id	sid	tid	token	lemma	pos
ejpam-3260	1	1	european	european	PROPN
ejpam-3260	1	2	journal	journal	PROPN
ejpam-3260	1	3	of	of	ADP
ejpam-3260	1	4	pure	pure	ADJ
ejpam-3260	1	5	and	and	CCONJ
ejpam-3260	1	6	applied	apply	VERB
ejpam-3260	1	7	mathematics	mathematic	NOUN
ejpam-3260	1	8	vol	vol	NOUN
ejpam-3260	1	9	.	.	PUNCT
ejpam-3260	2	1	11	11	NUM
ejpam-3260	2	2	,	,	PUNCT
ejpam-3260	2	3	no	no	INTJ
ejpam-3260	2	4	.	.	NOUN
ejpam-3260	2	5	3	3	NUM
ejpam-3260	2	6	,	,	PUNCT
ejpam-3260	2	7	2018	2018	NUM
ejpam-3260	2	8	,	,	PUNCT
ejpam-3260	2	9	580	580	NUM
ejpam-3260	2	10	-	-	SYM
ejpam-3260	2	11	588	588	NUM
ejpam-3260	2	12	issn	issn	PROPN
ejpam-3260	2	13	1307	1307	NUM
ejpam-3260	2	14	-	-	SYM
ejpam-3260	2	15	5543	5543	NUM
ejpam-3260	2	16	–	–	PUNCT
ejpam-3260	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3260	2	18	published	publish	VERB
ejpam-3260	2	19	by	by	ADP
ejpam-3260	2	20	new	new	PROPN
ejpam-3260	2	21	york	york	PROPN
ejpam-3260	2	22	business	business	PROPN
ejpam-3260	2	23	global	global	PROPN
ejpam-3260	2	24	left	leave	VERB
ejpam-3260	2	25	and	and	CCONJ
ejpam-3260	2	26	right	right	ADJ
ejpam-3260	2	27	magnifying	magnify	VERB
ejpam-3260	2	28	elements	element	NOUN
ejpam-3260	2	29	in	in	ADP
ejpam-3260	2	30	generalized	generalize	VERB
ejpam-3260	2	31	semigroups	semigroup	NOUN
ejpam-3260	2	32	of	of	ADP
ejpam-3260	2	33	transformations	transformation	NOUN
ejpam-3260	2	34	by	by	ADP
ejpam-3260	2	35	using	use	VERB
ejpam-3260	2	36	partitions	partition	NOUN
ejpam-3260	2	37	of	of	ADP
ejpam-3260	2	38	a	a	DET
ejpam-3260	2	39	set	set	VERB
ejpam-3260	2	40	ronnason	ronnason	NOUN
ejpam-3260	2	41	chinram1,4	chinram1,4	PROPN
ejpam-3260	2	42	,	,	PUNCT
ejpam-3260	2	43	pattarawan	pattarawan	NOUN
ejpam-3260	2	44	petchkaew2	petchkaew2	NOUN
ejpam-3260	2	45	,	,	PUNCT
ejpam-3260	2	46	samruam	samruam	PROPN
ejpam-3260	2	47	baupradist3,∗	baupradist3,∗	VERB
ejpam-3260	2	48	1	1	NUM
ejpam-3260	2	49	department	department	NOUN
ejpam-3260	2	50	of	of	ADP
ejpam-3260	2	51	mathematics	mathematic	NOUN
ejpam-3260	2	52	and	and	CCONJ
ejpam-3260	2	53	statistics	statistic	NOUN
ejpam-3260	2	54	,	,	PUNCT
ejpam-3260	2	55	faculty	faculty	NOUN
ejpam-3260	2	56	of	of	ADP
ejpam-3260	2	57	science	science	NOUN
ejpam-3260	2	58	,	,	PUNCT
ejpam-3260	2	59	prince	prince	NOUN
ejpam-3260	2	60	of	of	ADP
ejpam-3260	2	61	songkla	songkla	PROPN
ejpam-3260	2	62	university	university	PROPN
ejpam-3260	2	63	,	,	PUNCT
ejpam-3260	2	64	hat	hat	PROPN
ejpam-3260	2	65	yai	yai	PROPN
ejpam-3260	2	66	,	,	PUNCT
ejpam-3260	2	67	songkhla	songkhla	ADJ
ejpam-3260	2	68	,	,	PUNCT
ejpam-3260	2	69	90110	90110	NUM
ejpam-3260	2	70	,	,	PUNCT
ejpam-3260	2	71	thailand	thailand	PROPN
ejpam-3260	2	72	2	2	NUM
ejpam-3260	2	73	mathematics	mathematic	NOUN
ejpam-3260	2	74	and	and	CCONJ
ejpam-3260	2	75	statistics	statistic	NOUN
ejpam-3260	2	76	program	program	NOUN
ejpam-3260	2	77	,	,	PUNCT
ejpam-3260	2	78	faculty	faculty	NOUN
ejpam-3260	2	79	of	of	ADP
ejpam-3260	2	80	science	science	NOUN
ejpam-3260	2	81	and	and	CCONJ
ejpam-3260	2	82	technology	technology	NOUN
ejpam-3260	2	83	,	,	PUNCT
ejpam-3260	2	84	songkhla	songkhla	VERB
ejpam-3260	2	85	rajabhat	rajabhat	ADJ
ejpam-3260	2	86	university	university	NOUN
ejpam-3260	2	87	,	,	PUNCT
ejpam-3260	2	88	songkhla	songkhla	ADJ
ejpam-3260	2	89	,	,	PUNCT
ejpam-3260	2	90	90000	90000	NUM
ejpam-3260	2	91	,	,	PUNCT
ejpam-3260	2	92	thailand	thailand	PROPN
ejpam-3260	2	93	3	3	NUM
ejpam-3260	2	94	department	department	NOUN
ejpam-3260	2	95	of	of	ADP
ejpam-3260	2	96	mathematics	mathematic	NOUN
ejpam-3260	2	97	and	and	CCONJ
ejpam-3260	2	98	computer	computer	NOUN
ejpam-3260	2	99	science	science	NOUN
ejpam-3260	2	100	,	,	PUNCT
ejpam-3260	2	101	faculty	faculty	NOUN
ejpam-3260	2	102	of	of	ADP
ejpam-3260	2	103	science	science	NOUN
ejpam-3260	2	104	,	,	PUNCT
ejpam-3260	2	105	chulalongkorn	chulalongkorn	NOUN
ejpam-3260	2	106	university	university	NOUN
ejpam-3260	2	107	,	,	PUNCT
ejpam-3260	2	108	bangkok	bangkok	PROPN
ejpam-3260	2	109	,	,	PUNCT
ejpam-3260	2	110	10330	10330	NUM
ejpam-3260	2	111	,	,	PUNCT
ejpam-3260	2	112	thailand	thailand	PROPN
ejpam-3260	2	113	4	4	NUM
ejpam-3260	2	114	centre	centre	NOUN
ejpam-3260	2	115	of	of	ADP
ejpam-3260	2	116	excellence	excellence	NOUN
ejpam-3260	2	117	in	in	ADP
ejpam-3260	2	118	mathematics	mathematics	PROPN
ejpam-3260	2	119	,	,	PUNCT
ejpam-3260	2	120	che	che	PROPN
ejpam-3260	2	121	,	,	PUNCT
ejpam-3260	2	122	si	si	PROPN
ejpam-3260	2	123	ayuthaya	ayuthaya	PROPN
ejpam-3260	2	124	road	road	PROPN
ejpam-3260	2	125	,	,	PUNCT
ejpam-3260	2	126	bangkok	bangkok	PROPN
ejpam-3260	2	127	10400	10400	NUM
ejpam-3260	2	128	,	,	PUNCT
ejpam-3260	2	129	thailand	thailand	PROPN
ejpam-3260	2	130	abstract	abstract	PROPN
ejpam-3260	2	131	.	.	PUNCT
ejpam-3260	3	1	an	an	DET
ejpam-3260	3	2	element	element	NOUN
ejpam-3260	3	3	a	a	PRON
ejpam-3260	3	4	of	of	ADP
ejpam-3260	3	5	a	a	DET
ejpam-3260	3	6	semigroup	semigroup	NOUN
ejpam-3260	3	7	s	s	PART
ejpam-3260	3	8	is	be	AUX
ejpam-3260	3	9	called	call	VERB
ejpam-3260	3	10	left	leave	VERB
ejpam-3260	4	1	[	[	X
ejpam-3260	4	2	right	right	X
ejpam-3260	4	3	]	]	X
ejpam-3260	4	4	magnifying	magnify	VERB
ejpam-3260	4	5	if	if	SCONJ
ejpam-3260	4	6	there	there	PRON
ejpam-3260	4	7	exists	exist	VERB
ejpam-3260	4	8	a	a	DET
ejpam-3260	4	9	proper	proper	ADJ
ejpam-3260	4	10	subset	subset	NOUN
ejpam-3260	4	11	m	m	NOUN
ejpam-3260	4	12	of	of	ADP
ejpam-3260	4	13	s	s	PRON
ejpam-3260	4	14	such	such	ADJ
ejpam-3260	4	15	that	that	DET
ejpam-3260	4	16	s	s	PART
ejpam-3260	4	17	=	=	PRON
ejpam-3260	4	18	am	be	AUX
ejpam-3260	4	19	[	[	X
ejpam-3260	4	20	s	s	X
ejpam-3260	4	21	=	=	X
ejpam-3260	4	22	ma	ma	PROPN
ejpam-3260	4	23	]	]	X
ejpam-3260	4	24	.	.	PUNCT
ejpam-3260	5	1	let	let	VERB
ejpam-3260	5	2	x	x	PRON
ejpam-3260	5	3	be	be	AUX
ejpam-3260	5	4	a	a	DET
ejpam-3260	5	5	nonempty	nonempty	ADV
ejpam-3260	5	6	set	set	VERB
ejpam-3260	5	7	and	and	CCONJ
ejpam-3260	5	8	t	t	PROPN
ejpam-3260	5	9	(	(	PUNCT
ejpam-3260	5	10	x	x	X
ejpam-3260	5	11	)	)	PUNCT
ejpam-3260	5	12	be	be	VERB
ejpam-3260	5	13	the	the	DET
ejpam-3260	5	14	semigroup	semigroup	NOUN
ejpam-3260	5	15	of	of	ADP
ejpam-3260	5	16	all	all	DET
ejpam-3260	5	17	transformations	transformation	NOUN
ejpam-3260	5	18	from	from	ADP
ejpam-3260	5	19	x	x	PUNCT
ejpam-3260	5	20	into	into	ADP
ejpam-3260	5	21	itself	itself	PRON
ejpam-3260	5	22	under	under	ADP
ejpam-3260	5	23	the	the	DET
ejpam-3260	5	24	composition	composition	NOUN
ejpam-3260	5	25	of	of	ADP
ejpam-3260	5	26	functions	function	NOUN
ejpam-3260	5	27	.	.	PUNCT
ejpam-3260	6	1	for	for	ADP
ejpam-3260	6	2	a	a	DET
ejpam-3260	6	3	partition	partition	NOUN
ejpam-3260	6	4	p	p	NOUN
ejpam-3260	6	5	=	=	PUNCT
ejpam-3260	6	6	{	{	PUNCT
ejpam-3260	6	7	xα	xα	INTJ
ejpam-3260	7	1	|	|	ADV
ejpam-3260	7	2	α	α	NOUN
ejpam-3260	7	3	∈	∈	PROPN
ejpam-3260	8	1	i	i	X
ejpam-3260	8	2	}	}	PUNCT
ejpam-3260	8	3	of	of	ADP
ejpam-3260	8	4	the	the	DET
ejpam-3260	8	5	set	set	NOUN
ejpam-3260	8	6	x	x	NOUN
ejpam-3260	8	7	,	,	PUNCT
ejpam-3260	8	8	let	let	VERB
ejpam-3260	8	9	t	t	PROPN
ejpam-3260	8	10	(	(	PUNCT
ejpam-3260	8	11	x	x	X
ejpam-3260	8	12	,	,	PUNCT
ejpam-3260	8	13	p	p	NOUN
ejpam-3260	8	14	)	)	PUNCT
ejpam-3260	8	15	=	=	PUNCT
ejpam-3260	9	1	{	{	PUNCT
ejpam-3260	9	2	f	f	PROPN
ejpam-3260	9	3	∈	∈	PROPN
ejpam-3260	9	4	t	t	PROPN
ejpam-3260	9	5	(	(	PUNCT
ejpam-3260	9	6	x	x	X
ejpam-3260	9	7	)	)	PUNCT
ejpam-3260	9	8	|	|	ADV
ejpam-3260	9	9	(	(	PUNCT
ejpam-3260	9	10	xα)f	xα)f	PROPN
ejpam-3260	9	11	⊆	⊆	NUM
ejpam-3260	9	12	xα	xα	ADP
ejpam-3260	9	13	for	for	ADP
ejpam-3260	9	14	all	all	DET
ejpam-3260	9	15	α	α	NOUN
ejpam-3260	9	16	∈	∈	PROPN
ejpam-3260	9	17	i	i	X
ejpam-3260	9	18	}	}	PUNCT
ejpam-3260	9	19	.	.	PUNCT
ejpam-3260	10	1	then	then	ADV
ejpam-3260	10	2	t	t	PROPN
ejpam-3260	10	3	(	(	PUNCT
ejpam-3260	10	4	x	x	X
ejpam-3260	10	5	,	,	PUNCT
ejpam-3260	10	6	p	p	NOUN
ejpam-3260	10	7	)	)	PUNCT
ejpam-3260	10	8	is	be	AUX
ejpam-3260	10	9	a	a	DET
ejpam-3260	10	10	subsemigroup	subsemigroup	NOUN
ejpam-3260	10	11	of	of	ADP
ejpam-3260	10	12	t	t	PROPN
ejpam-3260	10	13	(	(	PUNCT
ejpam-3260	10	14	x	x	NOUN
ejpam-3260	10	15	)	)	PUNCT
ejpam-3260	10	16	and	and	CCONJ
ejpam-3260	10	17	if	if	SCONJ
ejpam-3260	10	18	p	p	X
ejpam-3260	10	19	=	=	X
ejpam-3260	10	20	{	{	PUNCT
ejpam-3260	10	21	x	x	NOUN
ejpam-3260	10	22	}	}	PUNCT
ejpam-3260	10	23	,	,	PUNCT
ejpam-3260	10	24	t	t	PROPN
ejpam-3260	10	25	(	(	PUNCT
ejpam-3260	10	26	x	x	X
ejpam-3260	10	27	,	,	PUNCT
ejpam-3260	10	28	p	p	NOUN
ejpam-3260	10	29	)	)	PUNCT
ejpam-3260	10	30	=	=	SYM
ejpam-3260	10	31	t	t	PROPN
ejpam-3260	10	32	(	(	PUNCT
ejpam-3260	10	33	x	x	NOUN
ejpam-3260	10	34	)	)	PUNCT
ejpam-3260	10	35	.	.	PUNCT
ejpam-3260	11	1	our	our	PRON
ejpam-3260	11	2	aim	aim	NOUN
ejpam-3260	11	3	in	in	ADP
ejpam-3260	11	4	this	this	DET
ejpam-3260	11	5	paper	paper	NOUN
ejpam-3260	11	6	is	be	AUX
ejpam-3260	11	7	to	to	PART
ejpam-3260	11	8	give	give	VERB
ejpam-3260	11	9	necessary	necessary	ADJ
ejpam-3260	11	10	and	and	CCONJ
ejpam-3260	11	11	sufficient	sufficient	ADJ
ejpam-3260	11	12	conditions	condition	NOUN
ejpam-3260	11	13	for	for	ADP
ejpam-3260	11	14	elements	element	NOUN
ejpam-3260	11	15	in	in	ADP
ejpam-3260	11	16	t	t	PROPN
ejpam-3260	11	17	(	(	PUNCT
ejpam-3260	11	18	x	x	X
ejpam-3260	11	19	,	,	PUNCT
ejpam-3260	11	20	p	p	NOUN
ejpam-3260	11	21	)	)	PUNCT
ejpam-3260	11	22	to	to	PART
ejpam-3260	11	23	be	be	AUX
ejpam-3260	11	24	left	leave	VERB
ejpam-3260	11	25	or	or	CCONJ
ejpam-3260	11	26	right	right	ADJ
ejpam-3260	11	27	magnifying	magnify	VERB
ejpam-3260	11	28	.	.	PUNCT
ejpam-3260	12	1	moreover	moreover	ADV
ejpam-3260	12	2	,	,	PUNCT
ejpam-3260	12	3	we	we	PRON
ejpam-3260	12	4	apply	apply	VERB
ejpam-3260	12	5	those	those	DET
ejpam-3260	12	6	conditions	condition	NOUN
ejpam-3260	12	7	to	to	PART
ejpam-3260	12	8	give	give	VERB
ejpam-3260	12	9	necessary	necessary	ADJ
ejpam-3260	12	10	and	and	CCONJ
ejpam-3260	12	11	sufficient	sufficient	ADJ
ejpam-3260	12	12	conditions	condition	NOUN
ejpam-3260	12	13	for	for	ADP
ejpam-3260	12	14	elements	element	NOUN
ejpam-3260	12	15	in	in	ADP
ejpam-3260	12	16	some	some	DET
ejpam-3260	12	17	generalized	generalize	VERB
ejpam-3260	12	18	linear	linear	NOUN
ejpam-3260	12	19	transformation	transformation	NOUN
ejpam-3260	12	20	semigroups	semigroup	NOUN
ejpam-3260	12	21	.	.	PUNCT
ejpam-3260	13	1	2010	2010	NUM
ejpam-3260	13	2	mathematics	mathematic	NOUN
ejpam-3260	13	3	subject	subject	NOUN
ejpam-3260	13	4	classifications	classification	NOUN
ejpam-3260	13	5	:	:	PUNCT
ejpam-3260	13	6	20m10	20m10	NUM
ejpam-3260	13	7	,	,	PUNCT
ejpam-3260	13	8	20m20	20m20	NUM
ejpam-3260	13	9	key	key	ADJ
ejpam-3260	13	10	words	word	NOUN
ejpam-3260	13	11	and	and	CCONJ
ejpam-3260	13	12	phrases	phrase	NOUN
ejpam-3260	13	13	:	:	PUNCT
ejpam-3260	13	14	functions	function	NOUN
ejpam-3260	13	15	,	,	PUNCT
ejpam-3260	13	16	transformation	transformation	NOUN
ejpam-3260	13	17	semigroups	semigroup	NOUN
ejpam-3260	13	18	,	,	PUNCT
ejpam-3260	13	19	partitions	partition	NOUN
ejpam-3260	13	20	,	,	PUNCT
ejpam-3260	13	21	left	leave	VERB
ejpam-3260	13	22	magnifying	magnify	VERB
ejpam-3260	13	23	elements	element	NOUN
ejpam-3260	13	24	,	,	PUNCT
ejpam-3260	13	25	right	right	ADJ
ejpam-3260	13	26	magnifying	magnify	VERB
ejpam-3260	13	27	elements	element	NOUN
ejpam-3260	13	28	.	.	PUNCT
ejpam-3260	14	1	1	1	X
ejpam-3260	14	2	.	.	X
ejpam-3260	14	3	introduction	introduction	NOUN
ejpam-3260	14	4	and	and	CCONJ
ejpam-3260	14	5	preliminaries	preliminary	NOUN
ejpam-3260	14	6	the	the	DET
ejpam-3260	14	7	notions	notion	NOUN
ejpam-3260	14	8	of	of	ADP
ejpam-3260	14	9	left	left	ADJ
ejpam-3260	14	10	and	and	CCONJ
ejpam-3260	14	11	right	right	ADJ
ejpam-3260	14	12	magnifying	magnify	VERB
ejpam-3260	14	13	elements	element	NOUN
ejpam-3260	14	14	of	of	ADP
ejpam-3260	14	15	semigroups	semigroup	NOUN
ejpam-3260	14	16	were	be	AUX
ejpam-3260	14	17	introduced	introduce	VERB
ejpam-3260	14	18	by	by	ADP
ejpam-3260	14	19	ljapin	ljapin	X
ejpam-3260	15	1	[	[	X
ejpam-3260	15	2	7	7	NUM
ejpam-3260	15	3	]	]	PUNCT
ejpam-3260	15	4	.	.	PUNCT
ejpam-3260	16	1	an	an	DET
ejpam-3260	16	2	element	element	NOUN
ejpam-3260	16	3	a	a	PRON
ejpam-3260	16	4	of	of	ADP
ejpam-3260	16	5	a	a	DET
ejpam-3260	16	6	semigroup	semigroup	NOUN
ejpam-3260	16	7	s	s	PART
ejpam-3260	16	8	is	be	AUX
ejpam-3260	16	9	called	call	VERB
ejpam-3260	16	10	left	leave	VERB
ejpam-3260	17	1	[	[	X
ejpam-3260	17	2	right	right	X
ejpam-3260	17	3	]	]	X
ejpam-3260	17	4	magnifying	magnify	VERB
ejpam-3260	17	5	if	if	SCONJ
ejpam-3260	17	6	there	there	PRON
ejpam-3260	17	7	exists	exist	VERB
ejpam-3260	17	8	a	a	DET
ejpam-3260	17	9	proper	proper	ADJ
ejpam-3260	17	10	subset	subset	NOUN
ejpam-3260	17	11	m	m	NOUN
ejpam-3260	17	12	of	of	ADP
ejpam-3260	17	13	s	s	PRON
ejpam-3260	17	14	such	such	ADJ
ejpam-3260	17	15	that	that	DET
ejpam-3260	17	16	s	s	PART
ejpam-3260	17	17	=	=	PRON
ejpam-3260	17	18	am	be	AUX
ejpam-3260	17	19	[	[	X
ejpam-3260	17	20	s	s	X
ejpam-3260	17	21	=	=	X
ejpam-3260	17	22	ma	ma	PROPN
ejpam-3260	17	23	]	]	X
ejpam-3260	17	24	.	.	PUNCT
ejpam-3260	18	1	minimal	minimal	ADJ
ejpam-3260	18	2	subsets	subset	NOUN
ejpam-3260	18	3	associated	associate	VERB
ejpam-3260	18	4	with	with	ADP
ejpam-3260	18	5	the	the	DET
ejpam-3260	18	6	magnifying	magnifying	ADJ
ejpam-3260	18	7	element	element	NOUN
ejpam-3260	18	8	,	,	PUNCT
ejpam-3260	18	9	were	be	AUX
ejpam-3260	18	10	introduced	introduce	VERB
ejpam-3260	18	11	and	and	CCONJ
ejpam-3260	18	12	studied	study	VERB
ejpam-3260	18	13	by	by	ADP
ejpam-3260	18	14	migliorini	migliorini	NOUN
ejpam-3260	18	15	in	in	ADP
ejpam-3260	18	16	[	[	X
ejpam-3260	18	17	9	9	NUM
ejpam-3260	18	18	]	]	PUNCT
ejpam-3260	18	19	and	and	CCONJ
ejpam-3260	18	20	[	[	X
ejpam-3260	18	21	10	10	NUM
ejpam-3260	18	22	]	]	PUNCT
ejpam-3260	18	23	.	.	PUNCT
ejpam-3260	19	1	in	in	ADP
ejpam-3260	19	2	[	[	X
ejpam-3260	19	3	2	2	NUM
ejpam-3260	19	4	]	]	PUNCT
ejpam-3260	19	5	,	,	PUNCT
ejpam-3260	19	6	catino	catino	NOUN
ejpam-3260	19	7	and	and	CCONJ
ejpam-3260	19	8	migliorini	migliorini	NOUN
ejpam-3260	19	9	gave	give	VERB
ejpam-3260	19	10	necessary	necessary	ADJ
ejpam-3260	19	11	and	and	CCONJ
ejpam-3260	19	12	sufficient	sufficient	ADJ
ejpam-3260	19	13	conditions	condition	NOUN
ejpam-3260	19	14	for	for	SCONJ
ejpam-3260	19	15	any	any	DET
ejpam-3260	19	16	semigroup	semigroup	NOUN
ejpam-3260	19	17	to	to	PART
ejpam-3260	19	18	contain	contain	VERB
ejpam-3260	19	19	left	left	ADJ
ejpam-3260	19	20	or	or	CCONJ
ejpam-3260	19	21	right	right	ADJ
ejpam-3260	19	22	magnifying	magnifying	ADJ
ejpam-3260	19	23	elements	element	NOUN
ejpam-3260	19	24	.	.	PUNCT
ejpam-3260	20	1	in	in	ADP
ejpam-3260	20	2	[	[	X
ejpam-3260	20	3	8	8	NUM
ejpam-3260	20	4	]	]	PUNCT
ejpam-3260	20	5	,	,	PUNCT
ejpam-3260	20	6	magill	magill	NOUN
ejpam-3260	20	7	,	,	PUNCT
ejpam-3260	20	8	jr	jr	PROPN
ejpam-3260	20	9	.	.	PROPN
ejpam-3260	20	10	gave	give	VERB
ejpam-3260	20	11	necessary	necessary	ADJ
ejpam-3260	20	12	and	and	CCONJ
ejpam-3260	20	13	sufficient	sufficient	ADJ
ejpam-3260	20	14	∗corresponding	∗corresponding	NOUN
ejpam-3260	20	15	author	author	NOUN
ejpam-3260	20	16	.	.	PUNCT
ejpam-3260	21	1	doi	doi	NOUN
ejpam-3260	21	2	:	:	PUNCT
ejpam-3260	21	3	https://doi.org/10.29020/nybg.ejpam.v11i3.3260	https://doi.org/10.29020/nybg.ejpam.v11i3.3260	PRON
ejpam-3260	21	4	email	email	NOUN
ejpam-3260	21	5	addresses	address	NOUN
ejpam-3260	21	6	:	:	PUNCT
ejpam-3260	21	7	ronnason.c@psu.ac.th	ronnason.c@psu.ac.th	PROPN
ejpam-3260	21	8	(	(	PUNCT
ejpam-3260	21	9	r.	r.	PROPN
ejpam-3260	21	10	chinram	chinram	PROPN
ejpam-3260	21	11	)	)	PUNCT
ejpam-3260	21	12	,	,	PUNCT
ejpam-3260	21	13	pattarawan.pe@gmail.com	pattarawan.pe@gmail.com	PROPN
ejpam-3260	21	14	(	(	PUNCT
ejpam-3260	21	15	p.	p.	NOUN
ejpam-3260	21	16	petchkaew	petchkaew	NOUN
ejpam-3260	21	17	)	)	PUNCT
ejpam-3260	21	18	,	,	PUNCT
ejpam-3260	21	19	samruam.b@chula.ac.th	samruam.b@chula.ac.th	PROPN
ejpam-3260	21	20	(	(	PUNCT
ejpam-3260	21	21	s.	s.	PROPN
ejpam-3260	21	22	baupradist	baupradist	PROPN
ejpam-3260	21	23	)	)	PUNCT
ejpam-3260	21	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3260	22	1	580	580	NUM
ejpam-3260	22	2	c	c	NOUN
ejpam-3260	22	3	©	©	PROPN
ejpam-3260	22	4	2018	2018	NUM
ejpam-3260	22	5	ejpam	ejpam	VERB
ejpam-3260	22	6	all	all	DET
ejpam-3260	22	7	rights	right	NOUN
ejpam-3260	22	8	reserved	reserve	VERB
ejpam-3260	22	9	.	.	PUNCT
ejpam-3260	23	1	r.	r.	PROPN
ejpam-3260	23	2	chinram	chinram	PROPN
ejpam-3260	23	3	,	,	PUNCT
ejpam-3260	23	4	p.	p.	NOUN
ejpam-3260	23	5	petchkaew	petchkaew	NOUN
ejpam-3260	23	6	,	,	PUNCT
ejpam-3260	23	7	s.	s.	PROPN
ejpam-3260	23	8	baupradist	baupradist	PROPN
ejpam-3260	23	9	/	/	SYM
ejpam-3260	23	10	eur	eur	PROPN
ejpam-3260	23	11	.	.	PUNCT
ejpam-3260	24	1	j.	j.	PROPN
ejpam-3260	24	2	pure	pure	PROPN
ejpam-3260	24	3	appl	appl	PROPN
ejpam-3260	24	4	.	.	PROPN
ejpam-3260	24	5	math	math	PROPN
ejpam-3260	24	6	,	,	PUNCT
ejpam-3260	24	7	11	11	NUM
ejpam-3260	24	8	(	(	PUNCT
ejpam-3260	24	9	3	3	NUM
ejpam-3260	24	10	)	)	PUNCT
ejpam-3260	24	11	(	(	PUNCT
ejpam-3260	24	12	2018	2018	NUM
ejpam-3260	24	13	)	)	PUNCT
ejpam-3260	24	14	,	,	PUNCT
ejpam-3260	24	15	580	580	NUM
ejpam-3260	24	16	-	-	SYM
ejpam-3260	24	17	588	588	NUM
ejpam-3260	24	18	581	581	NUM
ejpam-3260	24	19	conditions	condition	NOUN
ejpam-3260	24	20	for	for	ADP
ejpam-3260	24	21	elements	element	NOUN
ejpam-3260	24	22	in	in	ADP
ejpam-3260	24	23	transformation	transformation	NOUN
ejpam-3260	24	24	semigroups	semigroup	NOUN
ejpam-3260	24	25	to	to	PART
ejpam-3260	24	26	be	be	AUX
ejpam-3260	24	27	left	leave	VERB
ejpam-3260	24	28	or	or	CCONJ
ejpam-3260	24	29	right	right	ADJ
ejpam-3260	24	30	magnifying	magnify	VERB
ejpam-3260	24	31	and	and	CCONJ
ejpam-3260	24	32	applied	apply	VERB
ejpam-3260	24	33	those	those	DET
ejpam-3260	24	34	conditions	condition	NOUN
ejpam-3260	24	35	for	for	ADP
ejpam-3260	24	36	elements	element	NOUN
ejpam-3260	24	37	in	in	ADP
ejpam-3260	24	38	linear	linear	ADJ
ejpam-3260	24	39	transformation	transformation	NOUN
ejpam-3260	24	40	semigroups	semigroup	NOUN
ejpam-3260	24	41	and	and	CCONJ
ejpam-3260	24	42	semigroups	semigroup	NOUN
ejpam-3260	24	43	of	of	ADP
ejpam-3260	24	44	all	all	DET
ejpam-3260	24	45	continuous	continuous	ADJ
ejpam-3260	24	46	selfmaps	selfmap	NOUN
ejpam-3260	24	47	of	of	ADP
ejpam-3260	24	48	topological	topological	ADJ
ejpam-3260	24	49	spaces	space	NOUN
ejpam-3260	24	50	to	to	PART
ejpam-3260	24	51	be	be	AUX
ejpam-3260	24	52	left	leave	VERB
ejpam-3260	24	53	or	or	CCONJ
ejpam-3260	24	54	right	right	ADJ
ejpam-3260	24	55	magnifying	magnify	VERB
ejpam-3260	24	56	.	.	PUNCT
ejpam-3260	25	1	gutan	gutan	PROPN
ejpam-3260	25	2	studied	study	VERB
ejpam-3260	25	3	semigroups	semigroup	NOUN
ejpam-3260	25	4	with	with	ADP
ejpam-3260	25	5	strong	strong	ADJ
ejpam-3260	25	6	and	and	CCONJ
ejpam-3260	25	7	nonstrong	nonstrong	NOUN
ejpam-3260	25	8	magnifying	magnify	VERB
ejpam-3260	25	9	elements	element	NOUN
ejpam-3260	25	10	in	in	ADP
ejpam-3260	25	11	[	[	X
ejpam-3260	25	12	3	3	NUM
ejpam-3260	25	13	]	]	PUNCT
