id	sid	tid	token	lemma	pos
ejpam-3752	1	1	european	european	PROPN
ejpam-3752	1	2	journal	journal	PROPN
ejpam-3752	1	3	of	of	ADP
ejpam-3752	1	4	pure	pure	ADJ
ejpam-3752	1	5	and	and	CCONJ
ejpam-3752	1	6	applied	apply	VERB
ejpam-3752	1	7	mathematics	mathematic	NOUN
ejpam-3752	1	8	vol	vol	NOUN
ejpam-3752	1	9	.	.	PROPN
ejpam-3752	2	1	13	13	NUM
ejpam-3752	2	2	,	,	PUNCT
ejpam-3752	2	3	no	no	INTJ
ejpam-3752	2	4	.	.	NOUN
ejpam-3752	2	5	3	3	NUM
ejpam-3752	2	6	,	,	PUNCT
ejpam-3752	2	7	2020	2020	NUM
ejpam-3752	2	8	,	,	PUNCT
ejpam-3752	2	9	459	459	NUM
ejpam-3752	2	10	-	-	SYM
ejpam-3752	2	11	471	471	NUM
ejpam-3752	2	12	issn	issn	PROPN
ejpam-3752	2	13	1307	1307	NUM
ejpam-3752	2	14	-	-	SYM
ejpam-3752	2	15	5543	5543	NUM
ejpam-3752	2	16	–	–	PUNCT
ejpam-3752	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3752	2	18	published	publish	VERB
ejpam-3752	2	19	by	by	ADP
ejpam-3752	2	20	new	new	PROPN
ejpam-3752	2	21	york	york	PROPN
ejpam-3752	2	22	business	business	PROPN
ejpam-3752	2	23	global	global	ADJ
ejpam-3752	2	24	fuzzy	fuzzy	ADJ
ejpam-3752	2	25	duplex	duplex	NOUN
ejpam-3752	2	26	up	up	ADP
ejpam-3752	2	27	-	-	PUNCT
ejpam-3752	2	28	algebras†	algebras†	NOUN
ejpam-3752	2	29	aiyared	aiyared	NOUN
ejpam-3752	2	30	iampan1	iampan1	PROPN
ejpam-3752	2	31	,	,	PUNCT
ejpam-3752	2	32	metawee	metawee	NOUN
ejpam-3752	2	33	songsaeng1	songsaeng1	PROPN
ejpam-3752	2	34	,	,	PUNCT
ejpam-3752	2	35	g.	g.	PROPN
ejpam-3752	2	36	muhiuddin2,∗	muhiuddin2,∗	PROPN
ejpam-3752	2	37	1	1	NUM
ejpam-3752	2	38	department	department	NOUN
ejpam-3752	2	39	of	of	ADP
ejpam-3752	2	40	mathematics	mathematic	NOUN
ejpam-3752	2	41	,	,	PUNCT
ejpam-3752	2	42	school	school	NOUN
ejpam-3752	2	43	of	of	ADP
ejpam-3752	2	44	science	science	NOUN
ejpam-3752	2	45	,	,	PUNCT
ejpam-3752	2	46	university	university	NOUN
ejpam-3752	2	47	of	of	ADP
ejpam-3752	2	48	phayao	phayao	NOUN
ejpam-3752	2	49	,	,	PUNCT
ejpam-3752	2	50	phayao	phayao	NOUN
ejpam-3752	2	51	56000	56000	NUM
ejpam-3752	2	52	,	,	PUNCT
ejpam-3752	2	53	thailand	thailand	PROPN
ejpam-3752	2	54	2	2	NUM
ejpam-3752	2	55	department	department	NOUN
ejpam-3752	2	56	of	of	ADP
ejpam-3752	2	57	mathematics	mathematic	NOUN
ejpam-3752	2	58	,	,	PUNCT
ejpam-3752	2	59	university	university	PROPN
ejpam-3752	2	60	of	of	ADP
ejpam-3752	2	61	tabuk	tabuk	PROPN
ejpam-3752	2	62	,	,	PUNCT
ejpam-3752	2	63	tabuk	tabuk	NOUN
ejpam-3752	2	64	71491	71491	NUM
ejpam-3752	2	65	,	,	PUNCT
ejpam-3752	2	66	saudi	saudi	PROPN
ejpam-3752	2	67	arabia	arabia	PROPN
ejpam-3752	2	68	abstract	abstract	NOUN
ejpam-3752	2	69	.	.	PUNCT
ejpam-3752	3	1	using	use	VERB
ejpam-3752	3	2	the	the	DET
ejpam-3752	3	3	concept	concept	NOUN
ejpam-3752	3	4	of	of	ADP
ejpam-3752	3	5	a	a	DET
ejpam-3752	3	6	neutrosophic	neutrosophic	ADJ
ejpam-3752	3	7	quadruple	quadruple	NOUN
ejpam-3752	3	8	number	number	NOUN
ejpam-3752	3	9	to	to	ADP
ejpam-3752	3	10	a	a	DET
ejpam-3752	3	11	fuzzy	fuzzy	ADJ
ejpam-3752	3	12	duplex	duplex	NOUN
ejpam-3752	3	13	number	number	NOUN
ejpam-3752	3	14	,	,	PUNCT
ejpam-3752	3	15	we	we	PRON
ejpam-3752	3	16	introduce	introduce	VERB
ejpam-3752	3	17	the	the	DET
ejpam-3752	3	18	concept	concept	NOUN
ejpam-3752	3	19	of	of	ADP
ejpam-3752	3	20	a	a	DET
ejpam-3752	3	21	fuzzy	fuzzy	ADJ
ejpam-3752	3	22	duplex	duplex	NOUN
ejpam-3752	3	23	up	up	ADP
ejpam-3752	3	24	-	-	PUNCT
ejpam-3752	3	25	algebra	algebra	NOUN
ejpam-3752	3	26	,	,	PUNCT
ejpam-3752	3	27	and	and	CCONJ
ejpam-3752	3	28	investigate	investigate	VERB
ejpam-3752	3	29	some	some	DET
ejpam-3752	3	30	related	related	ADJ
ejpam-3752	3	31	properties	property	NOUN
ejpam-3752	3	32	.	.	PUNCT
ejpam-3752	4	1	also	also	ADV
ejpam-3752	4	2	,	,	PUNCT
ejpam-3752	4	3	we	we	PRON
ejpam-3752	4	4	find	find	VERB
ejpam-3752	4	5	the	the	DET
ejpam-3752	4	6	necessary	necessary	ADJ
ejpam-3752	4	7	condition	condition	NOUN
ejpam-3752	4	8	for	for	ADP
ejpam-3752	4	9	a	a	DET
ejpam-3752	4	10	fuzzy	fuzzy	ADJ
ejpam-3752	4	11	duplex	duplex	NOUN
ejpam-3752	4	12	up	up	ADV
ejpam-3752	4	13	-	-	PUNCT
ejpam-3752	4	14	set	set	NOUN
ejpam-3752	4	15	to	to	PART
ejpam-3752	4	16	be	be	AUX
ejpam-3752	4	17	a	a	DET
ejpam-3752	4	18	fuzzy	fuzzy	ADJ
ejpam-3752	4	19	duplex	duplex	NOUN
ejpam-3752	4	20	up	up	ADP
ejpam-3752	4	21	-	-	PUNCT
ejpam-3752	4	22	algebra	algebra	NOUN
ejpam-3752	4	23	.	.	PUNCT
ejpam-3752	5	1	furthermore	furthermore	ADV
ejpam-3752	5	2	,	,	PUNCT
ejpam-3752	5	3	we	we	PRON
ejpam-3752	5	4	study	study	VERB
ejpam-3752	5	5	the	the	DET
ejpam-3752	5	6	relationship	relationship	NOUN
ejpam-3752	5	7	between	between	ADP
ejpam-3752	5	8	special	special	ADJ
ejpam-3752	5	9	subsets	subset	NOUN
ejpam-3752	5	10	of	of	ADP
ejpam-3752	5	11	a	a	DET
ejpam-3752	5	12	up	up	NOUN
ejpam-3752	5	13	-	-	PUNCT
ejpam-3752	5	14	algebra	algebra	NOUN
ejpam-3752	5	15	and	and	CCONJ
ejpam-3752	5	16	special	special	ADJ
ejpam-3752	5	17	subsets	subset	NOUN
ejpam-3752	5	18	of	of	ADP
ejpam-3752	5	19	a	a	DET
ejpam-3752	5	20	fuzzy	fuzzy	ADJ
ejpam-3752	5	21	duplex	duplex	NOUN
ejpam-3752	5	22	up	up	ADV
ejpam-3752	5	23	-	-	PUNCT
ejpam-3752	5	24	set	set	NOUN
ejpam-3752	5	25	.	.	PUNCT
ejpam-3752	6	1	2020	2020	NUM
ejpam-3752	6	2	mathematics	mathematics	PROPN
ejpam-3752	6	3	subject	subject	NOUN
ejpam-3752	6	4	classifications	classification	NOUN
ejpam-3752	6	5	:	:	PUNCT
ejpam-3752	6	6	03g25	03g25	NUM
ejpam-3752	6	7	,	,	PUNCT
ejpam-3752	6	8	08a72	08a72	NOUN
ejpam-3752	6	9	key	key	ADJ
ejpam-3752	6	10	words	word	NOUN
ejpam-3752	6	11	and	and	CCONJ
ejpam-3752	6	12	phrases	phrase	NOUN
ejpam-3752	6	13	:	:	PUNCT
ejpam-3752	6	14	up	up	ADP
ejpam-3752	6	15	-	-	PUNCT
ejpam-3752	6	16	algebra	algebra	NOUN
ejpam-3752	6	17	,	,	PUNCT
ejpam-3752	6	18	up	up	ADP
ejpam-3752	6	19	-	-	PUNCT
ejpam-3752	6	20	subalgebra	subalgebra	NOUN
ejpam-3752	6	21	,	,	PUNCT
ejpam-3752	6	22	near	near	ADP
ejpam-3752	6	23	up	up	ADP
ejpam-3752	6	24	-	-	PUNCT
ejpam-3752	6	25	filter	filter	NOUN
ejpam-3752	6	26	,	,	PUNCT
ejpam-3752	6	27	up	up	ADP
ejpam-3752	6	28	-	-	PUNCT
ejpam-3752	6	29	filter	filter	NOUN
ejpam-3752	6	30	,	,	PUNCT
ejpam-3752	6	31	up	up	ADP
ejpam-3752	6	32	-	-	PUNCT
ejpam-3752	6	33	ideal	ideal	ADJ
ejpam-3752	6	34	,	,	PUNCT
ejpam-3752	6	35	strong	strong	ADJ
ejpam-3752	6	36	up	up	ADP
ejpam-3752	6	37	-	-	PUNCT
ejpam-3752	6	38	ideal	ideal	ADJ
ejpam-3752	6	39	,	,	PUNCT
ejpam-3752	6	40	fuzzy	fuzzy	ADJ
ejpam-3752	6	41	duplex	duplex	NOUN
ejpam-3752	6	42	up	up	ADP
ejpam-3752	6	43	-	-	PUNCT
ejpam-3752	6	44	set	set	ADJ
ejpam-3752	6	45	,	,	PUNCT
ejpam-3752	6	46	fuzzy	fuzzy	ADJ
ejpam-3752	6	47	duplex	duplex	NOUN
ejpam-3752	6	48	up	up	ADP
ejpam-3752	6	49	-	-	PUNCT
ejpam-3752	6	50	algebra	algebra	NOUN
ejpam-3752	6	51	1	1	NUM
ejpam-3752	6	52	.	.	PUNCT
ejpam-3752	6	53	introduction	introduction	NOUN
ejpam-3752	6	54	the	the	DET
ejpam-3752	6	55	type	type	NOUN
ejpam-3752	6	56	of	of	ADP
ejpam-3752	6	57	the	the	DET
ejpam-3752	6	58	logical	logical	ADJ
ejpam-3752	6	59	algebra	algebra	NOUN
ejpam-3752	6	60	,	,	PUNCT
ejpam-3752	6	61	a	a	DET
ejpam-3752	6	62	up	up	NOUN
ejpam-3752	6	63	-	-	PUNCT
ejpam-3752	6	64	algebra	algebra	NOUN
ejpam-3752	6	65	was	be	AUX
ejpam-3752	6	66	introduced	introduce	VERB
ejpam-3752	6	67	by	by	ADP
ejpam-3752	6	68	iampan	iampan	NOUN
ejpam-3752	6	69	[	[	X
ejpam-3752	6	70	9	9	NUM
ejpam-3752	6	71	]	]	PUNCT
ejpam-3752	6	72	,	,	PUNCT
ejpam-3752	6	73	and	and	CCONJ
ejpam-3752	6	74	it	it	PRON
ejpam-3752	6	75	is	be	AUX
ejpam-3752	6	76	known	know	VERB
ejpam-3752	6	77	that	that	SCONJ
ejpam-3752	6	78	the	the	DET
ejpam-3752	6	79	class	class	NOUN
ejpam-3752	6	80	of	of	ADP
ejpam-3752	6	81	ku	ku	PROPN
ejpam-3752	6	82	-	-	PUNCT
ejpam-3752	6	83	algebras	algebras	PROPN
ejpam-3752	6	84	is	be	AUX
ejpam-3752	6	85	a	a	DET
ejpam-3752	6	86	proper	proper	ADJ
ejpam-3752	6	87	subclass	subclass	NOUN
ejpam-3752	6	88	of	of	ADP
ejpam-3752	6	89	the	the	DET
ejpam-3752	6	90	class	class	NOUN
ejpam-3752	6	91	of	of	ADP
ejpam-3752	6	92	up	up	NOUN
ejpam-3752	6	93	-	-	PUNCT
ejpam-3752	6	94	algebras	algebras	X
ejpam-3752	6	95	.	.	PUNCT
ejpam-3752	7	1	later	later	ADV
ejpam-3752	7	2	somjanta	somjanta	VERB
ejpam-3752	7	3	et	et	PROPN
ejpam-3752	7	4	al	al	PROPN
ejpam-3752	7	5	.	.	PUNCT
ejpam-3752	8	1	[	[	X
ejpam-3752	8	2	29	29	NUM
ejpam-3752	8	3	]	]	PUNCT
ejpam-3752	8	4	studied	study	VERB
ejpam-3752	8	5	fuzzy	fuzzy	ADJ
ejpam-3752	8	6	up	up	ADP
ejpam-3752	8	7	-	-	PUNCT
ejpam-3752	8	8	subalgebras	subalgebras	X
ejpam-3752	8	9	,	,	PUNCT
ejpam-3752	8	10	fuzzy	fuzzy	ADJ
ejpam-3752	8	11	up	up	NOUN
ejpam-3752	8	12	-	-	PUNCT
ejpam-3752	8	13	ideals	ideal	NOUN
ejpam-3752	8	14	and	and	CCONJ
ejpam-3752	8	15	fuzzy	fuzzy	ADJ
ejpam-3752	8	16	up	up	NOUN
ejpam-3752	8	17	-	-	PUNCT
ejpam-3752	8	18	filters	filter	NOUN
ejpam-3752	8	19	of	of	ADP
ejpam-3752	8	20	up	up	ADP
ejpam-3752	8	21	-	-	PUNCT
ejpam-3752	8	22	algebras	algebras	X
ejpam-3752	8	23	.	.	PUNCT
ejpam-3752	9	1	guntasow	guntasow	PROPN
ejpam-3752	9	2	et	et	PROPN
ejpam-3752	9	3	al	al	PROPN
ejpam-3752	9	4	.	.	PUNCT
ejpam-3752	10	1	[	[	X
ejpam-3752	10	2	7	7	NUM
ejpam-3752	10	3	]	]	PUNCT
ejpam-3752	10	4	studied	study	VERB
ejpam-3752	10	5	fuzzy	fuzzy	ADJ
ejpam-3752	10	6	translations	translation	NOUN
ejpam-3752	10	7	of	of	ADP
ejpam-3752	10	8	a	a	DET
ejpam-3752	10	9	fuzzy	fuzzy	ADJ
ejpam-3752	10	10	set	set	NOUN
ejpam-3752	10	11	in	in	ADP
ejpam-3752	10	12	up	up	ADP
ejpam-3752	10	13	-	-	PUNCT
ejpam-3752	10	14	algebras	algebras	X
ejpam-3752	10	15	.	.	PUNCT
ejpam-3752	11	1	kesorn	kesorn	PROPN
ejpam-3752	11	2	et	et	PROPN
ejpam-3752	11	3	al	al	PROPN
ejpam-3752	11	4	.	.	PUNCT
ejpam-3752	12	1	[	[	X
ejpam-3752	12	2	16	16	NUM
ejpam-3752	12	3	]	]	PUNCT
ejpam-3752	12	4	studied	study	VERB
ejpam-3752	12	5	intuitionistic	intuitionistic	ADJ
ejpam-3752	12	6	fuzzy	fuzzy	ADJ
ejpam-3752	12	7	sets	set	NOUN
ejpam-3752	12	8	in	in	ADP
ejpam-3752	12	9	up	up	ADP
ejpam-3752	12	10	-	-	PUNCT
ejpam-3752	12	11	algebras	algebras	X
ejpam-3752	12	12	.	.	PUNCT
ejpam-3752	13	1	kaijae	kaijae	PROPN
ejpam-3752	13	2	et	et	PROPN
ejpam-3752	13	3	al	al	PROPN
ejpam-3752	13	4	.	.	PUNCT
ejpam-3752	14	1	[	[	X
ejpam-3752	14	2	15	15	NUM
ejpam-3752	14	3	]	]	PUNCT
ejpam-3752	14	4	studied	study	VERB
ejpam-3752	14	5	anti	anti	ADJ
ejpam-3752	14	6	-	-	ADJ
ejpam-3752	14	7	fuzzy	fuzzy	ADJ
ejpam-3752	14	8	up	up	ADJ
ejpam-3752	14	9	-	-	PUNCT
ejpam-3752	14	10	ideals	ideal	NOUN
ejpam-3752	14	11	and	and	CCONJ
ejpam-3752	14	12	anti	anti	ADJ
ejpam-3752	14	13	-	-	ADJ
ejpam-3752	14	14	fuzzy	fuzzy	ADJ
ejpam-3752	14	15	up	up	ADP
ejpam-3752	14	16	-	-	PUNCT
ejpam-3752	14	17	subalgebras	subalgebras	X
ejpam-3752	14	18	.	.	PUNCT
ejpam-3752	15	1	tanamoon	tanamoon	NOUN
ejpam-3752	15	2	et	et	PROPN
ejpam-3752	15	3	al	al	PROPN
ejpam-3752	15	4	.	.	PUNCT
ejpam-3752	16	1	[	[	X
ejpam-3752	16	2	35	35	NUM
ejpam-3752	16	3	]	]	PUNCT
ejpam-3752	16	4	and	and	CCONJ
ejpam-3752	16	5	sripaeng	sripaeng	PROPN
ejpam-3752	16	6	et	et	PROPN
ejpam-3752	16	7	al	al	PROPN
ejpam-3752	16	8	.	.	PUNCT
ejpam-3752	17	1	[	[	X
ejpam-3752	17	2	34	34	NUM
ejpam-3752	17	3	]	]	PUNCT
ejpam-3752	17	4	introduced	introduce	VERB
ejpam-3752	17	5	the	the	DET
ejpam-3752	17	6	concept	concept	NOUN
ejpam-3752	17	7	of	of	ADP
ejpam-3752	17	8	q	q	ADJ
ejpam-3752	17	9	-	-	PUNCT
ejpam-3752	17	10	fuzzy	fuzzy	ADJ
ejpam-3752	17	11	sets	set	NOUN
ejpam-3752	17	12	in	in	ADP
ejpam-3752	17	13	up	up	ADP
ejpam-3752	17	14	-	-	PUNCT
ejpam-3752	17	15	algebras	algebras	X
ejpam-3752	17	16	,	,	PUNCT
ejpam-3752	17	17	and	and	CCONJ
ejpam-3752	17	18	studied	study	VERB
ejpam-3752	17	19	anti	anti	ADJ
ejpam-3752	17	20	q	q	ADJ
ejpam-3752	17	21	-	-	ADJ
ejpam-3752	17	22	fuzzy	fuzzy	ADJ
ejpam-3752	17	23	up	up	NOUN
ejpam-3752	17	24	-	-	PUNCT
ejpam-3752	17	25	ideals	ideal	NOUN
ejpam-3752	17	26	and	and	CCONJ
ejpam-3752	17	27	anti	anti	ADJ
ejpam-3752	17	28	q	q	ADJ
ejpam-3752	17	29	-	-	ADJ
ejpam-3752	17	30	fuzzy	fuzzy	ADJ
ejpam-3752	17	31	up	up	ADP
ejpam-3752	17	32	-	-	PUNCT
ejpam-3752	17	33	subalgebras	subalgebra	NOUN
ejpam-3752	17	34	of	of	ADP
ejpam-3752	17	35	up	up	ADP
ejpam-3752	17	36	-	-	PUNCT
ejpam-3752	17	37	algebras	algebras	X
ejpam-3752	17	38	.	.	PUNCT
ejpam-3752	18	1	dokkhamdang	dokkhamdang	PROPN
ejpam-3752	18	2	et	et	PROPN
ejpam-3752	18	3	al	al	PROPN
ejpam-3752	18	4	.	.	PUNCT
ejpam-3752	19	1	[	[	X
ejpam-3752	19	2	6	6	NUM
ejpam-3752	19	3	]	]	PUNCT
ejpam-3752	19	4	introduced	introduce	VERB
ejpam-3752	19	5	the	the	DET
ejpam-3752	19	6	concept	concept	NOUN
ejpam-3752	19	7	of	of	ADP
ejpam-3752	19	8	fuzzy	fuzzy	ADJ
ejpam-3752	19	9	up	up	NOUN
ejpam-3752	19	10	-	-	PUNCT
ejpam-3752	19	11	subalgebras	subalgebras	X
ejpam-3752	19	12	(	(	PUNCT
ejpam-3752	19	13	fuzzy	fuzzy	ADJ
ejpam-3752	19	14	up	up	ADP
ejpam-3752	19	15	-	-	PUNCT
ejpam-3752	19	16	filters	filter	NOUN
ejpam-3752	19	17	,	,	PUNCT
ejpam-3752	19	18	fuzzy	fuzzy	ADJ
ejpam-3752	19	19	up	up	NOUN
ejpam-3752	19	20	-	-	PUNCT
ejpam-3752	19	21	ideals	ideal	NOUN
ejpam-3752	19	22	,	,	PUNCT
ejpam-3752	19	23	fuzzy	fuzzy	ADJ
ejpam-3752	19	24	strong	strong	ADJ
ejpam-3752	19	25	up	up	ADJ
ejpam-3752	19	26	-	-	PUNCT
ejpam-3752	19	27	ideals	ideal	NOUN
ejpam-3752	19	28	)	)	PUNCT
ejpam-3752	19	29	with	with	ADP
ejpam-3752	19	30	thresholds	threshold	NOUN
ejpam-3752	19	31	of	of	ADP
ejpam-3752	19	32	up	up	ADP
ejpam-3752	19	33	-	-	PUNCT
ejpam-3752	19	34	algebras	algebras	X
ejpam-3752	19	35	.	.	PUNCT
ejpam-3752	20	1	ansari	ansari	PROPN
ejpam-3752	20	2	et	et	PROPN
ejpam-3752	20	3	al	al	PROPN
ejpam-3752	20	4	.	.	PUNCT
ejpam-3752	21	1	[	[	X
ejpam-3752	21	2	3	3	X
ejpam-3752	21	3	]	]	PUNCT
ejpam-3752	21	4	introduced	introduce	VERB
ejpam-3752	21	5	the	the	DET
ejpam-3752	21	6	concept	concept	NOUN
ejpam-3752	21	7	of	of	ADP
ejpam-3752	21	8	graphs	graph	NOUN
ejpam-3752	21	9	associated	associate	VERB
ejpam-3752	21	10	with	with	ADP
ejpam-3752	21	11	commutative	commutative	ADJ
ejpam-3752	21	12	up	up	ADP
ejpam-3752	21	13	-	-	PUNCT
ejpam-3752	21	14	algebras	algebra	NOUN
ejpam-3752	21	15	and	and	CCONJ
ejpam-3752	21	16	defined	define	VERB
ejpam-3752	21	17	a	a	DET
ejpam-3752	21	18	graph	graph	NOUN
ejpam-3752	21	19	of	of	ADP
ejpam-3752	21	20	equivalence	equivalence	NOUN
ejpam-3752	21	21	classes	class	NOUN
ejpam-3752	21	22	of	of	ADP
ejpam-3752	21	23	commutative	commutative	ADJ
ejpam-3752	21	24	up	up	ADP
ejpam-3752	21	25	-	-	PUNCT
ejpam-3752	21	26	algebras	algebras	X
ejpam-3752	21	27	.	.	PUNCT
ejpam-3752	22	1	songsaeng	songsaeng	PROPN
ejpam-3752	22	2	and	and	CCONJ
ejpam-3752	22	3	iampan	iampan	PROPN
ejpam-3752	23	1	[	[	X
ejpam-3752	23	2	31–33	31–33	NUM
ejpam-3752	23	3	]	]	PUNCT
ejpam-3752	23	4	studied	study	VERB
ejpam-3752	23	5	n	n	NUM
ejpam-3752	23	6	-fuzzy	-fuzzy	NOUN
ejpam-3752	23	7	sets	set	NOUN
ejpam-3752	23	8	,	,	PUNCT
ejpam-3752	23	9	fuzzy	fuzzy	ADJ
ejpam-3752	23	10	proper	proper	ADJ
ejpam-3752	23	11	up	up	NOUN
ejpam-3752	23	12	-	-	PUNCT
ejpam-3752	23	13	filters	filter	NOUN
ejpam-3752	23	14	,	,	PUNCT
ejpam-3752	23	15	and	and	CCONJ
ejpam-3752	23	16	neutrosophic	neutrosophic	ADJ
ejpam-3752	23	17	sets	set	NOUN
ejpam-3752	23	18	in	in	ADP
ejpam-3752	23	19	up	up	ADP
ejpam-3752	23	20	-	-	PUNCT
ejpam-3752	23	21	algebras	algebras	X
ejpam-3752	23	22	.	.	PUNCT
ejpam-3752	24	1	senapati	senapati	PROPN
ejpam-3752	24	2	et	et	PROPN
ejpam-3752	24	3	al	al	PROPN
ejpam-3752	24	4	.	.	PUNCT
ejpam-3752	25	1	[	[	X
ejpam-3752	25	2	26	26	NUM
ejpam-3752	25	3	,	,	PUNCT
ejpam-3752	25	4	27	27	NUM
ejpam-3752	25	5	]	]	PUNCT
ejpam-3752	25	6	studies	study	NOUN
ejpam-3752	25	7	applied	apply	VERB
ejpam-3752	25	8	cubic	cubic	ADJ
ejpam-3752	25	9	set	set	NOUN
ejpam-3752	25	10	and	and	CCONJ
ejpam-3752	25	11	interval	interval	NOUN
ejpam-3752	25	12	-	-	PUNCT
ejpam-3752	25	13	valued	value	VERB
ejpam-3752	25	14	intuitionistic	intuitionistic	ADJ
ejpam-3752	25	15	fuzzy	fuzzy	ADJ
ejpam-3752	25	16	structure	structure	NOUN
ejpam-3752	25	17	in	in	ADP
ejpam-3752	25	18	up	up	ADV
ejpam-3752	25	19	-	-	PUNCT
ejpam-3752	25	20	algebras	algebras	X
ejpam-3752	25	21	.	.	PUNCT
ejpam-3752	26	1	†this	†this	DET
ejpam-3752	26	2	work	work	NOUN
ejpam-3752	26	3	was	be	AUX
ejpam-3752	26	4	supported	support	VERB
ejpam-3752	26	5	by	by	ADP
ejpam-3752	26	6	the	the	DET
ejpam-3752	26	7	unit	unit	NOUN
ejpam-3752	26	8	of	of	ADP
ejpam-3752	26	9	excellence	excellence	PROPN
ejpam-3752	26	10	,	,	PUNCT
ejpam-3752	26	11	university	university	NOUN
ejpam-3752	26	12	of	of	ADP
ejpam-3752	26	13	phayao	phayao	NOUN
ejpam-3752	26	14	.	.	PUNCT
ejpam-3752	27	1	∗corresponding	∗corresponde	VERB
ejpam-3752	27	2	author	author	NOUN
ejpam-3752	27	3	.	.	PUNCT
ejpam-3752	28	1	doi	doi	NOUN
ejpam-3752	28	2	:	:	PUNCT
ejpam-3752	28	3	https://doi.org/10.29020/nybg.ejpam.v13i3.3752	https://doi.org/10.29020/nybg.ejpam.v13i3.3752	PROPN
ejpam-3752	28	4	email	email	NOUN
ejpam-3752	28	5	addresses	address	VERB
ejpam-3752	28	6	:	:	PUNCT
ejpam-3752	29	1	chishtygm@gmail.com	chishtygm@gmail.com	X
ejpam-3752	29	2	(	(	PUNCT
ejpam-3752	29	3	g.	g.	PROPN
ejpam-3752	29	4	muhiuddin	muhiuddin	PROPN
ejpam-3752	29	5	)	)	PUNCT
ejpam-3752	29	6	,	,	PUNCT
ejpam-3752	29	7	metawee.faith@gmail.com	metawee.faith@gmail.com	NOUN
ejpam-3752	29	8	(	(	PUNCT
ejpam-3752	29	9	m.	m.	NOUN
ejpam-3752	29	10	songsaeng	songsaeng	PROPN
ejpam-3752	29	11	)	)	PUNCT
ejpam-3752	29	12	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-3752	29	13	(	(	PUNCT
ejpam-3752	29	14	a.	a.	NOUN
ejpam-3752	29	15	iampan	iampan	PROPN
ejpam-3752	29	16	)	)	PUNCT
ejpam-3752	29	17	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-3752	30	1	459	459	NUM
ejpam-3752	31	1	c	c	X
ejpam-3752	31	2	©	©	NOUN
ejpam-3752	31	3	2020	2020	NUM
ejpam-3752	31	4	ejpam	ejpam	VERB
ejpam-3752	31	5	all	all	DET
ejpam-3752	31	6	rights	right	NOUN
ejpam-3752	31	7	reserved	reserve	VERB
ejpam-3752	31	8	.	.	PUNCT
ejpam-3752	32	1	a.	a.	PROPN
ejpam-3752	32	2	iampan	iampan	PROPN
ejpam-3752	32	3	,	,	PUNCT
ejpam-3752	32	4	m.	m.	PROPN
ejpam-3752	32	5	songsaeng	songsaeng	PROPN
ejpam-3752	32	6	,	,	PUNCT
ejpam-3752	32	7	g.	g.	PROPN
ejpam-3752	32	8	muhiuddin	muhiuddin	PROPN
ejpam-3752	32	9	/	/	SYM
ejpam-3752	32	10	eur	eur	PROPN
ejpam-3752	32	11	.	.	PUNCT
ejpam-3752	33	1	j.	j.	PROPN
ejpam-3752	33	2	pure	pure	PROPN
ejpam-3752	33	3	appl	appl	PROPN
ejpam-3752	33	4	.	.	PROPN
ejpam-3752	33	5	math	math	PROPN
ejpam-3752	33	6	,	,	PUNCT
ejpam-3752	33	7	13	13	NUM
ejpam-3752	33	8	(	(	PUNCT
ejpam-3752	33	9	3	3	NUM
ejpam-3752	33	10	)	)	PUNCT
ejpam-3752	33	11	(	(	PUNCT
ejpam-3752	33	12	2020	2020	NUM
ejpam-3752	33	13	)	)	PUNCT
ejpam-3752	33	14	,	,	PUNCT
ejpam-3752	33	15	459	459	NUM
ejpam-3752	33	16	-	-	SYM
ejpam-3752	33	17	471	471	NUM
ejpam-3752	33	18	460	460	NUM
ejpam-3752	33	19	more	more	ADJ
ejpam-3752	33	20	concepts	concept	NOUN
ejpam-3752	33	21	on	on	ADP
ejpam-3752	33	22	up	up	ADV
ejpam-3752	33	23	-	-	PUNCT
ejpam-3752	33	24	algebras	algebra	NOUN
ejpam-3752	33	25	are	be	AUX
ejpam-3752	33	26	discussed	discuss	VERB
ejpam-3752	33	27	in	in	ADP
ejpam-3752	33	28	[	[	X
ejpam-3752	33	29	4	4	NUM
ejpam-3752	33	30	,	,	PUNCT
ejpam-3752	33	31	5	5	NUM
ejpam-3752	33	32	,	,	PUNCT
ejpam-3752	33	33	17	17	NUM
ejpam-3752	33	34	]	]	PUNCT
ejpam-3752	33	35	.	.	PUNCT
ejpam-3752	34	1	a	a	DET
ejpam-3752	34	2	fuzzy	fuzzy	ADJ
ejpam-3752	34	3	set	set	NOUN
ejpam-3752	34	4	f	f	PROPN
ejpam-3752	34	5	in	in	ADP
ejpam-3752	34	6	a	a	DET
ejpam-3752	34	7	nonempty	nonempty	ADJ
ejpam-3752	34	8	set	set	NOUN
ejpam-3752	34	9	s	s	PART
ejpam-3752	34	10	is	be	AUX
ejpam-3752	34	11	a	a	DET
ejpam-3752	34	12	function	function	NOUN
ejpam-3752	34	13	from	from	ADP
ejpam-3752	34	14	s	s	PRON
ejpam-3752	34	15	to	to	ADP
ejpam-3752	34	16	the	the	DET
ejpam-3752	34	17	closed	closed	ADJ
ejpam-3752	34	18	interval	interval	NOUN
ejpam-3752	34	19	[	[	X
ejpam-3752	34	20	0	0	NUM
ejpam-3752	34	21	,	,	PUNCT
ejpam-3752	34	22	1	1	NUM
ejpam-3752	34	23	]	]	PUNCT
ejpam-3752	34	24	.	.	PUNCT
ejpam-3752	35	1	the	the	DET
ejpam-3752	35	2	concept	concept	NOUN
ejpam-3752	35	3	of	of	ADP
ejpam-3752	35	4	a	a	DET
ejpam-3752	35	5	fuzzy	fuzzy	ADJ
ejpam-3752	35	6	set	set	NOUN
ejpam-3752	35	7	in	in	ADP
ejpam-3752	35	8	a	a	DET
ejpam-3752	35	9	nonempty	nonempty	ADJ
ejpam-3752	35	10	set	set	NOUN
ejpam-3752	35	11	was	be	AUX
ejpam-3752	35	12	first	first	ADV
ejpam-3752	35	13	considered	consider	VERB
ejpam-3752	35	14	by	by	ADP
ejpam-3752	35	15	zadeh	zadeh	PROPN
ejpam-3752	36	1	[	[	X
ejpam-3752	36	2	36	36	NUM
ejpam-3752	36	3	]	]	PUNCT
ejpam-3752	36	4	in	in	ADP
ejpam-3752	36	5	1965	1965	NUM
ejpam-3752	36	6	.	.	PUNCT
ejpam-3752	37	1	the	the	DET
ejpam-3752	37	2	fuzzy	fuzzy	ADJ
ejpam-3752	37	3	set	set	NOUN
ejpam-3752	37	4	theories	theory	NOUN
ejpam-3752	37	5	developed	develop	VERB
ejpam-3752	37	6	by	by	ADP
ejpam-3752	37	7	zadeh	zadeh	NOUN
ejpam-3752	37	8	and	and	CCONJ
ejpam-3752	37	9	others	other	NOUN
ejpam-3752	37	10	have	have	AUX
ejpam-3752	37	11	found	find	VERB
ejpam-3752	37	12	many	many	ADJ
ejpam-3752	37	13	applications	application	NOUN
ejpam-3752	37	14	in	in	ADP
ejpam-3752	37	15	the	the	DET
ejpam-3752	37	16	domain	domain	NOUN
ejpam-3752	37	17	of	of	ADP
ejpam-3752	37	18	mathematics	mathematic	NOUN
ejpam-3752	37	19	and	and	CCONJ
ejpam-3752	37	20	elsewhere	elsewhere	ADV
ejpam-3752	37	21	.	.	PUNCT
ejpam-3752	38	1	the	the	DET
ejpam-3752	38	2	concept	concept	NOUN
ejpam-3752	38	3	of	of	ADP
ejpam-3752	38	4	a	a	DET
ejpam-3752	38	5	neutrosophic	neutrosophic	ADJ
ejpam-3752	38	6	set	set	NOUN
ejpam-3752	38	7	was	be	AUX
ejpam-3752	38	8	introduced	introduce	VERB
ejpam-3752	38	9	by	by	ADP
ejpam-3752	38	10	smarandache	smarandache	NOUN
ejpam-3752	39	1	[	[	X
ejpam-3752	39	2	28	28	NUM
ejpam-3752	39	3	]	]	PUNCT
ejpam-3752	39	4	in	in	ADP
ejpam-3752	39	5	1999	1999	NUM
ejpam-3752	39	6	.	.	PUNCT
ejpam-3752	40	1	neutrosophic	neutrosophic	ADJ
ejpam-3752	40	2	algebraic	algebraic	ADJ
ejpam-3752	40	3	structures	structure	NOUN
ejpam-3752	40	4	in	in	ADP
ejpam-3752	40	5	bck	bck	PROPN
ejpam-3752	40	6	/	/	SYM
ejpam-3752	40	7	bci	bci	NOUN
ejpam-3752	40	8	-	-	PUNCT
ejpam-3752	40	9	algebras	algebra	NOUN
ejpam-3752	40	10	are	be	AUX
ejpam-3752	40	11	discussed	discuss	VERB
ejpam-3752	40	12	in	in	ADP
ejpam-3752	40	13	[	[	X
ejpam-3752	40	14	11	11	NUM
ejpam-3752	40	15	,	,	PUNCT
ejpam-3752	40	16	12	12	NUM
ejpam-3752	40	17	,	,	PUNCT
ejpam-3752	40	18	19	19	NUM
ejpam-3752	40	19	,	,	PUNCT
ejpam-3752	40	20	21	21	NUM
ejpam-3752	40	21	,	,	PUNCT
ejpam-3752	40	22	30	30	NUM
ejpam-3752	40	23	]	]	PUNCT
ejpam-3752	40	24	.	.	PUNCT
ejpam-3752	41	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	41	2	quadruple	quadruple	PROPN
ejpam-3752	41	3	algebraic	algebraic	PROPN
ejpam-3752	41	4	structures	structure	NOUN
ejpam-3752	41	5	and	and	CCONJ
ejpam-3752	41	6	hyperstructure	hyperstructure	NOUN
ejpam-3752	41	7	are	be	AUX
ejpam-3752	41	8	discussed	discuss	VERB
ejpam-3752	41	9	in	in	ADP
ejpam-3752	41	10	[	[	X
ejpam-3752	41	11	1	1	NUM
ejpam-3752	41	12	,	,	PUNCT
ejpam-3752	41	13	2	2	NUM
ejpam-3752	41	14	]	]	PUNCT
ejpam-3752	41	15	.	.	PUNCT
ejpam-3752	42	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	42	2	quadruple	quadruple	PROPN
ejpam-3752	42	3	algebraic	algebraic	PROPN
ejpam-3752	42	4	structures	structure	NOUN
ejpam-3752	42	5	in	in	ADP
ejpam-3752	42	6	bck	bck	PROPN
ejpam-3752	42	7	/	/	SYM
ejpam-3752	42	8	bci	bci	NOUN
ejpam-3752	42	9	-	-	PUNCT
ejpam-3752	42	10	algebras	algebra	NOUN
ejpam-3752	42	11	are	be	AUX
ejpam-3752	42	12	discussed	discuss	VERB
ejpam-3752	42	13	in	in	ADP
ejpam-3752	42	14	[	[	X
ejpam-3752	42	15	13	13	NUM
ejpam-3752	42	16	,	,	PUNCT
ejpam-3752	42	17	14	14	NUM
ejpam-3752	42	18	,	,	PUNCT
ejpam-3752	42	19	18	18	NUM
ejpam-3752	42	20	,	,	PUNCT
ejpam-3752	42	21	20	20	NUM
ejpam-3752	42	22	,	,	PUNCT
ejpam-3752	42	23	22	22	NUM
ejpam-3752	42	24	]	]	PUNCT
ejpam-3752	42	25	.	.	PUNCT
ejpam-3752	43	1	in	in	ADP
ejpam-3752	43	2	this	this	DET
ejpam-3752	43	3	paper	paper	NOUN
ejpam-3752	43	4	,	,	PUNCT
ejpam-3752	43	5	we	we	PRON
ejpam-3752	43	6	apply	apply	VERB
ejpam-3752	43	7	the	the	DET
ejpam-3752	43	8	concept	concept	NOUN
ejpam-3752	43	9	of	of	ADP
ejpam-3752	43	10	a	a	DET
ejpam-3752	43	11	neutrosophic	neutrosophic	ADJ
ejpam-3752	43	12	quadruple	quadruple	NOUN
ejpam-3752	43	13	number	number	NOUN
ejpam-3752	43	14	to	to	ADP
ejpam-3752	43	15	a	a	DET
ejpam-3752	43	16	fuzzy	fuzzy	ADJ
ejpam-3752	43	17	duplex	duplex	NOUN
ejpam-3752	43	18	number	number	NOUN
ejpam-3752	43	19	,	,	PUNCT
ejpam-3752	43	20	introduce	introduce	VERB
ejpam-3752	43	21	the	the	DET
ejpam-3752	43	22	concept	concept	NOUN
ejpam-3752	43	23	of	of	ADP
ejpam-3752	43	24	a	a	DET
ejpam-3752	43	25	fuzzy	fuzzy	ADJ
ejpam-3752	43	26	duplex	duplex	NOUN
ejpam-3752	43	27	set	set	VERB
ejpam-3752	43	28	base	base	NOUN
ejpam-3752	43	29	on	on	ADP
ejpam-3752	43	30	a	a	DET
ejpam-3752	43	31	up	up	NOUN
ejpam-3752	43	32	-	-	PUNCT
ejpam-3752	43	33	algebra	algebra	NOUN
ejpam-3752	43	34	,	,	PUNCT
ejpam-3752	43	35	which	which	PRON
ejpam-3752	43	36	is	be	AUX
ejpam-3752	43	37	called	call	VERB
ejpam-3752	43	38	a	a	DET
ejpam-3752	43	39	fuzzy	fuzzy	ADJ
ejpam-3752	43	40	duplex	duplex	NOUN
ejpam-3752	43	41	up	up	ADV
ejpam-3752	43	42	-	-	PUNCT
ejpam-3752	43	43	set	set	NOUN
ejpam-3752	43	44	,	,	PUNCT
ejpam-3752	43	45	and	and	CCONJ
ejpam-3752	43	46	investigate	investigate	VERB
ejpam-3752	43	47	some	some	DET
ejpam-3752	43	48	related	related	ADJ
ejpam-3752	43	49	properties	property	NOUN
ejpam-3752	43	50	.	.	PUNCT
ejpam-3752	44	1	we	we	PRON
ejpam-3752	44	2	find	find	VERB
ejpam-3752	44	3	the	the	DET
ejpam-3752	44	4	necessary	necessary	ADJ
ejpam-3752	44	5	conditions	condition	NOUN
ejpam-3752	44	6	that	that	SCONJ
ejpam-3752	44	7	a	a	DET
ejpam-3752	44	8	fuzzy	fuzzy	ADJ
ejpam-3752	44	9	duplex	duplex	NOUN
ejpam-3752	44	10	up	up	ADV
ejpam-3752	44	11	-	-	PUNCT
ejpam-3752	44	12	set	set	VERB
ejpam-3752	44	13	form	form	NOUN
ejpam-3752	44	14	a	a	DET
ejpam-3752	44	15	up	up	NOUN
ejpam-3752	44	16	-	-	PUNCT
ejpam-3752	44	17	algebra	algebra	NOUN
ejpam-3752	44	18	,	,	PUNCT
ejpam-3752	44	19	which	which	PRON
ejpam-3752	44	20	is	be	AUX
ejpam-3752	44	21	called	call	VERB
ejpam-3752	44	22	a	a	DET
ejpam-3752	44	23	fuzzy	fuzzy	ADJ
ejpam-3752	44	24	duplex	duplex	NOUN
ejpam-3752	44	25	up	up	ADP
ejpam-3752	44	26	-	-	PUNCT
ejpam-3752	44	27	algebra	algebra	NOUN
ejpam-3752	44	28	.	.	PUNCT
ejpam-3752	45	1	furthermore	furthermore	ADV
ejpam-3752	45	2	,	,	PUNCT
ejpam-3752	45	3	we	we	PRON
ejpam-3752	45	4	study	study	VERB
ejpam-3752	45	5	the	the	DET
ejpam-3752	45	6	relationship	relationship	NOUN
ejpam-3752	45	7	between	between	ADP
ejpam-3752	45	8	special	special	ADJ
ejpam-3752	45	9	subsets	subset	NOUN
ejpam-3752	45	10	of	of	ADP
ejpam-3752	45	11	a	a	DET
ejpam-3752	45	12	up	up	NOUN
ejpam-3752	45	13	-	-	PUNCT
ejpam-3752	45	14	algebra	algebra	NOUN
ejpam-3752	45	15	and	and	CCONJ
ejpam-3752	45	16	the	the	DET
ejpam-3752	45	17	same	same	ADJ
ejpam-3752	45	18	special	special	ADJ
ejpam-3752	45	19	subsets	subset	NOUN
ejpam-3752	45	20	of	of	ADP
ejpam-3752	45	21	a	a	DET
ejpam-3752	45	22	fuzzy	fuzzy	ADJ
ejpam-3752	45	23	duplex	duplex	NOUN
ejpam-3752	45	24	up	up	ADV
ejpam-3752	45	25	-	-	PUNCT
ejpam-3752	45	26	set	set	NOUN
ejpam-3752	45	27	.	.	PUNCT
ejpam-3752	46	1	2	2	X
ejpam-3752	46	2	.	.	NUM
ejpam-3752	46	3	basic	basic	ADJ
ejpam-3752	46	4	concepts	concept	NOUN
ejpam-3752	46	5	and	and	CCONJ
ejpam-3752	46	6	preliminary	preliminary	ADJ
ejpam-3752	46	7	notes	note	NOUN
ejpam-3752	46	8	on	on	ADP
ejpam-3752	46	9	up	up	ADV
ejpam-3752	46	10	-	-	PUNCT
ejpam-3752	46	11	algebras	algebra	NOUN
ejpam-3752	46	12	before	before	SCONJ
ejpam-3752	46	13	we	we	PRON
ejpam-3752	46	14	begin	begin	VERB
ejpam-3752	46	15	our	our	PRON
ejpam-3752	46	16	study	study	NOUN
ejpam-3752	46	17	,	,	PUNCT
ejpam-3752	46	18	we	we	PRON
ejpam-3752	46	19	will	will	AUX
ejpam-3752	46	20	give	give	VERB
ejpam-3752	46	21	the	the	DET
ejpam-3752	46	22	definition	definition	NOUN
ejpam-3752	46	23	and	and	CCONJ
ejpam-3752	46	24	useful	useful	ADJ
ejpam-3752	46	25	properties	property	NOUN
ejpam-3752	46	26	of	of	ADP
ejpam-3752	46	27	upalgebras	upalgebra	NOUN
ejpam-3752	46	28	.	.	PUNCT
ejpam-3752	47	1	definition	definition	NOUN
ejpam-3752	47	2	1	1	NUM
ejpam-3752	47	3	.	.	PUNCT
ejpam-3752	48	1	[	[	X
ejpam-3752	48	2	9	9	NUM
ejpam-3752	48	3	]	]	PUNCT
ejpam-3752	48	4	an	an	DET
ejpam-3752	48	5	algebra	algebra	NOUN
ejpam-3752	48	6	x	x	X
ejpam-3752	48	7	=	=	SYM
ejpam-3752	48	8	(	(	PUNCT
ejpam-3752	48	9	x	x	NOUN
ejpam-3752	48	10	,	,	PUNCT
ejpam-3752	48	11	·	·	PUNCT
ejpam-3752	48	12	,	,	PUNCT
ejpam-3752	48	13	0	0	NUM
ejpam-3752	48	14	)	)	PUNCT
ejpam-3752	48	15	of	of	ADP
ejpam-3752	48	16	type	type	NOUN
ejpam-3752	48	17	(	(	PUNCT
ejpam-3752	48	18	2	2	NUM
ejpam-3752	48	19	,	,	PUNCT
ejpam-3752	48	20	0	0	NUM
ejpam-3752	48	21	)	)	PUNCT
ejpam-3752	48	22	is	be	AUX
ejpam-3752	48	23	called	call	VERB
ejpam-3752	48	24	a	a	DET
ejpam-3752	48	25	up	up	NOUN
ejpam-3752	48	26	-	-	PUNCT
ejpam-3752	48	27	algebra	algebra	NOUN
ejpam-3752	48	28	,	,	PUNCT
ejpam-3752	48	29	where	where	SCONJ
ejpam-3752	48	30	x	x	PRON
ejpam-3752	48	31	is	be	AUX
ejpam-3752	48	32	a	a	DET
ejpam-3752	48	33	nonempty	nonempty	ADJ
ejpam-3752	48	34	set	set	VERB
ejpam-3752	48	35	,	,	PUNCT
ejpam-3752	48	36	·	·	PUNCT
ejpam-3752	48	37	is	be	AUX
ejpam-3752	48	38	a	a	DET
ejpam-3752	48	39	binary	binary	ADJ
ejpam-3752	48	40	operation	operation	NOUN
ejpam-3752	48	41	on	on	ADP
ejpam-3752	48	42	x	x	NOUN
ejpam-3752	48	43	,	,	PUNCT
ejpam-3752	48	44	and	and	CCONJ
ejpam-3752	48	45	0	0	NUM
ejpam-3752	48	46	is	be	AUX
ejpam-3752	48	47	a	a	DET
ejpam-3752	48	48	fixed	fix	VERB
ejpam-3752	48	49	element	element	NOUN
ejpam-3752	48	50	of	of	ADP
ejpam-3752	48	51	x	x	X
ejpam-3752	48	52	(	(	PUNCT
ejpam-3752	48	53	i.e.	i.e.	X
ejpam-3752	48	54	,	,	PUNCT
ejpam-3752	48	55	a	a	DET
ejpam-3752	48	56	nullary	nullary	ADJ
ejpam-3752	48	57	operation	operation	NOUN
ejpam-3752	48	58	)	)	PUNCT
ejpam-3752	48	59	if	if	SCONJ
ejpam-3752	48	60	it	it	PRON
ejpam-3752	48	61	satisfies	satisfy	VERB
ejpam-3752	48	62	the	the	DET
ejpam-3752	48	63	following	follow	VERB
ejpam-3752	48	64	axioms	axiom	NOUN
ejpam-3752	48	65	:	:	PUNCT
ejpam-3752	48	66	(	(	PUNCT
ejpam-3752	48	67	up-1	up-1	NOUN
ejpam-3752	48	68	)	)	PUNCT
ejpam-3752	48	69	(	(	PUNCT
ejpam-3752	48	70	∀x	∀x	X
ejpam-3752	48	71	,	,	PUNCT
ejpam-3752	48	72	y	y	PROPN
ejpam-3752	48	73	,	,	PUNCT
ejpam-3752	48	74	z	z	PROPN
ejpam-3752	48	75	∈	∈	PROPN
ejpam-3752	48	76	x)((y	x)((y	PROPN
ejpam-3752	48	77	·	·	PUNCT
ejpam-3752	49	1	z	z	X
ejpam-3752	49	2	)	)	PUNCT
ejpam-3752	49	3	·	·	PUNCT
ejpam-3752	49	4	(	(	PUNCT
ejpam-3752	49	5	(	(	PUNCT
ejpam-3752	49	6	x	x	SYM
ejpam-3752	49	7	·	·	PUNCT
ejpam-3752	49	8	y	y	X
ejpam-3752	49	9	)	)	PUNCT
ejpam-3752	49	10	·	·	PUNCT
ejpam-3752	50	1	(	(	PUNCT
ejpam-3752	50	2	x	x	X
ejpam-3752	50	3	·	·	PUNCT
ejpam-3752	50	4	z	z	NOUN
ejpam-3752	50	5	)	)	PUNCT
ejpam-3752	50	6	)	)	PUNCT
ejpam-3752	51	1	=	=	PUNCT
ejpam-3752	51	2	0	0	NUM
ejpam-3752	51	3	)	)	PUNCT
ejpam-3752	51	4	,	,	PUNCT
ejpam-3752	51	5	(	(	PUNCT
ejpam-3752	51	6	up-2	up-2	NUM
ejpam-3752	51	7	)	)	PUNCT
ejpam-3752	51	8	(	(	PUNCT
ejpam-3752	51	9	∀x	∀x	X
ejpam-3752	51	10	∈	∈	NOUN
ejpam-3752	51	11	x)(0	x)(0	X
ejpam-3752	51	12	·	·	PUNCT
ejpam-3752	52	1	x	x	PUNCT
ejpam-3752	52	2	=	=	PUNCT
ejpam-3752	52	3	x	x	NOUN
ejpam-3752	52	4	)	)	PUNCT
ejpam-3752	52	5	,	,	PUNCT
ejpam-3752	52	6	(	(	PUNCT
ejpam-3752	52	7	up-3	up-3	NOUN
ejpam-3752	52	8	)	)	PUNCT
ejpam-3752	52	9	(	(	PUNCT
ejpam-3752	52	10	∀x	∀x	X
ejpam-3752	52	11	∈	∈	PROPN
ejpam-3752	52	12	x)(x	x)(x	PROPN
ejpam-3752	52	13	·	·	PUNCT
ejpam-3752	52	14	0	0	PUNCT
ejpam-3752	53	1	=	=	SYM
ejpam-3752	53	2	0	0	NUM
ejpam-3752	53	3	)	)	PUNCT
ejpam-3752	53	4	,	,	PUNCT
ejpam-3752	53	5	and	and	CCONJ
ejpam-3752	53	6	(	(	PUNCT
ejpam-3752	53	7	up-4	up-4	ADV
ejpam-3752	53	8	)	)	PUNCT
ejpam-3752	53	9	(	(	PUNCT
ejpam-3752	53	10	∀x	∀x	X
ejpam-3752	53	11	,	,	PUNCT
ejpam-3752	53	12	y	y	PROPN
ejpam-3752	53	13	∈	∈	PROPN
ejpam-3752	53	14	x)(x	x)(x	PROPN
ejpam-3752	53	15	·	·	PUNCT
ejpam-3752	53	16	y	y	X
ejpam-3752	53	17	=	=	SYM
ejpam-3752	53	18	0	0	PROPN
ejpam-3752	53	19	,	,	PUNCT
ejpam-3752	53	20	y	y	PROPN
ejpam-3752	53	21	·	·	PUNCT
ejpam-3752	53	22	x	x	PUNCT
ejpam-3752	54	1	=	=	PUNCT
ejpam-3752	54	2	0⇒	0⇒	NUM
ejpam-3752	54	3	x	x	X
ejpam-3752	55	1	=	=	SYM
