id	sid	tid	token	lemma	pos
ejpam-3870	1	1	european	european	PROPN
ejpam-3870	1	2	journal	journal	PROPN
ejpam-3870	1	3	of	of	ADP
ejpam-3870	1	4	pure	pure	ADJ
ejpam-3870	1	5	and	and	CCONJ
ejpam-3870	1	6	applied	apply	VERB
ejpam-3870	1	7	mathematics	mathematic	NOUN
ejpam-3870	1	8	vol	vol	NOUN
ejpam-3870	1	9	.	.	PROPN
ejpam-3870	2	1	13	13	NUM
ejpam-3870	2	2	,	,	PUNCT
ejpam-3870	2	3	no	no	INTJ
ejpam-3870	2	4	.	.	NOUN
ejpam-3870	2	5	4	4	NUM
ejpam-3870	2	6	,	,	PUNCT
ejpam-3870	2	7	2020	2020	NUM
ejpam-3870	2	8	,	,	PUNCT
ejpam-3870	2	9	987	987	NUM
ejpam-3870	2	10	-	-	SYM
ejpam-3870	2	11	994	994	NUM
ejpam-3870	2	12	issn	issn	PROPN
ejpam-3870	2	13	1307	1307	NUM
ejpam-3870	2	14	-	-	SYM
ejpam-3870	2	15	5543	5543	NUM
ejpam-3870	2	16	–	–	PUNCT
ejpam-3870	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3870	2	18	published	publish	VERB
ejpam-3870	2	19	by	by	ADP
ejpam-3870	2	20	new	new	PROPN
ejpam-3870	2	21	york	york	PROPN
ejpam-3870	2	22	business	business	PROPN
ejpam-3870	2	23	global	global	PROPN
ejpam-3870	2	24	left	leave	VERB
ejpam-3870	2	25	and	and	CCONJ
ejpam-3870	2	26	right	right	ADJ
ejpam-3870	2	27	magnifying	magnify	VERB
ejpam-3870	2	28	elements	element	NOUN
ejpam-3870	2	29	in	in	ADP
ejpam-3870	2	30	the	the	DET
ejpam-3870	2	31	semigroup	semigroup	NOUN
ejpam-3870	2	32	of	of	ADP
ejpam-3870	2	33	all	all	DET
ejpam-3870	2	34	binary	binary	PROPN
ejpam-3870	2	35	relations	relation	NOUN
ejpam-3870	2	36	watchara	watchara	PROPN
ejpam-3870	3	1	teparos1	teparos1	PROPN
ejpam-3870	3	2	,	,	PUNCT
ejpam-3870	3	3	soontorn	soontorn	VERB
ejpam-3870	3	4	boonta1	boonta1	PROPN
ejpam-3870	3	5	,	,	PUNCT
ejpam-3870	3	6	thitiya	thitiya	PROPN
ejpam-3870	3	7	theparod2,∗	theparod2,∗	NOUN
ejpam-3870	3	8	1	1	NUM
ejpam-3870	3	9	department	department	NOUN
ejpam-3870	3	10	of	of	ADP
ejpam-3870	3	11	general	general	ADJ
ejpam-3870	3	12	science	science	NOUN
ejpam-3870	3	13	,	,	PUNCT
ejpam-3870	3	14	faculty	faculty	NOUN
ejpam-3870	3	15	of	of	ADP
ejpam-3870	3	16	science	science	NOUN
ejpam-3870	3	17	and	and	CCONJ
ejpam-3870	3	18	engineering	engineering	NOUN
ejpam-3870	3	19	,	,	PUNCT
ejpam-3870	3	20	kasetsart	kasetsart	PROPN
ejpam-3870	3	21	university	university	PROPN
ejpam-3870	3	22	,	,	PUNCT
ejpam-3870	3	23	chalermphrakiat	chalermphrakiat	PROPN
ejpam-3870	3	24	sakon	sakon	PROPN
ejpam-3870	3	25	nakhon	nakhon	PROPN
ejpam-3870	3	26	province	province	PROPN
ejpam-3870	3	27	campus	campus	PROPN
ejpam-3870	3	28	,	,	PUNCT
ejpam-3870	3	29	muang	muang	PROPN
ejpam-3870	3	30	,	,	PUNCT
ejpam-3870	3	31	sakon	sakon	PROPN
ejpam-3870	3	32	nakhon	nakhon	PROPN
ejpam-3870	3	33	,	,	PUNCT
ejpam-3870	3	34	thailand	thailand	PROPN
ejpam-3870	3	35	2	2	NUM
ejpam-3870	3	36	department	department	NOUN
ejpam-3870	3	37	of	of	ADP
ejpam-3870	3	38	mathematics	mathematic	NOUN
ejpam-3870	3	39	,	,	PUNCT
ejpam-3870	3	40	faculty	faculty	NOUN
ejpam-3870	3	41	of	of	ADP
ejpam-3870	3	42	science	science	NOUN
ejpam-3870	3	43	,	,	PUNCT
ejpam-3870	3	44	mahasarakham	mahasarakham	PROPN
ejpam-3870	3	45	university	university	PROPN
ejpam-3870	3	46	,	,	PUNCT
ejpam-3870	3	47	khamriang	khamriang	X
ejpam-3870	4	1	sub	sub	PROPN
ejpam-3870	4	2	-	-	NOUN
ejpam-3870	4	3	district	district	ADJ
ejpam-3870	4	4	,	,	PUNCT
ejpam-3870	4	5	kantarawichai	kantarawichai	PROPN
ejpam-3870	4	6	district	district	PROPN
ejpam-3870	4	7	,	,	PUNCT
ejpam-3870	4	8	maha	maha	PROPN
ejpam-3870	4	9	sarakham	sarakham	PROPN
ejpam-3870	4	10	,	,	PUNCT
ejpam-3870	4	11	thailand	thailand	PROPN
ejpam-3870	4	12	abstract	abstract	PROPN
ejpam-3870	4	13	.	.	PUNCT
ejpam-3870	5	1	an	an	DET
ejpam-3870	5	2	element	element	NOUN
ejpam-3870	5	3	a	a	PRON
ejpam-3870	5	4	of	of	ADP
ejpam-3870	5	5	a	a	DET
ejpam-3870	5	6	semigroup	semigroup	NOUN
ejpam-3870	5	7	s	s	PART
ejpam-3870	5	8	is	be	AUX
ejpam-3870	5	9	called	call	VERB
ejpam-3870	5	10	left	leave	VERB
ejpam-3870	6	1	[	[	X
ejpam-3870	6	2	right	right	X
ejpam-3870	6	3	]	]	X
ejpam-3870	6	4	magnifying	magnify	VERB
ejpam-3870	6	5	if	if	SCONJ
ejpam-3870	6	6	there	there	PRON
ejpam-3870	6	7	exists	exist	VERB
ejpam-3870	6	8	a	a	DET
ejpam-3870	6	9	proper	proper	ADJ
ejpam-3870	6	10	subset	subset	NOUN
ejpam-3870	6	11	m	m	NOUN
ejpam-3870	6	12	of	of	ADP
ejpam-3870	6	13	s	s	PRON
ejpam-3870	6	14	such	such	ADJ
ejpam-3870	6	15	that	that	DET
ejpam-3870	6	16	s	s	PART
ejpam-3870	6	17	=	=	PRON
ejpam-3870	6	18	am	be	AUX
ejpam-3870	6	19	[	[	X
ejpam-3870	6	20	s	s	X
ejpam-3870	6	21	=	=	X
ejpam-3870	6	22	ma	ma	PROPN
ejpam-3870	6	23	]	]	X
ejpam-3870	6	24	.	.	PUNCT
ejpam-3870	7	1	let	let	VERB
ejpam-3870	7	2	x	x	PRON
ejpam-3870	7	3	be	be	AUX
ejpam-3870	7	4	a	a	DET
ejpam-3870	7	5	nonempty	nonempty	ADV
ejpam-3870	7	6	set	set	VERB
ejpam-3870	7	7	and	and	CCONJ
ejpam-3870	7	8	bx	bx	VERB
ejpam-3870	7	9	the	the	DET
ejpam-3870	7	10	semigroup	semigroup	NOUN
ejpam-3870	7	11	of	of	ADP
ejpam-3870	7	12	binary	binary	ADJ
ejpam-3870	7	13	relations	relation	NOUN
ejpam-3870	7	14	on	on	ADP
ejpam-3870	7	15	x.	x.	NOUN
ejpam-3870	7	16	in	in	ADP
ejpam-3870	7	17	this	this	DET
ejpam-3870	7	18	paper	paper	NOUN
ejpam-3870	7	19	,	,	PUNCT
ejpam-3870	7	20	we	we	PRON
ejpam-3870	7	21	give	give	VERB
ejpam-3870	7	22	necessary	necessary	ADJ
ejpam-3870	7	23	and	and	CCONJ
ejpam-3870	7	24	sufficient	sufficient	ADJ
ejpam-3870	7	25	conditions	condition	NOUN
ejpam-3870	7	26	for	for	ADP
ejpam-3870	7	27	elements	element	NOUN
ejpam-3870	7	28	in	in	ADP
ejpam-3870	7	29	bx	bx	PROPN
ejpam-3870	7	30	to	to	PART
ejpam-3870	7	31	be	be	AUX
ejpam-3870	7	32	left	leave	VERB
ejpam-3870	7	33	or	or	CCONJ
ejpam-3870	7	34	right	right	ADJ
ejpam-3870	7	35	magnifying	magnifying	ADJ
ejpam-3870	7	36	.	.	PUNCT
ejpam-3870	8	1	2020	2020	NUM
ejpam-3870	8	2	mathematics	mathematic	NOUN
ejpam-3870	8	3	subject	subject	NOUN
ejpam-3870	8	4	classifications	classification	NOUN
ejpam-3870	8	5	:	:	PUNCT
ejpam-3870	8	6	20m20	20m20	NUM
ejpam-3870	8	7	key	key	ADJ
ejpam-3870	8	8	words	word	NOUN
ejpam-3870	8	9	and	and	CCONJ
ejpam-3870	8	10	phrases	phrase	NOUN
ejpam-3870	8	11	:	:	PUNCT
ejpam-3870	8	12	relations	relation	NOUN
ejpam-3870	8	13	,	,	PUNCT
ejpam-3870	8	14	functions	function	NOUN
ejpam-3870	8	15	,	,	PUNCT
ejpam-3870	8	16	magnifying	magnify	VERB
ejpam-3870	8	17	elements	element	NOUN
ejpam-3870	8	18	,	,	PUNCT
ejpam-3870	8	19	the	the	DET
ejpam-3870	8	20	semigroup	semigroup	NOUN
ejpam-3870	8	21	of	of	ADP
ejpam-3870	8	22	all	all	DET
ejpam-3870	8	23	binary	binary	ADJ
ejpam-3870	8	24	relations	relation	NOUN
ejpam-3870	8	25	1	1	NUM
ejpam-3870	8	26	.	.	PUNCT
ejpam-3870	8	27	introduction	introduction	NOUN
ejpam-3870	8	28	and	and	CCONJ
ejpam-3870	8	29	preliminaries	preliminary	NOUN
ejpam-3870	8	30	an	an	DET
ejpam-3870	8	31	element	element	NOUN
ejpam-3870	8	32	a	a	PRON
ejpam-3870	8	33	of	of	ADP
ejpam-3870	8	34	a	a	DET
ejpam-3870	8	35	semigroup	semigroup	NOUN
ejpam-3870	8	36	s	s	PART
ejpam-3870	8	37	is	be	AUX
ejpam-3870	8	38	called	call	VERB
ejpam-3870	8	39	left	leave	VERB
ejpam-3870	9	1	[	[	X
ejpam-3870	9	2	right	right	X
ejpam-3870	9	3	]	]	X
ejpam-3870	9	4	magnifying	magnify	VERB
ejpam-3870	9	5	if	if	SCONJ
ejpam-3870	9	6	there	there	PRON
ejpam-3870	9	7	exists	exist	VERB
ejpam-3870	9	8	a	a	DET
ejpam-3870	9	9	proper	proper	ADJ
ejpam-3870	9	10	subset	subset	NOUN
ejpam-3870	9	11	m	m	NOUN
ejpam-3870	9	12	of	of	ADP
ejpam-3870	9	13	s	s	PRON
ejpam-3870	9	14	such	such	ADJ
ejpam-3870	9	15	that	that	DET
ejpam-3870	9	16	s	s	PART
ejpam-3870	9	17	=	=	PRON
ejpam-3870	9	18	am	be	AUX
ejpam-3870	9	19	[	[	X
ejpam-3870	9	20	s	s	X
ejpam-3870	9	21	=	=	X
ejpam-3870	9	22	ma	ma	PROPN
ejpam-3870	9	23	]	]	X
ejpam-3870	9	24	in	in	ADP
ejpam-3870	9	25	which	which	PRON
ejpam-3870	9	26	the	the	DET
ejpam-3870	9	27	concept	concept	NOUN
ejpam-3870	9	28	of	of	ADP
ejpam-3870	9	29	such	such	ADJ
ejpam-3870	9	30	definition	definition	NOUN
ejpam-3870	9	31	was	be	AUX
ejpam-3870	9	32	first	first	ADV
ejpam-3870	9	33	introduced	introduce	VERB
ejpam-3870	9	34	by	by	ADP
ejpam-3870	9	35	ljapin	ljapin	X
ejpam-3870	10	1	[	[	X
ejpam-3870	10	2	4	4	NUM
ejpam-3870	10	3	]	]	PUNCT
ejpam-3870	10	4	.	.	PUNCT
ejpam-3870	11	1	in	in	ADP
ejpam-3870	11	2	1971	1971	NUM
ejpam-3870	11	3	,	,	PUNCT
ejpam-3870	11	4	migliorini	migliorini	NOUN
ejpam-3870	11	5	[	[	X
ejpam-3870	11	6	6	6	NUM
ejpam-3870	11	7	]	]	PUNCT
ejpam-3870	11	8	studies	study	NOUN
ejpam-3870	11	9	week	week	NOUN
ejpam-3870	11	10	left	leave	VERB
ejpam-3870	11	11	[	[	X
ejpam-3870	11	12	right	right	X
ejpam-3870	11	13	]	]	PUNCT
ejpam-3870	11	14	and	and	CCONJ
ejpam-3870	11	15	strong	strong	ADJ
ejpam-3870	11	16	left	leave	VERB
ejpam-3870	12	1	[	[	X
ejpam-3870	12	2	right	right	X
ejpam-3870	12	3	]	]	X
ejpam-3870	12	4	magnifying	magnifying	ADJ
ejpam-3870	12	5	element	element	NOUN
ejpam-3870	12	6	of	of	ADP
ejpam-3870	12	7	semigroups	semigroup	NOUN
ejpam-3870	12	8	which	which	PRON
ejpam-3870	12	9	specifically	specifically	ADV
ejpam-3870	12	10	gives	give	VERB
ejpam-3870	12	11	a	a	DET
ejpam-3870	12	12	definition	definition	NOUN
ejpam-3870	12	13	of	of	ADP
ejpam-3870	12	14	a	a	DET
ejpam-3870	12	15	proper	proper	ADJ
ejpam-3870	12	16	subset	subset	NOUN
ejpam-3870	12	17	m	m	NOUN
ejpam-3870	12	18	of	of	ADP
ejpam-3870	12	19	s	s	PRON
ejpam-3870	12	20	as	as	ADP
ejpam-3870	12	21	a	a	DET
ejpam-3870	12	22	subsemigroup	subsemigroup	NOUN
ejpam-3870	12	23	.	.	PUNCT
ejpam-3870	13	1	in	in	ADP
ejpam-3870	13	2	the	the	DET
ejpam-3870	13	3	following	following	ADJ
ejpam-3870	13	4	years	year	NOUN
ejpam-3870	13	5	,	,	PUNCT
ejpam-3870	13	6	there	there	PRON
ejpam-3870	13	7	are	be	VERB
ejpam-3870	13	8	several	several	ADJ
ejpam-3870	13	9	studies	study	NOUN
ejpam-3870	13	10	on	on	ADP
ejpam-3870	13	11	other	other	ADJ
ejpam-3870	13	12	properties	property	NOUN
ejpam-3870	13	13	of	of	ADP
ejpam-3870	13	14	magnifying	magnify	VERB
ejpam-3870	13	15	elements	element	NOUN
ejpam-3870	13	16	(	(	PUNCT
ejpam-3870	13	17	see	see	VERB
ejpam-3870	13	18	[	[	X
ejpam-3870	13	19	1–3	1–3	NOUN
ejpam-3870	13	20	,	,	PUNCT
ejpam-3870	13	21	5	5	NUM
ejpam-3870	13	22	,	,	PUNCT
ejpam-3870	13	23	7	7	NUM
ejpam-3870	13	24	]	]	NUM
ejpam-3870	13	25	)	)	PUNCT
ejpam-3870	13	26	.	.	PUNCT
ejpam-3870	14	1	the	the	DET
ejpam-3870	14	2	semigroup	semigroup	NOUN
ejpam-3870	14	3	of	of	ADP
ejpam-3870	14	4	all	all	DET
ejpam-3870	14	5	binary	binary	ADJ
ejpam-3870	14	6	relations	relation	NOUN
ejpam-3870	14	7	are	be	AUX
ejpam-3870	14	8	widely	widely	ADV
ejpam-3870	14	9	known	know	VERB
ejpam-3870	14	10	and	and	CCONJ
ejpam-3870	14	11	there	there	PRON
ejpam-3870	14	12	are	be	VERB
ejpam-3870	14	13	many	many	ADJ
ejpam-3870	14	14	research	research	NOUN
ejpam-3870	14	15	in	in	ADP
ejpam-3870	14	16	the	the	DET
ejpam-3870	14	17	area	area	NOUN
ejpam-3870	14	18	of	of	ADP
ejpam-3870	14	19	this	this	DET
ejpam-3870	14	20	type	type	NOUN
ejpam-3870	14	21	of	of	ADP
ejpam-3870	14	22	semigroup	semigroup	NOUN
ejpam-3870	14	23	(	(	PUNCT
ejpam-3870	14	24	[	[	X
ejpam-3870	14	25	8	8	NUM
ejpam-3870	14	26	,	,	PUNCT
ejpam-3870	14	27	11	11	NUM
ejpam-3870	14	28	,	,	PUNCT
ejpam-3870	14	29	12	12	NUM
ejpam-3870	14	30	]	]	PUNCT
ejpam-3870	14	31	)	)	PUNCT
ejpam-3870	14	32	.	.	PUNCT
ejpam-3870	15	1	in	in	ADP
ejpam-3870	15	2	2018	2018	NUM
ejpam-3870	15	3	,	,	PUNCT
ejpam-3870	15	4	chinram	chinram	NOUN
ejpam-3870	15	5	,	,	PUNCT
ejpam-3870	15	6	petchkaew	petchkaew	VERB
ejpam-3870	15	7	and	and	CCONJ
ejpam-3870	15	8	baupradist	baupradist	NOUN
ejpam-3870	15	9	[	[	X
ejpam-3870	15	10	9	9	NUM
ejpam-3870	15	11	]	]	PUNCT
ejpam-3870	15	12	give	give	VERB
ejpam-3870	15	13	necessary	necessary	ADJ
ejpam-3870	15	14	and	and	CCONJ
ejpam-3870	15	15	sufficient	sufficient	ADJ
ejpam-3870	15	16	conditions	condition	NOUN
ejpam-3870	15	17	for	for	ADP
ejpam-3870	15	18	elements	element	NOUN
ejpam-3870	15	19	in	in	ADP
ejpam-3870	15	20	some	some	DET
ejpam-3870	15	21	generalized	generalize	VERB
ejpam-3870	15	22	linear	linear	NOUN
ejpam-3870	15	23	transformation	transformation	NOUN
ejpam-3870	15	24	semigroups	semigroup	NOUN
ejpam-3870	15	25	.	.	PUNCT
ejpam-3870	16	1	then	then	ADV
ejpam-3870	16	2	in	in	ADP
ejpam-3870	16	3	the	the	DET
ejpam-3870	16	4	next	next	ADJ
ejpam-3870	16	5	year	year	NOUN
ejpam-3870	16	6	,	,	PUNCT
ejpam-3870	16	7	baupradist	baupradist	NOUN
ejpam-3870	16	8	,	,	PUNCT
ejpam-3870	16	9	panityakul	panityakul	NOUN
ejpam-3870	16	10	and	and	CCONJ
ejpam-3870	16	11	chinram	chinram	NOUN
ejpam-3870	17	1	[	[	X
ejpam-3870	17	2	10	10	NUM
ejpam-3870	17	3	]	]	PUNCT
ejpam-3870	17	4	give	give	VERB
ejpam-3870	17	5	necessary	necessary	ADJ
ejpam-3870	17	6	and	and	CCONJ
ejpam-3870	17	7	sufficient	sufficient	ADJ
ejpam-3870	17	8	conditions	condition	NOUN
ejpam-3870	17	9	for	for	ADP
ejpam-3870	17	10	elements	element	NOUN
ejpam-3870	17	11	in	in	ADP
ejpam-3870	17	12	semigroups	semigroup	NOUN
ejpam-3870	17	13	of	of	ADP
ejpam-3870	17	14	linear	linear	ADJ
ejpam-3870	17	15	transformations	transformation	NOUN
ejpam-3870	17	16	with	with	ADP
ejpam-3870	17	17	restricted	restricted	ADJ
ejpam-3870	17	18	range	range	NOUN
ejpam-3870	17	19	to	to	PART
ejpam-3870	17	20	be	be	AUX
ejpam-3870	17	21	left	leave	VERB
ejpam-3870	17	22	or	or	CCONJ
ejpam-3870	17	23	right	right	ADJ
ejpam-3870	17	24	magnifying	magnifying	NOUN
ejpam-3870	17	25	.	.	PUNCT
ejpam-3870	18	1	our	our	PRON
ejpam-3870	18	2	research	research	NOUN
ejpam-3870	18	3	is	be	AUX
ejpam-3870	18	4	motivated	motivate	VERB
ejpam-3870	18	5	by	by	ADP
ejpam-3870	18	6	these	these	DET
ejpam-3870	18	7	studies	study	NOUN
ejpam-3870	18	8	.	.	PUNCT
ejpam-3870	19	1	in	in	ADP
ejpam-3870	19	2	this	this	DET
ejpam-3870	19	3	paper	paper	NOUN
ejpam-3870	19	4	,	,	PUNCT
ejpam-3870	19	5	we	we	PRON
ejpam-3870	19	6	give	give	VERB
ejpam-3870	19	7	necessary	necessary	ADJ
ejpam-3870	19	8	and	and	CCONJ
ejpam-3870	19	9	sufficient	sufficient	ADJ
ejpam-3870	19	10	conditions	condition	NOUN
ejpam-3870	19	11	for	for	ADP
ejpam-3870	19	12	elements	element	NOUN
ejpam-3870	19	13	in	in	ADP
ejpam-3870	19	14	the	the	DET
ejpam-3870	19	15	semigroups	semigroup	NOUN
ejpam-3870	19	16	of	of	ADP
ejpam-3870	19	17	binary	binary	ADJ
ejpam-3870	19	18	relations	relation	NOUN
ejpam-3870	19	19	to	to	PART
ejpam-3870	19	20	be	be	AUX
ejpam-3870	19	21	left	leave	VERB
ejpam-3870	19	22	and	and	CCONJ
ejpam-3870	19	23	right	right	ADJ
ejpam-3870	19	24	magnifying	magnify	VERB
ejpam-3870	19	25	.	.	PUNCT
ejpam-3870	20	1	∗corresponding	∗corresponde	VERB
ejpam-3870	20	2	author	author	NOUN
ejpam-3870	20	3	.	.	PUNCT
ejpam-3870	21	1	doi	doi	NOUN
ejpam-3870	21	2	:	:	PUNCT
ejpam-3870	21	3	https://doi.org/10.29020/nybg.ejpam.v13i4.3870	https://doi.org/10.29020/nybg.ejpam.v13i4.3870	PROPN
ejpam-3870	21	4	email	email	NOUN
ejpam-3870	21	5	addresses	address	NOUN
ejpam-3870	21	6	:	:	PUNCT
ejpam-3870	21	7	watchara.tha@ku.th	watchara.tha@ku.th	PROPN
ejpam-3870	21	8	(	(	PUNCT
ejpam-3870	21	9	w.	w.	PROPN
ejpam-3870	21	10	teparos	teparos	PROPN
ejpam-3870	21	11	)	)	PUNCT
ejpam-3870	21	12	,	,	PUNCT
ejpam-3870	21	13	soontorn.bo@ku.th	soontorn.bo@ku.th	PROPN
ejpam-3870	21	14	(	(	PUNCT
ejpam-3870	21	15	s.	s.	PROPN
ejpam-3870	21	16	boonta	boonta	PROPN
ejpam-3870	21	17	)	)	PUNCT
ejpam-3870	21	18	,	,	PUNCT
ejpam-3870	21	19	thitiya.t@msu.ac.th	thitiya.t@msu.ac.th	X
ejpam-3870	21	20	(	(	PUNCT
ejpam-3870	21	21	t.	t.	PROPN
ejpam-3870	21	22	theparod	theparod	PROPN
ejpam-3870	21	23	)	)	PUNCT
ejpam-3870	21	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3870	22	1	987	987	NUM
ejpam-3870	22	2	c	c	X
ejpam-3870	22	3	©	©	NOUN
ejpam-3870	22	4	2020	2020	NUM
ejpam-3870	22	5	ejpam	ejpam	VERB
ejpam-3870	22	6	all	all	DET
ejpam-3870	22	7	rights	right	NOUN
ejpam-3870	22	8	reserved	reserve	VERB
ejpam-3870	22	9	.	.	PUNCT
ejpam-3870	23	1	w.	w.	PROPN
ejpam-3870	23	2	teparos	teparos	PROPN
ejpam-3870	23	3	,	,	PUNCT
ejpam-3870	23	4	s.	s.	PROPN
ejpam-3870	23	5	boonta	boonta	PROPN
ejpam-3870	23	6	,	,	PUNCT
ejpam-3870	23	7	t.	t.	PROPN
ejpam-3870	23	8	theparod	theparod	PROPN
ejpam-3870	23	9	/	/	SYM
ejpam-3870	23	10	eur	eur	PROPN
ejpam-3870	23	11	.	.	PUNCT
ejpam-3870	24	1	j.	j.	PROPN
ejpam-3870	24	2	pure	pure	PROPN
ejpam-3870	24	3	appl	appl	PROPN
ejpam-3870	24	4	.	.	PROPN
ejpam-3870	24	5	math	math	PROPN
ejpam-3870	24	6	,	,	PUNCT
ejpam-3870	24	7	13	13	NUM
ejpam-3870	24	8	(	(	PUNCT
ejpam-3870	24	9	4	4	NUM
ejpam-3870	24	10	)	)	PUNCT
ejpam-3870	24	11	(	(	PUNCT
ejpam-3870	24	12	2020	2020	NUM
ejpam-3870	24	13	)	)	PUNCT
ejpam-3870	24	14	,	,	PUNCT
ejpam-3870	24	15	987	987	NUM
ejpam-3870	24	16	-	-	SYM
ejpam-3870	24	17	994	994	NUM
ejpam-3870	24	18	988	988	NUM
ejpam-3870	24	19	throughout	throughout	ADP
ejpam-3870	24	20	this	this	DET
ejpam-3870	24	21	paper	paper	NOUN
