id	sid	tid	token	lemma	pos
ejpam-5511	1	1	european	european	PROPN
ejpam-5511	1	2	journal	journal	PROPN
ejpam-5511	1	3	of	of	ADP
ejpam-5511	1	4	pure	pure	ADJ
ejpam-5511	1	5	and	and	CCONJ
ejpam-5511	1	6	applied	apply	VERB
ejpam-5511	1	7	mathematics	mathematic	NOUN
ejpam-5511	1	8	vol	vol	NOUN
ejpam-5511	1	9	.	.	PROPN
ejpam-5511	2	1	17	17	NUM
ejpam-5511	2	2	,	,	PUNCT
ejpam-5511	2	3	no	no	INTJ
ejpam-5511	2	4	.	.	NOUN
ejpam-5511	2	5	4	4	NUM
ejpam-5511	2	6	,	,	PUNCT
ejpam-5511	2	7	2024	2024	NUM
ejpam-5511	2	8	,	,	PUNCT
ejpam-5511	2	9	4180	4180	NUM
ejpam-5511	2	10	-	-	SYM
ejpam-5511	2	11	4194	4194	NUM
ejpam-5511	2	12	issn	issn	PROPN
ejpam-5511	2	13	1307	1307	NUM
ejpam-5511	2	14	-	-	SYM
ejpam-5511	2	15	5543	5543	NUM
ejpam-5511	2	16	–	–	PUNCT
ejpam-5511	2	17	ejpam.com	ejpam.com	X
ejpam-5511	2	18	published	publish	VERB
ejpam-5511	2	19	by	by	ADP
ejpam-5511	2	20	new	new	PROPN
ejpam-5511	2	21	york	york	PROPN
ejpam-5511	2	22	business	business	PROPN
ejpam-5511	2	23	global	global	PROPN
ejpam-5511	2	24	implicative	implicative	PROPN
ejpam-5511	2	25	negatively	negatively	ADV
ejpam-5511	2	26	partially	partially	ADV
ejpam-5511	2	27	ordered	order	VERB
ejpam-5511	2	28	ternary	ternary	ADJ
ejpam-5511	2	29	semigroups	semigroup	NOUN
ejpam-5511	2	30	kansada	kansada	PROPN
ejpam-5511	2	31	nakwan1	nakwan1	PROPN
ejpam-5511	2	32	,	,	PUNCT
ejpam-5511	2	33	panuwat	panuwat	VERB
ejpam-5511	2	34	luangchaisri1	luangchaisri1	NOUN
ejpam-5511	2	35	,	,	PUNCT
ejpam-5511	2	36	thawhat	thawhat	PROPN
ejpam-5511	2	37	changphas1,∗	changphas1,∗	NOUN
ejpam-5511	2	38	1	1	NUM
ejpam-5511	2	39	department	department	NOUN
ejpam-5511	2	40	of	of	ADP
ejpam-5511	2	41	mathematics	mathematic	NOUN
ejpam-5511	2	42	,	,	PUNCT
ejpam-5511	2	43	faculty	faculty	NOUN
ejpam-5511	2	44	of	of	ADP
ejpam-5511	2	45	science	science	NOUN
ejpam-5511	2	46	,	,	PUNCT
ejpam-5511	2	47	khon	khon	PROPN
ejpam-5511	2	48	kaen	kaen	PROPN
ejpam-5511	2	49	university	university	PROPN
ejpam-5511	2	50	,	,	PUNCT
ejpam-5511	2	51	khon	khon	PROPN
ejpam-5511	2	52	kaen	kaen	PROPN
ejpam-5511	2	53	40002	40002	NUM
ejpam-5511	2	54	,	,	PUNCT
ejpam-5511	2	55	thailand	thailand	PROPN
ejpam-5511	2	56	abstract	abstract	NOUN
ejpam-5511	2	57	.	.	PUNCT
ejpam-5511	3	1	in	in	ADP
ejpam-5511	3	2	this	this	DET
ejpam-5511	3	3	paper	paper	NOUN
ejpam-5511	3	4	,	,	PUNCT
ejpam-5511	3	5	we	we	PRON
ejpam-5511	3	6	introduce	introduce	VERB
ejpam-5511	3	7	and	and	CCONJ
ejpam-5511	3	8	examine	examine	VERB
ejpam-5511	3	9	the	the	DET
ejpam-5511	3	10	notion	notion	NOUN
ejpam-5511	3	11	of	of	ADP
ejpam-5511	3	12	implicative	implicative	NOUN
ejpam-5511	3	13	negatively	negatively	ADV
ejpam-5511	3	14	partially	partially	ADV
ejpam-5511	3	15	ordered	order	VERB
ejpam-5511	3	16	ternary	ternary	ADJ
ejpam-5511	3	17	semigroups	semigroup	NOUN
ejpam-5511	3	18	,	,	PUNCT
ejpam-5511	3	19	for	for	ADP
ejpam-5511	3	20	short	short	ADJ
ejpam-5511	3	21	implicative	implicative	ADJ
ejpam-5511	3	22	n.p.o	n.p.o	NOUN
ejpam-5511	3	23	.	.	PUNCT
ejpam-5511	4	1	ternary	ternary	PROPN
ejpam-5511	4	2	semigroup	semigroup	PROPN
ejpam-5511	4	3	,	,	PUNCT
ejpam-5511	4	4	which	which	PRON
ejpam-5511	4	5	include	include	VERB
ejpam-5511	4	6	an	an	DET
ejpam-5511	4	7	element	element	NOUN
ejpam-5511	4	8	that	that	PRON
ejpam-5511	4	9	serves	serve	VERB
ejpam-5511	4	10	as	as	ADP
ejpam-5511	4	11	both	both	CCONJ
ejpam-5511	4	12	the	the	DET
ejpam-5511	4	13	greatest	great	ADJ
ejpam-5511	4	14	element	element	NOUN
ejpam-5511	4	15	and	and	CCONJ
ejpam-5511	4	16	the	the	DET
ejpam-5511	4	17	multiplicative	multiplicative	ADJ
ejpam-5511	4	18	identity	identity	NOUN
ejpam-5511	4	19	.	.	PUNCT
ejpam-5511	5	1	we	we	PRON
ejpam-5511	5	2	study	study	VERB
ejpam-5511	5	3	the	the	DET
ejpam-5511	5	4	notion	notion	NOUN
ejpam-5511	5	5	of	of	ADP
ejpam-5511	5	6	implicative	implicative	ADJ
ejpam-5511	5	7	homomorphisms	homomorphism	NOUN
ejpam-5511	5	8	between	between	ADP
ejpam-5511	5	9	these	these	DET
ejpam-5511	5	10	ternary	ternary	ADJ
ejpam-5511	5	11	semigroups	semigroup	NOUN
ejpam-5511	5	12	,	,	PUNCT
ejpam-5511	5	13	and	and	CCONJ
ejpam-5511	5	14	have	have	VERB
ejpam-5511	5	15	that	that	PRON
ejpam-5511	5	16	any	any	DET
ejpam-5511	5	17	implicative	implicative	ADJ
ejpam-5511	5	18	homomorphism	homomorphism	NOUN
ejpam-5511	5	19	is	be	AUX
ejpam-5511	5	20	a	a	DET
ejpam-5511	5	21	homomorphism	homomorphism	NOUN
ejpam-5511	5	22	.	.	PUNCT
ejpam-5511	6	1	let	let	VERB
ejpam-5511	6	2	φ	φ	PROPN
ejpam-5511	6	3	:	:	PUNCT
ejpam-5511	6	4	t1	t1	PROPN
ejpam-5511	6	5	−→	−→	ADJ
ejpam-5511	6	6	t2	t2	NOUN
ejpam-5511	6	7	be	be	VERB
ejpam-5511	6	8	an	an	DET
ejpam-5511	6	9	implicative	implicative	ADJ
ejpam-5511	6	10	homomorphism	homomorphism	NOUN
ejpam-5511	6	11	from	from	ADP
ejpam-5511	6	12	a	a	DET
ejpam-5511	6	13	commutative	commutative	ADJ
ejpam-5511	6	14	implicative	implicative	ADJ
ejpam-5511	6	15	n.p.o	n.p.o	NOUN
ejpam-5511	6	16	.	.	PUNCT
ejpam-5511	7	1	ternary	ternary	PROPN
ejpam-5511	7	2	semigroup	semigroup	PROPN
ejpam-5511	7	3	t1	t1	NOUN
ejpam-5511	7	4	onto	onto	ADP
ejpam-5511	7	5	t2	t2	NOUN
ejpam-5511	7	6	.	.	PUNCT
ejpam-5511	8	1	we	we	PRON
ejpam-5511	8	2	construct	construct	VERB
ejpam-5511	8	3	a	a	DET
ejpam-5511	8	4	quotient	quotient	NOUN
ejpam-5511	8	5	commutative	commutative	ADJ
ejpam-5511	8	6	implicative	implicative	ADJ
ejpam-5511	8	7	n.p.o	n.p.o	NOUN
ejpam-5511	8	8	.	.	PUNCT
ejpam-5511	9	1	ternary	ternary	PROPN
ejpam-5511	9	2	semigroup	semigroup	PROPN
ejpam-5511	9	3	t1	t1	PROPN
ejpam-5511	9	4	/	/	SYM
ejpam-5511	9	5	ρkerφ	ρkerφ	NOUN
ejpam-5511	9	6	,	,	PUNCT
ejpam-5511	9	7	where	where	SCONJ
ejpam-5511	9	8	ρkerφ	ρkerφ	NOUN
ejpam-5511	9	9	is	be	AUX
ejpam-5511	9	10	a	a	DET
ejpam-5511	9	11	congruence	congruence	NOUN
ejpam-5511	9	12	relation	relation	NOUN
ejpam-5511	9	13	defined	define	VERB
ejpam-5511	9	14	by	by	ADP
ejpam-5511	9	15	kerφ	kerφ	PROPN
ejpam-5511	9	16	.	.	PUNCT
ejpam-5511	10	1	we	we	PRON
ejpam-5511	10	2	prove	prove	VERB
ejpam-5511	10	3	that	that	SCONJ
ejpam-5511	10	4	there	there	PRON
ejpam-5511	10	5	exists	exist	VERB
ejpam-5511	10	6	an	an	DET
ejpam-5511	10	7	implicative	implicative	ADJ
ejpam-5511	10	8	homomorphism	homomorphism	NOUN
ejpam-5511	10	9	ψ	ψ	ADP
ejpam-5511	10	10	such	such	ADJ
ejpam-5511	10	11	that	that	SCONJ
ejpam-5511	10	12	ψ	ψ	ADP
ejpam-5511	10	13	◦	◦	NOUN
ejpam-5511	10	14	η	η	X
ejpam-5511	10	15	=	=	SYM
ejpam-5511	10	16	φ	φ	PROPN
ejpam-5511	10	17	,	,	PUNCT
ejpam-5511	10	18	where	where	SCONJ
ejpam-5511	10	19	η	η	PROPN
ejpam-5511	10	20	is	be	AUX
ejpam-5511	10	21	a	a	DET
ejpam-5511	10	22	canonical	canonical	ADJ
ejpam-5511	10	23	homomorphism	homomorphism	NOUN
ejpam-5511	10	24	from	from	ADP
ejpam-5511	10	25	t1	t1	PROPN
ejpam-5511	10	26	onto	onto	ADP
ejpam-5511	10	27	t1	t1	PROPN
ejpam-5511	10	28	/	/	SYM
ejpam-5511	10	29	ρkerφ	ρkerφ	VERB
ejpam-5511	10	30	.	.	PUNCT
ejpam-5511	11	1	2020	2020	NUM
ejpam-5511	11	2	mathematics	mathematics	PROPN
ejpam-5511	11	3	subject	subject	NOUN
ejpam-5511	11	4	classifications	classification	NOUN
ejpam-5511	11	5	:	:	PUNCT
ejpam-5511	11	6	20m12	20m12	NUM
ejpam-5511	11	7	,	,	PUNCT
ejpam-5511	11	8	06f99	06f99	NUM
ejpam-5511	11	9	,	,	PUNCT
ejpam-5511	11	10	06a06	06a06	NOUN
ejpam-5511	11	11	,	,	PUNCT
ejpam-5511	11	12	06a12	06a12	NUM
ejpam-5511	11	13	key	key	ADJ
ejpam-5511	11	14	words	word	NOUN
ejpam-5511	11	15	and	and	CCONJ
ejpam-5511	11	16	phrases	phrase	NOUN
ejpam-5511	11	17	:	:	PUNCT
ejpam-5511	11	18	implicative	implicative	ADJ
ejpam-5511	11	19	semilattice	semilattice	NOUN
ejpam-5511	11	20	,	,	PUNCT
ejpam-5511	11	21	implicative	implicative	ADJ
ejpam-5511	11	22	n.p.o	n.p.o	NOUN
ejpam-5511	11	23	.	.	PUNCT
ejpam-5511	12	1	(	(	PUNCT
ejpam-5511	12	2	negatively	negatively	ADV
ejpam-5511	12	3	partially	partially	ADV
ejpam-5511	12	4	ordered	order	VERB
ejpam-5511	12	5	)	)	PUNCT
ejpam-5511	12	6	ternary	ternary	ADJ
ejpam-5511	12	7	semigroup	semigroup	NOUN
ejpam-5511	12	8	,	,	PUNCT
ejpam-5511	12	9	implicative	implicative	ADJ
ejpam-5511	12	10	homomorphism	homomorphism	NOUN
ejpam-5511	12	11	,	,	PUNCT
ejpam-5511	12	12	filter	filter	NOUN
ejpam-5511	12	13	1	1	NUM
ejpam-5511	12	14	.	.	PUNCT
ejpam-5511	12	15	introduction	introduction	NOUN
ejpam-5511	12	16	an	an	DET
ejpam-5511	12	17	implicative	implicative	ADJ
ejpam-5511	12	18	semilattice	semilattice	NOUN
ejpam-5511	12	19	(	(	PUNCT
ejpam-5511	12	20	l,≤,∧	l,≤,∧	PROPN
ejpam-5511	12	21	,	,	PUNCT
ejpam-5511	12	22	∗	∗	NOUN
ejpam-5511	12	23	)	)	PUNCT
ejpam-5511	12	24	consists	consist	VERB
ejpam-5511	12	25	of	of	ADP
ejpam-5511	12	26	a	a	DET
ejpam-5511	12	27	non	non	ADJ
ejpam-5511	12	28	-	-	ADJ
ejpam-5511	12	29	empty	empty	ADJ
ejpam-5511	12	30	set	set	ADJ
ejpam-5511	12	31	l	l	NOUN
ejpam-5511	12	32	,	,	PUNCT
ejpam-5511	12	33	a	a	DET
ejpam-5511	12	34	partial	partial	ADJ
ejpam-5511	12	35	order	order	NOUN
ejpam-5511	12	36	≤	≤	NOUN
ejpam-5511	12	37	,	,	PUNCT
ejpam-5511	12	38	a	a	DET
ejpam-5511	12	39	greatest	greatest	ADV
ejpam-5511	12	40	lower	lower	ADV
ejpam-5511	12	41	bound	bind	VERB
ejpam-5511	12	42	(	(	PUNCT
ejpam-5511	12	43	with	with	ADP
ejpam-5511	12	44	respect	respect	NOUN
ejpam-5511	12	45	to	to	ADP
ejpam-5511	12	46	≤	≤	NUM
ejpam-5511	12	47	)	)	PUNCT
ejpam-5511	12	48	∧	∧	PROPN
ejpam-5511	12	49	,	,	PUNCT
ejpam-5511	12	50	and	and	CCONJ
ejpam-5511	12	51	a	a	DET
ejpam-5511	12	52	binary	binary	ADJ
ejpam-5511	12	53	multiplication	multiplication	NOUN
ejpam-5511	12	54	∗	∗	NOUN
ejpam-5511	12	55	such	such	ADJ
ejpam-5511	12	56	that	that	SCONJ
ejpam-5511	12	57	z	z	NOUN
ejpam-5511	12	58	≤	≤	NUM
ejpam-5511	12	59	x	x	PUNCT
ejpam-5511	12	60	∗	∗	PROPN
ejpam-5511	12	61	y	y	PROPN
ejpam-5511	12	62	⇔	⇔	PROPN
ejpam-5511	12	63	z	z	PROPN
ejpam-5511	12	64	∧	∧	PROPN
ejpam-5511	12	65	x	x	PUNCT
ejpam-5511	12	66	≤	≤	NUM
ejpam-5511	12	67	y	y	NOUN
ejpam-5511	12	68	for	for	ADP
ejpam-5511	12	69	any	any	DET
ejpam-5511	12	70	x	x	NOUN
ejpam-5511	12	71	,	,	PUNCT
ejpam-5511	12	72	y	y	PROPN
ejpam-5511	12	73	,	,	PUNCT
ejpam-5511	12	74	z	z	PROPN
ejpam-5511	12	75	∈	∈	PROPN
ejpam-5511	12	76	l.	l.	NOUN
ejpam-5511	12	77	the	the	DET
ejpam-5511	12	78	notion	notion	NOUN
ejpam-5511	12	79	have	have	AUX
ejpam-5511	12	80	been	be	AUX
ejpam-5511	12	81	explored	explore	VERB
ejpam-5511	12	82	in	in	ADP
ejpam-5511	12	83	the	the	DET
ejpam-5511	12	84	work	work	NOUN
ejpam-5511	12	85	of	of	ADP
ejpam-5511	12	86	w.	w.	PROPN
ejpam-5511	12	87	c.	c.	PROPN
ejpam-5511	12	88	nemitz	nemitz	PROPN
ejpam-5511	12	89	in	in	ADP
ejpam-5511	12	90	[	[	X
ejpam-5511	12	91	13	13	NUM
ejpam-5511	12	92	]	]	PUNCT
ejpam-5511	12	93	,	,	PUNCT
ejpam-5511	12	94	the	the	DET
ejpam-5511	12	95	author	author	NOUN
ejpam-5511	12	96	investigated	investigate	VERB
ejpam-5511	12	97	relationships	relationship	NOUN
ejpam-5511	12	98	between	between	ADP
ejpam-5511	12	99	homomorphisms	homomorphism	NOUN
ejpam-5511	12	100	of	of	ADP
ejpam-5511	12	101	implicative	implicative	ADJ
ejpam-5511	12	102	semilattices	semilattice	NOUN
ejpam-5511	12	103	and	and	CCONJ
ejpam-5511	12	104	their	their	PRON
ejpam-5511	12	105	kernels	kernel	NOUN
ejpam-5511	12	106	.	.	PUNCT
ejpam-5511	13	1	t.	t.	PROPN
ejpam-5511	13	2	s.	s.	PROPN
ejpam-5511	13	3	blyth	blyth	PROPN
ejpam-5511	13	4	in	in	ADP
ejpam-5511	13	5	[	[	X
ejpam-5511	13	6	1	1	NUM
ejpam-5511	13	7	]	]	PUNCT
ejpam-5511	13	8	generalized	generalize	VERB
ejpam-5511	13	9	some	some	DET
ejpam-5511	13	10	results	result	NOUN
ejpam-5511	13	11	of	of	ADP
ejpam-5511	13	12	nemitz	nemitz	NOUN
ejpam-5511	13	13	by	by	ADP
ejpam-5511	13	14	introducing	introduce	VERB
ejpam-5511	13	15	the	the	DET
ejpam-5511	13	16	notion	notion	NOUN
ejpam-5511	13	17	of	of	ADP
ejpam-5511	13	18	brouwerian	brouwerian	ADJ
ejpam-5511	13	19	semigroups	semigroup	NOUN
ejpam-5511	13	20	.	.	PUNCT
ejpam-5511	14	1	the	the	DET
ejpam-5511	14	2	results	result	NOUN
ejpam-5511	14	3	of	of	ADP
ejpam-5511	14	4	blyth	blyth	NOUN
ejpam-5511	14	5	[	[	X
ejpam-5511	14	6	1	1	X
ejpam-5511	14	7	]	]	PUNCT
ejpam-5511	14	8	have	have	AUX
ejpam-5511	14	9	been	be	AUX
ejpam-5511	14	10	generalized	generalize	VERB
ejpam-5511	14	11	further	far	ADV
ejpam-5511	14	12	by	by	ADP
ejpam-5511	14	13	m.	m.	PROPN
ejpam-5511	14	14	f.	f.	PROPN
ejpam-5511	14	15	janowitz	janowitz	PROPN
ejpam-5511	14	16	and	and	CCONJ
ejpam-5511	14	17	c.	c.	PROPN
ejpam-5511	14	18	s.	s.	PROPN
ejpam-5511	14	19	johnson	johnson	PROPN
ejpam-5511	14	20	jr	jr	PROPN
ejpam-5511	14	21	in	in	ADP
ejpam-5511	14	22	[	[	X
ejpam-5511	14	23	9	9	NUM
ejpam-5511	14	24	]	]	PUNCT
ejpam-5511	14	25	.	.	PUNCT
ejpam-5511	15	1	in	in	ADP
ejpam-5511	15	2	[	[	X
ejpam-5511	15	3	10	10	NUM
ejpam-5511	15	4	]	]	X
ejpam-5511	15	5	y.	y.	PROPN
ejpam-5511	15	6	b.	b.	PROPN
ejpam-5511	15	7	jun	jun	PROPN
ejpam-5511	15	8	introduced	introduce	VERB
ejpam-5511	15	9	a	a	DET
ejpam-5511	15	10	special	special	ADJ
ejpam-5511	15	11	set	set	NOUN
ejpam-5511	15	12	in	in	ADP
ejpam-5511	15	13	an	an	DET
ejpam-5511	15	14	implicative	implicative	ADJ
ejpam-5511	15	15	semigroup	semigroup	NOUN
ejpam-5511	15	16	,	,	PUNCT
ejpam-5511	15	17	from	from	ADP
ejpam-5511	15	18	which	which	PRON
ejpam-5511	15	19	the	the	DET
ejpam-5511	15	20	author	author	NOUN
ejpam-5511	15	21	derived	derive	VERB
ejpam-5511	15	22	an	an	DET
ejpam-5511	15	23	equivalent	equivalent	ADJ
ejpam-5511	15	24	condition	condition	NOUN
ejpam-5511	15	25	∗corresponding	∗corresponde	VERB
ejpam-5511	15	26	author	author	NOUN
ejpam-5511	15	27	.	.	PUNCT
ejpam-5511	16	1	doi	doi	NOUN
ejpam-5511	16	2	:	:	PUNCT
ejpam-5511	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5511	https://doi.org/10.29020/nybg.ejpam.v17i4.5511	NOUN
ejpam-5511	16	4	email	email	NOUN
ejpam-5511	16	5	addresses	address	NOUN
ejpam-5511	16	6	:	:	PUNCT
ejpam-5511	16	7	kansada.n@kkumail.com	kansada.n@kkumail.com	PROPN
ejpam-5511	16	8	(	(	PUNCT
ejpam-5511	16	9	k.	k.	PROPN
ejpam-5511	16	10	nakwan	nakwan	PROPN
ejpam-5511	16	11	)	)	PUNCT
ejpam-5511	16	12	,	,	PUNCT
ejpam-5511	16	13	panulu@kku.ac.th	panulu@kku.ac.th	NOUN
ejpam-5511	16	14	(	(	PUNCT
ejpam-5511	16	15	p.	p.	NOUN
ejpam-5511	16	16	luangchaisri	luangchaisri	PROPN
ejpam-5511	16	17	)	)	PUNCT
ejpam-5511	16	18	,	,	PUNCT
ejpam-5511	16	19	thacha@kku.ac.th	thacha@kku.ac.th	NOUN
ejpam-5511	16	20	(	(	PUNCT
ejpam-5511	16	21	t.	t.	NOUN
ejpam-5511	16	22	changphas	changphas	PROPN
ejpam-5511	16	23	)	)	PUNCT
ejpam-5511	16	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5511	16	25	4180	4180	NUM
ejpam-5511	17	1	copyright	copyright	NOUN
ejpam-5511	17	2	:	:	PUNCT
ejpam-5511	17	3	©	©	PROPN
ejpam-5511	17	4	2024	2024	NUM
ejpam-5511	17	5	the	the	DET
ejpam-5511	17	6	author(s	author(s	NOUN
ejpam-5511	17	7	)	)	PUNCT
ejpam-5511	17	8	.	.	PUNCT
ejpam-5511	18	1	(	(	PUNCT
ejpam-5511	18	2	cc	cc	NOUN
ejpam-5511	18	3	by	by	ADP
ejpam-5511	18	4	-	-	PUNCT
ejpam-5511	18	5	nc	nc	PROPN
ejpam-5511	18	6	4.0	4.0	NUM
ejpam-5511	18	7	)	)	PUNCT
ejpam-5511	18	8	k.	k.	PROPN
ejpam-5511	18	9	nakwan	nakwan	PROPN
ejpam-5511	18	10	,	,	PUNCT
ejpam-5511	18	11	p.	p.	PROPN
ejpam-5511	18	12	luangchaisri	luangchaisri	VERB
ejpam-5511	18	13	,	,	PUNCT
ejpam-5511	18	14	t.	t.	PROPN
ejpam-5511	18	15	changphas	changphas	PROPN
ejpam-5511	18	16	/	/	SYM
ejpam-5511	18	17	eur	eur	PROPN
ejpam-5511	18	18	.	.	PUNCT
ejpam-5511	19	1	j.	j.	PROPN
ejpam-5511	19	2	pure	pure	PROPN
ejpam-5511	19	3	appl	appl	PROPN
ejpam-5511	19	4	.	.	PROPN
ejpam-5511	19	5	math	math	PROPN
ejpam-5511	19	6	,	,	PUNCT
ejpam-5511	19	7	17	17	NUM
ejpam-5511	19	8	(	(	PUNCT
ejpam-5511	19	9	4	4	NUM
ejpam-5511	19	10	)	)	PUNCT
ejpam-5511	19	11	(	(	PUNCT
ejpam-5511	19	12	2024	2024	NUM
ejpam-5511	19	13	)	)	PUNCT
ejpam-5511	19	14	,	,	PUNCT
ejpam-5511	19	15	4180	4180	NUM
ejpam-5511	19	16	-	-	SYM
ejpam-5511	19	17	4194	4194	NUM
ejpam-5511	19	18	4181	4181	NUM
ejpam-5511	19	19	for	for	ADP
ejpam-5511	19	20	a	a	DET
ejpam-5511	19	21	filter	filter	NOUN
ejpam-5511	20	1	and	and	CCONJ
ejpam-5511	20	2	proved	prove	VERB
ejpam-5511	20	3	that	that	SCONJ
ejpam-5511	20	4	a	a	DET
ejpam-5511	20	5	filter	filter	NOUN
ejpam-5511	20	6	can	can	AUX
ejpam-5511	20	7	be	be	AUX
ejpam-5511	20	8	represented	represent	VERB
ejpam-5511	20	9	by	by	ADP
ejpam-5511	20	10	the	the	DET
ejpam-5511	20	11	union	union	NOUN
ejpam-5511	20	12	of	of	ADP
ejpam-5511	20	13	such	such	ADJ
ejpam-5511	20	14	sets	set	NOUN
ejpam-5511	20	15	.	.	PUNCT
ejpam-5511	21	1	in	in	ADP
ejpam-5511	21	2	[	[	X
ejpam-5511	21	3	14	14	NUM
ejpam-5511	21	4	]	]	X
ejpam-5511	21	5	d.	d.	PROPN
ejpam-5511	21	6	a.	a.	PROPN
ejpam-5511	21	7	romano	romano	PROPN
ejpam-5511	21	8	introduced	introduce	VERB
ejpam-5511	21	9	the	the	DET
ejpam-5511	21	10	concept	concept	NOUN
ejpam-5511	21	11	of	of	ADP
ejpam-5511	21	12	an	an	DET
ejpam-5511	21	13	anti	anti	ADJ
ejpam-5511	21	14	-	-	NOUN
ejpam-5511	21	15	filter	filter	NOUN
ejpam-5511	21	16	within	within	ADP
ejpam-5511	21	17	implicative	implicative	ADJ
ejpam-5511	21	18	semigroups	semigroup	NOUN
ejpam-5511	21	19	and	and	CCONJ
ejpam-5511	21	20	provided	provide	VERB
ejpam-5511	21	21	several	several	ADJ
ejpam-5511	21	22	equivalent	equivalent	ADJ
ejpam-5511	21	23	conditions	condition	NOUN
ejpam-5511	21	24	for	for	ADP
ejpam-5511	21	25	when	when	SCONJ
ejpam-5511	21	26	the	the	DET
ejpam-5511	21	27	special	special	ADJ
ejpam-5511	21	28	inhabited	inhabit	VERB
ejpam-5511	21	29	proper	proper	ADJ
ejpam-5511	21	30	subset	subset	NOUN
ejpam-5511	21	31	of	of	ADP
ejpam-5511	21	32	an	an	DET
ejpam-5511	21	33	implicative	implicative	ADJ
ejpam-5511	21	34	semigroup	semigroup	NOUN
ejpam-5511	21	35	qualifies	qualifie	NOUN
ejpam-5511	21	36	as	as	ADP
ejpam-5511	21	37	an	an	DET
ejpam-5511	21	38	ordered	ordered	ADJ
ejpam-5511	21	39	anti	anti	ADJ
ejpam-5511	21	40	-	-	NOUN
ejpam-5511	21	41	filter	filter	NOUN
ejpam-5511	21	42	.	.	PUNCT
ejpam-5511	22	1	in	in	ADP
ejpam-5511	22	2	[	[	X
ejpam-5511	22	3	6	6	NUM
ejpam-5511	22	4	]	]	PUNCT
ejpam-5511	22	5	,	,	PUNCT
ejpam-5511	22	6	a	a	DET
ejpam-5511	22	7	partially	partially	ADV
ejpam-5511	22	8	ordered	order	VERB
ejpam-5511	22	9	semigroup	semigroup	NOUN
ejpam-5511	22	10	(	(	PUNCT
ejpam-5511	22	11	s	s	PROPN
ejpam-5511	22	12	,	,	PUNCT
ejpam-5511	22	13	·	·	PUNCT
ejpam-5511	22	14	,	,	PUNCT
ejpam-5511	22	15	≤	≤	NUM
ejpam-5511	22	16	)	)	PUNCT
ejpam-5511	22	17	consists	consist	VERB
ejpam-5511	22	18	of	of	ADP
ejpam-5511	22	19	a	a	DET
ejpam-5511	22	20	semigroup	semigroup	NOUN
ejpam-5511	22	21	(	(	PUNCT
ejpam-5511	22	22	s	s	PROPN
ejpam-5511	22	23	,	,	PUNCT
ejpam-5511	22	24	·	·	PUNCT
ejpam-5511	22	25	)	)	PUNCT
ejpam-5511	22	26	together	together	ADV
ejpam-5511	22	27	with	with	ADP
ejpam-5511	22	28	a	a	DET
ejpam-5511	22	29	partial	partial	ADJ
ejpam-5511	22	30	order	order	NOUN
ejpam-5511	22	31	≤	≤	X
ejpam-5511	22	32	on	on	ADP
ejpam-5511	22	33	s	s	NOUN
ejpam-5511	22	34	that	that	PRON
ejpam-5511	22	35	is	be	AUX
ejpam-5511	22	36	compatible	compatible	ADJ
ejpam-5511	22	37	with	with	ADP
ejpam-5511	22	38	the	the	DET
ejpam-5511	22	39	semigroup	semigroup	PROPN
ejpam-5511	22	40	operation	operation	NOUN
ejpam-5511	22	41	,	,	PUNCT
ejpam-5511	22	42	that	that	PRON
ejpam-5511	22	43	is	be	AUX
ejpam-5511	22	44	for	for	ADP
ejpam-5511	22	45	any	any	DET
ejpam-5511	22	46	x	x	NOUN
ejpam-5511	22	47	,	,	PUNCT
ejpam-5511	22	48	y	y	PROPN
ejpam-5511	22	49	,	,	PUNCT
ejpam-5511	22	50	z	z	PROPN
ejpam-5511	22	51	∈	∈	PROPN
ejpam-5511	22	52	s	s	PART
ejpam-5511	22	53	,	,	PUNCT
ejpam-5511	22	54	if	if	SCONJ
ejpam-5511	22	55	x	x	ADP
ejpam-5511	22	56	≤	≤	NOUN
ejpam-5511	22	57	y	y	NOUN
ejpam-5511	22	58	then	then	ADV
ejpam-5511	22	59	xz	xz	PROPN
ejpam-5511	22	60	≤	≤	PROPN
ejpam-5511	22	61	yz	yz	PROPN
ejpam-5511	22	62	and	and	CCONJ
ejpam-5511	22	63	zx	zx	NUM
ejpam-5511	22	64	≤	≤	PROPN
ejpam-5511	22	65	zy	zy	PROPN
ejpam-5511	22	66	.	.	PUNCT
ejpam-5511	23	1	a	a	DET
ejpam-5511	23	2	partially	partially	ADV
ejpam-5511	23	3	ordered	order	VERB
ejpam-5511	23	4	semigroup	semigroup	NOUN
ejpam-5511	23	5	(	(	PUNCT
ejpam-5511	23	6	s	s	PROPN
ejpam-5511	23	7	,	,	PUNCT
ejpam-5511	23	8	·	·	PUNCT
ejpam-5511	23	9	,	,	PUNCT
ejpam-5511	23	10	≤	≤	NUM
ejpam-5511	23	11	)	)	PUNCT
ejpam-5511	23	12	is	be	AUX
ejpam-5511	23	13	called	call	VERB
ejpam-5511	23	14	a	a	DET
ejpam-5511	23	15	negatively	negatively	ADV
ejpam-5511	23	16	partially	partially	ADV
ejpam-5511	23	17	ordered	order	VERB
ejpam-5511	23	18	semigroup	semigroup	NOUN
ejpam-5511	23	19	,	,	PUNCT
ejpam-5511	23	20	for	for	ADP
ejpam-5511	23	21	short	short	ADJ
ejpam-5511	23	22	n.p.o	n.p.o	NOUN
ejpam-5511	23	23	.	.	PUNCT
ejpam-5511	24	1	semigroup	semigroup	PROPN
ejpam-5511	24	2	,	,	PUNCT
ejpam-5511	24	3	if	if	SCONJ
ejpam-5511	24	4	for	for	ADP
ejpam-5511	24	5	any	any	DET
ejpam-5511	24	6	x	x	NOUN
ejpam-5511	24	7	,	,	PUNCT
ejpam-5511	24	8	y	y	PROPN
ejpam-5511	24	9	,	,	PUNCT
ejpam-5511	24	10	z	z	PROPN
ejpam-5511	24	11	∈	∈	PROPN
ejpam-5511	24	12	s	s	PART
ejpam-5511	24	13	,	,	PUNCT
ejpam-5511	24	14	xy	xy	PROPN
ejpam-5511	24	15	≤	≤	NUM
ejpam-5511	24	16	x	x	PUNCT
ejpam-5511	24	17	and	and	CCONJ
ejpam-5511	24	18	xy	xy	X
ejpam-5511	24	19	≤	≤	PROPN
ejpam-5511	25	1	y.	y.	NOUN
ejpam-5511	25	2	an	an	DET
ejpam-5511	25	3	n.p.o	n.p.o	NOUN
ejpam-5511	25	4	.	.	PUNCT
ejpam-5511	26	1	semigroup	semigroup	PROPN
ejpam-5511	26	2	(	(	PUNCT
ejpam-5511	26	3	s	s	PROPN
ejpam-5511	26	4	,	,	PUNCT
ejpam-5511	26	5	·	·	PUNCT
ejpam-5511	26	6	,	,	PUNCT
ejpam-5511	26	7	≤	≤	NUM
ejpam-5511	26	8	)	)	PUNCT
ejpam-5511	26	9	with	with	ADP
ejpam-5511	26	10	an	an	DET
ejpam-5511	26	11	additional	additional	ADJ
ejpam-5511	26	12	binary	binary	ADJ
ejpam-5511	26	13	multiplication	multiplication	NOUN
ejpam-5511	26	14	∗	∗	NOUN
ejpam-5511	26	15	such	such	ADJ
ejpam-5511	26	16	that	that	SCONJ
ejpam-5511	26	17	z	z	NOUN
ejpam-5511	26	18	≤	≤	NUM
ejpam-5511	26	19	x	x	PUNCT
ejpam-5511	26	20	∗	∗	PROPN
ejpam-5511	26	21	y	y	PROPN
ejpam-5511	26	22	⇔	⇔	PROPN
ejpam-5511	26	23	zx	zx	PROPN
ejpam-5511	26	24	≤	≤	PROPN
ejpam-5511	26	25	y	y	PROPN
ejpam-5511	26	26	for	for	ADP
ejpam-5511	26	27	any	any	DET
ejpam-5511	26	28	x	x	NOUN
ejpam-5511	26	29	,	,	PUNCT
ejpam-5511	26	30	y	y	PROPN
ejpam-5511	26	31	,	,	PUNCT
ejpam-5511	26	32	z	z	PROPN
ejpam-5511	26	33	∈	∈	PROPN
ejpam-5511	26	34	s	s	VERB
ejpam-5511	26	35	is	be	AUX
ejpam-5511	26	36	called	call	VERB
ejpam-5511	26	37	an	an	DET
ejpam-5511	26	38	implicative	implicative	ADJ
ejpam-5511	26	39	n.p.o	n.p.o	NOUN
ejpam-5511	26	40	.	.	PUNCT
ejpam-5511	27	1	semigroup	semigroup	PROPN
ejpam-5511	27	2	.	.	PROPN
ejpam-5511	28	1	inspired	inspire	VERB
ejpam-5511	28	2	by	by	ADP
ejpam-5511	28	3	the	the	DET
ejpam-5511	28	4	works	work	NOUN
ejpam-5511	28	5	of	of	ADP
ejpam-5511	28	6	nemitz	nemitz	NOUN
ejpam-5511	29	1	[	[	X
ejpam-5511	29	2	13	13	NUM
ejpam-5511	29	3	]	]	PUNCT
ejpam-5511	29	4	and	and	CCONJ
ejpam-5511	29	5	blyth	blyth	PROPN
ejpam-5511	30	1	[	[	X
ejpam-5511	30	2	1	1	NUM
ejpam-5511	30	3	]	]	PUNCT
ejpam-5511	30	4	,	,	PUNCT
ejpam-5511	30	5	in	in	ADP
ejpam-5511	30	6	[	[	PUNCT
ejpam-5511	30	7	2	2	NUM
ejpam-5511	30	8	]	]	PUNCT
ejpam-5511	30	9	,	,	PUNCT
ejpam-5511	30	10	m.	m.	PROPN
ejpam-5511	30	11	w.	w.	PROPN
ejpam-5511	30	12	chan	chan	PROPN
ejpam-5511	30	13	and	and	CCONJ
ejpam-5511	30	14	k.	k.	PROPN
ejpam-5511	30	15	p.	p.	PROPN
ejpam-5511	30	16	shum	shum	PROPN
ejpam-5511	30	17	introduced	introduce	VERB
ejpam-5511	30	18	the	the	DET
ejpam-5511	30	19	concept	concept	NOUN
ejpam-5511	30	20	of	of	ADP
ejpam-5511	30	21	implicative	implicative	NOUN
ejpam-5511	30	22	negatively	negatively	ADV
ejpam-5511	30	23	partially	partially	ADV
ejpam-5511	30	24	ordered	order	VERB
ejpam-5511	30	25	semigroups	semigroup	NOUN
ejpam-5511	30	26	and	and	CCONJ
ejpam-5511	30	27	explored	explore	VERB
ejpam-5511	30	28	the	the	DET
ejpam-5511	30	29	homomorphisms	homomorphism	NOUN
ejpam-5511	30	30	between	between	ADP
ejpam-5511	30	31	these	these	DET
ejpam-5511	30	32	structures	structure	NOUN
ejpam-5511	30	33	.	.	PUNCT
ejpam-5511	31	1	their	their	PRON
ejpam-5511	31	2	work	work	NOUN
ejpam-5511	31	3	generalizes	generalize	VERB
ejpam-5511	31	4	and	and	CCONJ
ejpam-5511	31	5	expands	expand	VERB
ejpam-5511	31	6	upon	upon	SCONJ
ejpam-5511	31	7	some	some	DET
ejpam-5511	31	8	results	result	NOUN
ejpam-5511	31	9	by	by	ADP
ejpam-5511	31	10	nemitz	nemitz	NOUN
ejpam-5511	31	11	regarding	regard	VERB
ejpam-5511	31	12	implicative	implicative	ADJ
ejpam-5511	31	13	semilattices	semilattice	NOUN
ejpam-5511	31	14	.	.	PUNCT
ejpam-5511	32	1	a	a	DET
ejpam-5511	32	2	non	non	ADJ
ejpam-5511	32	3	-	-	ADJ
ejpam-5511	32	4	empty	empty	ADJ
ejpam-5511	32	5	set	set	ADJ
ejpam-5511	32	6	t	t	NOUN
ejpam-5511	32	7	together	together	ADV
ejpam-5511	32	8	with	with	ADP
ejpam-5511	32	9	a	a	DET
ejpam-5511	32	10	ternary	ternary	ADJ
ejpam-5511	32	11	multiplication	multiplication	NOUN
ejpam-5511	32	12	[	[	PUNCT
ejpam-5511	32	13	]	]	PUNCT
ejpam-5511	32	14	defined	define	VERB
ejpam-5511	32	15	on	on	ADP
ejpam-5511	32	16	the	the	DET
ejpam-5511	32	17	set	set	NOUN
ejpam-5511	32	18	t	t	PROPN
ejpam-5511	32	19	is	be	AUX
ejpam-5511	32	20	called	call	VERB
ejpam-5511	32	21	a	a	DET
ejpam-5511	32	22	ternary	ternary	ADJ
ejpam-5511	32	23	semigroup	semigroup	NOUN
ejpam-5511	32	24	if	if	SCONJ
ejpam-5511	32	25	the	the	DET
ejpam-5511	32	26	ternary	ternary	ADJ
ejpam-5511	32	27	multiplication	multiplication	NOUN
ejpam-5511	32	28	[	[	PUNCT
ejpam-5511	32	29	]	]	PUNCT
ejpam-5511	32	30	satisfies	satisfy	VERB
ejpam-5511	32	31	the	the	DET
ejpam-5511	32	32	following	following	ADJ
ejpam-5511	32	33	associative	associative	ADJ
ejpam-5511	32	34	law	law	NOUN
ejpam-5511	32	35	:	:	PUNCT
ejpam-5511	33	1	[	[	X
ejpam-5511	33	2	[	[	X
ejpam-5511	33	3	xyz]uv	xyz]uv	X
ejpam-5511	33	4	]	]	X
ejpam-5511	33	5	=	=	PUNCT
ejpam-5511	34	1	[	[	X
ejpam-5511	34	2	x[yzu]v	x[yzu]v	X
ejpam-5511	34	3	]	]	X
ejpam-5511	34	4	=	=	PUNCT
ejpam-5511	35	1	[	[	X
ejpam-5511	35	2	xy[zuv	xy[zuv	PROPN
ejpam-5511	35	3	]	]	X
ejpam-5511	35	4	]	]	PUNCT
ejpam-5511	35	5	for	for	ADP
ejpam-5511	35	6	all	all	DET
ejpam-5511	35	7	x	x	PROPN
ejpam-5511	35	8	,	,	PUNCT
ejpam-5511	35	9	y	y	PROPN
ejpam-5511	35	10	,	,	PUNCT
ejpam-5511	35	11	z	z	PROPN
ejpam-5511	35	12	,	,	PUNCT
ejpam-5511	35	13	u	u	NOUN
ejpam-5511	35	14	,	,	PUNCT
ejpam-5511	35	15	v	v	PROPN
ejpam-5511	35	16	∈	∈	PROPN
ejpam-5511	35	17	t	t	NOUN
ejpam-5511	35	18	.	.	PUNCT
ejpam-5511	36	1	this	this	DET
ejpam-5511	36	2	notion	notion	NOUN
ejpam-5511	36	3	has	have	AUX
ejpam-5511	36	4	been	be	AUX
ejpam-5511	36	5	introduced	introduce	VERB
ejpam-5511	36	6	and	and	CCONJ
ejpam-5511	36	7	studied	study	VERB
ejpam-5511	36	8	by	by	ADP
ejpam-5511	36	9	s.	s.	PROPN
ejpam-5511	36	10	banach	banach	PROPN
ejpam-5511	36	11	(	(	PUNCT
ejpam-5511	36	12	cf	cf	NOUN
ejpam-5511	36	13	.	.	PUNCT
ejpam-5511	37	1	j.	j.	PROPN
ejpam-5511	37	2	los	los	PROPN
ejpam-5511	38	1	[	[	X
ejpam-5511	38	2	12	12	NUM
ejpam-5511	38	3	]	]	PUNCT
ejpam-5511	38	4	)	)	PUNCT
ejpam-5511	38	5	who	who	PRON
ejpam-5511	38	6	is	be	AUX
ejpam-5511	38	7	credited	credit	VERB
ejpam-5511	38	8	with	with	ADP
ejpam-5511	38	9	an	an	DET
ejpam-5511	38	10	example	example	NOUN
ejpam-5511	38	11	of	of	ADP
ejpam-5511	38	12	a	a	DET
ejpam-5511	38	13	ternary	ternary	ADJ
ejpam-5511	38	14	semigroup	semigroup	NOUN
ejpam-5511	38	15	which	which	PRON
ejpam-5511	38	16	does	do	AUX
ejpam-5511	38	17	not	not	PART
ejpam-5511	38	18	reduce	reduce	VERB
ejpam-5511	38	19	to	to	ADP
ejpam-5511	38	20	a	a	DET
ejpam-5511	38	21	semigroup	semigroup	NOUN
ejpam-5511	38	22	.	.	PUNCT
ejpam-5511	39	1	d.	d.	PROPN
ejpam-5511	39	2	h.	h.	PROPN
ejpam-5511	39	3	lehmer	lehmer	PROPN
ejpam-5511	39	4	in	in	ADP
ejpam-5511	39	5	[	[	X
ejpam-5511	39	6	11	11	NUM
ejpam-5511	39	7	]	]	PUNCT
ejpam-5511	39	8	studied	study	VERB
ejpam-5511	39	9	a	a	DET
ejpam-5511	39	10	system	system	NOUN
ejpam-5511	39	11	called	call	VERB
ejpam-5511	39	12	triplexes	triplexe	NOUN
ejpam-5511	39	13	which	which	PRON
ejpam-5511	39	14	turns	turn	VERB
ejpam-5511	39	15	out	out	ADP
ejpam-5511	39	16	to	to	PART
ejpam-5511	39	17	be	be	AUX
ejpam-5511	39	18	a	a	DET
ejpam-5511	39	19	commutative	commutative	ADJ
ejpam-5511	39	20	ternary	ternary	ADJ
ejpam-5511	39	21	group	group	NOUN
ejpam-5511	39	22	.	.	PUNCT
ejpam-5511	40	1	j.	j.	PROPN
ejpam-5511	40	2	los	los	PROPN
ejpam-5511	40	3	in	in	ADP
ejpam-5511	40	4	[	[	X
ejpam-5511	40	5	12	12	NUM
ejpam-5511	40	6	]	]	PUNCT
ejpam-5511	40	7	proved	prove	VERB
ejpam-5511	40	8	that	that	SCONJ
ejpam-5511	40	9	any	any	DET
ejpam-5511	40	10	ternary	ternary	ADJ
ejpam-5511	40	11	semigroup	semigroup	NOUN
ejpam-5511	40	12	can	can	AUX
ejpam-5511	40	13	be	be	AUX
ejpam-5511	40	14	embedded	embed	VERB
ejpam-5511	40	15	in	in	ADP
ejpam-5511	40	16	a	a	DET
ejpam-5511	40	17	semigroup	semigroup	NOUN
ejpam-5511	40	18	.	.	PUNCT
ejpam-5511	41	1	f.	f.	PROPN
ejpam-5511	41	2	m.	m.	PROPN
ejpam-5511	41	3	sioson	sioson	PROPN
ejpam-5511	41	4	in	in	ADP
ejpam-5511	41	5	[	[	X
ejpam-5511	41	6	17	17	NUM
ejpam-5511	41	7	]	]	PUNCT
ejpam-5511	41	8	considered	consider	VERB
ejpam-5511	41	9	ideals	ideal	NOUN
ejpam-5511	41	10	and	and	CCONJ
ejpam-5511	41	11	radicals	radical	NOUN
ejpam-5511	41	12	of	of	ADP
ejpam-5511	41	13	ternary	ternary	ADJ
ejpam-5511	41	14	semigroups	semigroup	NOUN
ejpam-5511	41	15	;	;	PUNCT
ejpam-5511	41	16	various	various	ADJ
ejpam-5511	41	17	concepts	concept	NOUN
ejpam-5511	41	18	such	such	ADJ
ejpam-5511	41	19	as	as	ADP
ejpam-5511	41	20	primality	primality	NOUN
ejpam-5511	41	21	,	,	PUNCT
ejpam-5511	41	22	semiprimality	semiprimality	NOUN
ejpam-5511	41	23	,	,	PUNCT
ejpam-5511	41	24	and	and	CCONJ
ejpam-5511	41	25	regularity	regularity	NOUN
ejpam-5511	41	26	were	be	AUX
ejpam-5511	41	27	introduced	introduce	VERB
ejpam-5511	41	28	.	.	PUNCT
ejpam-5511	42	1	a.	a.	NOUN
ejpam-5511	42	2	chronowski	chronowski	PROPN
ejpam-5511	42	3	in	in	ADP
ejpam-5511	42	4	[	[	X
ejpam-5511	42	5	3	3	NUM
ejpam-5511	42	6	]	]	PUNCT
ejpam-5511	42	7	investigated	investigate	VERB
ejpam-5511	42	8	ternary	ternary	ADJ
ejpam-5511	42	9	semigroups	semigroup	NOUN
ejpam-5511	42	10	of	of	ADP
ejpam-5511	42	11	mappings	mapping	NOUN
ejpam-5511	42	12	of	of	ADP
ejpam-5511	42	13	sets	set	NOUN
ejpam-5511	42	14	;	;	PUNCT
ejpam-5511	42	15	these	these	DET
ejpam-5511	42	16	algebraic	algebraic	ADJ
ejpam-5511	42	17	structures	structure	NOUN
ejpam-5511	42	18	are	be	AUX
ejpam-5511	42	19	used	use	VERB
ejpam-5511	42	20	for	for	ADP
ejpam-5511	42	21	constructing	construct	VERB
ejpam-5511	42	22	the	the	DET
ejpam-5511	42	23	natural	natural	ADJ
ejpam-5511	42	24	examples	example	NOUN
ejpam-5511	42	25	of	of	ADP
ejpam-5511	42	26	ternary	ternary	ADJ
ejpam-5511	42	27	algebras	algebra	NOUN
ejpam-5511	42	28	.	.	PUNCT
ejpam-5511	43	1	v.	v.	ADP
ejpam-5511	43	2	n.	n.	PROPN
ejpam-5511	43	3	dixit	dixit	PROPN
ejpam-5511	43	4	and	and	CCONJ
ejpam-5511	43	5	s.	s.	PROPN
ejpam-5511	43	6	dewan	dewan	PROPN
ejpam-5511	43	7	in	in	ADP
ejpam-5511	43	8	[	[	X
ejpam-5511	43	9	5	5	NUM
ejpam-5511	43	10	]	]	PUNCT
ejpam-5511	43	11	studied	study	VERB
ejpam-5511	43	12	quasi	quasi	NOUN
ejpam-5511	43	13	-	-	NOUN
ejpam-5511	43	14	ideals	ideal	NOUN
ejpam-5511	43	15	and	and	CCONJ
ejpam-5511	43	16	bi	bi	NOUN
ejpam-5511	43	17	-	-	NOUN
ejpam-5511	43	18	ideals	ideal	NOUN
ejpam-5511	43	19	of	of	ADP
ejpam-5511	43	20	ternary	ternary	ADJ
ejpam-5511	43	21	semigroups	semigroup	NOUN
ejpam-5511	44	1	;	;	PUNCT
ejpam-5511	44	2	the	the	DET
ejpam-5511	44	3	authors	author	NOUN
ejpam-5511	44	4	proved	prove	VERB
ejpam-5511	44	5	that	that	SCONJ
ejpam-5511	44	6	every	every	DET
ejpam-5511	44	7	quasi	quasi	NOUN
ejpam-5511	44	8	-	-	NOUN
ejpam-5511	44	9	ideals	ideal	NOUN
ejpam-5511	44	10	is	be	AUX
ejpam-5511	44	11	a	a	DET
ejpam-5511	44	12	bi	bi	NOUN
ejpam-5511	44	13	-	-	NOUN
ejpam-5511	44	14	ideal	ideal	NOUN
ejpam-5511	44	15	and	and	CCONJ
ejpam-5511	44	16	gave	give	VERB
ejpam-5511	44	17	several	several	ADJ
ejpam-5511	44	18	examples	example	NOUN
ejpam-5511	44	19	in	in	ADP
ejpam-5511	44	20	different	different	ADJ
ejpam-5511	44	21	contexts	context	NOUN
ejpam-5511	44	22	to	to	PART
ejpam-5511	44	23	prove	prove	VERB
ejpam-5511	44	24	that	that	SCONJ
ejpam-5511	44	25	the	the	DET
ejpam-5511	44	26	converse	converse	NOUN
ejpam-5511	44	27	is	be	AUX
ejpam-5511	44	28	not	not	PART
ejpam-5511	44	29	true	true	ADJ
ejpam-5511	44	30	in	in	ADP
ejpam-5511	44	31	general	general	ADJ
ejpam-5511	44	32	.	.	PUNCT
ejpam-5511	45	1	m.	m.	PROPN
ejpam-5511	45	2	l.	l.	PROPN
ejpam-5511	45	3	santiago	santiago	PROPN
ejpam-5511	45	4	and	and	CCONJ
ejpam-5511	45	5	s.	s.	PROPN
ejpam-5511	45	6	sri	sri	PROPN
ejpam-5511	45	7	bala	bala	PROPN
ejpam-5511	45	8	in	in	ADP
ejpam-5511	45	9	[	[	X
ejpam-5511	45	10	15	15	NUM
ejpam-5511	45	11	]	]	PUNCT
ejpam-5511	45	12	investigated	investigate	VERB
ejpam-5511	45	13	regular	regular	ADJ
ejpam-5511	45	14	ternary	ternary	ADJ
ejpam-5511	45	15	semigroups	semigroup	NOUN
ejpam-5511	45	16	and	and	CCONJ
ejpam-5511	45	17	studied	study	VERB
ejpam-5511	45	18	several	several	ADJ
ejpam-5511	45	19	properties	property	NOUN
ejpam-5511	45	20	.	.	PUNCT
ejpam-5511	46	1	a	a	DET
ejpam-5511	46	2	ternary	ternary	ADJ
ejpam-5511	46	3	semigroup	semigroup	NOUN
ejpam-5511	46	4	(	(	PUNCT
ejpam-5511	46	5	t	t	PROPN
ejpam-5511	46	6	,	,	PUNCT
ejpam-5511	46	7	[	[	PUNCT
ejpam-5511	46	8	]	]	X
ejpam-5511	46	9	)	)	PUNCT
ejpam-5511	46	10	is	be	AUX
ejpam-5511	46	11	called	call	VERB
ejpam-5511	46	12	an	an	DET
ejpam-5511	46	13	ordered	order	VERB
ejpam-5511	46	14	ternary	ternary	ADJ
ejpam-5511	46	15	semigroup	semigroup	NOUN
ejpam-5511	46	16	if	if	SCONJ
ejpam-5511	46	17	there	there	PRON
ejpam-5511	46	18	is	be	VERB
ejpam-5511	46	19	a	a	DET
ejpam-5511	46	20	partial	partial	ADJ
ejpam-5511	46	21	order	order	NOUN
ejpam-5511	46	22	≤	≤	NUM
ejpam-5511	46	23	such	such	ADJ
ejpam-5511	46	24	that	that	PRON
ejpam-5511	46	25	for	for	ADP
ejpam-5511	46	26	any	any	DET
ejpam-5511	46	27	a	a	DET
ejpam-5511	46	28	,	,	PUNCT
ejpam-5511	46	29	b	b	NOUN
ejpam-5511	46	30	,	,	PUNCT
ejpam-5511	46	31	x	x	X
ejpam-5511	46	32	,	,	PUNCT
ejpam-5511	46	33	y	y	PROPN
ejpam-5511	46	34	∈	∈	PROPN
ejpam-5511	46	35	t	t	PROPN
ejpam-5511	46	36	,	,	PUNCT
ejpam-5511	46	37	if	if	SCONJ
ejpam-5511	46	38	a	a	DET
ejpam-5511	46	39	≤	≤	NUM
ejpam-5511	46	40	b	b	NOUN
ejpam-5511	46	41	then	then	ADV
ejpam-5511	46	42	[	[	X
ejpam-5511	46	43	axy	axy	X
ejpam-5511	46	44	]	]	X
ejpam-5511	46	45	≤	≤	NOUN
ejpam-5511	46	46	[	[	X
ejpam-5511	46	47	bxy	bxy	NOUN
ejpam-5511	46	48	]	]	X
ejpam-5511	46	49	,	,	PUNCT
ejpam-5511	46	50	[	[	X
ejpam-5511	46	51	xay	xay	X