ejpam-3752	55	2	y	y	PROPN
ejpam-3752	55	3	)	)	PUNCT
ejpam-3752	55	4	.	.	PUNCT
ejpam-3752	56	1	from	from	ADP
ejpam-3752	56	2	[	[	X
ejpam-3752	56	3	9	9	NUM
ejpam-3752	56	4	]	]	PUNCT
ejpam-3752	56	5	,	,	PUNCT
ejpam-3752	56	6	we	we	PRON
ejpam-3752	56	7	know	know	VERB
ejpam-3752	56	8	that	that	SCONJ
ejpam-3752	56	9	the	the	DET
ejpam-3752	56	10	concept	concept	NOUN
ejpam-3752	56	11	of	of	ADP
ejpam-3752	56	12	up	up	ADV
ejpam-3752	56	13	-	-	PUNCT
ejpam-3752	56	14	algebras	algebras	PROPN
ejpam-3752	56	15	is	be	AUX
ejpam-3752	56	16	a	a	DET
ejpam-3752	56	17	generalization	generalization	NOUN
ejpam-3752	56	18	of	of	ADP
ejpam-3752	56	19	ku	ku	PROPN
ejpam-3752	56	20	-	-	PUNCT
ejpam-3752	56	21	algebras	algebras	PROPN
ejpam-3752	56	22	(	(	PUNCT
ejpam-3752	56	23	see	see	VERB
ejpam-3752	56	24	[	[	X
ejpam-3752	56	25	23	23	NUM
ejpam-3752	56	26	]	]	NUM
ejpam-3752	56	27	)	)	PUNCT
ejpam-3752	56	28	.	.	PUNCT
ejpam-3752	57	1	for	for	ADP
ejpam-3752	57	2	more	more	ADJ
ejpam-3752	57	3	examples	example	NOUN
ejpam-3752	57	4	of	of	ADP
ejpam-3752	57	5	up	up	ADP
ejpam-3752	57	6	-	-	PUNCT
ejpam-3752	57	7	algebras	algebras	X
ejpam-3752	57	8	,	,	PUNCT
ejpam-3752	57	9	see	see	VERB
ejpam-3752	57	10	[	[	X
ejpam-3752	57	11	6	6	NUM
ejpam-3752	57	12	,	,	PUNCT
ejpam-3752	57	13	10	10	NUM
ejpam-3752	57	14	,	,	PUNCT
ejpam-3752	57	15	24–27	24–27	NUM
ejpam-3752	57	16	]	]	PUNCT
ejpam-3752	57	17	.	.	PUNCT
ejpam-3752	58	1	in	in	ADP
ejpam-3752	58	2	a	a	DET
ejpam-3752	58	3	up	up	NOUN
ejpam-3752	58	4	-	-	PUNCT
ejpam-3752	58	5	algebra	algebra	NOUN
ejpam-3752	58	6	x	x	PUNCT
ejpam-3752	58	7	=	=	SYM
ejpam-3752	58	8	(	(	PUNCT
ejpam-3752	58	9	x	x	NOUN
ejpam-3752	58	10	,	,	PUNCT
ejpam-3752	58	11	·	·	PUNCT
ejpam-3752	58	12	,	,	PUNCT
ejpam-3752	58	13	0	0	NUM
ejpam-3752	58	14	)	)	PUNCT
ejpam-3752	58	15	,	,	PUNCT
ejpam-3752	58	16	the	the	DET
ejpam-3752	58	17	following	follow	VERB
ejpam-3752	58	18	assertions	assertion	NOUN
ejpam-3752	58	19	are	be	AUX
ejpam-3752	58	20	valid	valid	ADJ
ejpam-3752	58	21	(	(	PUNCT
ejpam-3752	58	22	see	see	VERB
ejpam-3752	58	23	[	[	X
ejpam-3752	58	24	9	9	NUM
ejpam-3752	58	25	,	,	PUNCT
ejpam-3752	58	26	10	10	NUM
ejpam-3752	58	27	]	]	NUM
ejpam-3752	58	28	)	)	PUNCT
ejpam-3752	58	29	.	.	PUNCT
ejpam-3752	59	1	(	(	PUNCT
ejpam-3752	59	2	∀x	∀x	X
ejpam-3752	59	3	∈	∈	PROPN
ejpam-3752	59	4	x)(x	x)(x	PROPN
ejpam-3752	59	5	·	·	PUNCT
ejpam-3752	59	6	x	x	PUNCT
ejpam-3752	59	7	=	=	PUNCT
ejpam-3752	59	8	0	0	NUM
ejpam-3752	59	9	)	)	PUNCT
ejpam-3752	59	10	,	,	PUNCT
ejpam-3752	59	11	(	(	PUNCT
ejpam-3752	59	12	1	1	X
ejpam-3752	59	13	)	)	PUNCT
ejpam-3752	59	14	(	(	PUNCT
ejpam-3752	59	15	∀x	∀x	X
ejpam-3752	59	16	,	,	PUNCT
ejpam-3752	59	17	y	y	PROPN
ejpam-3752	59	18	,	,	PUNCT
ejpam-3752	59	19	z	z	PROPN
ejpam-3752	59	20	∈	∈	PROPN
ejpam-3752	59	21	x)(x	x)(x	PROPN
ejpam-3752	59	22	·	·	PUNCT
ejpam-3752	59	23	y	y	X
ejpam-3752	59	24	=	=	SYM
ejpam-3752	59	25	0	0	PROPN
ejpam-3752	59	26	,	,	PUNCT
ejpam-3752	59	27	y	y	PROPN
ejpam-3752	59	28	·	·	PUNCT
ejpam-3752	59	29	z	z	X
ejpam-3752	59	30	=	=	SYM
ejpam-3752	59	31	0⇒	0⇒	NUM
ejpam-3752	59	32	x	x	SYM
ejpam-3752	59	33	·	·	PUNCT
ejpam-3752	59	34	z	z	X
ejpam-3752	60	1	=	=	SYM
ejpam-3752	60	2	0	0	NUM
ejpam-3752	60	3	)	)	PUNCT
ejpam-3752	61	1	,	,	PUNCT
ejpam-3752	61	2	(	(	PUNCT
ejpam-3752	61	3	2	2	X
ejpam-3752	61	4	)	)	PUNCT
ejpam-3752	61	5	(	(	PUNCT
ejpam-3752	61	6	∀x	∀x	X
ejpam-3752	61	7	,	,	PUNCT
ejpam-3752	61	8	y	y	PROPN
ejpam-3752	61	9	,	,	PUNCT
ejpam-3752	61	10	z	z	PROPN
ejpam-3752	61	11	∈	∈	PROPN
ejpam-3752	61	12	x)(x	x)(x	PROPN
ejpam-3752	61	13	·	·	PUNCT
ejpam-3752	61	14	y	y	X
ejpam-3752	61	15	=	=	PUNCT
ejpam-3752	61	16	0⇒	0⇒	PROPN
ejpam-3752	61	17	(	(	PUNCT
ejpam-3752	61	18	z	z	NOUN
ejpam-3752	61	19	·	·	PUNCT
ejpam-3752	61	20	x	x	X
ejpam-3752	61	21	)	)	PUNCT
ejpam-3752	61	22	·	·	PUNCT
ejpam-3752	61	23	(	(	PUNCT
ejpam-3752	61	24	z	z	X
ejpam-3752	61	25	·	·	PUNCT
ejpam-3752	61	26	y	y	X
ejpam-3752	61	27	)	)	PUNCT
ejpam-3752	62	1	=	=	NOUN
ejpam-3752	62	2	0	0	NUM
ejpam-3752	62	3	)	)	PUNCT
ejpam-3752	62	4	,	,	PUNCT
ejpam-3752	62	5	(	(	PUNCT
ejpam-3752	62	6	3	3	X
ejpam-3752	62	7	)	)	PUNCT
ejpam-3752	62	8	(	(	PUNCT
ejpam-3752	62	9	∀x	∀x	X
ejpam-3752	62	10	,	,	PUNCT
ejpam-3752	62	11	y	y	PROPN
ejpam-3752	62	12	,	,	PUNCT
ejpam-3752	62	13	z	z	PROPN
ejpam-3752	62	14	∈	∈	PROPN
ejpam-3752	62	15	x)(x	x)(x	PROPN
ejpam-3752	62	16	·	·	PUNCT
ejpam-3752	63	1	y	y	X
ejpam-3752	63	2	=	=	PUNCT
ejpam-3752	63	3	0⇒	0⇒	PROPN
ejpam-3752	63	4	(	(	PUNCT
ejpam-3752	63	5	y	y	PROPN
ejpam-3752	63	6	·	·	PUNCT
ejpam-3752	63	7	z	z	X
ejpam-3752	63	8	)	)	PUNCT
ejpam-3752	63	9	·	·	PUNCT
ejpam-3752	63	10	(	(	PUNCT
ejpam-3752	63	11	x	x	X
ejpam-3752	63	12	·	·	PUNCT
ejpam-3752	64	1	z	z	X
ejpam-3752	64	2	)	)	PUNCT
ejpam-3752	64	3	=	=	SYM
ejpam-3752	64	4	0	0	NUM
ejpam-3752	64	5	)	)	PUNCT
ejpam-3752	64	6	,	,	PUNCT
ejpam-3752	64	7	(	(	PUNCT
ejpam-3752	64	8	4	4	X
ejpam-3752	64	9	)	)	PUNCT
ejpam-3752	64	10	(	(	PUNCT
ejpam-3752	64	11	∀x	∀x	X
ejpam-3752	64	12	,	,	PUNCT
ejpam-3752	64	13	y	y	PROPN
ejpam-3752	64	14	∈	∈	PROPN
ejpam-3752	64	15	x)(x	x)(x	PROPN
ejpam-3752	64	16	·	·	PUNCT
ejpam-3752	64	17	(	(	PUNCT
ejpam-3752	64	18	y	y	PROPN
ejpam-3752	64	19	·	·	PUNCT
ejpam-3752	64	20	x	x	X
ejpam-3752	64	21	)	)	PUNCT
ejpam-3752	64	22	=	=	SYM
ejpam-3752	64	23	0	0	NUM
ejpam-3752	64	24	)	)	PUNCT
ejpam-3752	64	25	,	,	PUNCT
ejpam-3752	64	26	(	(	PUNCT
ejpam-3752	64	27	5	5	X
ejpam-3752	64	28	)	)	PUNCT
ejpam-3752	64	29	a.	a.	NOUN
ejpam-3752	64	30	iampan	iampan	PROPN
ejpam-3752	64	31	,	,	PUNCT
ejpam-3752	64	32	m.	m.	PROPN
ejpam-3752	64	33	songsaeng	songsaeng	PROPN
ejpam-3752	64	34	,	,	PUNCT
ejpam-3752	64	35	g.	g.	PROPN
ejpam-3752	64	36	muhiuddin	muhiuddin	PROPN
ejpam-3752	64	37	/	/	SYM
ejpam-3752	64	38	eur	eur	PROPN
ejpam-3752	64	39	.	.	PUNCT
ejpam-3752	65	1	j.	j.	PROPN
ejpam-3752	65	2	pure	pure	PROPN
ejpam-3752	65	3	appl	appl	PROPN
ejpam-3752	65	4	.	.	PROPN
ejpam-3752	65	5	math	math	PROPN
ejpam-3752	65	6	,	,	PUNCT
ejpam-3752	65	7	13	13	NUM
ejpam-3752	65	8	(	(	PUNCT
ejpam-3752	65	9	3	3	NUM
ejpam-3752	65	10	)	)	PUNCT
ejpam-3752	65	11	(	(	PUNCT
ejpam-3752	65	12	2020	2020	NUM
ejpam-3752	65	13	)	)	PUNCT
ejpam-3752	65	14	,	,	PUNCT
ejpam-3752	65	15	459	459	NUM
ejpam-3752	65	16	-	-	SYM
ejpam-3752	65	17	471	471	NUM
ejpam-3752	65	18	461	461	NUM
ejpam-3752	65	19	(	(	PUNCT
ejpam-3752	65	20	∀x	∀x	NUM
ejpam-3752	65	21	,	,	PUNCT
ejpam-3752	65	22	y	y	PROPN
ejpam-3752	65	23	∈	∈	PROPN
ejpam-3752	65	24	x)((y	x)((y	PROPN
ejpam-3752	65	25	·	·	PUNCT
ejpam-3752	66	1	x	x	X
ejpam-3752	66	2	)	)	PUNCT
ejpam-3752	66	3	·	·	PUNCT
ejpam-3752	66	4	x	x	PUNCT
ejpam-3752	67	1	=	=	PUNCT
ejpam-3752	67	2	0⇔	0⇔	NOUN
ejpam-3752	67	3	x	x	X
ejpam-3752	68	1	=	=	PUNCT
ejpam-3752	68	2	y	y	PROPN
ejpam-3752	68	3	·	·	PUNCT
ejpam-3752	68	4	x	x	X
ejpam-3752	68	5	)	)	PUNCT
ejpam-3752	68	6	,	,	PUNCT
ejpam-3752	68	7	(	(	PUNCT
ejpam-3752	68	8	6	6	NUM
ejpam-3752	68	9	)	)	PUNCT
ejpam-3752	68	10	(	(	PUNCT
ejpam-3752	68	11	∀x	∀x	X
ejpam-3752	68	12	,	,	PUNCT
ejpam-3752	68	13	y	y	PROPN
ejpam-3752	68	14	∈	∈	PROPN
ejpam-3752	68	15	x)(x	x)(x	PROPN
ejpam-3752	68	16	·	·	PUNCT
ejpam-3752	68	17	(	(	PUNCT
ejpam-3752	68	18	y	y	PROPN
ejpam-3752	68	19	·	·	PUNCT
ejpam-3752	68	20	y	y	X
ejpam-3752	68	21	)	)	PUNCT
ejpam-3752	68	22	=	=	SYM
ejpam-3752	68	23	0	0	NUM
ejpam-3752	68	24	)	)	PUNCT
ejpam-3752	68	25	,	,	PUNCT
ejpam-3752	68	26	(	(	PUNCT
ejpam-3752	68	27	7	7	X
ejpam-3752	68	28	)	)	PUNCT
ejpam-3752	68	29	(	(	PUNCT
ejpam-3752	68	30	∀a	∀a	X
ejpam-3752	68	31	,	,	PUNCT
ejpam-3752	68	32	x	x	X
ejpam-3752	68	33	,	,	PUNCT
ejpam-3752	68	34	y	y	PROPN
ejpam-3752	68	35	,	,	PUNCT
ejpam-3752	68	36	z	z	PROPN
ejpam-3752	68	37	∈	∈	PROPN
ejpam-3752	68	38	x)((x	x)((x	NOUN
ejpam-3752	68	39	·	·	PUNCT
ejpam-3752	68	40	(	(	PUNCT
ejpam-3752	68	41	y	y	PROPN
ejpam-3752	68	42	·	·	PUNCT
ejpam-3752	68	43	z	z	NOUN
ejpam-3752	68	44	)	)	PUNCT
ejpam-3752	68	45	)	)	PUNCT
ejpam-3752	68	46	·	·	PUNCT
ejpam-3752	69	1	(	(	PUNCT
ejpam-3752	69	2	x	x	X
ejpam-3752	69	3	·	·	PUNCT
ejpam-3752	69	4	(	(	PUNCT
ejpam-3752	69	5	(	(	PUNCT
ejpam-3752	69	6	a	a	DET
ejpam-3752	69	7	·	·	PUNCT
ejpam-3752	69	8	y	y	NOUN
ejpam-3752	69	9	)	)	PUNCT
ejpam-3752	69	10	·	·	PUNCT
ejpam-3752	69	11	(	(	PUNCT
ejpam-3752	69	12	a	a	DET
ejpam-3752	69	13	·	·	PUNCT
ejpam-3752	69	14	z	z	NOUN
ejpam-3752	69	15	)	)	PUNCT
ejpam-3752	69	16	)	)	PUNCT
ejpam-3752	69	17	)	)	PUNCT
ejpam-3752	70	1	=	=	PUNCT
ejpam-3752	70	2	0	0	NUM
ejpam-3752	70	3	)	)	PUNCT
ejpam-3752	70	4	,	,	PUNCT
ejpam-3752	70	5	(	(	PUNCT
ejpam-3752	70	6	8)	8)	NUM
ejpam-3752	70	7	(	(	PUNCT
ejpam-3752	70	8	∀a	∀a	NOUN
ejpam-3752	70	9	,	,	PUNCT
ejpam-3752	70	10	x	x	X
ejpam-3752	70	11	,	,	PUNCT
ejpam-3752	70	12	y	y	PROPN
ejpam-3752	70	13	,	,	PUNCT
ejpam-3752	70	14	z	z	PROPN
ejpam-3752	70	15	∈	∈	PROPN
ejpam-3752	70	16	x)((((a	x)((((a	PROPN
ejpam-3752	70	17	·	·	PUNCT
ejpam-3752	70	18	x	x	X
ejpam-3752	70	19	)	)	PUNCT
ejpam-3752	70	20	·	·	PUNCT
ejpam-3752	70	21	(	(	PUNCT
ejpam-3752	70	22	a	a	DET
ejpam-3752	70	23	·	·	PUNCT
ejpam-3752	70	24	y	y	NOUN
ejpam-3752	70	25	)	)	PUNCT
ejpam-3752	70	26	)	)	PUNCT
ejpam-3752	70	27	·	·	PUNCT
ejpam-3752	71	1	z	z	X
ejpam-3752	71	2	)	)	PUNCT
ejpam-3752	71	3	·	·	PUNCT
ejpam-3752	71	4	(	(	PUNCT
ejpam-3752	71	5	(	(	PUNCT
ejpam-3752	71	6	x	x	SYM
ejpam-3752	71	7	·	·	PUNCT
ejpam-3752	71	8	y	y	X
ejpam-3752	71	9	)	)	PUNCT
ejpam-3752	71	10	·	·	PUNCT
ejpam-3752	72	1	z	z	X
ejpam-3752	72	2	)	)	PUNCT
ejpam-3752	72	3	=	=	SYM
ejpam-3752	72	4	0	0	NUM
ejpam-3752	72	5	)	)	PUNCT
ejpam-3752	72	6	,	,	PUNCT
ejpam-3752	72	7	(	(	PUNCT
ejpam-3752	72	8	9	9	X
ejpam-3752	72	9	)	)	PUNCT
ejpam-3752	72	10	(	(	PUNCT
ejpam-3752	72	11	∀x	∀x	X
ejpam-3752	72	12	,	,	PUNCT
ejpam-3752	72	13	y	y	PROPN
ejpam-3752	72	14	,	,	PUNCT
ejpam-3752	72	15	z	z	PROPN
ejpam-3752	72	16	∈	∈	PROPN
ejpam-3752	72	17	x)(((x	x)(((x	SYM
ejpam-3752	72	18	·	·	PUNCT
ejpam-3752	72	19	y	y	X
ejpam-3752	72	20	)	)	PUNCT
ejpam-3752	72	21	·	·	PUNCT
ejpam-3752	73	1	z	z	X
ejpam-3752	73	2	)	)	PUNCT
ejpam-3752	73	3	·	·	PUNCT
ejpam-3752	73	4	(	(	PUNCT
ejpam-3752	73	5	y	y	PROPN
ejpam-3752	73	6	·	·	PUNCT
ejpam-3752	73	7	z	z	X
ejpam-3752	73	8	)	)	PUNCT
ejpam-3752	73	9	=	=	SYM
ejpam-3752	73	10	0	0	NUM
ejpam-3752	73	11	)	)	PUNCT
ejpam-3752	73	12	,	,	PUNCT
ejpam-3752	73	13	(	(	PUNCT
ejpam-3752	73	14	10	10	NUM
ejpam-3752	73	15	)	)	PUNCT
ejpam-3752	73	16	(	(	PUNCT
ejpam-3752	73	17	∀x	∀x	X
ejpam-3752	73	18	,	,	PUNCT
ejpam-3752	73	19	y	y	PROPN
ejpam-3752	73	20	,	,	PUNCT
ejpam-3752	73	21	z	z	PROPN
ejpam-3752	73	22	∈	∈	PROPN
ejpam-3752	73	23	x)(x	x)(x	PROPN
ejpam-3752	73	24	·	·	PUNCT
ejpam-3752	74	1	y	y	X
ejpam-3752	74	2	=	=	SYM
ejpam-3752	74	3	0⇒	0⇒	PROPN
ejpam-3752	74	4	x	x	SYM
ejpam-3752	74	5	·	·	PUNCT
ejpam-3752	74	6	(	(	PUNCT
ejpam-3752	74	7	z	z	NOUN
ejpam-3752	74	8	·	·	PUNCT
ejpam-3752	74	9	y	y	X
ejpam-3752	74	10	)	)	PUNCT
ejpam-3752	74	11	=	=	NOUN
ejpam-3752	75	1	0	0	NUM
ejpam-3752	75	2	)	)	PUNCT
ejpam-3752	76	1	,	,	PUNCT
ejpam-3752	76	2	(	(	PUNCT
ejpam-3752	76	3	11	11	NUM
ejpam-3752	76	4	)	)	PUNCT
ejpam-3752	76	5	(	(	PUNCT
ejpam-3752	76	6	∀x	∀x	X
ejpam-3752	76	7	,	,	PUNCT
ejpam-3752	76	8	y	y	PROPN
ejpam-3752	76	9	,	,	PUNCT
ejpam-3752	76	10	z	z	PROPN
ejpam-3752	76	11	∈	∈	PROPN
ejpam-3752	76	12	x)(((x	x)(((x	SYM
ejpam-3752	76	13	·	·	PUNCT
ejpam-3752	76	14	y	y	X
ejpam-3752	76	15	)	)	PUNCT
ejpam-3752	76	16	·	·	PUNCT
ejpam-3752	77	1	z	z	X
ejpam-3752	77	2	)	)	PUNCT
ejpam-3752	77	3	·	·	PUNCT
ejpam-3752	77	4	(	(	PUNCT
ejpam-3752	77	5	x	x	X
ejpam-3752	77	6	·	·	PUNCT
ejpam-3752	77	7	(	(	PUNCT
ejpam-3752	77	8	y	y	PROPN
ejpam-3752	77	9	·	·	PUNCT
ejpam-3752	77	10	z	z	NOUN
ejpam-3752	77	11	)	)	PUNCT
ejpam-3752	77	12	)	)	PUNCT
ejpam-3752	78	1	=	=	PUNCT
ejpam-3752	78	2	0	0	NUM
ejpam-3752	78	3	)	)	PUNCT
ejpam-3752	78	4	,	,	PUNCT
ejpam-3752	78	5	and	and	CCONJ
ejpam-3752	78	6	(	(	PUNCT
ejpam-3752	78	7	12	12	NUM
ejpam-3752	78	8	)	)	PUNCT
ejpam-3752	78	9	(	(	PUNCT
ejpam-3752	78	10	∀a	∀a	X
ejpam-3752	78	11	,	,	PUNCT
ejpam-3752	78	12	x	x	X
ejpam-3752	78	13	,	,	PUNCT
ejpam-3752	78	14	y	y	PROPN
ejpam-3752	78	15	,	,	PUNCT
ejpam-3752	78	16	z	z	PROPN
ejpam-3752	78	17	∈	∈	PROPN
ejpam-3752	78	18	x)(((x	x)(((x	SYM
ejpam-3752	78	19	·	·	PUNCT
ejpam-3752	78	20	y	y	X
ejpam-3752	78	21	)	)	PUNCT
ejpam-3752	78	22	·	·	PUNCT
ejpam-3752	79	1	z	z	X
ejpam-3752	79	2	)	)	PUNCT
ejpam-3752	79	3	·	·	PUNCT
ejpam-3752	79	4	(	(	PUNCT
ejpam-3752	79	5	y	y	PROPN
ejpam-3752	79	6	·	·	PUNCT
ejpam-3752	79	7	(	(	PUNCT
ejpam-3752	79	8	a	a	DET
ejpam-3752	79	9	·	·	PUNCT
ejpam-3752	79	10	z	z	NOUN
ejpam-3752	79	11	)	)	PUNCT
ejpam-3752	79	12	)	)	PUNCT
ejpam-3752	80	1	=	=	PUNCT
ejpam-3752	80	2	0	0	NUM
ejpam-3752	80	3	)	)	PUNCT
ejpam-3752	80	4	.	.	PUNCT
ejpam-3752	81	1	(	(	PUNCT
ejpam-3752	81	2	13	13	NUM
ejpam-3752	81	3	)	)	PUNCT
ejpam-3752	81	4	from	from	ADP
ejpam-3752	81	5	[	[	X
ejpam-3752	81	6	9	9	NUM
ejpam-3752	81	7	]	]	PUNCT
ejpam-3752	81	8	,	,	PUNCT
ejpam-3752	81	9	the	the	DET
ejpam-3752	81	10	binary	binary	PROPN
ejpam-3752	81	11	relation	relation	NOUN
ejpam-3752	81	12	≤	≤	PUNCT
ejpam-3752	81	13	on	on	ADP
ejpam-3752	81	14	a	a	DET
ejpam-3752	81	15	up	up	NOUN
ejpam-3752	81	16	-	-	PUNCT
ejpam-3752	81	17	algebra	algebra	NOUN
ejpam-3752	81	18	x	x	PUNCT
ejpam-3752	81	19	=	=	SYM
ejpam-3752	81	20	(	(	PUNCT
ejpam-3752	81	21	x	x	NOUN
ejpam-3752	81	22	,	,	PUNCT
ejpam-3752	81	23	·	·	PUNCT
ejpam-3752	81	24	,	,	PUNCT
ejpam-3752	81	25	0	0	NUM
ejpam-3752	81	26	)	)	PUNCT
ejpam-3752	81	27	defined	define	VERB
ejpam-3752	81	28	as	as	SCONJ
ejpam-3752	81	29	follows	follow	VERB
ejpam-3752	81	30	:	:	PUNCT
ejpam-3752	81	31	(	(	PUNCT
ejpam-3752	81	32	∀x	∀x	X
ejpam-3752	81	33	,	,	PUNCT
ejpam-3752	81	34	y	y	PROPN
ejpam-3752	81	35	∈	∈	PROPN
ejpam-3752	81	36	x)(x	x)(x	PROPN
ejpam-3752	81	37	≤	≤	PROPN
ejpam-3752	82	1	y	y	PROPN
ejpam-3752	82	2	⇔	⇔	PROPN
ejpam-3752	82	3	x	x	PROPN
ejpam-3752	82	4	·	·	PUNCT
ejpam-3752	82	5	y	y	SYM
ejpam-3752	82	6	=	=	NOUN
ejpam-3752	82	7	0	0	NUM
ejpam-3752	82	8	)	)	PUNCT
ejpam-3752	82	9	.	.	PUNCT
ejpam-3752	83	1	(	(	PUNCT
ejpam-3752	83	2	14	14	NUM
ejpam-3752	83	3	)	)	PUNCT
ejpam-3752	83	4	definition	definition	NOUN
ejpam-3752	83	5	2	2	NUM
ejpam-3752	83	6	.	.	PUNCT
ejpam-3752	84	1	[	[	X
ejpam-3752	84	2	7–9	7–9	NUM
ejpam-3752	84	3	,	,	PUNCT
ejpam-3752	84	4	29	29	NUM
ejpam-3752	84	5	]	]	PUNCT
ejpam-3752	84	6	a	a	DET
ejpam-3752	84	7	nonempty	nonempty	ADV
ejpam-3752	84	8	subset	subset	VERB
ejpam-3752	84	9	s	s	NOUN
ejpam-3752	84	10	of	of	ADP
ejpam-3752	84	11	a	a	DET
ejpam-3752	84	12	up	up	NOUN
ejpam-3752	84	13	-	-	PUNCT
ejpam-3752	84	14	algebra	algebra	NOUN
ejpam-3752	84	15	x	x	PUNCT
ejpam-3752	84	16	=	=	SYM
ejpam-3752	84	17	(	(	PUNCT
ejpam-3752	84	18	x	x	NOUN
ejpam-3752	84	19	,	,	PUNCT
ejpam-3752	84	20	·	·	PUNCT
ejpam-3752	84	21	,	,	PUNCT
ejpam-3752	84	22	0	0	NUM
ejpam-3752	84	23	)	)	PUNCT
ejpam-3752	84	24	is	be	AUX
ejpam-3752	84	25	called	call	VERB
ejpam-3752	84	26	(	(	PUNCT
ejpam-3752	84	27	1	1	NUM
ejpam-3752	84	28	)	)	PUNCT
ejpam-3752	84	29	a	a	DET
ejpam-3752	84	30	up	up	ADJ
ejpam-3752	84	31	-	-	PUNCT
ejpam-3752	84	32	subalgebra	subalgebra	NOUN
ejpam-3752	84	33	of	of	ADP
ejpam-3752	84	34	x	x	PRON
ejpam-3752	84	35	if	if	SCONJ
ejpam-3752	84	36	(	(	PUNCT
ejpam-3752	84	37	∀x	∀x	X
ejpam-3752	84	38	,	,	PUNCT
ejpam-3752	84	39	y	y	PROPN
ejpam-3752	84	40	∈	∈	PROPN
ejpam-3752	84	41	s)(x	s)(x	PROPN
ejpam-3752	84	42	·	·	PUNCT
ejpam-3752	85	1	y	y	PROPN
ejpam-3752	85	2	∈	∈	PROPN
ejpam-3752	85	3	s	s	PART
ejpam-3752	85	4	)	)	PUNCT
ejpam-3752	85	5	.	.	PUNCT
ejpam-3752	86	1	(	(	PUNCT
ejpam-3752	86	2	2	2	X
ejpam-3752	86	3	)	)	PUNCT
ejpam-3752	86	4	a	a	DET
ejpam-3752	86	5	near	near	ADJ
ejpam-3752	86	6	up	up	NOUN
ejpam-3752	86	7	-	-	PUNCT
ejpam-3752	86	8	filter	filter	NOUN
ejpam-3752	86	9	of	of	ADP
ejpam-3752	86	10	x	x	SYM
ejpam-3752	86	11	if	if	SCONJ
ejpam-3752	86	12	(	(	PUNCT
ejpam-3752	86	13	i	i	NOUN
ejpam-3752	86	14	)	)	PUNCT
ejpam-3752	86	15	the	the	DET
ejpam-3752	86	16	constant	constant	ADJ
ejpam-3752	86	17	0	0	NUM
ejpam-3752	86	18	of	of	ADP
ejpam-3752	86	19	x	x	PRON
ejpam-3752	86	20	is	be	AUX
ejpam-3752	86	21	in	in	ADP
ejpam-3752	86	22	s	s	PROPN
ejpam-3752	86	23	,	,	PUNCT
ejpam-3752	86	24	and	and	CCONJ
ejpam-3752	86	25	(	(	PUNCT
ejpam-3752	86	26	ii	ii	NOUN
ejpam-3752	86	27	)	)	PUNCT
ejpam-3752	86	28	(	(	PUNCT
ejpam-3752	86	29	∀x	∀x	X
ejpam-3752	86	30	,	,	PUNCT
ejpam-3752	86	31	y	y	PROPN
ejpam-3752	86	32	∈	∈	PROPN
ejpam-3752	86	33	x)(y	x)(y	PUNCT
ejpam-3752	87	1	∈	∈	PROPN
ejpam-3752	87	2	s	s	PART
ejpam-3752	87	3	⇒	⇒	NOUN
ejpam-3752	87	4	x	x	X
ejpam-3752	87	5	·	·	PUNCT
ejpam-3752	87	6	y	y	X
ejpam-3752	87	7	∈	∈	PROPN
ejpam-3752	87	8	s	s	PART
ejpam-3752	87	9	)	)	PUNCT
ejpam-3752	87	10	.	.	PUNCT
ejpam-3752	88	1	(	(	PUNCT
ejpam-3752	88	2	3	3	X
ejpam-3752	88	3	)	)	PUNCT
ejpam-3752	88	4	a	a	DET
ejpam-3752	88	5	up	up	ADJ
ejpam-3752	88	6	-	-	PUNCT
ejpam-3752	88	7	filter	filter	NOUN
ejpam-3752	88	8	of	of	ADP
ejpam-3752	88	9	x	x	SYM
ejpam-3752	88	10	if	if	SCONJ
ejpam-3752	88	11	(	(	PUNCT
ejpam-3752	88	12	i	i	NOUN
ejpam-3752	88	13	)	)	PUNCT
ejpam-3752	88	14	the	the	DET
ejpam-3752	88	15	constant	constant	ADJ
ejpam-3752	88	16	0	0	NUM
ejpam-3752	88	17	of	of	ADP
ejpam-3752	88	18	x	x	PRON
ejpam-3752	88	19	is	be	AUX
ejpam-3752	88	20	in	in	ADP
ejpam-3752	88	21	s	s	PROPN
ejpam-3752	88	22	,	,	PUNCT
ejpam-3752	88	23	and	and	CCONJ
ejpam-3752	88	24	(	(	PUNCT
ejpam-3752	88	25	ii	ii	NOUN
ejpam-3752	88	26	)	)	PUNCT
ejpam-3752	88	27	(	(	PUNCT
ejpam-3752	88	28	∀x	∀x	X
ejpam-3752	88	29	,	,	PUNCT
ejpam-3752	88	30	y	y	PROPN
ejpam-3752	88	31	∈	∈	PROPN
ejpam-3752	88	32	x)(x	x)(x	PROPN
ejpam-3752	88	33	·	·	PUNCT
ejpam-3752	89	1	y	y	PROPN
ejpam-3752	89	2	∈	∈	PROPN
ejpam-3752	89	3	s	s	PROPN
ejpam-3752	89	4	,	,	PUNCT
ejpam-3752	89	5	x	x	SYM
ejpam-3752	89	6	∈	∈	PROPN
ejpam-3752	89	7	s	s	PART
ejpam-3752	89	8	⇒	⇒	NOUN
ejpam-3752	89	9	y	y	PROPN
ejpam-3752	89	10	∈	∈	PROPN
ejpam-3752	89	11	s	s	PART
ejpam-3752	89	12	)	)	PUNCT
ejpam-3752	89	13	.	.	PUNCT
ejpam-3752	90	1	(	(	PUNCT
ejpam-3752	90	2	4	4	X
ejpam-3752	90	3	)	)	PUNCT
ejpam-3752	90	4	a	a	DET
ejpam-3752	90	5	up	up	ADJ
ejpam-3752	90	6	-	-	PUNCT
ejpam-3752	90	7	ideal	ideal	NOUN
ejpam-3752	90	8	of	of	ADP
ejpam-3752	90	9	x	x	PRON
ejpam-3752	90	10	if	if	SCONJ
ejpam-3752	90	11	(	(	PUNCT
ejpam-3752	90	12	i	i	NOUN
ejpam-3752	90	13	)	)	PUNCT
ejpam-3752	90	14	the	the	DET
ejpam-3752	90	15	constant	constant	ADJ
ejpam-3752	90	16	0	0	NUM
ejpam-3752	90	17	of	of	ADP
ejpam-3752	90	18	x	x	PRON
ejpam-3752	90	19	is	be	AUX
ejpam-3752	90	20	in	in	ADP
ejpam-3752	90	21	s	s	PROPN
ejpam-3752	90	22	,	,	PUNCT
ejpam-3752	90	23	and	and	CCONJ
ejpam-3752	90	24	(	(	PUNCT
ejpam-3752	90	25	ii	ii	NOUN
ejpam-3752	90	26	)	)	PUNCT
ejpam-3752	90	27	(	(	PUNCT
ejpam-3752	90	28	∀x	∀x	X
ejpam-3752	90	29	,	,	PUNCT
ejpam-3752	90	30	y	y	PROPN
ejpam-3752	90	31	,	,	PUNCT
ejpam-3752	90	32	z	z	PROPN
ejpam-3752	90	33	∈	∈	PROPN
ejpam-3752	90	34	x)(x	x)(x	PROPN
ejpam-3752	90	35	·	·	PUNCT
ejpam-3752	90	36	(	(	PUNCT
ejpam-3752	90	37	y	y	PROPN
ejpam-3752	90	38	·	·	PUNCT
ejpam-3752	90	39	z	z	X
ejpam-3752	90	40	)	)	PUNCT
ejpam-3752	90	41	∈	∈	PROPN
ejpam-3752	90	42	s	s	PROPN
ejpam-3752	90	43	,	,	PUNCT
ejpam-3752	90	44	y	y	PROPN
ejpam-3752	90	45	∈	∈	PROPN
ejpam-3752	90	46	s	s	PART
ejpam-3752	90	47	⇒	⇒	NOUN
ejpam-3752	90	48	x	x	PUNCT
ejpam-3752	90	49	·	·	PUNCT
ejpam-3752	90	50	z	z	PUNCT
ejpam-3752	90	51	∈	∈	PROPN
ejpam-3752	90	52	s	s	NOUN
ejpam-3752	90	53	)	)	PUNCT
ejpam-3752	90	54	.	.	PUNCT
ejpam-3752	91	1	(	(	PUNCT
ejpam-3752	91	2	5	5	X
ejpam-3752	91	3	)	)	PUNCT
ejpam-3752	91	4	a	a	DET
ejpam-3752	91	5	strong	strong	ADJ
ejpam-3752	91	6	up	up	NOUN
ejpam-3752	91	7	-	-	PUNCT
ejpam-3752	91	8	ideal	ideal	NOUN
ejpam-3752	91	9	(	(	PUNCT
ejpam-3752	91	10	renamed	rename	VERB
ejpam-3752	91	11	from	from	ADP
ejpam-3752	91	12	a	a	DET
ejpam-3752	91	13	strongly	strongly	ADV
ejpam-3752	91	14	up	up	ADJ
ejpam-3752	91	15	-	-	PUNCT
ejpam-3752	91	16	ideal	ideal	NOUN
ejpam-3752	91	17	)	)	PUNCT
ejpam-3752	91	18	of	of	ADP
ejpam-3752	91	19	x	x	PRON
ejpam-3752	91	20	if	if	SCONJ
ejpam-3752	91	21	(	(	PUNCT
ejpam-3752	91	22	i	i	NOUN
ejpam-3752	91	23	)	)	PUNCT
ejpam-3752	91	24	the	the	DET
ejpam-3752	91	25	constant	constant	ADJ
ejpam-3752	91	26	0	0	NUM
ejpam-3752	91	27	of	of	ADP
ejpam-3752	91	28	x	x	PRON
ejpam-3752	91	29	is	be	AUX
ejpam-3752	91	30	in	in	ADP
ejpam-3752	91	31	s	s	PROPN
ejpam-3752	91	32	,	,	PUNCT
ejpam-3752	91	33	and	and	CCONJ
ejpam-3752	91	34	(	(	PUNCT
ejpam-3752	91	35	ii	ii	NOUN
ejpam-3752	91	36	)	)	PUNCT
ejpam-3752	91	37	(	(	PUNCT
ejpam-3752	91	38	∀x	∀x	X
ejpam-3752	91	39	,	,	PUNCT
ejpam-3752	91	40	y	y	PROPN
ejpam-3752	91	41	,	,	PUNCT
ejpam-3752	91	42	z	z	PROPN
ejpam-3752	91	43	∈	∈	PROPN
ejpam-3752	91	44	x)((z	x)((z	PROPN
ejpam-3752	91	45	·	·	PUNCT
ejpam-3752	92	1	y	y	X
ejpam-3752	92	2	)	)	PUNCT
ejpam-3752	92	3	·	·	PUNCT
ejpam-3752	93	1	(	(	PUNCT
ejpam-3752	93	2	z	z	NOUN
ejpam-3752	93	3	·	·	PUNCT
ejpam-3752	93	4	x	x	X
ejpam-3752	93	5	)	)	PUNCT
ejpam-3752	93	6	∈	∈	PROPN
ejpam-3752	93	7	s	s	PROPN
ejpam-3752	93	8	,	,	PUNCT
ejpam-3752	93	9	y	y	PROPN
ejpam-3752	93	10	∈	∈	PROPN
ejpam-3752	93	11	s	s	PART
ejpam-3752	93	12	⇒	⇒	NOUN
ejpam-3752	93	13	x	x	PUNCT
ejpam-3752	93	14	∈	∈	PROPN
ejpam-3752	93	15	s	s	PART
ejpam-3752	93	16	)	)	PUNCT
ejpam-3752	93	17	.	.	PUNCT
ejpam-3752	94	1	guntasow	guntasow	VERB
ejpam-3752	94	2	et	et	PROPN
ejpam-3752	94	3	al	al	PROPN
ejpam-3752	94	4	.	.	PUNCT
ejpam-3752	95	1	[	[	X
ejpam-3752	95	2	7	7	X
ejpam-3752	95	3	]	]	PUNCT
ejpam-3752	95	4	and	and	CCONJ
ejpam-3752	95	5	iampan	iampan	NOUN
ejpam-3752	95	6	[	[	X
ejpam-3752	95	7	8	8	NUM
ejpam-3752	95	8	]	]	PUNCT
ejpam-3752	95	9	proved	prove	VERB
ejpam-3752	95	10	that	that	SCONJ
ejpam-3752	95	11	the	the	DET
ejpam-3752	95	12	concept	concept	NOUN
ejpam-3752	95	13	of	of	ADP
ejpam-3752	95	14	up	up	ADV
ejpam-3752	95	15	-	-	PUNCT
ejpam-3752	95	16	subalgebras	subalgebras	PROPN
ejpam-3752	95	17	is	be	AUX
ejpam-3752	95	18	a	a	DET
ejpam-3752	95	19	generalization	generalization	NOUN
ejpam-3752	95	20	of	of	ADP
ejpam-3752	95	21	near	near	ADP
ejpam-3752	95	22	up	up	NOUN
ejpam-3752	95	23	-	-	PUNCT
ejpam-3752	95	24	filters	filter	NOUN
ejpam-3752	95	25	,	,	PUNCT
ejpam-3752	95	26	near	near	ADP
ejpam-3752	95	27	up	up	ADP
ejpam-3752	95	28	-	-	PUNCT
ejpam-3752	95	29	filters	filter	NOUN
ejpam-3752	95	30	is	be	AUX
ejpam-3752	95	31	a	a	DET
ejpam-3752	95	32	generalization	generalization	NOUN
ejpam-3752	95	33	of	of	ADP
ejpam-3752	95	34	up	up	ADJ
ejpam-3752	95	35	-	-	PUNCT
ejpam-3752	95	36	filters	filter	NOUN
ejpam-3752	95	37	,	,	PUNCT
ejpam-3752	95	38	up	up	ADP
ejpam-3752	95	39	-	-	PUNCT
ejpam-3752	95	40	filters	filter	NOUN
ejpam-3752	95	41	is	be	AUX
ejpam-3752	95	42	a	a	DET
ejpam-3752	95	43	generalization	generalization	NOUN
ejpam-3752	95	44	of	of	ADP
ejpam-3752	95	45	up	up	ADJ
ejpam-3752	95	46	-	-	PUNCT
ejpam-3752	95	47	ideals	ideal	NOUN
ejpam-3752	95	48	,	,	PUNCT
ejpam-3752	95	49	and	and	CCONJ
ejpam-3752	95	50	up	up	NOUN
ejpam-3752	95	51	-	-	PUNCT
ejpam-3752	95	52	ideals	ideal	NOUN
ejpam-3752	95	53	is	be	AUX
ejpam-3752	95	54	a	a	DET
ejpam-3752	95	55	generalization	generalization	NOUN
ejpam-3752	95	56	of	of	ADP
ejpam-3752	95	57	strong	strong	ADJ
ejpam-3752	95	58	up	up	NOUN
ejpam-3752	95	59	-	-	PUNCT
ejpam-3752	95	60	ideals	ideal	NOUN
ejpam-3752	95	61	.	.	PUNCT
ejpam-3752	96	1	furthermore	furthermore	ADV
ejpam-3752	96	2	,	,	PUNCT
ejpam-3752	96	3	they	they	PRON
ejpam-3752	96	4	proved	prove	VERB
ejpam-3752	96	5	that	that	SCONJ
ejpam-3752	96	6	the	the	DET
ejpam-3752	96	7	only	only	ADJ
ejpam-3752	96	8	strong	strong	ADJ
ejpam-3752	96	9	up	up	ADJ
ejpam-3752	96	10	-	-	PUNCT
ejpam-3752	96	11	ideal	ideal	NOUN
ejpam-3752	96	12	of	of	ADP
ejpam-3752	96	13	a	a	DET
ejpam-3752	96	14	up	up	NOUN
ejpam-3752	96	15	-	-	PUNCT
ejpam-3752	96	16	algebra	algebra	NOUN
ejpam-3752	96	17	x	x	PUNCT
ejpam-3752	96	18	is	be	AUX
ejpam-3752	96	19	x.	x.	NOUN
ejpam-3752	96	20	a.	a.	NOUN
ejpam-3752	96	21	iampan	iampan	PROPN
ejpam-3752	96	22	,	,	PUNCT
ejpam-3752	96	23	m.	m.	PROPN
ejpam-3752	96	24	songsaeng	songsaeng	PROPN
ejpam-3752	96	25	,	,	PUNCT
ejpam-3752	96	26	g.	g.	PROPN
ejpam-3752	96	27	muhiuddin	muhiuddin	PROPN
ejpam-3752	96	28	/	/	SYM
ejpam-3752	96	29	eur	eur	PROPN
ejpam-3752	96	30	.	.	PUNCT
ejpam-3752	97	1	j.	j.	PROPN
ejpam-3752	97	2	pure	pure	PROPN
ejpam-3752	97	3	appl	appl	PROPN
ejpam-3752	97	4	.	.	PROPN
ejpam-3752	97	5	math	math	PROPN
ejpam-3752	97	6	,	,	PUNCT
ejpam-3752	97	7	13	13	NUM
ejpam-3752	97	8	(	(	PUNCT
ejpam-3752	97	9	3	3	NUM
ejpam-3752	97	10	)	)	PUNCT
ejpam-3752	97	11	(	(	PUNCT
ejpam-3752	97	12	2020	2020	NUM
ejpam-3752	97	13	)	)	PUNCT
ejpam-3752	97	14	,	,	PUNCT
ejpam-3752	97	15	459	459	NUM
ejpam-3752	97	16	-	-	SYM
ejpam-3752	97	17	471	471	NUM
ejpam-3752	97	18	462	462	NUM
ejpam-3752	97	19	3	3	NUM
ejpam-3752	97	20	.	.	PUNCT
ejpam-3752	97	21	fuzzy	fuzzy	ADJ
ejpam-3752	97	22	duplex	duplex	PROPN
ejpam-3752	97	23	up	up	ADP
ejpam-3752	97	24	-	-	PUNCT
ejpam-3752	97	25	algebras	algebras	NOUN
ejpam-3752	97	26	in	in	ADP
ejpam-3752	97	27	this	this	DET
ejpam-3752	97	28	section	section	NOUN
ejpam-3752	97	29	,	,	PUNCT
ejpam-3752	97	30	we	we	PRON
ejpam-3752	97	31	introduce	introduce	VERB
ejpam-3752	97	32	the	the	DET
ejpam-3752	97	33	concepts	concept	NOUN
ejpam-3752	97	34	of	of	ADP
ejpam-3752	97	35	fuzzy	fuzzy	ADJ
ejpam-3752	97	36	duplex	duplex	NOUN
ejpam-3752	97	37	up	up	ADP
ejpam-3752	97	38	-	-	PUNCT
ejpam-3752	97	39	numbers	number	NOUN
ejpam-3752	97	40	and	and	CCONJ
ejpam-3752	97	41	fuzzy	fuzzy	ADJ
ejpam-3752	97	42	duplex	duplex	NOUN
ejpam-3752	97	43	up	up	ADP
ejpam-3752	97	44	-	-	PUNCT
ejpam-3752	97	45	sets	set	NOUN
ejpam-3752	97	46	,	,	PUNCT
ejpam-3752	97	47	and	and	CCONJ
ejpam-3752	97	48	investigate	investigate	VERB
ejpam-3752	97	49	some	some	DET
ejpam-3752	97	50	properties	property	NOUN
ejpam-3752	97	51	.	.	PUNCT
ejpam-3752	98	1	we	we	PRON
ejpam-3752	98	2	find	find	VERB
ejpam-3752	98	3	the	the	DET
ejpam-3752	98	4	necessary	necessary	ADJ
ejpam-3752	98	5	conditions	condition	NOUN
ejpam-3752	98	6	that	that	SCONJ
ejpam-3752	98	7	a	a	DET
ejpam-3752	98	8	fuzzy	fuzzy	ADJ
ejpam-3752	98	9	duplex	duplex	NOUN
ejpam-3752	98	10	up	up	ADV
ejpam-3752	98	11	-	-	PUNCT
ejpam-3752	98	12	set	set	VERB
ejpam-3752	98	13	form	form	NOUN
ejpam-3752	98	14	a	a	DET
ejpam-3752	98	15	up	up	NOUN
ejpam-3752	98	16	-	-	PUNCT
ejpam-3752	98	17	algebra	algebra	NOUN
ejpam-3752	98	18	.	.	PUNCT
ejpam-3752	99	1	furthermore	furthermore	ADV
ejpam-3752	99	2	,	,	PUNCT
ejpam-3752	99	3	we	we	PRON
ejpam-3752	99	4	study	study	VERB
ejpam-3752	99	5	the	the	DET
ejpam-3752	99	6	relationship	relationship	NOUN
ejpam-3752	99	7	between	between	ADP
ejpam-3752	99	8	special	special	ADJ
ejpam-3752	99	9	subsets	subset	NOUN
ejpam-3752	99	10	of	of	ADP
ejpam-3752	99	11	a	a	DET
ejpam-3752	99	12	up	up	NOUN
ejpam-3752	99	13	-	-	PUNCT
ejpam-3752	99	14	algebra	algebra	NOUN
ejpam-3752	99	15	and	and	CCONJ
ejpam-3752	99	16	the	the	DET
ejpam-3752	99	17	same	same	ADJ
ejpam-3752	99	18	special	special	ADJ
ejpam-3752	99	19	subsets	subset	NOUN
ejpam-3752	99	20	of	of	ADP
ejpam-3752	99	21	a	a	DET
ejpam-3752	99	22	fuzzy	fuzzy	ADJ
ejpam-3752	99	23	duplex	duplex	NOUN
ejpam-3752	99	24	up	up	ADV
ejpam-3752	99	25	-	-	PUNCT
ejpam-3752	99	26	set	set	NOUN
ejpam-3752	99	27	.	.	PUNCT
ejpam-3752	100	1	definition	definition	NOUN
ejpam-3752	100	2	3	3	X
ejpam-3752	100	3	.	.	PUNCT
ejpam-3752	101	1	let	let	VERB
ejpam-3752	101	2	x	x	PRON
ejpam-3752	101	3	and	and	CCONJ
ejpam-3752	101	4	y	y	PROPN
ejpam-3752	101	5	be	be	AUX
ejpam-3752	101	6	nonempty	nonempty	X
ejpam-3752	101	7	sets	set	NOUN
ejpam-3752	101	8	and	and	CCONJ
ejpam-3752	101	9	t	t	NOUN
ejpam-3752	101	10	:	:	PUNCT
ejpam-3752	101	11	x	x	X
ejpam-3752	101	12	→	→	SYM
ejpam-3752	101	13	y	y	X
ejpam-3752	101	14	be	be	AUX
ejpam-3752	101	15	a	a	DET
ejpam-3752	101	16	function	function	NOUN
ejpam-3752	101	17	.	.	PUNCT
ejpam-3752	102	1	a	a	DET
ejpam-3752	102	2	fuzzy	fuzzy	ADJ
ejpam-3752	102	3	duplex	duplex	NOUN
ejpam-3752	102	4	x	x	NOUN
ejpam-3752	102	5	-	-	NOUN
ejpam-3752	102	6	number	number	NOUN
ejpam-3752	102	7	is	be	AUX
ejpam-3752	102	8	an	an	DET
ejpam-3752	102	9	ordered	order	VERB
ejpam-3752	102	10	pair	pair	NOUN
ejpam-3752	102	11	(	(	PUNCT
ejpam-3752	102	12	x	x	X
ejpam-3752	102	13	,	,	PUNCT
ejpam-3752	102	14	yt	yt	PROPN
ejpam-3752	102	15	)	)	PUNCT
ejpam-3752	102	16	,	,	PUNCT
ejpam-3752	102	17	where	where	SCONJ
ejpam-3752	102	18	x	x	X
ejpam-3752	102	19	,	,	PUNCT
ejpam-3752	102	20	y	y	PROPN
ejpam-3752	102	21	∈	∈	PROPN
ejpam-3752	102	22	x	x	X
ejpam-3752	102	23	,	,	PUNCT
ejpam-3752	102	24	and	and	CCONJ
ejpam-3752	102	25	t	t	PROPN
ejpam-3752	102	26	(	(	PUNCT
ejpam-3752	102	27	y	y	NOUN
ejpam-3752	102	28	)	)	PUNCT
ejpam-3752	102	29	denoted	denote	VERB
ejpam-3752	102	30	by	by	ADP
ejpam-3752	102	31	yt	yt	NOUN
ejpam-3752	102	32	.	.	PUNCT
ejpam-3752	103	1	the	the	DET
ejpam-3752	103	2	cartesian	cartesian	ADJ
ejpam-3752	103	3	product	product	NOUN
ejpam-3752	103	4	x	x	X
ejpam-3752	103	5	×	×	NOUN
ejpam-3752	103	6	im(t	im(t	VERB
ejpam-3752	103	7	)	)	PUNCT
ejpam-3752	103	8	is	be	AUX
ejpam-3752	103	9	called	call	VERB
ejpam-3752	103	10	the	the	DET
ejpam-3752	103	11	fuzzy	fuzzy	ADJ
ejpam-3752	103	12	duplex	duplex	NOUN
ejpam-3752	103	13	set	set	VERB
ejpam-3752	103	14	based	base	VERB
ejpam-3752	103	15	on	on	ADP
ejpam-3752	103	16	x.	x.	NOUN
ejpam-3752	103	17	if	if	SCONJ
ejpam-3752	103	18	x	x	PRON
ejpam-3752	103	19	is	be	AUX
ejpam-3752	103	20	a	a	DET
ejpam-3752	103	21	up	up	NOUN
ejpam-3752	103	22	-	-	PUNCT
ejpam-3752	103	23	algebra	algebra	NOUN
ejpam-3752	103	24	,	,	PUNCT
ejpam-3752	103	25	a	a	DET
ejpam-3752	103	26	fuzzy	fuzzy	ADJ
ejpam-3752	103	27	duplex	duplex	NOUN
ejpam-3752	103	28	x	x	NOUN
ejpam-3752	103	29	-	-	NOUN
ejpam-3752	103	30	number	number	NOUN
ejpam-3752	103	31	is	be	AUX
ejpam-3752	103	32	called	call	VERB
ejpam-3752	103	33	a	a	DET
ejpam-3752	103	34	fuzzy	fuzzy	ADJ
ejpam-3752	103	35	duplex	duplex	NOUN
ejpam-3752	103	36	up	up	ADP
ejpam-3752	103	37	-	-	PUNCT
ejpam-3752	103	38	number	number	NOUN
ejpam-3752	103	39	and	and	CCONJ
ejpam-3752	103	40	we	we	PRON
ejpam-3752	103	41	say	say	VERB
ejpam-3752	103	42	that	that	SCONJ
ejpam-3752	103	43	x	x	X
ejpam-3752	103	44	×	×	NOUN
ejpam-3752	103	45	im(t	im(t	VERB
ejpam-3752	103	46	)	)	PUNCT
ejpam-3752	103	47	is	be	AUX
ejpam-3752	103	48	the	the	DET
ejpam-3752	103	49	fuzzy	fuzzy	ADJ
ejpam-3752	103	50	duplex	duplex	NOUN
ejpam-3752	103	51	up	up	ADV
ejpam-3752	103	52	-	-	PUNCT
ejpam-3752	103	53	set	set	NOUN
ejpam-3752	103	54	.	.	PUNCT
ejpam-3752	104	1	for	for	ADP
ejpam-3752	104	2	any	any	DET
ejpam-3752	104	3	two	two	NUM
ejpam-3752	104	4	nonempty	nonempty	ADJ
ejpam-3752	104	5	subsets	subset	NOUN
ejpam-3752	104	6	a	a	PRON
ejpam-3752	104	7	and	and	CCONJ
ejpam-3752	104	8	b	b	NOUN
ejpam-3752	104	9	of	of	ADP
ejpam-3752	104	10	x	x	PRON
ejpam-3752	104	11	,	,	PUNCT
ejpam-3752	104	12	we	we	PRON
ejpam-3752	104	13	see	see	VERB
ejpam-3752	104	14	that	that	SCONJ
ejpam-3752	104	15	a	a	DET
ejpam-3752	104	16	×	×	NOUN
ejpam-3752	104	17	t	t	NOUN
ejpam-3752	104	18	(	(	PUNCT
ejpam-3752	104	19	b	b	NOUN
ejpam-3752	104	20	)	)	PUNCT
ejpam-3752	104	21	is	be	AUX
ejpam-3752	104	22	a	a	DET
ejpam-3752	104	23	nonempty	nonempty	ADJ
ejpam-3752	104	24	subset	subset	NOUN
ejpam-3752	104	25	of	of	ADP
ejpam-3752	104	26	x	x	SYM
ejpam-3752	104	27	×	×	NOUN
ejpam-3752	104	28	im(t	im(t	ADJ
ejpam-3752	104	29	)	)	PUNCT
ejpam-3752	104	30	.	.	PUNCT
ejpam-3752	105	1	if	if	SCONJ
ejpam-3752	105	2	(	(	PUNCT
ejpam-3752	105	3	a	a	X
ejpam-3752	105	4	,	,	PUNCT
ejpam-3752	105	5	yt	yt	PROPN
ejpam-3752	105	6	)	)	PUNCT
ejpam-3752	105	7	∈	∈	PROPN
ejpam-3752	105	8	a	a	DET
ejpam-3752	105	9	×	×	PROPN
ejpam-3752	105	10	t	t	NOUN
ejpam-3752	105	11	(	(	PUNCT
ejpam-3752	105	12	b	b	NOUN
ejpam-3752	105	13	)	)	PUNCT
ejpam-3752	105	14	,	,	PUNCT
ejpam-3752	105	15	then	then	ADV
ejpam-3752	105	16	(	(	PUNCT
ejpam-3752	105	17	x	x	X
ejpam-3752	105	18	,	,	PUNCT
ejpam-3752	105	19	yt	yt	INTJ
ejpam-3752	105	20	)	)	PUNCT
ejpam-3752	105	21	∈	∈	PROPN
ejpam-3752	105	22	a×	a×	PROPN
