id	sid	tid	token	lemma	pos
ejpam-6436	1	1	european	european	PROPN
ejpam-6436	1	2	journal	journal	PROPN
ejpam-6436	1	3	of	of	ADP
ejpam-6436	1	4	pure	pure	ADJ
ejpam-6436	1	5	and	and	CCONJ
ejpam-6436	1	6	applied	applied	ADJ
ejpam-6436	1	7	mathematics	mathematic	NOUN
ejpam-6436	1	8	2025	2025	NUM
ejpam-6436	1	9	,	,	PUNCT
ejpam-6436	1	10	vol	vol	NOUN
ejpam-6436	1	11	.	.	PROPN
ejpam-6436	1	12	18	18	NUM
ejpam-6436	1	13	,	,	PUNCT
ejpam-6436	1	14	issue	issue	NOUN
ejpam-6436	1	15	3	3	NUM
ejpam-6436	1	16	,	,	PUNCT
ejpam-6436	1	17	article	article	NOUN
ejpam-6436	1	18	number	number	NOUN
ejpam-6436	1	19	6436	6436	NUM
ejpam-6436	1	20	issn	issn	VERB
ejpam-6436	1	21	1307	1307	NUM
ejpam-6436	1	22	-	-	SYM
ejpam-6436	1	23	5543	5543	NUM
ejpam-6436	1	24	–	–	PUNCT
ejpam-6436	1	25	ejpam.com	ejpam.com	X
ejpam-6436	1	26	published	publish	VERB
ejpam-6436	1	27	by	by	ADP
ejpam-6436	1	28	new	new	PROPN
ejpam-6436	1	29	york	york	PROPN
ejpam-6436	1	30	business	business	PROPN
ejpam-6436	1	31	global	global	PROPN
ejpam-6436	1	32	on	on	ADP
ejpam-6436	1	33	po	po	NOUN
ejpam-6436	1	34	-	-	ADJ
ejpam-6436	1	35	injective	injective	ADJ
ejpam-6436	1	36	and	and	CCONJ
ejpam-6436	1	37	po	po	NOUN
ejpam-6436	1	38	-	-	ADJ
ejpam-6436	1	39	surjective	surjective	ADJ
ejpam-6436	1	40	wreath	wreath	NOUN
ejpam-6436	1	41	product	product	NOUN
ejpam-6436	1	42	of	of	ADP
ejpam-6436	1	43	pomonoids	pomonoids	PROPN
ejpam-6436	1	44	bana	bana	PROPN
ejpam-6436	1	45	al	al	PROPN
ejpam-6436	1	46	subaiei1,∗	subaiei1,∗	PROPN
ejpam-6436	1	47	,	,	PUNCT
ejpam-6436	1	48	ahlam	ahlam	PROPN
ejpam-6436	1	49	almulhim1	almulhim1	PROPN
ejpam-6436	1	50	,	,	PUNCT
ejpam-6436	1	51	aftab	aftab	PROPN
ejpam-6436	1	52	hussain	hussain	PROPN
ejpam-6436	1	53	shah2	shah2	PROPN
ejpam-6436	1	54	,	,	PUNCT
ejpam-6436	1	55	syed	syed	ADJ
ejpam-6436	1	56	ahtisham	ahtisham	PROPN
ejpam-6436	1	57	ul	ul	INTJ
ejpam-6436	1	58	haq2	haq2	PROPN
ejpam-6436	1	59	1	1	NUM
ejpam-6436	1	60	department	department	NOUN
ejpam-6436	1	61	of	of	ADP
ejpam-6436	1	62	mathematics	mathematic	NOUN
ejpam-6436	1	63	and	and	CCONJ
ejpam-6436	1	64	statistics	statistic	NOUN
ejpam-6436	1	65	,	,	PUNCT
ejpam-6436	1	66	king	king	PROPN
ejpam-6436	1	67	faisal	faisal	PROPN
ejpam-6436	1	68	university	university	PROPN
ejpam-6436	1	69	,	,	PUNCT
ejpam-6436	1	70	al	al	PROPN
ejpam-6436	1	71	-	-	PUNCT
ejpam-6436	1	72	ahsa	ahsa	PROPN
ejpam-6436	1	73	,	,	PUNCT
ejpam-6436	1	74	saudi	saudi	PROPN
ejpam-6436	1	75	arabia	arabia	PROPN
ejpam-6436	1	76	2	2	NUM
ejpam-6436	1	77	department	department	NOUN
ejpam-6436	1	78	of	of	ADP
ejpam-6436	1	79	mathematics	mathematic	NOUN
ejpam-6436	1	80	,	,	PUNCT
ejpam-6436	1	81	central	central	ADJ
ejpam-6436	1	82	university	university	PROPN
ejpam-6436	1	83	of	of	ADP
ejpam-6436	1	84	kashmir	kashmir	PROPN
ejpam-6436	1	85	,	,	PUNCT
ejpam-6436	1	86	ganderbal	ganderbal	PROPN
ejpam-6436	1	87	,	,	PUNCT
ejpam-6436	1	88	india	india	PROPN
ejpam-6436	1	89	abstract	abstract	NOUN
ejpam-6436	1	90	.	.	PUNCT
ejpam-6436	2	1	let	let	VERB
ejpam-6436	2	2	r	r	NOUN
ejpam-6436	2	3	and	and	CCONJ
ejpam-6436	2	4	s	s	VERB
ejpam-6436	2	5	be	be	AUX
ejpam-6436	2	6	pomonoids	pomonoid	NOUN
ejpam-6436	2	7	and	and	CCONJ
ejpam-6436	2	8	ra	ra	PROPN
ejpam-6436	2	9	be	be	AUX
ejpam-6436	2	10	a	a	DET
ejpam-6436	2	11	left	left	ADJ
ejpam-6436	2	12	r	r	NOUN
ejpam-6436	2	13	-	-	PUNCT
ejpam-6436	2	14	poset	poset	NOUN
ejpam-6436	2	15	.	.	PUNCT
ejpam-6436	3	1	the	the	DET
ejpam-6436	3	2	wreath	wreath	NOUN
ejpam-6436	3	3	product	product	NOUN
ejpam-6436	3	4	of	of	ADP
ejpam-6436	3	5	the	the	DET
ejpam-6436	3	6	pomonoids	pomonoid	NOUN
ejpam-6436	3	7	r	r	NOUN
ejpam-6436	3	8	and	and	CCONJ
ejpam-6436	3	9	s	s	NOUN
ejpam-6436	3	10	by	by	ADP
ejpam-6436	3	11	ra	ra	PROPN
ejpam-6436	3	12	is	be	AUX
ejpam-6436	3	13	defined	define	VERB
ejpam-6436	3	14	as	as	ADP
ejpam-6436	3	15	the	the	DET
ejpam-6436	3	16	pomonoid	pomonoid	NOUN
ejpam-6436	3	17	t	t	PROPN
ejpam-6436	3	18	=	=	SYM
ejpam-6436	3	19	r×f	r×f	PROPN
ejpam-6436	3	20	(	(	PUNCT
ejpam-6436	3	21	a	a	DET
ejpam-6436	3	22	,	,	PUNCT
ejpam-6436	3	23	s	s	NOUN
ejpam-6436	3	24	)	)	PUNCT
ejpam-6436	3	25	while	while	SCONJ
ejpam-6436	3	26	,	,	PUNCT
ejpam-6436	3	27	the	the	DET
ejpam-6436	3	28	wreath	wreath	NOUN
ejpam-6436	3	29	product	product	NOUN
ejpam-6436	3	30	tc	tc	NOUN
ejpam-6436	3	31	of	of	ADP
ejpam-6436	3	32	the	the	DET
ejpam-6436	3	33	left	left	ADJ
ejpam-6436	3	34	r	r	NOUN
ejpam-6436	3	35	-	-	PUNCT
ejpam-6436	3	36	poset	poset	VERB
ejpam-6436	3	37	ra	ra	NOUN
ejpam-6436	3	38	with	with	ADP
ejpam-6436	3	39	the	the	DET
ejpam-6436	3	40	left	left	ADJ
ejpam-6436	3	41	s	s	NOUN
ejpam-6436	3	42	-	-	PUNCT
ejpam-6436	3	43	poset	poset	VERB
ejpam-6436	3	44	sb	sb	NOUN
ejpam-6436	3	45	over	over	ADP
ejpam-6436	3	46	the	the	DET
ejpam-6436	3	47	pomonoid	pomonoid	NOUN
ejpam-6436	3	48	t	t	PROPN
ejpam-6436	3	49	=	=	PUNCT
ejpam-6436	3	50	r	r	NOUN
ejpam-6436	3	51	×	×	PROPN
ejpam-6436	3	52	f	f	X
ejpam-6436	3	53	(	(	PUNCT
ejpam-6436	3	54	a	a	PRON
ejpam-6436	3	55	,	,	PUNCT
ejpam-6436	3	56	s	s	PART
ejpam-6436	3	57	)	)	PUNCT
ejpam-6436	3	58	is	be	AUX
ejpam-6436	3	59	the	the	DET
ejpam-6436	3	60	left	left	NOUN
ejpam-6436	3	61	t	t	NOUN
ejpam-6436	3	62	-poset	-poset	PROPN
ejpam-6436	4	1	tc	tc	NOUN
ejpam-6436	4	2	=	=	SYM
ejpam-6436	4	3	ra×	ra×	NOUN
ejpam-6436	4	4	sb	sb	PROPN
ejpam-6436	4	5	endowed	endow	VERB
ejpam-6436	4	6	with	with	ADP
ejpam-6436	4	7	the	the	DET
ejpam-6436	4	8	monotone	monotone	ADJ
ejpam-6436	4	9	action	action	NOUN
ejpam-6436	4	10	given	give	VERB
ejpam-6436	4	11	by	by	ADP
ejpam-6436	4	12	(	(	PUNCT
ejpam-6436	4	13	r	r	NOUN
ejpam-6436	4	14	,	,	PUNCT
ejpam-6436	4	15	f)(a	f)(a	NUM
ejpam-6436	4	16	,	,	PUNCT
ejpam-6436	4	17	b	b	NOUN
ejpam-6436	4	18	)	)	PUNCT
ejpam-6436	4	19	=	=	SYM
ejpam-6436	4	20	(	(	PUNCT
ejpam-6436	4	21	ra	ra	PROPN
ejpam-6436	4	22	,	,	PUNCT
ejpam-6436	4	23	f(a)b	f(a)b	PROPN
ejpam-6436	4	24	)	)	PUNCT
ejpam-6436	4	25	,	,	PUNCT
ejpam-6436	5	1	where	where	SCONJ
ejpam-6436	5	2	(	(	PUNCT
ejpam-6436	5	3	r	r	NOUN
ejpam-6436	5	4	,	,	PUNCT
ejpam-6436	5	5	f	f	X
ejpam-6436	5	6	)	)	PUNCT
ejpam-6436	5	7	∈	∈	PROPN
ejpam-6436	5	8	r×f	r×f	PROPN
ejpam-6436	5	9	(	(	PUNCT
ejpam-6436	5	10	a	a	PRON
ejpam-6436	5	11	,	,	PUNCT
ejpam-6436	5	12	s	s	PART
ejpam-6436	5	13	)	)	PUNCT
ejpam-6436	5	14	and	and	CCONJ
ejpam-6436	5	15	(	(	PUNCT
ejpam-6436	5	16	a	a	PRON
ejpam-6436	5	17	,	,	PUNCT
ejpam-6436	5	18	b	b	NOUN
ejpam-6436	5	19	)	)	PUNCT
ejpam-6436	5	20	∈	∈	PROPN
ejpam-6436	5	21	a×b	a×b	PROPN
ejpam-6436	5	22	.	.	PUNCT
ejpam-6436	6	1	the	the	DET
ejpam-6436	6	2	po	po	NOUN
ejpam-6436	6	3	-	-	PUNCT
ejpam-6436	6	4	injectivity	injectivity	PROPN
ejpam-6436	6	5	and	and	CCONJ
ejpam-6436	6	6	po	po	NOUN
ejpam-6436	6	7	-	-	PUNCT
ejpam-6436	6	8	cancellative	cancellative	ADJ
ejpam-6436	6	9	properties	property	NOUN
ejpam-6436	6	10	on	on	ADP
ejpam-6436	6	11	the	the	DET
ejpam-6436	6	12	wreath	wreath	NOUN
ejpam-6436	6	13	product	product	NOUN
ejpam-6436	6	14	tc	tc	NOUN
ejpam-6436	6	15	are	be	AUX
ejpam-6436	6	16	studied	study	VERB
ejpam-6436	6	17	and	and	CCONJ
ejpam-6436	6	18	the	the	DET
ejpam-6436	6	19	relations	relation	NOUN
ejpam-6436	6	20	between	between	ADP
ejpam-6436	6	21	them	they	PRON
ejpam-6436	6	22	are	be	AUX
ejpam-6436	6	23	established	establish	VERB
ejpam-6436	6	24	.	.	PUNCT
ejpam-6436	7	1	the	the	DET
ejpam-6436	7	2	relation	relation	NOUN
ejpam-6436	7	3	between	between	ADP
ejpam-6436	7	4	po	po	NOUN
ejpam-6436	7	5	-	-	ADJ
ejpam-6436	7	6	surjective	surjective	ADJ
ejpam-6436	7	7	property	property	NOUN
ejpam-6436	7	8	and	and	CCONJ
ejpam-6436	7	9	other	other	ADJ
ejpam-6436	7	10	properties	property	NOUN
ejpam-6436	7	11	on	on	ADP
ejpam-6436	7	12	the	the	DET
ejpam-6436	7	13	wreath	wreath	NOUN
ejpam-6436	7	14	product	product	NOUN
ejpam-6436	7	15	tc	tc	NOUN
ejpam-6436	7	16	are	be	AUX
ejpam-6436	7	17	also	also	ADV
ejpam-6436	7	18	established	establish	VERB
ejpam-6436	7	19	.	.	PUNCT
ejpam-6436	8	1	finally	finally	ADV
ejpam-6436	8	2	the	the	DET
ejpam-6436	8	3	characterization	characterization	NOUN
ejpam-6436	8	4	of	of	ADP
ejpam-6436	8	5	some	some	DET
ejpam-6436	8	6	properties	property	NOUN
ejpam-6436	8	7	of	of	ADP
ejpam-6436	8	8	po	po	NOUN
ejpam-6436	8	9	-	-	NOUN
ejpam-6436	8	10	flatness	flatness	NOUN
ejpam-6436	8	11	such	such	ADJ
ejpam-6436	8	12	as	as	ADP
ejpam-6436	8	13	po	po	NOUN
ejpam-6436	8	14	-	-	PUNCT
ejpam-6436	8	15	torsion	torsion	NOUN
ejpam-6436	8	16	free	free	ADJ
ejpam-6436	8	17	,	,	PUNCT
ejpam-6436	8	18	properties	property	NOUN
ejpam-6436	8	19	(	(	PUNCT
ejpam-6436	8	20	p	p	NOUN
ejpam-6436	8	21	)	)	PUNCT
ejpam-6436	8	22	,	,	PUNCT
ejpam-6436	8	23	(	(	PUNCT
ejpam-6436	8	24	e	e	NOUN
ejpam-6436	8	25	)	)	PUNCT
ejpam-6436	8	26	,	,	PUNCT
ejpam-6436	8	27	(	(	PUNCT
ejpam-6436	8	28	pe	pe	INTJ
ejpam-6436	8	29	)	)	PUNCT
ejpam-6436	8	30	,	,	PUNCT
ejpam-6436	8	31	and	and	CCONJ
ejpam-6436	8	32	strongly	strongly	ADV
ejpam-6436	8	33	flat	flat	ADJ
ejpam-6436	8	34	have	have	AUX
ejpam-6436	8	35	been	be	AUX
ejpam-6436	8	36	examined	examine	VERB
ejpam-6436	8	37	on	on	ADP
ejpam-6436	8	38	the	the	DET
ejpam-6436	8	39	wreath	wreath	NOUN
ejpam-6436	8	40	product	product	NOUN
ejpam-6436	8	41	tc	tc	NOUN
ejpam-6436	8	42	and	and	CCONJ
ejpam-6436	8	43	the	the	DET
ejpam-6436	8	44	relations	relation	NOUN
ejpam-6436	8	45	among	among	ADP
ejpam-6436	8	46	them	they	PRON
ejpam-6436	8	47	have	have	AUX
ejpam-6436	8	48	also	also	ADV
ejpam-6436	8	49	been	be	AUX
ejpam-6436	8	50	established	establish	VERB
ejpam-6436	8	51	.	.	PUNCT
ejpam-6436	9	1	2020	2020	NUM
ejpam-6436	9	2	mathematics	mathematics	PROPN
ejpam-6436	9	3	subject	subject	NOUN
ejpam-6436	9	4	classifications	classification	NOUN
ejpam-6436	9	5	:	:	PUNCT
ejpam-6436	9	6	20	20	NUM
ejpam-6436	9	7	-	-	SYM
ejpam-6436	9	8	xx	xx	NUM
ejpam-6436	9	9	,	,	PUNCT
ejpam-6436	9	10	20m15	20m15	NOUN
ejpam-6436	9	11	,	,	PUNCT
ejpam-6436	9	12	06f05	06f05	NUM
ejpam-6436	9	13	,	,	PUNCT
ejpam-6436	9	14	20m30	20m30	NUM
ejpam-6436	9	15	key	key	ADJ
ejpam-6436	9	16	words	word	NOUN
ejpam-6436	9	17	and	and	CCONJ
ejpam-6436	9	18	phrases	phrase	NOUN
ejpam-6436	9	19	:	:	PUNCT
ejpam-6436	9	20	wreath	wreath	NOUN
ejpam-6436	9	21	product	product	NOUN
ejpam-6436	9	22	,	,	PUNCT
ejpam-6436	9	23	po	po	NOUN
ejpam-6436	9	24	-	-	PUNCT
ejpam-6436	9	25	injective	injective	ADJ
ejpam-6436	9	26	,	,	PUNCT
ejpam-6436	9	27	po	po	NOUN
ejpam-6436	9	28	-	-	NOUN
ejpam-6436	9	29	surjective	surjective	ADJ
ejpam-6436	9	30	1	1	NUM
ejpam-6436	9	31	.	.	PUNCT
ejpam-6436	9	32	introduction	introduction	NOUN
ejpam-6436	9	33	in	in	ADP
ejpam-6436	9	34	group	group	NOUN
ejpam-6436	9	35	theory	theory	NOUN
ejpam-6436	9	36	the	the	DET
ejpam-6436	9	37	wreath	wreath	NOUN
ejpam-6436	9	38	product	product	NOUN
ejpam-6436	9	39	is	be	AUX
ejpam-6436	9	40	a	a	DET
ejpam-6436	9	41	generalization	generalization	NOUN
ejpam-6436	9	42	of	of	ADP
ejpam-6436	9	43	the	the	DET
ejpam-6436	9	44	semidirect	semidirect	NOUN
ejpam-6436	9	45	product	product	NOUN
ejpam-6436	9	46	.	.	PUNCT
ejpam-6436	10	1	the	the	DET
ejpam-6436	10	2	wreath	wreath	NOUN
ejpam-6436	10	3	product	product	NOUN
ejpam-6436	10	4	is	be	AUX
ejpam-6436	10	5	a	a	DET
ejpam-6436	10	6	way	way	NOUN
ejpam-6436	10	7	to	to	PART
ejpam-6436	10	8	combine	combine	VERB
ejpam-6436	10	9	two	two	NUM
ejpam-6436	10	10	groups	group	NOUN
ejpam-6436	10	11	,	,	PUNCT
ejpam-6436	10	12	h	h	NOUN
ejpam-6436	10	13	and	and	CCONJ
ejpam-6436	10	14	k	k	PROPN
ejpam-6436	10	15	,	,	PUNCT
ejpam-6436	10	16	using	use	VERB
ejpam-6436	10	17	the	the	DET
ejpam-6436	10	18	semidirect	semidirect	NOUN
ejpam-6436	10	19	product	product	NOUN
ejpam-6436	10	20	.	.	PUNCT
ejpam-6436	11	1	the	the	DET
ejpam-6436	11	2	key	key	ADJ
ejpam-6436	11	3	feature	feature	NOUN
ejpam-6436	11	4	is	be	AUX
ejpam-6436	11	5	that	that	SCONJ
ejpam-6436	11	6	one	one	NUM
ejpam-6436	11	7	group	group	NOUN
ejpam-6436	11	8	,	,	PUNCT
ejpam-6436	11	9	say	say	VERB
ejpam-6436	11	10	h	h	NOUN
ejpam-6436	11	11	acts	act	VERB
ejpam-6436	11	12	on	on	ADP
ejpam-6436	11	13	k	k	PROPN
ejpam-6436	11	14	in	in	ADP
ejpam-6436	11	15	a	a	DET
ejpam-6436	11	16	specific	specific	ADJ
ejpam-6436	11	17	way	way	NOUN
ejpam-6436	11	18	,	,	PUNCT
ejpam-6436	11	19	and	and	CCONJ
ejpam-6436	11	20	this	this	DET
ejpam-6436	11	21	action	action	NOUN
ejpam-6436	11	22	is	be	AUX
ejpam-6436	11	23	a	a	DET
ejpam-6436	11	24	crucial	crucial	ADJ
ejpam-6436	11	25	part	part	NOUN
ejpam-6436	11	26	of	of	ADP
ejpam-6436	11	27	the	the	DET
ejpam-6436	11	28	construction	construction	NOUN
ejpam-6436	11	29	.	.	PUNCT
ejpam-6436	12	1	the	the	DET
ejpam-6436	12	2	idea	idea	NOUN
ejpam-6436	12	3	of	of	ADP
ejpam-6436	12	4	wreath	wreath	NOUN
ejpam-6436	12	5	products	product	NOUN
ejpam-6436	12	6	has	have	AUX
ejpam-6436	12	7	been	be	AUX
ejpam-6436	12	8	extended	extend	VERB
ejpam-6436	12	9	to	to	ADP
ejpam-6436	12	10	semigroups	semigroup	NOUN
ejpam-6436	12	11	and	and	CCONJ
ejpam-6436	12	12	posemigroups	posemigroup	NOUN
ejpam-6436	12	13	as	as	ADV
ejpam-6436	12	14	well	well	ADV
ejpam-6436	12	15	,	,	PUNCT
ejpam-6436	12	16	allowing	allow	VERB
ejpam-6436	12	17	for	for	ADP
ejpam-6436	12	18	a	a	DET
ejpam-6436	12	19	broader	broad	ADJ
ejpam-6436	12	20	application	application	NOUN
ejpam-6436	12	21	of	of	ADP
ejpam-6436	12	22	this	this	DET
ejpam-6436	12	23	construction	construction	NOUN
ejpam-6436	12	24	beyond	beyond	ADP
ejpam-6436	12	25	just	just	ADV
ejpam-6436	12	26	groups	group	NOUN
ejpam-6436	12	27	.	.	PUNCT
ejpam-6436	13	1	the	the	DET
ejpam-6436	13	2	wreath	wreath	NOUN
ejpam-6436	13	3	product	product	NOUN
ejpam-6436	13	4	of	of	ADP
ejpam-6436	13	5	semigroups	semigroup	NOUN
ejpam-6436	13	6	is	be	AUX
ejpam-6436	13	7	a	a	DET
ejpam-6436	13	8	generalization	generalization	NOUN
ejpam-6436	13	9	of	of	ADP
ejpam-6436	13	10	the	the	DET
ejpam-6436	13	11	concept	concept	NOUN
ejpam-6436	13	12	for	for	ADP
ejpam-6436	13	13	groups	group	NOUN
ejpam-6436	13	14	,	,	PUNCT
ejpam-6436	13	15	but	but	CCONJ
ejpam-6436	13	16	with	with	ADP
ejpam-6436	13	17	some	some	DET
ejpam-6436	13	18	modifications	modification	NOUN
ejpam-6436	13	19	to	to	PART
ejpam-6436	13	20	accommodate	accommodate	VERB
ejpam-6436	13	21	the	the	DET
ejpam-6436	13	22	lack	lack	NOUN
ejpam-6436	13	23	of	of	ADP
ejpam-6436	13	24	inverses	inverse	NOUN
ejpam-6436	13	25	in	in	ADP
ejpam-6436	13	26	semigroups	semigroup	NOUN
ejpam-6436	13	27	.	.	PUNCT
ejpam-6436	14	1	the	the	DET
ejpam-6436	14	2	construction	construction	NOUN
ejpam-6436	14	3	involves	involve	VERB
ejpam-6436	14	4	not	not	PART
ejpam-6436	14	5	only	only	ADV
ejpam-6436	14	6	the	the	DET
ejpam-6436	14	7	direct	direct	ADJ
ejpam-6436	14	8	product	product	NOUN
ejpam-6436	14	9	of	of	ADP
ejpam-6436	14	10	copies	copy	NOUN
ejpam-6436	14	11	but	but	CCONJ
ejpam-6436	14	12	also	also	ADV
ejpam-6436	14	13	an	an	DET
ejpam-6436	14	14	action	action	NOUN
ejpam-6436	14	15	that	that	PRON
ejpam-6436	14	16	reflects	reflect	VERB
ejpam-6436	14	17	the	the	DET
ejpam-6436	14	18	interactions	interaction	NOUN
ejpam-6436	14	19	between	between	ADP
ejpam-6436	14	20	the	the	DET
ejpam-6436	14	21	two	two	NUM
ejpam-6436	14	22	semigroups	semigroup	NOUN
ejpam-6436	14	23	.	.	PUNCT
ejpam-6436	15	1	as	as	ADP
ejpam-6436	15	2	with	with	ADP
ejpam-6436	15	3	group	group	NOUN
ejpam-6436	15	4	wreath	wreath	NOUN
ejpam-6436	15	5	∗corresponding	∗corresponde	VERB
ejpam-6436	15	6	author	author	NOUN
ejpam-6436	15	7	.	.	PUNCT
ejpam-6436	16	1	doi	doi	NOUN
ejpam-6436	16	2	:	:	PUNCT
ejpam-6436	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6436	https://doi.org/10.29020/nybg.ejpam.v18i3.6436	PROPN
ejpam-6436	16	4	email	email	NOUN
ejpam-6436	16	5	addresses	address	VERB
ejpam-6436	16	6	:	:	PUNCT
ejpam-6436	16	7	banajawid@kfu.edu.sa	banajawid@kfu.edu.sa	PROPN
ejpam-6436	16	8	(	(	PUNCT
ejpam-6436	16	9	b.	b.	PROPN
ejpam-6436	16	10	al	al	PROPN
ejpam-6436	16	11	subaiei	subaiei	PROPN
ejpam-6436	16	12	)	)	PUNCT
ejpam-6436	16	13	,	,	PUNCT
ejpam-6436	16	14	ahmulhem@kfu.edu.sa	ahmulhem@kfu.edu.sa	PROPN
ejpam-6436	16	15	(	(	PUNCT
ejpam-6436	16	16	a.	a.	NOUN
ejpam-6436	16	17	almulhim	almulhim	PROPN
ejpam-6436	16	18	)	)	PUNCT
ejpam-6436	16	19	,	,	PUNCT
ejpam-6436	16	20	aftab@cukashmir.ac.in	aftab@cukashmir.ac.in	PROPN
ejpam-6436	16	21	(	(	PUNCT
ejpam-6436	16	22	a.	a.	NOUN
ejpam-6436	16	23	h.	h.	PROPN
ejpam-6436	16	24	shah	shah	PROPN
ejpam-6436	16	25	)	)	PUNCT
ejpam-6436	16	26	,	,	PUNCT
ejpam-6436	16	27	ahtishamulhaq1218@gmail.com	ahtishamulhaq1218@gmail.com	X
ejpam-6436	16	28	(	(	PUNCT
ejpam-6436	16	29	s.	s.	PROPN
ejpam-6436	16	30	a.	a.	PROPN
ejpam-6436	16	31	ul	ul	PROPN
ejpam-6436	16	32	haq	haq	PROPN
ejpam-6436	16	33	)	)	PUNCT
ejpam-6436	16	34	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6436	17	1	1	1	NUM
ejpam-6436	17	2	copyright	copyright	NOUN
ejpam-6436	17	3	:	:	PUNCT
ejpam-6436	17	4	©	©	PROPN
ejpam-6436	17	5	2025	2025	NUM
ejpam-6436	17	6	the	the	DET
ejpam-6436	17	7	author(s	author(s	NOUN
ejpam-6436	17	8	)	)	PUNCT
ejpam-6436	17	9	.	.	PUNCT
ejpam-6436	18	1	(	(	PUNCT
ejpam-6436	18	2	cc	cc	NOUN
ejpam-6436	18	3	by	by	ADP
ejpam-6436	18	4	-	-	PUNCT
ejpam-6436	18	5	nc	nc	PROPN
ejpam-6436	18	6	4.0	4.0	NUM
ejpam-6436	18	7	)	)	PUNCT
ejpam-6436	18	8	b.	b.	PROPN
ejpam-6436	19	1	al	al	PROPN
ejpam-6436	19	2	subaiei	subaiei	PROPN
ejpam-6436	19	3	et	et	PROPN
ejpam-6436	19	4	al	al	PROPN
ejpam-6436	19	5	.	.	PUNCT
ejpam-6436	19	6	/	/	SYM
ejpam-6436	19	7	eur	eur	PROPN
ejpam-6436	19	8	.	.	PUNCT
ejpam-6436	20	1	j.	j.	PROPN
ejpam-6436	20	2	pure	pure	PROPN
ejpam-6436	20	3	appl	appl	PROPN
ejpam-6436	20	4	.	.	PROPN
ejpam-6436	20	5	math	math	PROPN
ejpam-6436	20	6	,	,	PUNCT
ejpam-6436	20	7	18	18	NUM
ejpam-6436	20	8	(	(	PUNCT
ejpam-6436	20	9	3	3	NUM
ejpam-6436	20	10	)	)	PUNCT
ejpam-6436	20	11	(	(	PUNCT
ejpam-6436	20	12	2025	2025	NUM
ejpam-6436	20	13	)	)	PUNCT
ejpam-6436	20	14	,	,	PUNCT
ejpam-6436	20	15	6436	6436	NUM
ejpam-6436	20	16	2	2	NUM
ejpam-6436	20	17	of	of	ADP
ejpam-6436	20	18	14	14	NUM
ejpam-6436	20	19	products	product	NOUN
ejpam-6436	20	20	,	,	PUNCT
ejpam-6436	20	21	the	the	DET
ejpam-6436	20	22	wreath	wreath	NOUN
ejpam-6436	20	23	product	product	NOUN
ejpam-6436	20	24	of	of	ADP
ejpam-6436	20	25	semigroups	semigroup	NOUN
ejpam-6436	20	26	allows	allow	VERB
ejpam-6436	20	27	for	for	ADP
ejpam-6436	20	28	a	a	DET
ejpam-6436	20	29	structured	structured	ADJ
ejpam-6436	20	30	approach	approach	NOUN
ejpam-6436	20	31	to	to	ADP
ejpam-6436	20	32	understanding	understanding	NOUN
ejpam-6436	20	33	and	and	CCONJ
ejpam-6436	20	34	constructing	construct	VERB
ejpam-6436	20	35	certain	certain	ADJ
ejpam-6436	20	36	types	type	NOUN
ejpam-6436	20	37	of	of	ADP
ejpam-6436	20	38	semigroups	semigroup	NOUN
ejpam-6436	20	39	.	.	PUNCT
ejpam-6436	21	1	it	it	PRON
ejpam-6436	21	2	finds	find	VERB
ejpam-6436	21	3	applications	application	NOUN
ejpam-6436	21	4	in	in	ADP
ejpam-6436	21	5	areas	area	NOUN
ejpam-6436	21	6	like	like	ADP
ejpam-6436	21	7	automata	automata	NOUN
ejpam-6436	21	8	theory	theory	NOUN
ejpam-6436	21	9	and	and	CCONJ
ejpam-6436	21	10	formal	formal	ADJ
ejpam-6436	21	11	languages	language	NOUN
ejpam-6436	21	12	,	,	PUNCT
ejpam-6436	21	13	where	where	SCONJ
ejpam-6436	21	14	semigroups	semigroup	NOUN
ejpam-6436	21	15	play	play	VERB
ejpam-6436	21	16	a	a	DET
ejpam-6436	21	17	significant	significant	ADJ
ejpam-6436	21	18	role	role	NOUN
ejpam-6436	21	19	.	.	PUNCT
ejpam-6436	22	1	many	many	ADJ
ejpam-6436	22	2	researchers	researcher	NOUN
ejpam-6436	22	3	studied	study	VERB
ejpam-6436	22	4	the	the	DET
ejpam-6436	22	5	concept	concept	NOUN
ejpam-6436	22	6	of	of	ADP
ejpam-6436	22	7	wreath	wreath	NOUN
ejpam-6436	22	8	product	product	NOUN
ejpam-6436	22	9	of	of	ADP
ejpam-6436	22	10	semigroups	semigroup	NOUN
ejpam-6436	22	11	(	(	PUNCT
ejpam-6436	22	12	monoids	monoid	NOUN
ejpam-6436	22	13	)	)	PUNCT
ejpam-6436	22	14	in	in	ADP
ejpam-6436	22	15	numerous	numerous	ADJ
ejpam-6436	22	16	articles	article	NOUN
ejpam-6436	22	17	such	such	ADJ
ejpam-6436	22	18	as	as	ADP
ejpam-6436	22	19	[	[	X
ejpam-6436	22	20	1–5	1–5	X
ejpam-6436	22	21	]	]	X
ejpam-6436	22	22	.	.	PUNCT
ejpam-6436	23	1	many	many	ADJ
ejpam-6436	23	2	researchers	researcher	NOUN
ejpam-6436	23	3	are	be	AUX
ejpam-6436	23	4	interested	interested	ADJ
ejpam-6436	23	5	in	in	ADP
ejpam-6436	23	6	generalizing	generalize	VERB
ejpam-6436	23	7	results	result	NOUN
ejpam-6436	23	8	from	from	ADP
ejpam-6436	23	9	the	the	DET
ejpam-6436	23	10	category	category	NOUN
ejpam-6436	23	11	of	of	ADP
ejpam-6436	23	12	semigroups	semigroup	NOUN
ejpam-6436	23	13	to	to	ADP
ejpam-6436	23	14	that	that	PRON
ejpam-6436	23	15	of	of	ADP
ejpam-6436	23	16	posemigroups	posemigroup	NOUN
ejpam-6436	23	17	,	,	PUNCT
ejpam-6436	23	18	as	as	SCONJ
ejpam-6436	23	19	demonstrated	demonstrate	VERB
ejpam-6436	23	20	by	by	ADP
ejpam-6436	23	21	the	the	DET
ejpam-6436	23	22	work	work	NOUN
ejpam-6436	23	23	on	on	ADP
ejpam-6436	23	24	[	[	X
ejpam-6436	23	25	6–13	6–13	NOUN
ejpam-6436	23	26	]	]	PUNCT
ejpam-6436	23	27	.	.	PUNCT
ejpam-6436	24	1	knauer	knauer	PROPN
ejpam-6436	24	2	and	and	CCONJ
ejpam-6436	24	3	mikhalev	mikhalev	PROPN
ejpam-6436	25	1	[	[	X
ejpam-6436	25	2	14	14	NUM
ejpam-6436	25	3	]	]	PUNCT
ejpam-6436	25	4	,	,	PUNCT
ejpam-6436	25	5	initiated	initiate	VERB
ejpam-6436	25	6	the	the	DET
ejpam-6436	25	7	study	study	NOUN
ejpam-6436	25	8	of	of	ADP
ejpam-6436	25	9	wreath	wreath	NOUN
ejpam-6436	25	10	products	product	NOUN
ejpam-6436	25	11	of	of	ADP
ejpam-6436	25	12	ordered	order	VERB
ejpam-6436	25	13	semigroups	semigroup	NOUN
ejpam-6436	25	14	by	by	ADP
ejpam-6436	25	15	an	an	DET
ejpam-6436	25	16	ordered	order	VERB
ejpam-6436	25	17	action	action	NOUN
ejpam-6436	25	18	.	.	PUNCT
ejpam-6436	26	1	they	they	PRON
ejpam-6436	26	2	considered	consider	VERB
ejpam-6436	26	3	three	three	NUM
ejpam-6436	26	4	different	different	ADJ
ejpam-6436	26	5	types	type	NOUN
ejpam-6436	26	6	of	of	ADP
ejpam-6436	26	7	ordered	order	VERB
ejpam-6436	26	8	wreath	wreath	NOUN
ejpam-6436	26	9	products	product	NOUN
ejpam-6436	26	10	,	,	PUNCT
ejpam-6436	26	11	specifically	specifically	ADV
ejpam-6436	26	12	,	,	PUNCT
ejpam-6436	26	13	order	order	NOUN
ejpam-6436	26	14	preserving	preserve	VERB
ejpam-6436	26	15	,	,	PUNCT
ejpam-6436	26	16	order	order	NOUN
ejpam-6436	26	17	reversing	reverse	VERB
ejpam-6436	26	18	and	and	CCONJ
ejpam-6436	26	19	preserving	preserve	VERB
ejpam-6436	26	20	certain	certain	ADJ
ejpam-6436	26	21	zigzag	zigzag	NOUN
ejpam-6436	26	22	equivalence	equivalence	NOUN
ejpam-6436	26	23	.	.	PUNCT
ejpam-6436	27	1	kilp	kilp	PROPN
ejpam-6436	27	2	,	,	PUNCT
ejpam-6436	27	3	knauer	knauer	NOUN
ejpam-6436	27	4	and	and	CCONJ
ejpam-6436	27	5	mikhalev	mikhalev	PROPN
ejpam-6436	28	1	[	[	X
ejpam-6436	28	2	15	15	NUM
ejpam-6436	28	3	]	]	PUNCT
ejpam-6436	28	4	provided	provide	VERB
ejpam-6436	28	5	a	a	DET
ejpam-6436	28	6	characterization	characterization	NOUN
ejpam-6436	28	7	of	of	ADP
ejpam-6436	28	8	torsion	torsion	NOUN
ejpam-6436	28	9	free	free	ADJ
ejpam-6436	28	10	wreath	wreath	NOUN
ejpam-6436	28	11	products	product	NOUN
ejpam-6436	28	12	of	of	ADP
ejpam-6436	28	13	acts	act	NOUN
ejpam-6436	28	14	over	over	ADP
ejpam-6436	28	15	the	the	DET
ejpam-6436	28	16	wreath	wreath	NOUN
ejpam-6436	28	17	product	product	NOUN
ejpam-6436	28	18	of	of	ADP
ejpam-6436	28	19	monoids	monoid	NOUN
ejpam-6436	28	20	by	by	ADP
ejpam-6436	28	21	describing	describe	VERB
ejpam-6436	28	22	injective	injective	ADJ
ejpam-6436	28	23	,	,	PUNCT
ejpam-6436	28	24	surjective	surjective	ADJ
ejpam-6436	28	25	and	and	CCONJ
ejpam-6436	28	26	cancellative	cancellative	ADJ
ejpam-6436	28	27	elements	element	NOUN
ejpam-6436	28	28	of	of	ADP
ejpam-6436	28	29	the	the	DET
ejpam-6436	28	30	wreath	wreath	NOUN
ejpam-6436	28	31	product	product	NOUN
ejpam-6436	28	32	.	.	PUNCT
ejpam-6436	29	1	in	in	ADP
ejpam-6436	29	2	this	this	DET
ejpam-6436	29	3	paper	paper	NOUN
ejpam-6436	29	4	,	,	PUNCT
ejpam-6436	29	5	we	we	PRON
ejpam-6436	29	6	extend	extend	VERB
ejpam-6436	29	7	the	the	DET
ejpam-6436	29	8	work	work	NOUN
ejpam-6436	29	9	on	on	ADP
ejpam-6436	29	10	the	the	DET
ejpam-6436	29	11	ordered	order	VERB
ejpam-6436	29	12	(	(	PUNCT
ejpam-6436	29	13	monotone	monotone	ADJ
ejpam-6436	29	14	)	)	PUNCT
ejpam-6436	29	15	wreath	wreath	NOUN
ejpam-6436	29	16	product	product	NOUN
ejpam-6436	29	17	of	of	ADP
ejpam-6436	29	18	pomonoids	pomonoid	NOUN
ejpam-6436	29	19	over	over	ADP
ejpam-6436	29	20	a	a	DET
ejpam-6436	29	21	poset	poset	NOUN
ejpam-6436	29	22	by	by	ADP
ejpam-6436	29	23	generalizing	generalize	VERB
ejpam-6436	29	24	the	the	DET
ejpam-6436	29	25	work	work	NOUN
ejpam-6436	29	26	of	of	ADP
ejpam-6436	29	27	kilp	kilp	PROPN
ejpam-6436	29	28	,	,	PUNCT
ejpam-6436	29	29	knauer	knauer	NOUN
ejpam-6436	29	30	and	and	CCONJ
ejpam-6436	29	31	mikhalev	mikhalev	PROPN
ejpam-6436	29	32	on	on	ADP
ejpam-6436	29	33	monoids	monoid	NOUN
ejpam-6436	29	34	in	in	ADP
ejpam-6436	29	35	[	[	X
ejpam-6436	29	36	15	15	NUM
ejpam-6436	29	37	]	]	PUNCT
ejpam-6436	29	38	,	,	PUNCT
ejpam-6436	29	39	and	and	CCONJ
ejpam-6436	29	40	we	we	PRON
ejpam-6436	29	41	will	will	AUX
ejpam-6436	29	42	adopt	adopt	VERB
ejpam-6436	29	43	their	their	PRON
ejpam-6436	29	44	notations	notation	NOUN
ejpam-6436	29	45	for	for	ADP
ejpam-6436	29	46	the	the	DET
ejpam-6436	29	47	sake	sake	NOUN
ejpam-6436	29	48	of	of	ADP
ejpam-6436	29	49	simplicity	simplicity	NOUN
ejpam-6436	29	50	for	for	ADP
ejpam-6436	29	51	the	the	DET
ejpam-6436	29	52	reader	reader	NOUN
ejpam-6436	29	53	.	.	PUNCT
ejpam-6436	30	1	for	for	ADP
ejpam-6436	30	2	the	the	DET
ejpam-6436	30	3	initial	initial	ADJ
ejpam-6436	30	4	work	work	NOUN
ejpam-6436	30	5	on	on	ADP
ejpam-6436	30	6	ordered	order	VERB
ejpam-6436	30	7	wreath	wreath	NOUN
ejpam-6436	30	8	product	product	NOUN
ejpam-6436	30	9	of	of	ADP
ejpam-6436	30	10	posets	poset	NOUN
ejpam-6436	30	11	on	on	ADP
ejpam-6436	30	12	pomonoids	pomonoid	NOUN
ejpam-6436	30	13	the	the	DET
ejpam-6436	30	14	reader	reader	NOUN
ejpam-6436	30	15	is	be	AUX
ejpam-6436	30	16	refered	refer	VERB
ejpam-6436	30	17	to	to	ADP
ejpam-6436	30	18	[	[	X
ejpam-6436	30	19	14	14	NUM
ejpam-6436	30	20	,	,	PUNCT
ejpam-6436	30	21	16	16	NUM
ejpam-6436	30	22	,	,	PUNCT
ejpam-6436	30	23	17	17	NUM
ejpam-6436	30	24	]	]	PUNCT
ejpam-6436	30	25	.	.	PUNCT
ejpam-6436	31	1	a	a	DET
ejpam-6436	31	2	pomonoid	pomonoid	NOUN
ejpam-6436	31	3	s	s	VERB
ejpam-6436	31	4	is	be	AUX
ejpam-6436	31	5	a	a	DET
ejpam-6436	31	6	monoid	monoid	NOUN
ejpam-6436	31	7	endowed	endow	VERB
ejpam-6436	31	8	with	with	ADP
ejpam-6436	31	9	a	a	DET
ejpam-6436	31	10	partial	partial	ADJ
ejpam-6436	31	11	order	order	NOUN
ejpam-6436	31	12	usually	usually	ADV
ejpam-6436	31	13	denoted	denote	VERB
ejpam-6436	31	14	by	by	ADP
ejpam-6436	31	15	≤	≤	NOUN
ejpam-6436	31	16	such	such	ADJ
ejpam-6436	31	17	that	that	SCONJ
ejpam-6436	31	18	it	it	PRON
ejpam-6436	31	19	is	be	AUX
ejpam-6436	31	20	compatible	compatible	ADJ
ejpam-6436	31	21	with	with	ADP
ejpam-6436	31	22	the	the	DET
ejpam-6436	31	23	binary	binary	ADJ
ejpam-6436	31	24	operation	operation	NOUN
ejpam-6436	31	25	i.e.	i.e.	X
ejpam-6436	31	26	,	,	PUNCT
ejpam-6436	31	27	for	for	ADP
ejpam-6436	31	28	any	any	DET
ejpam-6436	31	29	s	s	NOUN
ejpam-6436	31	30	,	,	PUNCT
ejpam-6436	31	31	s′	s′	NUM
ejpam-6436	31	32	,	,	PUNCT
ejpam-6436	31	33	t	t	PROPN
ejpam-6436	31	34	∈	∈	PROPN
ejpam-6436	31	35	s	s	PROPN
ejpam-6436	31	36	,	,	PUNCT
ejpam-6436	31	37	s	s	PART
ejpam-6436	31	38	≤	≤	NOUN
ejpam-6436	31	39	s′	s′	NUM
ejpam-6436	31	40	implies	imply	VERB
ejpam-6436	31	41	ts	ts	ADP
ejpam-6436	31	42	≤	≤	NUM
ejpam-6436	31	43	ts′	ts′	NUM
ejpam-6436	31	44	and	and	CCONJ
ejpam-6436	31	45	st	st	PROPN
ejpam-6436	31	46	≤	≤	PROPN
ejpam-6436	31	47	s′t	s′t	NOUN
ejpam-6436	31	48	.	.	PUNCT
ejpam-6436	32	1	therefore	therefore	ADV
ejpam-6436	32	2	,	,	PUNCT
ejpam-6436	32	3	for	for	ADP
ejpam-6436	32	4	any	any	DET
ejpam-6436	32	5	pomonoid	pomonoid	NOUN
ejpam-6436	32	6	s	s	NOUN
ejpam-6436	32	7	and	and	CCONJ
ejpam-6436	32	8	r	r	NOUN
ejpam-6436	32	9	,	,	PUNCT
ejpam-6436	32	10	r′	r′	PROPN
ejpam-6436	32	11	,	,	PUNCT
ejpam-6436	32	12	p	p	X
ejpam-6436	32	13	,	,	PUNCT
ejpam-6436	32	14	p′	p′	NOUN
ejpam-6436	32	15	∈	∈	PROPN
ejpam-6436	32	16	s	s	NOUN
ejpam-6436	32	17	,	,	PUNCT
ejpam-6436	32	18	if	if	SCONJ
ejpam-6436	32	19	r	r	NOUN
ejpam-6436	32	20	≤	≤	X
ejpam-6436	32	21	r′	r′	NOUN
ejpam-6436	32	22	and	and	CCONJ
ejpam-6436	32	23	p	p	NOUN
ejpam-6436	32	24	≤	≤	PROPN
ejpam-6436	32	25	p′	p′	NOUN
ejpam-6436	32	26	,	,	PUNCT
ejpam-6436	32	27	then	then	ADV
ejpam-6436	32	28	rp	rp	PROPN
ejpam-6436	32	29	≤	≤	NUM
ejpam-6436	32	30	r′p′.	r′p′.	NOUN
ejpam-6436	32	31	let	let	VERB
ejpam-6436	32	32	a	a	PRON
ejpam-6436	32	33	and	and	CCONJ
ejpam-6436	32	34	b	b	NOUN
ejpam-6436	32	35	be	be	AUX
ejpam-6436	32	36	posets	poset	NOUN
ejpam-6436	32	37	,	,	PUNCT
ejpam-6436	32	38	a	a	DET
ejpam-6436	32	39	map	map	NOUN
ejpam-6436	32	40	f	f	X
ejpam-6436	32	41	:	:	PUNCT
ejpam-6436	32	42	a	a	DET
ejpam-6436	32	43	−→	−→	NOUN
ejpam-6436	32	44	b	b	PROPN
ejpam-6436	32	45	is	be	AUX
ejpam-6436	32	46	called	call	VERB
ejpam-6436	32	47	monotone	monotone	ADJ
ejpam-6436	32	48	if	if	SCONJ
ejpam-6436	32	49	it	it	PRON
ejpam-6436	32	50	preserves	preserve	VERB
ejpam-6436	32	51	the	the	DET
ejpam-6436	32	52	order	order	NOUN
ejpam-6436	32	53	i.e.	i.e.	X
ejpam-6436	32	54	,	,	PUNCT
ejpam-6436	32	55	a	a	DET
ejpam-6436	32	56	≤	≤	NOUN
ejpam-6436	32	57	a′	a′	NOUN
ejpam-6436	32	58	in	in	ADP
ejpam-6436	32	59	a	a	DET
ejpam-6436	32	60	implies	implie	NOUN
ejpam-6436	32	61	f(a	f(a	NOUN
ejpam-6436	32	62	)	)	PUNCT
ejpam-6436	32	63	≤	≤	NUM
ejpam-6436	32	64	f(a′	f(a′	NOUN
ejpam-6436	32	65	)	)	PUNCT
ejpam-6436	32	66	in	in	ADP
ejpam-6436	32	67	b.	b.	PROPN
ejpam-6436	32	68	the	the	DET
ejpam-6436	32	69	set	set	NOUN
ejpam-6436	32	70	of	of	ADP
ejpam-6436	32	71	all	all	DET
ejpam-6436	32	72	monotone	monotone	ADJ
ejpam-6436	32	73	mappings	mapping	NOUN
ejpam-6436	32	74	from	from	ADP
ejpam-6436	32	75	a	a	DET
ejpam-6436	32	76	to	to	PART
ejpam-6436	32	77	b	b	PROPN
ejpam-6436	32	78	(	(	PUNCT
ejpam-6436	32	79	resp	resp	NOUN
ejpam-6436	32	80	.	.	PUNCT
ejpam-6436	33	1	from	from	ADP
ejpam-6436	33	2	a	a	DET
ejpam-6436	33	3	to	to	ADP
ejpam-6436	33	4	a	a	PRON
ejpam-6436	33	5	)	)	PUNCT
ejpam-6436	33	6	is	be	AUX
ejpam-6436	33	7	usually	usually	ADV
ejpam-6436	33	8	denoted	denote	VERB
ejpam-6436	33	9	by	by	ADP
ejpam-6436	33	10	f	f	PROPN
ejpam-6436	33	11	(	(	PUNCT
ejpam-6436	33	12	a	a	DET
ejpam-6436	33	13	,	,	PUNCT
ejpam-6436	33	14	b	b	NOUN
ejpam-6436	33	15	)	)	PUNCT
ejpam-6436	33	16	(	(	PUNCT
ejpam-6436	33	17	resp	resp	NOUN
ejpam-6436	33	18	.	.	PUNCT
ejpam-6436	34	1	f	f	X
ejpam-6436	34	2	(	(	PUNCT
ejpam-6436	34	3	a	a	PRON
ejpam-6436	34	4	,	,	PUNCT
ejpam-6436	34	5	a	a	NOUN
ejpam-6436	34	6	)	)	PUNCT
ejpam-6436	34	7	)	)	PUNCT
ejpam-6436	35	1	and	and	CCONJ
ejpam-6436	35	2	it	it	PRON
ejpam-6436	35	3	inherits	inherit	VERB
ejpam-6436	35	4	a	a	DET
ejpam-6436	35	5	point	point	NOUN
ejpam-6436	35	6	-	-	PUNCT
ejpam-6436	35	7	wise	wise	ADJ
ejpam-6436	35	8	order	order	NOUN
ejpam-6436	35	9	as	as	SCONJ
ejpam-6436	35	10	follows	follow	VERB
ejpam-6436	35	11	:	:	PUNCT
ejpam-6436	35	12	f	f	PROPN
ejpam-6436	35	13	≤	≤	PROPN
ejpam-6436	35	14	g	g	PROPN
ejpam-6436	35	15	⇔	⇔	PROPN
ejpam-6436	35	16	f(a	f(a	PROPN
ejpam-6436	35	17	)	)	PUNCT
ejpam-6436	35	18	≤	≤	NOUN
ejpam-6436	35	19	g(a	g(a	PROPN
ejpam-6436	35	20	)	)	PUNCT
ejpam-6436	35	21	,	,	PUNCT
ejpam-6436	35	22	∀	∀	PUNCT
ejpam-6436	35	23	a	a	DET
ejpam-6436	35	24	∈	∈	PROPN
ejpam-6436	35	25	a.	a.	NOUN
ejpam-6436	35	26	for	for	ADP
ejpam-6436	35	27	each	each	DET
ejpam-6436	35	28	b	b	PROPN
ejpam-6436	35	29	∈	∈	PROPN
ejpam-6436	35	30	b	b	PROPN
ejpam-6436	35	31	,	,	PUNCT
ejpam-6436	35	32	cb	cb	PROPN
ejpam-6436	35	33	denotes	denote	VERB
ejpam-6436	35	34	the	the	DET
ejpam-6436	35	35	constant	constant	ADJ
ejpam-6436	35	36	map	map	NOUN
ejpam-6436	35	37	on	on	ADP
ejpam-6436	35	38	a	a	DET
ejpam-6436	35	39	with	with	ADP
ejpam-6436	35	40	range	range	NOUN
ejpam-6436	35	41	{	{	PUNCT
ejpam-6436	35	42	b	b	NOUN
ejpam-6436	35	43	}	}	PUNCT
ejpam-6436	35	44	and	and	CCONJ
ejpam-6436	35	45	such	such	DET
ejpam-6436	35	46	a	a	DET
ejpam-6436	35	47	map	map	NOUN
ejpam-6436	35	48	is	be	AUX
ejpam-6436	35	49	clearly	clearly	ADV
ejpam-6436	35	50	monotone	monotone	ADJ
ejpam-6436	35	51	.	.	PUNCT
ejpam-6436	36	1	let	let	VERB
ejpam-6436	36	2	r	r	PRON
ejpam-6436	36	3	be	be	AUX
ejpam-6436	36	4	a	a	DET
ejpam-6436	36	5	pomoniod	pomoniod	NOUN
ejpam-6436	36	6	and	and	CCONJ
ejpam-6436	36	7	a	a	DET
ejpam-6436	36	8	a	a	DET
ejpam-6436	36	9	poset	poset	NOUN
ejpam-6436	36	10	.	.	PUNCT
ejpam-6436	37	1	we	we	PRON
ejpam-6436	37	2	say	say	VERB
ejpam-6436	37	3	that	that	SCONJ
ejpam-6436	37	4	a	a	PRON
ejpam-6436	37	5	is	be	AUX
ejpam-6436	37	6	a	a	DET
ejpam-6436	37	7	left	left	ADJ
ejpam-6436	37	8	r	r	NOUN
ejpam-6436	37	9	-	-	PUNCT
ejpam-6436	37	10	poset	poset	NOUN
ejpam-6436	37	11	if	if	SCONJ
ejpam-6436	37	12	there	there	PRON
ejpam-6436	37	13	exists	exist	VERB
ejpam-6436	37	14	a	a	DET
ejpam-6436	37	15	monotone	monotone	ADJ
ejpam-6436	37	16	map	map	NOUN
ejpam-6436	37	17	r	r	NOUN
ejpam-6436	37	18	×	×	NOUN
ejpam-6436	37	19	a	a	DET
ejpam-6436	37	20	−→	−→	NOUN
ejpam-6436	37	21	a	a	DET
ejpam-6436	37	22	such	such	ADJ
ejpam-6436	37	23	that	that	SCONJ
ejpam-6436	37	24	1a	1a	PROPN
ejpam-6436	37	25	=	=	PUNCT
ejpam-6436	37	26	a	a	PROPN
ejpam-6436	37	27	and	and	CCONJ
ejpam-6436	37	28	(	(	PUNCT
ejpam-6436	37	29	rp)a	rp)a	NOUN
ejpam-6436	37	30	=	=	SYM
ejpam-6436	37	31	r(pa	r(pa	PROPN
ejpam-6436	37	32	)	)	PUNCT
ejpam-6436	37	33	for	for	ADP
ejpam-6436	37	34	all	all	DET
ejpam-6436	37	35	a	a	DET
ejpam-6436	37	36	∈	∈	PROPN
ejpam-6436	37	37	a	a	PRON
ejpam-6436	37	38	and	and	CCONJ
ejpam-6436	37	39	r	r	NOUN
ejpam-6436	37	40	,	,	PUNCT
ejpam-6436	37	41	p	p	PROPN
ejpam-6436	37	42	∈	∈	PROPN
ejpam-6436	37	43	r.	r.	NOUN
ejpam-6436	37	44	we	we	PRON
ejpam-6436	37	45	denote	denote	VERB
ejpam-6436	37	46	a	a	DET
ejpam-6436	37	47	left	left	ADJ
ejpam-6436	37	48	r	r	NOUN
ejpam-6436	37	49	-	-	PUNCT
ejpam-6436	37	50	poset	poset	NOUN
ejpam-6436	37	51	by	by	ADP
ejpam-6436	37	52	ra	ra	PROPN
ejpam-6436	37	53	.	.	PUNCT
ejpam-6436	38	1	the	the	DET
ejpam-6436	38	2	right	right	ADJ
ejpam-6436	38	3	r	r	NOUN
ejpam-6436	38	4	-	-	PUNCT
ejpam-6436	38	5	poset	poset	NOUN
ejpam-6436	38	6	is	be	AUX
ejpam-6436	38	7	defined	define	VERB
ejpam-6436	38	8	dually	dually	ADV
ejpam-6436	38	9	and	and	CCONJ
ejpam-6436	38	10	it	it	PRON
ejpam-6436	38	11	is	be	AUX
ejpam-6436	38	12	denoted	denote	VERB
ejpam-6436	38	13	by	by	ADP
ejpam-6436	38	14	ar	ar	PROPN
ejpam-6436	38	15	.	.	PROPN
ejpam-6436	39	1	let	let	VERB
ejpam-6436	39	2	r	r	NOUN
ejpam-6436	39	3	and	and	CCONJ
ejpam-6436	39	4	s	s	VERB
ejpam-6436	39	5	be	be	AUX
ejpam-6436	39	6	pomonoids	pomonoid	NOUN
ejpam-6436	39	7	.	.	PUNCT
ejpam-6436	40	1	the	the	DET
ejpam-6436	40	2	wreath	wreath	NOUN
ejpam-6436	40	3	product	product	NOUN
ejpam-6436	40	4	of	of	ADP
ejpam-6436	40	5	the	the	DET
ejpam-6436	40	6	pomonoids	pomonoid	NOUN
ejpam-6436	40	7	r	r	NOUN
ejpam-6436	40	8	and	and	CCONJ
ejpam-6436	40	9	s	s	NOUN
ejpam-6436	40	10	by	by	ADP
ejpam-6436	40	11	the	the	DET
ejpam-6436	40	12	left	left	ADJ
ejpam-6436	40	13	r	r	NOUN
ejpam-6436	40	14	-	-	PUNCT
ejpam-6436	40	15	poset	poset	NOUN
ejpam-6436	40	16	ra	ra	PROPN
ejpam-6436	40	17	is	be	AUX
ejpam-6436	40	18	the	the	DET
ejpam-6436	40	19	set	set	NOUN
ejpam-6436	40	20	t	t	NOUN
ejpam-6436	40	21	=	=	SYM
ejpam-6436	40	22	r×	r×	PROPN
ejpam-6436	40	23	f	f	X
ejpam-6436	40	24	(	(	PUNCT
ejpam-6436	40	25	a	a	PRON
ejpam-6436	40	26	,	,	PUNCT
ejpam-6436	40	27	s	s	PART
ejpam-6436	40	28	)	)	PUNCT
ejpam-6436	40	29	endowed	endow	VERB
ejpam-6436	40	30	with	with	ADP
ejpam-6436	40	31	the	the	DET
ejpam-6436	40	32	multiplication	multiplication	NOUN
ejpam-6436	40	33	given	give	VERB
ejpam-6436	40	34	by	by	ADP
ejpam-6436	40	35	(	(	PUNCT
ejpam-6436	40	36	r	r	NOUN
ejpam-6436	40	37	,	,	PUNCT
ejpam-6436	40	38	f)(p	f)(p	NOUN
ejpam-6436	40	39	,	,	PUNCT
ejpam-6436	40	40	g	g	NOUN
ejpam-6436	40	41	)	)	PUNCT
ejpam-6436	40	42	=	=	NOUN
ejpam-6436	40	43	(	(	PUNCT
ejpam-6436	40	44	rp	rp	NOUN
ejpam-6436	40	45	,	,	PUNCT
ejpam-6436	40	46	fpg	fpg	PROPN
ejpam-6436	40	47	)	)	PUNCT
ejpam-6436	40	48	,	,	PUNCT
ejpam-6436	40	49	where	where	SCONJ
ejpam-6436	40	50	fpg(a	fpg(a	NOUN
ejpam-6436	40	51	)	)	PUNCT
ejpam-6436	40	52	=	=	SYM
ejpam-6436	40	53	f(pa)g(a	f(pa)g(a	PROPN
ejpam-6436	40	54	)	)	PUNCT
ejpam-6436	40	55	for	for	ADP
ejpam-6436	40	56	all	all	DET
ejpam-6436	40	57	a	a	DET
ejpam-6436	40	58	∈	∈	PROPN
ejpam-6436	40	59	a	a	DET
ejpam-6436	40	60	,	,	PUNCT
ejpam-6436	40	61	r	r	NOUN
ejpam-6436	40	62	,	,	PUNCT
ejpam-6436	40	63	p	p	NOUN
ejpam-6436	40	64	∈	∈	PROPN
ejpam-6436	40	65	r	r	NOUN
ejpam-6436	40	66	,	,	PUNCT
ejpam-6436	40	67	f	f	PROPN
ejpam-6436	40	68	,	,	PUNCT
ejpam-6436	40	69	g	g	PROPN
ejpam-6436	40	70	∈	∈	PROPN
ejpam-6436	40	71	f	f	X
ejpam-6436	40	72	(	(	PUNCT
ejpam-6436	40	73	a	a	PRON
ejpam-6436	40	74	,	,	PUNCT
ejpam-6436	40	75	s	s	NOUN
ejpam-6436	40	76	)	)	PUNCT
ejpam-6436	40	77	.	.	PUNCT
ejpam-6436	41	1	the	the	DET
ejpam-6436	41	2	map	map	NOUN
ejpam-6436	41	3	fp	fp	X
ejpam-6436	41	4	means	mean	VERB
ejpam-6436	41	5	that	that	SCONJ
ejpam-6436	41	6	fp(a	fp(a	X
ejpam-6436	41	7	)	)	PUNCT
ejpam-6436	41	8	=	=	SYM
ejpam-6436	41	9	f(pa	f(pa	PROPN
ejpam-6436	41	10	)	)	PUNCT
ejpam-6436	41	11	.	.	PUNCT
ejpam-6436	42	1	by	by	ADP
ejpam-6436	42	2	[	[	X
ejpam-6436	42	3	14	14	NUM
ejpam-6436	42	4	]	]	PUNCT
ejpam-6436	42	5	proposition	proposition	NOUN
ejpam-6436	42	6	2.1	2.1	NUM
ejpam-6436	42	7	the	the	DET
ejpam-6436	42	8	wreath	wreath	NOUN
ejpam-6436	42	9	product	product	NOUN
ejpam-6436	42	10	t	t	NOUN
ejpam-6436	42	11	is	be	AUX
ejpam-6436	42	12	a	a	DET
ejpam-6436	42	13	semigroup	semigroup	NOUN
ejpam-6436	42	14	,	,	PUNCT
ejpam-6436	42	15	and	and	CCONJ
ejpam-6436	42	16	it	it	PRON
ejpam-6436	42	17	is	be	AUX
ejpam-6436	42	18	a	a	DET
ejpam-6436	42	19	monoid	monoid	NOUN
ejpam-6436	42	20	if	if	SCONJ
ejpam-6436	42	21	and	and	CCONJ
ejpam-6436	42	22	only	only	ADV
ejpam-6436	42	23	if	if	SCONJ
ejpam-6436	42	24	s	s	NOUN
ejpam-6436	42	25	is	be	AUX
ejpam-6436	42	26	a	a	DET
ejpam-6436	42	27	monoid	monoid	NOUN
ejpam-6436	42	28	.	.	PUNCT
ejpam-6436	42	29	again	again	ADV
ejpam-6436	42	30	by	by	ADP
ejpam-6436	42	31	[	[	X
ejpam-6436	42	32	14	14	NUM
ejpam-6436	42	33	]	]	PUNCT
ejpam-6436	42	34	proposition	proposition	NOUN
ejpam-6436	42	35	2.4	2.4	NUM
ejpam-6436	42	36	,	,	PUNCT
ejpam-6436	42	37	t	t	PROPN
ejpam-6436	42	38	is	be	AUX
ejpam-6436	42	39	a	a	DET
ejpam-6436	42	40	posemigroup	posemigroup	NOUN
ejpam-6436	42	41	with	with	ADP
ejpam-6436	42	42	componentwise	componentwise	NOUN
ejpam-6436	42	43	order	order	NOUN
ejpam-6436	42	44	.	.	PUNCT
ejpam-6436	43	1	knauer	knauer	NOUN
ejpam-6436	43	2	and	and	CCONJ
ejpam-6436	43	3	mikhalev	mikhalev	PROPN
ejpam-6436	44	1	[	[	X
ejpam-6436	44	2	14	14	NUM
ejpam-6436	44	3	]	]	PUNCT
ejpam-6436	44	4	studied	study	VERB
ejpam-6436	44	5	the	the	DET
ejpam-6436	44	6	ordered	order	VERB
ejpam-6436	44	7	wreath	wreath	NOUN
ejpam-6436	44	8	product	product	NOUN
ejpam-6436	44	9	where	where	SCONJ
ejpam-6436	44	10	they	they	PRON
ejpam-6436	44	11	assumed	assume	VERB
ejpam-6436	44	12	f	f	PROPN
ejpam-6436	44	13	(	(	PUNCT
ejpam-6436	44	14	a	a	PRON
ejpam-6436	44	15	,	,	PUNCT
ejpam-6436	44	16	s	s	NOUN
ejpam-6436	44	17	)	)	PUNCT
ejpam-6436	44	18	to	to	PART
ejpam-6436	44	19	contain	contain	VERB
ejpam-6436	44	20	all	all	DET
ejpam-6436	44	21	montone	montone	NOUN
ejpam-6436	44	22	(	(	PUNCT
ejpam-6436	44	23	isotone	isotone	NOUN
ejpam-6436	44	24	)	)	PUNCT
ejpam-6436	44	25	,	,	PUNCT
ejpam-6436	44	26	antimonotone	antimonotone	NOUN
ejpam-6436	44	27	(	(	PUNCT
ejpam-6436	44	28	antitone	antitone	NOUN
ejpam-6436	44	29	)	)	PUNCT
ejpam-6436	44	30	,	,	PUNCT
ejpam-6436	44	31	and	and	CCONJ
ejpam-6436	44	32	zigzag	zigzag	PROPN
ejpam-6436	44	33	b.	b.	PROPN