ejpam-3870	25	1	,	,	PUNCT
ejpam-3870	25	2	we	we	PRON
ejpam-3870	25	3	let	let	VERB
ejpam-3870	25	4	x	x	PART
ejpam-3870	25	5	be	be	AUX
ejpam-3870	25	6	a	a	DET
ejpam-3870	25	7	nonempty	nonempty	ADV
ejpam-3870	25	8	set	set	VERB
ejpam-3870	25	9	and	and	CCONJ
ejpam-3870	25	10	|x|	|x|	PROPN
ejpam-3870	25	11	be	be	AUX
ejpam-3870	25	12	the	the	DET
ejpam-3870	25	13	cardinality	cardinality	NOUN
ejpam-3870	25	14	of	of	ADP
ejpam-3870	25	15	x.	x.	NOUN
ejpam-3870	25	16	it	it	PRON
ejpam-3870	25	17	is	be	AUX
ejpam-3870	25	18	well	well	ADV
ejpam-3870	25	19	-	-	PUNCT
ejpam-3870	25	20	known	know	VERB
ejpam-3870	25	21	that	that	SCONJ
ejpam-3870	25	22	the	the	DET
ejpam-3870	25	23	set	set	NOUN
ejpam-3870	25	24	of	of	ADP
ejpam-3870	25	25	all	all	DET
ejpam-3870	25	26	binary	binary	ADJ
ejpam-3870	25	27	relations	relation	NOUN
ejpam-3870	25	28	on	on	ADP
ejpam-3870	25	29	x	x	PUNCT
ejpam-3870	25	30	form	form	VERB
ejpam-3870	25	31	a	a	DET
ejpam-3870	25	32	semigroup	semigroup	NOUN
ejpam-3870	25	33	,	,	PUNCT
ejpam-3870	25	34	denoted	denote	VERB
ejpam-3870	25	35	by	by	ADP
ejpam-3870	25	36	bx	bx	PROPN
ejpam-3870	25	37	,	,	PUNCT
ejpam-3870	25	38	under	under	ADP
ejpam-3870	25	39	composition	composition	NOUN
ejpam-3870	25	40	:	:	PUNCT
ejpam-3870	25	41	α	α	X
ejpam-3870	25	42	◦	◦	NOUN
ejpam-3870	25	43	β	β	X
ejpam-3870	25	44	=	=	NOUN
ejpam-3870	25	45	{	{	PUNCT
ejpam-3870	25	46	(	(	PUNCT
ejpam-3870	25	47	x	x	NOUN
ejpam-3870	25	48	,	,	PUNCT
ejpam-3870	25	49	y	y	NOUN
ejpam-3870	25	50	)	)	PUNCT
ejpam-3870	25	51	|	|	ADV
ejpam-3870	25	52	∃z	∃z	PROPN
ejpam-3870	25	53	∈	∈	PROPN
ejpam-3870	25	54	x	x	PUNCT
ejpam-3870	25	55	such	such	ADJ
ejpam-3870	25	56	that	that	SCONJ
ejpam-3870	25	57	(	(	PUNCT
ejpam-3870	25	58	x	x	X
ejpam-3870	25	59	,	,	PUNCT
ejpam-3870	25	60	z	z	NOUN
ejpam-3870	25	61	)	)	PUNCT
ejpam-3870	25	62	∈	∈	PROPN
ejpam-3870	25	63	α	α	NOUN
ejpam-3870	25	64	and	and	CCONJ
ejpam-3870	25	65	(	(	PUNCT
ejpam-3870	25	66	z	z	PROPN
ejpam-3870	25	67	,	,	PUNCT
ejpam-3870	25	68	y	y	PROPN
ejpam-3870	25	69	)	)	PUNCT
ejpam-3870	25	70	∈	∈	PROPN
ejpam-3870	25	71	β	β	X
ejpam-3870	25	72	}	}	PUNCT
ejpam-3870	25	73	for	for	ADP
ejpam-3870	25	74	all	all	DET
ejpam-3870	25	75	α	α	NOUN
ejpam-3870	25	76	,	,	PUNCT
ejpam-3870	25	77	β	β	X
ejpam-3870	25	78	∈	∈	PROPN
ejpam-3870	25	79	bx	bx	X
ejpam-3870	25	80	.	.	PUNCT
ejpam-3870	26	1	let	let	VERB
ejpam-3870	26	2	a	a	DET
ejpam-3870	26	3	,	,	PUNCT
ejpam-3870	26	4	b	b	PROPN
ejpam-3870	26	5	∈	∈	PROPN
ejpam-3870	26	6	x	x	NOUN
ejpam-3870	26	7	,	,	PUNCT
ejpam-3870	26	8	a	a	DET
ejpam-3870	26	9	⊆	⊆	NUM
ejpam-3870	26	10	x	x	SYM
ejpam-3870	26	11	and	and	CCONJ
ejpam-3870	26	12	α	α	NOUN
ejpam-3870	26	13	∈	∈	PROPN
ejpam-3870	26	14	bx	bx	NOUN
ejpam-3870	26	15	.	.	PUNCT
ejpam-3870	27	1	the	the	DET
ejpam-3870	27	2	domain	domain	NOUN
ejpam-3870	27	3	and	and	CCONJ
ejpam-3870	27	4	range	range	NOUN
ejpam-3870	27	5	of	of	ADP
ejpam-3870	27	6	α	α	PROPN
ejpam-3870	27	7	are	be	AUX
ejpam-3870	27	8	denoted	denote	VERB
ejpam-3870	27	9	by	by	ADP
ejpam-3870	27	10	domα	domα	NOUN
ejpam-3870	27	11	=	=	SYM
ejpam-3870	27	12	{	{	PUNCT
ejpam-3870	27	13	x	x	SYM
ejpam-3870	27	14	∈	∈	PROPN
ejpam-3870	27	15	x	x	INTJ
ejpam-3870	28	1	|	|	ADV
ejpam-3870	28	2	(	(	PUNCT
ejpam-3870	28	3	x	x	NOUN
ejpam-3870	28	4	,	,	PUNCT
ejpam-3870	28	5	y	y	NOUN
ejpam-3870	28	6	)	)	PUNCT
ejpam-3870	28	7	∈	∈	PROPN
ejpam-3870	28	8	α	α	NOUN
ejpam-3870	28	9	}	}	PUNCT
ejpam-3870	28	10	and	and	CCONJ
ejpam-3870	28	11	ranα	ranα	VERB
ejpam-3870	28	12	=	=	PUNCT
ejpam-3870	28	13	{	{	PUNCT
ejpam-3870	28	14	y	y	PROPN
ejpam-3870	28	15	∈	∈	PROPN
ejpam-3870	28	16	x	x	X
ejpam-3870	29	1	|	|	ADV
ejpam-3870	29	2	(	(	PUNCT
ejpam-3870	29	3	x	x	NOUN
ejpam-3870	29	4	,	,	PUNCT
ejpam-3870	29	5	y	y	NOUN
ejpam-3870	29	6	)	)	PUNCT
ejpam-3870	29	7	∈	∈	PROPN
ejpam-3870	29	8	α	α	NOUN
ejpam-3870	29	9	}	}	PUNCT
ejpam-3870	29	10	,	,	PUNCT
ejpam-3870	29	11	respectively	respectively	ADV
ejpam-3870	29	12	.	.	PUNCT
ejpam-3870	30	1	we	we	PRON
ejpam-3870	30	2	use	use	VERB
ejpam-3870	30	3	the	the	DET
ejpam-3870	30	4	following	follow	VERB
ejpam-3870	30	5	notions	notion	NOUN
ejpam-3870	30	6	:	:	PUNCT
ejpam-3870	30	7	α−1	α−1	PROPN
ejpam-3870	30	8	=	=	SYM
ejpam-3870	30	9	{	{	PUNCT
ejpam-3870	30	10	(	(	PUNCT
ejpam-3870	30	11	a	a	DET
ejpam-3870	30	12	,	,	PUNCT
ejpam-3870	30	13	b	b	NOUN
ejpam-3870	30	14	)	)	PUNCT
ejpam-3870	31	1	|	|	ADV
ejpam-3870	31	2	(	(	PUNCT
ejpam-3870	31	3	a	a	PRON
ejpam-3870	31	4	,	,	PUNCT
ejpam-3870	31	5	b	b	NOUN
ejpam-3870	31	6	)	)	PUNCT
ejpam-3870	31	7	∈	∈	PROPN
ejpam-3870	31	8	α	α	NOUN
ejpam-3870	31	9	}	}	PUNCT
ejpam-3870	31	10	,	,	PUNCT
ejpam-3870	31	11	(	(	PUNCT
ejpam-3870	31	12	a)α	a)α	X
ejpam-3870	31	13	=	=	SYM
ejpam-3870	31	14	{	{	PUNCT
ejpam-3870	31	15	y	y	PROPN
ejpam-3870	31	16	∈	∈	PROPN
ejpam-3870	31	17	x	x	X
ejpam-3870	32	1	|	|	ADV
ejpam-3870	32	2	(	(	PUNCT
ejpam-3870	32	3	a	a	PRON
ejpam-3870	32	4	,	,	PUNCT
ejpam-3870	32	5	y	y	NOUN
ejpam-3870	32	6	)	)	PUNCT
ejpam-3870	32	7	∈	∈	PROPN
ejpam-3870	32	8	α	α	NOUN
ejpam-3870	32	9	}	}	PUNCT
ejpam-3870	32	10	,	,	PUNCT
ejpam-3870	32	11	(	(	PUNCT
ejpam-3870	32	12	a)α−1	a)α−1	X
ejpam-3870	32	13	=	=	PRON
ejpam-3870	32	14	{	{	PUNCT
ejpam-3870	32	15	x	x	SYM
ejpam-3870	32	16	∈	∈	PROPN
ejpam-3870	32	17	x	x	INTJ
ejpam-3870	32	18	|	|	INTJ
ejpam-3870	32	19	(	(	PUNCT
ejpam-3870	32	20	x	x	NOUN
ejpam-3870	32	21	,	,	PUNCT
ejpam-3870	32	22	a	a	PRON
ejpam-3870	32	23	)	)	PUNCT
ejpam-3870	32	24	∈	∈	PROPN
ejpam-3870	32	25	α	α	NOUN
ejpam-3870	32	26	}	}	PUNCT
ejpam-3870	32	27	,	,	PUNCT
ejpam-3870	32	28	(	(	PUNCT
ejpam-3870	32	29	a)α	a)α	X
ejpam-3870	32	30	=	=	SYM
ejpam-3870	32	31	{	{	PUNCT
ejpam-3870	32	32	y	y	PROPN
ejpam-3870	32	33	∈	∈	PROPN
ejpam-3870	32	34	x	x	INTJ
ejpam-3870	32	35	|	|	ADV
ejpam-3870	32	36	y	y	PROPN
ejpam-3870	32	37	∈	∈	PROPN
ejpam-3870	32	38	(	(	PUNCT
ejpam-3870	32	39	a)α	a)α	X
ejpam-3870	32	40	for	for	ADP
ejpam-3870	32	41	some	some	DET
ejpam-3870	32	42	a	a	DET
ejpam-3870	32	43	∈	∈	PROPN
ejpam-3870	32	44	a	a	PRON
ejpam-3870	32	45	}	}	PUNCT
ejpam-3870	32	46	,	,	PUNCT
ejpam-3870	32	47	(	(	PUNCT
ejpam-3870	32	48	a)α−1	a)α−1	X
ejpam-3870	32	49	=	=	PRON
ejpam-3870	32	50	{	{	PUNCT
ejpam-3870	32	51	x	x	SYM
ejpam-3870	32	52	∈	∈	NOUN
ejpam-3870	32	53	x	x	PUNCT
ejpam-3870	32	54	|	|	ADV
ejpam-3870	32	55	x	x	SYM
ejpam-3870	32	56	∈	∈	PROPN
ejpam-3870	32	57	(	(	PUNCT
ejpam-3870	32	58	a)α−1	a)α−1	NOUN
ejpam-3870	32	59	for	for	ADP
ejpam-3870	32	60	some	some	DET
ejpam-3870	32	61	a	a	DET
ejpam-3870	32	62	∈	∈	PROPN
ejpam-3870	32	63	a	a	PRON
ejpam-3870	32	64	}	}	PUNCT
ejpam-3870	32	65	,	,	PUNCT
ejpam-3870	32	66	α|a	α|a	PUNCT
ejpam-3870	32	67	=	=	PRON
ejpam-3870	32	68	{	{	PUNCT
ejpam-3870	32	69	(	(	PUNCT
ejpam-3870	32	70	a	a	DET
ejpam-3870	32	71	,	,	PUNCT
ejpam-3870	32	72	b	b	NOUN
ejpam-3870	32	73	)	)	PUNCT
ejpam-3870	32	74	|	|	ADV
ejpam-3870	32	75	a	a	DET
ejpam-3870	32	76	∈	∈	PROPN
ejpam-3870	32	77	a	a	PRON
ejpam-3870	33	1	and	and	CCONJ
ejpam-3870	33	2	(	(	PUNCT
ejpam-3870	33	3	a	a	PRON
ejpam-3870	33	4	,	,	PUNCT
ejpam-3870	33	5	b	b	NOUN
ejpam-3870	33	6	)	)	PUNCT
ejpam-3870	33	7	∈	∈	PROPN
ejpam-3870	33	8	α	α	NOUN
ejpam-3870	33	9	}	}	PUNCT
ejpam-3870	33	10	note	note	NOUN
ejpam-3870	33	11	that	that	SCONJ
ejpam-3870	33	12	we	we	PRON
ejpam-3870	33	13	can	can	AUX
ejpam-3870	33	14	write	write	VERB
ejpam-3870	33	15	(	(	PUNCT
ejpam-3870	33	16	a)α	a)α	X
ejpam-3870	33	17	instead	instead	ADV
ejpam-3870	33	18	of	of	ADP
ejpam-3870	33	19	(	(	PUNCT
ejpam-3870	33	20	{	{	PUNCT
ejpam-3870	33	21	a})α	a})α	NOUN
ejpam-3870	33	22	.	.	PUNCT
ejpam-3870	34	1	the	the	DET
ejpam-3870	34	2	universal	universal	ADJ
ejpam-3870	34	3	relation	relation	PROPN
ejpam-3870	34	4	x×x	x×x	PROPN
ejpam-3870	34	5	is	be	AUX
ejpam-3870	34	6	denoted	denote	VERB
ejpam-3870	34	7	by	by	ADP
ejpam-3870	34	8	ω	ω	PROPN
ejpam-3870	34	9	and	and	CCONJ
ejpam-3870	34	10	the	the	DET
ejpam-3870	34	11	identity	identity	NOUN
ejpam-3870	34	12	relation	relation	NOUN
ejpam-3870	34	13	on	on	ADP
ejpam-3870	34	14	x	x	PUNCT
ejpam-3870	34	15	is	be	AUX
ejpam-3870	34	16	denoted	denote	VERB
ejpam-3870	34	17	by	by	ADP
ejpam-3870	34	18	ix	ix	PROPN
ejpam-3870	34	19	.	.	PUNCT
ejpam-3870	35	1	here	here	ADV
ejpam-3870	35	2	,	,	PUNCT
ejpam-3870	35	3	we	we	PRON
ejpam-3870	35	4	will	will	AUX
ejpam-3870	35	5	write	write	VERB
ejpam-3870	35	6	a	a	DET
ejpam-3870	35	7	relation	relation	NOUN
ejpam-3870	35	8	from	from	ADP
ejpam-3870	35	9	the	the	DET
ejpam-3870	35	10	right	right	NOUN
ejpam-3870	35	11	,	,	PUNCT
ejpam-3870	35	12	(	(	PUNCT
ejpam-3870	35	13	a)α	a)α	X
ejpam-3870	35	14	rather	rather	ADV
ejpam-3870	35	15	than	than	ADP
ejpam-3870	35	16	α(a	α(a	NOUN
ejpam-3870	35	17	)	)	PUNCT
ejpam-3870	35	18	and	and	CCONJ
ejpam-3870	35	19	compose	compose	VERB
ejpam-3870	35	20	from	from	ADP
ejpam-3870	35	21	the	the	DET
ejpam-3870	35	22	left	left	NOUN
ejpam-3870	35	23	to	to	ADP
ejpam-3870	35	24	the	the	DET
ejpam-3870	35	25	right	right	NOUN
ejpam-3870	35	26	,	,	PUNCT
ejpam-3870	35	27	(	(	PUNCT
ejpam-3870	35	28	a)(αβ	a)(αβ	NOUN
ejpam-3870	35	29	)	)	PUNCT
ejpam-3870	35	30	rather	rather	ADV
ejpam-3870	35	31	than	than	ADP
ejpam-3870	35	32	(	(	PUNCT
ejpam-3870	35	33	β	β	X
ejpam-3870	35	34	◦	◦	NOUN
ejpam-3870	35	35	α)(a	α)(a	NUM
ejpam-3870	35	36	)	)	PUNCT
ejpam-3870	35	37	,	,	PUNCT
ejpam-3870	35	38	for	for	ADP
ejpam-3870	35	39	α	α	NOUN
ejpam-3870	35	40	,	,	PUNCT
ejpam-3870	35	41	β	β	X
ejpam-3870	35	42	∈	∈	PROPN
ejpam-3870	35	43	bx	bx	NOUN
ejpam-3870	35	44	.	.	PUNCT
ejpam-3870	36	1	2	2	X
ejpam-3870	36	2	.	.	X
ejpam-3870	36	3	left	leave	VERB
ejpam-3870	36	4	magnifying	magnify	VERB
ejpam-3870	36	5	elements	element	NOUN
ejpam-3870	36	6	of	of	ADP
ejpam-3870	36	7	bx	bx	PROPN
ejpam-3870	36	8	lemma	lemma	PROPN
ejpam-3870	36	9	1	1	X
ejpam-3870	36	10	.	.	PUNCT
ejpam-3870	37	1	let	let	VERB
ejpam-3870	37	2	α	α	PRON
ejpam-3870	37	3	∈	∈	PROPN
ejpam-3870	37	4	bx	bx	X
ejpam-3870	37	5	.	.	PUNCT
ejpam-3870	38	1	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	38	2	=	=	PUNCT
ejpam-3870	38	3	1	1	NUM
ejpam-3870	38	4	for	for	ADP
ejpam-3870	38	5	all	all	DET
ejpam-3870	38	6	y	y	PROPN
ejpam-3870	38	7	∈	∈	PROPN
ejpam-3870	38	8	ranα	ranα	VERB
ejpam-3870	38	9	if	if	SCONJ
ejpam-3870	38	10	and	and	CCONJ
ejpam-3870	38	11	only	only	ADV
ejpam-3870	38	12	if	if	SCONJ
ejpam-3870	38	13	for	for	ADP
ejpam-3870	38	14	every	every	DET
ejpam-3870	38	15	a	a	PROPN
ejpam-3870	38	16	,	,	PUNCT
ejpam-3870	38	17	b	b	PROPN
ejpam-3870	38	18	∈	∈	PROPN
ejpam-3870	38	19	domα	domα	NOUN
ejpam-3870	38	20	,	,	PUNCT
ejpam-3870	38	21	(	(	PUNCT
ejpam-3870	38	22	a)α	a)α	X
ejpam-3870	38	23	∩	∩	NOUN
ejpam-3870	38	24	(	(	PUNCT
ejpam-3870	38	25	b)α	b)α	NOUN
ejpam-3870	38	26	6=	6=	NUM
ejpam-3870	38	27	∅	∅	NOUN
ejpam-3870	38	28	implies	imply	VERB
ejpam-3870	38	29	a	a	DET
ejpam-3870	38	30	=	=	NOUN
ejpam-3870	38	31	b.	b.	NOUN
ejpam-3870	38	32	proof	proof	NOUN
ejpam-3870	38	33	.	.	PUNCT
ejpam-3870	39	1	assume	assume	VERB
ejpam-3870	39	2	that	that	SCONJ
ejpam-3870	39	3	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	39	4	=	=	PUNCT
ejpam-3870	39	5	1	1	NUM
ejpam-3870	39	6	for	for	ADP
ejpam-3870	39	7	all	all	DET
ejpam-3870	39	8	y	y	PROPN
ejpam-3870	39	9	∈	∈	PROPN
ejpam-3870	39	10	ranα	ranα	VERB
ejpam-3870	39	11	.	.	PUNCT
ejpam-3870	40	1	let	let	VERB
ejpam-3870	40	2	a	a	DET
ejpam-3870	40	3	,	,	PUNCT
ejpam-3870	40	4	b	b	PROPN
ejpam-3870	40	5	∈	∈	PROPN
ejpam-3870	40	6	domα	domα	NOUN
ejpam-3870	40	7	.	.	PUNCT
ejpam-3870	41	1	suppose	suppose	VERB
ejpam-3870	42	1	that	that	SCONJ
ejpam-3870	42	2	(	(	PUNCT
ejpam-3870	42	3	a)α	a)α	X
ejpam-3870	42	4	∩	∩	NOUN
ejpam-3870	42	5	(	(	PUNCT
ejpam-3870	42	6	b)α	b)α	NOUN
ejpam-3870	42	7	6=	6=	ADP
ejpam-3870	42	8	∅.	∅.	NOUN
ejpam-3870	42	9	let	let	VERB
ejpam-3870	42	10	c	c	PROPN
ejpam-3870	42	11	∈	∈	PROPN
ejpam-3870	42	12	(	(	PUNCT
ejpam-3870	42	13	a)α	a)α	X
ejpam-3870	42	14	∩	∩	NOUN
ejpam-3870	42	15	(	(	PUNCT
ejpam-3870	42	16	b)α	b)α	NOUN
ejpam-3870	42	17	.	.	PUNCT
ejpam-3870	43	1	thus	thus	ADV
ejpam-3870	43	2	a	a	DET
ejpam-3870	43	3	∈	∈	PROPN
ejpam-3870	43	4	(	(	PUNCT
ejpam-3870	43	5	c)α−1	c)α−1	NOUN
ejpam-3870	43	6	and	and	CCONJ
ejpam-3870	43	7	b	b	NOUN
ejpam-3870	43	8	∈	∈	PROPN
ejpam-3870	43	9	(	(	PUNCT
ejpam-3870	43	10	c)α−1	c)α−1	NOUN
ejpam-3870	43	11	.	.	PUNCT
ejpam-3870	44	1	since	since	SCONJ
ejpam-3870	44	2	a	a	DET
ejpam-3870	44	3	,	,	PUNCT
ejpam-3870	44	4	b	b	PROPN
ejpam-3870	44	5	∈	∈	PROPN
ejpam-3870	44	6	ranα	ranα	NOUN
ejpam-3870	44	7	,	,	PUNCT
ejpam-3870	44	8	we	we	PRON
ejpam-3870	44	9	have	have	VERB
ejpam-3870	44	10	|(c)α−1|	|(c)α−1|	NUM
ejpam-3870	44	11	=	=	SYM
ejpam-3870	44	12	1	1	NUM
ejpam-3870	44	13	,	,	PUNCT
ejpam-3870	44	14	then	then	ADV
ejpam-3870	44	15	a	a	DET
ejpam-3870	44	16	=	=	X
ejpam-3870	44	17	b.	b.	PROPN
ejpam-3870	44	18	conversely	conversely	ADV
ejpam-3870	44	19	,	,	PUNCT
ejpam-3870	44	20	assume	assume	VERB
ejpam-3870	44	21	that	that	SCONJ
ejpam-3870	44	22	for	for	ADP
ejpam-3870	44	23	every	every	DET
ejpam-3870	44	24	a	a	PROPN
ejpam-3870	44	25	,	,	PUNCT
ejpam-3870	44	26	b	b	PROPN
ejpam-3870	44	27	∈	∈	PROPN
ejpam-3870	44	28	domα	domα	NOUN
ejpam-3870	44	29	,	,	PUNCT
ejpam-3870	44	30	(	(	PUNCT
ejpam-3870	44	31	a)α∩	a)α∩	ADJ
ejpam-3870	44	32	(	(	PUNCT
ejpam-3870	44	33	b)α	b)α	NOUN
ejpam-3870	44	34	6=	6=	NUM
ejpam-3870	44	35	∅	∅	NOUN
ejpam-3870	44	36	implies	imply	VERB
ejpam-3870	44	37	a	a	DET
ejpam-3870	44	38	=	=	X
ejpam-3870	44	39	b.	b.	NOUN
ejpam-3870	44	40	let	let	VERB
ejpam-3870	44	41	y	y	PROPN
ejpam-3870	44	42	∈	∈	PROPN
ejpam-3870	44	43	ranα	ranα	VERB
ejpam-3870	44	44	.	.	PUNCT
ejpam-3870	45	1	suppose	suppose	VERB
ejpam-3870	45	2	that	that	SCONJ
ejpam-3870	45	3	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	45	4	>	>	X
ejpam-3870	45	5	1	1	X
ejpam-3870	45	6	.	.	PUNCT
ejpam-3870	46	1	then	then	ADV
ejpam-3870	46	2	there	there	PRON
ejpam-3870	46	3	exist	exist	VERB
ejpam-3870	46	4	two	two	NUM
ejpam-3870	46	5	distinct	distinct	ADJ
ejpam-3870	46	6	elements	element	NOUN
ejpam-3870	46	7	a	a	PRON
ejpam-3870	46	8	,	,	PUNCT
ejpam-3870	46	9	b	b	PROPN
ejpam-3870	46	10	∈	∈	PROPN
ejpam-3870	46	11	domα	domα	NOUN
ejpam-3870	46	12	such	such	DET
ejpam-3870	46	13	that	that	SCONJ
ejpam-3870	46	14	a	a	PRON
ejpam-3870	46	15	,	,	PUNCT
ejpam-3870	46	16	b	b	PROPN
ejpam-3870	46	17	∈	∈	PROPN
ejpam-3870	46	18	(	(	PUNCT
ejpam-3870	46	19	y)α−1	y)α−1	NOUN
ejpam-3870	46	20	.	.	PUNCT
ejpam-3870	47	1	thus	thus	ADV
ejpam-3870	47	2	y	y	PROPN
ejpam-3870	47	3	∈	∈	PROPN
ejpam-3870	47	4	(	(	PUNCT
ejpam-3870	47	5	a)α	a)α	X
ejpam-3870	47	6	and	and	CCONJ
ejpam-3870	47	7	y	y	PROPN
ejpam-3870	47	8	∈	∈	PROPN
ejpam-3870	47	9	(	(	PUNCT
ejpam-3870	47	10	b)α	b)α	NOUN
ejpam-3870	47	11	.	.	PUNCT
ejpam-3870	48	1	that	that	PRON
ejpam-3870	48	2	is	be	AUX
ejpam-3870	48	3	,	,	PUNCT
ejpam-3870	48	4	(	(	PUNCT
ejpam-3870	48	5	a)α∩	a)α∩	ADJ
ejpam-3870	48	6	(	(	PUNCT
ejpam-3870	48	7	b)α	b)α	NOUN
ejpam-3870	48	8	6=	6=	ADP
ejpam-3870	48	9	∅.	∅.	ADV
ejpam-3870	48	10	as	as	ADP
ejpam-3870	48	11	a	a	DET
ejpam-3870	48	12	result	result	NOUN
ejpam-3870	48	13	,	,	PUNCT
ejpam-3870	48	14	a	a	DET
ejpam-3870	48	15	=	=	SYM
ejpam-3870	48	16	b	b	NOUN
ejpam-3870	48	17	in	in	ADP
ejpam-3870	48	18	which	which	PRON
ejpam-3870	48	19	we	we	PRON
ejpam-3870	48	20	obtain	obtain	VERB
ejpam-3870	48	21	a	a	DET
ejpam-3870	48	22	contradiction	contradiction	NOUN
ejpam-3870	48	23	.	.	PUNCT
ejpam-3870	49	1	therefore	therefore	ADV
ejpam-3870	49	2	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	49	3	=	=	PROPN
ejpam-3870	50	1	1	1	X
ejpam-3870	50	2	.	.	PUNCT
ejpam-3870	50	3	lemma	lemma	PROPN
ejpam-3870	50	4	2	2	X
ejpam-3870	50	5	.	.	PUNCT
ejpam-3870	51	1	let	let	VERB
ejpam-3870	51	2	α	α	PRON
ejpam-3870	51	3	∈	∈	PROPN
ejpam-3870	51	4	bx	bx	X
ejpam-3870	51	5	.	.	PUNCT
ejpam-3870	52	1	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	52	2	=	=	PUNCT
ejpam-3870	52	3	1	1	NUM
ejpam-3870	52	4	for	for	ADP
ejpam-3870	52	5	all	all	DET
ejpam-3870	52	6	y	y	PROPN
ejpam-3870	52	7	∈	∈	PROPN
ejpam-3870	52	8	ranα	ranα	VERB
ejpam-3870	52	9	if	if	SCONJ
ejpam-3870	52	10	and	and	CCONJ
ejpam-3870	52	11	only	only	ADV
ejpam-3870	52	12	if	if	SCONJ
ejpam-3870	52	13	(	(	PUNCT
ejpam-3870	52	14	aα)α−1	aα)α−1	X
ejpam-3870	52	15	=	=	SYM
ejpam-3870	52	16	a	a	NOUN
ejpam-3870	52	17	for	for	ADP
ejpam-3870	52	18	every	every	DET
ejpam-3870	52	19	a	a	DET
ejpam-3870	52	20	⊆	⊆	NUM
ejpam-3870	52	21	domα	domα	NOUN
ejpam-3870	52	22	.	.	PUNCT
ejpam-3870	53	1	proof	proof	NOUN
ejpam-3870	53	2	.	.	PUNCT
ejpam-3870	54	1	assume	assume	VERB
ejpam-3870	54	2	that	that	SCONJ