ejpam-3752	105	23	t	t	PROPN
ejpam-3752	105	24	(	(	PUNCT
ejpam-3752	105	25	b	b	NOUN
ejpam-3752	105	26	)	)	PUNCT
ejpam-3752	105	27	for	for	ADP
ejpam-3752	105	28	all	all	DET
ejpam-3752	105	29	x	x	SYM
ejpam-3752	105	30	∈	∈	NOUN
ejpam-3752	105	31	a.	a.	NOUN
ejpam-3752	105	32	in	in	ADP
ejpam-3752	105	33	what	what	PRON
ejpam-3752	105	34	follows	follow	VERB
ejpam-3752	105	35	,	,	PUNCT
ejpam-3752	105	36	x	x	PRON
ejpam-3752	105	37	will	will	AUX
ejpam-3752	105	38	denote	denote	VERB
ejpam-3752	105	39	a	a	DET
ejpam-3752	105	40	up	up	NOUN
ejpam-3752	105	41	-	-	PUNCT
ejpam-3752	105	42	algebra	algebra	NOUN
ejpam-3752	105	43	(	(	PUNCT
ejpam-3752	105	44	x	x	X
ejpam-3752	105	45	,	,	PUNCT
ejpam-3752	105	46	·	·	PUNCT
ejpam-3752	105	47	,	,	PUNCT
ejpam-3752	105	48	0	0	NUM
ejpam-3752	105	49	)	)	PUNCT
ejpam-3752	105	50	,	,	PUNCT
ejpam-3752	105	51	y	y	PROPN
ejpam-3752	105	52	will	will	AUX
ejpam-3752	105	53	denote	denote	VERB
ejpam-3752	105	54	a	a	DET
ejpam-3752	105	55	nonempty	nonempty	ADJ
ejpam-3752	105	56	set	set	NOUN
ejpam-3752	105	57	,	,	PUNCT
ejpam-3752	105	58	and	and	CCONJ
ejpam-3752	105	59	t	t	NOUN
ejpam-3752	105	60	:	:	PUNCT
ejpam-3752	105	61	x	x	X
ejpam-3752	105	62	→	→	SYM
ejpam-3752	105	63	y	y	PROPN
ejpam-3752	105	64	will	will	AUX
ejpam-3752	105	65	be	be	AUX
ejpam-3752	105	66	a	a	DET
ejpam-3752	105	67	function	function	NOUN
ejpam-3752	105	68	.	.	PUNCT
ejpam-3752	106	1	we	we	PRON
ejpam-3752	106	2	define	define	VERB
ejpam-3752	106	3	the	the	DET
ejpam-3752	106	4	binary	binary	PROPN
ejpam-3752	106	5	operation	operation	NOUN
ejpam-3752	106	6	�	�	PROPN
ejpam-3752	106	7	on	on	ADP
ejpam-3752	106	8	the	the	DET
ejpam-3752	106	9	fuzzy	fuzzy	ADJ
ejpam-3752	106	10	duplex	duplex	NOUN
ejpam-3752	106	11	up	up	ADV
ejpam-3752	106	12	-	-	PUNCT
ejpam-3752	106	13	set	set	ADJ
ejpam-3752	106	14	x	x	SYM
ejpam-3752	106	15	×	×	NOUN
ejpam-3752	106	16	im(t	im(t	NOUN
ejpam-3752	106	17	)	)	PUNCT
ejpam-3752	106	18	by	by	ADP
ejpam-3752	106	19	(	(	PUNCT
ejpam-3752	106	20	∀(a	∀(a	PROPN
ejpam-3752	106	21	,	,	PUNCT
ejpam-3752	106	22	xt	xt	X
ejpam-3752	106	23	)	)	PUNCT
ejpam-3752	106	24	,	,	PUNCT
ejpam-3752	106	25	(	(	PUNCT
ejpam-3752	106	26	b	b	X
ejpam-3752	106	27	,	,	PUNCT
ejpam-3752	106	28	yt	yt	ADJ
ejpam-3752	106	29	)	)	PUNCT
ejpam-3752	106	30	∈	∈	PROPN
ejpam-3752	107	1	x	x	X
ejpam-3752	107	2	×	×	NOUN
ejpam-3752	107	3	im(t	im(t	NOUN
ejpam-3752	107	4	)	)	PUNCT
ejpam-3752	107	5	)	)	PUNCT
ejpam-3752	108	1	(	(	PUNCT
ejpam-3752	108	2	(	(	PUNCT
ejpam-3752	108	3	a	a	X
ejpam-3752	108	4	,	,	PUNCT
ejpam-3752	108	5	xt	xt	PROPN
ejpam-3752	108	6	)	)	PUNCT
ejpam-3752	108	7	�	�	PROPN
ejpam-3752	108	8	(	(	PUNCT
ejpam-3752	108	9	b	b	PROPN
ejpam-3752	108	10	,	,	PUNCT
ejpam-3752	108	11	yt	yt	NOUN
ejpam-3752	108	12	)	)	PUNCT
ejpam-3752	108	13	=	=	SYM
ejpam-3752	108	14	(	(	PUNCT
ejpam-3752	108	15	a	a	DET
ejpam-3752	108	16	·	·	SYM
ejpam-3752	108	17	b	b	NOUN
ejpam-3752	108	18	,	,	PUNCT
ejpam-3752	108	19	(	(	PUNCT
ejpam-3752	108	20	x	x	X
ejpam-3752	108	21	·	·	PUNCT
ejpam-3752	108	22	y)t	y)t	NUM
ejpam-3752	108	23	)	)	PUNCT
ejpam-3752	108	24	)	)	PUNCT
ejpam-3752	108	25	.	.	PUNCT
ejpam-3752	109	1	(	(	PUNCT
ejpam-3752	109	2	15	15	NUM
ejpam-3752	109	3	)	)	PUNCT
ejpam-3752	109	4	if	if	SCONJ
ejpam-3752	109	5	the	the	DET
ejpam-3752	109	6	algebra	algebra	NOUN
ejpam-3752	109	7	(	(	PUNCT
ejpam-3752	109	8	x	x	SYM
ejpam-3752	109	9	×	×	NOUN
ejpam-3752	109	10	im(t	im(t	ADJ
ejpam-3752	109	11	)	)	PUNCT
ejpam-3752	109	12	,	,	PUNCT
ejpam-3752	109	13	�	�	PROPN
ejpam-3752	109	14	,	,	PUNCT
ejpam-3752	109	15	0̃	0̃	PROPN
ejpam-3752	109	16	)	)	PUNCT
ejpam-3752	109	17	is	be	AUX
ejpam-3752	109	18	a	a	DET
ejpam-3752	109	19	up	up	NOUN
ejpam-3752	109	20	-	-	PUNCT
ejpam-3752	109	21	algebra	algebra	NOUN
ejpam-3752	109	22	,	,	PUNCT
ejpam-3752	109	23	then	then	ADV
ejpam-3752	109	24	it	it	PRON
ejpam-3752	109	25	is	be	AUX
ejpam-3752	109	26	called	call	VERB
ejpam-3752	109	27	the	the	DET
ejpam-3752	109	28	fuzzy	fuzzy	ADJ
ejpam-3752	109	29	duplex	duplex	NOUN
ejpam-3752	109	30	upalgebra	upalgebra	NOUN
ejpam-3752	109	31	.	.	PUNCT
ejpam-3752	110	1	we	we	PRON
ejpam-3752	110	2	denote	denote	VERB
ejpam-3752	110	3	by	by	ADP
ejpam-3752	110	4	ã	ã	PROPN
ejpam-3752	110	5	the	the	DET
ejpam-3752	110	6	fuzzy	fuzzy	ADJ
ejpam-3752	110	7	duplex	duplex	NOUN
ejpam-3752	110	8	up	up	ADP
ejpam-3752	110	9	-	-	PUNCT
ejpam-3752	110	10	number	number	NOUN
ejpam-3752	110	11	,	,	PUNCT
ejpam-3752	110	12	that	that	ADV
ejpam-3752	110	13	is	is	ADV
ejpam-3752	110	14	,	,	PUNCT
ejpam-3752	110	15	ã	ã	PROPN
ejpam-3752	110	16	=	=	SYM
ejpam-3752	110	17	(	(	PUNCT
ejpam-3752	110	18	a1	a1	PROPN
ejpam-3752	110	19	,	,	PUNCT
ejpam-3752	110	20	a2	a2	PROPN
ejpam-3752	110	21	t	t	PROPN
ejpam-3752	110	22	)	)	PUNCT
ejpam-3752	110	23	for	for	ADP
ejpam-3752	110	24	some	some	DET
ejpam-3752	110	25	a1	a1	NOUN
ejpam-3752	110	26	,	,	PUNCT
ejpam-3752	110	27	a2	a2	PROPN
ejpam-3752	110	28	∈	∈	PROPN
ejpam-3752	110	29	x	x	NOUN
ejpam-3752	110	30	,	,	PUNCT
ejpam-3752	110	31	and	and	CCONJ
ejpam-3752	110	32	the	the	DET
ejpam-3752	110	33	zero	zero	NUM
ejpam-3752	110	34	fuzzy	fuzzy	ADJ
ejpam-3752	110	35	duplex	duplex	NOUN
ejpam-3752	110	36	up	up	ADP
ejpam-3752	110	37	-	-	PUNCT
ejpam-3752	110	38	number	number	NOUN
ejpam-3752	110	39	(	(	PUNCT
ejpam-3752	110	40	0	0	NUM
ejpam-3752	110	41	,	,	PUNCT
ejpam-3752	110	42	0	0	NUM
ejpam-3752	110	43	t	t	NOUN
ejpam-3752	110	44	)	)	PUNCT
ejpam-3752	110	45	is	be	AUX
ejpam-3752	110	46	denoted	denote	VERB
ejpam-3752	110	47	by	by	ADP
ejpam-3752	110	48	0̃.	0̃.	NOUN
ejpam-3752	110	49	we	we	PRON
ejpam-3752	110	50	define	define	VERB
ejpam-3752	110	51	the	the	DET
ejpam-3752	110	52	binary	binary	PROPN
ejpam-3752	110	53	relation	relation	PROPN
ejpam-3752	110	54	�	�	PROPN
ejpam-3752	110	55	and	and	CCONJ
ejpam-3752	110	56	the	the	DET
ejpam-3752	110	57	equality	equality	NOUN
ejpam-3752	110	58	.	.	PUNCT
ejpam-3752	111	1	=	=	PUNCT
ejpam-3752	112	1	on	on	ADP
ejpam-3752	112	2	x	x	SYM
ejpam-3752	112	3	×	×	NOUN
ejpam-3752	112	4	im(t	im(t	ADV
ejpam-3752	112	5	)	)	PUNCT
ejpam-3752	112	6	as	as	SCONJ
ejpam-3752	112	7	follows	follow	VERB
ejpam-3752	112	8	:	:	PUNCT
ejpam-3752	112	9	(	(	PUNCT
ejpam-3752	112	10	∀(a	∀(a	PROPN
ejpam-3752	112	11	,	,	PUNCT
ejpam-3752	112	12	xt	xt	X
ejpam-3752	112	13	)	)	PUNCT
ejpam-3752	112	14	,	,	PUNCT
ejpam-3752	112	15	(	(	PUNCT
ejpam-3752	112	16	b	b	X
ejpam-3752	112	17	,	,	PUNCT
ejpam-3752	112	18	yt	yt	ADJ
ejpam-3752	112	19	)	)	PUNCT
ejpam-3752	112	20	∈	∈	PROPN
ejpam-3752	112	21	x	x	X
ejpam-3752	112	22	×	×	NOUN
ejpam-3752	112	23	im(t	im(t	ADJ
ejpam-3752	112	24	)	)	PUNCT
ejpam-3752	112	25	)	)	PUNCT
ejpam-3752	113	1	(	(	PUNCT
ejpam-3752	113	2	(	(	PUNCT
ejpam-3752	113	3	a	a	X
ejpam-3752	113	4	,	,	PUNCT
ejpam-3752	113	5	xt	xt	PROPN
ejpam-3752	113	6	)	)	PUNCT
ejpam-3752	113	7	�	�	PROPN
ejpam-3752	113	8	(	(	PUNCT
ejpam-3752	113	9	b	b	PROPN
ejpam-3752	113	10	,	,	PUNCT
ejpam-3752	113	11	yt	yt	PROPN
ejpam-3752	113	12	)	)	PUNCT
ejpam-3752	113	13	⇔	⇔	X
ejpam-3752	113	14	a	a	DET
ejpam-3752	113	15	≤	≤	PROPN
ejpam-3752	113	16	b	b	NOUN
ejpam-3752	113	17	,	,	PUNCT
ejpam-3752	113	18	x	x	PUNCT
ejpam-3752	113	19	≤	≤	ADJ
ejpam-3752	113	20	y	y	PROPN
ejpam-3752	113	21	(	(	PUNCT
ejpam-3752	113	22	a	a	PROPN
ejpam-3752	113	23	,	,	PUNCT
ejpam-3752	113	24	xt	xt	PROPN
ejpam-3752	113	25	)	)	PUNCT
ejpam-3752	113	26	.	.	PUNCT
ejpam-3752	114	1	=	=	PUNCT
ejpam-3752	114	2	(	(	PUNCT
ejpam-3752	114	3	b	b	X
ejpam-3752	114	4	,	,	PUNCT
ejpam-3752	114	5	yt	yt	PROPN
ejpam-3752	114	6	)	)	PUNCT
ejpam-3752	114	7	⇔	⇔	X
ejpam-3752	114	8	(	(	PUNCT
ejpam-3752	114	9	a	a	PROPN
ejpam-3752	114	10	,	,	PUNCT
ejpam-3752	114	11	xt	xt	PROPN
ejpam-3752	114	12	)	)	PUNCT
ejpam-3752	114	13	�	�	PROPN
ejpam-3752	114	14	(	(	PUNCT
ejpam-3752	114	15	b	b	PROPN
ejpam-3752	114	16	,	,	PUNCT
ejpam-3752	114	17	yt	yt	PROPN
ejpam-3752	114	18	)	)	PUNCT
ejpam-3752	114	19	,	,	PUNCT
ejpam-3752	114	20	(	(	PUNCT
ejpam-3752	114	21	b	b	X
ejpam-3752	114	22	,	,	PUNCT
ejpam-3752	114	23	yt	yt	PROPN
ejpam-3752	114	24	)	)	PUNCT
ejpam-3752	114	25	�	�	PROPN
ejpam-3752	114	26	(	(	PUNCT
ejpam-3752	114	27	a	a	PROPN
ejpam-3752	114	28	,	,	PUNCT
ejpam-3752	114	29	xt	xt	PROPN
ejpam-3752	114	30	)	)	PUNCT
ejpam-3752	114	31	)	)	PUNCT
ejpam-3752	114	32	.	.	PUNCT
ejpam-3752	115	1	then	then	ADV
ejpam-3752	115	2	we	we	PRON
ejpam-3752	115	3	can	can	AUX
ejpam-3752	115	4	easily	easily	ADV
ejpam-3752	115	5	prove	prove	VERB
ejpam-3752	115	6	that	that	SCONJ
ejpam-3752	115	7	the	the	DET
ejpam-3752	115	8	binary	binary	PROPN
ejpam-3752	115	9	relation	relation	PROPN
ejpam-3752	115	10	�	�	PROPN
ejpam-3752	115	11	is	be	AUX
ejpam-3752	115	12	an	an	DET
ejpam-3752	115	13	order	order	NOUN
ejpam-3752	115	14	relation	relation	NOUN
ejpam-3752	115	15	on	on	ADP
ejpam-3752	115	16	x	x	SYM
ejpam-3752	115	17	×	×	NOUN
ejpam-3752	115	18	im(t	im(t	NOUN
ejpam-3752	115	19	)	)	PUNCT
ejpam-3752	115	20	and	and	CCONJ
ejpam-3752	115	21	(	(	PUNCT
ejpam-3752	115	22	∀(a	∀(a	PROPN
ejpam-3752	115	23	,	,	PUNCT
ejpam-3752	115	24	xt	xt	X
ejpam-3752	115	25	)	)	PUNCT
ejpam-3752	115	26	,	,	PUNCT
ejpam-3752	115	27	(	(	PUNCT
ejpam-3752	115	28	b	b	X
ejpam-3752	115	29	,	,	PUNCT
ejpam-3752	115	30	yt	yt	ADJ
ejpam-3752	115	31	)	)	PUNCT
ejpam-3752	115	32	∈	∈	PROPN
ejpam-3752	115	33	x	x	X
ejpam-3752	115	34	×	×	NOUN
ejpam-3752	115	35	im(t	im(t	ADJ
ejpam-3752	115	36	)	)	PUNCT
ejpam-3752	115	37	)	)	PUNCT
ejpam-3752	116	1	(	(	PUNCT
ejpam-3752	116	2	(	(	PUNCT
ejpam-3752	116	3	a	a	X
ejpam-3752	116	4	,	,	PUNCT
ejpam-3752	116	5	xt	xt	PROPN
ejpam-3752	116	6	)	)	PUNCT
ejpam-3752	116	7	�	�	PROPN
ejpam-3752	116	8	(	(	PUNCT
ejpam-3752	116	9	b	b	PROPN
ejpam-3752	116	10	,	,	PUNCT
ejpam-3752	116	11	yt	yt	PROPN
ejpam-3752	116	12	)	)	PUNCT
ejpam-3752	116	13	⇔	⇔	X
ejpam-3752	116	14	(	(	PUNCT
ejpam-3752	116	15	a	a	PROPN
ejpam-3752	116	16	,	,	PUNCT
ejpam-3752	116	17	xt	xt	PROPN
ejpam-3752	116	18	)	)	PUNCT
ejpam-3752	116	19	�	�	PROPN
ejpam-3752	116	20	(	(	PUNCT
ejpam-3752	116	21	b	b	PROPN
ejpam-3752	116	22	,	,	PUNCT
ejpam-3752	116	23	yt	yt	NOUN
ejpam-3752	116	24	)	)	PUNCT
ejpam-3752	116	25	=	=	SYM
ejpam-3752	116	26	0̃	0̃	NOUN
ejpam-3752	116	27	(	(	PUNCT
ejpam-3752	116	28	a	a	NOUN
ejpam-3752	116	29	,	,	PUNCT
ejpam-3752	116	30	xt	xt	PROPN
ejpam-3752	116	31	)	)	PUNCT
ejpam-3752	116	32	.	.	PUNCT
ejpam-3752	117	1	=	=	PUNCT
ejpam-3752	117	2	(	(	PUNCT
ejpam-3752	117	3	b	b	X
ejpam-3752	117	4	,	,	PUNCT
ejpam-3752	117	5	yt	yt	PROPN
ejpam-3752	117	6	)	)	PUNCT
ejpam-3752	117	7	⇔	⇔	PROPN
ejpam-3752	117	8	a	a	X
ejpam-3752	117	9	=	=	SYM
ejpam-3752	117	10	b	b	PROPN
ejpam-3752	117	11	,	,	PUNCT
ejpam-3752	117	12	x	x	PUNCT
ejpam-3752	117	13	=	=	SYM
ejpam-3752	117	14	y	y	PROPN
ejpam-3752	117	15	)	)	PUNCT
ejpam-3752	117	16	.	.	PUNCT
ejpam-3752	118	1	hence	hence	ADV
ejpam-3752	118	2	,	,	PUNCT
ejpam-3752	118	3	.	.	PUNCT
ejpam-3752	119	1	=	=	PRON
ejpam-3752	119	2	⊆=	⊆=	NOUN
ejpam-3752	119	3	on	on	ADP
ejpam-3752	119	4	x	x	X
ejpam-3752	119	5	×	×	NOUN
ejpam-3752	119	6	im(t	im(t	ADJ
ejpam-3752	119	7	)	)	PUNCT
ejpam-3752	119	8	.	.	PUNCT
ejpam-3752	120	1	example	example	NOUN
ejpam-3752	121	1	1	1	X
ejpam-3752	121	2	.	.	PUNCT
ejpam-3752	121	3	let	let	VERB
ejpam-3752	121	4	x	x	PUNCT
ejpam-3752	121	5	=	=	PUNCT
ejpam-3752	121	6	{	{	PUNCT
ejpam-3752	121	7	0	0	NUM
ejpam-3752	121	8	,	,	PUNCT
ejpam-3752	121	9	a	a	DET
ejpam-3752	121	10	,	,	PUNCT
ejpam-3752	121	11	b	b	NOUN
ejpam-3752	121	12	,	,	PUNCT
ejpam-3752	121	13	c	c	AUX
ejpam-3752	121	14	}	}	PUNCT
ejpam-3752	121	15	be	be	AUX
ejpam-3752	121	16	a	a	DET
ejpam-3752	121	17	up	up	NOUN
ejpam-3752	121	18	-	-	PUNCT
ejpam-3752	121	19	algebra	algebra	NOUN
ejpam-3752	121	20	with	with	ADP
ejpam-3752	121	21	a	a	DET
ejpam-3752	121	22	fixed	fix	VERB
ejpam-3752	121	23	element	element	NOUN
ejpam-3752	121	24	0	0	PUNCT
ejpam-3752	121	25	and	and	CCONJ
ejpam-3752	121	26	a	a	DET
ejpam-3752	121	27	binary	binary	ADJ
ejpam-3752	121	28	operation	operation	NOUN
ejpam-3752	121	29	·	·	PUNCT
ejpam-3752	121	30	defined	define	VERB
ejpam-3752	121	31	by	by	ADP
ejpam-3752	121	32	the	the	DET
ejpam-3752	121	33	following	following	ADJ
ejpam-3752	121	34	cayley	cayley	ADJ
ejpam-3752	121	35	table	table	NOUN
ejpam-3752	121	36	:	:	PUNCT
ejpam-3752	121	37	·	·	PUNCT
ejpam-3752	121	38	0	0	PUNCT
ejpam-3752	122	1	a	a	DET
ejpam-3752	122	2	b	b	X
ejpam-3752	122	3	c	c	NOUN
ejpam-3752	122	4	0	0	NUM
ejpam-3752	122	5	0	0	NUM
ejpam-3752	122	6	a	a	DET
ejpam-3752	122	7	b	b	NOUN
ejpam-3752	122	8	c	c	NOUN
ejpam-3752	122	9	a	a	PRON
ejpam-3752	122	10	0	0	NUM
ejpam-3752	122	11	0	0	NUM
ejpam-3752	122	12	b	b	PROPN
ejpam-3752	122	13	b	b	PROPN
ejpam-3752	122	14	b	b	PROPN
ejpam-3752	122	15	0	0	NUM
ejpam-3752	122	16	a	a	DET
ejpam-3752	122	17	0	0	NUM
ejpam-3752	122	18	b	b	NOUN
ejpam-3752	122	19	c	c	NOUN
ejpam-3752	122	20	0	0	NUM
ejpam-3752	123	1	a	a	DET
ejpam-3752	123	2	0	0	NUM
ejpam-3752	123	3	0	0	NUM
ejpam-3752	123	4	a.	a.	NOUN
ejpam-3752	123	5	iampan	iampan	PROPN
ejpam-3752	123	6	,	,	PUNCT
ejpam-3752	123	7	m.	m.	PROPN
ejpam-3752	123	8	songsaeng	songsaeng	PROPN
ejpam-3752	123	9	,	,	PUNCT
ejpam-3752	123	10	g.	g.	PROPN
ejpam-3752	123	11	muhiuddin	muhiuddin	PROPN
ejpam-3752	123	12	/	/	SYM
ejpam-3752	123	13	eur	eur	PROPN
ejpam-3752	123	14	.	.	PUNCT
ejpam-3752	124	1	j.	j.	PROPN
ejpam-3752	124	2	pure	pure	PROPN
ejpam-3752	124	3	appl	appl	PROPN
ejpam-3752	124	4	.	.	PROPN
ejpam-3752	124	5	math	math	PROPN
ejpam-3752	124	6	,	,	PUNCT
ejpam-3752	124	7	13	13	NUM
ejpam-3752	124	8	(	(	PUNCT
ejpam-3752	124	9	3	3	NUM
ejpam-3752	124	10	)	)	PUNCT
ejpam-3752	124	11	(	(	PUNCT
ejpam-3752	124	12	2020	2020	NUM
ejpam-3752	124	13	)	)	PUNCT
ejpam-3752	124	14	,	,	PUNCT
ejpam-3752	124	15	459	459	NUM
ejpam-3752	124	16	-	-	SYM
ejpam-3752	124	17	471	471	NUM
ejpam-3752	124	18	463	463	NUM
ejpam-3752	124	19	let	let	VERB
ejpam-3752	124	20	t	t	NOUN
ejpam-3752	124	21	:	:	PUNCT
ejpam-3752	124	22	x	x	X
ejpam-3752	124	23	→	→	X
ejpam-3752	124	24	{	{	PUNCT
ejpam-3752	124	25	0.5	0.5	NUM
ejpam-3752	124	26	,	,	PUNCT
ejpam-3752	124	27	1	1	NUM
ejpam-3752	124	28	}	}	PUNCT
ejpam-3752	124	29	be	be	AUX
ejpam-3752	124	30	a	a	DET
ejpam-3752	124	31	function	function	NOUN
ejpam-3752	124	32	defined	define	VERB
ejpam-3752	124	33	by	by	ADP
ejpam-3752	124	34	0	0	NUM
ejpam-3752	124	35	t	t	NOUN
ejpam-3752	124	36	=	=	PUNCT
ejpam-3752	124	37	at	at	ADP
ejpam-3752	124	38	=	=	PUNCT
ejpam-3752	124	39	bt	bt	NOUN
ejpam-3752	124	40	=	=	NOUN
ejpam-3752	124	41	0.5	0.5	NUM
ejpam-3752	124	42	,	,	PUNCT
ejpam-3752	124	43	ct	ct	NOUN
ejpam-3752	124	44	=	=	SYM
ejpam-3752	124	45	1	1	X
ejpam-3752	124	46	.	.	PUNCT
ejpam-3752	125	1	then	then	ADV
ejpam-3752	125	2	the	the	DET
ejpam-3752	125	3	axiom	axiom	NOUN
ejpam-3752	125	4	(	(	PUNCT
ejpam-3752	125	5	up-4	up-4	ADV
ejpam-3752	125	6	)	)	PUNCT
ejpam-3752	125	7	is	be	AUX
ejpam-3752	125	8	not	not	PART
ejpam-3752	125	9	satisfied	satisfied	ADJ
ejpam-3752	125	10	.	.	PUNCT
ejpam-3752	126	1	indeed	indeed	ADV
ejpam-3752	126	2	,	,	PUNCT
ejpam-3752	126	3	there	there	PRON
ejpam-3752	126	4	are	be	VERB
ejpam-3752	126	5	(	(	PUNCT
ejpam-3752	126	6	0	0	NUM
ejpam-3752	126	7	,	,	PUNCT
ejpam-3752	126	8	at	at	ADP
ejpam-3752	126	9	)	)	PUNCT
ejpam-3752	126	10	,	,	PUNCT
ejpam-3752	126	11	(	(	PUNCT
ejpam-3752	126	12	0	0	NUM
ejpam-3752	126	13	,	,	PUNCT
ejpam-3752	126	14	ct	ct	NUM
ejpam-3752	126	15	)	)	PUNCT
ejpam-3752	126	16	∈	∈	PROPN
ejpam-3752	126	17	x	x	X
ejpam-3752	126	18	×	×	NOUN
ejpam-3752	126	19	{	{	PUNCT
ejpam-3752	126	20	0.5	0.5	NUM
ejpam-3752	126	21	,	,	PUNCT
ejpam-3752	126	22	1	1	NUM
ejpam-3752	126	23	}	}	PUNCT
ejpam-3752	126	24	such	such	ADJ
ejpam-3752	126	25	that	that	SCONJ
ejpam-3752	126	26	(	(	PUNCT
ejpam-3752	126	27	0	0	NUM
ejpam-3752	126	28	,	,	PUNCT
ejpam-3752	126	29	at	at	ADP
ejpam-3752	126	30	)	)	PUNCT
ejpam-3752	126	31	=	=	SYM
ejpam-3752	126	32	(	(	PUNCT
ejpam-3752	126	33	0	0	NUM
ejpam-3752	126	34	,	,	PUNCT
ejpam-3752	126	35	0.5	0.5	NUM
ejpam-3752	126	36	)	)	PUNCT
ejpam-3752	126	37	6=	6=	NUM
ejpam-3752	126	38	(	(	PUNCT
ejpam-3752	126	39	0	0	NUM
ejpam-3752	126	40	,	,	PUNCT
ejpam-3752	126	41	1	1	NUM
ejpam-3752	126	42	)	)	PUNCT
ejpam-3752	126	43	=	=	SYM
ejpam-3752	126	44	(	(	PUNCT
ejpam-3752	126	45	0	0	NUM
ejpam-3752	126	46	,	,	PUNCT
ejpam-3752	126	47	ct	ct	PROPN
ejpam-3752	126	48	)	)	PUNCT
ejpam-3752	127	1	but	but	CCONJ
ejpam-3752	127	2	(	(	PUNCT
ejpam-3752	127	3	0	0	NUM
ejpam-3752	127	4	,	,	PUNCT
ejpam-3752	127	5	at	at	ADP
ejpam-3752	127	6	)	)	PUNCT
ejpam-3752	127	7	�	�	PROPN
ejpam-3752	127	8	(	(	PUNCT
ejpam-3752	127	9	0	0	NUM
ejpam-3752	127	10	,	,	PUNCT
ejpam-3752	127	11	ct	ct	NUM
ejpam-3752	127	12	)	)	PUNCT
ejpam-3752	128	1	=	=	PUNCT
ejpam-3752	128	2	(	(	PUNCT
ejpam-3752	128	3	0	0	NUM
ejpam-3752	128	4	·	·	SYM
ejpam-3752	128	5	0	0	NUM
ejpam-3752	128	6	,	,	PUNCT
ejpam-3752	128	7	(	(	PUNCT
ejpam-3752	128	8	a	a	DET
ejpam-3752	128	9	·	·	PUNCT
ejpam-3752	128	10	c)t	c)t	X
ejpam-3752	128	11	)	)	PUNCT
ejpam-3752	129	1	=	=	SYM
ejpam-3752	129	2	(	(	PUNCT
ejpam-3752	129	3	0	0	NUM
ejpam-3752	129	4	,	,	PUNCT
ejpam-3752	129	5	bt	bt	NOUN
ejpam-3752	129	6	)	)	PUNCT
ejpam-3752	129	7	=	=	PUNCT
ejpam-3752	130	1	(	(	PUNCT
ejpam-3752	130	2	0	0	NUM
ejpam-3752	130	3	,	,	PUNCT
ejpam-3752	130	4	0	0	NUM
ejpam-3752	130	5	t	t	NOUN
ejpam-3752	130	6	)	)	PUNCT
ejpam-3752	131	1	=	=	SYM
ejpam-3752	131	2	0̃	0̃	NOUN
ejpam-3752	131	3	and	and	CCONJ
ejpam-3752	131	4	(	(	PUNCT
ejpam-3752	131	5	0	0	NUM
ejpam-3752	131	6	,	,	PUNCT
ejpam-3752	131	7	ct	ct	PROPN
ejpam-3752	131	8	)	)	PUNCT
ejpam-3752	131	9	�	�	PROPN
ejpam-3752	131	10	(	(	PUNCT
ejpam-3752	131	11	0	0	NUM
ejpam-3752	131	12	,	,	PUNCT
ejpam-3752	131	13	at	at	ADP
ejpam-3752	131	14	)	)	PUNCT
ejpam-3752	131	15	=	=	SYM
ejpam-3752	131	16	(	(	PUNCT
ejpam-3752	131	17	0	0	NUM
ejpam-3752	131	18	·	·	PUNCT
ejpam-3752	131	19	0	0	NUM
ejpam-3752	131	20	,	,	PUNCT
ejpam-3752	131	21	(	(	PUNCT
ejpam-3752	131	22	c	c	X
ejpam-3752	131	23	·	·	PUNCT
ejpam-3752	131	24	a)t	a)t	X
ejpam-3752	131	25	)	)	PUNCT
ejpam-3752	132	1	=	=	SYM
ejpam-3752	132	2	(	(	PUNCT
ejpam-3752	132	3	0	0	NUM
ejpam-3752	132	4	,	,	PUNCT
ejpam-3752	132	5	at	at	ADP
ejpam-3752	132	6	)	)	PUNCT
ejpam-3752	132	7	=	=	SYM
ejpam-3752	132	8	(	(	PUNCT
ejpam-3752	132	9	0	0	NUM
ejpam-3752	132	10	,	,	PUNCT
ejpam-3752	132	11	0	0	NUM
ejpam-3752	132	12	t	t	NOUN
ejpam-3752	132	13	)	)	PUNCT
ejpam-3752	133	1	=	=	SYM
ejpam-3752	134	1	0̃.	0̃.	NOUN
ejpam-3752	134	2	hence	hence	ADV
ejpam-3752	134	3	,	,	PUNCT
ejpam-3752	134	4	the	the	DET
ejpam-3752	134	5	algebra	algebra	NOUN
ejpam-3752	134	6	(	(	PUNCT
ejpam-3752	134	7	x	x	SYM
ejpam-3752	134	8	×	×	NOUN
ejpam-3752	134	9	{	{	PUNCT
ejpam-3752	134	10	0.5	0.5	NUM
ejpam-3752	134	11	,	,	PUNCT
ejpam-3752	134	12	1	1	NUM
ejpam-3752	134	13	}	}	PUNCT
ejpam-3752	134	14	,	,	PUNCT
ejpam-3752	134	15	�	�	PROPN
ejpam-3752	134	16	,	,	PUNCT
ejpam-3752	134	17	0̃	0̃	NOUN
ejpam-3752	134	18	)	)	PUNCT
ejpam-3752	134	19	is	be	AUX
ejpam-3752	134	20	not	not	PART
ejpam-3752	134	21	a	a	DET
ejpam-3752	134	22	up	up	NOUN
ejpam-3752	134	23	-	-	PUNCT
ejpam-3752	134	24	algebra	algebra	NOUN
ejpam-3752	134	25	.	.	PUNCT
ejpam-3752	135	1	theorem	theorem	NOUN
ejpam-3752	135	2	1	1	NUM
ejpam-3752	135	3	.	.	PUNCT
ejpam-3752	136	1	the	the	DET
ejpam-3752	136	2	algebra	algebra	NOUN
ejpam-3752	136	3	(	(	PUNCT
ejpam-3752	136	4	x	x	SYM
ejpam-3752	136	5	×	×	NOUN
ejpam-3752	136	6	im(t	im(t	ADJ
ejpam-3752	136	7	)	)	PUNCT
ejpam-3752	136	8	,	,	PUNCT
ejpam-3752	136	9	�	�	PROPN
ejpam-3752	136	10	,	,	PUNCT
ejpam-3752	136	11	0̃	0̃	PROPN
ejpam-3752	136	12	)	)	PUNCT
ejpam-3752	136	13	satisfies	satisfy	VERB
ejpam-3752	136	14	the	the	DET
ejpam-3752	136	15	axioms	axiom	NOUN
ejpam-3752	136	16	(	(	PUNCT
ejpam-3752	136	17	up-1	up-1	NUM
ejpam-3752	136	18	)	)	PUNCT
ejpam-3752	136	19	,	,	PUNCT
ejpam-3752	136	20	(	(	PUNCT
ejpam-3752	136	21	up-2	up-2	NUM
ejpam-3752	136	22	)	)	PUNCT
ejpam-3752	136	23	,	,	PUNCT
ejpam-3752	136	24	and	and	CCONJ
ejpam-3752	136	25	(	(	PUNCT
ejpam-3752	136	26	up-3	up-3	NOUN
ejpam-3752	136	27	)	)	PUNCT
ejpam-3752	136	28	.	.	PUNCT
ejpam-3752	137	1	proof	proof	NOUN
ejpam-3752	137	2	.	.	PUNCT
ejpam-3752	138	1	(	(	PUNCT
ejpam-3752	138	2	up-1	up-1	NOUN
ejpam-3752	138	3	)	)	PUNCT
ejpam-3752	138	4	let	let	VERB
ejpam-3752	138	5	x̃	x̃	PROPN
ejpam-3752	138	6	,	,	PUNCT
ejpam-3752	138	7	ỹ	ỹ	PROPN
ejpam-3752	138	8	,	,	PUNCT
ejpam-3752	138	9	z̃	z̃	PROPN
ejpam-3752	138	10	∈	∈	PROPN
ejpam-3752	138	11	x	x	SYM
ejpam-3752	138	12	×	×	NOUN
ejpam-3752	138	13	im(t	im(t	NOUN
ejpam-3752	138	14	)	)	PUNCT
ejpam-3752	138	15	where	where	SCONJ
ejpam-3752	138	16	x̃	x̃	PROPN
ejpam-3752	138	17	=	=	SYM
ejpam-3752	138	18	(	(	PUNCT
ejpam-3752	138	19	x1	x1	PROPN
ejpam-3752	138	20	,	,	PUNCT
ejpam-3752	138	21	x2	x2	PROPN
ejpam-3752	138	22	t	t	PROPN
ejpam-3752	138	23	)	)	PUNCT
ejpam-3752	138	24	,	,	PUNCT
ejpam-3752	138	25	ỹ	ỹ	PROPN
ejpam-3752	138	26	=	=	SYM
ejpam-3752	138	27	(	(	PUNCT
ejpam-3752	138	28	y1	y1	PROPN
ejpam-3752	138	29	,	,	PUNCT
ejpam-3752	138	30	y2	y2	PROPN
ejpam-3752	138	31	t	t	PROPN
ejpam-3752	138	32	)	)	PUNCT
ejpam-3752	138	33	,	,	PUNCT
ejpam-3752	138	34	and	and	CCONJ
ejpam-3752	138	35	z̃	z̃	PROPN
ejpam-3752	138	36	=	=	SYM
ejpam-3752	138	37	(	(	PUNCT
ejpam-3752	138	38	z1	z1	PROPN
ejpam-3752	138	39	,	,	PUNCT
ejpam-3752	138	40	z2	z2	PROPN
ejpam-3752	138	41	t	t	PROPN
ejpam-3752	138	42	)	)	PUNCT
ejpam-3752	138	43	.	.	PUNCT
ejpam-3752	139	1	then	then	ADV
ejpam-3752	139	2	(	(	PUNCT
ejpam-3752	139	3	ỹ	ỹ	PROPN
ejpam-3752	139	4	�	�	PROPN
ejpam-3752	139	5	z̃	z̃	PROPN
ejpam-3752	139	6	)	)	PUNCT
ejpam-3752	139	7	�	�	PROPN
ejpam-3752	139	8	(	(	PUNCT
ejpam-3752	139	9	(	(	PUNCT
ejpam-3752	139	10	x̃	x̃	PROPN
ejpam-3752	139	11	�	�	PROPN
ejpam-3752	139	12	ỹ	ỹ	PROPN
ejpam-3752	139	13	)	)	PUNCT
ejpam-3752	139	14	�	�	PROPN
ejpam-3752	139	15	(	(	PUNCT
ejpam-3752	139	16	x̃	x̃	PROPN
ejpam-3752	139	17	�	�	PROPN
ejpam-3752	139	18	z̃	z̃	PROPN
ejpam-3752	139	19	)	)	PUNCT
ejpam-3752	139	20	)	)	PUNCT
ejpam-3752	140	1	=	=	SYM
ejpam-3752	140	2	(	(	PUNCT
ejpam-3752	140	3	(	(	PUNCT
ejpam-3752	140	4	y1	y1	INTJ
ejpam-3752	140	5	,	,	PUNCT
ejpam-3752	140	6	y2	y2	PROPN
ejpam-3752	140	7	t	t	PROPN
ejpam-3752	140	8	)	)	PUNCT
ejpam-3752	140	9	�	�	PROPN
ejpam-3752	140	10	(	(	PUNCT
ejpam-3752	140	11	z1	z1	PROPN
ejpam-3752	140	12	,	,	PUNCT
ejpam-3752	140	13	z2	z2	PROPN
ejpam-3752	140	14	t	t	PROPN
ejpam-3752	140	15	)	)	PUNCT
ejpam-3752	140	16	)	)	PUNCT
ejpam-3752	140	17	�	�	PROPN
ejpam-3752	140	18	(	(	PUNCT
ejpam-3752	140	19	(	(	PUNCT
ejpam-3752	140	20	(	(	PUNCT
ejpam-3752	140	21	x1	x1	ADJ
ejpam-3752	140	22	,	,	PUNCT
ejpam-3752	140	23	x2	x2	PROPN
ejpam-3752	140	24	t	t	PROPN
ejpam-3752	140	25	)	)	PUNCT
ejpam-3752	140	26	�	�	PROPN
ejpam-3752	140	27	(	(	PUNCT
ejpam-3752	140	28	y1	y1	PROPN
ejpam-3752	140	29	,	,	PUNCT
ejpam-3752	140	30	y2	y2	PROPN
ejpam-3752	140	31	t	t	PROPN
ejpam-3752	140	32	)	)	PUNCT
ejpam-3752	140	33	)	)	PUNCT
ejpam-3752	140	34	�	�	PROPN
ejpam-3752	140	35	(	(	PUNCT
ejpam-3752	140	36	(	(	PUNCT
ejpam-3752	140	37	x1	x1	PROPN
ejpam-3752	140	38	,	,	PUNCT
ejpam-3752	140	39	x2	x2	PROPN
ejpam-3752	140	40	t	t	PROPN
ejpam-3752	140	41	)	)	PUNCT
ejpam-3752	140	42	�	�	PROPN
ejpam-3752	140	43	(	(	PUNCT
ejpam-3752	140	44	z1	z1	PROPN
ejpam-3752	140	45	,	,	PUNCT
ejpam-3752	140	46	z2	z2	PROPN
ejpam-3752	140	47	t	t	PROPN
ejpam-3752	140	48	)	)	PUNCT
ejpam-3752	140	49	)	)	PUNCT
ejpam-3752	140	50	)	)	PUNCT
ejpam-3752	141	1	=	=	PUNCT
ejpam-3752	141	2	(	(	PUNCT
ejpam-3752	141	3	y1	y1	INTJ
ejpam-3752	141	4	·	·	PUNCT
ejpam-3752	141	5	z1	z1	PROPN
ejpam-3752	141	6	,	,	PUNCT
ejpam-3752	141	7	(	(	PUNCT
ejpam-3752	141	8	y2	y2	INTJ
ejpam-3752	141	9	·	·	PUNCT
ejpam-3752	141	10	z2)t	z2)t	PROPN
ejpam-3752	141	11	)	)	PUNCT
ejpam-3752	141	12	�	�	PROPN
ejpam-3752	141	13	(	(	PUNCT
ejpam-3752	141	14	(	(	PUNCT
ejpam-3752	141	15	x1	x1	PROPN
ejpam-3752	141	16	·	·	PUNCT
ejpam-3752	141	17	y1	y1	INTJ
ejpam-3752	141	18	,	,	PUNCT
ejpam-3752	141	19	(	(	PUNCT
ejpam-3752	141	20	x2	x2	PROPN
ejpam-3752	141	21	·	·	PUNCT
ejpam-3752	141	22	y2)t	y2)t	ADV
ejpam-3752	141	23	)	)	PUNCT
ejpam-3752	141	24	�	�	PROPN
ejpam-3752	141	25	(	(	PUNCT
ejpam-3752	141	26	x1	x1	PROPN
ejpam-3752	141	27	·	·	PUNCT
ejpam-3752	141	28	z1	z1	PROPN
ejpam-3752	141	29	,	,	PUNCT
ejpam-3752	141	30	(	(	PUNCT
ejpam-3752	141	31	x2	x2	PROPN
ejpam-3752	141	32	·	·	PUNCT
ejpam-3752	141	33	z2)t	z2)t	PROPN
ejpam-3752	141	34	)	)	PUNCT
ejpam-3752	141	35	)	)	PUNCT
ejpam-3752	142	1	=	=	PUNCT
ejpam-3752	143	1	(	(	PUNCT
ejpam-3752	143	2	y1	y1	INTJ
ejpam-3752	143	3	·	·	PUNCT
ejpam-3752	143	4	z1	z1	PROPN
ejpam-3752	143	5	,	,	PUNCT
ejpam-3752	143	6	(	(	PUNCT
ejpam-3752	143	7	y2	y2	INTJ
ejpam-3752	143	8	·	·	PUNCT
ejpam-3752	143	9	z2)t	z2)t	PROPN
ejpam-3752	143	10	)	)	PUNCT
ejpam-3752	143	11	�	�	PROPN
ejpam-3752	143	12	(	(	PUNCT
ejpam-3752	143	13	(	(	PUNCT
ejpam-3752	143	14	x1	x1	PROPN
ejpam-3752	143	15	·	·	PUNCT
ejpam-3752	143	16	y1	y1	PROPN
ejpam-3752	143	17	)	)	PUNCT
ejpam-3752	143	18	·	·	PUNCT
ejpam-3752	144	1	(	(	PUNCT
ejpam-3752	144	2	x1	x1	PROPN
ejpam-3752	144	3	·	·	PUNCT
ejpam-3752	144	4	z1	z1	PROPN
ejpam-3752	144	5	)	)	PUNCT
ejpam-3752	144	6	,	,	PUNCT
ejpam-3752	144	7	(	(	PUNCT
ejpam-3752	144	8	(	(	PUNCT
ejpam-3752	144	9	x2	x2	PROPN
ejpam-3752	144	10	·	·	PUNCT
ejpam-3752	144	11	y2	y2	NUM
ejpam-3752	144	12	)	)	PUNCT
ejpam-3752	144	13	·	·	PUNCT
ejpam-3752	145	1	(	(	PUNCT
ejpam-3752	145	2	x2	x2	X
ejpam-3752	145	3	·	·	PUNCT
ejpam-3752	145	4	z2))t	z2))t	NOUN
ejpam-3752	145	5	)	)	PUNCT
ejpam-3752	145	6	=	=	PUNCT
ejpam-3752	145	7	(	(	PUNCT
ejpam-3752	145	8	(	(	PUNCT
ejpam-3752	145	9	y1	y1	INTJ
ejpam-3752	145	10	·	·	PUNCT
ejpam-3752	145	11	z1	z1	PROPN
ejpam-3752	145	12	)	)	PUNCT
ejpam-3752	145	13	·	·	PUNCT
ejpam-3752	145	14	(	(	PUNCT
ejpam-3752	145	15	(	(	PUNCT
ejpam-3752	145	16	x1	x1	PROPN
ejpam-3752	145	17	·	·	PUNCT
ejpam-3752	145	18	y1	y1	PROPN
ejpam-3752	145	19	)	)	PUNCT
ejpam-3752	145	20	·	·	PUNCT
ejpam-3752	146	1	(	(	PUNCT
ejpam-3752	146	2	x1	x1	PROPN
ejpam-3752	146	3	·	·	PUNCT
ejpam-3752	146	4	z1	z1	PROPN
ejpam-3752	146	5	)	)	PUNCT
ejpam-3752	146	6	)	)	PUNCT
ejpam-3752	146	7	,	,	PUNCT
ejpam-3752	146	8	(	(	PUNCT
ejpam-3752	146	9	(	(	PUNCT
ejpam-3752	146	10	y2	y2	INTJ
ejpam-3752	146	11	·	·	SYM
ejpam-3752	146	12	z2	z2	NUM
ejpam-3752	146	13	)	)	PUNCT
ejpam-3752	146	14	·	·	PUNCT
ejpam-3752	146	15	(	(	PUNCT
ejpam-3752	146	16	(	(	PUNCT
ejpam-3752	146	17	x2	x2	PROPN
ejpam-3752	146	18	·	·	PUNCT
ejpam-3752	146	19	y2	y2	NUM
ejpam-3752	146	20	)	)	PUNCT
ejpam-3752	146	21	·	·	PUNCT
ejpam-3752	147	1	(	(	PUNCT
ejpam-3752	147	2	x2	x2	X
ejpam-3752	147	3	·	·	PUNCT
ejpam-3752	147	4	z2)))t	z2)))t	PROPN
ejpam-3752	147	5	)	)	PUNCT
ejpam-3752	148	1	=	=	PUNCT
ejpam-3752	148	2	(	(	PUNCT
ejpam-3752	148	3	0	0	NUM
ejpam-3752	148	4	,	,	PUNCT
ejpam-3752	148	5	0	0	NUM
ejpam-3752	148	6	t	t	NOUN
ejpam-3752	148	7	)	)	PUNCT
ejpam-3752	148	8	(	(	PUNCT
ejpam-3752	148	9	(	(	PUNCT
ejpam-3752	148	10	up-1	up-1	NOUN
ejpam-3752	148	11	)	)	PUNCT
ejpam-3752	148	12	)	)	PUNCT
ejpam-3752	149	1	=	=	SYM
ejpam-3752	149	2	0̃.	0̃.	NUM
ejpam-3752	149	3	(	(	PUNCT
ejpam-3752	149	4	up-2	up-2	NUM
ejpam-3752	149	5	)	)	PUNCT
ejpam-3752	149	6	let	let	VERB
ejpam-3752	149	7	x̃	x̃	PROPN
ejpam-3752	149	8	∈	∈	PROPN
ejpam-3752	149	9	x	x	X
ejpam-3752	149	10	×	×	NOUN
ejpam-3752	149	11	im(t	im(t	NOUN
ejpam-3752	149	12	)	)	PUNCT
ejpam-3752	149	13	where	where	SCONJ
ejpam-3752	149	14	x̃	x̃	PROPN
ejpam-3752	149	15	=	=	SYM
ejpam-3752	149	16	(	(	PUNCT
ejpam-3752	149	17	x1	x1	PROPN
ejpam-3752	149	18	,	,	PUNCT
ejpam-3752	149	19	x2	x2	PROPN
ejpam-3752	149	20	t	t	PROPN
ejpam-3752	149	21	)	)	PUNCT
ejpam-3752	149	22	.	.	PUNCT
ejpam-3752	150	1	then	then	ADV
ejpam-3752	150	2	0̃	0̃	PROPN
ejpam-3752	150	3	�	�	PROPN
ejpam-3752	150	4	x̃	x̃	PROPN
ejpam-3752	151	1	=	=	PUNCT
ejpam-3752	152	1	(	(	PUNCT
ejpam-3752	152	2	0	0	NUM
ejpam-3752	152	3	,	,	PUNCT
ejpam-3752	152	4	0	0	NUM
ejpam-3752	152	5	t	t	NOUN
ejpam-3752	152	6	)	)	PUNCT
ejpam-3752	152	7	�	�	PROPN
ejpam-3752	152	8	(	(	PUNCT
ejpam-3752	152	9	x1	x1	PROPN
ejpam-3752	152	10	,	,	PUNCT
ejpam-3752	152	11	x2	x2	PROPN
ejpam-3752	152	12	t	t	PROPN
ejpam-3752	152	13	)	)	PUNCT
ejpam-3752	153	1	=	=	PUNCT
ejpam-3752	153	2	(	(	PUNCT
ejpam-3752	153	3	0	0	NUM
ejpam-3752	153	4	·	·	SYM
ejpam-3752	153	5	x1	x1	NUM
ejpam-3752	153	6	,	,	PUNCT
ejpam-3752	153	7	(	(	PUNCT
ejpam-3752	153	8	0	0	NUM
ejpam-3752	153	9	·	·	PUNCT
ejpam-3752	153	10	x2)t	x2)t	ADJ
ejpam-3752	153	11	)	)	PUNCT
ejpam-3752	154	1	=	=	PUNCT
ejpam-3752	154	2	(	(	PUNCT
ejpam-3752	154	3	x1	x1	PROPN
ejpam-3752	154	4	,	,	PUNCT
ejpam-3752	154	5	x2	x2	PROPN
ejpam-3752	154	6	t	t	PROPN
ejpam-3752	154	7	)	)	PUNCT
ejpam-3752	154	8	(	(	PUNCT
ejpam-3752	154	9	(	(	PUNCT
ejpam-3752	154	10	up-2	up-2	NUM
ejpam-3752	154	11	)	)	PUNCT
ejpam-3752	154	12	)	)	PUNCT
ejpam-3752	155	1	=	=	PUNCT
ejpam-3752	155	2	x̃.	x̃.	ADJ
ejpam-3752	155	3	(	(	PUNCT
ejpam-3752	155	4	up-3	up-3	NOUN
ejpam-3752	155	5	)	)	PUNCT
ejpam-3752	155	6	let	let	VERB
ejpam-3752	155	7	x̃	x̃	PROPN
ejpam-3752	155	8	∈	∈	PROPN
ejpam-3752	155	9	x	x	X
ejpam-3752	155	10	×	×	NOUN
ejpam-3752	155	11	im(t	im(t	NOUN
ejpam-3752	155	12	)	)	PUNCT
ejpam-3752	155	13	where	where	SCONJ
ejpam-3752	155	14	x̃	x̃	PROPN
ejpam-3752	155	15	=	=	SYM
ejpam-3752	155	16	(	(	PUNCT
ejpam-3752	155	17	x1	x1	PROPN
ejpam-3752	155	18	,	,	PUNCT
ejpam-3752	155	19	x2	x2	PROPN
ejpam-3752	155	20	t	t	PROPN
ejpam-3752	155	21	)	)	PUNCT
ejpam-3752	155	22	.	.	PUNCT
ejpam-3752	156	1	then	then	ADV
ejpam-3752	156	2	x̃	x̃	PROPN
ejpam-3752	156	3	�	�	PROPN
ejpam-3752	156	4	0̃	0̃	PROPN
ejpam-3752	156	5	=	=	SYM
ejpam-3752	156	6	(	(	PUNCT
ejpam-3752	156	7	x1	x1	PROPN
ejpam-3752	156	8	,	,	PUNCT
ejpam-3752	156	9	x2	x2	PROPN
ejpam-3752	156	10	t	t	PROPN
ejpam-3752	156	11	)	)	PUNCT
ejpam-3752	156	12	�	�	PROPN
ejpam-3752	156	13	(	(	PUNCT
ejpam-3752	156	14	0	0	NUM
ejpam-3752	156	15	,	,	PUNCT
ejpam-3752	156	16	0	0	NUM
ejpam-3752	156	17	t	t	NOUN
ejpam-3752	156	18	)	)	PUNCT
ejpam-3752	156	19	=	=	SYM
ejpam-3752	157	1	(	(	PUNCT
ejpam-3752	157	2	x1	x1	PROPN
ejpam-3752	157	3	·	·	PUNCT
ejpam-3752	157	4	0	0	NUM
ejpam-3752	157	5	,	,	PUNCT
ejpam-3752	157	6	(	(	PUNCT
ejpam-3752	157	7	x2	x2	X
ejpam-3752	157	8	·	·	PUNCT
ejpam-3752	157	9	0)t	0)t	INTJ
ejpam-3752	157	10	)	)	PUNCT
ejpam-3752	158	1	=	=	PUNCT
ejpam-3752	158	2	(	(	PUNCT
ejpam-3752	158	3	0	0	NUM
ejpam-3752	158	4	,	,	PUNCT
ejpam-3752	158	5	0	0	NUM
ejpam-3752	158	6	t	t	NOUN
ejpam-3752	158	7	)	)	PUNCT
ejpam-3752	158	8	(	(	PUNCT
ejpam-3752	158	9	(	(	PUNCT
ejpam-3752	158	10	up-3	up-3	NOUN
ejpam-3752	158	11	)	)	PUNCT
ejpam-3752	158	12	)	)	PUNCT
ejpam-3752	159	1	=	=	SYM
ejpam-3752	159	2	0̃.	0̃.	NOUN
ejpam-3752	159	3	hence	hence	ADV
ejpam-3752	159	4	,	,	PUNCT
ejpam-3752	159	5	(	(	PUNCT
ejpam-3752	159	6	up-1	up-1	NOUN
ejpam-3752	159	7	)	)	PUNCT
ejpam-3752	159	8	,	,	PUNCT
ejpam-3752	159	9	(	(	PUNCT
ejpam-3752	159	10	up-2	up-2	NUM
ejpam-3752	159	11	)	)	PUNCT
ejpam-3752	159	12	,	,	PUNCT
ejpam-3752	159	13	and	and	CCONJ
ejpam-3752	159	14	(	(	PUNCT
ejpam-3752	159	15	up-3	up-3	NOUN
ejpam-3752	159	16	)	)	PUNCT
ejpam-3752	159	17	are	be	AUX
ejpam-3752	159	18	valid	valid	ADJ
ejpam-3752	159	19	.	.	PUNCT
ejpam-3752	160	1	a.	a.	PROPN
ejpam-3752	160	2	iampan	iampan	PROPN
ejpam-3752	160	3	,	,	PUNCT
ejpam-3752	160	4	m.	m.	PROPN
ejpam-3752	160	5	songsaeng	songsaeng	PROPN
ejpam-3752	160	6	,	,	PUNCT
ejpam-3752	160	7	g.	g.	PROPN
ejpam-3752	160	8	muhiuddin	muhiuddin	PROPN
ejpam-3752	160	9	/	/	SYM
ejpam-3752	160	10	eur	eur	PROPN
ejpam-3752	160	11	.	.	PUNCT
ejpam-3752	161	1	j.	j.	PROPN
ejpam-3752	161	2	pure	pure	PROPN
ejpam-3752	161	3	appl	appl	PROPN
ejpam-3752	161	4	.	.	PROPN
ejpam-3752	161	5	math	math	PROPN
ejpam-3752	161	6	,	,	PUNCT
ejpam-3752	161	7	13	13	NUM
ejpam-3752	161	8	(	(	PUNCT
ejpam-3752	161	9	3	3	NUM
ejpam-3752	161	10	)	)	PUNCT
ejpam-3752	161	11	(	(	PUNCT
ejpam-3752	161	12	2020	2020	NUM
ejpam-3752	161	13	)	)	PUNCT
ejpam-3752	161	14	,	,	PUNCT
ejpam-3752	161	15	459	459	NUM
ejpam-3752	161	16	-	-	SYM
ejpam-3752	161	17	471	471	NUM
ejpam-3752	161	18	464	464	NUM
ejpam-3752	161	19	proposition	proposition	NOUN