ejpam-6436	44	34	al	al	PROPN
ejpam-6436	44	35	subaiei	subaiei	PROPN
ejpam-6436	44	36	et	et	PROPN
ejpam-6436	44	37	al	al	PROPN
ejpam-6436	44	38	.	.	PUNCT
ejpam-6436	44	39	/	/	SYM
ejpam-6436	44	40	eur	eur	PROPN
ejpam-6436	44	41	.	.	PUNCT
ejpam-6436	45	1	j.	j.	PROPN
ejpam-6436	45	2	pure	pure	PROPN
ejpam-6436	45	3	appl	appl	PROPN
ejpam-6436	45	4	.	.	PROPN
ejpam-6436	45	5	math	math	PROPN
ejpam-6436	45	6	,	,	PUNCT
ejpam-6436	45	7	18	18	NUM
ejpam-6436	45	8	(	(	PUNCT
ejpam-6436	45	9	3	3	NUM
ejpam-6436	45	10	)	)	PUNCT
ejpam-6436	45	11	(	(	PUNCT
ejpam-6436	45	12	2025	2025	NUM
ejpam-6436	45	13	)	)	PUNCT
ejpam-6436	45	14	,	,	PUNCT
ejpam-6436	45	15	6436	6436	NUM
ejpam-6436	45	16	3	3	NUM
ejpam-6436	45	17	of	of	ADP
ejpam-6436	45	18	14	14	NUM
ejpam-6436	45	19	preserving	preserve	VERB
ejpam-6436	45	20	mappings	mapping	NOUN
ejpam-6436	45	21	.	.	PUNCT
ejpam-6436	46	1	in	in	ADP
ejpam-6436	46	2	this	this	DET
ejpam-6436	46	3	paper	paper	NOUN
ejpam-6436	46	4	,	,	PUNCT
ejpam-6436	46	5	we	we	PRON
ejpam-6436	46	6	only	only	ADV
ejpam-6436	46	7	consider	consider	VERB
ejpam-6436	46	8	the	the	DET
ejpam-6436	46	9	monotone	monotone	NOUN
ejpam-6436	46	10	(	(	PUNCT
ejpam-6436	46	11	isotone	isotone	NOUN
ejpam-6436	46	12	)	)	PUNCT
ejpam-6436	46	13	case	case	NOUN
ejpam-6436	46	14	and	and	CCONJ
ejpam-6436	46	15	thus	thus	ADV
ejpam-6436	46	16	under	under	ADP
ejpam-6436	46	17	the	the	DET
ejpam-6436	46	18	notations	notation	NOUN
ejpam-6436	46	19	introduced	introduce	VERB
ejpam-6436	46	20	in	in	ADP
ejpam-6436	46	21	[	[	X
ejpam-6436	46	22	14	14	NUM
ejpam-6436	46	23	]	]	PUNCT
ejpam-6436	46	24	,	,	PUNCT
ejpam-6436	46	25	f	f	PROPN
ejpam-6436	46	26	(	(	PUNCT
ejpam-6436	46	27	a	a	DET
ejpam-6436	46	28	,	,	PUNCT
ejpam-6436	46	29	s	s	PART
ejpam-6436	46	30	)	)	PUNCT
ejpam-6436	46	31	is	be	AUX
ejpam-6436	46	32	precisely	precisely	ADV
ejpam-6436	46	33	the	the	DET
ejpam-6436	46	34	set	set	NOUN
ejpam-6436	46	35	i(a	i(a	PROPN
ejpam-6436	46	36	,	,	PUNCT
ejpam-6436	46	37	s	s	PART
ejpam-6436	46	38	)	)	PUNCT
ejpam-6436	46	39	.	.	PUNCT
ejpam-6436	47	1	the	the	DET
ejpam-6436	47	2	wreath	wreath	NOUN
ejpam-6436	47	3	product	product	NOUN
ejpam-6436	47	4	tc	tc	NOUN
ejpam-6436	47	5	of	of	ADP
ejpam-6436	47	6	the	the	DET
ejpam-6436	47	7	left	left	ADJ
ejpam-6436	47	8	r	r	NOUN
ejpam-6436	47	9	-	-	PUNCT
ejpam-6436	47	10	poset	poset	VERB
ejpam-6436	47	11	ra	ra	NOUN
ejpam-6436	47	12	with	with	ADP
ejpam-6436	47	13	the	the	DET
ejpam-6436	47	14	left	left	ADJ
ejpam-6436	47	15	s	s	NOUN
ejpam-6436	47	16	-	-	PUNCT
ejpam-6436	47	17	poset	poset	VERB
ejpam-6436	47	18	sb	sb	NOUN
ejpam-6436	47	19	over	over	ADP
ejpam-6436	47	20	the	the	DET
ejpam-6436	47	21	pomonoid	pomonoid	NOUN
ejpam-6436	47	22	t	t	PROPN
ejpam-6436	47	23	=	=	SYM
ejpam-6436	47	24	r×f	r×f	PROPN
ejpam-6436	47	25	(	(	PUNCT
ejpam-6436	47	26	a	a	DET
ejpam-6436	47	27	,	,	PUNCT
ejpam-6436	47	28	s	s	PART
ejpam-6436	47	29	)	)	PUNCT
ejpam-6436	47	30	is	be	AUX
ejpam-6436	47	31	the	the	DET
ejpam-6436	47	32	left	left	NOUN
ejpam-6436	47	33	t	t	NOUN
ejpam-6436	47	34	-poset	-poset	PROPN
ejpam-6436	47	35	tc	tc	NOUN
ejpam-6436	47	36	=	=	SYM
ejpam-6436	47	37	ra×sb	ra×sb	PROPN
ejpam-6436	47	38	endowed	endow	VERB
ejpam-6436	47	39	with	with	ADP
ejpam-6436	47	40	the	the	DET
ejpam-6436	47	41	monotone	monotone	ADJ
ejpam-6436	47	42	action	action	NOUN
ejpam-6436	47	43	given	give	VERB
ejpam-6436	47	44	by	by	ADP
ejpam-6436	47	45	(	(	PUNCT
ejpam-6436	47	46	r	r	NOUN
ejpam-6436	47	47	,	,	PUNCT
ejpam-6436	47	48	f)(a	f)(a	NUM
ejpam-6436	47	49	,	,	PUNCT
ejpam-6436	47	50	b	b	NOUN
ejpam-6436	47	51	)	)	PUNCT
ejpam-6436	47	52	=	=	SYM
ejpam-6436	47	53	(	(	PUNCT
ejpam-6436	47	54	ra	ra	PROPN
ejpam-6436	47	55	,	,	PUNCT
ejpam-6436	47	56	f(a)b	f(a)b	PROPN
ejpam-6436	47	57	)	)	PUNCT
ejpam-6436	47	58	,	,	PUNCT
ejpam-6436	47	59	for	for	ADP
ejpam-6436	47	60	all	all	DET
ejpam-6436	47	61	(	(	PUNCT
ejpam-6436	47	62	r	r	NOUN
ejpam-6436	47	63	,	,	PUNCT
ejpam-6436	47	64	f	f	X
ejpam-6436	47	65	)	)	PUNCT
ejpam-6436	47	66	∈	∈	PROPN
ejpam-6436	47	67	r×	r×	NOUN
ejpam-6436	47	68	f	f	X
ejpam-6436	47	69	(	(	PUNCT
ejpam-6436	47	70	a	a	PRON
ejpam-6436	47	71	,	,	PUNCT
ejpam-6436	47	72	s	s	PART
ejpam-6436	47	73	)	)	PUNCT
ejpam-6436	47	74	and	and	CCONJ
ejpam-6436	47	75	(	(	PUNCT
ejpam-6436	47	76	a	a	PRON
ejpam-6436	47	77	,	,	PUNCT
ejpam-6436	47	78	b	b	NOUN
ejpam-6436	47	79	)	)	PUNCT
ejpam-6436	47	80	∈	∈	PROPN
ejpam-6436	47	81	a×b	a×b	PROPN
ejpam-6436	47	82	.	.	PROPN
ejpam-6436	48	1	for	for	ADP
ejpam-6436	48	2	simplicity	simplicity	NOUN
ejpam-6436	48	3	,	,	PUNCT
ejpam-6436	48	4	we	we	PRON
ejpam-6436	48	5	will	will	AUX
ejpam-6436	48	6	refer	refer	VERB
ejpam-6436	48	7	to	to	ADP
ejpam-6436	48	8	the	the	DET
ejpam-6436	48	9	wreath	wreath	NOUN
ejpam-6436	48	10	product	product	NOUN
ejpam-6436	48	11	t	t	NOUN
ejpam-6436	48	12	=	=	SYM
ejpam-6436	48	13	r×	r×	PROPN
ejpam-6436	48	14	f	f	X
ejpam-6436	48	15	(	(	PUNCT
ejpam-6436	48	16	a	a	DET
ejpam-6436	48	17	,	,	PUNCT
ejpam-6436	48	18	s	s	PART
ejpam-6436	48	19	)	)	PUNCT
ejpam-6436	48	20	simply	simply	ADV
ejpam-6436	48	21	as	as	ADP
ejpam-6436	48	22	t	t	PROPN
ejpam-6436	48	23	,	,	PUNCT
ejpam-6436	48	24	and	and	CCONJ
ejpam-6436	48	25	the	the	DET
ejpam-6436	48	26	wreath	wreath	NOUN
ejpam-6436	48	27	product	product	NOUN
ejpam-6436	48	28	t	t	X
ejpam-6436	48	29	-poset	-poset	PROPN
ejpam-6436	48	30	tc	tc	NOUN
ejpam-6436	48	31	=	=	SYM
ejpam-6436	48	32	ra×sb	ra×sb	PROPN
ejpam-6436	48	33	as	as	ADP
ejpam-6436	48	34	tc	tc	NUM
ejpam-6436	48	35	throughout	throughout	ADP
ejpam-6436	48	36	the	the	DET
ejpam-6436	48	37	paper	paper	NOUN
ejpam-6436	48	38	when	when	SCONJ
ejpam-6436	48	39	the	the	DET
ejpam-6436	48	40	context	context	NOUN
ejpam-6436	48	41	is	be	AUX
ejpam-6436	48	42	clear	clear	ADJ
ejpam-6436	48	43	.	.	PUNCT
ejpam-6436	49	1	in	in	ADP
ejpam-6436	49	2	this	this	DET
ejpam-6436	49	3	paper	paper	NOUN
ejpam-6436	49	4	,	,	PUNCT
ejpam-6436	49	5	we	we	PRON
ejpam-6436	49	6	first	first	ADV
ejpam-6436	49	7	find	find	VERB
ejpam-6436	49	8	the	the	DET
ejpam-6436	49	9	necessary	necessary	ADJ
ejpam-6436	49	10	conditions	condition	NOUN
ejpam-6436	49	11	for	for	ADP
ejpam-6436	49	12	an	an	DET
ejpam-6436	49	13	element	element	NOUN
ejpam-6436	49	14	of	of	ADP
ejpam-6436	49	15	a	a	DET
ejpam-6436	49	16	pomonoid	pomonoid	NOUN
ejpam-6436	49	17	r	r	NOUN
ejpam-6436	49	18	to	to	PART
ejpam-6436	49	19	act	act	VERB
ejpam-6436	49	20	po	po	X
ejpam-6436	49	21	-	-	PUNCT
ejpam-6436	49	22	injectively	injectively	ADV
ejpam-6436	49	23	and	and	CCONJ
ejpam-6436	49	24	to	to	PART
ejpam-6436	49	25	be	be	AUX
ejpam-6436	49	26	po	po	NOUN
ejpam-6436	49	27	-	-	NOUN
ejpam-6436	49	28	cancellable	cancellable	ADJ
ejpam-6436	49	29	respectively	respectively	ADV
ejpam-6436	49	30	on	on	ADP
ejpam-6436	49	31	the	the	DET
ejpam-6436	49	32	wreath	wreath	NOUN
ejpam-6436	49	33	product	product	NOUN
ejpam-6436	49	34	tc	tc	NOUN
ejpam-6436	49	35	.	.	PUNCT
ejpam-6436	50	1	we	we	PRON
ejpam-6436	50	2	also	also	ADV
ejpam-6436	50	3	establish	establish	VERB
ejpam-6436	50	4	necessary	necessary	ADJ
ejpam-6436	50	5	conditions	condition	NOUN
ejpam-6436	50	6	on	on	ADP
ejpam-6436	50	7	the	the	DET
ejpam-6436	50	8	wreath	wreath	NOUN
ejpam-6436	50	9	product	product	NOUN
ejpam-6436	50	10	t	t	PROPN
ejpam-6436	50	11	to	to	PART
ejpam-6436	50	12	act	act	VERB
ejpam-6436	50	13	po	po	X
ejpam-6436	50	14	-	-	PUNCT
ejpam-6436	50	15	injectively	injectively	ADV
ejpam-6436	50	16	and	and	CCONJ
ejpam-6436	50	17	to	to	PART
ejpam-6436	50	18	be	be	AUX
ejpam-6436	50	19	pocancellable	pocancellable	ADJ
ejpam-6436	50	20	on	on	ADP
ejpam-6436	50	21	the	the	DET
ejpam-6436	50	22	left	left	NOUN
ejpam-6436	50	23	t	t	PROPN
ejpam-6436	50	24	-poset	-poset	PROPN
ejpam-6436	50	25	tc	tc	NOUN
ejpam-6436	50	26	.	.	PUNCT
ejpam-6436	51	1	finally	finally	ADV
ejpam-6436	51	2	we	we	PRON
ejpam-6436	51	3	examine	examine	VERB
ejpam-6436	51	4	some	some	PRON
ejpam-6436	51	5	of	of	ADP
ejpam-6436	51	6	the	the	DET
ejpam-6436	51	7	well	well	ADV
ejpam-6436	51	8	known	know	VERB
ejpam-6436	51	9	properties	property	NOUN
ejpam-6436	51	10	of	of	ADP
ejpam-6436	51	11	s−posets	s−poset	NOUN
ejpam-6436	51	12	either	either	CCONJ
ejpam-6436	51	13	on	on	ADP
ejpam-6436	51	14	tc	tc	NOUN
ejpam-6436	51	15	or	or	CCONJ
ejpam-6436	51	16	on	on	ADP
ejpam-6436	51	17	t	t	PROPN
ejpam-6436	51	18	.	.	PUNCT
ejpam-6436	52	1	this	this	PRON
ejpam-6436	52	2	particularly	particularly	ADV
ejpam-6436	52	3	includes	include	VERB
ejpam-6436	52	4	the	the	DET
ejpam-6436	52	5	properties	property	NOUN
ejpam-6436	52	6	such	such	ADJ
ejpam-6436	52	7	as	as	ADP
ejpam-6436	52	8	po	po	NOUN
ejpam-6436	52	9	-	-	NOUN
ejpam-6436	52	10	surjectivity	surjectivity	NOUN
ejpam-6436	52	11	,	,	PUNCT
ejpam-6436	52	12	po	po	NOUN
ejpam-6436	52	13	-	-	PUNCT
ejpam-6436	52	14	torsion	torsion	NOUN
ejpam-6436	52	15	free	free	ADJ
ejpam-6436	52	16	,	,	PUNCT
ejpam-6436	52	17	property	property	NOUN
ejpam-6436	52	18	(	(	PUNCT
ejpam-6436	52	19	p	p	NOUN
ejpam-6436	52	20	)	)	PUNCT
ejpam-6436	52	21	,	,	PUNCT
ejpam-6436	52	22	property	property	NOUN
ejpam-6436	52	23	(	(	PUNCT
ejpam-6436	52	24	e	e	NOUN
ejpam-6436	52	25	)	)	PUNCT
ejpam-6436	52	26	,	,	PUNCT
ejpam-6436	52	27	property	property	NOUN
ejpam-6436	52	28	(	(	PUNCT
ejpam-6436	52	29	pe	pe	NOUN
ejpam-6436	52	30	)	)	PUNCT
ejpam-6436	52	31	,	,	PUNCT
ejpam-6436	52	32	strongly	strongly	ADV
ejpam-6436	52	33	flat	flat	ADJ
ejpam-6436	52	34	,	,	PUNCT
ejpam-6436	52	35	reversible	reversible	ADJ
ejpam-6436	52	36	,	,	PUNCT
ejpam-6436	52	37	and	and	CCONJ
ejpam-6436	52	38	solvable	solvable	ADJ
ejpam-6436	52	39	.	.	PUNCT
ejpam-6436	53	1	2	2	X
ejpam-6436	53	2	.	.	X
ejpam-6436	53	3	po	po	NOUN
ejpam-6436	53	4	-	-	ADJ
ejpam-6436	53	5	injective	injective	ADJ
ejpam-6436	53	6	action	action	NOUN
ejpam-6436	53	7	and	and	CCONJ
ejpam-6436	53	8	left	leave	VERB
ejpam-6436	53	9	po	po	NOUN
ejpam-6436	53	10	-	-	NOUN
ejpam-6436	53	11	cancellability	cancellability	NOUN
ejpam-6436	53	12	in	in	ADP
ejpam-6436	53	13	this	this	DET
ejpam-6436	53	14	section	section	NOUN
ejpam-6436	53	15	we	we	PRON
ejpam-6436	53	16	investigate	investigate	VERB
ejpam-6436	53	17	the	the	DET
ejpam-6436	53	18	po	po	NOUN
ejpam-6436	53	19	-	-	PUNCT
ejpam-6436	53	20	injective	injective	ADJ
ejpam-6436	53	21	and	and	CCONJ
ejpam-6436	53	22	po	po	NOUN
ejpam-6436	53	23	-	-	PUNCT
ejpam-6436	53	24	cancellable	cancellable	ADJ
ejpam-6436	53	25	properties	property	NOUN
ejpam-6436	53	26	on	on	ADP
ejpam-6436	53	27	the	the	DET
ejpam-6436	53	28	wreath	wreath	NOUN
ejpam-6436	53	29	product	product	NOUN
ejpam-6436	53	30	of	of	ADP
ejpam-6436	53	31	pomonoids	pomonoid	NOUN
ejpam-6436	53	32	and	and	CCONJ
ejpam-6436	53	33	the	the	DET
ejpam-6436	53	34	relation	relation	NOUN
ejpam-6436	53	35	between	between	ADP
ejpam-6436	53	36	these	these	DET
ejpam-6436	53	37	properties	property	NOUN
ejpam-6436	53	38	.	.	PUNCT
ejpam-6436	54	1	let	let	VERB
ejpam-6436	54	2	ra	ra	PROPN
ejpam-6436	54	3	be	be	AUX
ejpam-6436	54	4	a	a	DET
ejpam-6436	54	5	left	left	ADJ
ejpam-6436	54	6	r	r	NOUN
ejpam-6436	54	7	-	-	PUNCT
ejpam-6436	54	8	poset	poset	NOUN
ejpam-6436	54	9	and	and	CCONJ
ejpam-6436	54	10	let	let	VERB
ejpam-6436	54	11	r	r	PRON
ejpam-6436	54	12	be	be	AUX
ejpam-6436	54	13	any	any	DET
ejpam-6436	54	14	element	element	NOUN
ejpam-6436	54	15	of	of	ADP
ejpam-6436	54	16	r.	r.	PROPN
ejpam-6436	54	17	we	we	PRON
ejpam-6436	54	18	say	say	VERB
ejpam-6436	54	19	that	that	SCONJ
ejpam-6436	54	20	r	r	NOUN
ejpam-6436	54	21	acts	act	VERB
ejpam-6436	54	22	poinjectively	poinjectively	ADV
ejpam-6436	54	23	on	on	ADP
ejpam-6436	54	24	a	a	DET
ejpam-6436	54	25	if	if	SCONJ
ejpam-6436	54	26	ra	ra	NOUN
ejpam-6436	54	27	≤	≤	ADJ
ejpam-6436	54	28	ra′	ra′	NOUN
ejpam-6436	54	29	implies	imply	VERB
ejpam-6436	54	30	a	a	DET
ejpam-6436	54	31	≤	≤	NUM
ejpam-6436	54	32	a′	a′	PROPN
ejpam-6436	54	33	,	,	PUNCT
ejpam-6436	54	34	where	where	SCONJ
ejpam-6436	54	35	a	a	X
ejpam-6436	54	36	,	,	PUNCT
ejpam-6436	54	37	a′	a′	PROPN
ejpam-6436	54	38	∈	∈	PROPN
ejpam-6436	54	39	a.	a.	NOUN
ejpam-6436	54	40	if	if	SCONJ
ejpam-6436	54	41	this	this	DET
ejpam-6436	54	42	property	property	NOUN
ejpam-6436	54	43	holds	hold	VERB
ejpam-6436	54	44	for	for	ADP
ejpam-6436	54	45	every	every	DET
ejpam-6436	54	46	r	r	NOUN
ejpam-6436	54	47	∈	∈	NOUN
ejpam-6436	54	48	r	r	NOUN
ejpam-6436	54	49	,	,	PUNCT
ejpam-6436	54	50	then	then	ADV
ejpam-6436	54	51	it	it	PRON
ejpam-6436	54	52	can	can	AUX
ejpam-6436	54	53	be	be	AUX
ejpam-6436	54	54	said	say	VERB
ejpam-6436	54	55	that	that	SCONJ
ejpam-6436	54	56	r	r	NOUN
ejpam-6436	54	57	acts	act	VERB
ejpam-6436	54	58	po	po	NOUN
ejpam-6436	54	59	-	-	PUNCT
ejpam-6436	54	60	injectively	injectively	ADV
ejpam-6436	54	61	on	on	ADP
ejpam-6436	54	62	a.	a.	NOUN
ejpam-6436	54	63	the	the	DET
ejpam-6436	54	64	strong	strong	ADJ
ejpam-6436	54	65	version	version	NOUN
ejpam-6436	54	66	of	of	ADP
ejpam-6436	54	67	r	r	NOUN
ejpam-6436	54	68	being	be	AUX
ejpam-6436	54	69	acting	act	VERB
ejpam-6436	54	70	po	po	NOUN
ejpam-6436	54	71	-	-	PUNCT
ejpam-6436	54	72	injectively	injectively	ADV
ejpam-6436	54	73	on	on	ADP
ejpam-6436	54	74	a	a	PRON
ejpam-6436	54	75	is	be	AUX
ejpam-6436	54	76	that	that	PRON
ejpam-6436	54	77	of	of	ADP
ejpam-6436	54	78	r	r	NOUN
ejpam-6436	54	79	being	be	AUX
ejpam-6436	54	80	acting	act	VERB
ejpam-6436	54	81	strongly	strongly	ADV
ejpam-6436	54	82	po	po	NOUN
ejpam-6436	54	83	-	-	PUNCT
ejpam-6436	54	84	injectively	injectively	ADV
ejpam-6436	54	85	on	on	ADP
ejpam-6436	54	86	a	a	PRON
ejpam-6436	54	87	,	,	PUNCT
ejpam-6436	54	88	which	which	PRON
ejpam-6436	54	89	is	be	AUX
ejpam-6436	54	90	defined	define	VERB
ejpam-6436	54	91	as	as	ADP
ejpam-6436	54	92	:	:	PUNCT
ejpam-6436	54	93	r	r	NOUN
ejpam-6436	54	94	acts	act	VERB
ejpam-6436	54	95	strongly	strongly	ADV
ejpam-6436	54	96	po	po	NOUN
ejpam-6436	54	97	-	-	PUNCT
ejpam-6436	54	98	injectively	injectively	ADV
ejpam-6436	54	99	on	on	ADP
ejpam-6436	54	100	a	a	DET
ejpam-6436	54	101	if	if	NOUN
ejpam-6436	54	102	for	for	ADP
ejpam-6436	54	103	all	all	DET
ejpam-6436	54	104	r	r	NOUN
ejpam-6436	54	105	,	,	PUNCT
ejpam-6436	54	106	r′	r′	NOUN
ejpam-6436	54	107	∈	∈	PROPN
ejpam-6436	54	108	r	r	NOUN
ejpam-6436	54	109	,	,	PUNCT
ejpam-6436	54	110	a	a	PRON
ejpam-6436	54	111	,	,	PUNCT
ejpam-6436	55	1	a′	a′	PROPN
ejpam-6436	55	2	∈	∈	PROPN
ejpam-6436	55	3	a	a	PRON
ejpam-6436	55	4	,	,	PUNCT
ejpam-6436	55	5	if	if	SCONJ
ejpam-6436	55	6	ra	ra	PROPN
ejpam-6436	55	7	≤	≤	NUM
ejpam-6436	55	8	r′a′	r′a′	PROPN
ejpam-6436	55	9	and	and	CCONJ
ejpam-6436	55	10	r	r	PROPN
ejpam-6436	55	11	≤	≤	NUM
ejpam-6436	55	12	r′	r′	PROPN
ejpam-6436	55	13	then	then	ADV
ejpam-6436	55	14	a	a	DET
ejpam-6436	55	15	≤	≤	NOUN
ejpam-6436	55	16	a′.	a′.	NOUN
ejpam-6436	55	17	an	an	DET
ejpam-6436	55	18	element	element	NOUN
ejpam-6436	55	19	r	r	NOUN
ejpam-6436	55	20	∈	∈	NOUN
ejpam-6436	55	21	r	r	NOUN
ejpam-6436	55	22	is	be	AUX
ejpam-6436	55	23	called	call	VERB
ejpam-6436	55	24	left	left	ADJ
ejpam-6436	55	25	po	po	NOUN
ejpam-6436	55	26	-	-	NOUN
ejpam-6436	55	27	cancellable	cancellable	ADJ
ejpam-6436	55	28	if	if	SCONJ
ejpam-6436	55	29	for	for	ADP
ejpam-6436	55	30	all	all	DET
ejpam-6436	55	31	t	t	PROPN
ejpam-6436	55	32	,	,	PUNCT
ejpam-6436	55	33	t′	t′	NUM
ejpam-6436	55	34	∈	∈	PROPN
ejpam-6436	55	35	r	r	NOUN
ejpam-6436	55	36	,	,	PUNCT
ejpam-6436	55	37	rt	rt	PROPN
ejpam-6436	55	38	≤	≤	ADJ
ejpam-6436	55	39	rt′	rt′	PROPN
ejpam-6436	55	40	implies	imply	VERB
ejpam-6436	55	41	t	t	PROPN
ejpam-6436	55	42	≤	≤	NUM
ejpam-6436	55	43	t′.	t′.	NOUN
ejpam-6436	55	44	a	a	DET
ejpam-6436	55	45	pomoniod	pomoniod	NOUN
ejpam-6436	55	46	r	r	NOUN
ejpam-6436	55	47	is	be	AUX
ejpam-6436	55	48	called	call	VERB
ejpam-6436	55	49	left	left	ADJ
ejpam-6436	55	50	po	po	NOUN
ejpam-6436	55	51	-	-	NOUN
ejpam-6436	55	52	cancellative	cancellative	ADJ
ejpam-6436	55	53	if	if	SCONJ
ejpam-6436	55	54	every	every	DET
ejpam-6436	55	55	element	element	NOUN
ejpam-6436	55	56	in	in	ADP
ejpam-6436	55	57	r	r	NOUN
ejpam-6436	55	58	is	be	AUX
ejpam-6436	55	59	left	leave	VERB
ejpam-6436	55	60	po	po	NOUN
ejpam-6436	55	61	-	-	NOUN
ejpam-6436	55	62	cancellable	cancellable	ADJ
ejpam-6436	55	63	.	.	PUNCT
ejpam-6436	56	1	a	a	DET
ejpam-6436	56	2	pomonoid	pomonoid	NOUN
ejpam-6436	56	3	r	r	NOUN
ejpam-6436	56	4	is	be	AUX
ejpam-6436	56	5	called	call	VERB
ejpam-6436	56	6	strongly	strongly	ADV
ejpam-6436	56	7	left	leave	VERB
ejpam-6436	56	8	po	po	NOUN
ejpam-6436	56	9	-	-	NOUN
ejpam-6436	56	10	cancellative	cancellative	ADJ
ejpam-6436	56	11	if	if	SCONJ
ejpam-6436	56	12	for	for	ADP
ejpam-6436	56	13	all	all	DET
ejpam-6436	56	14	r	r	NOUN
ejpam-6436	56	15	,	,	PUNCT
ejpam-6436	56	16	r′	r′	PROPN
ejpam-6436	56	17	,	,	PUNCT
ejpam-6436	56	18	t	t	PROPN
ejpam-6436	56	19	,	,	PUNCT
ejpam-6436	56	20	t′	t′	NUM
ejpam-6436	56	21	∈	∈	NOUN
ejpam-6436	56	22	r	r	NOUN
ejpam-6436	56	23	,	,	PUNCT
ejpam-6436	56	24	r	r	NOUN
ejpam-6436	56	25	≤	≤	NUM
ejpam-6436	56	26	r′	r′	NUM
ejpam-6436	56	27	and	and	CCONJ
ejpam-6436	56	28	rt	rt	PROPN
ejpam-6436	56	29	≤	≤	NUM
ejpam-6436	56	30	r′t′	r′t′	PROPN
ejpam-6436	56	31	implies	imply	VERB
ejpam-6436	56	32	t	t	NOUN
ejpam-6436	56	33	≤	≤	NUM
ejpam-6436	56	34	t′.	t′.	NOUN
ejpam-6436	56	35	the	the	DET
ejpam-6436	56	36	right	right	ADJ
ejpam-6436	56	37	po	po	NOUN
ejpam-6436	56	38	-	-	NOUN
ejpam-6436	56	39	cancellable	cancellable	ADJ
ejpam-6436	56	40	,	,	PUNCT
ejpam-6436	56	41	right	right	ADJ
ejpam-6436	56	42	po	po	NOUN
ejpam-6436	56	43	-	-	NOUN
ejpam-6436	56	44	cancellative	cancellative	ADJ
ejpam-6436	56	45	,	,	PUNCT
ejpam-6436	56	46	and	and	CCONJ
ejpam-6436	56	47	strongly	strongly	ADV
ejpam-6436	56	48	right	right	ADJ
ejpam-6436	56	49	po	po	NOUN
ejpam-6436	56	50	-	-	ADJ
ejpam-6436	56	51	cancellative	cancellative	ADJ
ejpam-6436	56	52	are	be	AUX
ejpam-6436	56	53	defined	define	VERB
ejpam-6436	56	54	dually	dually	ADV
ejpam-6436	56	55	.	.	PUNCT
ejpam-6436	57	1	let	let	VERB
ejpam-6436	57	2	x	x	PRON
ejpam-6436	57	3	be	be	AUX
ejpam-6436	57	4	a	a	DET
ejpam-6436	57	5	left	left	ADJ
ejpam-6436	57	6	r	r	NOUN
ejpam-6436	57	7	-	-	PUNCT
ejpam-6436	57	8	poset	poset	NOUN
ejpam-6436	57	9	and	and	CCONJ
ejpam-6436	57	10	y	y	PROPN
ejpam-6436	57	11	a	a	DET
ejpam-6436	57	12	poset	poset	NOUN
ejpam-6436	57	13	.	.	PUNCT
ejpam-6436	58	1	let	let	VERB
ejpam-6436	58	2	t	t	NOUN
ejpam-6436	58	3	(	(	PUNCT
ejpam-6436	58	4	x	x	PROPN
ejpam-6436	58	5	×	×	PROPN
ejpam-6436	58	6	y	y	PROPN
ejpam-6436	58	7	)	)	PUNCT
ejpam-6436	58	8	be	be	AUX
ejpam-6436	58	9	a	a	DET
ejpam-6436	58	10	left	left	ADJ
ejpam-6436	58	11	t	t	NOUN
ejpam-6436	58	12	-poset	-poset	PROPN
ejpam-6436	58	13	where	where	SCONJ
ejpam-6436	58	14	t	t	NOUN
ejpam-6436	58	15	=	=	SYM
ejpam-6436	58	16	r×	r×	PROPN
ejpam-6436	58	17	f	f	X
ejpam-6436	58	18	(	(	PUNCT
ejpam-6436	58	19	a	a	PRON
ejpam-6436	58	20	,	,	PUNCT
ejpam-6436	58	21	s	s	PART
ejpam-6436	58	22	)	)	PUNCT
ejpam-6436	58	23	is	be	AUX
ejpam-6436	58	24	the	the	DET
ejpam-6436	58	25	wreath	wreath	NOUN
ejpam-6436	58	26	product	product	NOUN
ejpam-6436	58	27	defined	define	VERB
ejpam-6436	58	28	above	above	ADV
ejpam-6436	58	29	,	,	PUNCT
ejpam-6436	58	30	and	and	CCONJ
ejpam-6436	58	31	the	the	DET
ejpam-6436	58	32	action	action	NOUN
ejpam-6436	58	33	is	be	AUX
ejpam-6436	58	34	defined	define	VERB
ejpam-6436	58	35	through	through	ADP
ejpam-6436	58	36	some	some	DET
ejpam-6436	58	37	monotone	monotone	ADJ
ejpam-6436	58	38	mapping	mapping	NOUN
ejpam-6436	58	39	α	α	NOUN
ejpam-6436	58	40	:	:	PUNCT
ejpam-6436	59	1	f	f	X
ejpam-6436	59	2	(	(	PUNCT
ejpam-6436	59	3	a	a	PRON
ejpam-6436	59	4	,	,	PUNCT
ejpam-6436	59	5	s	s	NOUN
ejpam-6436	59	6	)	)	PUNCT
ejpam-6436	59	7	×	×	NOUN
ejpam-6436	59	8	x	x	SYM
ejpam-6436	59	9	×	×	NOUN
ejpam-6436	59	10	y	y	PROPN
ejpam-6436	59	11	−→	−→	NOUN
ejpam-6436	59	12	y	y	PROPN
ejpam-6436	59	13	such	such	ADJ
ejpam-6436	59	14	that	that	SCONJ
ejpam-6436	59	15	(	(	PUNCT
ejpam-6436	59	16	r	r	NOUN
ejpam-6436	59	17	,	,	PUNCT
ejpam-6436	59	18	f)(x	f)(x	PROPN
ejpam-6436	59	19	,	,	PUNCT
ejpam-6436	59	20	y	y	NOUN
ejpam-6436	59	21	)	)	PUNCT
ejpam-6436	59	22	=	=	PRON
ejpam-6436	59	23	(	(	PUNCT
ejpam-6436	59	24	rx	rx	PROPN
ejpam-6436	59	25	,	,	PUNCT
ejpam-6436	59	26	α(f	α(f	PROPN
ejpam-6436	59	27	,	,	PUNCT
ejpam-6436	59	28	x	x	NOUN
ejpam-6436	59	29	,	,	PUNCT
ejpam-6436	59	30	y	y	PROPN
ejpam-6436	59	31	)	)	PUNCT
ejpam-6436	59	32	)	)	PUNCT
ejpam-6436	59	33	.	.	PUNCT
ejpam-6436	60	1	this	this	PRON
ejpam-6436	60	2	is	be	AUX
ejpam-6436	60	3	equivalent	equivalent	ADJ
ejpam-6436	60	4	to	to	PART
ejpam-6436	60	5	say	say	VERB
ejpam-6436	60	6	that	that	SCONJ
ejpam-6436	60	7	α	α	PROPN
ejpam-6436	60	8	satisfies	satisfy	VERB
ejpam-6436	60	9	the	the	DET
ejpam-6436	60	10	identities	identity	NOUN
ejpam-6436	60	11	:	:	PUNCT
ejpam-6436	60	12	(	(	PUNCT
ejpam-6436	60	13	i	i	NOUN
ejpam-6436	60	14	)	)	PUNCT
ejpam-6436	60	15	α(c1	α(c1	PROPN
ejpam-6436	60	16	,	,	PUNCT
ejpam-6436	60	17	x	x	NOUN
ejpam-6436	60	18	,	,	PUNCT
ejpam-6436	60	19	y	y	NOUN
ejpam-6436	60	20	)	)	PUNCT
ejpam-6436	60	21	=	=	SYM
ejpam-6436	60	22	y.	y.	NOUN
ejpam-6436	60	23	(	(	PUNCT
ejpam-6436	60	24	ii	ii	PROPN
ejpam-6436	60	25	)	)	PUNCT
ejpam-6436	60	26	α(f	α(f	PROPN
ejpam-6436	60	27	,	,	PUNCT
ejpam-6436	60	28	px	px	PROPN
ejpam-6436	60	29	,	,	PUNCT
ejpam-6436	60	30	α(g	α(g	PROPN
ejpam-6436	60	31	,	,	PUNCT
ejpam-6436	60	32	x	x	NOUN
ejpam-6436	60	33	,	,	PUNCT
ejpam-6436	60	34	y	y	NOUN
ejpam-6436	60	35	)	)	PUNCT
ejpam-6436	60	36	)	)	PUNCT
ejpam-6436	61	1	=	=	SYM
ejpam-6436	61	2	α(fpg	α(fpg	NOUN
ejpam-6436	61	3	,	,	PUNCT
ejpam-6436	61	4	x	x	NOUN
ejpam-6436	61	5	,	,	PUNCT
ejpam-6436	61	6	y	y	PROPN
ejpam-6436	61	7	)	)	PUNCT
ejpam-6436	61	8	,	,	PUNCT
ejpam-6436	61	9	b.	b.	PROPN
ejpam-6436	61	10	al	al	PROPN
ejpam-6436	61	11	subaiei	subaiei	PROPN
ejpam-6436	61	12	et	et	PROPN
ejpam-6436	61	13	al	al	PROPN
ejpam-6436	61	14	.	.	PUNCT
ejpam-6436	61	15	/	/	SYM
ejpam-6436	61	16	eur	eur	PROPN
ejpam-6436	61	17	.	.	PUNCT
ejpam-6436	62	1	j.	j.	PROPN
ejpam-6436	62	2	pure	pure	PROPN
ejpam-6436	62	3	appl	appl	PROPN
ejpam-6436	62	4	.	.	PROPN
ejpam-6436	62	5	math	math	PROPN
ejpam-6436	62	6	,	,	PUNCT
ejpam-6436	62	7	18	18	NUM
ejpam-6436	62	8	(	(	PUNCT
ejpam-6436	62	9	3	3	NUM
ejpam-6436	62	10	)	)	PUNCT
ejpam-6436	62	11	(	(	PUNCT
ejpam-6436	62	12	2025	2025	NUM
ejpam-6436	62	13	)	)	PUNCT
ejpam-6436	62	14	,	,	PUNCT
ejpam-6436	62	15	6436	6436	NUM
ejpam-6436	62	16	4	4	NUM
ejpam-6436	62	17	of	of	ADP
ejpam-6436	62	18	14	14	NUM
ejpam-6436	62	19	for	for	ADP
ejpam-6436	62	20	all	all	PRON
ejpam-6436	62	21	x	x	SYM
ejpam-6436	62	22	∈	∈	PROPN
ejpam-6436	62	23	x	x	NOUN
ejpam-6436	62	24	,	,	PUNCT
ejpam-6436	62	25	y	y	PROPN
ejpam-6436	62	26	∈	∈	PROPN
ejpam-6436	62	27	y	y	PROPN
ejpam-6436	62	28	,	,	PUNCT
ejpam-6436	62	29	c1	c1	PROPN
ejpam-6436	62	30	,	,	PUNCT
ejpam-6436	62	31	f	f	PROPN
ejpam-6436	62	32	,	,	PUNCT
ejpam-6436	62	33	g	g	PROPN
ejpam-6436	62	34	∈	∈	PROPN
ejpam-6436	62	35	f	f	X
ejpam-6436	63	1	(	(	PUNCT
ejpam-6436	63	2	a	a	PRON
ejpam-6436	63	3	,	,	PUNCT
ejpam-6436	63	4	s	s	PART
ejpam-6436	63	5	)	)	PUNCT
ejpam-6436	64	1	and	and	CCONJ
ejpam-6436	64	2	p	p	PROPN
ejpam-6436	64	3	∈	∈	PROPN
ejpam-6436	64	4	r.	r.	PROPN
ejpam-6436	64	5	first	first	ADV
ejpam-6436	64	6	we	we	PRON
ejpam-6436	64	7	give	give	VERB
ejpam-6436	64	8	necessary	necessary	ADJ
ejpam-6436	64	9	and	and	CCONJ
ejpam-6436	64	10	sufficient	sufficient	ADJ
ejpam-6436	64	11	condition	condition	NOUN
ejpam-6436	64	12	for	for	ADP
ejpam-6436	64	13	an	an	DET
ejpam-6436	64	14	element	element	NOUN
ejpam-6436	64	15	of	of	ADP
ejpam-6436	64	16	t	t	PROPN
ejpam-6436	64	17	to	to	PART
ejpam-6436	64	18	act	act	VERB
ejpam-6436	64	19	po	po	VERB
ejpam-6436	64	20	-	-	PUNCT
ejpam-6436	64	21	injectively	injectively	ADV
ejpam-6436	64	22	on	on	ADP
ejpam-6436	64	23	tx	tx	PROPN
ejpam-6436	64	24	×	×	PROPN
ejpam-6436	64	25	y	y	PROPN
ejpam-6436	64	26	proposition	proposition	NOUN
ejpam-6436	64	27	1	1	X
ejpam-6436	64	28	.	.	PUNCT
ejpam-6436	65	1	the	the	DET
ejpam-6436	65	2	element	element	NOUN
ejpam-6436	65	3	(	(	PUNCT
ejpam-6436	65	4	r	r	NOUN
ejpam-6436	65	5	,	,	PUNCT
ejpam-6436	65	6	f	f	X
ejpam-6436	65	7	)	)	PUNCT
ejpam-6436	65	8	∈	∈	PROPN
ejpam-6436	65	9	t	t	PROPN
ejpam-6436	65	10	acts	act	VERB
ejpam-6436	65	11	po	po	NOUN
ejpam-6436	65	12	-	-	PUNCT
ejpam-6436	65	13	injectively	injectively	ADV
ejpam-6436	65	14	on	on	ADP
ejpam-6436	65	15	t	t	PROPN
ejpam-6436	65	16	(	(	PUNCT
ejpam-6436	65	17	x	x	PROPN
ejpam-6436	65	18	×	×	PROPN
ejpam-6436	65	19	y	y	PROPN
ejpam-6436	65	20	)	)	PUNCT
ejpam-6436	65	21	through	through	ADP
ejpam-6436	65	22	α	α	PROPN
ejpam-6436	65	23	:	:	PUNCT
ejpam-6436	65	24	f	f	X
ejpam-6436	65	25	(	(	PUNCT
ejpam-6436	65	26	a	a	DET
ejpam-6436	65	27	,	,	PUNCT
ejpam-6436	65	28	s)×x	s)×x	ADJ
ejpam-6436	65	29	×	×	PROPN
ejpam-6436	65	30	y	y	PROPN
ejpam-6436	65	31	→	→	SYM
ejpam-6436	65	32	y	y	PROPN
ejpam-6436	66	1	if	if	SCONJ
ejpam-6436	66	2	and	and	CCONJ
ejpam-6436	66	3	only	only	ADV
ejpam-6436	66	4	if	if	SCONJ
ejpam-6436	66	5	the	the	DET
ejpam-6436	66	6	following	follow	VERB
ejpam-6436	66	7	conditions	condition	NOUN
ejpam-6436	66	8	are	be	AUX
ejpam-6436	66	9	satisfied	satisfied	ADJ
ejpam-6436	66	10	.	.	PUNCT
ejpam-6436	67	1	1	1	X
ejpam-6436	67	2	)	)	PUNCT
ejpam-6436	67	3	if	if	SCONJ
ejpam-6436	67	4	x	x	ADP
ejpam-6436	67	5	≤	≤	NUM
ejpam-6436	67	6	x′	x′	PROPN
ejpam-6436	67	7	and	and	CCONJ
ejpam-6436	67	8	α(f	α(f	PROPN
ejpam-6436	67	9	,	,	PUNCT
ejpam-6436	67	10	x	x	X
ejpam-6436	67	11	,	,	PUNCT
ejpam-6436	67	12	y	y	NOUN
ejpam-6436	67	13	)	)	PUNCT
ejpam-6436	67	14	≤	≤	NOUN
ejpam-6436	67	15	α(f	α(f	PROPN
ejpam-6436	67	16	,	,	PUNCT
ejpam-6436	67	17	x′	x′	NUM
ejpam-6436	67	18	,	,	PUNCT
ejpam-6436	67	19	y′	y′	NUM
ejpam-6436	67	20	)	)	PUNCT
ejpam-6436	67	21	then	then	ADV
ejpam-6436	67	22	y	y	PROPN
ejpam-6436	67	23	≤	≤	ADV
ejpam-6436	67	24	y′	y′	PUNCT
ejpam-6436	67	25	,	,	PUNCT
ejpam-6436	67	26	where	where	SCONJ
ejpam-6436	67	27	x	x	X
ejpam-6436	67	28	,	,	PUNCT
ejpam-6436	67	29	x′	x′	PROPN
ejpam-6436	67	30	∈	∈	PROPN
ejpam-6436	67	31	x	x	X
ejpam-6436	67	32	and	and	CCONJ
ejpam-6436	67	33	y	y	PROPN
ejpam-6436	67	34	,	,	PUNCT
ejpam-6436	67	35	y′	y′	NOUN
ejpam-6436	67	36	∈	∈	PROPN
ejpam-6436	67	37	y	y	PROPN
ejpam-6436	67	38	.	.	PUNCT
ejpam-6436	68	1	2	2	X
ejpam-6436	68	2	)	)	PUNCT
ejpam-6436	68	3	if	if	SCONJ
ejpam-6436	68	4	rx	rx	VERB
ejpam-6436	68	5	≤	≤	NUM
ejpam-6436	68	6	rx′	rx′	NOUN
ejpam-6436	68	7	and	and	CCONJ
ejpam-6436	68	8	x	x	SYM
ejpam-6436	68	9	≰	≰	PROPN
ejpam-6436	68	10	x′	x′	PROPN
ejpam-6436	68	11	then	then	ADV
ejpam-6436	68	12	for	for	ADP
ejpam-6436	68	13	all	all	DET
ejpam-6436	68	14	y	y	PROPN
ejpam-6436	68	15	,	,	PUNCT
ejpam-6436	68	16	y′	y′	NOUN
ejpam-6436	68	17	∈	∈	PROPN
ejpam-6436	68	18	y	y	PROPN
ejpam-6436	68	19	,	,	PUNCT
ejpam-6436	68	20	α(f	α(f	PROPN
ejpam-6436	68	21	,	,	PUNCT
ejpam-6436	68	22	x	x	X
ejpam-6436	68	23	,	,	PUNCT
ejpam-6436	68	24	y	y	NOUN
ejpam-6436	68	25	)	)	PUNCT
ejpam-6436	68	26	≰	≰	PROPN
ejpam-6436	68	27	α(f	α(f	PROPN
ejpam-6436	68	28	,	,	PUNCT
ejpam-6436	68	29	x′	x′	NUM
ejpam-6436	68	30	,	,	PUNCT
ejpam-6436	68	31	y′	y′	NUM
ejpam-6436	68	32	)	)	PUNCT
ejpam-6436	68	33	where	where	SCONJ
ejpam-6436	68	34	x	x	X
ejpam-6436	68	35	,	,	PUNCT
ejpam-6436	68	36	x′	x′	PROPN
ejpam-6436	68	37	∈	∈	PROPN
ejpam-6436	68	38	x	x	X
ejpam-6436	68	39	and	and	CCONJ
ejpam-6436	68	40	r	r	PROPN
ejpam-6436	68	41	∈	∈	PROPN
ejpam-6436	68	42	r.	r.	NOUN
ejpam-6436	68	43	proof	proof	NOUN
ejpam-6436	68	44	.	.	PUNCT
ejpam-6436	69	1	let	let	AUX
ejpam-6436	69	2	(	(	PUNCT
ejpam-6436	69	3	r	r	NOUN
ejpam-6436	69	4	,	,	PUNCT
ejpam-6436	69	5	f	f	X
ejpam-6436	69	6	)	)	PUNCT
ejpam-6436	69	7	∈	∈	PROPN
ejpam-6436	69	8	t	t	PROPN
ejpam-6436	69	9	acts	act	VERB
ejpam-6436	69	10	po	po	NOUN
ejpam-6436	69	11	-	-	PUNCT
ejpam-6436	69	12	injectively	injectively	ADV
ejpam-6436	69	13	on	on	ADP
ejpam-6436	69	14	t	t	PROPN
ejpam-6436	69	15	(	(	PUNCT
ejpam-6436	69	16	x	x	PROPN
ejpam-6436	69	17	×	×	PROPN
ejpam-6436	69	18	y	y	PROPN
ejpam-6436	69	19	)	)	PUNCT
ejpam-6436	69	20	through	through	ADP
ejpam-6436	69	21	α	α	NUM
ejpam-6436	69	22	.	.	PROPN
ejpam-6436	69	23	1	1	NUM
ejpam-6436	69	24	)	)	PUNCT
ejpam-6436	69	25	first	first	ADV
ejpam-6436	69	26	suppose	suppose	VERB
ejpam-6436	69	27	that	that	SCONJ
ejpam-6436	69	28	x	x	PUNCT
ejpam-6436	69	29	≤	≤	NUM
ejpam-6436	69	30	x′	x′	PROPN
ejpam-6436	69	31	in	in	ADP
ejpam-6436	69	32	x	x	X
ejpam-6436	69	33	and	and	CCONJ
ejpam-6436	69	34	α(f	α(f	PROPN
ejpam-6436	69	35	,	,	PUNCT
ejpam-6436	69	36	x	x	X
ejpam-6436	69	37	,	,	PUNCT
ejpam-6436	69	38	y	y	NOUN
ejpam-6436	69	39	)	)	PUNCT
ejpam-6436	69	40	≤	≤	NOUN
ejpam-6436	69	41	α(f	α(f	PROPN
ejpam-6436	69	42	,	,	PUNCT
ejpam-6436	69	43	x′	x′	NUM
ejpam-6436	69	44	,	,	PUNCT
ejpam-6436	69	45	y′	y′	NUM
ejpam-6436	69	46	)	)	PUNCT
ejpam-6436	70	1	where	where	SCONJ
ejpam-6436	70	2	y	y	NOUN
ejpam-6436	70	3	,	,	PUNCT
ejpam-6436	70	4	y′	y′	NOUN
ejpam-6436	70	5	∈	∈	PROPN
ejpam-6436	70	6	y	y	PROPN
ejpam-6436	70	7	.	.	PUNCT
ejpam-6436	71	1	hence	hence	ADV
ejpam-6436	71	2	,	,	PUNCT
ejpam-6436	71	3	for	for	ADP
ejpam-6436	71	4	all	all	DET
ejpam-6436	71	5	(	(	PUNCT
ejpam-6436	71	6	r	r	NOUN
ejpam-6436	71	7	,	,	PUNCT
ejpam-6436	71	8	f	f	X
ejpam-6436	71	9	)	)	PUNCT
ejpam-6436	71	10	∈	∈	PROPN
ejpam-6436	71	11	t	t	NOUN
ejpam-6436	71	12	(	(	PUNCT
ejpam-6436	71	13	r	r	NOUN
ejpam-6436	71	14	,	,	PUNCT
ejpam-6436	71	15	f)(x	f)(x	PROPN
ejpam-6436	71	16	,	,	PUNCT
ejpam-6436	71	17	y	y	NOUN
ejpam-6436	71	18	)	)	PUNCT
ejpam-6436	71	19	=	=	PRON
ejpam-6436	71	20	(	(	PUNCT
ejpam-6436	71	21	rx	rx	PROPN
ejpam-6436	71	22	,	,	PUNCT
ejpam-6436	71	23	α(f	α(f	PROPN
ejpam-6436	71	24	,	,	PUNCT
ejpam-6436	71	25	x	x	NOUN
ejpam-6436	71	26	,	,	PUNCT
ejpam-6436	71	27	y	y	NOUN
ejpam-6436	71	28	)	)	PUNCT
ejpam-6436	71	29	)	)	PUNCT
ejpam-6436	71	30	≤	≤	NOUN
ejpam-6436	71	31	(	(	PUNCT
ejpam-6436	71	32	rx′	rx′	PROPN
ejpam-6436	71	33	,	,	PUNCT
ejpam-6436	71	34	α(f	α(f	PROPN
ejpam-6436	71	35	,	,	PUNCT
ejpam-6436	71	36	x′	x′	NUM
ejpam-6436	71	37	,	,	PUNCT
ejpam-6436	71	38	y′	y′	NUM
ejpam-6436	71	39	)	)	PUNCT
ejpam-6436	71	40	)	)	PUNCT
ejpam-6436	72	1	=	=	PRON
ejpam-6436	72	2	(	(	PUNCT
ejpam-6436	72	3	r	r	NOUN
ejpam-6436	72	4	,	,	PUNCT
ejpam-6436	72	5	f)(x′	f)(x′	PRON
ejpam-6436	72	6	,	,	PUNCT
ejpam-6436	72	7	y′	y′	NUM
ejpam-6436	72	8	)	)	PUNCT
ejpam-6436	72	9	.	.	PUNCT
ejpam-6436	73	1	since	since	SCONJ
ejpam-6436	73	2	(	(	PUNCT
ejpam-6436	73	3	r	r	NOUN
ejpam-6436	73	4	,	,	PUNCT
ejpam-6436	73	5	f	f	X
ejpam-6436	73	6	)	)	PUNCT
ejpam-6436	73	7	acts	act	VERB
ejpam-6436	73	8	po	po	NOUN
ejpam-6436	73	9	-	-	PUNCT
ejpam-6436	73	10	injectively	injectively	ADV
ejpam-6436	73	11	on	on	ADP
ejpam-6436	73	12	t	t	PROPN
ejpam-6436	73	13	(	(	PUNCT
ejpam-6436	73	14	x	x	PROPN
ejpam-6436	73	15	×	×	PROPN
ejpam-6436	73	16	y	y	PROPN
ejpam-6436	73	17	)	)	PUNCT
ejpam-6436	73	18	,	,	PUNCT
ejpam-6436	73	19	it	it	PRON
ejpam-6436	73	20	follows	follow	VERB
ejpam-6436	73	21	that	that	SCONJ
ejpam-6436	73	22	(	(	PUNCT
ejpam-6436	73	23	x	x	X
ejpam-6436	73	24	,	,	PUNCT
ejpam-6436	73	25	y	y	NOUN
ejpam-6436	73	26	)	)	PUNCT
ejpam-6436	73	27	≤	≤	NOUN
ejpam-6436	73	28	(	(	PUNCT
ejpam-6436	73	29	x′	x′	NUM
ejpam-6436	73	30	,	,	PUNCT
ejpam-6436	73	31	y′	y′	NUM
ejpam-6436	73	32	)	)	PUNCT
ejpam-6436	73	33	and	and	CCONJ
ejpam-6436	73	34	therefore	therefore	ADV
ejpam-6436	73	35	,	,	PUNCT
ejpam-6436	73	36	y	y	PROPN
ejpam-6436	73	37	≤	≤	PROPN
ejpam-6436	73	38	y′	y′	ADV
ejpam-6436	73	39	as	as	SCONJ
ejpam-6436	73	40	required	require	VERB
ejpam-6436	73	41	.	.	PUNCT
ejpam-6436	74	1	2	2	X
ejpam-6436	74	2	)	)	PUNCT
ejpam-6436	74	3	suppose	suppose	VERB
ejpam-6436	74	4	now	now	ADV
ejpam-6436	74	5	that	that	PRON
ejpam-6436	74	6	rx	rx	VERB
ejpam-6436	74	7	≤	≤	NUM
ejpam-6436	74	8	rx′	rx′	NOUN
ejpam-6436	74	9	and	and	CCONJ
ejpam-6436	74	10	x	x	SYM
ejpam-6436	74	11	≰	≰	PROPN
ejpam-6436	74	12	x′	x′	NUM
ejpam-6436	74	13	,	,	PUNCT
ejpam-6436	74	14	where	where	SCONJ
ejpam-6436	74	15	r	r	NOUN
ejpam-6436	74	16	∈	∈	NOUN
ejpam-6436	74	17	r	r	NOUN
ejpam-6436	74	18	and	and	CCONJ
ejpam-6436	74	19	x	x	NOUN
ejpam-6436	74	20	,	,	PUNCT
ejpam-6436	74	21	x′	x′	PROPN
ejpam-6436	74	22	∈	∈	PROPN
ejpam-6436	74	23	x.	x.	NOUN
ejpam-6436	74	24	also	also	ADV
ejpam-6436	74	25	,	,	PUNCT
ejpam-6436	74	26	suppose	suppose	VERB
ejpam-6436	74	27	that	that	SCONJ
ejpam-6436	74	28	α(f	α(f	PROPN
ejpam-6436	74	29	,	,	PUNCT
ejpam-6436	74	30	x	x	NOUN
ejpam-6436	74	31	,	,	PUNCT
ejpam-6436	74	32	y	y	NOUN
ejpam-6436	74	33	)	)	PUNCT
ejpam-6436	74	34	≤	≤	NOUN
ejpam-6436	74	35	α(f	α(f	PROPN
ejpam-6436	74	36	,	,	PUNCT
ejpam-6436	74	37	x′	x′	NUM
ejpam-6436	74	38	,	,	PUNCT
ejpam-6436	74	39	y′	y′	NUM
ejpam-6436	74	40	)	)	PUNCT
ejpam-6436	74	41	for	for	ADP
ejpam-6436	74	42	some	some	DET
ejpam-6436	74	43	y	y	NOUN
ejpam-6436	74	44	,	,	PUNCT
ejpam-6436	74	45	y′	y′	NOUN
ejpam-6436	74	46	∈	∈	PROPN
ejpam-6436	74	47	y	y	PROPN
ejpam-6436	74	48	.	.	PUNCT
ejpam-6436	75	1	hence	hence	ADV
ejpam-6436	75	2	,	,	PUNCT
ejpam-6436	75	3	(	(	PUNCT
ejpam-6436	75	4	r	r	NOUN
ejpam-6436	75	5	,	,	PUNCT
ejpam-6436	75	6	f)(x	f)(x	PROPN
ejpam-6436	75	7	,	,	PUNCT
ejpam-6436	75	8	y	y	NOUN
ejpam-6436	75	9	)	)	PUNCT
ejpam-6436	75	10	=	=	PRON
ejpam-6436	75	11	(	(	PUNCT
ejpam-6436	75	12	rx	rx	PROPN
ejpam-6436	75	13	,	,	PUNCT
ejpam-6436	75	14	α(f	α(f	PROPN
ejpam-6436	75	15	,	,	PUNCT
ejpam-6436	75	16	x	x	NOUN
ejpam-6436	75	17	,	,	PUNCT
ejpam-6436	75	18	y	y	NOUN
ejpam-6436	75	19	)	)	PUNCT
ejpam-6436	75	20	)	)	PUNCT
ejpam-6436	76	1	≤	≤	NOUN
ejpam-6436	76	2	(	(	PUNCT
ejpam-6436	76	3	rx′	rx′	PROPN
ejpam-6436	76	4	,	,	PUNCT
ejpam-6436	76	5	α(f	α(f	PROPN
ejpam-6436	76	6	,	,	PUNCT
ejpam-6436	76	7	x′	x′	NUM
ejpam-6436	76	8	,	,	PUNCT
ejpam-6436	76	9	y′	y′	NUM
ejpam-6436	76	10	)	)	PUNCT
ejpam-6436	76	11	)	)	PUNCT
ejpam-6436	77	1	=	=	PRON
ejpam-6436	77	2	(	(	PUNCT
ejpam-6436	77	3	r	r	NOUN
ejpam-6436	77	4	,	,	PUNCT
ejpam-6436	77	5	f)(x′	f)(x′	PRON
ejpam-6436	77	6	,	,	PUNCT
ejpam-6436	77	7	y′	y′	NUM
ejpam-6436	77	8	)	)	PUNCT
ejpam-6436	77	9	.	.	PUNCT
ejpam-6436	78	1	again	again	ADV
ejpam-6436	78	2	since	since	SCONJ
ejpam-6436	78	3	(	(	PUNCT
ejpam-6436	78	4	r	r	NOUN
ejpam-6436	78	5	,	,	PUNCT
ejpam-6436	78	6	f	f	X
ejpam-6436	78	7	)	)	PUNCT
ejpam-6436	78	8	acts	act	VERB
ejpam-6436	78	9	po	po	NOUN
ejpam-6436	78	10	-	-	PUNCT
ejpam-6436	78	11	injectively	injectively	ADV
ejpam-6436	78	12	on	on	ADP
ejpam-6436	78	13	t	t	PROPN
ejpam-6436	78	14	(	(	PUNCT
ejpam-6436	78	15	x	x	PROPN
ejpam-6436	78	16	×	×	PROPN
ejpam-6436	78	17	y	y	PROPN
ejpam-6436	78	18	)	)	PUNCT
ejpam-6436	78	19	,	,	PUNCT
ejpam-6436	78	20	we	we	PRON
ejpam-6436	78	21	must	must	AUX
ejpam-6436	78	22	have	have	VERB
ejpam-6436	78	23	(	(	PUNCT
ejpam-6436	78	24	x	x	NOUN
ejpam-6436	78	25	,	,	PUNCT
ejpam-6436	78	26	y	y	NOUN
ejpam-6436	78	27	)	)	PUNCT
ejpam-6436	78	28	≤	≤	NOUN
ejpam-6436	78	29	(	(	PUNCT
ejpam-6436	78	30	x′	x′	NUM
ejpam-6436	78	31	,	,	PUNCT
ejpam-6436	78	32	y′	y′	NUM
ejpam-6436	78	33	)	)	PUNCT
ejpam-6436	78	34	.	.	PUNCT
ejpam-6436	79	1	thus	thus	ADV
ejpam-6436	79	2	,	,	PUNCT
ejpam-6436	79	3	x	x	PUNCT
ejpam-6436	79	4	≤	≤	NUM
ejpam-6436	79	5	x′	x′	PROPN
ejpam-6436	79	6	and	and	CCONJ
ejpam-6436	79	7	this	this	PRON
ejpam-6436	79	8	contradicts	contradict	VERB
ejpam-6436	79	9	the	the	DET
ejpam-6436	79	10	assumption	assumption	NOUN
ejpam-6436	79	11	x	x	X
ejpam-6436	79	12	≰	≰	PROPN
ejpam-6436	79	13	x′.	x′.	PROPN
ejpam-6436	79	14	therefore	therefore	ADV
ejpam-6436	79	15	,	,	PUNCT
ejpam-6436	79	16	for	for	ADP
ejpam-6436	79	17	all	all	DET
ejpam-6436	79	18	y	y	PROPN
ejpam-6436	79	19	,	,	PUNCT
ejpam-6436	79	20	y′	y′	NOUN
ejpam-6436	79	21	∈	∈	PROPN
ejpam-6436	80	1	y	y	NOUN
ejpam-6436	81	1	we	we	PRON
ejpam-6436	81	2	have	have	VERB
ejpam-6436	81	3	α(f	α(f	PROPN
ejpam-6436	81	4	,	,	PUNCT
ejpam-6436	81	5	x	x	X
ejpam-6436	81	6	,	,	PUNCT
ejpam-6436	81	7	y	y	NOUN
ejpam-6436	81	8	)	)	PUNCT
ejpam-6436	81	9	≰	≰	PROPN
ejpam-6436	81	10	α(f	α(f	PROPN
ejpam-6436	81	11	,	,	PUNCT
ejpam-6436	81	12	x′	x′	NUM
ejpam-6436	81	13	,	,	PUNCT
ejpam-6436	81	14	y′	y′	NUM
ejpam-6436	81	15	)	)	PUNCT
ejpam-6436	81	16	.	.	PUNCT
ejpam-6436	82	1	for	for	ADP
ejpam-6436	82	2	the	the	DET
ejpam-6436	82	3	other	other	ADJ
ejpam-6436	82	4	direction	direction	NOUN
ejpam-6436	82	5	,	,	PUNCT
ejpam-6436	82	6	assume	assume	VERB
ejpam-6436	82	7	the	the	DET
ejpam-6436	82	8	two	two	NUM
ejpam-6436	82	9	conditions	condition	NOUN
ejpam-6436	82	10	are	be	AUX
ejpam-6436	82	11	satisfied	satisfied	ADJ
ejpam-6436	82	12	.	.	PUNCT
ejpam-6436	83	1	suppose	suppose	VERB
ejpam-6436	83	2	that	that	SCONJ
ejpam-6436	83	3	(	(	PUNCT
ejpam-6436	83	4	r	r	NOUN
ejpam-6436	83	5	,	,	PUNCT
ejpam-6436	83	6	f)(x	f)(x	PROPN
ejpam-6436	83	7	,	,	PUNCT
ejpam-6436	83	8	y	y	NOUN
ejpam-6436	83	9	)	)	PUNCT
ejpam-6436	83	10	≤	≤	NOUN
ejpam-6436	83	11	(	(	PUNCT
ejpam-6436	83	12	r	r	NOUN
ejpam-6436	83	13	,	,	PUNCT
ejpam-6436	83	14	f)(x′	f)(x′	PRON
ejpam-6436	83	15	,	,	PUNCT
ejpam-6436	83	16	y′	y′	NUM
ejpam-6436	83	17	)	)	PUNCT
ejpam-6436	83	18	.	.	PUNCT
ejpam-6436	84	1	this	this	PRON
ejpam-6436	84	2	implies	imply	VERB
ejpam-6436	84	3	(	(	PUNCT
ejpam-6436	84	4	rx	rx	ADJ
ejpam-6436	84	5	,	,	PUNCT
ejpam-6436	84	6	α(f	α(f	PROPN
ejpam-6436	84	7	,	,	PUNCT
ejpam-6436	84	8	x	x	NOUN
ejpam-6436	84	9	,	,	PUNCT
ejpam-6436	84	10	y	y	NOUN
ejpam-6436	84	11	)	)	PUNCT
ejpam-6436	84	12	)	)	PUNCT
ejpam-6436	84	13	≤	≤	NOUN
ejpam-6436	84	14	(	(	PUNCT
ejpam-6436	84	15	rx′	rx′	PROPN
ejpam-6436	84	16	,	,	PUNCT
ejpam-6436	84	17	α(f	α(f	PROPN
ejpam-6436	84	18	,	,	PUNCT
ejpam-6436	84	19	x′	x′	NUM
ejpam-6436	84	20	,	,	PUNCT
ejpam-6436	84	21	y′	y′	NUM
ejpam-6436	84	22	)	)	PUNCT
ejpam-6436	84	23	)	)	PUNCT
ejpam-6436	84	24	.	.	PUNCT
ejpam-6436	85	1	therefore	therefore	ADV
ejpam-6436	85	2	,	,	PUNCT
ejpam-6436	85	3	rx	rx	VERB
ejpam-6436	85	4	≤	≤	NUM
ejpam-6436	85	5	rx′	rx′	NOUN
ejpam-6436	85	6	and	and	CCONJ
ejpam-6436	85	7	α(f	α(f	PROPN
ejpam-6436	85	8	,	,	PUNCT
ejpam-6436	85	9	x	x	X
ejpam-6436	85	10	,	,	PUNCT
ejpam-6436	85	11	y	y	NOUN
ejpam-6436	85	12	)	)	PUNCT
ejpam-6436	85	13	≤	≤	NOUN
ejpam-6436	85	14	α(f	α(f	PROPN
ejpam-6436	85	15	,	,	PUNCT
ejpam-6436	85	16	x′	x′	NUM
ejpam-6436	85	17	,	,	PUNCT
ejpam-6436	85	18	y′	y′	NUM
ejpam-6436	85	19	)	)	PUNCT
ejpam-6436	85	20	.	.	PUNCT
ejpam-6436	86	1	the	the	DET
ejpam-6436	86	2	condition	condition	NOUN
ejpam-6436	86	3	(	(	PUNCT
ejpam-6436	86	4	2	2	NUM
ejpam-6436	86	5	)	)	PUNCT
ejpam-6436	86	6	implies	imply	VERB
ejpam-6436	86	7	x	x	PUNCT
ejpam-6436	86	8	≤	≤	NUM
ejpam-6436	86	9	x′	x′	PROPN
ejpam-6436	86	10	and	and	CCONJ
ejpam-6436	86	11	so	so	ADV
ejpam-6436	86	12	from	from	ADP
ejpam-6436	86	13	condition	condition	NOUN
ejpam-6436	86	14	(	(	PUNCT
ejpam-6436	86	15	1	1	X
ejpam-6436	86	16	)	)	PUNCT
ejpam-6436	86	17	we	we	PRON
ejpam-6436	86	18	get	get	VERB
ejpam-6436	86	19	y	y	NOUN
ejpam-6436	86	20	≤	≤	NUM
ejpam-6436	86	21	y′.	y′.	VERB
ejpam-6436	86	22	therefore	therefore	ADV
ejpam-6436	86	23	,	,	PUNCT
ejpam-6436	86	24	(	(	PUNCT
ejpam-6436	86	25	x	x	X
ejpam-6436	86	26	,	,	PUNCT
ejpam-6436	86	27	y	y	NOUN
ejpam-6436	86	28	)	)	PUNCT
ejpam-6436	86	29	≤	≤	NOUN
ejpam-6436	86	30	(	(	PUNCT
ejpam-6436	86	31	x′	x′	NUM
ejpam-6436	86	32	,	,	PUNCT
ejpam-6436	86	33	y′	y′	NUM
ejpam-6436	86	34	)	)	PUNCT
ejpam-6436	86	35	.	.	PUNCT
ejpam-6436	87	1	hence	hence	ADV
ejpam-6436	87	2	(	(	PUNCT
ejpam-6436	87	3	r	r	NOUN
ejpam-6436	87	4	,	,	PUNCT
ejpam-6436	87	5	f	f	X
ejpam-6436	87	6	)	)	PUNCT
ejpam-6436	87	7	acts	act	VERB
ejpam-6436	87	8	po	po	NOUN
ejpam-6436	87	9	-	-	PUNCT
ejpam-6436	87	10	injectively	injectively	ADV
ejpam-6436	87	11	on	on	ADP
ejpam-6436	87	12	t	t	PROPN
ejpam-6436	87	13	,	,	PUNCT
ejpam-6436	87	14	as	as	SCONJ
ejpam-6436	87	15	required	require	VERB
ejpam-6436	87	16	.	.	PUNCT
ejpam-6436	88	1	in	in	ADP
ejpam-6436	88	2	particular	particular	ADJ
ejpam-6436	88	3	,	,	PUNCT
ejpam-6436	88	4	by	by	ADP
