id	sid	tid	token	lemma	pos
ejpam-5835	1	1	european	european	PROPN
ejpam-5835	1	2	journal	journal	PROPN
ejpam-5835	1	3	of	of	ADP
ejpam-5835	1	4	pure	pure	ADJ
ejpam-5835	1	5	and	and	CCONJ
ejpam-5835	1	6	applied	applied	ADJ
ejpam-5835	1	7	mathematics	mathematic	NOUN
ejpam-5835	1	8	2025	2025	NUM
ejpam-5835	1	9	,	,	PUNCT
ejpam-5835	1	10	vol	vol	NOUN
ejpam-5835	1	11	.	.	PROPN
ejpam-5835	1	12	18	18	NUM
ejpam-5835	1	13	,	,	PUNCT
ejpam-5835	1	14	issue	issue	NOUN
ejpam-5835	1	15	2	2	NUM
ejpam-5835	1	16	,	,	PUNCT
ejpam-5835	1	17	article	article	NOUN
ejpam-5835	1	18	number	number	NOUN
ejpam-5835	1	19	5835	5835	NUM
ejpam-5835	1	20	issn	issn	VERB
ejpam-5835	1	21	1307	1307	NUM
ejpam-5835	1	22	-	-	SYM
ejpam-5835	1	23	5543	5543	NUM
ejpam-5835	1	24	–	–	PUNCT
ejpam-5835	1	25	ejpam.com	ejpam.com	X
ejpam-5835	1	26	published	publish	VERB
ejpam-5835	1	27	by	by	ADP
ejpam-5835	1	28	new	new	PROPN
ejpam-5835	1	29	york	york	PROPN
ejpam-5835	1	30	business	business	PROPN
ejpam-5835	1	31	global	global	PROPN
ejpam-5835	1	32	multisorted	multisorte	VERB
ejpam-5835	1	33	algebras	algebra	NOUN
ejpam-5835	1	34	of	of	ADP
ejpam-5835	1	35	trees	tree	NOUN
ejpam-5835	1	36	of	of	ADP
ejpam-5835	1	37	a	a	DET
ejpam-5835	1	38	weakly	weakly	ADJ
ejpam-5835	1	39	fixed	fix	VERB
ejpam-5835	1	40	variable	variable	ADJ
ejpam-5835	1	41	thodsaporn	thodsaporn	ADJ
ejpam-5835	1	42	kumduang1	kumduang1	NOUN
ejpam-5835	1	43	,	,	PUNCT
ejpam-5835	1	44	khwancheewa	khwancheewa	PROPN
ejpam-5835	1	45	wattanatripop2,∗	wattanatripop2,∗	VERB
ejpam-5835	1	46	1	1	NUM
ejpam-5835	1	47	department	department	NOUN
ejpam-5835	1	48	of	of	ADP
ejpam-5835	1	49	mathematics	mathematic	NOUN
ejpam-5835	1	50	,	,	PUNCT
ejpam-5835	1	51	faculty	faculty	NOUN
ejpam-5835	1	52	of	of	ADP
ejpam-5835	1	53	science	science	NOUN
ejpam-5835	1	54	and	and	CCONJ
ejpam-5835	1	55	technology	technology	NOUN
ejpam-5835	1	56	,	,	PUNCT
ejpam-5835	1	57	rajamangala	rajamangala	PROPN
ejpam-5835	1	58	university	university	PROPN
ejpam-5835	1	59	of	of	ADP
ejpam-5835	1	60	technology	technology	NOUN
ejpam-5835	1	61	rattanakosin	rattanakosin	NOUN
ejpam-5835	1	62	,	,	PUNCT
ejpam-5835	1	63	nakhon	nakhon	PROPN
ejpam-5835	1	64	pathom	pathom	PROPN
ejpam-5835	1	65	73170	73170	NUM
ejpam-5835	1	66	,	,	PUNCT
ejpam-5835	1	67	thailand	thailand	PROPN
ejpam-5835	1	68	2	2	NUM
ejpam-5835	1	69	department	department	NOUN
ejpam-5835	1	70	of	of	ADP
ejpam-5835	1	71	mathematics	mathematic	NOUN
ejpam-5835	1	72	,	,	PUNCT
ejpam-5835	1	73	faculty	faculty	NOUN
ejpam-5835	1	74	of	of	ADP
ejpam-5835	1	75	science	science	NOUN
ejpam-5835	1	76	and	and	CCONJ
ejpam-5835	1	77	agricultural	agricultural	ADJ
ejpam-5835	1	78	technology	technology	NOUN
ejpam-5835	1	79	,	,	PUNCT
ejpam-5835	1	80	rajamangala	rajamangala	PROPN
ejpam-5835	1	81	university	university	PROPN
ejpam-5835	1	82	of	of	ADP
ejpam-5835	1	83	technology	technology	PROPN
ejpam-5835	1	84	lanna	lanna	PROPN
ejpam-5835	1	85	,	,	PUNCT
ejpam-5835	1	86	chiang	chiang	PROPN
ejpam-5835	1	87	mai	mai	PROPN
ejpam-5835	1	88	50200	50200	NUM
ejpam-5835	1	89	,	,	PUNCT
ejpam-5835	1	90	thailand	thailand	PROPN
ejpam-5835	1	91	abstract	abstract	NOUN
ejpam-5835	1	92	.	.	PUNCT
ejpam-5835	2	1	for	for	ADP
ejpam-5835	2	2	any	any	DET
ejpam-5835	2	3	algebra	algebra	NOUN
ejpam-5835	2	4	of	of	ADP
ejpam-5835	2	5	type	type	NOUN
ejpam-5835	2	6	τ	τ	PROPN
ejpam-5835	2	7	,	,	PUNCT
ejpam-5835	2	8	this	this	DET
ejpam-5835	2	9	paper	paper	NOUN
ejpam-5835	2	10	introduces	introduce	VERB
ejpam-5835	2	11	a	a	DET
ejpam-5835	2	12	novel	novel	ADJ
ejpam-5835	2	13	class	class	NOUN
ejpam-5835	2	14	of	of	ADP
ejpam-5835	2	15	terms	term	NOUN
ejpam-5835	2	16	(	(	PUNCT
ejpam-5835	2	17	or	or	CCONJ
ejpam-5835	2	18	terms	term	NOUN
ejpam-5835	2	19	)	)	PUNCT
ejpam-5835	2	20	of	of	ADP
ejpam-5835	2	21	a	a	DET
ejpam-5835	2	22	weakly	weakly	ADJ
ejpam-5835	2	23	fixed	fixed	ADJ
ejpam-5835	2	24	variable	variable	NOUN
ejpam-5835	2	25	of	of	ADP
ejpam-5835	2	26	type	type	NOUN
ejpam-5835	2	27	τ	τ	PROPN
ejpam-5835	2	28	.	.	PUNCT
ejpam-5835	3	1	algebraic	algebraic	ADJ
ejpam-5835	3	2	structures	structure	NOUN
ejpam-5835	3	3	in	in	ADP
ejpam-5835	3	4	the	the	DET
ejpam-5835	3	5	sence	sence	NOUN
ejpam-5835	3	6	of	of	ADP
ejpam-5835	3	7	multisorted	multisorte	VERB
ejpam-5835	3	8	algebras	algebra	NOUN
ejpam-5835	3	9	are	be	AUX
ejpam-5835	3	10	studied	study	VERB
ejpam-5835	3	11	.	.	PUNCT
ejpam-5835	4	1	in	in	ADP
ejpam-5835	4	2	fact	fact	NOUN
ejpam-5835	4	3	,	,	PUNCT
ejpam-5835	4	4	it	it	PRON
ejpam-5835	4	5	is	be	AUX
ejpam-5835	4	6	shown	show	VERB
ejpam-5835	4	7	that	that	SCONJ
ejpam-5835	4	8	the	the	DET
ejpam-5835	4	9	set	set	NOUN
ejpam-5835	4	10	of	of	ADP
ejpam-5835	4	11	such	such	ADJ
ejpam-5835	4	12	terms	term	NOUN
ejpam-5835	4	13	and	and	CCONJ
ejpam-5835	4	14	the	the	DET
ejpam-5835	4	15	multisort	multisort	NOUN
ejpam-5835	4	16	operations	operation	NOUN
ejpam-5835	4	17	forms	form	VERB
ejpam-5835	4	18	a	a	DET
ejpam-5835	4	19	multisorted	multisorte	VERB
ejpam-5835	4	20	algebra	algebra	NOUN
ejpam-5835	4	21	that	that	PRON
ejpam-5835	4	22	satisfies	satisfy	VERB
ejpam-5835	4	23	some	some	DET
ejpam-5835	4	24	axioms	axiom	NOUN
ejpam-5835	4	25	from	from	ADP
ejpam-5835	4	26	the	the	DET
ejpam-5835	4	27	theory	theory	NOUN
ejpam-5835	4	28	of	of	ADP
ejpam-5835	4	29	clone	clone	NOUN
ejpam-5835	4	30	.	.	PUNCT
ejpam-5835	5	1	as	as	ADP
ejpam-5835	5	2	a	a	DET
ejpam-5835	5	3	tool	tool	NOUN
ejpam-5835	5	4	for	for	ADP
ejpam-5835	5	5	classifying	classify	VERB
ejpam-5835	5	6	arbitrary	arbitrary	ADJ
ejpam-5835	5	7	algebras	algebra	NOUN
ejpam-5835	5	8	to	to	ADP
ejpam-5835	5	9	subclasses	subclass	NOUN
ejpam-5835	5	10	called	call	VERB
ejpam-5835	5	11	weakly	weakly	ADV
ejpam-5835	5	12	fixed	fix	VERB
ejpam-5835	5	13	variable	variable	ADJ
ejpam-5835	5	14	solid	solid	ADJ
ejpam-5835	5	15	varieties	variety	NOUN
ejpam-5835	5	16	,	,	PUNCT
ejpam-5835	5	17	the	the	DET
ejpam-5835	5	18	seminearring	seminearring	NOUN
ejpam-5835	5	19	of	of	ADP
ejpam-5835	5	20	weakly	weakly	ADJ
ejpam-5835	5	21	fixed	fix	VERB
ejpam-5835	5	22	variable	variable	ADJ
ejpam-5835	5	23	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	5	24	is	be	AUX
ejpam-5835	5	25	proposed	propose	VERB
ejpam-5835	5	26	.	.	PUNCT
ejpam-5835	6	1	characterizations	characterization	NOUN
ejpam-5835	6	2	for	for	ADP
ejpam-5835	6	3	any	any	DET
ejpam-5835	6	4	variety	variety	NOUN
ejpam-5835	6	5	v	v	NOUN
ejpam-5835	6	6	of	of	ADP
ejpam-5835	6	7	algebras	algebra	NOUN
ejpam-5835	6	8	of	of	ADP
ejpam-5835	6	9	type	type	NOUN
ejpam-5835	6	10	τ	τ	PROPN
ejpam-5835	6	11	to	to	PART
ejpam-5835	6	12	be	be	AUX
ejpam-5835	6	13	a	a	DET
ejpam-5835	6	14	weakly	weakly	ADV
ejpam-5835	6	15	fixed	fix	VERB
ejpam-5835	6	16	variable	variable	ADJ
ejpam-5835	6	17	solid	solid	ADJ
ejpam-5835	6	18	variety	variety	NOUN
ejpam-5835	6	19	are	be	AUX
ejpam-5835	6	20	explored	explore	VERB
ejpam-5835	6	21	.	.	PUNCT
ejpam-5835	7	1	2020	2020	NUM
ejpam-5835	7	2	mathematics	mathematics	PROPN
ejpam-5835	7	3	subject	subject	NOUN
ejpam-5835	7	4	classifications	classification	NOUN
ejpam-5835	7	5	:	:	PUNCT
ejpam-5835	7	6	08a05	08a05	NUM
ejpam-5835	7	7	,	,	PUNCT
ejpam-5835	7	8	08b05	08b05	NUM
ejpam-5835	7	9	,	,	PUNCT
ejpam-5835	7	10	08a68	08a68	NUM
ejpam-5835	7	11	,	,	PUNCT
ejpam-5835	7	12	20n15	20n15	NUM
ejpam-5835	7	13	,	,	PUNCT
ejpam-5835	7	14	20m07	20m07	NUM
ejpam-5835	7	15	key	key	ADJ
ejpam-5835	7	16	words	word	NOUN
ejpam-5835	7	17	and	and	CCONJ
ejpam-5835	7	18	phrases	phrase	NOUN
ejpam-5835	7	19	:	:	PUNCT
ejpam-5835	7	20	term	term	NOUN
ejpam-5835	7	21	,	,	PUNCT
ejpam-5835	7	22	operation	operation	NOUN
ejpam-5835	7	23	,	,	PUNCT
ejpam-5835	7	24	multisorted	multisorte	VERB
ejpam-5835	7	25	set	set	NOUN
ejpam-5835	7	26	,	,	PUNCT
ejpam-5835	7	27	endomorphism	endomorphism	PROPN
ejpam-5835	7	28	,	,	PUNCT
ejpam-5835	7	29	semigroup	semigroup	PROPN
ejpam-5835	7	30	,	,	PUNCT
ejpam-5835	7	31	variety	variety	NOUN
ejpam-5835	7	32	,	,	PUNCT
ejpam-5835	7	33	hyperidentity	hyperidentity	NOUN
ejpam-5835	7	34	1	1	NUM
ejpam-5835	7	35	.	.	PUNCT
ejpam-5835	7	36	introduction	introduction	NOUN
ejpam-5835	7	37	and	and	CCONJ
ejpam-5835	7	38	background	background	NOUN
ejpam-5835	7	39	the	the	DET
ejpam-5835	7	40	concept	concept	NOUN
ejpam-5835	7	41	of	of	ADP
ejpam-5835	7	42	multisorted	multisorte	VERB
ejpam-5835	7	43	algebras	algebra	NOUN
ejpam-5835	7	44	(	(	PUNCT
ejpam-5835	7	45	also	also	ADV
ejpam-5835	7	46	called	call	VERB
ejpam-5835	7	47	many	many	ADJ
ejpam-5835	7	48	-	-	PUNCT
ejpam-5835	7	49	sorted	sort	VERB
ejpam-5835	7	50	algebras	algebra	NOUN
ejpam-5835	7	51	or	or	CCONJ
ejpam-5835	7	52	heterogeneous	heterogeneous	ADJ
ejpam-5835	7	53	algebras	algebra	NOUN
ejpam-5835	7	54	)	)	PUNCT
ejpam-5835	7	55	generalizes	generalize	VERB
ejpam-5835	7	56	the	the	DET
ejpam-5835	7	57	concept	concept	NOUN
ejpam-5835	7	58	of	of	ADP
ejpam-5835	7	59	one	one	NUM
ejpam-5835	7	60	-	-	PUNCT
ejpam-5835	7	61	sorted	sort	VERB
ejpam-5835	7	62	algebras	algebra	NOUN
ejpam-5835	7	63	.	.	PUNCT
ejpam-5835	8	1	any	any	DET
ejpam-5835	8	2	module	module	NOUN
ejpam-5835	8	3	and	and	CCONJ
ejpam-5835	8	4	vector	vector	NOUN
ejpam-5835	8	5	space	space	NOUN
ejpam-5835	8	6	are	be	AUX
ejpam-5835	8	7	basic	basic	ADJ
ejpam-5835	8	8	examples	example	NOUN
ejpam-5835	8	9	of	of	ADP
ejpam-5835	8	10	multisorted	multisorte	VERB
ejpam-5835	8	11	algebras	algebra	NOUN
ejpam-5835	8	12	.	.	PUNCT
ejpam-5835	9	1	in	in	ADP
ejpam-5835	9	2	general	general	ADJ
ejpam-5835	9	3	,	,	PUNCT
ejpam-5835	9	4	the	the	DET
ejpam-5835	9	5	s	s	NOUN
ejpam-5835	9	6	-	-	PUNCT
ejpam-5835	9	7	sorted	sort	VERB
ejpam-5835	9	8	sets	set	NOUN
ejpam-5835	9	9	a	a	PRON
ejpam-5835	9	10	=	=	X
ejpam-5835	9	11	(	(	PUNCT
ejpam-5835	9	12	as)s∈s	as)s∈s	PROPN
ejpam-5835	9	13	are	be	AUX
ejpam-5835	9	14	essential	essential	ADJ
ejpam-5835	9	15	.	.	PUNCT
ejpam-5835	10	1	the	the	DET
ejpam-5835	10	2	set	set	NOUN
ejpam-5835	10	3	s	s	PART
ejpam-5835	10	4	is	be	AUX
ejpam-5835	10	5	called	call	VERB
ejpam-5835	10	6	a	a	DET
ejpam-5835	10	7	set	set	NOUN
ejpam-5835	10	8	of	of	ADP
ejpam-5835	10	9	sorts	sort	NOUN
ejpam-5835	10	10	.	.	PUNCT
ejpam-5835	11	1	in	in	ADP
ejpam-5835	11	2	addition	addition	NOUN
ejpam-5835	11	3	,	,	PUNCT
ejpam-5835	11	4	the	the	DET
ejpam-5835	11	5	sort	sort	NOUN
ejpam-5835	11	6	mapping	map	VERB
ejpam-5835	11	7	ϕ	ϕ	NOUN
ejpam-5835	11	8	:	:	PUNCT
ejpam-5835	11	9	a	a	DET
ejpam-5835	11	10	→	→	SYM
ejpam-5835	11	11	b	b	PROPN
ejpam-5835	11	12	from	from	ADP
ejpam-5835	11	13	an	an	DET
ejpam-5835	11	14	s	s	NOUN
ejpam-5835	11	15	-	-	PUNCT
ejpam-5835	11	16	sorted	sorted	ADJ
ejpam-5835	11	17	set	set	NOUN
ejpam-5835	11	18	a	a	DET
ejpam-5835	11	19	=	=	X
ejpam-5835	11	20	(	(	PUNCT
ejpam-5835	11	21	as)s∈s	as)s∈s	PROPN
ejpam-5835	11	22	to	to	ADP
ejpam-5835	11	23	an	an	DET
ejpam-5835	11	24	s	s	ADV
ejpam-5835	11	25	-	-	PUNCT
ejpam-5835	11	26	sorted	sort	VERB
ejpam-5835	11	27	set	set	NOUN
ejpam-5835	11	28	b	b	NOUN
ejpam-5835	11	29	=	=	SYM
ejpam-5835	11	30	(	(	PUNCT
ejpam-5835	11	31	bs)s∈s	bs)s∈s	PROPN
ejpam-5835	11	32	is	be	AUX
ejpam-5835	11	33	an	an	DET
ejpam-5835	11	34	s	s	NOUN
ejpam-5835	11	35	-	-	PUNCT
ejpam-5835	11	36	sorted	sort	VERB
ejpam-5835	11	37	family	family	NOUN
ejpam-5835	11	38	ϕ	ϕ	NOUN
ejpam-5835	11	39	:	:	PUNCT
ejpam-5835	11	40	(	(	PUNCT
ejpam-5835	11	41	ϕs)s∈s	ϕs)s∈s	NUM
ejpam-5835	11	42	of	of	ADP
ejpam-5835	11	43	mappings	mapping	NOUN
ejpam-5835	11	44	ϕs	ϕs	ADP
ejpam-5835	11	45	:	:	PUNCT
ejpam-5835	11	46	as	as	SCONJ
ejpam-5835	11	47	→	→	SYM
ejpam-5835	11	48	bs	bs	X
ejpam-5835	11	49	where	where	SCONJ
ejpam-5835	11	50	s	s	VERB
ejpam-5835	11	51	∈	∈	PROPN
ejpam-5835	11	52	s.	s.	PROPN
ejpam-5835	11	53	the	the	DET
ejpam-5835	11	54	authors	author	NOUN
ejpam-5835	11	55	always	always	ADV
ejpam-5835	11	56	refer	refer	VERB
ejpam-5835	11	57	to	to	ADP
ejpam-5835	11	58	[	[	X
ejpam-5835	11	59	1	1	NUM
ejpam-5835	11	60	,	,	PUNCT
ejpam-5835	11	61	4	4	NUM
ejpam-5835	11	62	,	,	PUNCT
ejpam-5835	11	63	19	19	NUM
ejpam-5835	11	64	]	]	PUNCT
ejpam-5835	11	65	for	for	ADP
ejpam-5835	11	66	more	more	ADJ
ejpam-5835	11	67	details	detail	NOUN
ejpam-5835	11	68	.	.	PUNCT
ejpam-5835	12	1	terms	term	NOUN
ejpam-5835	12	2	or	or	CCONJ
ejpam-5835	12	3	trees	tree	NOUN
ejpam-5835	12	4	in	in	ADP
ejpam-5835	12	5	a	a	DET
ejpam-5835	12	6	study	study	NOUN
ejpam-5835	12	7	of	of	ADP
ejpam-5835	12	8	automata	automata	NOUN
ejpam-5835	12	9	and	and	CCONJ
ejpam-5835	12	10	logic	logic	NOUN
ejpam-5835	12	11	can	can	AUX
ejpam-5835	12	12	be	be	AUX
ejpam-5835	12	13	applied	apply	VERB
ejpam-5835	12	14	to	to	PART
ejpam-5835	12	15	form	form	NOUN
ejpam-5835	12	16	multisorted	multisorte	VERB
ejpam-5835	12	17	algebras	algebras	PROPN
ejpam-5835	12	18	called	call	VERB
ejpam-5835	12	19	the	the	DET
ejpam-5835	12	20	multisorted	multisorte	VERB
ejpam-5835	12	21	algebra	algebra	NOUN
ejpam-5835	12	22	of	of	ADP
ejpam-5835	12	23	terms	term	NOUN
ejpam-5835	12	24	of	of	ADP
ejpam-5835	12	25	type	type	NOUN
ejpam-5835	12	26	τ	τ	PROPN
ejpam-5835	12	27	.	.	PUNCT
ejpam-5835	13	1	to	to	PART
ejpam-5835	13	2	attain	attain	VERB
ejpam-5835	13	3	this	this	PRON
ejpam-5835	13	4	,	,	PUNCT
ejpam-5835	13	5	we	we	PRON
ejpam-5835	13	6	recall	recall	VERB
ejpam-5835	13	7	some	some	DET
ejpam-5835	13	8	important	important	ADJ
ejpam-5835	13	9	definitions	definition	NOUN
ejpam-5835	13	10	.	.	PUNCT
ejpam-5835	14	1	let	let	VERB
ejpam-5835	14	2	i	i	PRON
ejpam-5835	14	3	be	be	AUX
ejpam-5835	14	4	a	a	DET
ejpam-5835	14	5	nonempty	nonempty	ADV
ejpam-5835	14	6	indexed	index	VERB
ejpam-5835	14	7	set	set	VERB
ejpam-5835	14	8	and	and	CCONJ
ejpam-5835	14	9	(	(	PUNCT
ejpam-5835	14	10	fi)i∈i	fi)i∈i	NOUN
ejpam-5835	14	11	be	be	VERB
ejpam-5835	14	12	a	a	DET
ejpam-5835	14	13	sequence	sequence	NOUN
ejpam-5835	14	14	of	of	ADP
ejpam-5835	14	15	operation	operation	NOUN
ejpam-5835	14	16	symbols	symbol	NOUN
ejpam-5835	14	17	.	.	PUNCT
ejpam-5835	15	1	to	to	ADP
ejpam-5835	15	2	every	every	DET
ejpam-5835	15	3	operation	operation	NOUN
ejpam-5835	15	4	symbol	symbol	NOUN
ejpam-5835	15	5	fi	fi	NOUN
ejpam-5835	15	6	,	,	PUNCT
ejpam-5835	15	7	we	we	PRON
ejpam-5835	15	8	assign	assign	VERB
ejpam-5835	15	9	a	a	DET
ejpam-5835	15	10	natural	natural	ADJ
ejpam-5835	15	11	number	number	NOUN
ejpam-5835	15	12	ni	ni	PROPN
ejpam-5835	15	13	∈	∈	PROPN
ejpam-5835	15	14	n	n	NOUN
ejpam-5835	15	15	:	:	PUNCT
ejpam-5835	15	16	=	=	SYM
ejpam-5835	15	17	∗corresponding	∗corresponde	VERB
ejpam-5835	15	18	author	author	NOUN
ejpam-5835	15	19	.	.	PUNCT
ejpam-5835	16	1	doi	doi	NOUN
ejpam-5835	16	2	:	:	PUNCT
ejpam-5835	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5835	https://doi.org/10.29020/nybg.ejpam.v18i2.5835	NOUN
ejpam-5835	16	4	email	email	NOUN
ejpam-5835	16	5	addresses	address	NOUN
ejpam-5835	16	6	:	:	PUNCT
ejpam-5835	16	7	thodsaporn.kum@rmutr.ac.th	thodsaporn.kum@rmutr.ac.th	PROPN
ejpam-5835	16	8	(	(	PUNCT
ejpam-5835	16	9	t.	t.	PROPN
ejpam-5835	16	10	kumduang	kumduang	PROPN
ejpam-5835	16	11	)	)	PUNCT
ejpam-5835	16	12	,	,	PUNCT
ejpam-5835	16	13	khwancheewa.wat@rmutl.ac.th	khwancheewa.wat@rmutl.ac.th	PROPN
ejpam-5835	16	14	(	(	PUNCT
ejpam-5835	16	15	k.	k.	PROPN
ejpam-5835	16	16	wattanatripop	wattanatripop	PROPN
ejpam-5835	16	17	)	)	PUNCT
ejpam-5835	16	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5835	17	1	1	1	NUM
ejpam-5835	17	2	copyright	copyright	NOUN
ejpam-5835	17	3	:	:	PUNCT
ejpam-5835	17	4	©	©	PROPN
ejpam-5835	17	5	2025	2025	NUM
ejpam-5835	17	6	the	the	DET
ejpam-5835	17	7	author(s	author(s	NOUN
ejpam-5835	17	8	)	)	PUNCT
ejpam-5835	17	9	.	.	PUNCT
ejpam-5835	18	1	(	(	PUNCT
ejpam-5835	18	2	cc	cc	NOUN
ejpam-5835	18	3	by	by	ADP
ejpam-5835	18	4	-	-	PUNCT
ejpam-5835	18	5	nc	nc	PROPN
ejpam-5835	18	6	4.0	4.0	NUM
ejpam-5835	18	7	)	)	PUNCT
ejpam-5835	18	8	t.	t.	PROPN
ejpam-5835	18	9	kumduang	kumduang	PROPN
ejpam-5835	18	10	,	,	PUNCT
ejpam-5835	18	11	k.	k.	PROPN
ejpam-5835	18	12	wattanatripop	wattanatripop	PROPN
ejpam-5835	18	13	/	/	SYM
ejpam-5835	18	14	eur	eur	PROPN
ejpam-5835	18	15	.	.	PUNCT
ejpam-5835	19	1	j.	j.	PROPN
ejpam-5835	19	2	pure	pure	PROPN
ejpam-5835	19	3	appl	appl	PROPN
ejpam-5835	19	4	.	.	PROPN
ejpam-5835	19	5	math	math	PROPN
ejpam-5835	19	6	,	,	PUNCT
ejpam-5835	19	7	18	18	NUM
ejpam-5835	19	8	(	(	PUNCT
ejpam-5835	19	9	2	2	NUM
ejpam-5835	19	10	)	)	PUNCT
ejpam-5835	19	11	(	(	PUNCT
ejpam-5835	19	12	2025	2025	NUM
ejpam-5835	19	13	)	)	PUNCT
ejpam-5835	19	14	,	,	PUNCT
ejpam-5835	19	15	5835	5835	NUM
ejpam-5835	19	16	2	2	NUM
ejpam-5835	19	17	of	of	ADP
ejpam-5835	19	18	16	16	NUM
ejpam-5835	19	19	{	{	PUNCT
ejpam-5835	19	20	1	1	NUM
ejpam-5835	19	21	,	,	PUNCT
ejpam-5835	19	22	2	2	NUM
ejpam-5835	19	23	,	,	PUNCT
ejpam-5835	19	24	.	.	PUNCT
ejpam-5835	19	25	.	.	PUNCT
ejpam-5835	20	1	.	.	PUNCT
ejpam-5835	20	2	}	}	PUNCT
ejpam-5835	20	3	,	,	PUNCT
ejpam-5835	20	4	called	call	VERB
ejpam-5835	20	5	the	the	DET
ejpam-5835	20	6	arity	arity	NOUN
ejpam-5835	20	7	of	of	ADP
ejpam-5835	20	8	fi	fi	PROPN
ejpam-5835	20	9	.	.	PUNCT
ejpam-5835	21	1	the	the	DET
ejpam-5835	21	2	type	type	NOUN
ejpam-5835	21	3	is	be	AUX
ejpam-5835	21	4	a	a	DET
ejpam-5835	21	5	sequence	sequence	NOUN
ejpam-5835	21	6	τ	τ	NOUN
ejpam-5835	21	7	:	:	PUNCT
ejpam-5835	21	8	=	=	SYM
ejpam-5835	21	9	(	(	PUNCT
ejpam-5835	21	10	ni)i∈i	ni)i∈i	NUM
ejpam-5835	21	11	.	.	PUNCT
ejpam-5835	22	1	let	let	VERB
ejpam-5835	22	2	n	n	PRON
ejpam-5835	22	3	≥	≥	NOUN
ejpam-5835	22	4	1	1	NUM
ejpam-5835	22	5	,	,	PUNCT
ejpam-5835	22	6	we	we	PRON
ejpam-5835	22	7	denote	denote	VERB
ejpam-5835	22	8	by	by	ADP
ejpam-5835	22	9	xn	xn	PROPN
ejpam-5835	23	1	:	:	PUNCT
ejpam-5835	23	2	=	=	X
ejpam-5835	23	3	{	{	PUNCT
ejpam-5835	23	4	x1	x1	PROPN
ejpam-5835	23	5	,	,	PUNCT
ejpam-5835	23	6	.	.	PUNCT
ejpam-5835	23	7	.	.	PUNCT
ejpam-5835	24	1	.	.	PUNCT
ejpam-5835	25	1	,	,	PUNCT
ejpam-5835	25	2	xn	xn	X
ejpam-5835	25	3	}	}	PUNCT
ejpam-5835	25	4	a	a	DET
ejpam-5835	25	5	finite	finite	NOUN
ejpam-5835	25	6	set	set	NOUN
ejpam-5835	25	7	called	call	VERB
ejpam-5835	25	8	an	an	DET
ejpam-5835	25	9	alphabet	alphabet	NOUN
ejpam-5835	25	10	and	and	CCONJ
ejpam-5835	25	11	each	each	DET
ejpam-5835	25	12	xi	xi	X
ejpam-5835	25	13	in	in	ADP
ejpam-5835	25	14	xn	xn	PROPN
ejpam-5835	25	15	is	be	AUX
ejpam-5835	25	16	called	call	VERB
ejpam-5835	25	17	a	a	DET
ejpam-5835	25	18	variable	variable	NOUN
ejpam-5835	25	19	.	.	PUNCT
ejpam-5835	26	1	the	the	DET
ejpam-5835	26	2	set	set	NOUN
ejpam-5835	26	3	of	of	ADP
ejpam-5835	26	4	all	all	DET
ejpam-5835	26	5	n	n	CCONJ
ejpam-5835	26	6	-	-	PUNCT
ejpam-5835	26	7	ary	ary	NOUN
ejpam-5835	26	8	terms	term	NOUN
ejpam-5835	26	9	of	of	ADP
ejpam-5835	26	10	type	type	NOUN
ejpam-5835	26	11	τ	τ	PROPN
ejpam-5835	26	12	is	be	AUX
ejpam-5835	26	13	the	the	DET
ejpam-5835	26	14	smallest	small	ADJ
ejpam-5835	26	15	set	set	NOUN
ejpam-5835	26	16	which	which	PRON
ejpam-5835	26	17	contains	contain	VERB
ejpam-5835	26	18	xn	xn	PROPN
ejpam-5835	26	19	denoted	denote	VERB
ejpam-5835	26	20	by	by	ADP
ejpam-5835	26	21	wτ	wτ	PROPN
ejpam-5835	26	22	(	(	PUNCT
ejpam-5835	26	23	xn	xn	PROPN
ejpam-5835	26	24	)	)	PUNCT
ejpam-5835	26	25	inductively	inductively	ADV
ejpam-5835	26	26	defined	define	VERB
ejpam-5835	26	27	by	by	ADP
ejpam-5835	26	28	:	:	PUNCT
ejpam-5835	26	29	(	(	PUNCT
ejpam-5835	26	30	1	1	X
ejpam-5835	26	31	)	)	PUNCT
ejpam-5835	26	32	xn	xn	PROPN
ejpam-5835	27	1	⊆	⊆	NUM
ejpam-5835	27	2	wτ	wτ	NOUN
ejpam-5835	27	3	(	(	PUNCT
ejpam-5835	27	4	xn	xn	PROPN
ejpam-5835	27	5	)	)	PUNCT
ejpam-5835	27	6	and	and	CCONJ
ejpam-5835	27	7	(	(	PUNCT
ejpam-5835	27	8	2	2	X
ejpam-5835	27	9	)	)	PUNCT
ejpam-5835	27	10	if	if	SCONJ
ejpam-5835	27	11	t1	t1	PROPN
ejpam-5835	27	12	,	,	PUNCT
ejpam-5835	27	13	.	.	PUNCT
ejpam-5835	27	14	.	.	PUNCT
ejpam-5835	27	15	.	.	PUNCT
ejpam-5835	28	1	,	,	PUNCT
ejpam-5835	28	2	tni	tni	PROPN
ejpam-5835	28	3	∈	∈	PROPN
ejpam-5835	28	4	wτ	wτ	PROPN
ejpam-5835	28	5	(	(	PUNCT
ejpam-5835	28	6	xn	xn	PROPN
ejpam-5835	28	7	)	)	PUNCT
ejpam-5835	28	8	and	and	CCONJ
ejpam-5835	28	9	fi	fi	NOUN
ejpam-5835	28	10	is	be	AUX
ejpam-5835	28	11	an	an	DET
ejpam-5835	28	12	operation	operation	NOUN
ejpam-5835	28	13	symbol	symbol	NOUN
ejpam-5835	28	14	of	of	ADP
ejpam-5835	28	15	the	the	DET
ejpam-5835	28	16	arity	arity	NOUN
ejpam-5835	28	17	ni	ni	PROPN
ejpam-5835	28	18	,	,	PUNCT
ejpam-5835	28	19	then	then	ADV
ejpam-5835	28	20	fi(t1	fi(t1	NOUN
ejpam-5835	28	21	,	,	PUNCT
ejpam-5835	28	22	.	.	PUNCT
ejpam-5835	28	23	.	.	PUNCT
ejpam-5835	29	1	.	.	PUNCT
ejpam-5835	30	1	,	,	PUNCT
ejpam-5835	30	2	tni	tni	NOUN
ejpam-5835	30	3	)	)	PUNCT
ejpam-5835	30	4	∈	∈	PROPN
ejpam-5835	30	5	wτ	wτ	NOUN
ejpam-5835	30	6	(	(	PUNCT
ejpam-5835	30	7	xn	xn	PROPN
ejpam-5835	30	8	)	)	PUNCT
ejpam-5835	30	9	.	.	PUNCT
ejpam-5835	31	1	for	for	ADP
ejpam-5835	31	2	infinitely	infinitely	ADV
ejpam-5835	31	3	many	many	ADJ
ejpam-5835	31	4	variables	variable	NOUN
ejpam-5835	31	5	x	x	NOUN
ejpam-5835	31	6	,	,	PUNCT
ejpam-5835	31	7	we	we	PRON
ejpam-5835	31	8	denote	denote	VERB
ejpam-5835	31	9	by	by	ADP
ejpam-5835	31	10	wτ	wτ	PROPN
ejpam-5835	31	11	(	(	PUNCT
ejpam-5835	31	12	x	x	NOUN
ejpam-5835	31	13	)	)	PUNCT
ejpam-5835	31	14	:	:	PUNCT
ejpam-5835	32	1	=	=	SYM
ejpam-5835	32	2	(	(	PUNCT
ejpam-5835	32	3	wτ	wτ	INTJ
ejpam-5835	32	4	(	(	PUNCT
ejpam-5835	32	5	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	32	6	,	,	PUNCT
ejpam-5835	32	7	i.e.	i.e.	X
ejpam-5835	32	8	,	,	PUNCT
ejpam-5835	32	9	for	for	ADP
ejpam-5835	32	10	the	the	DET
ejpam-5835	32	11	infinite	infinite	ADJ
ejpam-5835	32	12	sequence	sequence	NOUN
ejpam-5835	32	13	(	(	PUNCT
ejpam-5835	32	14	wτ	wτ	NOUN
ejpam-5835	32	15	(	(	PUNCT
ejpam-5835	32	16	x1),wτ	x1),wτ	PROPN
ejpam-5835	32	17	(	(	PUNCT
ejpam-5835	32	18	x2),wτ	x2),wτ	PROPN
ejpam-5835	32	19	(	(	PUNCT
ejpam-5835	32	20	x3	x3	ADJ
ejpam-5835	32	21	)	)	PUNCT
ejpam-5835	32	22	,	,	PUNCT
ejpam-5835	32	23	.	.	PUNCT
ejpam-5835	32	24	.	.	PUNCT
ejpam-5835	32	25	.	.	PUNCT
ejpam-5835	32	26	)	)	PUNCT
ejpam-5835	33	1	the	the	DET
ejpam-5835	33	2	multisorted	multisorte	VERB
ejpam-5835	33	3	set	set	NOUN
ejpam-5835	33	4	of	of	ADP
ejpam-5835	33	5	all	all	DET
ejpam-5835	33	6	terms	term	NOUN
ejpam-5835	33	7	of	of	ADP
ejpam-5835	33	8	type	type	NOUN
ejpam-5835	33	9	τ	τ	PROPN
ejpam-5835	33	10	.	.	PUNCT
ejpam-5835	34	1	in	in	ADP
ejpam-5835	34	2	this	this	DET
ejpam-5835	34	3	matter	matter	NOUN
ejpam-5835	34	4	,	,	PUNCT
ejpam-5835	34	5	the	the	DET
ejpam-5835	34	6	sorts	sort	NOUN
ejpam-5835	34	7	are	be	AUX
ejpam-5835	34	8	the	the	DET
ejpam-5835	34	9	sets	set	NOUN
ejpam-5835	34	10	of	of	ADP
ejpam-5835	34	11	n	n	CCONJ
ejpam-5835	34	12	-	-	PUNCT
ejpam-5835	34	13	ary	ary	NOUN
ejpam-5835	34	14	terms	term	NOUN
ejpam-5835	34	15	of	of	ADP
ejpam-5835	34	16	type	type	NOUN
ejpam-5835	34	17	τ	τ	PROPN
ejpam-5835	34	18	for	for	ADP
ejpam-5835	34	19	all	all	DET
ejpam-5835	34	20	n	n	PRON
ejpam-5835	34	21	∈	∈	PROPN
ejpam-5835	34	22	n.	n.	NOUN
ejpam-5835	34	23	recent	recent	ADJ
ejpam-5835	34	24	developments	development	NOUN
ejpam-5835	34	25	of	of	ADP
ejpam-5835	34	26	terms	term	NOUN
ejpam-5835	34	27	in	in	ADP
ejpam-5835	34	28	various	various	ADJ
ejpam-5835	34	29	directions	direction	NOUN
ejpam-5835	34	30	can	can	AUX
ejpam-5835	34	31	be	be	AUX
ejpam-5835	34	32	found	find	VERB
ejpam-5835	34	33	,	,	PUNCT
ejpam-5835	34	34	for	for	ADP
ejpam-5835	34	35	instance	instance	NOUN
ejpam-5835	34	36	,	,	PUNCT
ejpam-5835	34	37	in	in	ADP
ejpam-5835	34	38	[	[	X
ejpam-5835	34	39	8	8	NUM
ejpam-5835	34	40	,	,	PUNCT
ejpam-5835	34	41	10	10	NUM
ejpam-5835	34	42	,	,	PUNCT
ejpam-5835	34	43	12	12	NUM
ejpam-5835	34	44	,	,	PUNCT
ejpam-5835	34	45	15	15	NUM
ejpam-5835	34	46	,	,	PUNCT
ejpam-5835	34	47	16	16	NUM
ejpam-5835	34	48	,	,	PUNCT
ejpam-5835	34	49	18	18	NUM
ejpam-5835	34	50	]	]	PUNCT
ejpam-5835	34	51	.	.	PUNCT
ejpam-5835	35	1	it	it	PRON
ejpam-5835	35	2	is	be	AUX
ejpam-5835	35	3	commonly	commonly	ADV
ejpam-5835	35	4	seen	see	VERB
ejpam-5835	35	5	that	that	SCONJ
ejpam-5835	35	6	any	any	DET
ejpam-5835	35	7	term	term	NOUN
ejpam-5835	35	8	can	can	AUX
ejpam-5835	35	9	be	be	AUX
ejpam-5835	35	10	represented	represent	VERB
ejpam-5835	35	11	as	as	ADP
ejpam-5835	35	12	a	a	DET
ejpam-5835	35	13	tree	tree	NOUN
ejpam-5835	35	14	diagram	diagram	NOUN
ejpam-5835	35	15	.	.	PUNCT
ejpam-5835	36	1	for	for	ADP
ejpam-5835	36	2	this	this	PRON
ejpam-5835	36	3	,	,	PUNCT
ejpam-5835	36	4	we	we	PRON
ejpam-5835	36	5	can	can	AUX
ejpam-5835	36	6	visualize	visualize	VERB
ejpam-5835	36	7	a	a	DET
ejpam-5835	36	8	term	term	NOUN
ejpam-5835	36	9	from	from	ADP
ejpam-5835	36	10	the	the	DET
ejpam-5835	36	11	left	left	NOUN
ejpam-5835	36	12	to	to	ADP
ejpam-5835	36	13	the	the	DET
ejpam-5835	36	14	right	right	NOUN
ejpam-5835	36	15	by	by	ADP
ejpam-5835	36	16	treating	treat	VERB
ejpam-5835	36	17	each	each	DET
ejpam-5835	36	18	operation	operation	NOUN
ejpam-5835	36	19	symbol	symbol	NOUN
ejpam-5835	36	20	as	as	ADP
ejpam-5835	36	21	a	a	DET
ejpam-5835	36	22	vertex	vertex	NOUN
ejpam-5835	36	23	and	and	CCONJ
ejpam-5835	36	24	each	each	DET
ejpam-5835	36	25	variable	variable	NOUN
ejpam-5835	36	26	as	as	ADP
ejpam-5835	36	27	a	a	DET
ejpam-5835	36	28	leaf	leaf	NOUN
ejpam-5835	36	29	of	of	ADP
ejpam-5835	36	30	the	the	DET
ejpam-5835	36	31	tree	tree	NOUN
ejpam-5835	36	32	.	.	PUNCT
ejpam-5835	37	1	for	for	ADP
ejpam-5835	37	2	example	example	NOUN
ejpam-5835	37	3	,	,	PUNCT
ejpam-5835	37	4	the	the	DET
ejpam-5835	37	5	term	term	NOUN
ejpam-5835	37	6	t	t	PROPN
ejpam-5835	37	7	=	=	SYM
ejpam-5835	37	8	f(g(f(x2	f(g(f(x2	PROPN
ejpam-5835	37	9	,	,	PUNCT
ejpam-5835	37	10	x1	x1	PROPN
ejpam-5835	37	11	)	)	PUNCT
ejpam-5835	37	12	)	)	PUNCT
ejpam-5835	37	13	,	,	PUNCT
ejpam-5835	37	14	f(h(x4	f(h(x4	NOUN
ejpam-5835	37	15	,	,	PUNCT
ejpam-5835	37	16	x5	x5	NOUN
ejpam-5835	37	17	,	,	PUNCT
ejpam-5835	37	18	x2	x2	PROPN
ejpam-5835	37	19	)	)	PUNCT
ejpam-5835	37	20	,	,	PUNCT
ejpam-5835	37	21	g(x2	g(x2	NOUN
ejpam-5835	37	22	)	)	PUNCT
ejpam-5835	37	23	)	)	PUNCT
ejpam-5835	37	24	)	)	PUNCT
ejpam-5835	37	25	can	can	AUX
ejpam-5835	37	26	be	be	AUX
ejpam-5835	37	27	visualized	visualize	VERB
ejpam-5835	37	28	as	as	ADP
ejpam-5835	37	29	the	the	DET
ejpam-5835	37	30	following	follow	VERB
ejpam-5835	37	31	figure	figure	NOUN
ejpam-5835	37	32	.	.	PUNCT
ejpam-5835	38	1	g	g	NOUN
ejpam-5835	38	2	f	f	PROPN
ejpam-5835	39	1	f	f	PROPN
ejpam-5835	39	2	g	g	PROPN
ejpam-5835	40	1	x2	x2	PROPN
ejpam-5835	40	2	f	f	PROPN
ejpam-5835	41	1	x2	x2	INTJ
ejpam-5835	42	1	x1	x1	PROPN
ejpam-5835	42	2	h	h	NOUN
ejpam-5835	42	3	x5	x5	PROPN
ejpam-5835	42	4	x2x4	x2x4	X
ejpam-5835	43	1	for	for	ADP
ejpam-5835	43	2	more	more	ADJ
ejpam-5835	43	3	backgrounds	background	NOUN
ejpam-5835	43	4	of	of	ADP
ejpam-5835	43	5	terms	term	NOUN
ejpam-5835	43	6	representative	representative	VERB
ejpam-5835	43	7	by	by	ADP
ejpam-5835	43	8	trees	tree	NOUN
ejpam-5835	43	9	,	,	PUNCT
ejpam-5835	43	10	we	we	PRON
ejpam-5835	43	11	refer	refer	VERB
ejpam-5835	43	12	to	to	ADP
ejpam-5835	43	13	[	[	X
ejpam-5835	43	14	7	7	NUM
ejpam-5835	43	15	]	]	PUNCT
ejpam-5835	43	16	.	.	PUNCT
ejpam-5835	44	1	the	the	DET
ejpam-5835	44	2	multisorted	multisorte	VERB
ejpam-5835	44	3	algebra	algebra	NOUN
ejpam-5835	44	4	of	of	ADP
ejpam-5835	44	5	terms	term	NOUN
ejpam-5835	44	6	belongs	belong	VERB
ejpam-5835	44	7	to	to	ADP
ejpam-5835	44	8	the	the	DET
ejpam-5835	44	9	variety	variety	NOUN
ejpam-5835	44	10	of	of	ADP
ejpam-5835	44	11	all	all	DET
ejpam-5835	44	12	abstract	abstract	ADJ
ejpam-5835	44	13	clones	clone	NOUN
ejpam-5835	44	14	which	which	PRON
ejpam-5835	44	15	is	be	AUX
ejpam-5835	44	16	a	a	DET
ejpam-5835	44	17	family	family	NOUN
ejpam-5835	44	18	of	of	ADP
ejpam-5835	44	19	n	n	ADV
ejpam-5835	44	20	-	-	PUNCT
ejpam-5835	44	21	sorted	sort	VERB
ejpam-5835	44	22	algebras	algebra	NOUN
ejpam-5835	44	23	satisfying	satisfy	VERB
ejpam-5835	44	24	the	the	DET
ejpam-5835	44	25	following	follow	VERB
ejpam-5835	44	26	three	three	NUM
ejpam-5835	44	27	identities	identity	NOUN
ejpam-5835	44	28	:	:	PUNCT
ejpam-5835	44	29	(	(	PUNCT
ejpam-5835	44	30	c1	c1	NOUN
ejpam-5835	44	31	)	)	PUNCT
ejpam-5835	44	32	s̃n	s̃n	VERB
ejpam-5835	44	33	m(s̃p	m(s̃p	PROPN
ejpam-5835	44	34	n(z̃	n(z̃	PROPN
ejpam-5835	44	35	,	,	PUNCT
ejpam-5835	44	36	ỹ1	ỹ1	PROPN
ejpam-5835	44	37	,	,	PUNCT
ejpam-5835	44	38	.	.	PUNCT
ejpam-5835	44	39	.	.	PUNCT
ejpam-5835	45	1	.	.	PUNCT
ejpam-5835	46	1	,	,	PUNCT
ejpam-5835	46	2	ỹp	ỹp	NOUN
ejpam-5835	46	3	)	)	PUNCT
ejpam-5835	46	4	,	,	PUNCT
ejpam-5835	46	5	x̃1	x̃1	PROPN
ejpam-5835	46	6	,	,	PUNCT
ejpam-5835	46	7	.	.	PUNCT
ejpam-5835	46	8	.	.	PUNCT
ejpam-5835	46	9	.	.	PUNCT
ejpam-5835	47	1	,	,	PUNCT
ejpam-5835	47	2	x̃n	x̃n	PROPN
ejpam-5835	47	3	)	)	PUNCT
ejpam-5835	48	1	≈	≈	PROPN
ejpam-5835	48	2	s̃p	s̃p	PROPN
ejpam-5835	48	3	m(z̃	m(z̃	PROPN
ejpam-5835	48	4	,	,	PUNCT
ejpam-5835	48	5	s̃n	s̃n	PROPN
ejpam-5835	48	6	m(ỹ1	m(ỹ1	PROPN
ejpam-5835	48	7	,	,	PUNCT
ejpam-5835	48	8	x̃1	x̃1	PROPN
ejpam-5835	48	9	,	,	PUNCT
ejpam-5835	48	10	.	.	PUNCT
ejpam-5835	48	11	.	.	PUNCT
ejpam-5835	48	12	.	.	PUNCT
ejpam-5835	49	1	,	,	PUNCT
ejpam-5835	49	2	x̃n	x̃n	PROPN
ejpam-5835	49	3	)	)	PUNCT
ejpam-5835	49	4	,	,	PUNCT
ejpam-5835	49	5	.	.	PUNCT
ejpam-5835	49	6	.	.	PUNCT
ejpam-5835	50	1	.	.	PUNCT
ejpam-5835	51	1	,	,	PUNCT
ejpam-5835	51	2	s̃	s̃	PROPN
ejpam-5835	51	3	n	n	PRON
ejpam-5835	51	4	m(ỹp	m(ỹp	PROPN
ejpam-5835	51	5	,	,	PUNCT
ejpam-5835	51	6	x̃1	x̃1	PROPN
ejpam-5835	51	7	,	,	PUNCT
ejpam-5835	51	8	.	.	PUNCT
ejpam-5835	51	9	.	.	PUNCT
ejpam-5835	52	1	.	.	PUNCT
ejpam-5835	53	1	,	,	PUNCT
ejpam-5835	53	2	x̃n)),m	x̃n)),m	ADJ
ejpam-5835	53	3	,	,	PUNCT
ejpam-5835	53	4	n	n	CCONJ
ejpam-5835	53	5	,	,	PUNCT
ejpam-5835	53	6	p	p	PROPN
ejpam-5835	53	7	∈	∈	PROPN
ejpam-5835	53	8	n	n	CCONJ
ejpam-5835	53	9	,	,	PUNCT
ejpam-5835	53	10	(	(	PUNCT
ejpam-5835	53	11	c2	c2	PROPN
ejpam-5835	53	12	)	)	PUNCT
ejpam-5835	53	13	s̃n	s̃n	VERB
ejpam-5835	53	14	m(λj	m(λj	NOUN
ejpam-5835	53	15	,	,	PUNCT
ejpam-5835	53	16	x̃1	x̃1	PROPN
ejpam-5835	53	17	,	,	PUNCT
ejpam-5835	53	18	.	.	PUNCT
ejpam-5835	53	19	.	.	PUNCT
ejpam-5835	53	20	.	.	PUNCT
ejpam-5835	54	1	,	,	PUNCT
ejpam-5835	54	2	x̃n	x̃n	PROPN
ejpam-5835	54	3	)	)	PUNCT
ejpam-5835	55	1	≈	≈	PROPN
ejpam-5835	55	2	x̃j	x̃j	INTJ
ejpam-5835	55	3	,	,	PUNCT
ejpam-5835	55	4	n	n	CCONJ
ejpam-5835	55	5	,	,	PUNCT
ejpam-5835	55	6	m	m	VERB
ejpam-5835	55	7	∈	∈	PROPN
ejpam-5835	55	8	n	n	CCONJ
ejpam-5835	55	9	,	,	PUNCT
ejpam-5835	55	10	1	1	NUM
ejpam-5835	55	11	≤	≤	NUM
ejpam-5835	55	12	j	j	PROPN
ejpam-5835	55	13	≤	≤	NUM
ejpam-5835	55	14	n	n	CCONJ
ejpam-5835	55	15	,	,	PUNCT
ejpam-5835	55	16	(	(	PUNCT
ejpam-5835	55	17	c3	c3	NOUN
ejpam-5835	55	18	)	)	PUNCT
ejpam-5835	55	19	s̃n	s̃n	VERB
ejpam-5835	55	20	n(ỹ	n(ỹ	NUM
ejpam-5835	55	21	,	,	PUNCT
ejpam-5835	55	22	λ1	λ1	ADJ
ejpam-5835	55	23	,	,	PUNCT
ejpam-5835	55	24	.	.	PUNCT
ejpam-5835	55	25	.	.	PUNCT
ejpam-5835	56	1	.	.	PUNCT
ejpam-5835	57	1	,	,	PUNCT
ejpam-5835	57	2	λn	λn	NOUN
ejpam-5835	57	3	)	)	PUNCT
ejpam-5835	58	1	≈	≈	PROPN
ejpam-5835	58	2	ỹ	ỹ	PROPN
ejpam-5835	58	3	,	,	PUNCT
ejpam-5835	58	4	n	n	PROPN
ejpam-5835	58	5	∈	∈	PROPN
ejpam-5835	58	6	n	n	CCONJ
ejpam-5835	58	7	,	,	PUNCT
ejpam-5835	58	8	where	where	SCONJ
ejpam-5835	58	9	s̃n	s̃n	PROPN
ejpam-5835	58	10	m	m	PROPN
ejpam-5835	58	11	,	,	PUNCT
ejpam-5835	58	12	s̃p	s̃p	NOUN
ejpam-5835	58	13	n	n	NOUN
ejpam-5835	58	14	,	,	PUNCT
ejpam-5835	58	15	s̃	s̃	PROPN
ejpam-5835	58	16	p	p	PROPN
ejpam-5835	58	17	m	m	PROPN
ejpam-5835	58	18	,	,	PUNCT
ejpam-5835	58	19	s̃n	s̃n	INTJ
ejpam-5835	58	20	n	n	PRON
ejpam-5835	58	21	are	be	AUX
ejpam-5835	58	22	operation	operation	NOUN
ejpam-5835	58	23	symbols	symbol	NOUN
ejpam-5835	58	24	,	,	PUNCT
ejpam-5835	58	25	z̃	z̃	PROPN
ejpam-5835	58	26	,	,	PUNCT
ejpam-5835	58	27	ỹ1	ỹ1	PROPN
ejpam-5835	58	28	,	,	PUNCT
ejpam-5835	58	29	.	.	PUNCT
ejpam-5835	58	30	.	.	PUNCT
ejpam-5835	59	1	.	.	PUNCT
ejpam-5835	60	1	,	,	PUNCT
ejpam-5835	60	2	ỹp	ỹp	NOUN
ejpam-5835	60	3	,	,	PUNCT
ejpam-5835	60	4	x̃1	x̃1	PROPN
ejpam-5835	60	5	,	,	PUNCT
ejpam-5835	60	6	.	.	PUNCT
ejpam-5835	60	7	.	.	PUNCT
ejpam-5835	60	8	.	.	PUNCT
ejpam-5835	61	1	,	,	PUNCT
ejpam-5835	61	2	x̃n	x̃n	PROPN
ejpam-5835	61	3	,	,	PUNCT
ejpam-5835	61	4	ỹ	ỹ	PROPN
ejpam-5835	61	5	are	be	AUX
ejpam-5835	61	6	variables	variable	NOUN
ejpam-5835	61	7	for	for	ADP
ejpam-5835	61	8	terms	term	NOUN
ejpam-5835	61	9	,	,	PUNCT
ejpam-5835	61	10	and	and	CCONJ
ejpam-5835	61	11	λj	λj	PROPN
ejpam-5835	61	12	are	be	AUX
ejpam-5835	61	13	symbols	symbol	NOUN
ejpam-5835	61	14	for	for	ADP
ejpam-5835	61	15	variables	variable	NOUN
ejpam-5835	61	16	.	.	PUNCT
ejpam-5835	62	1	in	in	ADP
ejpam-5835	62	2	general	general	ADJ
ejpam-5835	62	3	,	,	PUNCT
ejpam-5835	62	4	(	(	PUNCT
ejpam-5835	62	5	c1	c1	NOUN
ejpam-5835	62	6	)	)	PUNCT
ejpam-5835	62	7	is	be	AUX
ejpam-5835	62	8	said	say	VERB
ejpam-5835	62	9	to	to	PART
ejpam-5835	62	10	be	be	AUX
ejpam-5835	62	11	the	the	DET
ejpam-5835	62	12	superassociative	superassociative	ADJ
ejpam-5835	62	13	law	law	NOUN
ejpam-5835	62	14	since	since	SCONJ
ejpam-5835	62	15	it	it	PRON
ejpam-5835	62	16	generalizes	generalize	VERB
ejpam-5835	62	17	the	the	DET
ejpam-5835	62	18	associative	associative	ADJ
ejpam-5835	62	19	law	law	NOUN
ejpam-5835	62	20	.	.	PUNCT
ejpam-5835	63	1	a	a	DET
ejpam-5835	63	2	class	class	NOUN
ejpam-5835	63	3	of	of	ADP
ejpam-5835	63	4	algebras	algebra	NOUN
ejpam-5835	63	5	that	that	SCONJ
ejpam-5835	63	6	satisfies	satisfie	NOUN
ejpam-5835	63	7	(	(	PUNCT
ejpam-5835	63	8	c1	c1	PROPN
ejpam-5835	63	9	)	)	PUNCT
ejpam-5835	63	10	is	be	AUX
ejpam-5835	63	11	called	call	VERB
ejpam-5835	63	12	t.	t.	PROPN
ejpam-5835	63	13	kumduang	kumduang	PROPN
ejpam-5835	63	14	,	,	PUNCT
ejpam-5835	63	15	k.	k.	PROPN
ejpam-5835	63	16	wattanatripop	wattanatripop	PROPN
ejpam-5835	63	17	/	/	SYM
ejpam-5835	63	18	eur	eur	PROPN
ejpam-5835	63	19	.	.	PUNCT
ejpam-5835	64	1	j.	j.	PROPN
ejpam-5835	64	2	pure	pure	PROPN
ejpam-5835	64	3	appl	appl	PROPN
ejpam-5835	64	4	.	.	PROPN
ejpam-5835	64	5	math	math	PROPN
ejpam-5835	64	6	,	,	PUNCT
ejpam-5835	64	7	18	18	NUM
ejpam-5835	64	8	(	(	PUNCT
ejpam-5835	64	9	2	2	NUM
ejpam-5835	64	10	)	)	PUNCT
ejpam-5835	64	11	(	(	PUNCT
ejpam-5835	64	12	2025	2025	NUM
ejpam-5835	64	13	)	)	PUNCT
ejpam-5835	64	14	,	,	PUNCT
ejpam-5835	64	15	5835	5835	NUM
ejpam-5835	64	16	3	3	NUM
ejpam-5835	64	17	of	of	ADP
ejpam-5835	64	18	16	16	NUM
ejpam-5835	64	19	a	a	DET
ejpam-5835	64	20	menger	menger	PROPN
ejpam-5835	64	21	algebra	algebra	NOUN
ejpam-5835	64	22	or	or	CCONJ
ejpam-5835	64	23	a	a	DET
ejpam-5835	64	24	superassociative	superassociative	ADJ
ejpam-5835	64	25	algebra	algebra	NOUN
ejpam-5835	64	26	.	.	PUNCT
ejpam-5835	65	1	in	in	ADP
ejpam-5835	65	2	(	(	PUNCT
ejpam-5835	65	3	c1	c1	PROPN
ejpam-5835	65	4	)	)	PUNCT
ejpam-5835	65	5	,	,	PUNCT
ejpam-5835	65	6	if	if	SCONJ
ejpam-5835	65	7	n	n	NOUN
ejpam-5835	65	8	=	=	NOUN
ejpam-5835	65	9	m	m	PROPN
ejpam-5835	65	10	=	=	SYM
ejpam-5835	65	11	p	p	X
ejpam-5835	65	12	=	=	NOUN
ejpam-5835	65	13	1	1	NUM
ejpam-5835	65	14	,	,	PUNCT
ejpam-5835	65	15	then	then	ADV
ejpam-5835	65	16	it	it	PRON
ejpam-5835	65	17	reduces	reduce	VERB
ejpam-5835	65	18	to	to	ADP
ejpam-5835	65	19	the	the	DET
ejpam-5835	65	20	usual	usual	ADJ
ejpam-5835	65	21	associative	associative	ADJ
ejpam-5835	65	22	law	law	NOUN
ejpam-5835	65	23	.	.	PUNCT
