id	sid	tid	token	lemma	pos
ejpam-6472	1	1	european	european	PROPN
ejpam-6472	1	2	journal	journal	PROPN
ejpam-6472	1	3	of	of	ADP
ejpam-6472	1	4	pure	pure	ADJ
ejpam-6472	1	5	and	and	CCONJ
ejpam-6472	1	6	applied	applied	ADJ
ejpam-6472	1	7	mathematics	mathematic	NOUN
ejpam-6472	1	8	2025	2025	NUM
ejpam-6472	1	9	,	,	PUNCT
ejpam-6472	1	10	vol	vol	NOUN
ejpam-6472	1	11	.	.	PROPN
ejpam-6472	1	12	18	18	NUM
ejpam-6472	1	13	,	,	PUNCT
ejpam-6472	1	14	issue	issue	NOUN
ejpam-6472	1	15	3	3	NUM
ejpam-6472	1	16	,	,	PUNCT
ejpam-6472	1	17	article	article	NOUN
ejpam-6472	1	18	number	number	NOUN
ejpam-6472	1	19	6472	6472	NUM
ejpam-6472	1	20	issn	issn	VERB
ejpam-6472	1	21	1307	1307	NUM
ejpam-6472	1	22	-	-	SYM
ejpam-6472	1	23	5543	5543	NUM
ejpam-6472	1	24	–	–	PUNCT
ejpam-6472	1	25	ejpam.com	ejpam.com	X
ejpam-6472	1	26	published	publish	VERB
ejpam-6472	1	27	by	by	ADP
ejpam-6472	1	28	new	new	PROPN
ejpam-6472	1	29	york	york	PROPN
ejpam-6472	1	30	business	business	PROPN
ejpam-6472	1	31	global	global	PROPN
ejpam-6472	1	32	an	an	DET
ejpam-6472	1	33	inductive	inductive	ADJ
ejpam-6472	1	34	product	product	NOUN
ejpam-6472	1	35	of	of	ADP
ejpam-6472	1	36	terms	term	NOUN
ejpam-6472	1	37	pongsaphat	pongsaphat	ADP
ejpam-6472	1	38	prachumdang1	prachumdang1	NOUN
ejpam-6472	1	39	,	,	PUNCT
ejpam-6472	1	40	bundit	bundit	NOUN
ejpam-6472	1	41	pibaljommee1,∗	pibaljommee1,∗	NOUN
ejpam-6472	1	42	1	1	NUM
ejpam-6472	1	43	department	department	NOUN
ejpam-6472	1	44	of	of	ADP
ejpam-6472	1	45	mathematics	mathematic	NOUN
ejpam-6472	1	46	,	,	PUNCT
ejpam-6472	1	47	faculty	faculty	NOUN
ejpam-6472	1	48	of	of	ADP
ejpam-6472	1	49	science	science	NOUN
ejpam-6472	1	50	,	,	PUNCT
ejpam-6472	1	51	khon	khon	PROPN
ejpam-6472	1	52	kaen	kaen	PROPN
ejpam-6472	1	53	university	university	PROPN
ejpam-6472	1	54	,	,	PUNCT
ejpam-6472	1	55	khon	khon	PROPN
ejpam-6472	1	56	kaen	kaen	PROPN
ejpam-6472	1	57	40002	40002	NUM
ejpam-6472	1	58	,	,	PUNCT
ejpam-6472	1	59	thailand	thailand	PROPN
ejpam-6472	1	60	abstract	abstract	PROPN
ejpam-6472	1	61	.	.	PUNCT
ejpam-6472	2	1	over	over	ADP
ejpam-6472	2	2	the	the	DET
ejpam-6472	2	3	years	year	NOUN
ejpam-6472	2	4	,	,	PUNCT
ejpam-6472	2	5	many	many	ADJ
ejpam-6472	2	6	binary	binary	ADJ
ejpam-6472	2	7	operations	operation	NOUN
ejpam-6472	2	8	on	on	ADP
ejpam-6472	2	9	the	the	DET
ejpam-6472	2	10	set	set	NOUN
ejpam-6472	2	11	of	of	ADP
ejpam-6472	2	12	all	all	DET
ejpam-6472	2	13	n	n	CCONJ
ejpam-6472	2	14	-	-	PUNCT
ejpam-6472	2	15	ary	ary	NOUN
ejpam-6472	2	16	terms	term	NOUN
ejpam-6472	2	17	of	of	ADP
ejpam-6472	2	18	type	type	NOUN
ejpam-6472	2	19	τ	τ	PROPN
ejpam-6472	2	20	have	have	AUX
ejpam-6472	2	21	been	be	AUX
ejpam-6472	2	22	defined	define	VERB
ejpam-6472	2	23	,	,	PUNCT
ejpam-6472	2	24	derived	derive	VERB
ejpam-6472	2	25	from	from	ADP
ejpam-6472	2	26	superpositions	superposition	NOUN
ejpam-6472	2	27	and	and	CCONJ
ejpam-6472	2	28	forming	form	VERB
ejpam-6472	2	29	semigroups	semigroup	NOUN
ejpam-6472	2	30	.	.	PUNCT
ejpam-6472	3	1	later	later	ADV
ejpam-6472	3	2	,	,	PUNCT
ejpam-6472	3	3	an	an	DET
ejpam-6472	3	4	inductive	inductive	ADJ
ejpam-6472	3	5	composition	composition	NOUN
ejpam-6472	3	6	of	of	ADP
ejpam-6472	3	7	terms	term	NOUN
ejpam-6472	3	8	was	be	AUX
ejpam-6472	3	9	introduced	introduce	VERB
ejpam-6472	3	10	as	as	ADP
ejpam-6472	3	11	a	a	DET
ejpam-6472	3	12	generalization	generalization	NOUN
ejpam-6472	3	13	of	of	ADP
ejpam-6472	3	14	a	a	DET
ejpam-6472	3	15	superposition	superposition	NOUN
ejpam-6472	3	16	,	,	PUNCT
ejpam-6472	3	17	extending	extend	VERB
ejpam-6472	3	18	its	its	PRON
ejpam-6472	3	19	scope	scope	NOUN
ejpam-6472	3	20	from	from	ADP
ejpam-6472	3	21	variable	variable	ADJ
ejpam-6472	3	22	replacement	replacement	NOUN
ejpam-6472	3	23	to	to	PART
ejpam-6472	3	24	subterm	subterm	NOUN
ejpam-6472	3	25	replacement	replacement	NOUN
ejpam-6472	3	26	.	.	PUNCT
ejpam-6472	4	1	from	from	ADP
ejpam-6472	4	2	this	this	PRON
ejpam-6472	4	3	,	,	PUNCT
ejpam-6472	4	4	a	a	DET
ejpam-6472	4	5	binary	binary	ADJ
ejpam-6472	4	6	operation	operation	NOUN
ejpam-6472	4	7	called	call	VERB
ejpam-6472	4	8	an	an	DET
ejpam-6472	4	9	r	r	NOUN
ejpam-6472	4	10	-	-	PUNCT
ejpam-6472	4	11	inductive	inductive	ADJ
ejpam-6472	4	12	product	product	NOUN
ejpam-6472	4	13	was	be	AUX
ejpam-6472	4	14	introduced	introduce	VERB
ejpam-6472	4	15	by	by	ADP
ejpam-6472	4	16	fixing	fix	VERB
ejpam-6472	4	17	a	a	DET
ejpam-6472	4	18	specific	specific	ADJ
ejpam-6472	4	19	subterm	subterm	NOUN
ejpam-6472	4	20	to	to	PART
ejpam-6472	4	21	be	be	AUX
ejpam-6472	4	22	replaced	replace	VERB
ejpam-6472	4	23	.	.	PUNCT
ejpam-6472	5	1	in	in	ADP
ejpam-6472	5	2	this	this	DET
ejpam-6472	5	3	study	study	NOUN
ejpam-6472	5	4	,	,	PUNCT
ejpam-6472	5	5	we	we	PRON
ejpam-6472	5	6	define	define	VERB
ejpam-6472	5	7	a	a	DET
ejpam-6472	5	8	new	new	ADJ
ejpam-6472	5	9	binary	binary	ADJ
ejpam-6472	5	10	operation	operation	NOUN
ejpam-6472	5	11	,	,	PUNCT
ejpam-6472	5	12	called	call	VERB
ejpam-6472	5	13	an	an	DET
ejpam-6472	5	14	rs	rs	ADJ
ejpam-6472	5	15	-	-	PUNCT
ejpam-6472	5	16	inductive	inductive	ADJ
ejpam-6472	5	17	product	product	NOUN
ejpam-6472	5	18	,	,	PUNCT
ejpam-6472	5	19	which	which	PRON
ejpam-6472	5	20	generalizes	generalize	VERB
ejpam-6472	5	21	the	the	DET
ejpam-6472	5	22	r	r	NOUN
ejpam-6472	5	23	-	-	PUNCT
ejpam-6472	5	24	inductive	inductive	ADJ
ejpam-6472	5	25	product	product	NOUN
ejpam-6472	5	26	by	by	ADP
ejpam-6472	5	27	allowing	allow	VERB
ejpam-6472	5	28	the	the	DET
ejpam-6472	5	29	simultaneous	simultaneous	ADJ
ejpam-6472	5	30	replacement	replacement	NOUN
ejpam-6472	5	31	of	of	ADP
ejpam-6472	5	32	two	two	NUM
ejpam-6472	5	33	specific	specific	ADJ
ejpam-6472	5	34	subterms	subterm	NOUN
ejpam-6472	5	35	.	.	PUNCT
ejpam-6472	6	1	we	we	PRON
ejpam-6472	6	2	construct	construct	VERB
ejpam-6472	6	3	a	a	DET
ejpam-6472	6	4	semigroup	semigroup	NOUN
ejpam-6472	6	5	equipped	equip	VERB
ejpam-6472	6	6	with	with	ADP
ejpam-6472	6	7	the	the	DET
ejpam-6472	6	8	new	new	ADJ
ejpam-6472	6	9	operation	operation	NOUN
ejpam-6472	6	10	and	and	CCONJ
ejpam-6472	6	11	investigate	investigate	VERB
ejpam-6472	6	12	its	its	PRON
ejpam-6472	6	13	algebraic	algebraic	ADJ
ejpam-6472	6	14	properties	property	NOUN
ejpam-6472	6	15	,	,	PUNCT
ejpam-6472	6	16	including	include	VERB
ejpam-6472	6	17	regular	regular	ADJ
ejpam-6472	6	18	elements	element	NOUN
ejpam-6472	6	19	,	,	PUNCT
ejpam-6472	6	20	idempotent	idempotent	ADJ
ejpam-6472	6	21	elements	element	NOUN
ejpam-6472	6	22	,	,	PUNCT
ejpam-6472	6	23	and	and	CCONJ
ejpam-6472	6	24	green	green	PROPN
ejpam-6472	6	25	’s	’s	PART
ejpam-6472	6	26	relations	relation	NOUN
ejpam-6472	6	27	.	.	PUNCT
ejpam-6472	7	1	2020	2020	NUM
ejpam-6472	7	2	mathematics	mathematic	NOUN
ejpam-6472	7	3	subject	subject	NOUN
ejpam-6472	7	4	classifications	classification	NOUN
ejpam-6472	7	5	:	:	PUNCT
ejpam-6472	7	6	08a40	08a40	ADJ
ejpam-6472	7	7	,	,	PUNCT
ejpam-6472	7	8	08a70	08a70	NUM
ejpam-6472	7	9	,	,	PUNCT
ejpam-6472	7	10	20m10	20m10	NUM
ejpam-6472	7	11	key	key	ADJ
ejpam-6472	7	12	words	word	NOUN
ejpam-6472	7	13	and	and	CCONJ
ejpam-6472	7	14	phrases	phrase	NOUN
ejpam-6472	7	15	:	:	PUNCT
ejpam-6472	7	16	terms	term	NOUN
ejpam-6472	7	17	,	,	PUNCT
ejpam-6472	7	18	inductive	inductive	ADJ
ejpam-6472	7	19	composition	composition	NOUN
ejpam-6472	7	20	of	of	ADP
ejpam-6472	7	21	terms	term	NOUN
ejpam-6472	7	22	,	,	PUNCT
ejpam-6472	7	23	inductive	inductive	ADJ
ejpam-6472	7	24	product	product	NOUN
ejpam-6472	7	25	of	of	ADP
ejpam-6472	7	26	terms	term	NOUN
ejpam-6472	7	27	,	,	PUNCT
ejpam-6472	7	28	semigroups	semigroup	NOUN
ejpam-6472	7	29	,	,	PUNCT
ejpam-6472	7	30	regular	regular	ADJ
ejpam-6472	7	31	elements	element	NOUN
ejpam-6472	7	32	,	,	PUNCT
ejpam-6472	7	33	idempotent	idempotent	ADJ
ejpam-6472	7	34	elements	element	NOUN
ejpam-6472	7	35	,	,	PUNCT
ejpam-6472	7	36	green	green	PROPN
ejpam-6472	7	37	’s	’s	PART
ejpam-6472	7	38	relations	relation	NOUN
ejpam-6472	7	39	1	1	NUM
ejpam-6472	7	40	.	.	PUNCT
ejpam-6472	8	1	introduction	introduction	NOUN
ejpam-6472	8	2	in	in	ADP
ejpam-6472	8	3	universal	universal	ADJ
ejpam-6472	8	4	algebra	algebra	NOUN
ejpam-6472	8	5	,	,	PUNCT
ejpam-6472	8	6	the	the	DET
ejpam-6472	8	7	concept	concept	NOUN
ejpam-6472	8	8	of	of	ADP
ejpam-6472	8	9	terms	term	NOUN
ejpam-6472	8	10	plays	play	VERB
ejpam-6472	8	11	a	a	DET
ejpam-6472	8	12	crucial	crucial	ADJ
ejpam-6472	8	13	role	role	NOUN
ejpam-6472	8	14	as	as	ADP
ejpam-6472	8	15	formal	formal	ADJ
ejpam-6472	8	16	representations	representation	NOUN
ejpam-6472	8	17	in	in	ADP
ejpam-6472	8	18	equations	equation	NOUN
ejpam-6472	8	19	and	and	CCONJ
ejpam-6472	8	20	identities	identity	NOUN
ejpam-6472	8	21	within	within	ADP
ejpam-6472	8	22	algebraic	algebraic	ADJ
ejpam-6472	8	23	structures	structure	NOUN
ejpam-6472	8	24	.	.	PUNCT
ejpam-6472	9	1	in	in	ADP
ejpam-6472	9	2	addition	addition	NOUN
ejpam-6472	9	3	to	to	ADP
ejpam-6472	9	4	their	their	PRON
ejpam-6472	9	5	foundational	foundational	ADJ
ejpam-6472	9	6	role	role	NOUN
ejpam-6472	9	7	in	in	ADP
ejpam-6472	9	8	algebra	algebra	NOUN
ejpam-6472	9	9	,	,	PUNCT
ejpam-6472	9	10	terms	term	NOUN
ejpam-6472	9	11	have	have	AUX
ejpam-6472	9	12	found	find	VERB
ejpam-6472	9	13	applications	application	NOUN
ejpam-6472	9	14	in	in	ADP
ejpam-6472	9	15	other	other	ADJ
ejpam-6472	9	16	areas	area	NOUN
ejpam-6472	9	17	,	,	PUNCT
ejpam-6472	9	18	particularly	particularly	ADV
ejpam-6472	9	19	in	in	ADP
ejpam-6472	9	20	computer	computer	NOUN
ejpam-6472	9	21	science	science	NOUN
ejpam-6472	9	22	and	and	CCONJ
ejpam-6472	9	23	formal	formal	ADJ
ejpam-6472	9	24	languages	language	NOUN
ejpam-6472	9	25	.	.	PUNCT
ejpam-6472	10	1	for	for	ADP
ejpam-6472	10	2	further	further	ADJ
ejpam-6472	10	3	background	background	NOUN
ejpam-6472	10	4	and	and	CCONJ
ejpam-6472	10	5	applications	application	NOUN
ejpam-6472	10	6	,	,	PUNCT
ejpam-6472	10	7	the	the	DET
ejpam-6472	10	8	readers	reader	NOUN
ejpam-6472	10	9	are	be	AUX
ejpam-6472	10	10	referred	refer	VERB
ejpam-6472	10	11	to	to	ADP
ejpam-6472	10	12	[	[	X
ejpam-6472	10	13	1	1	NUM
ejpam-6472	10	14	]	]	PUNCT
ejpam-6472	10	15	.	.	PUNCT
ejpam-6472	11	1	in	in	ADP
ejpam-6472	11	2	the	the	DET
ejpam-6472	11	3	study	study	NOUN
ejpam-6472	11	4	of	of	ADP
ejpam-6472	11	5	terms	term	NOUN
ejpam-6472	11	6	,	,	PUNCT
ejpam-6472	11	7	various	various	ADJ
ejpam-6472	11	8	operations	operation	NOUN
ejpam-6472	11	9	on	on	ADP
ejpam-6472	11	10	the	the	DET
ejpam-6472	11	11	set	set	NOUN
ejpam-6472	11	12	of	of	ADP
ejpam-6472	11	13	terms	term	NOUN
ejpam-6472	11	14	have	have	AUX
ejpam-6472	11	15	been	be	AUX
ejpam-6472	11	16	introduced	introduce	VERB
ejpam-6472	11	17	over	over	ADP
ejpam-6472	11	18	the	the	DET
ejpam-6472	11	19	past	past	ADJ
ejpam-6472	11	20	decades	decade	NOUN
ejpam-6472	11	21	.	.	PUNCT
ejpam-6472	12	1	among	among	ADP
ejpam-6472	12	2	these	these	PRON
ejpam-6472	12	3	,	,	PUNCT
ejpam-6472	12	4	superpositions	superposition	NOUN
ejpam-6472	12	5	have	have	AUX
ejpam-6472	12	6	been	be	AUX
ejpam-6472	12	7	extensively	extensively	ADV
ejpam-6472	12	8	studied	study	VERB
ejpam-6472	12	9	due	due	ADP
ejpam-6472	12	10	to	to	ADP
ejpam-6472	12	11	their	their	PRON
ejpam-6472	12	12	satisfaction	satisfaction	NOUN
ejpam-6472	12	13	of	of	ADP
ejpam-6472	12	14	the	the	DET
ejpam-6472	12	15	superassociative	superassociative	ADJ
ejpam-6472	12	16	law	law	NOUN
ejpam-6472	12	17	,	,	PUNCT
ejpam-6472	12	18	a	a	DET
ejpam-6472	12	19	generalization	generalization	NOUN
ejpam-6472	12	20	of	of	ADP
ejpam-6472	12	21	associativity	associativity	NOUN
ejpam-6472	12	22	(	(	PUNCT
ejpam-6472	12	23	see	see	VERB
ejpam-6472	12	24	,	,	PUNCT
ejpam-6472	12	25	e.g.	e.g.	ADV
ejpam-6472	12	26	,	,	PUNCT
ejpam-6472	12	27	[	[	X
ejpam-6472	12	28	1	1	NUM
ejpam-6472	12	29	]	]	NUM
ejpam-6472	12	30	)	)	PUNCT
ejpam-6472	12	31	.	.	PUNCT
ejpam-6472	13	1	one	one	NUM
ejpam-6472	13	2	of	of	ADP
ejpam-6472	13	3	the	the	DET
ejpam-6472	13	4	earliest	early	ADJ
ejpam-6472	13	5	forms	form	NOUN
ejpam-6472	13	6	is	be	AUX
ejpam-6472	13	7	the	the	DET
ejpam-6472	13	8	superposition	superposition	NOUN
ejpam-6472	13	9	sn	sn	NOUN
ejpam-6472	13	10	m	m	PROPN
ejpam-6472	13	11	,	,	PUNCT
ejpam-6472	13	12	which	which	PRON
ejpam-6472	13	13	maps	map	VERB
ejpam-6472	13	14	an	an	DET
ejpam-6472	13	15	n	n	CCONJ
ejpam-6472	13	16	-	-	PUNCT
ejpam-6472	13	17	ary	ary	NOUN
ejpam-6472	13	18	term	term	NOUN
ejpam-6472	13	19	and	and	CCONJ
ejpam-6472	13	20	an	an	DET
ejpam-6472	13	21	n	n	NOUN
ejpam-6472	13	22	-	-	PUNCT
ejpam-6472	13	23	tuple	tuple	NOUN
ejpam-6472	13	24	of	of	ADP
ejpam-6472	13	25	m	m	PROPN
ejpam-6472	13	26	-	-	ADJ
ejpam-6472	13	27	ary	ary	PROPN
ejpam-6472	13	28	terms	term	NOUN
ejpam-6472	13	29	to	to	ADP
ejpam-6472	13	30	an	an	DET
ejpam-6472	13	31	m	m	ADJ
ejpam-6472	13	32	-	-	ADJ
ejpam-6472	13	33	ary	ary	ADJ
ejpam-6472	13	34	term	term	NOUN
ejpam-6472	13	35	by	by	ADP
ejpam-6472	13	36	substituting	substitute	VERB
ejpam-6472	13	37	each	each	DET
ejpam-6472	13	38	variable	variable	NOUN
ejpam-6472	13	39	in	in	ADP
ejpam-6472	13	40	the	the	DET
ejpam-6472	13	41	n	n	CCONJ
ejpam-6472	13	42	-	-	PUNCT
ejpam-6472	13	43	ary	ary	NOUN
ejpam-6472	13	44	term	term	NOUN
ejpam-6472	13	45	with	with	ADP
ejpam-6472	13	46	the	the	DET
ejpam-6472	13	47	corresponding	correspond	VERB
ejpam-6472	13	48	m	m	PROPN
ejpam-6472	13	49	-	-	ADJ
ejpam-6472	13	50	ary	ary	PROPN
ejpam-6472	13	51	term	term	NOUN
ejpam-6472	13	52	.	.	PUNCT
ejpam-6472	14	1	in	in	ADP
ejpam-6472	14	2	2001	2001	NUM
ejpam-6472	14	3	,	,	PUNCT
ejpam-6472	14	4	denecke	denecke	NOUN
ejpam-6472	14	5	and	and	CCONJ
ejpam-6472	14	6	leeratanavalee	leeratanavalee	NOUN
ejpam-6472	14	7	[	[	X
ejpam-6472	14	8	2	2	X
ejpam-6472	14	9	]	]	PUNCT
ejpam-6472	14	10	extended	extend	VERB
ejpam-6472	14	11	this	this	DET
ejpam-6472	14	12	operation	operation	NOUN
ejpam-6472	14	13	to	to	ADP
ejpam-6472	14	14	a	a	DET
ejpam-6472	14	15	more	more	ADV
ejpam-6472	14	16	general	general	ADJ
ejpam-6472	14	17	form	form	NOUN
ejpam-6472	14	18	,	,	PUNCT
ejpam-6472	14	19	denoted	denote	VERB
ejpam-6472	14	20	by	by	ADP
ejpam-6472	14	21	sn	sn	PROPN
ejpam-6472	14	22	g	g	PROPN
ejpam-6472	14	23	,	,	PUNCT
ejpam-6472	14	24	which	which	PRON
ejpam-6472	14	25	is	be	AUX
ejpam-6472	14	26	an	an	DET
ejpam-6472	14	27	(	(	PUNCT
ejpam-6472	14	28	n	n	NOUN
ejpam-6472	14	29	+	+	CCONJ
ejpam-6472	14	30	1)-ary	1)-ary	ADJ
ejpam-6472	14	31	operation	operation	NOUN
ejpam-6472	14	32	defined	define	VERB
ejpam-6472	14	33	on	on	ADP
ejpam-6472	14	34	terms	term	NOUN
ejpam-6472	14	35	of	of	ADP
ejpam-6472	14	36	arbitrary	arbitrary	ADJ
ejpam-6472	14	37	arity	arity	NOUN
ejpam-6472	14	38	.	.	PUNCT
ejpam-6472	15	1	a	a	DET
ejpam-6472	15	2	special	special	ADJ
ejpam-6472	15	3	case	case	NOUN
ejpam-6472	15	4	where	where	SCONJ
ejpam-6472	15	5	n	n	PROPN
ejpam-6472	15	6	=	=	SYM
ejpam-6472	15	7	m	m	PROPN
ejpam-6472	15	8	,	,	PUNCT
ejpam-6472	15	9	denoted	denote	VERB
ejpam-6472	15	10	sn	sn	PROPN
ejpam-6472	15	11	,	,	PUNCT
ejpam-6472	15	12	was	be	AUX
ejpam-6472	15	13	later	later	ADV
ejpam-6472	15	14	∗corresponding	∗corresponde	VERB
ejpam-6472	15	15	author	author	NOUN
ejpam-6472	15	16	.	.	PUNCT
ejpam-6472	16	1	doi	doi	NOUN
ejpam-6472	16	2	:	:	PUNCT
ejpam-6472	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6472	https://doi.org/10.29020/nybg.ejpam.v18i3.6472	ADJ
ejpam-6472	16	4	email	email	NOUN
ejpam-6472	16	5	addresses	address	NOUN
ejpam-6472	16	6	:	:	PUNCT
ejpam-6472	16	7	pong	pong	PROPN
ejpam-6472	16	8	sa	sa	PROPN
ejpam-6472	17	1	phat@kkumail.com	phat@kkumail.com	PROPN
ejpam-6472	18	1	(	(	PUNCT
ejpam-6472	18	2	p.	p.	NOUN
ejpam-6472	18	3	prachumdang	prachumdang	PROPN
ejpam-6472	18	4	)	)	PUNCT
ejpam-6472	18	5	,	,	PUNCT
ejpam-6472	19	1	banpib@kku.ac.th	banpib@kku.ac.th	PROPN
ejpam-6472	19	2	(	(	PUNCT
ejpam-6472	19	3	b.	b.	PROPN
ejpam-6472	19	4	pibaljommee	pibaljommee	PROPN
ejpam-6472	19	5	)	)	PUNCT
ejpam-6472	19	6	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6472	20	1	1	1	NUM
ejpam-6472	20	2	copyright	copyright	NOUN
ejpam-6472	20	3	:	:	PUNCT
ejpam-6472	20	4	©	©	PROPN
ejpam-6472	20	5	2025	2025	NUM
ejpam-6472	20	6	the	the	DET
ejpam-6472	20	7	author(s	author(s	NOUN
ejpam-6472	20	8	)	)	PUNCT
ejpam-6472	20	9	.	.	PUNCT
ejpam-6472	21	1	(	(	PUNCT
ejpam-6472	21	2	cc	cc	NOUN
ejpam-6472	21	3	by	by	ADP
ejpam-6472	21	4	-	-	PUNCT
ejpam-6472	21	5	nc	nc	PROPN
ejpam-6472	21	6	4.0	4.0	NUM
ejpam-6472	21	7	)	)	PUNCT
ejpam-6472	21	8	p.	p.	NOUN
ejpam-6472	21	9	prachumdang	prachumdang	PROPN
ejpam-6472	21	10	,	,	PUNCT
ejpam-6472	21	11	b.	b.	PROPN
ejpam-6472	21	12	pibaljommee	pibaljommee	PROPN
ejpam-6472	21	13	/	/	SYM
ejpam-6472	21	14	eur	eur	PROPN
ejpam-6472	21	15	.	.	PUNCT
ejpam-6472	22	1	j.	j.	PROPN
ejpam-6472	22	2	pure	pure	PROPN
ejpam-6472	22	3	appl	appl	PROPN
ejpam-6472	22	4	.	.	PROPN
ejpam-6472	22	5	math	math	PROPN
ejpam-6472	22	6	,	,	PUNCT
ejpam-6472	22	7	18	18	NUM
ejpam-6472	22	8	(	(	PUNCT
ejpam-6472	22	9	3	3	NUM
ejpam-6472	22	10	)	)	PUNCT
ejpam-6472	22	11	(	(	PUNCT
ejpam-6472	22	12	2025	2025	NUM
ejpam-6472	22	13	)	)	PUNCT
ejpam-6472	22	14	,	,	PUNCT
ejpam-6472	22	15	6472	6472	NUM
ejpam-6472	22	16	2	2	NUM
ejpam-6472	22	17	of	of	ADP
ejpam-6472	22	18	16	16	NUM
ejpam-6472	22	19	mentioned	mention	VERB
ejpam-6472	22	20	in	in	ADP
ejpam-6472	22	21	[	[	X
ejpam-6472	22	22	3	3	NUM
ejpam-6472	22	23	]	]	PUNCT
ejpam-6472	22	24	.	.	PUNCT
ejpam-6472	23	1	moreover	moreover	ADV
ejpam-6472	23	2	,	,	PUNCT
ejpam-6472	23	3	the	the	DET
ejpam-6472	23	4	idea	idea	NOUN
ejpam-6472	23	5	of	of	ADP
ejpam-6472	23	6	superpositions	superposition	NOUN
ejpam-6472	23	7	has	have	AUX
ejpam-6472	23	8	also	also	ADV
ejpam-6472	23	9	been	be	AUX
ejpam-6472	23	10	extended	extend	VERB
ejpam-6472	23	11	to	to	ADP
ejpam-6472	23	12	sets	set	NOUN
ejpam-6472	23	13	of	of	ADP
ejpam-6472	23	14	terms	term	NOUN
ejpam-6472	23	15	,	,	PUNCT
ejpam-6472	23	16	known	know	VERB
ejpam-6472	23	17	as	as	ADP
ejpam-6472	23	18	tree	tree	NOUN
ejpam-6472	23	19	languages	language	NOUN
ejpam-6472	23	20	.	.	PUNCT
ejpam-6472	24	1	this	this	DET
ejpam-6472	24	2	extension	extension	NOUN
ejpam-6472	24	3	,	,	PUNCT
ejpam-6472	24	4	denoted	denote	VERB
ejpam-6472	24	5	by	by	ADP
ejpam-6472	24	6	ŝn	ŝn	PROPN
ejpam-6472	24	7	m	m	NOUN
ejpam-6472	24	8	,	,	PUNCT
ejpam-6472	24	9	was	be	AUX
ejpam-6472	24	10	introduced	introduce	VERB
ejpam-6472	24	11	in	in	ADP
ejpam-6472	24	12	[	[	X
ejpam-6472	24	13	4	4	NUM
ejpam-6472	24	14	]	]	PUNCT
ejpam-6472	24	15	.	.	PUNCT
ejpam-6472	25	1	superpositions	superposition	NOUN
ejpam-6472	25	2	,	,	PUNCT
ejpam-6472	25	3	which	which	PRON
ejpam-6472	25	4	satisfy	satisfy	VERB
ejpam-6472	25	5	the	the	DET
ejpam-6472	25	6	superassociative	superassociative	ADJ
ejpam-6472	25	7	law	law	NOUN
ejpam-6472	25	8	,	,	PUNCT
ejpam-6472	25	9	have	have	AUX
ejpam-6472	25	10	inspired	inspire	VERB
ejpam-6472	25	11	many	many	ADJ
ejpam-6472	25	12	researchers	researcher	NOUN
ejpam-6472	25	13	to	to	PART
ejpam-6472	25	14	transform	transform	VERB
ejpam-6472	25	15	them	they	PRON
ejpam-6472	25	16	into	into	ADP
ejpam-6472	25	17	binary	binary	ADJ
ejpam-6472	25	18	operations	operation	NOUN
ejpam-6472	25	19	and	and	CCONJ
ejpam-6472	25	20	study	study	VERB
ejpam-6472	25	21	the	the	DET
ejpam-6472	25	22	semigroups	semigroup	NOUN
ejpam-6472	25	23	equipped	equip	VERB
ejpam-6472	25	24	with	with	ADP
ejpam-6472	25	25	these	these	DET
ejpam-6472	25	26	operations	operation	NOUN
ejpam-6472	25	27	.	.	PUNCT
ejpam-6472	26	1	following	follow	VERB
ejpam-6472	26	2	this	this	DET
ejpam-6472	26	3	approach	approach	NOUN
ejpam-6472	26	4	,	,	PUNCT
ejpam-6472	26	5	denecke	denecke	NOUN
ejpam-6472	26	6	and	and	CCONJ
ejpam-6472	26	7	jampachon	jampachon	ADJ
ejpam-6472	26	8	[	[	X
ejpam-6472	26	9	5	5	NUM
ejpam-6472	26	10	]	]	PUNCT
ejpam-6472	26	11	introduced	introduce	VERB
ejpam-6472	26	12	four	four	NUM
ejpam-6472	26	13	binary	binary	ADJ
ejpam-6472	26	14	operations	operation	NOUN
ejpam-6472	26	15	,	,	PUNCT
ejpam-6472	26	16	denoted	denote	VERB
ejpam-6472	26	17	by	by	ADP
ejpam-6472	26	18	+	+	ADJ
ejpam-6472	26	19	,	,	PUNCT
ejpam-6472	26	20	∗,+g	∗,+g	NOUN
ejpam-6472	26	21	,	,	PUNCT
ejpam-6472	26	22	and	and	CCONJ
ejpam-6472	26	23	∗g	∗g	NUM
ejpam-6472	26	24	,	,	PUNCT
ejpam-6472	26	25	derived	derive	VERB
ejpam-6472	26	26	from	from	ADP
ejpam-6472	26	27	the	the	DET
ejpam-6472	26	28	superposition	superposition	NOUN
ejpam-6472	26	29	sn	sn	NOUN
ejpam-6472	26	30	,	,	PUNCT
ejpam-6472	26	31	and	and	CCONJ
ejpam-6472	26	32	investigated	investigate	VERB
ejpam-6472	26	33	idempotent	idempotent	NOUN
ejpam-6472	26	34	and	and	CCONJ
ejpam-6472	26	35	regular	regular	ADJ
ejpam-6472	26	36	elements	element	NOUN
ejpam-6472	26	37	as	as	ADV
ejpam-6472	26	38	well	well	ADV
ejpam-6472	26	39	as	as	ADP
ejpam-6472	26	40	green	green	NOUN
ejpam-6472	26	41	’s	’s	PART
ejpam-6472	26	42	relations	relation	NOUN
ejpam-6472	26	43	in	in	ADP
ejpam-6472	26	44	the	the	DET
ejpam-6472	26	45	resulting	result	VERB
ejpam-6472	26	46	semigroups	semigroup	NOUN
ejpam-6472	26	47	.	.	PUNCT
ejpam-6472	27	1	similarly	similarly	ADV
ejpam-6472	27	2	,	,	PUNCT
ejpam-6472	27	3	in	in	ADP
ejpam-6472	27	4	the	the	DET
ejpam-6472	27	5	context	context	NOUN
ejpam-6472	27	6	of	of	ADP
ejpam-6472	27	7	tree	tree	NOUN
ejpam-6472	27	8	languages	language	NOUN
ejpam-6472	27	9	,	,	PUNCT
ejpam-6472	27	10	denecke	denecke	NOUN
ejpam-6472	27	11	and	and	CCONJ
ejpam-6472	27	12	sarasit	sarasit	NOUN
ejpam-6472	27	13	[	[	X
ejpam-6472	27	14	6	6	NUM
ejpam-6472	27	15	]	]	PUNCT
ejpam-6472	27	16	defined	define	VERB
ejpam-6472	27	17	a	a	DET
ejpam-6472	27	18	product	product	NOUN
ejpam-6472	27	19	of	of	ADP
ejpam-6472	27	20	tree	tree	NOUN
ejpam-6472	27	21	languages	language	NOUN
ejpam-6472	27	22	,	,	PUNCT
ejpam-6472	27	23	denoted	denote	VERB
ejpam-6472	27	24	by	by	ADP
ejpam-6472	27	25	·	·	PROPN
ejpam-6472	27	26	xi	xi	PROPN
ejpam-6472	27	27	,	,	PUNCT
ejpam-6472	27	28	which	which	PRON
ejpam-6472	27	29	is	be	AUX
ejpam-6472	27	30	a	a	DET
ejpam-6472	27	31	binary	binary	ADJ
ejpam-6472	27	32	operation	operation	NOUN
ejpam-6472	27	33	induced	induce	VERB
ejpam-6472	27	34	from	from	ADP
ejpam-6472	27	35	the	the	DET
ejpam-6472	27	36	superposition	superposition	NOUN
ejpam-6472	27	37	ŝn	ŝn	NOUN
ejpam-6472	27	38	m.	m.	NOUN
ejpam-6472	27	39	the	the	DET
ejpam-6472	27	40	binary	binary	PROPN
ejpam-6472	27	41	operation	operation	PROPN
ejpam-6472	27	42	·	·	PUNCT
ejpam-6472	27	43	xi	xi	X
ejpam-6472	27	44	can	can	AUX
ejpam-6472	27	45	also	also	ADV
ejpam-6472	27	46	be	be	AUX
ejpam-6472	27	47	restricted	restrict	VERB
ejpam-6472	27	48	to	to	ADP
ejpam-6472	27	49	the	the	DET
ejpam-6472	27	50	set	set	NOUN
ejpam-6472	27	51	of	of	ADP
ejpam-6472	27	52	terms	term	NOUN
ejpam-6472	27	53	,	,	PUNCT
ejpam-6472	27	54	as	as	SCONJ
ejpam-6472	27	55	shown	show	VERB
ejpam-6472	27	56	by	by	ADP
ejpam-6472	27	57	kumduang	kumduang	PROPN
ejpam-6472	27	58	and	and	CCONJ
ejpam-6472	27	59	leeratanavalee	leeratanavalee	NOUN
ejpam-6472	27	60	in	in	ADP
ejpam-6472	27	61	[	[	X
ejpam-6472	27	62	7	7	NUM
ejpam-6472	27	63	]	]	PUNCT
ejpam-6472	27	64	.	.	PUNCT
ejpam-6472	28	1	this	this	DET
ejpam-6472	28	2	restricted	restrict	VERB
ejpam-6472	28	3	operation	operation	NOUN
ejpam-6472	28	4	corresponds	correspond	VERB
ejpam-6472	28	5	to	to	ADP
ejpam-6472	28	6	substituting	substitute	VERB
ejpam-6472	28	7	every	every	DET
ejpam-6472	28	8	occurrence	occurrence	NOUN
ejpam-6472	28	9	of	of	ADP
ejpam-6472	28	10	the	the	DET
ejpam-6472	28	11	variable	variable	NOUN
ejpam-6472	28	12	xi	xi	X
ejpam-6472	28	13	in	in	ADP
ejpam-6472	28	14	a	a	DET
ejpam-6472	28	15	term	term	NOUN
ejpam-6472	28	16	with	with	ADP
ejpam-6472	28	17	another	another	DET
ejpam-6472	28	18	term	term	NOUN
ejpam-6472	28	19	.	.	PUNCT
ejpam-6472	29	1	in	in	ADP
ejpam-6472	29	2	a	a	DET
ejpam-6472	29	3	more	more	ADV
ejpam-6472	29	4	general	general	ADJ
ejpam-6472	29	5	approach	approach	NOUN
ejpam-6472	29	6	,	,	PUNCT
ejpam-6472	29	7	which	which	PRON
ejpam-6472	29	8	is	be	AUX
ejpam-6472	29	9	not	not	PART
ejpam-6472	29	10	limited	limit	VERB
ejpam-6472	29	11	to	to	ADP
ejpam-6472	29	12	variable	variable	ADJ
ejpam-6472	29	13	replacement	replacement	NOUN
ejpam-6472	29	14	but	but	CCONJ
ejpam-6472	29	15	also	also	ADV
ejpam-6472	29	16	extends	extend	VERB
ejpam-6472	29	17	to	to	ADP
ejpam-6472	29	18	subterm	subterm	PROPN
ejpam-6472	29	19	replacement	replacement	NOUN
ejpam-6472	29	20	,	,	PUNCT
ejpam-6472	29	21	shtrakov	shtrakov	NOUN
ejpam-6472	30	1	[	[	X
ejpam-6472	30	2	8	8	NUM
ejpam-6472	30	3	]	]	PUNCT
ejpam-6472	30	4	introduced	introduce	VERB
ejpam-6472	30	5	an	an	DET
ejpam-6472	30	6	inductive	inductive	ADJ
ejpam-6472	30	7	composition	composition	NOUN
ejpam-6472	30	8	,	,	PUNCT
ejpam-6472	30	9	a	a	DET
ejpam-6472	30	10	ternary	ternary	ADJ
ejpam-6472	30	11	operation	operation	NOUN
ejpam-6472	30	12	that	that	PRON
ejpam-6472	30	13	maps	map	VERB
ejpam-6472	30	14	a	a	DET
ejpam-6472	30	15	triple	triple	ADJ
ejpam-6472	30	16	(	(	PUNCT
ejpam-6472	30	17	t	t	PROPN
ejpam-6472	30	18	,	,	PUNCT
ejpam-6472	30	19	r	r	NOUN
ejpam-6472	30	20	,	,	PUNCT
ejpam-6472	30	21	q	q	NOUN
ejpam-6472	30	22	)	)	PUNCT
ejpam-6472	30	23	to	to	ADP
ejpam-6472	30	24	a	a	DET
ejpam-6472	30	25	term	term	NOUN
ejpam-6472	30	26	obtained	obtain	VERB
ejpam-6472	30	27	by	by	ADP
ejpam-6472	30	28	simultaneously	simultaneously	ADV
ejpam-6472	30	29	replacing	replace	VERB
ejpam-6472	30	30	every	every	DET
ejpam-6472	30	31	occurrence	occurrence	NOUN
ejpam-6472	30	32	of	of	ADP
ejpam-6472	30	33	the	the	DET
ejpam-6472	30	34	subterm	subterm	NOUN
ejpam-6472	30	35	r	r	NOUN
ejpam-6472	30	36	in	in	ADP
ejpam-6472	30	37	t	t	PROPN
ejpam-6472	30	38	with	with	ADP
ejpam-6472	30	39	q.	q.	PROPN
ejpam-6472	30	40	building	building	NOUN
ejpam-6472	30	41	on	on	ADP
ejpam-6472	30	42	this	this	PRON
ejpam-6472	30	43	,	,	PUNCT
ejpam-6472	30	44	kritpratyakul	kritpratyakul	PROPN
ejpam-6472	30	45	and	and	CCONJ
ejpam-6472	30	46	pibaljommee	pibaljommee	NOUN
ejpam-6472	31	1	[	[	X
ejpam-6472	31	2	9	9	NUM
ejpam-6472	31	3	]	]	PUNCT
ejpam-6472	31	4	defined	define	VERB
ejpam-6472	31	5	a	a	DET
ejpam-6472	31	6	binary	binary	ADJ
ejpam-6472	31	7	operation	operation	NOUN
ejpam-6472	31	8	,	,	PUNCT
ejpam-6472	31	9	called	call	VERB
ejpam-6472	31	10	the	the	DET
ejpam-6472	31	11	r	r	NOUN
ejpam-6472	31	12	-	-	PUNCT
ejpam-6472	31	13	inductive	inductive	ADJ
ejpam-6472	31	14	product	product	NOUN
ejpam-6472	31	15	and	and	CCONJ
ejpam-6472	31	16	denoted	denote	VERB
ejpam-6472	31	17	by	by	ADP
ejpam-6472	31	18	·	·	SYM
ejpam-6472	31	19	r	r	NOUN
ejpam-6472	31	20	,	,	PUNCT
ejpam-6472	31	21	by	by	ADP
ejpam-6472	31	22	fixing	fix	VERB
ejpam-6472	31	23	a	a	DET
ejpam-6472	31	24	specific	specific	ADJ
ejpam-6472	31	25	term	term	NOUN
ejpam-6472	31	26	r	r	NOUN
ejpam-6472	31	27	in	in	ADP
ejpam-6472	31	28	the	the	DET
ejpam-6472	31	29	inductive	inductive	ADJ
ejpam-6472	31	30	composition	composition	NOUN
ejpam-6472	31	31	.	.	PUNCT
ejpam-6472	32	1	unlike	unlike	ADP
ejpam-6472	32	2	other	other	ADJ
ejpam-6472	32	3	binary	binary	ADJ
ejpam-6472	32	4	operations	operation	NOUN
ejpam-6472	32	5	derived	derive	VERB
ejpam-6472	32	6	from	from	ADP
ejpam-6472	32	7	superpositions	superposition	NOUN
ejpam-6472	32	8	,	,	PUNCT
ejpam-6472	32	9	the	the	DET
ejpam-6472	32	10	r	r	NOUN
ejpam-6472	32	11	-	-	PUNCT
ejpam-6472	32	12	inductive	inductive	ADJ
ejpam-6472	32	13	product	product	NOUN
ejpam-6472	32	14	is	be	AUX
ejpam-6472	32	15	not	not	PART
ejpam-6472	32	16	associative	associative	ADJ
ejpam-6472	32	17	on	on	ADP
ejpam-6472	32	18	the	the	DET
ejpam-6472	32	19	entire	entire	ADJ
ejpam-6472	32	20	set	set	NOUN
ejpam-6472	32	21	of	of	ADP
ejpam-6472	32	22	terms	term	NOUN
ejpam-6472	32	23	,	,	PUNCT
ejpam-6472	32	24	as	as	SCONJ
ejpam-6472	32	25	demonstrated	demonstrate	VERB
ejpam-6472	32	26	by	by	ADP
ejpam-6472	32	27	kritpratyakul	kritpratyakul	PROPN
ejpam-6472	32	28	and	and	CCONJ
ejpam-6472	32	29	pibaljommee	pibaljommee	NOUN
ejpam-6472	33	1	[	[	X
ejpam-6472	33	2	9	9	NUM
ejpam-6472	33	3	]	]	PUNCT
ejpam-6472	33	4	.	.	PUNCT
ejpam-6472	34	1	however	however	ADV
ejpam-6472	34	2	,	,	PUNCT
ejpam-6472	34	3	they	they	PRON
ejpam-6472	34	4	showed	show	VERB
ejpam-6472	34	5	that	that	SCONJ
ejpam-6472	34	6	the	the	DET
ejpam-6472	34	7	operation	operation	NOUN
ejpam-6472	34	8	·	·	PUNCT
ejpam-6472	34	9	r	r	NOUN
ejpam-6472	34	10	becomes	become	VERB
ejpam-6472	34	11	associative	associative	ADJ
ejpam-6472	34	12	and	and	CCONJ
ejpam-6472	34	13	closed	close	VERB
ejpam-6472	34	14	on	on	ADP
ejpam-6472	34	15	a	a	DET
ejpam-6472	34	16	certain	certain	ADJ
ejpam-6472	34	17	subset	subset	NOUN
ejpam-6472	34	18	of	of	ADP
ejpam-6472	34	19	the	the	DET
ejpam-6472	34	20	set	set	NOUN
ejpam-6472	34	21	of	of	ADP
ejpam-6472	34	22	terms	term	NOUN
ejpam-6472	34	23	.	.	PUNCT
ejpam-6472	35	1	they	they	PRON
ejpam-6472	35	2	further	far	ADV
ejpam-6472	35	3	investigated	investigate	VERB
ejpam-6472	35	4	the	the	DET
ejpam-6472	35	5	algebraic	algebraic	ADJ
ejpam-6472	35	6	structure	structure	NOUN
ejpam-6472	35	7	of	of	ADP
ejpam-6472	35	8	the	the	DET
ejpam-6472	35	9	resulting	result	VERB
ejpam-6472	35	10	semigroup	semigroup	NOUN
ejpam-6472	35	11	,	,	PUNCT
ejpam-6472	35	12	examining	examine	VERB
ejpam-6472	35	13	properties	property	NOUN
ejpam-6472	35	14	such	such	ADJ
ejpam-6472	35	15	as	as	ADP
ejpam-6472	35	16	idempotent	idempotent	NOUN
ejpam-6472	35	17	and	and	CCONJ
ejpam-6472	35	18	regular	regular	ADJ
ejpam-6472	35	19	elements	element	NOUN
ejpam-6472	35	20	,	,	PUNCT
ejpam-6472	35	21	green	green	PROPN
ejpam-6472	35	22	’s	’s	PART
ejpam-6472	35	23	relations	relation	NOUN
ejpam-6472	35	24	,	,	PUNCT
ejpam-6472	35	25	ideals	ideal	NOUN
ejpam-6472	35	26	,	,	PUNCT
ejpam-6472	35	27	and	and	CCONJ
ejpam-6472	35	28	special	special	ADJ
ejpam-6472	35	29	substructures	substructure	NOUN
ejpam-6472	35	30	(	(	PUNCT
ejpam-6472	35	31	see	see	VERB
ejpam-6472	35	32	[	[	X
ejpam-6472	35	33	9–11	9–11	X
ejpam-6472	35	34	]	]	PUNCT
ejpam-6472	35	35	)	)	PUNCT
ejpam-6472	35	36	.	.	PUNCT
ejpam-6472	36	1	in	in	ADP
ejpam-6472	36	2	this	this	DET
ejpam-6472	36	3	paper	paper	NOUN
ejpam-6472	36	4	,	,	PUNCT
ejpam-6472	36	5	we	we	PRON
ejpam-6472	36	6	extend	extend	VERB
ejpam-6472	36	7	the	the	DET
ejpam-6472	36	8	concept	concept	NOUN
ejpam-6472	36	9	of	of	ADP
ejpam-6472	36	10	the	the	DET
ejpam-6472	36	11	r	r	NOUN
ejpam-6472	36	12	-	-	PUNCT
ejpam-6472	36	13	inductive	inductive	ADJ
ejpam-6472	36	14	product	product	NOUN
ejpam-6472	36	15	by	by	ADP
ejpam-6472	36	16	allowing	allow	VERB
ejpam-6472	36	17	two	two	NUM
ejpam-6472	36	18	specific	specific	ADJ
ejpam-6472	36	19	subterms	subterm	NOUN
ejpam-6472	36	20	to	to	PART
ejpam-6472	36	21	be	be	AUX
ejpam-6472	36	22	replaced	replace	VERB
ejpam-6472	36	23	simultaneously	simultaneously	ADV
ejpam-6472	36	24	.	.	PUNCT
ejpam-6472	37	1	the	the	DET
ejpam-6472	37	2	resulting	result	VERB
ejpam-6472	37	3	binary	binary	ADJ
ejpam-6472	37	4	operation	operation	NOUN
ejpam-6472	37	5	is	be	AUX
ejpam-6472	37	6	called	call	VERB
ejpam-6472	37	7	the	the	DET
ejpam-6472	37	8	rsinductive	rsinductive	ADJ
ejpam-6472	37	9	product	product	NOUN
ejpam-6472	37	10	and	and	CCONJ
ejpam-6472	37	11	is	be	AUX
ejpam-6472	37	12	denoted	denote	VERB
ejpam-6472	37	13	by	by	ADP
ejpam-6472	37	14	·	·	SYM
ejpam-6472	37	15	rs	rs	NOUN
ejpam-6472	37	16	,	,	PUNCT
ejpam-6472	37	17	where	where	SCONJ
ejpam-6472	37	18	r	r	NOUN
ejpam-6472	37	19	and	and	CCONJ
ejpam-6472	37	20	s	s	NOUN
ejpam-6472	37	21	are	be	AUX
ejpam-6472	37	22	the	the	DET
ejpam-6472	37	23	two	two	NUM
ejpam-6472	37	24	fixed	fix	VERB
ejpam-6472	37	25	terms	term	NOUN
ejpam-6472	37	26	.	.	PUNCT
ejpam-6472	38	1	this	this	DET
ejpam-6472	38	2	operation	operation	NOUN
ejpam-6472	38	3	generalizes	generalize	VERB
ejpam-6472	38	4	the	the	DET
ejpam-6472	38	5	binary	binary	PROPN
ejpam-6472	38	6	operation	operation	NOUN
ejpam-6472	38	7	·	·	PUNCT
ejpam-6472	38	8	ij	ij	INTJ
ejpam-6472	38	9	,	,	PUNCT
ejpam-6472	38	10	introduced	introduce	VERB
ejpam-6472	38	11	by	by	ADP
ejpam-6472	38	12	boonsol	boonsol	PROPN
ejpam-6472	38	13	et	et	PROPN
ejpam-6472	38	14	al	al	PROPN
ejpam-6472	38	15	.	.	PUNCT
ejpam-6472	39	1	[	[	X
ejpam-6472	39	2	12	12	NUM
ejpam-6472	39	3	]	]	PUNCT
ejpam-6472	39	4	on	on	ADP
ejpam-6472	39	5	the	the	DET
ejpam-6472	39	6	set	set	NOUN
ejpam-6472	39	7	of	of	ADP
ejpam-6472	39	8	tree	tree	NOUN
ejpam-6472	39	9	languages	language	NOUN
ejpam-6472	39	10	,	,	PUNCT
ejpam-6472	39	11	when	when	SCONJ
ejpam-6472	39	12	restricted	restrict	VERB
ejpam-6472	39	13	to	to	ADP
ejpam-6472	39	14	the	the	DET
ejpam-6472	39	15	set	set	NOUN
ejpam-6472	39	16	of	of	ADP
ejpam-6472	39	17	terms	term	NOUN
ejpam-6472	39	18	.	.	PUNCT
ejpam-6472	40	1	we	we	PRON
ejpam-6472	40	2	construct	construct	VERB
ejpam-6472	40	3	a	a	DET
ejpam-6472	40	4	semigroup	semigroup	NOUN
ejpam-6472	40	5	of	of	ADP
ejpam-6472	40	6	terms	term	NOUN
ejpam-6472	40	7	under	under	ADP
ejpam-6472	40	8	this	this	DET
ejpam-6472	40	9	new	new	ADJ
ejpam-6472	40	10	operation	operation	NOUN
ejpam-6472	40	11	and	and	CCONJ
ejpam-6472	40	12	investigate	investigate	VERB
ejpam-6472	40	13	its	its	PRON
ejpam-6472	40	14	algebraic	algebraic	ADJ
ejpam-6472	40	15	structure	structure	NOUN
ejpam-6472	40	16	,	,	PUNCT
ejpam-6472	40	17	focusing	focus	VERB
ejpam-6472	40	18	on	on	ADP
ejpam-6472	40	19	the	the	DET
ejpam-6472	40	20	characterization	characterization	NOUN
ejpam-6472	40	21	of	of	ADP
ejpam-6472	40	22	idempotent	idempotent	NOUN
ejpam-6472	40	23	and	and	CCONJ
ejpam-6472	40	24	regular	regular	ADJ
ejpam-6472	40	25	elements	element	NOUN
ejpam-6472	40	26	,	,	PUNCT
ejpam-6472	40	27	as	as	ADV
ejpam-6472	40	28	well	well	ADV
ejpam-6472	40	29	as	as	ADP
ejpam-6472	40	30	all	all	DET
ejpam-6472	40	31	five	five	NUM
ejpam-6472	40	32	types	type	NOUN
ejpam-6472	40	33	of	of	ADP
ejpam-6472	40	34	green	green	PROPN
ejpam-6472	40	35	’s	’s	PART
ejpam-6472	40	36	relations	relation	NOUN
ejpam-6472	40	37	.	.	PUNCT
ejpam-6472	41	1	2	2	X
ejpam-6472	41	2	.	.	X
ejpam-6472	41	3	preliminaries	preliminary	NOUN
ejpam-6472	41	4	we	we	PRON
ejpam-6472	41	5	begin	begin	VERB
ejpam-6472	41	6	by	by	ADP
ejpam-6472	41	7	recalling	recall	VERB
ejpam-6472	41	8	the	the	DET
ejpam-6472	41	9	definition	definition	NOUN
ejpam-6472	41	10	of	of	ADP
ejpam-6472	41	11	terms	term	NOUN
ejpam-6472	41	12	.	.	PUNCT
ejpam-6472	42	1	let	let	VERB
ejpam-6472	42	2	xn	xn	PUNCT
ejpam-6472	43	1	=	=	PUNCT
ejpam-6472	43	2	{	{	PUNCT
ejpam-6472	43	3	x1	x1	PROPN
ejpam-6472	43	4	,	,	PUNCT
ejpam-6472	43	5	.	.	PUNCT
ejpam-6472	43	6	.	.	PUNCT
ejpam-6472	43	7	.	.	PUNCT
ejpam-6472	44	1	,	,	PUNCT
ejpam-6472	44	2	xn	xn	X
ejpam-6472	44	3	}	}	PUNCT
ejpam-6472	44	4	be	be	AUX
ejpam-6472	44	5	a	a	DET
ejpam-6472	44	6	finite	finite	ADJ
ejpam-6472	44	7	set	set	NOUN
ejpam-6472	44	8	of	of	ADP
ejpam-6472	44	9	n	n	DET
ejpam-6472	44	10	elements	element	NOUN
ejpam-6472	44	11	,	,	PUNCT
ejpam-6472	44	12	called	call	VERB
ejpam-6472	44	13	the	the	DET
ejpam-6472	44	14	alphabet	alphabet	NOUN
ejpam-6472	44	15	,	,	PUNCT
ejpam-6472	44	16	whose	whose	DET
ejpam-6472	44	17	elements	element	NOUN
ejpam-6472	44	18	are	be	AUX
ejpam-6472	44	19	called	call	VERB
ejpam-6472	44	20	variables	variable	NOUN
ejpam-6472	44	21	.	.	PUNCT
ejpam-6472	45	1	let	let	VERB
ejpam-6472	45	2	{	{	PUNCT
ejpam-6472	45	3	fi	fi	NOUN
ejpam-6472	46	1	|	|	INTJ
ejpam-6472	46	2	i	i	PRON
ejpam-6472	46	3	∈	∈	PROPN
ejpam-6472	46	4	i	i	PRON
ejpam-6472	46	5	}	}	PUNCT
ejpam-6472	46	6	be	be	VERB
ejpam-6472	46	7	a	a	DET
ejpam-6472	46	8	set	set	NOUN
ejpam-6472	46	9	of	of	ADP
ejpam-6472	46	10	operation	operation	NOUN
ejpam-6472	46	11	symbols	symbol	NOUN
ejpam-6472	46	12	,	,	PUNCT
ejpam-6472	46	13	where	where	SCONJ
ejpam-6472	46	14	i	i	PRON
ejpam-6472	46	15	is	be	AUX
ejpam-6472	46	16	a	a	DET
ejpam-6472	46	17	non	non	ADJ
ejpam-6472	46	18	-	-	ADJ
ejpam-6472	46	19	empty	empty	ADJ
ejpam-6472	46	20	index	index	NOUN
ejpam-6472	46	21	set	set	NOUN
ejpam-6472	46	22	,	,	PUNCT
ejpam-6472	46	23	and	and	CCONJ
ejpam-6472	46	24	assume	assume	VERB
ejpam-6472	46	25	that	that	SCONJ
ejpam-6472	46	26	{	{	PUNCT
ejpam-6472	46	27	fi	fi	NOUN
ejpam-6472	46	28	|	|	INTJ
ejpam-6472	46	29	i	i	PRON
ejpam-6472	46	30	∈	∈	VERB
ejpam-6472	46	31	i	i	X
ejpam-6472	46	32	}	}	PUNCT
ejpam-6472	46	33	and	and	CCONJ
ejpam-6472	46	34	xn	xn	PROPN
ejpam-6472	46	35	are	be	AUX
ejpam-6472	46	36	disjoint	disjoint	ADJ
ejpam-6472	46	37	.	.	PUNCT
ejpam-6472	47	1	for	for	ADP
ejpam-6472	47	2	each	each	DET
ejpam-6472	47	3	fi	fi	NOUN
ejpam-6472	47	4	,	,	PUNCT
ejpam-6472	47	5	we	we	PRON
ejpam-6472	47	6	assign	assign	VERB
ejpam-6472	47	7	a	a	DET
ejpam-6472	47	8	positive	positive	ADJ
ejpam-6472	47	9	integer	integer	NOUN
ejpam-6472	47	10	ni	ni	PROPN
ejpam-6472	47	11	,	,	PUNCT
ejpam-6472	47	12	called	call	VERB
ejpam-6472	47	13	the	the	DET
ejpam-6472	47	14	arity	arity	NOUN
ejpam-6472	47	15	of	of	ADP
ejpam-6472	47	16	fi	fi	PROPN
ejpam-6472	47	17	.	.	PUNCT
ejpam-6472	48	1	the	the	DET
ejpam-6472	48	2	sequence	sequence	NOUN
ejpam-6472	48	3	τ	τ	X
ejpam-6472	48	4	=	=	SYM
ejpam-6472	48	5	(	(	PUNCT
ejpam-6472	48	6	ni)i∈i	ni)i∈i	NUM
ejpam-6472	48	7	is	be	AUX
ejpam-6472	48	8	called	call	VERB
ejpam-6472	48	9	the	the	DET
ejpam-6472	48	10	type	type	NOUN
ejpam-6472	48	11	.	.	PUNCT
ejpam-6472	49	1	the	the	DET
ejpam-6472	49	2	n	n	NUM
ejpam-6472	49	3	-	-	PUNCT
ejpam-6472	49	4	ary	ary	PROPN
ejpam-6472	49	5	terms	term	NOUN
ejpam-6472	49	6	of	of	ADP
ejpam-6472	49	7	type	type	NOUN
ejpam-6472	49	8	τ	τ	PROPN
ejpam-6472	49	9	are	be	AUX
ejpam-6472	49	10	inductively	inductively	ADV
ejpam-6472	49	11	defined	define	VERB
ejpam-6472	49	12	as	as	SCONJ
ejpam-6472	49	13	follows	follow	VERB
ejpam-6472	49	14	.	.	PUNCT
ejpam-6472	50	1	(	(	PUNCT
ejpam-6472	50	2	i	i	NOUN
ejpam-6472	50	3	)	)	PUNCT
ejpam-6472	50	4	every	every	DET
ejpam-6472	50	5	variable	variable	NOUN
ejpam-6472	50	6	xi	xi	X
ejpam-6472	50	7	is	be	AUX
ejpam-6472	50	8	an	an	DET
ejpam-6472	50	9	n	n	CCONJ
ejpam-6472	50	10	-	-	PUNCT
ejpam-6472	50	11	ary	ary	NOUN
ejpam-6472	50	12	term	term	NOUN
ejpam-6472	50	13	of	of	ADP
ejpam-6472	50	14	type	type	NOUN
ejpam-6472	50	15	τ	τ	PROPN
ejpam-6472	50	16	.	.	PUNCT
ejpam-6472	51	1	p.	p.	PROPN
ejpam-6472	51	2	prachumdang	prachumdang	PROPN
ejpam-6472	51	3	,	,	PUNCT
ejpam-6472	51	4	b.	b.	PROPN
ejpam-6472	51	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	51	6	/	/	SYM
ejpam-6472	51	7	eur	eur	PROPN
ejpam-6472	51	8	.	.	PUNCT
ejpam-6472	52	1	j.	j.	PROPN
ejpam-6472	52	2	pure	pure	PROPN
ejpam-6472	52	3	appl	appl	PROPN
ejpam-6472	52	4	.	.	PROPN
ejpam-6472	52	5	math	math	PROPN
ejpam-6472	52	6	,	,	PUNCT
ejpam-6472	52	7	18	18	NUM
ejpam-6472	52	8	(	(	PUNCT
ejpam-6472	52	9	3	3	NUM
ejpam-6472	52	10	)	)	PUNCT
ejpam-6472	52	11	(	(	PUNCT
ejpam-6472	52	12	2025	2025	NUM
ejpam-6472	52	13	)	)	PUNCT
ejpam-6472	52	14	,	,	PUNCT
ejpam-6472	52	15	6472	6472	NUM
ejpam-6472	52	16	3	3	NUM
ejpam-6472	52	17	of	of	ADP
ejpam-6472	52	18	16	16	NUM
ejpam-6472	52	19	(	(	PUNCT
ejpam-6472	52	20	ii	ii	NOUN
ejpam-6472	52	21	)	)	PUNCT
ejpam-6472	52	22	if	if	SCONJ
ejpam-6472	52	23	t1	t1	PROPN
ejpam-6472	52	24	,	,	PUNCT
ejpam-6472	52	25	.	.	PUNCT
ejpam-6472	52	26	.	.	PUNCT
ejpam-6472	53	1	.	.	PUNCT
ejpam-6472	54	1	,	,	PUNCT
ejpam-6472	54	2	tni	tni	NOUN
ejpam-6472	54	3	are	be	AUX
ejpam-6472	54	4	n	n	PRON
ejpam-6472	54	5	-	-	PUNCT
ejpam-6472	54	6	ary	ary	NOUN
ejpam-6472	54	7	terms	term	NOUN
ejpam-6472	54	8	of	of	ADP
ejpam-6472	54	9	type	type	NOUN
ejpam-6472	54	10	τ	τ	PROPN
ejpam-6472	54	11	and	and	CCONJ
ejpam-6472	54	12	fi	fi	NOUN
ejpam-6472	54	13	is	be	AUX
ejpam-6472	54	14	an	an	DET
ejpam-6472	54	15	operation	operation	NOUN
ejpam-6472	54	16	symbol	symbol	NOUN
ejpam-6472	54	17	of	of	ADP
ejpam-6472	54	18	arity	arity	NOUN
ejpam-6472	54	19	ni	ni	PROPN
ejpam-6472	54	20	,	,	PUNCT
ejpam-6472	54	21	then	then	ADV
ejpam-6472	54	22	fi(t1	fi(t1	NOUN
ejpam-6472	54	23	,	,	PUNCT
ejpam-6472	54	24	.	.	PUNCT
ejpam-6472	54	25	.	.	PUNCT
ejpam-6472	55	1	.	.	PUNCT
ejpam-6472	56	1	,	,	PUNCT
ejpam-6472	56	2	tni	tni	NOUN
ejpam-6472	56	3	)	)	PUNCT
ejpam-6472	56	4	is	be	AUX
ejpam-6472	56	5	an	an	DET
ejpam-6472	56	6	n	n	CCONJ
ejpam-6472	56	7	-	-	PUNCT
ejpam-6472	56	8	ary	ary	NOUN
ejpam-6472	56	9	term	term	NOUN
ejpam-6472	56	10	of	of	ADP
ejpam-6472	56	11	type	type	NOUN
ejpam-6472	56	12	τ	τ	PROPN
ejpam-6472	56	13	.	.	PUNCT
ejpam-6472	57	1	(	(	PUNCT
ejpam-6472	57	2	iii	iii	X
ejpam-6472	57	3	)	)	PUNCT
ejpam-6472	57	4	the	the	DET
ejpam-6472	57	5	set	set	VERB
ejpam-6472	57	6	wτ	wτ	PROPN
ejpam-6472	57	7	(	(	PUNCT
ejpam-6472	57	8	xn	xn	PROPN
ejpam-6472	57	9	)	)	PUNCT
ejpam-6472	57	10	of	of	ADP
ejpam-6472	57	11	all	all	DET
ejpam-6472	57	12	n	n	CCONJ
ejpam-6472	57	13	-	-	PUNCT
ejpam-6472	57	14	ary	ary	PROPN
ejpam-6472	57	15	terms	term	NOUN
ejpam-6472	57	16	is	be	AUX
ejpam-6472	57	17	the	the	DET
ejpam-6472	57	18	smallest	small	ADJ
ejpam-6472	57	19	set	set	NOUN
ejpam-6472	57	20	containing	contain	VERB
ejpam-6472	57	21	x1	x1	PROPN
ejpam-6472	57	22	,	,	PUNCT
ejpam-6472	57	23	.	.	PUNCT
ejpam-6472	57	24	.	.	PUNCT
ejpam-6472	58	1	.	.	PUNCT
ejpam-6472	59	1	,	,	PUNCT
ejpam-6472	59	2	xn	xn	PROPN
ejpam-6472	59	3	,	,	PUNCT
ejpam-6472	59	4	and	and	CCONJ
ejpam-6472	59	5	closed	close	VERB
ejpam-6472	59	6	under	under	ADP
ejpam-6472	59	7	finite	finite	ADJ
ejpam-6472	59	8	applications	application	NOUN
ejpam-6472	59	9	of	of	ADP
ejpam-6472	59	10	(	(	PUNCT
ejpam-6472	59	11	ii	ii	NOUN
ejpam-6472	59	12	)	)	PUNCT
ejpam-6472	59	13	.	.	PUNCT
ejpam-6472	60	1	as	as	SCONJ
ejpam-6472	60	2	subterm	subterm	NOUN
ejpam-6472	60	3	replacement	replacement	NOUN
ejpam-6472	60	4	plays	play	VERB
ejpam-6472	60	5	a	a	DET
ejpam-6472	60	6	crucial	crucial	ADJ
ejpam-6472	60	7	role	role	NOUN
ejpam-6472	60	8	in	in	ADP
ejpam-6472	60	9	our	our	PRON
ejpam-6472	60	10	study	study	NOUN
ejpam-6472	60	11	,	,	PUNCT
ejpam-6472	60	12	we	we	PRON
ejpam-6472	60	13	now	now	ADV
ejpam-6472	60	14	recall	recall	VERB
ejpam-6472	60	15	the	the	DET
ejpam-6472	60	16	formal	formal	ADJ
ejpam-6472	60	17	definition	definition	NOUN
ejpam-6472	60	18	of	of	ADP
ejpam-6472	60	19	subterms	subterm	NOUN
ejpam-6472	60	20	.	.	PUNCT
ejpam-6472	61	1	this	this	DET
ejpam-6472	61	2	notion	notion	NOUN
ejpam-6472	61	3	appears	appear	VERB
ejpam-6472	61	4	in	in	ADP
ejpam-6472	61	5	several	several	ADJ
ejpam-6472	61	6	works	work	NOUN
ejpam-6472	61	7	(	(	PUNCT
ejpam-6472	61	8	see	see	VERB
ejpam-6472	61	9	,	,	PUNCT
ejpam-6472	61	10	e.g.	e.g.	ADV
ejpam-6472	61	11	,	,	PUNCT
ejpam-6472	61	12	[	[	X
ejpam-6472	61	13	8	8	NUM
ejpam-6472	61	14	,	,	PUNCT
ejpam-6472	61	15	9	9	NUM