ejpam-3752	161	20	1	1	NUM
ejpam-3752	161	21	.	.	PUNCT
ejpam-3752	162	1	the	the	DET
ejpam-3752	162	2	algebra	algebra	NOUN
ejpam-3752	162	3	(	(	PUNCT
ejpam-3752	162	4	x	x	SYM
ejpam-3752	162	5	×	×	NOUN
ejpam-3752	162	6	im(t	im(t	ADJ
ejpam-3752	162	7	)	)	PUNCT
ejpam-3752	162	8	,	,	PUNCT
ejpam-3752	162	9	�	�	PROPN
ejpam-3752	162	10	,	,	PUNCT
ejpam-3752	162	11	0̃	0̃	PROPN
ejpam-3752	162	12	)	)	PUNCT
ejpam-3752	162	13	satisfies	satisfy	VERB
ejpam-3752	162	14	the	the	DET
ejpam-3752	162	15	following	follow	VERB
ejpam-3752	162	16	properties	property	NOUN
ejpam-3752	162	17	:	:	PUNCT
ejpam-3752	162	18	(	(	PUNCT
ejpam-3752	162	19	1	1	X
ejpam-3752	162	20	)	)	PUNCT
ejpam-3752	162	21	(	(	PUNCT
ejpam-3752	162	22	∀ã	∀ã	PROPN
ejpam-3752	162	23	∈	∈	PROPN
ejpam-3752	162	24	x	x	X
ejpam-3752	162	25	×	×	NOUN
ejpam-3752	162	26	im(t	im(t	NOUN
ejpam-3752	162	27	)	)	PUNCT
ejpam-3752	162	28	)	)	PUNCT
ejpam-3752	163	1	(	(	PUNCT
ejpam-3752	163	2	ã	ã	PROPN
ejpam-3752	163	3	�	�	PROPN
ejpam-3752	163	4	ã	ã	PROPN
ejpam-3752	163	5	)	)	PUNCT
ejpam-3752	163	6	,	,	PUNCT
ejpam-3752	163	7	(	(	PUNCT
ejpam-3752	163	8	2	2	X
ejpam-3752	163	9	)	)	PUNCT
ejpam-3752	163	10	(	(	PUNCT
ejpam-3752	163	11	∀ã	∀ã	PROPN
ejpam-3752	163	12	,	,	PUNCT
ejpam-3752	163	13	b̃	b̃	PROPN
ejpam-3752	163	14	,	,	PUNCT
ejpam-3752	163	15	c̃	c̃	PROPN
ejpam-3752	163	16	∈	∈	PROPN
ejpam-3752	164	1	x	x	SYM
ejpam-3752	164	2	×	×	NOUN
ejpam-3752	164	3	im(t	im(t	NOUN
ejpam-3752	164	4	)	)	PUNCT
ejpam-3752	164	5	)	)	PUNCT
ejpam-3752	165	1	(	(	PUNCT
ejpam-3752	165	2	ã	ã	PROPN
ejpam-3752	165	3	�	�	PROPN
ejpam-3752	165	4	b̃	b̃	PROPN
ejpam-3752	165	5	,	,	PUNCT
ejpam-3752	165	6	b̃	b̃	PROPN
ejpam-3752	165	7	�	�	PROPN
ejpam-3752	165	8	c̃⇒	c̃⇒	PROPN
ejpam-3752	165	9	ã	ã	PROPN
ejpam-3752	165	10	�	�	PROPN
ejpam-3752	165	11	c̃	c̃	PROPN
ejpam-3752	165	12	)	)	PUNCT
ejpam-3752	165	13	,	,	PUNCT
ejpam-3752	165	14	(	(	PUNCT
ejpam-3752	165	15	3	3	X
ejpam-3752	165	16	)	)	PUNCT
ejpam-3752	165	17	(	(	PUNCT
ejpam-3752	165	18	∀ã	∀ã	PROPN
ejpam-3752	165	19	,	,	PUNCT
ejpam-3752	165	20	b̃	b̃	PROPN
ejpam-3752	165	21	,	,	PUNCT
ejpam-3752	165	22	c̃	c̃	PROPN
ejpam-3752	165	23	∈	∈	PROPN
ejpam-3752	165	24	x	x	SYM
ejpam-3752	165	25	×	×	NOUN
ejpam-3752	165	26	im(t	im(t	NOUN
ejpam-3752	165	27	)	)	PUNCT
ejpam-3752	165	28	)	)	PUNCT
ejpam-3752	165	29	(	(	PUNCT
ejpam-3752	165	30	ã	ã	PROPN
ejpam-3752	165	31	�	�	PROPN
ejpam-3752	165	32	b̃⇒	b̃⇒	PROPN
ejpam-3752	165	33	c̃	c̃	PROPN
ejpam-3752	165	34	�	�	PROPN
ejpam-3752	165	35	ã	ã	PROPN
ejpam-3752	165	36	�	�	PROPN
ejpam-3752	165	37	c̃	c̃	PROPN
ejpam-3752	165	38	�	�	PROPN
ejpam-3752	165	39	b̃	b̃	PROPN
ejpam-3752	165	40	)	)	PUNCT
ejpam-3752	165	41	,	,	PUNCT
ejpam-3752	165	42	(	(	PUNCT
ejpam-3752	165	43	4	4	X
ejpam-3752	165	44	)	)	PUNCT
ejpam-3752	165	45	(	(	PUNCT
ejpam-3752	165	46	∀ã	∀ã	PROPN
ejpam-3752	165	47	,	,	PUNCT
ejpam-3752	165	48	b̃	b̃	PROPN
ejpam-3752	165	49	,	,	PUNCT
ejpam-3752	165	50	c̃	c̃	PROPN
ejpam-3752	165	51	∈	∈	PROPN
ejpam-3752	165	52	x	x	SYM
ejpam-3752	165	53	×	×	NOUN
ejpam-3752	165	54	im(t	im(t	NOUN
ejpam-3752	165	55	)	)	PUNCT
ejpam-3752	165	56	)	)	PUNCT
ejpam-3752	165	57	(	(	PUNCT
ejpam-3752	165	58	ã	ã	PROPN
ejpam-3752	165	59	�	�	PROPN
ejpam-3752	165	60	b̃⇒	b̃⇒	PROPN
ejpam-3752	165	61	b̃	b̃	PROPN
ejpam-3752	165	62	�	�	PROPN
ejpam-3752	165	63	c̃	c̃	PROPN
ejpam-3752	165	64	�	�	PROPN
ejpam-3752	165	65	ã	ã	PROPN
ejpam-3752	165	66	�	�	PROPN
ejpam-3752	165	67	c̃	c̃	PROPN
ejpam-3752	165	68	)	)	PUNCT
ejpam-3752	165	69	,	,	PUNCT
ejpam-3752	165	70	(	(	PUNCT
ejpam-3752	165	71	5	5	X
ejpam-3752	165	72	)	)	PUNCT
ejpam-3752	165	73	(	(	PUNCT
ejpam-3752	165	74	∀ã	∀ã	PROPN
ejpam-3752	165	75	,	,	PUNCT
ejpam-3752	165	76	b̃	b̃	PROPN
ejpam-3752	165	77	∈	∈	PROPN
ejpam-3752	165	78	x	x	X
ejpam-3752	165	79	×	×	NOUN
ejpam-3752	165	80	im(t	im(t	NOUN
ejpam-3752	165	81	)	)	PUNCT
ejpam-3752	165	82	)	)	PUNCT
ejpam-3752	165	83	(	(	PUNCT
ejpam-3752	165	84	ã	ã	PROPN
ejpam-3752	165	85	�	�	PROPN
ejpam-3752	165	86	b̃	b̃	PROPN
ejpam-3752	165	87	�	�	PROPN
ejpam-3752	165	88	ã	ã	PROPN
ejpam-3752	165	89	)	)	PUNCT
ejpam-3752	165	90	,	,	PUNCT
ejpam-3752	165	91	(	(	PUNCT
ejpam-3752	165	92	6	6	NUM
ejpam-3752	165	93	)	)	PUNCT
ejpam-3752	165	94	(	(	PUNCT
ejpam-3752	165	95	∀ã	∀ã	PROPN
ejpam-3752	165	96	,	,	PUNCT
ejpam-3752	165	97	b̃	b̃	PROPN
ejpam-3752	165	98	∈	∈	PROPN
ejpam-3752	165	99	x	x	X
ejpam-3752	165	100	×	×	NOUN
ejpam-3752	165	101	im(t	im(t	NOUN
ejpam-3752	165	102	)	)	PUNCT
ejpam-3752	165	103	)	)	PUNCT
ejpam-3752	165	104	(	(	PUNCT
ejpam-3752	165	105	ã	ã	PROPN
ejpam-3752	165	106	�	�	PROPN
ejpam-3752	165	107	b̃	b̃	PROPN
ejpam-3752	165	108	�	�	PROPN
ejpam-3752	165	109	b̃	b̃	PROPN
ejpam-3752	165	110	)	)	PUNCT
ejpam-3752	165	111	,	,	PUNCT
ejpam-3752	165	112	(	(	PUNCT
ejpam-3752	165	113	7	7	X
ejpam-3752	165	114	)	)	PUNCT
ejpam-3752	165	115	(	(	PUNCT
ejpam-3752	165	116	∀x̃	∀x̃	NOUN
ejpam-3752	165	117	,	,	PUNCT
ejpam-3752	165	118	ã	ã	PROPN
ejpam-3752	165	119	,	,	PUNCT
ejpam-3752	165	120	b̃	b̃	PROPN
ejpam-3752	165	121	,	,	PUNCT
ejpam-3752	165	122	c̃	c̃	PROPN
ejpam-3752	165	123	∈	∈	PROPN
ejpam-3752	166	1	x	x	SYM
ejpam-3752	167	1	×	×	NOUN
ejpam-3752	167	2	im(t	im(t	NOUN
ejpam-3752	167	3	)	)	PUNCT
ejpam-3752	167	4	)	)	PUNCT
ejpam-3752	168	1	(	(	PUNCT
ejpam-3752	168	2	ã	ã	PROPN
ejpam-3752	168	3	�	�	PROPN
ejpam-3752	168	4	(	(	PUNCT
ejpam-3752	168	5	b̃	b̃	PROPN
ejpam-3752	168	6	�	�	PROPN
ejpam-3752	168	7	c̃	c̃	PROPN
ejpam-3752	168	8	)	)	PUNCT
ejpam-3752	168	9	�	�	PROPN
ejpam-3752	168	10	ã	ã	PROPN
ejpam-3752	168	11	�	�	PROPN
ejpam-3752	168	12	(	(	PUNCT
ejpam-3752	168	13	(	(	PUNCT
ejpam-3752	168	14	x̃	x̃	PROPN
ejpam-3752	168	15	�	�	PROPN
ejpam-3752	168	16	b̃	b̃	PROPN
ejpam-3752	168	17	)	)	PUNCT
ejpam-3752	168	18	�	�	PROPN
ejpam-3752	168	19	(	(	PUNCT
ejpam-3752	168	20	x̃	x̃	PROPN
ejpam-3752	168	21	�	�	PROPN
ejpam-3752	168	22	c̃	c̃	PROPN
ejpam-3752	168	23	)	)	PUNCT
ejpam-3752	168	24	)	)	PUNCT
ejpam-3752	168	25	)	)	PUNCT
ejpam-3752	168	26	,	,	PUNCT
ejpam-3752	168	27	(	(	PUNCT
ejpam-3752	168	28	8)	8)	NUM
ejpam-3752	168	29	(	(	PUNCT
ejpam-3752	168	30	∀x̃	∀x̃	NOUN
ejpam-3752	168	31	,	,	PUNCT
ejpam-3752	168	32	ã	ã	PROPN
ejpam-3752	168	33	,	,	PUNCT
ejpam-3752	168	34	b̃	b̃	PROPN
ejpam-3752	168	35	,	,	PUNCT
ejpam-3752	168	36	c̃	c̃	PROPN
ejpam-3752	168	37	∈	∈	PROPN
ejpam-3752	168	38	x	x	SYM
ejpam-3752	168	39	×	×	NOUN
ejpam-3752	168	40	im(t	im(t	NOUN
ejpam-3752	168	41	)	)	PUNCT
ejpam-3752	168	42	)	)	PUNCT
ejpam-3752	168	43	(	(	PUNCT
ejpam-3752	168	44	(	(	PUNCT
ejpam-3752	168	45	(	(	PUNCT
ejpam-3752	168	46	x̃	x̃	PROPN
ejpam-3752	168	47	�	�	PROPN
ejpam-3752	168	48	ã	ã	PROPN
ejpam-3752	168	49	)	)	PUNCT
ejpam-3752	168	50	�	�	PROPN
ejpam-3752	168	51	(	(	PUNCT
ejpam-3752	168	52	x̃	x̃	PROPN
ejpam-3752	168	53	�	�	PROPN
ejpam-3752	168	54	b̃	b̃	PROPN
ejpam-3752	168	55	)	)	PUNCT
ejpam-3752	168	56	)	)	PUNCT
ejpam-3752	168	57	�	�	PROPN
ejpam-3752	168	58	c̃	c̃	PROPN
ejpam-3752	168	59	�	�	PROPN
ejpam-3752	168	60	(	(	PUNCT
ejpam-3752	168	61	ã	ã	PROPN
ejpam-3752	168	62	�	�	PROPN
ejpam-3752	168	63	b̃	b̃	PROPN
ejpam-3752	168	64	)	)	PUNCT
ejpam-3752	168	65	�	�	PROPN
ejpam-3752	168	66	c̃	c̃	PROPN
ejpam-3752	168	67	)	)	PUNCT
ejpam-3752	168	68	,	,	PUNCT
ejpam-3752	168	69	(	(	PUNCT
ejpam-3752	168	70	9	9	X
ejpam-3752	168	71	)	)	PUNCT
ejpam-3752	168	72	(	(	PUNCT
ejpam-3752	168	73	∀ã	∀ã	PROPN
ejpam-3752	168	74	,	,	PUNCT
ejpam-3752	168	75	b̃	b̃	PROPN
ejpam-3752	168	76	,	,	PUNCT
ejpam-3752	168	77	c̃	c̃	PROPN
ejpam-3752	168	78	∈	∈	PROPN
ejpam-3752	168	79	x	x	SYM
ejpam-3752	168	80	×	×	NOUN
ejpam-3752	168	81	im(t	im(t	NOUN
ejpam-3752	168	82	)	)	PUNCT
ejpam-3752	168	83	)	)	PUNCT
ejpam-3752	168	84	(	(	PUNCT
ejpam-3752	168	85	(	(	PUNCT
ejpam-3752	168	86	ã	ã	PROPN
ejpam-3752	168	87	�	�	PROPN
ejpam-3752	168	88	b̃	b̃	PROPN
ejpam-3752	168	89	)	)	PUNCT
ejpam-3752	168	90	�	�	PROPN
ejpam-3752	168	91	c̃	c̃	PROPN
ejpam-3752	168	92	�	�	PROPN
ejpam-3752	168	93	b̃	b̃	PROPN
ejpam-3752	168	94	�	�	PROPN
ejpam-3752	168	95	c̃	c̃	PROPN
ejpam-3752	168	96	)	)	PUNCT
ejpam-3752	168	97	,	,	PUNCT
ejpam-3752	168	98	(	(	PUNCT
ejpam-3752	168	99	10	10	NUM
ejpam-3752	168	100	)	)	PUNCT
ejpam-3752	168	101	(	(	PUNCT
ejpam-3752	168	102	∀ã	∀ã	PROPN
ejpam-3752	168	103	,	,	PUNCT
ejpam-3752	168	104	b̃	b̃	PROPN
ejpam-3752	168	105	,	,	PUNCT
ejpam-3752	168	106	c̃	c̃	PROPN
ejpam-3752	168	107	∈	∈	PROPN
ejpam-3752	168	108	x	x	SYM
ejpam-3752	168	109	×	×	NOUN
ejpam-3752	168	110	im(t	im(t	NOUN
ejpam-3752	168	111	)	)	PUNCT
ejpam-3752	168	112	)	)	PUNCT
ejpam-3752	168	113	(	(	PUNCT
ejpam-3752	168	114	ã	ã	PROPN
ejpam-3752	168	115	�	�	PROPN
ejpam-3752	168	116	b̃⇒	b̃⇒	PROPN
ejpam-3752	168	117	ã	ã	PROPN
ejpam-3752	168	118	�	�	PROPN
ejpam-3752	168	119	c̃	c̃	PROPN
ejpam-3752	168	120	�	�	PROPN
ejpam-3752	168	121	b̃	b̃	PROPN
ejpam-3752	168	122	)	)	PUNCT
ejpam-3752	168	123	,	,	PUNCT
ejpam-3752	168	124	(	(	PUNCT
ejpam-3752	168	125	11	11	NUM
ejpam-3752	168	126	)	)	PUNCT
ejpam-3752	168	127	(	(	PUNCT
ejpam-3752	168	128	∀ã	∀ã	PROPN
ejpam-3752	168	129	,	,	PUNCT
ejpam-3752	168	130	b̃	b̃	PROPN
ejpam-3752	168	131	,	,	PUNCT
ejpam-3752	168	132	c̃	c̃	PROPN
ejpam-3752	168	133	∈	∈	PROPN
ejpam-3752	168	134	x	x	SYM
ejpam-3752	168	135	×	×	NOUN
ejpam-3752	168	136	im(t	im(t	NOUN
ejpam-3752	168	137	)	)	PUNCT
ejpam-3752	168	138	)	)	PUNCT
ejpam-3752	168	139	(	(	PUNCT
ejpam-3752	168	140	(	(	PUNCT
ejpam-3752	168	141	ã	ã	PROPN
ejpam-3752	168	142	�	�	PROPN
ejpam-3752	168	143	b̃	b̃	PROPN
ejpam-3752	168	144	)	)	PUNCT
ejpam-3752	168	145	�	�	PROPN
ejpam-3752	168	146	c̃	c̃	PROPN
ejpam-3752	168	147	�	�	PROPN
ejpam-3752	168	148	ã	ã	PROPN
ejpam-3752	168	149	�	�	PROPN
ejpam-3752	168	150	(	(	PUNCT
ejpam-3752	168	151	b̃	b̃	PROPN
ejpam-3752	168	152	�	�	PROPN
ejpam-3752	168	153	c̃	c̃	PROPN
ejpam-3752	168	154	)	)	PUNCT
ejpam-3752	168	155	)	)	PUNCT
ejpam-3752	168	156	,	,	PUNCT
ejpam-3752	168	157	and	and	CCONJ
ejpam-3752	168	158	(	(	PUNCT
ejpam-3752	168	159	12	12	NUM
ejpam-3752	168	160	)	)	PUNCT
ejpam-3752	168	161	(	(	PUNCT
ejpam-3752	168	162	∀x̃	∀x̃	NOUN
ejpam-3752	168	163	,	,	PUNCT
ejpam-3752	168	164	ã	ã	PROPN
ejpam-3752	168	165	,	,	PUNCT
ejpam-3752	168	166	b̃	b̃	PROPN
ejpam-3752	168	167	,	,	PUNCT
ejpam-3752	168	168	c̃	c̃	PROPN
ejpam-3752	168	169	∈	∈	PROPN
ejpam-3752	168	170	x	x	SYM
ejpam-3752	168	171	×	×	NOUN
ejpam-3752	168	172	im(t	im(t	NOUN
ejpam-3752	168	173	)	)	PUNCT
ejpam-3752	168	174	)	)	PUNCT
ejpam-3752	168	175	(	(	PUNCT
ejpam-3752	168	176	(	(	PUNCT
ejpam-3752	168	177	ã	ã	PROPN
ejpam-3752	168	178	�	�	PROPN
ejpam-3752	168	179	b̃	b̃	PROPN
ejpam-3752	168	180	)	)	PUNCT
ejpam-3752	168	181	�	�	PROPN
ejpam-3752	168	182	c̃	c̃	PROPN
ejpam-3752	168	183	�	�	PROPN
ejpam-3752	168	184	b̃	b̃	PROPN
ejpam-3752	168	185	�	�	PROPN
ejpam-3752	168	186	(	(	PUNCT
ejpam-3752	168	187	x̃	x̃	PROPN
ejpam-3752	168	188	�	�	PROPN
ejpam-3752	168	189	c̃	c̃	PROPN
ejpam-3752	168	190	)	)	PUNCT
ejpam-3752	168	191	)	)	PUNCT
ejpam-3752	168	192	.	.	PUNCT
ejpam-3752	169	1	proof	proof	NOUN
ejpam-3752	169	2	.	.	PUNCT
ejpam-3752	170	1	by	by	ADP
ejpam-3752	170	2	theorem	theorem	NOUN
ejpam-3752	170	3	1	1	NUM
ejpam-3752	170	4	,	,	PUNCT
ejpam-3752	170	5	the	the	DET
ejpam-3752	170	6	algebra	algebra	NOUN
ejpam-3752	170	7	(	(	PUNCT
ejpam-3752	170	8	x	x	SYM
ejpam-3752	170	9	×	×	NOUN
ejpam-3752	170	10	im(t	im(t	ADJ
ejpam-3752	170	11	)	)	PUNCT
ejpam-3752	170	12	,	,	PUNCT
ejpam-3752	170	13	�	�	PROPN
ejpam-3752	170	14	,	,	PUNCT
ejpam-3752	170	15	0̃	0̃	PROPN
ejpam-3752	170	16	)	)	PUNCT
ejpam-3752	170	17	satisfies	satisfy	VERB
ejpam-3752	170	18	the	the	DET
ejpam-3752	170	19	axioms	axiom	NOUN
ejpam-3752	170	20	(	(	PUNCT
ejpam-3752	170	21	up-1	up-1	NUM
ejpam-3752	170	22	)	)	PUNCT
ejpam-3752	170	23	,	,	PUNCT
ejpam-3752	170	24	(	(	PUNCT
ejpam-3752	170	25	up-2	up-2	NUM
ejpam-3752	170	26	)	)	PUNCT
ejpam-3752	170	27	,	,	PUNCT
ejpam-3752	170	28	and	and	CCONJ
ejpam-3752	170	29	(	(	PUNCT
ejpam-3752	170	30	up-3	up-3	NOUN
ejpam-3752	170	31	)	)	PUNCT
ejpam-3752	170	32	.	.	PUNCT
ejpam-3752	171	1	(	(	PUNCT
ejpam-3752	171	2	1	1	X
ejpam-3752	171	3	)	)	PUNCT
ejpam-3752	171	4	let	let	VERB
ejpam-3752	171	5	ã	ã	PROPN
ejpam-3752	171	6	∈	∈	PROPN
ejpam-3752	171	7	x	x	SYM
ejpam-3752	171	8	×	×	NOUN
ejpam-3752	171	9	im(t	im(t	ADJ
ejpam-3752	171	10	)	)	PUNCT
ejpam-3752	171	11	.	.	PUNCT
ejpam-3752	172	1	then	then	ADV
ejpam-3752	172	2	0̃	0̃	NOUN
ejpam-3752	172	3	=	=	SYM
ejpam-3752	172	4	(	(	PUNCT
ejpam-3752	172	5	0̃	0̃	PROPN
ejpam-3752	172	6	�	�	PROPN
ejpam-3752	172	7	ã	ã	PROPN
ejpam-3752	172	8	)	)	PUNCT
ejpam-3752	172	9	�	�	PROPN
ejpam-3752	172	10	(	(	PUNCT
ejpam-3752	172	11	(	(	PUNCT
ejpam-3752	172	12	0̃	0̃	NOUN
ejpam-3752	172	13	�	�	PROPN
ejpam-3752	172	14	0̃	0̃	NOUN
ejpam-3752	172	15	)	)	PUNCT
ejpam-3752	172	16	�	�	PROPN
ejpam-3752	172	17	(	(	PUNCT
ejpam-3752	172	18	0̃	0̃	PROPN
ejpam-3752	172	19	�	�	PROPN
ejpam-3752	172	20	ã	ã	PROPN
ejpam-3752	172	21	)	)	PUNCT
ejpam-3752	172	22	)	)	PUNCT
ejpam-3752	172	23	(	(	PUNCT
ejpam-3752	172	24	(	(	PUNCT
ejpam-3752	172	25	up-1	up-1	NOUN
ejpam-3752	172	26	)	)	PUNCT
ejpam-3752	172	27	)	)	PUNCT
ejpam-3752	173	1	=	=	PRON
ejpam-3752	173	2	(	(	PUNCT
ejpam-3752	173	3	0̃	0̃	PROPN
ejpam-3752	173	4	�	�	PROPN
ejpam-3752	173	5	ã	ã	PROPN
ejpam-3752	173	6	)	)	PUNCT
ejpam-3752	173	7	�	�	PROPN
ejpam-3752	173	8	(	(	PUNCT
ejpam-3752	173	9	0̃	0̃	PROPN
ejpam-3752	173	10	�	�	PROPN
ejpam-3752	173	11	ã	ã	PROPN
ejpam-3752	173	12	)	)	PUNCT
ejpam-3752	173	13	(	(	PUNCT
ejpam-3752	173	14	(	(	PUNCT
ejpam-3752	173	15	up-2	up-2	NUM
ejpam-3752	173	16	)	)	PUNCT
ejpam-3752	173	17	)	)	PUNCT
ejpam-3752	174	1	=	=	PUNCT
ejpam-3752	174	2	ã	ã	PROPN
ejpam-3752	174	3	�	�	PROPN
ejpam-3752	174	4	ã.	ã.	PROPN
ejpam-3752	174	5	(	(	PUNCT
ejpam-3752	174	6	(	(	PUNCT
ejpam-3752	174	7	up-2	up-2	NUM
ejpam-3752	174	8	)	)	PUNCT
ejpam-3752	174	9	)	)	PUNCT
ejpam-3752	174	10	hence	hence	ADV
ejpam-3752	174	11	,	,	PUNCT
ejpam-3752	174	12	ã	ã	PROPN
ejpam-3752	174	13	�	�	PROPN
ejpam-3752	174	14	ã.	ã.	PROPN
ejpam-3752	174	15	(	(	PUNCT
ejpam-3752	174	16	2	2	X
ejpam-3752	174	17	)	)	PUNCT
ejpam-3752	174	18	let	let	VERB
ejpam-3752	174	19	ã	ã	PROPN
ejpam-3752	174	20	,	,	PUNCT
ejpam-3752	174	21	b̃	b̃	PROPN
ejpam-3752	174	22	,	,	PUNCT
ejpam-3752	174	23	c̃	c̃	PROPN
ejpam-3752	174	24	∈	∈	PROPN
ejpam-3752	174	25	x×im(t	x×im(t	PROPN
ejpam-3752	174	26	)	)	PUNCT
ejpam-3752	174	27	be	be	AUX
ejpam-3752	174	28	such	such	ADJ
ejpam-3752	174	29	that	that	SCONJ
ejpam-3752	174	30	ã	ã	PROPN
ejpam-3752	174	31	�	�	PROPN
ejpam-3752	174	32	b̃	b̃	PROPN
ejpam-3752	174	33	and	and	CCONJ
ejpam-3752	174	34	b̃	b̃	PROPN
ejpam-3752	174	35	�	�	PROPN
ejpam-3752	174	36	c̃.	c̃.	PROPN
ejpam-3752	174	37	then	then	ADV
ejpam-3752	174	38	ã	ã	PROPN
ejpam-3752	174	39	�	�	PROPN
ejpam-3752	174	40	b̃	b̃	PROPN
ejpam-3752	174	41	=	=	PUNCT
ejpam-3752	174	42	0̃	0̃	PROPN
ejpam-3752	174	43	and	and	CCONJ
ejpam-3752	174	44	b̃	b̃	PROPN
ejpam-3752	174	45	�	�	PROPN
ejpam-3752	175	1	c̃	c̃	PROPN
ejpam-3752	175	2	=	=	PROPN
ejpam-3752	175	3	0̃.	0̃.	NOUN
ejpam-3752	176	1	thus	thus	ADV
ejpam-3752	176	2	ã	ã	PROPN
ejpam-3752	176	3	�	�	PROPN
ejpam-3752	176	4	c̃	c̃	PROPN
ejpam-3752	176	5	=	=	PUNCT
ejpam-3752	176	6	0̃	0̃	PROPN
ejpam-3752	176	7	�	�	PROPN
ejpam-3752	176	8	(	(	PUNCT
ejpam-3752	176	9	0̃	0̃	PROPN
ejpam-3752	176	10	�	�	PROPN
ejpam-3752	176	11	(	(	PUNCT
ejpam-3752	176	12	ã	ã	PROPN
ejpam-3752	176	13	�	�	PROPN
ejpam-3752	176	14	c̃	c̃	PROPN
ejpam-3752	176	15	)	)	PUNCT
ejpam-3752	176	16	)	)	PUNCT
ejpam-3752	177	1	(	(	PUNCT
ejpam-3752	177	2	(	(	PUNCT
ejpam-3752	177	3	up-2	up-2	NUM
ejpam-3752	177	4	)	)	PUNCT
ejpam-3752	177	5	)	)	PUNCT
ejpam-3752	178	1	=	=	PRON
ejpam-3752	178	2	(	(	PUNCT
ejpam-3752	178	3	b̃	b̃	PROPN
ejpam-3752	178	4	�	�	PROPN
ejpam-3752	178	5	c̃	c̃	PROPN
ejpam-3752	178	6	)	)	PUNCT
ejpam-3752	178	7	�	�	PROPN
ejpam-3752	178	8	(	(	PUNCT
ejpam-3752	178	9	(	(	PUNCT
ejpam-3752	178	10	ã	ã	PROPN
ejpam-3752	178	11	�	�	PROPN
ejpam-3752	178	12	b̃	b̃	PROPN
ejpam-3752	178	13	)	)	PUNCT
ejpam-3752	178	14	�	�	PROPN
ejpam-3752	178	15	(	(	PUNCT
ejpam-3752	178	16	ã	ã	PROPN
ejpam-3752	178	17	�	�	PROPN
ejpam-3752	178	18	c̃	c̃	PROPN
ejpam-3752	178	19	)	)	PUNCT
ejpam-3752	178	20	)	)	PUNCT
ejpam-3752	179	1	=	=	PUNCT
ejpam-3752	179	2	0̃.	0̃.	NOUN
ejpam-3752	179	3	(	(	PUNCT
ejpam-3752	179	4	(	(	PUNCT
ejpam-3752	179	5	up-1	up-1	NOUN
ejpam-3752	179	6	)	)	PUNCT
ejpam-3752	179	7	)	)	PUNCT
ejpam-3752	179	8	hence	hence	ADV
ejpam-3752	179	9	,	,	PUNCT
ejpam-3752	179	10	ã	ã	PROPN
ejpam-3752	179	11	�	�	PROPN
ejpam-3752	179	12	c̃.	c̃.	PROPN
ejpam-3752	179	13	(	(	PUNCT
ejpam-3752	179	14	3	3	X
ejpam-3752	179	15	)	)	PUNCT
ejpam-3752	179	16	let	let	VERB
ejpam-3752	179	17	ã	ã	PROPN
ejpam-3752	179	18	,	,	PUNCT
ejpam-3752	179	19	b̃	b̃	PROPN
ejpam-3752	179	20	∈	∈	PROPN
ejpam-3752	179	21	x	x	X
ejpam-3752	179	22	×	×	NOUN
ejpam-3752	179	23	im(t	im(t	VERB
ejpam-3752	179	24	)	)	PUNCT
ejpam-3752	179	25	be	be	AUX
ejpam-3752	179	26	such	such	ADJ
ejpam-3752	179	27	that	that	SCONJ
ejpam-3752	179	28	ã	ã	PROPN
ejpam-3752	179	29	�	�	PROPN
ejpam-3752	179	30	b̃.	b̃.	PROPN
ejpam-3752	179	31	then	then	ADV
ejpam-3752	179	32	ã	ã	PROPN
ejpam-3752	179	33	�	�	PROPN
ejpam-3752	179	34	b̃	b̃	PROPN
ejpam-3752	179	35	=	=	PROPN
ejpam-3752	180	1	0̃.	0̃.	PROPN
ejpam-3752	180	2	(	(	PUNCT
ejpam-3752	180	3	c̃	c̃	PROPN
ejpam-3752	180	4	�	�	PROPN
ejpam-3752	180	5	ã	ã	PROPN
ejpam-3752	180	6	)	)	PUNCT
ejpam-3752	180	7	�	�	PROPN
ejpam-3752	180	8	(	(	PUNCT
ejpam-3752	180	9	c̃	c̃	PROPN
ejpam-3752	180	10	�	�	PROPN
ejpam-3752	180	11	b̃	b̃	PROPN
ejpam-3752	180	12	)	)	PUNCT
ejpam-3752	181	1	=	=	SYM
ejpam-3752	181	2	0̃	0̃	PROPN
ejpam-3752	181	3	�	�	PROPN
ejpam-3752	181	4	(	(	PUNCT
ejpam-3752	181	5	(	(	PUNCT
ejpam-3752	181	6	c̃	c̃	PROPN
ejpam-3752	181	7	�	�	PROPN
ejpam-3752	181	8	ã	ã	PROPN
ejpam-3752	181	9	)	)	PUNCT
ejpam-3752	181	10	�	�	PROPN
ejpam-3752	181	11	(	(	PUNCT
ejpam-3752	181	12	c̃	c̃	PROPN
ejpam-3752	181	13	�	�	PROPN
ejpam-3752	181	14	b̃	b̃	PROPN
ejpam-3752	181	15	)	)	PUNCT
ejpam-3752	181	16	)	)	PUNCT
ejpam-3752	181	17	(	(	PUNCT
ejpam-3752	181	18	(	(	PUNCT
ejpam-3752	181	19	up-2	up-2	NUM
ejpam-3752	181	20	)	)	PUNCT
ejpam-3752	181	21	)	)	PUNCT
ejpam-3752	182	1	a.	a.	NOUN
ejpam-3752	182	2	iampan	iampan	PROPN
ejpam-3752	182	3	,	,	PUNCT
ejpam-3752	182	4	m.	m.	PROPN
ejpam-3752	182	5	songsaeng	songsaeng	PROPN
ejpam-3752	182	6	,	,	PUNCT
ejpam-3752	182	7	g.	g.	PROPN
ejpam-3752	182	8	muhiuddin	muhiuddin	PROPN
ejpam-3752	182	9	/	/	SYM
ejpam-3752	182	10	eur	eur	PROPN
ejpam-3752	182	11	.	.	PUNCT
ejpam-3752	183	1	j.	j.	PROPN
ejpam-3752	183	2	pure	pure	PROPN
ejpam-3752	183	3	appl	appl	PROPN
ejpam-3752	183	4	.	.	PROPN
ejpam-3752	183	5	math	math	PROPN
ejpam-3752	183	6	,	,	PUNCT
ejpam-3752	183	7	13	13	NUM
ejpam-3752	183	8	(	(	PUNCT
ejpam-3752	183	9	3	3	NUM
ejpam-3752	183	10	)	)	PUNCT
ejpam-3752	183	11	(	(	PUNCT
ejpam-3752	183	12	2020	2020	NUM
ejpam-3752	183	13	)	)	PUNCT
ejpam-3752	183	14	,	,	PUNCT
ejpam-3752	183	15	459	459	NUM
ejpam-3752	183	16	-	-	SYM
ejpam-3752	183	17	471	471	NUM
ejpam-3752	183	18	465	465	NUM
ejpam-3752	183	19	=	=	SYM
ejpam-3752	183	20	(	(	PUNCT
ejpam-3752	183	21	ã	ã	PROPN
ejpam-3752	183	22	�	�	PROPN
ejpam-3752	183	23	b̃	b̃	PROPN
ejpam-3752	183	24	)	)	PUNCT
ejpam-3752	183	25	�	�	PROPN
ejpam-3752	183	26	(	(	PUNCT
ejpam-3752	183	27	(	(	PUNCT
ejpam-3752	183	28	c̃	c̃	PROPN
ejpam-3752	183	29	�	�	PROPN
ejpam-3752	183	30	ã	ã	PROPN
ejpam-3752	183	31	)	)	PUNCT
ejpam-3752	183	32	�	�	PROPN
ejpam-3752	183	33	(	(	PUNCT
ejpam-3752	183	34	c̃	c̃	PROPN
ejpam-3752	183	35	�	�	PROPN
ejpam-3752	183	36	b̃	b̃	PROPN
ejpam-3752	183	37	)	)	PUNCT
ejpam-3752	183	38	)	)	PUNCT
ejpam-3752	184	1	=	=	PUNCT
ejpam-3752	184	2	0̃.	0̃.	NOUN
ejpam-3752	184	3	(	(	PUNCT
ejpam-3752	184	4	(	(	PUNCT
ejpam-3752	184	5	up-1	up-1	NOUN
ejpam-3752	184	6	)	)	PUNCT
ejpam-3752	184	7	)	)	PUNCT
ejpam-3752	185	1	hence	hence	ADV
ejpam-3752	185	2	,	,	PUNCT
ejpam-3752	185	3	c̃	c̃	PROPN
ejpam-3752	185	4	�	�	PROPN
ejpam-3752	185	5	ã	ã	PROPN
ejpam-3752	185	6	�	�	PROPN
ejpam-3752	185	7	c̃	c̃	PROPN
ejpam-3752	185	8	�	�	PROPN
ejpam-3752	185	9	b̃.	b̃.	NOUN
ejpam-3752	185	10	(	(	PUNCT
ejpam-3752	185	11	4	4	X
ejpam-3752	185	12	)	)	PUNCT
ejpam-3752	185	13	let	let	VERB
ejpam-3752	185	14	ã	ã	PROPN
ejpam-3752	185	15	,	,	PUNCT
ejpam-3752	185	16	b̃	b̃	PROPN
ejpam-3752	185	17	∈	∈	PROPN
ejpam-3752	185	18	x	x	X
ejpam-3752	185	19	×	×	NOUN
ejpam-3752	185	20	im(t	im(t	VERB
ejpam-3752	185	21	)	)	PUNCT
ejpam-3752	185	22	be	be	AUX
ejpam-3752	185	23	such	such	ADJ
ejpam-3752	185	24	that	that	SCONJ
ejpam-3752	185	25	ã	ã	PROPN
ejpam-3752	185	26	�	�	PROPN
ejpam-3752	185	27	b̃.	b̃.	PROPN
ejpam-3752	185	28	then	then	ADV
ejpam-3752	185	29	ã	ã	PROPN
ejpam-3752	185	30	�	�	PROPN
ejpam-3752	185	31	b̃	b̃	PROPN
ejpam-3752	185	32	=	=	PROPN
ejpam-3752	186	1	0̃.	0̃.	PROPN
ejpam-3752	187	1	(	(	PUNCT
ejpam-3752	187	2	b̃	b̃	PROPN
ejpam-3752	187	3	�	�	PROPN
ejpam-3752	187	4	c̃	c̃	PROPN
ejpam-3752	187	5	)	)	PUNCT
ejpam-3752	187	6	�	�	PROPN
ejpam-3752	187	7	(	(	PUNCT
ejpam-3752	187	8	ã	ã	PROPN
ejpam-3752	187	9	�	�	PROPN
ejpam-3752	187	10	c̃	c̃	PROPN
ejpam-3752	187	11	)	)	PUNCT
ejpam-3752	187	12	=	=	PUNCT
ejpam-3752	188	1	(	(	PUNCT
ejpam-3752	188	2	b̃	b̃	PROPN
ejpam-3752	188	3	�	�	PROPN
ejpam-3752	188	4	c̃	c̃	PROPN
ejpam-3752	188	5	)	)	PUNCT
ejpam-3752	188	6	�	�	PROPN
ejpam-3752	188	7	(	(	PUNCT
ejpam-3752	188	8	0̃	0̃	PROPN
ejpam-3752	188	9	�	�	PROPN
ejpam-3752	188	10	(	(	PUNCT
ejpam-3752	188	11	ã	ã	PROPN
ejpam-3752	188	12	�	�	PROPN
ejpam-3752	188	13	c̃	c̃	PROPN
ejpam-3752	188	14	)	)	PUNCT
ejpam-3752	188	15	)	)	PUNCT
ejpam-3752	189	1	(	(	PUNCT
ejpam-3752	189	2	(	(	PUNCT
ejpam-3752	189	3	up-2	up-2	NUM
ejpam-3752	189	4	)	)	PUNCT
ejpam-3752	189	5	)	)	PUNCT
ejpam-3752	190	1	=	=	PRON
ejpam-3752	190	2	(	(	PUNCT
ejpam-3752	190	3	b̃	b̃	PROPN
ejpam-3752	190	4	�	�	PROPN
ejpam-3752	190	5	c̃	c̃	PROPN
ejpam-3752	190	6	)	)	PUNCT
ejpam-3752	190	7	�	�	PROPN
ejpam-3752	190	8	(	(	PUNCT
ejpam-3752	190	9	(	(	PUNCT
ejpam-3752	190	10	ã	ã	PROPN
ejpam-3752	190	11	�	�	PROPN
ejpam-3752	190	12	b̃	b̃	PROPN
ejpam-3752	190	13	)	)	PUNCT
ejpam-3752	190	14	�	�	PROPN
ejpam-3752	190	15	(	(	PUNCT
ejpam-3752	190	16	ã	ã	PROPN
ejpam-3752	190	17	�	�	PROPN
ejpam-3752	190	18	c̃	c̃	PROPN
ejpam-3752	190	19	)	)	PUNCT
ejpam-3752	190	20	)	)	PUNCT
ejpam-3752	191	1	=	=	PUNCT
ejpam-3752	191	2	0̃.	0̃.	NOUN
ejpam-3752	191	3	(	(	PUNCT
ejpam-3752	191	4	(	(	PUNCT
ejpam-3752	191	5	up-1	up-1	NOUN
ejpam-3752	191	6	)	)	PUNCT
ejpam-3752	191	7	)	)	PUNCT
ejpam-3752	192	1	hence	hence	ADV
ejpam-3752	192	2	,	,	PUNCT
ejpam-3752	192	3	b̃	b̃	PROPN
ejpam-3752	192	4	�	�	PROPN
ejpam-3752	192	5	c̃	c̃	PROPN
ejpam-3752	192	6	�	�	PROPN
ejpam-3752	192	7	ã	ã	PROPN
ejpam-3752	192	8	�	�	PROPN
ejpam-3752	192	9	c̃.	c̃.	PROPN
ejpam-3752	192	10	(	(	PUNCT
ejpam-3752	192	11	5	5	X
ejpam-3752	192	12	)	)	PUNCT
ejpam-3752	192	13	let	let	VERB
ejpam-3752	192	14	ã	ã	PROPN
ejpam-3752	192	15	,	,	PUNCT
ejpam-3752	192	16	b̃	b̃	PROPN
ejpam-3752	192	17	∈	∈	PROPN
ejpam-3752	192	18	x	x	X
ejpam-3752	192	19	×	×	NOUN
ejpam-3752	192	20	im(t	im(t	ADJ
ejpam-3752	192	21	)	)	PUNCT
ejpam-3752	192	22	.	.	PUNCT
ejpam-3752	193	1	then	then	ADV
ejpam-3752	193	2	ã	ã	PROPN
ejpam-3752	193	3	�	�	PROPN
ejpam-3752	193	4	(	(	PUNCT
ejpam-3752	193	5	b̃	b̃	PROPN
ejpam-3752	193	6	�	�	PROPN
ejpam-3752	193	7	ã	ã	PROPN
ejpam-3752	193	8	)	)	PUNCT
ejpam-3752	193	9	=	=	PUNCT
ejpam-3752	193	10	(	(	PUNCT
ejpam-3752	193	11	0̃	0̃	PROPN
ejpam-3752	193	12	�	�	PROPN
ejpam-3752	193	13	ã	ã	PROPN
ejpam-3752	193	14	)	)	PUNCT
ejpam-3752	193	15	�	�	PROPN
ejpam-3752	193	16	(	(	PUNCT
ejpam-3752	193	17	0̃	0̃	PROPN
ejpam-3752	193	18	�	�	PROPN
ejpam-3752	193	19	(	(	PUNCT
ejpam-3752	193	20	b̃	b̃	PROPN
ejpam-3752	193	21	�	�	PROPN
ejpam-3752	193	22	ã	ã	PROPN
ejpam-3752	193	23	)	)	PUNCT
ejpam-3752	193	24	)	)	PUNCT
ejpam-3752	193	25	(	(	PUNCT
ejpam-3752	193	26	(	(	PUNCT
ejpam-3752	193	27	up-2	up-2	NUM
ejpam-3752	193	28	)	)	PUNCT
ejpam-3752	193	29	)	)	PUNCT
ejpam-3752	194	1	=	=	PRON
ejpam-3752	194	2	(	(	PUNCT
ejpam-3752	194	3	0̃	0̃	PROPN
ejpam-3752	194	4	�	�	PROPN
ejpam-3752	194	5	ã	ã	PROPN
ejpam-3752	194	6	)	)	PUNCT
ejpam-3752	194	7	�	�	PROPN
ejpam-3752	194	8	(	(	PUNCT
ejpam-3752	194	9	(	(	PUNCT
ejpam-3752	194	10	b̃	b̃	PROPN
ejpam-3752	194	11	�	�	PROPN
ejpam-3752	194	12	0̃	0̃	PROPN
ejpam-3752	194	13	)	)	PUNCT
ejpam-3752	194	14	�	�	PROPN
ejpam-3752	194	15	(	(	PUNCT
ejpam-3752	194	16	b̃	b̃	PROPN
ejpam-3752	194	17	�	�	PROPN
ejpam-3752	194	18	ã	ã	PROPN
ejpam-3752	194	19	)	)	PUNCT
ejpam-3752	194	20	)	)	PUNCT
ejpam-3752	194	21	(	(	PUNCT
ejpam-3752	194	22	(	(	PUNCT
ejpam-3752	194	23	up-3	up-3	NOUN
ejpam-3752	194	24	)	)	PUNCT
ejpam-3752	194	25	)	)	PUNCT
ejpam-3752	195	1	=	=	SYM
ejpam-3752	195	2	0̃.	0̃.	NOUN
ejpam-3752	195	3	(	(	PUNCT
ejpam-3752	195	4	(	(	PUNCT
ejpam-3752	195	5	up-1	up-1	NOUN
ejpam-3752	195	6	)	)	PUNCT
ejpam-3752	195	7	)	)	PUNCT
ejpam-3752	195	8	hence	hence	ADV
ejpam-3752	195	9	,	,	PUNCT
ejpam-3752	195	10	ã	ã	PROPN
ejpam-3752	195	11	�	�	PROPN
ejpam-3752	195	12	b̃	b̃	PROPN
ejpam-3752	195	13	�	�	PROPN
ejpam-3752	195	14	ã.	ã.	PROPN
ejpam-3752	195	15	(	(	PUNCT
ejpam-3752	195	16	6	6	NUM
ejpam-3752	195	17	)	)	PUNCT
ejpam-3752	195	18	let	let	VERB
ejpam-3752	195	19	ã	ã	PROPN
ejpam-3752	195	20	,	,	PUNCT
ejpam-3752	195	21	b̃	b̃	PROPN
ejpam-3752	195	22	∈	∈	PROPN
ejpam-3752	195	23	x	x	X
ejpam-3752	195	24	×	×	NOUN
ejpam-3752	195	25	im(t	im(t	ADJ
ejpam-3752	195	26	)	)	PUNCT
ejpam-3752	195	27	.	.	PUNCT
ejpam-3752	196	1	by	by	ADP
ejpam-3752	196	2	(	(	PUNCT
ejpam-3752	196	3	up-3	up-3	NOUN
ejpam-3752	196	4	)	)	PUNCT
ejpam-3752	196	5	and	and	CCONJ
ejpam-3752	196	6	(	(	PUNCT
ejpam-3752	196	7	1	1	NUM
ejpam-3752	196	8	)	)	PUNCT
ejpam-3752	196	9	,	,	PUNCT
ejpam-3752	196	10	we	we	PRON
ejpam-3752	196	11	have	have	VERB
ejpam-3752	196	12	ã	ã	PROPN
ejpam-3752	196	13	�	�	PROPN
ejpam-3752	196	14	(	(	PUNCT
ejpam-3752	196	15	b̃	b̃	PROPN
ejpam-3752	196	16	�	�	PROPN
ejpam-3752	196	17	b̃	b̃	PROPN
ejpam-3752	196	18	)	)	PUNCT
ejpam-3752	196	19	=	=	PUNCT
ejpam-3752	196	20	ã	ã	PROPN
ejpam-3752	196	21	�	�	PROPN
ejpam-3752	196	22	0̃	0̃	PROPN
ejpam-3752	196	23	=	=	SYM
ejpam-3752	196	24	0̃.	0̃.	NOUN
ejpam-3752	196	25	hence	hence	ADV
ejpam-3752	196	26	,	,	PUNCT
ejpam-3752	196	27	ã	ã	PROPN
ejpam-3752	196	28	�	�	PROPN
ejpam-3752	196	29	b̃	b̃	PROPN
ejpam-3752	196	30	�	�	PROPN
ejpam-3752	196	31	b̃.	b̃.	NOUN
ejpam-3752	196	32	(	(	PUNCT
ejpam-3752	196	33	7	7	X
ejpam-3752	196	34	)	)	PUNCT
ejpam-3752	196	35	let	let	VERB
ejpam-3752	196	36	x̃	x̃	PROPN
ejpam-3752	196	37	,	,	PUNCT
ejpam-3752	196	38	ã	ã	PROPN
ejpam-3752	196	39	,	,	PUNCT
ejpam-3752	196	40	b̃	b̃	PROPN
ejpam-3752	196	41	,	,	PUNCT
ejpam-3752	196	42	c̃	c̃	PROPN
ejpam-3752	196	43	∈	∈	PROPN
ejpam-3752	196	44	x	x	SYM
ejpam-3752	196	45	×	×	NOUN
ejpam-3752	196	46	im(t	im(t	ADJ
ejpam-3752	196	47	)	)	PUNCT
ejpam-3752	196	48	.	.	PUNCT
ejpam-3752	197	1	by	by	ADP
ejpam-3752	197	2	(	(	PUNCT
ejpam-3752	197	3	up-1	up-1	NUM
ejpam-3752	197	4	)	)	PUNCT
ejpam-3752	197	5	,	,	PUNCT
ejpam-3752	197	6	we	we	PRON
ejpam-3752	197	7	have	have	VERB
ejpam-3752	197	8	(	(	PUNCT
ejpam-3752	197	9	b̃	b̃	PROPN
ejpam-3752	197	10	�	�	PROPN
ejpam-3752	197	11	c̃	c̃	PROPN
ejpam-3752	197	12	)	)	PUNCT
ejpam-3752	197	13	�	�	PROPN
ejpam-3752	197	14	(	(	PUNCT
ejpam-3752	197	15	(	(	PUNCT
ejpam-3752	197	16	x̃	x̃	PROPN
ejpam-3752	197	17	�	�	PROPN
ejpam-3752	197	18	b̃	b̃	PROPN
ejpam-3752	197	19	)	)	PUNCT
ejpam-3752	197	20	�	�	PROPN
ejpam-3752	197	21	(	(	PUNCT
ejpam-3752	197	22	x̃	x̃	PROPN
ejpam-3752	197	23	�	�	PROPN
ejpam-3752	197	24	c̃	c̃	PROPN
ejpam-3752	197	25	)	)	PUNCT
ejpam-3752	197	26	)	)	PUNCT
ejpam-3752	198	1	=	=	PUNCT
ejpam-3752	198	2	0̃.	0̃.	NOUN
ejpam-3752	199	1	thus	thus	ADV
ejpam-3752	199	2	b̃	b̃	PROPN
ejpam-3752	199	3	�	�	PROPN
ejpam-3752	199	4	c̃	c̃	PROPN
ejpam-3752	199	5	�	�	PROPN
ejpam-3752	199	6	(	(	PUNCT
ejpam-3752	199	7	x̃	x̃	PROPN
ejpam-3752	199	8	�	�	PROPN
ejpam-3752	199	9	b̃	b̃	PROPN
ejpam-3752	199	10	)	)	PUNCT
ejpam-3752	199	11	�	�	PROPN
ejpam-3752	199	12	(	(	PUNCT
ejpam-3752	199	13	x̃	x̃	PROPN
ejpam-3752	199	14	�	�	PROPN
ejpam-3752	199	15	c̃	c̃	PROPN
ejpam-3752	199	16	)	)	PUNCT
ejpam-3752	199	17	.	.	PUNCT
ejpam-3752	200	1	by	by	ADP
ejpam-3752	200	2	(	(	PUNCT
ejpam-3752	200	3	3	3	NUM
ejpam-3752	200	4	)	)	PUNCT
ejpam-3752	200	5	,	,	PUNCT
ejpam-3752	200	6	we	we	PRON
ejpam-3752	200	7	have	have	VERB
ejpam-3752	200	8	ã	ã	PROPN
ejpam-3752	200	9	�	�	PROPN
ejpam-3752	200	10	(	(	PUNCT
ejpam-3752	200	11	b̃	b̃	PROPN
ejpam-3752	200	12	�	�	PROPN
ejpam-3752	200	13	c̃	c̃	PROPN
ejpam-3752	200	14	)	)	PUNCT
ejpam-3752	200	15	�	�	PROPN
ejpam-3752	200	16	ã	ã	PROPN
ejpam-3752	200	17	�	�	PROPN
ejpam-3752	200	18	(	(	PUNCT
ejpam-3752	200	19	(	(	PUNCT
ejpam-3752	200	20	x̃	x̃	PROPN
ejpam-3752	200	21	�	�	PROPN
ejpam-3752	200	22	b̃	b̃	PROPN
ejpam-3752	200	23	)	)	PUNCT
ejpam-3752	200	24	�	�	PROPN
ejpam-3752	200	25	(	(	PUNCT
ejpam-3752	200	26	x̃	x̃	PROPN
ejpam-3752	200	27	�	�	PROPN
ejpam-3752	200	28	c̃	c̃	PROPN
ejpam-3752	200	29	)	)	PUNCT
ejpam-3752	200	30	)	)	PUNCT
ejpam-3752	200	31	.	.	PUNCT
ejpam-3752	201	1	(	(	PUNCT
ejpam-3752	201	2	8)	8)	NUM
ejpam-3752	201	3	let	let	VERB
ejpam-3752	201	4	x̃	x̃	PROPN
ejpam-3752	201	5	,	,	PUNCT
ejpam-3752	201	6	ã	ã	PROPN
ejpam-3752	201	7	,	,	PUNCT
ejpam-3752	201	8	b̃	b̃	PROPN
ejpam-3752	201	9	,	,	PUNCT
ejpam-3752	201	10	c̃	c̃	PROPN
ejpam-3752	201	11	∈	∈	PROPN
ejpam-3752	201	12	x	x	SYM
ejpam-3752	201	13	×	×	NOUN
ejpam-3752	201	14	im(t	im(t	ADJ
ejpam-3752	201	15	)	)	PUNCT
ejpam-3752	201	16	.	.	PUNCT
ejpam-3752	202	1	by	by	ADP
ejpam-3752	202	2	(	(	PUNCT
ejpam-3752	202	3	up-1	up-1	NUM
ejpam-3752	202	4	)	)	PUNCT
ejpam-3752	202	5	,	,	PUNCT
ejpam-3752	202	6	we	we	PRON
ejpam-3752	202	7	have	have	VERB
ejpam-3752	202	8	(	(	PUNCT
ejpam-3752	202	9	ã	ã	PROPN
ejpam-3752	202	10	�	�	PROPN
ejpam-3752	202	11	b̃	b̃	PROPN
ejpam-3752	202	12	)	)	PUNCT
ejpam-3752	202	13	�	�	PROPN
ejpam-3752	202	14	(	(	PUNCT
ejpam-3752	202	15	(	(	PUNCT
ejpam-3752	202	16	x̃	x̃	PROPN
ejpam-3752	202	17	�	�	PROPN
ejpam-3752	202	18	ã	ã	PROPN
ejpam-3752	202	19	)	)	PUNCT
ejpam-3752	202	20	�	�	PROPN
ejpam-3752	202	21	(	(	PUNCT
ejpam-3752	202	22	x̃	x̃	PROPN
ejpam-3752	202	23	�	�	PROPN
ejpam-3752	202	24	b̃	b̃	PROPN
ejpam-3752	202	25	)	)	PUNCT
ejpam-3752	202	26	)	)	PUNCT
ejpam-3752	203	1	=	=	PUNCT
ejpam-3752	203	2	0̃.	0̃.	NOUN
ejpam-3752	204	1	thus	thus	ADV
ejpam-3752	204	2	ã	ã	PROPN
ejpam-3752	204	3	�	�	PROPN
ejpam-3752	204	4	b̃	b̃	PROPN
ejpam-3752	204	5	�	�	PROPN
ejpam-3752	204	6	(	(	PUNCT
ejpam-3752	204	7	x̃	x̃	PROPN
ejpam-3752	204	8	�	�	PROPN
ejpam-3752	204	9	ã	ã	PROPN
ejpam-3752	204	10	)	)	PUNCT
ejpam-3752	204	11	�	�	PROPN
ejpam-3752	204	12	(	(	PUNCT
ejpam-3752	204	13	x̃	x̃	PROPN
ejpam-3752	204	14	�	�	PROPN
ejpam-3752	204	15	b̃	b̃	PROPN
ejpam-3752	204	16	)	)	PUNCT
ejpam-3752	204	17	.	.	PUNCT
ejpam-3752	205	1	by	by	ADP
ejpam-3752	205	2	(	(	PUNCT
ejpam-3752	205	3	4	4	NUM
ejpam-3752	205	4	)	)	PUNCT
ejpam-3752	205	5	,	,	PUNCT
ejpam-3752	205	6	we	we	PRON
ejpam-3752	205	7	have	have	AUX
ejpam-3752	205	8	(	(	PUNCT
ejpam-3752	205	9	(	(	PUNCT
ejpam-3752	205	10	x̃	x̃	PROPN
ejpam-3752	205	11	�	�	PROPN
ejpam-3752	205	12	ã	ã	PROPN
ejpam-3752	205	13	)	)	PUNCT
ejpam-3752	205	14	�	�	PROPN
ejpam-3752	205	15	(	(	PUNCT
ejpam-3752	205	16	x̃	x̃	PROPN
ejpam-3752	205	17	�	�	PROPN
ejpam-3752	205	18	b̃	b̃	PROPN
ejpam-3752	205	19	)	)	PUNCT
ejpam-3752	205	20	)	)	PUNCT
ejpam-3752	205	21	�	�	PROPN
ejpam-3752	205	22	c̃	c̃	PROPN
ejpam-3752	205	23	�	�	PROPN
ejpam-3752	205	24	(	(	PUNCT
ejpam-3752	205	25	ã	ã	PROPN
ejpam-3752	205	26	�	�	PROPN
ejpam-3752	205	27	b̃	b̃	PROPN
ejpam-3752	205	28	)	)	PUNCT
ejpam-3752	205	29	�	�	PROPN
ejpam-3752	205	30	c̃.	c̃.	PROPN
ejpam-3752	205	31	(	(	PUNCT
ejpam-3752	205	32	9	9	X
ejpam-3752	205	33	)	)	PUNCT
ejpam-3752	205	34	let	let	VERB
ejpam-3752	205	35	ã	ã	PROPN
ejpam-3752	205	36	,	,	PUNCT
ejpam-3752	205	37	b̃	b̃	PROPN
ejpam-3752	205	38	,	,	PUNCT
ejpam-3752	205	39	c̃	c̃	PROPN
ejpam-3752	205	40	∈	∈	PROPN
ejpam-3752	205	41	x	x	SYM
ejpam-3752	205	42	×	×	NOUN
ejpam-3752	205	43	im(t	im(t	ADJ
ejpam-3752	205	44	)	)	PUNCT