ejpam-5511	46	52	]	]	X
ejpam-5511	46	53	≤	≤	X
ejpam-5511	47	1	[	[	X
ejpam-5511	47	2	xby	xby	X
ejpam-5511	47	3	]	]	X
ejpam-5511	47	4	,	,	PUNCT
ejpam-5511	47	5	[	[	X
ejpam-5511	47	6	xya	xya	X
ejpam-5511	47	7	]	]	X
ejpam-5511	47	8	≤	≤	NOUN
ejpam-5511	48	1	[	[	X
ejpam-5511	48	2	xyb	xyb	X
ejpam-5511	48	3	]	]	PUNCT
ejpam-5511	48	4	.	.	PUNCT
ejpam-5511	49	1	a.	a.	PROPN
ejpam-5511	49	2	iampan	iampan	PROPN
ejpam-5511	49	3	in	in	ADP
ejpam-5511	49	4	(	(	PUNCT
ejpam-5511	49	5	[	[	X
ejpam-5511	49	6	7	7	NUM
ejpam-5511	49	7	]	]	PUNCT
ejpam-5511	49	8	,	,	PUNCT
ejpam-5511	50	1	[	[	X
ejpam-5511	50	2	8	8	NUM
ejpam-5511	50	3	]	]	PUNCT
ejpam-5511	50	4	)	)	PUNCT
ejpam-5511	50	5	discussed	discuss	VERB
ejpam-5511	50	6	ordered	order	VERB
ejpam-5511	50	7	ternary	ternary	ADJ
ejpam-5511	50	8	semigroups	semigroup	NOUN
ejpam-5511	50	9	and	and	CCONJ
ejpam-5511	50	10	characterized	characterize	VERB
ejpam-5511	50	11	the	the	DET
ejpam-5511	50	12	minimality	minimality	NOUN
ejpam-5511	50	13	and	and	CCONJ
ejpam-5511	50	14	maximality	maximality	PROPN
ejpam-5511	50	15	of	of	ADP
ejpam-5511	50	16	ordered	order	VERB
ejpam-5511	50	17	lateral	lateral	ADJ
ejpam-5511	50	18	ideals	ideal	NOUN
ejpam-5511	50	19	in	in	ADP
ejpam-5511	50	20	ordered	order	VERB
ejpam-5511	50	21	ternary	ternary	ADJ
ejpam-5511	50	22	semigroups	semigroup	NOUN
ejpam-5511	50	23	;	;	PUNCT
ejpam-5511	50	24	the	the	DET
ejpam-5511	50	25	author	author	NOUN
ejpam-5511	50	26	also	also	ADV
ejpam-5511	50	27	considered	consider	VERB
ejpam-5511	50	28	ideal	ideal	ADJ
ejpam-5511	50	29	extensions	extension	NOUN
ejpam-5511	50	30	.	.	PUNCT
ejpam-5511	51	1	v.	v.	ADP
ejpam-5511	51	2	r.	r.	PROPN
ejpam-5511	51	3	daddi	daddi	PROPN
ejpam-5511	51	4	and	and	CCONJ
ejpam-5511	51	5	y.	y.	PROPN
ejpam-5511	51	6	s.	s.	PROPN
ejpam-5511	51	7	pawar	pawar	PROPN
ejpam-5511	51	8	in	in	ADP
ejpam-5511	51	9	[	[	X
ejpam-5511	51	10	4	4	NUM
ejpam-5511	51	11	]	]	PUNCT
ejpam-5511	51	12	introduced	introduce	VERB
ejpam-5511	51	13	and	and	CCONJ
ejpam-5511	51	14	studied	study	VERB
ejpam-5511	51	15	quasi	quasi	NOUN
ejpam-5511	51	16	-	-	NOUN
ejpam-5511	51	17	ideals	ideal	NOUN
ejpam-5511	51	18	and	and	CCONJ
ejpam-5511	51	19	bi	bi	NOUN
ejpam-5511	51	20	-	-	NOUN
ejpam-5511	51	21	ideals	ideal	NOUN
ejpam-5511	51	22	in	in	ADP
ejpam-5511	51	23	ordered	order	VERB
ejpam-5511	51	24	ternary	ternary	ADJ
ejpam-5511	51	25	semigroups	semigroup	NOUN
ejpam-5511	51	26	.	.	PUNCT
ejpam-5511	52	1	the	the	DET
ejpam-5511	52	2	purpose	purpose	NOUN
ejpam-5511	52	3	of	of	ADP
ejpam-5511	52	4	this	this	DET
ejpam-5511	52	5	paper	paper	NOUN
ejpam-5511	52	6	is	be	AUX
ejpam-5511	52	7	to	to	PART
ejpam-5511	52	8	introduce	introduce	VERB
ejpam-5511	52	9	and	and	CCONJ
ejpam-5511	52	10	study	study	VERB
ejpam-5511	52	11	the	the	DET
ejpam-5511	52	12	notion	notion	NOUN
ejpam-5511	52	13	of	of	ADP
ejpam-5511	52	14	implicative	implicative	ADJ
ejpam-5511	52	15	n.p.o	n.p.o	NOUN
ejpam-5511	52	16	.	.	PUNCT
ejpam-5511	53	1	ternary	ternary	ADJ
ejpam-5511	53	2	semigroups	semigroup	NOUN
ejpam-5511	53	3	.	.	PUNCT
ejpam-5511	54	1	main	main	ADJ
ejpam-5511	54	2	idea	idea	NOUN
ejpam-5511	54	3	of	of	ADP
ejpam-5511	54	4	this	this	DET
ejpam-5511	54	5	work	work	NOUN
ejpam-5511	54	6	is	be	AUX
ejpam-5511	54	7	inspired	inspire	VERB
ejpam-5511	54	8	by	by	ADP
ejpam-5511	54	9	[	[	X
ejpam-5511	54	10	2	2	NUM
ejpam-5511	54	11	]	]	PUNCT
ejpam-5511	54	12	.	.	PUNCT
ejpam-5511	55	1	we	we	PRON
ejpam-5511	55	2	apply	apply	VERB
ejpam-5511	55	3	concept	concept	NOUN
ejpam-5511	55	4	of	of	ADP
ejpam-5511	55	5	implicative	implicative	ADJ
ejpam-5511	55	6	n.p.o	n.p.o	NOUN
ejpam-5511	55	7	.	.	PUNCT
ejpam-5511	56	1	semigroups	semigroup	NOUN
ejpam-5511	56	2	to	to	PART
ejpam-5511	56	3	establish	establish	VERB
ejpam-5511	56	4	implicative	implicative	ADJ
ejpam-5511	56	5	n.p.o	n.p.o	NOUN
ejpam-5511	56	6	.	.	PUNCT
ejpam-5511	57	1	ternary	ternary	ADJ
ejpam-5511	57	2	semigroups	semigroup	NOUN
ejpam-5511	57	3	.	.	PUNCT
ejpam-5511	58	1	in	in	ADP
ejpam-5511	58	2	addition	addition	NOUN
ejpam-5511	58	3	,	,	PUNCT
ejpam-5511	58	4	we	we	PRON
ejpam-5511	58	5	introduce	introduce	VERB
ejpam-5511	58	6	and	and	CCONJ
ejpam-5511	58	7	study	study	VERB
ejpam-5511	58	8	implicative	implicative	ADJ
ejpam-5511	58	9	homomorphisms	homomorphism	NOUN
ejpam-5511	58	10	related	relate	VERB
ejpam-5511	58	11	to	to	ADP
ejpam-5511	58	12	homomorphisms	homomorphism	NOUN
ejpam-5511	58	13	between	between	ADP
ejpam-5511	58	14	implicative	implicative	ADJ
ejpam-5511	58	15	n.p.o	n.p.o	NOUN
ejpam-5511	58	16	.	.	PUNCT
ejpam-5511	59	1	ternary	ternary	ADJ
ejpam-5511	59	2	semigroups	semigroup	NOUN
ejpam-5511	59	3	.	.	PUNCT
ejpam-5511	60	1	moreover	moreover	ADV
ejpam-5511	60	2	,	,	PUNCT
ejpam-5511	60	3	we	we	PRON
ejpam-5511	60	4	construct	construct	VERB
ejpam-5511	60	5	quotient	quotient	NOUN
ejpam-5511	60	6	commutative	commutative	ADJ
ejpam-5511	60	7	implicative	implicative	ADJ
ejpam-5511	60	8	n.p.o	n.p.o	NOUN
ejpam-5511	60	9	.	.	PUNCT
ejpam-5511	61	1	ternary	ternary	ADJ
ejpam-5511	61	2	semigroups	semigroup	NOUN
ejpam-5511	61	3	,	,	PUNCT
ejpam-5511	61	4	and	and	CCONJ
ejpam-5511	61	5	prove	prove	VERB
ejpam-5511	61	6	the	the	DET
ejpam-5511	61	7	homomorphism	homomorphism	NOUN
ejpam-5511	61	8	theorem	theorem	VERB
ejpam-5511	61	9	.	.	PUNCT
ejpam-5511	61	10	k.	k.	PROPN
ejpam-5511	61	11	nakwan	nakwan	PROPN
ejpam-5511	61	12	,	,	PUNCT
ejpam-5511	61	13	p.	p.	PROPN
ejpam-5511	61	14	luangchaisri	luangchaisri	VERB
ejpam-5511	61	15	,	,	PUNCT
ejpam-5511	61	16	t.	t.	PROPN
ejpam-5511	61	17	changphas	changphas	PROPN
ejpam-5511	61	18	/	/	SYM
ejpam-5511	61	19	eur	eur	PROPN
ejpam-5511	61	20	.	.	PUNCT
ejpam-5511	62	1	j.	j.	PROPN
ejpam-5511	62	2	pure	pure	PROPN
ejpam-5511	62	3	appl	appl	PROPN
ejpam-5511	62	4	.	.	PROPN
ejpam-5511	62	5	math	math	PROPN
ejpam-5511	62	6	,	,	PUNCT
ejpam-5511	62	7	17	17	NUM
ejpam-5511	62	8	(	(	PUNCT
ejpam-5511	62	9	4	4	NUM
ejpam-5511	62	10	)	)	PUNCT
ejpam-5511	62	11	(	(	PUNCT
ejpam-5511	62	12	2024	2024	NUM
ejpam-5511	62	13	)	)	PUNCT
ejpam-5511	62	14	,	,	PUNCT
ejpam-5511	62	15	4180	4180	NUM
ejpam-5511	62	16	-	-	SYM
ejpam-5511	62	17	4194	4194	NUM
ejpam-5511	62	18	4182	4182	NUM
ejpam-5511	62	19	2	2	NUM
ejpam-5511	62	20	.	.	X
ejpam-5511	62	21	implicative	implicative	ADJ
ejpam-5511	62	22	ternary	ternary	ADJ
ejpam-5511	62	23	semigroups	semigroup	NOUN
ejpam-5511	62	24	we	we	PRON
ejpam-5511	62	25	start	start	VERB
ejpam-5511	62	26	this	this	DET
ejpam-5511	62	27	section	section	NOUN
ejpam-5511	62	28	with	with	ADP
ejpam-5511	62	29	the	the	DET
ejpam-5511	62	30	definition	definition	NOUN
ejpam-5511	62	31	of	of	ADP
ejpam-5511	62	32	n.p.o	n.p.o	NOUN
ejpam-5511	62	33	.	.	PUNCT
ejpam-5511	63	1	ternary	ternary	ADJ
ejpam-5511	63	2	semigroups	semigroup	NOUN
ejpam-5511	63	3	.	.	PUNCT
ejpam-5511	64	1	definition	definition	NOUN
ejpam-5511	64	2	1	1	NUM
ejpam-5511	64	3	.	.	PUNCT
ejpam-5511	65	1	an	an	DET
ejpam-5511	65	2	n.p.o	n.p.o	NOUN
ejpam-5511	65	3	.	.	PUNCT
ejpam-5511	66	1	ternary	ternary	ADJ
ejpam-5511	66	2	semigroup	semigroup	PROPN
ejpam-5511	66	3	(	(	PUNCT
ejpam-5511	66	4	t	t	PROPN
ejpam-5511	66	5	,	,	PUNCT
ejpam-5511	66	6	[	[	PUNCT
ejpam-5511	66	7	]	]	X
ejpam-5511	66	8	,	,	PUNCT
ejpam-5511	66	9	≤	≤	NUM
ejpam-5511	66	10	)	)	PUNCT
ejpam-5511	66	11	consists	consist	VERB
ejpam-5511	66	12	of	of	ADP
ejpam-5511	66	13	a	a	DET
ejpam-5511	66	14	non	non	ADJ
ejpam-5511	66	15	-	-	ADJ
ejpam-5511	66	16	empty	empty	ADJ
ejpam-5511	66	17	set	set	ADJ
ejpam-5511	66	18	t	t	NOUN
ejpam-5511	66	19	together	together	ADV
ejpam-5511	66	20	with	with	ADP
ejpam-5511	66	21	a	a	DET
ejpam-5511	66	22	partial	partial	ADJ
ejpam-5511	66	23	order	order	NOUN
ejpam-5511	66	24	≤	≤	NOUN
ejpam-5511	66	25	and	and	CCONJ
ejpam-5511	66	26	a	a	DET
ejpam-5511	66	27	ternary	ternary	ADJ
ejpam-5511	66	28	multiplication	multiplication	NOUN
ejpam-5511	66	29	[	[	PUNCT
ejpam-5511	66	30	]	]	PUNCT
ejpam-5511	66	31	on	on	ADP
ejpam-5511	66	32	t	t	PROPN
ejpam-5511	66	33	such	such	ADJ
ejpam-5511	66	34	that	that	SCONJ
ejpam-5511	66	35	the	the	DET
ejpam-5511	66	36	following	follow	VERB
ejpam-5511	66	37	conditions	condition	NOUN
ejpam-5511	66	38	are	be	AUX
ejpam-5511	66	39	satisfied	satisfied	ADJ
ejpam-5511	66	40	:	:	PUNCT
ejpam-5511	66	41	for	for	ADP
ejpam-5511	66	42	any	any	DET
ejpam-5511	66	43	x	x	NOUN
ejpam-5511	66	44	,	,	PUNCT
ejpam-5511	66	45	y	y	PROPN
ejpam-5511	66	46	,	,	PUNCT
ejpam-5511	66	47	z	z	PROPN
ejpam-5511	66	48	,	,	PUNCT
ejpam-5511	66	49	u	u	NOUN
ejpam-5511	66	50	,	,	PUNCT
ejpam-5511	66	51	v	v	PROPN
ejpam-5511	66	52	∈	∈	PROPN
ejpam-5511	66	53	t	t	NOUN
ejpam-5511	66	54	,	,	PUNCT
ejpam-5511	66	55	(	(	PUNCT
ejpam-5511	66	56	1	1	X
ejpam-5511	66	57	)	)	PUNCT
ejpam-5511	67	1	[	[	X
ejpam-5511	67	2	[	[	X
ejpam-5511	67	3	xyz]uv	xyz]uv	X
ejpam-5511	67	4	]	]	X
ejpam-5511	67	5	=	=	PUNCT
ejpam-5511	68	1	[	[	X
ejpam-5511	68	2	x[yzu]v	x[yzu]v	X
ejpam-5511	68	3	]	]	X
ejpam-5511	68	4	=	=	PUNCT
ejpam-5511	69	1	[	[	X
ejpam-5511	69	2	xy[zuv	xy[zuv	PROPN
ejpam-5511	69	3	]	]	X
ejpam-5511	69	4	]	]	X
ejpam-5511	69	5	;	;	PUNCT
ejpam-5511	69	6	(	(	PUNCT
ejpam-5511	69	7	2	2	X
ejpam-5511	69	8	)	)	PUNCT
ejpam-5511	69	9	if	if	SCONJ
ejpam-5511	69	10	x	x	PROPN
ejpam-5511	69	11	≤	≤	NOUN
ejpam-5511	69	12	y	y	NOUN
ejpam-5511	69	13	,	,	PUNCT
ejpam-5511	69	14	then	then	ADV
ejpam-5511	69	15	[	[	X
ejpam-5511	69	16	xuv	xuv	X
ejpam-5511	69	17	]	]	X
ejpam-5511	69	18	≤	≤	X
ejpam-5511	70	1	[	[	X
ejpam-5511	70	2	yuv	yuv	X
ejpam-5511	70	3	]	]	PUNCT
ejpam-5511	70	4	,	,	PUNCT
ejpam-5511	70	5	[	[	X
ejpam-5511	70	6	uxv	uxv	X
ejpam-5511	70	7	]	]	X
ejpam-5511	70	8	≤	≤	NOUN
ejpam-5511	71	1	[	[	X
ejpam-5511	71	2	uyv	uyv	X
ejpam-5511	71	3	]	]	X
ejpam-5511	71	4	and	and	CCONJ
ejpam-5511	71	5	[	[	X
ejpam-5511	71	6	uvx	uvx	X
ejpam-5511	71	7	]	]	X
ejpam-5511	71	8	≤	≤	NOUN
ejpam-5511	72	1	[	[	X
ejpam-5511	72	2	uvy	uvy	NOUN
ejpam-5511	72	3	]	]	X
ejpam-5511	72	4	;	;	PUNCT
ejpam-5511	72	5	(	(	PUNCT
ejpam-5511	72	6	3	3	X
ejpam-5511	72	7	)	)	PUNCT
ejpam-5511	73	1	[	[	X
ejpam-5511	73	2	xyz	xyz	X
ejpam-5511	73	3	]	]	X
ejpam-5511	73	4	≤	≤	NUM
ejpam-5511	73	5	x	x	X
ejpam-5511	73	6	,	,	PUNCT
ejpam-5511	73	7	[	[	X
ejpam-5511	73	8	xyz	xyz	X
ejpam-5511	73	9	]	]	X
ejpam-5511	73	10	≤	≤	NUM
ejpam-5511	73	11	y	y	PROPN
ejpam-5511	73	12	and	and	CCONJ
ejpam-5511	73	13	[	[	X
ejpam-5511	73	14	xyz	xyz	X
ejpam-5511	73	15	]	]	X
ejpam-5511	73	16	≤	≤	NUM
ejpam-5511	73	17	z.	z.	PROPN
ejpam-5511	73	18	definition	definition	NOUN
ejpam-5511	73	19	2	2	NUM
ejpam-5511	73	20	.	.	PUNCT
ejpam-5511	74	1	an	an	DET
ejpam-5511	74	2	n.p.o	n.p.o	NOUN
ejpam-5511	74	3	.	.	PUNCT
ejpam-5511	75	1	ternary	ternary	ADJ
ejpam-5511	75	2	semigroup	semigroup	PROPN
ejpam-5511	75	3	(	(	PUNCT
ejpam-5511	75	4	t	t	PROPN
ejpam-5511	75	5	,	,	PUNCT
ejpam-5511	75	6	[	[	PUNCT
ejpam-5511	75	7	]	]	X
ejpam-5511	75	8	,	,	PUNCT
ejpam-5511	75	9	≤	≤	NUM
ejpam-5511	75	10	)	)	PUNCT
ejpam-5511	75	11	with	with	ADP
ejpam-5511	75	12	an	an	DET
ejpam-5511	75	13	additional	additional	ADJ
ejpam-5511	75	14	ternary	ternary	ADJ
ejpam-5511	75	15	multiplication	multiplication	NOUN
ejpam-5511	75	16	[	[	PUNCT
ejpam-5511	75	17	]	]	X
ejpam-5511	75	18	∗	∗	NOUN
ejpam-5511	75	19	on	on	ADP
ejpam-5511	75	20	t	t	PROPN
ejpam-5511	75	21	such	such	ADJ
ejpam-5511	75	22	that	that	SCONJ
ejpam-5511	75	23	u	u	NOUN
ejpam-5511	75	24	≤	≤	X
ejpam-5511	76	1	[	[	X
ejpam-5511	76	2	xyz]∗	xyz]∗	X
ejpam-5511	76	3	⇔	⇔	X
ejpam-5511	76	4	[	[	X
ejpam-5511	76	5	uxy	uxy	X
ejpam-5511	76	6	]	]	X
ejpam-5511	76	7	≤	≤	ADJ
ejpam-5511	76	8	z	z	NOUN
ejpam-5511	76	9	for	for	ADP
ejpam-5511	76	10	any	any	DET
ejpam-5511	76	11	x	x	NOUN
ejpam-5511	76	12	,	,	PUNCT
ejpam-5511	76	13	y	y	PROPN
ejpam-5511	76	14	,	,	PUNCT
ejpam-5511	76	15	z	z	PROPN
ejpam-5511	76	16	,	,	PUNCT
ejpam-5511	76	17	u	u	PROPN
ejpam-5511	76	18	∈	∈	PROPN
ejpam-5511	76	19	t	t	PROPN
ejpam-5511	76	20	is	be	AUX
ejpam-5511	76	21	called	call	VERB
ejpam-5511	76	22	an	an	DET
ejpam-5511	76	23	implicative	implicative	ADJ
ejpam-5511	76	24	n.p.o	n.p.o	NOUN
ejpam-5511	76	25	.	.	PUNCT
ejpam-5511	77	1	ternary	ternary	PROPN
ejpam-5511	77	2	semigroup	semigroup	PROPN
ejpam-5511	77	3	.	.	PUNCT
ejpam-5511	78	1	the	the	DET
ejpam-5511	78	2	ternary	ternary	ADJ
ejpam-5511	78	3	multiplication	multiplication	NOUN
ejpam-5511	78	4	[	[	PUNCT
ejpam-5511	78	5	]	]	PUNCT
ejpam-5511	78	6	∗	∗	NOUN
ejpam-5511	78	7	is	be	AUX
ejpam-5511	78	8	called	call	VERB
ejpam-5511	78	9	a	a	DET
ejpam-5511	78	10	ternary	ternary	ADJ
ejpam-5511	78	11	implication	implication	NOUN
ejpam-5511	78	12	.	.	PUNCT
ejpam-5511	79	1	an	an	DET
ejpam-5511	79	2	element	element	NOUN
ejpam-5511	79	3	1	1	NUM
ejpam-5511	79	4	of	of	ADP
ejpam-5511	79	5	a	a	DET
ejpam-5511	79	6	ternary	ternary	ADJ
ejpam-5511	79	7	semigroup	semigroup	NOUN
ejpam-5511	79	8	(	(	PUNCT
ejpam-5511	79	9	t	t	PROPN
ejpam-5511	79	10	,	,	PUNCT
ejpam-5511	79	11	[	[	X
ejpam-5511	79	12	]	]	X
ejpam-5511	79	13	)	)	PUNCT
ejpam-5511	79	14	is	be	AUX
ejpam-5511	79	15	a	a	DET
ejpam-5511	79	16	multiplicative	multiplicative	ADJ
ejpam-5511	79	17	identity	identity	NOUN
ejpam-5511	79	18	of	of	ADP
ejpam-5511	79	19	t	t	PROPN
ejpam-5511	79	20	if	if	SCONJ
ejpam-5511	79	21	[	[	X
ejpam-5511	79	22	11x	11x	NOUN
ejpam-5511	79	23	]	]	X
ejpam-5511	79	24	=	=	PUNCT
ejpam-5511	80	1	[	[	X
ejpam-5511	80	2	1x1	1x1	X
ejpam-5511	80	3	]	]	X
ejpam-5511	80	4	=	=	PUNCT
ejpam-5511	81	1	[	[	X
ejpam-5511	81	2	x11	x11	X
ejpam-5511	81	3	]	]	X
ejpam-5511	81	4	=	=	PUNCT
ejpam-5511	81	5	x	x	X
ejpam-5511	81	6	for	for	ADP
ejpam-5511	81	7	any	any	DET
ejpam-5511	81	8	x	x	SYM
ejpam-5511	81	9	∈	∈	PROPN
ejpam-5511	81	10	t	t	NOUN
ejpam-5511	81	11	.	.	PUNCT
ejpam-5511	82	1	the	the	DET
ejpam-5511	82	2	following	follow	VERB
ejpam-5511	82	3	example	example	NOUN
ejpam-5511	82	4	shows	show	VERB
ejpam-5511	82	5	that	that	SCONJ
ejpam-5511	82	6	the	the	DET
ejpam-5511	82	7	greatest	great	ADJ
ejpam-5511	82	8	element	element	NOUN
ejpam-5511	82	9	of	of	ADP
ejpam-5511	82	10	an	an	DET
ejpam-5511	82	11	implicative	implicative	ADJ
ejpam-5511	82	12	n.p.o	n.p.o	NOUN
ejpam-5511	82	13	.	.	PUNCT
ejpam-5511	83	1	ternary	ternary	ADJ
ejpam-5511	83	2	semigroup	semigroup	NOUN
ejpam-5511	83	3	need	need	AUX
ejpam-5511	83	4	not	not	PART
ejpam-5511	83	5	be	be	AUX
ejpam-5511	83	6	identity	identity	NOUN
ejpam-5511	83	7	.	.	PUNCT
ejpam-5511	83	8	example	example	NOUN
ejpam-5511	84	1	1	1	NUM
ejpam-5511	84	2	.	.	PUNCT
ejpam-5511	85	1	let	let	VERB
ejpam-5511	85	2	t	t	NOUN
ejpam-5511	85	3	=	=	SYM
ejpam-5511	85	4	{	{	PUNCT
ejpam-5511	85	5	1	1	NUM
ejpam-5511	85	6	,	,	PUNCT
ejpam-5511	85	7	a	a	PRON
ejpam-5511	85	8	,	,	PUNCT
ejpam-5511	85	9	0	0	NUM
ejpam-5511	85	10	}	}	PUNCT
ejpam-5511	85	11	.	.	PUNCT
ejpam-5511	86	1	let	let	VERB
ejpam-5511	86	2	us	we	PRON
ejpam-5511	86	3	consider	consider	VERB
ejpam-5511	86	4	the	the	DET
ejpam-5511	86	5	implicative	implicative	ADJ
ejpam-5511	86	6	n.p.o	n.p.o	NOUN
ejpam-5511	86	7	.	.	PUNCT
ejpam-5511	87	1	ternary	ternary	ADJ
ejpam-5511	87	2	semigroup	semigroup	PROPN
ejpam-5511	87	3	(	(	PUNCT
ejpam-5511	87	4	t	t	PROPN
ejpam-5511	87	5	,	,	PUNCT
ejpam-5511	87	6	[	[	PUNCT
ejpam-5511	87	7	]	]	X
ejpam-5511	87	8	,	,	PUNCT
ejpam-5511	87	9	≤	≤	NUM
ejpam-5511	87	10	,	,	PUNCT
ejpam-5511	87	11	[	[	PUNCT
ejpam-5511	87	12	]	]	X
ejpam-5511	87	13	∗	∗	NOUN
ejpam-5511	87	14	)	)	PUNCT
ejpam-5511	87	15	with	with	ADP
ejpam-5511	87	16	a	a	DET
ejpam-5511	87	17	ternary	ternary	ADJ
ejpam-5511	87	18	multiplication	multiplication	NOUN
ejpam-5511	87	19	,	,	PUNCT
ejpam-5511	87	20	a	a	DET
ejpam-5511	87	21	ternary	ternary	ADJ
ejpam-5511	87	22	implication	implication	NOUN
ejpam-5511	87	23	,	,	PUNCT
ejpam-5511	87	24	and	and	CCONJ
ejpam-5511	87	25	an	an	DET
ejpam-5511	87	26	order	order	NOUN
ejpam-5511	87	27	relation	relation	NOUN
ejpam-5511	87	28	defined	define	VERB
ejpam-5511	87	29	on	on	ADP
ejpam-5511	87	30	t	t	PROPN
ejpam-5511	87	31	as	as	SCONJ
ejpam-5511	87	32	follows	follow	VERB
ejpam-5511	87	33	:	:	PUNCT
ejpam-5511	87	34	[	[	PUNCT
ejpam-5511	87	35	]	]	X
ejpam-5511	87	36	1	1	NUM
ejpam-5511	87	37	a	a	DET
ejpam-5511	87	38	0	0	NUM
ejpam-5511	87	39	11	11	NUM
ejpam-5511	87	40	1	1	NUM
ejpam-5511	87	41	0	0	NUM
ejpam-5511	87	42	0	0	NUM
ejpam-5511	87	43	1a	1a	X
ejpam-5511	87	44	0	0	NUM
ejpam-5511	87	45	0	0	NUM
ejpam-5511	87	46	0	0	NUM
ejpam-5511	87	47	10	10	NUM
ejpam-5511	87	48	0	0	NUM
ejpam-5511	87	49	0	0	NUM
ejpam-5511	87	50	0	0	NUM
ejpam-5511	88	1	[	[	PUNCT
ejpam-5511	88	2	]	]	X
ejpam-5511	88	3	1	1	NUM
ejpam-5511	88	4	a	a	DET
ejpam-5511	88	5	0	0	NUM
ejpam-5511	88	6	aa	aa	NOUN
ejpam-5511	88	7	0	0	NUM
ejpam-5511	88	8	0	0	SYM
ejpam-5511	88	9	0	0	NUM
ejpam-5511	88	10	a1	a1	NOUN
ejpam-5511	88	11	0	0	NUM
ejpam-5511	88	12	0	0	NUM
ejpam-5511	88	13	0	0	NUM
ejpam-5511	88	14	a0	a0	NOUN
ejpam-5511	88	15	0	0	NUM
ejpam-5511	88	16	0	0	NUM
ejpam-5511	88	17	0	0	NUM
ejpam-5511	89	1	[	[	PUNCT
ejpam-5511	89	2	]	]	X
ejpam-5511	89	3	1	1	NUM
ejpam-5511	89	4	a	a	PRON
ejpam-5511	89	5	0	0	NUM
ejpam-5511	89	6	00	00	NUM
ejpam-5511	89	7	0	0	NUM
ejpam-5511	89	8	0	0	NUM
ejpam-5511	89	9	0	0	NUM
ejpam-5511	89	10	01	01	NUM
ejpam-5511	89	11	0	0	NUM
ejpam-5511	89	12	0	0	NUM
ejpam-5511	89	13	0	0	NUM
ejpam-5511	89	14	0a	0a	NOUN
ejpam-5511	89	15	0	0	NUM
ejpam-5511	89	16	0	0	NUM
ejpam-5511	89	17	0	0	NUM
ejpam-5511	90	1	[	[	PUNCT
ejpam-5511	90	2	]	]	X
ejpam-5511	90	3	∗	∗	NOUN
ejpam-5511	90	4	1	1	NUM
ejpam-5511	90	5	a	a	DET
ejpam-5511	90	6	0	0	NUM
ejpam-5511	90	7	11	11	NUM
ejpam-5511	90	8	1	1	NUM
ejpam-5511	90	9	1	1	NUM
ejpam-5511	90	10	1	1	NUM
ejpam-5511	90	11	1a	1a	NUM
ejpam-5511	90	12	1	1	NUM
ejpam-5511	90	13	1	1	NUM
ejpam-5511	90	14	1	1	NUM
ejpam-5511	90	15	10	10	NUM
ejpam-5511	90	16	1	1	NUM
ejpam-5511	90	17	1	1	NUM
ejpam-5511	90	18	1	1	NUM
ejpam-5511	90	19	[	[	PUNCT
ejpam-5511	90	20	]	]	X
ejpam-5511	90	21	∗	∗	NOUN
ejpam-5511	90	22	1	1	NUM
ejpam-5511	90	23	a	a	DET
ejpam-5511	90	24	0	0	NUM
ejpam-5511	90	25	aa	aa	NOUN
ejpam-5511	90	26	1	1	NUM
ejpam-5511	90	27	1	1	NUM
ejpam-5511	90	28	1	1	NUM
ejpam-5511	90	29	a1	a1	NOUN
ejpam-5511	90	30	1	1	NUM
ejpam-5511	90	31	1	1	NUM
ejpam-5511	90	32	1	1	NUM
ejpam-5511	90	33	a0	a0	NOUN
ejpam-5511	90	34	1	1	NUM
ejpam-5511	90	35	1	1	NUM
ejpam-5511	90	36	1	1	NUM
ejpam-5511	90	37	[	[	PUNCT
ejpam-5511	90	38	]	]	X
ejpam-5511	90	39	∗	∗	NOUN
ejpam-5511	90	40	1	1	NUM
ejpam-5511	90	41	a	a	DET
ejpam-5511	90	42	0	0	NUM
ejpam-5511	90	43	00	00	NUM
ejpam-5511	90	44	1	1	NUM
ejpam-5511	90	45	1	1	NUM
ejpam-5511	90	46	1	1	NUM
ejpam-5511	90	47	01	01	NUM
ejpam-5511	90	48	1	1	NUM
ejpam-5511	90	49	1	1	NUM
ejpam-5511	90	50	1	1	NUM
ejpam-5511	90	51	0a	0a	NUM
ejpam-5511	90	52	1	1	NUM
ejpam-5511	90	53	1	1	NUM
ejpam-5511	90	54	1	1	NUM
ejpam-5511	90	55	and	and	CCONJ
ejpam-5511	90	56	≤=	≤=	PROPN
ejpam-5511	90	57	{	{	PUNCT
ejpam-5511	90	58	(	(	PUNCT
ejpam-5511	90	59	0	0	NUM
ejpam-5511	90	60	,	,	PUNCT
ejpam-5511	90	61	0	0	NUM
ejpam-5511	90	62	)	)	PUNCT
ejpam-5511	90	63	,	,	PUNCT
ejpam-5511	90	64	(	(	PUNCT
ejpam-5511	90	65	1	1	NUM
ejpam-5511	90	66	,	,	PUNCT
ejpam-5511	90	67	1	1	NUM
ejpam-5511	90	68	)	)	PUNCT
ejpam-5511	90	69	,	,	PUNCT
ejpam-5511	90	70	(	(	PUNCT
ejpam-5511	90	71	a	a	X
ejpam-5511	90	72	,	,	PUNCT
ejpam-5511	90	73	a	a	NOUN
ejpam-5511	90	74	)	)	PUNCT
ejpam-5511	90	75	,	,	PUNCT
ejpam-5511	90	76	(	(	PUNCT
ejpam-5511	90	77	a	a	DET
ejpam-5511	90	78	,	,	PUNCT
ejpam-5511	90	79	1	1	NUM
ejpam-5511	90	80	)	)	PUNCT
ejpam-5511	90	81	,	,	PUNCT
ejpam-5511	90	82	(	(	PUNCT
ejpam-5511	90	83	0	0	NUM
ejpam-5511	90	84	,	,	PUNCT
ejpam-5511	90	85	a	a	PRON
ejpam-5511	90	86	)	)	PUNCT
ejpam-5511	90	87	,	,	PUNCT
ejpam-5511	90	88	(	(	PUNCT
ejpam-5511	90	89	0	0	NUM
ejpam-5511	90	90	,	,	PUNCT
ejpam-5511	90	91	1	1	NUM
ejpam-5511	90	92	)	)	PUNCT
ejpam-5511	90	93	}	}	PUNCT
ejpam-5511	90	94	.	.	PUNCT
ejpam-5511	91	1	to	to	PART
ejpam-5511	91	2	express	express	VERB
ejpam-5511	91	3	the	the	DET
ejpam-5511	91	4	calculation	calculation	NOUN
ejpam-5511	91	5	[	[	X
ejpam-5511	91	6	x1x2x3	x1x2x3	X
ejpam-5511	91	7	]	]	X
ejpam-5511	91	8	using	use	VERB
ejpam-5511	91	9	a	a	DET
ejpam-5511	91	10	multiplication	multiplication	NOUN
ejpam-5511	91	11	table	table	NOUN
ejpam-5511	91	12	,	,	PUNCT
ejpam-5511	91	13	we	we	PRON
ejpam-5511	91	14	place	place	VERB
ejpam-5511	91	15	x1x2	x1x2	PUNCT
ejpam-5511	92	1	in	in	ADP
ejpam-5511	92	2	the	the	DET
ejpam-5511	92	3	first	first	ADJ
ejpam-5511	92	4	column	column	NOUN
ejpam-5511	92	5	and	and	CCONJ
ejpam-5511	92	6	x3	x3	VERB
ejpam-5511	92	7	in	in	ADP
ejpam-5511	92	8	the	the	DET
ejpam-5511	92	9	first	first	ADJ
ejpam-5511	92	10	row	row	NOUN
ejpam-5511	92	11	.	.	PUNCT
ejpam-5511	93	1	it	it	PRON
ejpam-5511	93	2	is	be	AUX
ejpam-5511	93	3	observed	observe	VERB
ejpam-5511	93	4	that	that	SCONJ
ejpam-5511	93	5	1	1	NUM
ejpam-5511	93	6	is	be	AUX
ejpam-5511	93	7	the	the	DET
ejpam-5511	93	8	greatest	great	ADJ
ejpam-5511	93	9	element	element	NOUN
ejpam-5511	93	10	.	.	PUNCT
ejpam-5511	94	1	however	however	ADV
ejpam-5511	94	2	,	,	PUNCT
ejpam-5511	94	3	1	1	NUM
ejpam-5511	94	4	is	be	AUX
ejpam-5511	94	5	not	not	PART
ejpam-5511	94	6	the	the	DET
ejpam-5511	94	7	identity	identity	NOUN
ejpam-5511	94	8	since	since	SCONJ
ejpam-5511	94	9	[	[	X
ejpam-5511	94	10	11a	11a	NOUN
ejpam-5511	94	11	]	]	X
ejpam-5511	94	12	=	=	SYM
ejpam-5511	94	13	0	0	NUM
ejpam-5511	94	14	̸=	̸=	PROPN
ejpam-5511	94	15	a.	a.	NOUN
ejpam-5511	94	16	k.	k.	PROPN
ejpam-5511	94	17	nakwan	nakwan	PROPN
ejpam-5511	94	18	,	,	PUNCT
ejpam-5511	94	19	p.	p.	PROPN
ejpam-5511	94	20	luangchaisri	luangchaisri	VERB
ejpam-5511	94	21	,	,	PUNCT
ejpam-5511	94	22	t.	t.	PROPN
ejpam-5511	94	23	changphas	changphas	PROPN
ejpam-5511	94	24	/	/	SYM
ejpam-5511	94	25	eur	eur	PROPN
ejpam-5511	94	26	.	.	PUNCT
ejpam-5511	95	1	j.	j.	PROPN
ejpam-5511	95	2	pure	pure	PROPN
ejpam-5511	95	3	appl	appl	PROPN
ejpam-5511	95	4	.	.	PROPN
ejpam-5511	95	5	math	math	PROPN
ejpam-5511	95	6	,	,	PUNCT
ejpam-5511	95	7	17	17	NUM
ejpam-5511	95	8	(	(	PUNCT
ejpam-5511	95	9	4	4	NUM
ejpam-5511	95	10	)	)	PUNCT
ejpam-5511	95	11	(	(	PUNCT
ejpam-5511	95	12	2024	2024	NUM
ejpam-5511	95	13	)	)	PUNCT
ejpam-5511	95	14	,	,	PUNCT
ejpam-5511	95	15	4180	4180	NUM
ejpam-5511	95	16	-	-	SYM
ejpam-5511	95	17	4194	4194	NUM
ejpam-5511	95	18	4183	4183	NUM
ejpam-5511	96	1	the	the	DET
ejpam-5511	96	2	next	next	ADJ
ejpam-5511	96	3	example	example	NOUN
ejpam-5511	96	4	shows	show	VERB
ejpam-5511	96	5	that	that	SCONJ
ejpam-5511	96	6	not	not	PART
ejpam-5511	96	7	every	every	DET
ejpam-5511	96	8	n.p.o	n.p.o	NOUN
ejpam-5511	96	9	.	.	PUNCT
ejpam-5511	97	1	ternary	ternary	ADJ
ejpam-5511	97	2	semigroup	semigroup	NOUN
ejpam-5511	97	3	with	with	ADP
ejpam-5511	97	4	identity	identity	NOUN
ejpam-5511	97	5	admits	admit	VERB
ejpam-5511	97	6	the	the	DET
ejpam-5511	97	7	implicative	implicative	ADJ
ejpam-5511	97	8	structure	structure	NOUN
ejpam-5511	97	9	.	.	PUNCT
ejpam-5511	98	1	example	example	NOUN
ejpam-5511	99	1	2	2	NUM
ejpam-5511	99	2	.	.	PUNCT
ejpam-5511	99	3	let	let	VERB
ejpam-5511	99	4	t	t	NOUN
ejpam-5511	99	5	=	=	SYM
ejpam-5511	99	6	{	{	PUNCT
ejpam-5511	99	7	0	0	NUM
ejpam-5511	99	8	,	,	PUNCT
ejpam-5511	99	9	1	1	NUM
ejpam-5511	99	10	,	,	PUNCT
ejpam-5511	99	11	a	a	DET
ejpam-5511	99	12	,	,	PUNCT
ejpam-5511	99	13	b	b	NOUN
ejpam-5511	99	14	}	}	PUNCT
ejpam-5511	99	15	.	.	PUNCT
ejpam-5511	100	1	let	let	VERB
ejpam-5511	100	2	us	we	PRON
ejpam-5511	100	3	consider	consider	VERB
ejpam-5511	100	4	the	the	DET
ejpam-5511	100	5	n.p.o	n.p.o	NOUN
ejpam-5511	100	6	.	.	PUNCT
ejpam-5511	101	1	ternary	ternary	ADJ
ejpam-5511	101	2	semigroup	semigroup	PROPN
ejpam-5511	101	3	(	(	PUNCT
ejpam-5511	101	4	t	t	PROPN
ejpam-5511	101	5	,	,	PUNCT
ejpam-5511	101	6	[	[	PUNCT
ejpam-5511	101	7	]	]	X
ejpam-5511	101	8	,	,	PUNCT
ejpam-5511	101	9	≤	≤	NUM
ejpam-5511	101	10	)	)	PUNCT
ejpam-5511	101	11	with	with	ADP
ejpam-5511	101	12	a	a	DET
ejpam-5511	101	13	ternary	ternary	ADJ
ejpam-5511	101	14	multiplication	multiplication	NOUN
ejpam-5511	101	15	and	and	CCONJ
ejpam-5511	101	16	an	an	DET
ejpam-5511	101	17	order	order	NOUN
ejpam-5511	101	18	relation	relation	NOUN
ejpam-5511	101	19	defined	define	VERB
ejpam-5511	101	20	on	on	ADP
ejpam-5511	101	21	t	t	PROPN
ejpam-5511	101	22	as	as	SCONJ
ejpam-5511	101	23	follows	follow	VERB
ejpam-5511	101	24	:	:	PUNCT
ejpam-5511	101	25	[	[	PUNCT
ejpam-5511	101	26	]	]	X
ejpam-5511	101	27	1	1	NUM
ejpam-5511	101	28	a	a	DET
ejpam-5511	101	29	b	b	NOUN
ejpam-5511	101	30	0	0	NUM
ejpam-5511	101	31	11	11	NUM
ejpam-5511	101	32	1	1	NUM
ejpam-5511	101	33	a	a	DET
ejpam-5511	101	34	b	b	PROPN
ejpam-5511	101	35	0	0	PUNCT
ejpam-5511	101	36	1a	1a	PROPN
ejpam-5511	101	37	a	a	DET
ejpam-5511	101	38	0	0	NUM
ejpam-5511	101	39	0	0	NUM
ejpam-5511	101	40	0	0	NUM
ejpam-5511	101	41	1b	1b	NUM
ejpam-5511	101	42	b	b	X
ejpam-5511	101	43	0	0	NUM
ejpam-5511	101	44	b	b	NOUN
ejpam-5511	101	45	0	0	NUM
ejpam-5511	101	46	10	10	NUM
ejpam-5511	101	47	0	0	NUM
ejpam-5511	101	48	0	0	NUM
ejpam-5511	101	49	0	0	NUM
ejpam-5511	101	50	0	0	NUM
ejpam-5511	102	1	[	[	PUNCT
ejpam-5511	102	2	]	]	X
ejpam-5511	102	3	1	1	NUM
ejpam-5511	102	4	a	a	DET
ejpam-5511	102	5	b	b	PROPN
ejpam-5511	102	6	0	0	NUM
ejpam-5511	102	7	aa	aa	NOUN
ejpam-5511	102	8	0	0	NUM
ejpam-5511	102	9	0	0	NUM
ejpam-5511	102	10	0	0	SYM
ejpam-5511	102	11	0	0	NUM
ejpam-5511	102	12	a1	a1	NOUN
ejpam-5511	102	13	a	a	DET
ejpam-5511	102	14	0	0	NUM
ejpam-5511	102	15	0	0	NUM
ejpam-5511	102	16	0	0	NUM
ejpam-5511	103	1	ab	ab	NOUN
ejpam-5511	103	2	0	0	NUM
ejpam-5511	103	3	0	0	NUM
ejpam-5511	103	4	0	0	NUM
ejpam-5511	103	5	0	0	NUM
ejpam-5511	103	6	a0	a0	NOUN
ejpam-5511	103	7	0	0	NUM
ejpam-5511	103	8	0	0	NUM
ejpam-5511	103	9	0	0	NUM
ejpam-5511	103	10	0	0	NUM
ejpam-5511	104	1	[	[	PUNCT
ejpam-5511	104	2	]	]	X
ejpam-5511	104	3	1	1	NUM
ejpam-5511	104	4	a	a	DET
ejpam-5511	104	5	b	b	PROPN
ejpam-5511	104	6	0	0	NUM
ejpam-5511	104	7	bb	bb	NUM
ejpam-5511	104	8	b	b	NOUN
ejpam-5511	104	9	0	0	NUM
ejpam-5511	104	10	b	b	SYM
ejpam-5511	104	11	0	0	NUM
ejpam-5511	104	12	b1	b1	PROPN
ejpam-5511	104	13	b	b	PROPN
ejpam-5511	104	14	0	0	NUM
ejpam-5511	104	15	b	b	PROPN
ejpam-5511	104	16	0	0	NUM
ejpam-5511	104	17	ba	ba	NOUN
ejpam-5511	104	18	0	0	NUM
ejpam-5511	104	19	0	0	NUM
ejpam-5511	104	20	0	0	NUM
ejpam-5511	104	21	0	0	NUM
ejpam-5511	104	22	b0	b0	VERB
ejpam-5511	104	23	0	0	NUM
ejpam-5511	104	24	0	0	NUM
ejpam-5511	104	25	0	0	NUM
ejpam-5511	104	26	0	0	NUM
ejpam-5511	105	1	[	[	PUNCT
ejpam-5511	105	2	]	]	X
ejpam-5511	105	3	1	1	NUM
ejpam-5511	105	4	a	a	DET
ejpam-5511	105	5	b	b	NOUN
ejpam-5511	105	6	0	0	NUM
ejpam-5511	105	7	00	00	NUM
ejpam-5511	105	8	0	0	NUM
ejpam-5511	105	9	0	0	NUM
ejpam-5511	105	10	0	0	NUM
ejpam-5511	105	11	0	0	NUM
ejpam-5511	105	12	01	01	NUM
ejpam-5511	105	13	0	0	NUM
ejpam-5511	105	14	0	0	NUM
ejpam-5511	105	15	0	0	NUM
ejpam-5511	105	16	0	0	NUM
ejpam-5511	105	17	0a	0a	NOUN
ejpam-5511	105	18	0	0	NUM
ejpam-5511	105	19	0	0	NUM
ejpam-5511	105	20	0	0	NUM
ejpam-5511	105	21	0	0	NUM
ejpam-5511	105	22	0b	0b	NOUN
ejpam-5511	105	23	0	0	NUM
ejpam-5511	105	24	0	0	NUM
ejpam-5511	105	25	0	0	NUM
ejpam-5511	105	26	0	0	NUM
ejpam-5511	105	27	and	and	CCONJ
ejpam-5511	105	28	≤=	≤=	PROPN
ejpam-5511	105	29	{	{	PUNCT
ejpam-5511	105	30	(	(	PUNCT
ejpam-5511	105	31	0	0	NUM
ejpam-5511	105	32	,	,	PUNCT
ejpam-5511	105	33	0	0	NUM
ejpam-5511	105	34	)	)	PUNCT
ejpam-5511	105	35	,	,	PUNCT
ejpam-5511	105	36	(	(	PUNCT
ejpam-5511	105	37	1	1	NUM
ejpam-5511	105	38	,	,	PUNCT
ejpam-5511	105	39	1	1	NUM
ejpam-5511	105	40	)	)	PUNCT
ejpam-5511	105	41	,	,	PUNCT
ejpam-5511	105	42	(	(	PUNCT
ejpam-5511	105	43	a	a	X
ejpam-5511	105	44	,	,	PUNCT
ejpam-5511	105	45	a	a	NOUN
ejpam-5511	105	46	)	)	PUNCT
ejpam-5511	105	47	,	,	PUNCT
ejpam-5511	105	48	(	(	PUNCT
ejpam-5511	105	49	b	b	X
ejpam-5511	105	50	,	,	PUNCT
ejpam-5511	105	51	b	b	NOUN
ejpam-5511	105	52	)	)	PUNCT
ejpam-5511	105	53	,	,	PUNCT
ejpam-5511	105	54	(	(	PUNCT
ejpam-5511	105	55	0	0	NUM
ejpam-5511	105	56	,	,	PUNCT
ejpam-5511	105	57	a	a	PRON
ejpam-5511	105	58	)	)	PUNCT
ejpam-5511	105	59	,	,	PUNCT
ejpam-5511	105	60	(	(	PUNCT
ejpam-5511	105	61	0	0	NUM
ejpam-5511	105	62	,	,	PUNCT
ejpam-5511	105	63	b	b	NOUN
ejpam-5511	105	64	)	)	PUNCT
ejpam-5511	105	65	,	,	PUNCT
ejpam-5511	105	66	(	(	PUNCT
ejpam-5511	105	67	0	0	NUM
ejpam-5511	105	68	,	,	PUNCT
ejpam-5511	105	69	1	1	NUM
ejpam-5511	105	70	)	)	PUNCT
ejpam-5511	105	71	,	,	PUNCT
ejpam-5511	105	72	(	(	PUNCT
ejpam-5511	105	73	a	a	DET
ejpam-5511	105	74	,	,	PUNCT
ejpam-5511	105	75	1	1	NUM
ejpam-5511	105	76	)	)	PUNCT
ejpam-5511	105	77	,	,	PUNCT
ejpam-5511	105	78	(	(	PUNCT
ejpam-5511	105	79	b	b	X
ejpam-5511	105	80	,	,	PUNCT
ejpam-5511	105	81	1	1	NUM
ejpam-5511	105	82	)	)	PUNCT
ejpam-5511	105	83	}	}	PUNCT
ejpam-5511	105	84	.	.	PUNCT
ejpam-5511	106	1	observed	observe	VERB
ejpam-5511	106	2	that	that	SCONJ
ejpam-5511	106	3	1	1	NUM
ejpam-5511	106	4	is	be	AUX
ejpam-5511	106	5	the	the	DET
ejpam-5511	106	6	greatest	great	ADJ
ejpam-5511	106	7	element	element	NOUN
ejpam-5511	106	8	.	.	PUNCT
ejpam-5511	107	1	notice	notice	VERB
ejpam-5511	107	2	that	that	SCONJ
ejpam-5511	107	3	t	t	PROPN
ejpam-5511	107	4	is	be	AUX
ejpam-5511	107	5	not	not	PART
ejpam-5511	107	6	an	an	DET
ejpam-5511	107	7	implicative	implicative	ADJ
ejpam-5511	107	8	n.p.o	n.p.o	NOUN
ejpam-5511	107	9	.	.	PUNCT
ejpam-5511	108	1	ternary	ternary	PROPN
ejpam-5511	108	2	semigroup	semigroup	PROPN
ejpam-5511	108	3	.	.	PUNCT
ejpam-5511	109	1	indeed	indeed	ADV
ejpam-5511	109	2	,	,	PUNCT
ejpam-5511	109	3	if	if	SCONJ
ejpam-5511	109	4	t	t	PROPN
ejpam-5511	109	5	is	be	AUX
ejpam-5511	109	6	an	an	DET
ejpam-5511	109	7	implicative	implicative	ADJ
ejpam-5511	109	8	n.p.o	n.p.o	NOUN
ejpam-5511	109	9	.	.	PUNCT
ejpam-5511	110	1	ternary	ternary	PROPN
ejpam-5511	110	2	semigroup	semigroup	NOUN
ejpam-5511	110	3	with	with	ADP
ejpam-5511	110	4	a	a	DET
ejpam-5511	110	5	ternary	ternary	ADJ
ejpam-5511	110	6	implication	implication	NOUN
ejpam-5511	110	7	[	[	PUNCT
ejpam-5511	110	8	]	]	X
ejpam-5511	110	9	∗	∗	NOUN
ejpam-5511	110	10	,	,	PUNCT
ejpam-5511	110	11	then	then	ADV
ejpam-5511	110	12	a	a	DET
ejpam-5511	110	13	≤	≤	NOUN
ejpam-5511	111	1	[	[	PUNCT
ejpam-5511	111	2	1ab]∗	1ab]∗	NUM
ejpam-5511	111	3	and	and	CCONJ
ejpam-5511	111	4	b	b	NOUN
ejpam-5511	111	5	≤	≤	NOUN
ejpam-5511	112	1	[	[	X
ejpam-5511	112	2	1ab]∗	1ab]∗	NOUN
ejpam-5511	112	3	since	since	SCONJ
ejpam-5511	112	4	[	[	X
ejpam-5511	112	5	a1a	a1a	X
ejpam-5511	112	6	]	]	X
ejpam-5511	112	7	=	=	SYM
ejpam-5511	112	8	0	0	NUM
ejpam-5511	112	9	≤	≤	NUM
ejpam-5511	112	10	b	b	NOUN
ejpam-5511	112	11	and	and	CCONJ
ejpam-5511	113	1	[	[	X
ejpam-5511	113	2	b1a	b1a	X
ejpam-5511	113	3	]	]	X
ejpam-5511	113	4	=	=	SYM
ejpam-5511	113	5	0	0	NUM
ejpam-5511	113	6	≤	≤	NUM
ejpam-5511	113	7	b	b	NOUN
ejpam-5511	113	8	,	,	PUNCT
ejpam-5511	113	9	respectively	respectively	ADV
ejpam-5511	113	10	.	.	PUNCT
ejpam-5511	114	1	it	it	PRON
ejpam-5511	114	2	follows	follow	VERB
ejpam-5511	114	3	that	that	SCONJ
ejpam-5511	115	1	[	[	X
ejpam-5511	115	2	1ab]∗	1ab]∗	NUM
ejpam-5511	115	3	=	=	SYM
ejpam-5511	115	4	1	1	NUM
ejpam-5511	115	5	.	.	PUNCT
ejpam-5511	116	1	as	as	ADP
ejpam-5511	116	2	1	1	NUM
ejpam-5511	116	3	≤	≤	NOUN
ejpam-5511	117	1	[	[	PUNCT
ejpam-5511	117	2	1ab]∗	1ab]∗	NOUN
ejpam-5511	117	3	,	,	PUNCT
ejpam-5511	117	4	we	we	PRON
ejpam-5511	117	5	have	have	VERB
ejpam-5511	117	6	a	a	DET
ejpam-5511	117	7	=	=	SYM
ejpam-5511	117	8	[	[	X
ejpam-5511	117	9	11a	11a	NOUN
ejpam-5511	117	10	]	]	PUNCT
ejpam-5511	117	11	≤	≤	NUM
ejpam-5511	117	12	b.	b.	PROPN
ejpam-5511	117	13	this	this	PRON
ejpam-5511	117	14	is	be	AUX
ejpam-5511	117	15	a	a	DET
ejpam-5511	117	16	contradiction	contradiction	NOUN
ejpam-5511	117	17	.	.	PUNCT
ejpam-5511	118	1	an	an	DET
ejpam-5511	118	2	implicative	implicative	ADJ
ejpam-5511	118	3	n.p.o	n.p.o	NOUN
ejpam-5511	118	4	.	.	PUNCT
ejpam-5511	119	1	ternary	ternary	ADJ
ejpam-5511	119	2	semigroup	semigroup	PROPN
ejpam-5511	119	3	(	(	PUNCT
ejpam-5511	119	4	t	t	PROPN
ejpam-5511	119	5	,	,	PUNCT
ejpam-5511	119	6	[	[	PUNCT
ejpam-5511	119	7	]	]	X
ejpam-5511	119	8	,	,	PUNCT
ejpam-5511	119	9	≤	≤	NUM
ejpam-5511	119	10	,	,	PUNCT
ejpam-5511	119	11	[	[	PUNCT
ejpam-5511	119	12	]	]	X
ejpam-5511	119	13	∗	∗	NOUN
ejpam-5511	119	14	)	)	PUNCT
ejpam-5511	119	15	is	be	AUX
ejpam-5511	119	16	said	say	VERB
ejpam-5511	119	17	to	to	PART
ejpam-5511	119	18	be	be	AUX
ejpam-5511	119	19	commutative	commutative	ADJ
ejpam-5511	120	1	[	[	X
ejpam-5511	120	2	16	16	NUM
ejpam-5511	120	3	]	]	PUNCT
ejpam-5511	120	4	if	if	SCONJ
ejpam-5511	120	5	[	[	X
ejpam-5511	120	6	xyz	xyz	X
ejpam-5511	120	7	]	]	X
ejpam-5511	120	8	=	=	PUNCT
ejpam-5511	121	1	[	[	X
ejpam-5511	121	2	yzx	yzx	X
ejpam-5511	121	3	]	]	X
ejpam-5511	121	4	=	=	PUNCT
ejpam-5511	122	1	[	[	X
ejpam-5511	122	2	zxy	zxy	X
ejpam-5511	122	3	]	]	X
ejpam-5511	122	4	=	=	PUNCT
ejpam-5511	123	1	[	[	X
ejpam-5511	123	2	yxz	yxz	X
ejpam-5511	123	3	]	]	X
ejpam-5511	123	4	=	=	SYM
ejpam-5511	124	1	[	[	X
ejpam-5511	124	2	zyx	zyx	X
ejpam-5511	124	3	]	]	X
ejpam-5511	124	4	=	=	PUNCT
ejpam-5511	125	1	[	[	X
ejpam-5511	125	2	xzy	xzy	X
ejpam-5511	125	3	]	]	X
ejpam-5511	125	4	for	for	ADP
ejpam-5511	125	5	all	all	DET
ejpam-5511	125	6	elements	element	NOUN
ejpam-5511	125	7	x	x	X
ejpam-5511	125	8	,	,	PUNCT
ejpam-5511	125	9	y	y	PROPN
ejpam-5511	125	10	,	,	PUNCT
ejpam-5511	125	11	z	z	NOUN
ejpam-5511	125	12	in	in	ADP
ejpam-5511	125	13	t	t	PROPN
ejpam-5511	125	14	.	.	PUNCT
ejpam-5511	126	1	the	the	DET
ejpam-5511	126	2	following	follow	VERB
ejpam-5511	126	3	example	example	NOUN
ejpam-5511	126	4	shows	show	VERB
ejpam-5511	126	5	an	an	DET
ejpam-5511	126	6	infinite	infinite	ADJ
ejpam-5511	126	7	commutative	commutative	ADJ
ejpam-5511	126	8	implicative	implicative	ADJ
ejpam-5511	126	9	n.p.o	n.p.o	NOUN
ejpam-5511	126	10	.	.	PUNCT
ejpam-5511	127	1	ternary	ternary	PROPN
ejpam-5511	127	2	semigroup	semigroup	NOUN
ejpam-5511	127	3	with	with	ADP
ejpam-5511	127	4	1	1	NUM
ejpam-5511	127	5	as	as	ADP
ejpam-5511	127	6	its	its	PRON
ejpam-5511	127	7	greatest	great	ADJ
ejpam-5511	127	8	element	element	NOUN
ejpam-5511	127	9	.	.	PUNCT
ejpam-5511	128	1	example	example	NOUN
ejpam-5511	129	1	3	3	X
ejpam-5511	129	2	.	.	PUNCT
ejpam-5511	130	1	let	let	AUX
ejpam-5511	130	2	(	(	PUNCT
ejpam-5511	130	3	z+	z+	X
ejpam-5511	130	4	,	,	PUNCT
ejpam-5511	130	5	[	[	PUNCT
ejpam-5511	130	6	]	]	X
ejpam-5511	130	7	)	)	PUNCT
ejpam-5511	130	8	be	be	AUX
ejpam-5511	130	9	the	the	DET