ejpam-3870	54	3	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	54	4	=	=	PUNCT
ejpam-3870	54	5	1	1	NUM
ejpam-3870	54	6	for	for	ADP
ejpam-3870	54	7	all	all	DET
ejpam-3870	54	8	y	y	PROPN
ejpam-3870	54	9	∈	∈	PROPN
ejpam-3870	54	10	ranα	ranα	VERB
ejpam-3870	54	11	.	.	PUNCT
ejpam-3870	55	1	it	it	PRON
ejpam-3870	55	2	is	be	AUX
ejpam-3870	55	3	clear	clear	ADJ
ejpam-3870	55	4	that	that	SCONJ
ejpam-3870	55	5	a	a	DET
ejpam-3870	55	6	⊆	⊆	NUM
ejpam-3870	55	7	(	(	PUNCT
ejpam-3870	55	8	aα)α−1	aα)α−1	X
ejpam-3870	55	9	.	.	PUNCT
ejpam-3870	56	1	we	we	PRON
ejpam-3870	56	2	want	want	VERB
ejpam-3870	56	3	to	to	PART
ejpam-3870	56	4	show	show	VERB
ejpam-3870	56	5	that	that	SCONJ
ejpam-3870	56	6	(	(	PUNCT
ejpam-3870	56	7	aα)α−1	aα)α−1	NOUN
ejpam-3870	56	8	⊆	⊆	NUM
ejpam-3870	56	9	a.	a.	NOUN
ejpam-3870	56	10	let	let	VERB
ejpam-3870	56	11	x	x	X
ejpam-3870	56	12	∈	∈	PROPN
ejpam-3870	56	13	(	(	PUNCT
ejpam-3870	56	14	aα)α−1	aα)α−1	PROPN
ejpam-3870	56	15	.	.	PUNCT
ejpam-3870	57	1	then	then	ADV
ejpam-3870	57	2	there	there	PRON
ejpam-3870	57	3	exists	exist	VERB
ejpam-3870	57	4	b	b	PROPN
ejpam-3870	57	5	∈	∈	PROPN
ejpam-3870	57	6	aα	aα	NOUN
ejpam-3870	57	7	such	such	ADJ
ejpam-3870	57	8	that	that	SCONJ
ejpam-3870	57	9	x	x	SYM
ejpam-3870	57	10	∈	∈	PROPN
ejpam-3870	57	11	(	(	PUNCT
ejpam-3870	57	12	b)α−1	b)α−1	NOUN
ejpam-3870	57	13	.	.	PUNCT
ejpam-3870	58	1	we	we	PRON
ejpam-3870	58	2	have	have	VERB
ejpam-3870	58	3	that	that	DET
ejpam-3870	58	4	b	b	PROPN
ejpam-3870	58	5	∈	∈	PROPN
ejpam-3870	58	6	(	(	PUNCT
ejpam-3870	58	7	x)α	x)α	NOUN
ejpam-3870	58	8	and	and	CCONJ
ejpam-3870	58	9	therefore	therefore	ADV
ejpam-3870	58	10	there	there	PRON
ejpam-3870	58	11	exists	exist	VERB
ejpam-3870	58	12	a	a	DET
ejpam-3870	58	13	∈	∈	NOUN
ejpam-3870	59	1	a	a	DET
ejpam-3870	59	2	such	such	ADJ
ejpam-3870	59	3	that	that	PRON
ejpam-3870	59	4	b	b	PROPN
ejpam-3870	59	5	∈	∈	PROPN
ejpam-3870	59	6	(	(	PUNCT
ejpam-3870	59	7	a)α	a)α	X
ejpam-3870	59	8	.	.	PUNCT
ejpam-3870	60	1	that	that	PRON
ejpam-3870	60	2	is	be	AUX
ejpam-3870	60	3	,	,	PUNCT
ejpam-3870	60	4	b	b	X
ejpam-3870	60	5	∈	∈	PROPN
ejpam-3870	60	6	(	(	PUNCT
ejpam-3870	60	7	x)α	x)α	X
ejpam-3870	60	8	∩	∩	NOUN
ejpam-3870	60	9	(	(	PUNCT
ejpam-3870	60	10	a)α	a)α	X
ejpam-3870	60	11	.	.	PUNCT
ejpam-3870	61	1	as	as	ADP
ejpam-3870	61	2	a	a	DET
ejpam-3870	61	3	result	result	NOUN
ejpam-3870	61	4	,	,	PUNCT
ejpam-3870	61	5	(	(	PUNCT
ejpam-3870	61	6	x)α	x)α	X
ejpam-3870	61	7	∩	∩	NOUN
ejpam-3870	61	8	(	(	PUNCT
ejpam-3870	61	9	a)α	a)α	X
ejpam-3870	61	10	6=	6=	X
ejpam-3870	61	11	∅.	∅.	NOUN
ejpam-3870	61	12	by	by	ADP
ejpam-3870	61	13	lemma	lemma	PROPN
ejpam-3870	61	14	1	1	NUM
ejpam-3870	61	15	,	,	PUNCT
ejpam-3870	61	16	x	x	PUNCT
ejpam-3870	61	17	=	=	PUNCT
ejpam-3870	61	18	a	a	DET
ejpam-3870	61	19	∈	∈	PROPN
ejpam-3870	61	20	a.	a.	NOUN
ejpam-3870	61	21	w.	w.	PROPN
ejpam-3870	61	22	teparos	teparos	PROPN
ejpam-3870	61	23	,	,	PUNCT
ejpam-3870	61	24	s.	s.	PROPN
ejpam-3870	61	25	boonta	boonta	PROPN
ejpam-3870	61	26	,	,	PUNCT
ejpam-3870	61	27	t.	t.	PROPN
ejpam-3870	61	28	theparod	theparod	PROPN
ejpam-3870	61	29	/	/	SYM
ejpam-3870	61	30	eur	eur	PROPN
ejpam-3870	61	31	.	.	PUNCT
ejpam-3870	62	1	j.	j.	PROPN
ejpam-3870	62	2	pure	pure	PROPN
ejpam-3870	62	3	appl	appl	PROPN
ejpam-3870	62	4	.	.	PROPN
ejpam-3870	62	5	math	math	PROPN
ejpam-3870	62	6	,	,	PUNCT
ejpam-3870	62	7	13	13	NUM
ejpam-3870	62	8	(	(	PUNCT
ejpam-3870	62	9	4	4	NUM
ejpam-3870	62	10	)	)	PUNCT
ejpam-3870	62	11	(	(	PUNCT
ejpam-3870	62	12	2020	2020	NUM
ejpam-3870	62	13	)	)	PUNCT
ejpam-3870	62	14	,	,	PUNCT
ejpam-3870	62	15	987	987	NUM
ejpam-3870	62	16	-	-	SYM
ejpam-3870	62	17	994	994	NUM
ejpam-3870	62	18	989	989	NUM
ejpam-3870	62	19	conversely	conversely	ADV
ejpam-3870	62	20	,	,	PUNCT
ejpam-3870	62	21	assume	assume	VERB
ejpam-3870	62	22	that	that	SCONJ
ejpam-3870	62	23	(	(	PUNCT
ejpam-3870	62	24	aα)α−1	aα)α−1	X
ejpam-3870	62	25	=	=	SYM
ejpam-3870	62	26	a	a	X
ejpam-3870	62	27	for	for	ADP
ejpam-3870	62	28	all	all	DET
ejpam-3870	62	29	a	a	DET
ejpam-3870	62	30	⊆	⊆	NUM
ejpam-3870	62	31	domα	domα	NOUN
ejpam-3870	62	32	.	.	PUNCT
ejpam-3870	63	1	let	let	VERB
ejpam-3870	63	2	y	y	PROPN
ejpam-3870	63	3	∈	∈	PROPN
ejpam-3870	63	4	ranα	ranα	VERB
ejpam-3870	63	5	.	.	PUNCT
ejpam-3870	64	1	we	we	PRON
ejpam-3870	64	2	will	will	AUX
ejpam-3870	64	3	show	show	VERB
ejpam-3870	64	4	that	that	SCONJ
ejpam-3870	64	5	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	64	6	=	=	PROPN
ejpam-3870	65	1	1	1	X
ejpam-3870	65	2	.	.	PUNCT
ejpam-3870	65	3	since	since	SCONJ
ejpam-3870	65	4	y	y	PROPN
ejpam-3870	65	5	∈	∈	PROPN
ejpam-3870	65	6	ranα	ranα	VERB
ejpam-3870	65	7	,	,	PUNCT
ejpam-3870	65	8	there	there	PRON
ejpam-3870	65	9	exist	exist	VERB
ejpam-3870	65	10	a	a	DET
ejpam-3870	65	11	∈	∈	PROPN
ejpam-3870	65	12	domα	domα	NOUN
ejpam-3870	65	13	such	such	ADJ
ejpam-3870	65	14	that	that	SCONJ
ejpam-3870	65	15	y	y	PROPN
ejpam-3870	65	16	∈	∈	PROPN
ejpam-3870	65	17	(	(	PUNCT
ejpam-3870	65	18	a)α	a)α	X
ejpam-3870	65	19	.	.	PUNCT
ejpam-3870	66	1	clearly	clearly	ADV
ejpam-3870	66	2	,	,	PUNCT
ejpam-3870	66	3	a	a	DET
ejpam-3870	66	4	∈	∈	PROPN
ejpam-3870	66	5	(	(	PUNCT
ejpam-3870	66	6	y)α−1	y)α−1	NOUN
ejpam-3870	66	7	.	.	PUNCT
ejpam-3870	66	8	suppose	suppose	VERB
ejpam-3870	66	9	that	that	SCONJ
ejpam-3870	66	10	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	66	11	>	>	X
ejpam-3870	66	12	1	1	X
ejpam-3870	66	13	.	.	PUNCT
ejpam-3870	67	1	then	then	ADV
ejpam-3870	67	2	there	there	PRON
ejpam-3870	67	3	exist	exist	VERB
ejpam-3870	67	4	b	b	PROPN
ejpam-3870	67	5	∈	∈	PROPN
ejpam-3870	67	6	(	(	PUNCT
ejpam-3870	67	7	y)α−1	y)α−1	NOUN
ejpam-3870	67	8	such	such	DET
ejpam-3870	67	9	that	that	DET
ejpam-3870	67	10	b	b	PROPN
ejpam-3870	67	11	6=	6=	ADP
ejpam-3870	67	12	a.	a.	NOUN
ejpam-3870	67	13	since	since	SCONJ
ejpam-3870	67	14	{	{	PUNCT
ejpam-3870	67	15	a	a	DET
ejpam-3870	67	16	}	}	PUNCT
ejpam-3870	67	17	⊆	⊆	NUM
ejpam-3870	67	18	domα	domα	NOUN
ejpam-3870	67	19	and	and	CCONJ
ejpam-3870	67	20	by	by	ADP
ejpam-3870	67	21	assumption	assumption	NOUN
ejpam-3870	67	22	,	,	PUNCT
ejpam-3870	67	23	we	we	PRON
ejpam-3870	67	24	have	have	VERB
ejpam-3870	67	25	(	(	PUNCT
ejpam-3870	67	26	(	(	PUNCT
ejpam-3870	67	27	{	{	PUNCT
ejpam-3870	67	28	a})α)α−1	a})α)α−1	PROPN
ejpam-3870	67	29	=	=	SYM
ejpam-3870	67	30	{	{	PUNCT
ejpam-3870	67	31	a	a	NOUN
ejpam-3870	67	32	}	}	PUNCT
ejpam-3870	67	33	.	.	PUNCT
ejpam-3870	68	1	therefore	therefore	ADV
ejpam-3870	68	2	b	b	PROPN
ejpam-3870	68	3	∈	∈	PROPN
ejpam-3870	68	4	(	(	PUNCT
ejpam-3870	68	5	y)α−1	y)α−1	NOUN
ejpam-3870	68	6	⊆	⊆	NUM
ejpam-3870	68	7	(	(	PUNCT
ejpam-3870	68	8	(	(	PUNCT
ejpam-3870	68	9	a)α)α−1	a)α)α−1	X
ejpam-3870	68	10	=	=	PRON
ejpam-3870	68	11	{	{	PUNCT
ejpam-3870	68	12	a	a	NOUN
ejpam-3870	68	13	}	}	PUNCT
ejpam-3870	68	14	.	.	PUNCT
ejpam-3870	69	1	thus	thus	ADV
ejpam-3870	69	2	b	b	X
ejpam-3870	69	3	=	=	SYM
ejpam-3870	69	4	a	a	NOUN
ejpam-3870	69	5	,	,	PUNCT
ejpam-3870	69	6	a	a	DET
ejpam-3870	69	7	contradiction	contradiction	NOUN
ejpam-3870	69	8	.	.	PUNCT
ejpam-3870	70	1	as	as	ADP
ejpam-3870	70	2	a	a	DET
ejpam-3870	70	3	result	result	NOUN
ejpam-3870	70	4	,	,	PUNCT
ejpam-3870	70	5	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	70	6	=	=	SYM
ejpam-3870	70	7	1	1	X
ejpam-3870	70	8	.	.	X
ejpam-3870	70	9	combining	combine	VERB
ejpam-3870	70	10	lemmas	lemmas	PROPN
ejpam-3870	70	11	1	1	NUM
ejpam-3870	70	12	and	and	CCONJ
ejpam-3870	70	13	2	2	NUM
ejpam-3870	70	14	we	we	PRON
ejpam-3870	70	15	have	have	VERB
ejpam-3870	70	16	the	the	DET
ejpam-3870	70	17	following	follow	VERB
ejpam-3870	70	18	lemma	lemma	PROPN
ejpam-3870	70	19	.	.	PUNCT
ejpam-3870	71	1	lemma	lemma	PROPN
ejpam-3870	71	2	3	3	X
ejpam-3870	71	3	.	.	PUNCT
ejpam-3870	72	1	let	let	VERB
ejpam-3870	72	2	α	α	PRON
ejpam-3870	72	3	∈	∈	PROPN
ejpam-3870	72	4	bx	bx	X
ejpam-3870	72	5	.	.	PUNCT
ejpam-3870	73	1	then	then	ADV
ejpam-3870	73	2	the	the	DET
ejpam-3870	73	3	following	follow	VERB
ejpam-3870	73	4	are	be	AUX
ejpam-3870	73	5	equivalent	equivalent	ADJ
ejpam-3870	73	6	:	:	PUNCT
ejpam-3870	73	7	(	(	PUNCT
ejpam-3870	73	8	i	i	NOUN
ejpam-3870	73	9	)	)	PUNCT
ejpam-3870	73	10	for	for	ADP
ejpam-3870	73	11	every	every	DET
ejpam-3870	73	12	a	a	PROPN
ejpam-3870	73	13	,	,	PUNCT
ejpam-3870	73	14	b	b	PROPN
ejpam-3870	73	15	∈	∈	PROPN
ejpam-3870	73	16	domα	domα	NOUN
ejpam-3870	73	17	,	,	PUNCT
ejpam-3870	73	18	(	(	PUNCT
ejpam-3870	73	19	a)α	a)α	X
ejpam-3870	73	20	∩	∩	NOUN
ejpam-3870	73	21	(	(	PUNCT
ejpam-3870	73	22	b)α	b)α	NOUN
ejpam-3870	73	23	6=	6=	NUM
ejpam-3870	73	24	∅	∅	NOUN
ejpam-3870	73	25	implies	imply	VERB
ejpam-3870	73	26	a	a	DET
ejpam-3870	73	27	=	=	SYM
ejpam-3870	73	28	b	b	NOUN
ejpam-3870	73	29	;	;	PUNCT
ejpam-3870	73	30	(	(	PUNCT
ejpam-3870	73	31	ii	ii	NOUN
ejpam-3870	73	32	)	)	PUNCT
ejpam-3870	73	33	|(y)α−1|	|(y)α−1|	PROPN
ejpam-3870	73	34	=	=	PUNCT
ejpam-3870	73	35	1	1	NUM
ejpam-3870	73	36	for	for	ADP
ejpam-3870	73	37	all	all	DET
ejpam-3870	73	38	y	y	PROPN
ejpam-3870	73	39	∈	∈	PROPN
ejpam-3870	73	40	ranα	ranα	VERB
ejpam-3870	73	41	;	;	PUNCT
ejpam-3870	73	42	(	(	PUNCT
ejpam-3870	73	43	iii	iii	X
ejpam-3870	73	44	)	)	PUNCT
ejpam-3870	73	45	(	(	PUNCT
ejpam-3870	73	46	aα)α−1	aα)α−1	X
ejpam-3870	73	47	=	=	SYM
ejpam-3870	73	48	a	a	NOUN
ejpam-3870	73	49	for	for	ADP
ejpam-3870	73	50	every	every	DET
ejpam-3870	73	51	a	a	DET
ejpam-3870	73	52	⊆	⊆	NUM
ejpam-3870	73	53	domα	domα	NOUN
ejpam-3870	73	54	.	.	PUNCT
ejpam-3870	74	1	lemma	lemma	PROPN
ejpam-3870	74	2	4	4	X
ejpam-3870	74	3	.	.	PUNCT
ejpam-3870	75	1	let	let	VERB
ejpam-3870	75	2	α	α	PRON
ejpam-3870	75	3	∈	∈	PROPN
ejpam-3870	75	4	bx	bx	NOUN
ejpam-3870	75	5	.	.	PUNCT
ejpam-3870	76	1	if	if	SCONJ
ejpam-3870	76	2	α	α	PRON
ejpam-3870	76	3	is	be	AUX
ejpam-3870	76	4	a	a	DET
ejpam-3870	76	5	left	left	ADJ
ejpam-3870	76	6	magnifying	magnifying	ADJ
ejpam-3870	76	7	element	element	NOUN
ejpam-3870	76	8	of	of	ADP
ejpam-3870	76	9	bx	bx	PROPN
ejpam-3870	76	10	,	,	PUNCT
ejpam-3870	76	11	then	then	ADV
ejpam-3870	76	12	(	(	PUNCT
ejpam-3870	76	13	i	i	NOUN
ejpam-3870	76	14	)	)	PUNCT
ejpam-3870	76	15	dom(α	dom(α	PROPN
ejpam-3870	76	16	)	)	PUNCT
ejpam-3870	77	1	=	=	SYM
ejpam-3870	77	2	x	x	X
ejpam-3870	77	3	,	,	PUNCT
ejpam-3870	77	4	(	(	PUNCT
ejpam-3870	77	5	ii	ii	NOUN
ejpam-3870	77	6	)	)	PUNCT
ejpam-3870	77	7	for	for	ADP
ejpam-3870	77	8	any	any	DET
ejpam-3870	77	9	x	x	NOUN
ejpam-3870	77	10	,	,	PUNCT
ejpam-3870	77	11	y	y	PROPN
ejpam-3870	77	12	∈	∈	PROPN
ejpam-3870	77	13	dom(α	dom(α	PROPN
ejpam-3870	77	14	)	)	PUNCT
ejpam-3870	77	15	,	,	PUNCT
ejpam-3870	77	16	(	(	PUNCT
ejpam-3870	77	17	a)α	a)α	X
ejpam-3870	77	18	∩	∩	NOUN
ejpam-3870	77	19	(	(	PUNCT
ejpam-3870	77	20	b)α	b)α	NOUN
ejpam-3870	77	21	6=	6=	NUM
ejpam-3870	77	22	∅	∅	NOUN
ejpam-3870	77	23	implies	imply	VERB
ejpam-3870	77	24	a	a	DET
ejpam-3870	77	25	=	=	NOUN
ejpam-3870	77	26	b.	b.	NOUN
ejpam-3870	77	27	proof	proof	NOUN
ejpam-3870	77	28	.	.	PUNCT
ejpam-3870	78	1	assume	assume	VERB
ejpam-3870	78	2	that	that	SCONJ
ejpam-3870	78	3	α	α	PRON
ejpam-3870	78	4	is	be	AUX
ejpam-3870	78	5	a	a	DET
ejpam-3870	78	6	left	left	ADJ
ejpam-3870	78	7	magnifying	magnifying	ADJ
ejpam-3870	78	8	element	element	NOUN
ejpam-3870	78	9	of	of	ADP
ejpam-3870	78	10	bx	bx	PROPN
ejpam-3870	78	11	.	.	PUNCT
ejpam-3870	79	1	then	then	ADV
ejpam-3870	79	2	there	there	PRON
ejpam-3870	79	3	exists	exist	VERB
ejpam-3870	79	4	a	a	DET
ejpam-3870	79	5	proper	proper	ADJ
ejpam-3870	79	6	subset	subset	NOUN
ejpam-3870	79	7	m	m	NOUN
ejpam-3870	79	8	of	of	ADP
ejpam-3870	79	9	bx	bx	PRON
ejpam-3870	79	10	such	such	ADJ
ejpam-3870	79	11	that	that	DET
ejpam-3870	79	12	αm	αm	NOUN
ejpam-3870	79	13	=	=	NOUN
ejpam-3870	79	14	bx	bx	PROPN
ejpam-3870	79	15	.	.	PUNCT
ejpam-3870	80	1	since	since	SCONJ
ejpam-3870	80	2	ix	ix	PROPN
ejpam-3870	80	3	∈	∈	PROPN
ejpam-3870	80	4	bx	bx	NOUN
ejpam-3870	80	5	,	,	PUNCT
ejpam-3870	80	6	there	there	PRON
ejpam-3870	80	7	exists	exist	VERB
ejpam-3870	80	8	a	a	DET
ejpam-3870	80	9	relation	relation	NOUN
ejpam-3870	80	10	β	β	NOUN
ejpam-3870	80	11	∈m	∈m	NOUN
ejpam-3870	80	12	such	such	ADJ
ejpam-3870	80	13	that	that	SCONJ
ejpam-3870	81	1	αβ	αβ	PROPN
ejpam-3870	82	1	=	=	PRON
ejpam-3870	82	2	ix	ix	ADJ
ejpam-3870	82	3	and	and	CCONJ
ejpam-3870	82	4	since	since	SCONJ
ejpam-3870	82	5	dom(ix	dom(ix	NUM
ejpam-3870	82	6	)	)	PUNCT
ejpam-3870	83	1	=	=	SYM
ejpam-3870	83	2	x	x	X
ejpam-3870	83	3	,	,	PUNCT
ejpam-3870	83	4	we	we	PRON
ejpam-3870	83	5	obtain	obtain	VERB
ejpam-3870	83	6	domα	domα	NOUN
ejpam-3870	83	7	=	=	PUNCT
ejpam-3870	83	8	x.	x.	NOUN
ejpam-3870	83	9	let	let	VERB
ejpam-3870	83	10	x	x	PRON
ejpam-3870	83	11	,	,	PUNCT
ejpam-3870	83	12	y	y	PROPN
ejpam-3870	83	13	∈	∈	PROPN
ejpam-3870	83	14	domα	domα	NOUN
ejpam-3870	83	15	.	.	PUNCT
ejpam-3870	84	1	suppose	suppose	VERB
ejpam-3870	84	2	that	that	SCONJ
ejpam-3870	84	3	(	(	PUNCT
ejpam-3870	84	4	a)α	a)α	X
ejpam-3870	84	5	∩	∩	NOUN
ejpam-3870	84	6	(	(	PUNCT
ejpam-3870	84	7	b)α	b)α	NOUN
ejpam-3870	84	8	6=	6=	ADP
ejpam-3870	84	9	∅.	∅.	NOUN
ejpam-3870	84	10	then	then	ADV
ejpam-3870	84	11	there	there	PRON
ejpam-3870	84	12	exists	exist	VERB
ejpam-3870	84	13	an	an	DET
ejpam-3870	84	14	element	element	NOUN
ejpam-3870	84	15	z	z	PROPN
ejpam-3870	84	16	∈	∈	PROPN
ejpam-3870	84	17	(	(	PUNCT
ejpam-3870	84	18	x)α	x)α	X
ejpam-3870	84	19	∩	∩	X
ejpam-3870	84	20	(	(	PUNCT
ejpam-3870	84	21	y)α	y)α	NOUN
ejpam-3870	84	22	.	.	PUNCT
ejpam-3870	85	1	we	we	PRON
ejpam-3870	85	2	get	get	VERB
ejpam-3870	85	3	(	(	PUNCT
ejpam-3870	85	4	z)β	z)β	NOUN
ejpam-3870	85	5	⊆	⊆	NUM
ejpam-3870	85	6	(	(	PUNCT
ejpam-3870	85	7	(	(	PUNCT
ejpam-3870	85	8	x)α)β	x)α)β	NOUN
ejpam-3870	85	9	=	=	SYM
ejpam-3870	85	10	(	(	PUNCT
ejpam-3870	85	11	x)(αβ	x)(αβ	NUM
ejpam-3870	85	12	)	)	PUNCT
ejpam-3870	85	13	=	=	NOUN
ejpam-3870	86	1	(	(	PUNCT
ejpam-3870	86	2	x)ix	x)ix	PROPN
ejpam-3870	86	3	=	=	PRON
ejpam-3870	86	4	{	{	PUNCT
ejpam-3870	86	5	x	x	NOUN
ejpam-3870	86	6	}	}	PUNCT
ejpam-3870	86	7	,	,	PUNCT
ejpam-3870	86	8	and	and	CCONJ
ejpam-3870	86	9	(	(	PUNCT
ejpam-3870	86	10	z)β	z)β	NOUN
ejpam-3870	86	11	⊆	⊆	NUM
ejpam-3870	86	12	(	(	PUNCT
ejpam-3870	86	13	(	(	PUNCT
ejpam-3870	86	14	y)α)β	y)α)β	NOUN
ejpam-3870	86	15	=	=	SYM
ejpam-3870	86	16	(	(	PUNCT
ejpam-3870	86	17	y)(αβ	y)(αβ	NOUN
ejpam-3870	86	18	)	)	PUNCT
ejpam-3870	86	19	=	=	PUNCT
ejpam-3870	86	20	(	(	PUNCT
ejpam-3870	86	21	y)ix	y)ix	PROPN
ejpam-3870	86	22	=	=	SYM
ejpam-3870	86	23	{	{	PUNCT
ejpam-3870	86	24	y	y	NOUN
ejpam-3870	86	25	}	}	PUNCT
ejpam-3870	86	26	.	.	PUNCT
ejpam-3870	87	1	thus	thus	ADV
ejpam-3870	87	2	(	(	PUNCT
ejpam-3870	87	3	z)β	z)β	NOUN
ejpam-3870	87	4	⊆	⊆	NUM
ejpam-3870	87	5	{	{	PUNCT
ejpam-3870	87	6	x	x	NOUN
ejpam-3870	87	7	}	}	PUNCT
ejpam-3870	87	8	and	and	CCONJ
ejpam-3870	87	9	(	(	PUNCT
ejpam-3870	87	10	z)β	z)β	NOUN
ejpam-3870	87	11	⊆	⊆	NUM
ejpam-3870	87	12	{	{	PUNCT
ejpam-3870	87	13	y	y	NOUN
ejpam-3870	87	14	}	}	PUNCT
ejpam-3870	87	15	.	.	PUNCT
ejpam-3870	88	1	we	we	PRON
ejpam-3870	88	2	have	have	VERB
ejpam-3870	88	3	that	that	PRON
ejpam-3870	88	4	x	x	X
ejpam-3870	88	5	=	=	PUNCT
ejpam-3870	88	6	y.	y.	PROPN
ejpam-3870	88	7	therefore	therefore	ADV
ejpam-3870	88	8	(	(	PUNCT
ejpam-3870	88	9	x)α	x)α	X
ejpam-3870	88	10	∩	∩	X
ejpam-3870	88	11	(	(	PUNCT
ejpam-3870	88	12	y)α	y)α	NOUN
ejpam-3870	88	13	=	=	PUNCT
ejpam-3870	88	14	∅.	∅.	PRON
ejpam-3870	88	15	lemma	lemma	PROPN
ejpam-3870	88	16	5	5	NUM
ejpam-3870	88	17	.	.	PUNCT
ejpam-3870	89	1	let	let	VERB
ejpam-3870	89	2	α	α	PRON
ejpam-3870	89	3	∈	∈	PROPN
ejpam-3870	89	4	bx	bx	X
ejpam-3870	89	5	.	.	PUNCT
ejpam-3870	90	1	if	if	SCONJ
ejpam-3870	90	2	for	for	ADP
ejpam-3870	90	3	any	any	DET
ejpam-3870	90	4	x	x	NOUN
ejpam-3870	90	5	,	,	PUNCT
ejpam-3870	90	6	y	y	PROPN
ejpam-3870	90	7	∈	∈	PROPN
ejpam-3870	90	8	dom(α	dom(α	PROPN
ejpam-3870	90	9	)	)	PUNCT
ejpam-3870	90	10	such	such	ADJ
ejpam-3870	90	11	that	that	SCONJ
ejpam-3870	90	12	(	(	PUNCT
ejpam-3870	90	13	x)α	x)α	X
ejpam-3870	90	14	∩	∩	NOUN
ejpam-3870	90	15	(	(	PUNCT
ejpam-3870	90	16	y)α	y)α	NOUN
ejpam-3870	90	17	6=	6=	NUM
ejpam-3870	90	18	∅	∅	NOUN
ejpam-3870	90	19	,	,	PUNCT
ejpam-3870	90	20	x	x	PROPN
ejpam-3870	90	21	=	=	SYM
ejpam-3870	90	22	y	y	PROPN
ejpam-3870	90	23	and	and	CCONJ
ejpam-3870	90	24	α	α	PROPN
ejpam-3870	90	25	is	be	AUX
ejpam-3870	90	26	a	a	DET
ejpam-3870	90	27	function	function	NOUN
ejpam-3870	90	28	,	,	PUNCT
ejpam-3870	90	29	then	then	ADV
ejpam-3870	90	30	α	α	PROPN
ejpam-3870	90	31	is	be	AUX
ejpam-3870	90	32	a	a	DET
ejpam-3870	90	33	one	one	NUM
ejpam-3870	90	34	-	-	PUNCT
ejpam-3870	90	35	to	to	ADP
ejpam-3870	90	36	-	-	PUNCT
ejpam-3870	90	37	one	one	NUM
