejpam-3266	334	6	congruences	congruence	NOUN
ejpam-3266	334	7	on	on	ADP
ejpam-3266	334	8	ordered	order	VERB
ejpam-3266	334	9	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	334	10	let	let	VERB
ejpam-3266	334	11	us	we	PRON
ejpam-3266	334	12	consider	consider	VERB
ejpam-3266	334	13	now	now	ADV
ejpam-3266	334	14	the	the	DET
ejpam-3266	334	15	case	case	NOUN
ejpam-3266	334	16	of	of	ADP
ejpam-3266	334	17	ordered	order	VERB
ejpam-3266	334	18	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	334	19	.	.	PUNCT
ejpam-3266	335	1	for	for	ADP
ejpam-3266	335	2	the	the	DET
ejpam-3266	335	3	necessary	necessary	ADJ
ejpam-3266	335	4	definitions	definition	NOUN
ejpam-3266	335	5	and	and	CCONJ
ejpam-3266	335	6	notations	notation	NOUN
ejpam-3266	335	7	on	on	ADP
ejpam-3266	335	8	ordered	order	VERB
ejpam-3266	335	9	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	335	10	we	we	PRON
ejpam-3266	335	11	refer	refer	VERB
ejpam-3266	335	12	to	to	ADP
ejpam-3266	335	13	[	[	X
ejpam-3266	335	14	6	6	NUM
ejpam-3266	335	15	]	]	PUNCT
ejpam-3266	335	16	and	and	CCONJ
ejpam-3266	335	17	[	[	X
ejpam-3266	335	18	9	9	NUM
ejpam-3266	335	19	]	]	PUNCT
ejpam-3266	335	20	.	.	PUNCT
ejpam-3266	336	1	for	for	ADP
ejpam-3266	336	2	an	an	DET
ejpam-3266	336	3	ordered	order	VERB
ejpam-3266	336	4	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	336	5	,	,	PUNCT
ejpam-3266	336	6	the	the	DET
ejpam-3266	336	7	semilattice	semilattice	NOUN
ejpam-3266	336	8	congruence	congruence	NOUN
ejpam-3266	336	9	is	be	AUX
ejpam-3266	336	10	defined	define	VERB
ejpam-3266	336	11	exactly	exactly	ADV
ejpam-3266	336	12	as	as	ADP
ejpam-3266	336	13	in	in	ADP
ejpam-3266	336	14	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	336	15	.	.	PUNCT
ejpam-3266	337	1	the	the	DET
ejpam-3266	337	2	concept	concept	NOUN
ejpam-3266	337	3	of	of	ADP
ejpam-3266	337	4	complete	complete	ADJ
ejpam-3266	337	5	semilattice	semilattice	NOUN
ejpam-3266	337	6	congruences	congruence	NOUN
ejpam-3266	337	7	of	of	ADP
ejpam-3266	337	8	ordered	order	VERB
ejpam-3266	337	9	groupoids	groupoid	NOUN
ejpam-3266	337	10	introduced	introduce	VERB
ejpam-3266	337	11	by	by	ADP
ejpam-3266	337	12	kehayopulu	kehayopulu	ADJ
ejpam-3266	337	13	and	and	CCONJ
ejpam-3266	337	14	tsingelis	tsingeli	NOUN
ejpam-3266	337	15	in	in	ADP
ejpam-3266	337	16	[	[	X
ejpam-3266	337	17	11	11	NUM
ejpam-3266	337	18	]	]	PUNCT
ejpam-3266	337	19	can	can	AUX
ejpam-3266	337	20	be	be	AUX
ejpam-3266	337	21	naturally	naturally	ADV
ejpam-3266	337	22	transferred	transfer	VERB
ejpam-3266	337	23	to	to	ADP
ejpam-3266	337	24	ordered	order	VERB
ejpam-3266	337	25	hypergroupoids	hypergroupoid	NOUN
ejpam-3266	337	26	by	by	ADP
ejpam-3266	337	27	the	the	DET
ejpam-3266	337	28	following	follow	VERB
ejpam-3266	337	29	definition	definition	NOUN
ejpam-3266	337	30	.	.	PUNCT
ejpam-3266	338	1	definition	definition	NOUN
ejpam-3266	338	2	4.1	4.1	NUM
ejpam-3266	338	3	.	.	PUNCT
ejpam-3266	339	1	if	if	SCONJ
ejpam-3266	339	2	(	(	PUNCT
ejpam-3266	339	3	s	s	NOUN
ejpam-3266	339	4	,	,	PUNCT
ejpam-3266	339	5	◦	◦	NOUN
ejpam-3266	339	6	,	,	PUNCT
ejpam-3266	339	7	≤	≤	NUM
ejpam-3266	339	8	)	)	PUNCT
ejpam-3266	339	9	is	be	AUX
ejpam-3266	339	10	an	an	DET
ejpam-3266	339	11	ordered	ordered	ADJ
ejpam-3266	339	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	339	13	,	,	PUNCT
ejpam-3266	339	14	a	a	DET
ejpam-3266	339	15	semilattice	semilattice	NOUN
ejpam-3266	339	16	congruence	congruence	PROPN
ejpam-3266	339	17	σ	σ	PROPN
ejpam-3266	339	18	on	on	ADP
ejpam-3266	339	19	s	s	PROPN
ejpam-3266	339	20	is	be	AUX
ejpam-3266	339	21	called	call	VERB
ejpam-3266	339	22	complete	complete	ADJ
ejpam-3266	339	23	if	if	SCONJ
ejpam-3266	339	24	,	,	PUNCT
ejpam-3266	339	25	for	for	ADP
ejpam-3266	339	26	every	every	DET
ejpam-3266	339	27	a	a	PROPN
ejpam-3266	339	28	,	,	PUNCT
ejpam-3266	339	29	b	b	PROPN
ejpam-3266	339	30	∈	∈	PROPN
ejpam-3266	339	31	s	s	PROPN
ejpam-3266	339	32	,	,	PUNCT
ejpam-3266	339	33	the	the	DET
ejpam-3266	339	34	relation	relation	NOUN
ejpam-3266	339	35	a	a	DET
ejpam-3266	339	36	≤	≤	NUM
ejpam-3266	339	37	b	b	NOUN
ejpam-3266	339	38	implies	imply	VERB
ejpam-3266	339	39	(	(	PUNCT
ejpam-3266	339	40	a	a	PRON
ejpam-3266	339	41	,	,	PUNCT
ejpam-3266	339	42	a	a	DET
ejpam-3266	339	43	◦	◦	NOUN
ejpam-3266	339	44	b	b	NOUN
ejpam-3266	339	45	)	)	PUNCT
ejpam-3266	339	46	∈	∈	PROPN
ejpam-3266	339	47	σ	σ	PROPN
ejpam-3266	339	48	.	.	PUNCT
ejpam-3266	339	49	proposition	proposition	NOUN
ejpam-3266	339	50	4.2	4.2	NUM
ejpam-3266	339	51	.	.	PUNCT
ejpam-3266	340	1	let	let	VERB
ejpam-3266	340	2	(	(	PUNCT
ejpam-3266	340	3	s	s	X
ejpam-3266	340	4	,	,	PUNCT
ejpam-3266	340	5	·	·	PUNCT
ejpam-3266	340	6	,	,	PUNCT
ejpam-3266	340	7	≤	≤	NUM
ejpam-3266	340	8	)	)	PUNCT
ejpam-3266	340	9	be	be	AUX
ejpam-3266	340	10	an	an	DET
ejpam-3266	340	11	ordered	order	VERB
ejpam-3266	340	12	groupoid	groupoid	NOUN
ejpam-3266	340	13	and	and	CCONJ
ejpam-3266	340	14	“	"	PUNCT
ejpam-3266	340	15	◦	◦	NOUN
ejpam-3266	340	16	”	"	PUNCT
ejpam-3266	340	17	the	the	DET
ejpam-3266	340	18	hyperoperation	hyperoperation	NOUN
ejpam-3266	340	19	on	on	ADP
ejpam-3266	340	20	s	s	PRON
ejpam-3266	340	21	defined	define	VERB
ejpam-3266	340	22	by	by	ADP
ejpam-3266	340	23	a	a	DET
ejpam-3266	340	24	◦	◦	NOUN
ejpam-3266	340	25	b	b	X
ejpam-3266	340	26	:	:	PUNCT
ejpam-3266	340	27	=	=	SYM
ejpam-3266	340	28	{	{	PUNCT
ejpam-3266	340	29	ab	ab	NOUN
ejpam-3266	340	30	}	}	PUNCT
ejpam-3266	340	31	.	.	PUNCT
ejpam-3266	341	1	then	then	ADV
ejpam-3266	341	2	(	(	PUNCT
ejpam-3266	341	3	s	s	X
ejpam-3266	341	4	,	,	PUNCT
ejpam-3266	341	5	◦	◦	NOUN
ejpam-3266	341	6	,	,	PUNCT
ejpam-3266	341	7	≤	≤	NUM
ejpam-3266	341	8	)	)	PUNCT
ejpam-3266	341	9	is	be	AUX
ejpam-3266	341	10	an	an	DET
ejpam-3266	341	11	ordered	ordered	ADJ
ejpam-3266	341	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	341	13	.	.	PUNCT
ejpam-3266	342	1	the	the	DET
ejpam-3266	342	2	relation	relation	NOUN
ejpam-3266	342	3	σ	σ	PROPN
ejpam-3266	342	4	is	be	AUX
ejpam-3266	342	5	a	a	DET
ejpam-3266	342	6	semilattice	semilattice	NOUN
ejpam-3266	342	7	(	(	PUNCT
ejpam-3266	342	8	resp	resp	NOUN
ejpam-3266	342	9	.	.	PUNCT
ejpam-3266	343	1	complete	complete	ADJ
ejpam-3266	343	2	semilattice	semilattice	PROPN
ejpam-3266	343	3	)	)	PUNCT
ejpam-3266	343	4	congruence	congruence	NOUN
ejpam-3266	343	5	on	on	ADP
ejpam-3266	343	6	(	(	PUNCT
ejpam-3266	343	7	s	s	X
ejpam-3266	343	8	,	,	PUNCT
ejpam-3266	343	9	·	·	PUNCT
ejpam-3266	343	10	,	,	PUNCT
ejpam-3266	343	11	≤	≤	NUM
ejpam-3266	343	12	)	)	PUNCT
ejpam-3266	344	1	if	if	SCONJ
ejpam-3266	344	2	and	and	CCONJ
ejpam-3266	344	3	only	only	ADV
ejpam-3266	344	4	if	if	SCONJ
ejpam-3266	344	5	it	it	PRON
ejpam-3266	344	6	is	be	AUX
ejpam-3266	344	7	semilattice	semilattice	NOUN
ejpam-3266	344	8	(	(	PUNCT
ejpam-3266	344	9	resp	resp	NOUN
ejpam-3266	344	10	.	.	PUNCT
ejpam-3266	345	1	complete	complete	ADJ
ejpam-3266	345	2	semilattice	semilattice	PROPN
ejpam-3266	345	3	)	)	PUNCT
ejpam-3266	345	4	congruence	congruence	NOUN
ejpam-3266	345	5	on	on	ADP
ejpam-3266	345	6	(	(	PUNCT
ejpam-3266	345	7	s	s	NOUN
ejpam-3266	345	8	,	,	PUNCT
ejpam-3266	345	9	◦	◦	NOUN
ejpam-3266	345	10	,	,	PUNCT
ejpam-3266	345	11	≤	≤	NUM
ejpam-3266	345	12	)	)	PUNCT
ejpam-3266	345	13	.	.	PUNCT
ejpam-3266	346	1	if	if	SCONJ
ejpam-3266	346	2	(	(	PUNCT
ejpam-3266	346	3	s	s	X
ejpam-3266	346	4	,	,	PUNCT
ejpam-3266	346	5	·	·	PUNCT
ejpam-3266	346	6	,	,	PUNCT
ejpam-3266	346	7	≤	≤	NUM
ejpam-3266	346	8	)	)	PUNCT
ejpam-3266	346	9	is	be	AUX
ejpam-3266	346	10	an	an	DET
ejpam-3266	346	11	ordered	order	VERB
ejpam-3266	346	12	semigroup	semigroup	NOUN
ejpam-3266	346	13	,	,	PUNCT
ejpam-3266	346	14	then	then	ADV
ejpam-3266	346	15	(	(	PUNCT
ejpam-3266	346	16	s	s	X
ejpam-3266	346	17	,	,	PUNCT
ejpam-3266	346	18	◦	◦	NOUN
ejpam-3266	346	19	,	,	PUNCT
ejpam-3266	346	20	≤	≤	NUM
ejpam-3266	346	21	)	)	PUNCT
ejpam-3266	346	22	is	be	AUX
ejpam-3266	346	23	an	an	DET
ejpam-3266	346	24	ordered	order	VERB
ejpam-3266	346	25	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	346	26	as	as	ADV
ejpam-3266	346	27	well	well	ADV
ejpam-3266	346	28	.	.	PUNCT
ejpam-3266	347	1	proof	proof	NOUN
ejpam-3266	347	2	.	.	PUNCT
ejpam-3266	348	1	if	if	SCONJ
ejpam-3266	348	2	(	(	PUNCT
ejpam-3266	348	3	s	s	X
ejpam-3266	348	4	,	,	PUNCT
ejpam-3266	348	5	·	·	PUNCT
ejpam-3266	348	6	,	,	PUNCT
ejpam-3266	348	7	≤	≤	NUM
ejpam-3266	348	8	)	)	PUNCT
ejpam-3266	348	9	is	be	AUX
ejpam-3266	348	10	an	an	DET
ejpam-3266	348	11	ordered	ordered	ADJ
ejpam-3266	348	12	groupoid	groupoid	NOUN
ejpam-3266	348	13	,	,	PUNCT
ejpam-3266	348	14	a	a	DET
ejpam-3266	348	15	≤	≤	PROPN
ejpam-3266	348	16	b	b	NUM
ejpam-3266	348	17	,	,	PUNCT
ejpam-3266	348	18	c	c	PROPN
ejpam-3266	348	19	∈	∈	PROPN
ejpam-3266	348	20	s	s	PART
ejpam-3266	348	21	and	and	CCONJ
ejpam-3266	348	22	u	u	PROPN
ejpam-3266	348	23	∈	∈	PROPN
ejpam-3266	348	24	a	a	DET
ejpam-3266	348	25	◦	◦	NOUN
ejpam-3266	348	26	c	c	NOUN
ejpam-3266	348	27	,	,	PUNCT
ejpam-3266	348	28	then	then	ADV
ejpam-3266	348	29	u	u	X
ejpam-3266	348	30	=	=	SYM
ejpam-3266	348	31	ac	ac	PROPN
ejpam-3266	348	32	≤	≤	PUNCT
ejpam-3266	348	33	bc	bc	PROPN
ejpam-3266	348	34	,	,	PUNCT
ejpam-3266	348	35	so	so	ADV
ejpam-3266	348	36	for	for	SCONJ
ejpam-3266	348	37	the	the	DET
ejpam-3266	348	38	element	element	NOUN
ejpam-3266	348	39	v	v	NOUN
ejpam-3266	348	40	:	:	PUNCT
ejpam-3266	348	41	=	=	NUM
ejpam-3266	349	1	bc	bc	PROPN
ejpam-3266	349	2	∈	∈	PROPN
ejpam-3266	349	3	b	b	PROPN
ejpam-3266	349	4	◦	◦	NOUN
ejpam-3266	349	5	c	c	NOUN
ejpam-3266	349	6	we	we	PRON
ejpam-3266	349	7	have	have	VERB
ejpam-3266	349	8	u	u	NOUN
ejpam-3266	349	9	≤	≤	ADJ
ejpam-3266	349	10	v	v	NOUN
ejpam-3266	349	11	;	;	PUNCT
ejpam-3266	349	12	similarly	similarly	ADV
ejpam-3266	349	13	c	c	AUX
ejpam-3266	349	14	◦	◦	VERB
ejpam-3266	349	15	a	a	DET
ejpam-3266	349	16	�	�	PROPN
ejpam-3266	349	17	c	c	PROPN
ejpam-3266	349	18	◦	◦	NOUN
ejpam-3266	349	19	b	b	PROPN
ejpam-3266	349	20	and	and	CCONJ
ejpam-3266	349	21	so	so	ADV
ejpam-3266	349	22	(	(	PUNCT
ejpam-3266	349	23	s	s	NOUN
ejpam-3266	349	24	,	,	PUNCT
ejpam-3266	349	25	◦	◦	NOUN
ejpam-3266	349	26	,	,	PUNCT
ejpam-3266	349	27	≤	≤	NUM
ejpam-3266	349	28	)	)	PUNCT
ejpam-3266	349	29	is	be	AUX
ejpam-3266	349	30	an	an	DET
ejpam-3266	349	31	ordered	ordered	ADJ
ejpam-3266	349	32	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	349	33	.	.	PUNCT
ejpam-3266	350	1	let	let	VERB
ejpam-3266	350	2	σ	σ	NOUN
ejpam-3266	350	3	be	be	AUX
ejpam-3266	350	4	a	a	DET
ejpam-3266	350	5	semilattice	semilattice	NOUN
ejpam-3266	350	6	congruence	congruence	NOUN
ejpam-3266	350	7	on	on	ADP
ejpam-3266	350	8	(	(	PUNCT
ejpam-3266	350	9	s	s	X
ejpam-3266	350	10	,	,	PUNCT
ejpam-3266	350	11	·	·	PUNCT
ejpam-3266	350	12	,	,	PUNCT
ejpam-3266	350	13	≤	≤	NUM
ejpam-3266	350	14	)	)	PUNCT
ejpam-3266	350	15	.	.	PUNCT
ejpam-3266	351	1	if	if	SCONJ
ejpam-3266	351	2	(	(	PUNCT
ejpam-3266	351	3	a	a	PRON
ejpam-3266	351	4	,	,	PUNCT
ejpam-3266	351	5	b	b	NOUN
ejpam-3266	351	6	)	)	PUNCT
ejpam-3266	351	7	∈	∈	PROPN
ejpam-3266	351	8	σ	σ	NOUN
ejpam-3266	351	9	and	and	CCONJ
ejpam-3266	351	10	c	c	NOUN
ejpam-3266	351	11	∈	∈	PROPN
ejpam-3266	351	12	s	s	PART
ejpam-3266	351	13	,	,	PUNCT
ejpam-3266	351	14	then	then	ADV
ejpam-3266	351	15	(	(	PUNCT
ejpam-3266	351	16	a	a	DET
ejpam-3266	351	17	◦	◦	NOUN
ejpam-3266	351	18	c	c	NOUN
ejpam-3266	351	19	,	,	PUNCT
ejpam-3266	351	20	b	b	X
ejpam-3266	351	21	◦	◦	NOUN
ejpam-3266	351	22	c	c	NOUN
ejpam-3266	351	23	)	)	PUNCT
ejpam-3266	351	24	∈	∈	PROPN
ejpam-3266	351	25	σ	σ	PROPN
ejpam-3266	351	26	.	.	PUNCT
ejpam-3266	352	1	indeed	indeed	ADV
ejpam-3266	352	2	,	,	PUNCT
ejpam-3266	352	3	if	if	SCONJ
ejpam-3266	352	4	u	u	PROPN
ejpam-3266	352	5	∈	∈	VERB
ejpam-3266	352	6	a	a	DET
ejpam-3266	352	7	◦	◦	NOUN
ejpam-3266	352	8	c	c	NOUN
ejpam-3266	352	9	and	and	CCONJ
ejpam-3266	352	10	v	v	ADP
ejpam-3266	352	11	∈	∈	PROPN
ejpam-3266	352	12	b	b	PROPN
ejpam-3266	352	13	◦	◦	NOUN
ejpam-3266	352	14	c	c	NOUN
ejpam-3266	352	15	,	,	PUNCT
ejpam-3266	352	16	then	then	ADV
ejpam-3266	352	17	u	u	X
ejpam-3266	352	18	=	=	SYM
ejpam-3266	352	19	ac	ac	PROPN
ejpam-3266	352	20	,	,	PUNCT
ejpam-3266	352	21	v	v	NOUN
ejpam-3266	352	22	=	=	SYM
ejpam-3266	352	23	bc	bc	PROPN
ejpam-3266	352	24	and	and	CCONJ
ejpam-3266	352	25	(	(	PUNCT
ejpam-3266	352	26	ac	ac	PROPN
ejpam-3266	352	27	,	,	PUNCT
ejpam-3266	352	28	bc	bc	PROPN
ejpam-3266	352	29	)	)	PUNCT
ejpam-3266	352	30	∈	∈	PROPN
ejpam-3266	352	31	σ	σ	PROPN
ejpam-3266	352	32	,	,	PUNCT
ejpam-3266	352	33	so	so	CCONJ
ejpam-3266	352	34	(	(	PUNCT
ejpam-3266	352	35	u	u	NOUN
ejpam-3266	352	36	,	,	PUNCT
ejpam-3266	352	37	v	v	NOUN
ejpam-3266	352	38	)	)	PUNCT
ejpam-3266	352	39	∈	∈	PROPN
ejpam-3266	352	40	σ	σ	PROPN
ejpam-3266	352	41	.	.	PUNCT
ejpam-3266	352	42	similarly	similarly	ADV
ejpam-3266	352	43	σ	σ	PROPN
ejpam-3266	352	44	is	be	AUX
ejpam-3266	352	45	a	a	DET
ejpam-3266	352	46	left	left	ADJ
ejpam-3266	352	47	congruence	congruence	NOUN
ejpam-3266	352	48	on	on	ADP
ejpam-3266	352	49	(	(	PUNCT
ejpam-3266	352	50	s	s	NOUN
ejpam-3266	352	51	,	,	PUNCT
ejpam-3266	352	52	◦	◦	NOUN
ejpam-3266	352	53	,	,	PUNCT
ejpam-3266	352	54	≤	≤	NUM
ejpam-3266	352	55	)	)	PUNCT
ejpam-3266	352	56	.	.	PUNCT
ejpam-3266	353	1	let	let	VERB
ejpam-3266	353	2	a	a	DET
ejpam-3266	353	3	,	,	PUNCT
ejpam-3266	353	4	b	b	X
ejpam-3266	353	5	∈	∈	PROPN
ejpam-3266	353	6	s.	s.	PROPN
ejpam-3266	353	7	then	then	ADV
ejpam-3266	353	8	(	(	PUNCT
ejpam-3266	353	9	a	a	DET
ejpam-3266	353	10	◦	◦	NOUN
ejpam-3266	353	11	a	a	PRON
ejpam-3266	353	12	,	,	PUNCT
ejpam-3266	353	13	a	a	PRON
ejpam-3266	353	14	)	)	PUNCT
ejpam-3266	353	15	∈	∈	PROPN
ejpam-3266	353	16	σ	σ	PROPN
ejpam-3266	353	17	.	.	PUNCT
ejpam-3266	354	1	indeed	indeed	ADV
ejpam-3266	354	2	,	,	PUNCT
ejpam-3266	354	3	if	if	SCONJ
ejpam-3266	354	4	u	u	PROPN
ejpam-3266	354	5	∈	∈	VERB
ejpam-3266	354	6	a	a	DET
ejpam-3266	354	7	◦	◦	NOUN
ejpam-3266	354	8	a	a	PRON
ejpam-3266	354	9	,	,	PUNCT
ejpam-3266	354	10	then	then	ADV
ejpam-3266	354	11	u	u	PROPN
ejpam-3266	354	12	=	=	PROPN
ejpam-3266	354	13	a2	a2	PROPN
ejpam-3266	354	14	and	and	CCONJ
ejpam-3266	354	15	(	(	PUNCT
ejpam-3266	354	16	a2	a2	PROPN
ejpam-3266	354	17	,	,	PUNCT
ejpam-3266	354	18	a	a	PRON
ejpam-3266	354	19	)	)	PUNCT
ejpam-3266	354	20	∈	∈	PROPN
ejpam-3266	354	21	σ	σ	PROPN
ejpam-3266	354	22	,	,	PUNCT
ejpam-3266	354	23	thus	thus	ADV
ejpam-3266	354	24	we	we	PRON
ejpam-3266	354	25	get	get	VERB
ejpam-3266	354	26	(	(	PUNCT
ejpam-3266	354	27	u	u	NOUN
ejpam-3266	354	28	,	,	PUNCT
ejpam-3266	354	29	a	a	PRON
ejpam-3266	354	30	)	)	PUNCT
ejpam-3266	354	31	∈	∈	PROPN
ejpam-3266	354	32	σ	σ	PROPN
ejpam-3266	354	33	.	.	PUNCT
ejpam-3266	355	1	we	we	PRON
ejpam-3266	355	2	have	have	VERB
ejpam-3266	355	3	(	(	PUNCT
ejpam-3266	355	4	a	a	DET
ejpam-3266	355	5	◦	◦	NOUN
ejpam-3266	355	6	b	b	NUM
ejpam-3266	355	7	,	,	PUNCT
ejpam-3266	355	8	b	b	X
ejpam-3266	355	9	◦	◦	NOUN
ejpam-3266	355	10	a	a	X
ejpam-3266	355	11	)	)	PUNCT
ejpam-3266	355	12	∈	∈	PROPN
ejpam-3266	355	13	σ	σ	PROPN
ejpam-3266	355	14	.	.	PUNCT
ejpam-3266	356	1	indeed	indeed	ADV
ejpam-3266	356	2	,	,	PUNCT
ejpam-3266	356	3	if	if	SCONJ
ejpam-3266	356	4	u	u	PROPN
ejpam-3266	356	5	∈	∈	VERB
ejpam-3266	356	6	a	a	DET
ejpam-3266	356	7	◦	◦	NOUN
ejpam-3266	356	8	b	b	NOUN
ejpam-3266	356	9	and	and	CCONJ
ejpam-3266	356	10	v	v	ADP
ejpam-3266	356	11	∈	∈	PROPN
ejpam-3266	356	12	b	b	PROPN
ejpam-3266	356	13	◦	◦	NOUN
ejpam-3266	356	14	a	a	PRON
ejpam-3266	356	15	,	,	PUNCT
ejpam-3266	356	16	then	then	ADV
ejpam-3266	356	17	u	u	PROPN
ejpam-3266	356	18	=	=	PROPN
ejpam-3266	356	19	ab	ab	PROPN
ejpam-3266	356	20	,	,	PUNCT
ejpam-3266	356	21	v	v	NOUN
ejpam-3266	356	22	=	=	SYM
ejpam-3266	356	23	ba	ba	PROPN
ejpam-3266	356	24	and	and	CCONJ
ejpam-3266	356	25	(	(	PUNCT
ejpam-3266	356	26	ab	ab	PROPN
ejpam-3266	356	27	,	,	PUNCT
ejpam-3266	356	28	ba	ba	PROPN
ejpam-3266	356	29	)	)	PUNCT
ejpam-3266	356	30	∈	∈	PROPN
ejpam-3266	356	31	σ	σ	PROPN
ejpam-3266	356	32	,	,	PUNCT
ejpam-3266	356	33	thus	thus	ADV
ejpam-3266	356	34	we	we	PRON
ejpam-3266	356	35	get	get	VERB
ejpam-3266	356	36	(	(	PUNCT
ejpam-3266	356	37	u	u	NOUN
ejpam-3266	356	38	,	,	PUNCT
ejpam-3266	356	39	v	v	NOUN
ejpam-3266	356	40	)	)	PUNCT
ejpam-3266	356	41	∈	∈	PROPN
ejpam-3266	356	42	σ	σ	NOUN
ejpam-3266	357	1	and	and	CCONJ
ejpam-3266	357	2	so	so	ADV
ejpam-3266	357	3	σ	σ	PROPN
ejpam-3266	357	4	is	be	AUX
ejpam-3266	357	5	a	a	DET
ejpam-3266	357	6	semilattice	semilattice	NOUN
ejpam-3266	357	7	congruence	congruence	NOUN
ejpam-3266	357	8	on	on	ADP
ejpam-3266	357	9	(	(	PUNCT
ejpam-3266	357	10	s	s	NOUN
ejpam-3266	357	11	,	,	PUNCT
ejpam-3266	357	12	◦	◦	NOUN
ejpam-3266	357	13	,	,	PUNCT
ejpam-3266	357	14	≤	≤	NUM
ejpam-3266	357	15	)	)	PUNCT
ejpam-3266	357	16	.	.	PUNCT
ejpam-3266	358	1	let	let	VERB
ejpam-3266	358	2	σ	σ	NOUN
ejpam-3266	358	3	be	be	AUX
ejpam-3266	358	4	a	a	DET
ejpam-3266	358	5	complete	complete	ADJ
ejpam-3266	358	6	semilattice	semilattice	NOUN
ejpam-3266	358	7	congruence	congruence	NOUN
ejpam-3266	358	8	on	on	ADP
ejpam-3266	358	9	(	(	PUNCT
ejpam-3266	358	10	s	s	X
ejpam-3266	358	11	,	,	PUNCT
ejpam-3266	358	12	·	·	PUNCT
ejpam-3266	358	13	,	,	PUNCT
ejpam-3266	358	14	≤	≤	NUM
ejpam-3266	358	15	)	)	PUNCT
ejpam-3266	358	16	,	,	PUNCT
ejpam-3266	358	17	a	a	DET
ejpam-3266	358	18	≤	≤	NUM
ejpam-3266	358	19	b	b	NUM
ejpam-3266	358	20	,	,	PUNCT
ejpam-3266	358	21	and	and	CCONJ
ejpam-3266	358	22	u	u	PROPN
ejpam-3266	358	23	∈	∈	PROPN
ejpam-3266	358	24	a	a	DET
ejpam-3266	358	25	◦	◦	NOUN
ejpam-3266	358	26	b.	b.	NOUN
ejpam-3266	358	27	since	since	SCONJ
ejpam-3266	358	28	u	u	PROPN
ejpam-3266	358	29	=	=	PROPN
ejpam-3266	358	30	ab	ab	PROPN
ejpam-3266	358	31	and	and	CCONJ
ejpam-3266	358	32	n.	n.	PROPN
ejpam-3266	358	33	kehayopulu	kehayopulu	PROPN
ejpam-3266	358	34	/	/	SYM
ejpam-3266	358	35	eur	eur	PROPN
ejpam-3266	358	36	.	.	PUNCT
ejpam-3266	359	1	j.	j.	PROPN
ejpam-3266	359	2	pure	pure	PROPN
ejpam-3266	359	3	appl	appl	PROPN
ejpam-3266	359	4	.	.	PROPN
ejpam-3266	359	5	math	math	PROPN
ejpam-3266	359	6	,	,	PUNCT
ejpam-3266	359	7	11	11	NUM
ejpam-3266	359	8	(	(	PUNCT
ejpam-3266	359	9	2	2	NUM
ejpam-3266	359	10	)	)	PUNCT
ejpam-3266	359	11	(	(	PUNCT
ejpam-3266	359	12	2018	2018	NUM
ejpam-3266	359	13	)	)	PUNCT
ejpam-3266	359	14	,	,	PUNCT
ejpam-3266	359	15	476	476	NUM
ejpam-3266	359	16	-	-	SYM
ejpam-3266	359	17	492	492	NUM
ejpam-3266	359	18	485	485	NUM
ejpam-3266	359	19	a	a	DET
ejpam-3266	359	20	≤	≤	NUM
ejpam-3266	359	21	b	b	NOUN
ejpam-3266	359	22	,	,	PUNCT
ejpam-3266	359	23	we	we	PRON
ejpam-3266	359	24	have	have	AUX
ejpam-3266	359	25	(	(	PUNCT
ejpam-3266	359	26	a	a	PRON
ejpam-3266	359	27	,	,	PUNCT
ejpam-3266	359	28	ab	ab	NOUN
ejpam-3266	359	29	)	)	PUNCT
ejpam-3266	359	30	∈	∈	PROPN
ejpam-3266	359	31	σ	σ	PROPN
ejpam-3266	359	32	,	,	PUNCT
ejpam-3266	359	33	then	then	ADV
ejpam-3266	359	34	(	(	PUNCT
ejpam-3266	359	35	a	a	DET
ejpam-3266	359	36	,	,	PUNCT
ejpam-3266	359	37	u	u	NOUN
ejpam-3266	359	38	)	)	PUNCT
ejpam-3266	359	39	∈	∈	PROPN
ejpam-3266	359	40	σ	σ	NOUN
ejpam-3266	359	41	and	and	CCONJ
ejpam-3266	359	42	so	so	ADV
ejpam-3266	359	43	σ	σ	PROPN
ejpam-3266	359	44	is	be	AUX
ejpam-3266	359	45	a	a	DET
ejpam-3266	359	46	complete	complete	ADJ
ejpam-3266	359	47	semilattice	semilattice	NOUN
ejpam-3266	359	48	congruence	congruence	NOUN
ejpam-3266	359	49	on	on	ADP
ejpam-3266	359	50	(	(	PUNCT
ejpam-3266	359	51	s	s	NOUN
ejpam-3266	359	52	,	,	PUNCT
ejpam-3266	359	53	◦	◦	NOUN
ejpam-3266	359	54	,	,	PUNCT
ejpam-3266	359	55	≤	≤	NUM
ejpam-3266	359	56	)	)	PUNCT
ejpam-3266	359	57	.	.	PUNCT
ejpam-3266	360	1	let	let	VERB
ejpam-3266	360	2	σ	σ	NOUN
ejpam-3266	360	3	be	be	AUX
ejpam-3266	360	4	a	a	DET
ejpam-3266	360	5	semilattice	semilattice	NOUN
ejpam-3266	360	6	congruence	congruence	NOUN
ejpam-3266	360	7	on	on	ADP
ejpam-3266	360	8	(	(	PUNCT
ejpam-3266	360	9	s	s	NOUN
ejpam-3266	360	10	,	,	PUNCT
ejpam-3266	360	11	◦	◦	NOUN
ejpam-3266	360	12	,	,	PUNCT
ejpam-3266	360	13	≤	≤	NUM
ejpam-3266	360	14	)	)	PUNCT
ejpam-3266	360	15	.	.	PUNCT
ejpam-3266	361	1	if	if	SCONJ
ejpam-3266	361	2	(	(	PUNCT
ejpam-3266	361	3	a	a	PRON
ejpam-3266	361	4	,	,	PUNCT
ejpam-3266	361	5	b	b	NOUN
ejpam-3266	361	6	)	)	PUNCT
ejpam-3266	361	7	∈	∈	PROPN
ejpam-3266	361	8	σ	σ	NOUN
ejpam-3266	361	9	and	and	CCONJ
ejpam-3266	361	10	c	c	PROPN
ejpam-3266	361	11	∈	∈	PROPN
ejpam-3266	361	12	s	s	VERB
ejpam-3266	361	13	then	then	ADV
ejpam-3266	361	14	,	,	PUNCT
ejpam-3266	361	15	since	since	SCONJ
ejpam-3266	361	16	(	(	PUNCT
ejpam-3266	361	17	a	a	DET
ejpam-3266	361	18	◦	◦	NOUN
ejpam-3266	361	19	c	c	NOUN
ejpam-3266	361	20	,	,	PUNCT
ejpam-3266	361	21	b	b	X
ejpam-3266	361	22	◦	◦	NOUN
ejpam-3266	361	23	c	c	NOUN
ejpam-3266	361	24	)	)	PUNCT
ejpam-3266	361	25	∈	∈	PROPN
ejpam-3266	361	26	σ	σ	PROPN
ejpam-3266	361	27	,	,	PUNCT
ejpam-3266	361	28	ac	ac	PROPN
ejpam-3266	361	29	∈	∈	PROPN
ejpam-3266	361	30	a	a	DET
ejpam-3266	361	31	◦	◦	NOUN
ejpam-3266	361	32	c	c	NOUN
ejpam-3266	361	33	and	and	CCONJ
ejpam-3266	361	34	bc	bc	PROPN
ejpam-3266	361	35	∈	∈	PROPN
ejpam-3266	361	36	b	b	PROPN
ejpam-3266	361	37	◦	◦	NOUN
ejpam-3266	361	38	c	c	X
ejpam-3266	361	39	,	,	PUNCT
ejpam-3266	361	40	we	we	PRON
ejpam-3266	361	41	have	have	AUX
ejpam-3266	361	42	(	(	PUNCT
ejpam-3266	361	43	ac	ac	PROPN
ejpam-3266	361	44	,	,	PUNCT
ejpam-3266	361	45	bc	bc	PROPN
ejpam-3266	361	46	)	)	PUNCT
ejpam-3266	361	47	∈	∈	PROPN
ejpam-3266	361	48	σ	σ	PROPN
ejpam-3266	361	49	.	.	PUNCT
ejpam-3266	362	1	similarly	similarly	ADV
ejpam-3266	362	2	σ	σ	PROPN
ejpam-3266	362	3	is	be	AUX
ejpam-3266	362	4	a	a	DET
ejpam-3266	362	5	left	left	ADJ
ejpam-3266	362	6	congruence	congruence	NOUN
ejpam-3266	362	7	on	on	ADP
ejpam-3266	362	8	(	(	PUNCT
ejpam-3266	362	9	s	s	X
ejpam-3266	362	10	,	,	PUNCT
ejpam-3266	362	11	·	·	PUNCT
ejpam-3266	362	12	,	,	PUNCT
ejpam-3266	362	13	≤	≤	NUM
ejpam-3266	362	14	)	)	PUNCT
ejpam-3266	362	15	.	.	PUNCT
ejpam-3266	363	1	if	if	SCONJ
ejpam-3266	363	2	a	a	DET
ejpam-3266	363	3	∈	∈	PROPN
ejpam-3266	363	4	s	s	NOUN
ejpam-3266	363	5	,	,	PUNCT
ejpam-3266	363	6	then	then	ADV
ejpam-3266	363	7	(	(	PUNCT
ejpam-3266	363	8	a	a	DET
ejpam-3266	363	9	◦	◦	NOUN
ejpam-3266	363	10	a	a	PRON
ejpam-3266	363	11	,	,	PUNCT
ejpam-3266	363	12	a	a	PRON
ejpam-3266	363	13	)	)	PUNCT
ejpam-3266	363	14	∈	∈	PROPN
ejpam-3266	363	15	σ	σ	NOUN
ejpam-3266	363	16	and	and	CCONJ
ejpam-3266	363	17	,	,	PUNCT
ejpam-3266	363	18	since	since	SCONJ
ejpam-3266	363	19	a2	a2	PROPN
ejpam-3266	363	20	∈	∈	PROPN
ejpam-3266	363	21	a	a	DET
ejpam-3266	363	22	◦	◦	NOUN
ejpam-3266	363	23	a	a	X
ejpam-3266	363	24	,	,	PUNCT
ejpam-3266	363	25	we	we	PRON
ejpam-3266	363	26	have	have	VERB
ejpam-3266	363	27	(	(	PUNCT
ejpam-3266	363	28	a2	a2	PROPN
ejpam-3266	363	29	,	,	PUNCT
ejpam-3266	363	30	a	a	PRON
ejpam-3266	363	31	)	)	PUNCT
ejpam-3266	363	32	∈	∈	PROPN
ejpam-3266	363	33	σ	σ	PROPN
ejpam-3266	363	34	.	.	PUNCT
ejpam-3266	364	1	if	if	SCONJ
ejpam-3266	364	2	a	a	DET
ejpam-3266	364	3	,	,	PUNCT
ejpam-3266	364	4	b	b	PROPN
ejpam-3266	364	5	∈	∈	PROPN
ejpam-3266	364	6	s	s	NOUN
ejpam-3266	364	7	,	,	PUNCT
ejpam-3266	364	8	then	then	ADV
ejpam-3266	364	9	(	(	PUNCT
ejpam-3266	364	10	a	a	DET
ejpam-3266	364	11	◦	◦	NOUN
ejpam-3266	364	12	b	b	NUM
ejpam-3266	364	13	,	,	PUNCT
ejpam-3266	364	14	b	b	X
ejpam-3266	364	15	◦	◦	NOUN
ejpam-3266	364	16	a	a	X
ejpam-3266	364	17	)	)	PUNCT
ejpam-3266	364	18	∈	∈	PROPN
ejpam-3266	364	19	σ	σ	NOUN
ejpam-3266	364	20	and	and	CCONJ
ejpam-3266	364	21	,	,	PUNCT
ejpam-3266	364	22	since	since	SCONJ
ejpam-3266	364	23	ab	ab	PROPN
ejpam-3266	364	24	∈	∈	PROPN
ejpam-3266	364	25	a	a	DET
ejpam-3266	364	26	◦	◦	NOUN
ejpam-3266	364	27	b	b	NOUN
ejpam-3266	364	28	and	and	CCONJ
ejpam-3266	364	29	ba	ba	PROPN
ejpam-3266	364	30	∈	∈	PROPN
ejpam-3266	364	31	b	b	PROPN
ejpam-3266	364	32	◦	◦	NOUN
ejpam-3266	364	33	a	a	X
ejpam-3266	365	1	,	,	PUNCT
ejpam-3266	365	2	we	we	PRON
ejpam-3266	365	3	have	have	AUX
ejpam-3266	365	4	(	(	PUNCT
ejpam-3266	365	5	ab	ab	PROPN
ejpam-3266	365	6	,	,	PUNCT
ejpam-3266	365	7	ba	ba	PROPN
ejpam-3266	365	8	)	)	PUNCT
ejpam-3266	365	9	∈	∈	PROPN
ejpam-3266	365	10	σ	σ	PROPN
ejpam-3266	365	11	.	.	PUNCT
ejpam-3266	366	1	hence	hence	ADV
ejpam-3266	366	2	σ	σ	PROPN
ejpam-3266	366	3	is	be	AUX
ejpam-3266	366	4	a	a	DET
ejpam-3266	366	5	semilattice	semilattice	NOUN
ejpam-3266	366	6	congruence	congruence	NOUN
ejpam-3266	366	7	on	on	ADP
ejpam-3266	366	8	(	(	PUNCT
ejpam-3266	366	9	s	s	X
ejpam-3266	366	10	,	,	PUNCT
ejpam-3266	366	11	·	·	PUNCT
ejpam-3266	366	12	,	,	PUNCT
ejpam-3266	366	13	≤	≤	NUM
ejpam-3266	366	14	)	)	PUNCT
ejpam-3266	366	15	.	.	PUNCT
ejpam-3266	367	1	let	let	VERB
ejpam-3266	367	2	now	now	ADV
ejpam-3266	367	3	σ	σ	NOUN
ejpam-3266	367	4	be	be	AUX
ejpam-3266	367	5	a	a	DET