ejpam-5511	130	10	ternary	ternary	ADJ
ejpam-5511	130	11	semigroup	semigroup	NOUN
ejpam-5511	130	12	of	of	ADP
ejpam-5511	130	13	positive	positive	ADJ
ejpam-5511	130	14	integers	integer	NOUN
ejpam-5511	130	15	with	with	ADP
ejpam-5511	130	16	the	the	DET
ejpam-5511	130	17	ternary	ternary	ADJ
ejpam-5511	130	18	multiplication	multiplication	NOUN
ejpam-5511	130	19	induced	induce	VERB
ejpam-5511	130	20	by	by	ADP
ejpam-5511	130	21	usual	usual	ADJ
ejpam-5511	130	22	multiplication	multiplication	NOUN
ejpam-5511	130	23	.	.	PUNCT
ejpam-5511	131	1	for	for	ADP
ejpam-5511	131	2	a	a	DET
ejpam-5511	131	3	,	,	PUNCT
ejpam-5511	131	4	b	b	PROPN
ejpam-5511	131	5	∈	∈	PROPN
ejpam-5511	131	6	z+	z+	NUM
ejpam-5511	131	7	,	,	PUNCT
ejpam-5511	131	8	an	an	DET
ejpam-5511	131	9	order	order	NOUN
ejpam-5511	131	10	relation	relation	NOUN
ejpam-5511	131	11	≤	≤	NOUN
ejpam-5511	131	12	on	on	ADP
ejpam-5511	131	13	z+	z+	NUM
ejpam-5511	131	14	is	be	AUX
ejpam-5511	131	15	defined	define	VERB
ejpam-5511	131	16	by	by	ADP
ejpam-5511	131	17	a	a	DET
ejpam-5511	131	18	≤	≤	NUM
ejpam-5511	131	19	b⇔	b⇔	PROPN
ejpam-5511	131	20	b	b	NOUN
ejpam-5511	131	21	|	|	ADV
ejpam-5511	131	22	a.	a.	NOUN
ejpam-5511	131	23	here	here	ADV
ejpam-5511	131	24	,	,	PUNCT
ejpam-5511	131	25	b|a	b|a	PROPN
ejpam-5511	131	26	means	mean	VERB
ejpam-5511	131	27	b	b	NOUN
ejpam-5511	131	28	divides	divide	NOUN
ejpam-5511	131	29	a.	a.	NOUN
ejpam-5511	131	30	we	we	PRON
ejpam-5511	131	31	have	have	VERB
ejpam-5511	131	32	that	that	PRON
ejpam-5511	131	33	(	(	PUNCT
ejpam-5511	131	34	z+	z+	X
ejpam-5511	131	35	,	,	PUNCT
ejpam-5511	131	36	[	[	PUNCT
ejpam-5511	131	37	]	]	X
ejpam-5511	131	38	,	,	PUNCT
ejpam-5511	131	39	≤	≤	NUM
ejpam-5511	131	40	)	)	PUNCT
ejpam-5511	131	41	is	be	AUX
ejpam-5511	131	42	a	a	DET
ejpam-5511	131	43	commutative	commutative	ADJ
ejpam-5511	131	44	n.p.o	n.p.o	NOUN
ejpam-5511	131	45	.	.	PUNCT
ejpam-5511	132	1	ternary	ternary	PROPN
ejpam-5511	132	2	semigroup	semigroup	NOUN
ejpam-5511	132	3	with	with	ADP
ejpam-5511	132	4	1	1	NUM
ejpam-5511	132	5	as	as	ADP
ejpam-5511	132	6	its	its	PRON
ejpam-5511	132	7	greatest	great	ADJ
ejpam-5511	132	8	element	element	NOUN
ejpam-5511	132	9	.	.	PUNCT
ejpam-5511	133	1	indeed	indeed	ADV
ejpam-5511	133	2	:	:	PUNCT
ejpam-5511	133	3	it	it	PRON
ejpam-5511	133	4	is	be	AUX
ejpam-5511	133	5	easy	easy	ADJ
ejpam-5511	133	6	to	to	PART
ejpam-5511	133	7	see	see	VERB
ejpam-5511	133	8	that	that	PRON
ejpam-5511	133	9	(	(	PUNCT
ejpam-5511	133	10	z+	z+	X
ejpam-5511	133	11	,	,	PUNCT
ejpam-5511	133	12	[	[	PUNCT
ejpam-5511	133	13	]	]	X
ejpam-5511	133	14	)	)	PUNCT
ejpam-5511	133	15	is	be	AUX
ejpam-5511	133	16	a	a	DET
ejpam-5511	133	17	commutative	commutative	ADJ
ejpam-5511	133	18	ternary	ternary	ADJ
ejpam-5511	133	19	semigroup	semigroup	NOUN
ejpam-5511	133	20	.	.	PUNCT
ejpam-5511	134	1	let	let	VERB
ejpam-5511	134	2	x	x	PRON
ejpam-5511	134	3	,	,	PUNCT
ejpam-5511	134	4	y	y	PROPN
ejpam-5511	134	5	,	,	PUNCT
ejpam-5511	134	6	u	u	NOUN
ejpam-5511	134	7	,	,	PUNCT
ejpam-5511	134	8	v	v	PROPN
ejpam-5511	134	9	∈	∈	NOUN
ejpam-5511	134	10	z+	z+	NUM
ejpam-5511	134	11	with	with	ADP
ejpam-5511	134	12	x	x	SYM
ejpam-5511	134	13	≤	≤	X
ejpam-5511	134	14	y.	y.	NOUN
ejpam-5511	134	15	since	since	SCONJ
ejpam-5511	134	16	y	y	PROPN
ejpam-5511	134	17	|x	|x	PROPN
ejpam-5511	134	18	,	,	PUNCT
ejpam-5511	134	19	there	there	PRON
ejpam-5511	134	20	exists	exist	VERB
ejpam-5511	134	21	q	q	PROPN
ejpam-5511	134	22	∈	∈	PROPN
ejpam-5511	134	23	z+	z+	NUM
ejpam-5511	135	1	such	such	ADJ
ejpam-5511	135	2	that	that	SCONJ
ejpam-5511	135	3	x	x	X
ejpam-5511	135	4	=	=	SYM
ejpam-5511	135	5	qy	qy	PROPN
ejpam-5511	135	6	.	.	PROPN
ejpam-5511	136	1	from	from	ADP
ejpam-5511	136	2	xuv	xuv	PROPN
ejpam-5511	136	3	=	=	X
ejpam-5511	136	4	q(yuv	q(yuv	PROPN
ejpam-5511	136	5	)	)	PUNCT
ejpam-5511	136	6	,	,	PUNCT
ejpam-5511	136	7	it	it	PRON
ejpam-5511	136	8	follows	follow	VERB
ejpam-5511	136	9	that	that	SCONJ
ejpam-5511	136	10	yuv	yuv	PROPN
ejpam-5511	136	11	|xuv	|xuv	NOUN
ejpam-5511	136	12	.	.	PUNCT
ejpam-5511	137	1	hence	hence	ADV
ejpam-5511	137	2	,	,	PUNCT
ejpam-5511	137	3	[	[	X
ejpam-5511	137	4	xuv	xuv	X
ejpam-5511	137	5	]	]	X
ejpam-5511	137	6	≤	≤	X
ejpam-5511	138	1	[	[	X
ejpam-5511	138	2	yuv	yuv	X
ejpam-5511	138	3	]	]	PUNCT
ejpam-5511	138	4	.	.	PUNCT
ejpam-5511	139	1	similarly	similarly	ADV
ejpam-5511	139	2	,	,	PUNCT
ejpam-5511	139	3	we	we	PRON
ejpam-5511	139	4	get	get	VERB
ejpam-5511	139	5	[	[	X
ejpam-5511	139	6	uxv	uxv	X
ejpam-5511	139	7	]	]	X
ejpam-5511	139	8	≤	≤	NOUN
ejpam-5511	140	1	[	[	X
ejpam-5511	140	2	uyv	uyv	X
ejpam-5511	140	3	]	]	X
ejpam-5511	140	4	and	and	CCONJ
ejpam-5511	140	5	[	[	X
ejpam-5511	140	6	uvx	uvx	X
ejpam-5511	140	7	]	]	X
ejpam-5511	140	8	≤	≤	NOUN
ejpam-5511	141	1	[	[	X
ejpam-5511	141	2	uvy	uvy	NOUN
ejpam-5511	141	3	]	]	X
ejpam-5511	141	4	.	.	PUNCT
ejpam-5511	142	1	let	let	VERB
ejpam-5511	142	2	x	x	PRON
ejpam-5511	142	3	,	,	PUNCT
ejpam-5511	142	4	y	y	PROPN
ejpam-5511	142	5	,	,	PUNCT
ejpam-5511	142	6	z	z	PROPN
ejpam-5511	142	7	∈	∈	PROPN
ejpam-5511	142	8	z+	z+	PUNCT
ejpam-5511	142	9	.	.	PUNCT
ejpam-5511	143	1	since	since	SCONJ
ejpam-5511	143	2	xyz	xyz	PROPN
ejpam-5511	143	3	=	=	SYM
ejpam-5511	143	4	xyz	xyz	PROPN
ejpam-5511	143	5	,	,	PUNCT
ejpam-5511	143	6	x	x	PRON
ejpam-5511	143	7	|xyz	|xyz	NOUN
ejpam-5511	143	8	,	,	PUNCT
ejpam-5511	143	9	and	and	CCONJ
ejpam-5511	144	1	so	so	ADV
ejpam-5511	145	1	[	[	X
ejpam-5511	145	2	xyz	xyz	X
ejpam-5511	145	3	]	]	X
ejpam-5511	145	4	≤	≤	NUM
ejpam-5511	145	5	x.	x.	NOUN
ejpam-5511	145	6	similarly	similarly	ADV
ejpam-5511	145	7	,	,	PUNCT
ejpam-5511	145	8	we	we	PRON
ejpam-5511	145	9	get	get	VERB
ejpam-5511	145	10	[	[	X
ejpam-5511	145	11	xyz	xyz	X
ejpam-5511	145	12	]	]	X
ejpam-5511	145	13	≤	≤	NUM
ejpam-5511	145	14	y	y	PROPN
ejpam-5511	145	15	and	and	CCONJ
ejpam-5511	145	16	[	[	X
ejpam-5511	145	17	xyz	xyz	X
ejpam-5511	145	18	]	]	X
ejpam-5511	145	19	≤	≤	NUM
ejpam-5511	145	20	z.	z.	PROPN
ejpam-5511	146	1	since	since	SCONJ
ejpam-5511	146	2	1	1	NUM
ejpam-5511	146	3	|x	|x	NOUN
ejpam-5511	146	4	for	for	ADP
ejpam-5511	146	5	all	all	DET
ejpam-5511	146	6	x	x	SYM
ejpam-5511	146	7	∈	∈	PROPN
ejpam-5511	146	8	z+	z+	NUM
ejpam-5511	146	9	,	,	PUNCT
ejpam-5511	146	10	x	x	SYM
ejpam-5511	146	11	≤	≤	ADV
ejpam-5511	146	12	1	1	NUM
ejpam-5511	146	13	for	for	ADP
ejpam-5511	146	14	all	all	DET
ejpam-5511	146	15	x	x	SYM
ejpam-5511	146	16	∈	∈	PROPN
ejpam-5511	146	17	z+	z+	NUM
ejpam-5511	146	18	.	.	PUNCT
ejpam-5511	147	1	thus	thus	ADV
ejpam-5511	147	2	,	,	PUNCT
ejpam-5511	147	3	1	1	NUM
ejpam-5511	147	4	is	be	AUX
ejpam-5511	147	5	the	the	DET
ejpam-5511	147	6	greatest	great	ADJ
ejpam-5511	147	7	element	element	NOUN
ejpam-5511	147	8	.	.	PUNCT
ejpam-5511	148	1	moreover	moreover	ADV
ejpam-5511	148	2	,	,	PUNCT
ejpam-5511	148	3	we	we	PRON
ejpam-5511	148	4	have	have	VERB
ejpam-5511	148	5	the	the	DET
ejpam-5511	148	6	ternary	ternary	ADJ
ejpam-5511	148	7	implication	implication	NOUN
ejpam-5511	148	8	on	on	ADP
ejpam-5511	148	9	z+	z+	NUM
ejpam-5511	148	10	defined	define	VERB
ejpam-5511	148	11	by	by	ADP
ejpam-5511	148	12	[	[	X
ejpam-5511	148	13	xyz]∗	xyz]∗	X
ejpam-5511	148	14	=	=	SYM
ejpam-5511	148	15	z	z	NOUN
ejpam-5511	148	16	gcd(xy	gcd(xy	NOUN
ejpam-5511	148	17	,	,	PUNCT
ejpam-5511	148	18	z	z	NOUN
ejpam-5511	148	19	)	)	PUNCT
ejpam-5511	148	20	for	for	ADP
ejpam-5511	148	21	all	all	DET
ejpam-5511	148	22	x	x	NOUN
ejpam-5511	148	23	,	,	PUNCT
ejpam-5511	148	24	y	y	PROPN
ejpam-5511	148	25	,	,	PUNCT
ejpam-5511	148	26	z	z	PROPN
ejpam-5511	148	27	∈	∈	PROPN
ejpam-5511	148	28	z+	z+	NUM
ejpam-5511	148	29	.	.	PUNCT
ejpam-5511	148	30	to	to	PART
ejpam-5511	148	31	see	see	VERB
ejpam-5511	148	32	this	this	PRON
ejpam-5511	148	33	,	,	PUNCT
ejpam-5511	148	34	let	let	VERB
ejpam-5511	148	35	x	x	PRON
ejpam-5511	148	36	,	,	PUNCT
ejpam-5511	148	37	y	y	PROPN
ejpam-5511	148	38	,	,	PUNCT
ejpam-5511	148	39	z	z	PROPN
ejpam-5511	148	40	,	,	PUNCT
ejpam-5511	148	41	u	u	PROPN
ejpam-5511	148	42	∈	∈	PROPN
ejpam-5511	148	43	z+	z+	NUM
ejpam-5511	148	44	with	with	ADP
ejpam-5511	148	45	gcd(xy	gcd(xy	NOUN
ejpam-5511	148	46	,	,	PUNCT
ejpam-5511	148	47	z	z	NOUN
ejpam-5511	148	48	)	)	PUNCT
ejpam-5511	148	49	=	=	SYM
ejpam-5511	148	50	d.	d.	PROPN
ejpam-5511	148	51	assume	assume	VERB
ejpam-5511	148	52	that	that	SCONJ
ejpam-5511	148	53	[	[	X
ejpam-5511	148	54	uxy	uxy	X
ejpam-5511	148	55	]	]	X
ejpam-5511	148	56	≤	≤	ADJ
ejpam-5511	148	57	z	z	PROPN
ejpam-5511	148	58	;	;	PUNCT
ejpam-5511	148	59	k.	k.	PROPN
ejpam-5511	148	60	nakwan	nakwan	PROPN
ejpam-5511	148	61	,	,	PUNCT
ejpam-5511	148	62	p.	p.	PROPN
ejpam-5511	148	63	luangchaisri	luangchaisri	VERB
ejpam-5511	148	64	,	,	PUNCT
ejpam-5511	148	65	t.	t.	PROPN
ejpam-5511	148	66	changphas	changphas	PROPN
ejpam-5511	148	67	/	/	SYM
ejpam-5511	148	68	eur	eur	PROPN
ejpam-5511	148	69	.	.	PUNCT
ejpam-5511	149	1	j.	j.	PROPN
ejpam-5511	149	2	pure	pure	PROPN
ejpam-5511	149	3	appl	appl	PROPN
ejpam-5511	149	4	.	.	PROPN
ejpam-5511	149	5	math	math	PROPN
ejpam-5511	149	6	,	,	PUNCT
ejpam-5511	149	7	17	17	NUM
ejpam-5511	149	8	(	(	PUNCT
ejpam-5511	149	9	4	4	NUM
ejpam-5511	149	10	)	)	PUNCT
ejpam-5511	149	11	(	(	PUNCT
ejpam-5511	149	12	2024	2024	NUM
ejpam-5511	149	13	)	)	PUNCT
ejpam-5511	149	14	,	,	PUNCT
ejpam-5511	149	15	4180	4180	NUM
ejpam-5511	149	16	-	-	SYM
ejpam-5511	149	17	4194	4194	NUM
ejpam-5511	149	18	4184	4184	NUM
ejpam-5511	150	1	then	then	ADV
ejpam-5511	150	2	z	z	PROPN
ejpam-5511	150	3	d	d	PROPN
ejpam-5511	150	4	|u	|u	PROPN
ejpam-5511	150	5	xy	xy	PROPN
ejpam-5511	150	6	d	d	X
ejpam-5511	150	7	.	.	PUNCT
ejpam-5511	151	1	since	since	SCONJ
ejpam-5511	151	2	gcd(xyd	gcd(xyd	ADJ
ejpam-5511	151	3	,	,	PUNCT
ejpam-5511	151	4	z	z	NOUN
ejpam-5511	151	5	d	d	NOUN
ejpam-5511	151	6	)	)	PUNCT
ejpam-5511	151	7	=	=	SYM
ejpam-5511	151	8	1	1	NUM
ejpam-5511	151	9	,	,	PUNCT
ejpam-5511	151	10	z	z	NOUN
ejpam-5511	151	11	d	d	X
ejpam-5511	151	12	|u	|u	ADJ
ejpam-5511	151	13	.	.	PUNCT
ejpam-5511	151	14	therefore	therefore	ADV
ejpam-5511	151	15	,	,	PUNCT
ejpam-5511	151	16	u	u	NOUN
ejpam-5511	151	17	≤	≤	NOUN
ejpam-5511	151	18	z	z	NOUN
ejpam-5511	151	19	d	d	NOUN
ejpam-5511	151	20	.	.	PUNCT
ejpam-5511	152	1	conversely	conversely	ADV
ejpam-5511	152	2	,	,	PUNCT
ejpam-5511	152	3	assume	assume	VERB
ejpam-5511	152	4	that	that	SCONJ
ejpam-5511	152	5	u	u	PROPN
ejpam-5511	152	6	≤	≤	X
ejpam-5511	152	7	z	z	NOUN
ejpam-5511	152	8	d	d	NOUN
ejpam-5511	152	9	.	.	PUNCT
ejpam-5511	153	1	then	then	ADV
ejpam-5511	153	2	there	there	PRON
ejpam-5511	153	3	exists	exist	VERB
ejpam-5511	153	4	p	p	PROPN
ejpam-5511	153	5	∈	∈	PROPN
ejpam-5511	153	6	z+	z+	NUM
ejpam-5511	153	7	such	such	ADJ
ejpam-5511	153	8	that	that	DET
ejpam-5511	153	9	u	u	NOUN
ejpam-5511	153	10	=	=	PROPN
ejpam-5511	153	11	p	p	X
ejpam-5511	153	12	zd	zd	PROPN
ejpam-5511	153	13	,	,	PUNCT
ejpam-5511	153	14	and	and	CCONJ
ejpam-5511	153	15	then	then	ADV
ejpam-5511	153	16	uxy	uxy	PROPN
ejpam-5511	153	17	=	=	SYM
ejpam-5511	153	18	(	(	PUNCT
ejpam-5511	153	19	pxyd	pxyd	PROPN
ejpam-5511	153	20	)	)	PUNCT
ejpam-5511	154	1	z.	z.	PROPN
ejpam-5511	155	1	this	this	PRON
ejpam-5511	155	2	implies	imply	VERB
ejpam-5511	155	3	that	that	SCONJ
ejpam-5511	155	4	z	z	NOUN
ejpam-5511	155	5	|uxy	|uxy	PROPN
ejpam-5511	155	6	,	,	PUNCT
ejpam-5511	155	7	that	that	ADV
ejpam-5511	155	8	is	is	ADV
ejpam-5511	155	9	,	,	PUNCT
ejpam-5511	155	10	[	[	X
ejpam-5511	155	11	uxy	uxy	X
ejpam-5511	155	12	]	]	X
ejpam-5511	155	13	≤	≤	NUM
ejpam-5511	155	14	z.	z.	PROPN
ejpam-5511	156	1	the	the	DET
ejpam-5511	156	2	following	follow	VERB
ejpam-5511	156	3	theorem	theorem	NOUN
ejpam-5511	156	4	shows	show	VERB
ejpam-5511	156	5	that	that	SCONJ
ejpam-5511	156	6	an	an	DET
ejpam-5511	156	7	implicative	implicative	ADJ
ejpam-5511	156	8	n.p.o	n.p.o	NOUN
ejpam-5511	156	9	.	.	PUNCT
ejpam-5511	157	1	ternary	ternary	ADJ
ejpam-5511	157	2	semigroup	semigroup	PROPN
ejpam-5511	157	3	always	always	ADV
ejpam-5511	157	4	contains	contain	VERB
ejpam-5511	157	5	the	the	DET
ejpam-5511	157	6	greatest	great	ADJ
ejpam-5511	157	7	element	element	NOUN
ejpam-5511	157	8	.	.	PUNCT
ejpam-5511	158	1	theorem	theorem	NOUN
ejpam-5511	158	2	1	1	NUM
ejpam-5511	158	3	.	.	PUNCT
ejpam-5511	159	1	let	let	AUX
ejpam-5511	159	2	(	(	PUNCT
ejpam-5511	159	3	t	t	NOUN
ejpam-5511	159	4	,	,	PUNCT
ejpam-5511	159	5	[	[	PUNCT
ejpam-5511	159	6	]	]	X
ejpam-5511	159	7	,	,	PUNCT
ejpam-5511	159	8	≤	≤	NUM
ejpam-5511	159	9	,	,	PUNCT
ejpam-5511	159	10	[	[	PUNCT
ejpam-5511	159	11	]	]	X
ejpam-5511	159	12	∗	∗	NOUN
ejpam-5511	159	13	)	)	PUNCT
ejpam-5511	159	14	be	be	VERB
ejpam-5511	159	15	an	an	DET
ejpam-5511	159	16	implicative	implicative	ADJ
ejpam-5511	159	17	n.p.o	n.p.o	NOUN
ejpam-5511	159	18	.	.	PUNCT
ejpam-5511	160	1	ternary	ternary	PROPN
ejpam-5511	160	2	semigroup	semigroup	PROPN
ejpam-5511	160	3	.	.	PUNCT
ejpam-5511	161	1	then	then	ADV
ejpam-5511	161	2	the	the	DET
ejpam-5511	161	3	following	follow	VERB
ejpam-5511	161	4	properties	property	NOUN
ejpam-5511	161	5	hold	hold	VERB
ejpam-5511	161	6	:	:	PUNCT
ejpam-5511	161	7	(	(	PUNCT
ejpam-5511	161	8	1	1	X
ejpam-5511	161	9	)	)	PUNCT
ejpam-5511	161	10	x	x	SYM
ejpam-5511	161	11	≤	≤	NOUN
ejpam-5511	162	1	[	[	X
ejpam-5511	162	2	xxx]∗	xxx]∗	X
ejpam-5511	162	3	;	;	PUNCT
ejpam-5511	162	4	(	(	PUNCT
ejpam-5511	162	5	2	2	X
ejpam-5511	162	6	)	)	PUNCT
ejpam-5511	163	1	[	[	X
ejpam-5511	163	2	xxx]∗	xxx]∗	X
ejpam-5511	163	3	=	=	PUNCT
ejpam-5511	163	4	[	[	X
ejpam-5511	163	5	yyy]∗	yyy]∗	NOUN
ejpam-5511	163	6	;	;	PUNCT
ejpam-5511	163	7	(	(	PUNCT
ejpam-5511	163	8	3	3	X
ejpam-5511	163	9	)	)	PUNCT
ejpam-5511	163	10	t	t	NOUN
ejpam-5511	163	11	contains	contain	VERB
ejpam-5511	163	12	the	the	DET
ejpam-5511	163	13	greatest	great	ADJ
ejpam-5511	163	14	element	element	NOUN
ejpam-5511	163	15	,	,	PUNCT
ejpam-5511	163	16	namely	namely	ADV
ejpam-5511	163	17	[	[	X
ejpam-5511	163	18	xxx]∗	xxx]∗	NUM
ejpam-5511	163	19	,	,	PUNCT
ejpam-5511	163	20	for	for	ADP
ejpam-5511	163	21	any	any	DET
ejpam-5511	163	22	x	x	NOUN
ejpam-5511	163	23	,	,	PUNCT
ejpam-5511	163	24	y	y	PROPN
ejpam-5511	163	25	∈	∈	PROPN
ejpam-5511	163	26	t	t	PROPN
ejpam-5511	163	27	.	.	PUNCT
ejpam-5511	164	1	proof	proof	NOUN
ejpam-5511	164	2	.	.	PUNCT
ejpam-5511	165	1	as	as	ADP
ejpam-5511	165	2	[	[	X
ejpam-5511	165	3	xxx	xxx	X
ejpam-5511	165	4	]	]	X
ejpam-5511	165	5	≤	≤	NUM
ejpam-5511	165	6	x	x	X
ejpam-5511	165	7	,	,	PUNCT
ejpam-5511	165	8	x	x	SYM
ejpam-5511	165	9	≤	≤	NOUN
ejpam-5511	166	1	[	[	X
ejpam-5511	166	2	xxx]∗	xxx]∗	X
ejpam-5511	166	3	,	,	PUNCT
ejpam-5511	166	4	so	so	CCONJ
ejpam-5511	166	5	(	(	PUNCT
ejpam-5511	166	6	1	1	X
ejpam-5511	166	7	)	)	PUNCT
ejpam-5511	166	8	is	be	AUX
ejpam-5511	166	9	hold	hold	NOUN
ejpam-5511	166	10	.	.	PUNCT
ejpam-5511	167	1	since	since	SCONJ
ejpam-5511	167	2	[	[	X
ejpam-5511	167	3	[	[	X
ejpam-5511	167	4	xxx]∗yy	xxx]∗yy	X
ejpam-5511	167	5	]	]	X
ejpam-5511	167	6	≤	≤	NUM
ejpam-5511	167	7	y	y	NOUN
ejpam-5511	167	8	,	,	PUNCT
ejpam-5511	167	9	then	then	ADV
ejpam-5511	167	10	[	[	X
ejpam-5511	167	11	xxx]∗	xxx]∗	X
ejpam-5511	167	12	≤	≤	NOUN
ejpam-5511	168	1	[	[	X
ejpam-5511	168	2	yyy]∗.	yyy]∗.	NOUN
ejpam-5511	168	3	similarly	similarly	ADV
ejpam-5511	168	4	,	,	PUNCT
ejpam-5511	168	5	[	[	X
ejpam-5511	168	6	yyy]∗	yyy]∗	NOUN
ejpam-5511	168	7	≤	≤	X
ejpam-5511	169	1	[	[	X
ejpam-5511	169	2	xxx]∗.	xxx]∗.	PROPN
ejpam-5511	169	3	thus	thus	ADV
ejpam-5511	169	4	,	,	PUNCT
ejpam-5511	169	5	(	(	PUNCT
ejpam-5511	169	6	2	2	X
ejpam-5511	169	7	)	)	PUNCT
ejpam-5511	169	8	holds	hold	NOUN
ejpam-5511	169	9	.	.	PUNCT
ejpam-5511	170	1	by	by	ADP
ejpam-5511	170	2	y	y	PROPN
ejpam-5511	170	3	≤	≤	NOUN
ejpam-5511	171	1	[	[	X
ejpam-5511	171	2	yyy]∗	yyy]∗	NOUN
ejpam-5511	171	3	≤	≤	X
ejpam-5511	172	1	[	[	X
ejpam-5511	172	2	xxx]∗	xxx]∗	NUM
ejpam-5511	172	3	,	,	PUNCT
ejpam-5511	172	4	it	it	PRON
ejpam-5511	172	5	follows	follow	VERB
ejpam-5511	172	6	that	that	SCONJ
ejpam-5511	172	7	t	t	PROPN
ejpam-5511	172	8	contains	contain	VERB
ejpam-5511	172	9	greatest	great	ADJ
ejpam-5511	172	10	element	element	NOUN
ejpam-5511	172	11	,	,	PUNCT
ejpam-5511	172	12	namely	namely	ADV
ejpam-5511	172	13	[	[	X
ejpam-5511	172	14	xxx]∗.	xxx]∗.	PROPN
ejpam-5511	172	15	hence	hence	ADV
ejpam-5511	172	16	,	,	PUNCT
ejpam-5511	172	17	(	(	PUNCT
ejpam-5511	172	18	3	3	X
ejpam-5511	172	19	)	)	PUNCT
ejpam-5511	172	20	holds	hold	VERB
ejpam-5511	172	21	.	.	PUNCT
ejpam-5511	173	1	let	let	VERB
ejpam-5511	173	2	1	1	NUM
ejpam-5511	173	3	be	be	AUX
ejpam-5511	173	4	the	the	DET
ejpam-5511	173	5	greatest	great	ADJ
ejpam-5511	173	6	element	element	NOUN
ejpam-5511	173	7	of	of	ADP
ejpam-5511	173	8	an	an	DET
ejpam-5511	173	9	n.p.o	n.p.o	NOUN
ejpam-5511	173	10	.	.	PUNCT
ejpam-5511	174	1	ternary	ternary	ADJ
ejpam-5511	174	2	semigroup	semigroup	PROPN
ejpam-5511	174	3	(	(	PUNCT
ejpam-5511	174	4	t	t	PROPN
ejpam-5511	174	5	,	,	PUNCT
ejpam-5511	174	6	[	[	PUNCT
ejpam-5511	174	7	]	]	X
ejpam-5511	174	8	,	,	PUNCT
ejpam-5511	174	9	≤	≤	NUM
ejpam-5511	174	10	,	,	PUNCT
ejpam-5511	174	11	[	[	PUNCT
ejpam-5511	174	12	]	]	X
ejpam-5511	174	13	∗	∗	NOUN
ejpam-5511	174	14	)	)	PUNCT
ejpam-5511	174	15	if	if	SCONJ
ejpam-5511	174	16	exists	exist	VERB
ejpam-5511	174	17	.	.	PUNCT
ejpam-5511	175	1	it	it	PRON
ejpam-5511	175	2	is	be	AUX
ejpam-5511	175	3	observed	observe	VERB
ejpam-5511	175	4	that	that	SCONJ
ejpam-5511	175	5	if	if	SCONJ
ejpam-5511	175	6	1	1	NUM
ejpam-5511	175	7	is	be	AUX
ejpam-5511	175	8	the	the	DET
ejpam-5511	175	9	multiplicative	multiplicative	ADJ
ejpam-5511	175	10	identity	identity	NOUN
ejpam-5511	175	11	then	then	ADV
ejpam-5511	175	12	it	it	PRON
ejpam-5511	175	13	can	can	AUX
ejpam-5511	175	14	be	be	AUX
ejpam-5511	175	15	verified	verify	VERB
ejpam-5511	175	16	that	that	SCONJ
ejpam-5511	175	17	[	[	X
ejpam-5511	175	18	xyz	xyz	X
ejpam-5511	175	19	]	]	X
ejpam-5511	175	20	=	=	SYM
ejpam-5511	175	21	1	1	NUM
ejpam-5511	175	22	if	if	SCONJ
ejpam-5511	175	23	and	and	CCONJ
ejpam-5511	175	24	only	only	ADV
ejpam-5511	175	25	if	if	SCONJ
ejpam-5511	175	26	x	x	NOUN
ejpam-5511	175	27	=	=	PUNCT
ejpam-5511	175	28	y	y	NOUN
ejpam-5511	175	29	=	=	PUNCT
ejpam-5511	175	30	z	z	NOUN
ejpam-5511	175	31	=	=	SYM
ejpam-5511	175	32	1	1	NUM
ejpam-5511	175	33	for	for	ADP
ejpam-5511	175	34	any	any	DET
ejpam-5511	175	35	x	x	NOUN
ejpam-5511	175	36	,	,	PUNCT
ejpam-5511	175	37	y	y	PROPN
ejpam-5511	175	38	,	,	PUNCT
ejpam-5511	175	39	z	z	PROPN
ejpam-5511	175	40	∈	∈	PROPN
ejpam-5511	175	41	t	t	PROPN
ejpam-5511	175	42	.	.	PUNCT
ejpam-5511	176	1	indeed	indeed	ADV
ejpam-5511	176	2	,	,	PUNCT
ejpam-5511	176	3	if	if	SCONJ
ejpam-5511	176	4	x	x	PROPN
ejpam-5511	176	5	,	,	PUNCT
ejpam-5511	176	6	y	y	PROPN
ejpam-5511	176	7	,	,	PUNCT
ejpam-5511	176	8	z	z	PROPN
ejpam-5511	176	9	∈	∈	PROPN
ejpam-5511	176	10	t	t	NOUN
ejpam-5511	176	11	such	such	ADJ
ejpam-5511	176	12	that	that	SCONJ
ejpam-5511	177	1	[	[	X
ejpam-5511	177	2	xyz	xyz	X
ejpam-5511	177	3	]	]	X
ejpam-5511	177	4	=	=	SYM
ejpam-5511	177	5	1	1	NUM
ejpam-5511	177	6	then	then	ADV
ejpam-5511	177	7	1	1	NUM
ejpam-5511	177	8	=	=	SYM
ejpam-5511	178	1	[	[	X
ejpam-5511	178	2	xyz	xyz	X
ejpam-5511	178	3	]	]	X
ejpam-5511	178	4	≤	≤	NUM
ejpam-5511	178	5	x	x	SYM
ejpam-5511	178	6	≤	≤	NUM
ejpam-5511	178	7	1	1	NUM
ejpam-5511	178	8	;	;	PUNCT
ejpam-5511	178	9	so	so	ADV
ejpam-5511	178	10	x	x	SYM
ejpam-5511	178	11	=	=	SYM
ejpam-5511	178	12	1	1	X
ejpam-5511	178	13	.	.	PUNCT
ejpam-5511	178	14	in	in	ADP
ejpam-5511	178	15	a	a	DET
ejpam-5511	178	16	similar	similar	ADJ
ejpam-5511	178	17	argument	argument	NOUN
ejpam-5511	178	18	we	we	PRON
ejpam-5511	178	19	can	can	AUX
ejpam-5511	178	20	deduce	deduce	VERB
ejpam-5511	178	21	that	that	PRON
ejpam-5511	178	22	y	y	PROPN
ejpam-5511	178	23	=	=	SYM
ejpam-5511	178	24	1	1	NUM
ejpam-5511	178	25	and	and	CCONJ
ejpam-5511	178	26	z	z	NOUN
ejpam-5511	178	27	=	=	NOUN
ejpam-5511	178	28	1	1	X
ejpam-5511	178	29	.	.	PUNCT
ejpam-5511	178	30	clearly	clearly	ADV
ejpam-5511	178	31	,	,	PUNCT
ejpam-5511	178	32	if	if	SCONJ
ejpam-5511	178	33	x	x	ADP
ejpam-5511	178	34	=	=	PUNCT
ejpam-5511	178	35	y	y	NOUN
ejpam-5511	178	36	=	=	PUNCT
ejpam-5511	179	1	z	z	NOUN
ejpam-5511	179	2	=	=	PUNCT
ejpam-5511	179	3	1	1	NUM
ejpam-5511	179	4	then	then	ADV
ejpam-5511	180	1	[	[	X
ejpam-5511	180	2	xyz	xyz	X
ejpam-5511	180	3	]	]	X
ejpam-5511	180	4	=	=	SYM
ejpam-5511	180	5	1	1	X
ejpam-5511	180	6	.	.	PUNCT
ejpam-5511	180	7	throughout	throughout	ADP
ejpam-5511	180	8	the	the	DET
ejpam-5511	180	9	rest	rest	NOUN
ejpam-5511	180	10	of	of	ADP
ejpam-5511	180	11	the	the	DET
ejpam-5511	180	12	paper	paper	NOUN
ejpam-5511	180	13	,	,	PUNCT
ejpam-5511	180	14	we	we	PRON
ejpam-5511	180	15	deal	deal	VERB
ejpam-5511	180	16	with	with	ADP
ejpam-5511	180	17	an	an	DET
ejpam-5511	180	18	implicative	implicative	ADJ
ejpam-5511	180	19	n.p.o	n.p.o	NOUN
ejpam-5511	180	20	.	.	PUNCT
ejpam-5511	181	1	ternary	ternary	PROPN
ejpam-5511	181	2	semigroup	semigroup	NOUN
ejpam-5511	181	3	with	with	ADP
ejpam-5511	181	4	1	1	NUM
ejpam-5511	181	5	which	which	PRON
ejpam-5511	181	6	is	be	AUX
ejpam-5511	181	7	both	both	CCONJ
ejpam-5511	181	8	the	the	DET
ejpam-5511	181	9	greatest	great	ADJ
ejpam-5511	181	10	element	element	NOUN
ejpam-5511	181	11	and	and	CCONJ
ejpam-5511	181	12	the	the	DET
ejpam-5511	181	13	multiplicative	multiplicative	ADJ
ejpam-5511	181	14	identity	identity	NOUN
ejpam-5511	181	15	.	.	PUNCT
ejpam-5511	182	1	the	the	DET
ejpam-5511	182	2	following	follow	VERB
ejpam-5511	182	3	theorem	theorem	NOUN
ejpam-5511	182	4	collects	collect	VERB
ejpam-5511	182	5	several	several	ADJ
ejpam-5511	182	6	properties	property	NOUN
ejpam-5511	182	7	of	of	ADP
ejpam-5511	182	8	elements	element	NOUN
ejpam-5511	182	9	of	of	ADP
ejpam-5511	182	10	implicative	implicative	ADJ
ejpam-5511	182	11	n.p.o	n.p.o	NOUN
ejpam-5511	182	12	.	.	PUNCT
ejpam-5511	183	1	ternary	ternary	ADJ
ejpam-5511	183	2	semigroups	semigroup	NOUN
ejpam-5511	183	3	.	.	PUNCT
ejpam-5511	184	1	theorem	theorem	NOUN
ejpam-5511	184	2	2	2	NUM
ejpam-5511	184	3	.	.	PUNCT
ejpam-5511	185	1	let	let	AUX
ejpam-5511	185	2	(	(	PUNCT
ejpam-5511	185	3	t	t	NOUN
ejpam-5511	185	4	,	,	PUNCT
ejpam-5511	185	5	[	[	PUNCT
ejpam-5511	185	6	]	]	X
ejpam-5511	185	7	,	,	PUNCT
ejpam-5511	185	8	≤	≤	NUM
ejpam-5511	185	9	,	,	PUNCT
ejpam-5511	185	10	[	[	PUNCT
ejpam-5511	185	11	]	]	X
ejpam-5511	185	12	∗	∗	NOUN
ejpam-5511	185	13	)	)	PUNCT
ejpam-5511	185	14	be	be	VERB
ejpam-5511	185	15	an	an	DET
ejpam-5511	185	16	implicative	implicative	ADJ
ejpam-5511	185	17	n.p.o	n.p.o	NOUN
ejpam-5511	185	18	.	.	PUNCT
ejpam-5511	186	1	ternary	ternary	PROPN
ejpam-5511	186	2	semigroup	semigroup	PROPN
ejpam-5511	186	3	.	.	PUNCT
ejpam-5511	187	1	then	then	ADV
ejpam-5511	187	2	for	for	ADP
ejpam-5511	187	3	any	any	DET
ejpam-5511	187	4	x	x	NOUN
ejpam-5511	187	5	,	,	PUNCT
ejpam-5511	187	6	y	y	PROPN
ejpam-5511	187	7	,	,	PUNCT
ejpam-5511	187	8	z	z	PROPN
ejpam-5511	187	9	,	,	PUNCT
ejpam-5511	187	10	u	u	NOUN
ejpam-5511	187	11	,	,	PUNCT
ejpam-5511	187	12	v	v	PROPN
ejpam-5511	187	13	∈	∈	PROPN
ejpam-5511	187	14	t	t	NOUN
ejpam-5511	187	15	,	,	PUNCT
ejpam-5511	187	16	the	the	DET
ejpam-5511	187	17	following	follow	VERB
ejpam-5511	187	18	conditions	condition	NOUN
ejpam-5511	187	19	hold	hold	VERB
ejpam-5511	187	20	:	:	PUNCT
ejpam-5511	187	21	(	(	PUNCT
ejpam-5511	187	22	1	1	X
ejpam-5511	187	23	)	)	PUNCT
ejpam-5511	187	24	x	x	SYM
ejpam-5511	187	25	≤	≤	NUM
ejpam-5511	187	26	1	1	NUM
ejpam-5511	187	27	,	,	PUNCT
ejpam-5511	187	28	[	[	X
ejpam-5511	187	29	xxx]∗	xxx]∗	X
ejpam-5511	187	30	=	=	SYM
ejpam-5511	187	31	1	1	NUM
ejpam-5511	187	32	,	,	PUNCT
ejpam-5511	187	33	x	x	PUNCT
ejpam-5511	187	34	=	=	PUNCT
ejpam-5511	188	1	[	[	X
ejpam-5511	188	2	11x]∗	11x]∗	NUM
ejpam-5511	188	3	;	;	PUNCT
ejpam-5511	188	4	(	(	PUNCT
ejpam-5511	188	5	2	2	X
ejpam-5511	188	6	)	)	PUNCT
ejpam-5511	188	7	x	x	SYM
ejpam-5511	188	8	≤	≤	NOUN
ejpam-5511	189	1	[	[	X
ejpam-5511	189	2	yz[xyz]]∗	yz[xyz]]∗	NOUN
ejpam-5511	189	3	;	;	PUNCT
ejpam-5511	189	4	(	(	PUNCT
ejpam-5511	189	5	3	3	X
ejpam-5511	189	6	)	)	PUNCT
ejpam-5511	189	7	x	x	SYM
ejpam-5511	189	8	≤	≤	PUNCT
ejpam-5511	190	1	[	[	X
ejpam-5511	190	2	xx[xxx]]∗	xx[xxx]]∗	NOUN
ejpam-5511	190	3	;	;	PUNCT
ejpam-5511	190	4	(	(	PUNCT
ejpam-5511	190	5	4	4	X
ejpam-5511	190	6	)	)	PUNCT
ejpam-5511	190	7	x	x	SYM
ejpam-5511	190	8	≤	≤	NOUN
ejpam-5511	191	1	[	[	X
ejpam-5511	191	2	yzx]∗	yzx]∗	NOUN
ejpam-5511	191	3	;	;	PUNCT
ejpam-5511	191	4	(	(	PUNCT
ejpam-5511	191	5	5	5	X
ejpam-5511	191	6	)	)	PUNCT
ejpam-5511	191	7	if	if	SCONJ
ejpam-5511	191	8	x	x	PROPN
ejpam-5511	191	9	≤	≤	NOUN
ejpam-5511	191	10	y	y	NOUN
ejpam-5511	191	11	,	,	PUNCT
ejpam-5511	191	12	then	then	ADV
ejpam-5511	191	13	[	[	X
ejpam-5511	191	14	yuv]∗	yuv]∗	PROPN
ejpam-5511	191	15	≤	≤	X
ejpam-5511	192	1	[	[	X
ejpam-5511	192	2	xuv]∗	xuv]∗	NOUN
ejpam-5511	192	3	and	and	CCONJ
ejpam-5511	192	4	[	[	X
ejpam-5511	192	5	uvx]∗	uvx]∗	X
ejpam-5511	192	6	≤	≤	X
ejpam-5511	193	1	[	[	X
ejpam-5511	193	2	uvy]∗	uvy]∗	NOUN
ejpam-5511	193	3	;	;	PUNCT
ejpam-5511	193	4	(	(	PUNCT
ejpam-5511	193	5	6	6	NUM
ejpam-5511	193	6	)	)	PUNCT
ejpam-5511	193	7	x	x	PUNCT
ejpam-5511	193	8	≤	≤	PROPN
ejpam-5511	193	9	y	y	PROPN
ejpam-5511	193	10	⇔	⇔	X
ejpam-5511	193	11	[	[	X
ejpam-5511	193	12	x1y]∗	x1y]∗	NOUN
ejpam-5511	193	13	=	=	SYM
ejpam-5511	193	14	1	1	NUM
ejpam-5511	193	15	⇔	⇔	X
ejpam-5511	193	16	[	[	X
ejpam-5511	193	17	1xy]∗	1xy]∗	NUM
ejpam-5511	193	18	=	=	SYM
ejpam-5511	193	19	1	1	NUM
ejpam-5511	193	20	;	;	PUNCT
ejpam-5511	193	21	(	(	PUNCT
ejpam-5511	193	22	7	7	X
ejpam-5511	193	23	)	)	PUNCT
ejpam-5511	194	1	[	[	X
ejpam-5511	194	2	xy[zuv]∗]∗	xy[zuv]∗]∗	X
ejpam-5511	194	3	=	=	PUNCT
ejpam-5511	195	1	[	[	X
ejpam-5511	195	2	[	[	X
ejpam-5511	195	3	xyz]uv]∗	xyz]uv]∗	X
ejpam-5511	195	4	=	=	PUNCT
ejpam-5511	196	1	[	[	X
ejpam-5511	196	2	x[yzu]v]∗.	x[yzu]v]∗.	PROPN
ejpam-5511	196	3	k.	k.	PROPN
ejpam-5511	196	4	nakwan	nakwan	PROPN
ejpam-5511	196	5	,	,	PUNCT
ejpam-5511	196	6	p.	p.	PROPN
ejpam-5511	196	7	luangchaisri	luangchaisri	VERB
ejpam-5511	196	8	,	,	PUNCT
ejpam-5511	196	9	t.	t.	PROPN
ejpam-5511	196	10	changphas	changphas	PROPN
ejpam-5511	196	11	/	/	SYM
ejpam-5511	196	12	eur	eur	PROPN
ejpam-5511	196	13	.	.	PUNCT
ejpam-5511	197	1	j.	j.	PROPN
ejpam-5511	197	2	pure	pure	PROPN
ejpam-5511	197	3	appl	appl	PROPN
ejpam-5511	197	4	.	.	PROPN
ejpam-5511	197	5	math	math	PROPN
ejpam-5511	197	6	,	,	PUNCT
ejpam-5511	197	7	17	17	NUM
ejpam-5511	197	8	(	(	PUNCT
ejpam-5511	197	9	4	4	NUM
ejpam-5511	197	10	)	)	PUNCT
ejpam-5511	197	11	(	(	PUNCT
ejpam-5511	197	12	2024	2024	NUM
ejpam-5511	197	13	)	)	PUNCT
ejpam-5511	197	14	,	,	PUNCT
ejpam-5511	197	15	4180	4180	NUM
ejpam-5511	197	16	-	-	SYM
ejpam-5511	197	17	4194	4194	NUM
ejpam-5511	197	18	4185	4185	NUM
ejpam-5511	197	19	proof	proof	NOUN
ejpam-5511	197	20	.	.	PUNCT
ejpam-5511	198	1	(	(	PUNCT
ejpam-5511	198	2	1	1	X
ejpam-5511	198	3	)	)	PUNCT
ejpam-5511	198	4	it	it	PRON
ejpam-5511	198	5	is	be	AUX
ejpam-5511	198	6	clear	clear	ADJ
ejpam-5511	198	7	that	that	SCONJ
ejpam-5511	198	8	x	x	SYM
ejpam-5511	198	9	≤	≤	ADV
ejpam-5511	198	10	1	1	NUM
ejpam-5511	198	11	and	and	CCONJ
ejpam-5511	198	12	[	[	X
ejpam-5511	198	13	xxx]∗	xxx]∗	X
ejpam-5511	198	14	=	=	SYM
ejpam-5511	198	15	1	1	X
ejpam-5511	198	16	.	.	PUNCT
ejpam-5511	199	1	as	as	ADP
ejpam-5511	199	2	[	[	X
ejpam-5511	199	3	x11	x11	X
ejpam-5511	199	4	]	]	X
ejpam-5511	199	5	=	=	PUNCT
ejpam-5511	199	6	x	x	SYM
ejpam-5511	199	7	≤	≤	NUM
ejpam-5511	199	8	x	x	PUNCT
ejpam-5511	199	9	,	,	PUNCT
ejpam-5511	199	10	we	we	PRON
ejpam-5511	199	11	get	get	VERB
ejpam-5511	199	12	that	that	PRON
ejpam-5511	199	13	x	x	X
ejpam-5511	199	14	≤	≤	X
ejpam-5511	200	1	[	[	X
ejpam-5511	200	2	11x]∗.	11x]∗.	NOUN
ejpam-5511	200	3	since	since	SCONJ
ejpam-5511	200	4	[	[	X
ejpam-5511	200	5	11x]∗	11x]∗	NUM
ejpam-5511	200	6	≤	≤	NOUN
ejpam-5511	200	7	[	[	X
ejpam-5511	200	8	11x]∗	11x]∗	NUM
ejpam-5511	200	9	,	,	PUNCT
ejpam-5511	200	10	we	we	PRON
ejpam-5511	200	11	have	have	VERB
ejpam-5511	200	12	[	[	X
ejpam-5511	200	13	11x]∗	11x]∗	NUM
ejpam-5511	200	14	=	=	SYM
ejpam-5511	201	1	[	[	X
ejpam-5511	201	2	[	[	X
ejpam-5511	201	3	11x]∗11	11x]∗11	NUM
ejpam-5511	201	4	]	]	PUNCT
ejpam-5511	201	5	≤	≤	NUM
ejpam-5511	201	6	x.	x.	NOUN
ejpam-5511	201	7	(	(	PUNCT
ejpam-5511	201	8	2	2	NUM
ejpam-5511	201	9	)	)	PUNCT
ejpam-5511	201	10	from	from	ADP
ejpam-5511	201	11	[	[	X
ejpam-5511	201	12	xyz	xyz	X
ejpam-5511	201	13	]	]	X
ejpam-5511	201	14	≤	≤	NOUN
ejpam-5511	201	15	[	[	X
ejpam-5511	201	16	xyz	xyz	X
ejpam-5511	201	17	]	]	X
ejpam-5511	201	18	,	,	PUNCT
ejpam-5511	201	19	we	we	PRON
ejpam-5511	201	20	get	get	VERB
ejpam-5511	201	21	x	x	PUNCT
ejpam-5511	201	22	≤	≤	NUM
ejpam-5511	202	1	[	[	PUNCT
ejpam-5511	202	2	yz[xyz]]∗.	yz[xyz]]∗.	NOUN
ejpam-5511	202	3	(	(	PUNCT
ejpam-5511	202	4	3	3	NUM
ejpam-5511	202	5	)	)	PUNCT
ejpam-5511	202	6	the	the	DET
ejpam-5511	202	7	assertion	assertion	NOUN
ejpam-5511	202	8	follows	follow	VERB
ejpam-5511	202	9	by	by	ADP
ejpam-5511	202	10	(	(	PUNCT
ejpam-5511	202	11	2	2	NUM
ejpam-5511	202	12	)	)	PUNCT
ejpam-5511	202	13	.	.	PUNCT
ejpam-5511	203	1	(	(	PUNCT
ejpam-5511	203	2	4	4	X
ejpam-5511	203	3	)	)	PUNCT
ejpam-5511	203	4	this	this	PRON
ejpam-5511	203	5	is	be	AUX
ejpam-5511	203	6	clear	clear	ADJ
ejpam-5511	203	7	because	because	SCONJ
ejpam-5511	203	8	[	[	X
ejpam-5511	203	9	xyz	xyz	X
ejpam-5511	203	10	]	]	X
ejpam-5511	203	11	≤	≤	NUM
ejpam-5511	203	12	x.	x.	NOUN
ejpam-5511	203	13	(	(	PUNCT
ejpam-5511	203	14	5	5	X
ejpam-5511	203	15	)	)	PUNCT
ejpam-5511	203	16	assume	assume	VERB
ejpam-5511	203	17	that	that	SCONJ
ejpam-5511	203	18	x	x	X
ejpam-5511	203	19	≤	≤	X
ejpam-5511	203	20	y.	y.	NOUN
ejpam-5511	203	21	since	since	SCONJ
ejpam-5511	203	22	[	[	X
ejpam-5511	203	23	yuv]∗	yuv]∗	PROPN
ejpam-5511	203	24	≤	≤	PROPN
ejpam-5511	204	1	[	[	X
ejpam-5511	204	2	yuv]∗	yuv]∗	PROPN
ejpam-5511	204	3	,	,	PUNCT
ejpam-5511	204	4	[	[	X
ejpam-5511	204	5	[	[	X
ejpam-5511	204	6	yuv]∗yu	yuv]∗yu	X
ejpam-5511	204	7	]	]	X
ejpam-5511	204	8	≤	≤	NUM
ejpam-5511	204	9	v.	v.	ADP
ejpam-5511	204	10	by	by	ADP
ejpam-5511	204	11	assumption	assumption	NOUN
ejpam-5511	204	12	,	,	PUNCT
ejpam-5511	204	13	it	it	PRON
ejpam-5511	204	14	follows	follow	VERB
ejpam-5511	204	15	that	that	SCONJ
ejpam-5511	204	16	[	[	X
ejpam-5511	204	17	[	[	X
ejpam-5511	204	18	yuv]∗xu	yuv]∗xu	X
ejpam-5511	204	19	]	]	X
ejpam-5511	204	20	≤	≤	PUNCT
ejpam-5511	205	1	[	[	X
ejpam-5511	205	2	[	[	X
ejpam-5511	205	3	yuv∗]yu	yuv∗]yu	NOUN
ejpam-5511	205	4	]	]	X
ejpam-5511	205	5	≤	≤	NOUN
ejpam-5511	206	1	v.	v.	CCONJ
ejpam-5511	206	2	then	then	ADV
ejpam-5511	206	3	[	[	X
ejpam-5511	206	4	yuv]∗	yuv]∗	PROPN
ejpam-5511	206	5	≤	≤	X
ejpam-5511	207	1	[	[	X
ejpam-5511	207	2	xuv]∗.	xuv]∗.	PROPN
ejpam-5511	207	3	similarly	similarly	ADV
ejpam-5511	207	4	,	,	PUNCT
ejpam-5511	207	5	if	if	SCONJ
ejpam-5511	207	6	x	x	ADP
ejpam-5511	207	7	≤	≤	NOUN
ejpam-5511	207	8	y	y	NOUN
ejpam-5511	207	9	,	,	PUNCT
ejpam-5511	207	10	then	then	ADV
ejpam-5511	207	11	[	[	X
ejpam-5511	207	12	uvx]∗	uvx]∗	X
ejpam-5511	207	13	≤	≤	X
ejpam-5511	208	1	[	[	X
ejpam-5511	208	2	uvy]∗.	uvy]∗.	X
ejpam-5511	208	3	(	(	PUNCT
ejpam-5511	208	4	6	6	NUM
ejpam-5511	208	5	)	)	PUNCT
ejpam-5511	208	6	if	if	SCONJ
ejpam-5511	208	7	x	x	PROPN
ejpam-5511	208	8	≤	≤	NOUN
ejpam-5511	208	9	y	y	NOUN
ejpam-5511	208	10	,	,	PUNCT
ejpam-5511	208	11	then	then	ADV
ejpam-5511	208	12	[	[	X
ejpam-5511	208	13	1x1	1x1	X
ejpam-5511	208	14	]	]	X
ejpam-5511	208	15	≤	≤	NOUN
ejpam-5511	209	1	[	[	X
ejpam-5511	209	2	11y	11y	NOUN
ejpam-5511	209	3	]	]	PUNCT
ejpam-5511	209	4	.	.	PUNCT
ejpam-5511	210	1	hence	hence	ADV
ejpam-5511	210	2	,	,	PUNCT
ejpam-5511	210	3	1	1	NUM
ejpam-5511	210	4	≤	≤	NOUN
ejpam-5511	211	1	[	[	X
ejpam-5511	211	2	x1[11y]]∗	x1[11y]]∗	NOUN
ejpam-5511	211	3	=	=	SYM
ejpam-5511	211	4	[	[	X
ejpam-5511	211	5	x1y]∗	x1y]∗	NOUN
ejpam-5511	211	6	≤	≤	ADV
ejpam-5511	211	7	1	1	NUM
ejpam-5511	211	8	.	.	PUNCT
ejpam-5511	212	1	thus	thus	ADV
ejpam-5511	212	2	,	,	PUNCT
ejpam-5511	212	3	[	[	X
ejpam-5511	212	4	x1y]∗	x1y]∗	NOUN
ejpam-5511	212	5	=	=	SYM
ejpam-5511	212	6	1	1	X
ejpam-5511	212	7	.	.	PUNCT
ejpam-5511	212	8	similarly	similarly	ADV
ejpam-5511	212	9	,	,	PUNCT
ejpam-5511	212	10	if	if	SCONJ
ejpam-5511	212	11	[	[	X
ejpam-5511	212	12	x1y]∗	x1y]∗	NOUN
ejpam-5511	212	13	=	=	SYM
ejpam-5511	212	14	1	1	NUM
ejpam-5511	212	15	,	,	PUNCT
ejpam-5511	212	16	then	then	ADV
ejpam-5511	212	17	[	[	X
ejpam-5511	212	18	1xy]∗	1xy]∗	NUM
ejpam-5511	212	19	=	=	SYM
ejpam-5511	212	20	1	1	X
ejpam-5511	212	21	.	.	PUNCT
ejpam-5511	213	1	conversely	conversely	ADV
ejpam-5511	213	2	,	,	PUNCT
ejpam-5511	213	3	if	if	SCONJ
ejpam-5511	213	4	[	[	X
ejpam-5511	213	5	1xy]∗	1xy]∗	NUM
ejpam-5511	213	6	=	=	SYM
ejpam-5511	213	7	1	1	NUM
ejpam-5511	213	8	,	,	PUNCT
ejpam-5511	213	9	then	then	ADV
ejpam-5511	213	10	1	1	NUM
ejpam-5511	213	11	≤	≤	NOUN
ejpam-5511	214	1	[	[	X
ejpam-5511	214	2	1xy]∗	1xy]∗	NUM
ejpam-5511	214	3	,	,	PUNCT
ejpam-5511	214	4	and	and	CCONJ
ejpam-5511	214	5	so	so	ADV
ejpam-5511	214	6	x	x	X
ejpam-5511	214	7	=	=	PUNCT
ejpam-5511	214	8	[	[	X
ejpam-5511	214	9	11x	11x	NOUN
ejpam-5511	214	10	]	]	X
ejpam-5511	214	11	≤	≤	NUM
ejpam-5511	214	12	y.	y.	NOUN
ejpam-5511	214	13	(	(	PUNCT
ejpam-5511	214	14	7	7	X
ejpam-5511	214	15	)	)	PUNCT
ejpam-5511	214	16	let	let	VERB
ejpam-5511	214	17	s	s	NOUN
ejpam-5511	214	18	=	=	PUNCT
ejpam-5511	215	1	[	[	X
ejpam-5511	215	2	xy[zuv]∗]∗	xy[zuv]∗]∗	PROPN
ejpam-5511	215	3	and	and	CCONJ
ejpam-5511	215	4	t	t	NOUN
ejpam-5511	215	5	=	=	PUNCT
ejpam-5511	216	1	[	[	X
ejpam-5511	216	2	[	[	X
ejpam-5511	216	3	xyz]uv]∗.	xyz]uv]∗.	X
ejpam-5511	216	4	we	we	PRON
ejpam-5511	216	5	have	have	VERB
ejpam-5511	216	6	[	[	X
ejpam-5511	216	7	sxy	sxy	X
ejpam-5511	216	8	]	]	X
ejpam-5511	216	9	≤	≤	NOUN
ejpam-5511	217	1	[	[	X
ejpam-5511	217	2	zuv]∗	zuv]∗	NOUN
ejpam-5511	217	3	]	]	PUNCT
ejpam-5511	217	4	,	,	PUNCT
ejpam-5511	217	5	and	and	CCONJ
ejpam-5511	217	6	thus	thus	ADV
ejpam-5511	217	7	,	,	PUNCT
ejpam-5511	217	8	[	[	X
ejpam-5511	217	9	s[xyz]u	s[xyz]u	X
ejpam-5511	217	10	]	]	X
ejpam-5511	217	11	=	=	PUNCT
ejpam-5511	218	1	[	[	X
ejpam-5511	218	2	[	[	X
ejpam-5511	218	3	sxy]zu	sxy]zu	X
ejpam-5511	218	4	]	]	X
ejpam-5511	218	5	≤	≤	PROPN
ejpam-5511	218	6	v.	v.	ADP
ejpam-5511	218	7	hence	hence	ADV
ejpam-5511	218	8	,	,	PUNCT
ejpam-5511	218	9	s	s	VERB
ejpam-5511	218	10	≤	≤	X
ejpam-5511	219	1	[	[	X