ejpam-3870	90	38	function	function	NOUN
ejpam-3870	90	39	.	.	PUNCT
ejpam-3870	91	1	the	the	DET
ejpam-3870	91	2	proof	proof	NOUN
ejpam-3870	91	3	of	of	ADP
ejpam-3870	91	4	lemma	lemma	PROPN
ejpam-3870	91	5	5	5	NUM
ejpam-3870	91	6	is	be	AUX
ejpam-3870	91	7	obvious	obvious	ADJ
ejpam-3870	91	8	and	and	CCONJ
ejpam-3870	91	9	immediately	immediately	ADV
ejpam-3870	91	10	obtained	obtain	VERB
ejpam-3870	91	11	.	.	PUNCT
ejpam-3870	92	1	lemma	lemma	PROPN
ejpam-3870	92	2	6	6	NUM
ejpam-3870	92	3	.	.	PUNCT
ejpam-3870	93	1	let	let	VERB
ejpam-3870	93	2	α	α	PRON
ejpam-3870	93	3	∈	∈	PROPN
ejpam-3870	93	4	bx	bx	NOUN
ejpam-3870	93	5	.	.	PUNCT
ejpam-3870	94	1	if	if	SCONJ
ejpam-3870	94	2	α	α	PRON
ejpam-3870	94	3	is	be	AUX
ejpam-3870	94	4	a	a	DET
ejpam-3870	94	5	bijective	bijective	ADJ
ejpam-3870	94	6	function	function	NOUN
ejpam-3870	94	7	on	on	ADP
ejpam-3870	94	8	x	x	NOUN
ejpam-3870	94	9	,	,	PUNCT
ejpam-3870	94	10	then	then	ADV
ejpam-3870	94	11	α	α	PROPN
ejpam-3870	94	12	is	be	AUX
ejpam-3870	94	13	not	not	PART
ejpam-3870	94	14	left	leave	VERB
ejpam-3870	94	15	magnifying	magnify	VERB
ejpam-3870	94	16	element	element	NOUN
ejpam-3870	94	17	of	of	ADP
ejpam-3870	94	18	bx	bx	PROPN
ejpam-3870	94	19	.	.	PUNCT
ejpam-3870	95	1	proof	proof	NOUN
ejpam-3870	95	2	.	.	PUNCT
ejpam-3870	96	1	we	we	PRON
ejpam-3870	96	2	are	be	AUX
ejpam-3870	96	3	going	go	VERB
ejpam-3870	96	4	to	to	PART
ejpam-3870	96	5	proof	proof	VERB
ejpam-3870	96	6	this	this	DET
ejpam-3870	96	7	lemma	lemma	PROPN
ejpam-3870	96	8	similarly	similarly	ADV
ejpam-3870	96	9	to	to	ADP
ejpam-3870	96	10	[	[	X
ejpam-3870	96	11	9	9	NUM
ejpam-3870	96	12	,	,	PUNCT
ejpam-3870	96	13	lemma	lemma	PROPN
ejpam-3870	96	14	2	2	NUM
ejpam-3870	96	15	.	.	NUM
ejpam-3870	96	16	]	]	PUNCT
ejpam-3870	96	17	.	.	PUNCT
ejpam-3870	97	1	suppose	suppose	VERB
ejpam-3870	97	2	that	that	SCONJ
ejpam-3870	97	3	α	α	PROPN
ejpam-3870	97	4	is	be	AUX
ejpam-3870	97	5	a	a	DET
ejpam-3870	97	6	left	left	ADJ
ejpam-3870	97	7	magnifying	magnifying	ADJ
ejpam-3870	97	8	element	element	NOUN
ejpam-3870	97	9	of	of	ADP
ejpam-3870	97	10	bx	bx	PROPN
ejpam-3870	97	11	.	.	PUNCT
ejpam-3870	98	1	then	then	ADV
ejpam-3870	98	2	there	there	PRON
ejpam-3870	98	3	exists	exist	VERB
ejpam-3870	98	4	a	a	DET
ejpam-3870	98	5	proper	proper	ADJ
ejpam-3870	98	6	subset	subset	NOUN
ejpam-3870	98	7	m	m	NOUN
ejpam-3870	98	8	of	of	ADP
ejpam-3870	98	9	bx	bx	PRON
ejpam-3870	98	10	such	such	ADJ
ejpam-3870	98	11	that	that	DET
ejpam-3870	98	12	αm	αm	NOUN
ejpam-3870	98	13	=	=	NOUN
ejpam-3870	98	14	bx	bx	PROPN
ejpam-3870	98	15	.	.	PUNCT
ejpam-3870	99	1	since	since	SCONJ
ejpam-3870	99	2	α	α	PROPN
ejpam-3870	99	3	is	be	AUX
ejpam-3870	99	4	a	a	DET
ejpam-3870	99	5	bijective	bijective	ADJ
ejpam-3870	99	6	function	function	NOUN
ejpam-3870	99	7	,	,	PUNCT
ejpam-3870	99	8	αm	αm	NOUN
ejpam-3870	99	9	=	=	SYM
ejpam-3870	100	1	αα−1αm	αα−1αm	NUM
ejpam-3870	100	2	=	=	SYM
ejpam-3870	100	3	αα−1bx	αα−1bx	NUM
ejpam-3870	100	4	⊆	⊆	NUM
ejpam-3870	100	5	αbx	αbx	NOUN
ejpam-3870	100	6	⊆	⊆	NUM
ejpam-3870	100	7	bx	bx	NOUN
ejpam-3870	100	8	=	=	NOUN
ejpam-3870	100	9	αm	αm	PROPN
ejpam-3870	100	10	.	.	PUNCT
ejpam-3870	101	1	then	then	ADV
ejpam-3870	101	2	αm	αm	INTJ
ejpam-3870	101	3	=	=	PUNCT
ejpam-3870	101	4	αbx	αbx	NOUN
ejpam-3870	101	5	.	.	PUNCT
ejpam-3870	102	1	hence	hence	ADV
ejpam-3870	102	2	m	m	VERB
ejpam-3870	102	3	=	=	ADJ
ejpam-3870	102	4	α−1αm	α−1αm	NOUN
ejpam-3870	102	5	=	=	PUNCT
ejpam-3870	103	1	α−1αbx	α−1αbx	PROPN
ejpam-3870	103	2	=	=	PUNCT
ejpam-3870	103	3	bx	bx	X
ejpam-3870	103	4	;	;	PUNCT
ejpam-3870	103	5	we	we	PRON
ejpam-3870	103	6	achieve	achieve	VERB
ejpam-3870	103	7	a	a	DET
ejpam-3870	103	8	contradiction	contradiction	NOUN
ejpam-3870	103	9	.	.	PUNCT
ejpam-3870	104	1	therefore	therefore	ADV
ejpam-3870	104	2	α	α	PROPN
ejpam-3870	104	3	is	be	AUX
ejpam-3870	104	4	not	not	PART
ejpam-3870	104	5	a	a	DET
ejpam-3870	104	6	left	left	ADJ
ejpam-3870	104	7	magnifying	magnifying	ADJ
ejpam-3870	104	8	element	element	NOUN
ejpam-3870	104	9	of	of	ADP
ejpam-3870	104	10	bx	bx	PROPN
ejpam-3870	104	11	.	.	PUNCT
ejpam-3870	105	1	w.	w.	PROPN
ejpam-3870	105	2	teparos	teparos	PROPN
ejpam-3870	105	3	,	,	PUNCT
ejpam-3870	105	4	s.	s.	PROPN
ejpam-3870	105	5	boonta	boonta	PROPN
ejpam-3870	105	6	,	,	PUNCT
ejpam-3870	105	7	t.	t.	PROPN
ejpam-3870	105	8	theparod	theparod	PROPN
ejpam-3870	105	9	/	/	SYM
ejpam-3870	105	10	eur	eur	PROPN
ejpam-3870	105	11	.	.	PUNCT
ejpam-3870	106	1	j.	j.	PROPN
ejpam-3870	106	2	pure	pure	PROPN
ejpam-3870	106	3	appl	appl	PROPN
ejpam-3870	106	4	.	.	PROPN
ejpam-3870	106	5	math	math	PROPN
ejpam-3870	106	6	,	,	PUNCT
ejpam-3870	106	7	13	13	NUM
ejpam-3870	106	8	(	(	PUNCT
ejpam-3870	106	9	4	4	NUM
ejpam-3870	106	10	)	)	PUNCT
ejpam-3870	106	11	(	(	PUNCT
ejpam-3870	106	12	2020	2020	NUM
ejpam-3870	106	13	)	)	PUNCT
ejpam-3870	106	14	,	,	PUNCT
ejpam-3870	106	15	987	987	NUM
ejpam-3870	106	16	-	-	SYM
ejpam-3870	106	17	994	994	NUM
ejpam-3870	106	18	990	990	NUM
ejpam-3870	106	19	lemma	lemma	PROPN
ejpam-3870	106	20	7	7	NUM
ejpam-3870	106	21	.	.	PUNCT
ejpam-3870	107	1	let	let	VERB
ejpam-3870	107	2	α	α	PRON
ejpam-3870	107	3	∈	∈	PROPN
ejpam-3870	107	4	bx	bx	NOUN
ejpam-3870	107	5	and	and	CCONJ
ejpam-3870	107	6	domα	domα	NOUN
ejpam-3870	107	7	=	=	PUNCT
ejpam-3870	108	1	x.	x.	NOUN
ejpam-3870	108	2	if	if	SCONJ
ejpam-3870	108	3	α	α	PRON
ejpam-3870	108	4	is	be	AUX
ejpam-3870	108	5	not	not	PART
ejpam-3870	108	6	a	a	DET
ejpam-3870	108	7	bijective	bijective	ADJ
ejpam-3870	108	8	function	function	NOUN
ejpam-3870	108	9	on	on	ADP
ejpam-3870	108	10	x	x	PUNCT
ejpam-3870	108	11	and	and	CCONJ
ejpam-3870	108	12	for	for	ADP
ejpam-3870	108	13	every	every	DET
ejpam-3870	108	14	a	a	PROPN
ejpam-3870	108	15	,	,	PUNCT
ejpam-3870	108	16	b	b	PROPN
ejpam-3870	108	17	∈	∈	PROPN
ejpam-3870	108	18	domα	domα	NOUN
ejpam-3870	108	19	,	,	PUNCT
ejpam-3870	108	20	(	(	PUNCT
ejpam-3870	108	21	a)α	a)α	X
ejpam-3870	108	22	∩	∩	NOUN
ejpam-3870	108	23	(	(	PUNCT
ejpam-3870	108	24	b)α	b)α	NOUN
ejpam-3870	108	25	6=	6=	NUM
ejpam-3870	108	26	∅	∅	NOUN
ejpam-3870	108	27	implies	imply	VERB
ejpam-3870	108	28	a	a	DET
ejpam-3870	108	29	=	=	SYM
ejpam-3870	108	30	b	b	NOUN
ejpam-3870	108	31	,	,	PUNCT
ejpam-3870	108	32	then	then	ADV
ejpam-3870	108	33	α	α	PROPN
ejpam-3870	108	34	is	be	AUX
ejpam-3870	108	35	a	a	DET
ejpam-3870	108	36	left	left	ADJ
ejpam-3870	108	37	magnifying	magnifying	ADJ
ejpam-3870	108	38	element	element	NOUN
ejpam-3870	108	39	of	of	ADP
ejpam-3870	108	40	bx	bx	PROPN
ejpam-3870	108	41	.	.	PUNCT
ejpam-3870	109	1	proof	proof	NOUN
ejpam-3870	109	2	.	.	PUNCT
ejpam-3870	110	1	let	let	VERB
ejpam-3870	110	2	α	α	PRON
ejpam-3870	110	3	∈	∈	PROPN
ejpam-3870	110	4	bx	bx	NOUN
ejpam-3870	110	5	and	and	CCONJ
ejpam-3870	110	6	domα	domα	NOUN
ejpam-3870	110	7	=	=	SYM
ejpam-3870	110	8	x.	x.	NOUN
ejpam-3870	110	9	assume	assume	VERB
ejpam-3870	110	10	that	that	SCONJ
ejpam-3870	110	11	α	α	PRON
ejpam-3870	110	12	is	be	AUX
ejpam-3870	110	13	not	not	PART
ejpam-3870	110	14	a	a	DET
ejpam-3870	110	15	bijective	bijective	ADJ
ejpam-3870	110	16	function	function	NOUN
ejpam-3870	110	17	on	on	ADP
ejpam-3870	110	18	x	x	PUNCT
ejpam-3870	110	19	and	and	CCONJ
ejpam-3870	110	20	for	for	ADP
ejpam-3870	110	21	every	every	DET
ejpam-3870	110	22	a	a	PROPN
ejpam-3870	110	23	,	,	PUNCT
ejpam-3870	110	24	b	b	PROPN
ejpam-3870	110	25	∈	∈	PROPN
ejpam-3870	110	26	domα	domα	NOUN
ejpam-3870	110	27	,	,	PUNCT
ejpam-3870	110	28	(	(	PUNCT
ejpam-3870	111	1	a)α	a)α	X
ejpam-3870	111	2	∩	∩	NOUN
ejpam-3870	111	3	(	(	PUNCT
ejpam-3870	111	4	b)α	b)α	NOUN
ejpam-3870	111	5	6=	6=	NUM
ejpam-3870	111	6	∅	∅	NOUN
ejpam-3870	111	7	implies	imply	VERB
ejpam-3870	111	8	a	a	DET
ejpam-3870	111	9	=	=	X
ejpam-3870	111	10	b.	b.	NOUN
ejpam-3870	111	11	let	let	VERB
ejpam-3870	111	12	m	m	VERB
ejpam-3870	111	13	=	=	PRON
ejpam-3870	111	14	{	{	PUNCT
ejpam-3870	111	15	h	h	NOUN
ejpam-3870	111	16	∈	∈	PROPN
ejpam-3870	111	17	bx	bx	PROPN
ejpam-3870	111	18	|	|	ADV
ejpam-3870	111	19	domh	domh	PROPN
ejpam-3870	111	20	6=	6=	ADP
ejpam-3870	111	21	x	x	NOUN
ejpam-3870	111	22	or	or	CCONJ
ejpam-3870	111	23	h	h	NOUN
ejpam-3870	111	24	is	be	AUX
ejpam-3870	111	25	not	not	PART
ejpam-3870	111	26	a	a	DET
ejpam-3870	111	27	one	one	NUM
ejpam-3870	111	28	-	-	PUNCT
ejpam-3870	111	29	to	to	ADP
ejpam-3870	111	30	-	-	PUNCT
ejpam-3870	111	31	one	one	NUM
ejpam-3870	111	32	function	function	NOUN
ejpam-3870	111	33	}	}	PUNCT
ejpam-3870	111	34	.	.	PUNCT
ejpam-3870	112	1	then	then	ADV
ejpam-3870	112	2	m	m	PROPN
ejpam-3870	112	3	is	be	AUX
ejpam-3870	112	4	a	a	DET
ejpam-3870	112	5	proper	proper	ADJ
ejpam-3870	112	6	subset	subset	NOUN
ejpam-3870	112	7	of	of	ADP
ejpam-3870	112	8	bx	bx	PROPN
ejpam-3870	112	9	.	.	PUNCT
ejpam-3870	113	1	we	we	PRON
ejpam-3870	113	2	will	will	AUX
ejpam-3870	113	3	show	show	VERB
ejpam-3870	113	4	that	that	SCONJ
ejpam-3870	113	5	αm	αm	NOUN
ejpam-3870	113	6	=	=	NOUN
ejpam-3870	113	7	bx	bx	PROPN
ejpam-3870	113	8	.	.	PUNCT
ejpam-3870	114	1	let	let	VERB
ejpam-3870	114	2	β	β	X
ejpam-3870	114	3	be	be	AUX
ejpam-3870	114	4	a	a	DET
ejpam-3870	114	5	relation	relation	NOUN
ejpam-3870	114	6	in	in	ADP
ejpam-3870	114	7	bx	bx	PROPN
ejpam-3870	114	8	.	.	PUNCT
ejpam-3870	115	1	for	for	ADP
ejpam-3870	115	2	each	each	DET
ejpam-3870	115	3	x	x	SYM
ejpam-3870	115	4	∈	∈	PROPN
ejpam-3870	115	5	(	(	PUNCT
ejpam-3870	115	6	domβ)α	domβ)α	X
ejpam-3870	115	7	.	.	PUNCT
ejpam-3870	116	1	then	then	ADV
ejpam-3870	116	2	there	there	PRON
ejpam-3870	116	3	exists	exist	VERB
ejpam-3870	116	4	a	a	DET
ejpam-3870	116	5	unique	unique	ADJ
ejpam-3870	116	6	x′	x′	PROPN
ejpam-3870	116	7	∈	∈	PROPN
ejpam-3870	116	8	domβ	domβ	NOUN
ejpam-3870	116	9	such	such	ADJ
ejpam-3870	116	10	that	that	SCONJ
ejpam-3870	116	11	x	x	SYM
ejpam-3870	116	12	∈	∈	PROPN
ejpam-3870	116	13	(	(	PUNCT
ejpam-3870	116	14	x′)α	x′)α	PROPN
ejpam-3870	116	15	.	.	PUNCT
ejpam-3870	116	16	define	define	VERB
ejpam-3870	116	17	a	a	DET
ejpam-3870	116	18	relation	relation	NOUN
ejpam-3870	116	19	γ	γ	NOUN
ejpam-3870	116	20	in	in	ADP
ejpam-3870	116	21	bx	bx	PROPN
ejpam-3870	116	22	by	by	ADP
ejpam-3870	116	23	(	(	PUNCT
ejpam-3870	116	24	x)γ	x)γ	PUNCT
ejpam-3870	116	25	=	=	SYM
ejpam-3870	116	26	(	(	PUNCT
ejpam-3870	116	27	x′)β	x′)β	INTJ
ejpam-3870	116	28	where	where	SCONJ
ejpam-3870	116	29	x′	x′	PROPN
ejpam-3870	116	30	∈	∈	PROPN
ejpam-3870	116	31	domβ	domβ	VERB
ejpam-3870	116	32	such	such	ADJ
ejpam-3870	116	33	that	that	SCONJ
ejpam-3870	116	34	x	x	SYM
ejpam-3870	116	35	∈	∈	PROPN
ejpam-3870	116	36	(	(	PUNCT
ejpam-3870	116	37	x′)α	x′)α	PROPN
ejpam-3870	116	38	.	.	PUNCT
ejpam-3870	117	1	if	if	SCONJ
ejpam-3870	117	2	(	(	PUNCT
ejpam-3870	117	3	domβ)α	domβ)α	X
ejpam-3870	117	4	6=	6=	ADP
ejpam-3870	117	5	x	x	SYM
ejpam-3870	117	6	,	,	PUNCT
ejpam-3870	117	7	then	then	ADV
ejpam-3870	117	8	domγ	domγ	PROPN
ejpam-3870	117	9	6=	6=	PROPN
ejpam-3870	117	10	x.	x.	NOUN
ejpam-3870	118	1	so	so	ADV
ejpam-3870	118	2	γ	γ	X
ejpam-3870	118	3	∈m	∈m	NOUN
ejpam-3870	118	4	.	.	PUNCT
ejpam-3870	119	1	if	if	SCONJ
ejpam-3870	119	2	β	β	NOUN
ejpam-3870	119	3	is	be	AUX
ejpam-3870	119	4	not	not	PART
ejpam-3870	119	5	a	a	DET
ejpam-3870	119	6	function	function	NOUN
ejpam-3870	119	7	,	,	PUNCT
ejpam-3870	119	8	by	by	ADP
ejpam-3870	119	9	the	the	DET
ejpam-3870	119	10	definition	definition	NOUN
ejpam-3870	119	11	of	of	ADP
ejpam-3870	119	12	γ	γ	PROPN
ejpam-3870	119	13	,	,	PUNCT
ejpam-3870	119	14	clearly	clearly	ADV
ejpam-3870	119	15	,	,	PUNCT
ejpam-3870	119	16	γ	γ	PROPN
ejpam-3870	119	17	is	be	AUX
ejpam-3870	119	18	not	not	PART
ejpam-3870	119	19	a	a	DET
ejpam-3870	119	20	function	function	NOUN
ejpam-3870	119	21	.	.	PUNCT
ejpam-3870	120	1	consequently	consequently	ADV
ejpam-3870	120	2	γ	γ	PRON
ejpam-3870	120	3	∈m	∈m	NOUN
ejpam-3870	120	4	.	.	PUNCT
ejpam-3870	120	5	suppose	suppose	VERB
ejpam-3870	120	6	that	that	SCONJ
ejpam-3870	120	7	(	(	PUNCT
ejpam-3870	120	8	domβ)α	domβ)α	X
ejpam-3870	120	9	=	=	SYM
ejpam-3870	120	10	x	x	X
ejpam-3870	120	11	and	and	CCONJ
ejpam-3870	120	12	β	β	X
ejpam-3870	120	13	is	be	AUX
ejpam-3870	120	14	a	a	DET
ejpam-3870	120	15	function	function	NOUN
ejpam-3870	120	16	.	.	PUNCT
ejpam-3870	121	1	we	we	PRON
ejpam-3870	121	2	will	will	AUX
ejpam-3870	121	3	show	show	VERB
ejpam-3870	121	4	that	that	SCONJ
ejpam-3870	121	5	γ	γ	PROPN
ejpam-3870	121	6	is	be	AUX
ejpam-3870	121	7	not	not	PART
ejpam-3870	121	8	a	a	DET
ejpam-3870	121	9	one	one	NUM
ejpam-3870	121	10	-	-	PUNCT
ejpam-3870	121	11	toone	toone	NOUN
ejpam-3870	121	12	function	function	NOUN
ejpam-3870	121	13	.	.	PUNCT
ejpam-3870	122	1	let	let	VERB
ejpam-3870	122	2	x	x	PUNCT
ejpam-3870	122	3	∈	∈	PROPN
ejpam-3870	122	4	x	x	X
ejpam-3870	122	5	and	and	CCONJ
ejpam-3870	122	6	c	c	NOUN
ejpam-3870	122	7	∈	∈	PROPN
ejpam-3870	122	8	(	(	PUNCT
ejpam-3870	122	9	x)α	x)α	X
ejpam-3870	122	10	.	.	PUNCT
ejpam-3870	123	1	thus	thus	ADV
ejpam-3870	123	2	we	we	PRON
ejpam-3870	123	3	have	have	VERB
ejpam-3870	123	4	c	c	NOUN
ejpam-3870	123	5	∈	∈	NOUN
ejpam-3870	123	6	x	x	PUNCT
ejpam-3870	123	7	=	=	SYM
ejpam-3870	123	8	(	(	PUNCT
ejpam-3870	123	9	domβ)α	domβ)α	X
ejpam-3870	123	10	.	.	PUNCT
ejpam-3870	124	1	then	then	ADV
ejpam-3870	124	2	there	there	PRON
ejpam-3870	124	3	exists	exist	VERB
ejpam-3870	124	4	x′	x′	PROPN
ejpam-3870	124	5	∈	∈	PROPN
ejpam-3870	124	6	domβ	domβ	NOUN
ejpam-3870	124	7	such	such	ADJ
ejpam-3870	124	8	that	that	SCONJ
ejpam-3870	124	9	c	c	PROPN
ejpam-3870	124	10	∈	∈	PROPN
ejpam-3870	124	11	(	(	PUNCT
ejpam-3870	124	12	x′)α	x′)α	PROPN
ejpam-3870	124	13	.	.	PUNCT
ejpam-3870	125	1	that	that	PRON
ejpam-3870	125	2	is	be	AUX
ejpam-3870	125	3	,	,	PUNCT
ejpam-3870	125	4	(	(	PUNCT
ejpam-3870	125	5	x)α	x)α	X
ejpam-3870	125	6	∩	∩	NOUN
ejpam-3870	125	7	(	(	PUNCT
ejpam-3870	125	8	x′)α	x′)α	PROPN
ejpam-3870	125	9	6=	6=	PROPN
ejpam-3870	125	10	∅.	∅.	VERB
ejpam-3870	125	11	consequently	consequently	ADV
ejpam-3870	125	12	,	,	PUNCT
ejpam-3870	125	13	x	x	PUNCT
ejpam-3870	125	14	=	=	PUNCT
ejpam-3870	125	15	x′	x′	PROPN
ejpam-3870	125	16	∈	∈	PROPN
ejpam-3870	125	17	domβ	domβ	NOUN
ejpam-3870	125	18	.	.	PUNCT
ejpam-3870	126	1	therefore	therefore	ADV
ejpam-3870	126	2	domβ	domβ	X
ejpam-3870	126	3	=	=	PUNCT
ejpam-3870	127	1	x.	x.	NOUN
ejpam-3870	127	2	next	next	ADV
ejpam-3870	127	3	,	,	PUNCT
ejpam-3870	127	4	we	we	PRON
ejpam-3870	127	5	will	will	AUX
ejpam-3870	127	6	show	show	VERB
ejpam-3870	127	7	that	that	SCONJ
ejpam-3870	127	8	α	α	PRON
ejpam-3870	127	9	is	be	AUX
ejpam-3870	127	10	not	not	PART
ejpam-3870	127	11	a	a	DET
ejpam-3870	127	12	function	function	NOUN
ejpam-3870	127	13	from	from	ADP
ejpam-3870	127	14	domβ	domβ	NOUN
ejpam-3870	128	1	=	=	PUNCT
ejpam-3870	128	2	x	x	SYM
ejpam-3870	128	3	onto	onto	ADP
ejpam-3870	128	4	x.	x.	NOUN
ejpam-3870	128	5	suppose	suppose	VERB
ejpam-3870	128	6	the	the	DET
ejpam-3870	128	7	contrary	contrary	NOUN
ejpam-3870	128	8	that	that	SCONJ
ejpam-3870	128	9	α	α	PRON
ejpam-3870	128	10	is	be	AUX
ejpam-3870	128	11	a	a	DET
ejpam-3870	128	12	function	function	NOUN
ejpam-3870	128	13	from	from	ADP
ejpam-3870	128	14	x	x	PRON
ejpam-3870	128	15	onto	onto	ADP
ejpam-3870	128	16	x.	x.	NOUN
ejpam-3870	128	17	by	by	ADP
ejpam-3870	128	18	our	our	PRON
ejpam-3870	128	19	assumption	assumption	NOUN
ejpam-3870	128	20	and	and	CCONJ
ejpam-3870	128	21	lemma	lemma	PROPN
ejpam-3870	128	22	5	5	NUM
ejpam-3870	128	23	,	,	PUNCT
ejpam-3870	128	24	α	α	PROPN
ejpam-3870	128	25	is	be	AUX
ejpam-3870	128	26	a	a	DET
ejpam-3870	128	27	one	one	NUM
ejpam-3870	128	28	-	-	PUNCT
ejpam-3870	128	29	to	to	ADP
ejpam-3870	128	30	-	-	PUNCT
ejpam-3870	128	31	one	one	NUM
ejpam-3870	128	32	function	function	NOUN
ejpam-3870	128	33	.	.	PUNCT
ejpam-3870	129	1	hence	hence	ADV
ejpam-3870	129	2	α	α	PROPN
ejpam-3870	129	3	is	be	AUX
ejpam-3870	129	4	a	a	DET
ejpam-3870	129	5	bijective	bijective	ADJ
ejpam-3870	129	6	function	function	NOUN
ejpam-3870	129	7	on	on	ADP
ejpam-3870	129	8	x.	x.	NOUN
ejpam-3870	130	1	this	this	PRON
ejpam-3870	130	2	is	be	AUX
ejpam-3870	130	3	a	a	DET
ejpam-3870	130	4	contradiction	contradiction	NOUN
ejpam-3870	130	5	.	.	PUNCT
ejpam-3870	131	1	therefore	therefore	ADV
ejpam-3870	131	2	α	α	PROPN
ejpam-3870	131	3	is	be	AUX
ejpam-3870	131	4	not	not	PART
ejpam-3870	131	5	a	a	DET
ejpam-3870	131	6	function	function	NOUN
ejpam-3870	131	7	from	from	ADP
ejpam-3870	131	8	domβ	domβ	NOUN
ejpam-3870	132	1	=	=	PUNCT
ejpam-3870	132	2	x	x	SYM
ejpam-3870	132	3	onto	onto	ADP
ejpam-3870	132	4	x.	x.	NOUN
ejpam-3870	132	5	finally	finally	ADV
ejpam-3870	132	6	,	,	PUNCT
ejpam-3870	132	7	we	we	PRON
ejpam-3870	132	8	will	will	AUX
ejpam-3870	132	9	show	show	VERB