ejpam-3266	367	6	complete	complete	ADJ
ejpam-3266	367	7	semilattice	semilattice	NOUN
ejpam-3266	367	8	congruence	congruence	NOUN
ejpam-3266	367	9	on	on	ADP
ejpam-3266	367	10	(	(	PUNCT
ejpam-3266	367	11	s	s	NOUN
ejpam-3266	367	12	,	,	PUNCT
ejpam-3266	367	13	◦	◦	NOUN
ejpam-3266	367	14	,	,	PUNCT
ejpam-3266	367	15	≤	≤	NUM
ejpam-3266	367	16	)	)	PUNCT
ejpam-3266	367	17	and	and	CCONJ
ejpam-3266	367	18	a	a	DET
ejpam-3266	367	19	≤	≤	PROPN
ejpam-3266	367	20	b.	b.	PROPN
ejpam-3266	367	21	since	since	SCONJ
ejpam-3266	367	22	(	(	PUNCT
ejpam-3266	367	23	a	a	X
ejpam-3266	367	24	,	,	PUNCT
ejpam-3266	367	25	a	a	DET
ejpam-3266	367	26	◦	◦	NOUN
ejpam-3266	367	27	b	b	NOUN
ejpam-3266	367	28	)	)	PUNCT
ejpam-3266	367	29	∈	∈	PROPN
ejpam-3266	367	30	σ	σ	PROPN
ejpam-3266	367	31	and	and	CCONJ
ejpam-3266	367	32	ab	ab	PROPN
ejpam-3266	367	33	∈	∈	PROPN
ejpam-3266	367	34	a	a	DET
ejpam-3266	367	35	◦	◦	NOUN
ejpam-3266	367	36	b	b	NUM
ejpam-3266	367	37	,	,	PUNCT
ejpam-3266	367	38	we	we	PRON
ejpam-3266	367	39	have	have	VERB
ejpam-3266	367	40	(	(	PUNCT
ejpam-3266	367	41	a	a	DET
ejpam-3266	367	42	,	,	PUNCT
ejpam-3266	367	43	ab	ab	NOUN
ejpam-3266	367	44	)	)	PUNCT
ejpam-3266	367	45	∈	∈	PROPN
ejpam-3266	367	46	σ	σ	PROPN
ejpam-3266	367	47	,	,	PUNCT
ejpam-3266	367	48	so	so	SCONJ
ejpam-3266	367	49	σ	σ	PROPN
ejpam-3266	367	50	is	be	AUX
ejpam-3266	367	51	a	a	DET
ejpam-3266	367	52	complete	complete	ADJ
ejpam-3266	367	53	semilattice	semilattice	NOUN
ejpam-3266	367	54	congruence	congruence	NOUN
ejpam-3266	367	55	on	on	ADP
ejpam-3266	367	56	(	(	PUNCT
ejpam-3266	367	57	s	s	X
ejpam-3266	367	58	,	,	PUNCT
ejpam-3266	367	59	·	·	PUNCT
ejpam-3266	367	60	,	,	PUNCT
ejpam-3266	367	61	≤	≤	NUM
ejpam-3266	367	62	)	)	PUNCT
ejpam-3266	367	63	.	.	PUNCT
ejpam-3266	368	1	let	let	VERB
ejpam-3266	368	2	now	now	ADV
ejpam-3266	368	3	(	(	PUNCT
ejpam-3266	368	4	s	s	X
ejpam-3266	368	5	,	,	PUNCT
ejpam-3266	368	6	·	·	PUNCT
ejpam-3266	368	7	,	,	PUNCT
ejpam-3266	368	8	≤	≤	NUM
ejpam-3266	368	9	)	)	PUNCT
ejpam-3266	368	10	be	be	VERB
ejpam-3266	368	11	an	an	DET
ejpam-3266	368	12	ordered	order	VERB
ejpam-3266	368	13	semigroup	semigroup	NOUN
ejpam-3266	368	14	,	,	PUNCT
ejpam-3266	368	15	a	a	DET
ejpam-3266	368	16	,	,	PUNCT
ejpam-3266	368	17	b	b	NOUN
ejpam-3266	368	18	,	,	PUNCT
ejpam-3266	368	19	c	c	PROPN
ejpam-3266	368	20	∈	∈	PROPN
ejpam-3266	368	21	s	s	PART
ejpam-3266	368	22	and	and	CCONJ
ejpam-3266	368	23	x	x	PROPN
ejpam-3266	368	24	∈	∈	PROPN
ejpam-3266	368	25	{	{	PUNCT
ejpam-3266	368	26	a	a	NOUN
ejpam-3266	368	27	}	}	PUNCT
ejpam-3266	368	28	∗	∗	NOUN
ejpam-3266	368	29	(	(	PUNCT
ejpam-3266	368	30	b	b	X
ejpam-3266	368	31	◦	◦	NOUN
ejpam-3266	368	32	c	c	NOUN
ejpam-3266	368	33	)	)	PUNCT
ejpam-3266	368	34	.	.	PUNCT
ejpam-3266	369	1	then	then	ADV
ejpam-3266	369	2	x	x	X
ejpam-3266	369	3	∈	∈	PROPN
ejpam-3266	369	4	a	a	DET
ejpam-3266	369	5	◦	◦	NOUN
ejpam-3266	369	6	u	u	NOUN
ejpam-3266	369	7	for	for	ADP
ejpam-3266	369	8	some	some	DET
ejpam-3266	369	9	u	u	NOUN
ejpam-3266	369	10	∈	∈	PROPN
ejpam-3266	369	11	b	b	PROPN
ejpam-3266	369	12	◦	◦	NOUN
ejpam-3266	369	13	c	c	NOUN
ejpam-3266	369	14	,	,	PUNCT
ejpam-3266	369	15	then	then	ADV
ejpam-3266	369	16	x	x	ADP
ejpam-3266	369	17	=	=	PRON
ejpam-3266	369	18	au	au	X
ejpam-3266	369	19	and	and	CCONJ
ejpam-3266	369	20	u	u	X
ejpam-3266	369	21	=	=	PROPN
ejpam-3266	369	22	bc	bc	PROPN
ejpam-3266	369	23	.	.	PUNCT
ejpam-3266	370	1	then	then	ADV
ejpam-3266	370	2	we	we	PRON
ejpam-3266	370	3	have	have	VERB
ejpam-3266	370	4	x	x	X
ejpam-3266	370	5	=	=	SYM
ejpam-3266	370	6	a(bc	a(bc	PROPN
ejpam-3266	370	7	)	)	PUNCT
ejpam-3266	370	8	∈	∈	PROPN
ejpam-3266	370	9	{	{	PUNCT
ejpam-3266	370	10	a(bc	a(bc	NUM
ejpam-3266	370	11	)	)	PUNCT
ejpam-3266	370	12	}	}	PUNCT
ejpam-3266	370	13	=	=	SYM
ejpam-3266	370	14	{	{	PUNCT
ejpam-3266	370	15	(	(	PUNCT
ejpam-3266	370	16	ab)c	ab)c	NOUN
ejpam-3266	370	17	}	}	PUNCT
ejpam-3266	370	18	=	=	SYM
ejpam-3266	370	19	(	(	PUNCT
ejpam-3266	370	20	ab	ab	NOUN
ejpam-3266	370	21	)	)	PUNCT
ejpam-3266	370	22	◦	◦	NOUN
ejpam-3266	370	23	c	c	NOUN
ejpam-3266	370	24	⊆	⊆	NUM
ejpam-3266	370	25	{	{	PUNCT
ejpam-3266	370	26	ab	ab	NOUN
ejpam-3266	370	27	}	}	PUNCT
ejpam-3266	370	28	∗	∗	NOUN
ejpam-3266	370	29	{	{	PUNCT
ejpam-3266	370	30	c	c	NOUN
ejpam-3266	370	31	}	}	PUNCT
ejpam-3266	370	32	=	=	SYM
ejpam-3266	370	33	(	(	PUNCT
ejpam-3266	370	34	a	a	DET
ejpam-3266	370	35	◦	◦	NOUN
ejpam-3266	370	36	b	b	NOUN
ejpam-3266	370	37	)	)	PUNCT
ejpam-3266	370	38	∗	∗	NOUN
ejpam-3266	370	39	{	{	PUNCT
ejpam-3266	370	40	c	c	NOUN
ejpam-3266	370	41	}	}	PUNCT
ejpam-3266	370	42	,	,	PUNCT
ejpam-3266	370	43	then	then	ADV
ejpam-3266	370	44	{	{	PUNCT
ejpam-3266	370	45	a	a	DET
ejpam-3266	370	46	}	}	PUNCT
ejpam-3266	370	47	∗	∗	NOUN
ejpam-3266	370	48	(	(	PUNCT
ejpam-3266	370	49	b	b	X
ejpam-3266	370	50	◦	◦	NOUN
ejpam-3266	370	51	c	c	NOUN
ejpam-3266	370	52	)	)	PUNCT
ejpam-3266	370	53	⊆	⊆	NUM
ejpam-3266	370	54	(	(	PUNCT
ejpam-3266	370	55	a	a	DET
ejpam-3266	370	56	◦	◦	NOUN
ejpam-3266	370	57	b	b	NOUN
ejpam-3266	370	58	)	)	PUNCT
ejpam-3266	370	59	∗	∗	NOUN
ejpam-3266	370	60	{	{	PUNCT
ejpam-3266	370	61	c	c	NOUN
ejpam-3266	370	62	}	}	PUNCT
ejpam-3266	370	63	.	.	PUNCT
ejpam-3266	371	1	similarly	similarly	ADV
ejpam-3266	371	2	(	(	PUNCT
ejpam-3266	371	3	a	a	DET
ejpam-3266	371	4	◦	◦	NOUN
ejpam-3266	371	5	b	b	NOUN
ejpam-3266	371	6	)	)	PUNCT
ejpam-3266	371	7	∗	∗	NOUN
ejpam-3266	371	8	{	{	PUNCT
ejpam-3266	371	9	c	c	NOUN
ejpam-3266	371	10	}	}	PUNCT
ejpam-3266	371	11	⊆	⊆	NUM
ejpam-3266	371	12	{	{	PUNCT
ejpam-3266	371	13	a	a	DET
ejpam-3266	371	14	}	}	PUNCT
ejpam-3266	371	15	∗	∗	NOUN
ejpam-3266	371	16	(	(	PUNCT
ejpam-3266	371	17	b	b	X
ejpam-3266	371	18	◦	◦	NOUN
ejpam-3266	371	19	c	c	NOUN
ejpam-3266	371	20	)	)	PUNCT
ejpam-3266	371	21	and	and	CCONJ
ejpam-3266	371	22	so	so	ADV
ejpam-3266	371	23	(	(	PUNCT
ejpam-3266	371	24	s	s	NOUN
ejpam-3266	371	25	,	,	PUNCT
ejpam-3266	371	26	◦	◦	NOUN
ejpam-3266	371	27	,	,	PUNCT
ejpam-3266	371	28	≤	≤	NUM
ejpam-3266	371	29	)	)	PUNCT
ejpam-3266	371	30	is	be	AUX
ejpam-3266	371	31	an	an	DET
ejpam-3266	371	32	ordered	order	VERB
ejpam-3266	371	33	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	371	34	.	.	PUNCT
ejpam-3266	372	1	�	�	PROPN
ejpam-3266	372	2	definition	definition	NOUN
ejpam-3266	372	3	4.3	4.3	NUM
ejpam-3266	372	4	.	.	PUNCT
ejpam-3266	373	1	let	let	VERB
ejpam-3266	373	2	(	(	PUNCT
ejpam-3266	373	3	s	s	NOUN
ejpam-3266	373	4	,	,	PUNCT
ejpam-3266	373	5	◦	◦	NOUN
ejpam-3266	373	6	,	,	PUNCT
ejpam-3266	373	7	≤	≤	NUM
ejpam-3266	373	8	)	)	PUNCT
ejpam-3266	373	9	be	be	AUX
ejpam-3266	373	10	an	an	DET
ejpam-3266	373	11	ordered	ordered	ADJ
ejpam-3266	373	12	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	373	13	.	.	PUNCT
ejpam-3266	374	1	a	a	DET
ejpam-3266	374	2	subset	subset	NOUN
ejpam-3266	374	3	f	f	NOUN
ejpam-3266	374	4	of	of	ADP
ejpam-3266	374	5	s	s	PROPN
ejpam-3266	374	6	is	be	AUX
ejpam-3266	374	7	called	call	VERB
ejpam-3266	374	8	a	a	DET
ejpam-3266	374	9	filter	filter	NOUN
ejpam-3266	374	10	of	of	ADP
ejpam-3266	374	11	(	(	PUNCT
ejpam-3266	374	12	s	s	PROPN
ejpam-3266	374	13	,	,	PUNCT
ejpam-3266	374	14	◦	◦	NOUN
ejpam-3266	374	15	,	,	PUNCT
ejpam-3266	374	16	≤	≤	NUM
ejpam-3266	374	17	)	)	PUNCT
ejpam-3266	374	18	if	if	SCONJ
ejpam-3266	374	19	it	it	PRON
ejpam-3266	374	20	is	be	AUX
ejpam-3266	374	21	a	a	DET
ejpam-3266	374	22	filter	filter	NOUN
ejpam-3266	374	23	of	of	ADP
ejpam-3266	374	24	the	the	DET
ejpam-3266	374	25	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	374	26	(	(	PUNCT
ejpam-3266	374	27	s	s	NOUN
ejpam-3266	374	28	,	,	PUNCT
ejpam-3266	374	29	◦	◦	NOUN
ejpam-3266	374	30	)	)	PUNCT
ejpam-3266	374	31	and	and	CCONJ
ejpam-3266	374	32	,	,	PUNCT
ejpam-3266	374	33	in	in	ADP
ejpam-3266	374	34	addition	addition	NOUN
ejpam-3266	374	35	,	,	PUNCT
ejpam-3266	374	36	if	if	SCONJ
ejpam-3266	374	37	a	a	DET
ejpam-3266	374	38	∈	∈	PROPN
ejpam-3266	374	39	f	f	X
ejpam-3266	374	40	and	and	CCONJ
ejpam-3266	374	41	s	s	PROPN
ejpam-3266	374	42	3	3	NUM
ejpam-3266	374	43	b	b	NOUN
ejpam-3266	374	44	≥	≥	NOUN
ejpam-3266	374	45	a	a	DET
ejpam-3266	374	46	implies	implie	NOUN
ejpam-3266	374	47	b	b	PROPN
ejpam-3266	374	48	∈	∈	PROPN
ejpam-3266	374	49	f.	f.	PROPN
ejpam-3266	374	50	by	by	ADP
ejpam-3266	374	51	proposition	proposition	NOUN
ejpam-3266	374	52	3.4	3.4	NUM
ejpam-3266	374	53	,	,	PUNCT
ejpam-3266	374	54	we	we	PRON
ejpam-3266	374	55	have	have	VERB
ejpam-3266	374	56	the	the	DET
ejpam-3266	374	57	following	follow	VERB
ejpam-3266	374	58	proposition	proposition	NOUN
ejpam-3266	374	59	4.4	4.4	NUM
ejpam-3266	374	60	.	.	PUNCT
ejpam-3266	375	1	let	let	VERB
ejpam-3266	375	2	(	(	PUNCT
ejpam-3266	375	3	s	s	X
ejpam-3266	375	4	,	,	PUNCT
ejpam-3266	375	5	·	·	PUNCT
ejpam-3266	375	6	,	,	PUNCT
ejpam-3266	375	7	≤	≤	NUM
ejpam-3266	375	8	)	)	PUNCT
ejpam-3266	375	9	be	be	AUX
ejpam-3266	375	10	an	an	DET
ejpam-3266	375	11	ordered	order	VERB
ejpam-3266	375	12	groupoid	groupoid	NOUN
ejpam-3266	375	13	and	and	CCONJ
ejpam-3266	375	14	“	"	PUNCT
ejpam-3266	375	15	◦	◦	NOUN
ejpam-3266	375	16	”	"	PUNCT
ejpam-3266	375	17	the	the	DET
ejpam-3266	375	18	hyperoperation	hyperoperation	NOUN
ejpam-3266	375	19	on	on	ADP
ejpam-3266	375	20	s	s	PRON
ejpam-3266	375	21	defined	define	VERB
ejpam-3266	375	22	by	by	ADP
ejpam-3266	375	23	a	a	DET
ejpam-3266	375	24	◦	◦	NOUN
ejpam-3266	375	25	b	b	NOUN
ejpam-3266	375	26	:	:	PUNCT
ejpam-3266	375	27	=	=	SYM
ejpam-3266	375	28	{	{	PUNCT
ejpam-3266	375	29	ab	ab	NOUN
ejpam-3266	375	30	}	}	PUNCT
ejpam-3266	375	31	.	.	PUNCT
ejpam-3266	376	1	then	then	ADV
ejpam-3266	376	2	f	f	PROPN
ejpam-3266	376	3	is	be	AUX
ejpam-3266	376	4	a	a	DET
ejpam-3266	376	5	filter	filter	NOUN
ejpam-3266	376	6	of	of	ADP
ejpam-3266	376	7	(	(	PUNCT
ejpam-3266	376	8	s	s	PROPN
ejpam-3266	376	9	,	,	PUNCT
ejpam-3266	376	10	·	·	PUNCT
ejpam-3266	376	11	,	,	PUNCT
ejpam-3266	376	12	≤	≤	NUM
ejpam-3266	376	13	)	)	PUNCT
ejpam-3266	376	14	if	if	SCONJ
ejpam-3266	376	15	and	and	CCONJ
ejpam-3266	376	16	only	only	ADV
ejpam-3266	376	17	if	if	SCONJ
ejpam-3266	376	18	it	it	PRON
ejpam-3266	376	19	is	be	AUX
ejpam-3266	376	20	a	a	DET
ejpam-3266	376	21	filter	filter	NOUN
ejpam-3266	376	22	of	of	ADP
ejpam-3266	376	23	(	(	PUNCT
ejpam-3266	376	24	s	s	PROPN
ejpam-3266	376	25	,	,	PUNCT
ejpam-3266	376	26	◦	◦	NOUN
ejpam-3266	376	27	,	,	PUNCT
ejpam-3266	376	28	≤	≤	NUM
ejpam-3266	376	29	)	)	PUNCT
ejpam-3266	376	30	.	.	PUNCT
ejpam-3266	377	1	remark	remark	PROPN
ejpam-3266	377	2	4.5	4.5	NUM
ejpam-3266	377	3	.	.	PUNCT
ejpam-3266	378	1	according	accord	VERB
ejpam-3266	378	2	to	to	ADP
ejpam-3266	378	3	proposition	proposition	NOUN
ejpam-3266	378	4	4.4	4.4	NUM
ejpam-3266	378	5	,	,	PUNCT
ejpam-3266	378	6	if	if	SCONJ
ejpam-3266	378	7	the	the	DET
ejpam-3266	378	8	hyperoperation	hyperoperation	NOUN
ejpam-3266	378	9	“	"	PUNCT
ejpam-3266	378	10	◦	◦	NOUN
ejpam-3266	378	11	”	"	PUNCT
ejpam-3266	378	12	is	be	AUX
ejpam-3266	378	13	defined	define	VERB
ejpam-3266	378	14	by	by	ADP
ejpam-3266	378	15	a	a	DET
ejpam-3266	378	16	◦	◦	NOUN
ejpam-3266	378	17	b	b	NOUN
ejpam-3266	378	18	=	=	SYM
ejpam-3266	378	19	{	{	PUNCT
ejpam-3266	378	20	ab	ab	NOUN
ejpam-3266	378	21	}	}	PUNCT
ejpam-3266	378	22	,	,	PUNCT
ejpam-3266	378	23	then	then	ADV
ejpam-3266	378	24	the	the	DET
ejpam-3266	378	25	filters	filter	NOUN
ejpam-3266	378	26	of	of	ADP
ejpam-3266	378	27	the	the	DET
ejpam-3266	378	28	groupoid	groupoid	NOUN
ejpam-3266	378	29	(	(	PUNCT
ejpam-3266	378	30	s	s	PROPN
ejpam-3266	378	31	,	,	PUNCT
ejpam-3266	378	32	·	·	PUNCT
ejpam-3266	378	33	,	,	PUNCT
ejpam-3266	378	34	≤	≤	NUM
ejpam-3266	378	35	)	)	PUNCT
ejpam-3266	378	36	and	and	CCONJ
ejpam-3266	378	37	the	the	DET
ejpam-3266	378	38	filters	filter	NOUN
ejpam-3266	378	39	of	of	ADP
ejpam-3266	378	40	the	the	DET
ejpam-3266	378	41	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	378	42	(	(	PUNCT
ejpam-3266	378	43	s	s	NOUN
ejpam-3266	378	44	,	,	PUNCT
ejpam-3266	378	45	◦	◦	NOUN
ejpam-3266	378	46	,	,	PUNCT
ejpam-3266	378	47	≤	≤	NUM
ejpam-3266	378	48	)	)	PUNCT
ejpam-3266	378	49	are	be	AUX
ejpam-3266	378	50	the	the	DET
ejpam-3266	378	51	same	same	ADJ
ejpam-3266	378	52	.	.	PUNCT
ejpam-3266	379	1	also	also	ADV
ejpam-3266	379	2	,	,	PUNCT
ejpam-3266	379	3	by	by	ADP
ejpam-3266	379	4	proposition	proposition	NOUN
ejpam-3266	379	5	4.2	4.2	NUM
ejpam-3266	379	6	,	,	PUNCT
ejpam-3266	379	7	the	the	DET
ejpam-3266	379	8	semilattice	semilattice	NOUN
ejpam-3266	379	9	congruences	congruence	VERB
ejpam-3266	379	10	on	on	ADP
ejpam-3266	379	11	(	(	PUNCT
ejpam-3266	379	12	s	s	X
ejpam-3266	379	13	,	,	PUNCT
ejpam-3266	379	14	·	·	PUNCT
ejpam-3266	379	15	,	,	PUNCT
ejpam-3266	379	16	≤	≤	NUM
ejpam-3266	379	17	)	)	PUNCT
ejpam-3266	379	18	and	and	CCONJ
ejpam-3266	379	19	the	the	DET
ejpam-3266	379	20	semilattice	semilattice	NOUN
ejpam-3266	379	21	congruences	congruence	VERB
ejpam-3266	379	22	on	on	ADP
ejpam-3266	379	23	(	(	PUNCT
ejpam-3266	379	24	s	s	NOUN
ejpam-3266	379	25	,	,	PUNCT
ejpam-3266	379	26	◦	◦	NOUN
ejpam-3266	379	27	,	,	PUNCT
ejpam-3266	379	28	≤	≤	NUM
ejpam-3266	379	29	)	)	PUNCT
ejpam-3266	379	30	are	be	AUX
ejpam-3266	379	31	the	the	DET
ejpam-3266	379	32	same	same	ADJ
ejpam-3266	379	33	.	.	PUNCT
ejpam-3266	380	1	as	as	SCONJ
ejpam-3266	380	2	we	we	PRON
ejpam-3266	380	3	have	have	AUX
ejpam-3266	380	4	seen	see	VERB
ejpam-3266	380	5	in	in	ADP
ejpam-3266	380	6	[	[	X
ejpam-3266	380	7	11	11	NUM
ejpam-3266	380	8	]	]	PUNCT
ejpam-3266	380	9	,	,	PUNCT
ejpam-3266	380	10	in	in	ADP
ejpam-3266	380	11	an	an	DET
ejpam-3266	380	12	ordered	order	VERB
ejpam-3266	380	13	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	380	14	s	s	PROPN
ejpam-3266	380	15	,	,	PUNCT
ejpam-3266	380	16	the	the	DET
ejpam-3266	380	17	relation	relation	NOUN
ejpam-3266	380	18	n	n	CCONJ
ejpam-3266	380	19	is	be	AUX
ejpam-3266	380	20	not	not	PART
ejpam-3266	380	21	the	the	DET
ejpam-3266	380	22	least	least	ADJ
ejpam-3266	380	23	semilattice	semilattice	NOUN
ejpam-3266	380	24	congruence	congruence	NOUN
ejpam-3266	380	25	on	on	ADP
ejpam-3266	380	26	s	s	PRON
ejpam-3266	380	27	in	in	ADP
ejpam-3266	380	28	general	general	ADJ
ejpam-3266	380	29	,	,	PUNCT
ejpam-3266	380	30	so	so	SCONJ
ejpam-3266	380	31	according	accord	VERB
ejpam-3266	380	32	to	to	ADP
ejpam-3266	380	33	proposition	proposition	NOUN
ejpam-3266	380	34	4.2	4.2	NUM
ejpam-3266	380	35	,	,	PUNCT
ejpam-3266	380	36	in	in	ADP
ejpam-3266	380	37	an	an	DET
ejpam-3266	380	38	ordered	order	VERB
ejpam-3266	380	39	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	380	40	,	,	PUNCT
ejpam-3266	380	41	the	the	DET
ejpam-3266	380	42	relation	relation	NOUN
ejpam-3266	380	43	n	n	PRON
ejpam-3266	380	44	can	can	AUX
ejpam-3266	380	45	not	not	PART
ejpam-3266	380	46	be	be	AUX
ejpam-3266	380	47	the	the	DET
ejpam-3266	380	48	least	least	ADJ
ejpam-3266	380	49	semilattice	semilattice	NOUN
ejpam-3266	380	50	congruence	congruence	NOUN
ejpam-3266	380	51	as	as	ADV
ejpam-3266	380	52	well	well	ADV
ejpam-3266	380	53	,	,	PUNCT
ejpam-3266	380	54	in	in	ADP
ejpam-3266	380	55	general	general	ADJ
ejpam-3266	380	56	.	.	PUNCT
ejpam-3266	381	1	let	let	VERB
ejpam-3266	381	2	us	we	PRON
ejpam-3266	381	3	see	see	VERB
ejpam-3266	381	4	it	it	PRON
ejpam-3266	381	5	in	in	ADP
ejpam-3266	381	6	the	the	DET
ejpam-3266	381	7	following	follow	VERB
ejpam-3266	381	8	example	example	NOUN
ejpam-3266	381	9	.	.	PUNCT
ejpam-3266	382	1	example	example	NOUN
ejpam-3266	382	2	4.6	4.6	NUM
ejpam-3266	382	3	.	.	PUNCT
ejpam-3266	383	1	we	we	PRON
ejpam-3266	383	2	get	get	VERB
ejpam-3266	383	3	the	the	DET
ejpam-3266	383	4	ordered	order	VERB
ejpam-3266	383	5	semigroup	semigroup	NOUN
ejpam-3266	383	6	defined	define	VERB
ejpam-3266	383	7	in	in	ADP
ejpam-3266	383	8	[	[	X
ejpam-3266	383	9	11	11	NUM
ejpam-3266	383	10	]	]	PUNCT
ejpam-3266	383	11	with	with	ADP
ejpam-3266	383	12	the	the	DET
ejpam-3266	383	13	following	follow	VERB
ejpam-3266	383	14	table	table	NOUN
ejpam-3266	383	15	and	and	CCONJ
ejpam-3266	383	16	figure	figure	NOUN
ejpam-3266	383	17	.	.	PUNCT
ejpam-3266	383	18	·	·	PUNCT
ejpam-3266	384	1	a	a	DET
ejpam-3266	384	2	b	b	X
ejpam-3266	384	3	c	c	NOUN
ejpam-3266	385	1	d	d	X
ejpam-3266	385	2	f	f	PROPN
ejpam-3266	385	3	g	g	PROPN
ejpam-3266	385	4	a	a	DET
ejpam-3266	385	5	b	b	PROPN
ejpam-3266	385	6	b	b	PROPN
ejpam-3266	385	7	a	a	PROPN
ejpam-3266	385	8	d	d	X
ejpam-3266	385	9	a	a	DET
ejpam-3266	385	10	a	a	DET
ejpam-3266	385	11	b	b	PROPN
ejpam-3266	385	12	b	b	PROPN
ejpam-3266	385	13	b	b	PROPN
ejpam-3266	385	14	b	b	PROPN
ejpam-3266	385	15	d	d	PROPN
ejpam-3266	385	16	b	b	PROPN
ejpam-3266	385	17	b	b	PROPN
ejpam-3266	385	18	c	c	PROPN
ejpam-3266	385	19	a	a	DET
ejpam-3266	385	20	b	b	NOUN
ejpam-3266	385	21	c	c	NOUN
ejpam-3266	385	22	d	d	NOUN
ejpam-3266	385	23	c	c	NOUN
ejpam-3266	385	24	c	c	NOUN
ejpam-3266	386	1	d	d	PUNCT
ejpam-3266	386	2	d	d	PROPN
ejpam-3266	386	3	d	d	PROPN
ejpam-3266	386	4	d	d	PROPN
ejpam-3266	386	5	d	d	PROPN
ejpam-3266	386	6	d	d	PROPN
ejpam-3266	386	7	d	d	X
ejpam-3266	386	8	f	f	PROPN
ejpam-3266	386	9	a	a	DET
ejpam-3266	386	10	b	b	NOUN
ejpam-3266	386	11	c	c	NOUN
ejpam-3266	386	12	d	d	NOUN
ejpam-3266	386	13	c	c	NOUN
ejpam-3266	386	14	c	c	PROPN
ejpam-3266	386	15	g	g	PROPN
ejpam-3266	386	16	a	a	DET
ejpam-3266	386	17	b	b	NOUN
ejpam-3266	386	18	c	c	NOUN
ejpam-3266	387	1	d	d	X
ejpam-3266	387	2	f	f	PROPN
ejpam-3266	387	3	g	g	PROPN
ejpam-3266	387	4	table	table	NOUN
ejpam-3266	387	5	1	1	NUM
ejpam-3266	387	6	.	.	PUNCT
ejpam-3266	388	1	n.	n.	PROPN
ejpam-3266	388	2	kehayopulu	kehayopulu	PROPN
ejpam-3266	388	3	/	/	SYM
ejpam-3266	388	4	eur	eur	PROPN
ejpam-3266	388	5	.	.	PUNCT
ejpam-3266	389	1	j.	j.	PROPN
ejpam-3266	389	2	pure	pure	PROPN
ejpam-3266	389	3	appl	appl	PROPN
ejpam-3266	389	4	.	.	PROPN
ejpam-3266	389	5	math	math	PROPN
ejpam-3266	389	6	,	,	PUNCT
ejpam-3266	389	7	11	11	NUM
ejpam-3266	389	8	(	(	PUNCT
ejpam-3266	389	9	2	2	NUM
ejpam-3266	389	10	)	)	PUNCT
ejpam-3266	389	11	(	(	PUNCT
ejpam-3266	389	12	2018	2018	NUM
ejpam-3266	389	13	)	)	PUNCT
ejpam-3266	389	14	,	,	PUNCT
ejpam-3266	389	15	476	476	NUM
ejpam-3266	389	16	-	-	SYM
ejpam-3266	389	17	492	492	NUM
ejpam-3266	389	18	486	486	NUM
ejpam-3266	389	19	d	d	NOUN
ejpam-3266	389	20	gf	gf	NOUN
ejpam-3266	389	21	c	c	PROPN
ejpam-3266	389	22	ba	ba	PROPN
ejpam-3266	389	23	figure	figure	NOUN
ejpam-3266	389	24	1	1	NUM
ejpam-3266	389	25	.	.	PUNCT
ejpam-3266	390	1	for	for	ADP
ejpam-3266	390	2	this	this	DET
ejpam-3266	390	3	semigroup	semigroup	NOUN
ejpam-3266	390	4	,	,	PUNCT
ejpam-3266	390	5	n(a	n(a	PROPN
ejpam-3266	390	6	)	)	PUNCT
ejpam-3266	390	7	=	=	SYM
ejpam-3266	390	8	n(b	n(b	PROPN
ejpam-3266	390	9	)	)	PUNCT
ejpam-3266	391	1	=	=	PRON
ejpam-3266	391	2	{	{	PUNCT
ejpam-3266	391	3	a	a	PRON
ejpam-3266	391	4	,	,	PUNCT
ejpam-3266	391	5	b	b	NOUN
ejpam-3266	391	6	,	,	PUNCT
ejpam-3266	391	7	c	c	X
ejpam-3266	391	8	,	,	PUNCT
ejpam-3266	391	9	f	f	X
ejpam-3266	391	10	,	,	PUNCT
ejpam-3266	391	11	g	g	NOUN
ejpam-3266	391	12	}	}	PUNCT
ejpam-3266	391	13	,	,	PUNCT
ejpam-3266	391	14	n(c	n(c	NOUN
ejpam-3266	391	15	)	)	PUNCT
ejpam-3266	391	16	=	=	SYM
ejpam-3266	391	17	n(f	n(f	PROPN
ejpam-3266	391	18	)	)	PUNCT
ejpam-3266	391	19	=	=	SYM
ejpam-3266	391	20	n(g	n(g	NUM
ejpam-3266	391	21	)	)	PUNCT
ejpam-3266	391	22	=	=	PRON
ejpam-3266	391	23	{	{	PUNCT
ejpam-3266	391	24	c	c	NOUN
ejpam-3266	391	25	,	,	PUNCT
ejpam-3266	391	26	f	f	PROPN
ejpam-3266	391	27	,	,	PUNCT
ejpam-3266	391	28	g	g	NOUN
ejpam-3266	391	29	}	}	PUNCT
ejpam-3266	391	30	and	and	CCONJ
ejpam-3266	391	31	n(d	n(d	NUM
ejpam-3266	391	32	)	)	PUNCT
ejpam-3266	391	33	=	=	VERB
ejpam-3266	392	1	s.	s.	PROPN
ejpam-3266	392	2	we	we	PRON
ejpam-3266	392	3	consider	consider	VERB
ejpam-3266	392	4	the	the	DET
ejpam-3266	392	5	semilattice	semilattice	NOUN
ejpam-3266	392	6	congruences	congruence	VERB
ejpam-3266	392	7	on	on	ADP
ejpam-3266	392	8	s.	s.	PROPN
ejpam-3266	392	9	they	they	PRON
ejpam-3266	392	10	are	be	AUX
ejpam-3266	392	11	eight	eight	NUM
ejpam-3266	392	12	and	and	CCONJ
ejpam-3266	392	13	they	they	PRON
ejpam-3266	392	14	are	be	AUX
ejpam-3266	392	15	the	the	DET
ejpam-3266	392	16	following	follow	VERB
ejpam-3266	392	17	:	:	PUNCT
ejpam-3266	392	18	σ1	σ1	NOUN
ejpam-3266	392	19	=	=	SYM
ejpam-3266	392	20	{	{	PUNCT
ejpam-3266	392	21	(	(	PUNCT
ejpam-3266	392	22	a	a	PRON
ejpam-3266	392	23	,	,	PUNCT
ejpam-3266	392	24	a	a	NOUN
ejpam-3266	392	25	)	)	PUNCT
ejpam-3266	392	26	,	,	PUNCT
ejpam-3266	392	27	(	(	PUNCT
ejpam-3266	392	28	a	a	DET
ejpam-3266	392	29	,	,	PUNCT
ejpam-3266	392	30	b	b	NOUN
ejpam-3266	392	31	)	)	PUNCT
ejpam-3266	392	32	,	,	PUNCT
ejpam-3266	392	33	(	(	PUNCT
ejpam-3266	392	34	b	b	X
ejpam-3266	392	35	,	,	PUNCT
ejpam-3266	392	36	a	a	PRON
ejpam-3266	392	37	)	)	PUNCT
ejpam-3266	392	38	,	,	PUNCT
ejpam-3266	392	39	(	(	PUNCT
ejpam-3266	392	40	b	b	X
ejpam-3266	392	41	,	,	PUNCT
ejpam-3266	392	42	b	b	NOUN
ejpam-3266	392	43	)	)	PUNCT
ejpam-3266	392	44	,	,	PUNCT
ejpam-3266	392	45	(	(	PUNCT
ejpam-3266	392	46	c	c	X
ejpam-3266	392	47	,	,	PUNCT
ejpam-3266	392	48	c	c	NOUN
ejpam-3266	392	49	)	)	PUNCT
ejpam-3266	392	50	,	,	PUNCT
ejpam-3266	392	51	(	(	PUNCT
ejpam-3266	392	52	c	c	X
ejpam-3266	392	53	,	,	PUNCT
ejpam-3266	392	54	f	f	NOUN
ejpam-3266	392	55	)	)	PUNCT
ejpam-3266	392	56	,	,	PUNCT
ejpam-3266	392	57	(	(	PUNCT
ejpam-3266	392	58	d	d	X
ejpam-3266	392	59	,	,	PUNCT
ejpam-3266	392	60	d	d	NOUN
ejpam-3266	392	61	)	)	PUNCT
ejpam-3266	392	62	,	,	PUNCT
ejpam-3266	392	63	(	(	PUNCT
ejpam-3266	392	64	f	f	X
ejpam-3266	392	65	,	,	PUNCT
ejpam-3266	392	66	c	c	NOUN
ejpam-3266	392	67	)	)	PUNCT
ejpam-3266	392	68	,	,	PUNCT
ejpam-3266	392	69	(	(	PUNCT
ejpam-3266	392	70	f	f	X
ejpam-3266	392	71	,	,	PUNCT
ejpam-3266	392	72	f	f	PROPN
ejpam-3266	392	73	)	)	PUNCT
ejpam-3266	392	74	,	,	PUNCT
ejpam-3266	392	75	(	(	PUNCT
ejpam-3266	392	76	g	g	NOUN
ejpam-3266	392	77	,	,	PUNCT
ejpam-3266	392	78	g	g	NOUN
ejpam-3266	392	79	)	)	PUNCT
ejpam-3266	392	80	}	}	PUNCT
ejpam-3266	392	81	.	.	PUNCT
ejpam-3266	393	1	σ2	σ2	NOUN
ejpam-3266	393	2	=	=	SYM
ejpam-3266	393	3	{	{	PUNCT
ejpam-3266	393	4	(	(	PUNCT
ejpam-3266	393	5	a	a	PRON
ejpam-3266	393	6	,	,	PUNCT
ejpam-3266	393	7	a	a	NOUN
ejpam-3266	393	8	)	)	PUNCT
ejpam-3266	393	9	,	,	PUNCT
ejpam-3266	393	10	(	(	PUNCT
ejpam-3266	393	11	a	a	DET
ejpam-3266	393	12	,	,	PUNCT
ejpam-3266	393	13	b	b	NOUN
ejpam-3266	393	14	)	)	PUNCT
ejpam-3266	393	15	,	,	PUNCT
ejpam-3266	393	16	(	(	PUNCT
ejpam-3266	393	17	b	b	X
ejpam-3266	393	18	,	,	PUNCT
ejpam-3266	393	19	a	a	PRON
ejpam-3266	393	20	)	)	PUNCT
ejpam-3266	393	21	,	,	PUNCT
ejpam-3266	393	22	(	(	PUNCT
ejpam-3266	393	23	b	b	X
ejpam-3266	393	24	,	,	PUNCT
ejpam-3266	393	25	b	b	NOUN
ejpam-3266	393	26	)	)	PUNCT
ejpam-3266	393	27	,	,	PUNCT
ejpam-3266	393	28	(	(	PUNCT
ejpam-3266	393	29	c	c	X
ejpam-3266	393	30	,	,	PUNCT
ejpam-3266	393	31	c	c	NOUN
ejpam-3266	393	32	)	)	PUNCT
ejpam-3266	393	33	,	,	PUNCT
ejpam-3266	393	34	(	(	PUNCT
ejpam-3266	393	35	c	c	X
ejpam-3266	393	36	,	,	PUNCT
ejpam-3266	393	37	f	f	NOUN
ejpam-3266	393	38	)	)	PUNCT
ejpam-3266	393	39	,	,	PUNCT
ejpam-3266	393	40	(	(	PUNCT
ejpam-3266	393	41	c	c	X
ejpam-3266	393	42	,	,	PUNCT
ejpam-3266	393	43	g	g	NOUN
ejpam-3266	393	44	)	)	PUNCT
ejpam-3266	393	45	,	,	PUNCT
ejpam-3266	393	46	(	(	PUNCT
ejpam-3266	393	47	d	d	X
ejpam-3266	393	48	,	,	PUNCT
ejpam-3266	393	49	d	d	NOUN
ejpam-3266	393	50	)	)	PUNCT
ejpam-3266	393	51	,	,	PUNCT
ejpam-3266	393	52	(	(	PUNCT
ejpam-3266	393	53	f	f	X
ejpam-3266	393	54	,	,	PUNCT
ejpam-3266	393	55	c	c	NOUN
ejpam-3266	393	56	)	)	PUNCT
ejpam-3266	393	57	,	,	PUNCT
ejpam-3266	393	58	(	(	PUNCT
ejpam-3266	393	59	f	f	X
ejpam-3266	393	60	,	,	PUNCT
ejpam-3266	393	61	f	f	PROPN
ejpam-3266	393	62	)	)	PUNCT
ejpam-3266	393	63	,	,	PUNCT
ejpam-3266	393	64	(	(	PUNCT
ejpam-3266	393	65	f	f	X
ejpam-3266	393	66	,	,	PUNCT
ejpam-3266	393	67	g	g	PROPN
ejpam-3266	393	68	)	)	PUNCT
ejpam-3266	393	69	,	,	PUNCT
ejpam-3266	393	70	(	(	PUNCT
ejpam-3266	393	71	g	g	NOUN
ejpam-3266	393	72	,	,	PUNCT
ejpam-3266	393	73	c	c	NOUN
ejpam-3266	393	74	)	)	PUNCT
ejpam-3266	393	75	,	,	PUNCT
ejpam-3266	393	76	(	(	PUNCT
ejpam-3266	393	77	g	g	NOUN
ejpam-3266	393	78	,	,	PUNCT
ejpam-3266	393	79	f	f	PROPN
ejpam-3266	393	80	)	)	PUNCT
ejpam-3266	393	81	,	,	PUNCT
ejpam-3266	393	82	(	(	PUNCT
ejpam-3266	393	83	g	g	NOUN
ejpam-3266	393	84	,	,	PUNCT
ejpam-3266	393	85	g	g	NOUN
ejpam-3266	393	86	)	)	PUNCT
ejpam-3266	393	87	}	}	PUNCT
ejpam-3266	393	88	=	=	SYM
ejpam-3266	393	89	n	n	X
ejpam-3266	393	90	.	.	PUNCT
ejpam-3266	394	1	σ3	σ3	PROPN
ejpam-3266	394	2	=	=	PRON
ejpam-3266	394	3	{	{	PUNCT
ejpam-3266	394	4	(	(	PUNCT
ejpam-3266	394	5	a	a	PRON
ejpam-3266	394	6	,	,	PUNCT
ejpam-3266	394	7	a	a	NOUN
ejpam-3266	394	8	)	)	PUNCT