ejpam-6472	61	16	]	]	PUNCT
ejpam-6472	61	17	)	)	PUNCT
ejpam-6472	61	18	.	.	PUNCT
ejpam-6472	62	1	let	let	VERB
ejpam-6472	62	2	t	t	PROPN
ejpam-6472	62	3	∈	∈	PROPN
ejpam-6472	62	4	wτ	wτ	PROPN
ejpam-6472	62	5	(	(	PUNCT
ejpam-6472	62	6	xn	xn	PROPN
ejpam-6472	62	7	)	)	PUNCT
ejpam-6472	62	8	.	.	PUNCT
ejpam-6472	63	1	the	the	DET
ejpam-6472	63	2	set	set	NOUN
ejpam-6472	63	3	of	of	ADP
ejpam-6472	63	4	subterms	subterm	NOUN
ejpam-6472	63	5	of	of	ADP
ejpam-6472	63	6	t	t	PROPN
ejpam-6472	63	7	,	,	PUNCT
ejpam-6472	63	8	denoted	denote	VERB
ejpam-6472	63	9	by	by	ADP
ejpam-6472	63	10	sub(t	sub(t	PROPN
ejpam-6472	63	11	)	)	PUNCT
ejpam-6472	63	12	,	,	PUNCT
ejpam-6472	63	13	is	be	AUX
ejpam-6472	63	14	defined	define	VERB
ejpam-6472	63	15	inductively	inductively	ADV
ejpam-6472	63	16	as	as	SCONJ
ejpam-6472	63	17	follows	follow	VERB
ejpam-6472	63	18	:	:	PUNCT
ejpam-6472	63	19	(	(	PUNCT
ejpam-6472	63	20	i	i	NOUN
ejpam-6472	63	21	)	)	PUNCT
ejpam-6472	63	22	if	if	SCONJ
ejpam-6472	63	23	t	t	PROPN
ejpam-6472	63	24	∈	∈	PROPN
ejpam-6472	63	25	xn	xn	PROPN
ejpam-6472	63	26	,	,	PUNCT
ejpam-6472	63	27	then	then	ADV
ejpam-6472	63	28	sub(t	sub(t	PROPN
ejpam-6472	63	29	)	)	PUNCT
ejpam-6472	64	1	=	=	PRON
ejpam-6472	64	2	{	{	PUNCT
ejpam-6472	64	3	t	t	PROPN
ejpam-6472	64	4	}	}	PUNCT
ejpam-6472	64	5	;	;	PUNCT
ejpam-6472	64	6	(	(	PUNCT
ejpam-6472	64	7	ii	ii	NOUN
ejpam-6472	64	8	)	)	PUNCT
ejpam-6472	64	9	if	if	SCONJ
ejpam-6472	64	10	t	t	NOUN
ejpam-6472	64	11	=	=	SYM
ejpam-6472	64	12	fi(t1	fi(t1	NOUN
ejpam-6472	64	13	,	,	PUNCT
ejpam-6472	64	14	.	.	PUNCT
ejpam-6472	64	15	.	.	PUNCT
ejpam-6472	65	1	.	.	PUNCT
ejpam-6472	66	1	,	,	PUNCT
ejpam-6472	66	2	tni	tni	NOUN
ejpam-6472	66	3	)	)	PUNCT
ejpam-6472	66	4	,	,	PUNCT
ejpam-6472	66	5	then	then	ADV
ejpam-6472	66	6	sub(t	sub(t	PROPN
ejpam-6472	66	7	)	)	PUNCT
ejpam-6472	66	8	=	=	PRON
ejpam-6472	66	9	{	{	PUNCT
ejpam-6472	66	10	t	t	NOUN
ejpam-6472	66	11	}	}	PUNCT
ejpam-6472	66	12	∪	∪	ADJ
ejpam-6472	66	13	sub(t1	sub(t1	NOUN
ejpam-6472	66	14	)	)	PUNCT
ejpam-6472	66	15	∪	∪	X
ejpam-6472	66	16	·	·	PUNCT
ejpam-6472	66	17	·	·	PUNCT
ejpam-6472	66	18	·	·	PUNCT
ejpam-6472	66	19	∪	∪	ADP
ejpam-6472	66	20	sub(tni	sub(tni	NOUN
ejpam-6472	66	21	)	)	PUNCT
ejpam-6472	66	22	.	.	PUNCT
ejpam-6472	67	1	for	for	ADP
ejpam-6472	67	2	r	r	PROPN
ejpam-6472	67	3	,	,	PUNCT
ejpam-6472	67	4	t	t	PROPN
ejpam-6472	67	5	∈	∈	PROPN
ejpam-6472	67	6	wτ	wτ	PROPN
ejpam-6472	67	7	(	(	PUNCT
ejpam-6472	67	8	xn	xn	PROPN
ejpam-6472	67	9	)	)	PUNCT
ejpam-6472	67	10	,	,	PUNCT
ejpam-6472	67	11	let	let	VERB
ejpam-6472	67	12	nr(t	nr(t	NOUN
ejpam-6472	67	13	)	)	PUNCT
ejpam-6472	67	14	denote	denote	VERB
ejpam-6472	67	15	the	the	DET
ejpam-6472	67	16	number	number	NOUN
ejpam-6472	67	17	of	of	ADP
ejpam-6472	67	18	occurrences	occurrence	NOUN
ejpam-6472	67	19	of	of	ADP
ejpam-6472	67	20	r	r	NOUN
ejpam-6472	67	21	in	in	ADP
ejpam-6472	67	22	t.	t.	PROPN
ejpam-6472	67	23	this	this	DET
ejpam-6472	67	24	notion	notion	NOUN
ejpam-6472	67	25	was	be	AUX
ejpam-6472	67	26	introduced	introduce	VERB
ejpam-6472	67	27	in	in	ADP
ejpam-6472	67	28	[	[	X
ejpam-6472	67	29	9	9	NUM
ejpam-6472	67	30	]	]	PUNCT
ejpam-6472	67	31	.	.	PUNCT
ejpam-6472	68	1	it	it	PRON
ejpam-6472	68	2	is	be	AUX
ejpam-6472	68	3	defined	define	VERB
ejpam-6472	68	4	inductively	inductively	ADV
ejpam-6472	68	5	as	as	SCONJ
ejpam-6472	68	6	follows	follow	VERB
ejpam-6472	68	7	:	:	PUNCT
ejpam-6472	68	8	(	(	PUNCT
ejpam-6472	68	9	i	i	NOUN
ejpam-6472	68	10	)	)	PUNCT
ejpam-6472	68	11	nr(t	nr(t	PUNCT
ejpam-6472	68	12	)	)	PUNCT
ejpam-6472	69	1	=	=	SYM
ejpam-6472	69	2	0	0	PUNCT
ejpam-6472	70	1	if	if	SCONJ
ejpam-6472	70	2	r	r	NOUN
ejpam-6472	70	3	/∈	/∈	SYM
ejpam-6472	70	4	sub(t	sub(t	PROPN
ejpam-6472	70	5	)	)	PUNCT
ejpam-6472	70	6	;	;	PUNCT
ejpam-6472	70	7	(	(	PUNCT
ejpam-6472	70	8	ii	ii	NOUN
ejpam-6472	70	9	)	)	PUNCT
ejpam-6472	70	10	nr(t	nr(t	PUNCT
ejpam-6472	70	11	)	)	PUNCT
ejpam-6472	70	12	=	=	SYM
ejpam-6472	70	13	1	1	NUM
ejpam-6472	70	14	if	if	SCONJ
ejpam-6472	70	15	r	r	NOUN
ejpam-6472	70	16	=	=	SYM
ejpam-6472	70	17	t	t	PROPN
ejpam-6472	70	18	;	;	PUNCT
ejpam-6472	70	19	(	(	PUNCT
ejpam-6472	70	20	iii	iii	NOUN
ejpam-6472	70	21	)	)	PUNCT
ejpam-6472	70	22	nr(t	nr(t	NUM
ejpam-6472	70	23	)	)	PUNCT
ejpam-6472	70	24	=	=	SYM
ejpam-6472	70	25	∑ni	∑ni	VERB
ejpam-6472	70	26	j=1	j=1	PROPN
ejpam-6472	70	27	nr(tj	nr(tj	PROPN
ejpam-6472	70	28	)	)	PUNCT
ejpam-6472	71	1	if	if	SCONJ
ejpam-6472	71	2	t	t	NOUN
ejpam-6472	71	3	=	=	SYM
ejpam-6472	71	4	fi(t1	fi(t1	NOUN
ejpam-6472	71	5	,	,	PUNCT
ejpam-6472	71	6	.	.	PUNCT
ejpam-6472	71	7	.	.	PUNCT
ejpam-6472	72	1	.	.	PUNCT
ejpam-6472	73	1	,	,	PUNCT
ejpam-6472	73	2	tni	tni	NOUN
ejpam-6472	73	3	)	)	PUNCT
ejpam-6472	73	4	and	and	CCONJ
ejpam-6472	73	5	r	r	NOUN
ejpam-6472	73	6	∈	∈	PROPN
ejpam-6472	73	7	sub(t	sub(t	PROPN
ejpam-6472	73	8	)	)	PUNCT
ejpam-6472	73	9	\	\	PROPN
ejpam-6472	73	10	{	{	PUNCT
ejpam-6472	73	11	t	t	NOUN
ejpam-6472	73	12	}	}	PUNCT
ejpam-6472	73	13	.	.	PUNCT
ejpam-6472	74	1	to	to	PART
ejpam-6472	74	2	investigate	investigate	VERB
ejpam-6472	74	3	the	the	DET
ejpam-6472	74	4	structure	structure	NOUN
ejpam-6472	74	5	of	of	ADP
ejpam-6472	74	6	terms	term	NOUN
ejpam-6472	74	7	,	,	PUNCT
ejpam-6472	74	8	various	various	ADJ
ejpam-6472	74	9	measures	measure	NOUN
ejpam-6472	74	10	have	have	AUX
ejpam-6472	74	11	been	be	AUX
ejpam-6472	74	12	introduced	introduce	VERB
ejpam-6472	74	13	,	,	PUNCT
ejpam-6472	74	14	one	one	NUM
ejpam-6472	74	15	of	of	ADP
ejpam-6472	74	16	which	which	PRON
ejpam-6472	74	17	is	be	AUX
ejpam-6472	74	18	the	the	DET
ejpam-6472	74	19	operation	operation	NOUN
ejpam-6472	74	20	-	-	PUNCT
ejpam-6472	74	21	symbol	symbol	NOUN
ejpam-6472	74	22	count	count	NOUN
ejpam-6472	74	23	.	.	PUNCT
ejpam-6472	75	1	for	for	ADP
ejpam-6472	75	2	t	t	PROPN
ejpam-6472	75	3	∈	∈	PROPN
ejpam-6472	75	4	wτ	wτ	PROPN
ejpam-6472	75	5	(	(	PUNCT
ejpam-6472	75	6	xn	xn	PROPN
ejpam-6472	75	7	)	)	PUNCT
ejpam-6472	75	8	,	,	PUNCT
ejpam-6472	75	9	the	the	DET
ejpam-6472	75	10	operation	operation	NOUN
ejpam-6472	75	11	-	-	PUNCT
ejpam-6472	75	12	symbol	symbol	NOUN
ejpam-6472	75	13	count	count	NOUN
ejpam-6472	75	14	of	of	ADP
ejpam-6472	75	15	t	t	PROPN
ejpam-6472	75	16	,	,	PUNCT
ejpam-6472	75	17	denoted	denote	VERB
ejpam-6472	75	18	by	by	ADP
ejpam-6472	75	19	op(t	op(t	NOUN
ejpam-6472	75	20	)	)	PUNCT
ejpam-6472	75	21	,	,	PUNCT
ejpam-6472	75	22	is	be	AUX
ejpam-6472	75	23	defined	define	VERB
ejpam-6472	75	24	inductively	inductively	ADV
ejpam-6472	75	25	as	as	SCONJ
ejpam-6472	75	26	follows	follow	VERB
ejpam-6472	75	27	:	:	PUNCT
ejpam-6472	75	28	(	(	PUNCT
ejpam-6472	75	29	i	i	NOUN
ejpam-6472	75	30	)	)	PUNCT
ejpam-6472	75	31	op(t	op(t	NOUN
ejpam-6472	75	32	)	)	PUNCT
ejpam-6472	76	1	=	=	SYM
ejpam-6472	76	2	0	0	PUNCT
ejpam-6472	77	1	if	if	SCONJ
ejpam-6472	77	2	t	t	PROPN
ejpam-6472	77	3	∈	∈	PROPN
ejpam-6472	77	4	xn	xn	PROPN
ejpam-6472	77	5	;	;	PUNCT
ejpam-6472	77	6	(	(	PUNCT
ejpam-6472	77	7	ii	ii	NOUN
ejpam-6472	77	8	)	)	PUNCT
ejpam-6472	77	9	op(t	op(t	NOUN
ejpam-6472	77	10	)	)	PUNCT
ejpam-6472	77	11	=	=	SYM
ejpam-6472	77	12	1	1	NUM
ejpam-6472	77	13	+	+	NUM
ejpam-6472	77	14	ni∑	ni∑	NOUN
ejpam-6472	77	15	j=1	j=1	ADJ
ejpam-6472	77	16	op(tj	op(tj	PROPN
ejpam-6472	77	17	)	)	PUNCT
ejpam-6472	77	18	if	if	SCONJ
ejpam-6472	77	19	t	t	NOUN
ejpam-6472	77	20	=	=	SYM
ejpam-6472	77	21	fi(t1	fi(t1	NOUN
ejpam-6472	77	22	,	,	PUNCT
ejpam-6472	77	23	.	.	PUNCT
ejpam-6472	77	24	.	.	PUNCT
ejpam-6472	78	1	.	.	PUNCT
ejpam-6472	79	1	,	,	PUNCT
ejpam-6472	79	2	tni	tni	NOUN
ejpam-6472	79	3	)	)	PUNCT
ejpam-6472	79	4	.	.	PUNCT
ejpam-6472	80	1	we	we	PRON
ejpam-6472	80	2	refer	refer	VERB
ejpam-6472	80	3	the	the	DET
ejpam-6472	80	4	readers	reader	NOUN
ejpam-6472	80	5	to	to	ADP
ejpam-6472	80	6	[	[	X
ejpam-6472	80	7	13	13	NUM
ejpam-6472	80	8	]	]	PUNCT
ejpam-6472	80	9	for	for	ADP
ejpam-6472	80	10	further	further	ADJ
ejpam-6472	80	11	discussion	discussion	NOUN
ejpam-6472	80	12	on	on	ADP
ejpam-6472	80	13	term	term	NOUN
ejpam-6472	80	14	complexity	complexity	NOUN
ejpam-6472	80	15	measures	measure	NOUN
ejpam-6472	80	16	.	.	PUNCT
ejpam-6472	81	1	it	it	PRON
ejpam-6472	81	2	is	be	AUX
ejpam-6472	81	3	easy	easy	ADJ
ejpam-6472	81	4	to	to	PART
ejpam-6472	81	5	see	see	VERB
ejpam-6472	81	6	that	that	SCONJ
ejpam-6472	81	7	if	if	SCONJ
ejpam-6472	81	8	a	a	DET
ejpam-6472	81	9	term	term	NOUN
ejpam-6472	81	10	t	t	PROPN
ejpam-6472	81	11	∈	∈	PROPN
ejpam-6472	81	12	sub(q	sub(q	PROPN
ejpam-6472	81	13	)	)	PUNCT
ejpam-6472	81	14	,	,	PUNCT
ejpam-6472	81	15	then	then	ADV
ejpam-6472	81	16	op(t	op(t	NOUN
ejpam-6472	81	17	)	)	PUNCT
ejpam-6472	81	18	≤	≤	NOUN
ejpam-6472	81	19	op(q	op(q	NOUN
ejpam-6472	81	20	)	)	PUNCT
ejpam-6472	81	21	.	.	PUNCT
ejpam-6472	82	1	moreover	moreover	ADV
ejpam-6472	82	2	,	,	PUNCT
ejpam-6472	82	3	if	if	SCONJ
ejpam-6472	82	4	t	t	PROPN
ejpam-6472	82	5	̸=	̸=	PROPN
ejpam-6472	82	6	q	q	NOUN
ejpam-6472	82	7	,	,	PUNCT
ejpam-6472	82	8	then	then	ADV
ejpam-6472	82	9	op(t	op(t	NOUN
ejpam-6472	82	10	)	)	PUNCT
ejpam-6472	82	11	<	<	X
ejpam-6472	82	12	op(q	op(q	NOUN
ejpam-6472	82	13	)	)	PUNCT
ejpam-6472	82	14	.	.	PUNCT
ejpam-6472	83	1	3	3	X
ejpam-6472	83	2	.	.	X
ejpam-6472	83	3	the	the	DET
ejpam-6472	83	4	rs	rs	ADJ
ejpam-6472	83	5	-	-	PUNCT
ejpam-6472	83	6	inductive	inductive	ADJ
ejpam-6472	83	7	product	product	NOUN
ejpam-6472	83	8	we	we	PRON
ejpam-6472	83	9	define	define	VERB
ejpam-6472	83	10	a	a	DET
ejpam-6472	83	11	binary	binary	ADJ
ejpam-6472	83	12	operation	operation	NOUN
ejpam-6472	83	13	,	,	PUNCT
ejpam-6472	83	14	called	call	VERB
ejpam-6472	83	15	rs	r	VERB
ejpam-6472	83	16	-	-	PUNCT
ejpam-6472	83	17	inductive	inductive	ADJ
ejpam-6472	83	18	product	product	NOUN
ejpam-6472	83	19	on	on	ADP
ejpam-6472	83	20	the	the	DET
ejpam-6472	83	21	set	set	NOUN
ejpam-6472	83	22	of	of	ADP
ejpam-6472	83	23	terms	term	NOUN
ejpam-6472	83	24	wτ	wτ	INTJ
ejpam-6472	83	25	(	(	PUNCT
ejpam-6472	83	26	xn	xn	PROPN
ejpam-6472	83	27	)	)	PUNCT
ejpam-6472	83	28	,	,	PUNCT
ejpam-6472	83	29	which	which	PRON
ejpam-6472	83	30	extends	extend	VERB
ejpam-6472	83	31	the	the	DET
ejpam-6472	83	32	r	r	NOUN
ejpam-6472	83	33	-	-	PUNCT
ejpam-6472	83	34	inductive	inductive	ADJ
ejpam-6472	83	35	product	product	NOUN
ejpam-6472	83	36	by	by	ADP
ejpam-6472	83	37	allowing	allow	VERB
ejpam-6472	83	38	the	the	DET
ejpam-6472	83	39	simultaneous	simultaneous	ADJ
ejpam-6472	83	40	replacement	replacement	NOUN
ejpam-6472	83	41	of	of	ADP
ejpam-6472	83	42	two	two	NUM
ejpam-6472	83	43	fixed	fix	VERB
ejpam-6472	83	44	subterms	subterm	NOUN
ejpam-6472	83	45	within	within	ADP
ejpam-6472	83	46	a	a	DET
ejpam-6472	83	47	given	give	VERB
ejpam-6472	83	48	term	term	NOUN
ejpam-6472	83	49	.	.	PUNCT
ejpam-6472	84	1	definition	definition	NOUN
ejpam-6472	84	2	1	1	NUM
ejpam-6472	84	3	.	.	PUNCT
ejpam-6472	85	1	let	let	VERB
ejpam-6472	85	2	r	r	NOUN
ejpam-6472	85	3	,	,	PUNCT
ejpam-6472	85	4	s	s	NOUN
ejpam-6472	85	5	∈	∈	PROPN
ejpam-6472	85	6	wτ	wτ	NOUN
ejpam-6472	85	7	(	(	PUNCT
ejpam-6472	85	8	xn	xn	X
ejpam-6472	85	9	)	)	PUNCT
ejpam-6472	85	10	be	be	AUX
ejpam-6472	85	11	fixed	fix	VERB
ejpam-6472	85	12	terms	term	NOUN
ejpam-6472	85	13	and	and	CCONJ
ejpam-6472	85	14	let	let	VERB
ejpam-6472	85	15	t	t	PROPN
ejpam-6472	85	16	,	,	PUNCT
ejpam-6472	85	17	q	q	PROPN
ejpam-6472	85	18	∈	∈	PROPN
ejpam-6472	85	19	wτ	wτ	NOUN
ejpam-6472	85	20	(	(	PUNCT
ejpam-6472	85	21	xn	xn	PROPN
ejpam-6472	85	22	)	)	PUNCT
ejpam-6472	85	23	.	.	PUNCT
ejpam-6472	86	1	the	the	DET
ejpam-6472	86	2	binary	binary	PROPN
ejpam-6472	86	3	operation	operation	NOUN
ejpam-6472	86	4	rs	rs	ADJ
ejpam-6472	86	5	-	-	PUNCT
ejpam-6472	86	6	inductive	inductive	ADJ
ejpam-6472	86	7	product	product	NOUN
ejpam-6472	86	8	,	,	PUNCT
ejpam-6472	86	9	denoted	denote	VERB
ejpam-6472	86	10	by	by	ADP
ejpam-6472	86	11	·	·	SYM
ejpam-6472	86	12	rs	rs	NOUN
ejpam-6472	86	13	,	,	PUNCT
ejpam-6472	86	14	is	be	AUX
ejpam-6472	86	15	inductively	inductively	ADV
ejpam-6472	86	16	defined	define	VERB
ejpam-6472	86	17	as	as	SCONJ
ejpam-6472	86	18	follows	follow	VERB
ejpam-6472	86	19	:	:	PUNCT
ejpam-6472	86	20	(	(	PUNCT
ejpam-6472	86	21	i	i	NOUN
ejpam-6472	86	22	)	)	PUNCT
ejpam-6472	86	23	t	t	PROPN
ejpam-6472	86	24	·	·	PUNCT
ejpam-6472	86	25	rs	rs	NOUN
ejpam-6472	86	26	q	q	PROPN
ejpam-6472	87	1	=	=	PUNCT
ejpam-6472	87	2	t	t	NOUN
ejpam-6472	87	3	if	if	SCONJ
ejpam-6472	87	4	{	{	PUNCT
ejpam-6472	87	5	r	r	NOUN
ejpam-6472	87	6	,	,	PUNCT
ejpam-6472	87	7	s	s	NOUN
ejpam-6472	87	8	}	}	PUNCT
ejpam-6472	87	9	∩	∩	ADJ
ejpam-6472	87	10	sub(t	sub(t	NOUN
ejpam-6472	87	11	)	)	PUNCT
ejpam-6472	87	12	=	=	SYM
ejpam-6472	87	13	∅	∅	NOUN
ejpam-6472	87	14	;	;	PUNCT
ejpam-6472	87	15	(	(	PUNCT
ejpam-6472	87	16	ii	ii	NOUN
ejpam-6472	87	17	)	)	PUNCT
ejpam-6472	87	18	t	t	PROPN
ejpam-6472	87	19	·	·	PUNCT
ejpam-6472	87	20	rs	rs	NOUN
ejpam-6472	87	21	q	q	NOUN
ejpam-6472	88	1	=	=	PUNCT
ejpam-6472	88	2	q	q	NOUN
ejpam-6472	89	1	if	if	SCONJ
ejpam-6472	89	2	t	t	PROPN
ejpam-6472	89	3	∈	∈	PROPN
ejpam-6472	89	4	{	{	PUNCT
ejpam-6472	89	5	r	r	NOUN
ejpam-6472	89	6	,	,	PUNCT
ejpam-6472	89	7	s	s	PART
ejpam-6472	89	8	}	}	PUNCT
ejpam-6472	89	9	;	;	PUNCT
ejpam-6472	89	10	(	(	PUNCT
ejpam-6472	89	11	iii	iii	X
ejpam-6472	89	12	)	)	PUNCT
ejpam-6472	89	13	t	t	NOUN
ejpam-6472	89	14	·	·	PUNCT
ejpam-6472	89	15	rs	rs	NOUN
ejpam-6472	89	16	q	q	NOUN
ejpam-6472	90	1	=	=	PUNCT
ejpam-6472	90	2	fi(t1	fi(t1	NOUN
ejpam-6472	90	3	·	·	SYM
ejpam-6472	90	4	rs	rs	X
ejpam-6472	90	5	q	q	NOUN
ejpam-6472	90	6	,	,	PUNCT
ejpam-6472	90	7	.	.	PUNCT
ejpam-6472	90	8	.	.	PUNCT
ejpam-6472	90	9	.	.	PUNCT
ejpam-6472	91	1	,	,	PUNCT
ejpam-6472	91	2	tni	tni	NOUN
ejpam-6472	91	3	·	·	PUNCT
ejpam-6472	91	4	rs	rs	NOUN
ejpam-6472	91	5	q	q	NOUN
ejpam-6472	91	6	)	)	PUNCT
ejpam-6472	91	7	if	if	SCONJ
ejpam-6472	91	8	t	t	NOUN
ejpam-6472	91	9	=	=	SYM
ejpam-6472	91	10	fi(t1	fi(t1	NOUN
ejpam-6472	91	11	,	,	PUNCT
ejpam-6472	91	12	.	.	PUNCT
ejpam-6472	91	13	.	.	PUNCT
ejpam-6472	92	1	.	.	PUNCT
ejpam-6472	93	1	,	,	PUNCT
ejpam-6472	93	2	tni	tni	NOUN
ejpam-6472	93	3	)	)	PUNCT
ejpam-6472	93	4	,	,	PUNCT
ejpam-6472	93	5	{	{	PUNCT
ejpam-6472	93	6	r	r	NOUN
ejpam-6472	93	7	,	,	PUNCT
ejpam-6472	93	8	s}∩sub(t	s}∩sub(t	ADJ
ejpam-6472	93	9	)	)	PUNCT
ejpam-6472	93	10	̸=	̸=	NOUN
ejpam-6472	93	11	∅	∅	NOUN
ejpam-6472	93	12	,	,	PUNCT
ejpam-6472	93	13	and	and	CCONJ
ejpam-6472	93	14	t	t	X
ejpam-6472	93	15	̸∈	̸∈	PROPN
ejpam-6472	93	16	{	{	PUNCT
ejpam-6472	93	17	r	r	PROPN
ejpam-6472	93	18	,	,	PUNCT
ejpam-6472	93	19	s	s	PART
ejpam-6472	93	20	}	}	PUNCT
ejpam-6472	93	21	.	.	PUNCT
ejpam-6472	94	1	p.	p.	NOUN
ejpam-6472	94	2	prachumdang	prachumdang	PROPN
ejpam-6472	94	3	,	,	PUNCT
ejpam-6472	94	4	b.	b.	PROPN
ejpam-6472	94	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	94	6	/	/	SYM
ejpam-6472	94	7	eur	eur	PROPN
ejpam-6472	94	8	.	.	PUNCT
ejpam-6472	95	1	j.	j.	PROPN
ejpam-6472	95	2	pure	pure	PROPN
ejpam-6472	95	3	appl	appl	PROPN
ejpam-6472	95	4	.	.	PROPN
ejpam-6472	95	5	math	math	PROPN
ejpam-6472	95	6	,	,	PUNCT
ejpam-6472	95	7	18	18	NUM
ejpam-6472	95	8	(	(	PUNCT
ejpam-6472	95	9	3	3	NUM
ejpam-6472	95	10	)	)	PUNCT
ejpam-6472	95	11	(	(	PUNCT
ejpam-6472	95	12	2025	2025	NUM
ejpam-6472	95	13	)	)	PUNCT
ejpam-6472	95	14	,	,	PUNCT
ejpam-6472	95	15	6472	6472	NUM
ejpam-6472	95	16	4	4	NUM
ejpam-6472	95	17	of	of	ADP
ejpam-6472	95	18	16	16	NUM
ejpam-6472	95	19	example	example	NOUN
ejpam-6472	95	20	1	1	NUM
ejpam-6472	95	21	.	.	PUNCT
ejpam-6472	96	1	let	let	VERB
ejpam-6472	96	2	τ	τ	PROPN
ejpam-6472	96	3	=	=	PUNCT
ejpam-6472	96	4	(	(	PUNCT
ejpam-6472	96	5	1	1	NUM
ejpam-6472	96	6	,	,	PUNCT
ejpam-6472	96	7	2	2	NUM
ejpam-6472	96	8	,	,	PUNCT
ejpam-6472	96	9	3	3	NUM
ejpam-6472	96	10	)	)	PUNCT
ejpam-6472	96	11	with	with	ADP
ejpam-6472	96	12	a	a	DET
ejpam-6472	96	13	unary	unary	ADJ
ejpam-6472	96	14	operation	operation	NOUN
ejpam-6472	96	15	symbol	symbol	NOUN
ejpam-6472	96	16	g	g	PROPN
ejpam-6472	96	17	,	,	PUNCT
ejpam-6472	96	18	a	a	DET
ejpam-6472	96	19	binary	binary	ADJ
ejpam-6472	96	20	operation	operation	NOUN
ejpam-6472	96	21	f	f	PROPN
ejpam-6472	96	22	,	,	PUNCT
ejpam-6472	96	23	and	and	CCONJ
ejpam-6472	96	24	a	a	DET
ejpam-6472	96	25	ternary	ternary	ADJ
ejpam-6472	96	26	operation	operation	NOUN
ejpam-6472	96	27	symbol	symbol	NOUN
ejpam-6472	96	28	h.	h.	PROPN
ejpam-6472	96	29	fix	fix	VERB
ejpam-6472	96	30	the	the	DET
ejpam-6472	96	31	terms	term	NOUN
ejpam-6472	96	32	r	r	NOUN
ejpam-6472	96	33	=	=	NOUN
ejpam-6472	96	34	g(x2	g(x2	NOUN
ejpam-6472	96	35	)	)	PUNCT
ejpam-6472	96	36	and	and	CCONJ
ejpam-6472	96	37	s	s	NOUN
ejpam-6472	96	38	=	=	NOUN
ejpam-6472	96	39	f(x2	f(x2	NOUN
ejpam-6472	96	40	,	,	PUNCT
ejpam-6472	96	41	x1	x1	PROPN
ejpam-6472	96	42	)	)	PUNCT
ejpam-6472	96	43	.	.	PUNCT
ejpam-6472	97	1	consider	consider	VERB
ejpam-6472	97	2	3	3	NUM
ejpam-6472	97	3	-	-	PUNCT
ejpam-6472	97	4	ary	ary	NOUN
ejpam-6472	97	5	terms	term	NOUN
ejpam-6472	97	6	of	of	ADP
ejpam-6472	97	7	type	type	NOUN
ejpam-6472	97	8	τ	τ	PROPN
ejpam-6472	97	9	given	give	VERB
ejpam-6472	97	10	by	by	ADP
ejpam-6472	97	11	t	t	PROPN
ejpam-6472	97	12	=	=	SYM
ejpam-6472	97	13	h(f(x2	h(f(x2	NOUN
ejpam-6472	97	14	,	,	PUNCT
ejpam-6472	97	15	x1	x1	PROPN
ejpam-6472	97	16	)	)	PUNCT
ejpam-6472	97	17	,	,	PUNCT
ejpam-6472	97	18	x3	x3	ADJ
ejpam-6472	97	19	,	,	PUNCT
ejpam-6472	97	20	g(x2	g(x2	NOUN
ejpam-6472	97	21	)	)	PUNCT
ejpam-6472	97	22	)	)	PUNCT
ejpam-6472	97	23	and	and	CCONJ
ejpam-6472	97	24	q	q	NOUN
ejpam-6472	97	25	=	=	PUNCT
ejpam-6472	97	26	g(x3	g(x3	NOUN
ejpam-6472	97	27	)	)	PUNCT
ejpam-6472	97	28	.	.	PUNCT
ejpam-6472	98	1	then	then	ADV
ejpam-6472	98	2	we	we	PRON
ejpam-6472	98	3	have	have	VERB
ejpam-6472	98	4	t	t	NOUN
ejpam-6472	98	5	·	·	PUNCT
ejpam-6472	98	6	rs	rs	NOUN
ejpam-6472	98	7	q	q	NOUN
ejpam-6472	98	8	=	=	NOUN
ejpam-6472	98	9	h(f(x2	h(f(x2	NOUN
ejpam-6472	98	10	,	,	PUNCT
ejpam-6472	98	11	x1	x1	PROPN
ejpam-6472	98	12	)	)	PUNCT
ejpam-6472	98	13	,	,	PUNCT
ejpam-6472	98	14	x3	x3	ADJ
ejpam-6472	98	15	,	,	PUNCT
ejpam-6472	98	16	g(x2	g(x2	NOUN
ejpam-6472	98	17	)	)	PUNCT
ejpam-6472	98	18	)	)	PUNCT
ejpam-6472	98	19	·	·	PUNCT
ejpam-6472	98	20	rs	rs	NOUN
ejpam-6472	98	21	g(x3	g(x3	NOUN
ejpam-6472	98	22	)	)	PUNCT
ejpam-6472	99	1	=	=	SYM
ejpam-6472	99	2	h(f(x2	h(f(x2	NOUN
ejpam-6472	99	3	,	,	PUNCT
ejpam-6472	99	4	x1	x1	PROPN
ejpam-6472	99	5	)	)	PUNCT
ejpam-6472	99	6	·	·	PUNCT
ejpam-6472	99	7	rs	rs	NOUN
ejpam-6472	99	8	g(x3	g(x3	NOUN
ejpam-6472	99	9	)	)	PUNCT
ejpam-6472	99	10	,	,	PUNCT
ejpam-6472	99	11	x3	x3	ADJ
ejpam-6472	99	12	·	·	PUNCT
ejpam-6472	99	13	rs	rs	NOUN
ejpam-6472	99	14	g(x3	g(x3	NOUN
ejpam-6472	99	15	)	)	PUNCT
ejpam-6472	99	16	,	,	PUNCT
ejpam-6472	99	17	g(x2	g(x2	NOUN
ejpam-6472	99	18	)	)	PUNCT
ejpam-6472	99	19	·	·	PUNCT
ejpam-6472	99	20	rs	rs	NOUN
ejpam-6472	99	21	g(x3	g(x3	NOUN
ejpam-6472	99	22	)	)	PUNCT
ejpam-6472	99	23	)	)	PUNCT
ejpam-6472	100	1	=	=	PUNCT
ejpam-6472	100	2	h(g(x3	h(g(x3	PROPN
ejpam-6472	100	3	)	)	PUNCT
ejpam-6472	100	4	,	,	PUNCT
ejpam-6472	100	5	x3	x3	ADJ
ejpam-6472	100	6	,	,	PUNCT
ejpam-6472	100	7	g(x3	g(x3	NUM
ejpam-6472	100	8	)	)	PUNCT
ejpam-6472	100	9	)	)	PUNCT
ejpam-6472	100	10	.	.	PUNCT
ejpam-6472	101	1	unlike	unlike	ADP
ejpam-6472	101	2	the	the	DET
ejpam-6472	101	3	operation	operation	NOUN
ejpam-6472	101	4	·	·	PUNCT
ejpam-6472	101	5	r	r	NOUN
ejpam-6472	101	6	,	,	PUNCT
ejpam-6472	101	7	which	which	PRON
ejpam-6472	101	8	has	have	VERB
ejpam-6472	101	9	r	r	NOUN
ejpam-6472	101	10	as	as	ADP
ejpam-6472	101	11	an	an	DET
ejpam-6472	101	12	identity	identity	NOUN
ejpam-6472	101	13	element	element	NOUN
ejpam-6472	101	14	,	,	PUNCT
ejpam-6472	101	15	the	the	DET
ejpam-6472	101	16	operation	operation	NOUN
ejpam-6472	101	17	·	·	PUNCT
ejpam-6472	101	18	rs	rs	X
ejpam-6472	101	19	does	do	AUX
ejpam-6472	101	20	not	not	PART
ejpam-6472	101	21	possess	possess	VERB
ejpam-6472	101	22	an	an	DET
ejpam-6472	101	23	identity	identity	NOUN
ejpam-6472	101	24	element	element	NOUN
ejpam-6472	101	25	in	in	ADP
ejpam-6472	101	26	general	general	ADJ
ejpam-6472	101	27	.	.	PUNCT
ejpam-6472	102	1	in	in	ADP
ejpam-6472	102	2	fact	fact	NOUN
ejpam-6472	102	3	,	,	PUNCT
ejpam-6472	102	4	when	when	SCONJ
ejpam-6472	102	5	r	r	NOUN
ejpam-6472	102	6	̸=	̸=	PROPN
ejpam-6472	102	7	s	s	PART
ejpam-6472	102	8	,	,	PUNCT
ejpam-6472	102	9	the	the	DET
ejpam-6472	102	10	operation	operation	NOUN
ejpam-6472	102	11	has	have	VERB
ejpam-6472	102	12	no	no	DET
ejpam-6472	102	13	identity	identity	NOUN
ejpam-6472	102	14	element	element	NOUN
ejpam-6472	102	15	at	at	ADV
ejpam-6472	102	16	all	all	ADV
ejpam-6472	102	17	.	.	PUNCT
ejpam-6472	103	1	typically	typically	ADV
ejpam-6472	103	2	,	,	PUNCT
ejpam-6472	103	3	the	the	DET
ejpam-6472	103	4	terms	term	NOUN
ejpam-6472	103	5	r	r	NOUN
ejpam-6472	103	6	and	and	CCONJ
ejpam-6472	103	7	s	s	PART
ejpam-6472	103	8	serve	serve	VERB
ejpam-6472	103	9	only	only	ADV
ejpam-6472	103	10	as	as	SCONJ
ejpam-6472	103	11	left	leave	VERB
ejpam-6472	103	12	identities	identity	NOUN
ejpam-6472	103	13	of	of	ADP
ejpam-6472	103	14	·	·	SYM
ejpam-6472	103	15	rs	rs	NOUN
ejpam-6472	103	16	.	.	PUNCT
ejpam-6472	104	1	the	the	DET
ejpam-6472	104	2	next	next	ADJ
ejpam-6472	104	3	result	result	NOUN
ejpam-6472	104	4	establishes	establish	VERB
ejpam-6472	104	5	a	a	DET
ejpam-6472	104	6	formula	formula	NOUN
ejpam-6472	104	7	for	for	ADP
ejpam-6472	104	8	computing	compute	VERB
ejpam-6472	104	9	the	the	DET
ejpam-6472	104	10	operation	operation	NOUN
ejpam-6472	104	11	-	-	PUNCT
ejpam-6472	104	12	symbol	symbol	NOUN
ejpam-6472	104	13	count	count	NOUN
ejpam-6472	104	14	of	of	ADP
ejpam-6472	104	15	a	a	DET
ejpam-6472	104	16	term	term	NOUN
ejpam-6472	104	17	under	under	ADP
ejpam-6472	104	18	the	the	DET
ejpam-6472	104	19	binary	binary	ADJ
ejpam-6472	104	20	operation	operation	NOUN
ejpam-6472	104	21	·	·	SYM
ejpam-6472	104	22	rs	rs	X
ejpam-6472	104	23	.	.	PUNCT
ejpam-6472	105	1	this	this	DET
ejpam-6472	105	2	formula	formula	NOUN
ejpam-6472	105	3	reduces	reduce	VERB
ejpam-6472	105	4	to	to	ADP
ejpam-6472	105	5	the	the	DET
ejpam-6472	105	6	one	one	NOUN
ejpam-6472	105	7	given	give	VERB
ejpam-6472	105	8	for	for	ADP
ejpam-6472	105	9	the	the	DET
ejpam-6472	105	10	rinductive	rinductive	ADJ
ejpam-6472	105	11	product	product	NOUN
ejpam-6472	105	12	·	·	PUNCT
ejpam-6472	105	13	r	r	NOUN
ejpam-6472	105	14	in	in	ADP
ejpam-6472	105	15	[	[	X
ejpam-6472	105	16	9	9	NUM
ejpam-6472	105	17	]	]	PUNCT
ejpam-6472	105	18	when	when	SCONJ
ejpam-6472	105	19	r	r	NOUN
ejpam-6472	105	20	=	=	SYM
ejpam-6472	105	21	s.	s.	PROPN
ejpam-6472	105	22	note	note	VERB
ejpam-6472	105	23	that	that	SCONJ
ejpam-6472	105	24	for	for	ADP
ejpam-6472	105	25	any	any	DET
ejpam-6472	105	26	two	two	NUM
ejpam-6472	105	27	terms	term	NOUN
ejpam-6472	105	28	r	r	NOUN
ejpam-6472	105	29	and	and	CCONJ
ejpam-6472	105	30	s	s	PROPN
ejpam-6472	105	31	,	,	PUNCT
ejpam-6472	105	32	at	at	ADV
ejpam-6472	105	33	least	least	ADJ
ejpam-6472	105	34	one	one	NUM
ejpam-6472	105	35	of	of	ADP
ejpam-6472	105	36	them	they	PRON
ejpam-6472	105	37	is	be	AUX
ejpam-6472	105	38	not	not	PART
ejpam-6472	105	39	a	a	DET
ejpam-6472	105	40	proper	proper	ADJ
ejpam-6472	105	41	subterm	subterm	NOUN
ejpam-6472	105	42	of	of	ADP
ejpam-6472	105	43	the	the	DET
ejpam-6472	105	44	other	other	ADJ
ejpam-6472	105	45	.	.	PUNCT
ejpam-6472	106	1	theorem	theorem	NOUN
ejpam-6472	106	2	1	1	NUM
ejpam-6472	106	3	.	.	PUNCT
ejpam-6472	107	1	let	let	VERB
ejpam-6472	107	2	r	r	NOUN
ejpam-6472	107	3	,	,	PUNCT
ejpam-6472	107	4	s	s	NOUN
ejpam-6472	107	5	∈	∈	PROPN
ejpam-6472	107	6	wτ	wτ	NOUN
ejpam-6472	107	7	(	(	PUNCT
ejpam-6472	107	8	xn	xn	X
ejpam-6472	107	9	)	)	PUNCT
ejpam-6472	107	10	be	be	AUX
ejpam-6472	107	11	fixed	fix	VERB
ejpam-6472	107	12	terms	term	NOUN
ejpam-6472	107	13	such	such	ADJ
ejpam-6472	107	14	that	that	DET
ejpam-6472	107	15	r	r	NOUN
ejpam-6472	107	16	/∈	/∈	PUNCT
ejpam-6472	107	17	sub(s	sub(s	PROPN
ejpam-6472	107	18	)	)	PUNCT
ejpam-6472	107	19	\	\	NOUN
ejpam-6472	107	20	{	{	PUNCT
ejpam-6472	107	21	s	s	NOUN
ejpam-6472	107	22	}	}	PUNCT
ejpam-6472	107	23	,	,	PUNCT
ejpam-6472	107	24	and	and	CCONJ
ejpam-6472	107	25	let	let	VERB
ejpam-6472	107	26	t	t	PROPN
ejpam-6472	107	27	,	,	PUNCT
ejpam-6472	107	28	q	q	PROPN
ejpam-6472	107	29	∈	∈	PROPN
ejpam-6472	107	30	wτ	wτ	NOUN
ejpam-6472	107	31	(	(	PUNCT
ejpam-6472	107	32	xn	xn	PROPN
ejpam-6472	107	33	)	)	PUNCT
ejpam-6472	107	34	.	.	PUNCT
ejpam-6472	108	1	then	then	ADV
ejpam-6472	108	2	,	,	PUNCT
ejpam-6472	108	3	the	the	DET
ejpam-6472	108	4	operation	operation	NOUN
ejpam-6472	108	5	-	-	PUNCT
ejpam-6472	108	6	symbol	symbol	NOUN
ejpam-6472	108	7	count	count	NOUN
ejpam-6472	108	8	of	of	ADP
ejpam-6472	108	9	t	t	NOUN
ejpam-6472	108	10	·	·	PUNCT
ejpam-6472	108	11	rs	rs	X
ejpam-6472	108	12	q	q	NOUN
ejpam-6472	108	13	is	be	AUX
ejpam-6472	108	14	given	give	VERB
ejpam-6472	108	15	by	by	ADP
ejpam-6472	108	16	op(t	op(t	NOUN
ejpam-6472	108	17	·	·	PUNCT
ejpam-6472	108	18	rs	rs	X
ejpam-6472	108	19	q	q	NOUN
ejpam-6472	108	20	)	)	PUNCT
ejpam-6472	108	21	=	=	SYM
ejpam-6472	108	22	op(t	op(t	NOUN
ejpam-6472	108	23	)	)	PUNCT
ejpam-6472	108	24	+	+	CCONJ
ejpam-6472	108	25	nr(t)(op(q)−	nr(t)(op(q)−	PROPN
ejpam-6472	108	26	op(r	op(r	NUM
ejpam-6472	108	27	)	)	PUNCT
ejpam-6472	108	28	)	)	PUNCT
ejpam-6472	109	1	+	+	CCONJ
ejpam-6472	109	2	(	(	PUNCT
ejpam-6472	109	3	ns(t)−	ns(t)−	PROPN
ejpam-6472	109	4	ns(r)nr(t))(op(q)−	ns(r)nr(t))(op(q)−	PROPN
ejpam-6472	109	5	op(s	op(s	NUM
ejpam-6472	109	6	)	)	PUNCT
ejpam-6472	109	7	)	)	PUNCT
ejpam-6472	109	8	.	.	PUNCT
ejpam-6472	110	1	proof	proof	NOUN
ejpam-6472	110	2	.	.	PUNCT
ejpam-6472	111	1	we	we	PRON
ejpam-6472	111	2	proceed	proceed	VERB
ejpam-6472	111	3	by	by	ADP
ejpam-6472	111	4	induction	induction	NOUN
ejpam-6472	111	5	on	on	ADP
ejpam-6472	111	6	the	the	DET
ejpam-6472	111	7	structure	structure	NOUN
ejpam-6472	111	8	of	of	ADP
ejpam-6472	111	9	t.	t.	PROPN
ejpam-6472	111	10	if	if	SCONJ
ejpam-6472	111	11	{	{	PUNCT
ejpam-6472	111	12	r	r	NOUN
ejpam-6472	111	13	,	,	PUNCT
ejpam-6472	111	14	s	s	NOUN
ejpam-6472	111	15	}	}	PUNCT
ejpam-6472	111	16	∩	∩	ADJ
ejpam-6472	111	17	sub(t	sub(t	NOUN
ejpam-6472	111	18	)	)	PUNCT
ejpam-6472	111	19	=	=	NOUN
ejpam-6472	111	20	∅	∅	NOUN
ejpam-6472	111	21	,	,	PUNCT
ejpam-6472	111	22	then	then	ADV
ejpam-6472	111	23	t	t	PROPN
ejpam-6472	111	24	·	·	PUNCT
ejpam-6472	111	25	rs	rs	PROPN
ejpam-6472	111	26	q	q	PROPN
ejpam-6472	111	27	=	=	SYM
ejpam-6472	111	28	t	t	PROPN
ejpam-6472	111	29	,	,	PUNCT
ejpam-6472	111	30	and	and	CCONJ
ejpam-6472	111	31	we	we	PRON
ejpam-6472	111	32	have	have	VERB
ejpam-6472	111	33	nr(t	nr(t	NOUN
ejpam-6472	111	34	)	)	PUNCT
ejpam-6472	111	35	=	=	SYM
ejpam-6472	111	36	ns(t	ns(t	ADJ
ejpam-6472	111	37	)	)	PUNCT
ejpam-6472	111	38	=	=	SYM
ejpam-6472	112	1	0	0	X
ejpam-6472	112	2	.	.	PUNCT
ejpam-6472	113	1	the	the	DET
ejpam-6472	113	2	formula	formula	NOUN
ejpam-6472	113	3	holds	hold	VERB
ejpam-6472	113	4	trivially	trivially	ADV
ejpam-6472	113	5	.	.	PUNCT
ejpam-6472	114	1	if	if	SCONJ
ejpam-6472	114	2	t	t	NOUN
ejpam-6472	114	3	=	=	SYM
ejpam-6472	114	4	r	r	NOUN
ejpam-6472	114	5	,	,	PUNCT
ejpam-6472	114	6	then	then	ADV
ejpam-6472	114	7	t	t	PROPN
ejpam-6472	114	8	·	·	PUNCT
ejpam-6472	114	9	rs	rs	X
ejpam-6472	114	10	q	q	NOUN
ejpam-6472	114	11	=	=	PUNCT
ejpam-6472	114	12	q	q	NOUN
ejpam-6472	114	13	,	,	PUNCT
ejpam-6472	114	14	and	and	CCONJ
ejpam-6472	114	15	we	we	PRON
ejpam-6472	114	16	observe	observe	VERB
ejpam-6472	114	17	that	that	PRON
ejpam-6472	114	18	nr(t	nr(t	PUNCT
ejpam-6472	114	19	)	)	PUNCT
ejpam-6472	114	20	=	=	SYM
ejpam-6472	114	21	1	1	NUM
ejpam-6472	114	22	and	and	CCONJ
ejpam-6472	114	23	ns(t	ns(t	ADJ
ejpam-6472	114	24	)	)	PUNCT
ejpam-6472	114	25	=	=	SYM
ejpam-6472	114	26	ns(r	ns(r	PRON
ejpam-6472	114	27	)	)	PUNCT
ejpam-6472	114	28	.	.	PUNCT
ejpam-6472	115	1	the	the	DET
ejpam-6472	115	2	formula	formula	NOUN
ejpam-6472	115	3	follows	follow	VERB
ejpam-6472	115	4	by	by	ADP
ejpam-6472	115	5	substituting	substitute	VERB
ejpam-6472	115	6	these	these	DET
ejpam-6472	115	7	values	value	NOUN
ejpam-6472	115	8	.	.	PUNCT
ejpam-6472	116	1	if	if	SCONJ
ejpam-6472	116	2	t	t	PROPN
ejpam-6472	116	3	=	=	SYM
ejpam-6472	116	4	s	s	PROPN
ejpam-6472	116	5	,	,	PUNCT
ejpam-6472	116	6	then	then	ADV
ejpam-6472	116	7	t	t	PROPN
ejpam-6472	116	8	·	·	PUNCT
ejpam-6472	116	9	rs	rs	X
ejpam-6472	116	10	q	q	NOUN
ejpam-6472	116	11	=	=	PUNCT
ejpam-6472	116	12	q	q	X
ejpam-6472	116	13	and	and	CCONJ
ejpam-6472	116	14	ns(t	ns(t	ADJ
ejpam-6472	116	15	)	)	PUNCT
ejpam-6472	116	16	=	=	SYM
ejpam-6472	117	1	1	1	X
ejpam-6472	117	2	.	.	PUNCT
ejpam-6472	117	3	by	by	ADP
ejpam-6472	117	4	the	the	DET
ejpam-6472	117	5	assumption	assumption	NOUN
ejpam-6472	117	6	that	that	SCONJ
ejpam-6472	117	7	r	r	PROPN
ejpam-6472	117	8	̸∈	̸∈	PROPN
ejpam-6472	117	9	sub(s	sub(s	PROPN
ejpam-6472	117	10	)	)	PUNCT
ejpam-6472	117	11	\	\	NOUN
ejpam-6472	117	12	{	{	PUNCT
ejpam-6472	117	13	s	s	X
ejpam-6472	117	14	}	}	PUNCT
ejpam-6472	117	15	,	,	PUNCT
ejpam-6472	117	16	we	we	PRON
ejpam-6472	117	17	have	have	VERB
ejpam-6472	117	18	t	t	NOUN
ejpam-6472	117	19	=	=	SYM
ejpam-6472	117	20	r	r	NOUN
ejpam-6472	117	21	or	or	CCONJ
ejpam-6472	117	22	r	r	NOUN
ejpam-6472	117	23	̸∈	̸∈	PROPN
ejpam-6472	117	24	sub(t	sub(t	PROPN
ejpam-6472	117	25	)	)	PUNCT
ejpam-6472	117	26	.	.	PUNCT
ejpam-6472	118	1	the	the	DET
ejpam-6472	118	2	first	first	ADJ
ejpam-6472	118	3	case	case	NOUN
ejpam-6472	118	4	implies	imply	VERB
ejpam-6472	118	5	the	the	DET
ejpam-6472	118	6	formula	formula	NOUN
ejpam-6472	118	7	by	by	ADP
ejpam-6472	118	8	the	the	DET
ejpam-6472	118	9	argument	argument	NOUN
ejpam-6472	118	10	discussed	discuss	VERB
ejpam-6472	118	11	above	above	ADV
ejpam-6472	118	12	.	.	PUNCT
ejpam-6472	119	1	in	in	ADP
ejpam-6472	119	2	the	the	DET
ejpam-6472	119	3	second	second	ADJ
ejpam-6472	119	4	case	case	NOUN
ejpam-6472	119	5	,	,	PUNCT
ejpam-6472	119	6	we	we	PRON
ejpam-6472	119	7	have	have	VERB
ejpam-6472	119	8	nr(t	nr(t	NOUN
ejpam-6472	119	9	)	)	PUNCT
ejpam-6472	119	10	=	=	SYM
ejpam-6472	119	11	0	0	NUM
ejpam-6472	119	12	,	,	PUNCT
ejpam-6472	119	13	and	and	CCONJ
ejpam-6472	119	14	the	the	DET
ejpam-6472	119	15	formula	formula	NOUN
ejpam-6472	119	16	follows	follow	VERB
ejpam-6472	119	17	immediately	immediately	ADV
ejpam-6472	119	18	from	from	ADP
ejpam-6472	119	19	the	the	DET
ejpam-6472	119	20	known	know	VERB
ejpam-6472	119	21	values	value	NOUN
ejpam-6472	119	22	.	.	PUNCT
ejpam-6472	120	1	for	for	ADP
ejpam-6472	120	2	t	t	NOUN
ejpam-6472	120	3	=	=	SYM
ejpam-6472	120	4	fi(t1	fi(t1	PROPN
ejpam-6472	120	5	,	,	PUNCT
ejpam-6472	120	6	.	.	PUNCT
ejpam-6472	120	7	.	.	PUNCT
ejpam-6472	120	8	.	.	PUNCT
ejpam-6472	121	1	,	,	PUNCT
ejpam-6472	121	2	tni	tni	NOUN
ejpam-6472	121	3	)	)	PUNCT
ejpam-6472	121	4	with	with	ADP
ejpam-6472	121	5	{	{	PUNCT
ejpam-6472	121	6	r	r	NOUN
ejpam-6472	121	7	,	,	PUNCT
ejpam-6472	121	8	s	s	NOUN
ejpam-6472	121	9	}	}	PUNCT
ejpam-6472	121	10	∩	∩	ADJ
ejpam-6472	121	11	sub(t	sub(t	NOUN
ejpam-6472	121	12	)	)	PUNCT
ejpam-6472	121	13	̸=	̸=	PROPN
ejpam-6472	121	14	∅	∅	NOUN
ejpam-6472	121	15	and	and	CCONJ
ejpam-6472	121	16	t	t	X
ejpam-6472	121	17	̸∈	̸∈	PROPN
ejpam-6472	121	18	{	{	PUNCT
ejpam-6472	121	19	r	r	PROPN
ejpam-6472	121	20	,	,	PUNCT
ejpam-6472	121	21	s	s	PART
ejpam-6472	121	22	}	}	PUNCT
ejpam-6472	121	23	,	,	PUNCT
ejpam-6472	121	24	we	we	PRON
ejpam-6472	121	25	inductively	inductively	ADV
ejpam-6472	121	26	assume	assume	VERB
ejpam-6472	121	27	that	that	SCONJ
ejpam-6472	121	28	op(tj	op(tj	PROPN
ejpam-6472	121	29	·	·	PUNCT
ejpam-6472	121	30	rs	rs	X
ejpam-6472	121	31	q	q	NOUN
ejpam-6472	121	32	)	)	PUNCT
ejpam-6472	121	33	=	=	SYM
ejpam-6472	121	34	op(tj	op(tj	PROPN
ejpam-6472	121	35	)	)	PUNCT
ejpam-6472	122	1	+	+	CCONJ
ejpam-6472	122	2	nr(tj)(op(q)−	nr(tj)(op(q)−	PROPN
ejpam-6472	122	3	op(r	op(r	NOUN
ejpam-6472	122	4	)	)	PUNCT
ejpam-6472	122	5	)	)	PUNCT
ejpam-6472	123	1	+	+	CCONJ
ejpam-6472	123	2	(	(	PUNCT
ejpam-6472	123	3	ns(tj)−	ns(tj)−	ADP
ejpam-6472	123	4	ns(r)nr(tj))(op(q)−	ns(r)nr(tj))(op(q)−	ADJ
ejpam-6472	123	5	op(s	op(s	NUM
ejpam-6472	123	6	)	)	PUNCT
ejpam-6472	123	7	)	)	PUNCT
ejpam-6472	123	8	for	for	ADP
ejpam-6472	123	9	all	all	PRON
ejpam-6472	123	10	1	1	NUM
ejpam-6472	123	11	≤	≤	NUM
ejpam-6472	123	12	j	j	PROPN
ejpam-6472	123	13	≤	≤	PROPN
ejpam-6472	123	14	ni	ni	PROPN
ejpam-6472	123	15	.	.	PROPN
ejpam-6472	123	16	then	then	ADV
ejpam-6472	123	17	op(t	op(t	X
ejpam-6472	123	18	·	·	PUNCT
ejpam-6472	123	19	rs	rs	X
ejpam-6472	123	20	q	q	NOUN
ejpam-6472	123	21	)	)	PUNCT
ejpam-6472	123	22	=	=	VERB
ejpam-6472	123	23	op(fi(t1	op(fi(t1	NOUN
ejpam-6472	123	24	·	·	PUNCT
ejpam-6472	123	25	rs	rs	X
ejpam-6472	123	26	q	q	NOUN
ejpam-6472	123	27	,	,	PUNCT
ejpam-6472	123	28	.	.	PUNCT
ejpam-6472	123	29	.	.	PUNCT
ejpam-6472	123	30	.	.	PUNCT
ejpam-6472	124	1	,	,	PUNCT
ejpam-6472	124	2	tni	tni	NOUN
ejpam-6472	124	3	·	·	PUNCT
ejpam-6472	124	4	rs	rs	X
ejpam-6472	124	5	q	q	NOUN
ejpam-6472	124	6	)	)	PUNCT
ejpam-6472	124	7	)	)	PUNCT
ejpam-6472	125	1	=	=	SYM
ejpam-6472	125	2	1	1	NUM
ejpam-6472	125	3	+	+	NUM
ejpam-6472	125	4	ni∑	ni∑	NOUN
ejpam-6472	125	5	j=1	j=1	ADJ
ejpam-6472	125	6	op(tj	op(tj	PROPN
ejpam-6472	125	7	·	·	PUNCT
ejpam-6472	125	8	rs	rs	X
ejpam-6472	125	9	q	q	NOUN
ejpam-6472	125	10	)	)	PUNCT
ejpam-6472	125	11	=	=	SYM
ejpam-6472	125	12	1	1	NUM
ejpam-6472	125	13	+	+	NUM
ejpam-6472	125	14	ni∑	ni∑	NOUN
ejpam-6472	125	15	j=1	j=1	NOUN
ejpam-6472	125	16	[	[	PUNCT
ejpam-6472	125	17	op(tj	op(tj	PROPN
ejpam-6472	125	18	)	)	PUNCT
ejpam-6472	125	19	+	+	CCONJ
ejpam-6472	125	20	nr(tj)(op(q)−	nr(tj)(op(q)−	PROPN
ejpam-6472	125	21	op(r	op(r	NOUN
ejpam-6472	125	22	)	)	PUNCT
ejpam-6472	125	23	)	)	PUNCT
ejpam-6472	126	1	+	+	CCONJ
ejpam-6472	126	2	(	(	PUNCT
ejpam-6472	126	3	ns(tj)−	ns(tj)−	ADP
ejpam-6472	126	4	ns(r)nr(tj))(op(q)−	ns(r)nr(tj))(op(q)−	ADJ
ejpam-6472	126	5	op(s	op(s	NUM
ejpam-6472	126	6	)	)	PUNCT
ejpam-6472	126	7	)	)	PUNCT
ejpam-6472	126	8	]	]	PUNCT
ejpam-6472	127	1	=	=	SYM
ejpam-6472	127	2	1	1	NUM
ejpam-6472	127	3	+	+	NUM
ejpam-6472	127	4	ni∑	ni∑	NOUN
ejpam-6472	127	5	j=1	j=1	ADJ
ejpam-6472	127	6	op(tj	op(tj	PROPN
ejpam-6472	127	7	)	)	PUNCT
ejpam-6472	127	8	+	+	CCONJ
ejpam-6472	127	9	(	(	PUNCT
ejpam-6472	127	10	op(q)−	op(q)−	ADJ
ejpam-6472	127	11	op(r	op(r	NUM
ejpam-6472	127	12	)	)	PUNCT
ejpam-6472	127	13	)	)	PUNCT
ejpam-6472	128	1	ni∑	ni∑	PROPN
ejpam-6472	128	2	j=1	j=1	PROPN
ejpam-6472	128	3	nr(tj	nr(tj	PROPN
ejpam-6472	128	4	)	)	PUNCT
ejpam-6472	129	1	p.	p.	PROPN
ejpam-6472	129	2	prachumdang	prachumdang	PROPN
ejpam-6472	129	3	,	,	PUNCT
ejpam-6472	129	4	b.	b.	PROPN
ejpam-6472	129	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	129	6	/	/	SYM
ejpam-6472	129	7	eur	eur	PROPN
ejpam-6472	129	8	.	.	PUNCT
ejpam-6472	130	1	j.	j.	PROPN
ejpam-6472	130	2	pure	pure	PROPN
ejpam-6472	130	3	appl	appl	PROPN
ejpam-6472	130	4	.	.	PROPN
ejpam-6472	130	5	math	math	PROPN
ejpam-6472	130	6	,	,	PUNCT
ejpam-6472	130	7	18	18	NUM
ejpam-6472	130	8	(	(	PUNCT
ejpam-6472	130	9	3	3	NUM
ejpam-6472	130	10	)	)	PUNCT
ejpam-6472	130	11	(	(	PUNCT
ejpam-6472	130	12	2025	2025	NUM
ejpam-6472	130	13	)	)	PUNCT
ejpam-6472	130	14	,	,	PUNCT
ejpam-6472	130	15	6472	6472	NUM
ejpam-6472	130	16	5	5	NUM
ejpam-6472	130	17	of	of	ADP
ejpam-6472	130	18	16	16	NUM
ejpam-6472	130	19	+	+	CCONJ
ejpam-6472	130	20	(	(	PUNCT
ejpam-6472	130	21	op(q)−	op(q)−	ADJ
ejpam-6472	130	22	op(s	op(s	NUM
ejpam-6472	130	23	)	)	PUNCT
ejpam-6472	130	24	)	)	PUNCT
ejpam-6472	131	1	(	(	PUNCT
ejpam-6472	131	2	ni∑	ni∑	NOUN
ejpam-6472	131	3	j=1	j=1	PROPN
ejpam-6472	131	4	ns(tj)−	ns(tj)−	ADP
ejpam-6472	131	5	ns(r	ns(r	PRON
ejpam-6472	131	6	)	)	PUNCT
ejpam-6472	131	7	ni∑	ni∑	NOUN
ejpam-6472	131	8	j=1	j=1	PROPN
ejpam-6472	131	9	nr(tj	nr(tj	PROPN
ejpam-6472	131	10	)	)	PUNCT
ejpam-6472	131	11	)	)	PUNCT
ejpam-6472	132	1	=	=	SYM
ejpam-6472	132	2	op(t	op(t	NOUN
ejpam-6472	132	3	)	)	PUNCT
ejpam-6472	133	1	+	+	CCONJ
ejpam-6472	133	2	nr(t)(op(q)−	nr(t)(op(q)−	PROPN
ejpam-6472	133	3	op(r	op(r	NUM
ejpam-6472	133	4	)	)	PUNCT
ejpam-6472	133	5	)	)	PUNCT
ejpam-6472	134	1	+	+	CCONJ
ejpam-6472	134	2	(	(	PUNCT
ejpam-6472	134	3	ns(t)−	ns(t)−	PROPN
ejpam-6472	134	4	ns(r)nr(t))(op(q)−	ns(r)nr(t))(op(q)−	PROPN
ejpam-6472	134	5	op(s	op(s	NUM
ejpam-6472	134	6	)	)	PUNCT
ejpam-6472	134	7	)	)	PUNCT
ejpam-6472	134	8	.	.	PUNCT
ejpam-6472	135	1	this	this	PRON
ejpam-6472	135	2	completes	complete	VERB
ejpam-6472	135	3	the	the	DET
ejpam-6472	135	4	proof	proof	NOUN
ejpam-6472	135	5	.	.	PUNCT
ejpam-6472	136	1	as	as	ADP
ejpam-6472	136	2	a	a	DET
ejpam-6472	136	3	direct	direct	ADJ
ejpam-6472	136	4	consequence	consequence	NOUN
ejpam-6472	136	5	of	of	ADP
ejpam-6472	136	6	theorem	theorem	NOUN
ejpam-6472	136	7	1	1	NUM
ejpam-6472	136	8	,	,	PUNCT
ejpam-6472	136	9	we	we	PRON
ejpam-6472	136	10	obtain	obtain	VERB
ejpam-6472	136	11	the	the	DET
ejpam-6472	136	12	following	follow	VERB
ejpam-6472	136	13	corollary	corollary	NOUN
ejpam-6472	136	14	.	.	PUNCT
ejpam-6472	137	1	corollary	corollary	ADJ
ejpam-6472	137	2	1	1	NUM
ejpam-6472	137	3	.	.	PUNCT
ejpam-6472	138	1	let	let	VERB
ejpam-6472	138	2	r	r	NOUN
ejpam-6472	138	3	,	,	PUNCT
ejpam-6472	138	4	s	s	NOUN
ejpam-6472	138	5	∈	∈	PROPN
ejpam-6472	138	6	wτ	wτ	NOUN
ejpam-6472	138	7	(	(	PUNCT
ejpam-6472	138	8	xn	xn	X
ejpam-6472	138	9	)	)	PUNCT
ejpam-6472	138	10	be	be	AUX
ejpam-6472	138	11	fixed	fix	VERB
ejpam-6472	138	12	terms	term	NOUN
ejpam-6472	138	13	such	such	ADJ
ejpam-6472	138	14	that	that	SCONJ
ejpam-6472	138	15	r	r	PROPN
ejpam-6472	138	16	̸∈	̸∈	PROPN
ejpam-6472	138	17	sub(s	sub(s	PROPN
ejpam-6472	138	18	)	)	PUNCT
ejpam-6472	138	19	\	\	NOUN
ejpam-6472	139	1	{	{	PUNCT
ejpam-6472	139	2	s	s	NOUN
ejpam-6472	139	3	}	}	PUNCT
ejpam-6472	139	4	and	and	CCONJ
ejpam-6472	139	5	s	s	VERB
ejpam-6472	139	6	̸∈	̸∈	PROPN
ejpam-6472	139	7	sub(r){r	sub(r){r	PRON
ejpam-6472	139	8	}	}	PUNCT
ejpam-6472	139	9	.	.	PUNCT
ejpam-6472	140	1	for	for	ADP
ejpam-6472	140	2	each	each	DET
ejpam-6472	140	3	t	t	NOUN
ejpam-6472	140	4	,	,	PUNCT
ejpam-6472	140	5	q	q	PROPN
ejpam-6472	140	6	∈	∈	PROPN
ejpam-6472	140	7	wτ	wτ	NOUN
ejpam-6472	140	8	(	(	PUNCT
ejpam-6472	140	9	xn	xn	PROPN
ejpam-6472	140	10	)	)	PUNCT
ejpam-6472	140	11	,	,	PUNCT
ejpam-6472	140	12	the	the	DET
ejpam-6472	140	13	following	follow	VERB
ejpam-6472	140	14	statements	statement	NOUN
ejpam-6472	140	15	hold	hold	VERB
ejpam-6472	140	16	true	true	ADJ
ejpam-6472	140	17	.	.	PUNCT
ejpam-6472	141	1	(	(	PUNCT
ejpam-6472	141	2	i	i	NOUN
ejpam-6472	141	3	)	)	PUNCT
ejpam-6472	141	4	if	if	SCONJ
ejpam-6472	141	5	r	r	NOUN
ejpam-6472	141	6	=	=	SYM
ejpam-6472	141	7	s	s	PROPN
ejpam-6472	141	8	,	,	PUNCT
ejpam-6472	141	9	then	then	ADV
ejpam-6472	141	10	op(t	op(t	ADJ
ejpam-6472	141	11	·	·	PUNCT
ejpam-6472	141	12	rs	rs	X
ejpam-6472	141	13	q	q	NOUN
ejpam-6472	141	14	)	)	PUNCT
ejpam-6472	141	15	=	=	SYM
ejpam-6472	141	16	op(t	op(t	NOUN
ejpam-6472	141	17	)	)	PUNCT
ejpam-6472	141	18	+	+	CCONJ
ejpam-6472	141	19	nr(t)(op(q)−	nr(t)(op(q)−	PROPN
ejpam-6472	141	20	op(r	op(r	NUM
ejpam-6472	141	21	)	)	PUNCT
ejpam-6472	141	22	)	)	PUNCT
ejpam-6472	141	23	.	.	PUNCT
ejpam-6472	142	1	(	(	PUNCT
ejpam-6472	142	2	ii	ii	NOUN
ejpam-6472	142	3	)	)	PUNCT
ejpam-6472	142	4	if	if	SCONJ
ejpam-6472	142	5	r	r	PROPN
ejpam-6472	142	6	̸=	̸=	PROPN
ejpam-6472	142	7	s	s	PART
ejpam-6472	142	8	,	,	PUNCT
ejpam-6472	142	9	then	then	ADV
ejpam-6472	142	10	op(t	op(t	ADJ
ejpam-6472	142	11	·	·	PUNCT
ejpam-6472	142	12	rs	rs	X
ejpam-6472	142	13	q	q	NOUN
ejpam-6472	142	14	)	)	PUNCT
ejpam-6472	142	15	=	=	SYM
ejpam-6472	142	16	op(t	op(t	NOUN
ejpam-6472	142	17	)	)	PUNCT
ejpam-6472	142	18	+	+	CCONJ
ejpam-6472	142	19	nr(t)(op(q)−	nr(t)(op(q)−	PROPN
ejpam-6472	142	20	op(r	op(r	NUM
ejpam-6472	142	21	)	)	PUNCT
ejpam-6472	142	22	)	)	PUNCT
ejpam-6472	143	1	+	+	CCONJ
ejpam-6472	143	2	ns(t)(op(q)−	ns(t)(op(q)−	NOUN
ejpam-6472	143	3	op(s	op(s	NUM
ejpam-6472	143	4	)	)	PUNCT
ejpam-6472	143	5	)	)	PUNCT
ejpam-6472	143	6	.	.	PUNCT
ejpam-6472	144	1	we	we	PRON
ejpam-6472	144	2	now	now	ADV
ejpam-6472	144	3	establish	establish	VERB
ejpam-6472	144	4	some	some	DET
ejpam-6472	144	5	fundamental	fundamental	ADJ
ejpam-6472	144	6	properties	property	NOUN
ejpam-6472	144	7	of	of	ADP
ejpam-6472	144	8	the	the	DET
ejpam-6472	144	9	operation	operation	NOUN
ejpam-6472	144	10	·	·	SYM
ejpam-6472	144	11	rs	rs	X
ejpam-6472	144	12	.	.	PUNCT
ejpam-6472	145	1	lemma	lemma	PROPN
ejpam-6472	145	2	1	1	X
ejpam-6472	145	3	.	.	PUNCT
ejpam-6472	146	1	let	let	VERB
ejpam-6472	146	2	r	r	NOUN
ejpam-6472	146	3	,	,	PUNCT
ejpam-6472	146	4	s	s	NOUN
ejpam-6472	146	5	∈	∈	PROPN
ejpam-6472	146	6	wτ	wτ	NOUN
ejpam-6472	146	7	(	(	PUNCT
ejpam-6472	146	8	xn	xn	X
ejpam-6472	146	9	)	)	PUNCT
ejpam-6472	146	10	be	be	AUX
ejpam-6472	146	11	fixed	fix	VERB
ejpam-6472	146	12	terms	term	NOUN
ejpam-6472	146	13	and	and	CCONJ
ejpam-6472	146	14	t	t	PROPN
ejpam-6472	146	15	,	,	PUNCT
ejpam-6472	146	16	q	q	PROPN
ejpam-6472	146	17	∈	∈	PROPN
ejpam-6472	146	18	wτ	wτ	NOUN
ejpam-6472	146	19	(	(	PUNCT
ejpam-6472	146	20	xn	xn	PROPN
ejpam-6472	146	21	)	)	PUNCT
ejpam-6472	146	22	.	.	PUNCT
ejpam-6472	147	1	if	if	SCONJ
ejpam-6472	147	2	{	{	PUNCT
ejpam-6472	147	3	r	r	NOUN
ejpam-6472	147	4	,	,	PUNCT
ejpam-6472	147	5	s	s	NOUN
ejpam-6472	147	6	}	}	PUNCT
ejpam-6472	147	7	∩	∩	ADJ
ejpam-6472	147	8	sub(t	sub(t	NOUN
ejpam-6472	147	9	)	)	PUNCT
ejpam-6472	147	10	̸=	̸=	NOUN
ejpam-6472	147	11	∅	∅	NOUN
ejpam-6472	147	12	,	,	PUNCT
ejpam-6472	147	13	then	then	ADV
ejpam-6472	147	14	q	q	PROPN
ejpam-6472	147	15	∈	∈	PROPN
ejpam-6472	147	16	sub(t	sub(t	PROPN
ejpam-6472	147	17	·	·	SYM
ejpam-6472	147	18	rs	rs	X
ejpam-6472	147	19	q	q	NOUN
ejpam-6472	147	20	)	)	PUNCT
ejpam-6472	147	21	.	.	PUNCT
ejpam-6472	148	1	if	if	SCONJ
ejpam-6472	148	2	,	,	PUNCT
ejpam-6472	148	3	in	in	ADP
ejpam-6472	148	4	addition	addition	NOUN
ejpam-6472	148	5	,	,	PUNCT
ejpam-6472	148	6	t	t	PROPN
ejpam-6472	148	7	̸∈	̸∈	PROPN
ejpam-6472	148	8	{	{	PUNCT
ejpam-6472	148	9	r	r	PROPN
ejpam-6472	148	10	,	,	PUNCT
ejpam-6472	148	11	s	s	PART
ejpam-6472	148	12	}	}	PUNCT
ejpam-6472	148	13	,	,	PUNCT
ejpam-6472	148	14	then	then	ADV
ejpam-6472	148	15	q	q	PROPN
ejpam-6472	148	16	∈	∈	PROPN
ejpam-6472	148	17	sub(t	sub(t	PROPN
ejpam-6472	148	18	·	·	SYM
ejpam-6472	148	19	rs	rs	X
ejpam-6472	148	20	q	q	NOUN
ejpam-6472	148	21	)	)	PUNCT
ejpam-6472	148	22	\	\	NOUN
ejpam-6472	148	23	{	{	PUNCT
ejpam-6472	148	24	t	t	NOUN
ejpam-6472	148	25	·	·	SYM
ejpam-6472	148	26	rs	rs	NOUN
ejpam-6472	148	27	q	q	NOUN
ejpam-6472	148	28	}	}	PUNCT
ejpam-6472	148	29	.	.	PUNCT
ejpam-6472	149	1	proof	proof	NOUN