ejpam-3870	132	10	that	that	SCONJ
ejpam-3870	132	11	γ	γ	PROPN
ejpam-3870	132	12	is	be	AUX
ejpam-3870	132	13	not	not	PART
ejpam-3870	132	14	a	a	DET
ejpam-3870	132	15	one	one	NUM
ejpam-3870	132	16	-	-	PUNCT
ejpam-3870	132	17	to	to	ADP
ejpam-3870	132	18	-	-	PUNCT
ejpam-3870	132	19	one	one	NUM
ejpam-3870	132	20	function	function	NOUN
ejpam-3870	132	21	.	.	PUNCT
ejpam-3870	133	1	since	since	SCONJ
ejpam-3870	133	2	α	α	PROPN
ejpam-3870	133	3	is	be	AUX
ejpam-3870	133	4	not	not	PART
ejpam-3870	133	5	a	a	DET
ejpam-3870	133	6	function	function	NOUN
ejpam-3870	133	7	from	from	ADP
ejpam-3870	133	8	domβ	domβ	NOUN
ejpam-3870	133	9	onto	onto	ADP
ejpam-3870	133	10	x	x	PRON
ejpam-3870	133	11	,	,	PUNCT
ejpam-3870	133	12	there	there	PRON
ejpam-3870	133	13	exists	exist	VERB
ejpam-3870	133	14	x0	x0	PROPN
ejpam-3870	133	15	∈	∈	PROPN
ejpam-3870	133	16	domβ	domβ	NOUN
ejpam-3870	133	17	such	such	ADJ
ejpam-3870	133	18	that	that	ADV
ejpam-3870	133	19	|(x0)α|	|(x0)α|	NOUN
ejpam-3870	133	20	>	>	X
ejpam-3870	133	21	1	1	NUM
ejpam-3870	134	1	and	and	CCONJ
ejpam-3870	134	2	that	that	SCONJ
ejpam-3870	134	3	there	there	PRON
ejpam-3870	134	4	exist	exist	VERB
ejpam-3870	134	5	two	two	NUM
ejpam-3870	134	6	distinct	distinct	ADJ
ejpam-3870	134	7	elements	element	NOUN
ejpam-3870	134	8	u	u	NOUN
ejpam-3870	134	9	,	,	PUNCT
ejpam-3870	134	10	v	v	ADP
ejpam-3870	134	11	in	in	ADP
ejpam-3870	134	12	(	(	PUNCT
ejpam-3870	134	13	x0)α	x0)α	ADV
ejpam-3870	134	14	.	.	PUNCT
ejpam-3870	135	1	by	by	ADP
ejpam-3870	135	2	the	the	DET
ejpam-3870	135	3	definition	definition	NOUN
ejpam-3870	135	4	of	of	ADP
ejpam-3870	135	5	γ	γ	PROPN
ejpam-3870	135	6	,	,	PUNCT
ejpam-3870	135	7	we	we	PRON
ejpam-3870	135	8	have	have	VERB
ejpam-3870	135	9	(	(	PUNCT
ejpam-3870	135	10	u)γ	u)γ	NOUN
ejpam-3870	135	11	=	=	SYM
ejpam-3870	135	12	(	(	PUNCT
ejpam-3870	135	13	v)γ	v)γ	X
ejpam-3870	135	14	=	=	SYM
ejpam-3870	135	15	(	(	PUNCT
ejpam-3870	135	16	x0)β	x0)β	PROPN
ejpam-3870	135	17	.	.	PUNCT
ejpam-3870	136	1	therefore	therefore	ADV
ejpam-3870	136	2	γ	γ	PROPN
ejpam-3870	136	3	can	can	AUX
ejpam-3870	136	4	not	not	PART
ejpam-3870	136	5	be	be	AUX
ejpam-3870	136	6	a	a	DET
ejpam-3870	136	7	one	one	NUM
ejpam-3870	136	8	-	-	PUNCT
ejpam-3870	136	9	to	to	ADP
ejpam-3870	136	10	-	-	PUNCT
ejpam-3870	136	11	one	one	NUM
ejpam-3870	136	12	function	function	NOUN
ejpam-3870	136	13	.	.	PUNCT
ejpam-3870	137	1	hence	hence	ADV
ejpam-3870	137	2	γ	γ	X
ejpam-3870	137	3	∈m	∈m	NOUN
ejpam-3870	137	4	.	.	PUNCT
ejpam-3870	138	1	by	by	ADP
ejpam-3870	138	2	lemma	lemma	PROPN
ejpam-3870	138	3	3(iii	3(iii	NUM
ejpam-3870	138	4	)	)	PUNCT
ejpam-3870	138	5	,	,	PUNCT
ejpam-3870	138	6	we	we	PRON
ejpam-3870	138	7	obtain	obtain	VERB
ejpam-3870	138	8	dom(αγ	dom(αγ	NOUN
ejpam-3870	138	9	)	)	PUNCT
ejpam-3870	138	10	=	=	PUNCT
ejpam-3870	138	11	(	(	PUNCT
ejpam-3870	138	12	ranα	ranα	PROPN
ejpam-3870	138	13	∩	∩	ADJ
ejpam-3870	138	14	domγ)α−1	domγ)α−1	NUM
ejpam-3870	138	15	=	=	PUNCT
ejpam-3870	138	16	(	(	PUNCT
ejpam-3870	138	17	ranα	ranα	PROPN
ejpam-3870	138	18	∩	∩	NOUN
ejpam-3870	138	19	(	(	PUNCT
ejpam-3870	138	20	domβ)α)α−1	domβ)α)α−1	ADJ
ejpam-3870	138	21	=	=	SYM
ejpam-3870	138	22	(	(	PUNCT
ejpam-3870	138	23	(	(	PUNCT
ejpam-3870	138	24	domβ)α)α−1	domβ)α)α−1	ADJ
ejpam-3870	138	25	=	=	SYM
ejpam-3870	138	26	domβ	domβ	X
ejpam-3870	138	27	.	.	PUNCT
ejpam-3870	139	1	therefore	therefore	ADV
ejpam-3870	139	2	dom(αγ	dom(αγ	NOUN
ejpam-3870	139	3	)	)	PUNCT
ejpam-3870	139	4	=	=	SYM
ejpam-3870	139	5	domβ	domβ	PROPN
ejpam-3870	139	6	.	.	PUNCT
ejpam-3870	140	1	for	for	ADP
ejpam-3870	140	2	each	each	DET
ejpam-3870	140	3	x	x	SYM
ejpam-3870	140	4	∈	∈	NOUN
ejpam-3870	140	5	dom(αγ	dom(αγ	NOUN
ejpam-3870	140	6	)	)	PUNCT
ejpam-3870	140	7	,	,	PUNCT
ejpam-3870	140	8	we	we	PRON
ejpam-3870	140	9	have	have	VERB
ejpam-3870	140	10	(	(	PUNCT
ejpam-3870	140	11	x)(αγ	x)(αγ	NUM
ejpam-3870	140	12	)	)	PUNCT
ejpam-3870	140	13	=	=	SYM
ejpam-3870	140	14	(	(	PUNCT
ejpam-3870	140	15	(	(	PUNCT
ejpam-3870	140	16	x)α)γ	x)α)γ	X
ejpam-3870	140	17	=	=	SYM
ejpam-3870	140	18	(	(	PUNCT
ejpam-3870	140	19	x)β	x)β	PROPN
ejpam-3870	140	20	.	.	PUNCT
ejpam-3870	141	1	then	then	ADV
ejpam-3870	141	2	αγ	αγ	INTJ
ejpam-3870	141	3	=	=	SYM
ejpam-3870	141	4	β	β	X
ejpam-3870	141	5	,	,	PUNCT
ejpam-3870	141	6	and	and	CCONJ
ejpam-3870	141	7	as	as	ADP
ejpam-3870	141	8	a	a	DET
ejpam-3870	141	9	result	result	NOUN
ejpam-3870	141	10	,	,	PUNCT
ejpam-3870	141	11	αm	αm	NOUN
ejpam-3870	141	12	=	=	SYM
ejpam-3870	141	13	bx	bx	PROPN
ejpam-3870	141	14	.	.	PUNCT
ejpam-3870	142	1	hence	hence	ADV
ejpam-3870	142	2	the	the	DET
ejpam-3870	142	3	proof	proof	NOUN
ejpam-3870	142	4	is	be	AUX
ejpam-3870	142	5	complete	complete	ADJ
ejpam-3870	142	6	.	.	PUNCT
ejpam-3870	143	1	theorem	theorem	NOUN
ejpam-3870	143	2	1	1	NUM
ejpam-3870	143	3	.	.	PUNCT
ejpam-3870	144	1	let	let	VERB
ejpam-3870	144	2	α	α	PRON
ejpam-3870	144	3	∈	∈	PROPN
ejpam-3870	144	4	bx	bx	X
ejpam-3870	144	5	.	.	PUNCT
ejpam-3870	145	1	then	then	ADV
ejpam-3870	145	2	α	α	PROPN
ejpam-3870	145	3	is	be	AUX
ejpam-3870	145	4	a	a	DET
ejpam-3870	145	5	left	left	ADJ
ejpam-3870	145	6	magnifying	magnifying	ADJ
ejpam-3870	145	7	element	element	NOUN
ejpam-3870	145	8	of	of	ADP
ejpam-3870	145	9	bx	bx	PRON
ejpam-3870	145	10	if	if	SCONJ
ejpam-3870	145	11	and	and	CCONJ
ejpam-3870	145	12	only	only	ADV
ejpam-3870	145	13	if	if	SCONJ
ejpam-3870	145	14	(	(	PUNCT
ejpam-3870	145	15	i	i	NOUN
ejpam-3870	145	16	)	)	PUNCT
ejpam-3870	145	17	domα	domα	NOUN
ejpam-3870	145	18	=	=	PUNCT
ejpam-3870	145	19	x	x	X
ejpam-3870	145	20	,	,	PUNCT
ejpam-3870	145	21	(	(	PUNCT
ejpam-3870	145	22	ii	ii	NOUN
ejpam-3870	145	23	)	)	PUNCT
ejpam-3870	145	24	for	for	ADP
ejpam-3870	145	25	every	every	DET
ejpam-3870	145	26	x	x	PROPN
ejpam-3870	145	27	,	,	PUNCT
ejpam-3870	145	28	y	y	PROPN
ejpam-3870	145	29	∈	∈	PROPN
ejpam-3870	145	30	domα	domα	NOUN
ejpam-3870	145	31	,	,	PUNCT
ejpam-3870	145	32	(	(	PUNCT
ejpam-3870	145	33	x)α	x)α	X
ejpam-3870	145	34	∩	∩	NOUN
ejpam-3870	145	35	(	(	PUNCT
ejpam-3870	145	36	y)α	y)α	NOUN
ejpam-3870	145	37	6=	6=	PRON
ejpam-3870	145	38	∅	∅	NOUN
ejpam-3870	145	39	implies	imply	VERB
ejpam-3870	145	40	x	x	PUNCT
ejpam-3870	145	41	=	=	SYM
ejpam-3870	145	42	y	y	PROPN
ejpam-3870	145	43	,	,	PUNCT
ejpam-3870	145	44	and	and	CCONJ
ejpam-3870	145	45	(	(	PUNCT
ejpam-3870	145	46	iii	iii	X
ejpam-3870	145	47	)	)	PUNCT
ejpam-3870	145	48	α	α	NOUN
ejpam-3870	145	49	is	be	AUX
ejpam-3870	145	50	not	not	PART
ejpam-3870	145	51	a	a	DET
ejpam-3870	145	52	bijective	bijective	ADJ
ejpam-3870	145	53	function	function	NOUN
ejpam-3870	145	54	on	on	ADP
ejpam-3870	145	55	x.	x.	PROPN
ejpam-3870	145	56	w.	w.	PROPN
ejpam-3870	145	57	teparos	teparos	PROPN
ejpam-3870	145	58	,	,	PUNCT
ejpam-3870	145	59	s.	s.	PROPN
ejpam-3870	145	60	boonta	boonta	PROPN
ejpam-3870	145	61	,	,	PUNCT
ejpam-3870	145	62	t.	t.	PROPN
ejpam-3870	145	63	theparod	theparod	PROPN
ejpam-3870	145	64	/	/	SYM
ejpam-3870	145	65	eur	eur	PROPN
ejpam-3870	145	66	.	.	PUNCT
ejpam-3870	146	1	j.	j.	PROPN
ejpam-3870	146	2	pure	pure	PROPN
ejpam-3870	146	3	appl	appl	PROPN
ejpam-3870	146	4	.	.	PROPN
ejpam-3870	146	5	math	math	PROPN
ejpam-3870	146	6	,	,	PUNCT
ejpam-3870	146	7	13	13	NUM
ejpam-3870	146	8	(	(	PUNCT
ejpam-3870	146	9	4	4	NUM
ejpam-3870	146	10	)	)	PUNCT
ejpam-3870	146	11	(	(	PUNCT
ejpam-3870	146	12	2020	2020	NUM
ejpam-3870	146	13	)	)	PUNCT
ejpam-3870	146	14	,	,	PUNCT
ejpam-3870	146	15	987	987	NUM
ejpam-3870	146	16	-	-	SYM
ejpam-3870	146	17	994	994	NUM
ejpam-3870	146	18	991	991	NUM
ejpam-3870	146	19	proof	proof	NOUN
ejpam-3870	146	20	.	.	PUNCT
ejpam-3870	147	1	it	it	PRON
ejpam-3870	147	2	follows	follow	VERB
ejpam-3870	147	3	from	from	ADP
ejpam-3870	147	4	lemma	lemma	PROPN
ejpam-3870	147	5	4	4	NUM
ejpam-3870	147	6	,	,	PUNCT
ejpam-3870	147	7	lemma	lemma	PROPN
ejpam-3870	147	8	6	6	NUM
ejpam-3870	147	9	and	and	CCONJ
ejpam-3870	147	10	lemma	lemma	PROPN
ejpam-3870	147	11	7	7	PROPN
ejpam-3870	147	12	.	.	NOUN
ejpam-3870	147	13	example	example	NOUN
ejpam-3870	148	1	1	1	NUM
ejpam-3870	148	2	.	.	PUNCT
ejpam-3870	149	1	let	let	VERB
ejpam-3870	149	2	x	x	SYM
ejpam-3870	149	3	=	=	PUNCT
ejpam-3870	149	4	n	n	PROPN
ejpam-3870	149	5	and	and	CCONJ
ejpam-3870	149	6	α	α	PROPN
ejpam-3870	149	7	∈	∈	PROPN
ejpam-3870	149	8	bx	bx	NOUN
ejpam-3870	149	9	defined	define	VERB
ejpam-3870	149	10	by	by	ADP
ejpam-3870	149	11	(	(	PUNCT
ejpam-3870	149	12	x)α	x)α	NOUN
ejpam-3870	149	13	=	=	SYM
ejpam-3870	149	14	{	{	PUNCT
ejpam-3870	149	15	2x	2x	NUM
ejpam-3870	149	16	,	,	PUNCT
ejpam-3870	149	17	3x	3x	NUM
ejpam-3870	149	18	}	}	PUNCT
ejpam-3870	149	19	for	for	ADP
ejpam-3870	149	20	all	all	PRON
ejpam-3870	149	21	x	x	SYM
ejpam-3870	149	22	∈	∈	NOUN
ejpam-3870	149	23	x.	x.	NOUN
ejpam-3870	149	24	following	follow	VERB
ejpam-3870	149	25	the	the	DET
ejpam-3870	149	26	assumption	assumption	NOUN
ejpam-3870	149	27	we	we	PRON
ejpam-3870	149	28	have	have	VERB
ejpam-3870	149	29	domα	domα	NOUN
ejpam-3870	149	30	=	=	SYM
ejpam-3870	149	31	x	x	NOUN
ejpam-3870	149	32	,	,	PUNCT
ejpam-3870	149	33	for	for	ADP
ejpam-3870	149	34	every	every	DET
ejpam-3870	149	35	x	x	NOUN
ejpam-3870	149	36	,	,	PUNCT
ejpam-3870	149	37	y	y	PROPN
ejpam-3870	149	38	∈	∈	PROPN
ejpam-3870	149	39	x	x	PUNCT
ejpam-3870	149	40	such	such	ADJ
ejpam-3870	149	41	that	that	SCONJ
ejpam-3870	149	42	x	x	PROPN
ejpam-3870	149	43	6=	6=	PROPN
ejpam-3870	149	44	y	y	PROPN
ejpam-3870	149	45	,	,	PUNCT
ejpam-3870	149	46	(	(	PUNCT
ejpam-3870	149	47	x)α	x)α	X
ejpam-3870	149	48	∩	∩	NOUN
ejpam-3870	149	49	(	(	PUNCT
ejpam-3870	149	50	y)α	y)α	NOUN
ejpam-3870	149	51	=	=	SYM
ejpam-3870	149	52	∅	∅	NOUN
ejpam-3870	149	53	and	and	CCONJ
ejpam-3870	149	54	α	α	NOUN
ejpam-3870	149	55	is	be	AUX
ejpam-3870	149	56	not	not	PART
ejpam-3870	149	57	a	a	DET
ejpam-3870	149	58	function	function	NOUN
ejpam-3870	149	59	.	.	PUNCT
ejpam-3870	150	1	so	so	ADV
ejpam-3870	150	2	that	that	SCONJ
ejpam-3870	150	3	α	α	PRON
ejpam-3870	150	4	is	be	AUX
ejpam-3870	150	5	not	not	PART
ejpam-3870	150	6	a	a	DET
ejpam-3870	150	7	bijective	bijective	NOUN
ejpam-3870	150	8	on	on	ADP
ejpam-3870	150	9	x.	x.	NOUN
ejpam-3870	150	10	let	let	VERB
ejpam-3870	150	11	m	m	VERB
ejpam-3870	150	12	=	=	PRON
ejpam-3870	150	13	{	{	PUNCT
ejpam-3870	150	14	h	h	NOUN
ejpam-3870	150	15	∈	∈	PROPN
ejpam-3870	150	16	bx	bx	PROPN
ejpam-3870	150	17	|	|	ADV
ejpam-3870	150	18	domh	domh	PROPN
ejpam-3870	150	19	6=	6=	ADP
ejpam-3870	151	1	x	x	NOUN
ejpam-3870	151	2	or	or	CCONJ
ejpam-3870	151	3	h	h	NOUN
ejpam-3870	151	4	is	be	AUX
ejpam-3870	151	5	not	not	PART
ejpam-3870	151	6	a	a	DET
ejpam-3870	151	7	one	one	NUM
ejpam-3870	151	8	-	-	PUNCT
ejpam-3870	151	9	to	to	ADP
ejpam-3870	151	10	-	-	PUNCT
ejpam-3870	151	11	one	one	NUM
ejpam-3870	151	12	function	function	NOUN
ejpam-3870	151	13	}	}	PUNCT
ejpam-3870	151	14	.	.	PUNCT
ejpam-3870	152	1	let	let	VERB
ejpam-3870	152	2	β	β	PRON
ejpam-3870	152	3	be	be	AUX
ejpam-3870	152	4	any	any	DET
ejpam-3870	152	5	relation	relation	NOUN
ejpam-3870	152	6	in	in	ADP
ejpam-3870	152	7	bx	bx	PROPN
ejpam-3870	152	8	.	.	PUNCT
ejpam-3870	153	1	by	by	ADP
ejpam-3870	153	2	lemma	lemma	PROPN
ejpam-3870	153	3	7	7	NUM
ejpam-3870	153	4	,	,	PUNCT
ejpam-3870	153	5	we	we	PRON
ejpam-3870	153	6	can	can	AUX
ejpam-3870	153	7	define	define	VERB
ejpam-3870	153	8	a	a	DET
ejpam-3870	153	9	relation	relation	NOUN
ejpam-3870	153	10	γ	γ	X
ejpam-3870	153	11	∈	∈	PROPN
ejpam-3870	153	12	bx	bx	NOUN
ejpam-3870	153	13	such	such	ADJ
ejpam-3870	153	14	that	that	SCONJ
ejpam-3870	153	15	γ	γ	PROPN
ejpam-3870	153	16	∈	∈	PROPN
ejpam-3870	153	17	m	m	NOUN
ejpam-3870	153	18	and	and	CCONJ
ejpam-3870	153	19	γα	γα	X
ejpam-3870	153	20	=	=	NOUN
ejpam-3870	153	21	β	β	X
ejpam-3870	153	22	.	.	PUNCT
ejpam-3870	153	23	for	for	ADP
ejpam-3870	153	24	example	example	NOUN
ejpam-3870	153	25	,	,	PUNCT
ejpam-3870	153	26	if	if	SCONJ
ejpam-3870	153	27	β	β	X
ejpam-3870	153	28	is	be	AUX
ejpam-3870	153	29	a	a	DET
ejpam-3870	153	30	relation	relation	NOUN
ejpam-3870	153	31	in	in	ADP
ejpam-3870	153	32	bx	bx	NOUN
ejpam-3870	153	33	such	such	ADJ
ejpam-3870	153	34	that	that	PRON
ejpam-3870	153	35	(	(	PUNCT
ejpam-3870	153	36	x)β	x)β	NOUN
ejpam-3870	153	37	=	=	SYM
ejpam-3870	153	38	{	{	PUNCT
ejpam-3870	153	39	2x	2x	NUM
ejpam-3870	153	40	}	}	PUNCT
ejpam-3870	153	41	for	for	ADP
ejpam-3870	153	42	all	all	DET
ejpam-3870	153	43	odd	odd	ADJ
ejpam-3870	153	44	integer	integer	NOUN
ejpam-3870	153	45	x.	x.	NOUN
ejpam-3870	153	46	thus	thus	ADV
ejpam-3870	153	47	domβ	domβ	X
ejpam-3870	154	1	=	=	PUNCT
ejpam-3870	154	2	{	{	PUNCT
ejpam-3870	154	3	x	x	SYM
ejpam-3870	154	4	∈	∈	PROPN
ejpam-3870	154	5	n	n	PRON
ejpam-3870	154	6	|	|	ADV
ejpam-3870	154	7	x	x	INTJ
ejpam-3870	154	8	is	be	AUX
ejpam-3870	154	9	odd	odd	ADJ
ejpam-3870	154	10	}	}	PUNCT
ejpam-3870	154	11	.	.	PUNCT
ejpam-3870	155	1	so	so	ADV
ejpam-3870	155	2	(	(	PUNCT
ejpam-3870	155	3	domβ)α	domβ)α	X
ejpam-3870	155	4	=	=	PUNCT
ejpam-3870	155	5	{	{	PUNCT
ejpam-3870	155	6	2x	2x	NUM
ejpam-3870	155	7	|	|	ADV
ejpam-3870	155	8	x	x	INTJ
ejpam-3870	155	9	is	be	AUX
ejpam-3870	155	10	odd	odd	ADJ
ejpam-3870	155	11	}	}	PUNCT
ejpam-3870	155	12	∪	∪	X
ejpam-3870	155	13	{	{	PUNCT
ejpam-3870	155	14	3x	3x	NUM
ejpam-3870	155	15	|	|	ADV
ejpam-3870	155	16	x	x	PROPN
ejpam-3870	155	17	is	be	AUX
ejpam-3870	155	18	odd	odd	ADJ
ejpam-3870	155	19	}	}	PUNCT
ejpam-3870	155	20	.	.	PUNCT
ejpam-3870	156	1	define	define	VERB
ejpam-3870	156	2	a	a	DET
ejpam-3870	156	3	relation	relation	NOUN
ejpam-3870	156	4	γ	γ	NOUN
ejpam-3870	156	5	in	in	ADP
ejpam-3870	156	6	bx	bx	PROPN
ejpam-3870	156	7	by	by	ADP
ejpam-3870	156	8	(	(	PUNCT
ejpam-3870	156	9	x)γ	x)γ	PUNCT
ejpam-3870	156	10	=	=	SYM
ejpam-3870	156	11	(	(	PUNCT
ejpam-3870	156	12	y)β	y)β	VERB
ejpam-3870	156	13	if	if	SCONJ
ejpam-3870	156	14	x	x	X
ejpam-3870	156	15	=	=	NOUN
ejpam-3870	156	16	2y	2y	NUM
ejpam-3870	156	17	or	or	CCONJ
ejpam-3870	156	18	x	x	X
ejpam-3870	156	19	=	=	SYM
ejpam-3870	156	20	3y	3y	NUM
ejpam-3870	156	21	for	for	ADP
ejpam-3870	156	22	some	some	DET
ejpam-3870	156	23	odd	odd	ADJ
ejpam-3870	156	24	integer	integer	NOUN
ejpam-3870	156	25	y.	y.	NOUN
ejpam-3870	156	26	thus	thus	ADV
ejpam-3870	156	27	domγ	domγ	NOUN
ejpam-3870	156	28	=	=	SYM
ejpam-3870	156	29	{	{	PUNCT
ejpam-3870	156	30	2x	2x	NUM
ejpam-3870	156	31	|	|	ADV
ejpam-3870	156	32	x	x	ADP
ejpam-3870	156	33	is	be	AUX
ejpam-3870	156	34	odd}∪{3x	odd}∪{3x	NOUN
ejpam-3870	156	35	|	|	ADV
ejpam-3870	156	36	x	x	VERB
ejpam-3870	156	37	is	be	AUX
ejpam-3870	156	38	odd	odd	ADJ
ejpam-3870	156	39	}	}	PUNCT
ejpam-3870	156	40	6=	6=	ADP
ejpam-3870	156	41	x	x	SYM
ejpam-3870	156	42	and	and	CCONJ
ejpam-3870	156	43	domγ	domγ	NOUN
ejpam-3870	156	44	=	=	SYM
ejpam-3870	156	45	{	{	PUNCT
ejpam-3870	156	46	2x	2x	NUM
ejpam-3870	156	47	|	|	ADV
ejpam-3870	156	48	x	x	ADP
ejpam-3870	156	49	is	be	AUX
ejpam-3870	156	50	odd}∪{3x	odd}∪{3x	NOUN
ejpam-3870	157	1	|	|	ADV
ejpam-3870	157	2	x	x	VERB
ejpam-3870	157	3	is	be	AUX
ejpam-3870	157	4	odd	odd	ADJ
ejpam-3870	157	5	}	}	PUNCT
ejpam-3870	157	6	⊆	⊆	NUM
ejpam-3870	157	7	ranα	ranα	NOUN
ejpam-3870	157	8	.	.	PUNCT
ejpam-3870	158	1	we	we	PRON
ejpam-3870	158	2	have	have	VERB
ejpam-3870	158	3	dom(αγ	dom(αγ	NOUN
ejpam-3870	158	4	)	)	PUNCT
ejpam-3870	158	5	=	=	PUNCT
ejpam-3870	158	6	(	(	PUNCT
ejpam-3870	158	7	ranα	ranα	PROPN
ejpam-3870	158	8	∩	∩	ADJ
ejpam-3870	158	9	domγ)α−1	domγ)α−1	NUM
ejpam-3870	158	10	=	=	SYM
ejpam-3870	158	11	(	(	PUNCT
ejpam-3870	158	12	domγ)α−1	domγ)α−1	NUM
ejpam-3870	158	13	=	=	SYM
ejpam-3870	158	14	(	(	PUNCT
ejpam-3870	158	15	{	{	PUNCT
ejpam-3870	158	16	2x	2x	NUM
ejpam-3870	158	17	|	|	ADV
ejpam-3870	158	18	x	x	INTJ
ejpam-3870	158	19	is	be	AUX
ejpam-3870	158	20	odd	odd	ADJ
ejpam-3870	158	21	}	}	PUNCT
ejpam-3870	158	22	∪	∪	X
ejpam-3870	158	23	{	{	PUNCT
ejpam-3870	158	24	3x	3x	NUM
ejpam-3870	158	25	|	|	ADV
ejpam-3870	158	26	x	x	X
ejpam-3870	158	27	is	be	AUX
ejpam-3870	158	28	odd})α−1	odd})α−1	NOUN
ejpam-3870	158	29	=	=	SYM
ejpam-3870	158	30	{	{	PUNCT
ejpam-3870	158	31	x	x	SYM
ejpam-3870	158	32	∈	∈	PROPN
ejpam-3870	158	33	n	n	PRON
ejpam-3870	159	1	|	|	ADV
ejpam-3870	159	2	x	x	INTJ
ejpam-3870	159	3	is	be	AUX
ejpam-3870	159	4	odd	odd	ADJ
ejpam-3870	159	5	}	}	PUNCT
ejpam-3870	159	6	=	=	SYM
ejpam-3870	159	7	domβ	domβ	PROPN
ejpam-3870	159	8	.	.	PUNCT
ejpam-3870	160	1	that	that	PRON
ejpam-3870	160	2	is	be	AUX
ejpam-3870	160	3	,	,	PUNCT
ejpam-3870	160	4	dom(αγ	dom(αγ	NOUN
ejpam-3870	160	5	)	)	PUNCT
ejpam-3870	160	6	=	=	SYM
ejpam-3870	160	7	domβ	domβ	PROPN
ejpam-3870	160	8	.	.	PUNCT
ejpam-3870	161	1	for	for	ADP
ejpam-3870	161	2	each	each	PRON