ejpam-3266	394	9	,	,	PUNCT
ejpam-3266	394	10	(	(	PUNCT
ejpam-3266	394	11	a	a	DET
ejpam-3266	394	12	,	,	PUNCT
ejpam-3266	394	13	b	b	NOUN
ejpam-3266	394	14	)	)	PUNCT
ejpam-3266	394	15	,	,	PUNCT
ejpam-3266	394	16	(	(	PUNCT
ejpam-3266	394	17	a	a	DET
ejpam-3266	394	18	,	,	PUNCT
ejpam-3266	394	19	d	d	NOUN
ejpam-3266	394	20	)	)	PUNCT
ejpam-3266	394	21	,	,	PUNCT
ejpam-3266	394	22	(	(	PUNCT
ejpam-3266	394	23	b	b	X
ejpam-3266	394	24	,	,	PUNCT
ejpam-3266	394	25	a	a	PRON
ejpam-3266	394	26	)	)	PUNCT
ejpam-3266	394	27	,	,	PUNCT
ejpam-3266	394	28	(	(	PUNCT
ejpam-3266	394	29	b	b	X
ejpam-3266	394	30	,	,	PUNCT
ejpam-3266	394	31	b	b	NOUN
ejpam-3266	394	32	)	)	PUNCT
ejpam-3266	394	33	,	,	PUNCT
ejpam-3266	394	34	(	(	PUNCT
ejpam-3266	394	35	b	b	X
ejpam-3266	394	36	,	,	PUNCT
ejpam-3266	394	37	d	d	NOUN
ejpam-3266	394	38	)	)	PUNCT
ejpam-3266	394	39	,	,	PUNCT
ejpam-3266	394	40	(	(	PUNCT
ejpam-3266	394	41	c	c	X
ejpam-3266	394	42	,	,	PUNCT
ejpam-3266	394	43	c	c	NOUN
ejpam-3266	394	44	)	)	PUNCT
ejpam-3266	394	45	,	,	PUNCT
ejpam-3266	394	46	(	(	PUNCT
ejpam-3266	394	47	c	c	X
ejpam-3266	394	48	,	,	PUNCT
ejpam-3266	394	49	f	f	NOUN
ejpam-3266	394	50	)	)	PUNCT
ejpam-3266	394	51	,	,	PUNCT
ejpam-3266	394	52	(	(	PUNCT
ejpam-3266	394	53	d	d	X
ejpam-3266	394	54	,	,	PUNCT
ejpam-3266	394	55	a	a	NOUN
ejpam-3266	394	56	)	)	PUNCT
ejpam-3266	394	57	,	,	PUNCT
ejpam-3266	394	58	(	(	PUNCT
ejpam-3266	394	59	d	d	X
ejpam-3266	394	60	,	,	PUNCT
ejpam-3266	394	61	b	b	NOUN
ejpam-3266	394	62	)	)	PUNCT
ejpam-3266	394	63	,	,	PUNCT
ejpam-3266	394	64	(	(	PUNCT
ejpam-3266	394	65	d	d	X
ejpam-3266	394	66	,	,	PUNCT
ejpam-3266	394	67	d	d	NOUN
ejpam-3266	394	68	)	)	PUNCT
ejpam-3266	394	69	,	,	PUNCT
ejpam-3266	394	70	(	(	PUNCT
ejpam-3266	394	71	f	f	X
ejpam-3266	394	72	,	,	PUNCT
ejpam-3266	394	73	c	c	NOUN
ejpam-3266	394	74	)	)	PUNCT
ejpam-3266	394	75	,	,	PUNCT
ejpam-3266	394	76	(	(	PUNCT
ejpam-3266	394	77	f	f	X
ejpam-3266	394	78	,	,	PUNCT
ejpam-3266	394	79	f	f	PROPN
ejpam-3266	394	80	)	)	PUNCT
ejpam-3266	394	81	,	,	PUNCT
ejpam-3266	394	82	(	(	PUNCT
ejpam-3266	394	83	g	g	NOUN
ejpam-3266	394	84	,	,	PUNCT
ejpam-3266	394	85	g	g	NOUN
ejpam-3266	394	86	)	)	PUNCT
ejpam-3266	394	87	}	}	PUNCT
ejpam-3266	394	88	.	.	PUNCT
ejpam-3266	395	1	σ4	σ4	NOUN
ejpam-3266	395	2	=	=	SYM
ejpam-3266	395	3	{	{	PUNCT
ejpam-3266	395	4	(	(	PUNCT
ejpam-3266	395	5	a	a	PRON
ejpam-3266	395	6	,	,	PUNCT
ejpam-3266	395	7	a	a	NOUN
ejpam-3266	395	8	)	)	PUNCT
ejpam-3266	395	9	,	,	PUNCT
ejpam-3266	395	10	(	(	PUNCT
ejpam-3266	395	11	a	a	DET
ejpam-3266	395	12	,	,	PUNCT
ejpam-3266	395	13	b	b	NOUN
ejpam-3266	395	14	)	)	PUNCT
ejpam-3266	395	15	,	,	PUNCT
ejpam-3266	395	16	(	(	PUNCT
ejpam-3266	395	17	a	a	PRON
ejpam-3266	395	18	,	,	PUNCT
ejpam-3266	395	19	c	c	NOUN
ejpam-3266	395	20	)	)	PUNCT
ejpam-3266	395	21	,	,	PUNCT
ejpam-3266	395	22	(	(	PUNCT
ejpam-3266	395	23	a	a	X
ejpam-3266	395	24	,	,	PUNCT
ejpam-3266	395	25	f	f	NOUN
ejpam-3266	395	26	)	)	PUNCT
ejpam-3266	395	27	,	,	PUNCT
ejpam-3266	395	28	(	(	PUNCT
ejpam-3266	395	29	b	b	X
ejpam-3266	395	30	,	,	PUNCT
ejpam-3266	395	31	a	a	PRON
ejpam-3266	395	32	)	)	PUNCT
ejpam-3266	395	33	,	,	PUNCT
ejpam-3266	395	34	(	(	PUNCT
ejpam-3266	395	35	b	b	X
ejpam-3266	395	36	,	,	PUNCT
ejpam-3266	395	37	b	b	NOUN
ejpam-3266	395	38	)	)	PUNCT
ejpam-3266	395	39	,	,	PUNCT
ejpam-3266	395	40	(	(	PUNCT
ejpam-3266	395	41	b	b	X
ejpam-3266	395	42	,	,	PUNCT
ejpam-3266	395	43	c	c	NOUN
ejpam-3266	395	44	)	)	PUNCT
ejpam-3266	395	45	,	,	PUNCT
ejpam-3266	395	46	(	(	PUNCT
ejpam-3266	395	47	b	b	X
ejpam-3266	395	48	,	,	PUNCT
ejpam-3266	395	49	f	f	PROPN
ejpam-3266	395	50	)	)	PUNCT
ejpam-3266	395	51	,	,	PUNCT
ejpam-3266	395	52	(	(	PUNCT
ejpam-3266	395	53	c	c	X
ejpam-3266	395	54	,	,	PUNCT
ejpam-3266	395	55	a	a	NOUN
ejpam-3266	395	56	)	)	PUNCT
ejpam-3266	395	57	,	,	PUNCT
ejpam-3266	395	58	(	(	PUNCT
ejpam-3266	395	59	c	c	X
ejpam-3266	395	60	,	,	PUNCT
ejpam-3266	395	61	b	b	NOUN
ejpam-3266	395	62	)	)	PUNCT
ejpam-3266	395	63	,	,	PUNCT
ejpam-3266	395	64	(	(	PUNCT
ejpam-3266	395	65	c	c	X
ejpam-3266	395	66	,	,	PUNCT
ejpam-3266	395	67	c	c	NOUN
ejpam-3266	395	68	)	)	PUNCT
ejpam-3266	395	69	,	,	PUNCT
ejpam-3266	395	70	(	(	PUNCT
ejpam-3266	395	71	c	c	X
ejpam-3266	395	72	,	,	PUNCT
ejpam-3266	395	73	f	f	NOUN
ejpam-3266	395	74	)	)	PUNCT
ejpam-3266	395	75	,	,	PUNCT
ejpam-3266	395	76	(	(	PUNCT
ejpam-3266	395	77	d	d	X
ejpam-3266	395	78	,	,	PUNCT
ejpam-3266	395	79	d	d	NOUN
ejpam-3266	395	80	)	)	PUNCT
ejpam-3266	395	81	,	,	PUNCT
ejpam-3266	395	82	(	(	PUNCT
ejpam-3266	395	83	f	f	X
ejpam-3266	395	84	,	,	PUNCT
ejpam-3266	395	85	a	a	NOUN
ejpam-3266	395	86	)	)	PUNCT
ejpam-3266	395	87	,	,	PUNCT
ejpam-3266	395	88	(	(	PUNCT
ejpam-3266	395	89	f	f	X
ejpam-3266	395	90	,	,	PUNCT
ejpam-3266	395	91	b	b	NOUN
ejpam-3266	395	92	)	)	PUNCT
ejpam-3266	395	93	,	,	PUNCT
ejpam-3266	395	94	(	(	PUNCT
ejpam-3266	395	95	f	f	X
ejpam-3266	395	96	,	,	PUNCT
ejpam-3266	395	97	c	c	NOUN
ejpam-3266	395	98	)	)	PUNCT
ejpam-3266	395	99	,	,	PUNCT
ejpam-3266	395	100	(	(	PUNCT
ejpam-3266	395	101	f	f	X
ejpam-3266	395	102	,	,	PUNCT
ejpam-3266	395	103	f	f	PROPN
ejpam-3266	395	104	)	)	PUNCT
ejpam-3266	395	105	,	,	PUNCT
ejpam-3266	395	106	(	(	PUNCT
ejpam-3266	395	107	g	g	NOUN
ejpam-3266	395	108	,	,	PUNCT
ejpam-3266	395	109	g	g	NOUN
ejpam-3266	395	110	)	)	PUNCT
ejpam-3266	395	111	}	}	PUNCT
ejpam-3266	395	112	.	.	PUNCT
ejpam-3266	396	1	σ5	σ5	PROPN
ejpam-3266	396	2	=	=	PRON
ejpam-3266	396	3	{	{	PUNCT
ejpam-3266	396	4	(	(	PUNCT
ejpam-3266	396	5	a	a	PRON
ejpam-3266	396	6	,	,	PUNCT
ejpam-3266	396	7	a	a	NOUN
ejpam-3266	396	8	)	)	PUNCT
ejpam-3266	396	9	,	,	PUNCT
ejpam-3266	396	10	(	(	PUNCT
ejpam-3266	396	11	a	a	DET
ejpam-3266	396	12	,	,	PUNCT
ejpam-3266	396	13	b	b	NOUN
ejpam-3266	396	14	)	)	PUNCT
ejpam-3266	396	15	,	,	PUNCT
ejpam-3266	396	16	(	(	PUNCT
ejpam-3266	396	17	a	a	DET
ejpam-3266	396	18	,	,	PUNCT
ejpam-3266	396	19	d	d	NOUN
ejpam-3266	396	20	)	)	PUNCT
ejpam-3266	396	21	,	,	PUNCT
ejpam-3266	396	22	(	(	PUNCT
ejpam-3266	396	23	b	b	X
ejpam-3266	396	24	,	,	PUNCT
ejpam-3266	396	25	a	a	PRON
ejpam-3266	396	26	)	)	PUNCT
ejpam-3266	396	27	,	,	PUNCT
ejpam-3266	396	28	(	(	PUNCT
ejpam-3266	396	29	b	b	X
ejpam-3266	396	30	,	,	PUNCT
ejpam-3266	396	31	b	b	NOUN
ejpam-3266	396	32	)	)	PUNCT
ejpam-3266	396	33	,	,	PUNCT
ejpam-3266	396	34	(	(	PUNCT
ejpam-3266	396	35	b	b	X
ejpam-3266	396	36	,	,	PUNCT
ejpam-3266	396	37	d	d	NOUN
ejpam-3266	396	38	)	)	PUNCT
ejpam-3266	396	39	,	,	PUNCT
ejpam-3266	396	40	(	(	PUNCT
ejpam-3266	396	41	c	c	X
ejpam-3266	396	42	,	,	PUNCT
ejpam-3266	396	43	c	c	NOUN
ejpam-3266	396	44	)	)	PUNCT
ejpam-3266	396	45	,	,	PUNCT
ejpam-3266	396	46	(	(	PUNCT
ejpam-3266	396	47	c	c	X
ejpam-3266	396	48	,	,	PUNCT
ejpam-3266	396	49	f	f	NOUN
ejpam-3266	396	50	)	)	PUNCT
ejpam-3266	396	51	,	,	PUNCT
ejpam-3266	396	52	(	(	PUNCT
ejpam-3266	396	53	c	c	X
ejpam-3266	396	54	,	,	PUNCT
ejpam-3266	396	55	g	g	NOUN
ejpam-3266	396	56	)	)	PUNCT
ejpam-3266	396	57	,	,	PUNCT
ejpam-3266	396	58	(	(	PUNCT
ejpam-3266	396	59	d	d	X
ejpam-3266	396	60	,	,	PUNCT
ejpam-3266	396	61	a	a	NOUN
ejpam-3266	396	62	)	)	PUNCT
ejpam-3266	396	63	,	,	PUNCT
ejpam-3266	396	64	(	(	PUNCT
ejpam-3266	396	65	d	d	X
ejpam-3266	396	66	,	,	PUNCT
ejpam-3266	396	67	b	b	NOUN
ejpam-3266	396	68	)	)	PUNCT
ejpam-3266	396	69	,	,	PUNCT
ejpam-3266	396	70	(	(	PUNCT
ejpam-3266	396	71	d	d	X
ejpam-3266	396	72	,	,	PUNCT
ejpam-3266	396	73	d	d	NOUN
ejpam-3266	396	74	)	)	PUNCT
ejpam-3266	396	75	,	,	PUNCT
ejpam-3266	396	76	(	(	PUNCT
ejpam-3266	396	77	f	f	X
ejpam-3266	396	78	,	,	PUNCT
ejpam-3266	396	79	c	c	NOUN
ejpam-3266	396	80	)	)	PUNCT
ejpam-3266	396	81	,	,	PUNCT
ejpam-3266	396	82	(	(	PUNCT
ejpam-3266	396	83	f	f	X
ejpam-3266	396	84	,	,	PUNCT
ejpam-3266	396	85	f	f	PROPN
ejpam-3266	396	86	)	)	PUNCT
ejpam-3266	396	87	,	,	PUNCT
ejpam-3266	396	88	(	(	PUNCT
ejpam-3266	396	89	f	f	X
ejpam-3266	396	90	,	,	PUNCT
ejpam-3266	396	91	g	g	PROPN
ejpam-3266	396	92	)	)	PUNCT
ejpam-3266	396	93	,	,	PUNCT
ejpam-3266	396	94	(	(	PUNCT
ejpam-3266	396	95	g	g	NOUN
ejpam-3266	396	96	,	,	PUNCT
ejpam-3266	396	97	c	c	NOUN
ejpam-3266	396	98	)	)	PUNCT
ejpam-3266	396	99	,	,	PUNCT
ejpam-3266	396	100	(	(	PUNCT
ejpam-3266	396	101	g	g	NOUN
ejpam-3266	396	102	,	,	PUNCT
ejpam-3266	396	103	f	f	PROPN
ejpam-3266	396	104	)	)	PUNCT
ejpam-3266	396	105	,	,	PUNCT
ejpam-3266	396	106	(	(	PUNCT
ejpam-3266	396	107	g	g	NOUN
ejpam-3266	396	108	,	,	PUNCT
ejpam-3266	396	109	g	g	NOUN
ejpam-3266	396	110	)	)	PUNCT
ejpam-3266	396	111	}	}	PUNCT
ejpam-3266	396	112	.	.	PUNCT
ejpam-3266	397	1	σ6	σ6	NOUN
ejpam-3266	397	2	=	=	PRON
ejpam-3266	397	3	{	{	PUNCT
ejpam-3266	397	4	(	(	PUNCT
ejpam-3266	397	5	a	a	PRON
ejpam-3266	397	6	,	,	PUNCT
ejpam-3266	397	7	a	a	NOUN
ejpam-3266	397	8	)	)	PUNCT
ejpam-3266	397	9	,	,	PUNCT
ejpam-3266	397	10	(	(	PUNCT
ejpam-3266	397	11	a	a	DET
ejpam-3266	397	12	,	,	PUNCT
ejpam-3266	397	13	b	b	NOUN
ejpam-3266	397	14	)	)	PUNCT
ejpam-3266	397	15	,	,	PUNCT
ejpam-3266	397	16	(	(	PUNCT
ejpam-3266	397	17	a	a	DET
ejpam-3266	397	18	,	,	PUNCT
ejpam-3266	397	19	c	c	NOUN
ejpam-3266	397	20	)	)	PUNCT
ejpam-3266	397	21	,	,	PUNCT
ejpam-3266	397	22	(	(	PUNCT
ejpam-3266	397	23	a	a	DET
ejpam-3266	397	24	,	,	PUNCT
ejpam-3266	397	25	d	d	NOUN
ejpam-3266	397	26	)	)	PUNCT
ejpam-3266	397	27	,	,	PUNCT
ejpam-3266	397	28	(	(	PUNCT
ejpam-3266	397	29	a	a	X
ejpam-3266	397	30	,	,	PUNCT
ejpam-3266	397	31	f	f	NOUN
ejpam-3266	397	32	)	)	PUNCT
ejpam-3266	397	33	,	,	PUNCT
ejpam-3266	397	34	(	(	PUNCT
ejpam-3266	397	35	b	b	X
ejpam-3266	397	36	,	,	PUNCT
ejpam-3266	397	37	a	a	PRON
ejpam-3266	397	38	)	)	PUNCT
ejpam-3266	397	39	,	,	PUNCT
ejpam-3266	397	40	(	(	PUNCT
ejpam-3266	397	41	b	b	X
ejpam-3266	397	42	,	,	PUNCT
ejpam-3266	397	43	b	b	NOUN
ejpam-3266	397	44	)	)	PUNCT
ejpam-3266	397	45	,	,	PUNCT
ejpam-3266	397	46	(	(	PUNCT
ejpam-3266	397	47	b	b	X
ejpam-3266	397	48	,	,	PUNCT
ejpam-3266	397	49	c	c	NOUN
ejpam-3266	397	50	)	)	PUNCT
ejpam-3266	397	51	,	,	PUNCT
ejpam-3266	397	52	(	(	PUNCT
ejpam-3266	397	53	b	b	X
ejpam-3266	397	54	,	,	PUNCT
ejpam-3266	397	55	d	d	NOUN
ejpam-3266	397	56	)	)	PUNCT
ejpam-3266	397	57	,	,	PUNCT
ejpam-3266	397	58	(	(	PUNCT
ejpam-3266	397	59	b	b	X
ejpam-3266	397	60	,	,	PUNCT
ejpam-3266	397	61	f	f	PROPN
ejpam-3266	397	62	)	)	PUNCT
ejpam-3266	397	63	,	,	PUNCT
ejpam-3266	397	64	(	(	PUNCT
ejpam-3266	397	65	c	c	X
ejpam-3266	397	66	,	,	PUNCT
ejpam-3266	397	67	a	a	NOUN
ejpam-3266	397	68	)	)	PUNCT
ejpam-3266	397	69	,	,	PUNCT
ejpam-3266	397	70	(	(	PUNCT
ejpam-3266	397	71	c	c	X
ejpam-3266	397	72	,	,	PUNCT
ejpam-3266	397	73	b	b	NOUN
ejpam-3266	397	74	)	)	PUNCT
ejpam-3266	397	75	,	,	PUNCT
ejpam-3266	397	76	(	(	PUNCT
ejpam-3266	397	77	c	c	X
ejpam-3266	397	78	,	,	PUNCT
ejpam-3266	397	79	c	c	NOUN
ejpam-3266	397	80	)	)	PUNCT
ejpam-3266	397	81	,	,	PUNCT
ejpam-3266	397	82	(	(	PUNCT
ejpam-3266	397	83	c	c	X
ejpam-3266	397	84	,	,	PUNCT
ejpam-3266	397	85	d	d	NOUN
ejpam-3266	397	86	)	)	PUNCT
ejpam-3266	397	87	,	,	PUNCT
ejpam-3266	397	88	(	(	PUNCT
ejpam-3266	397	89	c	c	X
ejpam-3266	397	90	,	,	PUNCT
ejpam-3266	397	91	f	f	NOUN
ejpam-3266	397	92	)	)	PUNCT
ejpam-3266	397	93	,	,	PUNCT
ejpam-3266	397	94	(	(	PUNCT
ejpam-3266	397	95	d	d	X
ejpam-3266	397	96	,	,	PUNCT
ejpam-3266	397	97	a	a	NOUN
ejpam-3266	397	98	)	)	PUNCT
ejpam-3266	397	99	,	,	PUNCT
ejpam-3266	397	100	(	(	PUNCT
ejpam-3266	397	101	d	d	X
ejpam-3266	397	102	,	,	PUNCT
ejpam-3266	397	103	b	b	NOUN
ejpam-3266	397	104	)	)	PUNCT
ejpam-3266	397	105	,	,	PUNCT
ejpam-3266	397	106	(	(	PUNCT
ejpam-3266	397	107	d	d	X
ejpam-3266	397	108	,	,	PUNCT
ejpam-3266	397	109	c	c	NOUN
ejpam-3266	397	110	)	)	PUNCT
ejpam-3266	397	111	,	,	PUNCT
ejpam-3266	397	112	(	(	PUNCT
ejpam-3266	397	113	d	d	X
ejpam-3266	397	114	,	,	PUNCT
ejpam-3266	397	115	d	d	NOUN
ejpam-3266	397	116	)	)	PUNCT
ejpam-3266	397	117	,	,	PUNCT
ejpam-3266	397	118	(	(	PUNCT
ejpam-3266	397	119	d	d	X
ejpam-3266	397	120	,	,	PUNCT
ejpam-3266	397	121	f	f	NOUN
ejpam-3266	397	122	)	)	PUNCT
ejpam-3266	397	123	,	,	PUNCT
ejpam-3266	397	124	(	(	PUNCT
ejpam-3266	397	125	f	f	X
ejpam-3266	397	126	,	,	PUNCT
ejpam-3266	397	127	a	a	NOUN
ejpam-3266	397	128	)	)	PUNCT
ejpam-3266	397	129	,	,	PUNCT
ejpam-3266	397	130	(	(	PUNCT
ejpam-3266	397	131	f	f	X
ejpam-3266	397	132	,	,	PUNCT
ejpam-3266	397	133	b	b	NOUN
ejpam-3266	397	134	)	)	PUNCT
ejpam-3266	397	135	,	,	PUNCT
ejpam-3266	397	136	(	(	PUNCT
ejpam-3266	397	137	f	f	X
ejpam-3266	397	138	,	,	PUNCT
ejpam-3266	397	139	c	c	NOUN
ejpam-3266	397	140	)	)	PUNCT
ejpam-3266	397	141	,	,	PUNCT
ejpam-3266	397	142	(	(	PUNCT
ejpam-3266	397	143	f	f	X
ejpam-3266	397	144	,	,	PUNCT
ejpam-3266	397	145	d	d	NOUN
ejpam-3266	397	146	)	)	PUNCT
ejpam-3266	397	147	,	,	PUNCT
ejpam-3266	397	148	(	(	PUNCT
ejpam-3266	397	149	f	f	X
ejpam-3266	397	150	,	,	PUNCT
ejpam-3266	397	151	f	f	PROPN
ejpam-3266	397	152	)	)	PUNCT
ejpam-3266	397	153	,	,	PUNCT
ejpam-3266	397	154	(	(	PUNCT
ejpam-3266	397	155	g	g	NOUN
ejpam-3266	397	156	,	,	PUNCT
ejpam-3266	397	157	g	g	NOUN
ejpam-3266	397	158	)	)	PUNCT
ejpam-3266	397	159	}	}	PUNCT
ejpam-3266	397	160	.	.	PUNCT
ejpam-3266	398	1	σ7	σ7	VERB
ejpam-3266	398	2	=	=	SYM
ejpam-3266	398	3	{	{	PUNCT
ejpam-3266	398	4	(	(	PUNCT
ejpam-3266	398	5	a	a	PRON
ejpam-3266	398	6	,	,	PUNCT
ejpam-3266	398	7	a	a	NOUN
ejpam-3266	398	8	)	)	PUNCT
ejpam-3266	398	9	,	,	PUNCT
ejpam-3266	398	10	(	(	PUNCT
ejpam-3266	398	11	a	a	DET
ejpam-3266	398	12	,	,	PUNCT
ejpam-3266	398	13	b	b	NOUN
ejpam-3266	398	14	)	)	PUNCT
ejpam-3266	398	15	,	,	PUNCT
ejpam-3266	398	16	(	(	PUNCT
ejpam-3266	398	17	a	a	DET
ejpam-3266	398	18	,	,	PUNCT
ejpam-3266	398	19	c	c	NOUN
ejpam-3266	398	20	)	)	PUNCT
ejpam-3266	398	21	,	,	PUNCT
ejpam-3266	398	22	(	(	PUNCT
ejpam-3266	398	23	a	a	X
ejpam-3266	398	24	,	,	PUNCT
ejpam-3266	398	25	f	f	NOUN
ejpam-3266	398	26	)	)	PUNCT
ejpam-3266	398	27	,	,	PUNCT
ejpam-3266	398	28	(	(	PUNCT
ejpam-3266	398	29	a	a	X
ejpam-3266	398	30	,	,	PUNCT
ejpam-3266	398	31	g	g	NOUN
ejpam-3266	398	32	)	)	PUNCT
ejpam-3266	398	33	,	,	PUNCT
ejpam-3266	398	34	(	(	PUNCT
ejpam-3266	398	35	b	b	X
ejpam-3266	398	36	,	,	PUNCT
ejpam-3266	398	37	a	a	PRON
ejpam-3266	398	38	)	)	PUNCT
ejpam-3266	398	39	,	,	PUNCT
ejpam-3266	398	40	(	(	PUNCT
ejpam-3266	398	41	b	b	X
ejpam-3266	398	42	,	,	PUNCT
ejpam-3266	398	43	b	b	NOUN
ejpam-3266	398	44	)	)	PUNCT
ejpam-3266	398	45	,	,	PUNCT
ejpam-3266	398	46	(	(	PUNCT
ejpam-3266	398	47	b	b	X
ejpam-3266	398	48	,	,	PUNCT
ejpam-3266	398	49	c	c	NOUN
ejpam-3266	398	50	)	)	PUNCT
ejpam-3266	398	51	,	,	PUNCT
ejpam-3266	398	52	(	(	PUNCT
ejpam-3266	398	53	b	b	X
ejpam-3266	398	54	,	,	PUNCT
ejpam-3266	398	55	f	f	PROPN
ejpam-3266	398	56	)	)	PUNCT
ejpam-3266	398	57	,	,	PUNCT
ejpam-3266	398	58	(	(	PUNCT
ejpam-3266	398	59	b	b	X
ejpam-3266	398	60	,	,	PUNCT
ejpam-3266	398	61	g	g	NOUN
ejpam-3266	398	62	)	)	PUNCT
ejpam-3266	398	63	,	,	PUNCT
ejpam-3266	398	64	(	(	PUNCT
ejpam-3266	398	65	c	c	X
ejpam-3266	398	66	,	,	PUNCT
ejpam-3266	398	67	a	a	NOUN
ejpam-3266	398	68	)	)	PUNCT
ejpam-3266	398	69	,	,	PUNCT
ejpam-3266	398	70	(	(	PUNCT
ejpam-3266	398	71	c	c	X
ejpam-3266	398	72	,	,	PUNCT
ejpam-3266	398	73	b	b	NOUN
ejpam-3266	398	74	)	)	PUNCT
ejpam-3266	398	75	,	,	PUNCT
ejpam-3266	398	76	(	(	PUNCT
ejpam-3266	398	77	c	c	X
ejpam-3266	398	78	,	,	PUNCT
ejpam-3266	398	79	c	c	NOUN
ejpam-3266	398	80	)	)	PUNCT
ejpam-3266	398	81	,	,	PUNCT
ejpam-3266	398	82	(	(	PUNCT
ejpam-3266	398	83	c	c	X
ejpam-3266	398	84	,	,	PUNCT
ejpam-3266	398	85	f	f	NOUN
ejpam-3266	398	86	)	)	PUNCT
ejpam-3266	398	87	,	,	PUNCT
ejpam-3266	398	88	(	(	PUNCT
ejpam-3266	398	89	c	c	X
ejpam-3266	398	90	,	,	PUNCT
ejpam-3266	398	91	g	g	NOUN
ejpam-3266	398	92	)	)	PUNCT
ejpam-3266	398	93	,	,	PUNCT
ejpam-3266	398	94	(	(	PUNCT
ejpam-3266	398	95	d	d	X
ejpam-3266	398	96	,	,	PUNCT
ejpam-3266	398	97	d	d	NOUN
ejpam-3266	398	98	)	)	PUNCT
ejpam-3266	398	99	,	,	PUNCT
ejpam-3266	398	100	(	(	PUNCT
ejpam-3266	398	101	f	f	X
ejpam-3266	398	102	,	,	PUNCT
ejpam-3266	398	103	a	a	NOUN
ejpam-3266	398	104	)	)	PUNCT
ejpam-3266	398	105	,	,	PUNCT
ejpam-3266	398	106	(	(	PUNCT
ejpam-3266	398	107	f	f	X
ejpam-3266	398	108	,	,	PUNCT
ejpam-3266	398	109	b	b	NOUN
ejpam-3266	398	110	)	)	PUNCT
ejpam-3266	398	111	,	,	PUNCT
ejpam-3266	398	112	(	(	PUNCT
ejpam-3266	398	113	f	f	X
ejpam-3266	398	114	,	,	PUNCT
ejpam-3266	398	115	c	c	NOUN
ejpam-3266	398	116	)	)	PUNCT
ejpam-3266	398	117	,	,	PUNCT
ejpam-3266	398	118	(	(	PUNCT
ejpam-3266	398	119	f	f	X
ejpam-3266	398	120	,	,	PUNCT
ejpam-3266	398	121	f	f	PROPN
ejpam-3266	398	122	)	)	PUNCT
ejpam-3266	398	123	,	,	PUNCT
ejpam-3266	398	124	(	(	PUNCT
ejpam-3266	398	125	f	f	X
ejpam-3266	398	126	,	,	PUNCT
ejpam-3266	398	127	g	g	PROPN
ejpam-3266	398	128	)	)	PUNCT
ejpam-3266	398	129	,	,	PUNCT
ejpam-3266	398	130	(	(	PUNCT
ejpam-3266	398	131	g	g	NOUN
ejpam-3266	398	132	,	,	PUNCT
ejpam-3266	398	133	a	a	PRON
ejpam-3266	398	134	)	)	PUNCT
ejpam-3266	398	135	,	,	PUNCT
ejpam-3266	398	136	(	(	PUNCT
ejpam-3266	398	137	g	g	NOUN
ejpam-3266	398	138	,	,	PUNCT
ejpam-3266	398	139	b	b	NOUN
ejpam-3266	398	140	)	)	PUNCT
ejpam-3266	398	141	,	,	PUNCT
ejpam-3266	398	142	(	(	PUNCT
ejpam-3266	398	143	g	g	NOUN
ejpam-3266	398	144	,	,	PUNCT
ejpam-3266	398	145	c	c	NOUN
ejpam-3266	398	146	)	)	PUNCT
ejpam-3266	398	147	,	,	PUNCT
ejpam-3266	398	148	(	(	PUNCT
ejpam-3266	398	149	g	g	NOUN
ejpam-3266	398	150	,	,	PUNCT
ejpam-3266	398	151	f	f	PROPN
ejpam-3266	398	152	)	)	PUNCT
ejpam-3266	398	153	,	,	PUNCT
ejpam-3266	398	154	(	(	PUNCT
ejpam-3266	398	155	g	g	NOUN
ejpam-3266	398	156	,	,	PUNCT
ejpam-3266	398	157	g	g	NOUN
ejpam-3266	398	158	)	)	PUNCT
ejpam-3266	398	159	}	}	PUNCT
ejpam-3266	398	160	.	.	PUNCT
ejpam-3266	399	1	σ8	σ8	X
ejpam-3266	400	1	=	=	PUNCT
ejpam-3266	400	2	s	s	PART
ejpam-3266	400	3	×	×	PROPN
ejpam-3266	400	4	s.	s.	PROPN
ejpam-3266	400	5	σ1	σ1	PROPN
ejpam-3266	400	6	is	be	AUX
ejpam-3266	400	7	the	the	DET
ejpam-3266	400	8	least	least	ADJ
ejpam-3266	400	9	semilattice	semilattice	NOUN
ejpam-3266	400	10	congruence	congruence	NOUN
ejpam-3266	400	11	on	on	ADP
ejpam-3266	400	12	s	s	PROPN
ejpam-3266	400	13	,	,	PUNCT
ejpam-3266	400	14	the	the	DET
ejpam-3266	400	15	relations	relation	NOUN
ejpam-3266	400	16	σ2	σ2	PROPN
ejpam-3266	400	17	,	,	PUNCT
ejpam-3266	400	18	σ5	σ5	NOUN
ejpam-3266	400	19	,	,	PUNCT
ejpam-3266	400	20	σ7	σ7	VERB
ejpam-3266	400	21	,	,	PUNCT
ejpam-3266	400	22	σ8	σ8	PROPN
ejpam-3266	400	23	are	be	AUX
ejpam-3266	400	24	complete	complete	ADJ
ejpam-3266	400	25	semilattice	semilattice	NOUN
ejpam-3266	400	26	congruences	congruence	NOUN
ejpam-3266	400	27	on	on	ADP
ejpam-3266	400	28	s	s	PROPN
ejpam-3266	400	29	,	,	PUNCT
ejpam-3266	400	30	n	n	PRON
ejpam-3266	400	31	(=	(=	NOUN
ejpam-3266	400	32	σ2	σ2	NOUN
ejpam-3266	400	33	)	)	PUNCT
ejpam-3266	400	34	⊆	⊆	NUM
ejpam-3266	400	35	σ5	σ5	NOUN
ejpam-3266	400	36	,	,	PUNCT
ejpam-3266	400	37	σ7	σ7	PROPN
ejpam-3266	400	38	,	,	PUNCT
ejpam-3266	400	39	σ8	σ8	PROPN
ejpam-3266	400	40	,	,	PUNCT
ejpam-3266	400	41	that	that	PRON
ejpam-3266	400	42	is	be	AUX
ejpam-3266	400	43	n	n	PRON
ejpam-3266	400	44	is	be	AUX
ejpam-3266	400	45	the	the	DET
ejpam-3266	400	46	least	least	ADJ
ejpam-3266	400	47	complete	complete	ADJ
ejpam-3266	400	48	semilattice	semilattice	NOUN
ejpam-3266	400	49	congruence	congruence	NOUN
ejpam-3266	400	50	on	on	ADP
ejpam-3266	400	51	s	s	NOUN
ejpam-3266	400	52	and	and	CCONJ
ejpam-3266	400	53	σ1	σ1	PROPN
ejpam-3266	400	54	6=	6=	PROPN
ejpam-3266	400	55	n	n	PROPN
ejpam-3266	400	56	.	.	PUNCT
ejpam-3266	401	1	according	accord	VERB
ejpam-3266	401	2	to	to	ADP
ejpam-3266	401	3	proposition	proposition	NOUN
ejpam-3266	401	4	4.2	4.2	NUM
ejpam-3266	401	5	,	,	PUNCT
ejpam-3266	401	6	the	the	DET
ejpam-3266	401	7	ordered	order	VERB
ejpam-3266	401	8	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	401	9	(	(	PUNCT
ejpam-3266	401	10	s	s	NOUN
ejpam-3266	401	11	,	,	PUNCT
ejpam-3266	401	12	◦	◦	NOUN
ejpam-3266	401	13	,	,	PUNCT
ejpam-3266	401	14	≤	≤	NUM
ejpam-3266	401	15	)	)	PUNCT
ejpam-3266	401	16	defined	define	VERB
ejpam-3266	401	17	by	by	ADP
ejpam-3266	401	18	the	the	DET
ejpam-3266	401	19	table	table	NOUN
ejpam-3266	401	20	below	below	ADV
ejpam-3266	401	21	and	and	CCONJ
ejpam-3266	401	22	the	the	DET
ejpam-3266	401	23	same	same	ADJ
ejpam-3266	401	24	figure	figure	NOUN
ejpam-3266	401	25	1	1	NUM
ejpam-3266	401	26	is	be	AUX
ejpam-3266	401	27	an	an	DET
ejpam-3266	401	28	ordered	order	VERB
ejpam-3266	401	29	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	401	30	and	and	CCONJ
ejpam-3266	401	31	the	the	DET
ejpam-3266	401	32	semilattice	semilattice	NOUN
ejpam-3266	401	33	congruences	congruence	VERB
ejpam-3266	401	34	n.	n.	PROPN
ejpam-3266	401	35	kehayopulu	kehayopulu	PROPN
ejpam-3266	401	36	/	/	SYM
ejpam-3266	401	37	eur	eur	PROPN
ejpam-3266	401	38	.	.	PUNCT
ejpam-3266	402	1	j.	j.	PROPN
ejpam-3266	402	2	pure	pure	PROPN
ejpam-3266	402	3	appl	appl	PROPN
ejpam-3266	402	4	.	.	PROPN
ejpam-3266	402	5	math	math	PROPN
ejpam-3266	402	6	,	,	PUNCT
ejpam-3266	402	7	11	11	NUM
ejpam-3266	402	8	(	(	PUNCT
ejpam-3266	402	9	2	2	NUM
ejpam-3266	402	10	)	)	PUNCT
ejpam-3266	402	11	(	(	PUNCT
ejpam-3266	402	12	2018	2018	NUM
ejpam-3266	402	13	)	)	PUNCT
ejpam-3266	402	14	,	,	PUNCT
ejpam-3266	402	15	476	476	NUM
ejpam-3266	402	16	-	-	SYM
ejpam-3266	402	17	492	492	NUM
ejpam-3266	402	18	487	487	NUM
ejpam-3266	402	19	on	on	ADP
ejpam-3266	402	20	(	(	PUNCT
ejpam-3266	402	21	s	s	X
ejpam-3266	402	22	,	,	PUNCT
ejpam-3266	402	23	·	·	PUNCT
ejpam-3266	402	24	,	,	PUNCT
ejpam-3266	402	25	≤	≤	NUM
ejpam-3266	402	26	)	)	PUNCT
ejpam-3266	402	27	and	and	CCONJ
ejpam-3266	402	28	on	on	ADP
ejpam-3266	402	29	(	(	PUNCT
ejpam-3266	402	30	s	s	NOUN
ejpam-3266	402	31	,	,	PUNCT
ejpam-3266	402	32	◦	◦	NOUN
ejpam-3266	402	33	,	,	PUNCT
ejpam-3266	402	34	≤	≤	NUM
ejpam-3266	402	35	)	)	PUNCT
ejpam-3266	402	36	are	be	AUX
ejpam-3266	402	37	the	the	DET
ejpam-3266	402	38	same	same	ADJ
ejpam-3266	402	39	,	,	PUNCT
ejpam-3266	402	40	so	so	SCONJ
ejpam-3266	402	41	σ1	σ1	PROPN
ejpam-3266	402	42	is	be	AUX
ejpam-3266	402	43	the	the	DET
ejpam-3266	402	44	least	least	ADJ
ejpam-3266	402	45	semilattice	semilattice	NOUN
ejpam-3266	402	46	congruence	congruence	NOUN
ejpam-3266	402	47	on	on	ADP
ejpam-3266	402	48	(	(	PUNCT
ejpam-3266	402	49	s	s	NOUN
ejpam-3266	402	50	,	,	PUNCT
ejpam-3266	402	51	◦	◦	NOUN
ejpam-3266	402	52	,	,	PUNCT
ejpam-3266	402	53	≤	≤	NUM
ejpam-3266	402	54	)	)	PUNCT
ejpam-3266	402	55	,	,	PUNCT
ejpam-3266	402	56	n	n	PRON
ejpam-3266	402	57	is	be	AUX
ejpam-3266	402	58	the	the	DET
ejpam-3266	402	59	least	least	ADJ
ejpam-3266	402	60	complete	complete	ADJ
ejpam-3266	402	61	semilattice	semilattice	NOUN
ejpam-3266	402	62	congruence	congruence	NOUN
ejpam-3266	402	63	on	on	ADP
ejpam-3266	402	64	(	(	PUNCT
ejpam-3266	402	65	s	s	NOUN
ejpam-3266	402	66	,	,	PUNCT
ejpam-3266	402	67	◦	◦	NOUN
ejpam-3266	402	68	,	,	PUNCT
ejpam-3266	402	69	≤	≤	NUM
ejpam-3266	402	70	)	)	PUNCT
ejpam-3266	402	71	and	and	CCONJ
ejpam-3266	402	72	n	n	PRON
ejpam-3266	402	73	is	be	AUX
ejpam-3266	402	74	different	different	ADJ
ejpam-3266	402	75	than	than	ADP
ejpam-3266	402	76	σ1	σ1	PROPN
ejpam-3266	402	77	.	.	PUNCT
ejpam-3266	403	1	◦	◦	NOUN
ejpam-3266	403	2	{	{	PUNCT
ejpam-3266	403	3	a	a	NOUN
ejpam-3266	403	4	}	}	PUNCT
ejpam-3266	403	5	{	{	PUNCT
ejpam-3266	403	6	b	b	NOUN
ejpam-3266	403	7	}	}	PUNCT
ejpam-3266	403	8	{	{	PUNCT
ejpam-3266	403	9	c	c	NOUN
ejpam-3266	403	10	}	}	PUNCT
ejpam-3266	403	11	{	{	PUNCT
ejpam-3266	403	12	d	d	NOUN
ejpam-3266	403	13	}	}	PUNCT
ejpam-3266	403	14	{	{	PUNCT
ejpam-3266	403	15	f	f	X
ejpam-3266	403	16	}	}	PUNCT
ejpam-3266	403	17	{	{	PUNCT
ejpam-3266	403	18	g	g	NOUN
ejpam-3266	403	19	}	}	PUNCT
ejpam-3266	403	20	a	a	DET
ejpam-3266	403	21	{	{	PUNCT
ejpam-3266	403	22	b	b	NOUN
ejpam-3266	403	23	}	}	PUNCT
ejpam-3266	403	24	{	{	PUNCT
ejpam-3266	403	25	b	b	NOUN
ejpam-3266	403	26	}	}	PUNCT
ejpam-3266	403	27	{	{	PUNCT
ejpam-3266	403	28	a	a	NOUN
ejpam-3266	403	29	}	}	PUNCT
ejpam-3266	403	30	{	{	PUNCT
ejpam-3266	403	31	d	d	NOUN
ejpam-3266	403	32	}	}	PUNCT
ejpam-3266	403	33	{	{	PUNCT
ejpam-3266	403	34	a	a	NOUN
ejpam-3266	403	35	}	}	PUNCT
ejpam-3266	403	36	{	{	PUNCT
ejpam-3266	403	37	a	a	DET
ejpam-3266	403	38	}	}	PUNCT
ejpam-3266	403	39	b	b	PROPN
ejpam-3266	403	40	{	{	PUNCT
ejpam-3266	403	41	b	b	NOUN
ejpam-3266	403	42	}	}	PUNCT
ejpam-3266	403	43	{	{	PUNCT
ejpam-3266	403	44	b	b	NOUN
ejpam-3266	403	45	}	}	PUNCT
ejpam-3266	403	46	{	{	PUNCT
ejpam-3266	403	47	b	b	NOUN
ejpam-3266	403	48	}	}	PUNCT
ejpam-3266	403	49	{	{	PUNCT
ejpam-3266	403	50	d	d	NOUN
ejpam-3266	403	51	}	}	PUNCT
ejpam-3266	403	52	{	{	PUNCT
ejpam-3266	403	53	b	b	NOUN
ejpam-3266	403	54	}	}	PUNCT
ejpam-3266	403	55	{	{	PUNCT
ejpam-3266	403	56	b	b	NOUN
ejpam-3266	403	57	}	}	PUNCT
