id	sid	tid	token	lemma	pos
ejpam-3280	1	1	soft	soft	ADJ
ejpam-3280	1	2	hypervector	hypervector	NOUN
ejpam-3280	1	3	spaces	space	NOUN
ejpam-3280	1	4	and	and	CCONJ
ejpam-3280	1	5	fuzzy	fuzzy	ADJ
ejpam-3280	1	6	soft	soft	ADJ
ejpam-3280	1	7	hypervector	hypervector	NOUN
ejpam-3280	1	8	spaces	space	NOUN
ejpam-3280	1	9	european	european	ADJ
ejpam-3280	1	10	journal	journal	PROPN
ejpam-3280	1	11	of	of	ADP
ejpam-3280	1	12	pure	pure	ADJ
ejpam-3280	1	13	and	and	CCONJ
ejpam-3280	1	14	applied	apply	VERB
ejpam-3280	1	15	mathematics	mathematic	NOUN
ejpam-3280	1	16	vol	vol	NOUN
ejpam-3280	1	17	.	.	PROPN
ejpam-3280	2	1	12	12	NUM
ejpam-3280	2	2	,	,	PUNCT
ejpam-3280	2	3	no	no	INTJ
ejpam-3280	2	4	.	.	NOUN
ejpam-3280	2	5	1	1	NUM
ejpam-3280	2	6	,	,	PUNCT
ejpam-3280	2	7	2019	2019	NUM
ejpam-3280	2	8	,	,	PUNCT
ejpam-3280	2	9	118	118	NUM
ejpam-3280	2	10	-	-	SYM
ejpam-3280	2	11	134	134	NUM
ejpam-3280	2	12	issn	issn	PROPN
ejpam-3280	2	13	1307	1307	NUM
ejpam-3280	2	14	-	-	SYM
ejpam-3280	2	15	5543	5543	NUM
ejpam-3280	2	16	–	–	PUNCT
ejpam-3280	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3280	3	2	published	publish	VERB
ejpam-3280	3	3	by	by	ADP
ejpam-3280	3	4	new	new	PROPN
ejpam-3280	3	5	york	york	PROPN
ejpam-3280	3	6	business	business	PROPN
ejpam-3280	3	7	global	global	ADJ
ejpam-3280	3	8	soft	soft	ADJ
ejpam-3280	3	9	hypervector	hypervector	NOUN
ejpam-3280	3	10	spaces	space	NOUN
ejpam-3280	3	11	and	and	CCONJ
ejpam-3280	3	12	fuzzy	fuzzy	ADJ
ejpam-3280	3	13	soft	soft	ADJ
ejpam-3280	3	14	hypervector	hypervector	NOUN
ejpam-3280	3	15	spaces	space	NOUN
ejpam-3280	3	16	esmail	esmail	ADJ
ejpam-3280	3	17	ranjbar	ranjbar	NOUN
ejpam-3280	3	18	-	-	PUNCT
ejpam-3280	3	19	yanehsari1	yanehsari1	NOUN
ejpam-3280	3	20	,	,	PUNCT
ejpam-3280	3	21	mohsen	mohsen	PROPN
ejpam-3280	3	22	asghari	asghari	ADV
ejpam-3280	3	23	-	-	PUNCT
ejpam-3280	3	24	larimi1,∗	larimi1,∗	NOUN
ejpam-3280	3	25	,	,	PUNCT
ejpam-3280	3	26	reza	reza	PROPN
ejpam-3280	3	27	ameri2	ameri2	PROPN
ejpam-3280	3	28	1	1	NUM
ejpam-3280	3	29	department	department	NOUN
ejpam-3280	3	30	of	of	ADP
ejpam-3280	3	31	mathematics	mathematics	PROPN
ejpam-3280	3	32	,	,	PUNCT
ejpam-3280	3	33	golestan	golestan	PROPN
ejpam-3280	3	34	university	university	NOUN
ejpam-3280	3	35	,	,	PUNCT
ejpam-3280	3	36	gorgan	gorgan	NOUN
ejpam-3280	3	37	,	,	PUNCT
ejpam-3280	3	38	iran	iran	PROPN
ejpam-3280	3	39	2	2	NUM
ejpam-3280	3	40	department	department	NOUN
ejpam-3280	3	41	of	of	ADP
ejpam-3280	3	42	mathematics	mathematic	NOUN
ejpam-3280	3	43	,	,	PUNCT
ejpam-3280	3	44	university	university	PROPN
ejpam-3280	3	45	of	of	ADP
ejpam-3280	3	46	tehran	tehran	PROPN
ejpam-3280	3	47	,	,	PUNCT
ejpam-3280	3	48	tehran	tehran	PROPN
ejpam-3280	3	49	,	,	PUNCT
ejpam-3280	3	50	iran	iran	PROPN
ejpam-3280	3	51	abstract	abstract	ADJ
ejpam-3280	3	52	.	.	PUNCT
ejpam-3280	4	1	in	in	ADP
ejpam-3280	4	2	this	this	DET
ejpam-3280	4	3	paper	paper	NOUN
ejpam-3280	4	4	,	,	PUNCT
ejpam-3280	4	5	the	the	DET
ejpam-3280	4	6	notions	notion	NOUN
ejpam-3280	4	7	of	of	ADP
ejpam-3280	4	8	soft	soft	ADJ
ejpam-3280	4	9	hypervector	hypervector	NOUN
ejpam-3280	4	10	space	space	NOUN
ejpam-3280	4	11	and	and	CCONJ
ejpam-3280	4	12	fuzzy	fuzzy	ADJ
ejpam-3280	4	13	soft	soft	ADJ
ejpam-3280	4	14	hypervector	hypervector	NOUN
ejpam-3280	4	15	space	space	NOUN
ejpam-3280	4	16	are	be	AUX
ejpam-3280	4	17	introduced	introduce	VERB
ejpam-3280	4	18	,	,	PUNCT
ejpam-3280	4	19	and	and	CCONJ
ejpam-3280	4	20	several	several	ADJ
ejpam-3280	4	21	basic	basic	ADJ
ejpam-3280	4	22	properties	property	NOUN
ejpam-3280	4	23	are	be	AUX
ejpam-3280	4	24	provided	provide	VERB
ejpam-3280	4	25	.	.	PUNCT
ejpam-3280	5	1	also	also	ADV
ejpam-3280	5	2	,	,	PUNCT
ejpam-3280	5	3	we	we	PRON
ejpam-3280	5	4	define	define	VERB
ejpam-3280	5	5	and	and	CCONJ
ejpam-3280	5	6	analyze	analyze	VERB
ejpam-3280	5	7	the	the	DET
ejpam-3280	5	8	concept	concept	NOUN
ejpam-3280	5	9	of	of	ADP
ejpam-3280	5	10	image	image	NOUN
ejpam-3280	5	11	and	and	CCONJ
ejpam-3280	5	12	pre	pre	NOUN
ejpam-3280	5	13	-	-	NOUN
ejpam-3280	5	14	image	image	NOUN
ejpam-3280	5	15	of	of	ADP
ejpam-3280	5	16	fuzzy	fuzzy	ADJ
ejpam-3280	5	17	soft	soft	ADJ
ejpam-3280	5	18	hypervector	hypervector	NOUN
ejpam-3280	5	19	space	space	NOUN
ejpam-3280	5	20	.	.	PUNCT
ejpam-3280	6	1	2010	2010	NUM
ejpam-3280	6	2	mathematics	mathematic	NOUN
ejpam-3280	6	3	subject	subject	NOUN
ejpam-3280	6	4	classifications	classification	NOUN
ejpam-3280	6	5	:	:	PUNCT
ejpam-3280	6	6	20n20	20n20	NUM
ejpam-3280	6	7	key	key	ADJ
ejpam-3280	6	8	words	word	NOUN
ejpam-3280	6	9	and	and	CCONJ
ejpam-3280	6	10	phrases	phrase	NOUN
ejpam-3280	6	11	:	:	PUNCT
ejpam-3280	6	12	hypervector	hypervector	NOUN
ejpam-3280	6	13	space	space	NOUN
ejpam-3280	6	14	,	,	PUNCT
ejpam-3280	6	15	soft	soft	ADJ
ejpam-3280	6	16	hypervector	hypervector	NOUN
ejpam-3280	6	17	space	space	NOUN
ejpam-3280	6	18	,	,	PUNCT
ejpam-3280	6	19	fuzzy	fuzzy	ADJ
ejpam-3280	6	20	soft	soft	ADJ
ejpam-3280	6	21	hypervector	hypervector	NOUN
ejpam-3280	6	22	space	space	NOUN
ejpam-3280	6	23	,	,	PUNCT
ejpam-3280	6	24	fuzzy	fuzzy	ADJ
ejpam-3280	6	25	soft	soft	ADJ
ejpam-3280	6	26	image	image	NOUN
ejpam-3280	6	27	,	,	PUNCT
ejpam-3280	6	28	fuzzy	fuzzy	ADJ
ejpam-3280	6	29	soft	soft	ADJ
ejpam-3280	6	30	pre	pre	NOUN
ejpam-3280	6	31	-	-	NOUN
ejpam-3280	6	32	image	image	ADJ
ejpam-3280	6	33	1	1	NUM
ejpam-3280	6	34	.	.	PUNCT
ejpam-3280	6	35	introduction	introduction	NOUN
ejpam-3280	6	36	the	the	DET
ejpam-3280	6	37	concept	concept	NOUN
ejpam-3280	6	38	of	of	ADP
ejpam-3280	6	39	soft	soft	ADJ
ejpam-3280	6	40	set	set	NOUN
ejpam-3280	6	41	has	have	AUX
ejpam-3280	6	42	been	be	AUX
ejpam-3280	6	43	introduced	introduce	VERB
ejpam-3280	6	44	in	in	ADP
ejpam-3280	6	45	1999	1999	NUM
ejpam-3280	6	46	by	by	ADP
ejpam-3280	6	47	molodtsov	molodtsov	NOUN
ejpam-3280	7	1	[	[	X
ejpam-3280	7	2	15	15	NUM
ejpam-3280	7	3	]	]	PUNCT
ejpam-3280	7	4	as	as	ADP
ejpam-3280	7	5	a	a	DET
ejpam-3280	7	6	general	general	ADJ
ejpam-3280	7	7	mathematical	mathematical	ADJ
ejpam-3280	7	8	tool	tool	NOUN
ejpam-3280	7	9	for	for	ADP
ejpam-3280	7	10	dealing	deal	VERB
ejpam-3280	7	11	with	with	ADP
ejpam-3280	7	12	uncertainties	uncertainty	NOUN
ejpam-3280	7	13	and	and	CCONJ
ejpam-3280	7	14	imprecision	imprecision	NOUN
ejpam-3280	7	15	.	.	PUNCT
ejpam-3280	8	1	after	after	ADP
ejpam-3280	8	2	molodtsovs	molodtsovs	PROPN
ejpam-3280	8	3	work	work	NOUN
ejpam-3280	8	4	,	,	PUNCT
ejpam-3280	8	5	some	some	DET
ejpam-3280	8	6	research	research	NOUN
ejpam-3280	8	7	papers	paper	NOUN
ejpam-3280	8	8	have	have	AUX
ejpam-3280	8	9	appeared	appear	VERB
ejpam-3280	8	10	on	on	ADP
ejpam-3280	8	11	the	the	DET
ejpam-3280	8	12	algebraic	algebraic	ADJ
ejpam-3280	8	13	structures	structure	NOUN
ejpam-3280	8	14	of	of	ADP
ejpam-3280	8	15	soft	soft	ADJ
ejpam-3280	8	16	set	set	NOUN
ejpam-3280	8	17	theory	theory	NOUN
ejpam-3280	8	18	.	.	PUNCT
ejpam-3280	9	1	then	then	ADV
ejpam-3280	9	2	,	,	PUNCT
ejpam-3280	9	3	maji	maji	PROPN
ejpam-3280	9	4	et	et	PROPN
ejpam-3280	9	5	al	al	PROPN
ejpam-3280	9	6	.	.	PUNCT
ejpam-3280	10	1	[	[	X
ejpam-3280	10	2	17	17	NUM
ejpam-3280	10	3	]	]	PUNCT
ejpam-3280	10	4	introduced	introduce	VERB
ejpam-3280	10	5	and	and	CCONJ
ejpam-3280	10	6	analyzed	analyze	VERB
ejpam-3280	10	7	several	several	ADJ
ejpam-3280	10	8	operations	operation	NOUN
ejpam-3280	10	9	on	on	ADP
ejpam-3280	10	10	soft	soft	ADJ
ejpam-3280	10	11	sets	set	NOUN
ejpam-3280	10	12	.	.	PUNCT
ejpam-3280	11	1	in	in	ADP
ejpam-3280	11	2	2007	2007	NUM
ejpam-3280	11	3	,	,	PUNCT
ejpam-3280	11	4	aktas	akta	NOUN
ejpam-3280	11	5	and	and	CCONJ
ejpam-3280	11	6	cagman	cagman	ADJ
ejpam-3280	11	7	[	[	X
ejpam-3280	11	8	2	2	NUM
ejpam-3280	11	9	]	]	PUNCT
ejpam-3280	11	10	studied	study	VERB
ejpam-3280	11	11	the	the	DET
ejpam-3280	11	12	basic	basic	ADJ
ejpam-3280	11	13	concepts	concept	NOUN
ejpam-3280	11	14	of	of	ADP
ejpam-3280	11	15	soft	soft	ADJ
ejpam-3280	11	16	sets	set	NOUN
ejpam-3280	11	17	theory	theory	NOUN
ejpam-3280	11	18	and	and	CCONJ
ejpam-3280	11	19	soft	soft	ADJ
ejpam-3280	11	20	groups	group	NOUN
ejpam-3280	11	21	,	,	PUNCT
ejpam-3280	11	22	providing	provide	VERB
ejpam-3280	11	23	examples	example	NOUN
ejpam-3280	11	24	to	to	PART
ejpam-3280	11	25	clarify	clarify	VERB
ejpam-3280	11	26	their	their	PRON
ejpam-3280	11	27	differences	difference	NOUN
ejpam-3280	11	28	.	.	PUNCT
ejpam-3280	12	1	moreover	moreover	ADV
ejpam-3280	12	2	,	,	PUNCT
ejpam-3280	12	3	in	in	ADP
ejpam-3280	12	4	[	[	PUNCT
ejpam-3280	12	5	1	1	X
ejpam-3280	12	6	]	]	PUNCT
ejpam-3280	12	7	acar	acar	NOUN
ejpam-3280	12	8	et	et	PROPN
ejpam-3280	12	9	al	al	PROPN
ejpam-3280	12	10	.	.	PROPN
ejpam-3280	12	11	and	and	CCONJ
ejpam-3280	12	12	in	in	ADP
ejpam-3280	12	13	[	[	X
ejpam-3280	12	14	18	18	NUM
ejpam-3280	12	15	]	]	X
ejpam-3280	12	16	sun	sun	PROPN
ejpam-3280	12	17	et	et	PROPN
ejpam-3280	12	18	al	al	PROPN
ejpam-3280	12	19	.	.	PROPN
ejpam-3280	12	20	defined	define	VERB
ejpam-3280	12	21	the	the	DET
ejpam-3280	12	22	concepts	concept	NOUN
ejpam-3280	12	23	of	of	ADP
ejpam-3280	12	24	soft	soft	ADJ
ejpam-3280	12	25	rings	ring	NOUN
ejpam-3280	12	26	and	and	CCONJ
ejpam-3280	12	27	soft	soft	ADJ
ejpam-3280	12	28	modules	module	NOUN
ejpam-3280	12	29	,	,	PUNCT
ejpam-3280	12	30	respectively	respectively	ADV
ejpam-3280	12	31	.	.	PUNCT
ejpam-3280	13	1	the	the	DET
ejpam-3280	13	2	notion	notion	NOUN
ejpam-3280	13	3	of	of	ADP
ejpam-3280	13	4	a	a	DET
ejpam-3280	13	5	fuzzy	fuzzy	ADJ
ejpam-3280	13	6	subset	subset	NOUN
ejpam-3280	13	7	introduced	introduce	VERB
ejpam-3280	13	8	by	by	ADP
ejpam-3280	13	9	zadeh	zadeh	PROPN
ejpam-3280	13	10	in	in	ADP
ejpam-3280	13	11	1965	1965	NUM
ejpam-3280	13	12	[	[	X
ejpam-3280	13	13	22	22	NUM
ejpam-3280	13	14	]	]	PUNCT
ejpam-3280	13	15	.	.	PUNCT
ejpam-3280	14	1	in	in	ADP
ejpam-3280	14	2	[	[	X
ejpam-3280	14	3	12	12	NUM
ejpam-3280	14	4	]	]	X
ejpam-3280	14	5	maji	maji	PROPN
ejpam-3280	14	6	et	et	PROPN
ejpam-3280	14	7	al	al	PROPN
ejpam-3280	14	8	.	.	PROPN
ejpam-3280	14	9	presented	present	VERB
ejpam-3280	14	10	the	the	DET
ejpam-3280	14	11	concept	concept	NOUN
ejpam-3280	14	12	of	of	ADP
ejpam-3280	14	13	fuzzy	fuzzy	ADJ
ejpam-3280	14	14	soft	soft	ADJ
ejpam-3280	14	15	sets	set	NOUN
ejpam-3280	14	16	.	.	PUNCT
ejpam-3280	15	1	in	in	ADP
ejpam-3280	15	2	particular	particular	ADJ
ejpam-3280	15	3	,	,	PUNCT
ejpam-3280	15	4	fuzzy	fuzzy	ADJ
ejpam-3280	15	5	soft	soft	ADJ
ejpam-3280	15	6	set	set	NOUN
ejpam-3280	15	7	theory	theory	NOUN
ejpam-3280	15	8	has	have	AUX
ejpam-3280	15	9	been	be	AUX
ejpam-3280	15	10	investigated	investigate	VERB
ejpam-3280	15	11	by	by	ADP
ejpam-3280	15	12	some	some	DET
ejpam-3280	15	13	researchers	researcher	NOUN
ejpam-3280	15	14	,	,	PUNCT
ejpam-3280	15	15	for	for	ADP
ejpam-3280	15	16	examples	example	NOUN
ejpam-3280	15	17	,	,	PUNCT
ejpam-3280	15	18	see	see	VERB
ejpam-3280	15	19	[	[	X
ejpam-3280	15	20	6	6	NUM
ejpam-3280	15	21	]	]	PUNCT
ejpam-3280	15	22	,	,	PUNCT
ejpam-3280	16	1	[	[	X
ejpam-3280	16	2	12	12	NUM
ejpam-3280	16	3	]	]	PUNCT
ejpam-3280	16	4	,	,	PUNCT
ejpam-3280	16	5	[	[	X
ejpam-3280	16	6	13	13	NUM
ejpam-3280	16	7	]	]	PUNCT
ejpam-3280	16	8	and	and	CCONJ
ejpam-3280	16	9	[	[	X
ejpam-3280	16	10	20	20	NUM
ejpam-3280	16	11	]	]	PUNCT
ejpam-3280	16	12	.	.	PUNCT
ejpam-3280	17	1	the	the	DET
ejpam-3280	17	2	hyperstructure	hyperstructure	NOUN
ejpam-3280	17	3	theory	theory	NOUN
ejpam-3280	17	4	was	be	AUX
ejpam-3280	17	5	introduced	introduce	VERB
ejpam-3280	17	6	by	by	ADP
ejpam-3280	17	7	marty	marty	PROPN
ejpam-3280	18	1	[	[	X
ejpam-3280	18	2	14	14	NUM
ejpam-3280	18	3	]	]	PUNCT
ejpam-3280	18	4	at	at	ADP
ejpam-3280	18	5	the	the	DET
ejpam-3280	18	6	8th	8th	ADJ
ejpam-3280	18	7	congress	congress	PROPN
ejpam-3280	18	8	of	of	ADP
ejpam-3280	18	9	scandinavian	scandinavian	ADJ
ejpam-3280	18	10	mathematicians	mathematician	NOUN
ejpam-3280	18	11	in	in	ADP
ejpam-3280	18	12	1934	1934	NUM
ejpam-3280	18	13	.	.	PUNCT
ejpam-3280	19	1	as	as	ADP
ejpam-3280	19	2	a	a	DET
ejpam-3280	19	3	generalization	generalization	NOUN
ejpam-3280	19	4	of	of	ADP
ejpam-3280	19	5	hypervector	hypervector	NOUN
ejpam-3280	19	6	spaces	space	NOUN
ejpam-3280	19	7	,	,	PUNCT
ejpam-3280	19	8	the	the	DET
ejpam-3280	19	9	fuzzy	fuzzy	ADJ
ejpam-3280	19	10	hypervector	hypervector	NOUN
ejpam-3280	19	11	spaces	space	NOUN
ejpam-3280	19	12	are	be	AUX
ejpam-3280	19	13	studied	study	VERB
ejpam-3280	19	14	by	by	ADP
ejpam-3280	19	15	ameri	ameri	PROPN
ejpam-3280	19	16	and	and	CCONJ
ejpam-3280	19	17	et	et	NOUN
ejpam-3280	19	18	.	.	PUNCT
ejpam-3280	20	1	(	(	PUNCT
ejpam-3280	20	2	see	see	VERB
ejpam-3280	20	3	[	[	X
ejpam-3280	20	4	3	3	NUM
ejpam-3280	20	5	,	,	PUNCT
ejpam-3280	20	6	4	4	NUM
ejpam-3280	20	7	]	]	NUM
ejpam-3280	20	8	)	)	PUNCT
ejpam-3280	20	9	.	.	PUNCT
ejpam-3280	21	1	jun	jun	PROPN
ejpam-3280	21	2	et	et	PROPN
ejpam-3280	21	3	al	al	PROPN
ejpam-3280	21	4	.	.	PUNCT
ejpam-3280	22	1	[	[	X
ejpam-3280	22	2	8	8	NUM
ejpam-3280	22	3	]	]	PUNCT
ejpam-3280	22	4	discussed	discuss	VERB
ejpam-3280	22	5	the	the	DET
ejpam-3280	22	6	applications	application	NOUN
ejpam-3280	22	7	of	of	ADP
ejpam-3280	22	8	fuzzy	fuzzy	ADJ
ejpam-3280	22	9	soft	soft	ADJ
ejpam-3280	22	10	set	set	NOUN
ejpam-3280	22	11	in	in	ADP
ejpam-3280	22	12	bck	bck	PROPN
ejpam-3280	22	13	/	/	SYM
ejpam-3280	22	14	bci	bci	NOUN
ejpam-3280	22	15	-	-	PUNCT
ejpam-3280	22	16	algebras	algebras	X
ejpam-3280	22	17	.	.	PUNCT
ejpam-3280	23	1	fuzzy	fuzzy	ADJ
ejpam-3280	23	2	soft	soft	ADJ
ejpam-3280	23	3	hypergroups	hypergroup	NOUN
ejpam-3280	23	4	were	be	AUX
ejpam-3280	23	5	defined	define	VERB
ejpam-3280	23	6	and	and	CCONJ
ejpam-3280	23	7	analysed	analyse	VERB
ejpam-3280	23	8	by	by	ADP
ejpam-3280	23	9	leoreanu	leoreanu	PROPN
ejpam-3280	23	10	-	-	PUNCT
ejpam-3280	23	11	fotea	fotea	NOUN
ejpam-3280	23	12	et	et	PROPN
ejpam-3280	23	13	al	al	PROPN
ejpam-3280	23	14	.	.	PUNCT
ejpam-3280	24	1	[	[	X
ejpam-3280	24	2	10	10	NUM
ejpam-3280	24	3	]	]	PUNCT
ejpam-3280	24	4	.	.	PUNCT
ejpam-3280	25	1	in	in	ADP
ejpam-3280	25	2	[	[	X
ejpam-3280	25	3	5	5	NUM
ejpam-3280	25	4	]	]	X
ejpam-3280	25	5	ameri	ameri	PROPN
ejpam-3280	25	6	et	et	PROPN
ejpam-3280	25	7	al	al	PROPN
ejpam-3280	25	8	.	.	PROPN
ejpam-3280	25	9	extended	extend	VERB
ejpam-3280	25	10	the	the	DET
ejpam-3280	25	11	study	study	NOUN
ejpam-3280	25	12	application	application	NOUN
ejpam-3280	25	13	of	of	ADP
ejpam-3280	25	14	fuzzy	fuzzy	ADJ
ejpam-3280	25	15	sets	set	NOUN
ejpam-3280	25	16	and	and	CCONJ
ejpam-3280	25	17	fuzzy	fuzzy	ADJ
ejpam-3280	25	18	soft	soft	ADJ
ejpam-3280	25	19	sets	set	NOUN
ejpam-3280	25	20	in	in	ADP
ejpam-3280	25	21	hypermodules	hypermodule	NOUN
ejpam-3280	25	22	.	.	PUNCT
ejpam-3280	26	1	∗corresponding	∗corresponde	VERB
ejpam-3280	26	2	author	author	NOUN
ejpam-3280	26	3	.	.	PUNCT
ejpam-3280	27	1	doi	doi	NOUN
ejpam-3280	27	2	:	:	PUNCT
ejpam-3280	27	3	https://doi.org/10.29020/nybg.ejpam.v12i1.3280	https://doi.org/10.29020/nybg.ejpam.v12i1.3280	PROPN
ejpam-3280	27	4	email	email	NOUN
ejpam-3280	27	5	addresses	address	NOUN
ejpam-3280	27	6	:	:	PUNCT
ejpam-3280	27	7	es-ranjbar@yahoo.com	es-ranjbar@yahoo.com	X
ejpam-3280	27	8	(	(	PUNCT
ejpam-3280	27	9	e.	e.	PROPN
ejpam-3280	27	10	ranjbar	ranjbar	PROPN
ejpam-3280	27	11	-	-	PUNCT
ejpam-3280	27	12	yanehsari	yanehsari	NOUN
ejpam-3280	27	13	)	)	PUNCT
ejpam-3280	27	14	,	,	PUNCT
ejpam-3280	27	15	m.asghari@gu.ac.ir	m.asghari@gu.ac.ir	PROPN
ejpam-3280	27	16	(	(	PUNCT
ejpam-3280	27	17	m.	m.	NOUN
ejpam-3280	27	18	asghari	asghari	ADJ
ejpam-3280	27	19	-	-	PUNCT
ejpam-3280	27	20	larimi	larimi	NOUN
ejpam-3280	27	21	)	)	PUNCT
ejpam-3280	27	22	,	,	PUNCT
ejpam-3280	27	23	rameri@ut.ac.ir	rameri@ut.ac.ir	PROPN
ejpam-3280	27	24	(	(	PUNCT
ejpam-3280	27	25	r.	r.	PROPN
ejpam-3280	27	26	ameri	ameri	PROPN
ejpam-3280	27	27	)	)	PUNCT
ejpam-3280	27	28	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3280	28	1	118	118	NUM
ejpam-3280	28	2	c	c	X
ejpam-3280	28	3	©	©	PROPN
ejpam-3280	28	4	2019	2019	NUM
ejpam-3280	28	5	ejpam	ejpam	NOUN
ejpam-3280	28	6	all	all	DET
ejpam-3280	28	7	rights	right	NOUN
ejpam-3280	28	8	reserved	reserve	VERB
ejpam-3280	28	9	.	.	PUNCT
ejpam-3280	29	1	e.	e.	PROPN
ejpam-3280	29	2	ranjbar	ranjbar	PROPN
ejpam-3280	29	3	-	-	PUNCT
ejpam-3280	29	4	yanehsari	yanehsari	NOUN
ejpam-3280	29	5	,	,	PUNCT
ejpam-3280	29	6	m.	m.	NOUN
ejpam-3280	29	7	asghari	asghari	ADJ
ejpam-3280	29	8	-	-	PUNCT
ejpam-3280	29	9	larimi	larimi	PROPN
ejpam-3280	29	10	,	,	PUNCT
ejpam-3280	29	11	r.	r.	PROPN
ejpam-3280	29	12	ameri	ameri	PROPN
ejpam-3280	29	13	/	/	SYM
ejpam-3280	29	14	eur	eur	PROPN
ejpam-3280	29	15	.	.	PUNCT
ejpam-3280	30	1	j.	j.	PROPN
ejpam-3280	30	2	pure	pure	PROPN
ejpam-3280	30	3	appl	appl	PROPN
ejpam-3280	30	4	.	.	PROPN
ejpam-3280	30	5	math	math	PROPN
ejpam-3280	30	6	,	,	PUNCT
ejpam-3280	30	7	12	12	NUM
ejpam-3280	30	8	(	(	PUNCT
ejpam-3280	30	9	1	1	NUM
ejpam-3280	30	10	)	)	PUNCT
ejpam-3280	30	11	(	(	PUNCT
ejpam-3280	30	12	2019	2019	NUM
ejpam-3280	30	13	)	)	PUNCT
ejpam-3280	30	14	,	,	PUNCT
ejpam-3280	30	15	118	118	NUM
ejpam-3280	30	16	-	-	SYM
ejpam-3280	30	17	134	134	NUM
ejpam-3280	30	18	119	119	NUM
ejpam-3280	30	19	in	in	ADP
ejpam-3280	30	20	this	this	DET
ejpam-3280	30	21	paper	paper	NOUN
ejpam-3280	30	22	,	,	PUNCT
ejpam-3280	30	23	applying	apply	VERB
ejpam-3280	30	24	the	the	DET
ejpam-3280	30	25	notions	notion	NOUN
ejpam-3280	30	26	of	of	ADP
ejpam-3280	30	27	soft	soft	ADJ
ejpam-3280	30	28	sets	set	NOUN
ejpam-3280	30	29	and	and	CCONJ
ejpam-3280	30	30	fuzzy	fuzzy	ADJ
ejpam-3280	30	31	soft	soft	ADJ
ejpam-3280	30	32	sets	set	NOUN
ejpam-3280	30	33	to	to	ADP
ejpam-3280	30	34	the	the	DET
ejpam-3280	30	35	theory	theory	NOUN
ejpam-3280	30	36	of	of	ADP
ejpam-3280	30	37	hypervector	hypervector	NOUN
ejpam-3280	30	38	spaces	space	NOUN
ejpam-3280	30	39	,	,	PUNCT
ejpam-3280	30	40	we	we	PRON
ejpam-3280	30	41	introduce	introduce	VERB
ejpam-3280	30	42	soft	soft	ADJ
ejpam-3280	30	43	hypervector	hypervector	NOUN
ejpam-3280	30	44	spaces	space	NOUN
ejpam-3280	30	45	and	and	CCONJ
ejpam-3280	30	46	fuzzy	fuzzy	ADJ
ejpam-3280	30	47	soft	soft	ADJ
ejpam-3280	30	48	set	set	NOUN
ejpam-3280	30	49	to	to	ADP
ejpam-3280	30	50	hypervector	hypervector	NOUN
ejpam-3280	30	51	spaces	space	NOUN
ejpam-3280	30	52	,	,	PUNCT
ejpam-3280	30	53	and	and	CCONJ
ejpam-3280	30	54	study	study	VERB
ejpam-3280	30	55	some	some	DET
ejpam-3280	30	56	properties	property	NOUN
ejpam-3280	30	57	of	of	ADP
ejpam-3280	30	58	them	they	PRON
ejpam-3280	30	59	.	.	PUNCT
ejpam-3280	31	1	2	2	X
ejpam-3280	31	2	.	.	NUM
ejpam-3280	31	3	preliminaries	preliminary	NOUN
ejpam-3280	31	4	in	in	ADP
ejpam-3280	31	5	this	this	DET
ejpam-3280	31	6	section	section	NOUN
ejpam-3280	31	7	,	,	PUNCT
ejpam-3280	31	8	some	some	DET
ejpam-3280	31	9	definitions	definition	NOUN
ejpam-3280	31	10	and	and	CCONJ
ejpam-3280	31	11	various	various	ADJ
ejpam-3280	31	12	results	result	NOUN
ejpam-3280	31	13	of	of	ADP
ejpam-3280	31	14	hyperstructure	hyperstructure	NOUN
ejpam-3280	31	15	,	,	PUNCT
ejpam-3280	31	16	fuzzy	fuzzy	ADJ
ejpam-3280	31	17	sets	set	NOUN
ejpam-3280	31	18	and	and	CCONJ
ejpam-3280	31	19	soft	soft	ADJ
ejpam-3280	31	20	sets	set	NOUN
ejpam-3280	31	21	are	be	AUX
ejpam-3280	31	22	presented	present	VERB
ejpam-3280	31	23	.	.	PUNCT
ejpam-3280	32	1	a	a	DET
ejpam-3280	32	2	hyperstructure	hyperstructure	NOUN
ejpam-3280	32	3	is	be	AUX
ejpam-3280	32	4	a	a	DET
ejpam-3280	32	5	non	non	ADJ
ejpam-3280	32	6	-	-	ADJ
ejpam-3280	32	7	empty	empty	ADJ
ejpam-3280	32	8	set	set	ADJ
ejpam-3280	32	9	h	h	NOUN
ejpam-3280	32	10	together	together	ADV
ejpam-3280	32	11	with	with	ADP
ejpam-3280	32	12	a	a	DET
ejpam-3280	32	13	mapping	mapping	NOUN
ejpam-3280	32	14	◦	◦	NOUN
ejpam-3280	32	15	:	:	PUNCT
ejpam-3280	32	16	h	h	NOUN
ejpam-3280	32	17	×h	×h	PROPN
ejpam-3280	33	1	→	→	PUNCT
ejpam-3280	33	2	p	p	PROPN
ejpam-3280	33	3	∗(h	∗(h	PROPN
ejpam-3280	33	4	)	)	PUNCT
ejpam-3280	33	5	,	,	PUNCT
ejpam-3280	33	6	where	where	SCONJ
ejpam-3280	33	7	p	p	PROPN
ejpam-3280	33	8	∗(h	∗(h	PROPN
ejpam-3280	33	9	)	)	PUNCT
ejpam-3280	33	10	is	be	AUX
ejpam-3280	33	11	the	the	DET
ejpam-3280	33	12	set	set	NOUN
ejpam-3280	33	13	of	of	ADP
ejpam-3280	33	14	all	all	DET
ejpam-3280	33	15	the	the	DET
ejpam-3280	33	16	non	non	ADJ
ejpam-3280	33	17	-	-	ADJ
ejpam-3280	33	18	empty	empty	ADJ
ejpam-3280	33	19	subsets	subset	NOUN
ejpam-3280	33	20	of	of	ADP
ejpam-3280	33	21	h.	h.	NOUN
ejpam-3280	34	1	if	if	SCONJ
ejpam-3280	34	2	x	x	SYM
ejpam-3280	34	3	∈	∈	PROPN
ejpam-3280	34	4	h	h	NOUN
ejpam-3280	34	5	and	and	CCONJ
ejpam-3280	34	6	a	a	DET
ejpam-3280	34	7	,	,	PUNCT
ejpam-3280	34	8	b	b	PROPN
ejpam-3280	34	9	∈	∈	PROPN
ejpam-3280	34	10	p	p	PROPN
ejpam-3280	34	11	∗(h	∗(h	PROPN
ejpam-3280	34	12	)	)	PUNCT
ejpam-3280	34	13	,	,	PUNCT
ejpam-3280	34	14	then	then	ADV
ejpam-3280	34	15	by	by	ADP
ejpam-3280	34	16	a	a	DET
ejpam-3280	34	17	◦	◦	NOUN
ejpam-3280	34	18	b	b	NOUN
ejpam-3280	34	19	,	,	PUNCT
ejpam-3280	34	20	a	a	DET
ejpam-3280	34	21	◦	◦	NOUN
ejpam-3280	34	22	x	x	PUNCT
ejpam-3280	34	23	and	and	CCONJ
ejpam-3280	34	24	x	x	PART
ejpam-3280	34	25	◦	◦	NOUN
ejpam-3280	34	26	b	b	NUM
ejpam-3280	34	27	,	,	PUNCT
ejpam-3280	34	28	we	we	PRON
ejpam-3280	34	29	mean	mean	VERB
ejpam-3280	34	30	a	a	DET
ejpam-3280	34	31	◦	◦	NOUN
ejpam-3280	34	32	b	b	NOUN
ejpam-3280	34	33	=	=	PUNCT
ejpam-3280	34	34	⋃	⋃	NOUN
ejpam-3280	34	35	a∈a	a∈a	ADJ
ejpam-3280	34	36	,	,	PUNCT
ejpam-3280	34	37	b∈b	b∈b	VERB
ejpam-3280	34	38	a	a	DET
ejpam-3280	34	39	◦	◦	NOUN
ejpam-3280	34	40	b	b	NOUN
ejpam-3280	34	41	,	,	PUNCT
ejpam-3280	34	42	a	a	DET
ejpam-3280	34	43	◦	◦	NOUN
ejpam-3280	34	44	x	x	X
ejpam-3280	34	45	=	=	PUNCT
ejpam-3280	34	46	a	a	DET
ejpam-3280	34	47	◦	◦	NOUN
ejpam-3280	34	48	{	{	PUNCT
ejpam-3280	34	49	x	x	NOUN
ejpam-3280	34	50	}	}	PUNCT
ejpam-3280	34	51	and	and	CCONJ
ejpam-3280	34	52	x	x	PART
ejpam-3280	34	53	◦	◦	NOUN
ejpam-3280	34	54	b	b	NOUN
ejpam-3280	34	55	=	=	SYM
ejpam-3280	34	56	{	{	PUNCT
ejpam-3280	34	57	x	x	NOUN
ejpam-3280	34	58	}	}	PUNCT
ejpam-3280	34	59	◦	◦	NOUN
ejpam-3280	34	60	b	b	NOUN
ejpam-3280	34	61	,	,	PUNCT
ejpam-3280	34	62	respectively	respectively	ADV
ejpam-3280	34	63	.	.	PUNCT
ejpam-3280	35	1	definition	definition	NOUN
ejpam-3280	35	2	1	1	NUM
ejpam-3280	35	3	.	.	PUNCT
ejpam-3280	36	1	[	[	X
ejpam-3280	36	2	21	21	NUM
ejpam-3280	36	3	]	]	X
ejpam-3280	36	4	let	let	VERB
ejpam-3280	36	5	k	k	PRON
ejpam-3280	36	6	be	be	AUX
ejpam-3280	36	7	a	a	DET
ejpam-3280	36	8	field	field	NOUN
ejpam-3280	36	9	and	and	CCONJ
ejpam-3280	36	10	(	(	PUNCT
ejpam-3280	36	11	v,+	v,+	NUM
ejpam-3280	36	12	)	)	PUNCT
ejpam-3280	36	13	be	be	AUX
ejpam-3280	36	14	an	an	DET
ejpam-3280	36	15	abelian	abelian	ADJ
ejpam-3280	36	16	group	group	NOUN
ejpam-3280	36	17	.	.	PUNCT
ejpam-3280	37	1	a	a	DET
ejpam-3280	37	2	hypervector	hypervector	NOUN
ejpam-3280	37	3	space	space	NOUN
ejpam-3280	37	4	over	over	ADP
ejpam-3280	37	5	k	k	PROPN
ejpam-3280	37	6	is	be	AUX
ejpam-3280	37	7	defined	define	VERB
ejpam-3280	37	8	to	to	PART
ejpam-3280	37	9	be	be	AUX
ejpam-3280	37	10	the	the	DET
ejpam-3280	37	11	quadraple	quadraple	NOUN
ejpam-3280	37	12	(	(	PUNCT
ejpam-3280	37	13	v,+	v,+	NUM
ejpam-3280	37	14	,	,	PUNCT
ejpam-3280	37	15	◦	◦	NOUN
ejpam-3280	37	16	,	,	PUNCT
ejpam-3280	37	17	k	k	NOUN
ejpam-3280	37	18	)	)	PUNCT
ejpam-3280	37	19	,	,	PUNCT
ejpam-3280	37	20	where	where	SCONJ
ejpam-3280	37	21	“	"	PUNCT
ejpam-3280	37	22	◦	◦	NOUN
ejpam-3280	37	23	”	"	PUNCT
ejpam-3280	37	24	is	be	AUX
ejpam-3280	37	25	a	a	DET
ejpam-3280	37	26	mapping	mapping	NOUN
ejpam-3280	37	27	◦	◦	NOUN
ejpam-3280	37	28	:	:	PUNCT
ejpam-3280	37	29	k	k	X
ejpam-3280	37	30	×	×	PROPN
ejpam-3280	37	31	v	v	INTJ
ejpam-3280	37	32	→	→	SYM
ejpam-3280	37	33	p	p	NOUN
ejpam-3280	37	34	∗(v	∗(v	NOUN
ejpam-3280	37	35	)	)	PUNCT
ejpam-3280	37	36	such	such	ADJ
ejpam-3280	37	37	that	that	PRON
ejpam-3280	37	38	for	for	SCONJ
ejpam-3280	37	39	all	all	DET
ejpam-3280	37	40	a	a	DET
ejpam-3280	37	41	,	,	PUNCT
ejpam-3280	37	42	b	b	PROPN
ejpam-3280	37	43	∈	∈	PROPN
ejpam-3280	37	44	k	k	PROPN
ejpam-3280	37	45	and	and	CCONJ
ejpam-3280	37	46	x	x	PROPN
ejpam-3280	37	47	,	,	PUNCT
ejpam-3280	37	48	y	y	PROPN
ejpam-3280	37	49	∈	∈	PROPN
ejpam-3280	37	50	v	v	ADP
ejpam-3280	37	51	the	the	DET
ejpam-3280	37	52	following	follow	VERB
ejpam-3280	37	53	conditions	condition	NOUN
ejpam-3280	37	54	hold	hold	VERB
ejpam-3280	37	55	:	:	PUNCT
ejpam-3280	37	56	(	(	PUNCT
ejpam-3280	37	57	i	i	NOUN
ejpam-3280	37	58	)	)	PUNCT
ejpam-3280	37	59	a	a	DET
ejpam-3280	37	60	◦	◦	NOUN
ejpam-3280	37	61	(	(	PUNCT
ejpam-3280	37	62	x+	x+	ADJ
ejpam-3280	37	63	y	y	NOUN
ejpam-3280	37	64	)	)	PUNCT
ejpam-3280	38	1	⊆	⊆	PROPN
ejpam-3280	38	2	a	a	DET
ejpam-3280	38	3	◦	◦	NOUN
ejpam-3280	38	4	x+	x+	PUNCT
ejpam-3280	38	5	a	a	DET
ejpam-3280	38	6	◦	◦	NOUN
ejpam-3280	38	7	y	y	PROPN
ejpam-3280	38	8	(	(	PUNCT
ejpam-3280	38	9	ii	ii	PROPN
ejpam-3280	38	10	)	)	PUNCT
ejpam-3280	38	11	(	(	PUNCT
ejpam-3280	38	12	a+	a+	PUNCT
ejpam-3280	38	13	b	b	X
ejpam-3280	38	14	)	)	PUNCT
ejpam-3280	38	15	◦	◦	NOUN
ejpam-3280	38	16	x	x	SYM
ejpam-3280	38	17	⊆	⊆	NUM
ejpam-3280	38	18	a	a	DET
ejpam-3280	38	19	◦	◦	NOUN
ejpam-3280	38	20	x+	x+	X
ejpam-3280	38	21	b	b	X
ejpam-3280	38	22	◦	◦	NOUN
ejpam-3280	38	23	y	y	PROPN
ejpam-3280	38	24	(	(	PUNCT
ejpam-3280	38	25	iii	iii	PROPN
ejpam-3280	38	26	)	)	PUNCT
ejpam-3280	38	27	a	a	DET
ejpam-3280	38	28	◦	◦	NOUN
ejpam-3280	38	29	(	(	PUNCT
ejpam-3280	38	30	b	b	X
ejpam-3280	38	31	◦	◦	NOUN
ejpam-3280	38	32	x	x	NOUN
ejpam-3280	38	33	)	)	PUNCT
ejpam-3280	38	34	=	=	SYM
ejpam-3280	38	35	(	(	PUNCT
ejpam-3280	38	36	ab	ab	NOUN
ejpam-3280	38	37	)	)	PUNCT
ejpam-3280	38	38	◦	◦	NOUN
ejpam-3280	38	39	x	x	SYM
ejpam-3280	38	40	(	(	PUNCT
ejpam-3280	38	41	iv	iv	X
ejpam-3280	38	42	)	)	PUNCT
ejpam-3280	38	43	a	a	DET
ejpam-3280	38	44	◦	◦	NOUN
ejpam-3280	38	45	(	(	PUNCT
ejpam-3280	38	46	−x	−x	NOUN
ejpam-3280	38	47	)	)	PUNCT
ejpam-3280	38	48	=	=	PUNCT
ejpam-3280	38	49	(	(	PUNCT
ejpam-3280	38	50	−a	−a	ADJ
ejpam-3280	38	51	)	)	PUNCT
ejpam-3280	38	52	◦	◦	NOUN
ejpam-3280	38	53	x	x	X
ejpam-3280	38	54	=	=	SYM
ejpam-3280	38	55	−(a	−(a	ADJ
ejpam-3280	38	56	◦	◦	NOUN
ejpam-3280	38	57	x	x	X
ejpam-3280	38	58	)	)	PUNCT
ejpam-3280	38	59	(	(	PUNCT
ejpam-3280	38	60	v	v	NOUN
ejpam-3280	38	61	)	)	PUNCT
ejpam-3280	38	62	x	x	SYM
ejpam-3280	38	63	∈	∈	PROPN
ejpam-3280	38	64	1	1	NUM
ejpam-3280	38	65	◦	◦	NOUN
ejpam-3280	38	66	x.	x.	NOUN
ejpam-3280	38	67	v	v	NOUN
ejpam-3280	38	68	is	be	AUX
ejpam-3280	38	69	said	say	VERB
ejpam-3280	38	70	to	to	PART
ejpam-3280	38	71	be	be	AUX
ejpam-3280	38	72	anti	anti	ADJ
ejpam-3280	38	73	-	-	ADJ
ejpam-3280	38	74	left	left	ADJ
ejpam-3280	38	75	distributive	distributive	ADJ
ejpam-3280	38	76	if	if	SCONJ
ejpam-3280	38	77	it	it	PRON
ejpam-3280	38	78	satisfies	satisfy	VERB
ejpam-3280	38	79	the	the	DET
ejpam-3280	38	80	following	follow	VERB
ejpam-3280	38	81	condition	condition	NOUN
ejpam-3280	38	82	:	:	PUNCT
ejpam-3280	38	83	∀a	∀a	NOUN
ejpam-3280	38	84	,	,	PUNCT
ejpam-3280	38	85	b	b	X
ejpam-3280	38	86	∈	∈	PROPN
ejpam-3280	38	87	k	k	NOUN
ejpam-3280	38	88	,	,	PUNCT
ejpam-3280	38	89	∀x	∀x	X
ejpam-3280	38	90	∈	∈	PROPN
ejpam-3280	38	91	v	v	NOUN
ejpam-3280	38	92	,	,	PUNCT
ejpam-3280	38	93	(	(	PUNCT
ejpam-3280	38	94	a+	a+	X
ejpam-3280	38	95	b	b	X
ejpam-3280	38	96	)	)	PUNCT
ejpam-3280	38	97	◦	◦	NOUN
ejpam-3280	38	98	x	x	SYM
ejpam-3280	38	99	⊇	⊇	NOUN
ejpam-3280	38	100	a	a	DET
ejpam-3280	38	101	◦	◦	NOUN
ejpam-3280	38	102	x+	x+	X
ejpam-3280	38	103	b	b	X
ejpam-3280	38	104	◦	◦	NOUN
ejpam-3280	38	105	x	x	NOUN
ejpam-3280	38	106	,	,	PUNCT
ejpam-3280	38	107	and	and	CCONJ
ejpam-3280	38	108	strongly	strongly	ADV
ejpam-3280	38	109	left	leave	VERB
ejpam-3280	38	110	distributive	distributive	ADJ
ejpam-3280	38	111	,	,	PUNCT
ejpam-3280	38	112	if	if	SCONJ
ejpam-3280	38	113	∀a	∀a	NOUN
ejpam-3280	38	114	,	,	PUNCT
ejpam-3280	39	1	b	b	PROPN
ejpam-3280	39	2	∈	∈	PROPN
ejpam-3280	39	3	k	k	NOUN
ejpam-3280	39	4	,	,	PUNCT
ejpam-3280	39	5	∀x	∀x	X
ejpam-3280	39	6	∈	∈	PROPN
ejpam-3280	39	7	v	v	NOUN
ejpam-3280	39	8	,	,	PUNCT
ejpam-3280	39	9	(	(	PUNCT
ejpam-3280	39	10	a+	a+	X
ejpam-3280	39	11	b	b	X
ejpam-3280	39	12	)	)	PUNCT
ejpam-3280	39	13	◦	◦	NOUN
ejpam-3280	39	14	x	x	X
ejpam-3280	39	15	=	=	PUNCT
ejpam-3280	39	16	a	a	DET
ejpam-3280	39	17	◦	◦	NOUN
ejpam-3280	39	18	x+	x+	X
ejpam-3280	39	19	b	b	X
ejpam-3280	39	20	◦	◦	NOUN
ejpam-3280	39	21	x	x	SYM
ejpam-3280	39	22	in	in	ADP
ejpam-3280	39	23	similar	similar	ADJ
ejpam-3280	39	24	way	way	NOUN
ejpam-3280	39	25	,	,	PUNCT
ejpam-3280	39	26	the	the	DET
ejpam-3280	39	27	anti	anti	ADJ
ejpam-3280	39	28	right	right	NOUN
ejpam-3280	39	29	distributive	distributive	ADJ
ejpam-3280	39	30	and	and	CCONJ
ejpam-3280	39	31	strongly	strongly	ADV
ejpam-3280	39	32	right	right	ADJ
ejpam-3280	39	33	distributive	distributive	ADJ
ejpam-3280	39	34	hypervector	hypervector	NOUN
ejpam-3280	39	35	space	space	NOUN
ejpam-3280	39	36	are	be	AUX
ejpam-3280	39	37	defined	define	VERB
ejpam-3280	39	38	,	,	PUNCT
ejpam-3280	39	39	respectively	respectively	ADV
ejpam-3280	39	40	.	.	PUNCT
ejpam-3280	40	1	v	v	NOUN
ejpam-3280	40	2	is	be	AUX
ejpam-3280	40	3	called	call	VERB
ejpam-3280	40	4	strongly	strongly	ADV
ejpam-3280	40	5	distributive	distributive	ADJ
ejpam-3280	40	6	if	if	SCONJ
ejpam-3280	40	7	it	it	PRON
ejpam-3280	40	8	is	be	AUX
ejpam-3280	40	9	both	both	PRON
ejpam-3280	40	10	strongly	strongly	ADV
ejpam-3280	40	11	left	left	ADJ
ejpam-3280	40	12	and	and	CCONJ
ejpam-3280	40	13	strongly	strongly	ADV
ejpam-3280	40	14	right	right	ADJ
ejpam-3280	40	15	distributive	distributive	ADJ
ejpam-3280	40	16	.	.	PUNCT
ejpam-3280	40	17	example	example	NOUN
ejpam-3280	41	1	1	1	NUM
ejpam-3280	41	2	.	.	PUNCT
ejpam-3280	42	1	let	let	VERB
ejpam-3280	42	2	v	v	VERB
ejpam-3280	42	3	=	=	SYM
ejpam-3280	42	4	m2×2(r	m2×2(r	NOUN
ejpam-3280	42	5	)	)	PUNCT
ejpam-3280	42	6	and	and	CCONJ
ejpam-3280	42	7	w	w	NOUN
ejpam-3280	42	8	=	=	PUNCT
ejpam-3280	42	9	{	{	PUNCT
ejpam-3280	42	10	[	[	X
ejpam-3280	42	11	a	a	PRON
ejpam-3280	42	12	0	0	NUM
ejpam-3280	42	13	0	0	NUM
ejpam-3280	42	14	b	b	NOUN
ejpam-3280	42	15	]	]	X
ejpam-3280	42	16	:	:	PUNCT
ejpam-3280	42	17	a	a	PRON
ejpam-3280	42	18	,	,	PUNCT
ejpam-3280	42	19	b	b	X
ejpam-3280	42	20	∈	∈	PROPN
ejpam-3280	42	21	r	r	NOUN
ejpam-3280	42	22	}	}	PUNCT
ejpam-3280	42	23	and	and	CCONJ
ejpam-3280	42	24	◦	◦	NOUN
ejpam-3280	42	25	:	:	PUNCT
ejpam-3280	42	26	r×	r×	NOUN
ejpam-3280	42	27	v	v	NOUN
ejpam-3280	42	28	→	→	SYM
ejpam-3280	42	29	p	p	NOUN
ejpam-3280	42	30	∗(v	∗(v	NOUN
ejpam-3280	42	31	)	)	PUNCT
ejpam-3280	43	1	∀r	∀r	X
ejpam-3280	43	2	∈	∈	NOUN
ejpam-3280	43	3	r	r	NOUN
ejpam-3280	43	4	,	,	PUNCT
ejpam-3280	43	5	∀	∀	X
ejpam-3280	43	6	[	[	PUNCT
ejpam-3280	43	7	a	a	PRON
ejpam-3280	43	8	b	b	NOUN
ejpam-3280	43	9	c	c	NOUN
ejpam-3280	43	10	d	d	X
ejpam-3280	43	11	]	]	X
ejpam-3280	43	12	∈	∈	PROPN
ejpam-3280	43	13	v	v	NOUN
ejpam-3280	43	14	:	:	PUNCT
ejpam-3280	43	15	r	r	NOUN
ejpam-3280	43	16	◦	◦	NOUN
ejpam-3280	43	17	[	[	PUNCT
ejpam-3280	43	18	a	a	DET
ejpam-3280	43	19	b	b	NOUN
ejpam-3280	43	20	c	c	NOUN
ejpam-3280	43	21	d	d	X
ejpam-3280	43	22	]	]	X
ejpam-3280	44	1	=	=	PUNCT
ejpam-3280	44	2	[	[	PUNCT
ejpam-3280	44	3	0	0	NUM
ejpam-3280	44	4	rb	rb	PROPN
ejpam-3280	44	5	rc	rc	PROPN
ejpam-3280	44	6	0	0	NUM
ejpam-3280	44	7	]	]	PUNCT
ejpam-3280	45	1	+	+	X
ejpam-3280	45	2	w	w	ADJ
ejpam-3280	45	3	then	then	ADV
ejpam-3280	45	4	(	(	PUNCT
ejpam-3280	45	5	v,+	v,+	NUM
ejpam-3280	45	6	,	,	PUNCT
ejpam-3280	45	7	◦	◦	NOUN
ejpam-3280	45	8	,	,	PUNCT
ejpam-3280	45	9	r	r	NOUN
ejpam-3280	45	10	)	)	PUNCT
ejpam-3280	45	11	is	be	AUX
ejpam-3280	45	12	a	a	DET
ejpam-3280	45	13	strongly	strongly	ADV
ejpam-3280	45	14	distributive	distributive	ADJ
ejpam-3280	45	15	hypervector	hypervector	NOUN
ejpam-3280	45	16	space	space	NOUN
ejpam-3280	45	17	.	.	PUNCT
ejpam-3280	46	1	definition	definition	NOUN
ejpam-3280	46	2	2	2	NUM
ejpam-3280	46	3	.	.	PUNCT
ejpam-3280	47	1	[	[	X
ejpam-3280	47	2	19	19	NUM
ejpam-3280	47	3	]	]	PUNCT
ejpam-3280	47	4	a	a	DET
ejpam-3280	47	5	non	non	ADJ
ejpam-3280	47	6	-	-	ADJ
ejpam-3280	47	7	empty	empty	ADJ
ejpam-3280	47	8	subset	subset	NOUN
ejpam-3280	47	9	w	w	NOUN
ejpam-3280	47	10	of	of	ADP
ejpam-3280	47	11	v	v	NOUN
ejpam-3280	47	12	is	be	AUX
ejpam-3280	47	13	a	a	DET
ejpam-3280	47	14	sub	sub	ADJ
ejpam-3280	47	15	-	-	ADJ
ejpam-3280	47	16	hypervector	hypervector	ADJ
ejpam-3280	47	17	space	space	NOUN
ejpam-3280	47	18	if	if	SCONJ
ejpam-3280	47	19	w	w	NOUN
ejpam-3280	47	20	is	be	AUX
ejpam-3280	47	21	itself	itself	PRON
ejpam-3280	47	22	a	a	DET
ejpam-3280	47	23	hypervector	hypervector	NOUN
ejpam-3280	47	24	space	space	NOUN
ejpam-3280	47	25	with	with	ADP
ejpam-3280	47	26	the	the	DET
ejpam-3280	47	27	hyperoperation	hyperoperation	NOUN
ejpam-3280	47	28	on	on	ADP
ejpam-3280	47	29	v	v	NUM
ejpam-3280	47	30	,	,	PUNCT
ejpam-3280	47	31	i.e	i.e	PROPN
ejpam-3280	47	32	,	,	PUNCT
ejpam-3280	47	33	e.	e.	PROPN
ejpam-3280	47	34	ranjbar	ranjbar	PROPN
ejpam-3280	47	35	-	-	PUNCT
ejpam-3280	47	36	yanehsari	yanehsari	NOUN
ejpam-3280	47	37	,	,	PUNCT
ejpam-3280	47	38	m.	m.	NOUN
ejpam-3280	47	39	asghari	asghari	ADJ
ejpam-3280	47	40	-	-	PUNCT
ejpam-3280	47	41	larimi	larimi	PROPN
ejpam-3280	47	42	,	,	PUNCT
ejpam-3280	47	43	r.	r.	PROPN
ejpam-3280	47	44	ameri	ameri	PROPN
ejpam-3280	47	45	/	/	SYM
ejpam-3280	47	46	eur	eur	PROPN
ejpam-3280	47	47	.	.	PUNCT
ejpam-3280	48	1	j.	j.	PROPN
ejpam-3280	48	2	pure	pure	PROPN
ejpam-3280	48	3	appl	appl	PROPN
ejpam-3280	48	4	.	.	PROPN
ejpam-3280	48	5	math	math	PROPN
ejpam-3280	48	6	,	,	PUNCT
ejpam-3280	48	7	12	12	NUM
ejpam-3280	48	8	(	(	PUNCT
ejpam-3280	48	9	1	1	NUM
ejpam-3280	48	10	)	)	PUNCT
ejpam-3280	48	11	(	(	PUNCT
ejpam-3280	48	12	2019	2019	NUM
ejpam-3280	48	13	)	)	PUNCT
ejpam-3280	48	14	,	,	PUNCT
ejpam-3280	48	15	118	118	NUM
ejpam-3280	48	16	-	-	SYM
ejpam-3280	48	17	134	134	NUM
ejpam-3280	48	18	120	120	NUM
ejpam-3280	48	19	(	(	PUNCT
ejpam-3280	48	20	i	i	NOUN
ejpam-3280	48	21	)	)	PUNCT
ejpam-3280	48	22	w	w	PROPN
ejpam-3280	48	23	6=	6=	ADP
ejpam-3280	48	24	∅	∅	NOUN
ejpam-3280	48	25	(	(	PUNCT
ejpam-3280	48	26	ii	ii	NOUN
ejpam-3280	48	27	)	)	PUNCT
ejpam-3280	48	28	x	x	NOUN
ejpam-3280	48	29	,	,	PUNCT
ejpam-3280	48	30	y	y	PROPN
ejpam-3280	48	31	∈w	∈w	VERB
ejpam-3280	48	32	⇒	⇒	NOUN
ejpam-3280	48	33	x−	x−	PROPN
ejpam-3280	49	1	y	y	PROPN
ejpam-3280	49	2	∈w	∈w	PROPN
ejpam-3280	49	3	(	(	PUNCT
ejpam-3280	49	4	iii	iii	NOUN
ejpam-3280	49	5	)	)	PUNCT
ejpam-3280	49	6	a	a	DET
ejpam-3280	49	7	∈	∈	PROPN
ejpam-3280	49	8	k	k	NOUN
ejpam-3280	49	9	,	,	PUNCT
ejpam-3280	49	10	x	x	PART
ejpam-3280	49	11	∈w	∈w	VERB
ejpam-3280	49	12	⇒	⇒	NOUN
ejpam-3280	49	13	a	a	DET
ejpam-3280	49	14	◦	◦	NOUN
ejpam-3280	49	15	x	x	SYM
ejpam-3280	49	16	⊆w	⊆w	NOUN
ejpam-3280	49	17	in	in	ADP
ejpam-3280	49	18	this	this	DET
ejpam-3280	49	19	case	case	NOUN
ejpam-3280	49	20	,	,	PUNCT
ejpam-3280	49	21	we	we	PRON
ejpam-3280	49	22	write	write	VERB
ejpam-3280	49	23	w	w	PROPN
ejpam-3280	49	24	≤	≤	NUM
ejpam-3280	49	25	v	v	NOUN
ejpam-3280	49	26	.	.	PUNCT
ejpam-3280	50	1	where	where	SCONJ
ejpam-3280	50	2	fs(x	fs(x	NOUN
ejpam-3280	50	3	)	)	PUNCT
ejpam-3280	50	4	is	be	AUX
ejpam-3280	50	5	the	the	DET
ejpam-3280	50	6	set	set	NOUN
ejpam-3280	50	7	of	of	ADP
ejpam-3280	50	8	all	all	DET
ejpam-3280	50	9	fuzzy	fuzzy	ADJ
ejpam-3280	50	10	subset	subset	NOUN
ejpam-3280	50	11	of	of	ADP
ejpam-3280	50	12	x.	x.	NOUN
ejpam-3280	50	13	definition	definition	NOUN
ejpam-3280	50	14	3	3	NUM
ejpam-3280	50	15	.	.	PUNCT
ejpam-3280	51	1	[	[	X
ejpam-3280	51	2	19	19	NUM
ejpam-3280	51	3	]	]	X
ejpam-3280	51	4	let	let	VERB
ejpam-3280	51	5	f	f	PRON
ejpam-3280	51	6	:	:	PUNCT
ejpam-3280	51	7	x	x	X
ejpam-3280	51	8	→	→	SYM
ejpam-3280	51	9	y	y	X
ejpam-3280	51	10	be	be	AUX
ejpam-3280	51	11	a	a	DET
ejpam-3280	51	12	mapping	mapping	NOUN
ejpam-3280	51	13	and	and	CCONJ
ejpam-3280	51	14	let	let	VERB
ejpam-3280	51	15	µ	µ	PRON
ejpam-3280	51	16	∈	∈	PROPN
ejpam-3280	51	17	fs(x	fs(x	NOUN
ejpam-3280	51	18	)	)	PUNCT
ejpam-3280	51	19	and	and	CCONJ
ejpam-3280	51	20	ν	ν	X
ejpam-3280	51	21	∈	∈	PROPN
ejpam-3280	51	22	fs(y	fs(y	NUM
ejpam-3280	51	23	)	)	PUNCT
ejpam-3280	51	24	.	.	PUNCT
ejpam-3280	52	1	then	then	ADV
ejpam-3280	52	2	,	,	PUNCT
ejpam-3280	52	3	f(µ	f(µ	ADJ
ejpam-3280	52	4	)	)	PUNCT
ejpam-3280	52	5	∈	∈	NOUN