ejpam-3870	161	3	an	an	DET
ejpam-3870	161	4	odd	odd	ADJ
ejpam-3870	161	5	integer	integer	NOUN
ejpam-3870	161	6	x	x	X
ejpam-3870	161	7	,	,	PUNCT
ejpam-3870	161	8	(	(	PUNCT
ejpam-3870	161	9	x)(αγ	x)(αγ	PROPN
ejpam-3870	161	10	)	)	PUNCT
ejpam-3870	161	11	=	=	SYM
ejpam-3870	161	12	(	(	PUNCT
ejpam-3870	161	13	(	(	PUNCT
ejpam-3870	161	14	x)α)γ	x)α)γ	X
ejpam-3870	161	15	=	=	SYM
ejpam-3870	161	16	(	(	PUNCT
ejpam-3870	161	17	{	{	PUNCT
ejpam-3870	161	18	2x	2x	NUM
ejpam-3870	161	19	,	,	PUNCT
ejpam-3870	161	20	3x	3x	NUM
ejpam-3870	161	21	}	}	PUNCT
ejpam-3870	161	22	)	)	PUNCT
ejpam-3870	161	23	γ	γ	X
ejpam-3870	161	24	=	=	SYM
ejpam-3870	161	25	(	(	PUNCT
ejpam-3870	161	26	x)β	x)β	X
ejpam-3870	161	27	∪	∪	X
ejpam-3870	161	28	(	(	PUNCT
ejpam-3870	161	29	x)β	x)β	NOUN
ejpam-3870	161	30	=	=	SYM
ejpam-3870	161	31	(	(	PUNCT
ejpam-3870	161	32	x)β	x)β	PROPN
ejpam-3870	161	33	.	.	PUNCT
ejpam-3870	161	34	therefore	therefore	ADV
ejpam-3870	161	35	αγ	αγ	PROPN
ejpam-3870	161	36	=	=	SYM
ejpam-3870	161	37	β	β	X
ejpam-3870	161	38	.	.	NOUN
ejpam-3870	162	1	3	3	X
ejpam-3870	162	2	.	.	X
ejpam-3870	162	3	right	right	ADJ
ejpam-3870	162	4	magnifying	magnify	VERB
ejpam-3870	162	5	elements	element	NOUN
ejpam-3870	162	6	of	of	ADP
ejpam-3870	162	7	bx	bx	PROPN
ejpam-3870	162	8	lemma	lemma	PROPN
ejpam-3870	162	9	8	8	NUM
ejpam-3870	162	10	.	.	PUNCT
ejpam-3870	163	1	if	if	SCONJ
ejpam-3870	163	2	α	α	PRON
ejpam-3870	163	3	is	be	AUX
ejpam-3870	163	4	a	a	DET
ejpam-3870	163	5	right	right	ADJ
ejpam-3870	163	6	magnifying	magnify	VERB
ejpam-3870	163	7	element	element	NOUN
ejpam-3870	163	8	of	of	ADP
ejpam-3870	163	9	bx	bx	PROPN
ejpam-3870	163	10	,	,	PUNCT
ejpam-3870	163	11	then	then	ADV
ejpam-3870	163	12	there	there	PRON
ejpam-3870	163	13	exists	exist	VERB
ejpam-3870	163	14	a	a	DET
ejpam-3870	163	15	subset	subset	NOUN
ejpam-3870	163	16	a	a	PRON
ejpam-3870	163	17	of	of	ADP
ejpam-3870	163	18	x	x	SYM
ejpam-3870	163	19	such	such	ADJ
ejpam-3870	163	20	that	that	SCONJ
ejpam-3870	163	21	α|a	α|a	NOUN
ejpam-3870	163	22	is	be	AUX
ejpam-3870	163	23	an	an	PRON
ejpam-3870	163	24	onto	onto	ADP
ejpam-3870	163	25	function	function	NOUN
ejpam-3870	163	26	from	from	ADP
ejpam-3870	163	27	a	a	DET
ejpam-3870	163	28	to	to	NOUN
ejpam-3870	163	29	x.	x.	NOUN
ejpam-3870	163	30	proof	proof	NOUN
ejpam-3870	163	31	.	.	PUNCT
ejpam-3870	164	1	assume	assume	VERB
ejpam-3870	164	2	that	that	SCONJ
ejpam-3870	164	3	α	α	PRON
ejpam-3870	164	4	is	be	AUX
ejpam-3870	164	5	a	a	DET
ejpam-3870	164	6	right	right	ADJ
ejpam-3870	164	7	magnifying	magnify	VERB
ejpam-3870	164	8	element	element	NOUN
ejpam-3870	164	9	of	of	ADP
ejpam-3870	164	10	bx	bx	PROPN
ejpam-3870	164	11	.	.	PUNCT
ejpam-3870	165	1	then	then	ADV
ejpam-3870	165	2	there	there	PRON
ejpam-3870	165	3	exists	exist	VERB
ejpam-3870	165	4	a	a	DET
ejpam-3870	165	5	proper	proper	ADJ
ejpam-3870	165	6	subset	subset	NOUN
ejpam-3870	165	7	m	m	NOUN
ejpam-3870	165	8	of	of	ADP
ejpam-3870	165	9	bx	bx	PRON
ejpam-3870	165	10	such	such	ADJ
ejpam-3870	165	11	that	that	PRON
ejpam-3870	165	12	mα	mα	PROPN
ejpam-3870	165	13	=	=	NOUN
ejpam-3870	165	14	bx	bx	PROPN
ejpam-3870	165	15	.	.	PUNCT
ejpam-3870	166	1	since	since	SCONJ
ejpam-3870	166	2	ix	ix	PROPN
ejpam-3870	166	3	∈	∈	PROPN
ejpam-3870	166	4	bx	bx	NOUN
ejpam-3870	166	5	,	,	PUNCT
ejpam-3870	166	6	then	then	ADV
ejpam-3870	166	7	there	there	PRON
ejpam-3870	166	8	exists	exist	VERB
ejpam-3870	166	9	γ	γ	NOUN
ejpam-3870	166	10	∈m	∈m	NOUN
ejpam-3870	166	11	such	such	ADJ
ejpam-3870	166	12	that	that	SCONJ
ejpam-3870	166	13	γα	γα	ADP
ejpam-3870	166	14	=	=	X
ejpam-3870	166	15	ix	ix	ADJ
ejpam-3870	166	16	.	.	PUNCT
ejpam-3870	167	1	it	it	PRON
ejpam-3870	167	2	is	be	AUX
ejpam-3870	167	3	clear	clear	ADJ
ejpam-3870	167	4	that	that	PRON
ejpam-3870	167	5	ranγ	ranγ	VERB
ejpam-3870	167	6	∩domα	∩domα	PROPN
ejpam-3870	167	7	6=	6=	ADP
ejpam-3870	167	8	∅.	∅.	PRON
ejpam-3870	167	9	we	we	PRON
ejpam-3870	167	10	put	put	VERB
ejpam-3870	167	11	a	a	DET
ejpam-3870	167	12	:	:	PUNCT
ejpam-3870	167	13	=	=	NOUN
ejpam-3870	167	14	ranγ	ranγ	PROPN
ejpam-3870	167	15	∩domα	∩domα	PROPN
ejpam-3870	167	16	.	.	PUNCT
ejpam-3870	168	1	first	first	ADV
ejpam-3870	168	2	,	,	PUNCT
ejpam-3870	168	3	we	we	PRON
ejpam-3870	168	4	will	will	AUX
ejpam-3870	168	5	show	show	VERB
ejpam-3870	168	6	that	that	SCONJ
ejpam-3870	168	7	α|a	α|a	PROPN
ejpam-3870	168	8	is	be	AUX
ejpam-3870	168	9	a	a	DET
ejpam-3870	168	10	function	function	NOUN
ejpam-3870	168	11	from	from	ADP
ejpam-3870	168	12	a	a	DET
ejpam-3870	168	13	to	to	NOUN
ejpam-3870	168	14	x.	x.	NOUN
ejpam-3870	168	15	let	let	VERB
ejpam-3870	168	16	x	x	PUNCT
ejpam-3870	168	17	∈	∈	VERB
ejpam-3870	168	18	a.	a.	NOUN
ejpam-3870	168	19	then	then	ADV
ejpam-3870	168	20	there	there	PRON
ejpam-3870	168	21	exists	exist	VERB
ejpam-3870	168	22	u	u	PROPN
ejpam-3870	168	23	∈	∈	PROPN
ejpam-3870	168	24	domγ	domγ	NOUN
ejpam-3870	168	25	such	such	ADJ
ejpam-3870	168	26	that	that	SCONJ
ejpam-3870	168	27	x	x	SYM
ejpam-3870	168	28	∈	∈	PROPN
ejpam-3870	168	29	(	(	PUNCT
ejpam-3870	168	30	u)γ	u)γ	NOUN
ejpam-3870	168	31	.	.	PUNCT
ejpam-3870	169	1	therefore	therefore	ADV
ejpam-3870	169	2	(	(	PUNCT
ejpam-3870	169	3	x)α	x)α	NOUN
ejpam-3870	169	4	⊆	⊆	X
ejpam-3870	169	5	(	(	PUNCT
ejpam-3870	169	6	(	(	PUNCT
ejpam-3870	169	7	u)γ)α	u)γ)α	NOUN
ejpam-3870	169	8	=	=	SYM
ejpam-3870	169	9	(	(	PUNCT
ejpam-3870	169	10	u)(γα	u)(γα	NOUN
ejpam-3870	169	11	)	)	PUNCT
ejpam-3870	169	12	=	=	NOUN
ejpam-3870	169	13	(	(	PUNCT
ejpam-3870	169	14	u)ix	u)ix	PROPN
ejpam-3870	169	15	=	=	SYM
ejpam-3870	169	16	{	{	PUNCT
ejpam-3870	169	17	u	u	NOUN
ejpam-3870	169	18	}	}	PUNCT
ejpam-3870	169	19	.	.	PUNCT
ejpam-3870	170	1	thus	thus	ADV
ejpam-3870	170	2	|(x)α|	|(x)α|	PROPN
ejpam-3870	170	3	=	=	PUNCT
ejpam-3870	170	4	1	1	X
ejpam-3870	170	5	.	.	PUNCT
ejpam-3870	170	6	as	as	ADP
ejpam-3870	170	7	a	a	DET
ejpam-3870	170	8	result	result	NOUN
ejpam-3870	170	9	,	,	PUNCT
ejpam-3870	170	10	α|a	α|a	PROPN
ejpam-3870	170	11	is	be	AUX
ejpam-3870	170	12	a	a	DET
ejpam-3870	170	13	function	function	NOUN
ejpam-3870	170	14	from	from	ADP
ejpam-3870	170	15	a	a	DET
ejpam-3870	170	16	to	to	ADP
ejpam-3870	170	17	x.	x.	NOUN
ejpam-3870	170	18	next	next	ADV
ejpam-3870	170	19	,	,	PUNCT
ejpam-3870	170	20	we	we	PRON
ejpam-3870	170	21	will	will	AUX
ejpam-3870	170	22	show	show	VERB
ejpam-3870	170	23	that	that	SCONJ
ejpam-3870	170	24	α|a	α|a	PROPN
ejpam-3870	170	25	is	be	AUX
ejpam-3870	170	26	onto	onto	ADP
ejpam-3870	170	27	.	.	PUNCT
ejpam-3870	171	1	let	let	VERB
ejpam-3870	171	2	y	y	PROPN
ejpam-3870	171	3	∈	∈	PROPN
ejpam-3870	171	4	x.	x.	NOUN
ejpam-3870	172	1	then	then	ADV
ejpam-3870	172	2	y	y	PROPN
ejpam-3870	172	3	∈	∈	PROPN
ejpam-3870	172	4	ran(ix	ran(ix	NOUN
ejpam-3870	172	5	)	)	PUNCT
ejpam-3870	172	6	=	=	SYM
ejpam-3870	172	7	ran(γα	ran(γα	NOUN
ejpam-3870	172	8	)	)	PUNCT
ejpam-3870	172	9	,	,	PUNCT
ejpam-3870	172	10	giving	give	VERB
ejpam-3870	172	11	that	that	SCONJ
ejpam-3870	172	12	there	there	PRON
ejpam-3870	172	13	exists	exist	VERB
ejpam-3870	172	14	v	v	ADP
ejpam-3870	172	15	∈	∈	PROPN
ejpam-3870	172	16	dom(γα	dom(γα	NOUN
ejpam-3870	172	17	)	)	PUNCT
ejpam-3870	172	18	such	such	ADJ
ejpam-3870	172	19	that	that	SCONJ
ejpam-3870	172	20	y	y	PROPN
ejpam-3870	172	21	∈	∈	PROPN
ejpam-3870	172	22	(	(	PUNCT
ejpam-3870	172	23	v)(γα	v)(γα	X
ejpam-3870	172	24	)	)	PUNCT
ejpam-3870	172	25	=	=	SYM
ejpam-3870	172	26	(	(	PUNCT
ejpam-3870	172	27	(	(	PUNCT
ejpam-3870	172	28	v)γ)α	v)γ)α	NOUN
ejpam-3870	172	29	.	.	PUNCT
ejpam-3870	173	1	we	we	PRON
ejpam-3870	173	2	have	have	VERB
ejpam-3870	173	3	y	y	PROPN
ejpam-3870	173	4	∈	∈	PROPN
ejpam-3870	173	5	(	(	PUNCT
ejpam-3870	173	6	(	(	PUNCT
ejpam-3870	173	7	v)γ)α	v)γ)α	ADV
ejpam-3870	173	8	when	when	SCONJ
ejpam-3870	173	9	(	(	PUNCT
ejpam-3870	173	10	v)γ	v)γ	X
ejpam-3870	173	11	∈	∈	PROPN
ejpam-3870	173	12	(	(	PUNCT
ejpam-3870	173	13	ranγ	ranγ	X
ejpam-3870	173	14	∩	∩	ADJ
ejpam-3870	173	15	domα	domα	NOUN
ejpam-3870	173	16	)	)	PUNCT
ejpam-3870	173	17	.	.	PUNCT
ejpam-3870	174	1	this	this	PRON
ejpam-3870	174	2	leads	lead	VERB
ejpam-3870	174	3	us	we	PRON
ejpam-3870	174	4	to	to	ADP
ejpam-3870	174	5	a	a	DET
ejpam-3870	174	6	conclusion	conclusion	NOUN
ejpam-3870	174	7	that	that	SCONJ
ejpam-3870	174	8	α|a	α|a	PROPN
ejpam-3870	174	9	is	be	AUX
ejpam-3870	174	10	onto	onto	ADP
ejpam-3870	174	11	.	.	PUNCT
ejpam-3870	175	1	the	the	DET
ejpam-3870	175	2	proof	proof	NOUN
ejpam-3870	175	3	of	of	ADP
ejpam-3870	175	4	the	the	DET
ejpam-3870	175	5	following	follow	VERB
ejpam-3870	175	6	lemma	lemma	PROPN
ejpam-3870	175	7	is	be	AUX
ejpam-3870	175	8	done	do	VERB
ejpam-3870	175	9	similarly	similarly	ADV
ejpam-3870	175	10	to	to	ADP
ejpam-3870	175	11	[	[	X
ejpam-3870	175	12	9	9	NUM
ejpam-3870	175	13	,	,	PUNCT
ejpam-3870	175	14	lemma	lemma	PROPN
ejpam-3870	175	15	5	5	NUM
ejpam-3870	175	16	.	.	NUM
ejpam-3870	175	17	]	]	PUNCT
ejpam-3870	175	18	.	.	PUNCT
ejpam-3870	176	1	w.	w.	PROPN
ejpam-3870	176	2	teparos	teparos	PROPN
ejpam-3870	176	3	,	,	PUNCT
ejpam-3870	176	4	s.	s.	PROPN
ejpam-3870	176	5	boonta	boonta	PROPN
ejpam-3870	176	6	,	,	PUNCT
ejpam-3870	176	7	t.	t.	PROPN
ejpam-3870	176	8	theparod	theparod	PROPN
ejpam-3870	176	9	/	/	SYM
ejpam-3870	176	10	eur	eur	PROPN
ejpam-3870	176	11	.	.	PUNCT
ejpam-3870	177	1	j.	j.	PROPN
ejpam-3870	177	2	pure	pure	PROPN
ejpam-3870	177	3	appl	appl	PROPN
ejpam-3870	177	4	.	.	PROPN
ejpam-3870	177	5	math	math	PROPN
ejpam-3870	177	6	,	,	PUNCT
ejpam-3870	177	7	13	13	NUM
ejpam-3870	177	8	(	(	PUNCT
ejpam-3870	177	9	4	4	NUM
ejpam-3870	177	10	)	)	PUNCT
ejpam-3870	177	11	(	(	PUNCT
ejpam-3870	177	12	2020	2020	NUM
ejpam-3870	177	13	)	)	PUNCT
ejpam-3870	177	14	,	,	PUNCT
ejpam-3870	177	15	987	987	NUM
ejpam-3870	177	16	-	-	SYM
ejpam-3870	177	17	994	994	NUM
ejpam-3870	177	18	992	992	NUM
ejpam-3870	177	19	lemma	lemma	PROPN
ejpam-3870	177	20	9	9	NUM
ejpam-3870	177	21	.	.	PUNCT
ejpam-3870	178	1	if	if	SCONJ
ejpam-3870	178	2	α	α	PROPN
ejpam-3870	178	3	∈	∈	PROPN
ejpam-3870	178	4	bx	bx	PROPN
ejpam-3870	178	5	is	be	AUX
ejpam-3870	178	6	bijective	bijective	ADJ
ejpam-3870	178	7	,	,	PUNCT
ejpam-3870	178	8	then	then	ADV
ejpam-3870	178	9	α	α	PROPN
ejpam-3870	178	10	is	be	AUX
ejpam-3870	178	11	not	not	PART
ejpam-3870	178	12	a	a	DET
ejpam-3870	178	13	right	right	ADJ
ejpam-3870	178	14	magnifying	magnify	VERB
ejpam-3870	178	15	element	element	NOUN
ejpam-3870	178	16	.	.	PUNCT
ejpam-3870	179	1	proof	proof	NOUN
ejpam-3870	179	2	.	.	PUNCT
ejpam-3870	180	1	assume	assume	VERB
ejpam-3870	180	2	that	that	SCONJ
ejpam-3870	180	3	α	α	PRON
ejpam-3870	180	4	is	be	AUX
ejpam-3870	180	5	a	a	DET
ejpam-3870	180	6	right	right	ADJ
ejpam-3870	180	7	magnifying	magnify	VERB
ejpam-3870	180	8	element	element	NOUN
ejpam-3870	180	9	of	of	ADP
ejpam-3870	180	10	bx	bx	PROPN
ejpam-3870	180	11	.	.	PUNCT
ejpam-3870	181	1	then	then	ADV
ejpam-3870	181	2	there	there	PRON
ejpam-3870	181	3	exists	exist	VERB
ejpam-3870	181	4	a	a	DET
ejpam-3870	181	5	proper	proper	ADJ
ejpam-3870	181	6	subset	subset	NOUN
ejpam-3870	181	7	m	m	NOUN
ejpam-3870	181	8	of	of	ADP
ejpam-3870	181	9	bx	bx	PRON
ejpam-3870	181	10	such	such	ADJ
ejpam-3870	181	11	that	that	PRON
ejpam-3870	181	12	mα	mα	PROPN
ejpam-3870	181	13	=	=	NOUN
ejpam-3870	181	14	bx	bx	PROPN
ejpam-3870	181	15	.	.	PUNCT
ejpam-3870	182	1	since	since	SCONJ
ejpam-3870	182	2	α	α	PROPN
ejpam-3870	182	3	is	be	AUX
ejpam-3870	182	4	a	a	DET
ejpam-3870	182	5	bijective	bijective	ADJ
ejpam-3870	182	6	function	function	NOUN
ejpam-3870	182	7	,	,	PUNCT
ejpam-3870	182	8	mα	mα	PROPN
ejpam-3870	182	9	=	=	SYM
ejpam-3870	182	10	mαα−1α	mαα−1α	PROPN
ejpam-3870	182	11	=	=	PUNCT
ejpam-3870	182	12	bxα−1α	bxα−1α	PROPN
ejpam-3870	182	13	⊆	⊆	NUM
ejpam-3870	182	14	bxα	bxα	VERB
ejpam-3870	182	15	⊆	⊆	NUM
ejpam-3870	182	16	bx	bx	NOUN
ejpam-3870	182	17	=	=	PUNCT
ejpam-3870	182	18	mα	mα	PROPN
ejpam-3870	182	19	.	.	PUNCT
ejpam-3870	183	1	then	then	ADV
ejpam-3870	183	2	mα	mα	PROPN
ejpam-3870	183	3	=	=	PUNCT
ejpam-3870	183	4	bxα	bxα	PROPN
ejpam-3870	183	5	.	.	PROPN
ejpam-3870	184	1	hence	hence	ADV
ejpam-3870	184	2	m	m	VERB
ejpam-3870	184	3	=	=	PUNCT
ejpam-3870	184	4	mαα−1	mαα−1	NOUN
ejpam-3870	184	5	=	=	SYM
ejpam-3870	184	6	bxαα−1	bxαα−1	PROPN
ejpam-3870	184	7	=	=	SYM
ejpam-3870	184	8	bx	bx	PROPN
ejpam-3870	184	9	.	.	PUNCT
ejpam-3870	185	1	this	this	PRON
ejpam-3870	185	2	is	be	AUX
ejpam-3870	185	3	a	a	DET
ejpam-3870	185	4	contradiction	contradiction	NOUN
ejpam-3870	185	5	.	.	PUNCT
ejpam-3870	186	1	therefore	therefore	ADV
ejpam-3870	186	2	α	α	PROPN
ejpam-3870	186	3	is	be	AUX
ejpam-3870	186	4	not	not	PART
ejpam-3870	186	5	a	a	DET
ejpam-3870	186	6	right	right	ADJ
ejpam-3870	186	7	magnifying	magnify	VERB
ejpam-3870	186	8	element	element	NOUN
ejpam-3870	186	9	of	of	ADP
ejpam-3870	186	10	bx	bx	PROPN
ejpam-3870	186	11	.	.	PUNCT
ejpam-3870	187	1	lemma	lemma	PROPN
ejpam-3870	187	2	10	10	NUM
ejpam-3870	187	3	.	.	PUNCT
ejpam-3870	188	1	let	let	VERB
ejpam-3870	188	2	α	α	PRON
ejpam-3870	188	3	∈	∈	PROPN
ejpam-3870	188	4	bx	bx	NOUN
ejpam-3870	188	5	.	.	PUNCT
ejpam-3870	189	1	if	if	SCONJ
ejpam-3870	189	2	there	there	PRON
ejpam-3870	189	3	exists	exist	VERB
ejpam-3870	189	4	a	a	DET
ejpam-3870	189	5	subset	subset	NOUN
ejpam-3870	189	6	a	a	PRON
ejpam-3870	189	7	of	of	ADP
ejpam-3870	189	8	x	x	SYM
ejpam-3870	189	9	such	such	ADJ
ejpam-3870	189	10	that	that	SCONJ
ejpam-3870	189	11	α|a	α|a	NOUN
ejpam-3870	189	12	is	be	AUX
ejpam-3870	189	13	an	an	PRON
ejpam-3870	189	14	onto	onto	ADP
ejpam-3870	189	15	function	function	NOUN
ejpam-3870	189	16	from	from	ADP
ejpam-3870	189	17	a	a	PRON
ejpam-3870	189	18	to	to	PART
ejpam-3870	189	19	x	x	PUNCT
ejpam-3870	189	20	and	and	CCONJ
ejpam-3870	189	21	α	α	NOUN
ejpam-3870	189	22	is	be	AUX
ejpam-3870	189	23	not	not	PART
ejpam-3870	189	24	a	a	DET
ejpam-3870	189	25	bijective	bijective	ADJ
ejpam-3870	189	26	function	function	NOUN
ejpam-3870	189	27	on	on	ADP
ejpam-3870	189	28	x	x	NOUN
ejpam-3870	189	29	,	,	PUNCT
ejpam-3870	189	30	then	then	ADV
ejpam-3870	189	31	α	α	PROPN
ejpam-3870	189	32	is	be	AUX
ejpam-3870	189	33	a	a	DET
ejpam-3870	189	34	right	right	ADJ
ejpam-3870	189	35	magnifying	magnify	VERB
ejpam-3870	189	36	element	element	NOUN
ejpam-3870	189	37	of	of	ADP
ejpam-3870	189	38	bx	bx	PROPN
ejpam-3870	189	39	.	.	PUNCT
ejpam-3870	190	1	proof	proof	NOUN
ejpam-3870	190	2	.	.	PUNCT
ejpam-3870	191	1	assume	assume	VERB
ejpam-3870	191	2	that	that	SCONJ
ejpam-3870	191	3	there	there	PRON
ejpam-3870	191	4	exists	exist	VERB
ejpam-3870	191	5	a	a	DET
ejpam-3870	191	6	subset	subset	NOUN
ejpam-3870	191	7	a	a	PRON
ejpam-3870	191	8	of	of	ADP
ejpam-3870	191	9	x	x	SYM
ejpam-3870	191	10	such	such	ADJ
ejpam-3870	191	11	that	that	SCONJ
ejpam-3870	191	12	α|a	α|a	NOUN
ejpam-3870	191	13	is	be	AUX
ejpam-3870	191	14	an	an	PRON
ejpam-3870	191	15	onto	onto	ADP
ejpam-3870	191	16	function	function	NOUN
ejpam-3870	191	17	from	from	ADP
ejpam-3870	191	18	a	a	PRON
ejpam-3870	191	19	to	to	PART
ejpam-3870	191	20	x	x	PUNCT
ejpam-3870	191	21	and	and	CCONJ
ejpam-3870	191	22	α	α	NOUN
ejpam-3870	191	23	is	be	AUX
ejpam-3870	191	24	not	not	PART
ejpam-3870	191	25	a	a	DET
ejpam-3870	191	26	bijective	bijective	ADJ
ejpam-3870	191	27	function	function	NOUN
ejpam-3870	191	28	on	on	ADP
ejpam-3870	191	29	x.	x.	NOUN
ejpam-3870	191	30	let	let	VERB
ejpam-3870	191	31	m	m	VERB
ejpam-3870	191	32	=	=	PRON
ejpam-3870	191	33	{	{	PUNCT
ejpam-3870	191	34	h	h	NOUN
ejpam-3870	191	35	∈	∈	PROPN
ejpam-3870	191	36	bx	bx	NOUN
ejpam-3870	191	37	|	|	ADV
ejpam-3870	191	38	ranh	ranh	VERB
ejpam-3870	191	39	6=	6=	ADP
ejpam-3870	191	40	x	x	NOUN
ejpam-3870	191	41	}	}	PUNCT
ejpam-3870	191	42	.	.	PUNCT
ejpam-3870	192	1	then	then	ADV
ejpam-3870	192	2	m	m	PROPN
ejpam-3870	192	3	is	be	AUX
ejpam-3870	192	4	a	a	DET
ejpam-3870	192	5	proper	proper	ADJ
ejpam-3870	192	6	subset	subset	NOUN
ejpam-3870	192	7	of	of	ADP
ejpam-3870	192	8	bx	bx	PROPN
ejpam-3870	192	9	.	.	PUNCT
ejpam-3870	193	1	we	we	PRON
ejpam-3870	193	2	will	will	AUX
ejpam-3870	193	3	show	show	VERB
ejpam-3870	193	4	that	that	SCONJ
ejpam-3870	193	5	there	there	PRON
ejpam-3870	193	6	exists	exist	VERB
ejpam-3870	193	7	a	a	DET
ejpam-3870	193	8	proper	proper	ADJ
ejpam-3870	193	9	subset	subset	NOUN
ejpam-3870	193	10	c	c	NOUN
ejpam-3870	193	11	of	of	ADP
ejpam-3870	193	12	x	x	INTJ
ejpam-3870	193	13	such	such	ADJ
ejpam-3870	193	14	that	that	DET
ejpam-3870	193	15	α|c	α|c	PROPN
ejpam-3870	193	16	is	be	AUX
ejpam-3870	193	17	an	an	PRON
ejpam-3870	193	18	onto	onto	ADP
ejpam-3870	193	19	function	function	NOUN
ejpam-3870	193	20	from	from	ADP
ejpam-3870	193	21	c	c	NOUN