ejpam-3266	403	58	c	c	NOUN
ejpam-3266	403	59	{	{	PUNCT
ejpam-3266	403	60	a	a	NOUN
ejpam-3266	403	61	}	}	PUNCT
ejpam-3266	403	62	{	{	PUNCT
ejpam-3266	403	63	b	b	NOUN
ejpam-3266	403	64	}	}	PUNCT
ejpam-3266	403	65	{	{	PUNCT
ejpam-3266	403	66	c	c	NOUN
ejpam-3266	403	67	}	}	PUNCT
ejpam-3266	403	68	{	{	PUNCT
ejpam-3266	403	69	d	d	NOUN
ejpam-3266	403	70	}	}	PUNCT
ejpam-3266	403	71	{	{	PUNCT
ejpam-3266	403	72	c	c	NOUN
ejpam-3266	403	73	}	}	PUNCT
ejpam-3266	403	74	{	{	PUNCT
ejpam-3266	403	75	c	c	NOUN
ejpam-3266	403	76	}	}	PUNCT
ejpam-3266	403	77	d	d	NOUN
ejpam-3266	403	78	{	{	PUNCT
ejpam-3266	403	79	d	d	NOUN
ejpam-3266	403	80	}	}	PUNCT
ejpam-3266	403	81	{	{	PUNCT
ejpam-3266	403	82	d	d	NOUN
ejpam-3266	403	83	}	}	PUNCT
ejpam-3266	403	84	{	{	PUNCT
ejpam-3266	403	85	d	d	NOUN
ejpam-3266	403	86	}	}	PUNCT
ejpam-3266	403	87	{	{	PUNCT
ejpam-3266	403	88	d	d	NOUN
ejpam-3266	403	89	}	}	PUNCT
ejpam-3266	403	90	{	{	PUNCT
ejpam-3266	403	91	d	d	NOUN
ejpam-3266	403	92	}	}	PUNCT
ejpam-3266	403	93	{	{	PUNCT
ejpam-3266	403	94	d	d	NOUN
ejpam-3266	403	95	}	}	PUNCT
ejpam-3266	403	96	f	f	PROPN
ejpam-3266	403	97	{	{	PUNCT
ejpam-3266	403	98	a	a	PROPN
ejpam-3266	403	99	}	}	PUNCT
ejpam-3266	403	100	{	{	PUNCT
ejpam-3266	403	101	b	b	NOUN
ejpam-3266	403	102	}	}	PUNCT
ejpam-3266	403	103	{	{	PUNCT
ejpam-3266	403	104	c	c	NOUN
ejpam-3266	403	105	}	}	PUNCT
ejpam-3266	403	106	{	{	PUNCT
ejpam-3266	403	107	d	d	NOUN
ejpam-3266	403	108	}	}	PUNCT
ejpam-3266	403	109	{	{	PUNCT
ejpam-3266	403	110	c	c	NOUN
ejpam-3266	403	111	}	}	PUNCT
ejpam-3266	403	112	{	{	PUNCT
ejpam-3266	403	113	c	c	NOUN
ejpam-3266	403	114	}	}	PUNCT
ejpam-3266	403	115	g	g	NOUN
ejpam-3266	403	116	{	{	PUNCT
ejpam-3266	403	117	a	a	NOUN
ejpam-3266	403	118	}	}	PUNCT
ejpam-3266	403	119	{	{	PUNCT
ejpam-3266	403	120	b	b	NOUN
ejpam-3266	403	121	}	}	PUNCT
ejpam-3266	403	122	{	{	PUNCT
ejpam-3266	403	123	c	c	NOUN
ejpam-3266	403	124	}	}	PUNCT
ejpam-3266	403	125	{	{	PUNCT
ejpam-3266	403	126	d	d	NOUN
ejpam-3266	403	127	}	}	PUNCT
ejpam-3266	403	128	{	{	PUNCT
ejpam-3266	403	129	f	f	X
ejpam-3266	403	130	}	}	PUNCT
ejpam-3266	403	131	{	{	PUNCT
ejpam-3266	403	132	g	g	NOUN
ejpam-3266	403	133	}	}	PUNCT
ejpam-3266	403	134	table	table	NOUN
ejpam-3266	403	135	2	2	NUM
ejpam-3266	403	136	.	.	PUNCT
ejpam-3266	404	1	in	in	ADP
ejpam-3266	404	2	the	the	DET
ejpam-3266	404	3	above	above	ADJ
ejpam-3266	404	4	example	example	NOUN
ejpam-3266	404	5	the	the	DET
ejpam-3266	404	6	ordered	order	VERB
ejpam-3266	404	7	semigroup	semigroup	NOUN
ejpam-3266	404	8	has	have	AUX
ejpam-3266	404	9	been	be	AUX
ejpam-3266	404	10	found	find	VERB
ejpam-3266	404	11	using	use	VERB
ejpam-3266	404	12	our	our	PRON
ejpam-3266	404	13	computer	computer	NOUN
ejpam-3266	404	14	program	program	NOUN
ejpam-3266	404	15	.	.	PUNCT
ejpam-3266	405	1	let	let	VERB
ejpam-3266	405	2	us	we	PRON
ejpam-3266	405	3	give	give	VERB
ejpam-3266	405	4	another	another	DET
ejpam-3266	405	5	example	example	NOUN
ejpam-3266	405	6	which	which	PRON
ejpam-3266	405	7	is	be	AUX
ejpam-3266	405	8	easier	easy	ADJ
ejpam-3266	405	9	to	to	PART
ejpam-3266	405	10	check	check	VERB
ejpam-3266	405	11	by	by	ADP
ejpam-3266	405	12	hand	hand	NOUN
ejpam-3266	405	13	.	.	PUNCT
ejpam-3266	406	1	example	example	NOUN
ejpam-3266	406	2	4.7	4.7	NUM
ejpam-3266	406	3	.	.	PUNCT
ejpam-3266	407	1	(	(	PUNCT
ejpam-3266	407	2	cf	cf	NOUN
ejpam-3266	407	3	.	.	PUNCT
ejpam-3266	408	1	[	[	X
ejpam-3266	408	2	4	4	NUM
ejpam-3266	408	3	;	;	PUNCT
ejpam-3266	408	4	example	example	NOUN
ejpam-3266	408	5	1	1	NUM
ejpam-3266	408	6	]	]	PUNCT
ejpam-3266	408	7	)	)	PUNCT
ejpam-3266	408	8	the	the	DET
ejpam-3266	408	9	ordered	order	VERB
ejpam-3266	408	10	semigroup	semigroup	NOUN
ejpam-3266	408	11	given	give	VERB
ejpam-3266	408	12	by	by	ADP
ejpam-3266	408	13	the	the	DET
ejpam-3266	408	14	multiplication	multiplication	NOUN
ejpam-3266	408	15	“	"	PUNCT
ejpam-3266	408	16	·	·	PUNCT
ejpam-3266	408	17	”	"	PUNCT
ejpam-3266	408	18	and	and	CCONJ
ejpam-3266	408	19	the	the	DET
ejpam-3266	408	20	figure	figure	NOUN
ejpam-3266	408	21	below	below	ADV
ejpam-3266	408	22	is	be	AUX
ejpam-3266	408	23	an	an	DET
ejpam-3266	408	24	example	example	NOUN
ejpam-3266	408	25	of	of	ADP
ejpam-3266	408	26	an	an	DET
ejpam-3266	408	27	ordered	order	VERB
ejpam-3266	408	28	semigroup	semigroup	NOUN
ejpam-3266	408	29	for	for	ADP
ejpam-3266	408	30	which	which	PRON
ejpam-3266	408	31	the	the	DET
ejpam-3266	408	32	relation	relation	NOUN
ejpam-3266	408	33	n	n	CCONJ
ejpam-3266	408	34	is	be	AUX
ejpam-3266	408	35	not	not	PART
ejpam-3266	408	36	the	the	DET
ejpam-3266	408	37	least	least	ADJ
ejpam-3266	408	38	semilattice	semilattice	NOUN
ejpam-3266	408	39	congruence	congruence	NOUN
ejpam-3266	408	40	on	on	ADP
ejpam-3266	408	41	s.	s.	PROPN
ejpam-3266	408	42	·	·	PUNCT
ejpam-3266	409	1	a	a	DET
ejpam-3266	409	2	b	b	X
ejpam-3266	409	3	c	c	NOUN
ejpam-3266	409	4	d	d	PROPN
ejpam-3266	409	5	e	e	PROPN
ejpam-3266	409	6	a	a	PRON
ejpam-3266	409	7	b	b	NOUN
ejpam-3266	409	8	a	a	PRON
ejpam-3266	409	9	a	a	DET
ejpam-3266	409	10	a	a	DET
ejpam-3266	409	11	a	a	DET
ejpam-3266	409	12	b	b	NOUN
ejpam-3266	409	13	a	a	DET
ejpam-3266	409	14	b	b	PROPN
ejpam-3266	409	15	b	b	PROPN
ejpam-3266	409	16	b	b	PROPN
ejpam-3266	409	17	b	b	PROPN
ejpam-3266	409	18	c	c	PROPN
ejpam-3266	409	19	a	a	DET
ejpam-3266	409	20	b	b	PROPN
ejpam-3266	409	21	b	b	PROPN
ejpam-3266	409	22	b	b	PROPN
ejpam-3266	409	23	b	b	PROPN
ejpam-3266	410	1	d	d	PROPN
ejpam-3266	410	2	a	a	PRON
ejpam-3266	410	3	b	b	PROPN
ejpam-3266	410	4	b	b	PROPN
ejpam-3266	410	5	d	d	PROPN
ejpam-3266	410	6	d	d	PROPN
ejpam-3266	410	7	e	e	PROPN
ejpam-3266	410	8	a	a	DET
ejpam-3266	410	9	b	b	NOUN
ejpam-3266	410	10	c	c	NOUN
ejpam-3266	410	11	d	d	X
ejpam-3266	410	12	e	e	PROPN
ejpam-3266	410	13	table	table	NOUN
ejpam-3266	410	14	3	3	NUM
ejpam-3266	410	15	.	.	PUNCT
ejpam-3266	411	1	c	c	NOUN
ejpam-3266	411	2	e	e	PROPN
ejpam-3266	411	3	a	a	DET
ejpam-3266	411	4	b	b	NOUN
ejpam-3266	411	5	d	d	X
ejpam-3266	411	6	figure	figure	NOUN
ejpam-3266	411	7	2	2	X
ejpam-3266	411	8	.	.	X
ejpam-3266	412	1	we	we	PRON
ejpam-3266	412	2	have	have	VERB
ejpam-3266	412	3	n(a	n(a	NOUN
ejpam-3266	412	4	)	)	PUNCT
ejpam-3266	412	5	=	=	SYM
ejpam-3266	413	1	n(b	n(b	PROPN
ejpam-3266	413	2	)	)	PUNCT
ejpam-3266	413	3	=	=	SYM
ejpam-3266	413	4	n(c	n(c	NOUN
ejpam-3266	413	5	)	)	PUNCT
ejpam-3266	413	6	=	=	SYM
ejpam-3266	413	7	s	s	NOUN
ejpam-3266	413	8	and	and	CCONJ
ejpam-3266	413	9	n(d	n(d	NUM
ejpam-3266	413	10	)	)	PUNCT
ejpam-3266	413	11	=	=	SYM
ejpam-3266	413	12	n(f	n(f	PROPN
ejpam-3266	413	13	)	)	PUNCT
ejpam-3266	413	14	=	=	PRON
ejpam-3266	413	15	{	{	PUNCT
ejpam-3266	413	16	d	d	NOUN
ejpam-3266	413	17	,	,	PUNCT
ejpam-3266	413	18	e	e	NOUN
ejpam-3266	413	19	}	}	PUNCT
ejpam-3266	413	20	.	.	PUNCT
ejpam-3266	414	1	we	we	PRON
ejpam-3266	414	2	give	give	VERB
ejpam-3266	414	3	all	all	DET
ejpam-3266	414	4	the	the	DET
ejpam-3266	414	5	semilattice	semilattice	NOUN
ejpam-3266	414	6	congruences	congruence	VERB
ejpam-3266	414	7	on	on	ADP
ejpam-3266	414	8	s.	s.	PROPN
ejpam-3266	414	9	they	they	PRON
ejpam-3266	414	10	are	be	AUX
ejpam-3266	414	11	four	four	NUM
ejpam-3266	414	12	and	and	CCONJ
ejpam-3266	414	13	they	they	PRON
ejpam-3266	414	14	are	be	AUX
ejpam-3266	414	15	the	the	DET
ejpam-3266	414	16	following	follow	VERB
ejpam-3266	414	17	:	:	PUNCT
ejpam-3266	414	18	σ1	σ1	NOUN
ejpam-3266	414	19	=	=	SYM
ejpam-3266	414	20	{	{	PUNCT
ejpam-3266	414	21	(	(	PUNCT
ejpam-3266	414	22	a	a	PRON
ejpam-3266	414	23	,	,	PUNCT
ejpam-3266	414	24	a	a	NOUN
ejpam-3266	414	25	)	)	PUNCT
ejpam-3266	414	26	,	,	PUNCT
ejpam-3266	414	27	(	(	PUNCT
ejpam-3266	414	28	a	a	DET
ejpam-3266	414	29	,	,	PUNCT
ejpam-3266	414	30	b	b	NOUN
ejpam-3266	414	31	)	)	PUNCT
ejpam-3266	414	32	,	,	PUNCT
ejpam-3266	414	33	(	(	PUNCT
ejpam-3266	414	34	a	a	DET
ejpam-3266	414	35	,	,	PUNCT
ejpam-3266	414	36	c	c	NOUN
ejpam-3266	414	37	)	)	PUNCT
ejpam-3266	414	38	,	,	PUNCT
ejpam-3266	414	39	(	(	PUNCT
ejpam-3266	414	40	b	b	X
ejpam-3266	414	41	,	,	PUNCT
ejpam-3266	414	42	a	a	PRON
ejpam-3266	414	43	)	)	PUNCT
ejpam-3266	414	44	,	,	PUNCT
ejpam-3266	414	45	(	(	PUNCT
ejpam-3266	414	46	b	b	X
ejpam-3266	414	47	,	,	PUNCT
ejpam-3266	414	48	b	b	NOUN
ejpam-3266	414	49	)	)	PUNCT
ejpam-3266	414	50	,	,	PUNCT
ejpam-3266	414	51	(	(	PUNCT
ejpam-3266	414	52	b	b	X
ejpam-3266	414	53	,	,	PUNCT
ejpam-3266	414	54	c	c	NOUN
ejpam-3266	414	55	)	)	PUNCT
ejpam-3266	414	56	,	,	PUNCT
ejpam-3266	414	57	(	(	PUNCT
ejpam-3266	414	58	c	c	X
ejpam-3266	414	59	,	,	PUNCT
ejpam-3266	414	60	a	a	NOUN
ejpam-3266	414	61	)	)	PUNCT
ejpam-3266	414	62	,	,	PUNCT
ejpam-3266	414	63	(	(	PUNCT
ejpam-3266	414	64	c	c	X
ejpam-3266	414	65	,	,	PUNCT
ejpam-3266	414	66	b	b	NOUN
ejpam-3266	414	67	)	)	PUNCT
ejpam-3266	414	68	,	,	PUNCT
ejpam-3266	414	69	(	(	PUNCT
ejpam-3266	414	70	c	c	X
ejpam-3266	414	71	,	,	PUNCT
ejpam-3266	414	72	c	c	NOUN
ejpam-3266	414	73	)	)	PUNCT
ejpam-3266	414	74	,	,	PUNCT
ejpam-3266	414	75	n.	n.	PROPN
ejpam-3266	414	76	kehayopulu	kehayopulu	PROPN
ejpam-3266	414	77	/	/	SYM
ejpam-3266	414	78	eur	eur	PROPN
ejpam-3266	414	79	.	.	PUNCT
ejpam-3266	415	1	j.	j.	PROPN
ejpam-3266	415	2	pure	pure	PROPN
ejpam-3266	415	3	appl	appl	PROPN
ejpam-3266	415	4	.	.	PROPN
ejpam-3266	415	5	math	math	PROPN
ejpam-3266	415	6	,	,	PUNCT
ejpam-3266	415	7	11	11	NUM
ejpam-3266	415	8	(	(	PUNCT
ejpam-3266	415	9	2	2	NUM
ejpam-3266	415	10	)	)	PUNCT
ejpam-3266	415	11	(	(	PUNCT
ejpam-3266	415	12	2018	2018	NUM
ejpam-3266	415	13	)	)	PUNCT
ejpam-3266	415	14	,	,	PUNCT
ejpam-3266	415	15	476	476	NUM
ejpam-3266	415	16	-	-	SYM
ejpam-3266	415	17	492	492	NUM
ejpam-3266	415	18	488	488	NUM
ejpam-3266	415	19	(	(	PUNCT
ejpam-3266	415	20	d	d	NOUN
ejpam-3266	415	21	,	,	PUNCT
ejpam-3266	415	22	d	d	NOUN
ejpam-3266	415	23	)	)	PUNCT
ejpam-3266	415	24	,	,	PUNCT
ejpam-3266	415	25	(	(	PUNCT
ejpam-3266	415	26	e	e	NOUN
ejpam-3266	415	27	,	,	PUNCT
ejpam-3266	415	28	e	e	NOUN
ejpam-3266	415	29	)	)	PUNCT
ejpam-3266	415	30	}	}	PUNCT
ejpam-3266	415	31	.	.	PUNCT
ejpam-3266	416	1	σ2	σ2	NOUN
ejpam-3266	416	2	=	=	SYM
ejpam-3266	416	3	{	{	PUNCT
ejpam-3266	416	4	(	(	PUNCT
ejpam-3266	416	5	a	a	PRON
ejpam-3266	416	6	,	,	PUNCT
ejpam-3266	416	7	a	a	NOUN
ejpam-3266	416	8	)	)	PUNCT
ejpam-3266	416	9	,	,	PUNCT
ejpam-3266	416	10	(	(	PUNCT
ejpam-3266	416	11	a	a	DET
ejpam-3266	416	12	,	,	PUNCT
ejpam-3266	416	13	b	b	NOUN
ejpam-3266	416	14	)	)	PUNCT
ejpam-3266	416	15	,	,	PUNCT
ejpam-3266	416	16	(	(	PUNCT
ejpam-3266	416	17	a	a	DET
ejpam-3266	416	18	,	,	PUNCT
ejpam-3266	416	19	c	c	NOUN
ejpam-3266	416	20	)	)	PUNCT
ejpam-3266	416	21	,	,	PUNCT
ejpam-3266	416	22	(	(	PUNCT
ejpam-3266	416	23	b	b	X
ejpam-3266	416	24	,	,	PUNCT
ejpam-3266	416	25	a	a	PRON
ejpam-3266	416	26	)	)	PUNCT
ejpam-3266	416	27	,	,	PUNCT
ejpam-3266	416	28	(	(	PUNCT
ejpam-3266	416	29	b	b	X
ejpam-3266	416	30	,	,	PUNCT
ejpam-3266	416	31	b	b	NOUN
ejpam-3266	416	32	)	)	PUNCT
ejpam-3266	416	33	,	,	PUNCT
ejpam-3266	416	34	(	(	PUNCT
ejpam-3266	416	35	b	b	X
ejpam-3266	416	36	,	,	PUNCT
ejpam-3266	416	37	c	c	NOUN
ejpam-3266	416	38	)	)	PUNCT
ejpam-3266	416	39	,	,	PUNCT
ejpam-3266	416	40	(	(	PUNCT
ejpam-3266	416	41	c	c	X
ejpam-3266	416	42	,	,	PUNCT
ejpam-3266	416	43	a	a	NOUN
ejpam-3266	416	44	)	)	PUNCT
ejpam-3266	416	45	,	,	PUNCT
ejpam-3266	416	46	(	(	PUNCT
ejpam-3266	416	47	c	c	X
ejpam-3266	416	48	,	,	PUNCT
ejpam-3266	416	49	b	b	NOUN
ejpam-3266	416	50	)	)	PUNCT
ejpam-3266	416	51	,	,	PUNCT
ejpam-3266	416	52	(	(	PUNCT
ejpam-3266	416	53	c	c	X
ejpam-3266	416	54	,	,	PUNCT
ejpam-3266	416	55	c	c	NOUN
ejpam-3266	416	56	)	)	PUNCT
ejpam-3266	416	57	,	,	PUNCT
ejpam-3266	416	58	(	(	PUNCT
ejpam-3266	416	59	d	d	X
ejpam-3266	416	60	,	,	PUNCT
ejpam-3266	416	61	d	d	NOUN
ejpam-3266	416	62	)	)	PUNCT
ejpam-3266	416	63	(	(	PUNCT
ejpam-3266	416	64	d	d	X
ejpam-3266	416	65	,	,	PUNCT
ejpam-3266	416	66	e	e	NOUN
ejpam-3266	416	67	)	)	PUNCT
ejpam-3266	416	68	,	,	PUNCT
ejpam-3266	416	69	(	(	PUNCT
ejpam-3266	416	70	e	e	NOUN
ejpam-3266	416	71	,	,	PUNCT
ejpam-3266	416	72	d	d	NOUN
ejpam-3266	416	73	)	)	PUNCT
ejpam-3266	416	74	,	,	PUNCT
ejpam-3266	416	75	(	(	PUNCT
ejpam-3266	416	76	e	e	NOUN
ejpam-3266	416	77	,	,	PUNCT
ejpam-3266	416	78	e	e	NOUN
ejpam-3266	416	79	)	)	PUNCT
ejpam-3266	416	80	}	}	PUNCT
ejpam-3266	416	81	=	=	SYM
ejpam-3266	416	82	n	n	X
ejpam-3266	416	83	.	.	PUNCT
ejpam-3266	417	1	σ3	σ3	PROPN
ejpam-3266	417	2	=	=	PRON
ejpam-3266	417	3	{	{	PUNCT
ejpam-3266	417	4	(	(	PUNCT
ejpam-3266	417	5	a	a	PRON
ejpam-3266	417	6	,	,	PUNCT
ejpam-3266	417	7	a	a	NOUN
ejpam-3266	417	8	)	)	PUNCT
ejpam-3266	417	9	,	,	PUNCT
ejpam-3266	417	10	(	(	PUNCT
ejpam-3266	417	11	a	a	DET
ejpam-3266	417	12	,	,	PUNCT
ejpam-3266	417	13	b	b	NOUN
ejpam-3266	417	14	)	)	PUNCT
ejpam-3266	417	15	,	,	PUNCT
ejpam-3266	417	16	(	(	PUNCT
ejpam-3266	417	17	a	a	DET
ejpam-3266	417	18	,	,	PUNCT
ejpam-3266	417	19	c	c	NOUN
ejpam-3266	417	20	)	)	PUNCT
ejpam-3266	417	21	,	,	PUNCT
ejpam-3266	417	22	(	(	PUNCT
ejpam-3266	417	23	a	a	DET
ejpam-3266	417	24	,	,	PUNCT
ejpam-3266	417	25	d	d	NOUN
ejpam-3266	417	26	)	)	PUNCT
ejpam-3266	417	27	,	,	PUNCT
ejpam-3266	417	28	(	(	PUNCT
ejpam-3266	417	29	b	b	X
ejpam-3266	417	30	,	,	PUNCT
ejpam-3266	417	31	a	a	PRON
ejpam-3266	417	32	)	)	PUNCT
ejpam-3266	417	33	,	,	PUNCT
ejpam-3266	417	34	(	(	PUNCT
ejpam-3266	417	35	b	b	X
ejpam-3266	417	36	,	,	PUNCT
ejpam-3266	417	37	b	b	NOUN
ejpam-3266	417	38	)	)	PUNCT
ejpam-3266	417	39	,	,	PUNCT
ejpam-3266	417	40	(	(	PUNCT
ejpam-3266	417	41	b	b	X
ejpam-3266	417	42	,	,	PUNCT
ejpam-3266	417	43	c	c	NOUN
ejpam-3266	417	44	)	)	PUNCT
ejpam-3266	417	45	,	,	PUNCT
ejpam-3266	417	46	(	(	PUNCT
ejpam-3266	417	47	b	b	X
ejpam-3266	417	48	,	,	PUNCT
ejpam-3266	417	49	d	d	NOUN
ejpam-3266	417	50	)	)	PUNCT
ejpam-3266	417	51	,	,	PUNCT
ejpam-3266	417	52	(	(	PUNCT
ejpam-3266	417	53	c	c	X
ejpam-3266	417	54	,	,	PUNCT
ejpam-3266	417	55	a	a	NOUN
ejpam-3266	417	56	)	)	PUNCT
ejpam-3266	417	57	,	,	PUNCT
ejpam-3266	417	58	(	(	PUNCT
ejpam-3266	417	59	c	c	X
ejpam-3266	417	60	,	,	PUNCT
ejpam-3266	417	61	b	b	NOUN
ejpam-3266	417	62	)	)	PUNCT
ejpam-3266	417	63	,	,	PUNCT
ejpam-3266	417	64	(	(	PUNCT
ejpam-3266	417	65	c	c	X
ejpam-3266	417	66	,	,	PUNCT
ejpam-3266	417	67	c	c	NOUN
ejpam-3266	417	68	)	)	PUNCT
ejpam-3266	417	69	,	,	PUNCT
ejpam-3266	417	70	(	(	PUNCT
ejpam-3266	417	71	c	c	X
ejpam-3266	417	72	,	,	PUNCT
ejpam-3266	417	73	d	d	NOUN
ejpam-3266	417	74	)	)	PUNCT
ejpam-3266	417	75	,	,	PUNCT
ejpam-3266	417	76	(	(	PUNCT
ejpam-3266	417	77	d	d	X
ejpam-3266	417	78	,	,	PUNCT
ejpam-3266	417	79	a	a	NOUN
ejpam-3266	417	80	)	)	PUNCT
ejpam-3266	417	81	,	,	PUNCT
ejpam-3266	417	82	(	(	PUNCT
ejpam-3266	417	83	d	d	X
ejpam-3266	417	84	,	,	PUNCT
ejpam-3266	417	85	b	b	NOUN
ejpam-3266	417	86	)	)	PUNCT
ejpam-3266	417	87	,	,	PUNCT
ejpam-3266	417	88	(	(	PUNCT
ejpam-3266	417	89	d	d	X
ejpam-3266	417	90	,	,	PUNCT
ejpam-3266	417	91	c	c	NOUN
ejpam-3266	417	92	)	)	PUNCT
ejpam-3266	417	93	,	,	PUNCT
ejpam-3266	417	94	(	(	PUNCT
ejpam-3266	417	95	d	d	X
ejpam-3266	417	96	,	,	PUNCT
ejpam-3266	417	97	d	d	NOUN
ejpam-3266	417	98	)	)	PUNCT
ejpam-3266	417	99	,	,	PUNCT
ejpam-3266	417	100	(	(	PUNCT
ejpam-3266	417	101	e	e	NOUN
ejpam-3266	417	102	,	,	PUNCT
ejpam-3266	417	103	e	e	NOUN
ejpam-3266	417	104	)	)	PUNCT
ejpam-3266	417	105	}	}	PUNCT
ejpam-3266	417	106	.	.	PUNCT
ejpam-3266	418	1	σ4	σ4	NOUN
ejpam-3266	418	2	=	=	SYM
ejpam-3266	418	3	s	s	PART
ejpam-3266	418	4	×	×	PROPN
ejpam-3266	418	5	s.	s.	PROPN
ejpam-3266	418	6	the	the	DET
ejpam-3266	418	7	relation	relation	NOUN
ejpam-3266	418	8	σ1	σ1	PROPN
ejpam-3266	418	9	is	be	AUX
ejpam-3266	418	10	the	the	DET
ejpam-3266	418	11	least	least	ADJ
ejpam-3266	418	12	semilattice	semilattice	NOUN
ejpam-3266	418	13	congruence	congruence	NOUN
ejpam-3266	418	14	on	on	ADP
ejpam-3266	418	15	s	s	PROPN
ejpam-3266	418	16	,	,	PUNCT
ejpam-3266	418	17	the	the	DET
ejpam-3266	418	18	relationn	relationn	NOUN
ejpam-3266	418	19	is	be	AUX
ejpam-3266	418	20	the	the	DET
ejpam-3266	418	21	least	least	ADJ
ejpam-3266	418	22	complete	complete	ADJ
ejpam-3266	418	23	semilattice	semilattice	NOUN
ejpam-3266	418	24	congruence	congruence	NOUN
ejpam-3266	418	25	on	on	ADP
ejpam-3266	418	26	s	s	NOUN
ejpam-3266	418	27	,	,	PUNCT
ejpam-3266	418	28	and	and	CCONJ
ejpam-3266	418	29	σ1	σ1	PROPN
ejpam-3266	418	30	6=	6=	PROPN
ejpam-3266	418	31	n	n	PROPN
ejpam-3266	418	32	.	.	PUNCT
ejpam-3266	419	1	according	accord	VERB
ejpam-3266	419	2	to	to	ADP
ejpam-3266	419	3	proposition	proposition	NOUN
ejpam-3266	419	4	4.2	4.2	NUM
ejpam-3266	419	5	,	,	PUNCT
ejpam-3266	419	6	the	the	DET
ejpam-3266	419	7	ordered	order	VERB
ejpam-3266	419	8	semigroup	semigroup	NOUN
ejpam-3266	419	9	(	(	PUNCT
ejpam-3266	419	10	s	s	PROPN
ejpam-3266	419	11	,	,	PUNCT
ejpam-3266	419	12	·	·	PUNCT
ejpam-3266	419	13	,	,	PUNCT
ejpam-3266	419	14	≤	≤	NUM
ejpam-3266	419	15	)	)	PUNCT
ejpam-3266	419	16	with	with	ADP
ejpam-3266	419	17	the	the	DET
ejpam-3266	419	18	operation	operation	NOUN
ejpam-3266	419	19	“	"	PUNCT
ejpam-3266	419	20	◦	◦	NOUN
ejpam-3266	419	21	”	"	PUNCT
ejpam-3266	419	22	on	on	ADP
ejpam-3266	419	23	s	s	PRON
ejpam-3266	419	24	defined	define	VERB
ejpam-3266	419	25	by	by	ADP
ejpam-3266	419	26	a	a	DET
ejpam-3266	419	27	◦	◦	NOUN
ejpam-3266	419	28	b	b	NOUN
ejpam-3266	419	29	:	:	PUNCT
ejpam-3266	419	30	=	=	SYM
ejpam-3266	419	31	{	{	PUNCT
ejpam-3266	419	32	ab	ab	NOUN
ejpam-3266	419	33	}	}	PUNCT
ejpam-3266	419	34	is	be	AUX
ejpam-3266	419	35	an	an	DET
ejpam-3266	419	36	ordered	order	VERB
ejpam-3266	419	37	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	419	38	and	and	CCONJ
ejpam-3266	419	39	the	the	DET
ejpam-3266	419	40	semilattice	semilattice	NOUN
ejpam-3266	419	41	congruences	congruence	VERB
ejpam-3266	419	42	on	on	ADP
ejpam-3266	419	43	(	(	PUNCT
ejpam-3266	419	44	s	s	X
ejpam-3266	419	45	,	,	PUNCT
ejpam-3266	419	46	·	·	PUNCT
ejpam-3266	419	47	,	,	PUNCT
ejpam-3266	419	48	≤	≤	NUM
ejpam-3266	419	49	)	)	PUNCT
ejpam-3266	419	50	and	and	CCONJ
ejpam-3266	419	51	on	on	ADP
ejpam-3266	419	52	(	(	PUNCT
ejpam-3266	419	53	s	s	NOUN
ejpam-3266	419	54	,	,	PUNCT
ejpam-3266	419	55	◦	◦	NOUN
ejpam-3266	419	56	,	,	PUNCT
ejpam-3266	419	57	≤	≤	NOUN
ejpam-3266	419	58	)	)	PUNCT
ejpam-3266	419	59	coincide	coincide	NOUN
ejpam-3266	419	60	.	.	PUNCT
ejpam-3266	420	1	in	in	ADP
ejpam-3266	420	2	other	other	ADJ
ejpam-3266	420	3	words	word	NOUN
ejpam-3266	420	4	,	,	PUNCT
ejpam-3266	420	5	the	the	DET
ejpam-3266	420	6	set	set	NOUN
ejpam-3266	420	7	s	s	PROPN
ejpam-3266	420	8	with	with	ADP
ejpam-3266	420	9	the	the	DET
ejpam-3266	420	10	multiplication	multiplication	NOUN
ejpam-3266	420	11	given	give	VERB
ejpam-3266	420	12	by	by	ADP
ejpam-3266	420	13	the	the	DET
ejpam-3266	420	14	table	table	NOUN
ejpam-3266	420	15	◦	◦	VERB
ejpam-3266	420	16	a	a	DET
ejpam-3266	420	17	b	b	NOUN
ejpam-3266	420	18	c	c	NOUN
ejpam-3266	420	19	d	d	X
ejpam-3266	420	20	e	e	X
ejpam-3266	420	21	a	a	DET
ejpam-3266	420	22	{	{	PUNCT
ejpam-3266	420	23	b	b	NOUN
ejpam-3266	420	24	}	}	PUNCT
ejpam-3266	420	25	{	{	PUNCT
ejpam-3266	420	26	a	a	NOUN
ejpam-3266	420	27	}	}	PUNCT
ejpam-3266	420	28	{	{	PUNCT
ejpam-3266	420	29	a	a	NOUN
ejpam-3266	420	30	}	}	PUNCT
ejpam-3266	420	31	{	{	PUNCT
ejpam-3266	420	32	a	a	NOUN
ejpam-3266	420	33	}	}	PUNCT
ejpam-3266	420	34	{	{	PUNCT
ejpam-3266	420	35	a	a	PRON
ejpam-3266	420	36	}	}	PUNCT
ejpam-3266	420	37	b	b	PROPN
ejpam-3266	420	38	{	{	PUNCT
ejpam-3266	420	39	a	a	NOUN
ejpam-3266	420	40	}	}	PUNCT
ejpam-3266	420	41	{	{	PUNCT
ejpam-3266	420	42	b	b	NOUN
ejpam-3266	420	43	}	}	PUNCT
ejpam-3266	420	44	{	{	PUNCT
ejpam-3266	420	45	b	b	NOUN
ejpam-3266	420	46	}	}	PUNCT
ejpam-3266	420	47	{	{	PUNCT
ejpam-3266	420	48	b	b	NOUN
ejpam-3266	420	49	}	}	PUNCT
ejpam-3266	420	50	{	{	PUNCT
ejpam-3266	420	51	b	b	NOUN
ejpam-3266	420	52	}	}	PUNCT
ejpam-3266	420	53	c	c	NOUN
ejpam-3266	420	54	{	{	PUNCT
ejpam-3266	420	55	a	a	NOUN
ejpam-3266	420	56	}	}	PUNCT
ejpam-3266	420	57	{	{	PUNCT
ejpam-3266	420	58	b	b	NOUN
ejpam-3266	420	59	}	}	PUNCT
ejpam-3266	420	60	{	{	PUNCT
ejpam-3266	420	61	b	b	NOUN
ejpam-3266	420	62	}	}	PUNCT
ejpam-3266	420	63	{	{	PUNCT
ejpam-3266	420	64	b	b	NOUN
ejpam-3266	420	65	}	}	PUNCT
ejpam-3266	420	66	{	{	PUNCT
ejpam-3266	420	67	b	b	NOUN
ejpam-3266	420	68	}	}	PUNCT
ejpam-3266	420	69	d	d	NOUN
ejpam-3266	420	70	{	{	PUNCT
ejpam-3266	420	71	a	a	NOUN
ejpam-3266	420	72	}	}	PUNCT
ejpam-3266	420	73	{	{	PUNCT
ejpam-3266	420	74	b	b	NOUN
ejpam-3266	420	75	}	}	PUNCT
ejpam-3266	420	76	{	{	PUNCT
ejpam-3266	420	77	b	b	NOUN
ejpam-3266	420	78	}	}	PUNCT
ejpam-3266	420	79	{	{	PUNCT
ejpam-3266	420	80	d	d	NOUN
ejpam-3266	420	81	}	}	PUNCT
ejpam-3266	420	82	{	{	PUNCT
ejpam-3266	420	83	d	d	NOUN
ejpam-3266	420	84	}	}	PUNCT
ejpam-3266	420	85	e	e	X
ejpam-3266	420	86	{	{	PUNCT
ejpam-3266	420	87	a	a	NOUN
ejpam-3266	420	88	}	}	PUNCT
ejpam-3266	420	89	{	{	PUNCT
ejpam-3266	420	90	b	b	NOUN
ejpam-3266	420	91	}	}	PUNCT
ejpam-3266	420	92	{	{	PUNCT
ejpam-3266	420	93	c	c	NOUN
ejpam-3266	420	94	}	}	PUNCT
ejpam-3266	420	95	{	{	PUNCT
ejpam-3266	420	96	d	d	NOUN
ejpam-3266	420	97	}	}	PUNCT
ejpam-3266	420	98	{	{	PUNCT
ejpam-3266	420	99	e	e	NOUN
ejpam-3266	420	100	}	}	PUNCT
ejpam-3266	420	101	table	table	NOUN
ejpam-3266	420	102	4	4	NUM
ejpam-3266	420	103	.	.	PUNCT
ejpam-3266	421	1	and	and	CCONJ
ejpam-3266	421	2	the	the	DET
ejpam-3266	421	3	same	same	ADJ
ejpam-3266	421	4	order	order	NOUN
ejpam-3266	421	5	as	as	ADP
ejpam-3266	421	6	in	in	ADP
ejpam-3266	421	7	(	(	PUNCT
ejpam-3266	421	8	s	s	NOUN
ejpam-3266	421	9	,	,	PUNCT
ejpam-3266	421	10	·	·	PUNCT
ejpam-3266	421	11	,	,	PUNCT
ejpam-3266	421	12	≤	≤	NUM
ejpam-3266	421	13	)	)	PUNCT
ejpam-3266	421	14	(:	(:	NOUN
ejpam-3266	421	15	figure	figure	NOUN
ejpam-3266	421	16	2	2	NUM
ejpam-3266	421	17	)	)	PUNCT
ejpam-3266	421	18	is	be	AUX
ejpam-3266	421	19	an	an	DET
ejpam-3266	421	20	ordered	order	VERB
ejpam-3266	421	21	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	421	22	,	,	PUNCT
ejpam-3266	421	23	the	the	DET
ejpam-3266	421	24	relation	relation	NOUN
ejpam-3266	421	25	σ1	σ1	PROPN
ejpam-3266	421	26	is	be	AUX
ejpam-3266	421	27	the	the	DET
ejpam-3266	421	28	least	least	ADJ
ejpam-3266	421	29	semilattice	semilattice	NOUN
ejpam-3266	421	30	congruence	congruence	NOUN
ejpam-3266	421	31	on	on	ADP
ejpam-3266	421	32	s	s	PRON
ejpam-3266	421	33	and	and	CCONJ
ejpam-3266	421	34	it	it	PRON
ejpam-3266	421	35	is	be	AUX
ejpam-3266	421	36	different	different	ADJ
ejpam-3266	421	37	than	than	ADP
ejpam-3266	421	38	n	n	PROPN
ejpam-3266	421	39	.	.	PUNCT
ejpam-3266	422	1	in	in	ADP
ejpam-3266	422	2	[	[	X
ejpam-3266	422	3	4	4	X
ejpam-3266	422	4	]	]	PUNCT
ejpam-3266	422	5	there	there	PRON
ejpam-3266	422	6	are	be	VERB
ejpam-3266	422	7	also	also	ADV
ejpam-3266	422	8	examples	example	NOUN
ejpam-3266	422	9	of	of	ADP
ejpam-3266	422	10	ordered	order	VERB
ejpam-3266	422	11	semigroups	semigroup	NOUN
ejpam-3266	422	12	s	s	X
ejpam-3266	422	13	for	for	ADP
ejpam-3266	422	14	which	which	PRON
ejpam-3266	422	15	the	the	DET
ejpam-3266	422	16	complete	complete	ADJ
ejpam-3266	422	17	semilattice	semilattice	NOUN
ejpam-3266	422	18	congruence	congruence	NOUN
ejpam-3266	422	19	n	n	ADV
ejpam-3266	422	20	is	be	AUX
ejpam-3266	422	21	at	at	ADP
ejpam-3266	422	22	the	the	DET
ejpam-3266	422	23	same	same	ADJ
ejpam-3266	422	24	time	time	NOUN
ejpam-3266	422	25	the	the	DET
ejpam-3266	422	26	least	least	ADJ
ejpam-3266	422	27	semilattice	semilattice	NOUN
ejpam-3266	422	28	congruence	congruence	NOUN
ejpam-3266	422	29	on	on	ADP
ejpam-3266	422	30	s.	s.	PROPN
ejpam-3266	422	31	let	let	VERB
ejpam-3266	422	32	us	we	PRON
ejpam-3266	422	33	get	get	VERB
ejpam-3266	422	34	one	one	NUM
ejpam-3266	422	35	of	of	ADP
ejpam-3266	422	36	them	they	PRON
ejpam-3266	422	37	and	and	CCONJ
ejpam-3266	422	38	pass	pass	VERB
ejpam-3266	422	39	from	from	ADP
ejpam-3266	422	40	the	the	DET
ejpam-3266	422	41	ordered	order	VERB
ejpam-3266	422	42	semigroup	semigroup	NOUN
ejpam-3266	422	43	to	to	PART
ejpam-3266	422	44	ordered	order	VERB
ejpam-3266	422	45	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	422	46	.	.	PUNCT
ejpam-3266	423	1	example	example	NOUN
ejpam-3266	423	2	4.8	4.8	NUM
ejpam-3266	423	3	.	.	PUNCT
ejpam-3266	424	1	if	if	SCONJ
ejpam-3266	424	2	we	we	PRON
ejpam-3266	424	3	take	take	VERB
ejpam-3266	424	4	the	the	DET
ejpam-3266	424	5	ordered	order	VERB
ejpam-3266	424	6	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	424	7	(	(	PUNCT
ejpam-3266	424	8	s	s	PROPN
ejpam-3266	424	9	,	,	PUNCT
ejpam-3266	424	10	·	·	PUNCT
ejpam-3266	424	11	,	,	PUNCT
ejpam-3266	424	12	≤	≤	NUM
ejpam-3266	424	13	)	)	PUNCT
ejpam-3266	424	14	given	give	VERB
ejpam-3266	424	15	in	in	ADP
ejpam-3266	424	16	the	the	DET
ejpam-3266	424	17	example	example	NOUN
