id	sid	tid	token	lemma	pos
cana-3299	1	1	communications	communication	NOUN
cana-3299	1	2	on	on	ADP
cana-3299	1	3	applied	apply	VERB
cana-3299	1	4	nonlinear	nonlinear	ADJ
cana-3299	1	5	analysis	analysis	NOUN
cana-3299	1	6	issn	issn	NOUN
cana-3299	1	7	:	:	PUNCT
cana-3299	1	8	1074	1074	NUM
cana-3299	1	9	-	-	PUNCT
cana-3299	1	10	133x	133x	NUM
cana-3299	1	11	vol	vol	NOUN
cana-3299	1	12	32	32	NUM
cana-3299	1	13	no	no	NOUN
cana-3299	1	14	.	.	PUNCT
cana-3299	2	1	6s	6s	NUM
cana-3299	2	2	(	(	PUNCT
cana-3299	2	3	2025	2025	NUM
cana-3299	2	4	)	)	PUNCT
cana-3299	2	5	327	327	NUM
cana-3299	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	3	1	contra	contra	PROPN
cana-3299	3	2	𝑴-continuous	𝑴-continuous	PROPN
cana-3299	3	3	maps	map	NOUN
cana-3299	3	4	in	in	ADP
cana-3299	3	5	pythagorean	pythagorean	PROPN
cana-3299	3	6	fuzzy	fuzzy	ADJ
cana-3299	3	7	topological	topological	PROPN
cana-3299	3	8	spaces	space	NOUN
cana-3299	3	9	b.	b.	PROPN
cana-3299	3	10	vijayalakshmi	vijayalakshmi	PROPN
cana-3299	3	11	𝟏	𝟏	NUM
cana-3299	3	12	,	,	PUNCT
cana-3299	3	13	m.	m.	NOUN
cana-3299	3	14	ramalakshmi	ramalakshmi	NOUN
cana-3299	3	15	𝟐	𝟐	NUM
cana-3299	3	16	,	,	PUNCT
cana-3299	3	17	a.	a.	NOUN
cana-3299	3	18	vadivel	vadivel	NOUN
cana-3299	3	19	𝟑	𝟑	NUM
cana-3299	3	20	and	and	CCONJ
cana-3299	3	21	g.	g.	PROPN
cana-3299	3	22	saravanakumar4	saravanakumar4	PROPN
cana-3299	4	1	1department	1department	NUM
cana-3299	4	2	of	of	ADP
cana-3299	4	3	mathematics	mathematic	NOUN
cana-3299	4	4	,	,	PUNCT
cana-3299	4	5	government	government	NOUN
cana-3299	4	6	arts	arts	PROPN
cana-3299	4	7	college	college	PROPN
cana-3299	4	8	,	,	PUNCT
cana-3299	4	9	chidambaram	chidambaram	PROPN
cana-3299	4	10	,	,	PUNCT
cana-3299	4	11	tamil	tamil	PROPN
cana-3299	4	12	nadu-608	nadu-608	NOUN
cana-3299	4	13	102	102	NUM
cana-3299	4	14	;	;	PUNCT
cana-3299	4	15	mathematics	mathematic	NOUN
cana-3299	4	16	section	section	NOUN
cana-3299	4	17	(	(	PUNCT
cana-3299	4	18	feat	feat	PROPN
cana-3299	4	19	)	)	PUNCT
cana-3299	4	20	,	,	PUNCT
cana-3299	4	21	annamalai	annamalai	PROPN
cana-3299	4	22	university	university	PROPN
cana-3299	4	23	,	,	PUNCT
cana-3299	4	24	annamalai	annamalai	PROPN
cana-3299	4	25	nagar	nagar	VERB
cana-3299	4	26	608	608	NUM
cana-3299	4	27	002	002	NUM
cana-3299	4	28	,	,	PUNCT
cana-3299	4	29	tamilnadu	tamilnadu	NOUN
cana-3299	4	30	.	.	PUNCT
cana-3299	5	1	2department	2department	NUM
cana-3299	5	2	of	of	ADP
cana-3299	5	3	mathematics	mathematic	NOUN
cana-3299	5	4	,	,	PUNCT
cana-3299	5	5	sri	sri	PROPN
cana-3299	5	6	meenakshi	meenakshi	PROPN
cana-3299	5	7	government	government	PROPN
cana-3299	5	8	arts	arts	PROPN
cana-3299	5	9	college	college	PROPN
cana-3299	5	10	for	for	ADP
cana-3299	5	11	women	woman	NOUN
cana-3299	5	12	(	(	PUNCT
cana-3299	5	13	a	a	X
cana-3299	5	14	)	)	PUNCT
cana-3299	5	15	,	,	PUNCT
cana-3299	5	16	madurai625	madurai625	PROPN
cana-3299	5	17	002	002	NUM
cana-3299	5	18	3	3	NUM
cana-3299	5	19	arignar	arignar	NOUN
cana-3299	5	20	anna	anna	NOUN
cana-3299	5	21	government	government	PROPN
cana-3299	5	22	arts	arts	PROPN
cana-3299	5	23	college	college	PROPN
cana-3299	5	24	,	,	PUNCT
cana-3299	5	25	namakkal	namakkal	NOUN
cana-3299	5	26	637	637	NUM
cana-3299	5	27	002	002	NUM
cana-3299	5	28	,	,	PUNCT
cana-3299	5	29	india	india	PROPN
cana-3299	5	30	.	.	PUNCT
cana-3299	6	1	2,3department	2,3department	NUM
cana-3299	6	2	of	of	ADP
cana-3299	6	3	mathematics	mathematic	NOUN
cana-3299	6	4	,	,	PUNCT
cana-3299	6	5	annamalai	annamalai	PROPN