ejpam-5511	219	2	[	[	X
ejpam-5511	219	3	xyz]uv]∗	xyz]uv]∗	X
ejpam-5511	219	4	=	=	PUNCT
ejpam-5511	219	5	t.	t.	NOUN
ejpam-5511	219	6	by	by	ADP
ejpam-5511	220	1	[	[	X
ejpam-5511	220	2	[	[	X
ejpam-5511	220	3	txy]zu	txy]zu	X
ejpam-5511	220	4	]	]	X
ejpam-5511	221	1	=	=	PUNCT
ejpam-5511	222	1	[	[	X
ejpam-5511	222	2	t[xyz]u	t[xyz]u	X
ejpam-5511	222	3	]	]	PUNCT
ejpam-5511	222	4	≤	≤	NUM
ejpam-5511	222	5	v	v	NOUN
ejpam-5511	222	6	,	,	PUNCT
ejpam-5511	222	7	it	it	PRON
ejpam-5511	222	8	follows	follow	VERB
ejpam-5511	222	9	that	that	SCONJ
ejpam-5511	222	10	[	[	X
ejpam-5511	222	11	txy	txy	X
ejpam-5511	222	12	]	]	X
ejpam-5511	222	13	≤	≤	NOUN
ejpam-5511	223	1	[	[	X
ejpam-5511	223	2	zuv]∗.	zuv]∗.	NOUN
ejpam-5511	223	3	then	then	ADV
ejpam-5511	223	4	t	t	VERB
ejpam-5511	223	5	≤	≤	X
ejpam-5511	224	1	[	[	X
ejpam-5511	224	2	xy[zuv]∗]∗	xy[zuv]∗]∗	X
ejpam-5511	224	3	=	=	SYM
ejpam-5511	224	4	s.	s.	PROPN
ejpam-5511	224	5	hence	hence	ADV
ejpam-5511	224	6	,	,	PUNCT
ejpam-5511	224	7	s	s	PART
ejpam-5511	224	8	=	=	PUNCT
ejpam-5511	224	9	t.	t.	NOUN
ejpam-5511	224	10	now	now	ADV
ejpam-5511	224	11	,	,	PUNCT
ejpam-5511	224	12	let	let	VERB
ejpam-5511	224	13	s	s	PRON
ejpam-5511	224	14	=	=	PUNCT
ejpam-5511	225	1	[	[	X
ejpam-5511	225	2	xy[zuv]∗]∗	xy[zuv]∗]∗	PROPN
ejpam-5511	225	3	and	and	CCONJ
ejpam-5511	225	4	w	w	NOUN
ejpam-5511	225	5	=	=	SYM
ejpam-5511	226	1	[	[	X
ejpam-5511	226	2	x[yzu]v]∗.	x[yzu]v]∗.	PROPN
ejpam-5511	226	3	then	then	ADV
ejpam-5511	226	4	[	[	X
ejpam-5511	226	5	sxy	sxy	X
ejpam-5511	226	6	]	]	X
ejpam-5511	226	7	≤	≤	NOUN
ejpam-5511	227	1	[	[	X
ejpam-5511	227	2	zuv]∗	zuv]∗	NOUN
ejpam-5511	227	3	]	]	PUNCT
ejpam-5511	227	4	,	,	PUNCT
ejpam-5511	227	5	and	and	CCONJ
ejpam-5511	227	6	thus	thus	ADV
ejpam-5511	227	7	,	,	PUNCT
ejpam-5511	227	8	[	[	X
ejpam-5511	227	9	sx[yzu	sx[yzu	NOUN
ejpam-5511	227	10	]	]	X
ejpam-5511	227	11	]	]	PUNCT
ejpam-5511	227	12	=	=	PUNCT
ejpam-5511	228	1	[	[	X
ejpam-5511	228	2	[	[	X
ejpam-5511	228	3	sxy]zu	sxy]zu	X
ejpam-5511	228	4	]	]	X
ejpam-5511	228	5	≤	≤	NUM
ejpam-5511	228	6	v	v	NOUN
ejpam-5511	228	7	,	,	PUNCT
ejpam-5511	228	8	so	so	SCONJ
ejpam-5511	228	9	s	s	X
ejpam-5511	228	10	≤	≤	X
ejpam-5511	229	1	[	[	X
ejpam-5511	229	2	x[yzu]v]∗	x[yzu]v]∗	X
ejpam-5511	229	3	=	=	SYM
ejpam-5511	229	4	w.	w.	PROPN
ejpam-5511	229	5	as	as	ADP
ejpam-5511	229	6	[	[	X
ejpam-5511	229	7	[	[	X
ejpam-5511	229	8	wxy]zu	wxy]zu	X
ejpam-5511	229	9	]	]	X
ejpam-5511	229	10	=	=	PUNCT
ejpam-5511	230	1	[	[	X
ejpam-5511	230	2	wx[yzu	wx[yzu	PROPN
ejpam-5511	230	3	]	]	X
ejpam-5511	230	4	]	]	X
ejpam-5511	230	5	≤	≤	NUM
ejpam-5511	230	6	v	v	NOUN
ejpam-5511	230	7	,	,	PUNCT
ejpam-5511	230	8	we	we	PRON
ejpam-5511	230	9	have	have	VERB
ejpam-5511	230	10	[	[	X
ejpam-5511	230	11	wxy	wxy	X
ejpam-5511	230	12	]	]	X
ejpam-5511	230	13	≤	≤	NOUN
ejpam-5511	231	1	[	[	X
ejpam-5511	231	2	zuv]∗.	zuv]∗.	NOUN
ejpam-5511	231	3	then	then	ADV
ejpam-5511	231	4	w	w	PROPN
ejpam-5511	231	5	≤	≤	PROPN
ejpam-5511	232	1	[	[	X
ejpam-5511	232	2	xy[zuv]∗]∗	xy[zuv]∗]∗	X
ejpam-5511	232	3	=	=	SYM
ejpam-5511	232	4	s.	s.	PROPN
ejpam-5511	232	5	thus	thus	ADV
ejpam-5511	232	6	,	,	PUNCT
ejpam-5511	232	7	s	s	PART
ejpam-5511	232	8	=	=	PUNCT
ejpam-5511	232	9	w.	w.	PROPN
ejpam-5511	232	10	3	3	NUM
ejpam-5511	232	11	.	.	PUNCT
ejpam-5511	232	12	implicative	implicative	ADJ
ejpam-5511	232	13	homomorphisms	homomorphism	NOUN
ejpam-5511	232	14	we	we	PRON
ejpam-5511	232	15	begin	begin	VERB
ejpam-5511	232	16	this	this	DET
ejpam-5511	232	17	section	section	NOUN
ejpam-5511	232	18	with	with	ADP
ejpam-5511	232	19	the	the	DET
ejpam-5511	232	20	definition	definition	NOUN
ejpam-5511	232	21	of	of	ADP
ejpam-5511	232	22	implicative	implicative	ADJ
ejpam-5511	232	23	homomorphisms	homomorphism	NOUN
ejpam-5511	232	24	between	between	ADP
ejpam-5511	232	25	implicative	implicative	ADJ
ejpam-5511	232	26	n.p.o	n.p.o	NOUN
ejpam-5511	232	27	.	.	PUNCT
ejpam-5511	233	1	ternary	ternary	ADJ
ejpam-5511	233	2	semigroups	semigroup	NOUN
ejpam-5511	233	3	.	.	PUNCT
ejpam-5511	234	1	definition	definition	NOUN
ejpam-5511	234	2	3	3	NUM
ejpam-5511	234	3	.	.	PUNCT
ejpam-5511	235	1	let	let	AUX
ejpam-5511	235	2	(	(	PUNCT
ejpam-5511	235	3	t1	t1	VERB
ejpam-5511	235	4	,	,	PUNCT
ejpam-5511	235	5	[	[	PUNCT
ejpam-5511	235	6	]	]	X
ejpam-5511	235	7	1,≤1	1,≤1	ADJ
ejpam-5511	235	8	,	,	PUNCT
ejpam-5511	235	9	[	[	PUNCT
ejpam-5511	235	10	]	]	X
ejpam-5511	235	11	∗1	∗1	X
ejpam-5511	235	12	)	)	PUNCT
ejpam-5511	235	13	and	and	CCONJ
ejpam-5511	235	14	(	(	PUNCT
ejpam-5511	235	15	t2	t2	NOUN
ejpam-5511	235	16	,	,	PUNCT
ejpam-5511	235	17	[	[	PUNCT
ejpam-5511	235	18	]	]	X
ejpam-5511	235	19	2,≤2	2,≤2	NOUN
ejpam-5511	235	20	,	,	PUNCT
ejpam-5511	235	21	[	[	PUNCT
ejpam-5511	235	22	]	]	X
ejpam-5511	235	23	∗2	∗2	NOUN
ejpam-5511	235	24	)	)	PUNCT
ejpam-5511	235	25	be	be	AUX
ejpam-5511	235	26	implicative	implicative	ADJ
ejpam-5511	235	27	n.p.o	n.p.o	NOUN
ejpam-5511	235	28	.	.	PUNCT
ejpam-5511	236	1	ternary	ternary	ADJ
ejpam-5511	236	2	semigroups	semigroup	NOUN
ejpam-5511	236	3	.	.	PUNCT
ejpam-5511	237	1	a	a	DET
ejpam-5511	237	2	mapping	mapping	NOUN
ejpam-5511	237	3	φ	φ	NOUN
ejpam-5511	237	4	:	:	PUNCT
ejpam-5511	237	5	t1	t1	NUM
ejpam-5511	237	6	−→	−→	NOUN
ejpam-5511	237	7	t2	t2	PROPN
ejpam-5511	237	8	from	from	ADP
ejpam-5511	237	9	t1	t1	NOUN
ejpam-5511	237	10	onto	onto	ADP
ejpam-5511	237	11	t2	t2	NOUN
ejpam-5511	237	12	such	such	ADJ
ejpam-5511	237	13	that	that	PRON
ejpam-5511	237	14	φ([xyz]∗1	φ([xyz]∗1	ADJ
ejpam-5511	237	15	)	)	PUNCT
ejpam-5511	237	16	=	=	PUNCT
ejpam-5511	238	1	[	[	X
ejpam-5511	238	2	φ(x)φ(y)φ(z)]∗2	φ(x)φ(y)φ(z)]∗2	NOUN
ejpam-5511	238	3	for	for	ADP
ejpam-5511	238	4	all	all	DET
ejpam-5511	238	5	x	x	NOUN
ejpam-5511	238	6	,	,	PUNCT
ejpam-5511	238	7	y	y	PROPN
ejpam-5511	238	8	,	,	PUNCT
ejpam-5511	238	9	z	z	PROPN
ejpam-5511	238	10	∈	∈	PROPN
ejpam-5511	238	11	t1	t1	NOUN
ejpam-5511	238	12	is	be	AUX
ejpam-5511	238	13	called	call	VERB
ejpam-5511	238	14	an	an	DET
ejpam-5511	238	15	implicative	implicative	ADJ
ejpam-5511	238	16	homomorphism	homomorphism	NOUN
ejpam-5511	238	17	from	from	ADP
ejpam-5511	238	18	t1	t1	NOUN
ejpam-5511	238	19	onto	onto	ADP
ejpam-5511	238	20	t2	t2	NOUN
ejpam-5511	238	21	.	.	PUNCT
ejpam-5511	239	1	to	to	PART
ejpam-5511	239	2	study	study	VERB
ejpam-5511	239	3	the	the	DET
ejpam-5511	239	4	notion	notion	NOUN
ejpam-5511	239	5	of	of	ADP
ejpam-5511	239	6	quotient	quotient	NOUN
ejpam-5511	239	7	structures	structure	NOUN
ejpam-5511	239	8	of	of	ADP
ejpam-5511	239	9	implicative	implicative	ADJ
ejpam-5511	239	10	n.p.o	n.p.o	NOUN
ejpam-5511	239	11	.	.	PUNCT
ejpam-5511	240	1	ternary	ternary	ADJ
ejpam-5511	240	2	semigroups	semigroup	NOUN
ejpam-5511	240	3	,	,	PUNCT
ejpam-5511	240	4	we	we	PRON
ejpam-5511	240	5	need	need	VERB
ejpam-5511	240	6	the	the	DET
ejpam-5511	240	7	concept	concept	NOUN
ejpam-5511	240	8	of	of	ADP
ejpam-5511	240	9	filters	filter	NOUN
ejpam-5511	240	10	.	.	PUNCT
ejpam-5511	241	1	definition	definition	NOUN
ejpam-5511	241	2	4	4	NUM
ejpam-5511	241	3	.	.	PUNCT
ejpam-5511	242	1	let	let	VERB
ejpam-5511	242	2	(	(	PUNCT
ejpam-5511	242	3	t	t	NOUN
ejpam-5511	242	4	,	,	PUNCT
ejpam-5511	242	5	[	[	PUNCT
ejpam-5511	242	6	]	]	X
ejpam-5511	242	7	,	,	PUNCT
ejpam-5511	242	8	≤	≤	NUM
ejpam-5511	242	9	)	)	PUNCT
ejpam-5511	242	10	be	be	VERB
ejpam-5511	242	11	an	an	DET
ejpam-5511	242	12	n.p.o	n.p.o	NOUN
ejpam-5511	242	13	.	.	PUNCT
ejpam-5511	243	1	ternary	ternary	PROPN
ejpam-5511	243	2	semigroup	semigroup	PROPN
ejpam-5511	243	3	.	.	PUNCT
ejpam-5511	244	1	a	a	DET
ejpam-5511	244	2	non	non	ADJ
ejpam-5511	244	3	-	-	ADJ
ejpam-5511	244	4	empty	empty	ADJ
ejpam-5511	244	5	subset	subset	NOUN
ejpam-5511	244	6	f	f	PROPN
ejpam-5511	244	7	of	of	ADP
ejpam-5511	244	8	t	t	PROPN
ejpam-5511	244	9	is	be	AUX
ejpam-5511	244	10	called	call	VERB
ejpam-5511	244	11	a	a	DET
ejpam-5511	244	12	filter	filter	NOUN
ejpam-5511	244	13	of	of	ADP
ejpam-5511	244	14	t	t	PROPN
ejpam-5511	244	15	if	if	SCONJ
ejpam-5511	244	16	the	the	DET
ejpam-5511	244	17	following	follow	VERB
ejpam-5511	244	18	coditions	codition	NOUN
ejpam-5511	244	19	hold	hold	VERB
ejpam-5511	244	20	:	:	PUNCT
ejpam-5511	244	21	(	(	PUNCT
ejpam-5511	244	22	1	1	X
ejpam-5511	244	23	)	)	PUNCT
ejpam-5511	244	24	[	[	X
ejpam-5511	244	25	xyz	xyz	X
ejpam-5511	244	26	]	]	X
ejpam-5511	244	27	∈	∈	PROPN
ejpam-5511	244	28	f	f	PROPN
ejpam-5511	244	29	for	for	ADP
ejpam-5511	244	30	any	any	DET
ejpam-5511	244	31	x	x	NOUN
ejpam-5511	244	32	,	,	PUNCT
ejpam-5511	244	33	y	y	PROPN
ejpam-5511	244	34	,	,	PUNCT
ejpam-5511	244	35	z	z	PROPN
ejpam-5511	244	36	∈	∈	PROPN
ejpam-5511	244	37	f	f	X
ejpam-5511	244	38	,	,	PUNCT
ejpam-5511	244	39	that	that	PRON
ejpam-5511	244	40	is	is	ADV
ejpam-5511	244	41	f	f	PROPN
ejpam-5511	244	42	is	be	AUX
ejpam-5511	244	43	a	a	DET
ejpam-5511	244	44	ternary	ternary	ADJ
ejpam-5511	244	45	subsemigroup	subsemigroup	NOUN
ejpam-5511	244	46	of	of	ADP
ejpam-5511	244	47	t	t	PROPN
ejpam-5511	244	48	;	;	PUNCT
ejpam-5511	244	49	(	(	PUNCT
ejpam-5511	244	50	2	2	X
ejpam-5511	244	51	)	)	PUNCT
ejpam-5511	244	52	for	for	ADP
ejpam-5511	244	53	any	any	DET
ejpam-5511	244	54	x	x	NOUN
ejpam-5511	244	55	,	,	PUNCT
ejpam-5511	244	56	y	y	PROPN
ejpam-5511	244	57	∈	∈	PROPN
ejpam-5511	244	58	t	t	NOUN
ejpam-5511	244	59	,	,	PUNCT
ejpam-5511	244	60	if	if	SCONJ
ejpam-5511	244	61	x	x	ADP
ejpam-5511	244	62	≤	≤	ADJ
ejpam-5511	244	63	y	y	PROPN
ejpam-5511	244	64	and	and	CCONJ
ejpam-5511	244	65	x	x	SYM
ejpam-5511	244	66	∈	∈	PROPN
ejpam-5511	244	67	f	f	PROPN
ejpam-5511	244	68	,	,	PUNCT
ejpam-5511	244	69	then	then	ADV
ejpam-5511	244	70	y	y	PROPN
ejpam-5511	244	71	∈	∈	PROPN
ejpam-5511	244	72	f	f	PROPN
ejpam-5511	244	73	.	.	PUNCT
ejpam-5511	245	1	example	example	NOUN
ejpam-5511	246	1	4	4	NUM
ejpam-5511	246	2	.	.	PUNCT
ejpam-5511	247	1	let	let	VERB
ejpam-5511	247	2	t	t	NOUN
ejpam-5511	247	3	=	=	SYM
ejpam-5511	247	4	{	{	PUNCT
ejpam-5511	247	5	1	1	NUM
ejpam-5511	247	6	,	,	PUNCT
ejpam-5511	247	7	a	a	DET
ejpam-5511	247	8	,	,	PUNCT
ejpam-5511	247	9	b	b	NOUN
ejpam-5511	247	10	,	,	PUNCT
ejpam-5511	247	11	c	c	NOUN
ejpam-5511	247	12	,	,	PUNCT
ejpam-5511	247	13	d	d	NOUN
ejpam-5511	247	14	}	}	PUNCT
ejpam-5511	247	15	.	.	PUNCT
ejpam-5511	248	1	let	let	VERB
ejpam-5511	248	2	us	we	PRON
ejpam-5511	248	3	consider	consider	VERB
ejpam-5511	248	4	the	the	DET
ejpam-5511	248	5	n.p.o	n.p.o	NOUN
ejpam-5511	248	6	.	.	PUNCT
ejpam-5511	249	1	ternary	ternary	ADJ
ejpam-5511	249	2	semigroup	semigroup	PROPN
ejpam-5511	249	3	(	(	PUNCT
ejpam-5511	249	4	t	t	PROPN
ejpam-5511	249	5	,	,	PUNCT
ejpam-5511	249	6	[	[	PUNCT
ejpam-5511	249	7	]	]	X
ejpam-5511	249	8	,	,	PUNCT
ejpam-5511	249	9	≤	≤	NUM
ejpam-5511	249	10	)	)	PUNCT
ejpam-5511	249	11	with	with	ADP
ejpam-5511	249	12	a	a	DET
ejpam-5511	249	13	ternary	ternary	ADJ
ejpam-5511	249	14	multiplication	multiplication	NOUN
ejpam-5511	249	15	[	[	PUNCT
ejpam-5511	249	16	]	]	PUNCT
ejpam-5511	249	17	and	and	CCONJ
ejpam-5511	249	18	an	an	DET
ejpam-5511	249	19	order	order	NOUN
ejpam-5511	249	20	relation	relation	NOUN
ejpam-5511	249	21	≤	≤	NOUN
ejpam-5511	249	22	defined	define	VERB
ejpam-5511	249	23	on	on	ADP
ejpam-5511	249	24	t	t	PROPN
ejpam-5511	249	25	as	as	SCONJ
ejpam-5511	249	26	follows	follow	VERB
ejpam-5511	249	27	:	:	PUNCT
ejpam-5511	249	28	k.	k.	PROPN
ejpam-5511	249	29	nakwan	nakwan	PROPN
ejpam-5511	249	30	,	,	PUNCT
ejpam-5511	249	31	p.	p.	PROPN
ejpam-5511	249	32	luangchaisri	luangchaisri	VERB
ejpam-5511	249	33	,	,	PUNCT
ejpam-5511	249	34	t.	t.	PROPN
ejpam-5511	249	35	changphas	changphas	PROPN
ejpam-5511	249	36	/	/	SYM
ejpam-5511	249	37	eur	eur	PROPN
ejpam-5511	249	38	.	.	PUNCT
ejpam-5511	250	1	j.	j.	PROPN
ejpam-5511	250	2	pure	pure	PROPN
ejpam-5511	250	3	appl	appl	PROPN
ejpam-5511	250	4	.	.	PROPN
ejpam-5511	250	5	math	math	PROPN
ejpam-5511	250	6	,	,	PUNCT
ejpam-5511	250	7	17	17	NUM
ejpam-5511	250	8	(	(	PUNCT
ejpam-5511	250	9	4	4	NUM
ejpam-5511	250	10	)	)	PUNCT
ejpam-5511	250	11	(	(	PUNCT
ejpam-5511	250	12	2024	2024	NUM
ejpam-5511	250	13	)	)	PUNCT
ejpam-5511	250	14	,	,	PUNCT
ejpam-5511	250	15	4180	4180	NUM
ejpam-5511	250	16	-	-	SYM
ejpam-5511	250	17	4194	4194	NUM
ejpam-5511	250	18	4186	4186	NUM
ejpam-5511	250	19	[	[	PUNCT
ejpam-5511	250	20	]	]	X
ejpam-5511	250	21	1	1	NUM
ejpam-5511	250	22	a	a	DET
ejpam-5511	250	23	b	b	NOUN
ejpam-5511	250	24	c	c	NOUN
ejpam-5511	250	25	d	d	SYM
ejpam-5511	250	26	11	11	NUM
ejpam-5511	250	27	1	1	NUM
ejpam-5511	250	28	a	a	DET
ejpam-5511	250	29	b	b	NOUN
ejpam-5511	250	30	c	c	NOUN
ejpam-5511	251	1	d	d	X
ejpam-5511	251	2	1a	1a	X
ejpam-5511	251	3	a	a	DET
ejpam-5511	251	4	a	a	PROPN
ejpam-5511	251	5	d	d	X
ejpam-5511	251	6	c	c	NOUN
ejpam-5511	251	7	d	d	X
ejpam-5511	251	8	1b	1b	PROPN
ejpam-5511	251	9	b	b	PROPN
ejpam-5511	251	10	d	d	X
ejpam-5511	251	11	b	b	PROPN
ejpam-5511	251	12	d	d	PROPN
ejpam-5511	251	13	d	d	PROPN
ejpam-5511	251	14	1c	1c	NOUN
ejpam-5511	251	15	c	c	NOUN
ejpam-5511	251	16	c	c	NOUN
ejpam-5511	251	17	d	d	X
ejpam-5511	251	18	c	c	PROPN
ejpam-5511	251	19	d	d	X
ejpam-5511	251	20	1d	1d	NUM
ejpam-5511	251	21	d	d	NOUN
ejpam-5511	251	22	d	d	PROPN
ejpam-5511	251	23	d	d	PROPN
ejpam-5511	251	24	d	d	X
ejpam-5511	251	25	d	d	X
ejpam-5511	251	26	[	[	PUNCT
ejpam-5511	251	27	]	]	X
ejpam-5511	251	28	1	1	NUM
ejpam-5511	251	29	a	a	DET
ejpam-5511	251	30	b	b	NOUN
ejpam-5511	251	31	c	c	NOUN
ejpam-5511	251	32	d	d	NOUN
ejpam-5511	251	33	a1	a1	VERB
ejpam-5511	251	34	a	a	DET
ejpam-5511	251	35	a	a	NOUN
ejpam-5511	251	36	d	d	X
ejpam-5511	251	37	c	c	NOUN
ejpam-5511	252	1	d	d	X
ejpam-5511	252	2	aa	aa	PROPN
ejpam-5511	252	3	a	a	PRON
ejpam-5511	252	4	a	a	PROPN
ejpam-5511	252	5	d	d	X
ejpam-5511	252	6	c	c	NOUN
ejpam-5511	253	1	d	d	X
ejpam-5511	253	2	ab	ab	PROPN
ejpam-5511	254	1	d	d	PROPN
ejpam-5511	254	2	d	d	PROPN
ejpam-5511	255	1	d	d	PROPN
ejpam-5511	255	2	d	d	PROPN
ejpam-5511	255	3	d	d	X
ejpam-5511	255	4	ac	ac	PROPN
ejpam-5511	256	1	c	c	NOUN
ejpam-5511	256	2	c	c	PROPN
ejpam-5511	256	3	d	d	X
ejpam-5511	256	4	c	c	NOUN
ejpam-5511	256	5	d	d	X
ejpam-5511	256	6	ad	ad	NOUN
ejpam-5511	256	7	d	d	X
ejpam-5511	256	8	d	d	PROPN
ejpam-5511	256	9	d	d	PROPN
ejpam-5511	256	10	d	d	X
ejpam-5511	256	11	d	d	X
ejpam-5511	256	12	[	[	PUNCT
ejpam-5511	256	13	]	]	X
ejpam-5511	256	14	1	1	NUM
ejpam-5511	256	15	a	a	DET
ejpam-5511	256	16	b	b	NOUN
ejpam-5511	256	17	c	c	NOUN
ejpam-5511	256	18	d	d	PROPN
ejpam-5511	256	19	b1	b1	PROPN
ejpam-5511	256	20	b	b	PROPN
ejpam-5511	256	21	d	d	PROPN
ejpam-5511	256	22	b	b	PROPN
ejpam-5511	257	1	d	d	NOUN
ejpam-5511	257	2	d	d	X
ejpam-5511	257	3	ba	ba	PROPN
ejpam-5511	257	4	d	d	PROPN
ejpam-5511	257	5	d	d	PROPN
ejpam-5511	258	1	d	d	PROPN
ejpam-5511	258	2	d	d	X
ejpam-5511	258	3	d	d	X
ejpam-5511	258	4	bb	bb	NUM
ejpam-5511	258	5	b	b	PROPN
ejpam-5511	258	6	d	d	PROPN
ejpam-5511	258	7	b	b	PROPN
ejpam-5511	259	1	d	d	PROPN
ejpam-5511	259	2	d	d	PROPN
ejpam-5511	259	3	bc	bc	PROPN
ejpam-5511	260	1	d	d	PROPN
ejpam-5511	260	2	d	d	PROPN
ejpam-5511	260	3	d	d	PROPN
ejpam-5511	260	4	d	d	X
ejpam-5511	260	5	d	d	X
ejpam-5511	260	6	bd	bd	PROPN
ejpam-5511	260	7	d	d	PROPN
ejpam-5511	260	8	d	d	PROPN
ejpam-5511	260	9	d	d	PROPN
ejpam-5511	260	10	d	d	X
ejpam-5511	260	11	d	d	X
ejpam-5511	260	12	[	[	PUNCT
ejpam-5511	260	13	]	]	X
ejpam-5511	260	14	1	1	NUM
ejpam-5511	260	15	a	a	DET
ejpam-5511	260	16	b	b	NOUN
ejpam-5511	260	17	c	c	NOUN
ejpam-5511	260	18	d	d	PROPN
ejpam-5511	260	19	c1	c1	PROPN
ejpam-5511	261	1	c	c	PROPN
ejpam-5511	262	1	c	c	PROPN
ejpam-5511	263	1	d	d	X
ejpam-5511	263	2	c	c	NOUN
ejpam-5511	263	3	d	d	NOUN
ejpam-5511	263	4	ca	ca	NOUN
ejpam-5511	263	5	c	c	NOUN
ejpam-5511	263	6	c	c	NOUN
ejpam-5511	263	7	d	d	X
ejpam-5511	263	8	c	c	PROPN
ejpam-5511	264	1	d	d	X
ejpam-5511	264	2	cb	cb	PROPN
ejpam-5511	265	1	d	d	PROPN
ejpam-5511	265	2	d	d	PROPN
ejpam-5511	265	3	d	d	PROPN
ejpam-5511	265	4	d	d	X
ejpam-5511	265	5	d	d	X
ejpam-5511	265	6	cc	cc	X
ejpam-5511	265	7	c	c	NOUN
ejpam-5511	265	8	c	c	PROPN
ejpam-5511	265	9	d	d	X
ejpam-5511	265	10	c	c	X
ejpam-5511	265	11	d	d	PROPN
ejpam-5511	265	12	cd	cd	PROPN
ejpam-5511	265	13	d	d	PROPN
ejpam-5511	265	14	d	d	PROPN
ejpam-5511	265	15	d	d	PROPN
ejpam-5511	265	16	d	d	X
ejpam-5511	265	17	d	d	X
ejpam-5511	265	18	[	[	PUNCT
ejpam-5511	265	19	]	]	X
ejpam-5511	265	20	1	1	NUM
ejpam-5511	265	21	a	a	DET
ejpam-5511	265	22	b	b	NOUN
ejpam-5511	265	23	c	c	NOUN
ejpam-5511	265	24	d	d	NOUN
ejpam-5511	265	25	d1	d1	PROPN
ejpam-5511	266	1	d	d	PROPN
ejpam-5511	267	1	d	d	X
ejpam-5511	267	2	d	d	PROPN
ejpam-5511	267	3	d	d	PROPN
ejpam-5511	267	4	d	d	X
ejpam-5511	267	5	da	da	PROPN
ejpam-5511	267	6	d	d	PUNCT
ejpam-5511	267	7	d	d	PROPN
ejpam-5511	268	1	d	d	PROPN
ejpam-5511	268	2	d	d	PROPN
ejpam-5511	268	3	d	d	X
ejpam-5511	268	4	db	db	PROPN
ejpam-5511	269	1	d	d	X
ejpam-5511	269	2	d	d	PROPN
ejpam-5511	269	3	d	d	PROPN
ejpam-5511	269	4	d	d	PROPN
ejpam-5511	269	5	d	d	X
ejpam-5511	269	6	dc	dc	PROPN
ejpam-5511	270	1	d	d	PROPN
ejpam-5511	270	2	d	d	PROPN
ejpam-5511	270	3	d	d	X
ejpam-5511	270	4	d	d	X
ejpam-5511	270	5	d	d	X
ejpam-5511	270	6	dd	dd	NOUN
ejpam-5511	270	7	d	d	NOUN
ejpam-5511	270	8	d	d	PROPN
ejpam-5511	270	9	d	d	PROPN
ejpam-5511	270	10	d	d	PROPN
ejpam-5511	270	11	d	d	PROPN
ejpam-5511	270	12	and	and	CCONJ
ejpam-5511	270	13	≤	≤	NUM
ejpam-5511	270	14	=	=	SYM
ejpam-5511	270	15	{	{	PUNCT
ejpam-5511	270	16	(	(	PUNCT
ejpam-5511	270	17	1	1	NUM
ejpam-5511	270	18	,	,	PUNCT
ejpam-5511	270	19	1	1	NUM
ejpam-5511	270	20	)	)	PUNCT
ejpam-5511	270	21	,	,	PUNCT
ejpam-5511	270	22	(	(	PUNCT
ejpam-5511	270	23	a	a	X
ejpam-5511	270	24	,	,	PUNCT
ejpam-5511	270	25	a	a	NOUN
ejpam-5511	270	26	)	)	PUNCT
ejpam-5511	270	27	,	,	PUNCT
ejpam-5511	270	28	(	(	PUNCT
ejpam-5511	270	29	b	b	X
ejpam-5511	270	30	,	,	PUNCT
ejpam-5511	270	31	b	b	NOUN
ejpam-5511	270	32	)	)	PUNCT
ejpam-5511	270	33	,	,	PUNCT
ejpam-5511	270	34	(	(	PUNCT
ejpam-5511	270	35	c	c	X
ejpam-5511	270	36	,	,	PUNCT
ejpam-5511	270	37	c	c	NOUN
ejpam-5511	270	38	)	)	PUNCT
ejpam-5511	270	39	,	,	PUNCT
ejpam-5511	270	40	(	(	PUNCT
ejpam-5511	270	41	d	d	X
ejpam-5511	270	42	,	,	PUNCT
ejpam-5511	270	43	d	d	NOUN
ejpam-5511	270	44	)	)	PUNCT
ejpam-5511	270	45	,	,	PUNCT
ejpam-5511	270	46	(	(	PUNCT
ejpam-5511	270	47	b	b	X
ejpam-5511	270	48	,	,	PUNCT
ejpam-5511	270	49	1	1	NUM
ejpam-5511	270	50	)	)	PUNCT
ejpam-5511	270	51	,	,	PUNCT
ejpam-5511	270	52	(	(	PUNCT
ejpam-5511	270	53	a	a	PRON
ejpam-5511	270	54	,	,	PUNCT
ejpam-5511	270	55	1	1	NUM
ejpam-5511	270	56	)	)	PUNCT
ejpam-5511	270	57	,	,	PUNCT
ejpam-5511	270	58	(	(	PUNCT
ejpam-5511	270	59	c	c	X
ejpam-5511	270	60	,	,	PUNCT
ejpam-5511	270	61	a	a	NOUN
ejpam-5511	270	62	)	)	PUNCT
ejpam-5511	270	63	,	,	PUNCT
ejpam-5511	270	64	(	(	PUNCT
ejpam-5511	270	65	c	c	X
ejpam-5511	270	66	,	,	PUNCT
ejpam-5511	270	67	1	1	NUM
ejpam-5511	270	68	)	)	PUNCT
ejpam-5511	270	69	,	,	PUNCT
ejpam-5511	270	70	(	(	PUNCT
ejpam-5511	270	71	d	d	X
ejpam-5511	270	72	,	,	PUNCT
ejpam-5511	270	73	c	c	NOUN
ejpam-5511	270	74	)	)	PUNCT
ejpam-5511	270	75	,	,	PUNCT
ejpam-5511	270	76	(	(	PUNCT
ejpam-5511	270	77	d	d	X
ejpam-5511	270	78	,	,	PUNCT
ejpam-5511	270	79	a	a	NOUN
ejpam-5511	270	80	)	)	PUNCT
ejpam-5511	270	81	,	,	PUNCT
ejpam-5511	270	82	(	(	PUNCT
ejpam-5511	270	83	d	d	X
ejpam-5511	270	84	,	,	PUNCT
ejpam-5511	270	85	b	b	NOUN
ejpam-5511	270	86	)	)	PUNCT
ejpam-5511	270	87	,	,	PUNCT
ejpam-5511	270	88	(	(	PUNCT
ejpam-5511	270	89	d	d	X
ejpam-5511	270	90	,	,	PUNCT
ejpam-5511	270	91	1	1	NUM
ejpam-5511	270	92	)	)	PUNCT
ejpam-5511	270	93	}	}	PUNCT
ejpam-5511	270	94	.	.	PUNCT
ejpam-5511	271	1	observe	observe	VERB
ejpam-5511	271	2	that	that	SCONJ
ejpam-5511	271	3	1	1	NUM
ejpam-5511	271	4	is	be	AUX
ejpam-5511	271	5	the	the	DET
ejpam-5511	271	6	greatest	great	ADJ
ejpam-5511	271	7	element	element	NOUN
ejpam-5511	271	8	.	.	PUNCT
ejpam-5511	272	1	it	it	PRON
ejpam-5511	272	2	is	be	AUX
ejpam-5511	272	3	easy	easy	ADJ
ejpam-5511	272	4	to	to	PART
ejpam-5511	272	5	verify	verify	VERB
ejpam-5511	272	6	that	that	DET
ejpam-5511	272	7	f1	f1	NOUN
ejpam-5511	272	8	=	=	SYM
ejpam-5511	272	9	{	{	PUNCT
ejpam-5511	272	10	1	1	NUM
ejpam-5511	272	11	}	}	PUNCT
ejpam-5511	272	12	,	,	PUNCT
ejpam-5511	272	13	f2	f2	PROPN
ejpam-5511	272	14	=	=	SYM
ejpam-5511	272	15	{	{	PUNCT
ejpam-5511	272	16	1	1	NUM
ejpam-5511	272	17	,	,	PUNCT
ejpam-5511	272	18	a	a	PRON
ejpam-5511	272	19	}	}	PUNCT
ejpam-5511	272	20	,	,	PUNCT
ejpam-5511	272	21	f3	f3	PROPN
ejpam-5511	272	22	=	=	SYM
ejpam-5511	272	23	{	{	PUNCT
ejpam-5511	272	24	1	1	NUM
ejpam-5511	272	25	,	,	PUNCT
ejpam-5511	272	26	b	b	NOUN
ejpam-5511	272	27	}	}	PUNCT
ejpam-5511	272	28	,	,	PUNCT
ejpam-5511	272	29	f4	f4	NOUN
ejpam-5511	272	30	=	=	SYM
ejpam-5511	272	31	{	{	PUNCT
ejpam-5511	272	32	1	1	NUM
ejpam-5511	272	33	,	,	PUNCT
ejpam-5511	272	34	a	a	DET
ejpam-5511	272	35	,	,	PUNCT
ejpam-5511	272	36	c	c	NOUN
ejpam-5511	272	37	}	}	PUNCT
ejpam-5511	272	38	,	,	PUNCT
ejpam-5511	272	39	f5	f5	PROPN
ejpam-5511	272	40	=	=	SYM
ejpam-5511	272	41	t	t	PROPN
ejpam-5511	272	42	are	be	AUX
ejpam-5511	272	43	filters	filter	NOUN
ejpam-5511	272	44	,	,	PUNCT
ejpam-5511	272	45	but	but	CCONJ
ejpam-5511	272	46	{	{	PUNCT
ejpam-5511	272	47	1	1	NUM
ejpam-5511	272	48	,	,	PUNCT
ejpam-5511	272	49	a	a	DET
ejpam-5511	272	50	,	,	PUNCT
ejpam-5511	272	51	b	b	NOUN
ejpam-5511	272	52	}	}	PUNCT
ejpam-5511	272	53	is	be	AUX
ejpam-5511	272	54	not	not	PART
ejpam-5511	272	55	a	a	DET
ejpam-5511	272	56	filter	filter	NOUN
ejpam-5511	272	57	.	.	PUNCT
ejpam-5511	273	1	now	now	ADV
ejpam-5511	273	2	,	,	PUNCT
ejpam-5511	273	3	we	we	PRON
ejpam-5511	273	4	investigate	investigate	VERB
ejpam-5511	273	5	some	some	DET
ejpam-5511	273	6	properties	property	NOUN
ejpam-5511	273	7	of	of	ADP
ejpam-5511	273	8	implicative	implicative	ADJ
ejpam-5511	273	9	homomorphisms	homomorphism	NOUN
ejpam-5511	273	10	.	.	PUNCT
ejpam-5511	274	1	theorem	theorem	NOUN
ejpam-5511	274	2	3	3	X
ejpam-5511	274	3	.	.	PUNCT
ejpam-5511	275	1	let	let	AUX
ejpam-5511	275	2	(	(	PUNCT
ejpam-5511	275	3	t1	t1	VERB
ejpam-5511	275	4	,	,	PUNCT
ejpam-5511	275	5	[	[	PUNCT
ejpam-5511	275	6	]	]	X
ejpam-5511	275	7	1,≤1	1,≤1	ADJ
ejpam-5511	275	8	,	,	PUNCT
ejpam-5511	275	9	[	[	PUNCT
ejpam-5511	275	10	]	]	X
ejpam-5511	275	11	∗1	∗1	X
ejpam-5511	275	12	)	)	PUNCT
ejpam-5511	275	13	and	and	CCONJ
ejpam-5511	275	14	(	(	PUNCT
ejpam-5511	275	15	t2	t2	NOUN
ejpam-5511	275	16	,	,	PUNCT
ejpam-5511	275	17	[	[	PUNCT
ejpam-5511	275	18	]	]	X
ejpam-5511	275	19	2,≤2	2,≤2	NOUN
ejpam-5511	275	20	,	,	PUNCT
ejpam-5511	275	21	[	[	PUNCT
ejpam-5511	275	22	]	]	X
ejpam-5511	275	23	∗2	∗2	NOUN
ejpam-5511	275	24	)	)	PUNCT
ejpam-5511	275	25	be	be	AUX
ejpam-5511	275	26	implicative	implicative	ADJ
ejpam-5511	275	27	n.p.o	n.p.o	NOUN
ejpam-5511	275	28	.	.	PUNCT
ejpam-5511	276	1	ternary	ternary	ADJ
ejpam-5511	276	2	semigroups	semigroup	NOUN
ejpam-5511	276	3	.	.	PUNCT
ejpam-5511	277	1	let	let	VERB
ejpam-5511	277	2	φ	φ	PROPN
ejpam-5511	277	3	:	:	PUNCT
ejpam-5511	277	4	t1	t1	PROPN
ejpam-5511	277	5	−→	−→	ADJ
ejpam-5511	277	6	t2	t2	NOUN
ejpam-5511	277	7	be	be	VERB
ejpam-5511	277	8	an	an	DET
ejpam-5511	277	9	implicative	implicative	ADJ
ejpam-5511	277	10	homomorphism	homomorphism	NOUN
ejpam-5511	277	11	from	from	ADP
ejpam-5511	277	12	t1	t1	NOUN
ejpam-5511	277	13	onto	onto	ADP
ejpam-5511	277	14	t2	t2	NOUN
ejpam-5511	277	15	.	.	PUNCT
ejpam-5511	278	1	then	then	ADV
ejpam-5511	278	2	the	the	DET
ejpam-5511	278	3	following	follow	VERB
ejpam-5511	278	4	conditions	condition	NOUN
ejpam-5511	278	5	hold	hold	VERB
ejpam-5511	278	6	:	:	PUNCT
ejpam-5511	278	7	(	(	PUNCT
ejpam-5511	278	8	1	1	X
ejpam-5511	278	9	)	)	PUNCT
ejpam-5511	278	10	φ(1	φ(1	PROPN
ejpam-5511	278	11	)	)	PUNCT
ejpam-5511	278	12	=	=	SYM
ejpam-5511	279	1	1′	1′	NUM
ejpam-5511	279	2	,	,	PUNCT
ejpam-5511	279	3	where	where	SCONJ
ejpam-5511	279	4	1	1	NUM
ejpam-5511	279	5	and	and	CCONJ
ejpam-5511	279	6	1′	1′	NUM
ejpam-5511	279	7	are	be	AUX
ejpam-5511	279	8	the	the	DET
ejpam-5511	279	9	identities	identity	NOUN
ejpam-5511	279	10	as	as	ADV
ejpam-5511	279	11	well	well	ADV
ejpam-5511	279	12	as	as	ADP
ejpam-5511	279	13	the	the	DET
ejpam-5511	279	14	greatest	great	ADJ
ejpam-5511	279	15	elements	element	NOUN
ejpam-5511	279	16	of	of	ADP
ejpam-5511	279	17	t1	t1	NOUN
ejpam-5511	279	18	and	and	CCONJ
ejpam-5511	279	19	of	of	ADP
ejpam-5511	279	20	t2	t2	NOUN
ejpam-5511	279	21	,	,	PUNCT
ejpam-5511	279	22	respectively	respectively	ADV
ejpam-5511	279	23	;	;	PUNCT
ejpam-5511	279	24	(	(	PUNCT
ejpam-5511	279	25	2	2	X
ejpam-5511	279	26	)	)	PUNCT
ejpam-5511	279	27	φ	φ	PROPN
ejpam-5511	279	28	is	be	AUX
ejpam-5511	279	29	isotonic	isotonic	ADJ
ejpam-5511	279	30	,	,	PUNCT
ejpam-5511	279	31	that	that	PRON
ejpam-5511	279	32	is	be	AUX
ejpam-5511	279	33	for	for	ADP
ejpam-5511	279	34	any	any	DET
ejpam-5511	279	35	x	x	NOUN
ejpam-5511	279	36	,	,	PUNCT
ejpam-5511	279	37	y	y	PROPN
ejpam-5511	279	38	∈	∈	PROPN
ejpam-5511	279	39	t1	t1	NOUN
ejpam-5511	279	40	,	,	PUNCT
ejpam-5511	279	41	if	if	SCONJ
ejpam-5511	279	42	x	x	PROPN
ejpam-5511	279	43	≤1	≤1	PRON
ejpam-5511	279	44	y	y	PROPN
ejpam-5511	279	45	then	then	ADV
ejpam-5511	279	46	φ(x	φ(x	NOUN
ejpam-5511	279	47	)	)	PUNCT
ejpam-5511	279	48	≤2	≤2	NOUN
ejpam-5511	279	49	φ(y	φ(y	NOUN
ejpam-5511	279	50	)	)	PUNCT
ejpam-5511	279	51	;	;	PUNCT
ejpam-5511	279	52	(	(	PUNCT
ejpam-5511	279	53	3	3	X
ejpam-5511	279	54	)	)	PUNCT
ejpam-5511	279	55	φ	φ	PROPN
ejpam-5511	279	56	is	be	AUX
ejpam-5511	279	57	a	a	DET
ejpam-5511	279	58	(	(	PUNCT
ejpam-5511	279	59	ternary	ternary	ADJ
ejpam-5511	279	60	semigroup	semigroup	NOUN
ejpam-5511	279	61	)	)	PUNCT
ejpam-5511	279	62	homomorphism	homomorphism	NOUN
ejpam-5511	279	63	(	(	PUNCT
ejpam-5511	279	64	i.e.	i.e.	X
ejpam-5511	279	65	,	,	PUNCT
ejpam-5511	279	66	for	for	ADP
ejpam-5511	279	67	any	any	DET
ejpam-5511	279	68	x	x	NOUN
ejpam-5511	279	69	,	,	PUNCT
ejpam-5511	279	70	y	y	PROPN
ejpam-5511	279	71	,	,	PUNCT
ejpam-5511	279	72	z	z	PROPN
ejpam-5511	279	73	∈	∈	PROPN
ejpam-5511	279	74	t1	t1	NOUN
ejpam-5511	279	75	,	,	PUNCT
ejpam-5511	279	76	φ[xyz]1	φ[xyz]1	PUNCT
ejpam-5511	279	77	=	=	PUNCT
ejpam-5511	280	1	[	[	X
ejpam-5511	280	2	φ(x)φ(y)φ(z)]2	φ(x)φ(y)φ(z)]2	NOUN
ejpam-5511	280	3	)	)	PUNCT
ejpam-5511	280	4	;	;	PUNCT
ejpam-5511	280	5	(	(	PUNCT
ejpam-5511	280	6	4	4	X
ejpam-5511	280	7	)	)	PUNCT
ejpam-5511	280	8	φ−1(1′	φ−1(1′	NOUN
ejpam-5511	280	9	)	)	PUNCT
ejpam-5511	280	10	is	be	AUX
ejpam-5511	280	11	a	a	DET
ejpam-5511	280	12	filter	filter	NOUN
ejpam-5511	280	13	of	of	ADP
ejpam-5511	280	14	t1	t1	NOUN
ejpam-5511	280	15	,	,	PUNCT
ejpam-5511	280	16	when	when	SCONJ
ejpam-5511	280	17	φ	φ	PROPN
ejpam-5511	280	18	−1(1′	−1(1′	PROPN
ejpam-5511	280	19	)	)	PUNCT
ejpam-5511	280	20	=	=	PRON
ejpam-5511	281	1	{	{	PUNCT
ejpam-5511	281	2	x	x	PUNCT
ejpam-5511	281	3	∈	∈	PROPN
ejpam-5511	281	4	t1	t1	NOUN
ejpam-5511	281	5	:	:	PUNCT
ejpam-5511	281	6	φ(x	φ(x	X
ejpam-5511	281	7	)	)	PUNCT
ejpam-5511	281	8	=	=	SYM
ejpam-5511	281	9	1′	1′	NUM
ejpam-5511	281	10	}	}	PUNCT
ejpam-5511	281	11	;	;	PUNCT
ejpam-5511	281	12	(	(	PUNCT
ejpam-5511	281	13	5	5	X
ejpam-5511	281	14	)	)	PUNCT
ejpam-5511	281	15	φ	φ	PROPN
ejpam-5511	281	16	is	be	AUX
ejpam-5511	281	17	an	an	DET
ejpam-5511	281	18	(	(	PUNCT
ejpam-5511	281	19	ternary	ternary	ADJ
ejpam-5511	281	20	semigroup	semigroup	NOUN
ejpam-5511	281	21	)	)	PUNCT
ejpam-5511	281	22	isomorphism	isomorphism	NOUN
ejpam-5511	281	23	if	if	SCONJ
ejpam-5511	281	24	and	and	CCONJ
ejpam-5511	281	25	only	only	ADV
ejpam-5511	281	26	if	if	SCONJ
ejpam-5511	281	27	φ−1(1′	φ−1(1′	NOUN
ejpam-5511	281	28	)	)	PUNCT
ejpam-5511	281	29	=	=	PUNCT
ejpam-5511	281	30	{	{	PUNCT
ejpam-5511	281	31	1	1	NUM
ejpam-5511	281	32	}	}	PUNCT
ejpam-5511	281	33	.	.	PUNCT
ejpam-5511	282	1	k.	k.	PROPN
ejpam-5511	282	2	nakwan	nakwan	PROPN
ejpam-5511	282	3	,	,	PUNCT
ejpam-5511	282	4	p.	p.	PROPN
ejpam-5511	282	5	luangchaisri	luangchaisri	VERB
ejpam-5511	282	6	,	,	PUNCT
ejpam-5511	282	7	t.	t.	PROPN
ejpam-5511	282	8	changphas	changphas	PROPN
ejpam-5511	282	9	/	/	SYM
ejpam-5511	282	10	eur	eur	PROPN
ejpam-5511	282	11	.	.	PUNCT
ejpam-5511	283	1	j.	j.	PROPN
ejpam-5511	283	2	pure	pure	PROPN
ejpam-5511	283	3	appl	appl	PROPN
ejpam-5511	283	4	.	.	PROPN
ejpam-5511	283	5	math	math	PROPN
ejpam-5511	283	6	,	,	PUNCT
ejpam-5511	283	7	17	17	NUM
ejpam-5511	283	8	(	(	PUNCT
ejpam-5511	283	9	4	4	NUM
ejpam-5511	283	10	)	)	PUNCT
ejpam-5511	283	11	(	(	PUNCT
ejpam-5511	283	12	2024	2024	NUM
ejpam-5511	283	13	)	)	PUNCT
ejpam-5511	283	14	,	,	PUNCT
ejpam-5511	283	15	4180	4180	NUM
ejpam-5511	283	16	-	-	SYM
ejpam-5511	283	17	4194	4194	NUM
ejpam-5511	283	18	4187	4187	NUM
ejpam-5511	283	19	proof	proof	NOUN
ejpam-5511	283	20	.	.	PUNCT
ejpam-5511	284	1	(	(	PUNCT
ejpam-5511	284	2	1	1	X
ejpam-5511	284	3	)	)	PUNCT
ejpam-5511	284	4	by	by	ADP
ejpam-5511	284	5	theorem	theorem	ADJ
ejpam-5511	284	6	2	2	NUM
ejpam-5511	284	7	(	(	PUNCT
ejpam-5511	284	8	1	1	NUM
ejpam-5511	284	9	)	)	PUNCT
ejpam-5511	284	10	,	,	PUNCT
ejpam-5511	284	11	we	we	PRON
ejpam-5511	284	12	have	have	VERB
ejpam-5511	284	13	1	1	NUM
ejpam-5511	284	14	=	=	SYM
ejpam-5511	285	1	[	[	X
ejpam-5511	285	2	111]∗1	111]∗1	NOUN
ejpam-5511	285	3	.	.	PUNCT
ejpam-5511	286	1	consequently	consequently	ADV
ejpam-5511	286	2	,	,	PUNCT
ejpam-5511	286	3	φ(1	φ(1	PROPN
ejpam-5511	286	4	)	)	PUNCT
ejpam-5511	286	5	=	=	SYM
ejpam-5511	286	6	φ([111]∗1	φ([111]∗1	NOUN
ejpam-5511	286	7	)	)	PUNCT
ejpam-5511	286	8	=	=	PUNCT
ejpam-5511	287	1	[	[	X
ejpam-5511	287	2	φ(1)φ(1)φ(1)]∗2	φ(1)φ(1)φ(1)]∗2	X
ejpam-5511	287	3	=	=	PUNCT
ejpam-5511	287	4	1′.	1′.	NUM
ejpam-5511	287	5	(	(	PUNCT
ejpam-5511	287	6	2	2	NUM
ejpam-5511	287	7	)	)	PUNCT
ejpam-5511	287	8	if	if	SCONJ
ejpam-5511	287	9	x	x	X
ejpam-5511	287	10	,	,	PUNCT
ejpam-5511	287	11	y	y	PROPN
ejpam-5511	287	12	∈	∈	PROPN
ejpam-5511	287	13	t1	t1	NOUN
ejpam-5511	287	14	such	such	ADJ
ejpam-5511	287	15	that	that	SCONJ
ejpam-5511	287	16	x	x	PROPN
ejpam-5511	287	17	≤1	≤1	PROPN
ejpam-5511	287	18	y	y	PROPN
ejpam-5511	287	19	,	,	PUNCT
ejpam-5511	287	20	then	then	ADV
ejpam-5511	287	21	by	by	ADP
ejpam-5511	287	22	theorem	theorem	NOUN
ejpam-5511	287	23	2	2	NUM
ejpam-5511	287	24	(	(	PUNCT
ejpam-5511	287	25	6	6	NUM
ejpam-5511	287	26	)	)	PUNCT
ejpam-5511	287	27	we	we	PRON
ejpam-5511	287	28	get	get	VERB
ejpam-5511	287	29	that	that	PRON
ejpam-5511	288	1	[	[	X
ejpam-5511	288	2	x1y]∗1	x1y]∗1	X
ejpam-5511	288	3	=	=	SYM
ejpam-5511	288	4	1	1	X
ejpam-5511	288	5	.	.	PUNCT
ejpam-5511	289	1	hence	hence	ADV
ejpam-5511	289	2	,	,	PUNCT
ejpam-5511	289	3	[	[	X
ejpam-5511	289	4	φ(x)1′φ(y)]∗2	φ(x)1′φ(y)]∗2	X
ejpam-5511	289	5	=	=	PUNCT
ejpam-5511	290	1	[	[	X
ejpam-5511	290	2	φ(x)φ(1)φ(y)]∗2	φ(x)φ(1)φ(y)]∗2	X
ejpam-5511	290	3	=	=	SYM
ejpam-5511	290	4	φ([x1y]∗1	φ([x1y]∗1	ADJ
ejpam-5511	290	5	)	)	PUNCT
ejpam-5511	290	6	=	=	SYM
ejpam-5511	290	7	φ(1	φ(1	PROPN
ejpam-5511	290	8	)	)	PUNCT
ejpam-5511	290	9	=	=	PUNCT
ejpam-5511	290	10	1′.	1′.	NOUN
ejpam-5511	290	11	by	by	ADP
ejpam-5511	290	12	theorem	theorem	ADJ
ejpam-5511	290	13	2	2	NUM
ejpam-5511	290	14	(	(	PUNCT
ejpam-5511	290	15	6	6	NUM
ejpam-5511	290	16	)	)	PUNCT
ejpam-5511	290	17	,	,	PUNCT
ejpam-5511	290	18	we	we	PRON
ejpam-5511	290	19	have	have	VERB
ejpam-5511	290	20	φ(x	φ(x	NOUN
ejpam-5511	290	21	)	)	PUNCT
ejpam-5511	290	22	≤2	≤2	NOUN
ejpam-5511	290	23	φ(y	φ(y	NOUN
ejpam-5511	290	24	)	)	PUNCT
ejpam-5511	290	25	.	.	PUNCT
ejpam-5511	291	1	(	(	PUNCT
ejpam-5511	291	2	3	3	X
ejpam-5511	291	3	)	)	PUNCT
ejpam-5511	291	4	let	let	VERB
ejpam-5511	291	5	x	x	PRON
ejpam-5511	291	6	,	,	PUNCT
ejpam-5511	291	7	y	y	PROPN
ejpam-5511	291	8	,	,	PUNCT
ejpam-5511	291	9	z	z	PROPN
ejpam-5511	291	10	∈	∈	PROPN
ejpam-5511	291	11	t1	t1	NOUN
ejpam-5511	291	12	;	;	PUNCT
ejpam-5511	291	13	then	then	ADV
ejpam-5511	291	14	φ(u	φ(u	NOUN
ejpam-5511	291	15	)	)	PUNCT
ejpam-5511	291	16	=	=	PUNCT
ejpam-5511	292	1	[	[	X
ejpam-5511	292	2	φ(x)φ(y)φ(z)]2	φ(x)φ(y)φ(z)]2	PROPN
ejpam-5511	292	3	for	for	ADP
ejpam-5511	292	4	some	some	DET
ejpam-5511	292	5	u	u	PROPN
ejpam-5511	292	6	∈	∈	PROPN
ejpam-5511	292	7	t1	t1	NOUN
ejpam-5511	292	8	.	.	PUNCT
ejpam-5511	293	1	since	since	SCONJ
ejpam-5511	293	2	φ	φ	PROPN
ejpam-5511	293	3	is	be	AUX
ejpam-5511	293	4	an	an	DET
ejpam-5511	293	5	implicative	implicative	ADJ
ejpam-5511	293	6	homomorphism	homomorphism	NOUN
ejpam-5511	293	7	,	,	PUNCT
ejpam-5511	293	8	we	we	PRON
ejpam-5511	293	9	have	have	VERB
ejpam-5511	293	10	[	[	X
ejpam-5511	293	11	φ([xyz]1)φ(1)φ(u)]∗2	φ([xyz]1)φ(1)φ(u)]∗2	X
ejpam-5511	293	12	=	=	SYM
ejpam-5511	293	13	φ([[xyz]11u]∗1	φ([[xyz]11u]∗1	PROPN
ejpam-5511	293	14	)	)	PUNCT
ejpam-5511	293	15	=	=	SYM
ejpam-5511	293	16	φ([xy[z1u]1	φ([xy[z1u]1	NOUN
ejpam-5511	293	17	]	]	X
ejpam-5511	293	18	∗	∗	NOUN
ejpam-5511	293	19	1	1	NUM
ejpam-5511	293	20	)	)	PUNCT
ejpam-5511	293	21	=	=	NOUN
ejpam-5511	294	1	[	[	X
ejpam-5511	294	2	φ(x)φ(y)φ([z1u]1	φ(x)φ(y)φ([z1u]1	NOUN
ejpam-5511	294	3	)	)	PUNCT
ejpam-5511	294	4	]	]	PUNCT
ejpam-5511	294	5	∗	∗	NOUN
ejpam-5511	294	6	2	2	NUM
ejpam-5511	294	7	=	=	SYM
ejpam-5511	295	1	[	[	X
ejpam-5511	295	2	φ(x)φ(y)[φ(z)φ(1)φ(u)]2	φ(x)φ(y)[φ(z)φ(1)φ(u)]2	NOUN
ejpam-5511	295	3	]	]	X
ejpam-5511	295	4	∗	∗	NOUN
ejpam-5511	295	5	2	2	NUM
ejpam-5511	295	6	=	=	SYM
ejpam-5511	296	1	[	[	X
ejpam-5511	296	2	[	[	X
ejpam-5511	296	3	φ(x)φ(y)φ(z)]2φ(1)φ(u)]∗2	φ(x)φ(y)φ(z)]2φ(1)φ(u)]∗2	X
ejpam-5511	296	4	=	=	PUNCT
ejpam-5511	297	1	[	[	X
ejpam-5511	297	2	φ(u)φ(1)φ(u)]∗2	φ(u)φ(1)φ(u)]∗2	PROPN
ejpam-5511	297	3	=	=	PUNCT
ejpam-5511	297	4	1′.	1′.	NOUN
ejpam-5511	297	5	then	then	ADV
ejpam-5511	297	6	,	,	PUNCT
ejpam-5511	297	7	by	by	ADP
ejpam-5511	297	8	theorem	theorem	NOUN
ejpam-5511	297	9	2	2	NUM
ejpam-5511	297	10	(	(	PUNCT
ejpam-5511	297	11	6	6	NUM
ejpam-5511	297	12	)	)	PUNCT
ejpam-5511	297	13	,	,	PUNCT
ejpam-5511	297	14	φ([xyz]1	φ([xyz]1	PROPN
ejpam-5511	297	15	)	)	PUNCT
ejpam-5511	297	16	≤2	≤2	NOUN
ejpam-5511	297	17	[	[	X
ejpam-5511	297	18	φ(x)φ(y)φ(z)]2	φ(x)φ(y)φ(z)]2	NOUN
ejpam-5511	297	19	.	.	NOUN
ejpam-5511	297	20	from	from	ADP
ejpam-5511	297	21	[	[	X
ejpam-5511	297	22	xyz]1	xyz]1	PROPN
ejpam-5511	297	23	≤1	≤1	PROPN
ejpam-5511	297	24	[	[	X
ejpam-5511	297	25	xyz]1	xyz]1	PROPN
ejpam-5511	297	26	,	,	PUNCT
ejpam-5511	297	27	it	it	PRON
ejpam-5511	297	28	follows	follow	VERB
ejpam-5511	297	29	that	that	SCONJ
ejpam-5511	297	30	x	x	X
ejpam-5511	298	1	≤1	≤1	PROPN
ejpam-5511	299	1	[	[	X
ejpam-5511	299	2	yz[xyz]1	yz[xyz]1	X
ejpam-5511	299	3	]	]	X
ejpam-5511	299	4	∗	∗	PROPN
