id	sid	tid	token	lemma	pos
ejpam-6093	1	1	european	european	PROPN
ejpam-6093	1	2	journal	journal	PROPN
ejpam-6093	1	3	of	of	ADP
ejpam-6093	1	4	pure	pure	ADJ
ejpam-6093	1	5	and	and	CCONJ
ejpam-6093	1	6	applied	applied	ADJ
ejpam-6093	1	7	mathematics	mathematic	NOUN
ejpam-6093	1	8	2025	2025	NUM
ejpam-6093	1	9	,	,	PUNCT
ejpam-6093	1	10	vol	vol	NOUN
ejpam-6093	1	11	.	.	PROPN
ejpam-6093	1	12	18	18	NUM
ejpam-6093	1	13	,	,	PUNCT
ejpam-6093	1	14	issue	issue	NOUN
ejpam-6093	1	15	4	4	NUM
ejpam-6093	1	16	,	,	PUNCT
ejpam-6093	1	17	article	article	NOUN
ejpam-6093	1	18	number	number	NOUN
ejpam-6093	1	19	6093	6093	NUM
ejpam-6093	1	20	issn	issn	VERB
ejpam-6093	1	21	1307	1307	NUM
ejpam-6093	1	22	-	-	SYM
ejpam-6093	1	23	5543	5543	NUM
ejpam-6093	1	24	–	–	PUNCT
ejpam-6093	1	25	ejpam.com	ejpam.com	X
ejpam-6093	1	26	published	publish	VERB
ejpam-6093	1	27	by	by	ADP
ejpam-6093	1	28	new	new	PROPN
ejpam-6093	1	29	york	york	PROPN
ejpam-6093	1	30	business	business	PROPN
ejpam-6093	1	31	global	global	ADJ
ejpam-6093	1	32	implicative	implicative	ADJ
ejpam-6093	1	33	filters	filter	NOUN
ejpam-6093	1	34	of	of	ADP
ejpam-6093	1	35	implicative	implicative	NOUN
ejpam-6093	1	36	negatively	negatively	ADV
ejpam-6093	1	37	partially	partially	ADV
ejpam-6093	1	38	ordered	order	VERB
ejpam-6093	1	39	ternary	ternary	ADJ
ejpam-6093	1	40	semigroups	semigroup	NOUN
ejpam-6093	1	41	kansada	kansada	PROPN
ejpam-6093	1	42	nakwan1	nakwan1	PROPN
ejpam-6093	1	43	,	,	PUNCT
ejpam-6093	1	44	panuwat	panuwat	VERB
ejpam-6093	1	45	luangchaisri1	luangchaisri1	NOUN
ejpam-6093	1	46	,	,	PUNCT
ejpam-6093	1	47	thawhat	thawhat	PROPN
ejpam-6093	1	48	changphas1,∗	changphas1,∗	NOUN
ejpam-6093	1	49	1	1	NUM
ejpam-6093	1	50	department	department	NOUN
ejpam-6093	1	51	of	of	ADP
ejpam-6093	1	52	mathematics	mathematic	NOUN
ejpam-6093	1	53	,	,	PUNCT
ejpam-6093	1	54	faculty	faculty	NOUN
ejpam-6093	1	55	of	of	ADP
ejpam-6093	1	56	science	science	NOUN
ejpam-6093	1	57	,	,	PUNCT
ejpam-6093	1	58	khon	khon	PROPN
ejpam-6093	1	59	kaen	kaen	PROPN
ejpam-6093	1	60	university	university	PROPN
ejpam-6093	1	61	,	,	PUNCT
ejpam-6093	1	62	khon	khon	PROPN
ejpam-6093	1	63	kaen	kaen	PROPN
ejpam-6093	1	64	40002	40002	NUM
ejpam-6093	1	65	,	,	PUNCT
ejpam-6093	1	66	thailand	thailand	PROPN
ejpam-6093	1	67	abstract	abstract	NOUN
ejpam-6093	1	68	.	.	PUNCT
ejpam-6093	2	1	in	in	ADP
ejpam-6093	2	2	this	this	DET
ejpam-6093	2	3	paper	paper	NOUN
ejpam-6093	2	4	,	,	PUNCT
ejpam-6093	2	5	firstly	firstly	ADV
ejpam-6093	2	6	,	,	PUNCT
ejpam-6093	2	7	we	we	PRON
ejpam-6093	2	8	give	give	VERB
ejpam-6093	2	9	characterizations	characterization	NOUN
ejpam-6093	2	10	of	of	ADP
ejpam-6093	2	11	filters	filter	NOUN
ejpam-6093	2	12	in	in	ADP
ejpam-6093	2	13	implicative	implicative	NOUN
ejpam-6093	2	14	negatively	negatively	ADV
ejpam-6093	2	15	partially	partially	ADV
ejpam-6093	2	16	ordered	order	VERB
ejpam-6093	2	17	ternary	ternary	ADJ
ejpam-6093	2	18	semigroups	semigroup	NOUN
ejpam-6093	2	19	and	and	CCONJ
ejpam-6093	2	20	in	in	ADP
ejpam-6093	2	21	commutative	commutative	ADJ
ejpam-6093	2	22	implicative	implicative	NOUN
ejpam-6093	2	23	negatively	negatively	ADV
ejpam-6093	2	24	partially	partially	ADV
ejpam-6093	2	25	ordered	order	VERB
ejpam-6093	2	26	ternary	ternary	ADJ
ejpam-6093	2	27	semigroups	semigroup	NOUN
ejpam-6093	2	28	.	.	PUNCT
ejpam-6093	3	1	secondly	secondly	ADV
ejpam-6093	3	2	,	,	PUNCT
ejpam-6093	3	3	we	we	PRON
ejpam-6093	3	4	introduce	introduce	VERB
ejpam-6093	3	5	the	the	DET
ejpam-6093	3	6	notion	notion	NOUN
ejpam-6093	3	7	of	of	ADP
ejpam-6093	3	8	implicative	implicative	ADJ
ejpam-6093	3	9	filters	filter	NOUN
ejpam-6093	3	10	of	of	ADP
ejpam-6093	3	11	implicative	implicative	NOUN
ejpam-6093	3	12	negatively	negatively	ADV
ejpam-6093	3	13	partially	partially	ADV
ejpam-6093	3	14	ordered	order	VERB
ejpam-6093	3	15	ternary	ternary	ADJ
ejpam-6093	3	16	semigroups	semigroup	NOUN
ejpam-6093	3	17	;	;	PUNCT
ejpam-6093	3	18	an	an	DET
ejpam-6093	3	19	example	example	NOUN
ejpam-6093	3	20	is	be	AUX
ejpam-6093	3	21	established	establish	VERB
ejpam-6093	3	22	.	.	PUNCT
ejpam-6093	4	1	we	we	PRON
ejpam-6093	4	2	show	show	VERB
ejpam-6093	4	3	that	that	SCONJ
ejpam-6093	4	4	every	every	DET
ejpam-6093	4	5	implicative	implicative	ADJ
ejpam-6093	4	6	filter	filter	NOUN
ejpam-6093	4	7	is	be	AUX
ejpam-6093	4	8	a	a	DET
ejpam-6093	4	9	filter	filter	NOUN
ejpam-6093	4	10	and	and	CCONJ
ejpam-6093	4	11	give	give	VERB
ejpam-6093	4	12	an	an	DET
ejpam-6093	4	13	example	example	NOUN
ejpam-6093	4	14	to	to	PART
ejpam-6093	4	15	show	show	VERB
ejpam-6093	4	16	that	that	SCONJ
ejpam-6093	4	17	the	the	DET
ejpam-6093	4	18	converse	converse	NOUN
ejpam-6093	4	19	is	be	AUX
ejpam-6093	4	20	not	not	PART
ejpam-6093	4	21	true	true	ADJ
ejpam-6093	4	22	in	in	ADP
ejpam-6093	4	23	general	general	ADJ
ejpam-6093	4	24	.	.	PUNCT
ejpam-6093	5	1	moreover	moreover	ADV
ejpam-6093	5	2	,	,	PUNCT
ejpam-6093	5	3	we	we	PRON
ejpam-6093	5	4	state	state	VERB
ejpam-6093	5	5	some	some	DET
ejpam-6093	5	6	equivalent	equivalent	ADJ
ejpam-6093	5	7	conditions	condition	NOUN
ejpam-6093	5	8	for	for	ADP
ejpam-6093	5	9	an	an	DET
ejpam-6093	5	10	implicative	implicative	ADJ
ejpam-6093	5	11	filter	filter	NOUN
ejpam-6093	5	12	by	by	ADP
ejpam-6093	5	13	using	use	VERB
ejpam-6093	5	14	a	a	DET
ejpam-6093	5	15	particular	particular	ADJ
ejpam-6093	5	16	set	set	NOUN
ejpam-6093	5	17	defined	define	VERB
ejpam-6093	5	18	by	by	ADP
ejpam-6093	5	19	a	a	DET
ejpam-6093	5	20	filter	filter	NOUN
ejpam-6093	5	21	.	.	PUNCT
ejpam-6093	6	1	finally	finally	ADV
ejpam-6093	6	2	,	,	PUNCT
ejpam-6093	6	3	we	we	PRON
ejpam-6093	6	4	introduce	introduce	VERB
ejpam-6093	6	5	and	and	CCONJ
ejpam-6093	6	6	study	study	VERB
ejpam-6093	6	7	a	a	DET
ejpam-6093	6	8	generalization	generalization	NOUN
ejpam-6093	6	9	of	of	ADP
ejpam-6093	6	10	implicative	implicative	ADJ
ejpam-6093	6	11	filters	filter	NOUN
ejpam-6093	6	12	.	.	PUNCT
ejpam-6093	7	1	2020	2020	NUM
ejpam-6093	7	2	mathematics	mathematic	NOUN
ejpam-6093	7	3	subject	subject	NOUN
ejpam-6093	7	4	classifications	classification	NOUN
ejpam-6093	7	5	:	:	PUNCT
ejpam-6093	7	6	20m12	20m12	NUM
ejpam-6093	7	7	,	,	PUNCT
ejpam-6093	7	8	06f99	06f99	NUM
ejpam-6093	7	9	,	,	PUNCT
ejpam-6093	7	10	06a06	06a06	NOUN
ejpam-6093	7	11	,	,	PUNCT
ejpam-6093	7	12	06a12	06a12	NUM
ejpam-6093	7	13	key	key	ADJ
ejpam-6093	7	14	words	word	NOUN
ejpam-6093	7	15	and	and	CCONJ
ejpam-6093	7	16	phrases	phrase	NOUN
ejpam-6093	7	17	:	:	PUNCT
ejpam-6093	7	18	filter	filter	NOUN
ejpam-6093	7	19	,	,	PUNCT
ejpam-6093	7	20	implicative	implicative	ADJ
ejpam-6093	7	21	filter	filter	NOUN
ejpam-6093	7	22	,	,	PUNCT
ejpam-6093	7	23	generalized	generalize	VERB
ejpam-6093	7	24	implicative	implicative	ADJ
ejpam-6093	7	25	filter	filter	NOUN
ejpam-6093	7	26	,	,	PUNCT
ejpam-6093	7	27	implicative	implicative	ADJ
ejpam-6093	7	28	negatively	negatively	ADV
ejpam-6093	7	29	partially	partially	ADV
ejpam-6093	7	30	ordered	order	VERB
ejpam-6093	7	31	ternary	ternary	ADJ
ejpam-6093	7	32	semigroup	semigroup	NOUN
ejpam-6093	7	33	1	1	NUM
ejpam-6093	7	34	.	.	PUNCT
ejpam-6093	8	1	introduction	introduction	NOUN
ejpam-6093	8	2	in	in	ADP
ejpam-6093	8	3	[	[	X
ejpam-6093	8	4	1	1	NUM
ejpam-6093	8	5	]	]	PUNCT
ejpam-6093	8	6	,	,	PUNCT
ejpam-6093	8	7	m.	m.	PROPN
ejpam-6093	8	8	w.	w.	PROPN
ejpam-6093	8	9	chan	chan	PROPN
ejpam-6093	8	10	and	and	CCONJ
ejpam-6093	8	11	k.	k.	PROPN
ejpam-6093	8	12	p.	p.	PROPN
ejpam-6093	8	13	shum	shum	PROPN
ejpam-6093	8	14	introduced	introduce	VERB
ejpam-6093	8	15	and	and	CCONJ
ejpam-6093	8	16	studied	study	VERB
ejpam-6093	8	17	the	the	DET
ejpam-6093	8	18	concept	concept	NOUN
ejpam-6093	8	19	of	of	ADP
ejpam-6093	8	20	implicative	implicative	NOUN
ejpam-6093	8	21	negatively	negatively	ADV
ejpam-6093	8	22	partially	partially	ADV
ejpam-6093	8	23	ordered	order	VERB
ejpam-6093	8	24	semigroups	semigroup	NOUN
ejpam-6093	8	25	;	;	PUNCT
ejpam-6093	8	26	elementary	elementary	ADJ
ejpam-6093	8	27	properties	property	NOUN
ejpam-6093	8	28	are	be	AUX
ejpam-6093	8	29	established	establish	VERB
ejpam-6093	8	30	;	;	PUNCT
ejpam-6093	8	31	the	the	DET
ejpam-6093	8	32	authors	author	NOUN
ejpam-6093	8	33	obtained	obtain	VERB
ejpam-6093	8	34	the	the	DET
ejpam-6093	8	35	homomorphism	homomorphism	NOUN
ejpam-6093	8	36	theorems	theorem	NOUN
ejpam-6093	8	37	using	use	VERB
ejpam-6093	8	38	implicative	implicative	ADJ
ejpam-6093	8	39	homomorphisms	homomorphism	NOUN
ejpam-6093	8	40	and	and	CCONJ
ejpam-6093	8	41	filters	filter	NOUN
ejpam-6093	8	42	.	.	PUNCT
ejpam-6093	9	1	in	in	ADP
ejpam-6093	9	2	[	[	X
ejpam-6093	9	3	2	2	NUM
ejpam-6093	9	4	]	]	PUNCT
ejpam-6093	9	5	,	,	PUNCT
ejpam-6093	9	6	y.	y.	PROPN
ejpam-6093	9	7	b.	b.	PROPN
ejpam-6093	9	8	yun	yun	PROPN
ejpam-6093	9	9	introduced	introduce	VERB
ejpam-6093	9	10	and	and	CCONJ
ejpam-6093	9	11	studied	study	VERB
ejpam-6093	9	12	the	the	DET
ejpam-6093	9	13	notion	notion	NOUN
ejpam-6093	9	14	of	of	ADP
ejpam-6093	9	15	implicative	implicative	ADJ
ejpam-6093	9	16	filters	filter	NOUN
ejpam-6093	9	17	;	;	PUNCT
ejpam-6093	9	18	some	some	DET
ejpam-6093	9	19	characterizations	characterization	NOUN
ejpam-6093	9	20	were	be	AUX
ejpam-6093	9	21	given	give	VERB
ejpam-6093	9	22	by	by	ADP
ejpam-6093	9	23	using	use	VERB
ejpam-6093	9	24	a	a	DET
ejpam-6093	9	25	particular	particular	ADJ
ejpam-6093	9	26	set	set	NOUN
ejpam-6093	9	27	.	.	PUNCT
ejpam-6093	10	1	in	in	ADP
ejpam-6093	10	2	[	[	X
ejpam-6093	10	3	3	3	NUM
ejpam-6093	10	4	]	]	PUNCT
ejpam-6093	10	5	,	,	PUNCT
ejpam-6093	10	6	m.	m.	NOUN
ejpam-6093	10	7	sambasiva	sambasiva	PROPN
ejpam-6093	10	8	rao	rao	PROPN
ejpam-6093	10	9	and	and	CCONJ
ejpam-6093	10	10	k.	k.	PROPN
ejpam-6093	10	11	p.	p.	PROPN
ejpam-6093	10	12	shum	shum	PROPN
ejpam-6093	10	13	generalized	generalize	VERB
ejpam-6093	10	14	the	the	DET
ejpam-6093	10	15	notion	notion	NOUN
ejpam-6093	10	16	of	of	ADP
ejpam-6093	10	17	implicative	implicative	ADJ
ejpam-6093	10	18	filters	filter	NOUN
ejpam-6093	10	19	;	;	PUNCT
ejpam-6093	10	20	a	a	DET
ejpam-6093	10	21	sufficient	sufficient	ADJ
ejpam-6093	10	22	condition	condition	NOUN
ejpam-6093	10	23	is	be	AUX
ejpam-6093	10	24	derived	derive	VERB
ejpam-6093	10	25	for	for	ADP
ejpam-6093	10	26	a	a	DET
ejpam-6093	10	27	generalized	generalized	ADJ
ejpam-6093	10	28	implicative	implicative	ADJ
ejpam-6093	10	29	filter	filter	NOUN
ejpam-6093	10	30	of	of	ADP
ejpam-6093	10	31	an	an	DET
ejpam-6093	10	32	implicative	implicative	NOUN
ejpam-6093	10	33	negatively	negatively	ADV
ejpam-6093	10	34	partially	partially	ADV
ejpam-6093	10	35	ordered	order	VERB
ejpam-6093	10	36	semigroups	semigroup	NOUN
ejpam-6093	10	37	to	to	PART
ejpam-6093	10	38	become	become	VERB
ejpam-6093	10	39	a	a	DET
ejpam-6093	10	40	filter	filter	NOUN
ejpam-6093	10	41	.	.	PUNCT
ejpam-6093	11	1	in	in	ADP
ejpam-6093	11	2	[	[	X
ejpam-6093	11	3	4	4	NUM
ejpam-6093	11	4	]	]	PUNCT
ejpam-6093	11	5	,	,	PUNCT
ejpam-6093	11	6	k.	k.	PROPN
ejpam-6093	11	7	nakwan	nakwan	PROPN
ejpam-6093	11	8	,	,	PUNCT
ejpam-6093	11	9	p.	p.	PROPN
ejpam-6093	11	10	luangchaisri	luangchaisri	VERB
ejpam-6093	11	11	and	and	CCONJ
ejpam-6093	11	12	t.	t.	PROPN
ejpam-6093	11	13	changphas	changphas	PROPN
ejpam-6093	11	14	introduced	introduce	VERB
ejpam-6093	11	15	and	and	CCONJ
ejpam-6093	11	16	studied	study	VERB
ejpam-6093	11	17	the	the	DET
ejpam-6093	11	18	notion	notion	NOUN
ejpam-6093	11	19	of	of	ADP
ejpam-6093	11	20	implicative	implicative	NOUN
ejpam-6093	11	21	negatively	negatively	ADV
ejpam-6093	11	22	partially	partially	ADV
ejpam-6093	11	23	ordered	order	VERB
ejpam-6093	11	24	ternary	ternary	ADJ
ejpam-6093	11	25	semigroups	semigroup	NOUN
ejpam-6093	11	26	(	(	PUNCT
ejpam-6093	11	27	it	it	PRON
ejpam-6093	11	28	is	be	AUX
ejpam-6093	11	29	abbreviated	abbreviate	VERB
ejpam-6093	11	30	by	by	ADP
ejpam-6093	11	31	implicative	implicative	ADJ
ejpam-6093	11	32	n.p.o	n.p.o	NOUN
ejpam-6093	11	33	ternary	ternary	ADJ
ejpam-6093	11	34	semigroups	semigroup	NOUN
ejpam-6093	11	35	)	)	PUNCT
ejpam-6093	11	36	and	and	CCONJ
ejpam-6093	11	37	filters	filter	NOUN
ejpam-6093	11	38	.	.	PUNCT
ejpam-6093	12	1	the	the	DET
ejpam-6093	12	2	authors	author	NOUN
ejpam-6093	12	3	applied	apply	VERB
ejpam-6093	12	4	the	the	DET
ejpam-6093	12	5	concept	concept	NOUN
ejpam-6093	12	6	of	of	ADP
ejpam-6093	12	7	implicative	implicative	ADJ
ejpam-6093	12	8	n.p.o	n.p.o	NOUN
ejpam-6093	12	9	.	.	PUNCT
ejpam-6093	13	1	semigroups	semigroup	NOUN
ejpam-6093	13	2	to	to	PART
ejpam-6093	13	3	implicative	implicative	ADJ
ejpam-6093	13	4	n.p.o	n.p.o	NOUN
ejpam-6093	13	5	.	.	PUNCT
ejpam-6093	14	1	ternary	ternary	ADJ
ejpam-6093	14	2	semigroups	semigroup	NOUN
ejpam-6093	14	3	and	and	CCONJ
ejpam-6093	14	4	gave	give	VERB
ejpam-6093	14	5	elementary	elementary	ADJ
ejpam-6093	14	6	properties	property	NOUN
ejpam-6093	14	7	.	.	PUNCT
ejpam-6093	15	1	in	in	ADP
ejpam-6093	15	2	this	this	DET
ejpam-6093	15	3	paper	paper	NOUN
ejpam-6093	15	4	,	,	PUNCT
ejpam-6093	15	5	we	we	PRON
ejpam-6093	15	6	continue	continue	VERB
ejpam-6093	15	7	the	the	DET
ejpam-6093	15	8	investigation	investigation	NOUN
ejpam-6093	15	9	of	of	ADP
ejpam-6093	15	10	implicative	implicative	ADJ
ejpam-6093	15	11	n.p.o	n.p.o	NOUN
ejpam-6093	15	12	.	.	PUNCT
ejpam-6093	16	1	∗corresponding	∗corresponde	VERB
ejpam-6093	16	2	author	author	NOUN
ejpam-6093	16	3	.	.	PUNCT
ejpam-6093	17	1	doi	doi	NOUN
ejpam-6093	17	2	:	:	PUNCT
ejpam-6093	17	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6093	https://doi.org/10.29020/nybg.ejpam.v18i4.6093	PROPN
ejpam-6093	17	4	email	email	NOUN
ejpam-6093	17	5	addresses	address	NOUN
ejpam-6093	17	6	:	:	PUNCT
ejpam-6093	17	7	kansada.n@kkumail.com	kansada.n@kkumail.com	PROPN
ejpam-6093	17	8	(	(	PUNCT
ejpam-6093	17	9	k.	k.	PROPN
ejpam-6093	17	10	nakwan	nakwan	PROPN
ejpam-6093	17	11	)	)	PUNCT
ejpam-6093	17	12	,	,	PUNCT
ejpam-6093	17	13	panulu@kku.ac.th	panulu@kku.ac.th	NOUN
ejpam-6093	17	14	(	(	PUNCT
ejpam-6093	17	15	p.	p.	NOUN
ejpam-6093	17	16	luangchaisri	luangchaisri	PROPN
ejpam-6093	17	17	)	)	PUNCT
ejpam-6093	17	18	,	,	PUNCT
ejpam-6093	17	19	thacha@kku.ac.th	thacha@kku.ac.th	NOUN
ejpam-6093	17	20	(	(	PUNCT
ejpam-6093	17	21	t.	t.	NOUN
ejpam-6093	17	22	changphas	changphas	PROPN
ejpam-6093	17	23	)	)	PUNCT
ejpam-6093	17	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6093	18	1	1	1	NUM
ejpam-6093	18	2	copyright	copyright	NOUN
ejpam-6093	18	3	:	:	PUNCT
ejpam-6093	18	4	©	©	PROPN
ejpam-6093	18	5	2025	2025	NUM
ejpam-6093	18	6	the	the	DET
ejpam-6093	18	7	author(s	author(s	NOUN
ejpam-6093	18	8	)	)	PUNCT
ejpam-6093	18	9	.	.	PUNCT
ejpam-6093	19	1	(	(	PUNCT
ejpam-6093	19	2	cc	cc	NOUN
ejpam-6093	19	3	by	by	ADP
ejpam-6093	19	4	-	-	PUNCT
ejpam-6093	19	5	nc	nc	PROPN
ejpam-6093	19	6	4.0	4.0	NUM
ejpam-6093	19	7	)	)	PUNCT
ejpam-6093	19	8	k.	k.	PROPN
ejpam-6093	19	9	nakwan	nakwan	PROPN
ejpam-6093	19	10	,	,	PUNCT
ejpam-6093	19	11	p.	p.	PROPN
ejpam-6093	19	12	luangchaisri	luangchaisri	VERB
ejpam-6093	19	13	,	,	PUNCT
ejpam-6093	19	14	t.	t.	PROPN
ejpam-6093	19	15	changphas	changphas	PROPN
ejpam-6093	19	16	/	/	SYM
ejpam-6093	19	17	eur	eur	PROPN
ejpam-6093	19	18	.	.	PUNCT
ejpam-6093	20	1	j.	j.	PROPN
ejpam-6093	20	2	pure	pure	PROPN
ejpam-6093	20	3	appl	appl	PROPN
ejpam-6093	20	4	.	.	PROPN
ejpam-6093	20	5	math	math	PROPN
ejpam-6093	20	6	,	,	PUNCT
ejpam-6093	20	7	18	18	NUM
ejpam-6093	20	8	(	(	PUNCT
ejpam-6093	20	9	4	4	NUM
ejpam-6093	20	10	)	)	PUNCT
ejpam-6093	20	11	(	(	PUNCT
ejpam-6093	20	12	2025	2025	NUM
ejpam-6093	20	13	)	)	PUNCT
ejpam-6093	20	14	,	,	PUNCT
ejpam-6093	20	15	6093	6093	NUM
ejpam-6093	20	16	2	2	NUM
ejpam-6093	20	17	of	of	ADP
ejpam-6093	20	18	11	11	NUM
ejpam-6093	20	19	ternary	ternary	ADJ
ejpam-6093	20	20	semigroups	semigroup	NOUN
ejpam-6093	20	21	and	and	CCONJ
ejpam-6093	20	22	their	their	PRON
ejpam-6093	20	23	filters	filter	NOUN
ejpam-6093	20	24	which	which	PRON
ejpam-6093	20	25	was	be	AUX
ejpam-6093	20	26	started	start	VERB
ejpam-6093	20	27	in	in	ADP
ejpam-6093	20	28	the	the	DET
ejpam-6093	20	29	general	general	ADJ
ejpam-6093	20	30	case	case	NOUN
ejpam-6093	20	31	by	by	ADP
ejpam-6093	20	32	k.	k.	PROPN
ejpam-6093	20	33	nakwan	nakwan	PROPN
ejpam-6093	20	34	,	,	PUNCT
ejpam-6093	20	35	p.	p.	PROPN
ejpam-6093	20	36	luangchaisri	luangchaisri	VERB
ejpam-6093	20	37	and	and	CCONJ
ejpam-6093	20	38	t.	t.	PROPN
ejpam-6093	20	39	changphas	changphas	PROPN
ejpam-6093	20	40	in	in	ADP
ejpam-6093	20	41	[	[	X
ejpam-6093	20	42	4	4	NUM
ejpam-6093	20	43	]	]	PUNCT
ejpam-6093	20	44	.	.	PUNCT
ejpam-6093	21	1	we	we	PRON
ejpam-6093	21	2	also	also	ADV
ejpam-6093	21	3	give	give	VERB
ejpam-6093	21	4	equivalent	equivalent	ADJ
ejpam-6093	21	5	conditions	condition	NOUN
ejpam-6093	21	6	of	of	ADP
ejpam-6093	21	7	a	a	DET
ejpam-6093	21	8	filter	filter	NOUN
ejpam-6093	21	9	of	of	ADP
ejpam-6093	21	10	implicative	implicative	ADJ
ejpam-6093	21	11	and	and	CCONJ
ejpam-6093	21	12	commutative	commutative	ADJ
ejpam-6093	21	13	implicative	implicative	ADJ
ejpam-6093	21	14	n.p.o	n.p.o	NOUN
ejpam-6093	21	15	.	.	PUNCT
ejpam-6093	22	1	ternary	ternary	ADJ
ejpam-6093	22	2	semigroups	semigroup	NOUN
ejpam-6093	22	3	.	.	PUNCT
ejpam-6093	23	1	we	we	PRON
ejpam-6093	23	2	show	show	VERB
ejpam-6093	23	3	that	that	SCONJ
ejpam-6093	23	4	every	every	DET
ejpam-6093	23	5	implicative	implicative	ADJ
ejpam-6093	23	6	filter	filter	NOUN
ejpam-6093	23	7	is	be	AUX
ejpam-6093	23	8	a	a	DET
ejpam-6093	23	9	filter	filter	NOUN
ejpam-6093	23	10	and	and	CCONJ
ejpam-6093	23	11	give	give	VERB
ejpam-6093	23	12	an	an	DET
ejpam-6093	23	13	example	example	NOUN
ejpam-6093	23	14	to	to	PART
ejpam-6093	23	15	show	show	VERB
ejpam-6093	23	16	that	that	SCONJ
ejpam-6093	23	17	the	the	DET
ejpam-6093	23	18	converse	converse	NOUN
ejpam-6093	23	19	is	be	AUX
ejpam-6093	23	20	not	not	PART
ejpam-6093	23	21	true	true	ADJ
ejpam-6093	23	22	in	in	ADP
ejpam-6093	23	23	general	general	ADJ
ejpam-6093	23	24	.	.	PUNCT
ejpam-6093	24	1	we	we	PRON
ejpam-6093	24	2	state	state	VERB
ejpam-6093	24	3	some	some	DET
ejpam-6093	24	4	equivalent	equivalent	ADJ
ejpam-6093	24	5	conditions	condition	NOUN
ejpam-6093	24	6	for	for	ADP
ejpam-6093	24	7	an	an	DET
ejpam-6093	24	8	implicative	implicative	ADJ
ejpam-6093	24	9	filter	filter	NOUN
ejpam-6093	24	10	by	by	ADP
ejpam-6093	24	11	using	use	VERB
ejpam-6093	24	12	a	a	DET
ejpam-6093	24	13	particular	particular	ADJ
ejpam-6093	24	14	set	set	NOUN
ejpam-6093	24	15	defined	define	VERB
ejpam-6093	24	16	by	by	ADP
ejpam-6093	24	17	a	a	DET
ejpam-6093	24	18	filter	filter	NOUN
ejpam-6093	24	19	.	.	PUNCT
ejpam-6093	25	1	finally	finally	ADV
ejpam-6093	25	2	,	,	PUNCT
ejpam-6093	25	3	we	we	PRON
ejpam-6093	25	4	introduce	introduce	VERB
ejpam-6093	25	5	and	and	CCONJ
ejpam-6093	25	6	study	study	VERB
ejpam-6093	25	7	a	a	DET
ejpam-6093	25	8	generalization	generalization	NOUN
ejpam-6093	25	9	of	of	ADP
ejpam-6093	25	10	implicative	implicative	ADJ
ejpam-6093	25	11	filters	filter	NOUN
ejpam-6093	25	12	.	.	PUNCT
ejpam-6093	26	1	2	2	X
ejpam-6093	26	2	.	.	X
ejpam-6093	26	3	preliminaries	preliminary	NOUN
ejpam-6093	26	4	for	for	ADP
ejpam-6093	26	5	information	information	NOUN
ejpam-6093	26	6	in	in	ADP
ejpam-6093	26	7	this	this	DET
ejpam-6093	26	8	section	section	NOUN
ejpam-6093	26	9	,	,	PUNCT
ejpam-6093	26	10	we	we	PRON
ejpam-6093	26	11	refer	refer	VERB
ejpam-6093	26	12	to	to	ADP
ejpam-6093	26	13	the	the	DET
ejpam-6093	26	14	results	result	NOUN
ejpam-6093	26	15	obtained	obtain	VERB
ejpam-6093	26	16	in	in	ADP
ejpam-6093	26	17	[	[	X
ejpam-6093	26	18	4	4	NUM
ejpam-6093	26	19	]	]	PUNCT
ejpam-6093	26	20	.	.	PUNCT
ejpam-6093	27	1	a	a	DET
ejpam-6093	27	2	negatively	negatively	ADV
ejpam-6093	27	3	partially	partially	ADV
ejpam-6093	27	4	ordered	order	VERB
ejpam-6093	27	5	ternary	ternary	ADJ
ejpam-6093	27	6	semigroup	semigroup	NOUN
ejpam-6093	27	7	(	(	PUNCT
ejpam-6093	27	8	it	it	PRON
ejpam-6093	27	9	is	be	AUX
ejpam-6093	27	10	abbreviated	abbreviate	VERB
ejpam-6093	27	11	by	by	ADP
ejpam-6093	27	12	n.p.o	n.p.o	NOUN
ejpam-6093	27	13	.	.	PUNCT
ejpam-6093	28	1	ternary	ternary	PROPN
ejpam-6093	28	2	semigroup	semigroup	PROPN
ejpam-6093	28	3	)	)	PUNCT
ejpam-6093	28	4	(	(	PUNCT
ejpam-6093	28	5	t	t	PROPN
ejpam-6093	28	6	,	,	PUNCT
ejpam-6093	28	7	[	[	PUNCT
ejpam-6093	28	8	]	]	X
ejpam-6093	28	9	,	,	PUNCT
ejpam-6093	28	10	≤	≤	NUM
ejpam-6093	28	11	)	)	PUNCT
ejpam-6093	28	12	consists	consist	VERB
ejpam-6093	28	13	of	of	ADP
ejpam-6093	28	14	a	a	DET
ejpam-6093	28	15	non	non	ADJ
ejpam-6093	28	16	-	-	ADJ
ejpam-6093	28	17	empty	empty	ADJ
ejpam-6093	28	18	set	set	ADJ
ejpam-6093	28	19	t	t	NOUN
ejpam-6093	28	20	together	together	ADV
ejpam-6093	28	21	with	with	ADP
ejpam-6093	28	22	a	a	DET
ejpam-6093	28	23	partial	partial	ADJ
ejpam-6093	28	24	order	order	NOUN
ejpam-6093	28	25	≤	≤	NOUN
ejpam-6093	28	26	and	and	CCONJ
ejpam-6093	28	27	a	a	DET
ejpam-6093	28	28	ternary	ternary	ADJ
ejpam-6093	28	29	multiplication	multiplication	NOUN
ejpam-6093	28	30	[	[	PUNCT
ejpam-6093	28	31	]	]	PUNCT
ejpam-6093	28	32	on	on	ADP
ejpam-6093	28	33	t	t	PROPN
ejpam-6093	28	34	such	such	ADJ
ejpam-6093	28	35	that	that	SCONJ
ejpam-6093	28	36	the	the	DET
ejpam-6093	28	37	following	follow	VERB
ejpam-6093	28	38	conditions	condition	NOUN
ejpam-6093	28	39	are	be	AUX
ejpam-6093	28	40	satisfied	satisfied	ADJ
ejpam-6093	28	41	:	:	PUNCT
ejpam-6093	28	42	for	for	ADP
ejpam-6093	28	43	any	any	DET
ejpam-6093	28	44	x	x	NOUN
ejpam-6093	28	45	,	,	PUNCT
ejpam-6093	28	46	y	y	PROPN
ejpam-6093	28	47	,	,	PUNCT
ejpam-6093	28	48	z	z	PROPN
ejpam-6093	28	49	,	,	PUNCT
ejpam-6093	28	50	u	u	NOUN
ejpam-6093	28	51	,	,	PUNCT
ejpam-6093	28	52	v	v	PROPN
ejpam-6093	28	53	∈	∈	PROPN
ejpam-6093	28	54	t	t	NOUN
ejpam-6093	28	55	,	,	PUNCT
ejpam-6093	28	56	(	(	PUNCT
ejpam-6093	28	57	1	1	X
ejpam-6093	28	58	)	)	PUNCT
ejpam-6093	29	1	[	[	X
ejpam-6093	29	2	[	[	X
ejpam-6093	29	3	xyz]uv	xyz]uv	X
ejpam-6093	29	4	]	]	X
ejpam-6093	29	5	=	=	PUNCT
ejpam-6093	30	1	[	[	X
ejpam-6093	30	2	x[yzu]v	x[yzu]v	X
ejpam-6093	30	3	]	]	X
ejpam-6093	30	4	=	=	PUNCT
ejpam-6093	31	1	[	[	X
ejpam-6093	31	2	xy[zuv	xy[zuv	PROPN
ejpam-6093	31	3	]	]	X
ejpam-6093	31	4	]	]	X
ejpam-6093	31	5	;	;	PUNCT
ejpam-6093	31	6	(	(	PUNCT
ejpam-6093	31	7	2	2	X
ejpam-6093	31	8	)	)	PUNCT
ejpam-6093	31	9	if	if	SCONJ
ejpam-6093	31	10	x	x	PROPN
ejpam-6093	31	11	≤	≤	NOUN
ejpam-6093	31	12	y	y	NOUN
ejpam-6093	31	13	,	,	PUNCT
ejpam-6093	31	14	then	then	ADV
ejpam-6093	31	15	[	[	X
ejpam-6093	31	16	xuv	xuv	X
ejpam-6093	31	17	]	]	X
ejpam-6093	31	18	≤	≤	X
ejpam-6093	32	1	[	[	X
ejpam-6093	32	2	yuv	yuv	X
ejpam-6093	32	3	]	]	PUNCT
ejpam-6093	32	4	,	,	PUNCT
ejpam-6093	32	5	[	[	X
ejpam-6093	32	6	uxv	uxv	X
ejpam-6093	32	7	]	]	X
ejpam-6093	32	8	≤	≤	NOUN
ejpam-6093	33	1	[	[	X
ejpam-6093	33	2	uyv	uyv	X
ejpam-6093	33	3	]	]	X
ejpam-6093	33	4	,	,	PUNCT
ejpam-6093	33	5	and	and	CCONJ
ejpam-6093	33	6	[	[	X
ejpam-6093	33	7	uvx	uvx	X
ejpam-6093	33	8	]	]	X
ejpam-6093	33	9	≤	≤	NOUN
ejpam-6093	34	1	[	[	X
ejpam-6093	34	2	uvy	uvy	NOUN
ejpam-6093	34	3	]	]	X
ejpam-6093	34	4	;	;	PUNCT
ejpam-6093	34	5	(	(	PUNCT
ejpam-6093	34	6	3	3	X
ejpam-6093	34	7	)	)	PUNCT
ejpam-6093	35	1	[	[	X
ejpam-6093	35	2	xyz	xyz	X
ejpam-6093	35	3	]	]	X
ejpam-6093	35	4	≤	≤	NUM
ejpam-6093	35	5	x	x	X
ejpam-6093	35	6	,	,	PUNCT
ejpam-6093	35	7	[	[	X
ejpam-6093	35	8	xyz	xyz	X
ejpam-6093	35	9	]	]	X
ejpam-6093	35	10	≤	≤	NUM
ejpam-6093	35	11	y	y	PROPN
ejpam-6093	35	12	,	,	PUNCT
ejpam-6093	35	13	and	and	CCONJ
ejpam-6093	35	14	[	[	X
ejpam-6093	35	15	xyz	xyz	X
ejpam-6093	35	16	]	]	X
ejpam-6093	35	17	≤	≤	NUM
ejpam-6093	35	18	z.	z.	PROPN
ejpam-6093	35	19	an	an	DET
ejpam-6093	35	20	n.p.o	n.p.o	NOUN
ejpam-6093	35	21	.	.	PUNCT
ejpam-6093	36	1	ternary	ternary	ADJ
ejpam-6093	36	2	semigroup	semigroup	PROPN
ejpam-6093	36	3	(	(	PUNCT
ejpam-6093	36	4	t	t	PROPN
ejpam-6093	36	5	,	,	PUNCT
ejpam-6093	36	6	[	[	PUNCT
ejpam-6093	36	7	]	]	X
ejpam-6093	36	8	,	,	PUNCT
ejpam-6093	36	9	≤	≤	NUM
ejpam-6093	36	10	)	)	PUNCT
ejpam-6093	36	11	is	be	AUX
ejpam-6093	36	12	said	say	VERB
ejpam-6093	36	13	to	to	PART
ejpam-6093	36	14	be	be	AUX
ejpam-6093	36	15	commutative	commutative	ADJ
ejpam-6093	36	16	if	if	SCONJ
ejpam-6093	36	17	[	[	X
ejpam-6093	36	18	xyz	xyz	X