ejpam-3260	25	14	and	and	CCONJ
ejpam-3260	25	15	showed	show	VERB
ejpam-3260	25	16	that	that	SCONJ
ejpam-3260	25	17	every	every	DET
ejpam-3260	25	18	semigroup	semigroup	NOUN
ejpam-3260	25	19	containing	contain	VERB
ejpam-3260	25	20	magnifying	magnify	VERB
ejpam-3260	25	21	elements	element	NOUN
ejpam-3260	25	22	is	be	AUX
ejpam-3260	25	23	factorizable	factorizable	NOUN
ejpam-3260	25	24	in	in	ADP
ejpam-3260	25	25	[	[	X
ejpam-3260	25	26	4	4	NUM
ejpam-3260	25	27	]	]	PUNCT
ejpam-3260	25	28	.	.	PUNCT
ejpam-3260	26	1	in	in	ADP
ejpam-3260	26	2	[	[	X
ejpam-3260	26	3	5	5	NUM
ejpam-3260	26	4	]	]	PUNCT
ejpam-3260	26	5	,	,	PUNCT
ejpam-3260	26	6	semigroups	semigroup	NOUN
ejpam-3260	26	7	with	with	ADP
ejpam-3260	26	8	magnifiers	magnifier	NOUN
ejpam-3260	26	9	admitting	admit	VERB
ejpam-3260	26	10	minimal	minimal	ADJ
ejpam-3260	26	11	subsemigroups	subsemigroup	NOUN
ejpam-3260	26	12	were	be	AUX
ejpam-3260	26	13	studied	study	VERB
ejpam-3260	26	14	by	by	ADP
ejpam-3260	26	15	gutan	gutan	PROPN
ejpam-3260	26	16	.	.	PUNCT
ejpam-3260	27	1	semigroups	semigroup	NOUN
ejpam-3260	27	2	with	with	ADP
ejpam-3260	27	3	good	good	ADJ
ejpam-3260	27	4	and	and	CCONJ
ejpam-3260	27	5	bad	bad	ADJ
ejpam-3260	27	6	magnifying	magnifying	NOUN
ejpam-3260	27	7	were	be	AUX
ejpam-3260	27	8	investigated	investigate	VERB
ejpam-3260	27	9	by	by	ADP
ejpam-3260	27	10	gutan	gutan	PROPN
ejpam-3260	27	11	and	and	CCONJ
ejpam-3260	27	12	kisielewicz	kisielewicz	NOUN
ejpam-3260	27	13	in	in	ADP
ejpam-3260	27	14	[	[	X
ejpam-3260	27	15	6	6	NUM
ejpam-3260	27	16	]	]	PUNCT
ejpam-3260	27	17	.	.	PUNCT
ejpam-3260	28	1	let	let	VERB
ejpam-3260	28	2	x	x	PRON
ejpam-3260	28	3	be	be	AUX
ejpam-3260	28	4	a	a	DET
ejpam-3260	28	5	nonempty	nonempty	ADV
ejpam-3260	28	6	set	set	VERB
ejpam-3260	28	7	and	and	CCONJ
ejpam-3260	28	8	let	let	VERB
ejpam-3260	28	9	t	t	PROPN
ejpam-3260	28	10	(	(	PUNCT
ejpam-3260	28	11	x	x	X
ejpam-3260	28	12	)	)	PUNCT
ejpam-3260	28	13	be	be	VERB
ejpam-3260	28	14	the	the	DET
ejpam-3260	28	15	set	set	NOUN
ejpam-3260	28	16	of	of	ADP
ejpam-3260	28	17	all	all	DET
ejpam-3260	28	18	transformations	transformation	NOUN
ejpam-3260	28	19	from	from	ADP
ejpam-3260	28	20	x	x	PUNCT
ejpam-3260	28	21	into	into	ADP
ejpam-3260	28	22	itself	itself	PRON
ejpam-3260	28	23	,	,	PUNCT
ejpam-3260	28	24	that	that	ADV
ejpam-3260	28	25	is	is	ADV
ejpam-3260	28	26	,	,	PUNCT
ejpam-3260	28	27	t	t	PROPN
ejpam-3260	28	28	(	(	PUNCT
ejpam-3260	28	29	x	x	X
ejpam-3260	28	30	)	)	PUNCT
ejpam-3260	28	31	=	=	PRON
ejpam-3260	29	1	{	{	PUNCT
ejpam-3260	29	2	f	f	NOUN
ejpam-3260	29	3	:	:	PUNCT
ejpam-3260	29	4	x	x	X
ejpam-3260	29	5	→	→	PUNCT
ejpam-3260	29	6	x	x	SYM
ejpam-3260	29	7	|	|	ADV
ejpam-3260	29	8	f	f	PROPN
ejpam-3260	29	9	is	be	AUX
ejpam-3260	29	10	a	a	DET
ejpam-3260	29	11	function	function	NOUN
ejpam-3260	29	12	}	}	PUNCT
ejpam-3260	29	13	.	.	PUNCT
ejpam-3260	30	1	it	it	PRON
ejpam-3260	30	2	is	be	AUX
ejpam-3260	30	3	well	well	ADV
ejpam-3260	30	4	-	-	PUNCT
ejpam-3260	30	5	known	know	VERB
ejpam-3260	30	6	that	that	SCONJ
ejpam-3260	30	7	t	t	PROPN
ejpam-3260	30	8	(	(	PUNCT
ejpam-3260	30	9	x	x	X
ejpam-3260	30	10	)	)	PUNCT
ejpam-3260	30	11	is	be	AUX
ejpam-3260	30	12	a	a	DET
ejpam-3260	30	13	semigroup	semigroup	NOUN
ejpam-3260	30	14	under	under	ADP
ejpam-3260	30	15	the	the	DET
ejpam-3260	30	16	composition	composition	NOUN
ejpam-3260	30	17	of	of	ADP
ejpam-3260	30	18	functions	function	NOUN
ejpam-3260	30	19	and	and	CCONJ
ejpam-3260	30	20	it	it	PRON
ejpam-3260	30	21	is	be	AUX
ejpam-3260	30	22	called	call	VERB
ejpam-3260	30	23	the	the	DET
ejpam-3260	30	24	full	full	ADJ
ejpam-3260	30	25	transformation	transformation	NOUN
ejpam-3260	30	26	semigroup	semigroup	NOUN
ejpam-3260	30	27	on	on	ADP
ejpam-3260	30	28	x.	x.	PROPN
ejpam-3260	30	29	transformation	transformation	PROPN
ejpam-3260	30	30	semigroups	semigroup	NOUN
ejpam-3260	30	31	play	play	VERB
ejpam-3260	30	32	an	an	DET
ejpam-3260	30	33	important	important	ADJ
ejpam-3260	30	34	role	role	NOUN
ejpam-3260	30	35	in	in	ADP
ejpam-3260	30	36	semigroup	semigroup	PROPN
ejpam-3260	30	37	theory	theory	NOUN
ejpam-3260	30	38	since	since	SCONJ
ejpam-3260	30	39	it	it	PRON
ejpam-3260	30	40	is	be	AUX
ejpam-3260	30	41	well	well	ADV
ejpam-3260	30	42	-	-	PUNCT
ejpam-3260	30	43	known	know	VERB
ejpam-3260	30	44	that	that	SCONJ
ejpam-3260	30	45	every	every	DET
ejpam-3260	30	46	semigroup	semigroup	NOUN
ejpam-3260	30	47	is	be	AUX
ejpam-3260	30	48	isomorphic	isomorphic	ADJ
ejpam-3260	30	49	to	to	ADP
ejpam-3260	30	50	a	a	DET
ejpam-3260	30	51	subsemigroup	subsemigroup	NOUN
ejpam-3260	30	52	of	of	ADP
ejpam-3260	30	53	a	a	DET
ejpam-3260	30	54	suitable	suitable	ADJ
ejpam-3260	30	55	full	full	ADJ
ejpam-3260	30	56	transformation	transformation	NOUN
ejpam-3260	30	57	semigroup	semigroup	NOUN
ejpam-3260	30	58	.	.	PUNCT
ejpam-3260	31	1	we	we	PRON
ejpam-3260	31	2	will	will	AUX
ejpam-3260	31	3	write	write	VERB
ejpam-3260	31	4	functions	function	NOUN
ejpam-3260	31	5	from	from	ADP
ejpam-3260	31	6	the	the	DET
ejpam-3260	31	7	right	right	NOUN
ejpam-3260	31	8	,	,	PUNCT
ejpam-3260	31	9	(	(	PUNCT
ejpam-3260	31	10	x)f	x)f	X
ejpam-3260	31	11	rather	rather	ADV
ejpam-3260	31	12	than	than	ADP
ejpam-3260	31	13	f(x	f(x	PROPN
ejpam-3260	31	14	)	)	PUNCT
ejpam-3260	31	15	and	and	CCONJ
ejpam-3260	31	16	compose	compose	VERB
ejpam-3260	31	17	from	from	ADP
ejpam-3260	31	18	the	the	DET
ejpam-3260	31	19	left	left	NOUN
ejpam-3260	31	20	to	to	ADP
ejpam-3260	31	21	the	the	DET
ejpam-3260	31	22	right	right	NOUN
ejpam-3260	31	23	,	,	PUNCT
ejpam-3260	31	24	(	(	PUNCT
ejpam-3260	31	25	x)(fg	x)(fg	NOUN
ejpam-3260	31	26	)	)	PUNCT
ejpam-3260	31	27	rather	rather	ADV
ejpam-3260	31	28	than	than	ADP
ejpam-3260	31	29	(	(	PUNCT
ejpam-3260	31	30	g	g	PROPN
ejpam-3260	31	31	◦	◦	NOUN
ejpam-3260	31	32	f)(x	f)(x	NOUN
ejpam-3260	31	33	)	)	PUNCT
ejpam-3260	31	34	,	,	PUNCT
ejpam-3260	31	35	for	for	ADP
ejpam-3260	31	36	f	f	PROPN
ejpam-3260	31	37	,	,	PUNCT
ejpam-3260	31	38	g	g	PROPN
ejpam-3260	31	39	∈	∈	PROPN
ejpam-3260	31	40	t	t	PROPN
ejpam-3260	31	41	(	(	PUNCT
ejpam-3260	31	42	x	x	NOUN
ejpam-3260	31	43	)	)	PUNCT
ejpam-3260	31	44	and	and	CCONJ
ejpam-3260	31	45	x	x	PUNCT
ejpam-3260	31	46	∈	∈	NOUN
ejpam-3260	31	47	x.	x.	NOUN
ejpam-3260	31	48	for	for	ADP
ejpam-3260	31	49	a	a	DET
ejpam-3260	31	50	partition	partition	NOUN
ejpam-3260	31	51	p	p	NOUN
ejpam-3260	31	52	=	=	PUNCT
ejpam-3260	31	53	{	{	PUNCT
ejpam-3260	32	1	xα	xα	INTJ
ejpam-3260	32	2	|	|	ADV
ejpam-3260	32	3	α	α	NOUN
ejpam-3260	32	4	∈	∈	PROPN
ejpam-3260	33	1	i	i	X
ejpam-3260	33	2	}	}	PUNCT
ejpam-3260	33	3	of	of	ADP
ejpam-3260	33	4	a	a	DET
ejpam-3260	33	5	set	set	NOUN
ejpam-3260	33	6	x	x	NOUN
ejpam-3260	33	7	,	,	PUNCT
ejpam-3260	33	8	consider	consider	VERB
ejpam-3260	33	9	the	the	DET
ejpam-3260	33	10	semigroup	semigroup	PROPN
ejpam-3260	33	11	t	t	PROPN
ejpam-3260	33	12	(	(	PUNCT
ejpam-3260	33	13	x	x	X
ejpam-3260	33	14	,	,	PUNCT
ejpam-3260	33	15	p	p	NOUN
ejpam-3260	33	16	)	)	PUNCT
ejpam-3260	34	1	=	=	PUNCT
ejpam-3260	34	2	{	{	PUNCT
ejpam-3260	34	3	f	f	PROPN
ejpam-3260	34	4	∈	∈	PROPN
ejpam-3260	34	5	t	t	PROPN
ejpam-3260	34	6	(	(	PUNCT
ejpam-3260	34	7	x	x	X
ejpam-3260	34	8	)	)	PUNCT
ejpam-3260	34	9	|	|	ADV
ejpam-3260	34	10	(	(	PUNCT
ejpam-3260	34	11	xα)f	xα)f	PROPN
ejpam-3260	34	12	⊆	⊆	NUM
ejpam-3260	34	13	xα	xα	ADP
ejpam-3260	34	14	for	for	ADP
ejpam-3260	34	15	all	all	DET
ejpam-3260	34	16	α	α	NOUN
ejpam-3260	34	17	∈	∈	PROPN
ejpam-3260	34	18	i	i	X
ejpam-3260	34	19	}	}	PUNCT
ejpam-3260	34	20	.	.	PUNCT
ejpam-3260	35	1	we	we	PRON
ejpam-3260	35	2	have	have	VERB
ejpam-3260	35	3	that	that	DET
ejpam-3260	35	4	t	t	NOUN
ejpam-3260	35	5	(	(	PUNCT
ejpam-3260	35	6	x	x	X
ejpam-3260	35	7	,	,	PUNCT
ejpam-3260	35	8	p	p	NOUN
ejpam-3260	35	9	)	)	PUNCT
ejpam-3260	35	10	is	be	AUX
ejpam-3260	35	11	a	a	DET
ejpam-3260	35	12	subsemigroup	subsemigroup	NOUN
ejpam-3260	35	13	of	of	ADP
ejpam-3260	35	14	t	t	PROPN
ejpam-3260	35	15	(	(	PUNCT
ejpam-3260	35	16	x	x	NOUN
ejpam-3260	35	17	)	)	PUNCT
ejpam-3260	35	18	and	and	CCONJ
ejpam-3260	35	19	if	if	SCONJ
ejpam-3260	35	20	p	p	X
ejpam-3260	35	21	=	=	X
ejpam-3260	35	22	{	{	PUNCT
ejpam-3260	35	23	x	x	NOUN
ejpam-3260	35	24	}	}	PUNCT
ejpam-3260	35	25	,	,	PUNCT
ejpam-3260	35	26	then	then	ADV
ejpam-3260	35	27	t	t	PROPN
ejpam-3260	35	28	(	(	PUNCT
ejpam-3260	35	29	x	x	X
ejpam-3260	35	30	,	,	PUNCT
ejpam-3260	35	31	p	p	NOUN
ejpam-3260	35	32	)	)	PUNCT
ejpam-3260	35	33	=	=	SYM
ejpam-3260	35	34	t	t	PROPN
ejpam-3260	35	35	(	(	PUNCT
ejpam-3260	35	36	x	x	NOUN
ejpam-3260	35	37	)	)	PUNCT
ejpam-3260	35	38	.	.	PUNCT
ejpam-3260	36	1	in	in	ADP
ejpam-3260	36	2	2015	2015	NUM
ejpam-3260	36	3	,	,	PUNCT
ejpam-3260	36	4	araujo	araujo	PROPN
ejpam-3260	36	5	,	,	PUNCT
ejpam-3260	36	6	bentz	bentz	PROPN
ejpam-3260	36	7	,	,	PUNCT
ejpam-3260	36	8	mitchelll	mitchelll	NOUN
ejpam-3260	36	9	and	and	CCONJ
ejpam-3260	36	10	schneider	schneider	NOUN
ejpam-3260	37	1	[	[	X
ejpam-3260	37	2	1	1	X
ejpam-3260	37	3	]	]	PUNCT
ejpam-3260	37	4	solved	solve	VERB
ejpam-3260	37	5	the	the	DET
ejpam-3260	37	6	problem	problem	NOUN
ejpam-3260	37	7	of	of	ADP
ejpam-3260	37	8	finding	find	VERB
ejpam-3260	37	9	the	the	DET
ejpam-3260	37	10	minimum	minimum	ADJ
ejpam-3260	37	11	size	size	NOUN
ejpam-3260	37	12	of	of	ADP
ejpam-3260	37	13	the	the	DET
ejpam-3260	37	14	generating	generate	VERB
ejpam-3260	37	15	sets	set	NOUN
ejpam-3260	37	16	of	of	ADP
ejpam-3260	37	17	t	t	PROPN
ejpam-3260	37	18	(	(	PUNCT
ejpam-3260	37	19	x	x	X
ejpam-3260	37	20	,	,	PUNCT
ejpam-3260	37	21	p	p	NOUN
ejpam-3260	37	22	)	)	PUNCT
ejpam-3260	37	23	,	,	PUNCT
ejpam-3260	37	24	when	when	SCONJ
ejpam-3260	37	25	p	p	NOUN
ejpam-3260	37	26	is	be	AUX
ejpam-3260	37	27	an	an	DET
ejpam-3260	37	28	arbitrary	arbitrary	ADJ
ejpam-3260	37	29	partition	partition	NOUN
ejpam-3260	37	30	.	.	PUNCT
ejpam-3260	38	1	next	next	ADV
ejpam-3260	38	2	,	,	PUNCT
ejpam-3260	38	3	in	in	ADP
ejpam-3260	38	4	2016	2016	NUM
ejpam-3260	38	5	,	,	PUNCT
ejpam-3260	38	6	purisang	purisang	PROPN
ejpam-3260	38	7	and	and	CCONJ
ejpam-3260	38	8	rakbud	rakbud	NOUN
ejpam-3260	38	9	investigated	investigate	VERB
ejpam-3260	38	10	the	the	DET
ejpam-3260	38	11	regularity	regularity	NOUN
ejpam-3260	38	12	of	of	ADP
ejpam-3260	38	13	transformation	transformation	NOUN
ejpam-3260	38	14	semigroups	semigroup	NOUN
ejpam-3260	38	15	which	which	PRON
ejpam-3260	38	16	defined	define	VERB
ejpam-3260	38	17	by	by	ADP
ejpam-3260	38	18	a	a	DET
ejpam-3260	38	19	partition	partition	NOUN
ejpam-3260	38	20	in	in	ADP
ejpam-3260	38	21	[	[	X
ejpam-3260	38	22	11	11	NUM
ejpam-3260	38	23	]	]	PUNCT
ejpam-3260	38	24	.	.	PUNCT
ejpam-3260	39	1	these	these	PRON
ejpam-3260	39	2	are	be	AUX
ejpam-3260	39	3	our	our	PRON
ejpam-3260	39	4	motivation	motivation	NOUN
ejpam-3260	39	5	to	to	PART
ejpam-3260	39	6	do	do	AUX
ejpam-3260	39	7	this	this	DET
ejpam-3260	39	8	research	research	NOUN
ejpam-3260	39	9	.	.	PUNCT
ejpam-3260	40	1	our	our	PRON
ejpam-3260	40	2	aim	aim	NOUN
ejpam-3260	40	3	in	in	ADP
ejpam-3260	40	4	this	this	DET
ejpam-3260	40	5	paper	paper	NOUN
ejpam-3260	40	6	is	be	AUX
ejpam-3260	40	7	to	to	PART
ejpam-3260	40	8	give	give	VERB
ejpam-3260	40	9	necessary	necessary	ADJ
ejpam-3260	40	10	and	and	CCONJ
ejpam-3260	40	11	sufficient	sufficient	ADJ
ejpam-3260	40	12	conditions	condition	NOUN
ejpam-3260	40	13	for	for	ADP
ejpam-3260	40	14	elements	element	NOUN
ejpam-3260	40	15	in	in	ADP
ejpam-3260	40	16	t	t	PROPN
ejpam-3260	40	17	(	(	PUNCT
ejpam-3260	40	18	x	x	X
ejpam-3260	40	19	,	,	PUNCT
ejpam-3260	40	20	p	p	NOUN
ejpam-3260	40	21	)	)	PUNCT
ejpam-3260	40	22	to	to	PART
ejpam-3260	40	23	be	be	AUX
ejpam-3260	40	24	left	leave	VERB
ejpam-3260	40	25	or	or	CCONJ
ejpam-3260	40	26	right	right	ADJ
ejpam-3260	40	27	magnifying	magnify	VERB
ejpam-3260	40	28	.	.	PUNCT
ejpam-3260	41	1	2	2	X
ejpam-3260	41	2	.	.	X
ejpam-3260	41	3	left	leave	VERB
ejpam-3260	41	4	magnifying	magnify	VERB
ejpam-3260	41	5	elements	element	NOUN
ejpam-3260	41	6	of	of	ADP
ejpam-3260	41	7	t	t	PROPN
ejpam-3260	41	8	(	(	PUNCT
ejpam-3260	41	9	x	x	X
ejpam-3260	41	10	,	,	PUNCT
ejpam-3260	41	11	p	p	NOUN
ejpam-3260	41	12	)	)	PUNCT
ejpam-3260	41	13	our	our	PRON
ejpam-3260	41	14	purpose	purpose	NOUN
ejpam-3260	41	15	in	in	ADP
ejpam-3260	41	16	this	this	DET
ejpam-3260	41	17	section	section	NOUN
ejpam-3260	41	18	is	be	AUX
ejpam-3260	41	19	to	to	PART
ejpam-3260	41	20	give	give	VERB
ejpam-3260	41	21	necessary	necessary	ADJ
ejpam-3260	41	22	and	and	CCONJ
ejpam-3260	41	23	sufficient	sufficient	ADJ
ejpam-3260	41	24	conditions	condition	NOUN
ejpam-3260	41	25	for	for	ADP
ejpam-3260	41	26	elements	element	NOUN
ejpam-3260	41	27	in	in	ADP
ejpam-3260	41	28	t	t	PROPN
ejpam-3260	41	29	(	(	PUNCT
ejpam-3260	41	30	x	x	X
ejpam-3260	41	31	,	,	PUNCT
ejpam-3260	41	32	p	p	NOUN
ejpam-3260	41	33	)	)	PUNCT
ejpam-3260	41	34	to	to	PART
ejpam-3260	41	35	be	be	AUX
ejpam-3260	41	36	left	leave	VERB
ejpam-3260	41	37	magnifying	magnify	VERB
ejpam-3260	41	38	.	.	PUNCT
ejpam-3260	42	1	lemma	lemma	PROPN
ejpam-3260	42	2	1	1	NUM
ejpam-3260	42	3	.	.	PUNCT
ejpam-3260	43	1	if	if	SCONJ
ejpam-3260	43	2	a	a	DET
ejpam-3260	43	3	function	function	NOUN
ejpam-3260	43	4	f	f	PROPN
ejpam-3260	43	5	is	be	AUX
ejpam-3260	43	6	left	leave	VERB
ejpam-3260	43	7	magnifying	magnify	VERB
ejpam-3260	43	8	of	of	ADP
ejpam-3260	43	9	t	t	PROPN
ejpam-3260	43	10	(	(	PUNCT
ejpam-3260	43	11	x	x	X
ejpam-3260	43	12	,	,	PUNCT
ejpam-3260	43	13	p	p	NOUN
ejpam-3260	43	14	)	)	PUNCT
ejpam-3260	43	15	,	,	PUNCT
ejpam-3260	43	16	then	then	ADV
ejpam-3260	43	17	f	f	PROPN
ejpam-3260	43	18	is	be	AUX
ejpam-3260	43	19	one	one	NUM
ejpam-3260	43	20	-	-	PUNCT
ejpam-3260	43	21	to	to	ADP
ejpam-3260	43	22	-	-	PUNCT
ejpam-3260	43	23	one	one	NUM
ejpam-3260	43	24	.	.	PUNCT
ejpam-3260	44	1	proof	proof	NOUN
ejpam-3260	44	2	.	.	PUNCT
ejpam-3260	45	1	assume	assume	VERB
ejpam-3260	45	2	that	that	SCONJ
ejpam-3260	45	3	f	f	PROPN
ejpam-3260	45	4	is	be	AUX
ejpam-3260	45	5	a	a	DET
ejpam-3260	45	6	left	left	ADJ
ejpam-3260	45	7	magnifying	magnifying	ADJ
ejpam-3260	45	8	element	element	NOUN
ejpam-3260	45	9	of	of	ADP
ejpam-3260	45	10	t	t	PROPN
ejpam-3260	45	11	(	(	PUNCT
ejpam-3260	45	12	x	x	X
ejpam-3260	45	13	,	,	PUNCT
ejpam-3260	45	14	p	p	NOUN
ejpam-3260	45	15	)	)	PUNCT
ejpam-3260	45	16	.	.	PUNCT
ejpam-3260	46	1	then	then	ADV
ejpam-3260	46	2	there	there	PRON
ejpam-3260	46	3	exists	exist	VERB
ejpam-3260	46	4	a	a	DET
ejpam-3260	46	5	proper	proper	ADJ
ejpam-3260	46	6	subset	subset	NOUN
ejpam-3260	46	7	m	m	NOUN
ejpam-3260	46	8	of	of	ADP
ejpam-3260	46	9	t	t	PROPN
ejpam-3260	46	10	(	(	PUNCT
ejpam-3260	46	11	x	x	X
ejpam-3260	46	12	,	,	PUNCT
ejpam-3260	46	13	p	p	NOUN
ejpam-3260	46	14	)	)	PUNCT
ejpam-3260	46	15	such	such	ADJ
ejpam-3260	46	16	that	that	SCONJ
ejpam-3260	46	17	fm	fm	PROPN
ejpam-3260	46	18	=	=	SYM
ejpam-3260	46	19	t	t	PROPN
ejpam-3260	46	20	(	(	PUNCT
ejpam-3260	46	21	x	x	X
ejpam-3260	46	22	,	,	PUNCT
ejpam-3260	46	23	p	p	NOUN
ejpam-3260	46	24	)	)	PUNCT
ejpam-3260	46	25	.	.	PUNCT
ejpam-3260	47	1	let	let	VERB
ejpam-3260	47	2	idx	idx	NOUN
ejpam-3260	47	3	be	be	AUX
ejpam-3260	47	4	an	an	DET
ejpam-3260	47	5	identity	identity	NOUN
ejpam-3260	47	6	function	function	NOUN
ejpam-3260	47	7	on	on	ADP
ejpam-3260	47	8	x.	x.	NOUN
ejpam-3260	47	9	clearly	clearly	ADV
ejpam-3260	47	10	,	,	PUNCT
ejpam-3260	47	11	idx	idx	PROPN
ejpam-3260	47	12	∈	∈	PROPN
ejpam-3260	47	13	t	t	NOUN
ejpam-3260	47	14	(	(	PUNCT
ejpam-3260	47	15	x	x	X
ejpam-3260	47	16	,	,	PUNCT
ejpam-3260	47	17	p	p	NOUN
ejpam-3260	47	18	)	)	PUNCT
ejpam-3260	47	19	.	.	PUNCT
ejpam-3260	48	1	so	so	ADV
ejpam-3260	48	2	there	there	PRON
ejpam-3260	48	3	exists	exist	VERB
ejpam-3260	48	4	a	a	DET
ejpam-3260	48	5	function	function	NOUN
ejpam-3260	48	6	h	h	NOUN
ejpam-3260	48	7	∈	∈	PROPN
ejpam-3260	48	8	m	m	VERB
ejpam-3260	48	9	such	such	ADJ
ejpam-3260	48	10	that	that	SCONJ
ejpam-3260	48	11	fh	fh	PROPN
ejpam-3260	48	12	=	=	PUNCT
ejpam-3260	48	13	idx	idx	PROPN
ejpam-3260	48	14	.	.	PUNCT
ejpam-3260	49	1	this	this	PRON
ejpam-3260	49	2	implies	imply	VERB
ejpam-3260	49	3	that	that	SCONJ
ejpam-3260	49	4	f	f	PROPN
ejpam-3260	49	5	is	be	AUX
ejpam-3260	49	6	one	one	NUM
ejpam-3260	49	7	-	-	PUNCT
ejpam-3260	49	8	to	to	ADP
ejpam-3260	49	9	-	-	PUNCT
ejpam-3260	49	10	one	one	NUM
ejpam-3260	49	11	.	.	PUNCT
ejpam-3260	50	1	lemma	lemma	PROPN
ejpam-3260	50	2	2	2	NUM
ejpam-3260	50	3	.	.	PUNCT
ejpam-3260	51	1	if	if	SCONJ
ejpam-3260	51	2	f	f	PROPN
ejpam-3260	51	3	∈	∈	PROPN
ejpam-3260	51	4	t	t	PROPN
ejpam-3260	51	5	(	(	PUNCT
ejpam-3260	51	6	x	x	X
ejpam-3260	51	7	,	,	PUNCT
ejpam-3260	51	8	p	p	NOUN
ejpam-3260	51	9	)	)	PUNCT
ejpam-3260	51	10	is	be	AUX
ejpam-3260	51	11	bijective	bijective	ADJ
ejpam-3260	51	12	,	,	PUNCT
ejpam-3260	51	13	then	then	ADV
ejpam-3260	51	14	f	f	PROPN
ejpam-3260	51	15	is	be	AUX
ejpam-3260	51	16	not	not	PART
ejpam-3260	51	17	left	leave	VERB
ejpam-3260	51	18	magnifying	magnify	VERB
ejpam-3260	51	19	of	of	ADP
ejpam-3260	51	20	t	t	PROPN
ejpam-3260	51	21	(	(	PUNCT
ejpam-3260	51	22	x	x	X
ejpam-3260	51	23	,	,	PUNCT
ejpam-3260	51	24	p	p	NOUN
ejpam-3260	51	25	)	)	PUNCT
ejpam-3260	51	26	.	.	PUNCT
ejpam-3260	52	1	proof	proof	NOUN
ejpam-3260	52	2	.	.	PUNCT
ejpam-3260	53	1	suppose	suppose	VERB
ejpam-3260	53	2	that	that	SCONJ
ejpam-3260	53	3	f	f	PROPN
ejpam-3260	53	4	is	be	AUX
ejpam-3260	53	5	left	leave	VERB
ejpam-3260	53	6	magnifying	magnify	VERB
ejpam-3260	53	7	of	of	ADP
ejpam-3260	53	8	t	t	PROPN
ejpam-3260	53	9	(	(	PUNCT
ejpam-3260	53	10	x	x	X
ejpam-3260	53	11	,	,	PUNCT
ejpam-3260	53	12	p	p	NOUN
ejpam-3260	53	13	)	)	PUNCT
ejpam-3260	53	14	.	.	PUNCT
ejpam-3260	54	1	then	then	ADV
ejpam-3260	54	2	there	there	PRON
ejpam-3260	54	3	exists	exist	VERB
ejpam-3260	54	4	a	a	DET
ejpam-3260	54	5	proper	proper	ADJ
ejpam-3260	54	6	subset	subset	NOUN
ejpam-3260	54	7	m	m	NOUN
ejpam-3260	54	8	of	of	ADP
ejpam-3260	54	9	t	t	PROPN
ejpam-3260	54	10	(	(	PUNCT
ejpam-3260	54	11	x	x	X
ejpam-3260	54	12	,	,	PUNCT
ejpam-3260	54	13	p	p	NOUN
ejpam-3260	54	14	)	)	PUNCT
ejpam-3260	54	15	such	such	ADJ
ejpam-3260	54	16	that	that	SCONJ
ejpam-3260	54	17	fm	fm	PROPN
ejpam-3260	54	18	=	=	SYM
ejpam-3260	54	19	t	t	PROPN
ejpam-3260	54	20	(	(	PUNCT
ejpam-3260	54	21	x	x	X
ejpam-3260	54	22	,	,	PUNCT
ejpam-3260	54	23	p	p	NOUN
ejpam-3260	54	24	)	)	PUNCT
ejpam-3260	54	25	.	.	PUNCT
ejpam-3260	55	1	this	this	PRON
ejpam-3260	55	2	implies	imply	VERB
ejpam-3260	55	3	that	that	SCONJ
ejpam-3260	55	4	fm	fm	PROPN
ejpam-3260	55	5	=	=	SYM
ejpam-3260	55	6	ft	ft	PROPN
ejpam-3260	55	7	(	(	PUNCT
ejpam-3260	55	8	x	x	X
ejpam-3260	55	9	,	,	PUNCT
ejpam-3260	55	10	p	p	NOUN
ejpam-3260	55	11	)	)	PUNCT
ejpam-3260	55	12	.	.	PUNCT
ejpam-3260	56	1	since	since	SCONJ
ejpam-3260	56	2	f	f	PROPN
ejpam-3260	56	3	is	be	AUX
ejpam-3260	56	4	bijective	bijective	ADJ
ejpam-3260	56	5	,	,	PUNCT
ejpam-3260	56	6	its	its	PRON
ejpam-3260	56	7	inverse	inverse	NOUN
ejpam-3260	56	8	function	function	NOUN
ejpam-3260	56	9	f−1	f−1	PROPN
ejpam-3260	56	10	exists	exist	VERB
ejpam-3260	56	11	and	and	CCONJ
ejpam-3260	56	12	f−1	f−1	PROPN