ejpam-6436	88	5	taking	take	VERB
ejpam-6436	88	6	x	x	PUNCT
ejpam-6436	88	7	=	=	SYM
ejpam-6436	88	8	ra	ra	PROPN
ejpam-6436	88	9	,	,	PUNCT
ejpam-6436	88	10	y	y	PROPN
ejpam-6436	88	11	=	=	SYM
ejpam-6436	88	12	sb	sb	PROPN
ejpam-6436	88	13	and	and	CCONJ
ejpam-6436	88	14	defining	define	VERB
ejpam-6436	88	15	α	α	NOUN
ejpam-6436	88	16	:	:	PUNCT
ejpam-6436	88	17	f	f	X
ejpam-6436	88	18	(	(	PUNCT
ejpam-6436	88	19	a	a	DET
ejpam-6436	88	20	,	,	PUNCT
ejpam-6436	88	21	s)×a×	s)×a×	NOUN
ejpam-6436	88	22	s	s	PART
ejpam-6436	88	23	−→	−→	NOUN
ejpam-6436	88	24	b	b	PROPN
ejpam-6436	88	25	by	by	ADP
ejpam-6436	88	26	α(f	α(f	PROPN
ejpam-6436	88	27	,	,	PUNCT
ejpam-6436	88	28	a	a	DET
ejpam-6436	88	29	,	,	PUNCT
ejpam-6436	88	30	b	b	NOUN
ejpam-6436	88	31	)	)	PUNCT
ejpam-6436	88	32	=	=	SYM
ejpam-6436	88	33	f(a)b	f(a)b	PROPN
ejpam-6436	88	34	for	for	ADP
ejpam-6436	88	35	all	all	DET
ejpam-6436	88	36	a	a	DET
ejpam-6436	88	37	∈	∈	PROPN
ejpam-6436	89	1	a	a	DET
ejpam-6436	89	2	,	,	PUNCT
ejpam-6436	89	3	b	b	PROPN
ejpam-6436	89	4	∈	∈	PROPN
ejpam-6436	89	5	b	b	NOUN
ejpam-6436	89	6	,	,	PUNCT
ejpam-6436	89	7	in	in	ADP
ejpam-6436	89	8	proposition	proposition	NOUN
ejpam-6436	89	9	1	1	NUM
ejpam-6436	89	10	we	we	PRON
ejpam-6436	89	11	get	get	AUX
ejpam-6436	89	12	theorem	theorem	ADJ
ejpam-6436	89	13	1	1	X
ejpam-6436	89	14	.	.	PUNCT
ejpam-6436	90	1	however	however	ADV
ejpam-6436	90	2	for	for	ADP
ejpam-6436	90	3	the	the	DET
ejpam-6436	90	4	sake	sake	NOUN
ejpam-6436	90	5	of	of	ADP
ejpam-6436	90	6	clarity	clarity	NOUN
ejpam-6436	90	7	we	we	PRON
ejpam-6436	90	8	have	have	AUX
ejpam-6436	90	9	given	give	VERB
ejpam-6436	90	10	its	its	PRON
ejpam-6436	90	11	proof	proof	NOUN
ejpam-6436	90	12	.	.	PUNCT
ejpam-6436	91	1	theorem	theorem	NOUN
ejpam-6436	91	2	1	1	NUM
ejpam-6436	91	3	.	.	PUNCT
ejpam-6436	92	1	the	the	DET
ejpam-6436	92	2	element	element	NOUN
ejpam-6436	92	3	(	(	PUNCT
ejpam-6436	92	4	r	r	NOUN
ejpam-6436	92	5	,	,	PUNCT
ejpam-6436	92	6	f	f	X
ejpam-6436	92	7	)	)	PUNCT
ejpam-6436	92	8	∈	∈	PROPN
ejpam-6436	92	9	t	t	PROPN
ejpam-6436	92	10	acts	act	VERB
ejpam-6436	92	11	po	po	NOUN
ejpam-6436	92	12	-	-	PUNCT
ejpam-6436	92	13	injectively	injectively	ADV
ejpam-6436	92	14	on	on	ADP
ejpam-6436	92	15	tc	tc	PRON
ejpam-6436	92	16	if	if	SCONJ
ejpam-6436	92	17	and	and	CCONJ
ejpam-6436	92	18	only	only	ADV
ejpam-6436	92	19	if	if	SCONJ
ejpam-6436	92	20	:	:	PUNCT
ejpam-6436	92	21	1	1	X
ejpam-6436	92	22	)	)	PUNCT
ejpam-6436	92	23	if	if	SCONJ
ejpam-6436	92	24	a	a	DET
ejpam-6436	92	25	≤	≤	NOUN
ejpam-6436	92	26	a′	a′	NOUN
ejpam-6436	92	27	and	and	CCONJ
ejpam-6436	92	28	f(a)b	f(a)b	PROPN
ejpam-6436	92	29	≤	≤	X
ejpam-6436	92	30	f(a′)b′	f(a′)b′	INTJ
ejpam-6436	92	31	where	where	SCONJ
ejpam-6436	92	32	a	a	X
ejpam-6436	92	33	,	,	PUNCT
ejpam-6436	92	34	a′	a′	PROPN
ejpam-6436	92	35	∈	∈	PROPN
ejpam-6436	92	36	a	a	PRON
ejpam-6436	92	37	and	and	CCONJ
ejpam-6436	92	38	b	b	NOUN
ejpam-6436	92	39	,	,	PUNCT
ejpam-6436	92	40	b′	b′	NUM
ejpam-6436	92	41	∈	∈	PROPN
ejpam-6436	92	42	b	b	NOUN
ejpam-6436	92	43	,	,	PUNCT
ejpam-6436	92	44	then	then	ADV
ejpam-6436	92	45	b	b	X
ejpam-6436	92	46	≤	≤	X
ejpam-6436	92	47	b′	b′	NUM
ejpam-6436	92	48	,	,	PUNCT
ejpam-6436	92	49	and	and	CCONJ
ejpam-6436	92	50	2	2	X
ejpam-6436	92	51	)	)	PUNCT
ejpam-6436	92	52	if	if	SCONJ
ejpam-6436	92	53	ra	ra	NOUN
ejpam-6436	92	54	≤	≤	NOUN
ejpam-6436	92	55	ra′	ra′	NOUN
ejpam-6436	92	56	and	and	CCONJ
ejpam-6436	92	57	a	a	DET
ejpam-6436	92	58	≰	≰	PROPN
ejpam-6436	92	59	a′	a′	NOUN
ejpam-6436	92	60	where	where	SCONJ
ejpam-6436	92	61	a	a	PRON
ejpam-6436	92	62	,	,	PUNCT
ejpam-6436	92	63	a′	a′	PROPN
ejpam-6436	92	64	∈	∈	PROPN
ejpam-6436	92	65	a	a	PRON
ejpam-6436	92	66	,	,	PUNCT
ejpam-6436	92	67	then	then	ADV
ejpam-6436	92	68	f(a)b	f(a)b	PROPN
ejpam-6436	92	69	≰	≰	VERB
ejpam-6436	92	70	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	92	71	for	for	ADP
ejpam-6436	92	72	all	all	DET
ejpam-6436	92	73	b	b	NOUN
ejpam-6436	92	74	,	,	PUNCT
ejpam-6436	92	75	b′	b′	NUM
ejpam-6436	92	76	∈	∈	PROPN
ejpam-6436	92	77	b.	b.	NOUN
ejpam-6436	92	78	proof	proof	NOUN
ejpam-6436	92	79	.	.	PUNCT
ejpam-6436	93	1	let	let	AUX
ejpam-6436	93	2	(	(	PUNCT
ejpam-6436	93	3	r	r	NOUN
ejpam-6436	93	4	,	,	PUNCT
ejpam-6436	93	5	f	f	X
ejpam-6436	93	6	)	)	PUNCT
ejpam-6436	93	7	∈	∈	PROPN
ejpam-6436	93	8	t	t	PROPN
ejpam-6436	93	9	acts	act	VERB
ejpam-6436	93	10	po	po	NOUN
ejpam-6436	93	11	-	-	PUNCT
ejpam-6436	93	12	injectively	injectively	ADV
ejpam-6436	93	13	on	on	ADP
ejpam-6436	93	14	tc	tc	NUM
ejpam-6436	93	15	.	.	NOUN
ejpam-6436	93	16	1	1	NUM
ejpam-6436	93	17	)	)	PUNCT
ejpam-6436	93	18	first	first	ADV
ejpam-6436	93	19	suppose	suppose	VERB
ejpam-6436	93	20	that	that	SCONJ
ejpam-6436	93	21	a	a	DET
ejpam-6436	93	22	≤	≤	NOUN
ejpam-6436	93	23	a′	a′	NOUN
ejpam-6436	93	24	in	in	ADP
ejpam-6436	93	25	a	a	DET
ejpam-6436	93	26	and	and	CCONJ
ejpam-6436	93	27	f(a)b	f(a)b	PROPN
ejpam-6436	93	28	≤	≤	NUM
ejpam-6436	93	29	f(a′)b	f(a′)b	NOUN
ejpam-6436	93	30	where	where	SCONJ
ejpam-6436	93	31	a	a	X
ejpam-6436	93	32	,	,	PUNCT
ejpam-6436	93	33	a′	a′	PROPN
ejpam-6436	93	34	∈	∈	PROPN
ejpam-6436	93	35	a	a	DET
ejpam-6436	93	36	and	and	CCONJ
ejpam-6436	93	37	b	b	NOUN
ejpam-6436	93	38	,	,	PUNCT
ejpam-6436	93	39	b′	b′	NUM
ejpam-6436	93	40	∈	∈	PROPN
ejpam-6436	93	41	b.	b.	NOUN
ejpam-6436	93	42	then	then	ADV
ejpam-6436	93	43	,	,	PUNCT
ejpam-6436	93	44	(	(	PUNCT
ejpam-6436	93	45	r	r	NOUN
ejpam-6436	93	46	,	,	PUNCT
ejpam-6436	93	47	f)(a	f)(a	NUM
ejpam-6436	93	48	,	,	PUNCT
ejpam-6436	93	49	b	b	NOUN
ejpam-6436	93	50	)	)	PUNCT
ejpam-6436	93	51	=	=	SYM
ejpam-6436	93	52	(	(	PUNCT
ejpam-6436	93	53	ra	ra	PROPN
ejpam-6436	93	54	,	,	PUNCT
ejpam-6436	93	55	f(a)b	f(a)b	PROPN
ejpam-6436	93	56	)	)	PUNCT
ejpam-6436	93	57	≤	≤	NOUN
ejpam-6436	93	58	(	(	PUNCT
ejpam-6436	93	59	ra′	ra′	PROPN
ejpam-6436	93	60	,	,	PUNCT
ejpam-6436	93	61	f(a′)b′	f(a′)b′	X
ejpam-6436	93	62	)	)	PUNCT
ejpam-6436	93	63	=	=	SYM
ejpam-6436	93	64	(	(	PUNCT
ejpam-6436	93	65	r	r	NOUN
ejpam-6436	93	66	,	,	PUNCT
ejpam-6436	93	67	f)(a′	f)(a′	PROPN
ejpam-6436	93	68	,	,	PUNCT
ejpam-6436	93	69	b′	b′	NUM
ejpam-6436	93	70	)	)	PUNCT
ejpam-6436	93	71	.	.	PUNCT
ejpam-6436	94	1	since	since	SCONJ
ejpam-6436	94	2	(	(	PUNCT
ejpam-6436	94	3	r	r	NOUN
ejpam-6436	94	4	,	,	PUNCT
ejpam-6436	94	5	f	f	X
ejpam-6436	94	6	)	)	PUNCT
ejpam-6436	94	7	acts	act	VERB
ejpam-6436	94	8	po	po	NOUN
ejpam-6436	94	9	-	-	PUNCT
ejpam-6436	94	10	injectively	injectively	ADV
ejpam-6436	94	11	on	on	ADP
ejpam-6436	94	12	tc	tc	NOUN
ejpam-6436	94	13	=	=	NOUN
ejpam-6436	94	14	r	r	NOUN
ejpam-6436	94	15	a	a	DET
ejpam-6436	94	16	×s	×s	NOUN
ejpam-6436	94	17	b	b	NOUN
ejpam-6436	94	18	,	,	PUNCT
ejpam-6436	94	19	we	we	PRON
ejpam-6436	94	20	must	must	AUX
ejpam-6436	94	21	have	have	VERB
ejpam-6436	94	22	(	(	PUNCT
ejpam-6436	94	23	a	a	PRON
ejpam-6436	94	24	,	,	PUNCT
ejpam-6436	94	25	b	b	NOUN
ejpam-6436	94	26	)	)	PUNCT
ejpam-6436	94	27	≤	≤	NOUN
ejpam-6436	94	28	(	(	PUNCT
ejpam-6436	94	29	a′	a′	PROPN
ejpam-6436	94	30	,	,	PUNCT
ejpam-6436	94	31	b′	b′	NUM
ejpam-6436	94	32	)	)	PUNCT
ejpam-6436	94	33	and	and	CCONJ
ejpam-6436	95	1	so	so	ADV
ejpam-6436	95	2	b	b	PROPN
ejpam-6436	95	3	≤	≤	NUM
ejpam-6436	95	4	b′	b′	NUM
ejpam-6436	95	5	,	,	PUNCT
ejpam-6436	95	6	as	as	SCONJ
ejpam-6436	95	7	required	require	VERB
ejpam-6436	95	8	.	.	PUNCT
ejpam-6436	96	1	2	2	X
ejpam-6436	96	2	)	)	PUNCT
ejpam-6436	96	3	now	now	ADV
ejpam-6436	96	4	suppose	suppose	VERB
ejpam-6436	96	5	that	that	SCONJ
ejpam-6436	96	6	ra	ra	PROPN
ejpam-6436	96	7	≤	≤	ADJ
ejpam-6436	96	8	ra′	ra′	NOUN
ejpam-6436	96	9	and	and	CCONJ
ejpam-6436	96	10	a	a	DET
ejpam-6436	96	11	≰	≰	PROPN
ejpam-6436	96	12	a′	a′	PROPN
ejpam-6436	96	13	,	,	PUNCT
ejpam-6436	96	14	where	where	SCONJ
ejpam-6436	96	15	r	r	NOUN
ejpam-6436	96	16	∈	∈	NOUN
ejpam-6436	96	17	r	r	NOUN
ejpam-6436	96	18	and	and	CCONJ
ejpam-6436	96	19	a	a	PRON
ejpam-6436	96	20	,	,	PUNCT
ejpam-6436	96	21	a′	a′	PROPN
ejpam-6436	96	22	∈	∈	PROPN
ejpam-6436	96	23	a.	a.	NOUN
ejpam-6436	96	24	also	also	ADV
ejpam-6436	96	25	let	let	VERB
ejpam-6436	96	26	f(a)b	f(a)b	PROPN
ejpam-6436	96	27	≤	≤	VERB
ejpam-6436	96	28	f(a′)b′	f(a′)b′	NOUN
ejpam-6436	96	29	for	for	ADP
ejpam-6436	96	30	some	some	DET
ejpam-6436	96	31	b	b	NOUN
ejpam-6436	96	32	,	,	PUNCT
ejpam-6436	96	33	b′	b′	NUM
ejpam-6436	96	34	∈	∈	PROPN
ejpam-6436	96	35	b.	b.	NOUN
ejpam-6436	96	36	then	then	ADV
ejpam-6436	96	37	,	,	PUNCT
ejpam-6436	96	38	b.	b.	PROPN
ejpam-6436	96	39	al	al	PROPN
ejpam-6436	96	40	subaiei	subaiei	PROPN
ejpam-6436	96	41	et	et	PROPN
ejpam-6436	96	42	al	al	PROPN
ejpam-6436	96	43	.	.	PUNCT
ejpam-6436	96	44	/	/	SYM
ejpam-6436	96	45	eur	eur	PROPN
ejpam-6436	96	46	.	.	PUNCT
ejpam-6436	97	1	j.	j.	PROPN
ejpam-6436	97	2	pure	pure	PROPN
ejpam-6436	97	3	appl	appl	PROPN
ejpam-6436	97	4	.	.	PROPN
ejpam-6436	97	5	math	math	PROPN
ejpam-6436	97	6	,	,	PUNCT
ejpam-6436	97	7	18	18	NUM
ejpam-6436	97	8	(	(	PUNCT
ejpam-6436	97	9	3	3	NUM
ejpam-6436	97	10	)	)	PUNCT
ejpam-6436	97	11	(	(	PUNCT
ejpam-6436	97	12	2025	2025	NUM
ejpam-6436	97	13	)	)	PUNCT
ejpam-6436	97	14	,	,	PUNCT
ejpam-6436	97	15	6436	6436	NUM
ejpam-6436	97	16	5	5	NUM
ejpam-6436	97	17	of	of	ADP
ejpam-6436	97	18	14	14	NUM
ejpam-6436	97	19	(	(	PUNCT
ejpam-6436	97	20	r	r	NOUN
ejpam-6436	97	21	,	,	PUNCT
ejpam-6436	97	22	f)(a	f)(a	NUM
ejpam-6436	97	23	,	,	PUNCT
ejpam-6436	97	24	b	b	NOUN
ejpam-6436	97	25	)	)	PUNCT
ejpam-6436	97	26	=	=	SYM
ejpam-6436	97	27	(	(	PUNCT
ejpam-6436	97	28	ra	ra	PROPN
ejpam-6436	97	29	,	,	PUNCT
ejpam-6436	97	30	f(a)b	f(a)b	PROPN
ejpam-6436	97	31	)	)	PUNCT
ejpam-6436	97	32	≤	≤	NOUN
ejpam-6436	97	33	(	(	PUNCT
ejpam-6436	97	34	ra′	ra′	PROPN
ejpam-6436	97	35	,	,	PUNCT
ejpam-6436	97	36	f(a′)b′	f(a′)b′	X
ejpam-6436	97	37	)	)	PUNCT
ejpam-6436	97	38	=	=	SYM
ejpam-6436	98	1	(	(	PUNCT
ejpam-6436	98	2	r	r	NOUN
ejpam-6436	98	3	,	,	PUNCT
ejpam-6436	98	4	f)(a′	f)(a′	PROPN
ejpam-6436	98	5	,	,	PUNCT
ejpam-6436	98	6	b′	b′	NUM
ejpam-6436	98	7	)	)	PUNCT
ejpam-6436	98	8	.	.	PUNCT
ejpam-6436	99	1	since	since	SCONJ
ejpam-6436	99	2	(	(	PUNCT
ejpam-6436	99	3	r	r	NOUN
ejpam-6436	99	4	,	,	PUNCT
ejpam-6436	99	5	f	f	X
ejpam-6436	99	6	)	)	PUNCT
ejpam-6436	99	7	acts	act	VERB
ejpam-6436	99	8	po	po	NOUN
ejpam-6436	99	9	-	-	PUNCT
ejpam-6436	99	10	injectively	injectively	ADV
ejpam-6436	99	11	on	on	ADP
ejpam-6436	99	12	tc	tc	NOUN
ejpam-6436	99	13	we	we	PRON
ejpam-6436	99	14	must	must	AUX
ejpam-6436	99	15	have	have	VERB
ejpam-6436	99	16	(	(	PUNCT
ejpam-6436	99	17	a	a	DET
ejpam-6436	99	18	,	,	PUNCT
ejpam-6436	99	19	b	b	NOUN
ejpam-6436	99	20	)	)	PUNCT
ejpam-6436	99	21	≤	≤	NOUN
ejpam-6436	99	22	(	(	PUNCT
ejpam-6436	99	23	a′	a′	PROPN
ejpam-6436	99	24	,	,	PUNCT
ejpam-6436	99	25	b′	b′	NUM
ejpam-6436	99	26	)	)	PUNCT
ejpam-6436	99	27	.	.	PUNCT
ejpam-6436	100	1	thus	thus	ADV
ejpam-6436	100	2	,	,	PUNCT
ejpam-6436	100	3	a	a	DET
ejpam-6436	100	4	≤	≤	NOUN
ejpam-6436	100	5	a′	a′	NOUN
ejpam-6436	100	6	and	and	CCONJ
ejpam-6436	100	7	this	this	PRON
ejpam-6436	100	8	is	be	AUX
ejpam-6436	100	9	a	a	DET
ejpam-6436	100	10	contradiction	contradiction	NOUN
ejpam-6436	100	11	to	to	ADP
ejpam-6436	100	12	the	the	DET
ejpam-6436	100	13	assumption	assumption	NOUN
ejpam-6436	100	14	in	in	ADP
ejpam-6436	100	15	(	(	PUNCT
ejpam-6436	100	16	2	2	NUM
ejpam-6436	100	17	)	)	PUNCT
ejpam-6436	100	18	.	.	PUNCT
ejpam-6436	101	1	therefore	therefore	ADV
ejpam-6436	101	2	,	,	PUNCT
ejpam-6436	101	3	f(a)b	f(a)b	PROPN
ejpam-6436	101	4	≰	≰	VERB
ejpam-6436	101	5	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	101	6	for	for	ADP
ejpam-6436	101	7	all	all	DET
ejpam-6436	101	8	b	b	NOUN
ejpam-6436	101	9	,	,	PUNCT
ejpam-6436	101	10	b′	b′	NUM
ejpam-6436	101	11	∈	∈	PROPN
ejpam-6436	101	12	b.	b.	NOUN
ejpam-6436	101	13	for	for	ADP
ejpam-6436	101	14	the	the	DET
ejpam-6436	101	15	other	other	ADJ
ejpam-6436	101	16	direction	direction	NOUN
ejpam-6436	101	17	,	,	PUNCT
ejpam-6436	101	18	assume	assume	VERB
ejpam-6436	101	19	the	the	DET
ejpam-6436	101	20	given	give	VERB
ejpam-6436	101	21	conditions	condition	NOUN
ejpam-6436	101	22	(	(	PUNCT
ejpam-6436	101	23	1	1	NUM
ejpam-6436	101	24	)	)	PUNCT
ejpam-6436	101	25	and	and	CCONJ
ejpam-6436	101	26	(	(	PUNCT
ejpam-6436	101	27	2	2	X
ejpam-6436	101	28	)	)	PUNCT
ejpam-6436	101	29	are	be	AUX
ejpam-6436	101	30	satisfied	satisfied	ADJ
ejpam-6436	101	31	.	.	PUNCT
ejpam-6436	102	1	let	let	VERB
ejpam-6436	102	2	(	(	PUNCT
ejpam-6436	102	3	r	r	NOUN
ejpam-6436	102	4	,	,	PUNCT
ejpam-6436	102	5	f	f	X
ejpam-6436	102	6	)	)	PUNCT
ejpam-6436	102	7	∈	∈	PROPN
ejpam-6436	102	8	t	t	NOUN
ejpam-6436	102	9	and	and	CCONJ
ejpam-6436	102	10	suppose	suppose	VERB
ejpam-6436	102	11	that	that	SCONJ
ejpam-6436	102	12	(	(	PUNCT
ejpam-6436	102	13	r	r	NOUN
ejpam-6436	102	14	,	,	PUNCT
ejpam-6436	102	15	f)(a	f)(a	NUM
ejpam-6436	102	16	,	,	PUNCT
ejpam-6436	102	17	b	b	NOUN
ejpam-6436	102	18	)	)	PUNCT
ejpam-6436	102	19	≤	≤	NOUN
ejpam-6436	102	20	(	(	PUNCT
ejpam-6436	102	21	r	r	NOUN
ejpam-6436	102	22	,	,	PUNCT
ejpam-6436	102	23	f)(a′	f)(a′	PROPN
ejpam-6436	102	24	,	,	PUNCT
ejpam-6436	102	25	b′	b′	NUM
ejpam-6436	102	26	)	)	PUNCT
ejpam-6436	102	27	.	.	PUNCT
ejpam-6436	103	1	so	so	ADV
ejpam-6436	103	2	(	(	PUNCT
ejpam-6436	103	3	ra	ra	PROPN
ejpam-6436	103	4	,	,	PUNCT
ejpam-6436	103	5	f(a)b	f(a)b	PROPN
ejpam-6436	103	6	)	)	PUNCT
ejpam-6436	103	7	≤	≤	NOUN
ejpam-6436	103	8	(	(	PUNCT
ejpam-6436	103	9	ra′	ra′	PROPN
ejpam-6436	103	10	,	,	PUNCT
ejpam-6436	103	11	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	103	12	)	)	PUNCT
ejpam-6436	103	13	which	which	PRON
ejpam-6436	103	14	forces	force	VERB
ejpam-6436	103	15	ra	ra	NOUN
ejpam-6436	103	16	≤	≤	ADJ
ejpam-6436	103	17	ra′	ra′	NOUN
ejpam-6436	103	18	and	and	CCONJ
ejpam-6436	103	19	f(a)b	f(a)b	PROPN
ejpam-6436	103	20	≤	≤	NUM
ejpam-6436	103	21	f(a′)b′.	f(a′)b′.	NOUN
ejpam-6436	103	22	from	from	ADP
ejpam-6436	103	23	condition	condition	NOUN
ejpam-6436	103	24	(	(	PUNCT
ejpam-6436	103	25	2	2	X
ejpam-6436	103	26	)	)	PUNCT
ejpam-6436	103	27	we	we	PRON
ejpam-6436	103	28	have	have	VERB
ejpam-6436	103	29	a	a	DET
ejpam-6436	103	30	≤	≤	NOUN
ejpam-6436	103	31	a′	a′	NOUN
ejpam-6436	103	32	and	and	CCONJ
ejpam-6436	103	33	this	this	PRON
ejpam-6436	103	34	together	together	ADV
ejpam-6436	103	35	with	with	ADP
ejpam-6436	103	36	condition	condition	NOUN
ejpam-6436	103	37	(	(	PUNCT
ejpam-6436	103	38	1	1	X
ejpam-6436	103	39	)	)	PUNCT
ejpam-6436	103	40	gives	give	VERB
ejpam-6436	103	41	b	b	PROPN
ejpam-6436	103	42	≤	≤	X
ejpam-6436	103	43	b′.	b′.	X
ejpam-6436	103	44	therefore	therefore	ADV
ejpam-6436	103	45	(	(	PUNCT
ejpam-6436	103	46	a	a	PRON
ejpam-6436	103	47	,	,	PUNCT
ejpam-6436	103	48	b	b	NOUN
ejpam-6436	103	49	)	)	PUNCT
ejpam-6436	103	50	≤	≤	NOUN
ejpam-6436	103	51	(	(	PUNCT
ejpam-6436	103	52	a′	a′	PROPN
ejpam-6436	103	53	,	,	PUNCT
ejpam-6436	103	54	b′	b′	NUM
ejpam-6436	103	55	)	)	PUNCT
ejpam-6436	103	56	.	.	PUNCT
ejpam-6436	104	1	then	then	ADV
ejpam-6436	104	2	,	,	PUNCT
ejpam-6436	104	3	(	(	PUNCT
ejpam-6436	104	4	r	r	NOUN
ejpam-6436	104	5	,	,	PUNCT
ejpam-6436	104	6	f	f	X
ejpam-6436	104	7	)	)	PUNCT
ejpam-6436	104	8	acts	act	VERB
ejpam-6436	104	9	po	po	NOUN
ejpam-6436	104	10	-	-	PUNCT
ejpam-6436	104	11	injectively	injectively	ADV
ejpam-6436	104	12	on	on	ADP
ejpam-6436	104	13	tc	tc	ADP
ejpam-6436	104	14	,	,	PUNCT
ejpam-6436	104	15	as	as	SCONJ
ejpam-6436	104	16	required	require	VERB
ejpam-6436	104	17	.	.	PUNCT
ejpam-6436	105	1	in	in	ADP
ejpam-6436	105	2	the	the	DET
ejpam-6436	105	3	unordered	unordered	ADJ
ejpam-6436	105	4	case	case	NOUN
ejpam-6436	105	5	,	,	PUNCT
ejpam-6436	105	6	it	it	PRON
ejpam-6436	105	7	has	have	AUX
ejpam-6436	105	8	been	be	AUX
ejpam-6436	105	9	shown	show	VERB
ejpam-6436	105	10	in	in	ADP
ejpam-6436	105	11	[	[	X
ejpam-6436	105	12	15	15	NUM
ejpam-6436	105	13	]	]	PUNCT
ejpam-6436	105	14	that	that	SCONJ
ejpam-6436	105	15	the	the	DET
ejpam-6436	105	16	analogue	analogue	NOUN
ejpam-6436	105	17	of	of	ADP
ejpam-6436	105	18	condition	condition	NOUN
ejpam-6436	105	19	(	(	PUNCT
ejpam-6436	105	20	1	1	NUM
ejpam-6436	105	21	)	)	PUNCT
ejpam-6436	105	22	in	in	ADP
ejpam-6436	105	23	theorem	theorem	NOUN
ejpam-6436	105	24	1	1	NUM
ejpam-6436	105	25	above	above	ADV
ejpam-6436	105	26	is	be	AUX
ejpam-6436	105	27	that	that	DET
ejpam-6436	105	28	f(a	f(a	NOUN
ejpam-6436	105	29	)	)	PUNCT
ejpam-6436	105	30	acts	act	VERB
ejpam-6436	105	31	injectively	injectively	ADV
ejpam-6436	105	32	on	on	ADP
ejpam-6436	105	33	b.	b.	PROPN
ejpam-6436	105	34	however	however	ADV
ejpam-6436	105	35	,	,	PUNCT
ejpam-6436	105	36	in	in	ADP
ejpam-6436	105	37	ordered	order	VERB
ejpam-6436	105	38	case	case	NOUN
ejpam-6436	105	39	condition	condition	NOUN
ejpam-6436	105	40	(	(	PUNCT
ejpam-6436	105	41	1	1	X
ejpam-6436	105	42	)	)	PUNCT
ejpam-6436	105	43	does	do	AUX
ejpam-6436	105	44	not	not	PART
ejpam-6436	105	45	imply	imply	VERB
ejpam-6436	105	46	that	that	DET
ejpam-6436	105	47	f(a	f(a	NOUN
ejpam-6436	105	48	)	)	PUNCT
ejpam-6436	105	49	acts	act	VERB
ejpam-6436	105	50	po	po	NOUN
ejpam-6436	105	51	-	-	PUNCT
ejpam-6436	105	52	injectively	injectively	ADV
ejpam-6436	105	53	on	on	ADP
ejpam-6436	105	54	b	b	NOUN
ejpam-6436	105	55	and	and	CCONJ
ejpam-6436	105	56	conversely	conversely	ADV
ejpam-6436	105	57	it	it	PRON
ejpam-6436	105	58	is	be	AUX
ejpam-6436	105	59	not	not	PART
ejpam-6436	105	60	enough	enough	ADJ
ejpam-6436	105	61	to	to	PART
ejpam-6436	105	62	have	have	VERB
ejpam-6436	105	63	f(a	f(a	NOUN
ejpam-6436	105	64	)	)	PUNCT
ejpam-6436	105	65	acting	act	VERB
ejpam-6436	105	66	po	po	NOUN
ejpam-6436	105	67	-	-	PUNCT
ejpam-6436	105	68	injectively	injectively	ADV
ejpam-6436	105	69	or	or	CCONJ
ejpam-6436	105	70	even	even	ADV
ejpam-6436	105	71	strongly	strongly	ADV
ejpam-6436	105	72	po	po	NOUN
ejpam-6436	105	73	-	-	PUNCT
ejpam-6436	105	74	injectively	injectively	ADV
ejpam-6436	105	75	on	on	ADP
ejpam-6436	105	76	b	b	NOUN
ejpam-6436	105	77	to	to	PART
ejpam-6436	105	78	deduce	deduce	VERB
ejpam-6436	105	79	condition	condition	NOUN
ejpam-6436	105	80	(	(	PUNCT
ejpam-6436	105	81	1	1	NUM
ejpam-6436	105	82	)	)	PUNCT
ejpam-6436	105	83	.	.	PUNCT
ejpam-6436	106	1	therefore	therefore	ADV
ejpam-6436	106	2	it	it	PRON
ejpam-6436	106	3	will	will	AUX
ejpam-6436	106	4	be	be	AUX
ejpam-6436	106	5	interesting	interesting	ADJ
ejpam-6436	106	6	to	to	PART
ejpam-6436	106	7	find	find	VERB
ejpam-6436	106	8	that	that	SCONJ
ejpam-6436	106	9	under	under	ADP
ejpam-6436	106	10	what	what	DET
ejpam-6436	106	11	conditions	condition	NOUN
ejpam-6436	106	12	the	the	DET
ejpam-6436	106	13	result	result	NOUN
ejpam-6436	106	14	in	in	ADP
ejpam-6436	106	15	ordered	order	VERB
ejpam-6436	106	16	case	case	NOUN
ejpam-6436	106	17	is	be	AUX
ejpam-6436	106	18	similar	similar	ADJ
ejpam-6436	106	19	to	to	ADP
ejpam-6436	106	20	that	that	PRON
ejpam-6436	106	21	of	of	ADP
ejpam-6436	106	22	unordered	unordered	ADJ
ejpam-6436	106	23	case	case	NOUN
ejpam-6436	106	24	.	.	PUNCT
ejpam-6436	107	1	however	however	ADV
ejpam-6436	107	2	we	we	PRON
ejpam-6436	107	3	do	do	AUX
ejpam-6436	107	4	have	have	VERB
ejpam-6436	107	5	the	the	DET
ejpam-6436	107	6	following	following	NOUN
ejpam-6436	107	7	.	.	PUNCT
ejpam-6436	108	1	corollary	corollary	ADJ
ejpam-6436	108	2	1	1	NUM
ejpam-6436	108	3	.	.	PUNCT
ejpam-6436	109	1	if	if	SCONJ
ejpam-6436	109	2	(	(	PUNCT
ejpam-6436	109	3	r	r	NOUN
ejpam-6436	109	4	,	,	PUNCT
ejpam-6436	109	5	f	f	X
ejpam-6436	109	6	)	)	PUNCT
ejpam-6436	109	7	∈	∈	PROPN
ejpam-6436	109	8	t	t	PROPN
ejpam-6436	109	9	acts	act	VERB
ejpam-6436	109	10	po	po	NOUN
ejpam-6436	109	11	-	-	PUNCT
ejpam-6436	109	12	injectively	injectively	ADV
ejpam-6436	109	13	on	on	ADP
ejpam-6436	109	14	tc	tc	NUM
ejpam-6436	109	15	then	then	ADV
ejpam-6436	109	16	1	1	NUM
ejpam-6436	109	17	)	)	PUNCT
ejpam-6436	109	18	f(a	f(a	NOUN
ejpam-6436	109	19	)	)	PUNCT
ejpam-6436	109	20	acts	act	VERB
ejpam-6436	109	21	po	po	NOUN
ejpam-6436	109	22	-	-	PUNCT
ejpam-6436	109	23	injectively	injectively	ADV
ejpam-6436	109	24	on	on	ADP
ejpam-6436	109	25	b	b	NOUN
ejpam-6436	109	26	for	for	ADP
ejpam-6436	109	27	any	any	DET
ejpam-6436	109	28	a	a	DET
ejpam-6436	109	29	∈	∈	PROPN
ejpam-6436	109	30	a	a	PRON
ejpam-6436	109	31	,	,	PUNCT
ejpam-6436	109	32	and	and	CCONJ
ejpam-6436	109	33	2	2	X
ejpam-6436	109	34	)	)	PUNCT
ejpam-6436	109	35	if	if	SCONJ
ejpam-6436	109	36	ra	ra	NOUN
ejpam-6436	109	37	≤	≤	NOUN
ejpam-6436	109	38	ra′	ra′	NOUN
ejpam-6436	109	39	and	and	CCONJ
ejpam-6436	109	40	a	a	DET
ejpam-6436	109	41	≰	≰	PROPN
ejpam-6436	109	42	a′	a′	NOUN
ejpam-6436	109	43	,	,	PUNCT
ejpam-6436	109	44	then	then	ADV
ejpam-6436	109	45	for	for	ADP
ejpam-6436	109	46	any	any	DET
ejpam-6436	109	47	b	b	NOUN
ejpam-6436	109	48	,	,	PUNCT
ejpam-6436	109	49	b′	b′	NUM
ejpam-6436	109	50	∈	∈	PROPN
ejpam-6436	109	51	b	b	NOUN
ejpam-6436	109	52	,	,	PUNCT
ejpam-6436	109	53	f(a)b	f(a)b	PROPN
ejpam-6436	109	54	≰	≰	PROPN
ejpam-6436	109	55	f(a′)b′.	f(a′)b′.	VERB
ejpam-6436	109	56	the	the	DET
ejpam-6436	109	57	proof	proof	NOUN
ejpam-6436	109	58	of	of	ADP
ejpam-6436	109	59	the	the	DET
ejpam-6436	109	60	following	following	NOUN
ejpam-6436	109	61	is	be	AUX
ejpam-6436	109	62	similar	similar	ADJ
ejpam-6436	109	63	to	to	ADP
ejpam-6436	109	64	theorem	theorem	NOUN
ejpam-6436	109	65	1	1	NUM
ejpam-6436	109	66	,	,	PUNCT
ejpam-6436	109	67	however	however	ADV
ejpam-6436	109	68	we	we	PRON
ejpam-6436	109	69	add	add	VERB
ejpam-6436	109	70	the	the	DET
ejpam-6436	109	71	proof	proof	NOUN
ejpam-6436	109	72	for	for	ADP
ejpam-6436	109	73	completeness	completeness	NOUN
ejpam-6436	109	74	.	.	PUNCT
ejpam-6436	110	1	proposition	proposition	NOUN
ejpam-6436	110	2	2	2	NUM
ejpam-6436	110	3	.	.	PUNCT
ejpam-6436	111	1	the	the	DET
ejpam-6436	111	2	element	element	NOUN
ejpam-6436	111	3	(	(	PUNCT
ejpam-6436	111	4	r	r	NOUN
ejpam-6436	111	5	,	,	PUNCT
ejpam-6436	111	6	f	f	X
ejpam-6436	111	7	)	)	PUNCT
ejpam-6436	111	8	∈	∈	PROPN
ejpam-6436	111	9	t	t	PROPN
ejpam-6436	111	10	is	be	AUX
ejpam-6436	111	11	left	leave	VERB
ejpam-6436	111	12	po	po	NOUN
ejpam-6436	111	13	-	-	NOUN
ejpam-6436	111	14	cancellable	cancellable	ADJ
ejpam-6436	111	15	if	if	SCONJ
ejpam-6436	112	1	and	and	CCONJ
ejpam-6436	112	2	only	only	ADV
ejpam-6436	112	3	if	if	SCONJ
ejpam-6436	112	4	the	the	DET
ejpam-6436	112	5	following	follow	VERB
ejpam-6436	112	6	two	two	NUM
ejpam-6436	112	7	conditions	condition	NOUN
ejpam-6436	112	8	hold	hold	VERB
ejpam-6436	112	9	.	.	PUNCT
ejpam-6436	113	1	1	1	X
ejpam-6436	113	2	)	)	PUNCT
ejpam-6436	113	3	p	p	NOUN
ejpam-6436	113	4	≤	≤	ADJ
ejpam-6436	113	5	p′	p′	NOUN
ejpam-6436	113	6	and	and	CCONJ
ejpam-6436	113	7	fpg	fpg	PROPN
ejpam-6436	113	8	≤	≤	PROPN
ejpam-6436	113	9	fp′g	fp′g	NOUN
ejpam-6436	113	10	′	′	NUM
ejpam-6436	113	11	implies	imply	VERB
ejpam-6436	113	12	g	g	PROPN
ejpam-6436	113	13	≤	≤	ADJ
ejpam-6436	113	14	g′	g′	NOUN
ejpam-6436	113	15	,	,	PUNCT
ejpam-6436	113	16	where	where	SCONJ
ejpam-6436	113	17	p	p	X
ejpam-6436	113	18	,	,	PUNCT
ejpam-6436	113	19	p′	p′	NOUN
ejpam-6436	113	20	∈	∈	NOUN
ejpam-6436	113	21	r	r	NOUN
ejpam-6436	113	22	and	and	CCONJ
ejpam-6436	113	23	g	g	NOUN
ejpam-6436	113	24	,	,	PUNCT
ejpam-6436	113	25	g′	g′	NOUN
ejpam-6436	113	26	∈	∈	PROPN
ejpam-6436	113	27	f	f	X
ejpam-6436	113	28	(	(	PUNCT
ejpam-6436	113	29	a	a	PRON
ejpam-6436	113	30	,	,	PUNCT
ejpam-6436	113	31	s	s	NOUN
ejpam-6436	113	32	)	)	PUNCT
ejpam-6436	113	33	.	.	PUNCT
ejpam-6436	114	1	2	2	X
ejpam-6436	114	2	)	)	PUNCT
ejpam-6436	114	3	rp	rp	NOUN
ejpam-6436	114	4	≤	≤	PROPN
ejpam-6436	114	5	rp′	rp′	NOUN
ejpam-6436	114	6	and	and	CCONJ
ejpam-6436	114	7	p	p	PROPN
ejpam-6436	114	8	≰	≰	PROPN
ejpam-6436	114	9	p′	p′	NOUN
ejpam-6436	114	10	implies	imply	VERB
ejpam-6436	114	11	fpg	fpg	PROPN
ejpam-6436	114	12	≰	≰	PROPN
ejpam-6436	114	13	fp′g	fp′g	VERB
ejpam-6436	114	14	′	′	NOUN
ejpam-6436	114	15	for	for	ADP
ejpam-6436	114	16	any	any	DET
ejpam-6436	114	17	g	g	NOUN
ejpam-6436	114	18	,	,	PUNCT
ejpam-6436	114	19	g′	g′	NOUN
ejpam-6436	114	20	∈	∈	PROPN
ejpam-6436	114	21	f	f	X
ejpam-6436	114	22	(	(	PUNCT
ejpam-6436	114	23	a	a	PRON
ejpam-6436	114	24	,	,	PUNCT
ejpam-6436	114	25	s	s	NOUN
ejpam-6436	114	26	)	)	PUNCT
ejpam-6436	114	27	.	.	PUNCT
ejpam-6436	115	1	proof	proof	NOUN
ejpam-6436	115	2	.	.	PUNCT
ejpam-6436	116	1	let	let	VERB
ejpam-6436	116	2	(	(	PUNCT
ejpam-6436	116	3	r	r	NOUN
ejpam-6436	116	4	,	,	PUNCT
ejpam-6436	116	5	f	f	X
ejpam-6436	116	6	)	)	PUNCT
ejpam-6436	116	7	∈	∈	PROPN
ejpam-6436	116	8	t	t	PROPN
ejpam-6436	116	9	be	be	AUX
ejpam-6436	116	10	left	leave	VERB
ejpam-6436	116	11	po	po	NOUN
ejpam-6436	116	12	-	-	NOUN
ejpam-6436	116	13	cancellable	cancellable	ADJ
ejpam-6436	116	14	.	.	PUNCT
ejpam-6436	117	1	1	1	X
ejpam-6436	117	2	)	)	PUNCT
ejpam-6436	117	3	suppose	suppose	VERB
ejpam-6436	117	4	that	that	SCONJ
ejpam-6436	117	5	p	p	PROPN
ejpam-6436	117	6	≤	≤	ADJ
ejpam-6436	117	7	p′	p′	NOUN
ejpam-6436	117	8	in	in	ADP
ejpam-6436	117	9	r	r	NOUN
ejpam-6436	117	10	and	and	CCONJ
ejpam-6436	117	11	fpg	fpg	PROPN
ejpam-6436	117	12	≤	≤	PROPN
ejpam-6436	117	13	fp′g	fp′g	NOUN
ejpam-6436	117	14	′	′	PUNCT
ejpam-6436	117	15	where	where	SCONJ
ejpam-6436	117	16	g	g	NOUN
ejpam-6436	117	17	,	,	PUNCT
ejpam-6436	117	18	g′	g′	NOUN
ejpam-6436	117	19	∈	∈	PROPN
ejpam-6436	117	20	f	f	X
ejpam-6436	117	21	(	(	PUNCT
ejpam-6436	117	22	a	a	PRON
ejpam-6436	117	23	,	,	PUNCT
ejpam-6436	117	24	s	s	NOUN
ejpam-6436	117	25	)	)	PUNCT
ejpam-6436	117	26	.	.	PUNCT
ejpam-6436	118	1	therefore	therefore	ADV
ejpam-6436	118	2	,	,	PUNCT
ejpam-6436	118	3	(	(	PUNCT
ejpam-6436	118	4	r	r	NOUN
ejpam-6436	118	5	,	,	PUNCT
ejpam-6436	118	6	f)(p	f)(p	NOUN
ejpam-6436	118	7	,	,	PUNCT
ejpam-6436	118	8	g	g	NOUN
ejpam-6436	118	9	)	)	PUNCT
ejpam-6436	118	10	=	=	NOUN
ejpam-6436	118	11	(	(	PUNCT
ejpam-6436	118	12	rp	rp	NOUN
ejpam-6436	118	13	,	,	PUNCT
ejpam-6436	118	14	fpg	fpg	PROPN
ejpam-6436	118	15	)	)	PUNCT
ejpam-6436	118	16	≤	≤	NOUN
ejpam-6436	118	17	(	(	PUNCT
ejpam-6436	118	18	rp′	rp′	ADJ
ejpam-6436	118	19	,	,	PUNCT
ejpam-6436	118	20	fp′g	fp′g	NOUN
ejpam-6436	118	21	′	′	NOUN
ejpam-6436	118	22	)	)	PUNCT
ejpam-6436	118	23	=	=	PUNCT
ejpam-6436	118	24	(	(	PUNCT
ejpam-6436	118	25	r	r	NOUN
ejpam-6436	118	26	,	,	PUNCT
ejpam-6436	118	27	f)(p′	f)(p′	PROPN
ejpam-6436	118	28	,	,	PUNCT
ejpam-6436	118	29	g′	g′	NOUN
ejpam-6436	118	30	)	)	PUNCT
ejpam-6436	118	31	.	.	PUNCT
ejpam-6436	119	1	since	since	SCONJ
ejpam-6436	119	2	(	(	PUNCT
ejpam-6436	119	3	r	r	NOUN
ejpam-6436	119	4	,	,	PUNCT
ejpam-6436	119	5	f	f	X
ejpam-6436	119	6	)	)	PUNCT
ejpam-6436	119	7	is	be	AUX
ejpam-6436	119	8	left	leave	VERB
ejpam-6436	119	9	po	po	NOUN
ejpam-6436	119	10	-	-	NOUN
ejpam-6436	119	11	cancellable	cancellable	ADJ
ejpam-6436	119	12	,	,	PUNCT
ejpam-6436	119	13	we	we	PRON
ejpam-6436	119	14	must	must	AUX
ejpam-6436	119	15	have	have	VERB
ejpam-6436	119	16	(	(	PUNCT
ejpam-6436	119	17	p	p	X
ejpam-6436	119	18	,	,	PUNCT
ejpam-6436	119	19	g	g	NOUN
ejpam-6436	119	20	)	)	PUNCT
ejpam-6436	119	21	≤	≤	NOUN
ejpam-6436	119	22	(	(	PUNCT
ejpam-6436	119	23	p′	p′	NOUN
ejpam-6436	119	24	,	,	PUNCT
ejpam-6436	119	25	g′	g′	NOUN
ejpam-6436	119	26	)	)	PUNCT
ejpam-6436	119	27	.	.	PUNCT
ejpam-6436	120	1	thus	thus	ADV
ejpam-6436	120	2	g	g	X
ejpam-6436	120	3	≤	≤	NUM
ejpam-6436	120	4	g′	g′	NOUN
ejpam-6436	120	5	as	as	SCONJ
ejpam-6436	120	6	required	require	VERB
ejpam-6436	120	7	.	.	PUNCT
ejpam-6436	121	1	2	2	X
ejpam-6436	121	2	)	)	PUNCT
ejpam-6436	121	3	now	now	ADV
ejpam-6436	121	4	assume	assume	VERB
ejpam-6436	121	5	that	that	SCONJ
ejpam-6436	121	6	r	r	NOUN
ejpam-6436	121	7	,	,	PUNCT
ejpam-6436	121	8	p	p	NOUN
ejpam-6436	121	9	,	,	PUNCT
ejpam-6436	121	10	p′	p′	NOUN
ejpam-6436	121	11	∈	∈	PROPN
ejpam-6436	121	12	r	r	NOUN
ejpam-6436	121	13	,	,	PUNCT
ejpam-6436	121	14	rp	rp	NOUN
ejpam-6436	121	15	≤	≤	NUM
ejpam-6436	121	16	rp′	rp′	NOUN
ejpam-6436	121	17	and	and	CCONJ
ejpam-6436	121	18	p	p	PROPN
ejpam-6436	121	19	≰	≰	PROPN
ejpam-6436	121	20	p′.	p′.	NOUN
ejpam-6436	121	21	also	also	ADV
ejpam-6436	121	22	suppose	suppose	VERB
ejpam-6436	121	23	that	that	SCONJ
ejpam-6436	121	24	fpg	fpg	PROPN
ejpam-6436	121	25	≤	≤	PROPN
ejpam-6436	121	26	fp′g	fp′g	NOUN
ejpam-6436	121	27	′	′	NUM
ejpam-6436	121	28	for	for	ADP
ejpam-6436	121	29	some	some	DET
ejpam-6436	121	30	g	g	NOUN
ejpam-6436	121	31	,	,	PUNCT
ejpam-6436	121	32	g′	g′	NOUN
ejpam-6436	121	33	∈	∈	PROPN
ejpam-6436	121	34	f	f	X
ejpam-6436	121	35	(	(	PUNCT
ejpam-6436	121	36	a	a	PRON
ejpam-6436	121	37	,	,	PUNCT
ejpam-6436	121	38	s	s	NOUN
ejpam-6436	121	39	)	)	PUNCT
ejpam-6436	121	40	.	.	PUNCT
ejpam-6436	122	1	therefore	therefore	ADV
ejpam-6436	122	2	,	,	PUNCT
ejpam-6436	122	3	(	(	PUNCT
ejpam-6436	122	4	r	r	NOUN
ejpam-6436	122	5	,	,	PUNCT
ejpam-6436	122	6	f)(p	f)(p	NOUN
ejpam-6436	122	7	,	,	PUNCT
ejpam-6436	122	8	g	g	NOUN
ejpam-6436	122	9	)	)	PUNCT
ejpam-6436	122	10	=	=	NOUN
ejpam-6436	122	11	(	(	PUNCT
ejpam-6436	122	12	rp	rp	NOUN
ejpam-6436	122	13	,	,	PUNCT
ejpam-6436	122	14	fpg	fpg	PROPN
ejpam-6436	122	15	)	)	PUNCT
ejpam-6436	122	16	≤	≤	NOUN
ejpam-6436	122	17	(	(	PUNCT
ejpam-6436	122	18	rp′	rp′	ADJ
ejpam-6436	122	19	,	,	PUNCT
ejpam-6436	122	20	fp′g	fp′g	NOUN
ejpam-6436	122	21	′	′	NOUN
ejpam-6436	122	22	)	)	PUNCT
ejpam-6436	122	23	=	=	PUNCT
ejpam-6436	122	24	(	(	PUNCT
ejpam-6436	122	25	r	r	NOUN
ejpam-6436	122	26	,	,	PUNCT
ejpam-6436	122	27	f)(p′	f)(p′	PROPN
ejpam-6436	122	28	,	,	PUNCT
ejpam-6436	122	29	g′	g′	NOUN
ejpam-6436	122	30	)	)	PUNCT
ejpam-6436	122	31	.	.	PUNCT
ejpam-6436	123	1	since	since	SCONJ
ejpam-6436	123	2	(	(	PUNCT
ejpam-6436	123	3	r	r	NOUN
ejpam-6436	123	4	,	,	PUNCT
ejpam-6436	123	5	f	f	X
ejpam-6436	123	6	)	)	PUNCT
ejpam-6436	123	7	is	be	AUX
ejpam-6436	123	8	left	leave	VERB
ejpam-6436	123	9	po	po	NOUN
ejpam-6436	123	10	-	-	PUNCT
ejpam-6436	123	11	cancellable	cancellable	ADJ
ejpam-6436	123	12	,	,	PUNCT
ejpam-6436	123	13	we	we	PRON
ejpam-6436	123	14	have	have	VERB
ejpam-6436	123	15	(	(	PUNCT
ejpam-6436	123	16	p	p	X
ejpam-6436	123	17	,	,	PUNCT
ejpam-6436	123	18	g	g	NOUN
ejpam-6436	123	19	)	)	PUNCT
ejpam-6436	123	20	≤	≤	NOUN
ejpam-6436	123	21	(	(	PUNCT
ejpam-6436	123	22	p′	p′	NOUN
ejpam-6436	123	23	,	,	PUNCT
ejpam-6436	123	24	g′	g′	NOUN
ejpam-6436	123	25	)	)	PUNCT
ejpam-6436	123	26	.	.	PUNCT
ejpam-6436	124	1	thus	thus	ADV
ejpam-6436	124	2	,	,	PUNCT
ejpam-6436	124	3	p	p	ADJ
ejpam-6436	124	4	≤	≤	ADJ
ejpam-6436	124	5	p′	p′	NOUN
ejpam-6436	124	6	and	and	CCONJ
ejpam-6436	124	7	we	we	PRON
ejpam-6436	124	8	arrive	arrive	VERB
ejpam-6436	124	9	at	at	ADP
ejpam-6436	124	10	a	a	DET
ejpam-6436	124	11	contradiction	contradiction	NOUN
ejpam-6436	124	12	.	.	PUNCT
ejpam-6436	125	1	therefore	therefore	ADV
ejpam-6436	125	2	,	,	PUNCT
ejpam-6436	125	3	fpg	fpg	PROPN
ejpam-6436	125	4	≰	≰	PROPN
ejpam-6436	125	5	fp′g	fp′g	NOUN
ejpam-6436	125	6	′	′	NOUN
ejpam-6436	125	7	for	for	ADP
ejpam-6436	125	8	any	any	DET
ejpam-6436	125	9	g	g	NOUN
ejpam-6436	125	10	,	,	PUNCT
ejpam-6436	125	11	g′	g′	NOUN
ejpam-6436	125	12	∈	∈	PROPN
ejpam-6436	125	13	f	f	X
ejpam-6436	125	14	(	(	PUNCT
ejpam-6436	125	15	a	a	PRON
ejpam-6436	125	16	,	,	PUNCT
ejpam-6436	125	17	s	s	NOUN
ejpam-6436	125	18	)	)	PUNCT
ejpam-6436	125	19	as	as	SCONJ
ejpam-6436	125	20	required	require	VERB
ejpam-6436	125	21	.	.	PUNCT
ejpam-6436	126	1	for	for	ADP
ejpam-6436	126	2	the	the	DET
ejpam-6436	126	3	other	other	ADJ
ejpam-6436	126	4	direction	direction	NOUN
ejpam-6436	126	5	,	,	PUNCT
ejpam-6436	126	6	assume	assume	VERB
ejpam-6436	126	7	the	the	DET
ejpam-6436	126	8	given	give	VERB
ejpam-6436	126	9	conditions	condition	NOUN
ejpam-6436	126	10	are	be	AUX
ejpam-6436	126	11	satisfied	satisfied	ADJ
ejpam-6436	126	12	.	.	PUNCT
ejpam-6436	127	1	suppose	suppose	VERB
ejpam-6436	127	2	that	that	SCONJ
ejpam-6436	127	3	(	(	PUNCT
ejpam-6436	127	4	r	r	NOUN
ejpam-6436	127	5	,	,	PUNCT
ejpam-6436	127	6	f)(p	f)(p	NOUN
ejpam-6436	127	7	,	,	PUNCT
ejpam-6436	127	8	g	g	NOUN
ejpam-6436	127	9	)	)	PUNCT
ejpam-6436	127	10	≤	≤	NOUN
ejpam-6436	127	11	(	(	PUNCT
ejpam-6436	127	12	r	r	NOUN
ejpam-6436	127	13	,	,	PUNCT
ejpam-6436	127	14	f)(p′	f)(p′	PROPN
ejpam-6436	127	15	,	,	PUNCT
ejpam-6436	127	16	g′	g′	NOUN
ejpam-6436	127	17	)	)	PUNCT
ejpam-6436	127	18	.	.	PUNCT
ejpam-6436	128	1	so	so	ADV
ejpam-6436	128	2	,	,	PUNCT
ejpam-6436	128	3	(	(	PUNCT
ejpam-6436	128	4	rp	rp	NOUN
ejpam-6436	128	5	,	,	PUNCT
ejpam-6436	128	6	fpg	fpg	NOUN
ejpam-6436	128	7	)	)	PUNCT
ejpam-6436	128	8	≤	≤	NOUN
ejpam-6436	128	9	(	(	PUNCT
ejpam-6436	128	10	rp′	rp′	ADJ
ejpam-6436	128	11	,	,	PUNCT
ejpam-6436	128	12	fp′g	fp′g	NOUN
ejpam-6436	128	13	′	′	NOUN
ejpam-6436	128	14	)	)	PUNCT
ejpam-6436	128	15	.	.	PUNCT
ejpam-6436	129	1	thus	thus	ADV
ejpam-6436	129	2	rp	rp	X
ejpam-6436	129	3	≤	≤	NUM
ejpam-6436	129	4	rp′	rp′	NOUN
ejpam-6436	129	5	and	and	CCONJ
ejpam-6436	129	6	fpg	fpg	PROPN
ejpam-6436	129	7	≤	≤	PROPN
ejpam-6436	129	8	fp′g	fp′g	VERB
ejpam-6436	129	9	′.	′.	NOUN
ejpam-6436	129	10	from	from	ADP
ejpam-6436	129	11	condition	condition	NOUN
ejpam-6436	129	12	(	(	PUNCT
ejpam-6436	129	13	2	2	NUM
ejpam-6436	129	14	)	)	PUNCT
ejpam-6436	129	15	p	p	NOUN
ejpam-6436	129	16	≤	≤	ADJ
ejpam-6436	129	17	p′	p′	NOUN
ejpam-6436	129	18	and	and	CCONJ
ejpam-6436	129	19	condition	condition	NOUN
ejpam-6436	129	20	(	(	PUNCT
ejpam-6436	129	21	1	1	NUM
ejpam-6436	129	22	)	)	PUNCT
ejpam-6436	129	23	implies	imply	VERB
ejpam-6436	129	24	that	that	SCONJ
ejpam-6436	129	25	g	g	PROPN
ejpam-6436	129	26	≤	≤	ADV
ejpam-6436	129	27	g′.	g′.	X
ejpam-6436	129	28	therefore	therefore	ADV
ejpam-6436	129	29	(	(	PUNCT
ejpam-6436	129	30	p	p	X
ejpam-6436	129	31	,	,	PUNCT
ejpam-6436	129	32	g	g	NOUN
ejpam-6436	129	33	)	)	PUNCT
ejpam-6436	129	34	≤	≤	NOUN
ejpam-6436	129	35	(	(	PUNCT
ejpam-6436	129	36	p′	p′	NOUN
ejpam-6436	129	37	,	,	PUNCT
ejpam-6436	129	38	g′	g′	NOUN
ejpam-6436	129	39	)	)	PUNCT
ejpam-6436	129	40	.	.	PUNCT
ejpam-6436	130	1	hence	hence	ADV
ejpam-6436	130	2	(	(	PUNCT
ejpam-6436	130	3	r	r	NOUN
ejpam-6436	130	4	,	,	PUNCT
ejpam-6436	130	5	f	f	X
ejpam-6436	130	6	)	)	PUNCT
ejpam-6436	130	7	is	be	AUX
ejpam-6436	130	8	left	leave	VERB
ejpam-6436	130	9	po	po	NOUN
ejpam-6436	130	10	-	-	NOUN
ejpam-6436	130	11	cancellable	cancellable	ADJ
ejpam-6436	130	12	,	,	PUNCT
ejpam-6436	130	13	as	as	SCONJ
ejpam-6436	130	14	required	require	VERB
ejpam-6436	130	15	.	.	PUNCT
ejpam-6436	131	1	recall	recall	NOUN
ejpam-6436	131	2	from	from	ADP
ejpam-6436	131	3	[	[	X
ejpam-6436	131	4	16	16	NUM
ejpam-6436	131	5	]	]	PUNCT
ejpam-6436	131	6	that	that	SCONJ
ejpam-6436	131	7	a	a	DET
ejpam-6436	131	8	free	free	ADJ
ejpam-6436	131	9	posemigroup	posemigroup	NOUN
ejpam-6436	131	10	f	f	PROPN
ejpam-6436	131	11	is	be	AUX
ejpam-6436	131	12	a	a	DET
ejpam-6436	131	13	free	free	ADJ
ejpam-6436	131	14	semigroup	semigroup	NOUN
ejpam-6436	131	15	f	f	PROPN
ejpam-6436	131	16	with	with	ADP
ejpam-6436	131	17	order	order	NOUN
ejpam-6436	131	18	defined	define	VERB
ejpam-6436	131	19	as	as	ADP
ejpam-6436	131	20	:	:	PUNCT
ejpam-6436	131	21	b.	b.	PROPN
ejpam-6436	131	22	al	al	PROPN
ejpam-6436	131	23	subaiei	subaiei	PROPN
ejpam-6436	131	24	et	et	PROPN
ejpam-6436	131	25	al	al	PROPN
ejpam-6436	131	26	.	.	PUNCT
ejpam-6436	131	27	/	/	SYM
ejpam-6436	131	28	eur	eur	PROPN
ejpam-6436	131	29	.	.	PUNCT
ejpam-6436	132	1	j.	j.	PROPN
ejpam-6436	132	2	pure	pure	PROPN
ejpam-6436	132	3	appl	appl	PROPN
ejpam-6436	132	4	.	.	PROPN
ejpam-6436	132	5	math	math	PROPN
ejpam-6436	132	6	,	,	PUNCT
ejpam-6436	132	7	18	18	NUM
ejpam-6436	132	8	(	(	PUNCT
ejpam-6436	132	9	3	3	NUM
ejpam-6436	132	10	)	)	PUNCT
ejpam-6436	132	11	(	(	PUNCT
ejpam-6436	132	12	2025	2025	NUM
ejpam-6436	132	13	)	)	PUNCT
ejpam-6436	132	14	,	,	PUNCT
ejpam-6436	132	15	6436	6436	NUM
ejpam-6436	132	16	6	6	NUM
ejpam-6436	132	17	of	of	ADP
ejpam-6436	132	18	14	14	NUM
ejpam-6436	132	19	a1a2	a1a2	INTJ
ejpam-6436	132	20	.	.	PUNCT
ejpam-6436	132	21	.	.	PUNCT
ejpam-6436	132	22	.	.	PUNCT
ejpam-6436	133	1	an	an	DET
ejpam-6436	133	2	≤	≤	NUM
ejpam-6436	133	3	b1b2	b1b2	PROPN
ejpam-6436	133	4	.	.	PUNCT
ejpam-6436	133	5	.	.	PUNCT
ejpam-6436	133	6	.	.	PUNCT
ejpam-6436	134	1	bt	bt	PROPN
ejpam-6436	134	2	⇔	⇔	PROPN
ejpam-6436	134	3	n	n	PROPN
ejpam-6436	134	4	=	=	SYM
ejpam-6436	134	5	t	t	PROPN
ejpam-6436	134	6	and	and	CCONJ
ejpam-6436	134	7	ai	ai	VERB
ejpam-6436	134	8	≤	≤	ADJ
ejpam-6436	134	9	bi	bi	NOUN
ejpam-6436	134	10	where	where	SCONJ
ejpam-6436	134	11	1	1	NUM
ejpam-6436	134	12	≤	≤	NUM
ejpam-6436	134	13	i	i	PRON
ejpam-6436	134	14	≤	≤	ADJ
ejpam-6436	134	15	n.	n.	NOUN
ejpam-6436	134	16	in	in	ADP
ejpam-6436	134	17	example	example	NOUN
ejpam-6436	134	18	1.4	1.4	NUM
ejpam-6436	134	19	of	of	ADP
ejpam-6436	134	20	[	[	X
ejpam-6436	134	21	15	15	NUM
ejpam-6436	134	22	]	]	X
ejpam-6436	134	23	it	it	PRON
ejpam-6436	134	24	has	have	AUX
ejpam-6436	134	25	been	be	AUX
ejpam-6436	134	26	shown	show	VERB
ejpam-6436	134	27	that	that	SCONJ
ejpam-6436	134	28	there	there	PRON
ejpam-6436	134	29	exist	exist	VERB
ejpam-6436	134	30	left	leave	VERB
ejpam-6436	134	31	cancellable	cancellable	ADJ
ejpam-6436	134	32	elements	element	NOUN
ejpam-6436	134	33	in	in	ADP
ejpam-6436	134	34	the	the	DET
ejpam-6436	134	35	monoid	monoid	NOUN
ejpam-6436	134	36	t	t	NOUN
ejpam-6436	134	37	=	=	PUNCT
ejpam-6436	134	38	r	r	NOUN
ejpam-6436	134	39	×	×	PROPN
ejpam-6436	134	40	f	f	X
ejpam-6436	134	41	(	(	PUNCT
ejpam-6436	134	42	a	a	PRON
ejpam-6436	134	43	,	,	PUNCT
ejpam-6436	134	44	s	s	NOUN
ejpam-6436	134	45	)	)	PUNCT
ejpam-6436	134	46	for	for	ADP
ejpam-6436	134	47	which	which	PRON
ejpam-6436	134	48	the	the	DET
ejpam-6436	134	49	first	first	ADJ
ejpam-6436	134	50	components	component	NOUN
ejpam-6436	134	51	are	be	AUX
ejpam-6436	134	52	not	not	PART
ejpam-6436	134	53	left	leave	VERB
ejpam-6436	134	54	cancellable	cancellable	ADJ
ejpam-6436	134	55	in	in	ADP
ejpam-6436	134	56	r.	r.	PROPN
ejpam-6436	134	57	in	in	ADP
ejpam-6436	134	58	the	the	DET
ejpam-6436	134	59	next	next	ADJ
ejpam-6436	134	60	example	example	NOUN
ejpam-6436	134	61	we	we	PRON
ejpam-6436	134	62	show	show	VERB
ejpam-6436	134	63	that	that	SCONJ
ejpam-6436	134	64	the	the	DET
ejpam-6436	134	65	same	same	ADJ
ejpam-6436	134	66	example	example	NOUN
ejpam-6436	134	67	in	in	ADP
ejpam-6436	134	68	[	[	X
ejpam-6436	134	69	15	15	NUM
ejpam-6436	134	70	]	]	PUNCT
ejpam-6436	134	71	can	can	AUX
ejpam-6436	134	72	be	be	AUX
ejpam-6436	134	73	transformed	transform	VERB
ejpam-6436	134	74	in	in	ADP
ejpam-6436	134	75	the	the	DET
ejpam-6436	134	76	ordered	order	VERB
ejpam-6436	134	77	case	case	NOUN
ejpam-6436	134	78	by	by	ADP
ejpam-6436	134	79	replacing	replace	VERB
ejpam-6436	134	80	the	the	DET
ejpam-6436	134	81	free	free	ADJ
ejpam-6436	134	82	semigroup	semigroup	NOUN
ejpam-6436	134	83	by	by	ADP
ejpam-6436	134	84	the	the	DET
ejpam-6436	134	85	free	free	ADJ
ejpam-6436	134	86	posemigroup	posemigroup	NOUN
ejpam-6436	134	87	,	,	PUNCT
ejpam-6436	134	88	by	by	ADP
ejpam-6436	134	89	defining	define	VERB
ejpam-6436	134	90	suitable	suitable	ADJ
ejpam-6436	134	91	orders	order	NOUN
ejpam-6436	134	92	and	and	CCONJ
ejpam-6436	134	93	carefully	carefully	ADV
ejpam-6436	134	94	choosing	choose	VERB
ejpam-6436	134	95	the	the	DET
ejpam-6436	134	96	required	require	VERB
ejpam-6436	134	97	monotone	monotone	ADJ
ejpam-6436	134	98	maps	map	NOUN
ejpam-6436	134	99	.	.	PUNCT
ejpam-6436	135	1	thus	thus	ADV
ejpam-6436	135	2	there	there	PRON
ejpam-6436	135	3	exists	exist	VERB
ejpam-6436	135	4	a	a	DET
ejpam-6436	135	5	left	left	ADJ
ejpam-6436	135	6	po	po	NOUN
ejpam-6436	135	7	-	-	PUNCT
ejpam-6436	135	8	cancellable	cancellable	ADJ
ejpam-6436	135	9	element	element	NOUN
ejpam-6436	135	10	(	(	PUNCT
ejpam-6436	135	11	r	r	NOUN
ejpam-6436	135	12	,	,	PUNCT
ejpam-6436	135	13	f	f	X
ejpam-6436	135	14	)	)	PUNCT
ejpam-6436	135	15	∈	∈	PROPN
ejpam-6436	135	16	t	t	NOUN
ejpam-6436	135	17	but	but	CCONJ
ejpam-6436	135	18	r	r	NOUN
ejpam-6436	135	19	is	be	AUX
ejpam-6436	135	20	not	not	PART
ejpam-6436	135	21	left	leave	VERB
ejpam-6436	135	22	po	po	NOUN