ejpam-5835	66	1	for	for	ADP
ejpam-5835	66	2	an	an	DET
ejpam-5835	66	3	overview	overview	NOUN
ejpam-5835	66	4	of	of	ADP
ejpam-5835	66	5	clone	clone	NOUN
ejpam-5835	66	6	theory	theory	NOUN
ejpam-5835	66	7	we	we	PRON
ejpam-5835	66	8	refer	refer	VERB
ejpam-5835	66	9	to	to	ADP
ejpam-5835	66	10	[	[	X
ejpam-5835	66	11	2	2	NUM
ejpam-5835	66	12	,	,	PUNCT
ejpam-5835	66	13	3	3	NUM
ejpam-5835	66	14	,	,	PUNCT
ejpam-5835	66	15	9	9	NUM
ejpam-5835	66	16	]	]	PUNCT
ejpam-5835	66	17	.	.	PUNCT
ejpam-5835	67	1	the	the	DET
ejpam-5835	67	2	viewpoint	viewpoint	NOUN
ejpam-5835	67	3	taken	take	VERB
ejpam-5835	67	4	in	in	ADP
ejpam-5835	67	5	menger	menger	PROPN
ejpam-5835	67	6	algebras	algebras	PROPN
ejpam-5835	67	7	can	can	AUX
ejpam-5835	67	8	be	be	AUX
ejpam-5835	67	9	found	find	VERB
ejpam-5835	67	10	in	in	ADP
ejpam-5835	67	11	[	[	X
ejpam-5835	67	12	5	5	NUM
ejpam-5835	67	13	,	,	PUNCT
ejpam-5835	67	14	6	6	NUM
ejpam-5835	67	15	,	,	PUNCT
ejpam-5835	67	16	11	11	NUM
ejpam-5835	67	17	,	,	PUNCT
ejpam-5835	67	18	14	14	NUM
ejpam-5835	67	19	]	]	PUNCT
ejpam-5835	67	20	.	.	PUNCT
ejpam-5835	68	1	the	the	DET
ejpam-5835	68	2	multisorted	multisorte	VERB
ejpam-5835	68	3	superposition	superposition	NOUN
ejpam-5835	68	4	operation	operation	NOUN
ejpam-5835	68	5	defined	define	VERB
ejpam-5835	68	6	on	on	ADP
ejpam-5835	68	7	(	(	PUNCT
ejpam-5835	68	8	wτ	wτ	INTJ
ejpam-5835	68	9	(	(	PUNCT
ejpam-5835	68	10	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	68	11	is	be	AUX
ejpam-5835	68	12	a	a	DET
ejpam-5835	68	13	multisorted	multisorte	VERB
ejpam-5835	68	14	mapping	mapping	NOUN
ejpam-5835	68	15	sn	sn	INTJ
ejpam-5835	68	16	m	m	VERB
ejpam-5835	68	17	:	:	PUNCT
ejpam-5835	68	18	wτ	wτ	INTJ
ejpam-5835	68	19	(	(	PUNCT
ejpam-5835	68	20	xn)×	xn)×	X
ejpam-5835	68	21	(	(	PUNCT
ejpam-5835	68	22	wτ	wτ	INTJ
ejpam-5835	68	23	(	(	PUNCT
ejpam-5835	68	24	xm))n	xm))n	PROPN
ejpam-5835	68	25	→	→	SYM
ejpam-5835	68	26	wτ	wτ	PROPN
ejpam-5835	68	27	(	(	PUNCT
ejpam-5835	68	28	xm	xm	NOUN
ejpam-5835	68	29	)	)	PUNCT
ejpam-5835	68	30	defined	define	VERB
ejpam-5835	68	31	by	by	ADP
ejpam-5835	68	32	:	:	PUNCT
ejpam-5835	68	33	(	(	PUNCT
ejpam-5835	68	34	1	1	X
ejpam-5835	68	35	)	)	PUNCT
ejpam-5835	68	36	sn	sn	PROPN
ejpam-5835	68	37	m(xi	m(xi	PROPN
ejpam-5835	68	38	,	,	PUNCT
ejpam-5835	68	39	t1	t1	NOUN
ejpam-5835	68	40	,	,	PUNCT
ejpam-5835	68	41	.	.	PUNCT
ejpam-5835	68	42	.	.	PUNCT
ejpam-5835	68	43	.	.	PUNCT
ejpam-5835	69	1	,	,	PUNCT
ejpam-5835	69	2	tn	tn	PROPN
ejpam-5835	69	3	)	)	PUNCT
ejpam-5835	69	4	=	=	SYM
ejpam-5835	69	5	ti	ti	NOUN
ejpam-5835	69	6	if	if	SCONJ
ejpam-5835	69	7	xi	xi	PROPN
ejpam-5835	69	8	∈	∈	PROPN
ejpam-5835	69	9	xn	xn	PROPN
ejpam-5835	69	10	,	,	PUNCT
ejpam-5835	69	11	(	(	PUNCT
ejpam-5835	69	12	2	2	X
ejpam-5835	69	13	)	)	PUNCT
ejpam-5835	69	14	sn	sn	NOUN
ejpam-5835	69	15	m(fi(s1	m(fi(s1	ADJ
ejpam-5835	69	16	,	,	PUNCT
ejpam-5835	69	17	.	.	PUNCT
ejpam-5835	69	18	.	.	PUNCT
ejpam-5835	70	1	.	.	PUNCT
ejpam-5835	71	1	,	,	PUNCT
ejpam-5835	71	2	sni	sni	PROPN
ejpam-5835	71	3	)	)	PUNCT
ejpam-5835	71	4	,	,	PUNCT
ejpam-5835	71	5	t1	t1	PROPN
ejpam-5835	71	6	,	,	PUNCT
ejpam-5835	71	7	.	.	PUNCT
ejpam-5835	71	8	.	.	PUNCT
ejpam-5835	72	1	.	.	PUNCT
ejpam-5835	73	1	,	,	PUNCT
ejpam-5835	73	2	tn	tn	PROPN
ejpam-5835	73	3	)	)	PUNCT
ejpam-5835	73	4	=	=	NOUN
ejpam-5835	73	5	fi(s	fi(s	X
ejpam-5835	74	1	n	n	X
ejpam-5835	74	2	m(s1	m(s1	ADJ
ejpam-5835	74	3	,	,	PUNCT
ejpam-5835	74	4	t1	t1	NOUN
ejpam-5835	74	5	,	,	PUNCT
ejpam-5835	74	6	.	.	PUNCT
ejpam-5835	74	7	.	.	PUNCT
ejpam-5835	74	8	.	.	PUNCT
ejpam-5835	75	1	,	,	PUNCT
ejpam-5835	75	2	tn	tn	PROPN
ejpam-5835	75	3	)	)	PUNCT
ejpam-5835	75	4	,	,	PUNCT
ejpam-5835	75	5	.	.	PUNCT
ejpam-5835	75	6	.	.	PUNCT
ejpam-5835	76	1	.	.	PUNCT
ejpam-5835	77	1	,	,	PUNCT
ejpam-5835	77	2	s	s	VERB
ejpam-5835	77	3	n	n	PRON
ejpam-5835	77	4	m(sni	m(sni	PROPN
ejpam-5835	77	5	,	,	PUNCT
ejpam-5835	77	6	t1	t1	PROPN
ejpam-5835	77	7	,	,	PUNCT
ejpam-5835	77	8	.	.	PUNCT
ejpam-5835	77	9	.	.	PUNCT
ejpam-5835	78	1	.	.	PUNCT
ejpam-5835	79	1	,	,	PUNCT
ejpam-5835	79	2	tn	tn	PROPN
ejpam-5835	79	3	)	)	PUNCT
ejpam-5835	79	4	)	)	PUNCT
ejpam-5835	80	1	where	where	SCONJ
ejpam-5835	80	2	n	n	X
ejpam-5835	80	3	,	,	PUNCT
ejpam-5835	80	4	m	m	VERB
ejpam-5835	80	5	∈	∈	PROPN
ejpam-5835	80	6	n	n	NOUN
ejpam-5835	80	7	and	and	CCONJ
ejpam-5835	80	8	t1	t1	VERB
ejpam-5835	80	9	,	,	PUNCT
ejpam-5835	80	10	.	.	PUNCT
ejpam-5835	80	11	.	.	PUNCT
ejpam-5835	81	1	.	.	PUNCT
ejpam-5835	82	1	,	,	PUNCT
ejpam-5835	82	2	tn	tn	PROPN
ejpam-5835	82	3	∈	∈	PROPN
ejpam-5835	82	4	wτ	wτ	NOUN
ejpam-5835	82	5	(	(	PUNCT
ejpam-5835	82	6	xm	xm	PROPN
ejpam-5835	82	7	)	)	PUNCT
ejpam-5835	82	8	.	.	PUNCT
ejpam-5835	83	1	thus	thus	ADV
ejpam-5835	83	2	,	,	PUNCT
ejpam-5835	83	3	the	the	DET
ejpam-5835	83	4	multisorted	multisorte	VERB
ejpam-5835	83	5	algebra	algebra	NOUN
ejpam-5835	83	6	of	of	ADP
ejpam-5835	83	7	terms	term	NOUN
ejpam-5835	83	8	of	of	ADP
ejpam-5835	83	9	type	type	NOUN
ejpam-5835	83	10	τ	τ	PROPN
ejpam-5835	83	11	or	or	CCONJ
ejpam-5835	83	12	the	the	DET
ejpam-5835	83	13	clone	clone	NOUN
ejpam-5835	83	14	of	of	ADP
ejpam-5835	83	15	all	all	DET
ejpam-5835	83	16	terms	term	NOUN
ejpam-5835	83	17	of	of	ADP
ejpam-5835	83	18	type	type	NOUN
ejpam-5835	83	19	τ	τ	PROPN
ejpam-5835	83	20	denoted	denote	VERB
ejpam-5835	83	21	by	by	ADP
ejpam-5835	83	22	clone(τ	clone(τ	NOUN
ejpam-5835	83	23	)	)	PUNCT
ejpam-5835	83	24	=	=	SYM
ejpam-5835	83	25	(	(	PUNCT
ejpam-5835	83	26	(	(	PUNCT
ejpam-5835	83	27	wτ	wτ	INTJ
ejpam-5835	83	28	(	(	PUNCT
ejpam-5835	83	29	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	83	30	,	,	PUNCT
ejpam-5835	83	31	(	(	PUNCT
ejpam-5835	83	32	s	s	NOUN
ejpam-5835	83	33	n	n	PRON
ejpam-5835	83	34	m)m	m)m	NOUN
ejpam-5835	83	35	,	,	PUNCT
ejpam-5835	83	36	n∈n	n∈n	PROPN
ejpam-5835	83	37	,	,	PUNCT
ejpam-5835	83	38	(	(	PUNCT
ejpam-5835	83	39	xi)i≤n∈n	xi)i≤n∈n	NOUN
ejpam-5835	83	40	)	)	PUNCT
ejpam-5835	83	41	is	be	AUX
ejpam-5835	83	42	formed	form	VERB
ejpam-5835	83	43	.	.	PUNCT
ejpam-5835	84	1	actually	actually	ADV
ejpam-5835	84	2	,	,	PUNCT
ejpam-5835	84	3	it	it	PRON
ejpam-5835	84	4	also	also	ADV
ejpam-5835	84	5	satisfies	satisfy	VERB
ejpam-5835	84	6	the	the	DET
ejpam-5835	84	7	axioms	axiom	NOUN
ejpam-5835	84	8	(	(	PUNCT
ejpam-5835	84	9	c1	c1	NOUN
ejpam-5835	84	10	)	)	PUNCT
ejpam-5835	84	11	,	,	PUNCT
ejpam-5835	84	12	(	(	PUNCT
ejpam-5835	84	13	c2	c2	PROPN
ejpam-5835	84	14	)	)	PUNCT
ejpam-5835	84	15	and	and	CCONJ
ejpam-5835	84	16	(	(	PUNCT
ejpam-5835	84	17	c3	c3	PROPN
ejpam-5835	84	18	)	)	PUNCT
ejpam-5835	84	19	,	,	PUNCT
ejpam-5835	84	20	thus	thus	ADV
ejpam-5835	84	21	it	it	PRON
ejpam-5835	84	22	is	be	AUX
ejpam-5835	84	23	an	an	DET
ejpam-5835	84	24	example	example	NOUN
ejpam-5835	84	25	of	of	ADP
ejpam-5835	84	26	abstract	abstract	ADJ
ejpam-5835	84	27	clones	clone	NOUN
ejpam-5835	84	28	.	.	PUNCT
ejpam-5835	85	1	particularly	particularly	ADV
ejpam-5835	85	2	,	,	PUNCT
ejpam-5835	85	3	if	if	SCONJ
ejpam-5835	85	4	we	we	PRON
ejpam-5835	85	5	let	let	VERB
ejpam-5835	85	6	a	a	PRON
ejpam-5835	85	7	:	:	PUNCT
ejpam-5835	85	8	=	=	SYM
ejpam-5835	85	9	(	(	PUNCT
ejpam-5835	85	10	a	a	PRON
ejpam-5835	85	11	,	,	PUNCT
ejpam-5835	85	12	(	(	PUNCT
ejpam-5835	85	13	fa	fa	INTJ
ejpam-5835	85	14	i	i	NOUN
ejpam-5835	85	15	)	)	PUNCT
ejpam-5835	85	16	i∈i	i∈i	ADV
ejpam-5835	85	17	)	)	PUNCT
ejpam-5835	85	18	be	be	VERB
ejpam-5835	85	19	an	an	DET
ejpam-5835	85	20	algebra	algebra	NOUN
ejpam-5835	85	21	of	of	ADP
ejpam-5835	85	22	type	type	NOUN
ejpam-5835	85	23	τ	τ	PROPN
ejpam-5835	85	24	and	and	CCONJ
ejpam-5835	85	25	let	let	VERB
ejpam-5835	85	26	t	t	PROPN
ejpam-5835	85	27	be	be	AUX
ejpam-5835	85	28	an	an	DET
ejpam-5835	85	29	n	n	CCONJ
ejpam-5835	85	30	-	-	PUNCT
ejpam-5835	85	31	ary	ary	NOUN
ejpam-5835	85	32	term	term	NOUN
ejpam-5835	85	33	of	of	ADP
ejpam-5835	85	34	type	type	NOUN
ejpam-5835	85	35	τ	τ	PROPN
ejpam-5835	85	36	,	,	PUNCT
ejpam-5835	85	37	then	then	ADV
ejpam-5835	85	38	a	a	DET
ejpam-5835	85	39	term	term	NOUN
ejpam-5835	85	40	t	t	PROPN
ejpam-5835	85	41	induces	induce	VERB
ejpam-5835	85	42	an	an	DET
ejpam-5835	85	43	n	n	CCONJ
ejpam-5835	85	44	-	-	PUNCT
ejpam-5835	85	45	ary	ary	NOUN
ejpam-5835	85	46	operation	operation	NOUN
ejpam-5835	85	47	ta	ta	X
ejpam-5835	85	48	on	on	ADP
ejpam-5835	85	49	a	a	PRON
ejpam-5835	85	50	as	as	SCONJ
ejpam-5835	85	51	follows	follow	VERB
ejpam-5835	85	52	:	:	PUNCT
ejpam-5835	85	53	(	(	PUNCT
ejpam-5835	85	54	1	1	X
ejpam-5835	85	55	)	)	PUNCT
ejpam-5835	85	56	if	if	SCONJ
ejpam-5835	85	57	t	t	PROPN
ejpam-5835	85	58	=	=	PUNCT
ejpam-5835	85	59	xj	xj	PROPN
ejpam-5835	85	60	∈	∈	PROPN
ejpam-5835	85	61	xn	xn	PROPN
ejpam-5835	85	62	,	,	PUNCT
ejpam-5835	85	63	then	then	ADV
ejpam-5835	85	64	ta	ta	PROPN
ejpam-5835	85	65	=	=	SYM
ejpam-5835	85	66	xaj	xaj	PROPN
ejpam-5835	85	67	=	=	SYM
ejpam-5835	85	68	prn	prn	PROPN
ejpam-5835	85	69	,	,	PUNCT
ejpam-5835	85	70	aj	aj	PROPN
ejpam-5835	85	71	where	where	SCONJ
ejpam-5835	85	72	prn	prn	PROPN
ejpam-5835	85	73	,	,	PUNCT
ejpam-5835	85	74	aj	aj	PROPN
ejpam-5835	85	75	is	be	AUX
ejpam-5835	85	76	an	an	DET
ejpam-5835	85	77	n	n	CCONJ
ejpam-5835	85	78	-	-	PUNCT
ejpam-5835	85	79	ary	ary	NOUN
ejpam-5835	85	80	projection	projection	NOUN
ejpam-5835	85	81	mapping	mapping	NOUN
ejpam-5835	85	82	on	on	ADP
ejpam-5835	85	83	a	a	DET
ejpam-5835	85	84	,	,	PUNCT
ejpam-5835	85	85	(	(	PUNCT
ejpam-5835	85	86	2	2	X
ejpam-5835	85	87	)	)	PUNCT
ejpam-5835	85	88	if	if	SCONJ
ejpam-5835	85	89	t	t	NOUN
ejpam-5835	85	90	=	=	SYM
ejpam-5835	85	91	fi(t1	fi(t1	NOUN
ejpam-5835	85	92	,	,	PUNCT
ejpam-5835	85	93	.	.	PUNCT
ejpam-5835	85	94	.	.	PUNCT
ejpam-5835	86	1	.	.	PUNCT
ejpam-5835	87	1	,	,	PUNCT
ejpam-5835	87	2	tni	tni	NOUN
ejpam-5835	87	3	)	)	PUNCT
ejpam-5835	87	4	is	be	AUX
ejpam-5835	87	5	an	an	DET
ejpam-5835	87	6	n	n	CCONJ
ejpam-5835	87	7	-	-	PUNCT
ejpam-5835	87	8	ary	ary	NOUN
ejpam-5835	87	9	term	term	NOUN
ejpam-5835	87	10	of	of	ADP
ejpam-5835	87	11	type	type	NOUN
ejpam-5835	87	12	τ	τ	PROPN
ejpam-5835	87	13	and	and	CCONJ
ejpam-5835	87	14	ta1	ta1	PROPN
ejpam-5835	87	15	,	,	PUNCT
ejpam-5835	87	16	.	.	PUNCT
ejpam-5835	87	17	.	.	PUNCT
ejpam-5835	88	1	.	.	PUNCT
ejpam-5835	89	1	,	,	PUNCT
ejpam-5835	89	2	t	t	PROPN
ejpam-5835	89	3	a	a	DET
ejpam-5835	89	4	ni	ni	PROPN
ejpam-5835	89	5	are	be	AUX
ejpam-5835	89	6	the	the	DET
ejpam-5835	89	7	term	term	NOUN
ejpam-5835	89	8	operations	operation	NOUN
ejpam-5835	89	9	which	which	PRON
ejpam-5835	89	10	are	be	AUX
ejpam-5835	89	11	induced	induce	VERB
ejpam-5835	89	12	by	by	ADP
ejpam-5835	89	13	t1	t1	NOUN
ejpam-5835	89	14	,	,	PUNCT
ejpam-5835	89	15	.	.	PUNCT
ejpam-5835	89	16	.	.	PUNCT
ejpam-5835	90	1	.	.	PUNCT
ejpam-5835	91	1	,	,	PUNCT
ejpam-5835	91	2	tni	tni	NOUN
ejpam-5835	91	3	,	,	PUNCT
ejpam-5835	91	4	then	then	ADV
ejpam-5835	91	5	ta	ta	PROPN
ejpam-5835	92	1	=	=	SYM
ejpam-5835	92	2	fa	fa	INTJ
ejpam-5835	92	3	i	i	PRON
ejpam-5835	92	4	(	(	PUNCT
ejpam-5835	92	5	ta1	ta1	PROPN
ejpam-5835	92	6	,	,	PUNCT
ejpam-5835	92	7	.	.	PUNCT
ejpam-5835	92	8	.	.	PUNCT
ejpam-5835	92	9	.	.	PUNCT
ejpam-5835	93	1	,	,	PUNCT
ejpam-5835	93	2	t	t	PROPN
ejpam-5835	93	3	a	a	DET
ejpam-5835	93	4	ni	ni	PROPN
ejpam-5835	93	5	)	)	PUNCT
ejpam-5835	93	6	.	.	PUNCT
ejpam-5835	94	1	hence	hence	ADV
ejpam-5835	94	2	,	,	PUNCT
ejpam-5835	94	3	ta	ta	PROPN
ejpam-5835	94	4	is	be	AUX
ejpam-5835	94	5	called	call	VERB
ejpam-5835	94	6	the	the	DET
ejpam-5835	94	7	term	term	NOUN
ejpam-5835	94	8	operation	operation	NOUN
ejpam-5835	94	9	induced	induce	VERB
ejpam-5835	94	10	by	by	ADP
ejpam-5835	94	11	the	the	DET
ejpam-5835	94	12	term	term	NOUN
ejpam-5835	94	13	t	t	PROPN
ejpam-5835	94	14	on	on	ADP
ejpam-5835	94	15	the	the	DET
ejpam-5835	94	16	algebra	algebra	NOUN
ejpam-5835	94	17	a.	a.	NOUN
ejpam-5835	94	18	the	the	DET
ejpam-5835	94	19	set	set	NOUN
ejpam-5835	94	20	of	of	ADP
ejpam-5835	94	21	all	all	DET
ejpam-5835	94	22	n	n	CCONJ
ejpam-5835	94	23	-	-	PUNCT
ejpam-5835	94	24	ary	ary	NOUN
ejpam-5835	94	25	term	term	NOUN
ejpam-5835	94	26	operations	operation	NOUN
ejpam-5835	94	27	on	on	ADP
ejpam-5835	94	28	a	a	PRON
ejpam-5835	94	29	will	will	AUX
ejpam-5835	94	30	be	be	AUX
ejpam-5835	94	31	denoted	denote	VERB
ejpam-5835	94	32	by	by	ADP
ejpam-5835	94	33	wτ	wτ	PROPN
ejpam-5835	94	34	(	(	PUNCT
ejpam-5835	94	35	xn	xn	PROPN
ejpam-5835	94	36	)	)	PUNCT
ejpam-5835	94	37	a.	a.	NOUN
ejpam-5835	95	1	moreover	moreover	ADV
ejpam-5835	95	2	,	,	PUNCT
ejpam-5835	95	3	let	let	VERB
ejpam-5835	95	4	ida	ida	PROPN
ejpam-5835	95	5	=	=	PRON
ejpam-5835	95	6	{	{	PUNCT
ejpam-5835	95	7	s	s	PROPN
ejpam-5835	95	8	≈	≈	PROPN
ejpam-5835	95	9	t	t	PROPN
ejpam-5835	95	10	∈	∈	PROPN
ejpam-5835	95	11	wτ	wτ	PROPN
ejpam-5835	95	12	(	(	PUNCT
ejpam-5835	95	13	x)×wτ	x)×wτ	PROPN
ejpam-5835	95	14	(	(	PUNCT
ejpam-5835	95	15	x	x	X
ejpam-5835	95	16	)	)	PUNCT
ejpam-5835	96	1	|	|	ADV
ejpam-5835	96	2	sa	sa	ADP
ejpam-5835	96	3	=	=	SYM
ejpam-5835	96	4	ta	ta	PART
ejpam-5835	96	5	}	}	PUNCT
ejpam-5835	96	6	be	be	AUX
ejpam-5835	96	7	the	the	DET
ejpam-5835	96	8	set	set	NOUN
ejpam-5835	96	9	of	of	ADP
ejpam-5835	96	10	all	all	DET
ejpam-5835	96	11	identities	identity	NOUN
ejpam-5835	96	12	satsified	satsifie	VERB
ejpam-5835	96	13	in	in	ADP
ejpam-5835	96	14	a.	a.	NOUN
ejpam-5835	96	15	the	the	DET
ejpam-5835	96	16	multisorted	multisorte	VERB
ejpam-5835	96	17	algebra	algebra	NOUN
ejpam-5835	96	18	clonea	clonea	NOUN
ejpam-5835	96	19	=	=	PUNCT
ejpam-5835	96	20	(	(	PUNCT
ejpam-5835	96	21	(	(	PUNCT
ejpam-5835	96	22	wτ	wτ	INTJ
ejpam-5835	96	23	(	(	PUNCT
ejpam-5835	96	24	xn	xn	PROPN
ejpam-5835	96	25	)	)	PUNCT
ejpam-5835	96	26	a)n∈n	a)n∈n	PROPN
ejpam-5835	96	27	,	,	PUNCT
ejpam-5835	96	28	(	(	PUNCT
ejpam-5835	96	29	on	on	ADP
ejpam-5835	96	30	,	,	PUNCT
ejpam-5835	96	31	a	a	DET
ejpam-5835	96	32	m	m	NOUN
ejpam-5835	96	33	)	)	PUNCT
ejpam-5835	96	34	n	n	CCONJ
ejpam-5835	96	35	,	,	PUNCT
ejpam-5835	96	36	m∈n	m∈n	NOUN
ejpam-5835	96	37	,	,	PUNCT
ejpam-5835	96	38	(	(	PUNCT
ejpam-5835	96	39	pr	pr	NOUN
ejpam-5835	96	40	n	n	CCONJ
ejpam-5835	96	41	,	,	PUNCT
ejpam-5835	96	42	a	a	DET
ejpam-5835	96	43	i	i	NOUN
ejpam-5835	96	44	)	)	PUNCT
ejpam-5835	96	45	i≤n	i≤n	PROPN
ejpam-5835	96	46	,	,	PUNCT
ejpam-5835	96	47	n∈n	n∈n	NOUN
ejpam-5835	96	48	)	)	PUNCT
ejpam-5835	96	49	is	be	AUX
ejpam-5835	96	50	constructed	construct	VERB
ejpam-5835	96	51	.	.	PUNCT
ejpam-5835	97	1	another	another	DET
ejpam-5835	97	2	example	example	NOUN
ejpam-5835	97	3	is	be	AUX
ejpam-5835	97	4	the	the	DET
ejpam-5835	97	5	quotient	quotient	NOUN
ejpam-5835	97	6	algebra	algebra	NOUN
ejpam-5835	97	7	clone(v	clone(v	NOUN
ejpam-5835	97	8	)	)	PUNCT
ejpam-5835	98	1	=	=	SYM
ejpam-5835	98	2	clone(τ)/id(v	clone(τ)/id(v	PROPN
ejpam-5835	98	3	)	)	PUNCT
ejpam-5835	98	4	where	where	SCONJ
ejpam-5835	98	5	id(v	id(v	PUNCT
ejpam-5835	98	6	)	)	PUNCT
ejpam-5835	98	7	is	be	AUX
ejpam-5835	98	8	a	a	DET
ejpam-5835	98	9	congruence	congruence	NOUN
ejpam-5835	98	10	in	in	ADP
ejpam-5835	98	11	the	the	DET
ejpam-5835	98	12	form	form	NOUN
ejpam-5835	98	13	of	of	ADP
ejpam-5835	98	14	the	the	DET
ejpam-5835	98	15	multisorted	multisorte	VERB
ejpam-5835	98	16	set	set	NOUN
ejpam-5835	98	17	(	(	PUNCT
ejpam-5835	98	18	idn(v	idn(v	INTJ
ejpam-5835	98	19	)	)	PUNCT
ejpam-5835	98	20	)	)	PUNCT
ejpam-5835	98	21	n∈n	n∈n	NOUN
ejpam-5835	98	22	of	of	ADP
ejpam-5835	98	23	all	all	DET
ejpam-5835	98	24	n	n	CCONJ
ejpam-5835	98	25	-	-	PUNCT
ejpam-5835	98	26	ary	ary	PROPN
ejpam-5835	98	27	identities	identity	NOUN
ejpam-5835	98	28	s	s	PROPN
ejpam-5835	98	29	≈	≈	PROPN
ejpam-5835	98	30	t	t	PROPN
ejpam-5835	98	31	satisfied	satisfy	VERB
ejpam-5835	98	32	in	in	ADP
ejpam-5835	98	33	a	a	DET
ejpam-5835	98	34	variety	variety	NOUN
ejpam-5835	98	35	v	v	NOUN
ejpam-5835	98	36	of	of	ADP
ejpam-5835	98	37	algebras	algebra	NOUN
ejpam-5835	98	38	of	of	ADP
ejpam-5835	98	39	type	type	NOUN
ejpam-5835	98	40	τ	τ	PROPN
ejpam-5835	98	41	.	.	PUNCT
ejpam-5835	99	1	recall	recall	PROPN
ejpam-5835	99	2	from	from	ADP
ejpam-5835	99	3	[	[	X
ejpam-5835	99	4	3	3	X
ejpam-5835	99	5	]	]	PUNCT
ejpam-5835	99	6	that	that	SCONJ
ejpam-5835	99	7	a	a	DET
ejpam-5835	99	8	mapping	mapping	NOUN
ejpam-5835	99	9	σ	σ	NOUN
ejpam-5835	99	10	:	:	PUNCT
ejpam-5835	99	11	{	{	PUNCT
ejpam-5835	99	12	fi	fi	NOUN
ejpam-5835	99	13	|	|	INTJ
ejpam-5835	99	14	i	i	PRON
ejpam-5835	99	15	∈	∈	VERB
ejpam-5835	100	1	i	i	PRON
ejpam-5835	100	2	}	}	PUNCT
ejpam-5835	100	3	→	→	SYM
ejpam-5835	100	4	wτ	wτ	X
ejpam-5835	100	5	(	(	PUNCT
ejpam-5835	100	6	x	x	NOUN
ejpam-5835	100	7	)	)	PUNCT
ejpam-5835	100	8	such	such	ADJ
ejpam-5835	100	9	that	that	PRON
ejpam-5835	100	10	for	for	ADP
ejpam-5835	100	11	each	each	DET
ejpam-5835	100	12	i	i	PRON
ejpam-5835	100	13	∈	∈	PROPN
ejpam-5835	100	14	i	i	PRON
ejpam-5835	100	15	,	,	PUNCT
ejpam-5835	100	16	σ(fi	σ(fi	PROPN
ejpam-5835	100	17	)	)	PUNCT
ejpam-5835	100	18	∈	∈	PROPN
ejpam-5835	100	19	wτ	wτ	NOUN
ejpam-5835	100	20	(	(	PUNCT
ejpam-5835	100	21	xni	xni	PROPN
ejpam-5835	100	22	)	)	PUNCT
ejpam-5835	100	23	is	be	AUX
ejpam-5835	100	24	called	call	VERB
ejpam-5835	100	25	a	a	DET
ejpam-5835	100	26	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	100	27	of	of	ADP
ejpam-5835	100	28	type	type	NOUN
ejpam-5835	100	29	τ	τ	PROPN
ejpam-5835	100	30	.	.	PUNCT
ejpam-5835	101	1	moreover	moreover	ADV
ejpam-5835	101	2	,	,	PUNCT
ejpam-5835	101	3	each	each	DET
ejpam-5835	101	4	σ	σ	NOUN
ejpam-5835	101	5	:	:	PUNCT
ejpam-5835	101	6	{	{	PUNCT
ejpam-5835	101	7	fi	fi	NOUN
ejpam-5835	101	8	|	|	INTJ
ejpam-5835	101	9	i	i	PRON
ejpam-5835	101	10	∈	∈	VERB
ejpam-5835	101	11	i	i	PRON
ejpam-5835	101	12	}	}	PUNCT
ejpam-5835	101	13	→	→	SYM
ejpam-5835	101	14	wτ	wτ	X
ejpam-5835	101	15	(	(	PUNCT
ejpam-5835	101	16	x	x	X
ejpam-5835	101	17	)	)	PUNCT
ejpam-5835	101	18	can	can	AUX
ejpam-5835	101	19	be	be	AUX
ejpam-5835	101	20	uniquely	uniquely	ADV
ejpam-5835	101	21	extended	extend	VERB
ejpam-5835	101	22	to	to	ADP
ejpam-5835	101	23	the	the	DET
ejpam-5835	101	24	mapping	mapping	NOUN
ejpam-5835	101	25	σ̂	σ̂	X
ejpam-5835	101	26	:	:	PUNCT
ejpam-5835	101	27	wτ	wτ	INTJ
ejpam-5835	101	28	(	(	PUNCT
ejpam-5835	101	29	x	x	NOUN
ejpam-5835	101	30	)	)	PUNCT
ejpam-5835	101	31	→	→	SYM
ejpam-5835	101	32	wτ	wτ	X
ejpam-5835	101	33	(	(	PUNCT
ejpam-5835	101	34	x	x	NOUN
ejpam-5835	101	35	)	)	PUNCT
ejpam-5835	101	36	defined	define	VERB
ejpam-5835	101	37	by	by	ADP
ejpam-5835	101	38	:	:	PUNCT
ejpam-5835	101	39	t.	t.	PROPN
ejpam-5835	101	40	kumduang	kumduang	PROPN
ejpam-5835	101	41	,	,	PUNCT
ejpam-5835	101	42	k.	k.	PROPN
ejpam-5835	101	43	wattanatripop	wattanatripop	PROPN
ejpam-5835	101	44	/	/	SYM
ejpam-5835	101	45	eur	eur	PROPN
ejpam-5835	101	46	.	.	PUNCT
ejpam-5835	102	1	j.	j.	PROPN
ejpam-5835	102	2	pure	pure	PROPN
ejpam-5835	102	3	appl	appl	PROPN
ejpam-5835	102	4	.	.	PROPN
ejpam-5835	102	5	math	math	PROPN
ejpam-5835	102	6	,	,	PUNCT
ejpam-5835	102	7	18	18	NUM
ejpam-5835	102	8	(	(	PUNCT
ejpam-5835	102	9	2	2	NUM
ejpam-5835	102	10	)	)	PUNCT
ejpam-5835	102	11	(	(	PUNCT
ejpam-5835	102	12	2025	2025	NUM
ejpam-5835	102	13	)	)	PUNCT
ejpam-5835	102	14	,	,	PUNCT
ejpam-5835	102	15	5835	5835	NUM
ejpam-5835	102	16	4	4	NUM
ejpam-5835	102	17	of	of	ADP
ejpam-5835	102	18	16	16	NUM
ejpam-5835	102	19	(	(	PUNCT
ejpam-5835	102	20	1	1	NUM
ejpam-5835	102	21	)	)	PUNCT
ejpam-5835	102	22	σ̂[xi	σ̂[xi	NOUN
ejpam-5835	102	23	]	]	X
ejpam-5835	102	24	=	=	SYM
ejpam-5835	102	25	xi	xi	PROPN
ejpam-5835	102	26	for	for	ADP
ejpam-5835	102	27	every	every	DET
ejpam-5835	102	28	xi	xi	ADP
ejpam-5835	102	29	∈	∈	PROPN
ejpam-5835	102	30	x	x	X
ejpam-5835	102	31	,	,	PUNCT
ejpam-5835	102	32	(	(	PUNCT
ejpam-5835	102	33	2	2	X
ejpam-5835	102	34	)	)	PUNCT
ejpam-5835	102	35	σ̂[fi(t1	σ̂[fi(t1	NOUN
ejpam-5835	102	36	,	,	PUNCT
ejpam-5835	102	37	.	.	PUNCT
ejpam-5835	102	38	.	.	PUNCT
ejpam-5835	103	1	.	.	PUNCT
ejpam-5835	104	1	,	,	PUNCT
ejpam-5835	104	2	tni	tni	NOUN
ejpam-5835	104	3	)	)	PUNCT
ejpam-5835	104	4	]	]	PUNCT
ejpam-5835	105	1	=	=	PUNCT
ejpam-5835	105	2	sni	sni	PROPN
ejpam-5835	105	3	m	m	VERB
ejpam-5835	105	4	(	(	PUNCT
ejpam-5835	105	5	σ(fi	σ(fi	PROPN
ejpam-5835	105	6	)	)	PUNCT
ejpam-5835	105	7	,	,	PUNCT
ejpam-5835	105	8	σ̂[t1	σ̂[t1	PROPN
ejpam-5835	105	9	]	]	PUNCT
ejpam-5835	105	10	,	,	PUNCT
ejpam-5835	105	11	.	.	PUNCT
ejpam-5835	105	12	.	.	PUNCT
ejpam-5835	105	13	.	.	PUNCT
ejpam-5835	106	1	,	,	PUNCT
ejpam-5835	106	2	σ̂[tni	σ̂[tni	PROPN
ejpam-5835	106	3	]	]	PUNCT
ejpam-5835	106	4	)	)	PUNCT
ejpam-5835	106	5	.	.	PUNCT
ejpam-5835	107	1	the	the	DET
ejpam-5835	107	2	sethyp(τ	sethyp(τ	PROPN
ejpam-5835	107	3	)	)	PUNCT
ejpam-5835	107	4	of	of	ADP
ejpam-5835	107	5	all	all	DET
ejpam-5835	107	6	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	107	7	of	of	ADP
ejpam-5835	107	8	type	type	NOUN
ejpam-5835	107	9	τ	τ	PROPN
ejpam-5835	107	10	forms	form	VERB
ejpam-5835	107	11	a	a	DET
ejpam-5835	107	12	monoid	monoid	NOUN
ejpam-5835	107	13	under	under	ADP
ejpam-5835	107	14	the	the	DET
ejpam-5835	107	15	associative	associative	ADJ
ejpam-5835	107	16	binary	binary	ADJ
ejpam-5835	107	17	operation	operation	NOUN
ejpam-5835	107	18	defined	define	VERB
ejpam-5835	107	19	by	by	ADP
ejpam-5835	107	20	:	:	PUNCT
ejpam-5835	107	21	σ	σ	PROPN
ejpam-5835	107	22	◦	◦	NOUN
ejpam-5835	107	23	h	h	NOUN
ejpam-5835	107	24	α	α	NOUN
ejpam-5835	107	25	=	=	X
ejpam-5835	107	26	σ̂	σ̂	X
ejpam-5835	107	27	◦	◦	NOUN
ejpam-5835	107	28	α	α	NOUN
ejpam-5835	107	29	for	for	ADP
ejpam-5835	107	30	all	all	DET
ejpam-5835	107	31	σ	σ	PROPN
ejpam-5835	107	32	,	,	PUNCT
ejpam-5835	107	33	α	α	PROPN
ejpam-5835	107	34	∈	∈	PROPN
ejpam-5835	107	35	hyp(τ	hyp(τ	PROPN
ejpam-5835	107	36	)	)	PUNCT
ejpam-5835	107	37	and	and	CCONJ
ejpam-5835	107	38	the	the	DET
ejpam-5835	107	39	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	107	40	σid	σid	ADJ
ejpam-5835	107	41	:	:	PUNCT
ejpam-5835	107	42	{	{	PUNCT
ejpam-5835	107	43	fi	fi	NOUN
ejpam-5835	107	44	|	|	INTJ
ejpam-5835	107	45	i	i	PRON
ejpam-5835	107	46	∈	∈	VERB
ejpam-5835	107	47	i	i	PRON
ejpam-5835	107	48	}	}	PUNCT
ejpam-5835	107	49	→	→	SYM
ejpam-5835	107	50	wτ	wτ	X
ejpam-5835	107	51	(	(	PUNCT
ejpam-5835	107	52	x	x	NOUN
ejpam-5835	107	53	)	)	PUNCT
ejpam-5835	107	54	defined	define	VERB
ejpam-5835	107	55	by	by	ADP
ejpam-5835	107	56	σid(fi	σid(fi	NOUN
ejpam-5835	107	57	)	)	PUNCT
ejpam-5835	107	58	=	=	SYM
ejpam-5835	107	59	fi(x1	fi(x1	PROPN
ejpam-5835	107	60	,	,	PUNCT
ejpam-5835	107	61	.	.	PUNCT
ejpam-5835	107	62	.	.	PUNCT
ejpam-5835	108	1	.	.	PUNCT
ejpam-5835	109	1	,	,	PUNCT
ejpam-5835	109	2	xni	xni	PROPN
ejpam-5835	109	3	)	)	PUNCT
ejpam-5835	110	1	for	for	ADP
ejpam-5835	110	2	all	all	PRON
ejpam-5835	110	3	i	i	PRON
ejpam-5835	110	4	∈	∈	PROPN
ejpam-5835	110	5	i	i	PRON
ejpam-5835	110	6	which	which	PRON
ejpam-5835	110	7	acts	act	VERB
ejpam-5835	110	8	as	as	ADP
ejpam-5835	110	9	an	an	DET
ejpam-5835	110	10	identity	identity	NOUN
ejpam-5835	110	11	element	element	NOUN
ejpam-5835	110	12	.	.	PUNCT
ejpam-5835	111	1	in	in	ADP
ejpam-5835	111	2	fact	fact	NOUN
ejpam-5835	111	3	,	,	PUNCT
ejpam-5835	111	4	each	each	DET
ejpam-5835	111	5	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	111	6	can	can	AUX
ejpam-5835	111	7	be	be	AUX
ejpam-5835	111	8	considered	consider	VERB
ejpam-5835	111	9	as	as	ADP
ejpam-5835	111	10	a	a	DET
ejpam-5835	111	11	multisorted	multisorte	VERB
ejpam-5835	111	12	mapping	mapping	NOUN
ejpam-5835	111	13	.	.	PUNCT
ejpam-5835	112	1	for	for	ADP
ejpam-5835	112	2	n	n	PRON
ejpam-5835	112	3	∈	∈	PROPN
ejpam-5835	112	4	n	n	CCONJ
ejpam-5835	112	5	,	,	PUNCT
ejpam-5835	112	6	let	let	VERB
ejpam-5835	112	7	in	in	ADP
ejpam-5835	112	8	⊆	⊆	NUM
ejpam-5835	112	9	i	i	PRON
ejpam-5835	112	10	be	be	VERB
ejpam-5835	112	11	the	the	DET
ejpam-5835	112	12	set	set	NOUN
ejpam-5835	112	13	of	of	ADP
ejpam-5835	112	14	all	all	DET
ejpam-5835	112	15	indexes	index	NOUN
ejpam-5835	112	16	such	such	ADJ
ejpam-5835	112	17	that	that	SCONJ
ejpam-5835	112	18	fj	fj	PROPN
ejpam-5835	112	19	with	with	ADP
ejpam-5835	112	20	j	j	PROPN
ejpam-5835	112	21	∈	∈	PROPN
ejpam-5835	112	22	in	in	ADP
ejpam-5835	112	23	is	be	AUX
ejpam-5835	112	24	an	an	DET
ejpam-5835	112	25	n	n	CCONJ
ejpam-5835	112	26	-	-	PUNCT
ejpam-5835	112	27	ary	ary	NOUN
ejpam-5835	112	28	.	.	PUNCT
ejpam-5835	113	1	let	let	VERB
ejpam-5835	113	2	fn	fn	PRON
ejpam-5835	113	3	τ	τ	PROPN
ejpam-5835	113	4	=	=	PUNCT
ejpam-5835	113	5	{	{	PUNCT
ejpam-5835	113	6	fj	fj	INTJ
ejpam-5835	113	7	|	|	ADV
ejpam-5835	113	8	j	j	PROPN
ejpam-5835	113	9	∈	∈	PROPN
ejpam-5835	113	10	in	in	ADP
ejpam-5835	113	11	}	}	PUNCT
ejpam-5835	113	12	.	.	PUNCT
ejpam-5835	114	1	thus	thus	ADV
ejpam-5835	114	2	,	,	PUNCT
ejpam-5835	114	3	a	a	DET
ejpam-5835	114	4	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	114	5	is	be	AUX
ejpam-5835	114	6	the	the	DET
ejpam-5835	114	7	sequence	sequence	NOUN
ejpam-5835	114	8	(	(	PUNCT
ejpam-5835	114	9	σn)n∈n	σn)n∈n	X
ejpam-5835	114	10	where	where	SCONJ
ejpam-5835	114	11	σ	σ	X
ejpam-5835	114	12	:	:	PUNCT
ejpam-5835	114	13	fn	fn	PROPN
ejpam-5835	114	14	τ	τ	PROPN
ejpam-5835	114	15	→	→	SYM
ejpam-5835	114	16	wτ	wτ	PROPN
ejpam-5835	114	17	(	(	PUNCT
ejpam-5835	114	18	xn	xn	PROPN
ejpam-5835	114	19	)	)	PUNCT
ejpam-5835	114	20	.	.	PUNCT
ejpam-5835	115	1	let	let	VERB
ejpam-5835	115	2	(	(	PUNCT
ejpam-5835	115	3	hypn(τ))n∈n	hypn(τ))n∈n	X
ejpam-5835	115	4	be	be	AUX
ejpam-5835	115	5	the	the	DET
ejpam-5835	115	6	multisorted	multisorte	VERB
ejpam-5835	115	7	set	set	NOUN
ejpam-5835	115	8	of	of	ADP
ejpam-5835	115	9	all	all	DET
ejpam-5835	115	10	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	115	11	of	of	ADP
ejpam-5835	115	12	type	type	NOUN
ejpam-5835	115	13	τ	τ	PROPN
ejpam-5835	115	14	.	.	PUNCT
ejpam-5835	116	1	by	by	ADP
ejpam-5835	116	2	the	the	DET
ejpam-5835	116	3	definition	definition	NOUN
ejpam-5835	116	4	σ̂n[xi	σ̂n[xi	NOUN
ejpam-5835	116	5	]	]	X
ejpam-5835	116	6	=	=	SYM
ejpam-5835	116	7	xi	xi	PROPN
ejpam-5835	116	8	and	and	CCONJ
ejpam-5835	116	9	σ̂n[fi(t1	σ̂n[fi(t1	NOUN
ejpam-5835	116	10	,	,	PUNCT
ejpam-5835	116	11	.	.	PUNCT
ejpam-5835	116	12	.	.	PUNCT
ejpam-5835	116	13	.	.	PUNCT
ejpam-5835	117	1	,	,	PUNCT
ejpam-5835	117	2	tn	tn	PROPN
ejpam-5835	117	3	)	)	PUNCT
ejpam-5835	117	4	]	]	PUNCT
ejpam-5835	118	1	=	=	PUNCT
ejpam-5835	118	2	sn	sn	PROPN
ejpam-5835	118	3	n(σn(fi	n(σn(fi	PROPN
ejpam-5835	118	4	)	)	PUNCT
ejpam-5835	118	5	,	,	PUNCT
ejpam-5835	118	6	σ̂n[t1	σ̂n[t1	PROPN
ejpam-5835	118	7	]	]	PUNCT
ejpam-5835	118	8	,	,	PUNCT
ejpam-5835	118	9	.	.	PUNCT
ejpam-5835	118	10	.	.	PUNCT
ejpam-5835	118	11	.	.	PUNCT
ejpam-5835	119	1	,	,	PUNCT
ejpam-5835	119	2	σ̂n[tn	σ̂n[tn	X
ejpam-5835	119	3	]	]	X
ejpam-5835	119	4	)	)	PUNCT
ejpam-5835	119	5	we	we	PRON
ejpam-5835	119	6	obtain	obtain	VERB
ejpam-5835	119	7	the	the	DET
ejpam-5835	119	8	extension	extension	NOUN
ejpam-5835	119	9	of	of	ADP
ejpam-5835	119	10	each	each	DET
ejpam-5835	119	11	σn	σn	NOUN
ejpam-5835	119	12	in	in	ADP
ejpam-5835	119	13	(	(	PUNCT
ejpam-5835	119	14	σn)n∈n	σn)n∈n	PROPN
ejpam-5835	119	15	.	.	PUNCT
ejpam-5835	120	1	recently	recently	ADV
ejpam-5835	120	2	,	,	PUNCT
ejpam-5835	120	3	in	in	ADP
ejpam-5835	120	4	[	[	PUNCT
ejpam-5835	120	5	17	17	NUM
ejpam-5835	120	6	]	]	PUNCT
ejpam-5835	120	7	,	,	PUNCT
ejpam-5835	120	8	the	the	DET
ejpam-5835	120	9	multisorted	multisorte	VERB
ejpam-5835	120	10	set	set	NOUN
ejpam-5835	120	11	(	(	PUNCT
ejpam-5835	120	12	w	w	PROPN
ejpam-5835	120	13	fv	fv	X
ejpam-5835	120	14	τ	τ	PROPN
ejpam-5835	120	15	(	(	PUNCT
ejpam-5835	120	16	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	120	17	of	of	ADP
ejpam-5835	120	18	terms	term	NOUN
ejpam-5835	120	19	of	of	ADP
ejpam-5835	120	20	a	a	DET
ejpam-5835	120	21	fixed	fix	VERB
ejpam-5835	120	22	variable	variable	NOUN
ejpam-5835	120	23	is	be	AUX
ejpam-5835	120	24	introduced	introduce	VERB
ejpam-5835	120	25	.	.	PUNCT
ejpam-5835	121	1	for	for	ADP
ejpam-5835	121	2	instance	instance	NOUN
ejpam-5835	121	3	,	,	PUNCT
ejpam-5835	121	4	let	let	VERB
ejpam-5835	121	5	us	we	PRON
ejpam-5835	121	6	consider	consider	VERB
ejpam-5835	121	7	the	the	DET
ejpam-5835	121	8	type	type	NOUN
ejpam-5835	121	9	τ	τ	PROPN
ejpam-5835	121	10	=	=	SYM
ejpam-5835	121	11	(	(	PUNCT
ejpam-5835	121	12	2	2	NUM
ejpam-5835	121	13	)	)	PUNCT
ejpam-5835	121	14	with	with	ADP
ejpam-5835	121	15	a	a	DET
ejpam-5835	121	16	binary	binary	ADJ
ejpam-5835	121	17	operation	operation	NOUN
ejpam-5835	121	18	symbol	symbol	NOUN
ejpam-5835	121	19	f	f	PROPN
ejpam-5835	121	20	.	.	PUNCT
ejpam-5835	122	1	then	then	ADV
ejpam-5835	122	2	,	,	PUNCT
ejpam-5835	122	3	x1	x1	PROPN
ejpam-5835	122	4	,	,	PUNCT
ejpam-5835	122	5	x2	x2	PROPN
ejpam-5835	122	6	,	,	PUNCT
ejpam-5835	122	7	f(x1	f(x1	NOUN
ejpam-5835	122	8	,	,	PUNCT
ejpam-5835	122	9	x1	x1	PROPN
ejpam-5835	122	10	)	)	PUNCT
ejpam-5835	122	11	,	,	PUNCT
ejpam-5835	122	12	f(x2	f(x2	NOUN
ejpam-5835	122	13	,	,	PUNCT
ejpam-5835	122	14	x2	x2	PROPN
ejpam-5835	122	15	)	)	PUNCT
ejpam-5835	122	16	,	,	PUNCT
ejpam-5835	122	17	f(f(x1	f(f(x1	PROPN
ejpam-5835	122	18	,	,	PUNCT
ejpam-5835	122	19	x1	x1	PROPN
ejpam-5835	122	20	)	)	PUNCT
ejpam-5835	122	21	,	,	PUNCT
ejpam-5835	122	22	x1	x1	PROPN
ejpam-5835	122	23	)	)	PUNCT
ejpam-5835	122	24	,	,	PUNCT
ejpam-5835	122	25	f(x2	f(x2	NOUN
ejpam-5835	122	26	,	,	PUNCT
ejpam-5835	122	27	f(x2	f(x2	NOUN
ejpam-5835	122	28	,	,	PUNCT
ejpam-5835	122	29	x2	x2	PROPN
ejpam-5835	122	30	)	)	PUNCT
ejpam-5835	122	31	)	)	PUNCT
ejpam-5835	123	1	∈	∈	PROPN
ejpam-5835	123	2	w	w	PROPN
ejpam-5835	123	3	fv	fv	PROPN
ejpam-5835	123	4	τ	τ	PROPN
ejpam-5835	123	5	(	(	PUNCT
ejpam-5835	123	6	x2	x2	PROPN
ejpam-5835	123	7	)	)	PUNCT
ejpam-5835	123	8	,	,	PUNCT
ejpam-5835	123	9	x1	x1	PROPN
ejpam-5835	123	10	,	,	PUNCT
ejpam-5835	123	11	x2	x2	PROPN
ejpam-5835	123	12	,	,	PUNCT
ejpam-5835	123	13	x3	x3	ADJ
ejpam-5835	123	14	,	,	PUNCT
ejpam-5835	123	15	f(x1	f(x1	NOUN
ejpam-5835	123	16	,	,	PUNCT
ejpam-5835	123	17	x1	x1	PROPN
ejpam-5835	123	18	)	)	PUNCT
ejpam-5835	123	19	,	,	PUNCT
ejpam-5835	123	20	f(x3	f(x3	ADJ
ejpam-5835	123	21	,	,	PUNCT
ejpam-5835	123	22	x3	x3	ADJ
ejpam-5835	123	23	)	)	PUNCT
ejpam-5835	123	24	,	,	PUNCT
ejpam-5835	123	25	f(f(x3	f(f(x3	PROPN
ejpam-5835	123	26	,	,	PUNCT
ejpam-5835	123	27	x3	x3	ADJ
ejpam-5835	123	28	)	)	PUNCT
ejpam-5835	123	29	,	,	PUNCT
ejpam-5835	123	30	f(x3	f(x3	ADJ
ejpam-5835	123	31	,	,	PUNCT
ejpam-5835	123	32	x3	x3	ADJ
ejpam-5835	123	33	)	)	PUNCT
ejpam-5835	123	34	)	)	PUNCT
ejpam-5835	124	1	∈	∈	PROPN
ejpam-5835	124	2	w	w	PROPN
ejpam-5835	124	3	fv	fv	PROPN
ejpam-5835	124	4	τ	τ	PROPN
ejpam-5835	124	5	(	(	PUNCT
ejpam-5835	124	6	x3	x3	ADJ
ejpam-5835	124	7	)	)	PUNCT
ejpam-5835	124	8	.	.	PUNCT
ejpam-5835	125	1	conversely	conversely	ADV
ejpam-5835	125	2	,	,	PUNCT
ejpam-5835	125	3	f(x1	f(x1	ADJ
ejpam-5835	125	4	,	,	PUNCT
ejpam-5835	125	5	x2	x2	PROPN
ejpam-5835	125	6	)	)	PUNCT
ejpam-5835	125	7	,	,	PUNCT
ejpam-5835	125	8	f(x3	f(x3	ADJ
ejpam-5835	125	9	,	,	PUNCT
ejpam-5835	125	10	x1	x1	PROPN
ejpam-5835	125	11	)	)	PUNCT
ejpam-5835	125	12	,	,	PUNCT
ejpam-5835	125	13	f(x2	f(x2	NOUN
ejpam-5835	125	14	,	,	PUNCT
ejpam-5835	125	15	f(x1	f(x1	NOUN
ejpam-5835	125	16	,	,	PUNCT
ejpam-5835	125	17	x2	x2	PROPN
ejpam-5835	125	18	)	)	PUNCT
ejpam-5835	125	19	)	)	PUNCT
ejpam-5835	126	1	∈	∈	PROPN
ejpam-5835	126	2	wτ	wτ	NOUN
ejpam-5835	126	3	(	(	PUNCT
ejpam-5835	126	4	x3	x3	ADJ
ejpam-5835	126	5	)	)	PUNCT
ejpam-5835	126	6	\w	\w	ADJ
ejpam-5835	126	7	fv	fv	PROPN
ejpam-5835	126	8	τ	τ	PROPN
ejpam-5835	126	9	(	(	PUNCT
ejpam-5835	126	10	x3	x3	ADJ
ejpam-5835	126	11	)	)	PUNCT
ejpam-5835	126	12	.	.	PUNCT
ejpam-5835	127	1	by	by	ADP
ejpam-5835	127	2	the	the	DET
ejpam-5835	127	3	formal	formal	ADJ
ejpam-5835	127	4	definition	definition	NOUN
ejpam-5835	127	5	,	,	PUNCT
ejpam-5835	127	6	if	if	SCONJ
ejpam-5835	127	7	t	t	PROPN
ejpam-5835	127	8	is	be	AUX
ejpam-5835	127	9	a	a	DET
ejpam-5835	127	10	term	term	NOUN
ejpam-5835	127	11	,	,	PUNCT
ejpam-5835	127	12	then	then	ADV
ejpam-5835	127	13	the	the	DET
ejpam-5835	127	14	set	set	ADJ
ejpam-5835	127	15	var(t	var(t	NOUN
ejpam-5835	127	16	)	)	PUNCT
ejpam-5835	127	17	consisting	consist	VERB
ejpam-5835	127	18	of	of	ADP
ejpam-5835	127	19	all	all	DET
ejpam-5835	127	20	variables	variable	NOUN
ejpam-5835	127	21	of	of	ADP
ejpam-5835	127	22	x	x	PRON
ejpam-5835	127	23	that	that	PRON
ejpam-5835	127	24	appear	appear	VERB
ejpam-5835	127	25	in	in	ADP
ejpam-5835	127	26	t	t	PROPN
ejpam-5835	127	27	is	be	AUX
ejpam-5835	127	28	called	call	VERB
ejpam-5835	127	29	the	the	DET
ejpam-5835	127	30	set	set	NOUN
ejpam-5835	127	31	of	of	ADP
ejpam-5835	127	32	all	all	DET
ejpam-5835	127	33	variables	variable	NOUN
ejpam-5835	127	34	for	for	ADP
ejpam-5835	127	35	t.	t.	PROPN
ejpam-5835	127	36	thus	thus	ADV
ejpam-5835	127	37	,	,	PUNCT
ejpam-5835	127	38	an	an	DET
ejpam-5835	127	39	n	n	CCONJ
ejpam-5835	127	40	-	-	PUNCT
ejpam-5835	127	41	ary	ary	NOUN
ejpam-5835	127	42	term	term	NOUN
ejpam-5835	127	43	of	of	ADP
ejpam-5835	127	44	a	a	DET
ejpam-5835	127	45	fixed	fix	VERB
ejpam-5835	127	46	variable	variable	NOUN
ejpam-5835	127	47	of	of	ADP
ejpam-5835	127	48	type	type	NOUN
ejpam-5835	127	49	τ	τ	PROPN
ejpam-5835	127	50	is	be	AUX
ejpam-5835	127	51	inductively	inductively	ADV
ejpam-5835	127	52	defined	define	VERB
ejpam-5835	127	53	by	by	ADP
ejpam-5835	127	54	:	:	PUNCT
ejpam-5835	127	55	(	(	PUNCT
ejpam-5835	127	56	1	1	X
ejpam-5835	127	57	)	)	PUNCT
ejpam-5835	127	58	every	every	DET
ejpam-5835	127	59	xi	xi	PROPN
ejpam-5835	127	60	∈	∈	PROPN
ejpam-5835	127	61	xn	xn	PROPN
ejpam-5835	127	62	is	be	AUX
ejpam-5835	127	63	an	an	DET
ejpam-5835	127	64	n	n	CCONJ
ejpam-5835	127	65	-	-	PUNCT
ejpam-5835	127	66	ary	ary	NOUN
ejpam-5835	127	67	term	term	NOUN
ejpam-5835	127	68	of	of	ADP
ejpam-5835	127	69	a	a	DET
ejpam-5835	127	70	fixed	fix	VERB
ejpam-5835	127	71	variable	variable	NOUN
ejpam-5835	127	72	of	of	ADP
ejpam-5835	127	73	type	type	NOUN
ejpam-5835	127	74	τ	τ	PROPN
ejpam-5835	127	75	,	,	PUNCT
ejpam-5835	127	76	(	(	PUNCT
ejpam-5835	127	77	2	2	X
ejpam-5835	127	78	)	)	PUNCT
ejpam-5835	127	79	if	if	SCONJ
ejpam-5835	127	80	t1	t1	PROPN
ejpam-5835	127	81	,	,	PUNCT
ejpam-5835	127	82	.	.	PUNCT
ejpam-5835	127	83	.	.	PUNCT
ejpam-5835	127	84	.	.	PUNCT
ejpam-5835	128	1	,	,	PUNCT
ejpam-5835	128	2	tni	tni	NOUN
ejpam-5835	128	3	are	be	AUX
ejpam-5835	128	4	n	n	PRON
ejpam-5835	128	5	-	-	PUNCT
ejpam-5835	128	6	ary	ary	NOUN
ejpam-5835	128	7	terms	term	NOUN
ejpam-5835	128	8	of	of	ADP
ejpam-5835	128	9	a	a	DET
ejpam-5835	128	10	fixed	fix	VERB
ejpam-5835	128	11	variable	variable	NOUN
ejpam-5835	128	12	of	of	ADP
ejpam-5835	128	13	type	type	NOUN
ejpam-5835	128	14	τ	τ	PROPN
ejpam-5835	128	15	,	,	PUNCT
ejpam-5835	128	16	and	and	CCONJ
ejpam-5835	128	17	if	if	SCONJ
ejpam-5835	128	18	var(tj	var(tj	ADJ
ejpam-5835	128	19	)	)	PUNCT
ejpam-5835	128	20	=	=	SYM
ejpam-5835	128	21	var(tk	var(tk	NOUN
ejpam-5835	128	22	)	)	PUNCT
ejpam-5835	128	23	for	for	ADP
ejpam-5835	128	24	all	all	DET
ejpam-5835	128	25	1	1	NUM
ejpam-5835	128	26	≤	≤	NUM
ejpam-5835	128	27	j	j	NOUN
ejpam-5835	128	28	<	<	X
ejpam-5835	128	29	k	k	PROPN
ejpam-5835	128	30	≤	≤	PROPN
ejpam-5835	128	31	ni	ni	PROPN
ejpam-5835	128	32	,	,	PUNCT
ejpam-5835	128	33	then	then	ADV
ejpam-5835	128	34	fi(t1	fi(t1	NOUN
ejpam-5835	128	35	,	,	PUNCT
ejpam-5835	128	36	.	.	PUNCT
ejpam-5835	128	37	.	.	PUNCT
ejpam-5835	129	1	.	.	PUNCT