ejpam-3280	52	6	fs(y	fs(y	PUNCT
ejpam-3280	52	7	)	)	PUNCT
ejpam-3280	52	8	and	and	CCONJ
ejpam-3280	52	9	f−1(ν	f−1(ν	PROPN
ejpam-3280	52	10	)	)	PUNCT
ejpam-3280	52	11	∈	∈	PROPN
ejpam-3280	52	12	fs(x	fs(x	NOUN
ejpam-3280	52	13	)	)	PUNCT
ejpam-3280	52	14	respectively	respectively	ADV
ejpam-3280	52	15	,	,	PUNCT
ejpam-3280	52	16	are	be	AUX
ejpam-3280	52	17	defined	define	VERB
ejpam-3280	52	18	as	as	SCONJ
ejpam-3280	52	19	follows	follow	VERB
ejpam-3280	52	20	:	:	PUNCT
ejpam-3280	52	21	f(µ)(y	f(µ)(y	NUM
ejpam-3280	52	22	)	)	PUNCT
ejpam-3280	52	23	=	=	PRON
ejpam-3280	52	24	{	{	PUNCT
ejpam-3280	52	25	∨	∨	PROPN
ejpam-3280	52	26	x∈f−1(y	x∈f−1(y	NOUN
ejpam-3280	52	27	)	)	PUNCT
ejpam-3280	52	28	µ(x	µ(x	NOUN
ejpam-3280	52	29	)	)	PUNCT
ejpam-3280	52	30	if	if	SCONJ
ejpam-3280	52	31	f−1(y	f−1(y	PROPN
ejpam-3280	52	32	)	)	PUNCT
ejpam-3280	52	33	6=	6=	ADP
ejpam-3280	52	34	∅	∅	NOUN
ejpam-3280	52	35	0	0	NUM
ejpam-3280	53	1	otherwise	otherwise	ADV
ejpam-3280	53	2	.	.	PUNCT
ejpam-3280	54	1	for	for	ADP
ejpam-3280	54	2	all	all	DET
ejpam-3280	54	3	y	y	PROPN
ejpam-3280	54	4	∈	∈	PROPN
ejpam-3280	54	5	y	y	PROPN
ejpam-3280	54	6	and	and	CCONJ
ejpam-3280	54	7	f−1(ν)(x	f−1(ν)(x	PROPN
ejpam-3280	54	8	)	)	PUNCT
ejpam-3280	54	9	=	=	SYM
ejpam-3280	54	10	ν(f(x	ν(f(x	PROPN
ejpam-3280	54	11	)	)	PUNCT
ejpam-3280	54	12	)	)	PUNCT
ejpam-3280	54	13	,	,	PUNCT
ejpam-3280	54	14	for	for	ADP
ejpam-3280	54	15	all	all	PRON
ejpam-3280	54	16	x	x	SYM
ejpam-3280	54	17	∈	∈	NOUN
ejpam-3280	54	18	x.	x.	NOUN
ejpam-3280	54	19	let	let	VERB
ejpam-3280	54	20	u	u	PRON
ejpam-3280	54	21	and	and	CCONJ
ejpam-3280	54	22	e	e	NOUN
ejpam-3280	54	23	be	be	AUX
ejpam-3280	54	24	an	an	DET
ejpam-3280	54	25	initial	initial	ADJ
ejpam-3280	54	26	universe	universe	NOUN
ejpam-3280	54	27	set	set	VERB
ejpam-3280	54	28	and	and	CCONJ
ejpam-3280	54	29	a	a	DET
ejpam-3280	54	30	set	set	NOUN
ejpam-3280	54	31	of	of	ADP
ejpam-3280	54	32	parameters	parameter	NOUN
ejpam-3280	54	33	,	,	PUNCT
ejpam-3280	54	34	respectively	respectively	ADV
ejpam-3280	54	35	.	.	PUNCT
ejpam-3280	55	1	let	let	VERB
ejpam-3280	55	2	p	p	NOUN
ejpam-3280	55	3	(	(	PUNCT
ejpam-3280	55	4	u	u	NOUN
ejpam-3280	55	5	)	)	PUNCT
ejpam-3280	55	6	denote	denote	VERB
ejpam-3280	55	7	the	the	DET
ejpam-3280	55	8	power	power	NOUN
ejpam-3280	55	9	set	set	NOUN
ejpam-3280	55	10	of	of	ADP
ejpam-3280	55	11	u	u	PROPN
ejpam-3280	55	12	and	and	CCONJ
ejpam-3280	55	13	a	a	DET
ejpam-3280	55	14	⊆	⊆	NUM
ejpam-3280	55	15	e	e	NOUN
ejpam-3280	55	16	unless	unless	SCONJ
ejpam-3280	55	17	otherwise	otherwise	ADV
ejpam-3280	55	18	specified	specify	VERB
ejpam-3280	55	19	.	.	PUNCT
ejpam-3280	56	1	molodtsov	molodtsov	PROPN
ejpam-3280	56	2	defined	define	VERB
ejpam-3280	56	3	the	the	DET
ejpam-3280	56	4	notion	notion	NOUN
ejpam-3280	56	5	of	of	ADP
ejpam-3280	56	6	a	a	DET
ejpam-3280	56	7	soft	soft	ADJ
ejpam-3280	56	8	set	set	NOUN
ejpam-3280	56	9	in	in	ADP
ejpam-3280	56	10	the	the	DET
ejpam-3280	56	11	following	following	ADJ
ejpam-3280	56	12	way	way	NOUN
ejpam-3280	56	13	.	.	PUNCT
ejpam-3280	57	1	definition	definition	NOUN
ejpam-3280	57	2	4	4	NUM
ejpam-3280	57	3	.	.	PUNCT
ejpam-3280	58	1	[	[	X
ejpam-3280	58	2	15	15	NUM
ejpam-3280	58	3	]	]	X
ejpam-3280	58	4	a	a	DET
ejpam-3280	58	5	pair	pair	NOUN
ejpam-3280	58	6	(	(	PUNCT
ejpam-3280	58	7	f	f	X
ejpam-3280	58	8	,	,	PUNCT
ejpam-3280	58	9	a	a	PRON
ejpam-3280	58	10	)	)	PUNCT
ejpam-3280	58	11	is	be	AUX
ejpam-3280	58	12	called	call	VERB
ejpam-3280	58	13	a	a	DET
ejpam-3280	58	14	soft	soft	ADJ
ejpam-3280	58	15	set	set	NOUN
ejpam-3280	58	16	over	over	ADP
ejpam-3280	58	17	u	u	NOUN
ejpam-3280	58	18	where	where	SCONJ
ejpam-3280	58	19	f	f	PROPN
ejpam-3280	58	20	is	be	AUX
ejpam-3280	58	21	a	a	DET
ejpam-3280	58	22	mapping	mapping	NOUN
ejpam-3280	58	23	given	give	VERB
ejpam-3280	58	24	by	by	ADP
ejpam-3280	58	25	f	f	PROPN
ejpam-3280	58	26	:	:	PUNCT
ejpam-3280	58	27	a→	a→	PUNCT
ejpam-3280	58	28	p	p	X
ejpam-3280	58	29	(	(	PUNCT
ejpam-3280	58	30	u	u	NOUN
ejpam-3280	58	31	)	)	PUNCT
ejpam-3280	58	32	.	.	PUNCT
ejpam-3280	59	1	in	in	ADP
ejpam-3280	59	2	fact	fact	NOUN
ejpam-3280	59	3	,	,	PUNCT
ejpam-3280	59	4	a	a	DET
ejpam-3280	59	5	soft	soft	ADJ
ejpam-3280	59	6	set	set	NOUN
ejpam-3280	59	7	over	over	ADP
ejpam-3280	59	8	u	u	NOUN
ejpam-3280	59	9	is	be	AUX
ejpam-3280	59	10	a	a	DET
ejpam-3280	59	11	parameterized	parameterized	ADJ
ejpam-3280	59	12	family	family	NOUN
ejpam-3280	59	13	of	of	ADP
ejpam-3280	59	14	subsets	subset	NOUN
ejpam-3280	59	15	of	of	ADP
ejpam-3280	59	16	the	the	DET
ejpam-3280	59	17	universe	universe	ADJ
ejpam-3280	59	18	u	u	NOUN
ejpam-3280	59	19	.	.	PUNCT
ejpam-3280	60	1	for	for	ADP
ejpam-3280	60	2	all	all	DET
ejpam-3280	60	3	a	a	DET
ejpam-3280	60	4	∈	∈	PROPN
ejpam-3280	60	5	a	a	DET
ejpam-3280	60	6	,	,	PUNCT
ejpam-3280	60	7	f(a	f(a	PROPN
ejpam-3280	60	8	)	)	PUNCT
ejpam-3280	60	9	may	may	AUX
ejpam-3280	60	10	be	be	AUX
ejpam-3280	60	11	considered	consider	VERB
ejpam-3280	60	12	as	as	ADP
ejpam-3280	60	13	the	the	DET
ejpam-3280	60	14	set	set	NOUN
ejpam-3280	60	15	of	of	ADP
ejpam-3280	60	16	a	a	DET
ejpam-3280	60	17	-	-	PUNCT
ejpam-3280	60	18	approximate	approximate	ADJ
ejpam-3280	60	19	elements	element	NOUN
ejpam-3280	60	20	of	of	ADP
ejpam-3280	60	21	the	the	DET
ejpam-3280	60	22	soft	soft	ADJ
ejpam-3280	60	23	set	set	NOUN
ejpam-3280	60	24	(	(	PUNCT
ejpam-3280	60	25	f	f	X
ejpam-3280	60	26	,	,	PUNCT
ejpam-3280	60	27	a	a	PRON
ejpam-3280	60	28	)	)	PUNCT
ejpam-3280	60	29	.	.	PUNCT
ejpam-3280	61	1	definition	definition	NOUN
ejpam-3280	61	2	5	5	NUM
ejpam-3280	61	3	.	.	PUNCT
ejpam-3280	62	1	[	[	X
ejpam-3280	62	2	11	11	NUM
ejpam-3280	62	3	]	]	X
ejpam-3280	62	4	let	let	VERB
ejpam-3280	62	5	(	(	PUNCT
ejpam-3280	62	6	f	f	X
ejpam-3280	62	7	,	,	PUNCT
ejpam-3280	62	8	a	a	PRON
ejpam-3280	62	9	)	)	PUNCT
ejpam-3280	62	10	and	and	CCONJ
ejpam-3280	62	11	(	(	PUNCT
ejpam-3280	62	12	g	g	NOUN
ejpam-3280	62	13	,	,	PUNCT
ejpam-3280	62	14	b	b	NOUN
ejpam-3280	62	15	)	)	PUNCT
ejpam-3280	62	16	be	be	AUX
ejpam-3280	62	17	two	two	NUM
ejpam-3280	62	18	soft	soft	ADJ
ejpam-3280	62	19	sets	set	NOUN
ejpam-3280	62	20	over	over	ADP
ejpam-3280	62	21	common	common	ADJ
ejpam-3280	62	22	universe	universe	NOUN
ejpam-3280	62	23	u	u	NOUN
ejpam-3280	62	24	.	.	PUNCT
ejpam-3280	63	1	we	we	PRON
ejpam-3280	63	2	say	say	VERB
ejpam-3280	63	3	that	that	SCONJ
ejpam-3280	63	4	(	(	PUNCT
ejpam-3280	63	5	f	f	X
ejpam-3280	63	6	,	,	PUNCT
ejpam-3280	63	7	a	a	PRON
ejpam-3280	63	8	)	)	PUNCT
ejpam-3280	63	9	is	be	AUX
ejpam-3280	63	10	a	a	DET
ejpam-3280	63	11	soft	soft	ADJ
ejpam-3280	63	12	subset	subset	NOUN
ejpam-3280	63	13	of	of	ADP
ejpam-3280	63	14	(	(	PUNCT
ejpam-3280	63	15	g	g	PROPN
ejpam-3280	63	16	,	,	PUNCT
ejpam-3280	63	17	b	b	NOUN
ejpam-3280	63	18	)	)	PUNCT
ejpam-3280	63	19	if	if	SCONJ
ejpam-3280	63	20	(	(	PUNCT
ejpam-3280	63	21	i	i	NOUN
ejpam-3280	63	22	)	)	PUNCT
ejpam-3280	63	23	a	a	PRON
ejpam-3280	63	24	⊆	⊆	NUM
ejpam-3280	63	25	b	b	PROPN
ejpam-3280	63	26	(	(	PUNCT
ejpam-3280	63	27	ii	ii	NOUN
ejpam-3280	63	28	)	)	PUNCT
ejpam-3280	63	29	a	a	DET
ejpam-3280	63	30	∈	∈	PROPN
ejpam-3280	63	31	a⇒	a⇒	PRON
ejpam-3280	63	32	f(a	f(a	NOUN
ejpam-3280	63	33	)	)	PUNCT
ejpam-3280	63	34	⊆	⊆	NUM
ejpam-3280	63	35	g(a	g(a	PROPN
ejpam-3280	63	36	)	)	PUNCT
ejpam-3280	63	37	.	.	PUNCT
ejpam-3280	64	1	definition	definition	NOUN
ejpam-3280	64	2	6	6	NUM
ejpam-3280	64	3	.	.	PUNCT
ejpam-3280	65	1	[	[	X
ejpam-3280	65	2	11	11	NUM
ejpam-3280	65	3	]	]	X
ejpam-3280	65	4	let	let	VERB
ejpam-3280	65	5	(	(	PUNCT
ejpam-3280	65	6	f	f	X
ejpam-3280	65	7	,	,	PUNCT
ejpam-3280	65	8	a	a	PRON
ejpam-3280	65	9	)	)	PUNCT
ejpam-3280	65	10	and	and	CCONJ
ejpam-3280	65	11	(	(	PUNCT
ejpam-3280	65	12	g	g	NOUN
ejpam-3280	65	13	,	,	PUNCT
ejpam-3280	65	14	b	b	NOUN
ejpam-3280	65	15	)	)	PUNCT
ejpam-3280	65	16	be	be	AUX
ejpam-3280	65	17	two	two	NUM
ejpam-3280	65	18	soft	soft	ADJ
ejpam-3280	65	19	sets	set	NOUN
ejpam-3280	65	20	over	over	ADP
ejpam-3280	65	21	common	common	ADJ
ejpam-3280	65	22	universe	universe	NOUN
ejpam-3280	65	23	u	u	NOUN
ejpam-3280	65	24	.	.	PUNCT
ejpam-3280	66	1	the	the	DET
ejpam-3280	66	2	union	union	NOUN
ejpam-3280	66	3	of	of	ADP
ejpam-3280	66	4	two	two	NUM
ejpam-3280	66	5	soft	soft	ADJ
ejpam-3280	66	6	sets	set	NOUN
ejpam-3280	66	7	(	(	PUNCT
ejpam-3280	66	8	f	f	X
ejpam-3280	66	9	,	,	PUNCT
ejpam-3280	66	10	a	a	PRON
ejpam-3280	66	11	)	)	PUNCT
ejpam-3280	66	12	and	and	CCONJ
ejpam-3280	66	13	(	(	PUNCT
ejpam-3280	66	14	g	g	NOUN
ejpam-3280	66	15	,	,	PUNCT
ejpam-3280	66	16	b	b	NOUN
ejpam-3280	66	17	)	)	PUNCT
ejpam-3280	66	18	is	be	AUX
ejpam-3280	66	19	the	the	DET
ejpam-3280	66	20	soft	soft	ADJ
ejpam-3280	66	21	set	set	NOUN
ejpam-3280	66	22	(	(	PUNCT
ejpam-3280	66	23	h	h	NOUN
ejpam-3280	66	24	,	,	PUNCT
ejpam-3280	66	25	c	c	NOUN
ejpam-3280	66	26	)	)	PUNCT
ejpam-3280	66	27	,	,	PUNCT
ejpam-3280	66	28	where	where	SCONJ
ejpam-3280	66	29	c	c	NOUN
ejpam-3280	66	30	=	=	PUNCT
ejpam-3280	66	31	a	a	DET
ejpam-3280	66	32	∪	∪	X
ejpam-3280	66	33	b	b	NOUN
ejpam-3280	66	34	and	and	CCONJ
ejpam-3280	66	35	h	h	NOUN
ejpam-3280	66	36	is	be	AUX
ejpam-3280	66	37	defined	define	VERB
ejpam-3280	66	38	as	as	SCONJ
ejpam-3280	66	39	follows	follow	VERB
ejpam-3280	66	40	:	:	PUNCT
ejpam-3280	66	41	h(c	h(c	PROPN
ejpam-3280	66	42	)	)	PUNCT
ejpam-3280	66	43	=	=	PUNCT
ejpam-3280	66	44			PUNCT
ejpam-3280	66	45	f(c	f(c	PROPN
ejpam-3280	66	46	)	)	PUNCT
ejpam-3280	66	47	if	if	SCONJ
ejpam-3280	66	48	c	c	PROPN
ejpam-3280	66	49	∈	∈	PROPN
ejpam-3280	66	50	a−b	a−b	NOUN
ejpam-3280	66	51	g(c	g(c	NOUN
ejpam-3280	66	52	)	)	PUNCT
ejpam-3280	66	53	if	if	SCONJ
ejpam-3280	66	54	c	c	PROPN
ejpam-3280	66	55	∈	∈	PROPN
ejpam-3280	66	56	b	b	X
ejpam-3280	66	57	−a	−a	NOUN
ejpam-3280	66	58	f(c	f(c	PROPN
ejpam-3280	66	59	)	)	PUNCT
ejpam-3280	66	60	∪	∪	ADP
ejpam-3280	66	61	g(c	g(c	NOUN
ejpam-3280	66	62	)	)	PUNCT
ejpam-3280	66	63	if	if	SCONJ
ejpam-3280	66	64	c	c	PROPN
ejpam-3280	66	65	∈	∈	PROPN
ejpam-3280	66	66	a	a	DET
ejpam-3280	66	67	∩b	∩b	NOUN
ejpam-3280	66	68	.	.	PUNCT
ejpam-3280	67	1	definition	definition	NOUN
ejpam-3280	67	2	7	7	NUM
ejpam-3280	67	3	.	.	PUNCT
ejpam-3280	68	1	[	[	X
ejpam-3280	68	2	11	11	NUM
ejpam-3280	68	3	]	]	X
ejpam-3280	68	4	let	let	VERB
ejpam-3280	68	5	(	(	PUNCT
ejpam-3280	68	6	f	f	X
ejpam-3280	68	7	,	,	PUNCT
ejpam-3280	68	8	a	a	PRON
ejpam-3280	68	9	)	)	PUNCT
ejpam-3280	68	10	and	and	CCONJ
ejpam-3280	68	11	(	(	PUNCT
ejpam-3280	68	12	g	g	NOUN
ejpam-3280	68	13	,	,	PUNCT
ejpam-3280	68	14	b	b	NOUN
ejpam-3280	68	15	)	)	PUNCT
ejpam-3280	68	16	be	be	AUX
ejpam-3280	68	17	two	two	NUM
ejpam-3280	68	18	soft	soft	ADJ
ejpam-3280	68	19	sets	set	NOUN
ejpam-3280	68	20	over	over	ADP
ejpam-3280	68	21	common	common	ADJ
ejpam-3280	68	22	universe	universe	NOUN
ejpam-3280	68	23	u	u	NOUN
ejpam-3280	68	24	,	,	PUNCT
ejpam-3280	69	1	such	such	ADJ
ejpam-3280	69	2	that	that	SCONJ
ejpam-3280	69	3	a∩b	a∩b	PROPN
ejpam-3280	69	4	6=	6=	ADP
ejpam-3280	69	5	∅.	∅.	VERB
ejpam-3280	69	6	the	the	DET
ejpam-3280	69	7	intersection	intersection	NOUN
ejpam-3280	69	8	of	of	ADP
ejpam-3280	69	9	(	(	PUNCT
ejpam-3280	69	10	f	f	X
ejpam-3280	69	11	,	,	PUNCT
ejpam-3280	69	12	a	a	PRON
ejpam-3280	69	13	)	)	PUNCT
ejpam-3280	69	14	and	and	CCONJ
ejpam-3280	69	15	(	(	PUNCT
ejpam-3280	69	16	g	g	NOUN
ejpam-3280	69	17	,	,	PUNCT
ejpam-3280	69	18	b	b	NOUN
ejpam-3280	69	19	)	)	PUNCT
ejpam-3280	69	20	is	be	AUX
ejpam-3280	69	21	the	the	DET
ejpam-3280	69	22	soft	soft	ADJ
ejpam-3280	69	23	set	set	NOUN
ejpam-3280	69	24	(	(	PUNCT
ejpam-3280	69	25	h	h	NOUN
ejpam-3280	69	26	,	,	PUNCT
ejpam-3280	69	27	c	c	NOUN
ejpam-3280	69	28	)	)	PUNCT
ejpam-3280	69	29	,	,	PUNCT
ejpam-3280	69	30	where	where	SCONJ
ejpam-3280	69	31	c	c	NOUN
ejpam-3280	69	32	=	=	SYM
ejpam-3280	69	33	a∩b	a∩b	PROPN
ejpam-3280	69	34	and	and	CCONJ
ejpam-3280	69	35	h(c	h(c	PROPN
ejpam-3280	69	36	)	)	PUNCT
ejpam-3280	69	37	=	=	SYM
ejpam-3280	69	38	f(c	f(c	PROPN
ejpam-3280	69	39	)	)	PUNCT
ejpam-3280	69	40	∩	∩	ADJ
ejpam-3280	69	41	g(c	g(c	NOUN
ejpam-3280	69	42	)	)	PUNCT
ejpam-3280	69	43	for	for	ADP
ejpam-3280	69	44	all	all	DET
ejpam-3280	69	45	c	c	PROPN
ejpam-3280	69	46	∈	∈	PROPN
ejpam-3280	69	47	c.	c.	NOUN
ejpam-3280	69	48	definition	definition	NOUN
ejpam-3280	69	49	8	8	NUM
ejpam-3280	69	50	.	.	PUNCT
ejpam-3280	70	1	[	[	X
ejpam-3280	70	2	11	11	NUM
ejpam-3280	70	3	]	]	X
ejpam-3280	70	4	let	let	VERB
ejpam-3280	70	5	(	(	PUNCT
ejpam-3280	70	6	f	f	X
ejpam-3280	70	7	,	,	PUNCT
ejpam-3280	70	8	a	a	PRON
ejpam-3280	70	9	)	)	PUNCT
ejpam-3280	70	10	and	and	CCONJ
ejpam-3280	70	11	(	(	PUNCT
ejpam-3280	70	12	g	g	NOUN
ejpam-3280	70	13	,	,	PUNCT
ejpam-3280	70	14	b	b	NOUN
ejpam-3280	70	15	)	)	PUNCT
ejpam-3280	70	16	be	be	AUX
ejpam-3280	70	17	two	two	NUM
ejpam-3280	70	18	soft	soft	ADJ
ejpam-3280	70	19	sets	set	NOUN
ejpam-3280	70	20	over	over	ADP
ejpam-3280	70	21	common	common	ADJ
ejpam-3280	70	22	universe	universe	NOUN
ejpam-3280	70	23	u	u	NOUN
ejpam-3280	70	24	.	.	PUNCT
ejpam-3280	71	1	then	then	ADV
ejpam-3280	71	2	(	(	PUNCT
ejpam-3280	71	3	f	f	X
ejpam-3280	71	4	,	,	PUNCT
ejpam-3280	71	5	a	a	PRON
ejpam-3280	71	6	)	)	PUNCT
ejpam-3280	71	7	and	and	CCONJ
ejpam-3280	71	8	(	(	PUNCT
ejpam-3280	71	9	g	g	NOUN
ejpam-3280	71	10	,	,	PUNCT
ejpam-3280	71	11	b	b	NOUN
ejpam-3280	71	12	)	)	PUNCT
ejpam-3280	71	13	denoted	denote	VERB
ejpam-3280	71	14	by	by	ADP
ejpam-3280	71	15	(	(	PUNCT
ejpam-3280	71	16	f	f	X
ejpam-3280	71	17	,	,	PUNCT
ejpam-3280	71	18	a)∧	a)∧	PROPN
ejpam-3280	71	19	(	(	PUNCT
ejpam-3280	71	20	g	g	PROPN
ejpam-3280	71	21	,	,	PUNCT
ejpam-3280	71	22	b	b	NOUN
ejpam-3280	71	23	)	)	PUNCT
ejpam-3280	71	24	and	and	CCONJ
ejpam-3280	71	25	is	be	AUX
ejpam-3280	71	26	defined	define	VERB
ejpam-3280	71	27	by	by	ADP
ejpam-3280	71	28	(	(	PUNCT
ejpam-3280	71	29	f	f	X
ejpam-3280	71	30	,	,	PUNCT
ejpam-3280	71	31	a)∧	a)∧	PROPN
ejpam-3280	71	32	(	(	PUNCT
ejpam-3280	71	33	g	g	PROPN
ejpam-3280	71	34	,	,	PUNCT
ejpam-3280	71	35	b	b	NOUN
ejpam-3280	71	36	)	)	PUNCT
ejpam-3280	71	37	=	=	SYM
ejpam-3280	71	38	(	(	PUNCT
ejpam-3280	71	39	h	h	NOUN
ejpam-3280	71	40	,	,	PUNCT
ejpam-3280	71	41	a×b	a×b	PROPN
ejpam-3280	71	42	)	)	PUNCT
ejpam-3280	71	43	,	,	PUNCT
ejpam-3280	71	44	where	where	SCONJ
ejpam-3280	71	45	h((a	h((a	PROPN
ejpam-3280	71	46	,	,	PUNCT
ejpam-3280	71	47	b	b	NOUN
ejpam-3280	71	48	)	)	PUNCT
ejpam-3280	71	49	)	)	PUNCT
ejpam-3280	71	50	=	=	SYM
ejpam-3280	71	51	f(a	f(a	NOUN
ejpam-3280	71	52	)	)	PUNCT
ejpam-3280	71	53	∩	∩	NOUN
ejpam-3280	71	54	g(b	g(b	NOUN
ejpam-3280	71	55	)	)	PUNCT
ejpam-3280	71	56	,	,	PUNCT
ejpam-3280	71	57	for	for	ADP
ejpam-3280	71	58	all	all	PRON
ejpam-3280	71	59	(	(	PUNCT
ejpam-3280	71	60	a	a	PRON
ejpam-3280	71	61	,	,	PUNCT
ejpam-3280	71	62	b	b	NOUN
ejpam-3280	71	63	)	)	PUNCT
ejpam-3280	71	64	∈	∈	PROPN
ejpam-3280	71	65	a×b	a×b	PROPN
ejpam-3280	71	66	.	.	PUNCT
ejpam-3280	71	67	definition	definition	NOUN
ejpam-3280	71	68	9	9	NUM
ejpam-3280	71	69	.	.	PUNCT
ejpam-3280	72	1	[	[	X
ejpam-3280	72	2	12	12	NUM
ejpam-3280	72	3	]	]	PUNCT
ejpam-3280	72	4	let	let	VERB
ejpam-3280	72	5	i	i	PRON
ejpam-3280	72	6	=	=	PUNCT
ejpam-3280	73	1	[	[	X
ejpam-3280	73	2	0	0	NUM
ejpam-3280	73	3	,	,	PUNCT
ejpam-3280	73	4	1	1	NUM
ejpam-3280	73	5	]	]	PUNCT
ejpam-3280	73	6	and	and	CCONJ
ejpam-3280	73	7	iu	iu	ADP
ejpam-3280	73	8	denoted	denote	VERB
ejpam-3280	73	9	the	the	DET
ejpam-3280	73	10	set	set	NOUN
ejpam-3280	73	11	of	of	ADP
ejpam-3280	73	12	all	all	DET
ejpam-3280	73	13	fuzzy	fuzzy	ADJ
ejpam-3280	73	14	sets	set	NOUN
ejpam-3280	73	15	on	on	ADP
ejpam-3280	73	16	u	u	NOUN
ejpam-3280	73	17	and	and	CCONJ
ejpam-3280	73	18	a	a	DET
ejpam-3280	73	19	⊆	⊆	NUM
ejpam-3280	73	20	e.	e.	PROPN
ejpam-3280	73	21	a	a	DET
ejpam-3280	73	22	pair	pair	NOUN
ejpam-3280	73	23	(	(	PUNCT
ejpam-3280	73	24	f	f	X
ejpam-3280	73	25	,	,	PUNCT
ejpam-3280	73	26	a	a	PRON
ejpam-3280	73	27	)	)	PUNCT
ejpam-3280	73	28	is	be	AUX
ejpam-3280	73	29	called	call	VERB
ejpam-3280	73	30	a	a	DET
ejpam-3280	73	31	fuzzy	fuzzy	ADJ
ejpam-3280	73	32	soft	soft	ADJ
ejpam-3280	73	33	set	set	NOUN
ejpam-3280	73	34	over	over	ADP
ejpam-3280	73	35	u	u	PROPN
ejpam-3280	73	36	,	,	PUNCT
ejpam-3280	73	37	where	where	SCONJ
ejpam-3280	73	38	f	f	PROPN
ejpam-3280	73	39	is	be	AUX
ejpam-3280	73	40	a	a	DET
ejpam-3280	73	41	mapping	mapping	NOUN
ejpam-3280	73	42	from	from	ADP
ejpam-3280	73	43	a	a	PRON
ejpam-3280	73	44	into	into	ADP
ejpam-3280	73	45	iu	iu	NOUN
ejpam-3280	73	46	.	.	PUNCT
ejpam-3280	74	1	that	that	PRON
ejpam-3280	74	2	is	be	AUX
ejpam-3280	74	3	,	,	PUNCT
ejpam-3280	74	4	for	for	ADP
ejpam-3280	74	5	each	each	DET
ejpam-3280	74	6	a	a	DET
ejpam-3280	74	7	∈	∈	PROPN
ejpam-3280	74	8	a	a	PRON
ejpam-3280	74	9	,	,	PUNCT
ejpam-3280	74	10	f(a	f(a	NOUN
ejpam-3280	74	11	)	)	PUNCT
ejpam-3280	75	1	=	=	SYM
ejpam-3280	75	2	fa	fa	INTJ
ejpam-3280	75	3	:	:	PUNCT
ejpam-3280	75	4	u	u	PROPN
ejpam-3280	75	5	→	→	PROPN
ejpam-3280	75	6	i	i	PROPN
ejpam-3280	75	7	,	,	PUNCT
ejpam-3280	75	8	is	be	AUX
ejpam-3280	75	9	a	a	DET
ejpam-3280	75	10	fuzzy	fuzzy	ADJ
ejpam-3280	75	11	set	set	NOUN
ejpam-3280	75	12	on	on	ADP
ejpam-3280	75	13	u	u	PROPN
ejpam-3280	75	14	.	.	PUNCT
ejpam-3280	76	1	e.	e.	PROPN
ejpam-3280	76	2	ranjbar	ranjbar	PROPN
ejpam-3280	76	3	-	-	PUNCT
ejpam-3280	76	4	yanehsari	yanehsari	NOUN
ejpam-3280	76	5	,	,	PUNCT
ejpam-3280	76	6	m.	m.	NOUN
ejpam-3280	76	7	asghari	asghari	ADJ
ejpam-3280	76	8	-	-	PUNCT
ejpam-3280	76	9	larimi	larimi	PROPN
ejpam-3280	76	10	,	,	PUNCT
ejpam-3280	76	11	r.	r.	PROPN
ejpam-3280	76	12	ameri	ameri	PROPN
ejpam-3280	76	13	/	/	SYM
ejpam-3280	76	14	eur	eur	PROPN
ejpam-3280	76	15	.	.	PUNCT
ejpam-3280	77	1	j.	j.	PROPN
ejpam-3280	77	2	pure	pure	PROPN
ejpam-3280	77	3	appl	appl	PROPN
ejpam-3280	77	4	.	.	PROPN
ejpam-3280	77	5	math	math	PROPN
ejpam-3280	77	6	,	,	PUNCT
ejpam-3280	77	7	12	12	NUM
ejpam-3280	77	8	(	(	PUNCT
ejpam-3280	77	9	1	1	NUM
ejpam-3280	77	10	)	)	PUNCT
ejpam-3280	77	11	(	(	PUNCT
ejpam-3280	77	12	2019	2019	NUM
ejpam-3280	77	13	)	)	PUNCT
ejpam-3280	77	14	,	,	PUNCT
ejpam-3280	77	15	118	118	NUM
ejpam-3280	77	16	-	-	SYM
ejpam-3280	77	17	134	134	NUM
ejpam-3280	77	18	121	121	NUM
ejpam-3280	77	19	definition	definition	NOUN
ejpam-3280	77	20	10	10	NUM
ejpam-3280	77	21	.	.	PUNCT
ejpam-3280	78	1	[	[	X
ejpam-3280	78	2	12	12	NUM
ejpam-3280	78	3	]	]	X
ejpam-3280	78	4	let	let	NOUN
ejpam-3280	78	5	(	(	PUNCT
ejpam-3280	78	6	f	f	X
ejpam-3280	78	7	,	,	PUNCT
ejpam-3280	78	8	a	a	PRON
ejpam-3280	78	9	)	)	PUNCT
ejpam-3280	78	10	and	and	CCONJ
ejpam-3280	78	11	(	(	PUNCT
ejpam-3280	78	12	g	g	NOUN
ejpam-3280	78	13	,	,	PUNCT
ejpam-3280	78	14	b	b	NOUN
ejpam-3280	78	15	)	)	PUNCT
ejpam-3280	78	16	be	be	AUX
ejpam-3280	78	17	two	two	NUM
ejpam-3280	78	18	fuzzy	fuzzy	ADJ
ejpam-3280	78	19	soft	soft	ADJ
ejpam-3280	78	20	sets	set	NOUN
ejpam-3280	78	21	over	over	ADP
ejpam-3280	78	22	common	common	ADJ
ejpam-3280	78	23	universe	universe	NOUN
ejpam-3280	78	24	u	u	NOUN
ejpam-3280	78	25	.	.	PUNCT
ejpam-3280	79	1	we	we	PRON
ejpam-3280	79	2	say	say	VERB
ejpam-3280	79	3	that	that	SCONJ
ejpam-3280	79	4	(	(	PUNCT
ejpam-3280	79	5	f	f	X
ejpam-3280	79	6	,	,	PUNCT
ejpam-3280	79	7	a	a	PRON
ejpam-3280	79	8	)	)	PUNCT
ejpam-3280	79	9	is	be	AUX
ejpam-3280	79	10	a	a	DET
ejpam-3280	79	11	fuzzy	fuzzy	ADJ
ejpam-3280	79	12	soft	soft	ADJ
ejpam-3280	79	13	subset	subset	NOUN
ejpam-3280	79	14	of	of	ADP
ejpam-3280	79	15	(	(	PUNCT
ejpam-3280	79	16	g	g	PROPN
ejpam-3280	79	17	,	,	PUNCT
ejpam-3280	79	18	b	b	NOUN
ejpam-3280	79	19	)	)	PUNCT
ejpam-3280	79	20	and	and	CCONJ
ejpam-3280	79	21	write	write	VERB
ejpam-3280	79	22	(	(	PUNCT
ejpam-3280	79	23	f	f	X
ejpam-3280	79	24	,	,	PUNCT
ejpam-3280	79	25	a	a	PRON
ejpam-3280	79	26	)	)	PUNCT
ejpam-3280	79	27	v	v	NOUN
ejpam-3280	79	28	(	(	PUNCT
ejpam-3280	79	29	g	g	PROPN
ejpam-3280	79	30	,	,	PUNCT
ejpam-3280	79	31	b	b	NOUN
ejpam-3280	79	32	)	)	PUNCT
ejpam-3280	79	33	if	if	SCONJ
ejpam-3280	79	34	(	(	PUNCT
ejpam-3280	79	35	i	i	NOUN
ejpam-3280	79	36	)	)	PUNCT
ejpam-3280	79	37	a	a	DET
ejpam-3280	79	38	⊆	⊆	NUM
ejpam-3280	79	39	b	b	PROPN
ejpam-3280	79	40	(	(	PUNCT
ejpam-3280	79	41	ii	ii	NOUN
ejpam-3280	79	42	)	)	PUNCT
ejpam-3280	79	43	a	a	DET
ejpam-3280	79	44	∈	∈	NOUN
ejpam-3280	79	45	a⇒	a⇒	INTJ
ejpam-3280	79	46	fa	fa	PROPN
ejpam-3280	79	47	≤	≤	PROPN
ejpam-3280	79	48	ga	ga	PROPN
ejpam-3280	79	49	,	,	PUNCT
ejpam-3280	79	50	that	that	PRON
ejpam-3280	79	51	is	is	ADV
ejpam-3280	79	52	fa	fa	INTJ
ejpam-3280	79	53	is	be	AUX
ejpam-3280	79	54	a	a	DET
ejpam-3280	79	55	fuzzy	fuzzy	ADJ
ejpam-3280	79	56	subset	subset	NOUN
ejpam-3280	79	57	of	of	ADP
ejpam-3280	79	58	ga	ga	PROPN
ejpam-3280	79	59	.	.	PROPN
ejpam-3280	79	60	definition	definition	NOUN
ejpam-3280	79	61	11	11	NUM
ejpam-3280	79	62	.	.	PUNCT
ejpam-3280	80	1	[	[	X
ejpam-3280	80	2	12	12	NUM
ejpam-3280	80	3	]	]	X
ejpam-3280	80	4	union	union	NOUN
ejpam-3280	80	5	of	of	ADP
ejpam-3280	80	6	two	two	NUM
ejpam-3280	80	7	fuzzy	fuzzy	ADJ
ejpam-3280	80	8	soft	soft	ADJ
ejpam-3280	80	9	sets	set	NOUN
ejpam-3280	80	10	(	(	PUNCT
ejpam-3280	80	11	f	f	X
ejpam-3280	80	12	,	,	PUNCT
ejpam-3280	80	13	a	a	PRON
ejpam-3280	80	14	)	)	PUNCT
ejpam-3280	80	15	and	and	CCONJ
ejpam-3280	80	16	(	(	PUNCT
ejpam-3280	80	17	g	g	NOUN
ejpam-3280	80	18	,	,	PUNCT
ejpam-3280	80	19	b	b	NOUN
ejpam-3280	80	20	)	)	PUNCT
ejpam-3280	80	21	over	over	ADP
ejpam-3280	80	22	common	common	ADJ
ejpam-3280	80	23	universe	universe	NOUN
ejpam-3280	80	24	u	u	NOUN
ejpam-3280	80	25	,	,	PUNCT
ejpam-3280	80	26	denoted	denote	VERB
ejpam-3280	80	27	by	by	ADP
ejpam-3280	80	28	(	(	PUNCT
ejpam-3280	80	29	f	f	X
ejpam-3280	80	30	,	,	PUNCT
ejpam-3280	80	31	a	a	PRON
ejpam-3280	80	32	)	)	PUNCT
ejpam-3280	80	33	t	t	NOUN
ejpam-3280	80	34	(	(	PUNCT
ejpam-3280	80	35	g	g	PROPN
ejpam-3280	80	36	,	,	PUNCT
ejpam-3280	80	37	b	b	NOUN
ejpam-3280	80	38	)	)	PUNCT
ejpam-3280	80	39	is	be	AUX
ejpam-3280	80	40	the	the	DET
ejpam-3280	80	41	fuzzy	fuzzy	ADJ
ejpam-3280	80	42	soft	soft	ADJ
ejpam-3280	80	43	sets	set	NOUN
ejpam-3280	80	44	(	(	PUNCT
ejpam-3280	80	45	h	h	NOUN
ejpam-3280	80	46	,	,	PUNCT
ejpam-3280	80	47	c	c	NOUN
ejpam-3280	80	48	)	)	PUNCT
ejpam-3280	80	49	,	,	PUNCT
ejpam-3280	80	50	where	where	SCONJ
ejpam-3280	80	51	c	c	NOUN
ejpam-3280	80	52	=	=	PUNCT
ejpam-3280	80	53	a	a	DET
ejpam-3280	80	54	∪	∪	X
ejpam-3280	80	55	b	b	NOUN
ejpam-3280	80	56	and	and	CCONJ
ejpam-3280	80	57	for	for	ADP
ejpam-3280	80	58	all	all	DET
ejpam-3280	80	59	c	c	NOUN
ejpam-3280	80	60	∈	∈	PROPN
ejpam-3280	80	61	c	c	NOUN
ejpam-3280	80	62	,	,	PUNCT
ejpam-3280	80	63	h(c	h(c	PROPN
ejpam-3280	80	64	)	)	PUNCT
ejpam-3280	80	65	=	=	PUNCT
ejpam-3280	81	1			PUNCT
ejpam-3280	81	2	fc	fc	INTJ
ejpam-3280	81	3	if	if	SCONJ
ejpam-3280	81	4	c	c	PROPN
ejpam-3280	81	5	∈	∈	PROPN
ejpam-3280	81	6	a−b	a−b	NOUN
ejpam-3280	81	7	gc	gc	PROPN
ejpam-3280	81	8	if	if	SCONJ
ejpam-3280	81	9	c	c	PROPN
ejpam-3280	81	10	∈	∈	PROPN
ejpam-3280	81	11	b	b	X
ejpam-3280	81	12	−a	−a	ADJ
ejpam-3280	81	13	fc	fc	PROPN
ejpam-3280	81	14	∨	∨	NUM
ejpam-3280	81	15	gc	gc	PROPN
ejpam-3280	81	16	if	if	SCONJ
ejpam-3280	81	17	c	c	PROPN
ejpam-3280	81	18	∈	∈	PROPN
ejpam-3280	81	19	a	a	DET
ejpam-3280	81	20	∩b	∩b	NOUN
ejpam-3280	81	21	.	.	PUNCT
ejpam-3280	82	1	definition	definition	NOUN
ejpam-3280	82	2	12	12	NUM
ejpam-3280	82	3	.	.	PUNCT
ejpam-3280	83	1	[	[	X
ejpam-3280	83	2	12	12	NUM
ejpam-3280	83	3	]	]	X
ejpam-3280	83	4	intersection	intersection	NOUN
ejpam-3280	83	5	of	of	ADP
ejpam-3280	83	6	two	two	NUM
ejpam-3280	83	7	fuzzy	fuzzy	ADJ
ejpam-3280	83	8	soft	soft	ADJ
ejpam-3280	83	9	sets	set	NOUN
ejpam-3280	83	10	(	(	PUNCT
ejpam-3280	83	11	f	f	X
ejpam-3280	83	12	,	,	PUNCT
ejpam-3280	83	13	a	a	PRON
ejpam-3280	83	14	)	)	PUNCT
ejpam-3280	83	15	and	and	CCONJ
ejpam-3280	83	16	(	(	PUNCT
ejpam-3280	83	17	g	g	NOUN
ejpam-3280	83	18	,	,	PUNCT
ejpam-3280	83	19	b	b	NOUN
ejpam-3280	83	20	)	)	PUNCT
ejpam-3280	83	21	over	over	ADP
ejpam-3280	83	22	a	a	DET
ejpam-3280	83	23	common	common	ADJ
ejpam-3280	83	24	universe	universe	NOUN
ejpam-3280	83	25	u	u	NOUN
ejpam-3280	83	26	,	,	PUNCT
ejpam-3280	83	27	denoted	denote	VERB
ejpam-3280	83	28	by	by	ADP
ejpam-3280	83	29	(	(	PUNCT
ejpam-3280	83	30	f	f	X
ejpam-3280	83	31	,	,	PUNCT
ejpam-3280	83	32	a	a	PRON
ejpam-3280	83	33	)	)	PUNCT
ejpam-3280	83	34	u	u	NOUN
ejpam-3280	83	35	(	(	PUNCT
ejpam-3280	83	36	g	g	PROPN
ejpam-3280	83	37	,	,	PUNCT
ejpam-3280	83	38	b	b	NOUN
ejpam-3280	83	39	)	)	PUNCT
ejpam-3280	83	40	is	be	AUX
ejpam-3280	83	41	the	the	DET
ejpam-3280	83	42	fuzzy	fuzzy	ADJ
ejpam-3280	83	43	soft	soft	ADJ
ejpam-3280	83	44	set	set	NOUN
ejpam-3280	83	45	(	(	PUNCT
ejpam-3280	83	46	h	h	NOUN
ejpam-3280	83	47	,	,	PUNCT
ejpam-3280	83	48	c	c	NOUN
ejpam-3280	83	49	)	)	PUNCT
ejpam-3280	83	50	,	,	PUNCT
ejpam-3280	83	51	where	where	SCONJ
ejpam-3280	83	52	c	c	NOUN
ejpam-3280	83	53	=	=	PUNCT
ejpam-3280	83	54	a	a	DET
ejpam-3280	83	55	∩	∩	ADJ
ejpam-3280	83	56	b	b	NOUN
ejpam-3280	83	57	6=	6=	ADP
ejpam-3280	83	58	∅	∅	NOUN
ejpam-3280	83	59	and	and	CCONJ
ejpam-3280	83	60	hc	hc	PROPN
ejpam-3280	83	61	=	=	PUNCT
ejpam-3280	83	62	fc	fc	PROPN
ejpam-3280	83	63	∧	∧	PROPN
ejpam-3280	83	64	gc	gc	PROPN
ejpam-3280	83	65	for	for	ADP
ejpam-3280	83	66	all	all	DET
ejpam-3280	83	67	c	c	PROPN
ejpam-3280	83	68	∈	∈	PROPN
ejpam-3280	83	69	c.	c.	NOUN
ejpam-3280	83	70	definition	definition	NOUN
ejpam-3280	83	71	13	13	NUM
ejpam-3280	83	72	.	.	PUNCT
ejpam-3280	84	1	[	[	X
ejpam-3280	84	2	12	12	NUM
ejpam-3280	84	3	]	]	X
ejpam-3280	84	4	if	if	SCONJ
ejpam-3280	84	5	(	(	PUNCT
ejpam-3280	84	6	f	f	X
ejpam-3280	84	7	,	,	PUNCT
ejpam-3280	84	8	a	a	PRON
ejpam-3280	84	9	)	)	PUNCT
ejpam-3280	84	10	and	and	CCONJ
ejpam-3280	84	11	(	(	PUNCT
ejpam-3280	84	12	g	g	NOUN
ejpam-3280	84	13	,	,	PUNCT
ejpam-3280	84	14	b	b	NOUN
ejpam-3280	84	15	)	)	PUNCT
ejpam-3280	84	16	are	be	AUX
ejpam-3280	84	17	two	two	NUM
ejpam-3280	84	18	fuzzy	fuzzy	ADJ
ejpam-3280	84	19	soft	soft	ADJ
ejpam-3280	84	20	sets	set	NOUN
ejpam-3280	84	21	,	,	PUNCT
ejpam-3280	84	22	then	then	ADV
ejpam-3280	84	23	(	(	PUNCT
ejpam-3280	84	24	f	f	X
ejpam-3280	84	25	,	,	PUNCT
ejpam-3280	84	26	a	a	PRON
ejpam-3280	84	27	)	)	PUNCT
ejpam-3280	84	28	and	and	CCONJ
ejpam-3280	84	29	(	(	PUNCT
ejpam-3280	84	30	g	g	NOUN
ejpam-3280	84	31	,	,	PUNCT
ejpam-3280	84	32	b	b	NOUN
ejpam-3280	84	33	)	)	PUNCT
ejpam-3280	84	34	is	be	AUX
ejpam-3280	84	35	denoted	denote	VERB
ejpam-3280	84	36	by	by	ADP
ejpam-3280	84	37	(	(	PUNCT
ejpam-3280	84	38	f	f	X
ejpam-3280	84	39	,	,	PUNCT
ejpam-3280	84	40	a	a	PRON
ejpam-3280	84	41	)	)	PUNCT
ejpam-3280	84	42	∧	∧	NOUN
ejpam-3280	84	43	(	(	PUNCT
ejpam-3280	84	44	g	g	PROPN
ejpam-3280	84	45	,	,	PUNCT
ejpam-3280	84	46	b	b	NOUN
ejpam-3280	84	47	)	)	PUNCT
ejpam-3280	85	1	=	=	SYM
ejpam-3280	85	2	(	(	PUNCT
ejpam-3280	85	3	h	h	NOUN
ejpam-3280	85	4	,	,	PUNCT
ejpam-3280	85	5	a	a	DET
ejpam-3280	85	6	×	×	PROPN
ejpam-3280	85	7	b	b	NOUN
ejpam-3280	85	8	)	)	PUNCT
ejpam-3280	85	9	,	,	PUNCT
ejpam-3280	85	10	where	where	SCONJ
ejpam-3280	85	11	h((a	h((a	PROPN
ejpam-3280	85	12	,	,	PUNCT
ejpam-3280	85	13	b	b	NOUN
ejpam-3280	85	14	)	)	PUNCT
ejpam-3280	85	15	)	)	PUNCT
ejpam-3280	85	16	=	=	PUNCT
ejpam-3280	86	1	ha	ha	INTJ
ejpam-3280	86	2	,	,	PUNCT
ejpam-3280	86	3	b	b	NOUN
ejpam-3280	86	4	=	=	SYM
ejpam-3280	86	5	fa	fa	PROPN
ejpam-3280	86	6	∧	∧	PROPN
ejpam-3280	86	7	gb	gb	NOUN
ejpam-3280	86	8	,	,	PUNCT
ejpam-3280	86	9	for	for	ADP
ejpam-3280	86	10	all	all	PRON
ejpam-3280	86	11	(	(	PUNCT
ejpam-3280	86	12	a	a	PRON
ejpam-3280	86	13	,	,	PUNCT
ejpam-3280	86	14	b	b	NOUN
ejpam-3280	86	15	)	)	PUNCT
ejpam-3280	86	16	∈	∈	PROPN
ejpam-3280	86	17	a×b	a×b	PROPN
ejpam-3280	86	18	.	.	PROPN
ejpam-3280	86	19	3	3	NUM
ejpam-3280	86	20	.	.	NOUN
ejpam-3280	86	21	soft	soft	ADJ
ejpam-3280	86	22	hypervector	hypervector	NOUN
ejpam-3280	86	23	space	space	NOUN
ejpam-3280	86	24	in	in	ADP
ejpam-3280	86	25	this	this	DET
ejpam-3280	86	26	section	section	NOUN
ejpam-3280	86	27	,	,	PUNCT
ejpam-3280	86	28	we	we	PRON
ejpam-3280	86	29	introduce	introduce	VERB
ejpam-3280	86	30	the	the	DET
ejpam-3280	86	31	notions	notion	NOUN
ejpam-3280	86	32	of	of	ADP
ejpam-3280	86	33	soft	soft	ADJ
ejpam-3280	86	34	hypervector	hypervector	NOUN
ejpam-3280	86	35	space	space	NOUN
ejpam-3280	86	36	.	.	PUNCT
ejpam-3280	87	1	also	also	ADV
ejpam-3280	87	2	several	several	ADJ
ejpam-3280	87	3	basic	basic	ADJ
ejpam-3280	87	4	properties	property	NOUN
ejpam-3280	87	5	are	be	AUX
ejpam-3280	87	6	provided	provide	VERB
ejpam-3280	87	7	.	.	PUNCT
ejpam-3280	88	1	definition	definition	NOUN
ejpam-3280	88	2	14	14	NUM
ejpam-3280	88	3	.	.	PUNCT
ejpam-3280	89	1	let	let	VERB
ejpam-3280	89	2	v	v	PART
ejpam-3280	89	3	be	be	AUX
ejpam-3280	89	4	a	a	DET
ejpam-3280	89	5	hypervector	hypervector	NOUN
ejpam-3280	89	6	space	space	NOUN
ejpam-3280	89	7	over	over	ADP
ejpam-3280	89	8	a	a	DET
ejpam-3280	89	9	filed	file	VERB
ejpam-3280	89	10	k	k	PROPN
ejpam-3280	89	11	and	and	CCONJ
ejpam-3280	89	12	(	(	PUNCT
ejpam-3280	89	13	f	f	X
ejpam-3280	89	14	,	,	PUNCT
ejpam-3280	89	15	a	a	PRON
ejpam-3280	89	16	)	)	PUNCT
ejpam-3280	89	17	be	be	AUX
ejpam-3280	89	18	a	a	DET
ejpam-3280	89	19	soft	soft	ADJ
ejpam-3280	89	20	set	set	NOUN
ejpam-3280	89	21	over	over	ADP
ejpam-3280	89	22	v	v	NOUN
ejpam-3280	89	23	.	.	PUNCT
ejpam-3280	90	1	then	then	ADV
ejpam-3280	90	2	(	(	PUNCT
ejpam-3280	90	3	f	f	X
ejpam-3280	90	4	,	,	PUNCT
ejpam-3280	90	5	a	a	PRON
ejpam-3280	90	6	)	)	PUNCT
ejpam-3280	90	7	is	be	AUX
ejpam-3280	90	8	called	call	VERB
ejpam-3280	90	9	a	a	DET
ejpam-3280	90	10	soft	soft	ADJ
ejpam-3280	90	11	hypervector	hypervector	NOUN
ejpam-3280	90	12	space	space	NOUN
ejpam-3280	90	13	over	over	ADP
ejpam-3280	90	14	v	v	NOUN
ejpam-3280	90	15	if	if	SCONJ
ejpam-3280	90	16	and	and	CCONJ
ejpam-3280	90	17	only	only	ADV
ejpam-3280	90	18	if	if	SCONJ
ejpam-3280	90	19	f(a	f(a	NOUN
ejpam-3280	90	20	)	)	PUNCT
ejpam-3280	90	21	be	be	VERB
ejpam-3280	90	22	a	a	DET
ejpam-3280	90	23	sub	sub	ADJ
ejpam-3280	90	24	-	-	ADJ
ejpam-3280	90	25	hypervector	hypervector	ADJ
ejpam-3280	90	26	space	space	NOUN
ejpam-3280	90	27	of	of	ADP
ejpam-3280	90	28	v	v	NOUN
ejpam-3280	90	29	,	,	PUNCT
ejpam-3280	90	30	for	for	ADP
ejpam-3280	90	31	all	all	DET
ejpam-3280	90	32	a	a	DET
ejpam-3280	90	33	∈	∈	PROPN
ejpam-3280	90	34	a.	a.	NOUN
ejpam-3280	90	35	example	example	NOUN
ejpam-3280	91	1	2	2	X
ejpam-3280	91	2	.	.	PUNCT
ejpam-3280	91	3	let	let	VERB
ejpam-3280	91	4	v	v	VERB
ejpam-3280	91	5	=	=	SYM
ejpam-3280	91	6	{	{	PUNCT
ejpam-3280	91	7	p	p	X
ejpam-3280	91	8	(	(	PUNCT
ejpam-3280	91	9	x	x	NOUN
ejpam-3280	91	10	)	)	PUNCT
ejpam-3280	91	11	:	:	PUNCT
ejpam-3280	91	12	deg(p	deg(p	PROPN
ejpam-3280	91	13	(	(	PUNCT
ejpam-3280	91	14	x	x	NOUN
ejpam-3280	91	15	)	)	PUNCT
ejpam-3280	91	16	)	)	PUNCT
ejpam-3280	91	17	≤	≤	NUM
ejpam-3280	91	18	2	2	NUM
ejpam-3280	91	19	}	}	PUNCT
ejpam-3280	91	20	and	and	CCONJ
ejpam-3280	91	21	k	k	NOUN
ejpam-3280	91	22	=	=	NOUN
ejpam-3280	91	23	r	r	NOUN
ejpam-3280	91	24	with	with	ADP
ejpam-3280	91	25	the	the	DET
ejpam-3280	91	26	following	follow	VERB
ejpam-3280	91	27	hyperoperation	hyperoperation	NOUN
ejpam-3280	91	28	:	:	PUNCT
ejpam-3280	91	29	◦	◦	NOUN
ejpam-3280	91	30	:	:	PUNCT
ejpam-3280	91	31	r×	r×	NOUN
ejpam-3280	91	32	v	v	NOUN
ejpam-3280	91	33	→	→	SYM
ejpam-3280	91	34	p	p	X
ejpam-3280	91	35	(	(	PUNCT
ejpam-3280	91	36	v	v	NOUN
ejpam-3280	91	37	)	)	PUNCT
ejpam-3280	91	38	◦	◦	NOUN
ejpam-3280	91	39	(	(	PUNCT
ejpam-3280	91	40	r	r	NOUN
ejpam-3280	91	41	,	,	PUNCT
ejpam-3280	91	42	p	p	X
ejpam-3280	91	43	(	(	PUNCT
ejpam-3280	91	44	x	x	NOUN
ejpam-3280	91	45	)	)	PUNCT
ejpam-3280	91	46	)	)	PUNCT
ejpam-3280	92	1	=	=	PRON
ejpam-3280	92	2	{	{	PUNCT
ejpam-3280	92	3	r	r	NOUN
ejpam-3280	92	4	·	·	PUNCT
ejpam-3280	92	5	p	p	X
ejpam-3280	92	6	(	(	PUNCT
ejpam-3280	92	7	x	x	NOUN
ejpam-3280	92	8	)	)	PUNCT
ejpam-3280	92	9	}	}	PUNCT
ejpam-3280	92	10	.	.	PUNCT
ejpam-3280	93	1	then	then	ADV
ejpam-3280	93	2	(	(	PUNCT
ejpam-3280	93	3	v,+	v,+	NUM
ejpam-3280	93	4	,	,	PUNCT
ejpam-3280	93	5	◦	◦	NOUN
ejpam-3280	93	6	,	,	PUNCT
ejpam-3280	93	7	r	r	NOUN
ejpam-3280	93	8	)	)	PUNCT
ejpam-3280	93	9	is	be	AUX
ejpam-3280	93	10	a	a	DET
ejpam-3280	93	11	strongly	strongly	ADV
ejpam-3280	93	12	distributive	distributive	ADJ
ejpam-3280	93	13	hypervector	hypervector	NOUN
ejpam-3280	93	14	space	space	NOUN
ejpam-3280	93	15	.	.	PUNCT
ejpam-3280	94	1	if	if	SCONJ
ejpam-3280	94	2	a	a	PRON
ejpam-3280	94	3	=	=	PUNCT
ejpam-3280	94	4	{	{	PUNCT
ejpam-3280	94	5	◦	◦	NOUN
ejpam-3280	94	6	,	,	PUNCT
ejpam-3280	94	7	x	x	NOUN
ejpam-3280	94	8	,	,	PUNCT
ejpam-3280	94	9	x2	x2	PROPN
ejpam-3280	94	10	}	}	PUNCT
ejpam-3280	94	11	and	and	CCONJ
ejpam-3280	94	12	define	define	VERB
ejpam-3280	94	13	the	the	DET
ejpam-3280	94	14	set	set	NOUN
ejpam-3280	94	15	-	-	PUNCT
ejpam-3280	94	16	valued	value	VERB
ejpam-3280	94	17	function	function	NOUN
ejpam-3280	94	18	f	f	NOUN
ejpam-3280	94	19	:	:	PUNCT
ejpam-3280	94	20	a	a	DET
ejpam-3280	94	21	→	→	SYM
ejpam-3280	94	22	p	p	X
ejpam-3280	94	23	(	(	PUNCT
ejpam-3280	94	24	v	v	NOUN
ejpam-3280	94	25	)	)	PUNCT
ejpam-3280	94	26	by	by	ADP
ejpam-3280	94	27	f(a	f(a	PROPN
ejpam-3280	94	28	)	)	PUNCT
ejpam-3280	94	29	=	=	PUNCT
ejpam-3280	95	1	〈	〈	PROPN
ejpam-3280	95	2	a	a	DET
ejpam-3280	95	3	〉	〉	NOUN
ejpam-3280	95	4	=	=	SYM
ejpam-3280	95	5	{	{	PUNCT
ejpam-3280	95	6	r	r	NOUN
ejpam-3280	95	7	◦	◦	NOUN
ejpam-3280	95	8	a	a	PRON
ejpam-3280	95	9	:	:	PUNCT
ejpam-3280	95	10	r	r	NOUN
ejpam-3280	95	11	∈	∈	NOUN
ejpam-3280	95	12	r	r	NOUN
ejpam-3280	95	13	}	}	PUNCT
ejpam-3280	95	14	.	.	PUNCT
ejpam-3280	96	1	then	then	ADV
ejpam-3280	96	2	f(0	f(0	NOUN
ejpam-3280	96	3	)	)	PUNCT
ejpam-3280	96	4	=	=	PRON
ejpam-3280	96	5	{	{	PUNCT
ejpam-3280	96	6	{	{	PUNCT
ejpam-3280	96	7	0	0	NUM
ejpam-3280	96	8	}	}	PUNCT
ejpam-3280	96	9	}	}	PUNCT
ejpam-3280	96	10	,	,	PUNCT
ejpam-3280	96	11	f(x	f(x	PROPN
ejpam-3280	96	12	)	)	PUNCT
ejpam-3280	96	13	=	=	PRON
ejpam-3280	96	14	{	{	PUNCT
ejpam-3280	96	15	{	{	PUNCT
ejpam-3280	96	16	r	r	NOUN
ejpam-3280	96	17	·	·	PUNCT
ejpam-3280	96	18	x	x	X
ejpam-3280	96	19	}	}	PUNCT
ejpam-3280	96	20	:	:	PUNCT
ejpam-3280	96	21	r	r	NOUN
ejpam-3280	96	22	∈	∈	NOUN
ejpam-3280	96	23	r	r	NOUN
ejpam-3280	96	24	}	}	PUNCT
ejpam-3280	96	25	and	and	CCONJ
ejpam-3280	96	26	f(x2	f(x2	NOUN
ejpam-3280	96	27	)	)	PUNCT
ejpam-3280	96	28	=	=	PRON
ejpam-3280	96	29	{	{	PUNCT
ejpam-3280	96	30	{	{	PUNCT
ejpam-3280	96	31	r	r	NOUN
ejpam-3280	96	32	·	·	PUNCT
ejpam-3280	96	33	x2	x2	NOUN
ejpam-3280	96	34	}	}	PUNCT
ejpam-3280	96	35	:	:	PUNCT
ejpam-3280	96	36	r	r	NOUN
ejpam-3280	96	37	∈	∈	NOUN
ejpam-3280	96	38	r	r	NOUN
ejpam-3280	96	39	}	}	PUNCT
ejpam-3280	96	40	that	that	SCONJ
ejpam-3280	96	41	all	all	PRON
ejpam-3280	96	42	of	of	ADP
ejpam-3280	96	43	these	these	PRON
ejpam-3280	96	44	are	be	AUX
ejpam-3280	96	45	sub	sub	ADJ
ejpam-3280	96	46	-	-	ADJ
ejpam-3280	96	47	hypervector	hypervector	ADJ
ejpam-3280	96	48	space	space	NOUN
ejpam-3280	96	49	of	of	ADP
ejpam-3280	96	50	v	v	NOUN
ejpam-3280	96	51	.	.	PUNCT
ejpam-3280	97	1	hence	hence	ADV
ejpam-3280	97	2	,	,	PUNCT
ejpam-3280	97	3	(	(	PUNCT
ejpam-3280	97	4	f	f	X
ejpam-3280	97	5	,	,	PUNCT
ejpam-3280	97	6	a	a	PRON
ejpam-3280	97	7	)	)	PUNCT
ejpam-3280	97	8	is	be	AUX
ejpam-3280	97	9	a	a	DET
ejpam-3280	97	10	soft	soft	ADJ
ejpam-3280	97	11	hypervector	hypervector	NOUN
ejpam-3280	97	12	space	space	NOUN
ejpam-3280	97	13	over	over	ADP
ejpam-3280	97	14	v	v	NOUN
ejpam-3280	97	15	.	.	PUNCT
ejpam-3280	98	1	proposition	proposition	NOUN
ejpam-3280	98	2	1	1	NUM
ejpam-3280	98	3	.	.	PUNCT
ejpam-3280	99	1	let	let	VERB
ejpam-3280	99	2	v	v	PART
ejpam-3280	99	3	be	be	AUX
ejpam-3280	99	4	a	a	DET
ejpam-3280	99	5	hypervector	hypervector	NOUN
ejpam-3280	99	6	space	space	NOUN
ejpam-3280	99	7	over	over	ADP
ejpam-3280	99	8	a	a	DET
ejpam-3280	99	9	field	field	NOUN
ejpam-3280	99	10	k	k	NOUN
ejpam-3280	99	11	and	and	CCONJ
ejpam-3280	99	12	let	let	VERB
ejpam-3280	99	13	(	(	PUNCT
ejpam-3280	99	14	f	f	X
ejpam-3280	99	15	,	,	PUNCT
ejpam-3280	99	16	a	a	PRON
ejpam-3280	99	17	)	)	PUNCT
ejpam-3280	99	18	and	and	CCONJ
ejpam-3280	99	19	(	(	PUNCT
ejpam-3280	99	20	g	g	NOUN
ejpam-3280	99	21	,	,	PUNCT
ejpam-3280	99	22	b	b	NOUN
ejpam-3280	99	23	)	)	PUNCT
ejpam-3280	99	24	be	be	AUX
ejpam-3280	99	25	two	two	NUM
ejpam-3280	99	26	soft	soft	ADJ
ejpam-3280	99	27	hypervector	hypervector	NOUN
ejpam-3280	99	28	space	space	NOUN