ejpam-6093	36	19	]	]	X
ejpam-6093	36	20	=	=	PUNCT
ejpam-6093	37	1	[	[	X
ejpam-6093	37	2	yzx	yzx	X
ejpam-6093	37	3	]	]	X
ejpam-6093	37	4	=	=	PUNCT
ejpam-6093	38	1	[	[	X
ejpam-6093	38	2	zxy	zxy	X
ejpam-6093	38	3	]	]	X
ejpam-6093	38	4	=	=	PUNCT
ejpam-6093	39	1	[	[	X
ejpam-6093	39	2	yxz	yxz	X
ejpam-6093	39	3	]	]	X
ejpam-6093	39	4	=	=	SYM
ejpam-6093	40	1	[	[	X
ejpam-6093	40	2	zyx	zyx	X
ejpam-6093	40	3	]	]	X
ejpam-6093	40	4	=	=	PUNCT
ejpam-6093	41	1	[	[	X
ejpam-6093	41	2	xzy	xzy	X
ejpam-6093	41	3	]	]	X
ejpam-6093	41	4	for	for	ADP
ejpam-6093	41	5	all	all	DET
ejpam-6093	41	6	elements	element	NOUN
ejpam-6093	41	7	x	x	X
ejpam-6093	41	8	,	,	PUNCT
ejpam-6093	41	9	y	y	PROPN
ejpam-6093	41	10	,	,	PUNCT
ejpam-6093	41	11	z	z	PROPN
ejpam-6093	41	12	∈	∈	PROPN
ejpam-6093	41	13	t	t	NOUN
ejpam-6093	41	14	.	.	PUNCT
ejpam-6093	42	1	that	that	PRON
ejpam-6093	42	2	is	be	AUX
ejpam-6093	42	3	,	,	PUNCT
ejpam-6093	42	4	if	if	SCONJ
ejpam-6093	42	5	for	for	ADP
ejpam-6093	42	6	any	any	DET
ejpam-6093	42	7	x1	x1	PROPN
ejpam-6093	42	8	,	,	PUNCT
ejpam-6093	42	9	x2	x2	PROPN
ejpam-6093	42	10	,	,	PUNCT
ejpam-6093	42	11	x3	x3	PROPN
ejpam-6093	42	12	∈	∈	PROPN
ejpam-6093	42	13	t	t	NOUN
ejpam-6093	42	14	,	,	PUNCT
ejpam-6093	42	15	[	[	X
ejpam-6093	42	16	x1x2x3	x1x2x3	X
ejpam-6093	42	17	]	]	X
ejpam-6093	42	18	=	=	PUNCT
ejpam-6093	43	1	[	[	X
ejpam-6093	43	2	xσ(1)xσ(2)xσ(3	xσ(1)xσ(2)xσ(3	PROPN
ejpam-6093	43	3	)	)	PUNCT
ejpam-6093	43	4	]	]	PUNCT
ejpam-6093	43	5	for	for	ADP
ejpam-6093	43	6	any	any	DET
ejpam-6093	43	7	permutation	permutation	NOUN
ejpam-6093	43	8	σ	σ	NOUN
ejpam-6093	43	9	on	on	ADP
ejpam-6093	43	10	{	{	PUNCT
ejpam-6093	43	11	1	1	NUM
ejpam-6093	43	12	,	,	PUNCT
ejpam-6093	43	13	2	2	NUM
ejpam-6093	43	14	,	,	PUNCT
ejpam-6093	43	15	3	3	NUM
ejpam-6093	43	16	}	}	PUNCT
ejpam-6093	43	17	.	.	PUNCT
ejpam-6093	44	1	an	an	DET
ejpam-6093	44	2	n.p.o	n.p.o	NOUN
ejpam-6093	44	3	.	.	PUNCT
ejpam-6093	45	1	ternary	ternary	ADJ
ejpam-6093	45	2	semigroup	semigroup	PROPN
ejpam-6093	45	3	(	(	PUNCT
ejpam-6093	45	4	t	t	PROPN
ejpam-6093	45	5	,	,	PUNCT
ejpam-6093	45	6	[	[	PUNCT
ejpam-6093	45	7	]	]	X
ejpam-6093	45	8	,	,	PUNCT
ejpam-6093	45	9	≤	≤	NUM
ejpam-6093	45	10	)	)	PUNCT
ejpam-6093	45	11	with	with	ADP
ejpam-6093	45	12	an	an	DET
ejpam-6093	45	13	additional	additional	ADJ
ejpam-6093	45	14	ternary	ternary	ADJ
ejpam-6093	45	15	multiplication	multiplication	NOUN
ejpam-6093	45	16	[	[	PUNCT
ejpam-6093	45	17	]	]	X
ejpam-6093	45	18	∗	∗	NOUN
ejpam-6093	45	19	on	on	ADP
ejpam-6093	45	20	t	t	PROPN
ejpam-6093	45	21	such	such	ADJ
ejpam-6093	45	22	that	that	SCONJ
ejpam-6093	45	23	u	u	PROPN
ejpam-6093	45	24	≤	≤	X
ejpam-6093	46	1	[	[	X
ejpam-6093	46	2	xyz]∗	xyz]∗	X
ejpam-6093	46	3	⇐	⇐	ADJ
ejpam-6093	46	4	⇒	⇒	PROPN
ejpam-6093	46	5	[	[	X
ejpam-6093	46	6	uxy	uxy	X
ejpam-6093	46	7	]	]	X
ejpam-6093	46	8	≤	≤	ADJ
ejpam-6093	46	9	z	z	NOUN
ejpam-6093	46	10	for	for	ADP
ejpam-6093	46	11	any	any	DET
ejpam-6093	46	12	x	x	NOUN
ejpam-6093	46	13	,	,	PUNCT
ejpam-6093	46	14	y	y	PROPN
ejpam-6093	46	15	,	,	PUNCT
ejpam-6093	46	16	z	z	PROPN
ejpam-6093	46	17	,	,	PUNCT
ejpam-6093	46	18	u	u	PROPN
ejpam-6093	46	19	∈	∈	PROPN
ejpam-6093	46	20	t	t	PROPN
ejpam-6093	46	21	is	be	AUX
ejpam-6093	46	22	called	call	VERB
ejpam-6093	46	23	an	an	DET
ejpam-6093	46	24	implicative	implicative	ADJ
ejpam-6093	46	25	n.p.o	n.p.o	NOUN
ejpam-6093	46	26	.	.	PUNCT
ejpam-6093	47	1	ternary	ternary	PROPN
ejpam-6093	47	2	semigroup	semigroup	PROPN
ejpam-6093	47	3	.	.	PUNCT
ejpam-6093	48	1	the	the	DET
ejpam-6093	48	2	ternary	ternary	ADJ
ejpam-6093	48	3	multiplication	multiplication	NOUN
ejpam-6093	48	4	[	[	PUNCT
ejpam-6093	48	5	]	]	PUNCT
ejpam-6093	48	6	∗	∗	NOUN
ejpam-6093	48	7	is	be	AUX
ejpam-6093	48	8	called	call	VERB
ejpam-6093	48	9	a	a	DET
ejpam-6093	48	10	ternary	ternary	ADJ
ejpam-6093	48	11	implication	implication	NOUN
ejpam-6093	48	12	.	.	PUNCT
ejpam-6093	49	1	an	an	DET
ejpam-6093	49	2	element	element	NOUN
ejpam-6093	49	3	1	1	NUM
ejpam-6093	49	4	of	of	ADP
ejpam-6093	49	5	an	an	DET
ejpam-6093	49	6	n.p.o	n.p.o	NOUN
ejpam-6093	49	7	.	.	PUNCT
ejpam-6093	50	1	ternary	ternary	ADJ
ejpam-6093	50	2	semigroup	semigroup	PROPN
ejpam-6093	50	3	(	(	PUNCT
ejpam-6093	50	4	t	t	PROPN
ejpam-6093	50	5	,	,	PUNCT
ejpam-6093	50	6	[	[	PUNCT
ejpam-6093	50	7	]	]	X
ejpam-6093	50	8	,	,	PUNCT
ejpam-6093	50	9	≤	≤	NUM
ejpam-6093	50	10	)	)	PUNCT
ejpam-6093	50	11	is	be	AUX
ejpam-6093	50	12	an	an	DET
ejpam-6093	50	13	identity	identity	NOUN
ejpam-6093	50	14	of	of	ADP
ejpam-6093	50	15	t	t	PROPN
ejpam-6093	50	16	if	if	SCONJ
ejpam-6093	50	17	[	[	X
ejpam-6093	50	18	11x	11x	NOUN
ejpam-6093	50	19	]	]	X
ejpam-6093	50	20	=	=	PUNCT
ejpam-6093	51	1	[	[	X
ejpam-6093	51	2	1x1	1x1	X
ejpam-6093	51	3	]	]	X
ejpam-6093	51	4	=	=	PUNCT
ejpam-6093	52	1	[	[	X
ejpam-6093	52	2	x11	x11	X
ejpam-6093	52	3	]	]	X
ejpam-6093	52	4	=	=	PUNCT
ejpam-6093	53	1	x	x	X
ejpam-6093	53	2	for	for	ADP
ejpam-6093	53	3	any	any	DET
ejpam-6093	53	4	x	x	SYM
ejpam-6093	53	5	∈	∈	PROPN
ejpam-6093	53	6	t	t	NOUN
ejpam-6093	53	7	.	.	PUNCT
ejpam-6093	54	1	not	not	PART
ejpam-6093	54	2	every	every	DET
ejpam-6093	54	3	n.p.o	n.p.o	NOUN
ejpam-6093	54	4	.	.	PUNCT
ejpam-6093	55	1	ternary	ternary	ADJ
ejpam-6093	55	2	semigroup	semigroup	NOUN
ejpam-6093	55	3	with	with	ADP
ejpam-6093	55	4	the	the	DET
ejpam-6093	55	5	same	same	ADJ
ejpam-6093	55	6	identity	identity	NOUN
ejpam-6093	55	7	and	and	CCONJ
ejpam-6093	55	8	greatest	great	ADJ
ejpam-6093	55	9	element	element	NOUN
ejpam-6093	55	10	admits	admit	VERB
ejpam-6093	55	11	the	the	DET
ejpam-6093	55	12	implicative	implicative	ADJ
ejpam-6093	55	13	structure	structure	NOUN
ejpam-6093	55	14	,	,	PUNCT
ejpam-6093	55	15	see	see	VERB
ejpam-6093	55	16	example	example	NOUN
ejpam-6093	55	17	2	2	NUM
ejpam-6093	55	18	in	in	ADP
ejpam-6093	55	19	[	[	X
ejpam-6093	55	20	4	4	NUM
ejpam-6093	55	21	]	]	PUNCT
ejpam-6093	55	22	.	.	PUNCT
ejpam-6093	56	1	furthermore	furthermore	ADV
ejpam-6093	56	2	,	,	PUNCT
ejpam-6093	56	3	the	the	DET
ejpam-6093	56	4	greatest	great	ADJ
ejpam-6093	56	5	element	element	NOUN
ejpam-6093	56	6	of	of	ADP
ejpam-6093	56	7	implicative	implicative	ADJ
ejpam-6093	56	8	n.p.o	n.p.o	NOUN
ejpam-6093	56	9	.	.	PUNCT
ejpam-6093	57	1	ternary	ternary	ADJ
ejpam-6093	57	2	semigroup	semigroup	NOUN
ejpam-6093	57	3	need	need	AUX
ejpam-6093	57	4	not	not	PART
ejpam-6093	57	5	be	be	AUX
ejpam-6093	57	6	identity	identity	NOUN
ejpam-6093	57	7	,	,	PUNCT
ejpam-6093	57	8	see	see	VERB
ejpam-6093	57	9	example	example	NOUN
ejpam-6093	57	10	1	1	NUM
ejpam-6093	57	11	in	in	ADP
ejpam-6093	57	12	[	[	X
ejpam-6093	57	13	4	4	NUM
ejpam-6093	57	14	]	]	PUNCT
ejpam-6093	57	15	.	.	PUNCT
ejpam-6093	58	1	let	let	AUX
ejpam-6093	58	2	(	(	PUNCT
ejpam-6093	58	3	t	t	NOUN
ejpam-6093	58	4	,	,	PUNCT
ejpam-6093	58	5	[	[	PUNCT
ejpam-6093	58	6	]	]	X
ejpam-6093	58	7	,	,	PUNCT
ejpam-6093	58	8	≤	≤	NUM
ejpam-6093	58	9	,	,	PUNCT
ejpam-6093	58	10	[	[	PUNCT
ejpam-6093	58	11	]	]	X
ejpam-6093	58	12	∗	∗	NOUN
ejpam-6093	58	13	)	)	PUNCT
ejpam-6093	58	14	be	be	VERB
ejpam-6093	58	15	an	an	DET
ejpam-6093	58	16	implicative	implicative	ADJ
ejpam-6093	58	17	n.p.o	n.p.o	NOUN
ejpam-6093	58	18	.	.	PUNCT
ejpam-6093	59	1	ternary	ternary	PROPN
ejpam-6093	59	2	semigroup	semigroup	PROPN
ejpam-6093	59	3	.	.	PUNCT
ejpam-6093	60	1	then	then	ADV
ejpam-6093	60	2	the	the	DET
ejpam-6093	60	3	following	follow	VERB
ejpam-6093	60	4	properties	property	NOUN
ejpam-6093	60	5	hold	hold	VERB
ejpam-6093	60	6	:	:	PUNCT
ejpam-6093	60	7	(	(	PUNCT
ejpam-6093	60	8	1	1	X
ejpam-6093	60	9	)	)	PUNCT
ejpam-6093	60	10	x	x	SYM
ejpam-6093	60	11	≤	≤	NOUN
ejpam-6093	61	1	[	[	X
ejpam-6093	61	2	xxx]∗	xxx]∗	X
ejpam-6093	61	3	;	;	PUNCT
ejpam-6093	61	4	k.	k.	PROPN
ejpam-6093	61	5	nakwan	nakwan	PROPN
ejpam-6093	61	6	,	,	PUNCT
ejpam-6093	61	7	p.	p.	PROPN
ejpam-6093	61	8	luangchaisri	luangchaisri	VERB
ejpam-6093	61	9	,	,	PUNCT
ejpam-6093	61	10	t.	t.	PROPN
ejpam-6093	61	11	changphas	changphas	PROPN
ejpam-6093	61	12	/	/	SYM
ejpam-6093	61	13	eur	eur	PROPN
ejpam-6093	61	14	.	.	PUNCT
ejpam-6093	62	1	j.	j.	PROPN
ejpam-6093	62	2	pure	pure	PROPN
ejpam-6093	62	3	appl	appl	PROPN
ejpam-6093	62	4	.	.	PROPN
ejpam-6093	62	5	math	math	PROPN
ejpam-6093	62	6	,	,	PUNCT
ejpam-6093	62	7	18	18	NUM
ejpam-6093	62	8	(	(	PUNCT
ejpam-6093	62	9	4	4	NUM
ejpam-6093	62	10	)	)	PUNCT
ejpam-6093	62	11	(	(	PUNCT
ejpam-6093	62	12	2025	2025	NUM
ejpam-6093	62	13	)	)	PUNCT
ejpam-6093	62	14	,	,	PUNCT
ejpam-6093	62	15	6093	6093	NUM
ejpam-6093	62	16	3	3	NUM
ejpam-6093	62	17	of	of	ADP
ejpam-6093	62	18	11	11	NUM
ejpam-6093	62	19	(	(	PUNCT
ejpam-6093	62	20	2	2	NUM
ejpam-6093	62	21	)	)	PUNCT
ejpam-6093	63	1	[	[	X
ejpam-6093	63	2	xxx]∗	xxx]∗	X
ejpam-6093	63	3	=	=	PUNCT
ejpam-6093	63	4	[	[	X
ejpam-6093	63	5	yyy]∗	yyy]∗	NOUN
ejpam-6093	63	6	;	;	PUNCT
ejpam-6093	63	7	(	(	PUNCT
ejpam-6093	63	8	3	3	X
ejpam-6093	63	9	)	)	PUNCT
ejpam-6093	63	10	t	t	NOUN
ejpam-6093	63	11	contains	contain	VERB
ejpam-6093	63	12	the	the	DET
ejpam-6093	63	13	greatest	great	ADJ
ejpam-6093	63	14	element	element	NOUN
ejpam-6093	63	15	,	,	PUNCT
ejpam-6093	63	16	namely	namely	ADV
ejpam-6093	63	17	[	[	X
ejpam-6093	63	18	xxx]∗	xxx]∗	NUM
ejpam-6093	63	19	,	,	PUNCT
ejpam-6093	63	20	for	for	ADP
ejpam-6093	63	21	any	any	DET
ejpam-6093	63	22	x	x	NOUN
ejpam-6093	63	23	,	,	PUNCT
ejpam-6093	63	24	y	y	PROPN
ejpam-6093	63	25	∈	∈	PROPN
ejpam-6093	63	26	t	t	PROPN
ejpam-6093	63	27	.	.	PUNCT
ejpam-6093	64	1	let	let	VERB
ejpam-6093	64	2	1	1	NUM
ejpam-6093	64	3	be	be	AUX
ejpam-6093	64	4	the	the	DET
ejpam-6093	64	5	greatest	great	ADJ
ejpam-6093	64	6	element	element	NOUN
ejpam-6093	64	7	of	of	ADP
ejpam-6093	64	8	an	an	DET
ejpam-6093	64	9	n.p.o	n.p.o	NOUN
ejpam-6093	64	10	.	.	PUNCT
ejpam-6093	65	1	ternary	ternary	ADJ
ejpam-6093	65	2	semigroup	semigroup	PROPN
ejpam-6093	65	3	(	(	PUNCT
ejpam-6093	65	4	t	t	PROPN
ejpam-6093	65	5	,	,	PUNCT
ejpam-6093	65	6	[	[	PUNCT
ejpam-6093	65	7	]	]	X
ejpam-6093	65	8	,	,	PUNCT
ejpam-6093	65	9	≤	≤	NUM
ejpam-6093	65	10	)	)	PUNCT
ejpam-6093	65	11	if	if	SCONJ
ejpam-6093	65	12	exists	exist	VERB
ejpam-6093	65	13	.	.	PUNCT
ejpam-6093	66	1	it	it	PRON
ejpam-6093	66	2	is	be	AUX
ejpam-6093	66	3	observed	observe	VERB
ejpam-6093	66	4	that	that	SCONJ
ejpam-6093	66	5	if	if	SCONJ
ejpam-6093	66	6	1	1	NUM
ejpam-6093	66	7	is	be	AUX
ejpam-6093	66	8	the	the	DET
ejpam-6093	66	9	multiplicative	multiplicative	ADJ
ejpam-6093	66	10	identity	identity	NOUN
ejpam-6093	66	11	then	then	ADV
ejpam-6093	66	12	it	it	PRON
ejpam-6093	66	13	can	can	AUX
ejpam-6093	66	14	be	be	AUX
ejpam-6093	66	15	verified	verify	VERB
ejpam-6093	66	16	that	that	SCONJ
ejpam-6093	66	17	[	[	X
ejpam-6093	66	18	xyz	xyz	X
ejpam-6093	66	19	]	]	X
ejpam-6093	66	20	=	=	SYM
ejpam-6093	66	21	1	1	NUM
ejpam-6093	66	22	if	if	SCONJ
ejpam-6093	66	23	and	and	CCONJ
ejpam-6093	66	24	only	only	ADV
ejpam-6093	66	25	if	if	SCONJ
ejpam-6093	66	26	x	x	NOUN
ejpam-6093	66	27	=	=	PUNCT
ejpam-6093	66	28	y	y	NOUN
ejpam-6093	66	29	=	=	PUNCT
ejpam-6093	66	30	z	z	NOUN
ejpam-6093	66	31	=	=	SYM
ejpam-6093	66	32	1	1	NUM
ejpam-6093	66	33	for	for	ADP
ejpam-6093	66	34	any	any	DET
ejpam-6093	66	35	x	x	NOUN
ejpam-6093	66	36	,	,	PUNCT
ejpam-6093	66	37	y	y	PROPN
ejpam-6093	66	38	,	,	PUNCT
ejpam-6093	66	39	z	z	PROPN
ejpam-6093	66	40	∈	∈	PROPN
ejpam-6093	66	41	t	t	NOUN
ejpam-6093	66	42	.	.	PUNCT
ejpam-6093	67	1	throughout	throughout	ADP
ejpam-6093	67	2	the	the	DET
ejpam-6093	67	3	paper	paper	NOUN
ejpam-6093	67	4	,	,	PUNCT
ejpam-6093	67	5	we	we	PRON
ejpam-6093	67	6	deal	deal	VERB
ejpam-6093	67	7	with	with	ADP
ejpam-6093	67	8	an	an	DET
ejpam-6093	67	9	implicative	implicative	ADJ
ejpam-6093	67	10	n.p.o	n.p.o	NOUN
ejpam-6093	67	11	.	.	PUNCT
ejpam-6093	68	1	ternary	ternary	PROPN
ejpam-6093	68	2	semigroup	semigroup	NOUN
ejpam-6093	68	3	with	with	ADP
ejpam-6093	68	4	1	1	NUM
ejpam-6093	68	5	which	which	PRON
ejpam-6093	68	6	is	be	AUX
ejpam-6093	68	7	both	both	CCONJ
ejpam-6093	68	8	the	the	DET
ejpam-6093	68	9	greatest	great	ADJ
ejpam-6093	68	10	element	element	NOUN
ejpam-6093	68	11	and	and	CCONJ
ejpam-6093	68	12	the	the	DET
ejpam-6093	68	13	identity	identity	NOUN
ejpam-6093	68	14	.	.	PUNCT
ejpam-6093	69	1	the	the	DET
ejpam-6093	69	2	following	follow	VERB
ejpam-6093	69	3	theorem	theorem	NOUN
ejpam-6093	69	4	collects	collect	VERB
ejpam-6093	69	5	several	several	ADJ
ejpam-6093	69	6	properties	property	NOUN
ejpam-6093	69	7	of	of	ADP
ejpam-6093	69	8	elements	element	NOUN
ejpam-6093	69	9	of	of	ADP
ejpam-6093	69	10	implicative	implicative	ADJ
ejpam-6093	69	11	n.p.o	n.p.o	NOUN
ejpam-6093	69	12	.	.	PUNCT
ejpam-6093	70	1	ternary	ternary	ADJ
ejpam-6093	70	2	semigroups	semigroup	NOUN
ejpam-6093	70	3	.	.	PUNCT
ejpam-6093	70	4	theorem	theorem	NOUN
ejpam-6093	70	5	1	1	NUM
ejpam-6093	70	6	.	.	PUNCT
ejpam-6093	71	1	[	[	X
ejpam-6093	71	2	4	4	X
ejpam-6093	71	3	]	]	X
ejpam-6093	71	4	let	let	NOUN
ejpam-6093	71	5	(	(	PUNCT
ejpam-6093	71	6	t	t	NOUN
ejpam-6093	71	7	,	,	PUNCT
ejpam-6093	71	8	[	[	PUNCT
ejpam-6093	71	9	]	]	X
ejpam-6093	71	10	,	,	PUNCT
ejpam-6093	71	11	≤	≤	NUM
ejpam-6093	71	12	,	,	PUNCT
ejpam-6093	71	13	[	[	PUNCT
ejpam-6093	71	14	]	]	X
ejpam-6093	71	15	∗	∗	NOUN
ejpam-6093	71	16	)	)	PUNCT
ejpam-6093	71	17	be	be	VERB
ejpam-6093	71	18	an	an	DET
ejpam-6093	71	19	implicative	implicative	ADJ
ejpam-6093	71	20	n.p.o	n.p.o	NOUN
ejpam-6093	71	21	.	.	PUNCT
ejpam-6093	72	1	ternary	ternary	PROPN
ejpam-6093	72	2	semigroup	semigroup	PROPN
ejpam-6093	72	3	.	.	PUNCT
ejpam-6093	73	1	then	then	ADV
ejpam-6093	73	2	for	for	ADP
ejpam-6093	73	3	any	any	DET
ejpam-6093	73	4	x	x	NOUN
ejpam-6093	73	5	,	,	PUNCT
ejpam-6093	73	6	y	y	PROPN
ejpam-6093	73	7	,	,	PUNCT
ejpam-6093	73	8	z	z	PROPN
ejpam-6093	73	9	,	,	PUNCT
ejpam-6093	73	10	u	u	NOUN
ejpam-6093	73	11	,	,	PUNCT
ejpam-6093	73	12	v	v	PROPN
ejpam-6093	73	13	∈	∈	PROPN
ejpam-6093	73	14	t	t	NOUN
ejpam-6093	73	15	,	,	PUNCT
ejpam-6093	73	16	the	the	DET
ejpam-6093	73	17	following	follow	VERB
ejpam-6093	73	18	conditions	condition	NOUN
ejpam-6093	73	19	hold	hold	VERB
ejpam-6093	73	20	:	:	PUNCT
ejpam-6093	73	21	(	(	PUNCT
ejpam-6093	73	22	1	1	X
ejpam-6093	73	23	)	)	PUNCT
ejpam-6093	73	24	x	x	SYM
ejpam-6093	73	25	≤	≤	NUM
ejpam-6093	73	26	1	1	NUM
ejpam-6093	73	27	,	,	PUNCT
ejpam-6093	73	28	[	[	X
ejpam-6093	73	29	xxx]∗	xxx]∗	X
ejpam-6093	73	30	=	=	SYM
ejpam-6093	73	31	1	1	NUM
ejpam-6093	73	32	,	,	PUNCT
ejpam-6093	73	33	x	x	PUNCT
ejpam-6093	73	34	=	=	PUNCT
ejpam-6093	74	1	[	[	X
ejpam-6093	74	2	11x]∗	11x]∗	NUM
ejpam-6093	74	3	;	;	PUNCT
ejpam-6093	74	4	(	(	PUNCT
ejpam-6093	74	5	2	2	X
ejpam-6093	74	6	)	)	PUNCT
ejpam-6093	74	7	x	x	SYM
ejpam-6093	74	8	≤	≤	NOUN
ejpam-6093	75	1	[	[	X
ejpam-6093	75	2	yz[xyz]]∗	yz[xyz]]∗	NOUN
ejpam-6093	75	3	;	;	PUNCT
ejpam-6093	75	4	(	(	PUNCT
ejpam-6093	75	5	3	3	X
ejpam-6093	75	6	)	)	PUNCT
ejpam-6093	75	7	x	x	SYM
ejpam-6093	75	8	≤	≤	PUNCT
ejpam-6093	76	1	[	[	X
ejpam-6093	76	2	xx[xxx]]∗	xx[xxx]]∗	NOUN
ejpam-6093	76	3	;	;	PUNCT
ejpam-6093	76	4	(	(	PUNCT
ejpam-6093	76	5	4	4	X
ejpam-6093	76	6	)	)	PUNCT
ejpam-6093	76	7	x	x	SYM
ejpam-6093	76	8	≤	≤	NOUN
ejpam-6093	77	1	[	[	X
ejpam-6093	77	2	yzx]∗	yzx]∗	NOUN
ejpam-6093	77	3	;	;	PUNCT
ejpam-6093	77	4	(	(	PUNCT
ejpam-6093	77	5	5	5	X
ejpam-6093	77	6	)	)	PUNCT
ejpam-6093	77	7	if	if	SCONJ
ejpam-6093	77	8	x	x	PROPN
ejpam-6093	77	9	≤	≤	NOUN
ejpam-6093	77	10	y	y	NOUN
ejpam-6093	77	11	,	,	PUNCT
ejpam-6093	77	12	then	then	ADV
ejpam-6093	77	13	[	[	X
ejpam-6093	77	14	xuv]∗	xuv]∗	X
ejpam-6093	77	15	≥	≥	PRON
ejpam-6093	77	16	[	[	X
ejpam-6093	77	17	yuv]∗	yuv]∗	X
ejpam-6093	77	18	and	and	CCONJ
ejpam-6093	77	19	[	[	X
ejpam-6093	77	20	uvx]∗	uvx]∗	X
ejpam-6093	77	21	≤	≤	X
ejpam-6093	78	1	[	[	X
ejpam-6093	78	2	uvy]∗	uvy]∗	NOUN
ejpam-6093	78	3	;	;	PUNCT
ejpam-6093	78	4	(	(	PUNCT
ejpam-6093	78	5	6	6	NUM
ejpam-6093	78	6	)	)	PUNCT
ejpam-6093	78	7	x	x	PUNCT
ejpam-6093	78	8	≤	≤	NUM
ejpam-6093	78	9	y	y	NUM
ejpam-6093	78	10	⇐	⇐	ADJ
ejpam-6093	78	11	⇒	⇒	PROPN
ejpam-6093	78	12	[	[	X
ejpam-6093	78	13	x1y]∗	x1y]∗	NOUN
ejpam-6093	78	14	=	=	SYM
ejpam-6093	78	15	1	1	NUM
ejpam-6093	78	16	⇐	⇐	ADJ
ejpam-6093	78	17	⇒	⇒	NOUN
ejpam-6093	78	18	[	[	X
ejpam-6093	78	19	1xy]∗	1xy]∗	NUM
ejpam-6093	78	20	=	=	SYM
ejpam-6093	78	21	1	1	NUM
ejpam-6093	78	22	;	;	PUNCT
ejpam-6093	78	23	(	(	PUNCT
ejpam-6093	78	24	7	7	X
ejpam-6093	78	25	)	)	PUNCT
ejpam-6093	79	1	[	[	X
ejpam-6093	79	2	xy[zuv]∗]∗	xy[zuv]∗]∗	X
ejpam-6093	79	3	=	=	PUNCT
ejpam-6093	80	1	[	[	X
ejpam-6093	80	2	[	[	X
ejpam-6093	80	3	xyz]uv]∗	xyz]uv]∗	X
ejpam-6093	80	4	=	=	PUNCT
ejpam-6093	81	1	[	[	X
ejpam-6093	81	2	x[yzu]v]∗.	x[yzu]v]∗.	NUM
ejpam-6093	81	3	definition	definition	NOUN
ejpam-6093	81	4	1	1	NUM
ejpam-6093	81	5	.	.	PUNCT
ejpam-6093	82	1	[	[	X
ejpam-6093	82	2	4	4	X
ejpam-6093	82	3	]	]	X
ejpam-6093	82	4	let	let	NOUN
ejpam-6093	82	5	(	(	PUNCT
ejpam-6093	82	6	t	t	NOUN
ejpam-6093	82	7	,	,	PUNCT
ejpam-6093	82	8	[	[	PUNCT
ejpam-6093	82	9	]	]	X
ejpam-6093	82	10	,	,	PUNCT
ejpam-6093	82	11	≤	≤	NUM
ejpam-6093	82	12	,	,	PUNCT
ejpam-6093	82	13	[	[	PUNCT
ejpam-6093	82	14	]	]	X
ejpam-6093	82	15	∗	∗	NOUN
ejpam-6093	82	16	)	)	PUNCT
ejpam-6093	82	17	be	be	VERB
ejpam-6093	82	18	an	an	DET
ejpam-6093	82	19	implicative	implicative	ADJ
ejpam-6093	82	20	n.p.o	n.p.o	NOUN
ejpam-6093	82	21	.	.	PUNCT
ejpam-6093	83	1	ternary	ternary	PROPN
ejpam-6093	83	2	semigroup	semigroup	PROPN
ejpam-6093	83	3	.	.	PUNCT
ejpam-6093	84	1	a	a	DET
ejpam-6093	84	2	nonempty	nonempty	NOUN
ejpam-6093	84	3	subset	subset	VERB
ejpam-6093	84	4	f	f	PROPN
ejpam-6093	84	5	of	of	ADP
ejpam-6093	84	6	t	t	PROPN
ejpam-6093	84	7	is	be	AUX
ejpam-6093	84	8	called	call	VERB
ejpam-6093	84	9	a	a	DET
ejpam-6093	84	10	filter	filter	NOUN
ejpam-6093	84	11	of	of	ADP
ejpam-6093	84	12	t	t	PROPN
ejpam-6093	84	13	if	if	SCONJ
ejpam-6093	84	14	the	the	DET
ejpam-6093	84	15	following	follow	VERB
ejpam-6093	84	16	conditions	condition	NOUN
ejpam-6093	84	17	hold	hold	VERB
ejpam-6093	84	18	:	:	PUNCT
ejpam-6093	84	19	(	(	PUNCT
ejpam-6093	84	20	f1	f1	NOUN
ejpam-6093	84	21	)	)	PUNCT
ejpam-6093	85	1	[	[	X
ejpam-6093	85	2	xyz	xyz	X
ejpam-6093	85	3	]	]	X
ejpam-6093	85	4	∈	∈	PROPN
ejpam-6093	85	5	f	f	PROPN
ejpam-6093	85	6	for	for	ADP
ejpam-6093	85	7	any	any	DET
ejpam-6093	85	8	x	x	NOUN
ejpam-6093	85	9	,	,	PUNCT
ejpam-6093	85	10	y	y	PROPN
ejpam-6093	85	11	,	,	PUNCT
ejpam-6093	85	12	z	z	PROPN
ejpam-6093	85	13	∈	∈	PROPN
ejpam-6093	85	14	f	f	X
ejpam-6093	85	15	,	,	PUNCT
ejpam-6093	85	16	that	that	PRON
ejpam-6093	85	17	is	is	ADV
ejpam-6093	85	18	f	f	PROPN
ejpam-6093	85	19	is	be	AUX
ejpam-6093	85	20	a	a	DET
ejpam-6093	85	21	ternary	ternary	ADJ
ejpam-6093	85	22	subsemigroup	subsemigroup	NOUN
ejpam-6093	85	23	of	of	ADP
ejpam-6093	85	24	t	t	PROPN
ejpam-6093	85	25	;	;	PUNCT
ejpam-6093	85	26	(	(	PUNCT
ejpam-6093	85	27	f2	f2	X
ejpam-6093	85	28	)	)	PUNCT
ejpam-6093	85	29	for	for	ADP
ejpam-6093	85	30	any	any	DET
ejpam-6093	85	31	x	x	NOUN
ejpam-6093	85	32	,	,	PUNCT
ejpam-6093	85	33	y	y	PROPN
ejpam-6093	85	34	∈	∈	PROPN
ejpam-6093	85	35	t	t	NOUN
ejpam-6093	85	36	,	,	PUNCT
ejpam-6093	85	37	if	if	SCONJ
ejpam-6093	85	38	x	x	ADP
ejpam-6093	85	39	≤	≤	ADJ
ejpam-6093	85	40	y	y	PROPN
ejpam-6093	85	41	and	and	CCONJ
ejpam-6093	85	42	x	x	SYM
ejpam-6093	85	43	∈	∈	PROPN
ejpam-6093	85	44	f	f	PROPN
ejpam-6093	85	45	,	,	PUNCT
ejpam-6093	85	46	then	then	ADV
ejpam-6093	85	47	y	y	PROPN
ejpam-6093	85	48	∈	∈	PROPN
ejpam-6093	85	49	f	f	X
ejpam-6093	85	50	.	.	PUNCT
ejpam-6093	86	1	3	3	X
ejpam-6093	86	2	.	.	X
ejpam-6093	86	3	implicative	implicative	ADJ
ejpam-6093	86	4	filters	filter	NOUN
ejpam-6093	86	5	we	we	PRON
ejpam-6093	86	6	begin	begin	VERB
ejpam-6093	86	7	this	this	DET
ejpam-6093	86	8	section	section	NOUN
ejpam-6093	86	9	with	with	ADP
ejpam-6093	86	10	characterizations	characterization	NOUN
ejpam-6093	86	11	of	of	ADP
ejpam-6093	86	12	filters	filter	NOUN
ejpam-6093	86	13	in	in	ADP
ejpam-6093	86	14	implicative	implicative	ADJ
ejpam-6093	86	15	and	and	CCONJ
ejpam-6093	86	16	commutative	commutative	ADJ
ejpam-6093	86	17	implicative	implicative	ADJ
ejpam-6093	86	18	n.p.o	n.p.o	NOUN
ejpam-6093	86	19	.	.	PUNCT
ejpam-6093	87	1	ternary	ternary	ADJ
ejpam-6093	87	2	semigroups	semigroup	NOUN
ejpam-6093	87	3	.	.	PUNCT
ejpam-6093	88	1	theorem	theorem	NOUN
ejpam-6093	88	2	2	2	NUM
ejpam-6093	88	3	.	.	PUNCT
ejpam-6093	89	1	let	let	AUX
ejpam-6093	89	2	(	(	PUNCT
ejpam-6093	89	3	t	t	NOUN
ejpam-6093	89	4	,	,	PUNCT
ejpam-6093	89	5	[	[	PUNCT
ejpam-6093	89	6	]	]	X
ejpam-6093	89	7	,	,	PUNCT
ejpam-6093	89	8	≤	≤	NUM
ejpam-6093	89	9	,	,	PUNCT
ejpam-6093	89	10	[	[	PUNCT
ejpam-6093	89	11	]	]	X
ejpam-6093	89	12	∗	∗	NOUN
ejpam-6093	89	13	)	)	PUNCT
ejpam-6093	89	14	be	be	VERB
ejpam-6093	89	15	an	an	DET
ejpam-6093	89	16	implicative	implicative	ADJ
ejpam-6093	89	17	n.p.o	n.p.o	NOUN
ejpam-6093	89	18	.	.	PUNCT
ejpam-6093	90	1	ternary	ternary	PROPN
ejpam-6093	90	2	semigroup	semigroup	PROPN
ejpam-6093	90	3	.	.	PUNCT
ejpam-6093	91	1	a	a	DET
ejpam-6093	91	2	non	non	ADJ
ejpam-6093	91	3	-	-	ADJ
ejpam-6093	91	4	empty	empty	ADJ
ejpam-6093	91	5	subset	subset	NOUN
ejpam-6093	91	6	f	f	PROPN
ejpam-6093	91	7	of	of	ADP
ejpam-6093	91	8	t	t	PROPN
ejpam-6093	91	9	is	be	AUX
ejpam-6093	91	10	a	a	DET
ejpam-6093	91	11	filter	filter	NOUN
ejpam-6093	91	12	if	if	SCONJ
ejpam-6093	92	1	and	and	CCONJ
ejpam-6093	92	2	only	only	ADV
ejpam-6093	92	3	if	if	SCONJ
ejpam-6093	92	4	it	it	PRON
ejpam-6093	92	5	satisfies	satisfy	VERB
ejpam-6093	92	6	the	the	DET
ejpam-6093	92	7	following	follow	VERB
ejpam-6093	92	8	conditions	condition	NOUN
ejpam-6093	92	9	:	:	PUNCT
ejpam-6093	93	1	(	(	PUNCT
ejpam-6093	93	2	f3	f3	ADJ
ejpam-6093	93	3	)	)	PUNCT
ejpam-6093	93	4	1	1	NUM
ejpam-6093	93	5	∈	∈	PROPN
ejpam-6093	93	6	f	f	NOUN
ejpam-6093	93	7	;	;	PUNCT
ejpam-6093	93	8	(	(	PUNCT
ejpam-6093	93	9	f4	f4	NOUN
ejpam-6093	93	10	)	)	PUNCT
ejpam-6093	93	11	for	for	ADP
ejpam-6093	93	12	any	any	DET
ejpam-6093	93	13	x	x	NOUN
ejpam-6093	93	14	,	,	PUNCT
ejpam-6093	93	15	y	y	PROPN
ejpam-6093	93	16	,	,	PUNCT
ejpam-6093	93	17	z	z	PROPN
ejpam-6093	93	18	∈	∈	PROPN
ejpam-6093	93	19	t	t	NOUN
ejpam-6093	93	20	,	,	PUNCT
ejpam-6093	93	21	if	if	SCONJ
ejpam-6093	93	22	[	[	X
ejpam-6093	93	23	xyz]∗	xyz]∗	X
ejpam-6093	93	24	∈	∈	PROPN
ejpam-6093	93	25	f	f	PROPN
ejpam-6093	93	26	and	and	CCONJ
ejpam-6093	93	27	x	x	NOUN
ejpam-6093	93	28	,	,	PUNCT
ejpam-6093	93	29	y	y	PROPN
ejpam-6093	93	30	∈	∈	PROPN
ejpam-6093	93	31	f	f	PROPN
ejpam-6093	93	32	,	,	PUNCT
ejpam-6093	93	33	then	then	ADV
ejpam-6093	93	34	z	z	PROPN
ejpam-6093	93	35	∈	∈	PROPN
ejpam-6093	93	36	f	f	X
ejpam-6093	93	37	.	.	PUNCT
ejpam-6093	94	1	k.	k.	PROPN
ejpam-6093	94	2	nakwan	nakwan	PROPN
ejpam-6093	94	3	,	,	PUNCT
ejpam-6093	94	4	p.	p.	PROPN
ejpam-6093	94	5	luangchaisri	luangchaisri	VERB
ejpam-6093	94	6	,	,	PUNCT
ejpam-6093	94	7	t.	t.	PROPN
ejpam-6093	94	8	changphas	changphas	PROPN
ejpam-6093	94	9	/	/	SYM
ejpam-6093	94	10	eur	eur	PROPN
ejpam-6093	94	11	.	.	PUNCT
ejpam-6093	95	1	j.	j.	PROPN
ejpam-6093	95	2	pure	pure	PROPN
ejpam-6093	95	3	appl	appl	PROPN
ejpam-6093	95	4	.	.	PROPN
ejpam-6093	95	5	math	math	PROPN
ejpam-6093	95	6	,	,	PUNCT
ejpam-6093	95	7	18	18	NUM
ejpam-6093	95	8	(	(	PUNCT
ejpam-6093	95	9	4	4	NUM
ejpam-6093	95	10	)	)	PUNCT
ejpam-6093	95	11	(	(	PUNCT
ejpam-6093	95	12	2025	2025	NUM
ejpam-6093	95	13	)	)	PUNCT
ejpam-6093	95	14	,	,	PUNCT
ejpam-6093	95	15	6093	6093	NUM
ejpam-6093	95	16	4	4	NUM
ejpam-6093	95	17	of	of	ADP
ejpam-6093	95	18	11	11	NUM
ejpam-6093	95	19	proof	proof	NOUN
ejpam-6093	95	20	.	.	PUNCT
ejpam-6093	96	1	assume	assume	VERB
ejpam-6093	96	2	that	that	SCONJ
ejpam-6093	96	3	f	f	PROPN
ejpam-6093	96	4	is	be	AUX
ejpam-6093	96	5	a	a	DET
ejpam-6093	96	6	filter	filter	NOUN
ejpam-6093	96	7	of	of	ADP
ejpam-6093	96	8	t	t	PROPN
ejpam-6093	96	9	.	.	PUNCT
ejpam-6093	97	1	since	since	SCONJ
ejpam-6093	97	2	1	1	NUM
ejpam-6093	97	3	is	be	AUX
ejpam-6093	97	4	the	the	DET
ejpam-6093	97	5	greatest	great	ADJ
ejpam-6093	97	6	element	element	NOUN
ejpam-6093	97	7	of	of	ADP
ejpam-6093	97	8	t	t	PROPN
ejpam-6093	97	9	,	,	PUNCT
ejpam-6093	97	10	1	1	NUM
ejpam-6093	97	11	∈	∈	PROPN
ejpam-6093	97	12	f	f	X
ejpam-6093	97	13	.	.	PUNCT
ejpam-6093	98	1	let	let	VERB
ejpam-6093	98	2	x	x	PRON
ejpam-6093	98	3	,	,	PUNCT