ejpam-3752	205	45	.	.	PUNCT
ejpam-3752	206	1	then	then	ADV
ejpam-3752	206	2	0̃	0̃	NOUN
ejpam-3752	206	3	=	=	SYM
ejpam-3752	206	4	(	(	PUNCT
ejpam-3752	206	5	(	(	PUNCT
ejpam-3752	206	6	(	(	PUNCT
ejpam-3752	206	7	ã	ã	PROPN
ejpam-3752	206	8	�	�	PROPN
ejpam-3752	206	9	0̃	0̃	PROPN
ejpam-3752	206	10	)	)	PUNCT
ejpam-3752	206	11	�	�	PROPN
ejpam-3752	206	12	(	(	PUNCT
ejpam-3752	206	13	ã	ã	PROPN
ejpam-3752	206	14	�	�	PROPN
ejpam-3752	206	15	b̃	b̃	PROPN
ejpam-3752	206	16	)	)	PUNCT
ejpam-3752	206	17	)	)	PUNCT
ejpam-3752	206	18	�	�	PROPN
ejpam-3752	206	19	c̃	c̃	PROPN
ejpam-3752	206	20	)	)	PUNCT
ejpam-3752	206	21	�	�	PROPN
ejpam-3752	206	22	(	(	PUNCT
ejpam-3752	206	23	(	(	PUNCT
ejpam-3752	206	24	0̃	0̃	PROPN
ejpam-3752	206	25	�	�	PROPN
ejpam-3752	206	26	b̃	b̃	PROPN
ejpam-3752	206	27	)	)	PUNCT
ejpam-3752	206	28	�	�	PROPN
ejpam-3752	206	29	c̃	c̃	PROPN
ejpam-3752	206	30	)	)	PUNCT
ejpam-3752	206	31	(	(	PUNCT
ejpam-3752	206	32	(	(	PUNCT
ejpam-3752	206	33	8)	8)	NUM
ejpam-3752	206	34	)	)	PUNCT
ejpam-3752	206	35	=	=	SYM
ejpam-3752	206	36	(	(	PUNCT
ejpam-3752	206	37	(	(	PUNCT
ejpam-3752	206	38	0̃	0̃	PROPN
ejpam-3752	206	39	�	�	PROPN
ejpam-3752	206	40	(	(	PUNCT
ejpam-3752	206	41	ã	ã	PROPN
ejpam-3752	206	42	�	�	PROPN
ejpam-3752	206	43	b̃	b̃	PROPN
ejpam-3752	206	44	)	)	PUNCT
ejpam-3752	206	45	)	)	PUNCT
ejpam-3752	206	46	�	�	PROPN
ejpam-3752	206	47	c̃	c̃	PROPN
ejpam-3752	206	48	)	)	PUNCT
ejpam-3752	206	49	�	�	PROPN
ejpam-3752	206	50	(	(	PUNCT
ejpam-3752	206	51	b̃	b̃	PROPN
ejpam-3752	206	52	�	�	PROPN
ejpam-3752	206	53	c̃	c̃	PROPN
ejpam-3752	206	54	)	)	PUNCT
ejpam-3752	206	55	(	(	PUNCT
ejpam-3752	206	56	(	(	PUNCT
ejpam-3752	206	57	up-2	up-2	NUM
ejpam-3752	206	58	)	)	PUNCT
ejpam-3752	206	59	,	,	PUNCT
ejpam-3752	206	60	(	(	PUNCT
ejpam-3752	206	61	up-3	up-3	NOUN
ejpam-3752	206	62	)	)	PUNCT
ejpam-3752	206	63	)	)	PUNCT
ejpam-3752	207	1	=	=	SYM
ejpam-3752	207	2	(	(	PUNCT
ejpam-3752	207	3	(	(	PUNCT
ejpam-3752	207	4	ã	ã	PROPN
ejpam-3752	207	5	�	�	PROPN
ejpam-3752	207	6	b̃	b̃	PROPN
ejpam-3752	207	7	)	)	PUNCT
ejpam-3752	207	8	�	�	PROPN
ejpam-3752	207	9	c̃	c̃	PROPN
ejpam-3752	207	10	)	)	PUNCT
ejpam-3752	207	11	�	�	PROPN
ejpam-3752	207	12	(	(	PUNCT
ejpam-3752	207	13	b̃	b̃	PROPN
ejpam-3752	207	14	�	�	PROPN
ejpam-3752	207	15	c̃	c̃	PROPN
ejpam-3752	207	16	)	)	PUNCT
ejpam-3752	207	17	.	.	PUNCT
ejpam-3752	208	1	(	(	PUNCT
ejpam-3752	208	2	(	(	PUNCT
ejpam-3752	208	3	up-2	up-2	NUM
ejpam-3752	208	4	)	)	PUNCT
ejpam-3752	208	5	)	)	PUNCT
ejpam-3752	208	6	hence	hence	ADV
ejpam-3752	208	7	,	,	PUNCT
ejpam-3752	208	8	(	(	PUNCT
ejpam-3752	208	9	ã	ã	PROPN
ejpam-3752	208	10	�	�	PROPN
ejpam-3752	208	11	b̃	b̃	PROPN
ejpam-3752	208	12	)	)	PUNCT
ejpam-3752	208	13	�	�	PROPN
ejpam-3752	208	14	c̃	c̃	PROPN
ejpam-3752	208	15	�	�	PROPN
ejpam-3752	208	16	b̃	b̃	PROPN
ejpam-3752	208	17	�	�	PROPN
ejpam-3752	208	18	c̃.	c̃.	PROPN
ejpam-3752	208	19	(	(	PUNCT
ejpam-3752	208	20	10	10	NUM
ejpam-3752	208	21	)	)	PUNCT
ejpam-3752	208	22	let	let	VERB
ejpam-3752	208	23	ã	ã	PROPN
ejpam-3752	208	24	,	,	PUNCT
ejpam-3752	208	25	b̃	b̃	PROPN
ejpam-3752	208	26	,	,	PUNCT
ejpam-3752	208	27	c̃	c̃	PROPN
ejpam-3752	208	28	∈	∈	PROPN
ejpam-3752	208	29	x	x	SYM
ejpam-3752	208	30	×	×	NOUN
ejpam-3752	208	31	im(t	im(t	VERB
ejpam-3752	208	32	)	)	PUNCT
ejpam-3752	208	33	be	be	AUX
ejpam-3752	208	34	such	such	ADJ
ejpam-3752	208	35	that	that	SCONJ
ejpam-3752	208	36	ã	ã	PROPN
ejpam-3752	208	37	�	�	PROPN
ejpam-3752	208	38	b̃.	b̃.	NOUN
ejpam-3752	208	39	by	by	ADP
ejpam-3752	208	40	(	(	PUNCT
ejpam-3752	208	41	3	3	NUM
ejpam-3752	208	42	)	)	PUNCT
ejpam-3752	208	43	,	,	PUNCT
ejpam-3752	208	44	we	we	PRON
ejpam-3752	208	45	have	have	VERB
ejpam-3752	208	46	(	(	PUNCT
ejpam-3752	208	47	c̃	c̃	PROPN
ejpam-3752	208	48	�	�	PROPN
ejpam-3752	208	49	ã	ã	PROPN
ejpam-3752	208	50	)	)	PUNCT
ejpam-3752	208	51	�	�	PROPN
ejpam-3752	208	52	(	(	PUNCT
ejpam-3752	208	53	c̃	c̃	PROPN
ejpam-3752	208	54	�	�	PROPN
ejpam-3752	208	55	b̃	b̃	PROPN
ejpam-3752	208	56	)	)	PUNCT
ejpam-3752	209	1	=	=	SYM
ejpam-3752	209	2	0̃.	0̃.	NOUN
ejpam-3752	210	1	thus	thus	ADV
ejpam-3752	210	2	ã	ã	PROPN
ejpam-3752	210	3	�	�	PROPN
ejpam-3752	210	4	(	(	PUNCT
ejpam-3752	210	5	c̃	c̃	PROPN
ejpam-3752	210	6	�	�	PROPN
ejpam-3752	210	7	b̃	b̃	PROPN
ejpam-3752	210	8	)	)	PUNCT
ejpam-3752	211	1	=	=	SYM
ejpam-3752	211	2	0̃	0̃	PROPN
ejpam-3752	211	3	�	�	PROPN
ejpam-3752	211	4	(	(	PUNCT
ejpam-3752	211	5	ã	ã	PROPN
ejpam-3752	211	6	�	�	PROPN
ejpam-3752	211	7	(	(	PUNCT
ejpam-3752	211	8	c̃	c̃	PROPN
ejpam-3752	211	9	�	�	PROPN
ejpam-3752	211	10	b̃	b̃	PROPN
ejpam-3752	211	11	)	)	PUNCT
ejpam-3752	211	12	)	)	PUNCT
ejpam-3752	211	13	(	(	PUNCT
ejpam-3752	211	14	(	(	PUNCT
ejpam-3752	211	15	up-2	up-2	NUM
ejpam-3752	211	16	)	)	PUNCT
ejpam-3752	211	17	)	)	PUNCT
ejpam-3752	212	1	=	=	SYM
ejpam-3752	212	2	(	(	PUNCT
ejpam-3752	212	3	(	(	PUNCT
ejpam-3752	212	4	c̃	c̃	PROPN
ejpam-3752	212	5	�	�	PROPN
ejpam-3752	212	6	ã	ã	PROPN
ejpam-3752	212	7	)	)	PUNCT
ejpam-3752	212	8	�	�	PROPN
ejpam-3752	212	9	(	(	PUNCT
ejpam-3752	212	10	c̃	c̃	PROPN
ejpam-3752	212	11	�	�	PROPN
ejpam-3752	212	12	b̃	b̃	PROPN
ejpam-3752	212	13	)	)	PUNCT
ejpam-3752	212	14	)	)	PUNCT
ejpam-3752	212	15	�	�	PROPN
ejpam-3752	212	16	(	(	PUNCT
ejpam-3752	212	17	ã	ã	PROPN
ejpam-3752	212	18	�	�	PROPN
ejpam-3752	212	19	(	(	PUNCT
ejpam-3752	212	20	c̃	c̃	PROPN
ejpam-3752	212	21	�	�	PROPN
ejpam-3752	212	22	b̃	b̃	PROPN
ejpam-3752	212	23	)	)	PUNCT
ejpam-3752	212	24	)	)	PUNCT
ejpam-3752	213	1	=	=	PUNCT
ejpam-3752	213	2	0̃.	0̃.	NOUN
ejpam-3752	213	3	(	(	PUNCT
ejpam-3752	213	4	(	(	PUNCT
ejpam-3752	213	5	9	9	NUM
ejpam-3752	213	6	)	)	PUNCT
ejpam-3752	213	7	)	)	PUNCT
ejpam-3752	213	8	hence	hence	ADV
ejpam-3752	213	9	,	,	PUNCT
ejpam-3752	213	10	ã	ã	PROPN
ejpam-3752	213	11	�	�	PROPN
ejpam-3752	213	12	c̃	c̃	PROPN
ejpam-3752	213	13	�	�	PROPN
ejpam-3752	213	14	b̃.	b̃.	PROPN
ejpam-3752	213	15	a.	a.	NOUN
ejpam-3752	213	16	iampan	iampan	PROPN
ejpam-3752	213	17	,	,	PUNCT
ejpam-3752	213	18	m.	m.	NOUN
ejpam-3752	213	19	songsaeng	songsaeng	PROPN
ejpam-3752	213	20	,	,	PUNCT
ejpam-3752	213	21	g.	g.	PROPN
ejpam-3752	213	22	muhiuddin	muhiuddin	PROPN
ejpam-3752	213	23	/	/	SYM
ejpam-3752	213	24	eur	eur	PROPN
ejpam-3752	213	25	.	.	PUNCT
ejpam-3752	214	1	j.	j.	PROPN
ejpam-3752	214	2	pure	pure	PROPN
ejpam-3752	214	3	appl	appl	PROPN
ejpam-3752	214	4	.	.	PROPN
ejpam-3752	214	5	math	math	PROPN
ejpam-3752	214	6	,	,	PUNCT
ejpam-3752	214	7	13	13	NUM
ejpam-3752	214	8	(	(	PUNCT
ejpam-3752	214	9	3	3	NUM
ejpam-3752	214	10	)	)	PUNCT
ejpam-3752	214	11	(	(	PUNCT
ejpam-3752	214	12	2020	2020	NUM
ejpam-3752	214	13	)	)	PUNCT
ejpam-3752	214	14	,	,	PUNCT
ejpam-3752	214	15	459	459	NUM
ejpam-3752	214	16	-	-	SYM
ejpam-3752	214	17	471	471	NUM
ejpam-3752	214	18	466	466	NUM
ejpam-3752	214	19	(	(	PUNCT
ejpam-3752	214	20	11	11	NUM
ejpam-3752	214	21	)	)	PUNCT
ejpam-3752	214	22	let	let	VERB
ejpam-3752	214	23	ã	ã	PROPN
ejpam-3752	214	24	,	,	PUNCT
ejpam-3752	214	25	b̃	b̃	PROPN
ejpam-3752	214	26	,	,	PUNCT
ejpam-3752	214	27	c̃	c̃	PROPN
ejpam-3752	214	28	∈	∈	PROPN
ejpam-3752	214	29	x	x	SYM
ejpam-3752	214	30	×	×	NOUN
ejpam-3752	214	31	im(t	im(t	ADJ
ejpam-3752	214	32	)	)	PUNCT
ejpam-3752	214	33	.	.	PUNCT
ejpam-3752	215	1	by	by	ADP
ejpam-3752	215	2	(	(	PUNCT
ejpam-3752	215	3	9	9	NUM
ejpam-3752	215	4	)	)	PUNCT
ejpam-3752	215	5	,	,	PUNCT
ejpam-3752	215	6	we	we	PRON
ejpam-3752	215	7	have	have	VERB
ejpam-3752	215	8	(	(	PUNCT
ejpam-3752	215	9	ã	ã	PROPN
ejpam-3752	215	10	�	�	PROPN
ejpam-3752	215	11	b̃	b̃	PROPN
ejpam-3752	215	12	)	)	PUNCT
ejpam-3752	215	13	�	�	PROPN
ejpam-3752	215	14	c̃	c̃	PROPN
ejpam-3752	215	15	�	�	PROPN
ejpam-3752	215	16	b̃	b̃	PROPN
ejpam-3752	215	17	�	�	PROPN
ejpam-3752	215	18	c̃.	c̃.	PROPN
ejpam-3752	215	19	by	by	ADP
ejpam-3752	215	20	(	(	PUNCT
ejpam-3752	215	21	5	5	NUM
ejpam-3752	215	22	)	)	PUNCT
ejpam-3752	215	23	,	,	PUNCT
ejpam-3752	215	24	we	we	PRON
ejpam-3752	215	25	have	have	VERB
ejpam-3752	215	26	b̃	b̃	PROPN
ejpam-3752	215	27	�	�	PROPN
ejpam-3752	215	28	c̃	c̃	PROPN
ejpam-3752	215	29	�	�	PROPN
ejpam-3752	215	30	ã	ã	PROPN
ejpam-3752	215	31	�	�	PROPN
ejpam-3752	215	32	(	(	PUNCT
ejpam-3752	215	33	b̃	b̃	PROPN
ejpam-3752	215	34	�	�	PROPN
ejpam-3752	215	35	c̃	c̃	PROPN
ejpam-3752	215	36	)	)	PUNCT
ejpam-3752	215	37	.	.	PUNCT
ejpam-3752	216	1	it	it	PRON
ejpam-3752	216	2	follows	follow	VERB
ejpam-3752	216	3	from	from	ADP
ejpam-3752	216	4	(	(	PUNCT
ejpam-3752	216	5	2	2	NUM
ejpam-3752	216	6	)	)	PUNCT
ejpam-3752	216	7	that	that	SCONJ
ejpam-3752	216	8	(	(	PUNCT
ejpam-3752	216	9	ã	ã	PROPN
ejpam-3752	216	10	�	�	PROPN
ejpam-3752	216	11	b̃	b̃	PROPN
ejpam-3752	216	12	)	)	PUNCT
ejpam-3752	216	13	�	�	PROPN
ejpam-3752	216	14	c̃	c̃	PROPN
ejpam-3752	216	15	�	�	PROPN
ejpam-3752	216	16	ã	ã	PROPN
ejpam-3752	216	17	�	�	PROPN
ejpam-3752	216	18	(	(	PUNCT
ejpam-3752	216	19	b̃	b̃	PROPN
ejpam-3752	216	20	�	�	PROPN
ejpam-3752	216	21	c̃	c̃	PROPN
ejpam-3752	216	22	)	)	PUNCT
ejpam-3752	216	23	.	.	PUNCT
ejpam-3752	217	1	(	(	PUNCT
ejpam-3752	217	2	12	12	X
ejpam-3752	217	3	)	)	PUNCT
ejpam-3752	217	4	let	let	VERB
ejpam-3752	217	5	x̃	x̃	PROPN
ejpam-3752	217	6	,	,	PUNCT
ejpam-3752	217	7	ã	ã	PROPN
ejpam-3752	217	8	,	,	PUNCT
ejpam-3752	217	9	b̃	b̃	PROPN
ejpam-3752	217	10	,	,	PUNCT
ejpam-3752	217	11	c̃	c̃	PROPN
ejpam-3752	217	12	∈	∈	PROPN
ejpam-3752	217	13	x	x	SYM
ejpam-3752	217	14	×	×	NOUN
ejpam-3752	217	15	im(t	im(t	ADJ
ejpam-3752	217	16	)	)	PUNCT
ejpam-3752	217	17	.	.	PUNCT
ejpam-3752	218	1	by	by	ADP
ejpam-3752	218	2	(	(	PUNCT
ejpam-3752	218	3	5	5	NUM
ejpam-3752	218	4	)	)	PUNCT
ejpam-3752	218	5	,	,	PUNCT
ejpam-3752	218	6	we	we	PRON
ejpam-3752	218	7	have	have	VERB
ejpam-3752	218	8	b̃	b̃	PROPN
ejpam-3752	218	9	�	�	PROPN
ejpam-3752	218	10	ã	ã	PROPN
ejpam-3752	218	11	�	�	PROPN
ejpam-3752	218	12	b̃	b̃	PROPN
ejpam-3752	218	13	and	and	CCONJ
ejpam-3752	218	14	ã	ã	PROPN
ejpam-3752	218	15	�	�	PROPN
ejpam-3752	218	16	b̃	b̃	PROPN
ejpam-3752	218	17	�	�	PROPN
ejpam-3752	218	18	x̃	x̃	PROPN
ejpam-3752	218	19	�	�	PROPN
ejpam-3752	218	20	(	(	PUNCT
ejpam-3752	218	21	ã	ã	PROPN
ejpam-3752	218	22	�	�	PROPN
ejpam-3752	218	23	b̃	b̃	PROPN
ejpam-3752	218	24	)	)	PUNCT
ejpam-3752	218	25	.	.	PUNCT
ejpam-3752	219	1	by	by	ADP
ejpam-3752	219	2	(	(	PUNCT
ejpam-3752	219	3	2	2	NUM
ejpam-3752	219	4	)	)	PUNCT
ejpam-3752	219	5	,	,	PUNCT
ejpam-3752	219	6	we	we	PRON
ejpam-3752	219	7	have	have	VERB
ejpam-3752	219	8	b̃	b̃	PROPN
ejpam-3752	219	9	�	�	PROPN
ejpam-3752	219	10	x̃	x̃	PROPN
ejpam-3752	219	11	�	�	PROPN
ejpam-3752	219	12	(	(	PUNCT
ejpam-3752	219	13	ã	ã	PROPN
ejpam-3752	219	14	�	�	PROPN
ejpam-3752	219	15	b̃	b̃	PROPN
ejpam-3752	219	16	)	)	PUNCT
ejpam-3752	219	17	.	.	PUNCT
ejpam-3752	220	1	by	by	ADP
ejpam-3752	220	2	(	(	PUNCT
ejpam-3752	220	3	4	4	NUM
ejpam-3752	220	4	)	)	PUNCT
ejpam-3752	220	5	,	,	PUNCT
ejpam-3752	220	6	we	we	PRON
ejpam-3752	220	7	have	have	VERB
ejpam-3752	220	8	(	(	PUNCT
ejpam-3752	220	9	x̃	x̃	PROPN
ejpam-3752	220	10	�	�	PROPN
ejpam-3752	220	11	(	(	PUNCT
ejpam-3752	220	12	ã	ã	PROPN
ejpam-3752	220	13	�	�	PROPN
ejpam-3752	220	14	b̃	b̃	PROPN
ejpam-3752	220	15	)	)	PUNCT
ejpam-3752	220	16	)	)	PUNCT
ejpam-3752	220	17	�	�	PROPN
ejpam-3752	220	18	(	(	PUNCT
ejpam-3752	220	19	x̃	x̃	PROPN
ejpam-3752	220	20	�	�	PROPN
ejpam-3752	220	21	c̃	c̃	PROPN
ejpam-3752	220	22	)	)	PUNCT
ejpam-3752	220	23	�	�	PROPN
ejpam-3752	220	24	b̃	b̃	PROPN
ejpam-3752	220	25	�	�	PROPN
ejpam-3752	220	26	(	(	PUNCT
ejpam-3752	220	27	x̃	x̃	PROPN
ejpam-3752	220	28	�	�	PROPN
ejpam-3752	220	29	c̃	c̃	PROPN
ejpam-3752	220	30	)	)	PUNCT
ejpam-3752	220	31	.	.	PUNCT
ejpam-3752	221	1	by	by	ADP
ejpam-3752	221	2	(	(	PUNCT
ejpam-3752	221	3	up-1	up-1	NUM
ejpam-3752	221	4	)	)	PUNCT
ejpam-3752	221	5	,	,	PUNCT
ejpam-3752	221	6	we	we	PRON
ejpam-3752	221	7	have	have	VERB
ejpam-3752	221	8	(	(	PUNCT
ejpam-3752	221	9	(	(	PUNCT
ejpam-3752	221	10	ã	ã	PROPN
ejpam-3752	221	11	�	�	PROPN
ejpam-3752	221	12	b̃	b̃	PROPN
ejpam-3752	221	13	)	)	PUNCT
ejpam-3752	221	14	�	�	PROPN
ejpam-3752	221	15	c̃	c̃	PROPN
ejpam-3752	221	16	)	)	PUNCT
ejpam-3752	221	17	�	�	PROPN
ejpam-3752	221	18	(	(	PUNCT
ejpam-3752	221	19	(	(	PUNCT
ejpam-3752	221	20	x̃	x̃	PROPN
ejpam-3752	221	21	�	�	PROPN
ejpam-3752	221	22	(	(	PUNCT
ejpam-3752	221	23	ã	ã	PROPN
ejpam-3752	221	24	�	�	PROPN
ejpam-3752	221	25	b̃	b̃	PROPN
ejpam-3752	221	26	)	)	PUNCT
ejpam-3752	221	27	)	)	PUNCT
ejpam-3752	222	1	�	�	PROPN
ejpam-3752	222	2	(	(	PUNCT
ejpam-3752	222	3	x̃	x̃	PROPN
ejpam-3752	222	4	�	�	PROPN
ejpam-3752	222	5	c̃	c̃	PROPN
ejpam-3752	222	6	)	)	PUNCT
ejpam-3752	222	7	)	)	PUNCT
ejpam-3752	223	1	=	=	PUNCT
ejpam-3752	224	1	0̃.	0̃.	NUM
ejpam-3752	224	2	then	then	ADV
ejpam-3752	224	3	(	(	PUNCT
ejpam-3752	224	4	ã	ã	PROPN
ejpam-3752	224	5	�	�	PROPN
ejpam-3752	224	6	b̃	b̃	PROPN
ejpam-3752	224	7	)	)	PUNCT
ejpam-3752	224	8	�	�	PROPN
ejpam-3752	224	9	c̃	c̃	PROPN
ejpam-3752	224	10	�	�	PROPN
ejpam-3752	224	11	(	(	PUNCT
ejpam-3752	224	12	x̃	x̃	PROPN
ejpam-3752	224	13	�	�	PROPN
ejpam-3752	224	14	(	(	PUNCT
ejpam-3752	224	15	ã	ã	PROPN
ejpam-3752	224	16	�	�	PROPN
ejpam-3752	224	17	b̃	b̃	PROPN
ejpam-3752	224	18	)	)	PUNCT
ejpam-3752	224	19	)	)	PUNCT
ejpam-3752	224	20	�	�	PROPN
ejpam-3752	224	21	(	(	PUNCT
ejpam-3752	224	22	x̃	x̃	PROPN
ejpam-3752	224	23	�	�	PROPN
ejpam-3752	224	24	c̃	c̃	PROPN
ejpam-3752	224	25	)	)	PUNCT
ejpam-3752	224	26	.	.	PUNCT
ejpam-3752	225	1	it	it	PRON
ejpam-3752	225	2	follows	follow	VERB
ejpam-3752	225	3	from	from	ADP
ejpam-3752	225	4	(	(	PUNCT
ejpam-3752	225	5	2	2	NUM
ejpam-3752	225	6	)	)	PUNCT
ejpam-3752	225	7	that	that	SCONJ
ejpam-3752	225	8	(	(	PUNCT
ejpam-3752	225	9	ã	ã	PROPN
ejpam-3752	225	10	�	�	PROPN
ejpam-3752	225	11	b̃	b̃	PROPN
ejpam-3752	225	12	)	)	PUNCT
ejpam-3752	225	13	�	�	PROPN
ejpam-3752	225	14	c̃	c̃	PROPN
ejpam-3752	225	15	�	�	PROPN
ejpam-3752	225	16	b̃	b̃	PROPN
ejpam-3752	225	17	�	�	PROPN
ejpam-3752	225	18	(	(	PUNCT
ejpam-3752	225	19	x̃	x̃	PROPN
ejpam-3752	225	20	�	�	PROPN
ejpam-3752	225	21	c̃	c̃	PROPN
ejpam-3752	225	22	)	)	PUNCT
ejpam-3752	225	23	.	.	PUNCT
ejpam-3752	226	1	theorem	theorem	NOUN
ejpam-3752	226	2	2	2	NUM
ejpam-3752	226	3	.	.	PUNCT
ejpam-3752	227	1	if	if	SCONJ
ejpam-3752	227	2	t	t	NOUN
ejpam-3752	227	3	:	:	PUNCT
ejpam-3752	227	4	x	x	X
ejpam-3752	227	5	→	→	SYM
ejpam-3752	227	6	y	y	PROPN
ejpam-3752	227	7	is	be	AUX
ejpam-3752	227	8	a	a	DET
ejpam-3752	227	9	constant	constant	ADJ
ejpam-3752	227	10	function	function	NOUN
ejpam-3752	227	11	,	,	PUNCT
ejpam-3752	227	12	that	that	ADV
ejpam-3752	227	13	is	is	ADV
ejpam-3752	227	14	,	,	PUNCT
ejpam-3752	227	15	the	the	DET
ejpam-3752	227	16	inverse	inverse	NOUN
ejpam-3752	227	17	image	image	NOUN
ejpam-3752	227	18	t−1({0	t−1({0	ADP
ejpam-3752	227	19	t	t	NOUN
ejpam-3752	227	20	}	}	PUNCT
ejpam-3752	227	21	)	)	PUNCT
ejpam-3752	228	1	=	=	SYM
ejpam-3752	228	2	x	x	X
ejpam-3752	228	3	,	,	PUNCT
ejpam-3752	228	4	then	then	ADV
ejpam-3752	228	5	the	the	DET
ejpam-3752	228	6	algebra	algebra	NOUN
ejpam-3752	228	7	(	(	PUNCT
ejpam-3752	228	8	x	x	SYM
ejpam-3752	228	9	×	×	NOUN
ejpam-3752	228	10	im(t	im(t	ADJ
ejpam-3752	228	11	)	)	PUNCT
ejpam-3752	228	12	,	,	PUNCT
ejpam-3752	228	13	�	�	PROPN
ejpam-3752	228	14	,	,	PUNCT
ejpam-3752	228	15	0̃	0̃	PROPN
ejpam-3752	228	16	)	)	PUNCT
ejpam-3752	228	17	is	be	AUX
ejpam-3752	228	18	a	a	DET
ejpam-3752	228	19	up	up	NOUN
ejpam-3752	228	20	-	-	PUNCT
ejpam-3752	228	21	algebra	algebra	NOUN
ejpam-3752	228	22	which	which	PRON
ejpam-3752	228	23	is	be	AUX
ejpam-3752	228	24	up	up	ADV
ejpam-3752	228	25	-	-	PUNCT
ejpam-3752	228	26	isomorphic	isomorphic	ADJ
ejpam-3752	228	27	to	to	PART
ejpam-3752	228	28	x.	x.	NOUN
ejpam-3752	228	29	proof	proof	NOUN
ejpam-3752	228	30	.	.	PUNCT
ejpam-3752	229	1	(	(	PUNCT
ejpam-3752	229	2	up-4	up-4	ADV
ejpam-3752	229	3	)	)	PUNCT
ejpam-3752	229	4	let	let	AUX
ejpam-3752	229	5	x̃	x̃	PROPN
ejpam-3752	229	6	,	,	PUNCT
ejpam-3752	229	7	ỹ	ỹ	PROPN
ejpam-3752	229	8	∈	∈	PROPN
ejpam-3752	229	9	x	x	SYM
ejpam-3752	229	10	×	×	NOUN
ejpam-3752	229	11	im(t	im(t	VERB
ejpam-3752	229	12	)	)	PUNCT
ejpam-3752	229	13	be	be	AUX
ejpam-3752	229	14	such	such	ADJ
ejpam-3752	229	15	that	that	SCONJ
ejpam-3752	229	16	x̃	x̃	PROPN
ejpam-3752	229	17	�	�	PROPN
ejpam-3752	229	18	ỹ	ỹ	PROPN
ejpam-3752	229	19	=	=	SYM
ejpam-3752	229	20	0̃	0̃	NOUN
ejpam-3752	229	21	and	and	CCONJ
ejpam-3752	229	22	ỹ	ỹ	PROPN
ejpam-3752	229	23	�	�	NOUN
ejpam-3752	229	24	x̃	x̃	PROPN
ejpam-3752	229	25	=	=	PUNCT
ejpam-3752	229	26	0̃	0̃	PROPN
ejpam-3752	229	27	where	where	SCONJ
ejpam-3752	229	28	x̃	x̃	PROPN
ejpam-3752	229	29	=	=	SYM
ejpam-3752	229	30	(	(	PUNCT
ejpam-3752	229	31	x1	x1	PROPN
ejpam-3752	229	32	,	,	PUNCT
ejpam-3752	229	33	x2	x2	PROPN
ejpam-3752	229	34	t	t	PROPN
ejpam-3752	229	35	)	)	PUNCT
ejpam-3752	229	36	,	,	PUNCT
ejpam-3752	229	37	ỹ	ỹ	PROPN
ejpam-3752	229	38	=	=	SYM
ejpam-3752	229	39	(	(	PUNCT
ejpam-3752	229	40	y1	y1	PROPN
ejpam-3752	229	41	,	,	PUNCT
ejpam-3752	229	42	y2	y2	NOUN
ejpam-3752	229	43	t	t	PROPN
ejpam-3752	229	44	)	)	PUNCT
ejpam-3752	229	45	.	.	PUNCT
ejpam-3752	230	1	then	then	ADV
ejpam-3752	230	2	(	(	PUNCT
ejpam-3752	230	3	x1	x1	PROPN
ejpam-3752	230	4	·	·	PUNCT
ejpam-3752	230	5	y1	y1	INTJ
ejpam-3752	230	6	,	,	PUNCT
ejpam-3752	230	7	(	(	PUNCT
ejpam-3752	230	8	x2	x2	PROPN
ejpam-3752	230	9	·	·	PUNCT
ejpam-3752	230	10	y2)t	y2)t	ADV
ejpam-3752	230	11	)	)	PUNCT
ejpam-3752	230	12	=	=	SYM
ejpam-3752	230	13	(	(	PUNCT
ejpam-3752	230	14	x1	x1	PROPN
ejpam-3752	230	15	,	,	PUNCT
ejpam-3752	230	16	x2	x2	PROPN
ejpam-3752	230	17	t	t	PROPN
ejpam-3752	230	18	)	)	PUNCT
ejpam-3752	230	19	�	�	PROPN
ejpam-3752	230	20	(	(	PUNCT
ejpam-3752	230	21	y1	y1	PROPN
ejpam-3752	230	22	,	,	PUNCT
ejpam-3752	230	23	y2	y2	NOUN
ejpam-3752	230	24	t	t	PROPN
ejpam-3752	230	25	)	)	PUNCT
ejpam-3752	230	26	=	=	PUNCT
ejpam-3752	230	27	(	(	PUNCT
ejpam-3752	230	28	0	0	NUM
ejpam-3752	230	29	,	,	PUNCT
ejpam-3752	230	30	0	0	NUM
ejpam-3752	230	31	t	t	NOUN
ejpam-3752	230	32	)	)	PUNCT
ejpam-3752	230	33	and	and	CCONJ
ejpam-3752	230	34	(	(	PUNCT
ejpam-3752	230	35	y1	y1	INTJ
ejpam-3752	230	36	·	·	PUNCT
ejpam-3752	230	37	x1	x1	NUM
ejpam-3752	230	38	,	,	PUNCT
ejpam-3752	230	39	(	(	PUNCT
ejpam-3752	230	40	y2	y2	PROPN
ejpam-3752	230	41	·	·	PUNCT
ejpam-3752	230	42	x2)t	x2)t	PROPN
ejpam-3752	230	43	)	)	PUNCT
ejpam-3752	230	44	=	=	SYM
ejpam-3752	230	45	(	(	PUNCT
ejpam-3752	230	46	y1	y1	INTJ
ejpam-3752	230	47	,	,	PUNCT
ejpam-3752	230	48	y2	y2	PROPN
ejpam-3752	230	49	t	t	PROPN
ejpam-3752	230	50	)	)	PUNCT
ejpam-3752	230	51	�	�	PROPN
ejpam-3752	230	52	(	(	PUNCT
ejpam-3752	230	53	x1	x1	PROPN
ejpam-3752	230	54	,	,	PUNCT
ejpam-3752	230	55	x2	x2	PROPN
ejpam-3752	230	56	t	t	PROPN
ejpam-3752	230	57	)	)	PUNCT
ejpam-3752	230	58	=	=	PUNCT
ejpam-3752	230	59	(	(	PUNCT
ejpam-3752	230	60	0	0	NUM
ejpam-3752	230	61	,	,	PUNCT
ejpam-3752	230	62	0	0	NUM
ejpam-3752	230	63	t	t	NOUN
ejpam-3752	230	64	)	)	PUNCT
ejpam-3752	230	65	.	.	PUNCT
ejpam-3752	231	1	it	it	PRON
ejpam-3752	231	2	follows	follow	VERB
ejpam-3752	231	3	that	that	SCONJ
ejpam-3752	231	4	x1	x1	PROPN
ejpam-3752	231	5	·	·	PUNCT
ejpam-3752	231	6	y1	y1	X
ejpam-3752	231	7	=	=	SYM
ejpam-3752	231	8	0	0	NUM
ejpam-3752	231	9	and	and	CCONJ
ejpam-3752	231	10	y1	y1	INTJ
ejpam-3752	231	11	·	·	PUNCT
ejpam-3752	231	12	x1	x1	NOUN
ejpam-3752	231	13	=	=	SYM
ejpam-3752	231	14	0	0	X
ejpam-3752	231	15	.	.	PUNCT
ejpam-3752	232	1	by	by	ADP
ejpam-3752	232	2	(	(	PUNCT
ejpam-3752	232	3	up-4	up-4	ADV
ejpam-3752	232	4	)	)	PUNCT
ejpam-3752	232	5	,	,	PUNCT
ejpam-3752	232	6	we	we	PRON
ejpam-3752	232	7	have	have	VERB
ejpam-3752	232	8	x1	x1	PROPN
ejpam-3752	232	9	=	=	SYM
ejpam-3752	232	10	y1	y1	PROPN
ejpam-3752	232	11	.	.	PUNCT
ejpam-3752	233	1	since	since	SCONJ
ejpam-3752	233	2	t	t	PROPN
ejpam-3752	233	3	is	be	AUX
ejpam-3752	233	4	constant	constant	ADJ
ejpam-3752	233	5	,	,	PUNCT
ejpam-3752	233	6	we	we	PRON
ejpam-3752	233	7	have	have	VERB
ejpam-3752	233	8	x2	x2	PROPN
ejpam-3752	233	9	t	t	NOUN
ejpam-3752	233	10	=	=	PUNCT
ejpam-3752	233	11	y2	y2	PROPN
ejpam-3752	233	12	t	t	PROPN
ejpam-3752	233	13	.	.	PUNCT
ejpam-3752	234	1	thus	thus	ADV
ejpam-3752	234	2	x̃	x̃	PROPN
ejpam-3752	234	3	=	=	SYM
ejpam-3752	234	4	(	(	PUNCT
ejpam-3752	234	5	x1	x1	PROPN
ejpam-3752	234	6	,	,	PUNCT
ejpam-3752	234	7	x2	x2	PROPN
ejpam-3752	234	8	t	t	PROPN
ejpam-3752	234	9	)	)	PUNCT
ejpam-3752	235	1	=	=	SYM
ejpam-3752	235	2	(	(	PUNCT
ejpam-3752	235	3	y1	y1	INTJ
ejpam-3752	235	4	,	,	PUNCT
ejpam-3752	235	5	y2	y2	NOUN
ejpam-3752	235	6	t	t	PROPN
ejpam-3752	235	7	)	)	PUNCT
ejpam-3752	236	1	=	=	SYM
ejpam-3752	236	2	ỹ	ỹ	PROPN
ejpam-3752	236	3	,	,	PUNCT
ejpam-3752	236	4	(	(	PUNCT
ejpam-3752	236	5	up-4	up-4	ADV
ejpam-3752	236	6	)	)	PUNCT
ejpam-3752	236	7	holding	holding	NOUN
ejpam-3752	236	8	.	.	PUNCT
ejpam-3752	237	1	by	by	ADP
ejpam-3752	237	2	theorem	theorem	NOUN
ejpam-3752	237	3	1	1	NUM
ejpam-3752	237	4	,	,	PUNCT
ejpam-3752	237	5	we	we	PRON
ejpam-3752	237	6	have	have	VERB
ejpam-3752	237	7	(	(	PUNCT
ejpam-3752	237	8	x	x	SYM
ejpam-3752	237	9	×	×	NOUN
ejpam-3752	237	10	im(t	im(t	ADJ
ejpam-3752	237	11	)	)	PUNCT
ejpam-3752	237	12	,	,	PUNCT
ejpam-3752	237	13	�	�	PROPN
ejpam-3752	237	14	,	,	PUNCT
ejpam-3752	237	15	0̃	0̃	PROPN
ejpam-3752	237	16	)	)	PUNCT
ejpam-3752	237	17	is	be	AUX
ejpam-3752	237	18	a	a	DET
ejpam-3752	237	19	up	up	NOUN
ejpam-3752	237	20	-	-	PUNCT
ejpam-3752	237	21	algebra	algebra	NOUN
ejpam-3752	237	22	.	.	PUNCT
ejpam-3752	238	1	finally	finally	ADV
ejpam-3752	238	2	,	,	PUNCT
ejpam-3752	238	3	x	x	PUNCT
ejpam-3752	238	4	and	and	CCONJ
ejpam-3752	238	5	x	x	SYM
ejpam-3752	238	6	×	×	NOUN
ejpam-3752	238	7	im(t	im(t	VERB
ejpam-3752	238	8	)	)	PUNCT
ejpam-3752	238	9	are	be	AUX
ejpam-3752	238	10	up	up	ADV
ejpam-3752	238	11	-	-	PUNCT
ejpam-3752	238	12	isomorphic	isomorphic	ADJ
ejpam-3752	238	13	under	under	ADP
ejpam-3752	238	14	the	the	DET
ejpam-3752	238	15	up	up	NOUN
ejpam-3752	238	16	-	-	PUNCT
ejpam-3752	238	17	isomorphism	isomorphism	NOUN
ejpam-3752	238	18	sending	send	VERB
ejpam-3752	238	19	x	x	SYM
ejpam-3752	238	20	7→	7→	NUM
ejpam-3752	238	21	(	(	PUNCT
ejpam-3752	238	22	x	x	NOUN
ejpam-3752	238	23	,	,	PUNCT
ejpam-3752	238	24	0	0	NUM
ejpam-3752	238	25	t	t	NOUN
ejpam-3752	238	26	)	)	PUNCT
ejpam-3752	238	27	.	.	PUNCT
ejpam-3752	239	1	corollary	corollary	ADJ
ejpam-3752	239	2	1	1	NUM
ejpam-3752	239	3	.	.	PUNCT
ejpam-3752	240	1	if	if	SCONJ
ejpam-3752	240	2	y	y	PROPN
ejpam-3752	240	3	is	be	AUX
ejpam-3752	240	4	a	a	DET
ejpam-3752	240	5	singleton	singleton	NOUN
ejpam-3752	240	6	set	set	NOUN
ejpam-3752	240	7	,	,	PUNCT
ejpam-3752	240	8	then	then	ADV
ejpam-3752	240	9	the	the	DET
ejpam-3752	240	10	algebra	algebra	NOUN
ejpam-3752	240	11	(	(	PUNCT
ejpam-3752	240	12	x	x	SYM
ejpam-3752	240	13	×	×	NOUN
ejpam-3752	240	14	im(t	im(t	ADJ
ejpam-3752	240	15	)	)	PUNCT
ejpam-3752	240	16	,	,	PUNCT
ejpam-3752	240	17	�	�	PROPN
ejpam-3752	240	18	,	,	PUNCT
ejpam-3752	240	19	0̃	0̃	PROPN
ejpam-3752	240	20	)	)	PUNCT
ejpam-3752	240	21	is	be	AUX
ejpam-3752	240	22	a	a	DET
ejpam-3752	240	23	up	up	NOUN
ejpam-3752	240	24	-	-	PUNCT
ejpam-3752	240	25	algebra	algebra	NOUN
ejpam-3752	240	26	.	.	PUNCT
ejpam-3752	241	1	proof	proof	NOUN
ejpam-3752	241	2	.	.	PUNCT
ejpam-3752	242	1	if	if	SCONJ
ejpam-3752	242	2	y	y	PROPN
ejpam-3752	242	3	is	be	AUX
ejpam-3752	242	4	a	a	DET
ejpam-3752	242	5	singleton	singleton	NOUN
ejpam-3752	242	6	set	set	NOUN
ejpam-3752	242	7	,	,	PUNCT
ejpam-3752	242	8	then	then	ADV
ejpam-3752	242	9	t	t	X
ejpam-3752	242	10	:	:	PUNCT
ejpam-3752	242	11	x	x	X
ejpam-3752	242	12	→	→	SYM
ejpam-3752	242	13	y	y	PROPN
ejpam-3752	242	14	is	be	AUX
ejpam-3752	242	15	a	a	DET
ejpam-3752	242	16	constant	constant	ADJ
ejpam-3752	242	17	function	function	NOUN
ejpam-3752	242	18	.	.	PUNCT
ejpam-3752	243	1	by	by	ADP
ejpam-3752	243	2	theorem	theorem	NOUN
ejpam-3752	243	3	2	2	NUM
ejpam-3752	243	4	,	,	PUNCT
ejpam-3752	243	5	we	we	PRON
ejpam-3752	243	6	have	have	VERB
ejpam-3752	243	7	the	the	DET
ejpam-3752	243	8	algebra	algebra	NOUN
ejpam-3752	243	9	(	(	PUNCT
ejpam-3752	243	10	x	x	SYM
ejpam-3752	243	11	×	×	NOUN
ejpam-3752	243	12	im(t	im(t	ADJ
ejpam-3752	243	13	)	)	PUNCT
ejpam-3752	243	14	,	,	PUNCT
ejpam-3752	243	15	�	�	PROPN
ejpam-3752	243	16	,	,	PUNCT
ejpam-3752	243	17	0̃	0̃	PROPN
ejpam-3752	243	18	)	)	PUNCT
ejpam-3752	243	19	is	be	AUX
ejpam-3752	243	20	a	a	DET
ejpam-3752	243	21	up	up	NOUN
ejpam-3752	243	22	-	-	PUNCT
ejpam-3752	243	23	algebra	algebra	NOUN
ejpam-3752	243	24	.	.	PUNCT
ejpam-3752	244	1	theorem	theorem	NOUN
ejpam-3752	244	2	3	3	NUM
ejpam-3752	244	3	.	.	PUNCT
ejpam-3752	245	1	if	if	SCONJ
ejpam-3752	245	2	t	t	NOUN
ejpam-3752	245	3	:	:	PUNCT
ejpam-3752	245	4	x	x	X
ejpam-3752	245	5	→	→	SYM
ejpam-3752	245	6	y	y	PROPN
ejpam-3752	245	7	is	be	AUX
ejpam-3752	245	8	a	a	DET
ejpam-3752	245	9	function	function	NOUN
ejpam-3752	245	10	with	with	ADP
ejpam-3752	245	11	the	the	DET
ejpam-3752	245	12	inverse	inverse	NOUN
ejpam-3752	245	13	image	image	NOUN
ejpam-3752	245	14	t−1({0	t−1({0	ADP
ejpam-3752	245	15	t	t	NOUN
ejpam-3752	245	16	}	}	PUNCT
ejpam-3752	245	17	)	)	PUNCT
ejpam-3752	246	1	=	=	PUNCT
ejpam-3752	246	2	{	{	PUNCT
ejpam-3752	246	3	0	0	NUM
ejpam-3752	246	4	}	}	PUNCT
ejpam-3752	246	5	,	,	PUNCT
ejpam-3752	246	6	then	then	ADV
ejpam-3752	246	7	the	the	DET
ejpam-3752	246	8	algebra	algebra	NOUN
ejpam-3752	246	9	(	(	PUNCT
ejpam-3752	246	10	x	x	SYM
ejpam-3752	246	11	×	×	NOUN
ejpam-3752	246	12	im(t	im(t	ADJ
ejpam-3752	246	13	)	)	PUNCT
ejpam-3752	246	14	,	,	PUNCT
ejpam-3752	246	15	�	�	PROPN
ejpam-3752	246	16	,	,	PUNCT
ejpam-3752	246	17	0̃	0̃	PROPN
ejpam-3752	246	18	)	)	PUNCT
ejpam-3752	246	19	is	be	AUX
ejpam-3752	246	20	a	a	DET
ejpam-3752	246	21	up	up	NOUN
ejpam-3752	246	22	-	-	PUNCT
ejpam-3752	246	23	algebra	algebra	NOUN
ejpam-3752	246	24	.	.	PUNCT
ejpam-3752	247	1	proof	proof	NOUN
ejpam-3752	247	2	.	.	PUNCT
ejpam-3752	248	1	(	(	PUNCT
ejpam-3752	248	2	up-4	up-4	ADV
ejpam-3752	248	3	)	)	PUNCT
ejpam-3752	248	4	let	let	VERB
ejpam-3752	248	5	x̃	x̃	PROPN
ejpam-3752	248	6	,	,	PUNCT
ejpam-3752	248	7	ỹ	ỹ	PROPN
ejpam-3752	248	8	∈	∈	PROPN
ejpam-3752	248	9	x	x	SYM
ejpam-3752	248	10	×	×	NOUN
ejpam-3752	248	11	im(t	im(t	VERB
ejpam-3752	248	12	)	)	PUNCT
ejpam-3752	248	13	be	be	AUX
ejpam-3752	248	14	such	such	ADJ
ejpam-3752	248	15	that	that	SCONJ
ejpam-3752	248	16	x̃	x̃	PROPN
ejpam-3752	248	17	�	�	PROPN
ejpam-3752	248	18	ỹ	ỹ	PROPN
ejpam-3752	248	19	=	=	SYM
ejpam-3752	248	20	0̃	0̃	NOUN
ejpam-3752	248	21	and	and	CCONJ
ejpam-3752	248	22	ỹ	ỹ	PROPN
ejpam-3752	248	23	�	�	NOUN
ejpam-3752	248	24	x̃	x̃	PROPN
ejpam-3752	248	25	=	=	PUNCT
ejpam-3752	248	26	0̃	0̃	PROPN
ejpam-3752	248	27	where	where	SCONJ
ejpam-3752	248	28	x̃	x̃	PROPN
ejpam-3752	248	29	=	=	SYM
ejpam-3752	248	30	(	(	PUNCT
ejpam-3752	248	31	x1	x1	PROPN
ejpam-3752	248	32	,	,	PUNCT
ejpam-3752	248	33	x2	x2	PROPN
ejpam-3752	248	34	t	t	PROPN
ejpam-3752	248	35	)	)	PUNCT
ejpam-3752	248	36	,	,	PUNCT
ejpam-3752	248	37	ỹ	ỹ	PROPN
ejpam-3752	248	38	=	=	SYM
ejpam-3752	248	39	(	(	PUNCT
ejpam-3752	248	40	y1	y1	PROPN
ejpam-3752	248	41	,	,	PUNCT
ejpam-3752	248	42	y2	y2	NOUN
ejpam-3752	248	43	t	t	PROPN
ejpam-3752	248	44	)	)	PUNCT
ejpam-3752	248	45	.	.	PUNCT
ejpam-3752	249	1	then	then	ADV
ejpam-3752	249	2	(	(	PUNCT
ejpam-3752	249	3	x1	x1	PROPN
ejpam-3752	249	4	·	·	PUNCT
ejpam-3752	249	5	y1	y1	INTJ
ejpam-3752	249	6	,	,	PUNCT
ejpam-3752	249	7	(	(	PUNCT
ejpam-3752	249	8	x2	x2	PROPN
ejpam-3752	249	9	·	·	PUNCT
ejpam-3752	249	10	y2)t	y2)t	ADV
ejpam-3752	249	11	)	)	PUNCT
ejpam-3752	249	12	=	=	SYM
ejpam-3752	249	13	(	(	PUNCT
ejpam-3752	249	14	x1	x1	PROPN
ejpam-3752	249	15	,	,	PUNCT
ejpam-3752	249	16	x2	x2	PROPN
ejpam-3752	249	17	t	t	PROPN
ejpam-3752	249	18	)	)	PUNCT
ejpam-3752	249	19	�	�	PROPN
ejpam-3752	249	20	(	(	PUNCT
ejpam-3752	249	21	y1	y1	PROPN
ejpam-3752	249	22	,	,	PUNCT
ejpam-3752	249	23	y2	y2	NOUN
ejpam-3752	249	24	t	t	PROPN
ejpam-3752	249	25	)	)	PUNCT
ejpam-3752	249	26	=	=	PUNCT
ejpam-3752	249	27	(	(	PUNCT
ejpam-3752	249	28	0	0	NUM
ejpam-3752	249	29	,	,	PUNCT
ejpam-3752	249	30	0	0	NUM
ejpam-3752	249	31	t	t	NOUN
ejpam-3752	249	32	)	)	PUNCT
ejpam-3752	249	33	and	and	CCONJ
ejpam-3752	249	34	(	(	PUNCT
ejpam-3752	249	35	y1	y1	INTJ
ejpam-3752	249	36	·	·	PUNCT
ejpam-3752	249	37	x1	x1	NUM
ejpam-3752	249	38	,	,	PUNCT
ejpam-3752	249	39	(	(	PUNCT
ejpam-3752	249	40	y2	y2	PROPN
ejpam-3752	249	41	·	·	PUNCT
ejpam-3752	249	42	x2)t	x2)t	PROPN
ejpam-3752	249	43	)	)	PUNCT
ejpam-3752	249	44	=	=	SYM
ejpam-3752	249	45	(	(	PUNCT
ejpam-3752	249	46	y1	y1	INTJ
ejpam-3752	249	47	,	,	PUNCT
ejpam-3752	249	48	y2	y2	PROPN
ejpam-3752	249	49	t	t	PROPN
ejpam-3752	249	50	)	)	PUNCT
ejpam-3752	249	51	�	�	PROPN
ejpam-3752	249	52	(	(	PUNCT
ejpam-3752	249	53	x1	x1	PROPN
ejpam-3752	249	54	,	,	PUNCT
ejpam-3752	249	55	x2	x2	PROPN
ejpam-3752	249	56	t	t	PROPN
ejpam-3752	249	57	)	)	PUNCT
ejpam-3752	249	58	=	=	PUNCT
ejpam-3752	249	59	(	(	PUNCT
ejpam-3752	249	60	0	0	NUM
ejpam-3752	249	61	,	,	PUNCT
ejpam-3752	249	62	0	0	NUM
ejpam-3752	249	63	t	t	NOUN
ejpam-3752	249	64	)	)	PUNCT
ejpam-3752	249	65	.	.	PUNCT
ejpam-3752	250	1	it	it	PRON
ejpam-3752	250	2	follows	follow	VERB
ejpam-3752	250	3	that	that	SCONJ
ejpam-3752	250	4	x1	x1	PROPN
ejpam-3752	250	5	·	·	PUNCT
ejpam-3752	250	6	y1	y1	NOUN
ejpam-3752	250	7	=	=	SYM
ejpam-3752	250	8	0	0	NUM
ejpam-3752	250	9	and	and	CCONJ
ejpam-3752	250	10	y1	y1	PROPN
ejpam-3752	250	11	·	·	PUNCT
ejpam-3752	250	12	x1	x1	PUNCT
ejpam-3752	251	1	=	=	SYM
ejpam-3752	251	2	0	0	NUM
ejpam-3752	251	3	,	,	PUNCT
ejpam-3752	251	4	and	and	CCONJ
ejpam-3752	251	5	x2	x2	PROPN
ejpam-3752	251	6	·	·	PUNCT
ejpam-3752	251	7	y2	y2	INTJ
ejpam-3752	251	8	,	,	PUNCT
ejpam-3752	251	9	y2	y2	PROPN
ejpam-3752	251	10	·	·	PUNCT
ejpam-3752	252	1	x2	x2	PROPN
ejpam-3752	252	2	∈	∈	PROPN
ejpam-3752	252	3	t−1({0	t−1({0	PRON
ejpam-3752	252	4	t	t	NOUN
ejpam-3752	252	5	}	}	PUNCT
ejpam-3752	252	6	)	)	PUNCT
ejpam-3752	252	7	=	=	PUNCT
ejpam-3752	252	8	{	{	PUNCT
ejpam-3752	252	9	0	0	NUM
ejpam-3752	252	10	}	}	PUNCT
ejpam-3752	252	11	,	,	PUNCT
ejpam-3752	252	12	that	that	ADV
ejpam-3752	252	13	is	is	ADV
ejpam-3752	252	14	,	,	PUNCT
ejpam-3752	252	15	x2·y2	x2·y2	PROPN
ejpam-3752	252	16	=	=	SYM
ejpam-3752	252	17	0	0	NUM
ejpam-3752	252	18	and	and	CCONJ
ejpam-3752	252	19	y2·x2	y2·x2	NUM
ejpam-3752	252	20	=	=	SYM
ejpam-3752	252	21	0	0	X
ejpam-3752	252	22	.	.	PUNCT
ejpam-3752	252	23	by	by	ADP
ejpam-3752	252	24	(	(	PUNCT
ejpam-3752	252	25	up-4	up-4	ADV
ejpam-3752	252	26	)	)	PUNCT
ejpam-3752	252	27	,	,	PUNCT
ejpam-3752	252	28	we	we	PRON
ejpam-3752	252	29	have	have	VERB
ejpam-3752	252	30	x1	x1	NOUN
ejpam-3752	252	31	=	=	SYM
ejpam-3752	252	32	y1	y1	INTJ
ejpam-3752	252	33	and	and	CCONJ
ejpam-3752	252	34	x2	x2	NOUN
ejpam-3752	252	35	=	=	PUNCT
ejpam-3752	252	36	y2	y2	PROPN
ejpam-3752	252	37	.	.	PUNCT
ejpam-3752	253	1	thus	thus	ADV
ejpam-3752	253	2	x2	x2	NUM
ejpam-3752	253	3	t	t	NOUN
ejpam-3752	253	4	=	=	SYM
ejpam-3752	253	5	y2	y2	PROPN
ejpam-3752	253	6	t	t	PROPN
ejpam-3752	254	1	and	and	CCONJ
ejpam-3752	255	1	so	so	ADV
ejpam-3752	255	2	x̃	x̃	PROPN
ejpam-3752	255	3	=	=	PUNCT
ejpam-3752	255	4	(	(	PUNCT
ejpam-3752	255	5	x1	x1	PROPN
ejpam-3752	255	6	,	,	PUNCT
ejpam-3752	255	7	x2	x2	PROPN
ejpam-3752	255	8	t	t	PROPN
ejpam-3752	255	9	)	)	PUNCT
ejpam-3752	256	1	=	=	SYM
ejpam-3752	256	2	(	(	PUNCT
ejpam-3752	256	3	y1	y1	INTJ
ejpam-3752	256	4	,	,	PUNCT
ejpam-3752	256	5	y2	y2	NOUN
ejpam-3752	256	6	t	t	PROPN
ejpam-3752	256	7	)	)	PUNCT
ejpam-3752	257	1	=	=	SYM
ejpam-3752	257	2	ỹ	ỹ	PROPN
ejpam-3752	257	3	,	,	PUNCT
ejpam-3752	257	4	(	(	PUNCT
ejpam-3752	257	5	up-4	up-4	ADV
ejpam-3752	257	6	)	)	PUNCT
ejpam-3752	257	7	holding	holding	NOUN
ejpam-3752	257	8	.	.	PUNCT
ejpam-3752	258	1	by	by	ADP
ejpam-3752	258	2	theorem	theorem	NOUN
ejpam-3752	258	3	1	1	NUM
ejpam-3752	258	4	,	,	PUNCT
ejpam-3752	258	5	we	we	PRON
ejpam-3752	258	6	have	have	VERB
ejpam-3752	258	7	(	(	PUNCT
ejpam-3752	258	8	x	x	SYM
ejpam-3752	258	9	×	×	NOUN
ejpam-3752	258	10	im(t	im(t	ADJ
ejpam-3752	258	11	)	)	PUNCT
ejpam-3752	258	12	,	,	PUNCT
ejpam-3752	258	13	�	�	PROPN
ejpam-3752	258	14	,	,	PUNCT
ejpam-3752	258	15	0̃	0̃	PROPN
ejpam-3752	258	16	)	)	PUNCT
ejpam-3752	258	17	is	be	AUX