ejpam-5835	130	1	,	,	PUNCT
ejpam-5835	130	2	tni	tni	NOUN
ejpam-5835	130	3	)	)	PUNCT
ejpam-5835	130	4	is	be	AUX
ejpam-5835	130	5	an	an	DET
ejpam-5835	130	6	n	n	CCONJ
ejpam-5835	130	7	-	-	PUNCT
ejpam-5835	130	8	ary	ary	NOUN
ejpam-5835	130	9	term	term	NOUN
ejpam-5835	130	10	of	of	ADP
ejpam-5835	130	11	a	a	DET
ejpam-5835	130	12	fixed	fix	VERB
ejpam-5835	130	13	variable	variable	NOUN
ejpam-5835	130	14	of	of	ADP
ejpam-5835	130	15	type	type	NOUN
ejpam-5835	130	16	τ	τ	PROPN
ejpam-5835	130	17	,	,	PUNCT
ejpam-5835	130	18	(	(	PUNCT
ejpam-5835	130	19	3	3	X
ejpam-5835	130	20	)	)	PUNCT
ejpam-5835	130	21	the	the	DET
ejpam-5835	130	22	set	set	NOUN
ejpam-5835	130	23	w	w	PROPN
ejpam-5835	130	24	fv	fv	PROPN
ejpam-5835	130	25	τ	τ	PROPN
ejpam-5835	130	26	(	(	PUNCT
ejpam-5835	130	27	xn	xn	PROPN
ejpam-5835	130	28	)	)	PUNCT
ejpam-5835	130	29	is	be	AUX
ejpam-5835	130	30	the	the	DET
ejpam-5835	130	31	smallest	small	ADJ
ejpam-5835	130	32	set	set	NOUN
ejpam-5835	130	33	which	which	PRON
ejpam-5835	130	34	is	be	AUX
ejpam-5835	130	35	closed	close	VERB
ejpam-5835	130	36	under	under	ADP
ejpam-5835	130	37	finite	finite	ADJ
ejpam-5835	130	38	application	application	NOUN
ejpam-5835	130	39	of	of	ADP
ejpam-5835	130	40	(	(	PUNCT
ejpam-5835	130	41	2	2	NUM
ejpam-5835	130	42	)	)	PUNCT
ejpam-5835	130	43	.	.	PUNCT
ejpam-5835	131	1	this	this	DET
ejpam-5835	131	2	concept	concept	NOUN
ejpam-5835	131	3	always	always	ADV
ejpam-5835	131	4	plays	play	VERB
ejpam-5835	131	5	a	a	DET
ejpam-5835	131	6	key	key	ADJ
ejpam-5835	131	7	role	role	NOUN
ejpam-5835	131	8	in	in	ADP
ejpam-5835	131	9	a	a	DET
ejpam-5835	131	10	study	study	NOUN
ejpam-5835	131	11	of	of	ADP
ejpam-5835	131	12	the	the	DET
ejpam-5835	131	13	variety	variety	NOUN
ejpam-5835	131	14	of	of	ADP
ejpam-5835	131	15	bands	band	NOUN
ejpam-5835	131	16	,	,	PUNCT
ejpam-5835	131	17	i.e.	i.e.	X
ejpam-5835	131	18	all	all	DET
ejpam-5835	131	19	algebras	algebra	NOUN
ejpam-5835	131	20	of	of	ADP
ejpam-5835	131	21	type	type	NOUN
ejpam-5835	131	22	(	(	PUNCT
ejpam-5835	131	23	2	2	NUM
ejpam-5835	131	24	)	)	PUNCT
ejpam-5835	131	25	satisfying	satisfy	VERB
ejpam-5835	131	26	f(x	f(x	PROPN
ejpam-5835	131	27	,	,	PUNCT
ejpam-5835	131	28	x	x	X
ejpam-5835	131	29	)	)	PUNCT
ejpam-5835	132	1	≈	≈	PROPN
ejpam-5835	132	2	x.	x.	NOUN
ejpam-5835	132	3	closed	close	VERB
ejpam-5835	132	4	identities	identity	NOUN
ejpam-5835	132	5	of	of	ADP
ejpam-5835	132	6	a	a	DET
ejpam-5835	132	7	fixed	fix	VERB
ejpam-5835	132	8	variable	variable	NOUN
ejpam-5835	132	9	and	and	CCONJ
ejpam-5835	132	10	closed	closed	ADJ
ejpam-5835	132	11	varieties	variety	NOUN
ejpam-5835	132	12	of	of	ADP
ejpam-5835	132	13	a	a	DET
ejpam-5835	132	14	fixed	fix	VERB
ejpam-5835	132	15	variable	variable	NOUN
ejpam-5835	132	16	are	be	AUX
ejpam-5835	132	17	also	also	ADV
ejpam-5835	132	18	investigated	investigate	VERB
ejpam-5835	132	19	based	base	VERB
ejpam-5835	132	20	on	on	ADP
ejpam-5835	132	21	multisorted	multisorte	VERB
ejpam-5835	132	22	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	132	23	of	of	ADP
ejpam-5835	132	24	a	a	DET
ejpam-5835	132	25	fixed	fix	VERB
ejpam-5835	132	26	variable	variable	NOUN
ejpam-5835	132	27	.	.	PUNCT
ejpam-5835	133	1	the	the	DET
ejpam-5835	133	2	main	main	ADJ
ejpam-5835	133	3	purpose	purpose	NOUN
ejpam-5835	133	4	of	of	ADP
ejpam-5835	133	5	this	this	DET
ejpam-5835	133	6	paper	paper	NOUN
ejpam-5835	133	7	is	be	AUX
ejpam-5835	133	8	to	to	PART
ejpam-5835	133	9	generalize	generalize	VERB
ejpam-5835	133	10	the	the	DET
ejpam-5835	133	11	multisorted	multisorte	VERB
ejpam-5835	133	12	set	set	NOUN
ejpam-5835	133	13	of	of	ADP
ejpam-5835	133	14	terms	term	NOUN
ejpam-5835	133	15	of	of	ADP
ejpam-5835	133	16	a	a	DET
ejpam-5835	133	17	fixed	fix	VERB
ejpam-5835	133	18	variable	variable	NOUN
ejpam-5835	133	19	by	by	ADP
ejpam-5835	133	20	naturally	naturally	ADV
ejpam-5835	133	21	reducing	reduce	VERB
ejpam-5835	133	22	certain	certain	ADJ
ejpam-5835	133	23	conditions	condition	NOUN
ejpam-5835	133	24	and	and	CCONJ
ejpam-5835	133	25	constructing	construct	VERB
ejpam-5835	133	26	the	the	DET
ejpam-5835	133	27	multisorted	multisorte	VERB
ejpam-5835	133	28	algebras	algebra	NOUN
ejpam-5835	133	29	under	under	ADP
ejpam-5835	133	30	the	the	DET
ejpam-5835	133	31	superposition	superposition	NOUN
ejpam-5835	133	32	operation	operation	NOUN
ejpam-5835	133	33	.	.	PUNCT
ejpam-5835	134	1	the	the	DET
ejpam-5835	134	2	paper	paper	NOUN
ejpam-5835	134	3	is	be	AUX
ejpam-5835	134	4	organized	organize	VERB
ejpam-5835	134	5	as	as	SCONJ
ejpam-5835	134	6	follows	follow	VERB
ejpam-5835	134	7	.	.	PUNCT
ejpam-5835	135	1	section	section	NOUN
ejpam-5835	135	2	2	2	NUM
ejpam-5835	135	3	t.	t.	PROPN
ejpam-5835	135	4	kumduang	kumduang	PROPN
ejpam-5835	135	5	,	,	PUNCT
ejpam-5835	135	6	k.	k.	PROPN
ejpam-5835	135	7	wattanatripop	wattanatripop	PROPN
ejpam-5835	135	8	/	/	SYM
ejpam-5835	135	9	eur	eur	PROPN
ejpam-5835	135	10	.	.	PUNCT
ejpam-5835	136	1	j.	j.	PROPN
ejpam-5835	136	2	pure	pure	PROPN
ejpam-5835	136	3	appl	appl	PROPN
ejpam-5835	136	4	.	.	PROPN
ejpam-5835	136	5	math	math	PROPN
ejpam-5835	136	6	,	,	PUNCT
ejpam-5835	136	7	18	18	NUM
ejpam-5835	136	8	(	(	PUNCT
ejpam-5835	136	9	2	2	NUM
ejpam-5835	136	10	)	)	PUNCT
ejpam-5835	136	11	(	(	PUNCT
ejpam-5835	136	12	2025	2025	NUM
ejpam-5835	136	13	)	)	PUNCT
ejpam-5835	136	14	,	,	PUNCT
ejpam-5835	136	15	5835	5835	NUM
ejpam-5835	136	16	5	5	NUM
ejpam-5835	136	17	of	of	ADP
ejpam-5835	136	18	16	16	NUM
ejpam-5835	136	19	introduces	introduce	NOUN
ejpam-5835	136	20	the	the	DET
ejpam-5835	136	21	concept	concept	NOUN
ejpam-5835	136	22	of	of	ADP
ejpam-5835	136	23	terms	term	NOUN
ejpam-5835	136	24	of	of	ADP
ejpam-5835	136	25	a	a	DET
ejpam-5835	136	26	weakly	weakly	ADJ
ejpam-5835	136	27	fixed	fixed	ADJ
ejpam-5835	136	28	variable	variable	NOUN
ejpam-5835	136	29	of	of	ADP
ejpam-5835	136	30	type	type	NOUN
ejpam-5835	136	31	τ	τ	PROPN
ejpam-5835	136	32	and	and	CCONJ
ejpam-5835	136	33	provides	provide	VERB
ejpam-5835	136	34	some	some	DET
ejpam-5835	136	35	algebraic	algebraic	ADJ
ejpam-5835	136	36	properties	property	NOUN
ejpam-5835	136	37	.	.	PUNCT
ejpam-5835	137	1	in	in	ADP
ejpam-5835	137	2	section	section	NOUN
ejpam-5835	137	3	3	3	NUM
ejpam-5835	137	4	,	,	PUNCT
ejpam-5835	137	5	we	we	PRON
ejpam-5835	137	6	present	present	VERB
ejpam-5835	137	7	essential	essential	ADJ
ejpam-5835	137	8	tools	tool	NOUN
ejpam-5835	137	9	for	for	ADP
ejpam-5835	137	10	defining	define	VERB
ejpam-5835	137	11	a	a	DET
ejpam-5835	137	12	novel	novel	ADJ
ejpam-5835	137	13	class	class	NOUN
ejpam-5835	137	14	of	of	ADP
ejpam-5835	137	15	algebras	algebra	NOUN
ejpam-5835	137	16	that	that	SCONJ
ejpam-5835	137	17	satisfy	satisfy	NOUN
ejpam-5835	137	18	identities	identity	NOUN
ejpam-5835	137	19	generated	generate	VERB
ejpam-5835	137	20	by	by	ADP
ejpam-5835	137	21	terms	term	NOUN
ejpam-5835	137	22	of	of	ADP
ejpam-5835	137	23	a	a	DET
ejpam-5835	137	24	weakly	weakly	ADJ
ejpam-5835	137	25	fixed	fix	VERB
ejpam-5835	137	26	variable	variable	NOUN
ejpam-5835	137	27	.	.	PUNCT
ejpam-5835	138	1	additionally	additionally	ADV
ejpam-5835	138	2	,	,	PUNCT
ejpam-5835	138	3	the	the	DET
ejpam-5835	138	4	multisorted	multisorte	VERB
ejpam-5835	138	5	algebras	algebras	PROPN
ejpam-5835	138	6	consisting	consist	VERB
ejpam-5835	138	7	of	of	ADP
ejpam-5835	138	8	the	the	DET
ejpam-5835	138	9	multisorted	multisorte	VERB
ejpam-5835	138	10	set	set	NOUN
ejpam-5835	138	11	of	of	ADP
ejpam-5835	138	12	mapping	mapping	NOUN
ejpam-5835	138	13	whose	whose	DET
ejpam-5835	138	14	images	image	NOUN
ejpam-5835	138	15	are	be	AUX
ejpam-5835	138	16	terms	term	NOUN
ejpam-5835	138	17	of	of	ADP
ejpam-5835	138	18	a	a	DET
ejpam-5835	138	19	weakly	weakly	ADJ
ejpam-5835	138	20	fixed	fix	VERB
ejpam-5835	138	21	variable	variable	NOUN
ejpam-5835	138	22	and	and	CCONJ
ejpam-5835	138	23	two	two	NUM
ejpam-5835	138	24	associative	associative	ADJ
ejpam-5835	138	25	binary	binary	ADJ
ejpam-5835	138	26	operations	operation	NOUN
ejpam-5835	138	27	are	be	AUX
ejpam-5835	138	28	constructed	construct	VERB
ejpam-5835	138	29	.	.	PUNCT
ejpam-5835	139	1	applications	application	NOUN
ejpam-5835	139	2	of	of	ADP
ejpam-5835	139	3	the	the	DET
ejpam-5835	139	4	multisorted	multisorte	VERB
ejpam-5835	139	5	algebras	algebra	NOUN
ejpam-5835	139	6	of	of	ADP
ejpam-5835	139	7	terms	term	NOUN
ejpam-5835	139	8	of	of	ADP
ejpam-5835	139	9	a	a	DET
ejpam-5835	139	10	weakly	weakly	ADJ
ejpam-5835	139	11	fixed	fix	VERB
ejpam-5835	139	12	variable	variable	NOUN
ejpam-5835	139	13	are	be	AUX
ejpam-5835	139	14	given	give	VERB
ejpam-5835	139	15	in	in	ADP
ejpam-5835	139	16	section	section	NOUN
ejpam-5835	139	17	4	4	NUM
ejpam-5835	139	18	.	.	PUNCT
ejpam-5835	140	1	finally	finally	ADV
ejpam-5835	140	2	,	,	PUNCT
ejpam-5835	140	3	we	we	PRON
ejpam-5835	140	4	provide	provide	VERB
ejpam-5835	140	5	some	some	DET
ejpam-5835	140	6	concluding	conclude	VERB
ejpam-5835	140	7	remarks	remark	NOUN
ejpam-5835	140	8	in	in	ADP
ejpam-5835	140	9	section	section	NOUN
ejpam-5835	140	10	5	5	NUM
ejpam-5835	140	11	.	.	NOUN
ejpam-5835	140	12	2	2	NUM
ejpam-5835	140	13	.	.	PUNCT
ejpam-5835	140	14	terms	term	NOUN
ejpam-5835	140	15	of	of	ADP
ejpam-5835	140	16	a	a	DET
ejpam-5835	140	17	weakly	weakly	ADJ
ejpam-5835	140	18	fixed	fixed	ADJ
ejpam-5835	140	19	variable	variable	NOUN
ejpam-5835	140	20	this	this	DET
ejpam-5835	140	21	section	section	NOUN
ejpam-5835	140	22	begins	begin	VERB
ejpam-5835	140	23	with	with	ADP
ejpam-5835	140	24	the	the	DET
ejpam-5835	140	25	definition	definition	NOUN
ejpam-5835	140	26	of	of	ADP
ejpam-5835	140	27	terms	term	NOUN
ejpam-5835	140	28	of	of	ADP
ejpam-5835	140	29	a	a	DET
ejpam-5835	140	30	weakly	weakly	ADJ
ejpam-5835	140	31	fixed	fix	VERB
ejpam-5835	140	32	variable	variable	NOUN
ejpam-5835	140	33	.	.	PUNCT
ejpam-5835	141	1	we	we	PRON
ejpam-5835	141	2	also	also	ADV
ejpam-5835	141	3	construct	construct	VERB
ejpam-5835	141	4	the	the	DET
ejpam-5835	141	5	multisorted	multisorte	VERB
ejpam-5835	141	6	algebra	algebra	NOUN
ejpam-5835	141	7	of	of	ADP
ejpam-5835	141	8	such	such	ADJ
ejpam-5835	141	9	terms	term	NOUN
ejpam-5835	141	10	under	under	ADP
ejpam-5835	141	11	the	the	DET
ejpam-5835	141	12	multisorted	multisorte	VERB
ejpam-5835	141	13	superposition	superposition	NOUN
ejpam-5835	141	14	operation	operation	NOUN
ejpam-5835	141	15	and	and	CCONJ
ejpam-5835	141	16	projections	projection	NOUN
ejpam-5835	141	17	.	.	PUNCT
ejpam-5835	142	1	definition	definition	NOUN
ejpam-5835	142	2	1	1	NUM
ejpam-5835	142	3	.	.	PUNCT
ejpam-5835	143	1	for	for	ADP
ejpam-5835	143	2	a	a	DET
ejpam-5835	143	3	natural	natural	ADJ
ejpam-5835	143	4	number	number	NOUN
ejpam-5835	143	5	n	n	CCONJ
ejpam-5835	143	6	,	,	PUNCT
ejpam-5835	143	7	an	an	DET
ejpam-5835	143	8	n	n	CCONJ
ejpam-5835	143	9	-	-	PUNCT
ejpam-5835	143	10	ary	ary	NOUN
ejpam-5835	143	11	term	term	NOUN
ejpam-5835	143	12	of	of	ADP
ejpam-5835	143	13	a	a	DET
ejpam-5835	143	14	weakly	weakly	ADJ
ejpam-5835	143	15	fixed	fixed	ADJ
ejpam-5835	143	16	variable	variable	NOUN
ejpam-5835	143	17	of	of	ADP
ejpam-5835	143	18	type	type	NOUN
ejpam-5835	143	19	τ	τ	PROPN
ejpam-5835	143	20	is	be	AUX
ejpam-5835	143	21	inductively	inductively	ADV
ejpam-5835	143	22	defined	define	VERB
ejpam-5835	143	23	by	by	ADP
ejpam-5835	143	24	the	the	DET
ejpam-5835	143	25	following	following	NOUN
ejpam-5835	143	26	:	:	PUNCT
ejpam-5835	143	27	(	(	PUNCT
ejpam-5835	143	28	1	1	X
ejpam-5835	143	29	)	)	PUNCT
ejpam-5835	143	30	every	every	DET
ejpam-5835	143	31	variable	variable	NOUN
ejpam-5835	143	32	xi	xi	X
ejpam-5835	143	33	in	in	ADP
ejpam-5835	143	34	an	an	DET
ejpam-5835	143	35	alphabet	alphabet	NOUN
ejpam-5835	143	36	xn	xn	PROPN
ejpam-5835	143	37	is	be	AUX
ejpam-5835	143	38	an	an	DET
ejpam-5835	143	39	n	n	CCONJ
ejpam-5835	143	40	-	-	PUNCT
ejpam-5835	143	41	ary	ary	NOUN
ejpam-5835	143	42	term	term	NOUN
ejpam-5835	143	43	of	of	ADP
ejpam-5835	143	44	a	a	DET
ejpam-5835	143	45	weakly	weakly	ADJ
ejpam-5835	143	46	fixed	fixed	ADJ
ejpam-5835	143	47	variable	variable	NOUN
ejpam-5835	143	48	of	of	ADP
ejpam-5835	143	49	type	type	NOUN
ejpam-5835	143	50	τ	τ	PROPN
ejpam-5835	143	51	.	.	PUNCT
ejpam-5835	144	1	(	(	PUNCT
ejpam-5835	144	2	2	2	X
ejpam-5835	144	3	)	)	PUNCT
ejpam-5835	144	4	if	if	SCONJ
ejpam-5835	144	5	t1	t1	PROPN
ejpam-5835	144	6	,	,	PUNCT
ejpam-5835	144	7	.	.	PUNCT
ejpam-5835	144	8	.	.	PUNCT
ejpam-5835	144	9	.	.	PUNCT
ejpam-5835	145	1	,	,	PUNCT
ejpam-5835	145	2	tni	tni	NOUN
ejpam-5835	145	3	are	be	AUX
ejpam-5835	145	4	n	n	PRON
ejpam-5835	145	5	-	-	PUNCT
ejpam-5835	145	6	ary	ary	NOUN
ejpam-5835	145	7	terms	term	NOUN
ejpam-5835	145	8	of	of	ADP
ejpam-5835	145	9	a	a	DET
ejpam-5835	145	10	weakly	weakly	ADJ
ejpam-5835	145	11	fixed	fixed	ADJ
ejpam-5835	145	12	variable	variable	NOUN
ejpam-5835	145	13	of	of	ADP
ejpam-5835	145	14	type	type	NOUN
ejpam-5835	145	15	τ	τ	PROPN
ejpam-5835	145	16	and	and	CCONJ
ejpam-5835	145	17	var(tl	var(tl	NUM
ejpam-5835	145	18	)	)	PUNCT
ejpam-5835	145	19	=	=	SYM
ejpam-5835	145	20	var(tp	var(tp	NOUN
ejpam-5835	145	21	)	)	PUNCT
ejpam-5835	145	22	for	for	ADP
ejpam-5835	145	23	some	some	DET
ejpam-5835	145	24	1	1	NUM
ejpam-5835	145	25	≤	≤	NUM
ejpam-5835	146	1	l	l	NOUN
ejpam-5835	146	2	<	<	X
ejpam-5835	146	3	p	p	X
ejpam-5835	146	4	≤	≤	PROPN
ejpam-5835	146	5	ni	ni	PROPN
ejpam-5835	146	6	,	,	PUNCT
ejpam-5835	146	7	then	then	ADV
ejpam-5835	146	8	fi(t1	fi(t1	NOUN
ejpam-5835	146	9	,	,	PUNCT
ejpam-5835	146	10	.	.	PUNCT
ejpam-5835	146	11	.	.	PUNCT
ejpam-5835	146	12	.	.	PUNCT
ejpam-5835	147	1	,	,	PUNCT
ejpam-5835	147	2	tni	tni	NOUN
ejpam-5835	147	3	)	)	PUNCT
ejpam-5835	147	4	is	be	AUX
ejpam-5835	147	5	an	an	DET
ejpam-5835	147	6	n	n	CCONJ
ejpam-5835	147	7	-	-	PUNCT
ejpam-5835	147	8	ary	ary	NOUN
ejpam-5835	147	9	term	term	NOUN
ejpam-5835	147	10	of	of	ADP
ejpam-5835	147	11	a	a	DET
ejpam-5835	147	12	weakly	weakly	ADJ
ejpam-5835	147	13	fixed	fixed	ADJ
ejpam-5835	147	14	variable	variable	NOUN
ejpam-5835	147	15	of	of	ADP
ejpam-5835	147	16	type	type	NOUN
ejpam-5835	147	17	τ	τ	PROPN
ejpam-5835	147	18	.	.	PUNCT
ejpam-5835	148	1	(	(	PUNCT
ejpam-5835	148	2	3	3	X
ejpam-5835	148	3	)	)	PUNCT
ejpam-5835	148	4	the	the	DET
ejpam-5835	148	5	set	set	NOUN
ejpam-5835	148	6	wwfv	wwfv	NOUN
ejpam-5835	148	7	τ	τ	PROPN
ejpam-5835	148	8	(	(	PUNCT
ejpam-5835	148	9	xn	xn	PROPN
ejpam-5835	148	10	)	)	PUNCT
ejpam-5835	148	11	of	of	ADP
ejpam-5835	148	12	all	all	DET
ejpam-5835	148	13	n	n	CCONJ
ejpam-5835	148	14	-	-	PUNCT
ejpam-5835	148	15	ary	ary	NOUN
ejpam-5835	148	16	terms	term	NOUN
ejpam-5835	148	17	of	of	ADP
ejpam-5835	148	18	a	a	DET
ejpam-5835	148	19	weakly	weakly	ADJ
ejpam-5835	148	20	fixed	fixed	ADJ
ejpam-5835	148	21	variable	variable	NOUN
ejpam-5835	148	22	of	of	ADP
ejpam-5835	148	23	type	type	NOUN
ejpam-5835	148	24	τ	τ	PROPN
ejpam-5835	148	25	is	be	AUX
ejpam-5835	148	26	the	the	DET
ejpam-5835	148	27	smallest	small	ADJ
ejpam-5835	148	28	set	set	NOUN
ejpam-5835	148	29	closed	close	VERB
ejpam-5835	148	30	under	under	ADP
ejpam-5835	148	31	finite	finite	ADJ
ejpam-5835	148	32	application	application	NOUN
ejpam-5835	148	33	of	of	ADP
ejpam-5835	148	34	(	(	PUNCT
ejpam-5835	148	35	2	2	NUM
ejpam-5835	148	36	)	)	PUNCT
ejpam-5835	148	37	.	.	PUNCT
ejpam-5835	149	1	some	some	DET
ejpam-5835	149	2	concrete	concrete	ADJ
ejpam-5835	149	3	examples	example	NOUN
ejpam-5835	149	4	are	be	AUX
ejpam-5835	149	5	given	give	VERB
ejpam-5835	149	6	.	.	PUNCT
ejpam-5835	149	7	example	example	NOUN
ejpam-5835	150	1	1	1	NUM
ejpam-5835	150	2	.	.	X
ejpam-5835	150	3	consider	consider	VERB
ejpam-5835	150	4	a	a	DET
ejpam-5835	150	5	type	type	NOUN
ejpam-5835	150	6	(	(	PUNCT
ejpam-5835	150	7	3	3	NUM
ejpam-5835	150	8	,	,	PUNCT
ejpam-5835	150	9	2	2	NUM
ejpam-5835	150	10	)	)	PUNCT
ejpam-5835	150	11	with	with	ADP
ejpam-5835	150	12	a	a	DET
ejpam-5835	150	13	ternary	ternary	ADJ
ejpam-5835	150	14	operation	operation	NOUN
ejpam-5835	150	15	symbol	symbol	NOUN
ejpam-5835	150	16	⊞	⊞	NOUN
ejpam-5835	150	17	and	and	CCONJ
ejpam-5835	150	18	a	a	DET
ejpam-5835	150	19	binary	binary	ADJ
ejpam-5835	150	20	operation	operation	NOUN
ejpam-5835	150	21	symbol	symbol	NOUN
ejpam-5835	150	22	⊟	⊟	NOUN
ejpam-5835	150	23	and	and	CCONJ
ejpam-5835	150	24	an	an	DET
ejpam-5835	150	25	alphabet	alphabet	NOUN
ejpam-5835	150	26	x4	x4	PROPN
ejpam-5835	150	27	.	.	PUNCT
ejpam-5835	151	1	then	then	ADV
ejpam-5835	151	2	quaternary	quaternary	ADJ
ejpam-5835	151	3	terms	term	NOUN
ejpam-5835	151	4	of	of	ADP
ejpam-5835	151	5	type	type	NOUN
ejpam-5835	151	6	(	(	PUNCT
ejpam-5835	151	7	3	3	NUM
ejpam-5835	151	8	,	,	PUNCT
ejpam-5835	151	9	2	2	NUM
ejpam-5835	151	10	)	)	PUNCT
ejpam-5835	151	11	which	which	PRON
ejpam-5835	151	12	are	be	AUX
ejpam-5835	151	13	quaternary	quaternary	ADJ
ejpam-5835	151	14	terms	term	NOUN
ejpam-5835	151	15	of	of	ADP
ejpam-5835	151	16	a	a	DET
ejpam-5835	151	17	weakly	weakly	ADJ
ejpam-5835	151	18	fixed	fix	VERB
ejpam-5835	151	19	variable	variable	NOUN
ejpam-5835	151	20	are	be	AUX
ejpam-5835	151	21	listed	list	VERB
ejpam-5835	151	22	,	,	PUNCT
ejpam-5835	151	23	for	for	ADP
ejpam-5835	151	24	example	example	NOUN
ejpam-5835	151	25	,	,	PUNCT
ejpam-5835	151	26	as	as	SCONJ
ejpam-5835	151	27	follows	follow	VERB
ejpam-5835	151	28	:	:	PUNCT
ejpam-5835	151	29	x1	x1	NUM
ejpam-5835	151	30	,	,	PUNCT
ejpam-5835	151	31	x2	x2	PROPN
ejpam-5835	151	32	,	,	PUNCT
ejpam-5835	151	33	x3	x3	ADJ
ejpam-5835	151	34	,	,	PUNCT
ejpam-5835	151	35	x4,⊞(x1	x4,⊞(x1	PROPN
ejpam-5835	151	36	,	,	PUNCT
ejpam-5835	151	37	x1	x1	PROPN
ejpam-5835	151	38	,	,	PUNCT
ejpam-5835	151	39	x3),⊞(x2	x3),⊞(x2	PROPN
ejpam-5835	151	40	,	,	PUNCT
ejpam-5835	151	41	x2	x2	PROPN
ejpam-5835	151	42	,	,	PUNCT
ejpam-5835	151	43	x4),⊟(x4	x4),⊟(x4	PROPN
ejpam-5835	151	44	,	,	PUNCT
ejpam-5835	151	45	x4),⊞(⊟(x3	x4),⊞(⊟(x3	NOUN
ejpam-5835	151	46	,	,	PUNCT
ejpam-5835	151	47	x3	x3	ADJ
ejpam-5835	151	48	)	)	PUNCT
ejpam-5835	151	49	,	,	PUNCT
ejpam-5835	151	50	x3,⊞(x1	x3,⊞(x1	NOUN
ejpam-5835	151	51	,	,	PUNCT
ejpam-5835	151	52	x2	x2	PROPN
ejpam-5835	151	53	,	,	PUNCT
ejpam-5835	151	54	x1	x1	PROPN
ejpam-5835	151	55	)	)	PUNCT
ejpam-5835	151	56	)	)	PUNCT
ejpam-5835	151	57	.	.	PUNCT
ejpam-5835	152	1	on	on	ADP
ejpam-5835	152	2	the	the	DET
ejpam-5835	152	3	other	other	ADJ
ejpam-5835	152	4	hand	hand	NOUN
ejpam-5835	152	5	,	,	PUNCT
ejpam-5835	152	6	⊞(x1	⊞(x1	PROPN
ejpam-5835	152	7	,	,	PUNCT
ejpam-5835	152	8	x2	x2	PROPN
ejpam-5835	152	9	,	,	PUNCT
ejpam-5835	152	10	x3),⊞(x4	x3),⊞(x4	PROPN
ejpam-5835	152	11	,	,	PUNCT
ejpam-5835	152	12	x2	x2	PROPN
ejpam-5835	152	13	,	,	PUNCT
ejpam-5835	152	14	x1),⊟(x2,⊟(x1	x1),⊟(x2,⊟(x1	PROPN
ejpam-5835	152	15	,	,	PUNCT
ejpam-5835	152	16	x1)),⊞(x3,⊟(x1	x1)),⊞(x3,⊟(x1	PROPN
ejpam-5835	152	17	,	,	PUNCT
ejpam-5835	152	18	x1	x1	PROPN
ejpam-5835	152	19	)	)	PUNCT
ejpam-5835	152	20	,	,	PUNCT
ejpam-5835	152	21	x4	x4	PROPN
ejpam-5835	152	22	)	)	PUNCT
ejpam-5835	152	23	are	be	AUX
ejpam-5835	152	24	not	not	PART
ejpam-5835	152	25	quaternary	quaternary	ADJ
ejpam-5835	152	26	terms	term	NOUN
ejpam-5835	152	27	of	of	ADP
ejpam-5835	152	28	a	a	DET
ejpam-5835	152	29	weakly	weakly	ADJ
ejpam-5835	152	30	fixed	fixed	ADJ
ejpam-5835	152	31	variable	variable	NOUN
ejpam-5835	152	32	of	of	ADP
ejpam-5835	152	33	type	type	NOUN
ejpam-5835	152	34	(	(	PUNCT
ejpam-5835	152	35	3	3	NUM
ejpam-5835	152	36	,	,	PUNCT
ejpam-5835	152	37	2	2	NUM
ejpam-5835	152	38	)	)	PUNCT
ejpam-5835	152	39	.	.	PUNCT
ejpam-5835	153	1	we	we	PRON
ejpam-5835	153	2	note	note	VERB
ejpam-5835	153	3	that	that	SCONJ
ejpam-5835	153	4	the	the	DET
ejpam-5835	153	5	set	set	NOUN
ejpam-5835	153	6	of	of	ADP
ejpam-5835	153	7	terms	term	NOUN
ejpam-5835	153	8	of	of	ADP
ejpam-5835	153	9	a	a	DET
ejpam-5835	153	10	weakly	weakly	ADJ
ejpam-5835	153	11	fixed	fix	VERB
ejpam-5835	153	12	variable	variable	NOUN
ejpam-5835	153	13	can	can	AUX
ejpam-5835	153	14	be	be	AUX
ejpam-5835	153	15	viewed	view	VERB
ejpam-5835	153	16	as	as	ADP
ejpam-5835	153	17	a	a	DET
ejpam-5835	153	18	generalization	generalization	NOUN
ejpam-5835	153	19	of	of	ADP
ejpam-5835	153	20	the	the	DET
ejpam-5835	153	21	set	set	NOUN
ejpam-5835	153	22	of	of	ADP
ejpam-5835	153	23	terms	term	NOUN
ejpam-5835	153	24	of	of	ADP
ejpam-5835	153	25	a	a	DET
ejpam-5835	153	26	fixed	fix	VERB
ejpam-5835	153	27	variable	variable	NOUN
ejpam-5835	153	28	as	as	SCONJ
ejpam-5835	153	29	follows	follow	VERB
ejpam-5835	153	30	.	.	PUNCT
ejpam-5835	154	1	remark	remark	PROPN
ejpam-5835	154	2	1	1	NUM
ejpam-5835	154	3	.	.	PUNCT
ejpam-5835	155	1	for	for	ADP
ejpam-5835	155	2	any	any	DET
ejpam-5835	155	3	n	n	PRON
ejpam-5835	155	4	≥	≥	NOUN
ejpam-5835	155	5	1	1	NUM
ejpam-5835	155	6	,	,	PUNCT
ejpam-5835	155	7	the	the	DET
ejpam-5835	155	8	connection	connection	NOUN
ejpam-5835	155	9	between	between	ADP
ejpam-5835	155	10	the	the	DET
ejpam-5835	155	11	set	set	NOUN
ejpam-5835	155	12	wwfv	wwfv	NOUN
ejpam-5835	155	13	τ	τ	PROPN
ejpam-5835	155	14	(	(	PUNCT
ejpam-5835	155	15	xn	xn	PROPN
ejpam-5835	155	16	)	)	PUNCT
ejpam-5835	155	17	and	and	CCONJ
ejpam-5835	155	18	w	w	PROPN
ejpam-5835	155	19	fv	fv	PROPN
ejpam-5835	155	20	τ	τ	PROPN
ejpam-5835	155	21	(	(	PUNCT
ejpam-5835	155	22	xn	xn	PROPN
ejpam-5835	155	23	)	)	PUNCT
ejpam-5835	155	24	is	be	AUX
ejpam-5835	155	25	described	describe	VERB
ejpam-5835	155	26	as	as	SCONJ
ejpam-5835	155	27	follows	follow	VERB
ejpam-5835	155	28	:	:	PUNCT
ejpam-5835	155	29	(	(	PUNCT
ejpam-5835	155	30	1	1	X
ejpam-5835	155	31	)	)	PUNCT
ejpam-5835	155	32	if	if	SCONJ
ejpam-5835	155	33	τ	τ	X
ejpam-5835	155	34	=	=	SYM
ejpam-5835	155	35	(	(	PUNCT
ejpam-5835	155	36	1	1	NUM
ejpam-5835	155	37	,	,	PUNCT
ejpam-5835	155	38	1	1	NUM
ejpam-5835	155	39	,	,	PUNCT
ejpam-5835	155	40	.	.	PUNCT
ejpam-5835	155	41	.	.	PUNCT
ejpam-5835	156	1	.	.	PUNCT
ejpam-5835	157	1	,	,	PUNCT
ejpam-5835	157	2	)	)	PUNCT
ejpam-5835	157	3	or	or	CCONJ
ejpam-5835	157	4	τ	τ	X
ejpam-5835	157	5	=	=	SYM
ejpam-5835	157	6	(	(	PUNCT
ejpam-5835	157	7	2	2	NUM
ejpam-5835	157	8	,	,	PUNCT
ejpam-5835	157	9	2	2	NUM
ejpam-5835	157	10	,	,	PUNCT
ejpam-5835	157	11	.	.	PUNCT
ejpam-5835	157	12	.	.	PUNCT
ejpam-5835	157	13	.	.	PUNCT
ejpam-5835	157	14	)	)	PUNCT
ejpam-5835	157	15	,	,	PUNCT
ejpam-5835	157	16	then	then	ADV
ejpam-5835	157	17	wwfv	wwfv	VERB
ejpam-5835	157	18	τ	τ	PROPN
ejpam-5835	157	19	(	(	PUNCT
ejpam-5835	157	20	xn	xn	PROPN
ejpam-5835	157	21	)	)	PUNCT
ejpam-5835	157	22	=	=	SYM
ejpam-5835	158	1	w	w	PROPN
ejpam-5835	158	2	fv	fv	PROPN
ejpam-5835	158	3	τ	τ	PROPN
ejpam-5835	158	4	(	(	PUNCT
ejpam-5835	158	5	xn	xn	PROPN
ejpam-5835	158	6	)	)	PUNCT
ejpam-5835	158	7	.	.	PUNCT
ejpam-5835	159	1	t.	t.	PROPN
ejpam-5835	159	2	kumduang	kumduang	PROPN
ejpam-5835	159	3	,	,	PUNCT
ejpam-5835	159	4	k.	k.	PROPN
ejpam-5835	159	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	159	6	/	/	SYM
ejpam-5835	159	7	eur	eur	PROPN
ejpam-5835	159	8	.	.	PUNCT
ejpam-5835	160	1	j.	j.	PROPN
ejpam-5835	160	2	pure	pure	PROPN
ejpam-5835	160	3	appl	appl	PROPN
ejpam-5835	160	4	.	.	PROPN
ejpam-5835	160	5	math	math	PROPN
ejpam-5835	160	6	,	,	PUNCT
ejpam-5835	160	7	18	18	NUM
ejpam-5835	160	8	(	(	PUNCT
ejpam-5835	160	9	2	2	NUM
ejpam-5835	160	10	)	)	PUNCT
ejpam-5835	160	11	(	(	PUNCT
ejpam-5835	160	12	2025	2025	NUM
ejpam-5835	160	13	)	)	PUNCT
ejpam-5835	160	14	,	,	PUNCT
ejpam-5835	160	15	5835	5835	NUM
ejpam-5835	160	16	6	6	NUM
ejpam-5835	160	17	of	of	ADP
ejpam-5835	160	18	16	16	NUM
ejpam-5835	160	19	(	(	PUNCT
ejpam-5835	160	20	2	2	NUM
ejpam-5835	160	21	)	)	PUNCT
ejpam-5835	160	22	if	if	SCONJ
ejpam-5835	160	23	τ	τ	X
ejpam-5835	160	24	=	=	SYM
ejpam-5835	160	25	(	(	PUNCT
ejpam-5835	160	26	ni)i∈i	ni)i∈i	NUM
ejpam-5835	160	27	and	and	CCONJ
ejpam-5835	160	28	ni	ni	PROPN
ejpam-5835	160	29	>	>	X
ejpam-5835	160	30	2	2	NUM
ejpam-5835	160	31	for	for	ADP
ejpam-5835	160	32	some	some	DET
ejpam-5835	160	33	i	i	PRON
ejpam-5835	160	34	∈	∈	PROPN
ejpam-5835	161	1	i	i	PRON
ejpam-5835	161	2	,	,	PUNCT
ejpam-5835	161	3	then	then	ADV
ejpam-5835	161	4	w	w	PROPN
ejpam-5835	161	5	fv	fv	PROPN
ejpam-5835	161	6	τ	τ	PROPN
ejpam-5835	161	7	(	(	PUNCT
ejpam-5835	161	8	xn	xn	PROPN
ejpam-5835	161	9	)	)	PUNCT
ejpam-5835	161	10	⊂	⊂	PRON
ejpam-5835	161	11	wwfv	wwfv	VERB
ejpam-5835	161	12	τ	τ	PROPN
ejpam-5835	161	13	(	(	PUNCT
ejpam-5835	161	14	xn	xn	PROPN
ejpam-5835	161	15	)	)	PUNCT
ejpam-5835	161	16	.	.	PUNCT
ejpam-5835	162	1	to	to	PART
ejpam-5835	162	2	guaruntee	guaruntee	VERB
ejpam-5835	162	3	that	that	SCONJ
ejpam-5835	162	4	the	the	DET
ejpam-5835	162	5	multisorted	multisorte	VERB
ejpam-5835	162	6	superposition	superposition	NOUN
ejpam-5835	162	7	can	can	AUX
ejpam-5835	162	8	be	be	AUX
ejpam-5835	162	9	applied	apply	VERB
ejpam-5835	162	10	to	to	ADP
ejpam-5835	162	11	the	the	DET
ejpam-5835	162	12	family	family	NOUN
ejpam-5835	162	13	of	of	ADP
ejpam-5835	162	14	the	the	DET
ejpam-5835	162	15	set	set	NOUN
ejpam-5835	162	16	of	of	ADP
ejpam-5835	162	17	all	all	DET
ejpam-5835	162	18	terms	term	NOUN
ejpam-5835	162	19	of	of	ADP
ejpam-5835	162	20	a	a	DET
ejpam-5835	162	21	weakly	weakly	ADJ
ejpam-5835	162	22	fixed	fixed	ADJ
ejpam-5835	162	23	variable	variable	NOUN
ejpam-5835	162	24	of	of	ADP
ejpam-5835	162	25	type	type	NOUN
ejpam-5835	162	26	τ	τ	PROPN
ejpam-5835	162	27	,	,	PUNCT
ejpam-5835	162	28	the	the	DET
ejpam-5835	162	29	following	follow	VERB
ejpam-5835	162	30	lemma	lemma	PROPN
ejpam-5835	162	31	is	be	AUX
ejpam-5835	162	32	required	require	VERB
ejpam-5835	162	33	.	.	PUNCT
ejpam-5835	163	1	lemma	lemma	PROPN
ejpam-5835	163	2	1	1	NUM
ejpam-5835	163	3	.	.	PUNCT
ejpam-5835	163	4	for	for	ADP
ejpam-5835	163	5	m	m	PROPN
ejpam-5835	163	6	,	,	PUNCT
ejpam-5835	163	7	n	n	PROPN
ejpam-5835	163	8	∈	∈	PROPN
ejpam-5835	163	9	n	n	CCONJ
ejpam-5835	163	10	,	,	PUNCT
ejpam-5835	163	11	if	if	SCONJ
ejpam-5835	163	12	s	s	VERB
ejpam-5835	163	13	is	be	AUX
ejpam-5835	163	14	an	an	DET
ejpam-5835	163	15	n	n	CCONJ
ejpam-5835	163	16	-	-	PUNCT
ejpam-5835	163	17	ary	ary	NOUN
ejpam-5835	163	18	term	term	NOUN
ejpam-5835	163	19	of	of	ADP
ejpam-5835	163	20	a	a	DET
ejpam-5835	163	21	weakly	weakly	ADJ
ejpam-5835	163	22	fixed	fixed	ADJ
ejpam-5835	163	23	variable	variable	NOUN
ejpam-5835	163	24	of	of	ADP
ejpam-5835	163	25	type	type	NOUN
ejpam-5835	163	26	τ	τ	PROPN
ejpam-5835	163	27	and	and	CCONJ
ejpam-5835	163	28	t1	t1	NOUN
ejpam-5835	163	29	,	,	PUNCT
ejpam-5835	163	30	.	.	PUNCT
ejpam-5835	163	31	.	.	PUNCT
ejpam-5835	164	1	.	.	PUNCT
ejpam-5835	165	1	,	,	PUNCT
ejpam-5835	165	2	tn	tn	PROPN
ejpam-5835	165	3	are	be	AUX
ejpam-5835	165	4	m	m	ADJ
ejpam-5835	165	5	-	-	ADJ
ejpam-5835	165	6	ary	ary	ADJ
ejpam-5835	165	7	terms	term	NOUN
ejpam-5835	165	8	of	of	ADP
ejpam-5835	165	9	a	a	DET
ejpam-5835	165	10	weakly	weakly	ADJ
ejpam-5835	165	11	fixed	fixed	ADJ
ejpam-5835	165	12	variable	variable	NOUN
ejpam-5835	165	13	of	of	ADP
ejpam-5835	165	14	type	type	NOUN
ejpam-5835	165	15	τ	τ	PROPN
ejpam-5835	165	16	,	,	PUNCT
ejpam-5835	165	17	then	then	ADV
ejpam-5835	165	18	sn	sn	PROPN
ejpam-5835	165	19	m(s	m(s	PROPN
ejpam-5835	165	20	,	,	PUNCT
ejpam-5835	165	21	t1	t1	NOUN
ejpam-5835	165	22	,	,	PUNCT
ejpam-5835	165	23	.	.	PUNCT
ejpam-5835	165	24	.	.	PUNCT
ejpam-5835	166	1	.	.	PUNCT
ejpam-5835	167	1	,	,	PUNCT
ejpam-5835	167	2	tn	tn	NOUN
ejpam-5835	167	3	)	)	PUNCT
ejpam-5835	167	4	∈	∈	NOUN
ejpam-5835	167	5	wwfv	wwfv	NOUN
ejpam-5835	167	6	τ	τ	PROPN
ejpam-5835	167	7	(	(	PUNCT
ejpam-5835	167	8	xm	xm	PROPN
ejpam-5835	167	9	)	)	PUNCT
ejpam-5835	167	10	.	.	PUNCT
ejpam-5835	168	1	proof	proof	NOUN
ejpam-5835	168	2	.	.	PUNCT
ejpam-5835	169	1	suppose	suppose	VERB
ejpam-5835	169	2	that	that	SCONJ
ejpam-5835	169	3	s	s	VERB
ejpam-5835	169	4	∈	∈	PROPN
ejpam-5835	169	5	wwfv	wwfv	NOUN
ejpam-5835	169	6	τ	τ	PROPN
ejpam-5835	169	7	(	(	PUNCT
ejpam-5835	169	8	xn	xn	PROPN
ejpam-5835	169	9	)	)	PUNCT
ejpam-5835	169	10	and	and	CCONJ
ejpam-5835	169	11	t1	t1	VERB
ejpam-5835	169	12	,	,	PUNCT
ejpam-5835	169	13	.	.	PUNCT
ejpam-5835	169	14	.	.	PUNCT
ejpam-5835	170	1	.	.	PUNCT
ejpam-5835	171	1	,	,	PUNCT
ejpam-5835	171	2	tn	tn	PROPN
ejpam-5835	171	3	∈	∈	PROPN
ejpam-5835	171	4	wwfv	wwfv	NOUN
ejpam-5835	171	5	τ	τ	PROPN
ejpam-5835	171	6	(	(	PUNCT
ejpam-5835	171	7	xm	xm	PROPN
ejpam-5835	171	8	)	)	PUNCT
ejpam-5835	171	9	.	.	PUNCT
ejpam-5835	172	1	we	we	PRON
ejpam-5835	172	2	prove	prove	VERB
ejpam-5835	172	3	on	on	ADP
ejpam-5835	172	4	the	the	DET
ejpam-5835	172	5	complexity	complexity	NOUN
ejpam-5835	172	6	of	of	ADP
ejpam-5835	172	7	a	a	DET
ejpam-5835	172	8	term	term	NOUN
ejpam-5835	172	9	s	s	VERB
ejpam-5835	172	10	that	that	SCONJ
ejpam-5835	172	11	sn	sn	PROPN
ejpam-5835	172	12	m(s	m(s	PROPN
ejpam-5835	172	13	,	,	PUNCT
ejpam-5835	172	14	t1	t1	NOUN
ejpam-5835	172	15	,	,	PUNCT
ejpam-5835	172	16	.	.	PUNCT
ejpam-5835	172	17	.	.	PUNCT
ejpam-5835	173	1	.	.	PUNCT
ejpam-5835	174	1	,	,	PUNCT
ejpam-5835	174	2	tn	tn	NOUN
ejpam-5835	174	3	)	)	PUNCT
ejpam-5835	174	4	∈	∈	NOUN
ejpam-5835	174	5	wwfv	wwfv	NOUN
ejpam-5835	174	6	τ	τ	PROPN
ejpam-5835	174	7	(	(	PUNCT
ejpam-5835	174	8	xm	xm	PROPN
ejpam-5835	174	9	)	)	PUNCT
ejpam-5835	174	10	.	.	PUNCT
ejpam-5835	175	1	it	it	PRON
ejpam-5835	175	2	is	be	AUX
ejpam-5835	175	3	obvious	obvious	ADJ
ejpam-5835	175	4	that	that	SCONJ
ejpam-5835	175	5	sn	sn	PROPN
ejpam-5835	175	6	m(s	m(s	PROPN
ejpam-5835	175	7	,	,	PUNCT
ejpam-5835	175	8	t1	t1	NOUN
ejpam-5835	175	9	,	,	PUNCT
ejpam-5835	175	10	.	.	PUNCT
ejpam-5835	175	11	.	.	PUNCT
ejpam-5835	176	1	.	.	PUNCT
ejpam-5835	177	1	,	,	PUNCT
ejpam-5835	177	2	tn	tn	PROPN
ejpam-5835	177	3	)	)	PUNCT
ejpam-5835	177	4	is	be	AUX
ejpam-5835	177	5	a	a	DET
ejpam-5835	177	6	term	term	NOUN
ejpam-5835	177	7	of	of	ADP
ejpam-5835	177	8	a	a	DET
ejpam-5835	177	9	weakly	weakly	ADJ
ejpam-5835	177	10	fixed	fix	VERB
ejpam-5835	177	11	variable	variable	NOUN
ejpam-5835	177	12	in	in	ADP
ejpam-5835	177	13	wwfv	wwfv	PROPN
ejpam-5835	177	14	τ	τ	PROPN
ejpam-5835	177	15	(	(	PUNCT
ejpam-5835	177	16	xm	xm	PROPN
ejpam-5835	177	17	)	)	PUNCT
ejpam-5835	177	18	if	if	SCONJ
ejpam-5835	177	19	s	s	VERB
ejpam-5835	177	20	is	be	AUX
ejpam-5835	177	21	a	a	DET
ejpam-5835	177	22	variable	variable	ADJ
ejpam-5835	177	23	xk	xk	NOUN
ejpam-5835	177	24	for	for	ADP
ejpam-5835	177	25	all	all	DET
ejpam-5835	177	26	1	1	NUM
ejpam-5835	177	27	≤	≤	NUM
ejpam-5835	178	1	i	i	PRON
ejpam-5835	178	2	≤	≤	NUM
ejpam-5835	178	3	n.	n.	NOUN
ejpam-5835	178	4	we	we	PRON
ejpam-5835	178	5	now	now	ADV
ejpam-5835	178	6	inductively	inductively	ADV
ejpam-5835	178	7	assume	assume	VERB
ejpam-5835	178	8	that	that	SCONJ
ejpam-5835	178	9	s	s	VERB
ejpam-5835	178	10	=	=	ADJ
ejpam-5835	178	11	fi(s1	fi(s1	NOUN
ejpam-5835	178	12	,	,	PUNCT
ejpam-5835	178	13	.	.	PUNCT
ejpam-5835	178	14	.	.	PUNCT
ejpam-5835	179	1	.	.	PUNCT
ejpam-5835	180	1	,	,	PUNCT
ejpam-5835	180	2	sni	sni	PROPN
ejpam-5835	180	3	)	)	PUNCT
ejpam-5835	180	4	and	and	CCONJ
ejpam-5835	180	5	var(sl	var(sl	NOUN
ejpam-5835	180	6	)	)	PUNCT
ejpam-5835	180	7	=	=	SYM
ejpam-5835	180	8	var(sk	var(sk	X
ejpam-5835	180	9	)	)	PUNCT
ejpam-5835	180	10	for	for	ADP
ejpam-5835	180	11	some	some	DET
ejpam-5835	180	12	fixed	fix	VERB
ejpam-5835	180	13	integers	integer	NOUN
ejpam-5835	180	14	1	1	NUM
ejpam-5835	180	15	≤	≤	NUM
ejpam-5835	181	1	l	l	NOUN
ejpam-5835	181	2	<	<	X
ejpam-5835	181	3	k	k	PROPN
ejpam-5835	181	4	≤	≤	PROPN
ejpam-5835	181	5	ni	ni	PROPN
ejpam-5835	181	6	.	.	PROPN
ejpam-5835	181	7	from	from	ADP
ejpam-5835	181	8	the	the	DET
ejpam-5835	181	9	definition	definition	NOUN
ejpam-5835	181	10	of	of	ADP
ejpam-5835	181	11	multisorted	multisorte	VERB
ejpam-5835	181	12	superposition	superposition	NOUN
ejpam-5835	181	13	,	,	PUNCT
ejpam-5835	181	14	we	we	PRON
ejpam-5835	181	15	have	have	VERB
ejpam-5835	181	16	sn	sn	NOUN
ejpam-5835	181	17	m(fi(s1	m(fi(s1	ADJ
ejpam-5835	181	18	,	,	PUNCT
ejpam-5835	181	19	.	.	PUNCT
ejpam-5835	181	20	.	.	PUNCT
ejpam-5835	182	1	.	.	PUNCT
ejpam-5835	183	1	,	,	PUNCT
ejpam-5835	183	2	sni	sni	PROPN
ejpam-5835	183	3	)	)	PUNCT
ejpam-5835	183	4	,	,	PUNCT
ejpam-5835	183	5	t1	t1	PROPN
ejpam-5835	183	6	,	,	PUNCT
ejpam-5835	183	7	.	.	PUNCT
ejpam-5835	183	8	.	.	PUNCT
ejpam-5835	184	1	.	.	PUNCT
ejpam-5835	185	1	,	,	PUNCT
ejpam-5835	185	2	tn	tn	PROPN
ejpam-5835	185	3	)	)	PUNCT
ejpam-5835	185	4	=	=	NOUN
ejpam-5835	185	5	fi(s	fi(s	X
ejpam-5835	186	1	n	n	X
ejpam-5835	186	2	m(s1	m(s1	ADJ
ejpam-5835	186	3	,	,	PUNCT
ejpam-5835	186	4	t1	t1	NOUN
ejpam-5835	186	5	,	,	PUNCT
ejpam-5835	186	6	.	.	PUNCT
ejpam-5835	186	7	.	.	PUNCT
ejpam-5835	186	8	.	.	PUNCT
ejpam-5835	187	1	,	,	PUNCT
ejpam-5835	187	2	tn	tn	PROPN
ejpam-5835	187	3	)	)	PUNCT
ejpam-5835	187	4	,	,	PUNCT
ejpam-5835	187	5	.	.	PUNCT
ejpam-5835	187	6	.	.	PUNCT
ejpam-5835	188	1	.	.	PUNCT
ejpam-5835	189	1	,	,	PUNCT
ejpam-5835	189	2	s	s	VERB
ejpam-5835	189	3	n	n	PRON
ejpam-5835	189	4	m(sni	m(sni	PROPN
ejpam-5835	189	5	,	,	PUNCT
ejpam-5835	189	6	t1	t1	PROPN
ejpam-5835	189	7	,	,	PUNCT
ejpam-5835	189	8	.	.	PUNCT
ejpam-5835	189	9	.	.	PUNCT
ejpam-5835	190	1	.	.	PUNCT
ejpam-5835	191	1	,	,	PUNCT
ejpam-5835	191	2	tn	tn	PROPN
ejpam-5835	191	3	)	)	PUNCT
ejpam-5835	191	4	)	)	PUNCT
ejpam-5835	191	5	,	,	PUNCT
ejpam-5835	191	6	we	we	PRON
ejpam-5835	191	7	prove	prove	VERB
ejpam-5835	191	8	that	that	SCONJ
ejpam-5835	191	9	each	each	DET
ejpam-5835	191	10	sn	sn	PROPN
ejpam-5835	191	11	m(sj	m(sj	X
ejpam-5835	191	12	,	,	PUNCT
ejpam-5835	191	13	t1	t1	PROPN
ejpam-5835	191	14	,	,	PUNCT
ejpam-5835	191	15	.	.	PUNCT
ejpam-5835	191	16	.	.	PUNCT
ejpam-5835	192	1	.	.	PUNCT
ejpam-5835	193	1	,	,	PUNCT
ejpam-5835	193	2	tn	tn	PROPN
ejpam-5835	193	3	)	)	PUNCT
ejpam-5835	193	4	is	be	AUX
ejpam-5835	193	5	an	an	DET
ejpam-5835	193	6	m	m	ADJ
ejpam-5835	193	7	-	-	ADJ
ejpam-5835	193	8	ary	ary	ADJ
ejpam-5835	193	9	term	term	NOUN
ejpam-5835	193	10	of	of	ADP
ejpam-5835	193	11	a	a	DET
ejpam-5835	193	12	weakly	weakly	ADJ
ejpam-5835	193	13	fixed	fixed	ADJ
ejpam-5835	193	14	variable	variable	NOUN
ejpam-5835	193	15	of	of	ADP
ejpam-5835	193	16	type	type	NOUN
ejpam-5835	193	17	τ	τ	PROPN
ejpam-5835	193	18	for	for	ADP
ejpam-5835	193	19	every	every	DET
ejpam-5835	193	20	1	1	NUM
ejpam-5835	193	21	≤	≤	NUM
ejpam-5835	193	22	j	j	PROPN
ejpam-5835	193	23	≤	≤	PROPN
ejpam-5835	193	24	ni	ni	PROPN
ejpam-5835	193	25	and	and	CCONJ
ejpam-5835	193	26	var(sn	var(sn	PROPN
ejpam-5835	193	27	m(sl	m(sl	NUM
ejpam-5835	193	28	,	,	PUNCT
ejpam-5835	193	29	t1	t1	NOUN
ejpam-5835	193	30	,	,	PUNCT
ejpam-5835	193	31	.	.	PUNCT
ejpam-5835	193	32	.	.	PUNCT
ejpam-5835	194	1	.	.	PUNCT
ejpam-5835	195	1	,	,	PUNCT
ejpam-5835	195	2	tn	tn	PROPN
ejpam-5835	195	3	)	)	PUNCT
ejpam-5835	195	4	)	)	PUNCT
ejpam-5835	196	1	=	=	PRON
ejpam-5835	196	2	var(sn	var(sn	X
ejpam-5835	196	3	m(sk	m(sk	PROPN
ejpam-5835	196	4	,	,	PUNCT
ejpam-5835	196	5	t1	t1	NOUN
ejpam-5835	196	6	,	,	PUNCT
ejpam-5835	196	7	.	.	PUNCT
ejpam-5835	196	8	.	.	PUNCT
ejpam-5835	197	1	.	.	PUNCT
ejpam-5835	198	1	,	,	PUNCT
ejpam-5835	198	2	tn	tn	PROPN
ejpam-5835	198	3	)	)	PUNCT
ejpam-5835	198	4	)	)	PUNCT
ejpam-5835	199	1	for	for	ADP
ejpam-5835	199	2	some	some	DET
ejpam-5835	199	3	fixed	fix	VERB
ejpam-5835	199	4	integers	integer	NOUN
ejpam-5835	199	5	1	1	NUM
ejpam-5835	199	6	≤	≤	NUM
ejpam-5835	200	1	l	l	NOUN
ejpam-5835	200	2	<	<	X
ejpam-5835	200	3	k	k	PROPN
ejpam-5835	200	4	≤	≤	PROPN
ejpam-5835	200	5	ni	ni	PROPN