ejpam-6093	98	4	y	y	PROPN
ejpam-6093	98	5	,	,	PUNCT
ejpam-6093	98	6	z	z	PROPN
ejpam-6093	98	7	∈	∈	PROPN
ejpam-6093	98	8	t	t	NOUN
ejpam-6093	98	9	be	be	AUX
ejpam-6093	98	10	such	such	ADJ
ejpam-6093	98	11	that	that	SCONJ
ejpam-6093	98	12	[	[	X
ejpam-6093	98	13	xyz]∗	xyz]∗	X
ejpam-6093	98	14	∈	∈	PROPN
ejpam-6093	98	15	f	f	PROPN
ejpam-6093	98	16	and	and	CCONJ
ejpam-6093	98	17	x	x	NOUN
ejpam-6093	98	18	,	,	PUNCT
ejpam-6093	98	19	y	y	PROPN
ejpam-6093	98	20	∈	∈	PROPN
ejpam-6093	98	21	f	f	X
ejpam-6093	98	22	.	.	PUNCT
ejpam-6093	99	1	by	by	ADP
ejpam-6093	99	2	[	[	X
ejpam-6093	99	3	xyz]∗	xyz]∗	X
ejpam-6093	99	4	≤	≤	NOUN
ejpam-6093	100	1	[	[	X
ejpam-6093	100	2	xyz]∗	xyz]∗	X
ejpam-6093	100	3	,	,	PUNCT
ejpam-6093	100	4	[	[	X
ejpam-6093	100	5	[	[	X
ejpam-6093	100	6	xyz]∗xy	xyz]∗xy	X
ejpam-6093	100	7	]	]	X
ejpam-6093	100	8	≤	≤	NUM
ejpam-6093	100	9	z.	z.	X
ejpam-6093	100	10	by	by	ADP
ejpam-6093	100	11	(	(	PUNCT
ejpam-6093	100	12	f1	f1	NOUN
ejpam-6093	100	13	)	)	PUNCT
ejpam-6093	100	14	,	,	PUNCT
ejpam-6093	101	1	[	[	X
ejpam-6093	101	2	[	[	X
ejpam-6093	101	3	xyz]∗xy	xyz]∗xy	X
ejpam-6093	101	4	]	]	X
ejpam-6093	101	5	∈	∈	PROPN
ejpam-6093	101	6	f	f	NOUN
ejpam-6093	101	7	;	;	PUNCT
ejpam-6093	101	8	hence	hence	ADV
ejpam-6093	101	9	z	z	NOUN
ejpam-6093	101	10	∈	∈	PROPN
ejpam-6093	101	11	f	f	X
ejpam-6093	101	12	by	by	ADP
ejpam-6093	101	13	(	(	PUNCT
ejpam-6093	101	14	f2	f2	PROPN
ejpam-6093	101	15	)	)	PUNCT
ejpam-6093	101	16	.	.	PUNCT
ejpam-6093	102	1	conversely	conversely	ADV
ejpam-6093	102	2	,	,	PUNCT
ejpam-6093	102	3	assume	assume	VERB
ejpam-6093	102	4	that	that	SCONJ
ejpam-6093	102	5	f	f	PROPN
ejpam-6093	102	6	satisfies	satisfie	NOUN
ejpam-6093	102	7	(	(	PUNCT
ejpam-6093	102	8	f3	f3	ADJ
ejpam-6093	102	9	)	)	PUNCT
ejpam-6093	102	10	and	and	CCONJ
ejpam-6093	102	11	(	(	PUNCT
ejpam-6093	102	12	f4	f4	NOUN
ejpam-6093	102	13	)	)	PUNCT
ejpam-6093	102	14	.	.	PUNCT
ejpam-6093	103	1	let	let	VERB
ejpam-6093	103	2	x	x	PRON
ejpam-6093	103	3	,	,	PUNCT
ejpam-6093	103	4	y	y	PROPN
ejpam-6093	103	5	∈	∈	PROPN
ejpam-6093	103	6	t	t	NOUN
ejpam-6093	103	7	such	such	ADJ
ejpam-6093	103	8	that	that	SCONJ
ejpam-6093	103	9	x	x	X
ejpam-6093	103	10	≤	≤	ADJ
ejpam-6093	103	11	y	y	PROPN
ejpam-6093	103	12	and	and	CCONJ
ejpam-6093	103	13	x	x	SYM
ejpam-6093	103	14	∈	∈	PROPN
ejpam-6093	103	15	f	f	X
ejpam-6093	103	16	.	.	PUNCT
ejpam-6093	104	1	by	by	ADP
ejpam-6093	104	2	theorem	theorem	NOUN
ejpam-6093	104	3	1	1	NUM
ejpam-6093	104	4	(	(	PUNCT
ejpam-6093	104	5	6	6	NUM
ejpam-6093	104	6	)	)	PUNCT
ejpam-6093	104	7	,	,	PUNCT
ejpam-6093	104	8	[	[	X
ejpam-6093	104	9	1xy]∗	1xy]∗	NUM
ejpam-6093	104	10	=	=	SYM
ejpam-6093	104	11	1	1	NUM
ejpam-6093	104	12	.	.	PUNCT
ejpam-6093	105	1	then	then	ADV
ejpam-6093	105	2	[	[	X
ejpam-6093	105	3	1xy]∗	1xy]∗	NUM
ejpam-6093	105	4	∈	∈	ADJ
ejpam-6093	105	5	f	f	X
ejpam-6093	105	6	by	by	ADP
ejpam-6093	105	7	(	(	PUNCT
ejpam-6093	105	8	f3	f3	ADJ
ejpam-6093	105	9	)	)	PUNCT
ejpam-6093	105	10	.	.	PUNCT
ejpam-6093	106	1	since	since	SCONJ
ejpam-6093	106	2	1	1	NUM
ejpam-6093	106	3	,	,	PUNCT
ejpam-6093	106	4	x	x	SYM
ejpam-6093	106	5	∈	∈	PROPN
ejpam-6093	106	6	f	f	X
ejpam-6093	106	7	and	and	CCONJ
ejpam-6093	106	8	(	(	PUNCT
ejpam-6093	106	9	f4	f4	PROPN
ejpam-6093	106	10	)	)	PUNCT
ejpam-6093	106	11	,	,	PUNCT
ejpam-6093	106	12	y	y	PROPN
ejpam-6093	106	13	∈	∈	PROPN
ejpam-6093	106	14	f	f	X
ejpam-6093	106	15	.	.	PUNCT
ejpam-6093	107	1	thus	thus	ADV
ejpam-6093	107	2	f	f	X
ejpam-6093	107	3	satisfies	satisfie	NOUN
ejpam-6093	107	4	(	(	PUNCT
ejpam-6093	107	5	f2	f2	PROPN
ejpam-6093	107	6	)	)	PUNCT
ejpam-6093	107	7	.	.	PUNCT
ejpam-6093	108	1	to	to	PART
ejpam-6093	108	2	show	show	VERB
ejpam-6093	108	3	that	that	SCONJ
ejpam-6093	108	4	f	f	PROPN
ejpam-6093	108	5	satisfies	satisfie	NOUN
ejpam-6093	108	6	(	(	PUNCT
ejpam-6093	108	7	f1	f1	NOUN
ejpam-6093	108	8	)	)	PUNCT
ejpam-6093	108	9	,	,	PUNCT
ejpam-6093	108	10	let	let	VERB
ejpam-6093	108	11	x	x	PRON
ejpam-6093	108	12	,	,	PUNCT
ejpam-6093	108	13	y	y	PROPN
ejpam-6093	108	14	,	,	PUNCT
ejpam-6093	108	15	z	z	PROPN
ejpam-6093	108	16	∈	∈	PROPN
ejpam-6093	108	17	f	f	X
ejpam-6093	108	18	.	.	PUNCT
ejpam-6093	109	1	by	by	ADP
ejpam-6093	109	2	theorem	theorem	NOUN
ejpam-6093	109	3	1	1	NUM
ejpam-6093	109	4	(	(	PUNCT
ejpam-6093	109	5	2	2	NUM
ejpam-6093	109	6	)	)	PUNCT
ejpam-6093	109	7	,	,	PUNCT
ejpam-6093	109	8	x	x	X
ejpam-6093	109	9	≤	≤	NOUN
ejpam-6093	109	10	[	[	X
ejpam-6093	109	11	yz[xyz]]∗	yz[xyz]]∗	NOUN
ejpam-6093	109	12	,	,	PUNCT
ejpam-6093	109	13	and	and	CCONJ
ejpam-6093	109	14	so	so	ADV
ejpam-6093	109	15	by	by	ADP
ejpam-6093	109	16	(	(	PUNCT
ejpam-6093	109	17	f2	f2	PROPN
ejpam-6093	109	18	)	)	PUNCT
ejpam-6093	109	19	we	we	PRON
ejpam-6093	109	20	get	get	VERB
ejpam-6093	109	21	[	[	PUNCT
ejpam-6093	109	22	yz[xyz]]∗	yz[xyz]]∗	NOUN
ejpam-6093	109	23	∈	∈	ADJ
ejpam-6093	109	24	f	f	NOUN
ejpam-6093	109	25	.	.	PUNCT
ejpam-6093	110	1	this	this	PRON
ejpam-6093	110	2	implies	imply	VERB
ejpam-6093	110	3	by	by	ADP
ejpam-6093	110	4	(	(	PUNCT
ejpam-6093	110	5	f4	f4	PROPN
ejpam-6093	110	6	)	)	PUNCT
ejpam-6093	110	7	that	that	SCONJ
ejpam-6093	111	1	[	[	X
ejpam-6093	111	2	xyz	xyz	X
ejpam-6093	111	3	]	]	X
ejpam-6093	111	4	∈	∈	PROPN
ejpam-6093	111	5	f	f	X
ejpam-6093	111	6	.	.	PUNCT
ejpam-6093	112	1	therefore	therefore	ADV
ejpam-6093	112	2	,	,	PUNCT
ejpam-6093	112	3	f	f	PROPN
ejpam-6093	112	4	is	be	AUX
ejpam-6093	112	5	a	a	DET
ejpam-6093	112	6	filter	filter	NOUN
ejpam-6093	112	7	of	of	ADP
ejpam-6093	112	8	t	t	PROPN
ejpam-6093	112	9	.	.	PUNCT
ejpam-6093	113	1	now	now	ADV
ejpam-6093	113	2	we	we	PRON
ejpam-6093	113	3	denote	denote	VERB
ejpam-6093	113	4	important	important	ADJ
ejpam-6093	113	5	elementary	elementary	ADJ
ejpam-6093	113	6	properties	property	NOUN
ejpam-6093	113	7	of	of	ADP
ejpam-6093	113	8	a	a	DET
ejpam-6093	113	9	commutative	commutative	ADJ
ejpam-6093	113	10	implicative	implicative	ADJ
ejpam-6093	113	11	n.p.o	n.p.o	NOUN
ejpam-6093	113	12	.	.	PUNCT
ejpam-6093	114	1	ternary	ternary	PROPN
ejpam-6093	114	2	semigroup	semigroup	PROPN
ejpam-6093	114	3	.	.	PUNCT
ejpam-6093	115	1	lemma	lemma	PROPN
ejpam-6093	115	2	1	1	NUM
ejpam-6093	115	3	.	.	PUNCT
ejpam-6093	116	1	if	if	SCONJ
ejpam-6093	116	2	(	(	PUNCT
ejpam-6093	116	3	t	t	PROPN
ejpam-6093	116	4	,	,	PUNCT
ejpam-6093	116	5	[	[	PUNCT
ejpam-6093	116	6	]	]	X
ejpam-6093	116	7	,	,	PUNCT
ejpam-6093	116	8	≤	≤	NUM
ejpam-6093	116	9	,	,	PUNCT
ejpam-6093	116	10	[	[	PUNCT
ejpam-6093	116	11	]	]	X
ejpam-6093	116	12	∗	∗	NOUN
ejpam-6093	116	13	)	)	PUNCT
ejpam-6093	116	14	is	be	AUX
ejpam-6093	116	15	a	a	DET
ejpam-6093	116	16	commutative	commutative	ADJ
ejpam-6093	116	17	implicative	implicative	ADJ
ejpam-6093	116	18	n.p.o	n.p.o	NOUN
ejpam-6093	116	19	.	.	PUNCT
ejpam-6093	117	1	ternary	ternary	PROPN
ejpam-6093	117	2	semigroup	semigroup	PROPN
ejpam-6093	117	3	,	,	PUNCT
ejpam-6093	117	4	then	then	ADV
ejpam-6093	117	5	for	for	ADP
ejpam-6093	117	6	any	any	DET
ejpam-6093	117	7	x	x	NOUN
ejpam-6093	117	8	,	,	PUNCT
ejpam-6093	117	9	y	y	PROPN
ejpam-6093	117	10	,	,	PUNCT
ejpam-6093	117	11	z	z	PROPN
ejpam-6093	117	12	,	,	PUNCT
ejpam-6093	117	13	u	u	NOUN
ejpam-6093	117	14	,	,	PUNCT
ejpam-6093	117	15	v	v	PROPN
ejpam-6093	117	16	∈	∈	NOUN
ejpam-6093	117	17	t	t	NOUN
ejpam-6093	117	18	:	:	PUNCT
ejpam-6093	117	19	(	(	PUNCT
ejpam-6093	117	20	1	1	X
ejpam-6093	117	21	)	)	PUNCT
ejpam-6093	118	1	[	[	X
ejpam-6093	118	2	xy[zuv]∗]∗	xy[zuv]∗]∗	X
ejpam-6093	118	3	=	=	PUNCT
ejpam-6093	119	1	[	[	X
ejpam-6093	119	2	zu[xyv]∗]∗.	zu[xyv]∗]∗.	PROPN
ejpam-6093	119	3	(	(	PUNCT
ejpam-6093	119	4	2	2	NUM
ejpam-6093	119	5	)	)	PUNCT
ejpam-6093	119	6	x	x	NOUN
ejpam-6093	119	7	≤	≤	NOUN
ejpam-6093	120	1	[	[	X
ejpam-6093	120	2	[	[	X
ejpam-6093	120	3	xyz]∗yz]∗.	xyz]∗yz]∗.	NOUN
ejpam-6093	120	4	proof	proof	NOUN
ejpam-6093	120	5	.	.	PUNCT
ejpam-6093	121	1	(	(	PUNCT
ejpam-6093	121	2	1	1	X
ejpam-6093	121	3	)	)	PUNCT
ejpam-6093	121	4	we	we	PRON
ejpam-6093	121	5	have	have	VERB
ejpam-6093	121	6	[	[	X
ejpam-6093	121	7	xy[zuv]∗]∗	xy[zuv]∗]∗	X
ejpam-6093	121	8	=	=	PUNCT
ejpam-6093	122	1	[	[	X
ejpam-6093	122	2	[	[	X
ejpam-6093	122	3	xyz]uv]∗	xyz]uv]∗	X
ejpam-6093	122	4	=	=	PUNCT
ejpam-6093	123	1	[	[	X
ejpam-6093	123	2	[	[	X
ejpam-6093	123	3	zxy]uv]∗	zxy]uv]∗	X
ejpam-6093	123	4	=	=	PUNCT
ejpam-6093	124	1	[	[	X
ejpam-6093	124	2	z[xyu]v]∗	z[xyu]v]∗	NUM
ejpam-6093	124	3	=	=	PUNCT
ejpam-6093	125	1	[	[	X
ejpam-6093	125	2	z[uxy]v]∗	z[uxy]v]∗	X
ejpam-6093	125	3	=	=	PUNCT
ejpam-6093	126	1	[	[	X
ejpam-6093	126	2	zu[xyv]∗]∗.	zu[xyv]∗]∗.	PROPN
ejpam-6093	126	3	the	the	DET
ejpam-6093	126	4	first	first	ADJ
ejpam-6093	126	5	equality	equality	NOUN
ejpam-6093	126	6	follows	follow	VERB
ejpam-6093	126	7	from	from	ADP
ejpam-6093	126	8	theorem	theorem	ADJ
ejpam-6093	126	9	1	1	NUM
ejpam-6093	126	10	(	(	PUNCT
ejpam-6093	126	11	7	7	NUM
ejpam-6093	126	12	)	)	PUNCT
ejpam-6093	126	13	,	,	PUNCT
ejpam-6093	126	14	and	and	CCONJ
ejpam-6093	126	15	the	the	DET
ejpam-6093	126	16	second	second	ADJ
ejpam-6093	126	17	from	from	ADP
ejpam-6093	126	18	commutativity	commutativity	NOUN
ejpam-6093	126	19	.	.	PUNCT
ejpam-6093	127	1	(	(	PUNCT
ejpam-6093	127	2	2	2	NUM
ejpam-6093	127	3	)	)	PUNCT
ejpam-6093	127	4	since	since	SCONJ
ejpam-6093	127	5	[	[	X
ejpam-6093	127	6	xyz]∗	xyz]∗	X
ejpam-6093	127	7	≤	≤	NOUN
ejpam-6093	128	1	[	[	X
ejpam-6093	128	2	xyz]∗	xyz]∗	X
ejpam-6093	128	3	,	,	PUNCT
ejpam-6093	128	4	[	[	X
ejpam-6093	128	5	[	[	X
ejpam-6093	128	6	xyz]∗xy	xyz]∗xy	X
ejpam-6093	128	7	]	]	X
ejpam-6093	128	8	≤	≤	NUM
ejpam-6093	128	9	z.	z.	PROPN
ejpam-6093	128	10	using	use	VERB
ejpam-6093	128	11	the	the	DET
ejpam-6093	128	12	commutativity	commutativity	NOUN
ejpam-6093	128	13	,	,	PUNCT
ejpam-6093	128	14	we	we	PRON
ejpam-6093	128	15	have	have	VERB
ejpam-6093	128	16	[	[	X
ejpam-6093	128	17	x[xyz]∗y	x[xyz]∗y	X
ejpam-6093	128	18	]	]	X
ejpam-6093	128	19	=	=	PUNCT
ejpam-6093	129	1	[	[	X
ejpam-6093	129	2	[	[	X
ejpam-6093	129	3	xyz]∗xy	xyz]∗xy	X
ejpam-6093	129	4	]	]	X
ejpam-6093	129	5	≤	≤	NUM
ejpam-6093	129	6	z.	z.	PROPN
ejpam-6093	130	1	thus	thus	ADV
ejpam-6093	130	2	x	x	X
ejpam-6093	130	3	≤	≤	NOUN
ejpam-6093	131	1	[	[	X
ejpam-6093	131	2	[	[	X
ejpam-6093	131	3	xyz]∗yz]∗.	xyz]∗yz]∗.	NOUN
ejpam-6093	131	4	theorem	theorem	VERB
ejpam-6093	131	5	3	3	X
ejpam-6093	131	6	.	.	PUNCT
ejpam-6093	132	1	let	let	AUX
ejpam-6093	132	2	(	(	PUNCT
ejpam-6093	132	3	t	t	NOUN
ejpam-6093	132	4	,	,	PUNCT
ejpam-6093	132	5	[	[	PUNCT
ejpam-6093	132	6	]	]	X
ejpam-6093	132	7	,	,	PUNCT
ejpam-6093	132	8	≤	≤	NUM
ejpam-6093	132	9	,	,	PUNCT
ejpam-6093	132	10	[	[	PUNCT
ejpam-6093	132	11	]	]	X
ejpam-6093	132	12	∗	∗	NOUN
ejpam-6093	132	13	)	)	PUNCT
ejpam-6093	132	14	be	be	VERB
ejpam-6093	132	15	a	a	DET
ejpam-6093	132	16	commutative	commutative	ADJ
ejpam-6093	132	17	implicative	implicative	ADJ
ejpam-6093	132	18	n.p.o	n.p.o	NOUN
ejpam-6093	132	19	.	.	PUNCT
ejpam-6093	133	1	ternary	ternary	ADJ
ejpam-6093	133	2	semigroup	semigroup	NOUN
ejpam-6093	133	3	and	and	CCONJ
ejpam-6093	133	4	f	f	PROPN
ejpam-6093	133	5	be	be	AUX
ejpam-6093	133	6	a	a	DET
ejpam-6093	133	7	non	non	ADJ
ejpam-6093	133	8	-	-	ADJ
ejpam-6093	133	9	empty	empty	ADJ
ejpam-6093	133	10	subset	subset	NOUN
ejpam-6093	133	11	of	of	ADP
ejpam-6093	133	12	t	t	PROPN
ejpam-6093	133	13	.	.	PUNCT
ejpam-6093	134	1	then	then	ADV
ejpam-6093	134	2	f	f	PROPN
ejpam-6093	134	3	is	be	AUX
ejpam-6093	134	4	a	a	DET
ejpam-6093	134	5	filter	filter	NOUN
ejpam-6093	134	6	of	of	ADP
ejpam-6093	134	7	t	t	PROPN
ejpam-6093	134	8	if	if	SCONJ
ejpam-6093	135	1	and	and	CCONJ
ejpam-6093	135	2	only	only	ADV
ejpam-6093	135	3	if	if	SCONJ
ejpam-6093	135	4	it	it	PRON
ejpam-6093	135	5	satisfies	satisfy	VERB
ejpam-6093	135	6	for	for	ADP
ejpam-6093	135	7	all	all	DET
ejpam-6093	135	8	x	x	NOUN
ejpam-6093	135	9	,	,	PUNCT
ejpam-6093	135	10	y	y	PROPN
ejpam-6093	135	11	,	,	PUNCT
ejpam-6093	135	12	z	z	PROPN
ejpam-6093	135	13	∈	∈	PROPN
ejpam-6093	135	14	f	f	NOUN
ejpam-6093	135	15	and	and	CCONJ
ejpam-6093	135	16	u	u	PROPN
ejpam-6093	135	17	∈	∈	PROPN
ejpam-6093	135	18	t	t	NOUN
ejpam-6093	135	19	:	:	PUNCT
ejpam-6093	135	20	(	(	PUNCT
ejpam-6093	135	21	f5	f5	NOUN
ejpam-6093	135	22	)	)	PUNCT
ejpam-6093	135	23	x	x	SYM
ejpam-6093	135	24	≤	≤	NOUN
ejpam-6093	136	1	[	[	X
ejpam-6093	136	2	yzu]∗	yzu]∗	PROPN
ejpam-6093	136	3	implies	imply	VERB
ejpam-6093	136	4	u	u	PROPN
ejpam-6093	136	5	∈	∈	PROPN
ejpam-6093	136	6	f	f	X
ejpam-6093	136	7	.	.	PUNCT
ejpam-6093	137	1	proof	proof	NOUN
ejpam-6093	137	2	.	.	PUNCT
ejpam-6093	138	1	assume	assume	VERB
ejpam-6093	138	2	that	that	SCONJ
ejpam-6093	138	3	f	f	PROPN
ejpam-6093	138	4	is	be	AUX
ejpam-6093	138	5	a	a	DET
ejpam-6093	138	6	filter	filter	NOUN
ejpam-6093	138	7	of	of	ADP
ejpam-6093	138	8	t	t	PROPN
ejpam-6093	138	9	.	.	PUNCT
ejpam-6093	139	1	let	let	VERB
ejpam-6093	139	2	x	x	PRON
ejpam-6093	139	3	,	,	PUNCT
ejpam-6093	139	4	y	y	PROPN
ejpam-6093	139	5	,	,	PUNCT
ejpam-6093	139	6	z	z	PROPN
ejpam-6093	139	7	∈	∈	PROPN
ejpam-6093	139	8	f	f	NOUN
ejpam-6093	139	9	and	and	CCONJ
ejpam-6093	139	10	u	u	PROPN
ejpam-6093	139	11	∈	∈	PROPN
ejpam-6093	139	12	t	t	NOUN
ejpam-6093	139	13	such	such	ADJ
ejpam-6093	139	14	that	that	SCONJ
ejpam-6093	139	15	x	x	SYM
ejpam-6093	139	16	≤	≤	X
ejpam-6093	140	1	[	[	X
ejpam-6093	140	2	yzu]∗.	yzu]∗.	NOUN
ejpam-6093	140	3	then	then	ADV
ejpam-6093	140	4	by	by	ADP
ejpam-6093	140	5	theorem	theorem	NOUN
ejpam-6093	140	6	1	1	NUM
ejpam-6093	140	7	(	(	PUNCT
ejpam-6093	140	8	6	6	NUM
ejpam-6093	140	9	)	)	PUNCT
ejpam-6093	140	10	,	,	PUNCT
ejpam-6093	140	11	[	[	X
ejpam-6093	140	12	1x[yzu]∗]∗	1x[yzu]∗]∗	NUM
ejpam-6093	140	13	=	=	SYM
ejpam-6093	140	14	1	1	NUM
ejpam-6093	140	15	∈	∈	PROPN
ejpam-6093	140	16	f	f	NOUN
ejpam-6093	140	17	.	.	PUNCT
ejpam-6093	141	1	from	from	ADP
ejpam-6093	141	2	1	1	NUM
ejpam-6093	141	3	,	,	PUNCT
ejpam-6093	141	4	x	x	SYM
ejpam-6093	141	5	∈	∈	PROPN
ejpam-6093	141	6	f	f	NOUN
ejpam-6093	141	7	,	,	PUNCT
ejpam-6093	141	8	it	it	PRON
ejpam-6093	141	9	follows	follow	VERB
ejpam-6093	141	10	by	by	ADP
ejpam-6093	141	11	(	(	PUNCT
ejpam-6093	141	12	f4	f4	PROPN
ejpam-6093	141	13	)	)	PUNCT
ejpam-6093	141	14	that	that	SCONJ
ejpam-6093	142	1	[	[	X
ejpam-6093	142	2	yzu]∗	yzu]∗	NOUN
ejpam-6093	142	3	∈	∈	PROPN
ejpam-6093	142	4	f	f	X
ejpam-6093	142	5	.	.	PUNCT
ejpam-6093	143	1	since	since	SCONJ
ejpam-6093	143	2	y	y	PROPN
ejpam-6093	143	3	,	,	PUNCT
ejpam-6093	143	4	z	z	PROPN
ejpam-6093	143	5	∈	∈	PROPN
ejpam-6093	143	6	f	f	NOUN
ejpam-6093	143	7	,	,	PUNCT
ejpam-6093	143	8	u	u	PROPN
ejpam-6093	143	9	∈	∈	PROPN
ejpam-6093	143	10	f	f	X
ejpam-6093	143	11	.	.	PUNCT
ejpam-6093	144	1	conversely	conversely	ADV
ejpam-6093	144	2	,	,	PUNCT
ejpam-6093	144	3	suppose	suppose	VERB
ejpam-6093	144	4	f	f	PROPN
ejpam-6093	144	5	satisfies	satisfie	NOUN
ejpam-6093	144	6	(	(	PUNCT
ejpam-6093	144	7	f5	f5	PROPN
ejpam-6093	144	8	)	)	PUNCT
ejpam-6093	144	9	.	.	PUNCT
ejpam-6093	145	1	since	since	SCONJ
ejpam-6093	145	2	x	x	PROPN
ejpam-6093	145	3	≤	≤	X
ejpam-6093	145	4	[	[	X
ejpam-6093	145	5	xx1]∗	xx1]∗	X
ejpam-6093	145	6	for	for	ADP
ejpam-6093	145	7	all	all	DET
ejpam-6093	145	8	x	x	SYM
ejpam-6093	145	9	∈	∈	PROPN
ejpam-6093	145	10	f	f	NOUN
ejpam-6093	145	11	,	,	PUNCT
ejpam-6093	145	12	we	we	PRON
ejpam-6093	145	13	have	have	VERB
ejpam-6093	145	14	1	1	NUM
ejpam-6093	145	15	∈	∈	NOUN
ejpam-6093	145	16	f	f	X
ejpam-6093	145	17	by	by	ADP
ejpam-6093	145	18	(	(	PUNCT
ejpam-6093	145	19	f5	f5	NOUN
ejpam-6093	145	20	)	)	PUNCT
ejpam-6093	145	21	.	.	PUNCT
ejpam-6093	146	1	let	let	VERB
ejpam-6093	146	2	x	x	PRON
ejpam-6093	146	3	,	,	PUNCT
ejpam-6093	146	4	y	y	PROPN
ejpam-6093	146	5	,	,	PUNCT
ejpam-6093	146	6	z	z	PROPN
ejpam-6093	146	7	∈	∈	PROPN
ejpam-6093	146	8	t	t	NOUN
ejpam-6093	146	9	such	such	ADJ
ejpam-6093	146	10	that	that	SCONJ
ejpam-6093	147	1	[	[	X
ejpam-6093	147	2	xyz]∗	xyz]∗	X
ejpam-6093	147	3	∈	∈	PROPN
ejpam-6093	147	4	f	f	PROPN
ejpam-6093	147	5	and	and	CCONJ
ejpam-6093	147	6	x	x	NOUN
ejpam-6093	147	7	,	,	PUNCT
ejpam-6093	147	8	y	y	PROPN
ejpam-6093	147	9	∈	∈	PROPN
ejpam-6093	147	10	f	f	PROPN
ejpam-6093	147	11	.	.	PUNCT
ejpam-6093	148	1	note	note	VERB
ejpam-6093	148	2	that	that	SCONJ
ejpam-6093	148	3	x	x	X
ejpam-6093	148	4	≤	≤	X
ejpam-6093	149	1	[	[	X
ejpam-6093	149	2	[	[	X
ejpam-6093	149	3	xyz]∗yz]∗	xyz]∗yz]∗	X
ejpam-6093	149	4	by	by	ADP
ejpam-6093	149	5	lemma	lemma	PROPN
ejpam-6093	149	6	1	1	NUM
ejpam-6093	149	7	(	(	PUNCT
ejpam-6093	149	8	2	2	NUM
ejpam-6093	149	9	)	)	PUNCT
ejpam-6093	149	10	.	.	PUNCT
ejpam-6093	150	1	applies	apply	VERB
ejpam-6093	150	2	(	(	PUNCT
ejpam-6093	150	3	f5	f5	PROPN
ejpam-6093	150	4	)	)	PUNCT
ejpam-6093	150	5	with	with	ADP
ejpam-6093	150	6	(	(	PUNCT
ejpam-6093	150	7	x	x	NOUN
ejpam-6093	150	8	,	,	PUNCT
ejpam-6093	150	9	y	y	PROPN
ejpam-6093	150	10	,	,	PUNCT
ejpam-6093	150	11	z	z	PROPN
ejpam-6093	150	12	,	,	PUNCT
ejpam-6093	150	13	u	u	NOUN
ejpam-6093	150	14	)	)	PUNCT
ejpam-6093	150	15	7→	7→	NUM
ejpam-6093	150	16	(	(	PUNCT
ejpam-6093	150	17	x	x	X
ejpam-6093	150	18	,	,	PUNCT
ejpam-6093	150	19	[	[	X
ejpam-6093	150	20	xyz]∗	xyz]∗	X
ejpam-6093	150	21	,	,	PUNCT
ejpam-6093	150	22	y	y	PROPN
ejpam-6093	150	23	,	,	PUNCT
ejpam-6093	150	24	z	z	NOUN
ejpam-6093	150	25	)	)	PUNCT
ejpam-6093	150	26	,	,	PUNCT
ejpam-6093	150	27	we	we	PRON
ejpam-6093	150	28	get	get	VERB
ejpam-6093	150	29	z	z	NOUN
ejpam-6093	150	30	∈	∈	PROPN
ejpam-6093	150	31	f	f	PROPN
ejpam-6093	150	32	.	.	PUNCT
ejpam-6093	151	1	therefore	therefore	ADV
ejpam-6093	151	2	,	,	PUNCT
ejpam-6093	151	3	f	f	PROPN
ejpam-6093	151	4	is	be	AUX
ejpam-6093	151	5	a	a	DET
ejpam-6093	151	6	filter	filter	NOUN
ejpam-6093	151	7	of	of	ADP
ejpam-6093	151	8	t	t	PROPN
ejpam-6093	151	9	.	.	PUNCT
ejpam-6093	152	1	following	follow	VERB
ejpam-6093	152	2	,	,	PUNCT
ejpam-6093	152	3	we	we	PRON
ejpam-6093	152	4	give	give	VERB
ejpam-6093	152	5	the	the	DET
ejpam-6093	152	6	definition	definition	NOUN
ejpam-6093	152	7	of	of	ADP
ejpam-6093	152	8	implicative	implicative	ADJ
ejpam-6093	152	9	filters	filter	NOUN
ejpam-6093	152	10	.	.	PUNCT
ejpam-6093	153	1	definition	definition	NOUN
ejpam-6093	153	2	2	2	NUM
ejpam-6093	153	3	.	.	PUNCT
ejpam-6093	154	1	let	let	AUX
ejpam-6093	154	2	(	(	PUNCT
ejpam-6093	154	3	t	t	NOUN
ejpam-6093	154	4	,	,	PUNCT
ejpam-6093	154	5	[	[	PUNCT
ejpam-6093	154	6	]	]	X
ejpam-6093	154	7	,	,	PUNCT
ejpam-6093	154	8	≤	≤	NUM
ejpam-6093	154	9	,	,	PUNCT
ejpam-6093	154	10	[	[	PUNCT
ejpam-6093	154	11	]	]	X
ejpam-6093	154	12	∗	∗	NOUN
ejpam-6093	154	13	)	)	PUNCT
ejpam-6093	154	14	be	be	VERB
ejpam-6093	154	15	an	an	DET
ejpam-6093	154	16	implicative	implicative	ADJ
ejpam-6093	154	17	n.p.o	n.p.o	NOUN
ejpam-6093	154	18	.	.	PUNCT
ejpam-6093	155	1	ternary	ternary	PROPN
ejpam-6093	155	2	semigroup	semigroup	PROPN
ejpam-6093	155	3	.	.	PUNCT
ejpam-6093	156	1	a	a	DET
ejpam-6093	156	2	nonempty	nonempty	NOUN
ejpam-6093	156	3	subset	subset	VERB
ejpam-6093	156	4	f	f	PROPN
ejpam-6093	156	5	of	of	ADP
ejpam-6093	156	6	t	t	PROPN
ejpam-6093	156	7	is	be	AUX
ejpam-6093	156	8	called	call	VERB
ejpam-6093	156	9	an	an	DET
ejpam-6093	156	10	implicative	implicative	ADJ
ejpam-6093	156	11	filter	filter	NOUN
ejpam-6093	156	12	of	of	ADP
ejpam-6093	156	13	t	t	PROPN
ejpam-6093	156	14	if	if	SCONJ
ejpam-6093	156	15	it	it	PRON
ejpam-6093	156	16	satisfies	satisfy	VERB
ejpam-6093	156	17	(	(	PUNCT
ejpam-6093	156	18	f3	f3	ADJ
ejpam-6093	156	19	)	)	PUNCT
ejpam-6093	156	20	and	and	CCONJ
ejpam-6093	157	1	[	[	X
ejpam-6093	157	2	xy[zuv]∗]∗	xy[zuv]∗]∗	PROPN
ejpam-6093	157	3	∈	∈	PROPN
ejpam-6093	157	4	f	f	X
ejpam-6093	157	5	,	,	PUNCT
ejpam-6093	157	6	[	[	X
ejpam-6093	157	7	xyz]∗	xyz]∗	X
ejpam-6093	157	8	∈	∈	PROPN
ejpam-6093	157	9	f	f	X
ejpam-6093	157	10	,	,	PUNCT
ejpam-6093	157	11	and	and	CCONJ
ejpam-6093	157	12	[	[	X
ejpam-6093	157	13	xyu]∗	xyu]∗	PROPN
ejpam-6093	157	14	∈	∈	PROPN
ejpam-6093	157	15	f	f	AUX
ejpam-6093	157	16	imply	imply	VERB
ejpam-6093	158	1	[	[	X
ejpam-6093	158	2	xyv]∗	xyv]∗	PROPN
ejpam-6093	158	3	∈	∈	PROPN
ejpam-6093	158	4	f	f	PROPN
ejpam-6093	158	5	for	for	ADP
ejpam-6093	158	6	all	all	DET
ejpam-6093	158	7	x	x	PROPN
ejpam-6093	158	8	,	,	PUNCT
ejpam-6093	158	9	y	y	PROPN
ejpam-6093	158	10	,	,	PUNCT
ejpam-6093	158	11	z	z	PROPN
ejpam-6093	158	12	,	,	PUNCT
ejpam-6093	158	13	u	u	NOUN
ejpam-6093	158	14	,	,	PUNCT
ejpam-6093	158	15	v	v	PROPN
ejpam-6093	158	16	∈	∈	PROPN
ejpam-6093	158	17	t	t	NOUN
ejpam-6093	158	18	.	.	PUNCT
ejpam-6093	159	1	k.	k.	PROPN
ejpam-6093	159	2	nakwan	nakwan	PROPN
ejpam-6093	159	3	,	,	PUNCT
ejpam-6093	159	4	p.	p.	PROPN
ejpam-6093	159	5	luangchaisri	luangchaisri	VERB
ejpam-6093	159	6	,	,	PUNCT
ejpam-6093	159	7	t.	t.	PROPN
ejpam-6093	159	8	changphas	changphas	PROPN
ejpam-6093	159	9	/	/	SYM
ejpam-6093	159	10	eur	eur	PROPN
ejpam-6093	159	11	.	.	PUNCT
ejpam-6093	160	1	j.	j.	PROPN
ejpam-6093	160	2	pure	pure	PROPN
ejpam-6093	160	3	appl	appl	PROPN
ejpam-6093	160	4	.	.	PROPN
ejpam-6093	160	5	math	math	PROPN
ejpam-6093	160	6	,	,	PUNCT
ejpam-6093	160	7	18	18	NUM
ejpam-6093	160	8	(	(	PUNCT
ejpam-6093	160	9	4	4	NUM
ejpam-6093	160	10	)	)	PUNCT
ejpam-6093	160	11	(	(	PUNCT
ejpam-6093	160	12	2025	2025	NUM
ejpam-6093	160	13	)	)	PUNCT
ejpam-6093	160	14	,	,	PUNCT
ejpam-6093	160	15	6093	6093	NUM
ejpam-6093	160	16	5	5	NUM
ejpam-6093	160	17	of	of	ADP
ejpam-6093	160	18	11	11	NUM
ejpam-6093	160	19	example	example	NOUN
ejpam-6093	160	20	1	1	NUM
ejpam-6093	160	21	.	.	PUNCT
ejpam-6093	161	1	let	let	VERB
ejpam-6093	161	2	t	t	NOUN
ejpam-6093	161	3	=	=	SYM
ejpam-6093	161	4	{	{	PUNCT
ejpam-6093	161	5	1	1	NUM
ejpam-6093	161	6	,	,	PUNCT
ejpam-6093	161	7	2	2	NUM
ejpam-6093	161	8	,	,	PUNCT
ejpam-6093	161	9	3	3	NUM
ejpam-6093	161	10	,	,	PUNCT
ejpam-6093	161	11	5	5	NUM
ejpam-6093	161	12	,	,	PUNCT
ejpam-6093	161	13	7	7	NUM
ejpam-6093	161	14	,	,	PUNCT
ejpam-6093	161	15	9	9	NUM
ejpam-6093	161	16	}	}	PUNCT
ejpam-6093	161	17	.	.	PUNCT
ejpam-6093	162	1	let	let	VERB
ejpam-6093	162	2	us	we	PRON
ejpam-6093	162	3	consider	consider	VERB
ejpam-6093	162	4	the	the	DET
ejpam-6093	162	5	implicative	implicative	ADJ
ejpam-6093	162	6	n.p.o	n.p.o	NOUN
ejpam-6093	162	7	.	.	PUNCT
ejpam-6093	163	1	ternary	ternary	ADJ
ejpam-6093	163	2	semigroup	semigroup	PROPN
ejpam-6093	163	3	(	(	PUNCT
ejpam-6093	163	4	t	t	PROPN
ejpam-6093	163	5	,	,	PUNCT
ejpam-6093	163	6	[	[	PUNCT
ejpam-6093	163	7	]	]	X
ejpam-6093	163	8	,	,	PUNCT
ejpam-6093	163	9	≤	≤	NUM
ejpam-6093	163	10	,	,	PUNCT
ejpam-6093	163	11	[	[	PUNCT
ejpam-6093	163	12	]	]	X
ejpam-6093	163	13	∗	∗	NOUN
ejpam-6093	163	14	)	)	PUNCT
ejpam-6093	163	15	with	with	ADP
ejpam-6093	163	16	ternary	ternary	ADJ
ejpam-6093	163	17	multiplication	multiplication	NOUN
ejpam-6093	163	18	[	[	PUNCT
ejpam-6093	163	19	]	]	X
ejpam-6093	163	20	,	,	PUNCT
ejpam-6093	163	21	ternary	ternary	ADJ
ejpam-6093	163	22	implication	implication	NOUN
ejpam-6093	163	23	[	[	PUNCT
ejpam-6093	163	24	]	]	X
ejpam-6093	163	25	∗	∗	NOUN
ejpam-6093	163	26	,	,	PUNCT
ejpam-6093	163	27	and	and	CCONJ
ejpam-6093	163	28	order	order	NOUN
ejpam-6093	163	29	relation	relation	NOUN
ejpam-6093	163	30	≤	≤	NOUN
ejpam-6093	163	31	defined	define	VERB
ejpam-6093	163	32	as	as	SCONJ
ejpam-6093	163	33	follows	follow	VERB
ejpam-6093	163	34	:	:	PUNCT
ejpam-6093	163	35	[	[	PUNCT
ejpam-6093	163	36	]	]	X
ejpam-6093	163	37	1	1	NUM
ejpam-6093	163	38	2	2	NUM
ejpam-6093	163	39	3	3	NUM
ejpam-6093	163	40	5	5	NUM
ejpam-6093	163	41	7	7	NUM
ejpam-6093	163	42	9	9	NUM
ejpam-6093	163	43	11	11	NUM
ejpam-6093	163	44	1	1	NUM
ejpam-6093	163	45	2	2	NUM
ejpam-6093	163	46	3	3	NUM
ejpam-6093	163	47	5	5	NUM
ejpam-6093	163	48	7	7	NUM
ejpam-6093	163	49	9	9	NUM
ejpam-6093	163	50	12	12	NUM
ejpam-6093	163	51	2	2	NUM
ejpam-6093	163	52	3	3	NUM
ejpam-6093	163	53	3	3	NUM
ejpam-6093	163	54	7	7	NUM
ejpam-6093	163	55	9	9	NUM
ejpam-6093	163	56	9	9	NUM
ejpam-6093	163	57	13	13	NUM
ejpam-6093	163	58	3	3	NUM
ejpam-6093	163	59	3	3	NUM
ejpam-6093	163	60	3	3	NUM
ejpam-6093	163	61	9	9	NUM
ejpam-6093	163	62	9	9	NUM
ejpam-6093	163	63	9	9	NUM
ejpam-6093	163	64	15	15	NUM
ejpam-6093	163	65	5	5	NUM
ejpam-6093	163	66	7	7	NUM
ejpam-6093	163	67	9	9	NUM
ejpam-6093	163	68	5	5	NUM
ejpam-6093	163	69	7	7	NUM
ejpam-6093	163	70	9	9	NUM
ejpam-6093	163	71	17	17	NUM
ejpam-6093	163	72	7	7	NUM