ejpam-3752	258	18	a	a	DET
ejpam-3752	258	19	up	up	NOUN
ejpam-3752	258	20	-	-	PUNCT
ejpam-3752	258	21	algebra	algebra	NOUN
ejpam-3752	258	22	.	.	PUNCT
ejpam-3752	259	1	a.	a.	PROPN
ejpam-3752	259	2	iampan	iampan	PROPN
ejpam-3752	259	3	,	,	PUNCT
ejpam-3752	259	4	m.	m.	PROPN
ejpam-3752	259	5	songsaeng	songsaeng	PROPN
ejpam-3752	259	6	,	,	PUNCT
ejpam-3752	259	7	g.	g.	PROPN
ejpam-3752	259	8	muhiuddin	muhiuddin	PROPN
ejpam-3752	259	9	/	/	SYM
ejpam-3752	259	10	eur	eur	PROPN
ejpam-3752	259	11	.	.	PUNCT
ejpam-3752	260	1	j.	j.	PROPN
ejpam-3752	260	2	pure	pure	PROPN
ejpam-3752	260	3	appl	appl	PROPN
ejpam-3752	260	4	.	.	PROPN
ejpam-3752	260	5	math	math	PROPN
ejpam-3752	260	6	,	,	PUNCT
ejpam-3752	260	7	13	13	NUM
ejpam-3752	260	8	(	(	PUNCT
ejpam-3752	260	9	3	3	NUM
ejpam-3752	260	10	)	)	PUNCT
ejpam-3752	260	11	(	(	PUNCT
ejpam-3752	260	12	2020	2020	NUM
ejpam-3752	260	13	)	)	PUNCT
ejpam-3752	260	14	,	,	PUNCT
ejpam-3752	260	15	459	459	NUM
ejpam-3752	260	16	-	-	SYM
ejpam-3752	260	17	471	471	NUM
ejpam-3752	260	18	467	467	NUM
ejpam-3752	260	19	corollary	corollary	ADJ
ejpam-3752	260	20	2	2	NUM
ejpam-3752	260	21	.	.	PUNCT
ejpam-3752	261	1	if	if	SCONJ
ejpam-3752	261	2	t	t	NOUN
ejpam-3752	261	3	:	:	PUNCT
ejpam-3752	261	4	x	x	X
ejpam-3752	261	5	→	→	SYM
ejpam-3752	261	6	y	y	PROPN
ejpam-3752	261	7	is	be	AUX
ejpam-3752	261	8	an	an	DET
ejpam-3752	261	9	injective	injective	ADJ
ejpam-3752	261	10	function	function	NOUN
ejpam-3752	261	11	,	,	PUNCT
ejpam-3752	261	12	then	then	ADV
ejpam-3752	261	13	the	the	DET
ejpam-3752	261	14	algebra	algebra	NOUN
ejpam-3752	261	15	(	(	PUNCT
ejpam-3752	261	16	x	x	SYM
ejpam-3752	261	17	×	×	NOUN
ejpam-3752	261	18	im(t	im(t	ADJ
ejpam-3752	261	19	)	)	PUNCT
ejpam-3752	261	20	,	,	PUNCT
ejpam-3752	261	21	�	�	PROPN
ejpam-3752	261	22	,	,	PUNCT
ejpam-3752	261	23	0̃	0̃	PROPN
ejpam-3752	261	24	)	)	PUNCT
ejpam-3752	261	25	is	be	AUX
ejpam-3752	261	26	a	a	DET
ejpam-3752	261	27	up	up	NOUN
ejpam-3752	261	28	-	-	PUNCT
ejpam-3752	261	29	algebra	algebra	NOUN
ejpam-3752	261	30	.	.	PUNCT
ejpam-3752	262	1	proof	proof	NOUN
ejpam-3752	262	2	.	.	PUNCT
ejpam-3752	263	1	if	if	SCONJ
ejpam-3752	263	2	t	t	NOUN
ejpam-3752	263	3	:	:	PUNCT
ejpam-3752	263	4	x	x	X
ejpam-3752	263	5	→	→	SYM
ejpam-3752	263	6	y	y	PROPN
ejpam-3752	263	7	is	be	AUX
ejpam-3752	263	8	an	an	DET
ejpam-3752	263	9	injective	injective	ADJ
ejpam-3752	263	10	function	function	NOUN
ejpam-3752	263	11	,	,	PUNCT
ejpam-3752	263	12	then	then	ADV
ejpam-3752	263	13	the	the	DET
ejpam-3752	263	14	inverse	inverse	NOUN
ejpam-3752	263	15	image	image	NOUN
ejpam-3752	263	16	t−1({0	t−1({0	ADP
ejpam-3752	263	17	t	t	NOUN
ejpam-3752	263	18	}	}	PUNCT
ejpam-3752	263	19	)	)	PUNCT
ejpam-3752	264	1	=	=	PUNCT
ejpam-3752	264	2	{	{	PUNCT
ejpam-3752	264	3	0	0	NUM
ejpam-3752	264	4	}	}	PUNCT
ejpam-3752	264	5	.	.	PUNCT
ejpam-3752	265	1	by	by	ADP
ejpam-3752	265	2	theorem	theorem	NOUN
ejpam-3752	265	3	3	3	NUM
ejpam-3752	265	4	,	,	PUNCT
ejpam-3752	265	5	we	we	PRON
ejpam-3752	265	6	have	have	VERB
ejpam-3752	265	7	the	the	DET
ejpam-3752	265	8	algebra	algebra	NOUN
ejpam-3752	265	9	(	(	PUNCT
ejpam-3752	265	10	x	x	SYM
ejpam-3752	265	11	×	×	NOUN
ejpam-3752	265	12	im(t	im(t	ADJ
ejpam-3752	265	13	)	)	PUNCT
ejpam-3752	265	14	,	,	PUNCT
ejpam-3752	265	15	�	�	PROPN
ejpam-3752	265	16	,	,	PUNCT
ejpam-3752	265	17	0̃	0̃	PROPN
ejpam-3752	265	18	)	)	PUNCT
ejpam-3752	265	19	is	be	AUX
ejpam-3752	265	20	a	a	DET
ejpam-3752	265	21	up	up	NOUN
ejpam-3752	265	22	-	-	PUNCT
ejpam-3752	265	23	algebra	algebra	NOUN
ejpam-3752	265	24	.	.	PUNCT
ejpam-3752	266	1	theorem	theorem	NOUN
ejpam-3752	266	2	4	4	NUM
ejpam-3752	266	3	.	.	PUNCT
ejpam-3752	267	1	let	let	VERB
ejpam-3752	267	2	a	a	PRON
ejpam-3752	267	3	and	and	CCONJ
ejpam-3752	267	4	b	b	NOUN
ejpam-3752	267	5	be	be	AUX
ejpam-3752	267	6	nonempty	nonempty	X
ejpam-3752	267	7	subsets	subset	NOUN
ejpam-3752	267	8	of	of	ADP
ejpam-3752	267	9	a	a	DET
ejpam-3752	267	10	up	up	NOUN
ejpam-3752	267	11	-	-	PUNCT
ejpam-3752	267	12	algebra	algebra	NOUN
ejpam-3752	267	13	x	x	PUNCT
ejpam-3752	267	14	and	and	CCONJ
ejpam-3752	267	15	(	(	PUNCT
ejpam-3752	267	16	x×	x×	X
ejpam-3752	267	17	im(t	im(t	ADJ
ejpam-3752	267	18	)	)	PUNCT
ejpam-3752	267	19	,	,	PUNCT
ejpam-3752	267	20	�	�	PROPN
ejpam-3752	267	21	,	,	PUNCT
ejpam-3752	267	22	0̃	0̃	PROPN
ejpam-3752	267	23	)	)	PUNCT
ejpam-3752	267	24	be	be	VERB
ejpam-3752	267	25	a	a	DET
ejpam-3752	267	26	fuzzy	fuzzy	ADJ
ejpam-3752	267	27	duplex	duplex	NOUN
ejpam-3752	267	28	up	up	ADP
ejpam-3752	267	29	-	-	PUNCT
ejpam-3752	267	30	algebra	algebra	NOUN
ejpam-3752	267	31	.	.	PUNCT
ejpam-3752	268	1	(	(	PUNCT
ejpam-3752	268	2	1	1	X
ejpam-3752	268	3	)	)	PUNCT
ejpam-3752	268	4	if	if	SCONJ
ejpam-3752	268	5	a	a	PRON
ejpam-3752	268	6	and	and	CCONJ
ejpam-3752	268	7	b	b	NOUN
ejpam-3752	268	8	are	be	AUX
ejpam-3752	268	9	up	up	ADV
ejpam-3752	268	10	-	-	PUNCT
ejpam-3752	268	11	subalgebras	subalgebras	NOUN
ejpam-3752	268	12	of	of	ADP
ejpam-3752	268	13	x	x	PRON
ejpam-3752	268	14	,	,	PUNCT
ejpam-3752	268	15	then	then	ADV
ejpam-3752	268	16	a×t	a×t	PROPN
ejpam-3752	268	17	(	(	PUNCT
ejpam-3752	268	18	b	b	NOUN
ejpam-3752	268	19	)	)	PUNCT
ejpam-3752	268	20	is	be	AUX
ejpam-3752	268	21	a	a	DET
ejpam-3752	268	22	up	up	ADJ
ejpam-3752	268	23	-	-	PUNCT
ejpam-3752	268	24	subalgebra	subalgebra	NOUN
ejpam-3752	268	25	of	of	ADP
ejpam-3752	268	26	x×im(t	x×im(t	PROPN
ejpam-3752	268	27	)	)	PUNCT
ejpam-3752	268	28	.	.	PUNCT
ejpam-3752	269	1	(	(	PUNCT
ejpam-3752	269	2	2	2	X
ejpam-3752	269	3	)	)	PUNCT
ejpam-3752	269	4	if	if	SCONJ
ejpam-3752	269	5	a×	a×	PROPN
ejpam-3752	269	6	t	t	PROPN
ejpam-3752	269	7	(	(	PUNCT
ejpam-3752	269	8	b	b	NOUN
ejpam-3752	269	9	)	)	PUNCT
ejpam-3752	269	10	is	be	AUX
ejpam-3752	269	11	a	a	DET
ejpam-3752	269	12	up	up	ADJ
ejpam-3752	269	13	-	-	PUNCT
ejpam-3752	269	14	subalgebra	subalgebra	NOUN
ejpam-3752	269	15	of	of	ADP
ejpam-3752	269	16	x	x	SYM
ejpam-3752	269	17	×	×	NOUN
ejpam-3752	269	18	im(t	im(t	ADJ
ejpam-3752	269	19	)	)	PUNCT
ejpam-3752	269	20	,	,	PUNCT
ejpam-3752	269	21	then	then	ADV
ejpam-3752	269	22	a	a	PRON
ejpam-3752	269	23	is	be	AUX
ejpam-3752	269	24	a	a	DET
ejpam-3752	269	25	up	up	ADJ
ejpam-3752	269	26	-	-	PUNCT
ejpam-3752	269	27	subalgebra	subalgebra	NOUN
ejpam-3752	269	28	of	of	ADP
ejpam-3752	269	29	x.	x.	NOUN
ejpam-3752	269	30	proof	proof	NOUN
ejpam-3752	269	31	.	.	PUNCT
ejpam-3752	270	1	(	(	PUNCT
ejpam-3752	270	2	1	1	X
ejpam-3752	270	3	)	)	PUNCT
ejpam-3752	270	4	assume	assume	VERB
ejpam-3752	270	5	that	that	SCONJ
ejpam-3752	270	6	a	a	PRON
ejpam-3752	270	7	and	and	CCONJ
ejpam-3752	270	8	b	b	NOUN
ejpam-3752	270	9	are	be	AUX
ejpam-3752	270	10	up	up	ADV
ejpam-3752	270	11	-	-	PUNCT
ejpam-3752	270	12	subalgebras	subalgebra	NOUN
ejpam-3752	270	13	of	of	ADP
ejpam-3752	270	14	x	x	PUNCT
ejpam-3752	270	15	and	and	CCONJ
ejpam-3752	270	16	let	let	VERB
ejpam-3752	270	17	x̃	x̃	PROPN
ejpam-3752	270	18	,	,	PUNCT
ejpam-3752	270	19	ỹ	ỹ	PROPN
ejpam-3752	270	20	∈	∈	PROPN
ejpam-3752	270	21	a	a	DET
ejpam-3752	270	22	×	×	NOUN
ejpam-3752	270	23	t	t	NOUN
ejpam-3752	270	24	(	(	PUNCT
ejpam-3752	270	25	b	b	NOUN
ejpam-3752	270	26	)	)	PUNCT
ejpam-3752	270	27	where	where	SCONJ
ejpam-3752	270	28	x̃	x̃	PROPN
ejpam-3752	270	29	=	=	PROPN
ejpam-3752	270	30	(	(	PUNCT
ejpam-3752	270	31	a1	a1	PROPN
ejpam-3752	270	32	,	,	PUNCT
ejpam-3752	270	33	b1	b1	NOUN
ejpam-3752	270	34	t	t	PROPN
ejpam-3752	270	35	)	)	PUNCT
ejpam-3752	270	36	and	and	CCONJ
ejpam-3752	270	37	ỹ	ỹ	PROPN
ejpam-3752	270	38	=	=	SYM
ejpam-3752	270	39	(	(	PUNCT
ejpam-3752	270	40	a2	a2	PROPN
ejpam-3752	270	41	,	,	PUNCT
ejpam-3752	270	42	b2	b2	NOUN
ejpam-3752	270	43	t	t	PROPN
ejpam-3752	270	44	)	)	PUNCT
ejpam-3752	270	45	.	.	PUNCT
ejpam-3752	271	1	then	then	ADV
ejpam-3752	271	2	a1	a1	NOUN
ejpam-3752	271	3	·	·	PUNCT
ejpam-3752	271	4	a2	a2	PROPN
ejpam-3752	271	5	∈	∈	PROPN
ejpam-3752	271	6	a	a	PRON
ejpam-3752	271	7	and	and	CCONJ
ejpam-3752	271	8	b1	b1	NOUN
ejpam-3752	271	9	·	·	PUNCT
ejpam-3752	271	10	b2	b2	PROPN
ejpam-3752	271	11	∈	∈	PROPN
ejpam-3752	271	12	b.	b.	NOUN
ejpam-3752	272	1	thus	thus	ADV
ejpam-3752	272	2	x̃	x̃	PROPN
ejpam-3752	272	3	�	�	PROPN
ejpam-3752	272	4	ỹ	ỹ	PROPN
ejpam-3752	272	5	=	=	SYM
ejpam-3752	272	6	(	(	PUNCT
ejpam-3752	272	7	a1	a1	PROPN
ejpam-3752	272	8	,	,	PUNCT
ejpam-3752	272	9	b1	b1	NOUN
ejpam-3752	272	10	t	t	PROPN
ejpam-3752	272	11	)	)	PUNCT
ejpam-3752	272	12	�	�	PROPN
ejpam-3752	272	13	(	(	PUNCT
ejpam-3752	272	14	a2	a2	PROPN
ejpam-3752	272	15	,	,	PUNCT
ejpam-3752	272	16	b2	b2	NOUN
ejpam-3752	272	17	t	t	NOUN
ejpam-3752	272	18	)	)	PUNCT
ejpam-3752	272	19	=	=	PUNCT
ejpam-3752	272	20	(	(	PUNCT
ejpam-3752	272	21	a1	a1	PROPN
ejpam-3752	272	22	·	·	SYM
ejpam-3752	272	23	a2	a2	PROPN
ejpam-3752	272	24	,	,	PUNCT
ejpam-3752	272	25	(	(	PUNCT
ejpam-3752	272	26	b1	b1	NOUN
ejpam-3752	272	27	·	·	SYM
ejpam-3752	272	28	b2)t	b2)t	X
ejpam-3752	272	29	)	)	PUNCT
ejpam-3752	272	30	∈	∈	PROPN
ejpam-3752	273	1	a×t	a×t	PROPN
ejpam-3752	273	2	(	(	PUNCT
ejpam-3752	273	3	b	b	NOUN
ejpam-3752	273	4	)	)	PUNCT
ejpam-3752	273	5	.	.	PUNCT
ejpam-3752	274	1	hence	hence	ADV
ejpam-3752	274	2	,	,	PUNCT
ejpam-3752	274	3	a×t	a×t	PROPN
ejpam-3752	274	4	(	(	PUNCT
ejpam-3752	274	5	b	b	NOUN
ejpam-3752	274	6	)	)	PUNCT
ejpam-3752	274	7	is	be	AUX
ejpam-3752	274	8	a	a	DET
ejpam-3752	274	9	up	up	ADJ
ejpam-3752	274	10	-	-	PUNCT
ejpam-3752	274	11	subalgebra	subalgebra	NOUN
ejpam-3752	274	12	of	of	ADP
ejpam-3752	274	13	x	x	SYM
ejpam-3752	274	14	×	×	NOUN
ejpam-3752	274	15	im(t	im(t	NOUN
ejpam-3752	274	16	)	)	PUNCT
ejpam-3752	274	17	.	.	PUNCT
ejpam-3752	275	1	(	(	PUNCT
ejpam-3752	275	2	2	2	X
ejpam-3752	275	3	)	)	PUNCT
ejpam-3752	275	4	assume	assume	VERB
ejpam-3752	275	5	that	that	SCONJ
ejpam-3752	275	6	a	a	DET
ejpam-3752	275	7	×	×	PROPN
ejpam-3752	275	8	t	t	NOUN
ejpam-3752	275	9	(	(	PUNCT
ejpam-3752	275	10	b	b	NOUN
ejpam-3752	275	11	)	)	PUNCT
ejpam-3752	275	12	is	be	AUX
ejpam-3752	275	13	a	a	DET
ejpam-3752	275	14	up	up	ADJ
ejpam-3752	275	15	-	-	PUNCT
ejpam-3752	275	16	subalgebra	subalgebra	NOUN
ejpam-3752	275	17	of	of	ADP
ejpam-3752	275	18	x	x	SYM
ejpam-3752	275	19	×	×	NOUN
ejpam-3752	275	20	im(t	im(t	ADJ
ejpam-3752	275	21	)	)	PUNCT
ejpam-3752	275	22	.	.	PUNCT
ejpam-3752	276	1	let	let	VERB
ejpam-3752	276	2	x	x	PRON
ejpam-3752	276	3	,	,	PUNCT
ejpam-3752	276	4	y	y	PROPN
ejpam-3752	276	5	∈	∈	PROPN
ejpam-3752	276	6	a.	a.	AUX
ejpam-3752	276	7	since	since	SCONJ
ejpam-3752	276	8	(	(	PUNCT
ejpam-3752	276	9	0	0	NUM
ejpam-3752	276	10	,	,	PUNCT
ejpam-3752	276	11	0	0	NUM
ejpam-3752	276	12	t	t	NOUN
ejpam-3752	276	13	)	)	PUNCT
ejpam-3752	276	14	∈	∈	PROPN
ejpam-3752	276	15	a	a	DET
ejpam-3752	276	16	×	×	PROPN
ejpam-3752	276	17	t	t	NOUN
ejpam-3752	276	18	(	(	PUNCT
ejpam-3752	276	19	b	b	NOUN
ejpam-3752	276	20	)	)	PUNCT
ejpam-3752	276	21	,	,	PUNCT
ejpam-3752	276	22	we	we	PRON
ejpam-3752	276	23	have	have	VERB
ejpam-3752	276	24	then	then	ADV
ejpam-3752	276	25	(	(	PUNCT
ejpam-3752	276	26	x	x	X
ejpam-3752	276	27	,	,	PUNCT
ejpam-3752	276	28	0	0	NUM
ejpam-3752	276	29	t	t	NOUN
ejpam-3752	276	30	)	)	PUNCT
ejpam-3752	276	31	,	,	PUNCT
ejpam-3752	276	32	(	(	PUNCT
ejpam-3752	276	33	y	y	NOUN
ejpam-3752	276	34	,	,	PUNCT
ejpam-3752	276	35	0	0	NUM
ejpam-3752	276	36	t	t	NOUN
ejpam-3752	276	37	)	)	PUNCT
ejpam-3752	276	38	∈	∈	PROPN
ejpam-3752	276	39	a	a	DET
ejpam-3752	276	40	×	×	PROPN
ejpam-3752	276	41	t	t	NOUN
ejpam-3752	276	42	(	(	PUNCT
ejpam-3752	276	43	b	b	NOUN
ejpam-3752	276	44	)	)	PUNCT
ejpam-3752	276	45	.	.	PUNCT
ejpam-3752	277	1	thus	thus	ADV
ejpam-3752	277	2	(	(	PUNCT
ejpam-3752	277	3	x	x	X
ejpam-3752	277	4	·	·	PUNCT
ejpam-3752	277	5	y	y	NOUN
ejpam-3752	277	6	,	,	PUNCT
ejpam-3752	277	7	0	0	NUM
ejpam-3752	277	8	t	t	NOUN
ejpam-3752	277	9	)	)	PUNCT
ejpam-3752	277	10	=	=	SYM
ejpam-3752	277	11	(	(	PUNCT
ejpam-3752	277	12	x	x	X
ejpam-3752	277	13	·	·	PUNCT
ejpam-3752	277	14	y	y	NOUN
ejpam-3752	277	15	,	,	PUNCT
ejpam-3752	277	16	(	(	PUNCT
ejpam-3752	277	17	0	0	NUM
ejpam-3752	277	18	·	·	SYM
ejpam-3752	277	19	0)t	0)t	NOUN
ejpam-3752	277	20	)	)	PUNCT
ejpam-3752	278	1	=	=	SYM
ejpam-3752	278	2	(	(	PUNCT
ejpam-3752	278	3	x	x	X
ejpam-3752	278	4	,	,	PUNCT
ejpam-3752	278	5	0	0	NUM
ejpam-3752	278	6	t	t	NOUN
ejpam-3752	278	7	)	)	PUNCT
ejpam-3752	278	8	�	�	PROPN
ejpam-3752	278	9	(	(	PUNCT
ejpam-3752	278	10	y	y	PROPN
ejpam-3752	278	11	,	,	PUNCT
ejpam-3752	278	12	0	0	NUM
ejpam-3752	278	13	t	t	NOUN
ejpam-3752	279	1	)	)	PUNCT
ejpam-3752	279	2	∈	∈	PROPN
ejpam-3752	279	3	a×	a×	PROPN
ejpam-3752	279	4	t	t	PROPN
ejpam-3752	279	5	(	(	PUNCT
ejpam-3752	279	6	b	b	NOUN
ejpam-3752	279	7	)	)	PUNCT
ejpam-3752	279	8	,	,	PUNCT
ejpam-3752	279	9	so	so	ADV
ejpam-3752	279	10	x	x	SYM
ejpam-3752	279	11	·	·	PUNCT
ejpam-3752	279	12	y	y	SYM
ejpam-3752	279	13	∈	∈	PROPN
ejpam-3752	279	14	a.	a.	NOUN
ejpam-3752	279	15	hence	hence	ADV
ejpam-3752	279	16	,	,	PUNCT
ejpam-3752	279	17	a	a	PRON
ejpam-3752	279	18	is	be	AUX
ejpam-3752	279	19	a	a	DET
ejpam-3752	279	20	up	up	ADJ
ejpam-3752	279	21	-	-	PUNCT
ejpam-3752	279	22	subalgebra	subalgebra	NOUN
ejpam-3752	279	23	of	of	ADP
ejpam-3752	279	24	x.	x.	NOUN
ejpam-3752	279	25	theorem	theorem	VERB
ejpam-3752	279	26	5	5	NUM
ejpam-3752	279	27	.	.	PUNCT
ejpam-3752	280	1	let	let	VERB
ejpam-3752	280	2	a	a	PRON
ejpam-3752	280	3	and	and	CCONJ
ejpam-3752	280	4	b	b	NOUN
ejpam-3752	280	5	be	be	AUX
ejpam-3752	280	6	nonempty	nonempty	X
ejpam-3752	280	7	subsets	subset	NOUN
ejpam-3752	280	8	of	of	ADP
ejpam-3752	280	9	a	a	DET
ejpam-3752	280	10	up	up	NOUN
ejpam-3752	280	11	-	-	PUNCT
ejpam-3752	280	12	algebra	algebra	NOUN
ejpam-3752	280	13	x	x	PUNCT
ejpam-3752	280	14	and	and	CCONJ
ejpam-3752	280	15	(	(	PUNCT
ejpam-3752	280	16	x×	x×	X
ejpam-3752	280	17	im(t	im(t	ADJ
ejpam-3752	280	18	)	)	PUNCT
ejpam-3752	280	19	,	,	PUNCT
ejpam-3752	280	20	�	�	PROPN
ejpam-3752	280	21	,	,	PUNCT
ejpam-3752	280	22	0̃	0̃	PROPN
ejpam-3752	280	23	)	)	PUNCT
ejpam-3752	280	24	be	be	VERB
ejpam-3752	280	25	a	a	DET
ejpam-3752	280	26	fuzzy	fuzzy	ADJ
ejpam-3752	280	27	duplex	duplex	NOUN
ejpam-3752	280	28	up	up	ADP
ejpam-3752	280	29	-	-	PUNCT
ejpam-3752	280	30	algebra	algebra	NOUN
ejpam-3752	280	31	.	.	PUNCT
ejpam-3752	281	1	(	(	PUNCT
ejpam-3752	281	2	1	1	X
ejpam-3752	281	3	)	)	PUNCT
ejpam-3752	281	4	if	if	SCONJ
ejpam-3752	281	5	a	a	PRON
ejpam-3752	281	6	and	and	CCONJ
ejpam-3752	281	7	b	b	NOUN
ejpam-3752	281	8	are	be	AUX
ejpam-3752	281	9	near	near	ADP
ejpam-3752	281	10	up	up	ADP
ejpam-3752	281	11	-	-	PUNCT
ejpam-3752	281	12	filters	filter	NOUN
ejpam-3752	281	13	of	of	ADP
ejpam-3752	281	14	x	x	NOUN
ejpam-3752	281	15	,	,	PUNCT
ejpam-3752	281	16	then	then	ADV
ejpam-3752	281	17	a×t	a×t	PROPN
ejpam-3752	281	18	(	(	PUNCT
ejpam-3752	281	19	b	b	NOUN
ejpam-3752	281	20	)	)	PUNCT
ejpam-3752	281	21	is	be	AUX
ejpam-3752	281	22	a	a	DET
ejpam-3752	281	23	near	near	ADJ
ejpam-3752	281	24	up	up	NOUN
ejpam-3752	281	25	-	-	PUNCT
ejpam-3752	281	26	filter	filter	NOUN
ejpam-3752	281	27	of	of	ADP
ejpam-3752	281	28	x×im(t	x×im(t	PROPN
ejpam-3752	281	29	)	)	PUNCT
ejpam-3752	281	30	.	.	PUNCT
ejpam-3752	282	1	(	(	PUNCT
ejpam-3752	282	2	2	2	X
ejpam-3752	282	3	)	)	PUNCT
ejpam-3752	282	4	if	if	SCONJ
ejpam-3752	282	5	a×	a×	PROPN
ejpam-3752	282	6	t	t	PROPN
ejpam-3752	282	7	(	(	PUNCT
ejpam-3752	282	8	b	b	NOUN
ejpam-3752	282	9	)	)	PUNCT
ejpam-3752	282	10	is	be	AUX
ejpam-3752	282	11	a	a	DET
ejpam-3752	282	12	near	near	ADJ
ejpam-3752	282	13	up	up	NOUN
ejpam-3752	282	14	-	-	PUNCT
ejpam-3752	282	15	filter	filter	NOUN
ejpam-3752	282	16	of	of	ADP
ejpam-3752	282	17	x	x	SYM
ejpam-3752	282	18	×	×	NOUN
ejpam-3752	282	19	im(t	im(t	ADJ
ejpam-3752	282	20	)	)	PUNCT
ejpam-3752	282	21	,	,	PUNCT
ejpam-3752	282	22	then	then	ADV
ejpam-3752	282	23	a	a	PRON
ejpam-3752	282	24	is	be	AUX
ejpam-3752	282	25	a	a	DET
ejpam-3752	282	26	near	near	ADJ
ejpam-3752	282	27	up	up	NOUN
ejpam-3752	282	28	-	-	PUNCT
ejpam-3752	282	29	filter	filter	NOUN
ejpam-3752	282	30	of	of	ADP
ejpam-3752	282	31	x.	x.	NOUN
ejpam-3752	282	32	proof	proof	NOUN
ejpam-3752	282	33	.	.	PUNCT
ejpam-3752	283	1	(	(	PUNCT
ejpam-3752	283	2	1	1	X
ejpam-3752	283	3	)	)	PUNCT
ejpam-3752	283	4	assume	assume	VERB
ejpam-3752	283	5	that	that	SCONJ
ejpam-3752	283	6	a	a	PRON
ejpam-3752	283	7	and	and	CCONJ
ejpam-3752	283	8	b	b	NOUN
ejpam-3752	283	9	are	be	AUX
ejpam-3752	283	10	near	near	ADP
ejpam-3752	283	11	up	up	ADP
ejpam-3752	283	12	-	-	PUNCT
ejpam-3752	283	13	filters	filter	NOUN
ejpam-3752	283	14	of	of	ADP
ejpam-3752	283	15	x.	x.	NOUN
ejpam-3752	283	16	since	since	SCONJ
ejpam-3752	283	17	0	0	NUM
ejpam-3752	283	18	∈	∈	PROPN
ejpam-3752	283	19	a	a	DET
ejpam-3752	283	20	and	and	CCONJ
ejpam-3752	283	21	0	0	NUM
ejpam-3752	283	22	∈	∈	PROPN
ejpam-3752	283	23	b	b	NOUN
ejpam-3752	283	24	,	,	PUNCT
ejpam-3752	283	25	we	we	PRON
ejpam-3752	283	26	have	have	VERB
ejpam-3752	283	27	0̃	0̃	NOUN
ejpam-3752	283	28	=	=	SYM
ejpam-3752	283	29	(	(	PUNCT
ejpam-3752	283	30	0	0	NUM
ejpam-3752	283	31	,	,	PUNCT
ejpam-3752	283	32	0	0	NUM
ejpam-3752	283	33	t	t	NOUN
ejpam-3752	284	1	)	)	PUNCT
ejpam-3752	284	2	∈	∈	PROPN
ejpam-3752	284	3	a×	a×	PROPN
ejpam-3752	284	4	t	t	PROPN
ejpam-3752	284	5	(	(	PUNCT
ejpam-3752	284	6	b	b	NOUN
ejpam-3752	284	7	)	)	PUNCT
ejpam-3752	284	8	.	.	PUNCT
ejpam-3752	285	1	let	let	VERB
ejpam-3752	285	2	x̃	x̃	PROPN
ejpam-3752	285	3	∈	∈	PROPN
ejpam-3752	285	4	x	x	X
ejpam-3752	285	5	×	×	NOUN
ejpam-3752	285	6	im(t	im(t	ADJ
ejpam-3752	285	7	)	)	PUNCT
ejpam-3752	285	8	and	and	CCONJ
ejpam-3752	285	9	ỹ	ỹ	PROPN
ejpam-3752	285	10	∈	∈	PROPN
ejpam-3752	285	11	a×	a×	PROPN
ejpam-3752	285	12	t	t	PROPN
ejpam-3752	285	13	(	(	PUNCT
ejpam-3752	285	14	b	b	NOUN
ejpam-3752	285	15	)	)	PUNCT
ejpam-3752	285	16	where	where	SCONJ
ejpam-3752	285	17	x̃	x̃	PROPN
ejpam-3752	285	18	=	=	SYM
ejpam-3752	285	19	(	(	PUNCT
ejpam-3752	285	20	x1	x1	PROPN
ejpam-3752	285	21	,	,	PUNCT
ejpam-3752	285	22	x2	x2	PROPN
ejpam-3752	285	23	t	t	PROPN
ejpam-3752	285	24	)	)	PUNCT
ejpam-3752	285	25	and	and	CCONJ
ejpam-3752	285	26	ỹ	ỹ	PROPN
ejpam-3752	285	27	=	=	SYM
ejpam-3752	285	28	(	(	PUNCT
ejpam-3752	285	29	a	a	PRON
ejpam-3752	285	30	,	,	PUNCT
ejpam-3752	285	31	bt	bt	NOUN
ejpam-3752	285	32	)	)	PUNCT
ejpam-3752	285	33	.	.	PUNCT
ejpam-3752	286	1	thus	thus	ADV
ejpam-3752	286	2	x1	x1	PRON
ejpam-3752	286	3	·	·	PUNCT
ejpam-3752	286	4	a	a	DET
ejpam-3752	286	5	∈	∈	PROPN
ejpam-3752	286	6	a	a	PRON
ejpam-3752	286	7	and	and	CCONJ
ejpam-3752	286	8	x2	x2	PROPN
ejpam-3752	286	9	·	·	PUNCT
ejpam-3752	286	10	b	b	X
ejpam-3752	286	11	∈	∈	PROPN
ejpam-3752	286	12	b	b	PROPN
ejpam-3752	286	13	,	,	PUNCT
ejpam-3752	286	14	so	so	ADV
ejpam-3752	286	15	x̃	x̃	PROPN
ejpam-3752	286	16	�	�	PROPN
ejpam-3752	286	17	ỹ	ỹ	PROPN
ejpam-3752	286	18	=	=	SYM
ejpam-3752	286	19	(	(	PUNCT
ejpam-3752	286	20	x1	x1	PROPN
ejpam-3752	286	21	,	,	PUNCT
ejpam-3752	286	22	x2	x2	PROPN
ejpam-3752	286	23	t	t	PROPN
ejpam-3752	286	24	)	)	PUNCT
ejpam-3752	286	25	�	�	PROPN
ejpam-3752	286	26	(	(	PUNCT
ejpam-3752	286	27	a	a	PRON
ejpam-3752	286	28	,	,	PUNCT
ejpam-3752	286	29	bt	bt	NOUN
ejpam-3752	286	30	)	)	PUNCT
ejpam-3752	286	31	=	=	PRON
ejpam-3752	286	32	(	(	PUNCT
ejpam-3752	286	33	x1	x1	PROPN
ejpam-3752	286	34	·	·	PUNCT
ejpam-3752	286	35	a	a	X
ejpam-3752	286	36	,	,	PUNCT
ejpam-3752	286	37	(	(	PUNCT
ejpam-3752	286	38	x2	x2	PROPN
ejpam-3752	286	39	·	·	PUNCT
ejpam-3752	286	40	b)t	b)t	X
ejpam-3752	286	41	)	)	PUNCT
ejpam-3752	287	1	∈	∈	PROPN
ejpam-3752	288	1	a×	a×	PROPN
ejpam-3752	288	2	t	t	PROPN
ejpam-3752	288	3	(	(	PUNCT
ejpam-3752	288	4	b	b	NOUN
ejpam-3752	288	5	)	)	PUNCT
ejpam-3752	288	6	.	.	PUNCT
ejpam-3752	289	1	hence	hence	ADV
ejpam-3752	289	2	,	,	PUNCT
ejpam-3752	289	3	a×	a×	PROPN
ejpam-3752	289	4	t	t	PROPN
ejpam-3752	289	5	(	(	PUNCT
ejpam-3752	289	6	b	b	NOUN
ejpam-3752	289	7	)	)	PUNCT
ejpam-3752	289	8	is	be	AUX
ejpam-3752	289	9	a	a	DET
ejpam-3752	289	10	near	near	ADJ
ejpam-3752	289	11	up	up	NOUN
ejpam-3752	289	12	-	-	PUNCT
ejpam-3752	289	13	filter	filter	NOUN
ejpam-3752	289	14	of	of	ADP
ejpam-3752	289	15	x	x	SYM
ejpam-3752	289	16	×	×	NOUN
ejpam-3752	289	17	im(t	im(t	NOUN
ejpam-3752	289	18	)	)	PUNCT
ejpam-3752	289	19	.	.	PUNCT
ejpam-3752	290	1	(	(	PUNCT
ejpam-3752	290	2	2	2	X
ejpam-3752	290	3	)	)	PUNCT
ejpam-3752	290	4	assume	assume	VERB
ejpam-3752	290	5	that	that	SCONJ
ejpam-3752	290	6	a	a	DET
ejpam-3752	290	7	×	×	PROPN
ejpam-3752	290	8	t	t	NOUN
ejpam-3752	290	9	(	(	PUNCT
ejpam-3752	290	10	b	b	NOUN
ejpam-3752	290	11	)	)	PUNCT
ejpam-3752	290	12	is	be	AUX
ejpam-3752	290	13	a	a	DET
ejpam-3752	290	14	near	near	ADJ
ejpam-3752	290	15	up	up	NOUN
ejpam-3752	290	16	-	-	PUNCT
ejpam-3752	290	17	filter	filter	NOUN
ejpam-3752	290	18	of	of	ADP
ejpam-3752	290	19	x	x	SYM
ejpam-3752	290	20	×	×	NOUN
ejpam-3752	290	21	im(t	im(t	ADJ
ejpam-3752	290	22	)	)	PUNCT
ejpam-3752	290	23	.	.	PUNCT
ejpam-3752	291	1	since	since	SCONJ
ejpam-3752	291	2	0̃	0̃	NOUN
ejpam-3752	291	3	=	=	SYM
ejpam-3752	291	4	(	(	PUNCT
ejpam-3752	291	5	0	0	NUM
ejpam-3752	291	6	,	,	PUNCT
ejpam-3752	291	7	0	0	NUM
ejpam-3752	291	8	t	t	NOUN
ejpam-3752	291	9	)	)	PUNCT
ejpam-3752	291	10	∈	∈	PROPN
ejpam-3752	291	11	a	a	DET
ejpam-3752	291	12	×	×	PROPN
ejpam-3752	291	13	t	t	NOUN
ejpam-3752	291	14	(	(	PUNCT
ejpam-3752	291	15	b	b	NOUN
ejpam-3752	291	16	)	)	PUNCT
ejpam-3752	291	17	,	,	PUNCT
ejpam-3752	291	18	we	we	PRON
ejpam-3752	291	19	have	have	AUX
ejpam-3752	291	20	0	0	NUM
ejpam-3752	291	21	∈	∈	NOUN
ejpam-3752	291	22	a.	a.	NOUN
ejpam-3752	291	23	let	let	VERB
ejpam-3752	291	24	x	x	X
ejpam-3752	292	1	∈	∈	PROPN
ejpam-3752	292	2	x	x	X
ejpam-3752	292	3	and	and	CCONJ
ejpam-3752	292	4	a	a	DET
ejpam-3752	292	5	∈	∈	NOUN
ejpam-3752	292	6	a.	a.	NOUN
ejpam-3752	292	7	then	then	ADV
ejpam-3752	292	8	(	(	PUNCT
ejpam-3752	292	9	x	x	X
ejpam-3752	292	10	,	,	PUNCT
ejpam-3752	292	11	0	0	NUM
ejpam-3752	292	12	t	t	NOUN
ejpam-3752	292	13	)	)	PUNCT
ejpam-3752	292	14	∈	∈	PROPN
ejpam-3752	292	15	x	x	X
ejpam-3752	292	16	×	×	NOUN
ejpam-3752	292	17	im(t	im(t	ADJ
ejpam-3752	292	18	)	)	PUNCT
ejpam-3752	292	19	and	and	CCONJ
ejpam-3752	292	20	(	(	PUNCT
ejpam-3752	292	21	a	a	PRON
ejpam-3752	292	22	,	,	PUNCT
ejpam-3752	292	23	0	0	NUM
ejpam-3752	292	24	t	t	NOUN
ejpam-3752	292	25	)	)	PUNCT
ejpam-3752	292	26	∈	∈	PROPN
ejpam-3752	293	1	a×	a×	PROPN
ejpam-3752	293	2	t	t	PROPN
ejpam-3752	293	3	(	(	PUNCT
ejpam-3752	293	4	b	b	NOUN
ejpam-3752	293	5	)	)	PUNCT
ejpam-3752	293	6	.	.	PUNCT
ejpam-3752	294	1	thus	thus	ADV
ejpam-3752	294	2	(	(	PUNCT
ejpam-3752	294	3	x	x	X
ejpam-3752	294	4	·	·	PUNCT
ejpam-3752	294	5	a	a	X
ejpam-3752	294	6	,	,	PUNCT
ejpam-3752	294	7	0	0	NUM
ejpam-3752	294	8	t	t	NOUN
ejpam-3752	294	9	)	)	PUNCT
ejpam-3752	294	10	=	=	SYM
ejpam-3752	295	1	(	(	PUNCT
ejpam-3752	295	2	x	x	X
ejpam-3752	295	3	·	·	PUNCT
ejpam-3752	295	4	a	a	X
ejpam-3752	295	5	,	,	PUNCT
ejpam-3752	295	6	(	(	PUNCT
ejpam-3752	295	7	0	0	NUM
ejpam-3752	295	8	·	·	SYM
ejpam-3752	295	9	0)t	0)t	NOUN
ejpam-3752	295	10	)	)	PUNCT
ejpam-3752	296	1	=	=	SYM
ejpam-3752	296	2	(	(	PUNCT
ejpam-3752	296	3	x	x	X
ejpam-3752	296	4	,	,	PUNCT
ejpam-3752	296	5	0	0	NUM
ejpam-3752	296	6	t	t	NOUN
ejpam-3752	296	7	)	)	PUNCT
ejpam-3752	296	8	�	�	PROPN
ejpam-3752	296	9	(	(	PUNCT
ejpam-3752	296	10	a	a	PRON
ejpam-3752	296	11	,	,	PUNCT
ejpam-3752	296	12	0	0	NUM
ejpam-3752	296	13	t	t	NOUN
ejpam-3752	297	1	)	)	PUNCT
ejpam-3752	297	2	∈	∈	PROPN
ejpam-3752	297	3	a×	a×	PROPN
ejpam-3752	297	4	t	t	PROPN
ejpam-3752	297	5	(	(	PUNCT
ejpam-3752	297	6	b	b	NOUN
ejpam-3752	297	7	)	)	PUNCT
ejpam-3752	297	8	,	,	PUNCT
ejpam-3752	297	9	so	so	ADV
ejpam-3752	297	10	x	x	X
ejpam-3752	297	11	·	·	PUNCT
ejpam-3752	297	12	a	a	DET
ejpam-3752	297	13	∈	∈	PROPN
ejpam-3752	297	14	a.	a.	NOUN
ejpam-3752	297	15	hence	hence	ADV
ejpam-3752	297	16	,	,	PUNCT
ejpam-3752	297	17	a	a	PRON
ejpam-3752	297	18	is	be	AUX
ejpam-3752	297	19	a	a	DET
ejpam-3752	297	20	near	near	ADJ
ejpam-3752	297	21	up	up	NOUN
ejpam-3752	297	22	-	-	PUNCT
ejpam-3752	297	23	filter	filter	NOUN
ejpam-3752	297	24	of	of	ADP
ejpam-3752	297	25	x.	x.	PROPN
ejpam-3752	297	26	theorem	theorem	VERB
ejpam-3752	297	27	6	6	NUM
ejpam-3752	297	28	.	.	PUNCT
ejpam-3752	298	1	let	let	VERB
ejpam-3752	298	2	a	a	PRON
ejpam-3752	298	3	and	and	CCONJ
ejpam-3752	298	4	b	b	NOUN
ejpam-3752	298	5	be	be	AUX
ejpam-3752	298	6	nonempty	nonempty	X
ejpam-3752	298	7	subsets	subset	NOUN
ejpam-3752	298	8	of	of	ADP
ejpam-3752	298	9	a	a	DET
ejpam-3752	298	10	up	up	NOUN
ejpam-3752	298	11	-	-	PUNCT
ejpam-3752	298	12	algebra	algebra	NOUN
ejpam-3752	298	13	x	x	PUNCT
ejpam-3752	298	14	and	and	CCONJ
ejpam-3752	298	15	(	(	PUNCT
ejpam-3752	298	16	x×	x×	X
ejpam-3752	298	17	im(t	im(t	ADJ
ejpam-3752	298	18	)	)	PUNCT
ejpam-3752	298	19	,	,	PUNCT
ejpam-3752	298	20	�	�	PROPN
ejpam-3752	298	21	,	,	PUNCT
ejpam-3752	298	22	0̃	0̃	PROPN
ejpam-3752	298	23	)	)	PUNCT
ejpam-3752	298	24	be	be	VERB
ejpam-3752	298	25	a	a	DET
ejpam-3752	298	26	fuzzy	fuzzy	ADJ
ejpam-3752	298	27	duplex	duplex	NOUN
ejpam-3752	298	28	up	up	ADP
ejpam-3752	298	29	-	-	PUNCT
ejpam-3752	298	30	algebra	algebra	NOUN
ejpam-3752	298	31	.	.	PUNCT
ejpam-3752	299	1	if	if	SCONJ
ejpam-3752	299	2	a	a	DET
ejpam-3752	299	3	×	×	PROPN
ejpam-3752	299	4	t	t	NOUN
ejpam-3752	299	5	(	(	PUNCT
ejpam-3752	299	6	b	b	NOUN
ejpam-3752	299	7	)	)	PUNCT
ejpam-3752	299	8	is	be	AUX
ejpam-3752	299	9	a	a	DET
ejpam-3752	299	10	up	up	ADJ
ejpam-3752	299	11	-	-	PUNCT
ejpam-3752	299	12	filter	filter	NOUN
ejpam-3752	299	13	of	of	ADP
ejpam-3752	299	14	x	x	SYM
ejpam-3752	299	15	×	×	NOUN
ejpam-3752	299	16	im(t	im(t	ADJ
ejpam-3752	299	17	)	)	PUNCT
ejpam-3752	299	18	,	,	PUNCT
ejpam-3752	299	19	then	then	ADV
ejpam-3752	299	20	a	a	PRON
ejpam-3752	299	21	is	be	AUX
ejpam-3752	299	22	a	a	DET
ejpam-3752	299	23	up	up	ADJ
ejpam-3752	299	24	-	-	PUNCT
ejpam-3752	299	25	filter	filter	NOUN
ejpam-3752	299	26	of	of	ADP
ejpam-3752	299	27	x.	x.	NOUN
ejpam-3752	299	28	proof	proof	PROPN
ejpam-3752	299	29	.	.	PUNCT
ejpam-3752	300	1	assume	assume	VERB
ejpam-3752	300	2	that	that	SCONJ
ejpam-3752	300	3	a×t	a×t	PROPN
ejpam-3752	300	4	(	(	PUNCT
ejpam-3752	300	5	b	b	NOUN
ejpam-3752	300	6	)	)	PUNCT
ejpam-3752	300	7	is	be	AUX
ejpam-3752	300	8	a	a	DET
ejpam-3752	300	9	up	up	ADJ
ejpam-3752	300	10	-	-	PUNCT
ejpam-3752	300	11	filter	filter	NOUN
ejpam-3752	300	12	of	of	ADP
ejpam-3752	300	13	x×im(t	x×im(t	PROPN
ejpam-3752	300	14	)	)	PUNCT
ejpam-3752	300	15	.	.	PUNCT
ejpam-3752	301	1	since	since	SCONJ
ejpam-3752	301	2	0̃	0̃	NOUN
ejpam-3752	301	3	=	=	SYM
ejpam-3752	301	4	(	(	PUNCT
ejpam-3752	301	5	0	0	NUM
ejpam-3752	301	6	,	,	PUNCT
ejpam-3752	301	7	0	0	NUM
ejpam-3752	301	8	t	t	NOUN
ejpam-3752	301	9	)	)	PUNCT
ejpam-3752	301	10	∈	∈	PROPN
ejpam-3752	301	11	a×t	a×t	PROPN
ejpam-3752	301	12	(	(	PUNCT
ejpam-3752	301	13	b	b	NOUN
ejpam-3752	301	14	)	)	PUNCT
ejpam-3752	301	15	,	,	PUNCT
ejpam-3752	301	16	we	we	PRON
ejpam-3752	301	17	have	have	VERB
ejpam-3752	301	18	0	0	NUM
ejpam-3752	301	19	∈	∈	NOUN
ejpam-3752	301	20	a.	a.	NOUN
ejpam-3752	301	21	let	let	VERB
ejpam-3752	301	22	x	x	PRON
ejpam-3752	301	23	,	,	PUNCT
ejpam-3752	301	24	a	a	DET
ejpam-3752	301	25	∈	∈	NOUN
ejpam-3752	301	26	x	x	AUX
ejpam-3752	301	27	be	be	AUX
ejpam-3752	301	28	such	such	ADJ
ejpam-3752	301	29	that	that	SCONJ
ejpam-3752	301	30	a	a	DET
ejpam-3752	301	31	·	·	PUNCT
ejpam-3752	301	32	x	x	SYM
ejpam-3752	301	33	∈	∈	PROPN
ejpam-3752	301	34	a	a	PRON
ejpam-3752	301	35	and	and	CCONJ
ejpam-3752	301	36	a	a	DET
ejpam-3752	301	37	∈	∈	NOUN
ejpam-3752	301	38	a.	a.	NOUN
ejpam-3752	301	39	then	then	ADV
ejpam-3752	301	40	(	(	PUNCT
ejpam-3752	301	41	a	a	PRON
ejpam-3752	301	42	,	,	PUNCT
ejpam-3752	301	43	0	0	NUM
ejpam-3752	301	44	t	t	NOUN
ejpam-3752	301	45	)	)	PUNCT
ejpam-3752	301	46	�	�	PROPN
ejpam-3752	301	47	(	(	PUNCT
ejpam-3752	301	48	x	x	NOUN
ejpam-3752	301	49	,	,	PUNCT
ejpam-3752	301	50	0	0	NUM
ejpam-3752	301	51	t	t	NOUN
ejpam-3752	301	52	)	)	PUNCT
ejpam-3752	301	53	=	=	SYM
ejpam-3752	302	1	(	(	PUNCT
ejpam-3752	302	2	a	a	DET
ejpam-3752	302	3	·	·	SYM
ejpam-3752	302	4	x	x	NOUN
ejpam-3752	302	5	,	,	PUNCT
ejpam-3752	302	6	(	(	PUNCT
ejpam-3752	302	7	0	0	NUM
ejpam-3752	302	8	·	·	SYM
ejpam-3752	302	9	0)t	0)t	X
ejpam-3752	302	10	)	)	PUNCT
ejpam-3752	303	1	=	=	SYM
ejpam-3752	303	2	(	(	PUNCT
ejpam-3752	303	3	a	a	DET
ejpam-3752	303	4	·	·	SYM
ejpam-3752	303	5	x	x	NOUN
ejpam-3752	303	6	,	,	PUNCT
ejpam-3752	303	7	0	0	NUM
ejpam-3752	303	8	t	t	NOUN
ejpam-3752	303	9	)	)	PUNCT
ejpam-3752	303	10	∈	∈	PROPN
ejpam-3752	303	11	a×t	a×t	PROPN
ejpam-3752	303	12	(	(	PUNCT
ejpam-3752	303	13	b	b	NOUN
ejpam-3752	303	14	)	)	PUNCT
ejpam-3752	303	15	and	and	CCONJ
ejpam-3752	303	16	(	(	PUNCT
ejpam-3752	303	17	a	a	PRON
ejpam-3752	303	18	,	,	PUNCT
ejpam-3752	303	19	0	0	NUM
ejpam-3752	303	20	t	t	NOUN
ejpam-3752	303	21	)	)	PUNCT
ejpam-3752	303	22	∈	∈	PROPN
ejpam-3752	303	23	a×t	a×t	PROPN
ejpam-3752	303	24	(	(	PUNCT
ejpam-3752	303	25	b	b	NOUN
ejpam-3752	303	26	)	)	PUNCT
ejpam-3752	303	27	.	.	PUNCT
ejpam-3752	304	1	thus	thus	ADV
ejpam-3752	304	2	(	(	PUNCT
ejpam-3752	304	3	x	x	X
ejpam-3752	304	4	,	,	PUNCT
ejpam-3752	304	5	0	0	NUM
ejpam-3752	304	6	t	t	NOUN
ejpam-3752	304	7	)	)	PUNCT
ejpam-3752	304	8	∈	∈	PROPN
ejpam-3752	304	9	a×t	a×t	PROPN
ejpam-3752	304	10	(	(	PUNCT
ejpam-3752	304	11	b	b	NOUN
ejpam-3752	304	12	)	)	PUNCT
ejpam-3752	304	13	,	,	PUNCT
ejpam-3752	304	14	so	so	ADV
ejpam-3752	304	15	x	x	X
ejpam-3752	304	16	∈	∈	NOUN
ejpam-3752	304	17	a.	a.	NOUN
ejpam-3752	304	18	hence	hence	ADV
ejpam-3752	304	19	,	,	PUNCT
ejpam-3752	304	20	a	a	PRON
ejpam-3752	304	21	is	be	AUX
ejpam-3752	304	22	a	a	DET
ejpam-3752	304	23	up	up	ADJ
ejpam-3752	304	24	-	-	PUNCT
ejpam-3752	304	25	filter	filter	NOUN
ejpam-3752	304	26	of	of	ADP
ejpam-3752	304	27	x.	x.	PROPN
ejpam-3752	304	28	a.	a.	PROPN
ejpam-3752	304	29	iampan	iampan	PROPN
ejpam-3752	304	30	,	,	PUNCT
ejpam-3752	304	31	m.	m.	PROPN
ejpam-3752	304	32	songsaeng	songsaeng	PROPN
ejpam-3752	304	33	,	,	PUNCT
ejpam-3752	304	34	g.	g.	PROPN
ejpam-3752	304	35	muhiuddin	muhiuddin	PROPN
ejpam-3752	304	36	/	/	SYM
ejpam-3752	304	37	eur	eur	PROPN
ejpam-3752	304	38	.	.	PUNCT
ejpam-3752	305	1	j.	j.	PROPN
ejpam-3752	305	2	pure	pure	PROPN
ejpam-3752	305	3	appl	appl	PROPN
ejpam-3752	305	4	.	.	PROPN
ejpam-3752	305	5	math	math	PROPN
ejpam-3752	305	6	,	,	PUNCT
ejpam-3752	305	7	13	13	NUM
ejpam-3752	305	8	(	(	PUNCT
ejpam-3752	305	9	3	3	NUM
ejpam-3752	305	10	)	)	PUNCT
ejpam-3752	305	11	(	(	PUNCT
ejpam-3752	305	12	2020	2020	NUM
ejpam-3752	305	13	)	)	PUNCT
ejpam-3752	305	14	,	,	PUNCT
ejpam-3752	305	15	459	459	NUM
ejpam-3752	305	16	-	-	SYM
ejpam-3752	305	17	471	471	NUM
ejpam-3752	305	18	468	468	NUM
ejpam-3752	305	19	theorem	theorem	NOUN
ejpam-3752	305	20	7	7	NUM
ejpam-3752	305	21	.	.	PUNCT
ejpam-3752	306	1	let	let	VERB
ejpam-3752	306	2	a	a	PRON
ejpam-3752	306	3	and	and	CCONJ
ejpam-3752	306	4	b	b	NOUN
ejpam-3752	306	5	be	be	AUX
ejpam-3752	306	6	nonempty	nonempty	X
ejpam-3752	306	7	subsets	subset	NOUN
ejpam-3752	306	8	of	of	ADP
ejpam-3752	306	9	a	a	DET
ejpam-3752	306	10	up	up	NOUN
ejpam-3752	306	11	-	-	PUNCT
ejpam-3752	306	12	algebra	algebra	NOUN
ejpam-3752	306	13	x	x	PUNCT
ejpam-3752	306	14	and	and	CCONJ
ejpam-3752	306	15	(	(	PUNCT
ejpam-3752	306	16	x×	x×	X
ejpam-3752	306	17	im(t	im(t	ADJ
ejpam-3752	306	18	)	)	PUNCT
ejpam-3752	306	19	,	,	PUNCT
ejpam-3752	306	20	�	�	PROPN
ejpam-3752	306	21	,	,	PUNCT
ejpam-3752	306	22	0̃	0̃	PROPN
ejpam-3752	306	23	)	)	PUNCT
ejpam-3752	306	24	be	be	VERB
ejpam-3752	306	25	a	a	DET
ejpam-3752	306	26	fuzzy	fuzzy	ADJ
ejpam-3752	306	27	duplex	duplex	NOUN
ejpam-3752	306	28	up	up	ADP
ejpam-3752	306	29	-	-	PUNCT
ejpam-3752	306	30	algebra	algebra	NOUN
ejpam-3752	306	31	.	.	PUNCT
ejpam-3752	307	1	if	if	SCONJ
ejpam-3752	307	2	a×t	a×t	PROPN
ejpam-3752	307	3	(	(	PUNCT
ejpam-3752	307	4	b	b	NOUN
ejpam-3752	307	5	)	)	PUNCT
ejpam-3752	307	6	is	be	AUX
ejpam-3752	307	7	a	a	DET
ejpam-3752	307	8	up	up	ADJ
ejpam-3752	307	9	-	-	PUNCT
ejpam-3752	307	10	ideal	ideal	NOUN
ejpam-3752	307	11	of	of	ADP
ejpam-3752	307	12	x×im(t	x×im(t	PROPN
ejpam-3752	307	13	)	)	PUNCT
ejpam-3752	307	14	,	,	PUNCT
ejpam-3752	307	15	then	then	ADV
ejpam-3752	307	16	a	a	PRON
ejpam-3752	307	17	is	be	AUX
ejpam-3752	307	18	a	a	DET