cana-3299	6	6	university	university	PROPN
cana-3299	6	7	,	,	PUNCT
cana-3299	6	8	annamalai	annamalai	PROPN
cana-3299	6	9	nagar	nagar	VERB
cana-3299	6	10	608	608	NUM
cana-3299	6	11	002	002	NUM
cana-3299	6	12	,	,	PUNCT
cana-3299	6	13	india	india	PROPN
cana-3299	6	14	.	.	PUNCT
cana-3299	7	1	4department	4department	NUM
cana-3299	7	2	of	of	ADP
cana-3299	7	3	mathematics	mathematic	NOUN
cana-3299	7	4	,	,	PUNCT
cana-3299	8	1	vel	vel	PROPN
cana-3299	8	2	tech	tech	PROPN
cana-3299	8	3	rangarajan	rangarajan	PROPN
cana-3299	8	4	dr	dr	PROPN
cana-3299	8	5	.	.	PROPN
cana-3299	8	6	sagunthala	sagunthala	PROPN
cana-3299	8	7	r&d	r&d	PROPN
cana-3299	8	8	institute	institute	PROPN
cana-3299	8	9	of	of	ADP
cana-3299	8	10	science	science	NOUN
cana-3299	8	11	and	and	CCONJ
cana-3299	8	12	technology	technology	NOUN
cana-3299	8	13	(	(	PUNCT
cana-3299	8	14	deemed	deem	VERB
cana-3299	8	15	to	to	PART
cana-3299	8	16	be	be	AUX
cana-3299	8	17	university	university	NOUN
cana-3299	8	18	)	)	PUNCT
cana-3299	8	19	,	,	PUNCT
cana-3299	8	20	avadi	avadi	NOUN
cana-3299	8	21	,	,	PUNCT
cana-3299	8	22	chennai-600062	chennai-600062	NOUN
cana-3299	8	23	,	,	PUNCT
cana-3299	8	24	india	india	PROPN
cana-3299	8	25	∗correspondence	∗correspondence	NOUN
cana-3299	8	26	:	:	PUNCT
cana-3299	8	27	mathvijaya2006au@gmail.com	mathvijaya2006au@gmail.com	PROPN
cana-3299	8	28	,	,	PUNCT
cana-3299	8	29	avmaths@gmail.com	avmaths@gmail.com	X
cana-3299	9	1	1mathvijaya2006au@gmail.com	1mathvijaya2006au@gmail.com	NUM
cana-3299	9	2	2ramalakshmikrishnan23@gmail.com	2ramalakshmikrishnan23@gmail.com	NOUN
cana-3299	10	1	3	3	NUM
cana-3299	10	2	avmaths@gmail.com	avmaths@gmail.com	X
cana-3299	10	3	4saravananguru2612@gmail.com	4saravananguru2612@gmail.com	PROPN
cana-3299	10	4	,	,	PUNCT
cana-3299	10	5	article	article	NOUN
cana-3299	10	6	history	history	NOUN
cana-3299	10	7	:	:	PUNCT
cana-3299	10	8	received	receive	VERB
cana-3299	10	9	:	:	PUNCT
cana-3299	10	10	20	20	NUM
cana-3299	10	11	-	-	SYM
cana-3299	10	12	10	10	NUM
cana-3299	10	13	-	-	PUNCT
cana-3299	10	14	2024	2024	NUM
cana-3299	10	15	revised	revise	VERB
cana-3299	10	16	:	:	PUNCT
cana-3299	10	17	04	04	NUM
cana-3299	10	18	-	-	SYM
cana-3299	10	19	12	12	NUM
cana-3299	10	20	-	-	PUNCT
cana-3299	10	21	2024	2024	NUM
cana-3299	10	22	accepted	accept	VERB
cana-3299	10	23	:	:	PUNCT
cana-3299	10	24	11	11	NUM
cana-3299	10	25	-	-	SYM
cana-3299	10	26	12	12	NUM
cana-3299	10	27	-	-	PUNCT
cana-3299	10	28	2024	2024	NUM
cana-3299	10	29	abstract	abstract	NOUN
cana-3299	10	30	:	:	PUNCT
cana-3299	10	31	in	in	ADP
cana-3299	10	32	this	this	DET
cana-3299	10	33	paper	paper	NOUN
cana-3299	10	34	,	,	PUNCT
cana-3299	10	35	we	we	PRON
cana-3299	10	36	introduce	introduce	VERB
cana-3299	10	37	and	and	CCONJ
cana-3299	10	38	investigate	investigate	VERB
cana-3299	10	39	pythagorean	pythagorean	PROPN
cana-3299	10	40	fuzzy	fuzzy	ADJ
cana-3299	10	41	contra	contra	PROPN
cana-3299	10	42	𝑀-continuous	𝑀-continuous	ADJ
cana-3299	10	43	maps	map	NOUN
cana-3299	10	44	in	in	ADP
cana-3299	10	45	pythagorean	pythagorean	PROPN
cana-3299	10	46	fuzzy	fuzzy	ADJ
cana-3299	10	47	topological	topological	ADJ
cana-3299	10	48	spaces	space	NOUN
cana-3299	10	49	and	and	CCONJ
cana-3299	10	50	also	also	ADV
cana-3299	10	51	discuss	discuss	VERB
cana-3299	10	52	about	about	ADP
cana-3299	10	53	some	some	DET
cana-3299	10	54	properties	property	NOUN
cana-3299	10	55	and	and	CCONJ
cana-3299	10	56	characterization	characterization	NOUN
cana-3299	10	57	of	of	ADP
cana-3299	10	58	pythagorean	pythagorean	PROPN