ejpam-6436	135	23	-	-	NOUN
ejpam-6436	135	24	cancellable	cancellable	ADJ
ejpam-6436	135	25	in	in	ADP
ejpam-6436	135	26	r.	r.	PROPN
ejpam-6436	135	27	example	example	NOUN
ejpam-6436	136	1	1	1	NUM
ejpam-6436	136	2	.	.	PUNCT
ejpam-6436	136	3	let	let	VERB
ejpam-6436	136	4	a	a	DET
ejpam-6436	136	5	=	=	X
ejpam-6436	136	6	{	{	PUNCT
ejpam-6436	136	7	a	a	PROPN
ejpam-6436	136	8	,	,	PUNCT
ejpam-6436	136	9	b	b	NOUN
ejpam-6436	136	10	}	}	PUNCT
ejpam-6436	136	11	where	where	SCONJ
ejpam-6436	136	12	a	a	DET
ejpam-6436	136	13	≤	≤	PROPN
ejpam-6436	136	14	b	b	NOUN
ejpam-6436	136	15	and	and	CCONJ
ejpam-6436	136	16	s	s	NOUN
ejpam-6436	136	17	=	=	NOUN
ejpam-6436	136	18	<	<	X
ejpam-6436	136	19	u	u	NOUN
ejpam-6436	136	20	,	,	PUNCT
ejpam-6436	136	21	v	v	X
ejpam-6436	136	22	>	>	X
ejpam-6436	136	23	∪{1	∪{1	PROPN
ejpam-6436	136	24	}	}	PUNCT
ejpam-6436	136	25	,	,	PUNCT
ejpam-6436	136	26	where	where	SCONJ
ejpam-6436	136	27	u	u	PROPN
ejpam-6436	136	28	≤	≤	X
ejpam-6436	136	29	v	v	NOUN
ejpam-6436	136	30	,	,	PUNCT
ejpam-6436	136	31	be	be	AUX
ejpam-6436	136	32	the	the	DET
ejpam-6436	136	33	free	free	ADJ
ejpam-6436	136	34	pomonoid	pomonoid	NOUN
ejpam-6436	136	35	generated	generate	VERB
ejpam-6436	136	36	by	by	ADP
ejpam-6436	136	37	u	u	PROPN
ejpam-6436	136	38	,	,	PUNCT
ejpam-6436	136	39	v.	v.	CCONJ
ejpam-6436	136	40	let	let	VERB
ejpam-6436	136	41	p	p	NOUN
ejpam-6436	136	42	(	(	PUNCT
ejpam-6436	136	43	a	a	NOUN
ejpam-6436	136	44	)	)	PUNCT
ejpam-6436	136	45	=	=	PRON
ejpam-6436	136	46	{	{	PUNCT
ejpam-6436	136	47	ca	ca	NOUN
ejpam-6436	136	48	,	,	PUNCT
ejpam-6436	136	49	cb	cb	PROPN
ejpam-6436	136	50	,	,	PUNCT
ejpam-6436	136	51	1	1	NUM
ejpam-6436	136	52	}	}	PUNCT
ejpam-6436	136	53	be	be	AUX
ejpam-6436	136	54	the	the	DET
ejpam-6436	136	55	pomonoid	pomonoid	NOUN
ejpam-6436	136	56	which	which	PRON
ejpam-6436	136	57	is	be	AUX
ejpam-6436	136	58	also	also	ADV
ejpam-6436	136	59	an	an	DET
ejpam-6436	136	60	a	a	PRON
ejpam-6436	136	61	-	-	PUNCT
ejpam-6436	136	62	poset	poset	NOUN
ejpam-6436	136	63	under	under	ADP
ejpam-6436	136	64	the	the	DET
ejpam-6436	136	65	action	action	NOUN
ejpam-6436	136	66	given	give	VERB
ejpam-6436	136	67	by	by	ADP
ejpam-6436	136	68	ca.x	ca.x	X
ejpam-6436	136	69	=	=	SYM
ejpam-6436	136	70	a	a	PRON
ejpam-6436	136	71	,	,	PUNCT
ejpam-6436	136	72	cb.x	cb.x	NOUN
ejpam-6436	136	73	=	=	SYM
ejpam-6436	136	74	b	b	PROPN
ejpam-6436	136	75	for	for	ADP
ejpam-6436	136	76	all	all	PRON
ejpam-6436	136	77	x	x	SYM
ejpam-6436	136	78	∈	∈	NOUN
ejpam-6436	136	79	a.	a.	NOUN
ejpam-6436	136	80	consider	consider	VERB
ejpam-6436	136	81	t	t	NOUN
ejpam-6436	136	82	=	=	SYM
ejpam-6436	136	83	p	p	X
ejpam-6436	136	84	(	(	PUNCT
ejpam-6436	136	85	a	a	NOUN
ejpam-6436	136	86	)	)	PUNCT
ejpam-6436	136	87	×	×	NOUN
ejpam-6436	136	88	f	f	X
ejpam-6436	136	89	(	(	PUNCT
ejpam-6436	136	90	a	a	PRON
ejpam-6436	136	91	,	,	PUNCT
ejpam-6436	136	92	s	s	NOUN
ejpam-6436	136	93	)	)	PUNCT
ejpam-6436	136	94	.	.	PUNCT
ejpam-6436	137	1	let	let	VERB
ejpam-6436	137	2	f	f	PROPN
ejpam-6436	137	3	∈	∈	PROPN
ejpam-6436	137	4	f	f	PROPN
ejpam-6436	137	5	(	(	PUNCT
ejpam-6436	137	6	a	a	PRON
ejpam-6436	137	7	,	,	PUNCT
ejpam-6436	137	8	s	s	NOUN
ejpam-6436	137	9	)	)	PUNCT
ejpam-6436	137	10	such	such	ADJ
ejpam-6436	137	11	that	that	DET
ejpam-6436	137	12	f(a	f(a	NOUN
ejpam-6436	137	13	)	)	PUNCT
ejpam-6436	137	14	=	=	SYM
ejpam-6436	137	15	u	u	NOUN
ejpam-6436	137	16	and	and	CCONJ
ejpam-6436	137	17	f(b	f(b	PROPN
ejpam-6436	137	18	)	)	PUNCT
ejpam-6436	138	1	=	=	VERB
ejpam-6436	139	1	v.	v.	CCONJ
ejpam-6436	139	2	we	we	PRON
ejpam-6436	139	3	show	show	VERB
ejpam-6436	139	4	that	that	SCONJ
ejpam-6436	139	5	(	(	PUNCT
ejpam-6436	139	6	ca	ca	NOUN
ejpam-6436	139	7	,	,	PUNCT
ejpam-6436	139	8	f	f	X
ejpam-6436	139	9	)	)	PUNCT
ejpam-6436	139	10	∈	∈	PROPN
ejpam-6436	139	11	t	t	PROPN
ejpam-6436	139	12	is	be	AUX
ejpam-6436	139	13	left	leave	VERB
ejpam-6436	139	14	po	po	NOUN
ejpam-6436	139	15	-	-	NOUN
ejpam-6436	139	16	cancellable	cancellable	ADJ
ejpam-6436	139	17	while	while	SCONJ
ejpam-6436	139	18	ca	can	AUX
ejpam-6436	139	19	is	be	AUX
ejpam-6436	139	20	not	not	PART
ejpam-6436	139	21	left	leave	VERB
ejpam-6436	139	22	po	po	NOUN
ejpam-6436	139	23	-	-	NOUN
ejpam-6436	139	24	cancellable	cancellable	ADJ
ejpam-6436	139	25	,	,	PUNCT
ejpam-6436	139	26	as	as	SCONJ
ejpam-6436	139	27	clearly	clearly	ADV
ejpam-6436	139	28	cb	cb	X
ejpam-6436	139	29	≰	≰	PROPN
ejpam-6436	139	30	ca	can	AUX
ejpam-6436	139	31	as	as	ADP
ejpam-6436	139	32	b	b	PROPN
ejpam-6436	139	33	≰	≰	PROPN
ejpam-6436	139	34	a	a	DET
ejpam-6436	139	35	while	while	NOUN
ejpam-6436	139	36	cacb	cacb	PROPN
ejpam-6436	139	37	≤	≤	PROPN
ejpam-6436	139	38	caca	caca	PROPN
ejpam-6436	139	39	.	.	PUNCT
ejpam-6436	140	1	now	now	ADV
ejpam-6436	140	2	suppose	suppose	VERB
ejpam-6436	140	3	that	that	SCONJ
ejpam-6436	140	4	(	(	PUNCT
ejpam-6436	140	5	ca	ca	NOUN
ejpam-6436	140	6	,	,	PUNCT
ejpam-6436	140	7	f)(h1	f)(h1	PROPN
ejpam-6436	140	8	,	,	PUNCT
ejpam-6436	140	9	g1	g1	NOUN
ejpam-6436	140	10	)	)	PUNCT
ejpam-6436	140	11	≤	≤	NOUN
ejpam-6436	140	12	(	(	PUNCT
ejpam-6436	140	13	ca	ca	NOUN
ejpam-6436	140	14	,	,	PUNCT
ejpam-6436	140	15	f)(h2	f)(h2	NOUN
ejpam-6436	140	16	,	,	PUNCT
ejpam-6436	140	17	g2	g2	PROPN
ejpam-6436	140	18	)	)	PUNCT
ejpam-6436	140	19	where	where	SCONJ
ejpam-6436	140	20	(	(	PUNCT
ejpam-6436	140	21	h1	h1	PROPN
ejpam-6436	140	22	,	,	PUNCT
ejpam-6436	140	23	g1	g1	PROPN
ejpam-6436	140	24	)	)	PUNCT
ejpam-6436	140	25	,	,	PUNCT
ejpam-6436	140	26	(	(	PUNCT
ejpam-6436	140	27	h2	h2	NOUN
ejpam-6436	140	28	,	,	PUNCT
ejpam-6436	140	29	g2	g2	PROPN
ejpam-6436	140	30	)	)	PUNCT
ejpam-6436	140	31	∈	∈	PROPN
ejpam-6436	140	32	t	t	PROPN
ejpam-6436	140	33	.	.	PUNCT
ejpam-6436	141	1	then	then	ADV
ejpam-6436	141	2	,	,	PUNCT
ejpam-6436	141	3	(	(	PUNCT
ejpam-6436	141	4	cah1	cah1	PROPN
ejpam-6436	141	5	,	,	PUNCT
ejpam-6436	141	6	fh1g1	fh1g1	PROPN
ejpam-6436	141	7	)	)	PUNCT
ejpam-6436	141	8	≤	≤	NOUN
ejpam-6436	141	9	(	(	PUNCT
ejpam-6436	141	10	cah2	cah2	PROPN
ejpam-6436	141	11	,	,	PUNCT
ejpam-6436	141	12	fh2g2	fh2g2	PROPN
ejpam-6436	141	13	)	)	PUNCT
ejpam-6436	141	14	.	.	PUNCT
ejpam-6436	142	1	so	so	ADV
ejpam-6436	142	2	for	for	ADP
ejpam-6436	142	3	any	any	DET
ejpam-6436	142	4	a	a	DET
ejpam-6436	142	5	∈	∈	PROPN
ejpam-6436	142	6	a	a	DET
ejpam-6436	142	7	,	,	PUNCT
ejpam-6436	142	8	fh1g1(a	fh1g1(a	NOUN
ejpam-6436	142	9	)	)	PUNCT
ejpam-6436	142	10	=	=	SYM
ejpam-6436	142	11	f(h1(a))g1(a	f(h1(a))g1(a	PROPN
ejpam-6436	142	12	)	)	PUNCT
ejpam-6436	142	13	≤	≤	NUM
ejpam-6436	142	14	f(h2(a))g2(a	f(h2(a))g2(a	NOUN
ejpam-6436	142	15	)	)	PUNCT
ejpam-6436	142	16	=	=	SYM
ejpam-6436	142	17	fh2g2(a	fh2g2(a	NOUN
ejpam-6436	142	18	)	)	PUNCT
ejpam-6436	142	19	.	.	PUNCT
ejpam-6436	143	1	from	from	ADP
ejpam-6436	143	2	the	the	DET
ejpam-6436	143	3	definition	definition	NOUN
ejpam-6436	143	4	of	of	ADP
ejpam-6436	143	5	free	free	ADJ
ejpam-6436	143	6	posemigroup	posemigroup	NOUN
ejpam-6436	143	7	and	and	CCONJ
ejpam-6436	143	8	since	since	SCONJ
ejpam-6436	143	9	the	the	DET
ejpam-6436	143	10	image	image	NOUN
ejpam-6436	143	11	of	of	ADP
ejpam-6436	143	12	f	f	PROPN
ejpam-6436	143	13	is	be	AUX
ejpam-6436	143	14	one	one	NUM
ejpam-6436	143	15	letter	letter	NOUN
ejpam-6436	143	16	word	word	NOUN
ejpam-6436	143	17	we	we	PRON
ejpam-6436	143	18	get	get	VERB
ejpam-6436	143	19	that	that	PRON
ejpam-6436	143	20	h1	h1	VERB
ejpam-6436	143	21	≤	≤	ADJ
ejpam-6436	143	22	h2	h2	NOUN
ejpam-6436	143	23	and	and	CCONJ
ejpam-6436	143	24	g1	g1	VERB
ejpam-6436	143	25	≤	≤	PROPN
ejpam-6436	143	26	g2	g2	PROPN
ejpam-6436	143	27	.	.	PUNCT
ejpam-6436	144	1	so	so	ADV
ejpam-6436	144	2	(	(	PUNCT
ejpam-6436	144	3	h1	h1	PROPN
ejpam-6436	144	4	,	,	PUNCT
ejpam-6436	144	5	g1	g1	PROPN
ejpam-6436	144	6	)	)	PUNCT
ejpam-6436	144	7	≤	≤	NOUN
ejpam-6436	144	8	(	(	PUNCT
ejpam-6436	144	9	h2	h2	NOUN
ejpam-6436	144	10	,	,	PUNCT
ejpam-6436	144	11	g2	g2	PROPN
ejpam-6436	144	12	)	)	PUNCT
ejpam-6436	144	13	and	and	CCONJ
ejpam-6436	144	14	thus	thus	ADV
ejpam-6436	144	15	(	(	PUNCT
ejpam-6436	144	16	ca	ca	NOUN
ejpam-6436	144	17	,	,	PUNCT
ejpam-6436	144	18	f	f	X
ejpam-6436	144	19	)	)	PUNCT
ejpam-6436	144	20	is	be	AUX
ejpam-6436	144	21	left	leave	VERB
ejpam-6436	144	22	po	po	NOUN
ejpam-6436	144	23	-	-	NOUN
ejpam-6436	144	24	cancellable	cancellable	ADJ
ejpam-6436	144	25	.	.	PUNCT
ejpam-6436	145	1	next	next	ADV
ejpam-6436	145	2	we	we	PRON
ejpam-6436	145	3	discuss	discuss	VERB
ejpam-6436	145	4	the	the	DET
ejpam-6436	145	5	po	po	NOUN
ejpam-6436	145	6	-	-	NOUN
ejpam-6436	145	7	injectivity	injectivity	NOUN
ejpam-6436	145	8	of	of	ADP
ejpam-6436	145	9	the	the	DET
ejpam-6436	145	10	wreath	wreath	NOUN
ejpam-6436	145	11	product	product	NOUN
ejpam-6436	145	12	pomonoid	pomonoid	NOUN
ejpam-6436	145	13	t	t	PROPN
ejpam-6436	145	14	on	on	ADP
ejpam-6436	145	15	the	the	DET
ejpam-6436	145	16	wreath	wreath	NOUN
ejpam-6436	145	17	product	product	NOUN
ejpam-6436	145	18	t	t	X
ejpam-6436	145	19	-poset	-poset	PROPN
ejpam-6436	145	20	tc	tc	NUM
ejpam-6436	145	21	constructed	construct	VERB
ejpam-6436	145	22	above	above	ADV
ejpam-6436	145	23	.	.	PUNCT
ejpam-6436	146	1	theorem	theorem	NOUN
ejpam-6436	146	2	2	2	NUM
ejpam-6436	146	3	.	.	PUNCT
ejpam-6436	147	1	the	the	DET
ejpam-6436	147	2	pomonoid	pomonoid	PROPN
ejpam-6436	147	3	t	t	PROPN
ejpam-6436	147	4	acts	act	VERB
ejpam-6436	147	5	po	po	NOUN
ejpam-6436	147	6	-	-	PUNCT
ejpam-6436	147	7	injectively	injectively	ADV
ejpam-6436	147	8	on	on	ADP
ejpam-6436	147	9	tc	tc	PRON
ejpam-6436	147	10	if	if	SCONJ
ejpam-6436	148	1	and	and	CCONJ
ejpam-6436	148	2	only	only	ADV
ejpam-6436	148	3	if	if	SCONJ
ejpam-6436	148	4	the	the	DET
ejpam-6436	148	5	following	follow	VERB
ejpam-6436	148	6	conditions	condition	NOUN
ejpam-6436	148	7	are	be	AUX
ejpam-6436	148	8	satisfied	satisfied	ADJ
ejpam-6436	148	9	.	.	PUNCT
ejpam-6436	149	1	1	1	X
ejpam-6436	149	2	)	)	PUNCT
ejpam-6436	149	3	a	a	DET
ejpam-6436	149	4	≤	≤	NOUN
ejpam-6436	149	5	a′	a′	NOUN
ejpam-6436	149	6	and	and	CCONJ
ejpam-6436	149	7	f(a)b	f(a)b	PROPN
ejpam-6436	150	1	≤	≤	ADJ
ejpam-6436	150	2	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	150	3	implies	imply	VERB
ejpam-6436	150	4	b	b	PROPN
ejpam-6436	150	5	≤	≤	ADJ
ejpam-6436	150	6	b′	b′	NUM
ejpam-6436	150	7	where	where	SCONJ
ejpam-6436	150	8	f	f	PROPN
ejpam-6436	150	9	∈	∈	PROPN
ejpam-6436	150	10	f	f	PROPN
ejpam-6436	150	11	(	(	PUNCT
ejpam-6436	150	12	a	a	PRON
ejpam-6436	150	13	,	,	PUNCT
ejpam-6436	150	14	s	s	NOUN
ejpam-6436	150	15	)	)	PUNCT
ejpam-6436	150	16	,	,	PUNCT
ejpam-6436	150	17	a	a	PRON
ejpam-6436	150	18	,	,	PUNCT
ejpam-6436	150	19	a′	a′	PROPN
ejpam-6436	150	20	∈	∈	PROPN
ejpam-6436	150	21	a	a	PRON
ejpam-6436	150	22	,	,	PUNCT
ejpam-6436	150	23	and	and	CCONJ
ejpam-6436	150	24	b	b	NOUN
ejpam-6436	150	25	,	,	PUNCT
ejpam-6436	150	26	b′	b′	NUM
ejpam-6436	150	27	∈	∈	PROPN
ejpam-6436	150	28	b.	b.	NOUN
ejpam-6436	150	29	2	2	X
ejpam-6436	150	30	)	)	PUNCT
ejpam-6436	150	31	r	r	NOUN
ejpam-6436	150	32	acts	act	NOUN
ejpam-6436	150	33	po	po	NOUN
ejpam-6436	150	34	-	-	PUNCT
ejpam-6436	150	35	injectively	injectively	ADV
ejpam-6436	150	36	on	on	ADP
ejpam-6436	150	37	a.	a.	NOUN
ejpam-6436	150	38	proof	proof	NOUN
ejpam-6436	150	39	.	.	PUNCT
ejpam-6436	151	1	let	let	AUX
ejpam-6436	151	2	t	t	PROPN
ejpam-6436	151	3	acts	act	VERB
ejpam-6436	151	4	po	po	NOUN
ejpam-6436	151	5	-	-	PUNCT
ejpam-6436	151	6	injectively	injectively	ADV
ejpam-6436	151	7	on	on	ADP
ejpam-6436	151	8	tc	tc	NUM
ejpam-6436	151	9	.	.	NOUN
ejpam-6436	151	10	1	1	NUM
ejpam-6436	151	11	)	)	PUNCT
ejpam-6436	151	12	suppose	suppose	VERB
ejpam-6436	151	13	that	that	SCONJ
ejpam-6436	151	14	a	a	DET
ejpam-6436	151	15	≤	≤	NOUN
ejpam-6436	151	16	a′	a′	NOUN
ejpam-6436	151	17	and	and	CCONJ
ejpam-6436	151	18	f(a)b	f(a)b	PROPN
ejpam-6436	151	19	≤	≤	ADJ
ejpam-6436	151	20	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	151	21	,	,	PUNCT
ejpam-6436	151	22	where	where	SCONJ
ejpam-6436	151	23	a	a	X
ejpam-6436	151	24	,	,	PUNCT
ejpam-6436	151	25	a′	a′	PROPN
ejpam-6436	151	26	∈	∈	PROPN
ejpam-6436	151	27	a	a	PRON
ejpam-6436	151	28	and	and	CCONJ
ejpam-6436	151	29	b	b	NOUN
ejpam-6436	151	30	,	,	PUNCT
ejpam-6436	151	31	b′	b′	NUM
ejpam-6436	151	32	∈	∈	PROPN
ejpam-6436	151	33	b.	b.	NOUN
ejpam-6436	151	34	by	by	ADP
ejpam-6436	151	35	condition	condition	NOUN
ejpam-6436	151	36	(	(	PUNCT
ejpam-6436	151	37	1	1	NUM
ejpam-6436	151	38	)	)	PUNCT
ejpam-6436	151	39	of	of	ADP
ejpam-6436	151	40	theorem	theorem	NOUN
ejpam-6436	151	41	1	1	NUM
ejpam-6436	151	42	,	,	PUNCT
ejpam-6436	151	43	we	we	PRON
ejpam-6436	151	44	get	get	VERB
ejpam-6436	151	45	that	that	DET
ejpam-6436	151	46	b	b	PROPN
ejpam-6436	151	47	≤	≤	X
ejpam-6436	151	48	b′.	b′.	NOUN
ejpam-6436	151	49	2	2	NUM
ejpam-6436	151	50	)	)	PUNCT
ejpam-6436	151	51	next	next	ADV
ejpam-6436	151	52	suppose	suppose	VERB
ejpam-6436	151	53	that	that	SCONJ
ejpam-6436	151	54	ra	ra	PROPN
ejpam-6436	151	55	≤	≤	NOUN
ejpam-6436	151	56	ra′	ra′	NOUN
ejpam-6436	151	57	where	where	SCONJ
ejpam-6436	151	58	r	r	NOUN
ejpam-6436	151	59	∈	∈	PROPN
ejpam-6436	151	60	r	r	NOUN
ejpam-6436	151	61	and	and	CCONJ
ejpam-6436	151	62	a	a	PRON
ejpam-6436	151	63	,	,	PUNCT
ejpam-6436	151	64	a′	a′	PROPN
ejpam-6436	151	65	∈	∈	PROPN
ejpam-6436	151	66	a.	a.	NOUN
ejpam-6436	151	67	assume	assume	VERB
ejpam-6436	151	68	that	that	SCONJ
ejpam-6436	151	69	a	a	DET
ejpam-6436	151	70	≰	≰	PROPN
ejpam-6436	151	71	a′.	a′.	NOUN
ejpam-6436	151	72	using	use	VERB
ejpam-6436	151	73	condition	condition	NOUN
ejpam-6436	151	74	(	(	PUNCT
ejpam-6436	151	75	2	2	NUM
ejpam-6436	151	76	)	)	PUNCT
ejpam-6436	151	77	in	in	ADP
ejpam-6436	151	78	theorem	theorem	NOUN
ejpam-6436	151	79	1	1	NUM
ejpam-6436	151	80	we	we	PRON
ejpam-6436	151	81	have	have	VERB
ejpam-6436	151	82	ca(a)b	ca(a)b	NUM
ejpam-6436	151	83	≰	≰	PROPN
ejpam-6436	151	84	ca′(a	ca′(a	PROPN
ejpam-6436	151	85	′)b′	′)b′	PROPN
ejpam-6436	151	86	for	for	ADP
ejpam-6436	151	87	all	all	DET
ejpam-6436	151	88	b	b	NOUN
ejpam-6436	151	89	,	,	PUNCT
ejpam-6436	151	90	b′	b′	NUM
ejpam-6436	151	91	∈	∈	PROPN
ejpam-6436	151	92	b	b	NOUN
ejpam-6436	151	93	and	and	CCONJ
ejpam-6436	151	94	this	this	PRON
ejpam-6436	151	95	is	be	AUX
ejpam-6436	151	96	a	a	DET
ejpam-6436	151	97	contradiction	contradiction	NOUN
ejpam-6436	151	98	to	to	ADP
ejpam-6436	151	99	t	t	PROPN
ejpam-6436	151	100	acts	act	VERB
ejpam-6436	151	101	po	po	NOUN
ejpam-6436	151	102	-	-	PUNCT
ejpam-6436	151	103	injectively	injectively	ADV
ejpam-6436	151	104	on	on	ADP
ejpam-6436	151	105	tc	tc	NOUN
ejpam-6436	151	106	.	.	PUNCT
ejpam-6436	152	1	therefore	therefore	ADV
ejpam-6436	152	2	,	,	PUNCT
ejpam-6436	152	3	a	a	DET
ejpam-6436	152	4	≤	≤	NOUN
ejpam-6436	152	5	a′	a′	NOUN
ejpam-6436	153	1	and	and	CCONJ
ejpam-6436	153	2	so	so	ADV
ejpam-6436	153	3	r	r	NOUN
ejpam-6436	153	4	acts	act	VERB
ejpam-6436	153	5	po	po	NOUN
ejpam-6436	153	6	-	-	PUNCT
ejpam-6436	153	7	injectively	injectively	ADV
ejpam-6436	153	8	on	on	ADP
ejpam-6436	153	9	a.	a.	NOUN
ejpam-6436	153	10	conversely	conversely	ADV
ejpam-6436	153	11	assume	assume	VERB
ejpam-6436	153	12	that	that	SCONJ
ejpam-6436	153	13	the	the	DET
ejpam-6436	153	14	two	two	NUM
ejpam-6436	153	15	conditions	condition	NOUN
ejpam-6436	153	16	are	be	AUX
ejpam-6436	153	17	satisfied	satisfied	ADJ
ejpam-6436	153	18	.	.	PUNCT
ejpam-6436	154	1	take	take	VERB
ejpam-6436	154	2	any	any	DET
ejpam-6436	154	3	(	(	PUNCT
ejpam-6436	154	4	r	r	NOUN
ejpam-6436	154	5	,	,	PUNCT
ejpam-6436	154	6	f	f	X
ejpam-6436	154	7	)	)	PUNCT
ejpam-6436	154	8	∈	∈	PROPN
ejpam-6436	154	9	t	t	PROPN
ejpam-6436	154	10	and	and	CCONJ
ejpam-6436	154	11	(	(	PUNCT
ejpam-6436	154	12	a	a	DET
ejpam-6436	154	13	,	,	PUNCT
ejpam-6436	154	14	b	b	NOUN
ejpam-6436	154	15	)	)	PUNCT
ejpam-6436	154	16	,	,	PUNCT
ejpam-6436	154	17	(	(	PUNCT
ejpam-6436	154	18	a′	a′	PROPN
ejpam-6436	154	19	,	,	PUNCT
ejpam-6436	154	20	b′	b′	NUM
ejpam-6436	154	21	)	)	PUNCT
ejpam-6436	154	22	∈	∈	PROPN
ejpam-6436	154	23	t	t	PROPN
ejpam-6436	154	24	(	(	PUNCT
ejpam-6436	154	25	a	a	DET
ejpam-6436	154	26	×	×	PROPN
ejpam-6436	154	27	b	b	NOUN
ejpam-6436	154	28	)	)	PUNCT
ejpam-6436	154	29	and	and	CCONJ
ejpam-6436	154	30	suppose	suppose	VERB
ejpam-6436	154	31	that	that	SCONJ
ejpam-6436	154	32	(	(	PUNCT
ejpam-6436	154	33	r	r	NOUN
ejpam-6436	154	34	,	,	PUNCT
ejpam-6436	154	35	f)(a	f)(a	NUM
ejpam-6436	154	36	,	,	PUNCT
ejpam-6436	154	37	b	b	NOUN
ejpam-6436	154	38	)	)	PUNCT
ejpam-6436	154	39	≤	≤	NOUN
ejpam-6436	154	40	(	(	PUNCT
ejpam-6436	154	41	r	r	NOUN
ejpam-6436	154	42	,	,	PUNCT
ejpam-6436	154	43	f)(a′	f)(a′	PROPN
ejpam-6436	154	44	,	,	PUNCT
ejpam-6436	154	45	b′	b′	NUM
ejpam-6436	154	46	)	)	PUNCT
ejpam-6436	154	47	.	.	PUNCT
ejpam-6436	155	1	therefore	therefore	ADV
ejpam-6436	155	2	(	(	PUNCT
ejpam-6436	155	3	ra	ra	PROPN
ejpam-6436	155	4	,	,	PUNCT
ejpam-6436	155	5	f(a)b	f(a)b	PROPN
ejpam-6436	155	6	)	)	PUNCT
ejpam-6436	155	7	≤	≤	NOUN
ejpam-6436	155	8	(	(	PUNCT
ejpam-6436	155	9	ra′	ra′	PROPN
ejpam-6436	155	10	,	,	PUNCT
ejpam-6436	155	11	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	155	12	)	)	PUNCT
ejpam-6436	156	1	so	so	ADV
ejpam-6436	156	2	ra	ra	PROPN
ejpam-6436	156	3	≤	≤	ADJ
ejpam-6436	156	4	ra′	ra′	NOUN
ejpam-6436	156	5	and	and	CCONJ
ejpam-6436	156	6	f(a)b	f(a)b	PROPN
ejpam-6436	156	7	≤	≤	NUM
ejpam-6436	156	8	f(a′)b′.	f(a′)b′.	NOUN
ejpam-6436	156	9	from	from	ADP
ejpam-6436	156	10	condition	condition	NOUN
ejpam-6436	156	11	(	(	PUNCT
ejpam-6436	156	12	2	2	X
ejpam-6436	156	13	)	)	PUNCT
ejpam-6436	156	14	we	we	PRON
ejpam-6436	156	15	have	have	VERB
ejpam-6436	156	16	a	a	DET
ejpam-6436	156	17	≤	≤	NOUN
ejpam-6436	156	18	a′.	a′.	NOUN
ejpam-6436	156	19	since	since	SCONJ
ejpam-6436	156	20	a	a	DET
ejpam-6436	156	21	≤	≤	NOUN
ejpam-6436	156	22	a′	a′	NOUN
ejpam-6436	156	23	and	and	CCONJ
ejpam-6436	156	24	f(a)b	f(a)b	PROPN
ejpam-6436	156	25	≤	≤	ADJ
ejpam-6436	156	26	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	156	27	,	,	PUNCT
ejpam-6436	156	28	from	from	ADP
ejpam-6436	156	29	condition	condition	NOUN
ejpam-6436	156	30	(	(	PUNCT
ejpam-6436	156	31	1	1	X
ejpam-6436	156	32	)	)	PUNCT
ejpam-6436	156	33	we	we	PRON
ejpam-6436	156	34	get	get	VERB
ejpam-6436	156	35	b	b	PROPN
ejpam-6436	156	36	≤	≤	X
ejpam-6436	156	37	b′.	b′.	NOUN
ejpam-6436	156	38	hence	hence	ADV
ejpam-6436	156	39	(	(	PUNCT
ejpam-6436	156	40	a	a	PRON
ejpam-6436	156	41	,	,	PUNCT
ejpam-6436	156	42	b	b	NOUN
ejpam-6436	156	43	)	)	PUNCT
ejpam-6436	156	44	≤	≤	NOUN
ejpam-6436	156	45	(	(	PUNCT
ejpam-6436	156	46	a′	a′	PROPN
ejpam-6436	156	47	,	,	PUNCT
ejpam-6436	156	48	b′	b′	NUM
ejpam-6436	156	49	)	)	PUNCT
ejpam-6436	157	1	and	and	CCONJ
ejpam-6436	157	2	so	so	ADV
ejpam-6436	157	3	t	t	PROPN
ejpam-6436	157	4	acts	act	VERB
ejpam-6436	157	5	po	po	NOUN
ejpam-6436	157	6	-	-	PUNCT
ejpam-6436	157	7	injectively	injectively	ADV
ejpam-6436	157	8	on	on	ADP
ejpam-6436	157	9	tc	tc	ADP
ejpam-6436	157	10	,	,	PUNCT
ejpam-6436	157	11	as	as	SCONJ
ejpam-6436	157	12	required	require	VERB
ejpam-6436	157	13	.	.	PUNCT
ejpam-6436	158	1	corollary	corollary	ADJ
ejpam-6436	158	2	2	2	NUM
ejpam-6436	158	3	.	.	PUNCT
ejpam-6436	159	1	the	the	DET
ejpam-6436	159	2	pomonoid	pomonoid	PROPN
ejpam-6436	159	3	t	t	PROPN
ejpam-6436	159	4	acts	act	VERB
ejpam-6436	159	5	po	po	NOUN
ejpam-6436	159	6	-	-	PUNCT
ejpam-6436	159	7	injectively	injectively	ADV
ejpam-6436	159	8	on	on	ADP
ejpam-6436	159	9	tc	tc	PRON
ejpam-6436	159	10	if	if	SCONJ
ejpam-6436	160	1	and	and	CCONJ
ejpam-6436	160	2	only	only	ADV
ejpam-6436	160	3	if	if	SCONJ
ejpam-6436	160	4	r	r	NOUN
ejpam-6436	160	5	acts	act	VERB
ejpam-6436	160	6	po	po	NOUN
ejpam-6436	160	7	-	-	PUNCT
ejpam-6436	160	8	injectively	injectively	ADV
ejpam-6436	160	9	on	on	ADP
ejpam-6436	160	10	a	a	DET
ejpam-6436	160	11	and	and	CCONJ
ejpam-6436	160	12	s	s	NOUN
ejpam-6436	160	13	acts	act	NOUN
ejpam-6436	160	14	po	po	NOUN
ejpam-6436	160	15	-	-	PUNCT
ejpam-6436	160	16	injectively	injectively	ADV
ejpam-6436	160	17	on	on	ADP
ejpam-6436	160	18	b.	b.	PROPN
ejpam-6436	160	19	proof	proof	NOUN
ejpam-6436	160	20	.	.	PUNCT
ejpam-6436	161	1	suppose	suppose	VERB
ejpam-6436	161	2	that	that	SCONJ
ejpam-6436	161	3	t	t	PROPN
ejpam-6436	161	4	acts	act	VERB
ejpam-6436	161	5	po	po	NOUN
ejpam-6436	161	6	-	-	PUNCT
ejpam-6436	161	7	injectively	injectively	ADV
ejpam-6436	161	8	on	on	ADP
ejpam-6436	161	9	tc	tc	NUM
ejpam-6436	161	10	.	.	PUNCT
ejpam-6436	162	1	by	by	ADP
ejpam-6436	162	2	condition	condition	NOUN
ejpam-6436	162	3	(	(	PUNCT
ejpam-6436	162	4	2	2	NUM
ejpam-6436	162	5	)	)	PUNCT
ejpam-6436	162	6	of	of	ADP
ejpam-6436	162	7	theorem	theorem	NOUN
ejpam-6436	162	8	2	2	NUM
ejpam-6436	162	9	,	,	PUNCT
ejpam-6436	162	10	r	r	NOUN
ejpam-6436	162	11	acts	act	VERB
ejpam-6436	162	12	po	po	NOUN
ejpam-6436	162	13	-	-	PUNCT
ejpam-6436	162	14	injectively	injectively	ADV
ejpam-6436	162	15	on	on	ADP
ejpam-6436	162	16	a.	a.	NOUN
ejpam-6436	162	17	take	take	VERB
ejpam-6436	162	18	any	any	DET
ejpam-6436	162	19	s	s	NOUN
ejpam-6436	162	20	∈	∈	NOUN
ejpam-6436	162	21	s	s	X
ejpam-6436	162	22	and	and	CCONJ
ejpam-6436	162	23	b	b	NOUN
ejpam-6436	162	24	,	,	PUNCT
ejpam-6436	162	25	b′	b′	NUM
ejpam-6436	162	26	∈	∈	PROPN
ejpam-6436	162	27	b	b	NOUN
ejpam-6436	162	28	such	such	ADJ
ejpam-6436	162	29	that	that	SCONJ
ejpam-6436	162	30	sb	sb	PROPN
ejpam-6436	162	31	≤	≤	PROPN
ejpam-6436	162	32	sb′.	sb′.	VERB
ejpam-6436	162	33	clearly	clearly	ADV
ejpam-6436	162	34	b.	b.	PROPN
ejpam-6436	162	35	al	al	PROPN
ejpam-6436	162	36	subaiei	subaiei	PROPN
ejpam-6436	163	1	et	et	PROPN
ejpam-6436	163	2	al	al	PROPN
ejpam-6436	163	3	.	.	PUNCT
ejpam-6436	163	4	/	/	SYM
ejpam-6436	163	5	eur	eur	PROPN
ejpam-6436	163	6	.	.	PUNCT
ejpam-6436	164	1	j.	j.	PROPN
ejpam-6436	164	2	pure	pure	PROPN
ejpam-6436	164	3	appl	appl	PROPN
ejpam-6436	164	4	.	.	PROPN
ejpam-6436	164	5	math	math	PROPN
ejpam-6436	164	6	,	,	PUNCT
ejpam-6436	164	7	18	18	NUM
ejpam-6436	164	8	(	(	PUNCT
ejpam-6436	164	9	3	3	NUM
ejpam-6436	164	10	)	)	PUNCT
ejpam-6436	164	11	(	(	PUNCT
ejpam-6436	164	12	2025	2025	NUM
ejpam-6436	164	13	)	)	PUNCT
ejpam-6436	164	14	,	,	PUNCT
ejpam-6436	164	15	6436	6436	NUM
ejpam-6436	164	16	7	7	NUM
ejpam-6436	164	17	of	of	ADP
ejpam-6436	164	18	14	14	NUM
ejpam-6436	164	19	(	(	PUNCT
ejpam-6436	164	20	ra	ra	PROPN
ejpam-6436	164	21	,	,	PUNCT
ejpam-6436	164	22	sb	sb	PROPN
ejpam-6436	164	23	)	)	PUNCT
ejpam-6436	164	24	≤	≤	NOUN
ejpam-6436	164	25	(	(	PUNCT
ejpam-6436	164	26	ra	ra	NOUN
ejpam-6436	164	27	,	,	PUNCT
ejpam-6436	164	28	sb′	sb′	PROPN
ejpam-6436	164	29	)	)	PUNCT
ejpam-6436	164	30	and	and	CCONJ
ejpam-6436	164	31	so	so	ADV
ejpam-6436	164	32	(	(	PUNCT
ejpam-6436	164	33	r	r	NOUN
ejpam-6436	164	34	,	,	PUNCT
ejpam-6436	164	35	cs)(a	cs)(a	PROPN
ejpam-6436	164	36	,	,	PUNCT
ejpam-6436	164	37	b	b	NOUN
ejpam-6436	164	38	)	)	PUNCT
ejpam-6436	164	39	≤	≤	NOUN
ejpam-6436	164	40	(	(	PUNCT
ejpam-6436	164	41	r	r	NOUN
ejpam-6436	164	42	,	,	PUNCT
ejpam-6436	164	43	cs)(a	cs)(a	PROPN
ejpam-6436	164	44	,	,	PUNCT
ejpam-6436	164	45	b	b	NOUN
ejpam-6436	164	46	′	′	NOUN
ejpam-6436	164	47	)	)	PUNCT
ejpam-6436	164	48	.	.	PUNCT
ejpam-6436	165	1	since	since	SCONJ
ejpam-6436	165	2	t	t	PROPN
ejpam-6436	165	3	acts	act	VERB
ejpam-6436	165	4	po	po	NOUN
ejpam-6436	165	5	-	-	PUNCT
ejpam-6436	165	6	injectively	injectively	ADV
ejpam-6436	165	7	on	on	ADP
ejpam-6436	165	8	tc	tc	NUM
ejpam-6436	165	9	,	,	PUNCT
ejpam-6436	165	10	it	it	PRON
ejpam-6436	165	11	follows	follow	VERB
ejpam-6436	165	12	that	that	SCONJ
ejpam-6436	165	13	(	(	PUNCT
ejpam-6436	165	14	a	a	DET
ejpam-6436	165	15	,	,	PUNCT
ejpam-6436	165	16	b	b	NOUN
ejpam-6436	165	17	)	)	PUNCT
ejpam-6436	165	18	≤	≤	NOUN
ejpam-6436	165	19	(	(	PUNCT
ejpam-6436	165	20	a	a	PRON
ejpam-6436	165	21	,	,	PUNCT
ejpam-6436	165	22	b′	b′	NUM
ejpam-6436	165	23	)	)	PUNCT
ejpam-6436	165	24	.	.	PUNCT
ejpam-6436	166	1	thus	thus	ADV
ejpam-6436	166	2	b	b	X
ejpam-6436	166	3	≤	≤	NUM
ejpam-6436	166	4	b′	b′	NUM
ejpam-6436	167	1	and	and	CCONJ
ejpam-6436	167	2	so	so	ADV
ejpam-6436	167	3	s	s	X
ejpam-6436	167	4	acts	act	NOUN
ejpam-6436	167	5	po	po	NOUN
ejpam-6436	167	6	-	-	PUNCT
ejpam-6436	167	7	injectively	injectively	ADV
ejpam-6436	167	8	on	on	ADP
ejpam-6436	167	9	b	b	NOUN
ejpam-6436	167	10	as	as	SCONJ
ejpam-6436	167	11	required	require	VERB
ejpam-6436	167	12	.	.	PUNCT
ejpam-6436	168	1	conversely	conversely	ADV
ejpam-6436	168	2	if	if	SCONJ
ejpam-6436	168	3	r	r	NOUN
ejpam-6436	168	4	acts	act	VERB
ejpam-6436	168	5	po	po	NOUN
ejpam-6436	168	6	-	-	PUNCT
ejpam-6436	168	7	injectively	injectively	ADV
ejpam-6436	168	8	on	on	ADP
ejpam-6436	168	9	a	a	DET
ejpam-6436	168	10	and	and	CCONJ
ejpam-6436	168	11	s	s	NOUN
ejpam-6436	168	12	acts	act	NOUN
ejpam-6436	168	13	po	po	NOUN
ejpam-6436	168	14	-	-	PUNCT
ejpam-6436	168	15	injectively	injectively	ADV
ejpam-6436	168	16	on	on	ADP
ejpam-6436	168	17	b	b	NOUN
ejpam-6436	168	18	then	then	ADV
ejpam-6436	168	19	conditions	condition	NOUN
ejpam-6436	168	20	(	(	PUNCT
ejpam-6436	168	21	1	1	NUM
ejpam-6436	168	22	)	)	PUNCT
ejpam-6436	168	23	and	and	CCONJ
ejpam-6436	168	24	(	(	PUNCT
ejpam-6436	168	25	2	2	X
ejpam-6436	168	26	)	)	PUNCT
ejpam-6436	168	27	of	of	ADP
ejpam-6436	168	28	theorem	theorem	ADJ
ejpam-6436	168	29	2	2	NUM
ejpam-6436	168	30	are	be	AUX
ejpam-6436	168	31	clearly	clearly	ADV
ejpam-6436	168	32	satisfied	satisfied	ADJ
ejpam-6436	168	33	and	and	CCONJ
ejpam-6436	168	34	hence	hence	ADV
ejpam-6436	168	35	t	t	PROPN
ejpam-6436	168	36	acts	act	VERB
ejpam-6436	168	37	po	po	NOUN
ejpam-6436	168	38	-	-	PUNCT
ejpam-6436	168	39	injectively	injectively	ADV
ejpam-6436	168	40	on	on	ADP
ejpam-6436	168	41	tc	tc	NOUN
ejpam-6436	168	42	.	.	PUNCT
ejpam-6436	168	43	proposition	proposition	NOUN
ejpam-6436	168	44	3	3	NUM
ejpam-6436	168	45	.	.	PUNCT
ejpam-6436	169	1	if	if	SCONJ
ejpam-6436	169	2	(	(	PUNCT
ejpam-6436	169	3	r	r	NOUN
ejpam-6436	169	4	,	,	PUNCT
ejpam-6436	169	5	f	f	X
ejpam-6436	169	6	)	)	PUNCT
ejpam-6436	169	7	∈	∈	PROPN
ejpam-6436	169	8	t	t	PROPN
ejpam-6436	169	9	is	be	AUX
ejpam-6436	169	10	left	leave	VERB
ejpam-6436	169	11	po	po	NOUN
ejpam-6436	169	12	-	-	NOUN
ejpam-6436	169	13	cancellable	cancellable	ADJ
ejpam-6436	169	14	then	then	ADV
ejpam-6436	169	15	for	for	ADP
ejpam-6436	169	16	all	all	DET
ejpam-6436	169	17	a	a	DET
ejpam-6436	169	18	∈	∈	PROPN
ejpam-6436	169	19	a	a	DET
ejpam-6436	169	20	s	s	NOUN
ejpam-6436	169	21	,	,	PUNCT
ejpam-6436	169	22	s′	s′	ADJ
ejpam-6436	169	23	∈	∈	PROPN
ejpam-6436	169	24	s	s	NOUN
ejpam-6436	169	25	and	and	CCONJ
ejpam-6436	169	26	p	p	X
ejpam-6436	169	27	,	,	PUNCT
ejpam-6436	169	28	p′	p′	NOUN
ejpam-6436	169	29	∈	∈	PROPN
ejpam-6436	169	30	r	r	NOUN
ejpam-6436	169	31	,	,	PUNCT
ejpam-6436	169	32	rp	rp	NOUN
ejpam-6436	169	33	≤	≤	NUM
ejpam-6436	169	34	rp′	rp′	NOUN
ejpam-6436	169	35	and	and	CCONJ
ejpam-6436	169	36	p	p	PROPN
ejpam-6436	169	37	≰	≰	PROPN
ejpam-6436	169	38	p′	p′	NOUN
ejpam-6436	169	39	imply	imply	VERB
ejpam-6436	169	40	that	that	SCONJ
ejpam-6436	169	41	f(pa)s	f(pa)s	NOUN
ejpam-6436	169	42	≰	≰	PROPN
ejpam-6436	169	43	f(p′a)s′	f(p′a)s′	VERB
ejpam-6436	169	44	.	.	PUNCT
ejpam-6436	170	1	proof	proof	NOUN
ejpam-6436	170	2	.	.	PUNCT
ejpam-6436	171	1	let	let	VERB
ejpam-6436	171	2	(	(	PUNCT
ejpam-6436	171	3	r	r	NOUN
ejpam-6436	171	4	,	,	PUNCT
ejpam-6436	171	5	f	f	X
ejpam-6436	171	6	)	)	PUNCT
ejpam-6436	171	7	∈	∈	PROPN
ejpam-6436	171	8	t	t	PROPN
ejpam-6436	171	9	be	be	AUX
ejpam-6436	171	10	left	leave	VERB
ejpam-6436	171	11	po	po	NOUN
ejpam-6436	171	12	-	-	PUNCT
ejpam-6436	171	13	cancellable	cancellable	ADJ
ejpam-6436	171	14	.	.	PUNCT
ejpam-6436	172	1	assume	assume	VERB
ejpam-6436	172	2	that	that	SCONJ
ejpam-6436	172	3	for	for	ADP
ejpam-6436	172	4	all	all	DET
ejpam-6436	172	5	r	r	NOUN
ejpam-6436	172	6	,	,	PUNCT
ejpam-6436	172	7	p	p	NOUN
ejpam-6436	172	8	,	,	PUNCT
ejpam-6436	172	9	p′	p′	NOUN
ejpam-6436	172	10	∈	∈	PROPN
ejpam-6436	172	11	r	r	NOUN
ejpam-6436	172	12	,	,	PUNCT
ejpam-6436	172	13	rp	rp	NOUN
ejpam-6436	172	14	≤	≤	NUM
ejpam-6436	172	15	rp′	rp′	NOUN
ejpam-6436	172	16	and	and	CCONJ
ejpam-6436	172	17	p	p	PROPN
ejpam-6436	172	18	≰	≰	PROPN
ejpam-6436	172	19	p′	p′	NOUN
ejpam-6436	172	20	and	and	CCONJ
ejpam-6436	172	21	there	there	PRON
ejpam-6436	172	22	exist	exist	VERB
ejpam-6436	172	23	some	some	DET
ejpam-6436	172	24	s	s	NOUN
ejpam-6436	172	25	,	,	PUNCT
ejpam-6436	172	26	s′	s′	PUNCT
ejpam-6436	172	27	∈	∈	PROPN
ejpam-6436	172	28	s	s	VERB
ejpam-6436	172	29	such	such	ADJ
ejpam-6436	172	30	that	that	DET
ejpam-6436	172	31	f(pa)s	f(pa)s	PROPN
ejpam-6436	172	32	≤	≤	NOUN
ejpam-6436	172	33	f(p′a)s′	f(p′a)s′	NOUN
ejpam-6436	172	34	for	for	ADP
ejpam-6436	172	35	all	all	DET
ejpam-6436	172	36	a	a	DET
ejpam-6436	172	37	∈	∈	PROPN
ejpam-6436	172	38	a	a	PRON
ejpam-6436	172	39	.	.	PUNCT
ejpam-6436	173	1	therefore	therefore	ADV
ejpam-6436	173	2	fpcs	fpc	VERB
ejpam-6436	173	3	≤	≤	PROPN
ejpam-6436	173	4	fp′cs′	fp′cs′	PROPN
ejpam-6436	173	5	and	and	CCONJ
ejpam-6436	173	6	so	so	ADV
ejpam-6436	173	7	,	,	PUNCT
ejpam-6436	173	8	(	(	PUNCT
ejpam-6436	173	9	r	r	NOUN
ejpam-6436	173	10	,	,	PUNCT
ejpam-6436	173	11	f)(p	f)(p	NOUN
ejpam-6436	173	12	,	,	PUNCT
ejpam-6436	173	13	cs	cs	ADJ
ejpam-6436	173	14	)	)	PUNCT
ejpam-6436	173	15	=	=	SYM
ejpam-6436	173	16	(	(	PUNCT
ejpam-6436	173	17	rp	rp	NOUN
ejpam-6436	173	18	,	,	PUNCT
ejpam-6436	173	19	fpcs	fpc	NOUN
ejpam-6436	173	20	)	)	PUNCT
ejpam-6436	173	21	≤	≤	NOUN
ejpam-6436	173	22	(	(	PUNCT
ejpam-6436	173	23	rp′	rp′	X
ejpam-6436	173	24	,	,	PUNCT
ejpam-6436	173	25	fp′cs′	fp′cs′	X
ejpam-6436	173	26	)	)	PUNCT
ejpam-6436	173	27	=	=	PUNCT
ejpam-6436	174	1	(	(	PUNCT
ejpam-6436	174	2	r	r	NOUN
ejpam-6436	174	3	,	,	PUNCT
ejpam-6436	174	4	f)(p′	f)(p′	PROPN
ejpam-6436	174	5	,	,	PUNCT
ejpam-6436	174	6	cs′	cs′	NOUN
ejpam-6436	174	7	)	)	PUNCT
ejpam-6436	174	8	.	.	PUNCT
ejpam-6436	175	1	since	since	SCONJ
ejpam-6436	175	2	(	(	PUNCT
ejpam-6436	175	3	r	r	NOUN
ejpam-6436	175	4	,	,	PUNCT
ejpam-6436	175	5	f	f	X
ejpam-6436	175	6	)	)	PUNCT
ejpam-6436	175	7	is	be	AUX
ejpam-6436	175	8	left	leave	VERB
ejpam-6436	175	9	po	po	NOUN
ejpam-6436	175	10	-	-	NOUN
ejpam-6436	175	11	cancellable	cancellable	ADJ
ejpam-6436	175	12	it	it	PRON
ejpam-6436	175	13	follows	follow	VERB
ejpam-6436	175	14	that	that	SCONJ
ejpam-6436	175	15	(	(	PUNCT
ejpam-6436	175	16	p	p	X
ejpam-6436	175	17	,	,	PUNCT
ejpam-6436	175	18	cs	cs	ADJ
ejpam-6436	175	19	)	)	PUNCT
ejpam-6436	175	20	≤	≤	NOUN
ejpam-6436	175	21	(	(	PUNCT
ejpam-6436	175	22	p′	p′	NOUN
ejpam-6436	175	23	,	,	PUNCT
ejpam-6436	175	24	cs′	cs′	X
ejpam-6436	175	25	)	)	PUNCT
ejpam-6436	175	26	.	.	PUNCT
ejpam-6436	176	1	thus	thus	ADV
ejpam-6436	176	2	p	p	X
ejpam-6436	176	3	≤	≤	ADJ
ejpam-6436	176	4	p′	p′	NOUN
ejpam-6436	176	5	and	and	CCONJ
ejpam-6436	176	6	this	this	PRON
ejpam-6436	176	7	is	be	AUX
ejpam-6436	176	8	a	a	DET
ejpam-6436	176	9	contradiction	contradiction	NOUN
ejpam-6436	176	10	.	.	PUNCT
ejpam-6436	177	1	hence	hence	ADV
ejpam-6436	177	2	f(pa)s	f(pa)s	NOUN
ejpam-6436	177	3	≰	≰	PROPN
ejpam-6436	177	4	f(p′a)s′	f(p′a)s′	VERB
ejpam-6436	177	5	for	for	ADP
ejpam-6436	177	6	all	all	DET
ejpam-6436	177	7	s	s	PROPN
ejpam-6436	177	8	,	,	PUNCT
ejpam-6436	177	9	s′	s′	PUNCT
ejpam-6436	177	10	∈	∈	PROPN
ejpam-6436	177	11	s	s	NOUN
ejpam-6436	177	12	and	and	CCONJ
ejpam-6436	177	13	all	all	DET
ejpam-6436	177	14	a	a	DET
ejpam-6436	177	15	∈	∈	NOUN
ejpam-6436	177	16	a.	a.	NOUN
ejpam-6436	177	17	proposition	proposition	NOUN
ejpam-6436	177	18	4	4	NUM
ejpam-6436	177	19	.	.	PUNCT
ejpam-6436	178	1	the	the	DET
ejpam-6436	178	2	element	element	NOUN
ejpam-6436	178	3	(	(	PUNCT
ejpam-6436	178	4	r	r	NOUN
ejpam-6436	178	5	,	,	PUNCT
ejpam-6436	178	6	f	f	X
ejpam-6436	178	7	)	)	PUNCT
ejpam-6436	178	8	∈	∈	PROPN
ejpam-6436	178	9	t	t	PROPN
ejpam-6436	178	10	is	be	AUX
ejpam-6436	178	11	left	leave	VERB
ejpam-6436	178	12	po	po	NOUN
ejpam-6436	178	13	-	-	NOUN
ejpam-6436	178	14	cancellable	cancellable	ADJ
ejpam-6436	178	15	if	if	SCONJ
ejpam-6436	178	16	the	the	DET
ejpam-6436	178	17	following	follow	VERB
ejpam-6436	178	18	two	two	NUM
ejpam-6436	178	19	conditions	condition	NOUN
ejpam-6436	178	20	hold	hold	VERB
ejpam-6436	178	21	:	:	PUNCT
ejpam-6436	178	22	1	1	X
ejpam-6436	178	23	)	)	PUNCT
ejpam-6436	178	24	if	if	SCONJ
ejpam-6436	178	25	a	a	DET
ejpam-6436	178	26	≤	≤	NOUN
ejpam-6436	178	27	a′	a′	NOUN
ejpam-6436	178	28	and	and	CCONJ
ejpam-6436	178	29	f(a)s	f(a)s	VERB
ejpam-6436	178	30	≤	≤	NUM
ejpam-6436	178	31	f(a′)s′	f(a′)s′	NOUN
ejpam-6436	178	32	then	then	ADV
ejpam-6436	178	33	s	s	VERB
ejpam-6436	178	34	≤	≤	ADJ
ejpam-6436	179	1	s′.	s′.	X
ejpam-6436	179	2	2	2	X
ejpam-6436	179	3	)	)	PUNCT
ejpam-6436	179	4	if	if	SCONJ
ejpam-6436	179	5	rp	rp	NOUN
ejpam-6436	179	6	≤	≤	NUM
ejpam-6436	179	7	rp′	rp′	NOUN
ejpam-6436	179	8	and	and	CCONJ
ejpam-6436	179	9	p	p	PROPN
ejpam-6436	179	10	≰	≰	PROPN
ejpam-6436	179	11	p′	p′	NOUN
ejpam-6436	179	12	,	,	PUNCT
ejpam-6436	179	13	then	then	ADV
ejpam-6436	179	14	for	for	ADP
ejpam-6436	179	15	all	all	DET
ejpam-6436	179	16	a	a	DET
ejpam-6436	179	17	∈	∈	PROPN
ejpam-6436	179	18	a	a	DET
ejpam-6436	179	19	,	,	PUNCT
ejpam-6436	179	20	s	s	PROPN
ejpam-6436	179	21	,	,	PUNCT
ejpam-6436	179	22	s′	s′	ADJ
ejpam-6436	179	23	∈	∈	PROPN
ejpam-6436	179	24	s	s	NOUN
ejpam-6436	179	25	,	,	PUNCT
ejpam-6436	179	26	f(pa)s	f(pa)s	PROPN
ejpam-6436	179	27	≰	≰	PROPN
ejpam-6436	179	28	f(p′a)s′	f(p′a)s′	VERB
ejpam-6436	179	29	where	where	SCONJ
ejpam-6436	179	30	p	p	X
ejpam-6436	179	31	,	,	PUNCT
ejpam-6436	179	32	p′	p′	PROPN
ejpam-6436	179	33	∈	∈	PROPN
ejpam-6436	179	34	r.	r.	NOUN
ejpam-6436	179	35	proof	proof	NOUN
ejpam-6436	179	36	.	.	PUNCT
ejpam-6436	180	1	assume	assume	VERB
ejpam-6436	180	2	the	the	DET
ejpam-6436	180	3	two	two	NUM
ejpam-6436	180	4	conditions	condition	NOUN
ejpam-6436	180	5	are	be	AUX
ejpam-6436	180	6	satisfied	satisfied	ADJ
ejpam-6436	180	7	and	and	CCONJ
ejpam-6436	180	8	let	let	VERB
ejpam-6436	180	9	(	(	PUNCT
ejpam-6436	180	10	r	r	NOUN
ejpam-6436	180	11	,	,	PUNCT
ejpam-6436	180	12	f)(p	f)(p	NOUN
ejpam-6436	180	13	,	,	PUNCT
ejpam-6436	180	14	g1	g1	NOUN
ejpam-6436	180	15	)	)	PUNCT
ejpam-6436	180	16	≤	≤	NOUN
ejpam-6436	180	17	(	(	PUNCT
ejpam-6436	180	18	r	r	NOUN
ejpam-6436	180	19	,	,	PUNCT
ejpam-6436	180	20	f)(p′	f)(p′	PROPN
ejpam-6436	180	21	,	,	PUNCT
ejpam-6436	180	22	g2	g2	PROPN
ejpam-6436	180	23	)	)	PUNCT
ejpam-6436	180	24	.	.	PUNCT
ejpam-6436	181	1	therefore	therefore	ADV
ejpam-6436	181	2	,	,	PUNCT
ejpam-6436	181	3	(	(	PUNCT
ejpam-6436	181	4	rp	rp	NOUN
ejpam-6436	181	5	,	,	PUNCT
ejpam-6436	181	6	fpg1	fpg1	NOUN
ejpam-6436	181	7	)	)	PUNCT
ejpam-6436	181	8	≤	≤	NOUN
ejpam-6436	181	9	(	(	PUNCT
ejpam-6436	181	10	rp′	rp′	X
ejpam-6436	181	11	,	,	PUNCT
ejpam-6436	181	12	fp′g2	fp′g2	NUM
ejpam-6436	181	13	)	)	PUNCT
ejpam-6436	181	14	and	and	CCONJ
ejpam-6436	181	15	so	so	ADV
ejpam-6436	181	16	rp	rp	NOUN
ejpam-6436	181	17	≤	≤	NUM
ejpam-6436	181	18	rp′	rp′	NOUN
ejpam-6436	181	19	and	and	CCONJ
ejpam-6436	181	20	fpg1	fpg1	VERB
ejpam-6436	181	21	≤	≤	NUM
ejpam-6436	181	22	fp′g2	fp′g2	NUM
ejpam-6436	181	23	.	.	PUNCT
ejpam-6436	182	1	if	if	SCONJ
ejpam-6436	182	2	p	p	PROPN
ejpam-6436	182	3	≰	≰	PROPN
ejpam-6436	182	4	p′	p′	NOUN
ejpam-6436	182	5	then	then	ADV
ejpam-6436	182	6	from	from	ADP
ejpam-6436	182	7	condition	condition	NOUN
ejpam-6436	182	8	(	(	PUNCT
ejpam-6436	182	9	2	2	X
ejpam-6436	182	10	)	)	PUNCT
ejpam-6436	182	11	it	it	PRON
ejpam-6436	182	12	follows	follow	VERB
ejpam-6436	182	13	that	that	SCONJ
ejpam-6436	182	14	f(pa)s	f(pa)s	PROPN
ejpam-6436	182	15	≰	≰	NOUN
ejpam-6436	182	16	f(p′a)s′	f(p′a)s′	VERB
ejpam-6436	182	17	for	for	ADP
ejpam-6436	182	18	all	all	DET
ejpam-6436	182	19	a	a	DET
ejpam-6436	182	20	∈	∈	PROPN
ejpam-6436	182	21	a	a	PRON
ejpam-6436	182	22	and	and	CCONJ
ejpam-6436	182	23	s	s	NOUN
ejpam-6436	182	24	,	,	PUNCT
ejpam-6436	182	25	s′	s′	PUNCT
ejpam-6436	182	26	∈	∈	PROPN
ejpam-6436	182	27	s.	s.	PROPN
ejpam-6436	182	28	since	since	SCONJ
ejpam-6436	182	29	g1(a	g1(a	PROPN
ejpam-6436	182	30	)	)	PUNCT
ejpam-6436	182	31	,	,	PUNCT
ejpam-6436	182	32	g2(a	g2(a	NOUN
ejpam-6436	182	33	)	)	PUNCT
ejpam-6436	182	34	∈	∈	PROPN
ejpam-6436	182	35	s	s	PROPN
ejpam-6436	182	36	,	,	PUNCT
ejpam-6436	182	37	the	the	DET
ejpam-6436	182	38	condition	condition	NOUN
ejpam-6436	182	39	f(pa)s	f(pa)s	NOUN
ejpam-6436	182	40	≰	≰	PROPN
ejpam-6436	182	41	f(p′a)s′	f(p′a)s′	VERB
ejpam-6436	182	42	contradictions	contradiction	NOUN
ejpam-6436	182	43	the	the	DET
ejpam-6436	182	44	assumption	assumption	NOUN
ejpam-6436	182	45	fpg1	fpg1	VERB
ejpam-6436	182	46	≤	≤	NUM
ejpam-6436	182	47	fp′g2	fp′g2	PROPN
ejpam-6436	182	48	and	and	CCONJ
ejpam-6436	182	49	so	so	ADV
ejpam-6436	182	50	we	we	PRON
ejpam-6436	182	51	must	must	AUX
ejpam-6436	182	52	have	have	VERB
ejpam-6436	182	53	p	p	NOUN
ejpam-6436	182	54	≤	≤	NUM
ejpam-6436	182	55	p′.	p′.	NOUN
ejpam-6436	182	56	also	also	ADV
ejpam-6436	182	57	,	,	PUNCT
ejpam-6436	182	58	since	since	SCONJ
ejpam-6436	182	59	pa	pa	PROPN
ejpam-6436	182	60	≤	≤	PROPN
ejpam-6436	182	61	p′a	p′a	NOUN
ejpam-6436	182	62	and	and	CCONJ
ejpam-6436	182	63	fpg1(a	fpg1(a	NOUN
ejpam-6436	182	64	)	)	PUNCT
ejpam-6436	182	65	=	=	SYM
ejpam-6436	182	66	f(pa)g1(a	f(pa)g1(a	NOUN
ejpam-6436	182	67	)	)	PUNCT
ejpam-6436	182	68	≤	≤	NUM
ejpam-6436	182	69	f(p′a)g2(a	f(p′a)g2(a	NOUN
ejpam-6436	182	70	)	)	PUNCT
ejpam-6436	183	1	=	=	SYM
ejpam-6436	183	2	fp′g2(a	fp′g2(a	NOUN
ejpam-6436	183	3	)	)	PUNCT
ejpam-6436	184	1	for	for	ADP
ejpam-6436	184	2	all	all	DET
ejpam-6436	184	3	a	a	DET
ejpam-6436	184	4	∈	∈	PROPN
ejpam-6436	184	5	a	a	DET
ejpam-6436	184	6	so	so	ADV
ejpam-6436	184	7	from	from	ADP
ejpam-6436	184	8	condition	condition	NOUN
ejpam-6436	184	9	(	(	PUNCT
ejpam-6436	184	10	1	1	X
ejpam-6436	184	11	)	)	PUNCT
ejpam-6436	184	12	we	we	PRON
ejpam-6436	184	13	get	get	VERB
ejpam-6436	184	14	that	that	PRON
ejpam-6436	184	15	g1	g1	VERB
ejpam-6436	184	16	≤	≤	PUNCT
ejpam-6436	184	17	g2	g2	PROPN
ejpam-6436	184	18	.	.	PUNCT
ejpam-6436	185	1	hence	hence	ADV
ejpam-6436	185	2	(	(	PUNCT
ejpam-6436	185	3	r	r	NOUN
ejpam-6436	185	4	,	,	PUNCT
ejpam-6436	185	5	f	f	X
ejpam-6436	185	6	)	)	PUNCT
ejpam-6436	185	7	is	be	AUX
ejpam-6436	185	8	left	leave	VERB
ejpam-6436	185	9	po	po	NOUN
ejpam-6436	185	10	-	-	NOUN
ejpam-6436	185	11	cancellable	cancellable	ADJ
ejpam-6436	185	12	,	,	PUNCT
ejpam-6436	185	13	as	as	SCONJ
ejpam-6436	185	14	required	require	VERB
ejpam-6436	185	15	.	.	PUNCT
ejpam-6436	186	1	theorem	theorem	NOUN
ejpam-6436	186	2	3	3	NUM
ejpam-6436	186	3	.	.	PUNCT
ejpam-6436	187	1	the	the	DET
ejpam-6436	187	2	wreath	wreath	NOUN
ejpam-6436	187	3	product	product	NOUN
ejpam-6436	187	4	t	t	NOUN
ejpam-6436	187	5	is	be	AUX
ejpam-6436	187	6	left	leave	VERB
ejpam-6436	187	7	po	po	NOUN
ejpam-6436	187	8	-	-	NOUN
ejpam-6436	187	9	cancellative	cancellative	ADJ
ejpam-6436	187	10	if	if	SCONJ
ejpam-6436	188	1	and	and	CCONJ
ejpam-6436	188	2	only	only	ADV
ejpam-6436	188	3	if	if	SCONJ
ejpam-6436	188	4	r	r	NOUN
ejpam-6436	188	5	is	be	AUX
ejpam-6436	188	6	left	leave	VERB
ejpam-6436	188	7	pocancellable	pocancellable	ADJ
ejpam-6436	188	8	and	and	CCONJ
ejpam-6436	188	9	s	s	NOUN
ejpam-6436	188	10	is	be	AUX
ejpam-6436	188	11	strongly	strongly	ADV
ejpam-6436	188	12	left	leave	VERB
ejpam-6436	188	13	po	po	NOUN
ejpam-6436	188	14	-	-	PUNCT
ejpam-6436	188	15	cancellative	cancellative	ADJ
ejpam-6436	188	16	.	.	PUNCT
ejpam-6436	189	1	proof	proof	NOUN
ejpam-6436	189	2	.	.	PUNCT
ejpam-6436	190	1	suppose	suppose	VERB
ejpam-6436	190	2	that	that	SCONJ
ejpam-6436	190	3	t	t	PROPN
ejpam-6436	190	4	is	be	AUX
ejpam-6436	190	5	left	leave	VERB
ejpam-6436	190	6	po	po	NOUN
ejpam-6436	190	7	-	-	PUNCT
ejpam-6436	190	8	cancellative	cancellative	ADJ
ejpam-6436	190	9	.	.	PUNCT
ejpam-6436	191	1	therefore	therefore	ADV
ejpam-6436	191	2	for	for	SCONJ
ejpam-6436	191	3	all	all	DET
ejpam-6436	191	4	(	(	PUNCT
ejpam-6436	191	5	r	r	NOUN