ejpam-5835	200	6	.	.	PROPN
ejpam-5835	200	7	let	let	VERB
ejpam-5835	200	8	j	j	PROPN
ejpam-5835	200	9	∈	∈	PROPN
ejpam-5835	200	10	{	{	PUNCT
ejpam-5835	200	11	1	1	NUM
ejpam-5835	200	12	,	,	PUNCT
ejpam-5835	200	13	.	.	PUNCT
ejpam-5835	200	14	.	.	PUNCT
ejpam-5835	201	1	.	.	PUNCT
ejpam-5835	202	1	,	,	PUNCT
ejpam-5835	202	2	ni	ni	NOUN
ejpam-5835	202	3	}	}	PUNCT
ejpam-5835	202	4	.	.	PUNCT
ejpam-5835	203	1	if	if	SCONJ
ejpam-5835	203	2	sj	sj	VERB
ejpam-5835	203	3	=	=	PUNCT
ejpam-5835	203	4	xp	xp	INTJ
ejpam-5835	203	5	for	for	ADP
ejpam-5835	203	6	some	some	DET
ejpam-5835	203	7	xp	xp	NOUN
ejpam-5835	203	8	∈	∈	PROPN
ejpam-5835	203	9	xn	xn	PROPN
ejpam-5835	203	10	,	,	PUNCT
ejpam-5835	203	11	then	then	ADV
ejpam-5835	203	12	sn	sn	PROPN
ejpam-5835	203	13	m(sj	m(sj	X
ejpam-5835	203	14	,	,	PUNCT
ejpam-5835	203	15	t1	t1	PROPN
ejpam-5835	203	16	,	,	PUNCT
ejpam-5835	203	17	.	.	PUNCT
ejpam-5835	203	18	.	.	PUNCT
ejpam-5835	204	1	.	.	PUNCT
ejpam-5835	205	1	,	,	PUNCT
ejpam-5835	205	2	tn	tn	PROPN
ejpam-5835	205	3	)	)	PUNCT
ejpam-5835	205	4	=	=	SYM
ejpam-5835	206	1	sn	sn	PROPN
ejpam-5835	206	2	m(xp	m(xp	NOUN
ejpam-5835	206	3	,	,	PUNCT
ejpam-5835	206	4	t1	t1	NOUN
ejpam-5835	206	5	,	,	PUNCT
ejpam-5835	206	6	.	.	PUNCT
ejpam-5835	206	7	.	.	PUNCT
ejpam-5835	206	8	.	.	PUNCT
ejpam-5835	207	1	,	,	PUNCT
ejpam-5835	207	2	tn	tn	PROPN
ejpam-5835	207	3	)	)	PUNCT
ejpam-5835	207	4	=	=	PUNCT
ejpam-5835	207	5	tp	tp	PART
ejpam-5835	207	6	∈	∈	PROPN
ejpam-5835	207	7	wwfv	wwfv	NOUN
ejpam-5835	207	8	τ	τ	PROPN
ejpam-5835	207	9	(	(	PUNCT
ejpam-5835	207	10	xm	xm	PROPN
ejpam-5835	207	11	)	)	PUNCT
ejpam-5835	207	12	.	.	PUNCT
ejpam-5835	208	1	assume	assume	VERB
ejpam-5835	208	2	that	that	SCONJ
ejpam-5835	208	3	sj	sj	PROPN
ejpam-5835	208	4	=	=	SYM
ejpam-5835	208	5	fi(s	fi(s	X
ejpam-5835	208	6	′	′	NUM
ejpam-5835	208	7	1	1	NUM
ejpam-5835	208	8	,	,	PUNCT
ejpam-5835	208	9	.	.	PUNCT
ejpam-5835	208	10	.	.	PUNCT
ejpam-5835	209	1	.	.	PUNCT
ejpam-5835	210	1	,	,	PUNCT
ejpam-5835	210	2	s	s	VERB
ejpam-5835	210	3	′	′	NUM
ejpam-5835	210	4	ni	ni	PROPN
ejpam-5835	210	5	)	)	PUNCT
ejpam-5835	210	6	and	and	CCONJ
ejpam-5835	210	7	sn	sn	PROPN
ejpam-5835	210	8	m(s′p	m(s′p	PROPN
ejpam-5835	210	9	,	,	PUNCT
ejpam-5835	210	10	t1	t1	NOUN
ejpam-5835	210	11	,	,	PUNCT
ejpam-5835	210	12	.	.	PUNCT
ejpam-5835	210	13	.	.	PUNCT
ejpam-5835	211	1	.	.	PUNCT
ejpam-5835	212	1	,	,	PUNCT
ejpam-5835	212	2	tn	tn	NOUN
ejpam-5835	212	3	)	)	PUNCT
ejpam-5835	212	4	∈	∈	NOUN
ejpam-5835	212	5	wwfv	wwfv	NOUN
ejpam-5835	212	6	τ	τ	PROPN
ejpam-5835	212	7	(	(	PUNCT
ejpam-5835	212	8	xm	xm	PROPN
ejpam-5835	212	9	)	)	PUNCT
ejpam-5835	212	10	for	for	ADP
ejpam-5835	212	11	all	all	DET
ejpam-5835	212	12	p	p	NOUN
ejpam-5835	212	13	=	=	NOUN
ejpam-5835	212	14	1	1	NUM
ejpam-5835	212	15	,	,	PUNCT
ejpam-5835	212	16	.	.	PUNCT
ejpam-5835	212	17	.	.	PUNCT
ejpam-5835	212	18	.	.	PUNCT
ejpam-5835	213	1	,	,	PUNCT
ejpam-5835	213	2	ni	ni	PROPN
ejpam-5835	213	3	.	.	PROPN
ejpam-5835	213	4	without	without	ADP
ejpam-5835	213	5	loss	loss	NOUN
ejpam-5835	213	6	of	of	ADP
ejpam-5835	213	7	generality	generality	NOUN
ejpam-5835	213	8	,	,	PUNCT
ejpam-5835	213	9	suppose	suppose	VERB
ejpam-5835	213	10	that	that	SCONJ
ejpam-5835	213	11	var(s′l	var(s′l	VERB
ejpam-5835	213	12	)	)	PUNCT
ejpam-5835	213	13	=	=	SYM
ejpam-5835	213	14	var(s′k	var(s′k	PROPN
ejpam-5835	213	15	)	)	PUNCT
ejpam-5835	213	16	for	for	ADP
ejpam-5835	213	17	some	some	DET
ejpam-5835	213	18	1	1	NUM
ejpam-5835	213	19	≤	≤	NUM
ejpam-5835	214	1	l	l	NOUN
ejpam-5835	214	2	<	<	X
ejpam-5835	214	3	k	k	PROPN
ejpam-5835	214	4	≤	≤	PROPN
ejpam-5835	214	5	ni	ni	PROPN
ejpam-5835	214	6	.	.	PROPN
ejpam-5835	215	1	then	then	ADV
ejpam-5835	215	2	we	we	PRON
ejpam-5835	215	3	obtain	obtain	VERB
ejpam-5835	215	4	that	that	DET
ejpam-5835	215	5	sn	sn	PROPN
ejpam-5835	215	6	m(fi(s	m(fi(s	NOUN
ejpam-5835	215	7	′	′	NOUN
ejpam-5835	215	8	1	1	NUM
ejpam-5835	215	9	,	,	PUNCT
ejpam-5835	215	10	.	.	PUNCT
ejpam-5835	215	11	.	.	PUNCT
ejpam-5835	215	12	.	.	PUNCT
ejpam-5835	216	1	,	,	PUNCT
ejpam-5835	216	2	s	s	VERB
ejpam-5835	216	3	′	′	NUM
ejpam-5835	216	4	ni	ni	PROPN
ejpam-5835	216	5	)	)	PUNCT
ejpam-5835	216	6	,	,	PUNCT
ejpam-5835	216	7	t1	t1	PROPN
ejpam-5835	216	8	,	,	PUNCT
ejpam-5835	216	9	.	.	PUNCT
ejpam-5835	216	10	.	.	PUNCT
ejpam-5835	217	1	.	.	PUNCT
ejpam-5835	218	1	,	,	PUNCT
ejpam-5835	218	2	tn	tn	NOUN
ejpam-5835	218	3	)	)	PUNCT
ejpam-5835	218	4	∈	∈	NOUN
ejpam-5835	218	5	wwfv	wwfv	NOUN
ejpam-5835	218	6	τ	τ	PROPN
ejpam-5835	218	7	(	(	PUNCT
ejpam-5835	218	8	xm	xm	PROPN
ejpam-5835	218	9	)	)	PUNCT
ejpam-5835	218	10	.	.	PUNCT
ejpam-5835	219	1	actually	actually	ADV
ejpam-5835	219	2	,	,	PUNCT
ejpam-5835	219	3	since	since	SCONJ
ejpam-5835	219	4	we	we	PRON
ejpam-5835	219	5	know	know	VERB
ejpam-5835	219	6	that	that	PRON
ejpam-5835	219	7	var(sl	var(sl	NOUN
ejpam-5835	219	8	)	)	PUNCT
ejpam-5835	219	9	=	=	SYM
ejpam-5835	219	10	var(sk	var(sk	X
ejpam-5835	219	11	)	)	PUNCT
ejpam-5835	219	12	for	for	ADP
ejpam-5835	219	13	some	some	DET
ejpam-5835	219	14	fixed	fix	VERB
ejpam-5835	219	15	integers	integer	NOUN
ejpam-5835	219	16	1	1	NUM
ejpam-5835	219	17	≤	≤	NUM
ejpam-5835	220	1	l	l	NOUN
ejpam-5835	220	2	<	<	X
ejpam-5835	220	3	k	k	PROPN
ejpam-5835	220	4	≤	≤	PROPN
ejpam-5835	220	5	ni	ni	PROPN
ejpam-5835	220	6	,	,	PUNCT
ejpam-5835	220	7	then	then	ADV
ejpam-5835	220	8	we	we	PRON
ejpam-5835	220	9	have	have	VERB
ejpam-5835	220	10	var(sn	var(sn	VERB
ejpam-5835	220	11	m(sl	m(sl	NOUN
ejpam-5835	220	12	,	,	PUNCT
ejpam-5835	220	13	t1	t1	NOUN
ejpam-5835	220	14	,	,	PUNCT
ejpam-5835	220	15	.	.	PUNCT
ejpam-5835	220	16	.	.	PUNCT
ejpam-5835	221	1	.	.	PUNCT
ejpam-5835	222	1	,	,	PUNCT
ejpam-5835	222	2	tn	tn	PROPN
ejpam-5835	222	3	)	)	PUNCT
ejpam-5835	222	4	)	)	PUNCT
ejpam-5835	223	1	=	=	PRON
ejpam-5835	223	2	var(sn	var(sn	X
ejpam-5835	223	3	m(sk	m(sk	PROPN
ejpam-5835	223	4	,	,	PUNCT
ejpam-5835	223	5	t1	t1	NOUN
ejpam-5835	223	6	,	,	PUNCT
ejpam-5835	223	7	.	.	PUNCT
ejpam-5835	223	8	.	.	PUNCT
ejpam-5835	224	1	.	.	PUNCT
ejpam-5835	225	1	,	,	PUNCT
ejpam-5835	225	2	tn	tn	PROPN
ejpam-5835	225	3	)	)	PUNCT
ejpam-5835	225	4	)	)	PUNCT
ejpam-5835	225	5	,	,	PUNCT
ejpam-5835	225	6	which	which	PRON
ejpam-5835	225	7	completes	complete	VERB
ejpam-5835	225	8	the	the	DET
ejpam-5835	225	9	proof	proof	NOUN
ejpam-5835	225	10	.	.	PUNCT
ejpam-5835	226	1	to	to	PART
ejpam-5835	226	2	enhance	enhance	VERB
ejpam-5835	226	3	understanding	understanding	NOUN
ejpam-5835	226	4	of	of	ADP
ejpam-5835	226	5	the	the	DET
ejpam-5835	226	6	computation	computation	NOUN
ejpam-5835	226	7	process	process	NOUN
ejpam-5835	226	8	for	for	ADP
ejpam-5835	226	9	terms	term	NOUN
ejpam-5835	226	10	with	with	ADP
ejpam-5835	226	11	a	a	DET
ejpam-5835	226	12	weakly	weakly	ADJ
ejpam-5835	226	13	fixed	fix	VERB
ejpam-5835	226	14	variable	variable	NOUN
ejpam-5835	226	15	under	under	ADP
ejpam-5835	226	16	the	the	DET
ejpam-5835	226	17	multisorted	multisorte	VERB
ejpam-5835	226	18	superposition	superposition	NOUN
ejpam-5835	226	19	,	,	PUNCT
ejpam-5835	226	20	the	the	DET
ejpam-5835	226	21	following	follow	VERB
ejpam-5835	226	22	example	example	NOUN
ejpam-5835	226	23	is	be	AUX
ejpam-5835	226	24	provided	provide	VERB
ejpam-5835	226	25	.	.	PUNCT
ejpam-5835	226	26	example	example	NOUN
ejpam-5835	226	27	2	2	NUM
ejpam-5835	226	28	.	.	X
ejpam-5835	226	29	consider	consider	VERB
ejpam-5835	226	30	n	n	NOUN
ejpam-5835	226	31	=	=	SYM
ejpam-5835	226	32	3	3	NUM
ejpam-5835	226	33	and	and	CCONJ
ejpam-5835	226	34	m	m	PROPN
ejpam-5835	226	35	=	=	NOUN
ejpam-5835	226	36	4	4	NUM
ejpam-5835	226	37	and	and	CCONJ
ejpam-5835	226	38	the	the	DET
ejpam-5835	226	39	multisorted	multisorte	VERB
ejpam-5835	226	40	superposition	superposition	NOUN
ejpam-5835	226	41	s3	s3	PROPN
ejpam-5835	226	42	4	4	NUM
ejpam-5835	226	43	.	.	PUNCT
ejpam-5835	227	1	on	on	ADP
ejpam-5835	227	2	the	the	DET
ejpam-5835	227	3	sets	set	NOUN
ejpam-5835	227	4	wwfv	wwfv	NOUN
ejpam-5835	227	5	(	(	PUNCT
ejpam-5835	227	6	3,2)(x3	3,2)(x3	NUM
ejpam-5835	227	7	)	)	PUNCT
ejpam-5835	227	8	and	and	CCONJ
ejpam-5835	227	9	wwfv	wwfv	NOUN
ejpam-5835	227	10	(	(	PUNCT
ejpam-5835	227	11	3,2)(x4	3,2)(x4	NUM
ejpam-5835	227	12	)	)	PUNCT
ejpam-5835	227	13	,	,	PUNCT
ejpam-5835	227	14	if	if	SCONJ
ejpam-5835	227	15	we	we	PRON
ejpam-5835	227	16	put	put	VERB
ejpam-5835	227	17	a	a	DET
ejpam-5835	227	18	=	=	SYM
ejpam-5835	227	19	⊞(x1	⊞(x1	NOUN
ejpam-5835	227	20	,	,	PUNCT
ejpam-5835	227	21	x3	x3	ADJ
ejpam-5835	227	22	,	,	PUNCT
ejpam-5835	227	23	x1	x1	PROPN
ejpam-5835	227	24	)	)	PUNCT
ejpam-5835	227	25	,	,	PUNCT
ejpam-5835	227	26	b	b	X
ejpam-5835	227	27	=	=	SYM
ejpam-5835	227	28	⊞(x4,⊞(x2	⊞(x4,⊞(x2	PROPN
ejpam-5835	227	29	,	,	PUNCT
ejpam-5835	227	30	x1	x1	PROPN
ejpam-5835	227	31	,	,	PUNCT
ejpam-5835	227	32	x2	x2	PROPN
ejpam-5835	227	33	)	)	PUNCT
ejpam-5835	227	34	,	,	PUNCT
ejpam-5835	227	35	x4	x4	PROPN
ejpam-5835	227	36	)	)	PUNCT
ejpam-5835	227	37	,	,	PUNCT
ejpam-5835	227	38	c	c	NOUN
ejpam-5835	227	39	=	=	SYM
ejpam-5835	227	40	⊟(x4	⊟(x4	NOUN
ejpam-5835	227	41	,	,	PUNCT
ejpam-5835	227	42	x4	x4	PROPN
ejpam-5835	227	43	)	)	PUNCT
ejpam-5835	227	44	,	,	PUNCT
ejpam-5835	227	45	d	d	NOUN
ejpam-5835	227	46	=	=	SYM
ejpam-5835	227	47	⊟(x2,⊞(x2	⊟(x2,⊞(x2	PROPN
ejpam-5835	227	48	,	,	PUNCT
ejpam-5835	227	49	x2	x2	PROPN
ejpam-5835	227	50	,	,	PUNCT
ejpam-5835	227	51	x2	x2	PROPN
ejpam-5835	227	52	)	)	PUNCT
ejpam-5835	227	53	)	)	PUNCT
ejpam-5835	227	54	,	,	PUNCT
ejpam-5835	227	55	e	e	X
ejpam-5835	227	56	=	=	SYM
ejpam-5835	227	57	⊞(⊟(x4	⊞(⊟(x4	PROPN
ejpam-5835	227	58	,	,	PUNCT
ejpam-5835	227	59	x4),⊟(x4	x4),⊟(x4	PROPN
ejpam-5835	227	60	,	,	PUNCT
ejpam-5835	227	61	x4	x4	PROPN
ejpam-5835	227	62	)	)	PUNCT
ejpam-5835	227	63	,	,	PUNCT
ejpam-5835	227	64	x3	x3	ADJ
ejpam-5835	227	65	)	)	PUNCT
ejpam-5835	227	66	,	,	PUNCT
ejpam-5835	227	67	f	f	PROPN
ejpam-5835	227	68	=	=	SYM
ejpam-5835	227	69	⊟(x1	⊟(x1	PROPN
ejpam-5835	227	70	,	,	PUNCT
ejpam-5835	227	71	x1	x1	PROPN
ejpam-5835	227	72	)	)	PUNCT
ejpam-5835	227	73	,	,	PUNCT
ejpam-5835	227	74	t.	t.	PROPN
ejpam-5835	227	75	kumduang	kumduang	PROPN
ejpam-5835	227	76	,	,	PUNCT
ejpam-5835	227	77	k.	k.	PROPN
ejpam-5835	227	78	wattanatripop	wattanatripop	PROPN
ejpam-5835	227	79	/	/	SYM
ejpam-5835	227	80	eur	eur	PROPN
ejpam-5835	227	81	.	.	PUNCT
ejpam-5835	228	1	j.	j.	PROPN
ejpam-5835	228	2	pure	pure	PROPN
ejpam-5835	228	3	appl	appl	PROPN
ejpam-5835	228	4	.	.	PROPN
ejpam-5835	228	5	math	math	PROPN
ejpam-5835	228	6	,	,	PUNCT
ejpam-5835	228	7	18	18	NUM
ejpam-5835	228	8	(	(	PUNCT
ejpam-5835	228	9	2	2	NUM
ejpam-5835	228	10	)	)	PUNCT
ejpam-5835	228	11	(	(	PUNCT
ejpam-5835	228	12	2025	2025	NUM
ejpam-5835	228	13	)	)	PUNCT
ejpam-5835	228	14	,	,	PUNCT
ejpam-5835	228	15	5835	5835	NUM
ejpam-5835	228	16	7	7	NUM
ejpam-5835	228	17	of	of	ADP
ejpam-5835	228	18	16	16	NUM
ejpam-5835	228	19	then	then	ADV
ejpam-5835	228	20	s3	s3	PROPN
ejpam-5835	228	21	4(a	4(a	NUM
ejpam-5835	228	22	,	,	PUNCT
ejpam-5835	228	23	b	b	NOUN
ejpam-5835	228	24	,	,	PUNCT
ejpam-5835	228	25	c	c	NOUN
ejpam-5835	228	26	,	,	PUNCT
ejpam-5835	228	27	c	c	NOUN
ejpam-5835	228	28	)	)	PUNCT
ejpam-5835	228	29	=	=	SYM
ejpam-5835	228	30	s3	s3	PROPN
ejpam-5835	228	31	4(⊞(x1	4(⊞(x1	NUM
ejpam-5835	228	32	,	,	PUNCT
ejpam-5835	228	33	x3	x3	ADJ
ejpam-5835	228	34	,	,	PUNCT
ejpam-5835	228	35	x1),⊞(x4,⊞(x2	x1),⊞(x4,⊞(x2	PROPN
ejpam-5835	228	36	,	,	PUNCT
ejpam-5835	228	37	x1	x1	PROPN
ejpam-5835	228	38	,	,	PUNCT
ejpam-5835	228	39	x2	x2	PROPN
ejpam-5835	228	40	)	)	PUNCT
ejpam-5835	228	41	,	,	PUNCT
ejpam-5835	228	42	x4),⊟(x4	x4),⊟(x4	PROPN
ejpam-5835	228	43	,	,	PUNCT
ejpam-5835	228	44	x4),⊟(x4	x4),⊟(x4	PROPN
ejpam-5835	228	45	,	,	PUNCT
ejpam-5835	228	46	x4	x4	PROPN
ejpam-5835	228	47	)	)	PUNCT
ejpam-5835	228	48	)	)	PUNCT
ejpam-5835	229	1	=	=	SYM
ejpam-5835	229	2	⊞(⊞(x4,⊞(x2	⊞(⊞(x4,⊞(x2	NOUN
ejpam-5835	229	3	,	,	PUNCT
ejpam-5835	229	4	x1	x1	PROPN
ejpam-5835	229	5	,	,	PUNCT
ejpam-5835	229	6	x2	x2	PROPN
ejpam-5835	229	7	)	)	PUNCT
ejpam-5835	229	8	,	,	PUNCT
ejpam-5835	229	9	x4),⊟(x4	x4),⊟(x4	PROPN
ejpam-5835	229	10	,	,	PUNCT
ejpam-5835	229	11	x4),⊞(x4,⊞(x2	x4),⊞(x4,⊞(x2	PROPN
ejpam-5835	229	12	,	,	PUNCT
ejpam-5835	229	13	x1	x1	PROPN
ejpam-5835	229	14	,	,	PUNCT
ejpam-5835	229	15	x2	x2	PROPN
ejpam-5835	229	16	)	)	PUNCT
ejpam-5835	229	17	,	,	PUNCT
ejpam-5835	229	18	x4	x4	PROPN
ejpam-5835	229	19	)	)	PUNCT
ejpam-5835	229	20	)	)	PUNCT
ejpam-5835	229	21	belongs	belong	VERB
ejpam-5835	229	22	to	to	PART
ejpam-5835	229	23	wwfv	wwfv	VERB
ejpam-5835	229	24	(	(	PUNCT
ejpam-5835	229	25	3,2)(x4	3,2)(x4	NUM
ejpam-5835	229	26	)	)	PUNCT
ejpam-5835	229	27	because	because	SCONJ
ejpam-5835	229	28	the	the	DET
ejpam-5835	229	29	sets	set	NOUN
ejpam-5835	229	30	of	of	ADP
ejpam-5835	229	31	variables	variable	NOUN
ejpam-5835	229	32	in	in	ADP
ejpam-5835	229	33	the	the	DET
ejpam-5835	229	34	first	first	ADJ
ejpam-5835	229	35	and	and	CCONJ
ejpam-5835	229	36	the	the	DET
ejpam-5835	229	37	third	third	ADJ
ejpam-5835	229	38	positions	position	NOUN
ejpam-5835	229	39	are	be	AUX
ejpam-5835	229	40	equal	equal	ADJ
ejpam-5835	229	41	,	,	PUNCT
ejpam-5835	229	42	i.e.	i.e.	X
ejpam-5835	229	43	,	,	PUNCT
ejpam-5835	229	44	{	{	PUNCT
ejpam-5835	229	45	x1	x1	PROPN
ejpam-5835	229	46	,	,	PUNCT
ejpam-5835	229	47	x2	x2	PROPN
ejpam-5835	229	48	,	,	PUNCT
ejpam-5835	229	49	x4	x4	PROPN
ejpam-5835	229	50	}	}	PUNCT
ejpam-5835	229	51	.	.	PUNCT
ejpam-5835	230	1	moreover	moreover	ADV
ejpam-5835	230	2	,	,	PUNCT
ejpam-5835	230	3	s3	s3	PROPN
ejpam-5835	230	4	4(y	4(y	NUM
ejpam-5835	230	5	,	,	PUNCT
ejpam-5835	230	6	z1	z1	PROPN
ejpam-5835	230	7	,	,	PUNCT
ejpam-5835	230	8	z2	z2	PROPN
ejpam-5835	230	9	,	,	PUNCT
ejpam-5835	230	10	z3	z3	NOUN
ejpam-5835	230	11	)	)	PUNCT
ejpam-5835	230	12	∈	∈	NOUN
ejpam-5835	230	13	wwfv	wwfv	NOUN
ejpam-5835	230	14	(	(	PUNCT
ejpam-5835	230	15	3,2)(x4	3,2)(x4	NUM
ejpam-5835	230	16	)	)	PUNCT
ejpam-5835	230	17	if	if	SCONJ
ejpam-5835	230	18	y	y	PROPN
ejpam-5835	230	19	∈	∈	PROPN
ejpam-5835	230	20	{	{	PUNCT
ejpam-5835	230	21	a	a	NOUN
ejpam-5835	230	22	,	,	PUNCT
ejpam-5835	230	23	d	d	NOUN
ejpam-5835	230	24	,	,	PUNCT
ejpam-5835	230	25	f	f	NOUN
ejpam-5835	230	26	}	}	PUNCT
ejpam-5835	230	27	and	and	CCONJ
ejpam-5835	230	28	z1	z1	ADJ
ejpam-5835	230	29	,	,	PUNCT
ejpam-5835	230	30	z2	z2	PROPN
ejpam-5835	230	31	,	,	PUNCT
ejpam-5835	230	32	z3	z3	PROPN
ejpam-5835	230	33	∈	∈	PROPN
ejpam-5835	230	34	{	{	PUNCT
ejpam-5835	230	35	a	a	PROPN
ejpam-5835	230	36	,	,	PUNCT
ejpam-5835	230	37	b	b	NOUN
ejpam-5835	230	38	,	,	PUNCT
ejpam-5835	230	39	c	c	NOUN
ejpam-5835	230	40	,	,	PUNCT
ejpam-5835	230	41	d	d	NOUN
ejpam-5835	230	42	,	,	PUNCT
ejpam-5835	230	43	e	e	NOUN
ejpam-5835	230	44	,	,	PUNCT
ejpam-5835	230	45	f	f	NOUN
ejpam-5835	230	46	}	}	PUNCT
ejpam-5835	230	47	and	and	CCONJ
ejpam-5835	230	48	s4	s4	PROPN
ejpam-5835	230	49	3(u	3(u	NUM
ejpam-5835	230	50	,	,	PUNCT
ejpam-5835	230	51	w1	w1	NOUN
ejpam-5835	230	52	,	,	PUNCT
ejpam-5835	230	53	w2	w2	NOUN
ejpam-5835	230	54	,	,	PUNCT
ejpam-5835	230	55	w3	w3	PROPN
ejpam-5835	230	56	,	,	PUNCT
ejpam-5835	230	57	w4	w4	NOUN
ejpam-5835	230	58	)	)	PUNCT
ejpam-5835	230	59	∈	∈	NOUN
ejpam-5835	230	60	wwfv	wwfv	NOUN
ejpam-5835	230	61	(	(	PUNCT
ejpam-5835	230	62	3,2)(x3	3,2)(x3	NUM
ejpam-5835	230	63	)	)	PUNCT
ejpam-5835	230	64	if	if	SCONJ
ejpam-5835	230	65	u	u	PROPN
ejpam-5835	230	66	∈	∈	PROPN
ejpam-5835	230	67	{	{	PUNCT
ejpam-5835	230	68	a	a	PRON
ejpam-5835	230	69	,	,	PUNCT
ejpam-5835	230	70	b	b	NOUN
ejpam-5835	230	71	,	,	PUNCT
ejpam-5835	230	72	c	c	NOUN
ejpam-5835	230	73	,	,	PUNCT
ejpam-5835	230	74	d	d	NOUN
ejpam-5835	230	75	,	,	PUNCT
ejpam-5835	230	76	e	e	NOUN
ejpam-5835	230	77	,	,	PUNCT
ejpam-5835	230	78	f	f	NOUN
ejpam-5835	230	79	}	}	PUNCT
ejpam-5835	230	80	and	and	CCONJ
ejpam-5835	230	81	w1	w1	NOUN
ejpam-5835	230	82	,	,	PUNCT
ejpam-5835	230	83	w2	w2	NOUN
ejpam-5835	230	84	,	,	PUNCT
ejpam-5835	230	85	w3	w3	PROPN
ejpam-5835	230	86	,	,	PUNCT
ejpam-5835	230	87	w4	w4	NOUN
ejpam-5835	230	88	∈	∈	PROPN
ejpam-5835	230	89	{	{	PUNCT
ejpam-5835	230	90	a	a	NOUN
ejpam-5835	230	91	,	,	PUNCT
ejpam-5835	230	92	d	d	NOUN
ejpam-5835	230	93	,	,	PUNCT
ejpam-5835	230	94	f	f	NOUN
ejpam-5835	230	95	}	}	PUNCT
ejpam-5835	230	96	.	.	PUNCT
ejpam-5835	231	1	by	by	ADP
ejpam-5835	231	2	lemma	lemma	PROPN
ejpam-5835	231	3	1	1	NUM
ejpam-5835	231	4	,	,	PUNCT
ejpam-5835	231	5	the	the	DET
ejpam-5835	231	6	multisorted	multisorte	VERB
ejpam-5835	231	7	superpositions	superposition	NOUN
ejpam-5835	232	1	sn	sn	PROPN
ejpam-5835	232	2	m	m	VERB
ejpam-5835	232	3	can	can	AUX
ejpam-5835	232	4	be	be	AUX
ejpam-5835	232	5	applied	apply	VERB
ejpam-5835	232	6	to	to	ADP
ejpam-5835	232	7	the	the	DET
ejpam-5835	232	8	family	family	NOUN
ejpam-5835	232	9	(	(	PUNCT
ejpam-5835	232	10	wwfv	wwfv	PROPN
ejpam-5835	232	11	τ	τ	X
ejpam-5835	232	12	(	(	PUNCT
ejpam-5835	232	13	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	232	14	,	,	PUNCT
ejpam-5835	232	15	which	which	PRON
ejpam-5835	232	16	means	mean	VERB
ejpam-5835	232	17	that	that	SCONJ
ejpam-5835	232	18	we	we	PRON
ejpam-5835	232	19	have	have	AUX
ejpam-5835	232	20	following	follow	VERB
ejpam-5835	232	21	multisorted	multisorte	VERB
ejpam-5835	232	22	mappings	mapping	NOUN
ejpam-5835	232	23	sn	sn	PROPN
ejpam-5835	232	24	m	m	VERB
ejpam-5835	232	25	:	:	PUNCT
ejpam-5835	232	26	wwfv	wwfv	PROPN
ejpam-5835	232	27	τ	τ	PROPN
ejpam-5835	232	28	(	(	PUNCT
ejpam-5835	232	29	xn)×	xn)×	X
ejpam-5835	232	30	(	(	PUNCT
ejpam-5835	232	31	wwfv	wwfv	PROPN
ejpam-5835	232	32	τ	τ	PROPN
ejpam-5835	232	33	(	(	PUNCT
ejpam-5835	232	34	xm))n	xm))n	PROPN
ejpam-5835	232	35	→	→	NOUN
ejpam-5835	232	36	wwfv	wwfv	PROPN
ejpam-5835	232	37	τ	τ	PROPN
ejpam-5835	232	38	(	(	PUNCT
ejpam-5835	232	39	xm	xm	PROPN
ejpam-5835	232	40	)	)	PUNCT
ejpam-5835	232	41	for	for	ADP
ejpam-5835	232	42	m	m	PROPN
ejpam-5835	232	43	,	,	PUNCT
ejpam-5835	232	44	n	n	PROPN
ejpam-5835	232	45	∈	∈	PROPN
ejpam-5835	232	46	n.	n.	NOUN
ejpam-5835	232	47	as	as	ADP
ejpam-5835	232	48	a	a	DET
ejpam-5835	232	49	consequence	consequence	NOUN
ejpam-5835	232	50	,	,	PUNCT
ejpam-5835	232	51	the	the	DET
ejpam-5835	232	52	multisorted	multisorte	VERB
ejpam-5835	232	53	algebra	algebra	NOUN
ejpam-5835	232	54	wwfv	wwfv	NOUN
ejpam-5835	232	55	τ	τ	PROPN
ejpam-5835	232	56	(	(	PUNCT
ejpam-5835	232	57	x	x	NOUN
ejpam-5835	232	58	)	)	PUNCT
ejpam-5835	232	59	:	:	PUNCT
ejpam-5835	233	1	=	=	SYM
ejpam-5835	233	2	(	(	PUNCT
ejpam-5835	233	3	(	(	PUNCT
ejpam-5835	233	4	wwfv	wwfv	PROPN
ejpam-5835	233	5	τ	τ	X
ejpam-5835	233	6	(	(	PUNCT
ejpam-5835	233	7	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	233	8	,	,	PUNCT
ejpam-5835	233	9	(	(	PUNCT
ejpam-5835	233	10	s	s	NOUN
ejpam-5835	233	11	n	n	PRON
ejpam-5835	233	12	m)n	m)n	X
ejpam-5835	233	13	,	,	PUNCT
ejpam-5835	233	14	m∈n	m∈n	NOUN
ejpam-5835	233	15	,	,	PUNCT
ejpam-5835	233	16	(	(	PUNCT
ejpam-5835	233	17	xi)i≤n	xi)i≤n	NUM
ejpam-5835	233	18	,	,	PUNCT
ejpam-5835	233	19	n∈n	n∈n	NUM
ejpam-5835	233	20	)	)	PUNCT
ejpam-5835	233	21	is	be	AUX
ejpam-5835	233	22	formed	form	VERB
ejpam-5835	233	23	.	.	PUNCT
ejpam-5835	234	1	since	since	SCONJ
ejpam-5835	234	2	we	we	PRON
ejpam-5835	234	3	know	know	VERB
ejpam-5835	234	4	that	that	PRON
ejpam-5835	234	5	(	(	PUNCT
ejpam-5835	234	6	wwfv	wwfv	PROPN
ejpam-5835	234	7	τ	τ	X
ejpam-5835	234	8	(	(	PUNCT
ejpam-5835	234	9	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	234	10	⊆	⊆	NUM
ejpam-5835	234	11	(	(	PUNCT
ejpam-5835	234	12	wτ	wτ	NOUN
ejpam-5835	234	13	(	(	PUNCT
ejpam-5835	234	14	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	234	15	,	,	PUNCT
ejpam-5835	234	16	then	then	ADV
ejpam-5835	234	17	by	by	ADP
ejpam-5835	234	18	lemma	lemma	PROPN
ejpam-5835	234	19	1	1	NUM
ejpam-5835	234	20	the	the	DET
ejpam-5835	234	21	following	following	ADJ
ejpam-5835	234	22	result	result	NOUN
ejpam-5835	234	23	is	be	AUX
ejpam-5835	234	24	concluded	conclude	VERB
ejpam-5835	234	25	.	.	PUNCT
ejpam-5835	235	1	theorem	theorem	NOUN
ejpam-5835	235	2	1	1	NUM
ejpam-5835	235	3	.	.	PUNCT
ejpam-5835	236	1	the	the	DET
ejpam-5835	236	2	multisorted	multisorte	VERB
ejpam-5835	236	3	algebra	algebra	NOUN
ejpam-5835	236	4	wwfv	wwfv	NOUN
ejpam-5835	236	5	τ	τ	PROPN
ejpam-5835	236	6	(	(	PUNCT
ejpam-5835	236	7	x	x	NOUN
ejpam-5835	236	8	)	)	PUNCT
ejpam-5835	236	9	satisfies	satisfy	VERB
ejpam-5835	236	10	the	the	DET
ejpam-5835	236	11	axioms	axiom	NOUN
ejpam-5835	236	12	(	(	PUNCT
ejpam-5835	236	13	c1	c1	NOUN
ejpam-5835	236	14	)	)	PUNCT
ejpam-5835	236	15	,	,	PUNCT
ejpam-5835	236	16	(	(	PUNCT
ejpam-5835	236	17	c2	c2	PROPN
ejpam-5835	236	18	)	)	PUNCT
ejpam-5835	236	19	and	and	CCONJ
ejpam-5835	236	20	(	(	PUNCT
ejpam-5835	236	21	c3	c3	PROPN
ejpam-5835	236	22	)	)	PUNCT
ejpam-5835	236	23	.	.	PUNCT
ejpam-5835	237	1	3	3	X
ejpam-5835	237	2	.	.	X
ejpam-5835	237	3	weakly	weakly	ADJ
ejpam-5835	237	4	fixed	fix	VERB
ejpam-5835	237	5	variable	variable	ADJ
ejpam-5835	237	6	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	237	7	this	this	DET
ejpam-5835	237	8	section	section	NOUN
ejpam-5835	237	9	introduces	introduce	VERB
ejpam-5835	237	10	a	a	DET
ejpam-5835	237	11	mapping	mapping	NOUN
ejpam-5835	237	12	whose	whose	DET
ejpam-5835	237	13	images	image	NOUN
ejpam-5835	237	14	are	be	AUX
ejpam-5835	237	15	terms	term	NOUN
ejpam-5835	237	16	of	of	ADP
ejpam-5835	237	17	a	a	DET
ejpam-5835	237	18	weakly	weakly	ADJ
ejpam-5835	237	19	fixed	fix	VERB
ejpam-5835	237	20	variable	variable	NOUN
ejpam-5835	237	21	and	and	CCONJ
ejpam-5835	237	22	discusses	discuss	VERB
ejpam-5835	237	23	the	the	DET
ejpam-5835	237	24	multisorted	multisorte	VERB
ejpam-5835	237	25	composition	composition	NOUN
ejpam-5835	237	26	.	.	PUNCT
ejpam-5835	238	1	definition	definition	NOUN
ejpam-5835	238	2	2	2	NUM
ejpam-5835	238	3	.	.	PUNCT
ejpam-5835	239	1	a	a	DET
ejpam-5835	239	2	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	239	3	σ	σ	PROPN
ejpam-5835	239	4	∈	∈	PROPN
ejpam-5835	239	5	hyp(τ	hyp(τ	PROPN
ejpam-5835	239	6	)	)	PUNCT
ejpam-5835	239	7	is	be	AUX
ejpam-5835	239	8	called	call	VERB
ejpam-5835	239	9	a	a	DET
ejpam-5835	239	10	weakly	weakly	ADJ
ejpam-5835	239	11	fixed	fix	VERB
ejpam-5835	239	12	variable	variable	ADJ
ejpam-5835	239	13	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	239	14	of	of	ADP
ejpam-5835	239	15	type	type	NOUN
ejpam-5835	239	16	τ	τ	PROPN
ejpam-5835	239	17	if	if	SCONJ
ejpam-5835	239	18	for	for	ADP
ejpam-5835	239	19	all	all	PRON
ejpam-5835	240	1	i	i	PRON
ejpam-5835	240	2	∈	∈	PROPN
ejpam-5835	241	1	i	i	PRON
ejpam-5835	241	2	,	,	PUNCT
ejpam-5835	241	3	σ	σ	PROPN
ejpam-5835	241	4	maps	map	VERB
ejpam-5835	241	5	each	each	DET
ejpam-5835	241	6	operation	operation	NOUN
ejpam-5835	241	7	symbol	symbol	NOUN
ejpam-5835	241	8	fi	fi	NOUN
ejpam-5835	241	9	to	to	ADP
ejpam-5835	241	10	an	an	DET
ejpam-5835	241	11	ni	ni	ADJ
ejpam-5835	241	12	-	-	ADJ
ejpam-5835	241	13	ary	ary	PROPN
ejpam-5835	241	14	term	term	NOUN
ejpam-5835	241	15	of	of	ADP
ejpam-5835	241	16	a	a	DET
ejpam-5835	241	17	weakly	weakly	ADJ
ejpam-5835	241	18	fixed	fixed	ADJ
ejpam-5835	241	19	variable	variable	NOUN
ejpam-5835	241	20	of	of	ADP
ejpam-5835	241	21	type	type	NOUN
ejpam-5835	241	22	τ	τ	PROPN
ejpam-5835	241	23	.	.	PUNCT
ejpam-5835	242	1	the	the	DET
ejpam-5835	242	2	set	set	NOUN
ejpam-5835	242	3	of	of	ADP
ejpam-5835	242	4	all	all	DET
ejpam-5835	242	5	weakly	weakly	ADJ
ejpam-5835	242	6	fixed	fix	VERB
ejpam-5835	242	7	variable	variable	ADJ
ejpam-5835	242	8	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	242	9	of	of	ADP
ejpam-5835	242	10	type	type	NOUN
ejpam-5835	242	11	τ	τ	PROPN
ejpam-5835	242	12	is	be	AUX
ejpam-5835	242	13	denoted	denote	VERB
ejpam-5835	242	14	by	by	ADP
ejpam-5835	242	15	hypwfv(τ	hypwfv(τ	PROPN
ejpam-5835	242	16	)	)	PUNCT
ejpam-5835	242	17	,	,	PUNCT
ejpam-5835	242	18	i.e.	i.e.	X
ejpam-5835	242	19	,	,	PUNCT
ejpam-5835	242	20	hypwfv(τ	hypwfv(τ	NOUN
ejpam-5835	242	21	)	)	PUNCT
ejpam-5835	242	22	=	=	SYM
ejpam-5835	243	1	{	{	PUNCT
ejpam-5835	243	2	σ	σ	PROPN
ejpam-5835	243	3	|	|	NOUN
ejpam-5835	243	4	σ	σ	PROPN
ejpam-5835	243	5	:	:	PUNCT
ejpam-5835	243	6	{	{	PUNCT
ejpam-5835	243	7	fi	fi	NOUN
ejpam-5835	244	1	|	|	INTJ
ejpam-5835	244	2	i	i	PRON
ejpam-5835	244	3	∈	∈	VERB
ejpam-5835	244	4	i	i	PRON
ejpam-5835	244	5	}	}	PUNCT
ejpam-5835	244	6	→	→	PUNCT
ejpam-5835	244	7	wwfv	wwfv	NOUN
ejpam-5835	244	8	τ	τ	X
ejpam-5835	244	9	(	(	PUNCT
ejpam-5835	244	10	x	x	NOUN
ejpam-5835	244	11	)	)	PUNCT
ejpam-5835	244	12	}	}	PUNCT
ejpam-5835	244	13	.	.	PUNCT
ejpam-5835	245	1	for	for	ADP
ejpam-5835	245	2	instance	instance	NOUN
ejpam-5835	245	3	,	,	PUNCT
ejpam-5835	245	4	let	let	VERB
ejpam-5835	245	5	τ	τ	X
ejpam-5835	245	6	=	=	PUNCT
ejpam-5835	245	7	(	(	PUNCT
ejpam-5835	245	8	3	3	NUM
ejpam-5835	245	9	,	,	PUNCT
ejpam-5835	245	10	2	2	NUM
ejpam-5835	245	11	)	)	PUNCT
ejpam-5835	245	12	be	be	AUX
ejpam-5835	245	13	a	a	DET
ejpam-5835	245	14	type	type	NOUN
ejpam-5835	245	15	with	with	ADP
ejpam-5835	245	16	a	a	DET
ejpam-5835	245	17	ternary	ternary	ADJ
ejpam-5835	245	18	operation	operation	NOUN
ejpam-5835	245	19	symbol	symbol	NOUN
ejpam-5835	245	20	⊞	⊞	NOUN
ejpam-5835	245	21	and	and	CCONJ
ejpam-5835	245	22	a	a	DET
ejpam-5835	245	23	binary	binary	ADJ
ejpam-5835	245	24	operation	operation	NOUN
ejpam-5835	245	25	symbol	symbol	NOUN
ejpam-5835	245	26	⊟.	⊟.	ADP
ejpam-5835	245	27	a	a	DET
ejpam-5835	245	28	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	245	29	σ	σ	NOUN
ejpam-5835	245	30	:	:	PUNCT
ejpam-5835	246	1	{	{	PUNCT
ejpam-5835	246	2	⊞,⊟	⊞,⊟	NOUN
ejpam-5835	246	3	}	}	PUNCT
ejpam-5835	246	4	→	→	SYM
ejpam-5835	246	5	wτ	wτ	X
ejpam-5835	246	6	(	(	PUNCT
ejpam-5835	246	7	x	x	NOUN
ejpam-5835	246	8	)	)	PUNCT
ejpam-5835	246	9	such	such	ADJ
ejpam-5835	246	10	that	that	SCONJ
ejpam-5835	246	11	σ(⊞	σ(⊞	ADJ
ejpam-5835	246	12	)	)	PUNCT
ejpam-5835	246	13	=	=	SYM
ejpam-5835	246	14	⊞(x3,⊟(x2	⊞(x3,⊟(x2	PROPN
ejpam-5835	246	15	,	,	PUNCT
ejpam-5835	246	16	x2	x2	PROPN
ejpam-5835	246	17	)	)	PUNCT
ejpam-5835	246	18	,	,	PUNCT
ejpam-5835	246	19	x3	x3	ADJ
ejpam-5835	246	20	)	)	PUNCT
ejpam-5835	246	21	and	and	CCONJ
ejpam-5835	246	22	σ(⊟	σ(⊟	NOUN
ejpam-5835	246	23	)	)	PUNCT
ejpam-5835	246	24	=	=	SYM
ejpam-5835	246	25	⊟(x1	⊟(x1	PROPN
ejpam-5835	246	26	,	,	PUNCT
ejpam-5835	246	27	x1	x1	NUM
ejpam-5835	246	28	)	)	PUNCT
ejpam-5835	246	29	.	.	PUNCT
ejpam-5835	247	1	then	then	ADV
ejpam-5835	247	2	we	we	PRON
ejpam-5835	247	3	get	get	VERB
ejpam-5835	247	4	that	that	DET
ejpam-5835	247	5	σ	σ	NOUN
ejpam-5835	247	6	a	a	DET
ejpam-5835	247	7	weakly	weakly	ADJ
ejpam-5835	247	8	fixed	fix	VERB
ejpam-5835	247	9	variable	variable	ADJ
ejpam-5835	247	10	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	247	11	of	of	ADP
ejpam-5835	247	12	type	type	NOUN
ejpam-5835	247	13	τ	τ	PROPN
ejpam-5835	247	14	.	.	PUNCT
ejpam-5835	248	1	on	on	ADP
ejpam-5835	248	2	the	the	DET
ejpam-5835	248	3	other	other	ADJ
ejpam-5835	248	4	hand	hand	NOUN
ejpam-5835	248	5	,	,	PUNCT
ejpam-5835	248	6	we	we	PRON
ejpam-5835	248	7	let	let	VERB
ejpam-5835	248	8	β	β	PRON
ejpam-5835	248	9	:	:	PUNCT
ejpam-5835	248	10	{	{	PUNCT
ejpam-5835	248	11	⊞,⊟	⊞,⊟	NOUN
ejpam-5835	248	12	}	}	PUNCT
ejpam-5835	248	13	→	→	SYM
ejpam-5835	248	14	wτ	wτ	X
ejpam-5835	248	15	(	(	PUNCT
ejpam-5835	248	16	x	x	NOUN
ejpam-5835	248	17	)	)	PUNCT
ejpam-5835	248	18	such	such	ADJ
ejpam-5835	248	19	that	that	PRON
ejpam-5835	248	20	β(⊞	β(⊞	NUM
ejpam-5835	248	21	)	)	PUNCT
ejpam-5835	248	22	=	=	SYM
ejpam-5835	248	23	⊞(x1,⊟(x2	⊞(x1,⊟(x2	PROPN
ejpam-5835	248	24	,	,	PUNCT
ejpam-5835	248	25	x2	x2	PROPN
ejpam-5835	248	26	)	)	PUNCT
ejpam-5835	248	27	,	,	PUNCT
ejpam-5835	248	28	x3	x3	ADJ
ejpam-5835	248	29	)	)	PUNCT
ejpam-5835	248	30	and	and	CCONJ
ejpam-5835	248	31	β(⊟	β(⊟	PUNCT
ejpam-5835	248	32	)	)	PUNCT
ejpam-5835	248	33	=	=	SYM
ejpam-5835	248	34	⊟(x1	⊟(x1	ADJ
ejpam-5835	248	35	,	,	PUNCT
ejpam-5835	248	36	x2	x2	PROPN
ejpam-5835	248	37	)	)	PUNCT
ejpam-5835	248	38	.	.	PUNCT
ejpam-5835	249	1	then	then	ADV
ejpam-5835	249	2	β	β	PROPN
ejpam-5835	249	3	is	be	AUX
ejpam-5835	249	4	not	not	PART
ejpam-5835	249	5	a	a	DET
ejpam-5835	249	6	weakly	weakly	ADJ
ejpam-5835	249	7	fixed	fix	VERB
ejpam-5835	249	8	variable	variable	ADJ
ejpam-5835	249	9	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	249	10	of	of	ADP
ejpam-5835	249	11	type	type	NOUN
ejpam-5835	249	12	τ	τ	PROPN
ejpam-5835	249	13	since	since	SCONJ
ejpam-5835	249	14	β(⊞	β(⊞	NUM
ejpam-5835	249	15	)	)	PUNCT
ejpam-5835	249	16	/∈	/∈	PUNCT
ejpam-5835	250	1	wwfv	wwfv	PROPN
ejpam-5835	250	2	τ	τ	X
ejpam-5835	250	3	(	(	PUNCT
ejpam-5835	250	4	x	x	NOUN
ejpam-5835	250	5	)	)	PUNCT
ejpam-5835	250	6	and	and	CCONJ
ejpam-5835	250	7	β(⊟	β(⊟	PUNCT
ejpam-5835	250	8	)	)	PUNCT
ejpam-5835	250	9	/∈	/∈	PUNCT
ejpam-5835	251	1	wwfv	wwfv	PROPN
ejpam-5835	251	2	τ	τ	X
ejpam-5835	251	3	(	(	PUNCT
ejpam-5835	251	4	x	x	NOUN
ejpam-5835	251	5	)	)	PUNCT
ejpam-5835	251	6	.	.	PUNCT
ejpam-5835	252	1	to	to	PART
ejpam-5835	252	2	construct	construct	VERB
ejpam-5835	252	3	the	the	DET
ejpam-5835	252	4	algebra	algebra	NOUN
ejpam-5835	252	5	of	of	ADP
ejpam-5835	252	6	weakly	weakly	ADJ
ejpam-5835	252	7	fixed	fix	VERB
ejpam-5835	252	8	variable	variable	ADJ
ejpam-5835	252	9	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	252	10	,	,	PUNCT
ejpam-5835	252	11	we	we	PRON
ejpam-5835	252	12	need	need	VERB
ejpam-5835	252	13	the	the	DET
ejpam-5835	252	14	following	follow	VERB
ejpam-5835	252	15	result	result	NOUN
ejpam-5835	252	16	to	to	PART
ejpam-5835	252	17	confirm	confirm	VERB
ejpam-5835	252	18	that	that	SCONJ
ejpam-5835	252	19	each	each	DET
ejpam-5835	252	20	extension	extension	NOUN
ejpam-5835	252	21	of	of	ADP
ejpam-5835	252	22	σ	σ	PROPN
ejpam-5835	252	23	takes	take	VERB
ejpam-5835	252	24	from	from	ADP
ejpam-5835	252	25	the	the	DET
ejpam-5835	252	26	set	set	NOUN
ejpam-5835	252	27	of	of	ADP
ejpam-5835	252	28	terms	term	NOUN
ejpam-5835	252	29	of	of	ADP
ejpam-5835	252	30	a	a	DET
ejpam-5835	252	31	weakly	weakly	ADJ
ejpam-5835	252	32	fixed	fix	VERB
ejpam-5835	252	33	variable	variable	NOUN
ejpam-5835	252	34	into	into	ADP
ejpam-5835	252	35	itself	itself	PRON
ejpam-5835	252	36	.	.	PUNCT
ejpam-5835	253	1	t.	t.	PROPN
ejpam-5835	253	2	kumduang	kumduang	PROPN
ejpam-5835	253	3	,	,	PUNCT
ejpam-5835	253	4	k.	k.	PROPN
ejpam-5835	253	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	253	6	/	/	SYM
ejpam-5835	253	7	eur	eur	PROPN
ejpam-5835	253	8	.	.	PUNCT
ejpam-5835	254	1	j.	j.	PROPN
ejpam-5835	254	2	pure	pure	PROPN
ejpam-5835	254	3	appl	appl	PROPN
ejpam-5835	254	4	.	.	PROPN
ejpam-5835	254	5	math	math	PROPN
ejpam-5835	254	6	,	,	PUNCT
ejpam-5835	254	7	18	18	NUM
ejpam-5835	254	8	(	(	PUNCT
ejpam-5835	254	9	2	2	NUM
ejpam-5835	254	10	)	)	PUNCT
ejpam-5835	254	11	(	(	PUNCT
ejpam-5835	254	12	2025	2025	NUM
ejpam-5835	254	13	)	)	PUNCT
ejpam-5835	254	14	,	,	PUNCT
ejpam-5835	254	15	5835	5835	NUM
ejpam-5835	254	16	8	8	NUM
ejpam-5835	254	17	of	of	ADP
ejpam-5835	254	18	16	16	NUM
ejpam-5835	254	19	lemma	lemma	PROPN
ejpam-5835	254	20	2	2	NUM
ejpam-5835	254	21	.	.	PUNCT
ejpam-5835	255	1	for	for	ADP
ejpam-5835	255	2	any	any	DET
ejpam-5835	255	3	weakly	weakly	ADJ
ejpam-5835	255	4	fixed	fix	VERB
ejpam-5835	255	5	variable	variable	ADJ
ejpam-5835	255	6	hypersubstitution	hypersubstitution	PROPN
ejpam-5835	255	7	σ	σ	PROPN
ejpam-5835	255	8	,	,	PUNCT
ejpam-5835	255	9	we	we	PRON
ejpam-5835	255	10	have	have	VERB
ejpam-5835	255	11	σ̂	σ̂	NUM
ejpam-5835	255	12	:	:	PUNCT
ejpam-5835	255	13	wwfv	wwfv	PROPN
ejpam-5835	255	14	τ	τ	PROPN
ejpam-5835	255	15	(	(	PUNCT
ejpam-5835	255	16	x	x	NOUN
ejpam-5835	255	17	)	)	PUNCT
ejpam-5835	255	18	→	→	SYM
ejpam-5835	255	19	wwfv	wwfv	NOUN
ejpam-5835	255	20	τ	τ	X
ejpam-5835	255	21	(	(	PUNCT
ejpam-5835	255	22	x	x	NOUN
ejpam-5835	255	23	)	)	PUNCT
ejpam-5835	255	24	.	.	PUNCT
ejpam-5835	256	1	proof	proof	NOUN
ejpam-5835	256	2	.	.	PUNCT
ejpam-5835	257	1	let	let	VERB
ejpam-5835	257	2	σ	σ	NOUN
ejpam-5835	257	3	be	be	AUX
ejpam-5835	257	4	a	a	DET
ejpam-5835	257	5	mapping	mapping	NOUN
ejpam-5835	257	6	on	on	ADP
ejpam-5835	257	7	hypwfv(τ	hypwfv(τ	PROPN
ejpam-5835	257	8	)	)	PUNCT
ejpam-5835	257	9	and	and	CCONJ
ejpam-5835	257	10	t	t	PROPN
ejpam-5835	257	11	be	be	AUX
ejpam-5835	257	12	an	an	DET
ejpam-5835	257	13	element	element	NOUN
ejpam-5835	257	14	in	in	ADP
ejpam-5835	257	15	wwfv	wwfv	NOUN
ejpam-5835	257	16	τ	τ	PROPN
ejpam-5835	257	17	(	(	PUNCT
ejpam-5835	257	18	x	x	NOUN
ejpam-5835	257	19	)	)	PUNCT
ejpam-5835	257	20	.	.	PUNCT
ejpam-5835	258	1	we	we	PRON
ejpam-5835	258	2	show	show	VERB
ejpam-5835	258	3	that	that	SCONJ
ejpam-5835	258	4	σ̂[t	σ̂[t	PROPN
ejpam-5835	258	5	]	]	X
ejpam-5835	258	6	∈	∈	PROPN
ejpam-5835	258	7	wwfv	wwfv	NOUN
ejpam-5835	258	8	τ	τ	PROPN
ejpam-5835	258	9	(	(	PUNCT
ejpam-5835	258	10	x	x	NOUN
ejpam-5835	258	11	)	)	PUNCT
ejpam-5835	258	12	.	.	PUNCT
ejpam-5835	259	1	clearly	clearly	ADV
ejpam-5835	259	2	,	,	PUNCT
ejpam-5835	259	3	σ̂[xi	σ̂[xi	X
ejpam-5835	259	4	]	]	X
ejpam-5835	259	5	∈	∈	NOUN
ejpam-5835	259	6	wwfv	wwfv	NOUN
ejpam-5835	259	7	τ	τ	PROPN
ejpam-5835	259	8	(	(	PUNCT
ejpam-5835	259	9	x	x	NOUN
ejpam-5835	259	10	)	)	PUNCT
ejpam-5835	259	11	for	for	ADP
ejpam-5835	259	12	every	every	DET
ejpam-5835	259	13	variable	variable	NOUN
ejpam-5835	259	14	xi	xi	X
ejpam-5835	259	15	.	.	PUNCT
ejpam-5835	259	16	suppose	suppose	VERB
ejpam-5835	259	17	now	now	ADV
ejpam-5835	259	18	that	that	SCONJ
ejpam-5835	259	19	t	t	NOUN
ejpam-5835	259	20	=	=	SYM
ejpam-5835	259	21	fi(t1	fi(t1	NOUN
ejpam-5835	259	22	,	,	PUNCT
ejpam-5835	259	23	.	.	PUNCT
ejpam-5835	259	24	.	.	PUNCT
ejpam-5835	260	1	.	.	PUNCT
ejpam-5835	261	1	,	,	PUNCT
ejpam-5835	261	2	tni	tni	NOUN
ejpam-5835	261	3	)	)	PUNCT
ejpam-5835	261	4	such	such	ADJ
ejpam-5835	261	5	that	that	PRON
ejpam-5835	261	6	σ̂[tk	σ̂[tk	NOUN
ejpam-5835	261	7	]	]	X
ejpam-5835	261	8	∈	∈	PROPN
ejpam-5835	261	9	wwfv	wwfv	NOUN
ejpam-5835	261	10	τ	τ	PROPN
ejpam-5835	261	11	(	(	PUNCT
ejpam-5835	261	12	x	x	NOUN
ejpam-5835	261	13	)	)	PUNCT
ejpam-5835	261	14	for	for	ADP
ejpam-5835	261	15	all	all	DET
ejpam-5835	261	16	k	k	PROPN
ejpam-5835	261	17	∈	∈	PROPN
ejpam-5835	261	18	{	{	PUNCT
ejpam-5835	261	19	1	1	NUM
ejpam-5835	261	20	,	,	PUNCT
ejpam-5835	261	21	.	.	PUNCT
ejpam-5835	261	22	.	.	PUNCT
ejpam-5835	261	23	.	.	PUNCT
ejpam-5835	262	1	,	,	PUNCT
ejpam-5835	262	2	ni	ni	NOUN
ejpam-5835	262	3	}	}	PUNCT
ejpam-5835	262	4	.	.	PUNCT
ejpam-5835	263	1	without	without	ADP
ejpam-5835	263	2	loss	loss	NOUN
ejpam-5835	263	3	of	of	ADP
ejpam-5835	263	4	generality	generality	NOUN
ejpam-5835	263	5	,	,	PUNCT
ejpam-5835	263	6	we	we	PRON
ejpam-5835	263	7	may	may	AUX
ejpam-5835	263	8	assume	assume	VERB
ejpam-5835	263	9	here	here	ADV
ejpam-5835	263	10	that	that	PRON
ejpam-5835	263	11	var(tl	var(tl	VERB
ejpam-5835	263	12	)	)	PUNCT
ejpam-5835	263	13	=	=	SYM
ejpam-5835	263	14	var(tp	var(tp	NOUN
ejpam-5835	263	15	)	)	PUNCT
ejpam-5835	263	16	for	for	ADP
ejpam-5835	263	17	some	some	DET
ejpam-5835	263	18	l	l	NOUN
ejpam-5835	263	19	,	,	PUNCT
ejpam-5835	263	20	p	p	PROPN
ejpam-5835	263	21	∈	∈	PROPN
ejpam-5835	263	22	{	{	PUNCT
ejpam-5835	263	23	1	1	NUM
ejpam-5835	263	24	,	,	PUNCT
ejpam-5835	263	25	.	.	PUNCT
ejpam-5835	263	26	.	.	PUNCT
ejpam-5835	264	1	.	.	PUNCT
ejpam-5835	265	1	,	,	PUNCT