ejpam-3260	56	13	∈	∈	PROPN
ejpam-3260	56	14	t	t	PROPN
ejpam-3260	56	15	(	(	PUNCT
ejpam-3260	56	16	x	x	X
ejpam-3260	56	17	,	,	PUNCT
ejpam-3260	56	18	p	p	NOUN
ejpam-3260	56	19	)	)	PUNCT
ejpam-3260	56	20	.	.	PUNCT
ejpam-3260	57	1	so	so	ADV
ejpam-3260	57	2	m	m	VERB
ejpam-3260	57	3	=	=	X
ejpam-3260	58	1	f−1fm	f−1fm	ADJ
ejpam-3260	58	2	=	=	SYM
ejpam-3260	58	3	f−1	f−1	PROPN
ejpam-3260	58	4	ft	ft	PART
ejpam-3260	58	5	(	(	PUNCT
ejpam-3260	58	6	x	x	NOUN
ejpam-3260	58	7	,	,	PUNCT
ejpam-3260	58	8	p	p	NOUN
ejpam-3260	58	9	)	)	PUNCT
ejpam-3260	58	10	=	=	SYM
ejpam-3260	58	11	t	t	PROPN
ejpam-3260	58	12	(	(	PUNCT
ejpam-3260	58	13	x	x	X
ejpam-3260	58	14	,	,	PUNCT
ejpam-3260	58	15	p	p	NOUN
ejpam-3260	58	16	)	)	PUNCT
ejpam-3260	58	17	,	,	PUNCT
ejpam-3260	58	18	a	a	DET
ejpam-3260	58	19	contradiction	contradiction	NOUN
ejpam-3260	58	20	.	.	PUNCT
ejpam-3260	59	1	therefore	therefore	ADV
ejpam-3260	59	2	,	,	PUNCT
ejpam-3260	59	3	f	f	PROPN
ejpam-3260	59	4	is	be	AUX
ejpam-3260	59	5	not	not	PART
ejpam-3260	59	6	left	leave	VERB
ejpam-3260	59	7	magnifying	magnify	VERB
ejpam-3260	59	8	of	of	ADP
ejpam-3260	59	9	t	t	PROPN
ejpam-3260	59	10	(	(	PUNCT
ejpam-3260	59	11	x	x	X
ejpam-3260	59	12	,	,	PUNCT
ejpam-3260	59	13	p	p	NOUN
ejpam-3260	59	14	)	)	PUNCT
ejpam-3260	59	15	.	.	PUNCT
ejpam-3260	60	1	lemma	lemma	PROPN
ejpam-3260	61	1	3	3	X
ejpam-3260	61	2	.	.	PUNCT
ejpam-3260	62	1	if	if	SCONJ
ejpam-3260	62	2	f	f	PROPN
ejpam-3260	62	3	∈	∈	PROPN
ejpam-3260	62	4	t	t	PROPN
ejpam-3260	62	5	(	(	PUNCT
ejpam-3260	62	6	x	x	X
ejpam-3260	62	7	,	,	PUNCT
ejpam-3260	62	8	p	p	NOUN
ejpam-3260	62	9	)	)	PUNCT
ejpam-3260	62	10	is	be	AUX
ejpam-3260	62	11	one	one	NUM
ejpam-3260	62	12	-	-	PUNCT
ejpam-3260	62	13	to	to	ADP
ejpam-3260	62	14	-	-	PUNCT
ejpam-3260	62	15	one	one	NUM
ejpam-3260	62	16	but	but	CCONJ
ejpam-3260	62	17	not	not	PART
ejpam-3260	62	18	onto	onto	NOUN
ejpam-3260	62	19	,	,	PUNCT
ejpam-3260	62	20	then	then	ADV
ejpam-3260	62	21	f	f	PROPN
ejpam-3260	62	22	is	be	AUX
ejpam-3260	62	23	left	leave	VERB
ejpam-3260	62	24	magnifying	magnify	VERB
ejpam-3260	62	25	of	of	ADP
ejpam-3260	62	26	t	t	PROPN
ejpam-3260	62	27	(	(	PUNCT
ejpam-3260	62	28	x	x	X
ejpam-3260	62	29	,	,	PUNCT
ejpam-3260	62	30	p	p	NOUN
ejpam-3260	62	31	)	)	PUNCT
ejpam-3260	62	32	.	.	PUNCT
ejpam-3260	63	1	r.	r.	PROPN
ejpam-3260	63	2	chinram	chinram	PROPN
ejpam-3260	63	3	,	,	PUNCT
ejpam-3260	63	4	p.	p.	NOUN
ejpam-3260	63	5	petchkaew	petchkaew	NOUN
ejpam-3260	63	6	,	,	PUNCT
ejpam-3260	63	7	s.	s.	PROPN
ejpam-3260	63	8	baupradist	baupradist	PROPN
ejpam-3260	63	9	/	/	SYM
ejpam-3260	63	10	eur	eur	PROPN
ejpam-3260	63	11	.	.	PUNCT
ejpam-3260	64	1	j.	j.	PROPN
ejpam-3260	64	2	pure	pure	PROPN
ejpam-3260	64	3	appl	appl	PROPN
ejpam-3260	64	4	.	.	PROPN
ejpam-3260	64	5	math	math	PROPN
ejpam-3260	64	6	,	,	PUNCT
ejpam-3260	64	7	11	11	NUM
ejpam-3260	64	8	(	(	PUNCT
ejpam-3260	64	9	3	3	NUM
ejpam-3260	64	10	)	)	PUNCT
ejpam-3260	64	11	(	(	PUNCT
ejpam-3260	64	12	2018	2018	NUM
ejpam-3260	64	13	)	)	PUNCT
ejpam-3260	64	14	,	,	PUNCT
ejpam-3260	64	15	580	580	NUM
ejpam-3260	64	16	-	-	SYM
ejpam-3260	64	17	588	588	NUM
ejpam-3260	64	18	582	582	NUM
ejpam-3260	64	19	proof	proof	NOUN
ejpam-3260	64	20	.	.	PUNCT
ejpam-3260	65	1	assume	assume	VERB
ejpam-3260	65	2	that	that	SCONJ
ejpam-3260	65	3	f	f	PROPN
ejpam-3260	65	4	is	be	AUX
ejpam-3260	65	5	one	one	NUM
ejpam-3260	65	6	-	-	PUNCT
ejpam-3260	65	7	to	to	ADP
ejpam-3260	65	8	-	-	PUNCT
ejpam-3260	65	9	one	one	NUM
ejpam-3260	65	10	but	but	CCONJ
ejpam-3260	65	11	not	not	PART
ejpam-3260	65	12	onto	onto	ADP
ejpam-3260	65	13	.	.	PUNCT
ejpam-3260	66	1	let	let	VERB
ejpam-3260	66	2	m	m	VERB
ejpam-3260	66	3	=	=	PRON
ejpam-3260	66	4	{	{	PUNCT
ejpam-3260	66	5	h	h	NOUN
ejpam-3260	66	6	∈	∈	PROPN
ejpam-3260	66	7	t	t	PROPN
ejpam-3260	66	8	(	(	PUNCT
ejpam-3260	66	9	x	x	X
ejpam-3260	66	10	,	,	PUNCT
ejpam-3260	66	11	p	p	NOUN
ejpam-3260	66	12	)	)	PUNCT
ejpam-3260	66	13	|	|	ADV
ejpam-3260	66	14	(	(	PUNCT
ejpam-3260	66	15	x)h	x)h	PROPN
ejpam-3260	67	1	=	=	PUNCT
ejpam-3260	67	2	x	x	PROPN
ejpam-3260	67	3	for	for	ADP
ejpam-3260	67	4	all	all	PRON
ejpam-3260	67	5	x	x	PROPN
ejpam-3260	67	6	/∈	/∈	PROPN
ejpam-3260	67	7	ran	run	VERB
ejpam-3260	67	8	f	f	NUM
ejpam-3260	67	9	}	}	PUNCT
ejpam-3260	67	10	.	.	PUNCT
ejpam-3260	68	1	then	then	ADV
ejpam-3260	68	2	m	m	PROPN
ejpam-3260	68	3	is	be	AUX
ejpam-3260	68	4	a	a	DET
ejpam-3260	68	5	proper	proper	ADJ
ejpam-3260	68	6	subset	subset	NOUN
ejpam-3260	68	7	of	of	ADP
ejpam-3260	68	8	t	t	PROPN
ejpam-3260	68	9	(	(	PUNCT
ejpam-3260	68	10	x	x	X
ejpam-3260	68	11	,	,	PUNCT
ejpam-3260	68	12	p	p	NOUN
ejpam-3260	68	13	)	)	PUNCT
ejpam-3260	68	14	.	.	PUNCT
ejpam-3260	69	1	claim	claim	VERB
ejpam-3260	69	2	that	that	SCONJ
ejpam-3260	69	3	fm	fm	PROPN
ejpam-3260	69	4	=	=	SYM
ejpam-3260	69	5	t	t	PROPN
ejpam-3260	69	6	(	(	PUNCT
ejpam-3260	69	7	x	x	X
ejpam-3260	69	8	,	,	PUNCT
ejpam-3260	69	9	p	p	NOUN
ejpam-3260	69	10	)	)	PUNCT
ejpam-3260	69	11	.	.	PUNCT
ejpam-3260	70	1	let	let	VERB
ejpam-3260	70	2	g	g	PRON
ejpam-3260	70	3	be	be	AUX
ejpam-3260	70	4	any	any	DET
ejpam-3260	70	5	function	function	NOUN
ejpam-3260	70	6	in	in	ADP
ejpam-3260	70	7	t	t	PROPN
ejpam-3260	70	8	(	(	PUNCT
ejpam-3260	70	9	x	x	X
ejpam-3260	70	10	,	,	PUNCT
ejpam-3260	70	11	p	p	NOUN
ejpam-3260	70	12	)	)	PUNCT
ejpam-3260	70	13	.	.	PUNCT
ejpam-3260	71	1	define	define	VERB
ejpam-3260	71	2	a	a	DET
ejpam-3260	71	3	function	function	NOUN
ejpam-3260	71	4	h	h	NOUN
ejpam-3260	71	5	∈	∈	PROPN
ejpam-3260	71	6	t	t	PROPN
ejpam-3260	71	7	(	(	PUNCT
ejpam-3260	71	8	x	x	X
ejpam-3260	71	9	,	,	PUNCT
ejpam-3260	71	10	p	p	NOUN
ejpam-3260	71	11	)	)	PUNCT
ejpam-3260	71	12	by	by	ADP
ejpam-3260	71	13	for	for	ADP
ejpam-3260	71	14	all	all	DET
ejpam-3260	71	15	x	x	SYM
ejpam-3260	71	16	∈	∈	PROPN
ejpam-3260	71	17	x	x	X
ejpam-3260	71	18	,	,	PUNCT
ejpam-3260	71	19	(	(	PUNCT
ejpam-3260	71	20	x)h	x)h	SYM
ejpam-3260	71	21	=	=	X
ejpam-3260	71	22	{	{	PUNCT
ejpam-3260	71	23	(	(	PUNCT
ejpam-3260	71	24	x′)g	x′)g	PUNCT
ejpam-3260	71	25	if	if	SCONJ
ejpam-3260	71	26	x	x	SYM
ejpam-3260	71	27	∈	∈	PROPN
ejpam-3260	71	28	ran	run	VERB
ejpam-3260	71	29	f	f	PROPN
ejpam-3260	71	30	and	and	CCONJ
ejpam-3260	71	31	(	(	PUNCT
ejpam-3260	71	32	x′)f	x′)f	PUNCT
ejpam-3260	71	33	=	=	SYM
ejpam-3260	71	34	x	x	X
ejpam-3260	71	35	,	,	PUNCT
ejpam-3260	71	36	x	x	X
ejpam-3260	71	37	if	if	SCONJ
ejpam-3260	71	38	x	x	PROPN
ejpam-3260	71	39	/∈	/∈	PROPN
ejpam-3260	71	40	ran	run	VERB
ejpam-3260	71	41	f.	f.	PROPN
ejpam-3260	71	42	let	let	VERB
ejpam-3260	71	43	x′	x′	NUM
ejpam-3260	71	44	,	,	PUNCT
ejpam-3260	71	45	x	x	PUNCT
ejpam-3260	71	46	∈	∈	PROPN
ejpam-3260	71	47	x	x	VERB
ejpam-3260	71	48	be	be	AUX
ejpam-3260	71	49	such	such	ADJ
ejpam-3260	71	50	that	that	SCONJ
ejpam-3260	71	51	(	(	PUNCT
ejpam-3260	71	52	x′)f	x′)f	PUNCT
ejpam-3260	71	53	=	=	PUNCT
ejpam-3260	71	54	x	x	PUNCT
ejpam-3260	71	55	and	and	CCONJ
ejpam-3260	71	56	x	x	SYM
ejpam-3260	71	57	∈	∈	NOUN
ejpam-3260	71	58	xα	xα	ADP
ejpam-3260	71	59	for	for	ADP
ejpam-3260	71	60	some	some	DET
ejpam-3260	71	61	α	α	PROPN
ejpam-3260	71	62	∈	∈	PROPN
ejpam-3260	71	63	i.	i.	NOUN
ejpam-3260	71	64	clearly	clearly	ADV
ejpam-3260	71	65	,	,	PUNCT
ejpam-3260	71	66	x′	x′	PROPN
ejpam-3260	71	67	∈	∈	PROPN
ejpam-3260	72	1	xα	xα	PROPN
ejpam-3260	72	2	.	.	PUNCT
ejpam-3260	73	1	therefore	therefore	ADV
ejpam-3260	73	2	,	,	PUNCT
ejpam-3260	73	3	(	(	PUNCT
ejpam-3260	73	4	x)h	x)h	SYM
ejpam-3260	73	5	=	=	SYM
ejpam-3260	73	6	(	(	PUNCT
ejpam-3260	73	7	x′)g	x′)g	PROPN
ejpam-3260	73	8	∈	∈	PROPN
ejpam-3260	73	9	xα	xα	PROPN
ejpam-3260	73	10	.	.	PUNCT
ejpam-3260	74	1	then	then	ADV
ejpam-3260	74	2	h	h	NOUN
ejpam-3260	74	3	∈m	∈m	NOUN
ejpam-3260	74	4	.	.	PUNCT
ejpam-3260	75	1	for	for	ADP
ejpam-3260	75	2	all	all	DET
ejpam-3260	75	3	x	x	SYM
ejpam-3260	75	4	∈	∈	PROPN
ejpam-3260	75	5	x	x	NOUN
ejpam-3260	75	6	,	,	PUNCT
ejpam-3260	75	7	we	we	PRON
ejpam-3260	75	8	have	have	VERB
ejpam-3260	75	9	(	(	PUNCT
ejpam-3260	75	10	x)fh	x)fh	PROPN
ejpam-3260	75	11	=	=	PRON
ejpam-3260	75	12	(	(	PUNCT
ejpam-3260	75	13	(	(	PUNCT
ejpam-3260	75	14	x)f)h	x)f)h	PROPN
ejpam-3260	75	15	=	=	SYM
ejpam-3260	75	16	(	(	PUNCT
ejpam-3260	75	17	x)g	x)g	X
ejpam-3260	75	18	.	.	PUNCT
ejpam-3260	76	1	then	then	ADV
ejpam-3260	76	2	fh	fh	PROPN
ejpam-3260	76	3	=	=	SYM
ejpam-3260	76	4	g	g	PROPN
ejpam-3260	76	5	,	,	PUNCT
ejpam-3260	76	6	this	this	PRON
ejpam-3260	76	7	implies	imply	VERB
ejpam-3260	76	8	that	that	SCONJ
ejpam-3260	76	9	fm	fm	PROPN
ejpam-3260	76	10	=	=	SYM
ejpam-3260	76	11	t	t	PROPN
ejpam-3260	76	12	(	(	PUNCT
ejpam-3260	76	13	x	x	X
ejpam-3260	76	14	,	,	PUNCT
ejpam-3260	76	15	p	p	NOUN
ejpam-3260	76	16	)	)	PUNCT
ejpam-3260	76	17	.	.	PUNCT
ejpam-3260	77	1	hence	hence	ADV
ejpam-3260	77	2	f	f	PROPN
ejpam-3260	77	3	is	be	AUX
ejpam-3260	77	4	left	leave	VERB
ejpam-3260	77	5	magnifying	magnify	VERB
ejpam-3260	77	6	of	of	ADP
ejpam-3260	77	7	t	t	PROPN
ejpam-3260	77	8	(	(	PUNCT
ejpam-3260	77	9	x	x	X
ejpam-3260	77	10	,	,	PUNCT
ejpam-3260	77	11	p	p	NOUN
ejpam-3260	77	12	)	)	PUNCT
ejpam-3260	77	13	.	.	PUNCT
ejpam-3260	78	1	example	example	NOUN
ejpam-3260	79	1	1	1	X
ejpam-3260	79	2	.	.	X
ejpam-3260	79	3	consider	consider	VERB
ejpam-3260	79	4	x	x	X
ejpam-3260	79	5	=	=	PUNCT
ejpam-3260	79	6	n	n	PROPN
ejpam-3260	79	7	and	and	CCONJ
ejpam-3260	79	8	p	p	NOUN
ejpam-3260	79	9	=	=	X
ejpam-3260	79	10	{	{	PUNCT
ejpam-3260	79	11	{	{	PUNCT
ejpam-3260	79	12	x	x	INTJ
ejpam-3260	79	13	|	|	ADV
ejpam-3260	79	14	x	x	INTJ
ejpam-3260	79	15	is	be	AUX
ejpam-3260	79	16	odd	odd	ADJ
ejpam-3260	79	17	}	}	PUNCT
ejpam-3260	79	18	,	,	PUNCT
ejpam-3260	79	19	{	{	PUNCT
ejpam-3260	79	20	x	x	SYM
ejpam-3260	79	21	|	|	ADV
ejpam-3260	79	22	x	x	INTJ
ejpam-3260	79	23	is	be	AUX
ejpam-3260	79	24	even	even	ADV
ejpam-3260	79	25	}	}	PUNCT
ejpam-3260	79	26	}	}	PUNCT
ejpam-3260	79	27	.	.	PUNCT
ejpam-3260	80	1	let	let	VERB
ejpam-3260	80	2	f	f	PROPN
ejpam-3260	80	3	∈	∈	PROPN
ejpam-3260	80	4	t	t	PROPN
ejpam-3260	80	5	(	(	PUNCT
ejpam-3260	80	6	x	x	X
ejpam-3260	80	7	,	,	PUNCT
ejpam-3260	80	8	p	p	NOUN
ejpam-3260	80	9	)	)	PUNCT
ejpam-3260	80	10	by	by	ADP
ejpam-3260	80	11	(	(	PUNCT
ejpam-3260	80	12	x)f	x)f	X
ejpam-3260	80	13	=	=	SYM
ejpam-3260	80	14	{	{	PUNCT
ejpam-3260	80	15	x+	x+	SYM
ejpam-3260	80	16	2	2	NUM
ejpam-3260	80	17	if	if	SCONJ
ejpam-3260	80	18	x	x	PRON
ejpam-3260	80	19	is	be	AUX
ejpam-3260	80	20	even	even	ADV
ejpam-3260	80	21	,	,	PUNCT
ejpam-3260	80	22	x	x	SYM
ejpam-3260	80	23	if	if	SCONJ
ejpam-3260	80	24	x	x	PRON
ejpam-3260	80	25	is	be	AUX
ejpam-3260	80	26	odd	odd	ADJ
ejpam-3260	80	27	,	,	PUNCT
ejpam-3260	80	28	that	that	ADV
ejpam-3260	80	29	is	is	ADV
ejpam-3260	80	30	,	,	PUNCT
ejpam-3260	80	31	f	f	X
ejpam-3260	81	1	=	=	PRON
ejpam-3260	82	1	(	(	PUNCT
ejpam-3260	82	2	1	1	NUM
ejpam-3260	82	3	2	2	NUM
ejpam-3260	82	4	3	3	NUM
ejpam-3260	82	5	4	4	NUM
ejpam-3260	82	6	5	5	NUM
ejpam-3260	82	7	6	6	NUM
ejpam-3260	82	8	7	7	NUM
ejpam-3260	82	9	8	8	NUM
ejpam-3260	82	10	·	·	PUNCT
ejpam-3260	82	11	·	·	PUNCT
ejpam-3260	82	12	·	·	PUNCT
ejpam-3260	82	13	1	1	NUM
ejpam-3260	82	14	4	4	NUM
ejpam-3260	82	15	3	3	NUM
ejpam-3260	82	16	6	6	NUM
ejpam-3260	82	17	5	5	NUM
ejpam-3260	82	18	8	8	NUM
ejpam-3260	82	19	7	7	NUM
ejpam-3260	82	20	10	10	NUM
ejpam-3260	82	21	·	·	PUNCT
ejpam-3260	82	22	·	·	PUNCT
ejpam-3260	82	23	·	·	PUNCT
ejpam-3260	82	24	)	)	PUNCT
ejpam-3260	82	25	.	.	PUNCT
ejpam-3260	83	1	then	then	ADV
ejpam-3260	83	2	f	f	PROPN
ejpam-3260	83	3	∈	∈	PROPN
ejpam-3260	83	4	t	t	PROPN
ejpam-3260	83	5	(	(	PUNCT
ejpam-3260	83	6	x	x	X
ejpam-3260	83	7	,	,	PUNCT
ejpam-3260	83	8	p	p	NOUN
ejpam-3260	83	9	)	)	PUNCT
ejpam-3260	83	10	and	and	CCONJ
ejpam-3260	83	11	f	f	PROPN
ejpam-3260	83	12	is	be	AUX
ejpam-3260	83	13	one	one	NUM
ejpam-3260	83	14	-	-	PUNCT
ejpam-3260	83	15	to	to	ADP
ejpam-3260	83	16	-	-	PUNCT
ejpam-3260	83	17	one	one	NUM
ejpam-3260	83	18	but	but	CCONJ
ejpam-3260	83	19	not	not	PART
ejpam-3260	83	20	onto	onto	ADP
ejpam-3260	83	21	because	because	SCONJ
ejpam-3260	83	22	2	2	NUM
ejpam-3260	83	23	/∈	/∈	PUNCT
ejpam-3260	83	24	ran	run	VERB
ejpam-3260	83	25	f	f	PROPN
ejpam-3260	83	26	.	.	PUNCT
ejpam-3260	84	1	let	let	VERB
ejpam-3260	84	2	m	m	VERB
ejpam-3260	84	3	=	=	PRON
ejpam-3260	84	4	{	{	PUNCT
ejpam-3260	84	5	h	h	NOUN
ejpam-3260	84	6	∈	∈	PROPN
ejpam-3260	84	7	t	t	PROPN
ejpam-3260	84	8	(	(	PUNCT
ejpam-3260	84	9	x	x	X
ejpam-3260	84	10	,	,	PUNCT
ejpam-3260	84	11	p	p	NOUN
ejpam-3260	84	12	)	)	PUNCT
ejpam-3260	84	13	|	|	ADV
ejpam-3260	84	14	(	(	PUNCT
ejpam-3260	84	15	2)h	2)h	NUM
ejpam-3260	84	16	=	=	SYM
ejpam-3260	84	17	2	2	NUM
ejpam-3260	84	18	}	}	PUNCT
ejpam-3260	84	19	.	.	PUNCT
ejpam-3260	85	1	let	let	VERB
ejpam-3260	85	2	g	g	PROPN
ejpam-3260	85	3	∈	∈	PROPN
ejpam-3260	85	4	t	t	PROPN
ejpam-3260	85	5	(	(	PUNCT
ejpam-3260	85	6	x	x	X
ejpam-3260	85	7	,	,	PUNCT
ejpam-3260	85	8	p	p	NOUN
ejpam-3260	85	9	)	)	PUNCT
ejpam-3260	85	10	be	be	AUX
ejpam-3260	85	11	any	any	DET
ejpam-3260	85	12	function	function	NOUN
ejpam-3260	85	13	.	.	PUNCT
ejpam-3260	86	1	define	define	VERB
ejpam-3260	86	2	a	a	DET
ejpam-3260	86	3	function	function	NOUN
ejpam-3260	86	4	h	h	NOUN
ejpam-3260	86	5	∈	∈	PROPN
ejpam-3260	86	6	t	t	PROPN
ejpam-3260	86	7	(	(	PUNCT
ejpam-3260	86	8	x	x	X
ejpam-3260	86	9	,	,	PUNCT
ejpam-3260	86	10	p	p	NOUN
ejpam-3260	86	11	)	)	PUNCT
ejpam-3260	86	12	by	by	ADP
ejpam-3260	86	13	(	(	PUNCT
ejpam-3260	86	14	x)h	x)h	PROPN
ejpam-3260	86	15	=	=	SYM
ejpam-3260	86	16			NOUN
ejpam-3260	86	17	2	2	NUM
ejpam-3260	86	18	if	if	SCONJ
ejpam-3260	86	19	x	x	NOUN
ejpam-3260	86	20	=	=	SYM
ejpam-3260	86	21	2	2	NUM
ejpam-3260	86	22	,	,	PUNCT
ejpam-3260	86	23	(	(	PUNCT
ejpam-3260	86	24	x−	x−	PROPN
ejpam-3260	86	25	2)g	2)g	PROPN
ejpam-3260	86	26	if	if	SCONJ
ejpam-3260	86	27	x	x	PRON
ejpam-3260	86	28	is	be	AUX
ejpam-3260	86	29	even	even	ADV
ejpam-3260	86	30	and	and	CCONJ
ejpam-3260	86	31	x	x	X
ejpam-3260	86	32	>	>	X
ejpam-3260	86	33	2	2	NUM
ejpam-3260	86	34	,	,	PUNCT
ejpam-3260	86	35	(	(	PUNCT
ejpam-3260	86	36	x)g	x)g	X
ejpam-3260	86	37	if	if	SCONJ
ejpam-3260	86	38	x	x	PRON
ejpam-3260	86	39	is	be	AUX
ejpam-3260	86	40	odd	odd	ADJ
ejpam-3260	86	41	.	.	PUNCT
ejpam-3260	87	1	so	so	ADV
ejpam-3260	87	2	h	h	NOUN
ejpam-3260	88	1	∈	∈	PROPN
ejpam-3260	88	2	m	m	VERB
ejpam-3260	88	3	.	.	PUNCT
ejpam-3260	89	1	if	if	SCONJ
ejpam-3260	89	2	x	x	PRON
ejpam-3260	89	3	is	be	AUX
ejpam-3260	89	4	odd	odd	ADJ
ejpam-3260	89	5	,	,	PUNCT
ejpam-3260	89	6	we	we	PRON
ejpam-3260	89	7	have	have	VERB
ejpam-3260	89	8	(	(	PUNCT
ejpam-3260	90	1	x)fh	x)fh	PROPN
ejpam-3260	90	2	=	=	PRON
ejpam-3260	90	3	(	(	PUNCT
ejpam-3260	90	4	(	(	PUNCT
ejpam-3260	90	5	x)f)h	x)f)h	PROPN
ejpam-3260	90	6	=	=	SYM
ejpam-3260	90	7	(	(	PUNCT
ejpam-3260	90	8	x)h	x)h	PROPN
ejpam-3260	90	9	=	=	SYM
ejpam-3260	90	10	(	(	PUNCT
ejpam-3260	90	11	x)g	x)g	X
ejpam-3260	90	12	.	.	PUNCT
ejpam-3260	91	1	if	if	SCONJ
ejpam-3260	91	2	x	x	PRON
ejpam-3260	91	3	is	be	AUX
ejpam-3260	91	4	even	even	ADV
ejpam-3260	91	5	,	,	PUNCT
ejpam-3260	91	6	we	we	PRON
ejpam-3260	91	7	have	have	VERB
ejpam-3260	91	8	(	(	PUNCT
ejpam-3260	91	9	x)fh	x)fh	PROPN
ejpam-3260	91	10	=	=	PRON
ejpam-3260	91	11	(	(	PUNCT
ejpam-3260	91	12	(	(	PUNCT
ejpam-3260	91	13	x)f)h	x)f)h	PROPN
ejpam-3260	91	14	=	=	SYM
ejpam-3260	91	15	(	(	PUNCT
ejpam-3260	91	16	x+	x+	X
ejpam-3260	91	17	2)h	2)h	NUM
ejpam-3260	91	18	=	=	SYM
ejpam-3260	91	19	(	(	PUNCT
ejpam-3260	91	20	x)g	x)g	X
ejpam-3260	91	21	.	.	PUNCT
ejpam-3260	92	1	then	then	ADV
ejpam-3260	92	2	fh	fh	PROPN
ejpam-3260	92	3	=	=	PUNCT
ejpam-3260	92	4	g.	g.	PROPN
ejpam-3260	92	5	for	for	ADP
ejpam-3260	92	6	example	example	NOUN
ejpam-3260	92	7	,	,	PUNCT
ejpam-3260	92	8	if	if	SCONJ
ejpam-3260	92	9	g	g	PROPN
ejpam-3260	92	10	∈	∈	PROPN
ejpam-3260	92	11	t	t	PROPN
ejpam-3260	92	12	(	(	PUNCT
ejpam-3260	92	13	x	x	X
ejpam-3260	92	14	,	,	PUNCT
ejpam-3260	92	15	p	p	NOUN
ejpam-3260	92	16	)	)	PUNCT
ejpam-3260	92	17	such	such	ADJ
ejpam-3260	92	18	that	that	PRON
ejpam-3260	92	19	(	(	PUNCT
ejpam-3260	92	20	x)g	x)g	X
ejpam-3260	92	21	=	=	SYM
ejpam-3260	92	22	{	{	PUNCT
ejpam-3260	92	23	2x	2x	NUM
ejpam-3260	92	24	if	if	SCONJ
ejpam-3260	92	25	x	x	PRON
ejpam-3260	92	26	is	be	AUX
ejpam-3260	92	27	even	even	ADV
ejpam-3260	92	28	,	,	PUNCT
ejpam-3260	92	29	x	x	SYM
ejpam-3260	92	30	if	if	SCONJ
ejpam-3260	92	31	x	x	PRON
ejpam-3260	92	32	is	be	AUX
ejpam-3260	92	33	odd	odd	ADJ
ejpam-3260	92	34	,	,	PUNCT
ejpam-3260	92	35	that	that	ADV
ejpam-3260	92	36	is	is	ADV
ejpam-3260	92	37	,	,	PUNCT
ejpam-3260	92	38	g	g	PROPN
ejpam-3260	92	39	=	=	PUNCT
ejpam-3260	92	40	(	(	PUNCT
ejpam-3260	92	41	1	1	NUM
ejpam-3260	92	42	2	2	NUM
ejpam-3260	92	43	3	3	NUM
ejpam-3260	92	44	4	4	NUM
ejpam-3260	92	45	5	5	NUM
ejpam-3260	92	46	6	6	NUM
ejpam-3260	92	47	7	7	NUM
ejpam-3260	92	48	8	8	NUM
ejpam-3260	92	49	·	·	PUNCT
ejpam-3260	92	50	·	·	PUNCT
ejpam-3260	92	51	·	·	PUNCT
ejpam-3260	93	1	1	1	NUM
ejpam-3260	93	2	4	4	NUM
ejpam-3260	93	3	3	3	NUM
ejpam-3260	93	4	8	8	NUM
ejpam-3260	93	5	5	5	NUM
ejpam-3260	93	6	12	12	NUM
ejpam-3260	93	7	7	7	NUM
ejpam-3260	93	8	16	16	NUM
ejpam-3260	93	9	·	·	PUNCT
ejpam-3260	93	10	·	·	PUNCT
ejpam-3260	93	11	·	·	PUNCT
ejpam-3260	93	12	)	)	PUNCT
ejpam-3260	93	13	.	.	PUNCT
ejpam-3260	94	1	define	define	VERB
ejpam-3260	94	2	a	a	DET
ejpam-3260	94	3	function	function	NOUN
ejpam-3260	94	4	h	h	NOUN
ejpam-3260	94	5	∈	∈	PROPN
ejpam-3260	94	6	t	t	PROPN
ejpam-3260	94	7	(	(	PUNCT
ejpam-3260	94	8	x	x	X
ejpam-3260	94	9	,	,	PUNCT
ejpam-3260	94	10	p	p	NOUN
ejpam-3260	94	11	)	)	PUNCT
ejpam-3260	94	12	by	by	ADP
ejpam-3260	94	13	(	(	PUNCT
ejpam-3260	94	14	2)h	2)h	NUM
ejpam-3260	94	15	=	=	SYM
ejpam-3260	94	16	2	2	NUM
ejpam-3260	94	17	,	,	PUNCT
ejpam-3260	94	18	(	(	PUNCT
ejpam-3260	94	19	2x	2x	NUM
ejpam-3260	94	20	+	+	X
ejpam-3260	94	21	2)h	2)h	NUM
ejpam-3260	94	22	=	=	SYM
ejpam-3260	94	23	(	(	PUNCT
ejpam-3260	94	24	2x)g	2x)g	NUM
ejpam-3260	94	25	=	=	SYM
ejpam-3260	94	26	4x	4x	NOUN
ejpam-3260	94	27	and	and	CCONJ
ejpam-3260	94	28	(	(	PUNCT
ejpam-3260	94	29	2x	2x	NUM
ejpam-3260	94	30	−	−	PROPN
ejpam-3260	94	31	1)h	1)h	NUM
ejpam-3260	95	1	=	=	SYM
ejpam-3260	96	1	(	(	PUNCT
ejpam-3260	96	2	2x−	2x−	NUM
ejpam-3260	96	3	1)g	1)g	NOUN
ejpam-3260	97	1	=	=	SYM
ejpam-3260	97	2	2x−	2x−	NOUN
ejpam-3260	97	3	1	1	NUM
ejpam-3260	97	4	for	for	ADP
ejpam-3260	97	5	all	all	DET
ejpam-3260	97	6	x	x	SYM
ejpam-3260	97	7	∈	∈	PROPN
ejpam-3260	97	8	x	x	NOUN
ejpam-3260	97	9	,	,	PUNCT
ejpam-3260	97	10	that	that	ADV
ejpam-3260	97	11	is	is	ADV
ejpam-3260	97	12	,	,	PUNCT
ejpam-3260	97	13	h	h	NOUN
ejpam-3260	97	14	=	=	PUNCT
ejpam-3260	97	15	(	(	PUNCT
ejpam-3260	97	16	1	1	NUM
ejpam-3260	97	17	2	2	NUM
ejpam-3260	97	18	3	3	NUM
ejpam-3260	97	19	4	4	NUM
ejpam-3260	97	20	5	5	NUM
ejpam-3260	97	21	6	6	NUM
ejpam-3260	97	22	7	7	NUM
ejpam-3260	97	23	8	8	NUM
ejpam-3260	97	24	·	·	PUNCT
ejpam-3260	97	25	·	·	PUNCT
ejpam-3260	97	26	·	·	PUNCT
ejpam-3260	97	27	1	1	NUM
ejpam-3260	97	28	2	2	NUM
ejpam-3260	97	29	3	3	NUM
ejpam-3260	97	30	4	4	NUM
ejpam-3260	97	31	5	5	NUM
ejpam-3260	97	32	8	8	NUM
ejpam-3260	97	33	7	7	NUM