ejpam-3752	307	19	up	up	ADJ
ejpam-3752	307	20	-	-	PUNCT
ejpam-3752	307	21	ideal	ideal	NOUN
ejpam-3752	307	22	of	of	ADP
ejpam-3752	307	23	x.	x.	NOUN
ejpam-3752	307	24	proof	proof	PROPN
ejpam-3752	307	25	.	.	PUNCT
ejpam-3752	308	1	assume	assume	VERB
ejpam-3752	308	2	that	that	SCONJ
ejpam-3752	308	3	a	a	DET
ejpam-3752	308	4	×	×	PROPN
ejpam-3752	308	5	t	t	NOUN
ejpam-3752	308	6	(	(	PUNCT
ejpam-3752	308	7	b	b	NOUN
ejpam-3752	308	8	)	)	PUNCT
ejpam-3752	308	9	is	be	AUX
ejpam-3752	308	10	a	a	DET
ejpam-3752	308	11	up	up	ADJ
ejpam-3752	308	12	-	-	PUNCT
ejpam-3752	308	13	ideal	ideal	NOUN
ejpam-3752	308	14	of	of	ADP
ejpam-3752	308	15	x	x	SYM
ejpam-3752	308	16	×	×	NOUN
ejpam-3752	308	17	im(t	im(t	ADJ
ejpam-3752	308	18	)	)	PUNCT
ejpam-3752	308	19	.	.	PUNCT
ejpam-3752	309	1	since	since	SCONJ
ejpam-3752	309	2	0̃	0̃	NOUN
ejpam-3752	309	3	=	=	SYM
ejpam-3752	309	4	(	(	PUNCT
ejpam-3752	309	5	0	0	NUM
ejpam-3752	309	6	,	,	PUNCT
ejpam-3752	309	7	0	0	NUM
ejpam-3752	309	8	t	t	NOUN
ejpam-3752	309	9	)	)	PUNCT
ejpam-3752	309	10	∈	∈	PROPN
ejpam-3752	309	11	a	a	DET
ejpam-3752	309	12	×	×	PROPN
ejpam-3752	309	13	t	t	NOUN
ejpam-3752	309	14	(	(	PUNCT
ejpam-3752	309	15	b	b	NOUN
ejpam-3752	309	16	)	)	PUNCT
ejpam-3752	309	17	,	,	PUNCT
ejpam-3752	309	18	we	we	PRON
ejpam-3752	309	19	have	have	AUX
ejpam-3752	309	20	0	0	NUM
ejpam-3752	309	21	∈	∈	NOUN
ejpam-3752	309	22	a.	a.	NOUN
ejpam-3752	309	23	let	let	VERB
ejpam-3752	309	24	x	x	NOUN
ejpam-3752	309	25	,	,	PUNCT
ejpam-3752	309	26	y	y	PROPN
ejpam-3752	309	27	,	,	PUNCT
ejpam-3752	309	28	z	z	NOUN
ejpam-3752	309	29	∈	∈	PROPN
ejpam-3752	309	30	x	x	AUX
ejpam-3752	309	31	be	be	AUX
ejpam-3752	309	32	such	such	ADJ
ejpam-3752	309	33	that	that	SCONJ
ejpam-3752	309	34	x	x	PART
ejpam-3752	309	35	·	·	PUNCT
ejpam-3752	309	36	(	(	PUNCT
ejpam-3752	309	37	y	y	PROPN
ejpam-3752	309	38	·	·	PUNCT
ejpam-3752	309	39	z	z	X
ejpam-3752	309	40	)	)	PUNCT
ejpam-3752	309	41	∈	∈	PROPN
ejpam-3752	309	42	a	a	PRON
ejpam-3752	310	1	and	and	CCONJ
ejpam-3752	310	2	y	y	PROPN
ejpam-3752	310	3	∈	∈	PROPN
ejpam-3752	310	4	a.	a.	NOUN
ejpam-3752	310	5	then	then	ADV
ejpam-3752	310	6	(	(	PUNCT
ejpam-3752	310	7	x	x	X
ejpam-3752	310	8	,	,	PUNCT
ejpam-3752	310	9	0	0	NUM
ejpam-3752	310	10	t	t	NOUN
ejpam-3752	310	11	)	)	PUNCT
ejpam-3752	310	12	�	�	PROPN
ejpam-3752	310	13	(	(	PUNCT
ejpam-3752	310	14	(	(	PUNCT
ejpam-3752	310	15	y	y	NOUN
ejpam-3752	310	16	,	,	PUNCT
ejpam-3752	310	17	0	0	NUM
ejpam-3752	310	18	t	t	NOUN
ejpam-3752	310	19	)	)	PUNCT
ejpam-3752	310	20	�	�	PROPN
ejpam-3752	310	21	(	(	PUNCT
ejpam-3752	310	22	z	z	NOUN
ejpam-3752	310	23	,	,	PUNCT
ejpam-3752	310	24	0	0	NUM
ejpam-3752	310	25	t	t	NOUN
ejpam-3752	310	26	)	)	PUNCT
ejpam-3752	310	27	)	)	PUNCT
ejpam-3752	311	1	=	=	PRON
ejpam-3752	311	2	(	(	PUNCT
ejpam-3752	311	3	x	x	PART
ejpam-3752	311	4	·	·	PUNCT
ejpam-3752	311	5	(	(	PUNCT
ejpam-3752	311	6	y	y	PROPN
ejpam-3752	311	7	·	·	PUNCT
ejpam-3752	311	8	z	z	X
ejpam-3752	311	9	)	)	PUNCT
ejpam-3752	311	10	,	,	PUNCT
ejpam-3752	311	11	(	(	PUNCT
ejpam-3752	311	12	0	0	NUM
ejpam-3752	311	13	·	·	PUNCT
ejpam-3752	311	14	(	(	PUNCT
ejpam-3752	311	15	0	0	NUM
ejpam-3752	311	16	·	·	SYM
ejpam-3752	311	17	0))t	0))t	NUM
ejpam-3752	311	18	)	)	PUNCT
ejpam-3752	312	1	=	=	SYM
ejpam-3752	312	2	(	(	PUNCT
ejpam-3752	312	3	x	x	PART
ejpam-3752	312	4	·	·	PUNCT
ejpam-3752	312	5	(	(	PUNCT
ejpam-3752	312	6	y	y	PROPN
ejpam-3752	312	7	·	·	PUNCT
ejpam-3752	312	8	z	z	X
ejpam-3752	312	9	)	)	PUNCT
ejpam-3752	312	10	,	,	PUNCT
ejpam-3752	313	1	0	0	NUM
ejpam-3752	313	2	t	t	NOUN
ejpam-3752	313	3	)	)	PUNCT
ejpam-3752	313	4	∈	∈	PROPN
ejpam-3752	314	1	a×	a×	PROPN
ejpam-3752	314	2	t	t	PROPN
ejpam-3752	314	3	(	(	PUNCT
ejpam-3752	314	4	b	b	NOUN
ejpam-3752	314	5	)	)	PUNCT
ejpam-3752	314	6	and	and	CCONJ
ejpam-3752	314	7	(	(	PUNCT
ejpam-3752	314	8	y	y	PROPN
ejpam-3752	314	9	,	,	PUNCT
ejpam-3752	314	10	0	0	NUM
ejpam-3752	314	11	t	t	NOUN
ejpam-3752	314	12	)	)	PUNCT
ejpam-3752	314	13	∈	∈	PROPN
ejpam-3752	314	14	a×	a×	PROPN
ejpam-3752	314	15	t	t	PROPN
ejpam-3752	314	16	(	(	PUNCT
ejpam-3752	314	17	b	b	NOUN
ejpam-3752	314	18	)	)	PUNCT
ejpam-3752	314	19	.	.	PUNCT
ejpam-3752	315	1	thus	thus	ADV
ejpam-3752	315	2	(	(	PUNCT
ejpam-3752	315	3	x	x	X
ejpam-3752	315	4	·	·	PUNCT
ejpam-3752	315	5	z	z	X
ejpam-3752	315	6	,	,	PUNCT
ejpam-3752	315	7	0	0	NUM
ejpam-3752	315	8	t	t	NOUN
ejpam-3752	315	9	)	)	PUNCT
ejpam-3752	315	10	=	=	SYM
ejpam-3752	316	1	(	(	PUNCT
ejpam-3752	316	2	x	x	X
ejpam-3752	316	3	·	·	PUNCT
ejpam-3752	316	4	z	z	X
ejpam-3752	316	5	,	,	PUNCT
ejpam-3752	316	6	(	(	PUNCT
ejpam-3752	316	7	0	0	NUM
ejpam-3752	316	8	·	·	SYM
ejpam-3752	316	9	0)t	0)t	NOUN
ejpam-3752	316	10	)	)	PUNCT
ejpam-3752	316	11	=	=	SYM
ejpam-3752	316	12	(	(	PUNCT
ejpam-3752	316	13	x	x	X
ejpam-3752	316	14	,	,	PUNCT
ejpam-3752	316	15	0	0	NUM
ejpam-3752	316	16	t	t	NOUN
ejpam-3752	316	17	)	)	PUNCT
ejpam-3752	316	18	�	�	PROPN
ejpam-3752	316	19	(	(	PUNCT
ejpam-3752	316	20	z	z	NOUN
ejpam-3752	316	21	,	,	PUNCT
ejpam-3752	316	22	0	0	NUM
ejpam-3752	316	23	t	t	NOUN
ejpam-3752	317	1	)	)	PUNCT
ejpam-3752	317	2	∈	∈	PROPN
ejpam-3752	317	3	a×	a×	PROPN
ejpam-3752	317	4	t	t	PROPN
ejpam-3752	317	5	(	(	PUNCT
ejpam-3752	317	6	b	b	NOUN
ejpam-3752	317	7	)	)	PUNCT
ejpam-3752	317	8	,	,	PUNCT
ejpam-3752	317	9	so	so	ADV
ejpam-3752	317	10	x	x	X
ejpam-3752	317	11	·	·	PUNCT
ejpam-3752	317	12	z	z	SYM
ejpam-3752	317	13	∈	∈	PROPN
ejpam-3752	317	14	a.	a.	NOUN
ejpam-3752	317	15	hence	hence	ADV
ejpam-3752	317	16	,	,	PUNCT
ejpam-3752	317	17	a	a	PRON
ejpam-3752	317	18	is	be	AUX
ejpam-3752	317	19	a	a	DET
ejpam-3752	317	20	up	up	ADJ
ejpam-3752	317	21	-	-	PUNCT
ejpam-3752	317	22	ideal	ideal	NOUN
ejpam-3752	317	23	of	of	ADP
ejpam-3752	317	24	x.	x.	NOUN
ejpam-3752	317	25	the	the	DET
ejpam-3752	317	26	following	follow	VERB
ejpam-3752	317	27	example	example	NOUN
ejpam-3752	317	28	shows	show	VERB
ejpam-3752	317	29	that	that	SCONJ
ejpam-3752	317	30	the	the	DET
ejpam-3752	317	31	sentence	sentence	NOUN
ejpam-3752	317	32	“	"	PUNCT
ejpam-3752	317	33	if	if	SCONJ
ejpam-3752	317	34	a	a	PRON
ejpam-3752	317	35	and	and	CCONJ
ejpam-3752	317	36	b	b	NOUN
ejpam-3752	317	37	are	be	AUX
ejpam-3752	317	38	up	up	ADP
ejpam-3752	317	39	-	-	PUNCT
ejpam-3752	317	40	filters	filter	NOUN
ejpam-3752	317	41	(	(	PUNCT
ejpam-3752	317	42	resp	resp	NOUN
ejpam-3752	317	43	.	.	PUNCT
ejpam-3752	317	44	,	,	PUNCT
ejpam-3752	317	45	upideals	upideal	NOUN
ejpam-3752	317	46	)	)	PUNCT
ejpam-3752	317	47	of	of	ADP
ejpam-3752	317	48	x	x	PRON
ejpam-3752	317	49	,	,	PUNCT
ejpam-3752	317	50	then	then	ADV
ejpam-3752	317	51	a×	a×	PROPN
ejpam-3752	317	52	t	t	PROPN
ejpam-3752	317	53	(	(	PUNCT
ejpam-3752	317	54	b	b	NOUN
ejpam-3752	317	55	)	)	PUNCT
ejpam-3752	317	56	is	be	AUX
ejpam-3752	317	57	a	a	DET
ejpam-3752	317	58	up	up	ADJ
ejpam-3752	317	59	-	-	PUNCT
ejpam-3752	317	60	filter	filter	NOUN
ejpam-3752	317	61	(	(	PUNCT
ejpam-3752	317	62	resp	resp	NOUN
ejpam-3752	317	63	.	.	PUNCT
ejpam-3752	317	64	,	,	PUNCT
ejpam-3752	317	65	up	up	ADP
ejpam-3752	317	66	-	-	PUNCT
ejpam-3752	317	67	ideal	ideal	NOUN
ejpam-3752	317	68	)	)	PUNCT
ejpam-3752	317	69	of	of	ADP
ejpam-3752	317	70	x	x	SYM
ejpam-3752	317	71	×	×	NOUN
ejpam-3752	317	72	im(t	im(t	ADJ
ejpam-3752	317	73	)	)	PUNCT
ejpam-3752	317	74	”	"	PUNCT
ejpam-3752	317	75	does	do	AUX
ejpam-3752	317	76	not	not	PART
ejpam-3752	317	77	hold	hold	VERB
ejpam-3752	317	78	in	in	ADP
ejpam-3752	317	79	general	general	ADJ
ejpam-3752	317	80	.	.	PUNCT
ejpam-3752	318	1	example	example	NOUN
ejpam-3752	319	1	2	2	NUM
ejpam-3752	319	2	.	.	PUNCT
ejpam-3752	319	3	let	let	VERB
ejpam-3752	319	4	x	x	PUNCT
ejpam-3752	319	5	=	=	PUNCT
ejpam-3752	319	6	{	{	PUNCT
ejpam-3752	319	7	0	0	NUM
ejpam-3752	319	8	,	,	PUNCT
ejpam-3752	319	9	a	a	DET
ejpam-3752	319	10	,	,	PUNCT
ejpam-3752	319	11	b	b	NOUN
ejpam-3752	319	12	,	,	PUNCT
ejpam-3752	319	13	c	c	AUX
ejpam-3752	319	14	}	}	PUNCT
ejpam-3752	319	15	be	be	AUX
ejpam-3752	319	16	a	a	DET
ejpam-3752	319	17	up	up	NOUN
ejpam-3752	319	18	-	-	PUNCT
ejpam-3752	319	19	algebra	algebra	NOUN
ejpam-3752	319	20	with	with	ADP
ejpam-3752	319	21	a	a	DET
ejpam-3752	319	22	fixed	fix	VERB
ejpam-3752	319	23	element	element	NOUN
ejpam-3752	319	24	0	0	PUNCT
ejpam-3752	319	25	and	and	CCONJ
ejpam-3752	319	26	a	a	DET
ejpam-3752	319	27	binary	binary	ADJ
ejpam-3752	319	28	operation	operation	NOUN
ejpam-3752	319	29	·	·	PUNCT
ejpam-3752	319	30	defined	define	VERB
ejpam-3752	319	31	by	by	ADP
ejpam-3752	319	32	the	the	DET
ejpam-3752	319	33	following	following	ADJ
ejpam-3752	319	34	cayley	cayley	ADJ
ejpam-3752	319	35	table	table	NOUN
ejpam-3752	319	36	:	:	PUNCT
ejpam-3752	319	37	·	·	PUNCT
ejpam-3752	319	38	0	0	PUNCT
ejpam-3752	320	1	a	a	DET
ejpam-3752	320	2	b	b	X
ejpam-3752	320	3	c	c	NOUN
ejpam-3752	320	4	0	0	NUM
ejpam-3752	320	5	0	0	NUM
ejpam-3752	320	6	a	a	DET
ejpam-3752	320	7	b	b	NOUN
ejpam-3752	320	8	c	c	NOUN
ejpam-3752	320	9	a	a	PRON
ejpam-3752	320	10	0	0	NUM
ejpam-3752	320	11	0	0	NUM
ejpam-3752	320	12	b	b	PROPN
ejpam-3752	320	13	b	b	PROPN
ejpam-3752	320	14	b	b	PROPN
ejpam-3752	320	15	0	0	NUM
ejpam-3752	320	16	a	a	DET
ejpam-3752	320	17	0	0	NUM
ejpam-3752	320	18	a	a	DET
ejpam-3752	320	19	c	c	NOUN
ejpam-3752	320	20	0	0	NUM
ejpam-3752	320	21	0	0	NUM
ejpam-3752	320	22	0	0	NUM
ejpam-3752	320	23	0	0	NUM
ejpam-3752	320	24	let	let	VERB
ejpam-3752	320	25	t	t	NOUN
ejpam-3752	320	26	:	:	PUNCT
ejpam-3752	320	27	x	x	X
ejpam-3752	320	28	→	→	X
ejpam-3752	320	29	{	{	PUNCT
ejpam-3752	320	30	0.5	0.5	NUM
ejpam-3752	320	31	,	,	PUNCT
ejpam-3752	320	32	0.7	0.7	NUM
ejpam-3752	320	33	,	,	PUNCT
ejpam-3752	320	34	1	1	NUM
ejpam-3752	320	35	}	}	PUNCT
ejpam-3752	320	36	be	be	AUX
ejpam-3752	320	37	a	a	DET
ejpam-3752	320	38	function	function	NOUN
ejpam-3752	320	39	defined	define	VERB
ejpam-3752	320	40	by	by	ADP
ejpam-3752	320	41	0	0	NUM
ejpam-3752	320	42	t	t	NOUN
ejpam-3752	320	43	=	=	NUM
ejpam-3752	320	44	0.5	0.5	NUM
ejpam-3752	320	45	,	,	PUNCT
ejpam-3752	320	46	at	at	ADP
ejpam-3752	320	47	=	=	SYM
ejpam-3752	320	48	bt	bt	NOUN
ejpam-3752	321	1	=	=	NOUN
ejpam-3752	321	2	0.7	0.7	NUM
ejpam-3752	321	3	,	,	PUNCT
ejpam-3752	321	4	ct	ct	NOUN
ejpam-3752	321	5	=	=	SYM
ejpam-3752	321	6	1	1	X
ejpam-3752	321	7	.	.	PUNCT
ejpam-3752	321	8	let	let	VERB
ejpam-3752	321	9	a	a	PRON
ejpam-3752	321	10	=	=	PUNCT
ejpam-3752	321	11	{	{	PUNCT
ejpam-3752	321	12	0	0	NUM
ejpam-3752	321	13	,	,	PUNCT
ejpam-3752	321	14	a	a	PRON
ejpam-3752	321	15	}	}	PUNCT
ejpam-3752	321	16	.	.	PUNCT
ejpam-3752	322	1	then	then	ADV
ejpam-3752	322	2	a	a	PRON
ejpam-3752	322	3	is	be	AUX
ejpam-3752	322	4	a	a	DET
ejpam-3752	322	5	up	up	ADJ
ejpam-3752	322	6	-	-	PUNCT
ejpam-3752	322	7	ideal	ideal	NOUN
ejpam-3752	322	8	(	(	PUNCT
ejpam-3752	322	9	also	also	ADV
ejpam-3752	322	10	a	a	DET
ejpam-3752	322	11	up	up	ADJ
ejpam-3752	322	12	-	-	PUNCT
ejpam-3752	322	13	filter	filter	NOUN
ejpam-3752	322	14	)	)	PUNCT
ejpam-3752	322	15	of	of	ADP
ejpam-3752	322	16	x	x	PUNCT
ejpam-3752	322	17	and	and	CCONJ
ejpam-3752	322	18	a×	a×	PROPN
ejpam-3752	322	19	t	t	NOUN
ejpam-3752	322	20	(	(	PUNCT
ejpam-3752	322	21	a	a	X
ejpam-3752	322	22	)	)	PUNCT
ejpam-3752	322	23	=	=	SYM
ejpam-3752	322	24	{	{	PUNCT
ejpam-3752	322	25	(	(	PUNCT
ejpam-3752	322	26	0	0	NUM
ejpam-3752	322	27	,	,	PUNCT
ejpam-3752	322	28	0	0	NUM
ejpam-3752	322	29	t	t	NOUN
ejpam-3752	322	30	)	)	PUNCT
ejpam-3752	322	31	,	,	PUNCT
ejpam-3752	322	32	(	(	PUNCT
ejpam-3752	322	33	0	0	NUM
ejpam-3752	322	34	,	,	PUNCT
ejpam-3752	322	35	at	at	ADP
ejpam-3752	322	36	)	)	PUNCT
ejpam-3752	322	37	,	,	PUNCT
ejpam-3752	322	38	(	(	PUNCT
ejpam-3752	322	39	a	a	X
ejpam-3752	322	40	,	,	PUNCT
ejpam-3752	322	41	0	0	NUM
ejpam-3752	322	42	t	t	NOUN
ejpam-3752	322	43	)	)	PUNCT
ejpam-3752	322	44	,	,	PUNCT
ejpam-3752	322	45	(	(	PUNCT
ejpam-3752	322	46	a	a	X
ejpam-3752	322	47	,	,	PUNCT
ejpam-3752	322	48	at	at	ADP
ejpam-3752	322	49	)	)	PUNCT
ejpam-3752	322	50	}	}	PUNCT
ejpam-3752	322	51	.	.	PUNCT
ejpam-3752	323	1	since	since	SCONJ
ejpam-3752	323	2	(	(	PUNCT
ejpam-3752	323	3	0	0	NUM
ejpam-3752	323	4	,	,	PUNCT
ejpam-3752	323	5	at	at	ADP
ejpam-3752	323	6	)	)	PUNCT
ejpam-3752	323	7	�	�	PROPN
ejpam-3752	323	8	(	(	PUNCT
ejpam-3752	323	9	0	0	NUM
ejpam-3752	323	10	,	,	PUNCT
ejpam-3752	323	11	ct	ct	NUM
ejpam-3752	323	12	)	)	PUNCT
ejpam-3752	323	13	=	=	PUNCT
ejpam-3752	323	14	(	(	PUNCT
ejpam-3752	323	15	0	0	NUM
ejpam-3752	323	16	,	,	PUNCT
ejpam-3752	323	17	bt	bt	NOUN
ejpam-3752	323	18	)	)	PUNCT
ejpam-3752	323	19	=	=	PUNCT
ejpam-3752	323	20	(	(	PUNCT
ejpam-3752	323	21	0	0	NUM
ejpam-3752	323	22	,	,	PUNCT
ejpam-3752	323	23	at	at	ADP
ejpam-3752	323	24	)	)	PUNCT
ejpam-3752	323	25	∈	∈	PROPN
ejpam-3752	323	26	a	a	DET
ejpam-3752	323	27	×	×	PROPN
ejpam-3752	323	28	t	t	NOUN
ejpam-3752	323	29	(	(	PUNCT
ejpam-3752	323	30	a	a	NOUN
ejpam-3752	323	31	)	)	PUNCT
ejpam-3752	323	32	and	and	CCONJ
ejpam-3752	323	33	(	(	PUNCT
ejpam-3752	323	34	0	0	NUM
ejpam-3752	323	35	,	,	PUNCT
ejpam-3752	323	36	at	at	ADP
ejpam-3752	323	37	)	)	PUNCT
ejpam-3752	323	38	∈	∈	PROPN
ejpam-3752	323	39	a	a	DET
ejpam-3752	323	40	×	×	PROPN
ejpam-3752	323	41	t	t	NOUN
ejpam-3752	323	42	(	(	PUNCT
ejpam-3752	323	43	a	a	NOUN
ejpam-3752	323	44	)	)	PUNCT
ejpam-3752	323	45	but	but	CCONJ
ejpam-3752	323	46	(	(	PUNCT
ejpam-3752	323	47	0	0	NUM
ejpam-3752	323	48	,	,	PUNCT
ejpam-3752	323	49	ct	ct	PROPN
ejpam-3752	323	50	)	)	PUNCT
ejpam-3752	323	51	/∈	/∈	PUNCT
ejpam-3752	324	1	a×	a×	PROPN
ejpam-3752	324	2	t	t	NOUN
ejpam-3752	324	3	(	(	PUNCT
ejpam-3752	324	4	a	a	NOUN
ejpam-3752	324	5	)	)	PUNCT
ejpam-3752	324	6	.	.	PUNCT
ejpam-3752	325	1	hence	hence	ADV
ejpam-3752	325	2	,	,	PUNCT
ejpam-3752	325	3	a×	a×	PROPN
ejpam-3752	325	4	t	t	PROPN
ejpam-3752	325	5	(	(	PUNCT
ejpam-3752	325	6	a	a	NOUN
ejpam-3752	325	7	)	)	PUNCT
ejpam-3752	325	8	is	be	AUX
ejpam-3752	325	9	not	not	PART
ejpam-3752	325	10	a	a	DET
ejpam-3752	325	11	up	up	ADJ
ejpam-3752	325	12	-	-	PUNCT
ejpam-3752	325	13	filter	filter	NOUN
ejpam-3752	325	14	(	(	PUNCT
ejpam-3752	325	15	also	also	ADV
ejpam-3752	325	16	not	not	PART
ejpam-3752	325	17	a	a	DET
ejpam-3752	325	18	up	up	ADJ
ejpam-3752	325	19	-	-	PUNCT
ejpam-3752	325	20	ideal	ideal	NOUN
ejpam-3752	325	21	)	)	PUNCT
ejpam-3752	325	22	of	of	ADP
ejpam-3752	325	23	x.	x.	PROPN
ejpam-3752	325	24	theorem	theorem	VERB
ejpam-3752	325	25	8	8	NUM
ejpam-3752	325	26	.	.	PUNCT
ejpam-3752	326	1	let	let	VERB
ejpam-3752	326	2	a	a	PRON
ejpam-3752	326	3	and	and	CCONJ
ejpam-3752	326	4	b	b	NOUN
ejpam-3752	326	5	be	be	AUX
ejpam-3752	326	6	nonempty	nonempty	X
ejpam-3752	326	7	subsets	subset	NOUN
ejpam-3752	326	8	of	of	ADP
ejpam-3752	326	9	a	a	DET
ejpam-3752	326	10	up	up	NOUN
ejpam-3752	326	11	-	-	PUNCT
ejpam-3752	326	12	algebra	algebra	NOUN
ejpam-3752	326	13	x	x	PUNCT
ejpam-3752	326	14	and	and	CCONJ
ejpam-3752	326	15	(	(	PUNCT
ejpam-3752	326	16	x×	x×	X
ejpam-3752	326	17	im(t	im(t	ADJ
ejpam-3752	326	18	)	)	PUNCT
ejpam-3752	326	19	,	,	PUNCT
ejpam-3752	326	20	�	�	PROPN
ejpam-3752	326	21	,	,	PUNCT
ejpam-3752	326	22	0̃	0̃	PROPN
ejpam-3752	326	23	)	)	PUNCT
ejpam-3752	326	24	be	be	VERB
ejpam-3752	326	25	a	a	DET
ejpam-3752	326	26	fuzzy	fuzzy	ADJ
ejpam-3752	326	27	duplex	duplex	NOUN
ejpam-3752	326	28	up	up	ADP
ejpam-3752	326	29	-	-	PUNCT
ejpam-3752	326	30	algebra	algebra	NOUN
ejpam-3752	326	31	.	.	PUNCT
ejpam-3752	327	1	(	(	PUNCT
ejpam-3752	327	2	1	1	X
ejpam-3752	327	3	)	)	PUNCT
ejpam-3752	327	4	if	if	SCONJ
ejpam-3752	327	5	a	a	PRON
ejpam-3752	327	6	and	and	CCONJ
ejpam-3752	327	7	b	b	NOUN
ejpam-3752	327	8	are	be	AUX
ejpam-3752	327	9	strong	strong	ADJ
ejpam-3752	327	10	up	up	ADJ
ejpam-3752	327	11	-	-	PUNCT
ejpam-3752	327	12	ideals	ideal	NOUN
ejpam-3752	327	13	of	of	ADP
ejpam-3752	327	14	x	x	NOUN
ejpam-3752	327	15	,	,	PUNCT
ejpam-3752	327	16	then	then	ADV
ejpam-3752	327	17	a	a	DET
ejpam-3752	327	18	×	×	PROPN
ejpam-3752	327	19	t	t	NOUN
ejpam-3752	327	20	(	(	PUNCT
ejpam-3752	327	21	b	b	NOUN
ejpam-3752	327	22	)	)	PUNCT
ejpam-3752	327	23	is	be	AUX
ejpam-3752	327	24	a	a	DET
ejpam-3752	327	25	strong	strong	ADJ
ejpam-3752	327	26	up	up	ADJ
ejpam-3752	327	27	-	-	PUNCT
ejpam-3752	327	28	ideal	ideal	NOUN
ejpam-3752	327	29	of	of	ADP
ejpam-3752	327	30	x	x	SYM
ejpam-3752	327	31	×	×	NOUN
ejpam-3752	327	32	im(t	im(t	NOUN
ejpam-3752	327	33	)	)	PUNCT
ejpam-3752	327	34	.	.	PUNCT
ejpam-3752	328	1	(	(	PUNCT
ejpam-3752	328	2	2	2	X
ejpam-3752	328	3	)	)	PUNCT
ejpam-3752	328	4	if	if	SCONJ
ejpam-3752	328	5	a×	a×	PROPN
ejpam-3752	328	6	t	t	PROPN
ejpam-3752	328	7	(	(	PUNCT
ejpam-3752	328	8	b	b	NOUN
ejpam-3752	328	9	)	)	PUNCT
ejpam-3752	328	10	is	be	AUX
ejpam-3752	328	11	a	a	DET
ejpam-3752	328	12	strong	strong	ADJ
ejpam-3752	328	13	up	up	ADJ
ejpam-3752	328	14	-	-	PUNCT
ejpam-3752	328	15	ideal	ideal	NOUN
ejpam-3752	328	16	of	of	ADP
ejpam-3752	328	17	x	x	SYM
ejpam-3752	328	18	×	×	NOUN
ejpam-3752	328	19	im(t	im(t	ADJ
ejpam-3752	328	20	)	)	PUNCT
ejpam-3752	328	21	,	,	PUNCT
ejpam-3752	328	22	then	then	ADV
ejpam-3752	328	23	a	a	PRON
ejpam-3752	328	24	is	be	AUX
ejpam-3752	328	25	a	a	DET
ejpam-3752	328	26	strong	strong	ADJ
ejpam-3752	328	27	up	up	ADJ
ejpam-3752	328	28	-	-	PUNCT
ejpam-3752	328	29	ideal	ideal	NOUN
ejpam-3752	328	30	of	of	ADP
ejpam-3752	328	31	x.	x.	NOUN
ejpam-3752	328	32	proof	proof	NOUN
ejpam-3752	328	33	.	.	PUNCT
ejpam-3752	329	1	(	(	PUNCT
ejpam-3752	329	2	1	1	X
ejpam-3752	329	3	)	)	PUNCT
ejpam-3752	329	4	assume	assume	VERB
ejpam-3752	329	5	that	that	SCONJ
ejpam-3752	329	6	a	a	PRON
ejpam-3752	329	7	and	and	CCONJ
ejpam-3752	329	8	b	b	NOUN
ejpam-3752	329	9	are	be	AUX
ejpam-3752	329	10	strong	strong	ADJ
ejpam-3752	329	11	up	up	ADJ
ejpam-3752	329	12	-	-	PUNCT
ejpam-3752	329	13	ideals	ideal	NOUN
ejpam-3752	329	14	of	of	ADP
ejpam-3752	329	15	x.	x.	NOUN
ejpam-3752	329	16	then	then	ADV
ejpam-3752	329	17	a	a	DET
ejpam-3752	329	18	=	=	SYM
ejpam-3752	329	19	b	b	NOUN
ejpam-3752	329	20	=	=	SYM
ejpam-3752	329	21	x	x	NOUN
ejpam-3752	329	22	,	,	PUNCT
ejpam-3752	329	23	so	so	ADV
ejpam-3752	329	24	a×	a×	PROPN
ejpam-3752	329	25	t	t	PROPN
ejpam-3752	329	26	(	(	PUNCT
ejpam-3752	329	27	b	b	NOUN
ejpam-3752	329	28	)	)	PUNCT
ejpam-3752	329	29	=	=	PUNCT
ejpam-3752	330	1	x	x	SYM
ejpam-3752	330	2	×	×	NOUN
ejpam-3752	330	3	im(t	im(t	ADJ
ejpam-3752	330	4	)	)	PUNCT
ejpam-3752	330	5	.	.	PUNCT
ejpam-3752	331	1	hence	hence	ADV
ejpam-3752	331	2	,	,	PUNCT
ejpam-3752	331	3	a×	a×	PROPN
ejpam-3752	331	4	t	t	PROPN
ejpam-3752	331	5	(	(	PUNCT
ejpam-3752	331	6	b	b	NOUN
ejpam-3752	331	7	)	)	PUNCT
ejpam-3752	331	8	is	be	AUX
ejpam-3752	331	9	a	a	DET
ejpam-3752	331	10	strong	strong	ADJ
ejpam-3752	331	11	up	up	ADJ
ejpam-3752	331	12	-	-	PUNCT
ejpam-3752	331	13	ideal	ideal	NOUN
ejpam-3752	331	14	of	of	ADP
ejpam-3752	331	15	x	x	SYM
ejpam-3752	331	16	×	×	NOUN
ejpam-3752	331	17	im(t	im(t	NOUN
ejpam-3752	331	18	)	)	PUNCT
ejpam-3752	331	19	.	.	PUNCT
ejpam-3752	332	1	(	(	PUNCT
ejpam-3752	332	2	2	2	X
ejpam-3752	332	3	)	)	PUNCT
ejpam-3752	332	4	assume	assume	VERB
ejpam-3752	332	5	that	that	SCONJ
ejpam-3752	332	6	a	a	DET
ejpam-3752	332	7	×	×	PROPN
ejpam-3752	332	8	t	t	NOUN
ejpam-3752	332	9	(	(	PUNCT
ejpam-3752	332	10	b	b	NOUN
ejpam-3752	332	11	)	)	PUNCT
ejpam-3752	332	12	is	be	AUX
ejpam-3752	332	13	a	a	DET
ejpam-3752	332	14	strong	strong	ADJ
ejpam-3752	332	15	up	up	ADJ
ejpam-3752	332	16	-	-	PUNCT
ejpam-3752	332	17	ideal	ideal	NOUN
ejpam-3752	332	18	of	of	ADP
ejpam-3752	332	19	x	x	SYM
ejpam-3752	332	20	×	×	NOUN
ejpam-3752	332	21	im(t	im(t	ADJ
ejpam-3752	332	22	)	)	PUNCT
ejpam-3752	332	23	.	.	PUNCT
ejpam-3752	333	1	then	then	ADV
ejpam-3752	333	2	a	a	DET
ejpam-3752	333	3	×	×	PROPN
ejpam-3752	333	4	t	t	NOUN
ejpam-3752	333	5	(	(	PUNCT
ejpam-3752	333	6	b	b	NOUN
ejpam-3752	333	7	)	)	PUNCT
ejpam-3752	333	8	=	=	PUNCT
ejpam-3752	334	1	x	x	SYM
ejpam-3752	334	2	×	×	NOUN
ejpam-3752	334	3	im(t	im(t	ADJ
ejpam-3752	334	4	)	)	PUNCT
ejpam-3752	334	5	,	,	PUNCT
ejpam-3752	334	6	so	so	ADV
ejpam-3752	334	7	a	a	DET
ejpam-3752	334	8	=	=	NOUN
ejpam-3752	334	9	x.	x.	NOUN
ejpam-3752	334	10	hence	hence	ADV
ejpam-3752	334	11	,	,	PUNCT
ejpam-3752	334	12	a	a	PRON
ejpam-3752	334	13	is	be	AUX
ejpam-3752	334	14	a	a	DET
ejpam-3752	334	15	strong	strong	ADJ
ejpam-3752	334	16	up	up	ADJ
ejpam-3752	334	17	-	-	PUNCT
ejpam-3752	334	18	ideal	ideal	NOUN
ejpam-3752	334	19	of	of	ADP
ejpam-3752	334	20	x.	x.	PROPN
ejpam-3752	334	21	references	reference	VERB
ejpam-3752	334	22	469	469	NUM
ejpam-3752	334	23	4	4	NUM
ejpam-3752	334	24	.	.	PUNCT
ejpam-3752	335	1	conclusions	conclusion	NOUN
ejpam-3752	335	2	in	in	ADP
ejpam-3752	335	3	this	this	DET
ejpam-3752	335	4	paper	paper	NOUN
ejpam-3752	335	5	,	,	PUNCT
ejpam-3752	335	6	we	we	PRON
ejpam-3752	335	7	have	have	AUX
ejpam-3752	335	8	introduced	introduce	VERB
ejpam-3752	335	9	the	the	DET
ejpam-3752	335	10	concept	concept	NOUN
ejpam-3752	335	11	of	of	ADP
ejpam-3752	335	12	a	a	DET
ejpam-3752	335	13	fuzzy	fuzzy	ADJ
ejpam-3752	335	14	duplex	duplex	NOUN
ejpam-3752	335	15	set	set	VERB
ejpam-3752	335	16	base	base	NOUN
ejpam-3752	335	17	on	on	ADP
ejpam-3752	335	18	a	a	DET
ejpam-3752	335	19	upalgebra	upalgebra	NOUN
ejpam-3752	335	20	,	,	PUNCT
ejpam-3752	335	21	which	which	PRON
ejpam-3752	335	22	is	be	AUX
ejpam-3752	335	23	called	call	VERB
ejpam-3752	335	24	a	a	DET
ejpam-3752	335	25	fuzzy	fuzzy	ADJ
ejpam-3752	335	26	duplex	duplex	NOUN
ejpam-3752	335	27	up	up	ADV
ejpam-3752	335	28	-	-	PUNCT
ejpam-3752	335	29	set	set	NOUN
ejpam-3752	335	30	,	,	PUNCT
ejpam-3752	335	31	and	and	CCONJ
ejpam-3752	335	32	investigated	investigate	VERB
ejpam-3752	335	33	some	some	DET
ejpam-3752	335	34	related	relate	VERB
ejpam-3752	335	35	properties	property	NOUN
ejpam-3752	335	36	.	.	PUNCT
ejpam-3752	336	1	we	we	PRON
ejpam-3752	336	2	have	have	AUX
ejpam-3752	336	3	found	find	VERB
ejpam-3752	336	4	the	the	DET
ejpam-3752	336	5	necessary	necessary	ADJ
ejpam-3752	336	6	conditions	condition	NOUN
ejpam-3752	336	7	that	that	SCONJ
ejpam-3752	336	8	a	a	DET
ejpam-3752	336	9	fuzzy	fuzzy	ADJ
ejpam-3752	336	10	duplex	duplex	NOUN
ejpam-3752	336	11	up	up	ADV
ejpam-3752	336	12	-	-	PUNCT
ejpam-3752	336	13	set	set	VERB
ejpam-3752	336	14	form	form	NOUN
ejpam-3752	336	15	a	a	DET
ejpam-3752	336	16	up	up	NOUN
ejpam-3752	336	17	-	-	PUNCT
ejpam-3752	336	18	algebra	algebra	NOUN
ejpam-3752	336	19	,	,	PUNCT
ejpam-3752	336	20	which	which	PRON
ejpam-3752	336	21	is	be	AUX
ejpam-3752	336	22	called	call	VERB
ejpam-3752	336	23	a	a	DET
ejpam-3752	336	24	fuzzy	fuzzy	ADJ
ejpam-3752	336	25	duplex	duplex	NOUN
ejpam-3752	336	26	up	up	ADP
ejpam-3752	336	27	-	-	PUNCT
ejpam-3752	336	28	algebra	algebra	NOUN
ejpam-3752	336	29	.	.	PUNCT
ejpam-3752	337	1	furthermore	furthermore	ADV
ejpam-3752	337	2	,	,	PUNCT
ejpam-3752	337	3	we	we	PRON
ejpam-3752	337	4	have	have	AUX
ejpam-3752	337	5	studied	study	VERB
ejpam-3752	337	6	the	the	DET
ejpam-3752	337	7	relationship	relationship	NOUN
ejpam-3752	337	8	between	between	ADP
ejpam-3752	337	9	special	special	ADJ
ejpam-3752	337	10	subsets	subset	NOUN
ejpam-3752	337	11	of	of	ADP
ejpam-3752	337	12	a	a	DET
ejpam-3752	337	13	up	up	NOUN
ejpam-3752	337	14	-	-	PUNCT
ejpam-3752	337	15	algebra	algebra	NOUN
ejpam-3752	337	16	and	and	CCONJ
ejpam-3752	337	17	the	the	DET
ejpam-3752	337	18	same	same	ADJ
ejpam-3752	337	19	special	special	ADJ
ejpam-3752	337	20	subsets	subset	NOUN
ejpam-3752	337	21	of	of	ADP
ejpam-3752	337	22	a	a	DET
ejpam-3752	337	23	fuzzy	fuzzy	ADJ
ejpam-3752	337	24	duplex	duplex	NOUN
ejpam-3752	337	25	up	up	ADV
ejpam-3752	337	26	-	-	PUNCT
ejpam-3752	337	27	set	set	VERB
ejpam-3752	337	28	and	and	CCONJ
ejpam-3752	337	29	have	have	AUX
ejpam-3752	337	30	presented	present	VERB
ejpam-3752	337	31	conflicting	conflicting	ADJ
ejpam-3752	337	32	examples	example	NOUN
ejpam-3752	337	33	for	for	ADP
ejpam-3752	337	34	certain	certain	ADJ
ejpam-3752	337	35	relationships	relationship	NOUN
ejpam-3752	337	36	.	.	PUNCT
ejpam-3752	338	1	acknowledgements	acknowledgement	NOUN
ejpam-3752	338	2	the	the	DET
ejpam-3752	338	3	authors	author	NOUN
ejpam-3752	338	4	would	would	AUX
ejpam-3752	338	5	also	also	ADV
ejpam-3752	338	6	like	like	VERB
ejpam-3752	338	7	to	to	PART
ejpam-3752	338	8	thank	thank	VERB
ejpam-3752	338	9	the	the	DET
ejpam-3752	338	10	anonymous	anonymous	ADJ
ejpam-3752	338	11	referee	referee	NOUN
ejpam-3752	338	12	for	for	ADP
ejpam-3752	338	13	giving	give	VERB
ejpam-3752	338	14	many	many	ADJ
ejpam-3752	338	15	helpful	helpful	ADJ
ejpam-3752	338	16	suggestion	suggestion	NOUN
ejpam-3752	338	17	on	on	ADP
ejpam-3752	338	18	the	the	DET
ejpam-3752	338	19	revision	revision	NOUN
ejpam-3752	338	20	of	of	ADP
ejpam-3752	338	21	present	present	ADJ
ejpam-3752	338	22	paper	paper	NOUN
ejpam-3752	338	23	.	.	PUNCT
ejpam-3752	339	1	references	reference	NOUN
ejpam-3752	339	2	[	[	X
ejpam-3752	339	3	1	1	NUM
ejpam-3752	339	4	]	]	PUNCT
ejpam-3752	339	5	a.	a.	NOUN
ejpam-3752	339	6	a.	a.	PROPN
ejpam-3752	339	7	a.	a.	PROPN
ejpam-3752	339	8	agboola	agboola	PROPN
ejpam-3752	339	9	,	,	PUNCT
ejpam-3752	339	10	b.	b.	PROPN
ejpam-3752	339	11	davvaz	davvaz	PROPN
ejpam-3752	339	12	,	,	PUNCT
ejpam-3752	339	13	and	and	CCONJ
ejpam-3752	339	14	f.	f.	PROPN
ejpam-3752	339	15	smarandache	smarandache	PROPN
ejpam-3752	339	16	.	.	PUNCT
ejpam-3752	340	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	340	2	quadruple	quadruple	PROPN
ejpam-3752	340	3	algebraic	algebraic	PROPN
ejpam-3752	340	4	hyperstructures	hyperstructure	VERB
ejpam-3752	340	5	.	.	PUNCT
ejpam-3752	341	1	ann	ann	PROPN
ejpam-3752	341	2	.	.	PUNCT
ejpam-3752	341	3	fuzzy	fuzzy	ADJ
ejpam-3752	341	4	math	math	NOUN
ejpam-3752	341	5	.	.	PUNCT
ejpam-3752	342	1	inform	inform	NOUN
ejpam-3752	342	2	.	.	PUNCT
ejpam-3752	342	3	,	,	PUNCT
ejpam-3752	342	4	14(1):29–42	14(1):29–42	NUM
ejpam-3752	342	5	,	,	PUNCT
ejpam-3752	342	6	2017	2017	NUM
ejpam-3752	342	7	.	.	PUNCT
ejpam-3752	343	1	[	[	X
ejpam-3752	343	2	2	2	X
ejpam-3752	343	3	]	]	PUNCT
ejpam-3752	343	4	s.	s.	PROPN
ejpam-3752	343	5	a.	a.	PROPN
ejpam-3752	343	6	akinleye	akinleye	PROPN
ejpam-3752	343	7	,	,	PUNCT
ejpam-3752	343	8	f.	f.	PROPN
ejpam-3752	343	9	smarandache	smarandache	PROPN
ejpam-3752	343	10	,	,	PUNCT
ejpam-3752	343	11	and	and	CCONJ
ejpam-3752	343	12	a.	a.	NOUN
ejpam-3752	343	13	a.	a.	PROPN
ejpam-3752	343	14	a.	a.	PROPN
ejpam-3752	343	15	agboola	agboola	PROPN
ejpam-3752	343	16	.	.	PUNCT
ejpam-3752	344	1	on	on	ADP
ejpam-3752	344	2	neutrosophic	neutrosophic	PROPN
ejpam-3752	344	3	quadruple	quadruple	NOUN
ejpam-3752	344	4	algebraic	algebraic	ADJ
ejpam-3752	344	5	structures	structure	NOUN
ejpam-3752	344	6	.	.	PUNCT
ejpam-3752	345	1	neutrosophic	neutrosophic	ADJ
ejpam-3752	345	2	sets	set	VERB
ejpam-3752	345	3	syst	syst	PROPN
ejpam-3752	345	4	.	.	PUNCT
ejpam-3752	345	5	,	,	PUNCT
ejpam-3752	345	6	12:122–126	12:122–126	PROPN
ejpam-3752	345	7	,	,	PUNCT
ejpam-3752	345	8	2016	2016	NUM
ejpam-3752	345	9	.	.	PUNCT
ejpam-3752	346	1	[	[	X
ejpam-3752	346	2	3	3	X
ejpam-3752	346	3	]	]	PUNCT
ejpam-3752	346	4	m.	m.	NOUN
ejpam-3752	346	5	a.	a.	NOUN
ejpam-3752	346	6	ansari	ansari	PROPN
ejpam-3752	346	7	,	,	PUNCT
ejpam-3752	346	8	a.	a.	PROPN
ejpam-3752	346	9	haidar	haidar	NOUN
ejpam-3752	346	10	,	,	PUNCT
ejpam-3752	346	11	and	and	CCONJ
ejpam-3752	346	12	a.	a.	PROPN
ejpam-3752	346	13	n.	n.	PROPN
ejpam-3752	346	14	a.	a.	PROPN
ejpam-3752	346	15	koam	koam	PROPN
ejpam-3752	346	16	.	.	PUNCT
ejpam-3752	347	1	on	on	ADP
ejpam-3752	347	2	a	a	DET
ejpam-3752	347	3	graph	graph	NOUN
ejpam-3752	347	4	associated	associate	VERB
ejpam-3752	347	5	to	to	ADP
ejpam-3752	347	6	up	up	ADV
ejpam-3752	347	7	-	-	PUNCT
ejpam-3752	347	8	algebras	algebras	PROPN
ejpam-3752	347	9	.	.	PUNCT
ejpam-3752	347	10	math	math	NOUN
ejpam-3752	347	11	.	.	PUNCT
ejpam-3752	348	1	comput	comput	NOUN
ejpam-3752	348	2	.	.	PUNCT
ejpam-3752	349	1	appl	appl	PROPN
ejpam-3752	349	2	.	.	PROPN
ejpam-3752	350	1	,	,	PUNCT
ejpam-3752	350	2	23(4):61	23(4):61	NUM
ejpam-3752	350	3	,	,	PUNCT
ejpam-3752	350	4	2018	2018	NUM
ejpam-3752	350	5	.	.	PUNCT
ejpam-3752	351	1	[	[	X
ejpam-3752	351	2	4	4	X
ejpam-3752	351	3	]	]	PUNCT
ejpam-3752	351	4	m.	m.	NOUN
ejpam-3752	351	5	a.	a.	NOUN
ejpam-3752	351	6	ansari	ansari	PROPN
ejpam-3752	351	7	,	,	PUNCT
ejpam-3752	351	8	a.	a.	PROPN
ejpam-3752	351	9	n.	n.	PROPN
ejpam-3752	351	10	a.	a.	PROPN
ejpam-3752	351	11	koam	koam	PROPN
ejpam-3752	351	12	,	,	PUNCT
ejpam-3752	351	13	and	and	CCONJ
ejpam-3752	351	14	a.	a.	NOUN
ejpam-3752	351	15	haider	haider	PROPN
ejpam-3752	351	16	.	.	PUNCT
ejpam-3752	352	1	rough	rough	ADJ
ejpam-3752	352	2	set	set	NOUN
ejpam-3752	352	3	theory	theory	NOUN
ejpam-3752	352	4	applied	apply	VERB
ejpam-3752	352	5	to	to	ADP
ejpam-3752	352	6	upalgebras	upalgebra	NOUN
ejpam-3752	352	7	.	.	PUNCT
ejpam-3752	353	1	ital	ital	PROPN
ejpam-3752	353	2	.	.	PUNCT
ejpam-3752	354	1	j.	j.	PROPN
ejpam-3752	354	2	pure	pure	PROPN
ejpam-3752	354	3	appl	appl	PROPN
ejpam-3752	354	4	.	.	PUNCT
ejpam-3752	354	5	math	math	PROPN
ejpam-3752	354	6	.	.	PUNCT
ejpam-3752	354	7	,	,	PUNCT
ejpam-3752	354	8	42:388–402	42:388–402	PROPN
ejpam-3752	354	9	,	,	PUNCT
ejpam-3752	354	10	2019	2019	NUM
ejpam-3752	354	11	.	.	PUNCT
ejpam-3752	355	1	[	[	X
ejpam-3752	355	2	5	5	X
ejpam-3752	355	3	]	]	PUNCT
ejpam-3752	355	4	m.	m.	NOUN
ejpam-3752	355	5	a.	a.	NOUN
ejpam-3752	355	6	ansari	ansari	PROPN
ejpam-3752	355	7	,	,	PUNCT
ejpam-3752	355	8	a.	a.	PROPN
ejpam-3752	355	9	n.	n.	PROPN
ejpam-3752	355	10	a.	a.	PROPN
ejpam-3752	355	11	koam	koam	PROPN
ejpam-3752	355	12	,	,	PUNCT
ejpam-3752	355	13	and	and	CCONJ
ejpam-3752	355	14	a.	a.	NOUN
ejpam-3752	355	15	haider	haider	PROPN
ejpam-3752	355	16	.	.	PUNCT
ejpam-3752	356	1	on	on	ADP
ejpam-3752	356	2	binary	binary	ADJ
ejpam-3752	356	3	block	block	NOUN
ejpam-3752	356	4	codes	code	NOUN
ejpam-3752	356	5	associated	associate	VERB
ejpam-3752	356	6	to	to	ADP
ejpam-3752	356	7	up	up	ADV
ejpam-3752	356	8	-	-	PUNCT
ejpam-3752	356	9	algebras	algebras	X
ejpam-3752	356	10	.	.	PUNCT
ejpam-3752	357	1	manuscript	manuscript	NOUN
ejpam-3752	357	2	accepted	accept	VERB
ejpam-3752	357	3	for	for	ADP
ejpam-3752	357	4	publication	publication	NOUN
ejpam-3752	357	5	in	in	ADP
ejpam-3752	357	6	ital	ital	PROPN
ejpam-3752	357	7	.	.	PUNCT
ejpam-3752	358	1	j.	j.	PROPN
ejpam-3752	358	2	pure	pure	PROPN
ejpam-3752	358	3	appl	appl	PROPN
ejpam-3752	358	4	.	.	PUNCT
ejpam-3752	358	5	math	math	PROPN
ejpam-3752	358	6	.	.	PUNCT
ejpam-3752	358	7	,	,	PUNCT
ejpam-3752	358	8	february	february	PROPN
ejpam-3752	358	9	2020	2020	NUM
ejpam-3752	358	10	.	.	PUNCT
ejpam-3752	359	1	[	[	X
ejpam-3752	359	2	6	6	NUM
ejpam-3752	359	3	]	]	X
ejpam-3752	359	4	n.	n.	PROPN
ejpam-3752	359	5	dokkhamdang	dokkhamdang	PROPN
ejpam-3752	359	6	,	,	PUNCT
ejpam-3752	359	7	a.	a.	PROPN
ejpam-3752	359	8	kesorn	kesorn	PROPN
ejpam-3752	359	9	,	,	PUNCT
ejpam-3752	359	10	and	and	CCONJ
ejpam-3752	359	11	a.	a.	NOUN
ejpam-3752	359	12	iampan	iampan	PROPN
ejpam-3752	359	13	.	.	PUNCT
ejpam-3752	360	1	generalized	generalize	VERB
ejpam-3752	360	2	fuzzy	fuzzy	ADJ
ejpam-3752	360	3	sets	set	NOUN
ejpam-3752	360	4	in	in	ADP
ejpam-3752	360	5	up	up	ADP
ejpam-3752	360	6	-	-	PUNCT
ejpam-3752	360	7	algebras	algebras	X
ejpam-3752	360	8	.	.	PUNCT
ejpam-3752	361	1	ann	ann	PROPN
ejpam-3752	361	2	.	.	PUNCT
ejpam-3752	361	3	fuzzy	fuzzy	ADJ
ejpam-3752	361	4	math	math	NOUN
ejpam-3752	361	5	.	.	PUNCT
ejpam-3752	362	1	inform	inform	NOUN
ejpam-3752	362	2	.	.	PUNCT
ejpam-3752	362	3	,	,	PUNCT
ejpam-3752	362	4	16(2):171–190	16(2):171–190	NUM
ejpam-3752	362	5	,	,	PUNCT
ejpam-3752	362	6	2018	2018	NUM
ejpam-3752	362	7	.	.	PUNCT
ejpam-3752	363	1	[	[	X
ejpam-3752	363	2	7	7	X
ejpam-3752	363	3	]	]	X
ejpam-3752	363	4	t.	t.	NOUN
ejpam-3752	363	5	guntasow	guntasow	NOUN
ejpam-3752	363	6	,	,	PUNCT
ejpam-3752	363	7	s.	s.	PROPN
ejpam-3752	363	8	sajak	sajak	PROPN
ejpam-3752	363	9	,	,	PUNCT
ejpam-3752	363	10	a.	a.	PROPN
ejpam-3752	363	11	jomkham	jomkham	PROPN
ejpam-3752	363	12	,	,	PUNCT
ejpam-3752	363	13	and	and	CCONJ
ejpam-3752	363	14	a.	a.	NOUN
ejpam-3752	363	15	iampan	iampan	PROPN
ejpam-3752	363	16	.	.	PUNCT
ejpam-3752	364	1	fuzzy	fuzzy	ADJ
ejpam-3752	364	2	translations	translation	NOUN
ejpam-3752	364	3	of	of	ADP
ejpam-3752	364	4	a	a	DET
ejpam-3752	364	5	fuzzy	fuzzy	ADJ