ejpam-6436	191	6	,	,	PUNCT
ejpam-6436	191	7	f	f	NOUN
ejpam-6436	191	8	)	)	PUNCT
ejpam-6436	191	9	,	,	PUNCT
ejpam-6436	191	10	(	(	PUNCT
ejpam-6436	191	11	p	p	X
ejpam-6436	191	12	,	,	PUNCT
ejpam-6436	191	13	g	g	NOUN
ejpam-6436	191	14	)	)	PUNCT
ejpam-6436	191	15	and	and	CCONJ
ejpam-6436	191	16	(	(	PUNCT
ejpam-6436	191	17	p′	p′	NOUN
ejpam-6436	191	18	,	,	PUNCT
ejpam-6436	191	19	g′	g′	NOUN
ejpam-6436	191	20	)	)	PUNCT
ejpam-6436	191	21	∈	∈	PROPN
ejpam-6436	191	22	t	t	VERB
ejpam-6436	191	23	the	the	DET
ejpam-6436	191	24	inequality	inequality	NOUN
ejpam-6436	191	25	(	(	PUNCT
ejpam-6436	191	26	r	r	NOUN
ejpam-6436	191	27	,	,	PUNCT
ejpam-6436	191	28	f)(p	f)(p	NOUN
ejpam-6436	191	29	,	,	PUNCT
ejpam-6436	191	30	g	g	NOUN
ejpam-6436	191	31	)	)	PUNCT
ejpam-6436	191	32	≤	≤	NOUN
ejpam-6436	191	33	(	(	PUNCT
ejpam-6436	191	34	r	r	NOUN
ejpam-6436	191	35	,	,	PUNCT
ejpam-6436	191	36	f)(p′	f)(p′	PROPN
ejpam-6436	191	37	,	,	PUNCT
ejpam-6436	191	38	g′	g′	NOUN
ejpam-6436	191	39	)	)	PUNCT
ejpam-6436	191	40	implies	imply	VERB
ejpam-6436	191	41	that	that	SCONJ
ejpam-6436	191	42	rp	rp	NOUN
ejpam-6436	191	43	≤	≤	NUM
ejpam-6436	191	44	rp′	rp′	NOUN
ejpam-6436	191	45	and	and	CCONJ
ejpam-6436	191	46	fpg	fpg	PROPN
ejpam-6436	191	47	≤	≤	PROPN
ejpam-6436	191	48	fp′g	fp′g	VERB
ejpam-6436	191	49	′.	′.	NOUN
ejpam-6436	191	50	by	by	ADP
ejpam-6436	191	51	proposition	proposition	NOUN
ejpam-6436	191	52	3	3	NUM
ejpam-6436	191	53	we	we	PRON
ejpam-6436	191	54	have	have	VERB
ejpam-6436	191	55	p	p	ADJ
ejpam-6436	191	56	≤	≤	NUM
ejpam-6436	191	57	p′	p′	NOUN
ejpam-6436	191	58	,	,	PUNCT
ejpam-6436	191	59	proving	prove	VERB
ejpam-6436	191	60	that	that	SCONJ
ejpam-6436	191	61	r	r	NOUN
ejpam-6436	191	62	is	be	AUX
ejpam-6436	191	63	left	leave	VERB
ejpam-6436	191	64	po	po	NOUN
ejpam-6436	191	65	-	-	PUNCT
ejpam-6436	191	66	cancellative	cancellative	ADJ
ejpam-6436	191	67	.	.	PUNCT
ejpam-6436	192	1	let	let	VERB
ejpam-6436	192	2	s	s	NOUN
ejpam-6436	192	3	,	,	PUNCT
ejpam-6436	192	4	s′	s′	PROPN
ejpam-6436	192	5	,	,	PUNCT
ejpam-6436	192	6	t	t	PROPN
ejpam-6436	192	7	,	,	PUNCT
ejpam-6436	192	8	t′	t′	NUM
ejpam-6436	192	9	∈	∈	NOUN
ejpam-6436	192	10	s	s	VERB
ejpam-6436	192	11	such	such	ADJ
ejpam-6436	192	12	that	that	PRON
ejpam-6436	192	13	s	s	VERB
ejpam-6436	192	14	≤	≤	NOUN
ejpam-6436	192	15	s′	s′	NUM
ejpam-6436	192	16	and	and	CCONJ
ejpam-6436	192	17	st	st	PROPN
ejpam-6436	192	18	≤	≤	PROPN
ejpam-6436	192	19	s′t′.	s′t′.	PROPN
ejpam-6436	192	20	by	by	ADP
ejpam-6436	192	21	taking	take	VERB
ejpam-6436	192	22	fp	fp	X
ejpam-6436	192	23	=	=	SYM
ejpam-6436	192	24	cs	cs	PROPN
ejpam-6436	192	25	,	,	PUNCT
ejpam-6436	192	26	fp′	fp′	NOUN
ejpam-6436	193	1	=	=	SYM
ejpam-6436	193	2	cs′	cs′	X
ejpam-6436	193	3	,	,	PUNCT
ejpam-6436	193	4	g	g	PROPN
ejpam-6436	193	5	=	=	SYM
ejpam-6436	193	6	ct	ct	PROPN
ejpam-6436	193	7	and	and	CCONJ
ejpam-6436	193	8	g′	g′	NOUN
ejpam-6436	193	9	=	=	SYM
ejpam-6436	193	10	ct′	ct′	NOUN
ejpam-6436	193	11	and	and	CCONJ
ejpam-6436	193	12	using	use	VERB
ejpam-6436	193	13	condition	condition	NOUN
ejpam-6436	193	14	(	(	PUNCT
ejpam-6436	193	15	1	1	NUM
ejpam-6436	193	16	)	)	PUNCT
ejpam-6436	193	17	of	of	ADP
ejpam-6436	193	18	propostion	propostion	NOUN
ejpam-6436	193	19	2	2	NUM
ejpam-6436	193	20	,	,	PUNCT
ejpam-6436	193	21	we	we	PRON
ejpam-6436	193	22	have	have	VERB
ejpam-6436	193	23	t	t	NOUN
ejpam-6436	193	24	≤	≤	NUM
ejpam-6436	193	25	t′	t′	NUM
ejpam-6436	193	26	,	,	PUNCT
ejpam-6436	193	27	proving	prove	VERB
ejpam-6436	193	28	that	that	SCONJ
ejpam-6436	193	29	s	s	VERB
ejpam-6436	193	30	is	be	AUX
ejpam-6436	193	31	strongly	strongly	ADV
ejpam-6436	193	32	left	leave	VERB
ejpam-6436	193	33	po	po	NOUN
ejpam-6436	193	34	-	-	PUNCT
ejpam-6436	193	35	cancellative	cancellative	ADJ
ejpam-6436	193	36	.	.	PUNCT
ejpam-6436	194	1	conversely	conversely	ADV
ejpam-6436	194	2	assume	assume	VERB
ejpam-6436	194	3	that	that	SCONJ
ejpam-6436	194	4	r	r	NOUN
ejpam-6436	194	5	is	be	AUX
ejpam-6436	194	6	left	leave	VERB
ejpam-6436	194	7	po	po	NOUN
ejpam-6436	194	8	-	-	ADJ
ejpam-6436	194	9	cancellative	cancellative	ADJ
ejpam-6436	194	10	and	and	CCONJ
ejpam-6436	194	11	s	s	VERB
ejpam-6436	194	12	is	be	AUX
ejpam-6436	194	13	strongly	strongly	ADV
ejpam-6436	194	14	left	leave	VERB
ejpam-6436	194	15	po	po	NOUN
ejpam-6436	194	16	-	-	PUNCT
ejpam-6436	194	17	cancellative	cancellative	ADJ
ejpam-6436	194	18	.	.	PUNCT
ejpam-6436	195	1	let	let	VERB
ejpam-6436	195	2	(	(	PUNCT
ejpam-6436	195	3	r	r	NOUN
ejpam-6436	195	4	,	,	PUNCT
ejpam-6436	195	5	f	f	NOUN
ejpam-6436	195	6	)	)	PUNCT
ejpam-6436	195	7	,	,	PUNCT
ejpam-6436	195	8	(	(	PUNCT
ejpam-6436	195	9	p	p	X
ejpam-6436	195	10	,	,	PUNCT
ejpam-6436	195	11	g	g	NOUN
ejpam-6436	195	12	)	)	PUNCT
ejpam-6436	195	13	and	and	CCONJ
ejpam-6436	195	14	(	(	PUNCT
ejpam-6436	195	15	p′	p′	NOUN
ejpam-6436	195	16	,	,	PUNCT
ejpam-6436	195	17	g′	g′	NOUN
ejpam-6436	195	18	)	)	PUNCT
ejpam-6436	195	19	∈	∈	PROPN
ejpam-6436	195	20	t	t	NOUN
ejpam-6436	196	1	=	=	PUNCT
ejpam-6436	196	2	r	r	NOUN
ejpam-6436	196	3	×	×	PROPN
ejpam-6436	196	4	f	f	X
ejpam-6436	196	5	(	(	PUNCT
ejpam-6436	196	6	a	a	PRON
ejpam-6436	196	7	,	,	PUNCT
ejpam-6436	196	8	s	s	PART
ejpam-6436	196	9	)	)	PUNCT
ejpam-6436	196	10	be	be	AUX
ejpam-6436	196	11	such	such	ADJ
ejpam-6436	196	12	that	that	SCONJ
ejpam-6436	196	13	(	(	PUNCT
ejpam-6436	196	14	r	r	NOUN
ejpam-6436	196	15	,	,	PUNCT
ejpam-6436	196	16	f)(p	f)(p	NOUN
ejpam-6436	196	17	,	,	PUNCT
ejpam-6436	196	18	g	g	NOUN
ejpam-6436	196	19	)	)	PUNCT
ejpam-6436	196	20	≤	≤	NOUN
ejpam-6436	196	21	(	(	PUNCT
ejpam-6436	196	22	r	r	NOUN
ejpam-6436	196	23	,	,	PUNCT
ejpam-6436	196	24	f)(p′	f)(p′	PROPN
ejpam-6436	196	25	,	,	PUNCT
ejpam-6436	196	26	g′	g′	NOUN
ejpam-6436	196	27	)	)	PUNCT
ejpam-6436	196	28	.	.	PUNCT
ejpam-6436	197	1	this	this	PRON
ejpam-6436	197	2	implies	imply	VERB
ejpam-6436	197	3	rp	rp	NOUN
ejpam-6436	197	4	≤	≤	NUM
ejpam-6436	197	5	rp′	rp′	NOUN
ejpam-6436	197	6	and	and	CCONJ
ejpam-6436	197	7	fpg	fpg	PROPN
ejpam-6436	197	8	≤	≤	PROPN
ejpam-6436	197	9	fp′g	fp′g	NOUN
ejpam-6436	197	10	′.	′.	NOUN
ejpam-6436	197	11	left	leave	VERB
ejpam-6436	197	12	po	po	NOUN
ejpam-6436	197	13	-	-	ADJ
ejpam-6436	197	14	cancellative	cancellative	ADJ
ejpam-6436	197	15	property	property	NOUN
ejpam-6436	197	16	of	of	ADP
ejpam-6436	197	17	r	r	NOUN
ejpam-6436	197	18	forces	force	NOUN
ejpam-6436	197	19	p	p	NOUN
ejpam-6436	197	20	≤	≤	NUM
ejpam-6436	197	21	p′.	p′.	NOUN
ejpam-6436	197	22	for	for	ADP
ejpam-6436	197	23	all	all	DET
ejpam-6436	197	24	a	a	DET
ejpam-6436	197	25	∈	∈	PROPN
ejpam-6436	197	26	a	a	DET
ejpam-6436	197	27	,	,	PUNCT
ejpam-6436	197	28	pa	pa	PROPN
ejpam-6436	197	29	≤	≤	PROPN
ejpam-6436	197	30	p′a	p′a	NOUN
ejpam-6436	197	31	and	and	CCONJ
ejpam-6436	197	32	since	since	SCONJ
ejpam-6436	197	33	f	f	PROPN
ejpam-6436	197	34	is	be	AUX
ejpam-6436	197	35	monotone	monotone	ADJ
ejpam-6436	197	36	it	it	PRON
ejpam-6436	197	37	follows	follow	VERB
ejpam-6436	197	38	that	that	SCONJ
ejpam-6436	197	39	f(pa	f(pa	NOUN
ejpam-6436	197	40	)	)	PUNCT
ejpam-6436	197	41	≤	≤	NUM
ejpam-6436	197	42	f(p′a	f(p′a	NOUN
ejpam-6436	197	43	)	)	PUNCT
ejpam-6436	197	44	.	.	PUNCT
ejpam-6436	198	1	from	from	ADP
ejpam-6436	198	2	fpg	fpg	PROPN
ejpam-6436	198	3	≤	≤	PROPN
ejpam-6436	198	4	fp′g	fp′g	PROPN
ejpam-6436	198	5	′	′	NUM
ejpam-6436	198	6	b.	b.	PROPN
ejpam-6436	198	7	al	al	PROPN
ejpam-6436	198	8	subaiei	subaiei	PROPN
ejpam-6436	198	9	et	et	PROPN
ejpam-6436	198	10	al	al	PROPN
ejpam-6436	198	11	.	.	PUNCT
ejpam-6436	198	12	/	/	SYM
ejpam-6436	198	13	eur	eur	PROPN
ejpam-6436	198	14	.	.	PUNCT
ejpam-6436	199	1	j.	j.	PROPN
ejpam-6436	199	2	pure	pure	PROPN
ejpam-6436	199	3	appl	appl	PROPN
ejpam-6436	199	4	.	.	PROPN
ejpam-6436	199	5	math	math	PROPN
ejpam-6436	199	6	,	,	PUNCT
ejpam-6436	199	7	18	18	NUM
ejpam-6436	199	8	(	(	PUNCT
ejpam-6436	199	9	3	3	NUM
ejpam-6436	199	10	)	)	PUNCT
ejpam-6436	199	11	(	(	PUNCT
ejpam-6436	199	12	2025	2025	NUM
ejpam-6436	199	13	)	)	PUNCT
ejpam-6436	199	14	,	,	PUNCT
ejpam-6436	199	15	6436	6436	NUM
ejpam-6436	199	16	8	8	NUM
ejpam-6436	199	17	of	of	ADP
ejpam-6436	199	18	14	14	NUM
ejpam-6436	199	19	we	we	PRON
ejpam-6436	199	20	have	have	VERB
ejpam-6436	199	21	f(pa)g(a	f(pa)g(a	PROPN
ejpam-6436	199	22	)	)	PUNCT
ejpam-6436	199	23	≤	≤	NOUN
ejpam-6436	199	24	f(p′a)g′(a	f(p′a)g′(a	PROPN
ejpam-6436	199	25	)	)	PUNCT
ejpam-6436	199	26	for	for	ADP
ejpam-6436	199	27	all	all	DET
ejpam-6436	199	28	a	a	DET
ejpam-6436	199	29	∈	∈	NOUN
ejpam-6436	199	30	a.	a.	NOUN
ejpam-6436	199	31	since	since	SCONJ
ejpam-6436	199	32	s	s	NOUN
ejpam-6436	199	33	is	be	AUX
ejpam-6436	199	34	strongly	strongly	ADV
ejpam-6436	199	35	left	leave	VERB
ejpam-6436	199	36	po	po	NOUN
ejpam-6436	199	37	-	-	PUNCT
ejpam-6436	199	38	cancellative	cancellative	ADJ
ejpam-6436	199	39	g(a	g(a	PROPN
ejpam-6436	199	40	)	)	PUNCT
ejpam-6436	199	41	≤	≤	NUM
ejpam-6436	200	1	g′(a	g′(a	PROPN
ejpam-6436	200	2	)	)	PUNCT
ejpam-6436	200	3	for	for	ADP
ejpam-6436	200	4	all	all	DET
ejpam-6436	200	5	a	a	DET
ejpam-6436	200	6	∈	∈	PROPN
ejpam-6436	200	7	a	a	PRON
ejpam-6436	200	8	and	and	CCONJ
ejpam-6436	200	9	so	so	ADV
ejpam-6436	200	10	g	g	NOUN
ejpam-6436	200	11	≤	≤	ADJ
ejpam-6436	200	12	g′.	g′.	NOUN
ejpam-6436	200	13	hence	hence	ADV
ejpam-6436	200	14	(	(	PUNCT
ejpam-6436	200	15	p	p	X
ejpam-6436	200	16	,	,	PUNCT
ejpam-6436	200	17	g	g	NOUN
ejpam-6436	200	18	)	)	PUNCT
ejpam-6436	200	19	≤	≤	NOUN
ejpam-6436	200	20	(	(	PUNCT
ejpam-6436	200	21	p′	p′	NOUN
ejpam-6436	200	22	,	,	PUNCT
ejpam-6436	200	23	g′	g′	NOUN
ejpam-6436	200	24	)	)	PUNCT
ejpam-6436	200	25	as	as	SCONJ
ejpam-6436	200	26	required	require	VERB
ejpam-6436	200	27	.	.	PUNCT
ejpam-6436	201	1	theorem	theorem	NOUN
ejpam-6436	201	2	3	3	NUM
ejpam-6436	201	3	is	be	AUX
ejpam-6436	201	4	only	only	ADV
ejpam-6436	201	5	true	true	ADJ
ejpam-6436	201	6	for	for	ADP
ejpam-6436	201	7	left	leave	VERB
ejpam-6436	201	8	po	po	NOUN
ejpam-6436	201	9	-	-	NOUN
ejpam-6436	201	10	cancellative	cancellative	ADJ
ejpam-6436	201	11	.	.	PUNCT
ejpam-6436	202	1	for	for	ADP
ejpam-6436	202	2	the	the	DET
ejpam-6436	202	3	right	right	ADJ
ejpam-6436	202	4	po	po	NOUN
ejpam-6436	202	5	-	-	NOUN
ejpam-6436	202	6	cancellative	cancellative	ADJ
ejpam-6436	202	7	we	we	PRON
ejpam-6436	202	8	have	have	VERB
ejpam-6436	202	9	the	the	DET
ejpam-6436	202	10	following	following	ADJ
ejpam-6436	202	11	result	result	NOUN
ejpam-6436	202	12	whose	whose	DET
ejpam-6436	202	13	proof	proof	NOUN
ejpam-6436	202	14	is	be	AUX
ejpam-6436	202	15	straightforward	straightforward	ADJ
ejpam-6436	202	16	and	and	CCONJ
ejpam-6436	202	17	so	so	ADV
ejpam-6436	202	18	we	we	PRON
ejpam-6436	202	19	omitted	omit	VERB
ejpam-6436	202	20	it	it	PRON
ejpam-6436	202	21	.	.	PUNCT
ejpam-6436	203	1	proposition	proposition	NOUN
ejpam-6436	203	2	5	5	NUM
ejpam-6436	203	3	.	.	PUNCT
ejpam-6436	204	1	if	if	SCONJ
ejpam-6436	204	2	the	the	DET
ejpam-6436	204	3	element	element	NOUN
ejpam-6436	204	4	(	(	PUNCT
ejpam-6436	204	5	r	r	NOUN
ejpam-6436	204	6	,	,	PUNCT
ejpam-6436	204	7	f	f	X
ejpam-6436	204	8	)	)	PUNCT
ejpam-6436	204	9	∈	∈	PROPN
ejpam-6436	204	10	t	t	PROPN
ejpam-6436	204	11	is	be	AUX
ejpam-6436	204	12	right	right	ADJ
ejpam-6436	204	13	po	po	NOUN
ejpam-6436	204	14	-	-	NOUN
ejpam-6436	204	15	cancellable	cancellable	ADJ
ejpam-6436	204	16	then	then	ADV
ejpam-6436	204	17	r	r	NOUN
ejpam-6436	204	18	is	be	AUX
ejpam-6436	204	19	right	right	ADV
ejpam-6436	204	20	pocancellable	pocancellable	ADJ
ejpam-6436	204	21	in	in	ADP
ejpam-6436	204	22	r.	r.	PROPN
ejpam-6436	204	23	proposition	proposition	NOUN
ejpam-6436	204	24	6	6	NUM
ejpam-6436	204	25	.	.	PUNCT
ejpam-6436	205	1	if	if	SCONJ
ejpam-6436	205	2	r	r	NOUN
ejpam-6436	205	3	∈	∈	PROPN
ejpam-6436	205	4	r	r	NOUN
ejpam-6436	205	5	is	be	AUX
ejpam-6436	205	6	not	not	PART
ejpam-6436	205	7	left	leave	VERB
ejpam-6436	205	8	po	po	NOUN
ejpam-6436	205	9	-	-	NOUN
ejpam-6436	205	10	cancellable	cancellable	ADJ
ejpam-6436	205	11	then	then	ADV
ejpam-6436	205	12	(	(	PUNCT
ejpam-6436	205	13	r	r	NOUN
ejpam-6436	205	14	,	,	PUNCT
ejpam-6436	205	15	c1	c1	NOUN
ejpam-6436	205	16	)	)	PUNCT
ejpam-6436	205	17	∈	∈	PROPN
ejpam-6436	205	18	t	t	PROPN
ejpam-6436	205	19	is	be	AUX
ejpam-6436	205	20	not	not	PART
ejpam-6436	205	21	left	leave	VERB
ejpam-6436	205	22	po	po	NOUN
ejpam-6436	205	23	-	-	NOUN
ejpam-6436	205	24	cancellable	cancellable	ADJ
ejpam-6436	205	25	.	.	PUNCT
ejpam-6436	206	1	proof	proof	NOUN
ejpam-6436	206	2	.	.	PUNCT
ejpam-6436	207	1	assume	assume	VERB
ejpam-6436	207	2	that	that	SCONJ
ejpam-6436	207	3	r	r	NOUN
ejpam-6436	207	4	∈	∈	NOUN
ejpam-6436	207	5	r	r	NOUN
ejpam-6436	207	6	is	be	AUX
ejpam-6436	207	7	not	not	PART
ejpam-6436	207	8	left	leave	VERB
ejpam-6436	207	9	po	po	NOUN
ejpam-6436	207	10	-	-	NOUN
ejpam-6436	207	11	cancellable	cancellable	ADJ
ejpam-6436	207	12	and	and	CCONJ
ejpam-6436	207	13	(	(	PUNCT
ejpam-6436	207	14	r	r	NOUN
ejpam-6436	207	15	,	,	PUNCT
ejpam-6436	207	16	c1	c1	NOUN
ejpam-6436	207	17	)	)	PUNCT
ejpam-6436	207	18	is	be	AUX
ejpam-6436	207	19	left	leave	VERB
ejpam-6436	207	20	po	po	NOUN
ejpam-6436	207	21	-	-	NOUN
ejpam-6436	207	22	cancellable	cancellable	ADJ
ejpam-6436	207	23	.	.	PUNCT
ejpam-6436	208	1	then	then	ADV
ejpam-6436	208	2	there	there	PRON
ejpam-6436	208	3	exist	exist	VERB
ejpam-6436	208	4	p	p	PRON
ejpam-6436	208	5	,	,	PUNCT
ejpam-6436	208	6	p′	p′	NOUN
ejpam-6436	208	7	∈	∈	NOUN
ejpam-6436	208	8	r	r	NOUN
ejpam-6436	208	9	such	such	ADJ
ejpam-6436	208	10	that	that	DET
ejpam-6436	208	11	rp	rp	NOUN
ejpam-6436	208	12	≤	≤	NUM
ejpam-6436	208	13	rp′	rp′	NOUN
ejpam-6436	208	14	and	and	CCONJ
ejpam-6436	208	15	p	p	PROPN
ejpam-6436	208	16	≰	≰	PROPN
ejpam-6436	208	17	p′.	p′.	NOUN
ejpam-6436	208	18	from	from	ADP
ejpam-6436	208	19	proposition	proposition	NOUN
ejpam-6436	208	20	3	3	NUM
ejpam-6436	208	21	,	,	PUNCT
ejpam-6436	208	22	for	for	ADP
ejpam-6436	208	23	all	all	DET
ejpam-6436	208	24	a	a	DET
ejpam-6436	208	25	∈	∈	PROPN
ejpam-6436	208	26	a	a	DET
ejpam-6436	208	27	,	,	PUNCT
ejpam-6436	208	28	s	s	PROPN
ejpam-6436	208	29	,	,	PUNCT
ejpam-6436	208	30	s′	s′	ADJ
ejpam-6436	208	31	∈	∈	PROPN
ejpam-6436	208	32	s	s	NOUN
ejpam-6436	208	33	,	,	PUNCT
ejpam-6436	208	34	c1(pa)s	c1(pa)s	PROPN
ejpam-6436	208	35	≰	≰	PROPN
ejpam-6436	208	36	c1(p	c1(p	PRON
ejpam-6436	208	37	′a)s′.	′a)s′.	PROPN
ejpam-6436	208	38	therefore	therefore	ADV
ejpam-6436	208	39	,	,	PUNCT
ejpam-6436	208	40	s	s	PART
ejpam-6436	208	41	≰	≰	PROPN
ejpam-6436	208	42	s′	s′	VERB
ejpam-6436	208	43	for	for	ADP
ejpam-6436	208	44	all	all	DET
ejpam-6436	208	45	s	s	PROPN
ejpam-6436	208	46	,	,	PUNCT
ejpam-6436	208	47	s′	s′	PUNCT
ejpam-6436	208	48	∈	∈	PROPN
ejpam-6436	208	49	s	s	X
ejpam-6436	208	50	which	which	PRON
ejpam-6436	208	51	is	be	AUX
ejpam-6436	208	52	impossible	impossible	ADJ
ejpam-6436	208	53	as	as	SCONJ
ejpam-6436	208	54	s	s	PROPN
ejpam-6436	208	55	≤	≤	PROPN
ejpam-6436	208	56	s.	s.	PROPN
ejpam-6436	208	57	therefore	therefore	ADV
ejpam-6436	208	58	,	,	PUNCT
ejpam-6436	208	59	(	(	PUNCT
ejpam-6436	208	60	r	r	NOUN
ejpam-6436	208	61	,	,	PUNCT
ejpam-6436	208	62	c1	c1	NOUN
ejpam-6436	208	63	)	)	PUNCT
ejpam-6436	208	64	in	in	ADP
ejpam-6436	208	65	t	t	PROPN
ejpam-6436	208	66	is	be	AUX
ejpam-6436	208	67	not	not	PART
ejpam-6436	208	68	left	leave	VERB
ejpam-6436	208	69	po	po	NOUN
ejpam-6436	208	70	-	-	NOUN
ejpam-6436	208	71	cancellable	cancellable	ADJ
ejpam-6436	208	72	.	.	PUNCT
ejpam-6436	209	1	3	3	X
ejpam-6436	209	2	.	.	X
ejpam-6436	209	3	po	po	NOUN
ejpam-6436	209	4	-	-	PUNCT
ejpam-6436	209	5	surjective	surjective	ADJ
ejpam-6436	209	6	action	action	NOUN
ejpam-6436	209	7	and	and	CCONJ
ejpam-6436	209	8	po	po	NOUN
ejpam-6436	209	9	-	-	PUNCT
ejpam-6436	209	10	flatness	flatness	NOUN
ejpam-6436	209	11	properties	property	NOUN
ejpam-6436	209	12	of	of	ADP
ejpam-6436	209	13	posets	poset	NOUN
ejpam-6436	209	14	this	this	DET
ejpam-6436	209	15	section	section	NOUN
ejpam-6436	209	16	will	will	AUX
ejpam-6436	209	17	be	be	AUX
ejpam-6436	209	18	devoted	devote	VERB
ejpam-6436	209	19	for	for	ADP
ejpam-6436	209	20	studying	study	VERB
ejpam-6436	209	21	the	the	DET
ejpam-6436	209	22	po	po	NOUN
ejpam-6436	209	23	-	-	PUNCT
ejpam-6436	209	24	surjective	surjective	ADJ
ejpam-6436	209	25	and	and	CCONJ
ejpam-6436	209	26	po	po	NOUN
ejpam-6436	209	27	-	-	PUNCT
ejpam-6436	209	28	flatness	flatness	NOUN
ejpam-6436	209	29	properties	property	NOUN
ejpam-6436	209	30	of	of	ADP
ejpam-6436	209	31	posets	poset	NOUN
ejpam-6436	209	32	on	on	ADP
ejpam-6436	209	33	the	the	DET
ejpam-6436	209	34	wreath	wreath	NOUN
ejpam-6436	209	35	product	product	NOUN
ejpam-6436	209	36	of	of	ADP
ejpam-6436	209	37	pomonoids	pomonoid	NOUN
ejpam-6436	209	38	.	.	PUNCT
ejpam-6436	210	1	the	the	DET
ejpam-6436	210	2	relationships	relationship	NOUN
ejpam-6436	210	3	among	among	ADP
ejpam-6436	210	4	these	these	DET
ejpam-6436	210	5	properties	property	NOUN
ejpam-6436	210	6	have	have	AUX
ejpam-6436	210	7	also	also	ADV
ejpam-6436	210	8	been	be	AUX
ejpam-6436	210	9	obtained	obtain	VERB
ejpam-6436	210	10	in	in	ADP
ejpam-6436	210	11	this	this	DET
ejpam-6436	210	12	section	section	NOUN
ejpam-6436	210	13	.	.	PUNCT
ejpam-6436	211	1	definition	definition	NOUN
ejpam-6436	211	2	1	1	NUM
ejpam-6436	211	3	.	.	PUNCT
ejpam-6436	212	1	(	(	PUNCT
ejpam-6436	212	2	i	i	NOUN
ejpam-6436	212	3	)	)	PUNCT
ejpam-6436	212	4	an	an	DET
ejpam-6436	212	5	element	element	NOUN
ejpam-6436	212	6	r	r	NOUN
ejpam-6436	212	7	∈	∈	NOUN
ejpam-6436	212	8	r	r	NOUN
ejpam-6436	212	9	acts	act	VERB
ejpam-6436	212	10	po	po	NOUN
ejpam-6436	212	11	-	-	PUNCT
ejpam-6436	212	12	surjectively	surjectively	ADV
ejpam-6436	212	13	on	on	ADP
ejpam-6436	212	14	the	the	DET
ejpam-6436	212	15	left	left	ADJ
ejpam-6436	212	16	r	r	NOUN
ejpam-6436	212	17	-	-	PUNCT
ejpam-6436	212	18	poset	poset	VERB
ejpam-6436	212	19	ra	ra	NOUN
ejpam-6436	212	20	if	if	SCONJ
ejpam-6436	212	21	for	for	ADP
ejpam-6436	212	22	every	every	DET
ejpam-6436	212	23	a	a	DET
ejpam-6436	212	24	∈	∈	PROPN
ejpam-6436	212	25	a	a	DET
ejpam-6436	212	26	there	there	PRON
ejpam-6436	212	27	exists	exist	VERB
ejpam-6436	212	28	a′	a′	PROPN
ejpam-6436	212	29	∈	∈	PROPN
ejpam-6436	212	30	a	a	DET
ejpam-6436	212	31	such	such	ADJ
ejpam-6436	212	32	that	that	DET
ejpam-6436	212	33	ra′	ra′	VERB
ejpam-6436	212	34	≤	≤	NUM
ejpam-6436	212	35	a.	a.	NOUN
ejpam-6436	212	36	(	(	PUNCT
ejpam-6436	212	37	ii	ii	PROPN
ejpam-6436	212	38	)	)	PUNCT
ejpam-6436	212	39	r′	r′	PROPN
ejpam-6436	212	40	⊆	⊆	NUM
ejpam-6436	212	41	r	r	NOUN
ejpam-6436	212	42	acts	act	NOUN
ejpam-6436	212	43	po	po	NOUN
ejpam-6436	212	44	-	-	PUNCT
ejpam-6436	212	45	surjectively	surjectively	ADV
ejpam-6436	212	46	on	on	ADP
ejpam-6436	212	47	a	a	PRON
ejpam-6436	212	48	,	,	PUNCT
ejpam-6436	212	49	when	when	SCONJ
ejpam-6436	212	50	every	every	DET
ejpam-6436	212	51	r′	r′	NUM
ejpam-6436	212	52	∈	∈	PROPN
ejpam-6436	212	53	r′	r′	PROPN
ejpam-6436	212	54	acts	act	NOUN
ejpam-6436	212	55	po	po	NOUN
ejpam-6436	212	56	-	-	PUNCT
ejpam-6436	212	57	surjectively	surjectively	ADV
ejpam-6436	212	58	on	on	ADP
ejpam-6436	212	59	ra	ra	PROPN
ejpam-6436	212	60	.	.	PUNCT
ejpam-6436	213	1	(	(	PUNCT
ejpam-6436	213	2	iii	iii	NOUN
ejpam-6436	213	3	)	)	PUNCT
ejpam-6436	213	4	for	for	ADP
ejpam-6436	213	5	any	any	DET
ejpam-6436	213	6	fixed	fix	VERB
ejpam-6436	213	7	r	r	NOUN
ejpam-6436	213	8	∈	∈	NOUN
ejpam-6436	213	9	r	r	NOUN
ejpam-6436	213	10	and	and	CCONJ
ejpam-6436	213	11	a	a	DET
ejpam-6436	213	12	∈	∈	NOUN
ejpam-6436	213	13	ra	ra	NOUN
ejpam-6436	213	14	we	we	PRON
ejpam-6436	213	15	define	define	VERB
ejpam-6436	213	16	the	the	DET
ejpam-6436	213	17	set	set	NOUN
ejpam-6436	213	18	ar	ar	NOUN
ejpam-6436	213	19	:	:	PUNCT
ejpam-6436	213	20	=	=	SYM
ejpam-6436	213	21	{	{	PUNCT
ejpam-6436	213	22	x	x	PUNCT
ejpam-6436	213	23	∈	∈	PROPN
ejpam-6436	213	24	a	a	PRON
ejpam-6436	213	25	:	:	PUNCT
ejpam-6436	213	26	rx	rx	VERB
ejpam-6436	213	27	≤	≤	NOUN
ejpam-6436	213	28	a	a	PRON
ejpam-6436	213	29	}	}	PUNCT
ejpam-6436	213	30	.	.	PUNCT
ejpam-6436	214	1	(	(	PUNCT
ejpam-6436	214	2	iv	iv	AUX
ejpam-6436	214	3	)	)	PUNCT
ejpam-6436	214	4	let	let	VERB
ejpam-6436	214	5	sb	sb	PRON
ejpam-6436	214	6	be	be	AUX
ejpam-6436	214	7	a	a	DET
ejpam-6436	214	8	left	left	ADJ
ejpam-6436	214	9	s−poset	s−poset	NOUN
ejpam-6436	214	10	,	,	PUNCT
ejpam-6436	214	11	then	then	ADV
ejpam-6436	214	12	we	we	PRON
ejpam-6436	214	13	say	say	VERB
ejpam-6436	214	14	that	that	SCONJ
ejpam-6436	214	15	sb	sb	PROPN
ejpam-6436	214	16	≤	≤	PROPN
ejpam-6436	214	17	b	b	PROPN
ejpam-6436	215	1	if	if	SCONJ
ejpam-6436	215	2	for	for	ADP
ejpam-6436	215	3	all	all	DET
ejpam-6436	215	4	b	b	NOUN
ejpam-6436	215	5	∈	∈	ADP
ejpam-6436	215	6	b	b	NOUN
ejpam-6436	215	7	there	there	PRON
ejpam-6436	215	8	exist	exist	VERB
ejpam-6436	215	9	s	s	PROPN
ejpam-6436	215	10	∈	∈	PROPN
ejpam-6436	215	11	s	s	X
ejpam-6436	215	12	and	and	CCONJ
ejpam-6436	215	13	b′	b′	NUM
ejpam-6436	215	14	∈	∈	PROPN
ejpam-6436	215	15	b	b	NOUN
ejpam-6436	215	16	such	such	ADJ
ejpam-6436	215	17	that	that	DET
ejpam-6436	215	18	sb′	sb′	PROPN
ejpam-6436	215	19	≤	≤	PROPN
ejpam-6436	215	20	b.	b.	PROPN
ejpam-6436	215	21	proposition	proposition	NOUN
ejpam-6436	215	22	7	7	NUM
ejpam-6436	215	23	.	.	PUNCT
ejpam-6436	216	1	the	the	DET
ejpam-6436	216	2	element	element	NOUN
ejpam-6436	216	3	(	(	PUNCT
ejpam-6436	216	4	r	r	NOUN
ejpam-6436	216	5	,	,	PUNCT
ejpam-6436	216	6	f	f	X
ejpam-6436	216	7	)	)	PUNCT
ejpam-6436	216	8	∈	∈	PROPN
ejpam-6436	216	9	t	t	PROPN
ejpam-6436	216	10	acts	act	VERB
ejpam-6436	216	11	po	po	NOUN
ejpam-6436	216	12	-	-	PUNCT
ejpam-6436	216	13	surjectively	surjectively	ADV
ejpam-6436	216	14	on	on	ADP
ejpam-6436	216	15	tc	tc	PRON
ejpam-6436	216	16	if	if	SCONJ
ejpam-6436	217	1	and	and	CCONJ
ejpam-6436	217	2	only	only	ADV
ejpam-6436	217	3	if	if	SCONJ
ejpam-6436	217	4	f(ar)b	f(ar)b	PROPN
ejpam-6436	217	5	≤	≤	NOUN
ejpam-6436	217	6	b	b	NOUN
ejpam-6436	217	7	for	for	ADP
ejpam-6436	217	8	all	all	DET
ejpam-6436	217	9	a	a	DET
ejpam-6436	217	10	∈	∈	NOUN
ejpam-6436	217	11	a.	a.	NOUN
ejpam-6436	217	12	proof	proof	NOUN
ejpam-6436	217	13	.	.	PUNCT
ejpam-6436	218	1	suppose	suppose	VERB
ejpam-6436	218	2	(	(	PUNCT
ejpam-6436	218	3	r	r	NOUN
ejpam-6436	218	4	,	,	PUNCT
ejpam-6436	218	5	f	f	X
ejpam-6436	218	6	)	)	PUNCT
ejpam-6436	218	7	∈	∈	PROPN
ejpam-6436	218	8	t	t	PROPN
ejpam-6436	218	9	acts	act	VERB
ejpam-6436	218	10	po	po	NOUN
ejpam-6436	218	11	-	-	PUNCT
ejpam-6436	218	12	surjectively	surjectively	ADV
ejpam-6436	218	13	on	on	ADP
ejpam-6436	218	14	tc	tc	NOUN
ejpam-6436	218	15	.	.	PUNCT
ejpam-6436	219	1	therefore	therefore	ADV
ejpam-6436	219	2	for	for	ADP
ejpam-6436	219	3	every	every	DET
ejpam-6436	219	4	(	(	PUNCT
ejpam-6436	219	5	a	a	PRON
ejpam-6436	219	6	,	,	PUNCT
ejpam-6436	219	7	b	b	NOUN
ejpam-6436	219	8	)	)	PUNCT
ejpam-6436	219	9	∈	∈	PROPN
ejpam-6436	219	10	tc	tc	NOUN
ejpam-6436	220	1	it	it	PRON
ejpam-6436	220	2	can	can	AUX
ejpam-6436	220	3	be	be	AUX
ejpam-6436	220	4	found	find	VERB
ejpam-6436	220	5	that	that	SCONJ
ejpam-6436	220	6	(	(	PUNCT
ejpam-6436	220	7	a′	a′	PROPN
ejpam-6436	220	8	,	,	PUNCT
ejpam-6436	220	9	b′	b′	NUM
ejpam-6436	220	10	)	)	PUNCT
ejpam-6436	220	11	∈	∈	PROPN
ejpam-6436	220	12	tc	tc	ADP
ejpam-6436	220	13	such	such	ADJ
ejpam-6436	220	14	that	that	PRON
ejpam-6436	220	15	(	(	PUNCT
ejpam-6436	220	16	r	r	NOUN
ejpam-6436	220	17	,	,	PUNCT
ejpam-6436	220	18	f)(a′	f)(a′	PROPN
ejpam-6436	220	19	,	,	PUNCT
ejpam-6436	220	20	b′	b′	NUM
ejpam-6436	220	21	)	)	PUNCT
ejpam-6436	220	22	≤	≤	NOUN
ejpam-6436	221	1	(	(	PUNCT
ejpam-6436	221	2	a	a	DET
ejpam-6436	221	3	,	,	PUNCT
ejpam-6436	221	4	b	b	NOUN
ejpam-6436	221	5	)	)	PUNCT
ejpam-6436	221	6	.	.	PUNCT
ejpam-6436	222	1	this	this	PRON
ejpam-6436	222	2	implies	imply	VERB
ejpam-6436	222	3	ra′	ra′	VERB
ejpam-6436	222	4	≤	≤	NUM
ejpam-6436	222	5	a	a	PRON
ejpam-6436	222	6	and	and	CCONJ
ejpam-6436	222	7	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	222	8	≤	≤	PROPN
ejpam-6436	222	9	b.	b.	PROPN
ejpam-6436	223	1	thus	thus	ADV
ejpam-6436	223	2	a′	a′	PROPN
ejpam-6436	223	3	∈	∈	PROPN
ejpam-6436	223	4	ar	ar	PROPN
ejpam-6436	223	5	and	and	CCONJ
ejpam-6436	223	6	we	we	PRON
ejpam-6436	223	7	have	have	VERB
ejpam-6436	223	8	f(ar)b	f(ar)b	PROPN
ejpam-6436	223	9	≤	≤	NUM
ejpam-6436	223	10	b.	b.	PROPN
ejpam-6436	224	1	conversely	conversely	ADV
ejpam-6436	224	2	,	,	PUNCT
ejpam-6436	224	3	suppose	suppose	VERB
ejpam-6436	224	4	f(ar)b	f(ar)b	PROPN
ejpam-6436	224	5	≤	≤	PROPN
ejpam-6436	224	6	b.	b.	PROPN
ejpam-6436	224	7	specifically	specifically	ADV
ejpam-6436	224	8	,	,	PUNCT
ejpam-6436	224	9	the	the	DET
ejpam-6436	224	10	assumption	assumption	NOUN
ejpam-6436	224	11	implies	imply	VERB
ejpam-6436	224	12	that	that	SCONJ
ejpam-6436	224	13	ar	ar	PROPN
ejpam-6436	224	14	̸=	̸=	PROPN
ejpam-6436	224	15	ϕ.	ϕ.	PROPN
ejpam-6436	224	16	take	take	VERB
ejpam-6436	224	17	(	(	PUNCT
ejpam-6436	224	18	a	a	DET
ejpam-6436	224	19	,	,	PUNCT
ejpam-6436	224	20	b	b	NOUN
ejpam-6436	224	21	)	)	PUNCT
ejpam-6436	224	22	∈	∈	PROPN
ejpam-6436	224	23	tc	tc	NOUN
ejpam-6436	224	24	,	,	PUNCT
ejpam-6436	224	25	choose	choose	VERB
ejpam-6436	224	26	a′	a′	PROPN
ejpam-6436	224	27	∈	∈	PROPN
ejpam-6436	224	28	ar	ar	PROPN
ejpam-6436	224	29	and	and	CCONJ
ejpam-6436	224	30	b′	b′	NUM
ejpam-6436	224	31	∈	∈	PROPN
ejpam-6436	224	32	b	b	NOUN
ejpam-6436	224	33	where	where	SCONJ
ejpam-6436	224	34	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	224	35	≤	≤	PROPN
ejpam-6436	224	36	b.	b.	PROPN
ejpam-6436	224	37	hence	hence	ADV
ejpam-6436	224	38	,	,	PUNCT
ejpam-6436	224	39	(	(	PUNCT
ejpam-6436	224	40	r	r	NOUN
ejpam-6436	224	41	,	,	PUNCT
ejpam-6436	224	42	f)(a′	f)(a′	PROPN
ejpam-6436	224	43	,	,	PUNCT
ejpam-6436	224	44	b′	b′	NUM
ejpam-6436	224	45	)	)	PUNCT
ejpam-6436	225	1	=	=	SYM
ejpam-6436	225	2	(	(	PUNCT
ejpam-6436	225	3	ra′	ra′	PROPN
ejpam-6436	225	4	,	,	PUNCT
ejpam-6436	225	5	f(a′)b′	f(a′)b′	NOUN
ejpam-6436	225	6	)	)	PUNCT
ejpam-6436	225	7	≤	≤	NOUN
ejpam-6436	225	8	(	(	PUNCT
ejpam-6436	225	9	a	a	DET
ejpam-6436	225	10	,	,	PUNCT
ejpam-6436	225	11	b	b	NOUN
ejpam-6436	225	12	)	)	PUNCT
ejpam-6436	225	13	.	.	PUNCT
ejpam-6436	226	1	hence	hence	ADV
ejpam-6436	226	2	(	(	PUNCT
ejpam-6436	226	3	r	r	NOUN
ejpam-6436	226	4	,	,	PUNCT
ejpam-6436	226	5	f	f	X
ejpam-6436	226	6	)	)	PUNCT
ejpam-6436	226	7	∈	∈	PROPN
ejpam-6436	226	8	t	t	PROPN
ejpam-6436	226	9	acts	act	VERB
ejpam-6436	226	10	po	po	NOUN
ejpam-6436	226	11	-	-	PUNCT
ejpam-6436	226	12	surjectively	surjectively	ADV
ejpam-6436	226	13	on	on	ADP
ejpam-6436	226	14	tc	tc	ADP
ejpam-6436	226	15	,	,	PUNCT
ejpam-6436	226	16	as	as	SCONJ
ejpam-6436	226	17	required	require	VERB
ejpam-6436	226	18	.	.	PUNCT
ejpam-6436	227	1	proposition	proposition	NOUN
ejpam-6436	227	2	8	8	NUM
ejpam-6436	227	3	.	.	PUNCT
ejpam-6436	228	1	the	the	DET
ejpam-6436	228	2	element	element	NOUN
ejpam-6436	228	3	(	(	PUNCT
ejpam-6436	228	4	r	r	NOUN
ejpam-6436	228	5	,	,	PUNCT
ejpam-6436	228	6	f	f	X
ejpam-6436	228	7	)	)	PUNCT
ejpam-6436	228	8	∈	∈	PROPN
ejpam-6436	228	9	t	t	PROPN
ejpam-6436	228	10	acts	act	VERB
ejpam-6436	228	11	po	po	NOUN
ejpam-6436	228	12	-	-	PUNCT
ejpam-6436	228	13	surjectively	surjectively	ADV
ejpam-6436	228	14	on	on	ADP
ejpam-6436	228	15	tc	tc	PRON
ejpam-6436	228	16	if	if	SCONJ
ejpam-6436	229	1	and	and	CCONJ
ejpam-6436	229	2	only	only	ADV
ejpam-6436	229	3	if	if	SCONJ
ejpam-6436	229	4	s0	s0	PROPN
ejpam-6436	229	5	acts	act	VERB
ejpam-6436	229	6	po	po	NOUN
ejpam-6436	229	7	-	-	PUNCT
ejpam-6436	229	8	surjectively	surjectively	ADV
ejpam-6436	229	9	on	on	ADP
ejpam-6436	229	10	sb	sb	PROPN
ejpam-6436	229	11	for	for	ADP
ejpam-6436	229	12	some	some	DET
ejpam-6436	229	13	s0	s0	PROPN
ejpam-6436	229	14	∈	∈	PROPN
ejpam-6436	229	15	f(ar	f(ar	PROPN
ejpam-6436	229	16	)	)	PUNCT
ejpam-6436	229	17	for	for	ADP
ejpam-6436	229	18	all	all	DET
ejpam-6436	230	1	a	a	DET
ejpam-6436	230	2	∈	∈	PROPN
ejpam-6436	230	3	a.	a.	NOUN
ejpam-6436	230	4	b.	b.	PROPN
ejpam-6436	230	5	al	al	PROPN
ejpam-6436	230	6	subaiei	subaiei	PROPN
ejpam-6436	230	7	et	et	PROPN
ejpam-6436	230	8	al	al	PROPN
ejpam-6436	230	9	.	.	PUNCT
ejpam-6436	230	10	/	/	SYM
ejpam-6436	230	11	eur	eur	PROPN
ejpam-6436	230	12	.	.	PUNCT
ejpam-6436	231	1	j.	j.	PROPN
ejpam-6436	231	2	pure	pure	PROPN
ejpam-6436	231	3	appl	appl	PROPN
ejpam-6436	231	4	.	.	PROPN
ejpam-6436	231	5	math	math	PROPN
ejpam-6436	231	6	,	,	PUNCT
ejpam-6436	231	7	18	18	NUM
ejpam-6436	231	8	(	(	PUNCT
ejpam-6436	231	9	3	3	NUM
ejpam-6436	231	10	)	)	PUNCT
ejpam-6436	231	11	(	(	PUNCT
ejpam-6436	231	12	2025	2025	NUM
ejpam-6436	231	13	)	)	PUNCT
ejpam-6436	231	14	,	,	PUNCT
ejpam-6436	231	15	6436	6436	NUM
ejpam-6436	231	16	9	9	NUM
ejpam-6436	231	17	of	of	ADP
ejpam-6436	231	18	14	14	NUM
ejpam-6436	231	19	proof	proof	NOUN
ejpam-6436	231	20	.	.	PUNCT
ejpam-6436	232	1	let	let	VERB
ejpam-6436	232	2	a	a	DET
ejpam-6436	232	3	∈	∈	PROPN
ejpam-6436	232	4	a	a	PRON
ejpam-6436	232	5	and	and	CCONJ
ejpam-6436	232	6	b	b	PROPN
ejpam-6436	232	7	∈	∈	PROPN
ejpam-6436	232	8	b.	b.	PROPN
ejpam-6436	232	9	since	since	SCONJ
ejpam-6436	232	10	(	(	PUNCT
ejpam-6436	232	11	r	r	NOUN
ejpam-6436	232	12	,	,	PUNCT
ejpam-6436	232	13	f	f	X
ejpam-6436	232	14	)	)	PUNCT
ejpam-6436	232	15	∈	∈	PROPN
ejpam-6436	232	16	t	t	PROPN
ejpam-6436	232	17	acts	act	VERB
ejpam-6436	232	18	po	po	NOUN
ejpam-6436	232	19	-	-	PUNCT
ejpam-6436	232	20	surjectively	surjectively	ADV
ejpam-6436	232	21	on	on	ADP
ejpam-6436	232	22	tc	tc	NOUN
ejpam-6436	232	23	,	,	PUNCT
ejpam-6436	232	24	for	for	ADP
ejpam-6436	232	25	any	any	DET
ejpam-6436	232	26	(	(	PUNCT
ejpam-6436	232	27	a	a	PRON
ejpam-6436	232	28	,	,	PUNCT
ejpam-6436	232	29	b	b	NOUN
ejpam-6436	232	30	)	)	PUNCT
ejpam-6436	232	31	∈	∈	PROPN
ejpam-6436	232	32	tc	tc	NOUN
ejpam-6436	233	1	it	it	PRON
ejpam-6436	233	2	can	can	AUX
ejpam-6436	233	3	be	be	AUX
ejpam-6436	233	4	found	find	VERB
ejpam-6436	233	5	that	that	SCONJ
ejpam-6436	233	6	(	(	PUNCT
ejpam-6436	233	7	a′	a′	PROPN
ejpam-6436	233	8	,	,	PUNCT
ejpam-6436	233	9	b′	b′	NUM
ejpam-6436	233	10	)	)	PUNCT
ejpam-6436	233	11	∈	∈	PROPN
ejpam-6436	233	12	tc	tc	ADP
ejpam-6436	233	13	such	such	ADJ
ejpam-6436	233	14	that	that	PRON
ejpam-6436	233	15	(	(	PUNCT
ejpam-6436	233	16	r	r	NOUN
ejpam-6436	233	17	,	,	PUNCT
ejpam-6436	233	18	f)(a′	f)(a′	PROPN
ejpam-6436	233	19	,	,	PUNCT
ejpam-6436	233	20	b′	b′	NUM
ejpam-6436	233	21	)	)	PUNCT
ejpam-6436	233	22	≤	≤	NOUN
ejpam-6436	234	1	(	(	PUNCT
ejpam-6436	234	2	a	a	DET
ejpam-6436	234	3	,	,	PUNCT
ejpam-6436	234	4	b	b	NOUN
ejpam-6436	234	5	)	)	PUNCT
ejpam-6436	234	6	.	.	PUNCT
ejpam-6436	235	1	then	then	ADV
ejpam-6436	235	2	,	,	PUNCT
ejpam-6436	235	3	ra′	ra′	VERB
ejpam-6436	235	4	≤	≤	NOUN
ejpam-6436	235	5	a	a	PRON
ejpam-6436	235	6	and	and	CCONJ
ejpam-6436	235	7	f(a′)b′	f(a′)b′	X
ejpam-6436	235	8	≤	≤	NUM
ejpam-6436	235	9	b	b	NOUN
ejpam-6436	235	10	implying	imply	VERB
ejpam-6436	235	11	a′	a′	PROPN
ejpam-6436	235	12	∈	∈	PROPN
ejpam-6436	235	13	ar	ar	PROPN
ejpam-6436	235	14	.	.	PROPN
ejpam-6436	235	15	suppose	suppose	VERB
ejpam-6436	235	16	f(a′	f(a′	NUM
ejpam-6436	235	17	)	)	PUNCT
ejpam-6436	235	18	=	=	SYM
ejpam-6436	235	19	s0	s0	PROPN
ejpam-6436	235	20	.	.	PUNCT
ejpam-6436	236	1	thus	thus	ADV
ejpam-6436	236	2	for	for	ADP
ejpam-6436	236	3	any	any	DET
ejpam-6436	236	4	b	b	PROPN
ejpam-6436	236	5	∈	∈	PROPN
ejpam-6436	236	6	b	b	NOUN
ejpam-6436	236	7	there	there	PRON
ejpam-6436	236	8	exists	exist	VERB
ejpam-6436	236	9	b′	b′	NUM
ejpam-6436	236	10	∈	∈	PROPN
ejpam-6436	236	11	b	b	NOUN
ejpam-6436	236	12	such	such	ADJ
ejpam-6436	236	13	that	that	SCONJ
ejpam-6436	236	14	s0b	s0b	PROPN
ejpam-6436	236	15	′	′	NUM
ejpam-6436	236	16	≤	≤	NUM
ejpam-6436	236	17	b	b	NOUN
ejpam-6436	236	18	for	for	ADP
ejpam-6436	236	19	some	some	DET
ejpam-6436	236	20	s0	s0	PROPN
ejpam-6436	236	21	=	=	SYM
ejpam-6436	236	22	f(a′	f(a′	PROPN
ejpam-6436	236	23	)	)	PUNCT
ejpam-6436	236	24	∈	∈	PROPN
ejpam-6436	236	25	f(ar	f(ar	NOUN
ejpam-6436	236	26	)	)	PUNCT
ejpam-6436	236	27	.	.	PUNCT
ejpam-6436	237	1	hence	hence	ADV
ejpam-6436	237	2	some	some	DET
ejpam-6436	237	3	s0	s0	PROPN
ejpam-6436	237	4	∈	∈	PROPN
ejpam-6436	237	5	f(ar	f(ar	PROPN
ejpam-6436	237	6	)	)	PUNCT
ejpam-6436	237	7	acts	act	VERB
ejpam-6436	237	8	po	po	NOUN
ejpam-6436	237	9	-	-	PUNCT
ejpam-6436	237	10	surjectively	surjectively	ADV
ejpam-6436	237	11	on	on	ADP
ejpam-6436	237	12	sb	sb	PROPN
ejpam-6436	237	13	.	.	PUNCT
ejpam-6436	237	14	now	now	ADV
ejpam-6436	237	15	suppose	suppose	VERB
ejpam-6436	237	16	s0	s0	PROPN
ejpam-6436	237	17	∈	∈	PROPN
ejpam-6436	237	18	f(ar	f(ar	PROPN
ejpam-6436	237	19	)	)	PUNCT
ejpam-6436	237	20	acts	act	VERB
ejpam-6436	237	21	po	po	NOUN
ejpam-6436	237	22	-	-	PUNCT
ejpam-6436	237	23	surjectively	surjectively	ADV
ejpam-6436	237	24	on	on	ADP
ejpam-6436	237	25	sb	sb	PROPN
ejpam-6436	237	26	.	.	PROPN
ejpam-6436	237	27	therefore	therefore	ADV
ejpam-6436	237	28	for	for	ADP
ejpam-6436	237	29	any	any	DET
ejpam-6436	237	30	b	b	PROPN
ejpam-6436	237	31	∈	∈	ADP
ejpam-6436	237	32	b	b	NOUN
ejpam-6436	237	33	it	it	PRON
ejpam-6436	237	34	can	can	AUX
ejpam-6436	237	35	be	be	AUX
ejpam-6436	237	36	found	find	VERB
ejpam-6436	237	37	that	that	SCONJ
ejpam-6436	237	38	b′	b′	NUM
ejpam-6436	237	39	∈	∈	PROPN
ejpam-6436	237	40	b	b	NOUN
ejpam-6436	237	41	such	such	ADJ
ejpam-6436	237	42	that	that	SCONJ
ejpam-6436	237	43	s0b	s0b	PROPN
ejpam-6436	237	44	′	′	PROPN
ejpam-6436	237	45	≤	≤	NUM
ejpam-6436	237	46	b.	b.	PROPN
ejpam-6436	237	47	clearly	clearly	ADV
ejpam-6436	237	48	,	,	PUNCT
ejpam-6436	237	49	ar	ar	NOUN
ejpam-6436	237	50	̸=	̸=	PROPN
ejpam-6436	237	51	∅	∅	NOUN
ejpam-6436	237	52	as	as	SCONJ
ejpam-6436	237	53	there	there	PRON
ejpam-6436	237	54	exists	exist	VERB
ejpam-6436	237	55	some	some	DET
ejpam-6436	237	56	a′	a′	PROPN
ejpam-6436	237	57	∈	∈	PROPN
ejpam-6436	237	58	ar	ar	NOUN
ejpam-6436	237	59	such	such	ADJ
ejpam-6436	237	60	that	that	DET
ejpam-6436	237	61	f(a′	f(a′	NOUN
ejpam-6436	237	62	)	)	PUNCT
ejpam-6436	238	1	=	=	SYM
ejpam-6436	238	2	s0	s0	PROPN
ejpam-6436	238	3	.	.	PUNCT
ejpam-6436	239	1	now	now	ADV
ejpam-6436	239	2	for	for	ADP
ejpam-6436	239	3	any	any	DET
ejpam-6436	239	4	(	(	PUNCT
ejpam-6436	239	5	a	a	PRON
ejpam-6436	239	6	,	,	PUNCT
ejpam-6436	239	7	b	b	NOUN
ejpam-6436	239	8	)	)	PUNCT
ejpam-6436	239	9	∈	∈	PROPN
ejpam-6436	239	10	tc	tc	NOUN
ejpam-6436	239	11	=	=	SYM
ejpam-6436	239	12	ra	ra	PROPN
ejpam-6436	239	13	×	×	NOUN
ejpam-6436	239	14	sb	sb	PROPN
ejpam-6436	239	15	there	there	ADV
ejpam-6436	239	16	exists	exist	VERB
ejpam-6436	239	17	some	some	PRON
ejpam-6436	239	18	(	(	PUNCT
ejpam-6436	239	19	a′	a′	PROPN
ejpam-6436	239	20	,	,	PUNCT
ejpam-6436	239	21	b′	b′	NUM
ejpam-6436	239	22	)	)	PUNCT
ejpam-6436	239	23	∈	∈	PROPN
ejpam-6436	239	24	ra	ra	NOUN
ejpam-6436	239	25	r	r	NOUN
ejpam-6436	239	26	×	×	PROPN
ejpam-6436	239	27	sb	sb	PROPN
ejpam-6436	240	1	⊆	⊆	NUM
ejpam-6436	240	2	ra	ra	PROPN
ejpam-6436	240	3	×	×	PROPN
ejpam-6436	240	4	sb	sb	NOUN
ejpam-6436	240	5	such	such	ADJ
ejpam-6436	240	6	that	that	SCONJ
ejpam-6436	240	7	(	(	PUNCT
ejpam-6436	240	8	r	r	NOUN
ejpam-6436	240	9	,	,	PUNCT
ejpam-6436	240	10	f)(a′	f)(a′	PROPN
ejpam-6436	240	11	,	,	PUNCT
ejpam-6436	240	12	b′	b′	NUM
ejpam-6436	240	13	)	)	PUNCT
ejpam-6436	241	1	=	=	SYM
ejpam-6436	242	1	(	(	PUNCT
ejpam-6436	242	2	ra′	ra′	PROPN
ejpam-6436	242	3	,	,	PUNCT
ejpam-6436	242	4	f(a′)b′	f(a′)b′	X
ejpam-6436	242	5	)	)	PUNCT
ejpam-6436	242	6	=	=	SYM
ejpam-6436	242	7	(	(	PUNCT
ejpam-6436	242	8	ra′	ra′	PROPN
ejpam-6436	242	9	,	,	PUNCT
ejpam-6436	242	10	s0b	s0b	PROPN
ejpam-6436	242	11	′	′	NOUN
ejpam-6436	242	12	)	)	PUNCT
ejpam-6436	242	13	≤	≤	NOUN
ejpam-6436	242	14	(	(	PUNCT
ejpam-6436	242	15	a	a	DET
ejpam-6436	242	16	,	,	PUNCT
ejpam-6436	242	17	b	b	NOUN
ejpam-6436	242	18	)	)	PUNCT
ejpam-6436	242	19	.	.	PUNCT
ejpam-6436	243	1	hence	hence	ADV
ejpam-6436	243	2	,	,	PUNCT
ejpam-6436	243	3	(	(	PUNCT
ejpam-6436	243	4	r	r	NOUN
ejpam-6436	243	5	,	,	PUNCT
ejpam-6436	243	6	f	f	X
ejpam-6436	243	7	)	)	PUNCT
ejpam-6436	243	8	∈	∈	PROPN
ejpam-6436	243	9	t	t	NOUN
ejpam-6436	243	10	=	=	SYM
ejpam-6436	243	11	r×	r×	NOUN
ejpam-6436	243	12	f	f	X
ejpam-6436	243	13	(	(	PUNCT
ejpam-6436	243	14	a	a	DET
ejpam-6436	243	15	,	,	PUNCT
ejpam-6436	243	16	s	s	PART
ejpam-6436	243	17	)	)	PUNCT
ejpam-6436	243	18	acts	act	VERB
ejpam-6436	243	19	po	po	NOUN
ejpam-6436	243	20	-	-	PUNCT
ejpam-6436	243	21	surjectively	surjectively	ADV
ejpam-6436	243	22	on	on	ADP
ejpam-6436	243	23	tc	tc	NUM
ejpam-6436	243	24	.	.	PUNCT
ejpam-6436	243	25	theorem	theorem	NOUN
ejpam-6436	243	26	4	4	NUM
ejpam-6436	243	27	.	.	PUNCT
ejpam-6436	244	1	the	the	DET
ejpam-6436	244	2	pomonoid	pomonoid	PROPN
ejpam-6436	244	3	t	t	PROPN
ejpam-6436	244	4	acts	act	VERB
ejpam-6436	244	5	po	po	NOUN
ejpam-6436	244	6	-	-	PUNCT
ejpam-6436	244	7	surjectively	surjectively	ADV
ejpam-6436	244	8	on	on	ADP
ejpam-6436	244	9	tc	tc	PRON
ejpam-6436	244	10	if	if	SCONJ
ejpam-6436	245	1	and	and	CCONJ
ejpam-6436	245	2	only	only	ADV
ejpam-6436	245	3	if	if	SCONJ
ejpam-6436	245	4	r	r	NOUN
ejpam-6436	245	5	acts	act	VERB
ejpam-6436	245	6	posurjectively	posurjectively	ADV
ejpam-6436	245	7	on	on	ADP
ejpam-6436	245	8	ra	ra	PROPN
ejpam-6436	245	9	and	and	CCONJ
ejpam-6436	245	10	s	s	PROPN
ejpam-6436	245	11	acts	act	NOUN
ejpam-6436	245	12	po	po	NOUN
ejpam-6436	245	13	-	-	PUNCT
ejpam-6436	245	14	surjectively	surjectively	ADV
ejpam-6436	245	15	on	on	ADP
ejpam-6436	245	16	sb	sb	PROPN
ejpam-6436	245	17	.	.	PROPN
ejpam-6436	245	18	proof	proof	NOUN
ejpam-6436	245	19	.	.	PUNCT
ejpam-6436	246	1	take	take	VERB
ejpam-6436	246	2	(	(	PUNCT
ejpam-6436	246	3	r	r	NOUN
ejpam-6436	246	4	,	,	PUNCT
ejpam-6436	246	5	cs	cs	ADJ
ejpam-6436	246	6	)	)	PUNCT
ejpam-6436	246	7	∈	∈	PROPN
ejpam-6436	246	8	t	t	NOUN
ejpam-6436	246	9	for	for	ADP
ejpam-6436	246	10	any	any	DET
ejpam-6436	246	11	r	r	NOUN
ejpam-6436	246	12	∈	∈	NOUN
ejpam-6436	246	13	r	r	NOUN
ejpam-6436	246	14	and	and	CCONJ
ejpam-6436	246	15	s	s	PROPN
ejpam-6436	246	16	∈	∈	PROPN
ejpam-6436	246	17	s.	s.	PROPN
ejpam-6436	246	18	since	since	SCONJ
ejpam-6436	246	19	t	t	PROPN
ejpam-6436	246	20	acts	act	VERB
ejpam-6436	246	21	po	po	NOUN
ejpam-6436	246	22	-	-	PUNCT
ejpam-6436	246	23	surjectively	surjectively	ADV
ejpam-6436	246	24	on	on	ADP
ejpam-6436	246	25	tc	tc	NOUN
ejpam-6436	246	26	so	so	ADV
ejpam-6436	246	27	for	for	SCONJ
ejpam-6436	246	28	every	every	DET
ejpam-6436	246	29	(	(	PUNCT
ejpam-6436	246	30	a	a	PRON
ejpam-6436	246	31	,	,	PUNCT
ejpam-6436	246	32	b	b	NOUN
ejpam-6436	246	33	)	)	PUNCT
ejpam-6436	246	34	∈t	∈t	NOUN
ejpam-6436	247	1	c	c	NOUN
ejpam-6436	247	2	it	it	PRON
ejpam-6436	247	3	can	can	AUX
ejpam-6436	247	4	be	be	AUX
ejpam-6436	247	5	found	find	VERB
ejpam-6436	247	6	that	that	SCONJ
ejpam-6436	247	7	(	(	PUNCT
ejpam-6436	247	8	a′	a′	PROPN
ejpam-6436	247	9	,	,	PUNCT
ejpam-6436	247	10	b′	b′	NUM
ejpam-6436	247	11	)	)	PUNCT
ejpam-6436	247	12	∈	∈	PROPN
ejpam-6436	247	13	tc	tc	ADP
ejpam-6436	247	14	such	such	ADJ
ejpam-6436	247	15	that	that	PRON
ejpam-6436	247	16	(	(	PUNCT
ejpam-6436	247	17	r	r	NOUN
ejpam-6436	247	18	,	,	PUNCT
ejpam-6436	247	19	cs)(a	cs)(a	PROPN
ejpam-6436	247	20	′	′	NUM
ejpam-6436	247	21	,	,	PUNCT
ejpam-6436	247	22	b′	b′	NUM
ejpam-6436	247	23	)	)	PUNCT
ejpam-6436	247	24	≤	≤	NOUN
ejpam-6436	247	25	(	(	PUNCT
ejpam-6436	247	26	a	a	DET
ejpam-6436	247	27	,	,	PUNCT
ejpam-6436	247	28	b	b	NOUN
ejpam-6436	247	29	)	)	PUNCT
ejpam-6436	247	30	implying	implying	ADJ
ejpam-6436	247	31	(	(	PUNCT
ejpam-6436	247	32	ra′	ra′	PROPN
ejpam-6436	247	33	,	,	PUNCT
ejpam-6436	247	34	sb′	sb′	NOUN
ejpam-6436	247	35	)	)	PUNCT
ejpam-6436	247	36	≤	≤	NOUN
ejpam-6436	247	37	(	(	PUNCT
ejpam-6436	247	38	a	a	DET
ejpam-6436	247	39	,	,	PUNCT
ejpam-6436	247	40	b	b	NOUN
ejpam-6436	247	41	)	)	PUNCT
ejpam-6436	247	42	which	which	PRON
ejpam-6436	247	43	further	far	ADV
ejpam-6436	247	44	implies	imply	VERB
ejpam-6436	247	45	ra′	ra′	VERB
ejpam-6436	247	46	≤	≤	NUM
ejpam-6436	247	47	a	a	DET