cana-3299	10	59	fuzzy	fuzzy	ADJ
cana-3299	10	60	contra	contra	PROPN
cana-3299	10	61	𝑀-irresolute	𝑀-irresolute	PROPN
cana-3299	10	62	maps	map	NOUN
cana-3299	10	63	.	.	PUNCT
cana-3299	11	1	keywords	keyword	NOUN
cana-3299	11	2	:	:	PUNCT
cana-3299	11	3	pythagorean	pythagorean	PROPN
cana-3299	11	4	fuzzy	fuzzy	ADJ
cana-3299	11	5	𝑀-closed	𝑀-closed	ADJ
cana-3299	11	6	sets	set	NOUN
cana-3299	11	7	,	,	PUNCT
cana-3299	12	1	pythagorean	pythagorean	PROPN
cana-3299	12	2	fuzzy	fuzzy	ADJ
cana-3299	12	3	contra	contra	PROPN
cana-3299	12	4	𝑀-continuous	𝑀-continuous	ADJ
cana-3299	12	5	maps	map	NOUN
cana-3299	12	6	and	and	CCONJ
cana-3299	12	7	pythagorean	pythagorean	PROPN
cana-3299	12	8	fuzzy	fuzzy	ADJ
cana-3299	12	9	contra	contra	PROPN
cana-3299	12	10	𝑀-irresolute	𝑀-irresolute	PROPN
cana-3299	12	11	maps	map	NOUN
cana-3299	12	12	.	.	PUNCT
cana-3299	13	1	ams	am	NOUN
cana-3299	13	2	(	(	PUNCT
cana-3299	13	3	2000	2000	NUM
cana-3299	13	4	)	)	PUNCT
cana-3299	13	5	subject	subject	ADJ
cana-3299	13	6	classification	classification	NOUN
cana-3299	13	7	:	:	PUNCT
cana-3299	13	8	03e72	03e72	NUM
cana-3299	13	9	,	,	PUNCT
cana-3299	13	10	54a10	54a10	NUM
cana-3299	13	11	,	,	PUNCT
cana-3299	13	12	54a40	54a40	NUM
cana-3299	13	13	,	,	PUNCT
cana-3299	13	14	54c05	54c05	NUM
cana-3299	13	15	,	,	PUNCT
cana-3299	13	16	54c10	54c10	NUM
cana-3299	13	17	.	.	X
cana-3299	14	1	1	1	X
cana-3299	14	2	.	.	X
cana-3299	14	3	introduction	introduction	NOUN
cana-3299	14	4	considering	consider	VERB
cana-3299	14	5	the	the	DET
cana-3299	14	6	imprecision	imprecision	NOUN
cana-3299	14	7	in	in	ADP
cana-3299	14	8	decision	decision	NOUN
cana-3299	14	9	-	-	PUNCT
cana-3299	14	10	making	making	NOUN
cana-3299	14	11	,	,	PUNCT
cana-3299	14	12	zadeh	zadeh	PROPN
cana-3299	15	1	[	[	X
cana-3299	15	2	36	36	NUM
cana-3299	15	3	]	]	PUNCT
cana-3299	15	4	introduced	introduce	VERB
cana-3299	15	5	the	the	DET
cana-3299	15	6	idea	idea	NOUN
cana-3299	15	7	of	of	ADP
cana-3299	15	8	fuzzy	fuzzy	ADJ
cana-3299	15	9	set	set	NOUN
cana-3299	15	10	which	which	PRON
cana-3299	15	11	has	have	VERB
cana-3299	15	12	a	a	DET
cana-3299	15	13	membership	membership	NOUN
cana-3299	15	14	function	function	NOUN
cana-3299	15	15	,	,	PUNCT
cana-3299	15	16	𝜇	𝜇	ADP
cana-3299	15	17	that	that	DET
cana-3299	15	18	assigns	assign	NOUN
cana-3299	15	19	to	to	ADP
cana-3299	15	20	each	each	DET
cana-3299	15	21	element	element	NOUN
cana-3299	15	22	of	of	ADP
cana-3299	15	23	the	the	DET
cana-3299	15	24	universe	universe	NOUN
cana-3299	15	25	of	of	ADP
cana-3299	15	26	discourse	discourse	NOUN
cana-3299	15	27	,	,	PUNCT
cana-3299	15	28	a	a	DET
cana-3299	15	29	number	number	NOUN
cana-3299	15	30	from	from	ADP
cana-3299	15	31	the	the	DET
cana-3299	15	32	unit	unit	NOUN
cana-3299	15	33	interval	interval	NOUN
cana-3299	15	34	[	[	X
cana-3299	15	35	0,1	0,1	NUM
cana-3299	15	36	]	]	PUNCT
cana-3299	15	37	to	to	PART
cana-3299	15	38	indicate	indicate	VERB
cana-3299	15	39	the	the	DET
cana-3299	15	40	degree	degree	NOUN
cana-3299	15	41	of	of	ADP
cana-3299	15	42	belongingness	belongingness	NOUN
cana-3299	15	43	to	to	ADP
cana-3299	15	44	the	the	DET
cana-3299	15	45	set	set	NOUN
cana-3299	15	46	under	under	ADP
cana-3299	15	47	consideration	consideration	NOUN
cana-3299	15	48	.	.	PUNCT
cana-3299	16	1	the	the	DET
cana-3299	16	2	notion	notion	NOUN
cana-3299	16	3	of	of	ADP
cana-3299	16	4	fuzzy	fuzzy	ADJ
cana-3299	16	5	sets	set	NOUN
cana-3299	16	6	generalizes	generalize	VERB
cana-3299	16	7	classical	classical	ADJ