ejpam-6093	163	73	9	9	NUM
ejpam-6093	163	74	9	9	NUM
ejpam-6093	163	75	7	7	NUM
ejpam-6093	163	76	9	9	NUM
ejpam-6093	163	77	9	9	NUM
ejpam-6093	163	78	19	19	NUM
ejpam-6093	163	79	9	9	NUM
ejpam-6093	163	80	9	9	NUM
ejpam-6093	163	81	9	9	NUM
ejpam-6093	163	82	9	9	NUM
ejpam-6093	163	83	9	9	NUM
ejpam-6093	163	84	9	9	NUM
ejpam-6093	163	85	[	[	PUNCT
ejpam-6093	163	86	]	]	SYM
ejpam-6093	163	87	1	1	NUM
ejpam-6093	163	88	2	2	NUM
ejpam-6093	163	89	3	3	NUM
ejpam-6093	163	90	5	5	NUM
ejpam-6093	163	91	7	7	NUM
ejpam-6093	163	92	9	9	NUM
ejpam-6093	163	93	21	21	NUM
ejpam-6093	163	94	2	2	NUM
ejpam-6093	163	95	3	3	NUM
ejpam-6093	163	96	3	3	NUM
ejpam-6093	163	97	7	7	NUM
ejpam-6093	163	98	9	9	NUM
ejpam-6093	163	99	9	9	NUM
ejpam-6093	163	100	22	22	NUM
ejpam-6093	163	101	3	3	NUM
ejpam-6093	163	102	3	3	NUM
ejpam-6093	163	103	3	3	NUM
ejpam-6093	163	104	9	9	NUM
ejpam-6093	163	105	9	9	NUM
ejpam-6093	163	106	9	9	NUM
ejpam-6093	163	107	23	23	NUM
ejpam-6093	163	108	3	3	NUM
ejpam-6093	163	109	3	3	NUM
ejpam-6093	163	110	3	3	NUM
ejpam-6093	163	111	9	9	NUM
ejpam-6093	163	112	9	9	NUM
ejpam-6093	163	113	9	9	NUM
ejpam-6093	163	114	25	25	NUM
ejpam-6093	163	115	7	7	NUM
ejpam-6093	163	116	9	9	NUM
ejpam-6093	163	117	9	9	NUM
ejpam-6093	163	118	7	7	NUM
ejpam-6093	163	119	9	9	NUM
ejpam-6093	163	120	9	9	NUM
ejpam-6093	163	121	27	27	NUM
ejpam-6093	163	122	9	9	NUM
ejpam-6093	163	123	9	9	NUM
ejpam-6093	163	124	9	9	NUM
ejpam-6093	163	125	9	9	NUM
ejpam-6093	163	126	9	9	NUM
ejpam-6093	163	127	9	9	NUM
ejpam-6093	163	128	29	29	NUM
ejpam-6093	163	129	9	9	NUM
ejpam-6093	163	130	9	9	NUM
ejpam-6093	163	131	9	9	NUM
ejpam-6093	163	132	9	9	NUM
ejpam-6093	163	133	9	9	NUM
ejpam-6093	163	134	9	9	NUM
ejpam-6093	163	135	[	[	PUNCT
ejpam-6093	163	136	]	]	SYM
ejpam-6093	163	137	1	1	NUM
ejpam-6093	163	138	2	2	NUM
ejpam-6093	163	139	3	3	NUM
ejpam-6093	163	140	5	5	NUM
ejpam-6093	163	141	7	7	NUM
ejpam-6093	163	142	9	9	NUM
ejpam-6093	163	143	31	31	NUM
ejpam-6093	163	144	3	3	NUM
ejpam-6093	163	145	3	3	NUM
ejpam-6093	163	146	3	3	NUM
ejpam-6093	163	147	9	9	NUM
ejpam-6093	163	148	9	9	NUM
ejpam-6093	163	149	9	9	NUM
ejpam-6093	163	150	32	32	NUM
ejpam-6093	163	151	3	3	NUM
ejpam-6093	163	152	3	3	NUM
ejpam-6093	163	153	3	3	NUM
ejpam-6093	163	154	9	9	NUM
ejpam-6093	163	155	9	9	NUM
ejpam-6093	163	156	9	9	NUM
ejpam-6093	163	157	33	33	NUM
ejpam-6093	163	158	3	3	NUM
ejpam-6093	163	159	3	3	NUM
ejpam-6093	163	160	3	3	NUM
ejpam-6093	163	161	9	9	NUM
ejpam-6093	163	162	9	9	NUM
ejpam-6093	163	163	9	9	NUM
ejpam-6093	163	164	35	35	NUM
ejpam-6093	163	165	9	9	NUM
ejpam-6093	163	166	9	9	NUM
ejpam-6093	163	167	9	9	NUM
ejpam-6093	163	168	9	9	NUM
ejpam-6093	163	169	9	9	NUM
ejpam-6093	163	170	9	9	NUM
ejpam-6093	163	171	37	37	NUM
ejpam-6093	163	172	9	9	NUM
ejpam-6093	163	173	9	9	NUM
ejpam-6093	163	174	9	9	NUM
ejpam-6093	163	175	9	9	NUM
ejpam-6093	163	176	9	9	NUM
ejpam-6093	163	177	9	9	NUM
ejpam-6093	163	178	39	39	NUM
ejpam-6093	163	179	9	9	NUM
ejpam-6093	163	180	9	9	NUM
ejpam-6093	163	181	9	9	NUM
ejpam-6093	163	182	9	9	NUM
ejpam-6093	163	183	9	9	NUM
ejpam-6093	163	184	9	9	NUM
ejpam-6093	163	185	[	[	PUNCT
ejpam-6093	163	186	]	]	SYM
ejpam-6093	163	187	1	1	NUM
ejpam-6093	163	188	2	2	NUM
ejpam-6093	163	189	3	3	NUM
ejpam-6093	163	190	5	5	NUM
ejpam-6093	163	191	7	7	NUM
ejpam-6093	163	192	9	9	NUM
ejpam-6093	163	193	51	51	NUM
ejpam-6093	163	194	5	5	NUM
ejpam-6093	163	195	7	7	NUM
ejpam-6093	163	196	9	9	NUM
ejpam-6093	163	197	5	5	NUM
ejpam-6093	163	198	7	7	NUM
ejpam-6093	163	199	9	9	NUM
ejpam-6093	163	200	52	52	NUM
ejpam-6093	163	201	7	7	NUM
ejpam-6093	163	202	9	9	NUM
ejpam-6093	163	203	9	9	NUM
ejpam-6093	163	204	7	7	NUM
ejpam-6093	163	205	9	9	NUM
ejpam-6093	163	206	9	9	NUM
ejpam-6093	163	207	53	53	NUM
ejpam-6093	163	208	9	9	NUM
ejpam-6093	163	209	9	9	NUM
ejpam-6093	163	210	9	9	NUM
ejpam-6093	163	211	9	9	NUM
ejpam-6093	163	212	9	9	NUM
ejpam-6093	163	213	9	9	NUM
ejpam-6093	163	214	55	55	NUM
ejpam-6093	163	215	5	5	NUM
ejpam-6093	163	216	7	7	NUM
ejpam-6093	163	217	9	9	NUM
ejpam-6093	163	218	5	5	NUM
ejpam-6093	163	219	7	7	NUM
ejpam-6093	163	220	9	9	NUM
ejpam-6093	163	221	57	57	NUM
ejpam-6093	163	222	7	7	NUM
ejpam-6093	163	223	9	9	NUM
ejpam-6093	163	224	9	9	NUM
ejpam-6093	163	225	7	7	NUM
ejpam-6093	163	226	9	9	NUM
ejpam-6093	163	227	9	9	NUM
ejpam-6093	163	228	59	59	NUM
ejpam-6093	163	229	9	9	NUM
ejpam-6093	163	230	9	9	NUM
ejpam-6093	163	231	9	9	NUM
ejpam-6093	163	232	9	9	NUM
ejpam-6093	163	233	9	9	NUM
ejpam-6093	163	234	9	9	NUM
ejpam-6093	163	235	[	[	PUNCT
ejpam-6093	163	236	]	]	SYM
ejpam-6093	163	237	1	1	NUM
ejpam-6093	163	238	2	2	NUM
ejpam-6093	163	239	3	3	NUM
ejpam-6093	163	240	5	5	NUM
ejpam-6093	163	241	7	7	NUM
ejpam-6093	163	242	9	9	NUM
ejpam-6093	163	243	71	71	NUM
ejpam-6093	163	244	7	7	NUM
ejpam-6093	163	245	9	9	NUM
ejpam-6093	163	246	9	9	NUM
ejpam-6093	163	247	7	7	NUM
ejpam-6093	163	248	9	9	NUM
ejpam-6093	163	249	9	9	NUM
ejpam-6093	163	250	72	72	NUM
ejpam-6093	163	251	9	9	NUM
ejpam-6093	163	252	9	9	NUM
ejpam-6093	163	253	9	9	NUM
ejpam-6093	163	254	9	9	NUM
ejpam-6093	163	255	9	9	NUM
ejpam-6093	163	256	9	9	NUM
ejpam-6093	163	257	73	73	NUM
ejpam-6093	163	258	9	9	NUM
ejpam-6093	163	259	9	9	NUM
ejpam-6093	163	260	9	9	NUM
ejpam-6093	163	261	9	9	NUM
ejpam-6093	163	262	9	9	NUM
ejpam-6093	163	263	9	9	NUM
ejpam-6093	163	264	75	75	NUM
ejpam-6093	163	265	7	7	NUM
ejpam-6093	163	266	9	9	NUM
ejpam-6093	163	267	9	9	NUM
ejpam-6093	163	268	7	7	NUM
ejpam-6093	163	269	9	9	NUM
ejpam-6093	163	270	9	9	NUM
ejpam-6093	163	271	77	77	NUM
ejpam-6093	163	272	9	9	NUM
ejpam-6093	163	273	9	9	NUM
ejpam-6093	163	274	9	9	NUM
ejpam-6093	163	275	9	9	NUM
ejpam-6093	163	276	9	9	NUM
ejpam-6093	163	277	9	9	NUM
ejpam-6093	163	278	79	79	NUM
ejpam-6093	163	279	9	9	NUM
ejpam-6093	163	280	9	9	NUM
ejpam-6093	163	281	9	9	NUM
ejpam-6093	163	282	9	9	NUM
ejpam-6093	163	283	9	9	NUM
ejpam-6093	163	284	9	9	NUM
ejpam-6093	163	285	[	[	PUNCT
ejpam-6093	163	286	]	]	SYM
ejpam-6093	163	287	1	1	NUM
ejpam-6093	163	288	2	2	NUM
ejpam-6093	163	289	3	3	NUM
ejpam-6093	163	290	5	5	NUM
ejpam-6093	163	291	7	7	NUM
ejpam-6093	163	292	9	9	NUM
ejpam-6093	163	293	91	91	NUM
ejpam-6093	163	294	9	9	NUM
ejpam-6093	163	295	9	9	NUM
ejpam-6093	163	296	9	9	NUM
ejpam-6093	163	297	9	9	NUM
ejpam-6093	163	298	9	9	NUM
ejpam-6093	163	299	9	9	NUM
ejpam-6093	163	300	92	92	NUM
ejpam-6093	163	301	9	9	NUM
ejpam-6093	163	302	9	9	NUM
ejpam-6093	163	303	9	9	NUM
ejpam-6093	163	304	9	9	NUM
ejpam-6093	163	305	9	9	NUM
ejpam-6093	163	306	9	9	NUM
ejpam-6093	163	307	93	93	NUM
ejpam-6093	163	308	9	9	NUM
ejpam-6093	163	309	9	9	NUM
ejpam-6093	163	310	9	9	NUM
ejpam-6093	163	311	9	9	NUM
ejpam-6093	163	312	9	9	NUM
ejpam-6093	163	313	9	9	NUM
ejpam-6093	163	314	95	95	NUM
ejpam-6093	163	315	9	9	NUM
ejpam-6093	163	316	9	9	NUM
ejpam-6093	163	317	9	9	NUM
ejpam-6093	163	318	9	9	NUM
ejpam-6093	163	319	9	9	NUM
ejpam-6093	163	320	9	9	NUM
ejpam-6093	163	321	97	97	NUM
ejpam-6093	163	322	9	9	NUM
ejpam-6093	163	323	9	9	NUM
ejpam-6093	163	324	9	9	NUM
ejpam-6093	163	325	9	9	NUM
ejpam-6093	163	326	9	9	NUM
ejpam-6093	163	327	9	9	NUM
ejpam-6093	163	328	99	99	NUM
ejpam-6093	163	329	9	9	NUM
ejpam-6093	163	330	9	9	NUM
ejpam-6093	163	331	9	9	NUM
ejpam-6093	163	332	9	9	NUM
ejpam-6093	163	333	9	9	NUM
ejpam-6093	163	334	9	9	NUM
ejpam-6093	163	335	[	[	PUNCT
ejpam-6093	163	336	]	]	X
ejpam-6093	163	337	∗	∗	NOUN
ejpam-6093	163	338	1	1	NUM
ejpam-6093	163	339	2	2	NUM
ejpam-6093	163	340	3	3	NUM
ejpam-6093	163	341	5	5	NUM
ejpam-6093	163	342	7	7	NUM
ejpam-6093	163	343	9	9	NUM
ejpam-6093	163	344	11	11	NUM
ejpam-6093	163	345	1	1	NUM
ejpam-6093	163	346	2	2	NUM
ejpam-6093	163	347	3	3	NUM
ejpam-6093	163	348	5	5	NUM
ejpam-6093	163	349	7	7	NUM
ejpam-6093	163	350	9	9	NUM
ejpam-6093	163	351	12	12	NUM
ejpam-6093	163	352	1	1	NUM
ejpam-6093	163	353	1	1	NUM
ejpam-6093	163	354	2	2	NUM
ejpam-6093	163	355	5	5	NUM
ejpam-6093	163	356	5	5	NUM
ejpam-6093	163	357	7	7	NUM
ejpam-6093	163	358	13	13	NUM
ejpam-6093	163	359	1	1	NUM
ejpam-6093	163	360	1	1	NUM
ejpam-6093	163	361	1	1	NUM
ejpam-6093	163	362	5	5	NUM
ejpam-6093	163	363	5	5	NUM
ejpam-6093	163	364	5	5	NUM
ejpam-6093	163	365	15	15	NUM
ejpam-6093	163	366	1	1	NUM
ejpam-6093	163	367	2	2	NUM
ejpam-6093	163	368	3	3	NUM
ejpam-6093	163	369	1	1	NUM
ejpam-6093	163	370	2	2	NUM
ejpam-6093	163	371	3	3	NUM
ejpam-6093	163	372	17	17	NUM
ejpam-6093	163	373	1	1	NUM
ejpam-6093	163	374	1	1	NUM
ejpam-6093	163	375	2	2	NUM
ejpam-6093	163	376	1	1	NUM
ejpam-6093	163	377	1	1	NUM
ejpam-6093	163	378	2	2	NUM
ejpam-6093	163	379	19	19	NUM
ejpam-6093	163	380	1	1	NUM
ejpam-6093	163	381	1	1	NUM
ejpam-6093	163	382	1	1	NUM
ejpam-6093	163	383	1	1	NUM
ejpam-6093	163	384	1	1	NUM
ejpam-6093	163	385	1	1	NUM
ejpam-6093	163	386	[	[	PUNCT
ejpam-6093	163	387	]	]	X
ejpam-6093	163	388	∗	∗	NOUN
ejpam-6093	163	389	1	1	NUM
ejpam-6093	163	390	2	2	NUM
ejpam-6093	163	391	3	3	NUM
ejpam-6093	163	392	5	5	NUM
ejpam-6093	163	393	7	7	NUM
ejpam-6093	163	394	9	9	NUM
ejpam-6093	163	395	21	21	NUM
ejpam-6093	163	396	1	1	NUM
ejpam-6093	163	397	1	1	NUM
ejpam-6093	163	398	2	2	NUM
ejpam-6093	163	399	5	5	NUM
ejpam-6093	163	400	5	5	NUM
ejpam-6093	163	401	7	7	NUM
ejpam-6093	163	402	22	22	NUM
ejpam-6093	163	403	1	1	NUM
ejpam-6093	163	404	1	1	NUM
ejpam-6093	163	405	1	1	NUM
ejpam-6093	163	406	5	5	NUM
ejpam-6093	163	407	5	5	NUM
ejpam-6093	163	408	5	5	NUM
ejpam-6093	163	409	23	23	NUM
ejpam-6093	163	410	1	1	NUM
ejpam-6093	163	411	1	1	NUM
ejpam-6093	163	412	1	1	NUM
ejpam-6093	163	413	5	5	NUM
ejpam-6093	163	414	5	5	NUM
ejpam-6093	163	415	5	5	NUM
ejpam-6093	163	416	25	25	NUM
ejpam-6093	163	417	1	1	NUM
ejpam-6093	163	418	1	1	NUM
ejpam-6093	163	419	2	2	NUM
ejpam-6093	163	420	1	1	NUM
ejpam-6093	163	421	1	1	NUM
ejpam-6093	163	422	2	2	NUM
ejpam-6093	163	423	27	27	NUM
ejpam-6093	163	424	1	1	NUM
ejpam-6093	163	425	1	1	NUM
ejpam-6093	163	426	1	1	NUM
ejpam-6093	163	427	1	1	NUM
ejpam-6093	163	428	1	1	NUM
ejpam-6093	163	429	1	1	NUM
ejpam-6093	163	430	29	29	NUM
ejpam-6093	163	431	1	1	NUM
ejpam-6093	163	432	1	1	NUM
ejpam-6093	163	433	1	1	NUM
ejpam-6093	163	434	1	1	NUM
ejpam-6093	163	435	1	1	NUM
ejpam-6093	163	436	1	1	NUM
ejpam-6093	163	437	[	[	PUNCT
ejpam-6093	163	438	]	]	X
ejpam-6093	163	439	∗	∗	NOUN
ejpam-6093	163	440	1	1	NUM
ejpam-6093	163	441	2	2	NUM
ejpam-6093	163	442	3	3	NUM
ejpam-6093	163	443	5	5	NUM
ejpam-6093	163	444	7	7	NUM
ejpam-6093	163	445	9	9	NUM
ejpam-6093	163	446	31	31	NUM
ejpam-6093	163	447	1	1	NUM
ejpam-6093	163	448	1	1	NUM
ejpam-6093	163	449	1	1	NUM
ejpam-6093	163	450	5	5	NUM
ejpam-6093	163	451	5	5	NUM
ejpam-6093	163	452	5	5	NUM
ejpam-6093	163	453	32	32	NUM
ejpam-6093	163	454	1	1	NUM
ejpam-6093	163	455	1	1	NUM
ejpam-6093	163	456	1	1	NUM
ejpam-6093	163	457	5	5	NUM
ejpam-6093	163	458	5	5	NUM
ejpam-6093	163	459	5	5	NUM
ejpam-6093	163	460	33	33	NUM
ejpam-6093	163	461	1	1	NUM
ejpam-6093	163	462	1	1	NUM
ejpam-6093	163	463	1	1	NUM
ejpam-6093	163	464	5	5	NUM
ejpam-6093	163	465	5	5	NUM
ejpam-6093	163	466	5	5	NUM
ejpam-6093	163	467	35	35	NUM
ejpam-6093	163	468	1	1	NUM
ejpam-6093	163	469	1	1	NUM
ejpam-6093	163	470	1	1	NUM
ejpam-6093	163	471	1	1	NUM
ejpam-6093	163	472	1	1	NUM
ejpam-6093	163	473	1	1	NUM
ejpam-6093	163	474	37	37	NUM
ejpam-6093	163	475	1	1	NUM
ejpam-6093	163	476	1	1	NUM
ejpam-6093	163	477	1	1	NUM
ejpam-6093	163	478	1	1	NUM
ejpam-6093	163	479	1	1	NUM
ejpam-6093	163	480	1	1	NUM
ejpam-6093	163	481	39	39	NUM
ejpam-6093	163	482	1	1	NUM
ejpam-6093	163	483	1	1	NUM
ejpam-6093	163	484	1	1	NUM
ejpam-6093	163	485	1	1	NUM
ejpam-6093	163	486	1	1	NUM
ejpam-6093	163	487	1	1	NUM
ejpam-6093	163	488	[	[	PUNCT
ejpam-6093	163	489	]	]	X
ejpam-6093	163	490	∗	∗	NOUN
ejpam-6093	163	491	1	1	NUM
ejpam-6093	163	492	2	2	NUM
ejpam-6093	163	493	3	3	NUM
ejpam-6093	163	494	5	5	NUM
ejpam-6093	163	495	7	7	NUM
ejpam-6093	163	496	9	9	NUM
ejpam-6093	163	497	51	51	NUM
ejpam-6093	163	498	1	1	NUM
ejpam-6093	163	499	2	2	NUM
ejpam-6093	163	500	3	3	NUM
ejpam-6093	163	501	1	1	NUM
ejpam-6093	163	502	2	2	NUM
ejpam-6093	163	503	3	3	NUM
ejpam-6093	163	504	52	52	NUM
ejpam-6093	163	505	1	1	NUM
ejpam-6093	163	506	1	1	NUM
ejpam-6093	163	507	2	2	NUM
ejpam-6093	163	508	1	1	NUM
ejpam-6093	163	509	1	1	NUM
ejpam-6093	163	510	2	2	NUM
ejpam-6093	163	511	53	53	NUM
ejpam-6093	163	512	1	1	NUM
ejpam-6093	163	513	1	1	NUM
ejpam-6093	163	514	1	1	NUM
ejpam-6093	163	515	1	1	NUM
ejpam-6093	163	516	1	1	NUM
ejpam-6093	163	517	1	1	NUM
ejpam-6093	163	518	55	55	NUM
ejpam-6093	163	519	1	1	NUM
ejpam-6093	163	520	2	2	NUM
ejpam-6093	163	521	3	3	NUM
ejpam-6093	163	522	1	1	NUM
ejpam-6093	163	523	2	2	NUM
ejpam-6093	163	524	3	3	NUM
ejpam-6093	163	525	57	57	NUM
ejpam-6093	163	526	1	1	NUM
ejpam-6093	163	527	1	1	NUM
ejpam-6093	163	528	2	2	NUM
ejpam-6093	163	529	1	1	NUM
ejpam-6093	163	530	1	1	NUM
ejpam-6093	163	531	2	2	NUM
ejpam-6093	163	532	59	59	NUM
ejpam-6093	163	533	1	1	NUM
ejpam-6093	163	534	1	1	NUM
ejpam-6093	163	535	1	1	NUM
ejpam-6093	163	536	1	1	NUM
ejpam-6093	163	537	1	1	NUM
ejpam-6093	163	538	1	1	NUM
ejpam-6093	163	539	k.	k.	NOUN
ejpam-6093	163	540	nakwan	nakwan	PROPN
ejpam-6093	163	541	,	,	PUNCT
ejpam-6093	163	542	p.	p.	PROPN
ejpam-6093	163	543	luangchaisri	luangchaisri	VERB
ejpam-6093	163	544	,	,	PUNCT
ejpam-6093	163	545	t.	t.	PROPN
ejpam-6093	163	546	changphas	changphas	PROPN
ejpam-6093	163	547	/	/	SYM
ejpam-6093	163	548	eur	eur	PROPN
ejpam-6093	163	549	.	.	PUNCT
ejpam-6093	164	1	j.	j.	PROPN
ejpam-6093	164	2	pure	pure	PROPN
ejpam-6093	164	3	appl	appl	PROPN
ejpam-6093	164	4	.	.	PROPN
ejpam-6093	164	5	math	math	PROPN
ejpam-6093	164	6	,	,	PUNCT
ejpam-6093	164	7	18	18	NUM
ejpam-6093	164	8	(	(	PUNCT
ejpam-6093	164	9	4	4	NUM
ejpam-6093	164	10	)	)	PUNCT
ejpam-6093	164	11	(	(	PUNCT
ejpam-6093	164	12	2025	2025	NUM
ejpam-6093	164	13	)	)	PUNCT
ejpam-6093	164	14	,	,	PUNCT
ejpam-6093	164	15	6093	6093	NUM
ejpam-6093	164	16	6	6	NUM
ejpam-6093	164	17	of	of	ADP
ejpam-6093	164	18	11	11	NUM
ejpam-6093	164	19	[	[	PUNCT
ejpam-6093	164	20	]	]	X
ejpam-6093	164	21	∗	∗	NOUN
ejpam-6093	164	22	1	1	NUM
ejpam-6093	164	23	2	2	NUM
ejpam-6093	164	24	3	3	NUM
ejpam-6093	164	25	5	5	NUM
ejpam-6093	164	26	7	7	NUM
ejpam-6093	164	27	9	9	NUM
ejpam-6093	164	28	71	71	NUM
ejpam-6093	164	29	1	1	NUM
ejpam-6093	164	30	1	1	NUM
ejpam-6093	164	31	2	2	NUM
ejpam-6093	164	32	1	1	NUM
ejpam-6093	164	33	1	1	NUM
ejpam-6093	164	34	2	2	NUM
ejpam-6093	164	35	72	72	NUM
ejpam-6093	164	36	1	1	NUM
ejpam-6093	164	37	1	1	NUM
ejpam-6093	164	38	1	1	NUM
ejpam-6093	164	39	1	1	NUM
ejpam-6093	164	40	1	1	NUM
ejpam-6093	164	41	1	1	NUM
ejpam-6093	164	42	73	73	NUM
ejpam-6093	164	43	1	1	NUM
ejpam-6093	164	44	1	1	NUM
ejpam-6093	164	45	1	1	NUM
ejpam-6093	164	46	1	1	NUM
ejpam-6093	164	47	1	1	NUM
ejpam-6093	164	48	1	1	NUM
ejpam-6093	164	49	75	75	NUM
ejpam-6093	164	50	1	1	NUM
ejpam-6093	164	51	1	1	NUM
ejpam-6093	164	52	2	2	NUM
ejpam-6093	164	53	1	1	NUM
ejpam-6093	164	54	1	1	NUM
ejpam-6093	164	55	2	2	NUM
ejpam-6093	164	56	77	77	NUM
ejpam-6093	164	57	1	1	NUM
ejpam-6093	164	58	1	1	NUM
ejpam-6093	164	59	1	1	NUM
ejpam-6093	164	60	1	1	NUM
ejpam-6093	164	61	1	1	NUM
ejpam-6093	164	62	1	1	NUM
ejpam-6093	164	63	79	79	NUM
ejpam-6093	164	64	1	1	NUM
ejpam-6093	164	65	1	1	NUM
ejpam-6093	164	66	1	1	NUM
ejpam-6093	164	67	1	1	NUM
ejpam-6093	164	68	1	1	NUM
ejpam-6093	164	69	1	1	NUM
ejpam-6093	164	70	[	[	PUNCT
ejpam-6093	164	71	]	]	X
ejpam-6093	164	72	∗	∗	NOUN
ejpam-6093	164	73	1	1	NUM
ejpam-6093	164	74	2	2	NUM
ejpam-6093	164	75	3	3	NUM
ejpam-6093	164	76	5	5	NUM
ejpam-6093	164	77	7	7	NUM
ejpam-6093	164	78	9	9	NUM
ejpam-6093	164	79	91	91	NUM
ejpam-6093	164	80	1	1	NUM
ejpam-6093	164	81	1	1	NUM
ejpam-6093	164	82	1	1	NUM
ejpam-6093	164	83	1	1	NUM
ejpam-6093	164	84	1	1	NUM
ejpam-6093	164	85	1	1	NUM
ejpam-6093	164	86	92	92	NUM
ejpam-6093	164	87	1	1	NUM
ejpam-6093	164	88	1	1	NUM
ejpam-6093	164	89	1	1	NUM
ejpam-6093	164	90	1	1	NUM
ejpam-6093	164	91	1	1	NUM
ejpam-6093	164	92	1	1	NUM
ejpam-6093	164	93	93	93	NUM
ejpam-6093	164	94	1	1	NUM
ejpam-6093	164	95	1	1	NUM
ejpam-6093	164	96	1	1	NUM
ejpam-6093	164	97	1	1	NUM
ejpam-6093	164	98	1	1	NUM
ejpam-6093	164	99	1	1	NUM
ejpam-6093	164	100	95	95	NUM
ejpam-6093	164	101	1	1	NUM
ejpam-6093	164	102	1	1	NUM
ejpam-6093	164	103	1	1	NUM
ejpam-6093	164	104	1	1	NUM
ejpam-6093	164	105	1	1	NUM
ejpam-6093	164	106	1	1	NUM
ejpam-6093	164	107	97	97	NUM
ejpam-6093	164	108	1	1	NUM
ejpam-6093	164	109	1	1	NUM
ejpam-6093	164	110	1	1	NUM
ejpam-6093	164	111	1	1	NUM
ejpam-6093	164	112	1	1	NUM
ejpam-6093	164	113	1	1	NUM
ejpam-6093	164	114	99	99	NUM
ejpam-6093	164	115	1	1	NUM
ejpam-6093	164	116	1	1	NUM
ejpam-6093	164	117	1	1	NUM
ejpam-6093	164	118	1	1	NUM
ejpam-6093	164	119	1	1	NUM
ejpam-6093	164	120	1	1	NUM
ejpam-6093	164	121	and	and	CCONJ
ejpam-6093	164	122	≤	≤	NUM
ejpam-6093	164	123	:	:	PUNCT
ejpam-6093	164	124	=	=	SYM
ejpam-6093	164	125	{	{	PUNCT
ejpam-6093	164	126	(	(	PUNCT
ejpam-6093	164	127	1	1	NUM
ejpam-6093	164	128	,	,	PUNCT
ejpam-6093	164	129	1	1	NUM
ejpam-6093	164	130	)	)	PUNCT
ejpam-6093	164	131	,	,	PUNCT
ejpam-6093	164	132	(	(	PUNCT
ejpam-6093	164	133	2	2	NUM
ejpam-6093	164	134	,	,	PUNCT
ejpam-6093	164	135	2	2	NUM
ejpam-6093	164	136	)	)	PUNCT
ejpam-6093	164	137	,	,	PUNCT
ejpam-6093	164	138	(	(	PUNCT
ejpam-6093	164	139	2	2	NUM
ejpam-6093	164	140	,	,	PUNCT
ejpam-6093	164	141	1	1	NUM
ejpam-6093	164	142	)	)	PUNCT
ejpam-6093	164	143	,	,	PUNCT
ejpam-6093	164	144	(	(	PUNCT
ejpam-6093	164	145	3	3	NUM
ejpam-6093	164	146	,	,	PUNCT
ejpam-6093	164	147	3	3	NUM
ejpam-6093	164	148	)	)	PUNCT
ejpam-6093	164	149	,	,	PUNCT
ejpam-6093	164	150	(	(	PUNCT
ejpam-6093	164	151	3	3	NUM
ejpam-6093	164	152	,	,	PUNCT
ejpam-6093	164	153	1	1	NUM
ejpam-6093	164	154	)	)	PUNCT
ejpam-6093	164	155	,	,	PUNCT
ejpam-6093	164	156	(	(	PUNCT
ejpam-6093	164	157	3	3	NUM
ejpam-6093	164	158	,	,	PUNCT
ejpam-6093	164	159	2	2	NUM
ejpam-6093	164	160	)	)	PUNCT
ejpam-6093	164	161	,	,	PUNCT
ejpam-6093	164	162	(	(	PUNCT
ejpam-6093	164	163	5	5	NUM
ejpam-6093	164	164	,	,	PUNCT
ejpam-6093	164	165	5	5	NUM
ejpam-6093	164	166	)	)	PUNCT
ejpam-6093	164	167	,	,	PUNCT
ejpam-6093	164	168	(	(	PUNCT
ejpam-6093	164	169	5	5	NUM
ejpam-6093	164	170	,	,	PUNCT
ejpam-6093	164	171	1	1	NUM
ejpam-6093	164	172	)	)	PUNCT
ejpam-6093	164	173	,	,	PUNCT
ejpam-6093	164	174	(	(	PUNCT
ejpam-6093	164	175	7	7	NUM
ejpam-6093	164	176	,	,	PUNCT
ejpam-6093	164	177	7	7	NUM
ejpam-6093	164	178	)	)	PUNCT
ejpam-6093	164	179	,	,	PUNCT
ejpam-6093	164	180	(	(	PUNCT
ejpam-6093	164	181	7	7	NUM
ejpam-6093	164	182	,	,	PUNCT
ejpam-6093	164	183	1	1	NUM
ejpam-6093	164	184	)	)	PUNCT
ejpam-6093	164	185	,	,	PUNCT
ejpam-6093	164	186	(	(	PUNCT
ejpam-6093	164	187	7	7	NUM
ejpam-6093	164	188	,	,	PUNCT
ejpam-6093	164	189	2	2	NUM
ejpam-6093	164	190	)	)	PUNCT
ejpam-6093	164	191	,	,	PUNCT
ejpam-6093	164	192	(	(	PUNCT
ejpam-6093	164	193	7	7	NUM
ejpam-6093	164	194	,	,	PUNCT
ejpam-6093	164	195	5	5	NUM
ejpam-6093	164	196	)	)	PUNCT
ejpam-6093	164	197	,	,	PUNCT
ejpam-6093	164	198	(	(	PUNCT
ejpam-6093	164	199	9	9	NUM
ejpam-6093	164	200	,	,	PUNCT
ejpam-6093	164	201	9	9	NUM
ejpam-6093	164	202	)	)	PUNCT
ejpam-6093	164	203	,	,	PUNCT
ejpam-6093	164	204	(	(	PUNCT
ejpam-6093	164	205	9	9	NUM
ejpam-6093	164	206	,	,	PUNCT
ejpam-6093	164	207	1	1	NUM
ejpam-6093	164	208	)	)	PUNCT
ejpam-6093	164	209	,	,	PUNCT
ejpam-6093	164	210	(	(	PUNCT
ejpam-6093	164	211	9	9	NUM
ejpam-6093	164	212	,	,	PUNCT
ejpam-6093	164	213	2	2	NUM
ejpam-6093	164	214	)	)	PUNCT
ejpam-6093	164	215	,	,	PUNCT
ejpam-6093	164	216	(	(	PUNCT
ejpam-6093	164	217	9	9	NUM
ejpam-6093	164	218	,	,	PUNCT
ejpam-6093	164	219	3	3	NUM
ejpam-6093	164	220	)	)	PUNCT
ejpam-6093	164	221	,	,	PUNCT
ejpam-6093	164	222	(	(	PUNCT
ejpam-6093	164	223	9	9	NUM
ejpam-6093	164	224	,	,	PUNCT
ejpam-6093	164	225	5	5	NUM
ejpam-6093	164	226	)	)	PUNCT
ejpam-6093	164	227	,	,	PUNCT
ejpam-6093	164	228	(	(	PUNCT
ejpam-6093	164	229	9	9	NUM
ejpam-6093	164	230	,	,	PUNCT
ejpam-6093	164	231	7	7	NUM
ejpam-6093	164	232	)	)	PUNCT
ejpam-6093	164	233	}	}	PUNCT
ejpam-6093	164	234	.	.	PUNCT
ejpam-6093	165	1	2	2	NUM
ejpam-6093	165	2	3	3	NUM
ejpam-6093	165	3	5	5	NUM
ejpam-6093	165	4	1	1	NUM
ejpam-6093	165	5	7	7	NUM
ejpam-6093	165	6	9	9	NUM
ejpam-6093	165	7	it	it	PRON
ejpam-6093	165	8	is	be	AUX
ejpam-6093	165	9	easy	easy	ADJ
ejpam-6093	165	10	to	to	PART
ejpam-6093	165	11	verify	verify	VERB
ejpam-6093	165	12	that	that	PRON
ejpam-6093	165	13	f	f	PROPN
ejpam-6093	165	14	=	=	PRON
ejpam-6093	165	15	{	{	PUNCT
ejpam-6093	165	16	1	1	NUM
ejpam-6093	165	17	,	,	PUNCT
ejpam-6093	165	18	2	2	NUM
ejpam-6093	165	19	,	,	PUNCT
ejpam-6093	165	20	3	3	NUM
ejpam-6093	165	21	}	}	PUNCT
ejpam-6093	165	22	is	be	AUX
ejpam-6093	165	23	an	an	DET
ejpam-6093	165	24	implicative	implicative	ADJ
ejpam-6093	165	25	filter	filter	NOUN
ejpam-6093	165	26	of	of	ADP
ejpam-6093	165	27	t	t	PROPN
ejpam-6093	165	28	.	.	PUNCT
ejpam-6093	166	1	theorem	theorem	ADJ
ejpam-6093	166	2	4	4	NUM
ejpam-6093	166	3	.	.	X
ejpam-6093	166	4	for	for	ADP
ejpam-6093	166	5	an	an	DET
ejpam-6093	166	6	implicative	implicative	ADJ
ejpam-6093	166	7	n.p.o	n.p.o	NOUN
ejpam-6093	166	8	.	.	PUNCT
ejpam-6093	167	1	ternary	ternary	ADJ
ejpam-6093	167	2	semigroup	semigroup	PROPN
ejpam-6093	167	3	(	(	PUNCT
ejpam-6093	167	4	t	t	PROPN
ejpam-6093	167	5	,	,	PUNCT
ejpam-6093	167	6	[	[	PUNCT
ejpam-6093	167	7	]	]	X
ejpam-6093	167	8	,	,	PUNCT
ejpam-6093	167	9	≤	≤	NUM
ejpam-6093	167	10	,	,	PUNCT
ejpam-6093	167	11	[	[	PUNCT
ejpam-6093	167	12	]	]	X
ejpam-6093	167	13	∗	∗	NOUN
ejpam-6093	167	14	)	)	PUNCT
ejpam-6093	167	15	,	,	PUNCT
ejpam-6093	167	16	every	every	DET
ejpam-6093	167	17	implicative	implicative	ADJ
ejpam-6093	167	18	filter	filter	NOUN
ejpam-6093	167	19	of	of	ADP
ejpam-6093	167	20	t	t	PROPN
ejpam-6093	167	21	is	be	AUX
ejpam-6093	167	22	a	a	DET
ejpam-6093	167	23	filter	filter	NOUN
ejpam-6093	167	24	of	of	ADP
ejpam-6093	167	25	t	t	PROPN
ejpam-6093	167	26	.	.	PUNCT
ejpam-6093	168	1	proof	proof	NOUN
ejpam-6093	168	2	.	.	PUNCT
ejpam-6093	169	1	suppose	suppose	VERB
ejpam-6093	169	2	f	f	PROPN
ejpam-6093	169	3	is	be	AUX
ejpam-6093	169	4	an	an	DET
ejpam-6093	169	5	implicative	implicative	ADJ
ejpam-6093	169	6	filter	filter	NOUN
ejpam-6093	169	7	of	of	ADP
ejpam-6093	169	8	t	t	PROPN
ejpam-6093	169	9	.	.	PUNCT
ejpam-6093	170	1	let	let	VERB
ejpam-6093	170	2	x	x	PRON
ejpam-6093	170	3	,	,	PUNCT
ejpam-6093	170	4	y	y	PROPN
ejpam-6093	170	5	,	,	PUNCT
ejpam-6093	170	6	z	z	PROPN
ejpam-6093	170	7	∈	∈	PROPN
ejpam-6093	170	8	t	t	NOUN
ejpam-6093	170	9	such	such	ADJ
ejpam-6093	170	10	that	that	SCONJ
ejpam-6093	171	1	[	[	X
ejpam-6093	171	2	xyz]∗	xyz]∗	X
ejpam-6093	171	3	∈	∈	PROPN
ejpam-6093	171	4	f	f	PROPN
ejpam-6093	171	5	and	and	CCONJ
ejpam-6093	171	6	x	x	NOUN
ejpam-6093	171	7	,	,	PUNCT
ejpam-6093	171	8	y	y	PROPN
ejpam-6093	171	9	∈	∈	PROPN
ejpam-6093	171	10	f	f	X
ejpam-6093	171	11	.	.	PUNCT
ejpam-6093	172	1	by	by	ADP
ejpam-6093	172	2	theorem	theorem	NOUN
ejpam-6093	172	3	1	1	NUM
ejpam-6093	172	4	(	(	PUNCT
ejpam-6093	172	5	1	1	NUM
ejpam-6093	172	6	)	)	PUNCT
ejpam-6093	172	7	,	,	PUNCT
ejpam-6093	173	1	[	[	X
ejpam-6093	173	2	11[xyz]∗]∗	11[xyz]∗]∗	NUM
ejpam-6093	173	3	∈	∈	PROPN
ejpam-6093	173	4	f	f	X
ejpam-6093	173	5	,	,	PUNCT
ejpam-6093	173	6	[	[	X
ejpam-6093	173	7	11x]∗	11x]∗	NUM
ejpam-6093	173	8	∈	∈	PROPN
ejpam-6093	173	9	f	f	X
ejpam-6093	173	10	,	,	PUNCT
ejpam-6093	173	11	and	and	CCONJ
ejpam-6093	173	12	[	[	X
ejpam-6093	173	13	11y]∗	11y]∗	NUM
ejpam-6093	173	14	∈	∈	PROPN
ejpam-6093	173	15	f	f	NOUN
ejpam-6093	173	16	;	;	PUNCT
ejpam-6093	173	17	so	so	ADV
ejpam-6093	173	18	z	z	NOUN
ejpam-6093	173	19	=	=	PUNCT
ejpam-6093	174	1	[	[	X
ejpam-6093	174	2	11z]∗	11z]∗	NUM
ejpam-6093	174	3	∈	∈	NOUN
ejpam-6093	174	4	f	f	X
ejpam-6093	174	5	.	.	PUNCT
ejpam-6093	175	1	in	in	ADP
ejpam-6093	175	2	general	general	ADJ
ejpam-6093	175	3	,	,	PUNCT
ejpam-6093	175	4	the	the	DET
ejpam-6093	175	5	converse	converse	NOUN
ejpam-6093	175	6	of	of	ADP
ejpam-6093	175	7	theorem	theorem	NOUN
ejpam-6093	175	8	4	4	NUM
ejpam-6093	175	9	is	be	AUX
ejpam-6093	175	10	not	not	PART
ejpam-6093	175	11	true	true	ADJ
ejpam-6093	175	12	.	.	PUNCT
ejpam-6093	176	1	example	example	NOUN
ejpam-6093	176	2	2	2	NUM
ejpam-6093	176	3	.	.	X