ejpam-5511	299	5	1	1	NUM
ejpam-5511	299	6	.	.	PUNCT
ejpam-5511	300	1	by	by	ADP
ejpam-5511	300	2	(	(	PUNCT
ejpam-5511	300	3	2	2	NUM
ejpam-5511	300	4	)	)	PUNCT
ejpam-5511	300	5	,	,	PUNCT
ejpam-5511	300	6	φ(x	φ(x	NOUN
ejpam-5511	300	7	)	)	PUNCT
ejpam-5511	300	8	≤2	≤2	NOUN
ejpam-5511	300	9	φ([yz[xyz]1	φ([yz[xyz]1	PROPN
ejpam-5511	300	10	]	]	X
ejpam-5511	300	11	∗	∗	NOUN
ejpam-5511	300	12	1	1	NUM
ejpam-5511	300	13	)	)	PUNCT
ejpam-5511	300	14	=	=	NOUN
ejpam-5511	301	1	[	[	X
ejpam-5511	301	2	φ(y)φ(z)φ([xyz]1	φ(y)φ(z)φ([xyz]1	X
ejpam-5511	301	3	)	)	PUNCT
ejpam-5511	301	4	]	]	PUNCT
ejpam-5511	301	5	∗	∗	NOUN
ejpam-5511	301	6	2	2	NUM
ejpam-5511	301	7	.	.	PUNCT
ejpam-5511	302	1	that	that	PRON
ejpam-5511	302	2	is	be	AUX
ejpam-5511	302	3	,	,	PUNCT
ejpam-5511	302	4	[	[	X
ejpam-5511	302	5	φ(x)φ(y)φ(z)]2	φ(x)φ(y)φ(z)]2	DET
ejpam-5511	302	6	≤2	≤2	NOUN
ejpam-5511	302	7	φ([xyz]1	φ([xyz]1	NOUN
ejpam-5511	302	8	)	)	PUNCT
ejpam-5511	302	9	.	.	PUNCT
ejpam-5511	303	1	hence	hence	ADV
ejpam-5511	303	2	,	,	PUNCT
ejpam-5511	303	3	φ([xyz]1	φ([xyz]1	PROPN
ejpam-5511	303	4	)	)	PUNCT
ejpam-5511	303	5	=	=	PUNCT
ejpam-5511	304	1	[	[	X
ejpam-5511	304	2	φ(x)φ(y)φ(z)]2	φ(x)φ(y)φ(z)]2	X
ejpam-5511	304	3	.	.	PUNCT
ejpam-5511	305	1	(	(	PUNCT
ejpam-5511	305	2	4	4	X
ejpam-5511	305	3	)	)	PUNCT
ejpam-5511	305	4	let	let	VERB
ejpam-5511	305	5	x	x	PRON
ejpam-5511	305	6	,	,	PUNCT
ejpam-5511	305	7	y	y	PROPN
ejpam-5511	305	8	,	,	PUNCT
ejpam-5511	305	9	z	z	PROPN
ejpam-5511	305	10	∈	∈	PROPN
ejpam-5511	305	11	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	305	12	)	)	PUNCT
ejpam-5511	305	13	,	,	PUNCT
ejpam-5511	305	14	that	that	ADV
ejpam-5511	305	15	is	is	ADV
ejpam-5511	305	16	,	,	PUNCT
ejpam-5511	305	17	φ(x	φ(x	PROPN
ejpam-5511	305	18	)	)	PUNCT
ejpam-5511	305	19	=	=	SYM
ejpam-5511	305	20	φ(y	φ(y	NOUN
ejpam-5511	305	21	)	)	PUNCT
ejpam-5511	305	22	=	=	SYM
ejpam-5511	305	23	φ(z	φ(z	NOUN
ejpam-5511	305	24	)	)	PUNCT
ejpam-5511	306	1	=	=	SYM
ejpam-5511	306	2	1′.	1′.	NUM
ejpam-5511	306	3	by	by	ADP
ejpam-5511	306	4	(	(	PUNCT
ejpam-5511	306	5	3	3	NUM
ejpam-5511	306	6	)	)	PUNCT
ejpam-5511	306	7	,	,	PUNCT
ejpam-5511	306	8	φ([xyz]1	φ([xyz]1	PROPN
ejpam-5511	306	9	)	)	PUNCT
ejpam-5511	306	10	=	=	PUNCT
ejpam-5511	307	1	[	[	PUNCT
ejpam-5511	307	2	φ(x)φ(y)φ(z)]2	φ(x)φ(y)φ(z)]2	X
ejpam-5511	307	3	=	=	PUNCT
ejpam-5511	307	4	[	[	X
ejpam-5511	307	5	1′1′1′]2	1′1′1′]2	NUM
ejpam-5511	307	6	=	=	SYM
ejpam-5511	307	7	1′.	1′.	NOUN
ejpam-5511	307	8	thus	thus	ADV
ejpam-5511	307	9	,	,	PUNCT
ejpam-5511	307	10	[	[	X
ejpam-5511	307	11	xyz	xyz	X
ejpam-5511	307	12	]	]	X
ejpam-5511	307	13	∈	∈	PROPN
ejpam-5511	307	14	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	307	15	)	)	PUNCT
ejpam-5511	307	16	.	.	PUNCT
ejpam-5511	307	17	assume	assume	VERB
ejpam-5511	307	18	that	that	SCONJ
ejpam-5511	307	19	x	x	X
ejpam-5511	307	20	,	,	PUNCT
ejpam-5511	307	21	y	y	PROPN
ejpam-5511	307	22	∈	∈	PROPN
ejpam-5511	307	23	t1	t1	NOUN
ejpam-5511	307	24	such	such	ADJ
ejpam-5511	307	25	that	that	SCONJ
ejpam-5511	307	26	x	x	SYM
ejpam-5511	307	27	≤1	≤1	PRON
ejpam-5511	307	28	y	y	PROPN
ejpam-5511	307	29	and	and	CCONJ
ejpam-5511	307	30	x	x	PROPN
ejpam-5511	307	31	∈	∈	PROPN
ejpam-5511	307	32	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	307	33	)	)	PUNCT
ejpam-5511	307	34	.	.	PUNCT
ejpam-5511	308	1	then	then	ADV
ejpam-5511	308	2	1′	1′	NUM
ejpam-5511	308	3	=	=	SYM
ejpam-5511	308	4	φ(1	φ(1	PROPN
ejpam-5511	308	5	)	)	PUNCT
ejpam-5511	308	6	=	=	SYM
ejpam-5511	308	7	φ([x1y]∗1	φ([x1y]∗1	ADJ
ejpam-5511	308	8	)	)	PUNCT
ejpam-5511	308	9	=	=	PUNCT
ejpam-5511	309	1	[	[	X
ejpam-5511	309	2	φ(x)φ(1)φ(y)]∗2	φ(x)φ(1)φ(y)]∗2	X
ejpam-5511	309	3	=	=	PUNCT
ejpam-5511	310	1	[	[	X
ejpam-5511	310	2	1′1′φ(y)]∗2	1′1′φ(y)]∗2	NUM
ejpam-5511	310	3	=	=	SYM
ejpam-5511	310	4	φ(y	φ(y	NOUN
ejpam-5511	310	5	)	)	PUNCT
ejpam-5511	310	6	,	,	PUNCT
ejpam-5511	310	7	so	so	CCONJ
ejpam-5511	310	8	y	y	PROPN
ejpam-5511	310	9	∈	∈	PROPN
ejpam-5511	310	10	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	310	11	)	)	PUNCT
ejpam-5511	310	12	.	.	PUNCT
ejpam-5511	311	1	hence	hence	ADV
ejpam-5511	311	2	,	,	PUNCT
ejpam-5511	311	3	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	311	4	)	)	PUNCT
ejpam-5511	311	5	is	be	AUX
ejpam-5511	311	6	a	a	DET
ejpam-5511	311	7	filter	filter	NOUN
ejpam-5511	311	8	.	.	PUNCT
ejpam-5511	312	1	(	(	PUNCT
ejpam-5511	312	2	5	5	X
ejpam-5511	312	3	)	)	PUNCT
ejpam-5511	312	4	assume	assume	VERB
ejpam-5511	312	5	that	that	SCONJ
ejpam-5511	312	6	φ−1(1′	φ−1(1′	NOUN
ejpam-5511	312	7	)	)	PUNCT
ejpam-5511	312	8	=	=	PUNCT
ejpam-5511	312	9	{	{	PUNCT
ejpam-5511	312	10	1	1	NUM
ejpam-5511	312	11	}	}	PUNCT
ejpam-5511	312	12	.	.	PUNCT
ejpam-5511	313	1	let	let	VERB
ejpam-5511	313	2	x	x	PRON
ejpam-5511	313	3	,	,	PUNCT
ejpam-5511	313	4	y	y	PROPN
ejpam-5511	313	5	∈	∈	PROPN
ejpam-5511	313	6	t1	t1	NOUN
ejpam-5511	313	7	be	be	VERB
ejpam-5511	313	8	such	such	ADJ
ejpam-5511	313	9	that	that	SCONJ
ejpam-5511	313	10	φ(x	φ(x	NOUN
ejpam-5511	313	11	)	)	PUNCT
ejpam-5511	313	12	=	=	SYM
ejpam-5511	313	13	φ(y	φ(y	NOUN
ejpam-5511	313	14	)	)	PUNCT
ejpam-5511	313	15	.	.	PUNCT
ejpam-5511	314	1	thus	thus	ADV
ejpam-5511	314	2	,	,	PUNCT
ejpam-5511	314	3	φ([x1y]∗1	φ([x1y]∗1	ADJ
ejpam-5511	314	4	)	)	PUNCT
ejpam-5511	314	5	=	=	PUNCT
ejpam-5511	315	1	[	[	X
ejpam-5511	315	2	φ(x)φ(1)φ(y)]∗2	φ(x)φ(1)φ(y)]∗2	X
ejpam-5511	315	3	=	=	PUNCT
ejpam-5511	316	1	[	[	X
ejpam-5511	316	2	φ(x)1′φ(x)]∗2	φ(x)1′φ(x)]∗2	X
ejpam-5511	316	3	=	=	SYM
ejpam-5511	316	4	1′.	1′.	NOUN
ejpam-5511	316	5	this	this	PRON
ejpam-5511	316	6	means	mean	VERB
ejpam-5511	316	7	that	that	SCONJ
ejpam-5511	316	8	[	[	X
ejpam-5511	316	9	x1y]∗1	x1y]∗1	NOUN
ejpam-5511	316	10	∈	∈	PROPN
ejpam-5511	316	11	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	316	12	)	)	PUNCT
ejpam-5511	316	13	,	,	PUNCT
ejpam-5511	316	14	that	that	ADV
ejpam-5511	316	15	is	is	ADV
ejpam-5511	316	16	,	,	PUNCT
ejpam-5511	316	17	[	[	X
ejpam-5511	316	18	x1y]∗1	x1y]∗1	X
ejpam-5511	316	19	=	=	SYM
ejpam-5511	316	20	1	1	X
ejpam-5511	316	21	.	.	PUNCT
ejpam-5511	316	22	then	then	ADV
ejpam-5511	316	23	by	by	ADP
ejpam-5511	316	24	theorem	theorem	NOUN
ejpam-5511	316	25	2	2	NUM
ejpam-5511	316	26	(	(	PUNCT
ejpam-5511	316	27	6	6	NUM
ejpam-5511	316	28	)	)	PUNCT
ejpam-5511	316	29	,	,	PUNCT
ejpam-5511	316	30	we	we	PRON
ejpam-5511	316	31	get	get	VERB
ejpam-5511	316	32	that	that	SCONJ
ejpam-5511	316	33	x	x	PUNCT
ejpam-5511	316	34	≤1	≤1	PROPN
ejpam-5511	316	35	y.	y.	PROPN
ejpam-5511	316	36	similarly	similarly	ADV
ejpam-5511	316	37	,	,	PUNCT
ejpam-5511	316	38	we	we	PRON
ejpam-5511	316	39	have	have	VERB
ejpam-5511	316	40	[	[	X
ejpam-5511	316	41	y1x]∗1	y1x]∗1	NOUN
ejpam-5511	316	42	=	=	SYM
ejpam-5511	316	43	1	1	NUM
ejpam-5511	316	44	,	,	PUNCT
ejpam-5511	316	45	then	then	ADV
ejpam-5511	316	46	y	y	PROPN
ejpam-5511	316	47	≤1	≤1	PROPN
ejpam-5511	316	48	x.	x.	NOUN
ejpam-5511	316	49	hence	hence	ADV
ejpam-5511	316	50	,	,	PUNCT
ejpam-5511	316	51	x	x	PUNCT
ejpam-5511	316	52	=	=	PUNCT
ejpam-5511	316	53	y.	y.	NOUN
ejpam-5511	316	54	on	on	ADP
ejpam-5511	316	55	the	the	DET
ejpam-5511	316	56	other	other	ADJ
ejpam-5511	316	57	hand	hand	NOUN
ejpam-5511	316	58	,	,	PUNCT
ejpam-5511	316	59	assume	assume	VERB
ejpam-5511	316	60	that	that	SCONJ
ejpam-5511	316	61	φ	φ	PROPN
ejpam-5511	316	62	is	be	AUX
ejpam-5511	316	63	an	an	DET
ejpam-5511	316	64	isomorphism	isomorphism	NOUN
ejpam-5511	316	65	.	.	PUNCT
ejpam-5511	317	1	if	if	SCONJ
ejpam-5511	317	2	x	x	SYM
ejpam-5511	317	3	∈	∈	PROPN
ejpam-5511	317	4	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	317	5	)	)	PUNCT
ejpam-5511	317	6	,	,	PUNCT
ejpam-5511	317	7	then	then	ADV
ejpam-5511	317	8	φ(x	φ(x	NOUN
ejpam-5511	317	9	)	)	PUNCT
ejpam-5511	317	10	=	=	SYM
ejpam-5511	317	11	1′	1′	NUM
ejpam-5511	317	12	=	=	SYM
ejpam-5511	317	13	φ(1	φ(1	PROPN
ejpam-5511	317	14	)	)	PUNCT
ejpam-5511	317	15	,	,	PUNCT
ejpam-5511	317	16	so	so	CCONJ
ejpam-5511	317	17	by	by	ADP
ejpam-5511	317	18	assumption	assumption	NOUN
ejpam-5511	317	19	we	we	PRON
ejpam-5511	317	20	have	have	VERB
ejpam-5511	317	21	x	x	X
ejpam-5511	317	22	=	=	SYM
ejpam-5511	317	23	1	1	NUM
ejpam-5511	317	24	.	.	PUNCT
ejpam-5511	318	1	hence	hence	ADV
ejpam-5511	318	2	,	,	PUNCT
ejpam-5511	318	3	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	318	4	)	)	PUNCT
ejpam-5511	318	5	=	=	PUNCT
ejpam-5511	318	6	{	{	PUNCT
ejpam-5511	318	7	1	1	NUM
ejpam-5511	318	8	}	}	PUNCT
ejpam-5511	318	9	.	.	PUNCT
ejpam-5511	319	1	k.	k.	PROPN
ejpam-5511	319	2	nakwan	nakwan	PROPN
ejpam-5511	319	3	,	,	PUNCT
ejpam-5511	319	4	p.	p.	PROPN
ejpam-5511	319	5	luangchaisri	luangchaisri	VERB
ejpam-5511	319	6	,	,	PUNCT
ejpam-5511	319	7	t.	t.	PROPN
ejpam-5511	319	8	changphas	changphas	PROPN
ejpam-5511	319	9	/	/	SYM
ejpam-5511	319	10	eur	eur	PROPN
ejpam-5511	319	11	.	.	PUNCT
ejpam-5511	320	1	j.	j.	PROPN
ejpam-5511	320	2	pure	pure	PROPN
ejpam-5511	320	3	appl	appl	PROPN
ejpam-5511	320	4	.	.	PROPN
ejpam-5511	320	5	math	math	PROPN
ejpam-5511	320	6	,	,	PUNCT
ejpam-5511	320	7	17	17	NUM
ejpam-5511	320	8	(	(	PUNCT
ejpam-5511	320	9	4	4	NUM
ejpam-5511	320	10	)	)	PUNCT
ejpam-5511	320	11	(	(	PUNCT
ejpam-5511	320	12	2024	2024	NUM
ejpam-5511	320	13	)	)	PUNCT
ejpam-5511	320	14	,	,	PUNCT
ejpam-5511	320	15	4180	4180	NUM
ejpam-5511	320	16	-	-	SYM
ejpam-5511	320	17	4194	4194	NUM
ejpam-5511	320	18	4188	4188	NUM
ejpam-5511	320	19	4	4	NUM
ejpam-5511	320	20	.	.	PUNCT
ejpam-5511	320	21	commutative	commutative	ADJ
ejpam-5511	320	22	implicative	implicative	ADJ
ejpam-5511	320	23	n.p.o	n.p.o	NOUN
ejpam-5511	320	24	.	.	PUNCT
ejpam-5511	321	1	ternary	ternary	ADJ
ejpam-5511	321	2	semigroups	semigroup	NOUN
ejpam-5511	321	3	hereafter	hereafter	ADV
ejpam-5511	321	4	,	,	PUNCT
ejpam-5511	321	5	we	we	PRON
ejpam-5511	321	6	deal	deal	VERB
ejpam-5511	321	7	with	with	ADP
ejpam-5511	321	8	commutative	commutative	ADJ
ejpam-5511	321	9	implicative	implicative	ADJ
ejpam-5511	321	10	n.p.o	n.p.o	NOUN
ejpam-5511	321	11	.	.	PUNCT
ejpam-5511	322	1	ternary	ternary	ADJ
ejpam-5511	322	2	semigroups	semigroup	NOUN
ejpam-5511	322	3	.	.	PUNCT
ejpam-5511	323	1	proposition	proposition	NOUN
ejpam-5511	323	2	1	1	NUM
ejpam-5511	323	3	.	.	PUNCT
ejpam-5511	324	1	if	if	SCONJ
ejpam-5511	324	2	f	f	PROPN
ejpam-5511	324	3	is	be	AUX
ejpam-5511	324	4	a	a	DET
ejpam-5511	324	5	filter	filter	NOUN
ejpam-5511	324	6	of	of	ADP
ejpam-5511	324	7	a	a	DET
ejpam-5511	324	8	commutative	commutative	ADJ
ejpam-5511	324	9	implicative	implicative	ADJ
ejpam-5511	324	10	n.p.o	n.p.o	NOUN
ejpam-5511	324	11	.	.	PUNCT
ejpam-5511	325	1	ternary	ternary	PROPN
ejpam-5511	325	2	semigroup	semigroup	PROPN
ejpam-5511	325	3	(	(	PUNCT
ejpam-5511	325	4	t	t	PROPN
ejpam-5511	325	5	,	,	PUNCT
ejpam-5511	325	6	[	[	PUNCT
ejpam-5511	325	7	]	]	X
ejpam-5511	325	8	,	,	PUNCT
ejpam-5511	325	9	≤	≤	NUM
ejpam-5511	325	10	,	,	PUNCT
ejpam-5511	325	11	[	[	PUNCT
ejpam-5511	325	12	]	]	X
ejpam-5511	325	13	∗	∗	NOUN
ejpam-5511	325	14	)	)	PUNCT
ejpam-5511	325	15	,	,	PUNCT
ejpam-5511	325	16	then	then	ADV
ejpam-5511	325	17	1	1	NUM
ejpam-5511	325	18	∈	∈	PROPN
ejpam-5511	325	19	f	f	NOUN
ejpam-5511	325	20	.	.	PUNCT
ejpam-5511	326	1	proof	proof	NOUN
ejpam-5511	326	2	.	.	PUNCT
ejpam-5511	327	1	the	the	DET
ejpam-5511	327	2	assertion	assertion	NOUN
ejpam-5511	327	3	follows	follow	VERB
ejpam-5511	327	4	by	by	ADP
ejpam-5511	327	5	1	1	NUM
ejpam-5511	327	6	is	be	AUX
ejpam-5511	327	7	the	the	DET
ejpam-5511	327	8	greatest	great	ADJ
ejpam-5511	327	9	element	element	NOUN
ejpam-5511	327	10	of	of	ADP
ejpam-5511	327	11	t	t	PROPN
ejpam-5511	327	12	.	.	PUNCT
ejpam-5511	328	1	let	let	VERB
ejpam-5511	328	2	(	(	PUNCT
ejpam-5511	328	3	t	t	NOUN
ejpam-5511	328	4	,	,	PUNCT
ejpam-5511	328	5	[	[	PUNCT
ejpam-5511	328	6	]	]	X
ejpam-5511	328	7	)	)	PUNCT
ejpam-5511	328	8	be	be	AUX
ejpam-5511	328	9	a	a	DET
ejpam-5511	328	10	ternary	ternary	ADJ
ejpam-5511	328	11	semigroup	semigroup	NOUN
ejpam-5511	328	12	.	.	PUNCT
ejpam-5511	329	1	an	an	DET
ejpam-5511	329	2	equivalence	equivalence	NOUN
ejpam-5511	329	3	relation	relation	NOUN
ejpam-5511	329	4	α	α	PROPN
ejpam-5511	329	5	on	on	ADP
ejpam-5511	329	6	t	t	PROPN
ejpam-5511	329	7	is	be	AUX
ejpam-5511	329	8	called	call	VERB
ejpam-5511	329	9	a	a	DET
ejpam-5511	329	10	congruence	congruence	NOUN
ejpam-5511	329	11	if	if	SCONJ
ejpam-5511	329	12	for	for	ADP
ejpam-5511	329	13	any	any	DET
ejpam-5511	329	14	x	x	NOUN
ejpam-5511	329	15	,	,	PUNCT
ejpam-5511	329	16	y	y	PROPN
ejpam-5511	329	17	,	,	PUNCT
ejpam-5511	329	18	s	s	PROPN
ejpam-5511	329	19	,	,	PUNCT
ejpam-5511	329	20	t	t	PROPN
ejpam-5511	329	21	∈	∈	PROPN
ejpam-5511	329	22	t	t	PROPN
ejpam-5511	329	23	,	,	PUNCT
ejpam-5511	330	1	if	if	SCONJ
ejpam-5511	330	2	(	(	PUNCT
ejpam-5511	330	3	x	x	NOUN
ejpam-5511	330	4	,	,	PUNCT
ejpam-5511	330	5	y	y	NOUN
ejpam-5511	330	6	)	)	PUNCT
ejpam-5511	330	7	∈	∈	PROPN
ejpam-5511	330	8	α	α	NOUN
ejpam-5511	330	9	,	,	PUNCT
ejpam-5511	330	10	then	then	ADV
ejpam-5511	330	11	(	(	PUNCT
ejpam-5511	330	12	[	[	X
ejpam-5511	330	13	stx	stx	X
ejpam-5511	330	14	]	]	X
ejpam-5511	330	15	,	,	PUNCT
ejpam-5511	331	1	[	[	X
ejpam-5511	331	2	sty	sty	PROPN
ejpam-5511	331	3	]	]	X
ejpam-5511	331	4	)	)	PUNCT
ejpam-5511	331	5	,	,	PUNCT
ejpam-5511	331	6	(	(	PUNCT
ejpam-5511	332	1	[	[	X
ejpam-5511	332	2	xst	xst	X
ejpam-5511	332	3	]	]	X
ejpam-5511	332	4	,	,	PUNCT
ejpam-5511	333	1	[	[	X
ejpam-5511	333	2	yst	yst	NOUN
ejpam-5511	333	3	]	]	X
ejpam-5511	333	4	)	)	PUNCT
ejpam-5511	333	5	,	,	PUNCT
ejpam-5511	333	6	(	(	PUNCT
ejpam-5511	333	7	[	[	X
ejpam-5511	333	8	sxt	sxt	X
ejpam-5511	333	9	]	]	X
ejpam-5511	333	10	,	,	PUNCT
ejpam-5511	333	11	[	[	X
ejpam-5511	333	12	syt	syt	X
ejpam-5511	333	13	]	]	X
ejpam-5511	333	14	)	)	PUNCT
ejpam-5511	333	15	∈	∈	PROPN
ejpam-5511	333	16	α	α	X
ejpam-5511	333	17	.	.	PUNCT
ejpam-5511	333	18	definition	definition	NOUN
ejpam-5511	333	19	5	5	NUM
ejpam-5511	333	20	.	.	PUNCT
ejpam-5511	334	1	let	let	AUX
ejpam-5511	334	2	(	(	PUNCT
ejpam-5511	334	3	t	t	NOUN
ejpam-5511	334	4	,	,	PUNCT
ejpam-5511	334	5	[	[	PUNCT
ejpam-5511	334	6	]	]	X
ejpam-5511	334	7	,	,	PUNCT
ejpam-5511	334	8	≤	≤	NUM
ejpam-5511	334	9	,	,	PUNCT
ejpam-5511	334	10	[	[	PUNCT
ejpam-5511	334	11	]	]	X
ejpam-5511	334	12	∗	∗	NOUN
ejpam-5511	334	13	)	)	PUNCT
ejpam-5511	334	14	be	be	VERB
ejpam-5511	334	15	a	a	DET
ejpam-5511	334	16	commutative	commutative	ADJ
ejpam-5511	334	17	implicative	implicative	ADJ
ejpam-5511	334	18	n.p.o	n.p.o	NOUN
ejpam-5511	334	19	.	.	PUNCT
ejpam-5511	335	1	ternary	ternary	PROPN
ejpam-5511	335	2	semigroup	semigroup	PROPN
ejpam-5511	335	3	,	,	PUNCT
ejpam-5511	335	4	and	and	CCONJ
ejpam-5511	335	5	let	let	VERB
ejpam-5511	335	6	f	f	PRON
ejpam-5511	335	7	be	be	AUX
ejpam-5511	335	8	a	a	DET
ejpam-5511	335	9	filter	filter	NOUN
ejpam-5511	335	10	of	of	ADP
ejpam-5511	335	11	t	t	PROPN
ejpam-5511	335	12	.	.	PUNCT
ejpam-5511	336	1	for	for	ADP
ejpam-5511	336	2	any	any	DET
ejpam-5511	336	3	x	x	NOUN
ejpam-5511	336	4	,	,	PUNCT
ejpam-5511	336	5	y	y	PROPN
ejpam-5511	336	6	∈	∈	PROPN
ejpam-5511	336	7	t	t	PROPN
ejpam-5511	336	8	,	,	PUNCT
ejpam-5511	336	9	the	the	DET
ejpam-5511	336	10	relation	relation	NOUN
ejpam-5511	336	11	ρf	ρf	PRON
ejpam-5511	336	12	defined	define	VERB
ejpam-5511	336	13	on	on	ADP
ejpam-5511	336	14	t	t	PROPN
ejpam-5511	336	15	as	as	SCONJ
ejpam-5511	336	16	follows	follow	VERB
ejpam-5511	336	17	:	:	PUNCT
ejpam-5511	336	18	xρf	xρf	PROPN
ejpam-5511	336	19	y	y	PROPN
ejpam-5511	336	20	⇔	⇔	PROPN
ejpam-5511	336	21	there	there	PRON
ejpam-5511	336	22	exist	exist	VERB
ejpam-5511	336	23	a	a	DET
ejpam-5511	336	24	,	,	PUNCT
ejpam-5511	336	25	b	b	PROPN
ejpam-5511	336	26	∈	∈	PROPN
ejpam-5511	336	27	f	f	PROPN
ejpam-5511	337	1	such	such	ADJ
ejpam-5511	337	2	that	that	SCONJ
ejpam-5511	337	3	[	[	X
ejpam-5511	337	4	abx	abx	NOUN
ejpam-5511	337	5	]	]	X
ejpam-5511	337	6	≤	≤	ADJ
ejpam-5511	337	7	y	y	PROPN
ejpam-5511	337	8	and	and	CCONJ
ejpam-5511	337	9	[	[	X
ejpam-5511	337	10	aby	aby	X
ejpam-5511	337	11	]	]	X
ejpam-5511	337	12	≤	≤	NUM
ejpam-5511	337	13	x.	x.	PUNCT
ejpam-5511	337	14	lemma	lemma	PROPN
ejpam-5511	338	1	1	1	X
ejpam-5511	338	2	.	.	PUNCT
ejpam-5511	339	1	let	let	AUX
ejpam-5511	339	2	(	(	PUNCT
ejpam-5511	339	3	t	t	NOUN
ejpam-5511	339	4	,	,	PUNCT
ejpam-5511	339	5	[	[	PUNCT
ejpam-5511	339	6	]	]	X
ejpam-5511	339	7	,	,	PUNCT
ejpam-5511	339	8	≤	≤	NUM
ejpam-5511	339	9	,	,	PUNCT
ejpam-5511	339	10	[	[	PUNCT
ejpam-5511	339	11	]	]	X
ejpam-5511	339	12	∗	∗	NOUN
ejpam-5511	339	13	)	)	PUNCT
ejpam-5511	339	14	be	be	VERB
ejpam-5511	339	15	a	a	DET
ejpam-5511	339	16	commutative	commutative	ADJ
ejpam-5511	339	17	implicative	implicative	ADJ
ejpam-5511	339	18	n.p.o	n.p.o	NOUN
ejpam-5511	339	19	.	.	PUNCT
ejpam-5511	340	1	ternary	ternary	PROPN
ejpam-5511	340	2	semigroup	semigroup	PROPN
ejpam-5511	340	3	,	,	PUNCT
ejpam-5511	340	4	and	and	CCONJ
ejpam-5511	340	5	let	let	VERB
ejpam-5511	340	6	f	f	PRON
ejpam-5511	340	7	be	be	AUX
ejpam-5511	340	8	a	a	DET
ejpam-5511	340	9	filter	filter	NOUN
ejpam-5511	340	10	of	of	ADP
ejpam-5511	340	11	t	t	PROPN
ejpam-5511	340	12	.	.	PUNCT
ejpam-5511	341	1	then	then	ADV
ejpam-5511	341	2	the	the	DET
ejpam-5511	341	3	relation	relation	NOUN
ejpam-5511	341	4	ρf	ρf	NOUN
ejpam-5511	341	5	is	be	AUX
ejpam-5511	341	6	a	a	DET
ejpam-5511	341	7	congruence	congruence	NOUN
ejpam-5511	341	8	defined	define	VERB
ejpam-5511	341	9	on	on	ADP
ejpam-5511	341	10	t	t	PROPN
ejpam-5511	341	11	.	.	PUNCT
ejpam-5511	342	1	proof	proof	NOUN
ejpam-5511	342	2	.	.	PUNCT
ejpam-5511	343	1	let	let	VERB
ejpam-5511	343	2	x	x	PRON
ejpam-5511	343	3	,	,	PUNCT
ejpam-5511	343	4	y	y	PROPN
ejpam-5511	343	5	,	,	PUNCT
ejpam-5511	343	6	z	z	PROPN
ejpam-5511	343	7	∈	∈	PROPN
ejpam-5511	343	8	t	t	NOUN
ejpam-5511	343	9	.	.	PUNCT
ejpam-5511	344	1	as	as	ADP
ejpam-5511	344	2	1	1	NUM
ejpam-5511	344	3	∈	∈	PROPN
ejpam-5511	344	4	f	f	NOUN
ejpam-5511	344	5	and	and	CCONJ
ejpam-5511	344	6	[	[	X
ejpam-5511	344	7	11x	11x	NOUN
ejpam-5511	344	8	]	]	X
ejpam-5511	344	9	≤	≤	NUM
ejpam-5511	344	10	x	x	NOUN
ejpam-5511	344	11	,	,	PUNCT
ejpam-5511	344	12	we	we	PRON
ejpam-5511	344	13	have	have	VERB
ejpam-5511	344	14	xρfx	xρfx	PROPN
ejpam-5511	344	15	.	.	PUNCT
ejpam-5511	345	1	if	if	SCONJ
ejpam-5511	345	2	xρf	xρf	PROPN
ejpam-5511	345	3	y	y	PROPN
ejpam-5511	345	4	,	,	PUNCT
ejpam-5511	345	5	then	then	ADV
ejpam-5511	345	6	there	there	PRON
ejpam-5511	345	7	exist	exist	VERB
ejpam-5511	345	8	a	a	DET
ejpam-5511	345	9	,	,	PUNCT
ejpam-5511	345	10	b	b	PROPN
ejpam-5511	345	11	∈	∈	PROPN
ejpam-5511	345	12	f	f	PROPN
ejpam-5511	346	1	such	such	ADJ
ejpam-5511	346	2	that	that	SCONJ
ejpam-5511	347	1	[	[	X
ejpam-5511	347	2	abx	abx	NOUN
ejpam-5511	347	3	]	]	X
ejpam-5511	347	4	≤	≤	ADJ
ejpam-5511	347	5	y	y	PROPN
ejpam-5511	347	6	and	and	CCONJ
ejpam-5511	347	7	[	[	X
ejpam-5511	347	8	aby	aby	X
ejpam-5511	347	9	]	]	X
ejpam-5511	347	10	≤	≤	NUM
ejpam-5511	347	11	x	x	NOUN
ejpam-5511	347	12	,	,	PUNCT
ejpam-5511	347	13	hence	hence	ADV
ejpam-5511	347	14	,	,	PUNCT
ejpam-5511	347	15	yρfx	yρfx	PROPN
ejpam-5511	347	16	.	.	PUNCT
ejpam-5511	347	17	assume	assume	VERB
ejpam-5511	347	18	that	that	SCONJ
ejpam-5511	347	19	xρf	xρf	PROPN
ejpam-5511	347	20	y	y	PROPN
ejpam-5511	347	21	and	and	CCONJ
ejpam-5511	347	22	yρf	yρf	PROPN
ejpam-5511	347	23	z.	z.	PROPN
ejpam-5511	347	24	then	then	ADV
ejpam-5511	347	25	there	there	PRON
ejpam-5511	347	26	exist	exist	VERB
ejpam-5511	347	27	a	a	DET
ejpam-5511	347	28	,	,	PUNCT
ejpam-5511	347	29	b	b	NOUN
ejpam-5511	347	30	,	,	PUNCT
ejpam-5511	347	31	c	c	NOUN
ejpam-5511	347	32	,	,	PUNCT
ejpam-5511	348	1	d	d	PROPN
ejpam-5511	348	2	∈	∈	PROPN
ejpam-5511	348	3	f	f	PROPN
ejpam-5511	348	4	such	such	ADJ
ejpam-5511	349	1	that	that	SCONJ
ejpam-5511	350	1	[	[	X
ejpam-5511	350	2	abx	abx	NOUN
ejpam-5511	350	3	]	]	X
ejpam-5511	350	4	≤	≤	ADJ
ejpam-5511	350	5	y	y	PROPN
ejpam-5511	350	6	and	and	CCONJ
ejpam-5511	350	7	[	[	X
ejpam-5511	350	8	aby	aby	X
ejpam-5511	350	9	]	]	X
ejpam-5511	350	10	≤	≤	NUM
ejpam-5511	350	11	x	x	X
ejpam-5511	350	12	,	,	PUNCT
ejpam-5511	351	1	[	[	X
ejpam-5511	351	2	cdy	cdy	X
ejpam-5511	351	3	]	]	X
ejpam-5511	351	4	≤	≤	NUM
ejpam-5511	351	5	z	z	NOUN
ejpam-5511	351	6	and	and	CCONJ
ejpam-5511	351	7	[	[	X
ejpam-5511	351	8	cdz	cdz	X
ejpam-5511	351	9	]	]	X
ejpam-5511	351	10	≤	≤	NUM
ejpam-5511	351	11	y.	y.	NOUN
ejpam-5511	351	12	we	we	PRON
ejpam-5511	351	13	have	have	VERB
ejpam-5511	351	14	[	[	X
ejpam-5511	351	15	[	[	X
ejpam-5511	351	16	abc]dx	abc]dx	X
ejpam-5511	351	17	]	]	X
ejpam-5511	351	18	=	=	PUNCT
ejpam-5511	352	1	[	[	X
ejpam-5511	352	2	[	[	X
ejpam-5511	352	3	cab]dx	cab]dx	X
ejpam-5511	352	4	]	]	X
ejpam-5511	352	5	=	=	PUNCT
ejpam-5511	353	1	[	[	X
ejpam-5511	353	2	c[abd]x	c[abd]x	X
ejpam-5511	353	3	]	]	X
ejpam-5511	353	4	=	=	PUNCT
ejpam-5511	354	1	[	[	X
ejpam-5511	354	2	c[dab]x	c[dab]x	X
ejpam-5511	354	3	]	]	X
ejpam-5511	354	4	=	=	PUNCT
ejpam-5511	355	1	[	[	X
ejpam-5511	355	2	cd[abx	cd[abx	NOUN
ejpam-5511	355	3	]	]	X
ejpam-5511	355	4	]	]	X
ejpam-5511	355	5	≤	≤	X
ejpam-5511	356	1	[	[	X
ejpam-5511	356	2	cdy	cdy	X
ejpam-5511	356	3	]	]	X
ejpam-5511	356	4	≤	≤	NUM
ejpam-5511	356	5	z	z	NOUN
ejpam-5511	356	6	and	and	CCONJ
ejpam-5511	356	7	[	[	X
ejpam-5511	356	8	[	[	X
ejpam-5511	356	9	abc]dz	abc]dz	X
ejpam-5511	356	10	]	]	X
ejpam-5511	356	11	=	=	PUNCT
ejpam-5511	357	1	[	[	X
ejpam-5511	357	2	ab[cdz	ab[cdz	PROPN
ejpam-5511	357	3	]	]	X
ejpam-5511	357	4	]	]	X
ejpam-5511	357	5	≤	≤	NOUN
ejpam-5511	358	1	[	[	X
ejpam-5511	358	2	aby	aby	X
ejpam-5511	358	3	]	]	X
ejpam-5511	358	4	≤	≤	NUM
ejpam-5511	358	5	x.	x.	PUNCT
ejpam-5511	358	6	thus	thus	ADV
ejpam-5511	358	7	,	,	PUNCT
ejpam-5511	358	8	xρf	xρf	PROPN
ejpam-5511	358	9	z.	z.	PROPN
ejpam-5511	358	10	therefore	therefore	ADV
ejpam-5511	358	11	,	,	PUNCT
ejpam-5511	358	12	ρf	ρf	PRON
ejpam-5511	358	13	is	be	AUX
ejpam-5511	358	14	an	an	DET
ejpam-5511	358	15	equivalence	equivalence	NOUN
ejpam-5511	358	16	relation	relation	NOUN
ejpam-5511	358	17	on	on	ADP
ejpam-5511	358	18	t	t	PROPN
ejpam-5511	358	19	.	.	PUNCT
ejpam-5511	359	1	suppose	suppose	VERB
ejpam-5511	359	2	that	that	SCONJ
ejpam-5511	359	3	xρf	xρf	PROPN
ejpam-5511	359	4	y.	y.	PROPN
ejpam-5511	359	5	then	then	ADV
ejpam-5511	359	6	there	there	PRON
ejpam-5511	359	7	exist	exist	VERB
ejpam-5511	359	8	a	a	DET
ejpam-5511	359	9	,	,	PUNCT
ejpam-5511	359	10	b	b	PROPN
ejpam-5511	359	11	∈	∈	PROPN
ejpam-5511	359	12	f	f	PROPN
ejpam-5511	359	13	such	such	ADJ
ejpam-5511	359	14	that	that	SCONJ
ejpam-5511	359	15	[	[	X
ejpam-5511	359	16	abx	abx	NOUN
ejpam-5511	359	17	]	]	X
ejpam-5511	359	18	≤	≤	ADJ
ejpam-5511	359	19	y	y	PROPN
ejpam-5511	359	20	and	and	CCONJ
ejpam-5511	359	21	[	[	X
ejpam-5511	359	22	aby	aby	X
ejpam-5511	359	23	]	]	X
ejpam-5511	359	24	≤	≤	NUM
ejpam-5511	359	25	x.	x.	NOUN
ejpam-5511	359	26	let	let	VERB
ejpam-5511	359	27	s	s	NOUN
ejpam-5511	359	28	,	,	PUNCT
ejpam-5511	359	29	t	t	PROPN
ejpam-5511	359	30	∈	∈	PROPN
ejpam-5511	359	31	t	t	PROPN
ejpam-5511	359	32	.	.	PUNCT
ejpam-5511	360	1	we	we	PRON
ejpam-5511	360	2	have	have	VERB
ejpam-5511	360	3	[	[	X
ejpam-5511	360	4	ab[xst	ab[xst	NOUN
ejpam-5511	360	5	]	]	X
ejpam-5511	360	6	]	]	PUNCT
ejpam-5511	361	1	=	=	PUNCT
ejpam-5511	362	1	[	[	X
ejpam-5511	362	2	[	[	X
ejpam-5511	362	3	abx]st	abx]st	X
ejpam-5511	362	4	]	]	PUNCT
ejpam-5511	362	5	≤	≤	NOUN
ejpam-5511	363	1	[	[	X
ejpam-5511	363	2	yst	yst	X
ejpam-5511	363	3	]	]	X
ejpam-5511	363	4	and	and	CCONJ
ejpam-5511	363	5	[	[	X
ejpam-5511	363	6	ab[yst	ab[yst	X
ejpam-5511	363	7	]	]	X
ejpam-5511	363	8	]	]	PUNCT
ejpam-5511	364	1	=	=	PUNCT
ejpam-5511	365	1	[	[	X
ejpam-5511	365	2	[	[	X
ejpam-5511	365	3	aby]st	aby]st	X
ejpam-5511	365	4	]	]	PUNCT
ejpam-5511	365	5	≤	≤	NOUN
ejpam-5511	366	1	[	[	X
ejpam-5511	366	2	xst	xst	X
ejpam-5511	366	3	]	]	X
ejpam-5511	366	4	;	;	PUNCT
ejpam-5511	366	5	so	so	CCONJ
ejpam-5511	366	6	[	[	X
ejpam-5511	366	7	xst]ρf	xst]ρf	PROPN
ejpam-5511	366	8	[	[	X
ejpam-5511	366	9	yst	yst	NOUN
ejpam-5511	366	10	]	]	X
ejpam-5511	366	11	.	.	PUNCT
ejpam-5511	367	1	similarly	similarly	ADV
ejpam-5511	367	2	,	,	PUNCT
ejpam-5511	367	3	[	[	X
ejpam-5511	367	4	stx]ρf	stx]ρf	ADJ
ejpam-5511	367	5	[	[	X
ejpam-5511	367	6	sty	sty	X
ejpam-5511	367	7	]	]	PUNCT
ejpam-5511	367	8	and	and	CCONJ
ejpam-5511	367	9	[	[	AUX
ejpam-5511	367	10	sxt]ρf	sxt]ρf	X
ejpam-5511	367	11	[	[	X
ejpam-5511	367	12	syt	syt	X
ejpam-5511	367	13	]	]	X
ejpam-5511	367	14	.	.	PUNCT
ejpam-5511	368	1	hence	hence	ADV
ejpam-5511	368	2	,	,	PUNCT
ejpam-5511	368	3	ρf	ρf	PRON
ejpam-5511	368	4	is	be	AUX
ejpam-5511	368	5	a	a	DET
ejpam-5511	368	6	congruence	congruence	NOUN
ejpam-5511	368	7	relation	relation	NOUN
ejpam-5511	368	8	on	on	ADP
ejpam-5511	368	9	t	t	PROPN
ejpam-5511	368	10	.	.	PUNCT
ejpam-5511	369	1	let	let	VERB
ejpam-5511	369	2	(	(	PUNCT
ejpam-5511	369	3	t	t	NOUN
ejpam-5511	369	4	,	,	PUNCT
ejpam-5511	369	5	[	[	PUNCT
ejpam-5511	369	6	]	]	X
ejpam-5511	369	7	,	,	PUNCT
ejpam-5511	369	8	≤	≤	NUM
ejpam-5511	369	9	,	,	PUNCT
ejpam-5511	369	10	[	[	PUNCT
ejpam-5511	369	11	]	]	X
ejpam-5511	369	12	∗	∗	NOUN
ejpam-5511	369	13	)	)	PUNCT
ejpam-5511	369	14	be	be	VERB
ejpam-5511	369	15	a	a	DET
ejpam-5511	369	16	commutative	commutative	ADJ
ejpam-5511	369	17	implicative	implicative	ADJ
ejpam-5511	369	18	n.p.o	n.p.o	NOUN
ejpam-5511	369	19	.	.	PUNCT
ejpam-5511	370	1	ternary	ternary	PROPN
ejpam-5511	370	2	semigroup	semigroup	PROPN
ejpam-5511	370	3	,	,	PUNCT
ejpam-5511	370	4	and	and	CCONJ
ejpam-5511	370	5	let	let	VERB
ejpam-5511	370	6	f	f	PRON
ejpam-5511	370	7	be	be	AUX
ejpam-5511	370	8	a	a	DET
ejpam-5511	370	9	filter	filter	NOUN
ejpam-5511	370	10	of	of	ADP
ejpam-5511	370	11	t	t	PROPN
ejpam-5511	370	12	.	.	PUNCT
ejpam-5511	371	1	as	as	ADP
ejpam-5511	371	2	usual	usual	ADJ
ejpam-5511	371	3	,	,	PUNCT
ejpam-5511	371	4	for	for	SCONJ
ejpam-5511	371	5	each	each	DET
ejpam-5511	371	6	x	x	SYM
ejpam-5511	371	7	∈	∈	PROPN
ejpam-5511	371	8	t	t	NOUN
ejpam-5511	371	9	the	the	DET
ejpam-5511	371	10	corresponding	corresponding	ADJ
ejpam-5511	371	11	element	element	NOUN
ejpam-5511	371	12	in	in	ADP
ejpam-5511	371	13	t	t	PROPN
ejpam-5511	371	14	/	/	SYM
ejpam-5511	371	15	ρf	ρf	PROPN
ejpam-5511	371	16	,	,	PUNCT
ejpam-5511	371	17	denoted	denote	VERB
ejpam-5511	371	18	by	by	ADP
ejpam-5511	371	19	[	[	PUNCT
ejpam-5511	371	20	x]ρf	x]ρf	PROPN
ejpam-5511	371	21	,	,	PUNCT
ejpam-5511	371	22	is	be	AUX
ejpam-5511	371	23	the	the	DET
ejpam-5511	371	24	equivalence	equivalence	NOUN
ejpam-5511	371	25	class	class	NOUN
ejpam-5511	372	1	[	[	X
ejpam-5511	372	2	x]ρf	x]ρf	PROPN
ejpam-5511	372	3	=	=	SYM
ejpam-5511	372	4	{	{	PUNCT
ejpam-5511	372	5	y	y	PROPN
ejpam-5511	372	6	∈	∈	PROPN
ejpam-5511	372	7	t	t	PROPN
ejpam-5511	372	8	:	:	PUNCT
ejpam-5511	372	9	yρfx	yρfx	PROPN
ejpam-5511	372	10	}	}	PUNCT
ejpam-5511	372	11	,	,	PUNCT
ejpam-5511	372	12	that	that	PRON
ejpam-5511	372	13	is	be	AUX
ejpam-5511	372	14	t	t	PROPN
ejpam-5511	372	15	/	/	SYM
ejpam-5511	372	16	ρf	ρf	NOUN
ejpam-5511	372	17	=	=	PUNCT
ejpam-5511	372	18	{	{	PUNCT
ejpam-5511	373	1	[	[	X
ejpam-5511	373	2	x]ρf	x]ρf	PROPN
ejpam-5511	373	3	:	:	PUNCT
ejpam-5511	373	4	x	x	SYM
ejpam-5511	373	5	∈	∈	PROPN
ejpam-5511	373	6	t	t	PROPN
ejpam-5511	373	7	}	}	PUNCT
ejpam-5511	373	8	.	.	PUNCT
ejpam-5511	374	1	define	define	VERB
ejpam-5511	374	2	the	the	DET
ejpam-5511	374	3	ternary	ternary	ADJ
ejpam-5511	374	4	multiplication	multiplication	NOUN
ejpam-5511	374	5	[	[	X
ejpam-5511	374	6	[	[	X
ejpam-5511	374	7	]	]	X
ejpam-5511	374	8	]	]	X
ejpam-5511	374	9	:	:	PUNCT
ejpam-5511	374	10	t	t	X
ejpam-5511	374	11	/	/	SYM
ejpam-5511	374	12	ρf	ρf	PROPN
ejpam-5511	374	13	×	×	PROPN
ejpam-5511	374	14	t	t	PROPN
ejpam-5511	374	15	/	/	SYM
ejpam-5511	374	16	ρf	ρf	PROPN
ejpam-5511	374	17	×	×	PROPN
ejpam-5511	374	18	t	t	PROPN
ejpam-5511	374	19	/	/	SYM
ejpam-5511	374	20	ρf	ρf	PROPN
ejpam-5511	374	21	−→	−→	ADJ
ejpam-5511	374	22	t	t	PROPN
ejpam-5511	374	23	/	/	SYM
ejpam-5511	374	24	ρf	ρf	NOUN
ejpam-5511	374	25	by	by	ADP
ejpam-5511	374	26	[	[	X
ejpam-5511	374	27	[	[	X
ejpam-5511	374	28	[	[	X
ejpam-5511	374	29	x]ρf	x]ρf	PROPN
ejpam-5511	374	30	[	[	X
ejpam-5511	374	31	y]ρf	y]ρf	PRON
ejpam-5511	374	32	[	[	X
ejpam-5511	374	33	z]ρf	z]ρf	PROPN
ejpam-5511	374	34	]	]	X
ejpam-5511	374	35	]	]	X
ejpam-5511	375	1	=	=	PUNCT
ejpam-5511	376	1	[	[	X
ejpam-5511	376	2	[	[	X
ejpam-5511	376	3	xyz]]ρf	xyz]]ρf	ADJ
ejpam-5511	376	4	for	for	ADP
ejpam-5511	376	5	all	all	PRON
ejpam-5511	376	6	[	[	X
ejpam-5511	376	7	x]ρf	x]ρf	PROPN
ejpam-5511	376	8	,	,	PUNCT
ejpam-5511	376	9	[	[	X
ejpam-5511	376	10	y]ρf	y]ρf	X
ejpam-5511	376	11	,	,	PUNCT
ejpam-5511	376	12	[	[	X
ejpam-5511	376	13	z]ρf	z]ρf	PROPN
ejpam-5511	376	14	∈	∈	PROPN
ejpam-5511	376	15	t	t	PROPN
ejpam-5511	376	16	/	/	SYM
ejpam-5511	376	17	ρf	ρf	PROPN
ejpam-5511	376	18	.	.	PUNCT
ejpam-5511	377	1	then	then	ADV
ejpam-5511	377	2	(	(	PUNCT
ejpam-5511	377	3	t	t	PROPN
ejpam-5511	377	4	/	/	SYM
ejpam-5511	377	5	ρf	ρf	NOUN
ejpam-5511	377	6	,	,	PUNCT
ejpam-5511	378	1	[	[	X
ejpam-5511	378	2	[	[	X
ejpam-5511	378	3	]	]	X
ejpam-5511	378	4	]	]	X
ejpam-5511	378	5	)	)	PUNCT
ejpam-5511	378	6	is	be	AUX
ejpam-5511	378	7	a	a	DET
ejpam-5511	378	8	commutative	commutative	ADJ
ejpam-5511	378	9	ternary	ternary	ADJ
ejpam-5511	378	10	semigroup	semigroup	NOUN
ejpam-5511	378	11	.	.	PUNCT
ejpam-5511	379	1	indeed	indeed	ADV
ejpam-5511	379	2	,	,	PUNCT
ejpam-5511	379	3	let	let	VERB
ejpam-5511	379	4	[	[	PUNCT
ejpam-5511	379	5	x]ρf	x]ρf	PROPN
ejpam-5511	379	6	[	[	X
ejpam-5511	379	7	y]ρf	y]ρf	PRON
ejpam-5511	379	8	[	[	PUNCT
ejpam-5511	379	9	z]ρf	z]ρf	PROPN
ejpam-5511	379	10	∈	∈	PROPN
ejpam-5511	379	11	t	t	PROPN
ejpam-5511	379	12	/	/	SYM
ejpam-5511	379	13	ρf	ρf	PROPN
ejpam-5511	379	14	.	.	PUNCT
ejpam-5511	380	1	we	we	PRON
ejpam-5511	380	2	have	have	VERB
ejpam-5511	380	3	[	[	X
ejpam-5511	380	4	[	[	X
ejpam-5511	380	5	[	[	X
ejpam-5511	380	6	x]ρf	x]ρf	PROPN
ejpam-5511	380	7	[	[	X
ejpam-5511	380	8	y]ρf	y]ρf	PRON
ejpam-5511	380	9	[	[	X
ejpam-5511	380	10	z]ρf	z]ρf	PROPN
ejpam-5511	380	11	]	]	X
ejpam-5511	380	12	]	]	X
ejpam-5511	381	1	=	=	PUNCT
ejpam-5511	382	1	[	[	X
ejpam-5511	382	2	[	[	X
ejpam-5511	382	3	xyz]]ρf	xyz]]ρf	NOUN
ejpam-5511	382	4	=	=	PUNCT
ejpam-5511	383	1	[	[	X
ejpam-5511	383	2	[	[	X
ejpam-5511	383	3	yzx]]ρf	yzx]]ρf	ADJ
ejpam-5511	383	4	=	=	SYM
ejpam-5511	384	1	[	[	X
ejpam-5511	384	2	[	[	X
ejpam-5511	384	3	[	[	X
ejpam-5511	384	4	y]ρf	y]ρf	X
ejpam-5511	384	5	[	[	X
ejpam-5511	384	6	z]ρf	z]ρf	PROPN
ejpam-5511	384	7	[	[	X
ejpam-5511	384	8	x]ρf	x]ρf	PROPN
ejpam-5511	384	9	]	]	X
ejpam-5511	384	10	]	]	PUNCT
ejpam-5511	384	11	.	.	PUNCT
ejpam-5511	385	1	similarly	similarly	ADV
ejpam-5511	385	2	,	,	PUNCT
ejpam-5511	385	3	we	we	PRON
ejpam-5511	385	4	get	get	VERB
ejpam-5511	385	5	[	[	X
ejpam-5511	385	6	[	[	X
ejpam-5511	385	7	[	[	X
ejpam-5511	385	8	x]ρf	x]ρf	PROPN
ejpam-5511	385	9	[	[	X
ejpam-5511	385	10	y]ρf	y]ρf	PRON
ejpam-5511	385	11	[	[	X
ejpam-5511	385	12	z]ρf	z]ρf	PROPN
ejpam-5511	385	13	]	]	X
ejpam-5511	385	14	]	]	X
ejpam-5511	386	1	=	=	PUNCT
ejpam-5511	387	1	[	[	X
ejpam-5511	387	2	[	[	X
ejpam-5511	387	3	[	[	X
ejpam-5511	387	4	z]ρf	z]ρf	PROPN
ejpam-5511	387	5	[	[	X
ejpam-5511	387	6	x]ρf	x]ρf	PROPN
ejpam-5511	387	7	[	[	X
ejpam-5511	387	8	y]ρf	y]ρf	X
ejpam-5511	387	9	]	]	X
ejpam-5511	387	10	]	]	X
ejpam-5511	387	11	,	,	PUNCT
ejpam-5511	388	1	[	[	X
ejpam-5511	388	2	[	[	X
ejpam-5511	388	3	[	[	X
ejpam-5511	388	4	x]ρf	x]ρf	PROPN
ejpam-5511	388	5	[	[	X
ejpam-5511	388	6	y]ρf	y]ρf	PRON
ejpam-5511	388	7	[	[	X
ejpam-5511	388	8	z]ρf	z]ρf	PROPN
ejpam-5511	388	9	]	]	X
ejpam-5511	388	10	]	]	X
ejpam-5511	388	11	=	=	PUNCT
ejpam-5511	389	1	[	[	X
ejpam-5511	389	2	[	[	X
ejpam-5511	389	3	[	[	X
ejpam-5511	389	4	y]ρf	y]ρf	PRON
ejpam-5511	389	5	[	[	X
ejpam-5511	389	6	x]ρf	x]ρf	PROPN
ejpam-5511	389	7	[	[	X
ejpam-5511	389	8	z]ρf	z]ρf	PROPN
ejpam-5511	389	9	]	]	X
ejpam-5511	389	10	]	]	X
ejpam-5511	389	11	,	,	PUNCT
ejpam-5511	389	12	[	[	X
ejpam-5511	389	13	[	[	X
ejpam-5511	389	14	[	[	X
ejpam-5511	389	15	x]ρf	x]ρf	PROPN
ejpam-5511	389	16	[	[	X
ejpam-5511	389	17	y]ρf	y]ρf	PRON
ejpam-5511	389	18	[	[	X
ejpam-5511	389	19	z]ρf	z]ρf	PROPN
ejpam-5511	389	20	]	]	X
ejpam-5511	389	21	]	]	X
ejpam-5511	390	1	=	=	PUNCT
ejpam-5511	391	1	[	[	X
ejpam-5511	391	2	[	[	X
ejpam-5511	391	3	[	[	X
ejpam-5511	391	4	z]ρf	z]ρf	PROPN
ejpam-5511	391	5	[	[	X
ejpam-5511	391	6	y]ρf	y]ρf	PRON
ejpam-5511	391	7	[	[	X
ejpam-5511	391	8	x]ρf	x]ρf	PROPN
ejpam-5511	391	9	]	]	X
ejpam-5511	391	10	]	]	X
ejpam-5511	391	11	,	,	PUNCT
ejpam-5511	392	1	[	[	X
ejpam-5511	392	2	[	[	X
ejpam-5511	392	3	[	[	X
ejpam-5511	392	4	x]ρf	x]ρf	PROPN
ejpam-5511	392	5	[	[	X
ejpam-5511	392	6	y]ρf	y]ρf	PRON
ejpam-5511	392	7	[	[	X
ejpam-5511	392	8	z]ρf	z]ρf	PROPN
ejpam-5511	392	9	]	]	X
ejpam-5511	392	10	]	]	X
ejpam-5511	392	11	=	=	PUNCT
ejpam-5511	393	1	[	[	X
ejpam-5511	393	2	[	[	X
ejpam-5511	393	3	[	[	X
ejpam-5511	393	4	x]ρf	x]ρf	PROPN
ejpam-5511	393	5	[	[	X
ejpam-5511	393	6	z]ρf	z]ρf	PROPN
ejpam-5511	393	7	[	[	X
ejpam-5511	393	8	y]ρf	y]ρf	NOUN
ejpam-5511	393	9	]	]	X
ejpam-5511	393	10	]	]	PUNCT
ejpam-5511	393	11	.	.	PUNCT
ejpam-5511	394	1	the	the	DET
ejpam-5511	394	2	order	order	NOUN
ejpam-5511	394	3	relation	relation	NOUN
ejpam-5511	394	4	⪯	⪯	NOUN
ejpam-5511	394	5	on	on	ADP
ejpam-5511	394	6	t	t	PROPN
ejpam-5511	394	7	/	/	SYM
ejpam-5511	394	8	ρf	ρf	PROPN
ejpam-5511	394	9	is	be	AUX
ejpam-5511	394	10	induced	induce	VERB
ejpam-5511	394	11	by	by	ADP
ejpam-5511	394	12	the	the	DET
ejpam-5511	394	13	relation	relation	NOUN
ejpam-5511	394	14	≤	≤	PROPN
ejpam-5511	394	15	as	as	SCONJ
ejpam-5511	394	16	follows	follow	VERB
ejpam-5511	394	17	:	:	PUNCT
ejpam-5511	394	18	for	for	ADP
ejpam-5511	394	19	any	any	DET
ejpam-5511	394	20	[	[	X
ejpam-5511	394	21	x]ρf	x]ρf	PROPN
ejpam-5511	394	22	,	,	PUNCT
ejpam-5511	394	23	[	[	X
ejpam-5511	394	24	y]ρf	y]ρf	NOUN
ejpam-5511	394	25	∈	∈	PROPN
ejpam-5511	394	26	t	t	PROPN
ejpam-5511	394	27	/	/	SYM
ejpam-5511	394	28	ρf	ρf	PROPN
ejpam-5511	394	29	,	,	PUNCT
ejpam-5511	394	30	defined	define	VERB
ejpam-5511	394	31	⪯	⪯	NOUN
ejpam-5511	394	32	by	by	ADP
ejpam-5511	394	33	[	[	PUNCT
ejpam-5511	394	34	x]ρf	x]ρf	PROPN
ejpam-5511	394	35	⪯	⪯	NOUN
ejpam-5511	395	1	[	[	X
ejpam-5511	395	2	y]ρf	y]ρf	NOUN
ejpam-5511	395	3	if	if	SCONJ
ejpam-5511	395	4	for	for	ADP
ejpam-5511	395	5	any	any	DET
ejpam-5511	395	6	a	a	DET
ejpam-5511	395	7	∈	∈	NOUN