ejpam-3266	424	18	2	2	NUM
ejpam-3266	424	19	in	in	ADP
ejpam-3266	424	20	[	[	X
ejpam-3266	424	21	4	4	NUM
ejpam-3266	424	22	]	]	PUNCT
ejpam-3266	424	23	and	and	CCONJ
ejpam-3266	424	24	define	define	VERB
ejpam-3266	424	25	the	the	DET
ejpam-3266	424	26	hyperoperation	hyperoperation	NOUN
ejpam-3266	424	27	as	as	ADP
ejpam-3266	424	28	a	a	DET
ejpam-3266	424	29	◦	◦	NOUN
ejpam-3266	424	30	b	b	NOUN
ejpam-3266	424	31	:	:	PUNCT
ejpam-3266	424	32	=	=	SYM
ejpam-3266	424	33	{	{	PUNCT
ejpam-3266	424	34	ab	ab	NOUN
ejpam-3266	424	35	}	}	PUNCT
ejpam-3266	424	36	,	,	PUNCT
ejpam-3266	424	37	then	then	ADV
ejpam-3266	424	38	we	we	PRON
ejpam-3266	424	39	get	get	VERB
ejpam-3266	424	40	the	the	DET
ejpam-3266	424	41	ordered	order	VERB
ejpam-3266	424	42	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	424	43	defined	define	VERB
ejpam-3266	424	44	by	by	ADP
ejpam-3266	424	45	the	the	DET
ejpam-3266	424	46	table	table	NOUN
ejpam-3266	424	47	and	and	CCONJ
ejpam-3266	424	48	the	the	DET
ejpam-3266	424	49	figure	figure	NOUN
ejpam-3266	424	50	below	below	ADV
ejpam-3266	424	51	.	.	PUNCT
ejpam-3266	425	1	◦	◦	VERB
ejpam-3266	425	2	a	a	DET
ejpam-3266	425	3	b	b	NOUN
ejpam-3266	425	4	c	c	NOUN
ejpam-3266	426	1	d	d	X
ejpam-3266	426	2	f	f	PROPN
ejpam-3266	426	3	a	a	DET
ejpam-3266	426	4	{	{	PUNCT
ejpam-3266	426	5	b	b	NOUN
ejpam-3266	426	6	}	}	PUNCT
ejpam-3266	426	7	{	{	PUNCT
ejpam-3266	426	8	b	b	NOUN
ejpam-3266	426	9	}	}	PUNCT
ejpam-3266	426	10	{	{	PUNCT
ejpam-3266	426	11	d	d	NOUN
ejpam-3266	426	12	}	}	PUNCT
ejpam-3266	426	13	{	{	PUNCT
ejpam-3266	426	14	d	d	NOUN
ejpam-3266	426	15	}	}	PUNCT
ejpam-3266	426	16	{	{	PUNCT
ejpam-3266	426	17	d	d	NOUN
ejpam-3266	426	18	}	}	PUNCT
ejpam-3266	426	19	b	b	PROPN
ejpam-3266	426	20	{	{	PUNCT
ejpam-3266	426	21	b	b	NOUN
ejpam-3266	426	22	}	}	PUNCT
ejpam-3266	426	23	{	{	PUNCT
ejpam-3266	426	24	b	b	NOUN
ejpam-3266	426	25	}	}	PUNCT
ejpam-3266	426	26	{	{	PUNCT
ejpam-3266	426	27	d	d	NOUN
ejpam-3266	426	28	}	}	PUNCT
ejpam-3266	426	29	{	{	PUNCT
ejpam-3266	426	30	d	d	NOUN
ejpam-3266	426	31	}	}	PUNCT
ejpam-3266	426	32	{	{	PUNCT
ejpam-3266	426	33	d	d	NOUN
ejpam-3266	426	34	}	}	PUNCT
ejpam-3266	426	35	c	c	NOUN
ejpam-3266	426	36	{	{	PUNCT
ejpam-3266	426	37	d	d	NOUN
ejpam-3266	426	38	}	}	PUNCT
ejpam-3266	426	39	{	{	PUNCT
ejpam-3266	426	40	d	d	NOUN
ejpam-3266	426	41	}	}	PUNCT
ejpam-3266	426	42	{	{	PUNCT
ejpam-3266	426	43	c	c	NOUN
ejpam-3266	426	44	}	}	PUNCT
ejpam-3266	426	45	{	{	PUNCT
ejpam-3266	426	46	d	d	NOUN
ejpam-3266	426	47	}	}	PUNCT
ejpam-3266	426	48	{	{	PUNCT
ejpam-3266	426	49	c	c	NOUN
ejpam-3266	426	50	}	}	PUNCT
ejpam-3266	426	51	d	d	NOUN
ejpam-3266	426	52	{	{	PUNCT
ejpam-3266	426	53	d	d	NOUN
ejpam-3266	426	54	}	}	PUNCT
ejpam-3266	426	55	{	{	PUNCT
ejpam-3266	426	56	d	d	NOUN
ejpam-3266	426	57	}	}	PUNCT
ejpam-3266	426	58	{	{	PUNCT
ejpam-3266	426	59	d	d	NOUN
ejpam-3266	426	60	}	}	PUNCT
ejpam-3266	426	61	{	{	PUNCT
ejpam-3266	426	62	d	d	NOUN
ejpam-3266	426	63	}	}	PUNCT
ejpam-3266	426	64	{	{	PUNCT
ejpam-3266	426	65	d	d	NOUN
ejpam-3266	426	66	}	}	PUNCT
ejpam-3266	426	67	f	f	PROPN
ejpam-3266	426	68	{	{	PUNCT
ejpam-3266	426	69	d	d	NOUN
ejpam-3266	426	70	}	}	PUNCT
ejpam-3266	426	71	{	{	PUNCT
ejpam-3266	426	72	d	d	NOUN
ejpam-3266	426	73	}	}	PUNCT
ejpam-3266	426	74	{	{	PUNCT
ejpam-3266	426	75	c	c	NOUN
ejpam-3266	426	76	}	}	PUNCT
ejpam-3266	426	77	{	{	PUNCT
ejpam-3266	426	78	d	d	NOUN
ejpam-3266	426	79	}	}	PUNCT
ejpam-3266	426	80	{	{	PUNCT
ejpam-3266	426	81	c	c	NOUN
ejpam-3266	426	82	}	}	PUNCT
ejpam-3266	426	83	table	table	NOUN
ejpam-3266	426	84	5	5	NUM
ejpam-3266	426	85	.	.	PUNCT
ejpam-3266	427	1	n.	n.	PROPN
ejpam-3266	427	2	kehayopulu	kehayopulu	PROPN
ejpam-3266	427	3	/	/	SYM
ejpam-3266	427	4	eur	eur	PROPN
ejpam-3266	427	5	.	.	PUNCT
ejpam-3266	428	1	j.	j.	PROPN
ejpam-3266	428	2	pure	pure	PROPN
ejpam-3266	428	3	appl	appl	PROPN
ejpam-3266	428	4	.	.	PROPN
ejpam-3266	428	5	math	math	PROPN
ejpam-3266	428	6	,	,	PUNCT
ejpam-3266	428	7	11	11	NUM
ejpam-3266	428	8	(	(	PUNCT
ejpam-3266	428	9	2	2	NUM
ejpam-3266	428	10	)	)	PUNCT
ejpam-3266	428	11	(	(	PUNCT
ejpam-3266	428	12	2018	2018	NUM
ejpam-3266	428	13	)	)	PUNCT
ejpam-3266	428	14	,	,	PUNCT
ejpam-3266	428	15	476	476	NUM
ejpam-3266	428	16	-	-	SYM
ejpam-3266	428	17	492	492	NUM
ejpam-3266	428	18	489	489	NUM
ejpam-3266	428	19	a	a	DET
ejpam-3266	428	20	d	d	X
ejpam-3266	428	21	f	f	PROPN
ejpam-3266	428	22	b	b	PROPN
ejpam-3266	428	23	c	c	X
ejpam-3266	428	24	figure	figure	NOUN
ejpam-3266	429	1	3	3	X
ejpam-3266	429	2	.	.	PUNCT
ejpam-3266	430	1	we	we	PRON
ejpam-3266	430	2	have	have	VERB
ejpam-3266	430	3	n(a	n(a	NOUN
ejpam-3266	430	4	)	)	PUNCT
ejpam-3266	430	5	=	=	SYM
ejpam-3266	430	6	n(b	n(b	PROPN
ejpam-3266	430	7	)	)	PUNCT
ejpam-3266	431	1	=	=	PRON
ejpam-3266	431	2	{	{	PUNCT
ejpam-3266	431	3	a	a	PRON
ejpam-3266	431	4	,	,	PUNCT
ejpam-3266	431	5	b	b	NOUN
ejpam-3266	431	6	}	}	PUNCT
ejpam-3266	431	7	,	,	PUNCT
ejpam-3266	431	8	n(c	n(c	NOUN
ejpam-3266	431	9	)	)	PUNCT
ejpam-3266	431	10	=	=	SYM
ejpam-3266	431	11	n(f	n(f	PROPN
ejpam-3266	431	12	)	)	PUNCT
ejpam-3266	431	13	=	=	PRON
ejpam-3266	431	14	{	{	PUNCT
ejpam-3266	431	15	c	c	X
ejpam-3266	431	16	,	,	PUNCT
ejpam-3266	431	17	f	f	NOUN
ejpam-3266	431	18	}	}	PUNCT
ejpam-3266	431	19	and	and	CCONJ
ejpam-3266	431	20	n(d	n(d	NUM
ejpam-3266	431	21	)	)	PUNCT
ejpam-3266	431	22	=	=	VERB
ejpam-3266	432	1	s.	s.	PROPN
ejpam-3266	432	2	there	there	PRON
ejpam-3266	432	3	are	be	VERB
ejpam-3266	432	4	four	four	NUM
ejpam-3266	432	5	semilattice	semilattice	NOUN
ejpam-3266	432	6	congruences	congruence	NOUN
ejpam-3266	432	7	on	on	ADP
ejpam-3266	432	8	(	(	PUNCT
ejpam-3266	432	9	s	s	X
ejpam-3266	432	10	,	,	PUNCT
ejpam-3266	432	11	◦	◦	NOUN
ejpam-3266	432	12	≤	≤	NUM
ejpam-3266	432	13	)	)	PUNCT
ejpam-3266	432	14	and	and	CCONJ
ejpam-3266	432	15	they	they	PRON
ejpam-3266	432	16	are	be	AUX
ejpam-3266	432	17	the	the	DET
ejpam-3266	432	18	following	follow	VERB
ejpam-3266	432	19	σ1	σ1	NOUN
ejpam-3266	432	20	=	=	SYM
ejpam-3266	432	21	{	{	PUNCT
ejpam-3266	432	22	(	(	PUNCT
ejpam-3266	432	23	a	a	PRON
ejpam-3266	432	24	,	,	PUNCT
ejpam-3266	432	25	a	a	NOUN
ejpam-3266	432	26	)	)	PUNCT
ejpam-3266	432	27	,	,	PUNCT
ejpam-3266	432	28	(	(	PUNCT
ejpam-3266	432	29	a	a	DET
ejpam-3266	432	30	,	,	PUNCT
ejpam-3266	432	31	b	b	NOUN
ejpam-3266	432	32	)	)	PUNCT
ejpam-3266	432	33	,	,	PUNCT
ejpam-3266	432	34	(	(	PUNCT
ejpam-3266	432	35	b	b	X
ejpam-3266	432	36	,	,	PUNCT
ejpam-3266	432	37	a	a	PRON
ejpam-3266	432	38	)	)	PUNCT
ejpam-3266	432	39	,	,	PUNCT
ejpam-3266	432	40	(	(	PUNCT
ejpam-3266	432	41	b	b	X
ejpam-3266	432	42	,	,	PUNCT
ejpam-3266	432	43	b	b	NOUN
ejpam-3266	432	44	)	)	PUNCT
ejpam-3266	432	45	,	,	PUNCT
ejpam-3266	432	46	(	(	PUNCT
ejpam-3266	432	47	c	c	X
ejpam-3266	432	48	,	,	PUNCT
ejpam-3266	432	49	c	c	NOUN
ejpam-3266	432	50	)	)	PUNCT
ejpam-3266	432	51	,	,	PUNCT
ejpam-3266	432	52	(	(	PUNCT
ejpam-3266	432	53	c	c	X
ejpam-3266	432	54	,	,	PUNCT
ejpam-3266	432	55	f	f	NOUN
ejpam-3266	432	56	)	)	PUNCT
ejpam-3266	432	57	,	,	PUNCT
ejpam-3266	432	58	(	(	PUNCT
ejpam-3266	432	59	d	d	X
ejpam-3266	432	60	,	,	PUNCT
ejpam-3266	432	61	d	d	NOUN
ejpam-3266	432	62	)	)	PUNCT
ejpam-3266	432	63	,	,	PUNCT
ejpam-3266	432	64	(	(	PUNCT
ejpam-3266	432	65	f	f	X
ejpam-3266	432	66	,	,	PUNCT
ejpam-3266	432	67	c	c	NOUN
ejpam-3266	432	68	)	)	PUNCT
ejpam-3266	432	69	,	,	PUNCT
ejpam-3266	432	70	(	(	PUNCT
ejpam-3266	432	71	f	f	X
ejpam-3266	432	72	,	,	PUNCT
ejpam-3266	432	73	f	f	NOUN
ejpam-3266	432	74	)	)	PUNCT
ejpam-3266	432	75	}	}	PUNCT
ejpam-3266	432	76	=	=	SYM
ejpam-3266	432	77	n	n	NOUN
ejpam-3266	432	78	.	.	PUNCT
ejpam-3266	433	1	σ2	σ2	NOUN
ejpam-3266	433	2	=	=	SYM
ejpam-3266	433	3	{	{	PUNCT
ejpam-3266	433	4	(	(	PUNCT
ejpam-3266	433	5	a	a	PRON
ejpam-3266	433	6	,	,	PUNCT
ejpam-3266	433	7	a	a	NOUN
ejpam-3266	433	8	)	)	PUNCT
ejpam-3266	433	9	,	,	PUNCT
ejpam-3266	433	10	(	(	PUNCT
ejpam-3266	433	11	a	a	DET
ejpam-3266	433	12	,	,	PUNCT
ejpam-3266	433	13	b	b	NOUN
ejpam-3266	433	14	)	)	PUNCT
ejpam-3266	433	15	,	,	PUNCT
ejpam-3266	433	16	(	(	PUNCT
ejpam-3266	433	17	a	a	DET
ejpam-3266	433	18	,	,	PUNCT
ejpam-3266	433	19	d	d	NOUN
ejpam-3266	433	20	)	)	PUNCT
ejpam-3266	433	21	,	,	PUNCT
ejpam-3266	433	22	(	(	PUNCT
ejpam-3266	433	23	b	b	X
ejpam-3266	433	24	,	,	PUNCT
ejpam-3266	433	25	a	a	PRON
ejpam-3266	433	26	)	)	PUNCT
ejpam-3266	433	27	,	,	PUNCT
ejpam-3266	433	28	(	(	PUNCT
ejpam-3266	433	29	b	b	X
ejpam-3266	433	30	,	,	PUNCT
ejpam-3266	433	31	b	b	NOUN
ejpam-3266	433	32	)	)	PUNCT
ejpam-3266	433	33	,	,	PUNCT
ejpam-3266	433	34	(	(	PUNCT
ejpam-3266	433	35	b	b	X
ejpam-3266	433	36	,	,	PUNCT
ejpam-3266	433	37	d	d	NOUN
ejpam-3266	433	38	)	)	PUNCT
ejpam-3266	433	39	,	,	PUNCT
ejpam-3266	433	40	(	(	PUNCT
ejpam-3266	433	41	c	c	X
ejpam-3266	433	42	,	,	PUNCT
ejpam-3266	433	43	c	c	NOUN
ejpam-3266	433	44	)	)	PUNCT
ejpam-3266	433	45	,	,	PUNCT
ejpam-3266	433	46	(	(	PUNCT
ejpam-3266	433	47	c	c	X
ejpam-3266	433	48	,	,	PUNCT
ejpam-3266	433	49	f	f	NOUN
ejpam-3266	433	50	)	)	PUNCT
ejpam-3266	433	51	,	,	PUNCT
ejpam-3266	433	52	(	(	PUNCT
ejpam-3266	433	53	d	d	X
ejpam-3266	433	54	,	,	PUNCT
ejpam-3266	433	55	a	a	NOUN
ejpam-3266	433	56	)	)	PUNCT
ejpam-3266	433	57	,	,	PUNCT
ejpam-3266	433	58	(	(	PUNCT
ejpam-3266	433	59	d	d	X
ejpam-3266	433	60	,	,	PUNCT
ejpam-3266	433	61	b	b	NOUN
ejpam-3266	433	62	)	)	PUNCT
ejpam-3266	433	63	,	,	PUNCT
ejpam-3266	433	64	(	(	PUNCT
ejpam-3266	433	65	d	d	X
ejpam-3266	433	66	,	,	PUNCT
ejpam-3266	433	67	d	d	NOUN
ejpam-3266	433	68	)	)	PUNCT
ejpam-3266	433	69	,	,	PUNCT
ejpam-3266	433	70	(	(	PUNCT
ejpam-3266	433	71	f	f	X
ejpam-3266	433	72	,	,	PUNCT
ejpam-3266	433	73	c	c	NOUN
ejpam-3266	433	74	)	)	PUNCT
ejpam-3266	433	75	,	,	PUNCT
ejpam-3266	433	76	(	(	PUNCT
ejpam-3266	433	77	f	f	X
ejpam-3266	433	78	,	,	PUNCT
ejpam-3266	433	79	f	f	NOUN
ejpam-3266	433	80	)	)	PUNCT
ejpam-3266	433	81	}	}	PUNCT
ejpam-3266	433	82	.	.	PUNCT
ejpam-3266	434	1	σ3	σ3	PROPN
ejpam-3266	434	2	=	=	PRON
ejpam-3266	434	3	{	{	PUNCT
ejpam-3266	434	4	(	(	PUNCT
ejpam-3266	434	5	a	a	PRON
ejpam-3266	434	6	,	,	PUNCT
ejpam-3266	434	7	a	a	NOUN
ejpam-3266	434	8	)	)	PUNCT
ejpam-3266	434	9	,	,	PUNCT
ejpam-3266	434	10	(	(	PUNCT
ejpam-3266	434	11	a	a	DET
ejpam-3266	434	12	,	,	PUNCT
ejpam-3266	434	13	b	b	NOUN
ejpam-3266	434	14	)	)	PUNCT
ejpam-3266	434	15	,	,	PUNCT
ejpam-3266	434	16	(	(	PUNCT
ejpam-3266	434	17	b	b	X
ejpam-3266	434	18	,	,	PUNCT
ejpam-3266	434	19	a	a	PRON
ejpam-3266	434	20	)	)	PUNCT
ejpam-3266	434	21	,	,	PUNCT
ejpam-3266	434	22	(	(	PUNCT
ejpam-3266	434	23	b	b	X
ejpam-3266	434	24	,	,	PUNCT
ejpam-3266	434	25	b	b	NOUN
ejpam-3266	434	26	)	)	PUNCT
ejpam-3266	434	27	,	,	PUNCT
ejpam-3266	434	28	(	(	PUNCT
ejpam-3266	434	29	c	c	X
ejpam-3266	434	30	,	,	PUNCT
ejpam-3266	434	31	c	c	NOUN
ejpam-3266	434	32	)	)	PUNCT
ejpam-3266	434	33	,	,	PUNCT
ejpam-3266	434	34	(	(	PUNCT
ejpam-3266	434	35	c	c	X
ejpam-3266	434	36	,	,	PUNCT
ejpam-3266	434	37	d	d	NOUN
ejpam-3266	434	38	)	)	PUNCT
ejpam-3266	434	39	,	,	PUNCT
ejpam-3266	434	40	(	(	PUNCT
ejpam-3266	434	41	c	c	X
ejpam-3266	434	42	,	,	PUNCT
ejpam-3266	434	43	f	f	NOUN
ejpam-3266	434	44	)	)	PUNCT
ejpam-3266	434	45	,	,	PUNCT
ejpam-3266	434	46	(	(	PUNCT
ejpam-3266	434	47	d	d	X
ejpam-3266	434	48	,	,	PUNCT
ejpam-3266	434	49	c	c	NOUN
ejpam-3266	434	50	)	)	PUNCT
ejpam-3266	434	51	,	,	PUNCT
ejpam-3266	434	52	(	(	PUNCT
ejpam-3266	434	53	d	d	X
ejpam-3266	434	54	,	,	PUNCT
ejpam-3266	434	55	d	d	NOUN
ejpam-3266	434	56	)	)	PUNCT
ejpam-3266	434	57	,	,	PUNCT
ejpam-3266	434	58	(	(	PUNCT
ejpam-3266	434	59	d	d	X
ejpam-3266	434	60	,	,	PUNCT
ejpam-3266	434	61	f	f	NOUN
ejpam-3266	434	62	)	)	PUNCT
ejpam-3266	434	63	,	,	PUNCT
ejpam-3266	434	64	(	(	PUNCT
ejpam-3266	434	65	f	f	X
ejpam-3266	434	66	,	,	PUNCT
ejpam-3266	434	67	c	c	NOUN
ejpam-3266	434	68	)	)	PUNCT
ejpam-3266	434	69	,	,	PUNCT
ejpam-3266	434	70	(	(	PUNCT
ejpam-3266	434	71	f	f	X
ejpam-3266	434	72	,	,	PUNCT
ejpam-3266	434	73	d	d	NOUN
ejpam-3266	434	74	)	)	PUNCT
ejpam-3266	434	75	,	,	PUNCT
ejpam-3266	434	76	(	(	PUNCT
ejpam-3266	434	77	f	f	X
ejpam-3266	434	78	,	,	PUNCT
ejpam-3266	434	79	f	f	NOUN
ejpam-3266	434	80	)	)	PUNCT
ejpam-3266	434	81	}	}	PUNCT
ejpam-3266	434	82	.	.	PUNCT
ejpam-3266	435	1	σ4	σ4	NOUN
ejpam-3266	435	2	=	=	SYM
ejpam-3266	435	3	s	s	PART
ejpam-3266	435	4	×	×	PROPN
ejpam-3266	435	5	s.	s.	PROPN
ejpam-3266	435	6	the	the	DET
ejpam-3266	435	7	relation	relation	NOUN
ejpam-3266	435	8	σ1	σ1	PROPN
ejpam-3266	435	9	is	be	AUX
ejpam-3266	435	10	the	the	DET
ejpam-3266	435	11	least	least	ADJ
ejpam-3266	435	12	semilattice	semilattice	NOUN
ejpam-3266	435	13	congruence	congruence	NOUN
ejpam-3266	435	14	on	on	ADP
ejpam-3266	435	15	(	(	PUNCT
ejpam-3266	435	16	s	s	NOUN
ejpam-3266	435	17	,	,	PUNCT
ejpam-3266	435	18	◦	◦	NOUN
ejpam-3266	435	19	,	,	PUNCT
ejpam-3266	435	20	≤	≤	NUM
ejpam-3266	435	21	)	)	PUNCT
ejpam-3266	435	22	and	and	CCONJ
ejpam-3266	435	23	at	at	ADP
ejpam-3266	435	24	the	the	DET
ejpam-3266	435	25	same	same	ADJ
ejpam-3266	435	26	time	time	NOUN
ejpam-3266	435	27	the	the	DET
ejpam-3266	435	28	least	least	ADV
ejpam-3266	435	29	complete	complete	ADJ
ejpam-3266	435	30	semilattice	semilattice	NOUN
ejpam-3266	435	31	congruence	congruence	NOUN
ejpam-3266	435	32	on	on	ADP
ejpam-3266	435	33	(	(	PUNCT
ejpam-3266	435	34	s	s	NOUN
ejpam-3266	435	35	,	,	PUNCT
ejpam-3266	435	36	◦	◦	NOUN
ejpam-3266	435	37	,	,	PUNCT
ejpam-3266	435	38	≤	≤	NUM
ejpam-3266	435	39	)	)	PUNCT
ejpam-3266	435	40	.	.	PUNCT
ejpam-3266	436	1	in	in	ADP
ejpam-3266	436	2	the	the	DET
ejpam-3266	436	3	example	example	NOUN
ejpam-3266	436	4	3	3	NUM
ejpam-3266	436	5	in	in	ADP
ejpam-3266	436	6	[	[	X
ejpam-3266	436	7	4	4	NUM
ejpam-3266	436	8	]	]	PUNCT
ejpam-3266	436	9	and	and	CCONJ
ejpam-3266	436	10	in	in	ADP
ejpam-3266	436	11	its	its	PRON
ejpam-3266	436	12	“	"	PUNCT
ejpam-3266	436	13	dual	dual	ADJ
ejpam-3266	436	14	”	"	PUNCT
ejpam-3266	436	15	given	give	VERB
ejpam-3266	436	16	immediately	immediately	ADV
ejpam-3266	436	17	after	after	ADP
ejpam-3266	436	18	the	the	DET
ejpam-3266	436	19	example	example	NOUN
ejpam-3266	436	20	3	3	NUM
ejpam-3266	436	21	,	,	PUNCT
ejpam-3266	436	22	the	the	DET
ejpam-3266	436	23	relation	relation	NOUN
ejpam-3266	436	24	σ1	σ1	PROPN
ejpam-3266	436	25	mentioned	mention	VERB
ejpam-3266	436	26	in	in	ADP
ejpam-3266	436	27	them	they	PRON
ejpam-3266	436	28	is	be	AUX
ejpam-3266	436	29	at	at	ADP
ejpam-3266	436	30	the	the	DET
ejpam-3266	436	31	same	same	ADJ
ejpam-3266	436	32	time	time	NOUN
ejpam-3266	436	33	the	the	DET
ejpam-3266	436	34	least	least	ADJ
ejpam-3266	436	35	semilattice	semilattice	NOUN
ejpam-3266	436	36	congruence	congruence	NOUN
ejpam-3266	436	37	and	and	CCONJ
ejpam-3266	436	38	the	the	DET
ejpam-3266	436	39	least	least	ADJ
ejpam-3266	436	40	complete	complete	ADJ
ejpam-3266	436	41	semilattice	semilattice	NOUN
ejpam-3266	436	42	congruence	congruence	NOUN
ejpam-3266	436	43	;	;	PUNCT
ejpam-3266	436	44	as	as	ADP
ejpam-3266	436	45	a	a	DET
ejpam-3266	436	46	consequence	consequence	NOUN
ejpam-3266	436	47	it	it	PRON
ejpam-3266	436	48	is	be	AUX
ejpam-3266	436	49	so	so	ADV
ejpam-3266	436	50	in	in	ADP
ejpam-3266	436	51	the	the	DET
ejpam-3266	436	52	corresponding	corresponding	ADJ
ejpam-3266	436	53	ordered	order	VERB
ejpam-3266	436	54	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	436	55	defined	define	VERB
ejpam-3266	436	56	by	by	ADP
ejpam-3266	436	57	the	the	DET
ejpam-3266	436	58	hyperoperation	hyperoperation	NOUN
ejpam-3266	436	59	a	a	DET
ejpam-3266	436	60	◦	◦	NOUN
ejpam-3266	436	61	b	b	NOUN
ejpam-3266	436	62	=	=	SYM
ejpam-3266	436	63	{	{	PUNCT
ejpam-3266	436	64	ab	ab	NOUN
ejpam-3266	436	65	}	}	PUNCT
ejpam-3266	436	66	.	.	PUNCT
ejpam-3266	437	1	proposition	proposition	NOUN
ejpam-3266	437	2	4.9	4.9	NUM
ejpam-3266	437	3	.	.	PUNCT
ejpam-3266	438	1	(	(	PUNCT
ejpam-3266	438	2	cf	cf	NOUN
ejpam-3266	438	3	.	.	PUNCT
ejpam-3266	439	1	also	also	ADV
ejpam-3266	439	2	[	[	X
ejpam-3266	439	3	12	12	NUM
ejpam-3266	439	4	;	;	PUNCT
ejpam-3266	439	5	remark	remark	NOUN
ejpam-3266	439	6	1	1	NUM
ejpam-3266	439	7	]	]	PUNCT
ejpam-3266	439	8	)	)	PUNCT
ejpam-3266	439	9	if	if	SCONJ
ejpam-3266	439	10	(	(	PUNCT
ejpam-3266	439	11	h	h	NOUN
ejpam-3266	439	12	,	,	PUNCT
ejpam-3266	439	13	◦	◦	NOUN
ejpam-3266	439	14	,	,	PUNCT
ejpam-3266	439	15	≤	≤	NUM
ejpam-3266	439	16	)	)	PUNCT
ejpam-3266	439	17	is	be	AUX
ejpam-3266	439	18	an	an	DET
ejpam-3266	439	19	ordered	ordered	ADJ
ejpam-3266	439	20	hypergroupoid	hypergroupoid	NOUN
ejpam-3266	439	21	,	,	PUNCT
ejpam-3266	439	22	then	then	ADV
ejpam-3266	439	23	the	the	DET
ejpam-3266	439	24	semilattice	semilattice	NOUN
ejpam-3266	439	25	congruence	congruence	NOUN
ejpam-3266	439	26	n	n	PART
ejpam-3266	439	27	is	be	AUX
ejpam-3266	439	28	a	a	DET
ejpam-3266	439	29	complete	complete	ADJ
ejpam-3266	439	30	semilattice	semilattice	NOUN
ejpam-3266	439	31	congruence	congruence	NOUN
ejpam-3266	439	32	on	on	ADP
ejpam-3266	439	33	h.	h.	PROPN
ejpam-3266	439	34	proof	proof	NOUN
ejpam-3266	439	35	.	.	PUNCT
ejpam-3266	440	1	let	let	VERB
ejpam-3266	440	2	a	a	DET
ejpam-3266	440	3	≤	≤	PROPN
ejpam-3266	440	4	b.	b.	NOUN
ejpam-3266	441	1	then	then	ADV
ejpam-3266	441	2	(	(	PUNCT
ejpam-3266	441	3	a	a	X
ejpam-3266	441	4	,	,	PUNCT
ejpam-3266	441	5	a	a	DET
ejpam-3266	441	6	◦	◦	NOUN
ejpam-3266	441	7	b	b	NOUN
ejpam-3266	441	8	)	)	PUNCT
ejpam-3266	441	9	∈	∈	PROPN
ejpam-3266	441	10	n	n	NOUN
ejpam-3266	441	11	.	.	PUNCT
ejpam-3266	442	1	in	in	ADP
ejpam-3266	442	2	fact	fact	NOUN
ejpam-3266	442	3	:	:	PUNCT
ejpam-3266	442	4	let	let	VERB
ejpam-3266	442	5	u	u	PRON
ejpam-3266	442	6	∈	∈	PROPN
ejpam-3266	442	7	a	a	DET
ejpam-3266	442	8	◦	◦	NOUN
ejpam-3266	442	9	b.	b.	NOUN
ejpam-3266	442	10	then	then	ADV
ejpam-3266	442	11	(	(	PUNCT
ejpam-3266	442	12	a	a	PRON
ejpam-3266	442	13	,	,	PUNCT
ejpam-3266	442	14	u	u	NOUN
ejpam-3266	442	15	)	)	PUNCT
ejpam-3266	442	16	∈	∈	PROPN
ejpam-3266	442	17	n	n	PRON
ejpam-3266	442	18	,	,	PUNCT
ejpam-3266	442	19	that	that	ADV
ejpam-3266	442	20	is	be	AUX
ejpam-3266	442	21	n(a	n(a	NOUN
ejpam-3266	442	22	)	)	PUNCT
ejpam-3266	442	23	=	=	SYM
ejpam-3266	442	24	n(u	n(u	PROPN
ejpam-3266	442	25	)	)	PUNCT
ejpam-3266	442	26	.	.	PUNCT
ejpam-3266	443	1	indeed	indeed	ADV
ejpam-3266	443	2	:	:	PUNCT
ejpam-3266	443	3	since	since	SCONJ
ejpam-3266	443	4	n(a	n(a	NOUN
ejpam-3266	443	5	)	)	PUNCT
ejpam-3266	443	6	3	3	NUM
ejpam-3266	443	7	a	a	DET
ejpam-3266	443	8	≤	≤	NUM
ejpam-3266	443	9	b	b	NOUN
ejpam-3266	443	10	,	,	PUNCT
ejpam-3266	443	11	we	we	PRON
ejpam-3266	443	12	have	have	VERB
ejpam-3266	443	13	b	b	PROPN
ejpam-3266	443	14	∈	∈	PROPN
ejpam-3266	443	15	n(a	n(a	PROPN
ejpam-3266	443	16	)	)	PUNCT
ejpam-3266	443	17	.	.	PUNCT
ejpam-3266	444	1	since	since	SCONJ
ejpam-3266	444	2	a	a	DET
ejpam-3266	444	3	,	,	PUNCT
ejpam-3266	444	4	b	b	PROPN
ejpam-3266	444	5	∈	∈	PROPN
ejpam-3266	444	6	n(a	n(a	PROPN
ejpam-3266	444	7	)	)	PUNCT
ejpam-3266	444	8	,	,	PUNCT
ejpam-3266	444	9	we	we	PRON
ejpam-3266	444	10	have	have	VERB
ejpam-3266	444	11	a	a	DET
ejpam-3266	444	12	◦	◦	NOUN
ejpam-3266	444	13	b	b	NOUN
ejpam-3266	444	14	⊆	⊆	NUM
ejpam-3266	444	15	n(a	n(a	NOUN
ejpam-3266	444	16	)	)	PUNCT
ejpam-3266	444	17	,	,	PUNCT
ejpam-3266	444	18	then	then	ADV
ejpam-3266	444	19	u	u	PROPN
ejpam-3266	444	20	∈	∈	PROPN
ejpam-3266	444	21	n(a	n(a	PROPN
ejpam-3266	444	22	)	)	PUNCT
ejpam-3266	444	23	,	,	PUNCT
ejpam-3266	444	24	and	and	CCONJ
ejpam-3266	444	25	so	so	ADV
ejpam-3266	444	26	n(u	n(u	PROPN
ejpam-3266	444	27	)	)	PUNCT
ejpam-3266	444	28	⊆	⊆	NUM
ejpam-3266	444	29	n(a	n(a	NOUN
ejpam-3266	444	30	)	)	PUNCT
ejpam-3266	444	31	.	.	PUNCT
ejpam-3266	445	1	on	on	ADP
ejpam-3266	445	2	the	the	DET
ejpam-3266	445	3	other	other	ADJ
ejpam-3266	445	4	hand	hand	NOUN
ejpam-3266	445	5	,	,	PUNCT
ejpam-3266	445	6	since	since	SCONJ
ejpam-3266	445	7	u	u	PROPN
ejpam-3266	445	8	∈	∈	PROPN
ejpam-3266	445	9	a	a	DET
ejpam-3266	445	10	◦	◦	NOUN
ejpam-3266	445	11	b	b	NOUN
ejpam-3266	445	12	and	and	CCONJ
ejpam-3266	445	13	u	u	PROPN
ejpam-3266	445	14	∈	∈	PROPN
ejpam-3266	445	15	n(u	n(u	PROPN
ejpam-3266	445	16	)	)	PUNCT
ejpam-3266	445	17	,	,	PUNCT
ejpam-3266	445	18	we	we	PRON
ejpam-3266	445	19	have	have	VERB
ejpam-3266	445	20	(	(	PUNCT
ejpam-3266	445	21	a	a	DET
ejpam-3266	445	22	◦	◦	NOUN
ejpam-3266	445	23	b	b	NOUN
ejpam-3266	445	24	)	)	PUNCT
ejpam-3266	445	25	∩	∩	ADJ
ejpam-3266	445	26	n(u	n(u	PROPN
ejpam-3266	445	27	)	)	PUNCT
ejpam-3266	445	28	6=	6=	ADP
ejpam-3266	445	29	∅	∅	NOUN
ejpam-3266	445	30	,	,	PUNCT
ejpam-3266	445	31	then	then	ADV
ejpam-3266	445	32	a	a	DET
ejpam-3266	445	33	◦	◦	NOUN
ejpam-3266	445	34	b	b	NOUN
ejpam-3266	445	35	⊆	⊆	NUM
ejpam-3266	445	36	n(u	n(u	PROPN
ejpam-3266	445	37	)	)	PUNCT
ejpam-3266	445	38	,	,	PUNCT
ejpam-3266	445	39	then	then	ADV
ejpam-3266	445	40	a	a	DET
ejpam-3266	445	41	∈	∈	PROPN
ejpam-3266	445	42	n(u	n(u	PROPN
ejpam-3266	445	43	)	)	PUNCT
ejpam-3266	445	44	,	,	PUNCT
ejpam-3266	445	45	and	and	CCONJ
ejpam-3266	445	46	n(a	n(a	NOUN
ejpam-3266	445	47	)	)	PUNCT
ejpam-3266	446	1	⊆	⊆	NUM
ejpam-3266	446	2	n(u	n(u	PROPN
ejpam-3266	446	3	)	)	PUNCT
ejpam-3266	446	4	.	.	PUNCT
ejpam-3266	447	1	hence	hence	ADV
ejpam-3266	447	2	we	we	PRON
ejpam-3266	447	3	obtain	obtain	VERB
ejpam-3266	447	4	n(u	n(u	NOUN
ejpam-3266	447	5	)	)	PUNCT
ejpam-3266	447	6	=	=	SYM
ejpam-3266	447	7	n(a	n(a	NOUN
ejpam-3266	447	8	)	)	PUNCT
ejpam-3266	447	9	and	and	CCONJ
ejpam-3266	447	10	the	the	DET
ejpam-3266	447	11	proof	proof	NOUN
ejpam-3266	447	12	is	be	AUX
ejpam-3266	447	13	complete	complete	ADJ
ejpam-3266	447	14	.	.	PUNCT
ejpam-3266	448	1	�	�	PROPN
ejpam-3266	448	2	theorem	theorem	VERB
ejpam-3266	448	3	4.10	4.10	NUM
ejpam-3266	448	4	.	.	PUNCT
ejpam-3266	449	1	(	(	PUNCT
ejpam-3266	449	2	cf	cf	NOUN
ejpam-3266	449	3	.	.	PUNCT
ejpam-3266	450	1	also	also	ADV
ejpam-3266	450	2	[	[	X
ejpam-3266	450	3	11	11	NUM
ejpam-3266	450	4	]	]	PUNCT
ejpam-3266	450	5	)	)	PUNCT
ejpam-3266	450	6	let	let	VERB
ejpam-3266	450	7	h	h	NOUN
ejpam-3266	450	8	be	be	AUX
ejpam-3266	450	9	an	an	DET
ejpam-3266	450	10	ordered	order	VERB
ejpam-3266	450	11	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	450	12	and	and	CCONJ
ejpam-3266	450	13	σ	σ	NOUN
ejpam-3266	450	14	a	a	DET
ejpam-3266	450	15	complete	complete	ADJ
ejpam-3266	450	16	semilattice	semilattice	NOUN
ejpam-3266	450	17	congruence	congruence	NOUN
ejpam-3266	450	18	on	on	ADP
ejpam-3266	450	19	h.	h.	PROPN
ejpam-3266	450	20	then	then	ADV
ejpam-3266	450	21	there	there	PRON
ejpam-3266	450	22	exists	exist	VERB
ejpam-3266	450	23	a	a	DET
ejpam-3266	450	24	family	family	NOUN
ejpam-3266	450	25	a	a	PRON
ejpam-3266	450	26	of	of	ADP
ejpam-3266	450	27	proper	proper	ADJ
ejpam-3266	450	28	prime	prime	ADJ
ejpam-3266	450	29	ideals	ideal	NOUN
ejpam-3266	450	30	of	of	ADP
ejpam-3266	450	31	h	h	NOUN
ejpam-3266	450	32	such	such	ADJ
ejpam-3266	450	33	that	that	SCONJ
ejpam-3266	450	34	σ	σ	PROPN
ejpam-3266	450	35	=	=	SYM
ejpam-3266	450	36	⋂	⋂	PROPN
ejpam-3266	450	37	i∈a	i∈a	VERB
ejpam-3266	450	38	σi	σi	NOUN
ejpam-3266	450	39	.	.	PUNCT
ejpam-3266	451	1	proof	proof	NOUN
ejpam-3266	451	2	.	.	PUNCT
ejpam-3266	452	1	following	follow	VERB
ejpam-3266	452	2	theorem	theorem	VERB
ejpam-3266	452	3	3.1	3.1	NUM
ejpam-3266	452	4	,	,	PUNCT
ejpam-3266	452	5	it	it	PRON
ejpam-3266	452	6	remains	remain	VERB
ejpam-3266	452	7	to	to	PART
ejpam-3266	452	8	prove	prove	VERB
ejpam-3266	452	9	that	that	SCONJ
ejpam-3266	452	10	for	for	ADP
ejpam-3266	452	11	the	the	DET
ejpam-3266	452	12	set	set	ADJ
ejpam-3266	452	13	ax	ax	NOUN
ejpam-3266	452	14	:	:	PUNCT
ejpam-3266	452	15	=	=	SYM
ejpam-3266	452	16	{	{	PUNCT
ejpam-3266	452	17	y	y	PROPN
ejpam-3266	452	18	∈	∈	PROPN
ejpam-3266	452	19	h	h	NOUN
ejpam-3266	453	1	|	|	ADV
ejpam-3266	453	2	(	(	PUNCT
ejpam-3266	453	3	x	x	X
ejpam-3266	453	4	,	,	PUNCT
ejpam-3266	453	5	x	x	PUNCT
ejpam-3266	453	6	◦	◦	NOUN
ejpam-3266	453	7	y	y	NOUN
ejpam-3266	453	8	)	)	PUNCT
ejpam-3266	453	9	∈	∈	PROPN
ejpam-3266	453	10	σ	σ	PROPN
ejpam-3266	453	11	}	}	PUNCT
ejpam-3266	453	12	n.	n.	NOUN
ejpam-3266	453	13	kehayopulu	kehayopulu	PROPN
ejpam-3266	453	14	/	/	SYM
ejpam-3266	453	15	eur	eur	PROPN
ejpam-3266	453	16	.	.	PUNCT
ejpam-3266	454	1	j.	j.	PROPN
ejpam-3266	454	2	pure	pure	PROPN
ejpam-3266	454	3	appl	appl	PROPN
ejpam-3266	454	4	.	.	PROPN
ejpam-3266	454	5	math	math	PROPN
ejpam-3266	454	6	,	,	PUNCT
ejpam-3266	454	7	11	11	NUM
ejpam-3266	454	8	(	(	PUNCT
ejpam-3266	454	9	2	2	NUM
ejpam-3266	454	10	)	)	PUNCT
ejpam-3266	454	11	(	(	PUNCT
ejpam-3266	454	12	2018	2018	NUM
ejpam-3266	454	13	)	)	PUNCT
ejpam-3266	454	14	,	,	PUNCT
ejpam-3266	454	15	476	476	NUM
ejpam-3266	454	16	-	-	SYM
ejpam-3266	454	17	492	492	NUM
ejpam-3266	454	18	490	490	NUM