cana-3299	16	8	sets	set	NOUN
cana-3299	16	9	theory	theory	NOUN
cana-3299	16	10	by	by	ADP
cana-3299	16	11	allowing	allow	VERB
cana-3299	16	12	intermediate	intermediate	ADJ
cana-3299	16	13	situations	situation	NOUN
cana-3299	16	14	between	between	ADP
cana-3299	16	15	the	the	DET
cana-3299	16	16	whole	whole	NOUN
cana-3299	16	17	and	and	CCONJ
cana-3299	16	18	nothing	nothing	PRON
cana-3299	16	19	.	.	PUNCT
cana-3299	17	1	in	in	ADP
cana-3299	17	2	a	a	DET
cana-3299	17	3	fuzzy	fuzzy	ADJ
cana-3299	17	4	set	set	NOUN
cana-3299	17	5	,	,	PUNCT
cana-3299	17	6	a	a	DET
cana-3299	17	7	membership	membership	NOUN
cana-3299	17	8	function	function	NOUN
cana-3299	17	9	is	be	AUX
cana-3299	17	10	defined	define	VERB
cana-3299	17	11	to	to	PART
cana-3299	17	12	describe	describe	VERB
cana-3299	17	13	the	the	DET
cana-3299	17	14	degree	degree	NOUN
cana-3299	17	15	of	of	ADP
cana-3299	17	16	membership	membership	NOUN
cana-3299	17	17	of	of	ADP
cana-3299	17	18	an	an	DET
cana-3299	17	19	element	element	NOUN
cana-3299	17	20	to	to	ADP
cana-3299	17	21	a	a	DET
cana-3299	17	22	class	class	NOUN
cana-3299	17	23	.	.	PUNCT
cana-3299	18	1	the	the	DET
cana-3299	18	2	membership	membership	NOUN
cana-3299	18	3	value	value	NOUN
cana-3299	18	4	ranges	range	VERB
cana-3299	18	5	from	from	ADP
cana-3299	18	6	0	0	NUM
cana-3299	18	7	to	to	ADP
cana-3299	18	8	1	1	NUM
cana-3299	18	9	,	,	PUNCT
cana-3299	18	10	where	where	SCONJ
cana-3299	18	11	0	0	NUM
cana-3299	18	12	shows	show	VERB
cana-3299	18	13	that	that	SCONJ
cana-3299	18	14	the	the	DET
cana-3299	18	15	element	element	NOUN
cana-3299	18	16	does	do	AUX
cana-3299	18	17	not	not	PART
cana-3299	18	18	belong	belong	VERB
cana-3299	18	19	to	to	ADP
cana-3299	18	20	a	a	DET
cana-3299	18	21	class	class	NOUN
cana-3299	18	22	,	,	PUNCT
cana-3299	18	23	1	1	NUM
cana-3299	18	24	means	mean	NOUN
cana-3299	18	25	belongs	belong	NOUN
cana-3299	18	26	,	,	PUNCT
cana-3299	18	27	and	and	CCONJ
cana-3299	18	28	other	other	ADJ
cana-3299	18	29	values	value	NOUN
cana-3299	18	30	indicate	indicate	VERB
cana-3299	18	31	the	the	DET
cana-3299	18	32	degree	degree	NOUN
cana-3299	18	33	of	of	ADP
cana-3299	18	34	membership	membership	NOUN
cana-3299	18	35	to	to	ADP
cana-3299	18	36	a	a	DET
cana-3299	18	37	class	class	NOUN
cana-3299	18	38	.	.	PUNCT
cana-3299	19	1	for	for	ADP
cana-3299	19	2	fuzzy	fuzzy	ADJ
cana-3299	19	3	sets	set	NOUN
cana-3299	19	4	,	,	PUNCT
cana-3299	19	5	the	the	DET
cana-3299	19	6	membership	membership	NOUN
cana-3299	19	7	function	function	NOUN
cana-3299	19	8	replaced	replace	VERB
cana-3299	19	9	the	the	DET
cana-3299	19	10	characteristic	characteristic	ADJ
cana-3299	19	11	function	function	NOUN
cana-3299	19	12	in	in	ADP
cana-3299	19	13	crisp	crisp	ADJ
cana-3299	19	14	sets	set	NOUN
cana-3299	19	15	.	.	PUNCT
cana-3299	20	1	the	the	DET
cana-3299	20	2	concept	concept	NOUN
cana-3299	20	3	of	of	ADP
cana-3299	20	4	fuzzy	fuzzy	ADJ
cana-3299	20	5	set	set	NOUN
cana-3299	20	6	theory	theory	NOUN
cana-3299	20	7	seems	seem	VERB
cana-3299	20	8	to	to	PART
cana-3299	20	9	be	be	AUX
cana-3299	20	10	inconclusive	inconclusive	ADJ
cana-3299	20	11	because	because	SCONJ
cana-3299	20	12	of	of	ADP
cana-3299	20	13	the	the	DET
cana-3299	20	14	exclusion	exclusion	NOUN
cana-3299	20	15	of	of	ADP
cana-3299	20	16	nonmembership	nonmembership	NOUN
cana-3299	20	17	function	function	NOUN
cana-3299	20	18	and	and	CCONJ
cana-3299	20	19	the	the	DET
cana-3299	20	20	disregard	disregard	NOUN
cana-3299	20	21	for	for	ADP
cana-3299	20	22	the	the	DET