ejpam-3280	99	29	over	over	ADP
ejpam-3280	99	30	v	v	NOUN
ejpam-3280	99	31	.	.	PUNCT
ejpam-3280	100	1	if	if	SCONJ
ejpam-3280	100	2	a	a	DET
ejpam-3280	100	3	∩	∩	X
ejpam-3280	100	4	b	b	NOUN
ejpam-3280	100	5	6=	6=	ADP
ejpam-3280	100	6	∅	∅	NOUN
ejpam-3280	100	7	and	and	CCONJ
ejpam-3280	100	8	for	for	ADP
ejpam-3280	100	9	all	all	DET
ejpam-3280	100	10	x	x	SYM
ejpam-3280	100	11	∈	∈	PROPN
ejpam-3280	100	12	a	a	DET
ejpam-3280	100	13	∩	∩	ADJ
ejpam-3280	100	14	b	b	NOUN
ejpam-3280	100	15	,	,	PUNCT
ejpam-3280	100	16	f(x	f(x	PROPN
ejpam-3280	100	17	)	)	PUNCT
ejpam-3280	100	18	∩	∩	NOUN
ejpam-3280	100	19	g(x	g(x	NOUN
ejpam-3280	100	20	)	)	PUNCT
ejpam-3280	100	21	6=	6=	ADP
ejpam-3280	100	22	∅	∅	NOUN
ejpam-3280	100	23	,	,	PUNCT
ejpam-3280	100	24	then	then	ADV
ejpam-3280	100	25	their	their	PRON
ejpam-3280	100	26	intersection	intersection	NOUN
ejpam-3280	100	27	(	(	PUNCT
ejpam-3280	100	28	f	f	X
ejpam-3280	100	29	,	,	PUNCT
ejpam-3280	100	30	a	a	PRON
ejpam-3280	100	31	)	)	PUNCT
ejpam-3280	100	32	∩	∩	NOUN
ejpam-3280	100	33	(	(	PUNCT
ejpam-3280	100	34	g	g	PROPN
ejpam-3280	100	35	,	,	PUNCT
ejpam-3280	100	36	b	b	NOUN
ejpam-3280	100	37	)	)	PUNCT
ejpam-3280	100	38	is	be	AUX
ejpam-3280	100	39	a	a	DET
ejpam-3280	100	40	soft	soft	ADJ
ejpam-3280	100	41	hypervector	hypervector	NOUN
ejpam-3280	100	42	space	space	NOUN
ejpam-3280	100	43	over	over	ADP
ejpam-3280	100	44	v	v	NOUN
ejpam-3280	100	45	.	.	PUNCT
ejpam-3280	101	1	proof	proof	NOUN
ejpam-3280	101	2	.	.	PUNCT
ejpam-3280	102	1	straightforward	straightforward	ADJ
ejpam-3280	102	2	.	.	PUNCT
ejpam-3280	103	1	e.	e.	PROPN
ejpam-3280	103	2	ranjbar	ranjbar	PROPN
ejpam-3280	103	3	-	-	PUNCT
ejpam-3280	103	4	yanehsari	yanehsari	NOUN
ejpam-3280	103	5	,	,	PUNCT
ejpam-3280	103	6	m.	m.	NOUN
ejpam-3280	103	7	asghari	asghari	ADJ
ejpam-3280	103	8	-	-	PUNCT
ejpam-3280	103	9	larimi	larimi	PROPN
ejpam-3280	103	10	,	,	PUNCT
ejpam-3280	103	11	r.	r.	PROPN
ejpam-3280	103	12	ameri	ameri	PROPN
ejpam-3280	103	13	/	/	SYM
ejpam-3280	103	14	eur	eur	PROPN
ejpam-3280	103	15	.	.	PUNCT
ejpam-3280	104	1	j.	j.	PROPN
ejpam-3280	104	2	pure	pure	PROPN
ejpam-3280	104	3	appl	appl	PROPN
ejpam-3280	104	4	.	.	PROPN
ejpam-3280	104	5	math	math	PROPN
ejpam-3280	104	6	,	,	PUNCT
ejpam-3280	104	7	12	12	NUM
ejpam-3280	104	8	(	(	PUNCT
ejpam-3280	104	9	1	1	NUM
ejpam-3280	104	10	)	)	PUNCT
ejpam-3280	104	11	(	(	PUNCT
ejpam-3280	104	12	2019	2019	NUM
ejpam-3280	104	13	)	)	PUNCT
ejpam-3280	104	14	,	,	PUNCT
ejpam-3280	104	15	118	118	NUM
ejpam-3280	104	16	-	-	SYM
ejpam-3280	104	17	134	134	NUM
ejpam-3280	104	18	122	122	NUM
ejpam-3280	104	19	corollary	corollary	ADJ
ejpam-3280	104	20	1	1	NUM
ejpam-3280	104	21	.	.	PUNCT
ejpam-3280	105	1	let	let	VERB
ejpam-3280	105	2	v	v	PART
ejpam-3280	105	3	be	be	AUX
ejpam-3280	105	4	a	a	DET
ejpam-3280	105	5	hypervector	hypervector	NOUN
ejpam-3280	105	6	space	space	NOUN
ejpam-3280	105	7	over	over	ADP
ejpam-3280	105	8	field	field	NOUN
ejpam-3280	105	9	k	k	PROPN
ejpam-3280	105	10	and	and	CCONJ
ejpam-3280	105	11	{	{	PUNCT
ejpam-3280	105	12	(	(	PUNCT
ejpam-3280	105	13	fi	fi	NOUN
ejpam-3280	105	14	,	,	PUNCT
ejpam-3280	105	15	ai	ai	NOUN
ejpam-3280	105	16	)	)	PUNCT
ejpam-3280	105	17	:	:	PUNCT
ejpam-3280	106	1	i	i	PRON
ejpam-3280	106	2	∈	∈	VERB
ejpam-3280	106	3	i	i	PRON
ejpam-3280	106	4	}	}	PUNCT
ejpam-3280	106	5	be	be	VERB
ejpam-3280	106	6	a	a	DET
ejpam-3280	106	7	nonempty	nonempty	ADJ
ejpam-3280	106	8	family	family	NOUN
ejpam-3280	106	9	of	of	ADP
ejpam-3280	106	10	soft	soft	ADJ
ejpam-3280	106	11	hypervector	hypervector	NOUN
ejpam-3280	106	12	space	space	NOUN
ejpam-3280	106	13	over	over	ADP
ejpam-3280	106	14	common	common	ADJ
ejpam-3280	106	15	universe	universe	NOUN
ejpam-3280	106	16	v	v	NOUN
ejpam-3280	106	17	.	.	PUNCT
ejpam-3280	107	1	if	if	SCONJ
ejpam-3280	107	2	⋂	⋂	PROPN
ejpam-3280	107	3	i∈i	i∈i	ADV
ejpam-3280	107	4	ai	ai	VERB
ejpam-3280	107	5	6=	6=	ADP
ejpam-3280	107	6	∅	∅	NOUN
ejpam-3280	107	7	and	and	CCONJ
ejpam-3280	107	8	for	for	ADP
ejpam-3280	107	9	all	all	DET
ejpam-3280	107	10	x	x	SYM
ejpam-3280	107	11	∈	∈	PROPN
ejpam-3280	107	12	⋂	⋂	PROPN
ejpam-3280	107	13	i∈i	i∈i	ADJ
ejpam-3280	107	14	ai	ai	VERB
ejpam-3280	107	15	,	,	PUNCT
ejpam-3280	107	16	⋂	⋂	PROPN
ejpam-3280	107	17	i∈i	i∈i	ADJ
ejpam-3280	107	18	fi(x	fi(x	NUM
ejpam-3280	107	19	)	)	PUNCT
ejpam-3280	107	20	6=	6=	ADP
ejpam-3280	107	21	∅	∅	NOUN
ejpam-3280	107	22	,	,	PUNCT
ejpam-3280	107	23	then	then	ADV
ejpam-3280	107	24	⋂	⋂	PROPN
ejpam-3280	107	25	i∈i(fi	i∈i(fi	PROPN
ejpam-3280	107	26	,	,	PUNCT
ejpam-3280	107	27	ai	ai	VERB
ejpam-3280	107	28	)	)	PUNCT
ejpam-3280	107	29	is	be	AUX
ejpam-3280	107	30	a	a	DET
ejpam-3280	107	31	soft	soft	ADJ
ejpam-3280	107	32	hypervector	hypervector	NOUN
ejpam-3280	107	33	space	space	NOUN
ejpam-3280	107	34	over	over	ADP
ejpam-3280	107	35	v	v	NOUN
ejpam-3280	107	36	.	.	PUNCT
ejpam-3280	108	1	definition	definition	NOUN
ejpam-3280	108	2	15	15	NUM
ejpam-3280	108	3	.	.	PUNCT
ejpam-3280	109	1	let	let	AUX
ejpam-3280	109	2	(	(	PUNCT
ejpam-3280	109	3	f	f	X
ejpam-3280	109	4	,	,	PUNCT
ejpam-3280	109	5	a	a	PRON
ejpam-3280	109	6	)	)	PUNCT
ejpam-3280	109	7	be	be	AUX
ejpam-3280	109	8	a	a	DET
ejpam-3280	109	9	soft	soft	ADJ
ejpam-3280	109	10	hypervector	hypervector	NOUN
ejpam-3280	109	11	space	space	NOUN
ejpam-3280	109	12	over	over	ADP
ejpam-3280	109	13	v	v	NOUN
ejpam-3280	109	14	.	.	PUNCT
ejpam-3280	110	1	then	then	ADV
ejpam-3280	110	2	l(f	l(f	PROPN
ejpam-3280	110	3	,	,	PUNCT
ejpam-3280	110	4	a	a	PRON
ejpam-3280	110	5	)	)	PUNCT
ejpam-3280	110	6	is	be	AUX
ejpam-3280	110	7	defined	define	VERB
ejpam-3280	110	8	by	by	ADP
ejpam-3280	110	9	:	:	PUNCT
ejpam-3280	110	10	l(f	l(f	PROPN
ejpam-3280	110	11	,	,	PUNCT
ejpam-3280	110	12	a	a	PRON
ejpam-3280	110	13	)	)	PUNCT
ejpam-3280	110	14	=	=	SYM
ejpam-3280	110	15	⋂	⋂	PROPN
ejpam-3280	110	16	{	{	PUNCT
ejpam-3280	110	17	(	(	PUNCT
ejpam-3280	110	18	g	g	PROPN
ejpam-3280	110	19	,	,	PUNCT
ejpam-3280	110	20	b	b	NOUN
ejpam-3280	110	21	)	)	PUNCT
ejpam-3280	110	22	:	:	PUNCT
ejpam-3280	111	1	(	(	PUNCT
ejpam-3280	111	2	f	f	X
ejpam-3280	111	3	,	,	PUNCT
ejpam-3280	111	4	a	a	PRON
ejpam-3280	111	5	)	)	PUNCT
ejpam-3280	111	6	⊆	⊆	NUM
ejpam-3280	111	7	(	(	PUNCT
ejpam-3280	111	8	g	g	NOUN
ejpam-3280	111	9	,	,	PUNCT
ejpam-3280	111	10	b	b	NOUN
ejpam-3280	111	11	)	)	PUNCT
ejpam-3280	111	12	,	,	PUNCT
ejpam-3280	111	13	(	(	PUNCT
ejpam-3280	111	14	g	g	NOUN
ejpam-3280	111	15	,	,	PUNCT
ejpam-3280	111	16	b	b	NOUN
ejpam-3280	111	17	)	)	PUNCT
ejpam-3280	111	18	is	be	AUX
ejpam-3280	111	19	a	a	DET
ejpam-3280	111	20	soft	soft	ADJ
ejpam-3280	111	21	set	set	NOUN
ejpam-3280	111	22	of	of	ADP
ejpam-3280	111	23	v	v	NOUN
ejpam-3280	111	24	}	}	PUNCT
ejpam-3280	111	25	.	.	PUNCT
ejpam-3280	112	1	lemma	lemma	PROPN
ejpam-3280	112	2	1	1	NUM
ejpam-3280	112	3	.	.	PUNCT
ejpam-3280	113	1	l(f	l(f	PROPN
ejpam-3280	113	2	,	,	PUNCT
ejpam-3280	113	3	a	a	PRON
ejpam-3280	113	4	)	)	PUNCT
ejpam-3280	113	5	is	be	AUX
ejpam-3280	113	6	the	the	DET
ejpam-3280	113	7	smallest	small	ADJ
ejpam-3280	113	8	soft	soft	ADJ
ejpam-3280	113	9	hypervector	hypervector	NOUN
ejpam-3280	113	10	space	space	NOUN
ejpam-3280	113	11	over	over	ADP
ejpam-3280	113	12	v	v	NOUN
ejpam-3280	113	13	containing	contain	VERB
ejpam-3280	113	14	(	(	PUNCT
ejpam-3280	113	15	f	f	X
ejpam-3280	113	16	,	,	PUNCT
ejpam-3280	113	17	a	a	PRON
ejpam-3280	113	18	)	)	PUNCT
ejpam-3280	113	19	.	.	PUNCT
ejpam-3280	114	1	proof	proof	NOUN
ejpam-3280	114	2	.	.	PUNCT
ejpam-3280	115	1	obvious	obvious	ADJ
ejpam-3280	115	2	.	.	PUNCT
ejpam-3280	116	1	lemma	lemma	PROPN
ejpam-3280	116	2	2	2	NUM
ejpam-3280	116	3	.	.	PUNCT
ejpam-3280	117	1	(	(	PUNCT
ejpam-3280	117	2	i	i	NOUN
ejpam-3280	117	3	)	)	PUNCT
ejpam-3280	117	4	if	if	SCONJ
ejpam-3280	117	5	(	(	PUNCT
ejpam-3280	117	6	f	f	X
ejpam-3280	117	7	,	,	PUNCT
ejpam-3280	117	8	a	a	PRON
ejpam-3280	117	9	)	)	PUNCT
ejpam-3280	117	10	is	be	AUX
ejpam-3280	117	11	a	a	DET
ejpam-3280	117	12	soft	soft	ADJ
ejpam-3280	117	13	hypervector	hypervector	NOUN
ejpam-3280	117	14	space	space	NOUN
ejpam-3280	117	15	over	over	ADP
ejpam-3280	117	16	v	v	NUM
ejpam-3280	117	17	,	,	PUNCT
ejpam-3280	117	18	then	then	ADV
ejpam-3280	117	19	l(f	l(f	PROPN
ejpam-3280	117	20	,	,	PUNCT
ejpam-3280	117	21	a	a	PRON
ejpam-3280	117	22	)	)	PUNCT
ejpam-3280	117	23	=	=	SYM
ejpam-3280	117	24	(	(	PUNCT
ejpam-3280	117	25	f	f	X
ejpam-3280	117	26	,	,	PUNCT
ejpam-3280	117	27	a	a	PRON
ejpam-3280	117	28	)	)	PUNCT
ejpam-3280	117	29	.	.	PUNCT
ejpam-3280	118	1	(	(	PUNCT
ejpam-3280	118	2	ii	ii	NOUN
ejpam-3280	118	3	)	)	PUNCT
ejpam-3280	118	4	if	if	SCONJ
ejpam-3280	118	5	(	(	PUNCT
ejpam-3280	118	6	f	f	X
ejpam-3280	118	7	,	,	PUNCT
ejpam-3280	118	8	a	a	PRON
ejpam-3280	118	9	)	)	PUNCT
ejpam-3280	118	10	is	be	AUX
ejpam-3280	118	11	a	a	DET
ejpam-3280	118	12	soft	soft	ADJ
ejpam-3280	118	13	set	set	NOUN
ejpam-3280	118	14	over	over	ADP
ejpam-3280	118	15	v	v	NOUN
ejpam-3280	118	16	,	,	PUNCT
ejpam-3280	118	17	then	then	ADV
ejpam-3280	118	18	l(l(f	l(l(f	PROPN
ejpam-3280	118	19	,	,	PUNCT
ejpam-3280	118	20	a	a	PRON
ejpam-3280	118	21	)	)	PUNCT
ejpam-3280	118	22	)	)	PUNCT
ejpam-3280	119	1	=	=	SYM
ejpam-3280	119	2	l(f	l(f	PROPN
ejpam-3280	119	3	,	,	PUNCT
ejpam-3280	119	4	a	a	PRON
ejpam-3280	119	5	)	)	PUNCT
ejpam-3280	119	6	.	.	PUNCT
ejpam-3280	120	1	(	(	PUNCT
ejpam-3280	120	2	iii	iii	X
ejpam-3280	120	3	)	)	PUNCT
ejpam-3280	120	4	let	let	VERB
ejpam-3280	120	5	(	(	PUNCT
ejpam-3280	120	6	f	f	X
ejpam-3280	120	7	,	,	PUNCT
ejpam-3280	120	8	a	a	PRON
ejpam-3280	120	9	)	)	PUNCT
ejpam-3280	120	10	and	and	CCONJ
ejpam-3280	120	11	(	(	PUNCT
ejpam-3280	120	12	g	g	NOUN
ejpam-3280	120	13	,	,	PUNCT
ejpam-3280	120	14	b	b	NOUN
ejpam-3280	120	15	)	)	PUNCT
ejpam-3280	120	16	be	be	AUX
ejpam-3280	120	17	two	two	NUM
ejpam-3280	120	18	soft	soft	ADJ
ejpam-3280	120	19	sets	set	NOUN
ejpam-3280	120	20	over	over	ADP
ejpam-3280	120	21	v	v	NOUN
ejpam-3280	120	22	and	and	CCONJ
ejpam-3280	120	23	(	(	PUNCT
ejpam-3280	120	24	f	f	X
ejpam-3280	120	25	,	,	PUNCT
ejpam-3280	120	26	a	a	PRON
ejpam-3280	120	27	)	)	PUNCT
ejpam-3280	120	28	⊆	⊆	NUM
ejpam-3280	120	29	(	(	PUNCT
ejpam-3280	120	30	g	g	NOUN
ejpam-3280	120	31	,	,	PUNCT
ejpam-3280	120	32	b	b	NOUN
ejpam-3280	120	33	)	)	PUNCT
ejpam-3280	120	34	.	.	PUNCT
ejpam-3280	121	1	then	then	ADV
ejpam-3280	121	2	l(f	l(f	PROPN
ejpam-3280	121	3	,	,	PUNCT
ejpam-3280	121	4	a	a	PRON
ejpam-3280	121	5	)	)	PUNCT
ejpam-3280	121	6	⊆	⊆	NUM
ejpam-3280	121	7	l(g	l(g	PROPN
ejpam-3280	121	8	,	,	PUNCT
ejpam-3280	121	9	b	b	NOUN
ejpam-3280	121	10	)	)	PUNCT
ejpam-3280	121	11	.	.	PUNCT
ejpam-3280	122	1	proof	proof	NOUN
ejpam-3280	122	2	.	.	PUNCT
ejpam-3280	123	1	obvious	obvious	ADJ
ejpam-3280	123	2	.	.	PUNCT
ejpam-3280	124	1	lemma	lemma	PROPN
ejpam-3280	124	2	3	3	X
ejpam-3280	124	3	.	.	PUNCT
ejpam-3280	125	1	let	let	AUX
ejpam-3280	125	2	(	(	PUNCT
ejpam-3280	125	3	f1	f1	NOUN
ejpam-3280	125	4	,	,	PUNCT
ejpam-3280	125	5	a1	a1	NOUN
ejpam-3280	125	6	)	)	PUNCT
ejpam-3280	125	7	,	,	PUNCT
ejpam-3280	125	8	(	(	PUNCT
ejpam-3280	125	9	f2	f2	PROPN
ejpam-3280	125	10	,	,	PUNCT
ejpam-3280	125	11	a2	a2	PROPN
ejpam-3280	125	12	)	)	PUNCT
ejpam-3280	125	13	and	and	CCONJ
ejpam-3280	125	14	(	(	PUNCT
ejpam-3280	125	15	f3	f3	ADJ
ejpam-3280	125	16	,	,	PUNCT
ejpam-3280	125	17	a3	a3	NOUN
ejpam-3280	125	18	)	)	PUNCT
ejpam-3280	125	19	be	be	VERB
ejpam-3280	125	20	three	three	NUM
ejpam-3280	125	21	soft	soft	ADJ
ejpam-3280	125	22	sets	set	NOUN
ejpam-3280	125	23	over	over	ADP
ejpam-3280	125	24	v	v	NOUN
ejpam-3280	125	25	.	.	PUNCT
ejpam-3280	126	1	if	if	SCONJ
ejpam-3280	126	2	(	(	PUNCT
ejpam-3280	126	3	f1	f1	NOUN
ejpam-3280	126	4	,	,	PUNCT
ejpam-3280	126	5	a1	a1	PROPN
ejpam-3280	126	6	)	)	PUNCT
ejpam-3280	126	7	⊆	⊆	PROPN
ejpam-3280	126	8	l(f3	l(f3	NOUN
ejpam-3280	126	9	,	,	PUNCT
ejpam-3280	126	10	a3	a3	NOUN
ejpam-3280	126	11	)	)	PUNCT
ejpam-3280	126	12	and	and	CCONJ
ejpam-3280	126	13	(	(	PUNCT
ejpam-3280	126	14	f2	f2	PROPN
ejpam-3280	126	15	,	,	PUNCT
ejpam-3280	126	16	a2	a2	PROPN
ejpam-3280	126	17	)	)	PUNCT
ejpam-3280	126	18	⊆	⊆	PROPN
ejpam-3280	126	19	l(f3	l(f3	NOUN
ejpam-3280	126	20	,	,	PUNCT
ejpam-3280	126	21	a3	a3	NOUN
ejpam-3280	126	22	)	)	PUNCT
ejpam-3280	126	23	,	,	PUNCT
ejpam-3280	126	24	then	then	ADV
ejpam-3280	126	25	l((f1	l((f1	PROPN
ejpam-3280	126	26	,	,	PUNCT
ejpam-3280	126	27	a1	a1	NOUN
ejpam-3280	126	28	)	)	PUNCT
ejpam-3280	126	29	⋃	⋃	NOUN
ejpam-3280	126	30	(	(	PUNCT
ejpam-3280	126	31	f2	f2	PROPN
ejpam-3280	126	32	,	,	PUNCT
ejpam-3280	126	33	a2	a2	PROPN
ejpam-3280	126	34	)	)	PUNCT
ejpam-3280	126	35	)	)	PUNCT
ejpam-3280	127	1	⊆	⊆	NUM
ejpam-3280	127	2	l(f3	l(f3	NOUN
ejpam-3280	127	3	,	,	PUNCT
ejpam-3280	127	4	a3	a3	NOUN
ejpam-3280	127	5	)	)	PUNCT
ejpam-3280	127	6	.	.	PUNCT
ejpam-3280	128	1	proof	proof	NOUN
ejpam-3280	128	2	.	.	PUNCT
ejpam-3280	129	1	since	since	SCONJ
ejpam-3280	129	2	(	(	PUNCT
ejpam-3280	129	3	f1	f1	NOUN
ejpam-3280	129	4	,	,	PUNCT
ejpam-3280	129	5	a1	a1	PROPN
ejpam-3280	129	6	)	)	PUNCT
ejpam-3280	129	7	⊆	⊆	NUM
ejpam-3280	129	8	(	(	PUNCT
ejpam-3280	129	9	f3	f3	ADJ
ejpam-3280	129	10	,	,	PUNCT
ejpam-3280	129	11	a3	a3	NOUN
ejpam-3280	129	12	)	)	PUNCT
ejpam-3280	129	13	and	and	CCONJ
ejpam-3280	129	14	(	(	PUNCT
ejpam-3280	129	15	f2	f2	PROPN
ejpam-3280	129	16	,	,	PUNCT
ejpam-3280	129	17	a2	a2	PROPN
ejpam-3280	129	18	)	)	PUNCT
ejpam-3280	129	19	⊆	⊆	NUM
ejpam-3280	129	20	(	(	PUNCT
ejpam-3280	129	21	f3	f3	ADJ
ejpam-3280	129	22	,	,	PUNCT
ejpam-3280	129	23	a3	a3	NOUN
ejpam-3280	129	24	)	)	PUNCT
ejpam-3280	129	25	,	,	PUNCT
ejpam-3280	129	26	therefore	therefore	ADV
ejpam-3280	129	27	we	we	PRON
ejpam-3280	129	28	have	have	VERB
ejpam-3280	129	29	a1	a1	NOUN
ejpam-3280	129	30	∪	∪	NOUN
ejpam-3280	129	31	a2	a2	PROPN
ejpam-3280	129	32	⊆	⊆	NUM
ejpam-3280	129	33	a3	a3	NOUN
ejpam-3280	129	34	.	.	PUNCT
ejpam-3280	130	1	let	let	VERB
ejpam-3280	130	2	x	x	X
ejpam-3280	130	3	∈	∈	PROPN
ejpam-3280	130	4	a1	a1	NOUN
ejpam-3280	130	5	∪a2	∪a2	PRON
ejpam-3280	130	6	and	and	CCONJ
ejpam-3280	130	7	(	(	PUNCT
ejpam-3280	130	8	f	f	X
ejpam-3280	130	9	,	,	PUNCT
ejpam-3280	130	10	a	a	PRON
ejpam-3280	130	11	)	)	PUNCT
ejpam-3280	130	12	=	=	SYM
ejpam-3280	130	13	(	(	PUNCT
ejpam-3280	130	14	f1	f1	NOUN
ejpam-3280	130	15	,	,	PUNCT
ejpam-3280	130	16	a1	a1	NOUN
ejpam-3280	130	17	)	)	PUNCT
ejpam-3280	130	18	∪	∪	NOUN
ejpam-3280	130	19	(	(	PUNCT
ejpam-3280	130	20	f2	f2	PROPN
ejpam-3280	130	21	,	,	PUNCT
ejpam-3280	130	22	a2	a2	PROPN
ejpam-3280	130	23	)	)	PUNCT
ejpam-3280	130	24	.	.	PUNCT
ejpam-3280	131	1	if	if	SCONJ
ejpam-3280	131	2	x	x	SYM
ejpam-3280	131	3	∈	∈	PROPN
ejpam-3280	131	4	a1	a1	NOUN
ejpam-3280	131	5	−	−	PROPN
ejpam-3280	131	6	a2	a2	PROPN
ejpam-3280	131	7	,	,	PUNCT
ejpam-3280	131	8	then	then	ADV
ejpam-3280	131	9	f(x	f(x	PROPN
ejpam-3280	131	10	)	)	PUNCT
ejpam-3280	131	11	=	=	SYM
ejpam-3280	131	12	f1(x	f1(x	NUM
ejpam-3280	131	13	)	)	PUNCT
ejpam-3280	131	14	⊆	⊆	NUM
ejpam-3280	131	15	f3(x	f3(x	NUM
ejpam-3280	131	16	)	)	PUNCT
ejpam-3280	131	17	,	,	PUNCT
ejpam-3280	131	18	if	if	SCONJ
ejpam-3280	131	19	x	x	PROPN
ejpam-3280	131	20	∈	∈	PROPN
ejpam-3280	131	21	a2	a2	PROPN
ejpam-3280	131	22	−	−	PROPN
ejpam-3280	131	23	a1	a1	PROPN
ejpam-3280	131	24	,	,	PUNCT
ejpam-3280	131	25	then	then	ADV
ejpam-3280	131	26	f(x	f(x	PROPN
ejpam-3280	131	27	)	)	PUNCT
ejpam-3280	131	28	=	=	SYM
ejpam-3280	132	1	f2(x	f2(x	PROPN
ejpam-3280	132	2	)	)	PUNCT
ejpam-3280	132	3	⊆	⊆	NUM
ejpam-3280	132	4	f3(x	f3(x	NUM
ejpam-3280	132	5	)	)	PUNCT
ejpam-3280	132	6	,	,	PUNCT
ejpam-3280	132	7	if	if	SCONJ
ejpam-3280	132	8	x	x	SYM
ejpam-3280	132	9	∈	∈	NOUN
ejpam-3280	132	10	a1	a1	NOUN
ejpam-3280	132	11	∩	∩	ADJ
ejpam-3280	132	12	a2	a2	PROPN
ejpam-3280	132	13	,	,	PUNCT
ejpam-3280	132	14	then	then	ADV
ejpam-3280	132	15	f(x	f(x	PROPN
ejpam-3280	132	16	)	)	PUNCT
ejpam-3280	132	17	=	=	SYM
ejpam-3280	132	18	f1(x	f1(x	NOUN
ejpam-3280	132	19	)	)	PUNCT
ejpam-3280	132	20	∩	∩	NOUN
ejpam-3280	132	21	f2(x	f2(x	PROPN
ejpam-3280	132	22	)	)	PUNCT
ejpam-3280	132	23	⊆	⊆	NUM
ejpam-3280	132	24	f3(x	f3(x	NUM
ejpam-3280	132	25	)	)	PUNCT
ejpam-3280	132	26	.	.	PUNCT
ejpam-3280	133	1	thus	thus	ADV
ejpam-3280	133	2	(	(	PUNCT
ejpam-3280	133	3	f1	f1	NOUN
ejpam-3280	133	4	,	,	PUNCT
ejpam-3280	133	5	a1	a1	NOUN
ejpam-3280	133	6	)	)	PUNCT
ejpam-3280	133	7	∪	∪	NOUN
ejpam-3280	133	8	(	(	PUNCT
ejpam-3280	133	9	f2	f2	PROPN
ejpam-3280	133	10	,	,	PUNCT
ejpam-3280	133	11	a2	a2	PROPN
ejpam-3280	133	12	)	)	PUNCT
ejpam-3280	133	13	⊆	⊆	NUM
ejpam-3280	133	14	(	(	PUNCT
ejpam-3280	133	15	f3	f3	ADJ
ejpam-3280	133	16	,	,	PUNCT
ejpam-3280	133	17	a3	a3	NOUN
ejpam-3280	133	18	)	)	PUNCT
ejpam-3280	133	19	.	.	PUNCT
ejpam-3280	134	1	so	so	ADV
ejpam-3280	134	2	,	,	PUNCT
ejpam-3280	134	3	we	we	PRON
ejpam-3280	134	4	have	have	VERB
ejpam-3280	134	5	l((f1	l((f1	NOUN
ejpam-3280	134	6	,	,	PUNCT
ejpam-3280	134	7	a1	a1	NOUN
ejpam-3280	134	8	)	)	PUNCT
ejpam-3280	134	9	∪	∪	NOUN
ejpam-3280	134	10	(	(	PUNCT
ejpam-3280	134	11	f2	f2	PROPN
ejpam-3280	134	12	,	,	PUNCT
ejpam-3280	134	13	a2	a2	PROPN
ejpam-3280	134	14	)	)	PUNCT
ejpam-3280	134	15	)	)	PUNCT
ejpam-3280	135	1	⊆	⊆	NUM
ejpam-3280	135	2	l(f3	l(f3	NOUN
ejpam-3280	135	3	,	,	PUNCT
ejpam-3280	135	4	a3	a3	NOUN
ejpam-3280	135	5	)	)	PUNCT
ejpam-3280	135	6	.	.	PUNCT
ejpam-3280	136	1	lemma	lemma	PROPN
ejpam-3280	136	2	4	4	X
ejpam-3280	136	3	.	.	PUNCT
ejpam-3280	137	1	let	let	VERB
ejpam-3280	137	2	(	(	PUNCT
ejpam-3280	137	3	f	f	X
ejpam-3280	137	4	,	,	PUNCT
ejpam-3280	137	5	a	a	PRON
ejpam-3280	137	6	)	)	PUNCT
ejpam-3280	137	7	and	and	CCONJ
ejpam-3280	137	8	(	(	PUNCT
ejpam-3280	137	9	g	g	NOUN
ejpam-3280	137	10	,	,	PUNCT
ejpam-3280	137	11	b	b	NOUN
ejpam-3280	137	12	)	)	PUNCT
ejpam-3280	137	13	be	be	AUX
ejpam-3280	137	14	two	two	NUM
ejpam-3280	137	15	soft	soft	ADJ
ejpam-3280	137	16	sets	set	NOUN
ejpam-3280	137	17	over	over	ADP
ejpam-3280	137	18	v	v	NOUN
ejpam-3280	137	19	.	.	PUNCT
ejpam-3280	138	1	then	then	ADV
ejpam-3280	138	2	l((f	l((f	VERB
ejpam-3280	138	3	,	,	PUNCT
ejpam-3280	138	4	a	a	PRON
ejpam-3280	138	5	)	)	PUNCT
ejpam-3280	138	6	∪	∪	NOUN
ejpam-3280	138	7	(	(	PUNCT
ejpam-3280	138	8	g	g	NOUN
ejpam-3280	138	9	,	,	PUNCT
ejpam-3280	138	10	b	b	NOUN
ejpam-3280	138	11	)	)	PUNCT
ejpam-3280	138	12	)	)	PUNCT
ejpam-3280	139	1	=	=	SYM
ejpam-3280	139	2	l(l(f	l(l(f	PROPN
ejpam-3280	139	3	,	,	PUNCT
ejpam-3280	139	4	a	a	PRON
ejpam-3280	139	5	)	)	PUNCT
ejpam-3280	139	6	∪	∪	ADP
ejpam-3280	139	7	l(g	l(g	PROPN
ejpam-3280	139	8	,	,	PUNCT
ejpam-3280	139	9	b	b	NOUN
ejpam-3280	139	10	)	)	PUNCT
ejpam-3280	139	11	)	)	PUNCT
ejpam-3280	139	12	.	.	PUNCT
ejpam-3280	140	1	proof	proof	NOUN
ejpam-3280	140	2	.	.	PUNCT
ejpam-3280	141	1	clearly	clearly	ADV
ejpam-3280	141	2	,	,	PUNCT
ejpam-3280	141	3	l((f	l((f	PROPN
ejpam-3280	141	4	,	,	PUNCT
ejpam-3280	141	5	a	a	PRON
ejpam-3280	141	6	)	)	PUNCT
ejpam-3280	141	7	∪	∪	NOUN
ejpam-3280	141	8	(	(	PUNCT
ejpam-3280	141	9	g	g	NOUN
ejpam-3280	141	10	,	,	PUNCT
ejpam-3280	141	11	b	b	NOUN
ejpam-3280	141	12	)	)	PUNCT
ejpam-3280	141	13	)	)	PUNCT
ejpam-3280	141	14	⊆	⊆	X
ejpam-3280	141	15	l(l(f	l(l(f	PROPN
ejpam-3280	141	16	,	,	PUNCT
ejpam-3280	141	17	a	a	PRON
ejpam-3280	141	18	)	)	PUNCT
ejpam-3280	141	19	∪	∪	ADP
ejpam-3280	141	20	l(g	l(g	PROPN
ejpam-3280	141	21	,	,	PUNCT
ejpam-3280	141	22	b	b	NOUN
ejpam-3280	141	23	)	)	PUNCT
ejpam-3280	141	24	)	)	PUNCT
ejpam-3280	141	25	.	.	PUNCT
ejpam-3280	142	1	moreover	moreover	ADV
ejpam-3280	142	2	,	,	PUNCT
ejpam-3280	142	3	since	since	SCONJ
ejpam-3280	142	4	l(f	l(f	PROPN
ejpam-3280	142	5	,	,	PUNCT
ejpam-3280	142	6	a	a	PRON
ejpam-3280	142	7	)	)	PUNCT
ejpam-3280	142	8	⊆	⊆	NUM
ejpam-3280	142	9	l((f	l((f	ADJ
ejpam-3280	142	10	,	,	PUNCT
ejpam-3280	142	11	a)∪	a)∪	PROPN
ejpam-3280	142	12	(	(	PUNCT
ejpam-3280	142	13	g	g	NOUN
ejpam-3280	142	14	,	,	PUNCT
ejpam-3280	142	15	b	b	NOUN
ejpam-3280	142	16	)	)	PUNCT
ejpam-3280	142	17	)	)	PUNCT
ejpam-3280	142	18	and	and	CCONJ
ejpam-3280	142	19	l(g	l(g	PROPN
ejpam-3280	142	20	,	,	PUNCT
ejpam-3280	142	21	b	b	NOUN
ejpam-3280	142	22	)	)	PUNCT
ejpam-3280	142	23	⊆	⊆	NUM
ejpam-3280	142	24	l((f	l((f	ADJ
ejpam-3280	142	25	,	,	PUNCT
ejpam-3280	142	26	a)∪	a)∪	PROPN
ejpam-3280	142	27	(	(	PUNCT
ejpam-3280	142	28	g	g	NOUN
ejpam-3280	142	29	,	,	PUNCT
ejpam-3280	142	30	b	b	NOUN
ejpam-3280	142	31	)	)	PUNCT
ejpam-3280	142	32	)	)	PUNCT
ejpam-3280	142	33	,	,	PUNCT
ejpam-3280	142	34	thus	thus	ADV
ejpam-3280	142	35	l(l(f	l(l(f	PROPN
ejpam-3280	142	36	,	,	PUNCT
ejpam-3280	142	37	a)∪l(g	a)∪l(g	VERB
ejpam-3280	142	38	,	,	PUNCT
ejpam-3280	142	39	b	b	NOUN
ejpam-3280	142	40	)	)	PUNCT
ejpam-3280	142	41	)	)	PUNCT
ejpam-3280	143	1	⊆	⊆	NUM
ejpam-3280	143	2	l((f	l((f	VERB
ejpam-3280	143	3	,	,	PUNCT
ejpam-3280	143	4	a)∪	a)∪	PROPN
ejpam-3280	143	5	(	(	PUNCT
ejpam-3280	143	6	g	g	NOUN
ejpam-3280	143	7	,	,	PUNCT
ejpam-3280	143	8	b	b	NOUN
ejpam-3280	143	9	)	)	PUNCT
ejpam-3280	143	10	)	)	PUNCT
ejpam-3280	143	11	.	.	PUNCT
ejpam-3280	144	1	example	example	NOUN
ejpam-3280	145	1	3	3	X
ejpam-3280	145	2	.	.	X
ejpam-3280	145	3	consider	consider	VERB
ejpam-3280	145	4	v	v	NOUN
ejpam-3280	145	5	=	=	SYM
ejpam-3280	145	6	{	{	PUNCT
ejpam-3280	145	7	0	0	NUM
ejpam-3280	145	8	,	,	PUNCT
ejpam-3280	145	9	1	1	NUM
ejpam-3280	145	10	,	,	PUNCT
ejpam-3280	145	11	2	2	NUM
ejpam-3280	145	12	}	}	PUNCT
ejpam-3280	145	13	and	and	CCONJ
ejpam-3280	145	14	k	k	NOUN
ejpam-3280	145	15	=	=	X
ejpam-3280	145	16	{	{	PUNCT
ejpam-3280	145	17	0	0	NUM
ejpam-3280	145	18	,	,	PUNCT
ejpam-3280	145	19	1	1	NUM
ejpam-3280	145	20	,	,	PUNCT
ejpam-3280	145	21	2	2	NUM
ejpam-3280	145	22	}	}	PUNCT
ejpam-3280	145	23	with	with	ADP
ejpam-3280	145	24	the	the	DET
ejpam-3280	145	25	following	follow	VERB
ejpam-3280	145	26	operation	operation	NOUN
ejpam-3280	145	27	:	:	PUNCT
ejpam-3280	146	1	+	+	CCONJ
ejpam-3280	146	2	0	0	NUM
ejpam-3280	146	3	1	1	NUM
ejpam-3280	146	4	2	2	NUM
ejpam-3280	146	5	0	0	NUM
ejpam-3280	146	6	0	0	NUM
ejpam-3280	146	7	1	1	NUM
ejpam-3280	146	8	2	2	NUM
ejpam-3280	146	9	1	1	NUM
ejpam-3280	146	10	1	1	NUM
ejpam-3280	146	11	2	2	NUM
ejpam-3280	146	12	0	0	NUM
ejpam-3280	146	13	2	2	NUM
ejpam-3280	146	14	2	2	NUM
ejpam-3280	146	15	0	0	NUM
ejpam-3280	146	16	1	1	NUM
ejpam-3280	146	17	·	·	SYM
ejpam-3280	146	18	0	0	NUM
ejpam-3280	146	19	1	1	NUM
ejpam-3280	146	20	2	2	NUM
ejpam-3280	146	21	0	0	NUM
ejpam-3280	146	22	0	0	NUM
ejpam-3280	146	23	0	0	NUM
ejpam-3280	146	24	0	0	NUM
ejpam-3280	146	25	1	1	NUM
ejpam-3280	146	26	0	0	NUM
ejpam-3280	146	27	1	1	NUM
ejpam-3280	146	28	2	2	NUM
ejpam-3280	146	29	2	2	NUM
ejpam-3280	146	30	0	0	NUM
ejpam-3280	146	31	2	2	NUM
ejpam-3280	146	32	1	1	NUM
ejpam-3280	146	33	e.	e.	PROPN
ejpam-3280	146	34	ranjbar	ranjbar	PROPN
ejpam-3280	146	35	-	-	PUNCT
ejpam-3280	146	36	yanehsari	yanehsari	NOUN
ejpam-3280	146	37	,	,	PUNCT
ejpam-3280	146	38	m.	m.	NOUN
ejpam-3280	146	39	asghari	asghari	ADJ
ejpam-3280	146	40	-	-	PUNCT
ejpam-3280	146	41	larimi	larimi	PROPN
ejpam-3280	146	42	,	,	PUNCT
ejpam-3280	146	43	r.	r.	PROPN
ejpam-3280	146	44	ameri	ameri	PROPN
ejpam-3280	146	45	/	/	SYM
ejpam-3280	146	46	eur	eur	PROPN
ejpam-3280	146	47	.	.	PUNCT
ejpam-3280	147	1	j.	j.	PROPN
ejpam-3280	147	2	pure	pure	PROPN
ejpam-3280	147	3	appl	appl	PROPN
ejpam-3280	147	4	.	.	PROPN
ejpam-3280	147	5	math	math	PROPN
ejpam-3280	147	6	,	,	PUNCT
ejpam-3280	147	7	12	12	NUM
ejpam-3280	147	8	(	(	PUNCT
ejpam-3280	147	9	1	1	NUM
ejpam-3280	147	10	)	)	PUNCT
ejpam-3280	147	11	(	(	PUNCT
ejpam-3280	147	12	2019	2019	NUM
ejpam-3280	147	13	)	)	PUNCT
ejpam-3280	147	14	,	,	PUNCT
ejpam-3280	147	15	118	118	NUM
ejpam-3280	147	16	-	-	SYM
ejpam-3280	147	17	134	134	NUM
ejpam-3280	147	18	123	123	NUM
ejpam-3280	147	19	we	we	PRON
ejpam-3280	147	20	set	set	VERB
ejpam-3280	147	21	:	:	PUNCT
ejpam-3280	147	22	◦	◦	NOUN
ejpam-3280	147	23	:	:	PUNCT
ejpam-3280	147	24	k	k	X
ejpam-3280	147	25	×	×	PROPN
ejpam-3280	147	26	v	v	INTJ
ejpam-3280	147	27	→	→	SYM
ejpam-3280	147	28	p	p	X
ejpam-3280	147	29	(	(	PUNCT
ejpam-3280	147	30	v	v	NOUN
ejpam-3280	147	31	)	)	PUNCT
ejpam-3280	147	32	◦	◦	NOUN
ejpam-3280	147	33	(	(	PUNCT
ejpam-3280	147	34	a	a	DET
ejpam-3280	147	35	,	,	PUNCT
ejpam-3280	147	36	x	x	NOUN
ejpam-3280	147	37	)	)	PUNCT
ejpam-3280	147	38	=	=	PRON
ejpam-3280	147	39	{	{	PUNCT
ejpam-3280	147	40	{	{	PUNCT
ejpam-3280	147	41	1	1	NUM
ejpam-3280	147	42	}	}	PUNCT
ejpam-3280	147	43	if	if	SCONJ
ejpam-3280	147	44	a	a	PRON
ejpam-3280	147	45	=	=	SYM
ejpam-3280	147	46	x	x	SYM
ejpam-3280	147	47	=	=	SYM
ejpam-3280	147	48	2	2	NUM
ejpam-3280	147	49	{	{	PUNCT
ejpam-3280	147	50	a	a	PRON
ejpam-3280	147	51	·	·	PUNCT
ejpam-3280	147	52	x	x	X
ejpam-3280	147	53	}	}	PUNCT
ejpam-3280	147	54	otherwise	otherwise	ADV
ejpam-3280	147	55	.	.	PUNCT
ejpam-3280	148	1	then	then	ADV
ejpam-3280	148	2	(	(	PUNCT
ejpam-3280	148	3	v,+	v,+	NUM
ejpam-3280	148	4	,	,	PUNCT
ejpam-3280	148	5	◦	◦	NOUN
ejpam-3280	148	6	,	,	PUNCT
ejpam-3280	148	7	k	k	NOUN
ejpam-3280	148	8	)	)	PUNCT
ejpam-3280	148	9	is	be	AUX
ejpam-3280	148	10	a	a	DET
ejpam-3280	148	11	strongly	strongly	ADV
ejpam-3280	148	12	distributive	distributive	ADJ
ejpam-3280	148	13	hypervector	hypervector	NOUN
ejpam-3280	148	14	space	space	NOUN
ejpam-3280	148	15	over	over	ADP
ejpam-3280	148	16	k.	k.	PROPN
ejpam-3280	148	17	let	let	VERB
ejpam-3280	148	18	(	(	PUNCT
ejpam-3280	148	19	f	f	X
ejpam-3280	148	20	,	,	PUNCT
ejpam-3280	148	21	a	a	PRON
ejpam-3280	148	22	)	)	PUNCT
ejpam-3280	148	23	and	and	CCONJ
ejpam-3280	148	24	(	(	PUNCT
ejpam-3280	148	25	g	g	NOUN
ejpam-3280	148	26	,	,	PUNCT
ejpam-3280	148	27	b	b	NOUN
ejpam-3280	148	28	)	)	PUNCT
ejpam-3280	148	29	be	be	AUX
ejpam-3280	148	30	two	two	NUM
ejpam-3280	148	31	soft	soft	ADJ
ejpam-3280	148	32	sets	set	NOUN
ejpam-3280	148	33	over	over	ADP
ejpam-3280	148	34	v	v	NOUN
ejpam-3280	148	35	,	,	PUNCT
ejpam-3280	148	36	where	where	SCONJ
ejpam-3280	148	37	a	a	PRON
ejpam-3280	148	38	=	=	X
ejpam-3280	148	39	{	{	PUNCT
ejpam-3280	148	40	0	0	NUM
ejpam-3280	148	41	,	,	PUNCT
ejpam-3280	148	42	1	1	NUM
ejpam-3280	148	43	,	,	PUNCT
ejpam-3280	148	44	2	2	NUM
ejpam-3280	148	45	}	}	PUNCT
ejpam-3280	148	46	,	,	PUNCT
ejpam-3280	149	1	b	b	X
ejpam-3280	149	2	=	=	SYM
ejpam-3280	149	3	{	{	PUNCT
ejpam-3280	149	4	0	0	NUM
ejpam-3280	149	5	,	,	PUNCT
ejpam-3280	149	6	1	1	NUM
ejpam-3280	149	7	,	,	PUNCT
ejpam-3280	149	8	2	2	NUM
ejpam-3280	149	9	}	}	PUNCT
ejpam-3280	149	10	,	,	PUNCT
ejpam-3280	149	11	f(0	f(0	NOUN
ejpam-3280	149	12	)	)	PUNCT
ejpam-3280	149	13	=	=	PUNCT
ejpam-3280	149	14	{	{	PUNCT
ejpam-3280	149	15	0	0	NUM
ejpam-3280	149	16	}	}	PUNCT
ejpam-3280	149	17	,	,	PUNCT
ejpam-3280	149	18	f(1	f(1	PROPN
ejpam-3280	149	19	)	)	PUNCT
ejpam-3280	149	20	=	=	PRON
ejpam-3280	149	21	{	{	PUNCT
ejpam-3280	149	22	0	0	NUM
ejpam-3280	149	23	,	,	PUNCT
ejpam-3280	149	24	1	1	NUM
ejpam-3280	149	25	}	}	PUNCT
ejpam-3280	149	26	,	,	PUNCT
ejpam-3280	149	27	g(0	g(0	PROPN
ejpam-3280	149	28	)	)	PUNCT
ejpam-3280	149	29	=	=	PUNCT
ejpam-3280	149	30	{	{	PUNCT
ejpam-3280	149	31	0	0	NUM
ejpam-3280	149	32	}	}	PUNCT
ejpam-3280	149	33	,	,	PUNCT
ejpam-3280	149	34	g(1	g(1	NOUN
ejpam-3280	149	35	)	)	PUNCT
ejpam-3280	149	36	=	=	PUNCT
ejpam-3280	149	37	{	{	PUNCT
ejpam-3280	149	38	0	0	NUM
ejpam-3280	149	39	,	,	PUNCT
ejpam-3280	149	40	2	2	NUM
ejpam-3280	149	41	}	}	PUNCT
ejpam-3280	149	42	and	and	CCONJ
ejpam-3280	149	43	g(2	g(2	PROPN
ejpam-3280	149	44	)	)	PUNCT
ejpam-3280	149	45	=	=	PRON
ejpam-3280	149	46	{	{	PUNCT
ejpam-3280	149	47	2	2	NUM
ejpam-3280	149	48	}	}	PUNCT
ejpam-3280	149	49	.	.	PUNCT
ejpam-3280	150	1	suppose	suppose	VERB
ejpam-3280	150	2	c	c	NOUN
ejpam-3280	150	3	=	=	PUNCT
ejpam-3280	150	4	a∩b	a∩b	PROPN
ejpam-3280	150	5	and	and	CCONJ
ejpam-3280	150	6	(	(	PUNCT
ejpam-3280	150	7	h	h	NOUN
ejpam-3280	150	8	,	,	PUNCT
ejpam-3280	150	9	c	c	NOUN
ejpam-3280	150	10	)	)	PUNCT
ejpam-3280	150	11	=	=	SYM
ejpam-3280	150	12	(	(	PUNCT
ejpam-3280	150	13	f	f	PROPN
ejpam-3280	150	14	,	,	PUNCT
ejpam-3280	150	15	a)∩(g	a)∩(g	PROPN
ejpam-3280	150	16	,	,	PUNCT
ejpam-3280	150	17	b	b	NOUN
ejpam-3280	150	18	)	)	PUNCT
ejpam-3280	150	19	,	,	PUNCT
ejpam-3280	150	20	then	then	ADV
ejpam-3280	150	21	h(0	h(0	PROPN
ejpam-3280	150	22	)	)	PUNCT
ejpam-3280	151	1	=	=	SYM
ejpam-3280	151	2	f(0	f(0	NOUN
ejpam-3280	151	3	)	)	PUNCT
ejpam-3280	151	4	∩	∩	NOUN
ejpam-3280	151	5	g(0	g(0	PROPN
ejpam-3280	151	6	)	)	PUNCT
ejpam-3280	151	7	=	=	PUNCT
ejpam-3280	151	8	{	{	PUNCT
ejpam-3280	151	9	0	0	NUM
ejpam-3280	151	10	}	}	PUNCT
ejpam-3280	151	11	and	and	CCONJ
ejpam-3280	151	12	h(1	h(1	PROPN
ejpam-3280	151	13	)	)	PUNCT
ejpam-3280	151	14	=	=	SYM
ejpam-3280	151	15	f(1	f(1	PROPN
ejpam-3280	151	16	)	)	PUNCT
ejpam-3280	151	17	∩	∩	NOUN
ejpam-3280	151	18	g(1	g(1	NOUN
ejpam-3280	151	19	)	)	PUNCT
ejpam-3280	151	20	=	=	PRON
ejpam-3280	151	21	{	{	PUNCT
ejpam-3280	151	22	0	0	NUM
ejpam-3280	151	23	}	}	PUNCT
ejpam-3280	151	24	.	.	PUNCT
ejpam-3280	152	1	therefore	therefore	ADV
ejpam-3280	152	2	l((f	l((f	VERB
ejpam-3280	152	3	,	,	PUNCT
ejpam-3280	152	4	a	a	PRON
ejpam-3280	152	5	)	)	PUNCT
ejpam-3280	152	6	∩	∩	NOUN
ejpam-3280	152	7	(	(	PUNCT
ejpam-3280	152	8	g	g	PROPN
ejpam-3280	152	9	,	,	PUNCT
ejpam-3280	152	10	b	b	NOUN
ejpam-3280	152	11	)	)	PUNCT
ejpam-3280	152	12	)	)	PUNCT
ejpam-3280	152	13	=	=	SYM
ejpam-3280	153	1	l((h	l((h	PROPN
ejpam-3280	153	2	,	,	PUNCT
ejpam-3280	153	3	c	c	NOUN
ejpam-3280	153	4	)	)	PUNCT
ejpam-3280	153	5	)	)	PUNCT
ejpam-3280	154	1	=	=	PRON
ejpam-3280	154	2	(	(	PUNCT
ejpam-3280	154	3	h	h	NOUN
ejpam-3280	154	4	,	,	PUNCT
ejpam-3280	154	5	c	c	NOUN
ejpam-3280	154	6	)	)	PUNCT
ejpam-3280	154	7	.	.	PUNCT
ejpam-3280	155	1	let	let	VERB
ejpam-3280	155	2	l((f	l((f	ADJ
ejpam-3280	155	3	,	,	PUNCT
ejpam-3280	155	4	a	a	PRON
ejpam-3280	155	5	)	)	PUNCT
ejpam-3280	155	6	)	)	PUNCT
ejpam-3280	156	1	=	=	PRON
ejpam-3280	156	2	(	(	PUNCT
ejpam-3280	156	3	α	α	NOUN
ejpam-3280	156	4	,	,	PUNCT
ejpam-3280	156	5	a0	a0	NOUN
ejpam-3280	156	6	)	)	PUNCT
ejpam-3280	156	7	and	and	CCONJ
ejpam-3280	156	8	l((g	l((g	ADJ
ejpam-3280	156	9	,	,	PUNCT
ejpam-3280	156	10	b	b	NOUN
ejpam-3280	156	11	)	)	PUNCT
ejpam-3280	156	12	)	)	PUNCT
ejpam-3280	157	1	=	=	SYM
ejpam-3280	157	2	(	(	PUNCT
ejpam-3280	157	3	β	β	X
ejpam-3280	157	4	,	,	PUNCT
ejpam-3280	157	5	b0	b0	NOUN
ejpam-3280	157	6	)	)	PUNCT
ejpam-3280	157	7	.	.	PUNCT
ejpam-3280	158	1	then	then	ADV
ejpam-3280	158	2	α(0	α(0	PROPN
ejpam-3280	158	3	)	)	PUNCT
ejpam-3280	158	4	=	=	PRON
ejpam-3280	158	5	{	{	PUNCT
ejpam-3280	158	6	0	0	NUM
ejpam-3280	158	7	}	}	PUNCT
ejpam-3280	158	8	,	,	PUNCT
ejpam-3280	158	9	α(1	α(1	PROPN
ejpam-3280	158	10	)	)	PUNCT
ejpam-3280	158	11	=	=	SYM
ejpam-3280	158	12	v	v	NOUN
ejpam-3280	158	13	,	,	PUNCT
ejpam-3280	158	14	β(0	β(0	PROPN
ejpam-3280	158	15	)	)	PUNCT
ejpam-3280	158	16	=	=	PRON
ejpam-3280	158	17	{	{	PUNCT
ejpam-3280	158	18	0	0	NUM
ejpam-3280	158	19	}	}	PUNCT
ejpam-3280	158	20	and	and	CCONJ
ejpam-3280	158	21	β(1	β(1	NUM
ejpam-3280	158	22	)	)	PUNCT
ejpam-3280	158	23	=	=	SYM
ejpam-3280	158	24	β(2	β(2	PROPN
ejpam-3280	158	25	)	)	PUNCT
ejpam-3280	159	1	=	=	SYM
ejpam-3280	159	2	v	v	X
ejpam-3280	159	3	.	.	PUNCT
ejpam-3280	160	1	assume	assume	VERB
ejpam-3280	160	2	l((f	l((f	PROPN
ejpam-3280	160	3	,	,	PUNCT
ejpam-3280	160	4	a	a	PRON
ejpam-3280	160	5	)	)	PUNCT
ejpam-3280	160	6	)	)	PUNCT
ejpam-3280	161	1	∩	∩	PROPN
ejpam-3280	161	2	l((g	l((g	ADJ
ejpam-3280	161	3	,	,	PUNCT
ejpam-3280	161	4	b	b	NOUN
ejpam-3280	161	5	)	)	PUNCT
ejpam-3280	161	6	)	)	PUNCT
ejpam-3280	162	1	=	=	SYM
ejpam-3280	162	2	(	(	PUNCT
ejpam-3280	162	3	γ	γ	X
ejpam-3280	162	4	,	,	PUNCT
ejpam-3280	162	5	c0	c0	NOUN
ejpam-3280	162	6	)	)	PUNCT
ejpam-3280	162	7	,	,	PUNCT
ejpam-3280	162	8	where	where	SCONJ
ejpam-3280	162	9	c0	c0	PROPN
ejpam-3280	162	10	=	=	PROPN
ejpam-3280	162	11	a0	a0	PROPN
ejpam-3280	162	12	∩b0	∩b0	PROPN
ejpam-3280	162	13	and	and	CCONJ
ejpam-3280	162	14	γ(0	γ(0	PROPN
ejpam-3280	162	15	)	)	PUNCT
ejpam-3280	162	16	=	=	SYM
ejpam-3280	162	17	α(0	α(0	NOUN
ejpam-3280	162	18	)	)	PUNCT
ejpam-3280	162	19	∩	∩	NOUN
ejpam-3280	162	20	β(0	β(0	NOUN
ejpam-3280	162	21	)	)	PUNCT
ejpam-3280	162	22	=	=	PRON
ejpam-3280	162	23	{	{	PUNCT
ejpam-3280	162	24	0	0	NUM
ejpam-3280	162	25	}	}	PUNCT
ejpam-3280	162	26	and	and	CCONJ
ejpam-3280	162	27	γ(1	γ(1	PROPN
ejpam-3280	162	28	)	)	PUNCT
ejpam-3280	162	29	=	=	SYM
ejpam-3280	162	30	α(1	α(1	ADJ
ejpam-3280	162	31	)	)	PUNCT
ejpam-3280	162	32	∩	∩	NOUN
ejpam-3280	162	33	β(1	β(1	NUM
ejpam-3280	162	34	)	)	PUNCT
ejpam-3280	162	35	=	=	SYM
ejpam-3280	162	36	v	v	NOUN
ejpam-3280	162	37	.	.	PUNCT
ejpam-3280	163	1	so	so	ADV
ejpam-3280	163	2	,	,	PUNCT
ejpam-3280	163	3	l(l((f	l(l((f	PROPN
ejpam-3280	163	4	,	,	PUNCT
ejpam-3280	163	5	a	a	PRON
ejpam-3280	163	6	)	)	PUNCT
ejpam-3280	163	7	)	)	PUNCT
ejpam-3280	164	1	∩	∩	PROPN
ejpam-3280	164	2	l((g	l((g	ADJ
ejpam-3280	164	3	,	,	PUNCT
ejpam-3280	164	4	b	b	NOUN
ejpam-3280	164	5	)	)	PUNCT
ejpam-3280	164	6	)	)	PUNCT
ejpam-3280	164	7	)	)	PUNCT
ejpam-3280	165	1	=	=	SYM
ejpam-3280	165	2	l((γ	l((γ	PROPN
ejpam-3280	165	3	,	,	PUNCT
ejpam-3280	165	4	c0	c0	NOUN
ejpam-3280	165	5	)	)	PUNCT
ejpam-3280	165	6	)	)	PUNCT
ejpam-3280	166	1	=	=	PRON
ejpam-3280	166	2	(	(	PUNCT
ejpam-3280	166	3	γ	γ	X
ejpam-3280	166	4	,	,	PUNCT
ejpam-3280	166	5	c0	c0	NOUN
ejpam-3280	166	6	)	)	PUNCT
ejpam-3280	166	7	.	.	PUNCT
ejpam-3280	167	1	since	since	SCONJ
ejpam-3280	167	2	γ(1	γ(1	PROPN
ejpam-3280	167	3	)	)	PUNCT
ejpam-3280	167	4	6=	6=	PUNCT
ejpam-3280	167	5	h(1	h(1	PROPN
ejpam-3280	167	6	)	)	PUNCT
ejpam-3280	167	7	,	,	PUNCT
ejpam-3280	167	8	thus	thus	ADV
ejpam-3280	167	9	l(l((f	l(l((f	VERB
ejpam-3280	167	10	,	,	PUNCT
ejpam-3280	167	11	a	a	PRON
ejpam-3280	167	12	)	)	PUNCT
ejpam-3280	167	13	)	)	PUNCT
ejpam-3280	167	14	∩	∩	PROPN
ejpam-3280	167	15	l((g	l((g	ADJ
ejpam-3280	167	16	,	,	PUNCT
ejpam-3280	167	17	b	b	NOUN
ejpam-3280	167	18	)	)	PUNCT
ejpam-3280	167	19	)	)	PUNCT
ejpam-3280	167	20	)	)	PUNCT
ejpam-3280	167	21	6=	6=	PRON
ejpam-3280	167	22	l((f	l((f	PROPN
ejpam-3280	167	23	,	,	PUNCT
ejpam-3280	167	24	a	a	PRON
ejpam-3280	167	25	)	)	PUNCT
ejpam-3280	167	26	∩	∩	NOUN
ejpam-3280	167	27	(	(	PUNCT
ejpam-3280	167	28	g	g	PROPN
ejpam-3280	167	29	,	,	PUNCT
ejpam-3280	167	30	b	b	NOUN
ejpam-3280	167	31	)	)	PUNCT
ejpam-3280	167	32	)	)	PUNCT
ejpam-3280	167	33	.	.	PUNCT
ejpam-3280	168	1	remark	remark	PROPN
ejpam-3280	168	2	1	1	NUM
ejpam-3280	168	3	.	.	PUNCT
ejpam-3280	169	1	let	let	VERB
ejpam-3280	169	2	(	(	PUNCT
ejpam-3280	169	3	f	f	X
ejpam-3280	169	4	,	,	PUNCT
ejpam-3280	169	5	a	a	PRON
ejpam-3280	169	6	)	)	PUNCT
ejpam-3280	169	7	and	and	CCONJ
ejpam-3280	169	8	(	(	PUNCT
ejpam-3280	169	9	g	g	NOUN
ejpam-3280	169	10	,	,	PUNCT
ejpam-3280	169	11	b	b	NOUN
ejpam-3280	169	12	)	)	PUNCT
ejpam-3280	169	13	be	be	AUX
ejpam-3280	169	14	two	two	NUM
ejpam-3280	169	15	soft	soft	ADJ
ejpam-3280	169	16	sets	set	NOUN
ejpam-3280	169	17	over	over	ADP
ejpam-3280	169	18	v	v	NOUN
ejpam-3280	169	19	.	.	PUNCT
ejpam-3280	170	1	then	then	ADV
ejpam-3280	170	2	in	in	ADP
ejpam-3280	170	3	general	general	ADJ
ejpam-3280	170	4	,	,	PUNCT
ejpam-3280	170	5	l((f	l((f	PROPN
ejpam-3280	170	6	,	,	PUNCT
ejpam-3280	170	7	a	a	PRON
ejpam-3280	170	8	)	)	PUNCT
ejpam-3280	170	9	∩	∩	NOUN
ejpam-3280	170	10	(	(	PUNCT
ejpam-3280	170	11	g	g	PROPN
ejpam-3280	170	12	,	,	PUNCT
ejpam-3280	170	13	b	b	NOUN
ejpam-3280	170	14	)	)	PUNCT
ejpam-3280	170	15	)	)	PUNCT
ejpam-3280	171	1	6=	6=	ADP
ejpam-3280	171	2	l(l((f	l(l((f	PROPN
ejpam-3280	171	3	,	,	PUNCT
ejpam-3280	171	4	a	a	PRON
ejpam-3280	171	5	)	)	PUNCT
ejpam-3280	171	6	)	)	PUNCT
ejpam-3280	171	7	∩	∩	PROPN
ejpam-3280	171	8	l((g	l((g	ADJ
ejpam-3280	171	9	,	,	PUNCT
ejpam-3280	171	10	b	b	NOUN
ejpam-3280	171	11	)	)	PUNCT
ejpam-3280	171	12	)	)	PUNCT
ejpam-3280	171	13	)	)	PUNCT
ejpam-3280	171	14	.	.	PUNCT
ejpam-3280	172	1	theorem	theorem	NOUN
ejpam-3280	172	2	1	1	X
ejpam-3280	172	3	.	.	PUNCT
ejpam-3280	173	1	let	let	VERB
ejpam-3280	173	2	(	(	PUNCT
ejpam-3280	173	3	f	f	X
ejpam-3280	173	4	,	,	PUNCT
ejpam-3280	173	5	a	a	PRON
ejpam-3280	173	6	)	)	PUNCT
ejpam-3280	173	7	and	and	CCONJ
ejpam-3280	173	8	(	(	PUNCT
ejpam-3280	173	9	g	g	NOUN
ejpam-3280	173	10	,	,	PUNCT
ejpam-3280	173	11	b	b	NOUN
ejpam-3280	173	12	)	)	PUNCT
ejpam-3280	173	13	be	be	AUX
ejpam-3280	173	14	two	two	NUM
ejpam-3280	173	15	soft	soft	ADJ
ejpam-3280	173	16	hypervector	hypervector	NOUN