ejpam-6472	149	2	.	.	PUNCT
ejpam-6472	150	1	we	we	PRON
ejpam-6472	150	2	proceed	proceed	VERB
ejpam-6472	150	3	by	by	ADP
ejpam-6472	150	4	induction	induction	NOUN
ejpam-6472	150	5	on	on	ADP
ejpam-6472	150	6	the	the	DET
ejpam-6472	150	7	structure	structure	NOUN
ejpam-6472	150	8	of	of	ADP
ejpam-6472	150	9	t.	t.	PROPN
ejpam-6472	150	10	if	if	SCONJ
ejpam-6472	150	11	t	t	PROPN
ejpam-6472	150	12	∈	∈	PROPN
ejpam-6472	150	13	{	{	PUNCT
ejpam-6472	150	14	r	r	NOUN
ejpam-6472	150	15	,	,	PUNCT
ejpam-6472	150	16	s	s	PART
ejpam-6472	150	17	}	}	PUNCT
ejpam-6472	150	18	,	,	PUNCT
ejpam-6472	150	19	then	then	ADV
ejpam-6472	150	20	t	t	X
ejpam-6472	150	21	·	·	PUNCT
ejpam-6472	150	22	rs	rs	X
ejpam-6472	150	23	q	q	NOUN
ejpam-6472	151	1	=	=	PUNCT
ejpam-6472	151	2	q	q	NOUN
ejpam-6472	151	3	,	,	PUNCT
ejpam-6472	151	4	so	so	ADV
ejpam-6472	151	5	q	q	ADP
ejpam-6472	151	6	∈	∈	PROPN
ejpam-6472	151	7	sub(t	sub(t	NOUN
ejpam-6472	151	8	·	·	SYM
ejpam-6472	151	9	rs	rs	X
ejpam-6472	151	10	q	q	NOUN
ejpam-6472	151	11	)	)	PUNCT
ejpam-6472	151	12	.	.	PUNCT
ejpam-6472	152	1	for	for	ADP
ejpam-6472	152	2	t	t	NOUN
ejpam-6472	152	3	=	=	SYM
ejpam-6472	152	4	fi(t1	fi(t1	PROPN
ejpam-6472	152	5	,	,	PUNCT
ejpam-6472	152	6	.	.	PUNCT
ejpam-6472	152	7	.	.	PUNCT
ejpam-6472	153	1	.	.	PUNCT
ejpam-6472	154	1	,	,	PUNCT
ejpam-6472	154	2	tni	tni	NOUN
ejpam-6472	154	3	)	)	PUNCT
ejpam-6472	154	4	with	with	ADP
ejpam-6472	154	5	{	{	PUNCT
ejpam-6472	154	6	r	r	NOUN
ejpam-6472	154	7	,	,	PUNCT
ejpam-6472	154	8	s	s	NOUN
ejpam-6472	154	9	}	}	PUNCT
ejpam-6472	154	10	∩	∩	ADJ
ejpam-6472	154	11	sub(t	sub(t	NOUN
ejpam-6472	154	12	)	)	PUNCT
ejpam-6472	154	13	̸=	̸=	PROPN
ejpam-6472	154	14	∅	∅	NOUN
ejpam-6472	154	15	and	and	CCONJ
ejpam-6472	154	16	t	t	X
ejpam-6472	154	17	̸∈	̸∈	PROPN
ejpam-6472	154	18	{	{	PUNCT
ejpam-6472	154	19	r	r	PROPN
ejpam-6472	154	20	,	,	PUNCT
ejpam-6472	154	21	s	s	PART
ejpam-6472	154	22	}	}	PUNCT
ejpam-6472	154	23	,	,	PUNCT
ejpam-6472	154	24	we	we	PRON
ejpam-6472	154	25	assume	assume	VERB
ejpam-6472	154	26	that	that	SCONJ
ejpam-6472	154	27	{	{	PUNCT
ejpam-6472	154	28	r	r	NOUN
ejpam-6472	154	29	,	,	PUNCT
ejpam-6472	154	30	s}∩sub(tj	s}∩sub(tj	ADJ
ejpam-6472	154	31	)	)	PUNCT
ejpam-6472	154	32	̸=	̸=	PROPN
ejpam-6472	154	33	∅	∅	NOUN
ejpam-6472	154	34	implies	imply	VERB
ejpam-6472	154	35	q	q	PROPN
ejpam-6472	154	36	∈	∈	PROPN
ejpam-6472	154	37	sub(tj	sub(tj	NOUN
ejpam-6472	154	38	·	·	SYM
ejpam-6472	154	39	rs	rs	ADJ
ejpam-6472	154	40	q	q	NOUN
ejpam-6472	154	41	)	)	PUNCT
ejpam-6472	154	42	for	for	ADP
ejpam-6472	154	43	all	all	PRON
ejpam-6472	154	44	1	1	NUM
ejpam-6472	154	45	≤	≤	NUM
ejpam-6472	154	46	j	j	PROPN
ejpam-6472	154	47	≤	≤	PROPN
ejpam-6472	154	48	ni	ni	PROPN
ejpam-6472	154	49	.	.	PROPN
ejpam-6472	155	1	since	since	SCONJ
ejpam-6472	155	2	{	{	PUNCT
ejpam-6472	155	3	r	r	NOUN
ejpam-6472	155	4	,	,	PUNCT
ejpam-6472	155	5	s}∩sub(t	s}∩sub(t	ADJ
ejpam-6472	155	6	)	)	PUNCT
ejpam-6472	155	7	̸=	̸=	NOUN
ejpam-6472	155	8	∅	∅	NOUN
ejpam-6472	155	9	and	and	CCONJ
ejpam-6472	155	10	t	t	PROPN
ejpam-6472	155	11	̸=	̸=	PROPN
ejpam-6472	155	12	{	{	PUNCT
ejpam-6472	155	13	r	r	PROPN
ejpam-6472	155	14	,	,	PUNCT
ejpam-6472	155	15	s	s	PART
ejpam-6472	155	16	}	}	PUNCT
ejpam-6472	155	17	,	,	PUNCT
ejpam-6472	155	18	there	there	PRON
ejpam-6472	155	19	exists	exist	VERB
ejpam-6472	155	20	1	1	NUM
ejpam-6472	155	21	≤	≤	NUM
ejpam-6472	155	22	j	j	PROPN
ejpam-6472	155	23	≤	≤	PROPN
ejpam-6472	155	24	ni	ni	PROPN
ejpam-6472	155	25	such	such	ADJ
ejpam-6472	155	26	that	that	SCONJ
ejpam-6472	155	27	{	{	PUNCT
ejpam-6472	155	28	r	r	NOUN
ejpam-6472	155	29	,	,	PUNCT
ejpam-6472	155	30	s	s	NOUN
ejpam-6472	155	31	}	}	PUNCT
ejpam-6472	155	32	∩	∩	ADJ
ejpam-6472	155	33	sub(tj	sub(tj	NOUN
ejpam-6472	155	34	)	)	PUNCT
ejpam-6472	155	35	̸=	̸=	PROPN
ejpam-6472	155	36	∅.	∅.	VERB
ejpam-6472	155	37	by	by	ADP
ejpam-6472	155	38	inductive	inductive	ADJ
ejpam-6472	155	39	hypothesis	hypothesis	NOUN
ejpam-6472	155	40	,	,	PUNCT
ejpam-6472	155	41	it	it	PRON
ejpam-6472	155	42	follows	follow	VERB
ejpam-6472	155	43	that	that	SCONJ
ejpam-6472	155	44	q	q	PROPN
ejpam-6472	155	45	∈	∈	PROPN
ejpam-6472	155	46	sub(tj	sub(tj	NOUN
ejpam-6472	155	47	·	·	SYM
ejpam-6472	155	48	rs	rs	ADJ
ejpam-6472	155	49	q	q	NOUN
ejpam-6472	155	50	)	)	PUNCT
ejpam-6472	155	51	.	.	PUNCT
ejpam-6472	156	1	this	this	PRON
ejpam-6472	156	2	completes	complete	VERB
ejpam-6472	156	3	the	the	DET
ejpam-6472	156	4	first	first	ADJ
ejpam-6472	156	5	part	part	NOUN
ejpam-6472	156	6	.	.	PUNCT
ejpam-6472	157	1	for	for	ADP
ejpam-6472	157	2	the	the	DET
ejpam-6472	157	3	second	second	ADJ
ejpam-6472	157	4	part	part	NOUN
ejpam-6472	157	5	,	,	PUNCT
ejpam-6472	157	6	assume	assume	VERB
ejpam-6472	157	7	that	that	SCONJ
ejpam-6472	157	8	{	{	PUNCT
ejpam-6472	157	9	r	r	NOUN
ejpam-6472	157	10	,	,	PUNCT
ejpam-6472	157	11	s	s	NOUN
ejpam-6472	157	12	}	}	PUNCT
ejpam-6472	157	13	∩	∩	ADJ
ejpam-6472	157	14	sub(t	sub(t	NOUN
ejpam-6472	157	15	)	)	PUNCT
ejpam-6472	157	16	̸=	̸=	PROPN
ejpam-6472	157	17	∅	∅	NOUN
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ejpam-6472	157	19	t	t	PROPN
ejpam-6472	157	20	̸=	̸=	PROPN
ejpam-6472	157	21	{	{	PUNCT
ejpam-6472	157	22	r	r	PROPN
ejpam-6472	157	23	,	,	PUNCT
ejpam-6472	157	24	s	s	PART
ejpam-6472	157	25	}	}	PUNCT
ejpam-6472	157	26	.	.	PUNCT
ejpam-6472	158	1	then	then	ADV
ejpam-6472	158	2	t	t	PROPN
ejpam-6472	158	3	can	can	AUX
ejpam-6472	158	4	not	not	PART
ejpam-6472	158	5	be	be	AUX
ejpam-6472	158	6	a	a	DET
ejpam-6472	158	7	variable	variable	NOUN
ejpam-6472	158	8	,	,	PUNCT
ejpam-6472	158	9	so	so	ADV
ejpam-6472	158	10	let	let	VERB
ejpam-6472	158	11	t	t	NOUN
ejpam-6472	158	12	=	=	PUNCT
ejpam-6472	158	13	fi(t1	fi(t1	PROPN
ejpam-6472	158	14	,	,	PUNCT
ejpam-6472	158	15	.	.	PUNCT
ejpam-6472	158	16	.	.	PUNCT
ejpam-6472	158	17	.	.	PUNCT
ejpam-6472	159	1	,	,	PUNCT
ejpam-6472	159	2	tni	tni	NOUN
ejpam-6472	159	3	)	)	PUNCT
ejpam-6472	159	4	.	.	PUNCT
ejpam-6472	160	1	we	we	PRON
ejpam-6472	160	2	have	have	VERB
ejpam-6472	160	3	t	t	NOUN
ejpam-6472	160	4	·	·	PUNCT
ejpam-6472	160	5	rs	rs	NOUN
ejpam-6472	160	6	q	q	PROPN
ejpam-6472	160	7	=	=	PUNCT
ejpam-6472	160	8	fi(t1	fi(t1	NOUN
ejpam-6472	160	9	·	·	SYM
ejpam-6472	160	10	rs	rs	X
ejpam-6472	160	11	q	q	NOUN
ejpam-6472	160	12	,	,	PUNCT
ejpam-6472	160	13	.	.	PUNCT
ejpam-6472	160	14	.	.	PUNCT
ejpam-6472	161	1	.	.	PUNCT
ejpam-6472	162	1	,	,	PUNCT
ejpam-6472	162	2	tni	tni	NOUN
ejpam-6472	162	3	·	·	PUNCT
ejpam-6472	162	4	rs	rs	X
ejpam-6472	162	5	q	q	NOUN
ejpam-6472	162	6	)	)	PUNCT
ejpam-6472	162	7	,	,	PUNCT
ejpam-6472	162	8	and	and	CCONJ
ejpam-6472	162	9	as	as	ADP
ejpam-6472	162	10	above	above	ADV
ejpam-6472	162	11	,	,	PUNCT
ejpam-6472	162	12	there	there	PRON
ejpam-6472	162	13	is	be	VERB
ejpam-6472	162	14	1	1	NUM
ejpam-6472	162	15	≤	≤	NUM
ejpam-6472	162	16	j	j	PROPN
ejpam-6472	162	17	≤	≤	NOUN
ejpam-6472	162	18	such	such	ADJ
ejpam-6472	162	19	that	that	SCONJ
ejpam-6472	162	20	{	{	PUNCT
ejpam-6472	162	21	r	r	NOUN
ejpam-6472	162	22	,	,	PUNCT
ejpam-6472	162	23	s	s	NOUN
ejpam-6472	162	24	}	}	PUNCT
ejpam-6472	162	25	∩	∩	ADJ
ejpam-6472	162	26	sub(tj	sub(tj	NOUN
ejpam-6472	162	27	)	)	PUNCT
ejpam-6472	162	28	̸=	̸=	PROPN
ejpam-6472	162	29	∅.	∅.	VERB
ejpam-6472	162	30	by	by	ADP
ejpam-6472	162	31	the	the	DET
ejpam-6472	162	32	first	first	ADJ
ejpam-6472	162	33	part	part	NOUN
ejpam-6472	162	34	,	,	PUNCT
ejpam-6472	162	35	q	q	NOUN
ejpam-6472	162	36	∈	∈	PROPN
ejpam-6472	162	37	sub(tj	sub(tj	NOUN
ejpam-6472	162	38	·	·	SYM
ejpam-6472	162	39	rs	rs	ADJ
ejpam-6472	162	40	q	q	NOUN
ejpam-6472	162	41	)	)	PUNCT
ejpam-6472	162	42	.	.	PUNCT
ejpam-6472	163	1	thus	thus	ADV
ejpam-6472	163	2	,	,	PUNCT
ejpam-6472	163	3	q	q	PROPN
ejpam-6472	163	4	∈	∈	PROPN
ejpam-6472	163	5	sub(t	sub(t	NOUN
ejpam-6472	163	6	·	·	SYM
ejpam-6472	163	7	rs	rs	X
ejpam-6472	163	8	q	q	NOUN
ejpam-6472	163	9	)	)	PUNCT
ejpam-6472	163	10	\	\	NOUN
ejpam-6472	163	11	{	{	PUNCT
ejpam-6472	163	12	t	t	NOUN
ejpam-6472	163	13	·	·	SYM
ejpam-6472	163	14	rs	rs	NOUN
ejpam-6472	163	15	q	q	NOUN
ejpam-6472	163	16	}	}	PUNCT
ejpam-6472	163	17	.	.	PUNCT
ejpam-6472	164	1	lemma	lemma	PROPN
ejpam-6472	164	2	2	2	X
ejpam-6472	164	3	.	.	PUNCT
ejpam-6472	165	1	let	let	VERB
ejpam-6472	165	2	r	r	NOUN
ejpam-6472	165	3	,	,	PUNCT
ejpam-6472	165	4	s	s	NOUN
ejpam-6472	165	5	∈	∈	PROPN
ejpam-6472	165	6	wτ	wτ	NOUN
ejpam-6472	165	7	(	(	PUNCT
ejpam-6472	165	8	xn	xn	X
ejpam-6472	165	9	)	)	PUNCT
ejpam-6472	165	10	be	be	AUX
ejpam-6472	165	11	fixed	fix	VERB
ejpam-6472	165	12	terms	term	NOUN
ejpam-6472	165	13	and	and	CCONJ
ejpam-6472	165	14	t	t	PROPN
ejpam-6472	165	15	,	,	PUNCT
ejpam-6472	165	16	q	q	PROPN
ejpam-6472	165	17	∈	∈	PROPN
ejpam-6472	165	18	wτ	wτ	NOUN
ejpam-6472	165	19	(	(	PUNCT
ejpam-6472	165	20	xn	xn	PROPN
ejpam-6472	165	21	)	)	PUNCT
ejpam-6472	165	22	.	.	PUNCT
ejpam-6472	166	1	if	if	SCONJ
ejpam-6472	166	2	{	{	PUNCT
ejpam-6472	166	3	r	r	NOUN
ejpam-6472	166	4	,	,	PUNCT
ejpam-6472	166	5	s}∩sub(t	s}∩sub(t	ADJ
ejpam-6472	166	6	·	·	PUNCT
ejpam-6472	166	7	rs	rs	ADJ
ejpam-6472	166	8	q	q	NOUN
ejpam-6472	166	9	)	)	PUNCT
ejpam-6472	166	10	̸=	̸=	NOUN
ejpam-6472	166	11	∅	∅	NOUN
ejpam-6472	166	12	,	,	PUNCT
ejpam-6472	166	13	then	then	ADV
ejpam-6472	166	14	{	{	PUNCT
ejpam-6472	166	15	r	r	NOUN
ejpam-6472	166	16	,	,	PUNCT
ejpam-6472	166	17	s	s	NOUN
ejpam-6472	166	18	}	}	PUNCT
ejpam-6472	166	19	∩	∩	ADJ
ejpam-6472	166	20	sub(t	sub(t	NOUN
ejpam-6472	166	21	)	)	PUNCT
ejpam-6472	166	22	̸=	̸=	PROPN
ejpam-6472	166	23	∅.	∅.	ADP
ejpam-6472	166	24	proof	proof	NOUN
ejpam-6472	166	25	.	.	PUNCT
ejpam-6472	167	1	assume	assume	VERB
ejpam-6472	167	2	that	that	SCONJ
ejpam-6472	167	3	{	{	PUNCT
ejpam-6472	167	4	r	r	NOUN
ejpam-6472	167	5	,	,	PUNCT
ejpam-6472	167	6	s}∩	s}∩	PROPN
ejpam-6472	167	7	sub(t	sub(t	NOUN
ejpam-6472	167	8	)	)	PUNCT
ejpam-6472	168	1	=	=	PUNCT
ejpam-6472	168	2	∅.	∅.	VERB
ejpam-6472	168	3	then	then	ADV
ejpam-6472	168	4	t	t	NOUN
ejpam-6472	168	5	·	·	PUNCT
ejpam-6472	168	6	rs	rs	X
ejpam-6472	168	7	q	q	NOUN
ejpam-6472	169	1	=	=	PUNCT
ejpam-6472	169	2	t.	t.	NOUN
ejpam-6472	169	3	thus	thus	ADV
ejpam-6472	169	4	,	,	PUNCT
ejpam-6472	169	5	{	{	PUNCT
ejpam-6472	169	6	r	r	NOUN
ejpam-6472	169	7	,	,	PUNCT
ejpam-6472	169	8	s}∩	s}∩	PROPN
ejpam-6472	169	9	sub(t	sub(t	NOUN
ejpam-6472	169	10	·	·	SYM
ejpam-6472	169	11	rs	rs	X
ejpam-6472	169	12	q	q	NOUN
ejpam-6472	169	13	)	)	PUNCT
ejpam-6472	169	14	=	=	PUNCT
ejpam-6472	169	15	∅.	∅.	PRON
ejpam-6472	169	16	lemma	lemma	PROPN
ejpam-6472	169	17	3	3	NUM
ejpam-6472	169	18	.	.	PUNCT
ejpam-6472	170	1	let	let	VERB
ejpam-6472	170	2	r	r	NOUN
ejpam-6472	170	3	,	,	PUNCT
ejpam-6472	170	4	s	s	NOUN
ejpam-6472	170	5	∈	∈	PROPN
ejpam-6472	170	6	wτ	wτ	NOUN
ejpam-6472	170	7	(	(	PUNCT
ejpam-6472	170	8	xn	xn	X
ejpam-6472	170	9	)	)	PUNCT
ejpam-6472	170	10	be	be	AUX
ejpam-6472	170	11	fixed	fix	VERB
ejpam-6472	170	12	terms	term	NOUN
ejpam-6472	170	13	and	and	CCONJ
ejpam-6472	170	14	t	t	PROPN
ejpam-6472	170	15	,	,	PUNCT
ejpam-6472	170	16	q	q	PROPN
ejpam-6472	170	17	∈	∈	PROPN
ejpam-6472	170	18	wτ	wτ	NOUN
ejpam-6472	170	19	(	(	PUNCT
ejpam-6472	170	20	xn	xn	PROPN
ejpam-6472	170	21	)	)	PUNCT
ejpam-6472	170	22	.	.	PUNCT
ejpam-6472	171	1	then	then	ADV
ejpam-6472	171	2	the	the	DET
ejpam-6472	171	3	following	follow	VERB
ejpam-6472	171	4	statements	statement	NOUN
ejpam-6472	171	5	hold	hold	VERB
ejpam-6472	171	6	.	.	PUNCT
ejpam-6472	172	1	(	(	PUNCT
ejpam-6472	172	2	i	i	NOUN
ejpam-6472	172	3	)	)	PUNCT
ejpam-6472	172	4	if	if	SCONJ
ejpam-6472	172	5	{	{	PUNCT
ejpam-6472	172	6	r	r	NOUN
ejpam-6472	172	7	,	,	PUNCT
ejpam-6472	172	8	s	s	NOUN
ejpam-6472	172	9	}	}	PUNCT
ejpam-6472	172	10	∩	∩	ADJ
ejpam-6472	172	11	sub(t	sub(t	NOUN
ejpam-6472	172	12	)	)	PUNCT
ejpam-6472	172	13	̸=	̸=	PROPN
ejpam-6472	172	14	∅	∅	NOUN
ejpam-6472	172	15	and	and	CCONJ
ejpam-6472	172	16	r	r	NOUN
ejpam-6472	172	17	∈	∈	PROPN
ejpam-6472	172	18	sub(q	sub(q	PROPN
ejpam-6472	172	19	)	)	PUNCT
ejpam-6472	172	20	,	,	PUNCT
ejpam-6472	172	21	then	then	ADV
ejpam-6472	172	22	r	r	PROPN
ejpam-6472	172	23	∈	∈	PROPN
ejpam-6472	172	24	sub(t	sub(t	NOUN
ejpam-6472	172	25	·	·	SYM
ejpam-6472	172	26	rs	rs	X
ejpam-6472	172	27	q	q	NOUN
ejpam-6472	172	28	)	)	PUNCT
ejpam-6472	172	29	.	.	PUNCT
ejpam-6472	173	1	(	(	PUNCT
ejpam-6472	173	2	ii	ii	NOUN
ejpam-6472	173	3	)	)	PUNCT
ejpam-6472	173	4	if	if	SCONJ
ejpam-6472	173	5	{	{	PUNCT
ejpam-6472	173	6	r	r	NOUN
ejpam-6472	173	7	,	,	PUNCT
ejpam-6472	173	8	s	s	NOUN
ejpam-6472	173	9	}	}	PUNCT
ejpam-6472	173	10	∩	∩	ADJ
ejpam-6472	173	11	sub(t	sub(t	NOUN
ejpam-6472	173	12	)	)	PUNCT
ejpam-6472	173	13	̸=	̸=	PROPN
ejpam-6472	173	14	∅	∅	NOUN
ejpam-6472	173	15	and	and	CCONJ
ejpam-6472	173	16	s	s	NOUN
ejpam-6472	173	17	∈	∈	PROPN
ejpam-6472	173	18	sub(q	sub(q	PROPN
ejpam-6472	173	19	)	)	PUNCT
ejpam-6472	173	20	,	,	PUNCT
ejpam-6472	173	21	then	then	ADV
ejpam-6472	173	22	s	s	VERB
ejpam-6472	173	23	∈	∈	PROPN
ejpam-6472	173	24	sub(t	sub(t	NOUN
ejpam-6472	173	25	·	·	PUNCT
ejpam-6472	173	26	rs	rs	X
ejpam-6472	173	27	q	q	NOUN
ejpam-6472	173	28	)	)	PUNCT
ejpam-6472	173	29	.	.	PUNCT
ejpam-6472	174	1	proof	proof	NOUN
ejpam-6472	174	2	.	.	PUNCT
ejpam-6472	175	1	the	the	DET
ejpam-6472	175	2	second	second	ADJ
ejpam-6472	175	3	part	part	NOUN
ejpam-6472	175	4	follows	follow	VERB
ejpam-6472	175	5	by	by	ADP
ejpam-6472	175	6	a	a	DET
ejpam-6472	175	7	similar	similar	ADJ
ejpam-6472	175	8	argument	argument	NOUN
ejpam-6472	175	9	,	,	PUNCT
ejpam-6472	175	10	so	so	ADV
ejpam-6472	175	11	we	we	PRON
ejpam-6472	175	12	prove	prove	VERB
ejpam-6472	175	13	only	only	ADV
ejpam-6472	175	14	the	the	DET
ejpam-6472	175	15	first	first	ADJ
ejpam-6472	175	16	part	part	NOUN
ejpam-6472	175	17	.	.	PUNCT
ejpam-6472	176	1	assume	assume	VERB
ejpam-6472	176	2	{	{	PUNCT
ejpam-6472	176	3	r	r	NOUN
ejpam-6472	176	4	,	,	PUNCT
ejpam-6472	176	5	s	s	NOUN
ejpam-6472	176	6	}	}	PUNCT
ejpam-6472	176	7	∩	∩	ADJ
ejpam-6472	176	8	sub(t	sub(t	NOUN
ejpam-6472	176	9	)	)	PUNCT
ejpam-6472	176	10	̸=	̸=	PROPN
ejpam-6472	176	11	∅	∅	NOUN
ejpam-6472	176	12	and	and	CCONJ
ejpam-6472	176	13	r	r	NOUN
ejpam-6472	176	14	∈	∈	PROPN
ejpam-6472	176	15	sub(q	sub(q	PROPN
ejpam-6472	176	16	)	)	PUNCT
ejpam-6472	176	17	.	.	PUNCT
ejpam-6472	177	1	by	by	ADP
ejpam-6472	177	2	lemma	lemma	PROPN
ejpam-6472	177	3	1	1	NUM
ejpam-6472	177	4	,	,	PUNCT
ejpam-6472	177	5	we	we	PRON
ejpam-6472	177	6	have	have	VERB
ejpam-6472	177	7	q	q	PROPN
ejpam-6472	177	8	∈	∈	PROPN
ejpam-6472	177	9	sub(t	sub(t	NOUN
ejpam-6472	177	10	·	·	SYM
ejpam-6472	177	11	rs	rs	X
ejpam-6472	177	12	q	q	NOUN
ejpam-6472	177	13	)	)	PUNCT
ejpam-6472	177	14	.	.	PUNCT
ejpam-6472	178	1	thus	thus	ADV
ejpam-6472	178	2	,	,	PUNCT
ejpam-6472	178	3	r	r	PROPN
ejpam-6472	178	4	∈	∈	PROPN
ejpam-6472	178	5	sub(t	sub(t	NOUN
ejpam-6472	178	6	·	·	SYM
ejpam-6472	178	7	rs	rs	X
ejpam-6472	178	8	q	q	NOUN
ejpam-6472	178	9	)	)	PUNCT
ejpam-6472	178	10	.	.	PUNCT
ejpam-6472	179	1	p.	p.	PROPN
ejpam-6472	179	2	prachumdang	prachumdang	PROPN
ejpam-6472	179	3	,	,	PUNCT
ejpam-6472	179	4	b.	b.	PROPN
ejpam-6472	179	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	179	6	/	/	SYM
ejpam-6472	179	7	eur	eur	PROPN
ejpam-6472	179	8	.	.	PUNCT
ejpam-6472	180	1	j.	j.	PROPN
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ejpam-6472	180	3	appl	appl	PROPN
ejpam-6472	180	4	.	.	PROPN
ejpam-6472	180	5	math	math	PROPN
ejpam-6472	180	6	,	,	PUNCT
ejpam-6472	180	7	18	18	NUM
ejpam-6472	180	8	(	(	PUNCT
ejpam-6472	180	9	3	3	NUM
ejpam-6472	180	10	)	)	PUNCT
ejpam-6472	180	11	(	(	PUNCT
ejpam-6472	180	12	2025	2025	NUM
ejpam-6472	180	13	)	)	PUNCT
ejpam-6472	180	14	,	,	PUNCT
ejpam-6472	180	15	6472	6472	NUM
ejpam-6472	180	16	6	6	NUM
ejpam-6472	180	17	of	of	ADP
ejpam-6472	180	18	16	16	NUM
ejpam-6472	180	19	lemma	lemma	PROPN
ejpam-6472	180	20	4	4	NUM
ejpam-6472	180	21	.	.	PUNCT
ejpam-6472	181	1	let	let	VERB
ejpam-6472	181	2	r	r	NOUN
ejpam-6472	181	3	,	,	PUNCT
ejpam-6472	181	4	s	s	NOUN
ejpam-6472	181	5	∈	∈	PROPN
ejpam-6472	181	6	wτ	wτ	NOUN
ejpam-6472	181	7	(	(	PUNCT
ejpam-6472	181	8	xn	xn	X
ejpam-6472	181	9	)	)	PUNCT
ejpam-6472	181	10	be	be	AUX
ejpam-6472	181	11	fixed	fix	VERB
ejpam-6472	181	12	terms	term	NOUN
ejpam-6472	181	13	,	,	PUNCT
ejpam-6472	181	14	and	and	CCONJ
ejpam-6472	181	15	let	let	VERB
ejpam-6472	181	16	t	t	PROPN
ejpam-6472	181	17	,	,	PUNCT
ejpam-6472	181	18	q	q	PROPN
ejpam-6472	181	19	∈	∈	PROPN
ejpam-6472	181	20	wτ	wτ	NOUN
ejpam-6472	181	21	(	(	PUNCT
ejpam-6472	181	22	xn	xn	PROPN
ejpam-6472	181	23	)	)	PUNCT
ejpam-6472	181	24	.	.	PUNCT
ejpam-6472	182	1	then	then	ADV
ejpam-6472	182	2	the	the	DET
ejpam-6472	182	3	following	follow	VERB
ejpam-6472	182	4	statements	statement	NOUN
ejpam-6472	182	5	hold	hold	VERB
ejpam-6472	182	6	.	.	PUNCT
ejpam-6472	183	1	(	(	PUNCT
ejpam-6472	183	2	i	i	NOUN
ejpam-6472	183	3	)	)	PUNCT
ejpam-6472	183	4	if	if	SCONJ
ejpam-6472	183	5	t	t	NOUN
ejpam-6472	183	6	·	·	PUNCT
ejpam-6472	183	7	rs	rs	X
ejpam-6472	183	8	q	q	NOUN
ejpam-6472	183	9	=	=	SYM
ejpam-6472	183	10	r	r	NOUN
ejpam-6472	183	11	,	,	PUNCT
ejpam-6472	183	12	then	then	ADV
ejpam-6472	183	13	{	{	PUNCT
ejpam-6472	183	14	r	r	NOUN
ejpam-6472	183	15	,	,	PUNCT
ejpam-6472	183	16	s	s	NOUN
ejpam-6472	183	17	}	}	PUNCT
ejpam-6472	183	18	∩	∩	ADJ
ejpam-6472	183	19	sub(t	sub(t	NOUN
ejpam-6472	183	20	)	)	PUNCT
ejpam-6472	183	21	̸=	̸=	PROPN
ejpam-6472	183	22	∅	∅	NOUN
ejpam-6472	183	23	and	and	CCONJ
ejpam-6472	183	24	q	q	NOUN
ejpam-6472	183	25	∈	∈	PROPN
ejpam-6472	183	26	sub(r	sub(r	PROPN
ejpam-6472	183	27	)	)	PUNCT
ejpam-6472	183	28	.	.	PUNCT
ejpam-6472	184	1	(	(	PUNCT
ejpam-6472	184	2	ii	ii	NOUN
ejpam-6472	184	3	)	)	PUNCT
ejpam-6472	184	4	if	if	SCONJ
ejpam-6472	184	5	t	t	NOUN
ejpam-6472	184	6	·	·	PUNCT
ejpam-6472	184	7	rs	rs	X
ejpam-6472	184	8	q	q	PROPN
ejpam-6472	185	1	=	=	SYM
ejpam-6472	185	2	s	s	PROPN
ejpam-6472	185	3	,	,	PUNCT
ejpam-6472	185	4	then	then	ADV
ejpam-6472	185	5	{	{	PUNCT
ejpam-6472	185	6	r	r	NOUN
ejpam-6472	185	7	,	,	PUNCT
ejpam-6472	185	8	s	s	NOUN
ejpam-6472	185	9	}	}	PUNCT
ejpam-6472	185	10	∩	∩	ADJ
ejpam-6472	185	11	sub(t	sub(t	NOUN
ejpam-6472	185	12	)	)	PUNCT
ejpam-6472	185	13	̸=	̸=	PROPN
ejpam-6472	185	14	∅	∅	NOUN
ejpam-6472	185	15	and	and	CCONJ
ejpam-6472	185	16	q	q	NOUN
ejpam-6472	185	17	∈	∈	PROPN
ejpam-6472	185	18	sub(s	sub(s	PROPN
ejpam-6472	185	19	)	)	PUNCT
ejpam-6472	185	20	.	.	PUNCT
ejpam-6472	186	1	proof	proof	NOUN
ejpam-6472	186	2	.	.	PUNCT
ejpam-6472	187	1	we	we	PRON
ejpam-6472	187	2	prove	prove	VERB
ejpam-6472	187	3	only	only	ADV
ejpam-6472	187	4	the	the	DET
ejpam-6472	187	5	first	first	ADJ
ejpam-6472	187	6	part	part	NOUN
ejpam-6472	187	7	,	,	PUNCT
ejpam-6472	187	8	as	as	SCONJ
ejpam-6472	187	9	the	the	DET
ejpam-6472	187	10	second	second	NOUN
ejpam-6472	187	11	follows	follow	VERB
ejpam-6472	187	12	by	by	ADP
ejpam-6472	187	13	a	a	DET
ejpam-6472	187	14	similar	similar	ADJ
ejpam-6472	187	15	argument	argument	NOUN
ejpam-6472	187	16	.	.	PUNCT
ejpam-6472	188	1	assume	assume	VERB
ejpam-6472	188	2	that	that	SCONJ
ejpam-6472	188	3	t	t	NOUN
ejpam-6472	188	4	·	·	PUNCT
ejpam-6472	188	5	rs	rs	NOUN
ejpam-6472	188	6	q	q	PROPN
ejpam-6472	188	7	=	=	SYM
ejpam-6472	188	8	r.	r.	PROPN
ejpam-6472	188	9	then	then	ADV
ejpam-6472	188	10	r	r	PROPN
ejpam-6472	188	11	∈	∈	PROPN
ejpam-6472	188	12	sub(t	sub(t	NOUN
ejpam-6472	188	13	·	·	SYM
ejpam-6472	188	14	rs	rs	X
ejpam-6472	188	15	q	q	NOUN
ejpam-6472	188	16	)	)	PUNCT
ejpam-6472	188	17	.	.	PUNCT
ejpam-6472	189	1	by	by	ADP
ejpam-6472	189	2	lemma	lemma	PROPN
ejpam-6472	189	3	2	2	NUM
ejpam-6472	189	4	,	,	PUNCT
ejpam-6472	189	5	we	we	PRON
ejpam-6472	189	6	obtain	obtain	VERB
ejpam-6472	189	7	{	{	PUNCT
ejpam-6472	189	8	r	r	NOUN
ejpam-6472	189	9	,	,	PUNCT
ejpam-6472	189	10	s	s	NOUN
ejpam-6472	189	11	}	}	PUNCT
ejpam-6472	189	12	∩	∩	ADJ
ejpam-6472	189	13	sub(t	sub(t	NOUN
ejpam-6472	189	14	)	)	PUNCT
ejpam-6472	189	15	̸=	̸=	PROPN
ejpam-6472	189	16	∅.	∅.	AUX
ejpam-6472	189	17	applying	apply	VERB
ejpam-6472	189	18	lemma	lemma	PROPN
ejpam-6472	189	19	1	1	NUM
ejpam-6472	189	20	,	,	PUNCT
ejpam-6472	189	21	it	it	PRON
ejpam-6472	189	22	follows	follow	VERB
ejpam-6472	189	23	that	that	SCONJ
ejpam-6472	189	24	q	q	PROPN
ejpam-6472	189	25	∈	∈	PROPN
ejpam-6472	189	26	sub(t	sub(t	NOUN
ejpam-6472	189	27	·	·	SYM
ejpam-6472	189	28	rs	rs	X
ejpam-6472	189	29	q	q	NOUN
ejpam-6472	189	30	)	)	PUNCT
ejpam-6472	189	31	=	=	SYM
ejpam-6472	189	32	sub(r	sub(r	PROPN
ejpam-6472	189	33	)	)	PUNCT
ejpam-6472	189	34	.	.	PUNCT
ejpam-6472	190	1	as	as	ADP
ejpam-6472	190	2	in	in	ADP
ejpam-6472	190	3	the	the	DET
ejpam-6472	190	4	case	case	NOUN
ejpam-6472	190	5	of	of	ADP
ejpam-6472	190	6	·	·	SYM
ejpam-6472	190	7	r	r	NOUN
ejpam-6472	190	8	,	,	PUNCT
ejpam-6472	190	9	the	the	DET
ejpam-6472	190	10	operation	operation	NOUN
ejpam-6472	190	11	·	·	PUNCT
ejpam-6472	190	12	rs	rs	NOUN
ejpam-6472	190	13	is	be	AUX
ejpam-6472	190	14	not	not	PART
ejpam-6472	190	15	necessarily	necessarily	ADV
ejpam-6472	190	16	associative	associative	ADJ
ejpam-6472	190	17	over	over	ADP
ejpam-6472	190	18	wτ	wτ	PROPN
ejpam-6472	190	19	(	(	PUNCT
ejpam-6472	190	20	xn	xn	PROPN
ejpam-6472	190	21	)	)	PUNCT
ejpam-6472	190	22	.	.	PUNCT
ejpam-6472	191	1	the	the	DET
ejpam-6472	191	2	following	follow	VERB
ejpam-6472	191	3	example	example	NOUN
ejpam-6472	191	4	illustrates	illustrate	VERB
ejpam-6472	191	5	this	this	DET
ejpam-6472	191	6	fact	fact	NOUN
ejpam-6472	191	7	.	.	PUNCT
ejpam-6472	192	1	example	example	NOUN
ejpam-6472	193	1	2	2	NUM
ejpam-6472	193	2	.	.	PUNCT
ejpam-6472	193	3	let	let	VERB
ejpam-6472	193	4	τ	τ	PROPN
ejpam-6472	193	5	=	=	PUNCT
ejpam-6472	193	6	(	(	PUNCT
ejpam-6472	193	7	1	1	NUM
ejpam-6472	193	8	,	,	PUNCT
ejpam-6472	193	9	2	2	NUM
ejpam-6472	193	10	)	)	PUNCT
ejpam-6472	193	11	with	with	ADP
ejpam-6472	193	12	a	a	DET
ejpam-6472	193	13	unary	unary	ADJ
ejpam-6472	193	14	operation	operation	NOUN
ejpam-6472	193	15	symbol	symbol	NOUN
ejpam-6472	193	16	g	g	PROPN
ejpam-6472	193	17	and	and	CCONJ
ejpam-6472	193	18	a	a	DET
ejpam-6472	193	19	binary	binary	ADJ
ejpam-6472	193	20	operation	operation	NOUN
ejpam-6472	193	21	symbol	symbol	NOUN
ejpam-6472	193	22	f	f	PROPN
ejpam-6472	193	23	.	.	PUNCT
ejpam-6472	194	1	fix	fix	VERB
ejpam-6472	194	2	the	the	DET
ejpam-6472	194	3	terms	term	NOUN
ejpam-6472	194	4	r	r	NOUN
ejpam-6472	194	5	=	=	SYM
ejpam-6472	194	6	f(x1	f(x1	NOUN
ejpam-6472	194	7	,	,	PUNCT
ejpam-6472	194	8	x1	x1	PROPN
ejpam-6472	194	9	)	)	PUNCT
ejpam-6472	194	10	and	and	CCONJ
ejpam-6472	194	11	s	s	NOUN
ejpam-6472	194	12	=	=	NOUN
ejpam-6472	194	13	g(x2	g(x2	NOUN
ejpam-6472	194	14	)	)	PUNCT
ejpam-6472	194	15	.	.	PUNCT
ejpam-6472	195	1	let	let	VERB
ejpam-6472	195	2	t	t	NOUN
ejpam-6472	195	3	=	=	SYM
ejpam-6472	195	4	f(g(x2	f(g(x2	NOUN
ejpam-6472	195	5	)	)	PUNCT
ejpam-6472	195	6	,	,	PUNCT
ejpam-6472	195	7	f(x1	f(x1	NOUN
ejpam-6472	195	8	,	,	PUNCT
ejpam-6472	195	9	x1	x1	PROPN
ejpam-6472	195	10	)	)	PUNCT
ejpam-6472	195	11	)	)	PUNCT
ejpam-6472	195	12	,	,	PUNCT
ejpam-6472	195	13	q	q	NOUN
ejpam-6472	196	1	=	=	SYM
ejpam-6472	196	2	x1	x1	PROPN
ejpam-6472	196	3	,	,	PUNCT
ejpam-6472	196	4	and	and	CCONJ
ejpam-6472	196	5	h	h	NOUN
ejpam-6472	197	1	=	=	SYM
ejpam-6472	197	2	g(f(x1	g(f(x1	PROPN
ejpam-6472	197	3	,	,	PUNCT
ejpam-6472	197	4	x2	x2	PROPN
ejpam-6472	197	5	)	)	PUNCT
ejpam-6472	197	6	)	)	PUNCT
ejpam-6472	197	7	be	be	AUX
ejpam-6472	197	8	2	2	NUM
ejpam-6472	197	9	-	-	PUNCT
ejpam-6472	197	10	ary	ary	NOUN
ejpam-6472	197	11	terms	term	NOUN
ejpam-6472	197	12	of	of	ADP
ejpam-6472	197	13	type	type	NOUN
ejpam-6472	197	14	τ	τ	PROPN
ejpam-6472	197	15	.	.	PUNCT
ejpam-6472	198	1	we	we	PRON
ejpam-6472	198	2	have	have	VERB
ejpam-6472	198	3	(	(	PUNCT
ejpam-6472	198	4	t	t	NOUN
ejpam-6472	198	5	·	·	SYM
ejpam-6472	198	6	rs	rs	NOUN
ejpam-6472	198	7	q	q	NOUN
ejpam-6472	198	8	)	)	PUNCT
ejpam-6472	198	9	·	·	PUNCT
ejpam-6472	198	10	rs	rs	NOUN
ejpam-6472	198	11	h	h	NOUN
ejpam-6472	198	12	=	=	PUNCT
ejpam-6472	198	13	(	(	PUNCT
ejpam-6472	198	14	f(g(x2	f(g(x2	NOUN
ejpam-6472	198	15	)	)	PUNCT
ejpam-6472	198	16	,	,	PUNCT
ejpam-6472	198	17	f(x1	f(x1	NOUN
ejpam-6472	198	18	,	,	PUNCT
ejpam-6472	198	19	x1	x1	PROPN
ejpam-6472	198	20	)	)	PUNCT
ejpam-6472	198	21	)	)	PUNCT
ejpam-6472	199	1	·	·	PUNCT
ejpam-6472	199	2	rs	rs	X
ejpam-6472	199	3	x1	x1	PROPN
ejpam-6472	199	4	)	)	PUNCT
ejpam-6472	199	5	·	·	PUNCT
ejpam-6472	199	6	rs	rs	X
ejpam-6472	199	7	g(f(x1	g(f(x1	PROPN
ejpam-6472	199	8	,	,	PUNCT
ejpam-6472	199	9	x2	x2	PROPN
ejpam-6472	199	10	)	)	PUNCT
ejpam-6472	199	11	)	)	PUNCT
ejpam-6472	200	1	=	=	SYM
ejpam-6472	200	2	f(x1	f(x1	X
ejpam-6472	200	3	,	,	PUNCT
ejpam-6472	200	4	x1	x1	PROPN
ejpam-6472	200	5	)	)	PUNCT
ejpam-6472	200	6	·	·	PUNCT
ejpam-6472	200	7	rs	rs	X
ejpam-6472	200	8	g(f(x1	g(f(x1	PROPN
ejpam-6472	200	9	,	,	PUNCT
ejpam-6472	200	10	x2	x2	PROPN
ejpam-6472	200	11	)	)	PUNCT
ejpam-6472	200	12	)	)	PUNCT
ejpam-6472	201	1	=	=	SYM
ejpam-6472	201	2	g(f(x1	g(f(x1	PROPN
ejpam-6472	201	3	,	,	PUNCT
ejpam-6472	201	4	x2	x2	PROPN
ejpam-6472	201	5	)	)	PUNCT
ejpam-6472	201	6	)	)	PUNCT
ejpam-6472	201	7	.	.	PUNCT
ejpam-6472	202	1	on	on	ADP
ejpam-6472	202	2	the	the	DET
ejpam-6472	202	3	other	other	ADJ
ejpam-6472	202	4	hand	hand	NOUN
ejpam-6472	202	5	,	,	PUNCT
ejpam-6472	202	6	t	t	NOUN
ejpam-6472	202	7	·	·	PUNCT
ejpam-6472	202	8	rs	rs	X
ejpam-6472	202	9	(	(	PUNCT
ejpam-6472	202	10	q	q	NOUN
ejpam-6472	202	11	·	·	SYM
ejpam-6472	202	12	rs	rs	ADJ
ejpam-6472	202	13	h	h	NOUN
ejpam-6472	202	14	)	)	PUNCT
ejpam-6472	202	15	=	=	SYM
ejpam-6472	202	16	f(g(x2	f(g(x2	NOUN
ejpam-6472	202	17	)	)	PUNCT
ejpam-6472	202	18	,	,	PUNCT
ejpam-6472	202	19	f(x1	f(x1	NOUN
ejpam-6472	202	20	,	,	PUNCT
ejpam-6472	202	21	x1	x1	PROPN
ejpam-6472	202	22	)	)	PUNCT
ejpam-6472	202	23	)	)	PUNCT
ejpam-6472	202	24	·	·	PUNCT
ejpam-6472	202	25	rs	rs	X
ejpam-6472	202	26	(	(	PUNCT
ejpam-6472	202	27	x1	x1	ADJ
ejpam-6472	202	28	·	·	SYM
ejpam-6472	202	29	rs	rs	ADJ
ejpam-6472	202	30	g(f(x1	g(f(x1	PROPN
ejpam-6472	202	31	,	,	PUNCT
ejpam-6472	202	32	x2	x2	PROPN
ejpam-6472	202	33	)	)	PUNCT
ejpam-6472	202	34	)	)	PUNCT
ejpam-6472	202	35	)	)	PUNCT
ejpam-6472	203	1	=	=	SYM
ejpam-6472	203	2	f(g(x2	f(g(x2	NOUN
ejpam-6472	203	3	)	)	PUNCT
ejpam-6472	203	4	,	,	PUNCT
ejpam-6472	203	5	f(x1	f(x1	NOUN
ejpam-6472	203	6	,	,	PUNCT
ejpam-6472	203	7	x1	x1	PROPN
ejpam-6472	203	8	)	)	PUNCT
ejpam-6472	203	9	)	)	PUNCT
ejpam-6472	204	1	·	·	PUNCT
ejpam-6472	204	2	rs	rs	X
ejpam-6472	204	3	x1	x1	NOUN
ejpam-6472	204	4	=	=	SYM
ejpam-6472	204	5	f(x1	f(x1	X
ejpam-6472	204	6	,	,	PUNCT
ejpam-6472	204	7	x1	x1	PROPN
ejpam-6472	204	8	)	)	PUNCT
ejpam-6472	204	9	.	.	PUNCT
ejpam-6472	205	1	thus	thus	ADV
ejpam-6472	205	2	,	,	PUNCT
ejpam-6472	205	3	(	(	PUNCT
ejpam-6472	205	4	t	t	NOUN
ejpam-6472	205	5	·	·	SYM
ejpam-6472	205	6	rs	rs	NOUN
ejpam-6472	205	7	q	q	NOUN
ejpam-6472	205	8	)	)	PUNCT
ejpam-6472	205	9	·	·	PUNCT
ejpam-6472	205	10	rs	rs	NOUN
ejpam-6472	205	11	h	h	NOUN
ejpam-6472	205	12	̸=	̸=	PROPN
ejpam-6472	205	13	t	t	PROPN
ejpam-6472	205	14	·	·	PUNCT
ejpam-6472	205	15	rs	rs	X
ejpam-6472	205	16	(	(	PUNCT
ejpam-6472	205	17	q	q	NOUN
ejpam-6472	205	18	·	·	SYM
ejpam-6472	205	19	rs	rs	ADJ
ejpam-6472	205	20	h	h	NOUN
ejpam-6472	205	21	)	)	PUNCT
ejpam-6472	205	22	,	,	PUNCT
ejpam-6472	205	23	and	and	CCONJ
ejpam-6472	205	24	the	the	DET
ejpam-6472	205	25	operation	operation	NOUN
ejpam-6472	205	26	·	·	PUNCT
ejpam-6472	205	27	rs	rs	NOUN
ejpam-6472	205	28	is	be	AUX
ejpam-6472	205	29	not	not	PART
ejpam-6472	205	30	associative	associative	ADJ
ejpam-6472	205	31	on	on	ADP
ejpam-6472	205	32	wτ	wτ	PROPN
ejpam-6472	205	33	(	(	PUNCT
ejpam-6472	205	34	x2	x2	PROPN
ejpam-6472	205	35	)	)	PUNCT
ejpam-6472	205	36	.	.	PUNCT
ejpam-6472	206	1	next	next	ADV
ejpam-6472	206	2	,	,	PUNCT
ejpam-6472	206	3	we	we	PRON
ejpam-6472	206	4	investigate	investigate	VERB
ejpam-6472	206	5	the	the	DET
ejpam-6472	206	6	associativity	associativity	NOUN
ejpam-6472	206	7	of	of	ADP
ejpam-6472	206	8	the	the	DET
ejpam-6472	206	9	operation	operation	NOUN
ejpam-6472	206	10	·	·	SYM
ejpam-6472	206	11	rs	rs	NOUN
ejpam-6472	206	12	.	.	PUNCT
ejpam-6472	207	1	a	a	DET
ejpam-6472	207	2	necessary	necessary	ADJ
ejpam-6472	207	3	and	and	CCONJ
ejpam-6472	207	4	sufficient	sufficient	ADJ
ejpam-6472	207	5	condition	condition	NOUN
ejpam-6472	207	6	is	be	AUX
ejpam-6472	207	7	first	first	ADV
ejpam-6472	207	8	established	establish	VERB
ejpam-6472	207	9	to	to	PART
ejpam-6472	207	10	characterize	characterize	VERB
ejpam-6472	207	11	when	when	SCONJ
ejpam-6472	207	12	associativity	associativity	NOUN
ejpam-6472	207	13	holds	hold	VERB
ejpam-6472	207	14	on	on	ADP
ejpam-6472	207	15	a	a	DET
ejpam-6472	207	16	given	give	VERB
ejpam-6472	207	17	subset	subset	NOUN
ejpam-6472	207	18	of	of	ADP
ejpam-6472	207	19	wτ	wτ	PROPN
ejpam-6472	207	20	(	(	PUNCT
ejpam-6472	207	21	xn	xn	PROPN
ejpam-6472	207	22	)	)	PUNCT
ejpam-6472	207	23	.	.	PUNCT
ejpam-6472	208	1	using	use	VERB
ejpam-6472	208	2	this	this	DET
ejpam-6472	208	3	criterion	criterion	NOUN
ejpam-6472	208	4	,	,	PUNCT
ejpam-6472	208	5	we	we	PRON
ejpam-6472	208	6	construct	construct	VERB
ejpam-6472	208	7	a	a	DET
ejpam-6472	208	8	subset	subset	NOUN
ejpam-6472	208	9	of	of	ADP
ejpam-6472	208	10	wτ	wτ	PROPN
ejpam-6472	208	11	(	(	PUNCT
ejpam-6472	208	12	xn	xn	PROPN
ejpam-6472	208	13	)	)	PUNCT
ejpam-6472	208	14	on	on	ADP
ejpam-6472	208	15	which	which	PRON
ejpam-6472	208	16	·	·	PUNCT
ejpam-6472	208	17	rs	rs	X
ejpam-6472	208	18	is	be	AUX
ejpam-6472	208	19	both	both	PRON
ejpam-6472	208	20	associative	associative	ADJ
ejpam-6472	208	21	and	and	CCONJ
ejpam-6472	208	22	closed	closed	ADJ
ejpam-6472	208	23	,	,	PUNCT
ejpam-6472	208	24	which	which	PRON
ejpam-6472	208	25	leads	lead	VERB
ejpam-6472	208	26	to	to	ADP
ejpam-6472	208	27	a	a	DET
ejpam-6472	208	28	semigroup	semigroup	NOUN
ejpam-6472	208	29	under	under	ADP
ejpam-6472	208	30	the	the	DET
ejpam-6472	208	31	operation	operation	NOUN
ejpam-6472	208	32	.	.	PUNCT
ejpam-6472	209	1	theorem	theorem	NOUN
ejpam-6472	209	2	2	2	NUM
ejpam-6472	209	3	.	.	PUNCT
ejpam-6472	210	1	let	let	VERB
ejpam-6472	210	2	r	r	NOUN
ejpam-6472	210	3	,	,	PUNCT
ejpam-6472	210	4	s	s	NOUN
ejpam-6472	210	5	∈	∈	PROPN
ejpam-6472	210	6	wτ	wτ	NOUN
ejpam-6472	210	7	(	(	PUNCT
ejpam-6472	210	8	xn	xn	X
ejpam-6472	210	9	)	)	PUNCT
ejpam-6472	210	10	be	be	AUX
ejpam-6472	210	11	fixed	fix	VERB
ejpam-6472	210	12	terms	term	NOUN
ejpam-6472	210	13	and	and	CCONJ
ejpam-6472	210	14	a	a	DET
ejpam-6472	210	15	a	a	DET
ejpam-6472	210	16	non	non	ADJ
ejpam-6472	210	17	-	-	ADJ
ejpam-6472	210	18	empty	empty	ADJ
ejpam-6472	210	19	subset	subset	NOUN
ejpam-6472	210	20	of	of	ADP
ejpam-6472	210	21	wτ	wτ	PROPN
ejpam-6472	210	22	(	(	PUNCT
ejpam-6472	210	23	xn	xn	PROPN
ejpam-6472	210	24	)	)	PUNCT
ejpam-6472	210	25	.	.	PUNCT
ejpam-6472	211	1	the	the	DET
ejpam-6472	211	2	following	follow	VERB
ejpam-6472	211	3	statements	statement	NOUN
ejpam-6472	211	4	are	be	AUX
ejpam-6472	211	5	equivalent	equivalent	ADJ
ejpam-6472	211	6	:	:	PUNCT
ejpam-6472	211	7	(	(	PUNCT
ejpam-6472	211	8	i	i	NOUN
ejpam-6472	211	9	)	)	PUNCT
ejpam-6472	211	10	for	for	ADP
ejpam-6472	211	11	all	all	DET
ejpam-6472	211	12	t	t	NOUN
ejpam-6472	211	13	,	,	PUNCT
ejpam-6472	211	14	q	q	PROPN
ejpam-6472	211	15	∈	∈	PROPN
ejpam-6472	211	16	a	a	PRON
ejpam-6472	211	17	,	,	PUNCT
ejpam-6472	211	18	if	if	SCONJ
ejpam-6472	211	19	t	t	PROPN
ejpam-6472	211	20	̸∈	̸∈	PROPN
ejpam-6472	211	21	{	{	PUNCT
ejpam-6472	211	22	r	r	PROPN
ejpam-6472	211	23	,	,	PUNCT
ejpam-6472	211	24	s	s	PART
ejpam-6472	211	25	}	}	PUNCT
ejpam-6472	211	26	,	,	PUNCT
ejpam-6472	211	27	then	then	ADV
ejpam-6472	211	28	t	t	X
ejpam-6472	211	29	·	·	PUNCT
ejpam-6472	211	30	rs	rs	PROPN
ejpam-6472	211	31	q	q	PROPN
ejpam-6472	211	32	̸∈	̸∈	PROPN
ejpam-6472	211	33	{	{	PUNCT
ejpam-6472	211	34	r	r	PROPN
ejpam-6472	211	35	,	,	PUNCT
ejpam-6472	211	36	s	s	PART
ejpam-6472	211	37	}	}	PUNCT
ejpam-6472	211	38	.	.	PUNCT
ejpam-6472	212	1	(	(	PUNCT
ejpam-6472	212	2	ii	ii	NOUN
ejpam-6472	212	3	)	)	PUNCT
ejpam-6472	212	4	for	for	ADP
ejpam-6472	212	5	all	all	DET
ejpam-6472	212	6	t	t	PROPN
ejpam-6472	212	7	,	,	PUNCT
ejpam-6472	212	8	q	q	X
ejpam-6472	212	9	,	,	PUNCT
ejpam-6472	212	10	u	u	PROPN
ejpam-6472	212	11	∈	∈	PROPN
ejpam-6472	212	12	a	a	PRON
ejpam-6472	212	13	,	,	PUNCT
ejpam-6472	212	14	(	(	PUNCT
ejpam-6472	212	15	t	t	NOUN
ejpam-6472	212	16	·	·	SYM
ejpam-6472	212	17	rs	rs	NOUN
ejpam-6472	212	18	q	q	NOUN
ejpam-6472	212	19	)	)	PUNCT
ejpam-6472	212	20	·	·	PUNCT
ejpam-6472	212	21	rs	rs	PROPN
ejpam-6472	212	22	u	u	PROPN
ejpam-6472	212	23	=	=	PROPN
ejpam-6472	212	24	t	t	PROPN
ejpam-6472	212	25	·	·	PUNCT
ejpam-6472	212	26	rs	rs	X
ejpam-6472	212	27	(	(	PUNCT
ejpam-6472	212	28	q	q	NOUN
ejpam-6472	212	29	·	·	SYM
ejpam-6472	212	30	rs	rs	X
ejpam-6472	212	31	u	u	NOUN
ejpam-6472	212	32	)	)	PUNCT
ejpam-6472	212	33	.	.	PUNCT
ejpam-6472	213	1	proof	proof	NOUN
ejpam-6472	213	2	.	.	PUNCT
ejpam-6472	214	1	assume	assume	VERB
ejpam-6472	214	2	(	(	PUNCT
ejpam-6472	214	3	i	i	NOUN
ejpam-6472	214	4	)	)	PUNCT
ejpam-6472	214	5	and	and	CCONJ
ejpam-6472	214	6	let	let	VERB
ejpam-6472	214	7	t	t	PROPN
ejpam-6472	214	8	,	,	PUNCT
ejpam-6472	214	9	q	q	X
ejpam-6472	214	10	,	,	PUNCT
ejpam-6472	214	11	u	u	PROPN
ejpam-6472	214	12	∈	∈	NOUN
ejpam-6472	214	13	a.	a.	NOUN
ejpam-6472	214	14	we	we	PRON
ejpam-6472	214	15	prove	prove	VERB
ejpam-6472	214	16	by	by	ADP
ejpam-6472	214	17	induction	induction	NOUN
ejpam-6472	214	18	on	on	ADP
ejpam-6472	214	19	the	the	DET
ejpam-6472	214	20	structure	structure	NOUN
ejpam-6472	214	21	of	of	ADP
ejpam-6472	214	22	t.	t.	PROPN
ejpam-6472	214	23	if	if	SCONJ
ejpam-6472	214	24	{	{	PUNCT
ejpam-6472	214	25	r	r	NOUN
ejpam-6472	214	26	,	,	PUNCT
ejpam-6472	214	27	s	s	NOUN
ejpam-6472	214	28	}	}	PUNCT
ejpam-6472	214	29	∩	∩	ADJ
ejpam-6472	214	30	sub(t	sub(t	NOUN
ejpam-6472	214	31	)	)	PUNCT
ejpam-6472	214	32	=	=	SYM
ejpam-6472	214	33	∅	∅	NOUN
ejpam-6472	214	34	,	,	PUNCT
ejpam-6472	214	35	then	then	ADV
ejpam-6472	214	36	(	(	PUNCT
ejpam-6472	214	37	t	t	NOUN
ejpam-6472	214	38	·	·	SYM
ejpam-6472	214	39	rs	rs	NOUN
ejpam-6472	214	40	q	q	NOUN
ejpam-6472	214	41	)	)	PUNCT
ejpam-6472	214	42	·	·	PUNCT
ejpam-6472	214	43	rs	rs	PROPN
ejpam-6472	214	44	u	u	PROPN
ejpam-6472	214	45	=	=	PROPN
ejpam-6472	214	46	t	t	PROPN
ejpam-6472	214	47	·	·	PUNCT
ejpam-6472	214	48	rs	rs	NOUN
ejpam-6472	214	49	u	u	NOUN
ejpam-6472	214	50	=	=	PROPN
ejpam-6472	214	51	t	t	PROPN
ejpam-6472	214	52	=	=	SYM
ejpam-6472	214	53	t	t	PROPN
ejpam-6472	214	54	·	·	PUNCT
ejpam-6472	214	55	rs	rs	X
ejpam-6472	214	56	(	(	PUNCT
ejpam-6472	214	57	q	q	NOUN
ejpam-6472	214	58	·	·	SYM
ejpam-6472	214	59	rs	rs	X
ejpam-6472	214	60	u	u	NOUN
ejpam-6472	214	61	)	)	PUNCT
ejpam-6472	214	62	.	.	PUNCT
ejpam-6472	215	1	p.	p.	PROPN
ejpam-6472	215	2	prachumdang	prachumdang	PROPN
ejpam-6472	215	3	,	,	PUNCT
ejpam-6472	215	4	b.	b.	PROPN
ejpam-6472	215	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	215	6	/	/	SYM
ejpam-6472	215	7	eur	eur	PROPN
ejpam-6472	215	8	.	.	PUNCT
ejpam-6472	216	1	j.	j.	PROPN
ejpam-6472	216	2	pure	pure	PROPN
ejpam-6472	216	3	appl	appl	PROPN
ejpam-6472	216	4	.	.	PROPN
ejpam-6472	216	5	math	math	PROPN
ejpam-6472	216	6	,	,	PUNCT
ejpam-6472	216	7	18	18	NUM
ejpam-6472	216	8	(	(	PUNCT
ejpam-6472	216	9	3	3	NUM
ejpam-6472	216	10	)	)	PUNCT
ejpam-6472	216	11	(	(	PUNCT
ejpam-6472	216	12	2025	2025	NUM
ejpam-6472	216	13	)	)	PUNCT
ejpam-6472	216	14	,	,	PUNCT
ejpam-6472	216	15	6472	6472	NUM
ejpam-6472	216	16	7	7	NUM
ejpam-6472	216	17	of	of	ADP
ejpam-6472	216	18	16	16	NUM
ejpam-6472	216	19	if	if	SCONJ
ejpam-6472	216	20	t	t	PROPN
ejpam-6472	216	21	∈	∈	PROPN
ejpam-6472	216	22	{	{	PUNCT
ejpam-6472	216	23	r	r	NOUN
ejpam-6472	216	24	,	,	PUNCT
ejpam-6472	216	25	s	s	PART
ejpam-6472	216	26	}	}	PUNCT
ejpam-6472	216	27	,	,	PUNCT
ejpam-6472	216	28	then	then	ADV
ejpam-6472	216	29	(	(	PUNCT
ejpam-6472	216	30	t	t	NOUN
ejpam-6472	216	31	·	·	SYM
ejpam-6472	216	32	rs	rs	NOUN
ejpam-6472	216	33	q	q	NOUN
ejpam-6472	216	34	)	)	PUNCT
ejpam-6472	216	35	·	·	PUNCT
ejpam-6472	216	36	rs	rs	NOUN
ejpam-6472	216	37	u	u	NOUN
ejpam-6472	216	38	=	=	X
ejpam-6472	216	39	q	q	NOUN
ejpam-6472	216	40	·	·	PUNCT
ejpam-6472	216	41	rs	rs	NOUN
ejpam-6472	216	42	u	u	PROPN
ejpam-6472	216	43	=	=	PROPN
ejpam-6472	216	44	t	t	PROPN
ejpam-6472	216	45	·	·	PUNCT
ejpam-6472	216	46	rs	rs	X
ejpam-6472	216	47	(	(	PUNCT
ejpam-6472	216	48	q	q	NOUN
ejpam-6472	216	49	·	·	SYM
ejpam-6472	216	50	rs	rs	X
ejpam-6472	216	51	u	u	NOUN
ejpam-6472	216	52	)	)	PUNCT
ejpam-6472	216	53	.	.	PUNCT
ejpam-6472	217	1	for	for	ADP
ejpam-6472	217	2	t	t	NOUN
ejpam-6472	217	3	=	=	SYM
ejpam-6472	217	4	fi(t1	fi(t1	PROPN
ejpam-6472	217	5	,	,	PUNCT
ejpam-6472	217	6	.	.	PUNCT
ejpam-6472	217	7	.	.	PUNCT
ejpam-6472	218	1	.	.	PUNCT
ejpam-6472	219	1	,	,	PUNCT
ejpam-6472	219	2	tni	tni	NOUN
ejpam-6472	219	3	)	)	PUNCT
ejpam-6472	219	4	with	with	ADP
ejpam-6472	219	5	{	{	PUNCT
ejpam-6472	219	6	r	r	NOUN
ejpam-6472	219	7	,	,	PUNCT
ejpam-6472	219	8	s	s	NOUN
ejpam-6472	219	9	}	}	PUNCT
ejpam-6472	219	10	∩	∩	ADJ
ejpam-6472	219	11	sub(t	sub(t	NOUN
ejpam-6472	219	12	)	)	PUNCT
ejpam-6472	219	13	̸=	̸=	PROPN
ejpam-6472	219	14	∅	∅	NOUN
ejpam-6472	219	15	and	and	CCONJ
ejpam-6472	219	16	t	t	X
ejpam-6472	219	17	̸∈	̸∈	PROPN
ejpam-6472	219	18	{	{	PUNCT
ejpam-6472	219	19	r	r	PROPN
ejpam-6472	219	20	,	,	PUNCT
ejpam-6472	219	21	s	s	PART
ejpam-6472	219	22	}	}	PUNCT
ejpam-6472	219	23	,	,	PUNCT
ejpam-6472	219	24	assume	assume	VERB
ejpam-6472	219	25	inductively	inductively	ADV
ejpam-6472	219	26	that	that	SCONJ
ejpam-6472	219	27	(	(	PUNCT
ejpam-6472	219	28	tj	tj	NOUN
ejpam-6472	219	29	·	·	SYM
ejpam-6472	219	30	rs	rs	NOUN
ejpam-6472	219	31	q	q	NOUN
ejpam-6472	219	32	)	)	PUNCT
ejpam-6472	219	33	·	·	PUNCT
ejpam-6472	219	34	rs	rs	PROPN
ejpam-6472	219	35	u	u	NOUN
ejpam-6472	219	36	=	=	PROPN
ejpam-6472	219	37	tj	tj	PROPN
ejpam-6472	219	38	·	·	PUNCT
ejpam-6472	219	39	rs	rs	X
ejpam-6472	219	40	(	(	PUNCT
ejpam-6472	219	41	q	q	NOUN
ejpam-6472	219	42	·	·	SYM
ejpam-6472	219	43	rs	rs	X
ejpam-6472	219	44	u	u	NOUN
ejpam-6472	219	45	)	)	PUNCT
ejpam-6472	219	46	for	for	ADP
ejpam-6472	219	47	all	all	DET
ejpam-6472	219	48	j.	j.	PROPN
ejpam-6472	219	49	we	we	PRON
ejpam-6472	219	50	consider	consider	VERB
ejpam-6472	219	51	the	the	DET
ejpam-6472	219	52	following	follow	VERB
ejpam-6472	219	53	two	two	NUM
ejpam-6472	219	54	cases	case	NOUN
ejpam-6472	219	55	:	:	PUNCT
ejpam-6472	219	56	case	case	NOUN
ejpam-6472	219	57	1	1	NUM
ejpam-6472	219	58	:	:	PUNCT
ejpam-6472	219	59	{	{	PUNCT
ejpam-6472	219	60	r	r	NOUN
ejpam-6472	219	61	,	,	PUNCT
ejpam-6472	219	62	s	s	NOUN
ejpam-6472	219	63	}	}	PUNCT
ejpam-6472	219	64	∩	∩	ADJ
ejpam-6472	219	65	sub(t	sub(t	NOUN
ejpam-6472	219	66	·	·	SYM
ejpam-6472	219	67	rs	rs	X
ejpam-6472	219	68	q	q	NOUN
ejpam-6472	219	69	)	)	PUNCT
ejpam-6472	220	1	=	=	PUNCT
ejpam-6472	220	2	∅.	∅.	NOUN
ejpam-6472	220	3	then	then	ADV
ejpam-6472	220	4	(	(	PUNCT
ejpam-6472	220	5	t	t	NOUN
ejpam-6472	220	6	·	·	SYM
ejpam-6472	220	7	rs	rs	NOUN
ejpam-6472	220	8	q	q	NOUN
ejpam-6472	220	9	)	)	PUNCT
ejpam-6472	220	10	·	·	PUNCT
ejpam-6472	220	11	rs	rs	PROPN
ejpam-6472	220	12	u	u	PROPN
ejpam-6472	220	13	=	=	PROPN
ejpam-6472	220	14	t	t	PROPN
ejpam-6472	220	15	·	·	PUNCT
ejpam-6472	220	16	rs	rs	X
ejpam-6472	220	17	q.	q.	PROPN
ejpam-6472	220	18	since	since	SCONJ
ejpam-6472	220	19	{	{	PUNCT
ejpam-6472	220	20	r	r	NOUN
ejpam-6472	220	21	,	,	PUNCT
ejpam-6472	220	22	s	s	NOUN
ejpam-6472	220	23	}	}	PUNCT
ejpam-6472	220	24	∩	∩	ADJ
ejpam-6472	220	25	sub(t	sub(t	NOUN
ejpam-6472	220	26	)	)	PUNCT
ejpam-6472	220	27	̸=	̸=	NOUN
ejpam-6472	220	28	∅	∅	NOUN
ejpam-6472	220	29	,	,	PUNCT
ejpam-6472	220	30	lemma	lemma	PROPN
ejpam-6472	220	31	1	1	NUM
ejpam-6472	220	32	implies	imply	VERB
ejpam-6472	220	33	that	that	SCONJ
ejpam-6472	220	34	q	q	PROPN
ejpam-6472	220	35	∈	∈	PROPN
ejpam-6472	220	36	sub(t	sub(t	NOUN
ejpam-6472	220	37	·	·	SYM
ejpam-6472	220	38	rs	rs	X
ejpam-6472	220	39	q	q	NOUN
ejpam-6472	220	40	)	)	PUNCT
ejpam-6472	220	41	.	.	PUNCT
ejpam-6472	221	1	consequently	consequently	ADV
ejpam-6472	221	2	,	,	PUNCT
ejpam-6472	221	3	{	{	PUNCT
ejpam-6472	221	4	r	r	NOUN
ejpam-6472	221	5	,	,	PUNCT
ejpam-6472	221	6	s	s	NOUN
ejpam-6472	221	7	}	}	PUNCT
ejpam-6472	221	8	∩	∩	ADJ
ejpam-6472	221	9	sub(q	sub(q	PROPN
ejpam-6472	221	10	)	)	PUNCT
ejpam-6472	221	11	=	=	PUNCT
ejpam-6472	221	12	∅.	∅.	NOUN
ejpam-6472	221	13	it	it	PRON
ejpam-6472	221	14	follows	follow	VERB
ejpam-6472	221	15	that	that	SCONJ
ejpam-6472	221	16	t	t	NOUN
ejpam-6472	221	17	·	·	PUNCT
ejpam-6472	221	18	rs	rs	X
ejpam-6472	221	19	(	(	PUNCT
ejpam-6472	221	20	q	q	NOUN
ejpam-6472	221	21	·	·	SYM
ejpam-6472	221	22	rs	rs	X
ejpam-6472	221	23	u	u	NOUN
ejpam-6472	221	24	)	)	PUNCT
ejpam-6472	221	25	=	=	SYM
ejpam-6472	221	26	t	t	PROPN
ejpam-6472	221	27	·	·	PUNCT
ejpam-6472	221	28	rs	rs	PROPN
ejpam-6472	221	29	q.	q.	PROPN
ejpam-6472	221	30	thus	thus	ADV
ejpam-6472	221	31	,	,	PUNCT
ejpam-6472	221	32	(	(	PUNCT
ejpam-6472	221	33	t	t	NOUN
ejpam-6472	221	34	·	·	SYM
ejpam-6472	221	35	rs	rs	NOUN
ejpam-6472	221	36	q	q	NOUN
ejpam-6472	221	37	)	)	PUNCT
ejpam-6472	221	38	·	·	PUNCT
ejpam-6472	221	39	rs	rs	PROPN
ejpam-6472	221	40	u	u	PROPN
ejpam-6472	221	41	=	=	PROPN
ejpam-6472	221	42	t	t	PROPN
ejpam-6472	221	43	·	·	PUNCT
ejpam-6472	221	44	rs	rs	X
ejpam-6472	221	45	(	(	PUNCT
ejpam-6472	221	46	q	q	NOUN
ejpam-6472	221	47	·	·	SYM
ejpam-6472	221	48	rs	rs	X
ejpam-6472	221	49	u	u	NOUN
ejpam-6472	221	50	)	)	PUNCT
ejpam-6472	221	51	.	.	PUNCT
ejpam-6472	222	1	case	case	NOUN
ejpam-6472	222	2	2	2	NUM
ejpam-6472	222	3	:	:	PUNCT
ejpam-6472	222	4	{	{	PUNCT
ejpam-6472	222	5	r	r	NOUN
ejpam-6472	222	6	,	,	PUNCT
ejpam-6472	222	7	s	s	NOUN
ejpam-6472	222	8	}	}	PUNCT
ejpam-6472	222	9	∩	∩	ADJ
ejpam-6472	222	10	sub(t	sub(t	NOUN
ejpam-6472	222	11	·	·	SYM
ejpam-6472	222	12	rs	rs	X
ejpam-6472	222	13	q	q	NOUN
ejpam-6472	222	14	)	)	PUNCT
ejpam-6472	222	15	̸=	̸=	PROPN
ejpam-6472	222	16	∅.	∅.	VERB
ejpam-6472	222	17	by	by	ADP
ejpam-6472	222	18	(	(	PUNCT
ejpam-6472	222	19	i	i	NOUN
ejpam-6472	222	20	)	)	PUNCT
ejpam-6472	222	21	and	and	CCONJ
ejpam-6472	222	22	the	the	DET
ejpam-6472	222	23	fact	fact	NOUN
ejpam-6472	222	24	that	that	SCONJ
ejpam-6472	222	25	t	t	PROPN
ejpam-6472	222	26	̸∈	̸∈	PROPN
ejpam-6472	222	27	{	{	PUNCT
ejpam-6472	222	28	r	r	PROPN
ejpam-6472	222	29	,	,	PUNCT
ejpam-6472	222	30	s	s	PART
ejpam-6472	222	31	}	}	PUNCT
ejpam-6472	222	32	,	,	PUNCT
ejpam-6472	222	33	we	we	PRON
ejpam-6472	222	34	obtain	obtain	VERB
ejpam-6472	222	35	t	t	NOUN
ejpam-6472	222	36	·	·	PUNCT
ejpam-6472	222	37	rs	rs	PROPN