cana-3299	20	23	possibility	possibility	NOUN
cana-3299	20	24	of	of	ADP
cana-3299	20	25	hesitation	hesitation	NOUN
cana-3299	20	26	margin	margin	NOUN
cana-3299	20	27	.	.	PUNCT
cana-3299	21	1	atanassov	atanassov	PROPN
cana-3299	21	2	critically	critically	ADV
cana-3299	21	3	studied	study	VERB
cana-3299	21	4	these	these	DET
cana-3299	21	5	shortcomings	shortcoming	NOUN
cana-3299	21	6	and	and	CCONJ
cana-3299	21	7	proposed	propose	VERB
cana-3299	21	8	a	a	DET
cana-3299	21	9	concept	concept	NOUN
cana-3299	21	10	called	call	VERB
cana-3299	21	11	intuitionistic	intuitionistic	ADJ
cana-3299	21	12	fuzzy	fuzzy	ADJ
cana-3299	21	13	sets	set	NOUN
cana-3299	21	14	(	(	PUNCT
cana-3299	21	15	𝐼𝐹𝑆s	𝐼𝐹𝑆s	NOUN
cana-3299	21	16	)	)	PUNCT
cana-3299	22	1	[	[	X
cana-3299	22	2	1	1	NUM
cana-3299	22	3	,	,	PUNCT
cana-3299	22	4	2	2	NUM
cana-3299	22	5	,	,	PUNCT
cana-3299	22	6	4	4	NUM
cana-3299	22	7	,	,	PUNCT
cana-3299	22	8	5	5	NUM
cana-3299	22	9	]	]	PUNCT
cana-3299	22	10	.	.	PUNCT
cana-3299	23	1	the	the	DET
cana-3299	23	2	construct	construct	NOUN
cana-3299	23	3	(	(	PUNCT
cana-3299	23	4	that	that	PRON
cana-3299	23	5	is	is	ADV
cana-3299	23	6	,	,	PUNCT
cana-3299	23	7	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	23	8	’s	’s	PART
cana-3299	23	9	)	)	PUNCT
cana-3299	23	10	incorporates	incorporate	VERB
cana-3299	23	11	both	both	DET
cana-3299	23	12	membership	membership	NOUN
cana-3299	23	13	function	function	NOUN
cana-3299	23	14	,	,	PUNCT
cana-3299	23	15	𝜇	𝜇	ADP
cana-3299	23	16	and	and	CCONJ
cana-3299	23	17	nonmembership	nonmembership	NOUN
cana-3299	23	18	function	function	NOUN
cana-3299	23	19	,	,	PUNCT
cana-3299	23	20	𝜈	𝜈	X
cana-3299	23	21	with	with	ADP
cana-3299	23	22	hesitation	hesitation	NOUN
cana-3299	23	23	margin	margin	NOUN
cana-3299	23	24	,	,	PUNCT
cana-3299	23	25	𝜋	𝜋	X
cana-3299	23	26	(	(	PUNCT
cana-3299	23	27	that	that	PRON
cana-3299	23	28	is	is	ADV
cana-3299	23	29	,	,	PUNCT
cana-3299	23	30	neither	neither	CCONJ
cana-3299	23	31	membership	membership	NOUN
cana-3299	23	32	nor	nor	CCONJ
cana-3299	23	33	nonmembership	nonmembership	NOUN
cana-3299	23	34	functions	function	NOUN
cana-3299	23	35	)	)	PUNCT
cana-3299	23	36	,	,	PUNCT
cana-3299	23	37	such	such	ADJ
cana-3299	23	38	that	that	SCONJ
cana-3299	23	39	𝜇	𝜇	ADP
cana-3299	23	40	+	+	X
cana-3299	23	41	𝜈	𝜈	X
cana-3299	23	42	≤	≤	NUM
cana-3299	23	43	1	1	NUM
cana-3299	23	44	and	and	CCONJ
cana-3299	23	45	𝜇	𝜇	X
cana-3299	23	46	+	+	X
cana-3299	23	47	𝜈	𝜈	X
cana-3299	23	48	+	+	CCONJ
cana-3299	23	49	𝜋	𝜋	NOUN
cana-3299	23	50	=	=	ADJ
cana-3299	23	51	1	1	X
cana-3299	23	52	.	.	X
cana-3299	23	53	atanassov	atanassov	PROPN
cana-3299	23	54	[	[	X
cana-3299	23	55	3	3	NUM
cana-3299	23	56	]	]	PUNCT
cana-3299	23	57	introduced	introduce	VERB
cana-3299	23	58	intuitionistic	intuitionistic	ADJ
cana-3299	23	59	fuzzy	fuzzy	ADJ
cana-3299	23	60	sets	set	NOUN
cana-3299	23	61	of	of	ADP
cana-3299	23	62	second	second	ADJ
cana-3299	23	63	type	type	NOUN
cana-3299	23	64	(	(	PUNCT
cana-3299	23	65	𝐼𝐹𝑆𝑆𝑇	𝐼𝐹𝑆𝑆𝑇	PROPN
cana-3299	23	66	)	)	PUNCT
cana-3299	23	67	with	with	ADP
cana-3299	23	68	the	the	DET
cana-3299	23	69	property	property	NOUN
cana-3299	23	70	that	that	PRON
cana-3299	23	71	the	the	DET
cana-3299	23	72	sum	sum	NOUN
cana-3299	23	73	of	of	ADP
cana-3299	23	74	the	the	DET
cana-3299	23	75	square	square	NOUN
cana-3299	23	76	of	of	ADP
cana-3299	23	77	the	the	DET
cana-3299	23	78	membership	membership	NOUN
cana-3299	23	79	and	and	CCONJ
cana-3299	23	80	non	non	ADJ
cana-3299	23	81	-	-	ADJ
cana-3299	23	82	membership	membership	ADJ