ejpam-3870	193	22	to	to	PART
ejpam-3870	193	23	x.	x.	VERB
ejpam-3870	193	24	if	if	SCONJ
ejpam-3870	193	25	a	a	PRON
ejpam-3870	193	26	6=	6=	PRON
ejpam-3870	193	27	x	x	X
ejpam-3870	193	28	,	,	PUNCT
ejpam-3870	193	29	then	then	ADV
ejpam-3870	193	30	it	it	PRON
ejpam-3870	193	31	is	be	AUX
ejpam-3870	193	32	immediate	immediate	ADJ
ejpam-3870	193	33	by	by	ADP
ejpam-3870	193	34	setting	set	VERB
ejpam-3870	193	35	c	c	NOUN
ejpam-3870	193	36	:	:	PUNCT
ejpam-3870	193	37	=	=	PUNCT
ejpam-3870	193	38	a.	a.	NOUN
ejpam-3870	193	39	if	if	SCONJ
ejpam-3870	193	40	a	a	DET
ejpam-3870	193	41	=	=	SYM
ejpam-3870	193	42	x	x	NOUN
ejpam-3870	193	43	,	,	PUNCT
ejpam-3870	193	44	then	then	ADV
ejpam-3870	193	45	α	α	PROPN
ejpam-3870	193	46	is	be	AUX
ejpam-3870	193	47	an	an	PRON
ejpam-3870	193	48	onto	onto	ADP
ejpam-3870	193	49	function	function	NOUN
ejpam-3870	193	50	on	on	ADP
ejpam-3870	193	51	x	x	NOUN
ejpam-3870	193	52	,	,	PUNCT
ejpam-3870	193	53	but	but	CCONJ
ejpam-3870	193	54	as	as	SCONJ
ejpam-3870	193	55	α	α	PRON
ejpam-3870	193	56	is	be	AUX
ejpam-3870	193	57	not	not	PART
ejpam-3870	193	58	a	a	DET
ejpam-3870	193	59	bijective	bijective	ADJ
ejpam-3870	193	60	function	function	NOUN
ejpam-3870	193	61	on	on	ADP
ejpam-3870	193	62	x	x	PRON
ejpam-3870	193	63	,	,	PUNCT
ejpam-3870	193	64	α	α	PROPN
ejpam-3870	193	65	is	be	AUX
ejpam-3870	193	66	not	not	PART
ejpam-3870	193	67	a	a	DET
ejpam-3870	193	68	one	one	NUM
ejpam-3870	193	69	-	-	PUNCT
ejpam-3870	193	70	to	to	ADP
ejpam-3870	193	71	-	-	PUNCT
ejpam-3870	193	72	one	one	NUM
ejpam-3870	193	73	function	function	NOUN
ejpam-3870	193	74	on	on	ADP
ejpam-3870	193	75	x.	x.	NOUN
ejpam-3870	193	76	then	then	ADV
ejpam-3870	193	77	there	there	PRON
ejpam-3870	193	78	exists	exist	VERB
ejpam-3870	193	79	u	u	NOUN
ejpam-3870	193	80	∈	∈	PROPN
ejpam-3870	193	81	x	x	PUNCT
ejpam-3870	193	82	which	which	DET
ejpam-3870	193	83	α|x\{u	α|x\{u	NOUN
ejpam-3870	193	84	}	}	PUNCT
ejpam-3870	193	85	is	be	AUX
ejpam-3870	193	86	an	an	PRON
ejpam-3870	193	87	onto	onto	ADP
ejpam-3870	193	88	function	function	NOUN
ejpam-3870	193	89	from	from	ADP
ejpam-3870	193	90	x	x	X
ejpam-3870	193	91	\	\	PROPN
ejpam-3870	193	92	{	{	PUNCT
ejpam-3870	193	93	u	u	NOUN
ejpam-3870	193	94	}	}	PUNCT
ejpam-3870	193	95	to	to	PART
ejpam-3870	193	96	x.	x.	VERB
ejpam-3870	193	97	by	by	ADP
ejpam-3870	193	98	put	put	NOUN
ejpam-3870	193	99	c	c	NOUN
ejpam-3870	193	100	:	:	PUNCT
ejpam-3870	193	101	=	=	SYM
ejpam-3870	193	102	x	x	SYM
ejpam-3870	193	103	\	\	PROPN
ejpam-3870	193	104	{	{	PUNCT
ejpam-3870	193	105	u	u	NOUN
ejpam-3870	193	106	}	}	PUNCT
ejpam-3870	193	107	,	,	PUNCT
ejpam-3870	193	108	the	the	DET
ejpam-3870	193	109	proof	proof	NOUN
ejpam-3870	193	110	is	be	AUX
ejpam-3870	193	111	immediately	immediately	ADV
ejpam-3870	193	112	obtained	obtain	VERB
ejpam-3870	193	113	.	.	PUNCT
ejpam-3870	194	1	let	let	VERB
ejpam-3870	194	2	β	β	PRON
ejpam-3870	194	3	∈	∈	PROPN
ejpam-3870	194	4	bx	bx	PROPN
ejpam-3870	194	5	and	and	CCONJ
ejpam-3870	194	6	x	x	PUNCT
ejpam-3870	194	7	∈	∈	PROPN
ejpam-3870	194	8	domβ	domβ	NOUN
ejpam-3870	194	9	.	.	PUNCT
ejpam-3870	195	1	then	then	ADV
ejpam-3870	195	2	(	(	PUNCT
ejpam-3870	195	3	x)β	x)β	NOUN
ejpam-3870	195	4	⊆	⊆	NUM
ejpam-3870	195	5	x.	x.	NOUN
ejpam-3870	195	6	since	since	SCONJ
ejpam-3870	195	7	α|c	α|c	NOUN
ejpam-3870	195	8	is	be	AUX
ejpam-3870	195	9	onto	onto	ADP
ejpam-3870	195	10	,	,	PUNCT
ejpam-3870	195	11	there	there	PRON
ejpam-3870	195	12	exists	exist	VERB
ejpam-3870	195	13	a	a	DET
ejpam-3870	195	14	nonempty	nonempty	NOUN
ejpam-3870	195	15	subset	subset	VERB
ejpam-3870	195	16	cx	cx	NOUN
ejpam-3870	195	17	of	of	ADP
ejpam-3870	195	18	c	c	PROPN
ejpam-3870	195	19	such	such	ADJ
ejpam-3870	195	20	that	that	PRON
ejpam-3870	195	21	(	(	PUNCT
ejpam-3870	195	22	cx)α	cx)α	PROPN
ejpam-3870	195	23	=	=	SYM
ejpam-3870	195	24	(	(	PUNCT
ejpam-3870	195	25	x)β	x)β	PROPN
ejpam-3870	195	26	.	.	PUNCT
ejpam-3870	196	1	from	from	ADP
ejpam-3870	196	2	these	these	PRON
ejpam-3870	196	3	we	we	PRON
ejpam-3870	196	4	defined	define	VERB
ejpam-3870	196	5	a	a	DET
ejpam-3870	196	6	relation	relation	NOUN
ejpam-3870	196	7	γ	γ	X
ejpam-3870	196	8	∈	∈	PROPN
ejpam-3870	196	9	bx	bx	X
ejpam-3870	196	10	by	by	ADP
ejpam-3870	196	11	(	(	PUNCT
ejpam-3870	196	12	x)γ	x)γ	NOUN
ejpam-3870	196	13	=	=	SYM
ejpam-3870	196	14	cx	cx	PROPN
ejpam-3870	196	15	for	for	ADP
ejpam-3870	196	16	each	each	DET
ejpam-3870	196	17	x	x	SYM
ejpam-3870	196	18	∈	∈	PROPN
ejpam-3870	196	19	domβ	domβ	NOUN
ejpam-3870	196	20	.	.	PUNCT
ejpam-3870	197	1	it	it	PRON
ejpam-3870	197	2	is	be	AUX
ejpam-3870	197	3	clearly	clearly	ADV
ejpam-3870	197	4	that	that	PRON
ejpam-3870	197	5	ranγ	ranγ	VERB
ejpam-3870	197	6	⊆	⊆	NUM
ejpam-3870	197	7	c	c	NOUN
ejpam-3870	197	8	6=	6=	PROPN
ejpam-3870	197	9	x	x	PROPN
ejpam-3870	197	10	,	,	PUNCT
ejpam-3870	197	11	then	then	ADV
ejpam-3870	197	12	γ	γ	X
ejpam-3870	197	13	∈m	∈m	NOUN
ejpam-3870	197	14	.	.	PUNCT
ejpam-3870	198	1	consider	consider	VERB
ejpam-3870	198	2	(	(	PUNCT
ejpam-3870	198	3	x)β	x)β	NOUN
ejpam-3870	198	4	=	=	SYM
ejpam-3870	198	5	(	(	PUNCT
ejpam-3870	198	6	cx)α	cx)α	PROPN
ejpam-3870	198	7	=	=	SYM
ejpam-3870	198	8	(	(	PUNCT
ejpam-3870	198	9	(	(	PUNCT
ejpam-3870	198	10	x)γ)α	x)γ)α	PROPN
ejpam-3870	198	11	=	=	SYM
ejpam-3870	198	12	(	(	PUNCT
ejpam-3870	198	13	x)(γα	x)(γα	NUM
ejpam-3870	198	14	)	)	PUNCT
ejpam-3870	198	15	,	,	PUNCT
ejpam-3870	198	16	where	where	SCONJ
ejpam-3870	198	17	x	x	PUNCT
ejpam-3870	198	18	∈	∈	PROPN
ejpam-3870	198	19	domβ	domβ	NOUN
ejpam-3870	198	20	,	,	PUNCT
ejpam-3870	198	21	we	we	PRON
ejpam-3870	198	22	have	have	VERB
ejpam-3870	198	23	γα	γα	ADP
ejpam-3870	198	24	=	=	SYM
ejpam-3870	198	25	β	β	X
ejpam-3870	198	26	.	.	PUNCT
ejpam-3870	199	1	therefore	therefore	ADV
ejpam-3870	199	2	bx	bx	PROPN
ejpam-3870	199	3	=	=	SYM
ejpam-3870	199	4	mα	mα	PROPN
ejpam-3870	199	5	.	.	PUNCT
ejpam-3870	199	6	theorem	theorem	NOUN
ejpam-3870	199	7	2	2	NUM
ejpam-3870	199	8	.	.	PUNCT
ejpam-3870	200	1	let	let	VERB
ejpam-3870	200	2	α	α	PRON
ejpam-3870	200	3	∈	∈	PROPN
ejpam-3870	200	4	bx	bx	X
ejpam-3870	200	5	.	.	PUNCT
ejpam-3870	201	1	then	then	ADV
ejpam-3870	201	2	α	α	PROPN
ejpam-3870	201	3	is	be	AUX
ejpam-3870	201	4	a	a	DET
ejpam-3870	201	5	right	right	ADJ
ejpam-3870	201	6	magnifying	magnify	VERB
ejpam-3870	201	7	element	element	NOUN
ejpam-3870	201	8	of	of	ADP
ejpam-3870	201	9	bx	bx	PRON
ejpam-3870	201	10	if	if	SCONJ
ejpam-3870	201	11	and	and	CCONJ
ejpam-3870	201	12	only	only	ADV
ejpam-3870	201	13	if	if	SCONJ
ejpam-3870	201	14	there	there	PRON
ejpam-3870	201	15	exists	exist	VERB
ejpam-3870	201	16	a	a	DET
ejpam-3870	201	17	subset	subset	NOUN
ejpam-3870	201	18	a	a	PRON
ejpam-3870	201	19	of	of	ADP
ejpam-3870	201	20	x	x	SYM
ejpam-3870	201	21	such	such	ADJ
ejpam-3870	201	22	that	that	SCONJ
ejpam-3870	201	23	α	α	PRON
ejpam-3870	201	24	is	be	AUX
ejpam-3870	201	25	an	an	PRON
ejpam-3870	201	26	onto	onto	ADP
ejpam-3870	201	27	function	function	NOUN
ejpam-3870	201	28	from	from	ADP
ejpam-3870	201	29	a	a	PRON
ejpam-3870	201	30	to	to	PART
ejpam-3870	201	31	x	x	PUNCT
ejpam-3870	201	32	and	and	CCONJ
ejpam-3870	201	33	α	α	NOUN
ejpam-3870	201	34	is	be	AUX
ejpam-3870	201	35	not	not	PART
ejpam-3870	201	36	a	a	DET
ejpam-3870	201	37	bijective	bijective	ADJ
ejpam-3870	201	38	function	function	NOUN
ejpam-3870	201	39	on	on	ADP
ejpam-3870	201	40	x.	x.	NOUN
ejpam-3870	201	41	proof	proof	NOUN
ejpam-3870	201	42	.	.	PUNCT
ejpam-3870	202	1	trivial	trivial	ADJ
ejpam-3870	202	2	from	from	ADP
ejpam-3870	202	3	lemma	lemma	PROPN
ejpam-3870	202	4	8	8	NUM
ejpam-3870	202	5	,	,	PUNCT
ejpam-3870	202	6	lemma	lemma	PROPN
ejpam-3870	202	7	9	9	NUM
ejpam-3870	202	8	and	and	CCONJ
ejpam-3870	202	9	lemma	lemma	PROPN
ejpam-3870	202	10	10	10	NUM
ejpam-3870	202	11	.	.	PUNCT
ejpam-3870	202	12	example	example	NOUN
ejpam-3870	203	1	2	2	NUM
ejpam-3870	203	2	.	.	PUNCT
ejpam-3870	203	3	let	let	VERB
ejpam-3870	203	4	x	x	SYM
ejpam-3870	203	5	=	=	PUNCT
ejpam-3870	203	6	n	n	PROPN
ejpam-3870	203	7	and	and	CCONJ
ejpam-3870	203	8	α	α	PRON
ejpam-3870	203	9	be	be	VERB
ejpam-3870	203	10	a	a	DET
ejpam-3870	203	11	relation	relation	NOUN
ejpam-3870	203	12	in	in	ADP
ejpam-3870	203	13	bx	bx	NOUN
ejpam-3870	203	14	defined	define	VERB
ejpam-3870	203	15	by	by	ADP
ejpam-3870	203	16	(	(	PUNCT
ejpam-3870	203	17	x)α	x)α	NOUN
ejpam-3870	203	18	=	=	SYM
ejpam-3870	203	19	{	{	PUNCT
ejpam-3870	203	20	{	{	PUNCT
ejpam-3870	203	21	x	x	SYM
ejpam-3870	203	22	2	2	NUM
ejpam-3870	203	23	}	}	PUNCT
ejpam-3870	203	24	for	for	ADP
ejpam-3870	203	25	all	all	DET
ejpam-3870	203	26	even	even	ADV
ejpam-3870	203	27	x	x	X
ejpam-3870	203	28	,	,	PUNCT
ejpam-3870	203	29	{	{	PUNCT
ejpam-3870	203	30	x	x	NOUN
ejpam-3870	203	31	,	,	PUNCT
ejpam-3870	203	32	x+	x+	NUM
ejpam-3870	203	33	1	1	X
ejpam-3870	203	34	}	}	PUNCT
ejpam-3870	203	35	for	for	ADP
ejpam-3870	203	36	all	all	DET
ejpam-3870	203	37	odd	odd	ADJ
ejpam-3870	203	38	x.	x.	NOUN
ejpam-3870	203	39	then	then	ADV
ejpam-3870	203	40	α|a	α|a	PROPN
ejpam-3870	203	41	is	be	AUX
ejpam-3870	203	42	an	an	PRON
ejpam-3870	203	43	onto	onto	ADP
ejpam-3870	203	44	function	function	NOUN
ejpam-3870	203	45	from	from	ADP
ejpam-3870	203	46	a	a	PRON
ejpam-3870	203	47	to	to	ADP
ejpam-3870	203	48	n	n	CCONJ
ejpam-3870	203	49	,	,	PUNCT
ejpam-3870	203	50	where	where	SCONJ
ejpam-3870	203	51	a	a	DET
ejpam-3870	203	52	=	=	SYM
ejpam-3870	203	53	{	{	PUNCT
ejpam-3870	203	54	x	x	SYM
ejpam-3870	203	55	∈	∈	PROPN
ejpam-3870	203	56	n	n	PRON
ejpam-3870	203	57	|	|	ADV
ejpam-3870	203	58	x	x	INTJ
ejpam-3870	203	59	is	be	AUX
ejpam-3870	203	60	even	even	ADV
ejpam-3870	203	61	}	}	PUNCT
ejpam-3870	203	62	,	,	PUNCT
ejpam-3870	203	63	and	and	CCONJ
ejpam-3870	203	64	α	α	PRON
ejpam-3870	203	65	is	be	AUX
ejpam-3870	203	66	not	not	PART
ejpam-3870	203	67	a	a	DET
ejpam-3870	203	68	bijective	bijective	ADJ
ejpam-3870	203	69	function	function	NOUN
ejpam-3870	203	70	on	on	ADP
ejpam-3870	203	71	n.	n.	NOUN
ejpam-3870	203	72	we	we	PRON
ejpam-3870	203	73	put	put	VERB
ejpam-3870	203	74	m	m	VERB
ejpam-3870	203	75	:	:	PUNCT
ejpam-3870	203	76	=	=	SYM
ejpam-3870	203	77	{	{	PUNCT
ejpam-3870	203	78	h	h	NOUN
ejpam-3870	203	79	∈	∈	PROPN
ejpam-3870	203	80	bx	bx	NOUN
ejpam-3870	203	81	|	|	ADV
ejpam-3870	203	82	ranh	ranh	VERB
ejpam-3870	203	83	6=	6=	ADP
ejpam-3870	203	84	x	x	NOUN
ejpam-3870	203	85	}	}	PUNCT
ejpam-3870	203	86	.	.	PUNCT
ejpam-3870	204	1	let	let	VERB
ejpam-3870	204	2	β	β	PRON
ejpam-3870	204	3	∈	∈	PROPN
ejpam-3870	204	4	bx	bx	X
ejpam-3870	204	5	.	.	PUNCT
ejpam-3870	205	1	by	by	ADP
ejpam-3870	205	2	lemma	lemma	PROPN
ejpam-3870	205	3	3	3	NUM
ejpam-3870	205	4	,	,	PUNCT
ejpam-3870	205	5	there	there	PRON
ejpam-3870	205	6	exists	exist	VERB
ejpam-3870	205	7	a	a	DET
ejpam-3870	205	8	relation	relation	NOUN
ejpam-3870	205	9	γ	γ	NOUN
ejpam-3870	205	10	in	in	ADP
ejpam-3870	205	11	bx	bx	PRON
ejpam-3870	205	12	such	such	ADJ
ejpam-3870	205	13	that	that	SCONJ
ejpam-3870	205	14	γα	γα	ADP
ejpam-3870	205	15	=	=	SYM
ejpam-3870	205	16	β	β	X
ejpam-3870	205	17	.	.	PUNCT
ejpam-3870	206	1	w.	w.	PROPN
ejpam-3870	206	2	teparos	teparos	PROPN
ejpam-3870	206	3	,	,	PUNCT
ejpam-3870	206	4	s.	s.	PROPN
ejpam-3870	206	5	boonta	boonta	PROPN
ejpam-3870	206	6	,	,	PUNCT
ejpam-3870	206	7	t.	t.	PROPN
ejpam-3870	206	8	theparod	theparod	PROPN
ejpam-3870	206	9	/	/	SYM
ejpam-3870	206	10	eur	eur	PROPN
ejpam-3870	206	11	.	.	PUNCT
ejpam-3870	207	1	j.	j.	PROPN
ejpam-3870	207	2	pure	pure	PROPN
ejpam-3870	207	3	appl	appl	PROPN
ejpam-3870	207	4	.	.	PROPN
ejpam-3870	207	5	math	math	PROPN
ejpam-3870	207	6	,	,	PUNCT
ejpam-3870	207	7	13	13	NUM
ejpam-3870	207	8	(	(	PUNCT
ejpam-3870	207	9	4	4	NUM
ejpam-3870	207	10	)	)	PUNCT
ejpam-3870	207	11	(	(	PUNCT
ejpam-3870	207	12	2020	2020	NUM
ejpam-3870	207	13	)	)	PUNCT
ejpam-3870	207	14	,	,	PUNCT
ejpam-3870	207	15	987	987	NUM
ejpam-3870	207	16	-	-	SYM
ejpam-3870	207	17	994	994	NUM
ejpam-3870	207	18	993	993	NUM
ejpam-3870	207	19	for	for	ADP
ejpam-3870	207	20	example	example	NOUN
ejpam-3870	207	21	,	,	PUNCT
ejpam-3870	207	22	(	(	PUNCT
ejpam-3870	207	23	a	a	X
ejpam-3870	207	24	)	)	PUNCT
ejpam-3870	207	25	if	if	SCONJ
ejpam-3870	207	26	β	β	PROPN
ejpam-3870	207	27	∈	∈	PROPN
ejpam-3870	207	28	bx	bx	NOUN
ejpam-3870	207	29	such	such	ADJ
ejpam-3870	207	30	that	that	PRON
ejpam-3870	207	31	(	(	PUNCT
ejpam-3870	207	32	x)β	x)β	NOUN
ejpam-3870	207	33	=	=	SYM
ejpam-3870	207	34	{	{	PUNCT
ejpam-3870	207	35	x+	x+	NOUN
ejpam-3870	207	36	3	3	X
ejpam-3870	207	37	}	}	PUNCT
ejpam-3870	207	38	for	for	ADP
ejpam-3870	207	39	each	each	PRON
ejpam-3870	207	40	x	x	PUNCT
ejpam-3870	207	41	where	where	SCONJ
ejpam-3870	207	42	x	x	PRON
ejpam-3870	207	43	is	be	AUX
ejpam-3870	207	44	odd	odd	ADJ
ejpam-3870	207	45	.	.	PUNCT
ejpam-3870	208	1	then	then	ADV
ejpam-3870	208	2	domβ	domβ	VERB
ejpam-3870	208	3	=	=	PUNCT
ejpam-3870	208	4	{	{	PUNCT
ejpam-3870	208	5	x	x	SYM
ejpam-3870	208	6	∈	∈	PROPN
ejpam-3870	208	7	n	n	PRON
ejpam-3870	208	8	|	|	ADV
ejpam-3870	208	9	x	x	INTJ
ejpam-3870	208	10	is	be	AUX
ejpam-3870	208	11	odd	odd	ADJ
ejpam-3870	208	12	}	}	PUNCT
ejpam-3870	208	13	.	.	PUNCT
ejpam-3870	209	1	define	define	VERB
ejpam-3870	209	2	γ	γ	PROPN
ejpam-3870	209	3	∈	∈	PROPN
ejpam-3870	209	4	bx	bx	X
ejpam-3870	209	5	by	by	ADP
ejpam-3870	209	6	(	(	PUNCT
ejpam-3870	209	7	x)γ	x)γ	NOUN
ejpam-3870	209	8	=	=	SYM
ejpam-3870	209	9	2(x+	2(x+	NUM
ejpam-3870	209	10	3	3	X
ejpam-3870	209	11	)	)	PUNCT
ejpam-3870	209	12	for	for	ADP
ejpam-3870	209	13	all	all	DET
ejpam-3870	209	14	x	x	NOUN
ejpam-3870	209	15	that	that	PRON
ejpam-3870	209	16	is	be	AUX
ejpam-3870	209	17	odd	odd	ADJ
ejpam-3870	209	18	.	.	PUNCT
ejpam-3870	210	1	thus	thus	ADV
ejpam-3870	210	2	domγ	domγ	NOUN
ejpam-3870	210	3	=	=	SYM
ejpam-3870	210	4	domβ	domβ	NOUN
ejpam-3870	210	5	and	and	CCONJ
ejpam-3870	210	6	ranγ	ranγ	VERB
ejpam-3870	210	7	⊆	⊆	NUM
ejpam-3870	210	8	domα	domα	NOUN
ejpam-3870	210	9	6=	6=	NUM
ejpam-3870	210	10	x.	x.	NOUN
ejpam-3870	211	1	we	we	PRON
ejpam-3870	211	2	have	have	VERB
ejpam-3870	211	3	γ	γ	NOUN
ejpam-3870	211	4	∈	∈	PROPN
ejpam-3870	211	5	m	m	NOUN
ejpam-3870	211	6	.	.	PUNCT
ejpam-3870	212	1	for	for	ADP
ejpam-3870	212	2	each	each	DET
ejpam-3870	212	3	odd	odd	ADJ
ejpam-3870	212	4	integer	integer	NOUN
ejpam-3870	212	5	x	x	NOUN
ejpam-3870	212	6	,	,	PUNCT
ejpam-3870	212	7	then	then	ADV
ejpam-3870	212	8	(	(	PUNCT
ejpam-3870	212	9	x)(γα	x)(γα	X
ejpam-3870	212	10	)	)	PUNCT
ejpam-3870	213	1	=	=	SYM
ejpam-3870	213	2	(	(	PUNCT
ejpam-3870	213	3	(	(	PUNCT
ejpam-3870	213	4	x)γ)α	x)γ)α	PROPN
ejpam-3870	213	5	=	=	SYM
ejpam-3870	213	6	(	(	PUNCT
ejpam-3870	213	7	2(x+	2(x+	NUM
ejpam-3870	213	8	3))α	3))α	NUM
ejpam-3870	213	9	=	=	NOUN
ejpam-3870	213	10	{	{	PUNCT
ejpam-3870	213	11	2(x+	2(x+	NUM
ejpam-3870	213	12	3	3	NUM
ejpam-3870	213	13	)	)	PUNCT
ejpam-3870	213	14	2	2	NUM
ejpam-3870	213	15	}	}	PUNCT
ejpam-3870	213	16	=	=	SYM
ejpam-3870	213	17	{	{	PUNCT
ejpam-3870	213	18	x+	x+	ADJ
ejpam-3870	213	19	3	3	NUM
ejpam-3870	213	20	}	}	PUNCT
ejpam-3870	213	21	=	=	SYM
ejpam-3870	213	22	(	(	PUNCT
ejpam-3870	213	23	x)β	x)β	PROPN
ejpam-3870	213	24	.	.	PUNCT
ejpam-3870	214	1	therefore	therefore	ADV
ejpam-3870	214	2	γα	γα	ADP
ejpam-3870	214	3	=	=	NOUN
ejpam-3870	214	4	β	β	X
ejpam-3870	214	5	.	.	PUNCT
ejpam-3870	215	1	(	(	PUNCT
ejpam-3870	215	2	b	b	X
ejpam-3870	215	3	)	)	PUNCT
ejpam-3870	215	4	if	if	SCONJ
ejpam-3870	215	5	β	β	X
ejpam-3870	215	6	=	=	PRON
ejpam-3870	215	7	{	{	PUNCT
ejpam-3870	215	8	(	(	PUNCT
ejpam-3870	215	9	1	1	NUM
ejpam-3870	215	10	,	,	PUNCT
ejpam-3870	215	11	2	2	NUM
ejpam-3870	215	12	)	)	PUNCT
ejpam-3870	215	13	,	,	PUNCT
ejpam-3870	215	14	(	(	PUNCT
ejpam-3870	215	15	1	1	NUM
ejpam-3870	215	16	,	,	PUNCT
ejpam-3870	215	17	3	3	NUM
ejpam-3870	215	18	)	)	PUNCT
ejpam-3870	215	19	,	,	PUNCT
ejpam-3870	215	20	(	(	PUNCT
ejpam-3870	215	21	2	2	NUM
ejpam-3870	215	22	,	,	PUNCT
ejpam-3870	215	23	3	3	NUM
ejpam-3870	215	24	)	)	PUNCT
ejpam-3870	215	25	}	}	PUNCT
ejpam-3870	215	26	,	,	PUNCT
ejpam-3870	215	27	then	then	ADV
ejpam-3870	215	28	β	β	PROPN
ejpam-3870	215	29	∈	∈	PROPN
ejpam-3870	215	30	bx	bx	X
ejpam-3870	215	31	.	.	PUNCT
ejpam-3870	216	1	define	define	VERB
ejpam-3870	216	2	γ	γ	PROPN
ejpam-3870	216	3	∈	∈	PROPN
ejpam-3870	216	4	bx	bx	X
ejpam-3870	216	5	by	by	ADP
ejpam-3870	216	6	γ	γ	X
ejpam-3870	216	7	=	=	SYM
ejpam-3870	216	8	{	{	PUNCT
ejpam-3870	216	9	(	(	PUNCT
ejpam-3870	216	10	1	1	NUM
ejpam-3870	216	11	,	,	PUNCT
ejpam-3870	216	12	2	2	NUM
ejpam-3870	216	13	)	)	PUNCT
ejpam-3870	216	14	,	,	PUNCT
ejpam-3870	216	15	(	(	PUNCT
ejpam-3870	216	16	1	1	NUM
ejpam-3870	216	17	,	,	PUNCT
ejpam-3870	216	18	6	6	NUM