ejpam-6436	247	48	and	and	CCONJ
ejpam-6436	247	49	sb′	sb′	ADJ
ejpam-6436	247	50	≤	≤	NOUN
ejpam-6436	247	51	b	b	NOUN
ejpam-6436	247	52	for	for	ADP
ejpam-6436	247	53	arbitrary	arbitrary	ADJ
ejpam-6436	247	54	r	r	NOUN
ejpam-6436	247	55	∈	∈	PROPN
ejpam-6436	247	56	r	r	NOUN
ejpam-6436	247	57	,	,	PUNCT
ejpam-6436	247	58	s	s	PART
ejpam-6436	247	59	∈	∈	PROPN
ejpam-6436	247	60	s	s	PROPN
ejpam-6436	247	61	,	,	PUNCT
ejpam-6436	247	62	a	a	DET
ejpam-6436	247	63	∈	∈	PROPN
ejpam-6436	247	64	a	a	PRON
ejpam-6436	247	65	and	and	CCONJ
ejpam-6436	247	66	b	b	PROPN
ejpam-6436	247	67	∈	∈	PROPN
ejpam-6436	247	68	b.	b.	PROPN
ejpam-6436	248	1	thus	thus	ADV
ejpam-6436	248	2	,	,	PUNCT
ejpam-6436	248	3	r	r	NOUN
ejpam-6436	248	4	acts	act	VERB
ejpam-6436	248	5	po	po	NOUN
ejpam-6436	248	6	-	-	PUNCT
ejpam-6436	248	7	surjectively	surjectively	ADV
ejpam-6436	248	8	on	on	ADP
ejpam-6436	248	9	ra	ra	PROPN
ejpam-6436	248	10	and	and	CCONJ
ejpam-6436	248	11	s	s	PROPN
ejpam-6436	248	12	acts	act	NOUN
ejpam-6436	248	13	po	po	NOUN
ejpam-6436	248	14	-	-	PUNCT
ejpam-6436	248	15	surjectively	surjectively	ADV
ejpam-6436	248	16	on	on	ADP
ejpam-6436	248	17	sb	sb	PROPN
ejpam-6436	248	18	.	.	PUNCT
ejpam-6436	248	19	now	now	ADV
ejpam-6436	248	20	suppose	suppose	VERB
ejpam-6436	248	21	r	r	NOUN
ejpam-6436	248	22	acts	act	VERB
ejpam-6436	248	23	po	po	NOUN
ejpam-6436	248	24	-	-	PUNCT
ejpam-6436	248	25	surjectively	surjectively	ADV
ejpam-6436	248	26	on	on	ADP
ejpam-6436	248	27	ra	ra	PROPN
ejpam-6436	248	28	and	and	CCONJ
ejpam-6436	248	29	s	s	PROPN
ejpam-6436	248	30	acts	act	NOUN
ejpam-6436	248	31	po	po	NOUN
ejpam-6436	248	32	-	-	PUNCT
ejpam-6436	248	33	surjectively	surjectively	ADV
ejpam-6436	248	34	on	on	ADP
ejpam-6436	248	35	sb	sb	PROPN
ejpam-6436	248	36	.	.	PUNCT
ejpam-6436	249	1	we	we	PRON
ejpam-6436	249	2	need	need	VERB
ejpam-6436	249	3	to	to	PART
ejpam-6436	249	4	show	show	VERB
ejpam-6436	249	5	that	that	SCONJ
ejpam-6436	249	6	t	t	PROPN
ejpam-6436	249	7	acts	act	VERB
ejpam-6436	249	8	po	po	NOUN
ejpam-6436	249	9	-	-	PUNCT
ejpam-6436	249	10	surjectively	surjectively	ADV
ejpam-6436	249	11	on	on	ADP
ejpam-6436	249	12	tc	tc	X
ejpam-6436	249	13	.	.	PUNCT
ejpam-6436	249	14	assume	assume	VERB
ejpam-6436	249	15	on	on	ADP
ejpam-6436	249	16	contrary	contrary	ADV
ejpam-6436	249	17	that	that	SCONJ
ejpam-6436	249	18	t	t	PROPN
ejpam-6436	249	19	does	do	AUX
ejpam-6436	249	20	n’t	not	PART
ejpam-6436	249	21	act	act	VERB
ejpam-6436	249	22	posurjectively	posurjectively	ADV
ejpam-6436	249	23	on	on	ADP
ejpam-6436	249	24	tc	tc	NUM
ejpam-6436	249	25	,	,	PUNCT
ejpam-6436	249	26	there	there	PRON
ejpam-6436	249	27	exists	exist	VERB
ejpam-6436	249	28	(	(	PUNCT
ejpam-6436	249	29	r	r	NOUN
ejpam-6436	249	30	,	,	PUNCT
ejpam-6436	249	31	f	f	X
ejpam-6436	249	32	)	)	PUNCT
ejpam-6436	249	33	∈	∈	PROPN
ejpam-6436	249	34	t	t	NOUN
ejpam-6436	249	35	such	such	ADJ
ejpam-6436	249	36	that	that	SCONJ
ejpam-6436	249	37	(	(	PUNCT
ejpam-6436	249	38	r	r	NOUN
ejpam-6436	249	39	,	,	PUNCT
ejpam-6436	249	40	f)tc	f)tc	PROPN
ejpam-6436	249	41	≰	≰	PROPN
ejpam-6436	249	42	tc	tc	NOUN
ejpam-6436	249	43	.	.	PUNCT
ejpam-6436	250	1	therefore	therefore	ADV
ejpam-6436	250	2	there	there	PRON
ejpam-6436	250	3	exists	exist	VERB
ejpam-6436	250	4	(	(	PUNCT
ejpam-6436	250	5	a	a	PRON
ejpam-6436	250	6	,	,	PUNCT
ejpam-6436	250	7	b	b	NOUN
ejpam-6436	250	8	)	)	PUNCT
ejpam-6436	250	9	∈	∈	NOUN
ejpam-6436	250	10	tc	tc	ADP
ejpam-6436	250	11	such	such	ADJ
ejpam-6436	250	12	that	that	PRON
ejpam-6436	250	13	for	for	ADP
ejpam-6436	250	14	every	every	PRON
ejpam-6436	250	15	(	(	PUNCT
ejpam-6436	250	16	a′	a′	PROPN
ejpam-6436	250	17	,	,	PUNCT
ejpam-6436	250	18	b′	b′	NUM
ejpam-6436	250	19	)	)	PUNCT
ejpam-6436	250	20	∈	∈	PROPN
ejpam-6436	251	1	tc	tc	NOUN
ejpam-6436	251	2	we	we	PRON
ejpam-6436	251	3	have	have	VERB
ejpam-6436	251	4	(	(	PUNCT
ejpam-6436	251	5	r	r	NOUN
ejpam-6436	251	6	,	,	PUNCT
ejpam-6436	251	7	f)(a′	f)(a′	PROPN
ejpam-6436	251	8	,	,	PUNCT
ejpam-6436	251	9	b′	b′	NUM
ejpam-6436	251	10	)	)	PUNCT
ejpam-6436	251	11	≰	≰	PROPN
ejpam-6436	251	12	(	(	PUNCT
ejpam-6436	251	13	a	a	DET
ejpam-6436	251	14	,	,	PUNCT
ejpam-6436	251	15	b	b	NOUN
ejpam-6436	251	16	)	)	PUNCT
ejpam-6436	251	17	implying	imply	VERB
ejpam-6436	251	18	that	that	SCONJ
ejpam-6436	251	19	(	(	PUNCT
ejpam-6436	251	20	ra′	ra′	PROPN
ejpam-6436	251	21	,	,	PUNCT
ejpam-6436	251	22	f(a′)b′	f(a′)b′	X
ejpam-6436	251	23	)	)	PUNCT
ejpam-6436	251	24	≰	≰	PROPN
ejpam-6436	251	25	(	(	PUNCT
ejpam-6436	251	26	a	a	DET
ejpam-6436	251	27	,	,	PUNCT
ejpam-6436	251	28	b	b	NOUN
ejpam-6436	251	29	)	)	PUNCT
ejpam-6436	251	30	,	,	PUNCT
ejpam-6436	251	31	the	the	DET
ejpam-6436	251	32	following	follow	VERB
ejpam-6436	251	33	cases	case	NOUN
ejpam-6436	251	34	arise	arise	VERB
ejpam-6436	251	35	:	:	PUNCT
ejpam-6436	251	36	case	case	NOUN
ejpam-6436	251	37	1	1	NUM
ejpam-6436	251	38	:	:	PUNCT
ejpam-6436	251	39	if	if	SCONJ
ejpam-6436	251	40	ra′	ra′	NOUN
ejpam-6436	251	41	≰	≰	VERB
ejpam-6436	251	42	a	a	PRON
ejpam-6436	251	43	and	and	CCONJ
ejpam-6436	251	44	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	251	45	≰	≰	PROPN
ejpam-6436	251	46	b	b	PROPN
ejpam-6436	251	47	,	,	PUNCT
ejpam-6436	251	48	a	a	DET
ejpam-6436	251	49	contradiction	contradiction	NOUN
ejpam-6436	251	50	to	to	ADP
ejpam-6436	251	51	both	both	DET
ejpam-6436	251	52	r	r	NOUN
ejpam-6436	251	53	and	and	CCONJ
ejpam-6436	251	54	s	s	AUX
ejpam-6436	251	55	acting	act	VERB
ejpam-6436	251	56	po	po	NOUN
ejpam-6436	251	57	-	-	PUNCT
ejpam-6436	251	58	surjectively	surjectively	ADV
ejpam-6436	251	59	on	on	ADP
ejpam-6436	251	60	ra	ra	PROPN
ejpam-6436	251	61	and	and	CCONJ
ejpam-6436	251	62	sb	sb	PROPN
ejpam-6436	251	63	.	.	PROPN
ejpam-6436	251	64	case	case	NOUN
ejpam-6436	251	65	2	2	NUM
ejpam-6436	251	66	:	:	PUNCT
ejpam-6436	251	67	if	if	SCONJ
ejpam-6436	251	68	ra′	ra′	NOUN
ejpam-6436	251	69	≰	≰	VERB
ejpam-6436	251	70	a	a	PRON
ejpam-6436	251	71	and	and	CCONJ
ejpam-6436	251	72	f(a′)b′	f(a′)b′	X
ejpam-6436	251	73	≤	≤	NUM
ejpam-6436	251	74	b	b	NOUN
ejpam-6436	251	75	,	,	PUNCT
ejpam-6436	251	76	a	a	DET
ejpam-6436	251	77	contradiction	contradiction	NOUN
ejpam-6436	251	78	to	to	ADP
ejpam-6436	251	79	r	r	NOUN
ejpam-6436	251	80	acting	act	VERB
ejpam-6436	251	81	po	po	NOUN
ejpam-6436	251	82	-	-	PUNCT
ejpam-6436	251	83	surjectively	surjectively	ADV
ejpam-6436	251	84	on	on	ADP
ejpam-6436	251	85	ra	ra	PROPN
ejpam-6436	252	1	.	.	PUNCT
ejpam-6436	252	2	case	case	NOUN
ejpam-6436	253	1	3	3	NUM
ejpam-6436	253	2	:	:	PUNCT
ejpam-6436	253	3	if	if	SCONJ
ejpam-6436	253	4	ra′	ra′	VERB
ejpam-6436	253	5	≤	≤	NUM
ejpam-6436	253	6	a	a	PRON
ejpam-6436	253	7	and	and	CCONJ
ejpam-6436	253	8	f(a′)b′	f(a′)b′	PROPN
ejpam-6436	253	9	≰	≰	PROPN
ejpam-6436	253	10	b	b	PROPN
ejpam-6436	253	11	,	,	PUNCT
ejpam-6436	253	12	a	a	DET
ejpam-6436	253	13	contradiction	contradiction	NOUN
ejpam-6436	253	14	to	to	ADP
ejpam-6436	253	15	s	s	AUX
ejpam-6436	253	16	acting	act	VERB
ejpam-6436	253	17	po	po	NOUN
ejpam-6436	253	18	-	-	PUNCT
ejpam-6436	253	19	surjectively	surjectively	ADV
ejpam-6436	253	20	on	on	ADP
ejpam-6436	253	21	sb	sb	PROPN
ejpam-6436	253	22	.	.	PROPN
ejpam-6436	253	23	hence	hence	PROPN
ejpam-6436	253	24	t	t	PROPN
ejpam-6436	253	25	acts	act	VERB
ejpam-6436	253	26	po	po	NOUN
ejpam-6436	253	27	-	-	PUNCT
ejpam-6436	253	28	surjectively	surjectively	ADV
ejpam-6436	253	29	on	on	ADP
ejpam-6436	253	30	tc	tc	NOUN
ejpam-6436	253	31	.	.	PUNCT
ejpam-6436	253	32	definition	definition	NOUN
ejpam-6436	253	33	2	2	NUM
ejpam-6436	253	34	.	.	PUNCT
ejpam-6436	253	35	a	a	DET
ejpam-6436	253	36	subset	subset	NOUN
ejpam-6436	253	37	p	p	VERB
ejpam-6436	253	38	⊆	⊆	NUM
ejpam-6436	253	39	s	s	NOUN
ejpam-6436	253	40	is	be	AUX
ejpam-6436	253	41	referred	refer	VERB
ejpam-6436	253	42	to	to	ADP
ejpam-6436	253	43	as	as	ADV
ejpam-6436	253	44	simultaneously	simultaneously	ADV
ejpam-6436	253	45	right	right	ADJ
ejpam-6436	253	46	po	po	NOUN
ejpam-6436	253	47	-	-	NOUN
ejpam-6436	253	48	cancellable	cancellable	ADJ
ejpam-6436	253	49	in	in	ADP
ejpam-6436	253	50	s	s	PRON
ejpam-6436	253	51	if	if	SCONJ
ejpam-6436	253	52	sp	sp	ADP
ejpam-6436	253	53	≤	≤	NOUN
ejpam-6436	253	54	s′p	s′p	ADV
ejpam-6436	253	55	for	for	ADP
ejpam-6436	253	56	any	any	DET
ejpam-6436	253	57	p	p	NOUN
ejpam-6436	253	58	∈	∈	PROPN
ejpam-6436	253	59	p	p	NOUN
ejpam-6436	253	60	and	and	CCONJ
ejpam-6436	253	61	s	s	NOUN
ejpam-6436	253	62	,	,	PUNCT
ejpam-6436	253	63	s′	s′	PUNCT
ejpam-6436	253	64	∈	∈	PROPN
ejpam-6436	253	65	s	s	PART
ejpam-6436	253	66	implies	implie	NOUN
ejpam-6436	253	67	s	s	VERB
ejpam-6436	253	68	≤	≤	NUM
ejpam-6436	253	69	s′.	s′.	PROPN
ejpam-6436	253	70	proposition	proposition	NOUN
ejpam-6436	253	71	9	9	NUM
ejpam-6436	253	72	.	.	PUNCT
ejpam-6436	254	1	if	if	SCONJ
ejpam-6436	254	2	the	the	DET
ejpam-6436	254	3	element	element	NOUN
ejpam-6436	254	4	(	(	PUNCT
ejpam-6436	254	5	r	r	NOUN
ejpam-6436	254	6	,	,	PUNCT
ejpam-6436	254	7	f	f	X
ejpam-6436	254	8	)	)	PUNCT
ejpam-6436	254	9	∈	∈	PROPN
ejpam-6436	254	10	t	t	PROPN
ejpam-6436	254	11	is	be	AUX
ejpam-6436	254	12	right	right	ADJ
ejpam-6436	254	13	po	po	NOUN
ejpam-6436	254	14	-	-	NOUN
ejpam-6436	254	15	cancellable	cancellable	ADJ
ejpam-6436	254	16	,	,	PUNCT
ejpam-6436	254	17	then	then	ADV
ejpam-6436	254	18	r	r	NOUN
ejpam-6436	254	19	acts	act	VERB
ejpam-6436	254	20	po	po	NOUN
ejpam-6436	254	21	-	-	PUNCT
ejpam-6436	254	22	surjectively	surjectively	ADV
ejpam-6436	254	23	on	on	ADP
ejpam-6436	254	24	ra	ra	PROPN
ejpam-6436	254	25	,	,	PUNCT
ejpam-6436	254	26	r	r	NOUN
ejpam-6436	254	27	is	be	AUX
ejpam-6436	254	28	right	right	ADJ
ejpam-6436	254	29	po	po	NOUN
ejpam-6436	254	30	-	-	NOUN
ejpam-6436	254	31	cancellable	cancellable	ADJ
ejpam-6436	254	32	in	in	ADP
ejpam-6436	254	33	r	r	NOUN
ejpam-6436	254	34	,	,	PUNCT
ejpam-6436	254	35	and	and	CCONJ
ejpam-6436	254	36	for	for	ADP
ejpam-6436	254	37	any	any	DET
ejpam-6436	254	38	a	a	DET
ejpam-6436	254	39	∈	∈	PROPN
ejpam-6436	254	40	a	a	DET
ejpam-6436	254	41	the	the	DET
ejpam-6436	254	42	set	set	ADJ
ejpam-6436	254	43	f(a	f(a	NOUN
ejpam-6436	254	44	)	)	PUNCT
ejpam-6436	254	45	is	be	AUX
ejpam-6436	254	46	simultaneously	simultaneously	ADV
ejpam-6436	254	47	right	right	ADJ
ejpam-6436	254	48	po	po	NOUN
ejpam-6436	254	49	-	-	NOUN
ejpam-6436	254	50	cancellable	cancellable	ADJ
ejpam-6436	254	51	in	in	ADP
ejpam-6436	254	52	s.	s.	PROPN
ejpam-6436	254	53	proof	proof	PROPN
ejpam-6436	254	54	.	.	PUNCT
ejpam-6436	255	1	suppose	suppose	VERB
ejpam-6436	255	2	(	(	PUNCT
ejpam-6436	255	3	r	r	NOUN
ejpam-6436	255	4	,	,	PUNCT
ejpam-6436	255	5	f	f	X
ejpam-6436	255	6	)	)	PUNCT
ejpam-6436	255	7	∈	∈	PROPN
ejpam-6436	255	8	t	t	PROPN
ejpam-6436	255	9	is	be	AUX
ejpam-6436	255	10	right	right	ADJ
ejpam-6436	255	11	po	po	NOUN
ejpam-6436	255	12	-	-	NOUN
ejpam-6436	255	13	cancellable	cancellable	ADJ
ejpam-6436	255	14	.	.	PUNCT
ejpam-6436	256	1	assuming	assume	VERB
ejpam-6436	256	2	r	r	NOUN
ejpam-6436	256	3	is	be	AUX
ejpam-6436	256	4	not	not	PART
ejpam-6436	256	5	po	po	NOUN
ejpam-6436	256	6	-	-	VERB
ejpam-6436	256	7	surjectively	surjectively	ADV
ejpam-6436	256	8	on	on	ADP
ejpam-6436	256	9	ra	ra	PROPN
ejpam-6436	256	10	,	,	PUNCT
ejpam-6436	256	11	by	by	ADP
ejpam-6436	256	12	way	way	NOUN
ejpam-6436	256	13	of	of	ADP
ejpam-6436	256	14	contadiction	contadiction	NOUN
ejpam-6436	256	15	.	.	PUNCT
ejpam-6436	257	1	therefore	therefore	ADV
ejpam-6436	257	2	,	,	PUNCT
ejpam-6436	257	3	we	we	PRON
ejpam-6436	257	4	can	can	AUX
ejpam-6436	257	5	found	find	VERB
ejpam-6436	257	6	that	that	SCONJ
ejpam-6436	257	7	a	a	DET
ejpam-6436	257	8	∈	∈	PROPN
ejpam-6436	257	9	a	a	DET
ejpam-6436	257	10	such	such	ADJ
ejpam-6436	257	11	that	that	PRON
ejpam-6436	257	12	for	for	ADP
ejpam-6436	257	13	every	every	DET
ejpam-6436	257	14	a′	a′	PROPN
ejpam-6436	257	15	∈	∈	PROPN
ejpam-6436	257	16	a	a	PRON
ejpam-6436	257	17	,	,	PUNCT
ejpam-6436	257	18	ra′	ra′	PROPN
ejpam-6436	257	19	≰	≰	PROPN
ejpam-6436	257	20	a.	a.	NOUN
ejpam-6436	257	21	clearly	clearly	ADV
ejpam-6436	257	22	,	,	PUNCT
ejpam-6436	257	23	a	a	DET
ejpam-6436	257	24	⋂	⋂	PROPN
ejpam-6436	257	25	ra	ra	NOUN
ejpam-6436	257	26	=	=	NOUN
ejpam-6436	257	27	∅	∅	NOUN
ejpam-6436	257	28	,	,	PUNCT
ejpam-6436	257	29	for	for	ADP
ejpam-6436	257	30	if	if	SCONJ
ejpam-6436	257	31	x	x	SYM
ejpam-6436	257	32	∈	∈	PROPN
ejpam-6436	257	33	a	a	DET
ejpam-6436	257	34	⋂	⋂	PROPN
ejpam-6436	257	35	ra	ra	NOUN
ejpam-6436	257	36	then	then	ADV
ejpam-6436	257	37	x	x	X
ejpam-6436	257	38	=	=	PUNCT
ejpam-6436	257	39	a	a	PRON
ejpam-6436	257	40	and	and	CCONJ
ejpam-6436	257	41	x	x	SYM
ejpam-6436	257	42	=	=	NOUN
ejpam-6436	257	43	ra′′	ra′′	NOUN
ejpam-6436	257	44	for	for	ADP
ejpam-6436	257	45	some	some	DET
ejpam-6436	257	46	a′′	a′′	NOUN
ejpam-6436	257	47	∈	∈	PROPN
ejpam-6436	257	48	a	a	DET
ejpam-6436	257	49	implying	implying	ADJ
ejpam-6436	257	50	ra′′	ra′′	NOUN
ejpam-6436	257	51	=	=	PUNCT
ejpam-6436	257	52	a	a	PRON
ejpam-6436	257	53	for	for	ADP
ejpam-6436	257	54	some	some	DET
ejpam-6436	257	55	a′′	a′′	NOUN
ejpam-6436	257	56	∈	∈	PROPN
ejpam-6436	257	57	a	a	DET
ejpam-6436	257	58	implying	implying	ADJ
ejpam-6436	257	59	ra′′	ra′′	NOUN
ejpam-6436	257	60	≤	≤	NOUN
ejpam-6436	257	61	a	a	PRON
ejpam-6436	257	62	for	for	ADP
ejpam-6436	257	63	some	some	DET
ejpam-6436	257	64	a′′	a′′	PROPN
ejpam-6436	257	65	∈	∈	PROPN
ejpam-6436	257	66	a	a	PRON
ejpam-6436	257	67	which	which	PRON
ejpam-6436	257	68	is	be	AUX
ejpam-6436	257	69	not	not	PART
ejpam-6436	257	70	true	true	ADJ
ejpam-6436	257	71	.	.	PUNCT
ejpam-6436	258	1	let	let	VERB
ejpam-6436	258	2	g	g	NOUN
ejpam-6436	258	3	,	,	PUNCT
ejpam-6436	258	4	g′	g′	NOUN
ejpam-6436	258	5	∈	∈	PROPN
ejpam-6436	258	6	f	f	X
ejpam-6436	258	7	(	(	PUNCT
ejpam-6436	258	8	a	a	DET
ejpam-6436	258	9	,	,	PUNCT
ejpam-6436	258	10	s	s	NOUN
ejpam-6436	258	11	)	)	PUNCT
ejpam-6436	258	12	where	where	SCONJ
ejpam-6436	258	13	g(a	g(a	PROPN
ejpam-6436	258	14	)	)	PUNCT
ejpam-6436	258	15	≰	≰	PROPN
ejpam-6436	258	16	g′(a	g′(a	PROPN
ejpam-6436	258	17	)	)	PUNCT
ejpam-6436	258	18	and	and	CCONJ
ejpam-6436	258	19	g|ra	g|ra	NOUN
ejpam-6436	258	20	≤	≤	PROPN
ejpam-6436	258	21	g′|ra	g′|ra	PROPN
ejpam-6436	258	22	.	.	PUNCT
ejpam-6436	259	1	hence	hence	ADV
ejpam-6436	259	2	,	,	PUNCT
ejpam-6436	259	3	we	we	PRON
ejpam-6436	259	4	have	have	VERB
ejpam-6436	259	5	(	(	PUNCT
ejpam-6436	259	6	grf)(a	grf)(a	NOUN
ejpam-6436	259	7	′	′	NUM
ejpam-6436	259	8	)	)	PUNCT
ejpam-6436	259	9	=	=	SYM
ejpam-6436	259	10	g(ra′)f(a′	g(ra′)f(a′	PROPN
ejpam-6436	259	11	)	)	PUNCT
ejpam-6436	259	12	≤	≤	NUM
ejpam-6436	259	13	g′(ra′)f(a′	g′(ra′)f(a′	NOUN
ejpam-6436	259	14	)	)	PUNCT
ejpam-6436	259	15	=	=	PUNCT
ejpam-6436	260	1	(	(	PUNCT
ejpam-6436	260	2	g′rf)(a	g′rf)(a	NOUN
ejpam-6436	260	3	′	′	NUM
ejpam-6436	260	4	)	)	PUNCT
ejpam-6436	260	5	implying	imply	VERB
ejpam-6436	260	6	grf	grf	PROPN
ejpam-6436	260	7	≤	≤	PROPN
ejpam-6436	260	8	g′rf	g′rf	NOUN
ejpam-6436	260	9	,	,	PUNCT
ejpam-6436	260	10	where	where	SCONJ
ejpam-6436	260	11	a′	a′	PROPN
ejpam-6436	260	12	∈	∈	PROPN
ejpam-6436	260	13	a.	a.	NOUN
ejpam-6436	260	14	then	then	ADV
ejpam-6436	260	15	,	,	PUNCT
ejpam-6436	260	16	(	(	PUNCT
ejpam-6436	260	17	1	1	NUM
ejpam-6436	260	18	,	,	PUNCT
ejpam-6436	260	19	g)(r	g)(r	NOUN
ejpam-6436	260	20	,	,	PUNCT
ejpam-6436	260	21	f	f	X
ejpam-6436	260	22	)	)	PUNCT
ejpam-6436	260	23	=	=	SYM
ejpam-6436	260	24	(	(	PUNCT
ejpam-6436	260	25	r	r	NOUN
ejpam-6436	260	26	,	,	PUNCT
ejpam-6436	260	27	grf	grf	NOUN
ejpam-6436	260	28	)	)	PUNCT
ejpam-6436	260	29	≤	≤	NOUN
ejpam-6436	260	30	(	(	PUNCT
ejpam-6436	260	31	r	r	NOUN
ejpam-6436	260	32	,	,	PUNCT
ejpam-6436	260	33	g′rf	g′rf	NOUN
ejpam-6436	260	34	)	)	PUNCT
ejpam-6436	260	35	=	=	PUNCT
ejpam-6436	260	36	(	(	PUNCT
ejpam-6436	260	37	1	1	NUM
ejpam-6436	260	38	,	,	PUNCT
ejpam-6436	260	39	g′)(r	g′)(r	NOUN
ejpam-6436	260	40	,	,	PUNCT
ejpam-6436	260	41	f	f	PROPN
ejpam-6436	260	42	)	)	PUNCT
ejpam-6436	260	43	.	.	PUNCT
ejpam-6436	261	1	since	since	SCONJ
ejpam-6436	261	2	by	by	ADP
ejpam-6436	261	3	our	our	PRON
ejpam-6436	261	4	assumption	assumption	NOUN
ejpam-6436	261	5	(	(	PUNCT
ejpam-6436	261	6	r	r	NOUN
ejpam-6436	261	7	,	,	PUNCT
ejpam-6436	261	8	f	f	X
ejpam-6436	261	9	)	)	PUNCT
ejpam-6436	261	10	∈	∈	PROPN
ejpam-6436	261	11	t	t	PROPN
ejpam-6436	261	12	b.	b.	PROPN
ejpam-6436	261	13	al	al	PROPN
ejpam-6436	261	14	subaiei	subaiei	PROPN
ejpam-6436	261	15	et	et	PROPN
ejpam-6436	261	16	al	al	PROPN
ejpam-6436	261	17	.	.	PUNCT
ejpam-6436	261	18	/	/	SYM
ejpam-6436	261	19	eur	eur	PROPN
ejpam-6436	261	20	.	.	PUNCT
ejpam-6436	262	1	j.	j.	PROPN
ejpam-6436	262	2	pure	pure	PROPN
ejpam-6436	262	3	appl	appl	PROPN
ejpam-6436	262	4	.	.	PROPN
ejpam-6436	262	5	math	math	PROPN
ejpam-6436	262	6	,	,	PUNCT
ejpam-6436	262	7	18	18	NUM
ejpam-6436	262	8	(	(	PUNCT
ejpam-6436	262	9	3	3	NUM
ejpam-6436	262	10	)	)	PUNCT
ejpam-6436	262	11	(	(	PUNCT
ejpam-6436	262	12	2025	2025	NUM
ejpam-6436	262	13	)	)	PUNCT
ejpam-6436	262	14	,	,	PUNCT
ejpam-6436	262	15	6436	6436	NUM
ejpam-6436	262	16	10	10	NUM
ejpam-6436	262	17	of	of	ADP
ejpam-6436	262	18	14	14	NUM
ejpam-6436	262	19	is	be	AUX
ejpam-6436	262	20	right	right	ADJ
ejpam-6436	262	21	po	po	NOUN
ejpam-6436	262	22	-	-	NOUN
ejpam-6436	262	23	cancellable	cancellable	ADJ
ejpam-6436	262	24	so	so	CCONJ
ejpam-6436	262	25	(	(	PUNCT
ejpam-6436	262	26	1	1	NUM
ejpam-6436	262	27	,	,	PUNCT
ejpam-6436	262	28	g	g	NOUN
ejpam-6436	262	29	)	)	PUNCT
ejpam-6436	262	30	≤	≤	NOUN
ejpam-6436	262	31	(	(	PUNCT
ejpam-6436	262	32	1	1	NUM
ejpam-6436	262	33	,	,	PUNCT
ejpam-6436	262	34	g′	g′	NOUN
ejpam-6436	262	35	)	)	PUNCT
ejpam-6436	262	36	which	which	PRON
ejpam-6436	262	37	implies	imply	VERB
ejpam-6436	262	38	g	g	PROPN
ejpam-6436	262	39	≤	≤	NUM
ejpam-6436	262	40	g′	g′	NOUN
ejpam-6436	262	41	so	so	SCONJ
ejpam-6436	262	42	g(x	g(x	NOUN
ejpam-6436	262	43	)	)	PUNCT
ejpam-6436	262	44	≤	≤	NUM
ejpam-6436	262	45	g′(x	g′(x	NOUN
ejpam-6436	262	46	)	)	PUNCT
ejpam-6436	262	47	for	for	ADP
ejpam-6436	262	48	all	all	DET
ejpam-6436	262	49	x	x	SYM
ejpam-6436	262	50	∈	∈	PROPN
ejpam-6436	262	51	a	a	PRON
ejpam-6436	262	52	and	and	CCONJ
ejpam-6436	262	53	g(a	g(a	PROPN
ejpam-6436	262	54	)	)	PUNCT
ejpam-6436	262	55	≤	≤	NUM
ejpam-6436	263	1	g′(a	g′(a	PROPN
ejpam-6436	263	2	)	)	PUNCT
ejpam-6436	263	3	which	which	PRON
ejpam-6436	263	4	is	be	AUX
ejpam-6436	263	5	a	a	DET
ejpam-6436	263	6	contradiction	contradiction	NOUN
ejpam-6436	263	7	.	.	PUNCT
ejpam-6436	264	1	thus	thus	ADV
ejpam-6436	264	2	,	,	PUNCT
ejpam-6436	264	3	r	r	NOUN
ejpam-6436	264	4	acts	act	VERB
ejpam-6436	264	5	po	po	NOUN
ejpam-6436	264	6	-	-	PUNCT
ejpam-6436	264	7	surjectively	surjectively	ADV
ejpam-6436	264	8	on	on	ADP
ejpam-6436	264	9	ra	ra	PROPN
ejpam-6436	264	10	.	.	PUNCT
ejpam-6436	265	1	the	the	DET
ejpam-6436	265	2	remainder	remainder	NOUN
ejpam-6436	265	3	can	can	AUX
ejpam-6436	265	4	be	be	AUX
ejpam-6436	265	5	proved	prove	VERB
ejpam-6436	265	6	using	use	VERB
ejpam-6436	265	7	a	a	DET
ejpam-6436	265	8	similar	similar	ADJ
ejpam-6436	265	9	argument	argument	NOUN
ejpam-6436	265	10	to	to	PART
ejpam-6436	265	11	proposition	proposition	VERB
ejpam-6436	265	12	2.4	2.4	NUM
ejpam-6436	265	13	in	in	ADP
ejpam-6436	265	14	[	[	X
ejpam-6436	265	15	15	15	NUM
ejpam-6436	265	16	]	]	PUNCT
ejpam-6436	265	17	,	,	PUNCT
ejpam-6436	265	18	with	with	ADP
ejpam-6436	265	19	respect	respect	NOUN
ejpam-6436	265	20	to	to	ADP
ejpam-6436	265	21	the	the	DET
ejpam-6436	265	22	order	order	NOUN
ejpam-6436	265	23	relation	relation	NOUN
ejpam-6436	265	24	.	.	PUNCT
ejpam-6436	266	1	theorem	theorem	NOUN
ejpam-6436	266	2	5	5	NUM
ejpam-6436	266	3	.	.	PUNCT
ejpam-6436	267	1	if	if	SCONJ
ejpam-6436	267	2	the	the	DET
ejpam-6436	267	3	pomonoid	pomonoid	PROPN
ejpam-6436	267	4	t	t	PROPN
ejpam-6436	267	5	is	be	AUX
ejpam-6436	267	6	right	right	ADJ
ejpam-6436	267	7	po	po	NOUN
ejpam-6436	267	8	-	-	NOUN
ejpam-6436	267	9	cancellative	cancellative	ADJ
ejpam-6436	267	10	,	,	PUNCT
ejpam-6436	267	11	then	then	ADV
ejpam-6436	267	12	r	r	NOUN
ejpam-6436	267	13	acts	act	VERB
ejpam-6436	267	14	po	po	NOUN
ejpam-6436	267	15	-	-	PUNCT
ejpam-6436	267	16	surjectively	surjectively	ADV
ejpam-6436	267	17	on	on	ADP
ejpam-6436	267	18	ra	ra	PROPN
ejpam-6436	267	19	and	and	CCONJ
ejpam-6436	267	20	,	,	PUNCT
ejpam-6436	267	21	r	r	NOUN
ejpam-6436	267	22	and	and	CCONJ
ejpam-6436	267	23	s	s	NOUN
ejpam-6436	267	24	are	be	AUX
ejpam-6436	267	25	right	right	ADJ
ejpam-6436	267	26	po	po	NOUN
ejpam-6436	267	27	-	-	NOUN
ejpam-6436	267	28	cancellative	cancellative	ADJ
ejpam-6436	267	29	.	.	PUNCT
ejpam-6436	268	1	the	the	DET
ejpam-6436	268	2	proof	proof	NOUN
ejpam-6436	268	3	follows	follow	VERB
ejpam-6436	268	4	by	by	ADP
ejpam-6436	268	5	similar	similar	ADJ
ejpam-6436	268	6	argument	argument	NOUN
ejpam-6436	268	7	as	as	SCONJ
ejpam-6436	268	8	theorem	theorem	VERB
ejpam-6436	268	9	2.6	2.6	NUM
ejpam-6436	268	10	in	in	ADP
ejpam-6436	268	11	[	[	X
ejpam-6436	268	12	15	15	NUM
ejpam-6436	268	13	]	]	PUNCT
ejpam-6436	268	14	with	with	ADP
ejpam-6436	268	15	respect	respect	NOUN
ejpam-6436	268	16	to	to	ADP
ejpam-6436	268	17	the	the	DET
ejpam-6436	268	18	order	order	NOUN
ejpam-6436	268	19	relation	relation	NOUN
ejpam-6436	268	20	and	and	CCONJ
ejpam-6436	268	21	by	by	ADP
ejpam-6436	268	22	using	use	VERB
ejpam-6436	268	23	proposition	proposition	NOUN
ejpam-6436	268	24	9	9	NUM
ejpam-6436	268	25	above	above	ADV
ejpam-6436	268	26	.	.	PUNCT
ejpam-6436	269	1	in	in	ADP
ejpam-6436	269	2	[	[	X
ejpam-6436	269	3	11	11	NUM
ejpam-6436	269	4	,	,	PUNCT
ejpam-6436	269	5	13	13	NUM
ejpam-6436	269	6	,	,	PUNCT
ejpam-6436	269	7	18	18	NUM
ejpam-6436	269	8	,	,	PUNCT
ejpam-6436	269	9	19	19	NUM
ejpam-6436	269	10	]	]	X
ejpam-6436	269	11	many	many	ADJ
ejpam-6436	269	12	of	of	ADP
ejpam-6436	269	13	po	po	NOUN
ejpam-6436	269	14	-	-	PUNCT
ejpam-6436	269	15	flatness	flatness	NOUN
ejpam-6436	269	16	properties	property	NOUN
ejpam-6436	269	17	such	such	ADJ
ejpam-6436	269	18	as	as	ADP
ejpam-6436	269	19	po	po	NOUN
ejpam-6436	269	20	-	-	PUNCT
ejpam-6436	269	21	torsion	torsion	NOUN
ejpam-6436	269	22	free	free	ADJ
ejpam-6436	269	23	,	,	PUNCT
ejpam-6436	269	24	property	property	NOUN
ejpam-6436	269	25	(	(	PUNCT
ejpam-6436	269	26	e	e	NOUN
ejpam-6436	269	27	)	)	PUNCT
ejpam-6436	269	28	,	,	PUNCT
ejpam-6436	269	29	and	and	CCONJ
ejpam-6436	269	30	property	property	NOUN
ejpam-6436	269	31	(	(	PUNCT
ejpam-6436	269	32	p	p	NOUN
ejpam-6436	269	33	)	)	PUNCT
ejpam-6436	269	34	in	in	ADP
ejpam-6436	269	35	the	the	DET
ejpam-6436	269	36	category	category	NOUN
ejpam-6436	269	37	of	of	ADP
ejpam-6436	269	38	r	r	NOUN
ejpam-6436	269	39	-	-	PUNCT
ejpam-6436	269	40	posets	poset	NOUN
ejpam-6436	269	41	were	be	AUX
ejpam-6436	269	42	considered	consider	VERB
ejpam-6436	269	43	.	.	PUNCT
ejpam-6436	270	1	definition	definition	NOUN
ejpam-6436	270	2	3	3	X
ejpam-6436	270	3	.	.	PUNCT
ejpam-6436	271	1	let	let	VERB
ejpam-6436	271	2	ra	ra	PROPN
ejpam-6436	271	3	be	be	AUX
ejpam-6436	271	4	a	a	DET
ejpam-6436	271	5	left	left	ADJ
ejpam-6436	271	6	r	r	NOUN
ejpam-6436	271	7	-	-	PUNCT
ejpam-6436	271	8	poset	poset	NOUN
ejpam-6436	271	9	.	.	PUNCT
ejpam-6436	272	1	we	we	PRON
ejpam-6436	272	2	say	say	VERB
ejpam-6436	272	3	that	that	PRON
ejpam-6436	272	4	:	:	PUNCT
ejpam-6436	272	5	(	(	PUNCT
ejpam-6436	272	6	i	i	NOUN
ejpam-6436	272	7	)	)	PUNCT
ejpam-6436	272	8	ra	ra	PROPN
ejpam-6436	272	9	is	be	AUX
ejpam-6436	272	10	po	po	NOUN
ejpam-6436	272	11	-	-	PUNCT
ejpam-6436	272	12	torsion	torsion	NOUN
ejpam-6436	272	13	free	free	ADJ
ejpam-6436	272	14	over	over	ADP
ejpam-6436	272	15	r	r	NOUN
ejpam-6436	272	16	if	if	SCONJ
ejpam-6436	272	17	every	every	PRON
ejpam-6436	272	18	left	leave	VERB
ejpam-6436	272	19	po	po	NOUN
ejpam-6436	272	20	-	-	PUNCT
ejpam-6436	272	21	cancellable	cancellable	ADJ
ejpam-6436	272	22	element	element	NOUN
ejpam-6436	272	23	of	of	ADP
ejpam-6436	272	24	r	r	NOUN
ejpam-6436	272	25	acts	act	VERB
ejpam-6436	272	26	po	po	NOUN
ejpam-6436	272	27	-	-	PUNCT
ejpam-6436	272	28	injectively	injectively	ADV
ejpam-6436	272	29	on	on	ADP
ejpam-6436	272	30	ra	ra	PROPN
ejpam-6436	272	31	.	.	PUNCT
ejpam-6436	273	1	(	(	PUNCT
ejpam-6436	273	2	ii	ii	NOUN
ejpam-6436	273	3	)	)	PUNCT
ejpam-6436	273	4	ra	ra	PROPN
ejpam-6436	273	5	satisfies	satisfy	VERB
ejpam-6436	273	6	property	property	NOUN
ejpam-6436	273	7	(	(	PUNCT
ejpam-6436	273	8	p	p	NOUN
ejpam-6436	273	9	)	)	PUNCT
ejpam-6436	273	10	if	if	SCONJ
ejpam-6436	273	11	ra	ra	PROPN
ejpam-6436	273	12	≤	≤	PROPN
ejpam-6436	273	13	r′a′	r′a′	PROPN
ejpam-6436	273	14	where	where	SCONJ
ejpam-6436	273	15	r	r	NOUN
ejpam-6436	273	16	,	,	PUNCT
ejpam-6436	273	17	r′	r′	NOUN
ejpam-6436	273	18	∈	∈	PROPN
ejpam-6436	273	19	r	r	NOUN
ejpam-6436	273	20	and	and	CCONJ
ejpam-6436	273	21	a	a	PRON
ejpam-6436	273	22	,	,	PUNCT
ejpam-6436	273	23	a′	a′	PROPN
ejpam-6436	273	24	∈	∈	PROPN
ejpam-6436	273	25	a	a	PRON
ejpam-6436	273	26	,	,	PUNCT
ejpam-6436	273	27	then	then	ADV
ejpam-6436	273	28	a	a	DET
ejpam-6436	273	29	=	=	SYM
ejpam-6436	273	30	ua′′	ua′′	PROPN
ejpam-6436	273	31	,	,	PUNCT
ejpam-6436	273	32	a′	a′	PROPN
ejpam-6436	273	33	=	=	SYM
ejpam-6436	273	34	u′a′′	u′a′′	NOUN
ejpam-6436	273	35	with	with	ADP
ejpam-6436	273	36	ru	ru	PROPN
ejpam-6436	273	37	≤	≤	NUM
ejpam-6436	273	38	r′u′	r′u′	NOUN
ejpam-6436	273	39	for	for	ADP
ejpam-6436	273	40	some	some	DET
ejpam-6436	273	41	a′′	a′′	PROPN
ejpam-6436	273	42	∈	∈	PROPN
ejpam-6436	273	43	a	a	DET
ejpam-6436	273	44	,	,	PUNCT
ejpam-6436	273	45	u	u	NOUN
ejpam-6436	273	46	,	,	PUNCT
ejpam-6436	273	47	u′	u′	PROPN
ejpam-6436	273	48	∈	∈	PROPN
ejpam-6436	273	49	r.	r.	PROPN
ejpam-6436	273	50	(	(	PUNCT
ejpam-6436	273	51	iii	iii	X
ejpam-6436	273	52	)	)	PUNCT
ejpam-6436	273	53	ra	ra	PROPN
ejpam-6436	273	54	satisfies	satisfy	VERB
ejpam-6436	273	55	property	property	NOUN
ejpam-6436	273	56	(	(	PUNCT
ejpam-6436	273	57	e	e	NOUN
ejpam-6436	273	58	)	)	PUNCT
ejpam-6436	273	59	if	if	SCONJ
ejpam-6436	273	60	ra	ra	PROPN
ejpam-6436	273	61	≤	≤	X
ejpam-6436	274	1	r′a	r′a	INTJ
ejpam-6436	274	2	where	where	SCONJ
ejpam-6436	274	3	r	r	NOUN
ejpam-6436	274	4	,	,	PUNCT
ejpam-6436	274	5	r′	r′	NOUN
ejpam-6436	274	6	∈	∈	PROPN
ejpam-6436	274	7	r	r	NOUN
ejpam-6436	274	8	and	and	CCONJ
ejpam-6436	274	9	a	a	DET
ejpam-6436	274	10	∈	∈	PROPN
ejpam-6436	274	11	a	a	PRON
ejpam-6436	274	12	,	,	PUNCT
ejpam-6436	274	13	then	then	ADV
ejpam-6436	274	14	a	a	DET
ejpam-6436	274	15	=	=	X
ejpam-6436	274	16	ua′′	ua′′	NOUN
ejpam-6436	274	17	with	with	ADP
ejpam-6436	274	18	ru	ru	NOUN
ejpam-6436	274	19	≤	≤	NUM
ejpam-6436	274	20	r′u	r′u	NOUN
ejpam-6436	274	21	for	for	ADP
ejpam-6436	274	22	some	some	DET
ejpam-6436	274	23	a′′	a′′	PROPN
ejpam-6436	274	24	∈	∈	PROPN
ejpam-6436	274	25	a	a	PRON
ejpam-6436	274	26	,	,	PUNCT
ejpam-6436	274	27	u	u	PROPN
ejpam-6436	274	28	∈	∈	PROPN
ejpam-6436	274	29	r.	r.	PROPN
ejpam-6436	274	30	(	(	PUNCT
ejpam-6436	274	31	iv	iv	X
ejpam-6436	274	32	)	)	PUNCT
ejpam-6436	274	33	ra	ra	PROPN
ejpam-6436	274	34	satisfies	satisfy	VERB
ejpam-6436	274	35	property	property	NOUN
ejpam-6436	274	36	(	(	PUNCT
ejpam-6436	274	37	pe	pe	INTJ
ejpam-6436	274	38	)	)	PUNCT
ejpam-6436	274	39	if	if	SCONJ
ejpam-6436	274	40	ra	ra	PROPN
ejpam-6436	274	41	≤	≤	PROPN
ejpam-6436	274	42	r′a′	r′a′	PROPN
ejpam-6436	274	43	where	where	SCONJ
ejpam-6436	274	44	r	r	NOUN
ejpam-6436	274	45	,	,	PUNCT
ejpam-6436	274	46	r′	r′	NOUN
ejpam-6436	274	47	∈	∈	PROPN
ejpam-6436	274	48	r	r	NOUN
ejpam-6436	274	49	and	and	CCONJ
ejpam-6436	274	50	a	a	PRON
ejpam-6436	274	51	,	,	PUNCT
ejpam-6436	274	52	a′	a′	PROPN
ejpam-6436	274	53	∈	∈	PROPN
ejpam-6436	274	54	a	a	PRON
ejpam-6436	274	55	,	,	PUNCT
ejpam-6436	274	56	then	then	ADV
ejpam-6436	274	57	a	a	DET
ejpam-6436	274	58	≤	≤	PROPN
ejpam-6436	274	59	ua′′	ua′′	PROPN
ejpam-6436	274	60	and	and	CCONJ
ejpam-6436	274	61	u′a′′	u′a′′	NOUN
ejpam-6436	274	62	≤	≤	NOUN
ejpam-6436	274	63	a′	a′	NOUN
ejpam-6436	274	64	with	with	ADP
ejpam-6436	274	65	ru	ru	PROPN
ejpam-6436	274	66	≤	≤	NUM
ejpam-6436	274	67	r′u′	r′u′	NOUN
ejpam-6436	274	68	for	for	ADP
ejpam-6436	274	69	some	some	DET
ejpam-6436	274	70	a′′	a′′	PROPN
ejpam-6436	274	71	∈	∈	PROPN
ejpam-6436	274	72	a	a	DET
ejpam-6436	274	73	,	,	PUNCT
ejpam-6436	274	74	u	u	NOUN
ejpam-6436	274	75	,	,	PUNCT
ejpam-6436	274	76	u′	u′	PROPN
ejpam-6436	274	77	∈	∈	PROPN
ejpam-6436	274	78	r.	r.	PROPN
ejpam-6436	274	79	(	(	PUNCT
ejpam-6436	274	80	v	v	NOUN
ejpam-6436	274	81	)	)	PUNCT
ejpam-6436	274	82	ra	ra	PROPN
ejpam-6436	274	83	is	be	AUX
ejpam-6436	274	84	strongly	strongly	ADV
ejpam-6436	274	85	flat	flat	ADJ
ejpam-6436	274	86	if	if	SCONJ
ejpam-6436	274	87	it	it	PRON
ejpam-6436	274	88	satisfies	satisfy	VERB
ejpam-6436	274	89	properties	property	NOUN
ejpam-6436	274	90	(	(	PUNCT
ejpam-6436	274	91	p	p	NOUN
ejpam-6436	274	92	)	)	PUNCT
ejpam-6436	274	93	and	and	CCONJ
ejpam-6436	274	94	(	(	PUNCT
ejpam-6436	274	95	e	e	NOUN
ejpam-6436	274	96	)	)	PUNCT
ejpam-6436	274	97	.	.	PUNCT
ejpam-6436	275	1	theorem	theorem	VERB
ejpam-6436	275	2	6	6	NUM
ejpam-6436	275	3	.	.	PUNCT
ejpam-6436	276	1	if	if	SCONJ
ejpam-6436	276	2	the	the	DET
ejpam-6436	276	3	left	left	NOUN
ejpam-6436	276	4	t	t	X
ejpam-6436	276	5	-poset	-poset	PROPN
ejpam-6436	276	6	tc	tc	NOUN
ejpam-6436	276	7	is	be	AUX
ejpam-6436	276	8	po	po	NOUN
ejpam-6436	276	9	-	-	PUNCT
ejpam-6436	276	10	torsion	torsion	NOUN
ejpam-6436	276	11	free	free	ADJ
ejpam-6436	276	12	then	then	ADV
ejpam-6436	276	13	ra	ra	PROPN
ejpam-6436	276	14	and	and	CCONJ
ejpam-6436	276	15	sb	sb	PROPN
ejpam-6436	276	16	are	be	AUX
ejpam-6436	276	17	po	po	NOUN
ejpam-6436	276	18	-	-	PUNCT
ejpam-6436	276	19	torsion	torsion	NOUN
ejpam-6436	276	20	free	free	ADJ
ejpam-6436	276	21	.	.	PUNCT
ejpam-6436	277	1	proof	proof	NOUN
ejpam-6436	277	2	.	.	PUNCT
ejpam-6436	278	1	assume	assume	VERB
ejpam-6436	278	2	that	that	SCONJ
ejpam-6436	278	3	tc	tc	PROPN
ejpam-6436	278	4	is	be	AUX
ejpam-6436	278	5	po	po	NOUN
ejpam-6436	278	6	-	-	PUNCT
ejpam-6436	278	7	torsion	torsion	NOUN
ejpam-6436	278	8	free	free	ADJ
ejpam-6436	278	9	.	.	PUNCT
ejpam-6436	279	1	suppose	suppose	VERB
ejpam-6436	279	2	that	that	SCONJ
ejpam-6436	279	3	r	r	NOUN
ejpam-6436	279	4	∈	∈	PROPN
ejpam-6436	279	5	r	r	NOUN
ejpam-6436	279	6	is	be	AUX
ejpam-6436	279	7	a	a	DET
ejpam-6436	279	8	left	left	ADJ
ejpam-6436	279	9	po	po	NOUN
ejpam-6436	279	10	-	-	NOUN
ejpam-6436	279	11	cancellable	cancellable	ADJ
ejpam-6436	279	12	.	.	PUNCT
ejpam-6436	280	1	we	we	PRON
ejpam-6436	280	2	show	show	VERB
ejpam-6436	280	3	that	that	SCONJ
ejpam-6436	280	4	it	it	PRON
ejpam-6436	280	5	acts	act	VERB
ejpam-6436	280	6	po	po	NOUN
ejpam-6436	280	7	-	-	PUNCT
ejpam-6436	280	8	injectively	injectively	ADV
ejpam-6436	280	9	on	on	ADP
ejpam-6436	280	10	a.	a.	NOUN
ejpam-6436	280	11	let	let	VERB
ejpam-6436	280	12	ra	ra	PROPN
ejpam-6436	280	13	≤	≤	ADJ
ejpam-6436	280	14	ra′	ra′	NOUN
ejpam-6436	280	15	where	where	SCONJ
ejpam-6436	280	16	a	a	X
ejpam-6436	280	17	,	,	PUNCT
ejpam-6436	280	18	a′	a′	PROPN
ejpam-6436	280	19	∈	∈	PROPN
ejpam-6436	280	20	a.	a.	NOUN
ejpam-6436	280	21	we	we	PRON
ejpam-6436	280	22	first	first	ADV
ejpam-6436	280	23	show	show	VERB
ejpam-6436	280	24	that	that	SCONJ
ejpam-6436	280	25	(	(	PUNCT
ejpam-6436	280	26	r	r	NOUN
ejpam-6436	280	27	,	,	PUNCT
ejpam-6436	280	28	c1	c1	NOUN
ejpam-6436	280	29	)	)	PUNCT
ejpam-6436	280	30	is	be	AUX
ejpam-6436	280	31	left	leave	VERB
ejpam-6436	280	32	po	po	NOUN
ejpam-6436	280	33	-	-	NOUN
ejpam-6436	280	34	cancellable	cancellable	ADJ
ejpam-6436	280	35	by	by	ADP
ejpam-6436	280	36	using	use	VERB
ejpam-6436	280	37	proposition	proposition	NOUN
ejpam-6436	280	38	4	4	NUM
ejpam-6436	280	39	.	.	PUNCT
ejpam-6436	281	1	if	if	SCONJ
ejpam-6436	281	2	a1	a1	NOUN
ejpam-6436	281	3	≤	≤	NOUN
ejpam-6436	281	4	a2	a2	NOUN
ejpam-6436	281	5	and	and	CCONJ
ejpam-6436	281	6	c1(a1)s	c1(a1)s	NOUN
ejpam-6436	281	7	≤	≤	NOUN
ejpam-6436	281	8	c1(a2)s	c1(a2)s	ADJ
ejpam-6436	281	9	′	′	NOUN
ejpam-6436	281	10	,	,	PUNCT
ejpam-6436	281	11	then	then	ADV
ejpam-6436	281	12	s	s	VERB
ejpam-6436	281	13	≤	≤	NOUN
ejpam-6436	281	14	s′	s′	NUM
ejpam-6436	281	15	,	,	PUNCT
ejpam-6436	281	16	and	and	CCONJ
ejpam-6436	281	17	thus	thus	ADV
ejpam-6436	281	18	the	the	DET
ejpam-6436	281	19	first	first	ADJ
ejpam-6436	281	20	condition	condition	NOUN
ejpam-6436	281	21	holds	hold	VERB
ejpam-6436	281	22	.	.	PUNCT
ejpam-6436	282	1	for	for	ADP
ejpam-6436	282	2	the	the	DET
ejpam-6436	282	3	second	second	ADJ
ejpam-6436	282	4	condition	condition	NOUN
ejpam-6436	282	5	,	,	PUNCT
ejpam-6436	282	6	assume	assume	VERB
ejpam-6436	282	7	that	that	SCONJ
ejpam-6436	282	8	rp	rp	NOUN
ejpam-6436	282	9	≤	≤	NUM
ejpam-6436	282	10	rp′	rp′	NOUN
ejpam-6436	282	11	and	and	CCONJ
ejpam-6436	282	12	p	p	PROPN
ejpam-6436	282	13	≰	≰	PROPN
ejpam-6436	282	14	p′.	p′.	ADV
ejpam-6436	282	15	however	however	ADV
ejpam-6436	282	16	,	,	PUNCT
ejpam-6436	282	17	this	this	PRON
ejpam-6436	282	18	is	be	AUX
ejpam-6436	282	19	impossible	impossible	ADJ
ejpam-6436	282	20	as	as	SCONJ
ejpam-6436	282	21	r	r	NOUN
ejpam-6436	282	22	is	be	AUX
ejpam-6436	282	23	left	leave	VERB
ejpam-6436	282	24	po	po	NOUN
ejpam-6436	282	25	-	-	NOUN
ejpam-6436	282	26	cancellable	cancellable	ADJ
ejpam-6436	282	27	.	.	PUNCT
ejpam-6436	283	1	thus	thus	ADV
ejpam-6436	283	2	(	(	PUNCT
ejpam-6436	283	3	r	r	NOUN
ejpam-6436	283	4	,	,	PUNCT
ejpam-6436	283	5	c1	c1	NOUN
ejpam-6436	283	6	)	)	PUNCT
ejpam-6436	283	7	is	be	AUX
ejpam-6436	283	8	left	leave	VERB
ejpam-6436	283	9	po	po	NOUN
ejpam-6436	283	10	-	-	NOUN
ejpam-6436	283	11	cancellable	cancellable	ADJ
ejpam-6436	283	12	.	.	PUNCT
ejpam-6436	284	1	since	since	SCONJ
ejpam-6436	284	2	ra	ra	PROPN
ejpam-6436	284	3	×s	×s	ADV
ejpam-6436	284	4	b	b	PROPN
ejpam-6436	284	5	is	be	AUX
ejpam-6436	284	6	po	po	NOUN
ejpam-6436	284	7	-	-	PUNCT
ejpam-6436	284	8	torsion	torsion	NOUN
ejpam-6436	284	9	free	free	ADJ
ejpam-6436	284	10	,	,	PUNCT
ejpam-6436	284	11	(	(	PUNCT
ejpam-6436	284	12	r	r	NOUN
ejpam-6436	284	13	,	,	PUNCT
ejpam-6436	284	14	c1	c1	NOUN
ejpam-6436	284	15	)	)	PUNCT
ejpam-6436	284	16	acts	act	VERB
ejpam-6436	284	17	po	po	NOUN
ejpam-6436	284	18	-	-	PUNCT
ejpam-6436	284	19	injectively	injectively	ADV
ejpam-6436	284	20	on	on	ADP
ejpam-6436	284	21	ra	ra	PROPN
ejpam-6436	284	22	×s	×s	ADV
ejpam-6436	284	23	b.	b.	PROPN
ejpam-6436	285	1	therefore	therefore	ADV
ejpam-6436	285	2	for	for	ADP
ejpam-6436	285	3	any	any	DET
ejpam-6436	285	4	b	b	PROPN
ejpam-6436	285	5	∈	∈	PROPN
ejpam-6436	285	6	b	b	PROPN
ejpam-6436	285	7	,	,	PUNCT
ejpam-6436	285	8	(	(	PUNCT
ejpam-6436	285	9	r	r	NOUN
ejpam-6436	285	10	,	,	PUNCT
ejpam-6436	285	11	c1)(a	c1)(a	PROPN
ejpam-6436	285	12	,	,	PUNCT
ejpam-6436	285	13	b	b	NOUN
ejpam-6436	285	14	)	)	PUNCT
ejpam-6436	285	15	=	=	SYM
ejpam-6436	285	16	(	(	PUNCT
ejpam-6436	285	17	ra	ra	PROPN
ejpam-6436	285	18	,	,	PUNCT
ejpam-6436	285	19	b	b	NOUN
ejpam-6436	285	20	)	)	PUNCT
ejpam-6436	285	21	≤	≤	NOUN
ejpam-6436	285	22	(	(	PUNCT
ejpam-6436	285	23	ra′	ra′	PROPN
ejpam-6436	285	24	,	,	PUNCT
ejpam-6436	285	25	b	b	NOUN
ejpam-6436	285	26	)	)	PUNCT
ejpam-6436	285	27	=	=	SYM
ejpam-6436	285	28	(	(	PUNCT
ejpam-6436	285	29	r	r	NOUN
ejpam-6436	285	30	,	,	PUNCT
ejpam-6436	285	31	c1)(a	c1)(a	NOUN
ejpam-6436	285	32	′	′	NOUN
ejpam-6436	285	33	,	,	PUNCT
ejpam-6436	285	34	b	b	NOUN
ejpam-6436	285	35	)	)	PUNCT
ejpam-6436	285	36	.	.	PUNCT
ejpam-6436	286	1	so	so	ADV
ejpam-6436	286	2	(	(	PUNCT
ejpam-6436	286	3	a	a	PRON
ejpam-6436	286	4	,	,	PUNCT
ejpam-6436	286	5	b	b	NOUN
ejpam-6436	286	6	)	)	PUNCT
ejpam-6436	286	7	≤	≤	NOUN
ejpam-6436	286	8	(	(	PUNCT
ejpam-6436	286	9	a′	a′	PROPN
ejpam-6436	286	10	,	,	PUNCT
ejpam-6436	286	11	b	b	NOUN
ejpam-6436	286	12	)	)	PUNCT
ejpam-6436	286	13	and	and	CCONJ
ejpam-6436	286	14	then	then	ADV
ejpam-6436	286	15	a	a	DET
ejpam-6436	286	16	≤	≤	NOUN
ejpam-6436	286	17	a′.	a′.	NOUN
ejpam-6436	286	18	thus	thus	ADV
ejpam-6436	286	19	r	r	NOUN
ejpam-6436	286	20	acts	act	NOUN
ejpam-6436	286	21	po	po	NOUN
ejpam-6436	286	22	-	-	PUNCT
ejpam-6436	286	23	injectively	injectively	ADV
ejpam-6436	286	24	on	on	ADP
ejpam-6436	286	25	a	a	PRON
ejpam-6436	286	26	and	and	CCONJ
ejpam-6436	286	27	hence	hence	ADV
ejpam-6436	286	28	ra	ra	PROPN
ejpam-6436	286	29	is	be	AUX
ejpam-6436	286	30	po	po	NOUN
ejpam-6436	286	31	-	-	PUNCT
ejpam-6436	286	32	torsion	torsion	NOUN
ejpam-6436	286	33	free	free	ADJ
ejpam-6436	286	34	.	.	PUNCT
ejpam-6436	287	1	now	now	ADV
ejpam-6436	287	2	to	to	PART
ejpam-6436	287	3	prove	prove	VERB
ejpam-6436	287	4	that	that	SCONJ
ejpam-6436	287	5	sb	sb	PROPN
ejpam-6436	287	6	is	be	AUX
ejpam-6436	287	7	po	po	NOUN
ejpam-6436	287	8	-	-	PUNCT
ejpam-6436	287	9	torsion	torsion	NOUN
ejpam-6436	287	10	free	free	NOUN
ejpam-6436	287	11	suppose	suppose	VERB
ejpam-6436	287	12	that	that	SCONJ
ejpam-6436	287	13	s	s	VERB
ejpam-6436	287	14	∈	∈	NOUN
ejpam-6436	287	15	s	s	PART
ejpam-6436	287	16	is	be	AUX
ejpam-6436	287	17	left	leave	VERB
ejpam-6436	287	18	po	po	NOUN
ejpam-6436	287	19	-	-	NOUN
ejpam-6436	287	20	cancellable	cancellable	ADJ
ejpam-6436	287	21	and	and	CCONJ
ejpam-6436	287	22	sb	sb	PROPN
ejpam-6436	287	23	≤	≤	PROPN
ejpam-6436	287	24	sb′	sb′	PROPN
ejpam-6436	287	25	for	for	ADP
ejpam-6436	287	26	some	some	DET
ejpam-6436	287	27	b	b	NOUN
ejpam-6436	287	28	,	,	PUNCT
ejpam-6436	287	29	b′	b′	NUM
ejpam-6436	287	30	∈	∈	PROPN
ejpam-6436	287	31	b.	b.	NOUN
ejpam-6436	287	32	we	we	PRON
ejpam-6436	287	33	again	again	ADV
ejpam-6436	287	34	use	use	VERB
ejpam-6436	287	35	proposition	proposition	NOUN
ejpam-6436	287	36	4	4	NUM
ejpam-6436	287	37	to	to	PART
ejpam-6436	287	38	show	show	VERB
ejpam-6436	287	39	that	that	SCONJ
ejpam-6436	287	40	(	(	PUNCT
ejpam-6436	287	41	1	1	NUM
ejpam-6436	287	42	,	,	PUNCT
ejpam-6436	287	43	cs	cs	NOUN
ejpam-6436	287	44	)	)	PUNCT
ejpam-6436	287	45	is	be	AUX
ejpam-6436	287	46	left	leave	VERB
ejpam-6436	287	47	pocancellable	pocancellable	ADJ
ejpam-6436	287	48	.	.	PUNCT
ejpam-6436	288	1	if	if	SCONJ
ejpam-6436	288	2	a	a	DET
ejpam-6436	288	3	≤	≤	NOUN
ejpam-6436	288	4	a′	a′	NOUN
ejpam-6436	288	5	and	and	CCONJ
ejpam-6436	288	6	cs(a)s	cs(a)s	VERB
ejpam-6436	288	7	≤	≤	X
ejpam-6436	288	8	cs(a	cs(a	NOUN
ejpam-6436	288	9	′)s′	′)s′	NOUN
ejpam-6436	288	10	,	,	PUNCT
ejpam-6436	288	11	then	then	ADV
ejpam-6436	288	12	ss	ss	PROPN
ejpam-6436	288	13	≤	≤	ADJ
ejpam-6436	288	14	ss′.	ss′.	PROPN
ejpam-6436	288	15	as	as	SCONJ
ejpam-6436	288	16	s	s	PRON
ejpam-6436	288	17	is	be	AUX
ejpam-6436	288	18	left	leave	VERB
ejpam-6436	288	19	po	po	NOUN
ejpam-6436	288	20	-	-	PUNCT
ejpam-6436	288	21	cancellable	cancellable	ADJ
ejpam-6436	288	22	,	,	PUNCT
ejpam-6436	288	23	s	s	PART
ejpam-6436	288	24	≤	≤	PROPN
ejpam-6436	289	1	s′.	s′.	PROPN
ejpam-6436	289	2	b.	b.	PROPN
ejpam-6436	289	3	al	al	PROPN
ejpam-6436	289	4	subaiei	subaiei	PROPN
ejpam-6436	289	5	et	et	PROPN
ejpam-6436	289	6	al	al	PROPN
ejpam-6436	289	7	.	.	PUNCT
ejpam-6436	289	8	/	/	SYM
ejpam-6436	289	9	eur	eur	PROPN
ejpam-6436	289	10	.	.	PUNCT
ejpam-6436	290	1	j.	j.	PROPN
ejpam-6436	290	2	pure	pure	PROPN
ejpam-6436	290	3	appl	appl	PROPN
ejpam-6436	290	4	.	.	PROPN
ejpam-6436	290	5	math	math	PROPN
ejpam-6436	290	6	,	,	PUNCT
ejpam-6436	290	7	18	18	NUM
ejpam-6436	290	8	(	(	PUNCT
ejpam-6436	290	9	3	3	NUM
ejpam-6436	290	10	)	)	PUNCT
ejpam-6436	290	11	(	(	PUNCT
ejpam-6436	290	12	2025	2025	NUM
ejpam-6436	290	13	)	)	PUNCT
ejpam-6436	290	14	,	,	PUNCT
ejpam-6436	290	15	6436	6436	NUM
ejpam-6436	290	16	11	11	NUM
ejpam-6436	290	17	of	of	ADP
ejpam-6436	290	18	14	14	NUM
ejpam-6436	291	1	so	so	ADV
ejpam-6436	291	2	the	the	DET
ejpam-6436	291	3	first	first	ADJ
ejpam-6436	291	4	condition	condition	NOUN
ejpam-6436	291	5	holds	hold	VERB
ejpam-6436	291	6	.	.	PUNCT
ejpam-6436	292	1	suppose	suppose	VERB
ejpam-6436	292	2	that	that	SCONJ
ejpam-6436	292	3	p	p	PROPN
ejpam-6436	292	4	≤	≤	ADJ
ejpam-6436	292	5	p′	p′	NOUN
ejpam-6436	292	6	and	and	CCONJ
ejpam-6436	292	7	p	p	PROPN
ejpam-6436	292	8	≰	≰	PROPN
ejpam-6436	292	9	p′	p′	NOUN