cana-3299	23	83	degrees	degree	NOUN
cana-3299	23	84	is	be	AUX
cana-3299	23	85	less	less	ADJ
cana-3299	23	86	than	than	ADP
cana-3299	23	87	or	or	CCONJ
cana-3299	23	88	equal	equal	ADJ
cana-3299	23	89	to	to	ADP
cana-3299	23	90	one	one	NUM
cana-3299	23	91	.	.	PUNCT
cana-3299	24	1	this	this	DET
cana-3299	24	2	concept	concept	NOUN
cana-3299	24	3	generalizes	generalize	VERB
cana-3299	24	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	24	5	’s	’s	PART
cana-3299	24	6	in	in	ADP
cana-3299	24	7	a	a	DET
cana-3299	24	8	way	way	NOUN
cana-3299	24	9	.	.	PUNCT
cana-3299	25	1	the	the	DET
cana-3299	25	2	notion	notion	NOUN
cana-3299	25	3	of	of	ADP
cana-3299	25	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	25	5	’s	’s	PART
cana-3299	25	6	provides	provide	VERB
cana-3299	25	7	a	a	DET
cana-3299	25	8	flexible	flexible	ADJ
cana-3299	25	9	framework	framework	NOUN
cana-3299	25	10	to	to	PART
cana-3299	25	11	elaborate	elaborate	VERB
cana-3299	25	12	uncertainty	uncertainty	NOUN
cana-3299	25	13	and	and	CCONJ
cana-3299	25	14	vagueness	vagueness	NOUN
cana-3299	25	15	.	.	PUNCT
cana-3299	26	1	the	the	DET
cana-3299	26	2	idea	idea	NOUN
cana-3299	26	3	of	of	ADP
cana-3299	26	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	26	5	seems	seem	VERB
cana-3299	26	6	to	to	PART
cana-3299	26	7	be	be	AUX
cana-3299	26	8	resourceful	resourceful	ADJ
cana-3299	26	9	in	in	ADP
cana-3299	26	10	modelling	model	VERB
cana-3299	26	11	many	many	ADJ
cana-3299	26	12	real	real	ADJ
cana-3299	26	13	-	-	PUNCT
cana-3299	26	14	life	life	NOUN
cana-3299	26	15	situations	situation	NOUN
cana-3299	26	16	like	like	ADP
cana-3299	26	17	medical	medical	ADJ
cana-3299	26	18	diagnosis	diagnosis	NOUN
cana-3299	26	19	[	[	X
cana-3299	26	20	7	7	NUM
cana-3299	26	21	,	,	PUNCT
cana-3299	26	22	8	8	NUM
cana-3299	26	23	,	,	PUNCT
cana-3299	26	24	12	12	NUM
cana-3299	26	25	,	,	PUNCT
cana-3299	26	26	28	28	NUM
cana-3299	26	27	,	,	PUNCT
cana-3299	26	28	29	29	NUM
cana-3299	26	29	]	]	PUNCT
cana-3299	26	30	,	,	PUNCT
cana-3299	26	31	career	career	NOUN
cana-3299	26	32	determination	determination	NOUN
cana-3299	26	33	[	[	X
cana-3299	26	34	10	10	NUM
cana-3299	26	35	]	]	PUNCT
cana-3299	26	36	,	,	PUNCT
cana-3299	26	37	selection	selection	NOUN
cana-3299	26	38	process	process	NOUN
cana-3299	26	39	[	[	X
cana-3299	26	40	11	11	NUM
cana-3299	26	41	]	]	PUNCT
cana-3299	26	42	,	,	PUNCT
cana-3299	26	43	and	and	CCONJ
cana-3299	26	44	multi	multi	ADJ
cana-3299	26	45	-	-	NOUN
cana-3299	26	46	criteria	criterion	NOUN
cana-3299	26	47	decision	decision	NOUN
cana-3299	26	48	-	-	PUNCT
cana-3299	26	49	making	making	NOUN
cana-3299	26	50	[	[	X
cana-3299	26	51	15	15	NUM
cana-3299	26	52	,	,	PUNCT
cana-3299	26	53	16	16	NUM
cana-3299	26	54	,	,	PUNCT
cana-3299	26	55	17	17	NUM
cana-3299	26	56	]	]	PUNCT
cana-3299	26	57	,	,	PUNCT
cana-3299	26	58	among	among	ADP
cana-3299	26	59	others	other	NOUN
cana-3299	26	60	.	.	PUNCT
cana-3299	27	1	mailto:avmaths@gmail.com	mailto:avmaths@gmail.com	X
cana-3299	27	2	mailto:1mathvijaya2006au@gmail.com	mailto:1mathvijaya2006au@gmail.com	PROPN
cana-3299	27	3	mailto:2ramalakshmikrishnan23@gmail.com	mailto:2ramalakshmikrishnan23@gmail.com	PROPN
cana-3299	27	4	mailto:4saravananguru2612@gmail.com	mailto:4saravananguru2612@gmail.com	PROPN
cana-3299	27	5	communications	communication	NOUN
cana-3299	27	6	on	on	ADP
cana-3299	27	7	applied	apply	VERB
cana-3299	27	8	nonlinear	nonlinear	ADJ
cana-3299	27	9	analysis	analysis	NOUN
cana-3299	27	10	issn	issn	NOUN