ejpam-5511	396	1	[	[	X
ejpam-5511	396	2	x]ρf	x]ρf	PROPN
ejpam-5511	396	3	,	,	PUNCT
ejpam-5511	396	4	b	b	X
ejpam-5511	396	5	∈	∈	PROPN
ejpam-5511	396	6	[	[	X
ejpam-5511	396	7	y]ρf	y]ρf	NOUN
ejpam-5511	396	8	,	,	PUNCT
ejpam-5511	396	9	there	there	PRON
ejpam-5511	396	10	exist	exist	VERB
ejpam-5511	396	11	c	c	NOUN
ejpam-5511	396	12	,	,	PUNCT
ejpam-5511	396	13	d	d	PROPN
ejpam-5511	396	14	∈	∈	PROPN
ejpam-5511	396	15	f	f	PROPN
ejpam-5511	396	16	such	such	ADJ
ejpam-5511	396	17	that	that	SCONJ
ejpam-5511	396	18	[	[	X
ejpam-5511	396	19	cda	cda	X
ejpam-5511	396	20	]	]	X
ejpam-5511	396	21	≤	≤	PROPN
ejpam-5511	396	22	b.	b.	PROPN
ejpam-5511	396	23	k.	k.	PROPN
ejpam-5511	396	24	nakwan	nakwan	PROPN
ejpam-5511	396	25	,	,	PUNCT
ejpam-5511	396	26	p.	p.	PROPN
ejpam-5511	396	27	luangchaisri	luangchaisri	VERB
ejpam-5511	396	28	,	,	PUNCT
ejpam-5511	396	29	t.	t.	PROPN
ejpam-5511	396	30	changphas	changphas	PROPN
ejpam-5511	396	31	/	/	SYM
ejpam-5511	396	32	eur	eur	PROPN
ejpam-5511	396	33	.	.	PUNCT
ejpam-5511	397	1	j.	j.	PROPN
ejpam-5511	397	2	pure	pure	PROPN
ejpam-5511	397	3	appl	appl	PROPN
ejpam-5511	397	4	.	.	PROPN
ejpam-5511	397	5	math	math	PROPN
ejpam-5511	397	6	,	,	PUNCT
ejpam-5511	397	7	17	17	NUM
ejpam-5511	397	8	(	(	PUNCT
ejpam-5511	397	9	4	4	NUM
ejpam-5511	397	10	)	)	PUNCT
ejpam-5511	397	11	(	(	PUNCT
ejpam-5511	397	12	2024	2024	NUM
ejpam-5511	397	13	)	)	PUNCT
ejpam-5511	397	14	,	,	PUNCT
ejpam-5511	397	15	4180	4180	NUM
ejpam-5511	397	16	-	-	SYM
ejpam-5511	397	17	4194	4194	NUM
ejpam-5511	397	18	4189	4189	NUM
ejpam-5511	397	19	lemma	lemma	PROPN
ejpam-5511	397	20	2	2	X
ejpam-5511	397	21	.	.	PUNCT
ejpam-5511	398	1	let	let	AUX
ejpam-5511	398	2	(	(	PUNCT
ejpam-5511	398	3	t	t	NOUN
ejpam-5511	398	4	,	,	PUNCT
ejpam-5511	398	5	[	[	PUNCT
ejpam-5511	398	6	]	]	X
ejpam-5511	398	7	,	,	PUNCT
ejpam-5511	398	8	≤	≤	NUM
ejpam-5511	398	9	,	,	PUNCT
ejpam-5511	398	10	[	[	PUNCT
ejpam-5511	398	11	]	]	X
ejpam-5511	398	12	∗	∗	NOUN
ejpam-5511	398	13	)	)	PUNCT
ejpam-5511	398	14	be	be	VERB
ejpam-5511	398	15	a	a	DET
ejpam-5511	398	16	commutative	commutative	ADJ
ejpam-5511	398	17	implicative	implicative	ADJ
ejpam-5511	398	18	n.p.o	n.p.o	NOUN
ejpam-5511	398	19	.	.	PUNCT
ejpam-5511	399	1	ternary	ternary	PROPN
ejpam-5511	399	2	semigroup	semigroup	PROPN
ejpam-5511	399	3	,	,	PUNCT
ejpam-5511	399	4	and	and	CCONJ
ejpam-5511	399	5	let	let	VERB
ejpam-5511	399	6	f	f	PRON
ejpam-5511	399	7	be	be	AUX
ejpam-5511	399	8	a	a	DET
ejpam-5511	399	9	filter	filter	NOUN
ejpam-5511	399	10	of	of	ADP
ejpam-5511	399	11	t	t	PROPN
ejpam-5511	399	12	.	.	PUNCT
ejpam-5511	400	1	the	the	DET
ejpam-5511	400	2	ordered	order	VERB
ejpam-5511	400	3	relation	relation	NOUN
ejpam-5511	400	4	⪯	⪯	NOUN
ejpam-5511	400	5	is	be	AUX
ejpam-5511	400	6	a	a	DET
ejpam-5511	400	7	partial	partial	ADJ
ejpam-5511	400	8	order	order	NOUN
ejpam-5511	400	9	on	on	ADP
ejpam-5511	400	10	t	t	PROPN
ejpam-5511	400	11	/	/	SYM
ejpam-5511	400	12	ρf	ρf	PROPN
ejpam-5511	400	13	.	.	PUNCT
ejpam-5511	401	1	proof	proof	NOUN
ejpam-5511	401	2	.	.	PUNCT
ejpam-5511	402	1	if	if	SCONJ
ejpam-5511	402	2	x′	x′	PROPN
ejpam-5511	402	3	∈	∈	PROPN
ejpam-5511	402	4	[	[	X
ejpam-5511	402	5	x]ρf	x]ρf	PROPN
ejpam-5511	402	6	,	,	PUNCT
ejpam-5511	402	7	then	then	ADV
ejpam-5511	402	8	by	by	ADP
ejpam-5511	402	9	1	1	NUM
ejpam-5511	402	10	∈	∈	NOUN
ejpam-5511	402	11	f	f	NOUN
ejpam-5511	402	12	we	we	PRON
ejpam-5511	402	13	have	have	VERB
ejpam-5511	402	14	[	[	X
ejpam-5511	402	15	11x′	11x′	NUM
ejpam-5511	402	16	]	]	PUNCT
ejpam-5511	402	17	≤	≤	NUM
ejpam-5511	402	18	x′	x′	NUM
ejpam-5511	402	19	;	;	PUNCT
ejpam-5511	402	20	so	so	CCONJ
ejpam-5511	403	1	[	[	X
ejpam-5511	403	2	x]ρf	x]ρf	PROPN
ejpam-5511	403	3	⪯	⪯	NOUN
ejpam-5511	403	4	[	[	X
ejpam-5511	403	5	x]ρf	x]ρf	PROPN
ejpam-5511	403	6	.	.	PUNCT
ejpam-5511	404	1	assume	assume	VERB
ejpam-5511	404	2	[	[	PUNCT
ejpam-5511	404	3	x]ρf	x]ρf	PROPN
ejpam-5511	404	4	⪯	⪯	NOUN
ejpam-5511	404	5	[	[	X
ejpam-5511	404	6	y]ρf	y]ρf	NOUN
ejpam-5511	404	7	and	and	CCONJ
ejpam-5511	404	8	[	[	X
ejpam-5511	404	9	y]ρf	y]ρf	PRON
ejpam-5511	404	10	⪯	⪯	NOUN
ejpam-5511	405	1	[	[	X
ejpam-5511	405	2	x]ρf	x]ρf	PROPN
ejpam-5511	405	3	.	.	PUNCT
ejpam-5511	406	1	since	since	SCONJ
ejpam-5511	406	2	x	x	PROPN
ejpam-5511	406	3	∈	∈	PROPN
ejpam-5511	406	4	[	[	X
ejpam-5511	406	5	x]ρf	x]ρf	PROPN
ejpam-5511	406	6	and	and	CCONJ
ejpam-5511	406	7	y	y	PROPN
ejpam-5511	406	8	∈	∈	PROPN
ejpam-5511	406	9	[	[	X
ejpam-5511	406	10	x]ρf	x]ρf	PROPN
ejpam-5511	406	11	,	,	PUNCT
ejpam-5511	406	12	there	there	PRON
ejpam-5511	406	13	exist	exist	VERB
ejpam-5511	406	14	c1	c1	NOUN
ejpam-5511	406	15	,	,	PUNCT
ejpam-5511	406	16	d1	d1	PROPN
ejpam-5511	406	17	,	,	PUNCT
ejpam-5511	406	18	c2	c2	PROPN
ejpam-5511	406	19	,	,	PUNCT
ejpam-5511	406	20	d2	d2	PROPN
ejpam-5511	406	21	∈	∈	PROPN
ejpam-5511	406	22	f	f	PROPN
ejpam-5511	406	23	such	such	ADJ
ejpam-5511	406	24	that	that	SCONJ
ejpam-5511	407	1	[	[	X
ejpam-5511	407	2	c1d1x	c1d1x	X
ejpam-5511	407	3	]	]	X
ejpam-5511	407	4	≤	≤	NUM
ejpam-5511	407	5	y	y	PROPN
ejpam-5511	407	6	and	and	CCONJ
ejpam-5511	407	7	[	[	X
ejpam-5511	407	8	c2d2y	c2d2y	X
ejpam-5511	407	9	]	]	X
ejpam-5511	407	10	≤	≤	NUM
ejpam-5511	407	11	x.	x.	NOUN
ejpam-5511	408	1	we	we	PRON
ejpam-5511	408	2	have	have	VERB
ejpam-5511	408	3	[	[	X
ejpam-5511	408	4	[	[	X
ejpam-5511	408	5	c1d1c2]d2x	c1d1c2]d2x	NOUN
ejpam-5511	408	6	]	]	X
ejpam-5511	408	7	=	=	PUNCT
ejpam-5511	409	1	[	[	X
ejpam-5511	409	2	c1d1[c2d2x	c1d1[c2d2x	NOUN
ejpam-5511	409	3	]	]	X
ejpam-5511	409	4	]	]	X
ejpam-5511	409	5	=	=	PUNCT
ejpam-5511	410	1	[	[	X
ejpam-5511	410	2	c1d1[xc2d2	c1d1[xc2d2	X
ejpam-5511	410	3	]	]	X
ejpam-5511	410	4	]	]	X
ejpam-5511	410	5	=	=	PUNCT
ejpam-5511	411	1	[	[	X
ejpam-5511	411	2	[	[	X
ejpam-5511	411	3	c1d1x]c2d2	c1d1x]c2d2	X
ejpam-5511	411	4	]	]	X
ejpam-5511	411	5	≤	≤	X
ejpam-5511	412	1	[	[	X
ejpam-5511	412	2	yc2d2	yc2d2	X
ejpam-5511	412	3	]	]	X
ejpam-5511	412	4	≤	≤	PROPN
ejpam-5511	412	5	y.	y.	PROPN
ejpam-5511	412	6	also	also	ADV
ejpam-5511	412	7	,	,	PUNCT
ejpam-5511	412	8	[	[	X
ejpam-5511	412	9	[	[	X
ejpam-5511	412	10	c1d1c2]d2y	c1d1c2]d2y	NOUN
ejpam-5511	412	11	]	]	PUNCT
ejpam-5511	412	12	=	=	PUNCT
ejpam-5511	413	1	[	[	X
ejpam-5511	413	2	c1d1[c2d2y	c1d1[c2d2y	NOUN
ejpam-5511	413	3	]	]	X
ejpam-5511	413	4	]	]	X
ejpam-5511	413	5	≤	≤	X
ejpam-5511	414	1	[	[	X
ejpam-5511	414	2	c1d1x	c1d1x	X
ejpam-5511	414	3	]	]	X
ejpam-5511	414	4	≤	≤	NUM
ejpam-5511	414	5	x.	x.	PUNCT
ejpam-5511	415	1	thus	thus	ADV
ejpam-5511	415	2	,	,	PUNCT
ejpam-5511	415	3	xρf	xρf	PROPN
ejpam-5511	415	4	y	y	PROPN
ejpam-5511	415	5	,	,	PUNCT
ejpam-5511	415	6	that	that	ADV
ejpam-5511	415	7	is	is	ADV
ejpam-5511	415	8	,	,	PUNCT
ejpam-5511	415	9	[	[	X
ejpam-5511	415	10	x]ρf	x]ρf	X
ejpam-5511	415	11	=	=	PUNCT
ejpam-5511	416	1	[	[	X
ejpam-5511	416	2	y]ρf	y]ρf	NOUN
ejpam-5511	416	3	.	.	PUNCT
ejpam-5511	417	1	assume	assume	VERB
ejpam-5511	417	2	that	that	SCONJ
ejpam-5511	417	3	[	[	X
ejpam-5511	417	4	x]ρf	x]ρf	PROPN
ejpam-5511	417	5	⪯	⪯	NOUN
ejpam-5511	417	6	[	[	X
ejpam-5511	417	7	y]ρf	y]ρf	NOUN
ejpam-5511	417	8	and	and	CCONJ
ejpam-5511	417	9	[	[	X
ejpam-5511	417	10	y]ρf	y]ρf	PRON
ejpam-5511	417	11	⪯	⪯	NOUN
ejpam-5511	417	12	[	[	X
ejpam-5511	417	13	z]ρf	z]ρf	PROPN
ejpam-5511	417	14	.	.	PUNCT
ejpam-5511	418	1	let	let	VERB
ejpam-5511	418	2	x′	x′	PROPN
ejpam-5511	418	3	∈	∈	PROPN
ejpam-5511	419	1	[	[	X
ejpam-5511	419	2	x]ρf	x]ρf	PROPN
ejpam-5511	419	3	,	,	PUNCT
ejpam-5511	419	4	y′	y′	NOUN
ejpam-5511	419	5	∈	∈	PROPN
ejpam-5511	420	1	[	[	X
ejpam-5511	420	2	y]ρf	y]ρf	NOUN
ejpam-5511	420	3	and	and	CCONJ
ejpam-5511	420	4	z′	z′	NUM
ejpam-5511	420	5	∈	∈	PROPN
ejpam-5511	421	1	[	[	X
ejpam-5511	421	2	z]ρf	z]ρf	PROPN
ejpam-5511	421	3	.	.	PUNCT
ejpam-5511	422	1	then	then	ADV
ejpam-5511	422	2	there	there	PRON
ejpam-5511	422	3	exist	exist	VERB
ejpam-5511	422	4	c3	c3	PROPN
ejpam-5511	422	5	,	,	PUNCT
ejpam-5511	422	6	d3	d3	PROPN
ejpam-5511	422	7	,	,	PUNCT
ejpam-5511	422	8	c4	c4	NOUN
ejpam-5511	422	9	,	,	PUNCT
ejpam-5511	422	10	d4	d4	PROPN
ejpam-5511	422	11	∈	∈	PROPN
ejpam-5511	422	12	f	f	PROPN
ejpam-5511	423	1	such	such	ADJ
ejpam-5511	423	2	that	that	SCONJ
ejpam-5511	423	3	[	[	X
ejpam-5511	423	4	c3d3x	c3d3x	NUM
ejpam-5511	423	5	′	′	NUM
ejpam-5511	423	6	]	]	PUNCT
ejpam-5511	423	7	≤	≤	NUM
ejpam-5511	423	8	y′	y′	PUNCT
ejpam-5511	423	9	and	and	CCONJ
ejpam-5511	423	10	[	[	X
ejpam-5511	423	11	c4d4y	c4d4y	NOUN
ejpam-5511	423	12	′	′	NOUN
ejpam-5511	423	13	]	]	PUNCT
ejpam-5511	423	14	≤	≤	NUM
ejpam-5511	423	15	z′.	z′.	NOUN
ejpam-5511	423	16	from	from	ADP
ejpam-5511	423	17	[	[	X
ejpam-5511	423	18	[	[	X
ejpam-5511	423	19	c3d3c4]d4x	c3d3c4]d4x	NOUN
ejpam-5511	423	20	′	′	NOUN
ejpam-5511	423	21	]	]	X
ejpam-5511	423	22	=	=	PUNCT
ejpam-5511	424	1	[	[	X
ejpam-5511	424	2	c3d3[c4d4x	c3d3[c4d4x	NOUN
ejpam-5511	424	3	′	′	NOUN
ejpam-5511	424	4	]	]	X
ejpam-5511	424	5	]	]	PUNCT
ejpam-5511	425	1	=	=	PUNCT
ejpam-5511	426	1	[	[	X
ejpam-5511	426	2	c3d3[x	c3d3[x	PROPN
ejpam-5511	426	3	′c4d4	′c4d4	NOUN
ejpam-5511	426	4	]	]	X
ejpam-5511	426	5	]	]	PUNCT
ejpam-5511	426	6	=	=	PUNCT
ejpam-5511	427	1	[	[	X
ejpam-5511	427	2	[	[	X
ejpam-5511	427	3	c3d3x	c3d3x	ADJ
ejpam-5511	427	4	′]c4d4	′]c4d4	NOUN
ejpam-5511	427	5	]	]	PUNCT
ejpam-5511	427	6	≤	≤	NOUN
ejpam-5511	428	1	[	[	X
ejpam-5511	428	2	y′c4d4	y′c4d4	NOUN
ejpam-5511	428	3	]	]	X
ejpam-5511	428	4	=	=	PUNCT
ejpam-5511	429	1	[	[	X
ejpam-5511	429	2	c4d4y	c4d4y	NOUN
ejpam-5511	429	3	′	′	NOUN
ejpam-5511	429	4	]	]	PUNCT
ejpam-5511	429	5	≤	≤	NUM
ejpam-5511	429	6	z′	z′	NUM
ejpam-5511	429	7	it	it	PRON
ejpam-5511	429	8	follows	follow	VERB
ejpam-5511	429	9	that	that	SCONJ
ejpam-5511	429	10	[	[	X
ejpam-5511	429	11	x]ρf	x]ρf	PROPN
ejpam-5511	429	12	⪯	⪯	NOUN
ejpam-5511	429	13	[	[	X
ejpam-5511	429	14	z]ρf	z]ρf	PROPN
ejpam-5511	429	15	.	.	PUNCT
ejpam-5511	430	1	these	these	PRON
ejpam-5511	430	2	show	show	VERB
ejpam-5511	430	3	that	that	SCONJ
ejpam-5511	430	4	⪯	⪯	NOUN
ejpam-5511	430	5	is	be	AUX
ejpam-5511	430	6	a	a	DET
ejpam-5511	430	7	partial	partial	ADJ
ejpam-5511	430	8	order	order	NOUN
ejpam-5511	430	9	on	on	ADP
ejpam-5511	430	10	t	t	PROPN
ejpam-5511	430	11	/	/	SYM
ejpam-5511	430	12	ρf	ρf	PROPN
ejpam-5511	430	13	.	.	PUNCT
ejpam-5511	431	1	lemma	lemma	PROPN
ejpam-5511	431	2	3	3	X
ejpam-5511	431	3	.	.	PUNCT
ejpam-5511	432	1	let	let	VERB
ejpam-5511	432	2	(	(	PUNCT
ejpam-5511	432	3	t	t	NOUN
ejpam-5511	432	4	,	,	PUNCT
ejpam-5511	432	5	[	[	PUNCT
ejpam-5511	432	6	]	]	X
ejpam-5511	432	7	,	,	PUNCT
ejpam-5511	432	8	≤	≤	NUM
ejpam-5511	432	9	)	)	PUNCT
ejpam-5511	432	10	be	be	VERB
ejpam-5511	432	11	a	a	DET
ejpam-5511	432	12	commutative	commutative	ADJ
ejpam-5511	432	13	n.p.o	n.p.o	NOUN
ejpam-5511	432	14	.	.	PUNCT
ejpam-5511	433	1	ternary	ternary	ADJ
ejpam-5511	433	2	semigroup	semigroup	PROPN
ejpam-5511	433	3	,	,	PUNCT
ejpam-5511	433	4	and	and	CCONJ
ejpam-5511	433	5	let	let	VERB
ejpam-5511	433	6	f	f	PRON
ejpam-5511	433	7	be	be	AUX
ejpam-5511	433	8	a	a	DET
ejpam-5511	433	9	filter	filter	NOUN
ejpam-5511	433	10	of	of	ADP
ejpam-5511	433	11	t	t	PROPN
ejpam-5511	433	12	.	.	PUNCT
ejpam-5511	434	1	then	then	ADV
ejpam-5511	434	2	(	(	PUNCT
ejpam-5511	434	3	t	t	PROPN
ejpam-5511	434	4	/	/	SYM
ejpam-5511	434	5	ρf	ρf	NOUN
ejpam-5511	434	6	,	,	PUNCT
ejpam-5511	435	1	[	[	X
ejpam-5511	435	2	[	[	X
ejpam-5511	435	3	]	]	X
ejpam-5511	435	4	]	]	X
ejpam-5511	435	5	,	,	PUNCT
ejpam-5511	435	6	⪯	⪯	PROPN
ejpam-5511	435	7	)	)	PUNCT
ejpam-5511	435	8	is	be	AUX
ejpam-5511	435	9	a	a	DET
ejpam-5511	435	10	commutative	commutative	ADJ
ejpam-5511	435	11	n.p.o	n.p.o	NOUN
ejpam-5511	435	12	.	.	PUNCT
ejpam-5511	436	1	ternary	ternary	ADJ
ejpam-5511	436	2	semigroup	semigroup	PROPN
ejpam-5511	436	3	.	.	PUNCT
ejpam-5511	437	1	proof	proof	NOUN
ejpam-5511	437	2	.	.	PUNCT
ejpam-5511	438	1	we	we	PRON
ejpam-5511	438	2	have	have	AUX
ejpam-5511	438	3	seen	see	VERB
ejpam-5511	438	4	that	that	SCONJ
ejpam-5511	438	5	(	(	PUNCT
ejpam-5511	438	6	t	t	PROPN
ejpam-5511	438	7	/	/	SYM
ejpam-5511	438	8	ρf	ρf	NOUN
ejpam-5511	438	9	,	,	PUNCT
ejpam-5511	438	10	[	[	X
ejpam-5511	438	11	[	[	X
ejpam-5511	438	12	]	]	X
ejpam-5511	438	13	]	]	X
ejpam-5511	438	14	)	)	PUNCT
ejpam-5511	438	15	is	be	AUX
ejpam-5511	438	16	a	a	DET
ejpam-5511	438	17	commutative	commutative	ADJ
ejpam-5511	438	18	ternary	ternary	ADJ
ejpam-5511	438	19	semigroup	semigroup	NOUN
ejpam-5511	438	20	.	.	PUNCT
ejpam-5511	439	1	by	by	ADP
ejpam-5511	439	2	lemma	lemma	PROPN
ejpam-5511	439	3	2	2	NUM
ejpam-5511	439	4	,	,	PUNCT
ejpam-5511	439	5	⪯	⪯	NOUN
ejpam-5511	439	6	is	be	AUX
ejpam-5511	439	7	a	a	DET
ejpam-5511	439	8	partial	partial	ADJ
ejpam-5511	439	9	order	order	NOUN
ejpam-5511	439	10	on	on	ADP
ejpam-5511	439	11	t	t	PROPN
ejpam-5511	439	12	/	/	SYM
ejpam-5511	439	13	ρf	ρf	PROPN
ejpam-5511	439	14	.	.	PUNCT
ejpam-5511	440	1	let	let	VERB
ejpam-5511	441	1	[	[	PUNCT
ejpam-5511	441	2	x]ρf	x]ρf	PROPN
ejpam-5511	441	3	,	,	PUNCT
ejpam-5511	441	4	[	[	X
ejpam-5511	441	5	y]ρf	y]ρf	NOUN
ejpam-5511	441	6	,	,	PUNCT
ejpam-5511	441	7	[	[	X
ejpam-5511	441	8	u]ρf	u]ρf	NOUN
ejpam-5511	441	9	,	,	PUNCT
ejpam-5511	441	10	[	[	X
ejpam-5511	441	11	v]ρf	v]ρf	PROPN
ejpam-5511	441	12	∈	∈	PROPN
ejpam-5511	441	13	t	t	PROPN
ejpam-5511	441	14	/	/	SYM
ejpam-5511	441	15	ρf	ρf	NOUN
ejpam-5511	441	16	be	be	AUX
ejpam-5511	441	17	such	such	ADJ
ejpam-5511	441	18	that	that	SCONJ
ejpam-5511	441	19	[	[	X
ejpam-5511	441	20	x]ρf	x]ρf	PROPN
ejpam-5511	441	21	⪯	⪯	NOUN
ejpam-5511	441	22	[	[	X
ejpam-5511	441	23	y]ρf	y]ρf	NOUN
ejpam-5511	441	24	.	.	PUNCT
ejpam-5511	442	1	let	let	VERB
ejpam-5511	442	2	a	a	DET
ejpam-5511	442	3	∈	∈	NOUN
ejpam-5511	442	4	[	[	X
ejpam-5511	442	5	[	[	X
ejpam-5511	442	6	xuv]]ρf	xuv]]ρf	NOUN
ejpam-5511	442	7	and	and	CCONJ
ejpam-5511	442	8	b	b	X
ejpam-5511	442	9	∈	∈	PROPN
ejpam-5511	443	1	[	[	X
ejpam-5511	443	2	[	[	X
ejpam-5511	443	3	yuv]]ρf	yuv]]ρf	NOUN
ejpam-5511	443	4	.	.	PUNCT
ejpam-5511	444	1	since	since	SCONJ
ejpam-5511	444	2	x	x	PROPN
ejpam-5511	444	3	∈	∈	PROPN
ejpam-5511	444	4	[	[	X
ejpam-5511	444	5	x]ρf	x]ρf	PROPN
ejpam-5511	444	6	,	,	PUNCT
ejpam-5511	444	7	y	y	PROPN
ejpam-5511	444	8	∈	∈	PROPN
ejpam-5511	445	1	[	[	X
ejpam-5511	445	2	y]ρf	y]ρf	NOUN
ejpam-5511	445	3	,	,	PUNCT
ejpam-5511	445	4	and	and	CCONJ
ejpam-5511	445	5	[	[	X
ejpam-5511	445	6	x]ρf	x]ρf	PROPN
ejpam-5511	445	7	⪯	⪯	NOUN
ejpam-5511	445	8	[	[	X
ejpam-5511	445	9	y]ρf	y]ρf	NOUN
ejpam-5511	445	10	,	,	PUNCT
ejpam-5511	445	11	there	there	PRON
ejpam-5511	445	12	exist	exist	VERB
ejpam-5511	445	13	c	c	NOUN
ejpam-5511	445	14	,	,	PUNCT
ejpam-5511	445	15	d	d	PROPN
ejpam-5511	445	16	∈	∈	PROPN
ejpam-5511	445	17	f	f	PROPN
ejpam-5511	446	1	such	such	ADJ
ejpam-5511	446	2	that	that	SCONJ
ejpam-5511	446	3	[	[	X
ejpam-5511	446	4	cdx	cdx	NOUN
ejpam-5511	446	5	]	]	PUNCT
ejpam-5511	446	6	≤	≤	NUM
ejpam-5511	446	7	y.	y.	NOUN
ejpam-5511	446	8	from	from	ADP
ejpam-5511	446	9	a	a	DET
ejpam-5511	446	10	∈	∈	NOUN
ejpam-5511	447	1	[	[	X
ejpam-5511	447	2	[	[	X
ejpam-5511	447	3	xuv]]ρf	xuv]]ρf	NOUN
ejpam-5511	447	4	,	,	PUNCT
ejpam-5511	447	5	there	there	PRON
ejpam-5511	447	6	exist	exist	VERB
ejpam-5511	447	7	c1	c1	NOUN
ejpam-5511	447	8	,	,	PUNCT
ejpam-5511	447	9	d1	d1	PROPN
ejpam-5511	447	10	∈	∈	PROPN
ejpam-5511	448	1	f	f	PROPN
ejpam-5511	448	2	such	such	ADJ
ejpam-5511	448	3	that	that	SCONJ
ejpam-5511	449	1	[	[	X
ejpam-5511	449	2	c1d1[xuv	c1d1[xuv	NOUN
ejpam-5511	449	3	]	]	X
ejpam-5511	449	4	]	]	X
ejpam-5511	449	5	≤	≤	NOUN
ejpam-5511	449	6	a	a	DET
ejpam-5511	449	7	and	and	CCONJ
ejpam-5511	449	8	[	[	X
ejpam-5511	449	9	c1d1a	c1d1a	X
ejpam-5511	449	10	]	]	X
ejpam-5511	449	11	≤	≤	NOUN
ejpam-5511	450	1	[	[	X
ejpam-5511	450	2	xuv	xuv	X
ejpam-5511	450	3	]	]	PUNCT
ejpam-5511	450	4	.	.	PUNCT
ejpam-5511	451	1	similarly	similarly	ADV
ejpam-5511	451	2	,	,	PUNCT
ejpam-5511	451	3	by	by	ADP
ejpam-5511	451	4	b	b	PROPN
ejpam-5511	451	5	∈	∈	PROPN
ejpam-5511	452	1	[	[	X
ejpam-5511	452	2	[	[	X
ejpam-5511	452	3	yuv]]ρf	yuv]]ρf	NOUN
ejpam-5511	452	4	,	,	PUNCT
ejpam-5511	452	5	there	there	PRON
ejpam-5511	452	6	exist	exist	VERB
ejpam-5511	452	7	c2	c2	PROPN
ejpam-5511	452	8	,	,	PUNCT
ejpam-5511	452	9	d2	d2	PROPN
ejpam-5511	452	10	∈	∈	PROPN
ejpam-5511	452	11	f	f	PROPN
ejpam-5511	453	1	such	such	ADJ
ejpam-5511	453	2	that	that	SCONJ
ejpam-5511	454	1	[	[	X
ejpam-5511	454	2	c2d2[yuv	c2d2[yuv	X
ejpam-5511	454	3	]	]	X
ejpam-5511	454	4	]	]	X
ejpam-5511	454	5	≤	≤	NUM
ejpam-5511	454	6	b	b	NOUN
ejpam-5511	454	7	and	and	CCONJ
ejpam-5511	454	8	[	[	X
ejpam-5511	454	9	c2d2b	c2d2b	X
ejpam-5511	454	10	]	]	X
ejpam-5511	454	11	≤	≤	NOUN
ejpam-5511	455	1	[	[	X
ejpam-5511	455	2	yuv	yuv	X
ejpam-5511	455	3	]	]	PUNCT
ejpam-5511	455	4	.	.	PUNCT
ejpam-5511	456	1	consider	consider	VERB
ejpam-5511	456	2	:	:	PUNCT
ejpam-5511	457	1	[	[	X
ejpam-5511	457	2	[	[	X
ejpam-5511	457	3	c2d2[cdc1]]d1a	c2d2[cdc1]]d1a	X
ejpam-5511	457	4	]	]	X
ejpam-5511	457	5	=	=	PUNCT
ejpam-5511	457	6	[	[	X
ejpam-5511	457	7	c2d2[[cdc1]d1a	c2d2[[cdc1]d1a	X
ejpam-5511	457	8	]	]	X
ejpam-5511	457	9	]	]	PUNCT
ejpam-5511	457	10	=	=	PUNCT
ejpam-5511	458	1	[	[	X
ejpam-5511	458	2	c2d2[cd[c1d1a	c2d2[cd[c1d1a	X
ejpam-5511	458	3	]	]	X
ejpam-5511	458	4	]	]	X
ejpam-5511	458	5	]	]	X
ejpam-5511	458	6	≤	≤	NOUN
ejpam-5511	459	1	[	[	X
ejpam-5511	459	2	c2d2[cd[xuv	c2d2[cd[xuv	NOUN
ejpam-5511	459	3	]	]	X
ejpam-5511	459	4	]	]	X
ejpam-5511	459	5	]	]	X
ejpam-5511	459	6	=	=	PUNCT
ejpam-5511	460	1	[	[	X
ejpam-5511	460	2	c2d2[[cdx]uv	c2d2[[cdx]uv	X
ejpam-5511	460	3	]	]	X
ejpam-5511	460	4	]	]	X
ejpam-5511	460	5	≤	≤	NOUN
ejpam-5511	461	1	[	[	X
ejpam-5511	461	2	c2d2[yuv	c2d2[yuv	X
ejpam-5511	461	3	]	]	X
ejpam-5511	461	4	]	]	X
ejpam-5511	461	5	≤	≤	PROPN
ejpam-5511	461	6	b.	b.	PROPN
ejpam-5511	462	1	then	then	ADV
ejpam-5511	462	2	[	[	X
ejpam-5511	462	3	[	[	X
ejpam-5511	462	4	c2d2[cdc1]]d1a	c2d2[cdc1]]d1a	X
ejpam-5511	462	5	]	]	X
ejpam-5511	462	6	≤	≤	NUM
ejpam-5511	462	7	b	b	NOUN
ejpam-5511	462	8	,	,	PUNCT
ejpam-5511	462	9	so	so	SCONJ
ejpam-5511	463	1	[	[	X
ejpam-5511	463	2	[	[	X
ejpam-5511	463	3	xuv]]ρf	xuv]]ρf	ADP
ejpam-5511	463	4	⪯	⪯	NOUN
ejpam-5511	463	5	[	[	X
ejpam-5511	463	6	[	[	X
ejpam-5511	463	7	yuv]]ρf	yuv]]ρf	NOUN
ejpam-5511	463	8	.	.	PUNCT
ejpam-5511	464	1	hence	hence	ADV
ejpam-5511	464	2	,	,	PUNCT
ejpam-5511	464	3	[	[	X
ejpam-5511	464	4	[	[	X
ejpam-5511	464	5	[	[	X
ejpam-5511	464	6	x]ρf	x]ρf	PROPN
ejpam-5511	464	7	[	[	X
ejpam-5511	464	8	u]ρf	u]ρf	NOUN
ejpam-5511	464	9	[	[	X
ejpam-5511	464	10	v]ρf	v]ρf	NOUN
ejpam-5511	464	11	]	]	X
ejpam-5511	464	12	]	]	PUNCT
ejpam-5511	464	13	=	=	PUNCT
ejpam-5511	465	1	[	[	X
ejpam-5511	465	2	[	[	X
ejpam-5511	465	3	xuv]]ρf	xuv]]ρf	ADP
ejpam-5511	465	4	⪯	⪯	NOUN
ejpam-5511	466	1	[	[	X
ejpam-5511	466	2	[	[	X
ejpam-5511	466	3	yuv]]ρf	yuv]]ρf	NOUN
ejpam-5511	466	4	=	=	PUNCT
ejpam-5511	467	1	[	[	X
ejpam-5511	467	2	[	[	X
ejpam-5511	467	3	[	[	X
ejpam-5511	467	4	y]ρf	y]ρf	NOUN
ejpam-5511	467	5	[	[	X
ejpam-5511	467	6	u]ρf	u]ρf	NOUN
ejpam-5511	467	7	[	[	X
ejpam-5511	467	8	v]ρf	v]ρf	NOUN
ejpam-5511	467	9	]	]	SYM
ejpam-5511	467	10	]	]	PUNCT
ejpam-5511	467	11	.	.	PUNCT
ejpam-5511	468	1	similarly	similarly	ADV
ejpam-5511	468	2	,	,	PUNCT
ejpam-5511	468	3	[	[	X
ejpam-5511	468	4	[	[	X
ejpam-5511	468	5	[	[	X
ejpam-5511	468	6	u]ρf	u]ρf	NOUN
ejpam-5511	468	7	[	[	X
ejpam-5511	468	8	x]ρf	x]ρf	PROPN
ejpam-5511	469	1	[	[	X
ejpam-5511	469	2	v]ρf	v]ρf	NOUN
ejpam-5511	469	3	]	]	PUNCT
ejpam-5511	469	4	]	]	X
ejpam-5511	469	5	⪯	⪯	NOUN
ejpam-5511	470	1	[	[	X
ejpam-5511	470	2	[	[	X
ejpam-5511	470	3	[	[	X
ejpam-5511	470	4	u]ρf	u]ρf	NOUN
ejpam-5511	470	5	[	[	X
ejpam-5511	470	6	y]ρf	y]ρf	NOUN
ejpam-5511	470	7	[	[	X
ejpam-5511	470	8	v]ρf	v]ρf	NOUN
ejpam-5511	470	9	]	]	PUNCT
ejpam-5511	470	10	]	]	PUNCT
ejpam-5511	470	11	,	,	PUNCT
ejpam-5511	470	12	and	and	CCONJ
ejpam-5511	470	13	[	[	X
ejpam-5511	470	14	[	[	X
ejpam-5511	470	15	[	[	X
ejpam-5511	470	16	u]ρf	u]ρf	NOUN
ejpam-5511	470	17	[	[	X
ejpam-5511	470	18	v]ρf	v]ρf	PROPN
ejpam-5511	470	19	[	[	PUNCT
ejpam-5511	470	20	x]ρf	x]ρf	PROPN
ejpam-5511	470	21	]	]	X
ejpam-5511	470	22	]	]	X
ejpam-5511	470	23	⪯	⪯	NOUN
ejpam-5511	471	1	[	[	X
ejpam-5511	471	2	[	[	X
ejpam-5511	471	3	[	[	X
ejpam-5511	471	4	u]ρf	u]ρf	NOUN
ejpam-5511	471	5	[	[	X
ejpam-5511	471	6	v]ρf	v]ρf	NOUN
ejpam-5511	471	7	[	[	X
ejpam-5511	471	8	y]ρf	y]ρf	NOUN
ejpam-5511	471	9	]	]	X
ejpam-5511	471	10	]	]	PUNCT
ejpam-5511	471	11	.	.	PUNCT
ejpam-5511	472	1	let	let	VERB
ejpam-5511	472	2	[	[	PUNCT
ejpam-5511	472	3	x]ρf	x]ρf	PROPN
ejpam-5511	472	4	,	,	PUNCT
ejpam-5511	472	5	[	[	X
ejpam-5511	472	6	y]ρf	y]ρf	X
ejpam-5511	472	7	,	,	PUNCT
ejpam-5511	472	8	[	[	X
ejpam-5511	472	9	z]ρf	z]ρf	PROPN
ejpam-5511	472	10	∈	∈	PROPN
ejpam-5511	472	11	t	t	PROPN
ejpam-5511	472	12	/	/	SYM
ejpam-5511	472	13	ρf	ρf	PROPN
ejpam-5511	472	14	.	.	PUNCT
ejpam-5511	473	1	to	to	PART
ejpam-5511	473	2	show	show	VERB
ejpam-5511	473	3	that	that	SCONJ
ejpam-5511	473	4	[	[	X
ejpam-5511	473	5	[	[	X
ejpam-5511	473	6	[	[	X
ejpam-5511	473	7	x]ρf	x]ρf	PROPN
ejpam-5511	473	8	[	[	X
ejpam-5511	473	9	y]ρf	y]ρf	PRON
ejpam-5511	473	10	[	[	X
ejpam-5511	473	11	z]ρf	z]ρf	PROPN
ejpam-5511	473	12	]	]	X
ejpam-5511	473	13	]	]	X
ejpam-5511	473	14	⪯	⪯	NOUN
ejpam-5511	474	1	[	[	X
ejpam-5511	474	2	x]ρf	x]ρf	PROPN
ejpam-5511	474	3	,	,	PUNCT
ejpam-5511	474	4	let	let	VERB
ejpam-5511	474	5	a′	a′	PROPN
ejpam-5511	474	6	∈	∈	PROPN
ejpam-5511	474	7	[	[	X
ejpam-5511	474	8	[	[	X
ejpam-5511	474	9	xyz]]ρf	xyz]]ρf	ADJ
ejpam-5511	474	10	,	,	PUNCT
ejpam-5511	474	11	b′	b′	NUM
ejpam-5511	474	12	∈	∈	PROPN
ejpam-5511	475	1	[	[	X
ejpam-5511	475	2	x]ρf	x]ρf	PROPN
ejpam-5511	475	3	.	.	PUNCT
ejpam-5511	476	1	as	as	ADP
ejpam-5511	476	2	[	[	X
ejpam-5511	476	3	xyz]ρfa	xyz]ρfa	PROPN
ejpam-5511	476	4	′	′	NOUN
ejpam-5511	476	5	,	,	PUNCT
ejpam-5511	476	6	there	there	PRON
ejpam-5511	476	7	exist	exist	VERB
ejpam-5511	476	8	c1	c1	NOUN
ejpam-5511	476	9	,	,	PUNCT
ejpam-5511	476	10	d1	d1	PROPN
ejpam-5511	476	11	∈	∈	PROPN
ejpam-5511	477	1	f	f	PROPN
ejpam-5511	477	2	such	such	ADJ
ejpam-5511	477	3	that	that	SCONJ
ejpam-5511	477	4	[	[	X
ejpam-5511	477	5	c1d1[xyz	c1d1[xyz	X
ejpam-5511	477	6	]	]	X
ejpam-5511	477	7	]	]	X
ejpam-5511	477	8	≤	≤	NOUN
ejpam-5511	477	9	a′	a′	PROPN
ejpam-5511	478	1	and	and	CCONJ
ejpam-5511	478	2	[	[	X
ejpam-5511	478	3	c1d1a	c1d1a	X
ejpam-5511	478	4	′	′	NOUN
ejpam-5511	478	5	]	]	PUNCT
ejpam-5511	478	6	≤	≤	NOUN
ejpam-5511	479	1	[	[	X
ejpam-5511	479	2	xyz	xyz	X
ejpam-5511	479	3	]	]	X
ejpam-5511	479	4	.	.	PUNCT
ejpam-5511	480	1	by	by	ADP
ejpam-5511	480	2	xρf	xρf	PROPN
ejpam-5511	480	3	b	b	PROPN
ejpam-5511	480	4	′	′	PROPN
ejpam-5511	480	5	,	,	PUNCT
ejpam-5511	480	6	there	there	PRON
ejpam-5511	480	7	exist	exist	VERB
ejpam-5511	480	8	c2	c2	PROPN
ejpam-5511	480	9	,	,	PUNCT
ejpam-5511	480	10	d2	d2	PROPN
ejpam-5511	480	11	∈	∈	PROPN
ejpam-5511	480	12	f	f	PROPN
ejpam-5511	481	1	such	such	ADJ
ejpam-5511	481	2	that	that	SCONJ
ejpam-5511	482	1	[	[	X
ejpam-5511	482	2	c2d2x	c2d2x	X
ejpam-5511	482	3	]	]	X
ejpam-5511	482	4	≤	≤	NUM
ejpam-5511	482	5	b′	b′	NUM
ejpam-5511	482	6	and	and	CCONJ
ejpam-5511	482	7	[	[	X
ejpam-5511	482	8	c2d2b	c2d2b	X
ejpam-5511	482	9	′	′	NOUN
ejpam-5511	482	10	]	]	PUNCT
ejpam-5511	482	11	≤	≤	NUM
ejpam-5511	482	12	x.	x.	NOUN
ejpam-5511	482	13	we	we	PRON
ejpam-5511	482	14	have	have	VERB
ejpam-5511	482	15	k.	k.	PROPN
ejpam-5511	482	16	nakwan	nakwan	PROPN
ejpam-5511	482	17	,	,	PUNCT
ejpam-5511	482	18	p.	p.	PROPN
ejpam-5511	482	19	luangchaisri	luangchaisri	VERB
ejpam-5511	482	20	,	,	PUNCT
ejpam-5511	482	21	t.	t.	PROPN
ejpam-5511	482	22	changphas	changphas	PROPN
ejpam-5511	482	23	/	/	SYM
ejpam-5511	482	24	eur	eur	PROPN
ejpam-5511	482	25	.	.	PUNCT
ejpam-5511	483	1	j.	j.	PROPN
ejpam-5511	483	2	pure	pure	PROPN
ejpam-5511	483	3	appl	appl	PROPN
ejpam-5511	483	4	.	.	PROPN
ejpam-5511	483	5	math	math	PROPN
ejpam-5511	483	6	,	,	PUNCT
ejpam-5511	483	7	17	17	NUM
ejpam-5511	483	8	(	(	PUNCT
ejpam-5511	483	9	4	4	NUM
ejpam-5511	483	10	)	)	PUNCT
ejpam-5511	483	11	(	(	PUNCT
ejpam-5511	483	12	2024	2024	NUM
ejpam-5511	483	13	)	)	PUNCT
ejpam-5511	483	14	,	,	PUNCT
ejpam-5511	483	15	4180	4180	NUM
ejpam-5511	483	16	-	-	SYM
ejpam-5511	483	17	4194	4194	NUM
ejpam-5511	483	18	4190	4190	NUM
ejpam-5511	484	1	[	[	X
ejpam-5511	484	2	[	[	X
ejpam-5511	484	3	c1d1c2]d2a	c1d1c2]d2a	NOUN
ejpam-5511	484	4	′	′	X
ejpam-5511	484	5	]	]	X
ejpam-5511	484	6	=	=	PUNCT
ejpam-5511	485	1	[	[	X
ejpam-5511	485	2	c1d1[c2d2a	c1d1[c2d2a	NUM
ejpam-5511	485	3	′	′	NOUN
ejpam-5511	485	4	]	]	X
ejpam-5511	485	5	]	]	PUNCT
ejpam-5511	485	6	=	=	PUNCT
ejpam-5511	486	1	[	[	X
ejpam-5511	486	2	c1d1[a	c1d1[a	PROPN
ejpam-5511	486	3	′c2d2	′c2d2	PROPN
ejpam-5511	486	4	]	]	X
ejpam-5511	486	5	]	]	PUNCT
ejpam-5511	487	1	=	=	PUNCT
ejpam-5511	488	1	[	[	X
ejpam-5511	488	2	[	[	X
ejpam-5511	488	3	c1d1a	c1d1a	X
ejpam-5511	488	4	′]c2d2	′]c2d2	X
ejpam-5511	488	5	]	]	X
ejpam-5511	488	6	≤	≤	PUNCT
ejpam-5511	489	1	[	[	X
ejpam-5511	489	2	[	[	X
ejpam-5511	489	3	xyz]c2d2	xyz]c2d2	X
ejpam-5511	489	4	]	]	X
ejpam-5511	489	5	=	=	PUNCT
ejpam-5511	490	1	[	[	X
ejpam-5511	490	2	c2d2[xyz	c2d2[xyz	X
ejpam-5511	490	3	]	]	X
ejpam-5511	490	4	]	]	PUNCT
ejpam-5511	491	1	=	=	PUNCT
ejpam-5511	492	1	[	[	X
ejpam-5511	492	2	[	[	X
ejpam-5511	492	3	c2d2x]yz	c2d2x]yz	X
ejpam-5511	492	4	]	]	PUNCT
ejpam-5511	492	5	≤	≤	NOUN
ejpam-5511	493	1	[	[	X
ejpam-5511	493	2	b′yz	b′yz	NOUN
ejpam-5511	493	3	]	]	PUNCT
ejpam-5511	493	4	≤	≤	NUM
ejpam-5511	493	5	b′.	b′.	PROPN
ejpam-5511	494	1	then	then	ADV
ejpam-5511	494	2	[	[	X
ejpam-5511	494	3	[	[	X
ejpam-5511	494	4	c1d1c2]d2a	c1d1c2]d2a	NOUN
ejpam-5511	494	5	′	′	NOUN
ejpam-5511	494	6	]	]	X
ejpam-5511	494	7	≤	≤	NUM
ejpam-5511	494	8	b′	b′	NUM
ejpam-5511	494	9	;	;	PUNCT
ejpam-5511	494	10	hence	hence	ADV
ejpam-5511	494	11	,	,	PUNCT
ejpam-5511	494	12	[	[	X
ejpam-5511	494	13	[	[	X
ejpam-5511	494	14	xyz]]ρf	xyz]]ρf	X
ejpam-5511	494	15	⪯	⪯	NOUN
ejpam-5511	495	1	[	[	X
ejpam-5511	495	2	x]ρf	x]ρf	PROPN
ejpam-5511	495	3	.	.	PUNCT
ejpam-5511	496	1	that	that	PRON
ejpam-5511	496	2	is	be	AUX
ejpam-5511	496	3	[	[	X
ejpam-5511	496	4	[	[	X
ejpam-5511	496	5	[	[	X
ejpam-5511	496	6	x]ρf	x]ρf	PROPN
ejpam-5511	496	7	[	[	X
ejpam-5511	496	8	y]ρf	y]ρf	PRON
ejpam-5511	496	9	[	[	X
ejpam-5511	496	10	z]ρf	z]ρf	PROPN
ejpam-5511	496	11	]	]	X
ejpam-5511	496	12	]	]	X
ejpam-5511	496	13	⪯	⪯	NOUN
ejpam-5511	497	1	[	[	X
ejpam-5511	497	2	x]ρf	x]ρf	PROPN
ejpam-5511	497	3	.	.	PUNCT
ejpam-5511	498	1	in	in	ADP
ejpam-5511	498	2	the	the	DET
ejpam-5511	498	3	same	same	ADJ
ejpam-5511	498	4	manner	manner	NOUN
ejpam-5511	498	5	,	,	PUNCT
ejpam-5511	498	6	we	we	PRON
ejpam-5511	498	7	can	can	AUX
ejpam-5511	498	8	prove	prove	VERB
ejpam-5511	498	9	that	that	SCONJ
ejpam-5511	498	10	[	[	X
ejpam-5511	498	11	[	[	X
ejpam-5511	498	12	[	[	X
ejpam-5511	498	13	x]ρf	x]ρf	PROPN
ejpam-5511	498	14	[	[	X
ejpam-5511	498	15	y]ρf	y]ρf	PRON
ejpam-5511	498	16	[	[	X
ejpam-5511	498	17	z]ρf	z]ρf	PROPN
ejpam-5511	498	18	]	]	X
ejpam-5511	498	19	]	]	X
ejpam-5511	498	20	⪯	⪯	NOUN
ejpam-5511	499	1	[	[	X
ejpam-5511	499	2	y]ρf	y]ρf	NOUN
ejpam-5511	499	3	and	and	CCONJ
ejpam-5511	499	4	[	[	X
ejpam-5511	499	5	[	[	X
ejpam-5511	499	6	[	[	X
ejpam-5511	499	7	x]ρf	x]ρf	PROPN
ejpam-5511	499	8	[	[	X
ejpam-5511	499	9	y]ρf	y]ρf	PRON
ejpam-5511	499	10	[	[	X
ejpam-5511	499	11	z]ρf	z]ρf	PROPN
ejpam-5511	499	12	]	]	X
ejpam-5511	499	13	]	]	X
ejpam-5511	499	14	⪯	⪯	NOUN
ejpam-5511	500	1	[	[	X
ejpam-5511	500	2	z]ρf	z]ρf	PROPN
ejpam-5511	500	3	.	.	PUNCT
ejpam-5511	501	1	lemma	lemma	PROPN
ejpam-5511	501	2	4	4	X
ejpam-5511	501	3	.	.	PUNCT
ejpam-5511	502	1	let	let	AUX
ejpam-5511	502	2	(	(	PUNCT
ejpam-5511	502	3	t	t	NOUN
ejpam-5511	502	4	,	,	PUNCT
ejpam-5511	502	5	[	[	PUNCT
ejpam-5511	502	6	]	]	X
ejpam-5511	502	7	,	,	PUNCT
ejpam-5511	502	8	≤	≤	NUM
ejpam-5511	502	9	,	,	PUNCT
ejpam-5511	502	10	[	[	PUNCT
ejpam-5511	502	11	]	]	X
ejpam-5511	502	12	∗	∗	NOUN
ejpam-5511	502	13	)	)	PUNCT
ejpam-5511	502	14	be	be	VERB
ejpam-5511	502	15	a	a	DET
ejpam-5511	502	16	commutative	commutative	ADJ
ejpam-5511	502	17	implicative	implicative	ADJ
ejpam-5511	502	18	n.p.o	n.p.o	NOUN
ejpam-5511	502	19	.	.	PUNCT
ejpam-5511	503	1	ternary	ternary	PROPN
ejpam-5511	503	2	semigroup	semigroup	PROPN
ejpam-5511	503	3	,	,	PUNCT
ejpam-5511	503	4	and	and	CCONJ
ejpam-5511	503	5	let	let	VERB
ejpam-5511	503	6	f	f	PRON
ejpam-5511	503	7	be	be	AUX
ejpam-5511	503	8	a	a	DET
ejpam-5511	503	9	filter	filter	NOUN
ejpam-5511	503	10	of	of	ADP
ejpam-5511	503	11	t	t	PROPN
ejpam-5511	503	12	.	.	PUNCT
ejpam-5511	504	1	then	then	ADV
ejpam-5511	504	2	(	(	PUNCT
ejpam-5511	504	3	t	t	PROPN
ejpam-5511	504	4	/	/	SYM
ejpam-5511	504	5	ρf	ρf	NOUN
ejpam-5511	504	6	,	,	PUNCT
ejpam-5511	505	1	[	[	X
ejpam-5511	505	2	[	[	X
ejpam-5511	505	3	]	]	X
ejpam-5511	505	4	]	]	X
ejpam-5511	505	5	,	,	PUNCT
ejpam-5511	505	6	⪯	⪯	PROPN
ejpam-5511	505	7	,	,	PUNCT
ejpam-5511	505	8	[	[	X
ejpam-5511	505	9	[	[	X
ejpam-5511	505	10	]	]	X
ejpam-5511	505	11	]	]	X
ejpam-5511	505	12	∗	∗	NOUN
ejpam-5511	505	13	)	)	PUNCT
ejpam-5511	505	14	is	be	AUX
ejpam-5511	505	15	a	a	DET
ejpam-5511	505	16	commutative	commutative	ADJ
ejpam-5511	505	17	implicative	implicative	ADJ
ejpam-5511	505	18	n.p.o	n.p.o	NOUN
ejpam-5511	505	19	.	.	PUNCT
ejpam-5511	506	1	ternary	ternary	PROPN
ejpam-5511	506	2	semigroup	semigroup	NOUN
ejpam-5511	506	3	with	with	ADP
ejpam-5511	506	4	the	the	DET
ejpam-5511	506	5	ternary	ternary	ADJ
ejpam-5511	506	6	implication	implication	NOUN
ejpam-5511	507	1	[	[	X
ejpam-5511	507	2	[	[	X
ejpam-5511	507	3	[	[	X
ejpam-5511	507	4	x]ρf	x]ρf	PROPN
ejpam-5511	507	5	[	[	X
ejpam-5511	507	6	y]ρf	y]ρf	PRON
ejpam-5511	507	7	[	[	X
ejpam-5511	507	8	z]ρf	z]ρf	PROPN
ejpam-5511	507	9	]	]	X
ejpam-5511	507	10	]	]	X
ejpam-5511	507	11	∗	∗	NOUN
ejpam-5511	507	12	=	=	PUNCT
ejpam-5511	508	1	[	[	X
ejpam-5511	508	2	[	[	X
ejpam-5511	508	3	xyz]∗]ρf	xyz]∗]ρf	NUM
ejpam-5511	508	4	for	for	ADP
ejpam-5511	508	5	all	all	DET
ejpam-5511	508	6	[	[	X
ejpam-5511	508	7	x]ρf	x]ρf	PROPN
ejpam-5511	508	8	,	,	PUNCT
ejpam-5511	508	9	[	[	X
ejpam-5511	508	10	y]ρf	y]ρf	X
ejpam-5511	508	11	,	,	PUNCT
ejpam-5511	508	12	[	[	X
ejpam-5511	508	13	z]ρf	z]ρf	PROPN
ejpam-5511	508	14	∈	∈	PROPN
ejpam-5511	508	15	t	t	PROPN
ejpam-5511	508	16	/	/	SYM
ejpam-5511	508	17	ρf	ρf	PROPN
ejpam-5511	508	18	.	.	PUNCT
ejpam-5511	509	1	proof	proof	NOUN
ejpam-5511	509	2	.	.	PUNCT
ejpam-5511	510	1	we	we	PRON
ejpam-5511	510	2	first	first	ADV
ejpam-5511	510	3	show	show	VERB
ejpam-5511	510	4	that	that	SCONJ
ejpam-5511	510	5	[	[	X
ejpam-5511	510	6	[	[	X
ejpam-5511	510	7	]	]	X
ejpam-5511	510	8	]	]	X
ejpam-5511	510	9	∗	∗	NOUN
ejpam-5511	510	10	is	be	AUX
ejpam-5511	510	11	well	well	ADV
ejpam-5511	510	12	-	-	PUNCT
ejpam-5511	510	13	defined	define	VERB
ejpam-5511	510	14	on	on	ADP
ejpam-5511	510	15	t	t	PROPN
ejpam-5511	510	16	/	/	SYM
ejpam-5511	510	17	ρf	ρf	PROPN
ejpam-5511	510	18	.	.	PUNCT
ejpam-5511	511	1	let	let	VERB
ejpam-5511	512	1	[	[	PUNCT
ejpam-5511	512	2	x]ρf	x]ρf	PROPN
ejpam-5511	512	3	,	,	PUNCT
ejpam-5511	512	4	[	[	X
ejpam-5511	512	5	y]ρf	y]ρf	X
ejpam-5511	512	6	,	,	PUNCT
ejpam-5511	512	7	[	[	X
ejpam-5511	512	8	z]ρf	z]ρf	X
ejpam-5511	512	9	,	,	PUNCT
ejpam-5511	512	10	[	[	X
ejpam-5511	512	11	x′]ρf	x′]ρf	X
ejpam-5511	512	12	,	,	PUNCT
ejpam-5511	512	13	[	[	X
ejpam-5511	512	14	y′]ρf	y′]ρf	NOUN
ejpam-5511	512	15	,	,	PUNCT
ejpam-5511	512	16	[	[	X
ejpam-5511	512	17	z′]ρf	z′]ρf	PROPN
ejpam-5511	512	18	∈	∈	PROPN
ejpam-5511	512	19	t	t	PROPN
ejpam-5511	512	20	/	/	SYM
ejpam-5511	512	21	ρf	ρf	NOUN
ejpam-5511	512	22	be	be	AUX
ejpam-5511	512	23	such	such	ADJ
ejpam-5511	512	24	that	that	SCONJ
ejpam-5511	513	1	[	[	X
ejpam-5511	513	2	x]ρf	x]ρf	X
ejpam-5511	513	3	=	=	PUNCT
ejpam-5511	514	1	[	[	X
ejpam-5511	514	2	x′]ρf	x′]ρf	PROPN
ejpam-5511	514	3	,	,	PUNCT
ejpam-5511	514	4	[	[	X
ejpam-5511	514	5	y]ρf	y]ρf	NOUN
ejpam-5511	514	6	=	=	PUNCT
ejpam-5511	515	1	[	[	X
ejpam-5511	515	2	y′]ρf	y′]ρf	PROPN
ejpam-5511	515	3	and	and	CCONJ
ejpam-5511	515	4	[	[	X
ejpam-5511	515	5	z]ρf	z]ρf	PROPN
ejpam-5511	515	6	=	=	SYM
ejpam-5511	515	7	[	[	X
ejpam-5511	515	8	z′]ρf	z′]ρf	PROPN
ejpam-5511	515	9	.	.	PUNCT
ejpam-5511	516	1	then	then	ADV
ejpam-5511	516	2	there	there	PRON
ejpam-5511	516	3	exist	exist	VERB
ejpam-5511	516	4	c1	c1	NOUN
ejpam-5511	516	5	,	,	PUNCT
ejpam-5511	516	6	d1	d1	PROPN
ejpam-5511	516	7	,	,	PUNCT
ejpam-5511	516	8	c2	c2	PROPN
ejpam-5511	516	9	,	,	PUNCT
ejpam-5511	516	10	d2	d2	PROPN
ejpam-5511	516	11	,	,	PUNCT
ejpam-5511	516	12	c3	c3	PROPN
ejpam-5511	516	13	,	,	PUNCT
ejpam-5511	516	14	d3	d3	PROPN
ejpam-5511	516	15	∈	∈	PROPN
ejpam-5511	516	16	f	f	PROPN
ejpam-5511	516	17	such	such	ADJ
ejpam-5511	516	18	that	that	SCONJ
ejpam-5511	516	19	[	[	X
ejpam-5511	516	20	c1d1x	c1d1x	X
ejpam-5511	516	21	]	]	X
ejpam-5511	516	22	≤	≤	NUM
ejpam-5511	516	23	x′	x′	NUM
ejpam-5511	516	24	,	,	PUNCT
ejpam-5511	517	1	[	[	X
ejpam-5511	517	2	c1d1x	c1d1x	X
ejpam-5511	517	3	′	′	NUM
ejpam-5511	517	4	]	]	X
ejpam-5511	517	5	≤	≤	NUM
ejpam-5511	517	6	x	x	X
ejpam-5511	517	7	,	,	PUNCT
ejpam-5511	517	8	[	[	X
ejpam-5511	517	9	c2d2y	c2d2y	X
ejpam-5511	517	10	]	]	X
ejpam-5511	517	11	≤	≤	NUM
ejpam-5511	517	12	y′	y′	NUM
ejpam-5511	517	13	,	,	PUNCT
ejpam-5511	517	14	[	[	X
ejpam-5511	517	15	c2d2y	c2d2y	NUM
ejpam-5511	517	16	′	′	NOUN
ejpam-5511	517	17	]	]	PUNCT
ejpam-5511	517	18	≤	≤	NUM
ejpam-5511	517	19	y	y	NOUN
ejpam-5511	517	20	,	,	PUNCT
ejpam-5511	517	21	[	[	X
ejpam-5511	517	22	c3d3z	c3d3z	X
ejpam-5511	517	23	]	]	X
ejpam-5511	517	24	≤	≤	NUM
ejpam-5511	517	25	z′	z′	NUM
ejpam-5511	517	26	and	and	CCONJ
ejpam-5511	517	27	[	[	X
ejpam-5511	517	28	c3d3z	c3d3z	X
ejpam-5511	517	29	′	′	NOUN
ejpam-5511	517	30	]	]	PUNCT
ejpam-5511	517	31	≤	≤	NUM
ejpam-5511	517	32	z.	z.	PROPN
ejpam-5511	517	33	we	we	PRON
ejpam-5511	517	34	denote	denote	VERB
ejpam-5511	517	35	[	[	X
ejpam-5511	517	36	xyz]∗	xyz]∗	X
ejpam-5511	517	37	by	by	ADP
ejpam-5511	517	38	u	u	NOUN
ejpam-5511	517	39	and	and	CCONJ
ejpam-5511	517	40	[	[	X
ejpam-5511	517	41	x′y′z′]∗	x′y′z′]∗	PROPN
ejpam-5511	517	42	by	by	ADP
ejpam-5511	517	43	t.	t.	PROPN
ejpam-5511	517	44	since	since	SCONJ
ejpam-5511	517	45	u	u	NOUN
ejpam-5511	517	46	≤	≤	X
ejpam-5511	518	1	[	[	X
ejpam-5511	518	2	xyz]∗	xyz]∗	X
ejpam-5511	518	3	,	,	PUNCT
ejpam-5511	518	4	[	[	X
ejpam-5511	518	5	uxy	uxy	X
ejpam-5511	518	6	]	]	X
ejpam-5511	518	7	≤	≤	NUM
ejpam-5511	518	8	z.	z.	PROPN