ejpam-3280	173	17	space	space	NOUN
ejpam-3280	173	18	over	over	ADP
ejpam-3280	173	19	v	v	NOUN
ejpam-3280	173	20	.	.	PUNCT
ejpam-3280	174	1	if	if	SCONJ
ejpam-3280	174	2	(	(	PUNCT
ejpam-3280	174	3	f	f	X
ejpam-3280	174	4	,	,	PUNCT
ejpam-3280	174	5	a	a	PRON
ejpam-3280	174	6	)	)	PUNCT
ejpam-3280	174	7	⊆	⊆	NUM
ejpam-3280	174	8	(	(	PUNCT
ejpam-3280	174	9	g	g	NOUN
ejpam-3280	174	10	,	,	PUNCT
ejpam-3280	174	11	b	b	NOUN
ejpam-3280	174	12	)	)	PUNCT
ejpam-3280	174	13	,	,	PUNCT
ejpam-3280	174	14	then	then	ADV
ejpam-3280	174	15	(	(	PUNCT
ejpam-3280	174	16	f	f	X
ejpam-3280	174	17	,	,	PUNCT
ejpam-3280	174	18	a	a	PRON
ejpam-3280	174	19	)	)	PUNCT
ejpam-3280	174	20	∪	∪	NOUN
ejpam-3280	174	21	(	(	PUNCT
ejpam-3280	174	22	g	g	NOUN
ejpam-3280	174	23	,	,	PUNCT
ejpam-3280	174	24	b	b	NOUN
ejpam-3280	174	25	)	)	PUNCT
ejpam-3280	174	26	is	be	AUX
ejpam-3280	174	27	a	a	DET
ejpam-3280	174	28	soft	soft	ADJ
ejpam-3280	174	29	hypervector	hypervector	NOUN
ejpam-3280	174	30	space	space	NOUN
ejpam-3280	174	31	over	over	ADP
ejpam-3280	174	32	v	v	NOUN
ejpam-3280	174	33	.	.	PUNCT
ejpam-3280	175	1	proof	proof	NOUN
ejpam-3280	175	2	.	.	PUNCT
ejpam-3280	176	1	let	let	VERB
ejpam-3280	176	2	(	(	PUNCT
ejpam-3280	176	3	f	f	X
ejpam-3280	176	4	,	,	PUNCT
ejpam-3280	176	5	a)∪	a)∪	PROPN
ejpam-3280	176	6	(	(	PUNCT
ejpam-3280	176	7	g	g	NOUN
ejpam-3280	176	8	,	,	PUNCT
ejpam-3280	176	9	b	b	NOUN
ejpam-3280	176	10	)	)	PUNCT
ejpam-3280	176	11	=	=	SYM
ejpam-3280	176	12	(	(	PUNCT
ejpam-3280	176	13	h	h	NOUN
ejpam-3280	176	14	,	,	PUNCT
ejpam-3280	176	15	c	c	NOUN
ejpam-3280	176	16	)	)	PUNCT
ejpam-3280	176	17	.	.	PUNCT
ejpam-3280	177	1	since	since	SCONJ
ejpam-3280	177	2	(	(	PUNCT
ejpam-3280	177	3	f	f	X
ejpam-3280	177	4	,	,	PUNCT
ejpam-3280	177	5	a	a	PRON
ejpam-3280	177	6	)	)	PUNCT
ejpam-3280	177	7	⊆	⊆	NUM
ejpam-3280	177	8	(	(	PUNCT
ejpam-3280	177	9	g	g	NOUN
ejpam-3280	177	10	,	,	PUNCT
ejpam-3280	177	11	b	b	NOUN
ejpam-3280	177	12	)	)	PUNCT
ejpam-3280	177	13	,	,	PUNCT
ejpam-3280	177	14	thus	thus	ADV
ejpam-3280	177	15	a	a	DET
ejpam-3280	177	16	⊆	⊆	NUM
ejpam-3280	177	17	b	b	NOUN
ejpam-3280	177	18	and	and	CCONJ
ejpam-3280	177	19	f(a	f(a	NOUN
ejpam-3280	177	20	)	)	PUNCT
ejpam-3280	177	21	⊆	⊆	NUM
ejpam-3280	177	22	g(a	g(a	PROPN
ejpam-3280	177	23	)	)	PUNCT
ejpam-3280	177	24	for	for	ADP
ejpam-3280	177	25	all	all	DET
ejpam-3280	177	26	a	a	DET
ejpam-3280	177	27	∈	∈	NOUN
ejpam-3280	177	28	a.	a.	NOUN
ejpam-3280	177	29	hence	hence	ADV
ejpam-3280	177	30	c	c	X
ejpam-3280	177	31	=	=	PUNCT
ejpam-3280	177	32	a	a	PRON
ejpam-3280	177	33	∪b	∪b	X
ejpam-3280	177	34	=	=	SYM
ejpam-3280	177	35	b	b	NOUN
ejpam-3280	177	36	and	and	CCONJ
ejpam-3280	177	37	for	for	ADP
ejpam-3280	177	38	all	all	PRON
ejpam-3280	177	39	c	c	NOUN
ejpam-3280	177	40	∈	∈	PROPN
ejpam-3280	177	41	c	c	X
ejpam-3280	177	42	,	,	PUNCT
ejpam-3280	177	43	we	we	PRON
ejpam-3280	177	44	have	have	VERB
ejpam-3280	177	45	h(c	h(c	PROPN
ejpam-3280	177	46	)	)	PUNCT
ejpam-3280	178	1	=	=	PRON
ejpam-3280	178	2	{	{	PUNCT
ejpam-3280	178	3	g(c	g(c	NOUN
ejpam-3280	178	4	)	)	PUNCT
ejpam-3280	178	5	if	if	SCONJ
ejpam-3280	178	6	c	c	PROPN
ejpam-3280	178	7	∈	∈	PROPN
ejpam-3280	178	8	b	b	X
ejpam-3280	178	9	−a	−a	NOUN
ejpam-3280	178	10	f(c	f(c	PROPN
ejpam-3280	178	11	)	)	PUNCT
ejpam-3280	178	12	∪	∪	ADP
ejpam-3280	178	13	g(c	g(c	NOUN
ejpam-3280	178	14	)	)	PUNCT
ejpam-3280	178	15	if	if	SCONJ
ejpam-3280	178	16	c	c	PROPN
ejpam-3280	178	17	∈	∈	PROPN
ejpam-3280	178	18	a	a	DET
ejpam-3280	178	19	∩b	∩b	NOUN
ejpam-3280	178	20	=	=	PUNCT
ejpam-3280	178	21	a	a	DET
ejpam-3280	178	22	=	=	SYM
ejpam-3280	178	23	g(c	g(c	NOUN
ejpam-3280	178	24	)	)	PUNCT
ejpam-3280	178	25	since	since	SCONJ
ejpam-3280	178	26	g(c	g(c	NOUN
ejpam-3280	178	27	)	)	PUNCT
ejpam-3280	178	28	is	be	AUX
ejpam-3280	178	29	a	a	DET
ejpam-3280	178	30	sub	sub	ADJ
ejpam-3280	178	31	-	-	ADJ
ejpam-3280	178	32	hypervector	hypervector	ADJ
ejpam-3280	178	33	space	space	NOUN
ejpam-3280	178	34	of	of	ADP
ejpam-3280	178	35	v	v	NOUN
ejpam-3280	178	36	.	.	PUNCT
ejpam-3280	179	1	therefore	therefore	ADV
ejpam-3280	179	2	,	,	PUNCT
ejpam-3280	179	3	(	(	PUNCT
ejpam-3280	179	4	f	f	X
ejpam-3280	179	5	,	,	PUNCT
ejpam-3280	179	6	a)∪	a)∪	PROPN
ejpam-3280	179	7	(	(	PUNCT
ejpam-3280	179	8	g	g	NOUN
ejpam-3280	179	9	,	,	PUNCT
ejpam-3280	179	10	b	b	NOUN
ejpam-3280	179	11	)	)	PUNCT
ejpam-3280	179	12	is	be	AUX
ejpam-3280	179	13	a	a	DET
ejpam-3280	179	14	soft	soft	ADJ
ejpam-3280	179	15	hypervector	hypervector	NOUN
ejpam-3280	179	16	space	space	NOUN
ejpam-3280	179	17	over	over	ADP
ejpam-3280	179	18	v	v	NOUN
ejpam-3280	179	19	.	.	PUNCT
ejpam-3280	180	1	it	it	PRON
ejpam-3280	180	2	is	be	AUX
ejpam-3280	180	3	clear	clear	ADJ
ejpam-3280	180	4	that	that	SCONJ
ejpam-3280	180	5	we	we	PRON
ejpam-3280	180	6	have	have	VERB
ejpam-3280	180	7	the	the	DET
ejpam-3280	180	8	followings	following	NOUN
ejpam-3280	180	9	:	:	PUNCT
ejpam-3280	180	10	proposition	proposition	NOUN
ejpam-3280	180	11	2	2	NUM
ejpam-3280	180	12	.	.	PUNCT
ejpam-3280	181	1	let	let	VERB
ejpam-3280	181	2	(	(	PUNCT
ejpam-3280	181	3	f	f	X
ejpam-3280	181	4	,	,	PUNCT
ejpam-3280	181	5	a	a	PRON
ejpam-3280	181	6	)	)	PUNCT
ejpam-3280	181	7	and	and	CCONJ
ejpam-3280	181	8	(	(	PUNCT
ejpam-3280	181	9	g	g	NOUN
ejpam-3280	181	10	,	,	PUNCT
ejpam-3280	181	11	b	b	NOUN
ejpam-3280	181	12	)	)	PUNCT
ejpam-3280	181	13	be	be	AUX
ejpam-3280	181	14	two	two	NUM
ejpam-3280	181	15	soft	soft	ADJ
ejpam-3280	181	16	hypervector	hypervector	NOUN
ejpam-3280	181	17	space	space	NOUN
ejpam-3280	181	18	over	over	ADP
ejpam-3280	181	19	v	v	NOUN
ejpam-3280	181	20	.	.	PUNCT
ejpam-3280	182	1	then	then	ADV
ejpam-3280	182	2	(	(	PUNCT
ejpam-3280	182	3	f	f	X
ejpam-3280	182	4	,	,	PUNCT
ejpam-3280	182	5	a	a	PRON
ejpam-3280	182	6	)	)	PUNCT
ejpam-3280	182	7	and	and	CCONJ
ejpam-3280	182	8	(	(	PUNCT
ejpam-3280	182	9	g	g	NOUN
ejpam-3280	182	10	,	,	PUNCT
ejpam-3280	182	11	b	b	NOUN
ejpam-3280	182	12	)	)	PUNCT
ejpam-3280	182	13	is	be	AUX
ejpam-3280	182	14	a	a	DET
ejpam-3280	182	15	soft	soft	ADJ
ejpam-3280	182	16	hypervector	hypervector	NOUN
ejpam-3280	182	17	space	space	NOUN
ejpam-3280	182	18	over	over	ADP
ejpam-3280	182	19	v	v	NOUN
ejpam-3280	182	20	.	.	PUNCT
ejpam-3280	183	1	e.	e.	PROPN
ejpam-3280	183	2	ranjbar	ranjbar	PROPN
ejpam-3280	183	3	-	-	PUNCT
ejpam-3280	183	4	yanehsari	yanehsari	NOUN
ejpam-3280	183	5	,	,	PUNCT
ejpam-3280	183	6	m.	m.	NOUN
ejpam-3280	183	7	asghari	asghari	ADJ
ejpam-3280	183	8	-	-	PUNCT
ejpam-3280	183	9	larimi	larimi	PROPN
ejpam-3280	183	10	,	,	PUNCT
ejpam-3280	183	11	r.	r.	PROPN
ejpam-3280	183	12	ameri	ameri	PROPN
ejpam-3280	183	13	/	/	SYM
ejpam-3280	183	14	eur	eur	PROPN
ejpam-3280	183	15	.	.	PUNCT
ejpam-3280	184	1	j.	j.	PROPN
ejpam-3280	184	2	pure	pure	PROPN
ejpam-3280	184	3	appl	appl	PROPN
ejpam-3280	184	4	.	.	PROPN
ejpam-3280	184	5	math	math	PROPN
ejpam-3280	184	6	,	,	PUNCT
ejpam-3280	184	7	12	12	NUM
ejpam-3280	184	8	(	(	PUNCT
ejpam-3280	184	9	1	1	NUM
ejpam-3280	184	10	)	)	PUNCT
ejpam-3280	184	11	(	(	PUNCT
ejpam-3280	184	12	2019	2019	NUM
ejpam-3280	184	13	)	)	PUNCT
ejpam-3280	184	14	,	,	PUNCT
ejpam-3280	184	15	118	118	NUM
ejpam-3280	184	16	-	-	SYM
ejpam-3280	184	17	134	134	NUM
ejpam-3280	184	18	124	124	NUM
ejpam-3280	184	19	4	4	NUM
ejpam-3280	184	20	.	.	PUNCT
ejpam-3280	184	21	fuzzy	fuzzy	ADJ
ejpam-3280	184	22	soft	soft	ADJ
ejpam-3280	184	23	hypervector	hypervector	NOUN
ejpam-3280	184	24	space	space	NOUN
ejpam-3280	184	25	in	in	ADP
ejpam-3280	184	26	this	this	DET
ejpam-3280	184	27	section	section	NOUN
ejpam-3280	184	28	,	,	PUNCT
ejpam-3280	184	29	the	the	DET
ejpam-3280	184	30	notions	notion	NOUN
ejpam-3280	184	31	of	of	ADP
ejpam-3280	184	32	a	a	DET
ejpam-3280	184	33	fuzzy	fuzzy	ADJ
ejpam-3280	184	34	soft	soft	ADJ
ejpam-3280	184	35	hypervector	hypervector	NOUN
ejpam-3280	184	36	space	space	NOUN
ejpam-3280	184	37	is	be	AUX
ejpam-3280	184	38	introduced	introduce	VERB
ejpam-3280	184	39	,	,	PUNCT
ejpam-3280	184	40	and	and	CCONJ
ejpam-3280	184	41	several	several	ADJ
ejpam-3280	184	42	basic	basic	ADJ
ejpam-3280	184	43	properties	property	NOUN
ejpam-3280	184	44	of	of	ADP
ejpam-3280	184	45	fuzzy	fuzzy	ADJ
ejpam-3280	184	46	soft	soft	ADJ
ejpam-3280	184	47	hypervector	hypervector	NOUN
ejpam-3280	184	48	space	space	NOUN
ejpam-3280	184	49	are	be	AUX
ejpam-3280	184	50	provided	provide	VERB
ejpam-3280	184	51	.	.	PUNCT
ejpam-3280	185	1	definition	definition	NOUN
ejpam-3280	185	2	16	16	NUM
ejpam-3280	185	3	.	.	PUNCT
ejpam-3280	186	1	a	a	DET
ejpam-3280	186	2	fuzzy	fuzzy	ADJ
ejpam-3280	186	3	subset	subset	VERB
ejpam-3280	186	4	µ	µ	NOUN
ejpam-3280	186	5	of	of	ADP
ejpam-3280	186	6	a	a	DET
ejpam-3280	186	7	hypervector	hypervector	NOUN
ejpam-3280	186	8	space	space	NOUN
ejpam-3280	186	9	v	v	NOUN
ejpam-3280	186	10	over	over	ADP
ejpam-3280	186	11	a	a	DET
ejpam-3280	186	12	field	field	NOUN
ejpam-3280	186	13	k	k	NOUN
ejpam-3280	186	14	is	be	AUX
ejpam-3280	186	15	said	say	VERB
ejpam-3280	186	16	to	to	PART
ejpam-3280	186	17	be	be	AUX
ejpam-3280	186	18	a	a	DET
ejpam-3280	186	19	fuzzy	fuzzy	ADJ
ejpam-3280	186	20	sub	sub	ADJ
ejpam-3280	186	21	-	-	ADJ
ejpam-3280	186	22	hypervector	hypervector	ADJ
ejpam-3280	186	23	space	space	NOUN
ejpam-3280	186	24	of	of	ADP
ejpam-3280	186	25	v	v	NOUN
ejpam-3280	186	26	if	if	SCONJ
ejpam-3280	186	27	and	and	CCONJ
ejpam-3280	186	28	only	only	ADV
ejpam-3280	186	29	if	if	SCONJ
ejpam-3280	186	30	for	for	ADP
ejpam-3280	186	31	all	all	DET
ejpam-3280	186	32	x	x	NOUN
ejpam-3280	186	33	,	,	PUNCT
ejpam-3280	186	34	y	y	PROPN
ejpam-3280	186	35	∈	∈	PROPN
ejpam-3280	186	36	v	v	NOUN
ejpam-3280	186	37	and	and	CCONJ
ejpam-3280	186	38	r	r	NOUN
ejpam-3280	186	39	∈	∈	PROPN
ejpam-3280	186	40	k	k	NOUN
ejpam-3280	186	41	,	,	PUNCT
ejpam-3280	186	42	(	(	PUNCT
ejpam-3280	186	43	i	i	NOUN
ejpam-3280	186	44	)	)	PUNCT
ejpam-3280	186	45	µ(x+	µ(x+	PROPN
ejpam-3280	186	46	y	y	PROPN
ejpam-3280	186	47	)	)	PUNCT
ejpam-3280	186	48	≥	≥	NOUN
ejpam-3280	186	49	µ(x	µ(x	NOUN
ejpam-3280	186	50	)	)	PUNCT
ejpam-3280	186	51	∧	∧	PROPN
ejpam-3280	186	52	µ(y	µ(y	PROPN
ejpam-3280	186	53	)	)	PUNCT
ejpam-3280	186	54	(	(	PUNCT
ejpam-3280	186	55	ii	ii	NOUN
ejpam-3280	186	56	)	)	PUNCT
ejpam-3280	186	57	µ(−x	µ(−x	ADV
ejpam-3280	186	58	)	)	PUNCT
ejpam-3280	186	59	≥	≥	NOUN
ejpam-3280	186	60	µ(x	µ(x	VERB
ejpam-3280	186	61	)	)	PUNCT
ejpam-3280	186	62	(	(	PUNCT
ejpam-3280	186	63	iii	iii	X
ejpam-3280	186	64	)	)	PUNCT
ejpam-3280	186	65	inf	inf	NOUN
ejpam-3280	186	66	z∈r	z∈r	PROPN
ejpam-3280	186	67	◦	◦	NOUN
ejpam-3280	186	68	x	x	SYM
ejpam-3280	186	69	µ(z	µ(z	PROPN
ejpam-3280	186	70	)	)	PUNCT
ejpam-3280	186	71	≥	≥	NOUN
ejpam-3280	186	72	µ(x	µ(x	VERB
ejpam-3280	186	73	)	)	PUNCT
ejpam-3280	186	74	.	.	PUNCT
ejpam-3280	187	1	example	example	NOUN
ejpam-3280	188	1	4	4	NUM
ejpam-3280	188	2	.	.	X
ejpam-3280	188	3	in	in	ADP
ejpam-3280	188	4	example	example	NOUN
ejpam-3280	188	5	1	1	NUM
ejpam-3280	188	6	,	,	PUNCT
ejpam-3280	188	7	if	if	SCONJ
ejpam-3280	188	8	fuzzy	fuzzy	ADJ
ejpam-3280	188	9	subset	subset	VERB
ejpam-3280	188	10	µ	µ	PROPN
ejpam-3280	188	11	of	of	ADP
ejpam-3280	188	12	v	v	NOUN
ejpam-3280	188	13	is	be	AUX
ejpam-3280	188	14	defined	define	VERB
ejpam-3280	188	15	by	by	ADP
ejpam-3280	188	16	µ(x	µ(x	NOUN
ejpam-3280	188	17	)	)	PUNCT
ejpam-3280	188	18	=	=	PRON
ejpam-3280	188	19	{	{	PUNCT
ejpam-3280	188	20	1	1	NUM
ejpam-3280	188	21	if	if	SCONJ
ejpam-3280	188	22	x	x	PRON
ejpam-3280	188	23	∈w	∈w	VERB
ejpam-3280	188	24	t	t	NOUN
ejpam-3280	188	25	otherwise	otherwise	ADV
ejpam-3280	188	26	,	,	PUNCT
ejpam-3280	188	27	where	where	SCONJ
ejpam-3280	188	28	t	t	PROPN
ejpam-3280	188	29	∈	∈	PROPN
ejpam-3280	189	1	[	[	X
ejpam-3280	189	2	0	0	NUM
ejpam-3280	189	3	,	,	PUNCT
ejpam-3280	189	4	1	1	NUM
ejpam-3280	189	5	)	)	PUNCT
ejpam-3280	189	6	,	,	PUNCT
ejpam-3280	189	7	then	then	ADV
ejpam-3280	189	8	µ	µ	X
ejpam-3280	189	9	is	be	AUX
ejpam-3280	189	10	a	a	DET
ejpam-3280	189	11	fuzzy	fuzzy	ADJ
ejpam-3280	189	12	sub	sub	ADJ
ejpam-3280	189	13	-	-	ADJ
ejpam-3280	189	14	hypervector	hypervector	ADJ
ejpam-3280	189	15	space	space	NOUN
ejpam-3280	189	16	of	of	ADP
ejpam-3280	189	17	v	v	NOUN
ejpam-3280	189	18	.	.	PUNCT
ejpam-3280	190	1	definition	definition	NOUN
ejpam-3280	190	2	17	17	NUM
ejpam-3280	190	3	.	.	PUNCT
ejpam-3280	191	1	let	let	VERB
ejpam-3280	191	2	v	v	PART
ejpam-3280	191	3	be	be	AUX
ejpam-3280	191	4	a	a	DET
ejpam-3280	191	5	hypervector	hypervector	NOUN
ejpam-3280	191	6	space	space	NOUN
ejpam-3280	191	7	over	over	ADP
ejpam-3280	191	8	a	a	DET
ejpam-3280	191	9	field	field	NOUN
ejpam-3280	191	10	k	k	PROPN
ejpam-3280	192	1	and	and	CCONJ
ejpam-3280	192	2	(	(	PUNCT
ejpam-3280	192	3	f	f	X
ejpam-3280	192	4	,	,	PUNCT
ejpam-3280	192	5	a	a	PRON
ejpam-3280	192	6	)	)	PUNCT
ejpam-3280	192	7	be	be	AUX
ejpam-3280	192	8	a	a	DET
ejpam-3280	192	9	fuzzy	fuzzy	ADJ
ejpam-3280	192	10	soft	soft	ADJ
ejpam-3280	192	11	set	set	NOUN
ejpam-3280	192	12	over	over	ADP
ejpam-3280	192	13	v	v	NOUN
ejpam-3280	192	14	.	.	PUNCT
ejpam-3280	193	1	then	then	ADV
ejpam-3280	193	2	(	(	PUNCT
ejpam-3280	193	3	f	f	X
ejpam-3280	193	4	,	,	PUNCT
ejpam-3280	193	5	a	a	PRON
ejpam-3280	193	6	)	)	PUNCT
ejpam-3280	193	7	is	be	AUX
ejpam-3280	193	8	said	say	VERB
ejpam-3280	193	9	to	to	PART
ejpam-3280	193	10	be	be	AUX
ejpam-3280	193	11	a	a	DET
ejpam-3280	193	12	fuzzy	fuzzy	ADJ
ejpam-3280	193	13	soft	soft	ADJ
ejpam-3280	193	14	hypervector	hypervector	NOUN
ejpam-3280	193	15	space	space	NOUN
ejpam-3280	193	16	over	over	ADP
ejpam-3280	193	17	v	v	NOUN
ejpam-3280	193	18	if	if	SCONJ
ejpam-3280	193	19	and	and	CCONJ
ejpam-3280	193	20	only	only	ADV
ejpam-3280	193	21	if	if	SCONJ
ejpam-3280	193	22	for	for	ADP
ejpam-3280	193	23	all	all	DET
ejpam-3280	193	24	a	a	DET
ejpam-3280	193	25	∈	∈	PROPN
ejpam-3280	193	26	a	a	PRON
ejpam-3280	193	27	,	,	PUNCT
ejpam-3280	193	28	fa	fa	PROPN
ejpam-3280	193	29	is	be	AUX
ejpam-3280	193	30	a	a	DET
ejpam-3280	193	31	fuzzy	fuzzy	ADJ
ejpam-3280	193	32	sub	sub	ADJ
ejpam-3280	193	33	-	-	ADJ
ejpam-3280	193	34	hypervector	hypervector	ADJ
ejpam-3280	193	35	space	space	NOUN
ejpam-3280	193	36	of	of	ADP
ejpam-3280	193	37	v	v	NOUN
ejpam-3280	193	38	.	.	PUNCT
ejpam-3280	194	1	example	example	NOUN
ejpam-3280	195	1	5	5	NUM
ejpam-3280	195	2	.	.	PUNCT
ejpam-3280	196	1	in	in	ADP
ejpam-3280	196	2	example	example	NOUN
ejpam-3280	196	3	3	3	NUM
ejpam-3280	196	4	,	,	PUNCT
ejpam-3280	196	5	let	let	VERB
ejpam-3280	196	6	a	a	PRON
ejpam-3280	196	7	=	=	PUNCT
ejpam-3280	196	8	{	{	PUNCT
ejpam-3280	196	9	0	0	NUM
ejpam-3280	196	10	,	,	PUNCT
ejpam-3280	196	11	1	1	NUM
ejpam-3280	196	12	,	,	PUNCT
ejpam-3280	196	13	2	2	NUM
ejpam-3280	196	14	}	}	PUNCT
ejpam-3280	196	15	and	and	CCONJ
ejpam-3280	196	16	defined	define	VERB
ejpam-3280	196	17	the	the	DET
ejpam-3280	196	18	set	set	NOUN
ejpam-3280	196	19	-	-	PUNCT
ejpam-3280	196	20	valued	value	VERB
ejpam-3280	196	21	function	function	NOUN
ejpam-3280	196	22	f	f	NOUN
ejpam-3280	196	23	:	:	PUNCT
ejpam-3280	196	24	a→	a→	X
ejpam-3280	196	25	iv	iv	NUM
ejpam-3280	196	26	by	by	ADP
ejpam-3280	196	27	f0(x	f0(x	NOUN
ejpam-3280	196	28	)	)	PUNCT
ejpam-3280	196	29	=	=	SYM
ejpam-3280	197	1			NOUN
ejpam-3280	197	2	1	1	NUM
ejpam-3280	197	3	2	2	NUM
ejpam-3280	197	4	if	if	SCONJ
ejpam-3280	197	5	x	x	PROPN
ejpam-3280	197	6	=	=	SYM
ejpam-3280	197	7	0	0	NUM
ejpam-3280	197	8	0	0	NUM
ejpam-3280	198	1	otherwise	otherwise	ADV
ejpam-3280	198	2	,	,	PUNCT
ejpam-3280	198	3	f1(x	f1(x	NOUN
ejpam-3280	198	4	)	)	PUNCT
ejpam-3280	198	5	=	=	SYM
ejpam-3280	198	6	f2(x	f2(x	PROPN
ejpam-3280	198	7	)	)	PUNCT
ejpam-3280	198	8	=	=	SYM
ejpam-3280	198	9			NUM
ejpam-3280	198	10	1	1	NUM
ejpam-3280	198	11	3	3	NUM
ejpam-3280	198	12	if	if	SCONJ
ejpam-3280	198	13	x	x	PROPN
ejpam-3280	199	1	=	=	SYM
ejpam-3280	199	2	1	1	NUM
ejpam-3280	199	3	or	or	CCONJ
ejpam-3280	199	4	x	x	SYM
ejpam-3280	199	5	=	=	SYM
ejpam-3280	199	6	2	2	NUM
ejpam-3280	199	7	1	1	NUM
ejpam-3280	199	8	2	2	NUM
ejpam-3280	199	9	if	if	SCONJ
ejpam-3280	199	10	x	x	PROPN
ejpam-3280	199	11	=	=	SYM
ejpam-3280	199	12	0	0	NUM
ejpam-3280	199	13	since	since	SCONJ
ejpam-3280	199	14	f0	f0	PROPN
ejpam-3280	199	15	,	,	PUNCT
ejpam-3280	199	16	f1	f1	NOUN
ejpam-3280	199	17	and	and	CCONJ
ejpam-3280	199	18	f2	f2	PROPN
ejpam-3280	199	19	are	be	AUX
ejpam-3280	199	20	fuzzy	fuzzy	ADJ
ejpam-3280	199	21	sub	sub	ADJ
ejpam-3280	199	22	-	-	ADJ
ejpam-3280	199	23	hypervector	hypervector	ADJ
ejpam-3280	199	24	space	space	NOUN
ejpam-3280	199	25	of	of	ADP
ejpam-3280	199	26	v	v	NOUN
ejpam-3280	199	27	,	,	PUNCT
ejpam-3280	199	28	then	then	ADV
ejpam-3280	199	29	(	(	PUNCT
ejpam-3280	199	30	f	f	X
ejpam-3280	199	31	,	,	PUNCT
ejpam-3280	199	32	a	a	PRON
ejpam-3280	199	33	)	)	PUNCT
ejpam-3280	199	34	is	be	AUX
ejpam-3280	199	35	a	a	DET
ejpam-3280	199	36	fuzzy	fuzzy	ADJ
ejpam-3280	199	37	soft	soft	ADJ
ejpam-3280	199	38	hypervector	hypervector	NOUN
ejpam-3280	199	39	space	space	NOUN
ejpam-3280	199	40	over	over	ADP
ejpam-3280	199	41	v	v	NOUN
ejpam-3280	199	42	.	.	PUNCT
ejpam-3280	200	1	lemma	lemma	PROPN
ejpam-3280	200	2	5	5	X
ejpam-3280	200	3	.	.	PUNCT
ejpam-3280	201	1	let	let	AUX
ejpam-3280	201	2	(	(	PUNCT
ejpam-3280	201	3	f	f	X
ejpam-3280	201	4	,	,	PUNCT
ejpam-3280	201	5	a	a	PRON
ejpam-3280	201	6	)	)	PUNCT
ejpam-3280	201	7	be	be	AUX
ejpam-3280	201	8	a	a	DET
ejpam-3280	201	9	fuzzy	fuzzy	ADJ
ejpam-3280	201	10	soft	soft	ADJ
ejpam-3280	201	11	set	set	NOUN
ejpam-3280	201	12	over	over	ADP
ejpam-3280	201	13	hypervector	hypervector	NOUN
ejpam-3280	201	14	space	space	NOUN
ejpam-3280	201	15	v	v	NOUN
ejpam-3280	201	16	.	.	PUNCT
ejpam-3280	202	1	if	if	SCONJ
ejpam-3280	202	2	(	(	PUNCT
ejpam-3280	202	3	f	f	X
ejpam-3280	202	4	,	,	PUNCT
ejpam-3280	202	5	a	a	PRON
ejpam-3280	202	6	)	)	PUNCT
ejpam-3280	202	7	is	be	AUX
ejpam-3280	202	8	a	a	DET
ejpam-3280	202	9	fuzzy	fuzzy	ADJ
ejpam-3280	202	10	soft	soft	ADJ
ejpam-3280	202	11	hypervector	hypervector	NOUN
ejpam-3280	202	12	space	space	NOUN
ejpam-3280	202	13	,	,	PUNCT
ejpam-3280	202	14	then	then	ADV
ejpam-3280	202	15	for	for	ADP
ejpam-3280	202	16	all	all	DET
ejpam-3280	202	17	x	x	NOUN
ejpam-3280	202	18	,	,	PUNCT
ejpam-3280	202	19	y	y	PROPN
ejpam-3280	202	20	∈	∈	PROPN
ejpam-3280	202	21	v	v	NOUN
ejpam-3280	202	22	and	and	CCONJ
ejpam-3280	202	23	a	a	DET
ejpam-3280	202	24	∈	∈	PROPN
ejpam-3280	202	25	a	a	X
ejpam-3280	202	26	,	,	PUNCT
ejpam-3280	202	27	we	we	PRON
ejpam-3280	202	28	obtain	obtain	VERB
ejpam-3280	202	29	(	(	PUNCT
ejpam-3280	202	30	i	i	NOUN
ejpam-3280	202	31	)	)	PUNCT
ejpam-3280	202	32	fa(x−	fa(x−	ADP
ejpam-3280	202	33	y	y	PROPN
ejpam-3280	202	34	)	)	PUNCT
ejpam-3280	202	35	≥	≥	NOUN
ejpam-3280	202	36	fa(x	fa(x	NOUN
ejpam-3280	202	37	)	)	PUNCT
ejpam-3280	202	38	∧	∧	PROPN
ejpam-3280	202	39	fa(y	fa(y	NOUN
ejpam-3280	202	40	)	)	PUNCT
ejpam-3280	202	41	(	(	PUNCT
ejpam-3280	202	42	ii	ii	NOUN
ejpam-3280	202	43	)	)	PUNCT
ejpam-3280	202	44	fa(−x	fa(−x	NOUN
ejpam-3280	202	45	)	)	PUNCT
ejpam-3280	202	46	=	=	SYM
ejpam-3280	202	47	fa(x	fa(x	X
ejpam-3280	202	48	)	)	PUNCT
ejpam-3280	202	49	(	(	PUNCT
ejpam-3280	202	50	iii	iii	NOUN
ejpam-3280	202	51	)	)	PUNCT
ejpam-3280	202	52	fa(x	fa(x	PROPN
ejpam-3280	202	53	)	)	PUNCT
ejpam-3280	202	54	=	=	SYM
ejpam-3280	202	55	inf	inf	PROPN
ejpam-3280	202	56	z∈1	z∈1	PROPN
ejpam-3280	202	57	◦	◦	NOUN
ejpam-3280	202	58	x	x	NOUN
ejpam-3280	202	59	fa(z	fa(z	PRON
ejpam-3280	202	60	)	)	PUNCT
ejpam-3280	202	61	.	.	PUNCT
ejpam-3280	203	1	e.	e.	PROPN
ejpam-3280	203	2	ranjbar	ranjbar	PROPN
ejpam-3280	203	3	-	-	PUNCT
ejpam-3280	203	4	yanehsari	yanehsari	NOUN
ejpam-3280	203	5	,	,	PUNCT
ejpam-3280	203	6	m.	m.	NOUN
ejpam-3280	203	7	asghari	asghari	ADJ
ejpam-3280	203	8	-	-	PUNCT
ejpam-3280	203	9	larimi	larimi	PROPN
ejpam-3280	203	10	,	,	PUNCT
ejpam-3280	203	11	r.	r.	PROPN
ejpam-3280	203	12	ameri	ameri	PROPN
ejpam-3280	203	13	/	/	SYM
ejpam-3280	203	14	eur	eur	PROPN
ejpam-3280	203	15	.	.	PUNCT
ejpam-3280	204	1	j.	j.	PROPN
ejpam-3280	204	2	pure	pure	PROPN
ejpam-3280	204	3	appl	appl	PROPN
ejpam-3280	204	4	.	.	PROPN
ejpam-3280	204	5	math	math	PROPN
ejpam-3280	204	6	,	,	PUNCT
ejpam-3280	204	7	12	12	NUM
ejpam-3280	204	8	(	(	PUNCT
ejpam-3280	204	9	1	1	NUM
ejpam-3280	204	10	)	)	PUNCT
ejpam-3280	204	11	(	(	PUNCT
ejpam-3280	204	12	2019	2019	NUM
ejpam-3280	204	13	)	)	PUNCT
ejpam-3280	204	14	,	,	PUNCT
ejpam-3280	204	15	118	118	NUM
ejpam-3280	204	16	-	-	SYM
ejpam-3280	204	17	134	134	NUM
ejpam-3280	204	18	125	125	NUM
ejpam-3280	204	19	proof	proof	NOUN
ejpam-3280	204	20	.	.	PUNCT
ejpam-3280	205	1	(	(	PUNCT
ejpam-3280	205	2	i	i	NOUN
ejpam-3280	205	3	)	)	PUNCT
ejpam-3280	205	4	for	for	ADP
ejpam-3280	205	5	all	all	DET
ejpam-3280	205	6	x	x	NOUN
ejpam-3280	205	7	,	,	PUNCT
ejpam-3280	205	8	y	y	PROPN
ejpam-3280	205	9	∈	∈	PROPN
ejpam-3280	205	10	v	v	NOUN
ejpam-3280	205	11	,	,	PUNCT
ejpam-3280	205	12	a	a	DET
ejpam-3280	205	13	∈	∈	PROPN
ejpam-3280	205	14	a	a	X
ejpam-3280	205	15	,	,	PUNCT
ejpam-3280	205	16	we	we	PRON
ejpam-3280	205	17	obtain	obtain	VERB
ejpam-3280	205	18	fa(x−	fa(x−	NOUN
ejpam-3280	205	19	y	y	NOUN
ejpam-3280	205	20	)	)	PUNCT
ejpam-3280	205	21	=	=	PUNCT
ejpam-3280	205	22	fa(x+	fa(x+	PROPN
ejpam-3280	205	23	(	(	PUNCT
ejpam-3280	205	24	−y	−y	NOUN
ejpam-3280	205	25	)	)	PUNCT
ejpam-3280	205	26	)	)	PUNCT
ejpam-3280	205	27	≥	≥	NOUN
ejpam-3280	205	28	fa(x	fa(x	NOUN
ejpam-3280	205	29	)	)	PUNCT
ejpam-3280	205	30	∧	∧	NOUN
ejpam-3280	205	31	fa(−y	fa(−y	NOUN
ejpam-3280	205	32	)	)	PUNCT
ejpam-3280	205	33	≥	≥	NOUN
ejpam-3280	205	34	fa(x	fa(x	NOUN
ejpam-3280	205	35	)	)	PUNCT
ejpam-3280	205	36	∧	∧	PROPN
ejpam-3280	205	37	fa(y	fa(y	NOUN
ejpam-3280	205	38	)	)	PUNCT
ejpam-3280	205	39	(	(	PUNCT
ejpam-3280	205	40	ii	ii	NOUN
ejpam-3280	205	41	)	)	PUNCT
ejpam-3280	205	42	for	for	ADP
ejpam-3280	205	43	every	every	DET
ejpam-3280	205	44	x	x	SYM
ejpam-3280	205	45	∈	∈	PROPN
ejpam-3280	205	46	v	v	NOUN
ejpam-3280	205	47	,	,	PUNCT
ejpam-3280	205	48	a	a	DET
ejpam-3280	205	49	∈	∈	PROPN
ejpam-3280	205	50	a	a	X
ejpam-3280	205	51	,	,	PUNCT
ejpam-3280	205	52	we	we	PRON
ejpam-3280	205	53	have	have	VERB
ejpam-3280	205	54	fa(x	fa(x	NOUN
ejpam-3280	205	55	)	)	PUNCT
ejpam-3280	205	56	=	=	SYM
ejpam-3280	205	57	fa(−(−x	fa(−(−x	NOUN
ejpam-3280	205	58	)	)	PUNCT
ejpam-3280	205	59	)	)	PUNCT
ejpam-3280	205	60	≥	≥	NOUN
ejpam-3280	205	61	fa(−x	fa(−x	NOUN
ejpam-3280	205	62	)	)	PUNCT
ejpam-3280	205	63	≥	≥	NOUN
ejpam-3280	205	64	fa(x	fa(x	NOUN
ejpam-3280	205	65	)	)	PUNCT
ejpam-3280	205	66	thus	thus	ADV
ejpam-3280	205	67	fa(−x	fa(−x	NOUN
ejpam-3280	205	68	)	)	PUNCT
ejpam-3280	205	69	=	=	PUNCT
ejpam-3280	205	70	fa(x	fa(x	PROPN
ejpam-3280	205	71	)	)	PUNCT
ejpam-3280	205	72	.	.	PUNCT
ejpam-3280	206	1	(	(	PUNCT
ejpam-3280	206	2	iii	iii	NOUN
ejpam-3280	206	3	)	)	PUNCT
ejpam-3280	206	4	since	since	SCONJ
ejpam-3280	206	5	x	x	SYM
ejpam-3280	206	6	∈	∈	PROPN
ejpam-3280	206	7	1	1	NUM
ejpam-3280	206	8	◦	◦	NOUN
ejpam-3280	206	9	x	x	SYM
ejpam-3280	206	10	,	,	PUNCT
ejpam-3280	206	11	therefore	therefore	ADV
ejpam-3280	206	12	for	for	ADP
ejpam-3280	206	13	all	all	DET
ejpam-3280	206	14	x	x	SYM
ejpam-3280	206	15	∈	∈	PROPN
ejpam-3280	206	16	v	v	NOUN
ejpam-3280	206	17	and	and	CCONJ
ejpam-3280	206	18	a	a	DET
ejpam-3280	206	19	∈	∈	PROPN
ejpam-3280	206	20	a	a	X
ejpam-3280	206	21	,	,	PUNCT
ejpam-3280	206	22	we	we	PRON
ejpam-3280	206	23	obtain	obtain	VERB
ejpam-3280	206	24	fa(x	fa(x	NOUN
ejpam-3280	206	25	)	)	PUNCT
ejpam-3280	206	26	≥	≥	PROPN
ejpam-3280	206	27	inf	inf	PROPN
ejpam-3280	206	28	z∈1	z∈1	PROPN
ejpam-3280	206	29	◦	◦	NOUN
ejpam-3280	206	30	x	x	NOUN
ejpam-3280	206	31	fa(z	fa(z	PRON
ejpam-3280	206	32	)	)	PUNCT
ejpam-3280	206	33	≥	≥	NOUN
ejpam-3280	206	34	fa(x	fa(x	NOUN
ejpam-3280	206	35	)	)	PUNCT
ejpam-3280	206	36	.	.	PUNCT
ejpam-3280	207	1	hence	hence	ADV
ejpam-3280	207	2	fa(x	fa(x	VERB
ejpam-3280	207	3	)	)	PUNCT
ejpam-3280	207	4	=	=	SYM
ejpam-3280	207	5	inf	inf	PROPN
ejpam-3280	207	6	z∈1	z∈1	PROPN
ejpam-3280	207	7	◦	◦	NOUN
ejpam-3280	207	8	x	x	NOUN
ejpam-3280	207	9	fa(z	fa(z	PRON
ejpam-3280	207	10	)	)	PUNCT
ejpam-3280	207	11	.	.	PUNCT
ejpam-3280	208	1	theorem	theorem	NOUN
ejpam-3280	208	2	2	2	NUM
ejpam-3280	208	3	.	.	PUNCT
ejpam-3280	209	1	let	let	VERB
ejpam-3280	209	2	v	v	PART
ejpam-3280	209	3	be	be	AUX
ejpam-3280	209	4	a	a	DET
ejpam-3280	209	5	hypervector	hypervector	NOUN
ejpam-3280	209	6	space	space	NOUN
ejpam-3280	209	7	over	over	ADP
ejpam-3280	209	8	a	a	DET
ejpam-3280	209	9	field	field	NOUN
ejpam-3280	209	10	k.	k.	NOUN
ejpam-3280	210	1	if	if	SCONJ
ejpam-3280	210	2	(	(	PUNCT
ejpam-3280	210	3	f	f	X
ejpam-3280	210	4	,	,	PUNCT
ejpam-3280	210	5	a	a	PRON
ejpam-3280	210	6	)	)	PUNCT
ejpam-3280	210	7	and	and	CCONJ
ejpam-3280	210	8	(	(	PUNCT
ejpam-3280	210	9	g	g	NOUN
ejpam-3280	210	10	,	,	PUNCT
ejpam-3280	210	11	b	b	NOUN
ejpam-3280	210	12	)	)	PUNCT
ejpam-3280	210	13	are	be	AUX
ejpam-3280	210	14	two	two	NUM
ejpam-3280	210	15	fuzzy	fuzzy	ADJ
ejpam-3280	210	16	soft	soft	ADJ
ejpam-3280	210	17	hypervector	hypervector	NOUN
ejpam-3280	210	18	space	space	NOUN
ejpam-3280	210	19	over	over	ADP
ejpam-3280	210	20	v	v	NUM
ejpam-3280	210	21	,	,	PUNCT
ejpam-3280	210	22	then	then	ADV
ejpam-3280	210	23	(	(	PUNCT
ejpam-3280	210	24	f	f	X
ejpam-3280	210	25	,	,	PUNCT
ejpam-3280	210	26	a	a	PRON
ejpam-3280	210	27	)	)	PUNCT
ejpam-3280	210	28	u	u	NOUN
ejpam-3280	210	29	(	(	PUNCT
ejpam-3280	210	30	g	g	PROPN
ejpam-3280	210	31	,	,	PUNCT
ejpam-3280	210	32	b	b	NOUN
ejpam-3280	210	33	)	)	PUNCT
ejpam-3280	210	34	is	be	AUX
ejpam-3280	210	35	a	a	DET
ejpam-3280	210	36	fuzzy	fuzzy	ADJ
ejpam-3280	210	37	soft	soft	ADJ
ejpam-3280	210	38	hypervector	hypervector	NOUN
ejpam-3280	210	39	space	space	NOUN
ejpam-3280	210	40	over	over	ADP
ejpam-3280	210	41	v	v	NOUN
ejpam-3280	210	42	.	.	PUNCT
ejpam-3280	211	1	proof	proof	NOUN
ejpam-3280	211	2	.	.	PUNCT
ejpam-3280	212	1	let	let	VERB
ejpam-3280	212	2	(	(	PUNCT
ejpam-3280	212	3	f	f	X
ejpam-3280	212	4	,	,	PUNCT
ejpam-3280	212	5	a	a	PRON
ejpam-3280	212	6	)	)	PUNCT
ejpam-3280	212	7	u	u	NOUN
ejpam-3280	212	8	(	(	PUNCT
ejpam-3280	212	9	g	g	PROPN
ejpam-3280	212	10	,	,	PUNCT
ejpam-3280	212	11	b	b	NOUN
ejpam-3280	212	12	)	)	PUNCT
ejpam-3280	212	13	=	=	SYM
ejpam-3280	212	14	(	(	PUNCT
ejpam-3280	212	15	h	h	NOUN
ejpam-3280	212	16	,	,	PUNCT
ejpam-3280	212	17	c	c	NOUN
ejpam-3280	212	18	)	)	PUNCT
ejpam-3280	212	19	,	,	PUNCT
ejpam-3280	212	20	where	where	SCONJ
ejpam-3280	212	21	c	c	NOUN
ejpam-3280	212	22	=	=	PUNCT
ejpam-3280	212	23	a	a	DET
ejpam-3280	212	24	∩	∩	ADJ
ejpam-3280	212	25	b	b	NOUN
ejpam-3280	212	26	6=	6=	NOUN
ejpam-3280	212	27	∅	∅	NOUN
ejpam-3280	212	28	and	and	CCONJ
ejpam-3280	212	29	for	for	ADP
ejpam-3280	212	30	all	all	DET
ejpam-3280	212	31	x	x	SYM
ejpam-3280	212	32	∈	∈	PROPN
ejpam-3280	212	33	v	v	NOUN
ejpam-3280	212	34	,	,	PUNCT
ejpam-3280	212	35	c	c	PROPN
ejpam-3280	212	36	∈	∈	PROPN
ejpam-3280	212	37	c	c	NOUN
ejpam-3280	212	38	,	,	PUNCT
ejpam-3280	212	39	hc(x	hc(x	NOUN
ejpam-3280	212	40	)	)	PUNCT
ejpam-3280	212	41	=	=	SYM
ejpam-3280	212	42	fc(x	fc(x	X
ejpam-3280	212	43	)	)	PUNCT
ejpam-3280	212	44	∧	∧	NOUN
ejpam-3280	212	45	gc(x	gc(x	NOUN
ejpam-3280	212	46	)	)	PUNCT
ejpam-3280	212	47	.	.	PUNCT
ejpam-3280	213	1	if	if	SCONJ
ejpam-3280	213	2	y	y	PROPN
ejpam-3280	213	3	∈	∈	PROPN
ejpam-3280	213	4	v	v	NOUN
ejpam-3280	213	5	,	,	PUNCT
ejpam-3280	213	6	then	then	ADV
ejpam-3280	213	7	hc(x	hc(x	X
ejpam-3280	213	8	+	+	CCONJ
ejpam-3280	213	9	y	y	NOUN
ejpam-3280	213	10	)	)	PUNCT
ejpam-3280	213	11	=	=	SYM
ejpam-3280	213	12	fc(x	fc(x	NOUN
ejpam-3280	214	1	+	+	CCONJ
ejpam-3280	214	2	y	y	X
ejpam-3280	214	3	)	)	PUNCT
ejpam-3280	214	4	∧	∧	NOUN
ejpam-3280	214	5	gc(x	gc(x	NOUN
ejpam-3280	214	6	+	+	CCONJ
ejpam-3280	214	7	y	y	NOUN
ejpam-3280	214	8	)	)	PUNCT
ejpam-3280	214	9	≥	≥	NOUN
ejpam-3280	214	10	(	(	PUNCT
ejpam-3280	214	11	fc(x	fc(x	NOUN
ejpam-3280	214	12	)	)	PUNCT
ejpam-3280	214	13	∧	∧	NOUN
ejpam-3280	214	14	fc(y	fc(y	NOUN
ejpam-3280	214	15	)	)	PUNCT
ejpam-3280	214	16	)	)	PUNCT
ejpam-3280	215	1	∧	∧	NOUN
ejpam-3280	215	2	(	(	PUNCT
ejpam-3280	215	3	gc(x	gc(x	NOUN
ejpam-3280	215	4	)	)	PUNCT
ejpam-3280	215	5	∧	∧	NOUN
ejpam-3280	215	6	gc(y	gc(y	NOUN
ejpam-3280	215	7	)	)	PUNCT
ejpam-3280	215	8	)	)	PUNCT
ejpam-3280	216	1	=	=	SYM
ejpam-3280	216	2	(	(	PUNCT
ejpam-3280	216	3	fc(x	fc(x	NOUN
ejpam-3280	216	4	)	)	PUNCT
ejpam-3280	216	5	∧	∧	NOUN
ejpam-3280	216	6	gc(x	gc(x	NOUN
ejpam-3280	216	7	)	)	PUNCT
ejpam-3280	216	8	)	)	PUNCT
ejpam-3280	217	1	∧	∧	NOUN
ejpam-3280	217	2	(	(	PUNCT
ejpam-3280	217	3	fc(y	fc(y	NOUN
ejpam-3280	217	4	)	)	PUNCT
ejpam-3280	217	5	∧	∧	NOUN
ejpam-3280	217	6	gc(y	gc(y	NOUN
ejpam-3280	217	7	)	)	PUNCT
ejpam-3280	217	8	)	)	PUNCT
ejpam-3280	218	1	=	=	SYM
ejpam-3280	218	2	hc(x	hc(x	NOUN
ejpam-3280	218	3	)	)	PUNCT
ejpam-3280	218	4	∧	∧	NOUN
ejpam-3280	218	5	hc(y	hc(y	NOUN
ejpam-3280	218	6	)	)	PUNCT
ejpam-3280	218	7	.	.	PUNCT
ejpam-3280	219	1	moreover	moreover	ADV
ejpam-3280	219	2	,	,	PUNCT
ejpam-3280	219	3	hc(−x	hc(−x	NOUN
ejpam-3280	219	4	)	)	PUNCT
ejpam-3280	219	5	=	=	SYM
ejpam-3280	219	6	fc(−x	fc(−x	NOUN
ejpam-3280	219	7	)	)	PUNCT
ejpam-3280	219	8	∧	∧	NOUN
ejpam-3280	219	9	gc(−x	gc(−x	NOUN
ejpam-3280	219	10	)	)	PUNCT
ejpam-3280	219	11	≥	≥	NOUN
ejpam-3280	219	12	fc(x	fc(x	NOUN
ejpam-3280	219	13	)	)	PUNCT
ejpam-3280	219	14	∧	∧	NOUN
ejpam-3280	219	15	gc(x	gc(x	NOUN
ejpam-3280	219	16	)	)	PUNCT
ejpam-3280	219	17	=	=	SYM
ejpam-3280	219	18	hc(x	hc(x	NOUN
ejpam-3280	219	19	)	)	PUNCT
ejpam-3280	219	20	also	also	ADV
ejpam-3280	219	21	for	for	ADP
ejpam-3280	219	22	every	every	DET
ejpam-3280	219	23	r	r	NOUN
ejpam-3280	219	24	∈	∈	PROPN
ejpam-3280	219	25	k	k	NOUN
ejpam-3280	219	26	,	,	PUNCT
ejpam-3280	219	27	inf	inf	NOUN
ejpam-3280	219	28	z∈r	z∈r	PROPN
ejpam-3280	219	29	◦	◦	NOUN
ejpam-3280	219	30	x	x	NOUN
ejpam-3280	219	31	hc(z	hc(z	X
ejpam-3280	219	32	)	)	PUNCT
ejpam-3280	219	33	=	=	SYM
ejpam-3280	220	1	inf	inf	PROPN
ejpam-3280	220	2	z∈r	z∈r	NUM
ejpam-3280	220	3	◦	◦	NOUN
ejpam-3280	220	4	x	x	SYM
ejpam-3280	220	5	(	(	PUNCT
ejpam-3280	220	6	fc(z	fc(z	X
ejpam-3280	220	7	)	)	PUNCT
ejpam-3280	220	8	∧	∧	NOUN
ejpam-3280	220	9	gc(z	gc(z	NOUN
ejpam-3280	220	10	)	)	PUNCT
ejpam-3280	220	11	)	)	PUNCT
ejpam-3280	221	1	=	=	SYM
ejpam-3280	221	2	inf	inf	PROPN
ejpam-3280	221	3	z∈r	z∈r	NUM
ejpam-3280	221	4	◦	◦	NOUN
ejpam-3280	221	5	x	x	SYM
ejpam-3280	221	6	fc(z	fc(z	X
ejpam-3280	221	7	)	)	PUNCT
ejpam-3280	221	8	∧	∧	PROPN
ejpam-3280	221	9	inf	inf	NOUN
ejpam-3280	221	10	z∈r	z∈r	NUM
ejpam-3280	221	11	◦	◦	NOUN
ejpam-3280	221	12	x	x	SYM
ejpam-3280	221	13	gc(z	gc(z	X
ejpam-3280	221	14	)	)	PUNCT
ejpam-3280	221	15	≥	≥	NUM
ejpam-3280	221	16	fc(x	fc(x	SYM
ejpam-3280	221	17	)	)	PUNCT
ejpam-3280	221	18	∧	∧	NOUN
ejpam-3280	221	19	gc(x	gc(x	NOUN
ejpam-3280	221	20	)	)	PUNCT
ejpam-3280	221	21	=	=	SYM
ejpam-3280	221	22	hc(x	hc(x	NOUN
ejpam-3280	221	23	)	)	PUNCT
ejpam-3280	221	24	.	.	PUNCT
ejpam-3280	222	1	therefore	therefore	ADV
ejpam-3280	222	2	,	,	PUNCT
ejpam-3280	222	3	(	(	PUNCT
ejpam-3280	222	4	h	h	NOUN
ejpam-3280	222	5	,	,	PUNCT
ejpam-3280	222	6	c	c	NOUN
ejpam-3280	222	7	)	)	PUNCT
ejpam-3280	222	8	=	=	SYM
ejpam-3280	222	9	(	(	PUNCT
ejpam-3280	222	10	f	f	X
ejpam-3280	222	11	,	,	PUNCT
ejpam-3280	222	12	a	a	PRON
ejpam-3280	222	13	)	)	PUNCT
ejpam-3280	222	14	u	u	NOUN
ejpam-3280	222	15	(	(	PUNCT
ejpam-3280	222	16	g	g	PROPN
ejpam-3280	222	17	,	,	PUNCT
ejpam-3280	222	18	b	b	NOUN
ejpam-3280	222	19	)	)	PUNCT
ejpam-3280	222	20	is	be	AUX
ejpam-3280	222	21	a	a	DET
ejpam-3280	222	22	fuzzy	fuzzy	ADJ
ejpam-3280	222	23	soft	soft	ADJ
ejpam-3280	222	24	hypervector	hypervector	NOUN
ejpam-3280	222	25	space	space	NOUN
ejpam-3280	222	26	over	over	ADP
ejpam-3280	222	27	v	v	NOUN
ejpam-3280	222	28	.	.	PUNCT
ejpam-3280	223	1	theorem	theorem	NOUN
ejpam-3280	223	2	3	3	X
ejpam-3280	223	3	.	.	PUNCT
ejpam-3280	224	1	let	let	VERB
ejpam-3280	224	2	(	(	PUNCT
ejpam-3280	224	3	f	f	X
ejpam-3280	224	4	,	,	PUNCT
ejpam-3280	224	5	a	a	PRON
ejpam-3280	224	6	)	)	PUNCT
ejpam-3280	224	7	and	and	CCONJ
ejpam-3280	224	8	(	(	PUNCT
ejpam-3280	224	9	g	g	NOUN
ejpam-3280	224	10	,	,	PUNCT
ejpam-3280	224	11	b	b	NOUN
ejpam-3280	224	12	)	)	PUNCT
ejpam-3280	224	13	be	be	AUX
ejpam-3280	224	14	two	two	NUM
ejpam-3280	224	15	fuzzy	fuzzy	ADJ
ejpam-3280	224	16	soft	soft	ADJ
ejpam-3280	224	17	hypervector	hypervector	NOUN
ejpam-3280	224	18	space	space	NOUN
ejpam-3280	224	19	over	over	ADP
ejpam-3280	224	20	v	v	NOUN
ejpam-3280	224	21	.	.	PUNCT
ejpam-3280	225	1	if	if	SCONJ
ejpam-3280	225	2	a∩b	a∩b	PROPN
ejpam-3280	225	3	=	=	SYM
ejpam-3280	225	4	∅	∅	NOUN
ejpam-3280	225	5	,	,	PUNCT
ejpam-3280	225	6	then	then	ADV
ejpam-3280	225	7	(	(	PUNCT
ejpam-3280	225	8	f	f	X
ejpam-3280	225	9	,	,	PUNCT
ejpam-3280	225	10	a	a	PRON
ejpam-3280	225	11	)	)	PUNCT
ejpam-3280	225	12	t	t	NOUN
ejpam-3280	225	13	(	(	PUNCT
ejpam-3280	225	14	g	g	PROPN
ejpam-3280	225	15	,	,	PUNCT
ejpam-3280	225	16	b	b	NOUN
ejpam-3280	225	17	)	)	PUNCT
ejpam-3280	225	18	is	be	AUX
ejpam-3280	225	19	a	a	DET
ejpam-3280	225	20	fuzzy	fuzzy	ADJ
ejpam-3280	225	21	soft	soft	ADJ
ejpam-3280	225	22	hypervector	hypervector	NOUN
ejpam-3280	225	23	space	space	NOUN
ejpam-3280	225	24	over	over	ADP
ejpam-3280	225	25	v	v	NOUN
ejpam-3280	225	26	.	.	PUNCT
ejpam-3280	226	1	proof	proof	NOUN
ejpam-3280	226	2	.	.	PUNCT
ejpam-3280	227	1	let	let	VERB
ejpam-3280	227	2	(	(	PUNCT
ejpam-3280	227	3	f	f	X
ejpam-3280	227	4	,	,	PUNCT
ejpam-3280	227	5	a	a	PRON
ejpam-3280	227	6	)	)	PUNCT
ejpam-3280	227	7	t	t	NOUN
ejpam-3280	227	8	(	(	PUNCT
ejpam-3280	227	9	g	g	PROPN
ejpam-3280	227	10	,	,	PUNCT
ejpam-3280	227	11	b	b	NOUN
ejpam-3280	227	12	)	)	PUNCT
ejpam-3280	227	13	=	=	SYM
ejpam-3280	227	14	(	(	PUNCT
ejpam-3280	227	15	h	h	NOUN
ejpam-3280	227	16	,	,	PUNCT
ejpam-3280	227	17	c	c	NOUN
ejpam-3280	227	18	)	)	PUNCT
ejpam-3280	227	19	.	.	PUNCT
ejpam-3280	228	1	since	since	SCONJ
ejpam-3280	228	2	a	a	DET
ejpam-3280	228	3	∩b	∩b	NOUN
ejpam-3280	228	4	=	=	SYM
ejpam-3280	228	5	∅	∅	NOUN
ejpam-3280	228	6	,	,	PUNCT
ejpam-3280	228	7	thus	thus	ADV
ejpam-3280	228	8	for	for	ADP
ejpam-3280	228	9	all	all	PRON
ejpam-3280	228	10	c	c	NOUN
ejpam-3280	228	11	∈	∈	ADP
ejpam-3280	228	12	c	c	NOUN
ejpam-3280	228	13	=	=	PUNCT
ejpam-3280	228	14	a	a	PRON
ejpam-3280	228	15	∪b	∪b	NOUN
ejpam-3280	228	16	,	,	PUNCT
ejpam-3280	228	17	h(c	h(c	PROPN
ejpam-3280	228	18	)	)	PUNCT
ejpam-3280	228	19	=	=	SYM
ejpam-3280	228	20	hc	hc	PROPN
ejpam-3280	228	21	=	=	PUNCT
ejpam-3280	228	22	{	{	PUNCT
ejpam-3280	228	23	fc	fc	INTJ
ejpam-3280	228	24	if	if	SCONJ
ejpam-3280	228	25	c	c	PROPN
ejpam-3280	228	26	∈	∈	PROPN
ejpam-3280	228	27	a−b	a−b	NOUN
ejpam-3280	228	28	gc	gc	PROPN
ejpam-3280	228	29	if	if	SCONJ
ejpam-3280	228	30	c	c	PROPN
ejpam-3280	228	31	∈	∈	PROPN
ejpam-3280	228	32	b	b	X
ejpam-3280	228	33	−a	−a	NOUN
ejpam-3280	228	34	.	.	PUNCT
ejpam-3280	229	1	since	since	SCONJ
ejpam-3280	229	2	fc	fc	PROPN
ejpam-3280	229	3	and	and	CCONJ
ejpam-3280	229	4	gc	gc	PROPN
ejpam-3280	229	5	are	be	AUX
ejpam-3280	229	6	fuzzy	fuzzy	ADJ
ejpam-3280	229	7	sub	sub	ADJ
ejpam-3280	229	8	-	-	ADJ
ejpam-3280	229	9	hypervector	hypervector	ADJ
ejpam-3280	229	10	space	space	NOUN
ejpam-3280	229	11	of	of	ADP
ejpam-3280	229	12	v	v	NOUN
ejpam-3280	229	13	,	,	PUNCT
ejpam-3280	229	14	therefore	therefore	ADV
ejpam-3280	229	15	,	,	PUNCT
ejpam-3280	229	16	(	(	PUNCT
ejpam-3280	229	17	f	f	X
ejpam-3280	229	18	,	,	PUNCT
ejpam-3280	229	19	a	a	PRON
ejpam-3280	229	20	)	)	PUNCT
ejpam-3280	229	21	t	t	NOUN
ejpam-3280	229	22	(	(	PUNCT
ejpam-3280	229	23	g	g	PROPN
ejpam-3280	229	24	,	,	PUNCT
ejpam-3280	229	25	b	b	NOUN
ejpam-3280	229	26	)	)	PUNCT
ejpam-3280	229	27	is	be	AUX
ejpam-3280	229	28	a	a	DET
ejpam-3280	229	29	fuzzy	fuzzy	ADJ
ejpam-3280	229	30	soft	soft	ADJ
ejpam-3280	229	31	hypervector	hypervector	NOUN
ejpam-3280	229	32	space	space	NOUN
ejpam-3280	229	33	over	over	ADP
ejpam-3280	229	34	v	v	NOUN
ejpam-3280	229	35	.	.	PUNCT
ejpam-3280	230	1	theorem	theorem	ADJ
ejpam-3280	230	2	4	4	NUM
ejpam-3280	230	3	.	.	PUNCT
ejpam-3280	231	1	if	if	SCONJ
ejpam-3280	231	2	(	(	PUNCT
ejpam-3280	231	3	f	f	X
ejpam-3280	231	4	,	,	PUNCT
ejpam-3280	231	5	a	a	PRON
ejpam-3280	231	6	)	)	PUNCT
ejpam-3280	231	7	and	and	CCONJ
ejpam-3280	231	8	(	(	PUNCT
ejpam-3280	231	9	g	g	NOUN
ejpam-3280	231	10	,	,	PUNCT
ejpam-3280	231	11	b	b	NOUN
ejpam-3280	231	12	)	)	PUNCT