ejpam-3260	97	34	12	12	NUM
ejpam-3260	97	35	·	·	PUNCT
ejpam-3260	97	36	·	·	PUNCT
ejpam-3260	97	37	·	·	PUNCT
ejpam-3260	97	38	)	)	PUNCT
ejpam-3260	97	39	.	.	PUNCT
ejpam-3260	98	1	r.	r.	PROPN
ejpam-3260	98	2	chinram	chinram	PROPN
ejpam-3260	98	3	,	,	PUNCT
ejpam-3260	98	4	p.	p.	NOUN
ejpam-3260	98	5	petchkaew	petchkaew	NOUN
ejpam-3260	98	6	,	,	PUNCT
ejpam-3260	98	7	s.	s.	PROPN
ejpam-3260	98	8	baupradist	baupradist	PROPN
ejpam-3260	98	9	/	/	SYM
ejpam-3260	98	10	eur	eur	PROPN
ejpam-3260	98	11	.	.	PUNCT
ejpam-3260	99	1	j.	j.	PROPN
ejpam-3260	99	2	pure	pure	PROPN
ejpam-3260	99	3	appl	appl	PROPN
ejpam-3260	99	4	.	.	PROPN
ejpam-3260	99	5	math	math	PROPN
ejpam-3260	99	6	,	,	PUNCT
ejpam-3260	99	7	11	11	NUM
ejpam-3260	99	8	(	(	PUNCT
ejpam-3260	99	9	3	3	NUM
ejpam-3260	99	10	)	)	PUNCT
ejpam-3260	99	11	(	(	PUNCT
ejpam-3260	99	12	2018	2018	NUM
ejpam-3260	99	13	)	)	PUNCT
ejpam-3260	99	14	,	,	PUNCT
ejpam-3260	99	15	580	580	NUM
ejpam-3260	99	16	-	-	SYM
ejpam-3260	99	17	588	588	NUM
ejpam-3260	99	18	583	583	NUM
ejpam-3260	99	19	so	so	ADV
ejpam-3260	99	20	h	h	NOUN
ejpam-3260	99	21	∈m	∈m	NOUN
ejpam-3260	100	1	and	and	CCONJ
ejpam-3260	100	2	we	we	PRON
ejpam-3260	100	3	have	have	VERB
ejpam-3260	100	4	fh	fh	PROPN
ejpam-3260	100	5	=	=	SYM
ejpam-3260	100	6	(	(	PUNCT
ejpam-3260	100	7	1	1	NUM
ejpam-3260	100	8	2	2	NUM
ejpam-3260	100	9	3	3	NUM
ejpam-3260	100	10	4	4	NUM
ejpam-3260	100	11	5	5	NUM
ejpam-3260	100	12	6	6	NUM
ejpam-3260	100	13	7	7	NUM
ejpam-3260	100	14	8	8	NUM
ejpam-3260	100	15	·	·	PUNCT
ejpam-3260	100	16	·	·	PUNCT
ejpam-3260	100	17	·	·	PUNCT
ejpam-3260	101	1	1	1	NUM
ejpam-3260	101	2	4	4	NUM
ejpam-3260	101	3	3	3	NUM
ejpam-3260	101	4	6	6	NUM
ejpam-3260	101	5	5	5	NUM
ejpam-3260	101	6	8	8	NUM
ejpam-3260	101	7	7	7	NUM
ejpam-3260	101	8	10	10	NUM
ejpam-3260	101	9	·	·	PUNCT
ejpam-3260	101	10	·	·	PUNCT
ejpam-3260	101	11	·	·	PUNCT
ejpam-3260	101	12	)	)	PUNCT
ejpam-3260	101	13	(	(	PUNCT
ejpam-3260	101	14	1	1	NUM
ejpam-3260	101	15	2	2	NUM
ejpam-3260	101	16	3	3	NUM
ejpam-3260	101	17	4	4	NUM
ejpam-3260	101	18	5	5	NUM
ejpam-3260	101	19	6	6	NUM
ejpam-3260	101	20	7	7	NUM
ejpam-3260	101	21	8	8	NUM
ejpam-3260	101	22	·	·	PUNCT
ejpam-3260	101	23	·	·	PUNCT
ejpam-3260	101	24	·	·	PUNCT
ejpam-3260	101	25	1	1	NUM
ejpam-3260	101	26	2	2	NUM
ejpam-3260	101	27	3	3	NUM
ejpam-3260	101	28	4	4	NUM
ejpam-3260	101	29	5	5	NUM
ejpam-3260	101	30	8	8	NUM
ejpam-3260	101	31	7	7	NUM
ejpam-3260	101	32	12	12	NUM
ejpam-3260	101	33	·	·	PUNCT
ejpam-3260	101	34	·	·	PUNCT
ejpam-3260	101	35	·	·	PUNCT
ejpam-3260	101	36	)	)	PUNCT
ejpam-3260	102	1	=	=	PUNCT
ejpam-3260	102	2	(	(	PUNCT
ejpam-3260	102	3	1	1	NUM
ejpam-3260	102	4	2	2	NUM
ejpam-3260	102	5	3	3	NUM
ejpam-3260	102	6	4	4	NUM
ejpam-3260	102	7	5	5	NUM
ejpam-3260	102	8	6	6	NUM
ejpam-3260	102	9	7	7	NUM
ejpam-3260	102	10	8	8	NUM
ejpam-3260	102	11	·	·	PUNCT
ejpam-3260	102	12	·	·	PUNCT
ejpam-3260	102	13	·	·	PUNCT
ejpam-3260	103	1	1	1	NUM
ejpam-3260	103	2	4	4	NUM
ejpam-3260	103	3	3	3	NUM
ejpam-3260	103	4	8	8	NUM
ejpam-3260	103	5	5	5	NUM
ejpam-3260	103	6	12	12	NUM
ejpam-3260	103	7	7	7	NUM
ejpam-3260	103	8	16	16	NUM
ejpam-3260	103	9	·	·	PUNCT
ejpam-3260	103	10	·	·	PUNCT
ejpam-3260	103	11	·	·	PUNCT
ejpam-3260	103	12	)	)	PUNCT
ejpam-3260	104	1	=	=	PUNCT
ejpam-3260	104	2	g.	g.	PROPN
ejpam-3260	104	3	the	the	DET
ejpam-3260	104	4	following	follow	VERB
ejpam-3260	104	5	theorem	theorem	NOUN
ejpam-3260	104	6	is	be	AUX
ejpam-3260	104	7	the	the	DET
ejpam-3260	104	8	main	main	ADJ
ejpam-3260	104	9	result	result	NOUN
ejpam-3260	104	10	in	in	ADP
ejpam-3260	104	11	this	this	DET
ejpam-3260	104	12	section	section	NOUN
ejpam-3260	104	13	.	.	PUNCT
ejpam-3260	105	1	theorem	theorem	NOUN
ejpam-3260	105	2	1	1	NUM
ejpam-3260	105	3	.	.	PUNCT
ejpam-3260	106	1	let	let	VERB
ejpam-3260	106	2	p	p	NOUN
ejpam-3260	106	3	=	=	PUNCT
ejpam-3260	106	4	{	{	PUNCT
ejpam-3260	107	1	xα	xα	INTJ
ejpam-3260	107	2	|	|	ADV
ejpam-3260	107	3	α	α	NOUN
ejpam-3260	107	4	∈	∈	PROPN
ejpam-3260	108	1	i	i	PRON
ejpam-3260	108	2	}	}	PUNCT
ejpam-3260	108	3	be	be	VERB
ejpam-3260	108	4	a	a	DET
ejpam-3260	108	5	partition	partition	NOUN
ejpam-3260	108	6	of	of	ADP
ejpam-3260	108	7	a	a	DET
ejpam-3260	108	8	set	set	NOUN
ejpam-3260	108	9	x.	x.	NOUN
ejpam-3260	108	10	(	(	PUNCT
ejpam-3260	108	11	1	1	X
ejpam-3260	108	12	)	)	PUNCT
ejpam-3260	108	13	a	a	DET
ejpam-3260	108	14	semigroup	semigroup	PROPN
ejpam-3260	108	15	t	t	PROPN
ejpam-3260	108	16	(	(	PUNCT
ejpam-3260	108	17	x	x	X
ejpam-3260	108	18	,	,	PUNCT
ejpam-3260	108	19	p	p	NOUN
ejpam-3260	108	20	)	)	PUNCT
ejpam-3260	108	21	has	have	VERB
ejpam-3260	108	22	a	a	DET
ejpam-3260	108	23	left	left	ADJ
ejpam-3260	108	24	magnifying	magnifying	ADJ
ejpam-3260	108	25	element	element	NOUN
ejpam-3260	108	26	if	if	SCONJ
ejpam-3260	108	27	and	and	CCONJ
ejpam-3260	108	28	only	only	ADV
ejpam-3260	108	29	if	if	SCONJ
ejpam-3260	108	30	xα	xα	PRON
ejpam-3260	108	31	is	be	AUX
ejpam-3260	108	32	infinite	infinite	ADJ
ejpam-3260	108	33	for	for	ADP
ejpam-3260	108	34	some	some	DET
ejpam-3260	108	35	α	α	NOUN
ejpam-3260	108	36	∈	∈	PROPN
ejpam-3260	108	37	i.	i.	NOUN
ejpam-3260	108	38	(	(	PUNCT
ejpam-3260	108	39	2	2	X
ejpam-3260	108	40	)	)	PUNCT
ejpam-3260	108	41	a	a	DET
ejpam-3260	108	42	function	function	NOUN
ejpam-3260	108	43	f	f	PROPN
ejpam-3260	108	44	is	be	AUX
ejpam-3260	108	45	left	leave	VERB
ejpam-3260	108	46	magnifying	magnify	VERB
ejpam-3260	108	47	of	of	ADP
ejpam-3260	108	48	t	t	PROPN
ejpam-3260	108	49	(	(	PUNCT
ejpam-3260	108	50	x	x	X
ejpam-3260	108	51	,	,	PUNCT
ejpam-3260	108	52	p	p	NOUN
ejpam-3260	108	53	)	)	PUNCT
ejpam-3260	109	1	if	if	SCONJ
ejpam-3260	109	2	and	and	CCONJ
ejpam-3260	109	3	only	only	ADV
ejpam-3260	109	4	if	if	SCONJ
ejpam-3260	109	5	f	f	PROPN
ejpam-3260	109	6	is	be	AUX
ejpam-3260	109	7	one	one	NUM
ejpam-3260	109	8	-	-	PUNCT
ejpam-3260	109	9	to	to	ADP
ejpam-3260	109	10	-	-	PUNCT
ejpam-3260	109	11	one	one	NUM
ejpam-3260	109	12	but	but	CCONJ
ejpam-3260	109	13	not	not	PART
ejpam-3260	109	14	onto	onto	ADP
ejpam-3260	109	15	.	.	PUNCT
ejpam-3260	110	1	proof	proof	NOUN
ejpam-3260	110	2	.	.	PUNCT
ejpam-3260	111	1	this	this	PRON
ejpam-3260	111	2	follows	follow	VERB
ejpam-3260	111	3	by	by	ADP
ejpam-3260	111	4	lemma	lemma	PROPN
ejpam-3260	111	5	1	1	NUM
ejpam-3260	111	6	,	,	PUNCT
ejpam-3260	111	7	lemma	lemma	PROPN
ejpam-3260	111	8	2	2	NUM
ejpam-3260	111	9	and	and	CCONJ
ejpam-3260	111	10	lemma	lemma	PROPN
ejpam-3260	111	11	3	3	X
ejpam-3260	111	12	.	.	NOUN
ejpam-3260	111	13	example	example	NOUN
ejpam-3260	112	1	2	2	NUM
ejpam-3260	112	2	.	.	PUNCT
ejpam-3260	113	1	let	let	VERB
ejpam-3260	113	2	x	x	SYM
ejpam-3260	113	3	=	=	PUNCT
ejpam-3260	113	4	n	n	PROPN
ejpam-3260	113	5	and	and	CCONJ
ejpam-3260	113	6	p	p	NOUN
ejpam-3260	114	1	=	=	X
ejpam-3260	114	2	{	{	PUNCT
ejpam-3260	114	3	{	{	PUNCT
ejpam-3260	114	4	1	1	NUM
ejpam-3260	114	5	,	,	PUNCT
ejpam-3260	114	6	2	2	NUM
ejpam-3260	114	7	}	}	PUNCT
ejpam-3260	114	8	,	,	PUNCT
ejpam-3260	114	9	{	{	PUNCT
ejpam-3260	114	10	3	3	NUM
ejpam-3260	114	11	,	,	PUNCT
ejpam-3260	114	12	4	4	NUM
ejpam-3260	114	13	,	,	PUNCT
ejpam-3260	114	14	5	5	NUM
ejpam-3260	114	15	}	}	PUNCT
ejpam-3260	114	16	,	,	PUNCT
ejpam-3260	114	17	{	{	PUNCT
ejpam-3260	114	18	x	x	X
ejpam-3260	114	19	|	|	NOUN
ejpam-3260	114	20	x	x	X
ejpam-3260	114	21	>	>	X
ejpam-3260	114	22	5	5	NUM
ejpam-3260	114	23	}	}	PUNCT
ejpam-3260	114	24	}	}	PUNCT
ejpam-3260	114	25	.	.	PUNCT
ejpam-3260	115	1	by	by	ADP
ejpam-3260	115	2	theorem	theorem	NOUN
ejpam-3260	115	3	1(1	1(1	NUM
ejpam-3260	115	4	)	)	PUNCT
ejpam-3260	115	5	,	,	PUNCT
ejpam-3260	115	6	t	t	PROPN
ejpam-3260	115	7	(	(	PUNCT
ejpam-3260	115	8	x	x	X
ejpam-3260	115	9	,	,	PUNCT
ejpam-3260	115	10	p	p	NOUN
ejpam-3260	115	11	)	)	PUNCT
ejpam-3260	115	12	has	have	VERB
ejpam-3260	115	13	a	a	DET
ejpam-3260	115	14	left	left	ADJ
ejpam-3260	115	15	magnifying	magnifying	ADJ
ejpam-3260	115	16	element	element	NOUN
ejpam-3260	115	17	.	.	PUNCT
ejpam-3260	116	1	let	let	VERB
ejpam-3260	116	2	f	f	PROPN
ejpam-3260	116	3	∈	∈	PROPN
ejpam-3260	116	4	t	t	PROPN
ejpam-3260	116	5	(	(	PUNCT
ejpam-3260	116	6	x	x	X
ejpam-3260	116	7	,	,	PUNCT
ejpam-3260	116	8	p	p	NOUN
ejpam-3260	116	9	)	)	PUNCT
ejpam-3260	116	10	by	by	ADP
ejpam-3260	116	11	(	(	PUNCT
ejpam-3260	116	12	x)f	x)f	X
ejpam-3260	116	13	=	=	SYM
ejpam-3260	116	14	{	{	PUNCT
ejpam-3260	116	15	x	x	X
ejpam-3260	116	16	if	if	SCONJ
ejpam-3260	116	17	x	x	SYM
ejpam-3260	116	18	≤	≤	NOUN
ejpam-3260	116	19	6	6	NUM
ejpam-3260	116	20	,	,	PUNCT
ejpam-3260	116	21	x+	x+	NUM
ejpam-3260	116	22	1	1	NUM
ejpam-3260	116	23	if	if	SCONJ
ejpam-3260	116	24	x	x	PROPN
ejpam-3260	116	25	>	>	X
ejpam-3260	116	26	6	6	NUM
ejpam-3260	116	27	,	,	PUNCT
ejpam-3260	116	28	that	that	ADV
ejpam-3260	116	29	is	is	ADV
ejpam-3260	116	30	,	,	PUNCT
ejpam-3260	116	31	f	f	X
ejpam-3260	117	1	=	=	PRON
ejpam-3260	118	1	(	(	PUNCT
ejpam-3260	118	2	1	1	NUM
ejpam-3260	118	3	2	2	NUM
ejpam-3260	118	4	3	3	NUM
ejpam-3260	118	5	4	4	NUM
ejpam-3260	118	6	5	5	NUM
ejpam-3260	118	7	6	6	NUM
ejpam-3260	118	8	7	7	NUM
ejpam-3260	118	9	8	8	NUM
ejpam-3260	118	10	·	·	PUNCT
ejpam-3260	118	11	·	·	PUNCT
ejpam-3260	118	12	·	·	PUNCT
ejpam-3260	118	13	1	1	NUM
ejpam-3260	118	14	2	2	NUM
ejpam-3260	118	15	3	3	NUM
ejpam-3260	118	16	4	4	NUM
ejpam-3260	118	17	5	5	NUM
ejpam-3260	118	18	6	6	NUM
ejpam-3260	118	19	8	8	NUM
ejpam-3260	118	20	9	9	NUM
ejpam-3260	118	21	·	·	PUNCT
ejpam-3260	118	22	·	·	PUNCT
ejpam-3260	118	23	·	·	PUNCT
ejpam-3260	118	24	)	)	PUNCT
ejpam-3260	118	25	.	.	PUNCT
ejpam-3260	119	1	then	then	ADV
ejpam-3260	119	2	f	f	PROPN
ejpam-3260	119	3	is	be	AUX
ejpam-3260	119	4	one	one	NUM
ejpam-3260	119	5	-	-	PUNCT
ejpam-3260	119	6	to	to	ADP
ejpam-3260	119	7	-	-	PUNCT
ejpam-3260	119	8	one	one	NUM
ejpam-3260	119	9	but	but	CCONJ
ejpam-3260	119	10	not	not	PART
ejpam-3260	119	11	onto	onto	ADP
ejpam-3260	119	12	.	.	PUNCT
ejpam-3260	120	1	by	by	ADP
ejpam-3260	120	2	theorem	theorem	NOUN
ejpam-3260	120	3	1(2	1(2	NUM
ejpam-3260	120	4	)	)	PUNCT
ejpam-3260	120	5	,	,	PUNCT
ejpam-3260	120	6	f	f	PROPN
ejpam-3260	120	7	is	be	AUX
ejpam-3260	120	8	left	leave	VERB
ejpam-3260	120	9	magnifying	magnify	VERB
ejpam-3260	120	10	of	of	ADP
ejpam-3260	120	11	t	t	PROPN
ejpam-3260	120	12	(	(	PUNCT
ejpam-3260	120	13	x	x	X
ejpam-3260	120	14	,	,	PUNCT
ejpam-3260	120	15	p	p	NOUN
ejpam-3260	120	16	)	)	PUNCT
ejpam-3260	120	17	.	.	PUNCT
ejpam-3260	121	1	corollary	corollary	ADJ
ejpam-3260	121	2	1	1	NUM
ejpam-3260	121	3	.	.	PUNCT
ejpam-3260	122	1	the	the	DET
ejpam-3260	122	2	following	follow	VERB
ejpam-3260	122	3	statements	statement	NOUN
ejpam-3260	122	4	hold	hold	VERB
ejpam-3260	122	5	for	for	ADP
ejpam-3260	122	6	a	a	DET
ejpam-3260	122	7	semigroup	semigroup	PROPN
ejpam-3260	122	8	t	t	NOUN
ejpam-3260	122	9	(	(	PUNCT
ejpam-3260	122	10	x	x	NOUN
ejpam-3260	122	11	)	)	PUNCT
ejpam-3260	122	12	.	.	PUNCT
ejpam-3260	123	1	(	(	PUNCT
ejpam-3260	123	2	1	1	X
ejpam-3260	123	3	)	)	PUNCT
ejpam-3260	123	4	a	a	DET
ejpam-3260	123	5	semigroup	semigroup	PROPN
ejpam-3260	123	6	t	t	PROPN
ejpam-3260	123	7	(	(	PUNCT
ejpam-3260	123	8	x	x	X
ejpam-3260	123	9	)	)	PUNCT
ejpam-3260	123	10	has	have	VERB
ejpam-3260	123	11	a	a	DET
ejpam-3260	123	12	left	left	ADJ
ejpam-3260	123	13	magnifying	magnify	VERB
ejpam-3260	123	14	if	if	SCONJ
ejpam-3260	123	15	and	and	CCONJ
ejpam-3260	123	16	only	only	ADV
ejpam-3260	123	17	if	if	SCONJ
ejpam-3260	123	18	x	x	PRON
ejpam-3260	123	19	is	be	AUX
ejpam-3260	123	20	infinite	infinite	ADJ
ejpam-3260	123	21	.	.	PUNCT
ejpam-3260	124	1	(	(	PUNCT
ejpam-3260	124	2	2	2	X
ejpam-3260	124	3	)	)	PUNCT
ejpam-3260	124	4	a	a	DET
ejpam-3260	124	5	function	function	NOUN
ejpam-3260	124	6	f	f	PROPN
ejpam-3260	124	7	is	be	AUX
ejpam-3260	124	8	left	leave	VERB
ejpam-3260	124	9	magnifying	magnify	VERB
ejpam-3260	124	10	of	of	ADP
ejpam-3260	124	11	t	t	PROPN
ejpam-3260	124	12	(	(	PUNCT
ejpam-3260	124	13	x	x	NOUN
ejpam-3260	124	14	)	)	PUNCT
ejpam-3260	124	15	if	if	SCONJ
ejpam-3260	124	16	and	and	CCONJ
ejpam-3260	124	17	only	only	ADV
ejpam-3260	124	18	if	if	SCONJ
ejpam-3260	124	19	f	f	PROPN
ejpam-3260	124	20	is	be	AUX
ejpam-3260	124	21	one	one	NUM
ejpam-3260	124	22	-	-	PUNCT
ejpam-3260	124	23	to	to	ADP
ejpam-3260	124	24	-	-	PUNCT
ejpam-3260	124	25	one	one	NUM
ejpam-3260	124	26	but	but	CCONJ
ejpam-3260	124	27	not	not	PART
ejpam-3260	124	28	onto	onto	ADP
ejpam-3260	124	29	.	.	PUNCT
ejpam-3260	125	1	proof	proof	NOUN
ejpam-3260	125	2	.	.	PUNCT
ejpam-3260	126	1	this	this	PRON
ejpam-3260	126	2	follows	follow	VERB
ejpam-3260	126	3	by	by	ADP
ejpam-3260	126	4	theorem	theorem	NOUN
ejpam-3260	126	5	1	1	NUM
ejpam-3260	126	6	by	by	ADP
ejpam-3260	126	7	using	use	VERB
ejpam-3260	126	8	p	p	X
ejpam-3260	126	9	=	=	PUNCT
ejpam-3260	126	10	{	{	PUNCT
ejpam-3260	126	11	x	x	NOUN
ejpam-3260	126	12	}	}	PUNCT
ejpam-3260	126	13	.	.	PUNCT
ejpam-3260	127	1	3	3	X
ejpam-3260	127	2	.	.	X
ejpam-3260	127	3	right	right	ADJ
ejpam-3260	127	4	magnifying	magnify	VERB
ejpam-3260	127	5	elements	element	NOUN
ejpam-3260	127	6	of	of	ADP
ejpam-3260	127	7	t	t	PROPN
ejpam-3260	127	8	(	(	PUNCT
ejpam-3260	127	9	x	x	X
ejpam-3260	127	10	,	,	PUNCT
ejpam-3260	127	11	p	p	NOUN
ejpam-3260	127	12	)	)	PUNCT
ejpam-3260	127	13	in	in	ADP
ejpam-3260	127	14	this	this	DET
ejpam-3260	127	15	section	section	NOUN
ejpam-3260	127	16	,	,	PUNCT
ejpam-3260	127	17	we	we	PRON
ejpam-3260	127	18	give	give	VERB
ejpam-3260	127	19	necessary	necessary	ADJ
ejpam-3260	127	20	and	and	CCONJ
ejpam-3260	127	21	sufficient	sufficient	ADJ
ejpam-3260	127	22	conditions	condition	NOUN
ejpam-3260	127	23	for	for	ADP
ejpam-3260	127	24	elements	element	NOUN
ejpam-3260	127	25	in	in	ADP
ejpam-3260	127	26	t	t	PROPN
ejpam-3260	127	27	(	(	PUNCT
ejpam-3260	127	28	x	x	X
ejpam-3260	127	29	,	,	PUNCT
ejpam-3260	127	30	p	p	NOUN
ejpam-3260	127	31	)	)	PUNCT
ejpam-3260	127	32	to	to	PART
ejpam-3260	127	33	be	be	AUX
ejpam-3260	127	34	right	right	ADJ
ejpam-3260	127	35	magnifying	magnifying	NOUN
ejpam-3260	127	36	.	.	PUNCT
ejpam-3260	128	1	lemma	lemma	PROPN
ejpam-3260	128	2	4	4	X
ejpam-3260	128	3	.	.	PUNCT
ejpam-3260	129	1	if	if	SCONJ
ejpam-3260	129	2	f	f	PROPN
ejpam-3260	129	3	is	be	AUX
ejpam-3260	129	4	a	a	DET
ejpam-3260	129	5	right	right	ADJ
ejpam-3260	129	6	magnifying	magnify	VERB
ejpam-3260	129	7	element	element	NOUN
ejpam-3260	129	8	of	of	ADP
ejpam-3260	129	9	t	t	PROPN
ejpam-3260	129	10	(	(	PUNCT
ejpam-3260	129	11	x	x	X
ejpam-3260	129	12	,	,	PUNCT
ejpam-3260	129	13	p	p	NOUN
ejpam-3260	129	14	)	)	PUNCT
ejpam-3260	129	15	,	,	PUNCT
ejpam-3260	129	16	then	then	ADV
ejpam-3260	129	17	f	f	PROPN
ejpam-3260	129	18	is	be	AUX
ejpam-3260	129	19	onto	onto	ADP
ejpam-3260	129	20	.	.	PUNCT
ejpam-3260	130	1	proof	proof	NOUN
ejpam-3260	130	2	.	.	PUNCT
ejpam-3260	131	1	assume	assume	VERB
ejpam-3260	131	2	that	that	SCONJ
ejpam-3260	131	3	f	f	PROPN
ejpam-3260	131	4	is	be	AUX
ejpam-3260	131	5	a	a	DET
ejpam-3260	131	6	right	right	ADJ
ejpam-3260	131	7	magnifying	magnify	VERB
ejpam-3260	131	8	element	element	NOUN
ejpam-3260	131	9	of	of	ADP
ejpam-3260	131	10	t	t	PROPN
ejpam-3260	131	11	(	(	PUNCT
ejpam-3260	131	12	x	x	X
ejpam-3260	131	13	,	,	PUNCT
ejpam-3260	131	14	p	p	NOUN
ejpam-3260	131	15	)	)	PUNCT
ejpam-3260	131	16	.	.	PUNCT
ejpam-3260	132	1	then	then	ADV
ejpam-3260	132	2	there	there	PRON
ejpam-3260	132	3	exists	exist	VERB
ejpam-3260	132	4	a	a	DET
ejpam-3260	132	5	proper	proper	ADJ
ejpam-3260	132	6	subset	subset	NOUN
ejpam-3260	132	7	m	m	NOUN
ejpam-3260	132	8	of	of	ADP
ejpam-3260	132	9	t	t	PROPN
ejpam-3260	132	10	(	(	PUNCT
ejpam-3260	132	11	x	x	X
ejpam-3260	132	12	,	,	PUNCT
ejpam-3260	132	13	p	p	NOUN
ejpam-3260	132	14	)	)	PUNCT
ejpam-3260	132	15	such	such	ADJ
ejpam-3260	132	16	that	that	SCONJ
ejpam-3260	132	17	mf	mf	X
ejpam-3260	132	18	=	=	SYM
ejpam-3260	132	19	t	t	PROPN
ejpam-3260	132	20	(	(	PUNCT
ejpam-3260	132	21	x	x	X
ejpam-3260	132	22	,	,	PUNCT
ejpam-3260	132	23	p	p	NOUN
ejpam-3260	132	24	)	)	PUNCT
ejpam-3260	132	25	.	.	PUNCT
ejpam-3260	133	1	since	since	SCONJ
ejpam-3260	133	2	idx	idx	PROPN
ejpam-3260	133	3	∈	∈	PROPN
ejpam-3260	133	4	t	t	NOUN
ejpam-3260	133	5	(	(	PUNCT
ejpam-3260	133	6	x	x	X
ejpam-3260	133	7	,	,	PUNCT
ejpam-3260	133	8	p	p	NOUN
ejpam-3260	133	9	)	)	PUNCT
ejpam-3260	133	10	,	,	PUNCT
ejpam-3260	133	11	there	there	PRON
ejpam-3260	133	12	exists	exist	VERB
ejpam-3260	133	13	a	a	DET
ejpam-3260	133	14	function	function	NOUN
ejpam-3260	133	15	h	h	NOUN
ejpam-3260	133	16	∈m	∈m	NOUN
ejpam-3260	133	17	such	such	ADJ
ejpam-3260	133	18	that	that	DET
ejpam-3260	133	19	hf	hf	NOUN
ejpam-3260	133	20	=	=	PUNCT
ejpam-3260	133	21	idx	idx	PROPN
ejpam-3260	133	22	.	.	PUNCT
ejpam-3260	134	1	this	this	PRON
ejpam-3260	134	2	implies	imply	VERB
ejpam-3260	134	3	that	that	SCONJ
ejpam-3260	134	4	f	f	PROPN
ejpam-3260	134	5	is	be	AUX
ejpam-3260	134	6	onto	onto	ADP
ejpam-3260	134	7	.	.	PUNCT
ejpam-3260	135	1	r.	r.	PROPN
ejpam-3260	135	2	chinram	chinram	PROPN
ejpam-3260	135	3	,	,	PUNCT
ejpam-3260	135	4	p.	p.	NOUN
ejpam-3260	135	5	petchkaew	petchkaew	NOUN
ejpam-3260	135	6	,	,	PUNCT
ejpam-3260	135	7	s.	s.	PROPN
ejpam-3260	135	8	baupradist	baupradist	PROPN
ejpam-3260	135	9	/	/	SYM
ejpam-3260	135	10	eur	eur	PROPN
ejpam-3260	135	11	.	.	PUNCT
ejpam-3260	136	1	j.	j.	PROPN
ejpam-3260	136	2	pure	pure	PROPN
ejpam-3260	136	3	appl	appl	PROPN
ejpam-3260	136	4	.	.	PROPN
ejpam-3260	136	5	math	math	PROPN
ejpam-3260	136	6	,	,	PUNCT
ejpam-3260	136	7	11	11	NUM
ejpam-3260	136	8	(	(	PUNCT
ejpam-3260	136	9	3	3	NUM
ejpam-3260	136	10	)	)	PUNCT
ejpam-3260	136	11	(	(	PUNCT
ejpam-3260	136	12	2018	2018	NUM
ejpam-3260	136	13	)	)	PUNCT
ejpam-3260	136	14	,	,	PUNCT
ejpam-3260	136	15	580	580	NUM
ejpam-3260	136	16	-	-	SYM
ejpam-3260	136	17	588	588	NUM
ejpam-3260	136	18	584	584	NUM
ejpam-3260	136	19	lemma	lemma	PROPN
ejpam-3260	136	20	5	5	NUM
ejpam-3260	136	21	.	.	PUNCT
ejpam-3260	137	1	if	if	SCONJ
ejpam-3260	137	2	f	f	PROPN
ejpam-3260	137	3	∈	∈	PROPN
ejpam-3260	137	4	t	t	PROPN
ejpam-3260	137	5	(	(	PUNCT
ejpam-3260	137	6	x	x	X
ejpam-3260	137	7	,	,	PUNCT
ejpam-3260	137	8	p	p	NOUN
ejpam-3260	137	9	)	)	PUNCT
ejpam-3260	137	10	is	be	AUX
ejpam-3260	137	11	bijective	bijective	ADJ
ejpam-3260	137	12	,	,	PUNCT
ejpam-3260	137	13	then	then	ADV
ejpam-3260	137	14	f	f	PROPN
ejpam-3260	137	15	is	be	AUX
ejpam-3260	137	16	not	not	PART
ejpam-3260	137	17	right	right	ADJ
ejpam-3260	137	18	magnifying	magnifying	NOUN
ejpam-3260	137	19	of	of	ADP
ejpam-3260	137	20	t	t	PROPN
ejpam-3260	137	21	(	(	PUNCT
ejpam-3260	137	22	x	x	X
ejpam-3260	137	23	,	,	PUNCT
ejpam-3260	137	24	p	p	NOUN
ejpam-3260	137	25	)	)	PUNCT
ejpam-3260	137	26	.	.	PUNCT
ejpam-3260	138	1	proof	proof	NOUN
ejpam-3260	138	2	.	.	PUNCT
ejpam-3260	139	1	assume	assume	VERB
ejpam-3260	139	2	that	that	SCONJ
ejpam-3260	139	3	f	f	PROPN
ejpam-3260	139	4	is	be	AUX
ejpam-3260	139	5	bijective	bijective	ADJ
ejpam-3260	139	6	.	.	PUNCT
ejpam-3260	140	1	then	then	ADV
ejpam-3260	140	2	its	its	PRON
ejpam-3260	140	3	inverse	inverse	NOUN
ejpam-3260	140	4	function	function	NOUN
ejpam-3260	140	5	f−1	f−1	PROPN
ejpam-3260	140	6	exists	exist	VERB