ejpam-6472	222	38	q	q	PROPN
ejpam-6472	222	39	̸∈	̸∈	PROPN
ejpam-6472	222	40	{	{	PUNCT
ejpam-6472	222	41	r	r	PROPN
ejpam-6472	222	42	,	,	PUNCT
ejpam-6472	222	43	s	s	PART
ejpam-6472	222	44	}	}	PUNCT
ejpam-6472	222	45	.	.	PUNCT
ejpam-6472	223	1	from	from	ADP
ejpam-6472	223	2	the	the	DET
ejpam-6472	223	3	definition	definition	NOUN
ejpam-6472	223	4	of	of	ADP
ejpam-6472	223	5	·	·	PUNCT
ejpam-6472	223	6	rs	rs	X
ejpam-6472	223	7	and	and	CCONJ
ejpam-6472	223	8	the	the	DET
ejpam-6472	223	9	inductive	inductive	ADJ
ejpam-6472	223	10	hypothesis	hypothesis	NOUN
ejpam-6472	223	11	,	,	PUNCT
ejpam-6472	223	12	it	it	PRON
ejpam-6472	223	13	follows	follow	VERB
ejpam-6472	223	14	that	that	SCONJ
ejpam-6472	223	15	(	(	PUNCT
ejpam-6472	223	16	t	t	NOUN
ejpam-6472	223	17	·	·	SYM
ejpam-6472	223	18	rs	rs	NOUN
ejpam-6472	223	19	q	q	NOUN
ejpam-6472	223	20	)	)	PUNCT
ejpam-6472	223	21	·	·	PUNCT
ejpam-6472	223	22	rs	rs	PROPN
ejpam-6472	223	23	u	u	NOUN
ejpam-6472	223	24	=	=	PUNCT
ejpam-6472	223	25	(	(	PUNCT
ejpam-6472	223	26	fi(t1	fi(t1	NOUN
ejpam-6472	223	27	,	,	PUNCT
ejpam-6472	223	28	.	.	PUNCT
ejpam-6472	223	29	.	.	PUNCT
ejpam-6472	224	1	.	.	PUNCT
ejpam-6472	225	1	,	,	PUNCT
ejpam-6472	225	2	tni	tni	NOUN
ejpam-6472	225	3	)	)	PUNCT
ejpam-6472	225	4	·	·	PUNCT
ejpam-6472	225	5	rs	rs	X
ejpam-6472	225	6	q	q	NOUN
ejpam-6472	225	7	)	)	PUNCT
ejpam-6472	225	8	·	·	PUNCT
ejpam-6472	225	9	rs	rs	PROPN
ejpam-6472	225	10	u	u	PROPN
ejpam-6472	225	11	=	=	X
ejpam-6472	225	12	fi(t1	fi(t1	X
ejpam-6472	225	13	·	·	SYM
ejpam-6472	225	14	rs	rs	X
ejpam-6472	225	15	q	q	NOUN
ejpam-6472	225	16	,	,	PUNCT
ejpam-6472	225	17	.	.	PUNCT
ejpam-6472	225	18	.	.	PUNCT
ejpam-6472	226	1	.	.	PUNCT
ejpam-6472	227	1	,	,	PUNCT
ejpam-6472	227	2	tni	tni	NOUN
ejpam-6472	227	3	·	·	PUNCT
ejpam-6472	227	4	rs	rs	X
ejpam-6472	227	5	q	q	NOUN
ejpam-6472	227	6	)	)	PUNCT
ejpam-6472	227	7	·	·	PUNCT
ejpam-6472	227	8	rs	rs	PROPN
ejpam-6472	227	9	u	u	NOUN
ejpam-6472	227	10	=	=	PUNCT
ejpam-6472	227	11	fi((t1	fi((t1	X
ejpam-6472	227	12	·	·	PUNCT
ejpam-6472	227	13	rs	rs	X
ejpam-6472	227	14	q	q	NOUN
ejpam-6472	227	15	)	)	PUNCT
ejpam-6472	227	16	·	·	PUNCT
ejpam-6472	227	17	rs	rs	X
ejpam-6472	227	18	u	u	NOUN
ejpam-6472	227	19	,	,	PUNCT
ejpam-6472	227	20	.	.	PUNCT
ejpam-6472	227	21	.	.	PUNCT
ejpam-6472	227	22	.	.	PUNCT
ejpam-6472	228	1	,	,	PUNCT
ejpam-6472	228	2	(	(	PUNCT
ejpam-6472	228	3	tni	tni	NOUN
ejpam-6472	228	4	·	·	SYM
ejpam-6472	228	5	rs	rs	X
ejpam-6472	228	6	q	q	NOUN
ejpam-6472	228	7	)	)	PUNCT
ejpam-6472	228	8	·	·	PUNCT
ejpam-6472	228	9	rs	rs	X
ejpam-6472	228	10	u	u	NOUN
ejpam-6472	228	11	)	)	PUNCT
ejpam-6472	228	12	=	=	SYM
ejpam-6472	228	13	fi(t1	fi(t1	NOUN
ejpam-6472	228	14	·	·	PUNCT
ejpam-6472	228	15	rs	rs	X
ejpam-6472	228	16	(	(	PUNCT
ejpam-6472	228	17	q	q	NOUN
ejpam-6472	228	18	·	·	SYM
ejpam-6472	228	19	rs	rs	X
ejpam-6472	228	20	u	u	NOUN
ejpam-6472	228	21	)	)	PUNCT
ejpam-6472	228	22	,	,	PUNCT
ejpam-6472	228	23	.	.	PUNCT
ejpam-6472	228	24	.	.	PUNCT
ejpam-6472	228	25	.	.	PUNCT
ejpam-6472	229	1	,	,	PUNCT
ejpam-6472	229	2	tni	tni	NOUN
ejpam-6472	229	3	·	·	PUNCT
ejpam-6472	229	4	rs	rs	X
ejpam-6472	229	5	(	(	PUNCT
ejpam-6472	229	6	q	q	NOUN
ejpam-6472	229	7	·	·	SYM
ejpam-6472	229	8	rs	rs	X
ejpam-6472	229	9	u	u	NOUN
ejpam-6472	229	10	)	)	PUNCT
ejpam-6472	229	11	)	)	PUNCT
ejpam-6472	230	1	=	=	SYM
ejpam-6472	230	2	fi(t1	fi(t1	NOUN
ejpam-6472	230	3	,	,	PUNCT
ejpam-6472	230	4	.	.	PUNCT
ejpam-6472	230	5	.	.	PUNCT
ejpam-6472	230	6	.	.	PUNCT
ejpam-6472	231	1	,	,	PUNCT
ejpam-6472	231	2	tni	tni	NOUN
ejpam-6472	231	3	)	)	PUNCT
ejpam-6472	231	4	·	·	PUNCT
ejpam-6472	231	5	rs	rs	X
ejpam-6472	231	6	(	(	PUNCT
ejpam-6472	231	7	q	q	NOUN
ejpam-6472	231	8	·	·	SYM
ejpam-6472	231	9	rs	rs	X
ejpam-6472	231	10	u	u	NOUN
ejpam-6472	231	11	)	)	PUNCT
ejpam-6472	231	12	=	=	SYM
ejpam-6472	232	1	t	t	NOUN
ejpam-6472	232	2	·	·	PUNCT
ejpam-6472	232	3	rs	rs	X
ejpam-6472	232	4	(	(	PUNCT
ejpam-6472	232	5	q	q	NOUN
ejpam-6472	232	6	·	·	SYM
ejpam-6472	232	7	rs	rs	X
ejpam-6472	232	8	u	u	NOUN
ejpam-6472	232	9	)	)	PUNCT
ejpam-6472	232	10	.	.	PUNCT
ejpam-6472	233	1	conversely	conversely	ADV
ejpam-6472	233	2	,	,	PUNCT
ejpam-6472	233	3	assume	assume	VERB
ejpam-6472	233	4	(	(	PUNCT
ejpam-6472	233	5	ii	ii	NOUN
ejpam-6472	233	6	)	)	PUNCT
ejpam-6472	233	7	and	and	CCONJ
ejpam-6472	233	8	let	let	VERB
ejpam-6472	233	9	t	t	PROPN
ejpam-6472	233	10	,	,	PUNCT
ejpam-6472	233	11	q	q	PROPN
ejpam-6472	233	12	∈	∈	PROPN
ejpam-6472	233	13	a	a	DET
ejpam-6472	233	14	be	be	AUX
ejpam-6472	233	15	such	such	ADJ
ejpam-6472	233	16	that	that	SCONJ
ejpam-6472	233	17	t	t	PROPN
ejpam-6472	233	18	̸∈	̸∈	PROPN
ejpam-6472	233	19	{	{	PUNCT
ejpam-6472	233	20	r	r	PROPN
ejpam-6472	233	21	,	,	PUNCT
ejpam-6472	233	22	s	s	PART
ejpam-6472	233	23	}	}	PUNCT
ejpam-6472	233	24	.	.	PUNCT
ejpam-6472	234	1	suppose	suppose	VERB
ejpam-6472	234	2	t	t	NOUN
ejpam-6472	234	3	·	·	PUNCT
ejpam-6472	234	4	rs	rs	PROPN
ejpam-6472	234	5	q	q	PROPN
ejpam-6472	234	6	∈	∈	PROPN
ejpam-6472	234	7	{	{	PUNCT
ejpam-6472	234	8	r	r	NOUN
ejpam-6472	234	9	,	,	PUNCT
ejpam-6472	234	10	s	s	PART
ejpam-6472	234	11	}	}	PUNCT
ejpam-6472	234	12	,	,	PUNCT
ejpam-6472	234	13	say	say	VERB
ejpam-6472	234	14	t	t	NOUN
ejpam-6472	234	15	·	·	PUNCT
ejpam-6472	234	16	rs	rs	NOUN
ejpam-6472	235	1	q	q	PROPN
ejpam-6472	236	1	=	=	PUNCT
ejpam-6472	236	2	r.	r.	NOUN
ejpam-6472	236	3	by	by	ADP
ejpam-6472	236	4	lemma	lemma	PROPN
ejpam-6472	236	5	4	4	NUM
ejpam-6472	236	6	,	,	PUNCT
ejpam-6472	236	7	we	we	PRON
ejpam-6472	236	8	get	get	VERB
ejpam-6472	236	9	q	q	PROPN
ejpam-6472	236	10	∈	∈	PROPN
ejpam-6472	236	11	sub(r	sub(r	PROPN
ejpam-6472	236	12	)	)	PUNCT
ejpam-6472	236	13	and	and	CCONJ
ejpam-6472	236	14	{	{	PUNCT
ejpam-6472	236	15	r	r	NOUN
ejpam-6472	236	16	,	,	PUNCT
ejpam-6472	236	17	s	s	NOUN
ejpam-6472	236	18	}	}	PUNCT
ejpam-6472	236	19	∩	∩	ADJ
ejpam-6472	236	20	sub(t	sub(t	NOUN
ejpam-6472	236	21	)	)	PUNCT
ejpam-6472	236	22	̸=	̸=	PROPN
ejpam-6472	236	23	∅.	∅.	NOUN
ejpam-6472	236	24	we	we	PRON
ejpam-6472	236	25	consider	consider	VERB
ejpam-6472	236	26	the	the	DET
ejpam-6472	236	27	following	follow	VERB
ejpam-6472	236	28	two	two	NUM
ejpam-6472	236	29	cases	case	NOUN
ejpam-6472	236	30	:	:	PUNCT
ejpam-6472	236	31	case	case	NOUN
ejpam-6472	236	32	1	1	NUM
ejpam-6472	236	33	:	:	PUNCT
ejpam-6472	236	34	q	q	X
ejpam-6472	236	35	∈	∈	PROPN
ejpam-6472	236	36	{	{	PUNCT
ejpam-6472	236	37	r	r	NOUN
ejpam-6472	236	38	,	,	PUNCT
ejpam-6472	236	39	s	s	PART
ejpam-6472	236	40	}	}	PUNCT
ejpam-6472	236	41	.	.	PUNCT
ejpam-6472	237	1	by	by	ADP
ejpam-6472	237	2	the	the	DET
ejpam-6472	237	3	associativity	associativity	NOUN
ejpam-6472	237	4	of	of	ADP
ejpam-6472	237	5	·	·	PUNCT
ejpam-6472	237	6	rs	rs	X
ejpam-6472	237	7	,	,	PUNCT
ejpam-6472	237	8	we	we	PRON
ejpam-6472	237	9	have	have	VERB
ejpam-6472	237	10	t	t	NOUN
ejpam-6472	237	11	·	·	PUNCT
ejpam-6472	237	12	rs	rs	PROPN
ejpam-6472	237	13	t	t	PROPN
ejpam-6472	237	14	=	=	SYM
ejpam-6472	237	15	t	t	PROPN
ejpam-6472	237	16	·	·	PUNCT
ejpam-6472	237	17	rs	rs	X
ejpam-6472	237	18	(	(	PUNCT
ejpam-6472	237	19	q	q	NOUN
ejpam-6472	237	20	·	·	SYM
ejpam-6472	237	21	rs	rs	NOUN
ejpam-6472	237	22	t	t	PROPN
ejpam-6472	237	23	)	)	PUNCT
ejpam-6472	237	24	=	=	PUNCT
ejpam-6472	237	25	(	(	PUNCT
ejpam-6472	237	26	t	t	NOUN
ejpam-6472	237	27	·	·	SYM
ejpam-6472	237	28	rs	rs	NOUN
ejpam-6472	237	29	q	q	NOUN
ejpam-6472	237	30	)	)	PUNCT
ejpam-6472	237	31	·	·	PUNCT
ejpam-6472	237	32	rs	rs	X
ejpam-6472	237	33	t	t	NOUN
ejpam-6472	237	34	=	=	SYM
ejpam-6472	237	35	r	r	X
ejpam-6472	237	36	·	·	PUNCT
ejpam-6472	237	37	rs	rs	NOUN
ejpam-6472	237	38	t	t	NOUN
ejpam-6472	238	1	=	=	PUNCT
ejpam-6472	238	2	t.	t.	NOUN
ejpam-6472	238	3	since	since	SCONJ
ejpam-6472	238	4	{	{	PUNCT
ejpam-6472	238	5	r	r	NOUN
ejpam-6472	238	6	,	,	PUNCT
ejpam-6472	238	7	s}∩sub(t	s}∩sub(t	ADJ
ejpam-6472	238	8	)	)	PUNCT
ejpam-6472	238	9	̸=	̸=	NOUN
ejpam-6472	238	10	∅	∅	NOUN
ejpam-6472	238	11	and	and	CCONJ
ejpam-6472	238	12	t	t	X
ejpam-6472	238	13	̸∈	̸∈	PROPN
ejpam-6472	238	14	{	{	PUNCT
ejpam-6472	238	15	r	r	PROPN
ejpam-6472	238	16	,	,	PUNCT
ejpam-6472	238	17	s	s	PART
ejpam-6472	238	18	}	}	PUNCT
ejpam-6472	238	19	,	,	PUNCT
ejpam-6472	238	20	lemma	lemma	PROPN
ejpam-6472	238	21	1	1	NUM
ejpam-6472	238	22	gives	give	VERB
ejpam-6472	238	23	t	t	NOUN
ejpam-6472	238	24	∈	∈	PROPN
ejpam-6472	238	25	sub(t·rs	sub(t·rs	PROPN
ejpam-6472	238	26	t)\{t·rs	t)\{t·rs	PROPN
ejpam-6472	238	27	t	t	PROPN
ejpam-6472	238	28	}	}	PUNCT
ejpam-6472	238	29	=	=	SYM
ejpam-6472	238	30	sub(t)\{t	sub(t)\{t	X
ejpam-6472	238	31	}	}	PUNCT
ejpam-6472	238	32	,	,	PUNCT
ejpam-6472	238	33	a	a	DET
ejpam-6472	238	34	contradiction	contradiction	NOUN
ejpam-6472	238	35	.	.	PUNCT
ejpam-6472	239	1	case	case	NOUN
ejpam-6472	239	2	2	2	NUM
ejpam-6472	239	3	:	:	PUNCT
ejpam-6472	239	4	q	q	PROPN
ejpam-6472	239	5	̸∈	̸∈	PROPN
ejpam-6472	239	6	{	{	PUNCT
ejpam-6472	239	7	r	r	PROPN
ejpam-6472	239	8	,	,	PUNCT
ejpam-6472	239	9	s	s	PART
ejpam-6472	239	10	}	}	PUNCT
ejpam-6472	239	11	.	.	PUNCT
ejpam-6472	240	1	this	this	PRON
ejpam-6472	240	2	implies	imply	VERB
ejpam-6472	240	3	q	q	PROPN
ejpam-6472	240	4	∈	∈	PROPN
ejpam-6472	240	5	sub(r)\{r	sub(r)\{r	NOUN
ejpam-6472	240	6	}	}	PUNCT
ejpam-6472	240	7	,	,	PUNCT
ejpam-6472	240	8	so	so	SCONJ
ejpam-6472	240	9	op(q	op(q	NOUN
ejpam-6472	240	10	)	)	PUNCT
ejpam-6472	240	11	<	<	X
ejpam-6472	240	12	op(r	op(r	NOUN
ejpam-6472	240	13	)	)	PUNCT
ejpam-6472	240	14	.	.	PUNCT
ejpam-6472	241	1	hence	hence	ADV
ejpam-6472	241	2	,	,	PUNCT
ejpam-6472	241	3	r	r	PROPN
ejpam-6472	241	4	̸∈	̸∈	PROPN
ejpam-6472	241	5	sub(q	sub(q	PROPN
ejpam-6472	241	6	)	)	PUNCT
ejpam-6472	241	7	.	.	PUNCT
ejpam-6472	242	1	if	if	SCONJ
ejpam-6472	242	2	s	s	X
ejpam-6472	242	3	∈	∈	PROPN
ejpam-6472	242	4	sub(q	sub(q	PROPN
ejpam-6472	242	5	)	)	PUNCT
ejpam-6472	242	6	,	,	PUNCT
ejpam-6472	242	7	then	then	ADV
ejpam-6472	242	8	lemma	lemma	PROPN
ejpam-6472	242	9	1	1	NUM
ejpam-6472	242	10	provides	provide	VERB
ejpam-6472	242	11	that	that	SCONJ
ejpam-6472	242	12	t	t	PROPN
ejpam-6472	242	13	∈	∈	PROPN
ejpam-6472	242	14	sub(q	sub(q	PROPN
ejpam-6472	242	15	·	·	SYM
ejpam-6472	242	16	rs	rs	PROPN
ejpam-6472	242	17	t	t	PROPN
ejpam-6472	242	18	)	)	PUNCT
ejpam-6472	242	19	\	\	NOUN
ejpam-6472	242	20	{	{	PUNCT
ejpam-6472	242	21	q	q	NOUN
ejpam-6472	242	22	·	·	SYM
ejpam-6472	242	23	rs	rs	PROPN
ejpam-6472	242	24	t	t	PROPN
ejpam-6472	242	25	}	}	PUNCT
ejpam-6472	242	26	and	and	CCONJ
ejpam-6472	242	27	q	q	ADJ
ejpam-6472	242	28	·	·	PUNCT
ejpam-6472	242	29	rs	rs	PROPN
ejpam-6472	242	30	t	t	PROPN
ejpam-6472	242	31	∈	∈	PROPN
ejpam-6472	242	32	sub(t	sub(t	PROPN
ejpam-6472	242	33	·	·	PUNCT
ejpam-6472	242	34	rs	rs	X
ejpam-6472	242	35	(	(	PUNCT
ejpam-6472	242	36	q	q	NOUN
ejpam-6472	242	37	·	·	SYM
ejpam-6472	242	38	rs	rs	PROPN
ejpam-6472	242	39	t	t	PROPN
ejpam-6472	242	40	)	)	PUNCT
ejpam-6472	242	41	)	)	PUNCT
ejpam-6472	242	42	.	.	PUNCT
ejpam-6472	243	1	thus	thus	ADV
ejpam-6472	243	2	op(t	op(t	VERB
ejpam-6472	243	3	)	)	PUNCT
ejpam-6472	243	4	<	<	X
ejpam-6472	243	5	op(q	op(q	X
ejpam-6472	243	6	·	·	PUNCT
ejpam-6472	243	7	rs	rs	PROPN
ejpam-6472	243	8	t	t	PROPN
ejpam-6472	243	9	)	)	PUNCT
ejpam-6472	243	10	≤	≤	NOUN
ejpam-6472	243	11	op(t	op(t	X
ejpam-6472	243	12	·	·	PUNCT
ejpam-6472	243	13	rs	rs	X
ejpam-6472	243	14	(	(	PUNCT
ejpam-6472	243	15	q	q	NOUN
ejpam-6472	243	16	·	·	SYM
ejpam-6472	243	17	rs	rs	PROPN
ejpam-6472	243	18	t	t	PROPN
ejpam-6472	243	19	)	)	PUNCT
ejpam-6472	243	20	)	)	PUNCT
ejpam-6472	244	1	=	=	SYM
ejpam-6472	244	2	op((t	op((t	ADJ
ejpam-6472	244	3	·	·	PUNCT
ejpam-6472	244	4	rs	rs	ADJ
ejpam-6472	244	5	q	q	NOUN
ejpam-6472	244	6	)	)	PUNCT
ejpam-6472	244	7	·	·	PUNCT
ejpam-6472	244	8	rs	rs	PROPN
ejpam-6472	244	9	t	t	PROPN
ejpam-6472	244	10	)	)	PUNCT
ejpam-6472	244	11	=	=	SYM
ejpam-6472	244	12	op(r	op(r	X
ejpam-6472	244	13	·	·	PUNCT
ejpam-6472	244	14	rs	rs	PROPN
ejpam-6472	244	15	t	t	PROPN
ejpam-6472	244	16	)	)	PUNCT
ejpam-6472	244	17	=	=	SYM
ejpam-6472	244	18	op(t	op(t	NOUN
ejpam-6472	244	19	)	)	PUNCT
ejpam-6472	244	20	,	,	PUNCT
ejpam-6472	244	21	which	which	PRON
ejpam-6472	244	22	is	be	AUX
ejpam-6472	244	23	impossible	impossible	ADJ
ejpam-6472	244	24	.	.	PUNCT
ejpam-6472	245	1	it	it	PRON
ejpam-6472	245	2	follows	follow	VERB
ejpam-6472	245	3	that	that	SCONJ
ejpam-6472	245	4	{	{	PUNCT
ejpam-6472	245	5	r	r	NOUN
ejpam-6472	245	6	,	,	PUNCT
ejpam-6472	245	7	s	s	NOUN
ejpam-6472	245	8	}	}	PUNCT
ejpam-6472	245	9	∩	∩	ADJ
ejpam-6472	245	10	sub(q	sub(q	PROPN
ejpam-6472	245	11	)	)	PUNCT
ejpam-6472	245	12	=	=	NOUN
ejpam-6472	245	13	∅	∅	NOUN
ejpam-6472	245	14	,	,	PUNCT
ejpam-6472	245	15	so	so	ADV
ejpam-6472	245	16	q	q	ADJ
ejpam-6472	245	17	·	·	PUNCT
ejpam-6472	245	18	rs	rs	NOUN
ejpam-6472	245	19	t	t	NOUN
ejpam-6472	245	20	=	=	PUNCT
ejpam-6472	245	21	q.	q.	PROPN
ejpam-6472	245	22	as	as	ADP
ejpam-6472	245	23	a	a	DET
ejpam-6472	245	24	result	result	NOUN
ejpam-6472	245	25	,	,	PUNCT
ejpam-6472	245	26	r	r	NOUN
ejpam-6472	245	27	=	=	SYM
ejpam-6472	245	28	t	t	NOUN
ejpam-6472	245	29	·	·	PUNCT
ejpam-6472	245	30	rs	rs	NOUN
ejpam-6472	246	1	q	q	PROPN
ejpam-6472	247	1	=	=	SYM
ejpam-6472	247	2	t	t	NOUN
ejpam-6472	247	3	·	·	PUNCT
ejpam-6472	247	4	rs	rs	X
ejpam-6472	247	5	(	(	PUNCT
ejpam-6472	247	6	q	q	NOUN
ejpam-6472	247	7	·	·	SYM
ejpam-6472	247	8	rs	rs	NOUN
ejpam-6472	247	9	t	t	PROPN
ejpam-6472	247	10	)	)	PUNCT
ejpam-6472	247	11	=	=	PUNCT
ejpam-6472	247	12	(	(	PUNCT
ejpam-6472	247	13	t	t	NOUN
ejpam-6472	247	14	·	·	SYM
ejpam-6472	247	15	rs	rs	NOUN
ejpam-6472	247	16	q	q	NOUN
ejpam-6472	247	17	)	)	PUNCT
ejpam-6472	247	18	·	·	PUNCT
ejpam-6472	247	19	rs	rs	X
ejpam-6472	247	20	t	t	NOUN
ejpam-6472	247	21	=	=	SYM
ejpam-6472	247	22	r	r	X
ejpam-6472	247	23	·	·	PUNCT
ejpam-6472	247	24	rs	rs	NOUN
ejpam-6472	247	25	t	t	PROPN
ejpam-6472	247	26	=	=	SYM
ejpam-6472	247	27	t	t	PROPN
ejpam-6472	247	28	,	,	PUNCT
ejpam-6472	247	29	contradicting	contradict	VERB
ejpam-6472	247	30	t	t	PROPN
ejpam-6472	247	31	̸∈	̸∈	PROPN
ejpam-6472	247	32	{	{	PUNCT
ejpam-6472	247	33	r	r	PROPN
ejpam-6472	247	34	,	,	PUNCT
ejpam-6472	247	35	s	s	PART
ejpam-6472	247	36	}	}	PUNCT
ejpam-6472	247	37	.	.	PUNCT
ejpam-6472	248	1	theorem	theorem	NOUN
ejpam-6472	248	2	3	3	X
ejpam-6472	248	3	.	.	PUNCT
ejpam-6472	249	1	let	let	VERB
ejpam-6472	249	2	r	r	NOUN
ejpam-6472	249	3	,	,	PUNCT
ejpam-6472	249	4	s	s	NOUN
ejpam-6472	249	5	∈	∈	PROPN
ejpam-6472	249	6	wτ	wτ	NOUN
ejpam-6472	249	7	(	(	PUNCT
ejpam-6472	249	8	xn	xn	X
ejpam-6472	249	9	)	)	PUNCT
ejpam-6472	249	10	be	be	AUX
ejpam-6472	249	11	fixed	fix	VERB
ejpam-6472	249	12	terms	term	NOUN
ejpam-6472	249	13	,	,	PUNCT
ejpam-6472	249	14	and	and	CCONJ
ejpam-6472	249	15	define	define	VERB
ejpam-6472	249	16	w	w	NOUN
ejpam-6472	249	17	r	r	NOUN
ejpam-6472	249	18	,	,	PUNCT
ejpam-6472	249	19	s	s	PART
ejpam-6472	249	20	τ	τ	X
ejpam-6472	249	21	(	(	PUNCT
ejpam-6472	249	22	xn	xn	PROPN
ejpam-6472	249	23	)	)	PUNCT
ejpam-6472	250	1	=	=	PRON
ejpam-6472	250	2	wτ	wτ	INTJ
ejpam-6472	250	3	(	(	PUNCT
ejpam-6472	250	4	xn	xn	PROPN
ejpam-6472	250	5	)	)	PUNCT
ejpam-6472	250	6	\	\	PUNCT
ejpam-6472	251	1	[	[	PUNCT
ejpam-6472	251	2	(	(	PUNCT
ejpam-6472	251	3	sub(r	sub(r	PROPN
ejpam-6472	251	4	)	)	PUNCT
ejpam-6472	251	5	\	\	NOUN
ejpam-6472	251	6	{	{	PUNCT
ejpam-6472	251	7	r	r	NOUN
ejpam-6472	251	8	}	}	PUNCT
ejpam-6472	251	9	)	)	PUNCT
ejpam-6472	251	10	∪	∪	NOUN
ejpam-6472	251	11	(	(	PUNCT
ejpam-6472	251	12	sub(s	sub(s	PROPN
ejpam-6472	251	13	)	)	PUNCT
ejpam-6472	251	14	\	\	NOUN
ejpam-6472	252	1	{	{	PUNCT
ejpam-6472	252	2	s	s	NOUN
ejpam-6472	252	3	}	}	PUNCT
ejpam-6472	252	4	)	)	PUNCT
ejpam-6472	252	5	]	]	PUNCT
ejpam-6472	252	6	.	.	PUNCT
ejpam-6472	253	1	then	then	ADV
ejpam-6472	253	2	(	(	PUNCT
ejpam-6472	253	3	w	w	NOUN
ejpam-6472	253	4	r	r	NOUN
ejpam-6472	253	5	,	,	PUNCT
ejpam-6472	253	6	s	s	PART
ejpam-6472	253	7	τ	τ	X
ejpam-6472	253	8	(	(	PUNCT
ejpam-6472	253	9	xn	xn	PROPN
ejpam-6472	253	10	)	)	PUNCT
ejpam-6472	253	11	,	,	PUNCT
ejpam-6472	253	12	·	·	PUNCT
ejpam-6472	253	13	rs	rs	X
ejpam-6472	253	14	)	)	PUNCT
ejpam-6472	253	15	is	be	AUX
ejpam-6472	253	16	a	a	DET
ejpam-6472	253	17	semigroup	semigroup	NOUN
ejpam-6472	253	18	.	.	PUNCT
ejpam-6472	254	1	p.	p.	NOUN
ejpam-6472	254	2	prachumdang	prachumdang	PROPN
ejpam-6472	254	3	,	,	PUNCT
ejpam-6472	254	4	b.	b.	PROPN
ejpam-6472	254	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	254	6	/	/	SYM
ejpam-6472	254	7	eur	eur	PROPN
ejpam-6472	254	8	.	.	PUNCT
ejpam-6472	255	1	j.	j.	PROPN
ejpam-6472	255	2	pure	pure	PROPN
ejpam-6472	255	3	appl	appl	PROPN
ejpam-6472	255	4	.	.	PROPN
ejpam-6472	255	5	math	math	PROPN
ejpam-6472	255	6	,	,	PUNCT
ejpam-6472	255	7	18	18	NUM
ejpam-6472	255	8	(	(	PUNCT
ejpam-6472	255	9	3	3	NUM
ejpam-6472	255	10	)	)	PUNCT
ejpam-6472	255	11	(	(	PUNCT
ejpam-6472	255	12	2025	2025	NUM
ejpam-6472	255	13	)	)	PUNCT
ejpam-6472	255	14	,	,	PUNCT
ejpam-6472	255	15	6472	6472	NUM
ejpam-6472	255	16	8	8	NUM
ejpam-6472	255	17	of	of	ADP
ejpam-6472	255	18	16	16	NUM
ejpam-6472	255	19	proof	proof	NOUN
ejpam-6472	255	20	.	.	PUNCT
ejpam-6472	256	1	to	to	PART
ejpam-6472	256	2	show	show	VERB
ejpam-6472	256	3	closure	closure	NOUN
ejpam-6472	256	4	,	,	PUNCT
ejpam-6472	256	5	let	let	VERB
ejpam-6472	256	6	t	t	PROPN
ejpam-6472	256	7	,	,	PUNCT
ejpam-6472	256	8	q	q	PROPN
ejpam-6472	256	9	∈	∈	PROPN
ejpam-6472	256	10	w	w	NOUN
ejpam-6472	256	11	r	r	NOUN
ejpam-6472	256	12	,	,	PUNCT
ejpam-6472	256	13	s	s	PART
ejpam-6472	256	14	τ	τ	X
ejpam-6472	256	15	(	(	PUNCT
ejpam-6472	256	16	xn	xn	PROPN
ejpam-6472	256	17	)	)	PUNCT
ejpam-6472	256	18	.	.	PUNCT
ejpam-6472	257	1	if	if	SCONJ
ejpam-6472	257	2	{	{	PUNCT
ejpam-6472	257	3	r	r	NOUN
ejpam-6472	257	4	,	,	PUNCT
ejpam-6472	257	5	s	s	NOUN
ejpam-6472	257	6	}	}	PUNCT
ejpam-6472	257	7	∩	∩	ADJ
ejpam-6472	257	8	sub(t	sub(t	NOUN
ejpam-6472	257	9	)	)	PUNCT
ejpam-6472	257	10	=	=	NOUN
ejpam-6472	257	11	∅	∅	NOUN
ejpam-6472	257	12	,	,	PUNCT
ejpam-6472	257	13	then	then	ADV
ejpam-6472	257	14	t	t	PROPN
ejpam-6472	257	15	·	·	PUNCT
ejpam-6472	257	16	rs	rs	X
ejpam-6472	257	17	q	q	PROPN
ejpam-6472	258	1	=	=	PUNCT
ejpam-6472	258	2	t	t	X
ejpam-6472	258	3	∈	∈	PROPN
ejpam-6472	258	4	w	w	PROPN
ejpam-6472	258	5	r	r	PROPN
ejpam-6472	258	6	,	,	PUNCT
ejpam-6472	258	7	s	s	PART
ejpam-6472	258	8	τ	τ	X
ejpam-6472	258	9	(	(	PUNCT
ejpam-6472	258	10	xn	xn	PROPN
ejpam-6472	258	11	)	)	PUNCT
ejpam-6472	258	12	.	.	PUNCT
ejpam-6472	259	1	now	now	ADV
ejpam-6472	259	2	,	,	PUNCT
ejpam-6472	259	3	assume	assume	VERB
ejpam-6472	259	4	{	{	PUNCT
ejpam-6472	259	5	r	r	NOUN
ejpam-6472	259	6	,	,	PUNCT
ejpam-6472	259	7	s	s	NOUN
ejpam-6472	259	8	}	}	PUNCT
ejpam-6472	259	9	∩	∩	ADJ
ejpam-6472	259	10	sub(t	sub(t	NOUN
ejpam-6472	259	11	)	)	PUNCT
ejpam-6472	259	12	̸=	̸=	PROPN
ejpam-6472	259	13	∅.	∅.	PRON
ejpam-6472	259	14	by	by	ADP
ejpam-6472	259	15	lemma	lemma	PROPN
ejpam-6472	259	16	1	1	NUM
ejpam-6472	259	17	,	,	PUNCT
ejpam-6472	259	18	we	we	PRON
ejpam-6472	259	19	obtain	obtain	VERB
ejpam-6472	259	20	q	q	PROPN
ejpam-6472	259	21	∈	∈	PROPN
ejpam-6472	259	22	sub(t	sub(t	NOUN
ejpam-6472	259	23	·	·	SYM
ejpam-6472	259	24	rs	rs	X
ejpam-6472	259	25	q	q	NOUN
ejpam-6472	259	26	)	)	PUNCT
ejpam-6472	259	27	.	.	PUNCT
ejpam-6472	260	1	since	since	SCONJ
ejpam-6472	260	2	q	q	PROPN
ejpam-6472	260	3	is	be	AUX
ejpam-6472	260	4	not	not	PART
ejpam-6472	260	5	a	a	DET
ejpam-6472	260	6	proper	proper	ADJ
ejpam-6472	260	7	subterm	subterm	NOUN
ejpam-6472	260	8	of	of	ADP
ejpam-6472	260	9	either	either	CCONJ
ejpam-6472	260	10	r	r	NOUN
ejpam-6472	260	11	or	or	CCONJ
ejpam-6472	260	12	s	s	PROPN
ejpam-6472	260	13	,	,	PUNCT
ejpam-6472	260	14	the	the	DET
ejpam-6472	260	15	same	same	ADJ
ejpam-6472	260	16	must	must	AUX
ejpam-6472	260	17	hold	hold	VERB
ejpam-6472	260	18	for	for	ADP
ejpam-6472	260	19	t	t	NOUN
ejpam-6472	260	20	·	·	PUNCT
ejpam-6472	260	21	rs	rs	PROPN
ejpam-6472	260	22	q.	q.	PROPN
ejpam-6472	260	23	thus	thus	ADV
ejpam-6472	260	24	,	,	PUNCT
ejpam-6472	260	25	t	t	NOUN
ejpam-6472	260	26	·	·	PUNCT
ejpam-6472	260	27	rs	rs	X
ejpam-6472	260	28	q	q	PROPN
ejpam-6472	260	29	∈	∈	PROPN
ejpam-6472	260	30	w	w	PROPN
ejpam-6472	260	31	r	r	NOUN
ejpam-6472	260	32	,	,	PUNCT
ejpam-6472	260	33	s	s	PART
ejpam-6472	260	34	τ	τ	X
ejpam-6472	260	35	(	(	PUNCT
ejpam-6472	260	36	xn	xn	PROPN
ejpam-6472	260	37	)	)	PUNCT
ejpam-6472	260	38	.	.	PUNCT
ejpam-6472	261	1	next	next	ADV
ejpam-6472	261	2	,	,	PUNCT
ejpam-6472	261	3	we	we	PRON
ejpam-6472	261	4	establish	establish	VERB
ejpam-6472	261	5	associativity	associativity	NOUN
ejpam-6472	261	6	using	use	VERB
ejpam-6472	261	7	theorem	theorem	NOUN
ejpam-6472	261	8	2	2	NUM
ejpam-6472	261	9	.	.	PUNCT
ejpam-6472	262	1	let	let	VERB
ejpam-6472	262	2	t	t	PROPN
ejpam-6472	262	3	,	,	PUNCT
ejpam-6472	262	4	q	q	PROPN
ejpam-6472	262	5	∈	∈	PROPN
ejpam-6472	262	6	w	w	NOUN
ejpam-6472	262	7	r	r	NOUN
ejpam-6472	262	8	,	,	PUNCT
ejpam-6472	262	9	s	s	PART
ejpam-6472	262	10	τ	τ	X
ejpam-6472	262	11	(	(	PUNCT
ejpam-6472	262	12	xn	xn	PROPN
ejpam-6472	262	13	)	)	PUNCT
ejpam-6472	262	14	with	with	ADP
ejpam-6472	262	15	t	t	PROPN
ejpam-6472	262	16	̸∈	̸∈	PROPN
ejpam-6472	262	17	{	{	PUNCT
ejpam-6472	262	18	r	r	PROPN
ejpam-6472	262	19	,	,	PUNCT
ejpam-6472	262	20	s	s	PART
ejpam-6472	262	21	}	}	PUNCT
ejpam-6472	262	22	.	.	PUNCT
ejpam-6472	263	1	suppose	suppose	VERB
ejpam-6472	263	2	that	that	SCONJ
ejpam-6472	263	3	t	t	PROPN
ejpam-6472	263	4	·	·	SYM
ejpam-6472	263	5	rs	rs	NOUN
ejpam-6472	263	6	q	q	PROPN
ejpam-6472	263	7	∈	∈	PROPN
ejpam-6472	263	8	{	{	PUNCT
ejpam-6472	263	9	r	r	NOUN
ejpam-6472	263	10	,	,	PUNCT
ejpam-6472	263	11	s	s	PART
ejpam-6472	263	12	}	}	PUNCT
ejpam-6472	263	13	,	,	PUNCT
ejpam-6472	263	14	say	say	VERB
ejpam-6472	263	15	t	t	NOUN
ejpam-6472	263	16	·	·	PUNCT
ejpam-6472	263	17	rs	rs	NOUN
ejpam-6472	263	18	q	q	PROPN
ejpam-6472	264	1	=	=	PUNCT
ejpam-6472	264	2	r.	r.	NOUN
ejpam-6472	264	3	by	by	ADP
ejpam-6472	264	4	lemma	lemma	PROPN
ejpam-6472	264	5	4	4	NUM
ejpam-6472	264	6	,	,	PUNCT
ejpam-6472	264	7	we	we	PRON
ejpam-6472	264	8	have	have	AUX
ejpam-6472	264	9	{	{	PUNCT
ejpam-6472	264	10	r	r	NOUN
ejpam-6472	264	11	,	,	PUNCT
ejpam-6472	264	12	s	s	NOUN
ejpam-6472	264	13	}	}	PUNCT
ejpam-6472	264	14	∩	∩	ADJ
ejpam-6472	264	15	sub(t	sub(t	NOUN
ejpam-6472	264	16	)	)	PUNCT
ejpam-6472	264	17	̸=	̸=	PROPN
ejpam-6472	264	18	∅	∅	NOUN
ejpam-6472	264	19	and	and	CCONJ
ejpam-6472	264	20	q	q	NOUN
ejpam-6472	264	21	∈	∈	PROPN
ejpam-6472	264	22	sub(r	sub(r	PROPN
ejpam-6472	264	23	)	)	PUNCT
ejpam-6472	264	24	.	.	PUNCT
ejpam-6472	265	1	since	since	SCONJ
ejpam-6472	265	2	q	q	PROPN
ejpam-6472	265	3	is	be	AUX
ejpam-6472	265	4	not	not	PART
ejpam-6472	265	5	a	a	DET
ejpam-6472	265	6	proper	proper	ADJ
ejpam-6472	265	7	subterm	subterm	NOUN
ejpam-6472	265	8	of	of	ADP
ejpam-6472	265	9	r	r	NOUN
ejpam-6472	265	10	,	,	PUNCT
ejpam-6472	265	11	it	it	PRON
ejpam-6472	265	12	follows	follow	VERB
ejpam-6472	265	13	that	that	PRON
ejpam-6472	265	14	q	q	PROPN
ejpam-6472	265	15	=	=	SYM
ejpam-6472	265	16	r.	r.	NOUN
ejpam-6472	265	17	applying	apply	VERB
ejpam-6472	265	18	lemma	lemma	PROPN
ejpam-6472	265	19	1	1	NUM
ejpam-6472	265	20	,	,	PUNCT
ejpam-6472	265	21	we	we	PRON
ejpam-6472	265	22	deduce	deduce	VERB
ejpam-6472	265	23	r	r	NOUN
ejpam-6472	265	24	=	=	PUNCT
ejpam-6472	265	25	q	q	PUNCT
ejpam-6472	265	26	∈	∈	PROPN
ejpam-6472	265	27	sub(t	sub(t	NOUN
ejpam-6472	265	28	·	·	SYM
ejpam-6472	265	29	rs	rs	X
ejpam-6472	265	30	q	q	NOUN
ejpam-6472	265	31	)	)	PUNCT
ejpam-6472	265	32	\	\	NOUN
ejpam-6472	265	33	{	{	PUNCT
ejpam-6472	265	34	t	t	NOUN
ejpam-6472	265	35	·	·	SYM
ejpam-6472	265	36	rs	rs	X
ejpam-6472	265	37	q	q	NOUN
ejpam-6472	265	38	}	}	PUNCT
ejpam-6472	265	39	=	=	SYM
ejpam-6472	265	40	sub(r	sub(r	PROPN
ejpam-6472	265	41	)	)	PUNCT
ejpam-6472	265	42	\	\	NOUN
ejpam-6472	266	1	{	{	PUNCT
ejpam-6472	266	2	r	r	NOUN
ejpam-6472	266	3	}	}	PUNCT
ejpam-6472	266	4	,	,	PUNCT
ejpam-6472	266	5	a	a	DET
ejpam-6472	266	6	contradiction	contradiction	NOUN
ejpam-6472	266	7	.	.	PUNCT
ejpam-6472	267	1	therefore	therefore	ADV
ejpam-6472	267	2	,	,	PUNCT
ejpam-6472	267	3	t	t	NOUN
ejpam-6472	267	4	·	·	PUNCT
ejpam-6472	267	5	rs	rs	PROPN
ejpam-6472	267	6	q	q	PROPN
ejpam-6472	267	7	̸∈	̸∈	PROPN
ejpam-6472	267	8	{	{	PUNCT
ejpam-6472	267	9	r	r	PROPN
ejpam-6472	267	10	,	,	PUNCT
ejpam-6472	267	11	s	s	PART
ejpam-6472	267	12	}	}	PUNCT
ejpam-6472	267	13	.	.	PUNCT
ejpam-6472	268	1	we	we	PRON
ejpam-6472	268	2	further	far	ADV
ejpam-6472	268	3	show	show	VERB
ejpam-6472	268	4	that	that	SCONJ
ejpam-6472	268	5	w	w	ADP
ejpam-6472	268	6	r	r	NOUN
ejpam-6472	268	7	,	,	PUNCT
ejpam-6472	268	8	s	s	PART
ejpam-6472	268	9	τ	τ	X
ejpam-6472	268	10	(	(	PUNCT
ejpam-6472	268	11	xn	xn	PROPN
ejpam-6472	268	12	)	)	PUNCT
ejpam-6472	268	13	is	be	AUX
ejpam-6472	268	14	a	a	DET
ejpam-6472	268	15	maximal	maximal	ADJ
ejpam-6472	268	16	semigroup	semigroup	NOUN
ejpam-6472	268	17	in	in	ADP
ejpam-6472	268	18	wτ	wτ	PROPN
ejpam-6472	268	19	(	(	PUNCT
ejpam-6472	268	20	xn	xn	PROPN
ejpam-6472	268	21	)	)	PUNCT
ejpam-6472	268	22	with	with	ADP
ejpam-6472	268	23	respect	respect	NOUN
ejpam-6472	268	24	to	to	ADP
ejpam-6472	268	25	the	the	DET
ejpam-6472	268	26	operation	operation	NOUN
ejpam-6472	268	27	·	·	PUNCT
ejpam-6472	268	28	rs	rs	ADJ
ejpam-6472	268	29	,	,	PUNCT
ejpam-6472	268	30	assuming	assume	VERB
ejpam-6472	268	31	that	that	SCONJ
ejpam-6472	268	32	neither	neither	CCONJ
ejpam-6472	268	33	r	r	NOUN
ejpam-6472	268	34	nor	nor	CCONJ
ejpam-6472	268	35	s	s	NOUN
ejpam-6472	268	36	is	be	AUX
ejpam-6472	268	37	a	a	DET
ejpam-6472	268	38	proper	proper	ADJ
ejpam-6472	268	39	subterm	subterm	NOUN
ejpam-6472	268	40	of	of	ADP
ejpam-6472	268	41	the	the	DET
ejpam-6472	268	42	other	other	ADJ
ejpam-6472	268	43	.	.	PUNCT
ejpam-6472	269	1	theorem	theorem	ADJ
ejpam-6472	269	2	4	4	NUM
ejpam-6472	269	3	.	.	PUNCT
ejpam-6472	270	1	let	let	VERB
ejpam-6472	270	2	r	r	NOUN
ejpam-6472	270	3	,	,	PUNCT
ejpam-6472	270	4	s	s	NOUN
ejpam-6472	270	5	∈	∈	PROPN
ejpam-6472	270	6	wτ	wτ	NOUN
ejpam-6472	270	7	(	(	PUNCT
ejpam-6472	270	8	xn	xn	X
ejpam-6472	270	9	)	)	PUNCT
ejpam-6472	270	10	be	be	AUX
ejpam-6472	270	11	fixed	fix	VERB
ejpam-6472	270	12	terms	term	NOUN
ejpam-6472	270	13	such	such	ADJ
ejpam-6472	270	14	that	that	SCONJ
ejpam-6472	270	15	r	r	PROPN
ejpam-6472	270	16	̸∈	̸∈	PROPN
ejpam-6472	270	17	sub(s	sub(s	PROPN
ejpam-6472	270	18	)	)	PUNCT
ejpam-6472	270	19	\	\	NOUN
ejpam-6472	271	1	{	{	PUNCT
ejpam-6472	271	2	s	s	NOUN
ejpam-6472	271	3	}	}	PUNCT
ejpam-6472	271	4	and	and	CCONJ
ejpam-6472	271	5	s	s	VERB
ejpam-6472	271	6	̸∈	̸∈	PROPN
ejpam-6472	271	7	sub(r	sub(r	PROPN
ejpam-6472	271	8	)	)	PUNCT
ejpam-6472	271	9	\	\	NOUN
ejpam-6472	271	10	{	{	PUNCT
ejpam-6472	271	11	r	r	NOUN
ejpam-6472	271	12	}	}	PUNCT
ejpam-6472	271	13	.	.	PUNCT
ejpam-6472	272	1	then	then	ADV
ejpam-6472	272	2	w	w	PROPN
ejpam-6472	272	3	r	r	PROPN
ejpam-6472	272	4	,	,	PUNCT
ejpam-6472	272	5	s	s	PART
ejpam-6472	272	6	τ	τ	X
ejpam-6472	272	7	(	(	PUNCT
ejpam-6472	272	8	xn	xn	PROPN
ejpam-6472	272	9	)	)	PUNCT
ejpam-6472	272	10	is	be	AUX
ejpam-6472	272	11	a	a	DET
ejpam-6472	272	12	maximal	maximal	ADJ
ejpam-6472	272	13	subset	subset	NOUN
ejpam-6472	272	14	of	of	ADP
ejpam-6472	272	15	wτ	wτ	PROPN
ejpam-6472	272	16	(	(	PUNCT
ejpam-6472	272	17	xn	xn	PROPN
ejpam-6472	272	18	)	)	PUNCT
ejpam-6472	272	19	that	that	PRON
ejpam-6472	272	20	forms	form	VERB
ejpam-6472	272	21	a	a	DET
ejpam-6472	272	22	semigroup	semigroup	NOUN
ejpam-6472	272	23	under	under	ADP
ejpam-6472	272	24	the	the	DET
ejpam-6472	272	25	operation	operation	NOUN
ejpam-6472	272	26	·	·	SYM
ejpam-6472	272	27	rs	rs	NOUN
ejpam-6472	272	28	.	.	PUNCT
ejpam-6472	273	1	proof	proof	NOUN
ejpam-6472	273	2	.	.	PUNCT
ejpam-6472	274	1	by	by	ADP
ejpam-6472	274	2	theorem	theorem	NOUN
ejpam-6472	274	3	3	3	NUM
ejpam-6472	274	4	,	,	PUNCT
ejpam-6472	274	5	we	we	PRON
ejpam-6472	274	6	know	know	VERB
ejpam-6472	274	7	thatw	thatw	VERB
ejpam-6472	274	8	r	r	NOUN
ejpam-6472	274	9	,	,	PUNCT
ejpam-6472	274	10	s	s	PART
ejpam-6472	274	11	τ	τ	X
ejpam-6472	274	12	(	(	PUNCT
ejpam-6472	274	13	xn	xn	PROPN
ejpam-6472	274	14	)	)	PUNCT
ejpam-6472	274	15	is	be	AUX
ejpam-6472	274	16	a	a	DET
ejpam-6472	274	17	semigroup	semigroup	NOUN
ejpam-6472	274	18	.	.	PUNCT
ejpam-6472	275	1	we	we	PRON
ejpam-6472	275	2	now	now	ADV
ejpam-6472	275	3	proceed	proceed	VERB
ejpam-6472	275	4	to	to	PART
ejpam-6472	275	5	show	show	VERB
ejpam-6472	275	6	its	its	PRON
ejpam-6472	275	7	maximality	maximality	NOUN
ejpam-6472	275	8	.	.	PUNCT
ejpam-6472	276	1	note	note	VERB
ejpam-6472	276	2	that	that	SCONJ
ejpam-6472	276	3	when	when	SCONJ
ejpam-6472	276	4	r	r	NOUN
ejpam-6472	276	5	,	,	PUNCT
ejpam-6472	276	6	s	s	PART
ejpam-6472	276	7	∈	∈	PROPN
ejpam-6472	276	8	xn	xn	PROPN
ejpam-6472	276	9	,	,	PUNCT
ejpam-6472	276	10	the	the	DET
ejpam-6472	276	11	set	set	NOUN
ejpam-6472	276	12	w	w	NOUN
ejpam-6472	276	13	r	r	NOUN
ejpam-6472	276	14	,	,	PUNCT
ejpam-6472	276	15	s	s	PART
ejpam-6472	276	16	τ	τ	X
ejpam-6472	276	17	(	(	PUNCT
ejpam-6472	276	18	xn	xn	PROPN
ejpam-6472	276	19	)	)	PUNCT
ejpam-6472	276	20	becomes	become	VERB
ejpam-6472	276	21	equal	equal	ADJ
ejpam-6472	276	22	to	to	ADP
ejpam-6472	276	23	wτ	wτ	PROPN
ejpam-6472	276	24	(	(	PUNCT
ejpam-6472	276	25	xn	xn	PROPN
ejpam-6472	276	26	)	)	PUNCT
ejpam-6472	276	27	,	,	PUNCT
ejpam-6472	276	28	so	so	CCONJ
ejpam-6472	276	29	the	the	DET
ejpam-6472	276	30	maximality	maximality	NOUN
ejpam-6472	276	31	clearly	clearly	ADV
ejpam-6472	276	32	holds	hold	VERB
ejpam-6472	276	33	in	in	ADP
ejpam-6472	276	34	this	this	DET
ejpam-6472	276	35	case	case	NOUN
ejpam-6472	276	36	.	.	PUNCT
ejpam-6472	277	1	now	now	ADV
ejpam-6472	277	2	,	,	PUNCT
ejpam-6472	277	3	assume	assume	VERB
ejpam-6472	277	4	that	that	SCONJ
ejpam-6472	277	5	at	at	ADV
ejpam-6472	277	6	least	least	ADJ
ejpam-6472	277	7	one	one	NUM
ejpam-6472	277	8	of	of	ADP
ejpam-6472	277	9	r	r	NOUN
ejpam-6472	277	10	or	or	CCONJ
ejpam-6472	277	11	s	s	NOUN
ejpam-6472	277	12	is	be	AUX
ejpam-6472	277	13	a	a	DET
ejpam-6472	277	14	compound	compound	NOUN
ejpam-6472	277	15	term	term	NOUN
ejpam-6472	277	16	.	.	PUNCT
ejpam-6472	278	1	in	in	ADP
ejpam-6472	278	2	this	this	DET
ejpam-6472	278	3	case	case	NOUN
ejpam-6472	278	4	,	,	PUNCT
ejpam-6472	278	5	we	we	PRON
ejpam-6472	278	6	have	have	VERB
ejpam-6472	278	7	w	w	ADP
ejpam-6472	278	8	r	r	NOUN
ejpam-6472	278	9	,	,	PUNCT
ejpam-6472	278	10	s	s	PART
ejpam-6472	278	11	τ	τ	X
ejpam-6472	278	12	(	(	PUNCT
ejpam-6472	278	13	xn	xn	PROPN
ejpam-6472	278	14	)	)	PUNCT
ejpam-6472	278	15	⊊	⊊	VERB
ejpam-6472	278	16	wτ	wτ	NOUN
ejpam-6472	278	17	(	(	PUNCT
ejpam-6472	278	18	xn	xn	PROPN
ejpam-6472	278	19	)	)	PUNCT
ejpam-6472	278	20	.	.	PUNCT
ejpam-6472	279	1	let	let	VERB
ejpam-6472	279	2	q	q	PRON
ejpam-6472	279	3	be	be	AUX
ejpam-6472	279	4	a	a	DET
ejpam-6472	279	5	subset	subset	NOUN
ejpam-6472	279	6	of	of	ADP
ejpam-6472	279	7	wτ	wτ	PROPN
ejpam-6472	279	8	(	(	PUNCT
ejpam-6472	279	9	xn	xn	PROPN
ejpam-6472	279	10	)	)	PUNCT
ejpam-6472	279	11	such	such	ADJ
ejpam-6472	279	12	that	that	SCONJ
ejpam-6472	279	13	w	w	PROPN
ejpam-6472	279	14	r	r	NOUN
ejpam-6472	279	15	,	,	PUNCT
ejpam-6472	279	16	s	s	PART
ejpam-6472	279	17	τ	τ	X
ejpam-6472	279	18	(	(	PUNCT
ejpam-6472	279	19	xn	xn	PROPN
ejpam-6472	279	20	)	)	PUNCT
ejpam-6472	279	21	⊊	⊊	VERB
ejpam-6472	279	22	q.	q.	NOUN
ejpam-6472	279	23	this	this	PRON
ejpam-6472	279	24	implies	imply	VERB
ejpam-6472	279	25	that	that	SCONJ
ejpam-6472	279	26	there	there	PRON
ejpam-6472	279	27	exists	exist	VERB
ejpam-6472	279	28	an	an	DET
ejpam-6472	279	29	element	element	NOUN
ejpam-6472	279	30	a	a	DET
ejpam-6472	279	31	∈	∈	NOUN
ejpam-6472	279	32	q	q	NOUN
ejpam-6472	279	33	such	such	ADJ
ejpam-6472	279	34	that	that	SCONJ
ejpam-6472	279	35	a	a	DET
ejpam-6472	279	36	∈	∈	PROPN
ejpam-6472	279	37	(	(	PUNCT
ejpam-6472	279	38	sub(r)\{r})∪	sub(r)\{r})∪	NOUN
ejpam-6472	279	39	(	(	PUNCT
ejpam-6472	279	40	sub(s)\{s	sub(s)\{s	NOUN
ejpam-6472	279	41	}	}	PUNCT
ejpam-6472	279	42	)	)	PUNCT
ejpam-6472	279	43	.	.	PUNCT
ejpam-6472	280	1	without	without	ADP
ejpam-6472	280	2	loss	loss	NOUN
ejpam-6472	280	3	of	of	ADP
ejpam-6472	280	4	generality	generality	NOUN
ejpam-6472	280	5	,	,	PUNCT
ejpam-6472	280	6	assume	assume	VERB
ejpam-6472	280	7	that	that	SCONJ
ejpam-6472	280	8	a	a	DET
ejpam-6472	280	9	∈	∈	NOUN
ejpam-6472	280	10	sub(r)\{r	sub(r)\{r	NOUN
ejpam-6472	280	11	}	}	PUNCT
ejpam-6472	280	12	.	.	PUNCT
ejpam-6472	281	1	let	let	VERB
ejpam-6472	281	2	r	r	NOUN
ejpam-6472	281	3	=	=	PUNCT
ejpam-6472	281	4	fi(t1	fi(t1	NOUN
ejpam-6472	281	5	,	,	PUNCT
ejpam-6472	281	6	.	.	PUNCT
ejpam-6472	281	7	.	.	PUNCT
ejpam-6472	282	1	.	.	PUNCT
ejpam-6472	283	1	,	,	PUNCT
ejpam-6472	283	2	tni	tni	NOUN
ejpam-6472	283	3	)	)	PUNCT
ejpam-6472	283	4	,	,	PUNCT
ejpam-6472	283	5	and	and	CCONJ
ejpam-6472	283	6	let	let	VERB
ejpam-6472	283	7	1	1	NUM
ejpam-6472	283	8	≤	≤	NUM
ejpam-6472	284	1	l	l	NOUN
ejpam-6472	284	2	≤	≤	PROPN
ejpam-6472	284	3	ni	ni	PROPN
ejpam-6472	284	4	be	be	AUX
ejpam-6472	284	5	such	such	ADJ
ejpam-6472	284	6	that	that	SCONJ
ejpam-6472	284	7	a	a	DET
ejpam-6472	284	8	∈	∈	NOUN
ejpam-6472	284	9	sub(tl	sub(tl	NUM
ejpam-6472	284	10	)	)	PUNCT
ejpam-6472	284	11	.	.	PUNCT
ejpam-6472	285	1	we	we	PRON
ejpam-6472	285	2	will	will	AUX
ejpam-6472	285	3	demonstrate	demonstrate	VERB
ejpam-6472	285	4	that	that	SCONJ
ejpam-6472	285	5	q	q	NOUN
ejpam-6472	285	6	does	do	AUX
ejpam-6472	285	7	not	not	PART
ejpam-6472	285	8	satisfy	satisfy	VERB
ejpam-6472	285	9	associativity	associativity	NOUN
ejpam-6472	285	10	under	under	ADP
ejpam-6472	285	11	·	·	PUNCT
ejpam-6472	285	12	rs	r	VERB
ejpam-6472	285	13	by	by	ADP
ejpam-6472	285	14	applying	apply	VERB
ejpam-6472	285	15	theorem	theorem	NOUN
ejpam-6472	285	16	2	2	X
ejpam-6472	285	17	.	.	X
ejpam-6472	286	1	we	we	PRON
ejpam-6472	286	2	proceed	proceed	VERB
ejpam-6472	286	3	with	with	ADP
ejpam-6472	286	4	the	the	DET
ejpam-6472	286	5	following	follow	VERB
ejpam-6472	286	6	two	two	NUM
ejpam-6472	286	7	steps	step	NOUN
ejpam-6472	286	8	.	.	PUNCT
ejpam-6472	287	1	step	step	NOUN
ejpam-6472	287	2	1	1	NUM
ejpam-6472	287	3	.	.	PUNCT
ejpam-6472	288	1	we	we	PRON
ejpam-6472	288	2	show	show	VERB
ejpam-6472	288	3	that	that	SCONJ
ejpam-6472	288	4	there	there	PRON
ejpam-6472	288	5	is	be	VERB
ejpam-6472	288	6	b	b	NOUN
ejpam-6472	288	7	∈	∈	PROPN
ejpam-6472	288	8	w	w	NOUN
ejpam-6472	288	9	r	r	NOUN
ejpam-6472	288	10	,	,	PUNCT
ejpam-6472	288	11	s	s	PART
ejpam-6472	288	12	τ	τ	X
ejpam-6472	288	13	(	(	PUNCT
ejpam-6472	288	14	xn	xn	PROPN
ejpam-6472	288	15	)	)	PUNCT
ejpam-6472	288	16	such	such	ADJ
ejpam-6472	288	17	that	that	SCONJ
ejpam-6472	288	18	r	r	PROPN
ejpam-6472	288	19	∈	∈	PROPN
ejpam-6472	288	20	sub(b	sub(b	NOUN
ejpam-6472	288	21	)	)	PUNCT
ejpam-6472	288	22	and	and	CCONJ
ejpam-6472	288	23	b	b	X
ejpam-6472	288	24	·	·	PUNCT
ejpam-6472	288	25	rs	rs	NOUN
ejpam-6472	288	26	a	a	PRON
ejpam-6472	288	27	=	=	SYM
ejpam-6472	288	28	tl	tl	PROPN
ejpam-6472	288	29	.	.	PUNCT
ejpam-6472	289	1	we	we	PRON
ejpam-6472	289	2	prove	prove	VERB
ejpam-6472	289	3	by	by	ADP
ejpam-6472	289	4	induction	induction	NOUN
ejpam-6472	289	5	on	on	ADP
ejpam-6472	289	6	the	the	DET
ejpam-6472	289	7	complexity	complexity	NOUN
ejpam-6472	289	8	of	of	ADP
ejpam-6472	289	9	tl	tl	PROPN
ejpam-6472	289	10	.	.	PUNCT
ejpam-6472	290	1	if	if	SCONJ
ejpam-6472	290	2	tl	tl	PROPN
ejpam-6472	290	3	∈	∈	PROPN
ejpam-6472	290	4	xn	xn	PROPN
ejpam-6472	290	5	,	,	PUNCT
ejpam-6472	290	6	then	then	ADV
ejpam-6472	290	7	a	a	DET
ejpam-6472	290	8	∈	∈	NOUN
ejpam-6472	290	9	sub(tl	sub(tl	NUM
ejpam-6472	290	10	)	)	PUNCT
ejpam-6472	290	11	=	=	SYM
ejpam-6472	290	12	{	{	PUNCT
ejpam-6472	290	13	tl	tl	PROPN
ejpam-6472	290	14	}	}	PUNCT
ejpam-6472	290	15	,	,	PUNCT
ejpam-6472	290	16	which	which	PRON
ejpam-6472	290	17	implies	imply	VERB
ejpam-6472	290	18	a	a	DET
ejpam-6472	290	19	=	=	SYM
ejpam-6472	290	20	tl	tl	PROPN
ejpam-6472	290	21	.	.	PUNCT
ejpam-6472	291	1	in	in	ADP
ejpam-6472	291	2	this	this	DET
ejpam-6472	291	3	case	case	NOUN
ejpam-6472	291	4	,	,	PUNCT
ejpam-6472	291	5	we	we	PRON
ejpam-6472	291	6	set	set	VERB
ejpam-6472	291	7	b	b	PROPN
ejpam-6472	291	8	=	=	SYM
ejpam-6472	291	9	r.	r.	PROPN
ejpam-6472	291	10	for	for	ADP
ejpam-6472	291	11	tl	tl	PROPN
ejpam-6472	291	12	=	=	PUNCT
ejpam-6472	291	13	fj(q1	fj(q1	PROPN
ejpam-6472	291	14	,	,	PUNCT
ejpam-6472	291	15	.	.	PUNCT
ejpam-6472	291	16	.	.	PUNCT
ejpam-6472	292	1	.	.	PUNCT
ejpam-6472	293	1	,	,	PUNCT
ejpam-6472	293	2	qnj	qnj	VERB
ejpam-6472	293	3	)	)	PUNCT
ejpam-6472	293	4	,	,	PUNCT
ejpam-6472	293	5	assume	assume	VERB
ejpam-6472	293	6	that	that	SCONJ
ejpam-6472	293	7	for	for	ADP
ejpam-6472	293	8	each	each	DET
ejpam-6472	293	9	1	1	NUM
ejpam-6472	293	10	≤	≤	NUM
ejpam-6472	293	11	m	m	VERB
ejpam-6472	293	12	≤	≤	NOUN
ejpam-6472	293	13	nj	nj	PROPN
ejpam-6472	293	14	,	,	PUNCT
ejpam-6472	293	15	if	if	SCONJ
ejpam-6472	293	16	a	a	DET
ejpam-6472	293	17	∈	∈	PROPN
ejpam-6472	293	18	sub(qm	sub(qm	NOUN
ejpam-6472	293	19	)	)	PUNCT
ejpam-6472	293	20	,	,	PUNCT
ejpam-6472	293	21	then	then	ADV
ejpam-6472	293	22	there	there	PRON
ejpam-6472	293	23	exists	exist	VERB
ejpam-6472	293	24	bm	bm	PROPN
ejpam-6472	293	25	∈	∈	PROPN
ejpam-6472	293	26	w	w	PROPN
ejpam-6472	293	27	r	r	PROPN
ejpam-6472	293	28	,	,	PUNCT
ejpam-6472	293	29	s	s	PART
ejpam-6472	293	30	τ	τ	X
ejpam-6472	293	31	(	(	PUNCT
ejpam-6472	293	32	xn	xn	PROPN
ejpam-6472	293	33	)	)	PUNCT
ejpam-6472	293	34	such	such	ADJ
ejpam-6472	293	35	that	that	SCONJ
ejpam-6472	293	36	r	r	NOUN
ejpam-6472	293	37	∈	∈	PROPN
ejpam-6472	293	38	sub(bm	sub(bm	NOUN
ejpam-6472	293	39	)	)	PUNCT
ejpam-6472	293	40	and	and	CCONJ
ejpam-6472	293	41	bm	bm	PROPN
ejpam-6472	293	42	·	·	PUNCT
ejpam-6472	293	43	rs	rs	PROPN
ejpam-6472	293	44	a	a	DET
ejpam-6472	293	45	=	=	SYM
ejpam-6472	293	46	qm	qm	PROPN
ejpam-6472	293	47	.	.	PUNCT
ejpam-6472	294	1	if	if	SCONJ
ejpam-6472	294	2	a	a	DET
ejpam-6472	294	3	=	=	SYM
ejpam-6472	294	4	tl	tl	PROPN
ejpam-6472	294	5	,	,	PUNCT
ejpam-6472	294	6	then	then	ADV
ejpam-6472	294	7	we	we	PRON
ejpam-6472	294	8	set	set	VERB
ejpam-6472	294	9	b	b	NOUN
ejpam-6472	294	10	=	=	NOUN
ejpam-6472	294	11	r	r	NOUN
ejpam-6472	294	12	as	as	ADP
ejpam-6472	294	13	in	in	ADP
ejpam-6472	294	14	the	the	DET
ejpam-6472	294	15	base	base	NOUN
ejpam-6472	294	16	case	case	NOUN
ejpam-6472	294	17	.	.	PUNCT
ejpam-6472	295	1	next	next	ADV
ejpam-6472	295	2	,	,	PUNCT
ejpam-6472	295	3	consider	consider	VERB
ejpam-6472	295	4	the	the	DET
ejpam-6472	295	5	case	case	NOUN
ejpam-6472	295	6	where	where	SCONJ
ejpam-6472	295	7	a	a	DET
ejpam-6472	295	8	∈	∈	NOUN
ejpam-6472	295	9	sub(tl	sub(tl	NUM
ejpam-6472	295	10	)	)	PUNCT
ejpam-6472	295	11	\	\	PROPN
ejpam-6472	295	12	{	{	PUNCT
ejpam-6472	295	13	tl	tl	PROPN
ejpam-6472	295	14	}	}	PUNCT
ejpam-6472	295	15	.	.	PUNCT
ejpam-6472	296	1	we	we	PRON
ejpam-6472	296	2	obtain	obtain	VERB
ejpam-6472	296	3	that	that	SCONJ
ejpam-6472	296	4	a	a	DET
ejpam-6472	296	5	∈	∈	PROPN
ejpam-6472	296	6	sub(qm	sub(qm	NOUN
ejpam-6472	296	7	)	)	PUNCT
ejpam-6472	296	8	for	for	ADP
ejpam-6472	296	9	some	some	DET
ejpam-6472	296	10	1	1	NUM
ejpam-6472	296	11	≤	≤	NUM
ejpam-6472	296	12	m	m	VERB
ejpam-6472	296	13	≤	≤	NOUN
ejpam-6472	296	14	nj	nj	PROPN
ejpam-6472	296	15	.	.	PUNCT
ejpam-6472	297	1	by	by	ADP
ejpam-6472	297	2	inductive	inductive	ADJ
ejpam-6472	297	3	hypothesis	hypothesis	NOUN
ejpam-6472	297	4	,	,	PUNCT
ejpam-6472	297	5	there	there	PRON
ejpam-6472	297	6	exists	exist	VERB
ejpam-6472	297	7	bm	bm	PROPN
ejpam-6472	297	8	∈	∈	PROPN
ejpam-6472	297	9	w	w	PROPN
ejpam-6472	297	10	r	r	PROPN
ejpam-6472	297	11	,	,	PUNCT
ejpam-6472	297	12	s	s	PART
ejpam-6472	297	13	τ	τ	X
ejpam-6472	297	14	(	(	PUNCT
ejpam-6472	297	15	xn	xn	PROPN
ejpam-6472	297	16	)	)	PUNCT
ejpam-6472	297	17	such	such	ADJ
ejpam-6472	297	18	that	that	SCONJ
ejpam-6472	297	19	r	r	NOUN
ejpam-6472	297	20	∈	∈	PROPN
ejpam-6472	297	21	sub(bm	sub(bm	NOUN
ejpam-6472	297	22	)	)	PUNCT
ejpam-6472	297	23	and	and	CCONJ
ejpam-6472	297	24	bm	bm	PROPN
ejpam-6472	297	25	·	·	PUNCT
ejpam-6472	297	26	rs	rs	PROPN
ejpam-6472	297	27	a	a	DET
ejpam-6472	297	28	=	=	SYM
ejpam-6472	297	29	qm	qm	PROPN
ejpam-6472	297	30	.	.	PUNCT
ejpam-6472	298	1	we	we	PRON
ejpam-6472	298	2	define	define	VERB
ejpam-6472	298	3	b	b	NOUN
ejpam-6472	298	4	=	=	SYM
ejpam-6472	298	5	fj(q1	fj(q1	NOUN
ejpam-6472	298	6	,	,	PUNCT
ejpam-6472	298	7	.	.	PUNCT
ejpam-6472	298	8	.	.	PUNCT
ejpam-6472	299	1	.	.	PUNCT
ejpam-6472	300	1	,	,	PUNCT
ejpam-6472	300	2	qm−1	qm−1	NOUN
ejpam-6472	300	3	,	,	PUNCT
ejpam-6472	300	4	bm	bm	PROPN
ejpam-6472	300	5	,	,	PUNCT
ejpam-6472	300	6	qm+1	qm+1	PROPN
ejpam-6472	300	7	,	,	PUNCT
ejpam-6472	300	8	.	.	PUNCT
ejpam-6472	300	9	.	.	PUNCT
ejpam-6472	300	10	.	.	PUNCT
ejpam-6472	301	1	,	,	PUNCT
ejpam-6472	301	2	qnj	qnj	VERB
ejpam-6472	301	3	)	)	PUNCT
ejpam-6472	301	4	.	.	PUNCT
ejpam-6472	302	1	since	since	SCONJ
ejpam-6472	302	2	r	r	NOUN
ejpam-6472	302	3	∈	∈	PROPN
ejpam-6472	302	4	sub(bm	sub(bm	NOUN
ejpam-6472	302	5	)	)	PUNCT
ejpam-6472	302	6	⊆	⊆	NUM
ejpam-6472	302	7	sub(b	sub(b	NOUN
ejpam-6472	302	8	)	)	PUNCT
ejpam-6472	302	9	\	\	NOUN
ejpam-6472	302	10	{	{	PUNCT
ejpam-6472	302	11	b	b	NOUN
ejpam-6472	302	12	}	}	PUNCT
ejpam-6472	302	13	,	,	PUNCT
ejpam-6472	302	14	b	b	PROPN
ejpam-6472	302	15	̸∈	̸∈	PROPN
ejpam-6472	302	16	sub(r	sub(r	PROPN
ejpam-6472	302	17	)	)	PUNCT
ejpam-6472	302	18	.	.	PUNCT
ejpam-6472	303	1	additionally	additionally	ADV
ejpam-6472	303	2	,	,	PUNCT
ejpam-6472	303	3	since	since	SCONJ
ejpam-6472	303	4	r	r	PROPN
ejpam-6472	303	5	̸∈	̸∈	PROPN
ejpam-6472	303	6	sub(s	sub(s	PROPN
ejpam-6472	303	7	)	)	PUNCT
ejpam-6472	303	8	\	\	NOUN
ejpam-6472	303	9	{	{	PUNCT
ejpam-6472	303	10	s	s	NOUN
ejpam-6472	303	11	}	}	PUNCT
ejpam-6472	303	12	,	,	PUNCT
ejpam-6472	303	13	b	b	PROPN
ejpam-6472	303	14	̸∈	̸∈	PROPN
ejpam-6472	303	15	sub(s	sub(s	PROPN
ejpam-6472	303	16	)	)	PUNCT
ejpam-6472	303	17	.	.	PUNCT
ejpam-6472	304	1	thus	thus	ADV
ejpam-6472	304	2	,	,	PUNCT
ejpam-6472	304	3	b	b	PROPN
ejpam-6472	304	4	∈	∈	PROPN
ejpam-6472	304	5	w	w	NOUN
ejpam-6472	304	6	r	r	NOUN
ejpam-6472	304	7	,	,	PUNCT
ejpam-6472	304	8	s	s	PART
ejpam-6472	304	9	τ	τ	X
ejpam-6472	304	10	(	(	PUNCT
ejpam-6472	304	11	xn	xn	PROPN
ejpam-6472	304	12	)	)	PUNCT
ejpam-6472	304	13	and	and	CCONJ
ejpam-6472	304	14	b	b	X
ejpam-6472	304	15	̸∈	̸∈	PROPN
ejpam-6472	304	16	{	{	PUNCT
ejpam-6472	304	17	r	r	PROPN
ejpam-6472	304	18	,	,	PUNCT
ejpam-6472	304	19	s	s	PART
ejpam-6472	304	20	}	}	PUNCT
ejpam-6472	304	21	.	.	PUNCT
ejpam-6472	305	1	note	note	VERB
ejpam-6472	305	2	that	that	SCONJ
ejpam-6472	305	3	{	{	PUNCT