ejpam-3266	454	19	the	the	DET
ejpam-3266	454	20	following	follow	VERB
ejpam-3266	454	21	property	property	NOUN
ejpam-3266	454	22	is	be	AUX
ejpam-3266	454	23	satisfied	satisfied	ADJ
ejpam-3266	454	24	if	if	SCONJ
ejpam-3266	454	25	y	y	PROPN
ejpam-3266	454	26	∈	∈	PROPN
ejpam-3266	454	27	ax	ax	NOUN
ejpam-3266	454	28	and	and	CCONJ
ejpam-3266	454	29	h	h	NOUN
ejpam-3266	454	30	3	3	NUM
ejpam-3266	454	31	z	z	NOUN
ejpam-3266	454	32	≥	≥	NOUN
ejpam-3266	455	1	y	y	NOUN
ejpam-3266	455	2	,	,	PUNCT
ejpam-3266	455	3	then	then	ADV
ejpam-3266	455	4	z	z	NOUN
ejpam-3266	455	5	∈	∈	PROPN
ejpam-3266	455	6	ax	ax	NOUN
ejpam-3266	455	7	.	.	PUNCT
ejpam-3266	456	1	indeed	indeed	ADV
ejpam-3266	456	2	:	:	PUNCT
ejpam-3266	456	3	since	since	SCONJ
ejpam-3266	456	4	y	y	PROPN
ejpam-3266	456	5	∈	∈	PROPN
ejpam-3266	456	6	ax	ax	NOUN
ejpam-3266	456	7	,	,	PUNCT
ejpam-3266	456	8	we	we	PRON
ejpam-3266	456	9	have	have	VERB
ejpam-3266	456	10	(	(	PUNCT
ejpam-3266	456	11	x	x	NOUN
ejpam-3266	456	12	,	,	PUNCT
ejpam-3266	456	13	x	x	PROPN
ejpam-3266	456	14	◦	◦	NOUN
ejpam-3266	456	15	y	y	NOUN
ejpam-3266	456	16	)	)	PUNCT
ejpam-3266	456	17	∈	∈	PROPN
ejpam-3266	456	18	σ	σ	NOUN
ejpam-3266	456	19	then	then	ADV
ejpam-3266	456	20	,	,	PUNCT
ejpam-3266	456	21	by	by	ADP
ejpam-3266	456	22	lemma	lemma	PROPN
ejpam-3266	456	23	2.12	2.12	NUM
ejpam-3266	456	24	,	,	PUNCT
ejpam-3266	456	25	(	(	PUNCT
ejpam-3266	456	26	x	x	X
ejpam-3266	456	27	◦	◦	NOUN
ejpam-3266	456	28	z	z	NOUN
ejpam-3266	456	29	,	,	PUNCT
ejpam-3266	456	30	(	(	PUNCT
ejpam-3266	456	31	x	x	NOUN
ejpam-3266	456	32	◦	◦	NOUN
ejpam-3266	456	33	y)∗{z	y)∗{z	NOUN
ejpam-3266	456	34	}	}	PUNCT
ejpam-3266	456	35	)	)	PUNCT
ejpam-3266	456	36	∈	∈	PROPN
ejpam-3266	456	37	σ	σ	PROPN
ejpam-3266	456	38	,	,	PUNCT
ejpam-3266	456	39	that	that	ADV
ejpam-3266	456	40	is	is	ADV
ejpam-3266	456	41	(	(	PUNCT
ejpam-3266	456	42	(	(	PUNCT
ejpam-3266	456	43	x	x	SYM
ejpam-3266	456	44	◦	◦	VERB
ejpam-3266	456	45	y	y	NOUN
ejpam-3266	456	46	)	)	PUNCT
ejpam-3266	456	47	∗	∗	NOUN
ejpam-3266	456	48	{	{	PUNCT
ejpam-3266	456	49	z	z	NOUN
ejpam-3266	456	50	}	}	PUNCT
ejpam-3266	456	51	,	,	PUNCT
ejpam-3266	456	52	x	x	PUNCT
ejpam-3266	456	53	◦	◦	NOUN
ejpam-3266	456	54	z	z	NOUN
ejpam-3266	456	55	)	)	PUNCT
ejpam-3266	457	1	∈	∈	PROPN
ejpam-3266	457	2	σ	σ	PROPN
ejpam-3266	457	3	.	.	PUNCT
ejpam-3266	458	1	since	since	SCONJ
ejpam-3266	458	2	y	y	PROPN
ejpam-3266	458	3	≤	≤	PROPN
ejpam-3266	458	4	z	z	PROPN
ejpam-3266	458	5	and	and	CCONJ
ejpam-3266	458	6	σ	σ	PROPN
ejpam-3266	458	7	is	be	AUX
ejpam-3266	458	8	a	a	DET
ejpam-3266	458	9	complete	complete	ADJ
ejpam-3266	458	10	semilattice	semilattice	NOUN
ejpam-3266	458	11	congruence	congruence	NOUN
ejpam-3266	458	12	on	on	ADP
ejpam-3266	458	13	h	h	NOUN
ejpam-3266	458	14	,	,	PUNCT
ejpam-3266	458	15	we	we	PRON
ejpam-3266	458	16	have	have	VERB
ejpam-3266	458	17	(	(	PUNCT
ejpam-3266	458	18	y	y	NOUN
ejpam-3266	458	19	,	,	PUNCT
ejpam-3266	458	20	y	y	PROPN
ejpam-3266	458	21	◦	◦	PROPN
ejpam-3266	458	22	z	z	PROPN
ejpam-3266	458	23	)	)	PUNCT
ejpam-3266	458	24	∈	∈	PROPN
ejpam-3266	458	25	σ	σ	NOUN
ejpam-3266	458	26	and	and	CCONJ
ejpam-3266	458	27	,	,	PUNCT
ejpam-3266	458	28	by	by	ADP
ejpam-3266	458	29	lemma	lemma	PROPN
ejpam-3266	458	30	2.13	2.13	NUM
ejpam-3266	458	31	,	,	PUNCT
ejpam-3266	458	32	(	(	PUNCT
ejpam-3266	458	33	x	x	PUNCT
ejpam-3266	458	34	◦	◦	NOUN
ejpam-3266	458	35	y	y	PROPN
ejpam-3266	458	36	,	,	PUNCT
ejpam-3266	458	37	{	{	PUNCT
ejpam-3266	458	38	x	x	NOUN
ejpam-3266	458	39	}	}	PUNCT
ejpam-3266	458	40	∗	∗	NOUN
ejpam-3266	458	41	(	(	PUNCT
ejpam-3266	458	42	y	y	PROPN
ejpam-3266	458	43	◦	◦	PROPN
ejpam-3266	458	44	z	z	PROPN
ejpam-3266	458	45	)	)	PUNCT
ejpam-3266	458	46	)	)	PUNCT
ejpam-3266	459	1	∈	∈	PROPN
ejpam-3266	459	2	σ	σ	PROPN
ejpam-3266	459	3	.	.	PUNCT
ejpam-3266	460	1	hence	hence	ADV
ejpam-3266	460	2	we	we	PRON
ejpam-3266	460	3	obtain	obtain	VERB
ejpam-3266	460	4	(	(	PUNCT
ejpam-3266	460	5	x	x	X
ejpam-3266	460	6	,	,	PUNCT
ejpam-3266	460	7	x	x	PART
ejpam-3266	460	8	◦	◦	NOUN
ejpam-3266	460	9	z	z	NOUN
ejpam-3266	460	10	)	)	PUNCT
ejpam-3266	460	11	∈	∈	PROPN
ejpam-3266	460	12	σ	σ	NOUN
ejpam-3266	460	13	that	that	PRON
ejpam-3266	460	14	is	be	AUX
ejpam-3266	460	15	,	,	PUNCT
ejpam-3266	460	16	z	z	NOUN
ejpam-3266	460	17	∈	∈	PROPN
ejpam-3266	460	18	ax	ax	NOUN
ejpam-3266	460	19	.	.	PUNCT
ejpam-3266	460	20	�	�	PROPN
ejpam-3266	460	21	by	by	ADP
ejpam-3266	460	22	proposition	proposition	NOUN
ejpam-3266	460	23	3.2	3.2	NUM
ejpam-3266	460	24	,	,	PUNCT
ejpam-3266	460	25	proposition	proposition	NOUN
ejpam-3266	460	26	4.9	4.9	NUM
ejpam-3266	460	27	and	and	CCONJ
ejpam-3266	460	28	theorem	theorem	VERB
ejpam-3266	460	29	4.10	4.10	NUM
ejpam-3266	460	30	,	,	PUNCT
ejpam-3266	460	31	we	we	PRON
ejpam-3266	460	32	have	have	VERB
ejpam-3266	460	33	the	the	DET
ejpam-3266	460	34	following	follow	VERB
ejpam-3266	460	35	corollary	corollary	NOUN
ejpam-3266	460	36	4.11	4.11	NUM
ejpam-3266	460	37	.	.	PUNCT
ejpam-3266	461	1	(	(	PUNCT
ejpam-3266	461	2	cf	cf	NOUN
ejpam-3266	461	3	.	.	PUNCT
ejpam-3266	462	1	also	also	ADV
ejpam-3266	462	2	[	[	X
ejpam-3266	462	3	11	11	NUM
ejpam-3266	462	4	;	;	PUNCT
ejpam-3266	462	5	the	the	DET
ejpam-3266	462	6	proposition	proposition	NOUN
ejpam-3266	462	7	]	]	PUNCT
ejpam-3266	462	8	)	)	PUNCT
ejpam-3266	462	9	if	if	SCONJ
ejpam-3266	462	10	h	h	NOUN
ejpam-3266	462	11	is	be	AUX
ejpam-3266	462	12	an	an	DET
ejpam-3266	462	13	ordered	order	VERB
ejpam-3266	462	14	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	462	15	,	,	PUNCT
ejpam-3266	462	16	then	then	ADV
ejpam-3266	462	17	the	the	DET
ejpam-3266	462	18	relation	relation	NOUN
ejpam-3266	462	19	n	n	PRON
ejpam-3266	462	20	is	be	AUX
ejpam-3266	462	21	the	the	DET
ejpam-3266	462	22	least	least	ADJ
ejpam-3266	462	23	complete	complete	ADJ
ejpam-3266	462	24	semilattice	semilattice	NOUN
ejpam-3266	462	25	congruence	congruence	NOUN
ejpam-3266	462	26	on	on	ADP
ejpam-3266	462	27	h.	h.	PROPN
ejpam-3266	462	28	if	if	SCONJ
ejpam-3266	462	29	(	(	PUNCT
ejpam-3266	462	30	s	s	X
ejpam-3266	462	31	,	,	PUNCT
ejpam-3266	462	32	·	·	PUNCT
ejpam-3266	462	33	,	,	PUNCT
ejpam-3266	462	34	≤	≤	NUM
ejpam-3266	462	35	)	)	PUNCT
ejpam-3266	462	36	is	be	AUX
ejpam-3266	462	37	an	an	DET
ejpam-3266	462	38	ordered	order	VERB
ejpam-3266	462	39	groupoid	groupoid	NOUN
ejpam-3266	462	40	and	and	CCONJ
ejpam-3266	462	41	“	"	PUNCT
ejpam-3266	462	42	◦	◦	NOUN
ejpam-3266	462	43	”	"	PUNCT
ejpam-3266	462	44	the	the	DET
ejpam-3266	462	45	hyperoperation	hyperoperation	NOUN
ejpam-3266	462	46	on	on	ADP
ejpam-3266	462	47	s	s	PRON
ejpam-3266	462	48	defined	define	VERB
ejpam-3266	462	49	by	by	ADP
ejpam-3266	462	50	:	:	PUNCT
ejpam-3266	462	51	◦	◦	NOUN
ejpam-3266	462	52	:	:	PUNCT
ejpam-3266	462	53	s×s	s×s	PROPN
ejpam-3266	462	54	→	→	SYM
ejpam-3266	462	55	p∗(s	p∗(s	NOUN
ejpam-3266	462	56	)	)	PUNCT
ejpam-3266	462	57	|	|	NOUN
ejpam-3266	462	58	(	(	PUNCT
ejpam-3266	462	59	a	a	PRON
ejpam-3266	462	60	,	,	PUNCT
ejpam-3266	462	61	b)→	b)→	VERB
ejpam-3266	462	62	a	a	DET
ejpam-3266	462	63	◦	◦	NOUN
ejpam-3266	462	64	b	b	NOUN
ejpam-3266	462	65	,	,	PUNCT
ejpam-3266	462	66	where	where	SCONJ
ejpam-3266	462	67	a	a	DET
ejpam-3266	462	68	◦	◦	NOUN
ejpam-3266	462	69	b	b	NOUN
ejpam-3266	462	70	:	:	PUNCT
ejpam-3266	462	71	=	=	X
ejpam-3266	462	72	{	{	PUNCT
ejpam-3266	462	73	t	t	NOUN
ejpam-3266	462	74	∈	∈	PROPN
ejpam-3266	462	75	s	s	AUX
ejpam-3266	462	76	|	|	NOUN
ejpam-3266	462	77	t	t	X
ejpam-3266	462	78	≤	≤	PROPN
ejpam-3266	462	79	ab	ab	PROPN
ejpam-3266	462	80	}	}	PUNCT
ejpam-3266	462	81	,	,	PUNCT
ejpam-3266	462	82	then	then	ADV
ejpam-3266	462	83	(	(	PUNCT
ejpam-3266	462	84	s	s	X
ejpam-3266	462	85	,	,	PUNCT
ejpam-3266	462	86	◦	◦	NOUN
ejpam-3266	462	87	,	,	PUNCT
ejpam-3266	462	88	≤	≤	NUM
ejpam-3266	462	89	)	)	PUNCT
ejpam-3266	462	90	is	be	AUX
ejpam-3266	462	91	an	an	DET
ejpam-3266	462	92	ordered	order	VERB
ejpam-3266	462	93	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	463	1	[	[	X
ejpam-3266	463	2	10	10	NUM
ejpam-3266	463	3	;	;	PUNCT
ejpam-3266	463	4	lemma	lemma	PROPN
ejpam-3266	463	5	1	1	NUM
ejpam-3266	463	6	]	]	PUNCT
ejpam-3266	463	7	.	.	PUNCT
ejpam-3266	464	1	proposition	proposition	NOUN
ejpam-3266	464	2	4.12	4.12	NUM
ejpam-3266	464	3	.	.	PUNCT
ejpam-3266	465	1	let	let	VERB
ejpam-3266	465	2	(	(	PUNCT
ejpam-3266	465	3	s	s	X
ejpam-3266	465	4	,	,	PUNCT
ejpam-3266	465	5	·	·	PUNCT
ejpam-3266	465	6	,	,	PUNCT
ejpam-3266	465	7	≤	≤	NUM
ejpam-3266	465	8	)	)	PUNCT
ejpam-3266	465	9	be	be	AUX
ejpam-3266	465	10	an	an	DET
ejpam-3266	465	11	ordered	order	VERB
ejpam-3266	465	12	groupoid	groupoid	NOUN
ejpam-3266	465	13	and	and	CCONJ
ejpam-3266	465	14	“	"	PUNCT
ejpam-3266	465	15	◦	◦	NOUN
ejpam-3266	465	16	”	"	PUNCT
ejpam-3266	465	17	the	the	DET
ejpam-3266	465	18	hyperoperation	hyperoperation	NOUN
ejpam-3266	465	19	on	on	ADP
ejpam-3266	465	20	s	s	PRON
ejpam-3266	465	21	defined	define	VERB
ejpam-3266	465	22	by	by	ADP
ejpam-3266	465	23	◦	◦	NOUN
ejpam-3266	465	24	:	:	PUNCT
ejpam-3266	465	25	s	s	VERB
ejpam-3266	465	26	×	×	PROPN
ejpam-3266	465	27	s	s	X
ejpam-3266	465	28	→	→	SYM
ejpam-3266	465	29	p∗(s	p∗(s	NOUN
ejpam-3266	465	30	)	)	PUNCT
ejpam-3266	465	31	|	|	NOUN
ejpam-3266	465	32	(	(	PUNCT
ejpam-3266	465	33	a	a	PRON
ejpam-3266	465	34	,	,	PUNCT
ejpam-3266	465	35	b)→	b)→	VERB
ejpam-3266	465	36	a	a	DET
ejpam-3266	465	37	◦	◦	NOUN
ejpam-3266	465	38	b	b	NOUN
ejpam-3266	465	39	:	:	PUNCT
ejpam-3266	465	40	=	=	X
ejpam-3266	465	41	{	{	PUNCT
ejpam-3266	465	42	t	t	NOUN
ejpam-3266	465	43	∈	∈	PROPN
ejpam-3266	465	44	s	s	AUX
ejpam-3266	465	45	|	|	NOUN
ejpam-3266	465	46	t	t	X
ejpam-3266	465	47	≤	≤	PROPN
ejpam-3266	465	48	ab	ab	PROPN
ejpam-3266	465	49	}	}	PUNCT
ejpam-3266	465	50	.	.	PUNCT
ejpam-3266	466	1	if	if	SCONJ
ejpam-3266	466	2	f	f	PROPN
ejpam-3266	466	3	is	be	AUX
ejpam-3266	466	4	a	a	DET
ejpam-3266	466	5	filter	filter	NOUN
ejpam-3266	466	6	of	of	ADP
ejpam-3266	466	7	(	(	PUNCT
ejpam-3266	466	8	s	s	PROPN
ejpam-3266	466	9	,	,	PUNCT
ejpam-3266	466	10	◦	◦	NOUN
ejpam-3266	466	11	,	,	PUNCT
ejpam-3266	466	12	≤	≤	NUM
ejpam-3266	466	13	)	)	PUNCT
ejpam-3266	466	14	,	,	PUNCT
ejpam-3266	466	15	then	then	ADV
ejpam-3266	466	16	it	it	PRON
ejpam-3266	466	17	is	be	AUX
ejpam-3266	466	18	a	a	DET
ejpam-3266	466	19	filter	filter	NOUN
ejpam-3266	466	20	of	of	ADP
ejpam-3266	466	21	(	(	PUNCT
ejpam-3266	466	22	s	s	PROPN
ejpam-3266	466	23	,	,	PUNCT
ejpam-3266	466	24	·	·	PUNCT
ejpam-3266	466	25	,	,	PUNCT
ejpam-3266	466	26	≤	≤	NUM
ejpam-3266	466	27	)	)	PUNCT
ejpam-3266	466	28	as	as	ADV
ejpam-3266	466	29	well	well	ADV
ejpam-3266	466	30	.	.	PUNCT
ejpam-3266	467	1	the	the	DET
ejpam-3266	467	2	converse	converse	NOUN
ejpam-3266	467	3	statement	statement	NOUN
ejpam-3266	467	4	does	do	AUX
ejpam-3266	467	5	not	not	PART
ejpam-3266	467	6	hold	hold	VERB
ejpam-3266	467	7	in	in	ADP
ejpam-3266	467	8	general	general	ADJ
ejpam-3266	467	9	.	.	PUNCT
ejpam-3266	468	1	proof	proof	NOUN
ejpam-3266	468	2	.	.	PUNCT
ejpam-3266	469	1	let	let	VERB
ejpam-3266	469	2	a	a	DET
ejpam-3266	469	3	,	,	PUNCT
ejpam-3266	469	4	b	b	PROPN
ejpam-3266	469	5	∈	∈	PROPN
ejpam-3266	469	6	f	f	X
ejpam-3266	469	7	.	.	PUNCT
ejpam-3266	470	1	since	since	SCONJ
ejpam-3266	470	2	f	f	PROPN
ejpam-3266	470	3	is	be	AUX
ejpam-3266	470	4	a	a	DET
ejpam-3266	470	5	filter	filter	NOUN
ejpam-3266	470	6	of	of	ADP
ejpam-3266	470	7	(	(	PUNCT
ejpam-3266	470	8	s	s	PROPN
ejpam-3266	470	9	,	,	PUNCT
ejpam-3266	470	10	◦	◦	NOUN
ejpam-3266	470	11	,	,	PUNCT
ejpam-3266	470	12	≤	≤	NUM
ejpam-3266	470	13	)	)	PUNCT
ejpam-3266	470	14	,	,	PUNCT
ejpam-3266	470	15	we	we	PRON
ejpam-3266	470	16	have	have	VERB
ejpam-3266	470	17	a	a	DET
ejpam-3266	470	18	◦	◦	NOUN
ejpam-3266	470	19	b	b	NOUN
ejpam-3266	470	20	⊆	⊆	NUM
ejpam-3266	470	21	f	f	NOUN
ejpam-3266	470	22	.	.	PUNCT
ejpam-3266	471	1	since	since	SCONJ
ejpam-3266	471	2	ab	ab	PROPN
ejpam-3266	471	3	∈	∈	PROPN
ejpam-3266	471	4	a	a	DET
ejpam-3266	471	5	◦	◦	NOUN
ejpam-3266	471	6	b	b	NUM
ejpam-3266	471	7	,	,	PUNCT
ejpam-3266	471	8	we	we	PRON
ejpam-3266	471	9	have	have	VERB
ejpam-3266	471	10	ab	ab	PROPN
ejpam-3266	471	11	∈	∈	PROPN
ejpam-3266	471	12	f	f	PROPN
ejpam-3266	471	13	.	.	PUNCT
ejpam-3266	472	1	let	let	VERB
ejpam-3266	472	2	now	now	ADV
ejpam-3266	472	3	a	a	PRON
ejpam-3266	472	4	,	,	PUNCT
ejpam-3266	472	5	b	b	X
ejpam-3266	472	6	∈	∈	NOUN
ejpam-3266	472	7	s	s	VERB
ejpam-3266	472	8	such	such	ADJ
ejpam-3266	472	9	that	that	SCONJ
ejpam-3266	472	10	ab	ab	PROPN
ejpam-3266	472	11	∈	∈	PROPN
ejpam-3266	472	12	f	f	PROPN
ejpam-3266	472	13	.	.	PUNCT
ejpam-3266	473	1	since	since	SCONJ
ejpam-3266	473	2	ab	ab	PROPN
ejpam-3266	473	3	∈	∈	PROPN
ejpam-3266	473	4	a	a	DET
ejpam-3266	473	5	◦	◦	NOUN
ejpam-3266	473	6	b	b	NOUN
ejpam-3266	473	7	and	and	CCONJ
ejpam-3266	473	8	ab	ab	PROPN
ejpam-3266	473	9	∈	∈	PROPN
ejpam-3266	474	1	f	f	PROPN
ejpam-3266	474	2	,	,	PUNCT
ejpam-3266	474	3	we	we	PRON
ejpam-3266	474	4	have	have	VERB
ejpam-3266	474	5	(	(	PUNCT
ejpam-3266	474	6	a	a	DET
ejpam-3266	474	7	◦	◦	NOUN
ejpam-3266	474	8	b	b	NOUN
ejpam-3266	474	9	)	)	PUNCT
ejpam-3266	474	10	∩	∩	ADJ
ejpam-3266	474	11	f	f	PROPN
ejpam-3266	474	12	6=	6=	PROPN
ejpam-3266	474	13	∅	∅	NOUN
ejpam-3266	474	14	,	,	PUNCT
ejpam-3266	474	15	then	then	ADV
ejpam-3266	474	16	a	a	DET
ejpam-3266	474	17	◦	◦	NOUN
ejpam-3266	474	18	b	b	NOUN
ejpam-3266	474	19	⊆	⊆	NUM
ejpam-3266	474	20	f	f	NOUN
ejpam-3266	474	21	,	,	PUNCT
ejpam-3266	474	22	and	and	CCONJ
ejpam-3266	474	23	then	then	ADV
ejpam-3266	474	24	a	a	PRON
ejpam-3266	474	25	,	,	PUNCT
ejpam-3266	474	26	b	b	PROPN
ejpam-3266	474	27	∈	∈	PROPN
ejpam-3266	474	28	f	f	X
ejpam-3266	474	29	.	.	PUNCT
ejpam-3266	475	1	for	for	ADP
ejpam-3266	475	2	the	the	DET
ejpam-3266	475	3	converse	converse	NOUN
ejpam-3266	475	4	statement	statement	NOUN
ejpam-3266	475	5	,	,	PUNCT
ejpam-3266	475	6	consider	consider	VERB
ejpam-3266	475	7	the	the	DET
ejpam-3266	475	8	ordered	order	VERB
ejpam-3266	475	9	semigroup	semigroup	NOUN
ejpam-3266	475	10	(	(	PUNCT
ejpam-3266	475	11	s	s	PROPN
ejpam-3266	475	12	,	,	PUNCT
ejpam-3266	475	13	·	·	PUNCT
ejpam-3266	475	14	,	,	PUNCT
ejpam-3266	475	15	≤	≤	NUM
ejpam-3266	475	16	)	)	PUNCT
ejpam-3266	475	17	of	of	ADP
ejpam-3266	475	18	the	the	DET
ejpam-3266	475	19	example	example	NOUN
ejpam-3266	475	20	4.6	4.6	NUM
ejpam-3266	475	21	given	give	VERB
ejpam-3266	475	22	by	by	ADP
ejpam-3266	475	23	table	table	NOUN
ejpam-3266	475	24	1	1	NUM
ejpam-3266	475	25	and	and	CCONJ
ejpam-3266	475	26	figure	figure	VERB
ejpam-3266	475	27	1	1	NUM
ejpam-3266	475	28	and	and	CCONJ
ejpam-3266	475	29	the	the	DET
ejpam-3266	475	30	ordered	order	VERB
ejpam-3266	475	31	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	475	32	defined	define	VERB
ejpam-3266	475	33	by	by	ADP
ejpam-3266	475	34	the	the	DET
ejpam-3266	475	35	same	same	ADJ
ejpam-3266	475	36	order	order	NOUN
ejpam-3266	475	37	and	and	CCONJ
ejpam-3266	475	38	the	the	DET
ejpam-3266	475	39	hyperoperation	hyperoperation	NOUN
ejpam-3266	475	40	x	x	INTJ
ejpam-3266	475	41	◦	◦	NOUN
ejpam-3266	475	42	y	y	NOUN
ejpam-3266	475	43	:	:	PUNCT
ejpam-3266	475	44	=	=	SYM
ejpam-3266	475	45	{	{	PUNCT
ejpam-3266	475	46	t	t	NOUN
ejpam-3266	475	47	∈	∈	PROPN
ejpam-3266	475	48	s	s	AUX
ejpam-3266	475	49	|	|	NOUN
ejpam-3266	475	50	t	t	X
ejpam-3266	475	51	≤	≤	NUM
ejpam-3266	475	52	xy	xy	ADP
ejpam-3266	475	53	}	}	PUNCT
ejpam-3266	475	54	in	in	ADP
ejpam-3266	475	55	the	the	DET
ejpam-3266	475	56	following	follow	VERB
ejpam-3266	475	57	table	table	NOUN
ejpam-3266	475	58	.	.	PUNCT
ejpam-3266	476	1	◦	◦	VERB
ejpam-3266	476	2	a	a	DET
ejpam-3266	476	3	b	b	NOUN
ejpam-3266	476	4	c	c	NOUN
ejpam-3266	476	5	d	d	X
ejpam-3266	476	6	f	f	PROPN
ejpam-3266	476	7	g	g	PROPN
ejpam-3266	476	8	a	a	DET
ejpam-3266	476	9	{	{	PUNCT
ejpam-3266	476	10	b	b	NOUN
ejpam-3266	476	11	,	,	PUNCT
ejpam-3266	476	12	d	d	NOUN
ejpam-3266	476	13	}	}	PUNCT
ejpam-3266	476	14	{	{	PUNCT
ejpam-3266	476	15	b	b	NOUN
ejpam-3266	476	16	,	,	PUNCT
ejpam-3266	476	17	d	d	NOUN
ejpam-3266	476	18	}	}	PUNCT
ejpam-3266	476	19	{	{	PUNCT
ejpam-3266	476	20	a	a	PRON
ejpam-3266	476	21	,	,	PUNCT
ejpam-3266	476	22	d	d	NOUN
ejpam-3266	476	23	}	}	PUNCT
ejpam-3266	476	24	{	{	PUNCT
ejpam-3266	476	25	d	d	NOUN
ejpam-3266	476	26	}	}	PUNCT
ejpam-3266	476	27	{	{	PUNCT
ejpam-3266	476	28	a	a	PRON
ejpam-3266	476	29	,	,	PUNCT
ejpam-3266	476	30	d	d	NOUN
ejpam-3266	476	31	}	}	PUNCT
ejpam-3266	476	32	{	{	PUNCT
ejpam-3266	476	33	a	a	PRON
ejpam-3266	476	34	,	,	PUNCT
ejpam-3266	476	35	d	d	NOUN
ejpam-3266	476	36	}	}	PUNCT
ejpam-3266	476	37	b	b	PROPN
ejpam-3266	476	38	{	{	PUNCT
ejpam-3266	476	39	b	b	NOUN
ejpam-3266	476	40	,	,	PUNCT
ejpam-3266	476	41	d	d	NOUN
ejpam-3266	476	42	}	}	PUNCT
ejpam-3266	476	43	{	{	PUNCT
ejpam-3266	476	44	b	b	NOUN
ejpam-3266	476	45	,	,	PUNCT
ejpam-3266	476	46	d	d	NOUN
ejpam-3266	476	47	}	}	PUNCT
ejpam-3266	476	48	{	{	PUNCT
ejpam-3266	476	49	b	b	NOUN
ejpam-3266	476	50	,	,	PUNCT
ejpam-3266	476	51	d	d	NOUN
ejpam-3266	476	52	}	}	PUNCT
ejpam-3266	476	53	{	{	PUNCT
ejpam-3266	476	54	d	d	NOUN
ejpam-3266	476	55	}	}	PUNCT
ejpam-3266	476	56	{	{	PUNCT
ejpam-3266	476	57	b	b	NOUN
ejpam-3266	476	58	,	,	PUNCT
ejpam-3266	476	59	d	d	NOUN
ejpam-3266	476	60	}	}	PUNCT
ejpam-3266	476	61	{	{	PUNCT
ejpam-3266	476	62	b	b	NOUN
ejpam-3266	476	63	,	,	PUNCT
ejpam-3266	476	64	d	d	NOUN
ejpam-3266	476	65	}	}	PUNCT
ejpam-3266	476	66	c	c	NOUN
ejpam-3266	476	67	{	{	PUNCT
ejpam-3266	476	68	a	a	NOUN
ejpam-3266	476	69	,	,	PUNCT
ejpam-3266	476	70	d	d	NOUN
ejpam-3266	476	71	}	}	PUNCT
ejpam-3266	476	72	{	{	PUNCT
ejpam-3266	476	73	b	b	NOUN
ejpam-3266	476	74	,	,	PUNCT
ejpam-3266	476	75	d	d	NOUN
ejpam-3266	476	76	}	}	PUNCT
ejpam-3266	476	77	{	{	PUNCT
ejpam-3266	476	78	c	c	NOUN
ejpam-3266	476	79	,	,	PUNCT
ejpam-3266	476	80	d	d	NOUN
ejpam-3266	476	81	,	,	PUNCT
ejpam-3266	476	82	f	f	X
ejpam-3266	476	83	,	,	PUNCT
ejpam-3266	476	84	g	g	NOUN
ejpam-3266	476	85	}	}	PUNCT
ejpam-3266	476	86	{	{	PUNCT
ejpam-3266	476	87	d	d	NOUN
ejpam-3266	476	88	}	}	PUNCT
ejpam-3266	476	89	{	{	PUNCT
ejpam-3266	476	90	c	c	NOUN
ejpam-3266	476	91	,	,	PUNCT
ejpam-3266	476	92	d	d	NOUN
ejpam-3266	476	93	,	,	PUNCT
ejpam-3266	476	94	f	f	X
ejpam-3266	476	95	,	,	PUNCT
ejpam-3266	476	96	g	g	NOUN
ejpam-3266	476	97	}	}	PUNCT
ejpam-3266	476	98	{	{	PUNCT
ejpam-3266	476	99	c	c	NOUN
ejpam-3266	476	100	,	,	PUNCT
ejpam-3266	476	101	d	d	NOUN
ejpam-3266	476	102	,	,	PUNCT
ejpam-3266	476	103	f	f	X
ejpam-3266	476	104	,	,	PUNCT
ejpam-3266	476	105	g	g	NOUN
ejpam-3266	476	106	}	}	PUNCT
ejpam-3266	476	107	d	d	NOUN
ejpam-3266	476	108	{	{	PUNCT
ejpam-3266	476	109	d	d	NOUN
ejpam-3266	476	110	}	}	PUNCT
ejpam-3266	476	111	{	{	PUNCT
ejpam-3266	476	112	d	d	NOUN
ejpam-3266	476	113	}	}	PUNCT
ejpam-3266	476	114	{	{	PUNCT
ejpam-3266	476	115	d	d	NOUN
ejpam-3266	476	116	}	}	PUNCT
ejpam-3266	476	117	{	{	PUNCT
ejpam-3266	476	118	d	d	NOUN
ejpam-3266	476	119	}	}	PUNCT
ejpam-3266	476	120	{	{	PUNCT
ejpam-3266	476	121	d	d	NOUN
ejpam-3266	476	122	}	}	PUNCT
ejpam-3266	476	123	{	{	PUNCT
ejpam-3266	476	124	d	d	NOUN
ejpam-3266	476	125	}	}	PUNCT
ejpam-3266	476	126	f	f	PROPN
ejpam-3266	476	127	{	{	PUNCT
ejpam-3266	476	128	a	a	PROPN
ejpam-3266	476	129	,	,	PUNCT
ejpam-3266	476	130	d	d	NOUN
ejpam-3266	476	131	}	}	PUNCT
ejpam-3266	476	132	{	{	PUNCT
ejpam-3266	476	133	b	b	NOUN
ejpam-3266	476	134	,	,	PUNCT
ejpam-3266	476	135	d	d	NOUN
ejpam-3266	476	136	}	}	PUNCT
ejpam-3266	476	137	{	{	PUNCT
ejpam-3266	476	138	c	c	NOUN
ejpam-3266	476	139	,	,	PUNCT
ejpam-3266	476	140	d	d	NOUN
ejpam-3266	476	141	,	,	PUNCT
ejpam-3266	476	142	f	f	X
ejpam-3266	476	143	,	,	PUNCT
ejpam-3266	476	144	g	g	NOUN
ejpam-3266	476	145	}	}	PUNCT
ejpam-3266	476	146	{	{	PUNCT
ejpam-3266	476	147	d	d	NOUN
ejpam-3266	476	148	}	}	PUNCT
ejpam-3266	476	149	{	{	PUNCT
ejpam-3266	476	150	c	c	NOUN
ejpam-3266	476	151	,	,	PUNCT
ejpam-3266	476	152	d	d	NOUN
ejpam-3266	476	153	,	,	PUNCT
ejpam-3266	476	154	f	f	X
ejpam-3266	476	155	,	,	PUNCT
ejpam-3266	476	156	g	g	NOUN
ejpam-3266	476	157	}	}	PUNCT
ejpam-3266	476	158	{	{	PUNCT
ejpam-3266	476	159	c	c	NOUN
ejpam-3266	476	160	,	,	PUNCT
ejpam-3266	476	161	d	d	NOUN
ejpam-3266	476	162	,	,	PUNCT
ejpam-3266	476	163	f	f	X
ejpam-3266	476	164	,	,	PUNCT
ejpam-3266	476	165	g	g	NOUN
ejpam-3266	476	166	}	}	PUNCT
ejpam-3266	476	167	g	g	NOUN
ejpam-3266	476	168	{	{	PUNCT
ejpam-3266	476	169	a	a	NOUN
ejpam-3266	476	170	,	,	PUNCT
ejpam-3266	476	171	d	d	NOUN
ejpam-3266	476	172	}	}	PUNCT
ejpam-3266	476	173	{	{	PUNCT
ejpam-3266	476	174	b	b	NOUN
ejpam-3266	476	175	,	,	PUNCT
ejpam-3266	476	176	d	d	NOUN
ejpam-3266	476	177	}	}	PUNCT
ejpam-3266	476	178	{	{	PUNCT
ejpam-3266	476	179	c	c	NOUN
ejpam-3266	476	180	,	,	PUNCT
ejpam-3266	476	181	d	d	NOUN
ejpam-3266	476	182	,	,	PUNCT
ejpam-3266	476	183	f	f	X
ejpam-3266	476	184	,	,	PUNCT
ejpam-3266	476	185	g	g	NOUN
ejpam-3266	476	186	}	}	PUNCT
ejpam-3266	476	187	{	{	PUNCT
ejpam-3266	476	188	d	d	NOUN
ejpam-3266	476	189	}	}	PUNCT
ejpam-3266	476	190	{	{	PUNCT
ejpam-3266	476	191	d	d	NOUN
ejpam-3266	476	192	,	,	PUNCT
ejpam-3266	476	193	f	f	NOUN
ejpam-3266	476	194	}	}	PUNCT
ejpam-3266	476	195	{	{	PUNCT
ejpam-3266	476	196	d	d	NOUN
ejpam-3266	476	197	,	,	PUNCT
ejpam-3266	476	198	g	g	NOUN
ejpam-3266	476	199	}	}	PUNCT
ejpam-3266	476	200	table	table	NOUN
ejpam-3266	476	201	6	6	NUM
ejpam-3266	476	202	.	.	PUNCT
ejpam-3266	477	1	the	the	DET
ejpam-3266	477	2	set	set	NOUN
ejpam-3266	477	3	{	{	PUNCT
ejpam-3266	477	4	b	b	NOUN
ejpam-3266	477	5	,	,	PUNCT
ejpam-3266	477	6	c	c	NOUN
ejpam-3266	477	7	,	,	PUNCT
ejpam-3266	477	8	f	f	X
ejpam-3266	477	9	}	}	PUNCT
ejpam-3266	477	10	is	be	AUX
ejpam-3266	477	11	a	a	DET
ejpam-3266	477	12	filter	filter	NOUN
ejpam-3266	477	13	of	of	ADP
ejpam-3266	477	14	(	(	PUNCT
ejpam-3266	477	15	s	s	PROPN
ejpam-3266	477	16	,	,	PUNCT
ejpam-3266	477	17	·	·	PUNCT
ejpam-3266	477	18	,	,	PUNCT
ejpam-3266	477	19	≤	≤	NUM
ejpam-3266	477	20	)	)	PUNCT
ejpam-3266	477	21	,	,	PUNCT
ejpam-3266	477	22	but	but	CCONJ
ejpam-3266	477	23	it	it	PRON
ejpam-3266	477	24	is	be	AUX
ejpam-3266	477	25	not	not	PART
ejpam-3266	477	26	a	a	DET
ejpam-3266	477	27	filter	filter	NOUN
ejpam-3266	477	28	of	of	ADP
ejpam-3266	477	29	(	(	PUNCT
ejpam-3266	477	30	s	s	PROPN
ejpam-3266	477	31	,	,	PUNCT
ejpam-3266	477	32	◦	◦	NOUN
ejpam-3266	477	33	,	,	PUNCT
ejpam-3266	477	34	≤	≤	NUM
ejpam-3266	477	35	)	)	PUNCT
ejpam-3266	477	36	.	.	PUNCT
ejpam-3266	478	1	indeed	indeed	ADV
ejpam-3266	478	2	,	,	PUNCT
ejpam-3266	478	3	for	for	ADP
ejpam-3266	478	4	example	example	NOUN
ejpam-3266	478	5	,	,	PUNCT
ejpam-3266	478	6	b	b	X
ejpam-3266	478	7	◦	◦	NOUN
ejpam-3266	478	8	c	c	NOUN
ejpam-3266	478	9	=	=	SYM
ejpam-3266	478	10	{	{	PUNCT
ejpam-3266	478	11	d	d	PROPN
ejpam-3266	478	12	,	,	PUNCT
ejpam-3266	478	13	b	b	NOUN
ejpam-3266	478	14	}	}	PUNCT
ejpam-3266	478	15	*	*	PUNCT
ejpam-3266	478	16	{	{	PUNCT
ejpam-3266	478	17	b	b	NUM
ejpam-3266	478	18	,	,	PUNCT
ejpam-3266	478	19	c	c	X
ejpam-3266	478	20	,	,	PUNCT
ejpam-3266	478	21	f	f	NOUN
ejpam-3266	478	22	}	}	PUNCT
ejpam-3266	478	23	.	.	PUNCT
ejpam-3266	479	1	�	�	PROPN
ejpam-3266	479	2	proposition	proposition	NOUN
ejpam-3266	479	3	4.13	4.13	NUM
ejpam-3266	479	4	.	.	PUNCT
ejpam-3266	480	1	let	let	VERB
ejpam-3266	480	2	(	(	PUNCT
ejpam-3266	480	3	s	s	X
ejpam-3266	480	4	,	,	PUNCT
ejpam-3266	480	5	·	·	PUNCT
ejpam-3266	480	6	,	,	PUNCT
ejpam-3266	480	7	≤	≤	NUM
ejpam-3266	480	8	)	)	PUNCT
ejpam-3266	480	9	be	be	AUX
ejpam-3266	480	10	an	an	DET
ejpam-3266	480	11	ordered	order	VERB
ejpam-3266	480	12	groupoid	groupoid	NOUN
ejpam-3266	480	13	and	and	CCONJ
ejpam-3266	480	14	(	(	PUNCT
ejpam-3266	480	15	s	s	X
ejpam-3266	480	16	,	,	PUNCT
ejpam-3266	480	17	◦	◦	NOUN
ejpam-3266	480	18	,	,	PUNCT
ejpam-3266	480	19	≤	≤	NUM
ejpam-3266	480	20	)	)	PUNCT
ejpam-3266	480	21	the	the	DET
ejpam-3266	480	22	ordered	order	VERB
ejpam-3266	480	23	hypergroupoid	hypergroupoid	PROPN
ejpam-3266	480	24	defined	define	VERB
ejpam-3266	480	25	by	by	ADP
ejpam-3266	480	26	the	the	DET
ejpam-3266	480	27	hyperoperation	hyperoperation	NOUN
ejpam-3266	480	28	a	a	DET
ejpam-3266	480	29	◦	◦	NOUN
ejpam-3266	480	30	b	b	X
ejpam-3266	480	31	:	:	PUNCT
ejpam-3266	480	32	=	=	X
ejpam-3266	480	33	{	{	PUNCT
ejpam-3266	480	34	t	t	NOUN
ejpam-3266	480	35	∈	∈	PROPN
ejpam-3266	480	36	s	s	AUX
ejpam-3266	480	37	|	|	NOUN
ejpam-3266	480	38	t	t	X
ejpam-3266	480	39	≤	≤	PROPN
ejpam-3266	480	40	ab	ab	PROPN
ejpam-3266	480	41	}	}	PUNCT
ejpam-3266	480	42	.	.	PUNCT
ejpam-3266	481	1	if	if	SCONJ
ejpam-3266	481	2	σ	σ	PROPN
ejpam-3266	481	3	is	be	AUX
ejpam-3266	481	4	a	a	DET
ejpam-3266	481	5	semilattice	semilattice	NOUN
ejpam-3266	481	6	n.	n.	NOUN
ejpam-3266	481	7	kehayopulu	kehayopulu	PROPN
ejpam-3266	481	8	/	/	SYM
ejpam-3266	481	9	eur	eur	PROPN