ejpam-6436	292	10	,	,	PUNCT
ejpam-6436	292	11	but	but	CCONJ
ejpam-6436	292	12	this	this	PRON
ejpam-6436	292	13	is	be	AUX
ejpam-6436	292	14	impossible	impossible	ADJ
ejpam-6436	292	15	,	,	PUNCT
ejpam-6436	292	16	so	so	CCONJ
ejpam-6436	292	17	the	the	DET
ejpam-6436	292	18	second	second	ADJ
ejpam-6436	292	19	condition	condition	NOUN
ejpam-6436	292	20	holds	hold	VERB
ejpam-6436	292	21	.	.	PUNCT
ejpam-6436	293	1	thus	thus	ADV
ejpam-6436	293	2	(	(	PUNCT
ejpam-6436	293	3	1	1	NUM
ejpam-6436	293	4	,	,	PUNCT
ejpam-6436	293	5	cs	cs	NOUN
ejpam-6436	293	6	)	)	PUNCT
ejpam-6436	293	7	is	be	AUX
ejpam-6436	293	8	left	leave	VERB
ejpam-6436	293	9	po	po	NOUN
ejpam-6436	293	10	-	-	NOUN
ejpam-6436	293	11	cancellable	cancellable	ADJ
ejpam-6436	293	12	,	,	PUNCT
ejpam-6436	293	13	so	so	CCONJ
ejpam-6436	293	14	(	(	PUNCT
ejpam-6436	293	15	1	1	NUM
ejpam-6436	293	16	,	,	PUNCT
ejpam-6436	293	17	cs	cs	ADJ
ejpam-6436	293	18	)	)	PUNCT
ejpam-6436	293	19	acts	act	VERB
ejpam-6436	293	20	po	po	NOUN
ejpam-6436	293	21	-	-	PUNCT
ejpam-6436	293	22	injectively	injectively	ADV
ejpam-6436	293	23	on	on	ADP
ejpam-6436	293	24	ra×s	ra×s	PROPN
ejpam-6436	293	25	b.	b.	PROPN
ejpam-6436	293	26	therefore	therefore	ADV
ejpam-6436	293	27	for	for	ADP
ejpam-6436	293	28	any	any	DET
ejpam-6436	293	29	b	b	PROPN
ejpam-6436	293	30	∈	∈	PROPN
ejpam-6436	293	31	b	b	PROPN
ejpam-6436	293	32	,	,	PUNCT
ejpam-6436	293	33	(	(	PUNCT
ejpam-6436	293	34	1	1	NUM
ejpam-6436	293	35	,	,	PUNCT
ejpam-6436	293	36	cs)(a	cs)(a	PROPN
ejpam-6436	293	37	,	,	PUNCT
ejpam-6436	293	38	b	b	X
ejpam-6436	293	39	)	)	PUNCT
ejpam-6436	293	40	=	=	SYM
ejpam-6436	293	41	(	(	PUNCT
ejpam-6436	293	42	a	a	PRON
ejpam-6436	293	43	,	,	PUNCT
ejpam-6436	293	44	sb	sb	NOUN
ejpam-6436	293	45	)	)	PUNCT
ejpam-6436	293	46	≤	≤	NOUN
ejpam-6436	293	47	(	(	PUNCT
ejpam-6436	293	48	a	a	DET
ejpam-6436	293	49	,	,	PUNCT
ejpam-6436	293	50	sb′	sb′	NOUN
ejpam-6436	293	51	)	)	PUNCT
ejpam-6436	294	1	=	=	PUNCT
ejpam-6436	294	2	(	(	PUNCT
ejpam-6436	294	3	1	1	NUM
ejpam-6436	294	4	,	,	PUNCT
ejpam-6436	294	5	cs)(a	cs)(a	PROPN
ejpam-6436	294	6	,	,	PUNCT
ejpam-6436	294	7	b	b	NOUN
ejpam-6436	294	8	′	′	NOUN
ejpam-6436	294	9	)	)	PUNCT
ejpam-6436	294	10	.	.	PUNCT
ejpam-6436	295	1	so	so	ADV
ejpam-6436	295	2	(	(	PUNCT
ejpam-6436	295	3	a	a	DET
ejpam-6436	295	4	,	,	PUNCT
ejpam-6436	295	5	b	b	NOUN
ejpam-6436	295	6	)	)	PUNCT
ejpam-6436	295	7	≤	≤	NOUN
ejpam-6436	295	8	(	(	PUNCT
ejpam-6436	295	9	a	a	PRON
ejpam-6436	295	10	,	,	PUNCT
ejpam-6436	295	11	b′	b′	NUM
ejpam-6436	295	12	)	)	PUNCT
ejpam-6436	295	13	,	,	PUNCT
ejpam-6436	295	14	and	and	CCONJ
ejpam-6436	295	15	thus	thus	ADV
ejpam-6436	295	16	b	b	X
ejpam-6436	295	17	≤	≤	NUM
ejpam-6436	295	18	b′.	b′.	VERB
ejpam-6436	295	19	thus	thus	ADV
ejpam-6436	295	20	s	s	PART
ejpam-6436	295	21	acts	act	NOUN
ejpam-6436	295	22	po	po	NOUN
ejpam-6436	295	23	-	-	PUNCT
ejpam-6436	295	24	injectively	injectively	ADV
ejpam-6436	295	25	on	on	ADP
ejpam-6436	295	26	b	b	NOUN
ejpam-6436	295	27	and	and	CCONJ
ejpam-6436	295	28	hence	hence	ADV
ejpam-6436	295	29	sb	sb	PROPN
ejpam-6436	295	30	is	be	AUX
ejpam-6436	295	31	po	po	NOUN
ejpam-6436	295	32	-	-	PUNCT
ejpam-6436	295	33	torsion	torsion	NOUN
ejpam-6436	295	34	free	free	ADJ
ejpam-6436	295	35	as	as	SCONJ
ejpam-6436	295	36	required	require	VERB
ejpam-6436	295	37	.	.	PUNCT
ejpam-6436	296	1	recall	recall	VERB
ejpam-6436	296	2	that	that	PRON
ejpam-6436	296	3	in	in	ADP
ejpam-6436	296	4	unordered	unordered	ADJ
ejpam-6436	296	5	case	case	NOUN
ejpam-6436	296	6	,	,	PUNCT
ejpam-6436	296	7	when	when	SCONJ
ejpam-6436	296	8	tc	tc	NOUN
ejpam-6436	296	9	=	=	PUNCT
ejpam-6436	296	10	ra×	ra×	PROPN
ejpam-6436	296	11	sb	sb	PROPN
ejpam-6436	296	12	is	be	AUX
ejpam-6436	296	13	torsion	torsion	NOUN
ejpam-6436	296	14	free	free	ADJ
ejpam-6436	296	15	,	,	PUNCT
ejpam-6436	296	16	then	then	ADV
ejpam-6436	296	17	a	a	PRON
ejpam-6436	296	18	and	and	CCONJ
ejpam-6436	296	19	b	b	NOUN
ejpam-6436	296	20	are	be	AUX
ejpam-6436	296	21	both	both	PRON
ejpam-6436	296	22	torsion	torsion	NOUN
ejpam-6436	296	23	free	free	ADJ
ejpam-6436	296	24	.	.	PUNCT
ejpam-6436	297	1	therefore	therefore	ADV
ejpam-6436	297	2	the	the	DET
ejpam-6436	297	3	above	above	ADJ
ejpam-6436	297	4	theorem	theorem	NOUN
ejpam-6436	297	5	generalises	generalise	VERB
ejpam-6436	297	6	this	this	DET
ejpam-6436	297	7	result	result	NOUN
ejpam-6436	297	8	to	to	ADP
ejpam-6436	297	9	the	the	DET
ejpam-6436	297	10	ordered	order	VERB
ejpam-6436	297	11	case	case	NOUN
ejpam-6436	297	12	.	.	PUNCT
ejpam-6436	298	1	proposition	proposition	NOUN
ejpam-6436	298	2	10	10	NUM
ejpam-6436	298	3	.	.	PUNCT
ejpam-6436	299	1	for	for	ADP
ejpam-6436	299	2	the	the	DET
ejpam-6436	299	3	left	left	ADJ
ejpam-6436	299	4	t	t	PROPN
ejpam-6436	299	5	-poset	-poset	PROPN
ejpam-6436	299	6	tc	tc	ADP
ejpam-6436	299	7	the	the	DET
ejpam-6436	299	8	following	following	NOUN
ejpam-6436	299	9	are	be	AUX
ejpam-6436	299	10	true	true	ADJ
ejpam-6436	299	11	.	.	PUNCT
ejpam-6436	300	1	(	(	PUNCT
ejpam-6436	300	2	i	i	NOUN
ejpam-6436	300	3	)	)	PUNCT
ejpam-6436	300	4	if	if	SCONJ
ejpam-6436	300	5	tc	tc	NOUN
ejpam-6436	300	6	satisfies	satisfy	VERB
ejpam-6436	300	7	the	the	DET
ejpam-6436	300	8	property	property	NOUN
ejpam-6436	300	9	(	(	PUNCT
ejpam-6436	300	10	p	p	NOUN
ejpam-6436	300	11	)	)	PUNCT
ejpam-6436	300	12	then	then	ADV
ejpam-6436	300	13	so	so	ADV
ejpam-6436	300	14	does	do	VERB
ejpam-6436	300	15	ra	ra	PROPN
ejpam-6436	300	16	.	.	PUNCT
ejpam-6436	301	1	(	(	PUNCT
ejpam-6436	301	2	ii	ii	NOUN
ejpam-6436	301	3	)	)	PUNCT
ejpam-6436	301	4	if	if	SCONJ
ejpam-6436	301	5	tc	tc	NOUN
ejpam-6436	301	6	satisfies	satisfy	VERB
ejpam-6436	301	7	the	the	DET
ejpam-6436	301	8	property	property	NOUN
ejpam-6436	301	9	(	(	PUNCT
ejpam-6436	301	10	e	e	NOUN
ejpam-6436	301	11	)	)	PUNCT
ejpam-6436	301	12	then	then	ADV
ejpam-6436	301	13	so	so	ADV
ejpam-6436	301	14	does	do	VERB
ejpam-6436	301	15	ra	ra	PROPN
ejpam-6436	301	16	.	.	PUNCT
ejpam-6436	302	1	(	(	PUNCT
ejpam-6436	302	2	iii	iii	X
ejpam-6436	302	3	)	)	PUNCT
ejpam-6436	302	4	if	if	SCONJ
ejpam-6436	302	5	tc	tc	NOUN
ejpam-6436	302	6	is	be	AUX
ejpam-6436	302	7	strongly	strongly	ADV
ejpam-6436	302	8	flat	flat	ADJ
ejpam-6436	302	9	then	then	ADV
ejpam-6436	302	10	so	so	ADV
ejpam-6436	302	11	is	be	AUX
ejpam-6436	302	12	ra	ra	PROPN
ejpam-6436	302	13	.	.	PUNCT
ejpam-6436	303	1	(	(	PUNCT
ejpam-6436	303	2	iv	iv	X
ejpam-6436	303	3	)	)	PUNCT
ejpam-6436	303	4	if	if	SCONJ
ejpam-6436	303	5	tc	tc	NOUN
ejpam-6436	303	6	satisfies	satisfy	VERB
ejpam-6436	303	7	the	the	DET
ejpam-6436	303	8	property	property	NOUN
ejpam-6436	303	9	(	(	PUNCT
ejpam-6436	303	10	pe	pe	INTJ
ejpam-6436	303	11	)	)	PUNCT
ejpam-6436	303	12	then	then	ADV
ejpam-6436	303	13	so	so	ADV
ejpam-6436	303	14	does	do	VERB
ejpam-6436	303	15	ra	ra	PROPN
ejpam-6436	303	16	.	.	PUNCT
ejpam-6436	304	1	proof	proof	NOUN
ejpam-6436	304	2	.	.	PUNCT
ejpam-6436	305	1	1	1	X
ejpam-6436	305	2	)	)	PUNCT
ejpam-6436	305	3	suppose	suppose	VERB
ejpam-6436	305	4	that	that	SCONJ
ejpam-6436	305	5	t	t	PROPN
ejpam-6436	305	6	-poset	-poset	PROPN
ejpam-6436	305	7	tc	tc	NUM
ejpam-6436	305	8	satisfies	satisfie	NOUN
ejpam-6436	305	9	property	property	NOUN
ejpam-6436	305	10	(	(	PUNCT
ejpam-6436	305	11	p	p	NOUN
ejpam-6436	305	12	)	)	PUNCT
ejpam-6436	305	13	and	and	CCONJ
ejpam-6436	305	14	let	let	VERB
ejpam-6436	305	15	ra	ra	PROPN
ejpam-6436	305	16	≤	≤	NUM
ejpam-6436	305	17	r′a′	r′a′	NOUN
ejpam-6436	305	18	,	,	PUNCT
ejpam-6436	305	19	where	where	SCONJ
ejpam-6436	305	20	r	r	NOUN
ejpam-6436	305	21	,	,	PUNCT
ejpam-6436	305	22	r′	r′	NOUN
ejpam-6436	305	23	∈	∈	PROPN
ejpam-6436	305	24	r	r	NOUN
ejpam-6436	305	25	and	and	CCONJ
ejpam-6436	305	26	a	a	PRON
ejpam-6436	305	27	,	,	PUNCT
ejpam-6436	305	28	a′	a′	PROPN
ejpam-6436	305	29	∈	∈	PROPN
ejpam-6436	305	30	a.	a.	NOUN
ejpam-6436	305	31	now	now	ADV
ejpam-6436	305	32	for	for	ADP
ejpam-6436	305	33	any	any	DET
ejpam-6436	305	34	b	b	PROPN
ejpam-6436	305	35	∈	∈	PROPN
ejpam-6436	305	36	b	b	PROPN
ejpam-6436	305	37	,	,	PUNCT
ejpam-6436	305	38	(	(	PUNCT
ejpam-6436	305	39	r	r	NOUN
ejpam-6436	305	40	,	,	PUNCT
ejpam-6436	305	41	c1)(a	c1)(a	PROPN
ejpam-6436	305	42	,	,	PUNCT
ejpam-6436	305	43	b	b	NOUN
ejpam-6436	305	44	)	)	PUNCT
ejpam-6436	305	45	=	=	SYM
ejpam-6436	305	46	(	(	PUNCT
ejpam-6436	305	47	ra	ra	PROPN
ejpam-6436	305	48	,	,	PUNCT
ejpam-6436	305	49	b	b	NOUN
ejpam-6436	305	50	)	)	PUNCT
ejpam-6436	305	51	≤	≤	NOUN
ejpam-6436	305	52	(	(	PUNCT
ejpam-6436	305	53	r′a′	r′a′	NOUN
ejpam-6436	305	54	,	,	PUNCT
ejpam-6436	305	55	b	b	NOUN
ejpam-6436	305	56	)	)	PUNCT
ejpam-6436	305	57	=	=	SYM
ejpam-6436	305	58	(	(	PUNCT
ejpam-6436	305	59	r′	r′	PROPN
ejpam-6436	305	60	,	,	PUNCT
ejpam-6436	305	61	c1)(a	c1)(a	NOUN
ejpam-6436	305	62	′	′	NOUN
ejpam-6436	305	63	,	,	PUNCT
ejpam-6436	305	64	b	b	NOUN
ejpam-6436	305	65	)	)	PUNCT
ejpam-6436	305	66	.	.	PUNCT
ejpam-6436	306	1	since	since	SCONJ
ejpam-6436	306	2	tc	tc	NUM
ejpam-6436	306	3	satisfies	satisfie	NOUN
ejpam-6436	306	4	property	property	NOUN
ejpam-6436	306	5	(	(	PUNCT
ejpam-6436	306	6	p	p	X
ejpam-6436	306	7	)	)	PUNCT
ejpam-6436	306	8	there	there	PRON
ejpam-6436	306	9	exists	exist	VERB
ejpam-6436	306	10	some	some	PRON
ejpam-6436	306	11	(	(	PUNCT
ejpam-6436	306	12	a′′	a′′	PROPN
ejpam-6436	306	13	,	,	PUNCT
ejpam-6436	306	14	b′′	b′′	PROPN
ejpam-6436	306	15	)	)	PUNCT
ejpam-6436	306	16	∈	∈	PROPN
ejpam-6436	306	17	tc	tc	ADP
ejpam-6436	306	18	such	such	ADJ
ejpam-6436	306	19	that	that	PRON
ejpam-6436	306	20	(	(	PUNCT
ejpam-6436	306	21	a	a	DET
ejpam-6436	306	22	,	,	PUNCT
ejpam-6436	306	23	b	b	NOUN
ejpam-6436	306	24	)	)	PUNCT
ejpam-6436	306	25	=	=	SYM
ejpam-6436	307	1	(	(	PUNCT
ejpam-6436	307	2	r1	r1	PROPN
ejpam-6436	307	3	,	,	PUNCT
ejpam-6436	307	4	f1)(a	f1)(a	PROPN
ejpam-6436	307	5	′′	′′	PROPN
ejpam-6436	307	6	,	,	PUNCT
ejpam-6436	307	7	b′′	b′′	PROPN
ejpam-6436	307	8	)	)	PUNCT
ejpam-6436	307	9	=	=	PUNCT
ejpam-6436	307	10	(	(	PUNCT
ejpam-6436	307	11	r1a	r1a	PROPN
ejpam-6436	307	12	′′	′′	PROPN
ejpam-6436	307	13	,	,	PUNCT
ejpam-6436	307	14	f1(a	f1(a	PROPN
ejpam-6436	307	15	′′)b′′	′′)b′′	PUNCT
ejpam-6436	307	16	)	)	PUNCT
ejpam-6436	307	17	and	and	CCONJ
ejpam-6436	307	18	(	(	PUNCT
ejpam-6436	307	19	a′	a′	PROPN
ejpam-6436	307	20	,	,	PUNCT
ejpam-6436	307	21	b	b	NOUN
ejpam-6436	307	22	)	)	PUNCT
ejpam-6436	307	23	=	=	SYM
ejpam-6436	307	24	(	(	PUNCT
ejpam-6436	307	25	r2	r2	PROPN
ejpam-6436	307	26	,	,	PUNCT
ejpam-6436	307	27	f2)(a	f2)(a	PROPN
ejpam-6436	308	1	′′	′′	PROPN
ejpam-6436	308	2	,	,	PUNCT
ejpam-6436	308	3	b′′	b′′	PROPN
ejpam-6436	308	4	)	)	PUNCT
ejpam-6436	308	5	=	=	PUNCT
ejpam-6436	308	6	(	(	PUNCT
ejpam-6436	308	7	r2a	r2a	PROPN
ejpam-6436	308	8	′′	′′	PROPN
ejpam-6436	308	9	,	,	PUNCT
ejpam-6436	308	10	f2(a	f2(a	PROPN
ejpam-6436	308	11	′′)b′′	′′)b′′	PUNCT
ejpam-6436	308	12	)	)	PUNCT
ejpam-6436	308	13	with	with	ADP
ejpam-6436	308	14	(	(	PUNCT
ejpam-6436	308	15	r	r	NOUN
ejpam-6436	308	16	,	,	PUNCT
ejpam-6436	308	17	c1)(r1	c1)(r1	NOUN
ejpam-6436	308	18	,	,	PUNCT
ejpam-6436	308	19	f1	f1	NOUN
ejpam-6436	308	20	)	)	PUNCT
ejpam-6436	308	21	≤	≤	NOUN
ejpam-6436	308	22	(	(	PUNCT
ejpam-6436	308	23	r′	r′	NUM
ejpam-6436	308	24	,	,	PUNCT
ejpam-6436	308	25	c1)(r2	c1)(r2	NOUN
ejpam-6436	308	26	,	,	PUNCT
ejpam-6436	308	27	f2	f2	PROPN
ejpam-6436	308	28	)	)	PUNCT
ejpam-6436	308	29	.	.	PUNCT
ejpam-6436	309	1	therefore	therefore	ADV
ejpam-6436	309	2	a	a	DET
ejpam-6436	309	3	=	=	PUNCT
ejpam-6436	309	4	r1a	r1a	PROPN
ejpam-6436	309	5	′′	′′	PROPN
ejpam-6436	309	6	,	,	PUNCT
ejpam-6436	309	7	a′	a′	NOUN
ejpam-6436	309	8	=	=	PUNCT
ejpam-6436	309	9	r2a	r2a	PROPN
ejpam-6436	309	10	′′	′′	PROPN
ejpam-6436	309	11	and	and	CCONJ
ejpam-6436	309	12	(	(	PUNCT
ejpam-6436	309	13	rr1	rr1	NOUN
ejpam-6436	309	14	,	,	PUNCT
ejpam-6436	309	15	(	(	PUNCT
ejpam-6436	309	16	c1)r1f1	c1)r1f1	PROPN
ejpam-6436	309	17	)	)	PUNCT
ejpam-6436	309	18	≤	≤	NOUN
ejpam-6436	309	19	(	(	PUNCT
ejpam-6436	309	20	r′r2	r′r2	NOUN
ejpam-6436	309	21	,	,	PUNCT
ejpam-6436	309	22	(	(	PUNCT
ejpam-6436	309	23	c1)r2f2	c1)r2f2	PROPN
ejpam-6436	309	24	)	)	PUNCT
ejpam-6436	309	25	.	.	PUNCT
ejpam-6436	310	1	it	it	PRON
ejpam-6436	310	2	follows	follow	VERB
ejpam-6436	310	3	that	that	SCONJ
ejpam-6436	310	4	rr1	rr1	NOUN
ejpam-6436	310	5	≤	≤	NUM
ejpam-6436	310	6	r′r2	r′r2	NOUN
ejpam-6436	310	7	.	.	PUNCT
ejpam-6436	311	1	hence	hence	ADV
ejpam-6436	311	2	ra	ra	PROPN
ejpam-6436	311	3	satisfies	satisfy	VERB
ejpam-6436	311	4	property	property	NOUN
ejpam-6436	311	5	(	(	PUNCT
ejpam-6436	311	6	p	p	NOUN
ejpam-6436	311	7	)	)	PUNCT
ejpam-6436	311	8	.	.	PUNCT
ejpam-6436	312	1	2	2	X
ejpam-6436	312	2	)	)	PUNCT
ejpam-6436	312	3	it	it	PRON
ejpam-6436	312	4	can	can	AUX
ejpam-6436	312	5	be	be	AUX
ejpam-6436	312	6	proved	prove	VERB
ejpam-6436	312	7	by	by	ADP
ejpam-6436	312	8	an	an	DET
ejpam-6436	312	9	argument	argument	NOUN
ejpam-6436	312	10	similar	similar	ADJ
ejpam-6436	312	11	to	to	ADP
ejpam-6436	312	12	case	case	NOUN
ejpam-6436	312	13	(	(	PUNCT
ejpam-6436	312	14	1	1	NUM
ejpam-6436	312	15	)	)	PUNCT
ejpam-6436	312	16	.	.	PUNCT
ejpam-6436	313	1	3	3	X
ejpam-6436	313	2	)	)	PUNCT
ejpam-6436	313	3	it	it	PRON
ejpam-6436	313	4	follows	follow	VERB
ejpam-6436	313	5	from	from	ADP
ejpam-6436	313	6	cases	case	NOUN
ejpam-6436	313	7	(	(	PUNCT
ejpam-6436	313	8	1	1	NUM
ejpam-6436	313	9	)	)	PUNCT
ejpam-6436	313	10	and	and	CCONJ
ejpam-6436	313	11	(	(	PUNCT
ejpam-6436	313	12	2	2	NUM
ejpam-6436	313	13	)	)	PUNCT
ejpam-6436	313	14	.	.	PUNCT
ejpam-6436	314	1	4	4	X
ejpam-6436	314	2	)	)	PUNCT
ejpam-6436	314	3	suppose	suppose	VERB
ejpam-6436	314	4	that	that	SCONJ
ejpam-6436	314	5	tc	tc	PROPN
ejpam-6436	314	6	satisfies	satisfie	NOUN
ejpam-6436	314	7	property	property	NOUN
ejpam-6436	314	8	(	(	PUNCT
ejpam-6436	314	9	pe	pe	NOUN
ejpam-6436	314	10	)	)	PUNCT
ejpam-6436	314	11	and	and	CCONJ
ejpam-6436	314	12	let	let	VERB
ejpam-6436	314	13	ra	ra	PROPN
ejpam-6436	314	14	≤	≤	NUM
ejpam-6436	314	15	r′a′	r′a′	NOUN
ejpam-6436	314	16	,	,	PUNCT
ejpam-6436	314	17	where	where	SCONJ
ejpam-6436	314	18	r	r	NOUN
ejpam-6436	314	19	,	,	PUNCT
ejpam-6436	314	20	r′	r′	NOUN
ejpam-6436	314	21	∈	∈	PROPN
ejpam-6436	314	22	r	r	NOUN
ejpam-6436	314	23	and	and	CCONJ
ejpam-6436	314	24	a	a	PRON
ejpam-6436	314	25	,	,	PUNCT
ejpam-6436	314	26	a′	a′	PROPN
ejpam-6436	314	27	∈	∈	PROPN
ejpam-6436	314	28	a.	a.	NOUN
ejpam-6436	314	29	then	then	ADV
ejpam-6436	314	30	for	for	ADP
ejpam-6436	314	31	any	any	DET
ejpam-6436	314	32	b	b	PROPN
ejpam-6436	314	33	∈	∈	PROPN
ejpam-6436	314	34	b	b	PROPN
ejpam-6436	314	35	,	,	PUNCT
ejpam-6436	314	36	(	(	PUNCT
ejpam-6436	314	37	r	r	NOUN
ejpam-6436	314	38	,	,	PUNCT
ejpam-6436	314	39	c1)(a	c1)(a	PROPN
ejpam-6436	314	40	,	,	PUNCT
ejpam-6436	314	41	b	b	NOUN
ejpam-6436	314	42	)	)	PUNCT
ejpam-6436	314	43	=	=	SYM
ejpam-6436	314	44	(	(	PUNCT
ejpam-6436	314	45	ra	ra	PROPN
ejpam-6436	314	46	,	,	PUNCT
ejpam-6436	314	47	b	b	NOUN
ejpam-6436	314	48	)	)	PUNCT
ejpam-6436	314	49	≤	≤	NOUN
ejpam-6436	314	50	(	(	PUNCT
ejpam-6436	314	51	r′a′	r′a′	NOUN
ejpam-6436	314	52	,	,	PUNCT
ejpam-6436	314	53	b	b	NOUN
ejpam-6436	314	54	)	)	PUNCT
ejpam-6436	314	55	=	=	SYM
ejpam-6436	314	56	(	(	PUNCT
ejpam-6436	314	57	r′	r′	PROPN
ejpam-6436	314	58	,	,	PUNCT
ejpam-6436	314	59	c1)(a	c1)(a	NOUN
ejpam-6436	314	60	′	′	NOUN
ejpam-6436	314	61	,	,	PUNCT
ejpam-6436	314	62	b	b	NOUN
ejpam-6436	314	63	)	)	PUNCT
ejpam-6436	314	64	.	.	PUNCT
ejpam-6436	315	1	since	since	SCONJ
ejpam-6436	315	2	tc	tc	NUM
ejpam-6436	315	3	satisfies	satisfie	NOUN
ejpam-6436	315	4	property	property	NOUN
ejpam-6436	315	5	(	(	PUNCT
ejpam-6436	315	6	pe	pe	INTJ
ejpam-6436	315	7	)	)	PUNCT
ejpam-6436	315	8	there	there	PRON
ejpam-6436	315	9	exists	exist	VERB
ejpam-6436	315	10	(	(	PUNCT
ejpam-6436	315	11	a′′	a′′	NOUN
ejpam-6436	315	12	,	,	PUNCT
ejpam-6436	315	13	b′′	b′′	PROPN
ejpam-6436	315	14	)	)	PUNCT
ejpam-6436	315	15	∈	∈	PROPN
ejpam-6436	315	16	tc	tc	ADP
ejpam-6436	315	17	such	such	ADJ
ejpam-6436	315	18	that	that	PRON
ejpam-6436	315	19	(	(	PUNCT
ejpam-6436	315	20	a	a	DET
ejpam-6436	315	21	,	,	PUNCT
ejpam-6436	315	22	b	b	NOUN
ejpam-6436	315	23	)	)	PUNCT
ejpam-6436	315	24	≤	≤	NOUN
ejpam-6436	315	25	(	(	PUNCT
ejpam-6436	315	26	r1	r1	PROPN
ejpam-6436	315	27	,	,	PUNCT
ejpam-6436	315	28	f1)(a	f1)(a	PROPN
ejpam-6436	315	29	′′	′′	PROPN
ejpam-6436	315	30	,	,	PUNCT
ejpam-6436	315	31	b′′	b′′	PROPN
ejpam-6436	315	32	)	)	PUNCT
ejpam-6436	315	33	=	=	PUNCT
ejpam-6436	315	34	(	(	PUNCT
ejpam-6436	315	35	r1a	r1a	PROPN
ejpam-6436	315	36	′′	′′	PROPN
ejpam-6436	315	37	,	,	PUNCT
ejpam-6436	315	38	f1(a	f1(a	PROPN
ejpam-6436	315	39	′′)b′′	′′)b′′	PROPN
ejpam-6436	315	40	)	)	PUNCT
ejpam-6436	315	41	⇒	⇒	VERB
ejpam-6436	315	42	a	a	DET
ejpam-6436	315	43	≤	≤	ADJ
ejpam-6436	315	44	r1a	r1a	NOUN
ejpam-6436	315	45	′′	′′	PROPN
ejpam-6436	315	46	and	and	CCONJ
ejpam-6436	315	47	(	(	PUNCT
ejpam-6436	315	48	r2a	r2a	PROPN
ejpam-6436	315	49	′′	′′	PROPN
ejpam-6436	315	50	,	,	PUNCT
ejpam-6436	315	51	f2(a	f2(a	PROPN
ejpam-6436	315	52	′′)b′′	′′)b′′	PROPN
ejpam-6436	315	53	)	)	PUNCT
ejpam-6436	315	54	=	=	SYM
ejpam-6436	316	1	(	(	PUNCT
ejpam-6436	316	2	r2	r2	PROPN
ejpam-6436	316	3	,	,	PUNCT
ejpam-6436	316	4	f2)(a	f2)(a	PROPN
ejpam-6436	316	5	′′	′′	PROPN
ejpam-6436	316	6	,	,	PUNCT
ejpam-6436	316	7	b′′	b′′	PROPN
ejpam-6436	316	8	)	)	PUNCT
ejpam-6436	316	9	≤	≤	NOUN
ejpam-6436	316	10	(	(	PUNCT
ejpam-6436	316	11	a′	a′	PROPN
ejpam-6436	316	12	,	,	PUNCT
ejpam-6436	316	13	b	b	NOUN
ejpam-6436	316	14	)	)	PUNCT
ejpam-6436	316	15	⇒	⇒	NOUN
ejpam-6436	316	16	r2a	r2a	NOUN
ejpam-6436	316	17	′′	′′	PROPN
ejpam-6436	316	18	≤	≤	NOUN
ejpam-6436	316	19	a′	a′	PROPN
ejpam-6436	316	20	b.	b.	PROPN
ejpam-6436	316	21	al	al	PROPN
ejpam-6436	316	22	subaiei	subaiei	PROPN
ejpam-6436	316	23	et	et	PROPN
ejpam-6436	316	24	al	al	PROPN
ejpam-6436	316	25	.	.	PUNCT
ejpam-6436	316	26	/	/	SYM
ejpam-6436	316	27	eur	eur	PROPN
ejpam-6436	316	28	.	.	PUNCT
ejpam-6436	317	1	j.	j.	PROPN
ejpam-6436	317	2	pure	pure	PROPN
ejpam-6436	317	3	appl	appl	PROPN
ejpam-6436	317	4	.	.	PROPN
ejpam-6436	317	5	math	math	PROPN
ejpam-6436	317	6	,	,	PUNCT
ejpam-6436	317	7	18	18	NUM
ejpam-6436	317	8	(	(	PUNCT
ejpam-6436	317	9	3	3	NUM
ejpam-6436	317	10	)	)	PUNCT
ejpam-6436	317	11	(	(	PUNCT
ejpam-6436	317	12	2025	2025	NUM
ejpam-6436	317	13	)	)	PUNCT
ejpam-6436	317	14	,	,	PUNCT
ejpam-6436	317	15	6436	6436	NUM
ejpam-6436	317	16	12	12	NUM
ejpam-6436	317	17	of	of	ADP
ejpam-6436	317	18	14	14	NUM
ejpam-6436	317	19	with	with	ADP
ejpam-6436	317	20	(	(	PUNCT
ejpam-6436	317	21	r	r	NOUN
ejpam-6436	317	22	,	,	PUNCT
ejpam-6436	317	23	c1)(r1	c1)(r1	NOUN
ejpam-6436	317	24	,	,	PUNCT
ejpam-6436	317	25	f1	f1	NOUN
ejpam-6436	317	26	)	)	PUNCT
ejpam-6436	317	27	≤	≤	NOUN
ejpam-6436	317	28	(	(	PUNCT
ejpam-6436	317	29	r′	r′	NUM
ejpam-6436	317	30	,	,	PUNCT
ejpam-6436	317	31	c1)(r2	c1)(r2	NOUN
ejpam-6436	317	32	,	,	PUNCT
ejpam-6436	317	33	f2	f2	PROPN
ejpam-6436	317	34	)	)	PUNCT
ejpam-6436	317	35	.	.	PUNCT
ejpam-6436	318	1	thus	thus	ADV
ejpam-6436	318	2	,	,	PUNCT
ejpam-6436	318	3	(	(	PUNCT
ejpam-6436	318	4	rr1	rr1	NOUN
ejpam-6436	318	5	,	,	PUNCT
ejpam-6436	318	6	(	(	PUNCT
ejpam-6436	318	7	c1)r1f1	c1)r1f1	PROPN
ejpam-6436	318	8	)	)	PUNCT
ejpam-6436	318	9	≤	≤	NOUN
ejpam-6436	318	10	(	(	PUNCT
ejpam-6436	318	11	r′r2	r′r2	NOUN
ejpam-6436	318	12	,	,	PUNCT
ejpam-6436	318	13	(	(	PUNCT
ejpam-6436	318	14	c1)r2f2	c1)r2f2	PROPN
ejpam-6436	318	15	)	)	PUNCT
ejpam-6436	318	16	and	and	CCONJ
ejpam-6436	318	17	so	so	ADV
ejpam-6436	318	18	rr1	rr1	NOUN
ejpam-6436	318	19	≤	≤	NUM
ejpam-6436	318	20	r′r2	r′r2	NOUN
ejpam-6436	318	21	.	.	PUNCT
ejpam-6436	319	1	hence	hence	ADV
ejpam-6436	319	2	ra	ra	PROPN
ejpam-6436	319	3	satisfies	satisfy	VERB
ejpam-6436	319	4	property	property	NOUN
ejpam-6436	319	5	(	(	PUNCT
ejpam-6436	319	6	pe	pe	INTJ
ejpam-6436	319	7	)	)	PUNCT
ejpam-6436	319	8	as	as	SCONJ
ejpam-6436	319	9	required	require	VERB
ejpam-6436	319	10	.	.	PUNCT
ejpam-6436	320	1	the	the	DET
ejpam-6436	320	2	concepts	concept	NOUN
ejpam-6436	320	3	of	of	ADP
ejpam-6436	320	4	reversible	reversible	ADJ
ejpam-6436	320	5	and	and	CCONJ
ejpam-6436	320	6	weakly	weakly	ADJ
ejpam-6436	320	7	reversible	reversible	ADJ
ejpam-6436	320	8	were	be	AUX
ejpam-6436	320	9	considered	consider	VERB
ejpam-6436	320	10	in	in	ADP
ejpam-6436	320	11	the	the	DET
ejpam-6436	320	12	literature	literature	NOUN
ejpam-6436	320	13	,	,	PUNCT
ejpam-6436	320	14	see	see	VERB
ejpam-6436	320	15	for	for	ADP
ejpam-6436	320	16	example	example	NOUN
ejpam-6436	320	17	[	[	X
ejpam-6436	320	18	18	18	NUM
ejpam-6436	320	19	,	,	PUNCT
ejpam-6436	320	20	20	20	NUM
ejpam-6436	320	21	]	]	PUNCT
ejpam-6436	320	22	.	.	PUNCT
ejpam-6436	321	1	next	next	ADV
ejpam-6436	321	2	we	we	PRON
ejpam-6436	321	3	study	study	VERB
ejpam-6436	321	4	these	these	DET
ejpam-6436	321	5	concepts	concept	NOUN
ejpam-6436	321	6	for	for	ADP
ejpam-6436	321	7	the	the	DET
ejpam-6436	321	8	case	case	NOUN
ejpam-6436	321	9	of	of	ADP
ejpam-6436	321	10	wreath	wreath	NOUN
ejpam-6436	321	11	product	product	NOUN
ejpam-6436	321	12	and	and	CCONJ
ejpam-6436	321	13	obtain	obtain	VERB
ejpam-6436	321	14	some	some	DET
ejpam-6436	321	15	crucial	crucial	ADJ
ejpam-6436	321	16	results	result	NOUN
ejpam-6436	321	17	.	.	PUNCT
ejpam-6436	322	1	a	a	DET
ejpam-6436	322	2	pomonoid	pomonoid	NOUN
ejpam-6436	322	3	r	r	NOUN
ejpam-6436	322	4	is	be	AUX
ejpam-6436	322	5	said	say	VERB
ejpam-6436	322	6	to	to	PART
ejpam-6436	322	7	be	be	AUX
ejpam-6436	322	8	left	leave	VERB
ejpam-6436	322	9	reversible	reversible	ADJ
ejpam-6436	322	10	if	if	SCONJ
ejpam-6436	322	11	for	for	ADP
ejpam-6436	322	12	every	every	DET
ejpam-6436	322	13	r	r	NOUN
ejpam-6436	322	14	,	,	PUNCT
ejpam-6436	322	15	r′	r′	NOUN
ejpam-6436	322	16	∈	∈	PROPN
ejpam-6436	322	17	r	r	NOUN
ejpam-6436	322	18	,	,	PUNCT
ejpam-6436	322	19	rr	rr	NOUN
ejpam-6436	322	20	∩	∩	ADJ
ejpam-6436	322	21	r′r	r′r	PROPN
ejpam-6436	322	22	̸=	̸=	PROPN
ejpam-6436	322	23	∅.	∅.	ADV
ejpam-6436	322	24	if	if	SCONJ
ejpam-6436	322	25	z	z	NOUN
ejpam-6436	322	26	is	be	AUX
ejpam-6436	322	27	a	a	DET
ejpam-6436	322	28	subset	subset	NOUN
ejpam-6436	322	29	of	of	ADP
ejpam-6436	322	30	a	a	DET
ejpam-6436	322	31	poset	poset	NOUN
ejpam-6436	322	32	y	y	PROPN
ejpam-6436	322	33	,	,	PUNCT
ejpam-6436	322	34	the	the	DET
ejpam-6436	322	35	down	down	ADV
ejpam-6436	322	36	-	-	PUNCT
ejpam-6436	322	37	set	set	VERB
ejpam-6436	322	38	(	(	PUNCT
ejpam-6436	322	39	z	z	NOUN
ejpam-6436	322	40	]	]	X
ejpam-6436	322	41	of	of	ADP
ejpam-6436	322	42	y	y	PROPN
ejpam-6436	322	43	is	be	AUX
ejpam-6436	322	44	(	(	PUNCT
ejpam-6436	322	45	z	z	X
ejpam-6436	322	46	]	]	X
ejpam-6436	323	1	=	=	PUNCT
ejpam-6436	323	2	{	{	PUNCT
ejpam-6436	323	3	y	y	PROPN
ejpam-6436	323	4	∈	∈	PROPN
ejpam-6436	323	5	y	y	PROPN
ejpam-6436	323	6	|y	|y	NOUN
ejpam-6436	323	7	≤	≤	ADJ
ejpam-6436	323	8	z	z	NOUN
ejpam-6436	323	9	for	for	ADP
ejpam-6436	323	10	some	some	DET
ejpam-6436	323	11	z	z	NOUN
ejpam-6436	323	12	∈	∈	PROPN
ejpam-6436	323	13	z	z	NOUN
ejpam-6436	323	14	}	}	PUNCT
ejpam-6436	323	15	.	.	PUNCT
ejpam-6436	324	1	a	a	DET
ejpam-6436	324	2	pomonoid	pomonoid	NOUN
ejpam-6436	324	3	r	r	NOUN
ejpam-6436	324	4	is	be	AUX
ejpam-6436	324	5	called	call	VERB
ejpam-6436	324	6	weakly	weakly	ADV
ejpam-6436	324	7	left	left	ADJ
ejpam-6436	324	8	reversible	reversible	ADJ
ejpam-6436	324	9	if	if	SCONJ
ejpam-6436	324	10	for	for	ADP
ejpam-6436	324	11	every	every	DET
ejpam-6436	324	12	r	r	NOUN
ejpam-6436	324	13	,	,	PUNCT
ejpam-6436	324	14	r′	r′	NOUN
ejpam-6436	324	15	∈	∈	PROPN
ejpam-6436	324	16	r	r	NOUN
ejpam-6436	324	17	,	,	PUNCT
ejpam-6436	324	18	rr	rr	NOUN
ejpam-6436	324	19	∩	∩	NOUN
ejpam-6436	324	20	(	(	PUNCT
ejpam-6436	324	21	r′r	r′r	NOUN
ejpam-6436	324	22	]	]	X
ejpam-6436	324	23	̸=	̸=	PROPN
ejpam-6436	324	24	∅.	∅.	ADV
ejpam-6436	324	25	theorem	theorem	VERB
ejpam-6436	324	26	7	7	NUM
ejpam-6436	324	27	.	.	PUNCT
ejpam-6436	325	1	the	the	DET
ejpam-6436	325	2	wreath	wreath	NOUN
ejpam-6436	325	3	product	product	NOUN
ejpam-6436	325	4	t	t	NOUN
ejpam-6436	325	5	is	be	AUX
ejpam-6436	325	6	left	leave	VERB
ejpam-6436	325	7	reversible	reversible	ADJ
ejpam-6436	325	8	if	if	SCONJ
ejpam-6436	325	9	and	and	CCONJ
ejpam-6436	325	10	only	only	ADV
ejpam-6436	325	11	if	if	SCONJ
ejpam-6436	325	12	r	r	NOUN
ejpam-6436	325	13	and	and	CCONJ
ejpam-6436	325	14	s	s	NOUN
ejpam-6436	325	15	are	be	AUX
ejpam-6436	325	16	left	leave	VERB
ejpam-6436	325	17	reversible	reversible	ADJ
ejpam-6436	325	18	.	.	PUNCT
ejpam-6436	326	1	proof	proof	NOUN
ejpam-6436	326	2	.	.	PUNCT
ejpam-6436	327	1	let	let	VERB
ejpam-6436	327	2	r	r	NOUN
ejpam-6436	327	3	,	,	PUNCT
ejpam-6436	327	4	r′	r′	PROPN
ejpam-6436	327	5	∈	∈	PROPN
ejpam-6436	327	6	r.	r.	PROPN
ejpam-6436	327	7	suppose	suppose	VERB
ejpam-6436	327	8	that	that	SCONJ
ejpam-6436	327	9	t	t	PROPN
ejpam-6436	327	10	is	be	AUX
ejpam-6436	327	11	left	leave	VERB
ejpam-6436	327	12	reversible	reversible	ADJ
ejpam-6436	327	13	.	.	PUNCT
ejpam-6436	328	1	then	then	ADV
ejpam-6436	328	2	,	,	PUNCT
ejpam-6436	328	3	(	(	PUNCT
ejpam-6436	328	4	r	r	NOUN
ejpam-6436	328	5	,	,	PUNCT
ejpam-6436	328	6	c1)t	c1)t	NOUN
ejpam-6436	328	7	∩	∩	NOUN
ejpam-6436	328	8	(	(	PUNCT
ejpam-6436	328	9	r′	r′	PROPN
ejpam-6436	328	10	,	,	PUNCT
ejpam-6436	328	11	c1)t	c1)t	NOUN
ejpam-6436	328	12	̸=	̸=	PROPN
ejpam-6436	328	13	∅.	∅.	ADV
ejpam-6436	328	14	so	so	ADV
ejpam-6436	328	15	there	there	PRON
ejpam-6436	328	16	exist	exist	VERB
ejpam-6436	328	17	(	(	PUNCT
ejpam-6436	328	18	r1	r1	PROPN
ejpam-6436	328	19	,	,	PUNCT
ejpam-6436	328	20	f1	f1	NOUN
ejpam-6436	328	21	)	)	PUNCT
ejpam-6436	328	22	and	and	CCONJ
ejpam-6436	328	23	(	(	PUNCT
ejpam-6436	328	24	r2	r2	PROPN
ejpam-6436	328	25	,	,	PUNCT
ejpam-6436	328	26	f2	f2	PROPN
ejpam-6436	328	27	)	)	PUNCT
ejpam-6436	328	28	∈	∈	PROPN
ejpam-6436	328	29	t	t	NOUN
ejpam-6436	328	30	such	such	ADJ
ejpam-6436	328	31	that	that	SCONJ
ejpam-6436	328	32	(	(	PUNCT
ejpam-6436	328	33	r	r	NOUN
ejpam-6436	328	34	,	,	PUNCT
ejpam-6436	328	35	c1)(r1	c1)(r1	NOUN
ejpam-6436	328	36	,	,	PUNCT
ejpam-6436	328	37	f1	f1	NOUN
ejpam-6436	328	38	)	)	PUNCT
ejpam-6436	328	39	=	=	PUNCT
ejpam-6436	328	40	(	(	PUNCT
ejpam-6436	328	41	r′	r′	PROPN
ejpam-6436	328	42	,	,	PUNCT
ejpam-6436	328	43	c1)(r2	c1)(r2	NOUN
ejpam-6436	328	44	,	,	PUNCT
ejpam-6436	328	45	f2	f2	PROPN
ejpam-6436	328	46	)	)	PUNCT
ejpam-6436	328	47	and	and	CCONJ
ejpam-6436	328	48	so	so	ADV
ejpam-6436	328	49	(	(	PUNCT
ejpam-6436	328	50	rr1	rr1	NOUN
ejpam-6436	328	51	,	,	PUNCT
ejpam-6436	328	52	(	(	PUNCT
ejpam-6436	328	53	c1)r1f1	c1)r1f1	PROPN
ejpam-6436	328	54	)	)	PUNCT
ejpam-6436	328	55	=	=	SYM
ejpam-6436	328	56	(	(	PUNCT
ejpam-6436	328	57	r′r2	r′r2	PROPN
ejpam-6436	328	58	,	,	PUNCT
ejpam-6436	328	59	(	(	PUNCT
ejpam-6436	328	60	c1)r2f2	c1)r2f2	PROPN
ejpam-6436	328	61	)	)	PUNCT
ejpam-6436	328	62	.	.	PUNCT
ejpam-6436	329	1	therefore	therefore	ADV
ejpam-6436	329	2	rr1	rr1	NOUN
ejpam-6436	329	3	=	=	PUNCT
ejpam-6436	329	4	r′r2	r′r2	NOUN
ejpam-6436	329	5	and	and	CCONJ
ejpam-6436	329	6	thus	thus	ADV
ejpam-6436	329	7	rr	rr	ADJ
ejpam-6436	329	8	∩	∩	ADJ
ejpam-6436	329	9	r′r	r′r	PROPN
ejpam-6436	329	10	̸=	̸=	PROPN
ejpam-6436	329	11	∅.	∅.	ADV
ejpam-6436	329	12	hence	hence	ADV
ejpam-6436	329	13	r	r	NOUN
ejpam-6436	329	14	is	be	AUX
ejpam-6436	329	15	left	leave	VERB
ejpam-6436	329	16	reversible	reversible	ADJ
ejpam-6436	329	17	.	.	PUNCT
ejpam-6436	330	1	let	let	VERB
ejpam-6436	330	2	s	s	NOUN
ejpam-6436	330	3	,	,	PUNCT
ejpam-6436	330	4	s′	s′	PUNCT
ejpam-6436	330	5	∈	∈	PROPN
ejpam-6436	330	6	s.	s.	PROPN
ejpam-6436	330	7	as	as	ADP
ejpam-6436	330	8	(	(	PUNCT
ejpam-6436	330	9	r	r	NOUN
ejpam-6436	330	10	,	,	PUNCT
ejpam-6436	330	11	cs)t	cs)t	PROPN
ejpam-6436	330	12	∩	∩	NOUN
ejpam-6436	330	13	(	(	PUNCT
ejpam-6436	330	14	r	r	NOUN
ejpam-6436	330	15	,	,	PUNCT
ejpam-6436	330	16	cs′)t	cs′)t	NOUN
ejpam-6436	330	17	̸=	̸=	PROPN
ejpam-6436	330	18	∅	∅	NOUN
ejpam-6436	330	19	,	,	PUNCT
ejpam-6436	330	20	there	there	PRON
ejpam-6436	330	21	exist	exist	VERB
ejpam-6436	330	22	(	(	PUNCT
ejpam-6436	330	23	r1	r1	PROPN
ejpam-6436	330	24	,	,	PUNCT
ejpam-6436	330	25	f1	f1	NOUN
ejpam-6436	330	26	)	)	PUNCT
ejpam-6436	330	27	,	,	PUNCT
ejpam-6436	330	28	(	(	PUNCT
ejpam-6436	330	29	r2	r2	PROPN
ejpam-6436	330	30	,	,	PUNCT
ejpam-6436	330	31	f2	f2	PROPN
ejpam-6436	330	32	)	)	PUNCT
ejpam-6436	330	33	∈	∈	PROPN
ejpam-6436	330	34	t	t	NOUN
ejpam-6436	331	1	such	such	ADJ
ejpam-6436	331	2	that	that	SCONJ
ejpam-6436	331	3	(	(	PUNCT
ejpam-6436	331	4	r	r	NOUN
ejpam-6436	331	5	,	,	PUNCT
ejpam-6436	331	6	cs)(r1	cs)(r1	NOUN
ejpam-6436	331	7	,	,	PUNCT
ejpam-6436	331	8	f1	f1	NOUN
ejpam-6436	331	9	)	)	PUNCT
ejpam-6436	331	10	=	=	PUNCT
ejpam-6436	331	11	(	(	PUNCT
ejpam-6436	331	12	r	r	NOUN
ejpam-6436	331	13	,	,	PUNCT
ejpam-6436	331	14	cs′)(r2	cs′)(r2	NOUN
ejpam-6436	331	15	,	,	PUNCT
ejpam-6436	331	16	f2	f2	PROPN
ejpam-6436	331	17	)	)	PUNCT
ejpam-6436	331	18	.	.	PUNCT
ejpam-6436	332	1	thus	thus	ADV
ejpam-6436	332	2	(	(	PUNCT
ejpam-6436	332	3	rr1	rr1	NOUN
ejpam-6436	332	4	,	,	PUNCT
ejpam-6436	332	5	(	(	PUNCT
ejpam-6436	332	6	cs)r1f1	cs)r1f1	NOUN
ejpam-6436	332	7	)	)	PUNCT
ejpam-6436	332	8	=	=	SYM
ejpam-6436	332	9	(	(	PUNCT
ejpam-6436	332	10	rr2	rr2	PROPN
ejpam-6436	332	11	,	,	PUNCT
ejpam-6436	332	12	(	(	PUNCT
ejpam-6436	332	13	cs′)r2f2	cs′)r2f2	ADJ
ejpam-6436	332	14	)	)	PUNCT
ejpam-6436	332	15	and	and	CCONJ
ejpam-6436	332	16	so	so	ADV
ejpam-6436	332	17	(	(	PUNCT
ejpam-6436	332	18	cs)r1f1	cs)r1f1	NOUN
ejpam-6436	332	19	=	=	SYM
ejpam-6436	332	20	(	(	PUNCT
ejpam-6436	332	21	cs′)r2f2	cs′)r2f2	PROPN
ejpam-6436	332	22	.	.	PUNCT
ejpam-6436	333	1	take	take	VERB
ejpam-6436	333	2	any	any	PRON
ejpam-6436	333	3	a	a	DET
ejpam-6436	333	4	∈	∈	PROPN
ejpam-6436	333	5	a	a	PRON
ejpam-6436	333	6	,	,	PUNCT
ejpam-6436	333	7	then	then	ADV
ejpam-6436	333	8	cs(r1a)f1(a	cs(r1a)f1(a	PROPN
ejpam-6436	333	9	)	)	PUNCT
ejpam-6436	333	10	=	=	SYM
ejpam-6436	333	11	cs′(r2a)f2(a	cs′(r2a)f2(a	NOUN
ejpam-6436	333	12	)	)	PUNCT
ejpam-6436	333	13	.	.	PUNCT
ejpam-6436	334	1	this	this	PRON
ejpam-6436	334	2	implies	imply	VERB
ejpam-6436	334	3	sf1(a	sf1(a	NOUN
ejpam-6436	334	4	)	)	PUNCT
ejpam-6436	334	5	=	=	SYM
ejpam-6436	334	6	s′f2(a	s′f2(a	NOUN
ejpam-6436	334	7	)	)	PUNCT
ejpam-6436	334	8	.	.	PUNCT
ejpam-6436	335	1	as	as	ADP
ejpam-6436	335	2	f1(a	f1(a	PROPN
ejpam-6436	335	3	)	)	PUNCT
ejpam-6436	335	4	,	,	PUNCT
ejpam-6436	335	5	f2(a	f2(a	X
ejpam-6436	335	6	)	)	PUNCT
ejpam-6436	335	7	∈	∈	PROPN
ejpam-6436	335	8	s	s	PROPN
ejpam-6436	335	9	,	,	PUNCT
ejpam-6436	335	10	ss	ss	PROPN
ejpam-6436	335	11	∩	∩	NOUN
ejpam-6436	335	12	s′s	s′s	ADP
ejpam-6436	335	13	̸=	̸=	PROPN
ejpam-6436	335	14	∅.	∅.	VERB
ejpam-6436	335	15	hence	hence	ADV
ejpam-6436	335	16	s	s	PART
ejpam-6436	335	17	is	be	AUX
ejpam-6436	335	18	left	leave	VERB
ejpam-6436	335	19	reversible	reversible	ADJ
ejpam-6436	335	20	.	.	PUNCT
ejpam-6436	336	1	for	for	ADP
ejpam-6436	336	2	the	the	DET
ejpam-6436	336	3	other	other	ADJ
ejpam-6436	336	4	direction	direction	NOUN
ejpam-6436	336	5	,	,	PUNCT
ejpam-6436	336	6	let	let	VERB
ejpam-6436	336	7	(	(	PUNCT
ejpam-6436	336	8	r	r	NOUN
ejpam-6436	336	9	,	,	PUNCT
ejpam-6436	336	10	f	f	NOUN
ejpam-6436	336	11	)	)	PUNCT
ejpam-6436	336	12	,	,	PUNCT
ejpam-6436	336	13	(	(	PUNCT
ejpam-6436	336	14	p	p	X
ejpam-6436	336	15	,	,	PUNCT
ejpam-6436	336	16	g	g	NOUN
ejpam-6436	336	17	)	)	PUNCT
ejpam-6436	336	18	∈	∈	PROPN
ejpam-6436	336	19	t	t	PROPN
ejpam-6436	336	20	be	be	AUX
ejpam-6436	336	21	arbitrary	arbitrary	ADJ
ejpam-6436	336	22	.	.	PUNCT
ejpam-6436	337	1	since	since	SCONJ
ejpam-6436	337	2	r	r	NOUN
ejpam-6436	337	3	is	be	AUX
ejpam-6436	337	4	left	leave	VERB
ejpam-6436	337	5	reversible	reversible	ADJ
ejpam-6436	337	6	,	,	PUNCT
ejpam-6436	337	7	there	there	PRON
ejpam-6436	337	8	exist	exist	VERB
ejpam-6436	337	9	r′	r′	NOUN
ejpam-6436	337	10	,	,	PUNCT
ejpam-6436	337	11	r′′	r′′	VERB
ejpam-6436	337	12	∈	∈	NOUN
ejpam-6436	337	13	r	r	NOUN
ejpam-6436	337	14	such	such	DET
ejpam-6436	337	15	that	that	DET
ejpam-6436	337	16	rr′	rr′	NOUN
ejpam-6436	337	17	=	=	PUNCT
ejpam-6436	338	1	pr′′.	pr′′.	ADV
ejpam-6436	338	2	also	also	ADV
ejpam-6436	338	3	,	,	PUNCT
ejpam-6436	338	4	as	as	SCONJ
ejpam-6436	338	5	s	s	NOUN
ejpam-6436	338	6	is	be	AUX
ejpam-6436	338	7	left	leave	VERB
ejpam-6436	338	8	reversible	reversible	ADJ
ejpam-6436	338	9	and	and	CCONJ
ejpam-6436	338	10	f(r′a	f(r′a	NOUN
ejpam-6436	338	11	)	)	PUNCT
ejpam-6436	338	12	,	,	PUNCT
ejpam-6436	338	13	g(r′′a	g(r′′a	X
ejpam-6436	338	14	)	)	PUNCT
ejpam-6436	338	15	∈	∈	PROPN
ejpam-6436	338	16	s	s	NOUN
ejpam-6436	338	17	,	,	PUNCT
ejpam-6436	338	18	there	there	PRON
ejpam-6436	338	19	exist	exist	VERB
ejpam-6436	338	20	s′	s′	NOUN
ejpam-6436	338	21	,	,	PUNCT
ejpam-6436	338	22	s′′	s′′	PROPN
ejpam-6436	338	23	∈	∈	PROPN
ejpam-6436	338	24	s	s	VERB
ejpam-6436	338	25	such	such	ADJ
ejpam-6436	338	26	that	that	DET
ejpam-6436	338	27	f(r′a)s′	f(r′a)s′	NOUN
ejpam-6436	338	28	=	=	SYM
ejpam-6436	338	29	g(r′′a)s′′	g(r′′a)s′′	PROPN
ejpam-6436	338	30	,	,	PUNCT
ejpam-6436	338	31	so	so	ADV
ejpam-6436	338	32	f(r′a)cs′(a	f(r′a)cs′(a	PROPN
ejpam-6436	338	33	)	)	PUNCT
ejpam-6436	338	34	=	=	PUNCT
ejpam-6436	338	35	g(r′′a)cs′′(a	g(r′′a)cs′′(a	NUM
ejpam-6436	338	36	)	)	PUNCT
ejpam-6436	338	37	for	for	ADP
ejpam-6436	338	38	all	all	DET
ejpam-6436	338	39	a	a	DET
ejpam-6436	338	40	∈	∈	PROPN
ejpam-6436	338	41	a	a	DET
ejpam-6436	338	42	,	,	PUNCT
ejpam-6436	338	43	then	then	ADV
ejpam-6436	338	44	fr′cs′(a	fr′cs′(a	NOUN
ejpam-6436	338	45	)	)	PUNCT
ejpam-6436	338	46	=	=	SYM
ejpam-6436	339	1	gr′′cs′′(a	gr′′cs′′(a	PROPN
ejpam-6436	339	2	)	)	PUNCT
ejpam-6436	339	3	for	for	ADP
ejpam-6436	339	4	all	all	DET
ejpam-6436	339	5	a	a	DET
ejpam-6436	339	6	∈	∈	PROPN
ejpam-6436	339	7	a	a	PRON
ejpam-6436	339	8	,	,	PUNCT
ejpam-6436	339	9	which	which	PRON
ejpam-6436	339	10	implies	imply	VERB
ejpam-6436	339	11	fr′cs′	fr′cs′	X
ejpam-6436	339	12	=	=	SYM
ejpam-6436	339	13	gr′′cs′′	gr′′cs′′	NOUN
ejpam-6436	339	14	.	.	PUNCT
ejpam-6436	340	1	now	now	ADV
ejpam-6436	340	2	,	,	PUNCT
ejpam-6436	340	3	(	(	PUNCT
ejpam-6436	340	4	r	r	NOUN
ejpam-6436	340	5	,	,	PUNCT
ejpam-6436	340	6	f)(r′	f)(r′	NUM
ejpam-6436	340	7	,	,	PUNCT
ejpam-6436	340	8	cs′	cs′	X
ejpam-6436	340	9	)	)	PUNCT
ejpam-6436	340	10	=	=	SYM
ejpam-6436	340	11	(	(	PUNCT
ejpam-6436	340	12	rr′	rr′	PROPN
ejpam-6436	340	13	,	,	PUNCT
ejpam-6436	340	14	fr′cs′	fr′cs′	X
ejpam-6436	340	15	)	)	PUNCT
ejpam-6436	340	16	=	=	SYM
ejpam-6436	340	17	(	(	PUNCT
ejpam-6436	340	18	pr′′	pr′′	NOUN
ejpam-6436	340	19	,	,	PUNCT
ejpam-6436	340	20	gr′′cs′′	gr′′cs′′	NOUN
ejpam-6436	340	21	)	)	PUNCT
ejpam-6436	340	22	=	=	PUNCT
ejpam-6436	341	1	(	(	PUNCT
ejpam-6436	341	2	p	p	X
ejpam-6436	341	3	,	,	PUNCT
ejpam-6436	341	4	g)(r′′	g)(r′′	NOUN
ejpam-6436	341	5	,	,	PUNCT
ejpam-6436	341	6	cs′′	cs′′	PROPN
ejpam-6436	341	7	)	)	PUNCT
ejpam-6436	341	8	,	,	PUNCT
ejpam-6436	341	9	so	so	CCONJ
ejpam-6436	341	10	(	(	PUNCT
ejpam-6436	341	11	r	r	NOUN
ejpam-6436	341	12	,	,	PUNCT
ejpam-6436	341	13	f)t	f)t	NOUN
ejpam-6436	341	14	∩	∩	NOUN
ejpam-6436	341	15	(	(	PUNCT
ejpam-6436	341	16	p	p	X
ejpam-6436	341	17	,	,	PUNCT
ejpam-6436	341	18	g)t	g)t	X
ejpam-6436	341	19	̸=	̸=	PROPN
ejpam-6436	341	20	∅.	∅.	PRON
ejpam-6436	341	21	hence	hence	ADV
ejpam-6436	341	22	,	,	PUNCT
ejpam-6436	341	23	t	t	PROPN
ejpam-6436	341	24	is	be	AUX
ejpam-6436	341	25	left	leave	VERB
ejpam-6436	341	26	reversible	reversible	ADJ
ejpam-6436	341	27	.	.	PUNCT
ejpam-6436	342	1	proposition	proposition	NOUN
ejpam-6436	342	2	11	11	NUM
ejpam-6436	342	3	.	.	PUNCT
ejpam-6436	343	1	if	if	SCONJ
ejpam-6436	343	2	t	t	PROPN
ejpam-6436	343	3	is	be	AUX
ejpam-6436	343	4	weakly	weakly	ADV
ejpam-6436	343	5	left	leave	VERB
ejpam-6436	343	6	reversible	reversible	ADJ
ejpam-6436	343	7	,	,	PUNCT
ejpam-6436	343	8	then	then	ADV
ejpam-6436	343	9	r	r	NOUN
ejpam-6436	343	10	and	and	CCONJ
ejpam-6436	343	11	s	s	NOUN
ejpam-6436	343	12	are	be	AUX
ejpam-6436	343	13	weakly	weakly	ADV
ejpam-6436	343	14	left	leave	VERB
ejpam-6436	343	15	reversible	reversible	ADJ
ejpam-6436	343	16	.	.	PUNCT
ejpam-6436	344	1	proof	proof	NOUN
ejpam-6436	344	2	.	.	PUNCT
ejpam-6436	345	1	let	let	VERB
ejpam-6436	345	2	r	r	NOUN
ejpam-6436	345	3	,	,	PUNCT
ejpam-6436	345	4	r′	r′	PROPN
ejpam-6436	345	5	∈	∈	PROPN
ejpam-6436	345	6	r.	r.	PROPN
ejpam-6436	345	7	as	as	ADP
ejpam-6436	345	8	t	t	PROPN
ejpam-6436	345	9	is	be	AUX
ejpam-6436	345	10	weakly	weakly	ADV
ejpam-6436	345	11	left	leave	VERB
ejpam-6436	345	12	reversible	reversible	ADJ
ejpam-6436	345	13	,	,	PUNCT
ejpam-6436	345	14	(	(	PUNCT
ejpam-6436	345	15	r	r	NOUN
ejpam-6436	345	16	,	,	PUNCT
ejpam-6436	345	17	c1)t	c1)t	NOUN
ejpam-6436	345	18	∩	∩	NOUN
ejpam-6436	345	19	(	(	PUNCT
ejpam-6436	345	20	(	(	PUNCT
ejpam-6436	345	21	r′	r′	PROPN
ejpam-6436	345	22	,	,	PUNCT
ejpam-6436	345	23	c1)t	c1)t	NOUN
ejpam-6436	345	24	]	]	PUNCT
ejpam-6436	345	25	̸=	̸=	PROPN
ejpam-6436	345	26	∅.	∅.	PRON
ejpam-6436	345	27	so	so	ADV
ejpam-6436	345	28	,	,	PUNCT
ejpam-6436	345	29	we	we	PRON
ejpam-6436	345	30	can	can	AUX
ejpam-6436	345	31	found	find	VERB
ejpam-6436	345	32	(	(	PUNCT
ejpam-6436	345	33	p	p	X
ejpam-6436	345	34	,	,	PUNCT
ejpam-6436	345	35	g	g	NOUN
ejpam-6436	345	36	)	)	PUNCT
ejpam-6436	345	37	∈	∈	PROPN
ejpam-6436	345	38	t	t	NOUN
ejpam-6436	346	1	where	where	SCONJ
ejpam-6436	346	2	(	(	PUNCT
ejpam-6436	346	3	p	p	X
ejpam-6436	346	4	,	,	PUNCT
ejpam-6436	346	5	g	g	NOUN
ejpam-6436	346	6	)	)	PUNCT
ejpam-6436	346	7	=	=	SYM
ejpam-6436	347	1	(	(	PUNCT
ejpam-6436	347	2	r	r	NOUN
ejpam-6436	347	3	,	,	PUNCT
ejpam-6436	347	4	c1)(r1	c1)(r1	NOUN
ejpam-6436	347	5	,	,	PUNCT
ejpam-6436	347	6	f1	f1	NOUN
ejpam-6436	347	7	)	)	PUNCT
ejpam-6436	347	8	and	and	CCONJ
ejpam-6436	347	9	(	(	PUNCT
ejpam-6436	347	10	p	p	X
ejpam-6436	347	11	,	,	PUNCT
ejpam-6436	347	12	g	g	NOUN
ejpam-6436	347	13	)	)	PUNCT
ejpam-6436	347	14	≤	≤	NOUN
ejpam-6436	347	15	(	(	PUNCT
ejpam-6436	347	16	r′	r′	NUM
ejpam-6436	347	17	,	,	PUNCT
ejpam-6436	347	18	c1)(r2	c1)(r2	NOUN
ejpam-6436	347	19	,	,	PUNCT
ejpam-6436	347	20	f2	f2	PROPN
ejpam-6436	347	21	)	)	PUNCT
ejpam-6436	347	22	for	for	ADP
ejpam-6436	347	23	some	some	DET
ejpam-6436	347	24	(	(	PUNCT
ejpam-6436	347	25	r1	r1	PROPN
ejpam-6436	347	26	,	,	PUNCT
ejpam-6436	347	27	f1	f1	NOUN
ejpam-6436	347	28	)	)	PUNCT
ejpam-6436	347	29	,	,	PUNCT
ejpam-6436	347	30	(	(	PUNCT
ejpam-6436	347	31	r2	r2	PROPN
ejpam-6436	347	32	,	,	PUNCT
ejpam-6436	347	33	f2	f2	PROPN
ejpam-6436	347	34	)	)	PUNCT
ejpam-6436	347	35	∈	∈	PROPN
ejpam-6436	347	36	t	t	PROPN
ejpam-6436	347	37	.	.	PUNCT
ejpam-6436	348	1	now	now	ADV
ejpam-6436	348	2	(	(	PUNCT
ejpam-6436	348	3	p	p	X
ejpam-6436	348	4	,	,	PUNCT
ejpam-6436	348	5	g	g	NOUN
ejpam-6436	348	6	)	)	PUNCT
ejpam-6436	348	7	=	=	SYM
ejpam-6436	348	8	(	(	PUNCT
ejpam-6436	348	9	rr1	rr1	PROPN
ejpam-6436	348	10	,	,	PUNCT
ejpam-6436	348	11	(	(	PUNCT
ejpam-6436	348	12	c1)r1f1	c1)r1f1	PROPN
ejpam-6436	348	13	)	)	PUNCT
ejpam-6436	348	14	and	and	CCONJ
ejpam-6436	348	15	(	(	PUNCT
ejpam-6436	348	16	p	p	X
ejpam-6436	348	17	,	,	PUNCT
ejpam-6436	348	18	g	g	NOUN
ejpam-6436	348	19	)	)	PUNCT
ejpam-6436	348	20	≤	≤	NOUN
ejpam-6436	348	21	(	(	PUNCT
ejpam-6436	348	22	r′r2	r′r2	NOUN
ejpam-6436	348	23	,	,	PUNCT
ejpam-6436	348	24	(	(	PUNCT
ejpam-6436	348	25	c1)r2f2	c1)r2f2	PROPN
ejpam-6436	348	26	)	)	PUNCT
ejpam-6436	348	27	.	.	PUNCT
ejpam-6436	349	1	therefore	therefore	ADV
ejpam-6436	349	2	p	p	X
ejpam-6436	349	3	=	=	PUNCT
ejpam-6436	349	4	rr1	rr1	NOUN
ejpam-6436	349	5	and	and	CCONJ
ejpam-6436	349	6	p	p	NOUN
ejpam-6436	349	7	≤	≤	NUM
ejpam-6436	349	8	r′r2	r′r2	NOUN
ejpam-6436	349	9	.	.	PUNCT
ejpam-6436	350	1	thus	thus	ADV
ejpam-6436	350	2	p	p	PROPN
ejpam-6436	350	3	∈	∈	PROPN
ejpam-6436	350	4	rr	rr	NOUN
ejpam-6436	350	5	∩	∩	NOUN
ejpam-6436	350	6	(	(	PUNCT
ejpam-6436	350	7	r′r	r′r	NOUN
ejpam-6436	350	8	]	]	X
ejpam-6436	350	9	,	,	PUNCT