ejpam-6472	305	4	r	r	NOUN
ejpam-6472	305	5	,	,	PUNCT
ejpam-6472	305	6	s	s	NOUN
ejpam-6472	305	7	}	}	PUNCT
ejpam-6472	305	8	∩	∩	NOUN
ejpam-6472	305	9	sub(qk	sub(qk	NOUN
ejpam-6472	305	10	)	)	PUNCT
ejpam-6472	305	11	=	=	SYM
ejpam-6472	305	12	∅	∅	NOUN
ejpam-6472	305	13	for	for	ADP
ejpam-6472	305	14	all	all	DET
ejpam-6472	305	15	1	1	NUM
ejpam-6472	305	16	≤	≤	NOUN
ejpam-6472	305	17	qk	qk	ADP
ejpam-6472	305	18	≤	≤	ADJ
ejpam-6472	305	19	nj	nj	PROPN
ejpam-6472	305	20	because	because	SCONJ
ejpam-6472	305	21	each	each	DET
ejpam-6472	305	22	qk	qk	NOUN
ejpam-6472	305	23	is	be	AUX
ejpam-6472	305	24	a	a	DET
ejpam-6472	305	25	proper	proper	ADJ
ejpam-6472	305	26	subterm	subterm	NOUN
ejpam-6472	305	27	of	of	ADP
ejpam-6472	305	28	r	r	NOUN
ejpam-6472	305	29	and	and	CCONJ
ejpam-6472	305	30	s	s	PROPN
ejpam-6472	305	31	̸∈	̸∈	PROPN
ejpam-6472	305	32	sub(r	sub(r	PROPN
ejpam-6472	305	33	)	)	PUNCT
ejpam-6472	305	34	\	\	NOUN
ejpam-6472	306	1	{	{	PUNCT
ejpam-6472	306	2	r	r	NOUN
ejpam-6472	306	3	}	}	PUNCT
ejpam-6472	306	4	.	.	PUNCT
ejpam-6472	307	1	it	it	PRON
ejpam-6472	307	2	follows	follow	VERB
ejpam-6472	307	3	that	that	SCONJ
ejpam-6472	307	4	b	b	X
ejpam-6472	307	5	·	·	PUNCT
ejpam-6472	307	6	rs	rs	NOUN
ejpam-6472	307	7	a	a	DET
ejpam-6472	307	8	=	=	NOUN
ejpam-6472	307	9	fj(q1	fj(q1	NOUN
ejpam-6472	307	10	,	,	PUNCT
ejpam-6472	307	11	.	.	PUNCT
ejpam-6472	307	12	.	.	PUNCT
ejpam-6472	308	1	.	.	PUNCT
ejpam-6472	309	1	,	,	PUNCT
ejpam-6472	309	2	qm−1	qm−1	NOUN
ejpam-6472	309	3	,	,	PUNCT
ejpam-6472	309	4	bm	bm	PROPN
ejpam-6472	309	5	,	,	PUNCT
ejpam-6472	309	6	qm+1	qm+1	PROPN
ejpam-6472	309	7	,	,	PUNCT
ejpam-6472	309	8	.	.	PUNCT
ejpam-6472	309	9	.	.	PUNCT
ejpam-6472	309	10	.	.	PUNCT
ejpam-6472	310	1	,	,	PUNCT
ejpam-6472	310	2	qnj	qnj	VERB
ejpam-6472	310	3	)	)	PUNCT
ejpam-6472	310	4	·	·	PUNCT
ejpam-6472	310	5	rs	rs	NOUN
ejpam-6472	310	6	a	a	DET
ejpam-6472	310	7	=	=	NOUN
ejpam-6472	310	8	fj(q1	fj(q1	NOUN
ejpam-6472	310	9	·	·	PUNCT
ejpam-6472	310	10	rs	rs	NOUN
ejpam-6472	310	11	a	a	PRON
ejpam-6472	310	12	,	,	PUNCT
ejpam-6472	310	13	.	.	PUNCT
ejpam-6472	310	14	.	.	PUNCT
ejpam-6472	311	1	.	.	PUNCT
ejpam-6472	312	1	,	,	PUNCT
ejpam-6472	312	2	qm−1	qm−1	NOUN
ejpam-6472	312	3	·	·	PUNCT
ejpam-6472	312	4	rs	rs	NOUN
ejpam-6472	312	5	a	a	PRON
ejpam-6472	312	6	,	,	PUNCT
ejpam-6472	312	7	bm	bm	PROPN
ejpam-6472	312	8	·	·	PUNCT
ejpam-6472	312	9	rs	rs	PROPN
ejpam-6472	312	10	a	a	PROPN
ejpam-6472	312	11	,	,	PUNCT
ejpam-6472	312	12	qm+1	qm+1	PROPN
ejpam-6472	312	13	·	·	SYM
ejpam-6472	312	14	rs	rs	NOUN
ejpam-6472	312	15	a	a	PRON
ejpam-6472	312	16	,	,	PUNCT
ejpam-6472	312	17	.	.	PUNCT
ejpam-6472	312	18	.	.	PUNCT
ejpam-6472	313	1	.	.	PUNCT
ejpam-6472	314	1	,	,	PUNCT
ejpam-6472	314	2	qnj	qnj	VERB
ejpam-6472	314	3	·	·	SYM
ejpam-6472	314	4	rs	rs	NOUN
ejpam-6472	314	5	a	a	NOUN
ejpam-6472	314	6	)	)	PUNCT
ejpam-6472	314	7	=	=	SYM
ejpam-6472	314	8	fj(q1	fj(q1	NOUN
ejpam-6472	314	9	,	,	PUNCT
ejpam-6472	314	10	.	.	PUNCT
ejpam-6472	314	11	.	.	PUNCT
ejpam-6472	315	1	.	.	PUNCT
ejpam-6472	316	1	,	,	PUNCT
ejpam-6472	316	2	qm−1	qm−1	NOUN
ejpam-6472	316	3	,	,	PUNCT
ejpam-6472	316	4	qm	qm	PROPN
ejpam-6472	316	5	,	,	PUNCT
ejpam-6472	316	6	qm+1	qm+1	PROPN
ejpam-6472	316	7	,	,	PUNCT
ejpam-6472	316	8	.	.	PUNCT
ejpam-6472	316	9	.	.	PUNCT
ejpam-6472	316	10	.	.	PUNCT
ejpam-6472	317	1	,	,	PUNCT
ejpam-6472	317	2	qnj	qnj	INTJ
ejpam-6472	317	3	)	)	PUNCT
ejpam-6472	318	1	p.	p.	PROPN
ejpam-6472	318	2	prachumdang	prachumdang	PROPN
ejpam-6472	318	3	,	,	PUNCT
ejpam-6472	318	4	b.	b.	PROPN
ejpam-6472	318	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	318	6	/	/	SYM
ejpam-6472	318	7	eur	eur	PROPN
ejpam-6472	318	8	.	.	PUNCT
ejpam-6472	319	1	j.	j.	PROPN
ejpam-6472	319	2	pure	pure	PROPN
ejpam-6472	319	3	appl	appl	PROPN
ejpam-6472	319	4	.	.	PROPN
ejpam-6472	319	5	math	math	PROPN
ejpam-6472	319	6	,	,	PUNCT
ejpam-6472	319	7	18	18	NUM
ejpam-6472	319	8	(	(	PUNCT
ejpam-6472	319	9	3	3	NUM
ejpam-6472	319	10	)	)	PUNCT
ejpam-6472	319	11	(	(	PUNCT
ejpam-6472	319	12	2025	2025	NUM
ejpam-6472	319	13	)	)	PUNCT
ejpam-6472	319	14	,	,	PUNCT
ejpam-6472	319	15	6472	6472	NUM
ejpam-6472	319	16	9	9	NUM
ejpam-6472	319	17	of	of	ADP
ejpam-6472	319	18	16	16	NUM
ejpam-6472	319	19	=	=	SYM
ejpam-6472	319	20	tl	tl	PROPN
ejpam-6472	319	21	.	.	PUNCT
ejpam-6472	319	22	step	step	NOUN
ejpam-6472	319	23	2	2	NUM
ejpam-6472	319	24	.	.	PUNCT
ejpam-6472	320	1	we	we	PRON
ejpam-6472	320	2	establish	establish	VERB
ejpam-6472	320	3	the	the	DET
ejpam-6472	320	4	existence	existence	NOUN
ejpam-6472	320	5	of	of	ADP
ejpam-6472	320	6	c	c	PROPN
ejpam-6472	320	7	∈	∈	PROPN
ejpam-6472	320	8	w	w	PROPN
ejpam-6472	320	9	r	r	PROPN
ejpam-6472	320	10	,	,	PUNCT
ejpam-6472	320	11	s	s	PART
ejpam-6472	320	12	τ	τ	X
ejpam-6472	320	13	(	(	PUNCT
ejpam-6472	320	14	xn	xn	PROPN
ejpam-6472	320	15	)	)	PUNCT
ejpam-6472	320	16	such	such	ADJ
ejpam-6472	320	17	that	that	SCONJ
ejpam-6472	320	18	c	c	PROPN
ejpam-6472	320	19	̸∈	̸∈	PROPN
ejpam-6472	320	20	{	{	PUNCT
ejpam-6472	320	21	r	r	PROPN
ejpam-6472	320	22	,	,	PUNCT
ejpam-6472	320	23	s	s	PART
ejpam-6472	320	24	}	}	PUNCT
ejpam-6472	320	25	and	and	CCONJ
ejpam-6472	320	26	c	c	NOUN
ejpam-6472	320	27	·	·	PUNCT
ejpam-6472	320	28	rs	rs	NOUN
ejpam-6472	320	29	a	a	PRON
ejpam-6472	320	30	=	=	X
ejpam-6472	320	31	r.	r.	NOUN
ejpam-6472	320	32	let	let	VERB
ejpam-6472	320	33	b	b	X
ejpam-6472	320	34	be	be	AUX
ejpam-6472	320	35	the	the	DET
ejpam-6472	320	36	term	term	NOUN
ejpam-6472	320	37	constructed	construct	VERB
ejpam-6472	320	38	in	in	ADP
ejpam-6472	320	39	step	step	NOUN
ejpam-6472	320	40	1	1	NUM
ejpam-6472	320	41	.	.	PUNCT
ejpam-6472	321	1	we	we	PRON
ejpam-6472	321	2	define	define	VERB
ejpam-6472	321	3	c	c	NOUN
ejpam-6472	321	4	=	=	SYM
ejpam-6472	321	5	fi(t1	fi(t1	PROPN
ejpam-6472	321	6	,	,	PUNCT
ejpam-6472	321	7	.	.	PUNCT
ejpam-6472	321	8	.	.	PUNCT
ejpam-6472	321	9	.	.	PUNCT
ejpam-6472	322	1	,	,	PUNCT
ejpam-6472	322	2	tl−1	tl−1	PROPN
ejpam-6472	322	3	,	,	PUNCT
ejpam-6472	322	4	b	b	NOUN
ejpam-6472	322	5	,	,	PUNCT
ejpam-6472	322	6	tl+1	tl+1	PROPN
ejpam-6472	322	7	,	,	PUNCT
ejpam-6472	322	8	.	.	PUNCT
ejpam-6472	322	9	.	.	PUNCT
ejpam-6472	323	1	.	.	PUNCT
ejpam-6472	324	1	,	,	PUNCT
ejpam-6472	324	2	tni	tni	NOUN
ejpam-6472	324	3	)	)	PUNCT
ejpam-6472	324	4	.	.	PUNCT
ejpam-6472	325	1	since	since	SCONJ
ejpam-6472	325	2	r	r	PROPN
ejpam-6472	325	3	∈	∈	PROPN
ejpam-6472	325	4	sub(b	sub(b	NOUN
ejpam-6472	325	5	)	)	PUNCT
ejpam-6472	325	6	⊆	⊆	NUM
ejpam-6472	325	7	sub(c)\{c	sub(c)\{c	NUM
ejpam-6472	325	8	}	}	PUNCT
ejpam-6472	325	9	,	,	PUNCT
ejpam-6472	325	10	c	c	PROPN
ejpam-6472	325	11	̸∈	̸∈	PROPN
ejpam-6472	325	12	sub(r	sub(r	PROPN
ejpam-6472	325	13	)	)	PUNCT
ejpam-6472	325	14	.	.	PUNCT
ejpam-6472	326	1	furthermore	furthermore	ADV
ejpam-6472	326	2	,	,	PUNCT
ejpam-6472	326	3	since	since	SCONJ
ejpam-6472	326	4	r	r	PROPN
ejpam-6472	326	5	̸∈	̸∈	PROPN
ejpam-6472	326	6	sub(s)\{s	sub(s)\{s	PROPN
ejpam-6472	326	7	}	}	PUNCT
ejpam-6472	326	8	,	,	PUNCT
ejpam-6472	326	9	c	c	PROPN
ejpam-6472	326	10	̸∈	̸∈	PROPN
ejpam-6472	326	11	sub(s	sub(s	PROPN
ejpam-6472	326	12	)	)	PUNCT
ejpam-6472	326	13	.	.	PUNCT
ejpam-6472	327	1	thus	thus	ADV
ejpam-6472	327	2	,	,	PUNCT
ejpam-6472	327	3	c	c	PROPN
ejpam-6472	327	4	∈	∈	PROPN
ejpam-6472	327	5	w	w	PROPN
ejpam-6472	327	6	r	r	NOUN
ejpam-6472	327	7	,	,	PUNCT
ejpam-6472	327	8	s	s	PART
ejpam-6472	327	9	τ	τ	X
ejpam-6472	327	10	(	(	PUNCT
ejpam-6472	327	11	xn	xn	PROPN
ejpam-6472	327	12	)	)	PUNCT
ejpam-6472	327	13	and	and	CCONJ
ejpam-6472	327	14	c	c	PROPN
ejpam-6472	327	15	̸∈	̸∈	PROPN
ejpam-6472	327	16	{	{	PUNCT
ejpam-6472	327	17	r	r	PROPN
ejpam-6472	327	18	,	,	PUNCT
ejpam-6472	327	19	s	s	PART
ejpam-6472	327	20	}	}	PUNCT
ejpam-6472	327	21	.	.	PUNCT
ejpam-6472	328	1	observe	observe	VERB
ejpam-6472	328	2	that	that	SCONJ
ejpam-6472	328	3	{	{	PUNCT
ejpam-6472	328	4	r	r	NOUN
ejpam-6472	328	5	,	,	PUNCT
ejpam-6472	328	6	s	s	NOUN
ejpam-6472	328	7	}	}	PUNCT
ejpam-6472	328	8	∩	∩	ADJ
ejpam-6472	328	9	sub(tk	sub(tk	NOUN
ejpam-6472	328	10	)	)	PUNCT
ejpam-6472	328	11	=	=	NOUN
ejpam-6472	328	12	∅	∅	NOUN
ejpam-6472	328	13	for	for	ADP
ejpam-6472	328	14	all	all	DET
ejpam-6472	328	15	1	1	NUM
ejpam-6472	328	16	≤	≤	NUM
ejpam-6472	328	17	k	k	PROPN
ejpam-6472	328	18	≤	≤	PROPN
ejpam-6472	328	19	ni	ni	PROPN
ejpam-6472	328	20	as	as	SCONJ
ejpam-6472	328	21	each	each	DET
ejpam-6472	328	22	tk	tk	PROPN
ejpam-6472	328	23	is	be	AUX
ejpam-6472	328	24	a	a	DET
ejpam-6472	328	25	proper	proper	ADJ
ejpam-6472	328	26	subterm	subterm	NOUN
ejpam-6472	328	27	of	of	ADP
ejpam-6472	328	28	r	r	NOUN
ejpam-6472	328	29	and	and	CCONJ
ejpam-6472	328	30	s	s	PROPN
ejpam-6472	328	31	̸∈	̸∈	PROPN
ejpam-6472	328	32	sub(r	sub(r	PROPN
ejpam-6472	328	33	)	)	PUNCT
ejpam-6472	328	34	\	\	NOUN
ejpam-6472	328	35	{	{	PUNCT
ejpam-6472	328	36	r	r	NOUN
ejpam-6472	328	37	}	}	PUNCT
ejpam-6472	328	38	.	.	PUNCT
ejpam-6472	329	1	hence	hence	ADV
ejpam-6472	329	2	,	,	PUNCT
ejpam-6472	329	3	c	c	NOUN
ejpam-6472	329	4	·	·	PUNCT
ejpam-6472	329	5	rs	rs	NOUN
ejpam-6472	329	6	a	a	DET
ejpam-6472	329	7	=	=	NOUN
ejpam-6472	329	8	fi(t1	fi(t1	NOUN
ejpam-6472	329	9	,	,	PUNCT
ejpam-6472	329	10	.	.	PUNCT
ejpam-6472	329	11	.	.	PUNCT
ejpam-6472	329	12	.	.	PUNCT
ejpam-6472	330	1	,	,	PUNCT
ejpam-6472	330	2	tl−1	tl−1	PROPN
ejpam-6472	330	3	,	,	PUNCT
ejpam-6472	330	4	b	b	NOUN
ejpam-6472	330	5	,	,	PUNCT
ejpam-6472	330	6	tl+1	tl+1	PROPN
ejpam-6472	330	7	,	,	PUNCT
ejpam-6472	330	8	.	.	PUNCT
ejpam-6472	330	9	.	.	PUNCT
ejpam-6472	331	1	.	.	PUNCT
ejpam-6472	332	1	,	,	PUNCT
ejpam-6472	332	2	tni	tni	NOUN
ejpam-6472	332	3	)	)	PUNCT
ejpam-6472	332	4	·	·	PUNCT
ejpam-6472	332	5	rs	rs	NOUN
ejpam-6472	332	6	a	a	DET
ejpam-6472	332	7	=	=	NOUN
ejpam-6472	332	8	fi(t1	fi(t1	X
ejpam-6472	332	9	·	·	PUNCT
ejpam-6472	332	10	rs	rs	NOUN
ejpam-6472	332	11	a	a	PRON
ejpam-6472	332	12	,	,	PUNCT
ejpam-6472	332	13	.	.	PUNCT
ejpam-6472	332	14	.	.	PUNCT
ejpam-6472	333	1	.	.	PUNCT
ejpam-6472	334	1	,	,	PUNCT
ejpam-6472	334	2	tl−1	tl−1	NOUN
ejpam-6472	334	3	·	·	PUNCT
ejpam-6472	334	4	rs	rs	NOUN
ejpam-6472	334	5	a	a	PRON
ejpam-6472	334	6	,	,	PUNCT
ejpam-6472	334	7	b	b	NOUN
ejpam-6472	334	8	·	·	SYM
ejpam-6472	334	9	rs	rs	NOUN
ejpam-6472	334	10	a	a	X
ejpam-6472	334	11	,	,	PUNCT
ejpam-6472	334	12	tl+1	tl+1	PROPN
ejpam-6472	334	13	·	·	PUNCT
ejpam-6472	334	14	rs	rs	NOUN
ejpam-6472	334	15	a	a	PRON
ejpam-6472	334	16	,	,	PUNCT
ejpam-6472	334	17	.	.	PUNCT
ejpam-6472	334	18	.	.	PUNCT
ejpam-6472	334	19	.	.	PUNCT
ejpam-6472	335	1	,	,	PUNCT
ejpam-6472	335	2	tni	tni	NOUN
ejpam-6472	335	3	·	·	PUNCT
ejpam-6472	335	4	rs	rs	NOUN
ejpam-6472	335	5	a	a	NOUN
ejpam-6472	335	6	)	)	PUNCT
ejpam-6472	335	7	=	=	SYM
ejpam-6472	335	8	fi(t1	fi(t1	NOUN
ejpam-6472	335	9	,	,	PUNCT
ejpam-6472	335	10	.	.	PUNCT
ejpam-6472	335	11	.	.	PUNCT
ejpam-6472	335	12	.	.	PUNCT
ejpam-6472	336	1	,	,	PUNCT
ejpam-6472	336	2	tl−1	tl−1	PROPN
ejpam-6472	336	3	,	,	PUNCT
ejpam-6472	336	4	tl	tl	PROPN
ejpam-6472	336	5	,	,	PUNCT
ejpam-6472	336	6	tl+1	tl+1	PROPN
ejpam-6472	336	7	,	,	PUNCT
ejpam-6472	336	8	.	.	PUNCT
ejpam-6472	336	9	.	.	PUNCT
ejpam-6472	337	1	.	.	PUNCT
ejpam-6472	338	1	,	,	PUNCT
ejpam-6472	338	2	tni	tni	NOUN
ejpam-6472	338	3	)	)	PUNCT
ejpam-6472	338	4	=	=	VERB
ejpam-6472	339	1	r.	r.	NOUN
ejpam-6472	339	2	by	by	ADP
ejpam-6472	339	3	theorem	theorem	NOUN
ejpam-6472	339	4	2	2	NUM
ejpam-6472	339	5	,	,	PUNCT
ejpam-6472	339	6	q	q	PUNCT
ejpam-6472	339	7	is	be	AUX
ejpam-6472	339	8	not	not	PART
ejpam-6472	339	9	associative	associative	ADJ
ejpam-6472	339	10	under	under	ADP
ejpam-6472	339	11	·	·	SYM
ejpam-6472	339	12	rs	rs	X
ejpam-6472	339	13	.	.	PUNCT
ejpam-6472	340	1	we	we	PRON
ejpam-6472	340	2	conclude	conclude	VERB
ejpam-6472	340	3	this	this	DET
ejpam-6472	340	4	section	section	NOUN
ejpam-6472	340	5	with	with	ADP
ejpam-6472	340	6	two	two	NUM
ejpam-6472	340	7	lemmas	lemma	NOUN
ejpam-6472	340	8	,	,	PUNCT
ejpam-6472	340	9	which	which	PRON
ejpam-6472	340	10	show	show	VERB
ejpam-6472	340	11	that	that	SCONJ
ejpam-6472	340	12	the	the	DET
ejpam-6472	340	13	converses	converse	NOUN
ejpam-6472	340	14	of	of	ADP
ejpam-6472	340	15	lemma	lemma	PROPN
ejpam-6472	340	16	3	3	NUM
ejpam-6472	340	17	and	and	CCONJ
ejpam-6472	340	18	lemma	lemma	PROPN
ejpam-6472	340	19	4	4	NUM
ejpam-6472	340	20	hold	hold	VERB
ejpam-6472	340	21	when	when	SCONJ
ejpam-6472	340	22	restricted	restrict	VERB
ejpam-6472	340	23	to	to	ADP
ejpam-6472	340	24	the	the	DET
ejpam-6472	340	25	subset	subset	NOUN
ejpam-6472	340	26	w	w	PROPN
ejpam-6472	340	27	r	r	NOUN
ejpam-6472	340	28	,	,	PUNCT
ejpam-6472	340	29	s	s	PART
ejpam-6472	340	30	τ	τ	X
ejpam-6472	340	31	(	(	PUNCT
ejpam-6472	340	32	xn	xn	PROPN
ejpam-6472	340	33	)	)	PUNCT
ejpam-6472	340	34	.	.	PUNCT
ejpam-6472	341	1	these	these	DET
ejpam-6472	341	2	properties	property	NOUN
ejpam-6472	341	3	will	will	AUX
ejpam-6472	341	4	play	play	VERB
ejpam-6472	341	5	a	a	DET
ejpam-6472	341	6	key	key	ADJ
ejpam-6472	341	7	role	role	NOUN
ejpam-6472	341	8	in	in	ADP
ejpam-6472	341	9	establishing	establish	VERB
ejpam-6472	341	10	the	the	DET
ejpam-6472	341	11	algebraic	algebraic	ADJ
ejpam-6472	341	12	properties	property	NOUN
ejpam-6472	341	13	of	of	ADP
ejpam-6472	341	14	the	the	DET
ejpam-6472	341	15	semigroup	semigroup	NOUN
ejpam-6472	341	16	in	in	ADP
ejpam-6472	341	17	the	the	DET
ejpam-6472	341	18	next	next	ADJ
ejpam-6472	341	19	two	two	NUM
ejpam-6472	341	20	sections	section	NOUN
ejpam-6472	341	21	.	.	PUNCT
ejpam-6472	342	1	lemma	lemma	PROPN
ejpam-6472	342	2	5	5	X
ejpam-6472	342	3	.	.	PUNCT
ejpam-6472	343	1	let	let	VERB
ejpam-6472	343	2	r	r	NOUN
ejpam-6472	343	3	,	,	PUNCT
ejpam-6472	343	4	s	s	NOUN
ejpam-6472	343	5	∈	∈	PROPN
ejpam-6472	343	6	wτ	wτ	NOUN
ejpam-6472	343	7	(	(	PUNCT
ejpam-6472	343	8	xn	xn	X
ejpam-6472	343	9	)	)	PUNCT
ejpam-6472	343	10	be	be	AUX
ejpam-6472	343	11	fixed	fix	VERB
ejpam-6472	343	12	terms	term	NOUN
ejpam-6472	343	13	,	,	PUNCT
ejpam-6472	343	14	and	and	CCONJ
ejpam-6472	343	15	let	let	VERB
ejpam-6472	343	16	t	t	PROPN
ejpam-6472	343	17	,	,	PUNCT
ejpam-6472	343	18	q	q	PROPN
ejpam-6472	343	19	∈	∈	PROPN
ejpam-6472	343	20	w	w	NOUN
ejpam-6472	343	21	r	r	NOUN
ejpam-6472	343	22	,	,	PUNCT
ejpam-6472	343	23	s	s	PART
ejpam-6472	343	24	τ	τ	X
ejpam-6472	343	25	(	(	PUNCT
ejpam-6472	343	26	xn	xn	PROPN
ejpam-6472	343	27	)	)	PUNCT
ejpam-6472	343	28	.	.	PUNCT
ejpam-6472	344	1	then	then	ADV
ejpam-6472	344	2	the	the	DET
ejpam-6472	344	3	following	follow	VERB
ejpam-6472	344	4	statements	statement	NOUN
ejpam-6472	344	5	hold	hold	VERB
ejpam-6472	344	6	true	true	ADJ
ejpam-6472	344	7	:	:	PUNCT
ejpam-6472	344	8	(	(	PUNCT
ejpam-6472	344	9	i	i	NOUN
ejpam-6472	344	10	)	)	PUNCT
ejpam-6472	344	11	r	r	NOUN
ejpam-6472	344	12	∈	∈	PROPN
ejpam-6472	344	13	sub(t	sub(t	NOUN
ejpam-6472	344	14	·	·	SYM
ejpam-6472	344	15	rs	rs	X
ejpam-6472	344	16	q	q	NOUN
ejpam-6472	344	17	)	)	PUNCT
ejpam-6472	344	18	if	if	SCONJ
ejpam-6472	344	19	and	and	CCONJ
ejpam-6472	344	20	only	only	ADV
ejpam-6472	344	21	if	if	SCONJ
ejpam-6472	344	22	{	{	PUNCT
ejpam-6472	344	23	r	r	NOUN
ejpam-6472	344	24	,	,	PUNCT
ejpam-6472	344	25	s	s	NOUN
ejpam-6472	344	26	}	}	PUNCT
ejpam-6472	344	27	∩	∩	ADJ
ejpam-6472	344	28	sub(t	sub(t	NOUN
ejpam-6472	344	29	)	)	PUNCT
ejpam-6472	344	30	̸=	̸=	PROPN
ejpam-6472	344	31	∅	∅	NOUN
ejpam-6472	344	32	and	and	CCONJ
ejpam-6472	344	33	r	r	NOUN
ejpam-6472	344	34	∈	∈	PROPN
ejpam-6472	344	35	sub(q	sub(q	PROPN
ejpam-6472	344	36	)	)	PUNCT
ejpam-6472	344	37	.	.	PUNCT
ejpam-6472	345	1	(	(	PUNCT
ejpam-6472	345	2	ii	ii	NOUN
ejpam-6472	345	3	)	)	PUNCT
ejpam-6472	345	4	s	s	PART
ejpam-6472	345	5	∈	∈	PROPN
ejpam-6472	345	6	sub(t	sub(t	NOUN
ejpam-6472	345	7	·	·	SYM
ejpam-6472	345	8	rs	rs	X
ejpam-6472	345	9	q	q	NOUN
ejpam-6472	345	10	)	)	PUNCT
ejpam-6472	346	1	if	if	SCONJ
ejpam-6472	346	2	and	and	CCONJ
ejpam-6472	346	3	only	only	ADV
ejpam-6472	346	4	if	if	SCONJ
ejpam-6472	346	5	{	{	PUNCT
ejpam-6472	346	6	r	r	NOUN
ejpam-6472	346	7	,	,	PUNCT
ejpam-6472	346	8	s	s	NOUN
ejpam-6472	346	9	}	}	PUNCT
ejpam-6472	346	10	∩	∩	ADJ
ejpam-6472	346	11	sub(t	sub(t	NOUN
ejpam-6472	346	12	)	)	PUNCT
ejpam-6472	346	13	̸=	̸=	PROPN
ejpam-6472	346	14	∅	∅	NOUN
ejpam-6472	346	15	and	and	CCONJ
ejpam-6472	346	16	s	s	NOUN
ejpam-6472	346	17	∈	∈	PROPN
ejpam-6472	346	18	sub(q	sub(q	PROPN
ejpam-6472	346	19	)	)	PUNCT
ejpam-6472	346	20	.	.	PUNCT
ejpam-6472	347	1	proof	proof	NOUN
ejpam-6472	347	2	.	.	PUNCT
ejpam-6472	348	1	(	(	PUNCT
ejpam-6472	348	2	i	i	NOUN
ejpam-6472	348	3	)	)	PUNCT
ejpam-6472	348	4	the	the	DET
ejpam-6472	348	5	reverse	reverse	ADJ
ejpam-6472	348	6	direction	direction	NOUN
ejpam-6472	348	7	follows	follow	VERB
ejpam-6472	348	8	directly	directly	ADV
ejpam-6472	348	9	from	from	ADP
ejpam-6472	348	10	lemma	lemma	PROPN
ejpam-6472	348	11	3	3	NUM
ejpam-6472	348	12	.	.	PUNCT
ejpam-6472	348	13	additionally	additionally	ADV
ejpam-6472	348	14	,	,	PUNCT
ejpam-6472	348	15	lemma	lemma	PROPN
ejpam-6472	348	16	2	2	NUM
ejpam-6472	348	17	shows	show	VERB
ejpam-6472	348	18	that	that	SCONJ
ejpam-6472	348	19	r	r	NOUN
ejpam-6472	348	20	∈	∈	PROPN
ejpam-6472	348	21	sub(t	sub(t	NOUN
ejpam-6472	348	22	·	·	SYM
ejpam-6472	348	23	rs	rs	X
ejpam-6472	348	24	q	q	NOUN
ejpam-6472	348	25	)	)	PUNCT
ejpam-6472	348	26	implies	imply	VERB
ejpam-6472	348	27	{	{	PUNCT
ejpam-6472	348	28	r	r	NOUN
ejpam-6472	348	29	,	,	PUNCT
ejpam-6472	348	30	s	s	NOUN
ejpam-6472	348	31	}	}	PUNCT
ejpam-6472	348	32	∩	∩	ADJ
ejpam-6472	348	33	sub(t	sub(t	NOUN
ejpam-6472	348	34	)	)	PUNCT
ejpam-6472	348	35	̸=	̸=	PROPN
ejpam-6472	348	36	∅.	∅.	ADP
ejpam-6472	348	37	it	it	PRON
ejpam-6472	348	38	remains	remain	VERB
ejpam-6472	348	39	to	to	PART
ejpam-6472	348	40	demonstrate	demonstrate	VERB
ejpam-6472	348	41	that	that	SCONJ
ejpam-6472	348	42	r	r	NOUN
ejpam-6472	348	43	∈	∈	PROPN
ejpam-6472	348	44	sub(t	sub(t	NOUN
ejpam-6472	348	45	·	·	SYM
ejpam-6472	348	46	rs	rs	X
ejpam-6472	348	47	q	q	NOUN
ejpam-6472	348	48	)	)	PUNCT
ejpam-6472	348	49	implies	imply	VERB
ejpam-6472	348	50	r	r	NOUN
ejpam-6472	348	51	∈	∈	PROPN
ejpam-6472	348	52	sub(q	sub(q	PROPN
ejpam-6472	348	53	)	)	PUNCT
ejpam-6472	348	54	.	.	PUNCT
ejpam-6472	349	1	we	we	PRON
ejpam-6472	349	2	prove	prove	VERB
ejpam-6472	349	3	this	this	PRON
ejpam-6472	349	4	by	by	ADP
ejpam-6472	349	5	induction	induction	NOUN
ejpam-6472	349	6	on	on	ADP
ejpam-6472	349	7	the	the	DET
ejpam-6472	349	8	structure	structure	NOUN
ejpam-6472	349	9	of	of	ADP
ejpam-6472	349	10	t.	t.	PROPN
ejpam-6472	349	11	if	if	SCONJ
ejpam-6472	349	12	{	{	PUNCT
ejpam-6472	349	13	r	r	NOUN
ejpam-6472	349	14	,	,	PUNCT
ejpam-6472	349	15	s	s	NOUN
ejpam-6472	349	16	}	}	PUNCT
ejpam-6472	349	17	∩	∩	ADJ
ejpam-6472	349	18	sub(t	sub(t	NOUN
ejpam-6472	349	19	)	)	PUNCT
ejpam-6472	349	20	=	=	NOUN
ejpam-6472	349	21	∅	∅	NOUN
ejpam-6472	349	22	,	,	PUNCT
ejpam-6472	349	23	then	then	ADV
ejpam-6472	349	24	t	t	PROPN
ejpam-6472	349	25	·	·	PUNCT
ejpam-6472	349	26	rs	rs	PROPN
ejpam-6472	349	27	q	q	PROPN
ejpam-6472	349	28	=	=	SYM
ejpam-6472	349	29	t	t	PROPN
ejpam-6472	349	30	,	,	PUNCT
ejpam-6472	349	31	which	which	PRON
ejpam-6472	349	32	implies	imply	VERB
ejpam-6472	349	33	r	r	PROPN
ejpam-6472	349	34	̸∈	̸∈	PROPN
ejpam-6472	349	35	sub(t	sub(t	PROPN
ejpam-6472	349	36	·	·	PUNCT
ejpam-6472	349	37	rs	rs	X
ejpam-6472	349	38	q	q	NOUN
ejpam-6472	349	39	)	)	PUNCT
ejpam-6472	349	40	.	.	PUNCT
ejpam-6472	350	1	thus	thus	ADV
ejpam-6472	350	2	,	,	PUNCT
ejpam-6472	350	3	the	the	DET
ejpam-6472	350	4	claim	claim	NOUN
ejpam-6472	350	5	holds	hold	VERB
ejpam-6472	350	6	trivially	trivially	ADV
ejpam-6472	350	7	.	.	PUNCT
ejpam-6472	351	1	if	if	SCONJ
ejpam-6472	351	2	t	t	PROPN
ejpam-6472	351	3	∈	∈	PROPN
ejpam-6472	351	4	{	{	PUNCT
ejpam-6472	351	5	r	r	NOUN
ejpam-6472	351	6	,	,	PUNCT
ejpam-6472	351	7	s	s	PART
ejpam-6472	351	8	}	}	PUNCT
ejpam-6472	351	9	,	,	PUNCT
ejpam-6472	351	10	then	then	ADV
ejpam-6472	351	11	t	t	X
ejpam-6472	351	12	·	·	PUNCT
ejpam-6472	351	13	rs	rs	X
ejpam-6472	351	14	q	q	NOUN
ejpam-6472	352	1	=	=	PUNCT
ejpam-6472	352	2	q	q	NOUN
ejpam-6472	352	3	,	,	PUNCT
ejpam-6472	352	4	and	and	CCONJ
ejpam-6472	352	5	therefore	therefore	ADV
ejpam-6472	352	6	,	,	PUNCT
ejpam-6472	352	7	r	r	PROPN
ejpam-6472	352	8	∈	∈	PROPN
ejpam-6472	352	9	sub(t	sub(t	NOUN
ejpam-6472	352	10	·	·	SYM
ejpam-6472	352	11	rs	rs	X
ejpam-6472	352	12	q	q	NOUN
ejpam-6472	352	13	)	)	PUNCT
ejpam-6472	352	14	implies	imply	VERB
ejpam-6472	352	15	r	r	NOUN
ejpam-6472	352	16	∈	∈	PROPN
ejpam-6472	352	17	sub(q	sub(q	PROPN
ejpam-6472	352	18	)	)	PUNCT
ejpam-6472	352	19	.	.	PUNCT
ejpam-6472	353	1	for	for	ADP
ejpam-6472	353	2	t	t	NOUN
ejpam-6472	353	3	=	=	SYM
ejpam-6472	353	4	fi(t1	fi(t1	PROPN
ejpam-6472	353	5	,	,	PUNCT
ejpam-6472	353	6	.	.	PUNCT
ejpam-6472	353	7	.	.	PUNCT
ejpam-6472	354	1	.	.	PUNCT
ejpam-6472	355	1	,	,	PUNCT
ejpam-6472	355	2	tni	tni	NOUN
ejpam-6472	355	3	)	)	PUNCT
ejpam-6472	355	4	with	with	ADP
ejpam-6472	355	5	{	{	PUNCT
ejpam-6472	355	6	r	r	NOUN
ejpam-6472	355	7	,	,	PUNCT
ejpam-6472	355	8	s	s	NOUN
ejpam-6472	355	9	}	}	PUNCT
ejpam-6472	355	10	∩	∩	ADJ
ejpam-6472	355	11	sub(t	sub(t	NOUN
ejpam-6472	355	12	)	)	PUNCT
ejpam-6472	355	13	̸=	̸=	PROPN
ejpam-6472	355	14	∅	∅	NOUN
ejpam-6472	355	15	and	and	CCONJ
ejpam-6472	355	16	t	t	PROPN
ejpam-6472	355	17	̸=	̸=	PROPN
ejpam-6472	355	18	{	{	PUNCT
ejpam-6472	355	19	r	r	PROPN
ejpam-6472	355	20	,	,	PUNCT
ejpam-6472	355	21	s	s	PART
ejpam-6472	355	22	}	}	PUNCT
ejpam-6472	355	23	,	,	PUNCT
ejpam-6472	355	24	assume	assume	VERB
ejpam-6472	355	25	that	that	SCONJ
ejpam-6472	355	26	for	for	ADP
ejpam-6472	355	27	each	each	DET
ejpam-6472	355	28	1	1	NUM
ejpam-6472	355	29	≤	≤	NUM
ejpam-6472	355	30	j	j	PROPN
ejpam-6472	355	31	≤	≤	PROPN
ejpam-6472	355	32	ni	ni	PROPN
ejpam-6472	355	33	,	,	PUNCT
ejpam-6472	355	34	if	if	SCONJ
ejpam-6472	355	35	r	r	NOUN
ejpam-6472	355	36	∈	∈	NOUN
ejpam-6472	355	37	sub(tj	sub(tj	NOUN
ejpam-6472	355	38	·	·	SYM
ejpam-6472	355	39	rs	rs	ADJ
ejpam-6472	355	40	q	q	NOUN
ejpam-6472	355	41	)	)	PUNCT
ejpam-6472	355	42	,	,	PUNCT
ejpam-6472	355	43	then	then	ADV
ejpam-6472	355	44	r	r	NOUN
ejpam-6472	355	45	∈	∈	PROPN
ejpam-6472	355	46	sub(q	sub(q	PROPN
ejpam-6472	355	47	)	)	PUNCT
ejpam-6472	355	48	.	.	PUNCT
ejpam-6472	356	1	in	in	ADP
ejpam-6472	356	2	this	this	DET
ejpam-6472	356	3	case	case	NOUN
ejpam-6472	356	4	,	,	PUNCT
ejpam-6472	356	5	we	we	PRON
ejpam-6472	356	6	have	have	VERB
ejpam-6472	356	7	t	t	NOUN
ejpam-6472	356	8	·	·	PUNCT
ejpam-6472	356	9	rs	rs	NOUN
ejpam-6472	356	10	q	q	PROPN
ejpam-6472	356	11	=	=	PUNCT
ejpam-6472	356	12	fi(t1	fi(t1	NOUN
ejpam-6472	356	13	·	·	SYM
ejpam-6472	356	14	rs	rs	X
ejpam-6472	356	15	q	q	NOUN
ejpam-6472	356	16	,	,	PUNCT
ejpam-6472	356	17	.	.	PUNCT
ejpam-6472	356	18	.	.	PUNCT
ejpam-6472	357	1	.	.	PUNCT
ejpam-6472	358	1	,	,	PUNCT
ejpam-6472	358	2	tni	tni	NOUN
ejpam-6472	358	3	·	·	PUNCT
ejpam-6472	358	4	rs	rs	NOUN
ejpam-6472	358	5	q	q	NOUN
ejpam-6472	358	6	)	)	PUNCT
ejpam-6472	358	7	.	.	PUNCT
ejpam-6472	359	1	now	now	ADV
ejpam-6472	359	2	,	,	PUNCT
ejpam-6472	359	3	assume	assume	VERB
ejpam-6472	359	4	r	r	NOUN
ejpam-6472	359	5	∈	∈	PROPN
ejpam-6472	359	6	sub(t	sub(t	NOUN
ejpam-6472	359	7	·	·	SYM
ejpam-6472	359	8	rs	rs	X
ejpam-6472	359	9	q	q	NOUN
ejpam-6472	359	10	)	)	PUNCT
ejpam-6472	359	11	.	.	PUNCT
ejpam-6472	360	1	in	in	ADP
ejpam-6472	360	2	the	the	DET
ejpam-6472	360	3	case	case	NOUN
ejpam-6472	360	4	where	where	SCONJ
ejpam-6472	360	5	r	r	NOUN
ejpam-6472	360	6	=	=	SYM
ejpam-6472	360	7	t	t	NOUN
ejpam-6472	360	8	·	·	PUNCT
ejpam-6472	360	9	rs	rs	X
ejpam-6472	360	10	q	q	NOUN
ejpam-6472	360	11	,	,	PUNCT
ejpam-6472	360	12	lemma	lemma	PROPN
ejpam-6472	360	13	4	4	NUM
ejpam-6472	360	14	and	and	CCONJ
ejpam-6472	360	15	the	the	DET
ejpam-6472	360	16	fact	fact	NOUN
ejpam-6472	360	17	that	that	SCONJ
ejpam-6472	360	18	q	q	PROPN
ejpam-6472	360	19	∈	∈	PROPN
ejpam-6472	360	20	w	w	PROPN
ejpam-6472	360	21	r	r	NOUN
ejpam-6472	360	22	,	,	PUNCT
ejpam-6472	360	23	s	s	PART
ejpam-6472	360	24	τ	τ	X
ejpam-6472	360	25	(	(	PUNCT
ejpam-6472	360	26	xn	xn	PROPN
ejpam-6472	360	27	)	)	PUNCT
ejpam-6472	360	28	provides	provide	VERB
ejpam-6472	360	29	that	that	DET
ejpam-6472	360	30	q	q	NOUN
ejpam-6472	360	31	=	=	SYM
ejpam-6472	360	32	r	r	NOUN
ejpam-6472	360	33	,	,	PUNCT
ejpam-6472	360	34	and	and	CCONJ
ejpam-6472	360	35	thus	thus	ADV
ejpam-6472	360	36	r	r	NOUN
ejpam-6472	360	37	∈	∈	PROPN
ejpam-6472	360	38	sub(q	sub(q	PROPN
ejpam-6472	360	39	)	)	PUNCT
ejpam-6472	360	40	.	.	PUNCT
ejpam-6472	361	1	on	on	ADP
ejpam-6472	361	2	the	the	DET
ejpam-6472	361	3	other	other	ADJ
ejpam-6472	361	4	hand	hand	NOUN
ejpam-6472	361	5	,	,	PUNCT
ejpam-6472	361	6	if	if	SCONJ
ejpam-6472	361	7	r	r	NOUN
ejpam-6472	361	8	∈	∈	NOUN
ejpam-6472	361	9	sub(tj	sub(tj	NOUN
ejpam-6472	361	10	·	·	SYM
ejpam-6472	361	11	rs	rs	NOUN
ejpam-6472	361	12	q	q	NOUN
ejpam-6472	361	13	)	)	PUNCT
ejpam-6472	361	14	for	for	ADP
ejpam-6472	361	15	some	some	PRON
ejpam-6472	361	16	1	1	NUM
ejpam-6472	361	17	≤	≤	NUM
ejpam-6472	361	18	j	j	PROPN
ejpam-6472	361	19	≤	≤	PROPN
ejpam-6472	361	20	ni	ni	PROPN
ejpam-6472	361	21	,	,	PUNCT
ejpam-6472	361	22	then	then	ADV
ejpam-6472	361	23	the	the	DET
ejpam-6472	361	24	desired	desire	VERB
ejpam-6472	361	25	result	result	NOUN
ejpam-6472	361	26	follows	follow	VERB
ejpam-6472	361	27	directly	directly	ADV
ejpam-6472	361	28	from	from	ADP
ejpam-6472	361	29	the	the	DET
ejpam-6472	361	30	inductive	inductive	ADJ
ejpam-6472	361	31	hypothesis	hypothesis	NOUN
ejpam-6472	361	32	.	.	PUNCT
ejpam-6472	362	1	this	this	PRON
ejpam-6472	362	2	complete	complete	VERB
ejpam-6472	362	3	the	the	DET
ejpam-6472	362	4	proof	proof	NOUN
ejpam-6472	362	5	for	for	ADP
ejpam-6472	362	6	part	part	NOUN
ejpam-6472	362	7	(	(	PUNCT
ejpam-6472	362	8	i	i	NOUN
ejpam-6472	362	9	)	)	PUNCT
ejpam-6472	362	10	.	.	PUNCT
ejpam-6472	363	1	(	(	PUNCT
ejpam-6472	363	2	ii	ii	X
ejpam-6472	363	3	)	)	PUNCT
ejpam-6472	363	4	this	this	PRON
ejpam-6472	363	5	follows	follow	VERB
ejpam-6472	363	6	by	by	ADP
ejpam-6472	363	7	a	a	DET
ejpam-6472	363	8	similar	similar	ADJ
ejpam-6472	363	9	reasoning	reasoning	NOUN
ejpam-6472	363	10	.	.	PUNCT
ejpam-6472	364	1	lemma	lemma	PROPN
ejpam-6472	364	2	6	6	NUM
ejpam-6472	364	3	.	.	PUNCT
ejpam-6472	365	1	let	let	VERB
ejpam-6472	365	2	r	r	NOUN
ejpam-6472	365	3	,	,	PUNCT
ejpam-6472	365	4	s	s	NOUN
ejpam-6472	365	5	∈	∈	PROPN
ejpam-6472	365	6	wτ	wτ	NOUN
ejpam-6472	365	7	(	(	PUNCT
ejpam-6472	365	8	xn	xn	X
ejpam-6472	365	9	)	)	PUNCT
ejpam-6472	365	10	be	be	AUX
ejpam-6472	365	11	fixed	fix	VERB
ejpam-6472	365	12	terms	term	NOUN
ejpam-6472	365	13	,	,	PUNCT
ejpam-6472	365	14	and	and	CCONJ
ejpam-6472	365	15	let	let	VERB
ejpam-6472	365	16	t	t	PROPN
ejpam-6472	365	17	,	,	PUNCT
ejpam-6472	365	18	q	q	PROPN
ejpam-6472	365	19	∈	∈	PROPN
ejpam-6472	365	20	w	w	NOUN
ejpam-6472	365	21	r	r	NOUN
ejpam-6472	365	22	,	,	PUNCT
ejpam-6472	365	23	s	s	PART
ejpam-6472	365	24	τ	τ	X
ejpam-6472	365	25	(	(	PUNCT
ejpam-6472	365	26	xn	xn	PROPN
ejpam-6472	365	27	)	)	PUNCT
ejpam-6472	365	28	.	.	PUNCT
ejpam-6472	366	1	then	then	ADV
ejpam-6472	366	2	the	the	DET
ejpam-6472	366	3	following	following	ADJ
ejpam-6472	366	4	statements	statement	NOUN
ejpam-6472	366	5	hold	hold	VERB
ejpam-6472	366	6	:	:	PUNCT
ejpam-6472	366	7	(	(	PUNCT
ejpam-6472	366	8	i	i	NOUN
ejpam-6472	366	9	)	)	PUNCT
ejpam-6472	366	10	t	t	PROPN
ejpam-6472	366	11	·	·	PUNCT
ejpam-6472	366	12	rs	rs	NOUN
ejpam-6472	367	1	q	q	NOUN
ejpam-6472	368	1	=	=	PUNCT
ejpam-6472	368	2	r	r	NOUN
ejpam-6472	368	3	if	if	SCONJ
ejpam-6472	368	4	and	and	CCONJ
ejpam-6472	368	5	only	only	ADV
ejpam-6472	368	6	if	if	SCONJ
ejpam-6472	368	7	t	t	PROPN
ejpam-6472	368	8	∈	∈	PROPN
ejpam-6472	368	9	{	{	PUNCT
ejpam-6472	368	10	r	r	NOUN
ejpam-6472	368	11	,	,	PUNCT
ejpam-6472	368	12	s	s	PART
ejpam-6472	368	13	}	}	PUNCT
ejpam-6472	368	14	and	and	CCONJ
ejpam-6472	368	15	q	q	X
ejpam-6472	368	16	=	=	SYM
ejpam-6472	368	17	r.	r.	PROPN
ejpam-6472	368	18	p.	p.	PROPN
ejpam-6472	368	19	prachumdang	prachumdang	PROPN
ejpam-6472	368	20	,	,	PUNCT
ejpam-6472	368	21	b.	b.	PROPN
ejpam-6472	368	22	pibaljommee	pibaljommee	PROPN
ejpam-6472	368	23	/	/	SYM
ejpam-6472	368	24	eur	eur	PROPN
ejpam-6472	368	25	.	.	PUNCT
ejpam-6472	369	1	j.	j.	PROPN
ejpam-6472	369	2	pure	pure	PROPN
ejpam-6472	369	3	appl	appl	PROPN
ejpam-6472	369	4	.	.	PROPN
ejpam-6472	369	5	math	math	PROPN
ejpam-6472	369	6	,	,	PUNCT
ejpam-6472	369	7	18	18	NUM
ejpam-6472	369	8	(	(	PUNCT
ejpam-6472	369	9	3	3	NUM
ejpam-6472	369	10	)	)	PUNCT
ejpam-6472	369	11	(	(	PUNCT
ejpam-6472	369	12	2025	2025	NUM
ejpam-6472	369	13	)	)	PUNCT
ejpam-6472	369	14	,	,	PUNCT
ejpam-6472	369	15	6472	6472	NUM
ejpam-6472	369	16	10	10	NUM
ejpam-6472	369	17	of	of	ADP
ejpam-6472	369	18	16	16	NUM
ejpam-6472	369	19	(	(	PUNCT
ejpam-6472	369	20	ii	ii	NOUN
ejpam-6472	369	21	)	)	PUNCT
ejpam-6472	369	22	t	t	PROPN
ejpam-6472	369	23	·	·	PUNCT
ejpam-6472	369	24	rs	rs	NOUN
ejpam-6472	369	25	q	q	NOUN
ejpam-6472	370	1	=	=	SYM
ejpam-6472	370	2	s	s	X
ejpam-6472	370	3	if	if	SCONJ
ejpam-6472	371	1	and	and	CCONJ
ejpam-6472	371	2	only	only	ADV
ejpam-6472	371	3	if	if	SCONJ
ejpam-6472	371	4	t	t	PROPN
ejpam-6472	371	5	∈	∈	PROPN
ejpam-6472	371	6	{	{	PUNCT
ejpam-6472	371	7	r	r	NOUN
ejpam-6472	371	8	,	,	PUNCT
ejpam-6472	371	9	s	s	PART
ejpam-6472	371	10	}	}	PUNCT
ejpam-6472	371	11	and	and	CCONJ
ejpam-6472	371	12	q	q	X
ejpam-6472	371	13	=	=	PUNCT
ejpam-6472	371	14	s.	s.	PROPN
ejpam-6472	371	15	proof	proof	NOUN
ejpam-6472	371	16	.	.	PUNCT
ejpam-6472	372	1	we	we	PRON
ejpam-6472	372	2	will	will	AUX
ejpam-6472	372	3	prove	prove	VERB
ejpam-6472	372	4	only	only	ADV
ejpam-6472	372	5	(	(	PUNCT
ejpam-6472	372	6	i	i	NOUN
ejpam-6472	372	7	)	)	PUNCT
ejpam-6472	372	8	,	,	PUNCT
ejpam-6472	372	9	as	as	SCONJ
ejpam-6472	372	10	(	(	PUNCT
ejpam-6472	372	11	ii	ii	NOUN
ejpam-6472	372	12	)	)	PUNCT
ejpam-6472	372	13	follows	follow	VERB
ejpam-6472	372	14	by	by	ADP
ejpam-6472	372	15	a	a	DET
ejpam-6472	372	16	similar	similar	ADJ
ejpam-6472	372	17	argument	argument	NOUN
ejpam-6472	372	18	.	.	PUNCT
ejpam-6472	373	1	assume	assume	VERB
ejpam-6472	373	2	t	t	X
ejpam-6472	373	3	·	·	PUNCT
ejpam-6472	373	4	rs	rs	NOUN
ejpam-6472	373	5	q	q	PROPN
ejpam-6472	374	1	=	=	PUNCT
ejpam-6472	374	2	r.	r.	NOUN
ejpam-6472	374	3	by	by	ADP
ejpam-6472	374	4	lemma	lemma	PROPN
ejpam-6472	374	5	4	4	NUM
ejpam-6472	374	6	,	,	PUNCT
ejpam-6472	374	7	it	it	PRON
ejpam-6472	374	8	follows	follow	VERB
ejpam-6472	374	9	that	that	SCONJ
ejpam-6472	374	10	{	{	PUNCT
ejpam-6472	374	11	r	r	NOUN
ejpam-6472	374	12	,	,	PUNCT
ejpam-6472	374	13	s	s	NOUN
ejpam-6472	374	14	}	}	PUNCT
ejpam-6472	374	15	∩	∩	ADJ
ejpam-6472	374	16	sub(t	sub(t	NOUN
ejpam-6472	374	17	)	)	PUNCT
ejpam-6472	374	18	̸=	̸=	PROPN
ejpam-6472	374	19	∅	∅	NOUN
ejpam-6472	374	20	and	and	CCONJ
ejpam-6472	374	21	q	q	NOUN
ejpam-6472	374	22	∈	∈	PROPN
ejpam-6472	374	23	sub(r	sub(r	PROPN
ejpam-6472	374	24	)	)	PUNCT
ejpam-6472	374	25	.	.	PUNCT
ejpam-6472	375	1	since	since	SCONJ
ejpam-6472	375	2	q	q	PROPN
ejpam-6472	375	3	is	be	AUX
ejpam-6472	375	4	not	not	PART
ejpam-6472	375	5	a	a	DET
ejpam-6472	375	6	proper	proper	ADJ
ejpam-6472	375	7	subterm	subterm	NOUN
ejpam-6472	375	8	of	of	ADP
ejpam-6472	375	9	r	r	NOUN
ejpam-6472	375	10	,	,	PUNCT
ejpam-6472	375	11	q	q	X
ejpam-6472	375	12	=	=	SYM
ejpam-6472	375	13	r.	r.	PROPN
ejpam-6472	375	14	now	now	ADV
ejpam-6472	375	15	,	,	PUNCT
ejpam-6472	375	16	suppose	suppose	VERB
ejpam-6472	375	17	t	t	PROPN
ejpam-6472	375	18	̸∈	̸∈	PROPN
ejpam-6472	375	19	{	{	PUNCT
ejpam-6472	375	20	r	r	PROPN
ejpam-6472	375	21	,	,	PUNCT
ejpam-6472	375	22	s	s	PART
ejpam-6472	375	23	}	}	PUNCT
ejpam-6472	375	24	.	.	PUNCT
ejpam-6472	376	1	by	by	ADP
ejpam-6472	376	2	lemma	lemma	PROPN
ejpam-6472	376	3	1	1	NUM
ejpam-6472	376	4	,	,	PUNCT
ejpam-6472	376	5	r	r	NOUN
ejpam-6472	376	6	=	=	PUNCT
ejpam-6472	376	7	q	q	PUNCT
ejpam-6472	376	8	∈	∈	PROPN
ejpam-6472	376	9	sub(t	sub(t	NOUN
ejpam-6472	376	10	·	·	SYM
ejpam-6472	376	11	rs	rs	X
ejpam-6472	376	12	q	q	NOUN
ejpam-6472	376	13	)	)	PUNCT
ejpam-6472	376	14	\	\	NOUN
ejpam-6472	376	15	{	{	PUNCT
ejpam-6472	376	16	t	t	NOUN
ejpam-6472	376	17	·	·	SYM
ejpam-6472	376	18	rs	rs	X
ejpam-6472	376	19	q	q	NOUN
ejpam-6472	376	20	}	}	PUNCT
ejpam-6472	376	21	=	=	SYM
ejpam-6472	376	22	sub(r	sub(r	PROPN
ejpam-6472	376	23	)	)	PUNCT
ejpam-6472	376	24	\	\	NOUN
ejpam-6472	376	25	{	{	PUNCT
ejpam-6472	376	26	r	r	NOUN
ejpam-6472	376	27	}	}	PUNCT
ejpam-6472	376	28	,	,	PUNCT
ejpam-6472	376	29	which	which	PRON
ejpam-6472	376	30	is	be	AUX
ejpam-6472	376	31	a	a	DET
ejpam-6472	376	32	contradiction	contradiction	NOUN
ejpam-6472	376	33	.	.	PUNCT
ejpam-6472	377	1	hence	hence	ADV
ejpam-6472	377	2	,	,	PUNCT
ejpam-6472	377	3	t	t	PROPN
ejpam-6472	377	4	∈	∈	PROPN
ejpam-6472	377	5	{	{	PUNCT
ejpam-6472	377	6	r	r	NOUN
ejpam-6472	377	7	,	,	PUNCT
ejpam-6472	377	8	s	s	PART
ejpam-6472	377	9	}	}	PUNCT
ejpam-6472	377	10	.	.	PUNCT
ejpam-6472	378	1	the	the	DET
ejpam-6472	378	2	converse	converse	NOUN
ejpam-6472	378	3	is	be	AUX
ejpam-6472	378	4	straightforward	straightforward	ADJ
ejpam-6472	378	5	.	.	PUNCT
ejpam-6472	379	1	4	4	X
ejpam-6472	379	2	.	.	X
ejpam-6472	379	3	idempotent	idempotent	NOUN
ejpam-6472	379	4	and	and	CCONJ
ejpam-6472	379	5	regular	regular	ADJ
ejpam-6472	379	6	elements	element	NOUN
ejpam-6472	379	7	in	in	ADP
ejpam-6472	379	8	the	the	DET
ejpam-6472	379	9	semigroup	semigroup	NOUN
ejpam-6472	379	10	(	(	PUNCT
ejpam-6472	379	11	w	w	NOUN
ejpam-6472	379	12	r	r	NOUN
ejpam-6472	379	13	,	,	PUNCT
ejpam-6472	379	14	s	s	PART
ejpam-6472	379	15	τ	τ	X
ejpam-6472	379	16	(	(	PUNCT
ejpam-6472	379	17	xn	xn	PROPN
ejpam-6472	379	18	)	)	PUNCT
ejpam-6472	379	19	,	,	PUNCT
ejpam-6472	379	20	·	·	PUNCT
ejpam-6472	379	21	rs	rs	X
ejpam-6472	379	22	)	)	PUNCT
ejpam-6472	379	23	in	in	ADP
ejpam-6472	379	24	this	this	DET
ejpam-6472	379	25	section	section	NOUN
ejpam-6472	379	26	,	,	PUNCT
ejpam-6472	379	27	we	we	PRON
ejpam-6472	379	28	investigate	investigate	VERB
ejpam-6472	379	29	the	the	DET
ejpam-6472	379	30	idempotent	idempotent	NOUN
ejpam-6472	379	31	and	and	CCONJ
ejpam-6472	379	32	regular	regular	ADJ
ejpam-6472	379	33	elements	element	NOUN
ejpam-6472	379	34	with	with	ADP
ejpam-6472	379	35	respect	respect	NOUN
ejpam-6472	379	36	to	to	ADP
ejpam-6472	379	37	·	·	PUNCT
ejpam-6472	379	38	rs	rs	X
ejpam-6472	379	39	in	in	ADP
ejpam-6472	379	40	w	w	NOUN
ejpam-6472	379	41	r	r	NOUN
ejpam-6472	379	42	,	,	PUNCT
ejpam-6472	379	43	s	s	PART
ejpam-6472	379	44	τ	τ	X
ejpam-6472	379	45	(	(	PUNCT
ejpam-6472	379	46	xn	xn	PROPN
ejpam-6472	379	47	)	)	PUNCT
ejpam-6472	379	48	.	.	PUNCT
ejpam-6472	380	1	recall	recall	VERB
ejpam-6472	380	2	that	that	SCONJ
ejpam-6472	380	3	an	an	DET
ejpam-6472	380	4	element	element	NOUN
ejpam-6472	380	5	t	t	NOUN
ejpam-6472	380	6	in	in	ADP
ejpam-6472	380	7	a	a	DET
ejpam-6472	380	8	semigroup	semigroup	NOUN
ejpam-6472	380	9	s	s	PART
ejpam-6472	380	10	is	be	AUX
ejpam-6472	380	11	called	call	VERB
ejpam-6472	380	12	idempotent	idempotent	ADJ
ejpam-6472	380	13	if	if	SCONJ
ejpam-6472	380	14	t	t	PROPN
ejpam-6472	380	15	=	=	SYM
ejpam-6472	380	16	tt	tt	PROPN
ejpam-6472	380	17	,	,	PUNCT
ejpam-6472	380	18	and	and	CCONJ
ejpam-6472	380	19	is	be	AUX
ejpam-6472	380	20	called	call	VERB
ejpam-6472	380	21	regular	regular	ADV
ejpam-6472	380	22	if	if	SCONJ
ejpam-6472	380	23	there	there	PRON
ejpam-6472	380	24	exists	exist	VERB
ejpam-6472	380	25	q	q	PROPN
ejpam-6472	380	26	∈	∈	PROPN
ejpam-6472	380	27	s	s	VERB
ejpam-6472	380	28	such	such	ADJ
ejpam-6472	380	29	that	that	PRON
ejpam-6472	380	30	t	t	NOUN
ejpam-6472	380	31	=	=	PUNCT
ejpam-6472	380	32	tqt	tqt	PROPN
ejpam-6472	380	33	.	.	PUNCT
ejpam-6472	381	1	it	it	PRON
ejpam-6472	381	2	is	be	AUX
ejpam-6472	381	3	straightforward	straightforward	ADJ
ejpam-6472	381	4	that	that	SCONJ
ejpam-6472	381	5	every	every	DET
ejpam-6472	381	6	idempotent	idempotent	ADJ
ejpam-6472	381	7	element	element	NOUN
ejpam-6472	381	8	is	be	AUX
ejpam-6472	381	9	also	also	ADV
ejpam-6472	381	10	regular	regular	ADJ
ejpam-6472	381	11	.	.	PUNCT
ejpam-6472	382	1	theorem	theorem	NOUN
ejpam-6472	382	2	5	5	NUM
ejpam-6472	382	3	.	.	PUNCT
ejpam-6472	383	1	let	let	VERB
ejpam-6472	383	2	r	r	NOUN
ejpam-6472	383	3	,	,	PUNCT
ejpam-6472	383	4	s	s	NOUN
ejpam-6472	383	5	∈	∈	PROPN
ejpam-6472	383	6	wτ	wτ	NOUN
ejpam-6472	383	7	(	(	PUNCT
ejpam-6472	383	8	xn	xn	X
ejpam-6472	383	9	)	)	PUNCT
ejpam-6472	383	10	be	be	AUX
ejpam-6472	383	11	fixed	fix	VERB
ejpam-6472	383	12	terms	term	NOUN
ejpam-6472	383	13	and	and	CCONJ
ejpam-6472	383	14	t	t	NOUN
ejpam-6472	383	15	∈	∈	PROPN
ejpam-6472	383	16	w	w	PROPN
ejpam-6472	383	17	r	r	PROPN
ejpam-6472	383	18	,	,	PUNCT
ejpam-6472	383	19	s	s	PART
ejpam-6472	383	20	τ	τ	X
ejpam-6472	383	21	(	(	PUNCT
ejpam-6472	383	22	xn	xn	PROPN
ejpam-6472	383	23	)	)	PUNCT
ejpam-6472	383	24	.	.	PUNCT
ejpam-6472	384	1	then	then	ADV
ejpam-6472	384	2	t	t	PROPN
ejpam-6472	384	3	is	be	AUX
ejpam-6472	384	4	idempotent	idempotent	ADJ
ejpam-6472	384	5	with	with	ADP
ejpam-6472	384	6	respect	respect	NOUN
ejpam-6472	384	7	to	to	ADP
ejpam-6472	384	8	·	·	PUNCT
ejpam-6472	384	9	rs	rs	VERB
ejpam-6472	384	10	if	if	SCONJ
ejpam-6472	385	1	and	and	CCONJ
ejpam-6472	385	2	only	only	ADV
ejpam-6472	385	3	if	if	SCONJ
ejpam-6472	385	4	{	{	PUNCT
ejpam-6472	385	5	r	r	NOUN
ejpam-6472	385	6	,	,	PUNCT
ejpam-6472	385	7	s	s	NOUN
ejpam-6472	385	8	}	}	PUNCT
ejpam-6472	385	9	∩	∩	ADJ
ejpam-6472	385	10	sub(t	sub(t	NOUN
ejpam-6472	385	11	)	)	PUNCT
ejpam-6472	385	12	=	=	NOUN
ejpam-6472	386	1	∅	∅	NOUN
ejpam-6472	386	2	or	or	CCONJ
ejpam-6472	386	3	t	t	NOUN
ejpam-6472	386	4	∈	∈	PROPN
ejpam-6472	386	5	{	{	PUNCT
ejpam-6472	386	6	r	r	NOUN
ejpam-6472	386	7	,	,	PUNCT
ejpam-6472	386	8	s	s	PART
ejpam-6472	386	9	}	}	PUNCT
ejpam-6472	386	10	.	.	PUNCT
ejpam-6472	387	1	proof	proof	NOUN
ejpam-6472	387	2	.	.	PUNCT
ejpam-6472	388	1	assume	assume	VERB
ejpam-6472	388	2	that	that	SCONJ
ejpam-6472	388	3	{	{	PUNCT
ejpam-6472	388	4	r	r	NOUN
ejpam-6472	388	5	,	,	PUNCT
ejpam-6472	388	6	s	s	NOUN
ejpam-6472	388	7	}	}	PUNCT
ejpam-6472	388	8	∩	∩	ADJ
ejpam-6472	388	9	sub(t	sub(t	NOUN
ejpam-6472	388	10	)	)	PUNCT
ejpam-6472	388	11	̸=	̸=	PROPN
ejpam-6472	388	12	∅	∅	NOUN
ejpam-6472	388	13	and	and	CCONJ
ejpam-6472	388	14	t	t	X
ejpam-6472	388	15	̸∈	̸∈	PROPN
ejpam-6472	388	16	{	{	PUNCT
ejpam-6472	388	17	r	r	PROPN
ejpam-6472	388	18	,	,	PUNCT
ejpam-6472	388	19	s	s	PART
ejpam-6472	388	20	}	}	PUNCT
ejpam-6472	388	21	.	.	PUNCT
ejpam-6472	389	1	by	by	ADP
ejpam-6472	389	2	lemma	lemma	PROPN
ejpam-6472	389	3	1	1	NUM
ejpam-6472	389	4	,	,	PUNCT
ejpam-6472	389	5	t	t	PROPN
ejpam-6472	389	6	∈	∈	PROPN
ejpam-6472	389	7	sub(t	sub(t	PROPN
ejpam-6472	389	8	·	·	PUNCT
ejpam-6472	389	9	rs	rs	PROPN
ejpam-6472	389	10	t	t	PROPN
ejpam-6472	389	11	)	)	PUNCT
ejpam-6472	389	12	\	\	PROPN
ejpam-6472	389	13	{	{	PUNCT
ejpam-6472	389	14	t	t	NOUN
ejpam-6472	389	15	·	·	SYM
ejpam-6472	389	16	rs	rs	PROPN
ejpam-6472	389	17	t	t	PROPN
ejpam-6472	389	18	}	}	PUNCT
ejpam-6472	389	19	.	.	PUNCT
ejpam-6472	390	1	thus	thus	ADV
ejpam-6472	390	2	,	,	PUNCT
ejpam-6472	390	3	t	t	PROPN
ejpam-6472	390	4	̸=	̸=	PROPN
ejpam-6472	390	5	t	t	PROPN
ejpam-6472	390	6	·	·	PUNCT
ejpam-6472	390	7	rs	rs	PROPN
ejpam-6472	390	8	t	t	PROPN
ejpam-6472	390	9	,	,	PUNCT
ejpam-6472	390	10	which	which	PRON
ejpam-6472	390	11	implies	imply	VERB
ejpam-6472	390	12	that	that	SCONJ
ejpam-6472	390	13	t	t	PROPN
ejpam-6472	390	14	is	be	AUX
ejpam-6472	390	15	not	not	PART
ejpam-6472	390	16	idempotent	idempotent	ADJ
ejpam-6472	390	17	.	.	PUNCT
ejpam-6472	391	1	the	the	DET
ejpam-6472	391	2	converse	converse	NOUN
ejpam-6472	391	3	follows	follow	VERB
ejpam-6472	391	4	directly	directly	ADV
ejpam-6472	391	5	from	from	ADP
ejpam-6472	391	6	the	the	DET
ejpam-6472	391	7	definition	definition	NOUN
ejpam-6472	391	8	of	of	ADP
ejpam-6472	391	9	·	·	SYM
ejpam-6472	391	10	rs	rs	X
ejpam-6472	391	11	.	.	PUNCT
ejpam-6472	392	1	theorem	theorem	NOUN
ejpam-6472	392	2	6	6	NUM
ejpam-6472	392	3	.	.	PUNCT
ejpam-6472	393	1	let	let	VERB
ejpam-6472	393	2	r	r	NOUN
ejpam-6472	393	3	,	,	PUNCT
ejpam-6472	393	4	s	s	NOUN
ejpam-6472	393	5	∈	∈	PROPN
ejpam-6472	393	6	wτ	wτ	NOUN
ejpam-6472	393	7	(	(	PUNCT
ejpam-6472	393	8	xn	xn	X
ejpam-6472	393	9	)	)	PUNCT
ejpam-6472	393	10	be	be	AUX
ejpam-6472	393	11	fixed	fix	VERB
ejpam-6472	393	12	terms	term	NOUN
ejpam-6472	393	13	and	and	CCONJ
ejpam-6472	393	14	t	t	NOUN
ejpam-6472	393	15	∈	∈	PROPN
ejpam-6472	393	16	w	w	PROPN
ejpam-6472	393	17	r	r	PROPN
ejpam-6472	393	18	,	,	PUNCT
ejpam-6472	393	19	s	s	PART
ejpam-6472	393	20	τ	τ	X
ejpam-6472	393	21	(	(	PUNCT
ejpam-6472	393	22	xn	xn	PROPN
ejpam-6472	393	23	)	)	PUNCT
ejpam-6472	393	24	.	.	PUNCT
ejpam-6472	394	1	then	then	ADV
ejpam-6472	394	2	t	t	PROPN
ejpam-6472	394	3	is	be	AUX
ejpam-6472	394	4	regular	regular	ADJ
ejpam-6472	394	5	with	with	ADP
ejpam-6472	394	6	respect	respect	NOUN
ejpam-6472	394	7	to	to	ADP
ejpam-6472	394	8	·	·	PUNCT
ejpam-6472	394	9	rs	rs	VERB
ejpam-6472	394	10	if	if	SCONJ
ejpam-6472	395	1	and	and	CCONJ
ejpam-6472	395	2	only	only	ADV
ejpam-6472	395	3	if	if	SCONJ
ejpam-6472	395	4	t	t	PROPN
ejpam-6472	395	5	is	be	AUX
ejpam-6472	395	6	idempotent	idempotent	ADJ
ejpam-6472	395	7	.	.	PUNCT
ejpam-6472	396	1	proof	proof	NOUN
ejpam-6472	396	2	.	.	PUNCT
ejpam-6472	397	1	assume	assume	VERB
ejpam-6472	397	2	that	that	SCONJ
ejpam-6472	397	3	t	t	PROPN
ejpam-6472	397	4	is	be	AUX
ejpam-6472	397	5	regular	regular	ADJ
ejpam-6472	397	6	but	but	CCONJ
ejpam-6472	397	7	not	not	PART
ejpam-6472	397	8	idempotent	idempotent	ADJ
ejpam-6472	397	9	.	.	PUNCT
ejpam-6472	398	1	then	then	ADV
ejpam-6472	398	2	t	t	PROPN
ejpam-6472	398	3	=	=	SYM
ejpam-6472	398	4	t	t	PROPN
ejpam-6472	398	5	·	·	PUNCT
ejpam-6472	398	6	rs	rs	X
ejpam-6472	398	7	q	q	NOUN
ejpam-6472	398	8	·	·	PUNCT
ejpam-6472	398	9	rs	rs	NOUN
ejpam-6472	398	10	t	t	NOUN
ejpam-6472	398	11	for	for	ADP
ejpam-6472	398	12	some	some	DET
ejpam-6472	398	13	q	q	NOUN
ejpam-6472	398	14	∈	∈	PROPN
ejpam-6472	398	15	w	w	NOUN
ejpam-6472	398	16	r	r	NOUN
ejpam-6472	398	17	,	,	PUNCT
ejpam-6472	398	18	s	s	PART
ejpam-6472	398	19	τ	τ	X
ejpam-6472	398	20	(	(	PUNCT
ejpam-6472	398	21	xn	xn	PROPN
ejpam-6472	398	22	)	)	PUNCT
ejpam-6472	398	23	.	.	PUNCT
ejpam-6472	399	1	by	by	ADP
ejpam-6472	399	2	theorem	theorem	NOUN
ejpam-6472	399	3	5	5	NUM
ejpam-6472	399	4	,	,	PUNCT
ejpam-6472	399	5	we	we	PRON
ejpam-6472	399	6	obtain	obtain	VERB
ejpam-6472	399	7	{	{	PUNCT
ejpam-6472	399	8	r	r	NOUN
ejpam-6472	399	9	,	,	PUNCT
ejpam-6472	399	10	s	s	NOUN
ejpam-6472	399	11	}	}	PUNCT
ejpam-6472	399	12	∩	∩	ADJ
ejpam-6472	399	13	sub(t	sub(t	NOUN