ejpam-6093	177	1	consider	consider	VERB
ejpam-6093	177	2	the	the	DET
ejpam-6093	177	3	implicative	implicative	ADJ
ejpam-6093	177	4	n.p.o	n.p.o	NOUN
ejpam-6093	177	5	.	.	PUNCT
ejpam-6093	178	1	ternary	ternary	PROPN
ejpam-6093	178	2	semigroup	semigroup	PROPN
ejpam-6093	178	3	t	t	PROPN
ejpam-6093	178	4	defined	define	VERB
ejpam-6093	178	5	in	in	ADP
ejpam-6093	178	6	example	example	NOUN
ejpam-6093	178	7	1	1	X
ejpam-6093	178	8	.	.	PUNCT
ejpam-6093	179	1	it	it	PRON
ejpam-6093	179	2	is	be	AUX
ejpam-6093	179	3	observed	observe	VERB
ejpam-6093	179	4	that	that	SCONJ
ejpam-6093	179	5	{	{	PUNCT
ejpam-6093	179	6	1	1	X
ejpam-6093	179	7	}	}	PUNCT
ejpam-6093	179	8	is	be	AUX
ejpam-6093	179	9	a	a	DET
ejpam-6093	179	10	filter	filter	NOUN
ejpam-6093	179	11	of	of	ADP
ejpam-6093	179	12	t	t	PROPN
ejpam-6093	179	13	,	,	PUNCT
ejpam-6093	179	14	whereas	whereas	SCONJ
ejpam-6093	179	15	{	{	PUNCT
ejpam-6093	179	16	1	1	X
ejpam-6093	179	17	}	}	PUNCT
ejpam-6093	179	18	is	be	AUX
ejpam-6093	179	19	not	not	PART
ejpam-6093	179	20	an	an	DET
ejpam-6093	179	21	implicative	implicative	ADJ
ejpam-6093	179	22	filter	filter	NOUN
ejpam-6093	179	23	of	of	ADP
ejpam-6093	179	24	t	t	PROPN
ejpam-6093	179	25	.	.	PUNCT
ejpam-6093	180	1	indeed	indeed	ADV
ejpam-6093	180	2	,	,	PUNCT
ejpam-6093	180	3	[	[	X
ejpam-6093	180	4	71[719]∗]∗	71[719]∗]∗	X
ejpam-6093	180	5	=	=	PUNCT
ejpam-6093	181	1	[	[	X
ejpam-6093	181	2	712]∗	712]∗	NUM
ejpam-6093	181	3	=	=	SYM
ejpam-6093	181	4	1	1	NUM
ejpam-6093	181	5	∈	∈	NOUN
ejpam-6093	181	6	{	{	PUNCT
ejpam-6093	181	7	1	1	NUM
ejpam-6093	181	8	}	}	PUNCT
ejpam-6093	181	9	,	,	PUNCT
ejpam-6093	181	10	[	[	X
ejpam-6093	181	11	717]∗	717]∗	NUM
ejpam-6093	181	12	=	=	SYM
ejpam-6093	181	13	1	1	NUM
ejpam-6093	181	14	∈	∈	NOUN
ejpam-6093	181	15	{	{	PUNCT
ejpam-6093	181	16	1	1	NUM
ejpam-6093	181	17	}	}	PUNCT
ejpam-6093	181	18	,	,	PUNCT
ejpam-6093	181	19	and	and	CCONJ
ejpam-6093	181	20	[	[	X
ejpam-6093	181	21	711]∗	711]∗	X
ejpam-6093	181	22	=	=	SYM
ejpam-6093	181	23	1	1	NUM
ejpam-6093	181	24	∈	∈	NOUN
ejpam-6093	181	25	{	{	PUNCT
ejpam-6093	181	26	1	1	NUM
ejpam-6093	181	27	}	}	PUNCT
ejpam-6093	181	28	,	,	PUNCT
ejpam-6093	181	29	but	but	CCONJ
ejpam-6093	181	30	[	[	X
ejpam-6093	181	31	719]∗	719]∗	NUM
ejpam-6093	181	32	=	=	SYM
ejpam-6093	181	33	2	2	NUM
ejpam-6093	181	34	/∈	/∈	PUNCT
ejpam-6093	181	35	{	{	PUNCT
ejpam-6093	181	36	1	1	NUM
ejpam-6093	181	37	}	}	PUNCT
ejpam-6093	181	38	.	.	PUNCT
ejpam-6093	182	1	let	let	AUX
ejpam-6093	182	2	(	(	PUNCT
ejpam-6093	182	3	t	t	NOUN
ejpam-6093	182	4	,	,	PUNCT
ejpam-6093	182	5	[	[	PUNCT
ejpam-6093	182	6	]	]	X
ejpam-6093	182	7	,	,	PUNCT
ejpam-6093	182	8	≤	≤	NUM
ejpam-6093	182	9	,	,	PUNCT
ejpam-6093	182	10	[	[	PUNCT
ejpam-6093	182	11	]	]	X
ejpam-6093	182	12	∗	∗	NOUN
ejpam-6093	182	13	)	)	PUNCT
ejpam-6093	182	14	be	be	VERB
ejpam-6093	182	15	an	an	DET
ejpam-6093	182	16	implicative	implicative	ADJ
ejpam-6093	182	17	n.p.o	n.p.o	NOUN
ejpam-6093	182	18	.	.	PUNCT
ejpam-6093	183	1	ternary	ternary	PROPN
ejpam-6093	183	2	semigroup	semigroup	PROPN
ejpam-6093	183	3	.	.	PUNCT
ejpam-6093	184	1	for	for	ADP
ejpam-6093	184	2	a	a	DET
ejpam-6093	184	3	∈	∈	PROPN
ejpam-6093	184	4	t	t	NOUN
ejpam-6093	184	5	,	,	PUNCT
ejpam-6093	184	6	define	define	VERB
ejpam-6093	184	7	f	f	PROPN
ejpam-6093	184	8	(	(	PUNCT
ejpam-6093	184	9	a	a	NOUN
ejpam-6093	184	10	)	)	PUNCT
ejpam-6093	184	11	:	:	PUNCT
ejpam-6093	185	1	=	=	SYM
ejpam-6093	185	2	{	{	PUNCT
ejpam-6093	185	3	x	x	PUNCT
ejpam-6093	185	4	∈	∈	PROPN
ejpam-6093	185	5	t	t	NOUN
ejpam-6093	185	6	:	:	PUNCT
ejpam-6093	185	7	a	a	DET
ejpam-6093	185	8	≤	≤	NUM
ejpam-6093	185	9	x	x	X
ejpam-6093	185	10	}	}	PUNCT
ejpam-6093	185	11	.	.	PUNCT
ejpam-6093	186	1	observe	observe	VERB
ejpam-6093	186	2	that	that	SCONJ
ejpam-6093	186	3	1	1	NUM
ejpam-6093	186	4	,	,	PUNCT
ejpam-6093	186	5	a	a	DET
ejpam-6093	186	6	∈	∈	PROPN
ejpam-6093	186	7	f	f	X
ejpam-6093	186	8	(	(	PUNCT
ejpam-6093	186	9	a	a	NOUN
ejpam-6093	186	10	)	)	PUNCT
ejpam-6093	186	11	.	.	PUNCT
ejpam-6093	187	1	in	in	ADP
ejpam-6093	187	2	general	general	ADJ
ejpam-6093	187	3	,	,	PUNCT
ejpam-6093	187	4	f	f	PROPN
ejpam-6093	187	5	(	(	PUNCT
ejpam-6093	187	6	a	a	NOUN
ejpam-6093	187	7	)	)	PUNCT
ejpam-6093	187	8	is	be	AUX
ejpam-6093	187	9	not	not	PART
ejpam-6093	187	10	a	a	DET
ejpam-6093	187	11	filter	filter	NOUN
ejpam-6093	187	12	as	as	SCONJ
ejpam-6093	187	13	shown	show	VERB
ejpam-6093	187	14	in	in	ADP
ejpam-6093	187	15	the	the	DET
ejpam-6093	187	16	following	follow	VERB
ejpam-6093	187	17	example	example	NOUN
ejpam-6093	187	18	.	.	PUNCT
ejpam-6093	188	1	example	example	NOUN
ejpam-6093	189	1	3	3	X
ejpam-6093	189	2	.	.	PUNCT
ejpam-6093	189	3	let	let	VERB
ejpam-6093	189	4	us	we	PRON
ejpam-6093	189	5	consider	consider	VERB
ejpam-6093	189	6	the	the	DET
ejpam-6093	189	7	implicative	implicative	ADJ
ejpam-6093	189	8	n.p.o	n.p.o	NOUN
ejpam-6093	189	9	.	.	PUNCT
ejpam-6093	190	1	ternary	ternary	PROPN
ejpam-6093	190	2	semigroup	semigroup	PROPN
ejpam-6093	190	3	t	t	PROPN
ejpam-6093	190	4	defined	define	VERB
ejpam-6093	190	5	in	in	ADP
ejpam-6093	190	6	example	example	NOUN
ejpam-6093	190	7	1	1	X
ejpam-6093	190	8	.	.	PUNCT
ejpam-6093	191	1	we	we	PRON
ejpam-6093	191	2	have	have	VERB
ejpam-6093	191	3	f	f	X
ejpam-6093	191	4	(	(	PUNCT
ejpam-6093	191	5	1	1	NUM
ejpam-6093	191	6	)	)	PUNCT
ejpam-6093	191	7	=	=	NOUN
ejpam-6093	191	8	{	{	PUNCT
ejpam-6093	191	9	1	1	NUM
ejpam-6093	191	10	}	}	PUNCT
ejpam-6093	191	11	,	,	PUNCT
ejpam-6093	191	12	f	f	PROPN
ejpam-6093	191	13	(	(	PUNCT
ejpam-6093	191	14	2	2	NUM
ejpam-6093	191	15	)	)	PUNCT
ejpam-6093	191	16	=	=	NOUN
ejpam-6093	191	17	{	{	PUNCT
ejpam-6093	191	18	1	1	NUM
ejpam-6093	191	19	,	,	PUNCT
ejpam-6093	191	20	2	2	NUM
ejpam-6093	191	21	}	}	PUNCT
ejpam-6093	191	22	,	,	PUNCT
ejpam-6093	191	23	f	f	PROPN
ejpam-6093	191	24	(	(	PUNCT
ejpam-6093	191	25	3	3	NUM
ejpam-6093	191	26	)	)	PUNCT
ejpam-6093	191	27	=	=	NOUN
ejpam-6093	191	28	{	{	PUNCT
ejpam-6093	191	29	1	1	NUM
ejpam-6093	191	30	,	,	PUNCT
ejpam-6093	191	31	2	2	NUM
ejpam-6093	191	32	,	,	PUNCT
ejpam-6093	191	33	3	3	NUM
ejpam-6093	191	34	}	}	PUNCT
ejpam-6093	191	35	,	,	PUNCT
ejpam-6093	191	36	f	f	PROPN
ejpam-6093	191	37	(	(	PUNCT
ejpam-6093	191	38	5	5	NUM
ejpam-6093	191	39	)	)	PUNCT
ejpam-6093	191	40	=	=	NOUN
ejpam-6093	191	41	{	{	PUNCT
ejpam-6093	191	42	1	1	NUM
ejpam-6093	191	43	,	,	PUNCT
ejpam-6093	191	44	5	5	NUM
ejpam-6093	191	45	}	}	PUNCT
ejpam-6093	191	46	,	,	PUNCT
ejpam-6093	191	47	f	f	PROPN
ejpam-6093	191	48	(	(	PUNCT
ejpam-6093	191	49	7	7	NUM
ejpam-6093	191	50	)	)	PUNCT
ejpam-6093	191	51	=	=	NOUN
ejpam-6093	191	52	{	{	PUNCT
ejpam-6093	191	53	1	1	NUM
ejpam-6093	191	54	,	,	PUNCT
ejpam-6093	191	55	2	2	NUM
ejpam-6093	191	56	,	,	PUNCT
ejpam-6093	191	57	5	5	NUM
ejpam-6093	191	58	,	,	PUNCT
ejpam-6093	191	59	7	7	NUM
ejpam-6093	191	60	}	}	PUNCT
ejpam-6093	191	61	,	,	PUNCT
ejpam-6093	191	62	and	and	CCONJ
ejpam-6093	191	63	f	f	PROPN
ejpam-6093	191	64	(	(	PUNCT
ejpam-6093	191	65	9	9	NUM
ejpam-6093	191	66	)	)	PUNCT
ejpam-6093	191	67	=	=	NOUN
ejpam-6093	191	68	{	{	PUNCT
ejpam-6093	191	69	1	1	NUM
ejpam-6093	191	70	,	,	PUNCT
ejpam-6093	191	71	2	2	NUM
ejpam-6093	191	72	,	,	PUNCT
ejpam-6093	191	73	3	3	NUM
ejpam-6093	191	74	,	,	PUNCT
ejpam-6093	191	75	5	5	NUM
ejpam-6093	191	76	,	,	PUNCT
ejpam-6093	191	77	7	7	NUM
ejpam-6093	191	78	,	,	PUNCT
ejpam-6093	191	79	9	9	NUM
ejpam-6093	191	80	}	}	PUNCT
ejpam-6093	191	81	=	=	SYM
ejpam-6093	191	82	t	t	NOUN
ejpam-6093	191	83	.	.	PUNCT
ejpam-6093	192	1	it	it	PRON
ejpam-6093	192	2	is	be	AUX
ejpam-6093	192	3	observed	observe	VERB
ejpam-6093	192	4	that	that	SCONJ
ejpam-6093	192	5	f	f	PROPN
ejpam-6093	192	6	(	(	PUNCT
ejpam-6093	192	7	2	2	NUM
ejpam-6093	192	8	)	)	PUNCT
ejpam-6093	192	9	=	=	NOUN
ejpam-6093	192	10	{	{	PUNCT
ejpam-6093	192	11	1	1	NUM
ejpam-6093	192	12	,	,	PUNCT
ejpam-6093	192	13	2	2	NUM
ejpam-6093	192	14	}	}	PUNCT
ejpam-6093	192	15	is	be	AUX
ejpam-6093	192	16	not	not	PART
ejpam-6093	192	17	a	a	DET
ejpam-6093	192	18	filter	filter	NOUN
ejpam-6093	192	19	of	of	ADP
ejpam-6093	192	20	t	t	PROPN
ejpam-6093	192	21	,	,	PUNCT
ejpam-6093	192	22	since	since	SCONJ
ejpam-6093	192	23	[	[	X
ejpam-6093	192	24	123]∗	123]∗	NUM
ejpam-6093	192	25	=	=	SYM
ejpam-6093	192	26	2	2	NUM
ejpam-6093	192	27	∈	∈	NOUN
ejpam-6093	192	28	f	f	X
ejpam-6093	192	29	(	(	PUNCT
ejpam-6093	192	30	2	2	NUM
ejpam-6093	192	31	)	)	PUNCT
ejpam-6093	192	32	and	and	CCONJ
ejpam-6093	192	33	1	1	NUM
ejpam-6093	192	34	,	,	PUNCT
ejpam-6093	192	35	2	2	NUM
ejpam-6093	192	36	∈	∈	NOUN
ejpam-6093	192	37	f	f	X
ejpam-6093	192	38	(	(	PUNCT
ejpam-6093	192	39	2	2	NUM
ejpam-6093	192	40	)	)	PUNCT
ejpam-6093	192	41	,	,	PUNCT
ejpam-6093	192	42	but	but	CCONJ
ejpam-6093	192	43	3	3	NUM
ejpam-6093	192	44	/∈	/∈	SYM
ejpam-6093	192	45	f	f	X
ejpam-6093	192	46	(	(	PUNCT
ejpam-6093	192	47	2	2	NUM
ejpam-6093	192	48	)	)	PUNCT
ejpam-6093	192	49	.	.	PUNCT
ejpam-6093	193	1	k.	k.	PROPN
ejpam-6093	193	2	nakwan	nakwan	PROPN
ejpam-6093	193	3	,	,	PUNCT
ejpam-6093	193	4	p.	p.	PROPN
ejpam-6093	193	5	luangchaisri	luangchaisri	VERB
ejpam-6093	193	6	,	,	PUNCT
ejpam-6093	193	7	t.	t.	PROPN
ejpam-6093	193	8	changphas	changphas	PROPN
ejpam-6093	193	9	/	/	SYM
ejpam-6093	193	10	eur	eur	PROPN
ejpam-6093	193	11	.	.	PUNCT
ejpam-6093	194	1	j.	j.	PROPN
ejpam-6093	194	2	pure	pure	PROPN
ejpam-6093	194	3	appl	appl	PROPN
ejpam-6093	194	4	.	.	PROPN
ejpam-6093	194	5	math	math	PROPN
ejpam-6093	194	6	,	,	PUNCT
ejpam-6093	194	7	18	18	NUM
ejpam-6093	194	8	(	(	PUNCT
ejpam-6093	194	9	4	4	NUM
ejpam-6093	194	10	)	)	PUNCT
ejpam-6093	194	11	(	(	PUNCT
ejpam-6093	194	12	2025	2025	NUM
ejpam-6093	194	13	)	)	PUNCT
ejpam-6093	194	14	,	,	PUNCT
ejpam-6093	194	15	6093	6093	NUM
ejpam-6093	194	16	7	7	NUM
ejpam-6093	194	17	of	of	ADP
ejpam-6093	194	18	11	11	NUM
ejpam-6093	194	19	lemma	lemma	PROPN
ejpam-6093	194	20	2	2	NUM
ejpam-6093	194	21	.	.	PUNCT
ejpam-6093	195	1	let	let	AUX
ejpam-6093	195	2	(	(	PUNCT
ejpam-6093	195	3	t	t	NOUN
ejpam-6093	195	4	,	,	PUNCT
ejpam-6093	195	5	[	[	PUNCT
ejpam-6093	195	6	]	]	X
ejpam-6093	195	7	,	,	PUNCT
ejpam-6093	195	8	≤	≤	NUM
ejpam-6093	195	9	,	,	PUNCT
ejpam-6093	195	10	[	[	PUNCT
ejpam-6093	195	11	]	]	X
ejpam-6093	195	12	∗	∗	NOUN
ejpam-6093	195	13	)	)	PUNCT
ejpam-6093	195	14	be	be	VERB
ejpam-6093	195	15	an	an	DET
ejpam-6093	195	16	implicative	implicative	ADJ
ejpam-6093	195	17	n.p.o	n.p.o	NOUN
ejpam-6093	195	18	.	.	PUNCT
ejpam-6093	196	1	ternary	ternary	PROPN
ejpam-6093	196	2	semigroup	semigroup	PROPN
ejpam-6093	196	3	.	.	PUNCT
ejpam-6093	197	1	then	then	ADV
ejpam-6093	197	2	f	f	X
ejpam-6093	197	3	(	(	PUNCT
ejpam-6093	197	4	a	a	PRON
ejpam-6093	197	5	)	)	PUNCT
ejpam-6093	197	6	is	be	AUX
ejpam-6093	197	7	a	a	DET
ejpam-6093	197	8	filter	filter	NOUN
ejpam-6093	197	9	of	of	ADP
ejpam-6093	197	10	t	t	PROPN
ejpam-6093	197	11	for	for	ADP
ejpam-6093	197	12	all	all	DET
ejpam-6093	197	13	a	a	DET
ejpam-6093	197	14	∈	∈	NOUN
ejpam-6093	197	15	t	t	NOUN
ejpam-6093	197	16	if	if	SCONJ
ejpam-6093	197	17	and	and	CCONJ
ejpam-6093	197	18	only	only	ADV
ejpam-6093	197	19	if	if	SCONJ
ejpam-6093	197	20	,	,	PUNCT
ejpam-6093	197	21	for	for	ADP
ejpam-6093	197	22	all	all	DET
ejpam-6093	197	23	x	x	NOUN
ejpam-6093	197	24	,	,	PUNCT
ejpam-6093	197	25	y	y	PROPN
ejpam-6093	197	26	,	,	PUNCT
ejpam-6093	197	27	z	z	PROPN
ejpam-6093	197	28	,	,	PUNCT
ejpam-6093	197	29	u	u	PROPN
ejpam-6093	197	30	∈	∈	PROPN
ejpam-6093	197	31	t	t	PROPN
ejpam-6093	197	32	,	,	PUNCT
ejpam-6093	197	33	u	u	NOUN
ejpam-6093	197	34	≤	≤	X
ejpam-6093	198	1	[	[	X
ejpam-6093	198	2	xyz]∗	xyz]∗	PROPN
ejpam-6093	198	3	,	,	PUNCT
ejpam-6093	198	4	u	u	NOUN
ejpam-6093	198	5	≤	≤	X
ejpam-6093	198	6	x	x	X
ejpam-6093	198	7	,	,	PUNCT
ejpam-6093	198	8	and	and	CCONJ
ejpam-6093	198	9	u	u	NOUN
ejpam-6093	198	10	≤	≤	NOUN
ejpam-6093	198	11	y	y	PROPN
ejpam-6093	198	12	imply	imply	VERB
ejpam-6093	198	13	u	u	NOUN
ejpam-6093	198	14	≤	≤	X
ejpam-6093	198	15	z.	z.	PROPN
ejpam-6093	198	16	proof	proof	NOUN
ejpam-6093	198	17	.	.	PUNCT
ejpam-6093	199	1	assume	assume	VERB
ejpam-6093	199	2	that	that	SCONJ
ejpam-6093	199	3	f	f	PROPN
ejpam-6093	199	4	(	(	PUNCT
ejpam-6093	199	5	a	a	NOUN
ejpam-6093	199	6	)	)	PUNCT
ejpam-6093	199	7	is	be	AUX
ejpam-6093	199	8	a	a	DET
ejpam-6093	199	9	filter	filter	NOUN
ejpam-6093	199	10	of	of	ADP
ejpam-6093	199	11	t	t	PROPN
ejpam-6093	199	12	for	for	ADP
ejpam-6093	199	13	all	all	DET
ejpam-6093	199	14	a	a	DET
ejpam-6093	199	15	∈	∈	PROPN
ejpam-6093	199	16	t	t	NOUN
ejpam-6093	199	17	.	.	PUNCT
ejpam-6093	200	1	let	let	VERB
ejpam-6093	200	2	x	x	PRON
ejpam-6093	200	3	,	,	PUNCT
ejpam-6093	200	4	y	y	PROPN
ejpam-6093	200	5	,	,	PUNCT
ejpam-6093	200	6	z	z	PROPN
ejpam-6093	200	7	,	,	PUNCT
ejpam-6093	200	8	u	u	PROPN
ejpam-6093	200	9	∈	∈	PROPN
ejpam-6093	200	10	t	t	NOUN
ejpam-6093	200	11	such	such	ADJ
ejpam-6093	200	12	that	that	SCONJ
ejpam-6093	200	13	u	u	PROPN
ejpam-6093	200	14	≤	≤	X
ejpam-6093	201	1	[	[	X
ejpam-6093	201	2	xyz]∗	xyz]∗	PROPN
ejpam-6093	201	3	,	,	PUNCT
ejpam-6093	201	4	u	u	NOUN
ejpam-6093	201	5	≤	≤	X
ejpam-6093	201	6	x	x	PUNCT
ejpam-6093	201	7	and	and	CCONJ
ejpam-6093	201	8	u	u	PROPN
ejpam-6093	201	9	≤	≤	X
ejpam-6093	201	10	y.	y.	NOUN
ejpam-6093	201	11	then	then	ADV
ejpam-6093	202	1	[	[	X
ejpam-6093	202	2	xyz]∗	xyz]∗	X
ejpam-6093	202	3	∈	∈	PROPN
ejpam-6093	202	4	f	f	X
ejpam-6093	202	5	(	(	PUNCT
ejpam-6093	202	6	u	u	NOUN
ejpam-6093	202	7	)	)	PUNCT
ejpam-6093	202	8	,	,	PUNCT
ejpam-6093	202	9	x	x	PUNCT
ejpam-6093	202	10	∈	∈	PROPN
ejpam-6093	202	11	f	f	X
ejpam-6093	202	12	(	(	PUNCT
ejpam-6093	202	13	u	u	NOUN
ejpam-6093	202	14	)	)	PUNCT
ejpam-6093	202	15	and	and	CCONJ
ejpam-6093	202	16	y	y	PROPN
ejpam-6093	202	17	∈	∈	PROPN
ejpam-6093	202	18	f	f	X
ejpam-6093	202	19	(	(	PUNCT
ejpam-6093	202	20	u	u	NOUN
ejpam-6093	202	21	)	)	PUNCT
ejpam-6093	202	22	.	.	PUNCT
ejpam-6093	203	1	by	by	ADP
ejpam-6093	203	2	assumption	assumption	NOUN
ejpam-6093	203	3	,	,	PUNCT
ejpam-6093	203	4	z	z	PROPN
ejpam-6093	203	5	∈	∈	PROPN
ejpam-6093	203	6	f	f	X
ejpam-6093	203	7	(	(	PUNCT
ejpam-6093	203	8	u	u	NOUN
ejpam-6093	203	9	)	)	PUNCT
ejpam-6093	203	10	.	.	PUNCT
ejpam-6093	204	1	this	this	PRON
ejpam-6093	204	2	means	mean	VERB
ejpam-6093	204	3	that	that	SCONJ
ejpam-6093	204	4	u	u	PROPN
ejpam-6093	204	5	≤	≤	X
ejpam-6093	204	6	z.	z.	PROPN
ejpam-6093	204	7	conversely	conversely	ADV
ejpam-6093	204	8	,	,	PUNCT
ejpam-6093	204	9	assume	assume	VERB
ejpam-6093	204	10	that	that	SCONJ
ejpam-6093	204	11	u	u	PRON
ejpam-6093	204	12	≤	≤	X
ejpam-6093	205	1	[	[	X
ejpam-6093	205	2	xyz]∗	xyz]∗	PROPN
ejpam-6093	205	3	,	,	PUNCT
ejpam-6093	205	4	u	u	NOUN
ejpam-6093	205	5	≤	≤	X
ejpam-6093	205	6	x	x	PUNCT
ejpam-6093	205	7	and	and	CCONJ
ejpam-6093	205	8	u	u	PROPN
ejpam-6093	205	9	≤	≤	NOUN
ejpam-6093	205	10	y	y	NOUN
ejpam-6093	205	11	imply	imply	VERB
ejpam-6093	205	12	u	u	NOUN
ejpam-6093	205	13	≤	≤	ADJ
ejpam-6093	205	14	z	z	NOUN
ejpam-6093	205	15	for	for	ADP
ejpam-6093	205	16	all	all	DET
ejpam-6093	205	17	x	x	NOUN
ejpam-6093	205	18	,	,	PUNCT
ejpam-6093	205	19	y	y	PROPN
ejpam-6093	205	20	,	,	PUNCT
ejpam-6093	205	21	z	z	PROPN
ejpam-6093	205	22	,	,	PUNCT
ejpam-6093	205	23	u	u	PROPN
ejpam-6093	205	24	∈	∈	PROPN
ejpam-6093	205	25	t	t	PROPN
ejpam-6093	205	26	.	.	PUNCT
ejpam-6093	206	1	let	let	VERB
ejpam-6093	206	2	a	a	DET
ejpam-6093	206	3	∈	∈	PROPN
ejpam-6093	206	4	t	t	NOUN
ejpam-6093	206	5	.	.	PUNCT
ejpam-6093	207	1	clearly	clearly	ADV
ejpam-6093	207	2	,	,	PUNCT
ejpam-6093	207	3	1	1	NUM
ejpam-6093	207	4	∈	∈	PROPN
ejpam-6093	207	5	f	f	X
ejpam-6093	207	6	(	(	PUNCT
ejpam-6093	207	7	a	a	NOUN
ejpam-6093	207	8	)	)	PUNCT
ejpam-6093	207	9	.	.	PUNCT
ejpam-6093	208	1	let	let	VERB
ejpam-6093	208	2	[	[	PUNCT
ejpam-6093	208	3	xyz]∗	xyz]∗	X
ejpam-6093	208	4	∈	∈	PROPN
ejpam-6093	208	5	f	f	X
ejpam-6093	208	6	(	(	PUNCT
ejpam-6093	208	7	a	a	NOUN
ejpam-6093	208	8	)	)	PUNCT
ejpam-6093	208	9	and	and	CCONJ
ejpam-6093	208	10	x	x	X
ejpam-6093	208	11	,	,	PUNCT
ejpam-6093	208	12	y	y	PROPN
ejpam-6093	208	13	∈	∈	PROPN
ejpam-6093	208	14	f	f	X
ejpam-6093	208	15	(	(	PUNCT
ejpam-6093	208	16	a	a	NOUN
ejpam-6093	208	17	)	)	PUNCT
ejpam-6093	208	18	.	.	PUNCT
ejpam-6093	209	1	then	then	ADV
ejpam-6093	209	2	a	a	DET
ejpam-6093	209	3	≤	≤	PROPN
ejpam-6093	210	1	[	[	X
ejpam-6093	210	2	xyz]∗	xyz]∗	PROPN
ejpam-6093	210	3	,	,	PUNCT
ejpam-6093	210	4	a	a	DET
ejpam-6093	210	5	≤	≤	NOUN
ejpam-6093	210	6	x	x	PUNCT
ejpam-6093	210	7	and	and	CCONJ
ejpam-6093	210	8	a	a	DET
ejpam-6093	210	9	≤	≤	ADJ
ejpam-6093	210	10	y.	y.	NOUN
ejpam-6093	210	11	by	by	ADP
ejpam-6093	210	12	assumption	assumption	NOUN
ejpam-6093	210	13	,	,	PUNCT
ejpam-6093	210	14	a	a	DET
ejpam-6093	210	15	≤	≤	PROPN
ejpam-6093	210	16	z	z	NOUN
ejpam-6093	210	17	;	;	PUNCT
ejpam-6093	210	18	so	so	SCONJ
ejpam-6093	210	19	z	z	PROPN
ejpam-6093	210	20	∈	∈	PROPN
ejpam-6093	210	21	f	f	X
ejpam-6093	210	22	(	(	PUNCT
ejpam-6093	210	23	a	a	NOUN
ejpam-6093	210	24	)	)	PUNCT
ejpam-6093	210	25	.	.	PUNCT
ejpam-6093	211	1	proposition	proposition	NOUN
ejpam-6093	211	2	1	1	NUM
ejpam-6093	211	3	.	.	PUNCT
ejpam-6093	212	1	let	let	AUX
ejpam-6093	212	2	(	(	PUNCT
ejpam-6093	212	3	t	t	NOUN
ejpam-6093	212	4	,	,	PUNCT
ejpam-6093	212	5	[	[	PUNCT
ejpam-6093	212	6	]	]	X
ejpam-6093	212	7	,	,	PUNCT
ejpam-6093	212	8	≤	≤	NUM
ejpam-6093	212	9	,	,	PUNCT
ejpam-6093	212	10	[	[	PUNCT
ejpam-6093	212	11	]	]	X
ejpam-6093	212	12	∗	∗	NOUN
ejpam-6093	212	13	)	)	PUNCT
ejpam-6093	212	14	be	be	VERB
ejpam-6093	212	15	an	an	DET
ejpam-6093	212	16	implicative	implicative	ADJ
ejpam-6093	212	17	n.p.o	n.p.o	NOUN
ejpam-6093	212	18	.	.	PUNCT
ejpam-6093	213	1	ternary	ternary	ADJ
ejpam-6093	213	2	semigroup	semigroup	PROPN
ejpam-6093	213	3	.	.	PUNCT
ejpam-6093	214	1	if	if	SCONJ
ejpam-6093	214	2	{	{	PUNCT
ejpam-6093	214	3	1	1	NUM
ejpam-6093	214	4	}	}	PUNCT
ejpam-6093	214	5	is	be	AUX
ejpam-6093	214	6	an	an	DET
ejpam-6093	214	7	implicative	implicative	ADJ
ejpam-6093	214	8	filter	filter	NOUN
ejpam-6093	214	9	of	of	ADP
ejpam-6093	214	10	t	t	PROPN
ejpam-6093	214	11	,	,	PUNCT
ejpam-6093	214	12	then	then	ADV
ejpam-6093	214	13	f	f	X
ejpam-6093	214	14	(	(	PUNCT
ejpam-6093	214	15	a	a	PRON
ejpam-6093	214	16	)	)	PUNCT
ejpam-6093	214	17	is	be	AUX
ejpam-6093	214	18	a	a	DET
ejpam-6093	214	19	filter	filter	NOUN
ejpam-6093	214	20	of	of	ADP
ejpam-6093	214	21	t	t	PROPN
ejpam-6093	214	22	for	for	ADP
ejpam-6093	214	23	all	all	DET
ejpam-6093	214	24	a	a	DET
ejpam-6093	214	25	∈	∈	PROPN
ejpam-6093	214	26	t	t	NOUN
ejpam-6093	214	27	.	.	PUNCT
ejpam-6093	215	1	proof	proof	NOUN
ejpam-6093	215	2	.	.	PUNCT
ejpam-6093	216	1	suppose	suppose	VERB
ejpam-6093	216	2	{	{	PUNCT
ejpam-6093	216	3	1	1	X
ejpam-6093	216	4	}	}	PUNCT
ejpam-6093	216	5	is	be	AUX
ejpam-6093	216	6	an	an	DET
ejpam-6093	216	7	implicative	implicative	ADJ
ejpam-6093	216	8	filter	filter	NOUN
ejpam-6093	216	9	of	of	ADP
ejpam-6093	216	10	t	t	PROPN
ejpam-6093	216	11	.	.	PUNCT
ejpam-6093	217	1	let	let	VERB
ejpam-6093	217	2	a	a	DET
ejpam-6093	217	3	,	,	PUNCT
ejpam-6093	217	4	x	x	NOUN
ejpam-6093	217	5	,	,	PUNCT
ejpam-6093	217	6	y	y	PROPN
ejpam-6093	217	7	,	,	PUNCT
ejpam-6093	217	8	z	z	PROPN
ejpam-6093	217	9	∈	∈	PROPN
ejpam-6093	217	10	t	t	NOUN
ejpam-6093	217	11	such	such	ADJ
ejpam-6093	217	12	that	that	SCONJ
ejpam-6093	218	1	[	[	X
ejpam-6093	218	2	xyz]∗	xyz]∗	PROPN
ejpam-6093	218	3	,	,	PUNCT
ejpam-6093	218	4	x	x	PRON
ejpam-6093	218	5	,	,	PUNCT
ejpam-6093	218	6	y	y	PROPN
ejpam-6093	218	7	∈	∈	PROPN
ejpam-6093	218	8	f	f	X
ejpam-6093	218	9	(	(	PUNCT
ejpam-6093	218	10	a	a	NOUN
ejpam-6093	218	11	)	)	PUNCT
ejpam-6093	218	12	.	.	PUNCT
ejpam-6093	219	1	then	then	ADV
ejpam-6093	219	2	a	a	DET
ejpam-6093	219	3	≤	≤	PROPN
ejpam-6093	220	1	[	[	X
ejpam-6093	220	2	xyz]∗	xyz]∗	PROPN
ejpam-6093	220	3	,	,	PUNCT
ejpam-6093	220	4	a	a	DET
ejpam-6093	220	5	≤	≤	NOUN
ejpam-6093	220	6	x	x	X
ejpam-6093	220	7	,	,	PUNCT
ejpam-6093	220	8	and	and	CCONJ
ejpam-6093	220	9	a	a	DET
ejpam-6093	220	10	≤	≤	NUM
ejpam-6093	220	11	y.	y.	NOUN
ejpam-6093	220	12	thus	thus	ADV
ejpam-6093	220	13	,	,	PUNCT
ejpam-6093	220	14	by	by	ADP
ejpam-6093	220	15	theorem	theorem	NOUN
ejpam-6093	220	16	1	1	NUM
ejpam-6093	220	17	(	(	PUNCT
ejpam-6093	220	18	6	6	NUM
ejpam-6093	220	19	)	)	PUNCT
ejpam-6093	220	20	,	,	PUNCT
ejpam-6093	220	21	[	[	X
ejpam-6093	220	22	a1[xyz]∗]∗	a1[xyz]∗]∗	X
ejpam-6093	220	23	=	=	SYM
ejpam-6093	220	24	1	1	NUM
ejpam-6093	220	25	∈	∈	NOUN
ejpam-6093	220	26	{	{	PUNCT
ejpam-6093	220	27	1	1	NUM
ejpam-6093	220	28	}	}	PUNCT
ejpam-6093	220	29	,	,	PUNCT
ejpam-6093	220	30	[	[	X
ejpam-6093	220	31	a1x]∗	a1x]∗	NOUN
ejpam-6093	220	32	=	=	SYM
ejpam-6093	220	33	1	1	NUM
ejpam-6093	220	34	∈	∈	NOUN
ejpam-6093	220	35	{	{	PUNCT
ejpam-6093	220	36	1	1	NUM
ejpam-6093	220	37	}	}	PUNCT
ejpam-6093	220	38	,	,	PUNCT
ejpam-6093	220	39	and	and	CCONJ
ejpam-6093	220	40	[	[	X
ejpam-6093	220	41	a1y]∗	a1y]∗	NOUN
ejpam-6093	220	42	=	=	SYM
ejpam-6093	220	43	1	1	NUM
ejpam-6093	220	44	∈	∈	NOUN
ejpam-6093	220	45	{	{	PUNCT
ejpam-6093	220	46	1	1	NUM
ejpam-6093	220	47	}	}	PUNCT
ejpam-6093	220	48	.	.	PUNCT
ejpam-6093	221	1	by	by	ADP
ejpam-6093	221	2	assumption	assumption	NOUN
ejpam-6093	221	3	and	and	CCONJ
ejpam-6093	221	4	applying	apply	VERB
ejpam-6093	221	5	definition	definition	NOUN
ejpam-6093	221	6	2	2	NUM
ejpam-6093	221	7	with	with	ADP
ejpam-6093	221	8	(	(	PUNCT
ejpam-6093	221	9	x	x	NOUN
ejpam-6093	221	10	,	,	PUNCT
ejpam-6093	221	11	y	y	PROPN
ejpam-6093	221	12	,	,	PUNCT
ejpam-6093	221	13	z	z	PROPN
ejpam-6093	221	14	,	,	PUNCT
ejpam-6093	221	15	u	u	NOUN
ejpam-6093	221	16	,	,	PUNCT
ejpam-6093	221	17	v	v	NOUN
ejpam-6093	221	18	)	)	PUNCT
ejpam-6093	221	19	7→	7→	NOUN
ejpam-6093	221	20	(	(	PUNCT
ejpam-6093	221	21	a	a	PRON
ejpam-6093	221	22	,	,	PUNCT
ejpam-6093	221	23	1	1	NUM
ejpam-6093	221	24	,	,	PUNCT
ejpam-6093	221	25	x	x	NOUN
ejpam-6093	221	26	,	,	PUNCT
ejpam-6093	221	27	y	y	PROPN
ejpam-6093	221	28	,	,	PUNCT
ejpam-6093	221	29	z	z	NOUN
ejpam-6093	221	30	)	)	PUNCT
ejpam-6093	221	31	,	,	PUNCT
ejpam-6093	221	32	we	we	PRON
ejpam-6093	221	33	obtain	obtain	VERB
ejpam-6093	222	1	[	[	PUNCT
ejpam-6093	222	2	a1z]∗	a1z]∗	X
ejpam-6093	222	3	∈	∈	PROPN
ejpam-6093	222	4	{	{	PUNCT
ejpam-6093	222	5	1	1	NUM
ejpam-6093	222	6	}	}	PUNCT
ejpam-6093	222	7	.	.	PUNCT
ejpam-6093	223	1	therefore	therefore	ADV
ejpam-6093	223	2	,	,	PUNCT
ejpam-6093	223	3	[	[	X
ejpam-6093	223	4	a1z]∗	a1z]∗	X
ejpam-6093	223	5	=	=	SYM
ejpam-6093	223	6	1	1	NUM
ejpam-6093	223	7	,	,	PUNCT
ejpam-6093	223	8	that	that	ADV
ejpam-6093	223	9	is	is	ADV
ejpam-6093	223	10	,	,	PUNCT
ejpam-6093	223	11	a	a	DET
ejpam-6093	223	12	≤	≤	NOUN
ejpam-6093	223	13	z	z	NOUN
ejpam-6093	223	14	by	by	ADP
ejpam-6093	223	15	theorem	theorem	NOUN
ejpam-6093	223	16	1	1	NUM
ejpam-6093	223	17	(	(	PUNCT
ejpam-6093	223	18	6	6	NUM
ejpam-6093	223	19	)	)	PUNCT
ejpam-6093	223	20	.	.	PUNCT
ejpam-6093	224	1	hence	hence	ADV
ejpam-6093	224	2	z	z	PROPN
ejpam-6093	224	3	∈	∈	PROPN
ejpam-6093	224	4	f	f	X
ejpam-6093	224	5	(	(	PUNCT
ejpam-6093	224	6	a	a	NOUN
ejpam-6093	224	7	)	)	PUNCT
ejpam-6093	224	8	.	.	PUNCT
ejpam-6093	225	1	let	let	VERB
ejpam-6093	225	2	f	f	PRON
ejpam-6093	225	3	be	be	AUX
ejpam-6093	225	4	a	a	DET
ejpam-6093	225	5	filter	filter	NOUN
ejpam-6093	225	6	of	of	ADP
ejpam-6093	225	7	an	an	DET
ejpam-6093	225	8	implicative	implicative	ADJ
ejpam-6093	225	9	n.p.o	n.p.o	NOUN
ejpam-6093	225	10	.	.	PUNCT
ejpam-6093	226	1	ternary	ternary	ADJ
ejpam-6093	226	2	semigroup	semigroup	PROPN
ejpam-6093	226	3	(	(	PUNCT
ejpam-6093	226	4	t	t	PROPN
ejpam-6093	226	5	,	,	PUNCT
ejpam-6093	226	6	[	[	PUNCT
ejpam-6093	226	7	]	]	X
ejpam-6093	226	8	,	,	PUNCT
ejpam-6093	226	9	≤	≤	NUM
ejpam-6093	226	10	,	,	PUNCT
ejpam-6093	226	11	[	[	PUNCT
ejpam-6093	226	12	]	]	X
ejpam-6093	226	13	∗	∗	NOUN
ejpam-6093	226	14	)	)	PUNCT
ejpam-6093	226	15	.	.	PUNCT
ejpam-6093	227	1	for	for	ADP
ejpam-6093	227	2	a	a	DET
ejpam-6093	227	3	,	,	PUNCT
ejpam-6093	227	4	b	b	PROPN
ejpam-6093	227	5	∈	∈	PROPN
ejpam-6093	227	6	t	t	NOUN
ejpam-6093	227	7	,	,	PUNCT
ejpam-6093	227	8	define	define	VERB
ejpam-6093	227	9	fab	fab	NOUN
ejpam-6093	227	10	:	:	PUNCT
ejpam-6093	227	11	=	=	SYM
ejpam-6093	227	12	{	{	PUNCT
ejpam-6093	227	13	x	x	PUNCT
ejpam-6093	227	14	∈	∈	PROPN