ejpam-3280	231	13	be	be	AUX
ejpam-3280	231	14	two	two	NUM
ejpam-3280	231	15	fuzzy	fuzzy	ADJ
ejpam-3280	231	16	soft	soft	ADJ
ejpam-3280	231	17	hypervector	hypervector	NOUN
ejpam-3280	231	18	space	space	NOUN
ejpam-3280	231	19	over	over	ADP
ejpam-3280	231	20	v	v	NUM
ejpam-3280	231	21	,	,	PUNCT
ejpam-3280	231	22	then	then	ADV
ejpam-3280	231	23	(	(	PUNCT
ejpam-3280	231	24	f	f	X
ejpam-3280	231	25	,	,	PUNCT
ejpam-3280	231	26	a)∧	a)∧	PROPN
ejpam-3280	231	27	(	(	PUNCT
ejpam-3280	231	28	g	g	PROPN
ejpam-3280	231	29	,	,	PUNCT
ejpam-3280	231	30	b	b	NOUN
ejpam-3280	231	31	)	)	PUNCT
ejpam-3280	231	32	is	be	AUX
ejpam-3280	231	33	a	a	DET
ejpam-3280	231	34	fuzzy	fuzzy	ADJ
ejpam-3280	231	35	soft	soft	ADJ
ejpam-3280	231	36	hypervector	hypervector	NOUN
ejpam-3280	231	37	space	space	NOUN
ejpam-3280	231	38	over	over	ADP
ejpam-3280	231	39	v	v	NOUN
ejpam-3280	231	40	.	.	PUNCT
ejpam-3280	232	1	e.	e.	PROPN
ejpam-3280	232	2	ranjbar	ranjbar	PROPN
ejpam-3280	232	3	-	-	PUNCT
ejpam-3280	232	4	yanehsari	yanehsari	NOUN
ejpam-3280	232	5	,	,	PUNCT
ejpam-3280	232	6	m.	m.	NOUN
ejpam-3280	232	7	asghari	asghari	ADJ
ejpam-3280	232	8	-	-	PUNCT
ejpam-3280	232	9	larimi	larimi	PROPN
ejpam-3280	232	10	,	,	PUNCT
ejpam-3280	232	11	r.	r.	PROPN
ejpam-3280	232	12	ameri	ameri	PROPN
ejpam-3280	232	13	/	/	SYM
ejpam-3280	232	14	eur	eur	PROPN
ejpam-3280	232	15	.	.	PUNCT
ejpam-3280	233	1	j.	j.	PROPN
ejpam-3280	233	2	pure	pure	PROPN
ejpam-3280	233	3	appl	appl	PROPN
ejpam-3280	233	4	.	.	PROPN
ejpam-3280	233	5	math	math	PROPN
ejpam-3280	233	6	,	,	PUNCT
ejpam-3280	233	7	12	12	NUM
ejpam-3280	233	8	(	(	PUNCT
ejpam-3280	233	9	1	1	NUM
ejpam-3280	233	10	)	)	PUNCT
ejpam-3280	233	11	(	(	PUNCT
ejpam-3280	233	12	2019	2019	NUM
ejpam-3280	233	13	)	)	PUNCT
ejpam-3280	233	14	,	,	PUNCT
ejpam-3280	233	15	118	118	NUM
ejpam-3280	233	16	-	-	SYM
ejpam-3280	233	17	134	134	NUM
ejpam-3280	233	18	126	126	NUM
ejpam-3280	233	19	proof	proof	NOUN
ejpam-3280	233	20	.	.	PUNCT
ejpam-3280	234	1	let	let	VERB
ejpam-3280	234	2	(	(	PUNCT
ejpam-3280	234	3	f	f	X
ejpam-3280	234	4	,	,	PUNCT
ejpam-3280	234	5	a)∧	a)∧	PROPN
ejpam-3280	234	6	(	(	PUNCT
ejpam-3280	234	7	g	g	PROPN
ejpam-3280	234	8	,	,	PUNCT
ejpam-3280	234	9	b	b	NOUN
ejpam-3280	234	10	)	)	PUNCT
ejpam-3280	234	11	=	=	SYM
ejpam-3280	234	12	(	(	PUNCT
ejpam-3280	234	13	h	h	NOUN
ejpam-3280	234	14	,	,	PUNCT
ejpam-3280	234	15	a×b	a×b	PROPN
ejpam-3280	234	16	)	)	PUNCT
ejpam-3280	234	17	.	.	PUNCT
ejpam-3280	235	1	since	since	SCONJ
ejpam-3280	235	2	for	for	ADP
ejpam-3280	235	3	all	all	DET
ejpam-3280	235	4	a	a	DET
ejpam-3280	235	5	∈	∈	PROPN
ejpam-3280	235	6	a	a	PRON
ejpam-3280	235	7	,	,	PUNCT
ejpam-3280	235	8	b	b	PROPN
ejpam-3280	235	9	∈	∈	PROPN
ejpam-3280	235	10	b	b	PROPN
ejpam-3280	235	11	,	,	PUNCT
ejpam-3280	235	12	fa	fa	PROPN
ejpam-3280	235	13	and	and	CCONJ
ejpam-3280	235	14	gb	gb	PRON
ejpam-3280	235	15	are	be	AUX
ejpam-3280	235	16	fuzzy	fuzzy	ADJ
ejpam-3280	235	17	sub	sub	ADJ
ejpam-3280	235	18	-	-	ADJ
ejpam-3280	235	19	hypervector	hypervector	ADJ
ejpam-3280	235	20	space	space	NOUN
ejpam-3280	235	21	of	of	ADP
ejpam-3280	235	22	v	v	NOUN
ejpam-3280	235	23	,	,	PUNCT
ejpam-3280	235	24	so	so	ADV
ejpam-3280	235	25	is	be	AUX
ejpam-3280	235	26	h(a	h(a	PROPN
ejpam-3280	235	27	,	,	PUNCT
ejpam-3280	235	28	b	b	NOUN
ejpam-3280	235	29	)	)	PUNCT
ejpam-3280	235	30	=	=	SYM
ejpam-3280	236	1	ha	ha	INTJ
ejpam-3280	236	2	,	,	PUNCT
ejpam-3280	236	3	b	b	NOUN
ejpam-3280	236	4	=	=	SYM
ejpam-3280	236	5	fa	fa	PROPN
ejpam-3280	236	6	∧	∧	NOUN
ejpam-3280	236	7	gb	gb	NOUN
ejpam-3280	236	8	for	for	ADP
ejpam-3280	236	9	every	every	DET
ejpam-3280	236	10	(	(	PUNCT
ejpam-3280	236	11	a	a	PRON
ejpam-3280	236	12	,	,	PUNCT
ejpam-3280	236	13	b	b	NOUN
ejpam-3280	236	14	)	)	PUNCT
ejpam-3280	236	15	∈	∈	PROPN
ejpam-3280	236	16	a	a	DET
ejpam-3280	236	17	×	×	PROPN
ejpam-3280	236	18	b.	b.	NOUN
ejpam-3280	237	1	thus	thus	ADV
ejpam-3280	237	2	(	(	PUNCT
ejpam-3280	237	3	f	f	X
ejpam-3280	237	4	,	,	PUNCT
ejpam-3280	237	5	a	a	PRON
ejpam-3280	237	6	)	)	PUNCT
ejpam-3280	237	7	∧	∧	NOUN
ejpam-3280	237	8	(	(	PUNCT
ejpam-3280	237	9	g	g	PROPN
ejpam-3280	237	10	,	,	PUNCT
ejpam-3280	237	11	b	b	NOUN
ejpam-3280	237	12	)	)	PUNCT
ejpam-3280	237	13	is	be	AUX
ejpam-3280	237	14	a	a	DET
ejpam-3280	237	15	fuzzy	fuzzy	ADJ
ejpam-3280	237	16	soft	soft	ADJ
ejpam-3280	237	17	hypervector	hypervector	NOUN
ejpam-3280	237	18	space	space	NOUN
ejpam-3280	237	19	over	over	ADP
ejpam-3280	237	20	v	v	NOUN
ejpam-3280	237	21	.	.	PUNCT
ejpam-3280	238	1	definition	definition	NOUN
ejpam-3280	238	2	18	18	NUM
ejpam-3280	238	3	.	.	PUNCT
ejpam-3280	238	4	sum	sum	NOUN
ejpam-3280	238	5	of	of	ADP
ejpam-3280	238	6	two	two	NUM
ejpam-3280	238	7	fuzzy	fuzzy	ADJ
ejpam-3280	238	8	soft	soft	ADJ
ejpam-3280	238	9	sets	set	NOUN
ejpam-3280	238	10	(	(	PUNCT
ejpam-3280	238	11	f	f	X
ejpam-3280	238	12	,	,	PUNCT
ejpam-3280	238	13	a	a	PRON
ejpam-3280	238	14	)	)	PUNCT
ejpam-3280	238	15	and	and	CCONJ
ejpam-3280	238	16	(	(	PUNCT
ejpam-3280	238	17	g	g	NOUN
ejpam-3280	238	18	,	,	PUNCT
ejpam-3280	238	19	b	b	NOUN
ejpam-3280	238	20	)	)	PUNCT
ejpam-3280	238	21	over	over	ADP
ejpam-3280	238	22	a	a	DET
ejpam-3280	238	23	common	common	ADJ
ejpam-3280	238	24	universe	universe	NOUN
ejpam-3280	238	25	u	u	NOUN
ejpam-3280	238	26	,	,	PUNCT
ejpam-3280	238	27	denoted	denote	VERB
ejpam-3280	238	28	by	by	ADP
ejpam-3280	238	29	(	(	PUNCT
ejpam-3280	238	30	f	f	X
ejpam-3280	238	31	,	,	PUNCT
ejpam-3280	238	32	a	a	PRON
ejpam-3280	238	33	)	)	PUNCT
ejpam-3280	238	34	+	+	CCONJ
ejpam-3280	238	35	(	(	PUNCT
ejpam-3280	238	36	g	g	NOUN
ejpam-3280	238	37	,	,	PUNCT
ejpam-3280	238	38	b	b	NOUN
ejpam-3280	238	39	)	)	PUNCT
ejpam-3280	238	40	is	be	AUX
ejpam-3280	238	41	the	the	DET
ejpam-3280	238	42	fuzzy	fuzzy	ADJ
ejpam-3280	238	43	soft	soft	ADJ
ejpam-3280	238	44	set	set	NOUN
ejpam-3280	238	45	(	(	PUNCT
ejpam-3280	238	46	h	h	NOUN
ejpam-3280	238	47	,	,	PUNCT
ejpam-3280	238	48	c	c	NOUN
ejpam-3280	238	49	)	)	PUNCT
ejpam-3280	238	50	,	,	PUNCT
ejpam-3280	238	51	where	where	SCONJ
ejpam-3280	238	52	c	c	NOUN
ejpam-3280	238	53	=	=	SYM
ejpam-3280	238	54	a∪b	a∪b	NOUN
ejpam-3280	238	55	and	and	CCONJ
ejpam-3280	238	56	for	for	ADP
ejpam-3280	238	57	all	all	DET
ejpam-3280	238	58	c	c	NOUN
ejpam-3280	238	59	∈	∈	PROPN
ejpam-3280	238	60	c	c	NOUN
ejpam-3280	238	61	,	,	PUNCT
ejpam-3280	238	62	h(c	h(c	PROPN
ejpam-3280	238	63	)	)	PUNCT
ejpam-3280	238	64	=	=	PUNCT
ejpam-3280	239	1			PUNCT
ejpam-3280	239	2	fc	fc	PROPN
ejpam-3280	239	3	+	+	CCONJ
ejpam-3280	239	4	gc	gc	PROPN
ejpam-3280	239	5	if	if	SCONJ
ejpam-3280	239	6	c	c	PROPN
ejpam-3280	239	7	∈	∈	PROPN
ejpam-3280	239	8	a	a	DET
ejpam-3280	239	9	∩b	∩b	NOUN
ejpam-3280	239	10	fc	fc	PROPN
ejpam-3280	239	11	if	if	SCONJ
ejpam-3280	239	12	c	c	PROPN
ejpam-3280	239	13	∈	∈	PROPN
ejpam-3280	239	14	a−b	a−b	NOUN
ejpam-3280	239	15	gc	gc	PROPN
ejpam-3280	239	16	if	if	SCONJ
ejpam-3280	239	17	c	c	PROPN
ejpam-3280	239	18	∈	∈	PROPN
ejpam-3280	239	19	b	b	X
ejpam-3280	239	20	−a	−a	NOUN
ejpam-3280	239	21	.	.	PUNCT
ejpam-3280	240	1	and	and	CCONJ
ejpam-3280	240	2	for	for	ADP
ejpam-3280	240	3	every	every	DET
ejpam-3280	240	4	x	x	SYM
ejpam-3280	240	5	∈	∈	PROPN
ejpam-3280	240	6	v	v	NOUN
ejpam-3280	240	7	,	,	PUNCT
ejpam-3280	240	8	(	(	PUNCT
ejpam-3280	240	9	fc	fc	X
ejpam-3280	240	10	+	+	NUM
ejpam-3280	240	11	gc)(x	gc)(x	PROPN
ejpam-3280	240	12	)	)	PUNCT
ejpam-3280	240	13	=	=	PUNCT
ejpam-3280	240	14	∨	∨	X
ejpam-3280	240	15	{	{	PUNCT
ejpam-3280	240	16	fc(y	fc(y	NOUN
ejpam-3280	240	17	)	)	PUNCT
ejpam-3280	240	18	∧	∧	NOUN
ejpam-3280	240	19	gc(z	gc(z	NUM
ejpam-3280	240	20	)	)	PUNCT
ejpam-3280	240	21	:	:	PUNCT
ejpam-3280	240	22	y	y	X
ejpam-3280	240	23	,	,	PUNCT
ejpam-3280	240	24	z	z	PROPN
ejpam-3280	240	25	∈	∈	PROPN
ejpam-3280	240	26	v	v	NOUN
ejpam-3280	240	27	,	,	PUNCT
ejpam-3280	240	28	y	y	PROPN
ejpam-3280	241	1	+	+	NOUN
ejpam-3280	241	2	z	z	NOUN
ejpam-3280	241	3	=	=	SYM
ejpam-3280	241	4	x	x	NOUN
ejpam-3280	241	5	}	}	PUNCT
ejpam-3280	241	6	.	.	PUNCT
ejpam-3280	242	1	theorem	theorem	NOUN
ejpam-3280	242	2	5	5	NUM
ejpam-3280	242	3	.	.	PUNCT
ejpam-3280	243	1	let	let	VERB
ejpam-3280	243	2	(	(	PUNCT
ejpam-3280	243	3	f	f	X
ejpam-3280	243	4	,	,	PUNCT
ejpam-3280	243	5	a	a	PRON
ejpam-3280	243	6	)	)	PUNCT
ejpam-3280	243	7	and	and	CCONJ
ejpam-3280	243	8	(	(	PUNCT
ejpam-3280	243	9	g	g	NOUN
ejpam-3280	243	10	,	,	PUNCT
ejpam-3280	243	11	b	b	NOUN
ejpam-3280	243	12	)	)	PUNCT
ejpam-3280	243	13	be	be	AUX
ejpam-3280	243	14	two	two	NUM
ejpam-3280	243	15	fuzzy	fuzzy	ADJ
ejpam-3280	243	16	soft	soft	ADJ
ejpam-3280	243	17	hypervector	hypervector	NOUN
ejpam-3280	243	18	space	space	NOUN
ejpam-3280	243	19	over	over	ADP
ejpam-3280	243	20	v	v	NOUN
ejpam-3280	243	21	.	.	PUNCT
ejpam-3280	244	1	then	then	ADV
ejpam-3280	244	2	(	(	PUNCT
ejpam-3280	244	3	f	f	X
ejpam-3280	244	4	,	,	PUNCT
ejpam-3280	244	5	a	a	PRON
ejpam-3280	244	6	)	)	PUNCT
ejpam-3280	244	7	+	+	CCONJ
ejpam-3280	244	8	(	(	PUNCT
ejpam-3280	244	9	g	g	NOUN
ejpam-3280	244	10	,	,	PUNCT
ejpam-3280	244	11	b	b	NOUN
ejpam-3280	244	12	)	)	PUNCT
ejpam-3280	244	13	is	be	AUX
ejpam-3280	244	14	a	a	DET
ejpam-3280	244	15	fuzzy	fuzzy	ADJ
ejpam-3280	244	16	soft	soft	ADJ
ejpam-3280	244	17	hypervector	hypervector	NOUN
ejpam-3280	244	18	space	space	NOUN
ejpam-3280	244	19	over	over	ADP
ejpam-3280	244	20	v	v	NOUN
ejpam-3280	244	21	.	.	PUNCT
ejpam-3280	245	1	proof	proof	NOUN
ejpam-3280	245	2	.	.	PUNCT
ejpam-3280	246	1	let	let	VERB
ejpam-3280	246	2	(	(	PUNCT
ejpam-3280	246	3	f	f	X
ejpam-3280	246	4	,	,	PUNCT
ejpam-3280	246	5	a	a	PRON
ejpam-3280	246	6	)	)	PUNCT
ejpam-3280	246	7	+	+	CCONJ
ejpam-3280	246	8	(	(	PUNCT
ejpam-3280	246	9	g	g	NOUN
ejpam-3280	246	10	,	,	PUNCT
ejpam-3280	246	11	b	b	NOUN
ejpam-3280	246	12	)	)	PUNCT
ejpam-3280	246	13	=	=	SYM
ejpam-3280	246	14	(	(	PUNCT
ejpam-3280	246	15	h	h	NOUN
ejpam-3280	246	16	,	,	PUNCT
ejpam-3280	246	17	c	c	NOUN
ejpam-3280	246	18	)	)	PUNCT
ejpam-3280	246	19	,	,	PUNCT
ejpam-3280	247	1	where	where	SCONJ
ejpam-3280	247	2	c	c	NOUN
ejpam-3280	247	3	=	=	PUNCT
ejpam-3280	247	4	a	a	DET
ejpam-3280	247	5	∪b	∪b	X
ejpam-3280	247	6	and	and	CCONJ
ejpam-3280	247	7	hc(x	hc(x	NOUN
ejpam-3280	247	8	)	)	PUNCT
ejpam-3280	247	9	=	=	PUNCT
ejpam-3280	247	10			PUNCT
ejpam-3280	247	11	(	(	PUNCT
ejpam-3280	247	12	fc	fc	PROPN
ejpam-3280	247	13	+	+	NUM
ejpam-3280	247	14	gc)(x	gc)(x	PROPN
ejpam-3280	247	15	)	)	PUNCT
ejpam-3280	247	16	if	if	SCONJ
ejpam-3280	247	17	c	c	PROPN
ejpam-3280	247	18	∈	∈	VERB
ejpam-3280	247	19	a	a	DET
ejpam-3280	247	20	∩b	∩b	NOUN
ejpam-3280	247	21	fc(x	fc(x	NOUN
ejpam-3280	247	22	)	)	PUNCT
ejpam-3280	247	23	if	if	SCONJ
ejpam-3280	247	24	c	c	PROPN
ejpam-3280	247	25	∈	∈	PROPN
ejpam-3280	247	26	a−b	a−b	NOUN
ejpam-3280	247	27	gc(x	gc(x	NOUN
ejpam-3280	247	28	)	)	PUNCT
ejpam-3280	247	29	if	if	SCONJ
ejpam-3280	247	30	c	c	PROPN
ejpam-3280	247	31	∈	∈	PROPN
ejpam-3280	247	32	b	b	X
ejpam-3280	247	33	−a	−a	NOUN
ejpam-3280	247	34	for	for	ADP
ejpam-3280	247	35	all	all	DET
ejpam-3280	247	36	c	c	NOUN
ejpam-3280	247	37	∈	∈	PROPN
ejpam-3280	247	38	c	c	PROPN
ejpam-3280	247	39	and	and	CCONJ
ejpam-3280	247	40	x	x	PROPN
ejpam-3280	247	41	∈	∈	NOUN
ejpam-3280	247	42	v	v	NOUN
ejpam-3280	247	43	.	.	PUNCT
ejpam-3280	248	1	if	if	SCONJ
ejpam-3280	248	2	c	c	PROPN
ejpam-3280	248	3	∈	∈	PROPN
ejpam-3280	248	4	a−b	a−b	NOUN
ejpam-3280	248	5	or	or	CCONJ
ejpam-3280	248	6	c	c	NOUN
ejpam-3280	248	7	∈	∈	PROPN
ejpam-3280	248	8	b	b	NOUN
ejpam-3280	248	9	−a	−a	NOUN
ejpam-3280	248	10	,	,	PUNCT
ejpam-3280	248	11	the	the	DET
ejpam-3280	248	12	proof	proof	NOUN
ejpam-3280	248	13	is	be	AUX
ejpam-3280	248	14	straightforward	straightforward	ADJ
ejpam-3280	248	15	.	.	PUNCT
ejpam-3280	249	1	let	let	VERB
ejpam-3280	249	2	c	c	NOUN
ejpam-3280	249	3	∈	∈	VERB
ejpam-3280	249	4	a	a	DET
ejpam-3280	249	5	∩b	∩b	NOUN
ejpam-3280	249	6	,	,	PUNCT
ejpam-3280	249	7	hc(u+	hc(u+	PROPN
ejpam-3280	249	8	v	v	NOUN
ejpam-3280	249	9	)	)	PUNCT
ejpam-3280	249	10	=	=	SYM
ejpam-3280	249	11	a	a	PRON
ejpam-3280	249	12	,	,	PUNCT
ejpam-3280	249	13	hc(u	hc(u	PROPN
ejpam-3280	249	14	)	)	PUNCT
ejpam-3280	249	15	=	=	SYM
ejpam-3280	249	16	a′	a′	NOUN
ejpam-3280	249	17	and	and	CCONJ
ejpam-3280	249	18	hc(v	hc(v	NOUN
ejpam-3280	249	19	)	)	PUNCT
ejpam-3280	250	1	=	=	SYM
ejpam-3280	250	2	a′′	a′′	NOUN
ejpam-3280	250	3	for	for	ADP
ejpam-3280	250	4	all	all	DET
ejpam-3280	250	5	u	u	NOUN
ejpam-3280	250	6	,	,	PUNCT
ejpam-3280	250	7	v	v	NOUN
ejpam-3280	250	8	∈	∈	PROPN
ejpam-3280	250	9	v	v	NOUN
ejpam-3280	250	10	.	.	PUNCT
ejpam-3280	251	1	then	then	ADV
ejpam-3280	251	2	∃y0	∃y0	VERB
ejpam-3280	251	3	,	,	PUNCT
ejpam-3280	251	4	z0	z0	PROPN
ejpam-3280	251	5	∈	∈	PROPN
ejpam-3280	251	6	v	v	NOUN
ejpam-3280	251	7	:	:	PUNCT
ejpam-3280	251	8	y0	y0	NOUN
ejpam-3280	251	9	+	+	CCONJ
ejpam-3280	251	10	z0	z0	PROPN
ejpam-3280	251	11	=	=	PUNCT
ejpam-3280	251	12	u+	u+	NUM
ejpam-3280	251	13	v	v	NOUN
ejpam-3280	251	14	,	,	PUNCT
ejpam-3280	251	15	hc(u+	hc(u+	PROPN
ejpam-3280	251	16	v	v	NOUN
ejpam-3280	251	17	)	)	PUNCT
ejpam-3280	251	18	=	=	SYM
ejpam-3280	251	19	(	(	PUNCT
ejpam-3280	251	20	fc	fc	PROPN
ejpam-3280	251	21	+	+	CCONJ
ejpam-3280	251	22	gc)(u+	gc)(u+	PROPN
ejpam-3280	251	23	v	v	NOUN
ejpam-3280	251	24	)	)	PUNCT
ejpam-3280	251	25	=	=	SYM
ejpam-3280	251	26	fc(y0	fc(y0	NOUN
ejpam-3280	251	27	)	)	PUNCT
ejpam-3280	251	28	∧	∧	NOUN
ejpam-3280	251	29	gc(z0	gc(z0	NOUN
ejpam-3280	251	30	)	)	PUNCT
ejpam-3280	251	31	=	=	SYM
ejpam-3280	251	32	a	a	PRON
ejpam-3280	251	33	,	,	PUNCT
ejpam-3280	251	34	∃y′0	∃y′0	PROPN
ejpam-3280	251	35	,	,	PUNCT
ejpam-3280	251	36	z′0	z′0	X
ejpam-3280	251	37	∈	∈	PROPN
ejpam-3280	251	38	v	v	NOUN
ejpam-3280	251	39	:	:	PUNCT
ejpam-3280	251	40	y′0	y′0	X
ejpam-3280	252	1	+	+	CCONJ
ejpam-3280	252	2	z′0	z′0	X
ejpam-3280	252	3	=	=	SYM
ejpam-3280	252	4	u	u	NOUN
ejpam-3280	252	5	,	,	PUNCT
ejpam-3280	252	6	hc(u	hc(u	PROPN
ejpam-3280	252	7	)	)	PUNCT
ejpam-3280	252	8	=	=	SYM
ejpam-3280	252	9	(	(	PUNCT
ejpam-3280	252	10	fc	fc	X
ejpam-3280	252	11	+	+	CCONJ
ejpam-3280	252	12	gc)(u	gc)(u	PROPN
ejpam-3280	252	13	)	)	PUNCT
ejpam-3280	252	14	=	=	SYM
ejpam-3280	252	15	fc(y	fc(y	NOUN
ejpam-3280	252	16	′	′	NOUN
ejpam-3280	252	17	0	0	X
ejpam-3280	252	18	)	)	PUNCT
ejpam-3280	252	19	∧	∧	NOUN
ejpam-3280	252	20	gc(z′0	gc(z′0	NOUN
ejpam-3280	252	21	)	)	PUNCT
ejpam-3280	252	22	=	=	SYM
ejpam-3280	252	23	a′	a′	PROPN
ejpam-3280	252	24	,	,	PUNCT
ejpam-3280	252	25	and	and	CCONJ
ejpam-3280	252	26	∃y′′0	∃y′′0	PROPN
ejpam-3280	252	27	,	,	PUNCT
ejpam-3280	252	28	z′′0	z′′0	PROPN
ejpam-3280	252	29	∈	∈	PROPN
ejpam-3280	252	30	v	v	ADP
ejpam-3280	252	31	:	:	PUNCT
ejpam-3280	252	32	y′′0	y′′0	X
ejpam-3280	253	1	+	+	CCONJ
ejpam-3280	253	2	z′′0	z′′0	PROPN
ejpam-3280	253	3	=	=	SYM
ejpam-3280	253	4	v	v	NOUN
ejpam-3280	253	5	,	,	PUNCT
ejpam-3280	253	6	hc(v	hc(v	NUM
ejpam-3280	253	7	)	)	PUNCT
ejpam-3280	253	8	=	=	SYM
ejpam-3280	253	9	(	(	PUNCT
ejpam-3280	253	10	fc	fc	PROPN
ejpam-3280	253	11	+	+	CCONJ
ejpam-3280	253	12	gc)(u+	gc)(u+	PROPN
ejpam-3280	253	13	v	v	NOUN
ejpam-3280	253	14	)	)	PUNCT
ejpam-3280	253	15	=	=	SYM
ejpam-3280	253	16	fc(y	fc(y	X
ejpam-3280	253	17	′′	′′	PROPN
ejpam-3280	253	18	0	0	NUM
ejpam-3280	253	19	)	)	PUNCT
ejpam-3280	253	20	∧	∧	NOUN
ejpam-3280	253	21	gc(z′′0	gc(z′′0	NOUN
ejpam-3280	253	22	)	)	PUNCT
ejpam-3280	254	1	=	=	PUNCT
ejpam-3280	254	2	a′′.	a′′.	PROPN
ejpam-3280	254	3	since	since	SCONJ
ejpam-3280	254	4	a	a	DET
ejpam-3280	254	5	=	=	SYM
ejpam-3280	254	6	fc(y0	fc(y0	NOUN
ejpam-3280	254	7	)	)	PUNCT
ejpam-3280	254	8	∧	∧	NOUN
ejpam-3280	254	9	gc(z0	gc(z0	NOUN
ejpam-3280	254	10	)	)	PUNCT
ejpam-3280	254	11	≥	≥	NOUN
ejpam-3280	254	12	fc(y	fc(y	NOUN
ejpam-3280	255	1	′	′	NOUN
ejpam-3280	255	2	0	0	NUM
ejpam-3280	256	1	+	+	CCONJ
ejpam-3280	256	2	y′′0	y′′0	NOUN
ejpam-3280	256	3	)	)	PUNCT
ejpam-3280	256	4	∧	∧	NOUN
ejpam-3280	256	5	gc(z′0	gc(z′0	NOUN
ejpam-3280	256	6	+	+	CCONJ
ejpam-3280	256	7	z′′0	z′′0	NUM
ejpam-3280	256	8	)	)	PUNCT
ejpam-3280	256	9	≥	≥	NOUN
ejpam-3280	256	10	fc(y	fc(y	NOUN
ejpam-3280	256	11	′	′	NOUN
ejpam-3280	256	12	0	0	NUM
ejpam-3280	256	13	)	)	PUNCT
ejpam-3280	256	14	∧	∧	NOUN
ejpam-3280	256	15	fc(y′′0	fc(y′′0	NOUN
ejpam-3280	256	16	)	)	PUNCT
ejpam-3280	256	17	∧	∧	NOUN
ejpam-3280	256	18	gc(z′0	gc(z′0	NOUN
ejpam-3280	256	19	)	)	PUNCT
ejpam-3280	256	20	∧	∧	NOUN
ejpam-3280	256	21	gc(z′′0	gc(z′′0	NOUN
ejpam-3280	256	22	)	)	PUNCT
ejpam-3280	256	23	=	=	PUNCT
ejpam-3280	256	24	(	(	PUNCT
ejpam-3280	256	25	fc(y	fc(y	NOUN
ejpam-3280	256	26	′	′	NOUN
ejpam-3280	256	27	0	0	NUM
ejpam-3280	256	28	)	)	PUNCT
ejpam-3280	256	29	∧	∧	NOUN
ejpam-3280	256	30	gc(z′0	gc(z′0	NOUN
ejpam-3280	256	31	)	)	PUNCT
ejpam-3280	256	32	)	)	PUNCT
ejpam-3280	257	1	∧	∧	NOUN
ejpam-3280	257	2	(	(	PUNCT
ejpam-3280	257	3	fc(y	fc(y	NOUN
ejpam-3280	257	4	′′	′′	PROPN
ejpam-3280	257	5	0	0	NUM
ejpam-3280	257	6	)	)	PUNCT
ejpam-3280	257	7	∧	∧	NOUN
ejpam-3280	257	8	gc(z′′0	gc(z′′0	NOUN
ejpam-3280	257	9	)	)	PUNCT
ejpam-3280	257	10	)	)	PUNCT
ejpam-3280	258	1	=	=	PRON
ejpam-3280	258	2	a′	a′	PROPN
ejpam-3280	258	3	∧	∧	PROPN
ejpam-3280	258	4	a′′.	a′′.	PROPN
ejpam-3280	258	5	therefore	therefore	ADV
ejpam-3280	258	6	,	,	PUNCT
ejpam-3280	258	7	hc(u+	hc(u+	PROPN
ejpam-3280	258	8	v	v	NOUN
ejpam-3280	258	9	)	)	PUNCT
ejpam-3280	258	10	≥	≥	NOUN
ejpam-3280	258	11	hc(u	hc(u	NOUN
ejpam-3280	258	12	)	)	PUNCT
ejpam-3280	258	13	∧	∧	NOUN
ejpam-3280	258	14	hc(v	hc(v	NOUN
ejpam-3280	258	15	)	)	PUNCT
ejpam-3280	258	16	.	.	PUNCT
ejpam-3280	259	1	on	on	ADP
ejpam-3280	259	2	the	the	DET
ejpam-3280	259	3	other	other	ADJ
ejpam-3280	259	4	hand	hand	NOUN
ejpam-3280	259	5	,	,	PUNCT
ejpam-3280	259	6	since	since	SCONJ
ejpam-3280	259	7	fc	fc	PROPN
ejpam-3280	259	8	and	and	CCONJ
ejpam-3280	259	9	gc	gc	PROPN
ejpam-3280	259	10	are	be	AUX
ejpam-3280	259	11	fuzzy	fuzzy	ADJ
ejpam-3280	259	12	soft	soft	ADJ
ejpam-3280	259	13	hypervector	hypervector	NOUN
ejpam-3280	259	14	space	space	NOUN
ejpam-3280	259	15	,	,	PUNCT
ejpam-3280	259	16	thus	thus	ADV
ejpam-3280	259	17	fc(−y	fc(−y	NOUN
ejpam-3280	259	18	)	)	PUNCT
ejpam-3280	259	19	≥	≥	NOUN
ejpam-3280	259	20	fc(y	fc(y	NOUN
ejpam-3280	259	21	)	)	PUNCT
ejpam-3280	259	22	and	and	CCONJ
ejpam-3280	259	23	gc(−z	gc(−z	X
ejpam-3280	259	24	)	)	PUNCT
ejpam-3280	259	25	≥	≥	NOUN
ejpam-3280	259	26	gc(z	gc(z	X
ejpam-3280	259	27	)	)	PUNCT
ejpam-3280	259	28	for	for	ADP
ejpam-3280	259	29	all	all	DET
ejpam-3280	259	30	y	y	PROPN
ejpam-3280	259	31	,	,	PUNCT
ejpam-3280	259	32	z	z	PROPN
ejpam-3280	259	33	∈	∈	PROPN
ejpam-3280	259	34	v	v	NOUN
ejpam-3280	259	35	.	.	PUNCT
ejpam-3280	260	1	so∨	so∨	NOUN
ejpam-3280	260	2	{	{	PUNCT
ejpam-3280	260	3	fc(−y	fc(−y	NOUN
ejpam-3280	260	4	)	)	PUNCT
ejpam-3280	260	5	∧	∧	PROPN
ejpam-3280	260	6	gc(−z	gc(−z	PROPN
ejpam-3280	260	7	)	)	PUNCT
ejpam-3280	260	8	:	:	PUNCT
ejpam-3280	260	9	(	(	PUNCT
ejpam-3280	260	10	−y	−y	NOUN
ejpam-3280	260	11	)	)	PUNCT
ejpam-3280	260	12	+	+	CCONJ
ejpam-3280	260	13	(	(	PUNCT
ejpam-3280	260	14	−z	−z	NOUN
ejpam-3280	260	15	)	)	PUNCT
ejpam-3280	260	16	=	=	SYM
ejpam-3280	260	17	−v	−v	NOUN
ejpam-3280	260	18	}	}	PUNCT
ejpam-3280	260	19	≥	≥	NOUN
ejpam-3280	260	20	∨	∨	NUM
ejpam-3280	260	21	{	{	PUNCT
ejpam-3280	260	22	fc(y	fc(y	NOUN
ejpam-3280	260	23	)	)	PUNCT
ejpam-3280	260	24	∧	∧	NOUN
ejpam-3280	260	25	gc(z	gc(z	NUM
ejpam-3280	260	26	)	)	PUNCT
ejpam-3280	260	27	:	:	PUNCT
ejpam-3280	261	1	y	y	X
ejpam-3280	261	2	+	+	CCONJ
ejpam-3280	261	3	z	z	NOUN
ejpam-3280	261	4	=	=	SYM
ejpam-3280	261	5	v	v	NOUN
ejpam-3280	261	6	}	}	PUNCT
ejpam-3280	261	7	.	.	PUNCT
ejpam-3280	262	1	hence	hence	ADV
ejpam-3280	262	2	∨	∨	PROPN
ejpam-3280	262	3	{	{	PUNCT
ejpam-3280	262	4	fc(a	fc(a	NOUN
ejpam-3280	262	5	)	)	PUNCT
ejpam-3280	262	6	∧	∧	NOUN
ejpam-3280	262	7	gc(b	gc(b	PUNCT
ejpam-3280	262	8	)	)	PUNCT
ejpam-3280	262	9	:	:	PUNCT
ejpam-3280	262	10	a+	a+	PUNCT
ejpam-3280	262	11	b	b	X
ejpam-3280	262	12	=	=	SYM
ejpam-3280	262	13	−v	−v	PROPN
ejpam-3280	262	14	}	}	PUNCT
ejpam-3280	262	15	≥	≥	NOUN
ejpam-3280	262	16	∨	∨	NUM
ejpam-3280	262	17	{	{	PUNCT
ejpam-3280	262	18	fc(y	fc(y	NOUN
ejpam-3280	262	19	)	)	PUNCT
ejpam-3280	262	20	∧	∧	NOUN
ejpam-3280	262	21	gc(z	gc(z	NUM
ejpam-3280	262	22	)	)	PUNCT
ejpam-3280	262	23	:	:	PUNCT
ejpam-3280	263	1	y	y	X
ejpam-3280	263	2	+	+	CCONJ
ejpam-3280	263	3	z	z	NOUN
ejpam-3280	263	4	=	=	SYM
ejpam-3280	263	5	v	v	NOUN
ejpam-3280	263	6	}	}	PUNCT
ejpam-3280	263	7	.	.	PUNCT
ejpam-3280	264	1	e.	e.	PROPN
ejpam-3280	264	2	ranjbar	ranjbar	PROPN
ejpam-3280	264	3	-	-	PUNCT
ejpam-3280	264	4	yanehsari	yanehsari	NOUN
ejpam-3280	264	5	,	,	PUNCT
ejpam-3280	264	6	m.	m.	NOUN
ejpam-3280	264	7	asghari	asghari	ADJ
ejpam-3280	264	8	-	-	PUNCT
ejpam-3280	264	9	larimi	larimi	PROPN
ejpam-3280	264	10	,	,	PUNCT
ejpam-3280	264	11	r.	r.	PROPN
ejpam-3280	264	12	ameri	ameri	PROPN
ejpam-3280	264	13	/	/	SYM
ejpam-3280	264	14	eur	eur	PROPN
ejpam-3280	264	15	.	.	PUNCT
ejpam-3280	265	1	j.	j.	PROPN
ejpam-3280	265	2	pure	pure	PROPN
ejpam-3280	265	3	appl	appl	PROPN
ejpam-3280	265	4	.	.	PROPN
ejpam-3280	265	5	math	math	PROPN
ejpam-3280	265	6	,	,	PUNCT
ejpam-3280	265	7	12	12	NUM
ejpam-3280	265	8	(	(	PUNCT
ejpam-3280	265	9	1	1	NUM
ejpam-3280	265	10	)	)	PUNCT
ejpam-3280	265	11	(	(	PUNCT
ejpam-3280	265	12	2019	2019	NUM
ejpam-3280	265	13	)	)	PUNCT
ejpam-3280	265	14	,	,	PUNCT
ejpam-3280	265	15	118	118	NUM
ejpam-3280	265	16	-	-	SYM
ejpam-3280	265	17	134	134	NUM
ejpam-3280	265	18	127	127	NUM
ejpam-3280	265	19	therefore	therefore	ADV
ejpam-3280	265	20	hc(−v	hc(−v	PROPN
ejpam-3280	265	21	)	)	PUNCT
ejpam-3280	265	22	≥	≥	NOUN
ejpam-3280	265	23	hc(v	hc(v	X
ejpam-3280	265	24	)	)	PUNCT
ejpam-3280	265	25	∀v	∀v	PROPN
ejpam-3280	265	26	∈	∈	PROPN
ejpam-3280	265	27	v	v	NOUN
ejpam-3280	265	28	,	,	PUNCT
ejpam-3280	265	29	c	c	PROPN
ejpam-3280	265	30	∈	∈	PROPN
ejpam-3280	265	31	a	a	DET
ejpam-3280	265	32	∩b	∩b	NOUN
ejpam-3280	265	33	.	.	PUNCT
ejpam-3280	266	1	now	now	ADV
ejpam-3280	266	2	,	,	PUNCT
ejpam-3280	266	3	we	we	PRON
ejpam-3280	266	4	show	show	VERB
ejpam-3280	266	5	that	that	DET
ejpam-3280	266	6	inf	inf	PROPN
ejpam-3280	266	7	z∈r	z∈r	PROPN
ejpam-3280	266	8	◦	◦	NOUN
ejpam-3280	266	9	v	v	NOUN
ejpam-3280	266	10	(	(	PUNCT
ejpam-3280	266	11	f	f	PROPN
ejpam-3280	266	12	+	+	NUM
ejpam-3280	266	13	g)c(z	g)c(z	PROPN
ejpam-3280	266	14	)	)	PUNCT
ejpam-3280	266	15	≥	≥	NUM
ejpam-3280	266	16	(	(	PUNCT
ejpam-3280	266	17	f	f	X
ejpam-3280	266	18	+	+	CCONJ
ejpam-3280	266	19	g)c(v	g)c(v	PROPN
ejpam-3280	266	20	)	)	PUNCT
ejpam-3280	266	21	.	.	PUNCT
ejpam-3280	267	1	suppose	suppose	VERB
ejpam-3280	267	2	inf	inf	PROPN
ejpam-3280	267	3	z∈r	z∈r	PROPN
ejpam-3280	267	4	◦	◦	NOUN
ejpam-3280	267	5	v	v	NOUN
ejpam-3280	267	6	(	(	PUNCT
ejpam-3280	267	7	f	f	PROPN
ejpam-3280	267	8	+	+	NUM
ejpam-3280	267	9	g)c(z	g)c(z	NOUN
ejpam-3280	267	10	)	)	PUNCT
ejpam-3280	267	11	=	=	SYM
ejpam-3280	267	12	inf	inf	PROPN
ejpam-3280	267	13	z∈r	z∈r	NUM
ejpam-3280	267	14	◦	◦	NOUN
ejpam-3280	267	15	v	v	NOUN
ejpam-3280	267	16	(	(	PUNCT
ejpam-3280	267	17	∨	∨	X
ejpam-3280	267	18	{	{	PUNCT
ejpam-3280	267	19	fc(y	fc(y	NOUN
ejpam-3280	267	20	)	)	PUNCT
ejpam-3280	267	21	∧	∧	NOUN
ejpam-3280	267	22	gc(w	gc(w	NUM
ejpam-3280	267	23	)	)	PUNCT
ejpam-3280	267	24	:	:	PUNCT
ejpam-3280	268	1	y	y	X
ejpam-3280	268	2	+	+	CCONJ
ejpam-3280	268	3	w	w	PROPN
ejpam-3280	268	4	=	=	SYM
ejpam-3280	268	5	z	z	NOUN
ejpam-3280	268	6	}	}	PUNCT
ejpam-3280	268	7	)	)	PUNCT
ejpam-3280	268	8	,	,	PUNCT
ejpam-3280	268	9	and	and	CCONJ
ejpam-3280	268	10	(	(	PUNCT
ejpam-3280	268	11	f	f	PROPN
ejpam-3280	268	12	+	+	CCONJ
ejpam-3280	268	13	g)c(v	g)c(v	NOUN
ejpam-3280	268	14	)	)	PUNCT
ejpam-3280	268	15	=	=	SYM
ejpam-3280	268	16	∨	∨	X
ejpam-3280	268	17	{	{	PUNCT
ejpam-3280	268	18	fc(y′	fc(y′	PROPN
ejpam-3280	268	19	)	)	PUNCT
ejpam-3280	268	20	∧	∧	PROPN
ejpam-3280	268	21	gc(w′	gc(w′	PROPN
ejpam-3280	268	22	)	)	PUNCT
ejpam-3280	268	23	:	:	PUNCT
ejpam-3280	268	24	y′	y′	X
ejpam-3280	269	1	+	+	CCONJ
ejpam-3280	269	2	w′	w′	NOUN
ejpam-3280	269	3	=	=	SYM
ejpam-3280	269	4	v	v	NOUN
ejpam-3280	269	5	}	}	PUNCT
ejpam-3280	269	6	.	.	PUNCT
ejpam-3280	270	1	since	since	SCONJ
ejpam-3280	270	2	y′+w′	y′+w′	NUM
ejpam-3280	270	3	=	=	SYM
ejpam-3280	270	4	v	v	PROPN
ejpam-3280	270	5	,	,	PUNCT
ejpam-3280	270	6	this	this	PRON
ejpam-3280	270	7	implies	imply	VERB
ejpam-3280	270	8	that	that	SCONJ
ejpam-3280	270	9	r	r	NOUN
ejpam-3280	270	10	◦	◦	NOUN
ejpam-3280	270	11	v	v	NOUN
ejpam-3280	270	12	=	=	SYM
ejpam-3280	270	13	r	r	NOUN
ejpam-3280	270	14	◦	◦	NOUN
ejpam-3280	270	15	(y′+w′	(y′+w′	NOUN
ejpam-3280	270	16	)	)	PUNCT
ejpam-3280	270	17	⊆	⊆	NUM
ejpam-3280	270	18	r	r	NOUN
ejpam-3280	270	19	◦	◦	NOUN
ejpam-3280	270	20	y′+r	y′+r	NOUN
ejpam-3280	270	21	◦	◦	NOUN
ejpam-3280	270	22	w′.	w′.	NOUN
ejpam-3280	270	23	thus	thus	ADV
ejpam-3280	270	24	,	,	PUNCT
ejpam-3280	270	25	since	since	SCONJ
ejpam-3280	270	26	z	z	PROPN
ejpam-3280	270	27	∈	∈	PROPN
ejpam-3280	270	28	r	r	NOUN
ejpam-3280	270	29	◦	◦	NOUN
ejpam-3280	270	30	v	v	NOUN
ejpam-3280	270	31	,	,	PUNCT
ejpam-3280	270	32	then	then	ADV
ejpam-3280	270	33	there	there	PRON
ejpam-3280	270	34	exist	exist	VERB
ejpam-3280	270	35	a	a	DET
ejpam-3280	270	36	,	,	PUNCT
ejpam-3280	270	37	b	b	PROPN
ejpam-3280	270	38	∈	∈	NOUN
ejpam-3280	270	39	v	v	ADP
ejpam-3280	270	40	such	such	DET
ejpam-3280	270	41	that	that	SCONJ
ejpam-3280	270	42	a	a	DET
ejpam-3280	270	43	∈	∈	PROPN
ejpam-3280	270	44	r	r	NOUN
ejpam-3280	270	45	◦	◦	NOUN
ejpam-3280	270	46	y′	y′	NUM
ejpam-3280	270	47	,	,	PUNCT
ejpam-3280	270	48	b	b	X
ejpam-3280	270	49	∈	∈	PROPN
ejpam-3280	270	50	r	r	NOUN
ejpam-3280	270	51	◦	◦	NOUN
ejpam-3280	270	52	w′	w′	NOUN
ejpam-3280	270	53	and	and	CCONJ
ejpam-3280	270	54	z	z	NOUN
ejpam-3280	270	55	=	=	SYM
ejpam-3280	270	56	a+	a+	PUNCT
ejpam-3280	270	57	b.	b.	PROPN
ejpam-3280	270	58	also	also	ADV
ejpam-3280	270	59	,	,	PUNCT
ejpam-3280	270	60	since	since	SCONJ
ejpam-3280	270	61	inf	inf	PROPN
ejpam-3280	270	62	a∈r	a∈r	PROPN
ejpam-3280	270	63	◦	◦	NOUN
ejpam-3280	270	64	y′	y′	NOUN
ejpam-3280	270	65	fc(a	fc(a	X
ejpam-3280	270	66	)	)	PUNCT
ejpam-3280	270	67	≥	≥	PROPN
ejpam-3280	270	68	fc(y′	fc(y′	PROPN
ejpam-3280	270	69	)	)	PUNCT
ejpam-3280	270	70	,	,	PUNCT
ejpam-3280	270	71	inf	inf	PROPN
ejpam-3280	270	72	b∈r	b∈r	NOUN
ejpam-3280	270	73	◦	◦	NOUN
ejpam-3280	270	74	w′	w′	NOUN
ejpam-3280	270	75	gc(b	gc(b	PUNCT
ejpam-3280	270	76	)	)	PUNCT
ejpam-3280	270	77	≥	≥	X
ejpam-3280	271	1	gc(w′	gc(w′	NOUN
ejpam-3280	271	2	)	)	PUNCT
ejpam-3280	271	3	.	.	PUNCT
ejpam-3280	272	1	we	we	PRON
ejpam-3280	272	2	conclude	conclude	VERB
ejpam-3280	272	3	that	that	PRON
ejpam-3280	272	4	,	,	PUNCT
ejpam-3280	272	5	fc(a	fc(a	X
ejpam-3280	272	6	)	)	PUNCT
ejpam-3280	272	7	≥	≥	NOUN
ejpam-3280	272	8	fc(y′	fc(y′	PROPN
ejpam-3280	272	9	)	)	PUNCT
ejpam-3280	272	10	and	and	CCONJ
ejpam-3280	272	11	gc(b	gc(b	ADV
ejpam-3280	272	12	)	)	PUNCT
ejpam-3280	272	13	≥	≥	X
ejpam-3280	273	1	gc(w′	gc(w′	NOUN
ejpam-3280	273	2	)	)	PUNCT
ejpam-3280	273	3	for	for	ADP
ejpam-3280	273	4	all	all	DET
ejpam-3280	273	5	a	a	DET
ejpam-3280	273	6	∈	∈	NOUN
ejpam-3280	273	7	r	r	NOUN
ejpam-3280	273	8	◦	◦	NOUN
ejpam-3280	273	9	y′	y′	NUM
ejpam-3280	273	10	,	,	PUNCT
ejpam-3280	273	11	and	and	CCONJ
ejpam-3280	273	12	for	for	ADP
ejpam-3280	273	13	all	all	DET
ejpam-3280	273	14	b	b	NOUN
ejpam-3280	273	15	∈	∈	NOUN
ejpam-3280	273	16	r	r	NOUN
ejpam-3280	273	17	◦	◦	NOUN
ejpam-3280	273	18	w′.	w′.	X
ejpam-3280	273	19	therefore	therefore	ADV
ejpam-3280	273	20	,	,	PUNCT
ejpam-3280	273	21	fc(a)∧	fc(a)∧	NOUN
ejpam-3280	273	22	gc(b	gc(b	PUNCT
ejpam-3280	273	23	)	)	PUNCT
ejpam-3280	273	24	≥	≥	NOUN
ejpam-3280	274	1	fc(y′)∧	fc(y′)∧	VERB
ejpam-3280	274	2	gc(w′	gc(w′	NOUN
ejpam-3280	274	3	)	)	PUNCT
ejpam-3280	274	4	∀y′	∀y′	NUM
ejpam-3280	274	5	,	,	PUNCT
ejpam-3280	274	6	w′	w′	PROPN
ejpam-3280	274	7	∈	∈	PROPN
ejpam-3280	274	8	v	v	NOUN
ejpam-3280	274	9	,	,	PUNCT
ejpam-3280	274	10	where	where	SCONJ
ejpam-3280	274	11	y′+w′	y′+w′	NOUN
ejpam-3280	274	12	=	=	SYM
ejpam-3280	274	13	v	v	PROPN
ejpam-3280	274	14	for	for	ADP
ejpam-3280	274	15	all	all	DET
ejpam-3280	274	16	z	z	NOUN
ejpam-3280	274	17	=	=	SYM
ejpam-3280	274	18	a+	a+	PUNCT
ejpam-3280	274	19	b	b	X
ejpam-3280	274	20	∈	∈	PROPN
ejpam-3280	274	21	r	r	NOUN
ejpam-3280	274	22	◦	◦	NOUN
ejpam-3280	274	23	v.	v.	ADP
ejpam-3280	274	24	hence∨	hence∨	PROPN
ejpam-3280	274	25	{	{	PUNCT
ejpam-3280	274	26	fc(a	fc(a	NOUN
ejpam-3280	274	27	)	)	PUNCT
ejpam-3280	274	28	∧	∧	NOUN
ejpam-3280	274	29	gc(b	gc(b	PUNCT
ejpam-3280	274	30	)	)	PUNCT
ejpam-3280	274	31	:	:	PUNCT
ejpam-3280	274	32	a+	a+	PUNCT
ejpam-3280	275	1	b	b	X
ejpam-3280	275	2	=	=	SYM
ejpam-3280	275	3	z	z	PROPN
ejpam-3280	275	4	}	}	PUNCT
ejpam-3280	275	5	≥	≥	NOUN
ejpam-3280	275	6	∨	∨	NOUN
ejpam-3280	275	7	{	{	PUNCT
ejpam-3280	275	8	fc(y′	fc(y′	PROPN
ejpam-3280	275	9	)	)	PUNCT
ejpam-3280	275	10	∧	∧	PROPN
ejpam-3280	275	11	gc(w′	gc(w′	PROPN
ejpam-3280	275	12	)	)	PUNCT
ejpam-3280	275	13	:	:	PUNCT
ejpam-3280	275	14	y′	y′	X
ejpam-3280	276	1	+	+	CCONJ
ejpam-3280	276	2	w′	w′	NOUN
ejpam-3280	276	3	=	=	SYM
ejpam-3280	276	4	v	v	NOUN
ejpam-3280	276	5	}	}	PUNCT
ejpam-3280	276	6	.	.	PUNCT
ejpam-3280	277	1	so	so	ADV
ejpam-3280	277	2	inf	inf	ADJ
ejpam-3280	277	3	z∈r	z∈r	PROPN
ejpam-3280	277	4	◦	◦	NOUN
ejpam-3280	277	5	v	v	NOUN
ejpam-3280	277	6	(	(	PUNCT
ejpam-3280	277	7	∨	∨	X
ejpam-3280	277	8	{	{	PUNCT
ejpam-3280	277	9	fc(a	fc(a	NOUN
ejpam-3280	277	10	)	)	PUNCT
ejpam-3280	277	11	∧	∧	NOUN
ejpam-3280	277	12	gc(b	gc(b	PUNCT
ejpam-3280	277	13	)	)	PUNCT
ejpam-3280	277	14	:	:	PUNCT
ejpam-3280	277	15	a+	a+	PUNCT
ejpam-3280	278	1	b	b	X
ejpam-3280	278	2	=	=	SYM
ejpam-3280	278	3	z	z	NOUN
ejpam-3280	278	4	}	}	PUNCT
ejpam-3280	278	5	)	)	PUNCT
ejpam-3280	278	6	≥	≥	PROPN
ejpam-3280	278	7	∨	∨	NUM
ejpam-3280	278	8	{	{	PUNCT
ejpam-3280	278	9	fc(y′	fc(y′	PROPN
ejpam-3280	278	10	)	)	PUNCT
ejpam-3280	278	11	∧	∧	PROPN
ejpam-3280	278	12	gc(w′	gc(w′	PROPN
ejpam-3280	278	13	)	)	PUNCT
ejpam-3280	278	14	:	:	PUNCT
ejpam-3280	278	15	y′	y′	X
ejpam-3280	279	1	+	+	CCONJ
ejpam-3280	279	2	w′	w′	NOUN
ejpam-3280	279	3	=	=	SYM
ejpam-3280	279	4	v	v	NOUN
ejpam-3280	279	5	}	}	PUNCT
ejpam-3280	279	6	.	.	PUNCT
ejpam-3280	280	1	this	this	PRON
ejpam-3280	280	2	completes	complete	VERB
ejpam-3280	280	3	the	the	DET
ejpam-3280	280	4	proof	proof	NOUN
ejpam-3280	280	5	.	.	PUNCT
ejpam-3280	281	1	definition	definition	NOUN
ejpam-3280	281	2	19	19	NUM
ejpam-3280	281	3	.	.	PUNCT
ejpam-3280	282	1	[	[	X
ejpam-3280	282	2	5	5	NUM
ejpam-3280	282	3	]	]	X
ejpam-3280	282	4	let	let	VERB
ejpam-3280	282	5	(	(	PUNCT
ejpam-3280	282	6	f	f	X
ejpam-3280	282	7	,	,	PUNCT
ejpam-3280	282	8	a	a	PRON
ejpam-3280	282	9	)	)	PUNCT
ejpam-3280	282	10	be	be	AUX
ejpam-3280	282	11	a	a	DET
ejpam-3280	282	12	fuzzy	fuzzy	ADJ
ejpam-3280	282	13	soft	soft	ADJ
ejpam-3280	282	14	set	set	NOUN
ejpam-3280	282	15	over	over	ADP
ejpam-3280	282	16	hypervector	hypervector	NOUN
ejpam-3280	282	17	space	space	NOUN
ejpam-3280	282	18	v	v	NOUN
ejpam-3280	282	19	.	.	PUNCT
ejpam-3280	283	1	the	the	DET
ejpam-3280	283	2	soft	soft	ADJ
ejpam-3280	283	3	set	set	NOUN
ejpam-3280	283	4	(	(	PUNCT
ejpam-3280	283	5	f	f	NUM
ejpam-3280	283	6	,	,	PUNCT
ejpam-3280	283	7	a)α	a)α	X
ejpam-3280	283	8	=	=	PUNCT
ejpam-3280	283	9	{	{	PUNCT
ejpam-3280	283	10	(	(	PUNCT
ejpam-3280	283	11	fa)α	fa)α	ADV
ejpam-3280	283	12	:	:	PUNCT
ejpam-3280	283	13	a	a	DET
ejpam-3280	283	14	∈	∈	PROPN
ejpam-3280	283	15	a	a	X
ejpam-3280	283	16	}	}	PUNCT
ejpam-3280	283	17	where	where	SCONJ
ejpam-3280	283	18	(	(	PUNCT
ejpam-3280	283	19	fa)α	fa)α	NOUN
ejpam-3280	283	20	=	=	SYM
ejpam-3280	283	21	{	{	PUNCT
ejpam-3280	283	22	x	x	PROPN
ejpam-3280	283	23	∈	∈	PROPN
ejpam-3280	283	24	v	v	NOUN
ejpam-3280	283	25	:	:	PUNCT
ejpam-3280	283	26	fa(x	fa(x	PROPN
ejpam-3280	283	27	)	)	PUNCT
ejpam-3280	283	28	≥	≥	NOUN
ejpam-3280	283	29	α	α	NOUN
ejpam-3280	283	30	}	}	PUNCT
ejpam-3280	283	31	,	,	PUNCT
ejpam-3280	283	32	for	for	ADP
ejpam-3280	283	33	all	all	DET
ejpam-3280	283	34	α	α	DET
ejpam-3280	283	35	∈	∈	PROPN
ejpam-3280	283	36	(	(	PUNCT
ejpam-3280	283	37	0	0	NUM
ejpam-3280	283	38	,	,	PUNCT
ejpam-3280	283	39	1	1	NUM
ejpam-3280	283	40	]	]	PUNCT
ejpam-3280	283	41	,	,	PUNCT
ejpam-3280	283	42	is	be	AUX
ejpam-3280	283	43	called	call	VERB
ejpam-3280	283	44	an	an	DET
ejpam-3280	283	45	α	α	NUM
ejpam-3280	283	46	-	-	PUNCT
ejpam-3280	283	47	level	level	NOUN
ejpam-3280	283	48	soft	soft	ADJ
ejpam-3280	283	49	set	set	NOUN
ejpam-3280	283	50	of	of	ADP
ejpam-3280	283	51	the	the	DET
ejpam-3280	283	52	fuzzy	fuzzy	ADJ
ejpam-3280	283	53	soft	soft	ADJ
ejpam-3280	283	54	set	set	NOUN
ejpam-3280	283	55	(	(	PUNCT
ejpam-3280	283	56	f	f	X
ejpam-3280	283	57	,	,	PUNCT
ejpam-3280	283	58	a	a	PRON
ejpam-3280	283	59	)	)	PUNCT
ejpam-3280	283	60	,	,	PUNCT
ejpam-3280	283	61	where	where	SCONJ
ejpam-3280	283	62	(	(	PUNCT
ejpam-3280	283	63	fa)α	fa)α	NOUN
ejpam-3280	283	64	is	be	AUX
ejpam-3280	283	65	an	an	DET
ejpam-3280	283	66	α	α	NOUN
ejpam-3280	283	67	-	-	PUNCT
ejpam-3280	283	68	level	level	NOUN
ejpam-3280	283	69	subset	subset	NOUN
ejpam-3280	283	70	of	of	ADP
ejpam-3280	283	71	the	the	DET
ejpam-3280	283	72	fuzzy	fuzzy	ADJ
ejpam-3280	283	73	set	set	VERB
ejpam-3280	283	74	fa	fa	PROPN
ejpam-3280	283	75	.	.	PUNCT
ejpam-3280	283	76	theorem	theorem	NOUN
ejpam-3280	283	77	6	6	NUM
ejpam-3280	283	78	.	.	PUNCT
ejpam-3280	284	1	let	let	AUX
ejpam-3280	284	2	(	(	PUNCT
ejpam-3280	284	3	f	f	X
ejpam-3280	284	4	,	,	PUNCT
ejpam-3280	284	5	a	a	PRON
ejpam-3280	284	6	)	)	PUNCT
ejpam-3280	284	7	be	be	AUX
ejpam-3280	284	8	a	a	DET
ejpam-3280	284	9	fuzzy	fuzzy	ADJ
ejpam-3280	284	10	soft	soft	ADJ
ejpam-3280	284	11	set	set	NOUN
ejpam-3280	284	12	over	over	ADP
ejpam-3280	284	13	hypervector	hypervector	NOUN
ejpam-3280	284	14	space	space	NOUN
ejpam-3280	284	15	v	v	NOUN
ejpam-3280	284	16	of	of	ADP
ejpam-3280	284	17	field	field	NOUN
ejpam-3280	285	1	k.	k.	PROPN
ejpam-3280	285	2	then	then	ADV
ejpam-3280	285	3	(	(	PUNCT
ejpam-3280	285	4	f	f	X
ejpam-3280	285	5	,	,	PUNCT
ejpam-3280	285	6	a	a	PRON
ejpam-3280	285	7	)	)	PUNCT
ejpam-3280	285	8	is	be	AUX
ejpam-3280	285	9	a	a	DET
ejpam-3280	285	10	fuzzy	fuzzy	ADJ
ejpam-3280	285	11	soft	soft	ADJ
ejpam-3280	285	12	hypervector	hypervector	NOUN
ejpam-3280	285	13	space	space	NOUN
ejpam-3280	285	14	over	over	ADP
ejpam-3280	285	15	v	v	NOUN
ejpam-3280	285	16	if	if	SCONJ
ejpam-3280	286	1	and	and	CCONJ
ejpam-3280	286	2	only	only	ADV
ejpam-3280	286	3	if	if	SCONJ
ejpam-3280	286	4	for	for	ADP
ejpam-3280	286	5	all	all	DET
ejpam-3280	286	6	a	a	DET
ejpam-3280	286	7	∈	∈	NOUN
ejpam-3280	286	8	a	a	PRON
ejpam-3280	286	9	and	and	CCONJ
ejpam-3280	286	10	for	for	ADP
ejpam-3280	286	11	arbitrary	arbitrary	ADJ
ejpam-3280	286	12	α	α	PROPN
ejpam-3280	286	13	∈	∈	PROPN
ejpam-3280	286	14	(	(	PUNCT
ejpam-3280	286	15	0	0	NUM
ejpam-3280	286	16	,	,	PUNCT
ejpam-3280	286	17	1	1	NUM
ejpam-3280	286	18	]	]	PUNCT
ejpam-3280	286	19	with	with	ADP
ejpam-3280	286	20	(	(	PUNCT
ejpam-3280	286	21	fa)α	fa)α	PROPN
ejpam-3280	286	22	6=	6=	NUM
ejpam-3280	286	23	∅	∅	NOUN
ejpam-3280	286	24	,	,	PUNCT
ejpam-3280	286	25	the	the	DET
ejpam-3280	286	26	α	α	NOUN
ejpam-3280	286	27	-	-	PUNCT
ejpam-3280	286	28	level	level	NOUN
ejpam-3280	286	29	soft	soft	ADJ
ejpam-3280	286	30	set	set	NOUN
ejpam-3280	286	31	(	(	PUNCT
ejpam-3280	286	32	f	f	NUM
ejpam-3280	286	33	,	,	PUNCT
ejpam-3280	286	34	a)α	a)α	X
ejpam-3280	286	35	is	be	AUX
ejpam-3280	286	36	a	a	DET
ejpam-3280	286	37	soft	soft	ADJ
ejpam-3280	286	38	hypervector	hypervector	NOUN
ejpam-3280	286	39	space	space	NOUN
ejpam-3280	286	40	over	over	ADP
ejpam-3280	286	41	v	v	NOUN
ejpam-3280	286	42	.	.	PUNCT
ejpam-3280	287	1	proof	proof	NOUN
ejpam-3280	287	2	.	.	PUNCT
ejpam-3280	288	1	let	let	VERB
ejpam-3280	288	2	(	(	PUNCT
ejpam-3280	288	3	f	f	X
ejpam-3280	288	4	,	,	PUNCT
ejpam-3280	288	5	a	a	PRON
ejpam-3280	288	6	)	)	PUNCT
ejpam-3280	288	7	be	be	AUX
ejpam-3280	288	8	a	a	DET
ejpam-3280	288	9	fuzzy	fuzzy	ADJ
ejpam-3280	288	10	soft	soft	ADJ
ejpam-3280	288	11	hypervector	hypervector	NOUN
ejpam-3280	288	12	space	space	NOUN
ejpam-3280	288	13	over	over	ADP
ejpam-3280	288	14	v	v	NOUN
ejpam-3280	288	15	,	,	PUNCT
ejpam-3280	288	16	suppose	suppose	VERB
ejpam-3280	288	17	α	α	PRON
ejpam-3280	288	18	∈	∈	PROPN
ejpam-3280	288	19	(	(	PUNCT
ejpam-3280	288	20	0	0	NUM