cana-3299	27	11	:	:	PUNCT
cana-3299	27	12	1074	1074	NUM
cana-3299	27	13	-	-	PUNCT
cana-3299	27	14	133x	133x	NUM
cana-3299	27	15	vol	vol	NOUN
cana-3299	27	16	32	32	NUM
cana-3299	27	17	no	no	NOUN
cana-3299	27	18	.	.	PUNCT
cana-3299	28	1	6s	6s	NUM
cana-3299	28	2	(	(	PUNCT
cana-3299	28	3	2025	2025	NUM
cana-3299	28	4	)	)	PUNCT
cana-3299	28	5	328	328	NUM
cana-3299	28	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	28	7	there	there	PRON
cana-3299	28	8	are	be	VERB
cana-3299	28	9	situations	situation	NOUN
cana-3299	28	10	where	where	SCONJ
cana-3299	28	11	𝜇	𝜇	ADP
cana-3299	28	12	+	+	CCONJ
cana-3299	28	13	𝜈	𝜈	X
cana-3299	28	14	≥	≥	NOUN
cana-3299	28	15	1	1	NUM
cana-3299	28	16	unlike	unlike	ADP
cana-3299	28	17	the	the	DET
cana-3299	28	18	cases	case	NOUN
cana-3299	28	19	capture	capture	VERB
cana-3299	28	20	in	in	ADP
cana-3299	28	21	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	28	22	’s	’s	PART
cana-3299	28	23	.	.	PUNCT
cana-3299	29	1	this	this	DET
cana-3299	29	2	limitation	limitation	NOUN
cana-3299	29	3	in	in	ADP
cana-3299	29	4	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	29	5	naturally	naturally	ADV
cana-3299	29	6	led	lead	VERB
cana-3299	29	7	to	to	ADP
cana-3299	29	8	a	a	DET
cana-3299	29	9	construct	construct	NOUN
cana-3299	29	10	,	,	PUNCT
cana-3299	29	11	called	call	VERB
cana-3299	29	12	pythagorean	pythagorean	PROPN
cana-3299	29	13	fuzzy	fuzzy	ADJ
cana-3299	29	14	sets	set	NOUN
cana-3299	29	15	(	(	PUNCT
cana-3299	29	16	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	29	17	’s	’s	PART
cana-3299	29	18	)	)	PUNCT
cana-3299	29	19	.	.	PUNCT
cana-3299	30	1	pythagorean	pythagorean	PROPN
cana-3299	30	2	fuzzy	fuzzy	ADJ
cana-3299	30	3	set	set	NOUN
cana-3299	30	4	(	(	PUNCT
cana-3299	30	5	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	30	6	)	)	PUNCT
cana-3299	30	7	proposed	propose	VERB
cana-3299	30	8	in	in	ADP
cana-3299	30	9	[	[	X
cana-3299	30	10	33	33	NUM
cana-3299	30	11	,	,	PUNCT
cana-3299	30	12	34	34	NUM
cana-3299	30	13	,	,	PUNCT
cana-3299	30	14	35	35	NUM
cana-3299	30	15	]	]	PUNCT
cana-3299	30	16	is	be	AUX
cana-3299	30	17	a	a	DET
cana-3299	30	18	new	new	ADJ
cana-3299	30	19	tool	tool	NOUN
cana-3299	30	20	to	to	PART
cana-3299	30	21	deal	deal	VERB
cana-3299	30	22	with	with	ADP
cana-3299	30	23	vagueness	vagueness	NOUN
cana-3299	30	24	considering	consider	VERB
cana-3299	30	25	the	the	DET
cana-3299	30	26	membership	membership	NOUN
cana-3299	30	27	grade	grade	NOUN
cana-3299	30	28	,	,	PUNCT
cana-3299	30	29	𝜇	𝜇	ADP
cana-3299	30	30	and	and	CCONJ
cana-3299	30	31	non	non	ADJ
cana-3299	30	32	-	-	ADJ
cana-3299	30	33	membership	membership	ADJ
cana-3299	30	34	grade	grade	NOUN
cana-3299	30	35	,	,	PUNCT
cana-3299	31	1	𝜈	𝜈	X
cana-3299	31	2	satisfying	satisfy	VERB
cana-3299	31	3	the	the	DET
cana-3299	31	4	conditions	condition	NOUN
cana-3299	31	5	𝜇	𝜇	ADP
cana-3299	31	6	+	+	CCONJ
cana-3299	31	7	𝜈	𝜈	X
cana-3299	31	8	≤	≤	NUM
cana-3299	31	9	1	1	NUM
cana-3299	31	10	or	or	CCONJ
cana-3299	31	11	𝜇	𝜇	X
cana-3299	31	12	+	+	CCONJ
cana-3299	31	13	𝜈	𝜈	X
cana-3299	31	14	≥	≥	NUM
cana-3299	31	15	1	1	NUM
cana-3299	31	16	,	,	PUNCT
cana-3299	31	17	and	and	CCONJ
cana-3299	31	18	also	also	ADV
cana-3299	31	19	,	,	PUNCT
cana-3299	31	20	it	it	PRON
cana-3299	31	21	follows	follow	VERB
cana-3299	31	22	that	that	SCONJ
cana-3299	31	23	𝜇2	𝜇2	PROPN
cana-3299	31	24	+	+	CCONJ
cana-3299	31	25	𝜈2	𝜈2	NOUN
cana-3299	31	26	+	+	CCONJ
cana-3299	31	27	𝜋2	𝜋2	NOUN
cana-3299	31	28	=	=	SYM
cana-3299	31	29	1	1	NUM