ejpam-6093	227	15	t	t	NOUN
ejpam-6093	227	16	:	:	PUNCT
ejpam-6093	228	1	[	[	X
ejpam-6093	228	2	abx]∗	abx]∗	X
ejpam-6093	228	3	∈	∈	PROPN
ejpam-6093	228	4	f	f	X
ejpam-6093	228	5	}	}	PUNCT
ejpam-6093	228	6	.	.	PUNCT
ejpam-6093	229	1	by	by	ADP
ejpam-6093	229	2	theorem	theorem	NOUN
ejpam-6093	229	3	1	1	NUM
ejpam-6093	229	4	(	(	PUNCT
ejpam-6093	229	5	1	1	NUM
ejpam-6093	229	6	)	)	PUNCT
ejpam-6093	229	7	,	,	PUNCT
ejpam-6093	229	8	f11	f11	PROPN
ejpam-6093	229	9	=	=	SYM
ejpam-6093	229	10	f	f	PROPN
ejpam-6093	229	11	.	.	PUNCT
ejpam-6093	230	1	the	the	DET
ejpam-6093	230	2	set	set	ADJ
ejpam-6093	230	3	fab	fab	NOUN
ejpam-6093	230	4	may	may	AUX
ejpam-6093	230	5	not	not	PART
ejpam-6093	230	6	be	be	AUX
ejpam-6093	230	7	a	a	DET
ejpam-6093	230	8	filter	filter	NOUN
ejpam-6093	230	9	.	.	PUNCT
ejpam-6093	230	10	example	example	NOUN
ejpam-6093	231	1	4	4	NUM
ejpam-6093	231	2	.	.	PUNCT
ejpam-6093	231	3	again	again	ADV
ejpam-6093	231	4	,	,	PUNCT
ejpam-6093	231	5	let	let	VERB
ejpam-6093	231	6	us	we	PRON
ejpam-6093	231	7	consider	consider	VERB
ejpam-6093	231	8	the	the	DET
ejpam-6093	231	9	implicative	implicative	ADJ
ejpam-6093	231	10	n.p.o	n.p.o	NOUN
ejpam-6093	231	11	.	.	PUNCT
ejpam-6093	232	1	ternary	ternary	PROPN
ejpam-6093	232	2	semigroup	semigroup	PROPN
ejpam-6093	232	3	t	t	PROPN
ejpam-6093	232	4	defined	define	VERB
ejpam-6093	232	5	in	in	ADP
ejpam-6093	232	6	example	example	NOUN
ejpam-6093	232	7	1	1	X
ejpam-6093	232	8	.	.	PUNCT
ejpam-6093	233	1	we	we	PRON
ejpam-6093	233	2	have	have	VERB
ejpam-6093	233	3	f	f	NOUN
ejpam-6093	233	4	=	=	SYM
ejpam-6093	233	5	{	{	PUNCT
ejpam-6093	233	6	1	1	NUM
ejpam-6093	233	7	,	,	PUNCT
ejpam-6093	233	8	5	5	NUM
ejpam-6093	233	9	}	}	PUNCT
ejpam-6093	233	10	is	be	AUX
ejpam-6093	233	11	a	a	DET
ejpam-6093	233	12	filter	filter	NOUN
ejpam-6093	233	13	of	of	ADP
ejpam-6093	233	14	t	t	PROPN
ejpam-6093	233	15	.	.	PUNCT
ejpam-6093	234	1	note	note	VERB
ejpam-6093	234	2	that	that	SCONJ
ejpam-6093	234	3	f11	f11	PROPN
ejpam-6093	234	4	=	=	SYM
ejpam-6093	234	5	f15	f15	PROPN
ejpam-6093	234	6	=	=	SYM
ejpam-6093	234	7	f51	f51	PROPN
ejpam-6093	234	8	=	=	SYM
ejpam-6093	234	9	f55	f55	NOUN
ejpam-6093	234	10	=	=	PUNCT
ejpam-6093	234	11	{	{	PUNCT
ejpam-6093	234	12	1	1	NUM
ejpam-6093	234	13	,	,	PUNCT
ejpam-6093	234	14	5	5	NUM
ejpam-6093	234	15	}	}	PUNCT
ejpam-6093	234	16	,	,	PUNCT
ejpam-6093	234	17	f12	f12	NOUN
ejpam-6093	234	18	=	=	SYM
ejpam-6093	234	19	f17	f17	NOUN
ejpam-6093	234	20	=	=	SYM
ejpam-6093	234	21	f21	f21	NOUN
ejpam-6093	234	22	=	=	PROPN
ejpam-6093	234	23	f25	f25	NOUN
ejpam-6093	234	24	=	=	NOUN
ejpam-6093	235	1	f52	f52	NOUN
ejpam-6093	235	2	=	=	NOUN
ejpam-6093	235	3	f57	f57	VERB
ejpam-6093	235	4	=	=	SYM
ejpam-6093	235	5	f71	f71	ADJ
ejpam-6093	235	6	=	=	SYM
ejpam-6093	235	7	f75	f75	NOUN
ejpam-6093	235	8	=	=	SYM
ejpam-6093	235	9	{	{	PUNCT
ejpam-6093	235	10	1	1	NUM
ejpam-6093	235	11	,	,	PUNCT
ejpam-6093	235	12	2	2	NUM
ejpam-6093	235	13	,	,	PUNCT
ejpam-6093	235	14	5	5	NUM
ejpam-6093	235	15	,	,	PUNCT
ejpam-6093	235	16	7	7	NUM
ejpam-6093	235	17	}	}	PUNCT
ejpam-6093	235	18	,	,	PUNCT
ejpam-6093	235	19	and	and	CCONJ
ejpam-6093	235	20	f13	f13	X
ejpam-6093	235	21	=	=	SYM
ejpam-6093	235	22	f19	f19	PROPN
ejpam-6093	235	23	=	=	NOUN
ejpam-6093	235	24	f22	f22	NOUN
ejpam-6093	235	25	=	=	SYM
ejpam-6093	235	26	f23	f23	PROPN
ejpam-6093	235	27	=	=	PROPN
ejpam-6093	235	28	f27	f27	NOUN
ejpam-6093	235	29	=	=	PROPN
ejpam-6093	235	30	f29	f29	NOUN
ejpam-6093	235	31	=	=	SYM
ejpam-6093	235	32	f31	f31	NOUN
ejpam-6093	235	33	=	=	NOUN
ejpam-6093	235	34	f32	f32	NOUN
ejpam-6093	235	35	=	=	SYM
ejpam-6093	235	36	f33	f33	NOUN
ejpam-6093	235	37	=	=	PUNCT
ejpam-6093	235	38	f35	f35	NOUN
ejpam-6093	235	39	=	=	SYM
ejpam-6093	235	40	f37	f37	NOUN
ejpam-6093	236	1	=	=	PUNCT
ejpam-6093	236	2	f39	f39	NOUN
ejpam-6093	236	3	=	=	NOUN
ejpam-6093	236	4	f53	f53	NOUN
ejpam-6093	236	5	=	=	SYM
ejpam-6093	236	6	f59	f59	NOUN
ejpam-6093	236	7	=	=	SYM
ejpam-6093	236	8	f72	f72	NOUN
ejpam-6093	236	9	=	=	NOUN
ejpam-6093	236	10	f73	f73	NOUN
ejpam-6093	236	11	=	=	SYM
ejpam-6093	236	12	f77	f77	NOUN
ejpam-6093	236	13	=	=	SYM
ejpam-6093	236	14	f79	f79	NOUN
ejpam-6093	236	15	=	=	SYM
ejpam-6093	236	16	f91	f91	NOUN
ejpam-6093	236	17	=	=	SYM
ejpam-6093	236	18	f92	f92	NOUN
ejpam-6093	236	19	=	=	NOUN
ejpam-6093	236	20	f93	f93	NOUN
ejpam-6093	236	21	=	=	SYM
ejpam-6093	236	22	f95	f95	NOUN
ejpam-6093	236	23	=	=	SYM
ejpam-6093	236	24	f97	f97	NOUN
ejpam-6093	236	25	=	=	PUNCT
ejpam-6093	236	26	f99	f99	PROPN
ejpam-6093	236	27	=	=	SYM
ejpam-6093	236	28	{	{	PUNCT
ejpam-6093	236	29	1	1	NUM
ejpam-6093	236	30	,	,	PUNCT
ejpam-6093	236	31	2	2	NUM
ejpam-6093	236	32	,	,	PUNCT
ejpam-6093	236	33	3	3	NUM
ejpam-6093	236	34	,	,	PUNCT
ejpam-6093	236	35	5	5	NUM
ejpam-6093	236	36	,	,	PUNCT
ejpam-6093	236	37	7	7	NUM
ejpam-6093	236	38	,	,	PUNCT
ejpam-6093	236	39	9	9	NUM
ejpam-6093	236	40	}	}	PUNCT
ejpam-6093	236	41	=	=	SYM
ejpam-6093	236	42	t	t	NOUN
ejpam-6093	236	43	.	.	PUNCT
ejpam-6093	237	1	it	it	PRON
ejpam-6093	237	2	is	be	AUX
ejpam-6093	237	3	observed	observe	VERB
ejpam-6093	237	4	that	that	SCONJ
ejpam-6093	237	5	f25	f25	PROPN
ejpam-6093	237	6	=	=	PUNCT
ejpam-6093	237	7	{	{	PUNCT
ejpam-6093	237	8	1	1	NUM
ejpam-6093	237	9	,	,	PUNCT
ejpam-6093	237	10	2	2	NUM
ejpam-6093	237	11	,	,	PUNCT
ejpam-6093	237	12	5	5	NUM
ejpam-6093	237	13	,	,	PUNCT
ejpam-6093	237	14	7	7	NUM
ejpam-6093	237	15	}	}	PUNCT
ejpam-6093	237	16	is	be	AUX
ejpam-6093	237	17	not	not	PART
ejpam-6093	237	18	a	a	DET
ejpam-6093	237	19	filter	filter	NOUN
ejpam-6093	237	20	of	of	ADP
ejpam-6093	237	21	t	t	PROPN
ejpam-6093	237	22	.	.	PUNCT
ejpam-6093	238	1	in	in	ADP
ejpam-6093	238	2	fact	fact	NOUN
ejpam-6093	238	3	,	,	PUNCT
ejpam-6093	238	4	[	[	X
ejpam-6093	238	5	253]∗	253]∗	NUM
ejpam-6093	238	6	=	=	SYM
ejpam-6093	238	7	2	2	NUM
ejpam-6093	238	8	∈	∈	NOUN
ejpam-6093	238	9	f25	f25	NOUN
ejpam-6093	238	10	and	and	CCONJ
ejpam-6093	238	11	2	2	NUM
ejpam-6093	238	12	,	,	PUNCT
ejpam-6093	238	13	5	5	NUM
ejpam-6093	238	14	∈	∈	NOUN
ejpam-6093	238	15	f25	f25	NOUN
ejpam-6093	238	16	,	,	PUNCT
ejpam-6093	238	17	but	but	CCONJ
ejpam-6093	238	18	3	3	NUM
ejpam-6093	238	19	/∈	/∈	NOUN
ejpam-6093	238	20	f25	f25	PROPN
ejpam-6093	238	21	.	.	PUNCT
ejpam-6093	238	22	theorem	theorem	VERB
ejpam-6093	238	23	5	5	NUM
ejpam-6093	238	24	.	.	PUNCT
ejpam-6093	239	1	let	let	AUX
ejpam-6093	239	2	(	(	PUNCT
ejpam-6093	239	3	t	t	NOUN
ejpam-6093	239	4	,	,	PUNCT
ejpam-6093	239	5	[	[	PUNCT
ejpam-6093	239	6	]	]	X
ejpam-6093	239	7	,	,	PUNCT
ejpam-6093	239	8	≤	≤	NUM
ejpam-6093	239	9	,	,	PUNCT
ejpam-6093	239	10	[	[	PUNCT
ejpam-6093	239	11	]	]	X
ejpam-6093	239	12	∗	∗	NOUN
ejpam-6093	239	13	)	)	PUNCT
ejpam-6093	239	14	be	be	VERB
ejpam-6093	239	15	an	an	DET
ejpam-6093	239	16	implicative	implicative	ADJ
ejpam-6093	239	17	n.p.o	n.p.o	NOUN
ejpam-6093	239	18	.	.	PUNCT
ejpam-6093	240	1	ternary	ternary	ADJ
ejpam-6093	240	2	semigroup	semigroup	PROPN
ejpam-6093	240	3	,	,	PUNCT
ejpam-6093	240	4	and	and	CCONJ
ejpam-6093	240	5	let	let	VERB
ejpam-6093	240	6	f	f	PRON
ejpam-6093	240	7	be	be	AUX
ejpam-6093	240	8	a	a	DET
ejpam-6093	240	9	filter	filter	NOUN
ejpam-6093	240	10	of	of	ADP
ejpam-6093	240	11	t	t	PROPN
ejpam-6093	240	12	.	.	PUNCT
ejpam-6093	241	1	then	then	ADV
ejpam-6093	241	2	f	f	PROPN
ejpam-6093	241	3	is	be	AUX
ejpam-6093	241	4	an	an	DET
ejpam-6093	241	5	implicative	implicative	ADJ
ejpam-6093	241	6	filter	filter	NOUN
ejpam-6093	241	7	of	of	ADP
ejpam-6093	241	8	t	t	PROPN
ejpam-6093	241	9	if	if	SCONJ
ejpam-6093	241	10	and	and	CCONJ
ejpam-6093	241	11	only	only	ADV
ejpam-6093	241	12	if	if	SCONJ
ejpam-6093	241	13	for	for	ADP
ejpam-6093	241	14	any	any	DET
ejpam-6093	241	15	a	a	NOUN
ejpam-6093	241	16	,	,	PUNCT
ejpam-6093	241	17	b	b	PROPN
ejpam-6093	241	18	∈	∈	PROPN
ejpam-6093	241	19	t	t	NOUN
ejpam-6093	241	20	,	,	PUNCT
ejpam-6093	241	21	the	the	DET
ejpam-6093	241	22	set	set	VERB
ejpam-6093	241	23	fab	fab	NOUN
ejpam-6093	241	24	is	be	AUX
ejpam-6093	241	25	a	a	DET
ejpam-6093	241	26	filter	filter	NOUN
ejpam-6093	241	27	of	of	ADP
ejpam-6093	241	28	t	t	PROPN
ejpam-6093	241	29	.	.	PUNCT
ejpam-6093	242	1	proof	proof	NOUN
ejpam-6093	242	2	.	.	PUNCT
ejpam-6093	243	1	assume	assume	VERB
ejpam-6093	243	2	that	that	SCONJ
ejpam-6093	243	3	f	f	PROPN
ejpam-6093	243	4	is	be	AUX
ejpam-6093	243	5	an	an	DET
ejpam-6093	243	6	implicative	implicative	ADJ
ejpam-6093	243	7	filter	filter	NOUN
ejpam-6093	243	8	of	of	ADP
ejpam-6093	243	9	t	t	PROPN
ejpam-6093	243	10	.	.	PUNCT
ejpam-6093	244	1	let	let	VERB
ejpam-6093	244	2	a	a	DET
ejpam-6093	244	3	,	,	PUNCT
ejpam-6093	244	4	b	b	PROPN
ejpam-6093	244	5	∈	∈	PROPN
ejpam-6093	244	6	t	t	NOUN
ejpam-6093	244	7	.	.	PUNCT
ejpam-6093	245	1	by	by	ADP
ejpam-6093	245	2	theorem	theorem	NOUN
ejpam-6093	245	3	1	1	NUM
ejpam-6093	245	4	(	(	PUNCT
ejpam-6093	245	5	4	4	NUM
ejpam-6093	245	6	)	)	PUNCT
ejpam-6093	245	7	,	,	PUNCT
ejpam-6093	245	8	1	1	NUM
ejpam-6093	245	9	≤	≤	NOUN
ejpam-6093	246	1	[	[	X
ejpam-6093	246	2	ab1]∗	ab1]∗	NUM
ejpam-6093	246	3	≤	≤	NUM
ejpam-6093	246	4	1	1	NUM
ejpam-6093	246	5	.	.	PUNCT
ejpam-6093	247	1	thus	thus	ADV
ejpam-6093	247	2	[	[	X
ejpam-6093	247	3	ab1]∗	ab1]∗	X
ejpam-6093	247	4	=	=	SYM
ejpam-6093	247	5	1	1	NUM
ejpam-6093	247	6	∈	∈	PROPN
ejpam-6093	247	7	f	f	NOUN
ejpam-6093	247	8	,	,	PUNCT
ejpam-6093	247	9	that	that	ADV
ejpam-6093	247	10	is	is	ADV
ejpam-6093	247	11	,	,	PUNCT
ejpam-6093	247	12	1	1	NUM
ejpam-6093	247	13	∈	∈	PROPN
ejpam-6093	247	14	fab	fab	NOUN
ejpam-6093	247	15	.	.	PUNCT
ejpam-6093	248	1	let	let	VERB
ejpam-6093	248	2	x	x	PRON
ejpam-6093	248	3	,	,	PUNCT
ejpam-6093	248	4	y	y	PROPN
ejpam-6093	248	5	,	,	PUNCT
ejpam-6093	248	6	z	z	PROPN
ejpam-6093	248	7	∈	∈	PROPN
ejpam-6093	248	8	t	t	NOUN
ejpam-6093	248	9	such	such	ADJ
ejpam-6093	248	10	that	that	SCONJ
ejpam-6093	248	11	[	[	X
ejpam-6093	248	12	xyz]∗	xyz]∗	PROPN
ejpam-6093	248	13	,	,	PUNCT
ejpam-6093	248	14	x	x	PRON
ejpam-6093	248	15	,	,	PUNCT
ejpam-6093	248	16	y	y	PROPN
ejpam-6093	248	17	∈	∈	PROPN
ejpam-6093	248	18	fab	fab	NOUN
ejpam-6093	248	19	.	.	PUNCT
ejpam-6093	249	1	then	then	ADV
ejpam-6093	249	2	[	[	X
ejpam-6093	249	3	ab[xyz]∗]∗	ab[xyz]∗]∗	PROPN
ejpam-6093	249	4	∈	∈	PROPN
ejpam-6093	249	5	f	f	NOUN
ejpam-6093	249	6	,	,	PUNCT
ejpam-6093	249	7	[	[	X
ejpam-6093	249	8	abx]∗	abx]∗	X
ejpam-6093	249	9	∈	∈	PROPN
ejpam-6093	249	10	f	f	X
ejpam-6093	249	11	,	,	PUNCT
ejpam-6093	249	12	and	and	CCONJ
ejpam-6093	249	13	[	[	X
ejpam-6093	249	14	aby]∗	aby]∗	X
ejpam-6093	249	15	∈	∈	PROPN
ejpam-6093	249	16	f	f	X
ejpam-6093	249	17	.	.	PUNCT
ejpam-6093	250	1	by	by	ADP
ejpam-6093	250	2	assumption	assumption	NOUN
ejpam-6093	250	3	,	,	PUNCT
ejpam-6093	250	4	[	[	X
ejpam-6093	250	5	abz]∗	abz]∗	NOUN
ejpam-6093	250	6	∈	∈	PROPN
ejpam-6093	250	7	f	f	X
ejpam-6093	250	8	,	,	PUNCT
ejpam-6093	250	9	so	so	CCONJ
ejpam-6093	250	10	z	z	NOUN
ejpam-6093	250	11	∈	∈	PROPN
ejpam-6093	250	12	fab	fab	NOUN
ejpam-6093	250	13	.	.	PUNCT
ejpam-6093	251	1	hence	hence	ADV
ejpam-6093	251	2	fab	fab	NOUN
ejpam-6093	251	3	is	be	AUX
ejpam-6093	251	4	a	a	DET
ejpam-6093	251	5	filter	filter	NOUN
ejpam-6093	251	6	of	of	ADP
ejpam-6093	251	7	t	t	PROPN
ejpam-6093	251	8	.	.	PUNCT
ejpam-6093	252	1	conversely	conversely	ADV
ejpam-6093	252	2	,	,	PUNCT
ejpam-6093	252	3	suppose	suppose	VERB
ejpam-6093	252	4	that	that	SCONJ
ejpam-6093	252	5	fab	fab	NOUN
ejpam-6093	252	6	is	be	AUX
ejpam-6093	252	7	a	a	DET
ejpam-6093	252	8	filter	filter	NOUN
ejpam-6093	252	9	for	for	ADP
ejpam-6093	252	10	all	all	DET
ejpam-6093	252	11	a	a	DET
ejpam-6093	252	12	,	,	PUNCT
ejpam-6093	252	13	b	b	PROPN
ejpam-6093	252	14	∈	∈	PROPN
ejpam-6093	252	15	t	t	NOUN
ejpam-6093	252	16	.	.	PUNCT
ejpam-6093	253	1	let	let	VERB
ejpam-6093	253	2	x	x	PRON
ejpam-6093	253	3	,	,	PUNCT
ejpam-6093	253	4	y	y	PROPN
ejpam-6093	253	5	,	,	PUNCT
ejpam-6093	253	6	z	z	PROPN
ejpam-6093	253	7	,	,	PUNCT
ejpam-6093	253	8	u	u	NOUN
ejpam-6093	253	9	,	,	PUNCT
ejpam-6093	253	10	v	v	PROPN
ejpam-6093	253	11	∈	∈	PROPN
ejpam-6093	253	12	t	t	NOUN
ejpam-6093	253	13	such	such	ADJ
ejpam-6093	253	14	that	that	SCONJ
ejpam-6093	254	1	[	[	X
ejpam-6093	254	2	xy[zuv]∗]∗	xy[zuv]∗]∗	PROPN
ejpam-6093	254	3	∈	∈	PROPN
ejpam-6093	255	1	f	f	X
ejpam-6093	255	2	,	,	PUNCT
ejpam-6093	255	3	[	[	X
ejpam-6093	255	4	xyz]∗	xyz]∗	X
ejpam-6093	255	5	∈	∈	PROPN
ejpam-6093	255	6	f	f	X
ejpam-6093	255	7	,	,	PUNCT
ejpam-6093	255	8	and	and	CCONJ
ejpam-6093	255	9	[	[	X
ejpam-6093	255	10	xyu]∗	xyu]∗	PROPN
ejpam-6093	255	11	∈	∈	PROPN
ejpam-6093	255	12	f.	f.	NOUN
ejpam-6093	256	1	then	then	ADV
ejpam-6093	256	2	[	[	X
ejpam-6093	256	3	zuv]∗	zuv]∗	PROPN
ejpam-6093	256	4	∈	∈	PROPN
ejpam-6093	256	5	fxy	fxy	NOUN
ejpam-6093	256	6	,	,	PUNCT
ejpam-6093	256	7	z	z	PROPN
ejpam-6093	256	8	∈	∈	PROPN
ejpam-6093	256	9	fxy	fxy	NOUN
ejpam-6093	256	10	,	,	PUNCT
ejpam-6093	256	11	and	and	CCONJ
ejpam-6093	256	12	u	u	PROPN
ejpam-6093	256	13	∈	∈	PROPN
ejpam-6093	256	14	fxy	fxy	NOUN
ejpam-6093	256	15	.	.	PUNCT
ejpam-6093	257	1	by	by	ADP
ejpam-6093	257	2	assumption	assumption	NOUN
ejpam-6093	257	3	,	,	PUNCT
ejpam-6093	257	4	v	v	NOUN
ejpam-6093	257	5	∈	∈	PROPN
ejpam-6093	257	6	fxy	fxy	NOUN
ejpam-6093	257	7	,	,	PUNCT
ejpam-6093	257	8	that	that	ADV
ejpam-6093	257	9	is	is	ADV
ejpam-6093	257	10	,	,	PUNCT
ejpam-6093	257	11	[	[	X
ejpam-6093	257	12	xyv	xyv	X
ejpam-6093	257	13	]	]	X
ejpam-6093	257	14	∗	∗	NOUN
ejpam-6093	257	15	∈	∈	PROPN
ejpam-6093	257	16	f	f	X
ejpam-6093	257	17	.	.	PUNCT
ejpam-6093	258	1	thus	thus	ADV
ejpam-6093	258	2	f	f	PROPN
ejpam-6093	258	3	is	be	AUX
ejpam-6093	258	4	an	an	DET
ejpam-6093	258	5	implicative	implicative	ADJ
ejpam-6093	258	6	filter	filter	NOUN
ejpam-6093	258	7	of	of	ADP
ejpam-6093	258	8	t	t	PROPN
ejpam-6093	258	9	.	.	PUNCT
ejpam-6093	259	1	k.	k.	PROPN
ejpam-6093	259	2	nakwan	nakwan	PROPN
ejpam-6093	259	3	,	,	PUNCT
ejpam-6093	259	4	p.	p.	PROPN
ejpam-6093	259	5	luangchaisri	luangchaisri	VERB
ejpam-6093	259	6	,	,	PUNCT
ejpam-6093	259	7	t.	t.	PROPN
ejpam-6093	259	8	changphas	changphas	PROPN
ejpam-6093	259	9	/	/	SYM
ejpam-6093	259	10	eur	eur	PROPN
ejpam-6093	259	11	.	.	PUNCT
ejpam-6093	260	1	j.	j.	PROPN
ejpam-6093	260	2	pure	pure	PROPN
ejpam-6093	260	3	appl	appl	PROPN
ejpam-6093	260	4	.	.	PROPN
ejpam-6093	260	5	math	math	PROPN
ejpam-6093	260	6	,	,	PUNCT
ejpam-6093	260	7	18	18	NUM
ejpam-6093	260	8	(	(	PUNCT
ejpam-6093	260	9	4	4	NUM
ejpam-6093	260	10	)	)	PUNCT
ejpam-6093	260	11	(	(	PUNCT
ejpam-6093	260	12	2025	2025	NUM
ejpam-6093	260	13	)	)	PUNCT
ejpam-6093	260	14	,	,	PUNCT
ejpam-6093	260	15	6093	6093	NUM
ejpam-6093	260	16	8	8	NUM
ejpam-6093	260	17	of	of	ADP
ejpam-6093	260	18	11	11	NUM
ejpam-6093	260	19	example	example	NOUN
ejpam-6093	260	20	5	5	NUM
ejpam-6093	260	21	.	.	X
ejpam-6093	260	22	consider	consider	VERB
ejpam-6093	260	23	the	the	DET
ejpam-6093	260	24	implicative	implicative	ADJ
ejpam-6093	260	25	n.p.o	n.p.o	NOUN
ejpam-6093	260	26	.	.	PUNCT
ejpam-6093	261	1	ternary	ternary	PROPN
ejpam-6093	261	2	semigroup	semigroup	PROPN
ejpam-6093	261	3	t	t	PROPN
ejpam-6093	261	4	defined	define	VERB
ejpam-6093	261	5	in	in	ADP
ejpam-6093	261	6	example	example	NOUN
ejpam-6093	261	7	1	1	X
ejpam-6093	261	8	.	.	PUNCT
ejpam-6093	262	1	we	we	PRON
ejpam-6093	262	2	have	have	VERB
ejpam-6093	262	3	f	f	NOUN
ejpam-6093	262	4	=	=	SYM
ejpam-6093	262	5	{	{	PUNCT
ejpam-6093	262	6	1	1	NUM
ejpam-6093	262	7	,	,	PUNCT
ejpam-6093	262	8	2	2	NUM
ejpam-6093	262	9	,	,	PUNCT
ejpam-6093	262	10	3	3	NUM
ejpam-6093	262	11	}	}	PUNCT
ejpam-6093	262	12	is	be	AUX
ejpam-6093	262	13	a	a	DET
ejpam-6093	262	14	filter	filter	NOUN
ejpam-6093	262	15	of	of	ADP
ejpam-6093	262	16	t	t	PROPN
ejpam-6093	262	17	.	.	PUNCT
ejpam-6093	263	1	furthermore	furthermore	ADV
ejpam-6093	263	2	,	,	PUNCT
ejpam-6093	263	3	we	we	PRON
ejpam-6093	263	4	have	have	VERB
ejpam-6093	263	5	f11	f11	NOUN
ejpam-6093	263	6	=	=	SYM
ejpam-6093	263	7	f12	f12	NOUN
ejpam-6093	263	8	=	=	SYM
ejpam-6093	263	9	f13	f13	PROPN
ejpam-6093	263	10	=	=	PROPN
ejpam-6093	263	11	f21	f21	NOUN
ejpam-6093	263	12	=	=	NOUN
ejpam-6093	263	13	f22	f22	NOUN
ejpam-6093	263	14	=	=	SYM
ejpam-6093	263	15	f23	f23	NOUN
ejpam-6093	263	16	=	=	SYM
ejpam-6093	263	17	f31	f31	NOUN
ejpam-6093	263	18	=	=	NOUN
ejpam-6093	263	19	f32	f32	NOUN
ejpam-6093	263	20	=	=	SYM
ejpam-6093	263	21	f33	f33	NOUN
ejpam-6093	263	22	=	=	PUNCT
ejpam-6093	263	23	{	{	PUNCT
ejpam-6093	263	24	1	1	NUM
ejpam-6093	263	25	,	,	PUNCT
ejpam-6093	263	26	2	2	NUM
ejpam-6093	263	27	,	,	PUNCT
ejpam-6093	263	28	3	3	NUM
ejpam-6093	263	29	}	}	PUNCT
ejpam-6093	263	30	and	and	CCONJ
ejpam-6093	263	31	f15	f15	PROPN
ejpam-6093	263	32	=	=	NOUN
ejpam-6093	264	1	f17	f17	NOUN
ejpam-6093	264	2	=	=	SYM
ejpam-6093	264	3	f19	f19	PROPN
ejpam-6093	264	4	=	=	SYM
ejpam-6093	264	5	f25	f25	NOUN
ejpam-6093	264	6	=	=	PROPN
ejpam-6093	264	7	f27	f27	NOUN
ejpam-6093	264	8	=	=	NOUN
ejpam-6093	264	9	f29	f29	NOUN
ejpam-6093	264	10	=	=	NOUN
ejpam-6093	264	11	f35	f35	NOUN
ejpam-6093	264	12	=	=	SYM
ejpam-6093	264	13	f37	f37	NOUN
ejpam-6093	264	14	=	=	PUNCT
ejpam-6093	264	15	f39	f39	NOUN
ejpam-6093	264	16	=	=	NOUN
ejpam-6093	264	17	f51	f51	NOUN
ejpam-6093	264	18	=	=	SYM
ejpam-6093	264	19	f52	f52	NOUN
ejpam-6093	265	1	=	=	NOUN
ejpam-6093	265	2	f53	f53	NOUN
ejpam-6093	265	3	=	=	SYM
ejpam-6093	265	4	f55	f55	NOUN
ejpam-6093	265	5	=	=	NOUN
ejpam-6093	265	6	f57	f57	VERB
ejpam-6093	265	7	=	=	SYM
ejpam-6093	265	8	f59	f59	NOUN
ejpam-6093	266	1	=	=	SYM
ejpam-6093	266	2	f71	f71	ADJ
ejpam-6093	266	3	=	=	NOUN
ejpam-6093	266	4	f72	f72	NOUN
ejpam-6093	266	5	=	=	NOUN
ejpam-6093	266	6	f73	f73	NOUN
ejpam-6093	266	7	=	=	SYM
ejpam-6093	266	8	f75	f75	NOUN
ejpam-6093	266	9	=	=	SYM
ejpam-6093	266	10	f77	f77	NOUN
ejpam-6093	266	11	=	=	SYM
ejpam-6093	266	12	f79	f79	NOUN
ejpam-6093	266	13	=	=	SYM
ejpam-6093	266	14	f91	f91	NOUN
ejpam-6093	266	15	=	=	SYM
ejpam-6093	266	16	f92	f92	NOUN
ejpam-6093	266	17	=	=	NOUN
ejpam-6093	266	18	f93	f93	NOUN
ejpam-6093	266	19	=	=	SYM
ejpam-6093	266	20	f95	f95	NOUN
ejpam-6093	266	21	=	=	SYM
ejpam-6093	266	22	f97	f97	NOUN
ejpam-6093	266	23	=	=	PUNCT
ejpam-6093	266	24	f99	f99	PROPN
ejpam-6093	266	25	=	=	SYM
ejpam-6093	266	26	{	{	PUNCT
ejpam-6093	266	27	1	1	NUM
ejpam-6093	266	28	,	,	PUNCT
ejpam-6093	266	29	2	2	NUM
ejpam-6093	266	30	,	,	PUNCT
ejpam-6093	266	31	3	3	NUM
ejpam-6093	266	32	,	,	PUNCT
ejpam-6093	266	33	5	5	NUM
ejpam-6093	266	34	,	,	PUNCT
ejpam-6093	266	35	7	7	NUM
ejpam-6093	266	36	,	,	PUNCT
ejpam-6093	266	37	9	9	NUM
ejpam-6093	266	38	}	}	PUNCT
ejpam-6093	266	39	=	=	SYM
ejpam-6093	266	40	t	t	PROPN
ejpam-6093	266	41	.	.	PUNCT
ejpam-6093	267	1	from	from	ADP
ejpam-6093	267	2	{	{	PUNCT
ejpam-6093	267	3	1	1	NUM
ejpam-6093	267	4	,	,	PUNCT
ejpam-6093	267	5	2	2	NUM
ejpam-6093	267	6	,	,	PUNCT
ejpam-6093	267	7	3	3	NUM
ejpam-6093	267	8	}	}	PUNCT
ejpam-6093	267	9	and	and	CCONJ
ejpam-6093	267	10	t	t	PROPN
ejpam-6093	267	11	are	be	AUX
ejpam-6093	267	12	filters	filter	NOUN
ejpam-6093	267	13	of	of	ADP
ejpam-6093	267	14	t	t	NOUN
ejpam-6093	267	15	,	,	PUNCT
ejpam-6093	267	16	it	it	PRON
ejpam-6093	267	17	follows	follow	VERB
ejpam-6093	267	18	by	by	ADP
ejpam-6093	267	19	theorem	theorem	NOUN
ejpam-6093	267	20	5	5	NUM
ejpam-6093	267	21	that	that	SCONJ
ejpam-6093	267	22	f	f	AUX
ejpam-6093	267	23	=	=	PRON
ejpam-6093	267	24	{	{	PUNCT
ejpam-6093	267	25	1	1	NUM
ejpam-6093	267	26	,	,	PUNCT
ejpam-6093	267	27	2	2	NUM
ejpam-6093	267	28	,	,	PUNCT
ejpam-6093	267	29	3	3	NUM
ejpam-6093	267	30	}	}	PUNCT
ejpam-6093	267	31	is	be	AUX
ejpam-6093	267	32	an	an	DET
ejpam-6093	267	33	implicative	implicative	ADJ
ejpam-6093	267	34	filter	filter	NOUN
ejpam-6093	267	35	of	of	ADP
ejpam-6093	267	36	t	t	PROPN
ejpam-6093	267	37	.	.	PUNCT
ejpam-6093	268	1	4	4	X
ejpam-6093	268	2	.	.	X
ejpam-6093	268	3	generalized	generalize	VERB
ejpam-6093	268	4	implicative	implicative	ADJ
ejpam-6093	268	5	filters	filter	NOUN
ejpam-6093	268	6	we	we	PRON
ejpam-6093	268	7	generalize	generalize	VERB
ejpam-6093	268	8	the	the	DET
ejpam-6093	268	9	notion	notion	NOUN
ejpam-6093	268	10	of	of	ADP
ejpam-6093	268	11	implicative	implicative	ADJ
ejpam-6093	268	12	filter	filter	NOUN
ejpam-6093	268	13	as	as	SCONJ
ejpam-6093	268	14	follows	follow	VERB
ejpam-6093	268	15	.	.	PUNCT
ejpam-6093	269	1	definition	definition	NOUN
ejpam-6093	269	2	3	3	X
ejpam-6093	269	3	.	.	PUNCT
ejpam-6093	270	1	let	let	AUX
ejpam-6093	270	2	(	(	PUNCT
ejpam-6093	270	3	t	t	NOUN
ejpam-6093	270	4	,	,	PUNCT
ejpam-6093	270	5	[	[	PUNCT
ejpam-6093	270	6	]	]	X
ejpam-6093	270	7	,	,	PUNCT
ejpam-6093	270	8	≤	≤	NUM
ejpam-6093	270	9	,	,	PUNCT
ejpam-6093	270	10	[	[	PUNCT
ejpam-6093	270	11	]	]	X
ejpam-6093	270	12	∗	∗	NOUN
ejpam-6093	270	13	)	)	PUNCT
ejpam-6093	270	14	be	be	VERB
ejpam-6093	270	15	an	an	DET
ejpam-6093	270	16	implicative	implicative	ADJ
ejpam-6093	270	17	n.p.o	n.p.o	NOUN
ejpam-6093	270	18	.	.	PUNCT
ejpam-6093	271	1	ternary	ternary	PROPN
ejpam-6093	271	2	semigroup	semigroup	PROPN
ejpam-6093	271	3	.	.	PUNCT
ejpam-6093	272	1	a	a	DET
ejpam-6093	272	2	nonempty	nonempty	NOUN
ejpam-6093	272	3	subset	subset	VERB
ejpam-6093	272	4	f	f	PROPN
ejpam-6093	272	5	of	of	ADP
ejpam-6093	272	6	t	t	PROPN
ejpam-6093	272	7	is	be	AUX
ejpam-6093	272	8	called	call	VERB
ejpam-6093	272	9	a	a	DET
ejpam-6093	272	10	generalized	generalized	ADJ
ejpam-6093	272	11	implicative	implicative	ADJ
ejpam-6093	272	12	filter	filter	NOUN
ejpam-6093	272	13	of	of	ADP
ejpam-6093	272	14	t	t	PROPN
ejpam-6093	272	15	if	if	SCONJ
ejpam-6093	272	16	it	it	PRON
ejpam-6093	272	17	satisfies	satisfy	VERB
ejpam-6093	272	18	the	the	DET
ejpam-6093	272	19	following	follow	VERB
ejpam-6093	272	20	conditions	condition	NOUN
ejpam-6093	272	21	:	:	PUNCT
ejpam-6093	272	22	(	(	PUNCT
ejpam-6093	272	23	1	1	X
ejpam-6093	272	24	)	)	PUNCT
ejpam-6093	272	25	[	[	X
ejpam-6093	272	26	xyz	xyz	X
ejpam-6093	272	27	]	]	X
ejpam-6093	272	28	∈	∈	PROPN
ejpam-6093	272	29	f	f	PROPN
ejpam-6093	272	30	for	for	ADP
ejpam-6093	272	31	any	any	DET
ejpam-6093	272	32	x	x	NOUN
ejpam-6093	272	33	,	,	PUNCT
ejpam-6093	272	34	y	y	PROPN
ejpam-6093	272	35	,	,	PUNCT
ejpam-6093	272	36	z	z	PROPN
ejpam-6093	272	37	∈	∈	PROPN
ejpam-6093	272	38	f	f	X
ejpam-6093	272	39	,	,	PUNCT
ejpam-6093	272	40	that	that	PRON
ejpam-6093	272	41	is	is	ADV
ejpam-6093	272	42	f	f	PROPN
ejpam-6093	272	43	is	be	AUX
ejpam-6093	272	44	a	a	DET
ejpam-6093	272	45	ternary	ternary	ADJ
ejpam-6093	272	46	subsemigroup	subsemigroup	NOUN
ejpam-6093	272	47	of	of	ADP
ejpam-6093	272	48	t	t	PROPN
ejpam-6093	272	49	;	;	PUNCT
ejpam-6093	273	1	(	(	PUNCT
ejpam-6093	273	2	2	2	X
ejpam-6093	273	3	)	)	PUNCT
ejpam-6093	273	4	if	if	SCONJ
ejpam-6093	273	5	x	x	X
ejpam-6093	273	6	,	,	PUNCT
ejpam-6093	273	7	y	y	PROPN
ejpam-6093	273	8	∈	∈	PROPN
ejpam-6093	273	9	t	t	PROPN
ejpam-6093	273	10	and	and	CCONJ
ejpam-6093	273	11	z	z	PROPN
ejpam-6093	273	12	∈	∈	PROPN
ejpam-6093	273	13	f	f	NOUN
ejpam-6093	273	14	,	,	PUNCT
ejpam-6093	273	15	then	then	ADV
ejpam-6093	274	1	[	[	X
ejpam-6093	274	2	xyz]∗	xyz]∗	X
ejpam-6093	274	3	∈	∈	PROPN
ejpam-6093	274	4	f	f	PROPN
ejpam-6093	274	5	.	.	PUNCT
ejpam-6093	274	6	example	example	NOUN
ejpam-6093	275	1	6	6	NUM
ejpam-6093	275	2	.	.	PUNCT
ejpam-6093	276	1	let	let	VERB
ejpam-6093	276	2	t	t	NOUN
ejpam-6093	276	3	=	=	SYM
ejpam-6093	276	4	{	{	PUNCT
ejpam-6093	276	5	1	1	NUM
ejpam-6093	276	6	,	,	PUNCT
ejpam-6093	276	7	2	2	NUM
ejpam-6093	276	8	,	,	PUNCT
ejpam-6093	276	9	3	3	NUM
ejpam-6093	276	10	,	,	PUNCT
ejpam-6093	276	11	4	4	NUM
ejpam-6093	276	12	}	}	PUNCT
ejpam-6093	276	13	.	.	PUNCT
ejpam-6093	277	1	let	let	VERB
ejpam-6093	277	2	us	we	PRON
ejpam-6093	277	3	consider	consider	VERB
ejpam-6093	277	4	the	the	DET
ejpam-6093	277	5	implicative	implicative	ADJ
ejpam-6093	277	6	n.p.o	n.p.o	NOUN
ejpam-6093	277	7	.	.	PUNCT
ejpam-6093	278	1	ternary	ternary	ADJ
ejpam-6093	278	2	semigroup	semigroup	PROPN
ejpam-6093	278	3	(	(	PUNCT
ejpam-6093	278	4	t	t	PROPN
ejpam-6093	278	5	,	,	PUNCT
ejpam-6093	278	6	[	[	PUNCT
ejpam-6093	278	7	]	]	X
ejpam-6093	278	8	,	,	PUNCT
ejpam-6093	278	9	≤	≤	NUM
ejpam-6093	278	10	,	,	PUNCT
ejpam-6093	278	11	[	[	PUNCT
ejpam-6093	278	12	]	]	X
ejpam-6093	278	13	∗	∗	NOUN
ejpam-6093	278	14	)	)	PUNCT
ejpam-6093	278	15	with	with	ADP
ejpam-6093	278	16	ternary	ternary	ADJ