ejpam-5835	265	2	ni	ni	NOUN
ejpam-5835	265	3	}	}	PUNCT
ejpam-5835	265	4	and	and	CCONJ
ejpam-5835	265	5	l	l	PROPN
ejpam-5835	265	6	̸=	̸=	PROPN
ejpam-5835	265	7	p.	p.	NOUN
ejpam-5835	265	8	then	then	ADV
ejpam-5835	265	9	we	we	PRON
ejpam-5835	265	10	obtain	obtain	VERB
ejpam-5835	265	11	var(σ̂[tl	var(σ̂[tl	NOUN
ejpam-5835	265	12	]	]	PUNCT
ejpam-5835	265	13	)	)	PUNCT
ejpam-5835	265	14	=	=	SYM
ejpam-5835	265	15	var(σ̂[tp	var(σ̂[tp	PROPN
ejpam-5835	265	16	]	]	PUNCT
ejpam-5835	265	17	)	)	PUNCT
ejpam-5835	265	18	.	.	PUNCT
ejpam-5835	266	1	since	since	SCONJ
ejpam-5835	266	2	σ(fi	σ(fi	NUM
ejpam-5835	266	3	)	)	PUNCT
ejpam-5835	266	4	belongs	belong	VERB
ejpam-5835	266	5	to	to	PART
ejpam-5835	266	6	wwfv	wwfv	VERB
ejpam-5835	266	7	τ	τ	PROPN
ejpam-5835	266	8	(	(	PUNCT
ejpam-5835	266	9	x	x	NOUN
ejpam-5835	266	10	)	)	PUNCT
ejpam-5835	266	11	,	,	PUNCT
ejpam-5835	266	12	then	then	ADV
ejpam-5835	266	13	by	by	ADP
ejpam-5835	266	14	the	the	DET
ejpam-5835	266	15	hypothesis	hypothesis	NOUN
ejpam-5835	266	16	,	,	PUNCT
ejpam-5835	266	17	i.e.	i.e.	X
ejpam-5835	266	18	,	,	PUNCT
ejpam-5835	266	19	var(tl	var(tl	NUM
ejpam-5835	266	20	)	)	PUNCT
ejpam-5835	266	21	=	=	SYM
ejpam-5835	266	22	var(tp	var(tp	NOUN
ejpam-5835	266	23	)	)	PUNCT
ejpam-5835	266	24	,	,	PUNCT
ejpam-5835	266	25	we	we	PRON
ejpam-5835	266	26	have	have	VERB
ejpam-5835	266	27	σ̂[t	σ̂[t	PROPN
ejpam-5835	266	28	]	]	PUNCT
ejpam-5835	267	1	=	=	PUNCT
ejpam-5835	267	2	sni	sni	PROPN
ejpam-5835	267	3	m	m	VERB
ejpam-5835	267	4	(	(	PUNCT
ejpam-5835	267	5	σ(fi	σ(fi	PROPN
ejpam-5835	267	6	)	)	PUNCT
ejpam-5835	267	7	,	,	PUNCT
ejpam-5835	267	8	σ̂[t1	σ̂[t1	PROPN
ejpam-5835	267	9	]	]	PUNCT
ejpam-5835	267	10	,	,	PUNCT
ejpam-5835	267	11	.	.	PUNCT
ejpam-5835	267	12	.	.	PUNCT
ejpam-5835	267	13	.	.	PUNCT
ejpam-5835	268	1	,	,	PUNCT
ejpam-5835	268	2	σ̂[tni	σ̂[tni	PROPN
ejpam-5835	268	3	]	]	PUNCT
ejpam-5835	268	4	)	)	PUNCT
ejpam-5835	268	5	∈	∈	NOUN
ejpam-5835	268	6	wwfv	wwfv	NOUN
ejpam-5835	268	7	τ	τ	X
ejpam-5835	268	8	(	(	PUNCT
ejpam-5835	268	9	x	x	NOUN
ejpam-5835	268	10	)	)	PUNCT
ejpam-5835	268	11	.	.	PUNCT
ejpam-5835	269	1	this	this	PRON
ejpam-5835	269	2	finishes	finish	VERB
ejpam-5835	269	3	the	the	DET
ejpam-5835	269	4	proof	proof	NOUN
ejpam-5835	269	5	.	.	PUNCT
ejpam-5835	270	1	for	for	ADP
ejpam-5835	270	2	n	n	PRON
ejpam-5835	270	3	∈	∈	PROPN
ejpam-5835	270	4	n	n	CCONJ
ejpam-5835	270	5	,	,	PUNCT
ejpam-5835	270	6	the	the	DET
ejpam-5835	270	7	multisorted	multisorte	VERB
ejpam-5835	270	8	mapping	mapping	NOUN
ejpam-5835	270	9	σ̂n	σ̂n	NOUN
ejpam-5835	270	10	:	:	PUNCT
ejpam-5835	270	11	wwfv	wwfv	PROPN
ejpam-5835	270	12	τ	τ	PROPN
ejpam-5835	270	13	(	(	PUNCT
ejpam-5835	270	14	xn	xn	PROPN
ejpam-5835	270	15	)	)	PUNCT
ejpam-5835	270	16	→	→	SYM
ejpam-5835	270	17	wwfv	wwfv	NOUN
ejpam-5835	270	18	τ	τ	X
ejpam-5835	270	19	(	(	PUNCT
ejpam-5835	270	20	xn	xn	PROPN
ejpam-5835	270	21	)	)	PUNCT
ejpam-5835	270	22	can	can	AUX
ejpam-5835	270	23	be	be	AUX
ejpam-5835	270	24	defined	define	VERB
ejpam-5835	270	25	by	by	ADP
ejpam-5835	270	26	(	(	PUNCT
ejpam-5835	270	27	1	1	NUM
ejpam-5835	270	28	)	)	PUNCT
ejpam-5835	270	29	σ̂n[xi	σ̂n[xi	NOUN
ejpam-5835	270	30	]	]	X
ejpam-5835	270	31	=	=	SYM
ejpam-5835	270	32	xi	xi	PROPN
ejpam-5835	270	33	for	for	ADP
ejpam-5835	270	34	any	any	DET
ejpam-5835	270	35	xi	xi	ADP
ejpam-5835	270	36	∈	∈	PROPN
ejpam-5835	270	37	xn	xn	PROPN
ejpam-5835	271	1	and	and	CCONJ
ejpam-5835	271	2	(	(	PUNCT
ejpam-5835	271	3	2	2	X
ejpam-5835	271	4	)	)	PUNCT
ejpam-5835	271	5	σ̂n[fi(t1	σ̂n[fi(t1	NOUN
ejpam-5835	271	6	,	,	PUNCT
ejpam-5835	271	7	.	.	PUNCT
ejpam-5835	271	8	.	.	PUNCT
ejpam-5835	272	1	.	.	PUNCT
ejpam-5835	273	1	,	,	PUNCT
ejpam-5835	273	2	tni	tni	NOUN
ejpam-5835	273	3	)	)	PUNCT
ejpam-5835	273	4	]	]	PUNCT
ejpam-5835	274	1	=	=	PUNCT
ejpam-5835	274	2	sn(σni(fi	sn(σni(fi	NOUN
ejpam-5835	274	3	)	)	PUNCT
ejpam-5835	274	4	,	,	PUNCT
ejpam-5835	274	5	σ̂n[t1	σ̂n[t1	PROPN
ejpam-5835	274	6	]	]	PUNCT
ejpam-5835	274	7	,	,	PUNCT
ejpam-5835	274	8	.	.	PUNCT
ejpam-5835	274	9	.	.	PUNCT
ejpam-5835	275	1	.	.	PUNCT
ejpam-5835	276	1	,	,	PUNCT
ejpam-5835	276	2	σ̂n[tni	σ̂n[tni	NOUN
ejpam-5835	276	3	]	]	PUNCT
ejpam-5835	276	4	)	)	PUNCT
ejpam-5835	276	5	if	if	SCONJ
ejpam-5835	276	6	each	each	DET
ejpam-5835	276	7	σ̂n[tj	σ̂n[tj	NOUN
ejpam-5835	276	8	]	]	PUNCT
ejpam-5835	276	9	is	be	AUX
ejpam-5835	276	10	already	already	ADV
ejpam-5835	276	11	known	know	VERB
ejpam-5835	276	12	for	for	ADP
ejpam-5835	276	13	1	1	NUM
ejpam-5835	276	14	≤	≤	NUM
ejpam-5835	276	15	j	j	PROPN
ejpam-5835	276	16	≤	≤	PROPN
ejpam-5835	276	17	ni	ni	PROPN
ejpam-5835	276	18	.	.	PROPN
ejpam-5835	277	1	then	then	ADV
ejpam-5835	277	2	we	we	PRON
ejpam-5835	277	3	prove	prove	VERB
ejpam-5835	277	4	:	:	PUNCT
ejpam-5835	277	5	theorem	theorem	NOUN
ejpam-5835	277	6	2	2	NUM
ejpam-5835	277	7	.	.	PUNCT
ejpam-5835	278	1	the	the	DET
ejpam-5835	278	2	extension	extension	NOUN
ejpam-5835	278	3	σ̂	σ̂	NUM
ejpam-5835	278	4	of	of	ADP
ejpam-5835	278	5	each	each	DET
ejpam-5835	278	6	σ	σ	NOUN
ejpam-5835	278	7	in	in	ADP
ejpam-5835	278	8	hypwfv(τ	hypwfv(τ	NOUN
ejpam-5835	278	9	)	)	PUNCT
ejpam-5835	278	10	is	be	AUX
ejpam-5835	278	11	an	an	DET
ejpam-5835	278	12	endomorphism	endomorphism	NOUN
ejpam-5835	278	13	on	on	ADP
ejpam-5835	278	14	the	the	DET
ejpam-5835	278	15	superassociative	superassociative	ADJ
ejpam-5835	278	16	system	system	NOUN
ejpam-5835	278	17	wwfv	wwfv	NOUN
ejpam-5835	278	18	τ	τ	PROPN
ejpam-5835	278	19	(	(	PUNCT
ejpam-5835	278	20	x	x	NOUN
ejpam-5835	278	21	)	)	PUNCT
ejpam-5835	278	22	.	.	PUNCT
ejpam-5835	279	1	proof	proof	NOUN
ejpam-5835	279	2	.	.	PUNCT
ejpam-5835	280	1	let	let	VERB
ejpam-5835	280	2	σ	σ	NUM
ejpam-5835	280	3	∈	∈	PROPN
ejpam-5835	280	4	hypwfv(τ	hypwfv(τ	NOUN
ejpam-5835	280	5	)	)	PUNCT
ejpam-5835	280	6	.	.	PUNCT
ejpam-5835	281	1	to	to	PART
ejpam-5835	281	2	prove	prove	VERB
ejpam-5835	281	3	that	that	SCONJ
ejpam-5835	281	4	σ̂	σ̂	PROPN
ejpam-5835	281	5	is	be	AUX
ejpam-5835	281	6	an	an	DET
ejpam-5835	281	7	endomorphism	endomorphism	NOUN
ejpam-5835	281	8	on	on	ADP
ejpam-5835	281	9	wwfv	wwfv	NOUN
ejpam-5835	281	10	τ	τ	PROPN
ejpam-5835	281	11	(	(	PUNCT
ejpam-5835	281	12	x	x	NOUN
ejpam-5835	281	13	)	)	PUNCT
ejpam-5835	281	14	,	,	PUNCT
ejpam-5835	281	15	we	we	PRON
ejpam-5835	281	16	aim	aim	VERB
ejpam-5835	281	17	to	to	PART
ejpam-5835	281	18	show	show	VERB
ejpam-5835	281	19	that	that	SCONJ
ejpam-5835	281	20	the	the	DET
ejpam-5835	281	21	equation	equation	NOUN
ejpam-5835	281	22	σ̂m[sn	σ̂m[sn	VERB
ejpam-5835	281	23	m(s	m(s	PROPN
ejpam-5835	281	24	,	,	PUNCT
ejpam-5835	281	25	t1	t1	NOUN
ejpam-5835	281	26	,	,	PUNCT
ejpam-5835	281	27	.	.	PUNCT
ejpam-5835	281	28	.	.	PUNCT
ejpam-5835	282	1	.	.	PUNCT
ejpam-5835	283	1	,	,	PUNCT
ejpam-5835	283	2	tn	tn	PROPN
ejpam-5835	283	3	)	)	PUNCT
ejpam-5835	283	4	]	]	PUNCT
ejpam-5835	284	1	=	=	SYM
ejpam-5835	284	2	sn	sn	PROPN
ejpam-5835	284	3	m(σ̂n[s	m(σ̂n[	NOUN
ejpam-5835	284	4	]	]	PUNCT
ejpam-5835	284	5	,	,	PUNCT
ejpam-5835	284	6	σ̂m[t1	σ̂m[t1	X
ejpam-5835	284	7	]	]	PUNCT
ejpam-5835	284	8	,	,	PUNCT
ejpam-5835	284	9	.	.	PUNCT
ejpam-5835	284	10	.	.	PUNCT
ejpam-5835	284	11	.	.	PUNCT
ejpam-5835	285	1	,	,	PUNCT
ejpam-5835	285	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	285	3	]	]	X
ejpam-5835	285	4	)	)	PUNCT
ejpam-5835	285	5	(	(	PUNCT
ejpam-5835	285	6	1	1	X
ejpam-5835	285	7	)	)	PUNCT
ejpam-5835	285	8	holds	hold	VERB
ejpam-5835	285	9	for	for	ADP
ejpam-5835	285	10	any	any	DET
ejpam-5835	285	11	s	s	X
ejpam-5835	285	12	∈	∈	NOUN
ejpam-5835	285	13	wwfv	wwfv	NOUN
ejpam-5835	285	14	τ	τ	X
ejpam-5835	285	15	(	(	PUNCT
ejpam-5835	285	16	xn	xn	PROPN
ejpam-5835	285	17	)	)	PUNCT
ejpam-5835	285	18	,	,	PUNCT
ejpam-5835	285	19	t1	t1	NOUN
ejpam-5835	285	20	,	,	PUNCT
ejpam-5835	285	21	.	.	PUNCT
ejpam-5835	285	22	.	.	PUNCT
ejpam-5835	286	1	.	.	PUNCT
ejpam-5835	287	1	,	,	PUNCT
ejpam-5835	287	2	tn	tn	PROPN
ejpam-5835	287	3	∈	∈	PROPN
ejpam-5835	287	4	wwfv	wwfv	NOUN
ejpam-5835	287	5	τ	τ	PROPN
ejpam-5835	287	6	(	(	PUNCT
ejpam-5835	287	7	xm	xm	PROPN
ejpam-5835	287	8	)	)	PUNCT
ejpam-5835	287	9	.	.	PUNCT
ejpam-5835	288	1	to	to	PART
ejpam-5835	288	2	do	do	VERB
ejpam-5835	288	3	this	this	PRON
ejpam-5835	288	4	,	,	PUNCT
ejpam-5835	288	5	we	we	PRON
ejpam-5835	288	6	give	give	VERB
ejpam-5835	288	7	a	a	DET
ejpam-5835	288	8	proof	proof	NOUN
ejpam-5835	288	9	on	on	ADP
ejpam-5835	288	10	the	the	DET
ejpam-5835	288	11	complexity	complexity	NOUN
ejpam-5835	288	12	of	of	ADP
ejpam-5835	288	13	a	a	DET
ejpam-5835	288	14	term	term	NOUN
ejpam-5835	288	15	s.	s.	PROPN
ejpam-5835	288	16	if	if	SCONJ
ejpam-5835	288	17	s	s	PROPN
ejpam-5835	288	18	is	be	AUX
ejpam-5835	288	19	a	a	DET
ejpam-5835	288	20	variable	variable	ADJ
ejpam-5835	288	21	xj	xj	PROPN
ejpam-5835	288	22	in	in	ADP
ejpam-5835	288	23	xn	xn	PROPN
ejpam-5835	288	24	,	,	PUNCT
ejpam-5835	288	25	then	then	ADV
ejpam-5835	288	26	σ̂m[sn	σ̂m[sn	SCONJ
ejpam-5835	288	27	m(xj	m(xj	ADV
ejpam-5835	288	28	,	,	PUNCT
ejpam-5835	288	29	t1	t1	PROPN
ejpam-5835	288	30	,	,	PUNCT
ejpam-5835	288	31	.	.	PUNCT
ejpam-5835	288	32	.	.	PUNCT
ejpam-5835	289	1	.	.	PUNCT
ejpam-5835	290	1	,	,	PUNCT
ejpam-5835	290	2	tn	tn	PROPN
ejpam-5835	290	3	)	)	PUNCT
ejpam-5835	290	4	]	]	PUNCT
ejpam-5835	291	1	=	=	PUNCT
ejpam-5835	291	2	σ̂m[tj	σ̂m[tj	ADJ
ejpam-5835	291	3	]	]	X
ejpam-5835	292	1	=	=	SYM
ejpam-5835	292	2	sn	sn	PROPN
ejpam-5835	292	3	m(xj	m(xj	ADV
ejpam-5835	292	4	,	,	PUNCT
ejpam-5835	292	5	σ̂m[t1	σ̂m[t1	ADP
ejpam-5835	292	6	]	]	PUNCT
ejpam-5835	292	7	,	,	PUNCT
ejpam-5835	292	8	.	.	PUNCT
ejpam-5835	292	9	.	.	PUNCT
ejpam-5835	292	10	.	.	PUNCT
ejpam-5835	293	1	,	,	PUNCT
ejpam-5835	293	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	293	3	]	]	X
ejpam-5835	293	4	)	)	PUNCT
ejpam-5835	294	1	=	=	SYM
ejpam-5835	294	2	sn	sn	PROPN
ejpam-5835	294	3	m(σ̂n[xj	m(σ̂n[xj	X
ejpam-5835	294	4	]	]	PUNCT
ejpam-5835	294	5	,	,	PUNCT
ejpam-5835	294	6	σ̂m[t1	σ̂m[t1	X
ejpam-5835	294	7	]	]	PUNCT
ejpam-5835	294	8	,	,	PUNCT
ejpam-5835	294	9	.	.	PUNCT
ejpam-5835	294	10	.	.	PUNCT
ejpam-5835	294	11	.	.	PUNCT
ejpam-5835	295	1	,	,	PUNCT
ejpam-5835	295	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	295	3	]	]	X
ejpam-5835	295	4	)	)	PUNCT
ejpam-5835	295	5	.	.	PUNCT
ejpam-5835	295	6	suppose	suppose	VERB
ejpam-5835	295	7	that	that	SCONJ
ejpam-5835	295	8	s	s	AUX
ejpam-5835	295	9	=	=	SYM
ejpam-5835	295	10	fi(s1	fi(s1	NOUN
ejpam-5835	295	11	,	,	PUNCT
ejpam-5835	295	12	.	.	PUNCT
ejpam-5835	295	13	.	.	PUNCT
ejpam-5835	296	1	.	.	PUNCT
ejpam-5835	297	1	,	,	PUNCT
ejpam-5835	297	2	sni	sni	PROPN
ejpam-5835	297	3	)	)	PUNCT
ejpam-5835	297	4	and	and	CCONJ
ejpam-5835	297	5	inductively	inductively	ADV
ejpam-5835	297	6	assume	assume	VERB
ejpam-5835	297	7	that	that	SCONJ
ejpam-5835	297	8	the	the	DET
ejpam-5835	297	9	equation	equation	NOUN
ejpam-5835	297	10	(	(	PUNCT
ejpam-5835	297	11	1	1	X
ejpam-5835	297	12	)	)	PUNCT
ejpam-5835	297	13	is	be	AUX
ejpam-5835	297	14	satisfied	satisfied	ADJ
ejpam-5835	297	15	for	for	ADP
ejpam-5835	297	16	s1	s1	NOUN
ejpam-5835	297	17	,	,	PUNCT
ejpam-5835	297	18	.	.	PUNCT
ejpam-5835	297	19	.	.	PUNCT
ejpam-5835	298	1	.	.	PUNCT
ejpam-5835	299	1	,	,	PUNCT
ejpam-5835	299	2	sni	sni	PROPN
ejpam-5835	299	3	.	.	PUNCT
ejpam-5835	300	1	without	without	ADP
ejpam-5835	300	2	loss	loss	NOUN
ejpam-5835	300	3	of	of	ADP
ejpam-5835	300	4	generality	generality	NOUN
ejpam-5835	300	5	we	we	PRON
ejpam-5835	300	6	may	may	AUX
ejpam-5835	300	7	assume	assume	VERB
ejpam-5835	300	8	that	that	SCONJ
ejpam-5835	300	9	var(sl	var(sl	NOUN
ejpam-5835	300	10	)	)	PUNCT
ejpam-5835	300	11	=	=	SYM
ejpam-5835	301	1	var(sk	var(sk	X
ejpam-5835	301	2	)	)	PUNCT
ejpam-5835	301	3	for	for	ADP
ejpam-5835	301	4	some	some	DET
ejpam-5835	301	5	1	1	NUM
ejpam-5835	301	6	≤	≤	NUM
ejpam-5835	302	1	l	l	NOUN
ejpam-5835	302	2	<	<	X
ejpam-5835	302	3	k	k	PROPN
ejpam-5835	302	4	≤	≤	PROPN
ejpam-5835	302	5	ni	ni	PROPN
ejpam-5835	302	6	.	.	PROPN
ejpam-5835	302	7	then	then	ADV
ejpam-5835	302	8	by	by	ADP
ejpam-5835	302	9	theorem	theorem	NOUN
ejpam-5835	302	10	1	1	NUM
ejpam-5835	302	11	,	,	PUNCT
ejpam-5835	302	12	we	we	PRON
ejpam-5835	302	13	obtain	obtain	VERB
ejpam-5835	302	14	σ̂m[sn	σ̂m[sn	ADJ
ejpam-5835	302	15	m(fi(s1	m(fi(s1	ADJ
ejpam-5835	302	16	,	,	PUNCT
ejpam-5835	302	17	.	.	PUNCT
ejpam-5835	302	18	.	.	PUNCT
ejpam-5835	302	19	.	.	PUNCT
ejpam-5835	303	1	,	,	PUNCT
ejpam-5835	303	2	sni	sni	PROPN
ejpam-5835	303	3	)	)	PUNCT
ejpam-5835	303	4	,	,	PUNCT
ejpam-5835	303	5	t1	t1	PROPN
ejpam-5835	303	6	,	,	PUNCT
ejpam-5835	303	7	.	.	PUNCT
ejpam-5835	303	8	.	.	PUNCT
ejpam-5835	304	1	.	.	PUNCT
ejpam-5835	305	1	,	,	PUNCT
ejpam-5835	305	2	tn	tn	PROPN
ejpam-5835	305	3	)	)	PUNCT
ejpam-5835	305	4	]	]	PUNCT
ejpam-5835	306	1	=	=	PUNCT
ejpam-5835	306	2	σ̂m[fi(s	σ̂m[fi(s	NOUN
ejpam-5835	306	3	n	n	CCONJ
ejpam-5835	306	4	m(s1	m(s1	VERB
ejpam-5835	306	5	,	,	PUNCT
ejpam-5835	306	6	t1	t1	NOUN
ejpam-5835	306	7	,	,	PUNCT
ejpam-5835	306	8	.	.	PUNCT
ejpam-5835	306	9	.	.	PUNCT
ejpam-5835	307	1	.	.	PUNCT
ejpam-5835	308	1	,	,	PUNCT
ejpam-5835	308	2	tn	tn	PROPN
ejpam-5835	308	3	)	)	PUNCT
ejpam-5835	308	4	,	,	PUNCT
ejpam-5835	308	5	.	.	PUNCT
ejpam-5835	308	6	.	.	PUNCT
ejpam-5835	309	1	.	.	PUNCT
ejpam-5835	310	1	,	,	PUNCT
ejpam-5835	310	2	s	s	VERB
ejpam-5835	310	3	n	n	PRON
ejpam-5835	310	4	m(sni	m(sni	PROPN
ejpam-5835	310	5	,	,	PUNCT
ejpam-5835	310	6	t1	t1	PROPN
ejpam-5835	310	7	,	,	PUNCT
ejpam-5835	310	8	.	.	PUNCT
ejpam-5835	310	9	.	.	PUNCT
ejpam-5835	311	1	.	.	PUNCT
ejpam-5835	312	1	,	,	PUNCT
ejpam-5835	312	2	tn	tn	PROPN
ejpam-5835	312	3	)	)	PUNCT
ejpam-5835	312	4	)	)	PUNCT
ejpam-5835	312	5	]	]	PUNCT
ejpam-5835	313	1	=	=	PUNCT
ejpam-5835	313	2	sni	sni	PROPN
ejpam-5835	313	3	m	m	PROPN
ejpam-5835	313	4	(	(	PUNCT
ejpam-5835	313	5	σni(fi	σni(fi	X
ejpam-5835	313	6	)	)	PUNCT
ejpam-5835	313	7	,	,	PUNCT
ejpam-5835	313	8	σ̂m[sn	σ̂m[sn	SCONJ
ejpam-5835	313	9	m(s1	m(s1	X
ejpam-5835	313	10	,	,	PUNCT
ejpam-5835	313	11	t1	t1	NOUN
ejpam-5835	313	12	,	,	PUNCT
ejpam-5835	313	13	.	.	PUNCT
ejpam-5835	313	14	.	.	PUNCT
ejpam-5835	314	1	.	.	PUNCT
ejpam-5835	315	1	,	,	PUNCT
ejpam-5835	315	2	tn	tn	PROPN
ejpam-5835	315	3	)	)	PUNCT
ejpam-5835	315	4	]	]	PUNCT
ejpam-5835	315	5	,	,	PUNCT
ejpam-5835	315	6	.	.	PUNCT
ejpam-5835	315	7	.	.	PUNCT
ejpam-5835	315	8	.	.	PUNCT
ejpam-5835	316	1	,	,	PUNCT
ejpam-5835	316	2	σ̂m[sn	σ̂m[sn	ADJ
ejpam-5835	316	3	m(sni	m(sni	PROPN
ejpam-5835	316	4	,	,	PUNCT
ejpam-5835	316	5	t1	t1	PROPN
ejpam-5835	316	6	,	,	PUNCT
ejpam-5835	316	7	.	.	PUNCT
ejpam-5835	316	8	.	.	PUNCT
ejpam-5835	317	1	.	.	PUNCT
ejpam-5835	318	1	,	,	PUNCT
ejpam-5835	318	2	tn	tn	PROPN
ejpam-5835	318	3	)	)	PUNCT
ejpam-5835	318	4	]	]	PUNCT
ejpam-5835	318	5	)	)	PUNCT
ejpam-5835	319	1	=	=	SYM
ejpam-5835	319	2	sni	sni	PROPN
ejpam-5835	319	3	m	m	PROPN
ejpam-5835	319	4	(	(	PUNCT
ejpam-5835	319	5	σni(fi	σni(fi	X
ejpam-5835	319	6	)	)	PUNCT
ejpam-5835	319	7	,	,	PUNCT
ejpam-5835	319	8	s	s	VERB
ejpam-5835	319	9	n	n	PRON
ejpam-5835	319	10	m(σ̂n[s1	m(σ̂n[s1	NOUN
ejpam-5835	319	11	]	]	X
ejpam-5835	319	12	,	,	PUNCT
ejpam-5835	319	13	σ̂m[t1	σ̂m[t1	X
ejpam-5835	319	14	]	]	PUNCT
ejpam-5835	319	15	,	,	PUNCT
ejpam-5835	319	16	.	.	PUNCT
ejpam-5835	319	17	.	.	PUNCT
ejpam-5835	319	18	.	.	PUNCT
ejpam-5835	320	1	,	,	PUNCT
ejpam-5835	320	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	320	3	]	]	X
ejpam-5835	320	4	)	)	PUNCT
ejpam-5835	320	5	,	,	PUNCT
ejpam-5835	320	6	.	.	PUNCT
ejpam-5835	320	7	.	.	PUNCT
ejpam-5835	321	1	.	.	PUNCT
ejpam-5835	322	1	,	,	PUNCT
ejpam-5835	322	2	s	s	VERB
ejpam-5835	322	3	nm(σ̂n[sni	nm(σ̂n[sni	X
ejpam-5835	322	4	]	]	PUNCT
ejpam-5835	322	5	,	,	PUNCT
ejpam-5835	322	6	σ̂m[t1	σ̂m[t1	X
ejpam-5835	322	7	]	]	PUNCT
ejpam-5835	322	8	,	,	PUNCT
ejpam-5835	322	9	.	.	PUNCT
ejpam-5835	322	10	.	.	PUNCT
ejpam-5835	322	11	.	.	PUNCT
ejpam-5835	323	1	,	,	PUNCT
ejpam-5835	323	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	323	3	]	]	X
ejpam-5835	323	4	)	)	PUNCT
ejpam-5835	323	5	)	)	PUNCT
ejpam-5835	324	1	=	=	PUNCT
ejpam-5835	324	2	sn	sn	PROPN
ejpam-5835	324	3	m	m	VERB
ejpam-5835	324	4	(	(	PUNCT
ejpam-5835	324	5	sni	sni	PROPN
ejpam-5835	324	6	n	n	PROPN
ejpam-5835	324	7	(	(	PUNCT
ejpam-5835	324	8	σni(fi	σni(fi	X
ejpam-5835	324	9	)	)	PUNCT
ejpam-5835	324	10	,	,	PUNCT
ejpam-5835	324	11	σ̂n[s1	σ̂n[s1	ADV
ejpam-5835	324	12	]	]	PUNCT
ejpam-5835	324	13	,	,	PUNCT
ejpam-5835	324	14	.	.	PUNCT
ejpam-5835	324	15	.	.	PUNCT
ejpam-5835	324	16	.	.	PUNCT
ejpam-5835	325	1	,	,	PUNCT
ejpam-5835	325	2	σ̂n[sni	σ̂n[sni	VERB
ejpam-5835	325	3	]	]	PUNCT
ejpam-5835	325	4	)	)	PUNCT
ejpam-5835	325	5	,	,	PUNCT
ejpam-5835	325	6	σ̂m[t1	σ̂m[t1	ADP
ejpam-5835	325	7	]	]	PUNCT
ejpam-5835	325	8	,	,	PUNCT
ejpam-5835	325	9	.	.	PUNCT
ejpam-5835	325	10	.	.	PUNCT
ejpam-5835	326	1	.	.	PUNCT
ejpam-5835	327	1	,	,	PUNCT
ejpam-5835	327	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	327	3	]	]	X
ejpam-5835	327	4	)	)	PUNCT
ejpam-5835	328	1	=	=	SYM
ejpam-5835	328	2	sn	sn	PROPN
ejpam-5835	328	3	m	m	VERB
ejpam-5835	328	4	(	(	PUNCT
ejpam-5835	328	5	σ̂n[fi(s1	σ̂n[fi(s1	VERB
ejpam-5835	328	6	,	,	PUNCT
ejpam-5835	328	7	.	.	PUNCT
ejpam-5835	328	8	.	.	PUNCT
ejpam-5835	328	9	.	.	PUNCT
ejpam-5835	329	1	,	,	PUNCT
ejpam-5835	329	2	sni	sni	PROPN
ejpam-5835	329	3	)	)	PUNCT
ejpam-5835	329	4	]	]	PUNCT
ejpam-5835	329	5	,	,	PUNCT
ejpam-5835	329	6	σ̂m[t1	σ̂m[t1	X
ejpam-5835	329	7	]	]	PUNCT
ejpam-5835	329	8	,	,	PUNCT
ejpam-5835	329	9	.	.	PUNCT
ejpam-5835	329	10	.	.	PUNCT
ejpam-5835	330	1	.	.	PUNCT
ejpam-5835	331	1	,	,	PUNCT
ejpam-5835	331	2	σ̂m[tn	σ̂m[tn	PROPN
ejpam-5835	331	3	]	]	X
ejpam-5835	331	4	)	)	PUNCT
ejpam-5835	331	5	,	,	PUNCT
ejpam-5835	331	6	which	which	PRON
ejpam-5835	331	7	shows	show	VERB
ejpam-5835	331	8	that	that	SCONJ
ejpam-5835	331	9	(	(	PUNCT
ejpam-5835	331	10	1	1	X
ejpam-5835	331	11	)	)	PUNCT
ejpam-5835	331	12	holds	hold	VERB
ejpam-5835	331	13	for	for	ADP
ejpam-5835	331	14	s	s	NOUN
ejpam-5835	331	15	=	=	SYM
ejpam-5835	331	16	fi(s1	fi(s1	NOUN
ejpam-5835	331	17	,	,	PUNCT
ejpam-5835	331	18	.	.	PUNCT
ejpam-5835	331	19	.	.	PUNCT
ejpam-5835	332	1	.	.	PUNCT
ejpam-5835	333	1	,	,	PUNCT
ejpam-5835	333	2	sni	sni	PROPN
ejpam-5835	333	3	)	)	PUNCT
ejpam-5835	333	4	.	.	PUNCT
ejpam-5835	334	1	t.	t.	PROPN
ejpam-5835	334	2	kumduang	kumduang	PROPN
ejpam-5835	334	3	,	,	PUNCT
ejpam-5835	334	4	k.	k.	PROPN
ejpam-5835	334	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	334	6	/	/	SYM
ejpam-5835	334	7	eur	eur	PROPN
ejpam-5835	334	8	.	.	PUNCT
ejpam-5835	335	1	j.	j.	PROPN
ejpam-5835	335	2	pure	pure	PROPN
ejpam-5835	335	3	appl	appl	PROPN
ejpam-5835	335	4	.	.	PROPN
ejpam-5835	335	5	math	math	PROPN
ejpam-5835	335	6	,	,	PUNCT
ejpam-5835	335	7	18	18	NUM
ejpam-5835	335	8	(	(	PUNCT
ejpam-5835	335	9	2	2	NUM
ejpam-5835	335	10	)	)	PUNCT
ejpam-5835	335	11	(	(	PUNCT
ejpam-5835	335	12	2025	2025	NUM
ejpam-5835	335	13	)	)	PUNCT
ejpam-5835	335	14	,	,	PUNCT
ejpam-5835	335	15	5835	5835	NUM
ejpam-5835	335	16	9	9	NUM
ejpam-5835	335	17	of	of	ADP
ejpam-5835	335	18	16	16	NUM
ejpam-5835	335	19	acutally	acutally	ADV
ejpam-5835	335	20	,	,	PUNCT
ejpam-5835	335	21	weakly	weakly	ADJ
ejpam-5835	335	22	fixed	fix	VERB
ejpam-5835	335	23	variable	variable	ADJ
ejpam-5835	335	24	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	335	25	of	of	ADP
ejpam-5835	335	26	type	type	NOUN
ejpam-5835	335	27	τ	τ	PROPN
ejpam-5835	335	28	can	can	AUX
ejpam-5835	335	29	be	be	AUX
ejpam-5835	335	30	considered	consider	VERB
ejpam-5835	335	31	as	as	ADP
ejpam-5835	335	32	multisorted	multisorte	VERB
ejpam-5835	335	33	mappings	mapping	NOUN
ejpam-5835	335	34	(	(	PUNCT
ejpam-5835	335	35	σn)n∈n	σn)n∈n	X
ejpam-5835	335	36	.	.	PUNCT
ejpam-5835	336	1	let	let	VERB
ejpam-5835	336	2	hypn(τ	hypn(τ	NOUN
ejpam-5835	336	3	)	)	PUNCT
ejpam-5835	336	4	be	be	AUX
ejpam-5835	336	5	the	the	DET
ejpam-5835	336	6	set	set	NOUN
ejpam-5835	336	7	of	of	ADP
ejpam-5835	336	8	all	all	DET
ejpam-5835	336	9	σn	σn	NOUN
ejpam-5835	336	10	and	and	CCONJ
ejpam-5835	336	11	let	let	VERB
ejpam-5835	336	12	(	(	PUNCT
ejpam-5835	336	13	hypn(τ))n∈n	hypn(τ))n∈n	X
ejpam-5835	336	14	be	be	AUX
ejpam-5835	336	15	the	the	DET
ejpam-5835	336	16	multisorted	multisorte	VERB
ejpam-5835	336	17	sets	set	NOUN
ejpam-5835	336	18	of	of	ADP
ejpam-5835	336	19	all	all	DET
ejpam-5835	336	20	weakly	weakly	ADV
ejpam-5835	336	21	fixed	fix	VERB
ejpam-5835	336	22	variable	variable	ADJ
ejpam-5835	336	23	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	336	24	.	.	PUNCT
ejpam-5835	337	1	we	we	PRON
ejpam-5835	337	2	see	see	VERB
ejpam-5835	337	3	that	that	SCONJ
ejpam-5835	337	4	the	the	DET
ejpam-5835	337	5	composition	composition	NOUN
ejpam-5835	337	6	mapping	mapping	NOUN
ejpam-5835	337	7	(	(	PUNCT
ejpam-5835	337	8	f	f	PROPN
ejpam-5835	337	9	n	n	PROPN
ejpam-5835	337	10	τ	τ	PROPN
ejpam-5835	337	11	)	)	PUNCT
ejpam-5835	337	12	n∈n	n∈n	NOUN
ejpam-5835	337	13	(	(	PUNCT
ejpam-5835	337	14	αn)n∈n−−−−−→	αn)n∈n−−−−−→	INTJ
ejpam-5835	337	15	(	(	PUNCT
ejpam-5835	337	16	wwfv	wwfv	PROPN
ejpam-5835	337	17	τ	τ	X
ejpam-5835	337	18	(	(	PUNCT
ejpam-5835	337	19	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	337	20	(	(	PUNCT
ejpam-5835	337	21	σ̂n)n∈n−−−−−→	σ̂n)n∈n−−−−−→	X
ejpam-5835	337	22	(	(	PUNCT
ejpam-5835	337	23	wwfv	wwfv	PROPN
ejpam-5835	337	24	τ	τ	X
ejpam-5835	337	25	(	(	PUNCT
ejpam-5835	337	26	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	337	27	is	be	AUX
ejpam-5835	337	28	an	an	DET
ejpam-5835	337	29	element	element	NOUN
ejpam-5835	337	30	in	in	ADP
ejpam-5835	337	31	the	the	DET
ejpam-5835	337	32	multisorted	multisorte	VERB
ejpam-5835	337	33	set	set	NOUN
ejpam-5835	337	34	(	(	PUNCT
ejpam-5835	337	35	hypwfv	hypwfv	NOUN
ejpam-5835	337	36	n	n	CCONJ
ejpam-5835	337	37	(	(	PUNCT
ejpam-5835	337	38	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	337	39	.	.	PUNCT
ejpam-5835	338	1	consequently	consequently	ADV
ejpam-5835	338	2	,	,	PUNCT
ejpam-5835	338	3	as	as	ADP
ejpam-5835	338	4	in	in	ADP
ejpam-5835	338	5	the	the	DET
ejpam-5835	338	6	one	one	NUM
ejpam-5835	338	7	-	-	PUNCT
ejpam-5835	338	8	sorted	sort	VERB
ejpam-5835	338	9	case	case	NOUN
ejpam-5835	338	10	,	,	PUNCT
ejpam-5835	338	11	the	the	DET
ejpam-5835	338	12	composition	composition	NOUN
ejpam-5835	338	13	between	between	ADP
ejpam-5835	338	14	any	any	DET
ejpam-5835	338	15	two	two	NUM
ejpam-5835	338	16	mappings	mapping	NOUN
ejpam-5835	338	17	hypwfv	hypwfv	NOUN
ejpam-5835	338	18	n	n	CCONJ
ejpam-5835	338	19	(	(	PUNCT
ejpam-5835	338	20	τ	τ	X
ejpam-5835	338	21	)	)	PUNCT
ejpam-5835	338	22	is	be	AUX
ejpam-5835	338	23	defined	define	VERB
ejpam-5835	338	24	by	by	ADP
ejpam-5835	338	25	σn	σn	PROPN
ejpam-5835	338	26	◦	◦	NOUN
ejpam-5835	339	1	hn	hn	PROPN
ejpam-5835	339	2	αn	αn	NOUN
ejpam-5835	339	3	=	=	SYM
ejpam-5835	339	4	σ̂n	σ̂n	NOUN
ejpam-5835	339	5	◦	◦	NOUN
ejpam-5835	339	6	n	n	NUM
ejpam-5835	339	7	αn	αn	NOUN
ejpam-5835	339	8	where	where	SCONJ
ejpam-5835	339	9	◦	◦	NOUN
ejpam-5835	339	10	n	n	PART
ejpam-5835	339	11	is	be	AUX
ejpam-5835	339	12	a	a	DET
ejpam-5835	339	13	usual	usual	ADJ
ejpam-5835	339	14	composition	composition	NOUN
ejpam-5835	339	15	on	on	ADP
ejpam-5835	339	16	the	the	DET
ejpam-5835	339	17	nth	nth	NOUN
ejpam-5835	339	18	sort	sort	NOUN
ejpam-5835	339	19	.	.	PUNCT
ejpam-5835	340	1	then	then	ADV
ejpam-5835	340	2	we	we	PRON
ejpam-5835	340	3	prove	prove	VERB
ejpam-5835	340	4	:	:	PUNCT
ejpam-5835	340	5	theorem	theorem	NOUN
ejpam-5835	340	6	3	3	NUM
ejpam-5835	340	7	.	.	PUNCT
ejpam-5835	341	1	(	(	PUNCT
ejpam-5835	341	2	hypwfv	hypwfv	NOUN
ejpam-5835	341	3	n	n	CCONJ
ejpam-5835	341	4	(	(	PUNCT
ejpam-5835	341	5	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	341	6	is	be	AUX
ejpam-5835	341	7	a	a	DET
ejpam-5835	341	8	subsemigroup	subsemigroup	NOUN
ejpam-5835	341	9	of	of	ADP
ejpam-5835	341	10	(	(	PUNCT
ejpam-5835	341	11	hypn(τ))n∈n	hypn(τ))n∈n	X
ejpam-5835	341	12	with	with	ADP
ejpam-5835	341	13	respect	respect	NOUN
ejpam-5835	341	14	to	to	ADP
ejpam-5835	341	15	the	the	DET
ejpam-5835	341	16	multisorted	multisorte	VERB
ejpam-5835	341	17	operation	operation	NOUN
ejpam-5835	341	18	(	(	PUNCT
ejpam-5835	341	19	ohn)n∈n	ohn)n∈n	INTJ
ejpam-5835	341	20	.	.	PUNCT
ejpam-5835	342	1	proof	proof	NOUN
ejpam-5835	342	2	.	.	PUNCT
ejpam-5835	343	1	the	the	DET
ejpam-5835	343	2	proof	proof	NOUN
ejpam-5835	343	3	follows	follow	VERB
ejpam-5835	343	4	from	from	ADP
ejpam-5835	343	5	lemma	lemma	PROPN
ejpam-5835	343	6	2	2	NUM
ejpam-5835	343	7	.	.	PUNCT
ejpam-5835	343	8	note	note	VERB
ejpam-5835	343	9	that	that	SCONJ
ejpam-5835	343	10	there	there	PRON
ejpam-5835	343	11	is	be	VERB
ejpam-5835	343	12	no	no	DET
ejpam-5835	343	13	an	an	DET
ejpam-5835	343	14	identity	identity	NOUN
ejpam-5835	343	15	element	element	NOUN
ejpam-5835	343	16	in	in	ADP
ejpam-5835	343	17	(	(	PUNCT
ejpam-5835	343	18	hypwfv	hypwfv	NOUN
ejpam-5835	343	19	n	n	CCONJ
ejpam-5835	343	20	(	(	PUNCT
ejpam-5835	343	21	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	343	22	bacause	bacause	NOUN
ejpam-5835	343	23	the	the	DET
ejpam-5835	343	24	image	image	NOUN
ejpam-5835	343	25	of	of	ADP
ejpam-5835	343	26	the	the	DET
ejpam-5835	343	27	mapping	mapping	NOUN
ejpam-5835	343	28	σid	σid	VERB
ejpam-5835	343	29	given	give	VERB
ejpam-5835	343	30	by	by	ADP
ejpam-5835	343	31	σid(fi	σid(fi	NOUN
ejpam-5835	343	32	)	)	PUNCT
ejpam-5835	343	33	=	=	SYM
ejpam-5835	343	34	fi(x1	fi(x1	ADJ
ejpam-5835	343	35	,	,	PUNCT
ejpam-5835	343	36	x2	x2	PROPN
ejpam-5835	343	37	,	,	PUNCT
ejpam-5835	343	38	.	.	PUNCT
ejpam-5835	343	39	.	.	PUNCT
ejpam-5835	344	1	.	.	PUNCT
ejpam-5835	345	1	,	,	PUNCT
ejpam-5835	345	2	xni	xni	PROPN
ejpam-5835	345	3	)	)	PUNCT
ejpam-5835	345	4	is	be	AUX
ejpam-5835	345	5	not	not	PART
ejpam-5835	345	6	a	a	DET
ejpam-5835	345	7	term	term	NOUN
ejpam-5835	345	8	of	of	ADP
ejpam-5835	345	9	a	a	DET
ejpam-5835	345	10	weakly	weakly	ADJ
ejpam-5835	345	11	fixed	fix	VERB
ejpam-5835	345	12	variable	variable	NOUN
ejpam-5835	345	13	.	.	PUNCT
ejpam-5835	346	1	consequently	consequently	ADV
ejpam-5835	346	2	,	,	PUNCT
ejpam-5835	346	3	(	(	PUNCT
ejpam-5835	346	4	hypwfv	hypwfv	NOUN
ejpam-5835	346	5	n	n	CCONJ
ejpam-5835	346	6	(	(	PUNCT
ejpam-5835	346	7	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	346	8	does	do	AUX
ejpam-5835	346	9	not	not	PART
ejpam-5835	346	10	form	form	VERB
ejpam-5835	346	11	a	a	DET
ejpam-5835	346	12	monoid	monoid	NOUN
ejpam-5835	346	13	.	.	PUNCT
ejpam-5835	347	1	for	for	ADP
ejpam-5835	347	2	any	any	DET
ejpam-5835	347	3	σn	σn	NOUN
ejpam-5835	347	4	and	and	CCONJ
ejpam-5835	347	5	αn	αn	NOUN
ejpam-5835	347	6	on	on	ADP
ejpam-5835	347	7	hypwfv	hypwfv	PROPN
ejpam-5835	347	8	n	n	CCONJ
ejpam-5835	347	9	(	(	PUNCT
ejpam-5835	347	10	τ	τ	PROPN
ejpam-5835	347	11	)	)	PUNCT
ejpam-5835	347	12	,	,	PUNCT
ejpam-5835	347	13	we	we	PRON
ejpam-5835	347	14	define	define	VERB
ejpam-5835	347	15	the	the	DET
ejpam-5835	347	16	binary	binary	ADJ
ejpam-5835	347	17	operation	operation	NOUN
ejpam-5835	347	18	+	+	PROPN
ejpam-5835	347	19	n	n	PROPN
ejpam-5835	347	20	on	on	ADP
ejpam-5835	347	21	hypwfv	hypwfv	PROPN
ejpam-5835	347	22	n	n	CCONJ
ejpam-5835	347	23	(	(	PUNCT
ejpam-5835	347	24	τ	τ	PROPN
ejpam-5835	347	25	)	)	PUNCT
ejpam-5835	347	26	by	by	ADP
ejpam-5835	347	27	(	(	PUNCT
ejpam-5835	347	28	σn	σn	NOUN
ejpam-5835	347	29	+	+	PROPN
ejpam-5835	347	30	n	n	NOUN
ejpam-5835	347	31	αn)(fi	αn)(fi	NUM
ejpam-5835	347	32	)	)	PUNCT
ejpam-5835	347	33	=	=	SYM
ejpam-5835	347	34	sni	sni	PROPN
ejpam-5835	347	35	n	n	PROPN
ejpam-5835	347	36	(	(	PUNCT
ejpam-5835	347	37	σn(fi	σn(fi	PROPN
ejpam-5835	347	38	)	)	PUNCT
ejpam-5835	347	39	,	,	PUNCT
ejpam-5835	347	40	αn(fi	αn(fi	PROPN
ejpam-5835	347	41	)	)	PUNCT
ejpam-5835	347	42	,	,	PUNCT
ejpam-5835	347	43	.	.	PUNCT
ejpam-5835	347	44	.	.	PUNCT
ejpam-5835	348	1	.	.	PUNCT
ejpam-5835	349	1	,	,	PUNCT
ejpam-5835	349	2	αn(fi	αn(fi	PROPN
ejpam-5835	349	3	)	)	PUNCT
ejpam-5835	349	4	)	)	PUNCT
ejpam-5835	349	5	.	.	PUNCT
ejpam-5835	350	1	it	it	PRON
ejpam-5835	350	2	is	be	AUX
ejpam-5835	350	3	obvious	obvious	ADJ
ejpam-5835	350	4	that	that	SCONJ
ejpam-5835	350	5	σn	σn	PROPN
ejpam-5835	350	6	+	+	PROPN
ejpam-5835	350	7	n	n	NUM
ejpam-5835	350	8	αn	αn	NOUN
ejpam-5835	350	9	is	be	AUX
ejpam-5835	350	10	again	again	ADV
ejpam-5835	350	11	a	a	DET
ejpam-5835	350	12	weakly	weakly	ADJ
ejpam-5835	350	13	fixed	fix	VERB
ejpam-5835	350	14	variable	variable	ADJ
ejpam-5835	350	15	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	350	16	of	of	ADP
ejpam-5835	350	17	type	type	NOUN
ejpam-5835	350	18	τ	τ	PROPN
ejpam-5835	350	19	.	.	PUNCT
ejpam-5835	351	1	from	from	ADP
ejpam-5835	351	2	this	this	PRON
ejpam-5835	351	3	,	,	PUNCT
ejpam-5835	351	4	we	we	PRON
ejpam-5835	351	5	have	have	VERB
ejpam-5835	351	6	the	the	DET
ejpam-5835	351	7	following	follow	VERB
ejpam-5835	351	8	result	result	NOUN
ejpam-5835	351	9	.	.	PUNCT
ejpam-5835	352	1	theorem	theorem	ADJ
ejpam-5835	352	2	4	4	NUM
ejpam-5835	352	3	.	.	PUNCT
ejpam-5835	353	1	(	(	PUNCT
ejpam-5835	353	2	(	(	PUNCT
ejpam-5835	353	3	hypwfv	hypwfv	NOUN
ejpam-5835	353	4	n	n	CCONJ
ejpam-5835	353	5	(	(	PUNCT
ejpam-5835	353	6	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	353	7	,	,	PUNCT
ejpam-5835	353	8	(	(	PUNCT
ejpam-5835	353	9	◦	◦	NOUN
ejpam-5835	353	10	hn)n∈n	hn)n∈n	NUM
ejpam-5835	353	11	,	,	PUNCT
ejpam-5835	353	12	(	(	PUNCT
ejpam-5835	353	13	+	+	ADJ
ejpam-5835	353	14	n)n∈n	n)n∈n	NOUN
ejpam-5835	353	15	)	)	PUNCT
ejpam-5835	353	16	forms	form	VERB
ejpam-5835	353	17	a	a	DET
ejpam-5835	353	18	left	left	ADV
ejpam-5835	353	19	-	-	PUNCT
ejpam-5835	353	20	seminearring	seminearring	NOUN
ejpam-5835	353	21	.	.	PUNCT
ejpam-5835	354	1	proof	proof	NOUN
ejpam-5835	354	2	.	.	PUNCT
ejpam-5835	355	1	for	for	ADP
ejpam-5835	355	2	each	each	DET
ejpam-5835	355	3	n	n	PRON
ejpam-5835	355	4	∈	∈	PROPN
ejpam-5835	355	5	n	n	CCONJ
ejpam-5835	355	6	,	,	PUNCT
ejpam-5835	355	7	we	we	PRON
ejpam-5835	355	8	first	first	ADV
ejpam-5835	355	9	show	show	VERB
ejpam-5835	355	10	that	that	SCONJ
ejpam-5835	355	11	the	the	DET
ejpam-5835	355	12	operation	operation	NOUN
ejpam-5835	355	13	+	+	NOUN
ejpam-5835	355	14	n	n	ADJ
ejpam-5835	355	15	is	be	AUX
ejpam-5835	355	16	associative	associative	ADJ
ejpam-5835	355	17	,	,	PUNCT
ejpam-5835	355	18	i.e.	i.e.	X
ejpam-5835	355	19	,	,	PUNCT
ejpam-5835	355	20	(	(	PUNCT
ejpam-5835	355	21	(	(	PUNCT
ejpam-5835	355	22	σn	σn	X
ejpam-5835	355	23	+	+	PROPN
ejpam-5835	355	24	n	n	NUM
ejpam-5835	355	25	αn	αn	NOUN
ejpam-5835	355	26	)	)	PUNCT
ejpam-5835	355	27	+	+	CCONJ
ejpam-5835	355	28	βn	βn	NOUN
ejpam-5835	355	29	)	)	PUNCT
ejpam-5835	355	30	=	=	SYM
ejpam-5835	355	31	(	(	PUNCT
ejpam-5835	355	32	σ1	σ1	NOUN
ejpam-5835	355	33	+	+	CCONJ
ejpam-5835	355	34	(	(	PUNCT
ejpam-5835	355	35	σ2	σ2	PROPN
ejpam-5835	355	36	+	+	CCONJ
ejpam-5835	355	37	σ3	σ3	PROPN
ejpam-5835	355	38	)	)	PUNCT
ejpam-5835	355	39	)	)	PUNCT
ejpam-5835	355	40	for	for	ADP
ejpam-5835	355	41	all	all	DET
ejpam-5835	355	42	σn	σn	NOUN
ejpam-5835	355	43	,	,	PUNCT
ejpam-5835	355	44	αn	αn	VERB
ejpam-5835	355	45	,	,	PUNCT
ejpam-5835	355	46	βn	βn	NOUN
ejpam-5835	355	47	∈	∈	PROPN
ejpam-5835	355	48	hypwfv(τ	hypwfv(τ	NOUN
ejpam-5835	355	49	)	)	PUNCT
ejpam-5835	355	50	.	.	PUNCT
ejpam-5835	356	1	for	for	ADP
ejpam-5835	356	2	this	this	PRON
ejpam-5835	356	3	,	,	PUNCT
ejpam-5835	356	4	let	let	VERB
ejpam-5835	356	5	fi	fi	NOUN
ejpam-5835	356	6	be	be	AUX
ejpam-5835	356	7	an	an	DET
ejpam-5835	356	8	operation	operation	NOUN
ejpam-5835	356	9	symbol	symbol	NOUN
ejpam-5835	356	10	.	.	PUNCT
ejpam-5835	357	1	then	then	ADV
ejpam-5835	357	2	by	by	ADP
ejpam-5835	357	3	theorem	theorem	NOUN
ejpam-5835	357	4	1	1	NUM
ejpam-5835	357	5	,	,	PUNCT
ejpam-5835	357	6	we	we	PRON
ejpam-5835	357	7	obtain	obtain	VERB
ejpam-5835	357	8	(	(	PUNCT
ejpam-5835	357	9	(	(	PUNCT
ejpam-5835	357	10	σn	σn	X
ejpam-5835	357	11	+	+	PROPN
ejpam-5835	357	12	n	n	NUM
ejpam-5835	357	13	αn	αn	NOUN
ejpam-5835	357	14	)	)	PUNCT
ejpam-5835	357	15	+	+	CCONJ
ejpam-5835	357	16	βn)(fi	βn)(fi	PUNCT
ejpam-5835	357	17	)	)	PUNCT
ejpam-5835	357	18	=	=	SYM
ejpam-5835	357	19	sn	sn	X
ejpam-5835	357	20	n((σn	n((σn	X
ejpam-5835	357	21	+	+	PROPN
ejpam-5835	357	22	n	n	PROPN
ejpam-5835	357	23	αn)(fi	αn)(fi	NUM
ejpam-5835	357	24	)	)	PUNCT
ejpam-5835	357	25	,	,	PUNCT
ejpam-5835	357	26	βn(fi	βn(fi	PROPN
ejpam-5835	357	27	)	)	PUNCT
ejpam-5835	357	28	,	,	PUNCT
ejpam-5835	357	29	.	.	PUNCT
ejpam-5835	357	30	.	.	PUNCT
ejpam-5835	357	31	.	.	PUNCT
ejpam-5835	358	1	,	,	PUNCT
ejpam-5835	358	2	βn(fi	βn(fi	PROPN
ejpam-5835	358	3	)	)	PUNCT
ejpam-5835	358	4	)	)	PUNCT
ejpam-5835	359	1	=	=	SYM
ejpam-5835	359	2	sn	sn	PROPN
ejpam-5835	359	3	n(s	n(s	PROPN
ejpam-5835	359	4	n	n	CCONJ
ejpam-5835	359	5	n(σn(fi	n(σn(fi	NOUN
ejpam-5835	359	6	)	)	PUNCT
ejpam-5835	359	7	,	,	PUNCT
ejpam-5835	359	8	αn(fi	αn(fi	PROPN
ejpam-5835	359	9	)	)	PUNCT
ejpam-5835	359	10	,	,	PUNCT
ejpam-5835	359	11	.	.	PUNCT
ejpam-5835	359	12	.	.	PUNCT
ejpam-5835	360	1	.	.	PUNCT
ejpam-5835	361	1	,	,	PUNCT
ejpam-5835	361	2	αn(fi	αn(fi	PROPN
ejpam-5835	361	3	)	)	PUNCT
ejpam-5835	361	4	)	)	PUNCT
ejpam-5835	361	5	,	,	PUNCT
ejpam-5835	361	6	βn(fi	βn(fi	PROPN
ejpam-5835	361	7	)	)	PUNCT
ejpam-5835	361	8	,	,	PUNCT
ejpam-5835	361	9	.	.	PUNCT
ejpam-5835	361	10	.	.	PUNCT
ejpam-5835	362	1	.	.	PUNCT
ejpam-5835	363	1	,	,	PUNCT
ejpam-5835	363	2	βn(fi	βn(fi	PROPN
ejpam-5835	363	3	)	)	PUNCT
ejpam-5835	363	4	)	)	PUNCT
ejpam-5835	364	1	=	=	SYM
ejpam-5835	364	2	sn	sn	PROPN
ejpam-5835	364	3	n(σn(fi	n(σn(fi	PROPN
ejpam-5835	364	4	)	)	PUNCT
ejpam-5835	364	5	,	,	PUNCT
ejpam-5835	364	6	s	s	VERB
ejpam-5835	364	7	n	n	PRON
ejpam-5835	364	8	n(αn(fi	n(αn(fi	NUM
ejpam-5835	364	9	)	)	PUNCT
ejpam-5835	364	10	,	,	PUNCT
ejpam-5835	364	11	βn(fi	βn(fi	PROPN
ejpam-5835	364	12	)	)	PUNCT
ejpam-5835	364	13	,	,	PUNCT
ejpam-5835	364	14	.	.	PUNCT
ejpam-5835	364	15	.	.	PUNCT
ejpam-5835	365	1	.	.	PUNCT
ejpam-5835	366	1	,	,	PUNCT
ejpam-5835	366	2	βn(fi	βn(fi	PROPN
ejpam-5835	366	3	)	)	PUNCT
ejpam-5835	366	4	)	)	PUNCT
ejpam-5835	366	5	,	,	PUNCT
ejpam-5835	366	6	.	.	PUNCT
ejpam-5835	366	7	.	.	PUNCT
ejpam-5835	367	1	.	.	PUNCT
ejpam-5835	368	1	,	,	PUNCT
ejpam-5835	368	2	s	s	VERB
ejpam-5835	368	3	n	n	PRON
ejpam-5835	368	4	n(αn(fi	n(αn(fi	NUM
ejpam-5835	368	5	)	)	PUNCT
ejpam-5835	368	6	,	,	PUNCT
ejpam-5835	368	7	βn(fi	βn(fi	PROPN
ejpam-5835	368	8	)	)	PUNCT
ejpam-5835	368	9	,	,	PUNCT
ejpam-5835	368	10	.	.	PUNCT
ejpam-5835	368	11	.	.	PUNCT
ejpam-5835	369	1	.	.	PUNCT
ejpam-5835	370	1	,	,	PUNCT
ejpam-5835	370	2	βn(fi	βn(fi	PROPN
ejpam-5835	370	3	)	)	PUNCT
ejpam-5835	370	4	)	)	PUNCT
ejpam-5835	370	5	)	)	PUNCT
ejpam-5835	371	1	=	=	SYM
ejpam-5835	371	2	sn	sn	PROPN
ejpam-5835	371	3	n(σn(fi	n(σn(fi	PROPN
ejpam-5835	371	4	)	)	PUNCT
ejpam-5835	371	5	,	,	PUNCT
ejpam-5835	371	6	(	(	PUNCT
ejpam-5835	371	7	αn	αn	NOUN
ejpam-5835	371	8	+	+	NOUN
ejpam-5835	371	9	n	n	NOUN
ejpam-5835	371	10	βn)(fi	βn)(fi	PUNCT
ejpam-5835	371	11	)	)	PUNCT
ejpam-5835	371	12	,	,	PUNCT
ejpam-5835	371	13	.	.	PUNCT
ejpam-5835	371	14	.	.	PUNCT
ejpam-5835	371	15	.	.	PUNCT
ejpam-5835	372	1	,	,	PUNCT
ejpam-5835	372	2	(	(	PUNCT
ejpam-5835	372	3	αn	αn	INTJ
ejpam-5835	372	4	+	+	NOUN
ejpam-5835	372	5	n	n	NOUN
ejpam-5835	372	6	βn)(fi	βn)(fi	NUM
ejpam-5835	372	7	)	)	PUNCT
ejpam-5835	372	8	)	)	PUNCT