ejpam-5511	518	9	using	use	VERB
ejpam-5511	518	10	the	the	DET
ejpam-5511	518	11	associativity	associativity	NOUN
ejpam-5511	518	12	and	and	CCONJ
ejpam-5511	518	13	commutativity	commutativity	NOUN
ejpam-5511	518	14	of	of	ADP
ejpam-5511	518	15	t	t	PROPN
ejpam-5511	518	16	,	,	PUNCT
ejpam-5511	518	17	we	we	PRON
ejpam-5511	518	18	have	have	VERB
ejpam-5511	518	19	[	[	X
ejpam-5511	518	20	[	[	X
ejpam-5511	518	21	[	[	X
ejpam-5511	518	22	[	[	X
ejpam-5511	518	23	c1d1c2]d2c3]d3u]x′y′	c1d1c2]d2c3]d3u]x′y′	X
ejpam-5511	518	24	]	]	X
ejpam-5511	518	25	≤	≤	NUM
ejpam-5511	518	26	z′.	z′.	NOUN
ejpam-5511	519	1	this	this	PRON
ejpam-5511	519	2	shows	show	VERB
ejpam-5511	519	3	that	that	SCONJ
ejpam-5511	519	4	[	[	X
ejpam-5511	519	5	[	[	X
ejpam-5511	519	6	[	[	X
ejpam-5511	519	7	[	[	X
ejpam-5511	519	8	c1d1c2]d2c3]d3[xyz	c1d1c2]d2c3]d3[xyz	NOUN
ejpam-5511	519	9	]	]	X
ejpam-5511	519	10	∗	∗	NOUN
ejpam-5511	519	11	]	]	X
ejpam-5511	519	12	]	]	X
ejpam-5511	519	13	≤	≤	X
ejpam-5511	520	1	[	[	X
ejpam-5511	520	2	x′y′z′]∗.	x′y′z′]∗.	NOUN
ejpam-5511	520	3	in	in	ADP
ejpam-5511	520	4	the	the	DET
ejpam-5511	520	5	same	same	ADJ
ejpam-5511	520	6	manner	manner	NOUN
ejpam-5511	520	7	,	,	PUNCT
ejpam-5511	520	8	we	we	PRON
ejpam-5511	520	9	have	have	VERB
ejpam-5511	520	10	[	[	X
ejpam-5511	520	11	[	[	X
ejpam-5511	520	12	[	[	X
ejpam-5511	520	13	[	[	X
ejpam-5511	520	14	c1d1c2]d2c3]d3[x	c1d1c2]d2c3]d3[x	ADJ
ejpam-5511	520	15	′y′z′]∗	′y′z′]∗	PROPN
ejpam-5511	520	16	]	]	X
ejpam-5511	520	17	]	]	X
ejpam-5511	520	18	≤	≤	NOUN
ejpam-5511	521	1	[	[	X
ejpam-5511	521	2	xyz]∗.	xyz]∗.	NOUN
ejpam-5511	521	3	thus	thus	ADV
ejpam-5511	521	4	we	we	PRON
ejpam-5511	521	5	have	have	AUX
ejpam-5511	521	6	shown	show	VERB
ejpam-5511	521	7	that	that	SCONJ
ejpam-5511	522	1	[	[	X
ejpam-5511	522	2	xyz]∗ρf	xyz]∗ρf	NOUN
ejpam-5511	522	3	[	[	X
ejpam-5511	522	4	x′y′z′]∗	x′y′z′]∗	PROPN
ejpam-5511	522	5	and	and	CCONJ
ejpam-5511	522	6	hence	hence	ADV
ejpam-5511	522	7	[	[	X
ejpam-5511	522	8	[	[	X
ejpam-5511	522	9	xyz]∗]ρf	xyz]∗]ρf	NOUN
ejpam-5511	522	10	=	=	PUNCT
ejpam-5511	522	11	[	[	X
ejpam-5511	522	12	[	[	X
ejpam-5511	522	13	x′y′z′]∗]ρf	x′y′z′]∗]ρf	X
ejpam-5511	522	14	.	.	PUNCT
ejpam-5511	523	1	let	let	VERB
ejpam-5511	524	1	[	[	X
ejpam-5511	524	2	x]ρf	x]ρf	PROPN
ejpam-5511	524	3	,	,	PUNCT
ejpam-5511	524	4	[	[	X
ejpam-5511	524	5	y]ρf	y]ρf	X
ejpam-5511	524	6	,	,	PUNCT
ejpam-5511	524	7	[	[	X
ejpam-5511	524	8	z]ρf	z]ρf	X
ejpam-5511	524	9	,	,	PUNCT
ejpam-5511	524	10	[	[	X
ejpam-5511	524	11	u]ρf	u]ρf	PROPN
ejpam-5511	524	12	∈	∈	PROPN
ejpam-5511	524	13	t	t	PROPN
ejpam-5511	524	14	/	/	SYM
ejpam-5511	524	15	ρf	ρf	NOUN
ejpam-5511	524	16	be	be	AUX
ejpam-5511	524	17	such	such	ADJ
ejpam-5511	524	18	that	that	SCONJ
ejpam-5511	524	19	[	[	X
ejpam-5511	524	20	[	[	X
ejpam-5511	524	21	[	[	X
ejpam-5511	524	22	u]ρf	u]ρf	PROPN
ejpam-5511	524	23	[	[	X
ejpam-5511	524	24	x]ρf	x]ρf	PROPN
ejpam-5511	524	25	[	[	X
ejpam-5511	524	26	y]ρf	y]ρf	X
ejpam-5511	524	27	]	]	X
ejpam-5511	524	28	]	]	X
ejpam-5511	524	29	⪯	⪯	NOUN
ejpam-5511	525	1	[	[	X
ejpam-5511	525	2	z]ρf	z]ρf	PROPN
ejpam-5511	525	3	;	;	PUNCT
ejpam-5511	525	4	then	then	ADV
ejpam-5511	525	5	[	[	X
ejpam-5511	525	6	[	[	X
ejpam-5511	525	7	uxy]]ρf	uxy]]ρf	X
ejpam-5511	525	8	⪯	⪯	NOUN
ejpam-5511	525	9	[	[	X
ejpam-5511	525	10	z]ρf	z]ρf	PROPN
ejpam-5511	525	11	.	.	PUNCT
ejpam-5511	526	1	to	to	PART
ejpam-5511	526	2	show	show	VERB
ejpam-5511	526	3	that	that	SCONJ
ejpam-5511	527	1	[	[	X
ejpam-5511	527	2	u]ρf	u]ρf	ADJ
ejpam-5511	527	3	⪯	⪯	NOUN
ejpam-5511	527	4	[	[	X
ejpam-5511	527	5	[	[	X
ejpam-5511	527	6	xyz]∗]ρf	xyz]∗]ρf	NUM
ejpam-5511	527	7	,	,	PUNCT
ejpam-5511	527	8	that	that	ADV
ejpam-5511	527	9	is	is	ADV
ejpam-5511	527	10	,	,	PUNCT
ejpam-5511	527	11	[	[	X
ejpam-5511	527	12	u]ρf	u]ρf	NOUN
ejpam-5511	527	13	⪯	⪯	NOUN
ejpam-5511	528	1	[	[	X
ejpam-5511	528	2	[	[	X
ejpam-5511	528	3	[	[	X
ejpam-5511	528	4	x]ρf	x]ρf	PROPN
ejpam-5511	528	5	[	[	X
ejpam-5511	528	6	y]ρf	y]ρf	PRON
ejpam-5511	528	7	[	[	X
ejpam-5511	528	8	z]ρf	z]ρf	PROPN
ejpam-5511	528	9	]	]	X
ejpam-5511	528	10	]	]	PUNCT
ejpam-5511	528	11	∗.	∗.	PROPN
ejpam-5511	528	12	let	let	VERB
ejpam-5511	528	13	a	a	DET
ejpam-5511	528	14	∈	∈	NOUN
ejpam-5511	529	1	[	[	X
ejpam-5511	529	2	u]ρf	u]ρf	NOUN
ejpam-5511	529	3	and	and	CCONJ
ejpam-5511	529	4	b	b	NOUN
ejpam-5511	529	5	∈	∈	PROPN
ejpam-5511	530	1	[	[	X
ejpam-5511	530	2	[	[	X
ejpam-5511	530	3	xyz]∗]ρf	xyz]∗]ρf	X
ejpam-5511	530	4	.	.	PUNCT
ejpam-5511	531	1	since	since	SCONJ
ejpam-5511	531	2	[	[	X
ejpam-5511	531	3	[	[	X
ejpam-5511	531	4	uxy]]ρf	uxy]]ρf	X
ejpam-5511	531	5	⪯	⪯	NOUN
ejpam-5511	531	6	[	[	X
ejpam-5511	531	7	z]ρf	z]ρf	PROPN
ejpam-5511	531	8	,	,	PUNCT
ejpam-5511	531	9	there	there	PRON
ejpam-5511	531	10	exist	exist	VERB
ejpam-5511	531	11	c	c	NOUN
ejpam-5511	531	12	,	,	PUNCT
ejpam-5511	531	13	d	d	PROPN
ejpam-5511	531	14	∈	∈	PROPN
ejpam-5511	531	15	f	f	PROPN
ejpam-5511	531	16	such	such	ADJ
ejpam-5511	531	17	that	that	SCONJ
ejpam-5511	532	1	[	[	X
ejpam-5511	532	2	cd[uxy	cd[uxy	X
ejpam-5511	532	3	]	]	X
ejpam-5511	532	4	]	]	X
ejpam-5511	532	5	≤	≤	NUM
ejpam-5511	532	6	z.	z.	X
ejpam-5511	532	7	by	by	ADP
ejpam-5511	532	8	a	a	DET
ejpam-5511	532	9	∈	∈	PROPN
ejpam-5511	532	10	[	[	X
ejpam-5511	532	11	u]ρf	u]ρf	NOUN
ejpam-5511	532	12	,	,	PUNCT
ejpam-5511	532	13	there	there	PRON
ejpam-5511	532	14	exist	exist	VERB
ejpam-5511	532	15	c1	c1	NOUN
ejpam-5511	532	16	,	,	PUNCT
ejpam-5511	532	17	d1	d1	PROPN
ejpam-5511	532	18	∈	∈	PROPN
ejpam-5511	532	19	f	f	PROPN
ejpam-5511	533	1	such	such	ADJ
ejpam-5511	533	2	that	that	SCONJ
ejpam-5511	533	3	[	[	X
ejpam-5511	533	4	c1d1u	c1d1u	X
ejpam-5511	533	5	]	]	X
ejpam-5511	533	6	≤	≤	NUM
ejpam-5511	533	7	a	a	PRON
ejpam-5511	533	8	and	and	CCONJ
ejpam-5511	533	9	[	[	X
ejpam-5511	533	10	c1d1a	c1d1a	X
ejpam-5511	533	11	]	]	X
ejpam-5511	533	12	≤	≤	X
ejpam-5511	533	13	u.	u.	NOUN
ejpam-5511	533	14	similarly	similarly	ADV
ejpam-5511	533	15	,	,	PUNCT
ejpam-5511	533	16	by	by	ADP
ejpam-5511	533	17	b	b	PROPN
ejpam-5511	533	18	∈	∈	PROPN
ejpam-5511	534	1	[	[	X
ejpam-5511	534	2	[	[	X
ejpam-5511	534	3	xyz]∗]ρf	xyz]∗]ρf	ADP
ejpam-5511	534	4	,	,	PUNCT
ejpam-5511	534	5	there	there	PRON
ejpam-5511	534	6	exist	exist	VERB
ejpam-5511	534	7	c2	c2	PROPN
ejpam-5511	534	8	,	,	PUNCT
ejpam-5511	534	9	d2	d2	PROPN
ejpam-5511	534	10	∈	∈	PROPN
ejpam-5511	534	11	f	f	PROPN
ejpam-5511	534	12	such	such	ADJ
ejpam-5511	534	13	that	that	SCONJ
ejpam-5511	534	14	[	[	X
ejpam-5511	534	15	c2d2[xyz	c2d2[xyz	NOUN
ejpam-5511	534	16	]	]	X
ejpam-5511	534	17	∗	∗	NOUN
ejpam-5511	534	18	]	]	PUNCT
ejpam-5511	534	19	≤	≤	NUM
ejpam-5511	534	20	b	b	NOUN
ejpam-5511	534	21	and	and	CCONJ
ejpam-5511	534	22	[	[	X
ejpam-5511	534	23	c2d2b	c2d2b	X
ejpam-5511	534	24	]	]	X
ejpam-5511	534	25	≤	≤	NOUN
ejpam-5511	535	1	[	[	X
ejpam-5511	535	2	xyz]∗.	xyz]∗.	PROPN
ejpam-5511	535	3	as	as	ADP
ejpam-5511	535	4	[	[	X
ejpam-5511	535	5	cd[uxy	cd[uxy	X
ejpam-5511	535	6	]	]	X
ejpam-5511	535	7	]	]	X
ejpam-5511	535	8	≤	≤	PROPN
ejpam-5511	535	9	z	z	X
ejpam-5511	535	10	,	,	PUNCT
ejpam-5511	535	11	we	we	PRON
ejpam-5511	535	12	have	have	VERB
ejpam-5511	535	13	[	[	X
ejpam-5511	535	14	cdu	cdu	X
ejpam-5511	535	15	]	]	X
ejpam-5511	535	16	≤	≤	NOUN
ejpam-5511	536	1	[	[	X
ejpam-5511	536	2	xyz]∗.	xyz]∗.	NOUN
ejpam-5511	536	3	consider	consider	VERB
ejpam-5511	536	4	:	:	PUNCT
ejpam-5511	537	1	[	[	X
ejpam-5511	537	2	[	[	X
ejpam-5511	537	3	c2d2[cdc1]]d1a	c2d2[cdc1]]d1a	X
ejpam-5511	537	4	]	]	X
ejpam-5511	537	5	=	=	PUNCT
ejpam-5511	538	1	[	[	X
ejpam-5511	538	2	c2d2[[cdc1]d1a	c2d2[[cdc1]d1a	X
ejpam-5511	538	3	]	]	X
ejpam-5511	538	4	]	]	PUNCT
ejpam-5511	538	5	=	=	PUNCT
ejpam-5511	539	1	[	[	X
ejpam-5511	539	2	c2d2[cd[c1d1a	c2d2[cd[c1d1a	X
ejpam-5511	539	3	]	]	X
ejpam-5511	539	4	]	]	X
ejpam-5511	539	5	]	]	X
ejpam-5511	540	1	=	=	PUNCT
ejpam-5511	541	1	[	[	X
ejpam-5511	541	2	c2d2[cdu	c2d2[cdu	X
ejpam-5511	541	3	]	]	X
ejpam-5511	541	4	]	]	X
ejpam-5511	542	1	=	=	PUNCT
ejpam-5511	543	1	[	[	X
ejpam-5511	543	2	c2d2[xyz	c2d2[xyz	X
ejpam-5511	543	3	]	]	X
ejpam-5511	543	4	∗	∗	NOUN
ejpam-5511	543	5	]	]	PUNCT
ejpam-5511	543	6	≤	≤	NUM
ejpam-5511	543	7	b.	b.	PROPN
ejpam-5511	544	1	then	then	ADV
ejpam-5511	545	1	[	[	X
ejpam-5511	545	2	u]ρf	u]ρf	NOUN
ejpam-5511	545	3	⪯	⪯	NOUN
ejpam-5511	546	1	[	[	X
ejpam-5511	546	2	[	[	X
ejpam-5511	546	3	[	[	X
ejpam-5511	546	4	x]ρf	x]ρf	PROPN
ejpam-5511	546	5	[	[	X
ejpam-5511	546	6	y]ρf	y]ρf	PRON
ejpam-5511	546	7	[	[	X
ejpam-5511	546	8	z]ρf	z]ρf	PROPN
ejpam-5511	546	9	]	]	X
ejpam-5511	546	10	]	]	X
ejpam-5511	546	11	∗.	∗.	NOUN
ejpam-5511	546	12	conversely	conversely	ADV
ejpam-5511	546	13	,	,	PUNCT
ejpam-5511	546	14	suppose	suppose	VERB
ejpam-5511	546	15	that	that	SCONJ
ejpam-5511	547	1	[	[	X
ejpam-5511	547	2	u]ρf	u]ρf	NOUN
ejpam-5511	547	3	⪯	⪯	NOUN
ejpam-5511	547	4	[	[	X
ejpam-5511	547	5	[	[	X
ejpam-5511	547	6	[	[	X
ejpam-5511	547	7	x]ρf	x]ρf	PROPN
ejpam-5511	547	8	[	[	X
ejpam-5511	547	9	y]ρf	y]ρf	PRON
ejpam-5511	547	10	[	[	X
ejpam-5511	547	11	z]ρf	z]ρf	PROPN
ejpam-5511	547	12	]	]	X
ejpam-5511	547	13	]	]	X
ejpam-5511	547	14	∗	∗	NOUN
ejpam-5511	547	15	;	;	PUNCT
ejpam-5511	547	16	then	then	ADV
ejpam-5511	547	17	[	[	X
ejpam-5511	547	18	u]ρf	u]ρf	NOUN
ejpam-5511	547	19	⪯	⪯	NOUN
ejpam-5511	548	1	[	[	X
ejpam-5511	549	1	[	[	X
ejpam-5511	549	2	xyz]∗]ρf	xyz]∗]ρf	X
ejpam-5511	549	3	.	.	PUNCT
ejpam-5511	549	4	to	to	PART
ejpam-5511	549	5	show	show	VERB
ejpam-5511	549	6	that	that	SCONJ
ejpam-5511	549	7	[	[	X
ejpam-5511	549	8	[	[	X
ejpam-5511	549	9	[	[	X
ejpam-5511	549	10	u]ρf	u]ρf	PROPN
ejpam-5511	549	11	[	[	X
ejpam-5511	549	12	x]ρf	x]ρf	PROPN
ejpam-5511	549	13	[	[	X
ejpam-5511	549	14	y]ρf	y]ρf	X
ejpam-5511	549	15	]	]	X
ejpam-5511	549	16	]	]	X
ejpam-5511	549	17	⪯	⪯	NOUN
ejpam-5511	550	1	[	[	X
ejpam-5511	550	2	z]ρf	z]ρf	PROPN
ejpam-5511	550	3	,	,	PUNCT
ejpam-5511	550	4	that	that	ADV
ejpam-5511	550	5	is	is	ADV
ejpam-5511	550	6	,	,	PUNCT
ejpam-5511	550	7	[	[	X
ejpam-5511	550	8	uxy]ρf	uxy]ρf	X
ejpam-5511	550	9	⪯	⪯	NOUN
ejpam-5511	550	10	[	[	X
ejpam-5511	550	11	z]ρf	z]ρf	PROPN
ejpam-5511	550	12	.	.	PUNCT
ejpam-5511	551	1	let	let	VERB
ejpam-5511	551	2	s	s	PRON
ejpam-5511	551	3	∈	∈	NOUN
ejpam-5511	552	1	[	[	X
ejpam-5511	552	2	[	[	X
ejpam-5511	552	3	uxy]]ρf	uxy]]ρf	NOUN
ejpam-5511	552	4	and	and	CCONJ
ejpam-5511	552	5	t	t	PROPN
ejpam-5511	552	6	∈	∈	PROPN
ejpam-5511	552	7	[	[	X
ejpam-5511	552	8	z]ρf	z]ρf	PROPN
ejpam-5511	552	9	.	.	PUNCT
ejpam-5511	553	1	since	since	SCONJ
ejpam-5511	553	2	[	[	X
ejpam-5511	553	3	xyz]∗	xyz]∗	X
ejpam-5511	553	4	∈	∈	PROPN
ejpam-5511	554	1	[	[	X
ejpam-5511	554	2	[	[	X
ejpam-5511	554	3	xyz]∗]ρf	xyz]∗]ρf	X
ejpam-5511	554	4	,	,	PUNCT
ejpam-5511	554	5	u	u	PROPN
ejpam-5511	554	6	∈	∈	PROPN
ejpam-5511	555	1	[	[	X
ejpam-5511	555	2	u]ρf	u]ρf	NOUN
ejpam-5511	555	3	,	,	PUNCT
ejpam-5511	555	4	and	and	CCONJ
ejpam-5511	556	1	[	[	X
ejpam-5511	556	2	u]ρf	u]ρf	ADJ
ejpam-5511	556	3	⪯	⪯	NOUN
ejpam-5511	556	4	[	[	X
ejpam-5511	556	5	[	[	X
ejpam-5511	556	6	xyz]∗]ρf	xyz]∗]ρf	ADP
ejpam-5511	556	7	,	,	PUNCT
ejpam-5511	556	8	there	there	PRON
ejpam-5511	556	9	exist	exist	VERB
ejpam-5511	556	10	c′	c′	NOUN
ejpam-5511	556	11	,	,	PUNCT
ejpam-5511	557	1	d′	d′	X
ejpam-5511	557	2	∈	∈	PROPN
ejpam-5511	557	3	f	f	PROPN
ejpam-5511	557	4	such	such	ADJ
ejpam-5511	557	5	that	that	SCONJ
ejpam-5511	557	6	[	[	X
ejpam-5511	557	7	c′d′u	c′d′u	X
ejpam-5511	557	8	]	]	X
ejpam-5511	557	9	≤	≤	NOUN
ejpam-5511	558	1	[	[	X
ejpam-5511	558	2	xyz]∗.	xyz]∗.	NOUN
ejpam-5511	558	3	by	by	ADP
ejpam-5511	558	4	s	s	PROPN
ejpam-5511	558	5	∈	∈	PROPN
ejpam-5511	559	1	[	[	X
ejpam-5511	559	2	[	[	X
ejpam-5511	559	3	uxy]]ρf	uxy]]ρf	NOUN
ejpam-5511	559	4	,	,	PUNCT
ejpam-5511	559	5	there	there	PRON
ejpam-5511	559	6	exist	exist	VERB
ejpam-5511	559	7	c3	c3	NOUN
ejpam-5511	559	8	,	,	PUNCT
ejpam-5511	559	9	d3	d3	PROPN
ejpam-5511	559	10	∈	∈	PROPN
ejpam-5511	559	11	f	f	PROPN
ejpam-5511	560	1	such	such	ADJ
ejpam-5511	560	2	that	that	SCONJ
ejpam-5511	560	3	[	[	X
ejpam-5511	560	4	c3d3[uxy	c3d3[uxy	X
ejpam-5511	560	5	]	]	X
ejpam-5511	560	6	]	]	X
ejpam-5511	560	7	≤	≤	PROPN
ejpam-5511	560	8	s	s	X
ejpam-5511	560	9	and	and	CCONJ
ejpam-5511	560	10	[	[	X
ejpam-5511	560	11	c3d3s	c3d3s	X
ejpam-5511	560	12	]	]	X
ejpam-5511	560	13	≤	≤	NOUN
ejpam-5511	561	1	[	[	X
ejpam-5511	561	2	uxy	uxy	X
ejpam-5511	561	3	]	]	X
ejpam-5511	561	4	.	.	PUNCT
ejpam-5511	562	1	similarly	similarly	ADV
ejpam-5511	562	2	,	,	PUNCT
ejpam-5511	562	3	by	by	ADP
ejpam-5511	562	4	t	t	PROPN
ejpam-5511	562	5	∈	∈	PROPN
ejpam-5511	562	6	[	[	X
ejpam-5511	562	7	z]ρf	z]ρf	PROPN
ejpam-5511	562	8	,	,	PUNCT
ejpam-5511	562	9	there	there	PRON
ejpam-5511	562	10	exist	exist	VERB
ejpam-5511	562	11	c4	c4	NOUN
ejpam-5511	562	12	,	,	PUNCT
ejpam-5511	562	13	d4	d4	PROPN
ejpam-5511	562	14	∈	∈	PROPN
ejpam-5511	563	1	f	f	PROPN
ejpam-5511	563	2	such	such	ADJ
ejpam-5511	563	3	that	that	SCONJ
ejpam-5511	563	4	[	[	X
ejpam-5511	563	5	c4d4z	c4d4z	X
ejpam-5511	563	6	]	]	PUNCT
ejpam-5511	563	7	≤	≤	NUM
ejpam-5511	563	8	t	t	NOUN
ejpam-5511	563	9	and	and	CCONJ
ejpam-5511	563	10	[	[	X
ejpam-5511	563	11	c4d4	c4d4	NOUN
ejpam-5511	563	12	t	t	PROPN
ejpam-5511	563	13	]	]	PUNCT
ejpam-5511	563	14	≤	≤	NUM
ejpam-5511	563	15	z.	z.	PROPN
ejpam-5511	563	16	consider	consider	VERB
ejpam-5511	563	17	:	:	PUNCT
ejpam-5511	564	1	[	[	X
ejpam-5511	564	2	[	[	X
ejpam-5511	564	3	c5d5[c	c5d5[c	X
ejpam-5511	564	4	′d′c3]]d3s	′d′c3]]d3s	X
ejpam-5511	564	5	]	]	X
ejpam-5511	564	6	=	=	SYM
ejpam-5511	565	1	[	[	X
ejpam-5511	565	2	c5d5[[c	c5d5[[c	X
ejpam-5511	565	3	′d′c3]d3s	′d′c3]d3s	PROPN
ejpam-5511	565	4	]	]	X
ejpam-5511	565	5	]	]	PUNCT
ejpam-5511	565	6	k.	k.	PROPN
ejpam-5511	565	7	nakwan	nakwan	PROPN
ejpam-5511	565	8	,	,	PUNCT
ejpam-5511	565	9	p.	p.	PROPN
ejpam-5511	565	10	luangchaisri	luangchaisri	VERB
ejpam-5511	565	11	,	,	PUNCT
ejpam-5511	565	12	t.	t.	PROPN
ejpam-5511	565	13	changphas	changphas	PROPN
ejpam-5511	565	14	/	/	SYM
ejpam-5511	565	15	eur	eur	PROPN
ejpam-5511	565	16	.	.	PUNCT
ejpam-5511	566	1	j.	j.	PROPN
ejpam-5511	566	2	pure	pure	PROPN
ejpam-5511	566	3	appl	appl	PROPN
ejpam-5511	566	4	.	.	PROPN
ejpam-5511	566	5	math	math	PROPN
ejpam-5511	566	6	,	,	PUNCT
ejpam-5511	566	7	17	17	NUM
ejpam-5511	566	8	(	(	PUNCT
ejpam-5511	566	9	4	4	NUM
ejpam-5511	566	10	)	)	PUNCT
ejpam-5511	566	11	(	(	PUNCT
ejpam-5511	566	12	2024	2024	NUM
ejpam-5511	566	13	)	)	PUNCT
ejpam-5511	566	14	,	,	PUNCT
ejpam-5511	566	15	4180	4180	NUM
ejpam-5511	566	16	-	-	SYM
ejpam-5511	566	17	4194	4194	NUM
ejpam-5511	566	18	4191	4191	NUM
ejpam-5511	566	19	=	=	PUNCT
ejpam-5511	567	1	[	[	X
ejpam-5511	567	2	c5d5[c	c5d5[c	PROPN
ejpam-5511	567	3	′d′[c3d3s	′d′[c3d3	NOUN
ejpam-5511	567	4	]	]	X
ejpam-5511	567	5	]	]	X
ejpam-5511	567	6	]	]	X
ejpam-5511	567	7	≤	≤	X
ejpam-5511	568	1	[	[	X
ejpam-5511	568	2	c5d5[c	c5d5[c	PROPN
ejpam-5511	568	3	′d′[uxy	′d′[uxy	PROPN
ejpam-5511	568	4	]	]	X
ejpam-5511	568	5	]	]	X
ejpam-5511	568	6	]	]	X
ejpam-5511	568	7	=	=	PUNCT
ejpam-5511	569	1	[	[	X
ejpam-5511	569	2	c5d5[[c	c5d5[[c	PROPN
ejpam-5511	569	3	′d′u]xy	′d′u]xy	PROPN
ejpam-5511	569	4	]	]	X
ejpam-5511	569	5	]	]	X
ejpam-5511	569	6	≤	≤	NOUN
ejpam-5511	570	1	[	[	X
ejpam-5511	570	2	c5d5z	c5d5z	NUM
ejpam-5511	570	3	]	]	X
ejpam-5511	570	4	≤	≤	ADJ
ejpam-5511	570	5	t.	t.	NOUN
ejpam-5511	570	6	hence	hence	ADV
ejpam-5511	570	7	,	,	PUNCT
ejpam-5511	570	8	[	[	X
ejpam-5511	570	9	[	[	X
ejpam-5511	570	10	[	[	X
ejpam-5511	570	11	u]ρf	u]ρf	NOUN
ejpam-5511	570	12	[	[	X
ejpam-5511	570	13	x]ρf	x]ρf	PROPN
ejpam-5511	570	14	[	[	X
ejpam-5511	570	15	y]ρf	y]ρf	X
ejpam-5511	570	16	]	]	X
ejpam-5511	570	17	]	]	X
ejpam-5511	570	18	⪯	⪯	NOUN
ejpam-5511	571	1	[	[	X
ejpam-5511	571	2	z]ρf	z]ρf	PROPN
ejpam-5511	571	3	.	.	PUNCT
ejpam-5511	572	1	in	in	ADP
ejpam-5511	572	2	view	view	NOUN
ejpam-5511	572	3	of	of	ADP
ejpam-5511	572	4	lemma	lemma	PROPN
ejpam-5511	572	5	4	4	NUM
ejpam-5511	572	6	,	,	PUNCT
ejpam-5511	572	7	the	the	DET
ejpam-5511	572	8	mapping	mapping	NOUN
ejpam-5511	572	9	η	η	PROPN
ejpam-5511	572	10	:	:	PUNCT
ejpam-5511	572	11	(	(	PUNCT
ejpam-5511	572	12	t	t	NOUN
ejpam-5511	572	13	,	,	PUNCT
ejpam-5511	572	14	[	[	PUNCT
ejpam-5511	572	15	]	]	X
ejpam-5511	572	16	,	,	PUNCT
ejpam-5511	572	17	≤	≤	NUM
ejpam-5511	572	18	,	,	PUNCT
ejpam-5511	572	19	[	[	PUNCT
ejpam-5511	572	20	]	]	X
ejpam-5511	572	21	∗	∗	NOUN
ejpam-5511	572	22	)	)	PUNCT
ejpam-5511	572	23	−→	−→	NOUN
ejpam-5511	572	24	(	(	PUNCT
ejpam-5511	572	25	t	t	PROPN
ejpam-5511	572	26	/	/	SYM
ejpam-5511	572	27	ρf	ρf	NOUN
ejpam-5511	572	28	,	,	PUNCT
ejpam-5511	572	29	[	[	X
ejpam-5511	572	30	[	[	X
ejpam-5511	572	31	]	]	X
ejpam-5511	572	32	]	]	X
ejpam-5511	572	33	,	,	PUNCT
ejpam-5511	572	34	⪯	⪯	PROPN
ejpam-5511	572	35	,	,	PUNCT
ejpam-5511	572	36	[	[	X
ejpam-5511	572	37	[	[	X
ejpam-5511	572	38	]	]	X
ejpam-5511	572	39	]	]	X
ejpam-5511	572	40	∗	∗	NOUN
ejpam-5511	572	41	)	)	PUNCT
ejpam-5511	572	42	defined	define	VERB
ejpam-5511	572	43	by	by	ADP
ejpam-5511	572	44	x	x	PROPN
ejpam-5511	572	45	7→	7→	PROPN
ejpam-5511	573	1	[	[	X
ejpam-5511	573	2	x]ρf	x]ρf	PROPN
ejpam-5511	573	3	is	be	AUX
ejpam-5511	573	4	a	a	DET
ejpam-5511	573	5	surjective	surjective	ADJ
ejpam-5511	573	6	mapping	mapping	NOUN
ejpam-5511	573	7	.	.	PUNCT
ejpam-5511	574	1	definition	definition	NOUN
ejpam-5511	574	2	6	6	NUM
ejpam-5511	574	3	.	.	PUNCT
ejpam-5511	575	1	let	let	VERB
ejpam-5511	575	2	φ	φ	PROPN
ejpam-5511	575	3	be	be	AUX
ejpam-5511	575	4	an	an	DET
ejpam-5511	575	5	implicative	implicative	ADJ
ejpam-5511	575	6	homomorphism	homomorphism	NOUN
ejpam-5511	575	7	from	from	ADP
ejpam-5511	575	8	a	a	DET
ejpam-5511	575	9	commutative	commutative	ADJ
ejpam-5511	575	10	implicative	implicative	ADJ
ejpam-5511	575	11	n.p.o	n.p.o	NOUN
ejpam-5511	575	12	.	.	PUNCT
ejpam-5511	576	1	ternary	ternary	PROPN
ejpam-5511	576	2	semigroup	semigroup	PROPN
ejpam-5511	576	3	(	(	PUNCT
ejpam-5511	576	4	t1	t1	NOUN
ejpam-5511	576	5	,	,	PUNCT
ejpam-5511	576	6	[	[	PUNCT
ejpam-5511	576	7	]	]	X
ejpam-5511	576	8	1,≤1	1,≤1	ADJ
ejpam-5511	576	9	,	,	PUNCT
ejpam-5511	576	10	[	[	PUNCT
ejpam-5511	576	11	]	]	X
ejpam-5511	576	12	∗1	∗1	X
ejpam-5511	576	13	)	)	PUNCT
ejpam-5511	576	14	onto	onto	ADP
ejpam-5511	576	15	a	a	DET
ejpam-5511	576	16	commutative	commutative	ADJ
ejpam-5511	576	17	implicative	implicative	ADJ
ejpam-5511	576	18	n.p.o	n.p.o	NOUN
ejpam-5511	576	19	.	.	PUNCT
ejpam-5511	577	1	ternary	ternary	ADJ
ejpam-5511	577	2	semigroup	semigroup	PROPN
ejpam-5511	577	3	(	(	PUNCT
ejpam-5511	577	4	t2	t2	NOUN
ejpam-5511	577	5	,	,	PUNCT
ejpam-5511	577	6	[	[	PUNCT
ejpam-5511	577	7	]	]	X
ejpam-5511	577	8	2,≤2	2,≤2	NOUN
ejpam-5511	577	9	,	,	PUNCT
ejpam-5511	577	10	[	[	PUNCT
ejpam-5511	577	11	]	]	X
ejpam-5511	577	12	∗2	∗2	NOUN
ejpam-5511	577	13	)	)	PUNCT
ejpam-5511	577	14	.	.	PUNCT
ejpam-5511	578	1	the	the	DET
ejpam-5511	578	2	kernel	kernel	PROPN
ejpam-5511	578	3	of	of	ADP
ejpam-5511	578	4	φ	φ	PROPN
ejpam-5511	578	5	,	,	PUNCT
ejpam-5511	578	6	denoted	denote	VERB
ejpam-5511	578	7	by	by	ADP
ejpam-5511	578	8	kerφ	kerφ	PROPN
ejpam-5511	578	9	,	,	PUNCT
ejpam-5511	578	10	is	be	AUX
ejpam-5511	578	11	defined	define	VERB
ejpam-5511	578	12	to	to	PART
ejpam-5511	578	13	be	be	AUX
ejpam-5511	578	14	the	the	DET
ejpam-5511	578	15	set	set	NOUN
ejpam-5511	578	16	kerφ	kerφ	NOUN
ejpam-5511	578	17	=	=	SYM
ejpam-5511	578	18	{	{	PUNCT
ejpam-5511	578	19	x	x	PUNCT
ejpam-5511	578	20	∈	∈	PROPN
ejpam-5511	578	21	t1	t1	NOUN
ejpam-5511	578	22	:	:	PUNCT
ejpam-5511	578	23	φ(x	φ(x	X
ejpam-5511	578	24	)	)	PUNCT
ejpam-5511	578	25	=	=	SYM
ejpam-5511	578	26	1′	1′	NUM
ejpam-5511	578	27	}	}	PUNCT
ejpam-5511	578	28	,	,	PUNCT
ejpam-5511	578	29	where	where	SCONJ
ejpam-5511	578	30	1	1	NUM
ejpam-5511	578	31	and	and	CCONJ
ejpam-5511	578	32	1′	1′	NUM
ejpam-5511	578	33	are	be	AUX
ejpam-5511	578	34	the	the	DET
ejpam-5511	578	35	identities	identity	NOUN
ejpam-5511	578	36	and	and	CCONJ
ejpam-5511	578	37	the	the	DET
ejpam-5511	578	38	greatest	great	ADJ
ejpam-5511	578	39	elements	element	NOUN
ejpam-5511	578	40	of	of	ADP
ejpam-5511	578	41	t1	t1	NOUN
ejpam-5511	578	42	and	and	CCONJ
ejpam-5511	578	43	t2	t2	NOUN
ejpam-5511	578	44	,	,	PUNCT
ejpam-5511	578	45	respectively	respectively	ADV
ejpam-5511	578	46	.	.	PUNCT
ejpam-5511	579	1	remark	remark	PROPN
ejpam-5511	579	2	1	1	NUM
ejpam-5511	579	3	.	.	PUNCT
ejpam-5511	579	4	by	by	ADP
ejpam-5511	579	5	theorem	theorem	NOUN
ejpam-5511	579	6	3	3	NUM
ejpam-5511	579	7	,	,	PUNCT
ejpam-5511	579	8	we	we	PRON
ejpam-5511	579	9	get	get	VERB
ejpam-5511	579	10	that	that	PRON
ejpam-5511	579	11	kerφ	kerφ	PROPN
ejpam-5511	579	12	is	be	AUX
ejpam-5511	579	13	a	a	DET
ejpam-5511	579	14	filter	filter	NOUN
ejpam-5511	579	15	of	of	ADP
ejpam-5511	579	16	t1	t1	PROPN
ejpam-5511	579	17	.	.	PUNCT
ejpam-5511	580	1	lemma	lemma	PROPN
ejpam-5511	580	2	5	5	X
ejpam-5511	580	3	.	.	PUNCT
ejpam-5511	581	1	let	let	AUX
ejpam-5511	581	2	(	(	PUNCT
ejpam-5511	581	3	t	t	NOUN
ejpam-5511	581	4	,	,	PUNCT
ejpam-5511	581	5	[	[	PUNCT
ejpam-5511	581	6	]	]	X
ejpam-5511	581	7	,	,	PUNCT
ejpam-5511	581	8	≤	≤	NUM
ejpam-5511	581	9	,	,	PUNCT
ejpam-5511	581	10	[	[	PUNCT
ejpam-5511	581	11	]	]	X
ejpam-5511	581	12	∗	∗	NOUN
ejpam-5511	581	13	)	)	PUNCT
ejpam-5511	581	14	be	be	VERB
ejpam-5511	581	15	a	a	DET
ejpam-5511	581	16	commutative	commutative	ADJ
ejpam-5511	581	17	implicative	implicative	ADJ
ejpam-5511	581	18	n.p.o	n.p.o	NOUN
ejpam-5511	581	19	.	.	PUNCT
ejpam-5511	582	1	ternary	ternary	ADJ
ejpam-5511	582	2	semigroup	semigroup	NOUN
ejpam-5511	583	1	and	and	CCONJ
ejpam-5511	583	2	let	let	VERB
ejpam-5511	583	3	f	f	PRON
ejpam-5511	583	4	be	be	AUX
ejpam-5511	583	5	a	a	DET
ejpam-5511	583	6	filter	filter	NOUN
ejpam-5511	583	7	of	of	ADP
ejpam-5511	583	8	t	t	PROPN
ejpam-5511	583	9	and	and	CCONJ
ejpam-5511	583	10	ρf	ρf	ADP
ejpam-5511	583	11	a	a	DET
ejpam-5511	583	12	congruence	congruence	NOUN
ejpam-5511	583	13	on	on	ADP
ejpam-5511	583	14	t	t	PROPN
ejpam-5511	583	15	.	.	PUNCT
ejpam-5511	584	1	then	then	ADV
ejpam-5511	584	2	the	the	DET
ejpam-5511	584	3	canonical	canonical	ADJ
ejpam-5511	584	4	homomorphism	homomorphism	PROPN
ejpam-5511	584	5	η	η	PROPN
ejpam-5511	584	6	:	:	PUNCT
ejpam-5511	584	7	t	t	PROPN
ejpam-5511	584	8	−→	−→	NOUN
ejpam-5511	584	9	t	t	PROPN
ejpam-5511	584	10	/	/	SYM
ejpam-5511	584	11	ρf	ρf	PROPN
ejpam-5511	584	12	is	be	AUX
ejpam-5511	584	13	an	an	DET
ejpam-5511	584	14	implicative	implicative	ADJ
ejpam-5511	584	15	homomorphism	homomorphism	NOUN
ejpam-5511	584	16	from	from	ADP
ejpam-5511	584	17	(	(	PUNCT
ejpam-5511	584	18	t	t	PROPN
ejpam-5511	584	19	,	,	PUNCT
ejpam-5511	584	20	[	[	PUNCT
ejpam-5511	584	21	]	]	X
ejpam-5511	584	22	,	,	PUNCT
ejpam-5511	584	23	≤	≤	NUM
ejpam-5511	584	24	,	,	PUNCT
ejpam-5511	584	25	[	[	PUNCT
ejpam-5511	584	26	]	]	X
ejpam-5511	584	27	∗	∗	NOUN
ejpam-5511	584	28	)	)	PUNCT
ejpam-5511	584	29	onto	onto	ADP
ejpam-5511	584	30	(	(	PUNCT
ejpam-5511	584	31	t	t	PROPN
ejpam-5511	584	32	/	/	SYM
ejpam-5511	584	33	ρf	ρf	NOUN
ejpam-5511	584	34	,	,	PUNCT
ejpam-5511	584	35	[	[	X
ejpam-5511	584	36	[	[	X
ejpam-5511	584	37	]	]	X
ejpam-5511	584	38	]	]	X
ejpam-5511	584	39	,	,	PUNCT
ejpam-5511	584	40	⪯	⪯	PROPN
ejpam-5511	584	41	,	,	PUNCT
ejpam-5511	584	42	[	[	X
ejpam-5511	584	43	[	[	X
ejpam-5511	584	44	]	]	X
ejpam-5511	584	45	]	]	X
ejpam-5511	584	46	∗	∗	NOUN
ejpam-5511	584	47	)	)	PUNCT
ejpam-5511	584	48	.	.	PUNCT
ejpam-5511	585	1	proof	proof	NOUN
ejpam-5511	585	2	.	.	PUNCT
ejpam-5511	586	1	if	if	SCONJ
ejpam-5511	586	2	x	x	X
ejpam-5511	586	3	,	,	PUNCT
ejpam-5511	586	4	y	y	PROPN
ejpam-5511	586	5	,	,	PUNCT
ejpam-5511	586	6	z	z	PROPN
ejpam-5511	586	7	∈	∈	PROPN
ejpam-5511	586	8	t	t	PROPN
ejpam-5511	586	9	,	,	PUNCT
ejpam-5511	586	10	then	then	ADV
ejpam-5511	586	11	η([xyz]∗	η([xyz]∗	PROPN
ejpam-5511	586	12	)	)	PUNCT
ejpam-5511	586	13	=	=	PUNCT
ejpam-5511	587	1	[	[	X
ejpam-5511	587	2	[	[	X
ejpam-5511	587	3	xyz]∗]ρf	xyz]∗]ρf	NOUN
ejpam-5511	587	4	=	=	PUNCT
ejpam-5511	588	1	[	[	X
ejpam-5511	588	2	[	[	X
ejpam-5511	588	3	[	[	X
ejpam-5511	588	4	x]ρf	x]ρf	PROPN
ejpam-5511	588	5	[	[	X
ejpam-5511	588	6	y]ρf	y]ρf	PRON
ejpam-5511	588	7	[	[	X
ejpam-5511	588	8	z]ρf	z]ρf	PROPN
ejpam-5511	588	9	]	]	X
ejpam-5511	588	10	]	]	X
ejpam-5511	588	11	]	]	X
ejpam-5511	588	12	∗	∗	NOUN
ejpam-5511	588	13	=	=	PUNCT
ejpam-5511	589	1	[	[	X
ejpam-5511	589	2	[	[	X
ejpam-5511	589	3	η([x]ρf	η([x]ρf	NOUN
ejpam-5511	589	4	)	)	PUNCT
ejpam-5511	589	5	η([y]ρf	η([y]ρf	PUNCT
ejpam-5511	589	6	)	)	PUNCT
ejpam-5511	589	7	η([z]ρf	η([z]ρf	PROPN
ejpam-5511	589	8	)	)	PUNCT
ejpam-5511	589	9	]	]	PUNCT
ejpam-5511	589	10	]	]	X
ejpam-5511	589	11	∗.	∗.	NOUN
ejpam-5511	589	12	hence	hence	ADV
ejpam-5511	589	13	,	,	PUNCT
ejpam-5511	589	14	the	the	DET
ejpam-5511	589	15	assertion	assertion	NOUN
ejpam-5511	589	16	holds	hold	VERB
ejpam-5511	589	17	.	.	PUNCT
ejpam-5511	590	1	theorem	theorem	NOUN
ejpam-5511	590	2	4	4	NUM
ejpam-5511	590	3	.	.	PUNCT
ejpam-5511	591	1	let	let	AUX
ejpam-5511	591	2	(	(	PUNCT
ejpam-5511	591	3	t1	t1	VERB
ejpam-5511	591	4	,	,	PUNCT
ejpam-5511	591	5	[	[	PUNCT
ejpam-5511	591	6	]	]	X
ejpam-5511	591	7	1,≤1	1,≤1	ADJ
ejpam-5511	591	8	,	,	PUNCT
ejpam-5511	591	9	[	[	PUNCT
ejpam-5511	591	10	]	]	X
ejpam-5511	591	11	∗1	∗1	X
ejpam-5511	591	12	)	)	PUNCT
ejpam-5511	591	13	and	and	CCONJ
ejpam-5511	591	14	(	(	PUNCT
ejpam-5511	591	15	t2	t2	NOUN
ejpam-5511	591	16	,	,	PUNCT
ejpam-5511	591	17	[	[	PUNCT
ejpam-5511	591	18	]	]	X
ejpam-5511	591	19	2,≤2	2,≤2	NOUN
ejpam-5511	591	20	,	,	PUNCT
ejpam-5511	591	21	[	[	PUNCT
ejpam-5511	591	22	]	]	X
ejpam-5511	591	23	∗2	∗2	NOUN
ejpam-5511	591	24	)	)	PUNCT
ejpam-5511	591	25	be	be	VERB
ejpam-5511	591	26	any	any	DET
ejpam-5511	591	27	two	two	NUM
ejpam-5511	591	28	commutative	commutative	ADJ
ejpam-5511	591	29	implicative	implicative	ADJ
ejpam-5511	591	30	n.p.o	n.p.o	NOUN
ejpam-5511	591	31	.	.	PUNCT
ejpam-5511	592	1	ternary	ternary	ADJ
ejpam-5511	592	2	semigroups	semigroup	NOUN
ejpam-5511	592	3	,	,	PUNCT
ejpam-5511	592	4	with	with	ADP
ejpam-5511	592	5	1	1	NUM
ejpam-5511	592	6	and	and	CCONJ
ejpam-5511	592	7	1′	1′	NUM
ejpam-5511	592	8	are	be	AUX
ejpam-5511	592	9	the	the	DET
ejpam-5511	592	10	identities	identity	NOUN
ejpam-5511	592	11	and	and	CCONJ
ejpam-5511	592	12	the	the	DET
ejpam-5511	592	13	greatest	great	ADJ
ejpam-5511	592	14	elements	element	NOUN
ejpam-5511	592	15	of	of	ADP
ejpam-5511	592	16	t1	t1	NOUN
ejpam-5511	592	17	and	and	CCONJ
ejpam-5511	592	18	t2	t2	NOUN
ejpam-5511	592	19	,	,	PUNCT
ejpam-5511	592	20	respectively	respectively	ADV
ejpam-5511	592	21	.	.	PUNCT
ejpam-5511	593	1	let	let	VERB
ejpam-5511	593	2	φ	φ	PROPN
ejpam-5511	593	3	:	:	PUNCT
ejpam-5511	593	4	t1	t1	PROPN
ejpam-5511	593	5	−→	−→	ADJ
ejpam-5511	593	6	t2	t2	NOUN
ejpam-5511	593	7	be	be	VERB
ejpam-5511	593	8	an	an	DET
ejpam-5511	593	9	implicative	implicative	ADJ
ejpam-5511	593	10	homomorphism	homomorphism	NOUN
ejpam-5511	593	11	from	from	ADP
ejpam-5511	593	12	t1	t1	NOUN
ejpam-5511	593	13	onto	onto	ADP
ejpam-5511	593	14	t2	t2	NOUN
ejpam-5511	593	15	,	,	PUNCT
ejpam-5511	593	16	with	with	ADP
ejpam-5511	593	17	f	f	PROPN
ejpam-5511	593	18	=	=	SYM
ejpam-5511	593	19	kerφ	kerφ	PROPN
ejpam-5511	593	20	,	,	PUNCT
ejpam-5511	593	21	and	and	CCONJ
ejpam-5511	593	22	let	let	VERB
ejpam-5511	593	23	η	η	PROPN
ejpam-5511	593	24	:	:	PUNCT
ejpam-5511	593	25	t1	t1	PROPN
ejpam-5511	593	26	−→	−→	PROPN
ejpam-5511	593	27	t1	t1	NOUN
ejpam-5511	593	28	/	/	SYM
ejpam-5511	593	29	ρf	ρf	PRON
ejpam-5511	593	30	be	be	AUX
ejpam-5511	593	31	a	a	DET
ejpam-5511	593	32	canonical	canonical	ADJ
ejpam-5511	593	33	homomorphism	homomorphism	NOUN
ejpam-5511	593	34	from	from	ADP
ejpam-5511	593	35	t1	t1	PROPN
ejpam-5511	593	36	onto	onto	ADP
ejpam-5511	593	37	t1	t1	NOUN
ejpam-5511	593	38	/	/	SYM
ejpam-5511	593	39	ρf	ρf	X
ejpam-5511	593	40	.	.	PUNCT
ejpam-5511	594	1	then	then	ADV
ejpam-5511	594	2	there	there	PRON
ejpam-5511	594	3	exists	exist	VERB
ejpam-5511	594	4	an	an	DET
ejpam-5511	594	5	implicative	implicative	ADJ
ejpam-5511	594	6	homomorphism	homomorphism	NOUN
ejpam-5511	594	7	ψ	ψ	X
ejpam-5511	594	8	:	:	PUNCT
ejpam-5511	594	9	t1	t1	VERB
ejpam-5511	594	10	/	/	SYM
ejpam-5511	594	11	ρf	ρf	ADP
ejpam-5511	594	12	−→	−→	ADJ
ejpam-5511	594	13	t2	t2	NOUN
ejpam-5511	594	14	from	from	ADP
ejpam-5511	594	15	t1	t1	NOUN
ejpam-5511	594	16	/	/	SYM
ejpam-5511	594	17	ρf	ρf	X
ejpam-5511	594	18	onto	onto	ADP
ejpam-5511	594	19	t2	t2	NOUN
ejpam-5511	594	20	such	such	ADJ
ejpam-5511	594	21	that	that	SCONJ
ejpam-5511	594	22	the	the	DET
ejpam-5511	594	23	following	follow	VERB
ejpam-5511	594	24	diagram	diagram	NOUN
ejpam-5511	594	25	is	be	AUX
ejpam-5511	594	26	commutative	commutative	ADJ
ejpam-5511	594	27	:	:	PUNCT
ejpam-5511	594	28	(	(	PUNCT
ejpam-5511	594	29	t1	t1	NOUN
ejpam-5511	594	30	,	,	PUNCT
ejpam-5511	594	31	[	[	PUNCT
ejpam-5511	594	32	]	]	X
ejpam-5511	594	33	1,≤1	1,≤1	ADJ
ejpam-5511	594	34	,	,	PUNCT
ejpam-5511	594	35	[	[	PUNCT
ejpam-5511	594	36	]	]	X
ejpam-5511	594	37	∗1	∗1	X
ejpam-5511	594	38	)	)	PUNCT
ejpam-5511	594	39	(	(	PUNCT
ejpam-5511	594	40	t2	t2	NOUN
ejpam-5511	594	41	,	,	PUNCT
ejpam-5511	594	42	[	[	PUNCT
ejpam-5511	594	43	]	]	X
ejpam-5511	594	44	2,≤2	2,≤2	NOUN
ejpam-5511	594	45	,	,	PUNCT
ejpam-5511	594	46	[	[	PUNCT
ejpam-5511	594	47	]	]	X
ejpam-5511	594	48	∗2	∗2	NOUN
ejpam-5511	594	49	)	)	PUNCT
ejpam-5511	594	50	(	(	PUNCT
ejpam-5511	594	51	t1	t1	NOUN
ejpam-5511	594	52	/	/	SYM
ejpam-5511	594	53	ρf	ρf	NOUN
ejpam-5511	594	54	,	,	PUNCT
ejpam-5511	594	55	[	[	X
ejpam-5511	594	56	[	[	X
ejpam-5511	594	57	]	]	X
ejpam-5511	594	58	]	]	X
ejpam-5511	594	59	,	,	PUNCT
ejpam-5511	594	60	⪯	⪯	PROPN
ejpam-5511	594	61	,	,	PUNCT
ejpam-5511	594	62	[	[	X
ejpam-5511	594	63	[	[	X
ejpam-5511	594	64	]	]	X
ejpam-5511	594	65	]	]	X
ejpam-5511	594	66	∗	∗	NOUN
ejpam-5511	594	67	)	)	PUNCT
ejpam-5511	594	68	φ	φ	PROPN
ejpam-5511	594	69	η	η	PROPN
ejpam-5511	594	70	ψ	ψ	PROPN
ejpam-5511	594	71	k.	k.	PROPN
ejpam-5511	594	72	nakwan	nakwan	PROPN
ejpam-5511	594	73	,	,	PUNCT
ejpam-5511	594	74	p.	p.	PROPN
ejpam-5511	594	75	luangchaisri	luangchaisri	VERB
ejpam-5511	594	76	,	,	PUNCT
ejpam-5511	594	77	t.	t.	PROPN
ejpam-5511	594	78	changphas	changphas	PROPN
ejpam-5511	594	79	/	/	SYM
ejpam-5511	594	80	eur	eur	PROPN
ejpam-5511	594	81	.	.	PUNCT
ejpam-5511	595	1	j.	j.	PROPN
ejpam-5511	595	2	pure	pure	PROPN
ejpam-5511	595	3	appl	appl	PROPN
ejpam-5511	595	4	.	.	PROPN
ejpam-5511	595	5	math	math	PROPN
ejpam-5511	595	6	,	,	PUNCT
ejpam-5511	595	7	17	17	NUM
ejpam-5511	595	8	(	(	PUNCT
ejpam-5511	595	9	4	4	NUM
ejpam-5511	595	10	)	)	PUNCT
ejpam-5511	595	11	(	(	PUNCT
ejpam-5511	595	12	2024	2024	NUM
ejpam-5511	595	13	)	)	PUNCT
ejpam-5511	595	14	,	,	PUNCT
ejpam-5511	595	15	4180	4180	NUM
ejpam-5511	595	16	-	-	SYM
ejpam-5511	595	17	4194	4194	NUM
ejpam-5511	595	18	4192	4192	NUM
ejpam-5511	596	1	moreover	moreover	ADV
ejpam-5511	596	2	,	,	PUNCT
ejpam-5511	596	3	if	if	SCONJ
ejpam-5511	596	4	ker	ker	PROPN
ejpam-5511	596	5	η	η	PROPN
ejpam-5511	596	6	=	=	PROPN
ejpam-5511	596	7	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	596	8	)	)	PUNCT
ejpam-5511	596	9	,	,	PUNCT
ejpam-5511	596	10	then	then	ADV
ejpam-5511	596	11	ψ	ψ	X
ejpam-5511	596	12	is	be	AUX
ejpam-5511	596	13	an	an	DET
ejpam-5511	596	14	implicative	implicative	ADJ
ejpam-5511	596	15	isomorphism	isomorphism	NOUN
ejpam-5511	596	16	,	,	PUNCT
ejpam-5511	596	17	that	that	ADV
ejpam-5511	596	18	is	is	ADV
ejpam-5511	596	19	(	(	PUNCT
ejpam-5511	596	20	t1	t1	NOUN
ejpam-5511	596	21	/	/	SYM
ejpam-5511	596	22	ρf	ρf	NOUN
ejpam-5511	596	23	,	,	PUNCT
ejpam-5511	596	24	[	[	X
ejpam-5511	596	25	[	[	X
ejpam-5511	596	26	]	]	X
ejpam-5511	596	27	]	]	X
ejpam-5511	596	28	,	,	PUNCT
ejpam-5511	596	29	⪯	⪯	PROPN
ejpam-5511	596	30	,	,	PUNCT
ejpam-5511	596	31	[	[	X
ejpam-5511	596	32	[	[	X
ejpam-5511	596	33	]	]	X
ejpam-5511	596	34	]	]	X
ejpam-5511	596	35	∗	∗	NOUN
ejpam-5511	596	36	)	)	PUNCT
ejpam-5511	596	37	∼=	∼=	PROPN
ejpam-5511	596	38	(	(	PUNCT
ejpam-5511	596	39	t2	t2	NOUN
ejpam-5511	596	40	,	,	PUNCT
ejpam-5511	596	41	[	[	PUNCT
ejpam-5511	596	42	]	]	X
ejpam-5511	596	43	2,≤2	2,≤2	NOUN
ejpam-5511	596	44	,	,	PUNCT
ejpam-5511	596	45	[	[	PUNCT
ejpam-5511	596	46	]	]	X
ejpam-5511	596	47	∗2	∗2	NOUN
ejpam-5511	596	48	)	)	PUNCT
ejpam-5511	596	49	.	.	PUNCT
ejpam-5511	597	1	proof	proof	NOUN
ejpam-5511	597	2	.	.	PUNCT
ejpam-5511	598	1	define	define	VERB
ejpam-5511	598	2	ψ	ψ	X
ejpam-5511	598	3	:	:	PUNCT
ejpam-5511	598	4	t1	t1	VERB
ejpam-5511	598	5	/	/	SYM
ejpam-5511	598	6	ρf	ρf	ADP
ejpam-5511	598	7	−→	−→	NOUN
ejpam-5511	598	8	t2	t2	NOUN
ejpam-5511	598	9	by	by	ADP
ejpam-5511	598	10	ψ([x]ρf	ψ([x]ρf	NOUN
ejpam-5511	598	11	)	)	PUNCT
ejpam-5511	599	1	=	=	SYM
ejpam-5511	599	2	φ(x	φ(x	NOUN
ejpam-5511	599	3	)	)	PUNCT
ejpam-5511	599	4	for	for	ADP
ejpam-5511	599	5	any	any	DET
ejpam-5511	599	6	x	x	SYM
ejpam-5511	599	7	∈	∈	PROPN
ejpam-5511	599	8	t1	t1	NOUN
ejpam-5511	599	9	.	.	PUNCT
ejpam-5511	600	1	we	we	PRON
ejpam-5511	600	2	have	have	VERB
ejpam-5511	600	3	ψ	ψ	NOUN
ejpam-5511	600	4	is	be	AUX
ejpam-5511	600	5	well	well	ADV
ejpam-5511	600	6	-	-	PUNCT
ejpam-5511	600	7	defined	define	VERB
ejpam-5511	600	8	.	.	PUNCT
ejpam-5511	601	1	indeed	indeed	ADV
ejpam-5511	601	2	,	,	PUNCT
ejpam-5511	601	3	let	let	VERB
ejpam-5511	601	4	[	[	PUNCT
ejpam-5511	601	5	x]ρf	x]ρf	X
ejpam-5511	601	6	,	,	PUNCT
ejpam-5511	601	7	[	[	X
ejpam-5511	601	8	y]ρf	y]ρf	NOUN
ejpam-5511	601	9	∈	∈	PROPN
ejpam-5511	601	10	t1	t1	NOUN
ejpam-5511	601	11	/	/	SYM
ejpam-5511	601	12	ρf	ρf	PRON
ejpam-5511	601	13	be	be	AUX
ejpam-5511	601	14	such	such	ADJ
ejpam-5511	601	15	that	that	SCONJ
ejpam-5511	601	16	[	[	X
ejpam-5511	601	17	x]ρf	x]ρf	X
ejpam-5511	601	18	=	=	PUNCT
ejpam-5511	602	1	[	[	X
ejpam-5511	602	2	y]ρf	y]ρf	NOUN
ejpam-5511	602	3	.	.	PUNCT
ejpam-5511	603	1	since	since	SCONJ
ejpam-5511	603	2	xρf	xρf	PROPN
ejpam-5511	603	3	y	y	PROPN
ejpam-5511	603	4	,	,	PUNCT
ejpam-5511	603	5	there	there	PRON
ejpam-5511	603	6	exist	exist	VERB
ejpam-5511	603	7	c	c	NOUN
ejpam-5511	603	8	,	,	PUNCT
ejpam-5511	603	9	d	d	PROPN
ejpam-5511	603	10	∈	∈	PROPN
ejpam-5511	603	11	f	f	PROPN
ejpam-5511	603	12	such	such	ADJ
ejpam-5511	603	13	that	that	PRON
ejpam-5511	604	1	[	[	X
ejpam-5511	604	2	cdx]1	cdx]1	NOUN
ejpam-5511	604	3	≤1	≤1	PROPN
ejpam-5511	604	4	y	y	PROPN
ejpam-5511	604	5	and	and	CCONJ
ejpam-5511	604	6	[	[	X
ejpam-5511	604	7	cdy]1	cdy]1	X
ejpam-5511	604	8	≤1	≤1	INTJ