ejpam-3260	140	7	and	and	CCONJ
ejpam-3260	140	8	f−1	f−1	PROPN
ejpam-3260	140	9	∈	∈	PROPN
ejpam-3260	140	10	t	t	PROPN
ejpam-3260	140	11	(	(	PUNCT
ejpam-3260	140	12	x	x	X
ejpam-3260	140	13	,	,	PUNCT
ejpam-3260	140	14	p	p	NOUN
ejpam-3260	140	15	)	)	PUNCT
ejpam-3260	140	16	.	.	PUNCT
ejpam-3260	141	1	suppose	suppose	VERB
ejpam-3260	141	2	that	that	SCONJ
ejpam-3260	141	3	f	f	PROPN
ejpam-3260	141	4	is	be	AUX
ejpam-3260	141	5	a	a	DET
ejpam-3260	141	6	right	right	ADJ
ejpam-3260	141	7	magnifying	magnify	VERB
ejpam-3260	141	8	element	element	NOUN
ejpam-3260	141	9	of	of	ADP
ejpam-3260	141	10	t	t	PROPN
ejpam-3260	141	11	(	(	PUNCT
ejpam-3260	141	12	x	x	X
ejpam-3260	141	13	,	,	PUNCT
ejpam-3260	141	14	p	p	NOUN
ejpam-3260	141	15	)	)	PUNCT
ejpam-3260	141	16	.	.	PUNCT
ejpam-3260	142	1	then	then	ADV
ejpam-3260	142	2	there	there	PRON
ejpam-3260	142	3	exists	exist	VERB
ejpam-3260	142	4	a	a	DET
ejpam-3260	142	5	proper	proper	ADJ
ejpam-3260	142	6	subset	subset	NOUN
ejpam-3260	142	7	m	m	NOUN
ejpam-3260	142	8	of	of	ADP
ejpam-3260	142	9	t	t	PROPN
ejpam-3260	142	10	(	(	PUNCT
ejpam-3260	142	11	x	x	X
ejpam-3260	142	12	,	,	PUNCT
ejpam-3260	142	13	p	p	NOUN
ejpam-3260	142	14	)	)	PUNCT
ejpam-3260	142	15	such	such	ADJ
ejpam-3260	142	16	that	that	SCONJ
ejpam-3260	142	17	mf	mf	X
ejpam-3260	142	18	=	=	SYM
ejpam-3260	142	19	t	t	PROPN
ejpam-3260	142	20	(	(	PUNCT
ejpam-3260	142	21	x	x	X
ejpam-3260	142	22	,	,	PUNCT
ejpam-3260	142	23	p	p	NOUN
ejpam-3260	142	24	)	)	PUNCT
ejpam-3260	142	25	.	.	PUNCT
ejpam-3260	143	1	hence	hence	ADV
ejpam-3260	143	2	mf	mf	X
ejpam-3260	143	3	=	=	SYM
ejpam-3260	143	4	t	t	PROPN
ejpam-3260	143	5	(	(	PUNCT
ejpam-3260	143	6	x	x	X
ejpam-3260	143	7	,	,	PUNCT
ejpam-3260	143	8	p	p	NOUN
ejpam-3260	143	9	)	)	PUNCT
ejpam-3260	143	10	f	f	PROPN
ejpam-3260	143	11	and	and	CCONJ
ejpam-3260	143	12	m	m	PROPN
ejpam-3260	143	13	=	=	SYM
ejpam-3260	144	1	mff−1	mff−1	PROPN
ejpam-3260	144	2	=	=	SYM
ejpam-3260	144	3	t	t	PROPN
ejpam-3260	144	4	(	(	PUNCT
ejpam-3260	144	5	x	x	X
ejpam-3260	144	6	,	,	PUNCT
ejpam-3260	144	7	p	p	NOUN
ejpam-3260	144	8	)	)	PUNCT
ejpam-3260	144	9	ff−1	ff−1	PROPN
ejpam-3260	144	10	=	=	SYM
ejpam-3260	144	11	t	t	PROPN
ejpam-3260	144	12	(	(	PUNCT
ejpam-3260	144	13	x	x	X
ejpam-3260	144	14	,	,	PUNCT
ejpam-3260	144	15	p	p	NOUN
ejpam-3260	144	16	)	)	PUNCT
ejpam-3260	144	17	,	,	PUNCT
ejpam-3260	144	18	a	a	DET
ejpam-3260	144	19	contradiction	contradiction	NOUN
ejpam-3260	144	20	.	.	PUNCT
ejpam-3260	145	1	therefore	therefore	ADV
ejpam-3260	145	2	,	,	PUNCT
ejpam-3260	145	3	f	f	PROPN
ejpam-3260	145	4	is	be	AUX
ejpam-3260	145	5	not	not	PART
ejpam-3260	145	6	right	right	ADJ
ejpam-3260	145	7	magnifying	magnifying	NOUN
ejpam-3260	145	8	of	of	ADP
ejpam-3260	145	9	t	t	PROPN
ejpam-3260	145	10	(	(	PUNCT
ejpam-3260	145	11	x	x	X
ejpam-3260	145	12	,	,	PUNCT
ejpam-3260	145	13	p	p	NOUN
ejpam-3260	145	14	)	)	PUNCT
ejpam-3260	145	15	.	.	PUNCT
ejpam-3260	146	1	lemma	lemma	PROPN
ejpam-3260	146	2	6	6	NUM
ejpam-3260	146	3	.	.	PUNCT
ejpam-3260	147	1	let	let	VERB
ejpam-3260	147	2	f	f	PROPN
ejpam-3260	147	3	∈	∈	PROPN
ejpam-3260	147	4	t	t	PROPN
ejpam-3260	147	5	(	(	PUNCT
ejpam-3260	147	6	x	x	X
ejpam-3260	147	7	,	,	PUNCT
ejpam-3260	147	8	p	p	NOUN
ejpam-3260	147	9	)	)	PUNCT
ejpam-3260	147	10	be	be	AUX
ejpam-3260	147	11	onto	onto	ADP
ejpam-3260	147	12	but	but	CCONJ
ejpam-3260	147	13	not	not	PART
ejpam-3260	147	14	one	one	NUM
ejpam-3260	147	15	-	-	PUNCT
ejpam-3260	147	16	to	to	ADP
ejpam-3260	147	17	-	-	PUNCT
ejpam-3260	147	18	one	one	NUM
ejpam-3260	147	19	.	.	PUNCT
ejpam-3260	148	1	then	then	ADV
ejpam-3260	148	2	f	f	PROPN
ejpam-3260	148	3	is	be	AUX
ejpam-3260	148	4	right	right	ADJ
ejpam-3260	148	5	magnifying	magnifying	NOUN
ejpam-3260	148	6	of	of	ADP
ejpam-3260	148	7	t	t	PROPN
ejpam-3260	148	8	(	(	PUNCT
ejpam-3260	148	9	x	x	X
ejpam-3260	148	10	,	,	PUNCT
ejpam-3260	148	11	p	p	NOUN
ejpam-3260	148	12	)	)	PUNCT
ejpam-3260	148	13	.	.	PUNCT
ejpam-3260	149	1	proof	proof	NOUN
ejpam-3260	149	2	.	.	PUNCT
ejpam-3260	150	1	assume	assume	VERB
ejpam-3260	150	2	that	that	SCONJ
ejpam-3260	150	3	f	f	PROPN
ejpam-3260	150	4	is	be	AUX
ejpam-3260	150	5	onto	onto	ADP
ejpam-3260	150	6	but	but	CCONJ
ejpam-3260	150	7	not	not	PART
ejpam-3260	150	8	one	one	NUM
ejpam-3260	150	9	-	-	PUNCT
ejpam-3260	150	10	to	to	ADP
ejpam-3260	150	11	-	-	PUNCT
ejpam-3260	150	12	one	one	NUM
ejpam-3260	150	13	.	.	PUNCT
ejpam-3260	151	1	let	let	VERB
ejpam-3260	151	2	m	m	VERB
ejpam-3260	151	3	=	=	PRON
ejpam-3260	151	4	{	{	PUNCT
ejpam-3260	151	5	h	h	NOUN
ejpam-3260	151	6	∈	∈	PROPN
ejpam-3260	151	7	t	t	PROPN
ejpam-3260	151	8	(	(	PUNCT
ejpam-3260	151	9	x	x	X
ejpam-3260	151	10	,	,	PUNCT
ejpam-3260	151	11	p	p	NOUN
ejpam-3260	151	12	)	)	PUNCT
ejpam-3260	152	1	|	|	ADV
ejpam-3260	152	2	h	h	NOUN
ejpam-3260	152	3	is	be	AUX
ejpam-3260	152	4	not	not	PART
ejpam-3260	152	5	onto	onto	ADP
ejpam-3260	152	6	}	}	PUNCT
ejpam-3260	152	7	.	.	PUNCT
ejpam-3260	153	1	then	then	ADV
ejpam-3260	153	2	m	m	PROPN
ejpam-3260	153	3	6=	6=	PROPN
ejpam-3260	153	4	t	t	PROPN
ejpam-3260	153	5	(	(	PUNCT
ejpam-3260	153	6	x	x	X
ejpam-3260	153	7	,	,	PUNCT
ejpam-3260	153	8	p	p	NOUN
ejpam-3260	153	9	)	)	PUNCT
ejpam-3260	153	10	.	.	PUNCT
ejpam-3260	154	1	let	let	VERB
ejpam-3260	154	2	g	g	PRON
ejpam-3260	154	3	be	be	AUX
ejpam-3260	154	4	any	any	DET
ejpam-3260	154	5	function	function	NOUN
ejpam-3260	154	6	in	in	ADP
ejpam-3260	154	7	t	t	PROPN
ejpam-3260	154	8	(	(	PUNCT
ejpam-3260	154	9	x	x	X
ejpam-3260	154	10	,	,	PUNCT
ejpam-3260	154	11	p	p	NOUN
ejpam-3260	154	12	)	)	PUNCT
ejpam-3260	154	13	.	.	PUNCT
ejpam-3260	155	1	since	since	SCONJ
ejpam-3260	155	2	f	f	PROPN
ejpam-3260	155	3	is	be	AUX
ejpam-3260	155	4	onto	onto	ADP
ejpam-3260	155	5	,	,	PUNCT
ejpam-3260	155	6	there	there	PRON
ejpam-3260	155	7	exists	exist	VERB
ejpam-3260	155	8	for	for	ADP
ejpam-3260	155	9	each	each	DET
ejpam-3260	155	10	x	x	SYM
ejpam-3260	155	11	∈	∈	PROPN
ejpam-3260	155	12	xα	xα	PROPN
ejpam-3260	155	13	,	,	PUNCT
ejpam-3260	155	14	an	an	DET
ejpam-3260	155	15	element	element	NOUN
ejpam-3260	155	16	yx	yx	NOUN
ejpam-3260	155	17	∈	∈	PROPN
ejpam-3260	155	18	xα	xα	ADP
ejpam-3260	155	19	such	such	ADJ
ejpam-3260	155	20	that	that	SCONJ
ejpam-3260	155	21	(	(	PUNCT
ejpam-3260	155	22	yx)f	yx)f	X
ejpam-3260	155	23	=	=	SYM
ejpam-3260	155	24	(	(	PUNCT
ejpam-3260	155	25	x)g	x)g	X
ejpam-3260	155	26	(	(	PUNCT
ejpam-3260	155	27	if	if	SCONJ
ejpam-3260	155	28	(	(	PUNCT
ejpam-3260	155	29	x1)g	x1)g	NOUN
ejpam-3260	155	30	=	=	SYM
ejpam-3260	155	31	(	(	PUNCT
ejpam-3260	155	32	x2)g	x2)g	PROPN
ejpam-3260	155	33	,	,	PUNCT
ejpam-3260	155	34	we	we	PRON
ejpam-3260	155	35	must	must	AUX
ejpam-3260	155	36	choose	choose	VERB
ejpam-3260	155	37	yx1	yx1	NOUN
ejpam-3260	155	38	=	=	SYM
ejpam-3260	155	39	yx2	yx2	NOUN
ejpam-3260	155	40	)	)	PUNCT
ejpam-3260	155	41	.	.	PUNCT
ejpam-3260	156	1	define	define	VERB
ejpam-3260	156	2	a	a	DET
ejpam-3260	156	3	function	function	NOUN
ejpam-3260	156	4	h	h	NOUN
ejpam-3260	156	5	∈	∈	PROPN
ejpam-3260	156	6	t	t	PROPN
ejpam-3260	156	7	(	(	PUNCT
ejpam-3260	156	8	x	x	X
ejpam-3260	156	9	,	,	PUNCT
ejpam-3260	156	10	p	p	NOUN
ejpam-3260	156	11	)	)	PUNCT
ejpam-3260	156	12	by	by	ADP
ejpam-3260	156	13	(	(	PUNCT
ejpam-3260	156	14	x)h	x)h	PROPN
ejpam-3260	156	15	=	=	SYM
ejpam-3260	156	16	yx	yx	PROPN
ejpam-3260	156	17	for	for	ADP
ejpam-3260	156	18	all	all	PRON
ejpam-3260	156	19	x	x	SYM
ejpam-3260	156	20	∈	∈	ADJ
ejpam-3260	156	21	x.	x.	NOUN
ejpam-3260	157	1	we	we	PRON
ejpam-3260	157	2	claim	claim	VERB
ejpam-3260	157	3	that	that	SCONJ
ejpam-3260	157	4	h	h	NOUN
ejpam-3260	157	5	is	be	AUX
ejpam-3260	157	6	not	not	PART
ejpam-3260	157	7	onto	onto	ADP
ejpam-3260	157	8	.	.	PUNCT
ejpam-3260	158	1	since	since	SCONJ
ejpam-3260	158	2	f	f	PROPN
ejpam-3260	158	3	is	be	AUX
ejpam-3260	158	4	not	not	PART
ejpam-3260	158	5	one	one	NUM
ejpam-3260	158	6	-	-	PUNCT
ejpam-3260	158	7	to	to	ADP
ejpam-3260	158	8	-	-	PUNCT
ejpam-3260	158	9	one	one	NUM
ejpam-3260	158	10	,	,	PUNCT
ejpam-3260	158	11	there	there	PRON
ejpam-3260	158	12	exist	exist	VERB
ejpam-3260	158	13	an	an	DET
ejpam-3260	158	14	element	element	NOUN
ejpam-3260	158	15	y′	y′	NOUN
ejpam-3260	158	16	∈	∈	PROPN
ejpam-3260	158	17	x	x	X
ejpam-3260	158	18	and	and	CCONJ
ejpam-3260	158	19	distinct	distinct	ADJ
ejpam-3260	158	20	elements	element	NOUN
ejpam-3260	158	21	y1	y1	NOUN
ejpam-3260	158	22	,	,	PUNCT
ejpam-3260	158	23	y2	y2	NOUN
ejpam-3260	158	24	∈	∈	PROPN
ejpam-3260	158	25	x	x	PUNCT
ejpam-3260	159	1	such	such	ADJ
ejpam-3260	159	2	that	that	PRON
ejpam-3260	159	3	(	(	PUNCT
ejpam-3260	159	4	y1)f	y1)f	PROPN
ejpam-3260	159	5	=	=	SYM
ejpam-3260	159	6	(	(	PUNCT
ejpam-3260	159	7	y2)f	y2)f	NOUN
ejpam-3260	159	8	=	=	PUNCT
ejpam-3260	159	9	y′.	y′.	NOUN
ejpam-3260	159	10	if	if	SCONJ
ejpam-3260	159	11	y′	y′	NUM
ejpam-3260	159	12	/∈	/∈	PUNCT
ejpam-3260	159	13	ran	run	VERB
ejpam-3260	159	14	g	g	NOUN
ejpam-3260	159	15	,	,	PUNCT
ejpam-3260	159	16	we	we	PRON
ejpam-3260	159	17	have	have	VERB
ejpam-3260	159	18	y1	y1	NOUN
ejpam-3260	159	19	,	,	PUNCT
ejpam-3260	159	20	y2	y2	PROPN
ejpam-3260	159	21	/∈	/∈	PUNCT
ejpam-3260	160	1	ranh	ranh	ADJ
ejpam-3260	160	2	.	.	PUNCT
ejpam-3260	161	1	if	if	SCONJ
ejpam-3260	161	2	y′	y′	NOUN
ejpam-3260	161	3	∈	∈	PROPN
ejpam-3260	161	4	ran	run	VERB
ejpam-3260	161	5	g	g	NOUN
ejpam-3260	161	6	,	,	PUNCT
ejpam-3260	161	7	there	there	PRON
ejpam-3260	161	8	is	be	VERB
ejpam-3260	161	9	at	at	ADP
ejpam-3260	161	10	most	most	ADJ
ejpam-3260	161	11	one	one	NUM
ejpam-3260	161	12	between	between	ADP
ejpam-3260	161	13	y1	y1	NOUN
ejpam-3260	161	14	and	and	CCONJ
ejpam-3260	161	15	y2	y2	PROPN
ejpam-3260	161	16	in	in	ADP
ejpam-3260	161	17	ranh	ranh	VERB
ejpam-3260	161	18	.	.	PUNCT
ejpam-3260	162	1	then	then	ADV
ejpam-3260	162	2	h	h	NOUN
ejpam-3260	162	3	is	be	AUX
ejpam-3260	162	4	not	not	PART
ejpam-3260	162	5	onto	onto	ADP
ejpam-3260	162	6	.	.	PUNCT
ejpam-3260	163	1	hence	hence	ADV
ejpam-3260	163	2	h	h	NOUN
ejpam-3260	163	3	∈m	∈m	NOUN
ejpam-3260	163	4	and	and	CCONJ
ejpam-3260	163	5	for	for	ADP
ejpam-3260	163	6	all	all	DET
ejpam-3260	163	7	x	x	SYM
ejpam-3260	163	8	∈	∈	PROPN
ejpam-3260	163	9	x	x	NOUN
ejpam-3260	163	10	,	,	PUNCT
ejpam-3260	163	11	we	we	PRON
ejpam-3260	163	12	have	have	VERB
ejpam-3260	163	13	(	(	PUNCT
ejpam-3260	163	14	x)hf	x)hf	PROPN
ejpam-3260	163	15	=	=	SYM
ejpam-3260	163	16	(	(	PUNCT
ejpam-3260	163	17	yx)f	yx)f	X
ejpam-3260	163	18	=	=	SYM
ejpam-3260	163	19	(	(	PUNCT
ejpam-3260	163	20	x)g	x)g	X
ejpam-3260	163	21	.	.	PUNCT
ejpam-3260	164	1	then	then	ADV
ejpam-3260	164	2	hf	hf	PROPN
ejpam-3260	164	3	=	=	SYM
ejpam-3260	164	4	g	g	NOUN
ejpam-3260	164	5	,	,	PUNCT
ejpam-3260	164	6	hence	hence	ADV
ejpam-3260	164	7	mf	mf	X
ejpam-3260	164	8	=	=	SYM
ejpam-3260	164	9	t	t	PROPN
ejpam-3260	164	10	(	(	PUNCT
ejpam-3260	164	11	x	x	X
ejpam-3260	164	12	,	,	PUNCT
ejpam-3260	164	13	p	p	NOUN
ejpam-3260	164	14	)	)	PUNCT
ejpam-3260	164	15	.	.	PUNCT
ejpam-3260	165	1	therefore	therefore	ADV
ejpam-3260	165	2	,	,	PUNCT
ejpam-3260	165	3	f	f	PROPN
ejpam-3260	165	4	is	be	AUX
ejpam-3260	165	5	right	right	ADJ
ejpam-3260	165	6	magnifying	magnifying	NOUN
ejpam-3260	165	7	of	of	ADP
ejpam-3260	165	8	t	t	PROPN
ejpam-3260	165	9	(	(	PUNCT
ejpam-3260	165	10	x	x	X
ejpam-3260	165	11	,	,	PUNCT
ejpam-3260	165	12	p	p	NOUN
ejpam-3260	165	13	)	)	PUNCT
ejpam-3260	165	14	.	.	PUNCT
ejpam-3260	166	1	example	example	NOUN
ejpam-3260	167	1	3	3	X
ejpam-3260	167	2	.	.	X
ejpam-3260	168	1	consider	consider	VERB
ejpam-3260	168	2	x	x	X
ejpam-3260	168	3	=	=	PUNCT
ejpam-3260	168	4	n	n	PROPN
ejpam-3260	168	5	and	and	CCONJ
ejpam-3260	168	6	p	p	NOUN
ejpam-3260	168	7	=	=	X
ejpam-3260	168	8	{	{	PUNCT
ejpam-3260	168	9	{	{	PUNCT
ejpam-3260	168	10	x	x	INTJ
ejpam-3260	168	11	|	|	ADV
ejpam-3260	168	12	x	x	INTJ
ejpam-3260	168	13	is	be	AUX
ejpam-3260	168	14	odd	odd	ADJ
ejpam-3260	168	15	}	}	PUNCT
ejpam-3260	168	16	,	,	PUNCT
ejpam-3260	168	17	{	{	PUNCT
ejpam-3260	168	18	x	x	SYM
ejpam-3260	168	19	|	|	ADV
ejpam-3260	168	20	x	x	INTJ
ejpam-3260	168	21	is	be	AUX
ejpam-3260	168	22	even	even	ADV
ejpam-3260	168	23	}	}	PUNCT
ejpam-3260	168	24	}	}	PUNCT
ejpam-3260	168	25	.	.	PUNCT
ejpam-3260	169	1	let	let	VERB
ejpam-3260	169	2	f	f	PROPN
ejpam-3260	169	3	∈	∈	PROPN
ejpam-3260	169	4	t	t	PROPN
ejpam-3260	169	5	(	(	PUNCT
ejpam-3260	169	6	x	x	X
ejpam-3260	169	7	,	,	PUNCT
ejpam-3260	169	8	p	p	NOUN
ejpam-3260	169	9	)	)	PUNCT
ejpam-3260	169	10	by	by	ADP
ejpam-3260	169	11	f(1	f(1	PROPN
ejpam-3260	169	12	)	)	PUNCT
ejpam-3260	170	1	=	=	SYM
ejpam-3260	170	2	1	1	NUM
ejpam-3260	170	3	,	,	PUNCT
ejpam-3260	170	4	f(2	f(2	PROPN
ejpam-3260	170	5	)	)	PUNCT
ejpam-3260	170	6	=	=	SYM
ejpam-3260	170	7	2	2	NUM
ejpam-3260	170	8	and	and	CCONJ
ejpam-3260	170	9	(	(	PUNCT
ejpam-3260	170	10	x)f	x)f	X
ejpam-3260	170	11	=	=	PUNCT
ejpam-3260	171	1	x	x	SYM
ejpam-3260	171	2	−	−	PROPN
ejpam-3260	171	3	2	2	NUM
ejpam-3260	171	4	for	for	ADP
ejpam-3260	171	5	all	all	DET
ejpam-3260	171	6	positive	positive	ADJ
ejpam-3260	171	7	integer	integer	NOUN
ejpam-3260	171	8	x	x	X
ejpam-3260	171	9	>	>	X
ejpam-3260	171	10	2	2	NUM
ejpam-3260	171	11	,	,	PUNCT
ejpam-3260	171	12	that	that	ADV
ejpam-3260	171	13	is	is	ADV
ejpam-3260	171	14	,	,	PUNCT
ejpam-3260	171	15	f	f	X
ejpam-3260	171	16	=	=	PRON
ejpam-3260	171	17	(	(	PUNCT
ejpam-3260	171	18	1	1	NUM
ejpam-3260	171	19	2	2	NUM
ejpam-3260	171	20	3	3	NUM
ejpam-3260	171	21	4	4	NUM
ejpam-3260	171	22	5	5	NUM
ejpam-3260	171	23	6	6	NUM
ejpam-3260	171	24	7	7	NUM
ejpam-3260	171	25	8	8	NUM
ejpam-3260	171	26	·	·	PUNCT
ejpam-3260	171	27	·	·	PUNCT
ejpam-3260	171	28	·	·	PUNCT
ejpam-3260	172	1	1	1	NUM
ejpam-3260	172	2	2	2	NUM
ejpam-3260	172	3	1	1	NUM
ejpam-3260	172	4	2	2	NUM
ejpam-3260	172	5	3	3	NUM
ejpam-3260	172	6	4	4	NUM
ejpam-3260	172	7	5	5	NUM
ejpam-3260	172	8	6	6	NUM
ejpam-3260	172	9	·	·	PUNCT
ejpam-3260	172	10	·	·	PUNCT
ejpam-3260	172	11	·	·	PUNCT
ejpam-3260	172	12	)	)	PUNCT
ejpam-3260	172	13	.	.	PUNCT
ejpam-3260	173	1	then	then	ADV
ejpam-3260	173	2	f	f	PROPN
ejpam-3260	173	3	∈	∈	PROPN
ejpam-3260	173	4	t	t	PROPN
ejpam-3260	173	5	(	(	PUNCT
ejpam-3260	173	6	x	x	X
ejpam-3260	173	7	,	,	PUNCT
ejpam-3260	173	8	p	p	NOUN
ejpam-3260	173	9	)	)	PUNCT
ejpam-3260	173	10	and	and	CCONJ
ejpam-3260	173	11	f	f	PROPN
ejpam-3260	173	12	is	be	AUX
ejpam-3260	173	13	onto	onto	ADP
ejpam-3260	173	14	but	but	CCONJ
ejpam-3260	173	15	not	not	PART
ejpam-3260	173	16	one	one	NUM
ejpam-3260	173	17	-	-	PUNCT
ejpam-3260	173	18	to	to	ADP
ejpam-3260	173	19	-	-	PUNCT
ejpam-3260	173	20	one	one	NUM
ejpam-3260	173	21	.	.	PUNCT
ejpam-3260	174	1	let	let	VERB
ejpam-3260	174	2	m	m	VERB
ejpam-3260	174	3	=	=	PRON
ejpam-3260	174	4	{	{	PUNCT
ejpam-3260	174	5	h	h	NOUN
ejpam-3260	174	6	∈	∈	PROPN
ejpam-3260	174	7	t	t	PROPN
ejpam-3260	174	8	(	(	PUNCT
ejpam-3260	174	9	x	x	X
ejpam-3260	174	10	,	,	PUNCT
ejpam-3260	174	11	p	p	NOUN
ejpam-3260	174	12	)	)	PUNCT
ejpam-3260	175	1	|	|	ADV
ejpam-3260	175	2	h	h	NOUN
ejpam-3260	175	3	is	be	AUX
ejpam-3260	175	4	not	not	PART
ejpam-3260	175	5	onto	onto	ADP
ejpam-3260	175	6	}	}	PUNCT
ejpam-3260	175	7	.	.	PUNCT
ejpam-3260	176	1	let	let	VERB
ejpam-3260	176	2	g	g	PRON
ejpam-3260	176	3	be	be	AUX
ejpam-3260	176	4	any	any	DET
ejpam-3260	176	5	function	function	NOUN
ejpam-3260	176	6	in	in	ADP
ejpam-3260	176	7	t	t	PROPN
ejpam-3260	176	8	(	(	PUNCT
ejpam-3260	176	9	x	x	X
ejpam-3260	176	10	,	,	PUNCT
ejpam-3260	176	11	p	p	NOUN
ejpam-3260	176	12	)	)	PUNCT
ejpam-3260	176	13	.	.	PUNCT
ejpam-3260	177	1	by	by	ADP
ejpam-3260	177	2	lemma	lemma	PROPN
ejpam-3260	177	3	6	6	NUM
ejpam-3260	177	4	,	,	PUNCT
ejpam-3260	177	5	there	there	PRON
ejpam-3260	177	6	exists	exist	VERB
ejpam-3260	177	7	h	h	NOUN
ejpam-3260	177	8	∈	∈	PROPN
ejpam-3260	177	9	m	m	VERB
ejpam-3260	177	10	such	such	ADJ
ejpam-3260	177	11	that	that	SCONJ
ejpam-3260	177	12	hf	hf	PROPN
ejpam-3260	177	13	=	=	PUNCT
ejpam-3260	177	14	g.	g.	NOUN
ejpam-3260	177	15	for	for	ADP
ejpam-3260	177	16	example	example	NOUN
ejpam-3260	177	17	,	,	PUNCT
ejpam-3260	177	18	if	if	SCONJ
ejpam-3260	177	19	g	g	PROPN
ejpam-3260	177	20	∈	∈	PROPN
ejpam-3260	177	21	t	t	PROPN
ejpam-3260	177	22	(	(	PUNCT
ejpam-3260	177	23	x	x	X
ejpam-3260	177	24	,	,	PUNCT
ejpam-3260	177	25	p	p	NOUN
ejpam-3260	177	26	)	)	PUNCT
ejpam-3260	177	27	is	be	AUX
ejpam-3260	177	28	such	such	ADJ
ejpam-3260	177	29	that	that	SCONJ
ejpam-3260	177	30	(	(	PUNCT
ejpam-3260	177	31	x)g	x)g	X
ejpam-3260	177	32	=	=	SYM
ejpam-3260	177	33	x+	x+	PROPN
ejpam-3260	177	34	2	2	NUM
ejpam-3260	177	35	for	for	ADP
ejpam-3260	177	36	all	all	DET
ejpam-3260	177	37	x	x	SYM
ejpam-3260	177	38	∈	∈	PROPN
ejpam-3260	177	39	x	x	NOUN
ejpam-3260	177	40	,	,	PUNCT
ejpam-3260	177	41	that	that	ADV
ejpam-3260	177	42	is	is	ADV
ejpam-3260	177	43	,	,	PUNCT
ejpam-3260	177	44	g	g	PROPN
ejpam-3260	177	45	=	=	PUNCT
ejpam-3260	177	46	(	(	PUNCT
ejpam-3260	177	47	1	1	NUM
ejpam-3260	177	48	2	2	NUM
ejpam-3260	177	49	3	3	NUM
ejpam-3260	177	50	4	4	NUM
ejpam-3260	177	51	5	5	NUM
ejpam-3260	177	52	6	6	NUM
ejpam-3260	177	53	7	7	NUM
ejpam-3260	177	54	8	8	NUM
ejpam-3260	177	55	·	·	PUNCT
ejpam-3260	177	56	·	·	PUNCT
ejpam-3260	177	57	·	·	PUNCT
ejpam-3260	178	1	3	3	NUM
ejpam-3260	178	2	4	4	NUM
ejpam-3260	178	3	5	5	NUM
ejpam-3260	178	4	6	6	NUM
ejpam-3260	178	5	7	7	NUM
ejpam-3260	178	6	8	8	NUM
ejpam-3260	178	7	9	9	NUM
ejpam-3260	178	8	10	10	NUM
ejpam-3260	178	9	·	·	PUNCT
ejpam-3260	178	10	·	·	PUNCT
ejpam-3260	178	11	·	·	PUNCT
ejpam-3260	178	12	)	)	PUNCT
ejpam-3260	178	13	.	.	PUNCT
ejpam-3260	179	1	define	define	VERB
ejpam-3260	179	2	a	a	DET
ejpam-3260	179	3	function	function	NOUN
ejpam-3260	179	4	h	h	NOUN
ejpam-3260	179	5	∈	∈	PROPN
ejpam-3260	179	6	t	t	PROPN
ejpam-3260	179	7	(	(	PUNCT
ejpam-3260	179	8	x	x	X
ejpam-3260	179	9	,	,	PUNCT
ejpam-3260	179	10	p	p	NOUN
ejpam-3260	179	11	)	)	PUNCT
ejpam-3260	179	12	by	by	ADP
ejpam-3260	179	13	(	(	PUNCT
ejpam-3260	179	14	x)h	x)h	PROPN
ejpam-3260	179	15	=	=	PUNCT
ejpam-3260	179	16	x+	x+	SYM
ejpam-3260	179	17	4	4	NUM
ejpam-3260	179	18	for	for	ADP
ejpam-3260	179	19	all	all	DET
ejpam-3260	179	20	positive	positive	ADJ
ejpam-3260	179	21	integer	integer	NOUN
ejpam-3260	179	22	x	x	NOUN
ejpam-3260	179	23	,	,	PUNCT
ejpam-3260	179	24	that	that	ADV
ejpam-3260	179	25	is	is	ADV
ejpam-3260	179	26	,	,	PUNCT
ejpam-3260	179	27	h	h	NOUN
ejpam-3260	179	28	=	=	PUNCT
ejpam-3260	179	29	(	(	PUNCT
ejpam-3260	179	30	1	1	NUM
ejpam-3260	179	31	2	2	NUM
ejpam-3260	179	32	3	3	NUM
ejpam-3260	179	33	4	4	NUM
ejpam-3260	179	34	5	5	NUM
ejpam-3260	179	35	6	6	NUM
ejpam-3260	179	36	7	7	NUM
ejpam-3260	179	37	8	8	NUM
ejpam-3260	179	38	·	·	PUNCT
ejpam-3260	179	39	·	·	PUNCT
ejpam-3260	179	40	·	·	PUNCT
ejpam-3260	179	41	5	5	NUM
ejpam-3260	179	42	6	6	NUM
ejpam-3260	179	43	7	7	NUM
ejpam-3260	179	44	8	8	NUM
ejpam-3260	179	45	9	9	NUM
ejpam-3260	179	46	10	10	NUM
ejpam-3260	179	47	11	11	NUM
ejpam-3260	179	48	12	12	NUM
ejpam-3260	179	49	·	·	PUNCT
ejpam-3260	179	50	·	·	PUNCT
ejpam-3260	179	51	·	·	PUNCT
ejpam-3260	179	52	)	)	PUNCT
ejpam-3260	179	53	.	.	PUNCT
ejpam-3260	180	1	so	so	ADV