ejpam-5835	373	1	=	=	SYM
ejpam-5835	373	2	(	(	PUNCT
ejpam-5835	373	3	σn	σn	X
ejpam-5835	373	4	+	+	NOUN
ejpam-5835	373	5	n	n	NOUN
ejpam-5835	373	6	(	(	PUNCT
ejpam-5835	373	7	αn	αn	NOUN
ejpam-5835	373	8	+	+	CCONJ
ejpam-5835	373	9	βn))(fi	βn))(fi	NOUN
ejpam-5835	373	10	)	)	PUNCT
ejpam-5835	373	11	.	.	PUNCT
ejpam-5835	374	1	t.	t.	PROPN
ejpam-5835	374	2	kumduang	kumduang	PROPN
ejpam-5835	374	3	,	,	PUNCT
ejpam-5835	374	4	k.	k.	PROPN
ejpam-5835	374	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	374	6	/	/	SYM
ejpam-5835	374	7	eur	eur	PROPN
ejpam-5835	374	8	.	.	PUNCT
ejpam-5835	375	1	j.	j.	PROPN
ejpam-5835	375	2	pure	pure	PROPN
ejpam-5835	375	3	appl	appl	PROPN
ejpam-5835	375	4	.	.	PROPN
ejpam-5835	375	5	math	math	PROPN
ejpam-5835	375	6	,	,	PUNCT
ejpam-5835	375	7	18	18	NUM
ejpam-5835	375	8	(	(	PUNCT
ejpam-5835	375	9	2	2	NUM
ejpam-5835	375	10	)	)	PUNCT
ejpam-5835	375	11	(	(	PUNCT
ejpam-5835	375	12	2025	2025	NUM
ejpam-5835	375	13	)	)	PUNCT
ejpam-5835	375	14	,	,	PUNCT
ejpam-5835	375	15	5835	5835	NUM
ejpam-5835	375	16	10	10	NUM
ejpam-5835	375	17	of	of	ADP
ejpam-5835	375	18	16	16	NUM
ejpam-5835	375	19	furthermore	furthermore	ADV
ejpam-5835	375	20	,	,	PUNCT
ejpam-5835	375	21	the	the	DET
ejpam-5835	375	22	left	left	ADJ
ejpam-5835	375	23	distributive	distributive	ADJ
ejpam-5835	375	24	law	law	NOUN
ejpam-5835	375	25	,	,	PUNCT
ejpam-5835	375	26	i.e.	i.e.	X
ejpam-5835	375	27	,	,	PUNCT
ejpam-5835	375	28	σn	σn	PROPN
ejpam-5835	375	29	◦	◦	NOUN
ejpam-5835	375	30	hn	hn	PROPN
ejpam-5835	375	31	(	(	PUNCT
ejpam-5835	375	32	αn	αn	INTJ
ejpam-5835	375	33	+	+	ADV
ejpam-5835	375	34	n	n	ADJ
ejpam-5835	375	35	βn	βn	ADJ
ejpam-5835	375	36	)	)	PUNCT
ejpam-5835	375	37	=	=	SYM
ejpam-5835	375	38	(	(	PUNCT
ejpam-5835	375	39	σn	σn	NOUN
ejpam-5835	375	40	◦	◦	NOUN
ejpam-5835	375	41	hn	hn	PROPN
ejpam-5835	375	42	αn	αn	NOUN
ejpam-5835	375	43	)	)	PUNCT
ejpam-5835	376	1	+	+	NOUN
ejpam-5835	376	2	n	n	X
ejpam-5835	376	3	(	(	PUNCT
ejpam-5835	376	4	σn	σn	NOUN
ejpam-5835	376	5	◦	◦	NOUN
ejpam-5835	376	6	hn	hn	PROPN
ejpam-5835	376	7	βn	βn	NOUN
ejpam-5835	376	8	)	)	PUNCT
ejpam-5835	376	9	is	be	AUX
ejpam-5835	376	10	also	also	ADV
ejpam-5835	376	11	obtained	obtain	VERB
ejpam-5835	376	12	.	.	PUNCT
ejpam-5835	377	1	indeed	indeed	ADV
ejpam-5835	377	2	,	,	PUNCT
ejpam-5835	377	3	from	from	ADP
ejpam-5835	377	4	the	the	DET
ejpam-5835	377	5	fact	fact	NOUN
ejpam-5835	377	6	that	that	SCONJ
ejpam-5835	377	7	the	the	DET
ejpam-5835	377	8	extension	extension	NOUN
ejpam-5835	377	9	of	of	ADP
ejpam-5835	377	10	each	each	DET
ejpam-5835	377	11	mapping	mapping	NOUN
ejpam-5835	377	12	on	on	ADP
ejpam-5835	377	13	hypwfv(τ	hypwfv(τ	NOUN
ejpam-5835	377	14	)	)	PUNCT
ejpam-5835	377	15	preserves	preserve	VERB
ejpam-5835	377	16	the	the	DET
ejpam-5835	377	17	operations	operation	NOUN
ejpam-5835	377	18	on	on	ADP
ejpam-5835	377	19	the	the	DET
ejpam-5835	377	20	multisorted	multisorte	VERB
ejpam-5835	377	21	algebra	algebra	NOUN
ejpam-5835	377	22	wwfv	wwfv	NOUN
ejpam-5835	377	23	τ	τ	PROPN
ejpam-5835	377	24	(	(	PUNCT
ejpam-5835	377	25	x	x	NOUN
ejpam-5835	377	26	)	)	PUNCT
ejpam-5835	377	27	proved	prove	VERB
ejpam-5835	377	28	in	in	ADP
ejpam-5835	377	29	theorem	theorem	NOUN
ejpam-5835	377	30	2	2	NUM
ejpam-5835	377	31	,	,	PUNCT
ejpam-5835	377	32	we	we	PRON
ejpam-5835	377	33	have	have	AUX
ejpam-5835	377	34	(	(	PUNCT
ejpam-5835	377	35	σn	σn	NOUN
ejpam-5835	377	36	◦	◦	NOUN
ejpam-5835	377	37	hn	hn	PROPN
ejpam-5835	377	38	(	(	PUNCT
ejpam-5835	377	39	αn	αn	INTJ
ejpam-5835	377	40	+	+	NOUN
ejpam-5835	377	41	n	n	NOUN
ejpam-5835	377	42	βn))(fi	βn))(fi	NOUN
ejpam-5835	377	43	)	)	PUNCT
ejpam-5835	377	44	=	=	PUNCT
ejpam-5835	377	45	σ̂n[(αn	σ̂n[(αn	VERB
ejpam-5835	377	46	+	+	NOUN
ejpam-5835	377	47	n	n	NOUN
ejpam-5835	377	48	βn)(fi	βn)(fi	PUNCT
ejpam-5835	377	49	)	)	PUNCT
ejpam-5835	377	50	]	]	PUNCT
ejpam-5835	378	1	=	=	PUNCT
ejpam-5835	378	2	σ̂n[s	σ̂n[	NOUN
ejpam-5835	378	3	n	n	PRON
ejpam-5835	378	4	n(αn(fi	n(αn(fi	NUM
ejpam-5835	378	5	)	)	PUNCT
ejpam-5835	378	6	,	,	PUNCT
ejpam-5835	378	7	βn(fi	βn(fi	PROPN
ejpam-5835	378	8	)	)	PUNCT
ejpam-5835	378	9	,	,	PUNCT
ejpam-5835	378	10	.	.	PUNCT
ejpam-5835	378	11	.	.	PUNCT
ejpam-5835	378	12	.	.	PUNCT
ejpam-5835	378	13	,	,	PUNCT
ejpam-5835	378	14	βn(fi	βn(fi	PROPN
ejpam-5835	378	15	)	)	PUNCT
ejpam-5835	378	16	)	)	PUNCT
ejpam-5835	378	17	]	]	PUNCT
ejpam-5835	379	1	=	=	PUNCT
ejpam-5835	379	2	sn	sn	PROPN
ejpam-5835	379	3	n(σ̂n[αn(fi	n(σ̂n[αn(fi	PROPN
ejpam-5835	379	4	)	)	PUNCT
ejpam-5835	379	5	]	]	PUNCT
ejpam-5835	379	6	,	,	PUNCT
ejpam-5835	379	7	σ̂n[βn(fi	σ̂n[βn(fi	PROPN
ejpam-5835	379	8	)	)	PUNCT
ejpam-5835	379	9	]	]	PUNCT
ejpam-5835	379	10	,	,	PUNCT
ejpam-5835	379	11	.	.	PUNCT
ejpam-5835	379	12	.	.	PUNCT
ejpam-5835	379	13	.	.	PUNCT
ejpam-5835	380	1	,	,	PUNCT
ejpam-5835	380	2	σ̂n[βn(fi	σ̂n[βn(fi	PROPN
ejpam-5835	380	3	)	)	PUNCT
ejpam-5835	380	4	]	]	PUNCT
ejpam-5835	380	5	)	)	PUNCT
ejpam-5835	381	1	=	=	SYM
ejpam-5835	381	2	sn	sn	PROPN
ejpam-5835	381	3	n((σn	n((σn	X
ejpam-5835	381	4	◦	◦	NOUN
ejpam-5835	381	5	hn	hn	PROPN
ejpam-5835	381	6	αn)(fi	αn)(fi	PROPN
ejpam-5835	381	7	)	)	PUNCT
ejpam-5835	381	8	,	,	PUNCT
ejpam-5835	381	9	(	(	PUNCT
ejpam-5835	381	10	σn	σn	NOUN
ejpam-5835	381	11	◦	◦	NOUN
ejpam-5835	381	12	hn	hn	PROPN
ejpam-5835	381	13	βn)(fi	βn)(fi	PUNCT
ejpam-5835	381	14	)	)	PUNCT
ejpam-5835	381	15	,	,	PUNCT
ejpam-5835	381	16	.	.	PUNCT
ejpam-5835	381	17	.	.	PUNCT
ejpam-5835	381	18	.	.	PUNCT
ejpam-5835	382	1	,	,	PUNCT
ejpam-5835	382	2	(	(	PUNCT
ejpam-5835	382	3	σn	σn	NOUN
ejpam-5835	382	4	◦	◦	NOUN
ejpam-5835	382	5	hn	hn	PROPN
ejpam-5835	382	6	βn)(fi	βn)(fi	PUNCT
ejpam-5835	382	7	)	)	PUNCT
ejpam-5835	382	8	)	)	PUNCT
ejpam-5835	383	1	=	=	SYM
ejpam-5835	383	2	(	(	PUNCT
ejpam-5835	383	3	(	(	PUNCT
ejpam-5835	383	4	σn	σn	NOUN
ejpam-5835	383	5	◦	◦	NOUN
ejpam-5835	383	6	hn	hn	PROPN
ejpam-5835	383	7	αn	αn	NOUN
ejpam-5835	383	8	)	)	PUNCT
ejpam-5835	384	1	+	+	NOUN
ejpam-5835	384	2	n	n	X
ejpam-5835	384	3	(	(	PUNCT
ejpam-5835	384	4	σn	σn	NOUN
ejpam-5835	384	5	◦	◦	NOUN
ejpam-5835	384	6	hn	hn	PROPN
ejpam-5835	384	7	βn))(fi	βn))(fi	PROPN
ejpam-5835	384	8	)	)	PUNCT
ejpam-5835	384	9	.	.	PUNCT
ejpam-5835	385	1	therefore	therefore	ADV
ejpam-5835	385	2	,	,	PUNCT
ejpam-5835	385	3	(	(	PUNCT
ejpam-5835	385	4	(	(	PUNCT
ejpam-5835	385	5	hypwfv	hypwfv	NOUN
ejpam-5835	385	6	n	n	CCONJ
ejpam-5835	385	7	(	(	PUNCT
ejpam-5835	385	8	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	385	9	,	,	PUNCT
ejpam-5835	385	10	(	(	PUNCT
ejpam-5835	385	11	◦	◦	NOUN
ejpam-5835	385	12	hn)n∈n	hn)n∈n	NUM
ejpam-5835	385	13	,	,	PUNCT
ejpam-5835	385	14	(	(	PUNCT
ejpam-5835	385	15	+	+	ADV
ejpam-5835	385	16	n)n∈n	n)n∈n	NOUN
ejpam-5835	385	17	)	)	PUNCT
ejpam-5835	385	18	is	be	AUX
ejpam-5835	385	19	a	a	DET
ejpam-5835	385	20	left	left	ADV
ejpam-5835	385	21	-	-	PUNCT
ejpam-5835	385	22	seminearring	seminearring	NOUN
ejpam-5835	385	23	.	.	PUNCT
ejpam-5835	386	1	generally	generally	ADV
ejpam-5835	386	2	,	,	PUNCT
ejpam-5835	386	3	the	the	DET
ejpam-5835	386	4	right	right	ADJ
ejpam-5835	386	5	distributivity	distributivity	NOUN
ejpam-5835	386	6	does	do	AUX
ejpam-5835	386	7	not	not	PART
ejpam-5835	386	8	hold	hold	VERB
ejpam-5835	386	9	,	,	PUNCT
ejpam-5835	386	10	as	as	SCONJ
ejpam-5835	386	11	demonstrated	demonstrate	VERB
ejpam-5835	386	12	by	by	ADP
ejpam-5835	386	13	the	the	DET
ejpam-5835	386	14	following	follow	VERB
ejpam-5835	386	15	counterexample	counterexample	PROPN
ejpam-5835	386	16	.	.	PUNCT
ejpam-5835	386	17	example	example	NOUN
ejpam-5835	387	1	3	3	X
ejpam-5835	387	2	.	.	PUNCT
ejpam-5835	387	3	let	let	VERB
ejpam-5835	387	4	τ	τ	PROPN
ejpam-5835	387	5	=	=	PUNCT
ejpam-5835	387	6	(	(	PUNCT
ejpam-5835	387	7	3	3	X
ejpam-5835	387	8	)	)	PUNCT
ejpam-5835	387	9	be	be	AUX
ejpam-5835	387	10	a	a	DET
ejpam-5835	387	11	type	type	NOUN
ejpam-5835	387	12	with	with	ADP
ejpam-5835	387	13	a	a	DET
ejpam-5835	387	14	ternary	ternary	ADJ
ejpam-5835	387	15	operation	operation	NOUN
ejpam-5835	387	16	symbol	symbol	NOUN
ejpam-5835	387	17	⊞.	⊞.	PROPN
ejpam-5835	387	18	assume	assume	VERB
ejpam-5835	387	19	that	that	SCONJ
ejpam-5835	387	20	σ3	σ3	PROPN
ejpam-5835	387	21	,	,	PUNCT
ejpam-5835	387	22	α3	α3	NOUN
ejpam-5835	387	23	and	and	CCONJ
ejpam-5835	387	24	β3	β3	AUX
ejpam-5835	387	25	be	be	AUX
ejpam-5835	387	26	weakly	weakly	ADV
ejpam-5835	387	27	fixed	fix	VERB
ejpam-5835	387	28	variable	variable	ADJ
ejpam-5835	387	29	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	387	30	of	of	ADP
ejpam-5835	387	31	type	type	NOUN
ejpam-5835	387	32	(	(	PUNCT
ejpam-5835	387	33	3	3	NUM
ejpam-5835	387	34	)	)	PUNCT
ejpam-5835	387	35	which	which	PRON
ejpam-5835	387	36	are	be	AUX
ejpam-5835	387	37	defined	define	VERB
ejpam-5835	387	38	by	by	ADP
ejpam-5835	387	39	σ3(⊞	σ3(⊞	NUM
ejpam-5835	387	40	)	)	PUNCT
ejpam-5835	387	41	=	=	SYM
ejpam-5835	388	1	⊞(x1	⊞(x1	NOUN
ejpam-5835	388	2	,	,	PUNCT
ejpam-5835	388	3	x3	x3	ADJ
ejpam-5835	388	4	,	,	PUNCT
ejpam-5835	388	5	x1	x1	PROPN
ejpam-5835	388	6	)	)	PUNCT
ejpam-5835	388	7	,	,	PUNCT
ejpam-5835	388	8	α3(⊞	α3(⊞	NUM
ejpam-5835	388	9	)	)	PUNCT
ejpam-5835	388	10	=	=	PUNCT
ejpam-5835	388	11	⊞(x3	⊞(x3	PROPN
ejpam-5835	388	12	,	,	PUNCT
ejpam-5835	388	13	x1	x1	PROPN
ejpam-5835	388	14	,	,	PUNCT
ejpam-5835	388	15	x1	x1	PROPN
ejpam-5835	388	16	)	)	PUNCT
ejpam-5835	388	17	,	,	PUNCT
ejpam-5835	388	18	β3(⊞	β3(⊞	NUM
ejpam-5835	388	19	)	)	PUNCT
ejpam-5835	388	20	=	=	SYM
ejpam-5835	388	21	⊞(x2	⊞(x2	NOUN
ejpam-5835	388	22	,	,	PUNCT
ejpam-5835	388	23	x3	x3	ADJ
ejpam-5835	388	24	,	,	PUNCT
ejpam-5835	388	25	x3	x3	ADJ
ejpam-5835	388	26	)	)	PUNCT
ejpam-5835	388	27	.	.	PUNCT
ejpam-5835	389	1	consider	consider	VERB
ejpam-5835	389	2	(	(	PUNCT
ejpam-5835	389	3	(	(	PUNCT
ejpam-5835	389	4	σ3	σ3	PROPN
ejpam-5835	389	5	+3	+3	PROPN
ejpam-5835	389	6	α3	α3	NOUN
ejpam-5835	389	7	)	)	PUNCT
ejpam-5835	389	8	◦	◦	NOUN
ejpam-5835	389	9	h3	h3	NOUN
ejpam-5835	389	10	β3)(⊞	β3)(⊞	PRON
ejpam-5835	389	11	)	)	PUNCT
ejpam-5835	389	12	=	=	PUNCT
ejpam-5835	390	1	̂(σ3	̂(σ3	X
ejpam-5835	390	2	+3	+3	PROPN
ejpam-5835	390	3	α3)[⊞(x2	α3)[⊞(x2	NUM
ejpam-5835	390	4	,	,	PUNCT
ejpam-5835	390	5	x3	x3	ADJ
ejpam-5835	390	6	,	,	PUNCT
ejpam-5835	390	7	x3	x3	ADJ
ejpam-5835	390	8	)	)	PUNCT
ejpam-5835	390	9	]	]	PUNCT
ejpam-5835	391	1	=	=	SYM
ejpam-5835	391	2	s3	s3	PROPN
ejpam-5835	391	3	3((σ3	3((σ3	NUM
ejpam-5835	391	4	+3	+3	PROPN
ejpam-5835	391	5	α3)(⊞	α3)(⊞	PROPN
ejpam-5835	391	6	)	)	PUNCT
ejpam-5835	391	7	,	,	PUNCT
ejpam-5835	391	8	x2	x2	PROPN
ejpam-5835	391	9	,	,	PUNCT
ejpam-5835	391	10	x3	x3	ADJ
ejpam-5835	391	11	,	,	PUNCT
ejpam-5835	391	12	x3	x3	ADJ
ejpam-5835	391	13	)	)	PUNCT
ejpam-5835	391	14	=	=	SYM
ejpam-5835	391	15	s3	s3	PROPN
ejpam-5835	391	16	3(⊞(⊞(x3	3(⊞(⊞(x3	NUM
ejpam-5835	391	17	,	,	PUNCT
ejpam-5835	391	18	x1	x1	PROPN
ejpam-5835	391	19	,	,	PUNCT
ejpam-5835	391	20	x1),⊞(x3	x1),⊞(x3	PROPN
ejpam-5835	391	21	,	,	PUNCT
ejpam-5835	391	22	x1	x1	PROPN
ejpam-5835	391	23	,	,	PUNCT
ejpam-5835	391	24	x1),⊞(x3	x1),⊞(x3	PROPN
ejpam-5835	391	25	,	,	PUNCT
ejpam-5835	391	26	x1	x1	PROPN
ejpam-5835	391	27	,	,	PUNCT
ejpam-5835	391	28	x1	x1	PROPN
ejpam-5835	391	29	)	)	PUNCT
ejpam-5835	391	30	)	)	PUNCT
ejpam-5835	391	31	,	,	PUNCT
ejpam-5835	391	32	x2	x2	PROPN
ejpam-5835	391	33	,	,	PUNCT
ejpam-5835	391	34	x3	x3	ADJ
ejpam-5835	391	35	,	,	PUNCT
ejpam-5835	391	36	x3	x3	ADJ
ejpam-5835	391	37	)	)	PUNCT
ejpam-5835	391	38	=	=	SYM
ejpam-5835	391	39	⊞(⊞(x3	⊞(⊞(x3	NOUN
ejpam-5835	391	40	,	,	PUNCT
ejpam-5835	391	41	x2	x2	PROPN
ejpam-5835	391	42	,	,	PUNCT
ejpam-5835	391	43	x2),⊞(x3	x2),⊞(x3	PROPN
ejpam-5835	391	44	,	,	PUNCT
ejpam-5835	391	45	x2	x2	PROPN
ejpam-5835	391	46	,	,	PUNCT
ejpam-5835	391	47	x2),⊞(x3	x2),⊞(x3	PROPN
ejpam-5835	391	48	,	,	PUNCT
ejpam-5835	391	49	x2	x2	PROPN
ejpam-5835	391	50	,	,	PUNCT
ejpam-5835	391	51	x2	x2	PROPN
ejpam-5835	391	52	)	)	PUNCT
ejpam-5835	391	53	)	)	PUNCT
ejpam-5835	391	54	and	and	CCONJ
ejpam-5835	391	55	(	(	PUNCT
ejpam-5835	391	56	(	(	PUNCT
ejpam-5835	391	57	σ3	σ3	PROPN
ejpam-5835	391	58	◦	◦	NOUN
ejpam-5835	391	59	h3	h3	NOUN
ejpam-5835	391	60	β3	β3	NOUN
ejpam-5835	391	61	)	)	PUNCT
ejpam-5835	391	62	+3	+3	PROPN
ejpam-5835	391	63	(	(	PUNCT
ejpam-5835	391	64	α3	α3	PROPN
ejpam-5835	391	65	◦	◦	NOUN
ejpam-5835	391	66	h3	h3	NOUN
ejpam-5835	391	67	β3))(⊞	β3))(⊞	SYM
ejpam-5835	391	68	)	)	PUNCT
ejpam-5835	391	69	=	=	SYM
ejpam-5835	391	70	s3	s3	PROPN
ejpam-5835	391	71	3((σ3	3((σ3	NUM
ejpam-5835	391	72	◦	◦	NOUN
ejpam-5835	391	73	h3	h3	NOUN
ejpam-5835	391	74	β3)(⊞	β3)(⊞	PROPN
ejpam-5835	391	75	)	)	PUNCT
ejpam-5835	391	76	,	,	PUNCT
ejpam-5835	391	77	(	(	PUNCT
ejpam-5835	391	78	α3	α3	PROPN
ejpam-5835	391	79	◦	◦	NOUN
ejpam-5835	391	80	h3	h3	NOUN
ejpam-5835	391	81	β3)(⊞	β3)(⊞	PROPN
ejpam-5835	391	82	)	)	PUNCT
ejpam-5835	391	83	,	,	PUNCT
ejpam-5835	391	84	(	(	PUNCT
ejpam-5835	391	85	α3	α3	PROPN
ejpam-5835	391	86	◦	◦	NOUN
ejpam-5835	391	87	h3	h3	NOUN
ejpam-5835	391	88	β3)(⊞	β3)(⊞	PROPN
ejpam-5835	391	89	)	)	PUNCT
ejpam-5835	391	90	,	,	PUNCT
ejpam-5835	391	91	(	(	PUNCT
ejpam-5835	391	92	α3	α3	PROPN
ejpam-5835	391	93	◦	◦	NOUN
ejpam-5835	391	94	h3	h3	NOUN
ejpam-5835	391	95	β3)(⊞	β3)(⊞	PROPN
ejpam-5835	391	96	)	)	PUNCT
ejpam-5835	391	97	)	)	PUNCT
ejpam-5835	391	98	.	.	PUNCT
ejpam-5835	392	1	since	since	SCONJ
ejpam-5835	392	2	(	(	PUNCT
ejpam-5835	392	3	σ3	σ3	PROPN
ejpam-5835	392	4	◦	◦	NOUN
ejpam-5835	392	5	h3	h3	NOUN
ejpam-5835	392	6	β3)(⊞	β3)(⊞	PROPN
ejpam-5835	392	7	)	)	PUNCT
ejpam-5835	392	8	=	=	PRON
ejpam-5835	392	9	(	(	PUNCT
ejpam-5835	392	10	α3	α3	PROPN
ejpam-5835	392	11	◦	◦	NOUN
ejpam-5835	392	12	h3	h3	NOUN
ejpam-5835	392	13	β3)(⊞	β3)(⊞	SYM
ejpam-5835	392	14	)	)	PUNCT
ejpam-5835	392	15	=	=	SYM
ejpam-5835	392	16	⊞(⊞(x2	⊞(⊞(x2	PROPN
ejpam-5835	392	17	,	,	PUNCT
ejpam-5835	392	18	x3	x3	ADJ
ejpam-5835	392	19	,	,	PUNCT
ejpam-5835	392	20	x3),⊞(x2	x3),⊞(x2	NOUN
ejpam-5835	392	21	,	,	PUNCT
ejpam-5835	392	22	x3	x3	ADJ
ejpam-5835	392	23	,	,	PUNCT
ejpam-5835	392	24	x3),⊞(x2	x3),⊞(x2	NOUN
ejpam-5835	392	25	,	,	PUNCT
ejpam-5835	392	26	x3	x3	ADJ
ejpam-5835	392	27	,	,	PUNCT
ejpam-5835	392	28	x3	x3	ADJ
ejpam-5835	392	29	)	)	PUNCT
ejpam-5835	392	30	)	)	PUNCT
ejpam-5835	392	31	,	,	PUNCT
ejpam-5835	392	32	we	we	PRON
ejpam-5835	392	33	conclude	conclude	VERB
ejpam-5835	392	34	that	that	PRON
ejpam-5835	392	35	(	(	PUNCT
ejpam-5835	392	36	(	(	PUNCT
ejpam-5835	392	37	σ3	σ3	PROPN
ejpam-5835	392	38	+3	+3	PROPN
ejpam-5835	392	39	α3	α3	NOUN
ejpam-5835	392	40	)	)	PUNCT
ejpam-5835	392	41	◦	◦	NOUN
ejpam-5835	392	42	h3	h3	NOUN
ejpam-5835	392	43	β3)(⊞	β3)(⊞	SYM
ejpam-5835	392	44	)	)	PUNCT
ejpam-5835	392	45	̸=	̸=	PROPN
ejpam-5835	392	46	(	(	PUNCT
ejpam-5835	392	47	(	(	PUNCT
ejpam-5835	392	48	σ3	σ3	PROPN
ejpam-5835	392	49	◦	◦	NOUN
ejpam-5835	392	50	h3	h3	NOUN
ejpam-5835	392	51	β3	β3	NOUN
ejpam-5835	392	52	)	)	PUNCT
ejpam-5835	392	53	+3	+3	PROPN
ejpam-5835	392	54	(	(	PUNCT
ejpam-5835	392	55	α3	α3	PROPN
ejpam-5835	392	56	◦	◦	NOUN
ejpam-5835	392	57	h3	h3	NOUN
ejpam-5835	392	58	β3))(⊞	β3))(⊞	PUNCT
ejpam-5835	392	59	)	)	PUNCT
ejpam-5835	392	60	,	,	PUNCT
ejpam-5835	392	61	which	which	PRON
ejpam-5835	392	62	means	mean	VERB
ejpam-5835	392	63	that	that	SCONJ
ejpam-5835	392	64	the	the	DET
ejpam-5835	392	65	right	right	ADJ
ejpam-5835	392	66	distributivity	distributivity	NOUN
ejpam-5835	392	67	on	on	ADP
ejpam-5835	392	68	(	(	PUNCT
ejpam-5835	392	69	(	(	PUNCT
ejpam-5835	392	70	hypwfv	hypwfv	NOUN
ejpam-5835	392	71	n	n	CCONJ
ejpam-5835	392	72	(	(	PUNCT
ejpam-5835	392	73	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	392	74	,	,	PUNCT
ejpam-5835	392	75	(	(	PUNCT
ejpam-5835	392	76	◦	◦	NOUN
ejpam-5835	392	77	hn)n∈n	hn)n∈n	NUM
ejpam-5835	392	78	,	,	PUNCT
ejpam-5835	392	79	(	(	PUNCT
ejpam-5835	392	80	+	+	ADV
ejpam-5835	392	81	n)n∈n	n)n∈n	NOUN
ejpam-5835	392	82	)	)	PUNCT
ejpam-5835	392	83	does	do	AUX
ejpam-5835	392	84	not	not	PART
ejpam-5835	392	85	hold	hold	VERB
ejpam-5835	392	86	.	.	PUNCT
ejpam-5835	393	1	t.	t.	PROPN
ejpam-5835	393	2	kumduang	kumduang	PROPN
ejpam-5835	393	3	,	,	PUNCT
ejpam-5835	393	4	k.	k.	PROPN
ejpam-5835	393	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	393	6	/	/	SYM
ejpam-5835	393	7	eur	eur	PROPN
ejpam-5835	393	8	.	.	PUNCT
ejpam-5835	394	1	j.	j.	PROPN
ejpam-5835	394	2	pure	pure	PROPN
ejpam-5835	394	3	appl	appl	PROPN
ejpam-5835	394	4	.	.	PROPN
ejpam-5835	394	5	math	math	PROPN
ejpam-5835	394	6	,	,	PUNCT
ejpam-5835	394	7	18	18	NUM
ejpam-5835	394	8	(	(	PUNCT
ejpam-5835	394	9	2	2	NUM
ejpam-5835	394	10	)	)	PUNCT
ejpam-5835	394	11	(	(	PUNCT
ejpam-5835	394	12	2025	2025	NUM
ejpam-5835	394	13	)	)	PUNCT
ejpam-5835	394	14	,	,	PUNCT
ejpam-5835	394	15	5835	5835	NUM
ejpam-5835	394	16	11	11	NUM
ejpam-5835	394	17	of	of	ADP
ejpam-5835	394	18	16	16	NUM
ejpam-5835	394	19	4	4	NUM
ejpam-5835	394	20	.	.	PUNCT
ejpam-5835	394	21	weakly	weakly	ADJ
ejpam-5835	394	22	fixed	fix	VERB
ejpam-5835	394	23	variable	variable	ADJ
ejpam-5835	394	24	hyperidentities	hyperidentitie	NOUN
ejpam-5835	394	25	in	in	ADP
ejpam-5835	394	26	this	this	DET
ejpam-5835	394	27	section	section	NOUN
ejpam-5835	394	28	,	,	PUNCT
ejpam-5835	394	29	we	we	PRON
ejpam-5835	394	30	apply	apply	VERB
ejpam-5835	394	31	the	the	DET
ejpam-5835	394	32	concepts	concept	NOUN
ejpam-5835	394	33	of	of	ADP
ejpam-5835	394	34	terms	term	NOUN
ejpam-5835	394	35	of	of	ADP
ejpam-5835	394	36	a	a	DET
ejpam-5835	394	37	weakly	weakly	ADJ
ejpam-5835	394	38	fixed	fix	VERB
ejpam-5835	394	39	variable	variable	NOUN
ejpam-5835	394	40	and	and	CCONJ
ejpam-5835	394	41	wfvhypersubstitutions	wfvhypersubstitution	NOUN
ejpam-5835	394	42	to	to	PART
ejpam-5835	394	43	describe	describe	VERB
ejpam-5835	394	44	classes	class	NOUN
ejpam-5835	394	45	of	of	ADP
ejpam-5835	394	46	algebras	algebras	PROPN
ejpam-5835	394	47	.	.	PUNCT
ejpam-5835	395	1	we	we	PRON
ejpam-5835	395	2	start	start	VERB
ejpam-5835	395	3	with	with	ADP
ejpam-5835	395	4	the	the	DET
ejpam-5835	395	5	following	follow	VERB
ejpam-5835	395	6	definition	definition	NOUN
ejpam-5835	395	7	.	.	PUNCT
ejpam-5835	396	1	definition	definition	NOUN
ejpam-5835	396	2	3	3	X
ejpam-5835	396	3	.	.	PUNCT
ejpam-5835	397	1	let	let	VERB
ejpam-5835	397	2	v	v	PART
ejpam-5835	397	3	be	be	AUX
ejpam-5835	397	4	a	a	DET
ejpam-5835	397	5	variety	variety	NOUN
ejpam-5835	397	6	of	of	ADP
ejpam-5835	397	7	algebras	algebra	NOUN
ejpam-5835	397	8	of	of	ADP
ejpam-5835	397	9	type	type	NOUN
ejpam-5835	397	10	τ	τ	PROPN
ejpam-5835	397	11	.	.	PUNCT
ejpam-5835	398	1	an	an	DET
ejpam-5835	398	2	identity	identity	NOUN
ejpam-5835	398	3	s	s	PART
ejpam-5835	398	4	≈	≈	PROPN
ejpam-5835	398	5	t	t	PROPN
ejpam-5835	398	6	∈	∈	PROPN
ejpam-5835	398	7	id(v	id(v	PUNCT
ejpam-5835	398	8	)	)	PUNCT
ejpam-5835	398	9	is	be	AUX
ejpam-5835	398	10	said	say	VERB
ejpam-5835	398	11	to	to	PART
ejpam-5835	398	12	be	be	AUX
ejpam-5835	398	13	a	a	DET
ejpam-5835	398	14	weakly	weakly	ADJ
ejpam-5835	398	15	fixed	fix	VERB
ejpam-5835	398	16	variable	variable	ADJ
ejpam-5835	398	17	identity	identity	NOUN
ejpam-5835	398	18	of	of	ADP
ejpam-5835	398	19	v	v	NOUN
ejpam-5835	398	20	,	,	PUNCT
ejpam-5835	398	21	also	also	ADV
ejpam-5835	398	22	called	call	VERB
ejpam-5835	398	23	wfv	wfv	NOUN
ejpam-5835	398	24	-	-	PUNCT
ejpam-5835	398	25	identity	identity	NOUN
ejpam-5835	398	26	of	of	ADP
ejpam-5835	398	27	v	v	NOUN
ejpam-5835	398	28	,	,	PUNCT
ejpam-5835	398	29	if	if	SCONJ
ejpam-5835	398	30	both	both	PRON
ejpam-5835	398	31	s	s	X
ejpam-5835	398	32	and	and	CCONJ
ejpam-5835	398	33	t	t	PROPN
ejpam-5835	398	34	come	come	VERB
ejpam-5835	398	35	from	from	ADP
ejpam-5835	398	36	the	the	DET
ejpam-5835	398	37	set	set	NOUN
ejpam-5835	398	38	wwfv	wwfv	NOUN
ejpam-5835	398	39	τ	τ	PROPN
ejpam-5835	398	40	(	(	PUNCT
ejpam-5835	398	41	xn	xn	PROPN
ejpam-5835	398	42	)	)	PUNCT
ejpam-5835	398	43	for	for	ADP
ejpam-5835	398	44	some	some	DET
ejpam-5835	398	45	n	n	PRON
ejpam-5835	398	46	∈	∈	PROPN
ejpam-5835	398	47	n.	n.	NOUN
ejpam-5835	398	48	for	for	ADP
ejpam-5835	398	49	example	example	NOUN
ejpam-5835	398	50	,	,	PUNCT
ejpam-5835	398	51	the	the	DET
ejpam-5835	398	52	identity	identity	NOUN
ejpam-5835	398	53	f(a	f(a	NOUN
ejpam-5835	398	54	,	,	PUNCT
ejpam-5835	398	55	b	b	NOUN
ejpam-5835	398	56	,	,	PUNCT
ejpam-5835	398	57	a	a	PRON
ejpam-5835	398	58	)	)	PUNCT
ejpam-5835	398	59	=	=	NOUN
ejpam-5835	399	1	a	a	PRON
ejpam-5835	399	2	in	in	ADP
ejpam-5835	399	3	the	the	DET
ejpam-5835	399	4	variety	variety	NOUN
ejpam-5835	399	5	reg	reg	NOUN
ejpam-5835	399	6	of	of	ADP
ejpam-5835	399	7	regular	regular	ADJ
ejpam-5835	399	8	semigroups	semigroup	NOUN
ejpam-5835	399	9	is	be	AUX
ejpam-5835	399	10	a	a	DET
ejpam-5835	399	11	weakly	weakly	ADJ
ejpam-5835	399	12	fixed	fix	VERB
ejpam-5835	399	13	variable	variable	ADJ
ejpam-5835	399	14	identity	identity	NOUN
ejpam-5835	399	15	of	of	ADP
ejpam-5835	399	16	reg	reg	NOUN
ejpam-5835	399	17	.	.	PUNCT
ejpam-5835	400	1	for	for	ADP
ejpam-5835	400	2	the	the	DET
ejpam-5835	400	3	set	set	NOUN
ejpam-5835	400	4	idn(v	idn(v	PROPN
ejpam-5835	400	5	)	)	PUNCT
ejpam-5835	400	6	of	of	ADP
ejpam-5835	400	7	all	all	DET
ejpam-5835	400	8	n	n	CCONJ
ejpam-5835	400	9	-	-	PUNCT
ejpam-5835	400	10	ary	ary	PROPN
ejpam-5835	400	11	identities	identity	NOUN
ejpam-5835	400	12	of	of	ADP
ejpam-5835	400	13	the	the	DET
ejpam-5835	400	14	variety	variety	NOUN
ejpam-5835	400	15	v	v	NOUN
ejpam-5835	400	16	,	,	PUNCT
ejpam-5835	400	17	we	we	PRON
ejpam-5835	400	18	let	let	VERB
ejpam-5835	400	19	idwfv	idwfv	ADJ
ejpam-5835	400	20	n	n	CCONJ
ejpam-5835	400	21	(	(	PUNCT
ejpam-5835	400	22	v	v	NOUN
ejpam-5835	400	23	)	)	PUNCT
ejpam-5835	400	24	:	:	PUNCT
ejpam-5835	401	1	=	=	SYM
ejpam-5835	401	2	{	{	PUNCT
ejpam-5835	401	3	s	s	PROPN
ejpam-5835	401	4	≈	≈	PROPN
ejpam-5835	401	5	t	t	NOUN
ejpam-5835	402	1	|	|	NOUN
ejpam-5835	402	2	s	s	VERB
ejpam-5835	402	3	≈	≈	PROPN
ejpam-5835	402	4	t	t	PROPN
ejpam-5835	402	5	∈	∈	PROPN
ejpam-5835	402	6	id(v	id(v	NUM
ejpam-5835	402	7	)	)	PUNCT
ejpam-5835	402	8	,	,	PUNCT
ejpam-5835	402	9	s	s	AUX
ejpam-5835	402	10	,	,	PUNCT
ejpam-5835	402	11	t	t	PROPN
ejpam-5835	402	12	∈	∈	PROPN
ejpam-5835	402	13	wwfv	wwfv	NOUN
ejpam-5835	402	14	τ	τ	PROPN
ejpam-5835	402	15	(	(	PUNCT
ejpam-5835	402	16	xn	xn	PROPN
ejpam-5835	402	17	)	)	PUNCT
ejpam-5835	402	18	}	}	PUNCT
ejpam-5835	402	19	.	.	PUNCT
ejpam-5835	403	1	alternatively	alternatively	ADV
ejpam-5835	403	2	,	,	PUNCT
ejpam-5835	403	3	we	we	PRON
ejpam-5835	403	4	say	say	VERB
ejpam-5835	403	5	that	that	SCONJ
ejpam-5835	403	6	idwfv	idwfv	NOUN
ejpam-5835	403	7	n	n	CCONJ
ejpam-5835	403	8	(	(	PUNCT
ejpam-5835	403	9	v	v	NOUN
ejpam-5835	403	10	)	)	PUNCT
ejpam-5835	403	11	=	=	PUNCT
ejpam-5835	403	12	(	(	PUNCT
ejpam-5835	403	13	wwfv	wwfv	PROPN
ejpam-5835	403	14	τ	τ	PROPN
ejpam-5835	403	15	(	(	PUNCT
ejpam-5835	403	16	xn	xn	PROPN
ejpam-5835	403	17	)	)	PUNCT
ejpam-5835	403	18	)	)	PUNCT
ejpam-5835	403	19	2	2	NUM
ejpam-5835	403	20	∩	∩	X
ejpam-5835	403	21	idn(v	idn(v	ADJ
ejpam-5835	403	22	)	)	PUNCT
ejpam-5835	403	23	.	.	PUNCT
ejpam-5835	404	1	moreover	moreover	ADV
ejpam-5835	404	2	,	,	PUNCT
ejpam-5835	404	3	we	we	PRON
ejpam-5835	404	4	consider	consider	VERB
ejpam-5835	404	5	idwfv(v	idwfv(v	ADJ
ejpam-5835	404	6	)	)	PUNCT
ejpam-5835	404	7	:	:	PUNCT
ejpam-5835	405	1	=	=	SYM
ejpam-5835	405	2	(	(	PUNCT
ejpam-5835	405	3	idwfv	idwfv	NOUN
ejpam-5835	405	4	n	n	CCONJ
ejpam-5835	405	5	(	(	PUNCT
ejpam-5835	405	6	v	v	NOUN
ejpam-5835	405	7	)	)	PUNCT
ejpam-5835	405	8	)	)	PUNCT
ejpam-5835	405	9	n∈n	n∈n	X
ejpam-5835	405	10	.	.	PUNCT
ejpam-5835	406	1	then	then	ADV
ejpam-5835	406	2	we	we	PRON
ejpam-5835	406	3	prove	prove	VERB
ejpam-5835	406	4	:	:	PUNCT
ejpam-5835	406	5	theorem	theorem	NOUN
ejpam-5835	406	6	5	5	NUM
ejpam-5835	406	7	.	.	PUNCT
ejpam-5835	407	1	let	let	VERB
ejpam-5835	407	2	v	v	PART
ejpam-5835	407	3	be	be	AUX
ejpam-5835	407	4	a	a	DET
ejpam-5835	407	5	variety	variety	NOUN
ejpam-5835	407	6	of	of	ADP
ejpam-5835	407	7	algebras	algebra	NOUN
ejpam-5835	407	8	of	of	ADP
ejpam-5835	407	9	type	type	NOUN
ejpam-5835	407	10	τ	τ	PROPN
ejpam-5835	407	11	.	.	PUNCT
ejpam-5835	408	1	then	then	ADV
ejpam-5835	408	2	idwfv(v	idwfv(v	ADJ
ejpam-5835	408	3	)	)	PUNCT
ejpam-5835	408	4	is	be	AUX
ejpam-5835	408	5	a	a	DET
ejpam-5835	408	6	congruence	congruence	NOUN
ejpam-5835	408	7	on	on	ADP
ejpam-5835	408	8	the	the	DET
ejpam-5835	408	9	multisorted	multisorte	VERB
ejpam-5835	408	10	algebra	algebra	NOUN
ejpam-5835	408	11	wwfv	wwfv	NOUN
ejpam-5835	408	12	τ	τ	PROPN
ejpam-5835	408	13	(	(	PUNCT
ejpam-5835	408	14	x	x	NOUN
ejpam-5835	408	15	)	)	PUNCT
ejpam-5835	408	16	.	.	PUNCT
ejpam-5835	409	1	proof	proof	NOUN
ejpam-5835	409	2	.	.	PUNCT
ejpam-5835	410	1	it	it	PRON
ejpam-5835	410	2	is	be	AUX
ejpam-5835	410	3	clear	clear	ADJ
ejpam-5835	410	4	that	that	SCONJ
ejpam-5835	410	5	(	(	PUNCT
ejpam-5835	410	6	idfvn	idfvn	X
ejpam-5835	410	7	(	(	PUNCT
ejpam-5835	410	8	v	v	NOUN
ejpam-5835	410	9	)	)	PUNCT
ejpam-5835	410	10	)	)	PUNCT
ejpam-5835	410	11	n∈n+	n∈n+	PART
ejpam-5835	410	12	is	be	AUX
ejpam-5835	410	13	preserved	preserve	VERB
ejpam-5835	410	14	by	by	ADP
ejpam-5835	410	15	the	the	DET
ejpam-5835	410	16	constant	constant	ADJ
ejpam-5835	410	17	fundamental	fundamental	ADJ
ejpam-5835	410	18	operations	operation	NOUN
ejpam-5835	410	19	,	,	PUNCT
ejpam-5835	410	20	i.e.	i.e.	X
ejpam-5835	410	21	,	,	PUNCT
ejpam-5835	410	22	projections	projection	NOUN
ejpam-5835	410	23	,	,	PUNCT
ejpam-5835	410	24	of	of	ADP
ejpam-5835	410	25	wwfv	wwfv	NOUN
ejpam-5835	410	26	τ	τ	PROPN
ejpam-5835	410	27	(	(	PUNCT
ejpam-5835	410	28	x	x	NOUN
ejpam-5835	410	29	)	)	PUNCT
ejpam-5835	410	30	.	.	PUNCT
ejpam-5835	411	1	assume	assume	VERB
ejpam-5835	411	2	now	now	ADV
ejpam-5835	411	3	that	that	SCONJ
ejpam-5835	411	4	p	p	PROPN
ejpam-5835	411	5	≈	≈	PROPN
ejpam-5835	411	6	q	q	NOUN
ejpam-5835	411	7	∈	∈	PROPN
ejpam-5835	411	8	idwfv	idwfv	NOUN
ejpam-5835	411	9	n	n	CCONJ
ejpam-5835	411	10	(	(	PUNCT
ejpam-5835	411	11	v	v	NOUN
ejpam-5835	411	12	)	)	PUNCT
ejpam-5835	411	13	and	and	CCONJ
ejpam-5835	411	14	p1	p1	PROPN
ejpam-5835	411	15	≈	≈	PROPN
ejpam-5835	411	16	q1	q1	PROPN
ejpam-5835	411	17	,	,	PUNCT
ejpam-5835	411	18	.	.	PUNCT
ejpam-5835	411	19	.	.	PUNCT
ejpam-5835	412	1	.	.	PUNCT
ejpam-5835	413	1	,	,	PUNCT
ejpam-5835	413	2	pn	pn	PROPN
ejpam-5835	413	3	≈	≈	PROPN
ejpam-5835	413	4	qn	qn	PROPN
ejpam-5835	413	5	∈	∈	PROPN
ejpam-5835	413	6	idwfv	idwfv	NOUN
ejpam-5835	413	7	m	m	PROPN
ejpam-5835	413	8	(	(	PUNCT
ejpam-5835	413	9	v	v	NOUN
ejpam-5835	413	10	)	)	PUNCT
ejpam-5835	413	11	.	.	PUNCT
ejpam-5835	414	1	we	we	PRON
ejpam-5835	414	2	aim	aim	VERB
ejpam-5835	414	3	to	to	PART
ejpam-5835	414	4	show	show	VERB
ejpam-5835	414	5	that	that	SCONJ
ejpam-5835	414	6	sn	sn	PROPN
ejpam-5835	414	7	m(p	m(p	PROPN
ejpam-5835	414	8	,	,	PUNCT
ejpam-5835	414	9	p1	p1	NOUN
ejpam-5835	414	10	,	,	PUNCT
ejpam-5835	414	11	.	.	PUNCT
ejpam-5835	414	12	.	.	PUNCT
ejpam-5835	415	1	.	.	PUNCT
ejpam-5835	416	1	,	,	PUNCT
ejpam-5835	416	2	pn	pn	PROPN
ejpam-5835	416	3	)	)	PUNCT
ejpam-5835	416	4	≈	≈	PROPN
ejpam-5835	416	5	sn	sn	PROPN
ejpam-5835	416	6	m(q	m(q	PROPN
ejpam-5835	416	7	,	,	PUNCT
ejpam-5835	416	8	q1	q1	NOUN
ejpam-5835	416	9	,	,	PUNCT
ejpam-5835	416	10	.	.	PUNCT
ejpam-5835	416	11	.	.	PUNCT
ejpam-5835	417	1	.	.	PUNCT
ejpam-5835	418	1	,	,	PUNCT
ejpam-5835	418	2	qn	qn	INTJ
ejpam-5835	418	3	)	)	PUNCT
ejpam-5835	418	4	∈	∈	PROPN
ejpam-5835	418	5	idwfv	idwfv	NOUN
ejpam-5835	418	6	m	m	PROPN
ejpam-5835	418	7	(	(	PUNCT
ejpam-5835	418	8	v	v	NOUN
ejpam-5835	418	9	)	)	PUNCT
ejpam-5835	418	10	.	.	PUNCT
ejpam-5835	419	1	from	from	ADP
ejpam-5835	419	2	lemma	lemma	PROPN
ejpam-5835	419	3	1	1	NUM
ejpam-5835	419	4	,	,	PUNCT
ejpam-5835	419	5	we	we	PRON
ejpam-5835	419	6	have	have	VERB
ejpam-5835	419	7	that	that	SCONJ
ejpam-5835	419	8	the	the	DET
ejpam-5835	419	9	terms	term	NOUN
ejpam-5835	419	10	sn	sn	PROPN
ejpam-5835	419	11	m(p	m(p	PROPN
ejpam-5835	419	12	,	,	PUNCT
ejpam-5835	419	13	p1	p1	NOUN
ejpam-5835	419	14	,	,	PUNCT
ejpam-5835	419	15	.	.	PUNCT
ejpam-5835	419	16	.	.	PUNCT
ejpam-5835	420	1	.	.	PUNCT
ejpam-5835	421	1	,	,	PUNCT
ejpam-5835	421	2	pn	pn	PROPN
ejpam-5835	421	3	)	)	PUNCT
ejpam-5835	421	4	and	and	CCONJ
ejpam-5835	421	5	sn	sn	PROPN
ejpam-5835	421	6	m(q	m(q	PROPN
ejpam-5835	421	7	,	,	PUNCT
ejpam-5835	421	8	q1	q1	NOUN
ejpam-5835	421	9	,	,	PUNCT
ejpam-5835	421	10	.	.	PUNCT
ejpam-5835	421	11	.	.	PUNCT
ejpam-5835	422	1	.	.	PUNCT
ejpam-5835	423	1	,	,	PUNCT
ejpam-5835	423	2	qn	qn	NOUN
ejpam-5835	423	3	)	)	PUNCT
ejpam-5835	423	4	contain	contain	VERB
ejpam-5835	423	5	in	in	ADP
ejpam-5835	423	6	the	the	DET
ejpam-5835	423	7	set	set	NOUN
ejpam-5835	423	8	wwfv	wwfv	NOUN
ejpam-5835	423	9	τ	τ	PROPN
ejpam-5835	423	10	(	(	PUNCT
ejpam-5835	423	11	xm	xm	PROPN
ejpam-5835	423	12	)	)	PUNCT
ejpam-5835	423	13	.	.	PUNCT
ejpam-5835	424	1	thus	thus	ADV
ejpam-5835	424	2	sn	sn	PROPN
ejpam-5835	424	3	m(p	m(p	PROPN
ejpam-5835	424	4	,	,	PUNCT
ejpam-5835	424	5	p1	p1	NOUN
ejpam-5835	424	6	,	,	PUNCT
ejpam-5835	424	7	.	.	PUNCT
ejpam-5835	424	8	.	.	PUNCT
ejpam-5835	424	9	.	.	PUNCT
ejpam-5835	425	1	,	,	PUNCT
ejpam-5835	425	2	pn	pn	PROPN
ejpam-5835	425	3	)	)	PUNCT
ejpam-5835	425	4	≈	≈	PROPN
ejpam-5835	425	5	sn	sn	PROPN
ejpam-5835	425	6	m(q	m(q	PROPN
ejpam-5835	425	7	,	,	PUNCT
ejpam-5835	425	8	q1	q1	NOUN
ejpam-5835	425	9	,	,	PUNCT
ejpam-5835	425	10	.	.	PUNCT
ejpam-5835	425	11	.	.	PUNCT
ejpam-5835	426	1	.	.	PUNCT
ejpam-5835	427	1	,	,	PUNCT
ejpam-5835	427	2	qn	qn	INTJ
ejpam-5835	427	3	)	)	PUNCT
ejpam-5835	427	4	∈	∈	NOUN
ejpam-5835	427	5	idm(v	idm(v	PROPN
ejpam-5835	427	6	)	)	PUNCT
ejpam-5835	427	7	.	.	PUNCT
ejpam-5835	428	1	as	as	ADP
ejpam-5835	428	2	a	a	DET
ejpam-5835	428	3	result	result	NOUN
ejpam-5835	428	4	,	,	PUNCT
ejpam-5835	428	5	sn	sn	PROPN
ejpam-5835	428	6	m(p	m(p	PROPN
ejpam-5835	428	7	,	,	PUNCT
ejpam-5835	428	8	p1	p1	PROPN
ejpam-5835	428	9	,	,	PUNCT
ejpam-5835	428	10	.	.	PUNCT
ejpam-5835	428	11	.	.	PUNCT
ejpam-5835	428	12	.	.	PUNCT
ejpam-5835	429	1	,	,	PUNCT
ejpam-5835	429	2	pn	pn	PROPN
ejpam-5835	429	3	)	)	PUNCT
ejpam-5835	429	4	≈	≈	PROPN
ejpam-5835	429	5	sn	sn	PROPN
ejpam-5835	429	6	m(q	m(q	PROPN
ejpam-5835	429	7	,	,	PUNCT
ejpam-5835	429	8	q1	q1	NOUN
ejpam-5835	429	9	,	,	PUNCT
ejpam-5835	429	10	.	.	PUNCT
ejpam-5835	429	11	.	.	PUNCT
ejpam-5835	430	1	.	.	PUNCT
ejpam-5835	431	1	,	,	PUNCT
ejpam-5835	431	2	qn	qn	INTJ
ejpam-5835	431	3	)	)	PUNCT
ejpam-5835	431	4	∈	∈	PROPN
ejpam-5835	431	5	idwfv	idwfv	NOUN
ejpam-5835	431	6	m	m	PROPN
ejpam-5835	431	7	(	(	PUNCT
ejpam-5835	431	8	v	v	NOUN
ejpam-5835	431	9	)	)	PUNCT
ejpam-5835	431	10	.	.	PUNCT
ejpam-5835	432	1	theorem	theorem	NOUN
ejpam-5835	432	2	5	5	NUM
ejpam-5835	432	3	allows	allow	VERB
ejpam-5835	432	4	us	we	PRON
ejpam-5835	432	5	to	to	PART
ejpam-5835	432	6	consider	consider	VERB
ejpam-5835	432	7	the	the	DET
ejpam-5835	432	8	quotient	quotient	NOUN
ejpam-5835	432	9	systems	system	NOUN
ejpam-5835	432	10	of	of	ADP
ejpam-5835	432	11	the	the	DET
ejpam-5835	432	12	following	follow	VERB
ejpam-5835	432	13	form	form	NOUN
ejpam-5835	432	14	:	:	PUNCT
ejpam-5835	432	15	(	(	PUNCT
ejpam-5835	432	16	wwfv	wwfv	PROPN
ejpam-5835	432	17	τ	τ	X
ejpam-5835	432	18	(	(	PUNCT
ejpam-5835	432	19	xn))n∈n/(id	xn))n∈n/(id	PROPN
ejpam-5835	432	20	wfv	wfv	PROPN
ejpam-5835	432	21	n	n	PROPN
ejpam-5835	432	22	(	(	PUNCT
ejpam-5835	432	23	v	v	NOUN
ejpam-5835	432	24	)	)	PUNCT
ejpam-5835	432	25	)	)	PUNCT
ejpam-5835	433	1	n∈n	n∈n	PROPN
ejpam-5835	433	2	,	,	PUNCT
ejpam-5835	433	3	which	which	PRON
ejpam-5835	433	4	we	we	PRON
ejpam-5835	433	5	will	will	AUX
ejpam-5835	433	6	call	call	VERB
ejpam-5835	433	7	the	the	DET
ejpam-5835	433	8	quotient	quotient	NOUN
ejpam-5835	433	9	algebra	algebra	NOUN
ejpam-5835	433	10	of	of	ADP
ejpam-5835	433	11	terms	term	NOUN
ejpam-5835	433	12	of	of	ADP
ejpam-5835	433	13	a	a	DET
ejpam-5835	433	14	weakly	weakly	ADJ
ejpam-5835	433	15	fixed	fixed	ADJ
ejpam-5835	433	16	variable	variable	NOUN
ejpam-5835	433	17	of	of	ADP
ejpam-5835	433	18	a	a	DET
ejpam-5835	433	19	variety	variety	NOUN
ejpam-5835	433	20	v	v	NOUN
ejpam-5835	433	21	.	.	PUNCT
ejpam-5835	434	1	t.	t.	PROPN
ejpam-5835	434	2	kumduang	kumduang	PROPN
ejpam-5835	434	3	,	,	PUNCT
ejpam-5835	434	4	k.	k.	PROPN
ejpam-5835	434	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	434	6	/	/	SYM
ejpam-5835	434	7	eur	eur	PROPN
ejpam-5835	434	8	.	.	PUNCT
ejpam-5835	435	1	j.	j.	PROPN
ejpam-5835	435	2	pure	pure	PROPN
ejpam-5835	435	3	appl	appl	PROPN
ejpam-5835	435	4	.	.	PROPN
ejpam-5835	435	5	math	math	PROPN
ejpam-5835	435	6	,	,	PUNCT
ejpam-5835	435	7	18	18	NUM
ejpam-5835	435	8	(	(	PUNCT
ejpam-5835	435	9	2	2	NUM
ejpam-5835	435	10	)	)	PUNCT
ejpam-5835	435	11	(	(	PUNCT
ejpam-5835	435	12	2025	2025	NUM
ejpam-5835	435	13	)	)	PUNCT
ejpam-5835	435	14	,	,	PUNCT
ejpam-5835	435	15	5835	5835	NUM
ejpam-5835	435	16	12	12	NUM
ejpam-5835	435	17	of	of	ADP
ejpam-5835	435	18	16	16	NUM
ejpam-5835	435	19	moreover	moreover	ADV
ejpam-5835	435	20	,	,	PUNCT
ejpam-5835	435	21	the	the	DET
ejpam-5835	435	22	multisorted	multisorte	VERB
ejpam-5835	435	23	operations	operation	NOUN
ejpam-5835	435	24	on	on	ADP
ejpam-5835	435	25	(	(	PUNCT
ejpam-5835	435	26	wwfv	wwfv	PROPN
ejpam-5835	435	27	τ	τ	X
ejpam-5835	435	28	(	(	PUNCT
ejpam-5835	435	29	xn))n∈n/(id	xn))n∈n/(id	PROPN
ejpam-5835	435	30	wfv	wfv	PROPN
ejpam-5835	435	31	n	n	PROPN
ejpam-5835	435	32	(	(	PUNCT
ejpam-5835	435	33	v	v	NOUN
ejpam-5835	435	34	)	)	PUNCT
ejpam-5835	435	35	)	)	PUNCT
ejpam-5835	435	36	n∈n	n∈n	NOUN
ejpam-5835	435	37	denoted	denote	VERB
ejpam-5835	435	38	by	by	ADP
ejpam-5835	435	39	s	s	PROPN
ejpam-5835	435	40	n	n	PRON
ejpam-5835	435	41	m	m	VERB
ejpam-5835	435	42	:	:	PUNCT
ejpam-5835	435	43	wwfv	wwfv	PROPN
ejpam-5835	435	44	τ	τ	PROPN
ejpam-5835	435	45	(	(	PUNCT
ejpam-5835	435	46	xn)/id	xn)/id	PROPN
ejpam-5835	435	47	wfv	wfv	PROPN
ejpam-5835	435	48	n	n	PROPN
ejpam-5835	435	49	(	(	PUNCT
ejpam-5835	435	50	v	v	NOUN
ejpam-5835	435	51	)	)	PUNCT
ejpam-5835	435	52	×	×	NOUN
ejpam-5835	435	53	(	(	PUNCT
ejpam-5835	435	54	wwfv	wwfv	NOUN
ejpam-5835	435	55	τ	τ	X
ejpam-5835	435	56	(	(	PUNCT
ejpam-5835	435	57	xm)/idwfv	xm)/idwfv	PROPN
ejpam-5835	435	58	m	m	PROPN
ejpam-5835	435	59	(	(	PUNCT
ejpam-5835	435	60	v	v	NOUN
ejpam-5835	435	61	)	)	PUNCT
ejpam-5835	435	62	)	)	PUNCT
ejpam-5835	436	1	n	n	CCONJ
ejpam-5835	436	2	→	→	NOUN
ejpam-5835	436	3	wwfv	wwfv	NOUN
ejpam-5835	436	4	τ	τ	X
ejpam-5835	436	5	(	(	PUNCT
ejpam-5835	436	6	xm)/idwfv	xm)/idwfv	PROPN
ejpam-5835	436	7	m	m	PROPN
ejpam-5835	436	8	(	(	PUNCT
ejpam-5835	436	9	v	v	NOUN
ejpam-5835	436	10	)	)	PUNCT
ejpam-5835	436	11	can	can	AUX
ejpam-5835	436	12	be	be	AUX
ejpam-5835	436	13	naturally	naturally	ADV
ejpam-5835	436	14	defined	define	VERB
ejpam-5835	436	15	by	by	ADP
ejpam-5835	436	16	s	s	PROPN
ejpam-5835	436	17	n	n	PRON
ejpam-5835	436	18	m([t	m([t	PROPN
ejpam-5835	436	19	]	]	X
ejpam-5835	436	20	idwfv	idwfv	PROPN
ejpam-5835	436	21	n	n	PROPN
ejpam-5835	436	22	(	(	PUNCT
ejpam-5835	436	23	v	v	NOUN
ejpam-5835	436	24	)	)	PUNCT
ejpam-5835	436	25	,	,	PUNCT
ejpam-5835	437	1	[	[	X
ejpam-5835	437	2	t1]idwfv	t1]idwfv	X
ejpam-5835	437	3	m	m	PROPN
ejpam-5835	437	4	(	(	PUNCT
ejpam-5835	437	5	v	v	NOUN
ejpam-5835	437	6	)	)	PUNCT
ejpam-5835	437	7	,	,	PUNCT