ejpam-6093	278	17	multiplication	multiplication	NOUN
ejpam-6093	278	18	[	[	PUNCT
ejpam-6093	278	19	]	]	X
ejpam-6093	278	20	,	,	PUNCT
ejpam-6093	278	21	ternary	ternary	ADJ
ejpam-6093	278	22	implication	implication	NOUN
ejpam-6093	278	23	[	[	PUNCT
ejpam-6093	278	24	]	]	X
ejpam-6093	278	25	∗	∗	NOUN
ejpam-6093	278	26	,	,	PUNCT
ejpam-6093	278	27	and	and	CCONJ
ejpam-6093	278	28	order	order	NOUN
ejpam-6093	278	29	relation	relation	NOUN
ejpam-6093	278	30	≤	≤	NOUN
ejpam-6093	278	31	defined	define	VERB
ejpam-6093	278	32	as	as	SCONJ
ejpam-6093	278	33	follows	follow	VERB
ejpam-6093	278	34	:	:	PUNCT
ejpam-6093	278	35	[	[	PUNCT
ejpam-6093	278	36	]	]	X
ejpam-6093	278	37	1	1	NUM
ejpam-6093	278	38	2	2	NUM
ejpam-6093	278	39	3	3	NUM
ejpam-6093	278	40	4	4	NUM
ejpam-6093	278	41	11	11	NUM
ejpam-6093	278	42	1	1	NUM
ejpam-6093	278	43	2	2	NUM
ejpam-6093	278	44	3	3	NUM
ejpam-6093	278	45	4	4	NUM
ejpam-6093	278	46	12	12	NUM
ejpam-6093	278	47	2	2	NUM
ejpam-6093	278	48	4	4	NUM
ejpam-6093	278	49	4	4	NUM
ejpam-6093	278	50	4	4	NUM
ejpam-6093	278	51	13	13	NUM
ejpam-6093	278	52	3	3	NUM
ejpam-6093	278	53	4	4	NUM
ejpam-6093	278	54	4	4	NUM
ejpam-6093	278	55	4	4	NUM
ejpam-6093	278	56	14	14	NUM
ejpam-6093	278	57	4	4	NUM
ejpam-6093	278	58	4	4	NUM
ejpam-6093	278	59	4	4	NUM
ejpam-6093	278	60	4	4	NUM
ejpam-6093	278	61	[	[	PUNCT
ejpam-6093	278	62	]	]	SYM
ejpam-6093	278	63	1	1	NUM
ejpam-6093	278	64	2	2	NUM
ejpam-6093	278	65	3	3	NUM
ejpam-6093	278	66	4	4	NUM
ejpam-6093	278	67	21	21	NUM
ejpam-6093	278	68	2	2	NUM
ejpam-6093	278	69	4	4	NUM
ejpam-6093	278	70	4	4	NUM
ejpam-6093	278	71	4	4	NUM
ejpam-6093	278	72	22	22	NUM
ejpam-6093	278	73	4	4	NUM
ejpam-6093	278	74	4	4	NUM
ejpam-6093	278	75	4	4	NUM
ejpam-6093	278	76	4	4	NUM
ejpam-6093	278	77	23	23	NUM
ejpam-6093	278	78	4	4	NUM
ejpam-6093	278	79	4	4	NUM
ejpam-6093	278	80	4	4	NUM
ejpam-6093	278	81	4	4	NUM
ejpam-6093	278	82	24	24	NUM
ejpam-6093	278	83	4	4	NUM
ejpam-6093	278	84	4	4	NUM
ejpam-6093	278	85	4	4	NUM
ejpam-6093	278	86	4	4	NUM
ejpam-6093	278	87	[	[	PUNCT
ejpam-6093	278	88	]	]	SYM
ejpam-6093	278	89	1	1	NUM
ejpam-6093	278	90	2	2	NUM
ejpam-6093	278	91	3	3	NUM
ejpam-6093	278	92	4	4	NUM
ejpam-6093	278	93	31	31	NUM
ejpam-6093	278	94	3	3	NUM
ejpam-6093	278	95	4	4	NUM
ejpam-6093	278	96	4	4	NUM
ejpam-6093	278	97	4	4	NUM
ejpam-6093	278	98	32	32	NUM
ejpam-6093	278	99	4	4	NUM
ejpam-6093	278	100	4	4	NUM
ejpam-6093	278	101	4	4	NUM
ejpam-6093	278	102	4	4	NUM
ejpam-6093	278	103	33	33	NUM
ejpam-6093	278	104	4	4	NUM
ejpam-6093	278	105	4	4	NUM
ejpam-6093	278	106	4	4	NUM
ejpam-6093	278	107	4	4	NUM
ejpam-6093	278	108	34	34	NUM
ejpam-6093	278	109	4	4	NUM
ejpam-6093	278	110	4	4	NUM
ejpam-6093	278	111	4	4	NUM
ejpam-6093	278	112	4	4	NUM
ejpam-6093	278	113	[	[	PUNCT
ejpam-6093	278	114	]	]	SYM
ejpam-6093	278	115	1	1	NUM
ejpam-6093	278	116	2	2	NUM
ejpam-6093	278	117	3	3	NUM
ejpam-6093	278	118	4	4	NUM
ejpam-6093	278	119	41	41	NUM
ejpam-6093	278	120	4	4	NUM
ejpam-6093	278	121	4	4	NUM
ejpam-6093	278	122	4	4	NUM
ejpam-6093	278	123	4	4	NUM
ejpam-6093	278	124	42	42	NUM
ejpam-6093	278	125	4	4	NUM
ejpam-6093	278	126	4	4	NUM
ejpam-6093	278	127	4	4	NUM
ejpam-6093	278	128	4	4	NUM
ejpam-6093	278	129	43	43	NUM
ejpam-6093	278	130	4	4	NUM
ejpam-6093	278	131	4	4	NUM
ejpam-6093	278	132	4	4	NUM
ejpam-6093	278	133	4	4	NUM
ejpam-6093	278	134	44	44	NUM
ejpam-6093	278	135	4	4	NUM
ejpam-6093	278	136	4	4	NUM
ejpam-6093	278	137	4	4	NUM
ejpam-6093	278	138	4	4	NUM
ejpam-6093	278	139	[	[	PUNCT
ejpam-6093	278	140	]	]	X
ejpam-6093	278	141	∗	∗	NOUN
ejpam-6093	278	142	1	1	NUM
ejpam-6093	278	143	2	2	NUM
ejpam-6093	278	144	3	3	NUM
ejpam-6093	278	145	4	4	NUM
ejpam-6093	278	146	11	11	NUM
ejpam-6093	278	147	1	1	NUM
ejpam-6093	278	148	2	2	NUM
ejpam-6093	278	149	3	3	NUM
ejpam-6093	278	150	4	4	NUM
ejpam-6093	278	151	12	12	NUM
ejpam-6093	278	152	1	1	NUM
ejpam-6093	278	153	1	1	NUM
ejpam-6093	278	154	2	2	NUM
ejpam-6093	278	155	2	2	NUM
ejpam-6093	278	156	13	13	NUM
ejpam-6093	278	157	1	1	NUM
ejpam-6093	278	158	1	1	NUM
ejpam-6093	278	159	1	1	NUM
ejpam-6093	278	160	2	2	NUM
ejpam-6093	278	161	14	14	NUM
ejpam-6093	278	162	1	1	NUM
ejpam-6093	278	163	1	1	NUM
ejpam-6093	278	164	1	1	NUM
ejpam-6093	278	165	4	4	NUM
ejpam-6093	278	166	[	[	PUNCT
ejpam-6093	278	167	]	]	X
ejpam-6093	278	168	∗	∗	NOUN
ejpam-6093	278	169	1	1	NUM
ejpam-6093	278	170	2	2	NUM
ejpam-6093	278	171	3	3	NUM
ejpam-6093	278	172	4	4	NUM
ejpam-6093	278	173	21	21	NUM
ejpam-6093	278	174	1	1	NUM
ejpam-6093	278	175	1	1	NUM
ejpam-6093	278	176	2	2	NUM
ejpam-6093	278	177	2	2	NUM
ejpam-6093	278	178	22	22	NUM
ejpam-6093	278	179	1	1	NUM
ejpam-6093	278	180	1	1	NUM
ejpam-6093	278	181	1	1	NUM
ejpam-6093	278	182	1	1	NUM
ejpam-6093	278	183	23	23	NUM
ejpam-6093	278	184	1	1	NUM
ejpam-6093	278	185	1	1	NUM
ejpam-6093	278	186	1	1	NUM
ejpam-6093	278	187	1	1	NUM
ejpam-6093	278	188	24	24	NUM
ejpam-6093	278	189	1	1	NUM
ejpam-6093	278	190	1	1	NUM
ejpam-6093	278	191	1	1	NUM
ejpam-6093	278	192	1	1	NUM
ejpam-6093	278	193	[	[	PUNCT
ejpam-6093	278	194	]	]	X
ejpam-6093	278	195	∗	∗	NOUN
ejpam-6093	278	196	1	1	NUM
ejpam-6093	278	197	2	2	NUM
ejpam-6093	278	198	3	3	NUM
ejpam-6093	278	199	4	4	NUM
ejpam-6093	278	200	31	31	NUM
ejpam-6093	278	201	1	1	NUM
ejpam-6093	278	202	1	1	NUM
ejpam-6093	278	203	1	1	NUM
ejpam-6093	278	204	2	2	NUM
ejpam-6093	278	205	32	32	NUM
ejpam-6093	278	206	1	1	NUM
ejpam-6093	278	207	1	1	NUM
ejpam-6093	278	208	1	1	NUM
ejpam-6093	278	209	1	1	NUM
ejpam-6093	278	210	33	33	NUM
ejpam-6093	278	211	1	1	NUM
ejpam-6093	278	212	1	1	NUM
ejpam-6093	278	213	1	1	NUM
ejpam-6093	278	214	1	1	NUM
ejpam-6093	278	215	34	34	NUM
ejpam-6093	278	216	1	1	NUM
ejpam-6093	278	217	1	1	NUM
ejpam-6093	278	218	1	1	NUM
ejpam-6093	278	219	1	1	NUM
ejpam-6093	278	220	[	[	PUNCT
ejpam-6093	278	221	]	]	X
ejpam-6093	278	222	∗	∗	NOUN
ejpam-6093	278	223	1	1	NUM
ejpam-6093	278	224	2	2	NUM
ejpam-6093	278	225	3	3	NUM
ejpam-6093	278	226	4	4	NUM
ejpam-6093	278	227	41	41	NUM
ejpam-6093	278	228	1	1	NUM
ejpam-6093	278	229	1	1	NUM
ejpam-6093	278	230	1	1	NUM
ejpam-6093	278	231	1	1	NUM
ejpam-6093	278	232	42	42	NUM
ejpam-6093	278	233	1	1	NUM
ejpam-6093	278	234	1	1	NUM
ejpam-6093	278	235	1	1	NUM
ejpam-6093	278	236	1	1	NUM
ejpam-6093	278	237	43	43	NUM
ejpam-6093	278	238	1	1	NUM
ejpam-6093	278	239	1	1	NUM
ejpam-6093	278	240	1	1	NUM
ejpam-6093	278	241	1	1	NUM
ejpam-6093	278	242	44	44	NUM
ejpam-6093	278	243	1	1	NUM
ejpam-6093	278	244	1	1	NUM
ejpam-6093	278	245	1	1	NUM
ejpam-6093	278	246	1	1	NUM
ejpam-6093	278	247	k.	k.	NOUN
ejpam-6093	278	248	nakwan	nakwan	PROPN
ejpam-6093	278	249	,	,	PUNCT
ejpam-6093	278	250	p.	p.	PROPN
ejpam-6093	278	251	luangchaisri	luangchaisri	VERB
ejpam-6093	278	252	,	,	PUNCT
ejpam-6093	278	253	t.	t.	PROPN
ejpam-6093	278	254	changphas	changphas	PROPN
ejpam-6093	278	255	/	/	SYM
ejpam-6093	278	256	eur	eur	PROPN
ejpam-6093	278	257	.	.	PUNCT
ejpam-6093	279	1	j.	j.	PROPN
ejpam-6093	279	2	pure	pure	PROPN
ejpam-6093	279	3	appl	appl	PROPN
ejpam-6093	279	4	.	.	PROPN
ejpam-6093	279	5	math	math	PROPN
ejpam-6093	279	6	,	,	PUNCT
ejpam-6093	279	7	18	18	NUM
ejpam-6093	279	8	(	(	PUNCT
ejpam-6093	279	9	4	4	NUM
ejpam-6093	279	10	)	)	PUNCT
ejpam-6093	279	11	(	(	PUNCT
ejpam-6093	279	12	2025	2025	NUM
ejpam-6093	279	13	)	)	PUNCT
ejpam-6093	279	14	,	,	PUNCT
ejpam-6093	279	15	6093	6093	NUM
ejpam-6093	279	16	9	9	NUM
ejpam-6093	279	17	of	of	ADP
ejpam-6093	279	18	11	11	NUM
ejpam-6093	279	19	and	and	CCONJ
ejpam-6093	279	20	≤=	≤=	PROPN
ejpam-6093	279	21	{	{	PUNCT
ejpam-6093	279	22	(	(	PUNCT
ejpam-6093	279	23	1	1	NUM
ejpam-6093	279	24	,	,	PUNCT
ejpam-6093	279	25	1	1	NUM
ejpam-6093	279	26	)	)	PUNCT
ejpam-6093	279	27	,	,	PUNCT
ejpam-6093	279	28	(	(	PUNCT
ejpam-6093	279	29	2	2	NUM
ejpam-6093	279	30	,	,	PUNCT
ejpam-6093	279	31	2	2	NUM
ejpam-6093	279	32	)	)	PUNCT
ejpam-6093	279	33	,	,	PUNCT
ejpam-6093	279	34	(	(	PUNCT
ejpam-6093	279	35	2	2	NUM
ejpam-6093	279	36	,	,	PUNCT
ejpam-6093	279	37	1	1	NUM
ejpam-6093	279	38	)	)	PUNCT
ejpam-6093	279	39	,	,	PUNCT
ejpam-6093	279	40	(	(	PUNCT
ejpam-6093	279	41	3	3	NUM
ejpam-6093	279	42	,	,	PUNCT
ejpam-6093	279	43	3	3	NUM
ejpam-6093	279	44	)	)	PUNCT
ejpam-6093	279	45	,	,	PUNCT
ejpam-6093	279	46	(	(	PUNCT
ejpam-6093	279	47	3	3	NUM
ejpam-6093	279	48	,	,	PUNCT
ejpam-6093	279	49	1	1	NUM
ejpam-6093	279	50	)	)	PUNCT
ejpam-6093	279	51	,	,	PUNCT
ejpam-6093	279	52	(	(	PUNCT
ejpam-6093	279	53	3	3	NUM
ejpam-6093	279	54	,	,	PUNCT
ejpam-6093	279	55	2)(4	2)(4	NUM
ejpam-6093	279	56	,	,	PUNCT
ejpam-6093	279	57	4	4	NUM
ejpam-6093	279	58	)	)	PUNCT
ejpam-6093	279	59	,	,	PUNCT
ejpam-6093	279	60	(	(	PUNCT
ejpam-6093	279	61	4	4	NUM
ejpam-6093	279	62	,	,	PUNCT
ejpam-6093	279	63	1	1	NUM
ejpam-6093	279	64	)	)	PUNCT
ejpam-6093	279	65	,	,	PUNCT
ejpam-6093	279	66	(	(	PUNCT
ejpam-6093	279	67	4	4	NUM
ejpam-6093	279	68	,	,	PUNCT
ejpam-6093	279	69	2	2	NUM
ejpam-6093	279	70	)	)	PUNCT
ejpam-6093	279	71	,	,	PUNCT
ejpam-6093	279	72	(	(	PUNCT
ejpam-6093	279	73	4	4	NUM
ejpam-6093	279	74	,	,	PUNCT
ejpam-6093	279	75	3	3	NUM
ejpam-6093	279	76	)	)	PUNCT
ejpam-6093	279	77	}	}	PUNCT
ejpam-6093	279	78	.	.	PUNCT
ejpam-6093	280	1	1	1	NUM
ejpam-6093	280	2	2	2	NUM
ejpam-6093	280	3	3	3	NUM
ejpam-6093	280	4	4	4	NUM
ejpam-6093	280	5	then	then	ADV
ejpam-6093	280	6	clearly	clearly	ADV
ejpam-6093	280	7	{	{	PUNCT
ejpam-6093	280	8	1	1	NUM
ejpam-6093	280	9	,	,	PUNCT
ejpam-6093	280	10	2	2	NUM
ejpam-6093	280	11	,	,	PUNCT
ejpam-6093	280	12	4	4	NUM
ejpam-6093	280	13	}	}	PUNCT
ejpam-6093	280	14	is	be	AUX
ejpam-6093	280	15	a	a	DET
ejpam-6093	280	16	generalized	generalized	ADJ
ejpam-6093	280	17	implicative	implicative	ADJ
ejpam-6093	280	18	filter	filter	NOUN
ejpam-6093	280	19	of	of	ADP
ejpam-6093	280	20	t	t	PROPN
ejpam-6093	280	21	but	but	CCONJ
ejpam-6093	280	22	not	not	PART
ejpam-6093	280	23	a	a	DET
ejpam-6093	280	24	filter	filter	NOUN
ejpam-6093	280	25	of	of	ADP
ejpam-6093	280	26	t	t	PROPN
ejpam-6093	280	27	,	,	PUNCT
ejpam-6093	280	28	because	because	SCONJ
ejpam-6093	280	29	4	4	NUM
ejpam-6093	280	30	≤	≤	NUM
ejpam-6093	280	31	3	3	NUM
ejpam-6093	280	32	and	and	CCONJ
ejpam-6093	280	33	4	4	NUM
ejpam-6093	280	34	∈	∈	NOUN
ejpam-6093	280	35	{	{	PUNCT
ejpam-6093	280	36	1	1	NUM
ejpam-6093	280	37	,	,	PUNCT
ejpam-6093	280	38	2	2	NUM
ejpam-6093	280	39	,	,	PUNCT
ejpam-6093	280	40	4	4	NUM
ejpam-6093	280	41	}	}	PUNCT
ejpam-6093	280	42	but	but	CCONJ
ejpam-6093	280	43	3	3	NUM
ejpam-6093	280	44	/∈	/∈	PUNCT
ejpam-6093	280	45	{	{	PUNCT
ejpam-6093	280	46	1	1	NUM
ejpam-6093	280	47	,	,	PUNCT
ejpam-6093	280	48	2	2	NUM
ejpam-6093	280	49	,	,	PUNCT
ejpam-6093	280	50	4	4	NUM
ejpam-6093	280	51	}	}	PUNCT
ejpam-6093	280	52	.	.	PUNCT
ejpam-6093	281	1	we	we	PRON
ejpam-6093	281	2	have	have	VERB
ejpam-6093	281	3	that	that	DET
ejpam-6093	281	4	generalized	generalize	VERB
ejpam-6093	281	5	implicative	implicative	ADJ
ejpam-6093	281	6	filters	filter	NOUN
ejpam-6093	281	7	need	need	AUX
ejpam-6093	281	8	not	not	PART
ejpam-6093	281	9	be	be	AUX
ejpam-6093	281	10	implicative	implicative	ADJ
ejpam-6093	281	11	filters	filter	NOUN
ejpam-6093	281	12	.	.	PUNCT
ejpam-6093	281	13	example	example	NOUN
ejpam-6093	282	1	7	7	NUM
ejpam-6093	282	2	.	.	PUNCT
ejpam-6093	282	3	let	let	VERB
ejpam-6093	282	4	us	we	PRON
ejpam-6093	282	5	consider	consider	VERB
ejpam-6093	282	6	the	the	DET
ejpam-6093	282	7	implicative	implicative	ADJ
ejpam-6093	282	8	n.p.o	n.p.o	NOUN
ejpam-6093	282	9	.	.	PUNCT
ejpam-6093	283	1	ternary	ternary	PROPN
ejpam-6093	283	2	semigroup	semigroup	PROPN
ejpam-6093	283	3	t	t	PROPN
ejpam-6093	283	4	defined	define	VERB
ejpam-6093	283	5	in	in	ADP
ejpam-6093	283	6	example	example	NOUN
ejpam-6093	283	7	1	1	X
ejpam-6093	283	8	.	.	PUNCT
ejpam-6093	284	1	we	we	PRON
ejpam-6093	284	2	have	have	VERB
ejpam-6093	284	3	{	{	PUNCT
ejpam-6093	284	4	1	1	NUM
ejpam-6093	284	5	}	}	PUNCT
ejpam-6093	284	6	and	and	CCONJ
ejpam-6093	284	7	{	{	PUNCT
ejpam-6093	284	8	1	1	NUM
ejpam-6093	284	9	,	,	PUNCT
ejpam-6093	284	10	5	5	NUM
ejpam-6093	284	11	}	}	PUNCT
ejpam-6093	284	12	are	be	AUX
ejpam-6093	284	13	generalized	generalize	VERB
ejpam-6093	284	14	implicative	implicative	ADJ
ejpam-6093	284	15	filters	filter	NOUN
ejpam-6093	284	16	of	of	ADP
ejpam-6093	284	17	t	t	PROPN
ejpam-6093	284	18	whereas	whereas	SCONJ
ejpam-6093	284	19	the	the	DET
ejpam-6093	284	20	sets	set	NOUN
ejpam-6093	284	21	{	{	PUNCT
ejpam-6093	284	22	1	1	NUM
ejpam-6093	284	23	}	}	PUNCT
ejpam-6093	284	24	and	and	CCONJ
ejpam-6093	284	25	{	{	PUNCT
ejpam-6093	284	26	1	1	NUM
ejpam-6093	284	27	,	,	PUNCT
ejpam-6093	284	28	5	5	NUM
ejpam-6093	284	29	}	}	PUNCT
ejpam-6093	284	30	are	be	AUX
ejpam-6093	284	31	not	not	PART
ejpam-6093	284	32	implicative	implicative	ADJ
ejpam-6093	284	33	filters	filter	NOUN
ejpam-6093	284	34	of	of	ADP
ejpam-6093	284	35	t	t	PROPN
ejpam-6093	284	36	.	.	PUNCT
ejpam-6093	285	1	as	as	ADP
ejpam-6093	285	2	in	in	ADP
ejpam-6093	285	3	example	example	NOUN
ejpam-6093	285	4	2	2	NUM
ejpam-6093	285	5	,	,	PUNCT
ejpam-6093	285	6	{	{	PUNCT
ejpam-6093	285	7	1	1	X
ejpam-6093	285	8	}	}	PUNCT
ejpam-6093	285	9	is	be	AUX
ejpam-6093	285	10	not	not	PART
ejpam-6093	285	11	an	an	DET
ejpam-6093	285	12	implicative	implicative	ADJ
ejpam-6093	285	13	filter	filter	NOUN
ejpam-6093	285	14	of	of	ADP
ejpam-6093	285	15	t	t	PROPN
ejpam-6093	285	16	.	.	PUNCT
ejpam-6093	286	1	by	by	ADP
ejpam-6093	286	2	[	[	X
ejpam-6093	286	3	21[123]∗]∗	21[123]∗]∗	NOUN
ejpam-6093	286	4	=	=	PUNCT
ejpam-6093	287	1	[	[	X
ejpam-6093	287	2	212]∗	212]∗	NUM
ejpam-6093	287	3	=	=	SYM
ejpam-6093	287	4	1	1	NUM
ejpam-6093	287	5	∈	∈	NOUN
ejpam-6093	287	6	{	{	PUNCT
ejpam-6093	287	7	1	1	NUM
ejpam-6093	287	8	,	,	PUNCT
ejpam-6093	287	9	5	5	NUM
ejpam-6093	287	10	}	}	PUNCT
ejpam-6093	287	11	,	,	PUNCT
ejpam-6093	287	12	[	[	X
ejpam-6093	287	13	211]∗	211]∗	NUM
ejpam-6093	287	14	=	=	SYM
ejpam-6093	287	15	1	1	NUM
ejpam-6093	287	16	∈	∈	NOUN
ejpam-6093	287	17	{	{	PUNCT
ejpam-6093	287	18	1	1	NUM
ejpam-6093	287	19	,	,	PUNCT
ejpam-6093	287	20	5	5	NUM
ejpam-6093	287	21	}	}	PUNCT
ejpam-6093	287	22	,	,	PUNCT
ejpam-6093	287	23	[	[	X
ejpam-6093	287	24	212]∗	212]∗	NUM
ejpam-6093	287	25	=	=	SYM
ejpam-6093	287	26	1	1	NUM
ejpam-6093	287	27	∈	∈	NOUN
ejpam-6093	287	28	{	{	PUNCT
ejpam-6093	287	29	1	1	NUM
ejpam-6093	287	30	,	,	PUNCT
ejpam-6093	287	31	5	5	NUM
ejpam-6093	287	32	}	}	PUNCT
ejpam-6093	287	33	,	,	PUNCT
ejpam-6093	287	34	and	and	CCONJ
ejpam-6093	287	35	[	[	X
ejpam-6093	287	36	213]∗	213]∗	NUM
ejpam-6093	287	37	=	=	SYM
ejpam-6093	287	38	2	2	NUM
ejpam-6093	287	39	/∈	/∈	PUNCT
ejpam-6093	287	40	{	{	PUNCT
ejpam-6093	287	41	1	1	NUM
ejpam-6093	287	42	,	,	PUNCT
ejpam-6093	287	43	5	5	NUM
ejpam-6093	287	44	}	}	PUNCT
ejpam-6093	287	45	,	,	PUNCT
ejpam-6093	287	46	it	it	PRON
ejpam-6093	287	47	follows	follow	VERB
ejpam-6093	287	48	that	that	SCONJ
ejpam-6093	287	49	{	{	PUNCT
ejpam-6093	287	50	1	1	NUM
ejpam-6093	287	51	,	,	PUNCT
ejpam-6093	287	52	5	5	NUM
ejpam-6093	287	53	}	}	PUNCT
ejpam-6093	287	54	is	be	AUX
ejpam-6093	287	55	not	not	PART
ejpam-6093	287	56	an	an	DET
ejpam-6093	287	57	implicative	implicative	ADJ
ejpam-6093	287	58	filter	filter	NOUN
ejpam-6093	287	59	of	of	ADP
ejpam-6093	287	60	t	t	PROPN
ejpam-6093	287	61	.	.	PUNCT
ejpam-6093	288	1	proposition	proposition	NOUN
ejpam-6093	288	2	2	2	NUM
ejpam-6093	288	3	.	.	PUNCT
ejpam-6093	289	1	if	if	SCONJ
ejpam-6093	289	2	f	f	PROPN
ejpam-6093	289	3	is	be	AUX
ejpam-6093	289	4	a	a	DET
ejpam-6093	289	5	generalized	generalized	ADJ
ejpam-6093	289	6	implicative	implicative	ADJ
ejpam-6093	289	7	filter	filter	NOUN
ejpam-6093	289	8	of	of	ADP
ejpam-6093	289	9	an	an	DET
ejpam-6093	289	10	implicative	implicative	ADJ
ejpam-6093	289	11	n.p.o	n.p.o	NOUN
ejpam-6093	289	12	.	.	PUNCT
ejpam-6093	290	1	ternary	ternary	ADJ
ejpam-6093	290	2	semigroup	semigroup	PROPN
ejpam-6093	290	3	(	(	PUNCT
ejpam-6093	290	4	t	t	PROPN
ejpam-6093	290	5	,	,	PUNCT
ejpam-6093	290	6	[	[	PUNCT
ejpam-6093	290	7	]	]	X
ejpam-6093	290	8	,	,	PUNCT
ejpam-6093	290	9	≤	≤	NUM
ejpam-6093	290	10	,	,	PUNCT
ejpam-6093	290	11	[	[	PUNCT
ejpam-6093	290	12	]	]	X
ejpam-6093	290	13	∗	∗	NOUN
ejpam-6093	290	14	)	)	PUNCT
ejpam-6093	290	15	,	,	PUNCT
ejpam-6093	290	16	then	then	ADV
ejpam-6093	290	17	1	1	NUM
ejpam-6093	290	18	∈	∈	PROPN
ejpam-6093	290	19	f	f	NOUN
ejpam-6093	290	20	.	.	PUNCT
ejpam-6093	291	1	proof	proof	NOUN
ejpam-6093	291	2	.	.	PUNCT
ejpam-6093	292	1	let	let	VERB
ejpam-6093	292	2	x	x	SYM
ejpam-6093	292	3	∈	∈	PROPN
ejpam-6093	292	4	f	f	X
ejpam-6093	292	5	,	,	PUNCT
ejpam-6093	292	6	by	by	ADP
ejpam-6093	292	7	f	f	PROPN
ejpam-6093	292	8	is	be	AUX
ejpam-6093	292	9	a	a	DET
ejpam-6093	292	10	generalized	generalized	ADJ
ejpam-6093	292	11	implicative	implicative	ADJ
ejpam-6093	292	12	filter	filter	NOUN
ejpam-6093	292	13	of	of	ADP
ejpam-6093	292	14	t	t	PROPN
ejpam-6093	292	15	,	,	PUNCT
ejpam-6093	292	16	we	we	PRON
ejpam-6093	292	17	have	have	VERB
ejpam-6093	292	18	1	1	NUM
ejpam-6093	292	19	=	=	NOUN
ejpam-6093	293	1	[	[	X
ejpam-6093	293	2	xxx]∗	xxx]∗	PROPN
ejpam-6093	293	3	∈	∈	PROPN
ejpam-6093	293	4	f	f	PROPN
ejpam-6093	293	5	.	.	PUNCT
ejpam-6093	294	1	theorem	theorem	VERB
ejpam-6093	294	2	6	6	NUM
ejpam-6093	294	3	.	.	PUNCT
ejpam-6093	294	4	for	for	ADP
ejpam-6093	294	5	an	an	DET
ejpam-6093	294	6	implicative	implicative	ADJ
ejpam-6093	294	7	n.p.o	n.p.o	NOUN
ejpam-6093	294	8	.	.	PUNCT
ejpam-6093	295	1	ternary	ternary	ADJ
ejpam-6093	295	2	semigroup	semigroup	PROPN
ejpam-6093	295	3	(	(	PUNCT
ejpam-6093	295	4	t	t	PROPN
ejpam-6093	295	5	,	,	PUNCT
ejpam-6093	295	6	[	[	PUNCT
ejpam-6093	295	7	]	]	X
ejpam-6093	295	8	,	,	PUNCT
ejpam-6093	295	9	≤	≤	NUM
ejpam-6093	295	10	,	,	PUNCT
ejpam-6093	295	11	[	[	PUNCT
ejpam-6093	295	12	]	]	X
ejpam-6093	295	13	∗	∗	NOUN
ejpam-6093	295	14	)	)	PUNCT
ejpam-6093	295	15	,	,	PUNCT
ejpam-6093	295	16	every	every	DET
ejpam-6093	295	17	filter	filter	NOUN
ejpam-6093	295	18	is	be	AUX
ejpam-6093	295	19	a	a	DET
ejpam-6093	295	20	generalized	generalized	ADJ
ejpam-6093	295	21	implicative	implicative	ADJ
ejpam-6093	295	22	filter	filter	NOUN
ejpam-6093	295	23	of	of	ADP
ejpam-6093	295	24	t	t	PROPN
ejpam-6093	295	25	.	.	PUNCT
ejpam-6093	296	1	proof	proof	NOUN
ejpam-6093	296	2	.	.	PUNCT
ejpam-6093	297	1	assume	assume	VERB
ejpam-6093	297	2	that	that	SCONJ
ejpam-6093	297	3	f	f	PROPN
ejpam-6093	297	4	is	be	AUX
ejpam-6093	297	5	a	a	DET
ejpam-6093	297	6	filter	filter	NOUN
ejpam-6093	297	7	of	of	ADP
ejpam-6093	297	8	t	t	PROPN
ejpam-6093	297	9	;	;	PUNCT
ejpam-6093	297	10	then	then	ADV
ejpam-6093	297	11	f	f	PROPN
ejpam-6093	297	12	is	be	AUX
ejpam-6093	297	13	a	a	DET
ejpam-6093	297	14	ternary	ternary	ADJ
ejpam-6093	297	15	subsemigroup	subsemigroup	NOUN
ejpam-6093	297	16	of	of	ADP
ejpam-6093	297	17	t	t	PROPN
ejpam-6093	297	18	.	.	PUNCT
ejpam-6093	298	1	let	let	VERB
ejpam-6093	298	2	x	x	PRON
ejpam-6093	298	3	,	,	PUNCT
ejpam-6093	298	4	y	y	PROPN
ejpam-6093	298	5	∈	∈	PROPN
ejpam-6093	298	6	t	t	PROPN
ejpam-6093	298	7	and	and	CCONJ
ejpam-6093	298	8	z	z	PROPN
ejpam-6093	298	9	∈	∈	PROPN
ejpam-6093	299	1	f	f	X
ejpam-6093	299	2	.	.	PUNCT
ejpam-6093	300	1	since	since	SCONJ
ejpam-6093	300	2	[	[	X
ejpam-6093	300	3	zxy	zxy	X
ejpam-6093	300	4	]	]	X
ejpam-6093	300	5	≤	≤	PROPN
ejpam-6093	300	6	z	z	NOUN
ejpam-6093	300	7	,	,	PUNCT
ejpam-6093	300	8	z	z	NOUN
ejpam-6093	300	9	≤	≤	NOUN
ejpam-6093	301	1	[	[	PUNCT
ejpam-6093	301	2	xyz]∗.	xyz]∗.	NOUN
ejpam-6093	301	3	by	by	ADP
ejpam-6093	301	4	assumption	assumption	NOUN
ejpam-6093	301	5	,	,	PUNCT
ejpam-6093	301	6	[	[	X
ejpam-6093	301	7	xyz]∗	xyz]∗	X
ejpam-6093	301	8	∈	∈	PROPN
ejpam-6093	301	9	f	f	X
ejpam-6093	301	10	.	.	PUNCT
ejpam-6093	302	1	corollary	corollary	ADJ
ejpam-6093	302	2	1	1	NUM
ejpam-6093	302	3	.	.	PUNCT
ejpam-6093	303	1	for	for	ADP
ejpam-6093	303	2	an	an	DET
ejpam-6093	303	3	implicative	implicative	ADJ
ejpam-6093	303	4	n.p.o	n.p.o	NOUN
ejpam-6093	303	5	.	.	PUNCT
ejpam-6093	304	1	ternary	ternary	ADJ
ejpam-6093	304	2	semigroup	semigroup	PROPN
ejpam-6093	304	3	(	(	PUNCT
ejpam-6093	304	4	t	t	PROPN
ejpam-6093	304	5	,	,	PUNCT
ejpam-6093	304	6	[	[	PUNCT
ejpam-6093	304	7	]	]	X
ejpam-6093	304	8	,	,	PUNCT
ejpam-6093	304	9	≤	≤	NUM
ejpam-6093	304	10	,	,	PUNCT
ejpam-6093	304	11	[	[	PUNCT
ejpam-6093	304	12	]	]	X
ejpam-6093	304	13	∗	∗	NOUN
ejpam-6093	304	14	)	)	PUNCT
ejpam-6093	304	15	,	,	PUNCT
ejpam-6093	304	16	every	every	DET
ejpam-6093	304	17	implicative	implicative	ADJ
ejpam-6093	304	18	filter	filter	NOUN
ejpam-6093	304	19	of	of	ADP
ejpam-6093	304	20	t	t	PROPN
ejpam-6093	304	21	is	be	AUX
ejpam-6093	304	22	a	a	DET
ejpam-6093	304	23	generalized	generalized	ADJ
ejpam-6093	304	24	implicative	implicative	ADJ
ejpam-6093	304	25	filter	filter	NOUN
ejpam-6093	304	26	of	of	ADP
ejpam-6093	304	27	t	t	PROPN
ejpam-6093	304	28	.	.	PUNCT
ejpam-6093	305	1	proof	proof	NOUN
ejpam-6093	305	2	.	.	PUNCT
ejpam-6093	306	1	the	the	DET
ejpam-6093	306	2	assertion	assertion	NOUN
ejpam-6093	306	3	follows	follow	VERB
ejpam-6093	306	4	by	by	ADP
ejpam-6093	306	5	theorem	theorem	ADJ
ejpam-6093	306	6	4	4	NUM
ejpam-6093	306	7	and	and	CCONJ
ejpam-6093	306	8	theorem	theorem	VERB
ejpam-6093	306	9	6	6	NUM
ejpam-6093	306	10	.	.	PUNCT
ejpam-6093	306	11	in	in	ADP
ejpam-6093	306	12	the	the	DET
ejpam-6093	306	13	following	following	NOUN
ejpam-6093	306	14	,	,	PUNCT
ejpam-6093	306	15	a	a	DET
ejpam-6093	306	16	sufficient	sufficient	ADJ
ejpam-6093	306	17	condition	condition	NOUN
ejpam-6093	306	18	is	be	AUX
ejpam-6093	306	19	derived	derive	VERB
ejpam-6093	306	20	for	for	ADP
ejpam-6093	306	21	a	a	DET
ejpam-6093	306	22	generalized	generalized	ADJ
ejpam-6093	306	23	implicative	implicative	ADJ
ejpam-6093	306	24	filter	filter	NOUN
ejpam-6093	306	25	to	to	PART
ejpam-6093	306	26	become	become	VERB
ejpam-6093	306	27	a	a	DET
ejpam-6093	306	28	filter	filter	NOUN
ejpam-6093	306	29	.	.	PUNCT
ejpam-6093	307	1	theorem	theorem	ADJ
ejpam-6093	307	2	7	7	NUM
ejpam-6093	307	3	.	.	PUNCT
ejpam-6093	308	1	let	let	AUX
ejpam-6093	308	2	(	(	PUNCT
ejpam-6093	308	3	t	t	NOUN
ejpam-6093	308	4	,	,	PUNCT
ejpam-6093	308	5	[	[	PUNCT
ejpam-6093	308	6	]	]	X
ejpam-6093	308	7	,	,	PUNCT
ejpam-6093	308	8	≤	≤	NUM
ejpam-6093	308	9	,	,	PUNCT
ejpam-6093	308	10	[	[	PUNCT
ejpam-6093	308	11	]	]	X
ejpam-6093	308	12	∗	∗	NOUN
ejpam-6093	308	13	)	)	PUNCT
ejpam-6093	308	14	be	be	VERB
ejpam-6093	308	15	an	an	DET
ejpam-6093	308	16	implicative	implicative	ADJ
ejpam-6093	308	17	n.p.o	n.p.o	NOUN
ejpam-6093	308	18	.	.	PUNCT
ejpam-6093	309	1	ternary	ternary	PROPN
ejpam-6093	309	2	semigroup	semigroup	PROPN
ejpam-6093	309	3	.	.	PUNCT
ejpam-6093	310	1	then	then	ADV
ejpam-6093	310	2	every	every	DET
ejpam-6093	310	3	generalized	generalize	VERB
ejpam-6093	310	4	implicative	implicative	ADJ
ejpam-6093	310	5	filter	filter	NOUN
ejpam-6093	310	6	f	f	PROPN
ejpam-6093	310	7	of	of	ADP
ejpam-6093	310	8	t	t	PROPN
ejpam-6093	310	9	is	be	AUX
ejpam-6093	310	10	a	a	DET
ejpam-6093	310	11	filter	filter	NOUN
ejpam-6093	310	12	if	if	SCONJ
ejpam-6093	310	13	the	the	DET
ejpam-6093	310	14	following	follow	VERB
ejpam-6093	310	15	condition	condition	NOUN
ejpam-6093	310	16	satisfies	satisfy	VERB
ejpam-6093	310	17	:	:	PUNCT
ejpam-6093	310	18	for	for	ADP
ejpam-6093	310	19	all	all	DET
ejpam-6093	310	20	x	x	NOUN
ejpam-6093	310	21	,	,	PUNCT
ejpam-6093	310	22	y	y	PROPN
ejpam-6093	310	23	∈	∈	PROPN
ejpam-6093	310	24	t	t	PROPN
ejpam-6093	310	25	,	,	PUNCT
ejpam-6093	310	26	x	x	PUNCT
ejpam-6093	310	27	∈	∈	PROPN
ejpam-6093	310	28	f	f	NOUN
ejpam-6093	310	29	and	and	CCONJ
ejpam-6093	311	1	[	[	X
ejpam-6093	311	2	[	[	X
ejpam-6093	311	3	xxx]1y]∗	xxx]1y]∗	PROPN
ejpam-6093	311	4	∈	∈	PROPN
ejpam-6093	311	5	f	f	PROPN
ejpam-6093	311	6	or	or	CCONJ
ejpam-6093	311	7	[	[	X
ejpam-6093	311	8	[	[	X
ejpam-6093	311	9	xx1]xy]∗	xx1]xy]∗	X
ejpam-6093	311	10	∈	∈	PROPN
ejpam-6093	311	11	f	f	X
ejpam-6093	312	1	=	=	NOUN
ejpam-6093	312	2	⇒	⇒	VERB
ejpam-6093	312	3	y	y	PROPN
ejpam-6093	312	4	∈	∈	PROPN
ejpam-6093	312	5	f.	f.	PROPN
ejpam-6093	312	6	k.	k.	PROPN
ejpam-6093	312	7	nakwan	nakwan	PROPN
ejpam-6093	312	8	,	,	PUNCT
ejpam-6093	312	9	p.	p.	PROPN
ejpam-6093	312	10	luangchaisri	luangchaisri	VERB
ejpam-6093	312	11	,	,	PUNCT
ejpam-6093	312	12	t.	t.	PROPN
ejpam-6093	312	13	changphas	changphas	PROPN