ejpam-3260	180	2	h	h	NOUN
ejpam-3260	180	3	∈m	∈m	NOUN
ejpam-3260	181	1	and	and	CCONJ
ejpam-3260	181	2	we	we	PRON
ejpam-3260	181	3	have	have	VERB
ejpam-3260	181	4	hf	hf	NOUN
ejpam-3260	181	5	=	=	PUNCT
ejpam-3260	181	6	(	(	PUNCT
ejpam-3260	181	7	1	1	NUM
ejpam-3260	181	8	2	2	NUM
ejpam-3260	181	9	3	3	NUM
ejpam-3260	181	10	4	4	NUM
ejpam-3260	181	11	5	5	NUM
ejpam-3260	181	12	6	6	NUM
ejpam-3260	181	13	7	7	NUM
ejpam-3260	181	14	8	8	NUM
ejpam-3260	181	15	·	·	PUNCT
ejpam-3260	181	16	·	·	PUNCT
ejpam-3260	181	17	·	·	PUNCT
ejpam-3260	182	1	5	5	NUM
ejpam-3260	182	2	6	6	NUM
ejpam-3260	182	3	7	7	NUM
ejpam-3260	182	4	8	8	NUM
ejpam-3260	182	5	9	9	NUM
ejpam-3260	182	6	10	10	NUM
ejpam-3260	182	7	11	11	NUM
ejpam-3260	182	8	12	12	NUM
ejpam-3260	182	9	·	·	PUNCT
ejpam-3260	182	10	·	·	PUNCT
ejpam-3260	182	11	·	·	PUNCT
ejpam-3260	182	12	)	)	PUNCT
ejpam-3260	182	13	(	(	PUNCT
ejpam-3260	182	14	1	1	NUM
ejpam-3260	182	15	2	2	NUM
ejpam-3260	182	16	3	3	NUM
ejpam-3260	182	17	4	4	NUM
ejpam-3260	182	18	5	5	NUM
ejpam-3260	182	19	6	6	NUM
ejpam-3260	182	20	7	7	NUM
ejpam-3260	182	21	8	8	NUM
ejpam-3260	182	22	·	·	PUNCT
ejpam-3260	182	23	·	·	PUNCT
ejpam-3260	182	24	·	·	PUNCT
ejpam-3260	182	25	1	1	NUM
ejpam-3260	182	26	2	2	NUM
ejpam-3260	182	27	1	1	NUM
ejpam-3260	182	28	2	2	NUM
ejpam-3260	182	29	3	3	NUM
ejpam-3260	182	30	4	4	NUM
ejpam-3260	182	31	5	5	NUM
ejpam-3260	182	32	6	6	NUM
ejpam-3260	182	33	·	·	PUNCT
ejpam-3260	182	34	·	·	PUNCT
ejpam-3260	182	35	·	·	PUNCT
ejpam-3260	182	36	)	)	PUNCT
ejpam-3260	182	37	=	=	PUNCT
ejpam-3260	182	38	(	(	PUNCT
ejpam-3260	182	39	1	1	NUM
ejpam-3260	182	40	2	2	NUM
ejpam-3260	182	41	3	3	NUM
ejpam-3260	182	42	4	4	NUM
ejpam-3260	182	43	5	5	NUM
ejpam-3260	182	44	6	6	NUM
ejpam-3260	182	45	7	7	NUM
ejpam-3260	182	46	8	8	NUM
ejpam-3260	182	47	·	·	PUNCT
ejpam-3260	182	48	·	·	PUNCT
ejpam-3260	182	49	·	·	PUNCT
ejpam-3260	182	50	3	3	NUM
ejpam-3260	182	51	4	4	NUM
ejpam-3260	182	52	5	5	NUM
ejpam-3260	182	53	6	6	NUM
ejpam-3260	182	54	7	7	NUM
ejpam-3260	182	55	8	8	NUM
ejpam-3260	182	56	9	9	NUM
ejpam-3260	182	57	10	10	NUM
ejpam-3260	182	58	·	·	PUNCT
ejpam-3260	182	59	·	·	PUNCT
ejpam-3260	182	60	·	·	PUNCT
ejpam-3260	182	61	)	)	PUNCT
ejpam-3260	183	1	=	=	PUNCT
ejpam-3260	183	2	g.	g.	X
ejpam-3260	183	3	our	our	PRON
ejpam-3260	183	4	main	main	ADJ
ejpam-3260	183	5	result	result	NOUN
ejpam-3260	183	6	in	in	ADP
ejpam-3260	183	7	this	this	DET
ejpam-3260	183	8	section	section	NOUN
ejpam-3260	183	9	is	be	AUX
ejpam-3260	183	10	the	the	DET
ejpam-3260	183	11	following	follow	VERB
ejpam-3260	183	12	theorem	theorem	PROPN
ejpam-3260	183	13	.	.	PROPN
ejpam-3260	183	14	r.	r.	PROPN
ejpam-3260	183	15	chinram	chinram	PROPN
ejpam-3260	183	16	,	,	PUNCT
ejpam-3260	183	17	p.	p.	NOUN
ejpam-3260	183	18	petchkaew	petchkaew	NOUN
ejpam-3260	183	19	,	,	PUNCT
ejpam-3260	183	20	s.	s.	PROPN
ejpam-3260	183	21	baupradist	baupradist	PROPN
ejpam-3260	183	22	/	/	SYM
ejpam-3260	183	23	eur	eur	PROPN
ejpam-3260	183	24	.	.	PUNCT
ejpam-3260	184	1	j.	j.	PROPN
ejpam-3260	184	2	pure	pure	PROPN
ejpam-3260	184	3	appl	appl	PROPN
ejpam-3260	184	4	.	.	PROPN
ejpam-3260	184	5	math	math	PROPN
ejpam-3260	184	6	,	,	PUNCT
ejpam-3260	184	7	11	11	NUM
ejpam-3260	184	8	(	(	PUNCT
ejpam-3260	184	9	3	3	NUM
ejpam-3260	184	10	)	)	PUNCT
ejpam-3260	184	11	(	(	PUNCT
ejpam-3260	184	12	2018	2018	NUM
ejpam-3260	184	13	)	)	PUNCT
ejpam-3260	184	14	,	,	PUNCT
ejpam-3260	184	15	580	580	NUM
ejpam-3260	184	16	-	-	SYM
ejpam-3260	184	17	588	588	NUM
ejpam-3260	184	18	585	585	NUM
ejpam-3260	184	19	theorem	theorem	NOUN
ejpam-3260	184	20	2	2	NUM
ejpam-3260	184	21	.	.	PUNCT
ejpam-3260	185	1	let	let	VERB
ejpam-3260	185	2	p	p	NOUN
ejpam-3260	185	3	=	=	PUNCT
ejpam-3260	185	4	{	{	PUNCT
ejpam-3260	186	1	xα	xα	INTJ
ejpam-3260	186	2	|	|	ADV
ejpam-3260	186	3	α	α	NOUN
ejpam-3260	186	4	∈	∈	PROPN
ejpam-3260	187	1	i	i	PRON
ejpam-3260	187	2	}	}	PUNCT
ejpam-3260	187	3	be	be	VERB
ejpam-3260	187	4	a	a	DET
ejpam-3260	187	5	partition	partition	NOUN
ejpam-3260	187	6	of	of	ADP
ejpam-3260	187	7	a	a	DET
ejpam-3260	187	8	set	set	NOUN
ejpam-3260	187	9	x.	x.	NOUN
ejpam-3260	187	10	(	(	PUNCT
ejpam-3260	187	11	1	1	X
ejpam-3260	187	12	)	)	PUNCT
ejpam-3260	187	13	a	a	DET
ejpam-3260	187	14	semigroup	semigroup	PROPN
ejpam-3260	187	15	t	t	PROPN
ejpam-3260	187	16	(	(	PUNCT
ejpam-3260	187	17	x	x	X
ejpam-3260	187	18	,	,	PUNCT
ejpam-3260	187	19	p	p	NOUN
ejpam-3260	187	20	)	)	PUNCT
ejpam-3260	187	21	has	have	VERB
ejpam-3260	187	22	a	a	DET
ejpam-3260	187	23	right	right	ADJ
ejpam-3260	187	24	magnifying	magnify	VERB
ejpam-3260	187	25	element	element	NOUN
ejpam-3260	187	26	if	if	SCONJ
ejpam-3260	187	27	and	and	CCONJ
ejpam-3260	187	28	only	only	ADV
ejpam-3260	187	29	if	if	SCONJ
ejpam-3260	187	30	xα	xα	PRON
ejpam-3260	187	31	is	be	AUX
ejpam-3260	187	32	infinite	infinite	ADJ
ejpam-3260	187	33	for	for	ADP
ejpam-3260	187	34	some	some	DET
ejpam-3260	187	35	α	α	NOUN
ejpam-3260	187	36	∈	∈	PROPN
ejpam-3260	187	37	i.	i.	NOUN
ejpam-3260	187	38	(	(	PUNCT
ejpam-3260	187	39	2	2	X
ejpam-3260	187	40	)	)	PUNCT
ejpam-3260	187	41	a	a	DET
ejpam-3260	187	42	function	function	NOUN
ejpam-3260	187	43	f	f	PROPN
ejpam-3260	187	44	is	be	AUX
ejpam-3260	187	45	right	right	ADJ
ejpam-3260	187	46	magnifying	magnifying	NOUN
ejpam-3260	187	47	of	of	ADP
ejpam-3260	187	48	t	t	PROPN
ejpam-3260	187	49	(	(	PUNCT
ejpam-3260	187	50	x	x	X
ejpam-3260	187	51	,	,	PUNCT
ejpam-3260	187	52	p	p	NOUN
ejpam-3260	187	53	)	)	PUNCT
ejpam-3260	188	1	if	if	SCONJ
ejpam-3260	188	2	and	and	CCONJ
ejpam-3260	188	3	only	only	ADV
ejpam-3260	188	4	if	if	SCONJ
ejpam-3260	188	5	f	f	PROPN
ejpam-3260	188	6	is	be	AUX
ejpam-3260	188	7	onto	onto	ADP
ejpam-3260	188	8	but	but	CCONJ
ejpam-3260	188	9	not	not	PART
ejpam-3260	188	10	one	one	NUM
ejpam-3260	188	11	-	-	PUNCT
ejpam-3260	188	12	toone	toone	NOUN
ejpam-3260	188	13	.	.	PUNCT
ejpam-3260	189	1	proof	proof	NOUN
ejpam-3260	189	2	.	.	PUNCT
ejpam-3260	190	1	this	this	PRON
ejpam-3260	190	2	follows	follow	VERB
ejpam-3260	190	3	by	by	ADP
ejpam-3260	190	4	lemma	lemma	PROPN
ejpam-3260	190	5	4	4	NUM
ejpam-3260	190	6	,	,	PUNCT
ejpam-3260	190	7	lemma	lemma	PROPN
ejpam-3260	190	8	5	5	NUM
ejpam-3260	190	9	and	and	CCONJ
ejpam-3260	190	10	lemma	lemma	PROPN
ejpam-3260	190	11	6	6	NUM
ejpam-3260	190	12	.	.	PUNCT
ejpam-3260	190	13	example	example	NOUN
ejpam-3260	190	14	4	4	NUM
ejpam-3260	190	15	.	.	PUNCT
ejpam-3260	191	1	let	let	VERB
ejpam-3260	191	2	x	x	SYM
ejpam-3260	191	3	=	=	PUNCT
ejpam-3260	191	4	n	n	PROPN
ejpam-3260	191	5	and	and	CCONJ
ejpam-3260	191	6	p	p	NOUN
ejpam-3260	192	1	=	=	X
ejpam-3260	192	2	{	{	PUNCT
ejpam-3260	192	3	{	{	PUNCT
ejpam-3260	192	4	1	1	NUM
ejpam-3260	192	5	,	,	PUNCT
ejpam-3260	192	6	2	2	NUM
ejpam-3260	192	7	}	}	PUNCT
ejpam-3260	192	8	,	,	PUNCT
ejpam-3260	192	9	{	{	PUNCT
ejpam-3260	192	10	3	3	NUM
ejpam-3260	192	11	,	,	PUNCT
ejpam-3260	192	12	4	4	NUM
ejpam-3260	192	13	,	,	PUNCT
ejpam-3260	192	14	5	5	NUM
ejpam-3260	192	15	}	}	PUNCT
ejpam-3260	192	16	,	,	PUNCT
ejpam-3260	192	17	{	{	PUNCT
ejpam-3260	192	18	x	x	X
ejpam-3260	192	19	|	|	NOUN
ejpam-3260	192	20	x	x	X
ejpam-3260	192	21	>	>	X
ejpam-3260	192	22	5	5	NUM
ejpam-3260	192	23	}	}	PUNCT
ejpam-3260	192	24	}	}	PUNCT
ejpam-3260	192	25	.	.	PUNCT
ejpam-3260	193	1	by	by	ADP
ejpam-3260	193	2	theorem	theorem	NOUN
ejpam-3260	193	3	2(1	2(1	NUM
ejpam-3260	193	4	)	)	PUNCT
ejpam-3260	193	5	,	,	PUNCT
ejpam-3260	193	6	t	t	PROPN
ejpam-3260	193	7	(	(	PUNCT
ejpam-3260	193	8	x	x	X
ejpam-3260	193	9	,	,	PUNCT
ejpam-3260	193	10	p	p	NOUN
ejpam-3260	193	11	)	)	PUNCT
ejpam-3260	193	12	has	have	VERB
ejpam-3260	193	13	a	a	DET
ejpam-3260	193	14	right	right	ADJ
ejpam-3260	193	15	magnifying	magnify	VERB
ejpam-3260	193	16	element	element	NOUN
ejpam-3260	193	17	.	.	PUNCT
ejpam-3260	194	1	let	let	VERB
ejpam-3260	194	2	f	f	PROPN
ejpam-3260	194	3	∈	∈	PROPN
ejpam-3260	194	4	t	t	PROPN
ejpam-3260	194	5	(	(	PUNCT
ejpam-3260	194	6	x	x	X
ejpam-3260	194	7	,	,	PUNCT
ejpam-3260	194	8	p	p	NOUN
ejpam-3260	194	9	)	)	PUNCT
ejpam-3260	194	10	by	by	ADP
ejpam-3260	194	11	(	(	PUNCT
ejpam-3260	194	12	x)f	x)f	X
ejpam-3260	194	13	=	=	SYM
ejpam-3260	194	14	{	{	PUNCT
ejpam-3260	194	15	x	x	X
ejpam-3260	194	16	if	if	SCONJ
ejpam-3260	194	17	x	x	SYM
ejpam-3260	194	18	≤	≤	NUM
ejpam-3260	194	19	6	6	NUM
ejpam-3260	194	20	,	,	PUNCT
ejpam-3260	194	21	x−	x−	PROPN
ejpam-3260	194	22	1	1	NUM
ejpam-3260	194	23	if	if	SCONJ
ejpam-3260	194	24	x	x	PROPN
ejpam-3260	194	25	>	>	X
ejpam-3260	194	26	6	6	NUM
ejpam-3260	194	27	,	,	PUNCT
ejpam-3260	194	28	that	that	ADV
ejpam-3260	194	29	is	is	ADV
ejpam-3260	194	30	,	,	PUNCT
ejpam-3260	194	31	f	f	X
ejpam-3260	194	32	=	=	PRON
ejpam-3260	194	33	(	(	PUNCT
ejpam-3260	194	34	1	1	NUM
ejpam-3260	194	35	2	2	NUM
ejpam-3260	194	36	3	3	NUM
ejpam-3260	194	37	4	4	NUM
ejpam-3260	194	38	5	5	NUM
ejpam-3260	194	39	6	6	NUM
ejpam-3260	194	40	7	7	NUM
ejpam-3260	194	41	8	8	NUM
ejpam-3260	194	42	·	·	PUNCT
ejpam-3260	194	43	·	·	PUNCT
ejpam-3260	194	44	·	·	PUNCT
ejpam-3260	194	45	1	1	NUM
ejpam-3260	194	46	2	2	NUM
ejpam-3260	194	47	3	3	NUM
ejpam-3260	194	48	4	4	NUM
ejpam-3260	194	49	5	5	NUM
ejpam-3260	194	50	6	6	NUM
ejpam-3260	194	51	6	6	NUM
ejpam-3260	194	52	7	7	NUM
ejpam-3260	194	53	·	·	PUNCT
ejpam-3260	194	54	·	·	PUNCT
ejpam-3260	194	55	·	·	PUNCT
ejpam-3260	194	56	)	)	PUNCT
ejpam-3260	194	57	.	.	PUNCT
ejpam-3260	195	1	then	then	ADV
ejpam-3260	195	2	f	f	PROPN
ejpam-3260	195	3	is	be	AUX
ejpam-3260	195	4	onto	onto	ADP
ejpam-3260	195	5	but	but	CCONJ
ejpam-3260	195	6	not	not	PART
ejpam-3260	195	7	one	one	NUM
ejpam-3260	195	8	-	-	PUNCT
ejpam-3260	195	9	to	to	ADP
ejpam-3260	195	10	-	-	PUNCT
ejpam-3260	195	11	one	one	NUM
ejpam-3260	195	12	.	.	PUNCT
ejpam-3260	196	1	by	by	ADP
ejpam-3260	196	2	theorem	theorem	NOUN
ejpam-3260	196	3	2(2	2(2	NUM
ejpam-3260	196	4	)	)	PUNCT
ejpam-3260	196	5	,	,	PUNCT
ejpam-3260	196	6	f	f	PROPN
ejpam-3260	196	7	is	be	AUX
ejpam-3260	196	8	right	right	ADJ
ejpam-3260	196	9	magnifying	magnifying	NOUN
ejpam-3260	196	10	of	of	ADP
ejpam-3260	196	11	t	t	PROPN
ejpam-3260	196	12	(	(	PUNCT
ejpam-3260	196	13	x	x	X
ejpam-3260	196	14	,	,	PUNCT
ejpam-3260	196	15	p	p	NOUN
ejpam-3260	196	16	)	)	PUNCT
ejpam-3260	196	17	.	.	PUNCT
ejpam-3260	197	1	corollary	corollary	ADJ
ejpam-3260	197	2	2	2	NUM
ejpam-3260	197	3	.	.	PUNCT
ejpam-3260	198	1	the	the	DET
ejpam-3260	198	2	following	follow	VERB
ejpam-3260	198	3	statements	statement	NOUN
ejpam-3260	198	4	hold	hold	VERB
ejpam-3260	198	5	for	for	ADP
ejpam-3260	198	6	a	a	DET
ejpam-3260	198	7	semigroup	semigroup	PROPN
ejpam-3260	198	8	t	t	NOUN
ejpam-3260	198	9	(	(	PUNCT
ejpam-3260	198	10	x	x	NOUN
ejpam-3260	198	11	)	)	PUNCT
ejpam-3260	198	12	.	.	PUNCT
ejpam-3260	199	1	(	(	PUNCT
ejpam-3260	199	2	1	1	X
ejpam-3260	199	3	)	)	PUNCT
ejpam-3260	199	4	a	a	DET
ejpam-3260	199	5	semigroup	semigroup	PROPN
ejpam-3260	199	6	t	t	PROPN
ejpam-3260	199	7	(	(	PUNCT
ejpam-3260	199	8	x	x	X
ejpam-3260	199	9	)	)	PUNCT
ejpam-3260	199	10	has	have	VERB
ejpam-3260	199	11	a	a	DET
ejpam-3260	199	12	right	right	ADJ
ejpam-3260	199	13	magnifying	magnifying	NOUN
ejpam-3260	199	14	if	if	SCONJ
ejpam-3260	199	15	and	and	CCONJ
ejpam-3260	199	16	only	only	ADV
ejpam-3260	199	17	if	if	SCONJ
ejpam-3260	199	18	x	x	PRON
ejpam-3260	199	19	is	be	AUX
ejpam-3260	199	20	infinite	infinite	ADJ
ejpam-3260	199	21	.	.	PUNCT
ejpam-3260	200	1	(	(	PUNCT
ejpam-3260	200	2	2	2	X
ejpam-3260	200	3	)	)	PUNCT
ejpam-3260	200	4	a	a	DET
ejpam-3260	200	5	function	function	NOUN
ejpam-3260	200	6	f	f	PROPN
ejpam-3260	200	7	is	be	AUX
ejpam-3260	200	8	right	right	ADJ
ejpam-3260	200	9	magnifying	magnifying	NOUN
ejpam-3260	200	10	of	of	ADP
ejpam-3260	200	11	t	t	PROPN
ejpam-3260	200	12	(	(	PUNCT
ejpam-3260	200	13	x	x	NOUN
ejpam-3260	200	14	)	)	PUNCT
ejpam-3260	200	15	if	if	SCONJ
ejpam-3260	200	16	and	and	CCONJ
ejpam-3260	200	17	only	only	ADV
ejpam-3260	200	18	if	if	SCONJ
ejpam-3260	200	19	f	f	PROPN
ejpam-3260	200	20	is	be	AUX
ejpam-3260	200	21	onto	onto	ADP
ejpam-3260	200	22	but	but	CCONJ
ejpam-3260	200	23	not	not	PART
ejpam-3260	200	24	one	one	NUM
ejpam-3260	200	25	-	-	PUNCT
ejpam-3260	200	26	to	to	ADP
ejpam-3260	200	27	-	-	PUNCT
ejpam-3260	200	28	one	one	NUM
ejpam-3260	200	29	.	.	PUNCT
ejpam-3260	201	1	proof	proof	NOUN
ejpam-3260	201	2	.	.	PUNCT
ejpam-3260	202	1	this	this	PRON
ejpam-3260	202	2	follows	follow	VERB
ejpam-3260	202	3	by	by	ADP
ejpam-3260	202	4	theorem	theorem	NOUN
ejpam-3260	202	5	2	2	NUM
ejpam-3260	202	6	by	by	ADP
ejpam-3260	202	7	using	use	VERB
ejpam-3260	202	8	p	p	X
ejpam-3260	202	9	=	=	PUNCT
ejpam-3260	202	10	{	{	PUNCT
ejpam-3260	202	11	x	x	NOUN
ejpam-3260	202	12	}	}	PUNCT
ejpam-3260	202	13	.	.	PUNCT
ejpam-3260	203	1	4	4	X
ejpam-3260	203	2	.	.	X
ejpam-3260	203	3	application	application	NOUN
ejpam-3260	203	4	to	to	PART
ejpam-3260	203	5	left	left	VERB
ejpam-3260	203	6	and	and	CCONJ
ejpam-3260	203	7	right	right	ADJ
ejpam-3260	203	8	magnifying	magnify	VERB
ejpam-3260	203	9	elements	element	NOUN
ejpam-3260	203	10	of	of	ADP
ejpam-3260	203	11	some	some	DET
ejpam-3260	203	12	generalized	generalized	ADJ
ejpam-3260	203	13	transformation	transformation	NOUN
ejpam-3260	203	14	semigroup	semigroup	NOUN
ejpam-3260	203	15	let	let	VERB
ejpam-3260	203	16	v1	v1	VERB
ejpam-3260	203	17	and	and	CCONJ
ejpam-3260	203	18	v2	v2	VERB
ejpam-3260	203	19	be	be	AUX
ejpam-3260	203	20	subspaces	subspace	NOUN
ejpam-3260	203	21	of	of	ADP
ejpam-3260	203	22	a	a	DET
ejpam-3260	203	23	vector	vector	NOUN
ejpam-3260	203	24	space	space	NOUN
ejpam-3260	203	25	v	v	NOUN
ejpam-3260	203	26	over	over	ADP
ejpam-3260	203	27	a	a	DET
ejpam-3260	203	28	field	field	NOUN
ejpam-3260	203	29	f	f	NOUN
ejpam-3260	203	30	such	such	ADJ
ejpam-3260	203	31	that	that	DET
ejpam-3260	203	32	v	v	NOUN
ejpam-3260	203	33	=	=	SYM
ejpam-3260	203	34	v1	v1	PROPN
ejpam-3260	203	35	⊕	⊕	PROPN
ejpam-3260	203	36	v2	v2	PROPN
ejpam-3260	203	37	.	.	PUNCT
ejpam-3260	204	1	this	this	PRON
ejpam-3260	204	2	mean	mean	VERB
ejpam-3260	204	3	that	that	SCONJ
ejpam-3260	204	4	v	v	X
ejpam-3260	204	5	=	=	SYM
ejpam-3260	204	6	v1	v1	NOUN
ejpam-3260	204	7	+	+	CCONJ
ejpam-3260	204	8	v2	v2	NOUN
ejpam-3260	204	9	and	and	CCONJ
ejpam-3260	204	10	v1	v1	NOUN
ejpam-3260	204	11	∩	∩	ADJ
ejpam-3260	204	12	v2	v2	NOUN
ejpam-3260	204	13	=	=	SYM
ejpam-3260	204	14	{	{	PUNCT
ejpam-3260	204	15	0	0	NUM
ejpam-3260	204	16	}	}	PUNCT
ejpam-3260	204	17	.	.	PUNCT
ejpam-3260	205	1	let	let	VERB
ejpam-3260	205	2	l(v	l(v	NOUN
ejpam-3260	205	3	)	)	PUNCT
ejpam-3260	205	4	be	be	AUX
ejpam-3260	205	5	the	the	DET
ejpam-3260	205	6	semigroup	semigroup	NOUN
ejpam-3260	205	7	of	of	ADP
ejpam-3260	205	8	all	all	DET
ejpam-3260	205	9	linear	linear	ADJ
ejpam-3260	205	10	transformations	transformation	NOUN
ejpam-3260	205	11	from	from	ADP
ejpam-3260	205	12	v	v	NOUN
ejpam-3260	205	13	into	into	ADP
ejpam-3260	205	14	itself	itself	PRON
ejpam-3260	205	15	under	under	ADP
ejpam-3260	205	16	the	the	DET
ejpam-3260	205	17	composition	composition	NOUN
ejpam-3260	205	18	of	of	ADP
ejpam-3260	205	19	functions	function	NOUN
ejpam-3260	205	20	and	and	CCONJ
ejpam-3260	205	21	lp	lp	NOUN
ejpam-3260	205	22	(	(	PUNCT
ejpam-3260	205	23	v	v	NOUN
ejpam-3260	205	24	)	)	PUNCT
ejpam-3260	205	25	=	=	PUNCT
ejpam-3260	205	26	{	{	PUNCT
ejpam-3260	205	27	f	f	PROPN
ejpam-3260	205	28	∈	∈	PROPN
ejpam-3260	205	29	l(v	l(v	NOUN
ejpam-3260	205	30	)	)	PUNCT
ejpam-3260	205	31	|	|	CCONJ
ejpam-3260	205	32	(	(	PUNCT
ejpam-3260	205	33	v1)f	v1)f	VERB
ejpam-3260	205	34	⊆	⊆	NUM
ejpam-3260	205	35	v1	v1	NOUN
ejpam-3260	205	36	and	and	CCONJ
ejpam-3260	205	37	(	(	PUNCT
ejpam-3260	205	38	v2)f	v2)f	NOUN
ejpam-3260	205	39	⊆	⊆	NUM
ejpam-3260	205	40	v2	v2	NOUN
ejpam-3260	205	41	}	}	PUNCT
ejpam-3260	205	42	.	.	PUNCT
ejpam-3260	206	1	then	then	ADV
ejpam-3260	206	2	lp	lp	INTJ
ejpam-3260	206	3	(	(	PUNCT
ejpam-3260	206	4	v	v	NOUN
ejpam-3260	206	5	)	)	PUNCT
ejpam-3260	206	6	is	be	AUX
ejpam-3260	206	7	a	a	DET
ejpam-3260	206	8	subsemigroup	subsemigroup	NOUN
ejpam-3260	206	9	of	of	ADP
ejpam-3260	206	10	l(v	l(v	NOUN
ejpam-3260	206	11	)	)	PUNCT
ejpam-3260	206	12	.	.	PUNCT
ejpam-3260	207	1	if	if	SCONJ
ejpam-3260	207	2	v	v	NOUN
ejpam-3260	207	3	=	=	SYM
ejpam-3260	207	4	v1	v1	NOUN
ejpam-3260	207	5	and	and	CCONJ
ejpam-3260	207	6	v2	v2	NOUN
ejpam-3260	207	7	=	=	SYM
ejpam-3260	207	8	{	{	PUNCT
ejpam-3260	207	9	0	0	NUM
ejpam-3260	207	10	}	}	PUNCT
ejpam-3260	207	11	,	,	PUNCT
ejpam-3260	207	12	then	then	ADV
ejpam-3260	207	13	lp	lp	PROPN
ejpam-3260	207	14	(	(	PUNCT
ejpam-3260	207	15	v	v	NOUN
ejpam-3260	207	16	)	)	PUNCT
ejpam-3260	207	17	=	=	SYM
ejpam-3260	207	18	l(v	l(v	NOUN
ejpam-3260	207	19	)	)	PUNCT
ejpam-3260	207	20	.	.	PUNCT
ejpam-3260	208	1	our	our	PRON
ejpam-3260	208	2	purpose	purpose	NOUN
ejpam-3260	208	3	in	in	ADP
ejpam-3260	208	4	this	this	DET
ejpam-3260	208	5	section	section	NOUN
ejpam-3260	208	6	is	be	AUX
ejpam-3260	208	7	to	to	PART
ejpam-3260	208	8	give	give	VERB
ejpam-3260	208	9	necessary	necessary	ADJ
ejpam-3260	208	10	and	and	CCONJ
ejpam-3260	208	11	sufficient	sufficient	ADJ
ejpam-3260	208	12	condition	condition	NOUN
ejpam-3260	208	13	for	for	ADP
ejpam-3260	208	14	elements	element	NOUN
ejpam-3260	208	15	in	in	ADP
ejpam-3260	208	16	lp	lp	PROPN
ejpam-3260	208	17	(	(	PUNCT
ejpam-3260	208	18	v	v	NOUN
ejpam-3260	208	19	)	)	PUNCT
ejpam-3260	208	20	to	to	PART
ejpam-3260	208	21	be	be	AUX
ejpam-3260	208	22	right	right	ADJ
ejpam-3260	208	23	or	or	CCONJ
ejpam-3260	208	24	left	leave	VERB
ejpam-3260	208	25	magnifying	magnify	VERB
ejpam-3260	208	26	.	.	PUNCT
ejpam-3260	209	1	lemma	lemma	PROPN
ejpam-3260	209	2	7	7	X
ejpam-3260	209	3	.	.	PUNCT
ejpam-3260	210	1	if	if	SCONJ
ejpam-3260	210	2	a	a	DET
ejpam-3260	210	3	function	function	NOUN
ejpam-3260	210	4	f	f	PROPN
ejpam-3260	210	5	is	be	AUX
ejpam-3260	210	6	left	leave	VERB
ejpam-3260	210	7	magnifying	magnify	VERB
ejpam-3260	210	8	of	of	ADP
ejpam-3260	210	9	lp	lp	PROPN
ejpam-3260	210	10	(	(	PUNCT
ejpam-3260	210	11	v	v	NOUN
ejpam-3260	210	12	)	)	PUNCT
ejpam-3260	210	13	,	,	PUNCT
ejpam-3260	210	14	then	then	ADV
ejpam-3260	210	15	f	f	PROPN
ejpam-3260	210	16	is	be	AUX
ejpam-3260	210	17	one	one	NUM
ejpam-3260	210	18	-	-	PUNCT
ejpam-3260	210	19	to	to	ADP
ejpam-3260	210	20	-	-	PUNCT
ejpam-3260	210	21	one	one	NUM
ejpam-3260	210	22	.	.	PUNCT
ejpam-3260	211	1	proof	proof	NOUN
ejpam-3260	211	2	.	.	PUNCT
ejpam-3260	212	1	this	this	PRON
ejpam-3260	212	2	is	be	AUX
ejpam-3260	212	3	similar	similar	ADJ
ejpam-3260	212	4	to	to	ADP
ejpam-3260	212	5	the	the	DET
ejpam-3260	212	6	proof	proof	NOUN
ejpam-3260	212	7	of	of	ADP
ejpam-3260	212	8	lemma	lemma	PROPN
ejpam-3260	212	9	1	1	NUM
ejpam-3260	212	10	.	.	PUNCT
ejpam-3260	213	1	lemma	lemma	PROPN
ejpam-3260	213	2	8	8	NUM
ejpam-3260	213	3	.	.	PUNCT
ejpam-3260	214	1	if	if	SCONJ
ejpam-3260	214	2	f	f	PROPN
ejpam-3260	214	3	∈	∈	PROPN
ejpam-3260	214	4	lp	lp	PROPN
ejpam-3260	214	5	(	(	PUNCT
ejpam-3260	214	6	v	v	NOUN
ejpam-3260	214	7	)	)	PUNCT
ejpam-3260	214	8	is	be	AUX
ejpam-3260	214	9	bijective	bijective	ADJ
ejpam-3260	214	10	,	,	PUNCT