ejpam-6472	399	14	)	)	PUNCT
ejpam-6472	399	15	̸=	̸=	PROPN
ejpam-6472	399	16	∅	∅	NOUN
ejpam-6472	399	17	and	and	CCONJ
ejpam-6472	399	18	t	t	X
ejpam-6472	399	19	̸∈	̸∈	PROPN
ejpam-6472	399	20	{	{	PUNCT
ejpam-6472	399	21	r	r	PROPN
ejpam-6472	399	22	,	,	PUNCT
ejpam-6472	399	23	s	s	PART
ejpam-6472	399	24	}	}	PUNCT
ejpam-6472	399	25	.	.	PUNCT
ejpam-6472	400	1	now	now	ADV
ejpam-6472	400	2	we	we	PRON
ejpam-6472	400	3	have	have	VERB
ejpam-6472	400	4	{	{	PUNCT
ejpam-6472	400	5	r	r	NOUN
ejpam-6472	400	6	,	,	PUNCT
ejpam-6472	400	7	s	s	NOUN
ejpam-6472	400	8	}	}	PUNCT
ejpam-6472	400	9	∩	∩	NOUN
ejpam-6472	400	10	sub((t	sub((t	X
ejpam-6472	400	11	·	·	SYM
ejpam-6472	400	12	rs	rs	X
ejpam-6472	400	13	q	q	NOUN
ejpam-6472	400	14	)	)	PUNCT
ejpam-6472	400	15	·	·	PUNCT
ejpam-6472	400	16	rs	rs	PROPN
ejpam-6472	400	17	t	t	PROPN
ejpam-6472	400	18	)	)	PUNCT
ejpam-6472	400	19	̸=	̸=	PROPN
ejpam-6472	400	20	∅.	∅.	PRON
ejpam-6472	400	21	by	by	ADP
ejpam-6472	400	22	lemma	lemma	PROPN
ejpam-6472	400	23	5	5	NUM
ejpam-6472	400	24	,	,	PUNCT
ejpam-6472	400	25	it	it	PRON
ejpam-6472	400	26	follows	follow	VERB
ejpam-6472	400	27	that	that	SCONJ
ejpam-6472	400	28	{	{	PUNCT
ejpam-6472	400	29	r	r	NOUN
ejpam-6472	400	30	,	,	PUNCT
ejpam-6472	400	31	s	s	NOUN
ejpam-6472	400	32	}	}	PUNCT
ejpam-6472	400	33	∩	∩	ADJ
ejpam-6472	400	34	sub(t	sub(t	NOUN
ejpam-6472	400	35	·	·	SYM
ejpam-6472	400	36	rs	rs	X
ejpam-6472	400	37	q	q	NOUN
ejpam-6472	400	38	)	)	PUNCT
ejpam-6472	400	39	̸=	̸=	PROPN
ejpam-6472	400	40	∅.	∅.	VERB
ejpam-6472	400	41	by	by	ADP
ejpam-6472	400	42	using	use	VERB
ejpam-6472	400	43	lemma	lemma	PROPN
ejpam-6472	400	44	5	5	NUM
ejpam-6472	400	45	again	again	ADV
ejpam-6472	400	46	,	,	PUNCT
ejpam-6472	400	47	we	we	PRON
ejpam-6472	400	48	have	have	AUX
ejpam-6472	400	49	{	{	PUNCT
ejpam-6472	400	50	r	r	NOUN
ejpam-6472	400	51	,	,	PUNCT
ejpam-6472	400	52	s	s	NOUN
ejpam-6472	400	53	}	}	PUNCT
ejpam-6472	400	54	∩	∩	ADJ
ejpam-6472	400	55	sub(q	sub(q	PROPN
ejpam-6472	400	56	)	)	PUNCT
ejpam-6472	400	57	̸=	̸=	PROPN
ejpam-6472	400	58	∅.	∅.	ADP
ejpam-6472	400	59	lemma	lemma	PROPN
ejpam-6472	400	60	1	1	NUM
ejpam-6472	400	61	provides	provide	VERB
ejpam-6472	400	62	that	that	SCONJ
ejpam-6472	400	63	t	t	PROPN
ejpam-6472	400	64	∈	∈	PROPN
ejpam-6472	400	65	sub(q	sub(q	PROPN
ejpam-6472	400	66	·	·	SYM
ejpam-6472	400	67	rs	rs	PROPN
ejpam-6472	400	68	t	t	PROPN
ejpam-6472	400	69	)	)	PUNCT
ejpam-6472	400	70	and	and	CCONJ
ejpam-6472	400	71	q	q	ADJ
ejpam-6472	400	72	·	·	PUNCT
ejpam-6472	400	73	rs	rs	PROPN
ejpam-6472	400	74	t	t	PROPN
ejpam-6472	400	75	∈	∈	PROPN
ejpam-6472	400	76	sub(t	sub(t	PROPN
ejpam-6472	400	77	·	·	PUNCT
ejpam-6472	400	78	rs	rs	X
ejpam-6472	400	79	q	q	X
ejpam-6472	400	80	·	·	PUNCT
ejpam-6472	400	81	rs	rs	PROPN
ejpam-6472	400	82	t	t	PROPN
ejpam-6472	400	83	)	)	PUNCT
ejpam-6472	400	84	\	\	PROPN
ejpam-6472	400	85	{	{	PUNCT
ejpam-6472	400	86	t	t	NOUN
ejpam-6472	400	87	·	·	SYM
ejpam-6472	400	88	rs	rs	X
ejpam-6472	400	89	q	q	NOUN
ejpam-6472	400	90	·	·	PUNCT
ejpam-6472	400	91	rs	rs	X
ejpam-6472	400	92	t	t	PROPN
ejpam-6472	400	93	}	}	PUNCT
ejpam-6472	400	94	=	=	SYM
ejpam-6472	400	95	sub(t	sub(t	NOUN
ejpam-6472	400	96	)	)	PUNCT
ejpam-6472	400	97	\	\	NOUN
ejpam-6472	400	98	{	{	PUNCT
ejpam-6472	400	99	t	t	NOUN
ejpam-6472	400	100	}	}	PUNCT
ejpam-6472	400	101	.	.	PUNCT
ejpam-6472	401	1	hence	hence	ADV
ejpam-6472	401	2	,	,	PUNCT
ejpam-6472	401	3	t	t	PROPN
ejpam-6472	401	4	∈	∈	PROPN
ejpam-6472	401	5	sub(t	sub(t	PROPN
ejpam-6472	401	6	)	)	PUNCT
ejpam-6472	401	7	\	\	PROPN
ejpam-6472	401	8	{	{	PUNCT
ejpam-6472	401	9	t	t	PROPN
ejpam-6472	401	10	}	}	PUNCT
ejpam-6472	401	11	,	,	PUNCT
ejpam-6472	401	12	a	a	DET
ejpam-6472	401	13	contradiction	contradiction	NOUN
ejpam-6472	401	14	.	.	PUNCT
ejpam-6472	402	1	theorem	theorem	ADJ
ejpam-6472	402	2	5	5	NUM
ejpam-6472	402	3	and	and	CCONJ
ejpam-6472	402	4	theorem	theorem	VERB
ejpam-6472	402	5	6	6	NUM
ejpam-6472	402	6	show	show	VERB
ejpam-6472	402	7	that	that	SCONJ
ejpam-6472	402	8	idempotent	idempotent	ADJ
ejpam-6472	402	9	elements	element	NOUN
ejpam-6472	402	10	and	and	CCONJ
ejpam-6472	402	11	regular	regular	ADJ
ejpam-6472	402	12	elements	element	NOUN
ejpam-6472	402	13	are	be	AUX
ejpam-6472	402	14	coincide	coincide	ADJ
ejpam-6472	402	15	in	in	ADP
ejpam-6472	402	16	the	the	DET
ejpam-6472	402	17	semigroup	semigroup	NOUN
ejpam-6472	402	18	(	(	PUNCT
ejpam-6472	402	19	w	w	NOUN
ejpam-6472	402	20	r	r	NOUN
ejpam-6472	402	21	,	,	PUNCT
ejpam-6472	402	22	s	s	PART
ejpam-6472	402	23	τ	τ	X
ejpam-6472	402	24	(	(	PUNCT
ejpam-6472	402	25	xn	xn	PROPN
ejpam-6472	402	26	)	)	PUNCT
ejpam-6472	402	27	,	,	PUNCT
ejpam-6472	402	28	·	·	PUNCT
ejpam-6472	402	29	rs	rs	X
ejpam-6472	402	30	)	)	PUNCT
ejpam-6472	402	31	.	.	PUNCT
ejpam-6472	403	1	we	we	PRON
ejpam-6472	403	2	now	now	ADV
ejpam-6472	403	3	give	give	VERB
ejpam-6472	403	4	an	an	DET
ejpam-6472	403	5	example	example	NOUN
ejpam-6472	403	6	of	of	ADP
ejpam-6472	403	7	a	a	DET
ejpam-6472	403	8	term	term	NOUN
ejpam-6472	403	9	that	that	PRON
ejpam-6472	403	10	is	be	AUX
ejpam-6472	403	11	both	both	CCONJ
ejpam-6472	403	12	regular	regular	ADJ
ejpam-6472	403	13	and	and	CCONJ
ejpam-6472	403	14	idempotent	idempotent	NOUN
ejpam-6472	403	15	with	with	ADP
ejpam-6472	403	16	respect	respect	NOUN
ejpam-6472	403	17	to	to	ADP
ejpam-6472	403	18	·	·	PUNCT
ejpam-6472	403	19	rs	rs	ADP
ejpam-6472	403	20	in	in	ADP
ejpam-6472	403	21	order	order	NOUN
ejpam-6472	403	22	to	to	PART
ejpam-6472	403	23	better	well	ADV
ejpam-6472	403	24	demonstrate	demonstrate	VERB
ejpam-6472	403	25	this	this	DET
ejpam-6472	403	26	result	result	NOUN
ejpam-6472	403	27	.	.	PUNCT
ejpam-6472	404	1	example	example	NOUN
ejpam-6472	405	1	3	3	X
ejpam-6472	405	2	.	.	PUNCT
ejpam-6472	405	3	let	let	VERB
ejpam-6472	405	4	τ	τ	PROPN
ejpam-6472	405	5	=	=	PUNCT
ejpam-6472	405	6	(	(	PUNCT
ejpam-6472	405	7	1	1	NUM
ejpam-6472	405	8	,	,	PUNCT
ejpam-6472	405	9	2	2	NUM
ejpam-6472	405	10	)	)	PUNCT
ejpam-6472	405	11	with	with	ADP
ejpam-6472	405	12	a	a	DET
ejpam-6472	405	13	unary	unary	ADJ
ejpam-6472	405	14	operation	operation	NOUN
ejpam-6472	405	15	symbol	symbol	NOUN
ejpam-6472	405	16	g	g	PROPN
ejpam-6472	405	17	and	and	CCONJ
ejpam-6472	405	18	a	a	DET
ejpam-6472	405	19	binary	binary	ADJ
ejpam-6472	405	20	operation	operation	NOUN
ejpam-6472	405	21	symbol	symbol	NOUN
ejpam-6472	405	22	f	f	PROPN
ejpam-6472	405	23	.	.	PUNCT
ejpam-6472	406	1	fix	fix	VERB
ejpam-6472	406	2	the	the	DET
ejpam-6472	406	3	terms	term	NOUN
ejpam-6472	406	4	r	r	NOUN
ejpam-6472	406	5	=	=	SYM
ejpam-6472	406	6	f(x1	f(x1	NOUN
ejpam-6472	406	7	,	,	PUNCT
ejpam-6472	406	8	x1	x1	PROPN
ejpam-6472	406	9	)	)	PUNCT
ejpam-6472	406	10	and	and	CCONJ
ejpam-6472	406	11	s	s	NOUN
ejpam-6472	406	12	=	=	NOUN
ejpam-6472	406	13	g(x2	g(x2	NOUN
ejpam-6472	406	14	)	)	PUNCT
ejpam-6472	406	15	.	.	PUNCT
ejpam-6472	407	1	let	let	VERB
ejpam-6472	407	2	t	t	NOUN
ejpam-6472	407	3	=	=	SYM
ejpam-6472	407	4	g(f(x2	g(f(x2	PROPN
ejpam-6472	407	5	,	,	PUNCT
ejpam-6472	407	6	x1	x1	PROPN
ejpam-6472	407	7	)	)	PUNCT
ejpam-6472	407	8	)	)	PUNCT
ejpam-6472	407	9	and	and	CCONJ
ejpam-6472	407	10	q	q	NOUN
ejpam-6472	407	11	=	=	SYM
ejpam-6472	407	12	g(x1	g(x1	NOUN
ejpam-6472	407	13	)	)	PUNCT
ejpam-6472	407	14	be	be	VERB
ejpam-6472	407	15	2	2	NUM
ejpam-6472	407	16	-	-	PUNCT
ejpam-6472	407	17	ary	ary	NOUN
ejpam-6472	407	18	terms	term	NOUN
ejpam-6472	407	19	of	of	ADP
ejpam-6472	407	20	type	type	NOUN
ejpam-6472	407	21	τ	τ	PROPN
ejpam-6472	407	22	.	.	PUNCT
ejpam-6472	408	1	we	we	PRON
ejpam-6472	408	2	see	see	VERB
ejpam-6472	408	3	that	that	PRON
ejpam-6472	408	4	t	t	PROPN
ejpam-6472	408	5	and	and	CCONJ
ejpam-6472	408	6	q	q	NOUN
ejpam-6472	408	7	are	be	AUX
ejpam-6472	408	8	not	not	PART
ejpam-6472	408	9	subterms	subterm	NOUN
ejpam-6472	408	10	of	of	ADP
ejpam-6472	408	11	r	r	NOUN
ejpam-6472	408	12	and	and	CCONJ
ejpam-6472	408	13	s	s	NOUN
ejpam-6472	408	14	,	,	PUNCT
ejpam-6472	408	15	so	so	ADV
ejpam-6472	408	16	t	t	PROPN
ejpam-6472	408	17	,	,	PUNCT
ejpam-6472	408	18	q	q	PROPN
ejpam-6472	408	19	∈	∈	PROPN
ejpam-6472	408	20	w	w	NOUN
ejpam-6472	408	21	r	r	NOUN
ejpam-6472	408	22	,	,	PUNCT
ejpam-6472	408	23	s	s	PART
ejpam-6472	408	24	τ	τ	X
ejpam-6472	408	25	(	(	PUNCT
ejpam-6472	408	26	x2	x2	PROPN
ejpam-6472	408	27	)	)	PUNCT
ejpam-6472	408	28	.	.	PUNCT
ejpam-6472	409	1	moreover	moreover	ADV
ejpam-6472	409	2	,	,	PUNCT
ejpam-6472	409	3	{	{	PUNCT
ejpam-6472	409	4	r	r	NOUN
ejpam-6472	409	5	,	,	PUNCT
ejpam-6472	409	6	s	s	NOUN
ejpam-6472	409	7	}	}	PUNCT
ejpam-6472	409	8	∩	∩	ADJ
ejpam-6472	409	9	sub(t	sub(t	NOUN
ejpam-6472	409	10	)	)	PUNCT
ejpam-6472	409	11	=	=	PUNCT
ejpam-6472	410	1	∅.	∅.	NOUN
ejpam-6472	410	2	by	by	ADP
ejpam-6472	410	3	the	the	DET
ejpam-6472	410	4	definition	definition	NOUN
ejpam-6472	410	5	of	of	ADP
ejpam-6472	410	6	·	·	PUNCT
ejpam-6472	410	7	rs	rs	X
ejpam-6472	410	8	,	,	PUNCT
ejpam-6472	410	9	we	we	PRON
ejpam-6472	410	10	obtain	obtain	VERB
ejpam-6472	410	11	t	t	NOUN
ejpam-6472	410	12	=	=	SYM
ejpam-6472	410	13	t	t	PROPN
ejpam-6472	410	14	·	·	PUNCT
ejpam-6472	410	15	rs	rs	X
ejpam-6472	410	16	(	(	PUNCT
ejpam-6472	410	17	q	q	NOUN
ejpam-6472	410	18	·	·	SYM
ejpam-6472	410	19	rs	rs	PROPN
ejpam-6472	410	20	t	t	PROPN
ejpam-6472	410	21	)	)	PUNCT
ejpam-6472	410	22	and	and	CCONJ
ejpam-6472	410	23	t	t	PROPN
ejpam-6472	410	24	=	=	SYM
ejpam-6472	410	25	t	t	PROPN
ejpam-6472	410	26	·	·	PUNCT
ejpam-6472	410	27	rs	rs	X
ejpam-6472	410	28	t.	t.	PROPN
ejpam-6472	410	29	thus	thus	ADV
ejpam-6472	410	30	,	,	PUNCT
ejpam-6472	410	31	t	t	PROPN
ejpam-6472	410	32	is	be	AUX
ejpam-6472	410	33	both	both	CCONJ
ejpam-6472	410	34	regular	regular	ADJ
ejpam-6472	410	35	and	and	CCONJ
ejpam-6472	410	36	idempotent	idempotent	NOUN
ejpam-6472	410	37	under	under	ADP
ejpam-6472	410	38	·	·	SYM
ejpam-6472	410	39	rs	rs	X
ejpam-6472	410	40	.	.	PUNCT
ejpam-6472	411	1	p.	p.	NOUN
ejpam-6472	411	2	prachumdang	prachumdang	PROPN
ejpam-6472	411	3	,	,	PUNCT
ejpam-6472	411	4	b.	b.	PROPN
ejpam-6472	411	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	411	6	/	/	SYM
ejpam-6472	411	7	eur	eur	PROPN
ejpam-6472	411	8	.	.	PUNCT
ejpam-6472	412	1	j.	j.	PROPN
ejpam-6472	412	2	pure	pure	PROPN
ejpam-6472	412	3	appl	appl	PROPN
ejpam-6472	412	4	.	.	PROPN
ejpam-6472	412	5	math	math	PROPN
ejpam-6472	412	6	,	,	PUNCT
ejpam-6472	412	7	18	18	NUM
ejpam-6472	412	8	(	(	PUNCT
ejpam-6472	412	9	3	3	NUM
ejpam-6472	412	10	)	)	PUNCT
ejpam-6472	412	11	(	(	PUNCT
ejpam-6472	412	12	2025	2025	NUM
ejpam-6472	412	13	)	)	PUNCT
ejpam-6472	412	14	,	,	PUNCT
ejpam-6472	412	15	6472	6472	NUM
ejpam-6472	412	16	11	11	NUM
ejpam-6472	412	17	of	of	ADP
ejpam-6472	412	18	16	16	NUM
ejpam-6472	412	19	as	as	ADP
ejpam-6472	412	20	in	in	ADP
ejpam-6472	412	21	the	the	DET
ejpam-6472	412	22	case	case	NOUN
ejpam-6472	412	23	of	of	ADP
ejpam-6472	412	24	·	·	SYM
ejpam-6472	412	25	r	r	NOUN
ejpam-6472	412	26	,	,	PUNCT
ejpam-6472	412	27	where	where	SCONJ
ejpam-6472	412	28	it	it	PRON
ejpam-6472	412	29	was	be	AUX
ejpam-6472	412	30	shown	show	VERB
ejpam-6472	412	31	that	that	SCONJ
ejpam-6472	412	32	any	any	DET
ejpam-6472	412	33	term	term	NOUN
ejpam-6472	412	34	expressible	expressible	ADJ
ejpam-6472	412	35	as	as	ADP
ejpam-6472	412	36	a	a	DET
ejpam-6472	412	37	product	product	NOUN
ejpam-6472	412	38	of	of	ADP
ejpam-6472	412	39	several	several	ADJ
ejpam-6472	412	40	terms	term	NOUN
ejpam-6472	412	41	,	,	PUNCT
ejpam-6472	412	42	with	with	ADP
ejpam-6472	412	43	at	at	ADV
ejpam-6472	412	44	least	least	ADV
ejpam-6472	412	45	two	two	NUM
ejpam-6472	412	46	of	of	ADP
ejpam-6472	412	47	them	they	PRON
ejpam-6472	412	48	equal	equal	ADJ
ejpam-6472	412	49	to	to	ADP
ejpam-6472	412	50	the	the	DET
ejpam-6472	412	51	term	term	NOUN
ejpam-6472	412	52	itself	itself	PRON
ejpam-6472	412	53	,	,	PUNCT
ejpam-6472	412	54	is	be	AUX
ejpam-6472	412	55	idempotent	idempotent	ADJ
ejpam-6472	412	56	(	(	PUNCT
ejpam-6472	412	57	see	see	VERB
ejpam-6472	412	58	[	[	X
ejpam-6472	412	59	9	9	NUM
ejpam-6472	412	60	]	]	NUM
ejpam-6472	412	61	)	)	PUNCT
ejpam-6472	413	1	,	,	PUNCT
ejpam-6472	413	2	we	we	PRON
ejpam-6472	413	3	find	find	VERB
ejpam-6472	413	4	that	that	SCONJ
ejpam-6472	413	5	a	a	DET
ejpam-6472	413	6	similar	similar	ADJ
ejpam-6472	413	7	behavior	behavior	NOUN
ejpam-6472	413	8	holds	hold	VERB
ejpam-6472	413	9	in	in	ADP
ejpam-6472	413	10	the	the	DET
ejpam-6472	413	11	·	·	SYM
ejpam-6472	413	12	rs	rs	ADJ
ejpam-6472	413	13	setting	setting	NOUN
ejpam-6472	413	14	.	.	PUNCT
ejpam-6472	414	1	the	the	DET
ejpam-6472	414	2	next	next	ADJ
ejpam-6472	414	3	lemma	lemma	PROPN
ejpam-6472	414	4	plays	play	VERB
ejpam-6472	414	5	a	a	DET
ejpam-6472	414	6	key	key	ADJ
ejpam-6472	414	7	role	role	NOUN
ejpam-6472	414	8	in	in	ADP
ejpam-6472	414	9	verifying	verify	VERB
ejpam-6472	414	10	this	this	DET
ejpam-6472	414	11	implication	implication	NOUN
ejpam-6472	414	12	.	.	PUNCT
ejpam-6472	415	1	lemma	lemma	PROPN
ejpam-6472	415	2	7	7	X
ejpam-6472	415	3	.	.	PUNCT
ejpam-6472	416	1	let	let	VERB
ejpam-6472	416	2	r	r	NOUN
ejpam-6472	416	3	,	,	PUNCT
ejpam-6472	416	4	s	s	NOUN
ejpam-6472	416	5	∈	∈	PROPN
ejpam-6472	416	6	wτ	wτ	NOUN
ejpam-6472	416	7	(	(	PUNCT
ejpam-6472	416	8	xn	xn	X
ejpam-6472	416	9	)	)	PUNCT
ejpam-6472	416	10	be	be	AUX
ejpam-6472	416	11	fixed	fix	VERB
ejpam-6472	416	12	terms	term	NOUN
ejpam-6472	416	13	.	.	PUNCT
ejpam-6472	417	1	for	for	ADP
ejpam-6472	417	2	each	each	DET
ejpam-6472	417	3	t	t	PROPN
ejpam-6472	417	4	,	,	PUNCT
ejpam-6472	417	5	q	q	X
ejpam-6472	417	6	,	,	PUNCT
ejpam-6472	417	7	u	u	NOUN
ejpam-6472	417	8	∈	∈	PROPN
ejpam-6472	417	9	w	w	PROPN
ejpam-6472	417	10	r	r	NOUN
ejpam-6472	417	11	,	,	PUNCT
ejpam-6472	417	12	s	s	PART
ejpam-6472	417	13	τ	τ	X
ejpam-6472	417	14	(	(	PUNCT
ejpam-6472	417	15	xn	xn	PROPN
ejpam-6472	417	16	)	)	PUNCT
ejpam-6472	417	17	,	,	PUNCT
ejpam-6472	417	18	if	if	SCONJ
ejpam-6472	417	19	t	t	PROPN
ejpam-6472	417	20	=	=	SYM
ejpam-6472	417	21	u	u	X
ejpam-6472	417	22	·	·	PUNCT
ejpam-6472	417	23	rs	rs	X
ejpam-6472	417	24	t	t	PROPN
ejpam-6472	417	25	·	·	PUNCT
ejpam-6472	417	26	rs	rs	PROPN
ejpam-6472	417	27	q	q	NOUN
ejpam-6472	417	28	and	and	CCONJ
ejpam-6472	417	29	{	{	PUNCT
ejpam-6472	417	30	r	r	NOUN
ejpam-6472	417	31	,	,	PUNCT
ejpam-6472	417	32	s	s	NOUN
ejpam-6472	417	33	}	}	PUNCT
ejpam-6472	417	34	∩	∩	ADJ
ejpam-6472	417	35	sub(t	sub(t	NOUN
ejpam-6472	417	36	)	)	PUNCT
ejpam-6472	417	37	̸=	̸=	NOUN
ejpam-6472	417	38	∅	∅	NOUN
ejpam-6472	417	39	,	,	PUNCT
ejpam-6472	417	40	then	then	ADV
ejpam-6472	417	41	t	t	PROPN
ejpam-6472	417	42	=	=	SYM
ejpam-6472	417	43	u	u	PROPN
ejpam-6472	417	44	·	·	PUNCT
ejpam-6472	417	45	rs	rs	X
ejpam-6472	417	46	t	t	PROPN
ejpam-6472	417	47	and	and	CCONJ
ejpam-6472	417	48	q	q	PROPN
ejpam-6472	417	49	∈	∈	PROPN
ejpam-6472	417	50	{	{	PUNCT
ejpam-6472	417	51	r	r	NOUN
ejpam-6472	417	52	,	,	PUNCT
ejpam-6472	417	53	s	s	PART
ejpam-6472	417	54	}	}	PUNCT
ejpam-6472	417	55	.	.	PUNCT
ejpam-6472	418	1	proof	proof	NOUN
ejpam-6472	418	2	.	.	PUNCT
ejpam-6472	419	1	assume	assume	VERB
ejpam-6472	419	2	that	that	SCONJ
ejpam-6472	419	3	t	t	NOUN
ejpam-6472	419	4	=	=	SYM
ejpam-6472	419	5	u	u	PROPN
ejpam-6472	419	6	·	·	PUNCT
ejpam-6472	419	7	rs	rs	X
ejpam-6472	419	8	t	t	PROPN
ejpam-6472	419	9	·	·	PUNCT
ejpam-6472	419	10	rs	rs	PROPN
ejpam-6472	419	11	q	q	NOUN
ejpam-6472	419	12	and	and	CCONJ
ejpam-6472	419	13	{	{	PUNCT
ejpam-6472	419	14	r	r	NOUN
ejpam-6472	419	15	,	,	PUNCT
ejpam-6472	419	16	s	s	NOUN
ejpam-6472	419	17	}	}	PUNCT
ejpam-6472	419	18	∩	∩	ADJ
ejpam-6472	419	19	sub(t	sub(t	NOUN
ejpam-6472	419	20	)	)	PUNCT
ejpam-6472	419	21	̸=	̸=	PROPN
ejpam-6472	419	22	∅.	∅.	PRON
ejpam-6472	419	23	by	by	ADP
ejpam-6472	419	24	lemma	lemma	PROPN
ejpam-6472	419	25	5	5	NUM
ejpam-6472	419	26	,	,	PUNCT
ejpam-6472	419	27	we	we	PRON
ejpam-6472	419	28	have	have	VERB
ejpam-6472	419	29	{	{	PUNCT
ejpam-6472	419	30	r	r	NOUN
ejpam-6472	419	31	,	,	PUNCT
ejpam-6472	419	32	s	s	NOUN
ejpam-6472	419	33	}	}	PUNCT
ejpam-6472	419	34	∩	∩	ADJ
ejpam-6472	419	35	sub(u	sub(u	PROPN
ejpam-6472	419	36	·	·	SYM
ejpam-6472	419	37	rs	rs	PROPN
ejpam-6472	419	38	t	t	PROPN
ejpam-6472	419	39	)	)	PUNCT
ejpam-6472	419	40	̸=	̸=	PROPN
ejpam-6472	419	41	∅	∅	NOUN
ejpam-6472	419	42	and	and	CCONJ
ejpam-6472	419	43	{	{	PUNCT
ejpam-6472	419	44	r	r	NOUN
ejpam-6472	419	45	,	,	PUNCT
ejpam-6472	419	46	s	s	NOUN
ejpam-6472	419	47	}	}	PUNCT
ejpam-6472	419	48	∩	∩	ADJ
ejpam-6472	419	49	sub(u	sub(u	PROPN
ejpam-6472	419	50	)	)	PUNCT
ejpam-6472	419	51	̸=	̸=	PROPN
ejpam-6472	419	52	∅.	∅.	PRON
ejpam-6472	419	53	by	by	ADP
ejpam-6472	419	54	lemma	lemma	PROPN
ejpam-6472	419	55	1	1	NUM
ejpam-6472	419	56	,	,	PUNCT
ejpam-6472	419	57	we	we	PRON
ejpam-6472	419	58	obtain	obtain	VERB
ejpam-6472	419	59	q	q	NOUN
ejpam-6472	419	60	∈	∈	PROPN
ejpam-6472	419	61	sub((u	sub((u	NOUN
ejpam-6472	419	62	·	·	PUNCT
ejpam-6472	419	63	rs	rs	PROPN
ejpam-6472	419	64	t	t	PROPN
ejpam-6472	419	65	)	)	PUNCT
ejpam-6472	419	66	·	·	PUNCT
ejpam-6472	419	67	rs	rs	X
ejpam-6472	419	68	q	q	NOUN
ejpam-6472	419	69	)	)	PUNCT
ejpam-6472	419	70	=	=	SYM
ejpam-6472	419	71	sub(t	sub(t	PROPN
ejpam-6472	419	72	)	)	PUNCT
ejpam-6472	419	73	and	and	CCONJ
ejpam-6472	419	74	t	t	PROPN
ejpam-6472	419	75	∈	∈	PROPN
ejpam-6472	419	76	sub(u	sub(u	PROPN
ejpam-6472	419	77	·	·	SYM
ejpam-6472	419	78	rs	rs	PROPN
ejpam-6472	419	79	t	t	PROPN
ejpam-6472	419	80	)	)	PUNCT
ejpam-6472	419	81	.	.	PUNCT
ejpam-6472	420	1	we	we	PRON
ejpam-6472	420	2	claim	claim	VERB
ejpam-6472	420	3	the	the	DET
ejpam-6472	420	4	following	follow	VERB
ejpam-6472	420	5	statement	statement	NOUN
ejpam-6472	420	6	:	:	PUNCT
ejpam-6472	420	7	r	r	NOUN
ejpam-6472	420	8	∈	∈	PROPN
ejpam-6472	420	9	sub(t	sub(t	PROPN
ejpam-6472	420	10	)	)	PUNCT
ejpam-6472	420	11	⇔	⇔	PROPN
ejpam-6472	420	12	r	r	NOUN
ejpam-6472	420	13	∈	∈	PROPN
ejpam-6472	420	14	sub(u	sub(u	PROPN
ejpam-6472	420	15	·	·	SYM
ejpam-6472	420	16	rs	rs	PROPN
ejpam-6472	420	17	t	t	PROPN
ejpam-6472	420	18	)	)	PUNCT
ejpam-6472	420	19	⇔	⇔	PROPN
ejpam-6472	420	20	r	r	NOUN
ejpam-6472	420	21	∈	∈	PROPN
ejpam-6472	420	22	sub(q	sub(q	PROPN
ejpam-6472	420	23	)	)	PUNCT
ejpam-6472	420	24	.	.	PUNCT
ejpam-6472	421	1	(	(	PUNCT
ejpam-6472	421	2	1	1	X
ejpam-6472	421	3	)	)	PUNCT
ejpam-6472	421	4	to	to	PART
ejpam-6472	421	5	prove	prove	VERB
ejpam-6472	421	6	this	this	PRON
ejpam-6472	421	7	,	,	PUNCT
ejpam-6472	421	8	it	it	PRON
ejpam-6472	421	9	suffices	suffice	VERB
ejpam-6472	421	10	to	to	PART
ejpam-6472	421	11	show	show	VERB
ejpam-6472	421	12	both	both	DET
ejpam-6472	421	13	r	r	PROPN
ejpam-6472	421	14	∈	∈	PROPN
ejpam-6472	421	15	sub(t	sub(t	PROPN
ejpam-6472	421	16	)	)	PUNCT
ejpam-6472	421	17	⇔	⇔	PROPN
ejpam-6472	421	18	r	r	NOUN
ejpam-6472	421	19	∈	∈	PROPN
ejpam-6472	421	20	sub(u	sub(u	PROPN
ejpam-6472	421	21	·	·	SYM
ejpam-6472	421	22	rs	rs	PROPN
ejpam-6472	421	23	t	t	PROPN
ejpam-6472	421	24	)	)	PUNCT
ejpam-6472	421	25	and	and	CCONJ
ejpam-6472	421	26	r	r	NOUN
ejpam-6472	421	27	∈	∈	PROPN
ejpam-6472	421	28	sub(t	sub(t	PROPN
ejpam-6472	421	29	)	)	PUNCT
ejpam-6472	421	30	⇔	⇔	PROPN
ejpam-6472	421	31	r	r	NOUN
ejpam-6472	421	32	∈	∈	PROPN
ejpam-6472	421	33	sub(q	sub(q	PROPN
ejpam-6472	421	34	)	)	PUNCT
ejpam-6472	421	35	.	.	PUNCT
ejpam-6472	422	1	assume	assume	VERB
ejpam-6472	422	2	r	r	NOUN
ejpam-6472	422	3	∈	∈	PROPN
ejpam-6472	422	4	sub(t	sub(t	PROPN
ejpam-6472	422	5	)	)	PUNCT
ejpam-6472	422	6	.	.	PUNCT
ejpam-6472	423	1	since	since	SCONJ
ejpam-6472	423	2	t	t	PROPN
ejpam-6472	423	3	∈	∈	PROPN
ejpam-6472	423	4	sub(u	sub(u	PROPN
ejpam-6472	423	5	·	·	SYM
ejpam-6472	423	6	rs	rs	PROPN
ejpam-6472	423	7	t	t	PROPN
ejpam-6472	423	8	)	)	PUNCT
ejpam-6472	423	9	,	,	PUNCT
ejpam-6472	423	10	r	r	NOUN
ejpam-6472	423	11	∈	∈	PROPN
ejpam-6472	423	12	sub(u	sub(u	PROPN
ejpam-6472	423	13	·	·	SYM
ejpam-6472	423	14	rs	rs	PROPN
ejpam-6472	423	15	t	t	PROPN
ejpam-6472	423	16	)	)	PUNCT
ejpam-6472	423	17	.	.	PUNCT
ejpam-6472	424	1	moreover	moreover	ADV
ejpam-6472	424	2	,	,	PUNCT
ejpam-6472	424	3	by	by	ADP
ejpam-6472	424	4	lemma	lemma	PROPN
ejpam-6472	424	5	5	5	NUM
ejpam-6472	424	6	and	and	CCONJ
ejpam-6472	424	7	condition	condition	NOUN
ejpam-6472	424	8	t	t	NOUN
ejpam-6472	424	9	=	=	SYM
ejpam-6472	424	10	(	(	PUNCT
ejpam-6472	424	11	u	u	NOUN
ejpam-6472	424	12	·	·	SYM
ejpam-6472	424	13	rs	rs	PROPN
ejpam-6472	424	14	t	t	PROPN
ejpam-6472	424	15	)	)	PUNCT
ejpam-6472	424	16	·	·	PUNCT
ejpam-6472	424	17	rs	rs	X
ejpam-6472	424	18	q	q	NOUN
ejpam-6472	424	19	,	,	PUNCT
ejpam-6472	424	20	we	we	PRON
ejpam-6472	424	21	conclude	conclude	VERB
ejpam-6472	424	22	that	that	SCONJ
ejpam-6472	424	23	r	r	NOUN
ejpam-6472	424	24	∈	∈	NOUN
ejpam-6472	424	25	sub(q	sub(q	PROPN
ejpam-6472	424	26	)	)	PUNCT
ejpam-6472	424	27	.	.	PUNCT
ejpam-6472	425	1	conversely	conversely	ADV
ejpam-6472	425	2	,	,	PUNCT
ejpam-6472	425	3	assume	assume	VERB
ejpam-6472	425	4	that	that	SCONJ
ejpam-6472	425	5	r	r	NOUN
ejpam-6472	425	6	∈	∈	PROPN
ejpam-6472	425	7	sub(u	sub(u	PROPN
ejpam-6472	425	8	·	·	SYM
ejpam-6472	425	9	rs	rs	PROPN
ejpam-6472	425	10	t	t	PROPN
ejpam-6472	425	11	)	)	PUNCT
ejpam-6472	425	12	.	.	PUNCT
ejpam-6472	426	1	lemma	lemma	PROPN
ejpam-6472	426	2	5	5	NUM
ejpam-6472	426	3	provides	provide	VERB
ejpam-6472	426	4	that	that	SCONJ
ejpam-6472	426	5	r	r	NOUN
ejpam-6472	426	6	∈	∈	PROPN
ejpam-6472	426	7	sub(t	sub(t	PROPN
ejpam-6472	426	8	)	)	PUNCT
ejpam-6472	426	9	.	.	PUNCT
ejpam-6472	427	1	finally	finally	ADV
ejpam-6472	427	2	,	,	PUNCT
ejpam-6472	427	3	we	we	PRON
ejpam-6472	427	4	assume	assume	VERB
ejpam-6472	427	5	r	r	NOUN
ejpam-6472	427	6	∈	∈	NOUN
ejpam-6472	427	7	sub(q	sub(q	PROPN
ejpam-6472	427	8	)	)	PUNCT
ejpam-6472	427	9	.	.	PUNCT
ejpam-6472	428	1	since	since	SCONJ
ejpam-6472	428	2	q	q	PROPN
ejpam-6472	428	3	∈	∈	PROPN
ejpam-6472	428	4	sub(t	sub(t	PROPN
ejpam-6472	428	5	)	)	PUNCT
ejpam-6472	428	6	,	,	PUNCT
ejpam-6472	428	7	r	r	NOUN
ejpam-6472	428	8	∈	∈	PROPN
ejpam-6472	428	9	sub(t	sub(t	PROPN
ejpam-6472	428	10	)	)	PUNCT
ejpam-6472	428	11	.	.	PUNCT
ejpam-6472	429	1	this	this	PRON
ejpam-6472	429	2	establishes	establish	VERB
ejpam-6472	429	3	the	the	DET
ejpam-6472	429	4	statement	statement	NOUN
ejpam-6472	429	5	(	(	PUNCT
ejpam-6472	429	6	1	1	NUM
ejpam-6472	429	7	)	)	PUNCT
ejpam-6472	429	8	.	.	PUNCT
ejpam-6472	430	1	a	a	DET
ejpam-6472	430	2	similar	similar	ADJ
ejpam-6472	430	3	reasoning	reasoning	NOUN
ejpam-6472	430	4	shows	show	VERB
ejpam-6472	430	5	the	the	DET
ejpam-6472	430	6	corresponding	correspond	VERB
ejpam-6472	430	7	statement	statement	NOUN
ejpam-6472	430	8	for	for	ADP
ejpam-6472	430	9	s.	s.	PROPN
ejpam-6472	430	10	next	next	ADV
ejpam-6472	430	11	,	,	PUNCT
ejpam-6472	430	12	we	we	PRON
ejpam-6472	430	13	show	show	VERB
ejpam-6472	430	14	that	that	SCONJ
ejpam-6472	430	15	nr(u	nr(u	PUNCT
ejpam-6472	430	16	·	·	PUNCT
ejpam-6472	430	17	rs	rs	X
ejpam-6472	430	18	t)(op(q)−	t)(op(q)−	ADJ
ejpam-6472	430	19	op(r	op(r	NUM
ejpam-6472	430	20	)	)	PUNCT
ejpam-6472	430	21	)	)	PUNCT
ejpam-6472	430	22	≥	≥	NOUN
ejpam-6472	430	23	0	0	NUM
ejpam-6472	430	24	,	,	PUNCT
ejpam-6472	430	25	and	and	CCONJ
ejpam-6472	430	26	(	(	PUNCT
ejpam-6472	430	27	2	2	NUM
ejpam-6472	430	28	)	)	PUNCT
ejpam-6472	430	29	(	(	PUNCT
ejpam-6472	430	30	ns(u	ns(u	NOUN
ejpam-6472	430	31	·	·	PUNCT
ejpam-6472	430	32	rs	rs	NOUN
ejpam-6472	430	33	t)−	t)−	PROPN
ejpam-6472	430	34	ns(r)nr(u	ns(r)nr(u	PROPN
ejpam-6472	430	35	·	·	PUNCT
ejpam-6472	430	36	rs	rs	X
ejpam-6472	430	37	t))(op(q)−	t))(op(q)−	NOUN
ejpam-6472	430	38	op(s	op(s	NUM
ejpam-6472	430	39	)	)	PUNCT
ejpam-6472	430	40	)	)	PUNCT
ejpam-6472	430	41	≥	≥	NOUN
ejpam-6472	430	42	0	0	NUM
ejpam-6472	430	43	.	.	PUNCT
ejpam-6472	431	1	(	(	PUNCT
ejpam-6472	431	2	3	3	X
ejpam-6472	431	3	)	)	PUNCT
ejpam-6472	431	4	note	note	NOUN
ejpam-6472	431	5	that	that	SCONJ
ejpam-6472	431	6	nr(u	nr(u	PUNCT
ejpam-6472	431	7	·	·	PUNCT
ejpam-6472	431	8	rs	rs	PROPN
ejpam-6472	431	9	t	t	PROPN
ejpam-6472	431	10	)	)	PUNCT
ejpam-6472	431	11	≥	≥	NOUN
ejpam-6472	431	12	0	0	NUM
ejpam-6472	431	13	and	and	CCONJ
ejpam-6472	431	14	ns(u	ns(u	NOUN
ejpam-6472	431	15	·	·	PUNCT
ejpam-6472	431	16	rs	rs	X
ejpam-6472	431	17	t)−	t)−	PROPN
ejpam-6472	431	18	ns(r)nr(u	ns(r)nr(u	PROPN
ejpam-6472	431	19	·	·	PUNCT
ejpam-6472	431	20	rs	rs	PROPN
ejpam-6472	431	21	t	t	PROPN
ejpam-6472	431	22	)	)	PUNCT
ejpam-6472	431	23	≥	≥	NOUN
ejpam-6472	431	24	0	0	NUM
ejpam-6472	431	25	.	.	PUNCT
ejpam-6472	432	1	if	if	SCONJ
ejpam-6472	432	2	r	r	NOUN
ejpam-6472	432	3	∈	∈	PROPN
ejpam-6472	432	4	sub(t	sub(t	PROPN
ejpam-6472	432	5	)	)	PUNCT
ejpam-6472	432	6	,	,	PUNCT
ejpam-6472	432	7	then	then	ADV
ejpam-6472	432	8	by	by	ADP
ejpam-6472	432	9	(	(	PUNCT
ejpam-6472	432	10	1	1	NUM
ejpam-6472	432	11	)	)	PUNCT
ejpam-6472	432	12	,	,	PUNCT
ejpam-6472	432	13	we	we	PRON
ejpam-6472	432	14	have	have	VERB
ejpam-6472	432	15	r	r	NOUN
ejpam-6472	432	16	∈	∈	PROPN
ejpam-6472	432	17	sub(q	sub(q	PROPN
ejpam-6472	432	18	)	)	PUNCT
ejpam-6472	432	19	.	.	PUNCT
ejpam-6472	433	1	therefore	therefore	ADV
ejpam-6472	433	2	,	,	PUNCT
ejpam-6472	433	3	op(q	op(q	NOUN
ejpam-6472	433	4	)	)	PUNCT
ejpam-6472	433	5	−	−	NOUN
ejpam-6472	433	6	op(r	op(r	NUM
ejpam-6472	433	7	)	)	PUNCT
ejpam-6472	433	8	≥	≥	NOUN
ejpam-6472	433	9	0	0	NUM
ejpam-6472	433	10	,	,	PUNCT
ejpam-6472	433	11	and	and	CCONJ
ejpam-6472	433	12	inequality	inequality	NOUN
ejpam-6472	433	13	(	(	PUNCT
ejpam-6472	433	14	2	2	X
ejpam-6472	433	15	)	)	PUNCT
ejpam-6472	433	16	follows	follow	VERB
ejpam-6472	433	17	.	.	PUNCT
ejpam-6472	434	1	on	on	ADP
ejpam-6472	434	2	the	the	DET
ejpam-6472	434	3	other	other	ADJ
ejpam-6472	434	4	hand	hand	NOUN
ejpam-6472	434	5	,	,	PUNCT
ejpam-6472	434	6	if	if	SCONJ
ejpam-6472	434	7	r	r	NOUN
ejpam-6472	434	8	/∈	/∈	SYM
ejpam-6472	434	9	sub(t	sub(t	PROPN
ejpam-6472	434	10	)	)	PUNCT
ejpam-6472	434	11	,	,	PUNCT
ejpam-6472	434	12	then	then	ADV
ejpam-6472	434	13	by	by	ADP
ejpam-6472	434	14	(	(	PUNCT
ejpam-6472	434	15	1	1	NUM
ejpam-6472	434	16	)	)	PUNCT
ejpam-6472	434	17	,	,	PUNCT
ejpam-6472	434	18	we	we	PRON
ejpam-6472	434	19	also	also	ADV
ejpam-6472	434	20	have	have	VERB
ejpam-6472	434	21	r	r	NOUN
ejpam-6472	434	22	/∈	/∈	PUNCT
ejpam-6472	435	1	sub(u	sub(u	NOUN
ejpam-6472	435	2	·	·	PUNCT
ejpam-6472	435	3	rs	rs	PROPN
ejpam-6472	435	4	t	t	PROPN
ejpam-6472	435	5	)	)	PUNCT
ejpam-6472	435	6	.	.	PUNCT
ejpam-6472	436	1	in	in	ADP
ejpam-6472	436	2	this	this	DET
ejpam-6472	436	3	case	case	NOUN
ejpam-6472	436	4	,	,	PUNCT
ejpam-6472	436	5	we	we	PRON
ejpam-6472	436	6	have	have	VERB
ejpam-6472	436	7	nr(u	nr(u	PUNCT
ejpam-6472	436	8	·	·	PUNCT
ejpam-6472	436	9	rs	rs	PROPN
ejpam-6472	436	10	t	t	PROPN
ejpam-6472	436	11	)	)	PUNCT
ejpam-6472	436	12	=	=	SYM
ejpam-6472	436	13	0	0	NUM
ejpam-6472	436	14	,	,	PUNCT
ejpam-6472	436	15	which	which	PRON
ejpam-6472	436	16	implies	imply	VERB
ejpam-6472	436	17	inequality	inequality	NOUN
ejpam-6472	436	18	(	(	PUNCT
ejpam-6472	436	19	2	2	NUM
ejpam-6472	436	20	)	)	PUNCT
ejpam-6472	436	21	.	.	PUNCT
ejpam-6472	437	1	thus	thus	ADV
ejpam-6472	437	2	,	,	PUNCT
ejpam-6472	437	3	inequality	inequality	NOUN
ejpam-6472	437	4	(	(	PUNCT
ejpam-6472	437	5	2	2	X
ejpam-6472	437	6	)	)	PUNCT
ejpam-6472	437	7	always	always	ADV
ejpam-6472	437	8	holds	hold	VERB
ejpam-6472	437	9	.	.	PUNCT
ejpam-6472	438	1	a	a	DET
ejpam-6472	438	2	similar	similar	ADJ
ejpam-6472	438	3	argument	argument	NOUN
ejpam-6472	438	4	shows	show	VERB
ejpam-6472	438	5	that	that	SCONJ
ejpam-6472	438	6	inequality	inequality	NOUN
ejpam-6472	438	7	(	(	PUNCT
ejpam-6472	438	8	3	3	NUM
ejpam-6472	438	9	)	)	PUNCT
ejpam-6472	438	10	also	also	ADV
ejpam-6472	438	11	holds	hold	VERB
ejpam-6472	438	12	.	.	PUNCT
ejpam-6472	439	1	by	by	ADP
ejpam-6472	439	2	applying	apply	VERB
ejpam-6472	439	3	operation	operation	NOUN
ejpam-6472	439	4	-	-	PUNCT
ejpam-6472	439	5	symbol	symbol	NOUN
ejpam-6472	439	6	count	count	NOUN
ejpam-6472	439	7	formula	formula	NOUN
ejpam-6472	439	8	from	from	ADP
ejpam-6472	439	9	theorem	theorem	ADJ
ejpam-6472	439	10	1	1	NUM
ejpam-6472	439	11	,	,	PUNCT
ejpam-6472	439	12	we	we	PRON
ejpam-6472	439	13	have	have	VERB
ejpam-6472	439	14	op(t	op(t	NOUN
ejpam-6472	439	15	)	)	PUNCT
ejpam-6472	439	16	=	=	SYM
ejpam-6472	439	17	op(u	op(u	NUM
ejpam-6472	439	18	·	·	PUNCT
ejpam-6472	439	19	rs	rs	PROPN
ejpam-6472	439	20	t	t	PROPN
ejpam-6472	439	21	·	·	PUNCT
ejpam-6472	439	22	rs	rs	NOUN
ejpam-6472	439	23	q	q	NOUN
ejpam-6472	439	24	)	)	PUNCT
ejpam-6472	439	25	=	=	SYM
ejpam-6472	439	26	op(u	op(u	NUM
ejpam-6472	439	27	·	·	PUNCT
ejpam-6472	439	28	rs	rs	PROPN
ejpam-6472	439	29	t	t	PROPN
ejpam-6472	439	30	)	)	PUNCT
ejpam-6472	440	1	+	+	CCONJ
ejpam-6472	440	2	nr(u	nr(u	CCONJ
ejpam-6472	440	3	·	·	PUNCT
ejpam-6472	440	4	rs	rs	NOUN
ejpam-6472	440	5	t)(op(q)−	t)(op(q)−	ADJ
ejpam-6472	440	6	op(r	op(r	NUM
ejpam-6472	440	7	)	)	PUNCT
ejpam-6472	440	8	)	)	PUNCT
ejpam-6472	441	1	+	+	CCONJ
ejpam-6472	441	2	(	(	PUNCT
ejpam-6472	441	3	ns(u	ns(u	NOUN
ejpam-6472	441	4	·	·	PUNCT
ejpam-6472	441	5	rs	rs	NOUN
ejpam-6472	441	6	t)−	t)−	PROPN
ejpam-6472	441	7	ns(r)nr(u	ns(r)nr(u	PROPN
ejpam-6472	441	8	·	·	PUNCT
ejpam-6472	441	9	rs	rs	X
ejpam-6472	441	10	t))(op(q)−	t))(op(q)−	NOUN
ejpam-6472	441	11	op(s	op(s	NUM
ejpam-6472	441	12	)	)	PUNCT
ejpam-6472	441	13	)	)	PUNCT
ejpam-6472	441	14	≥	≥	NOUN
ejpam-6472	441	15	op(u	op(u	NUM
ejpam-6472	441	16	·	·	PUNCT
ejpam-6472	441	17	rs	rs	PROPN
ejpam-6472	441	18	t	t	PROPN
ejpam-6472	441	19	)	)	PUNCT
ejpam-6472	441	20	since	since	SCONJ
ejpam-6472	441	21	t	t	PROPN
ejpam-6472	441	22	∈	∈	PROPN
ejpam-6472	441	23	sub(u	sub(u	PROPN
ejpam-6472	441	24	·	·	SYM
ejpam-6472	441	25	rs	rs	PROPN
ejpam-6472	441	26	t	t	PROPN
ejpam-6472	441	27	)	)	PUNCT
ejpam-6472	441	28	,	,	PUNCT
ejpam-6472	441	29	we	we	PRON
ejpam-6472	441	30	have	have	VERB
ejpam-6472	441	31	op(t	op(t	NOUN
ejpam-6472	441	32	)	)	PUNCT
ejpam-6472	441	33	≤	≤	NOUN
ejpam-6472	441	34	op(u	op(u	NUM
ejpam-6472	441	35	·	·	PUNCT
ejpam-6472	441	36	rs	rs	PROPN
ejpam-6472	441	37	t	t	PROPN
ejpam-6472	441	38	)	)	PUNCT
ejpam-6472	441	39	.	.	PUNCT
ejpam-6472	442	1	therefore	therefore	ADV
ejpam-6472	442	2	,	,	PUNCT
ejpam-6472	442	3	op(t	op(t	NOUN
ejpam-6472	442	4	)	)	PUNCT
ejpam-6472	442	5	=	=	PRON
ejpam-6472	442	6	op(u	op(u	NUM
ejpam-6472	442	7	·	·	PUNCT
ejpam-6472	442	8	rs	rs	PROPN
ejpam-6472	442	9	t	t	PROPN
ejpam-6472	442	10	)	)	PUNCT
ejpam-6472	442	11	,	,	PUNCT
ejpam-6472	442	12	which	which	PRON
ejpam-6472	442	13	implies	imply	VERB
ejpam-6472	442	14	t	t	PROPN
ejpam-6472	442	15	=	=	SYM
ejpam-6472	442	16	u	u	PROPN
ejpam-6472	442	17	·	·	SYM
ejpam-6472	442	18	rs	rs	X
ejpam-6472	442	19	t.	t.	NOUN
ejpam-6472	442	20	substituting	substitute	VERB
ejpam-6472	442	21	this	this	PRON
ejpam-6472	442	22	into	into	ADP
ejpam-6472	442	23	the	the	DET
ejpam-6472	442	24	equation	equation	NOUN
ejpam-6472	442	25	above	above	ADV
ejpam-6472	442	26	shows	show	VERB
ejpam-6472	442	27	that	that	SCONJ
ejpam-6472	442	28	nr(u	nr(u	PUNCT
ejpam-6472	442	29	·	·	PUNCT
ejpam-6472	442	30	rs	rs	X
ejpam-6472	442	31	t)(op(q)−	t)(op(q)−	ADJ
ejpam-6472	442	32	op(r	op(r	NUM
ejpam-6472	442	33	)	)	PUNCT
ejpam-6472	442	34	)	)	PUNCT
ejpam-6472	443	1	=	=	PUNCT
ejpam-6472	443	2	0	0	NUM
ejpam-6472	443	3	,	,	PUNCT
ejpam-6472	443	4	and	and	CCONJ
ejpam-6472	443	5	(	(	PUNCT
ejpam-6472	443	6	ns(u	ns(u	NOUN
ejpam-6472	443	7	·	·	PUNCT
ejpam-6472	443	8	rs	rs	NOUN
ejpam-6472	443	9	t)−	t)−	PROPN
ejpam-6472	443	10	ns(r)nr(u	ns(r)nr(u	PROPN
ejpam-6472	443	11	·	·	PUNCT
ejpam-6472	443	12	rs	rs	X
ejpam-6472	443	13	t))(op(q)−	t))(op(q)−	NOUN
ejpam-6472	443	14	op(s	op(s	NUM
ejpam-6472	443	15	)	)	PUNCT
ejpam-6472	443	16	)	)	PUNCT
ejpam-6472	444	1	=	=	PUNCT
ejpam-6472	444	2	0	0	X
ejpam-6472	444	3	.	.	PUNCT
ejpam-6472	445	1	p.	p.	NOUN
ejpam-6472	445	2	prachumdang	prachumdang	PROPN
ejpam-6472	445	3	,	,	PUNCT
ejpam-6472	445	4	b.	b.	PROPN
ejpam-6472	445	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	445	6	/	/	SYM
ejpam-6472	445	7	eur	eur	PROPN
ejpam-6472	445	8	.	.	PUNCT
ejpam-6472	446	1	j.	j.	PROPN
ejpam-6472	446	2	pure	pure	PROPN
ejpam-6472	446	3	appl	appl	PROPN
ejpam-6472	446	4	.	.	PROPN
ejpam-6472	446	5	math	math	PROPN
ejpam-6472	446	6	,	,	PUNCT
ejpam-6472	446	7	18	18	NUM
ejpam-6472	446	8	(	(	PUNCT
ejpam-6472	446	9	3	3	NUM
ejpam-6472	446	10	)	)	PUNCT
ejpam-6472	446	11	(	(	PUNCT
ejpam-6472	446	12	2025	2025	NUM
ejpam-6472	446	13	)	)	PUNCT
ejpam-6472	446	14	,	,	PUNCT
ejpam-6472	446	15	6472	6472	NUM
ejpam-6472	446	16	12	12	NUM
ejpam-6472	446	17	of	of	ADP
ejpam-6472	446	18	16	16	NUM
ejpam-6472	446	19	if	if	SCONJ
ejpam-6472	446	20	r	r	NOUN
ejpam-6472	446	21	∈	∈	PROPN
ejpam-6472	446	22	sub(t	sub(t	PROPN
ejpam-6472	446	23	)	)	PUNCT
ejpam-6472	446	24	,	,	PUNCT
ejpam-6472	446	25	then	then	ADV
ejpam-6472	446	26	by	by	ADP
ejpam-6472	446	27	(	(	PUNCT
ejpam-6472	446	28	1	1	NUM
ejpam-6472	446	29	)	)	PUNCT
ejpam-6472	446	30	,	,	PUNCT
ejpam-6472	446	31	we	we	PRON
ejpam-6472	446	32	have	have	VERB
ejpam-6472	446	33	nr(u	nr(u	PUNCT
ejpam-6472	446	34	·	·	PUNCT
ejpam-6472	446	35	rs	rs	PROPN
ejpam-6472	446	36	t	t	PROPN
ejpam-6472	446	37	)	)	PUNCT
ejpam-6472	446	38	=	=	SYM
ejpam-6472	446	39	1	1	NUM
ejpam-6472	446	40	and	and	CCONJ
ejpam-6472	446	41	r	r	NOUN
ejpam-6472	446	42	∈	∈	PROPN
ejpam-6472	446	43	sub(q	sub(q	PROPN
ejpam-6472	446	44	)	)	PUNCT
ejpam-6472	446	45	.	.	PUNCT
ejpam-6472	447	1	thus	thus	ADV
ejpam-6472	447	2	,	,	PUNCT
ejpam-6472	447	3	op(q	op(q	NOUN
ejpam-6472	447	4	)	)	PUNCT
ejpam-6472	447	5	=	=	SYM
ejpam-6472	447	6	op(r	op(r	NOUN
ejpam-6472	447	7	)	)	PUNCT
ejpam-6472	447	8	,	,	PUNCT
ejpam-6472	447	9	which	which	PRON
ejpam-6472	447	10	implies	imply	VERB
ejpam-6472	447	11	q	q	NOUN
ejpam-6472	447	12	=	=	SYM
ejpam-6472	447	13	r.	r.	NOUN
ejpam-6472	447	14	if	if	SCONJ
ejpam-6472	447	15	r	r	PROPN
ejpam-6472	447	16	̸∈	̸∈	PROPN
ejpam-6472	447	17	sub(t	sub(t	PROPN
ejpam-6472	447	18	)	)	PUNCT
ejpam-6472	447	19	,	,	PUNCT
ejpam-6472	447	20	then	then	ADV
ejpam-6472	447	21	by	by	ADP
ejpam-6472	447	22	the	the	DET
ejpam-6472	447	23	assumption	assumption	NOUN
ejpam-6472	447	24	that	that	SCONJ
ejpam-6472	447	25	{	{	PUNCT
ejpam-6472	447	26	r	r	NOUN
ejpam-6472	447	27	,	,	PUNCT
ejpam-6472	447	28	s	s	NOUN
ejpam-6472	447	29	}	}	PUNCT
ejpam-6472	447	30	∩	∩	ADJ
ejpam-6472	447	31	sub(t	sub(t	NOUN
ejpam-6472	447	32	)	)	PUNCT
ejpam-6472	447	33	̸=	̸=	NOUN
ejpam-6472	447	34	∅	∅	NOUN
ejpam-6472	447	35	,	,	PUNCT
ejpam-6472	447	36	we	we	PRON
ejpam-6472	447	37	have	have	VERB
ejpam-6472	447	38	s	s	PROPN
ejpam-6472	447	39	∈	∈	PROPN
ejpam-6472	447	40	sub(t	sub(t	NOUN
ejpam-6472	447	41	)	)	PUNCT
ejpam-6472	447	42	.	.	PUNCT
ejpam-6472	448	1	by	by	ADP
ejpam-6472	448	2	a	a	DET
ejpam-6472	448	3	similar	similar	ADJ
ejpam-6472	448	4	reasoning	reasoning	NOUN
ejpam-6472	448	5	,	,	PUNCT
ejpam-6472	448	6	we	we	PRON
ejpam-6472	448	7	conclude	conclude	VERB
ejpam-6472	448	8	q	q	X
ejpam-6472	448	9	=	=	PUNCT
ejpam-6472	448	10	s.	s.	PROPN
ejpam-6472	448	11	this	this	PRON
ejpam-6472	448	12	completes	complete	VERB
ejpam-6472	448	13	the	the	DET
ejpam-6472	448	14	proof	proof	NOUN
ejpam-6472	448	15	.	.	PUNCT
ejpam-6472	449	1	the	the	DET
ejpam-6472	449	2	next	next	ADJ
ejpam-6472	449	3	theorem	theorem	NOUN
ejpam-6472	449	4	establishes	establish	VERB
ejpam-6472	449	5	that	that	SCONJ
ejpam-6472	449	6	any	any	DET
ejpam-6472	449	7	term	term	NOUN
ejpam-6472	449	8	in	in	ADP
ejpam-6472	449	9	(	(	PUNCT
ejpam-6472	449	10	w	w	NOUN
ejpam-6472	449	11	r	r	NOUN
ejpam-6472	449	12	,	,	PUNCT
ejpam-6472	449	13	s	s	PART
ejpam-6472	449	14	τ	τ	X
ejpam-6472	449	15	(	(	PUNCT
ejpam-6472	449	16	xn	xn	PROPN
ejpam-6472	449	17	)	)	PUNCT
ejpam-6472	449	18	,	,	PUNCT
ejpam-6472	449	19	·	·	PUNCT
ejpam-6472	449	20	rs	rs	X
ejpam-6472	449	21	)	)	PUNCT
ejpam-6472	449	22	that	that	PRON
ejpam-6472	449	23	can	can	AUX
ejpam-6472	449	24	be	be	AUX
ejpam-6472	449	25	written	write	VERB
ejpam-6472	449	26	as	as	ADP
ejpam-6472	449	27	a	a	DET
ejpam-6472	449	28	product	product	NOUN
ejpam-6472	449	29	of	of	ADP
ejpam-6472	449	30	several	several	ADJ
ejpam-6472	449	31	terms	term	NOUN
ejpam-6472	449	32	,	,	PUNCT
ejpam-6472	449	33	where	where	SCONJ
ejpam-6472	449	34	the	the	DET
ejpam-6472	449	35	term	term	NOUN
ejpam-6472	449	36	itself	itself	PRON
ejpam-6472	449	37	appears	appear	VERB
ejpam-6472	449	38	at	at	ADV
ejpam-6472	449	39	least	least	ADJ
ejpam-6472	449	40	twice	twice	ADV
ejpam-6472	449	41	,	,	PUNCT
ejpam-6472	449	42	is	be	AUX
ejpam-6472	449	43	necessarily	necessarily	ADV
ejpam-6472	449	44	idempotent	idempotent	ADJ
ejpam-6472	449	45	.	.	PUNCT
ejpam-6472	450	1	theorem	theorem	ADJ
ejpam-6472	450	2	7	7	NUM
ejpam-6472	450	3	.	.	PUNCT
ejpam-6472	451	1	let	let	VERB
ejpam-6472	451	2	r	r	NOUN
ejpam-6472	451	3	,	,	PUNCT
ejpam-6472	451	4	s	s	NOUN
ejpam-6472	451	5	∈	∈	PROPN
ejpam-6472	451	6	wτ	wτ	NOUN
ejpam-6472	451	7	(	(	PUNCT
ejpam-6472	451	8	xn	xn	X
ejpam-6472	451	9	)	)	PUNCT
ejpam-6472	451	10	be	be	AUX
ejpam-6472	451	11	fixed	fix	VERB
ejpam-6472	451	12	terms	term	NOUN
ejpam-6472	451	13	and	and	CCONJ
ejpam-6472	451	14	t	t	NOUN
ejpam-6472	451	15	∈	∈	PROPN
ejpam-6472	451	16	w	w	PROPN
ejpam-6472	451	17	r	r	PROPN
ejpam-6472	451	18	,	,	PUNCT
ejpam-6472	451	19	s	s	PART
ejpam-6472	451	20	τ	τ	X
ejpam-6472	451	21	(	(	PUNCT
ejpam-6472	451	22	xn	xn	PROPN
ejpam-6472	451	23	)	)	PUNCT
ejpam-6472	451	24	.	.	PUNCT
ejpam-6472	452	1	then	then	ADV
ejpam-6472	452	2	t	t	PROPN
ejpam-6472	452	3	is	be	AUX
ejpam-6472	452	4	idempotent	idempotent	ADJ
ejpam-6472	452	5	with	with	ADP
ejpam-6472	452	6	respect	respect	NOUN
ejpam-6472	452	7	to	to	ADP
ejpam-6472	452	8	·	·	PUNCT
ejpam-6472	452	9	rs	rs	VERB
ejpam-6472	452	10	if	if	SCONJ
ejpam-6472	453	1	and	and	CCONJ
ejpam-6472	453	2	only	only	ADV
ejpam-6472	453	3	if	if	SCONJ
ejpam-6472	453	4	there	there	PRON
ejpam-6472	453	5	exist	exist	VERB
ejpam-6472	453	6	t1	t1	NOUN
ejpam-6472	453	7	,	,	PUNCT
ejpam-6472	453	8	.	.	PUNCT
ejpam-6472	453	9	.	.	PUNCT
ejpam-6472	454	1	.	.	PUNCT
ejpam-6472	455	1	,	,	PUNCT
ejpam-6472	455	2	tm	tm	PROPN
ejpam-6472	455	3	∈	∈	PROPN
ejpam-6472	455	4	w	w	PROPN
ejpam-6472	455	5	r	r	PROPN
ejpam-6472	455	6	,	,	PUNCT
ejpam-6472	455	7	s	s	PART
ejpam-6472	455	8	τ	τ	X
ejpam-6472	455	9	(	(	PUNCT
ejpam-6472	455	10	xn	xn	PROPN
ejpam-6472	455	11	)	)	PUNCT
ejpam-6472	455	12	with	with	ADP
ejpam-6472	455	13	at	at	ADV
ejpam-6472	455	14	least	least	ADV
ejpam-6472	455	15	two	two	NUM
ejpam-6472	455	16	of	of	ADP
ejpam-6472	455	17	them	they	PRON
ejpam-6472	455	18	equal	equal	ADJ
ejpam-6472	455	19	to	to	ADP
ejpam-6472	455	20	t	t	NOUN
ejpam-6472	455	21	such	such	ADJ
ejpam-6472	455	22	that	that	DET
ejpam-6472	455	23	t	t	NOUN
ejpam-6472	455	24	=	=	SYM
ejpam-6472	455	25	t1	t1	NUM
ejpam-6472	455	26	·	·	SYM
ejpam-6472	455	27	rs	rs	ADJ
ejpam-6472	455	28	t2	t2	NOUN
ejpam-6472	455	29	·	·	PUNCT
ejpam-6472	455	30	rs	rs	X
ejpam-6472	455	31	·	·	PUNCT
ejpam-6472	455	32	·	·	PUNCT
ejpam-6472	455	33	·	·	PUNCT
ejpam-6472	455	34	·	·	PUNCT
ejpam-6472	455	35	rs	rs	PROPN
ejpam-6472	455	36	tm	tm	PROPN
ejpam-6472	455	37	.	.	PROPN
ejpam-6472	455	38	proof	proof	PROPN
ejpam-6472	455	39	.	.	PUNCT
ejpam-6472	456	1	assume	assume	VERB
ejpam-6472	456	2	that	that	SCONJ
ejpam-6472	456	3	t	t	NOUN
ejpam-6472	456	4	=	=	SYM
ejpam-6472	456	5	t1	t1	NUM
ejpam-6472	456	6	·	·	SYM
ejpam-6472	456	7	rs	rs	ADJ
ejpam-6472	456	8	t2	t2	NOUN
ejpam-6472	456	9	·	·	PUNCT
ejpam-6472	456	10	rs	rs	X
ejpam-6472	456	11	·	·	PUNCT
ejpam-6472	456	12	·	·	PUNCT
ejpam-6472	456	13	·	·	PUNCT
ejpam-6472	456	14	·	·	PUNCT
ejpam-6472	456	15	rs	rs	NOUN
ejpam-6472	456	16	tm	tm	NOUN
ejpam-6472	456	17	for	for	ADP
ejpam-6472	456	18	some	some	DET
ejpam-6472	456	19	t1	t1	NOUN
ejpam-6472	456	20	,	,	PUNCT
ejpam-6472	456	21	.	.	PUNCT
ejpam-6472	456	22	.	.	PUNCT
ejpam-6472	456	23	.	.	PUNCT
ejpam-6472	457	1	,	,	PUNCT
ejpam-6472	457	2	tm	tm	PROPN
ejpam-6472	457	3	∈	∈	PROPN
ejpam-6472	457	4	w	w	PROPN
ejpam-6472	457	5	r	r	PROPN
ejpam-6472	457	6	,	,	PUNCT
ejpam-6472	457	7	s	s	PART
ejpam-6472	457	8	τ	τ	X
ejpam-6472	457	9	(	(	PUNCT
ejpam-6472	457	10	xn	xn	PROPN
ejpam-6472	457	11	)	)	PUNCT
ejpam-6472	457	12	with	with	ADP
ejpam-6472	457	13	at	at	ADV
ejpam-6472	457	14	least	least	ADV
ejpam-6472	457	15	two	two	NUM
ejpam-6472	457	16	of	of	ADP
ejpam-6472	457	17	them	they	PRON
ejpam-6472	457	18	equal	equal	ADJ
ejpam-6472	457	19	to	to	ADP
ejpam-6472	457	20	t.	t.	PROPN
ejpam-6472	457	21	suppose	suppose	VERB
ejpam-6472	457	22	that	that	SCONJ
ejpam-6472	457	23	t	t	PROPN
ejpam-6472	457	24	is	be	AUX
ejpam-6472	457	25	not	not	PART
ejpam-6472	457	26	idempotent	idempotent	ADJ
ejpam-6472	457	27	.	.	PUNCT
ejpam-6472	458	1	by	by	ADP
ejpam-6472	458	2	theorem	theorem	NOUN
ejpam-6472	458	3	5	5	NUM
ejpam-6472	458	4	,	,	PUNCT
ejpam-6472	458	5	we	we	PRON
ejpam-6472	458	6	obtain	obtain	VERB
ejpam-6472	458	7	{	{	PUNCT
ejpam-6472	458	8	r	r	NOUN
ejpam-6472	458	9	,	,	PUNCT
ejpam-6472	458	10	s	s	NOUN
ejpam-6472	458	11	}	}	PUNCT
ejpam-6472	458	12	∩	∩	ADJ
ejpam-6472	458	13	sub(t	sub(t	NOUN
ejpam-6472	458	14	)	)	PUNCT
ejpam-6472	458	15	̸=	̸=	PROPN
ejpam-6472	458	16	∅	∅	NOUN
ejpam-6472	458	17	and	and	CCONJ
ejpam-6472	458	18	t	t	X
ejpam-6472	458	19	̸∈	̸∈	PROPN
ejpam-6472	458	20	{	{	PUNCT
ejpam-6472	458	21	r	r	PROPN
ejpam-6472	458	22	,	,	PUNCT
ejpam-6472	458	23	s	s	PART
ejpam-6472	458	24	}	}	PUNCT
ejpam-6472	458	25	.	.	PUNCT
ejpam-6472	459	1	we	we	PRON
ejpam-6472	459	2	first	first	ADV
ejpam-6472	459	3	consider	consider	VERB
ejpam-6472	459	4	the	the	DET
ejpam-6472	459	5	case	case	NOUN
ejpam-6472	459	6	where	where	SCONJ
ejpam-6472	459	7	tm	tm	PROPN
ejpam-6472	459	8	=	=	PROPN
ejpam-6472	459	9	t.	t.	PROPN
ejpam-6472	460	1	then	then	ADV
ejpam-6472	460	2	we	we	PRON
ejpam-6472	460	3	write	write	VERB
ejpam-6472	460	4	t	t	PROPN
ejpam-6472	460	5	=	=	PUNCT
ejpam-6472	460	6	a	a	DET
ejpam-6472	460	7	·	·	SYM
ejpam-6472	460	8	rs	rs	NOUN
ejpam-6472	460	9	t	t	PROPN
ejpam-6472	460	10	·	·	PUNCT
ejpam-6472	460	11	rs	rs	PROPN
ejpam-6472	460	12	b	b	PROPN
ejpam-6472	460	13	·	·	PUNCT
ejpam-6472	460	14	rs	rs	PROPN
ejpam-6472	460	15	t	t	PROPN
ejpam-6472	460	16	,	,	PUNCT
ejpam-6472	460	17	where	where	SCONJ
ejpam-6472	460	18	each	each	PRON
ejpam-6472	460	19	of	of	ADP
ejpam-6472	460	20	a	a	PRON
ejpam-6472	460	21	and	and	CCONJ
ejpam-6472	460	22	b	b	NOUN
ejpam-6472	460	23	is	be	AUX
ejpam-6472	460	24	either	either	CCONJ
ejpam-6472	460	25	a	a	DET
ejpam-6472	460	26	product	product	NOUN
ejpam-6472	460	27	of	of	ADP
ejpam-6472	460	28	tj	tj	NOUN
ejpam-6472	460	29	’s	’s	ADV
ejpam-6472	460	30	or	or	CCONJ
ejpam-6472	460	31	the	the	DET
ejpam-6472	460	32	element	element	NOUN
ejpam-6472	460	33	r	r	NOUN