ejpam-3280	288	21	,	,	PUNCT
ejpam-3280	288	22	1	1	NUM
ejpam-3280	288	23	]	]	PUNCT
ejpam-3280	288	24	with	with	ADP
ejpam-3280	288	25	(	(	PUNCT
ejpam-3280	288	26	fa)α	fa)α	NOUN
ejpam-3280	288	27	6=	6=	NOUN
ejpam-3280	288	28	∅	∅	NOUN
ejpam-3280	288	29	and	and	CCONJ
ejpam-3280	288	30	x	x	X
ejpam-3280	288	31	,	,	PUNCT
ejpam-3280	288	32	y	y	PROPN
ejpam-3280	288	33	∈	∈	PROPN
ejpam-3280	288	34	(	(	PUNCT
ejpam-3280	288	35	fa)α	fa)α	PROPN
ejpam-3280	288	36	.	.	PUNCT
ejpam-3280	288	37	since	since	SCONJ
ejpam-3280	288	38	fa(x	fa(x	NOUN
ejpam-3280	288	39	)	)	PUNCT
ejpam-3280	288	40	≥	≥	NOUN
ejpam-3280	288	41	α	α	NOUN
ejpam-3280	288	42	and	and	CCONJ
ejpam-3280	288	43	fa(y	fa(y	PROPN
ejpam-3280	288	44	)	)	PUNCT
ejpam-3280	288	45	≥	≥	NUM
ejpam-3280	288	46	α	α	NOUN
ejpam-3280	288	47	.	.	PUNCT
ejpam-3280	289	1	therefore	therefore	ADV
ejpam-3280	289	2	,	,	PUNCT
ejpam-3280	289	3	fa(x	fa(x	VERB
ejpam-3280	289	4	−	−	PROPN
ejpam-3280	289	5	y	y	PROPN
ejpam-3280	289	6	)	)	PUNCT
ejpam-3280	289	7	≥	≥	PROPN
ejpam-3280	289	8	α	α	NOUN
ejpam-3280	289	9	.	.	PUNCT
ejpam-3280	290	1	thus	thus	ADV
ejpam-3280	290	2	,	,	PUNCT
ejpam-3280	290	3	x	x	PUNCT
ejpam-3280	290	4	−	−	PROPN
ejpam-3280	290	5	y	y	PROPN
ejpam-3280	290	6	∈	∈	PROPN
ejpam-3280	290	7	fa	fa	PROPN
ejpam-3280	290	8	.	.	PUNCT
ejpam-3280	290	9	furthermore	furthermore	ADV
ejpam-3280	290	10	,	,	PUNCT
ejpam-3280	290	11	inf	inf	ADJ
ejpam-3280	290	12	z∈r	z∈r	PROPN
ejpam-3280	290	13	◦	◦	NOUN
ejpam-3280	290	14	x	x	NOUN
ejpam-3280	290	15	fa(z	fa(z	PRON
ejpam-3280	290	16	)	)	PUNCT
ejpam-3280	290	17	≥	≥	NOUN
ejpam-3280	290	18	fa(x	fa(x	PROPN
ejpam-3280	290	19	)	)	PUNCT
ejpam-3280	290	20	≥	≥	NUM
ejpam-3280	290	21	α	α	PRON
ejpam-3280	290	22	∀r	∀r	PROPN
ejpam-3280	290	23	∈	∈	PROPN
ejpam-3280	290	24	k	k	NOUN
ejpam-3280	290	25	,	,	PUNCT
ejpam-3280	290	26	∀z	∀z	PROPN
ejpam-3280	290	27	∈	∈	PROPN
ejpam-3280	290	28	r	r	NOUN
ejpam-3280	290	29	◦	◦	NOUN
ejpam-3280	290	30	x.	x.	NOUN
ejpam-3280	290	31	hence	hence	ADV
ejpam-3280	290	32	fa(z	fa(z	PUNCT
ejpam-3280	290	33	)	)	PUNCT
ejpam-3280	290	34	≥	≥	NUM
ejpam-3280	290	35	α	α	NOUN
ejpam-3280	290	36	,	,	PUNCT
ejpam-3280	290	37	so	so	SCONJ
ejpam-3280	290	38	z	z	NOUN
ejpam-3280	290	39	∈	∈	PROPN
ejpam-3280	290	40	(	(	PUNCT
ejpam-3280	290	41	fa)α	fa)α	NOUN
ejpam-3280	290	42	.	.	PUNCT
ejpam-3280	290	43	thus	thus	ADV
ejpam-3280	290	44	,	,	PUNCT
ejpam-3280	290	45	r	r	NOUN
ejpam-3280	290	46	◦	◦	NOUN
ejpam-3280	290	47	x	x	SYM
ejpam-3280	290	48	⊆	⊆	X
ejpam-3280	290	49	(	(	PUNCT
ejpam-3280	290	50	fa)α	fa)α	ADP
ejpam-3280	290	51	for	for	ADP
ejpam-3280	290	52	all	all	PRON
ejpam-3280	290	53	r	r	NOUN
ejpam-3280	290	54	∈	∈	PROPN
ejpam-3280	290	55	k.	k.	NOUN
ejpam-3280	290	56	we	we	PRON
ejpam-3280	290	57	obtain	obtain	VERB
ejpam-3280	290	58	that	that	PRON
ejpam-3280	290	59	(	(	PUNCT
ejpam-3280	290	60	fa)α	fa)α	ADV
ejpam-3280	290	61	is	be	AUX
ejpam-3280	290	62	a	a	DET
ejpam-3280	290	63	sub	sub	ADJ
ejpam-3280	290	64	-	-	ADJ
ejpam-3280	290	65	hypervector	hypervector	ADJ
ejpam-3280	290	66	space	space	NOUN
ejpam-3280	290	67	of	of	ADP
ejpam-3280	290	68	v	v	NOUN
ejpam-3280	290	69	for	for	ADP
ejpam-3280	290	70	all	all	DET
ejpam-3280	290	71	a	a	DET
ejpam-3280	290	72	∈	∈	NOUN
ejpam-3280	290	73	a.	a.	NOUN
ejpam-3280	290	74	consequently	consequently	ADV
ejpam-3280	290	75	,	,	PUNCT
ejpam-3280	290	76	(	(	PUNCT
ejpam-3280	290	77	f	f	X
ejpam-3280	290	78	,	,	PUNCT
ejpam-3280	290	79	a)α	a)α	X
ejpam-3280	290	80	is	be	AUX
ejpam-3280	290	81	a	a	DET
ejpam-3280	290	82	soft	soft	ADJ
ejpam-3280	290	83	hypervector	hypervector	NOUN
ejpam-3280	290	84	space	space	NOUN
ejpam-3280	290	85	over	over	ADP
ejpam-3280	290	86	v	v	NOUN
ejpam-3280	290	87	.	.	PUNCT
ejpam-3280	291	1	conversely	conversely	ADV
ejpam-3280	291	2	,	,	PUNCT
ejpam-3280	291	3	let	let	VERB
ejpam-3280	291	4	(	(	PUNCT
ejpam-3280	291	5	f	f	X
ejpam-3280	291	6	,	,	PUNCT
ejpam-3280	291	7	a)α	a)α	X
ejpam-3280	291	8	be	be	AUX
ejpam-3280	291	9	a	a	DET
ejpam-3280	291	10	fuzzy	fuzzy	ADJ
ejpam-3280	291	11	soft	soft	ADJ
ejpam-3280	291	12	hypervector	hypervector	NOUN
ejpam-3280	291	13	space	space	NOUN
ejpam-3280	291	14	over	over	ADP
ejpam-3280	291	15	v	v	NOUN
ejpam-3280	291	16	for	for	ADP
ejpam-3280	291	17	all	all	DET
ejpam-3280	291	18	α	α	PRON
ejpam-3280	291	19	∈	∈	NOUN
ejpam-3280	291	20	(	(	PUNCT
ejpam-3280	291	21	0	0	NUM
ejpam-3280	291	22	,	,	PUNCT
ejpam-3280	291	23	1	1	NUM
ejpam-3280	291	24	]	]	PUNCT
ejpam-3280	291	25	.	.	PUNCT
ejpam-3280	292	1	let	let	VERB
ejpam-3280	292	2	there	there	PRON
ejpam-3280	292	3	e.	e.	PROPN
ejpam-3280	292	4	ranjbar	ranjbar	PROPN
ejpam-3280	292	5	-	-	PUNCT
ejpam-3280	292	6	yanehsari	yanehsari	NOUN
ejpam-3280	292	7	,	,	PUNCT
ejpam-3280	292	8	m.	m.	NOUN
ejpam-3280	292	9	asghari	asghari	ADJ
ejpam-3280	292	10	-	-	PUNCT
ejpam-3280	292	11	larimi	larimi	PROPN
ejpam-3280	292	12	,	,	PUNCT
ejpam-3280	292	13	r.	r.	PROPN
ejpam-3280	292	14	ameri	ameri	PROPN
ejpam-3280	292	15	/	/	SYM
ejpam-3280	292	16	eur	eur	PROPN
ejpam-3280	292	17	.	.	PUNCT
ejpam-3280	293	1	j.	j.	PROPN
ejpam-3280	293	2	pure	pure	PROPN
ejpam-3280	293	3	appl	appl	PROPN
ejpam-3280	293	4	.	.	PROPN
ejpam-3280	293	5	math	math	PROPN
ejpam-3280	293	6	,	,	PUNCT
ejpam-3280	293	7	12	12	NUM
ejpam-3280	293	8	(	(	PUNCT
ejpam-3280	293	9	1	1	NUM
ejpam-3280	293	10	)	)	PUNCT
ejpam-3280	293	11	(	(	PUNCT
ejpam-3280	293	12	2019	2019	NUM
ejpam-3280	293	13	)	)	PUNCT
ejpam-3280	293	14	,	,	PUNCT
ejpam-3280	293	15	118	118	NUM
ejpam-3280	293	16	-	-	SYM
ejpam-3280	293	17	134	134	NUM
ejpam-3280	293	18	128	128	NUM
ejpam-3280	293	19	exist	exist	VERB
ejpam-3280	293	20	x0	x0	PROPN
ejpam-3280	293	21	,	,	PUNCT
ejpam-3280	293	22	y0	y0	PROPN
ejpam-3280	293	23	∈	∈	NOUN
ejpam-3280	293	24	v	v	ADP
ejpam-3280	293	25	such	such	ADJ
ejpam-3280	293	26	that	that	SCONJ
ejpam-3280	293	27	fa(x0+y0	fa(x0+y0	NOUN
ejpam-3280	293	28	)	)	PUNCT
ejpam-3280	293	29	<	<	X
ejpam-3280	293	30	fa(x0)∧fa(y0	fa(x0)∧fa(y0	PROPN
ejpam-3280	293	31	)	)	PUNCT
ejpam-3280	293	32	.	.	PUNCT
ejpam-3280	294	1	let	let	VERB
ejpam-3280	294	2	fa(x0+y0	fa(x0+y0	NOUN
ejpam-3280	294	3	)	)	PUNCT
ejpam-3280	294	4	=	=	SYM
ejpam-3280	294	5	δ	δ	PROPN
ejpam-3280	294	6	,	,	PUNCT
ejpam-3280	294	7	fa(x0	fa(x0	NOUN
ejpam-3280	294	8	)	)	PUNCT
ejpam-3280	294	9	=	=	SYM
ejpam-3280	294	10	β	β	X
ejpam-3280	294	11	and	and	CCONJ
ejpam-3280	294	12	fa(y0	fa(y0	ADJ
ejpam-3280	294	13	)	)	PUNCT
ejpam-3280	294	14	=	=	SYM
ejpam-3280	295	1	γ	γ	X
ejpam-3280	295	2	.	.	PUNCT
ejpam-3280	296	1	we	we	PRON
ejpam-3280	296	2	have	have	VERB
ejpam-3280	296	3	δ	δ	PROPN
ejpam-3280	296	4	<	<	X
ejpam-3280	296	5	min{β	min{β	PROPN
ejpam-3280	296	6	,	,	PUNCT
ejpam-3280	296	7	γ	γ	NOUN
ejpam-3280	296	8	}	}	PUNCT
ejpam-3280	296	9	.	.	PUNCT
ejpam-3280	297	1	let	let	VERB
ejpam-3280	297	2	α	α	NOUN
ejpam-3280	297	3	=	=	PUNCT
ejpam-3280	297	4	δ	δ	PROPN
ejpam-3280	297	5	+	+	PROPN
ejpam-3280	297	6	min{β	min{β	PROPN
ejpam-3280	297	7	,	,	PUNCT
ejpam-3280	297	8	γ	γ	NOUN
ejpam-3280	297	9	}	}	PUNCT
ejpam-3280	297	10	2	2	NUM
ejpam-3280	297	11	,	,	PUNCT
ejpam-3280	297	12	then	then	ADV
ejpam-3280	297	13	δ	δ	X
ejpam-3280	297	14	<	<	X
ejpam-3280	297	15	α	α	X
ejpam-3280	297	16	<	<	X
ejpam-3280	297	17	min{β	min{β	PROPN
ejpam-3280	297	18	,	,	PUNCT
ejpam-3280	297	19	γ	γ	NOUN
ejpam-3280	297	20	}	}	PUNCT
ejpam-3280	297	21	.	.	PUNCT
ejpam-3280	298	1	since	since	SCONJ
ejpam-3280	298	2	β	β	PROPN
ejpam-3280	298	3	>	>	X
ejpam-3280	298	4	min{β	min{β	PROPN
ejpam-3280	298	5	,	,	PUNCT
ejpam-3280	298	6	γ	γ	NOUN
ejpam-3280	298	7	}	}	PUNCT
ejpam-3280	298	8	>	>	X
ejpam-3280	298	9	α	α	PROPN
ejpam-3280	298	10	and	and	CCONJ
ejpam-3280	298	11	γ	γ	X
ejpam-3280	298	12	>	>	X
ejpam-3280	298	13	min{β	min{β	PROPN
ejpam-3280	298	14	,	,	PUNCT
ejpam-3280	298	15	γ	γ	NOUN
ejpam-3280	298	16	}	}	PUNCT
ejpam-3280	298	17	>	>	X
ejpam-3280	298	18	α	α	NOUN
ejpam-3280	298	19	,	,	PUNCT
ejpam-3280	298	20	we	we	PRON
ejpam-3280	298	21	obtain	obtain	VERB
ejpam-3280	298	22	fa(x0	fa(x0	NOUN
ejpam-3280	298	23	)	)	PUNCT
ejpam-3280	298	24	≥	≥	NOUN
ejpam-3280	298	25	α	α	NOUN
ejpam-3280	298	26	and	and	CCONJ
ejpam-3280	298	27	fa(y0	fa(y0	ADJ
ejpam-3280	298	28	)	)	PUNCT
ejpam-3280	298	29	≥	≥	NOUN
ejpam-3280	298	30	α	α	NOUN
ejpam-3280	298	31	,	,	PUNCT
ejpam-3280	298	32	that	that	PRON
ejpam-3280	298	33	is	be	AUX
ejpam-3280	298	34	x0	x0	PROPN
ejpam-3280	298	35	,	,	PUNCT
ejpam-3280	298	36	y0	y0	PROPN
ejpam-3280	298	37	∈	∈	NOUN
ejpam-3280	298	38	(	(	PUNCT
ejpam-3280	298	39	fa)α	fa)α	PROPN
ejpam-3280	298	40	.	.	NOUN
ejpam-3280	299	1	this	this	PRON
ejpam-3280	299	2	contradicts	contradict	VERB
ejpam-3280	299	3	with	with	ADP
ejpam-3280	299	4	the	the	DET
ejpam-3280	299	5	fact	fact	NOUN
ejpam-3280	299	6	(	(	PUNCT
ejpam-3280	299	7	f	f	X
ejpam-3280	299	8	,	,	PUNCT
ejpam-3280	299	9	a)α	a)α	X
ejpam-3280	299	10	is	be	AUX
ejpam-3280	299	11	a	a	DET
ejpam-3280	299	12	soft	soft	ADJ
ejpam-3280	299	13	hypervector	hypervector	NOUN
ejpam-3280	299	14	space	space	NOUN
ejpam-3280	299	15	over	over	ADP
ejpam-3280	299	16	v	v	NOUN
ejpam-3280	299	17	.	.	PUNCT
ejpam-3280	300	1	therefore	therefore	ADV
ejpam-3280	300	2	,	,	PUNCT
ejpam-3280	300	3	fa(x+	fa(x+	PROPN
ejpam-3280	300	4	y	y	X
ejpam-3280	300	5	)	)	PUNCT
ejpam-3280	300	6	≥	≥	NOUN
ejpam-3280	300	7	fa(x	fa(x	NOUN
ejpam-3280	300	8	)	)	PUNCT
ejpam-3280	300	9	∧	∧	PROPN
ejpam-3280	300	10	fa(y	fa(y	PROPN
ejpam-3280	300	11	)	)	PUNCT
ejpam-3280	300	12	for	for	ADP
ejpam-3280	300	13	all	all	DET
ejpam-3280	300	14	x	x	NOUN
ejpam-3280	300	15	,	,	PUNCT
ejpam-3280	300	16	y	y	PROPN
ejpam-3280	300	17	∈	∈	PROPN
ejpam-3280	300	18	v	v	NOUN
ejpam-3280	300	19	.	.	PUNCT
ejpam-3280	301	1	moreover	moreover	ADV
ejpam-3280	301	2	,	,	PUNCT
ejpam-3280	301	3	let	let	VERB
ejpam-3280	301	4	there	there	PRON
ejpam-3280	301	5	exists	exist	VERB
ejpam-3280	301	6	x0	x0	PROPN
ejpam-3280	301	7	∈	∈	PROPN
ejpam-3280	301	8	v	v	ADP
ejpam-3280	301	9	such	such	ADJ
ejpam-3280	301	10	that	that	DET
ejpam-3280	301	11	fa(−x0	fa(−x0	NOUN
ejpam-3280	301	12	)	)	PUNCT
ejpam-3280	301	13	<	<	X
ejpam-3280	301	14	fa(x0	fa(x0	NOUN
ejpam-3280	301	15	)	)	PUNCT
ejpam-3280	301	16	.	.	PUNCT
ejpam-3280	302	1	let	let	VERB
ejpam-3280	302	2	fa(−x0	fa(−x0	NOUN
ejpam-3280	302	3	)	)	PUNCT
ejpam-3280	302	4	=	=	SYM
ejpam-3280	303	1	β	β	NOUN
ejpam-3280	303	2	,	,	PUNCT
ejpam-3280	303	3	fa(x0	fa(x0	NOUN
ejpam-3280	303	4	)	)	PUNCT
ejpam-3280	303	5	=	=	SYM
ejpam-3280	303	6	γ	γ	NOUN
ejpam-3280	303	7	and	and	CCONJ
ejpam-3280	303	8	α	α	NOUN
ejpam-3280	303	9	=	=	SYM
ejpam-3280	303	10	β	β	X
ejpam-3280	303	11	+	+	X
ejpam-3280	303	12	γ	γ	X
ejpam-3280	303	13	2	2	NUM
ejpam-3280	303	14	.	.	PUNCT
ejpam-3280	304	1	since	since	SCONJ
ejpam-3280	304	2	β	β	X
ejpam-3280	304	3	<	<	X
ejpam-3280	304	4	α	α	X
ejpam-3280	304	5	<	<	X
ejpam-3280	304	6	γ	γ	X
ejpam-3280	304	7	and	and	CCONJ
ejpam-3280	304	8	fα(−x0	fα(−x0	NOUN
ejpam-3280	304	9	)	)	PUNCT
ejpam-3280	304	10	=	=	PUNCT
ejpam-3280	304	11	β	β	X
ejpam-3280	304	12	<	<	X
ejpam-3280	304	13	α	α	X
ejpam-3280	304	14	,	,	PUNCT
ejpam-3280	304	15	therefore	therefore	ADV
ejpam-3280	304	16	−x0	−x0	NOUN
ejpam-3280	304	17	/∈	/∈	PUNCT
ejpam-3280	304	18	(	(	PUNCT
ejpam-3280	304	19	fa)α	fa)α	PROPN
ejpam-3280	304	20	.	.	PROPN
ejpam-3280	304	21	but	but	CCONJ
ejpam-3280	304	22	,	,	PUNCT
ejpam-3280	304	23	fa(x0	fa(x0	NOUN
ejpam-3280	304	24	)	)	PUNCT
ejpam-3280	304	25	=	=	PUNCT
ejpam-3280	304	26	γ	γ	X
ejpam-3280	304	27	≥	≥	NUM
ejpam-3280	304	28	α	α	NOUN
ejpam-3280	304	29	,	,	PUNCT
ejpam-3280	304	30	that	that	ADV
ejpam-3280	304	31	is	is	ADV
ejpam-3280	304	32	,	,	PUNCT
ejpam-3280	304	33	x0	x0	PROPN
ejpam-3280	304	34	∈	∈	PROPN
ejpam-3280	304	35	(	(	PUNCT
ejpam-3280	304	36	fa)α	fa)α	PROPN
ejpam-3280	304	37	.	.	PUNCT
ejpam-3280	304	38	this	this	PRON
ejpam-3280	304	39	is	be	AUX
ejpam-3280	304	40	a	a	DET
ejpam-3280	304	41	contradiction	contradiction	NOUN
ejpam-3280	304	42	.	.	PUNCT
ejpam-3280	305	1	hence	hence	ADV
ejpam-3280	305	2	for	for	ADP
ejpam-3280	305	3	all	all	DET
ejpam-3280	305	4	x	x	SYM
ejpam-3280	305	5	∈	∈	PROPN
ejpam-3280	305	6	v	v	NOUN
ejpam-3280	305	7	,	,	PUNCT
ejpam-3280	305	8	fa(−x	fa(−x	PROPN
ejpam-3280	305	9	)	)	PUNCT
ejpam-3280	305	10	≥	≥	NOUN
ejpam-3280	305	11	fa(x	fa(x	NOUN
ejpam-3280	305	12	)	)	PUNCT
ejpam-3280	305	13	.	.	PUNCT
ejpam-3280	306	1	now	now	ADV
ejpam-3280	306	2	,	,	PUNCT
ejpam-3280	306	3	let	let	VERB
ejpam-3280	306	4	there	there	PRON
ejpam-3280	306	5	exists	exist	VERB
ejpam-3280	306	6	v0	v0	PROPN
ejpam-3280	306	7	∈	∈	PROPN
ejpam-3280	306	8	v	v	ADP
ejpam-3280	306	9	such	such	ADJ
ejpam-3280	306	10	that	that	DET
ejpam-3280	306	11	inf	inf	PROPN
ejpam-3280	306	12	z∈r	z∈r	PROPN
ejpam-3280	306	13	◦	◦	NOUN
ejpam-3280	306	14	v0	v0	NOUN
ejpam-3280	306	15	fa(z	fa(z	PUNCT
ejpam-3280	306	16	)	)	PUNCT
ejpam-3280	306	17	<	<	X
ejpam-3280	306	18	fa(v0	fa(v0	VERB
ejpam-3280	306	19	)	)	PUNCT
ejpam-3280	306	20	.	.	PUNCT
ejpam-3280	307	1	let	let	VERB
ejpam-3280	307	2	fa(v0	fa(v0	VERB
ejpam-3280	307	3	)	)	PUNCT
ejpam-3280	307	4	=	=	SYM
ejpam-3280	307	5	γ	γ	X
ejpam-3280	307	6	,	,	PUNCT
ejpam-3280	307	7	inf	inf	ADJ
ejpam-3280	307	8	z∈r	z∈r	PROPN
ejpam-3280	307	9	◦	◦	NOUN
ejpam-3280	307	10	v0	v0	NOUN
ejpam-3280	307	11	fa(z	fa(z	PUNCT
ejpam-3280	307	12	)	)	PUNCT
ejpam-3280	307	13	=	=	SYM
ejpam-3280	307	14	β	β	X
ejpam-3280	307	15	and	and	CCONJ
ejpam-3280	307	16	α	α	NOUN
ejpam-3280	307	17	=	=	X
ejpam-3280	307	18	β	β	X
ejpam-3280	307	19	+	+	X
ejpam-3280	307	20	γ	γ	X
ejpam-3280	307	21	2	2	NUM
ejpam-3280	307	22	.	.	PUNCT
ejpam-3280	308	1	since	since	SCONJ
ejpam-3280	308	2	β	β	X
ejpam-3280	308	3	<	<	X
ejpam-3280	308	4	α	α	X
ejpam-3280	308	5	<	<	X
ejpam-3280	308	6	γ	γ	X
ejpam-3280	308	7	and	and	CCONJ
ejpam-3280	308	8	fa(v0	fa(v0	VERB
ejpam-3280	308	9	)	)	PUNCT
ejpam-3280	308	10	=	=	SYM
ejpam-3280	308	11	γ	γ	X
ejpam-3280	308	12	>	>	X
ejpam-3280	308	13	α	α	PROPN
ejpam-3280	308	14	,	,	PUNCT
ejpam-3280	308	15	that	that	PRON
ejpam-3280	308	16	is	be	AUX
ejpam-3280	308	17	v0	v0	PROPN
ejpam-3280	308	18	∈	∈	PROPN
ejpam-3280	308	19	(	(	PUNCT
ejpam-3280	308	20	fa)α	fa)α	PROPN
ejpam-3280	308	21	,	,	PUNCT
ejpam-3280	308	22	so	so	SCONJ
ejpam-3280	308	23	r	r	NOUN
ejpam-3280	308	24	◦	◦	NOUN
ejpam-3280	308	25	v0	v0	NOUN
ejpam-3280	308	26	⊆	⊆	NUM
ejpam-3280	308	27	(	(	PUNCT
ejpam-3280	308	28	fa)α	fa)α	NOUN
ejpam-3280	308	29	,	,	PUNCT
ejpam-3280	308	30	∀r	∀r	PROPN
ejpam-3280	308	31	∈	∈	PROPN
ejpam-3280	308	32	k.	k.	PROPN
ejpam-3280	308	33	therefore	therefore	ADV
ejpam-3280	308	34	,	,	PUNCT
ejpam-3280	308	35	z	z	NOUN
ejpam-3280	308	36	∈	∈	PROPN
ejpam-3280	308	37	r	r	NOUN
ejpam-3280	308	38	◦	◦	NOUN
ejpam-3280	308	39	v0	v0	NOUN
ejpam-3280	308	40	⇒	⇒	PROPN
ejpam-3280	308	41	inf	inf	PROPN
ejpam-3280	308	42	z∈r	z∈r	PROPN
ejpam-3280	308	43	◦	◦	NOUN
ejpam-3280	308	44	v0	v0	NOUN
ejpam-3280	308	45	fa(z	fa(z	PUNCT
ejpam-3280	308	46	)	)	PUNCT
ejpam-3280	308	47	=	=	SYM
ejpam-3280	308	48	β	β	X
ejpam-3280	308	49	>	>	X
ejpam-3280	308	50	α	α	X
ejpam-3280	308	51	.	.	PUNCT
ejpam-3280	309	1	this	this	PRON
ejpam-3280	309	2	is	be	AUX
ejpam-3280	309	3	a	a	DET
ejpam-3280	309	4	contradiction	contradiction	NOUN
ejpam-3280	309	5	.	.	PUNCT
ejpam-3280	310	1	hence	hence	ADV
ejpam-3280	310	2	inf	inf	ADJ
ejpam-3280	310	3	z∈r	z∈r	NUM
ejpam-3280	310	4	◦	◦	NOUN
ejpam-3280	310	5	v	v	NOUN
ejpam-3280	310	6	fa(z	fa(z	PUNCT
ejpam-3280	310	7	)	)	PUNCT
ejpam-3280	310	8	≥	≥	NOUN
ejpam-3280	310	9	fa(v	fa(v	X
ejpam-3280	310	10	)	)	PUNCT
ejpam-3280	310	11	∀v	∀v	PROPN
ejpam-3280	310	12	∈	∈	PROPN
ejpam-3280	310	13	v	v	NOUN
ejpam-3280	310	14	,	,	PUNCT
ejpam-3280	310	15	for	for	ADP
ejpam-3280	310	16	all	all	DET
ejpam-3280	310	17	r	r	NOUN
ejpam-3280	310	18	∈	∈	PROPN
ejpam-3280	310	19	k.	k.	NOUN
ejpam-3280	310	20	therefore	therefore	ADV
ejpam-3280	310	21	,	,	PUNCT
ejpam-3280	310	22	(	(	PUNCT
ejpam-3280	310	23	f	f	X
ejpam-3280	310	24	,	,	PUNCT
ejpam-3280	310	25	a	a	PRON
ejpam-3280	310	26	)	)	PUNCT
ejpam-3280	310	27	is	be	AUX
ejpam-3280	310	28	a	a	DET
ejpam-3280	310	29	fuzzy	fuzzy	ADJ
ejpam-3280	310	30	soft	soft	ADJ
ejpam-3280	310	31	hypervector	hypervector	NOUN
ejpam-3280	310	32	space	space	NOUN
ejpam-3280	310	33	over	over	ADP
ejpam-3280	310	34	v	v	NOUN
ejpam-3280	310	35	.	.	PUNCT
ejpam-3280	311	1	definition	definition	NOUN
ejpam-3280	311	2	20	20	NUM
ejpam-3280	311	3	.	.	PUNCT
ejpam-3280	312	1	[	[	X
ejpam-3280	312	2	5	5	NUM
ejpam-3280	312	3	]	]	X
ejpam-3280	312	4	let	let	VERB
ejpam-3280	312	5	(	(	PUNCT
ejpam-3280	312	6	f	f	X
ejpam-3280	312	7	,	,	PUNCT
ejpam-3280	312	8	a	a	PRON
ejpam-3280	312	9	)	)	PUNCT
ejpam-3280	312	10	be	be	AUX
ejpam-3280	312	11	a	a	DET
ejpam-3280	312	12	fuzzy	fuzzy	ADJ
ejpam-3280	312	13	soft	soft	ADJ
ejpam-3280	312	14	hypervector	hypervector	NOUN
ejpam-3280	312	15	space	space	NOUN
ejpam-3280	312	16	over	over	ADP
ejpam-3280	312	17	v	v	NOUN
ejpam-3280	312	18	.	.	PUNCT
ejpam-3280	313	1	then	then	ADV
ejpam-3280	313	2	,	,	PUNCT
ejpam-3280	313	3	the	the	DET
ejpam-3280	313	4	soft	soft	ADJ
ejpam-3280	313	5	set	set	NOUN
ejpam-3280	313	6	(	(	PUNCT
ejpam-3280	313	7	f	f	X
ejpam-3280	313	8	,	,	PUNCT
ejpam-3280	313	9	a)0	a)0	PROPN
ejpam-3280	313	10	is	be	AUX
ejpam-3280	313	11	defined	define	VERB
ejpam-3280	313	12	by	by	ADP
ejpam-3280	313	13	:	:	PUNCT
ejpam-3280	313	14	(	(	PUNCT
ejpam-3280	313	15	f	f	X
ejpam-3280	313	16	,	,	PUNCT
ejpam-3280	313	17	a)0	a)0	PROPN
ejpam-3280	313	18	=	=	SYM
ejpam-3280	313	19	{	{	PUNCT
ejpam-3280	313	20	(	(	PUNCT
ejpam-3280	313	21	fa)0	fa)0	NOUN
ejpam-3280	313	22	:	:	PUNCT
ejpam-3280	313	23	a	a	DET
ejpam-3280	313	24	∈	∈	PROPN
ejpam-3280	313	25	a	a	X
ejpam-3280	313	26	}	}	PUNCT
ejpam-3280	313	27	where	where	SCONJ
ejpam-3280	313	28	(	(	PUNCT
ejpam-3280	313	29	fa)0	fa)0	NOUN
ejpam-3280	313	30	=	=	SYM
ejpam-3280	313	31	{	{	PUNCT
ejpam-3280	313	32	x	x	PROPN
ejpam-3280	313	33	∈	∈	PROPN
ejpam-3280	313	34	v	v	NOUN
ejpam-3280	313	35	:	:	PUNCT
ejpam-3280	313	36	fa(x	fa(x	NOUN
ejpam-3280	313	37	)	)	PUNCT
ejpam-3280	313	38	=	=	SYM
ejpam-3280	313	39	fa(0	fa(0	NOUN
ejpam-3280	313	40	)	)	PUNCT
ejpam-3280	313	41	}	}	PUNCT
ejpam-3280	313	42	.	.	PUNCT
ejpam-3280	314	1	theorem	theorem	VERB
ejpam-3280	314	2	7	7	NUM
ejpam-3280	314	3	.	.	PUNCT
ejpam-3280	315	1	let	let	AUX
ejpam-3280	315	2	(	(	PUNCT
ejpam-3280	315	3	f	f	X
ejpam-3280	315	4	,	,	PUNCT
ejpam-3280	315	5	a	a	PRON
ejpam-3280	315	6	)	)	PUNCT
ejpam-3280	315	7	be	be	AUX
ejpam-3280	315	8	a	a	DET
ejpam-3280	315	9	fuzzy	fuzzy	ADJ
ejpam-3280	315	10	soft	soft	ADJ
ejpam-3280	315	11	hypervector	hypervector	NOUN
ejpam-3280	315	12	space	space	NOUN
ejpam-3280	315	13	of	of	ADP
ejpam-3280	315	14	v	v	NOUN
ejpam-3280	315	15	over	over	ADP
ejpam-3280	315	16	field	field	NOUN
ejpam-3280	315	17	k.	k.	PROPN
ejpam-3280	316	1	then	then	ADV
ejpam-3280	316	2	(	(	PUNCT
ejpam-3280	316	3	f	f	X
ejpam-3280	316	4	,	,	PUNCT
ejpam-3280	316	5	a)0	a)0	PROPN
ejpam-3280	316	6	is	be	AUX
ejpam-3280	316	7	a	a	DET
ejpam-3280	316	8	soft	soft	ADJ
ejpam-3280	316	9	hypervector	hypervector	NOUN
ejpam-3280	316	10	space	space	NOUN
ejpam-3280	316	11	over	over	ADP
ejpam-3280	316	12	v	v	NOUN
ejpam-3280	316	13	.	.	PUNCT
ejpam-3280	317	1	proof	proof	NOUN
ejpam-3280	317	2	.	.	PUNCT
ejpam-3280	318	1	for	for	ADP
ejpam-3280	318	2	every	every	DET
ejpam-3280	318	3	a	a	DET
ejpam-3280	318	4	∈	∈	PROPN
ejpam-3280	318	5	a	a	PRON
ejpam-3280	318	6	and	and	CCONJ
ejpam-3280	318	7	for	for	ADP
ejpam-3280	318	8	all	all	DET
ejpam-3280	318	9	x	x	NOUN
ejpam-3280	318	10	,	,	PUNCT
ejpam-3280	318	11	y	y	PROPN
ejpam-3280	318	12	∈	∈	PROPN
ejpam-3280	318	13	(	(	PUNCT
ejpam-3280	318	14	fa)0	fa)0	NOUN
ejpam-3280	318	15	,	,	PUNCT
ejpam-3280	318	16	we	we	PRON
ejpam-3280	318	17	have	have	VERB
ejpam-3280	318	18	fa(x	fa(x	NOUN
ejpam-3280	318	19	)	)	PUNCT
ejpam-3280	318	20	=	=	SYM
ejpam-3280	318	21	fa(0	fa(0	NOUN
ejpam-3280	318	22	)	)	PUNCT
ejpam-3280	318	23	,	,	PUNCT
ejpam-3280	318	24	fa(y	fa(y	PROPN
ejpam-3280	318	25	)	)	PUNCT
ejpam-3280	318	26	=	=	SYM
ejpam-3280	319	1	fa(0	fa(0	NOUN
ejpam-3280	319	2	)	)	PUNCT
ejpam-3280	319	3	,	,	PUNCT
ejpam-3280	319	4	therefore	therefore	ADV
ejpam-3280	319	5	fa(x−y	fa(x−y	PROPN
ejpam-3280	319	6	)	)	PUNCT
ejpam-3280	319	7	≥	≥	NOUN
ejpam-3280	319	8	fa(x)∧fa(y	fa(x)∧fa(y	PROPN
ejpam-3280	319	9	)	)	PUNCT
ejpam-3280	319	10	=	=	SYM
ejpam-3280	320	1	fa(0	fa(0	NOUN
ejpam-3280	320	2	)	)	PUNCT
ejpam-3280	320	3	.	.	PUNCT
ejpam-3280	321	1	since	since	SCONJ
ejpam-3280	321	2	fa(0	fa(0	NOUN
ejpam-3280	321	3	)	)	PUNCT
ejpam-3280	321	4	≥	≥	NOUN
ejpam-3280	321	5	fa(x−y	fa(x−y	NUM
ejpam-3280	321	6	)	)	PUNCT
ejpam-3280	321	7	,	,	PUNCT
ejpam-3280	321	8	thus	thus	ADV
ejpam-3280	321	9	fa(x−y	fa(x−y	NUM
ejpam-3280	321	10	)	)	PUNCT
ejpam-3280	321	11	=	=	SYM
ejpam-3280	322	1	fa(0	fa(0	NOUN
ejpam-3280	322	2	)	)	PUNCT
ejpam-3280	322	3	.	.	PUNCT
ejpam-3280	323	1	hence	hence	ADV
ejpam-3280	323	2	x−y	x−y	PROPN
ejpam-3280	323	3	∈	∈	PROPN
ejpam-3280	323	4	(	(	PUNCT
ejpam-3280	323	5	fa)0	fa)0	NOUN
ejpam-3280	323	6	.	.	PUNCT
ejpam-3280	324	1	now	now	ADV
ejpam-3280	324	2	,	,	PUNCT
ejpam-3280	324	3	let	let	VERB
ejpam-3280	324	4	x	x	X
ejpam-3280	324	5	∈	∈	PROPN
ejpam-3280	324	6	(	(	PUNCT
ejpam-3280	324	7	fa)0	fa)0	NOUN
ejpam-3280	324	8	and	and	CCONJ
ejpam-3280	324	9	r	r	NOUN
ejpam-3280	324	10	∈	∈	PROPN
ejpam-3280	324	11	k.	k.	NOUN
ejpam-3280	324	12	since	since	SCONJ
ejpam-3280	324	13	inf	inf	PROPN
ejpam-3280	324	14	z∈r	z∈r	PROPN
ejpam-3280	324	15	◦	◦	NOUN
ejpam-3280	324	16	x	x	NOUN
ejpam-3280	324	17	fa(z	fa(z	PRON
ejpam-3280	324	18	)	)	PUNCT
ejpam-3280	324	19	≥	≥	NOUN
ejpam-3280	324	20	fa(x	fa(x	NOUN
ejpam-3280	324	21	)	)	PUNCT
ejpam-3280	324	22	=	=	SYM
ejpam-3280	324	23	fa(0	fa(0	NOUN
ejpam-3280	324	24	)	)	PUNCT
ejpam-3280	324	25	.	.	PUNCT
ejpam-3280	325	1	thus	thus	ADV
ejpam-3280	325	2	fa(z	fa(z	PUNCT
ejpam-3280	325	3	)	)	PUNCT
ejpam-3280	325	4	=	=	SYM
ejpam-3280	325	5	fa(0	fa(0	NOUN
ejpam-3280	325	6	)	)	PUNCT
ejpam-3280	325	7	for	for	ADP
ejpam-3280	325	8	all	all	DET
ejpam-3280	325	9	z	z	NOUN
ejpam-3280	325	10	∈	∈	NOUN
ejpam-3280	325	11	r	r	NOUN
ejpam-3280	325	12	◦	◦	NOUN
ejpam-3280	325	13	x.	x.	NOUN
ejpam-3280	325	14	hence	hence	ADV
ejpam-3280	325	15	r	r	NOUN
ejpam-3280	325	16	◦	◦	NOUN
ejpam-3280	325	17	x	x	SYM
ejpam-3280	325	18	⊆	⊆	X
ejpam-3280	325	19	(	(	PUNCT
ejpam-3280	325	20	fa)0	fa)0	NOUN
ejpam-3280	325	21	.	.	PUNCT
ejpam-3280	326	1	therefore	therefore	ADV
ejpam-3280	326	2	(	(	PUNCT
ejpam-3280	326	3	fa)0	fa)0	NOUN
ejpam-3280	326	4	is	be	AUX
ejpam-3280	326	5	a	a	DET
ejpam-3280	326	6	sub	sub	ADJ
ejpam-3280	326	7	-	-	ADJ
ejpam-3280	326	8	hypervector	hypervector	ADJ
ejpam-3280	326	9	space	space	NOUN
ejpam-3280	326	10	of	of	ADP
ejpam-3280	326	11	v	v	NOUN
ejpam-3280	326	12	,	,	PUNCT
ejpam-3280	326	13	consequently	consequently	ADV
ejpam-3280	326	14	(	(	PUNCT
ejpam-3280	326	15	f	f	X
ejpam-3280	326	16	,	,	PUNCT
ejpam-3280	326	17	a)0	a)0	PROPN
ejpam-3280	326	18	is	be	AUX
ejpam-3280	326	19	a	a	DET
ejpam-3280	326	20	soft	soft	ADJ
ejpam-3280	326	21	hypervector	hypervector	NOUN
ejpam-3280	326	22	space	space	NOUN
ejpam-3280	326	23	over	over	ADP
ejpam-3280	326	24	v	v	NOUN
ejpam-3280	326	25	.	.	PUNCT
ejpam-3280	327	1	definition	definition	NOUN
ejpam-3280	327	2	21	21	NUM
ejpam-3280	327	3	.	.	PUNCT
ejpam-3280	328	1	let	let	AUX
ejpam-3280	328	2	(	(	PUNCT
ejpam-3280	328	3	f	f	X
ejpam-3280	328	4	,	,	PUNCT
ejpam-3280	328	5	a	a	PRON
ejpam-3280	328	6	)	)	PUNCT
ejpam-3280	328	7	be	be	AUX
ejpam-3280	328	8	a	a	DET
ejpam-3280	328	9	fuzzy	fuzzy	ADJ
ejpam-3280	328	10	soft	soft	ADJ
ejpam-3280	328	11	hypervector	hypervector	NOUN
ejpam-3280	328	12	space	space	NOUN
ejpam-3280	328	13	over	over	ADP
ejpam-3280	328	14	v	v	NOUN
ejpam-3280	328	15	.	.	PUNCT
ejpam-3280	329	1	then	then	ADV
ejpam-3280	329	2	,	,	PUNCT
ejpam-3280	329	3	the	the	DET
ejpam-3280	329	4	soft	soft	ADJ
ejpam-3280	329	5	set	set	NOUN
ejpam-3280	329	6	(	(	PUNCT
ejpam-3280	329	7	f	f	X
ejpam-3280	329	8	,	,	PUNCT
ejpam-3280	329	9	a)0	a)0	PROPN
ejpam-3280	329	10	is	be	AUX
ejpam-3280	329	11	defined	define	VERB
ejpam-3280	329	12	by	by	ADP
ejpam-3280	329	13	:	:	PUNCT
ejpam-3280	329	14	(	(	PUNCT
ejpam-3280	329	15	f	f	X
ejpam-3280	329	16	,	,	PUNCT
ejpam-3280	329	17	a)0	a)0	PROPN
ejpam-3280	329	18	=	=	SYM
ejpam-3280	329	19	{	{	PUNCT
ejpam-3280	329	20	(	(	PUNCT
ejpam-3280	329	21	fa)0	fa)0	NOUN
ejpam-3280	329	22	:	:	PUNCT
ejpam-3280	329	23	a	a	DET
ejpam-3280	329	24	∈	∈	PROPN
ejpam-3280	329	25	a	a	X
ejpam-3280	329	26	}	}	PUNCT
ejpam-3280	329	27	where	where	SCONJ
ejpam-3280	329	28	(	(	PUNCT
ejpam-3280	329	29	fa	fa	NOUN
ejpam-3280	329	30	)	)	PUNCT
ejpam-3280	329	31	0	0	NUM
ejpam-3280	330	1	=	=	SYM
ejpam-3280	330	2	{	{	PUNCT
ejpam-3280	330	3	x	x	PUNCT
ejpam-3280	330	4	∈	∈	PROPN
ejpam-3280	330	5	v	v	NOUN
ejpam-3280	330	6	:	:	PUNCT
ejpam-3280	330	7	fa(x	fa(x	NOUN
ejpam-3280	330	8	)	)	PUNCT
ejpam-3280	330	9	>	>	X
ejpam-3280	330	10	0	0	NUM
ejpam-3280	330	11	}	}	PUNCT
ejpam-3280	330	12	.	.	PUNCT
ejpam-3280	331	1	it	it	PRON
ejpam-3280	331	2	is	be	AUX
ejpam-3280	331	3	clear	clear	ADJ
ejpam-3280	331	4	that	that	SCONJ
ejpam-3280	331	5	we	we	PRON
ejpam-3280	331	6	have	have	VERB
ejpam-3280	331	7	the	the	DET
ejpam-3280	331	8	followings	following	NOUN
ejpam-3280	331	9	:	:	PUNCT
ejpam-3280	331	10	theorem	theorem	VERB
ejpam-3280	331	11	8	8	NUM
ejpam-3280	331	12	.	.	PUNCT
ejpam-3280	332	1	let	let	AUX
ejpam-3280	332	2	(	(	PUNCT
ejpam-3280	332	3	f	f	X
ejpam-3280	332	4	,	,	PUNCT
ejpam-3280	332	5	a	a	PRON
ejpam-3280	332	6	)	)	PUNCT
ejpam-3280	332	7	be	be	AUX
ejpam-3280	332	8	a	a	DET
ejpam-3280	332	9	fuzzy	fuzzy	ADJ
ejpam-3280	332	10	soft	soft	ADJ
ejpam-3280	332	11	set	set	NOUN
ejpam-3280	332	12	over	over	ADP
ejpam-3280	332	13	hypervector	hypervector	NOUN
ejpam-3280	332	14	space	space	NOUN
ejpam-3280	332	15	v	v	NOUN
ejpam-3280	332	16	of	of	ADP
ejpam-3280	332	17	field	field	NOUN
ejpam-3280	333	1	k.	k.	PROPN
ejpam-3280	333	2	then	then	ADV
ejpam-3280	333	3	(	(	PUNCT
ejpam-3280	333	4	f	f	X
ejpam-3280	333	5	,	,	PUNCT
ejpam-3280	333	6	a)0	a)0	PROPN
ejpam-3280	333	7	is	be	AUX
ejpam-3280	333	8	a	a	DET
ejpam-3280	333	9	fuzzy	fuzzy	ADJ
ejpam-3280	333	10	soft	soft	ADJ
ejpam-3280	333	11	set	set	NOUN
ejpam-3280	333	12	over	over	ADP
ejpam-3280	333	13	hypervector	hypervector	NOUN
ejpam-3280	333	14	space	space	NOUN
ejpam-3280	333	15	v	v	NOUN
ejpam-3280	333	16	.	.	PUNCT
ejpam-3280	334	1	it	it	PRON
ejpam-3280	334	2	is	be	AUX
ejpam-3280	334	3	clear	clear	ADJ
ejpam-3280	334	4	that	that	SCONJ
ejpam-3280	334	5	we	we	PRON
ejpam-3280	334	6	have	have	VERB
ejpam-3280	334	7	the	the	DET
ejpam-3280	334	8	followings	following	NOUN
ejpam-3280	334	9	:	:	PUNCT
ejpam-3280	334	10	e.	e.	PROPN
ejpam-3280	334	11	ranjbar	ranjbar	PROPN
ejpam-3280	334	12	-	-	PUNCT
ejpam-3280	334	13	yanehsari	yanehsari	NOUN
ejpam-3280	334	14	,	,	PUNCT
ejpam-3280	334	15	m.	m.	NOUN
ejpam-3280	334	16	asghari	asghari	ADJ
ejpam-3280	334	17	-	-	PUNCT
ejpam-3280	334	18	larimi	larimi	PROPN
ejpam-3280	334	19	,	,	PUNCT
ejpam-3280	334	20	r.	r.	PROPN
ejpam-3280	334	21	ameri	ameri	PROPN
ejpam-3280	334	22	/	/	SYM
ejpam-3280	334	23	eur	eur	PROPN
ejpam-3280	334	24	.	.	PUNCT
ejpam-3280	335	1	j.	j.	PROPN
ejpam-3280	335	2	pure	pure	PROPN
ejpam-3280	335	3	appl	appl	PROPN
ejpam-3280	335	4	.	.	PROPN
ejpam-3280	335	5	math	math	PROPN
ejpam-3280	335	6	,	,	PUNCT
ejpam-3280	335	7	12	12	NUM
ejpam-3280	335	8	(	(	PUNCT
ejpam-3280	335	9	1	1	NUM
ejpam-3280	335	10	)	)	PUNCT
ejpam-3280	335	11	(	(	PUNCT
ejpam-3280	335	12	2019	2019	NUM
ejpam-3280	335	13	)	)	PUNCT
ejpam-3280	335	14	,	,	PUNCT
ejpam-3280	335	15	118	118	NUM
ejpam-3280	335	16	-	-	SYM
ejpam-3280	335	17	134	134	NUM
ejpam-3280	335	18	129	129	NUM
ejpam-3280	335	19	theorem	theorem	NOUN
ejpam-3280	335	20	9	9	NUM
ejpam-3280	335	21	.	.	PUNCT
ejpam-3280	336	1	let	let	VERB
ejpam-3280	336	2	(	(	PUNCT
ejpam-3280	336	3	f	f	X
ejpam-3280	336	4	,	,	PUNCT
ejpam-3280	336	5	a	a	PRON
ejpam-3280	336	6	)	)	PUNCT
ejpam-3280	336	7	and	and	CCONJ
ejpam-3280	336	8	(	(	PUNCT
ejpam-3280	336	9	g	g	NOUN
ejpam-3280	336	10	,	,	PUNCT
ejpam-3280	336	11	b	b	NOUN
ejpam-3280	336	12	)	)	PUNCT
ejpam-3280	336	13	be	be	AUX
ejpam-3280	336	14	two	two	NUM
ejpam-3280	336	15	fuzzy	fuzzy	ADJ
ejpam-3280	336	16	soft	soft	ADJ
ejpam-3280	336	17	set	set	NOUN
ejpam-3280	336	18	over	over	ADP
ejpam-3280	336	19	hypervector	hypervector	NOUN
ejpam-3280	336	20	space	space	NOUN
ejpam-3280	336	21	v	v	NOUN
ejpam-3280	336	22	.	.	PUNCT
ejpam-3280	337	1	then	then	ADV
ejpam-3280	337	2	(	(	PUNCT
ejpam-3280	337	3	i	i	NOUN
ejpam-3280	337	4	)	)	PUNCT
ejpam-3280	337	5	(	(	PUNCT
ejpam-3280	337	6	f	f	X
ejpam-3280	337	7	,	,	PUNCT
ejpam-3280	337	8	a)0	a)0	PROPN
ejpam-3280	337	9	u	u	NOUN
ejpam-3280	337	10	(	(	PUNCT
ejpam-3280	337	11	g	g	PROPN
ejpam-3280	337	12	,	,	PUNCT
ejpam-3280	337	13	b)0	b)0	PROPN
ejpam-3280	337	14	v	v	NOUN
ejpam-3280	337	15	(	(	PUNCT
ejpam-3280	337	16	h	h	NOUN
ejpam-3280	337	17	,	,	PUNCT
ejpam-3280	337	18	c)0	c)0	PROPN
ejpam-3280	337	19	(	(	PUNCT
ejpam-3280	337	20	ii	ii	NOUN
ejpam-3280	337	21	)	)	PUNCT
ejpam-3280	337	22	fc(0	fc(0	PROPN
ejpam-3280	337	23	)	)	PUNCT
ejpam-3280	337	24	=	=	SYM
ejpam-3280	337	25	gc(0)⇒	gc(0)⇒	PROPN
ejpam-3280	337	26	(	(	PUNCT
ejpam-3280	337	27	f	f	X
ejpam-3280	337	28	,	,	PUNCT
ejpam-3280	337	29	a)0	a)0	PROPN
ejpam-3280	337	30	u	u	NOUN
ejpam-3280	337	31	(	(	PUNCT
ejpam-3280	337	32	g	g	PROPN
ejpam-3280	337	33	,	,	PUNCT
ejpam-3280	337	34	b)0	b)0	PROPN
ejpam-3280	337	35	=	=	PUNCT
ejpam-3280	337	36	(	(	PUNCT
ejpam-3280	337	37	h	h	NOUN
ejpam-3280	337	38	,	,	PUNCT
ejpam-3280	337	39	c)0	c)0	PROPN
ejpam-3280	337	40	,	,	PUNCT
ejpam-3280	337	41	∀c	∀c	VERB
ejpam-3280	337	42	∈	∈	NOUN
ejpam-3280	337	43	a	a	DET
ejpam-3280	337	44	∩b	∩b	NOUN
ejpam-3280	337	45	.	.	PUNCT
ejpam-3280	338	1	5	5	NUM
ejpam-3280	338	2	.	.	X
ejpam-3280	338	3	image	image	NOUN
ejpam-3280	338	4	and	and	CCONJ
ejpam-3280	338	5	pre	pre	NOUN
ejpam-3280	338	6	-	-	NOUN
ejpam-3280	338	7	image	image	NOUN
ejpam-3280	338	8	of	of	ADP
ejpam-3280	338	9	fuzzy	fuzzy	ADJ
ejpam-3280	338	10	soft	soft	ADJ
ejpam-3280	338	11	hypervector	hypervector	NOUN
ejpam-3280	338	12	space	space	NOUN
ejpam-3280	338	13	in	in	ADP
ejpam-3280	338	14	this	this	DET
ejpam-3280	338	15	section	section	NOUN
ejpam-3280	338	16	,	,	PUNCT
ejpam-3280	338	17	the	the	DET
ejpam-3280	338	18	theorem	theorem	NOUN
ejpam-3280	338	19	of	of	ADP
ejpam-3280	338	20	homomorphic	homomorphic	ADJ
ejpam-3280	338	21	image	image	NOUN
ejpam-3280	338	22	and	and	CCONJ
ejpam-3280	338	23	homomorphic	homomorphic	ADJ
ejpam-3280	338	24	pre	pre	NOUN
ejpam-3280	338	25	-	-	NOUN
ejpam-3280	338	26	image	image	NOUN
ejpam-3280	338	27	of	of	ADP
ejpam-3280	338	28	fuzzy	fuzzy	ADJ
ejpam-3280	338	29	soft	soft	ADJ
ejpam-3280	338	30	hypervector	hypervector	NOUN
ejpam-3280	338	31	spaces	space	NOUN
ejpam-3280	338	32	are	be	AUX
ejpam-3280	338	33	studied	study	VERB
ejpam-3280	338	34	.	.	PUNCT
ejpam-3280	339	1	definition	definition	NOUN
ejpam-3280	339	2	22	22	NUM
ejpam-3280	339	3	.	.	PUNCT
ejpam-3280	340	1	let	let	VERB
ejpam-3280	340	2	f	f	PROPN
ejpam-3280	340	3	ss	ss	PROPN
ejpam-3280	340	4	(	(	PUNCT
ejpam-3280	340	5	v	v	NOUN
ejpam-3280	340	6	,	,	PUNCT
ejpam-3280	340	7	e	e	NOUN
ejpam-3280	340	8	)	)	PUNCT
ejpam-3280	340	9	=	=	SYM
ejpam-3280	340	10	{	{	PUNCT
ejpam-3280	340	11	(	(	PUNCT
ejpam-3280	340	12	f	f	NOUN
ejpam-3280	340	13	,	,	PUNCT
ejpam-3280	340	14	a	a	NOUN
ejpam-3280	340	15	)	)	PUNCT
ejpam-3280	340	16	:	:	PUNCT
ejpam-3280	340	17	a	a	DET
ejpam-3280	340	18	⊆	⊆	NUM
ejpam-3280	340	19	e	e	NOUN
ejpam-3280	340	20	and	and	CCONJ
ejpam-3280	340	21	(	(	PUNCT
ejpam-3280	340	22	f	f	X
ejpam-3280	340	23	,	,	PUNCT
ejpam-3280	340	24	a	a	PRON
ejpam-3280	340	25	)	)	PUNCT
ejpam-3280	340	26	is	be	AUX
ejpam-3280	340	27	a	a	DET
ejpam-3280	340	28	fuzzy	fuzzy	ADJ
ejpam-3280	340	29	soft	soft	ADJ
ejpam-3280	340	30	hypervector	hypervector	NOUN
ejpam-3280	340	31	space	space	NOUN
ejpam-3280	340	32	over	over	ADP
ejpam-3280	340	33	v	v	NOUN
ejpam-3280	340	34	}	}	PUNCT
ejpam-3280	340	35	,	,	PUNCT
ejpam-3280	340	36	then	then	ADV
ejpam-3280	340	37	f	f	PROPN
ejpam-3280	340	38	ss	ss	PROPN
ejpam-3280	340	39	(	(	PUNCT
ejpam-3280	340	40	v	v	NOUN
ejpam-3280	340	41	,	,	PUNCT
ejpam-3280	340	42	e	e	NOUN
ejpam-3280	340	43	)	)	PUNCT
ejpam-3280	340	44	is	be	AUX
ejpam-3280	340	45	called	call	VERB
ejpam-3280	340	46	a	a	DET
ejpam-3280	340	47	fuzzy	fuzzy	ADJ
ejpam-3280	340	48	soft	soft	ADJ
ejpam-3280	340	49	hypervector	hypervector	NOUN
ejpam-3280	340	50	space	space	NOUN
ejpam-3280	340	51	set	set	VERB
ejpam-3280	340	52	class	class	NOUN
ejpam-3280	340	53	over	over	ADP
ejpam-3280	340	54	v	v	NOUN
ejpam-3280	340	55	.	.	PUNCT
ejpam-3280	341	1	definition	definition	NOUN
ejpam-3280	341	2	23	23	NUM
ejpam-3280	341	3	.	.	PUNCT
ejpam-3280	342	1	[	[	X
ejpam-3280	342	2	5	5	X
ejpam-3280	342	3	]	]	PUNCT
ejpam-3280	342	4	let	let	VERB
ejpam-3280	342	5	φ	φ	NOUN
ejpam-3280	342	6	:	:	PUNCT
ejpam-3280	342	7	x	x	X
ejpam-3280	342	8	→	→	SYM
ejpam-3280	342	9	y	y	PROPN
ejpam-3280	342	10	and	and	CCONJ
ejpam-3280	342	11	ψ	ψ	X
ejpam-3280	342	12	:	:	PUNCT
ejpam-3280	342	13	a→	a→	PUNCT
ejpam-3280	342	14	b	b	NOUN
ejpam-3280	342	15	be	be	AUX
ejpam-3280	342	16	two	two	NUM
ejpam-3280	342	17	functions	function	NOUN
ejpam-3280	342	18	,	,	PUNCT
ejpam-3280	342	19	where	where	SCONJ
ejpam-3280	342	20	a	a	PRON
ejpam-3280	342	21	and	and	CCONJ
ejpam-3280	342	22	b	b	NOUN
ejpam-3280	342	23	are	be	AUX
ejpam-3280	342	24	parameter	parameter	NOUN
ejpam-3280	342	25	sets	set	NOUN
ejpam-3280	342	26	for	for	ADP
ejpam-3280	342	27	the	the	DET
ejpam-3280	342	28	crisp	crisp	ADJ
ejpam-3280	342	29	sets	set	NOUN
ejpam-3280	342	30	x	x	PUNCT
ejpam-3280	342	31	and	and	CCONJ
ejpam-3280	342	32	y	y	PROPN
ejpam-3280	342	33	,	,	PUNCT
ejpam-3280	342	34	respectively	respectively	ADV
ejpam-3280	342	35	.	.	PUNCT
ejpam-3280	343	1	then	then	ADV
ejpam-3280	343	2	the	the	DET
ejpam-3280	343	3	pair	pair	NOUN
ejpam-3280	343	4	(	(	PUNCT
ejpam-3280	343	5	ϕ,ψ	ϕ,ψ	NOUN
ejpam-3280	343	6	)	)	PUNCT
ejpam-3280	343	7	is	be	AUX
ejpam-3280	343	8	called	call	VERB
ejpam-3280	343	9	a	a	DET
ejpam-3280	343	10	fuzzy	fuzzy	ADJ
ejpam-3280	343	11	soft	soft	ADJ
ejpam-3280	343	12	function	function	NOUN
ejpam-3280	343	13	from	from	ADP
ejpam-3280	343	14	x	x	PUNCT
ejpam-3280	343	15	to	to	ADP
ejpam-3280	343	16	y	y	PROPN
ejpam-3280	343	17	.	.	PUNCT
ejpam-3280	344	1	definition	definition	NOUN
ejpam-3280	344	2	24	24	NUM
ejpam-3280	344	3	.	.	PUNCT
ejpam-3280	345	1	[	[	X
ejpam-3280	345	2	5	5	X
ejpam-3280	345	3	]	]	PUNCT
ejpam-3280	345	4	let	let	VERB
ejpam-3280	345	5	f	f	PROPN
ejpam-3280	345	6	ss	ss	PROPN
ejpam-3280	345	7	(	(	PUNCT
ejpam-3280	345	8	v	v	NOUN
ejpam-3280	345	9	,	,	PUNCT
ejpam-3280	345	10	e	e	NOUN
ejpam-3280	345	11	)	)	PUNCT
ejpam-3280	345	12	and	and	CCONJ
ejpam-3280	345	13	f	f	PROPN
ejpam-3280	345	14	ss	ss	PROPN
ejpam-3280	345	15	(	(	PUNCT
ejpam-3280	345	16	v	v	NOUN
ejpam-3280	345	17	′	′	NUM
ejpam-3280	345	18	,	,	PUNCT
ejpam-3280	345	19	e′	e′	ADJ
ejpam-3280	345	20	)	)	PUNCT
ejpam-3280	345	21	be	be	VERB
ejpam-3280	345	22	two	two	NUM
ejpam-3280	345	23	fuzzy	fuzzy	ADJ
ejpam-3280	345	24	soft	soft	ADJ
ejpam-3280	345	25	hypervector	hypervector	NOUN
ejpam-3280	345	26	space	space	NOUN
ejpam-3280	345	27	set	set	NOUN
ejpam-3280	345	28	classes	class	NOUN
ejpam-3280	345	29	.	.	PUNCT
ejpam-3280	346	1	let	let	VERB
ejpam-3280	346	2	φ	φ	PROPN
ejpam-3280	346	3	:	:	PUNCT
ejpam-3280	346	4	v	v	X
ejpam-3280	346	5	→	→	SYM
ejpam-3280	346	6	v	v	NOUN
ejpam-3280	346	7	′	′	NUM
ejpam-3280	346	8	and	and	CCONJ
ejpam-3280	346	9	ψ	ψ	X
ejpam-3280	346	10	:	:	PUNCT
ejpam-3280	346	11	e	e	X
ejpam-3280	346	12	→	→	SYM
ejpam-3280	346	13	e′	e′	X
ejpam-3280	346	14	be	be	AUX
ejpam-3280	346	15	mappings	mapping	NOUN
ejpam-3280	346	16	.	.	PUNCT
ejpam-3280	347	1	if	if	SCONJ
ejpam-3280	347	2	(	(	PUNCT
ejpam-3280	347	3	f	f	X
ejpam-3280	347	4	,	,	PUNCT
ejpam-3280	347	5	a	a	PRON
ejpam-3280	347	6	)	)	PUNCT
ejpam-3280	347	7	∈	∈	PROPN
ejpam-3280	347	8	f	f	X
ejpam-3280	347	9	ss	ss	PROPN
ejpam-3280	347	10	(	(	PUNCT
ejpam-3280	347	11	v	v	NOUN
ejpam-3280	347	12	,	,	PUNCT
ejpam-3280	347	13	e	e	NOUN
ejpam-3280	347	14	)	)	PUNCT
ejpam-3280	347	15	,	,	PUNCT
ejpam-3280	347	16	the	the	DET