ejpam-5511	604	9	x.	x.	NOUN
ejpam-5511	604	10	by	by	ADP
ejpam-5511	604	11	theorem	theorem	NOUN
ejpam-5511	604	12	3	3	NUM
ejpam-5511	604	13	,	,	PUNCT
ejpam-5511	604	14	φ([cdx]1	φ([cdx]1	PROPN
ejpam-5511	604	15	)	)	PUNCT
ejpam-5511	604	16	≤2	≤2	NOUN
ejpam-5511	604	17	φ(y	φ(y	NOUN
ejpam-5511	604	18	)	)	PUNCT
ejpam-5511	604	19	and	and	CCONJ
ejpam-5511	604	20	φ([cdy]1	φ([cdy]1	NUM
ejpam-5511	604	21	)	)	PUNCT
ejpam-5511	604	22	≤2	≤2	VERB
ejpam-5511	604	23	φ(x	φ(x	NOUN
ejpam-5511	604	24	)	)	PUNCT
ejpam-5511	604	25	.	.	PUNCT
ejpam-5511	605	1	since	since	SCONJ
ejpam-5511	605	2	c	c	PROPN
ejpam-5511	605	3	,	,	PUNCT
ejpam-5511	605	4	d	d	PROPN
ejpam-5511	605	5	∈	∈	PROPN
ejpam-5511	605	6	f	f	X
ejpam-5511	605	7	,	,	PUNCT
ejpam-5511	605	8	we	we	PRON
ejpam-5511	605	9	have	have	VERB
ejpam-5511	605	10	φ(c	φ(c	NOUN
ejpam-5511	605	11	)	)	PUNCT
ejpam-5511	605	12	=	=	SYM
ejpam-5511	605	13	1′	1′	NUM
ejpam-5511	605	14	and	and	CCONJ
ejpam-5511	605	15	φ(d	φ(d	NUM
ejpam-5511	605	16	)	)	PUNCT
ejpam-5511	606	1	=	=	SYM
ejpam-5511	606	2	1′.	1′.	NOUN
ejpam-5511	606	3	from	from	ADP
ejpam-5511	606	4	φ([cdx]1	φ([cdx]1	PROPN
ejpam-5511	606	5	)	)	PUNCT
ejpam-5511	606	6	=	=	PUNCT
ejpam-5511	607	1	[	[	X
ejpam-5511	607	2	φ(c)φ(d)φ(x)]2	φ(c)φ(d)φ(x)]2	X
ejpam-5511	607	3	=	=	PUNCT
ejpam-5511	607	4	[	[	X
ejpam-5511	607	5	1′1′φ(x)]2	1′1′φ(x)]2	NUM
ejpam-5511	607	6	=	=	SYM
ejpam-5511	607	7	φ(x	φ(x	PROPN
ejpam-5511	607	8	)	)	PUNCT
ejpam-5511	607	9	and	and	CCONJ
ejpam-5511	607	10	φ([cdy]1	φ([cdy]1	NUM
ejpam-5511	607	11	)	)	PUNCT
ejpam-5511	607	12	=	=	PUNCT
ejpam-5511	608	1	[	[	X
ejpam-5511	608	2	φ(c)φ(d)φ(y)]2	φ(c)φ(d)φ(y)]2	X
ejpam-5511	608	3	=	=	PUNCT
ejpam-5511	608	4	[	[	X
ejpam-5511	608	5	1′1′φ(y)]2	1′1′φ(y)]2	NUM
ejpam-5511	608	6	=	=	SYM
ejpam-5511	608	7	φ(y	φ(y	PROPN
ejpam-5511	608	8	)	)	PUNCT
ejpam-5511	608	9	it	it	PRON
ejpam-5511	608	10	follows	follow	VERB
ejpam-5511	608	11	that	that	SCONJ
ejpam-5511	608	12	φ(x	φ(x	NOUN
ejpam-5511	608	13	)	)	PUNCT
ejpam-5511	608	14	≤2	≤2	NOUN
ejpam-5511	608	15	φ(y	φ(y	NOUN
ejpam-5511	608	16	)	)	PUNCT
ejpam-5511	608	17	and	and	CCONJ
ejpam-5511	608	18	φ(y	φ(y	NOUN
ejpam-5511	608	19	)	)	PUNCT
ejpam-5511	608	20	≤2	≤2	NOUN
ejpam-5511	608	21	φ(x	φ(x	NOUN
ejpam-5511	608	22	)	)	PUNCT
ejpam-5511	608	23	.	.	PUNCT
ejpam-5511	609	1	hence	hence	ADV
ejpam-5511	609	2	,	,	PUNCT
ejpam-5511	609	3	φ(x	φ(x	PROPN
ejpam-5511	609	4	)	)	PUNCT
ejpam-5511	609	5	=	=	SYM
ejpam-5511	609	6	φ(y	φ(y	NOUN
ejpam-5511	609	7	)	)	PUNCT
ejpam-5511	609	8	.	.	PUNCT
ejpam-5511	610	1	next	next	ADV
ejpam-5511	610	2	,	,	PUNCT
ejpam-5511	610	3	we	we	PRON
ejpam-5511	610	4	have	have	AUX
ejpam-5511	610	5	ψ	ψ	NOUN
ejpam-5511	610	6	is	be	AUX
ejpam-5511	610	7	an	an	DET
ejpam-5511	610	8	implicative	implicative	ADJ
ejpam-5511	610	9	homomorphism	homomorphism	NOUN
ejpam-5511	610	10	.	.	PUNCT
ejpam-5511	611	1	in	in	ADP
ejpam-5511	611	2	fact	fact	NOUN
ejpam-5511	611	3	,	,	PUNCT
ejpam-5511	611	4	for	for	ADP
ejpam-5511	611	5	[	[	PUNCT
ejpam-5511	611	6	x]ρf	x]ρf	PROPN
ejpam-5511	611	7	,	,	PUNCT
ejpam-5511	611	8	[	[	X
ejpam-5511	611	9	y]ρf	y]ρf	X
ejpam-5511	611	10	,	,	PUNCT
ejpam-5511	611	11	[	[	X
ejpam-5511	611	12	z]ρf	z]ρf	PROPN
ejpam-5511	611	13	∈	∈	ADJ
ejpam-5511	611	14	t1	t1	NOUN
ejpam-5511	611	15	/	/	SYM
ejpam-5511	611	16	ρf	ρf	NOUN
ejpam-5511	611	17	,	,	PUNCT
ejpam-5511	611	18	we	we	PRON
ejpam-5511	611	19	have	have	VERB
ejpam-5511	611	20	ψ([[[x]ρf	ψ([[[x]ρf	NOUN
ejpam-5511	611	21	[	[	PUNCT
ejpam-5511	611	22	y]ρf	y]ρf	PRON
ejpam-5511	611	23	[	[	X
ejpam-5511	611	24	z]ρf	z]ρf	PROPN
ejpam-5511	611	25	]	]	PUNCT
ejpam-5511	611	26	]	]	X
ejpam-5511	611	27	∗	∗	NOUN
ejpam-5511	611	28	)	)	PUNCT
ejpam-5511	611	29	=	=	SYM
ejpam-5511	611	30	ψ([[xyz]∗1]ρf	ψ([[xyz]∗1]ρf	X
ejpam-5511	611	31	)	)	PUNCT
ejpam-5511	611	32	=	=	SYM
ejpam-5511	611	33	φ([xyz]∗1	φ([xyz]∗1	X
ejpam-5511	611	34	)	)	PUNCT
ejpam-5511	611	35	=	=	PUNCT
ejpam-5511	612	1	[	[	X
ejpam-5511	612	2	φ(x)φ(y)φ(z)]∗2	φ(x)φ(y)φ(z)]∗2	X
ejpam-5511	612	3	=	=	PUNCT
ejpam-5511	612	4	[	[	X
ejpam-5511	612	5	ψ([x]ρf	ψ([x]ρf	NOUN
ejpam-5511	612	6	)	)	PUNCT
ejpam-5511	612	7	ψ([y]ρf	ψ([y]ρf	NUM
ejpam-5511	612	8	)	)	PUNCT
ejpam-5511	612	9	ψ([z]ρf	ψ([z]ρf	PUNCT
ejpam-5511	612	10	)	)	PUNCT
ejpam-5511	612	11	]	]	SYM
ejpam-5511	612	12	∗2	∗2	NOUN
ejpam-5511	612	13	.	.	PUNCT
ejpam-5511	613	1	if	if	SCONJ
ejpam-5511	613	2	t	t	PROPN
ejpam-5511	613	3	∈	∈	PROPN
ejpam-5511	613	4	t2	t2	NOUN
ejpam-5511	613	5	,	,	PUNCT
ejpam-5511	613	6	since	since	SCONJ
ejpam-5511	613	7	φ	φ	PROPN
ejpam-5511	613	8	is	be	AUX
ejpam-5511	613	9	onto	onto	ADP
ejpam-5511	613	10	,	,	PUNCT
ejpam-5511	613	11	then	then	ADV
ejpam-5511	613	12	φ(s	φ(s	NOUN
ejpam-5511	613	13	)	)	PUNCT
ejpam-5511	614	1	=	=	SYM
ejpam-5511	614	2	t	t	NOUN
ejpam-5511	614	3	for	for	ADP
ejpam-5511	614	4	some	some	DET
ejpam-5511	614	5	s	s	PART
ejpam-5511	614	6	∈	∈	PROPN
ejpam-5511	614	7	t1	t1	NOUN
ejpam-5511	614	8	.	.	PUNCT
ejpam-5511	615	1	consequently	consequently	ADV
ejpam-5511	615	2	,	,	PUNCT
ejpam-5511	615	3	ψ(η(s	ψ(η(s	NOUN
ejpam-5511	615	4	)	)	PUNCT
ejpam-5511	615	5	)	)	PUNCT
ejpam-5511	616	1	=	=	PUNCT
ejpam-5511	616	2	ψ([s]ρf	ψ([s]ρf	PUNCT
ejpam-5511	616	3	)	)	PUNCT
ejpam-5511	616	4	=	=	SYM
ejpam-5511	616	5	φ(s	φ(s	NOUN
ejpam-5511	616	6	)	)	PUNCT
ejpam-5511	616	7	=	=	SYM
ejpam-5511	617	1	t.	t.	NOUN
ejpam-5511	617	2	for	for	ADP
ejpam-5511	617	3	any	any	DET
ejpam-5511	617	4	s	s	PROPN
ejpam-5511	617	5	∈	∈	PROPN
ejpam-5511	617	6	t1	t1	NOUN
ejpam-5511	617	7	,	,	PUNCT
ejpam-5511	617	8	we	we	PRON
ejpam-5511	617	9	have	have	VERB
ejpam-5511	617	10	ψ	ψ	PART
ejpam-5511	617	11	◦	◦	VERB
ejpam-5511	617	12	η(s	η(	NOUN
ejpam-5511	617	13	)	)	PUNCT
ejpam-5511	617	14	=	=	PUNCT
ejpam-5511	617	15	ψ(η(s	ψ(η(s	NOUN
ejpam-5511	617	16	)	)	PUNCT
ejpam-5511	617	17	)	)	PUNCT
ejpam-5511	618	1	=	=	PUNCT
ejpam-5511	618	2	ψ([s]ρf	ψ([s]ρf	PUNCT
ejpam-5511	618	3	)	)	PUNCT
ejpam-5511	618	4	=	=	SYM
ejpam-5511	618	5	φ(s	φ(s	NOUN
ejpam-5511	618	6	)	)	PUNCT
ejpam-5511	618	7	.	.	PUNCT
ejpam-5511	619	1	this	this	PRON
ejpam-5511	619	2	shows	show	VERB
ejpam-5511	619	3	that	that	SCONJ
ejpam-5511	619	4	the	the	DET
ejpam-5511	619	5	diagram	diagram	NOUN
ejpam-5511	619	6	is	be	AUX
ejpam-5511	619	7	commutative	commutative	ADJ
ejpam-5511	619	8	.	.	PUNCT
ejpam-5511	620	1	finally	finally	ADV
ejpam-5511	620	2	,	,	PUNCT
ejpam-5511	620	3	we	we	PRON
ejpam-5511	620	4	assume	assume	VERB
ejpam-5511	620	5	that	that	SCONJ
ejpam-5511	620	6	ker	ker	PROPN
ejpam-5511	620	7	η	η	PROPN
ejpam-5511	620	8	=	=	PROPN
ejpam-5511	620	9	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	620	10	)	)	PUNCT
ejpam-5511	620	11	.	.	PUNCT
ejpam-5511	621	1	to	to	PART
ejpam-5511	621	2	show	show	VERB
ejpam-5511	621	3	that	that	SCONJ
ejpam-5511	621	4	ψ	ψ	NOUN
ejpam-5511	621	5	is	be	AUX
ejpam-5511	621	6	an	an	DET
ejpam-5511	621	7	implicative	implicative	ADJ
ejpam-5511	621	8	isomorphism	isomorphism	NOUN
ejpam-5511	621	9	,	,	PUNCT
ejpam-5511	621	10	we	we	PRON
ejpam-5511	621	11	can	can	AUX
ejpam-5511	621	12	only	only	ADV
ejpam-5511	621	13	show	show	VERB
ejpam-5511	621	14	ψ	ψ	NOUN
ejpam-5511	621	15	is	be	AUX
ejpam-5511	621	16	one	one	NUM
ejpam-5511	621	17	-	-	PUNCT
ejpam-5511	621	18	to	to	ADP
ejpam-5511	621	19	-	-	PUNCT
ejpam-5511	621	20	one	one	NUM
ejpam-5511	621	21	.	.	PUNCT
ejpam-5511	622	1	let	let	VERB
ejpam-5511	622	2	[	[	PUNCT
ejpam-5511	622	3	x]ρf	x]ρf	PROPN
ejpam-5511	622	4	,	,	PUNCT
ejpam-5511	622	5	[	[	X
ejpam-5511	622	6	y]ρf	y]ρf	NOUN
ejpam-5511	622	7	∈	∈	PROPN
ejpam-5511	622	8	t1	t1	NOUN
ejpam-5511	622	9	/	/	SYM
ejpam-5511	622	10	ρf	ρf	PRON
ejpam-5511	622	11	be	be	AUX
ejpam-5511	622	12	such	such	ADJ
ejpam-5511	622	13	that	that	SCONJ
ejpam-5511	622	14	ψ([x]ρf	ψ([x]ρf	PUNCT
ejpam-5511	622	15	)	)	PUNCT
ejpam-5511	622	16	=	=	SYM
ejpam-5511	622	17	ψ([y]ρf	ψ([y]ρf	PROPN
ejpam-5511	622	18	)	)	PUNCT
ejpam-5511	622	19	;	;	PUNCT
ejpam-5511	622	20	then	then	ADV
ejpam-5511	622	21	φ(x	φ(x	PROPN
ejpam-5511	622	22	)	)	PUNCT
ejpam-5511	622	23	=	=	SYM
ejpam-5511	622	24	φ(y	φ(y	NOUN
ejpam-5511	622	25	)	)	PUNCT
ejpam-5511	622	26	.	.	PUNCT
ejpam-5511	623	1	by	by	ADP
ejpam-5511	623	2	theorem	theorem	NOUN
ejpam-5511	623	3	2	2	NUM
ejpam-5511	623	4	(	(	PUNCT
ejpam-5511	623	5	6	6	NUM
ejpam-5511	623	6	)	)	PUNCT
ejpam-5511	623	7	,	,	PUNCT
ejpam-5511	623	8	we	we	PRON
ejpam-5511	623	9	have	have	VERB
ejpam-5511	623	10	φ([1xy]∗1	φ([1xy]∗1	ADV
ejpam-5511	623	11	)	)	PUNCT
ejpam-5511	623	12	=	=	PUNCT
ejpam-5511	624	1	[	[	X
ejpam-5511	624	2	φ(1)φ(x)φ(y)]∗2	φ(1)φ(x)φ(y)]∗2	X
ejpam-5511	624	3	=	=	PUNCT
ejpam-5511	624	4	[	[	X
ejpam-5511	624	5	1′φ(x)φ(x)]∗2	1′φ(x)φ(x)]∗2	NUM
ejpam-5511	624	6	=	=	SYM
ejpam-5511	624	7	1′.	1′.	NOUN
ejpam-5511	624	8	hence	hence	ADV
ejpam-5511	624	9	,	,	PUNCT
ejpam-5511	624	10	[	[	X
ejpam-5511	624	11	1xy]∗1	1xy]∗1	NUM
ejpam-5511	624	12	∈	∈	PROPN
ejpam-5511	624	13	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	624	14	)	)	PUNCT
ejpam-5511	624	15	=	=	SYM
ejpam-5511	624	16	ker	ker	PROPN
ejpam-5511	624	17	η	η	PROPN
ejpam-5511	624	18	.	.	PROPN
ejpam-5511	624	19	similarly	similarly	ADV
ejpam-5511	624	20	,	,	PUNCT
ejpam-5511	624	21	[	[	X
ejpam-5511	624	22	1yx]∗1	1yx]∗1	NUM
ejpam-5511	624	23	∈	∈	PROPN
ejpam-5511	624	24	φ−1(1′	φ−1(1′	PROPN
ejpam-5511	624	25	)	)	PUNCT
ejpam-5511	624	26	=	=	SYM
ejpam-5511	624	27	ker	ker	PROPN
ejpam-5511	624	28	η	η	PROPN
ejpam-5511	624	29	.	.	PROPN
ejpam-5511	624	30	since	since	SCONJ
ejpam-5511	624	31	ker	ker	PROPN
ejpam-5511	624	32	η	η	PROPN
ejpam-5511	624	33	⊆	⊆	PROPN
ejpam-5511	624	34	kerφ	kerφ	PROPN
ejpam-5511	624	35	,	,	PUNCT
ejpam-5511	625	1	[	[	X
ejpam-5511	625	2	1xy]∗1	1xy]∗1	X
ejpam-5511	625	3	,	,	PUNCT
ejpam-5511	625	4	[	[	X
ejpam-5511	625	5	1yx]∗1	1yx]∗1	X
ejpam-5511	625	6	∈	∈	PROPN
ejpam-5511	625	7	kerφ	kerφ	PROPN
ejpam-5511	625	8	=	=	PUNCT
ejpam-5511	625	9	f	f	PROPN
ejpam-5511	625	10	.	.	PUNCT
ejpam-5511	626	1	let	let	VERB
ejpam-5511	626	2	us	we	PRON
ejpam-5511	626	3	denote	denote	VERB
ejpam-5511	626	4	[	[	X
ejpam-5511	626	5	1xy]∗1	1xy]∗1	ADV
ejpam-5511	626	6	by	by	ADP
ejpam-5511	626	7	c	c	PROPN
ejpam-5511	626	8	and	and	CCONJ
ejpam-5511	626	9	[	[	X
ejpam-5511	626	10	1yx]∗1	1yx]∗1	NUM
ejpam-5511	626	11	by	by	ADP
ejpam-5511	626	12	d.	d.	PROPN
ejpam-5511	626	13	since	since	SCONJ
ejpam-5511	626	14	c	c	PROPN
ejpam-5511	626	15	≤	≤	X
ejpam-5511	627	1	[	[	X
ejpam-5511	627	2	1xy]∗1	1xy]∗1	NUM
ejpam-5511	627	3	,	,	PUNCT
ejpam-5511	627	4	[	[	X
ejpam-5511	627	5	c1x]1	c1x]1	PUNCT
ejpam-5511	627	6	≤1	≤1	PROPN
ejpam-5511	627	7	y.	y.	PROPN
ejpam-5511	627	8	similarly	similarly	ADV
ejpam-5511	627	9	,	,	PUNCT
ejpam-5511	627	10	by	by	ADP
ejpam-5511	627	11	d	d	PROPN
ejpam-5511	627	12	≤	≤	X
ejpam-5511	627	13	[	[	X
ejpam-5511	627	14	1yx]∗1	1yx]∗1	NUM
ejpam-5511	627	15	,	,	PUNCT
ejpam-5511	627	16	we	we	PRON
ejpam-5511	627	17	have	have	VERB
ejpam-5511	627	18	[	[	X
ejpam-5511	627	19	d1y]1	d1y]1	PUNCT
ejpam-5511	627	20	≤1	≤1	PROPN
ejpam-5511	627	21	x.	x.	NOUN
ejpam-5511	627	22	hence	hence	ADV
ejpam-5511	627	23	,	,	PUNCT
ejpam-5511	627	24	[	[	X
ejpam-5511	627	25	[	[	X
ejpam-5511	627	26	c1d]11x]1	c1d]11x]1	X
ejpam-5511	627	27	=	=	PUNCT
ejpam-5511	628	1	[	[	X
ejpam-5511	628	2	c1[d1x]1]1	c1[d1x]1]1	NOUN
ejpam-5511	628	3	=	=	PUNCT
ejpam-5511	629	1	[	[	X
ejpam-5511	629	2	c1[xd1]1]1	c1[xd1]1]1	X
ejpam-5511	629	3	=	=	PUNCT
ejpam-5511	630	1	[	[	X
ejpam-5511	630	2	[	[	X
ejpam-5511	630	3	c1x]1d1]1	c1x]1d1]1	NOUN
ejpam-5511	630	4	≤1	≤1	PROPN
ejpam-5511	631	1	[	[	X
ejpam-5511	631	2	yd1]1	yd1]1	PROPN
ejpam-5511	631	3	≤1	≤1	PROPN
ejpam-5511	631	4	y	y	PROPN
ejpam-5511	631	5	and	and	CCONJ
ejpam-5511	631	6	[	[	X
ejpam-5511	631	7	[	[	X
ejpam-5511	631	8	c1d]11y]1	c1d]11y]1	X
ejpam-5511	631	9	=	=	PUNCT
ejpam-5511	632	1	[	[	X
ejpam-5511	632	2	c1[d1y]1]1	c1[d1y]1]1	VERB
ejpam-5511	632	3	≤1	≤1	PROPN
ejpam-5511	633	1	[	[	X
ejpam-5511	633	2	c1x]1	c1x]1	PUNCT
ejpam-5511	633	3	≤1	≤1	NOUN
ejpam-5511	633	4	x.	x.	NOUN
ejpam-5511	634	1	so	so	ADV
ejpam-5511	634	2	xρf	xρf	PROPN
ejpam-5511	634	3	y	y	PROPN
ejpam-5511	634	4	,	,	PUNCT
ejpam-5511	634	5	and	and	CCONJ
ejpam-5511	634	6	[	[	X
ejpam-5511	634	7	x]ρf	x]ρf	PROPN
ejpam-5511	634	8	=	=	PUNCT
ejpam-5511	635	1	[	[	X
ejpam-5511	635	2	y]ρf	y]ρf	NOUN
ejpam-5511	635	3	.	.	PUNCT
ejpam-5511	636	1	therefore	therefore	ADV
ejpam-5511	636	2	,	,	PUNCT
ejpam-5511	636	3	ψ	ψ	X
ejpam-5511	636	4	is	be	AUX
ejpam-5511	636	5	one	one	NUM
ejpam-5511	636	6	-	-	PUNCT
ejpam-5511	636	7	to	to	ADP
ejpam-5511	636	8	-	-	PUNCT
ejpam-5511	636	9	one	one	NUM
ejpam-5511	636	10	.	.	PUNCT
ejpam-5511	637	1	references	reference	NOUN
ejpam-5511	637	2	4193	4193	NUM
ejpam-5511	637	3	5	5	NUM
ejpam-5511	637	4	.	.	PUNCT
ejpam-5511	637	5	conclusions	conclusion	NOUN
ejpam-5511	637	6	in	in	ADP
ejpam-5511	637	7	this	this	DET
ejpam-5511	637	8	paper	paper	NOUN
ejpam-5511	637	9	,	,	PUNCT
ejpam-5511	637	10	we	we	PRON
ejpam-5511	637	11	introduce	introduce	VERB
ejpam-5511	637	12	the	the	DET
ejpam-5511	637	13	definition	definition	NOUN
ejpam-5511	637	14	of	of	ADP
ejpam-5511	637	15	n.p.o	n.p.o	NOUN
ejpam-5511	637	16	.	.	PUNCT
ejpam-5511	638	1	ternary	ternary	ADJ
ejpam-5511	638	2	semigroups	semigroup	NOUN
ejpam-5511	638	3	and	and	CCONJ
ejpam-5511	638	4	implicative	implicative	ADJ
ejpam-5511	638	5	n.p.o	n.p.o	NOUN
ejpam-5511	638	6	.	.	PUNCT
ejpam-5511	639	1	ternary	ternary	ADJ
ejpam-5511	639	2	semigroups	semigroup	NOUN
ejpam-5511	639	3	in	in	ADP
ejpam-5511	639	4	definition	definition	NOUN
ejpam-5511	639	5	1	1	NUM
ejpam-5511	639	6	and	and	CCONJ
ejpam-5511	639	7	definition	definition	NOUN
ejpam-5511	639	8	2	2	NUM
ejpam-5511	639	9	,	,	PUNCT
ejpam-5511	639	10	respectively	respectively	ADV
ejpam-5511	639	11	.	.	PUNCT
ejpam-5511	640	1	we	we	PRON
ejpam-5511	640	2	observe	observe	VERB
ejpam-5511	640	3	that	that	SCONJ
ejpam-5511	640	4	an	an	DET
ejpam-5511	640	5	n.p.o	n.p.o	NOUN
ejpam-5511	640	6	.	.	PUNCT
ejpam-5511	641	1	ternary	ternary	ADJ
ejpam-5511	641	2	semigroup	semigroup	NOUN
ejpam-5511	641	3	with	with	ADP
ejpam-5511	641	4	identity	identity	NOUN
ejpam-5511	641	5	need	need	VERB
ejpam-5511	641	6	not	not	PART
ejpam-5511	641	7	to	to	PART
ejpam-5511	641	8	be	be	AUX
ejpam-5511	641	9	implicative	implicative	ADJ
ejpam-5511	641	10	and	and	CCONJ
ejpam-5511	641	11	the	the	DET
ejpam-5511	641	12	greatest	great	ADJ
ejpam-5511	641	13	element	element	NOUN
ejpam-5511	641	14	of	of	ADP
ejpam-5511	641	15	an	an	DET
ejpam-5511	641	16	implicative	implicative	ADJ
ejpam-5511	641	17	n.p.o	n.p.o	NOUN
ejpam-5511	641	18	.	.	PUNCT
ejpam-5511	642	1	ternary	ternary	ADJ
ejpam-5511	642	2	semigroup	semigroup	PROPN
ejpam-5511	642	3	need	need	AUX
ejpam-5511	642	4	not	not	PART
ejpam-5511	642	5	to	to	PART
ejpam-5511	642	6	be	be	AUX
ejpam-5511	642	7	identity	identity	NOUN
ejpam-5511	642	8	.	.	PUNCT
ejpam-5511	643	1	throughout	throughout	ADP
ejpam-5511	643	2	this	this	DET
ejpam-5511	643	3	paper	paper	NOUN
ejpam-5511	643	4	,	,	PUNCT
ejpam-5511	643	5	we	we	PRON
ejpam-5511	643	6	assume	assume	VERB
ejpam-5511	643	7	that	that	SCONJ
ejpam-5511	643	8	implicative	implicative	ADJ
ejpam-5511	643	9	n.p.o	n.p.o	NOUN
ejpam-5511	643	10	.	.	PUNCT
ejpam-5511	644	1	ternary	ternary	ADJ
ejpam-5511	644	2	semigroups	semigroup	NOUN
ejpam-5511	644	3	consists	consist	VERB
ejpam-5511	644	4	an	an	DET
ejpam-5511	644	5	element	element	NOUN
ejpam-5511	644	6	1	1	NUM
ejpam-5511	644	7	which	which	PRON
ejpam-5511	644	8	is	be	AUX
ejpam-5511	644	9	both	both	CCONJ
ejpam-5511	644	10	the	the	DET
ejpam-5511	644	11	greatest	great	ADJ
ejpam-5511	644	12	element	element	NOUN
ejpam-5511	644	13	and	and	CCONJ
ejpam-5511	644	14	the	the	DET
ejpam-5511	644	15	multiplicative	multiplicative	ADJ
ejpam-5511	644	16	identity	identity	NOUN
ejpam-5511	644	17	.	.	PUNCT
ejpam-5511	645	1	then	then	ADV
ejpam-5511	645	2	we	we	PRON
ejpam-5511	645	3	define	define	VERB
ejpam-5511	645	4	an	an	DET
ejpam-5511	645	5	implicative	implicative	ADJ
ejpam-5511	645	6	homomorphism	homomorphism	NOUN
ejpam-5511	645	7	between	between	ADP
ejpam-5511	645	8	two	two	NUM
ejpam-5511	645	9	implicative	implicative	ADJ
ejpam-5511	645	10	n.p.o	n.p.o	NOUN
ejpam-5511	645	11	.	.	PUNCT
ejpam-5511	646	1	ternary	ternary	ADJ
ejpam-5511	646	2	semigroups	semigroup	NOUN
ejpam-5511	646	3	in	in	ADP
ejpam-5511	646	4	definition	definition	NOUN
ejpam-5511	646	5	3	3	NUM
ejpam-5511	646	6	.	.	PUNCT
ejpam-5511	647	1	the	the	DET
ejpam-5511	647	2	algebraic	algebraic	ADJ
ejpam-5511	647	3	properties	property	NOUN
ejpam-5511	647	4	of	of	ADP
ejpam-5511	647	5	such	such	ADJ
ejpam-5511	647	6	homomorphism	homomorphism	NOUN
ejpam-5511	647	7	are	be	AUX
ejpam-5511	647	8	presented	present	VERB
ejpam-5511	647	9	in	in	ADP
ejpam-5511	647	10	theorem	theorem	NOUN
ejpam-5511	647	11	3	3	NUM
ejpam-5511	647	12	.	.	PUNCT
ejpam-5511	648	1	in	in	ADP
ejpam-5511	648	2	the	the	DET
ejpam-5511	648	3	last	last	ADJ
ejpam-5511	648	4	section	section	NOUN
ejpam-5511	648	5	,	,	PUNCT
ejpam-5511	648	6	we	we	PRON
ejpam-5511	648	7	consider	consider	VERB
ejpam-5511	648	8	commutative	commutative	ADJ
ejpam-5511	648	9	implicative	implicative	ADJ
ejpam-5511	648	10	n.p.o	n.p.o	NOUN
ejpam-5511	648	11	.	.	PUNCT
ejpam-5511	649	1	ternary	ternary	ADJ
ejpam-5511	649	2	semigroups	semigroup	NOUN
ejpam-5511	649	3	.	.	PUNCT
ejpam-5511	650	1	under	under	ADP
ejpam-5511	650	2	certain	certain	ADJ
ejpam-5511	650	3	conditions	condition	NOUN
ejpam-5511	650	4	,	,	PUNCT
ejpam-5511	650	5	the	the	DET
ejpam-5511	650	6	diagram	diagram	NOUN
ejpam-5511	650	7	of	of	ADP
ejpam-5511	650	8	homomorphism	homomorphism	PROPN
ejpam-5511	650	9	is	be	AUX
ejpam-5511	650	10	presented	present	VERB
ejpam-5511	650	11	in	in	ADP
ejpam-5511	650	12	theorem	theorem	ADJ
ejpam-5511	650	13	4	4	NUM
ejpam-5511	650	14	.	.	PUNCT
ejpam-5511	650	15	acknowledgements	acknowledgement	VERB
ejpam-5511	650	16	the	the	DET
ejpam-5511	650	17	research	research	NOUN
ejpam-5511	650	18	on	on	ADP
ejpam-5511	650	19	”	"	PUNCT
ejpam-5511	650	20	implicative	implicative	ADJ
ejpam-5511	650	21	negatively	negatively	ADV
ejpam-5511	650	22	partially	partially	ADV
ejpam-5511	650	23	ordered	order	VERB
ejpam-5511	650	24	ternary	ternary	ADJ
ejpam-5511	650	25	semigroups	semigroup	NOUN
ejpam-5511	650	26	”	"	PUNCT
ejpam-5511	650	27	by	by	ADP
ejpam-5511	650	28	khon	khon	PROPN
ejpam-5511	650	29	kaen	kaen	PROPN
ejpam-5511	650	30	university	university	PROPN
ejpam-5511	650	31	has	have	AUX
ejpam-5511	650	32	received	receive	VERB
ejpam-5511	650	33	funding	funding	NOUN
ejpam-5511	650	34	support	support	NOUN
ejpam-5511	650	35	from	from	ADP
ejpam-5511	650	36	the	the	DET
ejpam-5511	650	37	national	national	ADJ
ejpam-5511	650	38	science	science	NOUN
ejpam-5511	650	39	,	,	PUNCT
ejpam-5511	650	40	research	research	NOUN
ejpam-5511	650	41	and	and	CCONJ
ejpam-5511	650	42	innovation	innovation	NOUN
ejpam-5511	650	43	fund	fund	NOUN
ejpam-5511	650	44	(	(	PUNCT
ejpam-5511	650	45	nsrf	nsrf	NOUN
ejpam-5511	650	46	)	)	PUNCT
ejpam-5511	650	47	.	.	PUNCT
ejpam-5511	651	1	we	we	PRON
ejpam-5511	651	2	express	express	VERB
ejpam-5511	651	3	our	our	PRON
ejpam-5511	651	4	warmest	warm	ADJ
ejpam-5511	651	5	thanks	thank	NOUN
ejpam-5511	651	6	to	to	ADP
ejpam-5511	651	7	referees	referee	NOUN
ejpam-5511	651	8	of	of	ADP
ejpam-5511	651	9	the	the	DET
ejpam-5511	651	10	paper	paper	NOUN
ejpam-5511	651	11	for	for	ADP
ejpam-5511	651	12	their	their	PRON
ejpam-5511	651	13	time	time	NOUN
ejpam-5511	651	14	to	to	PART
ejpam-5511	651	15	read	read	VERB
ejpam-5511	651	16	the	the	DET
ejpam-5511	651	17	manuscript	manuscript	NOUN
ejpam-5511	651	18	carefully	carefully	ADV
ejpam-5511	651	19	and	and	CCONJ
ejpam-5511	651	20	their	their	PRON
ejpam-5511	651	21	useful	useful	ADJ
ejpam-5511	651	22	comments	comment	NOUN
ejpam-5511	651	23	.	.	PUNCT
ejpam-5511	652	1	references	reference	NOUN
ejpam-5511	652	2	[	[	X
ejpam-5511	652	3	1	1	X
ejpam-5511	652	4	]	]	PUNCT
ejpam-5511	652	5	t.	t.	PROPN
ejpam-5511	652	6	s.	s.	PROPN
ejpam-5511	652	7	blyth	blyth	PROPN
ejpam-5511	652	8	.	.	PUNCT
ejpam-5511	653	1	pseudo	pseudo	NOUN
ejpam-5511	653	2	-	-	NOUN
ejpam-5511	653	3	residuals	residual	NOUN
ejpam-5511	653	4	in	in	ADP
ejpam-5511	653	5	semigroups	semigroup	NOUN
ejpam-5511	653	6	.	.	PUNCT
ejpam-5511	654	1	journal	journal	NOUN
ejpam-5511	654	2	of	of	ADP
ejpam-5511	654	3	the	the	DET
ejpam-5511	654	4	london	london	PROPN
ejpam-5511	654	5	mathematical	mathematical	ADJ
ejpam-5511	654	6	society	society	NOUN
ejpam-5511	654	7	,	,	PUNCT
ejpam-5511	654	8	1(1):441–454	1(1):441–454	NUM
ejpam-5511	654	9	,	,	PUNCT
ejpam-5511	654	10	1965	1965	NUM
ejpam-5511	654	11	.	.	PUNCT
ejpam-5511	655	1	[	[	X
ejpam-5511	655	2	2	2	NUM
ejpam-5511	655	3	]	]	PUNCT
ejpam-5511	655	4	m.	m.	NOUN
ejpam-5511	655	5	w.	w.	PROPN
ejpam-5511	655	6	chan	chan	PROPN
ejpam-5511	655	7	and	and	CCONJ
ejpam-5511	655	8	k.	k.	PROPN
ejpam-5511	655	9	p.	p.	PROPN
ejpam-5511	655	10	shum	shum	PROPN
ejpam-5511	655	11	.	.	PUNCT
ejpam-5511	656	1	homomorphisms	homomorphism	NOUN
ejpam-5511	656	2	of	of	ADP
ejpam-5511	656	3	implicative	implicative	ADJ
ejpam-5511	656	4	semigroups	semigroup	NOUN
ejpam-5511	656	5	.	.	PUNCT
ejpam-5511	657	1	in	in	ADP
ejpam-5511	657	2	semigroup	semigroup	PROPN
ejpam-5511	657	3	forum	forum	PROPN
ejpam-5511	657	4	,	,	PUNCT
ejpam-5511	657	5	volume	volume	NOUN
ejpam-5511	657	6	46	46	NUM
ejpam-5511	657	7	,	,	PUNCT
ejpam-5511	657	8	pages	page	NOUN
ejpam-5511	657	9	7–15	7–15	PROPN
ejpam-5511	657	10	.	.	PUNCT
ejpam-5511	658	1	springer	springer	NOUN
ejpam-5511	658	2	,	,	PUNCT
ejpam-5511	658	3	1993	1993	NUM
ejpam-5511	658	4	.	.	PUNCT
ejpam-5511	659	1	[	[	X
ejpam-5511	659	2	3	3	NUM
ejpam-5511	659	3	]	]	PUNCT
ejpam-5511	659	4	a.	a.	NOUN
ejpam-5511	659	5	chronowski	chronowski	NOUN
ejpam-5511	659	6	.	.	PUNCT
ejpam-5511	660	1	a	a	DET
ejpam-5511	660	2	ternary	ternary	ADJ
ejpam-5511	660	3	semigroup	semigroup	NOUN
ejpam-5511	660	4	of	of	ADP
ejpam-5511	660	5	mappings	mapping	NOUN
ejpam-5511	660	6	.	.	PUNCT
ejpam-5511	661	1	demonstratio	demonstratio	PROPN
ejpam-5511	661	2	mathematica	mathematica	PROPN
ejpam-5511	661	3	,	,	PUNCT
ejpam-5511	661	4	27(34):781–792	27(34):781–792	NUM
ejpam-5511	661	5	,	,	PUNCT
ejpam-5511	661	6	1994	1994	NUM
ejpam-5511	661	7	.	.	PUNCT
ejpam-5511	662	1	[	[	X
ejpam-5511	662	2	4	4	X
ejpam-5511	662	3	]	]	X
ejpam-5511	662	4	v.	v.	ADP
ejpam-5511	662	5	r.	r.	PROPN
ejpam-5511	662	6	daddi	daddi	PROPN
ejpam-5511	662	7	and	and	CCONJ
ejpam-5511	662	8	y.	y.	PROPN
ejpam-5511	662	9	s.	s.	PROPN
ejpam-5511	662	10	pawar	pawar	PROPN
ejpam-5511	662	11	.	.	PUNCT
ejpam-5511	663	1	on	on	ADP
ejpam-5511	663	2	ordered	order	VERB
ejpam-5511	663	3	ternary	ternary	ADJ
ejpam-5511	663	4	semigroups	semigroup	NOUN
ejpam-5511	663	5	.	.	PUNCT
ejpam-5511	664	1	kyungpook	kyungpook	PROPN
ejpam-5511	664	2	mathematical	mathematical	PROPN
ejpam-5511	664	3	journal	journal	PROPN
ejpam-5511	664	4	,	,	PUNCT
ejpam-5511	664	5	52(4):375–381	52(4):375–381	NUM
ejpam-5511	664	6	,	,	PUNCT
ejpam-5511	664	7	2012	2012	NUM
ejpam-5511	664	8	.	.	PUNCT
ejpam-5511	665	1	[	[	X
ejpam-5511	665	2	5	5	X
ejpam-5511	665	3	]	]	PUNCT
ejpam-5511	665	4	v.	v.	ADP
ejpam-5511	665	5	n.	n.	PROPN
ejpam-5511	665	6	dixit	dixit	PROPN
ejpam-5511	665	7	and	and	CCONJ
ejpam-5511	665	8	s.	s.	PROPN
ejpam-5511	665	9	dewan	dewan	PROPN
ejpam-5511	665	10	.	.	PUNCT
ejpam-5511	666	1	a	a	DET
ejpam-5511	666	2	note	note	NOUN
ejpam-5511	666	3	on	on	ADP
ejpam-5511	666	4	quasi	quasi	NOUN
ejpam-5511	666	5	and	and	CCONJ
ejpam-5511	666	6	bi	bi	NOUN
ejpam-5511	666	7	-	-	NOUN
ejpam-5511	666	8	ideals	ideal	NOUN
ejpam-5511	666	9	in	in	ADP
ejpam-5511	666	10	ternary	ternary	ADJ
ejpam-5511	666	11	semigroups	semigroup	NOUN
ejpam-5511	666	12	.	.	PUNCT
ejpam-5511	667	1	international	international	ADJ
ejpam-5511	667	2	journal	journal	NOUN
ejpam-5511	667	3	of	of	ADP
ejpam-5511	667	4	mathematics	mathematics	PROPN
ejpam-5511	667	5	and	and	CCONJ
ejpam-5511	667	6	mathematical	mathematical	ADJ
ejpam-5511	667	7	sciences	science	NOUN
ejpam-5511	667	8	,	,	PUNCT
ejpam-5511	667	9	18(3):501–508	18(3):501–508	NUM
ejpam-5511	667	10	,	,	PUNCT
ejpam-5511	667	11	1995	1995	NUM
ejpam-5511	667	12	.	.	PUNCT
ejpam-5511	668	1	[	[	X
ejpam-5511	668	2	6	6	NUM
ejpam-5511	668	3	]	]	PUNCT
ejpam-5511	668	4	l.	l.	PROPN
ejpam-5511	668	5	fuchs	fuchs	PROPN
ejpam-5511	668	6	.	.	PUNCT
ejpam-5511	669	1	partially	partially	ADV
ejpam-5511	669	2	ordered	order	VERB
ejpam-5511	669	3	algebraic	algebraic	ADJ
ejpam-5511	669	4	systems	system	NOUN
ejpam-5511	669	5	.	.	PUNCT
ejpam-5511	670	1	courier	courier	NOUN
ejpam-5511	670	2	corporation	corporation	NOUN
ejpam-5511	670	3	,	,	PUNCT
ejpam-5511	670	4	2014	2014	NUM
ejpam-5511	670	5	.	.	PUNCT
ejpam-5511	671	1	[	[	X
ejpam-5511	671	2	7	7	NUM
ejpam-5511	671	3	]	]	PUNCT
ejpam-5511	671	4	a.	a.	NOUN
ejpam-5511	671	5	iampan	iampan	PROPN
ejpam-5511	671	6	.	.	PUNCT
ejpam-5511	672	1	characterizing	characterize	VERB
ejpam-5511	672	2	the	the	DET
ejpam-5511	672	3	minimality	minimality	NOUN
ejpam-5511	672	4	and	and	CCONJ
ejpam-5511	672	5	maximality	maximality	PROPN
ejpam-5511	672	6	of	of	ADP
ejpam-5511	672	7	ordered	order	VERB
ejpam-5511	672	8	lateral	lateral	ADJ
ejpam-5511	672	9	ideals	ideal	NOUN
ejpam-5511	672	10	in	in	ADP
ejpam-5511	672	11	ordered	order	VERB
ejpam-5511	672	12	ternary	ternary	ADJ
ejpam-5511	672	13	semigroups	semigroup	NOUN
ejpam-5511	672	14	.	.	PUNCT
ejpam-5511	673	1	journal	journal	NOUN
ejpam-5511	673	2	of	of	ADP
ejpam-5511	673	3	the	the	DET
ejpam-5511	673	4	korean	korean	PROPN
ejpam-5511	673	5	mathematical	mathematical	ADJ
ejpam-5511	673	6	society	society	NOUN
ejpam-5511	673	7	,	,	PUNCT
ejpam-5511	673	8	46(4):775	46(4):775	NUM
ejpam-5511	673	9	–	–	PUNCT
ejpam-5511	673	10	784	784	NUM
ejpam-5511	673	11	,	,	PUNCT
ejpam-5511	673	12	2009	2009	NUM
ejpam-5511	673	13	.	.	PUNCT
ejpam-5511	674	1	[	[	X
ejpam-5511	674	2	8	8	NUM
ejpam-5511	674	3	]	]	PUNCT
ejpam-5511	674	4	a.	a.	NOUN
ejpam-5511	674	5	iampan	iampan	PROPN
ejpam-5511	674	6	.	.	PUNCT
ejpam-5511	675	1	on	on	ADP
ejpam-5511	675	2	ordered	order	VERB
ejpam-5511	675	3	ideal	ideal	ADJ
ejpam-5511	675	4	extensions	extension	NOUN
ejpam-5511	675	5	of	of	ADP
ejpam-5511	675	6	ordered	order	VERB
ejpam-5511	675	7	ternary	ternary	ADJ
ejpam-5511	675	8	semigroups	semigroup	NOUN
ejpam-5511	675	9	.	.	PUNCT
ejpam-5511	676	1	lobachevskii	lobachevskii	PROPN
ejpam-5511	676	2	journal	journal	PROPN
ejpam-5511	676	3	of	of	ADP
ejpam-5511	676	4	mathematics	mathematic	NOUN
ejpam-5511	676	5	,	,	PUNCT
ejpam-5511	676	6	31:13–17	31:13–17	NUM
ejpam-5511	676	7	,	,	PUNCT
ejpam-5511	676	8	2010	2010	NUM
ejpam-5511	676	9	.	.	PUNCT
ejpam-5511	677	1	references	reference	NOUN
ejpam-5511	677	2	4194	4194	NUM
ejpam-5511	678	1	[	[	X
ejpam-5511	678	2	9	9	NUM
ejpam-5511	678	3	]	]	PUNCT
ejpam-5511	678	4	m.	m.	NOUN
ejpam-5511	678	5	f.	f.	PROPN
ejpam-5511	678	6	janowitz	janowitz	PROPN
ejpam-5511	678	7	and	and	CCONJ
ejpam-5511	678	8	c.	c.	PROPN
ejpam-5511	678	9	s.	s.	PROPN
ejpam-5511	678	10	johnson	johnson	PROPN
ejpam-5511	678	11	jr	jr	PROPN
ejpam-5511	678	12	.	.	PUNCT
ejpam-5511	679	1	a	a	DET
ejpam-5511	679	2	note	note	NOUN
ejpam-5511	679	3	on	on	ADP
ejpam-5511	679	4	brouwerian	brouwerian	ADJ
ejpam-5511	679	5	and	and	CCONJ
ejpam-5511	679	6	glivenko	glivenko	ADJ
ejpam-5511	679	7	semigroups	semigroup	NOUN
ejpam-5511	679	8	.	.	PUNCT
ejpam-5511	680	1	journal	journal	NOUN
ejpam-5511	680	2	of	of	ADP
ejpam-5511	680	3	the	the	DET
ejpam-5511	680	4	london	london	PROPN
ejpam-5511	680	5	mathematical	mathematical	ADJ
ejpam-5511	680	6	society	society	NOUN
ejpam-5511	680	7	,	,	PUNCT
ejpam-5511	680	8	2(1):733–736	2(1):733–736	PROPN
ejpam-5511	680	9	,	,	PUNCT
ejpam-5511	680	10	1969	1969	NUM
ejpam-5511	680	11	.	.	PUNCT
ejpam-5511	681	1	[	[	X
ejpam-5511	681	2	10	10	NUM
ejpam-5511	681	3	]	]	X
ejpam-5511	681	4	y.	y.	PROPN
ejpam-5511	681	5	b.	b.	PROPN
ejpam-5511	681	6	jun	jun	PROPN
ejpam-5511	681	7	.	.	PUNCT
ejpam-5511	682	1	some	some	DET
ejpam-5511	682	2	results	result	NOUN
ejpam-5511	682	3	on	on	ADP
ejpam-5511	682	4	ordered	order	VERB
ejpam-5511	682	5	filters	filter	NOUN
ejpam-5511	682	6	of	of	ADP
ejpam-5511	682	7	implicative	implicative	ADJ
ejpam-5511	682	8	semigroups	semigroup	NOUN
ejpam-5511	682	9	.	.	PUNCT
ejpam-5511	683	1	international	international	ADJ
ejpam-5511	683	2	journal	journal	NOUN
ejpam-5511	683	3	of	of	ADP
ejpam-5511	683	4	mathematics	mathematics	PROPN
ejpam-5511	683	5	and	and	CCONJ
ejpam-5511	683	6	mathematical	mathematical	ADJ
ejpam-5511	683	7	sciences	science	NOUN
ejpam-5511	683	8	,	,	PUNCT
ejpam-5511	683	9	26(12):731–735	26(12):731–735	NUM
ejpam-5511	683	10	,	,	PUNCT
ejpam-5511	683	11	2001	2001	NUM
ejpam-5511	683	12	.	.	PUNCT
ejpam-5511	684	1	[	[	X
ejpam-5511	684	2	11	11	NUM
ejpam-5511	684	3	]	]	X
ejpam-5511	684	4	d.	d.	PROPN
ejpam-5511	684	5	h.	h.	PROPN
ejpam-5511	684	6	lehmer	lehmer	PROPN
ejpam-5511	684	7	.	.	PUNCT
ejpam-5511	685	1	a	a	DET
ejpam-5511	685	2	ternary	ternary	ADJ
ejpam-5511	685	3	analogue	analogue	NOUN
ejpam-5511	685	4	of	of	ADP
ejpam-5511	685	5	abelian	abelian	ADJ
ejpam-5511	685	6	groups	group	NOUN
ejpam-5511	685	7	.	.	PUNCT
ejpam-5511	686	1	american	american	ADJ
ejpam-5511	686	2	journal	journal	PROPN
ejpam-5511	686	3	of	of	ADP
ejpam-5511	686	4	mathematics	mathematics	PROPN
ejpam-5511	686	5	,	,	PUNCT
ejpam-5511	686	6	54(2):329–338	54(2):329–338	PROPN
ejpam-5511	686	7	,	,	PUNCT
ejpam-5511	686	8	1932	1932	NUM
ejpam-5511	686	9	.	.	PUNCT
ejpam-5511	687	1	[	[	X
ejpam-5511	687	2	12	12	NUM
ejpam-5511	687	3	]	]	X
ejpam-5511	687	4	j.	j.	PROPN
ejpam-5511	687	5	loś.	loś.	PROPN
ejpam-5511	687	6	on	on	ADP
ejpam-5511	687	7	the	the	DET
ejpam-5511	687	8	extending	extending	NOUN
ejpam-5511	687	9	of	of	ADP
ejpam-5511	687	10	models	model	NOUN
ejpam-5511	687	11	(	(	PUNCT
ejpam-5511	687	12	i	i	NOUN
ejpam-5511	687	13	)	)	PUNCT
ejpam-5511	687	14	.	.	PUNCT
ejpam-5511	688	1	fundamenta	fundamenta	PROPN
ejpam-5511	688	2	mathematicae	mathematicae	PROPN
ejpam-5511	688	3	,	,	PUNCT
ejpam-5511	688	4	42:38–54	42:38–54	NUM
ejpam-5511	688	5	,	,	PUNCT
ejpam-5511	688	6	1955	1955	NUM
ejpam-5511	688	7	.	.	PUNCT
ejpam-5511	689	1	[	[	X
ejpam-5511	689	2	13	13	NUM
ejpam-5511	689	3	]	]	PUNCT
ejpam-5511	689	4	w.	w.	PROPN
ejpam-5511	689	5	c.	c.	PROPN
ejpam-5511	689	6	nemitz	nemitz	PROPN
ejpam-5511	689	7	.	.	PUNCT
ejpam-5511	690	1	implicative	implicative	ADJ
ejpam-5511	690	2	semi	semi	NOUN
ejpam-5511	690	3	-	-	NOUN
ejpam-5511	690	4	lattices	lattice	NOUN
ejpam-5511	690	5	.	.	PUNCT
ejpam-5511	691	1	transactions	transaction	NOUN
ejpam-5511	691	2	of	of	ADP
ejpam-5511	691	3	the	the	DET
ejpam-5511	691	4	american	american	PROPN
ejpam-5511	691	5	mathematical	mathematical	PROPN
ejpam-5511	691	6	society	society	NOUN
ejpam-5511	691	7	,	,	PUNCT
ejpam-5511	691	8	117:128–142	117:128–142	NUM
ejpam-5511	691	9	,	,	PUNCT
ejpam-5511	691	10	1965	1965	NUM
ejpam-5511	691	11	.	.	PUNCT
ejpam-5511	692	1	[	[	X
ejpam-5511	692	2	14	14	NUM
ejpam-5511	692	3	]	]	X
ejpam-5511	692	4	d.	d.	PROPN
ejpam-5511	692	5	a.	a.	PROPN
ejpam-5511	692	6	romano	romano	PROPN
ejpam-5511	692	7	.	.	PUNCT
ejpam-5511	693	1	an	an	DET
ejpam-5511	693	2	introduction	introduction	NOUN
ejpam-5511	693	3	to	to	AUX
ejpam-5511	693	4	implicative	implicative	VERB
ejpam-5511	693	5	semigroups	semigroup	NOUN
ejpam-5511	693	6	with	with	ADP
ejpam-5511	693	7	apartness	apartness	PROPN
ejpam-5511	693	8	.	.	PUNCT
ejpam-5511	694	1	sarajevo	sarajevo	PROPN
ejpam-5511	694	2	j.	j.	PROPN
ejpam-5511	694	3	math	math	PROPN
ejpam-5511	694	4	,	,	PUNCT
ejpam-5511	694	5	12(2):155–165	12(2):155–165	PROPN
ejpam-5511	694	6	,	,	PUNCT
ejpam-5511	694	7	2016	2016	NUM
ejpam-5511	694	8	.	.	PUNCT
ejpam-5511	695	1	[	[	X
ejpam-5511	695	2	15	15	NUM
ejpam-5511	695	3	]	]	X
ejpam-5511	695	4	m.	m.	NOUN
ejpam-5511	695	5	l.	l.	PROPN
ejpam-5511	695	6	santiago	santiago	PROPN
ejpam-5511	695	7	and	and	CCONJ
ejpam-5511	695	8	s.	s.	PROPN
ejpam-5511	695	9	sri	sri	PROPN
ejpam-5511	695	10	bala	bala	PROPN
ejpam-5511	695	11	.	.	PUNCT
ejpam-5511	696	1	ternary	ternary	ADJ
ejpam-5511	696	2	semigroups	semigroup	NOUN
ejpam-5511	696	3	.	.	PUNCT
ejpam-5511	697	1	in	in	ADP
ejpam-5511	697	2	semigroup	semigroup	PROPN
ejpam-5511	697	3	forum	forum	PROPN
ejpam-5511	697	4	,	,	PUNCT
ejpam-5511	697	5	volume	volume	NOUN
ejpam-5511	697	6	81	81	NUM
ejpam-5511	697	7	,	,	PUNCT
ejpam-5511	697	8	pages	page	NOUN
ejpam-5511	697	9	380–388	380–388	NUM
ejpam-5511	697	10	.	.	PUNCT
ejpam-5511	697	11	springer	springer	NOUN
ejpam-5511	697	12	,	,	PUNCT
ejpam-5511	697	13	2010	2010	NUM
ejpam-5511	697	14	.	.	PUNCT
ejpam-5511	698	1	[	[	X
ejpam-5511	698	2	16	16	NUM
ejpam-5511	698	3	]	]	X
ejpam-5511	698	4	y.	y.	PROPN
ejpam-5511	698	5	sarala	sarala	PROPN
ejpam-5511	698	6	,	,	PUNCT
ejpam-5511	698	7	a.	a.	PROPN
ejpam-5511	698	8	anjaneyulu	anjaneyulu	VERB
ejpam-5511	698	9	,	,	PUNCT
ejpam-5511	698	10	and	and	CCONJ
ejpam-5511	698	11	d.	d.	PROPN
ejpam-5511	698	12	madhusudhana	madhusudhana	PROPN
ejpam-5511	698	13	rao	rao	PROPN
ejpam-5511	698	14	.	.	PUNCT
ejpam-5511	699	1	ternary	ternary	ADJ
ejpam-5511	699	2	semigroups	semigroup	NOUN
ejpam-5511	699	3	.	.	PUNCT
ejpam-5511	700	1	international	international	ADJ
ejpam-5511	700	2	journal	journal	PROPN
ejpam-5511	700	3	of	of	ADP
ejpam-5511	700	4	mathematics	mathematics	PROPN
ejpam-5511	700	5	sciences	science	NOUN
ejpam-5511	700	6	,	,	PUNCT
ejpam-5511	700	7	technology	technology	NOUN
ejpam-5511	700	8	and	and	CCONJ
ejpam-5511	700	9	humanities	humanity	NOUN
ejpam-5511	700	10	,	,	PUNCT
ejpam-5511	700	11	76:848–859	76:848–859	NUM
ejpam-5511	700	12	,	,	PUNCT
ejpam-5511	700	13	2013	2013	NUM
ejpam-5511	700	14	.	.	PUNCT
ejpam-5511	701	1	[	[	X
ejpam-5511	701	2	17	17	NUM
ejpam-5511	701	3	]	]	X
ejpam-5511	701	4	f.	f.	PROPN
ejpam-5511	701	5	m.	m.	PROPN
ejpam-5511	701	6	sioson	sioson	PROPN
ejpam-5511	701	7	.	.	PUNCT
ejpam-5511	702	1	ideal	ideal	PROPN
ejpam-5511	702	2	theory	theory	NOUN
ejpam-5511	702	3	in	in	ADP
ejpam-5511	702	4	ternary	ternary	ADJ
ejpam-5511	702	5	semigroups	semigroup	NOUN
ejpam-5511	702	6	.	.	PUNCT
ejpam-5511	703	1	math	math	NOUN
ejpam-5511	703	2	.	.	PUNCT
ejpam-5511	704	1	japon	japon	PROPN
ejpam-5511	704	2	,	,	PUNCT
ejpam-5511	704	3	10(84):63	10(84):63	NUM
ejpam-5511	704	4	,	,	PUNCT
ejpam-5511	704	5	1965	1965	NUM
ejpam-5511	704	6	.	.	PUNCT