ejpam-6472	460	34	,	,	PUNCT
ejpam-6472	460	35	which	which	PRON
ejpam-6472	460	36	is	be	AUX
ejpam-6472	460	37	the	the	DET
ejpam-6472	460	38	left	left	ADJ
ejpam-6472	460	39	identity	identity	NOUN
ejpam-6472	460	40	in	in	ADP
ejpam-6472	460	41	w	w	NOUN
ejpam-6472	460	42	r	r	NOUN
ejpam-6472	460	43	,	,	PUNCT
ejpam-6472	460	44	s	s	PART
ejpam-6472	460	45	τ	τ	X
ejpam-6472	460	46	(	(	PUNCT
ejpam-6472	460	47	xn	xn	PROPN
ejpam-6472	460	48	)	)	PUNCT
ejpam-6472	460	49	.	.	PUNCT
ejpam-6472	461	1	by	by	ADP
ejpam-6472	461	2	lemma	lemma	PROPN
ejpam-6472	461	3	5	5	NUM
ejpam-6472	461	4	,	,	PUNCT
ejpam-6472	461	5	we	we	PRON
ejpam-6472	461	6	obtain	obtain	VERB
ejpam-6472	461	7	{	{	PUNCT
ejpam-6472	461	8	r	r	NOUN
ejpam-6472	461	9	,	,	PUNCT
ejpam-6472	461	10	s	s	NOUN
ejpam-6472	461	11	}	}	PUNCT
ejpam-6472	461	12	∩	∩	ADJ
ejpam-6472	461	13	sub(a	sub(a	PROPN
ejpam-6472	461	14	)	)	PUNCT
ejpam-6472	461	15	̸=	̸=	PROPN
ejpam-6472	461	16	∅	∅	NOUN
ejpam-6472	461	17	and	and	CCONJ
ejpam-6472	461	18	{	{	PUNCT
ejpam-6472	461	19	r	r	NOUN
ejpam-6472	461	20	,	,	PUNCT
ejpam-6472	461	21	s	s	NOUN
ejpam-6472	461	22	}	}	PUNCT
ejpam-6472	461	23	∩	∩	ADJ
ejpam-6472	461	24	sub(b	sub(b	NOUN
ejpam-6472	461	25	)	)	PUNCT
ejpam-6472	461	26	̸=	̸=	PROPN
ejpam-6472	461	27	∅.	∅.	AUX
ejpam-6472	461	28	applying	apply	VERB
ejpam-6472	461	29	lemma	lemma	PROPN
ejpam-6472	461	30	1	1	NUM
ejpam-6472	461	31	,	,	PUNCT
ejpam-6472	461	32	it	it	PRON
ejpam-6472	461	33	follows	follow	VERB
ejpam-6472	461	34	that	that	SCONJ
ejpam-6472	461	35	t	t	PROPN
ejpam-6472	461	36	∈	∈	PROPN
ejpam-6472	461	37	sub(b	sub(b	PROPN
ejpam-6472	461	38	·	·	PUNCT
ejpam-6472	461	39	rs	rs	PROPN
ejpam-6472	461	40	t	t	PROPN
ejpam-6472	461	41	)	)	PUNCT
ejpam-6472	461	42	,	,	PUNCT
ejpam-6472	461	43	b	b	X
ejpam-6472	461	44	·	·	SYM
ejpam-6472	461	45	rs	rs	PROPN
ejpam-6472	461	46	t	t	PROPN
ejpam-6472	461	47	∈	∈	PROPN
ejpam-6472	461	48	sub(t	sub(t	PROPN
ejpam-6472	461	49	·	·	PUNCT
ejpam-6472	461	50	rs	rs	PROPN
ejpam-6472	461	51	b	b	PROPN
ejpam-6472	461	52	·	·	SYM
ejpam-6472	461	53	rs	rs	PROPN
ejpam-6472	461	54	t	t	PROPN
ejpam-6472	461	55	)	)	PUNCT
ejpam-6472	461	56	\	\	PROPN
ejpam-6472	461	57	{	{	PUNCT
ejpam-6472	461	58	t	t	NOUN
ejpam-6472	461	59	·	·	SYM
ejpam-6472	461	60	rs	rs	PROPN
ejpam-6472	461	61	b	b	PROPN
ejpam-6472	461	62	·	·	PUNCT
ejpam-6472	461	63	rs	rs	X
ejpam-6472	461	64	t	t	PROPN
ejpam-6472	461	65	}	}	PUNCT
ejpam-6472	461	66	,	,	PUNCT
ejpam-6472	461	67	and	and	CCONJ
ejpam-6472	461	68	t	t	PROPN
ejpam-6472	461	69	·	·	PUNCT
ejpam-6472	461	70	rs	rs	PROPN
ejpam-6472	461	71	b	b	PROPN
ejpam-6472	461	72	·	·	PUNCT
ejpam-6472	461	73	rs	rs	PROPN
ejpam-6472	461	74	t	t	PROPN
ejpam-6472	461	75	∈	∈	PROPN
ejpam-6472	461	76	sub(a	sub(a	PROPN
ejpam-6472	461	77	·	·	SYM
ejpam-6472	461	78	rs	rs	X
ejpam-6472	461	79	t	t	PROPN
ejpam-6472	461	80	·	·	PUNCT
ejpam-6472	461	81	rs	rs	PROPN
ejpam-6472	461	82	b	b	PROPN
ejpam-6472	461	83	·	·	PUNCT
ejpam-6472	461	84	rs	rs	PROPN
ejpam-6472	461	85	t	t	PROPN
ejpam-6472	461	86	)	)	PUNCT
ejpam-6472	461	87	.	.	PUNCT
ejpam-6472	462	1	hence	hence	ADV
ejpam-6472	462	2	,	,	PUNCT
ejpam-6472	462	3	op(t	op(t	NOUN
ejpam-6472	462	4	)	)	PUNCT
ejpam-6472	462	5	≤	≤	NOUN
ejpam-6472	462	6	op(b	op(b	ADP
ejpam-6472	462	7	·	·	PUNCT
ejpam-6472	462	8	rs	rs	PROPN
ejpam-6472	462	9	t	t	PROPN
ejpam-6472	462	10	)	)	PUNCT
ejpam-6472	462	11	<	<	X
ejpam-6472	462	12	op(t	op(t	X
ejpam-6472	462	13	·	·	PUNCT
ejpam-6472	462	14	rs	rs	PROPN
ejpam-6472	462	15	b	b	PROPN
ejpam-6472	462	16	·	·	SYM
ejpam-6472	462	17	rs	rs	PROPN
ejpam-6472	462	18	t	t	PROPN
ejpam-6472	462	19	)	)	PUNCT
ejpam-6472	462	20	≤	≤	NOUN
ejpam-6472	462	21	op(a	op(a	NUM
ejpam-6472	462	22	·	·	PUNCT
ejpam-6472	462	23	rs	rs	X
ejpam-6472	462	24	t	t	PROPN
ejpam-6472	462	25	·	·	PUNCT
ejpam-6472	462	26	rs	rs	PROPN
ejpam-6472	462	27	b	b	PROPN
ejpam-6472	462	28	·	·	SYM
ejpam-6472	462	29	rs	rs	PROPN
ejpam-6472	462	30	t	t	PROPN
ejpam-6472	462	31	)	)	PUNCT
ejpam-6472	462	32	=	=	SYM
ejpam-6472	462	33	op(t	op(t	NOUN
ejpam-6472	462	34	)	)	PUNCT
ejpam-6472	462	35	,	,	PUNCT
ejpam-6472	462	36	a	a	DET
ejpam-6472	462	37	contradiction	contradiction	NOUN
ejpam-6472	462	38	.	.	PUNCT
ejpam-6472	463	1	now	now	ADV
ejpam-6472	463	2	,	,	PUNCT
ejpam-6472	463	3	assume	assume	VERB
ejpam-6472	463	4	tm	tm	PROPN
ejpam-6472	463	5	̸=	̸=	PROPN
ejpam-6472	463	6	t.	t.	PROPN
ejpam-6472	463	7	then	then	ADV
ejpam-6472	463	8	t	t	PROPN
ejpam-6472	463	9	can	can	AUX
ejpam-6472	463	10	be	be	AUX
ejpam-6472	463	11	written	write	VERB
ejpam-6472	463	12	as	as	ADP
ejpam-6472	463	13	t	t	PROPN
ejpam-6472	463	14	=	=	SYM
ejpam-6472	464	1	a	a	DET
ejpam-6472	464	2	·	·	SYM
ejpam-6472	464	3	rs	rs	NOUN
ejpam-6472	464	4	t	t	PROPN
ejpam-6472	464	5	·	·	PUNCT
ejpam-6472	464	6	rs	rs	PROPN
ejpam-6472	464	7	b	b	PROPN
ejpam-6472	464	8	·	·	SYM
ejpam-6472	464	9	rs	rs	X
ejpam-6472	464	10	t	t	PROPN
ejpam-6472	464	11	·	·	PUNCT
ejpam-6472	464	12	rs	rs	PROPN
ejpam-6472	464	13	c	c	X
ejpam-6472	464	14	,	,	PUNCT
ejpam-6472	464	15	where	where	SCONJ
ejpam-6472	464	16	c	c	PROPN
ejpam-6472	464	17	is	be	AUX
ejpam-6472	464	18	a	a	DET
ejpam-6472	464	19	product	product	NOUN
ejpam-6472	464	20	of	of	ADP
ejpam-6472	464	21	tj	tj	PROPN
ejpam-6472	464	22	’	'	PUNCT
ejpam-6472	464	23	s.	s.	PROPN
ejpam-6472	464	24	by	by	ADP
ejpam-6472	464	25	lemma	lemma	PROPN
ejpam-6472	464	26	7	7	NUM
ejpam-6472	464	27	,	,	PUNCT
ejpam-6472	464	28	we	we	PRON
ejpam-6472	464	29	have	have	VERB
ejpam-6472	464	30	t	t	NOUN
ejpam-6472	464	31	=	=	SYM
ejpam-6472	464	32	a	a	DET
ejpam-6472	464	33	·	·	SYM
ejpam-6472	464	34	rs	rs	NOUN
ejpam-6472	464	35	t	t	PROPN
ejpam-6472	464	36	·	·	PUNCT
ejpam-6472	464	37	rs	rs	PROPN
ejpam-6472	464	38	b	b	PROPN
ejpam-6472	464	39	·	·	PUNCT
ejpam-6472	464	40	rs	rs	PROPN
ejpam-6472	464	41	t	t	PROPN
ejpam-6472	464	42	,	,	PUNCT
ejpam-6472	464	43	and	and	CCONJ
ejpam-6472	464	44	the	the	DET
ejpam-6472	464	45	same	same	ADJ
ejpam-6472	464	46	contradiction	contradiction	NOUN
ejpam-6472	464	47	follows	follow	VERB
ejpam-6472	464	48	as	as	ADP
ejpam-6472	464	49	in	in	ADP
ejpam-6472	464	50	the	the	DET
ejpam-6472	464	51	previous	previous	ADJ
ejpam-6472	464	52	case	case	NOUN
ejpam-6472	464	53	.	.	PUNCT
ejpam-6472	465	1	5	5	X
ejpam-6472	465	2	.	.	X
ejpam-6472	465	3	green	green	PROPN
ejpam-6472	465	4	’s	’s	PART
ejpam-6472	465	5	relations	relation	NOUN
ejpam-6472	465	6	on	on	ADP
ejpam-6472	465	7	the	the	DET
ejpam-6472	465	8	semigroup	semigroup	NOUN
ejpam-6472	465	9	(	(	PUNCT
ejpam-6472	465	10	w	w	NOUN
ejpam-6472	465	11	r	r	NOUN
ejpam-6472	465	12	,	,	PUNCT
ejpam-6472	465	13	s	s	PART
ejpam-6472	465	14	τ	τ	X
ejpam-6472	465	15	(	(	PUNCT
ejpam-6472	465	16	xn	xn	PROPN
ejpam-6472	465	17	)	)	PUNCT
ejpam-6472	465	18	,	,	PUNCT
ejpam-6472	465	19	·	·	PUNCT
ejpam-6472	465	20	rs	rs	X
ejpam-6472	465	21	)	)	PUNCT
ejpam-6472	465	22	in	in	ADP
ejpam-6472	465	23	this	this	DET
ejpam-6472	465	24	section	section	NOUN
ejpam-6472	465	25	,	,	PUNCT
ejpam-6472	465	26	we	we	PRON
ejpam-6472	465	27	provide	provide	VERB
ejpam-6472	465	28	explicit	explicit	ADJ
ejpam-6472	465	29	characterizations	characterization	NOUN
ejpam-6472	465	30	for	for	ADP
ejpam-6472	465	31	all	all	DET
ejpam-6472	465	32	five	five	NUM
ejpam-6472	465	33	types	type	NOUN
ejpam-6472	465	34	of	of	ADP
ejpam-6472	465	35	green	green	PROPN
ejpam-6472	465	36	’s	’s	PART
ejpam-6472	465	37	relations	relation	NOUN
ejpam-6472	465	38	on	on	ADP
ejpam-6472	465	39	the	the	DET
ejpam-6472	465	40	semigroup	semigroup	NOUN
ejpam-6472	465	41	(	(	PUNCT
ejpam-6472	465	42	w	w	NOUN
ejpam-6472	465	43	r	r	NOUN
ejpam-6472	465	44	,	,	PUNCT
ejpam-6472	465	45	s	s	PART
ejpam-6472	465	46	τ	τ	X
ejpam-6472	465	47	(	(	PUNCT
ejpam-6472	465	48	xn	xn	PROPN
ejpam-6472	465	49	)	)	PUNCT
ejpam-6472	465	50	,	,	PUNCT
ejpam-6472	465	51	·	·	PUNCT
ejpam-6472	465	52	rs	rs	X
ejpam-6472	465	53	)	)	PUNCT
ejpam-6472	465	54	.	.	PUNCT
ejpam-6472	466	1	let	let	VERB
ejpam-6472	466	2	s	s	PRON
ejpam-6472	466	3	be	be	AUX
ejpam-6472	466	4	a	a	DET
ejpam-6472	466	5	semigroup	semigroup	NOUN
ejpam-6472	466	6	and	and	CCONJ
ejpam-6472	466	7	s1	s1	NOUN
ejpam-6472	466	8	denote	denote	VERB
ejpam-6472	466	9	the	the	DET
ejpam-6472	466	10	monoid	monoid	NOUN
ejpam-6472	466	11	obtained	obtain	VERB
ejpam-6472	466	12	by	by	ADP
ejpam-6472	466	13	adjoining	adjoin	VERB
ejpam-6472	466	14	an	an	DET
ejpam-6472	466	15	identity	identity	NOUN
ejpam-6472	466	16	element	element	NOUN
ejpam-6472	466	17	1	1	NUM
ejpam-6472	466	18	to	to	ADP
ejpam-6472	466	19	s	s	PRON
ejpam-6472	466	20	,	,	PUNCT
ejpam-6472	466	21	if	if	SCONJ
ejpam-6472	466	22	necessary	necessary	ADJ
ejpam-6472	466	23	.	.	PUNCT
ejpam-6472	467	1	for	for	ADP
ejpam-6472	467	2	elements	element	NOUN
ejpam-6472	467	3	x	x	X
ejpam-6472	467	4	,	,	PUNCT
ejpam-6472	467	5	y	y	PROPN
ejpam-6472	467	6	∈	∈	PROPN
ejpam-6472	467	7	s	s	X
ejpam-6472	467	8	,	,	PUNCT
ejpam-6472	467	9	we	we	PRON
ejpam-6472	467	10	say	say	VERB
ejpam-6472	467	11	that	that	SCONJ
ejpam-6472	467	12	xl	xl	PROPN
ejpam-6472	467	13	y	y	PROPN
ejpam-6472	468	1	if	if	SCONJ
ejpam-6472	469	1	and	and	CCONJ
ejpam-6472	469	2	only	only	ADV
ejpam-6472	469	3	if	if	SCONJ
ejpam-6472	469	4	there	there	PRON
ejpam-6472	469	5	exist	exist	VERB
ejpam-6472	469	6	u	u	NOUN
ejpam-6472	469	7	,	,	PUNCT
ejpam-6472	469	8	v	v	NOUN
ejpam-6472	469	9	∈	∈	NOUN
ejpam-6472	469	10	s1	s1	NOUN
ejpam-6472	469	11	such	such	ADJ
ejpam-6472	469	12	that	that	PRON
ejpam-6472	469	13	ux	ux	PROPN
ejpam-6472	469	14	=	=	SYM
ejpam-6472	469	15	y	y	PROPN
ejpam-6472	469	16	and	and	CCONJ
ejpam-6472	469	17	vy	vy	NOUN
ejpam-6472	469	18	=	=	PUNCT
ejpam-6472	469	19	x.	x.	NOUN
ejpam-6472	469	20	similarly	similarly	ADV
ejpam-6472	469	21	,	,	PUNCT
ejpam-6472	469	22	xr	xr	PROPN
ejpam-6472	469	23	y	y	PROPN
ejpam-6472	470	1	if	if	SCONJ
ejpam-6472	470	2	and	and	CCONJ
ejpam-6472	470	3	only	only	ADV
ejpam-6472	470	4	if	if	SCONJ
ejpam-6472	470	5	there	there	PRON
ejpam-6472	470	6	exist	exist	VERB
ejpam-6472	470	7	u	u	NOUN
ejpam-6472	470	8	,	,	PUNCT
ejpam-6472	470	9	v	v	NOUN
ejpam-6472	470	10	∈	∈	NOUN
ejpam-6472	470	11	s1	s1	NOUN
ejpam-6472	470	12	such	such	ADJ
ejpam-6472	470	13	that	that	SCONJ
ejpam-6472	470	14	xu	xu	PROPN
ejpam-6472	470	15	=	=	SYM
ejpam-6472	470	16	y	y	PROPN
ejpam-6472	470	17	and	and	CCONJ
ejpam-6472	470	18	yv	yv	PROPN
ejpam-6472	470	19	=	=	PUNCT
ejpam-6472	470	20	x.	x.	NOUN
ejpam-6472	471	1	the	the	DET
ejpam-6472	471	2	relation	relation	NOUN
ejpam-6472	471	3	h	h	NOUN
ejpam-6472	471	4	is	be	AUX
ejpam-6472	471	5	defined	define	VERB
ejpam-6472	471	6	as	as	ADP
ejpam-6472	471	7	the	the	DET
ejpam-6472	471	8	intersection	intersection	NOUN
ejpam-6472	471	9	of	of	ADP
ejpam-6472	471	10	l	l	PROPN
ejpam-6472	471	11	and	and	CCONJ
ejpam-6472	471	12	r.	r.	X
ejpam-6472	471	13	the	the	DET
ejpam-6472	471	14	relation	relation	NOUN
ejpam-6472	472	1	d	d	PROPN
ejpam-6472	472	2	is	be	AUX
ejpam-6472	472	3	defined	define	VERB
ejpam-6472	472	4	as	as	ADP
ejpam-6472	472	5	the	the	DET
ejpam-6472	472	6	composition	composition	NOUN
ejpam-6472	472	7	l	l	NOUN
ejpam-6472	472	8	◦	◦	NOUN
ejpam-6472	472	9	r	r	NOUN
ejpam-6472	472	10	=	=	SYM
ejpam-6472	472	11	r	r	NOUN
ejpam-6472	472	12	◦	◦	NOUN
ejpam-6472	472	13	l	l	NOUN
ejpam-6472	472	14	,	,	PUNCT
ejpam-6472	472	15	where	where	SCONJ
ejpam-6472	472	16	◦	◦	NOUN
ejpam-6472	472	17	denotes	denote	VERB
ejpam-6472	472	18	the	the	DET
ejpam-6472	472	19	composition	composition	NOUN
ejpam-6472	472	20	of	of	ADP
ejpam-6472	472	21	binary	binary	ADJ
ejpam-6472	472	22	relations	relation	NOUN
ejpam-6472	472	23	.	.	PUNCT
ejpam-6472	473	1	finally	finally	ADV
ejpam-6472	473	2	,	,	PUNCT
ejpam-6472	473	3	xj	xj	PROPN
ejpam-6472	473	4	y	y	PROPN
ejpam-6472	473	5	if	if	SCONJ
ejpam-6472	473	6	and	and	CCONJ
ejpam-6472	473	7	only	only	ADV
ejpam-6472	473	8	if	if	SCONJ
ejpam-6472	473	9	there	there	PRON
ejpam-6472	473	10	exist	exist	VERB
ejpam-6472	473	11	u	u	NOUN
ejpam-6472	473	12	,	,	PUNCT
ejpam-6472	473	13	v	v	PROPN
ejpam-6472	473	14	,	,	PUNCT
ejpam-6472	473	15	a	a	DET
ejpam-6472	473	16	,	,	PUNCT
ejpam-6472	473	17	b	b	PROPN
ejpam-6472	473	18	∈	∈	PROPN
ejpam-6472	473	19	s1	s1	NOUN
ejpam-6472	473	20	such	such	ADJ
ejpam-6472	473	21	that	that	DET
ejpam-6472	473	22	uxv	uxv	NOUN
ejpam-6472	473	23	=	=	SYM
ejpam-6472	473	24	y	y	PROPN
ejpam-6472	473	25	and	and	CCONJ
ejpam-6472	473	26	ayb	ayb	PROPN
ejpam-6472	473	27	=	=	SYM
ejpam-6472	473	28	x.	x.	NOUN
ejpam-6472	473	29	for	for	ADP
ejpam-6472	473	30	further	further	ADJ
ejpam-6472	473	31	background	background	NOUN
ejpam-6472	473	32	on	on	ADP
ejpam-6472	473	33	green	green	PROPN
ejpam-6472	473	34	’s	’s	PART
ejpam-6472	473	35	relations	relation	NOUN
ejpam-6472	473	36	,	,	PUNCT
ejpam-6472	473	37	we	we	PRON
ejpam-6472	473	38	refer	refer	VERB
ejpam-6472	473	39	the	the	DET
ejpam-6472	473	40	reader	reader	NOUN
ejpam-6472	473	41	to	to	ADP
ejpam-6472	473	42	[	[	X
ejpam-6472	473	43	14	14	NUM
ejpam-6472	473	44	]	]	PUNCT
ejpam-6472	473	45	.	.	PUNCT
ejpam-6472	474	1	theorem	theorem	ADJ
ejpam-6472	474	2	8	8	NUM
ejpam-6472	474	3	.	.	PUNCT
ejpam-6472	475	1	let	let	VERB
ejpam-6472	475	2	r	r	NOUN
ejpam-6472	475	3	,	,	PUNCT
ejpam-6472	475	4	s	s	NOUN
ejpam-6472	475	5	∈	∈	PROPN
ejpam-6472	475	6	wτ	wτ	NOUN
ejpam-6472	475	7	(	(	PUNCT
ejpam-6472	475	8	xn	xn	X
ejpam-6472	475	9	)	)	PUNCT
ejpam-6472	475	10	be	be	AUX
ejpam-6472	475	11	fixed	fix	VERB
ejpam-6472	475	12	terms	term	NOUN
ejpam-6472	475	13	,	,	PUNCT
ejpam-6472	475	14	and	and	CCONJ
ejpam-6472	475	15	let	let	VERB
ejpam-6472	475	16	t	t	PROPN
ejpam-6472	475	17	,	,	PUNCT
ejpam-6472	475	18	q	q	PROPN
ejpam-6472	475	19	∈	∈	PROPN
ejpam-6472	475	20	w	w	NOUN
ejpam-6472	475	21	r	r	NOUN
ejpam-6472	475	22	,	,	PUNCT
ejpam-6472	475	23	s	s	PART
ejpam-6472	475	24	τ	τ	X
ejpam-6472	475	25	(	(	PUNCT
ejpam-6472	475	26	xn	xn	PROPN
ejpam-6472	475	27	)	)	PUNCT
ejpam-6472	475	28	.	.	PUNCT
ejpam-6472	476	1	then	then	ADV
ejpam-6472	476	2	tl	tl	PROPN
ejpam-6472	476	3	q	q	X
ejpam-6472	476	4	if	if	SCONJ
ejpam-6472	476	5	and	and	CCONJ
ejpam-6472	476	6	only	only	ADV
ejpam-6472	476	7	if	if	SCONJ
ejpam-6472	476	8	{	{	PUNCT
ejpam-6472	476	9	r	r	NOUN
ejpam-6472	476	10	,	,	PUNCT
ejpam-6472	476	11	s	s	NOUN
ejpam-6472	476	12	}	}	PUNCT
ejpam-6472	476	13	∩	∩	NOUN
ejpam-6472	476	14	(	(	PUNCT
ejpam-6472	476	15	sub(t	sub(t	NOUN
ejpam-6472	476	16	)	)	PUNCT
ejpam-6472	476	17	∪	∪	ADP
ejpam-6472	476	18	sub(q	sub(q	PROPN
ejpam-6472	476	19	)	)	PUNCT
ejpam-6472	476	20	)	)	PUNCT
ejpam-6472	477	1	=	=	NOUN
ejpam-6472	477	2	∅	∅	NOUN
ejpam-6472	477	3	or	or	CCONJ
ejpam-6472	477	4	t	t	NOUN
ejpam-6472	477	5	=	=	PUNCT
ejpam-6472	478	1	q.	q.	PROPN
ejpam-6472	478	2	p.	p.	PROPN
ejpam-6472	478	3	prachumdang	prachumdang	PROPN
ejpam-6472	478	4	,	,	PUNCT
ejpam-6472	478	5	b.	b.	PROPN
ejpam-6472	478	6	pibaljommee	pibaljommee	PROPN
ejpam-6472	478	7	/	/	SYM
ejpam-6472	478	8	eur	eur	PROPN
ejpam-6472	478	9	.	.	PUNCT
ejpam-6472	479	1	j.	j.	PROPN
ejpam-6472	479	2	pure	pure	PROPN
ejpam-6472	479	3	appl	appl	PROPN
ejpam-6472	479	4	.	.	PROPN
ejpam-6472	479	5	math	math	PROPN
ejpam-6472	479	6	,	,	PUNCT
ejpam-6472	479	7	18	18	NUM
ejpam-6472	479	8	(	(	PUNCT
ejpam-6472	479	9	3	3	NUM
ejpam-6472	479	10	)	)	PUNCT
ejpam-6472	479	11	(	(	PUNCT
ejpam-6472	479	12	2025	2025	NUM
ejpam-6472	479	13	)	)	PUNCT
ejpam-6472	479	14	,	,	PUNCT
ejpam-6472	479	15	6472	6472	NUM
ejpam-6472	479	16	13	13	NUM
ejpam-6472	479	17	of	of	ADP
ejpam-6472	479	18	16	16	NUM
ejpam-6472	479	19	proof	proof	NOUN
ejpam-6472	479	20	.	.	PUNCT
ejpam-6472	480	1	assume	assume	VERB
ejpam-6472	480	2	that	that	SCONJ
ejpam-6472	480	3	tl	tl	PROPN
ejpam-6472	480	4	q	q	PROPN
ejpam-6472	480	5	and	and	CCONJ
ejpam-6472	480	6	{	{	PUNCT
ejpam-6472	480	7	r	r	NOUN
ejpam-6472	480	8	,	,	PUNCT
ejpam-6472	480	9	s}∩	s}∩	PROPN
ejpam-6472	480	10	(	(	PUNCT
ejpam-6472	480	11	sub(t)∪	sub(t)∪	NOUN
ejpam-6472	480	12	sub(q	sub(q	PROPN
ejpam-6472	480	13	)	)	PUNCT
ejpam-6472	480	14	)	)	PUNCT
ejpam-6472	481	1	̸=	̸=	PROPN
ejpam-6472	481	2	∅.	∅.	ADV
ejpam-6472	481	3	without	without	ADP
ejpam-6472	481	4	loss	loss	NOUN
ejpam-6472	481	5	of	of	ADP
ejpam-6472	481	6	generality	generality	NOUN
ejpam-6472	481	7	,	,	PUNCT
ejpam-6472	481	8	assume	assume	VERB
ejpam-6472	481	9	{	{	PUNCT
ejpam-6472	481	10	r	r	NOUN
ejpam-6472	481	11	,	,	PUNCT
ejpam-6472	481	12	s	s	NOUN
ejpam-6472	481	13	}	}	PUNCT
ejpam-6472	481	14	∩	∩	ADJ
ejpam-6472	481	15	sub(t	sub(t	NOUN
ejpam-6472	481	16	)	)	PUNCT
ejpam-6472	481	17	̸=	̸=	PROPN
ejpam-6472	481	18	∅.	∅.	ADV
ejpam-6472	481	19	since	since	SCONJ
ejpam-6472	481	20	tl	tl	PROPN
ejpam-6472	481	21	q	q	X
ejpam-6472	481	22	,	,	PUNCT
ejpam-6472	481	23	there	there	PRON
ejpam-6472	481	24	exist	exist	VERB
ejpam-6472	481	25	u	u	NOUN
ejpam-6472	481	26	,	,	PUNCT
ejpam-6472	481	27	v	v	PROPN
ejpam-6472	481	28	∈	∈	PROPN
ejpam-6472	481	29	(	(	PUNCT
ejpam-6472	481	30	w	w	NOUN
ejpam-6472	481	31	r	r	NOUN
ejpam-6472	481	32	,	,	PUNCT
ejpam-6472	481	33	s	s	PART
ejpam-6472	481	34	τ	τ	X
ejpam-6472	481	35	(	(	PUNCT
ejpam-6472	481	36	xn	xn	PROPN
ejpam-6472	481	37	)	)	PUNCT
ejpam-6472	481	38	)	)	PUNCT
ejpam-6472	482	1	1	1	NUM
ejpam-6472	482	2	such	such	ADJ
ejpam-6472	482	3	that	that	SCONJ
ejpam-6472	482	4	u	u	NOUN
ejpam-6472	482	5	·	·	PUNCT
ejpam-6472	482	6	rs	rs	X
ejpam-6472	482	7	t	t	PROPN
ejpam-6472	482	8	=	=	PUNCT
ejpam-6472	482	9	q	q	PROPN
ejpam-6472	482	10	and	and	CCONJ
ejpam-6472	482	11	v	v	ADP
ejpam-6472	482	12	·	·	PUNCT
ejpam-6472	482	13	rs	rs	NOUN
ejpam-6472	482	14	q	q	NOUN
ejpam-6472	482	15	=	=	PUNCT
ejpam-6472	482	16	t.	t.	NOUN
ejpam-6472	482	17	if	if	SCONJ
ejpam-6472	482	18	u	u	PROPN
ejpam-6472	482	19	=	=	NOUN
ejpam-6472	482	20	1	1	NUM
ejpam-6472	482	21	or	or	CCONJ
ejpam-6472	482	22	v	v	NOUN
ejpam-6472	482	23	=	=	SYM
ejpam-6472	482	24	1	1	NUM
ejpam-6472	482	25	,	,	PUNCT
ejpam-6472	482	26	then	then	ADV
ejpam-6472	482	27	t	t	PROPN
ejpam-6472	482	28	=	=	SYM
ejpam-6472	483	1	q	q	X
ejpam-6472	483	2	,	,	PUNCT
ejpam-6472	483	3	and	and	CCONJ
ejpam-6472	483	4	we	we	PRON
ejpam-6472	483	5	are	be	AUX
ejpam-6472	483	6	done	do	VERB
ejpam-6472	483	7	.	.	PUNCT
ejpam-6472	484	1	next	next	ADV
ejpam-6472	484	2	,	,	PUNCT
ejpam-6472	484	3	assume	assume	VERB
ejpam-6472	484	4	u	u	NOUN
ejpam-6472	484	5	,	,	PUNCT
ejpam-6472	484	6	v	v	NOUN
ejpam-6472	484	7	∈	∈	PROPN
ejpam-6472	484	8	w	w	NOUN
ejpam-6472	484	9	r	r	NOUN
ejpam-6472	484	10	,	,	PUNCT
ejpam-6472	484	11	s	s	PART
ejpam-6472	484	12	τ	τ	X
ejpam-6472	484	13	(	(	PUNCT
ejpam-6472	484	14	xn	xn	PROPN
ejpam-6472	484	15	)	)	PUNCT
ejpam-6472	484	16	.	.	PUNCT
ejpam-6472	485	1	by	by	ADP
ejpam-6472	485	2	lemma	lemma	PROPN
ejpam-6472	485	3	5	5	NUM
ejpam-6472	485	4	,	,	PUNCT
ejpam-6472	485	5	we	we	PRON
ejpam-6472	485	6	have	have	VERB
ejpam-6472	485	7	{	{	PUNCT
ejpam-6472	485	8	r	r	NOUN
ejpam-6472	485	9	,	,	PUNCT
ejpam-6472	485	10	s	s	NOUN
ejpam-6472	485	11	}	}	PUNCT
ejpam-6472	485	12	∩	∩	ADJ
ejpam-6472	485	13	sub(v	sub(v	NOUN
ejpam-6472	485	14	)	)	PUNCT
ejpam-6472	485	15	̸=	̸=	PROPN
ejpam-6472	485	16	∅	∅	NOUN
ejpam-6472	485	17	and	and	CCONJ
ejpam-6472	485	18	{	{	PUNCT
ejpam-6472	485	19	r	r	NOUN
ejpam-6472	485	20	,	,	PUNCT
ejpam-6472	485	21	s	s	NOUN
ejpam-6472	485	22	}	}	PUNCT
ejpam-6472	485	23	∩	∩	ADJ
ejpam-6472	485	24	sub(u	sub(u	PROPN
ejpam-6472	485	25	)	)	PUNCT
ejpam-6472	485	26	̸=	̸=	PROPN
ejpam-6472	485	27	∅.	∅.	NOUN
ejpam-6472	485	28	then	then	ADV
ejpam-6472	485	29	,	,	PUNCT
ejpam-6472	485	30	by	by	ADP
ejpam-6472	485	31	lemma	lemma	PROPN
ejpam-6472	485	32	1	1	NUM
ejpam-6472	485	33	,	,	PUNCT
ejpam-6472	485	34	it	it	PRON
ejpam-6472	485	35	follows	follow	VERB
ejpam-6472	485	36	that	that	SCONJ
ejpam-6472	485	37	t	t	PROPN
ejpam-6472	485	38	∈	∈	PROPN
ejpam-6472	485	39	sub(u	sub(u	PROPN
ejpam-6472	485	40	·	·	SYM
ejpam-6472	485	41	rs	rs	PROPN
ejpam-6472	485	42	t	t	PROPN
ejpam-6472	485	43	)	)	PUNCT
ejpam-6472	485	44	=	=	SYM
ejpam-6472	485	45	sub(q	sub(q	PROPN
ejpam-6472	485	46	)	)	PUNCT
ejpam-6472	485	47	and	and	CCONJ
ejpam-6472	485	48	q	q	PROPN
ejpam-6472	485	49	∈	∈	PROPN
ejpam-6472	485	50	sub(v	sub(v	NOUN
ejpam-6472	485	51	·	·	SYM
ejpam-6472	485	52	rs	rs	X
ejpam-6472	485	53	q	q	NOUN
ejpam-6472	485	54	)	)	PUNCT
ejpam-6472	485	55	=	=	SYM
ejpam-6472	485	56	sub(t	sub(t	PROPN
ejpam-6472	485	57	)	)	PUNCT
ejpam-6472	485	58	.	.	PUNCT
ejpam-6472	486	1	hence	hence	ADV
ejpam-6472	486	2	,	,	PUNCT
ejpam-6472	486	3	t	t	PROPN
ejpam-6472	486	4	=	=	PUNCT
ejpam-6472	486	5	q.	q.	NOUN
ejpam-6472	486	6	the	the	DET
ejpam-6472	486	7	converse	converse	NOUN
ejpam-6472	486	8	is	be	AUX
ejpam-6472	486	9	clear	clear	ADJ
ejpam-6472	486	10	.	.	PUNCT
ejpam-6472	487	1	theorem	theorem	ADJ
ejpam-6472	487	2	9	9	NUM
ejpam-6472	487	3	.	.	PUNCT
ejpam-6472	488	1	let	let	VERB
ejpam-6472	488	2	r	r	NOUN
ejpam-6472	488	3	,	,	PUNCT
ejpam-6472	488	4	s	s	NOUN
ejpam-6472	488	5	∈	∈	PROPN
ejpam-6472	488	6	wτ	wτ	NOUN
ejpam-6472	488	7	(	(	PUNCT
ejpam-6472	488	8	xn	xn	X
ejpam-6472	488	9	)	)	PUNCT
ejpam-6472	488	10	be	be	AUX
ejpam-6472	488	11	fixed	fix	VERB
ejpam-6472	488	12	terms	term	NOUN
ejpam-6472	488	13	,	,	PUNCT
ejpam-6472	488	14	and	and	CCONJ
ejpam-6472	488	15	let	let	VERB
ejpam-6472	488	16	t	t	PROPN
ejpam-6472	488	17	,	,	PUNCT
ejpam-6472	488	18	q	q	PROPN
ejpam-6472	488	19	∈	∈	PROPN
ejpam-6472	488	20	w	w	NOUN
ejpam-6472	488	21	r	r	NOUN
ejpam-6472	488	22	,	,	PUNCT
ejpam-6472	488	23	s	s	PART
ejpam-6472	488	24	τ	τ	X
ejpam-6472	488	25	(	(	PUNCT
ejpam-6472	488	26	xn	xn	PROPN
ejpam-6472	488	27	)	)	PUNCT
ejpam-6472	488	28	.	.	PUNCT
ejpam-6472	489	1	then	then	ADV
ejpam-6472	489	2	tr	tr	VERB
ejpam-6472	489	3	q	q	PROPN
ejpam-6472	489	4	if	if	SCONJ
ejpam-6472	489	5	and	and	CCONJ
ejpam-6472	489	6	only	only	ADV
ejpam-6472	489	7	if	if	SCONJ
ejpam-6472	489	8	t	t	NOUN
ejpam-6472	489	9	=	=	SYM
ejpam-6472	489	10	q	q	X
ejpam-6472	489	11	or	or	CCONJ
ejpam-6472	489	12	there	there	ADV
ejpam-6472	489	13	exists	exist	VERB
ejpam-6472	489	14	u	u	NOUN
ejpam-6472	489	15	,	,	PUNCT
ejpam-6472	489	16	v	v	PROPN
ejpam-6472	489	17	∈	∈	PROPN
ejpam-6472	489	18	{	{	PUNCT
ejpam-6472	489	19	r	r	NOUN
ejpam-6472	489	20	,	,	PUNCT
ejpam-6472	489	21	s	s	PART
ejpam-6472	489	22	}	}	PUNCT
ejpam-6472	489	23	such	such	ADJ
ejpam-6472	489	24	that	that	SCONJ
ejpam-6472	489	25	t	t	NOUN
ejpam-6472	489	26	·	·	PUNCT
ejpam-6472	489	27	rs	rs	NOUN
ejpam-6472	489	28	u	u	NOUN
ejpam-6472	489	29	=	=	PROPN
ejpam-6472	489	30	q	q	X
ejpam-6472	489	31	and	and	CCONJ
ejpam-6472	489	32	q	q	ADJ
ejpam-6472	489	33	·	·	PUNCT
ejpam-6472	489	34	rs	rs	NOUN
ejpam-6472	489	35	v	v	NOUN
ejpam-6472	489	36	=	=	PUNCT
ejpam-6472	489	37	t.	t.	NOUN
ejpam-6472	489	38	proof	proof	NOUN
ejpam-6472	489	39	.	.	PUNCT
ejpam-6472	490	1	assume	assume	VERB
ejpam-6472	490	2	that	that	SCONJ
ejpam-6472	490	3	tr	tr	NOUN
ejpam-6472	490	4	q.	q.	NOUN
ejpam-6472	490	5	then	then	ADV
ejpam-6472	490	6	there	there	PRON
ejpam-6472	490	7	exists	exist	VERB
ejpam-6472	490	8	u	u	NOUN
ejpam-6472	490	9	,	,	PUNCT
ejpam-6472	490	10	v	v	NOUN
ejpam-6472	490	11	∈	∈	PROPN
ejpam-6472	490	12	(	(	PUNCT
ejpam-6472	490	13	w	w	NOUN
ejpam-6472	490	14	r	r	NOUN
ejpam-6472	490	15	,	,	PUNCT
ejpam-6472	490	16	s	s	PART
ejpam-6472	490	17	τ	τ	X
ejpam-6472	490	18	(	(	PUNCT
ejpam-6472	490	19	xn	xn	PROPN
ejpam-6472	490	20	)	)	PUNCT
ejpam-6472	490	21	)	)	PUNCT
ejpam-6472	491	1	1	1	NUM
ejpam-6472	491	2	such	such	ADJ
ejpam-6472	491	3	that	that	SCONJ
ejpam-6472	491	4	t	t	NOUN
ejpam-6472	491	5	·	·	PUNCT
ejpam-6472	491	6	rs	rs	NOUN
ejpam-6472	491	7	u	u	NOUN
ejpam-6472	491	8	=	=	PROPN
ejpam-6472	491	9	q	q	X
ejpam-6472	491	10	and	and	CCONJ
ejpam-6472	491	11	q	q	ADJ
ejpam-6472	491	12	·	·	PUNCT
ejpam-6472	491	13	rs	rs	NOUN
ejpam-6472	491	14	v	v	NOUN
ejpam-6472	491	15	=	=	PUNCT
ejpam-6472	491	16	t.	t.	NOUN
ejpam-6472	491	17	if	if	SCONJ
ejpam-6472	491	18	u	u	PROPN
ejpam-6472	491	19	=	=	NOUN
ejpam-6472	491	20	1	1	NUM
ejpam-6472	491	21	or	or	CCONJ
ejpam-6472	491	22	v	v	NOUN
ejpam-6472	491	23	=	=	SYM
ejpam-6472	491	24	1	1	NUM
ejpam-6472	491	25	,	,	PUNCT
ejpam-6472	491	26	then	then	ADV
ejpam-6472	491	27	t	t	PROPN
ejpam-6472	491	28	=	=	SYM
ejpam-6472	491	29	q	q	X
ejpam-6472	491	30	,	,	PUNCT
ejpam-6472	491	31	and	and	CCONJ
ejpam-6472	491	32	the	the	DET
ejpam-6472	491	33	result	result	NOUN
ejpam-6472	491	34	follows	follow	VERB
ejpam-6472	491	35	.	.	PUNCT
ejpam-6472	492	1	now	now	ADV
ejpam-6472	492	2	,	,	PUNCT
ejpam-6472	492	3	we	we	PRON
ejpam-6472	492	4	assume	assume	VERB
ejpam-6472	492	5	that	that	SCONJ
ejpam-6472	492	6	u	u	NOUN
ejpam-6472	492	7	,	,	PUNCT
ejpam-6472	492	8	v	v	ADP
ejpam-6472	492	9	∈	∈	PROPN
ejpam-6472	492	10	w	w	NOUN
ejpam-6472	492	11	r	r	NOUN
ejpam-6472	492	12	,	,	PUNCT
ejpam-6472	492	13	s	s	PART
ejpam-6472	492	14	τ	τ	X
ejpam-6472	492	15	(	(	PUNCT
ejpam-6472	492	16	xn	xn	PROPN
ejpam-6472	492	17	)	)	PUNCT
ejpam-6472	492	18	.	.	PUNCT
ejpam-6472	493	1	if	if	SCONJ
ejpam-6472	493	2	{	{	PUNCT
ejpam-6472	493	3	r	r	NOUN
ejpam-6472	493	4	,	,	PUNCT
ejpam-6472	493	5	s	s	NOUN
ejpam-6472	493	6	}	}	PUNCT
ejpam-6472	493	7	∩	∩	ADJ
ejpam-6472	493	8	sub(t	sub(t	NOUN
ejpam-6472	493	9	)	)	PUNCT
ejpam-6472	493	10	=	=	NOUN
ejpam-6472	493	11	∅	∅	NOUN
ejpam-6472	493	12	,	,	PUNCT
ejpam-6472	493	13	then	then	ADV
ejpam-6472	493	14	t	t	PROPN
ejpam-6472	493	15	=	=	SYM
ejpam-6472	493	16	t	t	PROPN
ejpam-6472	493	17	·	·	PUNCT
ejpam-6472	493	18	rs	rs	NOUN
ejpam-6472	493	19	u	u	NOUN
ejpam-6472	493	20	=	=	X
ejpam-6472	493	21	q.	q.	PROPN
ejpam-6472	494	1	if	if	SCONJ
ejpam-6472	494	2	{	{	PUNCT
ejpam-6472	494	3	r	r	NOUN
ejpam-6472	494	4	,	,	PUNCT
ejpam-6472	494	5	s	s	NOUN
ejpam-6472	494	6	}	}	PUNCT
ejpam-6472	494	7	∩	∩	ADJ
ejpam-6472	494	8	sub(t	sub(t	NOUN
ejpam-6472	494	9	)	)	PUNCT
ejpam-6472	494	10	̸=	̸=	NOUN
ejpam-6472	494	11	∅	∅	NOUN
ejpam-6472	494	12	,	,	PUNCT
ejpam-6472	494	13	we	we	PRON
ejpam-6472	494	14	consider	consider	VERB
ejpam-6472	494	15	t	t	NOUN
ejpam-6472	494	16	=	=	SYM
ejpam-6472	494	17	q	q	X
ejpam-6472	494	18	·	·	PUNCT
ejpam-6472	494	19	rs	rs	NOUN
ejpam-6472	494	20	v	v	NOUN
ejpam-6472	494	21	=	=	SYM
ejpam-6472	494	22	t	t	NOUN
ejpam-6472	494	23	·	·	PUNCT
ejpam-6472	494	24	rs	rs	X
ejpam-6472	494	25	u	u	NOUN
ejpam-6472	494	26	·	·	PUNCT
ejpam-6472	494	27	rs	rs	NOUN
ejpam-6472	494	28	v	v	NOUN
ejpam-6472	494	29	=	=	SYM
ejpam-6472	494	30	r	r	NOUN
ejpam-6472	494	31	·	·	PUNCT
ejpam-6472	494	32	rs	rs	NOUN
ejpam-6472	494	33	t	t	PROPN
ejpam-6472	494	34	·	·	PUNCT
ejpam-6472	494	35	rs	rs	X
ejpam-6472	494	36	u	u	NOUN
ejpam-6472	494	37	·	·	PUNCT
ejpam-6472	494	38	rs	rs	X
ejpam-6472	494	39	v.	v.	ADV
ejpam-6472	494	40	by	by	ADP
ejpam-6472	494	41	lemma	lemma	PROPN
ejpam-6472	494	42	7	7	NUM
ejpam-6472	494	43	,	,	PUNCT
ejpam-6472	494	44	we	we	PRON
ejpam-6472	494	45	obtain	obtain	VERB
ejpam-6472	494	46	that	that	SCONJ
ejpam-6472	494	47	u·rsv	u·rsv	PROPN
ejpam-6472	494	48	∈	∈	PROPN
ejpam-6472	494	49	{	{	PUNCT
ejpam-6472	494	50	r	r	NOUN
ejpam-6472	494	51	,	,	PUNCT
ejpam-6472	494	52	s	s	PART
ejpam-6472	494	53	}	}	PUNCT
ejpam-6472	494	54	.	.	PUNCT
ejpam-6472	495	1	then	then	ADV
ejpam-6472	495	2	,	,	PUNCT
ejpam-6472	495	3	by	by	ADP
ejpam-6472	495	4	lemma	lemma	PROPN
ejpam-6472	495	5	6	6	NUM
ejpam-6472	495	6	,	,	PUNCT
ejpam-6472	495	7	it	it	PRON
ejpam-6472	495	8	follows	follow	VERB
ejpam-6472	495	9	that	that	SCONJ
ejpam-6472	495	10	u	u	NOUN
ejpam-6472	495	11	,	,	PUNCT
ejpam-6472	495	12	v	v	PROPN
ejpam-6472	495	13	∈	∈	PROPN
ejpam-6472	495	14	{	{	PUNCT
ejpam-6472	495	15	r	r	NOUN
ejpam-6472	495	16	,	,	PUNCT
ejpam-6472	495	17	s	s	PART
ejpam-6472	495	18	}	}	PUNCT
ejpam-6472	495	19	.	.	PUNCT
ejpam-6472	496	1	the	the	DET
ejpam-6472	496	2	converse	converse	NOUN
ejpam-6472	496	3	is	be	AUX
ejpam-6472	496	4	straightforward	straightforward	ADJ
ejpam-6472	496	5	.	.	PUNCT
ejpam-6472	497	1	theorem	theorem	ADJ
ejpam-6472	497	2	10	10	NUM
ejpam-6472	497	3	.	.	PUNCT
ejpam-6472	498	1	let	let	VERB
ejpam-6472	498	2	r	r	NOUN
ejpam-6472	498	3	,	,	PUNCT
ejpam-6472	498	4	s	s	NOUN
ejpam-6472	498	5	∈	∈	PROPN
ejpam-6472	498	6	wτ	wτ	NOUN
ejpam-6472	498	7	(	(	PUNCT
ejpam-6472	498	8	xn	xn	X
ejpam-6472	498	9	)	)	PUNCT
ejpam-6472	498	10	be	be	AUX
ejpam-6472	498	11	fixed	fix	VERB
ejpam-6472	498	12	terms	term	NOUN
ejpam-6472	498	13	,	,	PUNCT
ejpam-6472	498	14	and	and	CCONJ
ejpam-6472	498	15	let	let	VERB
ejpam-6472	498	16	t	t	PROPN
ejpam-6472	498	17	,	,	PUNCT
ejpam-6472	498	18	q	q	PROPN
ejpam-6472	498	19	∈	∈	PROPN
ejpam-6472	498	20	w	w	NOUN
ejpam-6472	498	21	r	r	NOUN
ejpam-6472	498	22	,	,	PUNCT
ejpam-6472	498	23	s	s	PART
ejpam-6472	498	24	τ	τ	X
ejpam-6472	498	25	(	(	PUNCT
ejpam-6472	498	26	xn	xn	PROPN
ejpam-6472	498	27	)	)	PUNCT
ejpam-6472	498	28	.	.	PUNCT
ejpam-6472	499	1	then	then	ADV
ejpam-6472	499	2	th	th	X
ejpam-6472	499	3	q	q	NOUN
ejpam-6472	499	4	if	if	SCONJ
ejpam-6472	499	5	and	and	CCONJ
ejpam-6472	499	6	only	only	ADV
ejpam-6472	499	7	if	if	SCONJ
ejpam-6472	499	8	t	t	NOUN
ejpam-6472	499	9	=	=	SYM
ejpam-6472	499	10	q.	q.	NOUN
ejpam-6472	499	11	proof	proof	NOUN
ejpam-6472	499	12	.	.	PUNCT
ejpam-6472	500	1	assume	assume	VERB
ejpam-6472	500	2	th	th	X
ejpam-6472	500	3	q	q	PUNCT
ejpam-6472	500	4	and	and	CCONJ
ejpam-6472	500	5	suppose	suppose	VERB
ejpam-6472	500	6	t	t	PROPN
ejpam-6472	500	7	̸=	̸=	PROPN
ejpam-6472	500	8	q.	q.	NOUN
ejpam-6472	500	9	then	then	ADV
ejpam-6472	500	10	tl	tl	PROPN
ejpam-6472	500	11	q	q	PROPN
ejpam-6472	501	1	and	and	CCONJ
ejpam-6472	501	2	tr	tr	PROPN
ejpam-6472	501	3	q.	q.	PROPN
ejpam-6472	501	4	therefore	therefore	ADV
ejpam-6472	501	5	,	,	PUNCT
ejpam-6472	501	6	there	there	PRON
ejpam-6472	501	7	is	be	VERB
ejpam-6472	501	8	u	u	NOUN
ejpam-6472	501	9	∈	∈	PROPN
ejpam-6472	501	10	w	w	PROPN
ejpam-6472	501	11	r	r	NOUN
ejpam-6472	501	12	,	,	PUNCT
ejpam-6472	501	13	s	s	PART
ejpam-6472	501	14	τ	τ	X
ejpam-6472	501	15	(	(	PUNCT
ejpam-6472	501	16	xn	xn	PROPN
ejpam-6472	501	17	)	)	PUNCT
ejpam-6472	501	18	such	such	ADJ
ejpam-6472	501	19	that	that	SCONJ
ejpam-6472	501	20	t	t	NOUN
ejpam-6472	501	21	·	·	PUNCT
ejpam-6472	501	22	rs	rs	NOUN
ejpam-6472	501	23	u	u	NOUN
ejpam-6472	501	24	=	=	PUNCT
ejpam-6472	501	25	q.	q.	NOUN
ejpam-6472	501	26	by	by	ADP
ejpam-6472	501	27	theorem	theorem	NOUN
ejpam-6472	501	28	8	8	NUM
ejpam-6472	501	29	,	,	PUNCT
ejpam-6472	501	30	it	it	PRON
ejpam-6472	501	31	follows	follow	VERB
ejpam-6472	501	32	that	that	SCONJ
ejpam-6472	501	33	{	{	PUNCT
ejpam-6472	501	34	r	r	NOUN
ejpam-6472	501	35	,	,	PUNCT
ejpam-6472	501	36	s	s	NOUN
ejpam-6472	501	37	}	}	PUNCT
ejpam-6472	501	38	∩	∩	ADJ
ejpam-6472	501	39	sub(t	sub(t	NOUN
ejpam-6472	501	40	)	)	PUNCT
ejpam-6472	501	41	=	=	PUNCT
ejpam-6472	501	42	∅.	∅.	ADP
ejpam-6472	501	43	thus	thus	ADV
ejpam-6472	501	44	,	,	PUNCT
ejpam-6472	501	45	t	t	PROPN
ejpam-6472	501	46	=	=	SYM
ejpam-6472	501	47	t	t	PROPN
ejpam-6472	501	48	·	·	PUNCT
ejpam-6472	501	49	rs	rs	NOUN
ejpam-6472	501	50	u	u	NOUN
ejpam-6472	501	51	=	=	PROPN
ejpam-6472	501	52	q	q	PROPN
ejpam-6472	501	53	,	,	PUNCT
ejpam-6472	501	54	a	a	DET
ejpam-6472	501	55	contradiction	contradiction	NOUN
ejpam-6472	501	56	.	.	PUNCT
ejpam-6472	502	1	the	the	DET
ejpam-6472	502	2	reverse	reverse	ADJ
ejpam-6472	502	3	implication	implication	NOUN
ejpam-6472	502	4	holds	hold	VERB
ejpam-6472	502	5	by	by	ADP
ejpam-6472	502	6	the	the	DET
ejpam-6472	502	7	reflexivity	reflexivity	NOUN
ejpam-6472	502	8	of	of	ADP
ejpam-6472	502	9	h.	h.	PROPN
ejpam-6472	502	10	theorem	theorem	PROPN
ejpam-6472	502	11	11	11	NUM
ejpam-6472	502	12	.	.	PUNCT
ejpam-6472	503	1	let	let	VERB
ejpam-6472	503	2	r	r	NOUN
ejpam-6472	503	3	,	,	PUNCT
ejpam-6472	503	4	s	s	NOUN
ejpam-6472	503	5	∈	∈	PROPN
ejpam-6472	503	6	wτ	wτ	NOUN
ejpam-6472	503	7	(	(	PUNCT
ejpam-6472	503	8	xn	xn	X
ejpam-6472	503	9	)	)	PUNCT
ejpam-6472	503	10	be	be	AUX
ejpam-6472	503	11	fixed	fix	VERB
ejpam-6472	503	12	terms	term	NOUN
ejpam-6472	503	13	,	,	PUNCT
ejpam-6472	503	14	and	and	CCONJ
ejpam-6472	503	15	let	let	VERB
ejpam-6472	503	16	t	t	PROPN
ejpam-6472	503	17	,	,	PUNCT
ejpam-6472	503	18	q	q	PROPN
ejpam-6472	503	19	∈	∈	PROPN
ejpam-6472	503	20	w	w	NOUN
ejpam-6472	503	21	r	r	NOUN
ejpam-6472	503	22	,	,	PUNCT
ejpam-6472	503	23	s	s	PART
ejpam-6472	503	24	τ	τ	X
ejpam-6472	503	25	(	(	PUNCT
ejpam-6472	503	26	xn	xn	PROPN
ejpam-6472	503	27	)	)	PUNCT
ejpam-6472	503	28	.	.	PUNCT
ejpam-6472	504	1	then	then	ADV
ejpam-6472	504	2	the	the	DET
ejpam-6472	504	3	following	following	ADJ
ejpam-6472	504	4	statements	statement	NOUN
ejpam-6472	504	5	hold	hold	VERB
ejpam-6472	504	6	:	:	PUNCT
ejpam-6472	504	7	(	(	PUNCT
ejpam-6472	504	8	i	i	NOUN
ejpam-6472	504	9	)	)	PUNCT
ejpam-6472	504	10	if	if	SCONJ
ejpam-6472	504	11	{	{	PUNCT
ejpam-6472	504	12	r	r	NOUN
ejpam-6472	504	13	,	,	PUNCT
ejpam-6472	504	14	s	s	NOUN
ejpam-6472	504	15	}	}	PUNCT
ejpam-6472	504	16	∩	∩	ADJ
ejpam-6472	504	17	sub(t	sub(t	NOUN
ejpam-6472	504	18	)	)	PUNCT
ejpam-6472	504	19	=	=	NOUN
ejpam-6472	504	20	∅	∅	NOUN
ejpam-6472	504	21	,	,	PUNCT
ejpam-6472	504	22	then	then	ADV
ejpam-6472	504	23	td	td	VERB
ejpam-6472	504	24	q	q	PUNCT
ejpam-6472	504	25	if	if	SCONJ
ejpam-6472	505	1	and	and	CCONJ
ejpam-6472	505	2	only	only	ADV
ejpam-6472	505	3	if	if	SCONJ
ejpam-6472	505	4	tl	tl	PROPN
ejpam-6472	505	5	q.	q.	PROPN
ejpam-6472	505	6	(	(	PUNCT
ejpam-6472	505	7	ii	ii	PROPN
ejpam-6472	505	8	)	)	PUNCT
ejpam-6472	505	9	if	if	SCONJ
ejpam-6472	505	10	{	{	PUNCT
ejpam-6472	505	11	r	r	NOUN
ejpam-6472	505	12	,	,	PUNCT
ejpam-6472	505	13	s	s	NOUN
ejpam-6472	505	14	}	}	PUNCT
ejpam-6472	505	15	∩	∩	ADJ
ejpam-6472	505	16	sub(t	sub(t	NOUN
ejpam-6472	505	17	)	)	PUNCT
ejpam-6472	505	18	̸=	̸=	NOUN
ejpam-6472	505	19	∅	∅	NOUN
ejpam-6472	505	20	,	,	PUNCT
ejpam-6472	505	21	then	then	ADV
ejpam-6472	505	22	td	td	VERB
ejpam-6472	505	23	q	q	PUNCT
ejpam-6472	505	24	if	if	SCONJ
ejpam-6472	505	25	and	and	CCONJ
ejpam-6472	505	26	only	only	ADV
ejpam-6472	505	27	if	if	SCONJ
ejpam-6472	505	28	tr	tr	VERB
ejpam-6472	505	29	q.	q.	NOUN
ejpam-6472	505	30	proof	proof	NOUN
ejpam-6472	505	31	.	.	PUNCT
ejpam-6472	506	1	(	(	PUNCT
ejpam-6472	506	2	i	i	NOUN
ejpam-6472	506	3	)	)	PUNCT
ejpam-6472	506	4	assume	assume	VERB
ejpam-6472	506	5	that	that	SCONJ
ejpam-6472	506	6	{	{	PUNCT
ejpam-6472	506	7	r	r	NOUN
ejpam-6472	506	8	,	,	PUNCT
ejpam-6472	506	9	s	s	NOUN
ejpam-6472	506	10	}	}	PUNCT
ejpam-6472	506	11	∩	∩	ADJ
ejpam-6472	506	12	sub(t	sub(t	NOUN
ejpam-6472	506	13	)	)	PUNCT
ejpam-6472	506	14	=	=	NOUN
ejpam-6472	506	15	∅	∅	NOUN
ejpam-6472	506	16	and	and	CCONJ
ejpam-6472	506	17	td	td	NOUN
ejpam-6472	506	18	q.	q.	NOUN
ejpam-6472	506	19	then	then	ADV
ejpam-6472	506	20	there	there	PRON
ejpam-6472	506	21	exists	exist	VERB
ejpam-6472	506	22	u	u	NOUN
ejpam-6472	506	23	∈	∈	PROPN
ejpam-6472	506	24	w	w	PROPN
ejpam-6472	506	25	r	r	NOUN
ejpam-6472	506	26	,	,	PUNCT
ejpam-6472	506	27	s	s	PART
ejpam-6472	506	28	τ	τ	X
ejpam-6472	506	29	(	(	PUNCT
ejpam-6472	506	30	xn	xn	PROPN
ejpam-6472	506	31	)	)	PUNCT
ejpam-6472	506	32	such	such	ADJ
ejpam-6472	506	33	that	that	SCONJ
ejpam-6472	506	34	tlu	tlu	PROPN
ejpam-6472	506	35	and	and	CCONJ
ejpam-6472	506	36	ur	ur	INTJ
ejpam-6472	506	37	q.	q.	PROPN
ejpam-6472	506	38	by	by	ADP
ejpam-6472	506	39	lemma	lemma	PROPN
ejpam-6472	506	40	5	5	NUM
ejpam-6472	506	41	,	,	PUNCT
ejpam-6472	506	42	it	it	PRON
ejpam-6472	506	43	follows	follow	VERB
ejpam-6472	506	44	that	that	SCONJ
ejpam-6472	506	45	{	{	PUNCT
ejpam-6472	506	46	r	r	NOUN
ejpam-6472	506	47	,	,	PUNCT
ejpam-6472	506	48	s	s	NOUN
ejpam-6472	506	49	}	}	PUNCT
ejpam-6472	506	50	∩	∩	ADJ
ejpam-6472	506	51	sub(u	sub(u	PROPN
ejpam-6472	506	52	)	)	PUNCT
ejpam-6472	506	53	=	=	NOUN
ejpam-6472	506	54	∅	∅	NOUN
ejpam-6472	506	55	,	,	PUNCT
ejpam-6472	506	56	and	and	CCONJ
ejpam-6472	506	57	hence	hence	ADV
ejpam-6472	506	58	{	{	PUNCT
ejpam-6472	506	59	r	r	NOUN
ejpam-6472	506	60	,	,	PUNCT
ejpam-6472	506	61	s}∩	s}∩	PROPN
ejpam-6472	506	62	sub(q	sub(q	PROPN
ejpam-6472	506	63	)	)	PUNCT
ejpam-6472	506	64	=	=	PUNCT
ejpam-6472	506	65	∅.	∅.	ADP
ejpam-6472	506	66	applying	apply	VERB
ejpam-6472	506	67	theorem	theorem	NOUN
ejpam-6472	506	68	8	8	NUM
ejpam-6472	506	69	,	,	PUNCT
ejpam-6472	506	70	we	we	PRON
ejpam-6472	506	71	conclude	conclude	VERB
ejpam-6472	506	72	that	that	SCONJ
ejpam-6472	506	73	tl	tl	PROPN
ejpam-6472	506	74	q.	q.	VERB
ejpam-6472	506	75	the	the	DET
ejpam-6472	506	76	converse	converse	NOUN
ejpam-6472	506	77	is	be	AUX
ejpam-6472	506	78	obvious	obvious	ADJ
ejpam-6472	506	79	.	.	PUNCT
ejpam-6472	507	1	(	(	PUNCT
ejpam-6472	507	2	ii	ii	NOUN
ejpam-6472	507	3	)	)	PUNCT
ejpam-6472	507	4	assume	assume	VERB
ejpam-6472	507	5	that	that	SCONJ
ejpam-6472	507	6	{	{	PUNCT
ejpam-6472	507	7	r	r	NOUN
ejpam-6472	507	8	,	,	PUNCT
ejpam-6472	507	9	s	s	NOUN
ejpam-6472	507	10	}	}	PUNCT
ejpam-6472	507	11	∩	∩	ADJ
ejpam-6472	507	12	sub(t	sub(t	NOUN
ejpam-6472	507	13	)	)	PUNCT
ejpam-6472	507	14	̸=	̸=	PROPN
ejpam-6472	507	15	∅	∅	NOUN
ejpam-6472	507	16	and	and	CCONJ
ejpam-6472	507	17	td	td	NOUN
ejpam-6472	507	18	q.	q.	NOUN
ejpam-6472	507	19	then	then	ADV
ejpam-6472	507	20	there	there	PRON
ejpam-6472	507	21	is	be	VERB
ejpam-6472	507	22	u	u	NOUN
ejpam-6472	507	23	∈	∈	PROPN
ejpam-6472	507	24	w	w	PROPN
ejpam-6472	507	25	r	r	NOUN
ejpam-6472	507	26	,	,	PUNCT
ejpam-6472	507	27	s	s	PART
ejpam-6472	507	28	τ	τ	X
ejpam-6472	507	29	(	(	PUNCT
ejpam-6472	507	30	xn	xn	PROPN
ejpam-6472	507	31	)	)	PUNCT
ejpam-6472	507	32	such	such	ADJ
ejpam-6472	507	33	that	that	SCONJ
ejpam-6472	507	34	tlu	tlu	PROPN
ejpam-6472	507	35	and	and	CCONJ
ejpam-6472	507	36	ur	ur	INTJ
ejpam-6472	507	37	q.	q.	PROPN
ejpam-6472	507	38	by	by	ADP
ejpam-6472	507	39	theorem	theorem	NOUN
ejpam-6472	507	40	8	8	NUM
ejpam-6472	507	41	,	,	PUNCT
ejpam-6472	507	42	we	we	PRON
ejpam-6472	507	43	have	have	VERB
ejpam-6472	507	44	t	t	NOUN
ejpam-6472	507	45	=	=	SYM
ejpam-6472	507	46	u	u	NOUN
ejpam-6472	507	47	,	,	PUNCT
ejpam-6472	507	48	and	and	CCONJ
ejpam-6472	507	49	thus	thus	ADV
ejpam-6472	507	50	tr	tr	VERB
ejpam-6472	507	51	q.	q.	NOUN
ejpam-6472	507	52	the	the	DET
ejpam-6472	507	53	converse	converse	NOUN
ejpam-6472	507	54	is	be	AUX
ejpam-6472	507	55	clear	clear	ADJ
ejpam-6472	507	56	.	.	PUNCT
ejpam-6472	508	1	p.	p.	NOUN
ejpam-6472	508	2	prachumdang	prachumdang	PROPN
ejpam-6472	508	3	,	,	PUNCT
ejpam-6472	508	4	b.	b.	PROPN
ejpam-6472	508	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	508	6	/	/	SYM
ejpam-6472	508	7	eur	eur	PROPN
ejpam-6472	508	8	.	.	PUNCT
ejpam-6472	509	1	j.	j.	PROPN
ejpam-6472	509	2	pure	pure	PROPN
ejpam-6472	509	3	appl	appl	PROPN
ejpam-6472	509	4	.	.	PROPN
ejpam-6472	509	5	math	math	PROPN
ejpam-6472	509	6	,	,	PUNCT
ejpam-6472	509	7	18	18	NUM
ejpam-6472	509	8	(	(	PUNCT
ejpam-6472	509	9	3	3	NUM
ejpam-6472	509	10	)	)	PUNCT
ejpam-6472	509	11	(	(	PUNCT
ejpam-6472	509	12	2025	2025	NUM
ejpam-6472	509	13	)	)	PUNCT
ejpam-6472	509	14	,	,	PUNCT
ejpam-6472	509	15	6472	6472	NUM
ejpam-6472	509	16	14	14	NUM
ejpam-6472	509	17	of	of	ADP
ejpam-6472	509	18	16	16	NUM
ejpam-6472	509	19	theorem	theorem	NOUN
ejpam-6472	509	20	12	12	NUM
ejpam-6472	509	21	.	.	PUNCT
ejpam-6472	510	1	let	let	VERB
ejpam-6472	510	2	r	r	NOUN
ejpam-6472	510	3	,	,	PUNCT
ejpam-6472	510	4	s	s	NOUN
ejpam-6472	510	5	∈	∈	PROPN
ejpam-6472	510	6	wτ	wτ	NOUN
ejpam-6472	510	7	(	(	PUNCT
ejpam-6472	510	8	xn	xn	X
ejpam-6472	510	9	)	)	PUNCT
ejpam-6472	510	10	be	be	AUX
ejpam-6472	510	11	fixed	fix	VERB
ejpam-6472	510	12	terms	term	NOUN
ejpam-6472	510	13	,	,	PUNCT
ejpam-6472	510	14	and	and	CCONJ
ejpam-6472	510	15	let	let	VERB
ejpam-6472	510	16	t	t	PROPN
ejpam-6472	510	17	,	,	PUNCT
ejpam-6472	510	18	q	q	PROPN
ejpam-6472	510	19	∈	∈	PROPN
ejpam-6472	510	20	w	w	NOUN
ejpam-6472	510	21	r	r	NOUN
ejpam-6472	510	22	,	,	PUNCT
ejpam-6472	510	23	s	s	PART
ejpam-6472	510	24	τ	τ	X
ejpam-6472	510	25	(	(	PUNCT
ejpam-6472	510	26	xn	xn	PROPN
ejpam-6472	510	27	)	)	PUNCT
ejpam-6472	510	28	.	.	PUNCT
ejpam-6472	511	1	then	then	ADV
ejpam-6472	511	2	the	the	DET
ejpam-6472	511	3	following	following	ADJ
ejpam-6472	511	4	statements	statement	NOUN
ejpam-6472	511	5	hold	hold	VERB
ejpam-6472	511	6	:	:	PUNCT
ejpam-6472	511	7	(	(	PUNCT
ejpam-6472	511	8	i	i	NOUN
ejpam-6472	511	9	)	)	PUNCT
ejpam-6472	511	10	if	if	SCONJ
ejpam-6472	511	11	{	{	PUNCT
ejpam-6472	511	12	r	r	NOUN
ejpam-6472	511	13	,	,	PUNCT
ejpam-6472	511	14	s	s	NOUN
ejpam-6472	511	15	}	}	PUNCT
ejpam-6472	511	16	∩	∩	ADJ
ejpam-6472	511	17	sub(t	sub(t	NOUN
ejpam-6472	511	18	)	)	PUNCT
ejpam-6472	511	19	=	=	NOUN
ejpam-6472	511	20	∅	∅	NOUN
ejpam-6472	511	21	,	,	PUNCT
ejpam-6472	511	22	then	then	ADV
ejpam-6472	511	23	tj	tj	X
ejpam-6472	511	24	q	q	NOUN
ejpam-6472	511	25	if	if	SCONJ
ejpam-6472	512	1	and	and	CCONJ
ejpam-6472	512	2	only	only	ADV
ejpam-6472	512	3	if	if	SCONJ
ejpam-6472	512	4	tl	tl	PROPN
ejpam-6472	512	5	q.	q.	PROPN
ejpam-6472	512	6	(	(	PUNCT
ejpam-6472	512	7	ii	ii	PROPN
ejpam-6472	512	8	)	)	PUNCT
ejpam-6472	512	9	if	if	SCONJ
ejpam-6472	512	10	{	{	PUNCT
ejpam-6472	512	11	r	r	NOUN
ejpam-6472	512	12	,	,	PUNCT
ejpam-6472	512	13	s	s	NOUN
ejpam-6472	512	14	}	}	PUNCT
ejpam-6472	512	15	∩	∩	ADJ
ejpam-6472	512	16	sub(t	sub(t	NOUN
ejpam-6472	512	17	)	)	PUNCT
ejpam-6472	512	18	̸=	̸=	NOUN
ejpam-6472	512	19	∅	∅	NOUN
ejpam-6472	512	20	,	,	PUNCT
ejpam-6472	512	21	then	then	ADV
ejpam-6472	512	22	tj	tj	X
ejpam-6472	512	23	q	q	NOUN
ejpam-6472	512	24	if	if	SCONJ
ejpam-6472	513	1	and	and	CCONJ
ejpam-6472	513	2	only	only	ADV
ejpam-6472	513	3	if	if	SCONJ
ejpam-6472	513	4	tr	tr	VERB
ejpam-6472	513	5	q.	q.	NOUN
ejpam-6472	513	6	proof	proof	NOUN
ejpam-6472	513	7	.	.	PUNCT
ejpam-6472	514	1	part	part	NOUN
ejpam-6472	514	2	(	(	PUNCT
ejpam-6472	514	3	i	i	NOUN
ejpam-6472	514	4	)	)	PUNCT
ejpam-6472	514	5	follows	follow	VERB
ejpam-6472	514	6	from	from	ADP
ejpam-6472	514	7	the	the	DET
ejpam-6472	514	8	same	same	ADJ
ejpam-6472	514	9	reasoning	reasoning	NOUN
ejpam-6472	514	10	as	as	ADP
ejpam-6472	514	11	in	in	ADP
ejpam-6472	514	12	part	part	NOUN
ejpam-6472	514	13	(	(	PUNCT
ejpam-6472	514	14	i	i	NOUN
ejpam-6472	514	15	)	)	PUNCT
ejpam-6472	514	16	of	of	ADP
ejpam-6472	514	17	theorem	theorem	NOUN
ejpam-6472	514	18	11	11	NUM
ejpam-6472	514	19	.	.	PUNCT
ejpam-6472	515	1	for	for	ADP
ejpam-6472	515	2	part	part	NOUN
ejpam-6472	515	3	(	(	PUNCT
ejpam-6472	515	4	ii	ii	NOUN
ejpam-6472	515	5	)	)	PUNCT
ejpam-6472	515	6	,	,	PUNCT
ejpam-6472	515	7	assume	assume	VERB
ejpam-6472	515	8	{	{	PUNCT
ejpam-6472	515	9	r	r	NOUN
ejpam-6472	515	10	,	,	PUNCT
ejpam-6472	515	11	s}∩	s}∩	PROPN
ejpam-6472	515	12	sub(t	sub(t	NOUN
ejpam-6472	515	13	)	)	PUNCT
ejpam-6472	515	14	̸=	̸=	PROPN
ejpam-6472	515	15	∅	∅	NOUN
ejpam-6472	515	16	and	and	CCONJ
ejpam-6472	515	17	tj	tj	NOUN