ejpam-3260	214	11	then	then	ADV
ejpam-3260	214	12	f	f	PROPN
ejpam-3260	214	13	is	be	AUX
ejpam-3260	214	14	not	not	PART
ejpam-3260	214	15	left	leave	VERB
ejpam-3260	214	16	magnifying	magnify	VERB
ejpam-3260	214	17	of	of	ADP
ejpam-3260	214	18	lp	lp	PROPN
ejpam-3260	214	19	(	(	PUNCT
ejpam-3260	214	20	v	v	NOUN
ejpam-3260	214	21	)	)	PUNCT
ejpam-3260	214	22	.	.	PUNCT
ejpam-3260	215	1	proof	proof	NOUN
ejpam-3260	215	2	.	.	PUNCT
ejpam-3260	216	1	this	this	PRON
ejpam-3260	216	2	is	be	AUX
ejpam-3260	216	3	similar	similar	ADJ
ejpam-3260	216	4	to	to	ADP
ejpam-3260	216	5	the	the	DET
ejpam-3260	216	6	proof	proof	NOUN
ejpam-3260	216	7	of	of	ADP
ejpam-3260	216	8	lemma	lemma	PROPN
ejpam-3260	216	9	2	2	NUM
ejpam-3260	216	10	.	.	PUNCT
ejpam-3260	216	11	r.	r.	PROPN
ejpam-3260	216	12	chinram	chinram	PROPN
ejpam-3260	216	13	,	,	PUNCT
ejpam-3260	216	14	p.	p.	NOUN
ejpam-3260	216	15	petchkaew	petchkaew	NOUN
ejpam-3260	216	16	,	,	PUNCT
ejpam-3260	216	17	s.	s.	PROPN
ejpam-3260	216	18	baupradist	baupradist	PROPN
ejpam-3260	216	19	/	/	SYM
ejpam-3260	216	20	eur	eur	PROPN
ejpam-3260	216	21	.	.	PUNCT
ejpam-3260	217	1	j.	j.	PROPN
ejpam-3260	217	2	pure	pure	PROPN
ejpam-3260	217	3	appl	appl	PROPN
ejpam-3260	217	4	.	.	PROPN
ejpam-3260	217	5	math	math	PROPN
ejpam-3260	217	6	,	,	PUNCT
ejpam-3260	217	7	11	11	NUM
ejpam-3260	217	8	(	(	PUNCT
ejpam-3260	217	9	3	3	NUM
ejpam-3260	217	10	)	)	PUNCT
ejpam-3260	217	11	(	(	PUNCT
ejpam-3260	217	12	2018	2018	NUM
ejpam-3260	217	13	)	)	PUNCT
ejpam-3260	217	14	,	,	PUNCT
ejpam-3260	217	15	580	580	NUM
ejpam-3260	217	16	-	-	SYM
ejpam-3260	217	17	588	588	NUM
ejpam-3260	217	18	586	586	NUM
ejpam-3260	217	19	lemma	lemma	PROPN
ejpam-3260	217	20	9	9	NUM
ejpam-3260	217	21	.	.	PUNCT
ejpam-3260	218	1	if	if	SCONJ
ejpam-3260	218	2	f	f	PROPN
ejpam-3260	218	3	∈	∈	PROPN
ejpam-3260	218	4	lp	lp	PROPN
ejpam-3260	218	5	(	(	PUNCT
ejpam-3260	218	6	v	v	NOUN
ejpam-3260	218	7	)	)	PUNCT
ejpam-3260	218	8	is	be	AUX
ejpam-3260	218	9	one	one	NUM
ejpam-3260	218	10	-	-	PUNCT
ejpam-3260	218	11	to	to	ADP
ejpam-3260	218	12	-	-	PUNCT
ejpam-3260	218	13	one	one	NUM
ejpam-3260	218	14	but	but	CCONJ
ejpam-3260	218	15	not	not	PART
ejpam-3260	218	16	onto	onto	NOUN
ejpam-3260	218	17	,	,	PUNCT
ejpam-3260	218	18	then	then	ADV
ejpam-3260	218	19	f	f	PROPN
ejpam-3260	218	20	is	be	AUX
ejpam-3260	218	21	left	leave	VERB
ejpam-3260	218	22	magnifying	magnify	VERB
ejpam-3260	218	23	of	of	ADP
ejpam-3260	218	24	lp	lp	PROPN
ejpam-3260	218	25	(	(	PUNCT
ejpam-3260	218	26	v	v	NOUN
ejpam-3260	218	27	)	)	PUNCT
ejpam-3260	218	28	.	.	PUNCT
ejpam-3260	219	1	proof	proof	NOUN
ejpam-3260	219	2	.	.	PUNCT
ejpam-3260	220	1	assume	assume	VERB
ejpam-3260	220	2	that	that	SCONJ
ejpam-3260	220	3	f	f	PROPN
ejpam-3260	220	4	is	be	AUX
ejpam-3260	220	5	one	one	NUM
ejpam-3260	220	6	-	-	PUNCT
ejpam-3260	220	7	to	to	ADP
ejpam-3260	220	8	-	-	PUNCT
ejpam-3260	220	9	one	one	NUM
ejpam-3260	220	10	but	but	CCONJ
ejpam-3260	220	11	not	not	PART
ejpam-3260	220	12	onto	onto	ADP
ejpam-3260	220	13	.	.	PUNCT
ejpam-3260	221	1	let	let	VERB
ejpam-3260	221	2	m	m	VERB
ejpam-3260	221	3	=	=	PRON
ejpam-3260	221	4	{	{	PUNCT
ejpam-3260	221	5	h	h	NOUN
ejpam-3260	221	6	∈	∈	PROPN
ejpam-3260	221	7	lp	lp	NOUN
ejpam-3260	221	8	(	(	PUNCT
ejpam-3260	221	9	v	v	NOUN
ejpam-3260	221	10	)	)	PUNCT
ejpam-3260	221	11	|	|	ADV
ejpam-3260	221	12	(	(	PUNCT
ejpam-3260	221	13	v)h	v)h	NOUN
ejpam-3260	221	14	=	=	SYM
ejpam-3260	221	15	0	0	NUM
ejpam-3260	221	16	for	for	ADP
ejpam-3260	221	17	all	all	DET
ejpam-3260	221	18	v	v	NOUN
ejpam-3260	221	19	/∈	/∈	PUNCT
ejpam-3260	221	20	ran	run	VERB
ejpam-3260	221	21	f	f	NOUN
ejpam-3260	221	22	}	}	PUNCT
ejpam-3260	221	23	.	.	PUNCT
ejpam-3260	222	1	claim	claim	NOUN
ejpam-3260	222	2	that	that	SCONJ
ejpam-3260	222	3	fm	fm	PROPN
ejpam-3260	222	4	=	=	SYM
ejpam-3260	222	5	lp	lp	PROPN
ejpam-3260	222	6	(	(	PUNCT
ejpam-3260	222	7	v	v	NOUN
ejpam-3260	222	8	)	)	PUNCT
ejpam-3260	222	9	.	.	PUNCT
ejpam-3260	223	1	let	let	VERB
ejpam-3260	223	2	g	g	PRON
ejpam-3260	223	3	be	be	AUX
ejpam-3260	223	4	any	any	DET
ejpam-3260	223	5	linear	linear	ADJ
ejpam-3260	223	6	transformation	transformation	NOUN
ejpam-3260	223	7	in	in	ADP
ejpam-3260	223	8	lp	lp	PROPN
ejpam-3260	223	9	(	(	PUNCT
ejpam-3260	223	10	v	v	NOUN
ejpam-3260	223	11	)	)	PUNCT
ejpam-3260	223	12	.	.	PUNCT
ejpam-3260	224	1	let	let	VERB
ejpam-3260	224	2	b1	b1	NOUN
ejpam-3260	224	3	and	and	CCONJ
ejpam-3260	224	4	b2	b2	NOUN
ejpam-3260	224	5	be	be	VERB
ejpam-3260	224	6	bases	basis	NOUN
ejpam-3260	224	7	of	of	ADP
ejpam-3260	224	8	v1	v1	NOUN
ejpam-3260	224	9	and	and	CCONJ
ejpam-3260	224	10	v2	v2	NOUN
ejpam-3260	224	11	,	,	PUNCT
ejpam-3260	224	12	respectively	respectively	ADV
ejpam-3260	224	13	.	.	PUNCT
ejpam-3260	225	1	clearly	clearly	ADV
ejpam-3260	225	2	,	,	PUNCT
ejpam-3260	225	3	b1	b1	NOUN
ejpam-3260	225	4	+	+	NOUN
ejpam-3260	225	5	b2	b2	NOUN
ejpam-3260	225	6	is	be	AUX
ejpam-3260	225	7	a	a	DET
ejpam-3260	225	8	basis	basis	NOUN
ejpam-3260	225	9	of	of	ADP
ejpam-3260	225	10	v	v	NOUN
ejpam-3260	225	11	.	.	PUNCT
ejpam-3260	226	1	define	define	VERB
ejpam-3260	226	2	a	a	DET
ejpam-3260	226	3	linear	linear	ADJ
ejpam-3260	226	4	transformation	transformation	NOUN
ejpam-3260	226	5	h	h	NOUN
ejpam-3260	226	6	∈	∈	PROPN
ejpam-3260	226	7	lp	lp	PROPN
ejpam-3260	226	8	(	(	PUNCT
ejpam-3260	226	9	v	v	NOUN
ejpam-3260	226	10	)	)	PUNCT
ejpam-3260	226	11	by	by	ADP
ejpam-3260	226	12	for	for	ADP
ejpam-3260	226	13	all	all	DET
ejpam-3260	226	14	v	v	NOUN
ejpam-3260	226	15	∈	∈	NOUN
ejpam-3260	226	16	b1	b1	NOUN
ejpam-3260	226	17	∪b2	∪b2	ADV
ejpam-3260	226	18	,	,	PUNCT
ejpam-3260	226	19	(	(	PUNCT
ejpam-3260	226	20	v)h	v)h	X
ejpam-3260	226	21	=	=	X
ejpam-3260	226	22	{	{	PUNCT
ejpam-3260	226	23	(	(	PUNCT
ejpam-3260	226	24	v′)g	v′)g	NOUN
ejpam-3260	226	25	if	if	SCONJ
ejpam-3260	226	26	v	v	NUM
ejpam-3260	226	27	∈	∈	PROPN
ejpam-3260	226	28	ran	run	VERB
ejpam-3260	226	29	f	f	PROPN
ejpam-3260	226	30	and	and	CCONJ
ejpam-3260	226	31	(	(	PUNCT
ejpam-3260	226	32	v′)f	v′)f	PROPN
ejpam-3260	226	33	=	=	SYM
ejpam-3260	226	34	v	v	NOUN
ejpam-3260	226	35	,	,	PUNCT
ejpam-3260	226	36	0	0	NUM
ejpam-3260	226	37	if	if	SCONJ
ejpam-3260	226	38	v	v	NUM
ejpam-3260	226	39	/∈	/∈	PUNCT
ejpam-3260	227	1	ran	run	VERB
ejpam-3260	227	2	f.	f.	PROPN
ejpam-3260	227	3	let	let	VERB
ejpam-3260	227	4	v′	v′	NOUN
ejpam-3260	227	5	,	,	PUNCT
ejpam-3260	227	6	v	v	PROPN
ejpam-3260	227	7	∈	∈	PROPN
ejpam-3260	227	8	v	v	AUX
ejpam-3260	227	9	be	be	AUX
ejpam-3260	227	10	such	such	ADJ
ejpam-3260	227	11	that	that	SCONJ
ejpam-3260	227	12	(	(	PUNCT
ejpam-3260	227	13	v′)f	v′)f	PROPN
ejpam-3260	227	14	=	=	PUNCT
ejpam-3260	227	15	v.	v.	PROPN
ejpam-3260	227	16	assume	assume	VERB
ejpam-3260	227	17	that	that	SCONJ
ejpam-3260	227	18	v	v	NUM
ejpam-3260	227	19	∈	∈	PROPN
ejpam-3260	227	20	b1	b1	NOUN
ejpam-3260	227	21	.	.	PUNCT
ejpam-3260	228	1	clearly	clearly	ADV
ejpam-3260	228	2	,	,	PUNCT
ejpam-3260	228	3	v′	v′	PROPN
ejpam-3260	228	4	∈	∈	PROPN
ejpam-3260	228	5	v1	v1	NOUN
ejpam-3260	228	6	.	.	PUNCT
ejpam-3260	229	1	therefore	therefore	ADV
ejpam-3260	229	2	,	,	PUNCT
ejpam-3260	229	3	(	(	PUNCT
ejpam-3260	229	4	v)h	v)h	X
ejpam-3260	229	5	=	=	SYM
ejpam-3260	229	6	(	(	PUNCT
ejpam-3260	229	7	v′)g	v′)g	NOUN
ejpam-3260	229	8	∈	∈	NOUN
ejpam-3260	229	9	v1	v1	NOUN
ejpam-3260	229	10	.	.	PUNCT
ejpam-3260	230	1	similarly	similarly	ADV
ejpam-3260	230	2	,	,	PUNCT
ejpam-3260	230	3	if	if	SCONJ
ejpam-3260	230	4	v	v	NUM
ejpam-3260	230	5	∈	∈	PROPN
ejpam-3260	230	6	b2	b2	NOUN
ejpam-3260	230	7	,	,	PUNCT
ejpam-3260	230	8	then	then	ADV
ejpam-3260	230	9	(	(	PUNCT
ejpam-3260	230	10	v)h	v)h	NOUN
ejpam-3260	230	11	=	=	SYM
ejpam-3260	230	12	(	(	PUNCT
ejpam-3260	230	13	v′)g	v′)g	NOUN
ejpam-3260	230	14	∈	∈	NOUN
ejpam-3260	230	15	v2	v2	PROPN
ejpam-3260	230	16	.	.	PUNCT
ejpam-3260	231	1	thus	thus	ADV
ejpam-3260	231	2	h	h	NOUN
ejpam-3260	231	3	∈	∈	PROPN
ejpam-3260	231	4	m	m	PROPN
ejpam-3260	231	5	and	and	CCONJ
ejpam-3260	231	6	fh	fh	PROPN
ejpam-3260	231	7	=	=	SYM
ejpam-3260	231	8	g	g	PROPN
ejpam-3260	231	9	,	,	PUNCT
ejpam-3260	231	10	this	this	PRON
ejpam-3260	231	11	implies	imply	VERB
ejpam-3260	231	12	that	that	SCONJ
ejpam-3260	231	13	fm	fm	PROPN
ejpam-3260	231	14	=	=	SYM
ejpam-3260	231	15	lp	lp	PROPN
ejpam-3260	231	16	(	(	PUNCT
ejpam-3260	231	17	v	v	NOUN
ejpam-3260	231	18	)	)	PUNCT
ejpam-3260	231	19	.	.	PUNCT
ejpam-3260	232	1	hence	hence	ADV
ejpam-3260	232	2	f	f	PROPN
ejpam-3260	232	3	is	be	AUX
ejpam-3260	232	4	left	leave	VERB
ejpam-3260	232	5	magnifying	magnify	VERB
ejpam-3260	232	6	of	of	ADP
ejpam-3260	232	7	lp	lp	PROPN
ejpam-3260	232	8	(	(	PUNCT
ejpam-3260	232	9	v	v	NOUN
ejpam-3260	232	10	)	)	PUNCT
ejpam-3260	232	11	.	.	PUNCT
ejpam-3260	233	1	theorem	theorem	NOUN
ejpam-3260	233	2	3	3	NUM
ejpam-3260	233	3	.	.	PUNCT
ejpam-3260	234	1	the	the	DET
ejpam-3260	234	2	following	follow	VERB
ejpam-3260	234	3	statements	statement	NOUN
ejpam-3260	234	4	hold	hold	VERB
ejpam-3260	234	5	for	for	ADP
ejpam-3260	234	6	a	a	DET
ejpam-3260	234	7	semigroup	semigroup	ADJ
ejpam-3260	234	8	lp	lp	NOUN
ejpam-3260	234	9	(	(	PUNCT
ejpam-3260	234	10	v	v	NOUN
ejpam-3260	234	11	)	)	PUNCT
ejpam-3260	234	12	.	.	PUNCT
ejpam-3260	235	1	(	(	PUNCT
ejpam-3260	235	2	1	1	X
ejpam-3260	235	3	)	)	PUNCT
ejpam-3260	235	4	a	a	DET
ejpam-3260	235	5	semigroup	semigroup	ADJ
ejpam-3260	235	6	lp	lp	NOUN
ejpam-3260	235	7	(	(	PUNCT
ejpam-3260	235	8	v	v	NOUN
ejpam-3260	235	9	)	)	PUNCT
ejpam-3260	235	10	has	have	VERB
ejpam-3260	235	11	a	a	DET
ejpam-3260	235	12	left	left	ADJ
ejpam-3260	235	13	magnifying	magnifying	ADJ
ejpam-3260	235	14	element	element	NOUN
ejpam-3260	235	15	if	if	SCONJ
ejpam-3260	235	16	and	and	CCONJ
ejpam-3260	235	17	only	only	ADV
ejpam-3260	235	18	if	if	SCONJ
ejpam-3260	235	19	dimv1	dimv1	ADJ
ejpam-3260	235	20	is	be	AUX
ejpam-3260	235	21	infinite	infinite	ADJ
ejpam-3260	235	22	or	or	CCONJ
ejpam-3260	235	23	dimv2	dimv2	NOUN
ejpam-3260	235	24	is	be	AUX
ejpam-3260	235	25	infinite	infinite	ADJ
ejpam-3260	235	26	.	.	PUNCT
ejpam-3260	236	1	(	(	PUNCT
ejpam-3260	236	2	2	2	X
ejpam-3260	236	3	)	)	PUNCT
ejpam-3260	236	4	a	a	DET
ejpam-3260	236	5	linear	linear	ADJ
ejpam-3260	236	6	transformation	transformation	NOUN
ejpam-3260	236	7	f	f	PROPN
ejpam-3260	236	8	is	be	AUX
ejpam-3260	236	9	left	leave	VERB
ejpam-3260	236	10	magnifying	magnify	VERB
ejpam-3260	236	11	of	of	ADP
ejpam-3260	236	12	lp	lp	PROPN
ejpam-3260	236	13	(	(	PUNCT
ejpam-3260	236	14	v	v	NOUN
ejpam-3260	236	15	)	)	PUNCT
ejpam-3260	236	16	if	if	SCONJ
ejpam-3260	236	17	and	and	CCONJ
ejpam-3260	236	18	only	only	ADV
ejpam-3260	236	19	if	if	SCONJ
ejpam-3260	236	20	f	f	PROPN
ejpam-3260	236	21	is	be	AUX
ejpam-3260	236	22	one	one	NUM
ejpam-3260	236	23	-	-	PUNCT
ejpam-3260	236	24	to	to	ADP
ejpam-3260	236	25	-	-	PUNCT
ejpam-3260	236	26	one	one	NUM
ejpam-3260	236	27	but	but	CCONJ
ejpam-3260	236	28	not	not	PART
ejpam-3260	236	29	onto	onto	ADP
ejpam-3260	236	30	.	.	PUNCT
ejpam-3260	237	1	proof	proof	NOUN
ejpam-3260	237	2	.	.	PUNCT
ejpam-3260	238	1	this	this	PRON
ejpam-3260	238	2	follows	follow	VERB
ejpam-3260	238	3	by	by	ADP
ejpam-3260	238	4	lemma	lemma	PROPN
ejpam-3260	238	5	7	7	NUM
ejpam-3260	238	6	,	,	PUNCT
ejpam-3260	238	7	lemma	lemma	PROPN
ejpam-3260	238	8	8	8	NUM
ejpam-3260	238	9	and	and	CCONJ
ejpam-3260	238	10	lemma	lemma	PROPN
ejpam-3260	238	11	9	9	NUM
ejpam-3260	238	12	.	.	PUNCT
ejpam-3260	238	13	corollary	corollary	ADJ
ejpam-3260	238	14	3	3	NUM
ejpam-3260	238	15	.	.	PUNCT
ejpam-3260	239	1	let	let	VERB
ejpam-3260	239	2	l(v	l(v	NOUN
ejpam-3260	239	3	)	)	PUNCT
ejpam-3260	239	4	be	be	AUX
ejpam-3260	239	5	the	the	DET
ejpam-3260	239	6	linear	linear	PROPN
ejpam-3260	239	7	transformation	transformation	NOUN
ejpam-3260	239	8	semigroup	semigroup	NOUN
ejpam-3260	239	9	on	on	ADP
ejpam-3260	239	10	a	a	DET
ejpam-3260	239	11	vector	vector	NOUN
ejpam-3260	239	12	space	space	NOUN
ejpam-3260	239	13	v	v	NOUN
ejpam-3260	239	14	.	.	PUNCT
ejpam-3260	240	1	(	(	PUNCT
ejpam-3260	240	2	1	1	X
ejpam-3260	240	3	)	)	PUNCT
ejpam-3260	240	4	a	a	DET
ejpam-3260	240	5	semigroup	semigroup	PROPN
ejpam-3260	240	6	l(v	l(v	NOUN
ejpam-3260	240	7	)	)	PUNCT
ejpam-3260	240	8	has	have	VERB
ejpam-3260	240	9	a	a	DET
ejpam-3260	240	10	left	left	ADJ
ejpam-3260	240	11	magnifying	magnify	VERB
ejpam-3260	240	12	if	if	SCONJ
ejpam-3260	240	13	and	and	CCONJ
ejpam-3260	240	14	only	only	ADV
ejpam-3260	240	15	if	if	SCONJ
ejpam-3260	240	16	dimv	dimv	NOUN
ejpam-3260	240	17	is	be	AUX
ejpam-3260	240	18	infinite	infinite	ADJ
ejpam-3260	240	19	.	.	PUNCT
ejpam-3260	241	1	(	(	PUNCT
ejpam-3260	241	2	2	2	X
ejpam-3260	241	3	)	)	PUNCT
ejpam-3260	241	4	a	a	DET
ejpam-3260	241	5	linear	linear	ADJ
ejpam-3260	241	6	transformation	transformation	NOUN
ejpam-3260	241	7	f	f	PROPN
ejpam-3260	241	8	is	be	AUX
ejpam-3260	241	9	left	leave	VERB
ejpam-3260	241	10	magnifying	magnify	VERB
ejpam-3260	241	11	of	of	ADP
ejpam-3260	241	12	l(v	l(v	NOUN
ejpam-3260	241	13	)	)	PUNCT
ejpam-3260	242	1	if	if	SCONJ
ejpam-3260	242	2	and	and	CCONJ
ejpam-3260	242	3	only	only	ADV
ejpam-3260	242	4	if	if	SCONJ
ejpam-3260	242	5	f	f	PROPN
ejpam-3260	242	6	is	be	AUX
ejpam-3260	242	7	one	one	NUM
ejpam-3260	242	8	-	-	PUNCT
ejpam-3260	242	9	to	to	ADP
ejpam-3260	242	10	-	-	PUNCT
ejpam-3260	242	11	one	one	NUM
ejpam-3260	242	12	but	but	CCONJ
ejpam-3260	242	13	not	not	PART
ejpam-3260	242	14	onto	onto	ADP
ejpam-3260	242	15	.	.	PUNCT
ejpam-3260	243	1	proof	proof	NOUN
ejpam-3260	243	2	.	.	PUNCT
ejpam-3260	244	1	this	this	PRON
ejpam-3260	244	2	follows	follow	VERB
ejpam-3260	244	3	by	by	ADP
ejpam-3260	244	4	theorem	theorem	NOUN
ejpam-3260	244	5	3	3	NUM
ejpam-3260	244	6	by	by	ADP
ejpam-3260	244	7	using	use	VERB
ejpam-3260	244	8	v	v	NOUN
ejpam-3260	244	9	=	=	SYM
ejpam-3260	244	10	v1	v1	NOUN
ejpam-3260	244	11	and	and	CCONJ
ejpam-3260	244	12	v2	v2	NOUN
ejpam-3260	244	13	=	=	SYM
ejpam-3260	244	14	{	{	PUNCT
ejpam-3260	244	15	0	0	NUM
ejpam-3260	244	16	}	}	PUNCT
ejpam-3260	244	17	.	.	PUNCT
ejpam-3260	245	1	lemma	lemma	PROPN
ejpam-3260	245	2	10	10	NUM
ejpam-3260	245	3	.	.	PUNCT
ejpam-3260	246	1	if	if	SCONJ
ejpam-3260	246	2	f	f	PROPN
ejpam-3260	246	3	is	be	AUX
ejpam-3260	246	4	a	a	DET
ejpam-3260	246	5	right	right	ADJ
ejpam-3260	246	6	magnifying	magnify	VERB
ejpam-3260	246	7	element	element	NOUN
ejpam-3260	246	8	of	of	ADP
ejpam-3260	246	9	lp	lp	PROPN
ejpam-3260	246	10	(	(	PUNCT
ejpam-3260	246	11	v	v	NOUN
ejpam-3260	246	12	)	)	PUNCT
ejpam-3260	246	13	.	.	PUNCT
ejpam-3260	247	1	then	then	ADV
ejpam-3260	247	2	f	f	PROPN
ejpam-3260	247	3	is	be	AUX
ejpam-3260	247	4	onto	onto	ADP
ejpam-3260	247	5	.	.	PUNCT
ejpam-3260	248	1	proof	proof	NOUN
ejpam-3260	248	2	.	.	PUNCT
ejpam-3260	249	1	this	this	PRON
ejpam-3260	249	2	is	be	AUX
ejpam-3260	249	3	similar	similar	ADJ
ejpam-3260	249	4	to	to	ADP
ejpam-3260	249	5	the	the	DET
ejpam-3260	249	6	proof	proof	NOUN
ejpam-3260	249	7	of	of	ADP
ejpam-3260	249	8	lemma	lemma	PROPN
ejpam-3260	249	9	4	4	NUM
ejpam-3260	249	10	.	.	PUNCT
ejpam-3260	249	11	lemma	lemma	PROPN
ejpam-3260	249	12	11	11	NUM
ejpam-3260	249	13	.	.	PUNCT
ejpam-3260	250	1	if	if	SCONJ
ejpam-3260	250	2	f	f	PROPN
ejpam-3260	250	3	∈	∈	PROPN
ejpam-3260	250	4	lp	lp	PROPN
ejpam-3260	250	5	(	(	PUNCT
ejpam-3260	250	6	v	v	NOUN
ejpam-3260	250	7	)	)	PUNCT
ejpam-3260	250	8	is	be	AUX
ejpam-3260	250	9	bijective	bijective	ADJ
ejpam-3260	250	10	,	,	PUNCT
ejpam-3260	250	11	then	then	ADV
ejpam-3260	250	12	f	f	PROPN
ejpam-3260	250	13	is	be	AUX
ejpam-3260	250	14	not	not	PART
ejpam-3260	250	15	right	right	ADJ
ejpam-3260	250	16	magnifying	magnifying	NOUN
ejpam-3260	250	17	of	of	ADP
ejpam-3260	250	18	lp	lp	PROPN
ejpam-3260	250	19	(	(	PUNCT
ejpam-3260	250	20	v	v	NOUN
ejpam-3260	250	21	)	)	PUNCT
ejpam-3260	250	22	.	.	PUNCT
ejpam-3260	251	1	proof	proof	NOUN
ejpam-3260	251	2	.	.	PUNCT
ejpam-3260	252	1	this	this	PRON
ejpam-3260	252	2	is	be	AUX
ejpam-3260	252	3	similar	similar	ADJ
ejpam-3260	252	4	to	to	ADP
ejpam-3260	252	5	the	the	DET
ejpam-3260	252	6	proof	proof	NOUN
ejpam-3260	252	7	of	of	ADP
ejpam-3260	252	8	lemma	lemma	PROPN
ejpam-3260	252	9	5	5	NUM
ejpam-3260	252	10	.	.	PUNCT
ejpam-3260	252	11	lemma	lemma	PROPN
ejpam-3260	252	12	12	12	NUM
ejpam-3260	252	13	.	.	PUNCT
ejpam-3260	253	1	let	let	VERB
ejpam-3260	253	2	f	f	PROPN
ejpam-3260	253	3	∈	∈	PROPN
ejpam-3260	253	4	lp	lp	PROPN
ejpam-3260	253	5	(	(	PUNCT
ejpam-3260	253	6	v	v	NOUN
ejpam-3260	253	7	)	)	PUNCT
ejpam-3260	253	8	be	be	AUX
ejpam-3260	253	9	onto	onto	ADP
ejpam-3260	253	10	but	but	CCONJ
ejpam-3260	253	11	not	not	PART
ejpam-3260	253	12	one	one	NUM
ejpam-3260	253	13	-	-	PUNCT
ejpam-3260	253	14	to	to	ADP
ejpam-3260	253	15	-	-	PUNCT
ejpam-3260	253	16	one	one	NUM
ejpam-3260	253	17	,	,	PUNCT
ejpam-3260	253	18	then	then	ADV
ejpam-3260	253	19	f	f	PROPN
ejpam-3260	253	20	is	be	AUX
ejpam-3260	253	21	right	right	ADJ
ejpam-3260	253	22	magnifying	magnifying	NOUN
ejpam-3260	253	23	of	of	ADP
ejpam-3260	253	24	lp	lp	PROPN
ejpam-3260	253	25	(	(	PUNCT
ejpam-3260	253	26	v	v	NOUN
ejpam-3260	253	27	)	)	PUNCT
ejpam-3260	253	28	.	.	PUNCT
ejpam-3260	254	1	references	reference	NOUN
ejpam-3260	254	2	587	587	NUM
ejpam-3260	254	3	proof	proof	NOUN
ejpam-3260	254	4	.	.	PUNCT
ejpam-3260	255	1	assume	assume	VERB
ejpam-3260	255	2	that	that	SCONJ
ejpam-3260	255	3	f	f	PROPN
ejpam-3260	255	4	is	be	AUX
ejpam-3260	255	5	onto	onto	ADP
ejpam-3260	255	6	but	but	CCONJ
ejpam-3260	255	7	not	not	PART
ejpam-3260	255	8	one	one	NUM
ejpam-3260	255	9	-	-	PUNCT
ejpam-3260	255	10	to	to	ADP
ejpam-3260	255	11	-	-	PUNCT
ejpam-3260	255	12	one	one	NUM
ejpam-3260	255	13	.	.	PUNCT
ejpam-3260	256	1	let	let	VERB
ejpam-3260	256	2	m	m	VERB
ejpam-3260	256	3	=	=	PRON
ejpam-3260	256	4	{	{	PUNCT
ejpam-3260	256	5	f	f	PROPN
ejpam-3260	256	6	∈	∈	PROPN
ejpam-3260	256	7	lp	lp	PROPN
ejpam-3260	256	8	(	(	PUNCT
ejpam-3260	256	9	v	v	NOUN
ejpam-3260	256	10	)	)	PUNCT
ejpam-3260	257	1	|	|	ADV
ejpam-3260	257	2	f	f	PROPN
ejpam-3260	257	3	is	be	AUX
ejpam-3260	257	4	not	not	PART
ejpam-3260	257	5	onto	onto	ADP
ejpam-3260	257	6	}	}	PUNCT
ejpam-3260	257	7	.	.	PUNCT
ejpam-3260	258	1	then	then	ADV
ejpam-3260	258	2	m	m	VERB
ejpam-3260	258	3	6=	6=	NUM
ejpam-3260	258	4	lp	lp	PROPN
ejpam-3260	258	5	(	(	PUNCT
ejpam-3260	258	6	v	v	NOUN
ejpam-3260	258	7	)	)	PUNCT
ejpam-3260	258	8	.	.	PUNCT
ejpam-3260	259	1	let	let	VERB
ejpam-3260	259	2	g	g	PRON
ejpam-3260	259	3	be	be	AUX
ejpam-3260	259	4	any	any	DET
ejpam-3260	259	5	linear	linear	ADJ
ejpam-3260	259	6	transformation	transformation	NOUN
ejpam-3260	259	7	in	in	ADP
ejpam-3260	259	8	lp	lp	PROPN
ejpam-3260	259	9	(	(	PUNCT
ejpam-3260	259	10	v	v	NOUN
ejpam-3260	259	11	)	)	PUNCT
ejpam-3260	259	12	.	.	PUNCT
ejpam-3260	260	1	let	let	VERB
ejpam-3260	260	2	b1	b1	NOUN
ejpam-3260	260	3	and	and	CCONJ
ejpam-3260	260	4	b2	b2	NOUN
ejpam-3260	260	5	be	be	VERB
ejpam-3260	260	6	bases	basis	NOUN
ejpam-3260	260	7	of	of	ADP
ejpam-3260	260	8	v1	v1	NOUN
ejpam-3260	260	9	and	and	CCONJ
ejpam-3260	260	10	v2	v2	NOUN
ejpam-3260	260	11	,	,	PUNCT
ejpam-3260	260	12	respectively	respectively	ADV