ejpam-3870	216	19	)	)	PUNCT
ejpam-3870	216	20	,	,	PUNCT
ejpam-3870	216	21	(	(	PUNCT
ejpam-3870	216	22	2	2	NUM
ejpam-3870	216	23	,	,	PUNCT
ejpam-3870	216	24	6	6	NUM
ejpam-3870	216	25	)	)	PUNCT
ejpam-3870	216	26	}	}	PUNCT
ejpam-3870	216	27	.	.	PUNCT
ejpam-3870	217	1	thus	thus	ADV
ejpam-3870	217	2	(	(	PUNCT
ejpam-3870	217	3	1)(γα	1)(γα	NUM
ejpam-3870	217	4	)	)	PUNCT
ejpam-3870	217	5	=	=	SYM
ejpam-3870	217	6	(	(	PUNCT
ejpam-3870	217	7	(	(	PUNCT
ejpam-3870	217	8	1)γ)α	1)γ)α	NUM
ejpam-3870	217	9	=	=	SYM
ejpam-3870	217	10	(	(	PUNCT
ejpam-3870	217	11	{	{	PUNCT
ejpam-3870	217	12	2	2	NUM
ejpam-3870	217	13	,	,	PUNCT
ejpam-3870	217	14	6})α	6})α	NUM
ejpam-3870	217	15	=	=	SYM
ejpam-3870	217	16	{	{	PUNCT
ejpam-3870	217	17	1	1	NUM
ejpam-3870	217	18	,	,	PUNCT
ejpam-3870	217	19	3	3	NUM
ejpam-3870	217	20	}	}	PUNCT
ejpam-3870	217	21	,	,	PUNCT
ejpam-3870	217	22	and	and	CCONJ
ejpam-3870	217	23	(	(	PUNCT
ejpam-3870	217	24	2)γα	2)γα	PROPN
ejpam-3870	217	25	=	=	SYM
ejpam-3870	217	26	(	(	PUNCT
ejpam-3870	217	27	(	(	PUNCT
ejpam-3870	217	28	1)γ)α	1)γ)α	NUM
ejpam-3870	217	29	=	=	SYM
ejpam-3870	217	30	(	(	PUNCT
ejpam-3870	217	31	{	{	PUNCT
ejpam-3870	217	32	6})α	6})α	NUM
ejpam-3870	217	33	=	=	SYM
ejpam-3870	217	34	{	{	PUNCT
ejpam-3870	217	35	3	3	NUM
ejpam-3870	217	36	}	}	PUNCT
ejpam-3870	217	37	.	.	PUNCT
ejpam-3870	218	1	therefore	therefore	ADV
ejpam-3870	218	2	,	,	PUNCT
ejpam-3870	218	3	γα	γα	ADP
ejpam-3870	218	4	=	=	SYM
ejpam-3870	218	5	β	β	X
ejpam-3870	218	6	.	.	PUNCT
ejpam-3870	219	1	(	(	PUNCT
ejpam-3870	219	2	c	c	X
ejpam-3870	219	3	)	)	PUNCT
ejpam-3870	219	4	if	if	SCONJ
ejpam-3870	219	5	β	β	PROPN
ejpam-3870	219	6	∈	∈	PROPN
ejpam-3870	219	7	bx	bx	NOUN
ejpam-3870	219	8	such	such	ADJ
ejpam-3870	219	9	that	that	PRON
ejpam-3870	219	10	(	(	PUNCT
ejpam-3870	219	11	x)β	x)β	NOUN
ejpam-3870	219	12	=	=	SYM
ejpam-3870	219	13	{	{	PUNCT
ejpam-3870	219	14	x	x	NOUN
ejpam-3870	219	15	,	,	PUNCT
ejpam-3870	219	16	x+	x+	X
ejpam-3870	219	17	2	2	X
ejpam-3870	219	18	}	}	PUNCT
ejpam-3870	219	19	for	for	ADP
ejpam-3870	219	20	all	all	DET
ejpam-3870	219	21	x	x	SYM
ejpam-3870	219	22	∈	∈	PROPN
ejpam-3870	219	23	n.	n.	NOUN
ejpam-3870	219	24	define	define	VERB
ejpam-3870	219	25	γ	γ	PROPN
ejpam-3870	219	26	∈	∈	PROPN
ejpam-3870	219	27	bx	bx	X
ejpam-3870	219	28	by	by	ADP
ejpam-3870	219	29	(	(	PUNCT
ejpam-3870	219	30	x)γ	x)γ	NOUN
ejpam-3870	219	31	=	=	SYM
ejpam-3870	219	32	{	{	PUNCT
ejpam-3870	219	33	2x	2x	NUM
ejpam-3870	219	34	,	,	PUNCT
ejpam-3870	219	35	2(x+	2(x+	NUM
ejpam-3870	219	36	2	2	NUM
ejpam-3870	219	37	)	)	PUNCT
ejpam-3870	219	38	}	}	PUNCT
ejpam-3870	219	39	for	for	ADP
ejpam-3870	219	40	all	all	PRON
ejpam-3870	219	41	x	x	VERB
ejpam-3870	219	42	is	be	AUX
ejpam-3870	219	43	an	an	DET
ejpam-3870	219	44	integer	integer	NOUN
ejpam-3870	219	45	.	.	PUNCT
ejpam-3870	220	1	clearly	clearly	ADV
ejpam-3870	220	2	that	that	SCONJ
ejpam-3870	220	3	dom(γα	dom(γα	NOUN
ejpam-3870	220	4	)	)	PUNCT
ejpam-3870	220	5	=	=	SYM
ejpam-3870	220	6	domβ	domβ	PROPN
ejpam-3870	220	7	.	.	PUNCT
ejpam-3870	221	1	let	let	VERB
ejpam-3870	221	2	x	x	SYM
ejpam-3870	221	3	∈	∈	PROPN
ejpam-3870	221	4	n.	n.	NOUN
ejpam-3870	221	5	then	then	ADV
ejpam-3870	221	6	(	(	PUNCT
ejpam-3870	221	7	x)(γα	x)(γα	X
ejpam-3870	221	8	)	)	PUNCT
ejpam-3870	222	1	=	=	SYM
ejpam-3870	222	2	(	(	PUNCT
ejpam-3870	222	3	(	(	PUNCT
ejpam-3870	222	4	x)γ)α	x)γ)α	PROPN
ejpam-3870	222	5	=	=	SYM
ejpam-3870	222	6	(	(	PUNCT
ejpam-3870	222	7	{	{	PUNCT
ejpam-3870	222	8	2x	2x	NUM
ejpam-3870	222	9	,	,	PUNCT
ejpam-3870	222	10	2(x+	2(x+	NUM
ejpam-3870	222	11	2)})α	2)})α	NUM
ejpam-3870	222	12	=	=	SYM
ejpam-3870	222	13	{	{	PUNCT
ejpam-3870	222	14	2x	2x	NUM
ejpam-3870	222	15	2	2	NUM
ejpam-3870	222	16	,	,	PUNCT
ejpam-3870	222	17	2(x+	2(x+	NUM
ejpam-3870	222	18	2	2	NUM
ejpam-3870	222	19	)	)	PUNCT
ejpam-3870	222	20	2	2	NUM
ejpam-3870	222	21	}	}	PUNCT
ejpam-3870	222	22	=	=	SYM
ejpam-3870	222	23	{	{	PUNCT
ejpam-3870	222	24	x	x	NOUN
ejpam-3870	222	25	,	,	PUNCT
ejpam-3870	222	26	x+	x+	NUM
ejpam-3870	222	27	2	2	NUM
ejpam-3870	222	28	}	}	PUNCT
ejpam-3870	222	29	=	=	SYM
ejpam-3870	222	30	(	(	PUNCT
ejpam-3870	222	31	x)β	x)β	PROPN
ejpam-3870	222	32	.	.	PUNCT
ejpam-3870	223	1	therefore	therefore	ADV
ejpam-3870	223	2	(	(	PUNCT
ejpam-3870	223	3	x)(γα	x)(γα	NUM
ejpam-3870	223	4	)	)	PUNCT
ejpam-3870	223	5	=	=	SYM
ejpam-3870	223	6	(	(	PUNCT
ejpam-3870	223	7	x)β	x)β	NOUN
ejpam-3870	223	8	for	for	ADP
ejpam-3870	223	9	all	all	DET
ejpam-3870	223	10	x	x	SYM
ejpam-3870	223	11	∈	∈	PROPN
ejpam-3870	223	12	n.	n.	NOUN
ejpam-3870	223	13	acknowledgements	acknowledgement	VERB
ejpam-3870	223	14	the	the	DET
ejpam-3870	223	15	authors	author	NOUN
ejpam-3870	223	16	thank	thank	VERB
ejpam-3870	223	17	faculty	faculty	NOUN
ejpam-3870	223	18	of	of	ADP
ejpam-3870	223	19	science	science	NOUN
ejpam-3870	223	20	and	and	CCONJ
ejpam-3870	223	21	engineering	engineering	NOUN
ejpam-3870	223	22	,	,	PUNCT
ejpam-3870	223	23	kasetsart	kasetsart	PROPN
ejpam-3870	223	24	university	university	PROPN
ejpam-3870	223	25	,	,	PUNCT
ejpam-3870	223	26	chalermphrakiat	chalermphrakiat	PROPN
ejpam-3870	223	27	sakon	sakon	PROPN
ejpam-3870	223	28	nakhon	nakhon	PROPN
ejpam-3870	223	29	province	province	PROPN
ejpam-3870	223	30	campus	campus	PROPN
ejpam-3870	223	31	,	,	PUNCT
ejpam-3870	223	32	for	for	ADP
ejpam-3870	223	33	support	support	NOUN
ejpam-3870	223	34	.	.	PUNCT
ejpam-3870	224	1	tt	tt	PROPN
ejpam-3870	224	2	was	be	AUX
ejpam-3870	224	3	financially	financially	ADV
ejpam-3870	224	4	supported	support	VERB
ejpam-3870	224	5	by	by	ADP
ejpam-3870	224	6	faculty	faculty	NOUN
ejpam-3870	224	7	of	of	ADP
ejpam-3870	224	8	science	science	NOUN
ejpam-3870	224	9	,	,	PUNCT
ejpam-3870	224	10	mahasarakham	mahasarakham	PROPN
ejpam-3870	224	11	university	university	PROPN
ejpam-3870	224	12	grant	grant	PROPN
ejpam-3870	224	13	year	year	NOUN
ejpam-3870	224	14	2018	2018	NUM
ejpam-3870	224	15	.	.	PUNCT
ejpam-3870	225	1	references	reference	NOUN
ejpam-3870	225	2	994	994	NUM
ejpam-3870	225	3	references	reference	NOUN
ejpam-3870	225	4	[	[	X
ejpam-3870	225	5	1	1	NUM
ejpam-3870	225	6	]	]	X
ejpam-3870	225	7	f	f	PROPN
ejpam-3870	225	8	catino	catino	NOUN
ejpam-3870	225	9	and	and	CCONJ
ejpam-3870	225	10	f	f	PROPN
ejpam-3870	225	11	migliorini	migliorini	NOUN
ejpam-3870	225	12	.	.	PUNCT
ejpam-3870	226	1	magnifying	magnify	VERB
ejpam-3870	226	2	elements	element	NOUN
ejpam-3870	226	3	in	in	ADP
ejpam-3870	226	4	semigroups	semigroup	NOUN
ejpam-3870	226	5	.	.	PUNCT
ejpam-3870	227	1	semigroup	semigroup	PROPN
ejpam-3870	227	2	forum	forum	PROPN
ejpam-3870	227	3	,	,	PUNCT
ejpam-3870	227	4	44(1):314–319	44(1):314–319	PROPN
ejpam-3870	227	5	,	,	PUNCT
ejpam-3870	227	6	1992	1992	NUM
ejpam-3870	227	7	.	.	PUNCT
ejpam-3870	228	1	[	[	X
ejpam-3870	228	2	2	2	NUM
ejpam-3870	228	3	]	]	X
ejpam-3870	228	4	m	m	VERB
ejpam-3870	228	5	gutan	gutan	ADJ
ejpam-3870	228	6	.	.	PUNCT
ejpam-3870	229	1	semigroups	semigroup	NOUN
ejpam-3870	229	2	with	with	ADP
ejpam-3870	229	3	strong	strong	ADJ
ejpam-3870	229	4	and	and	CCONJ
ejpam-3870	229	5	nonstrong	nonstrong	NOUN
ejpam-3870	229	6	magnifying	magnify	VERB
ejpam-3870	229	7	elements	element	NOUN
ejpam-3870	229	8	.	.	PUNCT
ejpam-3870	230	1	semigroup	semigroup	PROPN
ejpam-3870	230	2	forum	forum	PROPN
ejpam-3870	230	3	,	,	PUNCT
ejpam-3870	230	4	53(1):384–386	53(1):384–386	NUM
ejpam-3870	230	5	,	,	PUNCT
ejpam-3870	230	6	1996	1996	NUM
ejpam-3870	230	7	.	.	PUNCT
ejpam-3870	231	1	[	[	X
ejpam-3870	231	2	3	3	NUM
ejpam-3870	231	3	]	]	X
ejpam-3870	231	4	m	m	VERB
ejpam-3870	231	5	gutan	gutan	ADJ
ejpam-3870	231	6	.	.	PUNCT
ejpam-3870	232	1	semigroups	semigroup	NOUN
ejpam-3870	232	2	which	which	PRON
ejpam-3870	232	3	contain	contain	VERB
ejpam-3870	232	4	magnifying	magnifying	ADJ
ejpam-3870	232	5	elements	element	NOUN
ejpam-3870	232	6	are	be	AUX
ejpam-3870	232	7	factorizable	factorizable	ADJ
ejpam-3870	232	8	.	.	PUNCT
ejpam-3870	233	1	communications	communication	NOUN
ejpam-3870	233	2	in	in	ADP
ejpam-3870	233	3	algebra	algebra	NOUN
ejpam-3870	233	4	,	,	PUNCT
ejpam-3870	233	5	25(12):3953–3963	25(12):3953–3963	NUM
ejpam-3870	233	6	,	,	PUNCT
ejpam-3870	233	7	1997	1997	NUM
ejpam-3870	233	8	.	.	PUNCT
ejpam-3870	234	1	[	[	X
ejpam-3870	234	2	4	4	NUM
ejpam-3870	234	3	]	]	X
ejpam-3870	234	4	e	e	X
ejpam-3870	234	5	s	s	X
ejpam-3870	234	6	ljapin	ljapin	NOUN
ejpam-3870	234	7	.	.	PUNCT
ejpam-3870	235	1	semigroups	semigroup	NOUN
ejpam-3870	235	2	.	.	PUNCT
ejpam-3870	236	1	translations	translation	NOUN
ejpam-3870	236	2	of	of	ADP
ejpam-3870	236	3	mathematical	mathematical	ADJ
ejpam-3870	236	4	monographs	monograph	NOUN
ejpam-3870	236	5	,	,	PUNCT
ejpam-3870	236	6	volume	volume	NOUN
ejpam-3870	236	7	3	3	NUM
ejpam-3870	236	8	,	,	PUNCT
ejpam-3870	236	9	american	american	PROPN
ejpam-3870	236	10	mathematical	mathematical	ADJ
ejpam-3870	236	11	society	society	NOUN
ejpam-3870	236	12	,	,	PUNCT
ejpam-3870	236	13	providence	providence	NOUN
ejpam-3870	236	14	,	,	PUNCT
ejpam-3870	236	15	rhode	rhode	NOUN
ejpam-3870	236	16	island	island	NOUN
ejpam-3870	236	17	,	,	PUNCT
ejpam-3870	236	18	1963	1963	NUM
ejpam-3870	236	19	.	.	PUNCT
ejpam-3870	237	1	[	[	X
ejpam-3870	237	2	5	5	NUM
ejpam-3870	237	3	]	]	X
ejpam-3870	237	4	k	k	PROPN
ejpam-3870	237	5	d	d	PROPN
ejpam-3870	237	6	magill	magill	NOUN
ejpam-3870	237	7	.	.	PUNCT
ejpam-3870	238	1	magnifying	magnify	VERB
ejpam-3870	238	2	elements	element	NOUN
ejpam-3870	238	3	of	of	ADP
ejpam-3870	238	4	transformation	transformation	NOUN
ejpam-3870	238	5	semigroups	semigroup	NOUN
ejpam-3870	238	6	.	.	PUNCT
ejpam-3870	239	1	semigroup	semigroup	PROPN
ejpam-3870	239	2	forum	forum	PROPN
ejpam-3870	239	3	,	,	PUNCT
ejpam-3870	239	4	48(1):119–126	48(1):119–126	PROPN
ejpam-3870	239	5	,	,	PUNCT
ejpam-3870	239	6	1994	1994	NUM
ejpam-3870	239	7	.	.	PUNCT
ejpam-3870	240	1	[	[	X
ejpam-3870	240	2	6	6	NUM
ejpam-3870	240	3	]	]	SYM
ejpam-3870	240	4	f	f	PROPN
ejpam-3870	240	5	migliorini	migliorini	NOUN
ejpam-3870	240	6	.	.	PUNCT
ejpam-3870	241	1	some	some	PRON
ejpam-3870	241	2	researches	research	VERB
ejpam-3870	241	3	on	on	ADP
ejpam-3870	241	4	semigroups	semigroup	NOUN
ejpam-3870	241	5	with	with	ADP
ejpam-3870	241	6	magnifying	magnify	VERB
ejpam-3870	241	7	elements	element	NOUN
ejpam-3870	241	8	.	.	PUNCT
ejpam-3870	242	1	periodica	periodica	PROPN
ejpam-3870	242	2	mathematica	mathematica	PROPN
ejpam-3870	242	3	hungarica	hungarica	PROPN
ejpam-3870	242	4	,	,	PUNCT
ejpam-3870	242	5	1(4):279–286	1(4):279–286	NUM
ejpam-3870	242	6	,	,	PUNCT
ejpam-3870	242	7	1971	1971	NUM
ejpam-3870	242	8	.	.	PUNCT
ejpam-3870	243	1	[	[	X
ejpam-3870	243	2	7	7	NUM
ejpam-3870	243	3	]	]	SYM
ejpam-3870	243	4	f	f	PROPN
ejpam-3870	243	5	migliorini	migliorini	NOUN
ejpam-3870	243	6	.	.	PUNCT
ejpam-3870	244	1	magnifying	magnify	VERB
ejpam-3870	244	2	elements	element	NOUN
ejpam-3870	244	3	and	and	CCONJ
ejpam-3870	244	4	minimal	minimal	ADJ
ejpam-3870	244	5	subsemigroups	subsemigroup	NOUN
ejpam-3870	244	6	in	in	ADP
ejpam-3870	244	7	semigroups	semigroup	NOUN
ejpam-3870	244	8	.	.	PUNCT
ejpam-3870	245	1	periodica	periodica	PROPN
ejpam-3870	245	2	mathematica	mathematica	PROPN
ejpam-3870	245	3	hungarica	hungarica	PROPN
ejpam-3870	245	4	,	,	PUNCT
ejpam-3870	245	5	5(4):279–288	5(4):279–288	PROPN
ejpam-3870	245	6	,	,	PUNCT
ejpam-3870	245	7	1974	1974	NUM
ejpam-3870	245	8	.	.	PUNCT
ejpam-3870	246	1	[	[	X
ejpam-3870	246	2	8	8	NUM
ejpam-3870	246	3	]	]	X
ejpam-3870	246	4	r	r	NOUN
ejpam-3870	246	5	j	j	PROPN
ejpam-3870	246	6	plemmons	plemmon	NOUN
ejpam-3870	246	7	and	and	CCONJ
ejpam-3870	246	8	m	m	PROPN
ejpam-3870	246	9	t	t	NOUN
ejpam-3870	246	10	west	west	NOUN
ejpam-3870	246	11	.	.	PUNCT
ejpam-3870	247	1	on	on	ADP
ejpam-3870	247	2	the	the	DET
ejpam-3870	247	3	semigroups	semigroup	NOUN
ejpam-3870	247	4	of	of	ADP
ejpam-3870	247	5	binary	binary	NOUN
ejpam-3870	247	6	relations	relation	NOUN
ejpam-3870	247	7	.	.	PUNCT
ejpam-3870	248	1	pacific	pacific	PROPN
ejpam-3870	248	2	journal	journal	PROPN
ejpam-3870	248	3	of	of	ADP
ejpam-3870	248	4	mathematics	mathematic	NOUN
ejpam-3870	248	5	,	,	PUNCT
ejpam-3870	248	6	35(3):743–753	35(3):743–753	PROPN
ejpam-3870	248	7	,	,	PUNCT
ejpam-3870	248	8	1970	1970	NUM
ejpam-3870	248	9	.	.	PUNCT
ejpam-3870	249	1	[	[	X
ejpam-3870	249	2	9	9	NUM
ejpam-3870	249	3	]	]	SYM
ejpam-3870	249	4	r	r	NOUN
ejpam-3870	249	5	chinram	chinram	NOUN
ejpam-3870	249	6	,	,	PUNCT
ejpam-3870	249	7	p	p	NOUN
ejpam-3870	249	8	petchkaew	petchkaew	NOUN
ejpam-3870	249	9	and	and	CCONJ
ejpam-3870	249	10	s	s	NOUN
ejpam-3870	249	11	baupradist	baupradist	NOUN
ejpam-3870	249	12	.	.	PUNCT
ejpam-3870	250	1	left	leave	VERB
ejpam-3870	250	2	and	and	CCONJ
ejpam-3870	250	3	right	right	ADJ
ejpam-3870	250	4	magnifying	magnify	VERB
ejpam-3870	250	5	elements	element	NOUN
ejpam-3870	250	6	in	in	ADP
ejpam-3870	250	7	generalized	generalize	VERB
ejpam-3870	250	8	semigroups	semigroup	NOUN
ejpam-3870	250	9	of	of	ADP
ejpam-3870	250	10	transformations	transformation	NOUN
ejpam-3870	250	11	by	by	ADP
ejpam-3870	250	12	using	use	VERB
ejpam-3870	250	13	partitions	partition	NOUN
ejpam-3870	250	14	of	of	ADP
ejpam-3870	250	15	a	a	DET
ejpam-3870	250	16	set	set	NOUN
ejpam-3870	250	17	.	.	PUNCT
ejpam-3870	251	1	european	european	PROPN
ejpam-3870	251	2	journal	journal	PROPN
ejpam-3870	251	3	of	of	ADP
ejpam-3870	251	4	pure	pure	ADJ
ejpam-3870	251	5	and	and	CCONJ
ejpam-3870	251	6	applied	applied	ADJ
ejpam-3870	251	7	mathematics	mathematic	NOUN
ejpam-3870	251	8	,	,	PUNCT
ejpam-3870	251	9	11(3):580–588	11(3):580–588	NUM
ejpam-3870	251	10	,	,	PUNCT
ejpam-3870	251	11	2018	2018	NUM
ejpam-3870	251	12	.	.	PUNCT
ejpam-3870	252	1	[	[	X
ejpam-3870	252	2	10	10	NUM
ejpam-3870	252	3	]	]	PUNCT
ejpam-3870	252	4	s	s	PART
ejpam-3870	252	5	baupradist	baupradist	NOUN
ejpam-3870	252	6	,	,	PUNCT
ejpam-3870	252	7	t	t	NOUN
ejpam-3870	252	8	panityakul	panityakul	NOUN
ejpam-3870	252	9	and	and	CCONJ
ejpam-3870	252	10	r	r	NOUN
ejpam-3870	252	11	chinram	chinram	NOUN
ejpam-3870	252	12	.	.	PUNCT
ejpam-3870	253	1	left	leave	VERB
ejpam-3870	253	2	and	and	CCONJ
ejpam-3870	253	3	right	right	ADJ
ejpam-3870	253	4	magnifying	magnify	VERB
ejpam-3870	253	5	elements	element	NOUN
ejpam-3870	253	6	in	in	ADP
ejpam-3870	253	7	semigroups	semigroup	NOUN
ejpam-3870	253	8	of	of	ADP
ejpam-3870	253	9	linear	linear	ADJ
ejpam-3870	253	10	transformations	transformation	NOUN
ejpam-3870	253	11	with	with	ADP
ejpam-3870	253	12	restricted	restricted	ADJ
ejpam-3870	253	13	range	range	NOUN
ejpam-3870	253	14	.	.	PUNCT
ejpam-3870	254	1	international	international	ADJ
ejpam-3870	254	2	journal	journal	PROPN
ejpam-3870	254	3	of	of	ADP
ejpam-3870	254	4	mathematics	mathematic	NOUN
ejpam-3870	254	5	and	and	CCONJ
ejpam-3870	254	6	computer	computer	NOUN
ejpam-3870	254	7	science	science	NOUN
ejpam-3870	254	8	,	,	PUNCT
ejpam-3870	254	9	14(1):1–8	14(1):1–8	PROPN
ejpam-3870	254	10	,	,	PUNCT
ejpam-3870	254	11	2019	2019	NUM
ejpam-3870	254	12	.	.	PUNCT
ejpam-3870	255	1	[	[	X
ejpam-3870	255	2	11	11	NUM
ejpam-3870	255	3	]	]	SYM
ejpam-3870	255	4	b	b	PROPN
ejpam-3870	255	5	m	m	PROPN
ejpam-3870	255	6	schein	schein	NOUN
ejpam-3870	255	7	.	.	PUNCT
ejpam-3870	256	1	regular	regular	ADJ
ejpam-3870	256	2	elements	element	NOUN
ejpam-3870	256	3	of	of	ADP
ejpam-3870	256	4	the	the	DET
ejpam-3870	256	5	semigroup	semigroup	NOUN
ejpam-3870	256	6	of	of	ADP
ejpam-3870	256	7	all	all	DET
ejpam-3870	256	8	binary	binary	ADJ
ejpam-3870	256	9	relations	relation	NOUN
ejpam-3870	256	10	.	.	PUNCT
ejpam-3870	257	1	semigroup	semigroup	PROPN
ejpam-3870	257	2	forum	forum	PROPN
ejpam-3870	257	3	,	,	PUNCT
ejpam-3870	257	4	13(1):95102	13(1):95102	NUM
ejpam-3870	257	5	,	,	PUNCT
ejpam-3870	257	6	1976	1976	NUM
ejpam-3870	257	7	.	.	PUNCT
ejpam-3870	258	1	[	[	X
ejpam-3870	258	2	12	12	NUM
ejpam-3870	258	3	]	]	X
ejpam-3870	258	4	s	s	PART
ejpam-3870	258	5	schwarz	schwarz	PROPN
ejpam-3870	258	6	.	.	PUNCT
ejpam-3870	259	1	on	on	ADP
ejpam-3870	259	2	the	the	DET
ejpam-3870	259	3	semigroup	semigroup	NOUN
ejpam-3870	259	4	of	of	ADP
ejpam-3870	259	5	binary	binary	ADJ
ejpam-3870	259	6	relations	relation	NOUN
ejpam-3870	259	7	on	on	ADP
ejpam-3870	259	8	a	a	DET
ejpam-3870	259	9	finite	finite	ADJ
ejpam-3870	259	10	set	set	NOUN
ejpam-3870	259	11	.	.	PUNCT
ejpam-3870	260	1	czechoslovak	czechoslovak	ADJ
ejpam-3870	260	2	mathematical	mathematical	PROPN
ejpam-3870	260	3	journal	journal	PROPN
ejpam-3870	260	4	,	,	PUNCT
ejpam-3870	260	5	20(4):632–679	20(4):632–679	PROPN
ejpam-3870	260	6	,	,	PUNCT
ejpam-3870	260	7	1970	1970	NUM
ejpam-3870	260	8	.	.	PUNCT