ejpam-6436	350	10	and	and	CCONJ
ejpam-6436	350	11	so	so	ADV
ejpam-6436	350	12	r	r	NOUN
ejpam-6436	350	13	is	be	AUX
ejpam-6436	350	14	weakly	weakly	ADV
ejpam-6436	350	15	left	leave	VERB
ejpam-6436	350	16	reversible	reversible	ADJ
ejpam-6436	350	17	.	.	PUNCT
ejpam-6436	351	1	next	next	ADV
ejpam-6436	351	2	take	take	VERB
ejpam-6436	351	3	any	any	DET
ejpam-6436	351	4	s	s	NOUN
ejpam-6436	351	5	,	,	PUNCT
ejpam-6436	351	6	s′	s′	PUNCT
ejpam-6436	351	7	∈	∈	PROPN
ejpam-6436	351	8	s.	s.	PROPN
ejpam-6436	351	9	again	again	ADV
ejpam-6436	351	10	as	as	SCONJ
ejpam-6436	351	11	t	t	PROPN
ejpam-6436	351	12	is	be	AUX
ejpam-6436	351	13	weakly	weakly	ADV
ejpam-6436	351	14	left	leave	VERB
ejpam-6436	351	15	reversible	reversible	ADJ
ejpam-6436	351	16	,	,	PUNCT
ejpam-6436	351	17	(	(	PUNCT
ejpam-6436	351	18	1	1	NUM
ejpam-6436	351	19	,	,	PUNCT
ejpam-6436	351	20	cs)t	cs)t	PROPN
ejpam-6436	351	21	∩	∩	NOUN
ejpam-6436	351	22	(	(	PUNCT
ejpam-6436	351	23	(	(	PUNCT
ejpam-6436	351	24	1	1	NUM
ejpam-6436	351	25	,	,	PUNCT
ejpam-6436	351	26	cs′)t	cs′)t	NOUN
ejpam-6436	351	27	]	]	PUNCT
ejpam-6436	351	28	̸=	̸=	PROPN
ejpam-6436	351	29	∅.	∅.	ADV
ejpam-6436	351	30	so	so	ADV
ejpam-6436	351	31	there	there	PRON
ejpam-6436	351	32	exists	exist	VERB
ejpam-6436	351	33	(	(	PUNCT
ejpam-6436	351	34	q	q	X
ejpam-6436	351	35	,	,	PUNCT
ejpam-6436	351	36	h	h	NOUN
ejpam-6436	351	37	)	)	PUNCT
ejpam-6436	351	38	∈	∈	PROPN
ejpam-6436	351	39	t	t	NOUN
ejpam-6436	351	40	such	such	ADJ
ejpam-6436	351	41	that	that	PRON
ejpam-6436	351	42	(	(	PUNCT
ejpam-6436	351	43	q	q	X
ejpam-6436	351	44	,	,	PUNCT
ejpam-6436	351	45	h	h	NOUN
ejpam-6436	351	46	)	)	PUNCT
ejpam-6436	351	47	=	=	SYM
ejpam-6436	352	1	(	(	PUNCT
ejpam-6436	352	2	1	1	NUM
ejpam-6436	352	3	,	,	PUNCT
ejpam-6436	352	4	cs)(p1	cs)(p1	NOUN
ejpam-6436	352	5	,	,	PUNCT
ejpam-6436	352	6	h1	h1	PROPN
ejpam-6436	352	7	)	)	PUNCT
ejpam-6436	352	8	and	and	CCONJ
ejpam-6436	352	9	(	(	PUNCT
ejpam-6436	352	10	q	q	ADJ
ejpam-6436	352	11	,	,	PUNCT
ejpam-6436	352	12	h	h	NOUN
ejpam-6436	352	13	)	)	PUNCT
ejpam-6436	352	14	≤	≤	NOUN
ejpam-6436	352	15	(	(	PUNCT
ejpam-6436	352	16	1	1	NUM
ejpam-6436	352	17	,	,	PUNCT
ejpam-6436	352	18	cs′)(p2	cs′)(p2	PROPN
ejpam-6436	352	19	,	,	PUNCT
ejpam-6436	352	20	h2	h2	NOUN
ejpam-6436	352	21	)	)	PUNCT
ejpam-6436	352	22	for	for	ADP
ejpam-6436	352	23	some	some	PRON
ejpam-6436	352	24	(	(	PUNCT
ejpam-6436	352	25	p1	p1	PROPN
ejpam-6436	352	26	,	,	PUNCT
ejpam-6436	352	27	h1	h1	PROPN
ejpam-6436	352	28	)	)	PUNCT
ejpam-6436	352	29	,	,	PUNCT
ejpam-6436	352	30	(	(	PUNCT
ejpam-6436	352	31	p2	p2	X
ejpam-6436	352	32	,	,	PUNCT
ejpam-6436	352	33	h2	h2	NOUN
ejpam-6436	352	34	)	)	PUNCT
ejpam-6436	352	35	∈	∈	PROPN
ejpam-6436	352	36	t	t	PROPN
ejpam-6436	352	37	.	.	PUNCT
ejpam-6436	353	1	now	now	ADV
ejpam-6436	353	2	(	(	PUNCT
ejpam-6436	353	3	q	q	ADJ
ejpam-6436	353	4	,	,	PUNCT
ejpam-6436	353	5	h	h	NOUN
ejpam-6436	353	6	)	)	PUNCT
ejpam-6436	353	7	=	=	SYM
ejpam-6436	353	8	(	(	PUNCT
ejpam-6436	353	9	p1	p1	PROPN
ejpam-6436	353	10	,	,	PUNCT
ejpam-6436	353	11	(	(	PUNCT
ejpam-6436	353	12	cs)p1h1	cs)p1h1	NOUN
ejpam-6436	353	13	)	)	PUNCT
ejpam-6436	353	14	and	and	CCONJ
ejpam-6436	353	15	(	(	PUNCT
ejpam-6436	353	16	q	q	ADJ
ejpam-6436	353	17	,	,	PUNCT
ejpam-6436	353	18	h	h	NOUN
ejpam-6436	353	19	)	)	PUNCT
ejpam-6436	353	20	≤	≤	NOUN
ejpam-6436	353	21	(	(	PUNCT
ejpam-6436	353	22	p2	p2	NOUN
ejpam-6436	353	23	,	,	PUNCT
ejpam-6436	353	24	(	(	PUNCT
ejpam-6436	353	25	cs′)p2h2	cs′)p2h2	INTJ
ejpam-6436	353	26	)	)	PUNCT
ejpam-6436	353	27	.	.	PUNCT
ejpam-6436	354	1	so	so	ADV
ejpam-6436	354	2	h	h	NOUN
ejpam-6436	354	3	=	=	SYM
ejpam-6436	354	4	(	(	PUNCT
ejpam-6436	354	5	cs)p1h1	cs)p1h1	PROPN
ejpam-6436	354	6	and	and	CCONJ
ejpam-6436	354	7	h	h	NOUN
ejpam-6436	354	8	≤	≤	NOUN
ejpam-6436	354	9	(	(	PUNCT
ejpam-6436	354	10	cs′)p2h2	cs′)p2h2	INTJ
ejpam-6436	354	11	.	.	PUNCT
ejpam-6436	355	1	take	take	VERB
ejpam-6436	355	2	any	any	PRON
ejpam-6436	355	3	a	a	DET
ejpam-6436	355	4	∈	∈	PROPN
ejpam-6436	355	5	a	a	PRON
ejpam-6436	355	6	,	,	PUNCT
ejpam-6436	355	7	then	then	ADV
ejpam-6436	355	8	h(a	h(a	PROPN
ejpam-6436	355	9	)	)	PUNCT
ejpam-6436	356	1	=	=	SYM
ejpam-6436	356	2	cs(p1a)h1(a	cs(p1a)h1(a	PROPN
ejpam-6436	356	3	)	)	PUNCT
ejpam-6436	356	4	and	and	CCONJ
ejpam-6436	356	5	h(a	h(a	PROPN
ejpam-6436	356	6	)	)	PUNCT
ejpam-6436	356	7	≤	≤	NUM
ejpam-6436	356	8	cs′(p2a)h2(a	cs′(p2a)h2(a	NOUN
ejpam-6436	356	9	)	)	PUNCT
ejpam-6436	356	10	.	.	PUNCT
ejpam-6436	357	1	so	so	ADV
ejpam-6436	357	2	h(a	h(a	PROPN
ejpam-6436	357	3	)	)	PUNCT
ejpam-6436	357	4	=	=	SYM
ejpam-6436	357	5	sh1(a	sh1(a	PROPN
ejpam-6436	357	6	)	)	PUNCT
ejpam-6436	357	7	and	and	CCONJ
ejpam-6436	357	8	h(a	h(a	PROPN
ejpam-6436	357	9	)	)	PUNCT
ejpam-6436	357	10	≤	≤	NUM
ejpam-6436	357	11	s′h2(a	s′h2(a	NOUN
ejpam-6436	357	12	)	)	PUNCT
ejpam-6436	357	13	.	.	PUNCT
ejpam-6436	358	1	thus	thus	ADV
ejpam-6436	358	2	h(a	h(a	PROPN
ejpam-6436	358	3	)	)	PUNCT
ejpam-6436	358	4	∈	∈	PROPN
ejpam-6436	358	5	ss	ss	NOUN
ejpam-6436	358	6	∩	∩	NOUN
ejpam-6436	358	7	(	(	PUNCT
ejpam-6436	358	8	s′s	s′s	NOUN
ejpam-6436	358	9	]	]	X
ejpam-6436	358	10	,	,	PUNCT
ejpam-6436	358	11	and	and	CCONJ
ejpam-6436	358	12	so	so	ADV
ejpam-6436	358	13	s	s	VERB
ejpam-6436	358	14	is	be	AUX
ejpam-6436	358	15	weakly	weakly	ADV
ejpam-6436	358	16	left	leave	VERB
ejpam-6436	358	17	reversible	reversible	ADJ
ejpam-6436	358	18	,	,	PUNCT
ejpam-6436	358	19	as	as	SCONJ
ejpam-6436	358	20	required	require	VERB
ejpam-6436	358	21	.	.	PUNCT
ejpam-6436	359	1	b.	b.	PROPN
ejpam-6436	359	2	al	al	PROPN
ejpam-6436	359	3	subaiei	subaiei	PROPN
ejpam-6436	359	4	et	et	PROPN
ejpam-6436	359	5	al	al	PROPN
ejpam-6436	359	6	.	.	PUNCT
ejpam-6436	359	7	/	/	SYM
ejpam-6436	359	8	eur	eur	PROPN
ejpam-6436	359	9	.	.	PUNCT
ejpam-6436	360	1	j.	j.	PROPN
ejpam-6436	360	2	pure	pure	PROPN
ejpam-6436	360	3	appl	appl	PROPN
ejpam-6436	360	4	.	.	PROPN
ejpam-6436	360	5	math	math	PROPN
ejpam-6436	360	6	,	,	PUNCT
ejpam-6436	360	7	18	18	NUM
ejpam-6436	360	8	(	(	PUNCT
ejpam-6436	360	9	3	3	NUM
ejpam-6436	360	10	)	)	PUNCT
ejpam-6436	360	11	(	(	PUNCT
ejpam-6436	360	12	2025	2025	NUM
ejpam-6436	360	13	)	)	PUNCT
ejpam-6436	360	14	,	,	PUNCT
ejpam-6436	360	15	6436	6436	NUM
ejpam-6436	360	16	13	13	NUM
ejpam-6436	360	17	of	of	ADP
ejpam-6436	360	18	14	14	NUM
ejpam-6436	360	19	recall	recall	NOUN
ejpam-6436	360	20	that	that	SCONJ
ejpam-6436	360	21	a	a	DET
ejpam-6436	360	22	posemigroup	posemigroup	NOUN
ejpam-6436	360	23	s	s	VERB
ejpam-6436	360	24	is	be	AUX
ejpam-6436	360	25	termed	term	VERB
ejpam-6436	360	26	left	leave	VERB
ejpam-6436	360	27	solvable	solvable	ADJ
ejpam-6436	360	28	if	if	SCONJ
ejpam-6436	360	29	for	for	ADP
ejpam-6436	360	30	any	any	DET
ejpam-6436	360	31	u	u	NOUN
ejpam-6436	360	32	,	,	PUNCT
ejpam-6436	360	33	v	v	ADP
ejpam-6436	360	34	∈	∈	NOUN
ejpam-6436	360	35	s	s	VERB
ejpam-6436	360	36	there	there	PRON
ejpam-6436	360	37	exist	exist	VERB
ejpam-6436	360	38	s	s	NOUN
ejpam-6436	360	39	∈	∈	NOUN
ejpam-6436	360	40	s	s	VERB
ejpam-6436	360	41	such	such	ADJ
ejpam-6436	360	42	that	that	DET
ejpam-6436	360	43	su	su	PROPN
ejpam-6436	361	1	=	=	NOUN
ejpam-6436	361	2	v.	v.	CCONJ
ejpam-6436	361	3	however	however	ADV
ejpam-6436	361	4	,	,	PUNCT
ejpam-6436	361	5	if	if	SCONJ
ejpam-6436	361	6	for	for	ADP
ejpam-6436	361	7	any	any	DET
ejpam-6436	361	8	u	u	NOUN
ejpam-6436	361	9	,	,	PUNCT
ejpam-6436	361	10	v	v	ADP
ejpam-6436	361	11	∈	∈	NOUN
ejpam-6436	361	12	s	s	VERB
ejpam-6436	361	13	there	there	PRON
ejpam-6436	361	14	exist	exist	VERB
ejpam-6436	361	15	a	a	DET
ejpam-6436	361	16	unique	unique	ADJ
ejpam-6436	361	17	s	s	X
ejpam-6436	361	18	∈	∈	NOUN
ejpam-6436	361	19	s	s	VERB
ejpam-6436	361	20	such	such	ADJ
ejpam-6436	361	21	that	that	PRON
ejpam-6436	361	22	su	su	PROPN
ejpam-6436	362	1	=	=	NOUN
ejpam-6436	362	2	v	v	PROPN
ejpam-6436	362	3	then	then	ADV
ejpam-6436	362	4	s	s	VERB
ejpam-6436	362	5	is	be	AUX
ejpam-6436	362	6	called	call	VERB
ejpam-6436	362	7	left	leave	VERB
ejpam-6436	362	8	uniquely	uniquely	ADV
ejpam-6436	362	9	solvable	solvable	ADJ
ejpam-6436	362	10	.	.	PUNCT
ejpam-6436	363	1	the	the	DET
ejpam-6436	363	2	right	right	ADJ
ejpam-6436	363	3	solvable	solvable	ADJ
ejpam-6436	363	4	and	and	CCONJ
ejpam-6436	363	5	uniquely	uniquely	ADV
ejpam-6436	363	6	solvable	solvable	ADJ
ejpam-6436	363	7	is	be	AUX
ejpam-6436	363	8	defined	define	VERB
ejpam-6436	363	9	dually	dually	ADV
ejpam-6436	363	10	.	.	PUNCT
ejpam-6436	364	1	as	as	SCONJ
ejpam-6436	364	2	known	know	VERB
ejpam-6436	364	3	that	that	SCONJ
ejpam-6436	364	4	left	leave	VERB
ejpam-6436	364	5	(	(	PUNCT
ejpam-6436	364	6	resp	resp	NOUN
ejpam-6436	364	7	.	.	PUNCT
ejpam-6436	365	1	right	right	ADJ
ejpam-6436	365	2	)	)	PUNCT
ejpam-6436	365	3	uniquely	uniquely	ADV
ejpam-6436	365	4	solvable	solvable	ADJ
ejpam-6436	365	5	semigroup	semigroup	NOUN
ejpam-6436	365	6	is	be	AUX
ejpam-6436	365	7	called	call	VERB
ejpam-6436	365	8	left	left	ADJ
ejpam-6436	365	9	(	(	PUNCT
ejpam-6436	365	10	resp	resp	NOUN
ejpam-6436	365	11	.	.	PUNCT
ejpam-6436	366	1	right	right	ADJ
ejpam-6436	366	2	)	)	PUNCT
ejpam-6436	366	3	group	group	NOUN
ejpam-6436	366	4	.	.	PUNCT
ejpam-6436	367	1	theorem	theorem	VERB
ejpam-6436	367	2	8	8	NUM
ejpam-6436	367	3	.	.	PUNCT
ejpam-6436	368	1	the	the	DET
ejpam-6436	368	2	posemigroup	posemigroup	PROPN
ejpam-6436	368	3	t	t	PROPN
ejpam-6436	368	4	is	be	AUX
ejpam-6436	368	5	a	a	DET
ejpam-6436	368	6	left	left	ADJ
ejpam-6436	368	7	solvable	solvable	NOUN
ejpam-6436	368	8	if	if	SCONJ
ejpam-6436	368	9	and	and	CCONJ
ejpam-6436	368	10	only	only	ADV
ejpam-6436	368	11	if	if	SCONJ
ejpam-6436	368	12	r	r	NOUN
ejpam-6436	368	13	and	and	CCONJ
ejpam-6436	368	14	s	s	NOUN
ejpam-6436	368	15	are	be	AUX
ejpam-6436	368	16	both	both	PRON
ejpam-6436	368	17	left	leave	VERB
ejpam-6436	368	18	solvable	solvable	ADJ
ejpam-6436	368	19	.	.	PUNCT
ejpam-6436	369	1	proof	proof	NOUN
ejpam-6436	369	2	.	.	PUNCT
ejpam-6436	370	1	suppose	suppose	VERB
ejpam-6436	370	2	that	that	SCONJ
ejpam-6436	370	3	t	t	PROPN
ejpam-6436	370	4	is	be	AUX
ejpam-6436	370	5	a	a	DET
ejpam-6436	370	6	left	left	ADJ
ejpam-6436	370	7	solvable	solvable	NOUN
ejpam-6436	370	8	.	.	PUNCT
ejpam-6436	371	1	for	for	ADP
ejpam-6436	371	2	all	all	DET
ejpam-6436	371	3	p	p	NOUN
ejpam-6436	371	4	,	,	PUNCT
ejpam-6436	371	5	t	t	PROPN
ejpam-6436	371	6	∈	∈	PROPN
ejpam-6436	371	7	r	r	NOUN
ejpam-6436	371	8	,	,	PUNCT
ejpam-6436	371	9	we	we	PRON
ejpam-6436	371	10	know	know	VERB
ejpam-6436	371	11	that	that	SCONJ
ejpam-6436	371	12	(	(	PUNCT
ejpam-6436	371	13	p	p	X
ejpam-6436	371	14	,	,	PUNCT
ejpam-6436	371	15	g	g	NOUN
ejpam-6436	371	16	)	)	PUNCT
ejpam-6436	371	17	,	,	PUNCT
ejpam-6436	371	18	(	(	PUNCT
ejpam-6436	371	19	t	t	PROPN
ejpam-6436	371	20	,	,	PUNCT
ejpam-6436	371	21	k	k	NOUN
ejpam-6436	371	22	)	)	PUNCT
ejpam-6436	371	23	∈	∈	PROPN
ejpam-6436	371	24	t	t	PROPN
ejpam-6436	371	25	.	.	PUNCT
ejpam-6436	372	1	then	then	ADV
ejpam-6436	372	2	there	there	PRON
ejpam-6436	372	3	exist	exist	VERB
ejpam-6436	372	4	(	(	PUNCT
ejpam-6436	372	5	r	r	NOUN
ejpam-6436	372	6	,	,	PUNCT
ejpam-6436	372	7	f	f	X
ejpam-6436	372	8	)	)	PUNCT
ejpam-6436	372	9	∈	∈	PROPN
ejpam-6436	372	10	t	t	NOUN
ejpam-6436	372	11	such	such	ADJ
ejpam-6436	372	12	that	that	SCONJ
ejpam-6436	372	13	(	(	PUNCT
ejpam-6436	372	14	r	r	NOUN
ejpam-6436	372	15	,	,	PUNCT
ejpam-6436	372	16	f)(p	f)(p	NOUN
ejpam-6436	372	17	,	,	PUNCT
ejpam-6436	372	18	g	g	NOUN
ejpam-6436	372	19	)	)	PUNCT
ejpam-6436	372	20	=	=	SYM
ejpam-6436	372	21	(	(	PUNCT
ejpam-6436	372	22	t	t	PROPN
ejpam-6436	372	23	,	,	PUNCT
ejpam-6436	372	24	k	k	NOUN
ejpam-6436	372	25	)	)	PUNCT
ejpam-6436	372	26	.	.	PUNCT
ejpam-6436	373	1	hence	hence	ADV
ejpam-6436	373	2	,	,	PUNCT
ejpam-6436	373	3	(	(	PUNCT
ejpam-6436	373	4	rp	rp	NOUN
ejpam-6436	373	5	,	,	PUNCT
ejpam-6436	373	6	fpg	fpg	PROPN
ejpam-6436	373	7	)	)	PUNCT
ejpam-6436	373	8	=	=	PUNCT
ejpam-6436	373	9	(	(	PUNCT
ejpam-6436	373	10	t	t	PROPN
ejpam-6436	373	11	,	,	PUNCT
ejpam-6436	373	12	k	k	NOUN
ejpam-6436	373	13	)	)	PUNCT
ejpam-6436	373	14	.	.	PUNCT
ejpam-6436	374	1	then	then	ADV
ejpam-6436	374	2	,	,	PUNCT
ejpam-6436	374	3	rp	rp	NOUN
ejpam-6436	374	4	=	=	SYM
ejpam-6436	374	5	t	t	PROPN
ejpam-6436	375	1	and	and	CCONJ
ejpam-6436	375	2	so	so	ADV
ejpam-6436	375	3	r	r	NOUN
ejpam-6436	375	4	is	be	AUX
ejpam-6436	375	5	left	leave	VERB
ejpam-6436	375	6	solvable	solvable	ADJ
ejpam-6436	375	7	.	.	PUNCT
ejpam-6436	376	1	now	now	ADV
ejpam-6436	376	2	,	,	PUNCT
ejpam-6436	376	3	for	for	ADP
ejpam-6436	376	4	any	any	DET
ejpam-6436	376	5	s	s	NOUN
ejpam-6436	376	6	,	,	PUNCT
ejpam-6436	376	7	s′	s′	PUNCT
ejpam-6436	376	8	∈	∈	PROPN
ejpam-6436	376	9	s	s	VERB
ejpam-6436	376	10	we	we	PRON
ejpam-6436	376	11	know	know	VERB
ejpam-6436	376	12	that	that	SCONJ
ejpam-6436	376	13	(	(	PUNCT
ejpam-6436	376	14	p	p	X
ejpam-6436	376	15	,	,	PUNCT
ejpam-6436	376	16	cs	cs	PROPN
ejpam-6436	376	17	)	)	PUNCT
ejpam-6436	376	18	,	,	PUNCT
ejpam-6436	376	19	(	(	PUNCT
ejpam-6436	376	20	t	t	PROPN
ejpam-6436	376	21	,	,	PUNCT
ejpam-6436	376	22	cs′	cs′	X
ejpam-6436	376	23	)	)	PUNCT
ejpam-6436	376	24	∈	∈	PROPN
ejpam-6436	376	25	t	t	NOUN
ejpam-6436	376	26	.	.	PUNCT
ejpam-6436	377	1	hence	hence	ADV
ejpam-6436	377	2	,	,	PUNCT
ejpam-6436	377	3	there	there	PRON
ejpam-6436	377	4	exist	exist	VERB
ejpam-6436	377	5	(	(	PUNCT
ejpam-6436	377	6	r	r	NOUN
ejpam-6436	377	7	,	,	PUNCT
ejpam-6436	377	8	f	f	X
ejpam-6436	377	9	)	)	PUNCT
ejpam-6436	377	10	∈	∈	PROPN
ejpam-6436	377	11	t	t	NOUN
ejpam-6436	377	12	such	such	ADJ
ejpam-6436	377	13	that	that	SCONJ
ejpam-6436	377	14	(	(	PUNCT
ejpam-6436	377	15	r	r	NOUN
ejpam-6436	377	16	,	,	PUNCT
ejpam-6436	377	17	f)(p	f)(p	NOUN
ejpam-6436	377	18	,	,	PUNCT
ejpam-6436	377	19	cs	cs	ADJ
ejpam-6436	377	20	)	)	PUNCT
ejpam-6436	377	21	=	=	SYM
ejpam-6436	377	22	(	(	PUNCT
ejpam-6436	377	23	t	t	PROPN
ejpam-6436	377	24	,	,	PUNCT
ejpam-6436	377	25	cs′	cs′	X
ejpam-6436	377	26	)	)	PUNCT
ejpam-6436	377	27	.	.	PUNCT
ejpam-6436	378	1	hence	hence	ADV
ejpam-6436	378	2	,	,	PUNCT
ejpam-6436	378	3	(	(	PUNCT
ejpam-6436	378	4	rp	rp	NOUN
ejpam-6436	378	5	,	,	PUNCT
ejpam-6436	378	6	fpcs	fpc	NOUN
ejpam-6436	378	7	)	)	PUNCT
ejpam-6436	378	8	=	=	SYM
ejpam-6436	378	9	(	(	PUNCT
ejpam-6436	378	10	t	t	PROPN
ejpam-6436	378	11	,	,	PUNCT
ejpam-6436	378	12	cs′	cs′	X
ejpam-6436	378	13	)	)	PUNCT
ejpam-6436	378	14	.	.	PUNCT
ejpam-6436	379	1	so	so	ADV
ejpam-6436	379	2	fpcs(a	fpcs(a	ADJ
ejpam-6436	379	3	)	)	PUNCT
ejpam-6436	379	4	=	=	SYM
ejpam-6436	379	5	f(pa)cs(a	f(pa)cs(a	PROPN
ejpam-6436	379	6	)	)	PUNCT
ejpam-6436	380	1	=	=	SYM
ejpam-6436	380	2	f(pa)s	f(pa)s	NOUN
ejpam-6436	380	3	=	=	SYM
ejpam-6436	380	4	cs′(a	cs′(a	NOUN
ejpam-6436	380	5	)	)	PUNCT
ejpam-6436	381	1	=	=	SYM
ejpam-6436	381	2	s′.	s′.	PROPN
ejpam-6436	381	3	therefore	therefore	ADV
ejpam-6436	381	4	,	,	PUNCT
ejpam-6436	381	5	s	s	VERB
ejpam-6436	381	6	is	be	AUX
ejpam-6436	381	7	left	leave	VERB
ejpam-6436	381	8	solvable	solvable	ADJ
ejpam-6436	381	9	.	.	PUNCT
ejpam-6436	382	1	now	now	ADV
ejpam-6436	382	2	,	,	PUNCT
ejpam-6436	382	3	suppose	suppose	VERB
ejpam-6436	382	4	that	that	SCONJ
ejpam-6436	382	5	r	r	NOUN
ejpam-6436	382	6	and	and	CCONJ
ejpam-6436	382	7	s	s	NOUN
ejpam-6436	382	8	are	be	AUX
ejpam-6436	382	9	both	both	PRON
ejpam-6436	382	10	left	leave	VERB
ejpam-6436	382	11	solvable	solvable	ADJ
ejpam-6436	382	12	.	.	PUNCT
ejpam-6436	383	1	suppose	suppose	VERB
ejpam-6436	383	2	that	that	SCONJ
ejpam-6436	383	3	(	(	PUNCT
ejpam-6436	383	4	p	p	X
ejpam-6436	383	5	,	,	PUNCT
ejpam-6436	383	6	g	g	NOUN
ejpam-6436	383	7	)	)	PUNCT
ejpam-6436	383	8	,	,	PUNCT
ejpam-6436	383	9	(	(	PUNCT
ejpam-6436	383	10	t	t	PROPN
ejpam-6436	383	11	,	,	PUNCT
ejpam-6436	383	12	k	k	NOUN
ejpam-6436	383	13	)	)	PUNCT
ejpam-6436	383	14	∈	∈	PROPN
ejpam-6436	383	15	t	t	NOUN
ejpam-6436	383	16	.	.	PUNCT
ejpam-6436	384	1	since	since	SCONJ
ejpam-6436	384	2	r	r	NOUN
ejpam-6436	384	3	is	be	AUX
ejpam-6436	384	4	left	leave	VERB
ejpam-6436	384	5	solvable	solvable	ADV
ejpam-6436	384	6	there	there	ADV
ejpam-6436	384	7	exist	exist	VERB
ejpam-6436	384	8	r	r	NOUN
ejpam-6436	384	9	∈	∈	NOUN
ejpam-6436	384	10	r	r	NOUN
ejpam-6436	384	11	such	such	ADJ
ejpam-6436	384	12	that	that	DET
ejpam-6436	384	13	rp	rp	NOUN
ejpam-6436	384	14	=	=	PUNCT
ejpam-6436	384	15	t.	t.	NOUN
ejpam-6436	384	16	since	since	ADV
ejpam-6436	384	17	,	,	PUNCT
ejpam-6436	384	18	g(a	g(a	PROPN
ejpam-6436	384	19	)	)	PUNCT
ejpam-6436	384	20	,	,	PUNCT
ejpam-6436	384	21	k(a	k(a	PROPN
ejpam-6436	384	22	)	)	PUNCT
ejpam-6436	384	23	∈	∈	PROPN
ejpam-6436	384	24	s	s	PART
ejpam-6436	384	25	for	for	ADP
ejpam-6436	384	26	any	any	DET
ejpam-6436	384	27	a	a	DET
ejpam-6436	384	28	∈	∈	PROPN
ejpam-6436	384	29	a	a	PRON
ejpam-6436	384	30	and	and	CCONJ
ejpam-6436	384	31	since	since	SCONJ
ejpam-6436	384	32	s	s	NOUN
ejpam-6436	384	33	is	be	AUX
ejpam-6436	384	34	left	leave	VERB
ejpam-6436	384	35	solvable	solvable	ADJ
ejpam-6436	384	36	then	then	ADV
ejpam-6436	384	37	there	there	PRON
ejpam-6436	384	38	exist	exist	VERB
ejpam-6436	384	39	s	s	NOUN
ejpam-6436	384	40	∈	∈	NOUN
ejpam-6436	384	41	s	s	VERB
ejpam-6436	384	42	such	such	ADJ
ejpam-6436	384	43	that	that	PRON
ejpam-6436	384	44	sg(a	sg(a	NOUN
ejpam-6436	384	45	)	)	PUNCT
ejpam-6436	384	46	=	=	SYM
ejpam-6436	384	47	k(a	k(a	NOUN
ejpam-6436	384	48	)	)	PUNCT
ejpam-6436	384	49	.	.	PUNCT
ejpam-6436	385	1	hence	hence	ADV
ejpam-6436	385	2	,	,	PUNCT
ejpam-6436	385	3	cs(a)g(a	cs(a)g(a	PROPN
ejpam-6436	385	4	)	)	PUNCT
ejpam-6436	385	5	=	=	SYM
ejpam-6436	385	6	k(a	k(a	PROPN
ejpam-6436	385	7	)	)	PUNCT
ejpam-6436	385	8	.	.	PUNCT
ejpam-6436	386	1	then	then	ADV
ejpam-6436	386	2	(	(	PUNCT
ejpam-6436	386	3	cs)pg(a	cs)pg(a	PROPN
ejpam-6436	386	4	)	)	PUNCT
ejpam-6436	386	5	=	=	SYM
ejpam-6436	386	6	cs(pa)g(a	cs(pa)g(a	X
ejpam-6436	386	7	)	)	PUNCT
ejpam-6436	386	8	=	=	SYM
ejpam-6436	386	9	cs(a)g(a	cs(a)g(a	PROPN
ejpam-6436	386	10	)	)	PUNCT
ejpam-6436	386	11	=	=	SYM
ejpam-6436	386	12	k(a	k(a	PROPN
ejpam-6436	386	13	)	)	PUNCT
ejpam-6436	386	14	.	.	PUNCT
ejpam-6436	387	1	therefore	therefore	ADV
ejpam-6436	387	2	,	,	PUNCT
ejpam-6436	387	3	(	(	PUNCT
ejpam-6436	387	4	cs)pg	cs)pg	X
ejpam-6436	387	5	=	=	PUNCT
ejpam-6436	387	6	k.	k.	PROPN
ejpam-6436	387	7	thus	thus	ADV
ejpam-6436	387	8	,	,	PUNCT
ejpam-6436	387	9	(	(	PUNCT
ejpam-6436	387	10	r	r	NOUN
ejpam-6436	387	11	,	,	PUNCT
ejpam-6436	387	12	cs)(p	cs)(p	NOUN
ejpam-6436	387	13	,	,	PUNCT
ejpam-6436	387	14	g	g	NOUN
ejpam-6436	387	15	)	)	PUNCT
ejpam-6436	387	16	=	=	NOUN
ejpam-6436	387	17	(	(	PUNCT
ejpam-6436	387	18	rp	rp	NOUN
ejpam-6436	387	19	,	,	PUNCT
ejpam-6436	387	20	(	(	PUNCT
ejpam-6436	387	21	cs)pg	cs)pg	X
ejpam-6436	387	22	)	)	PUNCT
ejpam-6436	387	23	=	=	SYM
ejpam-6436	387	24	(	(	PUNCT
ejpam-6436	387	25	t	t	PROPN
ejpam-6436	387	26	,	,	PUNCT
ejpam-6436	387	27	k	k	NOUN
ejpam-6436	387	28	)	)	PUNCT
ejpam-6436	387	29	as	as	SCONJ
ejpam-6436	387	30	required	require	VERB
ejpam-6436	387	31	.	.	PUNCT
ejpam-6436	388	1	corollary	corollary	ADJ
ejpam-6436	388	2	3	3	NUM
ejpam-6436	388	3	.	.	PUNCT
ejpam-6436	389	1	the	the	DET
ejpam-6436	389	2	left	left	ADJ
ejpam-6436	389	3	r	r	NOUN
ejpam-6436	389	4	-	-	PUNCT
ejpam-6436	389	5	poset	poset	VERB
ejpam-6436	389	6	t	t	NOUN
ejpam-6436	389	7	is	be	AUX
ejpam-6436	389	8	a	a	DET
ejpam-6436	389	9	left	left	NOUN
ejpam-6436	389	10	uniquely	uniquely	ADV
ejpam-6436	389	11	solvable	solvable	ADJ
ejpam-6436	389	12	if	if	SCONJ
ejpam-6436	389	13	and	and	CCONJ
ejpam-6436	389	14	only	only	ADV
ejpam-6436	389	15	if	if	SCONJ
ejpam-6436	389	16	r	r	NOUN
ejpam-6436	389	17	and	and	CCONJ
ejpam-6436	389	18	s	s	NOUN
ejpam-6436	389	19	are	be	AUX
ejpam-6436	389	20	both	both	PRON
ejpam-6436	389	21	left	leave	VERB
ejpam-6436	389	22	uniquely	uniquely	ADV
ejpam-6436	389	23	solvable	solvable	ADJ
ejpam-6436	389	24	.	.	PUNCT
ejpam-6436	390	1	acknowledgements	acknowledgement	NOUN
ejpam-6436	390	2	the	the	DET
ejpam-6436	390	3	authors	author	NOUN
ejpam-6436	390	4	thank	thank	VERB
ejpam-6436	390	5	the	the	DET
ejpam-6436	390	6	reviewers	reviewer	NOUN
ejpam-6436	390	7	for	for	ADP
ejpam-6436	390	8	their	their	PRON
ejpam-6436	390	9	valuable	valuable	ADJ
ejpam-6436	390	10	comments	comment	NOUN
ejpam-6436	390	11	,	,	PUNCT
ejpam-6436	390	12	which	which	PRON
ejpam-6436	390	13	contributed	contribute	VERB
ejpam-6436	390	14	to	to	ADP
ejpam-6436	390	15	improving	improve	VERB
ejpam-6436	390	16	the	the	DET
ejpam-6436	390	17	manuscript	manuscript	NOUN
ejpam-6436	390	18	.	.	PUNCT
ejpam-6436	391	1	the	the	DET
ejpam-6436	391	2	third	third	ADJ
ejpam-6436	391	3	author	author	NOUN
ejpam-6436	391	4	acknowledges	acknowledge	VERB
ejpam-6436	391	5	support	support	NOUN
ejpam-6436	391	6	from	from	ADP
ejpam-6436	391	7	the	the	DET
ejpam-6436	391	8	serb	serb	ADJ
ejpam-6436	391	9	matrics	matric	NOUN
ejpam-6436	391	10	grant	grant	VERB
ejpam-6436	391	11	mtr/2023/000944	mtr/2023/000944	NOUN
ejpam-6436	391	12	.	.	PUNCT
ejpam-6436	392	1	references	reference	NOUN
ejpam-6436	392	2	[	[	X
ejpam-6436	392	3	1	1	NUM
ejpam-6436	392	4	]	]	PUNCT
ejpam-6436	392	5	l.	l.	PROPN
ejpam-6436	392	6	a.	a.	PROPN
ejpam-6436	392	7	skornjakov	skornjakov	PROPN
ejpam-6436	392	8	.	.	PUNCT
ejpam-6436	393	1	regularity	regularity	NOUN
ejpam-6436	393	2	of	of	ADP
ejpam-6436	393	3	the	the	DET
ejpam-6436	393	4	wreath	wreath	NOUN
ejpam-6436	393	5	product	product	NOUN
ejpam-6436	393	6	of	of	ADP
ejpam-6436	393	7	monoids	monoid	NOUN
ejpam-6436	393	8	.	.	PUNCT
ejpam-6436	394	1	semigroup	semigroup	PROPN
ejpam-6436	394	2	forum	forum	PROPN
ejpam-6436	394	3	,	,	PUNCT
ejpam-6436	394	4	18:83–86	18:83–86	NUM
ejpam-6436	394	5	,	,	PUNCT
ejpam-6436	394	6	1979	1979	NUM
ejpam-6436	394	7	.	.	PUNCT
ejpam-6436	395	1	[	[	X
ejpam-6436	395	2	2	2	NUM
ejpam-6436	395	3	]	]	X
ejpam-6436	395	4	u.	u.	NOUN
ejpam-6436	395	5	knauer	knauer	PROPN
ejpam-6436	395	6	and	and	CCONJ
ejpam-6436	395	7	a.	a.	PROPN
ejpam-6436	395	8	mikhalev	mikhalev	PROPN
ejpam-6436	395	9	.	.	PUNCT
ejpam-6436	396	1	endomorphism	endomorphism	PROPN
ejpam-6436	396	2	monoids	monoid	NOUN
ejpam-6436	396	3	of	of	ADP
ejpam-6436	396	4	free	free	ADJ
ejpam-6436	396	5	acts	act	NOUN
ejpam-6436	396	6	and	and	CCONJ
ejpam-6436	396	7	0	0	NUM
ejpam-6436	396	8	-	-	PUNCT
ejpam-6436	396	9	wreath	wreath	NOUN
ejpam-6436	396	10	products	product	NOUN
ejpam-6436	396	11	of	of	ADP
ejpam-6436	396	12	monoids	monoid	NOUN
ejpam-6436	396	13	.	.	PUNCT
ejpam-6436	397	1	semigroup	semigroup	PROPN
ejpam-6436	397	2	forum	forum	PROPN
ejpam-6436	397	3	,	,	PUNCT
ejpam-6436	397	4	19:177–187	19:177–187	NUM
ejpam-6436	397	5	,	,	PUNCT
ejpam-6436	397	6	1980	1980	NUM
ejpam-6436	397	7	.	.	PUNCT
ejpam-6436	398	1	[	[	X
ejpam-6436	398	2	3	3	X
ejpam-6436	398	3	]	]	PUNCT
ejpam-6436	398	4	s.	s.	PROPN
ejpam-6436	398	5	a.	a.	PROPN
ejpam-6436	398	6	wazzana	wazzana	PROPN
ejpam-6436	398	7	,	,	PUNCT
ejpam-6436	398	8	f.	f.	PROPN
ejpam-6436	398	9	ates	ates	PROPN
ejpam-6436	398	10	,	,	PUNCT
ejpam-6436	398	11	and	and	CCONJ
ejpam-6436	398	12	a.	a.	PROPN
ejpam-6436	398	13	s.	s.	PROPN
ejpam-6436	398	14	cevik	cevik	PROPN
ejpam-6436	398	15	.	.	PUNCT
ejpam-6436	399	1	the	the	DET
ejpam-6436	399	2	new	new	ADJ
ejpam-6436	399	3	derivation	derivation	NOUN
ejpam-6436	399	4	for	for	ADP
ejpam-6436	399	5	wreath	wreath	NOUN
ejpam-6436	399	6	products	product	NOUN
ejpam-6436	399	7	of	of	ADP
ejpam-6436	399	8	monoids	monoid	NOUN
ejpam-6436	399	9	.	.	PUNCT
ejpam-6436	400	1	filomat	filomat	NOUN
ejpam-6436	400	2	,	,	PUNCT
ejpam-6436	400	3	34(2):683–689	34(2):683–689	PROPN
ejpam-6436	400	4	,	,	PUNCT
ejpam-6436	400	5	2020	2020	NUM
ejpam-6436	400	6	.	.	PUNCT
ejpam-6436	401	1	[	[	X
ejpam-6436	401	2	4	4	X
ejpam-6436	401	3	]	]	PUNCT
ejpam-6436	401	4	j.	j.	PROPN
ejpam-6436	401	5	d.	d.	PROPN
ejpam-6436	401	6	p.	p.	PROPN
ejpam-6436	401	7	meldrum	meldrum	PROPN
ejpam-6436	401	8	.	.	PUNCT
ejpam-6436	402	1	wreath	wreath	NOUN
ejpam-6436	402	2	products	product	NOUN
ejpam-6436	402	3	of	of	ADP
ejpam-6436	402	4	groups	group	NOUN
ejpam-6436	402	5	and	and	CCONJ
ejpam-6436	402	6	semigroups	semigroup	NOUN
ejpam-6436	402	7	.	.	PUNCT
ejpam-6436	403	1	longman	longman	NOUN
ejpam-6436	403	2	,	,	PUNCT
ejpam-6436	403	3	harlow	harlow	NOUN
ejpam-6436	403	4	,	,	PUNCT
ejpam-6436	403	5	1995	1995	NUM
ejpam-6436	403	6	.	.	PUNCT
ejpam-6436	404	1	[	[	X
ejpam-6436	404	2	5	5	X
ejpam-6436	404	3	]	]	X
ejpam-6436	404	4	u.	u.	NOUN
ejpam-6436	404	5	knauer	knauer	PROPN
ejpam-6436	404	6	and	and	CCONJ
ejpam-6436	404	7	a.	a.	NOUN
ejpam-6436	404	8	mikhalev	mikhalev	PROPN
ejpam-6436	404	9	.	.	PUNCT
ejpam-6436	405	1	wreath	wreath	NOUN
ejpam-6436	405	2	products	product	NOUN
ejpam-6436	405	3	of	of	ADP
ejpam-6436	405	4	acts	act	NOUN
ejpam-6436	405	5	over	over	ADP
ejpam-6436	405	6	monoids	monoid	NOUN
ejpam-6436	405	7	:	:	PUNCT
ejpam-6436	405	8	i.	i.	PROPN
ejpam-6436	405	9	regular	regular	ADJ
ejpam-6436	405	10	and	and	CCONJ
ejpam-6436	405	11	inverse	inverse	ADJ
ejpam-6436	405	12	acts	act	NOUN
ejpam-6436	405	13	.	.	PUNCT
ejpam-6436	406	1	journal	journal	NOUN
ejpam-6436	406	2	of	of	ADP
ejpam-6436	406	3	pure	pure	ADJ
ejpam-6436	406	4	and	and	CCONJ
ejpam-6436	406	5	applied	applied	ADJ
ejpam-6436	406	6	algebra	algebra	NOUN
ejpam-6436	406	7	,	,	PUNCT
ejpam-6436	406	8	51:251–260	51:251–260	PROPN
ejpam-6436	406	9	,	,	PUNCT
ejpam-6436	406	10	1988	1988	NUM
ejpam-6436	406	11	.	.	PUNCT
ejpam-6436	407	1	[	[	X
ejpam-6436	407	2	6	6	NUM
ejpam-6436	407	3	]	]	PUNCT
ejpam-6436	407	4	b.	b.	PROPN
ejpam-6436	407	5	al	al	PROPN
ejpam-6436	407	6	subaiei	subaiei	PROPN
ejpam-6436	407	7	and	and	CCONJ
ejpam-6436	407	8	j.	j.	PROPN
ejpam-6436	407	9	renshaw	renshaw	PROPN
ejpam-6436	407	10	.	.	PUNCT
ejpam-6436	408	1	on	on	ADP
ejpam-6436	408	2	free	free	ADJ
ejpam-6436	408	3	products	product	NOUN
ejpam-6436	408	4	and	and	CCONJ
ejpam-6436	408	5	amalgams	amalgam	NOUN
ejpam-6436	408	6	of	of	ADP
ejpam-6436	408	7	pomonoids	pomonoid	NOUN
ejpam-6436	408	8	.	.	PUNCT
ejpam-6436	409	1	communications	communication	NOUN
ejpam-6436	409	2	in	in	ADP
ejpam-6436	409	3	algebra	algebra	NOUN
ejpam-6436	409	4	,	,	PUNCT
ejpam-6436	409	5	44:2455–2474	44:2455–2474	PROPN
ejpam-6436	409	6	,	,	PUNCT
ejpam-6436	409	7	2016	2016	NUM
ejpam-6436	409	8	.	.	PUNCT
ejpam-6436	410	1	b.	b.	PROPN
ejpam-6436	410	2	al	al	PROPN
ejpam-6436	410	3	subaiei	subaiei	PROPN
ejpam-6436	410	4	et	et	PROPN
ejpam-6436	410	5	al	al	PROPN
ejpam-6436	410	6	.	.	PUNCT
ejpam-6436	410	7	/	/	SYM
ejpam-6436	410	8	eur	eur	PROPN
ejpam-6436	410	9	.	.	PUNCT
ejpam-6436	411	1	j.	j.	PROPN
ejpam-6436	411	2	pure	pure	PROPN
ejpam-6436	411	3	appl	appl	PROPN
ejpam-6436	411	4	.	.	PROPN
ejpam-6436	411	5	math	math	PROPN
ejpam-6436	411	6	,	,	PUNCT
ejpam-6436	411	7	18	18	NUM
ejpam-6436	411	8	(	(	PUNCT
ejpam-6436	411	9	3	3	NUM
ejpam-6436	411	10	)	)	PUNCT
ejpam-6436	411	11	(	(	PUNCT
ejpam-6436	411	12	2025	2025	NUM
ejpam-6436	411	13	)	)	PUNCT
ejpam-6436	411	14	,	,	PUNCT
ejpam-6436	411	15	6436	6436	NUM
ejpam-6436	411	16	14	14	NUM
ejpam-6436	411	17	of	of	ADP
ejpam-6436	411	18	14	14	NUM
ejpam-6436	411	19	[	[	X
ejpam-6436	411	20	7	7	NUM
ejpam-6436	411	21	]	]	PUNCT
ejpam-6436	411	22	b.	b.	PROPN
ejpam-6436	411	23	al	al	PROPN
ejpam-6436	411	24	subaiei	subaiei	PROPN
ejpam-6436	411	25	and	and	CCONJ
ejpam-6436	411	26	j.	j.	PROPN
ejpam-6436	411	27	renshaw	renshaw	PROPN
ejpam-6436	411	28	.	.	PUNCT
ejpam-6436	412	1	on	on	ADP
ejpam-6436	412	2	subamalgams	subamalgam	NOUN
ejpam-6436	412	3	of	of	ADP
ejpam-6436	412	4	partially	partially	ADV
ejpam-6436	412	5	ordered	order	VERB
ejpam-6436	412	6	monoids	monoid	NOUN
ejpam-6436	412	7	.	.	PUNCT
ejpam-6436	413	1	semigroup	semigroup	PROPN
ejpam-6436	413	2	forum	forum	PROPN
ejpam-6436	413	3	,	,	PUNCT
ejpam-6436	413	4	105:916–945	105:916–945	NUM
ejpam-6436	413	5	,	,	PUNCT
ejpam-6436	413	6	2022	2022	NUM
ejpam-6436	413	7	.	.	PUNCT
ejpam-6436	414	1	[	[	X
ejpam-6436	414	2	8	8	NUM
ejpam-6436	414	3	]	]	X
ejpam-6436	414	4	v.	v.	ADP
ejpam-6436	414	5	gould	gould	PROPN
ejpam-6436	414	6	and	and	CCONJ
ejpam-6436	414	7	l.	l.	PROPN
ejpam-6436	414	8	shaheen	shaheen	PROPN
ejpam-6436	414	9	.	.	PUNCT
ejpam-6436	415	1	perfection	perfection	NOUN
ejpam-6436	415	2	for	for	ADP
ejpam-6436	415	3	pomonoids	pomonoid	NOUN
ejpam-6436	415	4	.	.	PUNCT
ejpam-6436	416	1	semigroup	semigroup	PROPN
ejpam-6436	416	2	forum	forum	PROPN
ejpam-6436	416	3	,	,	PUNCT
ejpam-6436	416	4	81:102–127	81:102–127	NUM
ejpam-6436	416	5	,	,	PUNCT
ejpam-6436	416	6	2010	2010	NUM
ejpam-6436	416	7	.	.	PUNCT
ejpam-6436	417	1	[	[	X
ejpam-6436	417	2	9	9	NUM
ejpam-6436	417	3	]	]	PUNCT
ejpam-6436	417	4	b.	b.	PROPN
ejpam-6436	417	5	al	al	PROPN
ejpam-6436	417	6	subaiei	subaiei	PROPN
ejpam-6436	417	7	.	.	PUNCT
ejpam-6436	418	1	examples	example	NOUN
ejpam-6436	418	2	of	of	ADP
ejpam-6436	418	3	pomonoids	pomonoid	NOUN
ejpam-6436	418	4	of	of	ADP
ejpam-6436	418	5	full	full	ADJ
ejpam-6436	418	6	transformations	transformation	NOUN
ejpam-6436	418	7	of	of	ADP
ejpam-6436	418	8	a	a	DET
ejpam-6436	418	9	poset	poset	NOUN
ejpam-6436	418	10	.	.	PUNCT
ejpam-6436	419	1	the	the	DET
ejpam-6436	419	2	scientific	scientific	ADJ
ejpam-6436	419	3	journal	journal	NOUN
ejpam-6436	419	4	of	of	ADP
ejpam-6436	419	5	king	king	PROPN
ejpam-6436	419	6	faisal	faisal	PROPN
ejpam-6436	419	7	university	university	PROPN
ejpam-6436	419	8	:	:	PUNCT
ejpam-6436	419	9	basic	basic	ADJ
ejpam-6436	419	10	and	and	CCONJ
ejpam-6436	419	11	applied	applied	ADJ
ejpam-6436	419	12	sciences	science	NOUN
ejpam-6436	419	13	,	,	PUNCT
ejpam-6436	419	14	23(1):26–29	23(1):26–29	NUM
ejpam-6436	419	15	,	,	PUNCT
ejpam-6436	419	16	2022	2022	NUM
ejpam-6436	419	17	.	.	PUNCT
ejpam-6436	420	1	[	[	X
ejpam-6436	420	2	10	10	NUM
ejpam-6436	420	3	]	]	X
ejpam-6436	420	4	b.	b.	PROPN
ejpam-6436	420	5	al	al	PROPN
ejpam-6436	420	6	subaiei	subaiei	PROPN
ejpam-6436	420	7	.	.	PUNCT
ejpam-6436	421	1	on	on	ADP
ejpam-6436	421	2	pomonoid	pomonoid	NOUN
ejpam-6436	421	3	of	of	ADP
ejpam-6436	421	4	partial	partial	ADJ
ejpam-6436	421	5	transformations	transformation	NOUN
ejpam-6436	421	6	of	of	ADP
ejpam-6436	421	7	a	a	DET
ejpam-6436	421	8	poset	poset	NOUN
ejpam-6436	421	9	.	.	PUNCT
ejpam-6436	422	1	open	open	ADJ
ejpam-6436	422	2	mathematics	mathematic	NOUN
ejpam-6436	422	3	,	,	PUNCT
ejpam-6436	422	4	21(1):20230161	21(1):20230161	NUM
ejpam-6436	422	5	,	,	PUNCT
ejpam-6436	422	6	2023	2023	NUM
ejpam-6436	422	7	.	.	PUNCT
ejpam-6436	423	1	[	[	X
ejpam-6436	423	2	11	11	NUM
ejpam-6436	423	3	]	]	X
ejpam-6436	423	4	v.	v.	PROPN
ejpam-6436	423	5	gould	gould	PROPN
ejpam-6436	423	6	and	and	CCONJ
ejpam-6436	423	7	l.	l.	PROPN
ejpam-6436	423	8	shaheen	shaheen	PROPN
ejpam-6436	423	9	.	.	PUNCT
ejpam-6436	424	1	axiomatisability	axiomatisability	NOUN
ejpam-6436	424	2	problems	problem	NOUN
ejpam-6436	424	3	for	for	ADP
ejpam-6436	424	4	s	s	NOUN
ejpam-6436	424	5	-	-	NOUN
ejpam-6436	424	6	posets	poset	NOUN
ejpam-6436	424	7	.	.	PUNCT
ejpam-6436	425	1	semigroup	semigroup	PROPN
ejpam-6436	425	2	forum	forum	PROPN
ejpam-6436	425	3	,	,	PUNCT
ejpam-6436	425	4	82:199–228	82:199–228	PROPN
ejpam-6436	425	5	,	,	PUNCT
ejpam-6436	425	6	2011	2011	NUM
ejpam-6436	425	7	.	.	PUNCT
ejpam-6436	426	1	[	[	X
ejpam-6436	426	2	12	12	NUM
ejpam-6436	426	3	]	]	PUNCT
ejpam-6436	426	4	x.	x.	PROPN
ejpam-6436	426	5	shi	shi	PROPN
ejpam-6436	426	6	,	,	PUNCT
ejpam-6436	426	7	z.	z.	PROPN
ejpam-6436	426	8	liu	liu	PROPN
ejpam-6436	426	9	,	,	PUNCT
ejpam-6436	426	10	f.	f.	PROPN
ejpam-6436	426	11	wang	wang	PROPN
ejpam-6436	426	12	,	,	PUNCT
ejpam-6436	426	13	and	and	CCONJ
ejpam-6436	426	14	s.	s.	PROPN
ejpam-6436	426	15	bulman	bulman	PROPN
ejpam-6436	426	16	-	-	PUNCT
ejpam-6436	426	17	fleming	fleming	NOUN
ejpam-6436	426	18	.	.	PUNCT
ejpam-6436	427	1	indecomposable	indecomposable	ADJ
ejpam-6436	427	2	,	,	PUNCT
ejpam-6436	427	3	projective	projective	ADJ
ejpam-6436	427	4	,	,	PUNCT
ejpam-6436	427	5	and	and	CCONJ
ejpam-6436	427	6	flat	flat	ADJ
ejpam-6436	427	7	s	s	NOUN
ejpam-6436	427	8	-	-	NOUN
ejpam-6436	427	9	posets	poset	NOUN
ejpam-6436	427	10	.	.	PUNCT
ejpam-6436	428	1	communications	communication	NOUN
ejpam-6436	428	2	in	in	ADP
ejpam-6436	428	3	algebra	algebra	NOUN
ejpam-6436	428	4	,	,	PUNCT
ejpam-6436	428	5	33:235–251	33:235–251	PROPN
ejpam-6436	428	6	,	,	PUNCT
ejpam-6436	428	7	2005	2005	NUM
ejpam-6436	428	8	.	.	PUNCT
ejpam-6436	429	1	[	[	X
ejpam-6436	429	2	13	13	NUM
ejpam-6436	429	3	]	]	X
ejpam-6436	429	4	r.	r.	PROPN
ejpam-6436	429	5	khosravi	khosravi	PROPN
ejpam-6436	429	6	and	and	CCONJ
ejpam-6436	429	7	x.	x.	NOUN
ejpam-6436	429	8	liang	liang	PROPN
ejpam-6436	429	9	.	.	PUNCT
ejpam-6436	430	1	on	on	ADP
ejpam-6436	430	2	(	(	PUNCT
ejpam-6436	430	3	po-)torsion	po-)torsion	NOUN
ejpam-6436	430	4	free	free	ADJ
ejpam-6436	430	5	and	and	CCONJ
ejpam-6436	430	6	principally	principally	ADV
ejpam-6436	430	7	weakly	weakly	ADJ
ejpam-6436	430	8	(	(	PUNCT
ejpam-6436	430	9	po-)flat	po-)flat	PROPN
ejpam-6436	430	10	sposets	sposet	VERB
ejpam-6436	430	11	.	.	PUNCT
ejpam-6436	431	1	categories	category	NOUN
ejpam-6436	431	2	and	and	CCONJ
ejpam-6436	431	3	general	general	ADJ
ejpam-6436	431	4	algebraic	algebraic	ADJ
ejpam-6436	431	5	structure	structure	NOUN
ejpam-6436	431	6	with	with	ADP
ejpam-6436	431	7	applications	application	NOUN
ejpam-6436	431	8	,	,	PUNCT
ejpam-6436	431	9	8(1):35–49	8(1):35–49	NUM
ejpam-6436	431	10	,	,	PUNCT
ejpam-6436	431	11	2018	2018	NUM
ejpam-6436	431	12	.	.	PUNCT
ejpam-6436	432	1	[	[	X
ejpam-6436	432	2	14	14	NUM
ejpam-6436	432	3	]	]	X
ejpam-6436	432	4	u.	u.	NOUN
ejpam-6436	432	5	knauer	knauer	PROPN
ejpam-6436	432	6	and	and	CCONJ
ejpam-6436	432	7	a.	a.	NOUN
ejpam-6436	432	8	mikhalev	mikhalev	PROPN
ejpam-6436	432	9	.	.	PUNCT
ejpam-6436	433	1	wreath	wreath	NOUN
ejpam-6436	433	2	products	product	NOUN
ejpam-6436	433	3	of	of	ADP
ejpam-6436	433	4	ordered	order	VERB
ejpam-6436	433	5	semigroups	semigroup	NOUN
ejpam-6436	433	6	.	.	PUNCT
ejpam-6436	434	1	semigroup	semigroup	PROPN
ejpam-6436	434	2	forum	forum	PROPN
ejpam-6436	434	3	,	,	PUNCT
ejpam-6436	434	4	27:331–350	27:331–350	PROPN
ejpam-6436	434	5	,	,	PUNCT
ejpam-6436	434	6	1983	1983	NUM
ejpam-6436	434	7	.	.	PUNCT
ejpam-6436	435	1	[	[	X
ejpam-6436	435	2	15	15	NUM
ejpam-6436	435	3	]	]	X
ejpam-6436	435	4	m.	m.	NOUN
ejpam-6436	435	5	kilp	kilp	PROPN
ejpam-6436	435	6	,	,	PUNCT
ejpam-6436	435	7	u.	u.	PROPN
ejpam-6436	435	8	knauer	knauer	PROPN
ejpam-6436	435	9	,	,	PUNCT
ejpam-6436	435	10	and	and	CCONJ
ejpam-6436	435	11	a.	a.	NOUN
ejpam-6436	435	12	mikhalev	mikhalev	PROPN
ejpam-6436	435	13	.	.	PUNCT
ejpam-6436	436	1	wreath	wreath	NOUN
ejpam-6436	436	2	products	product	NOUN
ejpam-6436	436	3	of	of	ADP
ejpam-6436	436	4	acts	act	NOUN
ejpam-6436	436	5	over	over	ADP
ejpam-6436	436	6	monoids	monoids	PROPN
ejpam-6436	436	7	:	:	PUNCT
ejpam-6436	436	8	ii	ii	PROPN
ejpam-6436	436	9	.	.	PUNCT
ejpam-6436	436	10	torsion	torsion	NOUN
ejpam-6436	436	11	free	free	ADJ
ejpam-6436	436	12	and	and	CCONJ
ejpam-6436	436	13	divisible	divisible	ADJ
ejpam-6436	436	14	acts	act	NOUN
ejpam-6436	436	15	.	.	PUNCT
ejpam-6436	437	1	journal	journal	NOUN
ejpam-6436	437	2	of	of	ADP
ejpam-6436	437	3	pure	pure	ADJ
ejpam-6436	437	4	and	and	CCONJ
ejpam-6436	437	5	applied	applied	ADJ
ejpam-6436	437	6	algebra	algebra	NOUN
ejpam-6436	437	7	,	,	PUNCT
ejpam-6436	437	8	58:19–27	58:19–27	NUM
ejpam-6436	437	9	,	,	PUNCT
ejpam-6436	437	10	1989	1989	NUM
ejpam-6436	437	11	.	.	PUNCT
ejpam-6436	438	1	[	[	X
ejpam-6436	438	2	16	16	NUM
ejpam-6436	438	3	]	]	X
ejpam-6436	438	4	j.	j.	PROPN
ejpam-6436	438	5	pin	pin	PROPN
ejpam-6436	438	6	and	and	CCONJ
ejpam-6436	438	7	p.	p.	PROPN
ejpam-6436	438	8	weil	weil	PROPN
ejpam-6436	438	9	.	.	PUNCT
ejpam-6436	439	1	the	the	DET
ejpam-6436	439	2	wreath	wreath	NOUN
ejpam-6436	439	3	products	product	NOUN
ejpam-6436	439	4	principle	principle	NOUN
ejpam-6436	439	5	for	for	ADP
ejpam-6436	439	6	ordered	order	VERB
ejpam-6436	439	7	semigroups	semigroup	NOUN
ejpam-6436	439	8	.	.	PUNCT
ejpam-6436	440	1	communications	communication	NOUN
ejpam-6436	440	2	in	in	ADP
ejpam-6436	440	3	algebra	algebra	NOUN
ejpam-6436	440	4	,	,	PUNCT
ejpam-6436	440	5	30:5677–5713	30:5677–5713	NUM
ejpam-6436	440	6	,	,	PUNCT
ejpam-6436	440	7	2002	2002	NUM
ejpam-6436	440	8	.	.	PUNCT
ejpam-6436	441	1	[	[	X
ejpam-6436	441	2	17	17	NUM
ejpam-6436	441	3	]	]	X
ejpam-6436	441	4	j.	j.	PROPN
ejpam-6436	441	5	pin	pin	PROPN
ejpam-6436	441	6	and	and	CCONJ
ejpam-6436	441	7	p.	p.	PROPN
ejpam-6436	441	8	weil	weil	PROPN
ejpam-6436	441	9	.	.	PUNCT
ejpam-6436	441	10	semidirect	semidirect	PROPN
ejpam-6436	441	11	products	product	NOUN
ejpam-6436	441	12	of	of	ADP
ejpam-6436	441	13	ordered	order	VERB
ejpam-6436	441	14	semigroups	semigroup	NOUN
ejpam-6436	441	15	.	.	PUNCT
ejpam-6436	442	1	communications	communication	NOUN
ejpam-6436	442	2	in	in	ADP
ejpam-6436	442	3	algebra	algebra	NOUN
ejpam-6436	442	4	,	,	PUNCT
ejpam-6436	442	5	30(1):149–169	30(1):149–169	PROPN
ejpam-6436	442	6	,	,	PUNCT
ejpam-6436	442	7	2002	2002	NUM
ejpam-6436	442	8	.	.	PUNCT
ejpam-6436	443	1	[	[	X
ejpam-6436	443	2	18	18	NUM
ejpam-6436	443	3	]	]	X
ejpam-6436	443	4	s.	s.	PROPN
ejpam-6436	443	5	bulman	bulman	PROPN
ejpam-6436	443	6	-	-	PUNCT
ejpam-6436	443	7	fleming	fleming	NOUN
ejpam-6436	443	8	,	,	PUNCT
ejpam-6436	443	9	d.	d.	PROPN
ejpam-6436	443	10	gutermuth	gutermuth	PROPN
ejpam-6436	443	11	,	,	PUNCT
ejpam-6436	443	12	a.	a.	NOUN
ejpam-6436	443	13	gilmour	gilmour	PROPN
ejpam-6436	443	14	,	,	PUNCT
ejpam-6436	443	15	and	and	CCONJ
ejpam-6436	443	16	m.	m.	PROPN
ejpam-6436	443	17	kilp	kilp	PROPN
ejpam-6436	443	18	.	.	PROPN
ejpam-6436	444	1	flatness	flatness	PROPN
ejpam-6436	444	2	properties	property	NOUN
ejpam-6436	444	3	of	of	ADP
ejpam-6436	444	4	s	s	NOUN
ejpam-6436	444	5	-	-	NOUN
ejpam-6436	444	6	posets	poset	NOUN
ejpam-6436	444	7	.	.	PUNCT
ejpam-6436	445	1	communications	communication	NOUN
ejpam-6436	445	2	in	in	ADP
ejpam-6436	445	3	algebra	algebra	NOUN
ejpam-6436	445	4	,	,	PUNCT
ejpam-6436	445	5	34:1291–1317	34:1291–1317	NUM
ejpam-6436	445	6	,	,	PUNCT
ejpam-6436	445	7	2006	2006	NUM
ejpam-6436	445	8	.	.	PUNCT
ejpam-6436	446	1	[	[	X
ejpam-6436	446	2	19	19	NUM
ejpam-6436	446	3	]	]	PUNCT
ejpam-6436	446	4	a.	a.	NOUN
ejpam-6436	446	5	golchin	golchin	NOUN
ejpam-6436	446	6	and	and	CCONJ
ejpam-6436	446	7	p.	p.	PROPN
ejpam-6436	446	8	rezaei	rezaei	PROPN
ejpam-6436	446	9	.	.	PUNCT
ejpam-6436	447	1	(	(	PUNCT
ejpam-6436	447	2	homo	homo	NOUN
ejpam-6436	447	3	)	)	PUNCT
ejpam-6436	447	4	flatness	flatness	NOUN
ejpam-6436	447	5	of	of	ADP
ejpam-6436	447	6	posets	poset	NOUN
ejpam-6436	447	7	on	on	ADP
ejpam-6436	447	8	poideal	poideal	NOUN
ejpam-6436	447	9	extensions	extension	NOUN
ejpam-6436	447	10	.	.	PUNCT
ejpam-6436	448	1	semigroup	semigroup	PROPN
ejpam-6436	448	2	forum	forum	PROPN
ejpam-6436	448	3	,	,	PUNCT
ejpam-6436	448	4	79:65–78	79:65–78	PROPN
ejpam-6436	448	5	,	,	PUNCT
ejpam-6436	448	6	2009	2009	NUM
ejpam-6436	448	7	.	.	PUNCT
ejpam-6436	449	1	[	[	X
ejpam-6436	449	2	20	20	NUM
ejpam-6436	449	3	]	]	PUNCT
ejpam-6436	449	4	b.	b.	PROPN
ejpam-6436	449	5	al	al	PROPN
ejpam-6436	449	6	subaiei	subaiei	PROPN
ejpam-6436	449	7	.	.	PUNCT
ejpam-6436	450	1	connectivity	connectivity	NOUN
ejpam-6436	450	2	,	,	PUNCT
ejpam-6436	450	3	indecomposable	indecomposable	ADJ
ejpam-6436	450	4	,	,	PUNCT
ejpam-6436	450	5	and	and	CCONJ
ejpam-6436	450	6	weakly	weakly	ADJ
ejpam-6436	450	7	reversible	reversible	ADJ
ejpam-6436	450	8	in	in	ADP
ejpam-6436	450	9	$	$	SYM
ejpam-6436	450	10	s-$posets	s-$poset	NOUN
ejpam-6436	450	11	.	.	PUNCT
ejpam-6436	451	1	asian	asian	ADJ
ejpam-6436	451	2	-	-	PUNCT
ejpam-6436	451	3	european	european	ADJ
ejpam-6436	451	4	journal	journal	NOUN
ejpam-6436	451	5	of	of	ADP
ejpam-6436	451	6	mathematics	mathematic	NOUN
ejpam-6436	451	7	,	,	PUNCT
ejpam-6436	451	8	14(8):2150139	14(8):2150139	NUM
ejpam-6436	451	9	,	,	PUNCT
ejpam-6436	451	10	2021	2021	NUM
ejpam-6436	451	11	.	.	PUNCT