ejpam-5835	437	8	.	.	PUNCT
ejpam-5835	437	9	.	.	PUNCT
ejpam-5835	437	10	.	.	PUNCT
ejpam-5835	438	1	,	,	PUNCT
ejpam-5835	439	1	[	[	X
ejpam-5835	439	2	tn]idwfv	tn]idwfv	NOUN
ejpam-5835	439	3	m	m	VERB
ejpam-5835	439	4	(	(	PUNCT
ejpam-5835	439	5	v	v	NOUN
ejpam-5835	439	6	)	)	PUNCT
ejpam-5835	439	7	)	)	PUNCT
ejpam-5835	440	1	=	=	PUNCT
ejpam-5835	441	1	[	[	X
ejpam-5835	441	2	s	s	X
ejpam-5835	441	3	]	]	X
ejpam-5835	441	4	idwfv	idwfv	ADJ
ejpam-5835	441	5	m	m	PROPN
ejpam-5835	441	6	(	(	PUNCT
ejpam-5835	441	7	v	v	NOUN
ejpam-5835	441	8	)	)	PUNCT
ejpam-5835	441	9	.	.	PUNCT
ejpam-5835	442	1	thus	thus	ADV
ejpam-5835	442	2	,	,	PUNCT
ejpam-5835	442	3	we	we	PRON
ejpam-5835	442	4	denote	denote	VERB
ejpam-5835	442	5	qwfv	qwfv	PROPN
ejpam-5835	442	6	τ	τ	PROPN
ejpam-5835	442	7	(	(	PUNCT
ejpam-5835	442	8	v	v	NOUN
ejpam-5835	442	9	)	)	PUNCT
ejpam-5835	442	10	:	:	PUNCT
ejpam-5835	443	1	=	=	SYM
ejpam-5835	443	2	(	(	PUNCT
ejpam-5835	443	3	(	(	PUNCT
ejpam-5835	443	4	wwfv	wwfv	NOUN
ejpam-5835	443	5	τ	τ	X
ejpam-5835	443	6	(	(	PUNCT
ejpam-5835	443	7	xn))n∈n/(id	xn))n∈n/(id	PROPN
ejpam-5835	443	8	wfv	wfv	PROPN
ejpam-5835	443	9	n	n	PROPN
ejpam-5835	443	10	(	(	PUNCT
ejpam-5835	443	11	v	v	NOUN
ejpam-5835	443	12	)	)	PUNCT
ejpam-5835	443	13	)	)	PUNCT
ejpam-5835	443	14	n∈n	n∈n	PROPN
ejpam-5835	443	15	,	,	PUNCT
ejpam-5835	443	16	(	(	PUNCT
ejpam-5835	443	17	s	s	NOUN
ejpam-5835	443	18	n	n	PRON
ejpam-5835	443	19	m)n	m)n	X
ejpam-5835	443	20	,	,	PUNCT
ejpam-5835	443	21	m∈n	m∈n	NOUN
ejpam-5835	443	22	)	)	PUNCT
ejpam-5835	443	23	.	.	PUNCT
ejpam-5835	444	1	normally	normally	ADV
ejpam-5835	444	2	,	,	PUNCT
ejpam-5835	444	3	the	the	DET
ejpam-5835	444	4	natural	natural	ADJ
ejpam-5835	444	5	homomorphism	homomorphism	NOUN
ejpam-5835	444	6	is	be	AUX
ejpam-5835	444	7	the	the	DET
ejpam-5835	444	8	multisorted	multisorte	VERB
ejpam-5835	444	9	mapping	mapping	NOUN
ejpam-5835	444	10	(	(	PUNCT
ejpam-5835	444	11	natwfvidwfvvn)n∈n	natwfvidwfvvn)n∈n	ADV
ejpam-5835	444	12	:	:	PUNCT
ejpam-5835	444	13	(	(	PUNCT
ejpam-5835	444	14	wwfv	wwfv	NOUN
ejpam-5835	444	15	τ	τ	X
ejpam-5835	444	16	(	(	PUNCT
ejpam-5835	444	17	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	444	18	→	→	PUNCT
ejpam-5835	444	19	(	(	PUNCT
ejpam-5835	444	20	wwfv	wwfv	PROPN
ejpam-5835	444	21	τ	τ	X
ejpam-5835	444	22	(	(	PUNCT
ejpam-5835	444	23	xn))n∈n/(id	xn))n∈n/(id	PROPN
ejpam-5835	444	24	wfv	wfv	PROPN
ejpam-5835	444	25	n	n	PROPN
ejpam-5835	444	26	(	(	PUNCT
ejpam-5835	444	27	v	v	NOUN
ejpam-5835	444	28	)	)	PUNCT
ejpam-5835	444	29	)	)	PUNCT
ejpam-5835	444	30	n∈n	n∈n	NOUN
ejpam-5835	444	31	defined	define	VERB
ejpam-5835	444	32	by	by	ADP
ejpam-5835	444	33	natwfvidwfvvn(t	natwfvidwfvvn(t	NUM
ejpam-5835	444	34	)	)	PUNCT
ejpam-5835	444	35	=	=	PUNCT
ejpam-5835	445	1	[	[	X
ejpam-5835	445	2	t	t	X
ejpam-5835	445	3	]	]	X
ejpam-5835	445	4	idwfv	idwfv	PROPN
ejpam-5835	445	5	n	n	PROPN
ejpam-5835	445	6	(	(	PUNCT
ejpam-5835	445	7	v	v	NOUN
ejpam-5835	445	8	)	)	PUNCT
ejpam-5835	445	9	for	for	ADP
ejpam-5835	445	10	all	all	PRON
ejpam-5835	445	11	t	t	NOUN
ejpam-5835	445	12	∈	∈	PROPN
ejpam-5835	445	13	wwfv	wwfv	NOUN
ejpam-5835	445	14	τ	τ	PROPN
ejpam-5835	445	15	(	(	PUNCT
ejpam-5835	445	16	xn	xn	PROPN
ejpam-5835	445	17	)	)	PUNCT
ejpam-5835	445	18	.	.	PUNCT
ejpam-5835	446	1	clearly	clearly	ADV
ejpam-5835	446	2	,	,	PUNCT
ejpam-5835	446	3	(	(	PUNCT
ejpam-5835	446	4	natwfvidwfvvn)n∈n	natwfvidwfvvn)n∈n	ADV
ejpam-5835	446	5	is	be	AUX
ejpam-5835	446	6	a	a	DET
ejpam-5835	446	7	homomorphism	homomorphism	NOUN
ejpam-5835	446	8	from	from	ADP
ejpam-5835	446	9	wwfv	wwfv	PROPN
ejpam-5835	446	10	τ	τ	PROPN
ejpam-5835	446	11	(	(	PUNCT
ejpam-5835	446	12	x	x	NOUN
ejpam-5835	446	13	)	)	PUNCT
ejpam-5835	446	14	to	to	ADP
ejpam-5835	446	15	qwfv	qwfv	PROPN
ejpam-5835	446	16	τ	τ	PROPN
ejpam-5835	446	17	(	(	PUNCT
ejpam-5835	446	18	v	v	NOUN
ejpam-5835	446	19	)	)	PUNCT
ejpam-5835	446	20	.	.	PUNCT
ejpam-5835	447	1	in	in	ADP
ejpam-5835	447	2	the	the	DET
ejpam-5835	447	3	study	study	NOUN
ejpam-5835	447	4	of	of	ADP
ejpam-5835	447	5	algebra	algebra	PROPN
ejpam-5835	447	6	,	,	PUNCT
ejpam-5835	447	7	the	the	DET
ejpam-5835	447	8	concept	concept	NOUN
ejpam-5835	447	9	of	of	ADP
ejpam-5835	447	10	hyperidentities	hyperidentitie	NOUN
ejpam-5835	447	11	represents	represent	VERB
ejpam-5835	447	12	an	an	DET
ejpam-5835	447	13	extension	extension	NOUN
ejpam-5835	447	14	of	of	ADP
ejpam-5835	447	15	identities	identity	NOUN
ejpam-5835	447	16	to	to	ADP
ejpam-5835	447	17	a	a	DET
ejpam-5835	447	18	higher	high	ADJ
ejpam-5835	447	19	level	level	NOUN
ejpam-5835	447	20	,	,	PUNCT
ejpam-5835	447	21	see	see	VERB
ejpam-5835	447	22	[	[	X
ejpam-5835	447	23	3	3	NUM
ejpam-5835	447	24	,	,	PUNCT
ejpam-5835	447	25	13	13	NUM
ejpam-5835	447	26	]	]	PUNCT
ejpam-5835	447	27	.	.	PUNCT
ejpam-5835	448	1	we	we	PRON
ejpam-5835	448	2	now	now	ADV
ejpam-5835	448	3	discuss	discuss	VERB
ejpam-5835	448	4	identities	identity	NOUN
ejpam-5835	448	5	that	that	PRON
ejpam-5835	448	6	involve	involve	VERB
ejpam-5835	448	7	terms	term	NOUN
ejpam-5835	448	8	of	of	ADP
ejpam-5835	448	9	a	a	DET
ejpam-5835	448	10	weakly	weakly	ADJ
ejpam-5835	448	11	fixed	fix	VERB
ejpam-5835	448	12	variable	variable	NOUN
ejpam-5835	448	13	.	.	PUNCT
ejpam-5835	449	1	definition	definition	NOUN
ejpam-5835	449	2	4	4	NUM
ejpam-5835	449	3	.	.	PUNCT
ejpam-5835	450	1	let	let	VERB
ejpam-5835	450	2	v	v	PART
ejpam-5835	450	3	be	be	AUX
ejpam-5835	450	4	a	a	DET
ejpam-5835	450	5	variety	variety	NOUN
ejpam-5835	450	6	of	of	ADP
ejpam-5835	450	7	algebras	algebra	NOUN
ejpam-5835	450	8	of	of	ADP
ejpam-5835	450	9	type	type	NOUN
ejpam-5835	450	10	τ	τ	PROPN
ejpam-5835	450	11	and	and	CCONJ
ejpam-5835	450	12	let	let	VERB
ejpam-5835	450	13	(	(	PUNCT
ejpam-5835	450	14	hypwfv	hypwfv	VERB
ejpam-5835	450	15	n	n	CCONJ
ejpam-5835	450	16	(	(	PUNCT
ejpam-5835	450	17	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	450	18	be	be	AUX
ejpam-5835	450	19	the	the	DET
ejpam-5835	450	20	multisorted	multisorte	VERB
ejpam-5835	450	21	semigroup	semigroup	NOUN
ejpam-5835	450	22	of	of	ADP
ejpam-5835	450	23	weakly	weakly	ADJ
ejpam-5835	450	24	fixed	fix	VERB
ejpam-5835	450	25	variable	variable	ADJ
ejpam-5835	450	26	hypersubstitutions	hypersubstitution	NOUN
ejpam-5835	450	27	of	of	ADP
ejpam-5835	450	28	type	type	NOUN
ejpam-5835	450	29	τ	τ	PROPN
ejpam-5835	450	30	.	.	PUNCT
ejpam-5835	451	1	a	a	DET
ejpam-5835	451	2	weakly	weakly	ADJ
ejpam-5835	451	3	fixed	fix	VERB
ejpam-5835	451	4	variable	variable	ADJ
ejpam-5835	451	5	identity	identity	NOUN
ejpam-5835	451	6	s	s	PART
ejpam-5835	451	7	≈	≈	PROPN
ejpam-5835	451	8	t	t	PROPN
ejpam-5835	451	9	in	in	ADP
ejpam-5835	451	10	v	v	NUM
ejpam-5835	451	11	is	be	AUX
ejpam-5835	451	12	said	say	VERB
ejpam-5835	451	13	to	to	PART
ejpam-5835	451	14	be	be	AUX
ejpam-5835	451	15	a	a	DET
ejpam-5835	451	16	weakly	weakly	ADJ
ejpam-5835	451	17	fixed	fix	VERB
ejpam-5835	451	18	variable	variable	ADJ
ejpam-5835	451	19	hyperidentity	hyperidentity	NOUN
ejpam-5835	451	20	in	in	ADP
ejpam-5835	451	21	v	v	NOUN
ejpam-5835	451	22	if	if	SCONJ
ejpam-5835	451	23	σ̂n[s	σ̂n[	NOUN
ejpam-5835	451	24	]	]	PUNCT
ejpam-5835	452	1	≈	≈	PROPN
ejpam-5835	452	2	σ̂n[t	σ̂n[t	PROPN
ejpam-5835	452	3	]	]	X
ejpam-5835	452	4	∈	∈	PROPN
ejpam-5835	453	1	idn(v	idn(v	PROPN
ejpam-5835	453	2	)	)	PUNCT
ejpam-5835	453	3	for	for	ADP
ejpam-5835	453	4	s	s	PROPN
ejpam-5835	453	5	,	,	PUNCT
ejpam-5835	453	6	t	t	PROPN
ejpam-5835	453	7	∈	∈	PROPN
ejpam-5835	453	8	wwfv	wwfv	NOUN
ejpam-5835	453	9	τ	τ	PROPN
ejpam-5835	453	10	(	(	PUNCT
ejpam-5835	453	11	xn	xn	PROPN
ejpam-5835	453	12	)	)	PUNCT
ejpam-5835	453	13	,	,	PUNCT
ejpam-5835	453	14	σn	σn	PROPN
ejpam-5835	453	15	∈	∈	PROPN
ejpam-5835	453	16	hypwfv	hypwfv	NOUN
ejpam-5835	453	17	n	n	CCONJ
ejpam-5835	453	18	(	(	PUNCT
ejpam-5835	453	19	τ	τ	PROPN
ejpam-5835	453	20	)	)	PUNCT
ejpam-5835	453	21	and	and	CCONJ
ejpam-5835	453	22	n	n	DET
ejpam-5835	453	23	∈	∈	PROPN
ejpam-5835	453	24	n.	n.	NOUN
ejpam-5835	453	25	furthermore	furthermore	ADV
ejpam-5835	453	26	,	,	PUNCT
ejpam-5835	453	27	we	we	PRON
ejpam-5835	453	28	call	call	VERB
ejpam-5835	453	29	a	a	DET
ejpam-5835	453	30	variety	variety	NOUN
ejpam-5835	453	31	v	v	ADP
ejpam-5835	453	32	a	a	DET
ejpam-5835	453	33	weakly	weakly	ADV
ejpam-5835	453	34	fixed	fix	VERB
ejpam-5835	453	35	variable	variable	ADJ
ejpam-5835	453	36	solid	solid	ADJ
ejpam-5835	453	37	variety	variety	NOUN
ejpam-5835	453	38	if	if	SCONJ
ejpam-5835	453	39	σ̂n[s	σ̂n[	NOUN
ejpam-5835	453	40	]	]	PUNCT
ejpam-5835	454	1	≈	≈	PROPN
ejpam-5835	454	2	σ̂n[t	σ̂n[t	PROPN
ejpam-5835	454	3	]	]	X
ejpam-5835	454	4	∈	∈	PROPN
ejpam-5835	455	1	idn(v	idn(v	PROPN
ejpam-5835	455	2	)	)	PUNCT
ejpam-5835	455	3	for	for	ADP
ejpam-5835	455	4	s	s	PROPN
ejpam-5835	455	5	,	,	PUNCT
ejpam-5835	455	6	t	t	PROPN
ejpam-5835	455	7	∈	∈	PROPN
ejpam-5835	455	8	wwfv	wwfv	NOUN
ejpam-5835	455	9	τ	τ	PROPN
ejpam-5835	455	10	(	(	PUNCT
ejpam-5835	455	11	xn	xn	PROPN
ejpam-5835	455	12	)	)	PUNCT
ejpam-5835	455	13	,	,	PUNCT
ejpam-5835	455	14	σn	σn	PROPN
ejpam-5835	455	15	∈	∈	PROPN
ejpam-5835	455	16	hypwfv	hypwfv	NOUN
ejpam-5835	455	17	n	n	CCONJ
ejpam-5835	455	18	(	(	PUNCT
ejpam-5835	455	19	τ	τ	PROPN
ejpam-5835	455	20	)	)	PUNCT
ejpam-5835	455	21	and	and	CCONJ
ejpam-5835	455	22	n	n	DET
ejpam-5835	455	23	∈	∈	PROPN
ejpam-5835	455	24	n.	n.	NOUN
ejpam-5835	455	25	from	from	ADP
ejpam-5835	455	26	definition	definition	NOUN
ejpam-5835	455	27	4	4	NUM
ejpam-5835	455	28	,	,	PUNCT
ejpam-5835	455	29	we	we	PRON
ejpam-5835	455	30	define	define	VERB
ejpam-5835	455	31	hidwfv	hidwfv	PROPN
ejpam-5835	455	32	n	n	CCONJ
ejpam-5835	455	33	(	(	PUNCT
ejpam-5835	455	34	v	v	NOUN
ejpam-5835	455	35	)	)	PUNCT
ejpam-5835	455	36	:	:	PUNCT
ejpam-5835	455	37	=	=	SYM
ejpam-5835	455	38	{	{	PUNCT
ejpam-5835	455	39	s	s	PROPN
ejpam-5835	455	40	≈	≈	PROPN
ejpam-5835	455	41	t	t	PROPN
ejpam-5835	456	1	|	|	NOUN
ejpam-5835	456	2	s	s	PROPN
ejpam-5835	456	3	,	,	PUNCT
ejpam-5835	456	4	t	t	PROPN
ejpam-5835	456	5	∈	∈	PROPN
ejpam-5835	456	6	wwfv	wwfv	NOUN
ejpam-5835	456	7	τ	τ	PROPN
ejpam-5835	456	8	(	(	PUNCT
ejpam-5835	456	9	xn	xn	PROPN
ejpam-5835	456	10	)	)	PUNCT
ejpam-5835	456	11	,	,	PUNCT
ejpam-5835	456	12	σ̂n[s	σ̂n[	NOUN
ejpam-5835	456	13	]	]	PUNCT
ejpam-5835	457	1	≈	≈	PROPN
ejpam-5835	457	2	σ̂n[t	σ̂n[t	PROPN
ejpam-5835	457	3	]	]	X
ejpam-5835	457	4	∈	∈	PROPN
ejpam-5835	458	1	idn(v	idn(v	PROPN
ejpam-5835	458	2	)	)	PUNCT
ejpam-5835	458	3	,	,	PUNCT
ejpam-5835	458	4	σn	σn	PROPN
ejpam-5835	458	5	∈	∈	PROPN
ejpam-5835	458	6	hypwfv	hypwfv	NOUN
ejpam-5835	458	7	n	n	CCONJ
ejpam-5835	458	8	(	(	PUNCT
ejpam-5835	458	9	τ	τ	PROPN
ejpam-5835	458	10	)	)	PUNCT
ejpam-5835	458	11	}	}	PUNCT
ejpam-5835	458	12	.	.	PUNCT
ejpam-5835	459	1	then	then	ADV
ejpam-5835	459	2	(	(	PUNCT
ejpam-5835	459	3	hidwfv	hidwfv	PROPN
ejpam-5835	459	4	n	n	CCONJ
ejpam-5835	459	5	(	(	PUNCT
ejpam-5835	459	6	v	v	NOUN
ejpam-5835	459	7	)	)	PUNCT
ejpam-5835	459	8	)	)	PUNCT
ejpam-5835	459	9	n∈n	n∈n	NOUN
ejpam-5835	459	10	is	be	AUX
ejpam-5835	459	11	a	a	DET
ejpam-5835	459	12	multisorted	multisorte	VERB
ejpam-5835	459	13	equivalence	equivalence	NOUN
ejpam-5835	459	14	on	on	ADP
ejpam-5835	459	15	(	(	PUNCT
ejpam-5835	459	16	wwfv	wwfv	PROPN
ejpam-5835	459	17	τ	τ	X
ejpam-5835	459	18	(	(	PUNCT
ejpam-5835	459	19	xn))n∈n	xn))n∈n	PROPN
ejpam-5835	459	20	.	.	PROPN
ejpam-5835	459	21	theorem	theorem	VERB
ejpam-5835	459	22	6	6	NUM
ejpam-5835	459	23	.	.	PUNCT
ejpam-5835	460	1	let	let	VERB
ejpam-5835	460	2	v	v	PART
ejpam-5835	460	3	be	be	AUX
ejpam-5835	460	4	a	a	DET
ejpam-5835	460	5	variety	variety	NOUN
ejpam-5835	460	6	of	of	ADP
ejpam-5835	460	7	type	type	NOUN
ejpam-5835	460	8	τ	τ	PROPN
ejpam-5835	460	9	.	.	PUNCT
ejpam-5835	461	1	then	then	ADV
ejpam-5835	461	2	(	(	PUNCT
ejpam-5835	461	3	hidwfv	hidwfv	PROPN
ejpam-5835	461	4	n	n	CCONJ
ejpam-5835	461	5	(	(	PUNCT
ejpam-5835	461	6	v	v	NOUN
ejpam-5835	461	7	)	)	PUNCT
ejpam-5835	461	8	)	)	PUNCT
ejpam-5835	461	9	n∈n	n∈n	NOUN
ejpam-5835	461	10	is	be	AUX
ejpam-5835	461	11	a	a	DET
ejpam-5835	461	12	congruence	congruence	NOUN
ejpam-5835	461	13	on	on	ADP
ejpam-5835	461	14	wwfv	wwfv	PROPN
ejpam-5835	461	15	τ	τ	PROPN
ejpam-5835	461	16	(	(	PUNCT
ejpam-5835	461	17	x	x	NOUN
ejpam-5835	461	18	)	)	PUNCT
ejpam-5835	461	19	.	.	PUNCT
ejpam-5835	462	1	t.	t.	PROPN
ejpam-5835	462	2	kumduang	kumduang	PROPN
ejpam-5835	462	3	,	,	PUNCT
ejpam-5835	462	4	k.	k.	PROPN
ejpam-5835	462	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	462	6	/	/	SYM
ejpam-5835	462	7	eur	eur	PROPN
ejpam-5835	462	8	.	.	PUNCT
ejpam-5835	463	1	j.	j.	PROPN
ejpam-5835	463	2	pure	pure	PROPN
ejpam-5835	463	3	appl	appl	PROPN
ejpam-5835	463	4	.	.	PROPN
ejpam-5835	463	5	math	math	PROPN
ejpam-5835	463	6	,	,	PUNCT
ejpam-5835	463	7	18	18	NUM
ejpam-5835	463	8	(	(	PUNCT
ejpam-5835	463	9	2	2	NUM
ejpam-5835	463	10	)	)	PUNCT
ejpam-5835	463	11	(	(	PUNCT
ejpam-5835	463	12	2025	2025	NUM
ejpam-5835	463	13	)	)	PUNCT
ejpam-5835	463	14	,	,	PUNCT
ejpam-5835	463	15	5835	5835	NUM
ejpam-5835	463	16	13	13	NUM
ejpam-5835	463	17	of	of	ADP
ejpam-5835	463	18	16	16	NUM
ejpam-5835	463	19	proof	proof	NOUN
ejpam-5835	463	20	.	.	PUNCT
ejpam-5835	464	1	let	let	VERB
ejpam-5835	464	2	p	p	PROPN
ejpam-5835	464	3	≈	≈	PROPN
ejpam-5835	464	4	q	q	PROPN
ejpam-5835	464	5	∈	∈	PROPN
ejpam-5835	464	6	hidwfv	hidwfv	PROPN
ejpam-5835	464	7	n	n	CCONJ
ejpam-5835	464	8	(	(	PUNCT
ejpam-5835	464	9	v	v	NOUN
ejpam-5835	464	10	)	)	PUNCT
ejpam-5835	464	11	and	and	CCONJ
ejpam-5835	464	12	let	let	VERB
ejpam-5835	464	13	pj	pj	PROPN
ejpam-5835	464	14	≈	≈	PROPN
ejpam-5835	464	15	qj	qj	PROPN
ejpam-5835	464	16	∈	∈	PROPN
ejpam-5835	464	17	hidwfv	hidwfv	PROPN
ejpam-5835	464	18	m	m	PROPN
ejpam-5835	464	19	(	(	PUNCT
ejpam-5835	464	20	v	v	NOUN
ejpam-5835	464	21	)	)	PUNCT
ejpam-5835	464	22	for	for	ADP
ejpam-5835	464	23	j	j	PROPN
ejpam-5835	464	24	=	=	SYM
ejpam-5835	464	25	1	1	PROPN
ejpam-5835	464	26	,	,	PUNCT
ejpam-5835	464	27	.	.	PUNCT
ejpam-5835	464	28	.	.	PUNCT
ejpam-5835	465	1	.	.	PUNCT
ejpam-5835	466	1	,	,	PUNCT
ejpam-5835	466	2	n.	n.	PROPN
ejpam-5835	466	3	according	accord	VERB
ejpam-5835	466	4	to	to	ADP
ejpam-5835	466	5	the	the	DET
ejpam-5835	466	6	definition	definition	NOUN
ejpam-5835	466	7	of	of	ADP
ejpam-5835	466	8	weakly	weakly	ADJ
ejpam-5835	466	9	fixed	fix	VERB
ejpam-5835	466	10	variable	variable	ADJ
ejpam-5835	466	11	hyperidentities	hyperidentitie	NOUN
ejpam-5835	466	12	in	in	ADP
ejpam-5835	466	13	a	a	DET
ejpam-5835	466	14	variety	variety	NOUN
ejpam-5835	466	15	v	v	NOUN
ejpam-5835	466	16	,	,	PUNCT
ejpam-5835	466	17	we	we	PRON
ejpam-5835	466	18	have	have	AUX
ejpam-5835	466	19	σ̂n[p	σ̂n[p	VERB
ejpam-5835	466	20	]	]	X
ejpam-5835	467	1	≈	≈	PROPN
ejpam-5835	467	2	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	467	3	]	]	PUNCT
ejpam-5835	467	4	∈	∈	PROPN
ejpam-5835	467	5	idwfv	idwfv	NOUN
ejpam-5835	467	6	n	n	CCONJ
ejpam-5835	467	7	(	(	PUNCT
ejpam-5835	467	8	v	v	NOUN
ejpam-5835	467	9	)	)	PUNCT
ejpam-5835	467	10	and	and	CCONJ
ejpam-5835	467	11	σ̂m[pj	σ̂m[pj	VERB
ejpam-5835	467	12	]	]	PUNCT
ejpam-5835	468	1	≈	≈	PROPN
ejpam-5835	468	2	σ̂m[qj	σ̂m[qj	NOUN
ejpam-5835	468	3	]	]	PUNCT
ejpam-5835	468	4	∈	∈	PROPN
ejpam-5835	468	5	idwfv	idwfv	NOUN
ejpam-5835	468	6	m	m	PROPN
ejpam-5835	468	7	(	(	PUNCT
ejpam-5835	468	8	v	v	NOUN
ejpam-5835	468	9	)	)	PUNCT
ejpam-5835	468	10	for	for	ADP
ejpam-5835	468	11	all	all	PRON
ejpam-5835	468	12	j	j	NOUN
ejpam-5835	468	13	=	=	SYM
ejpam-5835	468	14	1	1	NUM
ejpam-5835	468	15	,	,	PUNCT
ejpam-5835	468	16	.	.	PUNCT
ejpam-5835	468	17	.	.	PUNCT
ejpam-5835	469	1	.	.	PUNCT
ejpam-5835	470	1	,	,	PUNCT
ejpam-5835	470	2	n	n	PROPN
ejpam-5835	470	3	and	and	CCONJ
ejpam-5835	470	4	σ	σ	NUM
ejpam-5835	470	5	∈	∈	PROPN
ejpam-5835	470	6	(	(	PUNCT
ejpam-5835	470	7	hypwfv	hypwfv	NOUN
ejpam-5835	470	8	n	n	CCONJ
ejpam-5835	470	9	(	(	PUNCT
ejpam-5835	470	10	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	470	11	.	.	PUNCT
ejpam-5835	471	1	our	our	PRON
ejpam-5835	471	2	aim	aim	NOUN
ejpam-5835	471	3	is	be	AUX
ejpam-5835	471	4	to	to	PART
ejpam-5835	471	5	show	show	VERB
ejpam-5835	471	6	that	that	SCONJ
ejpam-5835	471	7	σ̂m[sn	σ̂m[sn	ADJ
ejpam-5835	471	8	m(p	m(p	PROPN
ejpam-5835	471	9	,	,	PUNCT
ejpam-5835	471	10	p1	p1	NOUN
ejpam-5835	471	11	,	,	PUNCT
ejpam-5835	471	12	.	.	PUNCT
ejpam-5835	471	13	.	.	PUNCT
ejpam-5835	472	1	.	.	PUNCT
ejpam-5835	473	1	,	,	PUNCT
ejpam-5835	473	2	pn	pn	PROPN
ejpam-5835	473	3	)	)	PUNCT
ejpam-5835	473	4	]	]	PUNCT
ejpam-5835	474	1	≈	≈	NUM
ejpam-5835	474	2	σ̂m[sn	σ̂m[sn	VERB
ejpam-5835	474	3	m(q	m(q	PROPN
ejpam-5835	474	4	,	,	PUNCT
ejpam-5835	474	5	q1	q1	NOUN
ejpam-5835	474	6	,	,	PUNCT
ejpam-5835	474	7	.	.	PUNCT
ejpam-5835	474	8	.	.	PUNCT
ejpam-5835	474	9	.	.	PUNCT
ejpam-5835	475	1	,	,	PUNCT
ejpam-5835	475	2	qn	qn	NOUN
ejpam-5835	475	3	)	)	PUNCT
ejpam-5835	475	4	]	]	PUNCT
ejpam-5835	476	1	∈	∈	PROPN
ejpam-5835	477	1	idwfv	idwfv	NOUN
ejpam-5835	477	2	m	m	PROPN
ejpam-5835	477	3	(	(	PUNCT
ejpam-5835	477	4	v	v	NOUN
ejpam-5835	477	5	)	)	PUNCT
ejpam-5835	477	6	for	for	ADP
ejpam-5835	477	7	all	all	DET
ejpam-5835	477	8	σ	σ	X
ejpam-5835	477	9	∈	∈	PROPN
ejpam-5835	477	10	(	(	PUNCT
ejpam-5835	477	11	hypwfv	hypwfv	NOUN
ejpam-5835	477	12	n	n	CCONJ
ejpam-5835	477	13	(	(	PUNCT
ejpam-5835	477	14	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	477	15	.	.	PUNCT
ejpam-5835	478	1	for	for	ADP
ejpam-5835	478	2	this	this	PRON
ejpam-5835	478	3	,	,	PUNCT
ejpam-5835	478	4	we	we	PRON
ejpam-5835	478	5	let	let	VERB
ejpam-5835	478	6	σ	σ	NOUN
ejpam-5835	478	7	be	be	AUX
ejpam-5835	478	8	a	a	DET
ejpam-5835	478	9	weakly	weakly	ADJ
ejpam-5835	478	10	fixed	fix	VERB
ejpam-5835	478	11	variable	variable	ADJ
ejpam-5835	478	12	hypersubstitution	hypersubstitution	NOUN
ejpam-5835	478	13	on	on	ADP
ejpam-5835	478	14	the	the	DET
ejpam-5835	478	15	multisorted	multisorte	VERB
ejpam-5835	478	16	semigroup	semigroup	NOUN
ejpam-5835	478	17	(	(	PUNCT
ejpam-5835	478	18	hypwfv	hypwfv	NOUN
ejpam-5835	478	19	n	n	CCONJ
ejpam-5835	478	20	(	(	PUNCT
ejpam-5835	478	21	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	478	22	.	.	PUNCT
ejpam-5835	479	1	from	from	ADP
ejpam-5835	479	2	σ̂n[p	σ̂n[p	PROPN
ejpam-5835	479	3	]	]	X
ejpam-5835	480	1	≈	≈	PROPN
ejpam-5835	480	2	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	480	3	]	]	PUNCT
ejpam-5835	480	4	∈	∈	PROPN
ejpam-5835	480	5	idwfv	idwfv	NOUN
ejpam-5835	480	6	n	n	CCONJ
ejpam-5835	480	7	(	(	PUNCT
ejpam-5835	480	8	v	v	NOUN
ejpam-5835	480	9	)	)	PUNCT
ejpam-5835	480	10	,	,	PUNCT
ejpam-5835	480	11	we	we	PRON
ejpam-5835	480	12	have	have	VERB
ejpam-5835	480	13	that	that	DET
ejpam-5835	480	14	σ̂n[p	σ̂n[p	NOUN
ejpam-5835	480	15	]	]	PUNCT
ejpam-5835	480	16	and	and	CCONJ
ejpam-5835	480	17	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	480	18	]	]	PUNCT
ejpam-5835	480	19	are	be	AUX
ejpam-5835	480	20	m	m	ADJ
ejpam-5835	480	21	-	-	ADJ
ejpam-5835	481	1	ary	ary	ADJ
ejpam-5835	481	2	terms	term	NOUN
ejpam-5835	481	3	of	of	ADP
ejpam-5835	481	4	a	a	DET
ejpam-5835	481	5	weakly	weakly	ADJ
ejpam-5835	481	6	fixed	fixed	ADJ
ejpam-5835	481	7	variable	variable	NOUN
ejpam-5835	481	8	of	of	ADP
ejpam-5835	481	9	type	type	NOUN
ejpam-5835	481	10	τ	τ	PROPN
ejpam-5835	481	11	and	and	CCONJ
ejpam-5835	481	12	thus	thus	ADV
ejpam-5835	481	13	σ̂n[p	σ̂n[p	VERB
ejpam-5835	481	14	]	]	X
ejpam-5835	482	1	≈	≈	PROPN
ejpam-5835	482	2	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	482	3	]	]	PUNCT
ejpam-5835	482	4	is	be	AUX
ejpam-5835	482	5	an	an	DET
ejpam-5835	482	6	identity	identity	NOUN
ejpam-5835	482	7	in	in	ADP
ejpam-5835	482	8	v	v	NUM
ejpam-5835	482	9	,	,	PUNCT
ejpam-5835	482	10	i.e.	i.e.	X
ejpam-5835	482	11	,	,	PUNCT
ejpam-5835	482	12	σ̂n[p	σ̂n[p	NOUN
ejpam-5835	482	13	]	]	X
ejpam-5835	483	1	≈	≈	PROPN
ejpam-5835	483	2	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	483	3	]	]	X
ejpam-5835	483	4	∈	∈	PROPN
ejpam-5835	483	5	idn(v	idn(v	PROPN
ejpam-5835	483	6	)	)	PUNCT
ejpam-5835	483	7	.	.	PUNCT
ejpam-5835	484	1	similarly	similarly	ADV
ejpam-5835	484	2	,	,	PUNCT
ejpam-5835	484	3	because	because	SCONJ
ejpam-5835	484	4	for	for	ADP
ejpam-5835	484	5	every	every	DET
ejpam-5835	484	6	j	j	NOUN
ejpam-5835	484	7	=	=	SYM
ejpam-5835	484	8	1	1	NUM
ejpam-5835	484	9	,	,	PUNCT
ejpam-5835	484	10	.	.	PUNCT
ejpam-5835	484	11	.	.	PUNCT
ejpam-5835	484	12	.	.	PUNCT
ejpam-5835	485	1	,	,	PUNCT
ejpam-5835	485	2	n	n	CCONJ
ejpam-5835	485	3	,	,	PUNCT
ejpam-5835	485	4	σ̂m[pj	σ̂m[pj	VERB
ejpam-5835	485	5	]	]	PUNCT
ejpam-5835	486	1	≈	≈	PROPN
ejpam-5835	486	2	σ̂m[qj	σ̂m[qj	NOUN
ejpam-5835	486	3	]	]	PUNCT
ejpam-5835	486	4	∈	∈	PROPN
ejpam-5835	486	5	idwfv	idwfv	NOUN
ejpam-5835	486	6	m	m	PROPN
ejpam-5835	486	7	(	(	PUNCT
ejpam-5835	486	8	v	v	NOUN
ejpam-5835	486	9	)	)	PUNCT
ejpam-5835	486	10	,	,	PUNCT
ejpam-5835	486	11	then	then	ADV
ejpam-5835	486	12	σ̂m[pj	σ̂m[pj	VERB
ejpam-5835	486	13	]	]	PUNCT
ejpam-5835	487	1	≈	≈	PROPN
ejpam-5835	487	2	σ̂m[qj	σ̂m[qj	NOUN
ejpam-5835	487	3	]	]	PUNCT
ejpam-5835	487	4	∈	∈	PROPN
ejpam-5835	487	5	idm(v	idm(v	PROPN
ejpam-5835	487	6	)	)	PUNCT
ejpam-5835	487	7	for	for	ADP
ejpam-5835	487	8	all	all	DET
ejpam-5835	487	9	j	j	NOUN
ejpam-5835	487	10	=	=	SYM
ejpam-5835	487	11	1	1	NUM
ejpam-5835	487	12	,	,	PUNCT
ejpam-5835	487	13	.	.	PUNCT
ejpam-5835	487	14	.	.	PUNCT
ejpam-5835	487	15	.	.	PUNCT
ejpam-5835	487	16	,	,	PUNCT
ejpam-5835	487	17	n	n	CCONJ
ejpam-5835	487	18	,	,	PUNCT
ejpam-5835	487	19	and	and	CCONJ
ejpam-5835	487	20	σ̂m[p1	σ̂m[p1	NOUN
ejpam-5835	487	21	]	]	PUNCT
ejpam-5835	487	22	,	,	PUNCT
ejpam-5835	487	23	.	.	PUNCT
ejpam-5835	487	24	.	.	PUNCT
ejpam-5835	487	25	.	.	PUNCT
ejpam-5835	488	1	,	,	PUNCT
ejpam-5835	488	2	σ̂m[pn	σ̂m[pn	NOUN
ejpam-5835	488	3	]	]	X
ejpam-5835	488	4	,	,	PUNCT
ejpam-5835	488	5	σ̂m[q1	σ̂m[q1	PROPN
ejpam-5835	488	6	]	]	X
ejpam-5835	488	7	,	,	PUNCT
ejpam-5835	488	8	.	.	PUNCT
ejpam-5835	488	9	.	.	PUNCT
ejpam-5835	489	1	.	.	PUNCT
ejpam-5835	490	1	,	,	PUNCT
ejpam-5835	490	2	σ̂m[qn	σ̂m[qn	X
ejpam-5835	490	3	]	]	X
ejpam-5835	490	4	∈	∈	PROPN
ejpam-5835	490	5	wwfv	wwfv	NOUN
ejpam-5835	490	6	τ	τ	PROPN
ejpam-5835	490	7	(	(	PUNCT
ejpam-5835	490	8	xm	xm	PROPN
ejpam-5835	490	9	)	)	PUNCT
ejpam-5835	490	10	.	.	PUNCT
ejpam-5835	491	1	by	by	ADP
ejpam-5835	491	2	the	the	DET
ejpam-5835	491	3	fact	fact	NOUN
ejpam-5835	491	4	that	that	SCONJ
ejpam-5835	491	5	σ̂n[p	σ̂n[p	VERB
ejpam-5835	491	6	]	]	X
ejpam-5835	492	1	≈	≈	PROPN
ejpam-5835	492	2	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	492	3	]	]	X
ejpam-5835	492	4	∈	∈	PROPN
ejpam-5835	492	5	idn(v	idn(v	ADJ
ejpam-5835	492	6	)	)	PUNCT
ejpam-5835	492	7	and	and	CCONJ
ejpam-5835	492	8	σ̂m[pj	σ̂m[pj	VERB
ejpam-5835	492	9	]	]	X
ejpam-5835	493	1	≈	≈	PROPN
ejpam-5835	493	2	σ̂m[qj	σ̂m[qj	NOUN
ejpam-5835	493	3	]	]	PUNCT
ejpam-5835	493	4	∈	∈	PROPN
ejpam-5835	493	5	idm(v	idm(v	PROPN
ejpam-5835	493	6	)	)	PUNCT
ejpam-5835	493	7	,	,	PUNCT
ejpam-5835	493	8	we	we	PRON
ejpam-5835	493	9	obtain	obtain	VERB
ejpam-5835	493	10	sn	sn	PROPN
ejpam-5835	493	11	m(σ̂n[p	m(σ̂n[p	NOUN
ejpam-5835	493	12	]	]	X
ejpam-5835	493	13	,	,	PUNCT
ejpam-5835	493	14	σ̂m[p1	σ̂m[p1	PROPN
ejpam-5835	493	15	]	]	PUNCT
ejpam-5835	493	16	,	,	PUNCT
ejpam-5835	493	17	.	.	PUNCT
ejpam-5835	493	18	.	.	PUNCT
ejpam-5835	493	19	.	.	PUNCT
ejpam-5835	494	1	,	,	PUNCT
ejpam-5835	494	2	σ̂m[pn	σ̂m[pn	NOUN
ejpam-5835	494	3	]	]	X
ejpam-5835	494	4	)	)	PUNCT
ejpam-5835	495	1	≈	≈	PROPN
ejpam-5835	495	2	sn	sn	PROPN
ejpam-5835	495	3	m(σ̂n[q	m(σ̂n[q	PROPN
ejpam-5835	495	4	]	]	X
ejpam-5835	495	5	,	,	PUNCT
ejpam-5835	495	6	σ̂m[q1	σ̂m[q1	PROPN
ejpam-5835	495	7	]	]	X
ejpam-5835	495	8	,	,	PUNCT
ejpam-5835	495	9	.	.	PUNCT
ejpam-5835	495	10	.	.	PUNCT
ejpam-5835	495	11	.	.	PUNCT
ejpam-5835	496	1	,	,	PUNCT
ejpam-5835	496	2	σ̂m[qn	σ̂m[qn	NOUN
ejpam-5835	496	3	]	]	X
ejpam-5835	496	4	)	)	PUNCT
ejpam-5835	496	5	∈	∈	PROPN
ejpam-5835	496	6	idm(v	idm(v	PROPN
ejpam-5835	496	7	)	)	PUNCT
ejpam-5835	496	8	because	because	SCONJ
ejpam-5835	496	9	(	(	PUNCT
ejpam-5835	496	10	idn(v	idn(v	INTJ
ejpam-5835	496	11	)	)	PUNCT
ejpam-5835	496	12	)	)	PUNCT
ejpam-5835	496	13	n∈n	n∈n	NOUN
ejpam-5835	496	14	is	be	AUX
ejpam-5835	496	15	a	a	DET
ejpam-5835	496	16	congruence	congruence	NOUN
ejpam-5835	496	17	on	on	ADP
ejpam-5835	496	18	the	the	DET
ejpam-5835	496	19	multisorted	multisorte	VERB
ejpam-5835	496	20	algebra	algebra	NOUN
ejpam-5835	496	21	of	of	ADP
ejpam-5835	496	22	terms	term	NOUN
ejpam-5835	496	23	.	.	PUNCT
ejpam-5835	497	1	from	from	ADP
ejpam-5835	497	2	σ̂n[p	σ̂n[p	PROPN
ejpam-5835	497	3	]	]	PUNCT
ejpam-5835	497	4	,	,	PUNCT
ejpam-5835	497	5	σ̂n[q	σ̂n[q	PROPN
ejpam-5835	497	6	]	]	PUNCT
ejpam-5835	497	7	∈	∈	PROPN
ejpam-5835	497	8	wwfv	wwfv	NOUN
ejpam-5835	497	9	τ	τ	PROPN
ejpam-5835	497	10	(	(	PUNCT
ejpam-5835	497	11	xn	xn	PROPN
ejpam-5835	497	12	)	)	PUNCT
ejpam-5835	497	13	and	and	CCONJ
ejpam-5835	497	14	σ̂m[p1	σ̂m[p1	NOUN
ejpam-5835	497	15	]	]	PUNCT
ejpam-5835	497	16	,	,	PUNCT
ejpam-5835	497	17	.	.	PUNCT
ejpam-5835	497	18	.	.	PUNCT
ejpam-5835	497	19	.	.	PUNCT
ejpam-5835	498	1	,	,	PUNCT
ejpam-5835	498	2	σ̂m[pn	σ̂m[pn	NOUN
ejpam-5835	498	3	]	]	X
ejpam-5835	498	4	,	,	PUNCT
ejpam-5835	498	5	σ̂m[q1	σ̂m[q1	PROPN
ejpam-5835	498	6	]	]	X
ejpam-5835	498	7	,	,	PUNCT
ejpam-5835	498	8	.	.	PUNCT
ejpam-5835	498	9	.	.	PUNCT
ejpam-5835	499	1	.	.	PUNCT
ejpam-5835	500	1	,	,	PUNCT
ejpam-5835	500	2	σ̂m[qn	σ̂m[qn	X
ejpam-5835	500	3	]	]	X
ejpam-5835	500	4	∈	∈	PROPN
ejpam-5835	500	5	wwfv	wwfv	NOUN
ejpam-5835	500	6	τ	τ	PROPN
ejpam-5835	500	7	(	(	PUNCT
ejpam-5835	500	8	xm	xm	PROPN
ejpam-5835	500	9	)	)	PUNCT
ejpam-5835	500	10	,	,	PUNCT
ejpam-5835	500	11	we	we	PRON
ejpam-5835	500	12	also	also	ADV
ejpam-5835	500	13	conclude	conclude	VERB
ejpam-5835	500	14	that	that	SCONJ
ejpam-5835	500	15	sn	sn	PROPN
ejpam-5835	500	16	m(σ̂n[p	m(σ̂n[p	PROPN
ejpam-5835	500	17	]	]	PROPN
ejpam-5835	500	18	,	,	PUNCT
ejpam-5835	500	19	σ̂m[p1	σ̂m[p1	PROPN
ejpam-5835	500	20	]	]	PUNCT
ejpam-5835	500	21	,	,	PUNCT
ejpam-5835	500	22	.	.	PUNCT
ejpam-5835	500	23	.	.	PUNCT
ejpam-5835	501	1	.	.	PUNCT
ejpam-5835	502	1	,	,	PUNCT
ejpam-5835	502	2	σ̂m[pn	σ̂m[pn	NOUN
ejpam-5835	502	3	]	]	X
ejpam-5835	502	4	)	)	PUNCT
ejpam-5835	503	1	≈	≈	PROPN
ejpam-5835	503	2	sn	sn	PROPN
ejpam-5835	503	3	m(σ̂n[q	m(σ̂n[q	PROPN
ejpam-5835	503	4	]	]	X
ejpam-5835	503	5	,	,	PUNCT
ejpam-5835	503	6	σ̂m[q1	σ̂m[q1	PROPN
ejpam-5835	503	7	]	]	X
ejpam-5835	503	8	,	,	PUNCT
ejpam-5835	503	9	.	.	PUNCT
ejpam-5835	503	10	.	.	PUNCT
ejpam-5835	503	11	.	.	PUNCT
ejpam-5835	504	1	,	,	PUNCT
ejpam-5835	504	2	σ̂m[qn	σ̂m[qn	NOUN
ejpam-5835	504	3	]	]	X
ejpam-5835	504	4	)	)	PUNCT
ejpam-5835	504	5	∈	∈	NOUN
ejpam-5835	504	6	wwfv	wwfv	NOUN
ejpam-5835	504	7	τ	τ	PROPN
ejpam-5835	504	8	(	(	PUNCT
ejpam-5835	504	9	xm	xm	PROPN
ejpam-5835	504	10	)	)	PUNCT
ejpam-5835	504	11	.	.	PUNCT
ejpam-5835	505	1	this	this	PRON
ejpam-5835	505	2	implies	imply	VERB
ejpam-5835	505	3	that	that	SCONJ
ejpam-5835	505	4	sn	sn	PROPN
ejpam-5835	505	5	m(σ̂n[p	m(σ̂n[p	PROPN
ejpam-5835	505	6	]	]	PROPN
ejpam-5835	505	7	,	,	PUNCT
ejpam-5835	505	8	σ̂m[p1	σ̂m[p1	PROPN
ejpam-5835	505	9	]	]	PUNCT
ejpam-5835	505	10	,	,	PUNCT
ejpam-5835	505	11	.	.	PUNCT
ejpam-5835	505	12	.	.	PUNCT
ejpam-5835	505	13	.	.	PUNCT
ejpam-5835	506	1	,	,	PUNCT
ejpam-5835	506	2	σ̂m[pn	σ̂m[pn	NOUN
ejpam-5835	506	3	]	]	X
ejpam-5835	506	4	)	)	PUNCT
ejpam-5835	507	1	≈	≈	PROPN
ejpam-5835	507	2	sn	sn	PROPN
ejpam-5835	507	3	m(σ̂n[q	m(σ̂n[q	PROPN
ejpam-5835	507	4	]	]	X
ejpam-5835	507	5	,	,	PUNCT
ejpam-5835	507	6	σ̂m[q1	σ̂m[q1	PROPN
ejpam-5835	507	7	]	]	X
ejpam-5835	507	8	,	,	PUNCT
ejpam-5835	507	9	.	.	PUNCT
ejpam-5835	507	10	.	.	PUNCT
ejpam-5835	507	11	.	.	PUNCT
ejpam-5835	508	1	,	,	PUNCT
ejpam-5835	508	2	σ̂m[qn	σ̂m[qn	NOUN
ejpam-5835	508	3	]	]	X
ejpam-5835	508	4	)	)	PUNCT
ejpam-5835	508	5	∈	∈	PROPN
ejpam-5835	509	1	idwfv	idwfv	NOUN
ejpam-5835	509	2	m	m	PROPN
ejpam-5835	509	3	(	(	PUNCT
ejpam-5835	509	4	v	v	NOUN
ejpam-5835	509	5	)	)	PUNCT
ejpam-5835	509	6	.	.	PUNCT
ejpam-5835	510	1	from	from	ADP
ejpam-5835	510	2	the	the	DET
ejpam-5835	510	3	fact	fact	NOUN
ejpam-5835	510	4	that	that	SCONJ
ejpam-5835	510	5	(	(	PUNCT
ejpam-5835	510	6	σ̂n)n∈n	σ̂n)n∈n	PROPN
ejpam-5835	510	7	is	be	AUX
ejpam-5835	510	8	an	an	DET
ejpam-5835	510	9	endomorphism	endomorphism	NOUN
ejpam-5835	510	10	on	on	ADP
ejpam-5835	510	11	the	the	DET
ejpam-5835	510	12	multisorted	multisorte	VERB
ejpam-5835	510	13	algebra	algebra	NOUN
ejpam-5835	510	14	wwfv	wwfv	NOUN
ejpam-5835	510	15	τ	τ	PROPN
ejpam-5835	510	16	(	(	PUNCT
ejpam-5835	510	17	x	x	NOUN
ejpam-5835	510	18	)	)	PUNCT
ejpam-5835	510	19	proved	prove	VERB
ejpam-5835	510	20	in	in	ADP
ejpam-5835	510	21	theorem	theorem	NOUN
ejpam-5835	510	22	2	2	NUM
ejpam-5835	510	23	,	,	PUNCT
ejpam-5835	510	24	we	we	PRON
ejpam-5835	510	25	have	have	VERB
ejpam-5835	510	26	σ̂m[sn	σ̂m[sn	ADJ
ejpam-5835	510	27	m(p	m(p	PROPN
ejpam-5835	510	28	,	,	PUNCT
ejpam-5835	510	29	p1	p1	NOUN
ejpam-5835	510	30	,	,	PUNCT
ejpam-5835	510	31	.	.	PUNCT
ejpam-5835	510	32	.	.	PUNCT
ejpam-5835	511	1	.	.	PUNCT
ejpam-5835	512	1	,	,	PUNCT
ejpam-5835	512	2	pn	pn	PROPN
ejpam-5835	512	3	)	)	PUNCT
ejpam-5835	512	4	]	]	PUNCT
ejpam-5835	513	1	≈	≈	NUM
ejpam-5835	513	2	σ̂m[sn	σ̂m[sn	VERB
ejpam-5835	513	3	m(q	m(q	PROPN
ejpam-5835	513	4	,	,	PUNCT
ejpam-5835	513	5	q1	q1	NOUN
ejpam-5835	513	6	,	,	PUNCT
ejpam-5835	513	7	.	.	PUNCT
ejpam-5835	513	8	.	.	PUNCT
ejpam-5835	513	9	.	.	PUNCT
ejpam-5835	514	1	,	,	PUNCT
ejpam-5835	514	2	qn	qn	NOUN
ejpam-5835	514	3	)	)	PUNCT
ejpam-5835	514	4	]	]	PUNCT
ejpam-5835	515	1	∈	∈	PROPN
ejpam-5835	516	1	idwfv	idwfv	NOUN
ejpam-5835	516	2	m	m	PROPN
ejpam-5835	516	3	(	(	PUNCT
ejpam-5835	516	4	v	v	NOUN
ejpam-5835	516	5	)	)	PUNCT
ejpam-5835	516	6	.	.	PUNCT
ejpam-5835	517	1	t.	t.	PROPN
ejpam-5835	517	2	kumduang	kumduang	PROPN
ejpam-5835	517	3	,	,	PUNCT
ejpam-5835	517	4	k.	k.	PROPN
ejpam-5835	517	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	517	6	/	/	SYM
ejpam-5835	517	7	eur	eur	PROPN
ejpam-5835	517	8	.	.	PUNCT
ejpam-5835	518	1	j.	j.	PROPN
ejpam-5835	518	2	pure	pure	PROPN
ejpam-5835	518	3	appl	appl	PROPN
ejpam-5835	518	4	.	.	PROPN
ejpam-5835	518	5	math	math	PROPN
ejpam-5835	518	6	,	,	PUNCT
ejpam-5835	518	7	18	18	NUM
ejpam-5835	518	8	(	(	PUNCT
ejpam-5835	518	9	2	2	NUM
ejpam-5835	518	10	)	)	PUNCT
ejpam-5835	518	11	(	(	PUNCT
ejpam-5835	518	12	2025	2025	NUM
ejpam-5835	518	13	)	)	PUNCT
ejpam-5835	518	14	,	,	PUNCT
ejpam-5835	518	15	5835	5835	NUM
ejpam-5835	518	16	14	14	NUM
ejpam-5835	518	17	of	of	ADP
ejpam-5835	518	18	16	16	NUM
ejpam-5835	518	19	therefore	therefore	ADV
ejpam-5835	518	20	,	,	PUNCT
ejpam-5835	518	21	(	(	PUNCT
ejpam-5835	518	22	hidwfv	hidwfv	NOUN
ejpam-5835	518	23	n	n	CCONJ
ejpam-5835	518	24	(	(	PUNCT
ejpam-5835	518	25	v	v	NOUN
ejpam-5835	518	26	)	)	PUNCT
ejpam-5835	518	27	)	)	PUNCT
ejpam-5835	519	1	n∈n	n∈n	NOUN
ejpam-5835	519	2	is	be	AUX
ejpam-5835	519	3	a	a	DET
ejpam-5835	519	4	congruence	congruence	NOUN
ejpam-5835	519	5	on	on	ADP
ejpam-5835	519	6	wwfv	wwfv	PROPN
ejpam-5835	519	7	τ	τ	PROPN
ejpam-5835	519	8	(	(	PUNCT
ejpam-5835	519	9	x	x	NOUN
ejpam-5835	519	10	)	)	PUNCT
ejpam-5835	519	11	.	.	PUNCT
ejpam-5835	520	1	a	a	DET
ejpam-5835	520	2	congruence	congruence	NOUN
ejpam-5835	520	3	(	(	PUNCT
ejpam-5835	520	4	hidwfv	hidwfv	PROPN
ejpam-5835	520	5	n	n	CCONJ
ejpam-5835	520	6	(	(	PUNCT
ejpam-5835	520	7	v	v	NOUN
ejpam-5835	520	8	)	)	PUNCT
ejpam-5835	520	9	)	)	PUNCT
ejpam-5835	520	10	n∈n	n∈n	NOUN
ejpam-5835	520	11	on	on	ADP
ejpam-5835	520	12	wwfv	wwfv	PROPN
ejpam-5835	520	13	τ	τ	PROPN
ejpam-5835	520	14	(	(	PUNCT
ejpam-5835	520	15	x	x	X
ejpam-5835	520	16	)	)	PUNCT
ejpam-5835	520	17	is	be	AUX
ejpam-5835	520	18	said	say	VERB
ejpam-5835	520	19	to	to	PART
ejpam-5835	520	20	be	be	AUX
ejpam-5835	520	21	fully	fully	ADV
ejpam-5835	520	22	invariant	invariant	ADJ
ejpam-5835	520	23	if	if	SCONJ
ejpam-5835	520	24	it	it	PRON
ejpam-5835	520	25	is	be	AUX
ejpam-5835	520	26	compatible	compatible	ADJ
ejpam-5835	520	27	with	with	ADP
ejpam-5835	520	28	all	all	DET
ejpam-5835	520	29	endomorphism	endomorphism	PROPN
ejpam-5835	520	30	σ̂	σ̂	X
ejpam-5835	520	31	on	on	ADP
ejpam-5835	520	32	wwfv	wwfv	PROPN
ejpam-5835	520	33	τ	τ	PROPN
ejpam-5835	520	34	(	(	PUNCT
ejpam-5835	520	35	x	x	NOUN
ejpam-5835	520	36	)	)	PUNCT
ejpam-5835	520	37	.	.	PUNCT
ejpam-5835	521	1	then	then	ADV
ejpam-5835	521	2	we	we	PRON
ejpam-5835	521	3	prove	prove	VERB
ejpam-5835	521	4	the	the	DET
ejpam-5835	521	5	following	follow	VERB
ejpam-5835	521	6	theorem	theorem	NOUN
ejpam-5835	521	7	which	which	PRON
ejpam-5835	521	8	gives	give	VERB
ejpam-5835	521	9	a	a	DET
ejpam-5835	521	10	necessary	necessary	ADJ
ejpam-5835	521	11	condition	condition	NOUN
ejpam-5835	521	12	for	for	SCONJ
ejpam-5835	521	13	any	any	DET
ejpam-5835	521	14	variety	variety	NOUN
ejpam-5835	521	15	v	v	NOUN
ejpam-5835	521	16	to	to	PART
ejpam-5835	521	17	be	be	AUX
ejpam-5835	521	18	weakly	weakly	ADV
ejpam-5835	521	19	fixed	fix	VERB
ejpam-5835	521	20	variable	variable	NOUN
ejpam-5835	521	21	.	.	PUNCT
ejpam-5835	522	1	theorem	theorem	VERB
ejpam-5835	522	2	7	7	NUM
ejpam-5835	522	3	.	.	PUNCT
ejpam-5835	523	1	let	let	VERB
ejpam-5835	523	2	v	v	PART
ejpam-5835	523	3	be	be	AUX
ejpam-5835	523	4	a	a	DET
ejpam-5835	523	5	variety	variety	NOUN
ejpam-5835	523	6	of	of	ADP
ejpam-5835	523	7	type	type	NOUN
ejpam-5835	523	8	τ	τ	PROPN
ejpam-5835	523	9	.	.	PUNCT
ejpam-5835	524	1	if	if	SCONJ
ejpam-5835	524	2	a	a	DET
ejpam-5835	524	3	congruence	congruence	NOUN
ejpam-5835	524	4	(	(	PUNCT
ejpam-5835	524	5	hidwfv	hidwfv	PROPN
ejpam-5835	524	6	n	n	CCONJ
ejpam-5835	524	7	(	(	PUNCT
ejpam-5835	524	8	v	v	NOUN
ejpam-5835	524	9	)	)	PUNCT
ejpam-5835	524	10	)	)	PUNCT
ejpam-5835	524	11	n∈n	n∈n	NOUN
ejpam-5835	524	12	is	be	AUX
ejpam-5835	524	13	fully	fully	ADV
ejpam-5835	524	14	invariant	invariant	ADJ
ejpam-5835	524	15	,	,	PUNCT
ejpam-5835	524	16	then	then	ADV
ejpam-5835	524	17	v	v	NOUN
ejpam-5835	524	18	is	be	AUX
ejpam-5835	524	19	a	a	DET
ejpam-5835	524	20	weakly	weakly	ADJ
ejpam-5835	524	21	fixed	fix	VERB
ejpam-5835	524	22	variable	variable	ADJ
ejpam-5835	524	23	solid	solid	ADJ
ejpam-5835	524	24	variety	variety	NOUN
ejpam-5835	524	25	.	.	PUNCT
ejpam-5835	525	1	proof	proof	NOUN
ejpam-5835	525	2	.	.	PUNCT
ejpam-5835	526	1	suppose	suppose	VERB
ejpam-5835	526	2	first	first	ADV
ejpam-5835	526	3	that	that	SCONJ
ejpam-5835	526	4	a	a	DET
ejpam-5835	526	5	congruence	congruence	NOUN
ejpam-5835	526	6	(	(	PUNCT
ejpam-5835	526	7	hidwfv	hidwfv	PROPN
ejpam-5835	526	8	n	n	CCONJ
ejpam-5835	526	9	(	(	PUNCT
ejpam-5835	526	10	v	v	NOUN
ejpam-5835	526	11	)	)	PUNCT
ejpam-5835	526	12	)	)	PUNCT
ejpam-5835	526	13	n∈n	n∈n	NOUN
ejpam-5835	526	14	is	be	AUX
ejpam-5835	526	15	fully	fully	ADV
ejpam-5835	526	16	invariant	invariant	ADJ
ejpam-5835	526	17	.	.	PUNCT
ejpam-5835	527	1	on	on	ADP
ejpam-5835	527	2	a	a	DET
ejpam-5835	527	3	variety	variety	NOUN
ejpam-5835	527	4	v	v	NOUN
ejpam-5835	527	5	of	of	ADP
ejpam-5835	527	6	type	type	NOUN
ejpam-5835	527	7	τ	τ	PROPN
ejpam-5835	527	8	,	,	PUNCT
ejpam-5835	527	9	we	we	PRON
ejpam-5835	527	10	let	let	VERB
ejpam-5835	527	11	s	s	PRON
ejpam-5835	527	12	≈	≈	PROPN
ejpam-5835	527	13	t	t	PROPN
ejpam-5835	527	14	∈	∈	PROPN
ejpam-5835	527	15	hidwfv	hidwfv	PROPN