ejpam-6472	515	18	q.	q.	PROPN
ejpam-6472	515	19	then	then	ADV
ejpam-6472	515	20	there	there	PRON
ejpam-6472	515	21	are	be	VERB
ejpam-6472	515	22	u	u	NOUN
ejpam-6472	515	23	,	,	PUNCT
ejpam-6472	515	24	v	v	NOUN
ejpam-6472	515	25	,	,	PUNCT
ejpam-6472	515	26	a	a	PRON
ejpam-6472	515	27	,	,	PUNCT
ejpam-6472	515	28	b	b	X
ejpam-6472	515	29	∈	∈	PROPN
ejpam-6472	515	30	(	(	PUNCT
ejpam-6472	515	31	w	w	NOUN
ejpam-6472	515	32	r	r	NOUN
ejpam-6472	515	33	,	,	PUNCT
ejpam-6472	515	34	s	s	PART
ejpam-6472	515	35	τ	τ	X
ejpam-6472	515	36	(	(	PUNCT
ejpam-6472	515	37	xn	xn	PROPN
ejpam-6472	515	38	)	)	PUNCT
ejpam-6472	515	39	)	)	PUNCT
ejpam-6472	515	40	1	1	NUM
ejpam-6472	515	41	such	such	ADJ
ejpam-6472	515	42	that	that	SCONJ
ejpam-6472	515	43	u	u	NOUN
ejpam-6472	515	44	·	·	PUNCT
ejpam-6472	515	45	rs	rs	X
ejpam-6472	515	46	t	t	PROPN
ejpam-6472	515	47	·	·	PUNCT
ejpam-6472	515	48	rs	rs	NOUN
ejpam-6472	515	49	v	v	NOUN
ejpam-6472	515	50	=	=	PUNCT
ejpam-6472	515	51	q	q	X
ejpam-6472	515	52	and	and	CCONJ
ejpam-6472	515	53	a	a	DET
ejpam-6472	515	54	·	·	SYM
ejpam-6472	515	55	rs	rs	NOUN
ejpam-6472	515	56	q	q	NOUN
ejpam-6472	515	57	·	·	PUNCT
ejpam-6472	515	58	rs	rs	NOUN
ejpam-6472	515	59	b	b	NOUN
ejpam-6472	515	60	=	=	PUNCT
ejpam-6472	515	61	t.	t.	NOUN
ejpam-6472	515	62	(	(	PUNCT
ejpam-6472	515	63	4	4	NUM
ejpam-6472	515	64	)	)	PUNCT
ejpam-6472	515	65	then	then	ADV
ejpam-6472	515	66	t	t	PROPN
ejpam-6472	515	67	=	=	SYM
ejpam-6472	515	68	(	(	PUNCT
ejpam-6472	515	69	a	a	DET
ejpam-6472	515	70	·	·	SYM
ejpam-6472	515	71	rs	rs	NOUN
ejpam-6472	515	72	u	u	NOUN
ejpam-6472	515	73	)	)	PUNCT
ejpam-6472	515	74	·	·	PUNCT
ejpam-6472	515	75	rs	rs	X
ejpam-6472	515	76	t	t	PROPN
ejpam-6472	515	77	·	·	PUNCT
ejpam-6472	515	78	rs	rs	X
ejpam-6472	515	79	(	(	PUNCT
ejpam-6472	515	80	v	v	NOUN
ejpam-6472	515	81	·	·	SYM
ejpam-6472	515	82	rs	rs	NOUN
ejpam-6472	515	83	b	b	NOUN
ejpam-6472	515	84	)	)	PUNCT
ejpam-6472	515	85	.	.	PUNCT
ejpam-6472	516	1	we	we	PRON
ejpam-6472	516	2	consider	consider	VERB
ejpam-6472	516	3	the	the	DET
ejpam-6472	516	4	following	follow	VERB
ejpam-6472	516	5	cases	case	NOUN
ejpam-6472	516	6	.	.	PUNCT
ejpam-6472	517	1	case	case	NOUN
ejpam-6472	517	2	1	1	NUM
ejpam-6472	517	3	:	:	SYM
ejpam-6472	517	4	v	v	NOUN
ejpam-6472	517	5	=	=	SYM
ejpam-6472	517	6	b	b	NOUN
ejpam-6472	517	7	=	=	SYM
ejpam-6472	517	8	1	1	X
ejpam-6472	517	9	.	.	PUNCT
ejpam-6472	518	1	in	in	ADP
ejpam-6472	518	2	this	this	DET
ejpam-6472	518	3	case	case	NOUN
ejpam-6472	518	4	,	,	PUNCT
ejpam-6472	518	5	we	we	PRON
ejpam-6472	518	6	have	have	VERB
ejpam-6472	518	7	tl	tl	PROPN
ejpam-6472	518	8	q.	q.	PROPN
ejpam-6472	518	9	by	by	ADP
ejpam-6472	518	10	theorem	theorem	NOUN
ejpam-6472	518	11	8	8	NUM
ejpam-6472	518	12	,	,	PUNCT
ejpam-6472	518	13	it	it	PRON
ejpam-6472	518	14	follows	follow	VERB
ejpam-6472	518	15	that	that	DET
ejpam-6472	518	16	t	t	NOUN
ejpam-6472	518	17	=	=	SYM
ejpam-6472	518	18	q	q	NOUN
ejpam-6472	518	19	,	,	PUNCT
ejpam-6472	518	20	which	which	PRON
ejpam-6472	518	21	clearly	clearly	ADV
ejpam-6472	518	22	implies	imply	VERB
ejpam-6472	518	23	tr	tr	VERB
ejpam-6472	518	24	q.	q.	NOUN
ejpam-6472	518	25	case	case	NOUN
ejpam-6472	518	26	2	2	NUM
ejpam-6472	518	27	:	:	PUNCT
ejpam-6472	518	28	one	one	NUM
ejpam-6472	518	29	of	of	ADP
ejpam-6472	518	30	v	v	NOUN
ejpam-6472	518	31	or	or	CCONJ
ejpam-6472	518	32	b	b	NOUN
ejpam-6472	518	33	belong	belong	VERB
ejpam-6472	518	34	to	to	ADP
ejpam-6472	518	35	w	w	NOUN
ejpam-6472	518	36	r	r	NOUN
ejpam-6472	518	37	,	,	PUNCT
ejpam-6472	518	38	s	s	PART
ejpam-6472	518	39	τ	τ	X
ejpam-6472	518	40	(	(	PUNCT
ejpam-6472	518	41	xn	xn	PROPN
ejpam-6472	518	42	)	)	PUNCT
ejpam-6472	518	43	.	.	PUNCT
ejpam-6472	519	1	then	then	ADV
ejpam-6472	519	2	v	v	X
ejpam-6472	519	3	·	·	SYM
ejpam-6472	519	4	rs	rs	PROPN
ejpam-6472	519	5	b	b	PROPN
ejpam-6472	519	6	∈	∈	PROPN
ejpam-6472	519	7	w	w	NOUN
ejpam-6472	519	8	r	r	NOUN
ejpam-6472	519	9	,	,	PUNCT
ejpam-6472	519	10	s	s	PART
ejpam-6472	519	11	τ	τ	X
ejpam-6472	519	12	(	(	PUNCT
ejpam-6472	519	13	xn	xn	PROPN
ejpam-6472	519	14	)	)	PUNCT
ejpam-6472	519	15	.	.	PUNCT
ejpam-6472	520	1	if	if	SCONJ
ejpam-6472	520	2	u	u	PROPN
ejpam-6472	520	3	=	=	NOUN
ejpam-6472	520	4	1	1	NUM
ejpam-6472	520	5	or	or	CCONJ
ejpam-6472	520	6	a	a	DET
ejpam-6472	520	7	=	=	ADJ
ejpam-6472	520	8	1	1	NUM
ejpam-6472	520	9	,	,	PUNCT
ejpam-6472	520	10	we	we	PRON
ejpam-6472	520	11	may	may	AUX
ejpam-6472	520	12	substitute	substitute	VERB
ejpam-6472	520	13	it	it	PRON
ejpam-6472	520	14	with	with	ADP
ejpam-6472	520	15	r	r	NOUN
ejpam-6472	520	16	,	,	PUNCT
ejpam-6472	520	17	which	which	PRON
ejpam-6472	520	18	is	be	AUX
ejpam-6472	520	19	a	a	DET
ejpam-6472	520	20	left	left	ADJ
ejpam-6472	520	21	identity	identity	NOUN
ejpam-6472	520	22	in	in	ADP
ejpam-6472	520	23	w	w	NOUN
ejpam-6472	520	24	r	r	NOUN
ejpam-6472	520	25	,	,	PUNCT
ejpam-6472	520	26	s	s	PART
ejpam-6472	520	27	τ	τ	X
ejpam-6472	520	28	(	(	PUNCT
ejpam-6472	520	29	xn	xn	PROPN
ejpam-6472	520	30	)	)	PUNCT
ejpam-6472	520	31	,	,	PUNCT
ejpam-6472	520	32	without	without	ADP
ejpam-6472	520	33	affecting	affect	VERB
ejpam-6472	520	34	the	the	DET
ejpam-6472	520	35	equality	equality	NOUN
ejpam-6472	520	36	in	in	ADP
ejpam-6472	520	37	(	(	PUNCT
ejpam-6472	520	38	4	4	NUM
ejpam-6472	520	39	)	)	PUNCT
ejpam-6472	520	40	.	.	PUNCT
ejpam-6472	521	1	thus	thus	ADV
ejpam-6472	521	2	,	,	PUNCT
ejpam-6472	521	3	we	we	PRON
ejpam-6472	521	4	may	may	AUX
ejpam-6472	521	5	assume	assume	VERB
ejpam-6472	521	6	u	u	NOUN
ejpam-6472	521	7	,	,	PUNCT
ejpam-6472	521	8	a	a	DET
ejpam-6472	521	9	∈	∈	PROPN
ejpam-6472	521	10	w	w	NOUN
ejpam-6472	521	11	r	r	NOUN
ejpam-6472	521	12	,	,	PUNCT
ejpam-6472	521	13	s	s	PART
ejpam-6472	521	14	τ	τ	X
ejpam-6472	521	15	(	(	PUNCT
ejpam-6472	521	16	xn	xn	PROPN
ejpam-6472	521	17	)	)	PUNCT
ejpam-6472	521	18	.	.	PUNCT
ejpam-6472	522	1	by	by	ADP
ejpam-6472	522	2	lemma	lemma	PROPN
ejpam-6472	522	3	7	7	NUM
ejpam-6472	522	4	,	,	PUNCT
ejpam-6472	522	5	we	we	PRON
ejpam-6472	522	6	obtain	obtain	VERB
ejpam-6472	522	7	t	t	NOUN
ejpam-6472	522	8	=	=	PUNCT
ejpam-6472	522	9	(	(	PUNCT
ejpam-6472	522	10	a·rsu)·rs	a·rsu)·rs	ADJ
ejpam-6472	522	11	t.	t.	NOUN
ejpam-6472	522	12	applying	apply	VERB
ejpam-6472	522	13	lemma	lemma	PROPN
ejpam-6472	522	14	5	5	NUM
ejpam-6472	522	15	with	with	ADP
ejpam-6472	522	16	the	the	DET
ejpam-6472	522	17	condition	condition	NOUN
ejpam-6472	522	18	{	{	PUNCT
ejpam-6472	522	19	r	r	NOUN
ejpam-6472	522	20	,	,	PUNCT
ejpam-6472	522	21	s}∩sub((a·rsu)·rs(t·rs(v	s}∩sub((a·rsu)·rs(t·rs(v	PROPN
ejpam-6472	522	22	·	·	SYM
ejpam-6472	522	23	rsb	rsb	PROPN
ejpam-6472	522	24	)	)	PUNCT
ejpam-6472	522	25	)	)	PUNCT
ejpam-6472	522	26	)	)	PUNCT
ejpam-6472	523	1	̸=	̸=	NOUN
ejpam-6472	523	2	∅	∅	NOUN
ejpam-6472	523	3	,	,	PUNCT
ejpam-6472	523	4	we	we	PRON
ejpam-6472	523	5	have	have	AUX
ejpam-6472	523	6	{	{	PUNCT
ejpam-6472	523	7	r	r	NOUN
ejpam-6472	523	8	,	,	PUNCT
ejpam-6472	523	9	s	s	NOUN
ejpam-6472	523	10	}	}	PUNCT
ejpam-6472	523	11	∩	∩	NOUN
ejpam-6472	523	12	sub(a	sub(a	PROPN
ejpam-6472	523	13	·	·	SYM
ejpam-6472	523	14	rs	rs	X
ejpam-6472	523	15	u	u	NOUN
ejpam-6472	523	16	)	)	PUNCT
ejpam-6472	523	17	̸=	̸=	PROPN
ejpam-6472	523	18	∅.	∅.	ADV
ejpam-6472	523	19	if	if	SCONJ
ejpam-6472	523	20	a	a	DET
ejpam-6472	523	21	·	·	SYM
ejpam-6472	523	22	rs	rs	NOUN
ejpam-6472	523	23	u	u	NOUN
ejpam-6472	523	24	/∈	/∈	PUNCT
ejpam-6472	523	25	{	{	PUNCT
ejpam-6472	523	26	r	r	NOUN
ejpam-6472	523	27	,	,	PUNCT
ejpam-6472	523	28	s	s	PART
ejpam-6472	523	29	}	}	PUNCT
ejpam-6472	523	30	,	,	PUNCT
ejpam-6472	523	31	then	then	ADV
ejpam-6472	523	32	lemma	lemma	PROPN
ejpam-6472	523	33	1	1	NUM
ejpam-6472	523	34	yields	yield	NOUN
ejpam-6472	523	35	t	t	PROPN
ejpam-6472	523	36	∈	∈	PROPN
ejpam-6472	523	37	sub((a	sub((a	PROPN
ejpam-6472	523	38	·	·	SYM
ejpam-6472	523	39	rs	rs	X
ejpam-6472	523	40	u	u	NOUN
ejpam-6472	523	41	)	)	PUNCT
ejpam-6472	523	42	·	·	PUNCT
ejpam-6472	523	43	rs	rs	PROPN
ejpam-6472	523	44	t	t	PROPN
ejpam-6472	523	45	)	)	PUNCT
ejpam-6472	523	46	\	\	NOUN
ejpam-6472	523	47	{	{	PUNCT
ejpam-6472	523	48	(	(	PUNCT
ejpam-6472	523	49	a	a	DET
ejpam-6472	523	50	·	·	SYM
ejpam-6472	523	51	rs	rs	NOUN
ejpam-6472	523	52	u	u	NOUN
ejpam-6472	523	53	)	)	PUNCT
ejpam-6472	523	54	·	·	PUNCT
ejpam-6472	523	55	rs	rs	PROPN
ejpam-6472	523	56	t	t	PROPN
ejpam-6472	523	57	}	}	PUNCT
ejpam-6472	523	58	=	=	SYM
ejpam-6472	523	59	sub(t	sub(t	NOUN
ejpam-6472	523	60	)	)	PUNCT
ejpam-6472	523	61	\	\	NOUN
ejpam-6472	523	62	{	{	PUNCT
ejpam-6472	523	63	t	t	PROPN
ejpam-6472	523	64	}	}	PUNCT
ejpam-6472	523	65	,	,	PUNCT
ejpam-6472	523	66	a	a	DET
ejpam-6472	523	67	contradiction	contradiction	NOUN
ejpam-6472	523	68	.	.	PUNCT
ejpam-6472	524	1	consequently	consequently	ADV
ejpam-6472	524	2	,	,	PUNCT
ejpam-6472	524	3	a	a	DET
ejpam-6472	524	4	·	·	SYM
ejpam-6472	524	5	rs	rs	NOUN
ejpam-6472	524	6	u	u	PROPN
ejpam-6472	524	7	∈	∈	PROPN
ejpam-6472	524	8	{	{	PUNCT
ejpam-6472	524	9	r	r	NOUN
ejpam-6472	524	10	,	,	PUNCT
ejpam-6472	524	11	s	s	PART
ejpam-6472	524	12	}	}	PUNCT
ejpam-6472	524	13	,	,	PUNCT
ejpam-6472	524	14	and	and	CCONJ
ejpam-6472	524	15	then	then	ADV
ejpam-6472	524	16	lemma	lemma	PROPN
ejpam-6472	524	17	6	6	NUM
ejpam-6472	524	18	implies	imply	VERB
ejpam-6472	524	19	a	a	PRON
ejpam-6472	524	20	,	,	PUNCT
ejpam-6472	524	21	u	u	PROPN
ejpam-6472	524	22	∈	∈	PROPN
ejpam-6472	524	23	{	{	PUNCT
ejpam-6472	524	24	r	r	NOUN
ejpam-6472	524	25	,	,	PUNCT
ejpam-6472	524	26	s	s	PART
ejpam-6472	524	27	}	}	PUNCT
ejpam-6472	524	28	.	.	PUNCT
ejpam-6472	525	1	as	as	ADV
ejpam-6472	525	2	both	both	DET
ejpam-6472	525	3	r	r	NOUN
ejpam-6472	525	4	and	and	CCONJ
ejpam-6472	525	5	s	s	NOUN
ejpam-6472	525	6	act	act	NOUN
ejpam-6472	525	7	as	as	ADP
ejpam-6472	525	8	left	leave	VERB
ejpam-6472	525	9	identities	identity	NOUN
ejpam-6472	525	10	,	,	PUNCT
ejpam-6472	525	11	we	we	PRON
ejpam-6472	525	12	conclude	conclude	VERB
ejpam-6472	525	13	that	that	SCONJ
ejpam-6472	525	14	t	t	NOUN
ejpam-6472	525	15	·	·	PUNCT
ejpam-6472	525	16	rs	rs	NOUN
ejpam-6472	525	17	v	v	NOUN
ejpam-6472	525	18	=	=	PUNCT
ejpam-6472	525	19	q	q	NOUN
ejpam-6472	525	20	and	and	CCONJ
ejpam-6472	525	21	q	q	ADJ
ejpam-6472	525	22	·	·	PUNCT
ejpam-6472	525	23	rs	rs	PROPN
ejpam-6472	525	24	b	b	PROPN
ejpam-6472	525	25	=	=	SYM
ejpam-6472	525	26	t	t	PROPN
ejpam-6472	525	27	,	,	PUNCT
ejpam-6472	525	28	which	which	PRON
ejpam-6472	525	29	implies	imply	VERB
ejpam-6472	525	30	tr	tr	NOUN
ejpam-6472	525	31	q	q	ADJ
ejpam-6472	525	32	,	,	PUNCT
ejpam-6472	525	33	as	as	SCONJ
ejpam-6472	525	34	desired	desire	VERB
ejpam-6472	525	35	.	.	PUNCT
ejpam-6472	526	1	the	the	DET
ejpam-6472	526	2	characterizations	characterization	NOUN
ejpam-6472	526	3	of	of	ADP
ejpam-6472	526	4	green	green	PROPN
ejpam-6472	526	5	’s	’s	PART
ejpam-6472	526	6	relations	relation	NOUN
ejpam-6472	526	7	for	for	ADP
ejpam-6472	526	8	(	(	PUNCT
ejpam-6472	526	9	w	w	NOUN
ejpam-6472	526	10	r	r	NOUN
ejpam-6472	526	11	,	,	PUNCT
ejpam-6472	526	12	s	s	PART
ejpam-6472	526	13	τ	τ	X
ejpam-6472	526	14	(	(	PUNCT
ejpam-6472	526	15	xn	xn	PROPN
ejpam-6472	526	16	)	)	PUNCT
ejpam-6472	526	17	,	,	PUNCT
ejpam-6472	526	18	·	·	PUNCT
ejpam-6472	526	19	rs	rs	X
ejpam-6472	526	20	)	)	PUNCT
ejpam-6472	526	21	exhibit	exhibit	VERB
ejpam-6472	526	22	notable	notable	ADJ
ejpam-6472	526	23	differences	difference	NOUN
ejpam-6472	526	24	from	from	ADP
ejpam-6472	526	25	those	those	PRON
ejpam-6472	526	26	in	in	ADP
ejpam-6472	526	27	the	the	DET
ejpam-6472	526	28	case	case	NOUN
ejpam-6472	526	29	of	of	ADP
ejpam-6472	526	30	·	·	PUNCT
ejpam-6472	526	31	r.	r.	NOUN
ejpam-6472	526	32	for	for	ADP
ejpam-6472	526	33	the	the	DET
ejpam-6472	526	34	operation	operation	NOUN
ejpam-6472	526	35	·	·	PUNCT
ejpam-6472	526	36	r	r	NOUN
ejpam-6472	526	37	,	,	PUNCT
ejpam-6472	526	38	the	the	DET
ejpam-6472	526	39	relations	relation	NOUN
ejpam-6472	526	40	satisfy	satisfy	VERB
ejpam-6472	526	41	l	l	X
ejpam-6472	527	1	=	=	PUNCT
ejpam-6472	527	2	d	d	X
ejpam-6472	527	3	=	=	SYM
ejpam-6472	527	4	j	j	PROPN
ejpam-6472	527	5	and	and	CCONJ
ejpam-6472	527	6	r	r	PROPN
ejpam-6472	527	7	=	=	SYM
ejpam-6472	527	8	h	h	NOUN
ejpam-6472	527	9	(	(	PUNCT
ejpam-6472	527	10	see	see	VERB
ejpam-6472	527	11	[	[	X
ejpam-6472	527	12	9	9	NUM
ejpam-6472	527	13	]	]	NUM
ejpam-6472	527	14	)	)	PUNCT
ejpam-6472	527	15	.	.	PUNCT
ejpam-6472	528	1	however	however	ADV
ejpam-6472	528	2	,	,	PUNCT
ejpam-6472	528	3	under	under	ADP
ejpam-6472	528	4	·	·	SYM
ejpam-6472	528	5	rs	rs	X
ejpam-6472	528	6	,	,	PUNCT
ejpam-6472	528	7	we	we	PRON
ejpam-6472	528	8	generally	generally	ADV
ejpam-6472	528	9	have	have	VERB
ejpam-6472	528	10	only	only	ADV
ejpam-6472	528	11	d	d	PROPN
ejpam-6472	528	12	=	=	SYM
ejpam-6472	528	13	j	j	PROPN
ejpam-6472	528	14	,	,	PUNCT
ejpam-6472	528	15	while	while	SCONJ
ejpam-6472	528	16	l	l	PROPN
ejpam-6472	528	17	̸=	̸=	PROPN
ejpam-6472	528	18	j	j	PROPN
ejpam-6472	528	19	and	and	CCONJ
ejpam-6472	528	20	r	r	PROPN
ejpam-6472	528	21	̸=	̸=	PROPN
ejpam-6472	528	22	h	h	NOUN
ejpam-6472	528	23	may	may	AUX
ejpam-6472	528	24	occur	occur	VERB
ejpam-6472	528	25	.	.	PUNCT
ejpam-6472	529	1	for	for	ADP
ejpam-6472	529	2	instance	instance	NOUN
ejpam-6472	529	3	,	,	PUNCT
ejpam-6472	529	4	let	let	VERB
ejpam-6472	529	5	r	r	NOUN
ejpam-6472	529	6	=	=	SYM
ejpam-6472	529	7	x1	x1	PROPN
ejpam-6472	529	8	,	,	PUNCT
ejpam-6472	529	9	s	s	NOUN
ejpam-6472	529	10	=	=	NOUN
ejpam-6472	529	11	g(x2	g(x2	NOUN
ejpam-6472	529	12	)	)	PUNCT
ejpam-6472	529	13	,	,	PUNCT
ejpam-6472	529	14	t	t	NOUN
ejpam-6472	529	15	=	=	PUNCT
ejpam-6472	529	16	f(x1	f(x1	X
ejpam-6472	529	17	,	,	PUNCT
ejpam-6472	529	18	x1	x1	PROPN
ejpam-6472	529	19	)	)	PUNCT
ejpam-6472	529	20	,	,	PUNCT
ejpam-6472	529	21	and	and	CCONJ
ejpam-6472	529	22	q	q	NOUN
ejpam-6472	529	23	=	=	SYM
ejpam-6472	529	24	f(g(x2	f(g(x2	NOUN
ejpam-6472	529	25	)	)	PUNCT
ejpam-6472	529	26	,	,	PUNCT
ejpam-6472	529	27	g(x2	g(x2	NOUN
ejpam-6472	529	28	)	)	PUNCT
ejpam-6472	529	29	)	)	PUNCT
ejpam-6472	529	30	.	.	PUNCT
ejpam-6472	530	1	it	it	PRON
ejpam-6472	530	2	can	can	AUX
ejpam-6472	530	3	be	be	AUX
ejpam-6472	530	4	verified	verify	VERB
ejpam-6472	530	5	that	that	SCONJ
ejpam-6472	530	6	t	t	NOUN
ejpam-6472	530	7	·	·	PUNCT
ejpam-6472	530	8	rs	rs	PROPN
ejpam-6472	530	9	s	s	PART
ejpam-6472	530	10	=	=	X
ejpam-6472	530	11	q	q	X
ejpam-6472	530	12	and	and	CCONJ
ejpam-6472	530	13	q	q	ADJ
ejpam-6472	530	14	·	·	PUNCT
ejpam-6472	530	15	rs	rs	NOUN
ejpam-6472	530	16	r	r	NOUN
ejpam-6472	530	17	=	=	SYM
ejpam-6472	530	18	t	t	PROPN
ejpam-6472	530	19	,	,	PUNCT
ejpam-6472	530	20	so	so	ADV
ejpam-6472	530	21	tr	tr	ADV
ejpam-6472	530	22	q.	q.	PROPN
ejpam-6472	530	23	however	however	ADV
ejpam-6472	530	24	,	,	PUNCT
ejpam-6472	530	25	since	since	SCONJ
ejpam-6472	530	26	t	t	PROPN
ejpam-6472	530	27	̸=	̸=	PROPN
ejpam-6472	530	28	q	q	NUM
ejpam-6472	530	29	,	,	PUNCT
ejpam-6472	530	30	it	it	PRON
ejpam-6472	530	31	follows	follow	VERB
ejpam-6472	530	32	from	from	ADP
ejpam-6472	530	33	theorem	theorem	ADJ
ejpam-6472	530	34	10	10	NUM
ejpam-6472	530	35	that	that	PRON
ejpam-6472	530	36	(	(	PUNCT
ejpam-6472	530	37	t	t	PROPN
ejpam-6472	530	38	,	,	PUNCT
ejpam-6472	530	39	q	q	NOUN
ejpam-6472	530	40	)	)	PUNCT
ejpam-6472	530	41	/∈	/∈	PUNCT
ejpam-6472	531	1	h.	h.	PROPN
ejpam-6472	531	2	in	in	ADP
ejpam-6472	531	3	the	the	DET
ejpam-6472	531	4	same	same	ADJ
ejpam-6472	531	5	example	example	NOUN
ejpam-6472	531	6	,	,	PUNCT
ejpam-6472	531	7	we	we	PRON
ejpam-6472	531	8	also	also	ADV
ejpam-6472	531	9	have	have	VERB
ejpam-6472	531	10	r	r	NOUN
ejpam-6472	531	11	·	·	SYM
ejpam-6472	531	12	rs	rs	X
ejpam-6472	531	13	t	t	PROPN
ejpam-6472	531	14	·	·	PUNCT
ejpam-6472	531	15	rs	rs	PROPN
ejpam-6472	531	16	s	s	PART
ejpam-6472	531	17	=	=	X
ejpam-6472	531	18	q	q	X
ejpam-6472	531	19	and	and	CCONJ
ejpam-6472	531	20	r	r	NOUN
ejpam-6472	531	21	·	·	PUNCT
ejpam-6472	531	22	rs	rs	X
ejpam-6472	531	23	q	q	NOUN
ejpam-6472	531	24	·	·	PUNCT
ejpam-6472	531	25	rs	rs	NOUN
ejpam-6472	531	26	r	r	NOUN
ejpam-6472	531	27	=	=	SYM
ejpam-6472	531	28	t	t	PROPN
ejpam-6472	531	29	,	,	PUNCT
ejpam-6472	531	30	which	which	PRON
ejpam-6472	531	31	implies	imply	VERB
ejpam-6472	531	32	tj	tj	PROPN
ejpam-6472	531	33	q.	q.	PROPN
ejpam-6472	531	34	nevertheless	nevertheless	ADV
ejpam-6472	531	35	,	,	PUNCT
ejpam-6472	531	36	(	(	PUNCT
ejpam-6472	531	37	t	t	PROPN
ejpam-6472	531	38	,	,	PUNCT
ejpam-6472	531	39	q	q	NOUN
ejpam-6472	531	40	)	)	PUNCT
ejpam-6472	531	41	/∈	/∈	PUNCT
ejpam-6472	532	1	l	l	NOUN
ejpam-6472	532	2	by	by	ADP
ejpam-6472	532	3	theorem	theorem	NOUN
ejpam-6472	532	4	8	8	NUM
ejpam-6472	532	5	,	,	PUNCT
ejpam-6472	532	6	as	as	ADP
ejpam-6472	532	7	t	t	PROPN
ejpam-6472	532	8	̸=	̸=	PROPN
ejpam-6472	532	9	q	q	PROPN
ejpam-6472	532	10	and	and	CCONJ
ejpam-6472	532	11	both	both	DET
ejpam-6472	532	12	terms	term	NOUN
ejpam-6472	532	13	contain	contain	VERB
ejpam-6472	532	14	either	either	DET
ejpam-6472	532	15	r	r	NOUN
ejpam-6472	532	16	or	or	CCONJ
ejpam-6472	532	17	s	s	NOUN
ejpam-6472	532	18	as	as	ADP
ejpam-6472	532	19	subterms	subterm	NOUN
ejpam-6472	532	20	.	.	PUNCT
ejpam-6472	533	1	6	6	X
ejpam-6472	533	2	.	.	X
ejpam-6472	533	3	conclusion	conclusion	NOUN
ejpam-6472	533	4	in	in	ADP
ejpam-6472	533	5	this	this	DET
ejpam-6472	533	6	paper	paper	NOUN
ejpam-6472	533	7	,	,	PUNCT
ejpam-6472	533	8	we	we	PRON
ejpam-6472	533	9	introduced	introduce	VERB
ejpam-6472	533	10	a	a	DET
ejpam-6472	533	11	binary	binary	ADJ
ejpam-6472	533	12	operation	operation	NOUN
ejpam-6472	533	13	·	·	PUNCT
ejpam-6472	533	14	rs	rs	NOUN
ejpam-6472	533	15	on	on	ADP
ejpam-6472	533	16	terms	term	NOUN
ejpam-6472	533	17	,	,	PUNCT
ejpam-6472	533	18	extending	extend	VERB
ejpam-6472	533	19	the	the	DET
ejpam-6472	533	20	r	r	NOUN
ejpam-6472	533	21	-	-	PUNCT
ejpam-6472	533	22	inductive	inductive	ADJ
ejpam-6472	533	23	product	product	NOUN
ejpam-6472	533	24	by	by	ADP
ejpam-6472	533	25	simultaneously	simultaneously	ADV
ejpam-6472	533	26	replacing	replace	VERB
ejpam-6472	533	27	two	two	NUM
ejpam-6472	533	28	fixed	fix	VERB
ejpam-6472	533	29	subterms	subterm	NOUN
ejpam-6472	533	30	.	.	PUNCT
ejpam-6472	534	1	since	since	SCONJ
ejpam-6472	534	2	·	·	NUM
ejpam-6472	534	3	rs	rs	X
ejpam-6472	534	4	is	be	AUX
ejpam-6472	534	5	not	not	PART
ejpam-6472	534	6	associative	associative	ADJ
ejpam-6472	534	7	on	on	ADP
ejpam-6472	534	8	the	the	DET
ejpam-6472	534	9	entire	entire	ADJ
ejpam-6472	534	10	set	set	NOUN
ejpam-6472	534	11	of	of	ADP
ejpam-6472	534	12	terms	term	NOUN
ejpam-6472	534	13	,	,	PUNCT
ejpam-6472	534	14	we	we	PRON
ejpam-6472	534	15	constructed	construct	VERB
ejpam-6472	534	16	the	the	DET
ejpam-6472	534	17	subsetw	subsetw	NOUN
ejpam-6472	534	18	r	r	NOUN
ejpam-6472	534	19	,	,	PUNCT
ejpam-6472	534	20	s	s	PART
ejpam-6472	534	21	τ	τ	X
ejpam-6472	534	22	(	(	PUNCT
ejpam-6472	534	23	xn	xn	PROPN
ejpam-6472	534	24	)	)	PUNCT
ejpam-6472	534	25	by	by	ADP
ejpam-6472	534	26	excluding	exclude	VERB
ejpam-6472	534	27	all	all	DET
ejpam-6472	534	28	proper	proper	ADJ
ejpam-6472	534	29	subterms	subterm	NOUN
ejpam-6472	534	30	of	of	ADP
ejpam-6472	534	31	r	r	NOUN
ejpam-6472	534	32	and	and	CCONJ
ejpam-6472	534	33	s	s	NOUN
ejpam-6472	534	34	,	,	PUNCT
ejpam-6472	534	35	and	and	CCONJ
ejpam-6472	534	36	showed	show	VERB
ejpam-6472	534	37	that	that	SCONJ
ejpam-6472	534	38	this	this	DET
ejpam-6472	534	39	set	set	NOUN
ejpam-6472	534	40	forms	form	VERB
ejpam-6472	534	41	a	a	DET
ejpam-6472	534	42	semigroup	semigroup	NOUN
ejpam-6472	534	43	under	under	ADP
ejpam-6472	534	44	·	·	SYM
ejpam-6472	534	45	rs	rs	X
ejpam-6472	534	46	.	.	PUNCT
ejpam-6472	535	1	however	however	ADV
ejpam-6472	535	2	,	,	PUNCT
ejpam-6472	535	3	we	we	PRON
ejpam-6472	535	4	were	be	AUX
ejpam-6472	535	5	only	only	ADV
ejpam-6472	535	6	able	able	ADJ
ejpam-6472	535	7	to	to	PART
ejpam-6472	535	8	prove	prove	VERB
ejpam-6472	535	9	that	that	SCONJ
ejpam-6472	535	10	this	this	DET
ejpam-6472	535	11	semigroup	semigroup	NOUN
ejpam-6472	535	12	is	be	AUX
ejpam-6472	535	13	maximal	maximal	ADJ
ejpam-6472	535	14	under	under	ADP
ejpam-6472	535	15	the	the	DET
ejpam-6472	535	16	condition	condition	NOUN
ejpam-6472	535	17	that	that	SCONJ
ejpam-6472	535	18	r	r	NOUN
ejpam-6472	535	19	and	and	CCONJ
ejpam-6472	535	20	s	s	NOUN
ejpam-6472	535	21	are	be	AUX
ejpam-6472	535	22	not	not	PART
ejpam-6472	535	23	proper	proper	ADJ
ejpam-6472	535	24	p.	p.	PROPN
ejpam-6472	535	25	prachumdang	prachumdang	PROPN
ejpam-6472	535	26	,	,	PUNCT
ejpam-6472	535	27	b.	b.	PROPN
ejpam-6472	535	28	pibaljommee	pibaljommee	PROPN
ejpam-6472	535	29	/	/	SYM
ejpam-6472	535	30	eur	eur	PROPN
ejpam-6472	535	31	.	.	PUNCT
ejpam-6472	536	1	j.	j.	PROPN
ejpam-6472	536	2	pure	pure	PROPN
ejpam-6472	536	3	appl	appl	PROPN
ejpam-6472	536	4	.	.	PROPN
ejpam-6472	536	5	math	math	PROPN
ejpam-6472	536	6	,	,	PUNCT
ejpam-6472	536	7	18	18	NUM
ejpam-6472	536	8	(	(	PUNCT
ejpam-6472	536	9	3	3	NUM
ejpam-6472	536	10	)	)	PUNCT
ejpam-6472	536	11	(	(	PUNCT
ejpam-6472	536	12	2025	2025	NUM
ejpam-6472	536	13	)	)	PUNCT
ejpam-6472	536	14	,	,	PUNCT
ejpam-6472	536	15	6472	6472	NUM
ejpam-6472	536	16	15	15	NUM
ejpam-6472	536	17	of	of	ADP
ejpam-6472	536	18	16	16	NUM
ejpam-6472	536	19	subterms	subterm	NOUN
ejpam-6472	536	20	of	of	ADP
ejpam-6472	536	21	each	each	DET
ejpam-6472	536	22	other	other	ADJ
ejpam-6472	536	23	,	,	PUNCT
ejpam-6472	536	24	while	while	SCONJ
ejpam-6472	536	25	the	the	DET
ejpam-6472	536	26	general	general	ADJ
ejpam-6472	536	27	case	case	NOUN
ejpam-6472	536	28	remains	remain	VERB
ejpam-6472	536	29	open	open	ADJ
ejpam-6472	536	30	.	.	PUNCT
ejpam-6472	537	1	we	we	PRON
ejpam-6472	537	2	showed	show	VERB
ejpam-6472	537	3	that	that	SCONJ
ejpam-6472	537	4	idempotent	idempotent	NOUN
ejpam-6472	537	5	and	and	CCONJ
ejpam-6472	537	6	regular	regular	ADJ
ejpam-6472	537	7	elements	element	NOUN
ejpam-6472	537	8	coincide	coincide	VERB
ejpam-6472	537	9	in	in	ADP
ejpam-6472	537	10	this	this	DET
ejpam-6472	537	11	semigroup	semigroup	NOUN
ejpam-6472	537	12	,	,	PUNCT
ejpam-6472	537	13	and	and	CCONJ
ejpam-6472	537	14	that	that	SCONJ
ejpam-6472	537	15	any	any	DET
ejpam-6472	537	16	term	term	NOUN
ejpam-6472	537	17	expressible	expressible	ADJ
ejpam-6472	537	18	as	as	ADP
ejpam-6472	537	19	a	a	DET
ejpam-6472	537	20	product	product	NOUN
ejpam-6472	537	21	in	in	ADP
ejpam-6472	537	22	which	which	PRON
ejpam-6472	537	23	it	it	PRON
ejpam-6472	537	24	occurs	occur	VERB
ejpam-6472	537	25	at	at	ADV
ejpam-6472	537	26	least	least	ADJ
ejpam-6472	537	27	twice	twice	ADJ
ejpam-6472	537	28	is	be	AUX
ejpam-6472	537	29	necessarily	necessarily	ADV
ejpam-6472	537	30	idempotent	idempotent	ADJ
ejpam-6472	537	31	.	.	PUNCT
ejpam-6472	538	1	moreover	moreover	ADV
ejpam-6472	538	2	,	,	PUNCT
ejpam-6472	538	3	we	we	PRON
ejpam-6472	538	4	provided	provide	VERB
ejpam-6472	538	5	complete	complete	ADJ
ejpam-6472	538	6	characterizations	characterization	NOUN
ejpam-6472	538	7	for	for	ADP
ejpam-6472	538	8	all	all	DET
ejpam-6472	538	9	five	five	NUM
ejpam-6472	538	10	types	type	NOUN
ejpam-6472	538	11	of	of	ADP
ejpam-6472	538	12	green	green	PROPN
ejpam-6472	538	13	’s	’s	PART
ejpam-6472	538	14	relations	relation	NOUN
ejpam-6472	538	15	on	on	ADP
ejpam-6472	538	16	this	this	DET
ejpam-6472	538	17	semigroup	semigroup	NOUN
ejpam-6472	538	18	,	,	PUNCT
ejpam-6472	538	19	highlighting	highlight	VERB
ejpam-6472	538	20	that	that	SCONJ
ejpam-6472	538	21	d	d	PROPN
ejpam-6472	538	22	=	=	SYM
ejpam-6472	538	23	j	j	PROPN
ejpam-6472	538	24	still	still	ADV
ejpam-6472	538	25	holds	hold	VERB
ejpam-6472	538	26	,	,	PUNCT
ejpam-6472	538	27	whereas	whereas	SCONJ
ejpam-6472	538	28	r	r	NOUN
ejpam-6472	538	29	=	=	SYM
ejpam-6472	538	30	̸	̸	NUM
ejpam-6472	538	31	h	h	NOUN
ejpam-6472	538	32	and	and	CCONJ
ejpam-6472	538	33	l	l	NOUN
ejpam-6472	538	34	=	=	NOUN
ejpam-6472	538	35	̸	̸	ADV
ejpam-6472	538	36	j	j	NOUN
ejpam-6472	538	37	can	can	AUX
ejpam-6472	538	38	occur	occur	VERB
ejpam-6472	538	39	,	,	PUNCT
ejpam-6472	538	40	unlike	unlike	ADP
ejpam-6472	538	41	in	in	ADP
ejpam-6472	538	42	the	the	DET
ejpam-6472	538	43	case	case	NOUN
ejpam-6472	538	44	of	of	ADP
ejpam-6472	538	45	rinductive	rinductive	ADJ
ejpam-6472	538	46	product	product	NOUN
ejpam-6472	538	47	.	.	PUNCT
ejpam-6472	539	1	future	future	ADJ
ejpam-6472	539	2	research	research	NOUN
ejpam-6472	539	3	could	could	AUX
ejpam-6472	539	4	further	far	ADV
ejpam-6472	539	5	explore	explore	VERB
ejpam-6472	539	6	other	other	ADJ
ejpam-6472	539	7	algebraic	algebraic	ADJ
ejpam-6472	539	8	properties	property	NOUN
ejpam-6472	539	9	of	of	ADP
ejpam-6472	539	10	this	this	DET
ejpam-6472	539	11	semigroup	semigroup	NOUN
ejpam-6472	539	12	,	,	PUNCT
ejpam-6472	539	13	such	such	ADJ
ejpam-6472	539	14	as	as	ADP
ejpam-6472	539	15	ideals	ideal	NOUN
ejpam-6472	539	16	and	and	CCONJ
ejpam-6472	539	17	special	special	ADJ
ejpam-6472	539	18	subsemigroups	subsemigroup	NOUN
ejpam-6472	539	19	.	.	PUNCT
ejpam-6472	540	1	additionally	additionally	ADV
ejpam-6472	540	2	,	,	PUNCT
ejpam-6472	540	3	one	one	PRON
ejpam-6472	540	4	might	might	AUX
ejpam-6472	540	5	investigate	investigate	VERB
ejpam-6472	540	6	the	the	DET
ejpam-6472	540	7	behavior	behavior	NOUN
ejpam-6472	540	8	of	of	ADP
ejpam-6472	540	9	semigroups	semigroup	NOUN
ejpam-6472	540	10	under	under	ADP
ejpam-6472	540	11	more	more	ADJ
ejpam-6472	540	12	general	general	ADJ
ejpam-6472	540	13	forms	form	NOUN
ejpam-6472	540	14	of	of	ADP
ejpam-6472	540	15	subterm	subterm	NOUN
ejpam-6472	540	16	replacement	replacement	NOUN
ejpam-6472	540	17	or	or	CCONJ
ejpam-6472	540	18	define	define	VERB
ejpam-6472	540	19	new	new	ADJ
ejpam-6472	540	20	operations	operation	NOUN
ejpam-6472	540	21	inspired	inspire	VERB
ejpam-6472	540	22	by	by	ADP
ejpam-6472	540	23	inductive	inductive	ADJ
ejpam-6472	540	24	compositions	composition	NOUN
ejpam-6472	540	25	.	.	PUNCT
ejpam-6472	541	1	acknowledgements	acknowledgement	NOUN
ejpam-6472	541	2	this	this	DET
ejpam-6472	541	3	research	research	NOUN
ejpam-6472	541	4	is	be	AUX
ejpam-6472	541	5	supported	support	VERB
ejpam-6472	541	6	by	by	ADP
ejpam-6472	541	7	the	the	DET
ejpam-6472	541	8	development	development	NOUN
ejpam-6472	541	9	and	and	CCONJ
ejpam-6472	541	10	promotion	promotion	NOUN
ejpam-6472	541	11	of	of	ADP
ejpam-6472	541	12	science	science	NOUN
ejpam-6472	541	13	and	and	CCONJ
ejpam-6472	541	14	technology	technology	NOUN
ejpam-6472	541	15	talents	talent	NOUN
ejpam-6472	541	16	project	project	NOUN
ejpam-6472	541	17	(	(	PUNCT
ejpam-6472	541	18	dpst	dpst	NOUN
ejpam-6472	541	19	)	)	PUNCT
ejpam-6472	541	20	,	,	PUNCT
ejpam-6472	541	21	thai	thai	ADJ
ejpam-6472	541	22	government	government	NOUN
ejpam-6472	541	23	scholarship	scholarship	NOUN
ejpam-6472	541	24	.	.	PUNCT
ejpam-6472	542	1	references	reference	NOUN
ejpam-6472	542	2	[	[	X
ejpam-6472	542	3	1	1	NUM
ejpam-6472	542	4	]	]	X
ejpam-6472	542	5	k	k	X
ejpam-6472	542	6	denecke	denecke	NOUN
ejpam-6472	542	7	and	and	CCONJ
ejpam-6472	542	8	s	s	PROPN
ejpam-6472	542	9	l	l	NOUN
ejpam-6472	542	10	wismath	wismath	NOUN
ejpam-6472	542	11	.	.	PUNCT
ejpam-6472	543	1	universal	universal	ADJ
ejpam-6472	543	2	algebra	algebra	NOUN
ejpam-6472	543	3	and	and	CCONJ
ejpam-6472	543	4	applications	application	NOUN
ejpam-6472	543	5	in	in	ADP
ejpam-6472	543	6	theoretical	theoretical	ADJ
ejpam-6472	543	7	computer	computer	NOUN
ejpam-6472	543	8	science	science	NOUN
ejpam-6472	543	9	.	.	PUNCT
ejpam-6472	544	1	chapman	chapman	PROPN
ejpam-6472	544	2	&	&	CCONJ
ejpam-6472	544	3	hall	hall	PROPN
ejpam-6472	544	4	/	/	SYM
ejpam-6472	544	5	crc	crc	PROPN
ejpam-6472	544	6	,	,	PUNCT
ejpam-6472	544	7	boca	boca	PROPN
ejpam-6472	544	8	raton	raton	PROPN
ejpam-6472	544	9	,	,	PUNCT
ejpam-6472	544	10	fl	fl	PROPN
ejpam-6472	544	11	,	,	PUNCT
ejpam-6472	544	12	2002	2002	NUM
ejpam-6472	544	13	.	.	PUNCT
ejpam-6472	545	1	[	[	X
ejpam-6472	545	2	2	2	NUM
ejpam-6472	545	3	]	]	X
ejpam-6472	545	4	k	k	X
ejpam-6472	545	5	denecke	denecke	NOUN
ejpam-6472	545	6	and	and	CCONJ
ejpam-6472	545	7	s	s	NOUN
ejpam-6472	545	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6472	545	9	.	.	PUNCT
ejpam-6472	546	1	kernels	kernel	NOUN
ejpam-6472	546	2	of	of	ADP
ejpam-6472	546	3	generalized	generalized	ADJ
ejpam-6472	546	4	hypersubstitutions	hypersubstitution	NOUN
ejpam-6472	546	5	.	.	PUNCT
ejpam-6472	547	1	in	in	ADP
ejpam-6472	547	2	discrete	discrete	ADJ
ejpam-6472	547	3	mathematics	mathematic	NOUN
ejpam-6472	547	4	and	and	CCONJ
ejpam-6472	547	5	applications	application	NOUN
ejpam-6472	547	6	(	(	PUNCT
ejpam-6472	547	7	bansko	bansko	PROPN
ejpam-6472	547	8	,	,	PUNCT
ejpam-6472	547	9	2001	2001	NUM
ejpam-6472	547	10	)	)	PUNCT
ejpam-6472	547	11	,	,	PUNCT
ejpam-6472	547	12	volume	volume	NOUN
ejpam-6472	547	13	6	6	NUM
ejpam-6472	547	14	of	of	ADP
ejpam-6472	547	15	res	re	NOUN
ejpam-6472	547	16	.	.	PUNCT
ejpam-6472	547	17	math	math	NOUN
ejpam-6472	547	18	.	.	PUNCT
ejpam-6472	548	1	comput	comput	NOUN
ejpam-6472	548	2	.	.	PUNCT
ejpam-6472	549	1	sci	sci	PROPN
ejpam-6472	549	2	.	.	PROPN
ejpam-6472	549	3	,	,	PUNCT
ejpam-6472	549	4	pages	page	NOUN
ejpam-6472	549	5	87–96	87–96	NUM
ejpam-6472	549	6	.	.	PUNCT
ejpam-6472	550	1	south	south	PROPN
ejpam-6472	550	2	-	-	PUNCT
ejpam-6472	550	3	west	west	PROPN
ejpam-6472	550	4	univ	univ	PROPN
ejpam-6472	550	5	.	.	PROPN
ejpam-6472	550	6	,	,	PUNCT
ejpam-6472	550	7	blagoevgrad	blagoevgrad	PROPN
ejpam-6472	550	8	,	,	PUNCT
ejpam-6472	550	9	2002	2002	NUM
ejpam-6472	550	10	.	.	PUNCT
ejpam-6472	551	1	[	[	X
ejpam-6472	551	2	3	3	NUM
ejpam-6472	551	3	]	]	X
ejpam-6472	551	4	k	k	X
ejpam-6472	551	5	denecke	denecke	PROPN
ejpam-6472	551	6	.	.	PUNCT
ejpam-6472	552	1	menger	menger	PROPN
ejpam-6472	552	2	algebras	algebras	PROPN
ejpam-6472	552	3	and	and	CCONJ
ejpam-6472	552	4	clones	clone	NOUN
ejpam-6472	552	5	of	of	ADP
ejpam-6472	552	6	terms	term	NOUN
ejpam-6472	552	7	.	.	PUNCT
ejpam-6472	553	1	east	east	PROPN
ejpam-6472	553	2	-	-	PUNCT
ejpam-6472	553	3	west	west	PROPN
ejpam-6472	553	4	j.	j.	PROPN
ejpam-6472	553	5	math	math	PROPN
ejpam-6472	553	6	.	.	PUNCT
ejpam-6472	553	7	,	,	PUNCT
ejpam-6472	553	8	5(2):179–193	5(2):179–193	NUM
ejpam-6472	553	9	,	,	PUNCT
ejpam-6472	553	10	2003	2003	NUM
ejpam-6472	553	11	.	.	PUNCT
ejpam-6472	554	1	[	[	X
ejpam-6472	554	2	4	4	NUM
ejpam-6472	554	3	]	]	X
ejpam-6472	554	4	k	k	X
ejpam-6472	554	5	denecke	denecke	PROPN
ejpam-6472	554	6	,	,	PUNCT
ejpam-6472	554	7	p	p	NOUN
ejpam-6472	554	8	glubudom	glubudom	NOUN
ejpam-6472	554	9	,	,	PUNCT
ejpam-6472	554	10	and	and	CCONJ
ejpam-6472	554	11	j	j	PROPN
ejpam-6472	554	12	koppitz	koppitz	PROPN
ejpam-6472	554	13	.	.	PUNCT
ejpam-6472	555	1	power	power	NOUN
ejpam-6472	555	2	clones	clone	NOUN
ejpam-6472	555	3	and	and	CCONJ
ejpam-6472	555	4	non	non	ADJ
ejpam-6472	555	5	-	-	ADJ
ejpam-6472	555	6	deterministic	deterministic	ADJ
ejpam-6472	555	7	hypersubstitutions	hypersubstitution	NOUN
ejpam-6472	555	8	.	.	PUNCT
ejpam-6472	556	1	asian	asian	ADJ
ejpam-6472	556	2	-	-	PUNCT
ejpam-6472	556	3	eur	eur	NOUN
ejpam-6472	556	4	.	.	PUNCT
ejpam-6472	557	1	j.	j.	PROPN
ejpam-6472	557	2	math	math	PROPN
ejpam-6472	557	3	.	.	PUNCT
ejpam-6472	557	4	,	,	PUNCT
ejpam-6472	557	5	1(2):177–188	1(2):177–188	NUM
ejpam-6472	557	6	,	,	PUNCT
ejpam-6472	557	7	2008	2008	NUM
ejpam-6472	557	8	.	.	PUNCT
ejpam-6472	558	1	[	[	X
ejpam-6472	558	2	5	5	NUM
ejpam-6472	558	3	]	]	X
ejpam-6472	558	4	k	k	X
ejpam-6472	558	5	denecke	denecke	NOUN
ejpam-6472	558	6	and	and	CCONJ
ejpam-6472	558	7	p	p	NOUN
ejpam-6472	558	8	jampachon	jampachon	PROPN
ejpam-6472	558	9	.	.	PUNCT
ejpam-6472	559	1	regular	regular	ADJ
ejpam-6472	559	2	elements	element	NOUN
ejpam-6472	559	3	and	and	CCONJ
ejpam-6472	559	4	green	green	PROPN
ejpam-6472	559	5	’s	’s	PART
ejpam-6472	559	6	relations	relation	NOUN
ejpam-6472	559	7	in	in	ADP
ejpam-6472	559	8	menger	menger	PROPN
ejpam-6472	559	9	algebras	algebras	PROPN
ejpam-6472	559	10	of	of	ADP
ejpam-6472	559	11	terms	term	NOUN
ejpam-6472	559	12	.	.	PUNCT
ejpam-6472	560	1	discuss	discuss	PROPN
ejpam-6472	560	2	.	.	PUNCT
ejpam-6472	560	3	math	math	NOUN
ejpam-6472	560	4	.	.	PUNCT
ejpam-6472	561	1	gen	gen	PROPN
ejpam-6472	561	2	.	.	PROPN
ejpam-6472	561	3	algebra	algebra	PROPN
ejpam-6472	561	4	appl	appl	PROPN
ejpam-6472	561	5	.	.	PROPN
ejpam-6472	561	6	,	,	PUNCT
ejpam-6472	561	7	26(1):85–109	26(1):85–109	NUM
ejpam-6472	561	8	,	,	PUNCT
ejpam-6472	561	9	2006	2006	NUM
ejpam-6472	561	10	.	.	PUNCT
ejpam-6472	562	1	[	[	X
ejpam-6472	562	2	6	6	NUM
ejpam-6472	562	3	]	]	X
ejpam-6472	562	4	k	k	X
ejpam-6472	562	5	denecke	denecke	NOUN
ejpam-6472	562	6	and	and	CCONJ
ejpam-6472	562	7	n	n	PRON
ejpam-6472	562	8	sarasit	sarasit	NOUN
ejpam-6472	562	9	.	.	PUNCT
ejpam-6472	563	1	products	product	NOUN
ejpam-6472	563	2	of	of	ADP
ejpam-6472	563	3	tree	tree	NOUN
ejpam-6472	563	4	languages	language	NOUN
ejpam-6472	563	5	.	.	PUNCT
ejpam-6472	564	1	bull	bull	NOUN
ejpam-6472	564	2	.	.	PUNCT
ejpam-6472	565	1	sect	sect	NOUN
ejpam-6472	565	2	.	.	PUNCT
ejpam-6472	566	1	logic	logic	PROPN
ejpam-6472	566	2	univ	univ	PROPN
ejpam-6472	566	3	.	.	PUNCT
ejpam-6472	567	1	lódź	lódź	PROPN
ejpam-6472	567	2	,	,	PUNCT
ejpam-6472	567	3	40(1	40(1	NOUN
ejpam-6472	567	4	-	-	SYM
ejpam-6472	567	5	2):13–36	2):13–36	NUM
ejpam-6472	567	6	,	,	PUNCT
ejpam-6472	567	7	2011	2011	NUM
ejpam-6472	567	8	.	.	PUNCT
ejpam-6472	568	1	[	[	X
ejpam-6472	568	2	7	7	NUM
ejpam-6472	568	3	]	]	X
ejpam-6472	568	4	t	t	PROPN
ejpam-6472	568	5	kumduang	kumduang	PROPN
ejpam-6472	568	6	and	and	CCONJ
ejpam-6472	568	7	s	s	PROPN
ejpam-6472	568	8	leeratanavalee	leeratanavalee	PROPN
ejpam-6472	568	9	.	.	PUNCT
ejpam-6472	569	1	semigroups	semigroup	NOUN
ejpam-6472	569	2	of	of	ADP
ejpam-6472	569	3	terms	term	NOUN
ejpam-6472	569	4	,	,	PUNCT
ejpam-6472	569	5	tree	tree	NOUN
ejpam-6472	569	6	languages	language	NOUN
ejpam-6472	569	7	,	,	PUNCT
ejpam-6472	569	8	menger	menger	PROPN
ejpam-6472	569	9	algebra	algebra	PROPN
ejpam-6472	569	10	of	of	ADP
ejpam-6472	569	11	n	n	CCONJ
ejpam-6472	569	12	-	-	PUNCT
ejpam-6472	569	13	ary	ary	NOUN
ejpam-6472	569	14	functions	function	NOUN
ejpam-6472	569	15	and	and	CCONJ
ejpam-6472	569	16	their	their	PRON
ejpam-6472	569	17	embedding	embed	VERB
ejpam-6472	569	18	theorems	theorem	NOUN
ejpam-6472	569	19	.	.	PUNCT
ejpam-6472	569	20	symmetry	symmetry	NOUN
ejpam-6472	569	21	,	,	PUNCT
ejpam-6472	569	22	13:558	13:558	NUM
ejpam-6472	569	23	,	,	PUNCT
ejpam-6472	569	24	2021	2021	NUM
ejpam-6472	569	25	.	.	PUNCT
ejpam-6472	570	1	[	[	X
ejpam-6472	570	2	8	8	NUM
ejpam-6472	570	3	]	]	SYM
ejpam-6472	570	4	s	s	PART
ejpam-6472	570	5	shtrakov	shtrakov	NOUN
ejpam-6472	570	6	.	.	PUNCT
ejpam-6472	571	1	multi	multi	ADJ
ejpam-6472	571	2	-	-	ADJ
ejpam-6472	571	3	solid	solid	ADJ
ejpam-6472	571	4	varieties	variety	NOUN
ejpam-6472	571	5	and	and	CCONJ
ejpam-6472	571	6	mh	mh	PROPN
ejpam-6472	571	7	-	-	PUNCT
ejpam-6472	571	8	transducers	transducer	NOUN
ejpam-6472	571	9	.	.	PUNCT
ejpam-6472	572	1	algebra	algebra	NOUN
ejpam-6472	572	2	discrete	discrete	ADJ
ejpam-6472	572	3	math	math	NOUN
ejpam-6472	572	4	.	.	PUNCT
ejpam-6472	572	5	,	,	PUNCT
ejpam-6472	572	6	(	(	PUNCT
ejpam-6472	572	7	3):113–131	3):113–131	NUM
ejpam-6472	572	8	,	,	PUNCT
ejpam-6472	572	9	2007	2007	NUM
ejpam-6472	572	10	.	.	PUNCT
ejpam-6472	573	1	[	[	X
ejpam-6472	573	2	9	9	NUM
ejpam-6472	573	3	]	]	X
ejpam-6472	573	4	p	p	X
ejpam-6472	573	5	kitpratyakul	kitpratyakul	PROPN
ejpam-6472	573	6	and	and	CCONJ
ejpam-6472	573	7	b	b	NOUN
ejpam-6472	573	8	pibaljommee	pibaljommee	NOUN
ejpam-6472	573	9	.	.	PUNCT
ejpam-6472	574	1	semigroups	semigroup	NOUN
ejpam-6472	574	2	of	of	ADP
ejpam-6472	574	3	an	an	DET
ejpam-6472	574	4	inductive	inductive	ADJ
ejpam-6472	574	5	composition	composition	NOUN
ejpam-6472	574	6	of	of	ADP
ejpam-6472	574	7	terms	term	NOUN
ejpam-6472	574	8	.	.	PUNCT
ejpam-6472	575	1	asian	asian	ADJ
ejpam-6472	575	2	-	-	PUNCT
ejpam-6472	575	3	eur	eur	NOUN
ejpam-6472	575	4	.	.	PUNCT
ejpam-6472	576	1	j.	j.	PROPN
ejpam-6472	576	2	math	math	PROPN
ejpam-6472	576	3	.	.	PUNCT
ejpam-6472	576	4	,	,	PUNCT
ejpam-6472	576	5	15(2):paper	15(2):paper	NUM
ejpam-6472	576	6	no	no	NOUN
ejpam-6472	576	7	.	.	PUNCT
ejpam-6472	577	1	2250038	2250038	NUM
ejpam-6472	577	2	,	,	PUNCT
ejpam-6472	577	3	16	16	NUM
ejpam-6472	577	4	,	,	PUNCT
ejpam-6472	577	5	2022	2022	NUM
ejpam-6472	577	6	.	.	PUNCT
ejpam-6472	578	1	[	[	X
ejpam-6472	578	2	10	10	NUM
ejpam-6472	578	3	]	]	X
ejpam-6472	578	4	p	p	X
ejpam-6472	578	5	kitpratyakul	kitpratyakul	PROPN
ejpam-6472	578	6	and	and	CCONJ
ejpam-6472	578	7	b	b	NOUN
ejpam-6472	578	8	pibaljommee	pibaljommee	NOUN
ejpam-6472	578	9	.	.	PUNCT
ejpam-6472	579	1	ideal	ideal	ADJ
ejpam-6472	579	2	characterizations	characterization	NOUN
ejpam-6472	579	3	of	of	ADP
ejpam-6472	579	4	semigroups	semigroup	NOUN
ejpam-6472	579	5	of	of	ADP
ejpam-6472	579	6	inductive	inductive	ADJ
ejpam-6472	579	7	terms	term	NOUN
ejpam-6472	579	8	.	.	PUNCT
ejpam-6472	580	1	international	international	ADJ
ejpam-6472	580	2	journal	journal	NOUN
ejpam-6472	580	3	of	of	ADP
ejpam-6472	580	4	innovative	innovative	ADJ
ejpam-6472	580	5	computing	computing	NOUN
ejpam-6472	580	6	,	,	PUNCT
ejpam-6472	580	7	information	information	NOUN
ejpam-6472	580	8	and	and	CCONJ
ejpam-6472	580	9	control	control	NOUN
ejpam-6472	580	10	,	,	PUNCT
ejpam-6472	580	11	18:801–813	18:801–813	NUM
ejpam-6472	580	12	,	,	PUNCT
ejpam-6472	580	13	2022	2022	NUM
ejpam-6472	580	14	.	.	PUNCT
ejpam-6472	581	1	[	[	X
ejpam-6472	581	2	11	11	NUM
ejpam-6472	581	3	]	]	X
ejpam-6472	581	4	p	p	X
ejpam-6472	581	5	kitpratyakul	kitpratyakul	PROPN
ejpam-6472	581	6	and	and	CCONJ
ejpam-6472	581	7	b	b	NOUN
ejpam-6472	581	8	pibaljommee	pibaljommee	NOUN
ejpam-6472	581	9	.	.	PUNCT
ejpam-6472	582	1	on	on	ADP
ejpam-6472	582	2	substructures	substructure	NOUN
ejpam-6472	582	3	of	of	ADP
ejpam-6472	582	4	semigroups	semigroup	NOUN
ejpam-6472	582	5	of	of	ADP
ejpam-6472	582	6	inductive	inductive	ADJ
ejpam-6472	582	7	terms	term	NOUN
ejpam-6472	582	8	.	.	PUNCT
ejpam-6472	583	1	aims	aim	VERB
ejpam-6472	583	2	math	math	NOUN
ejpam-6472	583	3	.	.	PUNCT
ejpam-6472	583	4	,	,	PUNCT
ejpam-6472	584	1	7(6):9835–9845	7(6):9835–9845	NOUN
ejpam-6472	584	2	,	,	PUNCT
ejpam-6472	584	3	2022	2022	NUM
ejpam-6472	584	4	.	.	PUNCT
ejpam-6472	585	1	[	[	X
ejpam-6472	585	2	12	12	NUM
ejpam-6472	585	3	]	]	X
ejpam-6472	585	4	j	j	PROPN
ejpam-6472	585	5	boonsol	boonsol	NOUN
ejpam-6472	585	6	,	,	PUNCT
ejpam-6472	585	7	p	p	PROPN
ejpam-6472	585	8	kitpratyakul	kitpratyakul	PROPN
ejpam-6472	585	9	,	,	PUNCT
ejpam-6472	585	10	t	t	PROPN
ejpam-6472	585	11	changphas	changpha	NOUN
ejpam-6472	585	12	,	,	PUNCT
ejpam-6472	585	13	and	and	CCONJ
ejpam-6472	585	14	b	b	X
ejpam-6472	585	15	pibaljommee	pibaljommee	NOUN
ejpam-6472	585	16	.	.	PUNCT
ejpam-6472	586	1	a	a	DET
ejpam-6472	586	2	product	product	NOUN
ejpam-6472	586	3	of	of	ADP
ejpam-6472	586	4	tree	tree	NOUN
ejpam-6472	586	5	languages	language	NOUN
ejpam-6472	586	6	.	.	PUNCT
ejpam-6472	587	1	int	int	NOUN
ejpam-6472	587	2	.	.	PUNCT
ejpam-6472	588	1	j.	j.	PROPN
ejpam-6472	588	2	math	math	PROPN
ejpam-6472	588	3	.	.	PUNCT
ejpam-6472	589	1	comput	comput	NOUN
ejpam-6472	589	2	.	.	PUNCT
ejpam-6472	590	1	sci	sci	PROPN
ejpam-6472	590	2	.	.	PROPN
ejpam-6472	590	3	,	,	PUNCT
ejpam-6472	590	4	19(2):279–288	19(2):279–288	PROPN
ejpam-6472	590	5	,	,	PUNCT
ejpam-6472	590	6	2024	2024	NUM
ejpam-6472	590	7	.	.	PUNCT
ejpam-6472	591	1	p.	p.	NOUN
ejpam-6472	591	2	prachumdang	prachumdang	PROPN
ejpam-6472	591	3	,	,	PUNCT
ejpam-6472	591	4	b.	b.	PROPN
ejpam-6472	591	5	pibaljommee	pibaljommee	PROPN
ejpam-6472	591	6	/	/	SYM
ejpam-6472	591	7	eur	eur	PROPN
ejpam-6472	591	8	.	.	PUNCT
ejpam-6472	592	1	j.	j.	PROPN
ejpam-6472	592	2	pure	pure	PROPN
ejpam-6472	592	3	appl	appl	PROPN
ejpam-6472	592	4	.	.	PROPN
ejpam-6472	592	5	math	math	PROPN
ejpam-6472	592	6	,	,	PUNCT
ejpam-6472	592	7	18	18	NUM
ejpam-6472	592	8	(	(	PUNCT
ejpam-6472	592	9	3	3	NUM
ejpam-6472	592	10	)	)	PUNCT
ejpam-6472	592	11	(	(	PUNCT
ejpam-6472	592	12	2025	2025	NUM
ejpam-6472	592	13	)	)	PUNCT
ejpam-6472	592	14	,	,	PUNCT
ejpam-6472	592	15	6472	6472	NUM
ejpam-6472	592	16	16	16	NUM
ejpam-6472	592	17	of	of	ADP
ejpam-6472	592	18	16	16	NUM
ejpam-6472	593	1	[	[	X
ejpam-6472	593	2	13	13	NUM
ejpam-6472	593	3	]	]	X
ejpam-6472	593	4	k	k	X
ejpam-6472	593	5	denecke	denecke	NOUN
ejpam-6472	593	6	and	and	CCONJ
ejpam-6472	593	7	s	s	PROPN
ejpam-6472	593	8	l	l	NOUN
ejpam-6472	593	9	wismath	wismath	NOUN
ejpam-6472	593	10	.	.	PUNCT
ejpam-6472	594	1	complexity	complexity	NOUN
ejpam-6472	594	2	of	of	ADP
ejpam-6472	594	3	terms	term	NOUN
ejpam-6472	594	4	,	,	PUNCT
ejpam-6472	594	5	composition	composition	NOUN
ejpam-6472	594	6	,	,	PUNCT
ejpam-6472	594	7	and	and	CCONJ
ejpam-6472	594	8	hypersubstitution	hypersubstitution	NOUN
ejpam-6472	594	9	.	.	PUNCT
ejpam-6472	595	1	int	int	NOUN
ejpam-6472	595	2	.	.	PUNCT
ejpam-6472	596	1	j.	j.	PROPN
ejpam-6472	596	2	math	math	PROPN
ejpam-6472	596	3	.	.	PUNCT
ejpam-6472	597	1	math	math	NOUN
ejpam-6472	597	2	.	.	PUNCT
ejpam-6472	598	1	sci	sci	PROPN
ejpam-6472	598	2	.	.	PROPN
ejpam-6472	598	3	,	,	PUNCT
ejpam-6472	598	4	(	(	PUNCT
ejpam-6472	598	5	15):959–969	15):959–969	PROPN
ejpam-6472	598	6	,	,	PUNCT
ejpam-6472	598	7	2003	2003	NUM
ejpam-6472	598	8	.	.	PUNCT
ejpam-6472	599	1	[	[	X
ejpam-6472	599	2	14	14	NUM
ejpam-6472	599	3	]	]	X
ejpam-6472	599	4	j	j	PROPN
ejpam-6472	599	5	m	m	PROPN
ejpam-6472	599	6	howie	howie	NOUN
ejpam-6472	599	7	.	.	PUNCT
ejpam-6472	600	1	fundamentals	fundamental	NOUN
ejpam-6472	600	2	of	of	ADP
ejpam-6472	600	3	semigroup	semigroup	PROPN
ejpam-6472	600	4	theory	theory	NOUN
ejpam-6472	600	5	,	,	PUNCT
ejpam-6472	600	6	volume	volume	NOUN
ejpam-6472	600	7	12	12	NUM
ejpam-6472	600	8	of	of	ADP
ejpam-6472	600	9	london	london	PROPN
ejpam-6472	600	10	mathematical	mathematical	ADJ
ejpam-6472	600	11	society	society	NOUN
ejpam-6472	600	12	monographs	monograph	NOUN
ejpam-6472	600	13	.	.	PUNCT
ejpam-6472	601	1	new	new	ADJ
ejpam-6472	601	2	series	series	NOUN
ejpam-6472	601	3	.	.	PUNCT
ejpam-6472	602	1	the	the	DET
ejpam-6472	602	2	clarendon	clarendon	PROPN
ejpam-6472	602	3	press	press	NOUN
ejpam-6472	602	4	,	,	PUNCT
ejpam-6472	602	5	oxford	oxford	PROPN
ejpam-6472	602	6	university	university	PROPN
ejpam-6472	602	7	press	press	NOUN
ejpam-6472	602	8	,	,	PUNCT
ejpam-6472	602	9	new	new	PROPN
ejpam-6472	602	10	york	york	PROPN
ejpam-6472	602	11	,	,	PUNCT
ejpam-6472	602	12	1995	1995	NUM
ejpam-6472	602	13	.	.	PUNCT
ejpam-6472	603	1	oxford	oxford	PROPN
ejpam-6472	603	2	science	science	PROPN
ejpam-6472	603	3	publications	publication	NOUN
ejpam-6472	603	4	.	.	PUNCT