ejpam-3260	260	13	.	.	PUNCT
ejpam-3260	261	1	since	since	SCONJ
ejpam-3260	261	2	f	f	PROPN
ejpam-3260	261	3	is	be	AUX
ejpam-3260	261	4	onto	onto	ADP
ejpam-3260	261	5	,	,	PUNCT
ejpam-3260	261	6	there	there	PRON
ejpam-3260	261	7	exists	exist	VERB
ejpam-3260	261	8	for	for	ADP
ejpam-3260	261	9	each	each	DET
ejpam-3260	261	10	v	v	PROPN
ejpam-3260	261	11	∈	∈	PROPN
ejpam-3260	261	12	b1	b1	NOUN
ejpam-3260	261	13	,	,	PUNCT
ejpam-3260	261	14	an	an	DET
ejpam-3260	261	15	element	element	NOUN
ejpam-3260	261	16	uv	uv	PROPN
ejpam-3260	261	17	∈	∈	PROPN
ejpam-3260	261	18	b1	b1	NOUN
ejpam-3260	261	19	such	such	ADJ
ejpam-3260	261	20	that	that	SCONJ
ejpam-3260	261	21	(	(	PUNCT
ejpam-3260	261	22	uv)f	uv)f	PROPN
ejpam-3260	261	23	=	=	SYM
ejpam-3260	261	24	(	(	PUNCT
ejpam-3260	261	25	v)g	v)g	NOUN
ejpam-3260	261	26	and	and	CCONJ
ejpam-3260	261	27	there	there	PRON
ejpam-3260	261	28	exists	exist	VERB
ejpam-3260	261	29	for	for	ADP
ejpam-3260	261	30	each	each	DET
ejpam-3260	261	31	v	v	PROPN
ejpam-3260	261	32	∈	∈	PROPN
ejpam-3260	261	33	b2	b2	NOUN
ejpam-3260	261	34	,	,	PUNCT
ejpam-3260	261	35	an	an	DET
ejpam-3260	261	36	element	element	NOUN
ejpam-3260	261	37	uv	uv	PROPN
ejpam-3260	261	38	∈	∈	PROPN
ejpam-3260	261	39	b2	b2	NOUN
ejpam-3260	261	40	such	such	ADJ
ejpam-3260	261	41	that	that	SCONJ
ejpam-3260	261	42	(	(	PUNCT
ejpam-3260	261	43	uv)f	uv)f	PROPN
ejpam-3260	261	44	=	=	SYM
ejpam-3260	261	45	(	(	PUNCT
ejpam-3260	261	46	v)g	v)g	NOUN
ejpam-3260	261	47	.	.	PUNCT
ejpam-3260	262	1	define	define	VERB
ejpam-3260	262	2	a	a	DET
ejpam-3260	262	3	linear	linear	ADJ
ejpam-3260	262	4	transformation	transformation	NOUN
ejpam-3260	262	5	h	h	NOUN
ejpam-3260	262	6	∈	∈	PROPN
ejpam-3260	262	7	lp	lp	PROPN
ejpam-3260	262	8	(	(	PUNCT
ejpam-3260	262	9	v	v	NOUN
ejpam-3260	262	10	)	)	PUNCT
ejpam-3260	262	11	by	by	ADP
ejpam-3260	262	12	(	(	PUNCT
ejpam-3260	262	13	v)h	v)h	X
ejpam-3260	262	14	=	=	SYM
ejpam-3260	262	15	uv	uv	NOUN
ejpam-3260	262	16	for	for	ADP
ejpam-3260	262	17	all	all	DET
ejpam-3260	262	18	v	v	PRON
ejpam-3260	262	19	∈	∈	NOUN
ejpam-3260	262	20	b1	b1	NOUN
ejpam-3260	262	21	∪	∪	NOUN
ejpam-3260	262	22	b2	b2	PROPN
ejpam-3260	262	23	.	.	PUNCT
ejpam-3260	263	1	then	then	ADV
ejpam-3260	263	2	h	h	PROPN
ejpam-3260	263	3	∈	∈	PROPN
ejpam-3260	263	4	lp	lp	PROPN
ejpam-3260	263	5	(	(	PUNCT
ejpam-3260	263	6	v	v	NOUN
ejpam-3260	263	7	)	)	PUNCT
ejpam-3260	263	8	.	.	PUNCT
ejpam-3260	264	1	since	since	SCONJ
ejpam-3260	264	2	f	f	PROPN
ejpam-3260	264	3	is	be	AUX
ejpam-3260	264	4	not	not	PART
ejpam-3260	264	5	one	one	NUM
ejpam-3260	264	6	-	-	PUNCT
ejpam-3260	264	7	to	to	ADP
ejpam-3260	264	8	-	-	PUNCT
ejpam-3260	264	9	one	one	NUM
ejpam-3260	264	10	,	,	PUNCT
ejpam-3260	264	11	h	h	NOUN
ejpam-3260	264	12	is	be	AUX
ejpam-3260	264	13	not	not	PART
ejpam-3260	264	14	onto	onto	ADP
ejpam-3260	264	15	,	,	PUNCT
ejpam-3260	264	16	and	and	CCONJ
ejpam-3260	264	17	so	so	ADV
ejpam-3260	264	18	h	h	NOUN
ejpam-3260	265	1	∈	∈	PROPN
ejpam-3260	265	2	m	m	VERB
ejpam-3260	265	3	.	.	PUNCT
ejpam-3260	266	1	then	then	ADV
ejpam-3260	266	2	hf	hf	PROPN
ejpam-3260	266	3	=	=	SYM
ejpam-3260	266	4	g	g	NOUN
ejpam-3260	266	5	,	,	PUNCT
ejpam-3260	266	6	and	and	CCONJ
ejpam-3260	266	7	hence	hence	ADV
ejpam-3260	266	8	mf	mf	X
ejpam-3260	266	9	=	=	SYM
ejpam-3260	266	10	lp	lp	PROPN
ejpam-3260	266	11	(	(	PUNCT
ejpam-3260	266	12	v	v	NOUN
ejpam-3260	266	13	)	)	PUNCT
ejpam-3260	266	14	.	.	PUNCT
ejpam-3260	267	1	therefore	therefore	ADV
ejpam-3260	267	2	,	,	PUNCT
ejpam-3260	267	3	f	f	PROPN
ejpam-3260	267	4	is	be	AUX
ejpam-3260	267	5	right	right	ADJ
ejpam-3260	267	6	magnifying	magnifying	NOUN
ejpam-3260	267	7	of	of	ADP
ejpam-3260	267	8	lp	lp	PROPN
ejpam-3260	267	9	(	(	PUNCT
ejpam-3260	267	10	v	v	NOUN
ejpam-3260	267	11	)	)	PUNCT
ejpam-3260	267	12	.	.	PUNCT
ejpam-3260	268	1	theorem	theorem	ADJ
ejpam-3260	268	2	4	4	NUM
ejpam-3260	268	3	.	.	PUNCT
ejpam-3260	269	1	the	the	DET
ejpam-3260	269	2	following	follow	VERB
ejpam-3260	269	3	statements	statement	NOUN
ejpam-3260	269	4	hold	hold	VERB
ejpam-3260	269	5	for	for	ADP
ejpam-3260	269	6	a	a	DET
ejpam-3260	269	7	semigroup	semigroup	ADJ
ejpam-3260	269	8	lp	lp	NOUN
ejpam-3260	269	9	(	(	PUNCT
ejpam-3260	269	10	v	v	NOUN
ejpam-3260	269	11	)	)	PUNCT
ejpam-3260	269	12	.	.	PUNCT
ejpam-3260	270	1	(	(	PUNCT
ejpam-3260	270	2	1	1	X
ejpam-3260	270	3	)	)	PUNCT
ejpam-3260	270	4	a	a	DET
ejpam-3260	270	5	semigroup	semigroup	ADJ
ejpam-3260	270	6	lp	lp	NOUN
ejpam-3260	270	7	(	(	PUNCT
ejpam-3260	270	8	v	v	NOUN
ejpam-3260	270	9	)	)	PUNCT
ejpam-3260	270	10	has	have	VERB
ejpam-3260	270	11	a	a	DET
ejpam-3260	270	12	right	right	ADJ
ejpam-3260	270	13	magnifying	magnify	VERB
ejpam-3260	270	14	element	element	NOUN
ejpam-3260	270	15	if	if	SCONJ
ejpam-3260	270	16	and	and	CCONJ
ejpam-3260	270	17	only	only	ADV
ejpam-3260	270	18	if	if	SCONJ
ejpam-3260	270	19	dimv1	dimv1	ADJ
ejpam-3260	270	20	is	be	AUX
ejpam-3260	270	21	infinite	infinite	ADJ
ejpam-3260	270	22	or	or	CCONJ
ejpam-3260	270	23	dimv2	dimv2	NOUN
ejpam-3260	270	24	is	be	AUX
ejpam-3260	270	25	infinite	infinite	ADJ
ejpam-3260	270	26	.	.	PUNCT
ejpam-3260	271	1	(	(	PUNCT
ejpam-3260	271	2	2	2	X
ejpam-3260	271	3	)	)	PUNCT
ejpam-3260	271	4	a	a	DET
ejpam-3260	271	5	linear	linear	ADJ
ejpam-3260	271	6	transformation	transformation	NOUN
ejpam-3260	271	7	f	f	PROPN
ejpam-3260	271	8	is	be	AUX
ejpam-3260	271	9	right	right	ADJ
ejpam-3260	271	10	magnifying	magnifying	NOUN
ejpam-3260	271	11	of	of	ADP
ejpam-3260	271	12	lp	lp	PROPN
ejpam-3260	271	13	(	(	PUNCT
ejpam-3260	271	14	v	v	NOUN
ejpam-3260	271	15	)	)	PUNCT
ejpam-3260	271	16	if	if	SCONJ
ejpam-3260	271	17	and	and	CCONJ
ejpam-3260	271	18	only	only	ADV
ejpam-3260	271	19	if	if	SCONJ
ejpam-3260	271	20	f	f	PROPN
ejpam-3260	271	21	is	be	AUX
ejpam-3260	271	22	onto	onto	ADP
ejpam-3260	271	23	but	but	CCONJ
ejpam-3260	271	24	not	not	PART
ejpam-3260	271	25	one	one	NUM
ejpam-3260	271	26	-	-	PUNCT
ejpam-3260	271	27	to	to	ADP
ejpam-3260	271	28	-	-	PUNCT
ejpam-3260	271	29	one	one	NUM
ejpam-3260	271	30	.	.	PUNCT
ejpam-3260	272	1	proof	proof	NOUN
ejpam-3260	272	2	.	.	PUNCT
ejpam-3260	273	1	this	this	PRON
ejpam-3260	273	2	follows	follow	VERB
ejpam-3260	273	3	by	by	ADP
ejpam-3260	273	4	lemma	lemma	PROPN
ejpam-3260	273	5	10	10	NUM
ejpam-3260	273	6	,	,	PUNCT
ejpam-3260	273	7	lemma	lemma	PROPN
ejpam-3260	273	8	11	11	NUM
ejpam-3260	273	9	and	and	CCONJ
ejpam-3260	273	10	lemma	lemma	PROPN
ejpam-3260	273	11	12	12	NUM
ejpam-3260	273	12	.	.	PUNCT
ejpam-3260	274	1	corollary	corollary	ADJ
ejpam-3260	274	2	4	4	NUM
ejpam-3260	274	3	.	.	PUNCT
ejpam-3260	275	1	let	let	VERB
ejpam-3260	275	2	l(v	l(v	NOUN
ejpam-3260	275	3	)	)	PUNCT
ejpam-3260	275	4	be	be	AUX
ejpam-3260	275	5	the	the	DET
ejpam-3260	275	6	linear	linear	PROPN
ejpam-3260	275	7	transformation	transformation	NOUN
ejpam-3260	275	8	semigroup	semigroup	NOUN
ejpam-3260	275	9	on	on	ADP
ejpam-3260	275	10	a	a	DET
ejpam-3260	275	11	vector	vector	NOUN
ejpam-3260	275	12	space	space	NOUN
ejpam-3260	275	13	v	v	NOUN
ejpam-3260	275	14	.	.	PUNCT
ejpam-3260	276	1	(	(	PUNCT
ejpam-3260	276	2	1	1	X
ejpam-3260	276	3	)	)	PUNCT
ejpam-3260	276	4	a	a	DET
ejpam-3260	276	5	semigroup	semigroup	PROPN
ejpam-3260	276	6	l(v	l(v	NOUN
ejpam-3260	276	7	)	)	PUNCT
ejpam-3260	276	8	has	have	VERB
ejpam-3260	276	9	a	a	DET
ejpam-3260	276	10	right	right	ADJ
ejpam-3260	276	11	magnifying	magnifying	NOUN
ejpam-3260	276	12	if	if	SCONJ
ejpam-3260	276	13	and	and	CCONJ
ejpam-3260	276	14	only	only	ADV
ejpam-3260	276	15	if	if	SCONJ
ejpam-3260	276	16	dimv	dimv	NOUN
ejpam-3260	276	17	is	be	AUX
ejpam-3260	276	18	infinite	infinite	ADJ
ejpam-3260	276	19	.	.	PUNCT
ejpam-3260	277	1	(	(	PUNCT
ejpam-3260	277	2	2	2	X
ejpam-3260	277	3	)	)	PUNCT
ejpam-3260	277	4	a	a	DET
ejpam-3260	277	5	linear	linear	ADJ
ejpam-3260	277	6	transformation	transformation	NOUN
ejpam-3260	277	7	f	f	PROPN
ejpam-3260	277	8	is	be	AUX
ejpam-3260	277	9	right	right	ADJ
ejpam-3260	277	10	magnifying	magnifying	NOUN
ejpam-3260	277	11	of	of	ADP
ejpam-3260	277	12	l(v	l(v	NOUN
ejpam-3260	277	13	)	)	PUNCT
ejpam-3260	277	14	if	if	SCONJ
ejpam-3260	277	15	and	and	CCONJ
ejpam-3260	277	16	only	only	ADV
ejpam-3260	277	17	if	if	SCONJ
ejpam-3260	277	18	f	f	PROPN
ejpam-3260	277	19	is	be	AUX
ejpam-3260	277	20	onto	onto	ADP
ejpam-3260	277	21	but	but	CCONJ
ejpam-3260	277	22	not	not	PART
ejpam-3260	277	23	one	one	NUM
ejpam-3260	277	24	-	-	PUNCT
ejpam-3260	277	25	to	to	ADP
ejpam-3260	277	26	-	-	PUNCT
ejpam-3260	277	27	one	one	NUM
ejpam-3260	277	28	.	.	PUNCT
ejpam-3260	278	1	proof	proof	NOUN
ejpam-3260	278	2	.	.	PUNCT
ejpam-3260	279	1	this	this	PRON
ejpam-3260	279	2	follows	follow	VERB
ejpam-3260	279	3	by	by	ADP
ejpam-3260	279	4	theorem	theorem	NOUN
ejpam-3260	279	5	4	4	NUM
ejpam-3260	279	6	by	by	ADP
ejpam-3260	279	7	using	use	VERB
ejpam-3260	279	8	v	v	NOUN
ejpam-3260	279	9	=	=	SYM
ejpam-3260	279	10	v1	v1	NOUN
ejpam-3260	279	11	and	and	CCONJ
ejpam-3260	279	12	v2	v2	NOUN
ejpam-3260	279	13	=	=	SYM
ejpam-3260	279	14	{	{	PUNCT
ejpam-3260	279	15	0	0	NUM
ejpam-3260	279	16	}	}	PUNCT
ejpam-3260	279	17	.	.	PUNCT
ejpam-3260	280	1	acknowledgements	acknowledgement	NOUN
ejpam-3260	280	2	this	this	DET
ejpam-3260	280	3	paper	paper	NOUN
ejpam-3260	280	4	was	be	AUX
ejpam-3260	280	5	supported	support	VERB
ejpam-3260	280	6	by	by	ADP
ejpam-3260	280	7	algebra	algebra	NOUN
ejpam-3260	280	8	and	and	CCONJ
ejpam-3260	280	9	applications	application	NOUN
ejpam-3260	280	10	research	research	NOUN
ejpam-3260	280	11	unit	unit	NOUN
ejpam-3260	280	12	,	,	PUNCT
ejpam-3260	280	13	prince	prince	NOUN
ejpam-3260	280	14	of	of	ADP
ejpam-3260	280	15	songkla	songkla	PROPN
ejpam-3260	280	16	university	university	PROPN
ejpam-3260	280	17	.	.	PUNCT
ejpam-3260	281	1	references	reference	NOUN
ejpam-3260	281	2	[	[	X
ejpam-3260	281	3	1	1	NUM
ejpam-3260	281	4	]	]	PUNCT
ejpam-3260	281	5	j	j	PROPN
ejpam-3260	281	6	araujo	araujo	PROPN
ejpam-3260	281	7	,	,	PUNCT
ejpam-3260	281	8	w	w	PROPN
ejpam-3260	281	9	bentz	bentz	PROPN
ejpam-3260	281	10	,	,	PUNCT
ejpam-3260	281	11	j	j	PROPN
ejpam-3260	282	1	d	d	NOUN
ejpam-3260	282	2	mitchelll	mitchelll	NOUN
ejpam-3260	282	3	and	and	CCONJ
ejpam-3260	282	4	c	c	PROPN
ejpam-3260	282	5	schneider	schneider	NOUN
ejpam-3260	282	6	.	.	PUNCT
ejpam-3260	283	1	the	the	DET
ejpam-3260	283	2	rank	rank	NOUN
ejpam-3260	283	3	of	of	ADP
ejpam-3260	283	4	the	the	DET
ejpam-3260	283	5	semigroup	semigroup	NOUN
ejpam-3260	283	6	of	of	ADP
ejpam-3260	283	7	transformations	transformation	NOUN
ejpam-3260	283	8	stabilising	stabilise	VERB
ejpam-3260	283	9	a	a	DET
ejpam-3260	283	10	partition	partition	NOUN
ejpam-3260	283	11	of	of	ADP
ejpam-3260	283	12	a	a	DET
ejpam-3260	283	13	finite	finite	ADJ
ejpam-3260	283	14	set	set	NOUN
ejpam-3260	283	15	,	,	PUNCT
ejpam-3260	283	16	mathematical	mathematical	ADJ
ejpam-3260	283	17	proceedings	proceeding	NOUN
ejpam-3260	283	18	of	of	ADP
ejpam-3260	283	19	the	the	DET
ejpam-3260	283	20	cambridge	cambridge	PROPN
ejpam-3260	283	21	philosophical	philosophical	ADJ
ejpam-3260	283	22	society	society	NOUN
ejpam-3260	283	23	,	,	PUNCT
ejpam-3260	283	24	159:339–353	159:339–353	NUM
ejpam-3260	283	25	,	,	PUNCT
ejpam-3260	283	26	2015	2015	NUM
ejpam-3260	283	27	.	.	PUNCT
ejpam-3260	284	1	[	[	X
ejpam-3260	284	2	2	2	NUM
ejpam-3260	284	3	]	]	SYM
ejpam-3260	284	4	f	f	PROPN
ejpam-3260	284	5	catino	catino	NOUN
ejpam-3260	284	6	and	and	CCONJ
ejpam-3260	284	7	f	f	PROPN
ejpam-3260	284	8	migliorini	migliorini	NOUN
ejpam-3260	284	9	.	.	PUNCT
ejpam-3260	285	1	magnifying	magnify	VERB
ejpam-3260	285	2	elements	element	NOUN
ejpam-3260	285	3	in	in	ADP
ejpam-3260	285	4	semigroups	semigroup	NOUN
ejpam-3260	285	5	.	.	PUNCT
ejpam-3260	286	1	semigroup	semigroup	PROPN
ejpam-3260	286	2	forum	forum	PROPN
ejpam-3260	286	3	,	,	PUNCT
ejpam-3260	286	4	44:314–319	44:314–319	PROPN
ejpam-3260	286	5	,	,	PUNCT
ejpam-3260	286	6	1992	1992	NUM
ejpam-3260	286	7	.	.	PUNCT
ejpam-3260	287	1	[	[	X
ejpam-3260	287	2	3	3	NUM
ejpam-3260	287	3	]	]	X
ejpam-3260	287	4	m	m	VERB
ejpam-3260	287	5	gutan	gutan	ADJ
ejpam-3260	287	6	.	.	PUNCT
ejpam-3260	288	1	semigroups	semigroup	NOUN
ejpam-3260	288	2	with	with	ADP
ejpam-3260	288	3	strong	strong	ADJ
ejpam-3260	288	4	and	and	CCONJ
ejpam-3260	288	5	nonstrong	nonstrong	NOUN
ejpam-3260	288	6	magnifying	magnify	VERB
ejpam-3260	288	7	elements	element	NOUN
ejpam-3260	288	8	.	.	PUNCT
ejpam-3260	289	1	semigroup	semigroup	PROPN
ejpam-3260	289	2	forum	forum	PROPN
ejpam-3260	289	3	,	,	PUNCT
ejpam-3260	289	4	53:384–386	53:384–386	NUM
ejpam-3260	289	5	,	,	PUNCT
ejpam-3260	289	6	1996	1996	NUM
ejpam-3260	289	7	.	.	PUNCT
ejpam-3260	290	1	[	[	X
ejpam-3260	290	2	4	4	NUM
ejpam-3260	290	3	]	]	X
ejpam-3260	290	4	m	m	VERB
ejpam-3260	290	5	gutan	gutan	ADJ
ejpam-3260	290	6	.	.	PUNCT
ejpam-3260	291	1	semigroups	semigroup	NOUN
ejpam-3260	291	2	which	which	PRON
ejpam-3260	291	3	contain	contain	VERB
ejpam-3260	291	4	magnifying	magnifying	ADJ
ejpam-3260	291	5	elements	element	NOUN
ejpam-3260	291	6	are	be	AUX
ejpam-3260	291	7	factorizable	factorizable	ADJ
ejpam-3260	291	8	.	.	PUNCT
ejpam-3260	292	1	communications	communication	NOUN
ejpam-3260	292	2	in	in	ADP
ejpam-3260	292	3	algebra	algebra	NOUN
ejpam-3260	292	4	,	,	PUNCT
ejpam-3260	292	5	25:3953–3963	25:3953–3963	NUM
ejpam-3260	292	6	,	,	PUNCT
ejpam-3260	292	7	1997	1997	NUM
ejpam-3260	292	8	.	.	PUNCT
ejpam-3260	293	1	references	reference	NOUN
ejpam-3260	293	2	588	588	NUM
ejpam-3260	293	3	[	[	X
ejpam-3260	293	4	5	5	NUM
ejpam-3260	293	5	]	]	PUNCT
ejpam-3260	293	6	m	m	VERB
ejpam-3260	293	7	gutan	gutan	ADJ
ejpam-3260	293	8	.	.	PUNCT
ejpam-3260	294	1	semigroups	semigroup	NOUN
ejpam-3260	294	2	with	with	ADP
ejpam-3260	294	3	magnifiers	magnifier	NOUN
ejpam-3260	294	4	admitting	admit	VERB
ejpam-3260	294	5	minimal	minimal	ADJ
ejpam-3260	294	6	subsemigroups	subsemigroup	NOUN
ejpam-3260	294	7	,	,	PUNCT
ejpam-3260	294	8	communications	communication	NOUN
ejpam-3260	294	9	in	in	ADP
ejpam-3260	294	10	algebra	algebra	NOUN
ejpam-3260	294	11	,	,	PUNCT
ejpam-3260	294	12	27:1975–1996	27:1975–1996	PROPN
ejpam-3260	294	13	,	,	PUNCT
ejpam-3260	294	14	1999	1999	NUM
ejpam-3260	294	15	.	.	PUNCT
ejpam-3260	295	1	[	[	X
ejpam-3260	295	2	6	6	NUM
ejpam-3260	295	3	]	]	PUNCT
ejpam-3260	295	4	m	m	VERB
ejpam-3260	295	5	gutan	gutan	ADJ
ejpam-3260	295	6	and	and	CCONJ
ejpam-3260	295	7	a	a	DET
ejpam-3260	295	8	kisielewicz	kisielewicz	NOUN
ejpam-3260	295	9	.	.	PUNCT
ejpam-3260	296	1	semigroups	semigroup	NOUN
ejpam-3260	296	2	with	with	ADP
ejpam-3260	296	3	good	good	ADJ
ejpam-3260	296	4	and	and	CCONJ
ejpam-3260	296	5	bad	bad	ADJ
ejpam-3260	296	6	magnifiers	magnifier	NOUN
ejpam-3260	296	7	,	,	PUNCT
ejpam-3260	296	8	journal	journal	NOUN
ejpam-3260	296	9	of	of	ADP
ejpam-3260	296	10	algebra	algebra	PROPN
ejpam-3260	296	11	,	,	PUNCT
ejpam-3260	296	12	267:587–607	267:587–607	NUM
ejpam-3260	296	13	,	,	PUNCT
ejpam-3260	296	14	2003	2003	NUM
ejpam-3260	296	15	.	.	PUNCT
ejpam-3260	297	1	[	[	X
ejpam-3260	297	2	7	7	NUM
ejpam-3260	297	3	]	]	X
ejpam-3260	297	4	e	e	X
ejpam-3260	297	5	s	s	X
ejpam-3260	297	6	ljapin	ljapin	NOUN
ejpam-3260	297	7	,	,	PUNCT
ejpam-3260	297	8	semigroups	semigroup	NOUN
ejpam-3260	297	9	,	,	PUNCT
ejpam-3260	297	10	transl	transl	PROPN
ejpam-3260	297	11	.	.	PUNCT
ejpam-3260	297	12	math	math	NOUN
ejpam-3260	297	13	.	.	PUNCT
ejpam-3260	298	1	monographs	monograph	NOUN
ejpam-3260	298	2	,	,	PUNCT
ejpam-3260	298	3	vol	vol	NOUN
ejpam-3260	298	4	.	.	PROPN
ejpam-3260	298	5	3	3	NUM
ejpam-3260	298	6	,	,	PUNCT
ejpam-3260	298	7	providence	providence	NOUN
ejpam-3260	298	8	rhode	rhode	PROPN
ejpam-3260	298	9	island	island	NOUN
ejpam-3260	298	10	,	,	PUNCT
ejpam-3260	298	11	1963	1963	NUM
ejpam-3260	298	12	.	.	PUNCT
ejpam-3260	299	1	[	[	X
ejpam-3260	299	2	8	8	NUM
ejpam-3260	299	3	]	]	X
ejpam-3260	299	4	k	k	PROPN
ejpam-3260	299	5	d	d	PROPN
ejpam-3260	299	6	magill	magill	PROPN
ejpam-3260	299	7	jr	jr	PROPN
ejpam-3260	299	8	.	.	PUNCT
ejpam-3260	299	9	magnifying	magnify	VERB
ejpam-3260	299	10	elements	element	NOUN
ejpam-3260	299	11	of	of	ADP
ejpam-3260	299	12	transformation	transformation	NOUN
ejpam-3260	299	13	semigroups	semigroup	NOUN
ejpam-3260	299	14	,	,	PUNCT
ejpam-3260	299	15	semigroup	semigroup	PROPN
ejpam-3260	299	16	forum	forum	PROPN
ejpam-3260	299	17	,	,	PUNCT
ejpam-3260	299	18	48:119–126	48:119–126	PROPN
ejpam-3260	299	19	,	,	PUNCT
ejpam-3260	299	20	1994	1994	NUM
ejpam-3260	299	21	.	.	PUNCT
ejpam-3260	300	1	[	[	X
ejpam-3260	300	2	9	9	NUM
ejpam-3260	300	3	]	]	SYM
ejpam-3260	300	4	f	f	NOUN
ejpam-3260	300	5	migliorini	migliorini	NOUN
ejpam-3260	300	6	.	.	PUNCT
ejpam-3260	301	1	some	some	DET
ejpam-3260	301	2	research	research	NOUN
ejpam-3260	301	3	on	on	ADP
ejpam-3260	301	4	semigroups	semigroup	NOUN
ejpam-3260	301	5	with	with	ADP
ejpam-3260	301	6	magnifying	magnify	VERB
ejpam-3260	301	7	elements	element	NOUN
ejpam-3260	301	8	,	,	PUNCT
ejpam-3260	301	9	periodica	periodica	PROPN
ejpam-3260	301	10	mathematica	mathematica	PROPN
ejpam-3260	301	11	hungarica	hungarica	PROPN
ejpam-3260	301	12	,	,	PUNCT
ejpam-3260	301	13	1:279–286	1:279–286	NUM
ejpam-3260	301	14	,	,	PUNCT
ejpam-3260	301	15	1971	1971	NUM
ejpam-3260	301	16	.	.	PUNCT
ejpam-3260	302	1	[	[	X
ejpam-3260	302	2	10	10	NUM
ejpam-3260	302	3	]	]	X
ejpam-3260	302	4	f	f	PROPN
ejpam-3260	302	5	migliorini	migliorini	NOUN
ejpam-3260	302	6	.	.	PUNCT
ejpam-3260	303	1	magnifying	magnify	VERB
ejpam-3260	303	2	elements	element	NOUN
ejpam-3260	303	3	and	and	CCONJ
ejpam-3260	303	4	minimal	minimal	ADJ
ejpam-3260	303	5	subsemigroups	subsemigroup	NOUN
ejpam-3260	303	6	in	in	ADP
ejpam-3260	303	7	semigroups	semigroup	NOUN
ejpam-3260	303	8	,	,	PUNCT
ejpam-3260	303	9	periodica	periodica	PROPN
ejpam-3260	303	10	mathematica	mathematica	PROPN
ejpam-3260	303	11	hungarica	hungarica	PROPN
ejpam-3260	303	12	,	,	PUNCT
ejpam-3260	303	13	5:279–288	5:279–288	NUM
ejpam-3260	303	14	,	,	PUNCT
ejpam-3260	303	15	1974	1974	NUM
ejpam-3260	303	16	.	.	PUNCT
ejpam-3260	304	1	[	[	X
ejpam-3260	304	2	11	11	NUM
ejpam-3260	304	3	]	]	X
ejpam-3260	304	4	p	p	X
ejpam-3260	304	5	purisang	purisang	PROPN
ejpam-3260	304	6	and	and	CCONJ
ejpam-3260	304	7	j	j	PROPN
ejpam-3260	304	8	rakbud	rakbud	NOUN
ejpam-3260	304	9	.	.	PUNCT
ejpam-3260	305	1	regularity	regularity	NOUN
ejpam-3260	305	2	of	of	ADP
ejpam-3260	305	3	transformation	transformation	NOUN
ejpam-3260	305	4	semigroups	semigroup	NOUN
ejpam-3260	305	5	defined	define	VERB
ejpam-3260	305	6	by	by	ADP
ejpam-3260	305	7	a	a	DET
ejpam-3260	305	8	partition	partition	NOUN
ejpam-3260	305	9	,	,	PUNCT
ejpam-3260	305	10	communications	communication	NOUN
ejpam-3260	305	11	of	of	ADP
ejpam-3260	305	12	the	the	DET
ejpam-3260	305	13	korean	korean	ADJ
ejpam-3260	305	14	mathematical	mathematical	ADJ
ejpam-3260	305	15	society	society	NOUN
ejpam-3260	305	16	,	,	PUNCT
ejpam-3260	305	17	31:217	31:217	NUM
ejpam-3260	305	18	-	-	SYM
ejpam-3260	305	19	227	227	NUM
ejpam-3260	305	20	,	,	PUNCT
ejpam-3260	305	21	2016	2016	NUM
ejpam-3260	305	22	.	.	PUNCT