ejpam-3752	364	6	set	set	NOUN
ejpam-3752	364	7	in	in	ADP
ejpam-3752	364	8	up	up	ADP
ejpam-3752	364	9	-	-	PUNCT
ejpam-3752	364	10	algebras	algebras	X
ejpam-3752	364	11	.	.	PUNCT
ejpam-3752	365	1	j.	j.	PROPN
ejpam-3752	365	2	indones	indones	PROPN
ejpam-3752	365	3	.	.	PUNCT
ejpam-3752	366	1	math	math	NOUN
ejpam-3752	366	2	.	.	PUNCT
ejpam-3752	367	1	soc	soc	PROPN
ejpam-3752	367	2	.	.	PROPN
ejpam-3752	367	3	,	,	PUNCT
ejpam-3752	367	4	23(2):1–19	23(2):1–19	NUM
ejpam-3752	367	5	,	,	PUNCT
ejpam-3752	367	6	2017	2017	NUM
ejpam-3752	367	7	.	.	PUNCT
ejpam-3752	368	1	[	[	X
ejpam-3752	368	2	8	8	NUM
ejpam-3752	368	3	]	]	PUNCT
ejpam-3752	368	4	a.	a.	NOUN
ejpam-3752	368	5	iampan	iampan	PROPN
ejpam-3752	368	6	.	.	PUNCT
ejpam-3752	369	1	multipliers	multiplier	NOUN
ejpam-3752	369	2	and	and	CCONJ
ejpam-3752	369	3	near	near	ADP
ejpam-3752	369	4	up	up	ADP
ejpam-3752	369	5	-	-	PUNCT
ejpam-3752	369	6	filters	filter	NOUN
ejpam-3752	369	7	of	of	ADP
ejpam-3752	369	8	up	up	ADP
ejpam-3752	369	9	-	-	PUNCT
ejpam-3752	369	10	algebras	algebras	X
ejpam-3752	369	11	.	.	PUNCT
ejpam-3752	370	1	j.	j.	PROPN
ejpam-3752	370	2	discrete	discrete	PROPN
ejpam-3752	370	3	math	math	PROPN
ejpam-3752	370	4	.	.	PUNCT
ejpam-3752	371	1	sci	sci	PROPN
ejpam-3752	371	2	.	.	PUNCT
ejpam-3752	371	3	cryptography	cryptography	NOUN
ejpam-3752	371	4	,	,	PUNCT
ejpam-3752	371	5	page	page	NOUN
ejpam-3752	371	6	to	to	PART
ejpam-3752	371	7	appear	appear	VERB
ejpam-3752	371	8	.	.	PUNCT
ejpam-3752	372	1	[	[	X
ejpam-3752	372	2	9	9	NUM
ejpam-3752	372	3	]	]	PUNCT
ejpam-3752	372	4	a.	a.	NOUN
ejpam-3752	372	5	iampan	iampan	PROPN
ejpam-3752	372	6	.	.	PUNCT
ejpam-3752	373	1	a	a	DET
ejpam-3752	373	2	new	new	ADJ
ejpam-3752	373	3	branch	branch	NOUN
ejpam-3752	373	4	of	of	ADP
ejpam-3752	373	5	the	the	DET
ejpam-3752	373	6	logical	logical	ADJ
ejpam-3752	373	7	algebra	algebra	NOUN
ejpam-3752	373	8	:	:	PUNCT
ejpam-3752	373	9	up	up	ADP
ejpam-3752	373	10	-	-	PUNCT
ejpam-3752	373	11	algebras	algebras	X
ejpam-3752	373	12	.	.	PUNCT
ejpam-3752	374	1	j.	j.	PROPN
ejpam-3752	374	2	algebra	algebra	PROPN
ejpam-3752	374	3	relat	relat	PROPN
ejpam-3752	374	4	.	.	PUNCT
ejpam-3752	375	1	top	top	PROPN
ejpam-3752	375	2	.	.	PROPN
ejpam-3752	375	3	,	,	PUNCT
ejpam-3752	375	4	5(1):35–54	5(1):35–54	NUM
ejpam-3752	375	5	,	,	PUNCT
ejpam-3752	375	6	2017	2017	NUM
ejpam-3752	375	7	.	.	PUNCT
ejpam-3752	376	1	[	[	X
ejpam-3752	376	2	10	10	NUM
ejpam-3752	376	3	]	]	PUNCT
ejpam-3752	376	4	a.	a.	NOUN
ejpam-3752	376	5	iampan	iampan	PROPN
ejpam-3752	376	6	.	.	PUNCT
ejpam-3752	377	1	introducing	introduce	VERB
ejpam-3752	377	2	fully	fully	ADV
ejpam-3752	377	3	up	up	ADP
ejpam-3752	377	4	-	-	PUNCT
ejpam-3752	377	5	semigroups	semigroup	NOUN
ejpam-3752	377	6	.	.	PUNCT
ejpam-3752	378	1	discuss	discuss	PROPN
ejpam-3752	378	2	.	.	PUNCT
ejpam-3752	378	3	math	math	PROPN
ejpam-3752	378	4	.	.	PUNCT
ejpam-3752	378	5	,	,	PUNCT
ejpam-3752	379	1	gen	gen	PROPN
ejpam-3752	379	2	.	.	PROPN
ejpam-3752	379	3	algebra	algebra	PROPN
ejpam-3752	379	4	appl	appl	PROPN
ejpam-3752	379	5	.	.	PROPN
ejpam-3752	379	6	,	,	PUNCT
ejpam-3752	379	7	38(2):297–306	38(2):297–306	NUM
ejpam-3752	379	8	,	,	PUNCT
ejpam-3752	379	9	2018	2018	NUM
ejpam-3752	379	10	.	.	PUNCT
ejpam-3752	380	1	references	reference	NOUN
ejpam-3752	380	2	470	470	NUM
ejpam-3752	381	1	[	[	X
ejpam-3752	381	2	11	11	NUM
ejpam-3752	381	3	]	]	X
ejpam-3752	381	4	y.	y.	PROPN
ejpam-3752	381	5	b.	b.	PROPN
ejpam-3752	381	6	jun	jun	PROPN
ejpam-3752	381	7	,	,	PUNCT
ejpam-3752	381	8	f.	f.	PROPN
ejpam-3752	381	9	smarandache	smarandache	PROPN
ejpam-3752	381	10	,	,	PUNCT
ejpam-3752	381	11	and	and	CCONJ
ejpam-3752	381	12	h.	h.	PROPN
ejpam-3752	381	13	bordbar	bordbar	PROPN
ejpam-3752	381	14	.	.	PUNCT
ejpam-3752	382	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	382	2	n	n	PRON
ejpam-3752	382	3	-structures	-structure	NOUN
ejpam-3752	382	4	applied	apply	VERB
ejpam-3752	382	5	to	to	PART
ejpam-3752	382	6	bck	bck	VERB
ejpam-3752	382	7	/	/	SYM
ejpam-3752	382	8	bci	bci	NOUN
ejpam-3752	382	9	-	-	PUNCT
ejpam-3752	382	10	algebras	algebra	NOUN
ejpam-3752	382	11	.	.	PUNCT
ejpam-3752	383	1	inform	inform	NOUN
ejpam-3752	383	2	.	.	PUNCT
ejpam-3752	383	3	,	,	PUNCT
ejpam-3752	383	4	8(4):128	8(4):128	NUM
ejpam-3752	383	5	,	,	PUNCT
ejpam-3752	383	6	2017	2017	NUM
ejpam-3752	383	7	.	.	PUNCT
ejpam-3752	384	1	[	[	X
ejpam-3752	384	2	12	12	NUM
ejpam-3752	384	3	]	]	X
ejpam-3752	384	4	y.	y.	PROPN
ejpam-3752	384	5	b.	b.	PROPN
ejpam-3752	384	6	jun	jun	PROPN
ejpam-3752	384	7	,	,	PUNCT
ejpam-3752	384	8	f.	f.	PROPN
ejpam-3752	384	9	smarandache	smarandache	PROPN
ejpam-3752	384	10	,	,	PUNCT
ejpam-3752	384	11	s.-z	s.-z	PROPN
ejpam-3752	384	12	.	.	PUNCT
ejpam-3752	385	1	song	song	NOUN
ejpam-3752	385	2	,	,	PUNCT
ejpam-3752	385	3	and	and	CCONJ
ejpam-3752	385	4	m.	m.	PROPN
ejpam-3752	385	5	khan	khan	PROPN
ejpam-3752	385	6	.	.	PUNCT
ejpam-3752	386	1	neutrosophic	neutrosophic	ADJ
ejpam-3752	386	2	positive	positive	ADJ
ejpam-3752	386	3	implicative	implicative	ADJ
ejpam-3752	386	4	n	n	PRON
ejpam-3752	386	5	-ideals	-ideal	NOUN
ejpam-3752	386	6	in	in	ADP
ejpam-3752	386	7	bck	bck	NOUN
ejpam-3752	386	8	-	-	PUNCT
ejpam-3752	386	9	algebras	algebra	NOUN
ejpam-3752	386	10	.	.	PUNCT
ejpam-3752	387	1	axioms	axiom	NOUN
ejpam-3752	387	2	,	,	PUNCT
ejpam-3752	387	3	7(1):3	7(1):3	PROPN
ejpam-3752	387	4	,	,	PUNCT
ejpam-3752	387	5	2018	2018	NUM
ejpam-3752	387	6	.	.	PUNCT
ejpam-3752	388	1	[	[	X
ejpam-3752	388	2	13	13	NUM
ejpam-3752	388	3	]	]	X
ejpam-3752	388	4	y.	y.	PROPN
ejpam-3752	388	5	b.	b.	PROPN
ejpam-3752	388	6	jun	jun	PROPN
ejpam-3752	388	7	,	,	PUNCT
ejpam-3752	388	8	s.	s.	PROPN
ejpam-3752	388	9	z.	z.	PROPN
ejpam-3752	388	10	song	song	PROPN
ejpam-3752	388	11	,	,	PUNCT
ejpam-3752	388	12	and	and	CCONJ
ejpam-3752	388	13	s.	s.	PROPN
ejpam-3752	388	14	j.	j.	PROPN
ejpam-3752	388	15	kim	kim	PROPN
ejpam-3752	388	16	.	.	PROPN
ejpam-3752	388	17	neutrosophic	neutrosophic	PROPN
ejpam-3752	388	18	quadruple	quadruple	PROPN
ejpam-3752	388	19	bci	bci	ADJ
ejpam-3752	388	20	-	-	ADJ
ejpam-3752	388	21	positive	positive	ADJ
ejpam-3752	388	22	implicative	implicative	ADJ
ejpam-3752	388	23	ideals	ideal	NOUN
ejpam-3752	388	24	.	.	PUNCT
ejpam-3752	389	1	mathematics	mathematic	NOUN
ejpam-3752	389	2	,	,	PUNCT
ejpam-3752	389	3	7(5):385	7(5):385	NUM
ejpam-3752	389	4	,	,	PUNCT
ejpam-3752	389	5	2019	2019	NUM
ejpam-3752	389	6	.	.	PUNCT
ejpam-3752	390	1	[	[	X
ejpam-3752	390	2	14	14	NUM
ejpam-3752	390	3	]	]	X
ejpam-3752	390	4	y.	y.	PROPN
ejpam-3752	390	5	b.	b.	PROPN
ejpam-3752	390	6	jun	jun	PROPN
ejpam-3752	390	7	,	,	PUNCT
ejpam-3752	390	8	s.	s.	PROPN
ejpam-3752	390	9	z.	z.	PROPN
ejpam-3752	390	10	song	song	PROPN
ejpam-3752	390	11	,	,	PUNCT
ejpam-3752	390	12	f.	f.	PROPN
ejpam-3752	390	13	smarandache	smarandache	PROPN
ejpam-3752	390	14	,	,	PUNCT
ejpam-3752	390	15	and	and	CCONJ
ejpam-3752	390	16	h.	h.	PROPN
ejpam-3752	390	17	bordbar	bordbar	PROPN
ejpam-3752	390	18	.	.	PUNCT
ejpam-3752	391	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	391	2	quadruple	quadruple	PROPN
ejpam-3752	391	3	bck	bck	PROPN
ejpam-3752	391	4	/	/	SYM
ejpam-3752	391	5	bci	bci	NOUN
ejpam-3752	391	6	-	-	PUNCT
ejpam-3752	391	7	algebras	algebra	NOUN
ejpam-3752	391	8	.	.	PUNCT
ejpam-3752	392	1	axioms	axiom	NOUN
ejpam-3752	392	2	,	,	PUNCT
ejpam-3752	392	3	7(2):41	7(2):41	NUM
ejpam-3752	392	4	,	,	PUNCT
ejpam-3752	392	5	2018	2018	NUM
ejpam-3752	392	6	.	.	PUNCT
ejpam-3752	393	1	[	[	X
ejpam-3752	393	2	15	15	NUM
ejpam-3752	393	3	]	]	X
ejpam-3752	393	4	w.	w.	PROPN
ejpam-3752	393	5	kaijae	kaijae	PROPN
ejpam-3752	393	6	,	,	PUNCT
ejpam-3752	393	7	p.	p.	PROPN
ejpam-3752	393	8	poungsumpao	poungsumpao	PROPN
ejpam-3752	393	9	,	,	PUNCT
ejpam-3752	393	10	s.	s.	PROPN
ejpam-3752	393	11	arayarangsi	arayarangsi	PROPN
ejpam-3752	393	12	,	,	PUNCT
ejpam-3752	393	13	and	and	CCONJ
ejpam-3752	393	14	a.	a.	NOUN
ejpam-3752	393	15	iampan	iampan	PROPN
ejpam-3752	393	16	.	.	PUNCT
ejpam-3752	394	1	up	up	ADV
ejpam-3752	394	2	-	-	PUNCT
ejpam-3752	394	3	algebras	algebras	PROPN
ejpam-3752	394	4	characterized	characterize	VERB
ejpam-3752	394	5	by	by	ADP
ejpam-3752	394	6	their	their	PRON
ejpam-3752	394	7	anti	anti	ADJ
ejpam-3752	394	8	-	-	ADJ
ejpam-3752	394	9	fuzzy	fuzzy	ADJ
ejpam-3752	394	10	up	up	ADJ
ejpam-3752	394	11	-	-	PUNCT
ejpam-3752	394	12	ideals	ideal	NOUN
ejpam-3752	394	13	and	and	CCONJ
ejpam-3752	394	14	anti	anti	ADJ
ejpam-3752	394	15	-	-	ADJ
ejpam-3752	394	16	fuzzy	fuzzy	ADJ
ejpam-3752	394	17	up	up	ADP
ejpam-3752	394	18	-	-	PUNCT
ejpam-3752	394	19	subalgebras	subalgebras	PROPN
ejpam-3752	394	20	.	.	PUNCT
ejpam-3752	395	1	ital	ital	PROPN
ejpam-3752	395	2	.	.	PUNCT
ejpam-3752	396	1	j.	j.	PROPN
ejpam-3752	396	2	pure	pure	PROPN
ejpam-3752	396	3	appl	appl	PROPN
ejpam-3752	396	4	.	.	PUNCT
ejpam-3752	396	5	math	math	PROPN
ejpam-3752	396	6	.	.	PUNCT
ejpam-3752	396	7	,	,	PUNCT
ejpam-3752	397	1	36:667–692	36:667–692	NUM
ejpam-3752	397	2	,	,	PUNCT
ejpam-3752	397	3	2016	2016	NUM
ejpam-3752	397	4	.	.	PUNCT
ejpam-3752	398	1	[	[	X
ejpam-3752	398	2	16	16	NUM
ejpam-3752	398	3	]	]	X
ejpam-3752	398	4	b.	b.	PROPN
ejpam-3752	398	5	kesorn	kesorn	PROPN
ejpam-3752	398	6	,	,	PUNCT
ejpam-3752	398	7	k.	k.	PROPN
ejpam-3752	398	8	maimun	maimun	PROPN
ejpam-3752	398	9	,	,	PUNCT
ejpam-3752	398	10	w.	w.	PROPN
ejpam-3752	398	11	ratbandan	ratbandan	PROPN
ejpam-3752	398	12	,	,	PUNCT
ejpam-3752	398	13	and	and	CCONJ
ejpam-3752	398	14	a.	a.	NOUN
ejpam-3752	398	15	iampan	iampan	PROPN
ejpam-3752	398	16	.	.	PUNCT
ejpam-3752	399	1	intuitionistic	intuitionistic	ADJ
ejpam-3752	399	2	fuzzy	fuzzy	ADJ
ejpam-3752	399	3	sets	set	NOUN
ejpam-3752	399	4	in	in	ADP
ejpam-3752	399	5	up	up	ADP
ejpam-3752	399	6	-	-	PUNCT
ejpam-3752	399	7	algebras	algebras	X
ejpam-3752	399	8	.	.	PUNCT
ejpam-3752	400	1	ital	ital	PROPN
ejpam-3752	400	2	.	.	PUNCT
ejpam-3752	401	1	j.	j.	PROPN
ejpam-3752	401	2	pure	pure	PROPN
ejpam-3752	401	3	appl	appl	PROPN
ejpam-3752	401	4	.	.	PUNCT
ejpam-3752	401	5	math	math	PROPN
ejpam-3752	401	6	.	.	PUNCT
ejpam-3752	401	7	,	,	PUNCT
ejpam-3752	402	1	34:339–364	34:339–364	NUM
ejpam-3752	402	2	,	,	PUNCT
ejpam-3752	402	3	2015	2015	NUM
ejpam-3752	402	4	.	.	PUNCT
ejpam-3752	403	1	[	[	X
ejpam-3752	403	2	17	17	NUM
ejpam-3752	403	3	]	]	PUNCT
ejpam-3752	403	4	a.	a.	PROPN
ejpam-3752	403	5	n.	n.	PROPN
ejpam-3752	403	6	a.	a.	PROPN
ejpam-3752	403	7	koam	koam	PROPN
ejpam-3752	403	8	,	,	PUNCT
ejpam-3752	403	9	m.	m.	NOUN
ejpam-3752	403	10	a.	a.	NOUN
ejpam-3752	403	11	ansari	ansari	PROPN
ejpam-3752	403	12	,	,	PUNCT
ejpam-3752	403	13	and	and	CCONJ
ejpam-3752	403	14	a.	a.	NOUN
ejpam-3752	403	15	haidar	haidar	PROPN
ejpam-3752	403	16	.	.	PUNCT
ejpam-3752	404	1	n	n	CCONJ
ejpam-3752	404	2	-	-	PUNCT
ejpam-3752	404	3	ary	ary	PROPN
ejpam-3752	405	1	block	block	NOUN
ejpam-3752	405	2	codes	code	NOUN
ejpam-3752	405	3	related	relate	VERB
ejpam-3752	405	4	to	to	ADP
ejpam-3752	405	5	kualgebras	kualgebras	PROPN
ejpam-3752	405	6	.	.	PUNCT
ejpam-3752	406	1	j.	j.	PROPN
ejpam-3752	406	2	taibah	taibah	PROPN
ejpam-3752	406	3	univ	univ	PROPN
ejpam-3752	406	4	.	.	PUNCT
ejpam-3752	407	1	sci	sci	PROPN
ejpam-3752	407	2	.	.	PROPN
ejpam-3752	407	3	,	,	PUNCT
ejpam-3752	407	4	14(1):172–176	14(1):172–176	PROPN
ejpam-3752	407	5	,	,	PUNCT
ejpam-3752	407	6	2020	2020	NUM
ejpam-3752	407	7	.	.	PUNCT
ejpam-3752	408	1	[	[	X
ejpam-3752	408	2	18	18	NUM
ejpam-3752	408	3	]	]	X
ejpam-3752	408	4	g.	g.	PROPN
ejpam-3752	408	5	muhiuddin	muhiuddin	PROPN
ejpam-3752	408	6	,	,	PUNCT
ejpam-3752	408	7	a.	a.	PROPN
ejpam-3752	408	8	n.	n.	PROPN
ejpam-3752	408	9	al	al	PROPN
ejpam-3752	408	10	-	-	PUNCT
ejpam-3752	408	11	kenani	kenani	PROPN
ejpam-3752	408	12	,	,	PUNCT
ejpam-3752	408	13	e.	e.	PROPN
ejpam-3752	408	14	h.	h.	PROPN
ejpam-3752	408	15	roh	roh	PROPN
ejpam-3752	408	16	,	,	PUNCT
ejpam-3752	408	17	and	and	CCONJ
ejpam-3752	408	18	y.	y.	PROPN
ejpam-3752	408	19	b.	b.	PROPN
ejpam-3752	408	20	jun	jun	PROPN
ejpam-3752	408	21	.	.	PROPN
ejpam-3752	408	22	implicative	implicative	PROPN
ejpam-3752	408	23	neutrosophic	neutrosophic	PROPN
ejpam-3752	408	24	quadruple	quadruple	PROPN
ejpam-3752	408	25	bck	bck	PROPN
ejpam-3752	408	26	-	-	PUNCT
ejpam-3752	408	27	algebras	algebra	NOUN
ejpam-3752	408	28	and	and	CCONJ
ejpam-3752	408	29	ideals	ideal	NOUN
ejpam-3752	408	30	.	.	PUNCT
ejpam-3752	409	1	symmetry	symmetry	NOUN
ejpam-3752	409	2	,	,	PUNCT
ejpam-3752	409	3	11(2):277	11(2):277	NOUN
ejpam-3752	409	4	,	,	PUNCT
ejpam-3752	409	5	2019	2019	NUM
ejpam-3752	409	6	.	.	PUNCT
ejpam-3752	410	1	[	[	X
ejpam-3752	410	2	19	19	NUM
ejpam-3752	410	3	]	]	X
ejpam-3752	410	4	g.	g.	PROPN
ejpam-3752	410	5	muhiuddin	muhiuddin	PROPN
ejpam-3752	410	6	,	,	PUNCT
ejpam-3752	410	7	h.	h.	PROPN
ejpam-3752	410	8	bordbar	bordbar	PROPN
ejpam-3752	410	9	,	,	PUNCT
ejpam-3752	410	10	f.	f.	PROPN
ejpam-3752	410	11	smarandache	smarandache	PROPN
ejpam-3752	410	12	,	,	PUNCT
ejpam-3752	410	13	and	and	CCONJ
ejpam-3752	410	14	y.	y.	PROPN
ejpam-3752	410	15	b.	b.	PROPN
ejpam-3752	410	16	jun	jun	PROPN
ejpam-3752	410	17	.	.	PROPN
ejpam-3752	411	1	further	further	ADJ
ejpam-3752	411	2	results	result	NOUN
ejpam-3752	411	3	on	on	ADP
ejpam-3752	411	4	(	(	PUNCT
ejpam-3752	411	5	∈,∈)-neutrosophic	∈,∈)-neutrosophic	ADJ
ejpam-3752	411	6	subalgebras	subalgebra	NOUN
ejpam-3752	411	7	and	and	CCONJ
ejpam-3752	411	8	ideals	ideal	NOUN
ejpam-3752	411	9	in	in	ADP
ejpam-3752	411	10	bck	bck	PROPN
ejpam-3752	411	11	/	/	SYM
ejpam-3752	411	12	bci	bci	NOUN
ejpam-3752	411	13	-	-	PUNCT
ejpam-3752	411	14	algebras	algebra	NOUN
ejpam-3752	411	15	.	.	PUNCT
ejpam-3752	412	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	412	2	sets	set	VERB
ejpam-3752	412	3	syst	syst	PROPN
ejpam-3752	412	4	.	.	PUNCT
ejpam-3752	412	5	,	,	PUNCT
ejpam-3752	412	6	20:36–43	20:36–43	PROPN
ejpam-3752	412	7	,	,	PUNCT
ejpam-3752	412	8	2018	2018	NUM
ejpam-3752	412	9	.	.	PUNCT
ejpam-3752	413	1	[	[	X
ejpam-3752	413	2	20	20	NUM
ejpam-3752	413	3	]	]	X
ejpam-3752	413	4	g.	g.	PROPN
ejpam-3752	413	5	muhiuddin	muhiuddin	PROPN
ejpam-3752	413	6	and	and	CCONJ
ejpam-3752	413	7	y.	y.	PROPN
ejpam-3752	413	8	b.	b.	PROPN
ejpam-3752	413	9	jun	jun	PROPN
ejpam-3752	413	10	.	.	PROPN
ejpam-3752	414	1	p	p	NOUN
ejpam-3752	414	2	-	-	PUNCT
ejpam-3752	414	3	semisimple	semisimple	NOUN
ejpam-3752	414	4	neutrosophic	neutrosophic	PROPN
ejpam-3752	414	5	quadruple	quadruple	PROPN
ejpam-3752	414	6	bci	bci	NOUN
ejpam-3752	414	7	-	-	PUNCT
ejpam-3752	414	8	algebras	algebra	NOUN
ejpam-3752	414	9	and	and	CCONJ
ejpam-3752	414	10	neutrosophic	neutrosophic	ADJ
ejpam-3752	414	11	quadruple	quadruple	NOUN
ejpam-3752	414	12	p	p	NOUN
ejpam-3752	414	13	-	-	PUNCT
ejpam-3752	414	14	ideals	ideal	NOUN
ejpam-3752	414	15	.	.	PUNCT
ejpam-3752	415	1	ann	ann	AUX
ejpam-3752	415	2	.	.	PUNCT
ejpam-3752	415	3	commun	commun	PROPN
ejpam-3752	415	4	.	.	PUNCT
ejpam-3752	416	1	math	math	PROPN
ejpam-3752	416	2	.	.	PUNCT
ejpam-3752	416	3	,	,	PUNCT
ejpam-3752	416	4	1(1):26–37	1(1):26–37	NUM
ejpam-3752	416	5	,	,	PUNCT
ejpam-3752	416	6	2018	2018	NUM
ejpam-3752	416	7	.	.	PUNCT
ejpam-3752	417	1	[	[	X
ejpam-3752	417	2	21	21	NUM
ejpam-3752	417	3	]	]	X
ejpam-3752	417	4	g.	g.	PROPN
ejpam-3752	417	5	muhiuddin	muhiuddin	PROPN
ejpam-3752	417	6	,	,	PUNCT
ejpam-3752	417	7	s.	s.	PROPN
ejpam-3752	417	8	j.	j.	PROPN
ejpam-3752	417	9	kim	kim	PROPN
ejpam-3752	417	10	,	,	PUNCT
ejpam-3752	417	11	and	and	CCONJ
ejpam-3752	417	12	y.	y.	PROPN
ejpam-3752	417	13	b.	b.	PROPN
ejpam-3752	417	14	jun	jun	PROPN
ejpam-3752	417	15	.	.	PROPN
ejpam-3752	417	16	implicative	implicative	ADJ
ejpam-3752	417	17	n	n	PRON
ejpam-3752	417	18	-ideals	-ideal	NOUN
ejpam-3752	417	19	of	of	ADP
ejpam-3752	417	20	bck	bck	NOUN
ejpam-3752	417	21	-	-	PUNCT
ejpam-3752	417	22	algebras	algebras	PROPN
ejpam-3752	417	23	based	base	VERB
ejpam-3752	417	24	on	on	ADP
ejpam-3752	417	25	neutrosophic	neutrosophic	ADJ
ejpam-3752	417	26	n	n	PRON
ejpam-3752	417	27	-structures	-structure	NOUN
ejpam-3752	417	28	.	.	PUNCT
ejpam-3752	418	1	discrete	discrete	ADJ
ejpam-3752	418	2	math	math	NOUN
ejpam-3752	418	3	.	.	PUNCT
ejpam-3752	419	1	algorithms	algorithms	PROPN
ejpam-3752	419	2	appl	appl	PROPN
ejpam-3752	419	3	.	.	PROPN
ejpam-3752	419	4	,	,	PUNCT
ejpam-3752	419	5	11(1):1950011	11(1):1950011	NUM
ejpam-3752	419	6	,	,	PUNCT
ejpam-3752	419	7	2019	2019	NUM
ejpam-3752	419	8	.	.	PUNCT
ejpam-3752	420	1	[	[	X
ejpam-3752	420	2	22	22	NUM
ejpam-3752	420	3	]	]	X
ejpam-3752	420	4	g.	g.	PROPN
ejpam-3752	420	5	muhiuddin	muhiuddin	PROPN
ejpam-3752	420	6	,	,	PUNCT
ejpam-3752	420	7	f.	f.	PROPN
ejpam-3752	420	8	smarandache	smarandache	PROPN
ejpam-3752	420	9	,	,	PUNCT
ejpam-3752	420	10	and	and	CCONJ
ejpam-3752	420	11	y.	y.	PROPN
ejpam-3752	420	12	b.	b.	PROPN
ejpam-3752	420	13	jun	jun	PROPN
ejpam-3752	420	14	.	.	PROPN
ejpam-3752	420	15	neutrosophic	neutrosophic	PROPN
ejpam-3752	420	16	quadruple	quadruple	NOUN
ejpam-3752	420	17	ideals	ideal	NOUN
ejpam-3752	420	18	in	in	ADP
ejpam-3752	420	19	neutrosophic	neutrosophic	PROPN
ejpam-3752	420	20	quadruple	quadruple	PROPN
ejpam-3752	420	21	bci	bci	NOUN
ejpam-3752	420	22	-	-	PUNCT
ejpam-3752	420	23	algebras	algebra	NOUN
ejpam-3752	420	24	.	.	PUNCT
ejpam-3752	420	25	neutrosophic	neutrosophic	PROPN
ejpam-3752	420	26	sets	set	VERB
ejpam-3752	420	27	syst	syst	PROPN
ejpam-3752	420	28	.	.	PUNCT
ejpam-3752	420	29	,	,	PUNCT
ejpam-3752	420	30	25:161–173	25:161–173	PROPN
ejpam-3752	420	31	,	,	PUNCT
ejpam-3752	420	32	2019	2019	NUM
ejpam-3752	420	33	.	.	PUNCT
ejpam-3752	421	1	[	[	X
ejpam-3752	421	2	23	23	NUM
ejpam-3752	421	3	]	]	X
ejpam-3752	421	4	c.	c.	NOUN
ejpam-3752	421	5	prabpayak	prabpayak	NOUN
ejpam-3752	421	6	and	and	CCONJ
ejpam-3752	421	7	u.	u.	NOUN
ejpam-3752	421	8	leerawat	leerawat	PROPN
ejpam-3752	421	9	.	.	PUNCT
ejpam-3752	422	1	on	on	ADP
ejpam-3752	422	2	ideals	ideal	NOUN
ejpam-3752	422	3	and	and	CCONJ
ejpam-3752	422	4	congruences	congruence	NOUN
ejpam-3752	422	5	in	in	ADP
ejpam-3752	422	6	ku	ku	PROPN
ejpam-3752	422	7	-	-	PUNCT
ejpam-3752	422	8	algebras	algebras	PROPN
ejpam-3752	422	9	.	.	PUNCT
ejpam-3752	423	1	sci	sci	PROPN
ejpam-3752	423	2	.	.	PROPN
ejpam-3752	423	3	magna	magna	PROPN
ejpam-3752	423	4	,	,	PUNCT
ejpam-3752	423	5	5(1):54–57	5(1):54–57	NUM
ejpam-3752	423	6	,	,	PUNCT
ejpam-3752	423	7	2009	2009	NUM
ejpam-3752	423	8	.	.	PUNCT
ejpam-3752	424	1	[	[	X
ejpam-3752	424	2	24	24	NUM
ejpam-3752	424	3	]	]	PUNCT
ejpam-3752	424	4	a.	a.	NOUN
ejpam-3752	424	5	satirad	satirad	PROPN
ejpam-3752	424	6	,	,	PUNCT
ejpam-3752	424	7	p.	p.	PROPN
ejpam-3752	424	8	mosrijai	mosrijai	PROPN
ejpam-3752	424	9	,	,	PUNCT
ejpam-3752	424	10	and	and	CCONJ
ejpam-3752	424	11	a.	a.	NOUN
ejpam-3752	424	12	iampan	iampan	PROPN
ejpam-3752	424	13	.	.	PUNCT
ejpam-3752	425	1	formulas	formula	NOUN
ejpam-3752	425	2	for	for	ADP
ejpam-3752	425	3	finding	find	VERB
ejpam-3752	425	4	up	up	ADP
ejpam-3752	425	5	-	-	PUNCT
ejpam-3752	425	6	algebras	algebras	X
ejpam-3752	425	7	.	.	PUNCT
ejpam-3752	426	1	int	int	NOUN
ejpam-3752	426	2	.	.	PUNCT
ejpam-3752	427	1	j.	j.	PROPN
ejpam-3752	427	2	math	math	PROPN
ejpam-3752	427	3	.	.	PUNCT
ejpam-3752	428	1	comput	comput	NOUN
ejpam-3752	428	2	.	.	PUNCT
ejpam-3752	429	1	sci	sci	PROPN
ejpam-3752	429	2	.	.	PROPN
ejpam-3752	429	3	,	,	PUNCT
ejpam-3752	429	4	14(2):403–409	14(2):403–409	PROPN
ejpam-3752	429	5	,	,	PUNCT
ejpam-3752	429	6	2019	2019	NUM
ejpam-3752	429	7	.	.	PUNCT
ejpam-3752	430	1	[	[	X
ejpam-3752	430	2	25	25	NUM
ejpam-3752	430	3	]	]	PUNCT
ejpam-3752	430	4	a.	a.	NOUN
ejpam-3752	430	5	satirad	satirad	PROPN
ejpam-3752	430	6	,	,	PUNCT
ejpam-3752	430	7	p.	p.	PROPN
ejpam-3752	430	8	mosrijai	mosrijai	PROPN
ejpam-3752	430	9	,	,	PUNCT
ejpam-3752	430	10	and	and	CCONJ
ejpam-3752	430	11	a.	a.	NOUN
ejpam-3752	430	12	iampan	iampan	PROPN
ejpam-3752	430	13	.	.	PUNCT
ejpam-3752	431	1	generalized	generalized	ADJ
ejpam-3752	431	2	power	power	NOUN
ejpam-3752	431	3	up	up	ADP
ejpam-3752	431	4	-	-	PUNCT
ejpam-3752	431	5	algebras	algebras	PROPN
ejpam-3752	431	6	.	.	PUNCT
ejpam-3752	432	1	int	int	NOUN
ejpam-3752	432	2	.	.	PUNCT
ejpam-3752	433	1	j.	j.	PROPN
ejpam-3752	433	2	math	math	PROPN
ejpam-3752	433	3	.	.	PUNCT
ejpam-3752	434	1	comput	comput	NOUN
ejpam-3752	434	2	.	.	PUNCT
ejpam-3752	435	1	sci	sci	PROPN
ejpam-3752	435	2	.	.	PROPN
ejpam-3752	435	3	,	,	PUNCT
ejpam-3752	435	4	14(1):17–25	14(1):17–25	NUM
ejpam-3752	435	5	,	,	PUNCT
ejpam-3752	435	6	2019	2019	NUM
ejpam-3752	435	7	.	.	PUNCT
ejpam-3752	436	1	[	[	X
ejpam-3752	436	2	26	26	NUM
ejpam-3752	436	3	]	]	PUNCT
ejpam-3752	436	4	t.	t.	NOUN
ejpam-3752	436	5	senapati	senapati	PROPN
ejpam-3752	436	6	,	,	PUNCT
ejpam-3752	436	7	y.	y.	PROPN
ejpam-3752	436	8	b.	b.	PROPN
ejpam-3752	436	9	jun	jun	PROPN
ejpam-3752	436	10	,	,	PUNCT
ejpam-3752	436	11	and	and	CCONJ
ejpam-3752	436	12	k.	k.	PROPN
ejpam-3752	436	13	p.	p.	PROPN
ejpam-3752	436	14	shum	shum	PROPN
ejpam-3752	436	15	.	.	PUNCT
ejpam-3752	437	1	cubic	cubic	ADJ
ejpam-3752	437	2	set	set	VERB
ejpam-3752	437	3	structure	structure	NOUN
ejpam-3752	437	4	applied	apply	VERB
ejpam-3752	437	5	in	in	ADP
ejpam-3752	437	6	up	up	ADP
ejpam-3752	437	7	-	-	PUNCT
ejpam-3752	437	8	algebras	algebras	X
ejpam-3752	437	9	.	.	PUNCT
ejpam-3752	438	1	discrete	discrete	ADJ
ejpam-3752	438	2	math	math	NOUN
ejpam-3752	438	3	.	.	PUNCT
ejpam-3752	439	1	algorithms	algorithms	PROPN
ejpam-3752	439	2	appl	appl	PROPN
ejpam-3752	439	3	.	.	PROPN
ejpam-3752	439	4	,	,	PUNCT
ejpam-3752	439	5	10(4):1850049	10(4):1850049	NUM
ejpam-3752	439	6	,	,	PUNCT
ejpam-3752	439	7	2018	2018	NUM
ejpam-3752	439	8	.	.	PUNCT
ejpam-3752	440	1	references	reference	NOUN
ejpam-3752	440	2	471	471	NUM
ejpam-3752	441	1	[	[	X
ejpam-3752	441	2	27	27	NUM
ejpam-3752	441	3	]	]	PUNCT
ejpam-3752	441	4	t.	t.	NOUN
ejpam-3752	441	5	senapati	senapati	PROPN
ejpam-3752	441	6	,	,	PUNCT
ejpam-3752	441	7	g.	g.	PROPN
ejpam-3752	441	8	muhiuddin	muhiuddin	PROPN
ejpam-3752	441	9	,	,	PUNCT
ejpam-3752	441	10	and	and	CCONJ
ejpam-3752	441	11	k.	k.	PROPN
ejpam-3752	441	12	p.	p.	PROPN
ejpam-3752	441	13	shum	shum	PROPN
ejpam-3752	441	14	.	.	PUNCT
ejpam-3752	442	1	representation	representation	NOUN
ejpam-3752	442	2	of	of	ADP
ejpam-3752	442	3	up	up	ADV
ejpam-3752	442	4	-	-	PUNCT
ejpam-3752	442	5	algebras	algebras	NOUN
ejpam-3752	442	6	in	in	ADP
ejpam-3752	442	7	interval	interval	NOUN
ejpam-3752	442	8	-	-	PUNCT
ejpam-3752	442	9	valued	value	VERB
ejpam-3752	442	10	intuitionistic	intuitionistic	ADJ
ejpam-3752	442	11	fuzzy	fuzzy	ADJ
ejpam-3752	442	12	environment	environment	NOUN
ejpam-3752	442	13	.	.	PUNCT
ejpam-3752	443	1	ital	ital	PROPN
ejpam-3752	443	2	.	.	PUNCT
ejpam-3752	444	1	j.	j.	PROPN
ejpam-3752	444	2	pure	pure	PROPN
ejpam-3752	444	3	appl	appl	PROPN
ejpam-3752	444	4	.	.	PUNCT
ejpam-3752	444	5	math	math	PROPN
ejpam-3752	444	6	.	.	PUNCT
ejpam-3752	444	7	,	,	PUNCT
ejpam-3752	444	8	38:497	38:497	NUM
ejpam-3752	444	9	–	–	PUNCT
ejpam-3752	444	10	517	517	NUM
ejpam-3752	444	11	,	,	PUNCT
ejpam-3752	444	12	2017	2017	NUM
ejpam-3752	444	13	.	.	PUNCT
ejpam-3752	445	1	[	[	X
ejpam-3752	445	2	28	28	NUM
ejpam-3752	445	3	]	]	X
ejpam-3752	445	4	f.	f.	PROPN
ejpam-3752	445	5	smarandache	smarandache	PROPN
ejpam-3752	445	6	.	.	PUNCT
ejpam-3752	446	1	a	a	DET
ejpam-3752	446	2	unifying	unifying	ADJ
ejpam-3752	446	3	field	field	NOUN
ejpam-3752	446	4	in	in	ADP
ejpam-3752	446	5	logic	logic	NOUN
ejpam-3752	446	6	:	:	PUNCT
ejpam-3752	446	7	neutrosophic	neutrosophic	ADJ
ejpam-3752	446	8	logic	logic	NOUN
ejpam-3752	446	9	.	.	PUNCT
ejpam-3752	447	1	neutrosophy	neutrosophy	NOUN
ejpam-3752	447	2	,	,	PUNCT
ejpam-3752	447	3	neutrosophic	neutrosophic	ADJ
ejpam-3752	447	4	set	set	NOUN
ejpam-3752	447	5	,	,	PUNCT
ejpam-3752	447	6	neutrosophic	neutrosophic	ADJ
ejpam-3752	447	7	probability	probability	NOUN
ejpam-3752	447	8	.	.	PUNCT
ejpam-3752	448	1	american	american	PROPN
ejpam-3752	448	2	research	research	PROPN
ejpam-3752	448	3	press	press	PROPN
ejpam-3752	448	4	,	,	PUNCT
ejpam-3752	448	5	rehoboth	rehoboth	PROPN
ejpam-3752	448	6	,	,	PUNCT
ejpam-3752	448	7	nm	nm	PROPN
ejpam-3752	448	8	,	,	PUNCT
ejpam-3752	448	9	1999	1999	NUM
ejpam-3752	448	10	.	.	PUNCT
ejpam-3752	449	1	[	[	X
ejpam-3752	449	2	29	29	NUM
ejpam-3752	449	3	]	]	PUNCT
ejpam-3752	449	4	j.	j.	PROPN
ejpam-3752	449	5	somjanta	somjanta	PROPN
ejpam-3752	449	6	,	,	PUNCT
ejpam-3752	449	7	n.	n.	PROPN
ejpam-3752	449	8	thuekaew	thuekaew	PROPN
ejpam-3752	449	9	,	,	PUNCT
ejpam-3752	449	10	p.	p.	NOUN
ejpam-3752	449	11	kumpeangkeaw	kumpeangkeaw	PROPN
ejpam-3752	449	12	,	,	PUNCT
ejpam-3752	449	13	and	and	CCONJ
ejpam-3752	449	14	a.	a.	NOUN
ejpam-3752	449	15	iampan	iampan	PROPN
ejpam-3752	449	16	.	.	PUNCT
ejpam-3752	450	1	fuzzy	fuzzy	ADJ
ejpam-3752	450	2	sets	set	NOUN
ejpam-3752	450	3	in	in	ADP
ejpam-3752	450	4	upalgebras	upalgebra	NOUN
ejpam-3752	450	5	.	.	PUNCT
ejpam-3752	451	1	ann	ann	PROPN
ejpam-3752	451	2	.	.	PUNCT
ejpam-3752	451	3	fuzzy	fuzzy	ADJ
ejpam-3752	451	4	math	math	NOUN
ejpam-3752	451	5	.	.	PUNCT
ejpam-3752	452	1	inform	inform	NOUN
ejpam-3752	452	2	.	.	PUNCT
ejpam-3752	452	3	,	,	PUNCT
ejpam-3752	452	4	12(6):739–756	12(6):739–756	PROPN
ejpam-3752	452	5	,	,	PUNCT
ejpam-3752	452	6	2016	2016	NUM
ejpam-3752	452	7	.	.	PUNCT
ejpam-3752	453	1	[	[	X
ejpam-3752	453	2	30	30	NUM
ejpam-3752	453	3	]	]	PUNCT
ejpam-3752	453	4	s.	s.	PROPN
ejpam-3752	453	5	z.	z.	PROPN
ejpam-3752	453	6	song	song	PROPN
ejpam-3752	453	7	,	,	PUNCT
ejpam-3752	453	8	f.	f.	PROPN
ejpam-3752	453	9	smarandache	smarandache	PROPN
ejpam-3752	453	10	,	,	PUNCT
ejpam-3752	453	11	and	and	CCONJ
ejpam-3752	453	12	y.	y.	PROPN
ejpam-3752	453	13	b.	b.	PROPN
ejpam-3752	453	14	jun	jun	PROPN
ejpam-3752	453	15	.	.	PROPN
ejpam-3752	453	16	neutrosophic	neutrosophic	PROPN
ejpam-3752	453	17	commutative	commutative	ADJ
ejpam-3752	453	18	n	n	PRON
ejpam-3752	453	19	-ideals	-ideal	NOUN
ejpam-3752	453	20	in	in	ADP
ejpam-3752	453	21	bck	bck	NOUN
ejpam-3752	453	22	-	-	PUNCT
ejpam-3752	453	23	algebras	algebras	PROPN
ejpam-3752	453	24	.	.	PUNCT
ejpam-3752	454	1	inform	inform	NOUN
ejpam-3752	454	2	.	.	PUNCT
ejpam-3752	454	3	,	,	PUNCT
ejpam-3752	454	4	8:130	8:130	NUM
ejpam-3752	454	5	,	,	PUNCT
ejpam-3752	454	6	2017	2017	NUM
ejpam-3752	454	7	.	.	PUNCT
ejpam-3752	455	1	[	[	X
ejpam-3752	455	2	31	31	NUM
ejpam-3752	455	3	]	]	PUNCT
ejpam-3752	455	4	m.	m.	NOUN
ejpam-3752	455	5	songsaeng	songsaeng	PROPN
ejpam-3752	455	6	and	and	CCONJ
ejpam-3752	455	7	a.	a.	NOUN
ejpam-3752	455	8	iampan	iampan	PROPN
ejpam-3752	455	9	.	.	PUNCT
ejpam-3752	456	1	n	n	PRON
ejpam-3752	456	2	-fuzzy	-fuzzy	NOUN
ejpam-3752	456	3	up	up	ADV
ejpam-3752	456	4	-	-	PUNCT
ejpam-3752	456	5	algebras	algebra	NOUN
ejpam-3752	456	6	and	and	CCONJ
ejpam-3752	456	7	its	its	PRON
ejpam-3752	456	8	level	level	NOUN
ejpam-3752	456	9	subsets	subset	NOUN
ejpam-3752	456	10	.	.	PUNCT
ejpam-3752	457	1	j.	j.	PROPN
ejpam-3752	457	2	algebra	algebra	PROPN
ejpam-3752	457	3	relat	relat	PROPN
ejpam-3752	457	4	.	.	PUNCT
ejpam-3752	458	1	top	top	NOUN
ejpam-3752	458	2	.	.	PUNCT
ejpam-3752	458	3	,	,	PUNCT
ejpam-3752	458	4	6(1):1–24	6(1):1–24	NUM
ejpam-3752	458	5	,	,	PUNCT
ejpam-3752	458	6	2018	2018	NUM
ejpam-3752	458	7	.	.	PUNCT
ejpam-3752	459	1	[	[	X
ejpam-3752	459	2	32	32	NUM
ejpam-3752	459	3	]	]	PUNCT
ejpam-3752	459	4	m.	m.	NOUN
ejpam-3752	459	5	songsaeng	songsaeng	PROPN
ejpam-3752	459	6	and	and	CCONJ
ejpam-3752	459	7	a.	a.	NOUN
ejpam-3752	459	8	iampan	iampan	PROPN
ejpam-3752	459	9	.	.	PUNCT
ejpam-3752	460	1	fuzzy	fuzzy	ADJ
ejpam-3752	460	2	proper	proper	ADJ
ejpam-3752	460	3	up	up	NOUN
ejpam-3752	460	4	-	-	PUNCT
ejpam-3752	460	5	filters	filter	NOUN
ejpam-3752	460	6	of	of	ADP
ejpam-3752	460	7	up	up	NOUN
ejpam-3752	460	8	-	-	PUNCT
ejpam-3752	460	9	algebras	algebras	X
ejpam-3752	460	10	.	.	PUNCT
ejpam-3752	461	1	honam	honam	PROPN
ejpam-3752	461	2	math	math	PROPN
ejpam-3752	461	3	.	.	PUNCT
ejpam-3752	462	1	j.	j.	PROPN
ejpam-3752	462	2	,	,	PUNCT
ejpam-3752	462	3	41(3):515–530	41(3):515–530	PROPN
ejpam-3752	462	4	,	,	PUNCT
ejpam-3752	462	5	2019	2019	NUM
ejpam-3752	462	6	.	.	PUNCT
ejpam-3752	463	1	[	[	X
ejpam-3752	463	2	33	33	NUM
ejpam-3752	463	3	]	]	PUNCT
ejpam-3752	463	4	m.	m.	NOUN
ejpam-3752	463	5	songsaeng	songsaeng	PROPN
ejpam-3752	463	6	and	and	CCONJ
ejpam-3752	463	7	a.	a.	NOUN
ejpam-3752	463	8	iampan	iampan	PROPN
ejpam-3752	463	9	.	.	PUNCT
ejpam-3752	464	1	neutrosophic	neutrosophic	PROPN
ejpam-3752	464	2	set	set	PROPN
ejpam-3752	464	3	theory	theory	NOUN
ejpam-3752	464	4	applied	apply	VERB
ejpam-3752	464	5	to	to	ADP
ejpam-3752	464	6	up	up	ADV
ejpam-3752	464	7	-	-	PUNCT
ejpam-3752	464	8	algebras	algebras	X
ejpam-3752	464	9	.	.	PUNCT
ejpam-3752	465	1	eur	eur	PROPN
ejpam-3752	465	2	.	.	PUNCT
ejpam-3752	466	1	j.	j.	PROPN
ejpam-3752	466	2	pure	pure	PROPN
ejpam-3752	466	3	appl	appl	PROPN
ejpam-3752	466	4	.	.	PUNCT
ejpam-3752	466	5	math	math	PROPN
ejpam-3752	466	6	.	.	PUNCT
ejpam-3752	466	7	,	,	PUNCT
ejpam-3752	466	8	12(4):1382–1409	12(4):1382–1409	NUM
ejpam-3752	466	9	,	,	PUNCT
ejpam-3752	466	10	2019	2019	NUM
ejpam-3752	466	11	.	.	PUNCT
ejpam-3752	467	1	[	[	X
ejpam-3752	467	2	34	34	NUM
ejpam-3752	467	3	]	]	X
ejpam-3752	467	4	s.	s.	PROPN
ejpam-3752	467	5	sripaeng	sripaeng	PROPN
ejpam-3752	467	6	,	,	PUNCT
ejpam-3752	467	7	k.	k.	PROPN
ejpam-3752	467	8	tanamoon	tanamoon	PROPN
ejpam-3752	467	9	,	,	PUNCT
ejpam-3752	467	10	and	and	CCONJ
ejpam-3752	467	11	a.	a.	NOUN
ejpam-3752	467	12	iampan	iampan	PROPN
ejpam-3752	467	13	.	.	PUNCT
ejpam-3752	468	1	on	on	ADP
ejpam-3752	468	2	anti	anti	ADJ
ejpam-3752	468	3	q	q	ADJ
ejpam-3752	468	4	-	-	ADJ
ejpam-3752	468	5	fuzzy	fuzzy	ADJ
ejpam-3752	468	6	up	up	NOUN
ejpam-3752	468	7	-	-	PUNCT
ejpam-3752	468	8	ideals	ideal	NOUN
ejpam-3752	468	9	and	and	CCONJ
ejpam-3752	468	10	anti	anti	ADJ
ejpam-3752	468	11	q	q	ADJ
ejpam-3752	468	12	-	-	ADJ
ejpam-3752	468	13	fuzzy	fuzzy	ADJ
ejpam-3752	468	14	up	up	ADP
ejpam-3752	468	15	-	-	PUNCT
ejpam-3752	468	16	subalgebras	subalgebra	NOUN
ejpam-3752	468	17	of	of	ADP
ejpam-3752	468	18	up	up	ADP
ejpam-3752	468	19	-	-	PUNCT
ejpam-3752	468	20	algebras	algebras	X
ejpam-3752	468	21	.	.	PUNCT
ejpam-3752	469	1	j.	j.	PROPN
ejpam-3752	469	2	inf	inf	PROPN
ejpam-3752	469	3	.	.	PROPN
ejpam-3752	469	4	optim	optim	PROPN
ejpam-3752	469	5	.	.	PUNCT
ejpam-3752	470	1	sci	sci	PROPN
ejpam-3752	470	2	.	.	PROPN
ejpam-3752	470	3	,	,	PUNCT
ejpam-3752	470	4	39(5):1095–1127	39(5):1095–1127	NUM
ejpam-3752	470	5	,	,	PUNCT
ejpam-3752	470	6	2018	2018	NUM
ejpam-3752	470	7	.	.	PUNCT
ejpam-3752	471	1	[	[	X
ejpam-3752	471	2	35	35	NUM
ejpam-3752	471	3	]	]	PUNCT
ejpam-3752	471	4	k.	k.	PROPN
ejpam-3752	471	5	tanamoon	tanamoon	PROPN
ejpam-3752	471	6	,	,	PUNCT
ejpam-3752	471	7	s.	s.	PROPN
ejpam-3752	471	8	sripaeng	sripaeng	PROPN
ejpam-3752	471	9	,	,	PUNCT
ejpam-3752	471	10	and	and	CCONJ
ejpam-3752	471	11	a.	a.	NOUN
ejpam-3752	471	12	iampan	iampan	PROPN
ejpam-3752	471	13	.	.	PUNCT
ejpam-3752	472	1	q	q	ADJ
ejpam-3752	472	2	-	-	ADJ
ejpam-3752	472	3	fuzzy	fuzzy	ADJ
ejpam-3752	472	4	sets	set	NOUN
ejpam-3752	472	5	in	in	ADP
ejpam-3752	472	6	up	up	ADP
ejpam-3752	472	7	-	-	PUNCT
ejpam-3752	472	8	algebras	algebras	X
ejpam-3752	472	9	.	.	PUNCT
ejpam-3752	473	1	songklanakarin	songklanakarin	PROPN
ejpam-3752	473	2	j.	j.	PROPN
ejpam-3752	473	3	sci	sci	PROPN
ejpam-3752	473	4	.	.	PROPN
ejpam-3752	473	5	technol	technol	PROPN
ejpam-3752	473	6	.	.	PROPN
ejpam-3752	473	7	,	,	PUNCT
ejpam-3752	473	8	40(1):9–29	40(1):9–29	NUM
ejpam-3752	473	9	,	,	PUNCT
ejpam-3752	473	10	2018	2018	NUM
ejpam-3752	473	11	.	.	PUNCT
ejpam-3752	474	1	[	[	X
ejpam-3752	474	2	36	36	NUM
ejpam-3752	474	3	]	]	X
ejpam-3752	474	4	l.	l.	PROPN
ejpam-3752	474	5	a.	a.	PROPN
ejpam-3752	474	6	zadeh	zadeh	PROPN
ejpam-3752	474	7	.	.	PUNCT
ejpam-3752	474	8	fuzzy	fuzzy	ADJ
ejpam-3752	474	9	sets	set	NOUN
ejpam-3752	474	10	.	.	PUNCT
ejpam-3752	475	1	inf	inf	PROPN
ejpam-3752	475	2	.	.	PUNCT
ejpam-3752	475	3	cont	cont	PROPN
ejpam-3752	475	4	.	.	PROPN
ejpam-3752	475	5	,	,	PUNCT
ejpam-3752	475	6	8:338–353	8:338–353	NUM
ejpam-3752	475	7	,	,	PUNCT
ejpam-3752	475	8	1965	1965	NUM
ejpam-3752	475	9	.	.	PUNCT