ejpam-6093	312	14	/	/	SYM
ejpam-6093	312	15	eur	eur	PROPN
ejpam-6093	312	16	.	.	PUNCT
ejpam-6093	313	1	j.	j.	PROPN
ejpam-6093	313	2	pure	pure	PROPN
ejpam-6093	313	3	appl	appl	PROPN
ejpam-6093	313	4	.	.	PROPN
ejpam-6093	313	5	math	math	PROPN
ejpam-6093	313	6	,	,	PUNCT
ejpam-6093	313	7	18	18	NUM
ejpam-6093	313	8	(	(	PUNCT
ejpam-6093	313	9	4	4	NUM
ejpam-6093	313	10	)	)	PUNCT
ejpam-6093	313	11	(	(	PUNCT
ejpam-6093	313	12	2025	2025	NUM
ejpam-6093	313	13	)	)	PUNCT
ejpam-6093	313	14	,	,	PUNCT
ejpam-6093	313	15	6093	6093	NUM
ejpam-6093	313	16	10	10	NUM
ejpam-6093	313	17	of	of	ADP
ejpam-6093	313	18	11	11	NUM
ejpam-6093	313	19	proof	proof	NOUN
ejpam-6093	313	20	.	.	PUNCT
ejpam-6093	314	1	let	let	VERB
ejpam-6093	314	2	f	f	PRON
ejpam-6093	314	3	be	be	AUX
ejpam-6093	314	4	a	a	DET
ejpam-6093	314	5	generalized	generalized	ADJ
ejpam-6093	314	6	implicative	implicative	ADJ
ejpam-6093	314	7	filter	filter	NOUN
ejpam-6093	314	8	of	of	ADP
ejpam-6093	314	9	t	t	PROPN
ejpam-6093	314	10	.	.	PUNCT
ejpam-6093	315	1	there	there	PRON
ejpam-6093	315	2	are	be	VERB
ejpam-6093	315	3	two	two	NUM
ejpam-6093	315	4	cases	case	NOUN
ejpam-6093	315	5	to	to	PART
ejpam-6093	315	6	consider	consider	VERB
ejpam-6093	315	7	.	.	PUNCT
ejpam-6093	316	1	case	case	NOUN
ejpam-6093	316	2	1	1	NUM
ejpam-6093	316	3	:	:	PUNCT
ejpam-6093	316	4	assume	assume	VERB
ejpam-6093	316	5	that	that	SCONJ
ejpam-6093	316	6	x	x	SYM
ejpam-6093	316	7	∈	∈	PROPN
ejpam-6093	316	8	f	f	NOUN
ejpam-6093	316	9	and	and	CCONJ
ejpam-6093	316	10	[	[	X
ejpam-6093	316	11	[	[	X
ejpam-6093	316	12	xxx]1y]∗	xxx]1y]∗	PROPN
ejpam-6093	316	13	∈	∈	PROPN
ejpam-6093	316	14	f	f	X
ejpam-6093	316	15	imply	imply	VERB
ejpam-6093	316	16	y	y	PROPN
ejpam-6093	316	17	∈	∈	PROPN
ejpam-6093	316	18	f	f	PROPN
ejpam-6093	316	19	for	for	ADP
ejpam-6093	316	20	all	all	DET
ejpam-6093	316	21	x	x	NOUN
ejpam-6093	316	22	,	,	PUNCT
ejpam-6093	316	23	y	y	PROPN
ejpam-6093	316	24	∈	∈	PROPN
ejpam-6093	316	25	t	t	PROPN
ejpam-6093	316	26	.	.	PUNCT
ejpam-6093	317	1	clearly	clearly	ADV
ejpam-6093	317	2	,	,	PUNCT
ejpam-6093	317	3	f	f	PROPN
ejpam-6093	317	4	is	be	AUX
ejpam-6093	317	5	a	a	DET
ejpam-6093	317	6	ternary	ternary	ADJ
ejpam-6093	317	7	subsemigroup	subsemigroup	NOUN
ejpam-6093	317	8	of	of	ADP
ejpam-6093	317	9	t	t	PROPN
ejpam-6093	317	10	.	.	PUNCT
ejpam-6093	318	1	let	let	VERB
ejpam-6093	318	2	x	x	PRON
ejpam-6093	318	3	,	,	PUNCT
ejpam-6093	318	4	y	y	PROPN
ejpam-6093	318	5	∈	∈	PROPN
ejpam-6093	318	6	t	t	NOUN
ejpam-6093	318	7	such	such	ADJ
ejpam-6093	318	8	that	that	SCONJ
ejpam-6093	318	9	x	x	SYM
ejpam-6093	318	10	∈	∈	PROPN
ejpam-6093	318	11	f	f	PROPN
ejpam-6093	318	12	and	and	CCONJ
ejpam-6093	318	13	x	x	SYM
ejpam-6093	318	14	≤	≤	PROPN
ejpam-6093	318	15	y.	y.	NOUN
ejpam-6093	318	16	then	then	ADV
ejpam-6093	318	17	by	by	ADP
ejpam-6093	318	18	theorem	theorem	NOUN
ejpam-6093	318	19	1	1	NUM
ejpam-6093	318	20	(	(	PUNCT
ejpam-6093	318	21	6	6	NUM
ejpam-6093	318	22	)	)	PUNCT
ejpam-6093	318	23	,	,	PUNCT
ejpam-6093	319	1	[	[	X
ejpam-6093	319	2	x1y]∗	x1y]∗	NOUN
ejpam-6093	319	3	=	=	SYM
ejpam-6093	319	4	1	1	NUM
ejpam-6093	319	5	∈	∈	PROPN
ejpam-6093	319	6	f	f	NOUN
ejpam-6093	319	7	.	.	PUNCT
ejpam-6093	320	1	since	since	SCONJ
ejpam-6093	320	2	x	x	PROPN
ejpam-6093	320	3	∈	∈	PROPN
ejpam-6093	320	4	f	f	X
ejpam-6093	320	5	,	,	PUNCT
ejpam-6093	320	6	[	[	X
ejpam-6093	320	7	x1y]∗	x1y]∗	NOUN
ejpam-6093	320	8	∈	∈	PROPN
ejpam-6093	320	9	f	f	X
ejpam-6093	320	10	,	,	PUNCT
ejpam-6093	320	11	and	and	CCONJ
ejpam-6093	320	12	f	f	PROPN
ejpam-6093	320	13	is	be	AUX
ejpam-6093	320	14	a	a	DET
ejpam-6093	320	15	generalized	generalized	ADJ
ejpam-6093	320	16	implicative	implicative	ADJ
ejpam-6093	320	17	filter	filter	NOUN
ejpam-6093	320	18	of	of	ADP
ejpam-6093	320	19	t	t	PROPN
ejpam-6093	320	20	,	,	PUNCT
ejpam-6093	320	21	we	we	PRON
ejpam-6093	320	22	get	get	VERB
ejpam-6093	320	23	that	that	PRON
ejpam-6093	321	1	[	[	X
ejpam-6093	321	2	xx[x1y]∗]∗	xx[x1y]∗]∗	X
ejpam-6093	321	3	∈	∈	PROPN
ejpam-6093	321	4	f	f	PROPN
ejpam-6093	321	5	.	.	PUNCT
ejpam-6093	322	1	then	then	ADV
ejpam-6093	322	2	by	by	ADP
ejpam-6093	322	3	theorem	theorem	NOUN
ejpam-6093	322	4	1	1	NUM
ejpam-6093	322	5	(	(	PUNCT
ejpam-6093	322	6	7	7	NUM
ejpam-6093	322	7	)	)	PUNCT
ejpam-6093	322	8	,	,	PUNCT
ejpam-6093	322	9	[	[	X
ejpam-6093	322	10	xx[x1y]∗]∗	xx[x1y]∗]∗	X
ejpam-6093	322	11	=	=	PUNCT
ejpam-6093	323	1	[	[	X
ejpam-6093	323	2	[	[	X
ejpam-6093	323	3	xxx]1y]∗	xxx]1y]∗	PROPN
ejpam-6093	323	4	,	,	PUNCT
ejpam-6093	323	5	and	and	CCONJ
ejpam-6093	323	6	from	from	ADP
ejpam-6093	323	7	assumption	assumption	NOUN
ejpam-6093	323	8	,	,	PUNCT
ejpam-6093	323	9	we	we	PRON
ejpam-6093	323	10	have	have	VERB
ejpam-6093	323	11	y	y	PROPN
ejpam-6093	323	12	∈	∈	PROPN
ejpam-6093	323	13	f	f	PROPN
ejpam-6093	323	14	.	.	PUNCT
ejpam-6093	324	1	case	case	NOUN
ejpam-6093	324	2	2	2	NUM
ejpam-6093	324	3	:	:	PUNCT
ejpam-6093	324	4	assume	assume	VERB
ejpam-6093	324	5	that	that	SCONJ
ejpam-6093	324	6	x	x	SYM
ejpam-6093	324	7	∈	∈	PROPN
ejpam-6093	324	8	f	f	NOUN
ejpam-6093	324	9	and	and	CCONJ
ejpam-6093	324	10	[	[	X
ejpam-6093	324	11	[	[	X
ejpam-6093	324	12	xx1]xy]∗	xx1]xy]∗	PROPN
ejpam-6093	324	13	∈	∈	PROPN
ejpam-6093	324	14	f	f	X
ejpam-6093	324	15	imply	imply	VERB
ejpam-6093	324	16	y	y	PROPN
ejpam-6093	324	17	∈	∈	PROPN
ejpam-6093	324	18	f	f	PROPN
ejpam-6093	324	19	for	for	ADP
ejpam-6093	324	20	all	all	DET
ejpam-6093	324	21	x	x	NOUN
ejpam-6093	324	22	,	,	PUNCT
ejpam-6093	324	23	y	y	PROPN
ejpam-6093	324	24	∈	∈	PROPN
ejpam-6093	324	25	t	t	PROPN
ejpam-6093	324	26	.	.	PUNCT
ejpam-6093	325	1	clearly	clearly	ADV
ejpam-6093	325	2	,	,	PUNCT
ejpam-6093	325	3	f	f	PROPN
ejpam-6093	325	4	is	be	AUX
ejpam-6093	325	5	a	a	DET
ejpam-6093	325	6	ternary	ternary	ADJ
ejpam-6093	325	7	subsemigroup	subsemigroup	NOUN
ejpam-6093	325	8	of	of	ADP
ejpam-6093	325	9	t	t	PROPN
ejpam-6093	325	10	.	.	PUNCT
ejpam-6093	326	1	let	let	VERB
ejpam-6093	326	2	x	x	PRON
ejpam-6093	326	3	,	,	PUNCT
ejpam-6093	326	4	y	y	PROPN
ejpam-6093	326	5	∈	∈	PROPN
ejpam-6093	326	6	t	t	NOUN
ejpam-6093	326	7	such	such	ADJ
ejpam-6093	326	8	that	that	SCONJ
ejpam-6093	326	9	x	x	SYM
ejpam-6093	326	10	∈	∈	PROPN
ejpam-6093	326	11	f	f	PROPN
ejpam-6093	326	12	and	and	CCONJ
ejpam-6093	326	13	x	x	SYM
ejpam-6093	326	14	≤	≤	PROPN
ejpam-6093	326	15	y.	y.	NOUN
ejpam-6093	326	16	then	then	ADV
ejpam-6093	326	17	by	by	ADP
ejpam-6093	326	18	theorem	theorem	NOUN
ejpam-6093	326	19	1	1	NUM
ejpam-6093	326	20	(	(	PUNCT
ejpam-6093	326	21	6	6	NUM
ejpam-6093	326	22	)	)	PUNCT
ejpam-6093	326	23	,	,	PUNCT
ejpam-6093	327	1	[	[	X
ejpam-6093	327	2	1xy]∗	1xy]∗	NUM
ejpam-6093	327	3	=	=	SYM
ejpam-6093	327	4	1	1	NUM
ejpam-6093	327	5	∈	∈	PROPN
ejpam-6093	327	6	f	f	NOUN
ejpam-6093	327	7	.	.	PUNCT
ejpam-6093	328	1	since	since	SCONJ
ejpam-6093	328	2	x	x	PROPN
ejpam-6093	328	3	∈	∈	PROPN
ejpam-6093	328	4	f	f	X
ejpam-6093	328	5	,	,	PUNCT
ejpam-6093	328	6	[	[	X
ejpam-6093	328	7	1xy]∗	1xy]∗	NUM
ejpam-6093	328	8	∈	∈	ADJ
ejpam-6093	328	9	f	f	X
ejpam-6093	328	10	,	,	PUNCT
ejpam-6093	328	11	and	and	CCONJ
ejpam-6093	328	12	f	f	PROPN
ejpam-6093	328	13	is	be	AUX
ejpam-6093	328	14	a	a	DET
ejpam-6093	328	15	generalized	generalized	ADJ
ejpam-6093	328	16	implicative	implicative	ADJ
ejpam-6093	328	17	filter	filter	NOUN
ejpam-6093	328	18	of	of	ADP
ejpam-6093	328	19	t	t	PROPN
ejpam-6093	328	20	,	,	PUNCT
ejpam-6093	328	21	we	we	PRON
ejpam-6093	328	22	get	get	VERB
ejpam-6093	328	23	that	that	PRON
ejpam-6093	329	1	[	[	X
ejpam-6093	329	2	xx[1xy]∗]∗	xx[1xy]∗]∗	X
ejpam-6093	329	3	∈	∈	PROPN
ejpam-6093	329	4	f	f	X
ejpam-6093	329	5	.	.	PUNCT
ejpam-6093	330	1	then	then	ADV
ejpam-6093	330	2	by	by	ADP
ejpam-6093	330	3	theorem	theorem	NOUN
ejpam-6093	330	4	1	1	NUM
ejpam-6093	330	5	(	(	PUNCT
ejpam-6093	330	6	7	7	NUM
ejpam-6093	330	7	)	)	PUNCT
ejpam-6093	330	8	,	,	PUNCT
ejpam-6093	331	1	[	[	X
ejpam-6093	331	2	xx[1xy]∗]∗	xx[1xy]∗]∗	X
ejpam-6093	331	3	=	=	PUNCT
ejpam-6093	332	1	[	[	X
ejpam-6093	332	2	[	[	X
ejpam-6093	332	3	xx1]xy]∗	xx1]xy]∗	NOUN
ejpam-6093	332	4	,	,	PUNCT
ejpam-6093	332	5	and	and	CCONJ
ejpam-6093	332	6	from	from	ADP
ejpam-6093	332	7	assumption	assumption	NOUN
ejpam-6093	332	8	,	,	PUNCT
ejpam-6093	332	9	we	we	PRON
ejpam-6093	332	10	have	have	VERB
ejpam-6093	332	11	y	y	PROPN
ejpam-6093	332	12	∈	∈	PROPN
ejpam-6093	332	13	f	f	PROPN
ejpam-6093	332	14	.	.	PUNCT
ejpam-6093	333	1	5	5	X
ejpam-6093	333	2	.	.	X
ejpam-6093	333	3	conclusions	conclusion	NOUN
ejpam-6093	333	4	in	in	ADP
ejpam-6093	333	5	this	this	DET
ejpam-6093	333	6	paper	paper	NOUN
ejpam-6093	333	7	,	,	PUNCT
ejpam-6093	333	8	we	we	PRON
ejpam-6093	333	9	consider	consider	VERB
ejpam-6093	333	10	filters	filter	NOUN
ejpam-6093	333	11	,	,	PUNCT
ejpam-6093	333	12	implicative	implicative	ADJ
ejpam-6093	333	13	filters	filter	NOUN
ejpam-6093	333	14	and	and	CCONJ
ejpam-6093	333	15	generalized	generalized	ADJ
ejpam-6093	333	16	implicative	implicative	ADJ
ejpam-6093	333	17	filters	filter	NOUN
ejpam-6093	333	18	on	on	ADP
ejpam-6093	333	19	implicative	implicative	ADJ
ejpam-6093	333	20	n.p.o	n.p.o	NOUN
ejpam-6093	333	21	ternary	ternary	ADJ
ejpam-6093	333	22	semigroups	semigroup	NOUN
ejpam-6093	333	23	.	.	PUNCT
ejpam-6093	334	1	in	in	ADP
ejpam-6093	334	2	section	section	NOUN
ejpam-6093	334	3	3	3	NUM
ejpam-6093	334	4	,	,	PUNCT
ejpam-6093	334	5	we	we	PRON
ejpam-6093	334	6	give	give	VERB
ejpam-6093	334	7	characterizations	characterization	NOUN
ejpam-6093	334	8	of	of	ADP
ejpam-6093	334	9	filters	filter	NOUN
ejpam-6093	334	10	in	in	ADP
ejpam-6093	334	11	implicative	implicative	ADJ
ejpam-6093	334	12	and	and	CCONJ
ejpam-6093	334	13	commutative	commutative	ADJ
ejpam-6093	334	14	implicative	implicative	ADJ
ejpam-6093	334	15	n.p.o	n.p.o	NOUN
ejpam-6093	334	16	.	.	PUNCT
ejpam-6093	335	1	ternary	ternary	ADJ
ejpam-6093	335	2	semigroups	semigroup	NOUN
ejpam-6093	335	3	(	(	PUNCT
ejpam-6093	335	4	see	see	VERB
ejpam-6093	335	5	theorem	theorem	ADJ
ejpam-6093	335	6	2	2	NUM
ejpam-6093	335	7	and	and	CCONJ
ejpam-6093	335	8	theorem	theorem	VERB
ejpam-6093	335	9	3	3	NUM
ejpam-6093	335	10	)	)	PUNCT
ejpam-6093	335	11	.	.	PUNCT
ejpam-6093	336	1	we	we	PRON
ejpam-6093	336	2	introduce	introduce	VERB
ejpam-6093	336	3	the	the	DET
ejpam-6093	336	4	notion	notion	NOUN
ejpam-6093	336	5	of	of	ADP
ejpam-6093	336	6	implicative	implicative	ADJ
ejpam-6093	336	7	filters	filter	NOUN
ejpam-6093	336	8	of	of	ADP
ejpam-6093	336	9	implicative	implicative	ADJ
ejpam-6093	336	10	n.p.o	n.p.o	NOUN
ejpam-6093	336	11	.	.	PUNCT
ejpam-6093	337	1	ternary	ternary	ADJ
ejpam-6093	337	2	semigroups	semigroup	NOUN
ejpam-6093	337	3	(	(	PUNCT
ejpam-6093	337	4	see	see	VERB
ejpam-6093	337	5	definition	definition	NOUN
ejpam-6093	337	6	2	2	NUM
ejpam-6093	337	7	)	)	PUNCT
ejpam-6093	337	8	.	.	PUNCT
ejpam-6093	338	1	an	an	DET
ejpam-6093	338	2	example	example	NOUN
ejpam-6093	338	3	of	of	ADP
ejpam-6093	338	4	implicative	implicative	ADJ
ejpam-6093	338	5	filter	filter	NOUN
ejpam-6093	338	6	is	be	AUX
ejpam-6093	338	7	also	also	ADV
ejpam-6093	338	8	established	establish	VERB
ejpam-6093	338	9	.	.	PUNCT
ejpam-6093	339	1	then	then	ADV
ejpam-6093	339	2	we	we	PRON
ejpam-6093	339	3	show	show	VERB
ejpam-6093	339	4	that	that	SCONJ
ejpam-6093	339	5	every	every	DET
ejpam-6093	339	6	implicative	implicative	ADJ
ejpam-6093	339	7	filter	filter	NOUN
ejpam-6093	339	8	is	be	AUX
ejpam-6093	339	9	a	a	DET
ejpam-6093	339	10	filter	filter	NOUN
ejpam-6093	339	11	and	and	CCONJ
ejpam-6093	339	12	give	give	VERB
ejpam-6093	339	13	an	an	DET
ejpam-6093	339	14	example	example	NOUN
ejpam-6093	339	15	to	to	PART
ejpam-6093	339	16	show	show	VERB
ejpam-6093	339	17	that	that	SCONJ
ejpam-6093	339	18	the	the	DET
ejpam-6093	339	19	converse	converse	NOUN
ejpam-6093	339	20	is	be	AUX
ejpam-6093	339	21	not	not	PART
ejpam-6093	339	22	true	true	ADJ
ejpam-6093	339	23	in	in	ADP
ejpam-6093	339	24	general	general	ADJ
ejpam-6093	339	25	.	.	PUNCT
ejpam-6093	340	1	finally	finally	ADV
ejpam-6093	340	2	,	,	PUNCT
ejpam-6093	340	3	we	we	PRON
ejpam-6093	340	4	state	state	VERB
ejpam-6093	340	5	some	some	DET
ejpam-6093	340	6	equivalent	equivalent	ADJ
ejpam-6093	340	7	conditions	condition	NOUN
ejpam-6093	340	8	for	for	ADP
ejpam-6093	340	9	an	an	DET
ejpam-6093	340	10	implicative	implicative	ADJ
ejpam-6093	340	11	filter	filter	NOUN
ejpam-6093	340	12	by	by	ADP
ejpam-6093	340	13	using	use	VERB
ejpam-6093	340	14	a	a	DET
ejpam-6093	340	15	particular	particular	ADJ
ejpam-6093	340	16	set	set	NOUN
ejpam-6093	340	17	defined	define	VERB
ejpam-6093	340	18	by	by	ADP
ejpam-6093	340	19	a	a	DET
ejpam-6093	340	20	filter	filter	NOUN
ejpam-6093	340	21	.	.	PUNCT
ejpam-6093	341	1	indeed	indeed	ADV
ejpam-6093	341	2	,	,	PUNCT
ejpam-6093	341	3	let	let	VERB
ejpam-6093	341	4	f	f	PRON
ejpam-6093	341	5	be	be	AUX
ejpam-6093	341	6	a	a	DET
ejpam-6093	341	7	filter	filter	NOUN
ejpam-6093	341	8	of	of	ADP
ejpam-6093	341	9	an	an	DET
ejpam-6093	341	10	implicative	implicative	ADJ
ejpam-6093	341	11	n.p.o	n.p.o	NOUN
ejpam-6093	341	12	.	.	PUNCT
ejpam-6093	342	1	ternary	ternary	ADJ
ejpam-6093	342	2	semigroup	semigroup	PROPN
ejpam-6093	342	3	(	(	PUNCT
ejpam-6093	342	4	t	t	PROPN
ejpam-6093	342	5	,	,	PUNCT
ejpam-6093	342	6	[	[	PUNCT
ejpam-6093	342	7	]	]	X
ejpam-6093	342	8	,	,	PUNCT
ejpam-6093	342	9	≤	≤	NUM
ejpam-6093	342	10	,	,	PUNCT
ejpam-6093	342	11	[	[	PUNCT
ejpam-6093	342	12	]	]	X
ejpam-6093	342	13	∗	∗	NOUN
ejpam-6093	342	14	)	)	PUNCT
ejpam-6093	342	15	.	.	PUNCT
ejpam-6093	343	1	for	for	ADP
ejpam-6093	343	2	a	a	DET
ejpam-6093	343	3	,	,	PUNCT
ejpam-6093	343	4	b	b	PROPN
ejpam-6093	343	5	∈	∈	PROPN
ejpam-6093	343	6	t	t	NOUN
ejpam-6093	343	7	,	,	PUNCT
ejpam-6093	343	8	define	define	VERB
ejpam-6093	343	9	fab	fab	NOUN
ejpam-6093	343	10	:	:	PUNCT
ejpam-6093	343	11	=	=	SYM
ejpam-6093	343	12	{	{	PUNCT
ejpam-6093	343	13	x	x	PUNCT
ejpam-6093	343	14	∈	∈	PROPN
ejpam-6093	343	15	t	t	NOUN
ejpam-6093	343	16	:	:	PUNCT
ejpam-6093	344	1	[	[	X
ejpam-6093	344	2	abx]∗	abx]∗	X
ejpam-6093	344	3	∈	∈	PROPN
ejpam-6093	344	4	f	f	X
ejpam-6093	344	5	}	}	PUNCT
ejpam-6093	344	6	.	.	PUNCT
ejpam-6093	345	1	we	we	PRON
ejpam-6093	345	2	obtain	obtain	VERB
ejpam-6093	345	3	that	that	SCONJ
ejpam-6093	345	4	a	a	DET
ejpam-6093	345	5	filter	filter	NOUN
ejpam-6093	345	6	f	f	PROPN
ejpam-6093	345	7	is	be	AUX
ejpam-6093	345	8	an	an	DET
ejpam-6093	345	9	implicative	implicative	ADJ
ejpam-6093	345	10	filter	filter	NOUN
ejpam-6093	345	11	if	if	SCONJ
ejpam-6093	345	12	and	and	CCONJ
ejpam-6093	345	13	only	only	ADV
ejpam-6093	345	14	if	if	SCONJ
ejpam-6093	345	15	for	for	ADP
ejpam-6093	345	16	any	any	DET
ejpam-6093	345	17	a	a	NOUN
ejpam-6093	345	18	,	,	PUNCT
ejpam-6093	345	19	b	b	PROPN
ejpam-6093	345	20	∈	∈	PROPN
ejpam-6093	345	21	t	t	NOUN
ejpam-6093	345	22	,	,	PUNCT
ejpam-6093	345	23	the	the	DET
ejpam-6093	345	24	set	set	VERB
ejpam-6093	345	25	fab	fab	NOUN
ejpam-6093	345	26	is	be	AUX
ejpam-6093	345	27	a	a	DET
ejpam-6093	345	28	filter	filter	NOUN
ejpam-6093	345	29	of	of	ADP
ejpam-6093	345	30	t	t	PROPN
ejpam-6093	345	31	.	.	PUNCT
ejpam-6093	346	1	in	in	ADP
ejpam-6093	346	2	section	section	NOUN
ejpam-6093	346	3	4	4	NUM
ejpam-6093	346	4	,	,	PUNCT
ejpam-6093	346	5	we	we	PRON
ejpam-6093	346	6	define	define	VERB
ejpam-6093	346	7	a	a	DET
ejpam-6093	346	8	generalized	generalized	ADJ
ejpam-6093	346	9	implicative	implicative	ADJ
ejpam-6093	346	10	filters	filter	NOUN
ejpam-6093	346	11	on	on	ADP
ejpam-6093	346	12	implicative	implicative	ADJ
ejpam-6093	346	13	n.p.o	n.p.o	NOUN
ejpam-6093	346	14	ternary	ternary	ADJ
ejpam-6093	346	15	semigroups	semigroup	NOUN
ejpam-6093	346	16	.	.	PUNCT
ejpam-6093	347	1	then	then	ADV
ejpam-6093	347	2	we	we	PRON
ejpam-6093	347	3	consider	consider	VERB
ejpam-6093	347	4	relationships	relationship	NOUN
ejpam-6093	347	5	among	among	ADP
ejpam-6093	347	6	filters	filter	NOUN
ejpam-6093	347	7	,	,	PUNCT
ejpam-6093	347	8	implicative	implicative	ADJ
ejpam-6093	347	9	filters	filter	NOUN
ejpam-6093	347	10	and	and	CCONJ
ejpam-6093	347	11	generalized	generalized	ADJ
ejpam-6093	347	12	implicative	implicative	ADJ
ejpam-6093	347	13	filters	filter	NOUN
ejpam-6093	347	14	.	.	PUNCT
ejpam-6093	348	1	we	we	PRON
ejpam-6093	348	2	have	have	VERB
ejpam-6093	348	3	that	that	SCONJ
ejpam-6093	348	4	every	every	DET
ejpam-6093	348	5	filter	filter	NOUN
ejpam-6093	348	6	is	be	AUX
ejpam-6093	348	7	a	a	DET
ejpam-6093	348	8	generalized	generalized	ADJ
ejpam-6093	348	9	implicative	implicative	ADJ
ejpam-6093	348	10	filter	filter	NOUN
ejpam-6093	348	11	and	and	CCONJ
ejpam-6093	348	12	every	every	DET
ejpam-6093	348	13	implicative	implicative	ADJ
ejpam-6093	348	14	filter	filter	NOUN
ejpam-6093	348	15	is	be	AUX
ejpam-6093	348	16	also	also	ADV
ejpam-6093	348	17	a	a	DET
ejpam-6093	348	18	generalized	generalized	ADJ
ejpam-6093	348	19	implicative	implicative	ADJ
ejpam-6093	348	20	filter	filter	NOUN
ejpam-6093	348	21	.	.	PUNCT
ejpam-6093	349	1	the	the	DET
ejpam-6093	349	2	converse	converse	NOUN
ejpam-6093	349	3	of	of	ADP
ejpam-6093	349	4	these	these	DET
ejpam-6093	349	5	statement	statement	NOUN
ejpam-6093	349	6	is	be	AUX
ejpam-6093	349	7	not	not	PART
ejpam-6093	349	8	generally	generally	ADV
ejpam-6093	349	9	true	true	ADJ
ejpam-6093	349	10	.	.	PUNCT
ejpam-6093	350	1	now	now	ADV
ejpam-6093	350	2	,	,	PUNCT
ejpam-6093	350	3	we	we	PRON
ejpam-6093	350	4	conclude	conclude	VERB
ejpam-6093	350	5	the	the	DET
ejpam-6093	350	6	connections	connection	NOUN
ejpam-6093	350	7	of	of	ADP
ejpam-6093	350	8	filters	filter	NOUN
ejpam-6093	350	9	,	,	PUNCT
ejpam-6093	350	10	implicative	implicative	ADJ
ejpam-6093	350	11	filters	filter	NOUN
ejpam-6093	350	12	,	,	PUNCT
ejpam-6093	350	13	and	and	CCONJ
ejpam-6093	350	14	generalized	generalized	ADJ
ejpam-6093	350	15	implicative	implicative	ADJ
ejpam-6093	350	16	filters	filter	NOUN
ejpam-6093	350	17	as	as	ADP
ejpam-6093	350	18	the	the	DET
ejpam-6093	350	19	picture	picture	NOUN
ejpam-6093	350	20	.	.	PUNCT
ejpam-6093	351	1	filter	filter	NOUN
ejpam-6093	351	2	generalized	generalize	VERB
ejpam-6093	351	3	implicative	implicative	ADJ
ejpam-6093	351	4	filter	filter	NOUN
ejpam-6093	351	5	implicative	implicative	ADJ
ejpam-6093	351	6	filter	filter	PROPN
ejpam-6093	351	7	k.	k.	PROPN
ejpam-6093	351	8	nakwan	nakwan	PROPN
ejpam-6093	351	9	,	,	PUNCT
ejpam-6093	351	10	p.	p.	PROPN
ejpam-6093	351	11	luangchaisri	luangchaisri	VERB
ejpam-6093	351	12	,	,	PUNCT
ejpam-6093	351	13	t.	t.	PROPN
ejpam-6093	351	14	changphas	changphas	PROPN
ejpam-6093	351	15	/	/	SYM
ejpam-6093	351	16	eur	eur	PROPN
ejpam-6093	351	17	.	.	PUNCT
ejpam-6093	352	1	j.	j.	PROPN
ejpam-6093	352	2	pure	pure	PROPN
ejpam-6093	352	3	appl	appl	PROPN
ejpam-6093	352	4	.	.	PROPN
ejpam-6093	352	5	math	math	PROPN
ejpam-6093	352	6	,	,	PUNCT
ejpam-6093	352	7	18	18	NUM
ejpam-6093	352	8	(	(	PUNCT
ejpam-6093	352	9	4	4	NUM
ejpam-6093	352	10	)	)	PUNCT
ejpam-6093	352	11	(	(	PUNCT
ejpam-6093	352	12	2025	2025	NUM
ejpam-6093	352	13	)	)	PUNCT
ejpam-6093	352	14	,	,	PUNCT
ejpam-6093	352	15	6093	6093	NUM
ejpam-6093	352	16	11	11	NUM
ejpam-6093	352	17	of	of	ADP
ejpam-6093	352	18	11	11	NUM
ejpam-6093	352	19	acknowledgements	acknowledgement	NOUN
ejpam-6093	352	20	the	the	DET
ejpam-6093	352	21	research	research	NOUN
ejpam-6093	352	22	on	on	ADP
ejpam-6093	352	23	”	"	PUNCT
ejpam-6093	352	24	implicative	implicative	ADJ
ejpam-6093	352	25	filters	filter	NOUN
ejpam-6093	352	26	of	of	ADP
ejpam-6093	352	27	implicative	implicative	NOUN
ejpam-6093	352	28	negatively	negatively	ADV
ejpam-6093	352	29	partially	partially	ADV
ejpam-6093	352	30	ordered	order	VERB
ejpam-6093	352	31	ternary	ternary	ADJ
ejpam-6093	352	32	semigroups	semigroup	NOUN
ejpam-6093	352	33	”	"	PUNCT
ejpam-6093	352	34	by	by	ADP
ejpam-6093	352	35	khon	khon	PROPN
ejpam-6093	352	36	kaen	kaen	PROPN
ejpam-6093	352	37	university	university	PROPN
ejpam-6093	352	38	has	have	AUX
ejpam-6093	352	39	received	receive	VERB
ejpam-6093	352	40	funding	funding	NOUN
ejpam-6093	352	41	support	support	NOUN
ejpam-6093	352	42	from	from	ADP
ejpam-6093	352	43	the	the	DET
ejpam-6093	352	44	national	national	ADJ
ejpam-6093	352	45	science	science	NOUN
ejpam-6093	352	46	,	,	PUNCT
ejpam-6093	352	47	research	research	NOUN
ejpam-6093	352	48	and	and	CCONJ
ejpam-6093	352	49	innovation	innovation	NOUN
ejpam-6093	352	50	fund	fund	NOUN
ejpam-6093	352	51	(	(	PUNCT
ejpam-6093	352	52	nsrf	nsrf	NOUN
ejpam-6093	352	53	)	)	PUNCT
ejpam-6093	352	54	.	.	PUNCT
ejpam-6093	353	1	references	reference	NOUN
ejpam-6093	353	2	[	[	X
ejpam-6093	353	3	1	1	NUM
ejpam-6093	353	4	]	]	PUNCT
ejpam-6093	353	5	m.	m.	NOUN
ejpam-6093	353	6	w.	w.	PROPN
ejpam-6093	353	7	chan	chan	PROPN
ejpam-6093	353	8	and	and	CCONJ
ejpam-6093	353	9	k.	k.	PROPN
ejpam-6093	353	10	p.	p.	PROPN
ejpam-6093	353	11	shum	shum	PROPN
ejpam-6093	353	12	.	.	PUNCT
ejpam-6093	354	1	homomorphisms	homomorphism	NOUN
ejpam-6093	354	2	of	of	ADP
ejpam-6093	354	3	implicative	implicative	ADJ
ejpam-6093	354	4	semigroups	semigroup	NOUN
ejpam-6093	354	5	.	.	PUNCT
ejpam-6093	355	1	semigroup	semigroup	PROPN
ejpam-6093	355	2	forum	forum	PROPN
ejpam-6093	355	3	,	,	PUNCT
ejpam-6093	355	4	46:7–15	46:7–15	NUM
ejpam-6093	355	5	,	,	PUNCT
ejpam-6093	355	6	1993	1993	NUM
ejpam-6093	355	7	.	.	PUNCT
ejpam-6093	356	1	[	[	X
ejpam-6093	356	2	2	2	NUM
ejpam-6093	356	3	]	]	X
ejpam-6093	356	4	y.b	y.b	PROPN
ejpam-6093	356	5	.	.	PROPN
ejpam-6093	356	6	jun	jun	PROPN
ejpam-6093	356	7	.	.	PROPN
ejpam-6093	356	8	implicative	implicative	PROPN
ejpam-6093	356	9	ordered	order	VERB
ejpam-6093	356	10	filters	filter	NOUN
ejpam-6093	356	11	of	of	ADP
ejpam-6093	356	12	implicative	implicative	ADJ
ejpam-6093	356	13	semigroups	semigroup	NOUN
ejpam-6093	356	14	.	.	PUNCT
ejpam-6093	357	1	communications	communication	NOUN
ejpam-6093	357	2	of	of	ADP
ejpam-6093	357	3	the	the	DET
ejpam-6093	357	4	korean	korean	ADJ
ejpam-6093	357	5	mathematical	mathematical	ADJ
ejpam-6093	357	6	society	society	NOUN
ejpam-6093	357	7	,	,	PUNCT
ejpam-6093	357	8	14(1):47–55	14(1):47–55	NUM
ejpam-6093	357	9	,	,	PUNCT
ejpam-6093	357	10	1999	1999	NUM
ejpam-6093	357	11	.	.	PUNCT
ejpam-6093	358	1	[	[	X
ejpam-6093	358	2	3	3	X
ejpam-6093	358	3	]	]	PUNCT
ejpam-6093	358	4	m.	m.	NOUN
ejpam-6093	358	5	sambasiva	sambasiva	PROPN
ejpam-6093	358	6	rao	rao	PROPN
ejpam-6093	358	7	and	and	CCONJ
ejpam-6093	358	8	k.	k.	PROPN
ejpam-6093	358	9	p.	p.	PROPN
ejpam-6093	358	10	shum	shum	PROPN
ejpam-6093	358	11	.	.	PUNCT
ejpam-6093	359	1	on	on	ADP
ejpam-6093	359	2	filters	filter	NOUN
ejpam-6093	359	3	of	of	ADP
ejpam-6093	359	4	implicative	implicative	ADJ
ejpam-6093	359	5	npo	npo	PROPN
ejpam-6093	359	6	semigroups	semigroup	NOUN
ejpam-6093	359	7	.	.	PUNCT
ejpam-6093	359	8	asianeuropean	asianeuropean	PROPN
ejpam-6093	359	9	journal	journal	PROPN
ejpam-6093	359	10	of	of	ADP
ejpam-6093	359	11	mathematics	mathematic	NOUN
ejpam-6093	359	12	,	,	PUNCT
ejpam-6093	359	13	5(03):1250044	5(03):1250044	NUM
ejpam-6093	359	14	,	,	PUNCT
ejpam-6093	359	15	2012	2012	NUM
ejpam-6093	359	16	.	.	PUNCT
ejpam-6093	360	1	[	[	X
ejpam-6093	360	2	4	4	X
ejpam-6093	360	3	]	]	PUNCT
ejpam-6093	360	4	k.	k.	PROPN
ejpam-6093	360	5	nakwan	nakwan	PROPN
ejpam-6093	360	6	,	,	PUNCT
ejpam-6093	360	7	p.	p.	PROPN
ejpam-6093	360	8	luangchaisri	luangchaisri	VERB
ejpam-6093	360	9	,	,	PUNCT
ejpam-6093	360	10	and	and	CCONJ
ejpam-6093	360	11	t.	t.	PROPN
ejpam-6093	360	12	changphas	changphas	PROPN
ejpam-6093	360	13	.	.	PUNCT
ejpam-6093	361	1	implicative	implicative	PROPN
ejpam-6093	361	2	negatively	negatively	ADV
ejpam-6093	361	3	partially	partially	ADV
ejpam-6093	361	4	ordered	order	VERB
ejpam-6093	361	5	ternary	ternary	ADJ
ejpam-6093	361	6	semigroups	semigroup	NOUN
ejpam-6093	361	7	.	.	PUNCT
ejpam-6093	362	1	european	european	ADJ
ejpam-6093	362	2	journal	journal	PROPN
ejpam-6093	362	3	of	of	ADP
ejpam-6093	362	4	pure	pure	ADJ
ejpam-6093	362	5	and	and	CCONJ
ejpam-6093	362	6	applied	applied	ADJ
ejpam-6093	362	7	mathematics	mathematic	NOUN
ejpam-6093	362	8	.	.	PUNCT
ejpam-6093	362	9	,	,	PUNCT
ejpam-6093	362	10	17(4):4180–4194	17(4):4180–4194	NUM
ejpam-6093	362	11	,	,	PUNCT
ejpam-6093	362	12	2024	2024	NUM
ejpam-6093	362	13	.	.	PUNCT