ejpam-3266	481	10	.	.	PUNCT
ejpam-3266	482	1	j.	j.	PROPN
ejpam-3266	482	2	pure	pure	PROPN
ejpam-3266	482	3	appl	appl	PROPN
ejpam-3266	482	4	.	.	PROPN
ejpam-3266	482	5	math	math	PROPN
ejpam-3266	482	6	,	,	PUNCT
ejpam-3266	482	7	11	11	NUM
ejpam-3266	482	8	(	(	PUNCT
ejpam-3266	482	9	2	2	NUM
ejpam-3266	482	10	)	)	PUNCT
ejpam-3266	482	11	(	(	PUNCT
ejpam-3266	482	12	2018	2018	NUM
ejpam-3266	482	13	)	)	PUNCT
ejpam-3266	482	14	,	,	PUNCT
ejpam-3266	482	15	476	476	NUM
ejpam-3266	482	16	-	-	SYM
ejpam-3266	482	17	492	492	NUM
ejpam-3266	482	18	491	491	NUM
ejpam-3266	482	19	(	(	PUNCT
ejpam-3266	482	20	resp	resp	NOUN
ejpam-3266	482	21	.	.	PUNCT
ejpam-3266	483	1	complete	complete	ADJ
ejpam-3266	483	2	semilattice	semilattice	PROPN
ejpam-3266	483	3	)	)	PUNCT
ejpam-3266	483	4	congruence	congruence	NOUN
ejpam-3266	483	5	on	on	ADP
ejpam-3266	483	6	(	(	PUNCT
ejpam-3266	483	7	s	s	NOUN
ejpam-3266	483	8	,	,	PUNCT
ejpam-3266	483	9	◦	◦	NOUN
ejpam-3266	483	10	,	,	PUNCT
ejpam-3266	483	11	≤	≤	NUM
ejpam-3266	483	12	)	)	PUNCT
ejpam-3266	483	13	,	,	PUNCT
ejpam-3266	483	14	then	then	ADV
ejpam-3266	483	15	it	it	PRON
ejpam-3266	483	16	is	be	AUX
ejpam-3266	483	17	a	a	DET
ejpam-3266	483	18	semilattice	semilattice	NOUN
ejpam-3266	483	19	(	(	PUNCT
ejpam-3266	483	20	resp	resp	NOUN
ejpam-3266	483	21	.	.	PUNCT
ejpam-3266	484	1	complete	complete	ADJ
ejpam-3266	484	2	semilattice	semilattice	PROPN
ejpam-3266	484	3	)	)	PUNCT
ejpam-3266	484	4	congruence	congruence	NOUN
ejpam-3266	484	5	on	on	ADP
ejpam-3266	484	6	(	(	PUNCT
ejpam-3266	484	7	s	s	X
ejpam-3266	484	8	,	,	PUNCT
ejpam-3266	484	9	·	·	PUNCT
ejpam-3266	484	10	,	,	PUNCT
ejpam-3266	484	11	≤	≤	NUM
ejpam-3266	484	12	)	)	PUNCT
ejpam-3266	484	13	.	.	PUNCT
ejpam-3266	485	1	if	if	SCONJ
ejpam-3266	485	2	σ	σ	PROPN
ejpam-3266	485	3	is	be	AUX
ejpam-3266	485	4	a	a	DET
ejpam-3266	485	5	semilattice	semilattice	NOUN
ejpam-3266	485	6	congruence	congruence	NOUN
ejpam-3266	485	7	on	on	ADP
ejpam-3266	485	8	(	(	PUNCT
ejpam-3266	485	9	s	s	X
ejpam-3266	485	10	,	,	PUNCT
ejpam-3266	485	11	·	·	PUNCT
ejpam-3266	485	12	,	,	PUNCT
ejpam-3266	485	13	≤	≤	NUM
ejpam-3266	485	14	)	)	PUNCT
ejpam-3266	485	15	,	,	PUNCT
ejpam-3266	485	16	then	then	ADV
ejpam-3266	485	17	it	it	PRON
ejpam-3266	485	18	is	be	AUX
ejpam-3266	485	19	not	not	PART
ejpam-3266	485	20	a	a	DET
ejpam-3266	485	21	semilattice	semilattice	NOUN
ejpam-3266	485	22	congruence	congruence	NOUN
ejpam-3266	485	23	on	on	ADP
ejpam-3266	485	24	(	(	PUNCT
ejpam-3266	485	25	s	s	NOUN
ejpam-3266	485	26	,	,	PUNCT
ejpam-3266	485	27	◦	◦	NOUN
ejpam-3266	485	28	,	,	PUNCT
ejpam-3266	485	29	≤	≤	NUM
ejpam-3266	485	30	)	)	PUNCT
ejpam-3266	485	31	in	in	ADP
ejpam-3266	485	32	general	general	ADJ
ejpam-3266	485	33	.	.	PUNCT
ejpam-3266	486	1	proof	proof	NOUN
ejpam-3266	486	2	.	.	PUNCT
ejpam-3266	487	1	let	let	VERB
ejpam-3266	487	2	σ	σ	NOUN
ejpam-3266	487	3	be	be	AUX
ejpam-3266	487	4	a	a	DET
ejpam-3266	487	5	semilattice	semilattice	NOUN
ejpam-3266	487	6	congruence	congruence	NOUN
ejpam-3266	487	7	on	on	ADP
ejpam-3266	487	8	(	(	PUNCT
ejpam-3266	487	9	s	s	NOUN
ejpam-3266	487	10	,	,	PUNCT
ejpam-3266	487	11	◦	◦	NOUN
ejpam-3266	487	12	,	,	PUNCT
ejpam-3266	487	13	≤	≤	NUM
ejpam-3266	487	14	)	)	PUNCT
ejpam-3266	487	15	.	.	PUNCT
ejpam-3266	488	1	let	let	VERB
ejpam-3266	488	2	(	(	PUNCT
ejpam-3266	488	3	a	a	PRON
ejpam-3266	488	4	,	,	PUNCT
ejpam-3266	488	5	b	b	NOUN
ejpam-3266	488	6	)	)	PUNCT
ejpam-3266	488	7	∈	∈	PROPN
ejpam-3266	488	8	σ	σ	NOUN
ejpam-3266	488	9	and	and	CCONJ
ejpam-3266	488	10	c	c	PROPN
ejpam-3266	488	11	∈	∈	PROPN
ejpam-3266	488	12	s.	s.	PROPN
ejpam-3266	488	13	since	since	SCONJ
ejpam-3266	488	14	(	(	PUNCT
ejpam-3266	488	15	a	a	DET
ejpam-3266	488	16	◦	◦	NOUN
ejpam-3266	488	17	c	c	NOUN
ejpam-3266	488	18	,	,	PUNCT
ejpam-3266	488	19	b	b	NOUN
ejpam-3266	488	20	◦	◦	NOUN
ejpam-3266	488	21	c	c	NOUN
ejpam-3266	488	22	)	)	PUNCT
ejpam-3266	488	23	∈	∈	PROPN
ejpam-3266	488	24	σ	σ	PROPN
ejpam-3266	488	25	,	,	PUNCT
ejpam-3266	488	26	ac	ac	PROPN
ejpam-3266	488	27	∈	∈	PROPN
ejpam-3266	488	28	a	a	DET
ejpam-3266	488	29	◦	◦	NOUN
ejpam-3266	488	30	c	c	NOUN
ejpam-3266	488	31	,	,	PUNCT
ejpam-3266	488	32	and	and	CCONJ
ejpam-3266	488	33	bc	bc	PROPN
ejpam-3266	488	34	∈	∈	PROPN
ejpam-3266	488	35	b	b	PROPN
ejpam-3266	488	36	◦	◦	NOUN
ejpam-3266	488	37	c	c	NOUN
ejpam-3266	488	38	,	,	PUNCT
ejpam-3266	488	39	we	we	PRON
ejpam-3266	488	40	have	have	VERB
ejpam-3266	488	41	(	(	PUNCT
ejpam-3266	488	42	ac	ac	PROPN
ejpam-3266	488	43	,	,	PUNCT
ejpam-3266	488	44	bc	bc	PROPN
ejpam-3266	488	45	)	)	PUNCT
ejpam-3266	488	46	∈	∈	PROPN
ejpam-3266	488	47	σ	σ	PROPN
ejpam-3266	488	48	.	.	PUNCT
ejpam-3266	489	1	similarly	similarly	ADV
ejpam-3266	489	2	we	we	PRON
ejpam-3266	489	3	get	get	VERB
ejpam-3266	489	4	(	(	PUNCT
ejpam-3266	489	5	ca	ca	NOUN
ejpam-3266	489	6	,	,	PUNCT
ejpam-3266	489	7	cb	cb	PROPN
ejpam-3266	489	8	)	)	PUNCT
ejpam-3266	489	9	∈	∈	PROPN
ejpam-3266	489	10	σ	σ	PROPN
ejpam-3266	489	11	,	,	PUNCT
ejpam-3266	489	12	and	and	CCONJ
ejpam-3266	489	13	σ	σ	PROPN
ejpam-3266	489	14	is	be	AUX
ejpam-3266	489	15	a	a	DET
ejpam-3266	489	16	congruence	congruence	NOUN
ejpam-3266	489	17	on	on	ADP
ejpam-3266	489	18	(	(	PUNCT
ejpam-3266	489	19	s	s	X
ejpam-3266	489	20	,	,	PUNCT
ejpam-3266	489	21	·	·	PUNCT
ejpam-3266	489	22	,	,	PUNCT
ejpam-3266	489	23	≤	≤	NUM
ejpam-3266	489	24	)	)	PUNCT
ejpam-3266	489	25	.	.	PUNCT
ejpam-3266	490	1	let	let	VERB
ejpam-3266	490	2	now	now	ADV
ejpam-3266	490	3	a	a	PRON
ejpam-3266	490	4	,	,	PUNCT
ejpam-3266	490	5	b	b	X
ejpam-3266	490	6	∈	∈	PROPN
ejpam-3266	490	7	s.	s.	PROPN
ejpam-3266	490	8	since	since	SCONJ
ejpam-3266	490	9	(	(	PUNCT
ejpam-3266	490	10	a	a	DET
ejpam-3266	490	11	◦	◦	NOUN
ejpam-3266	490	12	a	a	DET
ejpam-3266	490	13	,	,	PUNCT
ejpam-3266	490	14	a	a	DET
ejpam-3266	490	15	)	)	PUNCT
ejpam-3266	490	16	∈	∈	PROPN
ejpam-3266	490	17	σ	σ	PROPN
ejpam-3266	490	18	and	and	CCONJ
ejpam-3266	490	19	a2	a2	PROPN
ejpam-3266	490	20	∈	∈	PROPN
ejpam-3266	490	21	a	a	DET
ejpam-3266	490	22	◦	◦	NOUN
ejpam-3266	490	23	a	a	X
ejpam-3266	490	24	,	,	PUNCT
ejpam-3266	490	25	we	we	PRON
ejpam-3266	490	26	have	have	VERB
ejpam-3266	490	27	(	(	PUNCT
ejpam-3266	490	28	a2	a2	PROPN
ejpam-3266	490	29	,	,	PUNCT
ejpam-3266	490	30	a	a	PRON
ejpam-3266	490	31	)	)	PUNCT
ejpam-3266	490	32	∈	∈	PROPN
ejpam-3266	490	33	σ	σ	PROPN
ejpam-3266	490	34	.	.	PUNCT
ejpam-3266	491	1	since	since	SCONJ
ejpam-3266	491	2	(	(	PUNCT
ejpam-3266	491	3	a	a	DET
ejpam-3266	491	4	◦	◦	NOUN
ejpam-3266	491	5	b	b	NUM
ejpam-3266	491	6	,	,	PUNCT
ejpam-3266	491	7	b	b	X
ejpam-3266	491	8	◦	◦	NOUN
ejpam-3266	491	9	a	a	X
ejpam-3266	491	10	)	)	PUNCT
ejpam-3266	491	11	∈	∈	PROPN
ejpam-3266	491	12	σ	σ	PROPN
ejpam-3266	491	13	,	,	PUNCT
ejpam-3266	491	14	ab	ab	PROPN
ejpam-3266	491	15	∈	∈	PROPN
ejpam-3266	491	16	a	a	DET
ejpam-3266	491	17	◦	◦	NOUN
ejpam-3266	491	18	b	b	NOUN
ejpam-3266	491	19	and	and	CCONJ
ejpam-3266	491	20	ba	ba	PROPN
ejpam-3266	491	21	∈	∈	PROPN
ejpam-3266	491	22	b	b	PROPN
ejpam-3266	491	23	◦	◦	NOUN
ejpam-3266	491	24	a	a	X
ejpam-3266	491	25	,	,	PUNCT
ejpam-3266	491	26	we	we	PRON
ejpam-3266	491	27	have	have	VERB
ejpam-3266	491	28	(	(	PUNCT
ejpam-3266	491	29	ab	ab	PROPN
ejpam-3266	491	30	,	,	PUNCT
ejpam-3266	491	31	ba	ba	PROPN
ejpam-3266	491	32	)	)	PUNCT
ejpam-3266	491	33	∈	∈	PROPN
ejpam-3266	491	34	σ	σ	PROPN
ejpam-3266	491	35	,	,	PUNCT
ejpam-3266	491	36	so	so	SCONJ
ejpam-3266	491	37	σ	σ	PROPN
ejpam-3266	491	38	is	be	AUX
ejpam-3266	491	39	a	a	DET
ejpam-3266	491	40	semilattice	semilattice	NOUN
ejpam-3266	491	41	congruence	congruence	NOUN
ejpam-3266	491	42	on	on	ADP
ejpam-3266	491	43	(	(	PUNCT
ejpam-3266	491	44	s	s	X
ejpam-3266	491	45	,	,	PUNCT
ejpam-3266	491	46	·	·	PUNCT
ejpam-3266	491	47	,	,	PUNCT
ejpam-3266	491	48	≤	≤	NUM
ejpam-3266	491	49	)	)	PUNCT
ejpam-3266	491	50	.	.	PUNCT
ejpam-3266	492	1	let	let	VERB
ejpam-3266	492	2	σ	σ	NOUN
ejpam-3266	492	3	be	be	AUX
ejpam-3266	492	4	a	a	DET
ejpam-3266	492	5	complete	complete	ADJ
ejpam-3266	492	6	semilattice	semilattice	NOUN
ejpam-3266	492	7	congruence	congruence	NOUN
ejpam-3266	492	8	on	on	ADP
ejpam-3266	492	9	(	(	PUNCT
ejpam-3266	492	10	s	s	NOUN
ejpam-3266	492	11	,	,	PUNCT
ejpam-3266	492	12	◦	◦	NOUN
ejpam-3266	492	13	,	,	PUNCT
ejpam-3266	492	14	≤	≤	NUM
ejpam-3266	492	15	)	)	PUNCT
ejpam-3266	492	16	and	and	CCONJ
ejpam-3266	492	17	a	a	DET
ejpam-3266	492	18	≤	≤	PROPN
ejpam-3266	492	19	b.	b.	PROPN
ejpam-3266	492	20	since	since	SCONJ
ejpam-3266	492	21	(	(	PUNCT
ejpam-3266	492	22	a	a	X
ejpam-3266	492	23	,	,	PUNCT
ejpam-3266	492	24	a	a	DET
ejpam-3266	492	25	◦	◦	NOUN
ejpam-3266	492	26	b	b	NOUN
ejpam-3266	492	27	)	)	PUNCT
ejpam-3266	492	28	∈	∈	PROPN
ejpam-3266	492	29	σ	σ	PROPN
ejpam-3266	492	30	and	and	CCONJ
ejpam-3266	492	31	ab	ab	PROPN
ejpam-3266	492	32	∈	∈	PROPN
ejpam-3266	492	33	a	a	DET
ejpam-3266	492	34	◦	◦	NOUN
ejpam-3266	492	35	b	b	NUM
ejpam-3266	492	36	,	,	PUNCT
ejpam-3266	492	37	we	we	PRON
ejpam-3266	492	38	have	have	VERB
ejpam-3266	492	39	(	(	PUNCT
ejpam-3266	492	40	a	a	PRON
ejpam-3266	492	41	,	,	PUNCT
ejpam-3266	492	42	ab	ab	NOUN
ejpam-3266	492	43	)	)	PUNCT
ejpam-3266	492	44	∈	∈	PROPN
ejpam-3266	492	45	σ	σ	PROPN
ejpam-3266	492	46	,	,	PUNCT
ejpam-3266	492	47	thus	thus	ADV
ejpam-3266	492	48	σ	σ	PROPN
ejpam-3266	492	49	is	be	AUX
ejpam-3266	492	50	a	a	DET
ejpam-3266	492	51	complete	complete	ADJ
ejpam-3266	492	52	semilattice	semilattice	NOUN
ejpam-3266	492	53	congruence	congruence	NOUN
ejpam-3266	492	54	on	on	ADP
ejpam-3266	492	55	(	(	PUNCT
ejpam-3266	492	56	s	s	X
ejpam-3266	492	57	,	,	PUNCT
ejpam-3266	492	58	·	·	PUNCT
ejpam-3266	492	59	,	,	PUNCT
ejpam-3266	492	60	≤	≤	NUM
ejpam-3266	492	61	)	)	PUNCT
ejpam-3266	492	62	.	.	PUNCT
ejpam-3266	493	1	for	for	ADP
ejpam-3266	493	2	the	the	DET
ejpam-3266	493	3	converse	converse	NOUN
ejpam-3266	493	4	statement	statement	NOUN
ejpam-3266	493	5	,	,	PUNCT
ejpam-3266	493	6	consider	consider	VERB
ejpam-3266	493	7	the	the	DET
ejpam-3266	493	8	ordered	order	VERB
ejpam-3266	493	9	semigroup	semigroup	NOUN
ejpam-3266	493	10	of	of	ADP
ejpam-3266	493	11	the	the	DET
ejpam-3266	493	12	example	example	NOUN
ejpam-3266	493	13	4.6	4.6	NUM
ejpam-3266	493	14	given	give	VERB
ejpam-3266	493	15	by	by	ADP
ejpam-3266	493	16	table	table	NOUN
ejpam-3266	493	17	1	1	NUM
ejpam-3266	493	18	and	and	CCONJ
ejpam-3266	493	19	figure	figure	VERB
ejpam-3266	493	20	1	1	NUM
ejpam-3266	493	21	and	and	CCONJ
ejpam-3266	493	22	the	the	DET
ejpam-3266	493	23	ordered	order	VERB
ejpam-3266	493	24	hypersemigroup	hypersemigroup	NOUN
ejpam-3266	493	25	defined	define	VERB
ejpam-3266	493	26	by	by	ADP
ejpam-3266	493	27	the	the	DET
ejpam-3266	493	28	same	same	ADJ
ejpam-3266	493	29	order	order	NOUN
ejpam-3266	493	30	and	and	CCONJ
ejpam-3266	493	31	the	the	DET
ejpam-3266	493	32	hyperoperation	hyperoperation	NOUN
ejpam-3266	493	33	x	x	INTJ
ejpam-3266	493	34	◦	◦	NOUN
ejpam-3266	493	35	y	y	NOUN
ejpam-3266	494	1	:	:	PUNCT
ejpam-3266	494	2	=	=	SYM
ejpam-3266	494	3	{	{	PUNCT
ejpam-3266	494	4	t	t	NOUN
ejpam-3266	494	5	∈	∈	PROPN
ejpam-3266	494	6	s	s	AUX
ejpam-3266	494	7	|	|	NOUN
ejpam-3266	494	8	t	t	X
ejpam-3266	494	9	≤	≤	NUM
ejpam-3266	494	10	xy	xy	ADP
ejpam-3266	494	11	}	}	PUNCT
ejpam-3266	494	12	in	in	ADP
ejpam-3266	494	13	table	table	NOUN
ejpam-3266	494	14	6	6	NUM
ejpam-3266	494	15	.	.	PUNCT
ejpam-3266	495	1	as	as	SCONJ
ejpam-3266	495	2	we	we	PRON
ejpam-3266	495	3	have	have	AUX
ejpam-3266	495	4	seen	see	VERB
ejpam-3266	495	5	,	,	PUNCT
ejpam-3266	495	6	the	the	DET
ejpam-3266	495	7	relation	relation	NOUN
ejpam-3266	495	8	σ1	σ1	PROPN
ejpam-3266	496	1	=	=	PUNCT
ejpam-3266	496	2	{	{	PUNCT
ejpam-3266	496	3	(	(	PUNCT
ejpam-3266	496	4	a	a	PRON
ejpam-3266	496	5	,	,	PUNCT
ejpam-3266	496	6	a	a	NOUN
ejpam-3266	496	7	)	)	PUNCT
ejpam-3266	496	8	,	,	PUNCT
ejpam-3266	496	9	(	(	PUNCT
ejpam-3266	496	10	a	a	DET
ejpam-3266	496	11	,	,	PUNCT
ejpam-3266	496	12	b	b	NOUN
ejpam-3266	496	13	)	)	PUNCT
ejpam-3266	496	14	,	,	PUNCT
ejpam-3266	496	15	(	(	PUNCT
ejpam-3266	496	16	b	b	X
ejpam-3266	496	17	,	,	PUNCT
ejpam-3266	496	18	a	a	PRON
ejpam-3266	496	19	)	)	PUNCT
ejpam-3266	496	20	,	,	PUNCT
ejpam-3266	496	21	(	(	PUNCT
ejpam-3266	496	22	b	b	X
ejpam-3266	496	23	,	,	PUNCT
ejpam-3266	496	24	b	b	NOUN
ejpam-3266	496	25	)	)	PUNCT
ejpam-3266	496	26	,	,	PUNCT
ejpam-3266	496	27	(	(	PUNCT
ejpam-3266	496	28	c	c	X
ejpam-3266	496	29	,	,	PUNCT
ejpam-3266	496	30	c	c	NOUN
ejpam-3266	496	31	)	)	PUNCT
ejpam-3266	496	32	,	,	PUNCT
ejpam-3266	496	33	(	(	PUNCT
ejpam-3266	496	34	c	c	X
ejpam-3266	496	35	,	,	PUNCT
ejpam-3266	496	36	f	f	NOUN
ejpam-3266	496	37	)	)	PUNCT
ejpam-3266	496	38	,	,	PUNCT
ejpam-3266	496	39	(	(	PUNCT
ejpam-3266	496	40	d	d	X
ejpam-3266	496	41	,	,	PUNCT
ejpam-3266	496	42	d	d	NOUN
ejpam-3266	496	43	)	)	PUNCT
ejpam-3266	496	44	,	,	PUNCT
ejpam-3266	496	45	(	(	PUNCT
ejpam-3266	496	46	f	f	X
ejpam-3266	496	47	,	,	PUNCT
ejpam-3266	496	48	c	c	NOUN
ejpam-3266	496	49	)	)	PUNCT
ejpam-3266	496	50	,	,	PUNCT
ejpam-3266	496	51	(	(	PUNCT
ejpam-3266	496	52	f	f	X
ejpam-3266	496	53	,	,	PUNCT
ejpam-3266	496	54	f	f	PROPN
ejpam-3266	496	55	)	)	PUNCT
ejpam-3266	496	56	,	,	PUNCT
ejpam-3266	496	57	(	(	PUNCT
ejpam-3266	496	58	g	g	NOUN
ejpam-3266	496	59	,	,	PUNCT
ejpam-3266	496	60	g	g	NOUN
ejpam-3266	496	61	)	)	PUNCT
ejpam-3266	496	62	}	}	PUNCT
ejpam-3266	496	63	is	be	AUX
ejpam-3266	496	64	a	a	DET
ejpam-3266	496	65	semilattice	semilattice	NOUN
ejpam-3266	496	66	congruence	congruence	NOUN
ejpam-3266	496	67	on	on	ADP
ejpam-3266	496	68	(	(	PUNCT
ejpam-3266	496	69	s	s	X
ejpam-3266	496	70	,	,	PUNCT
ejpam-3266	496	71	·	·	PUNCT
ejpam-3266	496	72	,	,	PUNCT
ejpam-3266	496	73	≤	≤	NUM
ejpam-3266	496	74	)	)	PUNCT
ejpam-3266	496	75	.	.	PUNCT
ejpam-3266	497	1	on	on	ADP
ejpam-3266	497	2	the	the	DET
ejpam-3266	497	3	other	other	ADJ
ejpam-3266	497	4	site	site	NOUN
ejpam-3266	497	5	,	,	PUNCT
ejpam-3266	497	6	σ1	σ1	PROPN
ejpam-3266	497	7	is	be	AUX
ejpam-3266	497	8	not	not	PART
ejpam-3266	497	9	a	a	DET
ejpam-3266	497	10	semilattice	semilattice	NOUN
ejpam-3266	497	11	congruence	congruence	NOUN
ejpam-3266	497	12	on	on	ADP
ejpam-3266	497	13	(	(	PUNCT
ejpam-3266	497	14	s	s	NOUN
ejpam-3266	497	15	,	,	PUNCT
ejpam-3266	497	16	◦	◦	NOUN
ejpam-3266	497	17	,	,	PUNCT
ejpam-3266	497	18	≤	≤	NUM
ejpam-3266	497	19	)	)	PUNCT
ejpam-3266	497	20	.	.	PUNCT
ejpam-3266	498	1	it	it	PRON
ejpam-3266	498	2	is	be	AUX
ejpam-3266	498	3	enough	enough	ADJ
ejpam-3266	498	4	to	to	PART
ejpam-3266	498	5	observe	observe	VERB
ejpam-3266	498	6	that	that	SCONJ
ejpam-3266	498	7	(	(	PUNCT
ejpam-3266	498	8	a	a	DET
ejpam-3266	498	9	,	,	PUNCT
ejpam-3266	498	10	b	b	NOUN
ejpam-3266	498	11	)	)	PUNCT
ejpam-3266	498	12	∈	∈	PROPN
ejpam-3266	498	13	σ1	σ1	PROPN
ejpam-3266	498	14	but	but	CCONJ
ejpam-3266	498	15	(	(	PUNCT
ejpam-3266	498	16	a	a	DET
ejpam-3266	498	17	◦	◦	NOUN
ejpam-3266	498	18	c	c	NOUN
ejpam-3266	498	19	,	,	PUNCT
ejpam-3266	498	20	b	b	X
ejpam-3266	498	21	◦	◦	NOUN
ejpam-3266	498	22	c	c	NOUN
ejpam-3266	498	23	)	)	PUNCT
ejpam-3266	498	24	/∈	/∈	PUNCT
ejpam-3266	499	1	σ1	σ1	PROPN
ejpam-3266	499	2	,	,	PUNCT
ejpam-3266	499	3	since	since	SCONJ
ejpam-3266	499	4	a	a	DET
ejpam-3266	499	5	∈	∈	PROPN
ejpam-3266	499	6	a	a	DET
ejpam-3266	499	7	◦	◦	NOUN
ejpam-3266	499	8	c	c	NOUN
ejpam-3266	499	9	,	,	PUNCT
ejpam-3266	499	10	d	d	PROPN
ejpam-3266	499	11	∈	∈	PROPN
ejpam-3266	499	12	b	b	PROPN
ejpam-3266	499	13	◦	◦	NOUN
ejpam-3266	499	14	c	c	PROPN
ejpam-3266	499	15	but	but	CCONJ
ejpam-3266	499	16	(	(	PUNCT
ejpam-3266	499	17	a	a	PRON
ejpam-3266	499	18	,	,	PUNCT
ejpam-3266	499	19	d	d	NOUN
ejpam-3266	499	20	)	)	PUNCT
ejpam-3266	499	21	/∈	/∈	PUNCT
ejpam-3266	500	1	σ1	σ1	PROPN
ejpam-3266	500	2	.	.	PUNCT
ejpam-3266	501	1	�	�	PROPN
ejpam-3266	502	1	the	the	DET
ejpam-3266	502	2	following	following	ADJ
ejpam-3266	502	3	question	question	NOUN
ejpam-3266	502	4	is	be	AUX
ejpam-3266	502	5	natural	natural	ADJ
ejpam-3266	502	6	.	.	PUNCT
ejpam-3266	503	1	under	under	ADP
ejpam-3266	503	2	what	what	PRON
ejpam-3266	503	3	restrictions	restriction	NOUN
ejpam-3266	503	4	a	a	DET
ejpam-3266	503	5	semilattice	semilattice	NOUN
ejpam-3266	503	6	congruence	congruence	NOUN
ejpam-3266	503	7	on	on	ADP
ejpam-3266	503	8	(	(	PUNCT
ejpam-3266	503	9	s	s	X
ejpam-3266	503	10	,	,	PUNCT
ejpam-3266	503	11	·	·	PUNCT
ejpam-3266	503	12	,	,	PUNCT
ejpam-3266	503	13	≤	≤	NUM
ejpam-3266	503	14	)	)	PUNCT
ejpam-3266	503	15	is	be	AUX
ejpam-3266	503	16	a	a	DET
ejpam-3266	503	17	semilattice	semilattice	NOUN
ejpam-3266	503	18	congruence	congruence	NOUN
ejpam-3266	503	19	on	on	ADP
ejpam-3266	503	20	(	(	PUNCT
ejpam-3266	503	21	s	s	NOUN
ejpam-3266	503	22	,	,	PUNCT
ejpam-3266	503	23	◦	◦	NOUN
ejpam-3266	503	24	,	,	PUNCT
ejpam-3266	503	25	≤	≤	NUM
ejpam-3266	503	26	)	)	PUNCT
ejpam-3266	503	27	?	?	PUNCT
ejpam-3266	504	1	for	for	ADP
ejpam-3266	504	2	this	this	DET
ejpam-3266	504	3	purpose	purpose	NOUN
ejpam-3266	504	4	,	,	PUNCT
ejpam-3266	504	5	we	we	PRON
ejpam-3266	504	6	introduce	introduce	VERB
ejpam-3266	504	7	the	the	DET
ejpam-3266	504	8	concept	concept	NOUN
ejpam-3266	504	9	of	of	ADP
ejpam-3266	504	10	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	504	11	semilattice	semilattice	NOUN
ejpam-3266	504	12	congruences	congruence	NOUN
ejpam-3266	504	13	as	as	SCONJ
ejpam-3266	504	14	follows	follow	VERB
ejpam-3266	504	15	:	:	PUNCT
ejpam-3266	504	16	definition	definition	NOUN
ejpam-3266	504	17	4.14	4.14	NUM
ejpam-3266	504	18	.	.	PUNCT
ejpam-3266	505	1	let	let	VERB
ejpam-3266	505	2	(	(	PUNCT
ejpam-3266	505	3	s	s	X
ejpam-3266	505	4	,	,	PUNCT
ejpam-3266	505	5	·	·	PUNCT
ejpam-3266	505	6	,	,	PUNCT
ejpam-3266	505	7	≤	≤	NUM
ejpam-3266	505	8	)	)	PUNCT
ejpam-3266	505	9	be	be	AUX
ejpam-3266	505	10	an	an	DET
ejpam-3266	505	11	ordered	ordered	ADJ
ejpam-3266	505	12	groupoid	groupoid	NOUN
ejpam-3266	505	13	.	.	PUNCT
ejpam-3266	506	1	a	a	DET
ejpam-3266	506	2	semilattice	semilattice	NOUN
ejpam-3266	506	3	congruence	congruence	PROPN
ejpam-3266	506	4	σ	σ	PROPN
ejpam-3266	506	5	on	on	ADP
ejpam-3266	506	6	s	s	PROPN
ejpam-3266	506	7	is	be	AUX
ejpam-3266	506	8	called	call	VERB
ejpam-3266	506	9	pseudocomplete	pseudocomplete	NOUN
ejpam-3266	506	10	if	if	SCONJ
ejpam-3266	506	11	≤⊆	≤⊆	PROPN
ejpam-3266	506	12	σ	σ	PROPN
ejpam-3266	506	13	.	.	PROPN
ejpam-3266	506	14	example	example	NOUN
ejpam-3266	506	15	4.15	4.15	NUM
ejpam-3266	506	16	.	.	PUNCT
ejpam-3266	507	1	the	the	DET
ejpam-3266	507	2	relation	relation	NOUN
ejpam-3266	507	3	σ2	σ2	PROPN
ejpam-3266	507	4	(=	(=	X
ejpam-3266	507	5	n	n	CCONJ
ejpam-3266	507	6	)	)	PUNCT
ejpam-3266	507	7	in	in	ADP
ejpam-3266	507	8	the	the	DET
ejpam-3266	507	9	example	example	NOUN
ejpam-3266	507	10	4.7	4.7	NUM
ejpam-3266	507	11	is	be	AUX
ejpam-3266	507	12	an	an	DET
ejpam-3266	507	13	example	example	NOUN
ejpam-3266	507	14	of	of	ADP
ejpam-3266	507	15	a	a	DET
ejpam-3266	507	16	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	507	17	semilattice	semilattice	NOUN
ejpam-3266	507	18	congruence	congruence	NOUN
ejpam-3266	507	19	on	on	ADP
ejpam-3266	507	20	(	(	PUNCT
ejpam-3266	507	21	s	s	X
ejpam-3266	507	22	,	,	PUNCT
ejpam-3266	507	23	·	·	PUNCT
ejpam-3266	507	24	,	,	PUNCT
ejpam-3266	507	25	≤	≤	NUM
ejpam-3266	507	26	)	)	PUNCT
ejpam-3266	507	27	.	.	PUNCT
ejpam-3266	508	1	there	there	PRON
ejpam-3266	508	2	is	be	VERB
ejpam-3266	508	3	no	no	DET
ejpam-3266	508	4	proper	proper	ADJ
ejpam-3266	508	5	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	508	6	semilattice	semilattice	NOUN
ejpam-3266	508	7	congruence	congruence	NOUN
ejpam-3266	508	8	on	on	ADP
ejpam-3266	508	9	(	(	PUNCT
ejpam-3266	508	10	s	s	X
ejpam-3266	508	11	,	,	PUNCT
ejpam-3266	508	12	·	·	PUNCT
ejpam-3266	508	13	,	,	PUNCT
ejpam-3266	508	14	≤	≤	NUM
ejpam-3266	508	15	)	)	PUNCT
ejpam-3266	508	16	in	in	ADP
ejpam-3266	508	17	the	the	DET
ejpam-3266	508	18	example	example	NOUN
ejpam-3266	508	19	4.6	4.6	NUM
ejpam-3266	508	20	,	,	PUNCT
ejpam-3266	508	21	in	in	ADP
ejpam-3266	508	22	fact	fact	NOUN
ejpam-3266	508	23	the	the	DET
ejpam-3266	508	24	only	only	ADJ
ejpam-3266	508	25	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	508	26	semilattice	semilattice	NOUN
ejpam-3266	508	27	congruence	congruence	NOUN
ejpam-3266	508	28	on	on	ADP
ejpam-3266	508	29	(	(	PUNCT
ejpam-3266	508	30	s	s	X
ejpam-3266	508	31	,	,	PUNCT
ejpam-3266	508	32	·	·	PUNCT
ejpam-3266	508	33	,	,	PUNCT
ejpam-3266	508	34	≤	≤	NUM
ejpam-3266	508	35	)	)	PUNCT
ejpam-3266	508	36	is	be	AUX
ejpam-3266	508	37	the	the	DET
ejpam-3266	508	38	set	set	NOUN
ejpam-3266	508	39	s	s	PART
ejpam-3266	508	40	×	×	PROPN
ejpam-3266	508	41	s.	s.	PROPN
ejpam-3266	508	42	proposition	proposition	PROPN
ejpam-3266	508	43	4.16	4.16	NUM
ejpam-3266	508	44	.	.	PUNCT
ejpam-3266	509	1	let	let	VERB
ejpam-3266	509	2	(	(	PUNCT
ejpam-3266	509	3	s	s	X
ejpam-3266	509	4	,	,	PUNCT
ejpam-3266	509	5	·	·	PUNCT
ejpam-3266	509	6	,	,	PUNCT
ejpam-3266	509	7	≤	≤	NUM
ejpam-3266	509	8	)	)	PUNCT
ejpam-3266	509	9	be	be	AUX
ejpam-3266	509	10	an	an	DET
ejpam-3266	509	11	ordered	order	VERB
ejpam-3266	509	12	groupoid	groupoid	NOUN
ejpam-3266	509	13	and	and	CCONJ
ejpam-3266	509	14	σ	σ	NOUN
ejpam-3266	509	15	a	a	DET
ejpam-3266	509	16	semilattice	semilattice	NOUN
ejpam-3266	509	17	congruence	congruence	NOUN
ejpam-3266	509	18	on	on	ADP
ejpam-3266	509	19	s.	s.	PROPN
ejpam-3266	509	20	if	if	SCONJ
ejpam-3266	509	21	σ	σ	PROPN
ejpam-3266	509	22	is	be	AUX
ejpam-3266	509	23	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	509	24	,	,	PUNCT
ejpam-3266	509	25	then	then	ADV
ejpam-3266	509	26	it	it	PRON
ejpam-3266	509	27	is	be	AUX
ejpam-3266	509	28	complete	complete	ADJ
ejpam-3266	509	29	.	.	PUNCT
ejpam-3266	510	1	proof	proof	NOUN
ejpam-3266	510	2	.	.	PUNCT
ejpam-3266	511	1	let	let	VERB
ejpam-3266	511	2	a	a	DET
ejpam-3266	511	3	≤	≤	PROPN
ejpam-3266	511	4	b.	b.	NOUN
ejpam-3266	512	1	then	then	ADV
ejpam-3266	512	2	(	(	PUNCT
ejpam-3266	512	3	a	a	PRON
ejpam-3266	512	4	,	,	PUNCT
ejpam-3266	512	5	ab	ab	PROPN
ejpam-3266	512	6	)	)	PUNCT
ejpam-3266	512	7	∈	∈	PROPN
ejpam-3266	512	8	σ	σ	PROPN
ejpam-3266	512	9	.	.	PUNCT
ejpam-3266	513	1	indeed	indeed	ADV
ejpam-3266	513	2	:	:	PUNCT
ejpam-3266	513	3	since	since	SCONJ
ejpam-3266	513	4	a	a	DET
ejpam-3266	513	5	≤	≤	NUM
ejpam-3266	513	6	b	b	NOUN
ejpam-3266	513	7	and	and	CCONJ
ejpam-3266	513	8	σ	σ	PROPN
ejpam-3266	513	9	is	be	AUX
ejpam-3266	513	10	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	513	11	,	,	PUNCT
ejpam-3266	513	12	we	we	PRON
ejpam-3266	513	13	have	have	VERB
ejpam-3266	513	14	(	(	PUNCT
ejpam-3266	513	15	a	a	DET
ejpam-3266	513	16	,	,	PUNCT
ejpam-3266	513	17	b	b	NOUN
ejpam-3266	513	18	)	)	PUNCT
ejpam-3266	513	19	∈	∈	PROPN
ejpam-3266	513	20	σ	σ	PROPN
ejpam-3266	513	21	.	.	PROPN
ejpam-3266	514	1	since	since	SCONJ
ejpam-3266	514	2	σ	σ	PROPN
ejpam-3266	514	3	is	be	AUX
ejpam-3266	514	4	a	a	DET
ejpam-3266	514	5	semilattice	semilattice	NOUN
ejpam-3266	514	6	congruence	congruence	NOUN
ejpam-3266	514	7	,	,	PUNCT
ejpam-3266	514	8	we	we	PRON
ejpam-3266	514	9	have	have	VERB
ejpam-3266	514	10	(	(	PUNCT
ejpam-3266	514	11	a2	a2	PROPN
ejpam-3266	514	12	,	,	PUNCT
ejpam-3266	514	13	ab	ab	PROPN
ejpam-3266	514	14	)	)	PUNCT
ejpam-3266	514	15	∈	∈	PROPN
ejpam-3266	514	16	σ	σ	PROPN
ejpam-3266	514	17	and	and	CCONJ
ejpam-3266	514	18	(	(	PUNCT
ejpam-3266	514	19	a	a	DET
ejpam-3266	514	20	,	,	PUNCT
ejpam-3266	514	21	a2	a2	PROPN
ejpam-3266	514	22	)	)	PUNCT
ejpam-3266	514	23	∈	∈	PROPN
ejpam-3266	514	24	σ	σ	PROPN
ejpam-3266	514	25	,	,	PUNCT
ejpam-3266	514	26	thus	thus	ADV
ejpam-3266	514	27	we	we	PRON
ejpam-3266	514	28	get	get	VERB
ejpam-3266	514	29	(	(	PUNCT
ejpam-3266	514	30	a	a	DET
ejpam-3266	514	31	,	,	PUNCT
ejpam-3266	514	32	ab	ab	NOUN
ejpam-3266	514	33	)	)	PUNCT
ejpam-3266	514	34	∈	∈	PROPN
ejpam-3266	514	35	σ	σ	PROPN
ejpam-3266	514	36	.	.	PUNCT
ejpam-3266	514	37	�	�	PROPN
ejpam-3266	514	38	proposition	proposition	NOUN
ejpam-3266	514	39	4.17	4.17	NUM
ejpam-3266	514	40	.	.	PUNCT
ejpam-3266	515	1	let	let	VERB
ejpam-3266	515	2	(	(	PUNCT
ejpam-3266	515	3	s	s	X
ejpam-3266	515	4	,	,	PUNCT
ejpam-3266	515	5	·	·	PUNCT
ejpam-3266	515	6	,	,	PUNCT
ejpam-3266	515	7	≤	≤	NUM
ejpam-3266	515	8	)	)	PUNCT
ejpam-3266	515	9	be	be	AUX
ejpam-3266	515	10	an	an	DET
ejpam-3266	515	11	ordered	order	VERB
ejpam-3266	515	12	groupoid	groupoid	NOUN
ejpam-3266	515	13	and	and	CCONJ
ejpam-3266	515	14	“	"	PUNCT
ejpam-3266	515	15	◦	◦	NOUN
ejpam-3266	515	16	”	"	PUNCT
ejpam-3266	515	17	the	the	DET
ejpam-3266	515	18	hyperoperation	hyperoperation	NOUN
ejpam-3266	515	19	on	on	ADP
ejpam-3266	515	20	s	s	PRON
ejpam-3266	515	21	defined	define	VERB
ejpam-3266	515	22	by	by	ADP
ejpam-3266	515	23	◦	◦	NOUN
ejpam-3266	515	24	:	:	PUNCT