ejpam-3280	347	17	image	image	NOUN
ejpam-3280	347	18	of	of	ADP
ejpam-3280	347	19	(	(	PUNCT
ejpam-3280	347	20	f	f	X
ejpam-3280	347	21	,	,	PUNCT
ejpam-3280	347	22	a	a	PRON
ejpam-3280	347	23	)	)	PUNCT
ejpam-3280	347	24	under	under	ADP
ejpam-3280	347	25	the	the	DET
ejpam-3280	347	26	function	function	NOUN
ejpam-3280	347	27	(	(	PUNCT
ejpam-3280	347	28	φ	φ	PROPN
ejpam-3280	347	29	,	,	PUNCT
ejpam-3280	347	30	ψ	ψ	NOUN
ejpam-3280	347	31	)	)	PUNCT
ejpam-3280	347	32	,	,	PUNCT
ejpam-3280	347	33	denoted	denote	VERB
ejpam-3280	347	34	by	by	ADP
ejpam-3280	347	35	(	(	PUNCT
ejpam-3280	347	36	φ	φ	PROPN
ejpam-3280	347	37	,	,	PUNCT
ejpam-3280	347	38	ψ)(f	ψ)(f	NUM
ejpam-3280	347	39	,	,	PUNCT
ejpam-3280	347	40	a	a	PRON
ejpam-3280	347	41	)	)	PUNCT
ejpam-3280	347	42	=	=	SYM
ejpam-3280	347	43	(	(	PUNCT
ejpam-3280	347	44	φ(f	φ(f	PROPN
ejpam-3280	347	45	)	)	PUNCT
ejpam-3280	347	46	,	,	PUNCT
ejpam-3280	347	47	ψ(a	ψ(a	PROPN
ejpam-3280	347	48	)	)	PUNCT
ejpam-3280	347	49	)	)	PUNCT
ejpam-3280	347	50	,	,	PUNCT
ejpam-3280	347	51	where	where	SCONJ
ejpam-3280	347	52	φ(f)b(v	φ(f)b(v	NOUN
ejpam-3280	347	53	′	′	NOUN
ejpam-3280	347	54	)	)	PUNCT
ejpam-3280	347	55	=	=	PUNCT
ejpam-3280	347	56			PUNCT
ejpam-3280	347	57	∨	∨	NUM
ejpam-3280	347	58	x∈φ−1(v′	x∈φ−1(v′	PROPN
ejpam-3280	347	59	)	)	PUNCT
ejpam-3280	347	60	∨	∨	NUM
ejpam-3280	347	61	a∈a∩φ−1(b	a∈a∩φ−1(b	PROPN
ejpam-3280	347	62	)	)	PUNCT
ejpam-3280	347	63	fa(x	fa(x	PROPN
ejpam-3280	347	64	)	)	PUNCT
ejpam-3280	347	65	if	if	SCONJ
ejpam-3280	347	66	φ−1(v′	φ−1(v′	NOUN
ejpam-3280	347	67	)	)	PUNCT
ejpam-3280	347	68	6=	6=	ADP
ejpam-3280	347	69	∅	∅	NOUN
ejpam-3280	347	70	0	0	NUM
ejpam-3280	347	71	otherwise	otherwise	ADV
ejpam-3280	347	72	,	,	PUNCT
ejpam-3280	347	73	for	for	ADP
ejpam-3280	347	74	all	all	DET
ejpam-3280	347	75	b	b	PROPN
ejpam-3280	347	76	∈	∈	PROPN
ejpam-3280	347	77	ψ(a	ψ(a	PROPN
ejpam-3280	347	78	)	)	PUNCT
ejpam-3280	347	79	and	and	CCONJ
ejpam-3280	347	80	v′	v′	NOUN
ejpam-3280	347	81	∈	∈	PROPN
ejpam-3280	347	82	v	v	ADP
ejpam-3280	347	83	′.	′.	NOUN
ejpam-3280	347	84	definition	definition	NOUN
ejpam-3280	347	85	25	25	NUM
ejpam-3280	347	86	.	.	PUNCT
ejpam-3280	348	1	[	[	X
ejpam-3280	348	2	5	5	NUM
ejpam-3280	348	3	]	]	X
ejpam-3280	348	4	let	let	VERB
ejpam-3280	348	5	(	(	PUNCT
ejpam-3280	348	6	g	g	NOUN
ejpam-3280	348	7	,	,	PUNCT
ejpam-3280	348	8	b	b	NOUN
ejpam-3280	348	9	)	)	PUNCT
ejpam-3280	348	10	∈	∈	PROPN
ejpam-3280	348	11	f	f	X
ejpam-3280	348	12	ss	ss	PROPN
ejpam-3280	348	13	(	(	PUNCT
ejpam-3280	348	14	v	v	NOUN
ejpam-3280	348	15	′	′	NUM
ejpam-3280	348	16	,	,	PUNCT
ejpam-3280	348	17	e′	e′	ADJ
ejpam-3280	348	18	)	)	PUNCT
ejpam-3280	348	19	,	,	PUNCT
ejpam-3280	348	20	then	then	ADV
ejpam-3280	348	21	the	the	DET
ejpam-3280	348	22	pre	pre	NOUN
ejpam-3280	348	23	-	-	NOUN
ejpam-3280	348	24	image	image	NOUN
ejpam-3280	348	25	of	of	ADP
ejpam-3280	348	26	(	(	PUNCT
ejpam-3280	348	27	g	g	PROPN
ejpam-3280	348	28	,	,	PUNCT
ejpam-3280	348	29	b	b	NOUN
ejpam-3280	348	30	)	)	PUNCT
ejpam-3280	348	31	under	under	ADP
ejpam-3280	348	32	the	the	DET
ejpam-3280	348	33	fuzzy	fuzzy	ADJ
ejpam-3280	348	34	soft	soft	ADJ
ejpam-3280	348	35	function	function	NOUN
ejpam-3280	348	36	(	(	PUNCT
ejpam-3280	348	37	φ	φ	PROPN
ejpam-3280	348	38	,	,	PUNCT
ejpam-3280	348	39	ψ	ψ	NOUN
ejpam-3280	348	40	)	)	PUNCT
ejpam-3280	348	41	,	,	PUNCT
ejpam-3280	348	42	denoted	denote	VERB
ejpam-3280	348	43	(	(	PUNCT
ejpam-3280	348	44	φ	φ	NOUN
ejpam-3280	348	45	,	,	PUNCT
ejpam-3280	348	46	ψ)−1(g	ψ)−1(g	NUM
ejpam-3280	348	47	,	,	PUNCT
ejpam-3280	348	48	b	b	NOUN
ejpam-3280	348	49	)	)	PUNCT
ejpam-3280	348	50	=	=	SYM
ejpam-3280	348	51	(	(	PUNCT
ejpam-3280	348	52	φ−1(g	φ−1(g	PROPN
ejpam-3280	348	53	)	)	PUNCT
ejpam-3280	348	54	,	,	PUNCT
ejpam-3280	348	55	ψ−1(b	ψ−1(b	NOUN
ejpam-3280	348	56	)	)	PUNCT
ejpam-3280	348	57	)	)	PUNCT
ejpam-3280	348	58	,	,	PUNCT
ejpam-3280	348	59	where	where	SCONJ
ejpam-3280	348	60	φ−1(g)α(v	φ−1(g)α(v	NUM
ejpam-3280	348	61	)	)	PUNCT
ejpam-3280	348	62	=	=	SYM
ejpam-3280	348	63	gψ(α)(φ(v	gψ(α)(φ(v	NOUN
ejpam-3280	348	64	)	)	PUNCT
ejpam-3280	348	65	)	)	PUNCT
ejpam-3280	348	66	,	,	PUNCT
ejpam-3280	348	67	for	for	ADP
ejpam-3280	348	68	all	all	DET
ejpam-3280	348	69	α	α	PRON
ejpam-3280	348	70	∈	∈	PROPN
ejpam-3280	348	71	ψ−1(b	ψ−1(b	NOUN
ejpam-3280	348	72	)	)	PUNCT
ejpam-3280	348	73	and	and	CCONJ
ejpam-3280	348	74	v	v	ADP
ejpam-3280	348	75	∈	∈	PROPN
ejpam-3280	348	76	v.	v.	ADP
ejpam-3280	348	77	theorem	theorem	ADJ
ejpam-3280	348	78	10	10	NUM
ejpam-3280	348	79	.	.	PUNCT
ejpam-3280	349	1	let	let	VERB
ejpam-3280	349	2	v	v	NOUN
ejpam-3280	349	3	and	and	CCONJ
ejpam-3280	349	4	v	v	NOUN
ejpam-3280	349	5	′	′	NUM
ejpam-3280	349	6	be	be	AUX
ejpam-3280	349	7	two	two	NUM
ejpam-3280	349	8	hypervector	hypervector	NOUN
ejpam-3280	349	9	space	space	NOUN
ejpam-3280	349	10	over	over	ADP
ejpam-3280	349	11	a	a	DET
ejpam-3280	349	12	field	field	NOUN
ejpam-3280	349	13	k.	k.	NOUN
ejpam-3280	350	1	if	if	SCONJ
ejpam-3280	350	2	(	(	PUNCT
ejpam-3280	350	3	g	g	NOUN
ejpam-3280	350	4	,	,	PUNCT
ejpam-3280	350	5	b	b	NOUN
ejpam-3280	350	6	)	)	PUNCT
ejpam-3280	350	7	∈	∈	PROPN
ejpam-3280	350	8	f	f	X
ejpam-3280	350	9	ss	ss	PROPN
ejpam-3280	350	10	(	(	PUNCT
ejpam-3280	350	11	v	v	NOUN
ejpam-3280	350	12	′	′	NUM
ejpam-3280	350	13	,	,	PUNCT
ejpam-3280	350	14	e′	e′	ADJ
ejpam-3280	350	15	)	)	PUNCT
ejpam-3280	350	16	and	and	CCONJ
ejpam-3280	350	17	(	(	PUNCT
ejpam-3280	350	18	φ	φ	PROPN
ejpam-3280	350	19	,	,	PUNCT
ejpam-3280	350	20	ψ	ψ	NOUN
ejpam-3280	350	21	)	)	PUNCT
ejpam-3280	350	22	is	be	AUX
ejpam-3280	350	23	a	a	DET
ejpam-3280	350	24	fuzzy	fuzzy	ADJ
ejpam-3280	350	25	soft	soft	ADJ
ejpam-3280	350	26	homomorphism	homomorphism	NOUN
ejpam-3280	350	27	from	from	ADP
ejpam-3280	350	28	v	v	NUM
ejpam-3280	350	29	to	to	ADP
ejpam-3280	350	30	v	v	NOUN
ejpam-3280	350	31	′	′	NOUN
ejpam-3280	350	32	,	,	PUNCT
ejpam-3280	350	33	then	then	ADV
ejpam-3280	350	34	(	(	PUNCT
ejpam-3280	350	35	φ	φ	NOUN
ejpam-3280	350	36	,	,	PUNCT
ejpam-3280	350	37	ψ)−1(g	ψ)−1(g	NUM
ejpam-3280	350	38	,	,	PUNCT
ejpam-3280	350	39	b	b	NOUN
ejpam-3280	350	40	)	)	PUNCT
ejpam-3280	350	41	∈	∈	PROPN
ejpam-3280	350	42	f	f	X
ejpam-3280	350	43	ss	ss	PROPN
ejpam-3280	350	44	(	(	PUNCT
ejpam-3280	350	45	v	v	NOUN
ejpam-3280	350	46	,	,	PUNCT
ejpam-3280	350	47	e	e	NOUN
ejpam-3280	350	48	)	)	PUNCT
ejpam-3280	350	49	.	.	PUNCT
ejpam-3280	351	1	proof	proof	NOUN
ejpam-3280	351	2	.	.	PUNCT
ejpam-3280	352	1	if	if	SCONJ
ejpam-3280	352	2	α	α	PROPN
ejpam-3280	352	3	∈	∈	PROPN
ejpam-3280	352	4	ψ−1(b	ψ−1(b	PROPN
ejpam-3280	352	5	)	)	PUNCT
ejpam-3280	352	6	,	,	PUNCT
ejpam-3280	352	7	u	u	NOUN
ejpam-3280	352	8	,	,	PUNCT
ejpam-3280	352	9	v	v	NOUN
ejpam-3280	352	10	∈	∈	PROPN
ejpam-3280	352	11	v	v	NOUN
ejpam-3280	352	12	,	,	PUNCT
ejpam-3280	352	13	then	then	ADV
ejpam-3280	352	14	φ−1(g)α(v	φ−1(g)α(v	PROPN
ejpam-3280	352	15	+	+	CCONJ
ejpam-3280	352	16	u	u	NOUN
ejpam-3280	352	17	)	)	PUNCT
ejpam-3280	352	18	=	=	SYM
ejpam-3280	352	19	gψ(α)(φ(v	gψ(α)(φ(v	X
ejpam-3280	352	20	+	+	NUM
ejpam-3280	352	21	u	u	NOUN
ejpam-3280	352	22	)	)	PUNCT
ejpam-3280	352	23	)	)	PUNCT
ejpam-3280	353	1	=	=	PUNCT
ejpam-3280	353	2	gψ(α)(ϕ(v	gψ(α)(ϕ(v	NOUN
ejpam-3280	353	3	)	)	PUNCT
ejpam-3280	354	1	+	+	CCONJ
ejpam-3280	354	2	ψ(u	ψ(u	NOUN
ejpam-3280	354	3	)	)	PUNCT
ejpam-3280	354	4	)	)	PUNCT
ejpam-3280	354	5	≥	≥	NOUN
ejpam-3280	354	6	gψ(α)(φ(v	gψ(α)(φ(v	NOUN
ejpam-3280	354	7	)	)	PUNCT
ejpam-3280	354	8	)	)	PUNCT
ejpam-3280	355	1	∧	∧	NOUN
ejpam-3280	355	2	gψ(α)(φ(u	gψ(α)(φ(u	NOUN
ejpam-3280	355	3	)	)	PUNCT
ejpam-3280	355	4	)	)	PUNCT
ejpam-3280	356	1	=	=	PUNCT
ejpam-3280	356	2	φ−1(g)α(u	φ−1(g)α(u	PROPN
ejpam-3280	356	3	)	)	PUNCT
ejpam-3280	356	4	∧	∧	PROPN
ejpam-3280	356	5	φ−1(g)α(v	φ−1(g)α(v	NOUN
ejpam-3280	356	6	)	)	PUNCT
ejpam-3280	356	7	.	.	PUNCT
ejpam-3280	357	1	moreover	moreover	ADV
ejpam-3280	357	2	,	,	PUNCT
ejpam-3280	357	3	for	for	ADP
ejpam-3280	357	4	all	all	DET
ejpam-3280	357	5	v	v	ADP
ejpam-3280	357	6	∈	∈	NUM
ejpam-3280	357	7	v	v	NOUN
ejpam-3280	357	8	,	,	PUNCT
ejpam-3280	357	9	φ−1(g)α(−v	φ−1(g)α(−v	X
ejpam-3280	357	10	)	)	PUNCT
ejpam-3280	357	11	=	=	SYM
ejpam-3280	357	12	gψ(α)(φ(−v	gψ(α)(φ(−v	NOUN
ejpam-3280	357	13	)	)	PUNCT
ejpam-3280	357	14	)	)	PUNCT
ejpam-3280	358	1	=	=	PUNCT
ejpam-3280	358	2	gψ(α)(−φ(v	gψ(α)(−φ(v	PROPN
ejpam-3280	358	3	)	)	PUNCT
ejpam-3280	358	4	)	)	PUNCT
ejpam-3280	358	5	≥	≥	NOUN
ejpam-3280	358	6	gψ(α)(φ(v	gψ(α)(φ(v	NOUN
ejpam-3280	358	7	)	)	PUNCT
ejpam-3280	358	8	)	)	PUNCT
ejpam-3280	359	1	=	=	SYM
ejpam-3280	359	2	φ−1(g)α(v	φ−1(g)α(v	NOUN
ejpam-3280	359	3	)	)	PUNCT
ejpam-3280	359	4	.	.	PUNCT
ejpam-3280	360	1	e.	e.	PROPN
ejpam-3280	360	2	ranjbar	ranjbar	PROPN
ejpam-3280	360	3	-	-	PUNCT
ejpam-3280	360	4	yanehsari	yanehsari	NOUN
ejpam-3280	360	5	,	,	PUNCT
ejpam-3280	360	6	m.	m.	NOUN
ejpam-3280	360	7	asghari	asghari	ADJ
ejpam-3280	360	8	-	-	PUNCT
ejpam-3280	360	9	larimi	larimi	PROPN
ejpam-3280	360	10	,	,	PUNCT
ejpam-3280	360	11	r.	r.	PROPN
ejpam-3280	360	12	ameri	ameri	PROPN
ejpam-3280	360	13	/	/	SYM
ejpam-3280	360	14	eur	eur	PROPN
ejpam-3280	360	15	.	.	PUNCT
ejpam-3280	361	1	j.	j.	PROPN
ejpam-3280	361	2	pure	pure	PROPN
ejpam-3280	361	3	appl	appl	PROPN
ejpam-3280	361	4	.	.	PROPN
ejpam-3280	361	5	math	math	PROPN
ejpam-3280	361	6	,	,	PUNCT
ejpam-3280	361	7	12	12	NUM
ejpam-3280	361	8	(	(	PUNCT
ejpam-3280	361	9	1	1	NUM
ejpam-3280	361	10	)	)	PUNCT
ejpam-3280	361	11	(	(	PUNCT
ejpam-3280	361	12	2019	2019	NUM
ejpam-3280	361	13	)	)	PUNCT
ejpam-3280	361	14	,	,	PUNCT
ejpam-3280	361	15	118	118	NUM
ejpam-3280	361	16	-	-	SYM
ejpam-3280	361	17	134	134	NUM
ejpam-3280	361	18	130	130	NUM
ejpam-3280	361	19	also	also	ADV
ejpam-3280	361	20	,	,	PUNCT
ejpam-3280	361	21	for	for	ADP
ejpam-3280	361	22	all	all	DET
ejpam-3280	361	23	r	r	NOUN
ejpam-3280	361	24	∈	∈	PROPN
ejpam-3280	361	25	k	k	NOUN
ejpam-3280	361	26	,	,	PUNCT
ejpam-3280	361	27	v	v	NOUN
ejpam-3280	361	28	∈	∈	PROPN
ejpam-3280	361	29	v	v	NOUN
ejpam-3280	361	30	and	and	CCONJ
ejpam-3280	361	31	z	z	NOUN
ejpam-3280	361	32	∈	∈	PROPN
ejpam-3280	361	33	r	r	NOUN
ejpam-3280	361	34	◦	◦	NOUN
ejpam-3280	361	35	v	v	NOUN
ejpam-3280	361	36	,	,	PUNCT
ejpam-3280	361	37	we	we	PRON
ejpam-3280	361	38	have	have	AUX
ejpam-3280	361	39	inf	inf	VERB
ejpam-3280	361	40	z∈r	z∈r	NUM
ejpam-3280	361	41	◦	◦	NOUN
ejpam-3280	361	42	v	v	NOUN
ejpam-3280	361	43	φ−1(g)α(z	φ−1(g)α(z	NOUN
ejpam-3280	361	44	)	)	PUNCT
ejpam-3280	361	45	=	=	SYM
ejpam-3280	361	46	inf	inf	NOUN
ejpam-3280	361	47	φ(z)∈r	φ(z)∈r	PROPN
ejpam-3280	361	48	◦	◦	NOUN
ejpam-3280	361	49	φ(v	φ(v	NUM
ejpam-3280	361	50	)	)	PUNCT
ejpam-3280	361	51	gψ(α)(φ(z	gψ(α)(φ(z	NOUN
ejpam-3280	361	52	)	)	PUNCT
ejpam-3280	361	53	)	)	PUNCT
ejpam-3280	361	54	≥	≥	NOUN
ejpam-3280	361	55	gψ(α)(φ(v	gψ(α)(φ(v	NOUN
ejpam-3280	361	56	)	)	PUNCT
ejpam-3280	361	57	)	)	PUNCT
ejpam-3280	362	1	=	=	SYM
ejpam-3280	362	2	φ−1(g)α(v	φ−1(g)α(v	NUM
ejpam-3280	362	3	)	)	PUNCT
ejpam-3280	362	4	.	.	PUNCT
ejpam-3280	363	1	therefore	therefore	ADV
ejpam-3280	363	2	,	,	PUNCT
ejpam-3280	363	3	(	(	PUNCT
ejpam-3280	363	4	φ	φ	NOUN
ejpam-3280	363	5	,	,	PUNCT
ejpam-3280	363	6	ψ)−1(g	ψ)−1(g	NUM
ejpam-3280	363	7	,	,	PUNCT
ejpam-3280	363	8	b	b	NOUN
ejpam-3280	363	9	)	)	PUNCT
ejpam-3280	363	10	∈	∈	PROPN
ejpam-3280	363	11	f	f	X
ejpam-3280	363	12	ss	ss	PROPN
ejpam-3280	363	13	(	(	PUNCT
ejpam-3280	363	14	v	v	NOUN
ejpam-3280	363	15	,	,	PUNCT
ejpam-3280	363	16	e	e	NOUN
ejpam-3280	363	17	)	)	PUNCT
ejpam-3280	363	18	.	.	PUNCT
ejpam-3280	364	1	theorem	theorem	NOUN
ejpam-3280	364	2	11	11	NUM
ejpam-3280	364	3	.	.	PUNCT
ejpam-3280	365	1	let	let	VERB
ejpam-3280	365	2	v	v	NOUN
ejpam-3280	365	3	,	,	PUNCT
ejpam-3280	365	4	v	v	NOUN
ejpam-3280	365	5	′	′	NUM
ejpam-3280	365	6	and	and	CCONJ
ejpam-3280	365	7	v	v	ADP
ejpam-3280	365	8	′′	′′	PROPN
ejpam-3280	365	9	be	be	VERB
ejpam-3280	365	10	three	three	NUM
ejpam-3280	365	11	hypervector	hypervector	NOUN
ejpam-3280	365	12	space	space	NOUN
ejpam-3280	365	13	over	over	ADP
ejpam-3280	365	14	a	a	DET
ejpam-3280	365	15	field	field	NOUN
ejpam-3280	365	16	k.	k.	NOUN
ejpam-3280	366	1	if	if	SCONJ
ejpam-3280	366	2	(	(	PUNCT
ejpam-3280	366	3	h	h	NOUN
ejpam-3280	366	4	,	,	PUNCT
ejpam-3280	366	5	c	c	NOUN
ejpam-3280	366	6	)	)	PUNCT
ejpam-3280	366	7	∈	∈	PROPN
ejpam-3280	366	8	f	f	X
ejpam-3280	366	9	ss	ss	PROPN
ejpam-3280	366	10	(	(	PUNCT
ejpam-3280	366	11	v	v	PROPN
ejpam-3280	366	12	′′	′′	PROPN
ejpam-3280	366	13	,	,	PUNCT
ejpam-3280	366	14	e′′	e′′	PROPN
ejpam-3280	366	15	)	)	PUNCT
ejpam-3280	366	16	and	and	CCONJ
ejpam-3280	366	17	(	(	PUNCT
ejpam-3280	366	18	φ1	φ1	PROPN
ejpam-3280	366	19	,	,	PUNCT
ejpam-3280	366	20	ψ1	ψ1	NOUN
ejpam-3280	366	21	)	)	PUNCT
ejpam-3280	366	22	,	,	PUNCT
ejpam-3280	366	23	(	(	PUNCT
ejpam-3280	366	24	φ2	φ2	PROPN
ejpam-3280	366	25	,	,	PUNCT
ejpam-3280	366	26	ψ2	ψ2	NOUN
ejpam-3280	366	27	)	)	PUNCT
ejpam-3280	366	28	are	be	AUX
ejpam-3280	366	29	two	two	NUM
ejpam-3280	366	30	fuzzy	fuzzy	ADJ
ejpam-3280	366	31	soft	soft	ADJ
ejpam-3280	366	32	homomorphisms	homomorphism	NOUN
ejpam-3280	366	33	from	from	ADP
ejpam-3280	366	34	v	v	NUM
ejpam-3280	366	35	to	to	ADP
ejpam-3280	366	36	v	v	NOUN
ejpam-3280	366	37	′	′	NUM
ejpam-3280	366	38	and	and	CCONJ
ejpam-3280	366	39	from	from	ADP
ejpam-3280	366	40	v	v	NUM
ejpam-3280	366	41	′	′	NUM
ejpam-3280	366	42	to	to	ADP
ejpam-3280	366	43	v	v	PROPN
ejpam-3280	366	44	′′	′′	PROPN
ejpam-3280	366	45	,	,	PUNCT
ejpam-3280	366	46	respectively	respectively	ADV
ejpam-3280	366	47	.	.	PUNCT
ejpam-3280	367	1	then	then	ADV
ejpam-3280	367	2	,	,	PUNCT
ejpam-3280	367	3	(	(	PUNCT
ejpam-3280	367	4	φ2	φ2	PROPN
ejpam-3280	367	5	◦	◦	PROPN
ejpam-3280	367	6	φ1	φ1	PROPN
ejpam-3280	367	7	,	,	PUNCT
ejpam-3280	367	8	ψ2	ψ2	NOUN
ejpam-3280	367	9	◦	◦	NOUN
ejpam-3280	367	10	ψ1	ψ1	NOUN
ejpam-3280	367	11	)	)	PUNCT
ejpam-3280	367	12	−1(h	−1(h	NOUN
ejpam-3280	367	13	,	,	PUNCT
ejpam-3280	367	14	c	c	NOUN
ejpam-3280	367	15	)	)	PUNCT
ejpam-3280	367	16	∈	∈	PROPN
ejpam-3280	367	17	f	f	X
ejpam-3280	367	18	ss	ss	PROPN
ejpam-3280	367	19	(	(	PUNCT
ejpam-3280	367	20	v	v	NOUN
ejpam-3280	367	21	,	,	PUNCT
ejpam-3280	367	22	e	e	NOUN
ejpam-3280	367	23	)	)	PUNCT
ejpam-3280	367	24	.	.	PUNCT
ejpam-3280	368	1	proof	proof	NOUN
ejpam-3280	368	2	.	.	PUNCT
ejpam-3280	369	1	show	show	VERB
ejpam-3280	369	2	that	that	SCONJ
ejpam-3280	369	3	,	,	PUNCT
ejpam-3280	369	4	for	for	ADP
ejpam-3280	369	5	all	all	DET
ejpam-3280	369	6	a	a	DET
ejpam-3280	369	7	∈	∈	NOUN
ejpam-3280	369	8	ψ−11	ψ−11	X
ejpam-3280	369	9	(	(	PUNCT
ejpam-3280	369	10	ψ−12	ψ−12	X
ejpam-3280	369	11	(	(	PUNCT
ejpam-3280	369	12	c	c	NOUN
ejpam-3280	369	13	)	)	PUNCT
ejpam-3280	369	14	)	)	PUNCT
ejpam-3280	369	15	and	and	CCONJ
ejpam-3280	369	16	v	v	ADP
ejpam-3280	369	17	∈	∈	PROPN
ejpam-3280	369	18	v	v	NOUN
ejpam-3280	369	19	,	,	PUNCT
ejpam-3280	369	20	(	(	PUNCT
ejpam-3280	369	21	φ2	φ2	PROPN
ejpam-3280	369	22	◦	◦	NOUN
ejpam-3280	369	23	φ1)−1(h	φ1)−1(h	NOUN
ejpam-3280	369	24	)	)	PUNCT
ejpam-3280	369	25	=	=	SYM
ejpam-3280	369	26	φ−11	φ−11	PROPN
ejpam-3280	369	27	(	(	PUNCT
ejpam-3280	369	28	φ−12	φ−12	PROPN
ejpam-3280	369	29	(	(	PUNCT
ejpam-3280	369	30	h))a(v	h))a(v	PROPN
ejpam-3280	369	31	)	)	PUNCT
ejpam-3280	369	32	=	=	SYM
ejpam-3280	369	33	φ−12	φ−12	NOUN
ejpam-3280	369	34	(	(	PUNCT
ejpam-3280	369	35	h)ψ1(a)(φ1(v	h)ψ1(a)(φ1(v	PROPN
ejpam-3280	369	36	)	)	PUNCT
ejpam-3280	369	37	)	)	PUNCT
ejpam-3280	370	1	=	=	SYM
ejpam-3280	370	2	hψ2(ψ1(a))(φ2(φ1(v	hψ2(ψ1(a))(φ2(φ1(v	NOUN
ejpam-3280	370	3	)	)	PUNCT
ejpam-3280	370	4	)	)	PUNCT
ejpam-3280	370	5	)	)	PUNCT
ejpam-3280	371	1	=	=	PUNCT
ejpam-3280	372	1	h(ψ2	h(ψ2	PROPN
ejpam-3280	372	2	◦	◦	NOUN
ejpam-3280	372	3	ψ1)(a)((φ2	ψ1)(a)((φ2	ADP
ejpam-3280	372	4	◦	◦	NOUN
ejpam-3280	372	5	φ1)(v	φ1)(v	NOUN
ejpam-3280	372	6	)	)	PUNCT
ejpam-3280	372	7	)	)	PUNCT
ejpam-3280	372	8	,	,	PUNCT
ejpam-3280	372	9	is	be	AUX
ejpam-3280	372	10	a	a	DET
ejpam-3280	372	11	fuzzy	fuzzy	ADJ
ejpam-3280	372	12	soft	soft	ADJ
ejpam-3280	372	13	hypervector	hypervector	NOUN
ejpam-3280	372	14	space	space	NOUN
ejpam-3280	372	15	over	over	ADP
ejpam-3280	372	16	v	v	NOUN
ejpam-3280	372	17	.	.	PUNCT
ejpam-3280	373	1	let	let	VERB
ejpam-3280	373	2	a	a	DET
ejpam-3280	373	3	∈	∈	NOUN
ejpam-3280	373	4	ψ−11	ψ−11	X
ejpam-3280	373	5	(	(	PUNCT
ejpam-3280	373	6	ψ−12	ψ−12	X
ejpam-3280	373	7	(	(	PUNCT
ejpam-3280	373	8	c	c	NOUN
ejpam-3280	373	9	)	)	PUNCT
ejpam-3280	373	10	)	)	PUNCT
ejpam-3280	373	11	,	,	PUNCT
ejpam-3280	373	12	u	u	NOUN
ejpam-3280	373	13	,	,	PUNCT
ejpam-3280	373	14	v	v	NOUN
ejpam-3280	373	15	∈	∈	PROPN
ejpam-3280	373	16	v	v	NOUN
ejpam-3280	373	17	.	.	PUNCT
ejpam-3280	374	1	then	then	ADV
ejpam-3280	374	2	(	(	PUNCT
ejpam-3280	374	3	φ2	φ2	PROPN
ejpam-3280	374	4	◦	◦	NOUN
ejpam-3280	374	5	φ1)−1(h)a(u+	φ1)−1(h)a(u+	NOUN
ejpam-3280	374	6	v	v	NOUN
ejpam-3280	374	7	)	)	PUNCT
ejpam-3280	374	8	=	=	SYM
ejpam-3280	375	1	h(ψ2	h(ψ2	NOUN
ejpam-3280	375	2	◦	◦	NOUN
ejpam-3280	375	3	ψ1)(a)(φ2	ψ1)(a)(φ2	NOUN
ejpam-3280	375	4	◦	◦	NOUN
ejpam-3280	375	5	φ1)(v	φ1)(v	X
ejpam-3280	376	1	+	+	CCONJ
ejpam-3280	376	2	u	u	NOUN
ejpam-3280	376	3	)	)	PUNCT
ejpam-3280	376	4	=	=	SYM
ejpam-3280	376	5	h(ψ2	h(ψ2	NOUN
ejpam-3280	376	6	◦	◦	NOUN
ejpam-3280	376	7	ψ1)(a)(φ2(φ1(v	ψ1)(a)(φ2(φ1(v	NOUN
ejpam-3280	376	8	)	)	PUNCT
ejpam-3280	376	9	)	)	PUNCT
ejpam-3280	377	1	+	+	CCONJ
ejpam-3280	377	2	φ2(φ1(u	φ2(φ1(u	NOUN
ejpam-3280	377	3	)	)	PUNCT
ejpam-3280	377	4	)	)	PUNCT
ejpam-3280	377	5	)	)	PUNCT
ejpam-3280	378	1	≥	≥	PROPN
ejpam-3280	378	2	h(ψ2	h(ψ2	NOUN
ejpam-3280	378	3	◦	◦	NOUN
ejpam-3280	378	4	ψ1)(a)(φ2	ψ1)(a)(φ2	PROPN
ejpam-3280	378	5	◦	◦	NOUN
ejpam-3280	378	6	φ1(v	φ1(v	NOUN
ejpam-3280	378	7	)	)	PUNCT
ejpam-3280	378	8	)	)	PUNCT
ejpam-3280	379	1	∧	∧	PROPN
ejpam-3280	379	2	h(ψ2	h(ψ2	NOUN
ejpam-3280	379	3	◦	◦	NOUN
ejpam-3280	379	4	ψ1)(a)(φ1	ψ1)(a)(φ1	PROPN
ejpam-3280	379	5	◦	◦	NOUN
ejpam-3280	379	6	φ2(u	φ2(u	NUM
ejpam-3280	379	7	)	)	PUNCT
ejpam-3280	379	8	)	)	PUNCT
ejpam-3280	379	9	.	.	PUNCT
ejpam-3280	380	1	moreover	moreover	ADV
ejpam-3280	380	2	,	,	PUNCT
ejpam-3280	380	3	for	for	ADP
ejpam-3280	380	4	all	all	DET
ejpam-3280	380	5	v	v	ADP
ejpam-3280	380	6	∈	∈	NOUN
ejpam-3280	380	7	v	v	NOUN
ejpam-3280	380	8	,	,	PUNCT
ejpam-3280	380	9	we	we	PRON
ejpam-3280	380	10	have	have	VERB
ejpam-3280	380	11	(	(	PUNCT
ejpam-3280	380	12	φ2	φ2	PROPN
ejpam-3280	380	13	◦	◦	NOUN
ejpam-3280	380	14	φ1)−1(h)a(−v	φ1)−1(h)a(−v	NUM
ejpam-3280	380	15	)	)	PUNCT
ejpam-3280	380	16	=	=	PUNCT
ejpam-3280	381	1	h(ψ2	h(ψ2	NOUN
ejpam-3280	381	2	◦	◦	NOUN
ejpam-3280	381	3	ψ1)(a)(φ2	ψ1)(a)(φ2	NOUN
ejpam-3280	381	4	◦	◦	NOUN
ejpam-3280	381	5	φ1)(−v	φ1)(−v	NOUN
ejpam-3280	381	6	)	)	PUNCT
ejpam-3280	382	1	=	=	PUNCT
ejpam-3280	383	1	h(ψ2	h(ψ2	NOUN
ejpam-3280	383	2	◦	◦	NOUN
ejpam-3280	383	3	ψ1)(a)(−(φ2	ψ1)(a)(−(φ2	NUM
ejpam-3280	383	4	◦	◦	NOUN
ejpam-3280	383	5	φ1(v	φ1(v	NUM
ejpam-3280	383	6	)	)	PUNCT
ejpam-3280	383	7	)	)	PUNCT
ejpam-3280	383	8	≥	≥	PROPN
ejpam-3280	383	9	h(ψ2	h(ψ2	NOUN
ejpam-3280	383	10	◦	◦	NOUN
ejpam-3280	383	11	ψ1)(a)(φ2	ψ1)(a)(φ2	NOUN
ejpam-3280	383	12	◦	◦	NOUN
ejpam-3280	383	13	φ1)(v	φ1)(v	X
ejpam-3280	383	14	)	)	PUNCT
ejpam-3280	384	1	=	=	SYM
ejpam-3280	384	2	(	(	PUNCT
ejpam-3280	384	3	ψ2	ψ2	NOUN
ejpam-3280	384	4	◦	◦	VERB
ejpam-3280	384	5	ψ1	ψ1	NOUN
ejpam-3280	384	6	)	)	PUNCT
ejpam-3280	384	7	−1(h)a(v	−1(h)a(v	NOUN
ejpam-3280	384	8	)	)	PUNCT
ejpam-3280	384	9	,	,	PUNCT
ejpam-3280	384	10	and	and	CCONJ
ejpam-3280	384	11	also	also	ADV
ejpam-3280	384	12	,	,	PUNCT
ejpam-3280	384	13	for	for	ADP
ejpam-3280	384	14	all	all	DET
ejpam-3280	384	15	r	r	NOUN
ejpam-3280	384	16	∈	∈	PROPN
ejpam-3280	384	17	k	k	NOUN
ejpam-3280	384	18	,	,	PUNCT
ejpam-3280	384	19	v	v	NOUN
ejpam-3280	384	20	∈	∈	PROPN
ejpam-3280	384	21	v	v	NOUN
ejpam-3280	384	22	and	and	CCONJ
ejpam-3280	384	23	z	z	NOUN
ejpam-3280	384	24	∈	∈	PROPN
ejpam-3280	384	25	r	r	NOUN
ejpam-3280	384	26	◦	◦	NOUN
ejpam-3280	384	27	v	v	NOUN
ejpam-3280	384	28	,	,	PUNCT
ejpam-3280	384	29	we	we	PRON
ejpam-3280	384	30	have	have	AUX
ejpam-3280	384	31	inf	inf	VERB
ejpam-3280	384	32	z∈r	z∈r	NUM
ejpam-3280	384	33	◦	◦	NOUN
ejpam-3280	384	34	v	v	NOUN
ejpam-3280	384	35	(	(	PUNCT
ejpam-3280	384	36	φ2	φ2	PROPN
ejpam-3280	384	37	◦	◦	NOUN
ejpam-3280	384	38	φ1)−1(h)a(z	φ1)−1(h)a(z	PROPN
ejpam-3280	384	39	)	)	PUNCT
ejpam-3280	385	1	=	=	SYM
ejpam-3280	385	2	inf	inf	PROPN
ejpam-3280	385	3	z∈r	z∈r	NUM
ejpam-3280	385	4	◦	◦	NOUN
ejpam-3280	385	5	v	v	NOUN
ejpam-3280	385	6	h(ψ2	h(ψ2	NOUN
ejpam-3280	385	7	◦	◦	NOUN
ejpam-3280	385	8	ψ1)(a)(φ2	ψ1)(a)(φ2	NOUN
ejpam-3280	385	9	◦	◦	VERB
ejpam-3280	385	10	φ1)(z	φ1)(z	NOUN
ejpam-3280	385	11	)	)	PUNCT
ejpam-3280	385	12	=	=	SYM
ejpam-3280	385	13	inf	inf	PROPN
ejpam-3280	385	14	φ2(φ1(z))∈r	φ2(φ1(z))∈r	PROPN
ejpam-3280	385	15	◦	◦	NOUN
ejpam-3280	385	16	φ2(φ1(v	φ2(φ1(v	PUNCT
ejpam-3280	385	17	)	)	PUNCT
ejpam-3280	385	18	)	)	PUNCT
ejpam-3280	386	1	h(ψ2	h(ψ2	VERB
ejpam-3280	386	2	◦	◦	NOUN
ejpam-3280	386	3	ψ1)(a)(φ2	ψ1)(a)(φ2	NOUN
ejpam-3280	386	4	◦	◦	NOUN
ejpam-3280	386	5	φ1(z	φ1(z	NUM
ejpam-3280	386	6	)	)	PUNCT
ejpam-3280	386	7	)	)	PUNCT
ejpam-3280	386	8	≥	≥	NOUN
ejpam-3280	386	9	h(ψ2	h(ψ2	NOUN
ejpam-3280	386	10	◦	◦	NOUN
ejpam-3280	386	11	ψ1)(a)(φ2(φ1(v	ψ1)(a)(φ2(φ1(v	NOUN
ejpam-3280	386	12	)	)	PUNCT
ejpam-3280	386	13	)	)	PUNCT
ejpam-3280	386	14	)	)	PUNCT
ejpam-3280	387	1	=	=	PRON
ejpam-3280	387	2	(	(	PUNCT
ejpam-3280	387	3	φ2	φ2	PROPN
ejpam-3280	387	4	◦	◦	NOUN
ejpam-3280	387	5	φ1)−1(h)a(v	φ1)−1(h)a(v	ADJ
ejpam-3280	387	6	)	)	PUNCT
ejpam-3280	387	7	.	.	PUNCT
ejpam-3280	388	1	consequently	consequently	ADV
ejpam-3280	388	2	,	,	PUNCT
ejpam-3280	388	3	(	(	PUNCT
ejpam-3280	388	4	φ2	φ2	PROPN
ejpam-3280	388	5	◦	◦	PROPN
ejpam-3280	388	6	φ1	φ1	PROPN
ejpam-3280	388	7	,	,	PUNCT
ejpam-3280	388	8	ψ2	ψ2	NOUN
ejpam-3280	388	9	◦	◦	NOUN
ejpam-3280	388	10	ψ1	ψ1	NOUN
ejpam-3280	388	11	)	)	PUNCT
ejpam-3280	388	12	−1(h	−1(h	NOUN
ejpam-3280	388	13	,	,	PUNCT
ejpam-3280	388	14	c	c	NOUN
ejpam-3280	388	15	)	)	PUNCT
ejpam-3280	388	16	∈	∈	PROPN
ejpam-3280	388	17	f	f	X
ejpam-3280	388	18	ss	ss	PROPN
ejpam-3280	388	19	(	(	PUNCT
ejpam-3280	388	20	v	v	NOUN
ejpam-3280	388	21	,	,	PUNCT
ejpam-3280	388	22	e	e	NOUN
ejpam-3280	388	23	)	)	PUNCT
ejpam-3280	388	24	.	.	PUNCT
ejpam-3280	389	1	theorem	theorem	NOUN
ejpam-3280	389	2	12	12	NUM
ejpam-3280	389	3	.	.	PUNCT
ejpam-3280	390	1	let	let	VERB
ejpam-3280	390	2	v	v	NOUN
ejpam-3280	390	3	and	and	CCONJ
ejpam-3280	390	4	v	v	NOUN
ejpam-3280	390	5	′	′	NUM
ejpam-3280	390	6	be	be	AUX
ejpam-3280	390	7	two	two	NUM
ejpam-3280	390	8	hypervector	hypervector	NOUN
ejpam-3280	390	9	space	space	NOUN
ejpam-3280	390	10	over	over	ADP
ejpam-3280	390	11	a	a	DET
ejpam-3280	390	12	field	field	NOUN
ejpam-3280	390	13	k.	k.	NOUN
ejpam-3280	391	1	if	if	SCONJ
ejpam-3280	391	2	(	(	PUNCT
ejpam-3280	391	3	f	f	X
ejpam-3280	391	4	,	,	PUNCT
ejpam-3280	391	5	a	a	PRON
ejpam-3280	391	6	)	)	PUNCT
ejpam-3280	391	7	∈	∈	PROPN
ejpam-3280	391	8	f	f	X
ejpam-3280	391	9	ss	ss	PROPN
ejpam-3280	391	10	(	(	PUNCT
ejpam-3280	391	11	v	v	NOUN
ejpam-3280	391	12	,	,	PUNCT
ejpam-3280	391	13	e	e	NOUN
ejpam-3280	391	14	)	)	PUNCT
ejpam-3280	391	15	and	and	CCONJ
ejpam-3280	391	16	(	(	PUNCT
ejpam-3280	391	17	φ	φ	PROPN
ejpam-3280	391	18	,	,	PUNCT
ejpam-3280	391	19	ψ	ψ	NOUN
ejpam-3280	391	20	)	)	PUNCT
ejpam-3280	391	21	is	be	AUX
ejpam-3280	391	22	a	a	DET
ejpam-3280	391	23	fuzzy	fuzzy	ADJ
ejpam-3280	391	24	soft	soft	ADJ
ejpam-3280	391	25	homomorphism	homomorphism	NOUN
ejpam-3280	391	26	from	from	ADP
ejpam-3280	391	27	v	v	NUM
ejpam-3280	391	28	to	to	ADP
ejpam-3280	391	29	v	v	NOUN
ejpam-3280	391	30	′	′	NOUN
ejpam-3280	391	31	,	,	PUNCT
ejpam-3280	391	32	then	then	ADV
ejpam-3280	391	33	(	(	PUNCT
ejpam-3280	391	34	φ	φ	NOUN
ejpam-3280	391	35	,	,	PUNCT
ejpam-3280	391	36	ψ)(f	ψ)(f	NUM
ejpam-3280	391	37	,	,	PUNCT
ejpam-3280	391	38	a	a	PRON
ejpam-3280	391	39	)	)	PUNCT
ejpam-3280	391	40	∈	∈	PROPN
ejpam-3280	391	41	f	f	X
ejpam-3280	391	42	ss	ss	PROPN
ejpam-3280	391	43	(	(	PUNCT
ejpam-3280	391	44	v	v	NOUN
ejpam-3280	391	45	′	′	NUM
ejpam-3280	391	46	,	,	PUNCT
ejpam-3280	391	47	e′	e′	NOUN
ejpam-3280	391	48	)	)	PUNCT
ejpam-3280	391	49	.	.	PUNCT
ejpam-3280	392	1	e.	e.	PROPN
ejpam-3280	392	2	ranjbar	ranjbar	PROPN
ejpam-3280	392	3	-	-	PUNCT
ejpam-3280	392	4	yanehsari	yanehsari	NOUN
ejpam-3280	392	5	,	,	PUNCT
ejpam-3280	392	6	m.	m.	NOUN
ejpam-3280	392	7	asghari	asghari	ADJ
ejpam-3280	392	8	-	-	PUNCT
ejpam-3280	392	9	larimi	larimi	PROPN
ejpam-3280	392	10	,	,	PUNCT
ejpam-3280	392	11	r.	r.	PROPN
ejpam-3280	392	12	ameri	ameri	PROPN
ejpam-3280	392	13	/	/	SYM
ejpam-3280	392	14	eur	eur	PROPN
ejpam-3280	392	15	.	.	PUNCT
ejpam-3280	393	1	j.	j.	PROPN
ejpam-3280	393	2	pure	pure	PROPN
ejpam-3280	393	3	appl	appl	PROPN
ejpam-3280	393	4	.	.	PROPN
ejpam-3280	393	5	math	math	PROPN
ejpam-3280	393	6	,	,	PUNCT
ejpam-3280	393	7	12	12	NUM
ejpam-3280	393	8	(	(	PUNCT
ejpam-3280	393	9	1	1	NUM
ejpam-3280	393	10	)	)	PUNCT
ejpam-3280	393	11	(	(	PUNCT
ejpam-3280	393	12	2019	2019	NUM
ejpam-3280	393	13	)	)	PUNCT
ejpam-3280	393	14	,	,	PUNCT
ejpam-3280	393	15	118	118	NUM
ejpam-3280	393	16	-	-	SYM
ejpam-3280	393	17	134	134	NUM
ejpam-3280	393	18	131	131	NUM
ejpam-3280	393	19	proof	proof	NOUN
ejpam-3280	393	20	.	.	PUNCT
ejpam-3280	394	1	let	let	VERB
ejpam-3280	394	2	b	b	X
ejpam-3280	394	3	∈	∈	PROPN
ejpam-3280	394	4	ψ(a	ψ(a	PROPN
ejpam-3280	394	5	)	)	PUNCT
ejpam-3280	394	6	,	,	PUNCT
ejpam-3280	394	7	v′	v′	PROPN
ejpam-3280	394	8	,	,	PUNCT
ejpam-3280	394	9	u′	u′	PROPN
ejpam-3280	394	10	∈	∈	PROPN
ejpam-3280	394	11	v	v	NOUN
ejpam-3280	394	12	′.	′.	NOUN
ejpam-3280	394	13	if	if	SCONJ
ejpam-3280	394	14	φ−1(v′	φ−1(v′	NOUN
ejpam-3280	394	15	)	)	PUNCT
ejpam-3280	394	16	=	=	SYM
ejpam-3280	394	17	∅	∅	NOUN
ejpam-3280	394	18	or	or	CCONJ
ejpam-3280	394	19	φ−1(u′	φ−1(u′	NUM
ejpam-3280	394	20	)	)	PUNCT
ejpam-3280	395	1	=	=	SYM
ejpam-3280	395	2	∅	∅	NOUN
ejpam-3280	395	3	,	,	PUNCT
ejpam-3280	395	4	the	the	DET
ejpam-3280	395	5	proof	proof	NOUN
ejpam-3280	395	6	is	be	AUX
ejpam-3280	395	7	straightforward	straightforward	ADJ
ejpam-3280	395	8	.	.	PUNCT
ejpam-3280	396	1	assume	assume	VERB
ejpam-3280	396	2	that	that	SCONJ
ejpam-3280	396	3	there	there	PRON
ejpam-3280	396	4	exist	exist	VERB
ejpam-3280	396	5	v	v	ADP
ejpam-3280	396	6	,	,	PUNCT
ejpam-3280	396	7	u	u	PROPN
ejpam-3280	396	8	∈	∈	PROPN
ejpam-3280	396	9	v	v	NOUN
ejpam-3280	396	10	,	,	PUNCT
ejpam-3280	396	11	such	such	ADJ
ejpam-3280	396	12	that	that	SCONJ
ejpam-3280	396	13	φ(v	φ(v	NOUN
ejpam-3280	396	14	)	)	PUNCT
ejpam-3280	396	15	=	=	SYM
ejpam-3280	396	16	v′	v′	NOUN
ejpam-3280	396	17	and	and	CCONJ
ejpam-3280	396	18	φ(u	φ(u	NOUN
ejpam-3280	396	19	)	)	PUNCT
ejpam-3280	396	20	=	=	SYM
ejpam-3280	397	1	u′.	u′.	NOUN
ejpam-3280	397	2	then	then	ADV
ejpam-3280	397	3	ϕ(f)b(u	ϕ(f)b(u	X
ejpam-3280	397	4	′	′	NOUN
ejpam-3280	398	1	+	+	NUM
ejpam-3280	398	2	v′	v′	NUM
ejpam-3280	398	3	)	)	PUNCT
ejpam-3280	399	1	=	=	PUNCT
ejpam-3280	399	2	∨	∨	NUM
ejpam-3280	399	3	ui∈φ−1(u′	ui∈φ−1(u′	NOUN
ejpam-3280	399	4	)	)	PUNCT
ejpam-3280	399	5	vj∈φ−1(v′	vj∈φ−1(v′	PROPN
ejpam-3280	399	6	)	)	PUNCT
ejpam-3280	399	7	i∈i	i∈i	NOUN
ejpam-3280	399	8	,	,	PUNCT
ejpam-3280	399	9	j∈j	j∈j	NOUN
ejpam-3280	399	10	∨	∨	PROPN
ejpam-3280	399	11	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	399	12	)	)	PUNCT
ejpam-3280	400	1	fa(ui	fa(ui	PROPN
ejpam-3280	401	1	+	+	NUM
ejpam-3280	401	2	vj	vj	NOUN
ejpam-3280	401	3	)	)	PUNCT
ejpam-3280	401	4	≥	≥	NOUN
ejpam-3280	401	5	∨	∨	NUM
ejpam-3280	401	6	ui∈φ−1(u′	ui∈φ−1(u′	NOUN
ejpam-3280	401	7	)	)	PUNCT
ejpam-3280	401	8	vj∈φ−1(v′	vj∈φ−1(v′	PROPN
ejpam-3280	401	9	)	)	PUNCT
ejpam-3280	401	10	i∈i	i∈i	NOUN
ejpam-3280	401	11	,	,	PUNCT
ejpam-3280	401	12	j∈j	j∈j	NOUN
ejpam-3280	401	13	∨	∨	PROPN
ejpam-3280	401	14	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	401	15	)	)	PUNCT
ejpam-3280	401	16	(	(	PUNCT
ejpam-3280	401	17	fa(ui	fa(ui	ADJ
ejpam-3280	401	18	)	)	PUNCT
ejpam-3280	401	19	∧	∧	PROPN
ejpam-3280	401	20	fa(vj	fa(vj	PROPN
ejpam-3280	401	21	)	)	PUNCT
ejpam-3280	401	22	)	)	PUNCT
ejpam-3280	402	1	=	=	PUNCT
ejpam-3280	402	2	∨	∨	NUM
ejpam-3280	402	3	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	402	4	)	)	PUNCT
ejpam-3280	402	5	[	[	PUNCT
ejpam-3280	402	6	(	(	PUNCT
ejpam-3280	402	7	∨	∨	NUM
ejpam-3280	402	8	vj∈φ−1(v′	vj∈φ−1(v′	PROPN
ejpam-3280	402	9	)	)	PUNCT
ejpam-3280	402	10	j∈j	j∈j	NOUN
ejpam-3280	402	11	(	(	PUNCT
ejpam-3280	402	12	fa(u1	fa(u1	NOUN
ejpam-3280	402	13	)	)	PUNCT
ejpam-3280	402	14	∧	∧	NOUN
ejpam-3280	402	15	fa(vj	fa(vj	NOUN
ejpam-3280	402	16	)	)	PUNCT
ejpam-3280	402	17	)	)	PUNCT
ejpam-3280	402	18	)	)	PUNCT
ejpam-3280	403	1	∨	∨	NUM
ejpam-3280	403	2	(	(	PUNCT
ejpam-3280	403	3	∨	∨	NUM
ejpam-3280	403	4	vj∈φ−1(v′	vj∈φ−1(v′	PROPN
ejpam-3280	403	5	)	)	PUNCT
ejpam-3280	403	6	j∈j	j∈j	NOUN
ejpam-3280	403	7	(	(	PUNCT
ejpam-3280	403	8	fa(u2	fa(u2	ADJ
ejpam-3280	403	9	)	)	PUNCT
ejpam-3280	403	10	∧	∧	PROPN
ejpam-3280	403	11	fa(vj	fa(vj	PROPN
ejpam-3280	403	12	)	)	PUNCT
ejpam-3280	403	13	)	)	PUNCT
ejpam-3280	403	14	)	)	PUNCT
ejpam-3280	404	1	∨	∨	NUM
ejpam-3280	404	2	·	·	PUNCT
ejpam-3280	404	3	·	·	PUNCT
ejpam-3280	404	4	·	·	PUNCT
ejpam-3280	404	5	]	]	PUNCT
ejpam-3280	405	1	=	=	PUNCT
ejpam-3280	405	2	∨	∨	NUM
ejpam-3280	405	3	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	405	4	)	)	PUNCT
ejpam-3280	405	5	(	(	PUNCT
ejpam-3280	405	6	[	[	PUNCT
ejpam-3280	405	7	fa(u1	fa(u1	NOUN
ejpam-3280	405	8	)	)	PUNCT
ejpam-3280	405	9	∧	∧	NOUN
ejpam-3280	405	10	(	(	PUNCT
ejpam-3280	405	11	∨	∨	NUM
ejpam-3280	405	12	vj∈φ−1(v′	vj∈φ−1(v′	PROPN
ejpam-3280	405	13	)	)	PUNCT
ejpam-3280	405	14	j∈j	j∈j	NOUN
ejpam-3280	405	15	fa(vj	fa(vj	PROPN
ejpam-3280	405	16	)	)	PUNCT
ejpam-3280	405	17	)	)	PUNCT
ejpam-3280	405	18	]	]	PUNCT
ejpam-3280	406	1	∨	∨	NUM
ejpam-3280	406	2	[	[	PUNCT
ejpam-3280	406	3	fa(u2	fa(u2	ADJ
ejpam-3280	406	4	)	)	PUNCT
ejpam-3280	406	5	∧	∧	PROPN
ejpam-3280	406	6	(	(	PUNCT
ejpam-3280	406	7	∨	∨	NUM
ejpam-3280	406	8	vj∈φ−1(v′	vj∈φ−1(v′	PROPN
ejpam-3280	406	9	)	)	PUNCT
ejpam-3280	406	10	j∈j	j∈j	NOUN
ejpam-3280	406	11	fa(vj	fa(vj	PROPN
ejpam-3280	406	12	)	)	PUNCT
ejpam-3280	406	13	)	)	PUNCT
ejpam-3280	406	14	]	]	PUNCT
ejpam-3280	407	1	∨	∨	X
ejpam-3280	407	2	·	·	PUNCT
ejpam-3280	407	3	·	·	PUNCT
ejpam-3280	407	4	·	·	PUNCT
ejpam-3280	407	5	)	)	PUNCT
ejpam-3280	408	1	=	=	PUNCT
ejpam-3280	408	2	∨	∨	NUM
ejpam-3280	408	3	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	408	4	)	)	PUNCT
ejpam-3280	408	5	(	(	PUNCT
ejpam-3280	408	6	∨	∨	NUM
ejpam-3280	408	7	ui∈φ−1(u′	ui∈φ−1(u′	NOUN
ejpam-3280	408	8	)	)	PUNCT
ejpam-3280	408	9	i∈i	i∈i	ADJ
ejpam-3280	408	10	fa(ui	fa(ui	PROPN
ejpam-3280	408	11	)	)	PUNCT
ejpam-3280	408	12	)	)	PUNCT
ejpam-3280	409	1	∧	∧	PROPN
ejpam-3280	409	2	(	(	PUNCT
ejpam-3280	409	3	∨	∨	NUM
ejpam-3280	409	4	vi∈φ−1(v′	vi∈φ−1(v′	NOUN
ejpam-3280	409	5	)	)	PUNCT
ejpam-3280	409	6	j∈j	j∈j	NOUN
ejpam-3280	409	7	fa(vj	fa(vj	PROPN
ejpam-3280	409	8	)	)	PUNCT
ejpam-3280	409	9	)	)	PUNCT
ejpam-3280	410	1	=	=	SYM
ejpam-3280	410	2	(	(	PUNCT
ejpam-3280	410	3	∨	∨	NUM
ejpam-3280	410	4	ui∈φ−1(u′	ui∈φ−1(u′	NOUN
ejpam-3280	410	5	)	)	PUNCT
ejpam-3280	410	6	i∈i	i∈i	ADJ
ejpam-3280	410	7	∨	∨	NUM
ejpam-3280	410	8	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	410	9	)	)	PUNCT
ejpam-3280	410	10	fa(ui	fa(ui	PROPN
ejpam-3280	410	11	)	)	PUNCT
ejpam-3280	410	12	)	)	PUNCT
ejpam-3280	411	1	∧	∧	PROPN
ejpam-3280	411	2	(	(	PUNCT
ejpam-3280	411	3	∨	∨	NUM
ejpam-3280	411	4	vi∈φ−1(v′	vi∈φ−1(v′	NOUN
ejpam-3280	411	5	)	)	PUNCT
ejpam-3280	411	6	j∈j	j∈j	NOUN
ejpam-3280	411	7	∨	∨	PROPN
ejpam-3280	411	8	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	411	9	)	)	PUNCT
ejpam-3280	411	10	fa(vj	fa(vj	NOUN
ejpam-3280	411	11	)	)	PUNCT
ejpam-3280	412	1	=	=	PUNCT
ejpam-3280	412	2	φ(f)b(u	φ(f)b(u	NUM
ejpam-3280	412	3	′	′	NUM
ejpam-3280	412	4	)	)	PUNCT
ejpam-3280	412	5	∧	∧	PROPN
ejpam-3280	412	6	φ(f)b(v	φ(f)b(v	NOUN
ejpam-3280	412	7	′	′	NUM
ejpam-3280	412	8	)	)	PUNCT
ejpam-3280	412	9	.	.	PUNCT
ejpam-3280	413	1	moreover	moreover	ADV
ejpam-3280	413	2	,	,	PUNCT
ejpam-3280	413	3	for	for	ADP
ejpam-3280	413	4	all	all	DET
ejpam-3280	413	5	v′	v′	NOUN
ejpam-3280	413	6	∈	∈	PROPN
ejpam-3280	413	7	v	v	ADP
ejpam-3280	413	8	′	′	NOUN
ejpam-3280	413	9	,	,	PUNCT
ejpam-3280	413	10	where	where	SCONJ
ejpam-3280	413	11	φ(v	φ(v	NOUN
ejpam-3280	413	12	)	)	PUNCT
ejpam-3280	413	13	=	=	SYM
ejpam-3280	413	14	v′	v′	NOUN
ejpam-3280	413	15	and	and	CCONJ
ejpam-3280	413	16	v	v	ADP
ejpam-3280	413	17	∈	∈	NOUN
ejpam-3280	413	18	v	v	NOUN
ejpam-3280	413	19	,	,	PUNCT
ejpam-3280	413	20	we	we	PRON
ejpam-3280	413	21	have	have	AUX
ejpam-3280	413	22	ϕ(f)b(−v′	ϕ(f)b(−v′	VERB
ejpam-3280	413	23	)	)	PUNCT
ejpam-3280	414	1	=	=	SYM
ejpam-3280	415	1	∨	∨	NUM
ejpam-3280	415	2	−v∈φ−1(−v′	−v∈φ−1(−v′	NOUN
ejpam-3280	415	3	)	)	PUNCT
ejpam-3280	415	4	∨	∨	NUM
ejpam-3280	415	5	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	415	6	)	)	PUNCT
ejpam-3280	415	7	fa(−v	fa(−v	NOUN
ejpam-3280	415	8	)	)	PUNCT
ejpam-3280	415	9	≥	≥	PROPN
ejpam-3280	415	10	∨	∨	PROPN
ejpam-3280	415	11	v∈φ−1(v′	v∈φ−1(v′	PROPN
ejpam-3280	415	12	)	)	PUNCT
ejpam-3280	415	13	∨	∨	PROPN
ejpam-3280	415	14	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	415	15	)	)	PUNCT
ejpam-3280	415	16	fa(v	fa(v	PUNCT
ejpam-3280	415	17	)	)	PUNCT
ejpam-3280	415	18	=	=	SYM
ejpam-3280	415	19	ϕ(f)b(v	ϕ(f)b(v	NOUN
ejpam-3280	415	20	)	)	PUNCT
ejpam-3280	415	21	.	.	PUNCT
ejpam-3280	416	1	also	also	ADV
ejpam-3280	416	2	,	,	PUNCT
ejpam-3280	416	3	let	let	VERB
ejpam-3280	416	4	r	r	PRON
ejpam-3280	416	5	∈	∈	PROPN
ejpam-3280	416	6	k	k	X
ejpam-3280	416	7	,	,	PUNCT
ejpam-3280	416	8	v′	v′	PROPN
ejpam-3280	416	9	∈	∈	PROPN
ejpam-3280	416	10	v	v	ADP
ejpam-3280	416	11	′.	′.	NOUN
ejpam-3280	416	12	if	if	SCONJ
ejpam-3280	416	13	φ−1(v′	φ−1(v′	NOUN
ejpam-3280	416	14	)	)	PUNCT
ejpam-3280	416	15	=	=	SYM
ejpam-3280	416	16	∅	∅	NOUN
ejpam-3280	416	17	,	,	PUNCT
ejpam-3280	416	18	the	the	DET
ejpam-3280	416	19	proof	proof	NOUN
ejpam-3280	416	20	is	be	AUX
ejpam-3280	416	21	straightforward	straightforward	ADJ
ejpam-3280	416	22	.	.	PUNCT
ejpam-3280	417	1	assume	assume	VERB
ejpam-3280	417	2	that	that	SCONJ
ejpam-3280	417	3	there	there	PRON
ejpam-3280	417	4	exists	exist	VERB
ejpam-3280	417	5	v	v	ADP
ejpam-3280	417	6	∈	∈	PROPN
ejpam-3280	417	7	v	v	NOUN
ejpam-3280	417	8	,	,	PUNCT
ejpam-3280	417	9	such	such	ADJ
ejpam-3280	417	10	that	that	SCONJ
ejpam-3280	417	11	φ(v	φ(v	NOUN
ejpam-3280	417	12	)	)	PUNCT
ejpam-3280	417	13	=	=	VERB
ejpam-3280	418	1	v′.	v′.	ADV
ejpam-3280	418	2	hence	hence	ADV
ejpam-3280	418	3	,	,	PUNCT
ejpam-3280	418	4	for	for	ADP
ejpam-3280	418	5	all	all	DET
ejpam-3280	418	6	z′	z′	NUM
ejpam-3280	418	7	∈	∈	PROPN
ejpam-3280	418	8	r	r	NOUN
ejpam-3280	418	9	◦	◦	NOUN
ejpam-3280	418	10	v′	v′	NOUN
ejpam-3280	418	11	,	,	PUNCT
ejpam-3280	418	12	such	such	ADJ
ejpam-3280	418	13	that	that	SCONJ
ejpam-3280	418	14	ϕ(z	ϕ(z	NOUN
ejpam-3280	418	15	)	)	PUNCT
ejpam-3280	419	1	=	=	SYM
ejpam-3280	419	2	z′	z′	PROPN
ejpam-3280	419	3	,	,	PUNCT
ejpam-3280	419	4	we	we	PRON
ejpam-3280	419	5	have	have	VERB
ejpam-3280	419	6	inf	inf	VERB
ejpam-3280	419	7	z′∈r	z′∈r	PROPN
ejpam-3280	419	8	◦	◦	NOUN
ejpam-3280	419	9	v′	v′	PROPN
ejpam-3280	419	10	φ(f)b(z	φ(f)b(z	NOUN
ejpam-3280	419	11	′	′	NUM
ejpam-3280	419	12	)	)	PUNCT
ejpam-3280	419	13	=	=	SYM
ejpam-3280	419	14	inf	inf	PROPN
ejpam-3280	419	15	z∈r	z∈r	NUM
ejpam-3280	419	16	◦	◦	NOUN
ejpam-3280	419	17	v	v	NOUN
ejpam-3280	419	18	φ(f)b(z	φ(f)b(z	NOUN
ejpam-3280	419	19	)	)	PUNCT
ejpam-3280	419	20	=	=	SYM
ejpam-3280	419	21	inf	inf	PROPN
ejpam-3280	419	22	z∈r	z∈r	NUM
ejpam-3280	419	23	◦	◦	NOUN
ejpam-3280	419	24	v	v	ADP
ejpam-3280	419	25	∨	∨	NUM
ejpam-3280	419	26	z∈ψ−1(z′	z∈ψ−1(z′	PROPN
ejpam-3280	419	27	)	)	PUNCT
ejpam-3280	419	28	∨	∨	PROPN
ejpam-3280	419	29	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	419	30	)	)	PUNCT
ejpam-3280	419	31	fa(z	fa(z	PUNCT
ejpam-3280	419	32	)	)	PUNCT
ejpam-3280	419	33	≥	≥	NOUN
ejpam-3280	419	34	∨	∨	NUM
ejpam-3280	419	35	z∈ψ−1(z′	z∈ψ−1(z′	PROPN
ejpam-3280	419	36	)	)	PUNCT
ejpam-3280	420	1	∨	∨	PROPN
ejpam-3280	420	2	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	420	3	)	)	PUNCT
ejpam-3280	420	4	inf	inf	NOUN
ejpam-3280	420	5	z∈r	z∈r	PROPN