ejpam-5835	527	16	n	n	CCONJ
ejpam-5835	527	17	(	(	PUNCT
ejpam-5835	527	18	v	v	NOUN
ejpam-5835	527	19	)	)	PUNCT
ejpam-5835	527	20	and	and	CCONJ
ejpam-5835	527	21	(	(	PUNCT
ejpam-5835	527	22	σn)n∈n	σn)n∈n	X
ejpam-5835	527	23	∈	∈	PROPN
ejpam-5835	527	24	(	(	PUNCT
ejpam-5835	527	25	hypwfv	hypwfv	NOUN
ejpam-5835	527	26	n	n	CCONJ
ejpam-5835	527	27	(	(	PUNCT
ejpam-5835	527	28	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	527	29	.	.	PUNCT
ejpam-5835	528	1	applying	apply	VERB
ejpam-5835	528	2	theorem	theorem	NOUN
ejpam-5835	528	3	2	2	NUM
ejpam-5835	528	4	,	,	PUNCT
ejpam-5835	528	5	we	we	PRON
ejpam-5835	528	6	have	have	VERB
ejpam-5835	528	7	σ̂n[s	σ̂n[	NOUN
ejpam-5835	528	8	]	]	PUNCT
ejpam-5835	529	1	≈	≈	PROPN
ejpam-5835	529	2	σ̂n[t	σ̂n[t	PROPN
ejpam-5835	529	3	]	]	X
ejpam-5835	529	4	∈	∈	PROPN
ejpam-5835	530	1	idn(v	idn(v	PROPN
ejpam-5835	530	2	)	)	PUNCT
ejpam-5835	530	3	for	for	ADP
ejpam-5835	530	4	all	all	PRON
ejpam-5835	530	5	n	n	DET
ejpam-5835	530	6	∈	∈	PROPN
ejpam-5835	530	7	n.	n.	NOUN
ejpam-5835	530	8	hence	hence	ADV
ejpam-5835	530	9	,	,	PUNCT
ejpam-5835	530	10	s	s	PROPN
ejpam-5835	530	11	≈	≈	PROPN
ejpam-5835	530	12	t	t	PROPN
ejpam-5835	530	13	is	be	AUX
ejpam-5835	530	14	a	a	DET
ejpam-5835	530	15	weakly	weakly	ADJ
ejpam-5835	530	16	fixed	fix	VERB
ejpam-5835	530	17	variable	variable	ADJ
ejpam-5835	530	18	hyperidentity	hyperidentity	NOUN
ejpam-5835	530	19	in	in	ADP
ejpam-5835	530	20	v	v	NUM
ejpam-5835	530	21	,	,	PUNCT
ejpam-5835	530	22	whence	whence	NOUN
ejpam-5835	530	23	,	,	PUNCT
ejpam-5835	530	24	a	a	DET
ejpam-5835	530	25	variety	variety	NOUN
ejpam-5835	530	26	v	v	NOUN
ejpam-5835	530	27	is	be	AUX
ejpam-5835	530	28	weakly	weakly	ADV
ejpam-5835	530	29	fixed	fix	VERB
ejpam-5835	530	30	variable	variable	NOUN
ejpam-5835	530	31	.	.	PUNCT
ejpam-5835	531	1	we	we	PRON
ejpam-5835	531	2	close	close	VERB
ejpam-5835	531	3	this	this	DET
ejpam-5835	531	4	section	section	NOUN
ejpam-5835	531	5	with	with	ADP
ejpam-5835	531	6	the	the	DET
ejpam-5835	531	7	following	follow	VERB
ejpam-5835	531	8	theorem	theorem	NOUN
ejpam-5835	531	9	which	which	PRON
ejpam-5835	531	10	gives	give	VERB
ejpam-5835	531	11	connection	connection	NOUN
ejpam-5835	531	12	between	between	ADP
ejpam-5835	531	13	weakly	weakly	ADJ
ejpam-5835	531	14	fixed	fix	VERB
ejpam-5835	531	15	variable	variable	ADJ
ejpam-5835	531	16	identities	identity	NOUN
ejpam-5835	531	17	and	and	CCONJ
ejpam-5835	531	18	weakly	weakly	ADJ
ejpam-5835	531	19	fixed	fix	VERB
ejpam-5835	531	20	variable	variable	ADJ
ejpam-5835	531	21	hyperidentities	hyperidentitie	NOUN
ejpam-5835	531	22	in	in	ADP
ejpam-5835	531	23	a	a	DET
ejpam-5835	531	24	variety	variety	NOUN
ejpam-5835	531	25	v	v	NOUN
ejpam-5835	531	26	of	of	ADP
ejpam-5835	531	27	algebras	algebra	NOUN
ejpam-5835	531	28	of	of	ADP
ejpam-5835	531	29	type	type	NOUN
ejpam-5835	531	30	τ	τ	PROPN
ejpam-5835	531	31	.	.	PUNCT
ejpam-5835	532	1	theorem	theorem	VERB
ejpam-5835	532	2	8	8	NUM
ejpam-5835	532	3	.	.	PUNCT
ejpam-5835	533	1	every	every	DET
ejpam-5835	533	2	weakly	weakly	ADJ
ejpam-5835	533	3	fixed	fix	VERB
ejpam-5835	533	4	variable	variable	ADJ
ejpam-5835	533	5	identity	identity	NOUN
ejpam-5835	533	6	in	in	ADP
ejpam-5835	533	7	a	a	DET
ejpam-5835	533	8	variety	variety	NOUN
ejpam-5835	533	9	v	v	NOUN
ejpam-5835	533	10	is	be	AUX
ejpam-5835	533	11	a	a	DET
ejpam-5835	533	12	weakly	weakly	ADJ
ejpam-5835	533	13	fixed	fix	VERB
ejpam-5835	533	14	variable	variable	ADJ
ejpam-5835	533	15	hyperidentity	hyperidentity	NOUN
ejpam-5835	533	16	in	in	ADP
ejpam-5835	533	17	v	v	NOUN
ejpam-5835	533	18	.	.	PUNCT
ejpam-5835	534	1	proof	proof	NOUN
ejpam-5835	534	2	.	.	PUNCT
ejpam-5835	535	1	suppose	suppose	VERB
ejpam-5835	535	2	first	first	ADV
ejpam-5835	535	3	that	that	PRON
ejpam-5835	535	4	s	s	VERB
ejpam-5835	535	5	≈	≈	PROPN
ejpam-5835	535	6	t	t	PROPN
ejpam-5835	535	7	∈	∈	PROPN
ejpam-5835	535	8	idwfv(v	idwfv(v	NOUN
ejpam-5835	535	9	)	)	PUNCT
ejpam-5835	535	10	is	be	AUX
ejpam-5835	535	11	an	an	DET
ejpam-5835	535	12	identity	identity	NOUN
ejpam-5835	535	13	in	in	ADP
ejpam-5835	535	14	the	the	DET
ejpam-5835	535	15	multisorted	multisorte	VERB
ejpam-5835	535	16	quotient	quotient	NOUN
ejpam-5835	536	1	algebra	algebra	VERB
ejpam-5835	536	2	qwfv	qwfv	PROPN
ejpam-5835	536	3	τ	τ	PROPN
ejpam-5835	536	4	(	(	PUNCT
ejpam-5835	536	5	v	v	NOUN
ejpam-5835	536	6	)	)	PUNCT
ejpam-5835	536	7	.	.	PUNCT
ejpam-5835	537	1	let	let	VERB
ejpam-5835	537	2	σ	σ	NUM
ejpam-5835	537	3	∈	∈	PROPN
ejpam-5835	537	4	hypwfv(τ	hypwfv(τ	NOUN
ejpam-5835	537	5	)	)	PUNCT
ejpam-5835	537	6	.	.	PUNCT
ejpam-5835	538	1	by	by	ADP
ejpam-5835	538	2	theorem	theorem	NOUN
ejpam-5835	538	3	2	2	NUM
ejpam-5835	538	4	and	and	CCONJ
ejpam-5835	538	5	the	the	DET
ejpam-5835	538	6	property	property	NOUN
ejpam-5835	538	7	of	of	ADP
ejpam-5835	538	8	a	a	DET
ejpam-5835	538	9	natural	natural	ADJ
ejpam-5835	538	10	homomorphism	homomorphism	NOUN
ejpam-5835	538	11	,	,	PUNCT
ejpam-5835	538	12	thus	thus	ADV
ejpam-5835	538	13	the	the	DET
ejpam-5835	538	14	composition	composition	NOUN
ejpam-5835	538	15	mapping	mapping	NOUN
ejpam-5835	538	16	natn	natn	ADJ
ejpam-5835	538	17	,	,	PUNCT
ejpam-5835	538	18	idwfv(v	idwfv(v	ADJ
ejpam-5835	538	19	)	)	PUNCT
ejpam-5835	538	20	◦	◦	NOUN
ejpam-5835	538	21	σ̂n	σ̂n	NOUN
ejpam-5835	538	22	:	:	PUNCT
ejpam-5835	538	23	wwfv	wwfv	PROPN
ejpam-5835	538	24	τ	τ	PROPN
ejpam-5835	538	25	(	(	PUNCT
ejpam-5835	538	26	x	x	NOUN
ejpam-5835	538	27	)	)	PUNCT
ejpam-5835	538	28	→	→	SYM
ejpam-5835	538	29	qwfv	qwfv	PROPN
ejpam-5835	538	30	τ	τ	X
ejpam-5835	538	31	(	(	PUNCT
ejpam-5835	538	32	v	v	NOUN
ejpam-5835	538	33	)	)	PUNCT
ejpam-5835	538	34	is	be	AUX
ejpam-5835	538	35	a	a	DET
ejpam-5835	538	36	homomorphism	homomorphism	NOUN
ejpam-5835	538	37	.	.	PUNCT
ejpam-5835	539	1	by	by	ADP
ejpam-5835	539	2	the	the	DET
ejpam-5835	539	3	hypothesis	hypothesis	NOUN
ejpam-5835	539	4	,	,	PUNCT
ejpam-5835	539	5	we	we	PRON
ejpam-5835	539	6	obtain	obtain	VERB
ejpam-5835	539	7	natn	natn	ADJ
ejpam-5835	539	8	,	,	PUNCT
ejpam-5835	539	9	idvf	idvf	ADJ
ejpam-5835	539	10	(	(	PUNCT
ejpam-5835	539	11	v	v	NOUN
ejpam-5835	539	12	)	)	PUNCT
ejpam-5835	539	13	◦	◦	NOUN
ejpam-5835	539	14	σ̂n(s	σ̂n(s	NUM
ejpam-5835	539	15	)	)	PUNCT
ejpam-5835	539	16	=	=	SYM
ejpam-5835	539	17	natn	natn	ADJ
ejpam-5835	539	18	,	,	PUNCT
ejpam-5835	539	19	idvf	idvf	NOUN
ejpam-5835	539	20	(	(	PUNCT
ejpam-5835	539	21	v	v	NOUN
ejpam-5835	539	22	)	)	PUNCT
ejpam-5835	539	23	◦	◦	NOUN
ejpam-5835	539	24	σ̂n(t	σ̂n(t	NUM
ejpam-5835	539	25	)	)	PUNCT
ejpam-5835	539	26	.	.	PUNCT
ejpam-5835	540	1	that	that	PRON
ejpam-5835	540	2	is	be	AUX
ejpam-5835	540	3	,	,	PUNCT
ejpam-5835	540	4	natn	natn	ADJ
ejpam-5835	540	5	,	,	PUNCT
ejpam-5835	540	6	idwfv(v	idwfv(v	ADJ
ejpam-5835	540	7	)	)	PUNCT
ejpam-5835	540	8	(	(	PUNCT
ejpam-5835	540	9	σ̂n[s	σ̂n[	NOUN
ejpam-5835	540	10	]	]	PUNCT
ejpam-5835	540	11	)	)	PUNCT
ejpam-5835	541	1	=	=	SYM
ejpam-5835	541	2	natn	natn	ADJ
ejpam-5835	541	3	,	,	PUNCT
ejpam-5835	541	4	idwfv(v	idwfv(v	ADJ
ejpam-5835	541	5	)	)	PUNCT
ejpam-5835	541	6	(	(	PUNCT
ejpam-5835	541	7	σ̂n[t	σ̂n[t	PROPN
ejpam-5835	541	8	]	]	PUNCT
ejpam-5835	541	9	)	)	PUNCT
ejpam-5835	541	10	.	.	PUNCT
ejpam-5835	542	1	again	again	ADV
ejpam-5835	542	2	by	by	ADP
ejpam-5835	542	3	a	a	DET
ejpam-5835	542	4	natural	natural	ADJ
ejpam-5835	542	5	homomorphism	homomorphism	NOUN
ejpam-5835	542	6	natn	natn	ADJ
ejpam-5835	542	7	,	,	PUNCT
ejpam-5835	542	8	idwfv(v	idwfv(v	ADJ
ejpam-5835	542	9	)	)	PUNCT
ejpam-5835	542	10	,	,	PUNCT
ejpam-5835	542	11	we	we	PRON
ejpam-5835	542	12	also	also	ADV
ejpam-5835	542	13	get	get	VERB
ejpam-5835	542	14	[	[	X
ejpam-5835	542	15	σ̂n[s]]idwfv(v	σ̂n[s]]idwfv(v	NOUN
ejpam-5835	542	16	)	)	PUNCT
ejpam-5835	542	17	=	=	PUNCT
ejpam-5835	543	1	[	[	X
ejpam-5835	543	2	σ̂n[t]]idwfv(v	σ̂n[t]]idwfv(v	NOUN
ejpam-5835	543	3	)	)	PUNCT
ejpam-5835	543	4	,	,	PUNCT
ejpam-5835	543	5	which	which	PRON
ejpam-5835	543	6	means	mean	VERB
ejpam-5835	543	7	that	that	SCONJ
ejpam-5835	543	8	σ̂n[s	σ̂n[	NOUN
ejpam-5835	543	9	]	]	PUNCT
ejpam-5835	543	10	≈	≈	PROPN
ejpam-5835	543	11	σ̂n[t	σ̂n[t	PROPN
ejpam-5835	543	12	]	]	X
ejpam-5835	543	13	∈	∈	PROPN
ejpam-5835	543	14	idwfv(v	idwfv(v	PROPN
ejpam-5835	543	15	)	)	PUNCT
ejpam-5835	543	16	.	.	PUNCT
ejpam-5835	544	1	thus	thus	ADV
ejpam-5835	544	2	,	,	PUNCT
ejpam-5835	544	3	s	s	PROPN
ejpam-5835	544	4	≈	≈	PROPN
ejpam-5835	544	5	t	t	PROPN
ejpam-5835	544	6	is	be	AUX
ejpam-5835	544	7	a	a	DET
ejpam-5835	544	8	weakly	weakly	ADJ
ejpam-5835	544	9	fixed	fix	VERB
ejpam-5835	544	10	variable	variable	ADJ
ejpam-5835	544	11	hyperidentity	hyperidentity	NOUN
ejpam-5835	544	12	in	in	ADP
ejpam-5835	544	13	v	v	NOUN
ejpam-5835	544	14	.	.	PUNCT
ejpam-5835	545	1	t.	t.	PROPN
ejpam-5835	545	2	kumduang	kumduang	PROPN
ejpam-5835	545	3	,	,	PUNCT
ejpam-5835	545	4	k.	k.	PROPN
ejpam-5835	545	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	545	6	/	/	SYM
ejpam-5835	545	7	eur	eur	PROPN
ejpam-5835	545	8	.	.	PUNCT
ejpam-5835	546	1	j.	j.	PROPN
ejpam-5835	546	2	pure	pure	PROPN
ejpam-5835	546	3	appl	appl	PROPN
ejpam-5835	546	4	.	.	PROPN
ejpam-5835	546	5	math	math	PROPN
ejpam-5835	546	6	,	,	PUNCT
ejpam-5835	546	7	18	18	NUM
ejpam-5835	546	8	(	(	PUNCT
ejpam-5835	546	9	2	2	NUM
ejpam-5835	546	10	)	)	PUNCT
ejpam-5835	546	11	(	(	PUNCT
ejpam-5835	546	12	2025	2025	NUM
ejpam-5835	546	13	)	)	PUNCT
ejpam-5835	546	14	,	,	PUNCT
ejpam-5835	546	15	5835	5835	NUM
ejpam-5835	546	16	15	15	NUM
ejpam-5835	546	17	of	of	ADP
ejpam-5835	546	18	16	16	NUM
ejpam-5835	546	19	5	5	NUM
ejpam-5835	546	20	.	.	PUNCT
ejpam-5835	546	21	concluding	conclude	VERB
ejpam-5835	546	22	remarks	remark	NOUN
ejpam-5835	546	23	as	as	ADP
ejpam-5835	546	24	a	a	DET
ejpam-5835	546	25	generalization	generalization	NOUN
ejpam-5835	546	26	of	of	ADP
ejpam-5835	546	27	terms	term	NOUN
ejpam-5835	546	28	of	of	ADP
ejpam-5835	546	29	fixed	fix	VERB
ejpam-5835	546	30	variable	variable	NOUN
ejpam-5835	546	31	introduced	introduce	VERB
ejpam-5835	546	32	in	in	ADP
ejpam-5835	546	33	[	[	X
ejpam-5835	546	34	17	17	NUM
ejpam-5835	546	35	]	]	PUNCT
ejpam-5835	546	36	,	,	PUNCT
ejpam-5835	546	37	this	this	DET
ejpam-5835	546	38	work	work	NOUN
ejpam-5835	546	39	presents	present	VERB
ejpam-5835	546	40	an	an	DET
ejpam-5835	546	41	extension	extension	NOUN
ejpam-5835	546	42	called	call	VERB
ejpam-5835	546	43	terms	term	NOUN
ejpam-5835	546	44	of	of	ADP
ejpam-5835	546	45	a	a	DET
ejpam-5835	546	46	weakly	weakly	ADJ
ejpam-5835	546	47	fixed	fix	VERB
ejpam-5835	546	48	variable	variable	NOUN
ejpam-5835	546	49	by	by	ADP
ejpam-5835	546	50	relaxing	relax	VERB
ejpam-5835	546	51	the	the	DET
ejpam-5835	546	52	conditions	condition	NOUN
ejpam-5835	546	53	on	on	ADP
ejpam-5835	546	54	inductive	inductive	ADJ
ejpam-5835	546	55	construction	construction	NOUN
ejpam-5835	546	56	of	of	ADP
ejpam-5835	546	57	any	any	DET
ejpam-5835	546	58	term	term	NOUN
ejpam-5835	546	59	t	t	NOUN
ejpam-5835	546	60	from	from	ADP
ejpam-5835	546	61	an	an	DET
ejpam-5835	546	62	alphabet	alphabet	NOUN
ejpam-5835	546	63	xn	xn	PROPN
ejpam-5835	546	64	.	.	PUNCT
ejpam-5835	547	1	several	several	ADJ
ejpam-5835	547	2	multibased	multibase	VERB
ejpam-5835	547	3	structures	structure	NOUN
ejpam-5835	547	4	for	for	ADP
ejpam-5835	547	5	such	such	ADJ
ejpam-5835	547	6	terms	term	NOUN
ejpam-5835	547	7	are	be	AUX
ejpam-5835	547	8	developed	develop	VERB
ejpam-5835	547	9	,	,	PUNCT
ejpam-5835	547	10	including	include	VERB
ejpam-5835	547	11	the	the	DET
ejpam-5835	547	12	superassociative	superassociative	ADJ
ejpam-5835	547	13	system	system	NOUN
ejpam-5835	547	14	with	with	ADP
ejpam-5835	547	15	respect	respect	NOUN
ejpam-5835	547	16	to	to	ADP
ejpam-5835	547	17	the	the	DET
ejpam-5835	547	18	multisorted	multisorte	VERB
ejpam-5835	547	19	superposition	superposition	NOUN
ejpam-5835	547	20	operation	operation	NOUN
ejpam-5835	547	21	,	,	PUNCT
ejpam-5835	547	22	the	the	DET
ejpam-5835	547	23	seminearring	seminearring	NOUN
ejpam-5835	547	24	of	of	ADP
ejpam-5835	547	25	mappings	mapping	NOUN
ejpam-5835	547	26	which	which	DET
ejpam-5835	547	27	images	image	NOUN
ejpam-5835	547	28	are	be	AUX
ejpam-5835	547	29	terms	term	NOUN
ejpam-5835	547	30	of	of	ADP
ejpam-5835	547	31	a	a	DET
ejpam-5835	547	32	weakly	weakly	ADJ
ejpam-5835	547	33	fixed	fix	VERB
ejpam-5835	547	34	variable	variable	NOUN
ejpam-5835	547	35	,	,	PUNCT
ejpam-5835	547	36	the	the	DET
ejpam-5835	547	37	quotient	quotient	NOUN
ejpam-5835	547	38	multisorted	multisorte	VERB
ejpam-5835	547	39	set	set	NOUN
ejpam-5835	547	40	obtained	obtain	VERB
ejpam-5835	547	41	by	by	ADP
ejpam-5835	547	42	dividing	divide	VERB
ejpam-5835	547	43	the	the	DET
ejpam-5835	547	44	set	set	NOUN
ejpam-5835	547	45	of	of	ADP
ejpam-5835	547	46	all	all	DET
ejpam-5835	547	47	identities	identity	NOUN
ejpam-5835	547	48	induced	induce	VERB
ejpam-5835	547	49	by	by	ADP
ejpam-5835	547	50	terms	term	NOUN
ejpam-5835	547	51	of	of	ADP
ejpam-5835	547	52	a	a	DET
ejpam-5835	547	53	weakly	weakly	ADJ
ejpam-5835	547	54	fixed	fix	VERB
ejpam-5835	547	55	variable	variable	NOUN
ejpam-5835	547	56	,	,	PUNCT
ejpam-5835	547	57	which	which	PRON
ejpam-5835	547	58	acts	act	VERB
ejpam-5835	547	59	as	as	ADP
ejpam-5835	547	60	a	a	DET
ejpam-5835	547	61	congruence	congruence	NOUN
ejpam-5835	547	62	.	.	PUNCT
ejpam-5835	548	1	furthermore	furthermore	ADV
ejpam-5835	548	2	,	,	PUNCT
ejpam-5835	548	3	applications	application	NOUN
ejpam-5835	548	4	of	of	ADP
ejpam-5835	548	5	terms	term	NOUN
ejpam-5835	548	6	of	of	ADP
ejpam-5835	548	7	a	a	DET
ejpam-5835	548	8	weakly	weakly	ADJ
ejpam-5835	548	9	fixed	fix	VERB
ejpam-5835	548	10	variable	variable	NOUN
ejpam-5835	548	11	for	for	ADP
ejpam-5835	548	12	classifying	classify	VERB
ejpam-5835	548	13	a	a	DET
ejpam-5835	548	14	variety	variety	NOUN
ejpam-5835	548	15	v	v	NOUN
ejpam-5835	548	16	of	of	ADP
ejpam-5835	548	17	algebras	algebra	NOUN
ejpam-5835	548	18	of	of	ADP
ejpam-5835	548	19	type	type	NOUN
ejpam-5835	548	20	τ	τ	PROPN
ejpam-5835	548	21	are	be	AUX
ejpam-5835	548	22	discussed	discuss	VERB
ejpam-5835	548	23	.	.	PUNCT
ejpam-5835	549	1	another	another	DET
ejpam-5835	549	2	direction	direction	NOUN
ejpam-5835	549	3	of	of	ADP
ejpam-5835	549	4	the	the	DET
ejpam-5835	549	5	future	future	ADJ
ejpam-5835	549	6	research	research	NOUN
ejpam-5835	549	7	in	in	ADP
ejpam-5835	549	8	this	this	DET
ejpam-5835	549	9	domain	domain	NOUN
ejpam-5835	549	10	should	should	AUX
ejpam-5835	549	11	be	be	AUX
ejpam-5835	549	12	devoted	devote	VERB
ejpam-5835	549	13	to	to	PART
ejpam-5835	549	14	characterize	characterize	VERB
ejpam-5835	549	15	the	the	DET
ejpam-5835	549	16	set	set	NOUN
ejpam-5835	549	17	of	of	ADP
ejpam-5835	549	18	idempotent	idempotent	NOUN
ejpam-5835	549	19	and	and	CCONJ
ejpam-5835	549	20	regular	regular	ADJ
ejpam-5835	549	21	elements	element	NOUN
ejpam-5835	549	22	on	on	ADP
ejpam-5835	549	23	the	the	DET
ejpam-5835	549	24	semigroup	semigroup	NOUN
ejpam-5835	549	25	(	(	PUNCT
ejpam-5835	549	26	hypwfv	hypwfv	NOUN
ejpam-5835	549	27	n	n	CCONJ
ejpam-5835	549	28	(	(	PUNCT
ejpam-5835	549	29	τ))n∈n	τ))n∈n	PROPN
ejpam-5835	549	30	.	.	PUNCT
ejpam-5835	550	1	acknowledgements	acknowledgement	NOUN
ejpam-5835	550	2	support	support	NOUN
ejpam-5835	550	3	of	of	ADP
ejpam-5835	550	4	the	the	DET
ejpam-5835	550	5	research	research	NOUN
ejpam-5835	550	6	of	of	ADP
ejpam-5835	550	7	the	the	DET
ejpam-5835	550	8	first	first	ADJ
ejpam-5835	550	9	author	author	NOUN
ejpam-5835	550	10	by	by	ADP
ejpam-5835	550	11	national	national	PROPN
ejpam-5835	550	12	research	research	PROPN
ejpam-5835	550	13	council	council	PROPN
ejpam-5835	550	14	of	of	ADP
ejpam-5835	550	15	thailand	thailand	PROPN
ejpam-5835	550	16	,	,	PUNCT
ejpam-5835	550	17	project	project	NOUN
ejpam-5835	550	18	n42a670114	n42a670114	NOUN
ejpam-5835	550	19	,	,	PUNCT
ejpam-5835	550	20	is	be	AUX
ejpam-5835	550	21	gratefully	gratefully	ADV
ejpam-5835	550	22	acknowledged	acknowledge	VERB
ejpam-5835	550	23	.	.	PUNCT
ejpam-5835	551	1	the	the	DET
ejpam-5835	551	2	second	second	ADJ
ejpam-5835	551	3	author	author	NOUN
ejpam-5835	551	4	was	be	AUX
ejpam-5835	551	5	supported	support	VERB
ejpam-5835	551	6	by	by	ADP
ejpam-5835	551	7	rajamangala	rajamangala	PROPN
ejpam-5835	551	8	university	university	PROPN
ejpam-5835	551	9	of	of	ADP
ejpam-5835	551	10	technology	technology	PROPN
ejpam-5835	551	11	lanna	lanna	PROPN
ejpam-5835	551	12	,	,	PUNCT
ejpam-5835	551	13	thailand	thailand	PROPN
ejpam-5835	551	14	.	.	PUNCT
ejpam-5835	552	1	this	this	DET
ejpam-5835	552	2	research	research	NOUN
ejpam-5835	552	3	was	be	AUX
ejpam-5835	552	4	supported	support	VERB
ejpam-5835	552	5	in	in	ADP
ejpam-5835	552	6	whole	whole	ADJ
ejpam-5835	552	7	or	or	CCONJ
ejpam-5835	552	8	in	in	ADP
ejpam-5835	552	9	part	part	NOUN
ejpam-5835	552	10	by	by	ADP
ejpam-5835	552	11	rajamangala	rajamangala	PROPN
ejpam-5835	552	12	university	university	PROPN
ejpam-5835	552	13	of	of	ADP
ejpam-5835	552	14	technology	technology	NOUN
ejpam-5835	552	15	rattanakosin	rattanakosin	NOUN
ejpam-5835	552	16	,	,	PUNCT
ejpam-5835	552	17	thailand	thailand	PROPN
ejpam-5835	552	18	.	.	PUNCT
ejpam-5835	553	1	references	reference	NOUN
ejpam-5835	553	2	[	[	X
ejpam-5835	553	3	1	1	NUM
ejpam-5835	553	4	]	]	PUNCT
ejpam-5835	553	5	l.	l.	PROPN
ejpam-5835	553	6	barto	barto	PROPN
ejpam-5835	553	7	and	and	CCONJ
ejpam-5835	553	8	m.	m.	PROPN
ejpam-5835	553	9	kapytka	kapytka	PROPN
ejpam-5835	553	10	.	.	PUNCT
ejpam-5835	554	1	multisorted	multisorte	VERB
ejpam-5835	554	2	boolean	boolean	ADJ
ejpam-5835	554	3	clones	clone	NOUN
ejpam-5835	554	4	determined	determine	VERB
ejpam-5835	554	5	by	by	ADP
ejpam-5835	554	6	binary	binary	ADJ
ejpam-5835	554	7	relations	relation	NOUN
ejpam-5835	554	8	up	up	ADP
ejpam-5835	554	9	to	to	ADP
ejpam-5835	554	10	minion	minion	NOUN
ejpam-5835	554	11	homomorphisms	homomorphism	NOUN
ejpam-5835	554	12	.	.	PUNCT
ejpam-5835	555	1	algebra	algebra	PROPN
ejpam-5835	555	2	universalis	universali	VERB
ejpam-5835	555	3	,	,	PUNCT
ejpam-5835	555	4	86:1	86:1	NOUN
ejpam-5835	555	5	,	,	PUNCT
ejpam-5835	555	6	2025	2025	NUM
ejpam-5835	555	7	.	.	PUNCT
ejpam-5835	556	1	[	[	X
ejpam-5835	556	2	2	2	NUM
ejpam-5835	556	3	]	]	PUNCT
ejpam-5835	556	4	a.	a.	NOUN
ejpam-5835	556	5	bucciarelli	bucciarelli	PROPN
ejpam-5835	556	6	and	and	CCONJ
ejpam-5835	556	7	a.	a.	NOUN
ejpam-5835	556	8	salibra	salibra	PROPN
ejpam-5835	556	9	.	.	PUNCT
ejpam-5835	557	1	an	an	DET
ejpam-5835	557	2	algebraic	algebraic	ADJ
ejpam-5835	557	3	theory	theory	NOUN
ejpam-5835	557	4	of	of	ADP
ejpam-5835	557	5	clones	clone	NOUN
ejpam-5835	557	6	.	.	PUNCT
ejpam-5835	558	1	algebra	algebra	NOUN
ejpam-5835	558	2	universalis	universali	VERB
ejpam-5835	558	3	,	,	PUNCT
ejpam-5835	558	4	83:14	83:14	NUM
ejpam-5835	558	5	,	,	PUNCT
ejpam-5835	558	6	2022	2022	NUM
ejpam-5835	558	7	.	.	PUNCT
ejpam-5835	559	1	[	[	X
ejpam-5835	559	2	3	3	X
ejpam-5835	559	3	]	]	PUNCT
ejpam-5835	559	4	k.	k.	PROPN
ejpam-5835	559	5	denecke	denecke	PROPN
ejpam-5835	559	6	.	.	PUNCT
ejpam-5835	559	7	partial	partial	ADJ
ejpam-5835	559	8	clones	clone	NOUN
ejpam-5835	559	9	.	.	PUNCT
ejpam-5835	560	1	asian	asian	ADJ
ejpam-5835	560	2	-	-	PUNCT
ejpam-5835	560	3	european	european	ADJ
ejpam-5835	560	4	journal	journal	NOUN
ejpam-5835	560	5	of	of	ADP
ejpam-5835	560	6	mathematics	mathematic	NOUN
ejpam-5835	560	7	,	,	PUNCT
ejpam-5835	560	8	13(8):2050161	13(8):2050161	NUM
ejpam-5835	560	9	,	,	PUNCT
ejpam-5835	560	10	2020	2020	NUM
ejpam-5835	560	11	.	.	PUNCT
ejpam-5835	561	1	[	[	X
ejpam-5835	561	2	4	4	X
ejpam-5835	561	3	]	]	PUNCT
ejpam-5835	561	4	k.	k.	PROPN
ejpam-5835	561	5	denecke	denecke	PROPN
ejpam-5835	561	6	.	.	PUNCT
ejpam-5835	561	7	partial	partial	ADJ
ejpam-5835	561	8	clones	clone	NOUN
ejpam-5835	561	9	of	of	ADP
ejpam-5835	561	10	terms	term	NOUN
ejpam-5835	561	11	:	:	PUNCT
ejpam-5835	561	12	an	an	DET
ejpam-5835	561	13	algebraic	algebraic	ADJ
ejpam-5835	561	14	approach	approach	NOUN
ejpam-5835	561	15	to	to	ADP
ejpam-5835	561	16	trees	tree	NOUN
ejpam-5835	561	17	,	,	PUNCT
ejpam-5835	561	18	formulas	formula	NOUN
ejpam-5835	561	19	and	and	CCONJ
ejpam-5835	561	20	languages	language	NOUN
ejpam-5835	561	21	.	.	PUNCT
ejpam-5835	562	1	eliva	eliva	PROPN
ejpam-5835	562	2	press	press	PROPN
ejpam-5835	562	3	,	,	PUNCT
ejpam-5835	562	4	chis	chis	PROPN
ejpam-5835	562	5	,	,	PUNCT
ejpam-5835	562	6	inău	inău	PROPN
ejpam-5835	562	7	,	,	PUNCT
ejpam-5835	562	8	2024	2024	NUM
ejpam-5835	562	9	.	.	PUNCT
ejpam-5835	563	1	[	[	X
ejpam-5835	563	2	5	5	X
ejpam-5835	563	3	]	]	PUNCT
ejpam-5835	563	4	w.	w.	PROPN
ejpam-5835	563	5	a.	a.	PROPN
ejpam-5835	563	6	dudek	dudek	PROPN
ejpam-5835	563	7	and	and	CCONJ
ejpam-5835	563	8	v.	v.	PROPN
ejpam-5835	563	9	s.	s.	PROPN
ejpam-5835	563	10	trokhimenko	trokhimenko	PROPN
ejpam-5835	563	11	.	.	PUNCT
ejpam-5835	564	1	algebras	algebras	PROPN
ejpam-5835	564	2	of	of	ADP
ejpam-5835	564	3	multiplace	multiplace	NOUN
ejpam-5835	564	4	functions	function	NOUN
ejpam-5835	564	5	.	.	PUNCT
ejpam-5835	565	1	de	de	ADP
ejpam-5835	565	2	gruyter	gruyter	NOUN
ejpam-5835	565	3	,	,	PUNCT
ejpam-5835	565	4	berlin	berlin	PROPN
ejpam-5835	565	5	,	,	PUNCT
ejpam-5835	565	6	2012	2012	NUM
ejpam-5835	565	7	.	.	PUNCT
ejpam-5835	566	1	[	[	X
ejpam-5835	566	2	6	6	NUM
ejpam-5835	566	3	]	]	PUNCT
ejpam-5835	566	4	w.	w.	PROPN
ejpam-5835	566	5	a.	a.	PROPN
ejpam-5835	566	6	dudek	dudek	PROPN
ejpam-5835	566	7	and	and	CCONJ
ejpam-5835	566	8	v.	v.	PROPN
ejpam-5835	566	9	s.	s.	PROPN
ejpam-5835	566	10	trokhimenko	trokhimenko	PROPN
ejpam-5835	566	11	.	.	PUNCT
ejpam-5835	567	1	menger	menger	PROPN
ejpam-5835	567	2	algebras	algebras	PROPN
ejpam-5835	567	3	of	of	ADP
ejpam-5835	567	4	associative	associative	ADJ
ejpam-5835	567	5	and	and	CCONJ
ejpam-5835	567	6	selfdistributive	selfdistributive	ADJ
ejpam-5835	567	7	n	n	CCONJ
ejpam-5835	567	8	-	-	PUNCT
ejpam-5835	567	9	ary	ary	NOUN
ejpam-5835	567	10	operations	operation	NOUN
ejpam-5835	567	11	.	.	PUNCT
ejpam-5835	568	1	quasigroups	quasigroup	NOUN
ejpam-5835	568	2	and	and	CCONJ
ejpam-5835	568	3	related	related	ADJ
ejpam-5835	568	4	systems	system	NOUN
ejpam-5835	568	5	,	,	PUNCT
ejpam-5835	568	6	26:45–52	26:45–52	NUM
ejpam-5835	568	7	,	,	PUNCT
ejpam-5835	568	8	2018	2018	NUM
ejpam-5835	568	9	.	.	PUNCT
ejpam-5835	569	1	[	[	X
ejpam-5835	569	2	7	7	X
ejpam-5835	569	3	]	]	X
ejpam-5835	569	4	y.	y.	PROPN
ejpam-5835	569	5	guellouma	guellouma	PROPN
ejpam-5835	569	6	and	and	CCONJ
ejpam-5835	569	7	h.	h.	PROPN
ejpam-5835	569	8	cherroun	cherroun	PROPN
ejpam-5835	569	9	.	.	PUNCT
ejpam-5835	570	1	from	from	ADP
ejpam-5835	570	2	tree	tree	NOUN
ejpam-5835	570	3	automata	automata	NOUN
ejpam-5835	570	4	to	to	ADP
ejpam-5835	570	5	rational	rational	ADJ
ejpam-5835	570	6	tree	tree	NOUN
ejpam-5835	570	7	expressions	expression	NOUN
ejpam-5835	570	8	.	.	PUNCT
ejpam-5835	571	1	international	international	ADJ
ejpam-5835	571	2	journal	journal	NOUN
ejpam-5835	571	3	of	of	ADP
ejpam-5835	571	4	foundations	foundation	NOUN
ejpam-5835	571	5	of	of	ADP
ejpam-5835	571	6	computer	computer	NOUN
ejpam-5835	571	7	science	science	NOUN
ejpam-5835	571	8	,	,	PUNCT
ejpam-5835	571	9	29(6):1045–1062	29(6):1045–1062	NUM
ejpam-5835	571	10	,	,	PUNCT
ejpam-5835	571	11	2018	2018	NUM
ejpam-5835	571	12	.	.	PUNCT
ejpam-5835	572	1	[	[	X
ejpam-5835	572	2	8	8	NUM
ejpam-5835	572	3	]	]	X
ejpam-5835	572	4	p.	p.	NOUN
ejpam-5835	572	5	junlouchai	junlouchai	PROPN
ejpam-5835	572	6	,	,	PUNCT
ejpam-5835	572	7	t.	t.	PROPN
ejpam-5835	572	8	kumduang	kumduang	PROPN
ejpam-5835	572	9	,	,	PUNCT
ejpam-5835	572	10	and	and	CCONJ
ejpam-5835	572	11	c.	c.	PROPN
ejpam-5835	572	12	siwapornanan	siwapornanan	PROPN
ejpam-5835	572	13	.	.	PUNCT
ejpam-5835	573	1	the	the	DET
ejpam-5835	573	2	structures	structure	NOUN
ejpam-5835	573	3	of	of	ADP
ejpam-5835	573	4	full	full	ADJ
ejpam-5835	573	5	terms	term	NOUN
ejpam-5835	573	6	preserving	preserve	VERB
ejpam-5835	573	7	a	a	DET
ejpam-5835	573	8	partition	partition	NOUN
ejpam-5835	573	9	under	under	ADP
ejpam-5835	573	10	different	different	ADJ
ejpam-5835	573	11	operations	operation	NOUN
ejpam-5835	573	12	.	.	PUNCT
ejpam-5835	574	1	quasigroups	quasigroup	NOUN
ejpam-5835	574	2	and	and	CCONJ
ejpam-5835	574	3	related	related	ADJ
ejpam-5835	574	4	systems	system	NOUN
ejpam-5835	574	5	,	,	PUNCT
ejpam-5835	574	6	32(2):261–276	32(2):261–276	PROPN
ejpam-5835	574	7	,	,	PUNCT
ejpam-5835	574	8	2024	2024	NUM
ejpam-5835	574	9	.	.	PUNCT
ejpam-5835	575	1	[	[	X
ejpam-5835	575	2	9	9	NUM
ejpam-5835	575	3	]	]	PUNCT
ejpam-5835	575	4	s.	s.	PROPN
ejpam-5835	575	5	kerhoff	kerhoff	PROPN
ejpam-5835	575	6	,	,	PUNCT
ejpam-5835	575	7	r.	r.	PROPN
ejpam-5835	575	8	pöschel	pöschel	PROPN
ejpam-5835	575	9	,	,	PUNCT
ejpam-5835	575	10	and	and	CCONJ
ejpam-5835	575	11	f.	f.	PROPN
ejpam-5835	575	12	m.	m.	PROPN
ejpam-5835	575	13	schneider	schneider	PROPN
ejpam-5835	575	14	.	.	PUNCT
ejpam-5835	576	1	a	a	DET
ejpam-5835	576	2	short	short	ADJ
ejpam-5835	576	3	introduction	introduction	NOUN
ejpam-5835	576	4	to	to	ADP
ejpam-5835	576	5	clones	clone	NOUN
ejpam-5835	576	6	.	.	PUNCT
ejpam-5835	577	1	electronic	electronic	ADJ
ejpam-5835	577	2	notes	note	NOUN
ejpam-5835	577	3	in	in	ADP
ejpam-5835	577	4	theoretical	theoretical	ADJ
ejpam-5835	577	5	computer	computer	NOUN
ejpam-5835	577	6	science	science	NOUN
ejpam-5835	577	7	,	,	PUNCT
ejpam-5835	577	8	303:107–120	303:107–120	NUM
ejpam-5835	577	9	,	,	PUNCT
ejpam-5835	577	10	2014	2014	NUM
ejpam-5835	577	11	.	.	PUNCT
ejpam-5835	578	1	t.	t.	PROPN
ejpam-5835	578	2	kumduang	kumduang	PROPN
ejpam-5835	578	3	,	,	PUNCT
ejpam-5835	578	4	k.	k.	PROPN
ejpam-5835	578	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	578	6	/	/	SYM
ejpam-5835	578	7	eur	eur	PROPN
ejpam-5835	578	8	.	.	PUNCT
ejpam-5835	579	1	j.	j.	PROPN
ejpam-5835	579	2	pure	pure	PROPN
ejpam-5835	579	3	appl	appl	PROPN
ejpam-5835	579	4	.	.	PROPN
ejpam-5835	579	5	math	math	PROPN
ejpam-5835	579	6	,	,	PUNCT
ejpam-5835	579	7	18	18	NUM
ejpam-5835	579	8	(	(	PUNCT
ejpam-5835	579	9	2	2	NUM
ejpam-5835	579	10	)	)	PUNCT
ejpam-5835	579	11	(	(	PUNCT
ejpam-5835	579	12	2025	2025	NUM
ejpam-5835	579	13	)	)	PUNCT
ejpam-5835	579	14	,	,	PUNCT
ejpam-5835	579	15	5835	5835	NUM
ejpam-5835	579	16	16	16	NUM
ejpam-5835	579	17	of	of	ADP
ejpam-5835	579	18	16	16	NUM
ejpam-5835	580	1	[	[	X
ejpam-5835	580	2	10	10	NUM
ejpam-5835	580	3	]	]	PUNCT
ejpam-5835	580	4	p.	p.	NOUN
ejpam-5835	580	5	kitpratyakul	kitpratyakul	PROPN
ejpam-5835	580	6	and	and	CCONJ
ejpam-5835	580	7	b.	b.	PROPN
ejpam-5835	580	8	pibaljommee	pibaljommee	PROPN
ejpam-5835	580	9	.	.	PUNCT
ejpam-5835	581	1	clones	clone	NOUN
ejpam-5835	581	2	of	of	ADP
ejpam-5835	581	3	inductive	inductive	ADJ
ejpam-5835	581	4	superpositions	superposition	NOUN
ejpam-5835	581	5	of	of	ADP
ejpam-5835	581	6	terms	term	NOUN
ejpam-5835	581	7	.	.	PUNCT
ejpam-5835	582	1	aims	aim	VERB
ejpam-5835	582	2	mathematics	mathematic	NOUN
ejpam-5835	582	3	,	,	PUNCT
ejpam-5835	582	4	8(4):7747–7765	8(4):7747–7765	PROPN
ejpam-5835	582	5	,	,	PUNCT
ejpam-5835	582	6	2023	2023	NUM
ejpam-5835	582	7	.	.	PUNCT
ejpam-5835	583	1	[	[	X
ejpam-5835	583	2	11	11	NUM
ejpam-5835	583	3	]	]	PUNCT
ejpam-5835	583	4	t.	t.	PROPN
ejpam-5835	583	5	kumduang	kumduang	PROPN
ejpam-5835	583	6	.	.	PUNCT
ejpam-5835	584	1	weak	weak	ADJ
ejpam-5835	584	2	embeddability	embeddability	NOUN
ejpam-5835	584	3	of	of	ADP
ejpam-5835	584	4	the	the	DET
ejpam-5835	584	5	partial	partial	ADJ
ejpam-5835	584	6	menger	menger	PROPN
ejpam-5835	584	7	algebra	algebra	PROPN
ejpam-5835	584	8	of	of	ADP
ejpam-5835	584	9	formulas	formula	NOUN
ejpam-5835	584	10	.	.	PUNCT
ejpam-5835	585	1	quasigroups	quasigroup	NOUN
ejpam-5835	585	2	and	and	CCONJ
ejpam-5835	585	3	related	related	ADJ
ejpam-5835	585	4	systems	system	NOUN
ejpam-5835	585	5	,	,	PUNCT
ejpam-5835	585	6	31(2):269–284	31(2):269–284	NUM
ejpam-5835	585	7	,	,	PUNCT
ejpam-5835	585	8	2023	2023	NUM
ejpam-5835	585	9	.	.	PUNCT
ejpam-5835	586	1	[	[	X
ejpam-5835	586	2	12	12	NUM
ejpam-5835	586	3	]	]	PUNCT
ejpam-5835	586	4	t.	t.	PROPN
ejpam-5835	586	5	kumduang	kumduang	PROPN
ejpam-5835	586	6	and	and	CCONJ
ejpam-5835	586	7	s.	s.	PROPN
ejpam-5835	586	8	sriwongsa	sriwongsa	PROPN
ejpam-5835	586	9	.	.	PUNCT
ejpam-5835	587	1	superassociative	superassociative	ADJ
ejpam-5835	587	2	structures	structure	NOUN
ejpam-5835	587	3	of	of	ADP
ejpam-5835	587	4	terms	term	NOUN
ejpam-5835	587	5	and	and	CCONJ
ejpam-5835	587	6	formulas	formula	NOUN
ejpam-5835	587	7	defined	define	VERB
ejpam-5835	587	8	by	by	ADP
ejpam-5835	587	9	transformations	transformation	NOUN
ejpam-5835	587	10	preserving	preserve	VERB
ejpam-5835	587	11	a	a	DET
ejpam-5835	587	12	partition	partition	NOUN
ejpam-5835	587	13	.	.	PUNCT
ejpam-5835	588	1	communications	communication	NOUN
ejpam-5835	588	2	in	in	ADP
ejpam-5835	588	3	algebra	algebra	NOUN
ejpam-5835	588	4	,	,	PUNCT
ejpam-5835	588	5	51(8):3203–3220	51(8):3203–3220	NOUN
ejpam-5835	588	6	,	,	PUNCT
ejpam-5835	588	7	2023	2023	NUM
ejpam-5835	588	8	.	.	PUNCT
ejpam-5835	589	1	[	[	X
ejpam-5835	589	2	13	13	NUM
ejpam-5835	589	3	]	]	SYM
ejpam-5835	589	4	yu	yu	PROPN
ejpam-5835	589	5	.	.	PROPN
ejpam-5835	589	6	m.	m.	NOUN
ejpam-5835	589	7	movsisyan	movsisyan	PROPN
ejpam-5835	589	8	.	.	PUNCT
ejpam-5835	590	1	hyperidentities	hyperidentitie	NOUN
ejpam-5835	590	2	and	and	CCONJ
ejpam-5835	590	3	related	related	ADJ
ejpam-5835	590	4	concepts	concept	NOUN
ejpam-5835	590	5	,	,	PUNCT
ejpam-5835	590	6	i.	i.	PROPN
ejpam-5835	590	7	armenian	armenian	PROPN
ejpam-5835	590	8	journal	journal	NOUN
ejpam-5835	590	9	of	of	ADP
ejpam-5835	590	10	mathematics	mathematics	PROPN
ejpam-5835	590	11	,	,	PUNCT
ejpam-5835	590	12	9(2):146–222	9(2):146–222	NOUN
ejpam-5835	590	13	,	,	PUNCT
ejpam-5835	590	14	2017	2017	NUM
ejpam-5835	590	15	.	.	PUNCT
ejpam-5835	591	1	[	[	X
ejpam-5835	591	2	14	14	NUM
ejpam-5835	591	3	]	]	PUNCT
ejpam-5835	591	4	a.	a.	NOUN
ejpam-5835	591	5	nongmanee	nongmanee	NOUN
ejpam-5835	591	6	and	and	CCONJ
ejpam-5835	591	7	s.	s.	PROPN
ejpam-5835	591	8	leeratanavalee	leeratanavalee	PROPN
ejpam-5835	591	9	.	.	PUNCT
ejpam-5835	592	1	ternary	ternary	ADJ
ejpam-5835	592	2	menger	menger	PROPN
ejpam-5835	592	3	algebras	algebra	VERB
ejpam-5835	592	4	:	:	PUNCT
ejpam-5835	592	5	a	a	DET
ejpam-5835	592	6	generalization	generalization	NOUN
ejpam-5835	592	7	of	of	ADP
ejpam-5835	592	8	ternary	ternary	ADJ
ejpam-5835	592	9	semigroups	semigroup	NOUN
ejpam-5835	592	10	.	.	PUNCT
ejpam-5835	593	1	mathematics	mathematic	NOUN
ejpam-5835	593	2	,	,	PUNCT
ejpam-5835	593	3	9:553	9:553	NUM
ejpam-5835	593	4	,	,	PUNCT
ejpam-5835	593	5	2021	2021	NUM
ejpam-5835	593	6	.	.	PUNCT
ejpam-5835	594	1	[	[	X
ejpam-5835	594	2	15	15	NUM
ejpam-5835	594	3	]	]	X
ejpam-5835	594	4	s.	s.	PROPN
ejpam-5835	594	5	phuapong	phuapong	PROPN
ejpam-5835	594	6	,	,	PUNCT
ejpam-5835	594	7	n.	n.	PROPN
ejpam-5835	594	8	chansuriya	chansuriya	PROPN
ejpam-5835	594	9	,	,	PUNCT
ejpam-5835	594	10	and	and	CCONJ
ejpam-5835	594	11	t.	t.	PROPN
ejpam-5835	594	12	kumduang	kumduang	PROPN
ejpam-5835	594	13	.	.	PUNCT
ejpam-5835	595	1	algebras	algebras	PROPN
ejpam-5835	595	2	of	of	ADP
ejpam-5835	595	3	generalized	generalized	ADJ
ejpam-5835	595	4	tree	tree	NOUN
ejpam-5835	595	5	languages	language	NOUN
ejpam-5835	595	6	with	with	ADP
ejpam-5835	595	7	fixed	fix	VERB
ejpam-5835	595	8	variables	variable	NOUN
ejpam-5835	595	9	.	.	PUNCT
ejpam-5835	596	1	algebra	algebra	NOUN
ejpam-5835	596	2	and	and	CCONJ
ejpam-5835	596	3	discrete	discrete	ADJ
ejpam-5835	596	4	mathematics	mathematic	NOUN
ejpam-5835	596	5	,	,	PUNCT
ejpam-5835	596	6	36(2):202–216	36(2):202–216	NUM
ejpam-5835	596	7	,	,	PUNCT
ejpam-5835	596	8	2023	2023	NUM
ejpam-5835	596	9	.	.	PUNCT
ejpam-5835	597	1	[	[	X
ejpam-5835	597	2	16	16	NUM
ejpam-5835	597	3	]	]	X
ejpam-5835	597	4	d.	d.	PROPN
ejpam-5835	597	5	phusanga	phusanga	PROPN
ejpam-5835	597	6	and	and	CCONJ
ejpam-5835	597	7	j.	j.	PROPN
ejpam-5835	597	8	koppitz	koppitz	PROPN
ejpam-5835	597	9	.	.	PUNCT
ejpam-5835	598	1	the	the	DET
ejpam-5835	598	2	semigroup	semigroup	NOUN
ejpam-5835	598	3	of	of	ADP
ejpam-5835	598	4	linear	linear	PROPN
ejpam-5835	598	5	terms	term	NOUN
ejpam-5835	598	6	.	.	PUNCT
ejpam-5835	599	1	asian	asian	ADJ
ejpam-5835	599	2	-	-	PUNCT
ejpam-5835	599	3	european	european	ADJ
ejpam-5835	599	4	journal	journal	NOUN
ejpam-5835	599	5	of	of	ADP
ejpam-5835	599	6	mathematics	mathematic	NOUN
ejpam-5835	599	7	,	,	PUNCT
ejpam-5835	599	8	13(1):2050005	13(1):2050005	NUM
ejpam-5835	599	9	,	,	PUNCT
ejpam-5835	599	10	2020	2020	NUM
ejpam-5835	599	11	.	.	PUNCT
ejpam-5835	600	1	[	[	X
ejpam-5835	600	2	17	17	NUM
ejpam-5835	600	3	]	]	PUNCT
ejpam-5835	600	4	k.	k.	PROPN
ejpam-5835	600	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	600	6	and	and	CCONJ
ejpam-5835	600	7	t.	t.	PROPN
ejpam-5835	600	8	changphas	changphas	PROPN
ejpam-5835	600	9	.	.	PUNCT
ejpam-5835	601	1	clones	clone	NOUN
ejpam-5835	601	2	of	of	ADP
ejpam-5835	601	3	terms	term	NOUN
ejpam-5835	601	4	of	of	ADP
ejpam-5835	601	5	a	a	DET
ejpam-5835	601	6	fixed	fix	VERB
ejpam-5835	601	7	variable	variable	NOUN
ejpam-5835	601	8	.	.	PUNCT
ejpam-5835	602	1	mathematics	mathematic	NOUN
ejpam-5835	602	2	,	,	PUNCT
ejpam-5835	602	3	8:260	8:260	NUM
ejpam-5835	602	4	,	,	PUNCT
ejpam-5835	602	5	2020	2020	NUM
ejpam-5835	602	6	.	.	PUNCT
ejpam-5835	603	1	[	[	X
ejpam-5835	603	2	18	18	NUM
ejpam-5835	603	3	]	]	PUNCT
ejpam-5835	603	4	k.	k.	PROPN
ejpam-5835	603	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	603	6	and	and	CCONJ
ejpam-5835	603	7	t.	t.	PROPN
ejpam-5835	603	8	changphas	changphas	PROPN
ejpam-5835	603	9	.	.	PUNCT
ejpam-5835	604	1	the	the	DET
ejpam-5835	604	2	menger	menger	PROPN
ejpam-5835	604	3	algebra	algebra	PROPN
ejpam-5835	604	4	of	of	ADP
ejpam-5835	604	5	terms	term	NOUN
ejpam-5835	604	6	induced	induce	VERB
ejpam-5835	604	7	by	by	ADP
ejpam-5835	604	8	orderdecreasing	orderdecrease	VERB
ejpam-5835	604	9	transformations	transformation	NOUN
ejpam-5835	604	10	.	.	PUNCT
ejpam-5835	605	1	communications	communication	NOUN
ejpam-5835	605	2	in	in	ADP
ejpam-5835	605	3	algebra	algebra	NOUN
ejpam-5835	605	4	,	,	PUNCT
ejpam-5835	605	5	49(7):3114–3123	49(7):3114–3123	NUM
ejpam-5835	605	6	,	,	PUNCT
ejpam-5835	605	7	2021	2021	NUM
ejpam-5835	605	8	.	.	PUNCT
ejpam-5835	606	1	[	[	X
ejpam-5835	606	2	19	19	NUM
ejpam-5835	606	3	]	]	PUNCT
ejpam-5835	606	4	k.	k.	PROPN
ejpam-5835	606	5	wattanatripop	wattanatripop	PROPN
ejpam-5835	606	6	and	and	CCONJ
ejpam-5835	606	7	t.	t.	PROPN
ejpam-5835	606	8	kumduang	kumduang	PROPN
ejpam-5835	606	9	.	.	PUNCT
ejpam-5835	607	1	the	the	DET
ejpam-5835	607	2	partial	partial	ADJ
ejpam-5835	607	3	clone	clone	NOUN
ejpam-5835	607	4	of	of	ADP
ejpam-5835	607	5	completely	completely	ADV
ejpam-5835	607	6	expanded	expand	VERB
ejpam-5835	607	7	terms	term	NOUN
ejpam-5835	607	8	.	.	PUNCT
ejpam-5835	608	1	asian	asian	ADJ
ejpam-5835	608	2	-	-	PUNCT
ejpam-5835	608	3	european	european	ADJ
ejpam-5835	608	4	journal	journal	NOUN
ejpam-5835	608	5	of	of	ADP
ejpam-5835	608	6	mathematics	mathematic	NOUN
ejpam-5835	608	7	,	,	PUNCT
ejpam-5835	608	8	17(10):2450063	17(10):2450063	NUM
ejpam-5835	608	9	,	,	PUNCT
ejpam-5835	608	10	2024	2024	NUM
ejpam-5835	608	11	.	.	PUNCT