ejpam-3266	515	25	s	s	VERB
ejpam-3266	515	26	×	×	PROPN
ejpam-3266	515	27	s	s	X
ejpam-3266	515	28	→	→	SYM
ejpam-3266	515	29	s	s	X
ejpam-3266	516	1	|	|	ADV
ejpam-3266	516	2	(	(	PUNCT
ejpam-3266	516	3	a	a	PRON
ejpam-3266	516	4	,	,	PUNCT
ejpam-3266	516	5	b)→	b)→	VERB
ejpam-3266	516	6	a	a	DET
ejpam-3266	516	7	◦	◦	NOUN
ejpam-3266	516	8	b	b	NOUN
ejpam-3266	516	9	:	:	PUNCT
ejpam-3266	516	10	=	=	X
ejpam-3266	516	11	{	{	PUNCT
ejpam-3266	516	12	t	t	NOUN
ejpam-3266	516	13	∈	∈	PROPN
ejpam-3266	516	14	s	s	AUX
ejpam-3266	516	15	|	|	NOUN
ejpam-3266	516	16	t	t	X
ejpam-3266	516	17	≤	≤	PROPN
ejpam-3266	516	18	ab	ab	PROPN
ejpam-3266	516	19	}	}	PUNCT
ejpam-3266	516	20	.	.	PUNCT
ejpam-3266	517	1	if	if	SCONJ
ejpam-3266	517	2	σ	σ	PROPN
ejpam-3266	517	3	is	be	AUX
ejpam-3266	517	4	a	a	DET
ejpam-3266	517	5	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	517	6	semilattice	semilattice	NOUN
ejpam-3266	517	7	congruence	congruence	NOUN
ejpam-3266	517	8	on	on	ADP
ejpam-3266	517	9	(	(	PUNCT
ejpam-3266	517	10	s	s	X
ejpam-3266	517	11	,	,	PUNCT
ejpam-3266	517	12	·	·	PUNCT
ejpam-3266	517	13	,	,	PUNCT
ejpam-3266	517	14	≤	≤	NUM
ejpam-3266	517	15	)	)	PUNCT
ejpam-3266	517	16	,	,	PUNCT
ejpam-3266	517	17	then	then	ADV
ejpam-3266	517	18	it	it	PRON
ejpam-3266	517	19	is	be	AUX
ejpam-3266	517	20	a	a	DET
ejpam-3266	517	21	complete	complete	ADJ
ejpam-3266	517	22	semilattice	semilattice	NOUN
ejpam-3266	517	23	congruence	congruence	NOUN
ejpam-3266	517	24	on	on	ADP
ejpam-3266	517	25	(	(	PUNCT
ejpam-3266	517	26	s	s	NOUN
ejpam-3266	517	27	,	,	PUNCT
ejpam-3266	517	28	◦	◦	NOUN
ejpam-3266	517	29	,	,	PUNCT
ejpam-3266	517	30	≤	≤	NUM
ejpam-3266	517	31	)	)	PUNCT
ejpam-3266	517	32	.	.	PUNCT
ejpam-3266	518	1	proof	proof	NOUN
ejpam-3266	518	2	.	.	PUNCT
ejpam-3266	519	1	let	let	VERB
ejpam-3266	519	2	(	(	PUNCT
ejpam-3266	519	3	a	a	PRON
ejpam-3266	519	4	,	,	PUNCT
ejpam-3266	519	5	b	b	NOUN
ejpam-3266	519	6	)	)	PUNCT
ejpam-3266	519	7	∈	∈	PROPN
ejpam-3266	519	8	σ	σ	NOUN
ejpam-3266	519	9	and	and	CCONJ
ejpam-3266	519	10	c	c	PROPN
ejpam-3266	519	11	∈	∈	PROPN
ejpam-3266	519	12	s.	s.	PROPN
ejpam-3266	519	13	then	then	ADV
ejpam-3266	519	14	(	(	PUNCT
ejpam-3266	519	15	a	a	DET
ejpam-3266	519	16	◦	◦	NOUN
ejpam-3266	519	17	c	c	NOUN
ejpam-3266	519	18	,	,	PUNCT
ejpam-3266	519	19	b	b	X
ejpam-3266	519	20	◦	◦	NOUN
ejpam-3266	519	21	c	c	NOUN
ejpam-3266	519	22	)	)	PUNCT
ejpam-3266	519	23	∈	∈	PROPN
ejpam-3266	519	24	σ	σ	PROPN
ejpam-3266	519	25	and	and	CCONJ
ejpam-3266	519	26	(	(	PUNCT
ejpam-3266	519	27	c	c	AUX
ejpam-3266	519	28	◦	◦	NOUN
ejpam-3266	519	29	a	a	PRON
ejpam-3266	519	30	,	,	PUNCT
ejpam-3266	519	31	c	c	PROPN
ejpam-3266	519	32	◦	◦	NOUN
ejpam-3266	519	33	b	b	NUM
ejpam-3266	519	34	)	)	PUNCT
ejpam-3266	519	35	∈	∈	PROPN
ejpam-3266	519	36	σ	σ	PROPN
ejpam-3266	519	37	.	.	PUNCT
ejpam-3266	520	1	indeed	indeed	ADV
ejpam-3266	520	2	:	:	PUNCT
ejpam-3266	520	3	let	let	VERB
ejpam-3266	520	4	u	u	PRON
ejpam-3266	520	5	∈	∈	PROPN
ejpam-3266	520	6	a	a	DET
ejpam-3266	520	7	◦	◦	NOUN
ejpam-3266	520	8	c	c	NOUN
ejpam-3266	520	9	and	and	CCONJ
ejpam-3266	520	10	v	v	ADP
ejpam-3266	520	11	∈	∈	PROPN
ejpam-3266	520	12	b	b	PROPN
ejpam-3266	520	13	◦	◦	NOUN
ejpam-3266	520	14	c.	c.	NOUN
ejpam-3266	520	15	then	then	ADV
ejpam-3266	520	16	u	u	X
ejpam-3266	520	17	≤	≤	X
ejpam-3266	520	18	ac	ac	PROPN
ejpam-3266	520	19	and	and	CCONJ
ejpam-3266	520	20	v	v	X
ejpam-3266	520	21	≤	≤	NUM
ejpam-3266	520	22	bc	bc	PROPN
ejpam-3266	520	23	.	.	PROPN
ejpam-3266	521	1	since	since	SCONJ
ejpam-3266	521	2	σ	σ	PROPN
ejpam-3266	521	3	is	be	AUX
ejpam-3266	521	4	pseudocomplete	pseudocomplete	ADJ
ejpam-3266	521	5	,	,	PUNCT
ejpam-3266	521	6	we	we	PRON
ejpam-3266	521	7	have	have	VERB
ejpam-3266	521	8	references	reference	NOUN
ejpam-3266	521	9	492	492	NUM
ejpam-3266	521	10	(	(	PUNCT
ejpam-3266	521	11	u	u	NOUN
ejpam-3266	521	12	,	,	PUNCT
ejpam-3266	521	13	ac	ac	PROPN
ejpam-3266	521	14	)	)	PUNCT
ejpam-3266	521	15	∈	∈	PROPN
ejpam-3266	521	16	σ	σ	PROPN
ejpam-3266	521	17	and	and	CCONJ
ejpam-3266	521	18	(	(	PUNCT
ejpam-3266	521	19	v	v	NOUN
ejpam-3266	521	20	,	,	PUNCT
ejpam-3266	521	21	bc	bc	PROPN
ejpam-3266	521	22	)	)	PUNCT
ejpam-3266	521	23	∈	∈	PROPN
ejpam-3266	521	24	σ	σ	PROPN
ejpam-3266	521	25	.	.	PUNCT
ejpam-3266	522	1	moreover	moreover	ADV
ejpam-3266	522	2	(	(	PUNCT
ejpam-3266	522	3	ac	ac	PROPN
ejpam-3266	522	4	,	,	PUNCT
ejpam-3266	522	5	bc	bc	PROPN
ejpam-3266	522	6	)	)	PUNCT
ejpam-3266	522	7	∈	∈	PROPN
ejpam-3266	522	8	σ	σ	PROPN
ejpam-3266	522	9	,	,	PUNCT
ejpam-3266	522	10	thus	thus	ADV
ejpam-3266	522	11	we	we	PRON
ejpam-3266	522	12	get	get	VERB
ejpam-3266	522	13	(	(	PUNCT
ejpam-3266	522	14	u	u	NOUN
ejpam-3266	522	15	,	,	PUNCT
ejpam-3266	522	16	v	v	NOUN
ejpam-3266	522	17	)	)	PUNCT
ejpam-3266	522	18	∈	∈	PROPN
ejpam-3266	522	19	σ	σ	PROPN
ejpam-3266	522	20	,	,	PUNCT
ejpam-3266	522	21	and	and	CCONJ
ejpam-3266	522	22	σ	σ	PROPN
ejpam-3266	522	23	is	be	AUX
ejpam-3266	522	24	a	a	DET
ejpam-3266	522	25	right	right	ADJ
ejpam-3266	522	26	congruence	congruence	NOUN
ejpam-3266	522	27	on	on	ADP
ejpam-3266	522	28	(	(	PUNCT
ejpam-3266	522	29	s	s	NOUN
ejpam-3266	522	30	,	,	PUNCT
ejpam-3266	522	31	◦	◦	NOUN
ejpam-3266	522	32	,	,	PUNCT
ejpam-3266	522	33	≤	≤	NUM
ejpam-3266	522	34	)	)	PUNCT
ejpam-3266	522	35	.	.	PUNCT
ejpam-3266	523	1	similarly	similarly	ADV
ejpam-3266	523	2	σ	σ	PROPN
ejpam-3266	523	3	is	be	AUX
ejpam-3266	523	4	a	a	DET
ejpam-3266	523	5	left	left	ADJ
ejpam-3266	523	6	congruence	congruence	NOUN
ejpam-3266	523	7	on	on	ADP
ejpam-3266	523	8	(	(	PUNCT
ejpam-3266	523	9	s	s	NOUN
ejpam-3266	523	10	,	,	PUNCT
ejpam-3266	523	11	◦	◦	NOUN
ejpam-3266	523	12	,	,	PUNCT
ejpam-3266	523	13	≤	≤	NUM
ejpam-3266	523	14	)	)	PUNCT
ejpam-3266	523	15	.	.	PUNCT
ejpam-3266	524	1	let	let	VERB
ejpam-3266	524	2	a	a	DET
ejpam-3266	524	3	∈	∈	NOUN
ejpam-3266	524	4	s.	s.	PROPN
ejpam-3266	524	5	then	then	ADV
ejpam-3266	524	6	(	(	PUNCT
ejpam-3266	524	7	a	a	DET
ejpam-3266	524	8	◦	◦	NOUN
ejpam-3266	524	9	a	a	PRON
ejpam-3266	524	10	,	,	PUNCT
ejpam-3266	524	11	a	a	PRON
ejpam-3266	524	12	)	)	PUNCT
ejpam-3266	524	13	∈	∈	PROPN
ejpam-3266	524	14	σ	σ	PROPN
ejpam-3266	524	15	.	.	PUNCT
ejpam-3266	525	1	in	in	ADP
ejpam-3266	525	2	fact	fact	NOUN
ejpam-3266	525	3	:	:	PUNCT
ejpam-3266	525	4	let	let	VERB
ejpam-3266	525	5	u	u	PRON
ejpam-3266	525	6	∈	∈	PROPN
ejpam-3266	525	7	a	a	DET
ejpam-3266	525	8	◦	◦	NOUN
ejpam-3266	525	9	a.	a.	NOUN
ejpam-3266	525	10	then	then	ADV
ejpam-3266	525	11	u	u	NOUN
ejpam-3266	525	12	≤	≤	PROPN
ejpam-3266	525	13	a2	a2	NOUN
ejpam-3266	525	14	,	,	PUNCT
ejpam-3266	525	15	thus	thus	ADV
ejpam-3266	525	16	(	(	PUNCT
ejpam-3266	525	17	u	u	NOUN
ejpam-3266	525	18	,	,	PUNCT
ejpam-3266	525	19	a2	a2	PROPN
ejpam-3266	525	20	)	)	PUNCT
ejpam-3266	525	21	∈	∈	PROPN
ejpam-3266	525	22	σ	σ	PROPN
ejpam-3266	525	23	.	.	PUNCT
ejpam-3266	526	1	moreover	moreover	ADV
ejpam-3266	526	2	(	(	PUNCT
ejpam-3266	526	3	a2	a2	PROPN
ejpam-3266	526	4	,	,	PUNCT
ejpam-3266	526	5	a	a	PRON
ejpam-3266	526	6	)	)	PUNCT
ejpam-3266	526	7	∈	∈	PROPN
ejpam-3266	526	8	σ	σ	PROPN
ejpam-3266	526	9	,	,	PUNCT
ejpam-3266	526	10	and	and	CCONJ
ejpam-3266	526	11	then	then	ADV
ejpam-3266	526	12	(	(	PUNCT
ejpam-3266	526	13	u	u	NOUN
ejpam-3266	526	14	,	,	PUNCT
ejpam-3266	526	15	a	a	PRON
ejpam-3266	526	16	)	)	PUNCT
ejpam-3266	526	17	∈	∈	PROPN
ejpam-3266	526	18	σ	σ	PROPN
ejpam-3266	526	19	.	.	PUNCT
ejpam-3266	527	1	let	let	VERB
ejpam-3266	527	2	a	a	DET
ejpam-3266	527	3	,	,	PUNCT
ejpam-3266	527	4	b	b	X
ejpam-3266	527	5	∈	∈	PROPN
ejpam-3266	527	6	s.	s.	PROPN
ejpam-3266	527	7	then	then	ADV
ejpam-3266	527	8	(	(	PUNCT
ejpam-3266	527	9	a	a	DET
ejpam-3266	527	10	◦	◦	NOUN
ejpam-3266	527	11	b	b	NUM
ejpam-3266	527	12	,	,	PUNCT
ejpam-3266	527	13	b	b	X
ejpam-3266	527	14	◦	◦	NOUN
ejpam-3266	527	15	a	a	X
ejpam-3266	527	16	)	)	PUNCT
ejpam-3266	527	17	∈	∈	PROPN
ejpam-3266	527	18	σ	σ	PROPN
ejpam-3266	527	19	.	.	PUNCT
ejpam-3266	528	1	in	in	ADP
ejpam-3266	528	2	fact	fact	NOUN
ejpam-3266	528	3	:	:	PUNCT
ejpam-3266	528	4	let	let	VERB
ejpam-3266	528	5	u	u	PRON
ejpam-3266	528	6	∈	∈	PROPN
ejpam-3266	528	7	a	a	DET
ejpam-3266	528	8	◦	◦	NOUN
ejpam-3266	528	9	b	b	NOUN
ejpam-3266	528	10	and	and	CCONJ
ejpam-3266	528	11	v	v	ADP
ejpam-3266	528	12	∈	∈	PROPN
ejpam-3266	528	13	b	b	NOUN
ejpam-3266	528	14	◦	◦	NOUN
ejpam-3266	528	15	a.	a.	NOUN
ejpam-3266	528	16	then	then	ADV
ejpam-3266	528	17	u	u	PROPN
ejpam-3266	528	18	≤	≤	PROPN
ejpam-3266	528	19	ab	ab	PROPN
ejpam-3266	528	20	,	,	PUNCT
ejpam-3266	528	21	v	v	NOUN
ejpam-3266	528	22	≤	≤	NUM
ejpam-3266	528	23	ba	ba	NOUN
ejpam-3266	528	24	,	,	PUNCT
ejpam-3266	528	25	from	from	ADP
ejpam-3266	528	26	which	which	PRON
ejpam-3266	528	27	(	(	PUNCT
ejpam-3266	528	28	u	u	NOUN
ejpam-3266	528	29	,	,	PUNCT
ejpam-3266	528	30	ab	ab	PROPN
ejpam-3266	528	31	)	)	PUNCT
ejpam-3266	528	32	∈	∈	PROPN
ejpam-3266	528	33	σ	σ	PROPN
ejpam-3266	528	34	,	,	PUNCT
ejpam-3266	528	35	(	(	PUNCT
ejpam-3266	528	36	v	v	NOUN
ejpam-3266	528	37	,	,	PUNCT
ejpam-3266	528	38	ba	ba	NOUN
ejpam-3266	528	39	)	)	PUNCT
ejpam-3266	528	40	∈	∈	PROPN
ejpam-3266	529	1	σ	σ	PROPN
ejpam-3266	529	2	.	.	PUNCT
ejpam-3266	530	1	moreover	moreover	ADV
ejpam-3266	530	2	(	(	PUNCT
ejpam-3266	530	3	ab	ab	PROPN
ejpam-3266	530	4	,	,	PUNCT
ejpam-3266	530	5	ba	ba	PROPN
ejpam-3266	530	6	)	)	PUNCT
ejpam-3266	530	7	∈	∈	PROPN
ejpam-3266	530	8	σ	σ	PROPN
ejpam-3266	530	9	,	,	PUNCT
ejpam-3266	530	10	thus	thus	ADV
ejpam-3266	530	11	we	we	PRON
ejpam-3266	530	12	get	get	VERB
ejpam-3266	530	13	(	(	PUNCT
ejpam-3266	530	14	u	u	NOUN
ejpam-3266	530	15	,	,	PUNCT
ejpam-3266	530	16	v	v	NOUN
ejpam-3266	530	17	)	)	PUNCT
ejpam-3266	530	18	∈	∈	PROPN
ejpam-3266	530	19	σ	σ	PROPN
ejpam-3266	530	20	.	.	PUNCT
ejpam-3266	530	21	let	let	VERB
ejpam-3266	530	22	a	a	DET
ejpam-3266	530	23	≤	≤	PROPN
ejpam-3266	530	24	b.	b.	NOUN
ejpam-3266	531	1	then	then	ADV
ejpam-3266	531	2	(	(	PUNCT
ejpam-3266	531	3	a	a	X
ejpam-3266	531	4	,	,	PUNCT
ejpam-3266	531	5	a	a	DET
ejpam-3266	531	6	◦	◦	NOUN
ejpam-3266	531	7	b	b	NOUN
ejpam-3266	531	8	)	)	PUNCT
ejpam-3266	531	9	∈	∈	PROPN
ejpam-3266	531	10	σ	σ	PROPN
ejpam-3266	531	11	.	.	PUNCT
ejpam-3266	532	1	indeed	indeed	ADV
ejpam-3266	532	2	:	:	PUNCT
ejpam-3266	532	3	let	let	VERB
ejpam-3266	532	4	u	u	PRON
ejpam-3266	532	5	∈	∈	PROPN
ejpam-3266	532	6	a	a	DET
ejpam-3266	532	7	◦	◦	NOUN
ejpam-3266	532	8	b.	b.	NOUN
ejpam-3266	532	9	then	then	ADV
ejpam-3266	532	10	u	u	PROPN
ejpam-3266	532	11	≤	≤	X
ejpam-3266	532	12	ab	ab	PROPN
ejpam-3266	532	13	,	,	PUNCT
ejpam-3266	532	14	so	so	CCONJ
ejpam-3266	532	15	(	(	PUNCT
ejpam-3266	532	16	u	u	NOUN
ejpam-3266	532	17	,	,	PUNCT
ejpam-3266	532	18	ab	ab	PROPN
ejpam-3266	532	19	)	)	PUNCT
ejpam-3266	532	20	∈	∈	PROPN
ejpam-3266	532	21	σ	σ	PROPN
ejpam-3266	532	22	.	.	PUNCT
ejpam-3266	533	1	since	since	SCONJ
ejpam-3266	533	2	a	a	DET
ejpam-3266	533	3	≤	≤	NUM
ejpam-3266	533	4	b	b	NOUN
ejpam-3266	533	5	,	,	PUNCT
ejpam-3266	533	6	we	we	PRON
ejpam-3266	533	7	have	have	VERB
ejpam-3266	533	8	(	(	PUNCT
ejpam-3266	533	9	a	a	DET
ejpam-3266	533	10	,	,	PUNCT
ejpam-3266	533	11	b	b	NOUN
ejpam-3266	533	12	)	)	PUNCT
ejpam-3266	533	13	∈	∈	PROPN
ejpam-3266	533	14	σ	σ	PROPN
ejpam-3266	533	15	,	,	PUNCT
ejpam-3266	533	16	then	then	ADV
ejpam-3266	533	17	(	(	PUNCT
ejpam-3266	533	18	a2	a2	PROPN
ejpam-3266	533	19	,	,	PUNCT
ejpam-3266	533	20	ab	ab	PROPN
ejpam-3266	533	21	)	)	PUNCT
ejpam-3266	533	22	∈	∈	PROPN
ejpam-3266	533	23	σ	σ	PROPN
ejpam-3266	533	24	.	.	PUNCT
ejpam-3266	534	1	moreover	moreover	ADV
ejpam-3266	534	2	(	(	PUNCT
ejpam-3266	534	3	a	a	PRON
ejpam-3266	534	4	,	,	PUNCT
ejpam-3266	534	5	a2	a2	PROPN
ejpam-3266	534	6	)	)	PUNCT
ejpam-3266	534	7	∈	∈	PROPN
ejpam-3266	534	8	σ	σ	PROPN
ejpam-3266	534	9	,	,	PUNCT
ejpam-3266	534	10	and	and	CCONJ
ejpam-3266	534	11	then	then	ADV
ejpam-3266	534	12	(	(	PUNCT
ejpam-3266	534	13	a	a	PRON
ejpam-3266	534	14	,	,	PUNCT
ejpam-3266	534	15	u	u	NOUN
ejpam-3266	534	16	)	)	PUNCT
ejpam-3266	534	17	∈	∈	PROPN
ejpam-3266	534	18	σ	σ	PROPN
ejpam-3266	534	19	.	.	PUNCT
ejpam-3266	535	1	hence	hence	ADV
ejpam-3266	535	2	σ	σ	PROPN
ejpam-3266	535	3	is	be	AUX
ejpam-3266	535	4	a	a	DET
ejpam-3266	535	5	complete	complete	ADJ
ejpam-3266	535	6	semilattice	semilattice	NOUN
ejpam-3266	535	7	congruence	congruence	NOUN
ejpam-3266	535	8	on	on	ADP
ejpam-3266	535	9	(	(	PUNCT
ejpam-3266	535	10	s	s	NOUN
ejpam-3266	535	11	,	,	PUNCT
ejpam-3266	535	12	◦	◦	NOUN
ejpam-3266	535	13	,	,	PUNCT
ejpam-3266	535	14	≤	≤	NUM
ejpam-3266	535	15	)	)	PUNCT
ejpam-3266	535	16	.	.	PUNCT
ejpam-3266	536	1	�	�	PROPN
ejpam-3266	536	2	with	with	ADP
ejpam-3266	536	3	my	my	PRON
ejpam-3266	536	4	best	good	ADJ
ejpam-3266	536	5	thanks	thank	NOUN
ejpam-3266	536	6	to	to	ADP
ejpam-3266	536	7	the	the	DET
ejpam-3266	536	8	two	two	NUM
ejpam-3266	536	9	anonymous	anonymous	ADJ
ejpam-3266	536	10	referees	referee	NOUN
ejpam-3266	536	11	for	for	ADP
ejpam-3266	536	12	their	their	PRON
ejpam-3266	536	13	time	time	NOUN
ejpam-3266	536	14	to	to	PART
ejpam-3266	536	15	read	read	VERB
ejpam-3266	536	16	the	the	DET
ejpam-3266	536	17	paper	paper	NOUN
ejpam-3266	536	18	carefully	carefully	ADV
ejpam-3266	536	19	,	,	PUNCT
ejpam-3266	536	20	their	their	PRON
ejpam-3266	536	21	interest	interest	NOUN
ejpam-3266	536	22	on	on	ADP
ejpam-3266	536	23	my	my	PRON
ejpam-3266	536	24	work	work	NOUN
ejpam-3266	536	25	and	and	CCONJ
ejpam-3266	536	26	their	their	PRON
ejpam-3266	536	27	prompt	prompt	ADJ
ejpam-3266	536	28	reply	reply	NOUN
ejpam-3266	536	29	.	.	PUNCT
ejpam-3266	537	1	references	reference	NOUN
ejpam-3266	537	2	[	[	X
ejpam-3266	537	3	1	1	NUM
ejpam-3266	537	4	]	]	PUNCT
ejpam-3266	537	5	n.	n.	NOUN
ejpam-3266	537	6	kehayopulu	kehayopulu	PROPN
ejpam-3266	537	7	.	.	PUNCT
ejpam-3266	538	1	on	on	ADP
ejpam-3266	538	2	weakly	weakly	ADJ
ejpam-3266	538	3	commutative	commutative	ADJ
ejpam-3266	538	4	poe	poe	PROPN
ejpam-3266	538	5	-	-	PUNCT
ejpam-3266	538	6	semigroups	semigroup	NOUN
ejpam-3266	538	7	.	.	PUNCT
ejpam-3266	539	1	semigroup	semigroup	PROPN
ejpam-3266	539	2	forum	forum	PROPN
ejpam-3266	539	3	34(3):367–370	34(3):367–370	NUM
ejpam-3266	539	4	,	,	PUNCT
ejpam-3266	539	5	1987	1987	NUM
ejpam-3266	539	6	.	.	PUNCT
ejpam-3266	540	1	[	[	X
ejpam-3266	540	2	2	2	NUM
ejpam-3266	540	3	]	]	PUNCT
ejpam-3266	540	4	n.	n.	NOUN
ejpam-3266	540	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	540	6	.	.	PUNCT
ejpam-3266	541	1	on	on	ADP
ejpam-3266	541	2	weakly	weakly	ADJ
ejpam-3266	541	3	prime	prime	ADJ
ejpam-3266	541	4	ideals	ideal	NOUN
ejpam-3266	541	5	of	of	ADP
ejpam-3266	541	6	ordered	order	VERB
ejpam-3266	541	7	semigroups	semigroup	NOUN
ejpam-3266	541	8	.	.	PUNCT
ejpam-3266	541	9	math	math	NOUN
ejpam-3266	541	10	.	.	PUNCT
ejpam-3266	542	1	japon	japon	PROPN
ejpam-3266	542	2	.	.	PUNCT
ejpam-3266	543	1	35(6):1051–1056	35(6):1051–1056	NUM
ejpam-3266	543	2	,	,	PUNCT
ejpam-3266	543	3	1990	1990	NUM
ejpam-3266	543	4	.	.	PUNCT
ejpam-3266	544	1	[	[	X
ejpam-3266	544	2	3	3	X
ejpam-3266	544	3	]	]	X
ejpam-3266	544	4	n.	n.	NOUN
ejpam-3266	544	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	544	6	.	.	PUNCT
ejpam-3266	545	1	remark	remark	PROPN
ejpam-3266	545	2	on	on	ADP
ejpam-3266	545	3	ordered	order	VERB
ejpam-3266	545	4	semigroups	semigroup	NOUN
ejpam-3266	545	5	.	.	PUNCT
ejpam-3266	546	1	math	math	NOUN
ejpam-3266	546	2	.	.	PUNCT
ejpam-3266	547	1	japon	japon	PROPN
ejpam-3266	547	2	.	.	PUNCT
ejpam-3266	548	1	35(6):1061–1063	35(6):1061–1063	NUM
ejpam-3266	548	2	,	,	PUNCT
ejpam-3266	548	3	1990	1990	NUM
ejpam-3266	548	4	.	.	PUNCT
ejpam-3266	549	1	[	[	X
ejpam-3266	549	2	4	4	X
ejpam-3266	549	3	]	]	X
ejpam-3266	549	4	n.	n.	NOUN
ejpam-3266	549	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	549	6	.	.	PUNCT
ejpam-3266	550	1	on	on	ADP
ejpam-3266	550	2	intra	intra	ADJ
ejpam-3266	550	3	-	-	ADJ
ejpam-3266	550	4	regular	regular	ADJ
ejpam-3266	550	5	ordered	order	VERB
ejpam-3266	550	6	semigroups	semigroup	NOUN
ejpam-3266	550	7	.	.	PUNCT
ejpam-3266	551	1	semigroup	semigroup	PROPN
ejpam-3266	551	2	forum	forum	PROPN
ejpam-3266	551	3	46(3):271–278	46(3):271–278	PROPN
ejpam-3266	551	4	,	,	PUNCT
ejpam-3266	551	5	1993	1993	NUM
ejpam-3266	551	6	.	.	PUNCT
ejpam-3266	552	1	[	[	X
ejpam-3266	552	2	5	5	NUM
ejpam-3266	552	3	]	]	PUNCT
ejpam-3266	552	4	n.	n.	NOUN
ejpam-3266	552	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	552	6	.	.	PUNCT
ejpam-3266	553	1	green	green	PROPN
ejpam-3266	553	2	’s	’s	PART
ejpam-3266	553	3	relations	relation	NOUN
ejpam-3266	553	4	and	and	CCONJ
ejpam-3266	553	5	the	the	DET
ejpam-3266	553	6	relation	relation	NOUN
ejpam-3266	553	7	n	n	CCONJ
ejpam-3266	553	8	in	in	ADP
ejpam-3266	553	9	γ	γ	NOUN
ejpam-3266	553	10	-	-	PUNCT
ejpam-3266	553	11	semigroups	semigroup	NOUN
ejpam-3266	553	12	.	.	PUNCT
ejpam-3266	554	1	quasigroups	quasigroup	NOUN
ejpam-3266	554	2	related	related	ADJ
ejpam-3266	554	3	systems	system	NOUN
ejpam-3266	554	4	22(1):89–96	22(1):89–96	NUM
ejpam-3266	554	5	,	,	PUNCT
ejpam-3266	554	6	2014	2014	NUM
ejpam-3266	554	7	.	.	PUNCT
ejpam-3266	555	1	[	[	X
ejpam-3266	555	2	6	6	NUM
ejpam-3266	555	3	]	]	PUNCT
ejpam-3266	555	4	n.	n.	NOUN
ejpam-3266	555	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	555	6	.	.	PUNCT
ejpam-3266	556	1	left	leave	VERB
ejpam-3266	556	2	regular	regular	ADJ
ejpam-3266	556	3	and	and	CCONJ
ejpam-3266	556	4	intra	intra	ADJ
ejpam-3266	556	5	-	-	ADJ
ejpam-3266	556	6	regular	regular	ADJ
ejpam-3266	556	7	ordered	order	VERB
ejpam-3266	556	8	nypersemigroups	nypersemigroup	NOUN
ejpam-3266	556	9	in	in	ADP
ejpam-3266	556	10	terms	term	NOUN
ejpam-3266	556	11	of	of	ADP
ejpam-3266	556	12	semiprime	semiprime	NOUN
ejpam-3266	556	13	and	and	CCONJ
ejpam-3266	556	14	fuzzy	fuzzy	ADJ
ejpam-3266	556	15	semiprime	semiprime	NOUN
ejpam-3266	556	16	subsets	subset	NOUN
ejpam-3266	556	17	.	.	PUNCT
ejpam-3266	557	1	sci	sci	PROPN
ejpam-3266	557	2	.	.	PROPN
ejpam-3266	557	3	math	math	PROPN
ejpam-3266	557	4	.	.	PUNCT
ejpam-3266	558	1	jpn	jpn	PROPN
ejpam-3266	558	2	.	.	PUNCT
ejpam-3266	559	1	80(3):295–305	80(3):295–305	PROPN
ejpam-3266	559	2	,	,	PUNCT
ejpam-3266	559	3	2017	2017	NUM
ejpam-3266	559	4	.	.	PUNCT
ejpam-3266	560	1	[	[	X
ejpam-3266	560	2	7	7	X
ejpam-3266	560	3	]	]	X
ejpam-3266	560	4	n.	n.	NOUN
ejpam-3266	560	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	560	6	.	.	PUNCT
ejpam-3266	561	1	fuzzy	fuzzy	ADJ
ejpam-3266	561	2	sets	set	NOUN
ejpam-3266	561	3	in	in	ADP
ejpam-3266	561	4	≤-hypergroupoids	≤-hypergroupoids	PROPN
ejpam-3266	561	5	.	.	PUNCT
ejpam-3266	562	1	sci	sci	PROPN
ejpam-3266	562	2	.	.	PUNCT
ejpam-3266	562	3	math	math	PROPN
ejpam-3266	562	4	.	.	PUNCT
ejpam-3266	563	1	jpn	jpn	PROPN
ejpam-3266	563	2	.	.	PUNCT
ejpam-3266	564	1	80(3):307–314	80(3):307–314	PROPN
ejpam-3266	564	2	,	,	PUNCT
ejpam-3266	564	3	2017	2017	NUM
ejpam-3266	564	4	.	.	PUNCT
ejpam-3266	565	1	[	[	X
ejpam-3266	565	2	8	8	NUM
ejpam-3266	565	3	]	]	X
ejpam-3266	565	4	n.	n.	NOUN
ejpam-3266	565	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	565	6	.	.	PUNCT
ejpam-3266	566	1	how	how	SCONJ
ejpam-3266	566	2	we	we	PRON
ejpam-3266	566	3	pass	pass	VERB
ejpam-3266	566	4	from	from	ADP
ejpam-3266	566	5	semigroups	semigroup	NOUN
ejpam-3266	566	6	to	to	ADP
ejpam-3266	566	7	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	566	8	.	.	PUNCT
ejpam-3266	567	1	lobachevskii	lobachevskii	PROPN
ejpam-3266	567	2	j.	j.	PROPN
ejpam-3266	567	3	math	math	PROPN
ejpam-3266	567	4	.	.	PUNCT
ejpam-3266	568	1	39(1):121–128	39(1):121–128	NUM
ejpam-3266	568	2	,	,	PUNCT
ejpam-3266	568	3	2018	2018	NUM
ejpam-3266	568	4	.	.	PUNCT
ejpam-3266	569	1	[	[	X
ejpam-3266	569	2	9	9	NUM
ejpam-3266	569	3	]	]	X
ejpam-3266	569	4	n.	n.	NOUN
ejpam-3266	569	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	569	6	.	.	PUNCT
ejpam-3266	570	1	on	on	ADP
ejpam-3266	570	2	ordered	order	VERB
ejpam-3266	570	3	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	570	4	with	with	ADP
ejpam-3266	570	5	idempotent	idempotent	ADJ
ejpam-3266	570	6	ideals	ideal	NOUN
ejpam-3266	570	7	,	,	PUNCT
ejpam-3266	570	8	prime	prime	ADJ
ejpam-3266	570	9	or	or	CCONJ
ejpam-3266	570	10	weakly	weakly	ADJ
ejpam-3266	570	11	prime	prime	ADJ
ejpam-3266	570	12	ideals	ideal	NOUN
ejpam-3266	570	13	.	.	PUNCT
ejpam-3266	571	1	eur	eur	PROPN
ejpam-3266	571	2	.	.	PUNCT
ejpam-3266	572	1	j.	j.	PROPN
ejpam-3266	572	2	pure	pure	PROPN
ejpam-3266	572	3	appl	appl	PROPN
ejpam-3266	572	4	.	.	PUNCT
ejpam-3266	572	5	math	math	NOUN
ejpam-3266	572	6	.	.	PUNCT
ejpam-3266	573	1	11(1):10–22	11(1):10–22	NUM
ejpam-3266	573	2	,	,	PUNCT
ejpam-3266	573	3	2018	2018	NUM
ejpam-3266	573	4	.	.	PUNCT
ejpam-3266	574	1	[	[	X
ejpam-3266	574	2	10	10	NUM
ejpam-3266	574	3	]	]	X
ejpam-3266	574	4	n.	n.	NOUN
ejpam-3266	574	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	574	6	.	.	PUNCT
ejpam-3266	575	1	on	on	ADP
ejpam-3266	575	2	ordered	order	VERB
ejpam-3266	575	3	hypersemigroups	hypersemigroup	NOUN
ejpam-3266	575	4	given	give	VERB
ejpam-3266	575	5	by	by	ADP
ejpam-3266	575	6	a	a	DET
ejpam-3266	575	7	table	table	NOUN
ejpam-3266	575	8	of	of	ADP
ejpam-3266	575	9	multiplication	multiplication	NOUN
ejpam-3266	575	10	and	and	CCONJ
ejpam-3266	575	11	a	a	DET
ejpam-3266	575	12	figure	figure	NOUN
ejpam-3266	575	13	.	.	PUNCT
ejpam-3266	576	1	turkish	turkish	ADJ
ejpam-3266	576	2	j.	j.	PROPN
ejpam-3266	576	3	math	math	PROPN
ejpam-3266	576	4	.	.	PROPN
ejpam-3266	576	5	,	,	PUNCT
ejpam-3266	576	6	submitted	submit	VERB
ejpam-3266	576	7	.	.	PUNCT
ejpam-3266	577	1	[	[	X
ejpam-3266	577	2	11	11	NUM
ejpam-3266	577	3	]	]	X
ejpam-3266	577	4	n.	n.	PROPN
ejpam-3266	577	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	577	6	,	,	PUNCT
ejpam-3266	577	7	m.	m.	NOUN
ejpam-3266	577	8	tsingelis	tsingelis	PROPN
ejpam-3266	577	9	.	.	PUNCT
ejpam-3266	578	1	remark	remark	PROPN
ejpam-3266	578	2	on	on	ADP
ejpam-3266	578	3	ordered	order	VERB
ejpam-3266	578	4	semigroups	semigroup	NOUN
ejpam-3266	578	5	.	.	PUNCT
ejpam-3266	579	1	in	in	ADP
ejpam-3266	579	2	:	:	PUNCT
ejpam-3266	579	3	partitions	partition	NOUN
ejpam-3266	579	4	and	and	CCONJ
ejpam-3266	579	5	holomorphic	holomorphic	ADJ
ejpam-3266	579	6	mappings	mapping	NOUN
ejpam-3266	579	7	of	of	ADP
ejpam-3266	579	8	semigroups	semigroup	NOUN
ejpam-3266	579	9	(	(	PUNCT
ejpam-3266	579	10	russian	russian	ADJ
ejpam-3266	579	11	)	)	PUNCT
ejpam-3266	579	12	50–55	50–55	NUM
ejpam-3266	579	13	,	,	PUNCT
ejpam-3266	579	14	“	"	PUNCT
ejpam-3266	579	15	obrazovanie	obrazovanie	NOUN
ejpam-3266	579	16	”	"	PUNCT
ejpam-3266	579	17	,	,	PUNCT
ejpam-3266	579	18	st	st	PROPN
ejpam-3266	579	19	.	.	PROPN
ejpam-3266	579	20	petersburg	petersburg	PROPN
ejpam-3266	579	21	1992	1992	NUM
ejpam-3266	579	22	.	.	PUNCT
ejpam-3266	580	1	[	[	X
ejpam-3266	580	2	12	12	NUM
ejpam-3266	580	3	]	]	X
ejpam-3266	580	4	n.	n.	PROPN
ejpam-3266	580	5	kehayopulu	kehayopulu	PROPN
ejpam-3266	580	6	,	,	PUNCT
ejpam-3266	580	7	m.	m.	NOUN
ejpam-3266	580	8	tsingelis	tsingelis	PROPN
ejpam-3266	580	9	.	.	PUNCT
ejpam-3266	581	1	on	on	ADP
ejpam-3266	581	2	the	the	DET
ejpam-3266	581	3	decomposition	decomposition	NOUN
ejpam-3266	581	4	of	of	ADP
ejpam-3266	581	5	prime	prime	ADJ
ejpam-3266	581	6	ideals	ideal	NOUN
ejpam-3266	581	7	of	of	ADP
ejpam-3266	581	8	ordered	order	VERB
ejpam-3266	581	9	semigroups	semigroup	NOUN
ejpam-3266	581	10	into	into	ADP
ejpam-3266	581	11	their	their	PRON
ejpam-3266	581	12	n	n	NUM
ejpam-3266	581	13	-classes	-classe	NOUN
ejpam-3266	581	14	.	.	PUNCT
ejpam-3266	582	1	semigroup	semigroup	PROPN
ejpam-3266	582	2	forum	forum	PROPN
ejpam-3266	582	3	47(3):393–395	47(3):393–395	PROPN
ejpam-3266	582	4	,	,	PUNCT
ejpam-3266	582	5	1993	1993	NUM
ejpam-3266	582	6	.	.	PUNCT
ejpam-3266	583	1	[	[	X
ejpam-3266	583	2	13	13	NUM
ejpam-3266	583	3	]	]	PUNCT
ejpam-3266	583	4	m.	m.	NOUN
ejpam-3266	583	5	petrich	petrich	PROPN
ejpam-3266	583	6	.	.	PUNCT
ejpam-3266	584	1	introduction	introduction	NOUN
ejpam-3266	584	2	to	to	ADP
ejpam-3266	584	3	semigroups	semigroup	NOUN
ejpam-3266	584	4	,	,	PUNCT
ejpam-3266	584	5	charles	charles	PROPN
ejpam-3266	584	6	e.	e.	PROPN
ejpam-3266	584	7	merrill	merrill	PROPN
ejpam-3266	584	8	publishing	publishing	PROPN
ejpam-3266	584	9	company	company	NOUN
ejpam-3266	584	10	,	,	PUNCT
ejpam-3266	584	11	a	a	DET
ejpam-3266	584	12	bell	bell	PROPN
ejpam-3266	584	13	&	&	CCONJ
ejpam-3266	584	14	howell	howell	PROPN
ejpam-3266	584	15	company	company	PROPN
ejpam-3266	584	16	.	.	PUNCT
ejpam-3266	585	1	columbus	columbus	PROPN
ejpam-3266	585	2	,	,	PUNCT
ejpam-3266	585	3	ohio	ohio	PROPN
ejpam-3266	585	4	1973	1973	NUM
ejpam-3266	585	5	.	.	PUNCT
ejpam-3266	586	1	viii+198	viii+198	NOUN
ejpam-3266	586	2	pp	pp	PROPN
ejpam-3266	586	3	.	.	PUNCT