ejpam-3280	420	6	◦	◦	NOUN
ejpam-3280	420	7	v	v	NOUN
ejpam-3280	420	8	fa(z	fa(z	PUNCT
ejpam-3280	420	9	)	)	PUNCT
ejpam-3280	420	10	=	=	PUNCT
ejpam-3280	421	1	∨	∨	NUM
ejpam-3280	421	2	z∈φ−1(z′	z∈φ−1(z′	PROPN
ejpam-3280	421	3	)	)	PUNCT
ejpam-3280	421	4	∨	∨	PROPN
ejpam-3280	421	5	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	421	6	)	)	PUNCT
ejpam-3280	421	7	fa(v	fa(v	PUNCT
ejpam-3280	421	8	)	)	PUNCT
ejpam-3280	421	9	=	=	SYM
ejpam-3280	421	10	∨	∨	NUM
ejpam-3280	421	11	v∈φ−1(v′	v∈φ−1(v′	PROPN
ejpam-3280	421	12	)	)	PUNCT
ejpam-3280	421	13	∨	∨	PROPN
ejpam-3280	421	14	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	421	15	)	)	PUNCT
ejpam-3280	421	16	fa(v	fa(v	PUNCT
ejpam-3280	421	17	)	)	PUNCT
ejpam-3280	422	1	=	=	SYM
ejpam-3280	422	2	φ(f)b(v	φ(f)b(v	NOUN
ejpam-3280	422	3	′	′	NUM
ejpam-3280	422	4	)	)	PUNCT
ejpam-3280	422	5	.	.	PUNCT
ejpam-3280	423	1	therefore	therefore	ADV
ejpam-3280	423	2	,	,	PUNCT
ejpam-3280	423	3	(	(	PUNCT
ejpam-3280	423	4	φ	φ	NOUN
ejpam-3280	423	5	,	,	PUNCT
ejpam-3280	423	6	ψ)(f	ψ)(f	NUM
ejpam-3280	423	7	,	,	PUNCT
ejpam-3280	423	8	a	a	DET
ejpam-3280	423	9	)	)	PUNCT
ejpam-3280	423	10	∈	∈	PROPN
ejpam-3280	423	11	f	f	X
ejpam-3280	423	12	ss	ss	PROPN
ejpam-3280	423	13	(	(	PUNCT
ejpam-3280	423	14	v	v	NOUN
ejpam-3280	423	15	′	′	NUM
ejpam-3280	423	16	,	,	PUNCT
ejpam-3280	423	17	e′	e′	NOUN
ejpam-3280	423	18	)	)	PUNCT
ejpam-3280	423	19	.	.	PUNCT
ejpam-3280	424	1	lemma	lemma	PROPN
ejpam-3280	424	2	6	6	NUM
ejpam-3280	424	3	.	.	PUNCT
ejpam-3280	425	1	let	let	VERB
ejpam-3280	425	2	v	v	NOUN
ejpam-3280	425	3	and	and	CCONJ
ejpam-3280	425	4	v	v	NOUN
ejpam-3280	425	5	′	′	NUM
ejpam-3280	425	6	be	be	AUX
ejpam-3280	425	7	two	two	NUM
ejpam-3280	425	8	hypervector	hypervector	NOUN
ejpam-3280	425	9	space	space	NOUN
ejpam-3280	425	10	over	over	ADP
ejpam-3280	425	11	a	a	DET
ejpam-3280	425	12	field	field	NOUN
ejpam-3280	425	13	k.	k.	NOUN
ejpam-3280	426	1	if	if	SCONJ
ejpam-3280	426	2	(	(	PUNCT
ejpam-3280	426	3	f	f	X
ejpam-3280	426	4	,	,	PUNCT
ejpam-3280	426	5	a	a	PRON
ejpam-3280	426	6	)	)	PUNCT
ejpam-3280	426	7	∈	∈	PROPN
ejpam-3280	426	8	f	f	X
ejpam-3280	426	9	ss	ss	PROPN
ejpam-3280	426	10	(	(	PUNCT
ejpam-3280	426	11	v	v	NOUN
ejpam-3280	426	12	,	,	PUNCT
ejpam-3280	426	13	e	e	NOUN
ejpam-3280	426	14	)	)	PUNCT
ejpam-3280	426	15	,	,	PUNCT
ejpam-3280	426	16	then	then	ADV
ejpam-3280	426	17	(	(	PUNCT
ejpam-3280	426	18	f	f	X
ejpam-3280	426	19	,	,	PUNCT
ejpam-3280	426	20	a	a	PRON
ejpam-3280	426	21	)	)	PUNCT
ejpam-3280	426	22	v	v	NOUN
ejpam-3280	426	23	(	(	PUNCT
ejpam-3280	426	24	φ	φ	PROPN
ejpam-3280	426	25	,	,	PUNCT
ejpam-3280	426	26	ψ)−1((φ	ψ)−1((φ	X
ejpam-3280	426	27	,	,	PUNCT
ejpam-3280	426	28	ψ)(f	ψ)(f	NUM
ejpam-3280	426	29	,	,	PUNCT
ejpam-3280	426	30	a	a	PRON
ejpam-3280	426	31	)	)	PUNCT
ejpam-3280	426	32	)	)	PUNCT
ejpam-3280	426	33	.	.	PUNCT
ejpam-3280	427	1	e.	e.	PROPN
ejpam-3280	427	2	ranjbar	ranjbar	PROPN
ejpam-3280	427	3	-	-	PUNCT
ejpam-3280	427	4	yanehsari	yanehsari	NOUN
ejpam-3280	427	5	,	,	PUNCT
ejpam-3280	427	6	m.	m.	NOUN
ejpam-3280	427	7	asghari	asghari	ADJ
ejpam-3280	427	8	-	-	PUNCT
ejpam-3280	427	9	larimi	larimi	PROPN
ejpam-3280	427	10	,	,	PUNCT
ejpam-3280	427	11	r.	r.	PROPN
ejpam-3280	427	12	ameri	ameri	PROPN
ejpam-3280	427	13	/	/	SYM
ejpam-3280	427	14	eur	eur	PROPN
ejpam-3280	427	15	.	.	PUNCT
ejpam-3280	428	1	j.	j.	PROPN
ejpam-3280	428	2	pure	pure	PROPN
ejpam-3280	428	3	appl	appl	PROPN
ejpam-3280	428	4	.	.	PROPN
ejpam-3280	428	5	math	math	PROPN
ejpam-3280	428	6	,	,	PUNCT
ejpam-3280	428	7	12	12	NUM
ejpam-3280	428	8	(	(	PUNCT
ejpam-3280	428	9	1	1	NUM
ejpam-3280	428	10	)	)	PUNCT
ejpam-3280	428	11	(	(	PUNCT
ejpam-3280	428	12	2019	2019	NUM
ejpam-3280	428	13	)	)	PUNCT
ejpam-3280	428	14	,	,	PUNCT
ejpam-3280	428	15	118	118	NUM
ejpam-3280	428	16	-	-	SYM
ejpam-3280	428	17	134	134	NUM
ejpam-3280	428	18	132	132	NUM
ejpam-3280	428	19	proof	proof	NOUN
ejpam-3280	428	20	.	.	PUNCT
ejpam-3280	429	1	it	it	PRON
ejpam-3280	429	2	is	be	AUX
ejpam-3280	429	3	obviously	obviously	ADV
ejpam-3280	429	4	that	that	PRON
ejpam-3280	429	5	,	,	PUNCT
ejpam-3280	429	6	a	a	DET
ejpam-3280	429	7	⊆	⊆	NUM
ejpam-3280	429	8	ψ−1(ψ(a	ψ−1(ψ(a	NOUN
ejpam-3280	429	9	)	)	PUNCT
ejpam-3280	429	10	)	)	PUNCT
ejpam-3280	429	11	.	.	PUNCT
ejpam-3280	430	1	let	let	VERB
ejpam-3280	430	2	v	v	NUM
ejpam-3280	430	3	∈	∈	PROPN
ejpam-3280	430	4	v	v	NOUN
ejpam-3280	430	5	and	and	CCONJ
ejpam-3280	430	6	a	a	DET
ejpam-3280	430	7	∈	∈	NOUN
ejpam-3280	430	8	a.	a.	NOUN
ejpam-3280	430	9	since	since	SCONJ
ejpam-3280	430	10	φ−1(φ(v	φ−1(φ(v	NOUN
ejpam-3280	430	11	)	)	PUNCT
ejpam-3280	430	12	)	)	PUNCT
ejpam-3280	431	1	6=	6=	ADP
ejpam-3280	431	2	∅	∅	NOUN
ejpam-3280	431	3	,	,	PUNCT
ejpam-3280	431	4	thus	thus	ADV
ejpam-3280	431	5	φ−1(φ(f))a(v	φ−1(φ(f))a(v	ADJ
ejpam-3280	431	6	)	)	PUNCT
ejpam-3280	431	7	=	=	SYM
ejpam-3280	431	8	φ(f)ψ(a)(φ(v	φ(f)ψ(a)(φ(v	PROPN
ejpam-3280	431	9	)	)	PUNCT
ejpam-3280	431	10	)	)	PUNCT
ejpam-3280	432	1	=	=	PUNCT
ejpam-3280	432	2	∨	∨	NOUN
ejpam-3280	432	3	x∈φ−1(φ(v	x∈φ−1(φ(v	NUM
ejpam-3280	432	4	)	)	PUNCT
ejpam-3280	432	5	)	)	PUNCT
ejpam-3280	433	1	∨	∨	PROPN
ejpam-3280	433	2	a∈a∩ψ−1(b	a∈a∩ψ−1(b	PROPN
ejpam-3280	433	3	)	)	PUNCT
ejpam-3280	433	4	fa(x	fa(x	PROPN
ejpam-3280	433	5	)	)	PUNCT
ejpam-3280	433	6	≥	≥	NOUN
ejpam-3280	433	7	fa(v	fa(v	NUM
ejpam-3280	433	8	)	)	PUNCT
ejpam-3280	433	9	.	.	PUNCT
ejpam-3280	434	1	consequently	consequently	ADV
ejpam-3280	434	2	,	,	PUNCT
ejpam-3280	434	3	fa	fa	PROPN
ejpam-3280	434	4	≤	≤	NUM
ejpam-3280	434	5	φ−1(φ(f))a	φ−1(φ(f))a	PROPN
ejpam-3280	434	6	,	,	PUNCT
ejpam-3280	434	7	∀	∀	X
ejpam-3280	434	8	a	a	DET
ejpam-3280	434	9	∈	∈	PROPN
ejpam-3280	434	10	a.	a.	NOUN
ejpam-3280	434	11	therefore	therefore	ADV
ejpam-3280	434	12	,	,	PUNCT
ejpam-3280	434	13	(	(	PUNCT
ejpam-3280	434	14	f	f	X
ejpam-3280	434	15	,	,	PUNCT
ejpam-3280	434	16	a	a	PRON
ejpam-3280	434	17	)	)	PUNCT
ejpam-3280	434	18	v	v	NOUN
ejpam-3280	434	19	(	(	PUNCT
ejpam-3280	434	20	φ	φ	PROPN
ejpam-3280	434	21	,	,	PUNCT
ejpam-3280	434	22	ψ)−1((φ	ψ)−1((φ	X
ejpam-3280	434	23	,	,	PUNCT
ejpam-3280	434	24	ψ)(f	ψ)(f	NUM
ejpam-3280	434	25	,	,	PUNCT
ejpam-3280	434	26	a	a	PRON
ejpam-3280	434	27	)	)	PUNCT
ejpam-3280	434	28	)	)	PUNCT
ejpam-3280	434	29	.	.	PUNCT
ejpam-3280	435	1	in	in	ADP
ejpam-3280	435	2	particular	particular	ADJ
ejpam-3280	435	3	,	,	PUNCT
ejpam-3280	435	4	if	if	SCONJ
ejpam-3280	435	5	φ	φ	PROPN
ejpam-3280	435	6	and	and	CCONJ
ejpam-3280	435	7	ψ	ψ	PROPN
ejpam-3280	435	8	are	be	AUX
ejpam-3280	435	9	injection	injection	NOUN
ejpam-3280	435	10	,	,	PUNCT
ejpam-3280	435	11	then	then	ADV
ejpam-3280	435	12	(	(	PUNCT
ejpam-3280	435	13	φ	φ	PROPN
ejpam-3280	435	14	,	,	PUNCT
ejpam-3280	435	15	ψ)−1((φ	ψ)−1((φ	X
ejpam-3280	435	16	,	,	PUNCT
ejpam-3280	435	17	ψ)(f	ψ)(f	NUM
ejpam-3280	435	18	,	,	PUNCT
ejpam-3280	435	19	a	a	PRON
ejpam-3280	435	20	)	)	PUNCT
ejpam-3280	435	21	)	)	PUNCT
ejpam-3280	436	1	=	=	PUNCT
ejpam-3280	436	2	(	(	PUNCT
ejpam-3280	436	3	f	f	X
ejpam-3280	436	4	,	,	PUNCT
ejpam-3280	436	5	a	a	PRON
ejpam-3280	436	6	)	)	PUNCT
ejpam-3280	436	7	.	.	PUNCT
ejpam-3280	437	1	lemma	lemma	PROPN
ejpam-3280	437	2	7	7	X
ejpam-3280	437	3	.	.	PUNCT
ejpam-3280	438	1	let	let	VERB
ejpam-3280	438	2	v	v	NOUN
ejpam-3280	438	3	and	and	CCONJ
ejpam-3280	438	4	v	v	NOUN
ejpam-3280	438	5	′	′	NUM
ejpam-3280	438	6	be	be	AUX
ejpam-3280	438	7	two	two	NUM
ejpam-3280	438	8	hypervector	hypervector	NOUN
ejpam-3280	438	9	space	space	NOUN
ejpam-3280	438	10	over	over	ADP
ejpam-3280	438	11	a	a	DET
ejpam-3280	438	12	field	field	NOUN
ejpam-3280	438	13	k.	k.	NOUN
ejpam-3280	439	1	if	if	SCONJ
ejpam-3280	439	2	(	(	PUNCT
ejpam-3280	439	3	g	g	NOUN
ejpam-3280	439	4	,	,	PUNCT
ejpam-3280	439	5	b	b	NOUN
ejpam-3280	439	6	)	)	PUNCT
ejpam-3280	439	7	∈	∈	PROPN
ejpam-3280	439	8	f	f	X
ejpam-3280	439	9	ss	ss	PROPN
ejpam-3280	439	10	(	(	PUNCT
ejpam-3280	439	11	v	v	NOUN
ejpam-3280	439	12	′	′	NUM
ejpam-3280	439	13	,	,	PUNCT
ejpam-3280	439	14	e′	e′	ADJ
ejpam-3280	439	15	)	)	PUNCT
ejpam-3280	439	16	,	,	PUNCT
ejpam-3280	439	17	then	then	ADV
ejpam-3280	439	18	(	(	PUNCT
ejpam-3280	439	19	φ	φ	NOUN
ejpam-3280	439	20	,	,	PUNCT
ejpam-3280	439	21	ψ)((φ	ψ)((φ	NOUN
ejpam-3280	439	22	,	,	PUNCT
ejpam-3280	439	23	ψ)−1(g	ψ)−1(g	NUM
ejpam-3280	439	24	,	,	PUNCT
ejpam-3280	439	25	b	b	NOUN
ejpam-3280	439	26	)	)	PUNCT
ejpam-3280	439	27	)	)	PUNCT
ejpam-3280	439	28	v	v	NOUN
ejpam-3280	439	29	(	(	PUNCT
ejpam-3280	439	30	g	g	PROPN
ejpam-3280	439	31	,	,	PUNCT
ejpam-3280	439	32	b	b	NOUN
ejpam-3280	439	33	)	)	PUNCT
ejpam-3280	439	34	.	.	PUNCT
ejpam-3280	440	1	proof	proof	NOUN
ejpam-3280	440	2	.	.	PUNCT
ejpam-3280	441	1	for	for	ADP
ejpam-3280	441	2	all	all	DET
ejpam-3280	441	3	v′	v′	NOUN
ejpam-3280	441	4	∈	∈	PROPN
ejpam-3280	441	5	v	v	ADP
ejpam-3280	441	6	′	′	NUM
ejpam-3280	441	7	and	and	CCONJ
ejpam-3280	441	8	b	b	X
ejpam-3280	441	9	∈	∈	PROPN
ejpam-3280	441	10	ψ(ψ−1(b	ψ(ψ−1(b	PROPN
ejpam-3280	441	11	)	)	PUNCT
ejpam-3280	441	12	)	)	PUNCT
ejpam-3280	441	13	,	,	PUNCT
ejpam-3280	441	14	we	we	PRON
ejpam-3280	441	15	have	have	VERB
ejpam-3280	441	16	φ(φ−1(g))b(v	φ(φ−1(g))b(v	NOUN
ejpam-3280	441	17	′	′	NUM
ejpam-3280	441	18	)	)	PUNCT
ejpam-3280	441	19	=	=	PUNCT
ejpam-3280	442	1			PUNCT
ejpam-3280	442	2	∨	∨	NUM
ejpam-3280	442	3	x∈φ−1(v′	x∈φ−1(v′	PROPN
ejpam-3280	442	4	)	)	PUNCT
ejpam-3280	442	5	∨	∨	NUM
ejpam-3280	442	6	a∈ψ−1(b)∩φ−1(b	a∈ψ−1(b)∩φ−1(b	NOUN
ejpam-3280	442	7	)	)	PUNCT
ejpam-3280	442	8	φ−1(g)a(x	φ−1(g)a(x	NOUN
ejpam-3280	442	9	)	)	PUNCT
ejpam-3280	442	10	if	if	SCONJ
ejpam-3280	442	11	φ−1(v′	φ−1(v′	NOUN
ejpam-3280	442	12	)	)	PUNCT
ejpam-3280	442	13	6=	6=	ADP
ejpam-3280	442	14	∅	∅	NOUN
ejpam-3280	442	15	0	0	NUM
ejpam-3280	443	1	otherwise	otherwise	ADV
ejpam-3280	443	2	.	.	PUNCT
ejpam-3280	444	1	=	=	PUNCT
ejpam-3280	444	2			PUNCT
ejpam-3280	444	3	∨	∨	NUM
ejpam-3280	444	4	φ(x)=v′	φ(x)=v′	PROPN
ejpam-3280	444	5	∨	∨	NUM
ejpam-3280	444	6	a∈ψ−1(b)∩φ−1(b	a∈ψ−1(b)∩φ−1(b	NOUN
ejpam-3280	444	7	)	)	PUNCT
ejpam-3280	444	8	gψ(a)(φ(x	gψ(a)(φ(x	ADJ
ejpam-3280	444	9	)	)	PUNCT
ejpam-3280	444	10	)	)	PUNCT
ejpam-3280	445	1	if	if	SCONJ
ejpam-3280	445	2	φ−1(v′	φ−1(v′	NOUN
ejpam-3280	445	3	)	)	PUNCT
ejpam-3280	445	4	6=	6=	ADP
ejpam-3280	445	5	∅	∅	NOUN
ejpam-3280	445	6	0	0	NUM
ejpam-3280	445	7	otherwise	otherwise	ADV
ejpam-3280	445	8	.	.	PUNCT
ejpam-3280	446	1	≤	≤	ADJ
ejpam-3280	446	2	gψ(a)(v′	gψ(a)(v′	NOUN
ejpam-3280	446	3	)	)	PUNCT
ejpam-3280	446	4	=	=	SYM
ejpam-3280	446	5	gb(v	gb(v	NOUN
ejpam-3280	446	6	′	′	NOUN
ejpam-3280	446	7	)	)	PUNCT
ejpam-3280	446	8	.	.	PUNCT
ejpam-3280	447	1	hence	hence	ADV
ejpam-3280	447	2	,	,	PUNCT
ejpam-3280	447	3	for	for	ADP
ejpam-3280	447	4	all	all	DET
ejpam-3280	447	5	b	b	PROPN
ejpam-3280	447	6	∈	∈	PROPN
ejpam-3280	447	7	ψ(ψ−1(b	ψ(ψ−1(b	PROPN
ejpam-3280	447	8	)	)	PUNCT
ejpam-3280	447	9	)	)	PUNCT
ejpam-3280	447	10	,	,	PUNCT
ejpam-3280	447	11	we	we	PRON
ejpam-3280	447	12	have	have	VERB
ejpam-3280	447	13	φ(φ−1(g))b	φ(φ−1(g))b	NOUN
ejpam-3280	447	14	≤	≤	NOUN
ejpam-3280	447	15	gb	gb	PRON
ejpam-3280	447	16	.	.	PUNCT
ejpam-3280	448	1	therefore	therefore	ADV
ejpam-3280	448	2	,	,	PUNCT
ejpam-3280	448	3	(	(	PUNCT
ejpam-3280	448	4	φ	φ	NOUN
ejpam-3280	448	5	,	,	PUNCT
ejpam-3280	448	6	ψ)((φ	ψ)((φ	NOUN
ejpam-3280	448	7	,	,	PUNCT
ejpam-3280	448	8	ψ)−1(g	ψ)−1(g	NUM
ejpam-3280	448	9	,	,	PUNCT
ejpam-3280	448	10	b	b	NOUN
ejpam-3280	448	11	)	)	PUNCT
ejpam-3280	448	12	)	)	PUNCT
ejpam-3280	448	13	v	v	NOUN
ejpam-3280	448	14	(	(	PUNCT
ejpam-3280	448	15	g	g	PROPN
ejpam-3280	448	16	,	,	PUNCT
ejpam-3280	448	17	b	b	NOUN
ejpam-3280	448	18	)	)	PUNCT
ejpam-3280	448	19	.	.	PUNCT
ejpam-3280	449	1	in	in	ADP
ejpam-3280	449	2	particular	particular	ADJ
ejpam-3280	449	3	,	,	PUNCT
ejpam-3280	449	4	if	if	SCONJ
ejpam-3280	449	5	φ	φ	PROPN
ejpam-3280	449	6	and	and	CCONJ
ejpam-3280	449	7	ψ	ψ	PROPN
ejpam-3280	449	8	are	be	AUX
ejpam-3280	449	9	surjection	surjection	NOUN
ejpam-3280	449	10	,	,	PUNCT
ejpam-3280	449	11	then	then	ADV
ejpam-3280	449	12	(	(	PUNCT
ejpam-3280	449	13	φ	φ	NOUN
ejpam-3280	449	14	,	,	PUNCT
ejpam-3280	449	15	ψ)((φ	ψ)((φ	NOUN
ejpam-3280	449	16	,	,	PUNCT
ejpam-3280	449	17	ψ)−1(g	ψ)−1(g	NUM
ejpam-3280	449	18	,	,	PUNCT
ejpam-3280	449	19	b	b	NOUN
ejpam-3280	449	20	)	)	PUNCT
ejpam-3280	449	21	)	)	PUNCT
ejpam-3280	450	1	=	=	PRON
ejpam-3280	450	2	(	(	PUNCT
ejpam-3280	450	3	g	g	PROPN
ejpam-3280	450	4	,	,	PUNCT
ejpam-3280	450	5	b	b	NOUN
ejpam-3280	450	6	)	)	PUNCT
ejpam-3280	450	7	.	.	PUNCT
ejpam-3280	451	1	corollary	corollary	ADJ
ejpam-3280	451	2	2	2	NUM
ejpam-3280	451	3	.	.	PUNCT
ejpam-3280	452	1	let	let	VERB
ejpam-3280	452	2	v	v	NOUN
ejpam-3280	452	3	and	and	CCONJ
ejpam-3280	452	4	v	v	NOUN
ejpam-3280	452	5	′	′	NUM
ejpam-3280	452	6	be	be	AUX
ejpam-3280	452	7	two	two	NUM
ejpam-3280	452	8	hypervector	hypervector	NOUN
ejpam-3280	452	9	space	space	NOUN
ejpam-3280	452	10	over	over	ADP
ejpam-3280	452	11	a	a	DET
ejpam-3280	452	12	field	field	NOUN
ejpam-3280	452	13	k.	k.	NOUN
ejpam-3280	453	1	if	if	SCONJ
ejpam-3280	453	2	(	(	PUNCT
ejpam-3280	453	3	f	f	X
ejpam-3280	453	4	,	,	PUNCT
ejpam-3280	453	5	a	a	PRON
ejpam-3280	453	6	)	)	PUNCT
ejpam-3280	453	7	∈	∈	PROPN
ejpam-3280	453	8	f	f	X
ejpam-3280	453	9	ss	ss	PROPN
ejpam-3280	453	10	(	(	PUNCT
ejpam-3280	453	11	v	v	NOUN
ejpam-3280	453	12	,	,	PUNCT
ejpam-3280	453	13	e	e	NOUN
ejpam-3280	453	14	)	)	PUNCT
ejpam-3280	453	15	and	and	CCONJ
ejpam-3280	453	16	(	(	PUNCT
ejpam-3280	453	17	g	g	NOUN
ejpam-3280	453	18	,	,	PUNCT
ejpam-3280	453	19	b	b	NOUN
ejpam-3280	453	20	)	)	PUNCT
ejpam-3280	453	21	∈	∈	PROPN
ejpam-3280	453	22	f	f	X
ejpam-3280	453	23	ss	ss	PROPN
ejpam-3280	453	24	(	(	PUNCT
ejpam-3280	453	25	v	v	NOUN
ejpam-3280	453	26	′	′	NUM
ejpam-3280	453	27	,	,	PUNCT
ejpam-3280	453	28	e′	e′	ADJ
ejpam-3280	453	29	)	)	PUNCT
ejpam-3280	453	30	,	,	PUNCT
ejpam-3280	453	31	then	then	ADV
ejpam-3280	453	32	(	(	PUNCT
ejpam-3280	453	33	φ	φ	NOUN
ejpam-3280	453	34	,	,	PUNCT
ejpam-3280	453	35	ψ)(f	ψ)(f	NUM
ejpam-3280	453	36	,	,	PUNCT
ejpam-3280	453	37	a	a	PRON
ejpam-3280	453	38	)	)	PUNCT
ejpam-3280	453	39	v	v	NOUN
ejpam-3280	453	40	(	(	PUNCT
ejpam-3280	453	41	g	g	PROPN
ejpam-3280	453	42	,	,	PUNCT
ejpam-3280	453	43	b)⇔	b)⇔	PROPN
ejpam-3280	453	44	(	(	PUNCT
ejpam-3280	453	45	f	f	PROPN
ejpam-3280	453	46	,	,	PUNCT
ejpam-3280	453	47	a	a	PRON
ejpam-3280	453	48	)	)	PUNCT
ejpam-3280	453	49	v	v	NOUN
ejpam-3280	453	50	(	(	PUNCT
ejpam-3280	453	51	φ−1	φ−1	PROPN
ejpam-3280	453	52	,	,	PUNCT
ejpam-3280	453	53	ψ−1)(g	ψ−1)(g	PROPN
ejpam-3280	453	54	,	,	PUNCT
ejpam-3280	453	55	b	b	NOUN
ejpam-3280	453	56	)	)	PUNCT
ejpam-3280	453	57	.	.	PUNCT
ejpam-3280	454	1	acknowledgements	acknowledgement	NOUN
ejpam-3280	454	2	the	the	DET
ejpam-3280	454	3	authors	author	NOUN
ejpam-3280	454	4	are	be	AUX
ejpam-3280	454	5	highly	highly	ADV
ejpam-3280	454	6	grateful	grateful	ADJ
ejpam-3280	454	7	to	to	ADP
ejpam-3280	454	8	the	the	DET
ejpam-3280	454	9	anonymous	anonymous	ADJ
ejpam-3280	454	10	reviewers	reviewer	NOUN
ejpam-3280	454	11	and	and	CCONJ
ejpam-3280	454	12	the	the	DET
ejpam-3280	454	13	editor	editor	NOUN
ejpam-3280	454	14	in	in	ADP
ejpam-3280	454	15	chief	chief	ADJ
ejpam-3280	454	16	prof	prof	NOUN
ejpam-3280	454	17	.	.	PUNCT
ejpam-3280	455	1	eyup	eyup	NOUN
ejpam-3280	455	2	cetin	cetin	NOUN
ejpam-3280	455	3	for	for	ADP
ejpam-3280	455	4	their	their	PRON
ejpam-3280	455	5	helpful	helpful	ADJ
ejpam-3280	455	6	comments	comment	NOUN
ejpam-3280	455	7	and	and	CCONJ
ejpam-3280	455	8	suggestions	suggestion	NOUN
ejpam-3280	455	9	for	for	ADP
ejpam-3280	455	10	improving	improve	VERB
ejpam-3280	455	11	the	the	DET
ejpam-3280	455	12	paper	paper	NOUN
ejpam-3280	455	13	.	.	PUNCT
ejpam-3280	456	1	references	reference	NOUN
ejpam-3280	456	2	133	133	NUM
ejpam-3280	456	3	references	reference	NOUN
ejpam-3280	456	4	[	[	X
ejpam-3280	456	5	1	1	NUM
ejpam-3280	456	6	]	]	X
ejpam-3280	456	7	u	u	NOUN
ejpam-3280	456	8	acar	acar	VERB
ejpam-3280	456	9	,	,	PUNCT
ejpam-3280	456	10	f	f	PROPN
ejpam-3280	456	11	koyuncu	koyuncu	PROPN
ejpam-3280	456	12	and	and	CCONJ
ejpam-3280	456	13	b	b	PROPN
ejpam-3280	456	14	tanay	tanay	NOUN
ejpam-3280	456	15	.	.	PUNCT
ejpam-3280	457	1	soft	soft	ADJ
ejpam-3280	457	2	sets	set	NOUN
ejpam-3280	457	3	and	and	CCONJ
ejpam-3280	457	4	soft	soft	ADJ
ejpam-3280	457	5	rings	ring	NOUN
ejpam-3280	457	6	.	.	PUNCT
ejpam-3280	458	1	computers	computer	NOUN
ejpam-3280	458	2	mathematics	mathematic	NOUN
ejpam-3280	458	3	with	with	ADP
ejpam-3280	458	4	applications	application	NOUN
ejpam-3280	458	5	,	,	PUNCT
ejpam-3280	458	6	59(11):3458	59(11):3458	NUM
ejpam-3280	458	7	-	-	SYM
ejpam-3280	458	8	3463	3463	NUM
ejpam-3280	458	9	,	,	PUNCT
ejpam-3280	458	10	2010	2010	NUM
ejpam-3280	458	11	.	.	PUNCT
ejpam-3280	459	1	[	[	X
ejpam-3280	459	2	2	2	NUM
ejpam-3280	459	3	]	]	PUNCT
ejpam-3280	459	4	h	h	NOUN
ejpam-3280	459	5	aktas	akta	NOUN
ejpam-3280	459	6	and	and	CCONJ
ejpam-3280	459	7	n	n	PRON
ejpam-3280	459	8	cogman	cogman	NOUN
ejpam-3280	459	9	.	.	PUNCT
ejpam-3280	460	1	soft	soft	ADJ
ejpam-3280	460	2	sets	set	NOUN
ejpam-3280	460	3	and	and	CCONJ
ejpam-3280	460	4	soft	soft	ADJ
ejpam-3280	460	5	groups	group	NOUN
ejpam-3280	460	6	,	,	PUNCT
ejpam-3280	460	7	information	information	NOUN
ejpam-3280	460	8	sciences	science	NOUN
ejpam-3280	460	9	,	,	PUNCT
ejpam-3280	460	10	177(13):27262735	177(13):27262735	PROPN
ejpam-3280	460	11	,	,	PUNCT
ejpam-3280	460	12	2007	2007	NUM
ejpam-3280	460	13	.	.	PUNCT
ejpam-3280	461	1	[	[	X
ejpam-3280	461	2	3	3	NUM
ejpam-3280	461	3	]	]	X
ejpam-3280	461	4	r	r	NOUN
ejpam-3280	461	5	ameri	ameri	PROPN
ejpam-3280	461	6	.	.	PUNCT
ejpam-3280	462	1	fuzzy	fuzzy	ADJ
ejpam-3280	462	2	hypervector	hypervector	NOUN
ejpam-3280	462	3	spaces	space	NOUN
ejpam-3280	462	4	over	over	ADP
ejpam-3280	462	5	valued	value	VERB
ejpam-3280	462	6	fields	field	NOUN
ejpam-3280	462	7	.	.	PUNCT
ejpam-3280	463	1	iranian	iranian	ADJ
ejpam-3280	463	2	journal	journal	PROPN
ejpam-3280	463	3	of	of	ADP
ejpam-3280	463	4	fuzzy	fuzzy	ADJ
ejpam-3280	463	5	systems	system	NOUN
ejpam-3280	463	6	,	,	PUNCT
ejpam-3280	463	7	2(1):37	2(1):37	NUM
ejpam-3280	463	8	-	-	SYM
ejpam-3280	463	9	47	47	NUM
ejpam-3280	463	10	,	,	PUNCT
ejpam-3280	463	11	2005	2005	NUM
ejpam-3280	463	12	.	.	PUNCT
ejpam-3280	464	1	[	[	X
ejpam-3280	464	2	4	4	NUM
ejpam-3280	464	3	]	]	X
ejpam-3280	464	4	r	r	NOUN
ejpam-3280	464	5	ameri	ameri	NOUN
ejpam-3280	464	6	and	and	CCONJ
ejpam-3280	464	7	o	o	NOUN
ejpam-3280	464	8	r	r	NOUN
ejpam-3280	464	9	dehghan	dehghan	NOUN
ejpam-3280	464	10	.	.	PUNCT
ejpam-3280	465	1	on	on	ADP
ejpam-3280	465	2	dimension	dimension	NOUN
ejpam-3280	465	3	of	of	ADP
ejpam-3280	465	4	hypervector	hypervector	NOUN
ejpam-3280	465	5	spaces	space	NOUN
ejpam-3280	465	6	,	,	PUNCT
ejpam-3280	465	7	european	european	PROPN
ejpam-3280	465	8	journal	journal	PROPN
ejpam-3280	465	9	of	of	ADP
ejpam-3280	465	10	pure	pure	ADJ
ejpam-3280	465	11	and	and	CCONJ
ejpam-3280	465	12	applied	applied	ADJ
ejpam-3280	465	13	mathematics	mathematic	NOUN
ejpam-3280	465	14	,	,	PUNCT
ejpam-3280	465	15	1(2):32	1(2):32	NOUN
ejpam-3280	465	16	-	-	PUNCT
ejpam-3280	465	17	50	50	NUM
ejpam-3280	465	18	,	,	PUNCT
ejpam-3280	465	19	2008	2008	NUM
ejpam-3280	465	20	.	.	PUNCT
ejpam-3280	466	1	[	[	X
ejpam-3280	466	2	5	5	NUM
ejpam-3280	466	3	]	]	X
ejpam-3280	466	4	r	r	NOUN
ejpam-3280	466	5	ameri	ameri	PROPN
ejpam-3280	466	6	,	,	PUNCT
ejpam-3280	466	7	m	m	VERB
ejpam-3280	466	8	norouzi	norouzi	VERB
ejpam-3280	466	9	and	and	CCONJ
ejpam-3280	466	10	h	h	PROPN
ejpam-3280	466	11	hedayati	hedayati	PROPN
ejpam-3280	466	12	.	.	PUNCT
ejpam-3280	467	1	application	application	NOUN
ejpam-3280	467	2	of	of	ADP
ejpam-3280	467	3	fuzzy	fuzzy	ADJ
ejpam-3280	467	4	sets	set	NOUN
ejpam-3280	467	5	and	and	CCONJ
ejpam-3280	467	6	fuzzy	fuzzy	ADJ
ejpam-3280	467	7	soft	soft	ADJ
ejpam-3280	467	8	sets	set	NOUN
ejpam-3280	467	9	in	in	ADP
ejpam-3280	467	10	hypermodules	hypermodule	NOUN
ejpam-3280	467	11	,	,	PUNCT
ejpam-3280	467	12	revista	revista	PROPN
ejpam-3280	467	13	de	de	X
ejpam-3280	467	14	la	la	PROPN
ejpam-3280	467	15	real	real	PROPN
ejpam-3280	467	16	academia	academia	PROPN
ejpam-3280	467	17	de	de	PROPN
ejpam-3280	467	18	ciencias	ciencias	PROPN
ejpam-3280	467	19	exactas	exacta	NOUN
ejpam-3280	467	20	,	,	PUNCT
ejpam-3280	467	21	fisicas	fisicas	PROPN
ejpam-3280	467	22	y	y	PROPN
ejpam-3280	467	23	naturales	naturales	PROPN
ejpam-3280	467	24	.	.	PUNCT
ejpam-3280	468	1	serie	serie	PROPN
ejpam-3280	468	2	a.	a.	PROPN
ejpam-3280	468	3	matematicas	matematicas	PROPN
ejpam-3280	468	4	,	,	PUNCT
ejpam-3280	468	5	107(2):327	107(2):327	NUM
ejpam-3280	468	6	-	-	SYM
ejpam-3280	468	7	338	338	NUM
ejpam-3280	468	8	,	,	PUNCT
ejpam-3280	468	9	2013	2013	NUM
ejpam-3280	468	10	.	.	PUNCT
ejpam-3280	469	1	[	[	X
ejpam-3280	469	2	6	6	NUM
ejpam-3280	469	3	]	]	PUNCT
ejpam-3280	469	4	m	m	VERB
ejpam-3280	469	5	asghari	asghari	ADV
ejpam-3280	469	6	-	-	PUNCT
ejpam-3280	469	7	larimi	larimi	PROPN
ejpam-3280	469	8	and	and	CCONJ
ejpam-3280	469	9	e.	e.	PROPN
ejpam-3280	469	10	ranjbar	ranjbar	PROPN
ejpam-3280	469	11	-	-	PUNCT
ejpam-3280	469	12	yanehsari	yanehsari	PROPN
ejpam-3280	469	13	.	.	PUNCT
ejpam-3280	470	1	a	a	DET
ejpam-3280	470	2	new	new	ADJ
ejpam-3280	470	3	view	view	NOUN
ejpam-3280	470	4	of	of	ADP
ejpam-3280	470	5	fuzzy	fuzzy	ADJ
ejpam-3280	470	6	vector	vector	NOUN
ejpam-3280	470	7	space	space	NOUN
ejpam-3280	470	8	over	over	ADP
ejpam-3280	470	9	fuzzy	fuzzy	ADJ
ejpam-3280	470	10	field	field	NOUN
ejpam-3280	470	11	,	,	PUNCT
ejpam-3280	470	12	jordan	jordan	PROPN
ejpam-3280	470	13	journal	journal	PROPN
ejpam-3280	470	14	of	of	ADP
ejpam-3280	470	15	mathematics	mathematics	PROPN
ejpam-3280	470	16	and	and	CCONJ
ejpam-3280	470	17	statistics	statistic	NOUN
ejpam-3280	470	18	,	,	PUNCT
ejpam-3280	470	19	2018	2018	NUM
ejpam-3280	470	20	,	,	PUNCT
ejpam-3280	470	21	accepted	accept	VERB
ejpam-3280	470	22	for	for	ADP
ejpam-3280	470	23	publication	publication	NOUN
ejpam-3280	470	24	.	.	PUNCT
ejpam-3280	471	1	[	[	X
ejpam-3280	471	2	7	7	X
ejpam-3280	471	3	]	]	X
ejpam-3280	471	4	p	p	X
ejpam-3280	471	5	corsini	corsini	NOUN
ejpam-3280	471	6	and	and	CCONJ
ejpam-3280	471	7	v	v	ADP
ejpam-3280	471	8	leoreanu	leoreanu	NOUN
ejpam-3280	471	9	.	.	PUNCT
ejpam-3280	472	1	applications	application	NOUN
ejpam-3280	472	2	of	of	ADP
ejpam-3280	472	3	hyperstructure	hyperstructure	PROPN
ejpam-3280	472	4	theory	theory	NOUN
ejpam-3280	472	5	(	(	PUNCT
ejpam-3280	472	6	vol	vol	NOUN
ejpam-3280	472	7	.	.	PROPN
ejpam-3280	472	8	5	5	NUM
ejpam-3280	472	9	)	)	PUNCT
ejpam-3280	472	10	,	,	PUNCT
ejpam-3280	472	11	springer	springer	NOUN
ejpam-3280	472	12	science	science	NOUN
ejpam-3280	472	13	business	business	NOUN
ejpam-3280	472	14	media	medium	NOUN
ejpam-3280	472	15	,	,	PUNCT
ejpam-3280	472	16	2013	2013	NUM
ejpam-3280	472	17	.	.	PUNCT
ejpam-3280	473	1	[	[	X
ejpam-3280	473	2	8	8	NUM
ejpam-3280	473	3	]	]	X
ejpam-3280	473	4	y	y	PROPN
ejpam-3280	473	5	b	b	PROPN
ejpam-3280	473	6	jun	jun	PROPN
ejpam-3280	473	7	,	,	PUNCT
ejpam-3280	473	8	k	k	PROPN
ejpam-3280	473	9	j	j	PROPN
ejpam-3280	473	10	lee	lee	PROPN
ejpam-3280	473	11	and	and	CCONJ
ejpam-3280	473	12	c	c	PROPN
ejpam-3280	473	13	h	h	PROPN
ejpam-3280	473	14	park	park	PROPN
ejpam-3280	473	15	.	.	PUNCT
ejpam-3280	474	1	soft	soft	ADJ
ejpam-3280	474	2	set	set	ADJ
ejpam-3280	474	3	theory	theory	NOUN
ejpam-3280	474	4	applied	apply	VERB
ejpam-3280	474	5	to	to	ADP
ejpam-3280	474	6	ideals	ideal	NOUN
ejpam-3280	474	7	in	in	ADP
ejpam-3280	474	8	d	d	NOUN
ejpam-3280	474	9	-	-	PUNCT
ejpam-3280	474	10	algebras	algebra	NOUN
ejpam-3280	474	11	.	.	PUNCT
ejpam-3280	475	1	computers	computer	NOUN
ejpam-3280	475	2	mathematics	mathematic	NOUN
ejpam-3280	475	3	with	with	ADP
ejpam-3280	475	4	applications	application	NOUN
ejpam-3280	475	5	,	,	PUNCT
ejpam-3280	475	6	57(3):367	57(3):367	PROPN
ejpam-3280	475	7	-	-	SYM
ejpam-3280	475	8	378	378	NUM
ejpam-3280	475	9	,	,	PUNCT
ejpam-3280	475	10	2009	2009	NUM
ejpam-3280	475	11	.	.	PUNCT
ejpam-3280	476	1	[	[	X
ejpam-3280	476	2	9	9	NUM
ejpam-3280	476	3	]	]	SYM
ejpam-3280	476	4	v	v	PRON
ejpam-3280	476	5	leoreanu	leoreanu	NOUN
ejpam-3280	476	6	-	-	PUNCT
ejpam-3280	476	7	fotea	fotea	NOUN
ejpam-3280	476	8	and	and	CCONJ
ejpam-3280	476	9	p	p	NOUN
ejpam-3280	476	10	corsini	corsini	PROPN
ejpam-3280	476	11	.	.	PUNCT
ejpam-3280	477	1	soft	soft	ADJ
ejpam-3280	477	2	hypergroups	hypergroup	NOUN
ejpam-3280	477	3	,	,	PUNCT
ejpam-3280	477	4	critical	critical	ADJ
ejpam-3280	477	5	review	review	NOUN
ejpam-3280	477	6	,	,	PUNCT
ejpam-3280	477	7	vol	vol	NOUN
ejpam-3280	477	8	.	.	PUNCT
ejpam-3280	478	1	iv	iv	NUM
ejpam-3280	478	2	.	.	PUNCT
ejpam-3280	478	3	center	center	NOUN
ejpam-3280	478	4	for	for	ADP
ejpam-3280	478	5	mathemativs	mathemativs	ADJ
ejpam-3280	478	6	of	of	ADP
ejpam-3280	478	7	uncertianty	uncertianty	NOUN
ejpam-3280	478	8	,	,	PUNCT
ejpam-3280	478	9	creighton	creighton	PROPN
ejpam-3280	478	10	university	university	PROPN
ejpam-3280	478	11	,	,	PUNCT
ejpam-3280	478	12	2010	2010	NUM
ejpam-3280	478	13	.	.	PUNCT
ejpam-3280	479	1	[	[	X
ejpam-3280	479	2	10	10	NUM
ejpam-3280	479	3	]	]	SYM
ejpam-3280	479	4	v	v	PRON
ejpam-3280	479	5	leoreanu	leoreanu	NOUN
ejpam-3280	479	6	-	-	PUNCT
ejpam-3280	479	7	fotea	fotea	NOUN
ejpam-3280	479	8	,	,	PUNCT
ejpam-3280	479	9	f	f	PROPN
ejpam-3280	479	10	feng	feng	PROPN
ejpam-3280	479	11	and	and	CCONJ
ejpam-3280	479	12	j	j	PROPN
ejpam-3280	479	13	zhan	zhan	PROPN
ejpam-3280	479	14	.	.	PUNCT
ejpam-3280	480	1	fuzzy	fuzzy	ADJ
ejpam-3280	480	2	soft	soft	ADJ
ejpam-3280	480	3	hypergroups	hypergroup	NOUN
ejpam-3280	480	4	,	,	PUNCT
ejpam-3280	480	5	international	international	ADJ
ejpam-3280	480	6	journal	journal	NOUN
ejpam-3280	480	7	of	of	ADP
ejpam-3280	480	8	computer	computer	NOUN
ejpam-3280	480	9	mathematics	mathematic	NOUN
ejpam-3280	480	10	,	,	PUNCT
ejpam-3280	480	11	89(8):963	89(8):963	NUM
ejpam-3280	480	12	-	-	SYM
ejpam-3280	480	13	974	974	NUM
ejpam-3280	480	14	,	,	PUNCT
ejpam-3280	480	15	2012	2012	NUM
ejpam-3280	480	16	.	.	PUNCT
ejpam-3280	481	1	[	[	X
ejpam-3280	481	2	11	11	NUM
ejpam-3280	481	3	]	]	X
ejpam-3280	481	4	p	p	X
ejpam-3280	481	5	k	k	PROPN
ejpam-3280	481	6	maji	maji	PROPN
ejpam-3280	481	7	,	,	PUNCT
ejpam-3280	481	8	r	r	NOUN
ejpam-3280	481	9	biswas	biswas	PROPN
ejpam-3280	481	10	and	and	CCONJ
ejpam-3280	481	11	a	a	DET
ejpam-3280	481	12	roy	roy	PROPN
ejpam-3280	481	13	.	.	PROPN
ejpam-3280	481	14	soft	soft	ADJ
ejpam-3280	481	15	set	set	NOUN
ejpam-3280	481	16	theory	theory	NOUN
ejpam-3280	481	17	.	.	PUNCT
ejpam-3280	482	1	computers	computer	NOUN
ejpam-3280	482	2	mathematics	mathematic	NOUN
ejpam-3280	482	3	with	with	ADP
ejpam-3280	482	4	applications	application	NOUN
ejpam-3280	482	5	,	,	PUNCT
ejpam-3280	482	6	45(4	45(4	NUM
ejpam-3280	482	7	-	-	PUNCT
ejpam-3280	482	8	5):555	5):555	NUM
ejpam-3280	482	9	-	-	PUNCT
ejpam-3280	482	10	562	562	NUM
ejpam-3280	482	11	,	,	PUNCT
ejpam-3280	482	12	2003	2003	NUM
ejpam-3280	482	13	.	.	PUNCT
ejpam-3280	483	1	[	[	X
ejpam-3280	483	2	12	12	NUM
ejpam-3280	483	3	]	]	X
ejpam-3280	483	4	p	p	X
ejpam-3280	483	5	k	k	PROPN
ejpam-3280	483	6	maji	maji	PROPN
ejpam-3280	483	7	,	,	PUNCT
ejpam-3280	483	8	r	r	NOUN
ejpam-3280	483	9	biswas	biswas	PROPN
ejpam-3280	483	10	and	and	CCONJ
ejpam-3280	483	11	a	a	DET
ejpam-3280	483	12	r	r	NOUN
ejpam-3280	483	13	roy	roy	PROPN
ejpam-3280	483	14	.	.	PROPN
ejpam-3280	483	15	fuzzy	fuzzy	ADJ
ejpam-3280	483	16	soft	soft	ADJ
ejpam-3280	483	17	sets	set	NOUN
ejpam-3280	483	18	,	,	PUNCT
ejpam-3280	483	19	journal	journal	NOUN
ejpam-3280	483	20	of	of	ADP
ejpam-3280	483	21	fuzzy	fuzzy	ADJ
ejpam-3280	483	22	mathematics	mathematic	NOUN
ejpam-3280	483	23	,	,	PUNCT
ejpam-3280	483	24	9(3):589	9(3):589	NUM
ejpam-3280	483	25	-	-	SYM
ejpam-3280	483	26	602	602	NUM
ejpam-3280	483	27	,	,	PUNCT
ejpam-3280	483	28	2001	2001	NUM
ejpam-3280	483	29	.	.	PUNCT
ejpam-3280	484	1	[	[	X
ejpam-3280	484	2	13	13	NUM
ejpam-3280	484	3	]	]	X
ejpam-3280	484	4	p	p	PROPN
ejpam-3280	484	5	majumdar	majumdar	PROPN
ejpam-3280	484	6	and	and	CCONJ
ejpam-3280	484	7	s	s	PROPN
ejpam-3280	484	8	k	k	PROPN
ejpam-3280	484	9	samanta	samanta	PROPN
ejpam-3280	484	10	.	.	PUNCT
ejpam-3280	485	1	generalized	generalize	VERB
ejpam-3280	485	2	fuzzy	fuzzy	ADJ
ejpam-3280	485	3	soft	soft	ADJ
ejpam-3280	485	4	sets	set	NOUN
ejpam-3280	485	5	.	.	PUNCT
ejpam-3280	486	1	computers	computer	NOUN
ejpam-3280	486	2	mathematics	mathematic	NOUN
ejpam-3280	486	3	with	with	ADP
ejpam-3280	486	4	applications	application	NOUN
ejpam-3280	486	5	,	,	PUNCT
ejpam-3280	486	6	59(4):1425	59(4):1425	NUM
ejpam-3280	486	7	-	-	SYM
ejpam-3280	486	8	1432	1432	NUM
ejpam-3280	486	9	,	,	PUNCT
ejpam-3280	486	10	2010	2010	NUM
ejpam-3280	486	11	.	.	PUNCT
ejpam-3280	487	1	[	[	X
ejpam-3280	487	2	14	14	NUM
ejpam-3280	487	3	]	]	X
ejpam-3280	487	4	f	f	PROPN
ejpam-3280	487	5	marty	marty	PROPN
ejpam-3280	487	6	.	.	PUNCT
ejpam-3280	488	1	sur	sur	PROPN
ejpam-3280	488	2	une	une	PROPN
ejpam-3280	488	3	generalization	generalization	PROPN
ejpam-3280	488	4	de	de	X
ejpam-3280	488	5	la	la	PROPN
ejpam-3280	488	6	notion	notion	PROPN
ejpam-3280	488	7	de	de	X
ejpam-3280	488	8	groupe	groupe	PROPN
ejpam-3280	488	9	,	,	PUNCT
ejpam-3280	488	10	8th	8th	ADJ
ejpam-3280	488	11	congress	congress	PROPN
ejpam-3280	488	12	math	math	NOUN
ejpam-3280	488	13	.	.	PUNCT
ejpam-3280	489	1	scandenaves	scandenave	NOUN
ejpam-3280	489	2	,	,	PUNCT
ejpam-3280	489	3	stockholm	stockholm	PROPN
ejpam-3280	489	4	,	,	PUNCT
ejpam-3280	489	5	45	45	NUM
ejpam-3280	489	6	-	-	SYM
ejpam-3280	489	7	49	49	NUM
ejpam-3280	489	8	,	,	PUNCT
ejpam-3280	489	9	1934	1934	NUM
ejpam-3280	489	10	.	.	PUNCT
ejpam-3280	490	1	[	[	X
ejpam-3280	490	2	15	15	NUM
ejpam-3280	490	3	]	]	X
ejpam-3280	490	4	d	d	X
ejpam-3280	490	5	molodtsov	molodtsov	PROPN
ejpam-3280	490	6	.	.	PUNCT
ejpam-3280	491	1	soft	soft	ADJ
ejpam-3280	491	2	set	set	NOUN
ejpam-3280	491	3	theory	theory	NOUN
ejpam-3280	491	4	-	-	PUNCT
ejpam-3280	491	5	first	first	ADJ
ejpam-3280	491	6	results	result	NOUN
ejpam-3280	491	7	.	.	PUNCT
ejpam-3280	492	1	computers	computer	NOUN
ejpam-3280	492	2	mathematics	mathematic	NOUN
ejpam-3280	492	3	with	with	ADP
ejpam-3280	492	4	applications	application	NOUN
ejpam-3280	492	5	,	,	PUNCT
ejpam-3280	492	6	37(4	37(4	PROPN
ejpam-3280	492	7	-	-	PUNCT
ejpam-3280	492	8	5):19	5):19	NUM
ejpam-3280	492	9	-	-	SYM
ejpam-3280	492	10	31	31	NUM
ejpam-3280	492	11	,	,	PUNCT
ejpam-3280	492	12	1999	1999	NUM
ejpam-3280	492	13	.	.	PUNCT
ejpam-3280	493	1	references	reference	NOUN
ejpam-3280	493	2	134	134	NUM
ejpam-3280	494	1	[	[	X
ejpam-3280	494	2	16	16	NUM
ejpam-3280	494	3	]	]	X
ejpam-3280	494	4	m	m	NOUN
ejpam-3280	494	5	davender	davender	NOUN
ejpam-3280	494	6	and	and	CCONJ
ejpam-3280	494	7	j	j	PROPN
ejpam-3280	494	8	mordeson	mordeson	NOUN
ejpam-3280	494	9	.	.	PUNCT
ejpam-3280	495	1	fuzzy	fuzzy	ADJ
ejpam-3280	495	2	commutative	commutative	ADJ
ejpam-3280	495	3	algebra	algebra	NOUN
ejpam-3280	495	4	,	,	PUNCT
ejpam-3280	495	5	world	world	NOUN
ejpam-3280	495	6	sceintific	sceintific	PROPN
ejpam-3280	495	7	publishing	publishing	PROPN
ejpam-3280	495	8	co.	co.	PROPN
ejpam-3280	495	9	,	,	PUNCT
ejpam-3280	495	10	1998	1998	NUM
ejpam-3280	495	11	.	.	PUNCT
ejpam-3280	496	1	[	[	X
ejpam-3280	496	2	17	17	NUM
ejpam-3280	496	3	]	]	X
ejpam-3280	496	4	e	e	X
ejpam-3280	496	5	k	k	PROPN
ejpam-3280	496	6	r	r	NOUN
ejpam-3280	496	7	nagarajan	nagarajan	NOUN
ejpam-3280	496	8	and	and	CCONJ
ejpam-3280	496	9	g	g	PROPN
ejpam-3280	496	10	meenambigai	meenambigai	PROPN
ejpam-3280	496	11	.	.	PUNCT
ejpam-3280	497	1	an	an	DET
ejpam-3280	497	2	application	application	NOUN
ejpam-3280	497	3	of	of	ADP
ejpam-3280	497	4	soft	soft	ADJ
ejpam-3280	497	5	sets	set	NOUN
ejpam-3280	497	6	to	to	ADP
ejpam-3280	497	7	lattices	lattice	NOUN
ejpam-3280	497	8	.	.	PUNCT
ejpam-3280	498	1	kragujevac	kragujevac	PROPN
ejpam-3280	498	2	journal	journal	PROPN
ejpam-3280	498	3	of	of	ADP
ejpam-3280	498	4	mathematics	mathematic	NOUN
ejpam-3280	498	5	,	,	PUNCT
ejpam-3280	498	6	35(35):75	35(35):75	NUM
ejpam-3280	498	7	-	-	SYM
ejpam-3280	498	8	87	87	NUM
ejpam-3280	498	9	,	,	PUNCT
ejpam-3280	498	10	2011	2011	NUM
ejpam-3280	498	11	.	.	PUNCT
ejpam-3280	499	1	[	[	X
ejpam-3280	499	2	18	18	NUM
ejpam-3280	499	3	]	]	X
ejpam-3280	499	4	q	q	X
ejpam-3280	499	5	m	m	PROPN
ejpam-3280	499	6	sun	sun	NOUN
ejpam-3280	499	7	,	,	PUNCT
ejpam-3280	499	8	z	z	PROPN
ejpam-3280	499	9	l	l	PROPN
ejpam-3280	499	10	zhang	zhang	PROPN
ejpam-3280	499	11	and	and	CCONJ
ejpam-3280	499	12	j	j	PROPN
ejpam-3280	499	13	liu	liu	PROPN
ejpam-3280	499	14	.	.	PROPN
ejpam-3280	499	15	soft	soft	ADJ
ejpam-3280	499	16	sets	set	NOUN
ejpam-3280	499	17	and	and	CCONJ
ejpam-3280	499	18	soft	soft	ADJ
ejpam-3280	499	19	modules	module	NOUN
ejpam-3280	499	20	,	,	PUNCT
ejpam-3280	499	21	rough	rough	ADJ
ejpam-3280	499	22	sets	set	NOUN
ejpam-3280	499	23	and	and	CCONJ
ejpam-3280	499	24	knowledge	knowledge	NOUN
ejpam-3280	499	25	technology	technology	NOUN
ejpam-3280	499	26	,	,	PUNCT
ejpam-3280	499	27	403	403	NUM
ejpam-3280	499	28	-	-	SYM
ejpam-3280	499	29	409	409	NUM
ejpam-3280	499	30	,	,	PUNCT
ejpam-3280	499	31	2008	2008	NUM
ejpam-3280	499	32	.	.	PUNCT
ejpam-3280	500	1	[	[	X
ejpam-3280	500	2	19	19	NUM
ejpam-3280	500	3	]	]	PUNCT
ejpam-3280	500	4	a	a	DET
ejpam-3280	500	5	rosenfeld	rosenfeld	PROPN
ejpam-3280	500	6	.	.	PUNCT
ejpam-3280	501	1	fuzzy	fuzzy	ADJ
ejpam-3280	501	2	groups	group	NOUN
ejpam-3280	501	3	.	.	PUNCT
ejpam-3280	502	1	journal	journal	PROPN
ejpam-3280	502	2	of	of	ADP
ejpam-3280	502	3	mathematical	mathematical	ADJ
ejpam-3280	502	4	analysis	analysis	NOUN
ejpam-3280	502	5	and	and	CCONJ
ejpam-3280	502	6	applications	application	NOUN
ejpam-3280	502	7	,	,	PUNCT
ejpam-3280	502	8	35(3):512	35(3):512	PROPN
ejpam-3280	502	9	-	-	SYM
ejpam-3280	502	10	517	517	NUM
ejpam-3280	502	11	,	,	PUNCT
ejpam-3280	502	12	1971	1971	NUM
ejpam-3280	502	13	.	.	PUNCT
ejpam-3280	503	1	[	[	X
ejpam-3280	503	2	20	20	NUM
ejpam-3280	503	3	]	]	X
ejpam-3280	503	4	y	y	PROPN
ejpam-3280	503	5	shao	shao	PROPN
ejpam-3280	503	6	and	and	CCONJ
ejpam-3280	503	7	k	k	PROPN
ejpam-3280	503	8	qin	qin	PROPN
ejpam-3280	503	9	.	.	PROPN
ejpam-3280	503	10	fuzzy	fuzzy	ADJ
ejpam-3280	503	11	soft	soft	ADJ
ejpam-3280	503	12	sets	set	NOUN
ejpam-3280	503	13	and	and	CCONJ
ejpam-3280	503	14	fuzzy	fuzzy	ADJ
ejpam-3280	503	15	soft	soft	ADJ
ejpam-3280	503	16	lattices	lattice	NOUN
ejpam-3280	503	17	,	,	PUNCT
ejpam-3280	503	18	international	international	ADJ
ejpam-3280	503	19	journal	journal	NOUN
ejpam-3280	503	20	of	of	ADP
ejpam-3280	503	21	computational	computational	ADJ
ejpam-3280	503	22	intelligence	intelligence	NOUN
ejpam-3280	503	23	systems	system	NOUN
ejpam-3280	503	24	,	,	PUNCT
ejpam-3280	503	25	5(6):1135	5(6):1135	NUM
ejpam-3280	503	26	-	-	SYM
ejpam-3280	503	27	1147	1147	NUM
ejpam-3280	503	28	,	,	PUNCT
ejpam-3280	503	29	2012	2012	NUM
ejpam-3280	503	30	.	.	PUNCT
ejpam-3280	504	1	[	[	X
ejpam-3280	504	2	21	21	NUM
ejpam-3280	504	3	]	]	X
ejpam-3280	504	4	m	m	PROPN
ejpam-3280	504	5	s	s	NOUN
ejpam-3280	504	6	tallini	tallini	PROPN
ejpam-3280	504	7	.	.	PUNCT
ejpam-3280	504	8	matroidal	matroidal	ADJ
ejpam-3280	504	9	hypervector	hypervector	NOUN
ejpam-3280	504	10	spaces	space	NOUN
ejpam-3280	504	11	,	,	PUNCT
ejpam-3280	504	12	journal	journal	NOUN
ejpam-3280	504	13	of	of	ADP
ejpam-3280	504	14	geometry	geometry	NOUN
ejpam-3280	504	15	,	,	PUNCT
ejpam-3280	504	16	42(1):132	42(1):132	NUM
ejpam-3280	504	17	-	-	PUNCT
ejpam-3280	504	18	140	140	NUM
ejpam-3280	504	19	,	,	PUNCT
ejpam-3280	504	20	1991	1991	NUM
ejpam-3280	504	21	.	.	PUNCT
ejpam-3280	505	1	[	[	X
ejpam-3280	505	2	22	22	NUM
ejpam-3280	505	3	]	]	PUNCT
ejpam-3280	505	4	l	l	NOUN
ejpam-3280	506	1	a	a	DET
ejpam-3280	506	2	zadeh	zadeh	PROPN
ejpam-3280	506	3	.	.	PUNCT
ejpam-3280	506	4	information	information	NOUN
ejpam-3280	506	5	and	and	CCONJ
ejpam-3280	506	6	control	control	NOUN
ejpam-3280	506	7	,	,	PUNCT
ejpam-3280	506	8	fuzzy	fuzzy	ADJ
ejpam-3280	506	9	sets	set	NOUN
ejpam-3280	506	10	,	,	PUNCT
ejpam-3280	506	11	8(3):338	8(3):338	NUM
ejpam-3280	506	12	-	-	SYM
ejpam-3280	506	13	353	353	NUM
ejpam-3280	506	14	,	,	PUNCT
ejpam-3280	506	15	1965	1965	NUM
ejpam-3280	506	16	.	.	PUNCT