cana-3299	31	30	,	,	PUNCT
cana-3299	31	31	where	where	SCONJ
cana-3299	31	32	𝜋	𝜋	NOUN
cana-3299	31	33	is	be	AUX
cana-3299	31	34	the	the	DET
cana-3299	31	35	pythagorean	pythagorean	PROPN
cana-3299	31	36	fuzzy	fuzzy	ADJ
cana-3299	31	37	set	set	PROPN
cana-3299	31	38	index	index	NOUN
cana-3299	31	39	.	.	PUNCT
cana-3299	32	1	in	in	ADP
cana-3299	32	2	fact	fact	NOUN
cana-3299	32	3	,	,	PUNCT
cana-3299	32	4	the	the	DET
cana-3299	32	5	origin	origin	NOUN
cana-3299	32	6	of	of	ADP
cana-3299	32	7	pythagorean	pythagorean	PROPN
cana-3299	32	8	fuzzy	fuzzy	ADJ
cana-3299	32	9	sets	set	NOUN
cana-3299	32	10	emanated	emanate	VERB
cana-3299	32	11	from	from	ADP
cana-3299	32	12	𝐼𝐹𝑆𝑆𝑇	𝐼𝐹𝑆𝑆𝑇	PROPN
cana-3299	32	13	earlier	early	ADV
cana-3299	32	14	studied	study	VERB
cana-3299	32	15	in	in	ADP
cana-3299	32	16	the	the	DET
cana-3299	32	17	literature	literature	NOUN
cana-3299	32	18	.	.	PUNCT
cana-3299	33	1	as	as	ADP
cana-3299	33	2	a	a	DET
cana-3299	33	3	generalized	generalized	ADJ
cana-3299	33	4	set	set	NOUN
cana-3299	33	5	,	,	PUNCT
cana-3299	33	6	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-3299	33	7	has	have	VERB
cana-3299	33	8	close	close	ADJ
cana-3299	33	9	relationship	relationship	NOUN
cana-3299	33	10	with	with	ADP
cana-3299	33	11	𝐼𝐹𝑆.	𝐼𝐹𝑆.	PUNCT
cana-3299	33	12	the	the	DET
cana-3299	33	13	construct	construct	NOUN
cana-3299	33	14	of	of	ADP
cana-3299	33	15	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-3299	33	16	’s	’s	PART
cana-3299	33	17	can	can	AUX
cana-3299	33	18	be	be	AUX
cana-3299	33	19	used	use	VERB
cana-3299	33	20	to	to	PART
cana-3299	33	21	characterize	characterize	VERB
cana-3299	33	22	uncertain	uncertain	ADJ
cana-3299	33	23	information	information	NOUN
cana-3299	33	24	more	more	ADV
cana-3299	33	25	sufficiently	sufficiently	ADV
cana-3299	33	26	and	and	CCONJ
cana-3299	33	27	accurately	accurately	ADV
cana-3299	33	28	than	than	ADP
cana-3299	33	29	𝐼𝐹𝑆.	𝐼𝐹𝑆.	NUM
cana-3299	33	30	garg	garg	NOUN
cana-3299	34	1	[	[	X
cana-3299	34	2	14	14	NUM
cana-3299	34	3	]	]	PUNCT
cana-3299	34	4	presented	present	VERB
cana-3299	34	5	an	an	DET
cana-3299	34	6	improved	improved	ADJ
cana-3299	34	7	score	score	NOUN
cana-3299	34	8	function	function	NOUN
cana-3299	34	9	for	for	ADP
cana-3299	34	10	the	the	DET
cana-3299	34	11	ranking	ranking	ADJ
cana-3299	34	12	order	order	NOUN
cana-3299	34	13	of	of	ADP
cana-3299	34	14	intervalvalued	intervalvalue	VERB
cana-3299	34	15	pythagorean	pythagorean	PROPN
cana-3299	34	16	fuzzy	fuzzy	ADJ
cana-3299	34	17	sets	set	NOUN
cana-3299	34	18	(	(	PUNCT
cana-3299	34	19	𝐼𝑉𝑃𝐹𝑆s	𝐼𝑉𝑃𝐹𝑆	NOUN
cana-3299	34	20	)	)	PUNCT
cana-3299	34	21	.	.	PUNCT
cana-3299	35	1	based	base	VERB
cana-3299	35	2	on	on	ADP
cana-3299	35	3	it	it	PRON
cana-3299	35	4	,	,	PUNCT
cana-3299	35	5	a	a	DET
cana-3299	35	6	pythagorean	pythagorean	ADJ
cana-3299	35	7	fuzzy	fuzzy	ADJ
cana-3299	35	8	technique	technique	NOUN
cana-3299	35	9	for	for	ADP
cana-3299	35	10	order	order	NOUN
cana-3299	35	11	of	of	ADP
cana-3299	35	12	preference	preference	NOUN
cana-3299	35	13	by	by	ADP
cana-3299	35	14	similarity	similarity	NOUN
cana-3299	35	15	to	to	ADP
cana-3299	35	16	ideal	ideal	ADJ
cana-3299	35	17	solution	solution	NOUN
cana-3299	35	18	(	(	PUNCT
cana-3299	35	19	𝑇𝑂𝑃𝑆𝐼𝑆	𝑇𝑂𝑃𝑆𝐼𝑆	PROPN
cana-3299	35	20	)	)	PUNCT
cana-3299	35	21	method	method	NOUN
cana-3299	35	22	by	by	ADP
cana-3299	35	23	taking	take	VERB
cana-3299	35	24	the	the	DET
cana-3299	35	25	preferences	preference	NOUN
cana-3299	35	26	of	of	ADP
cana-3299	35	27	the	the	DET
cana-3299	35	28	experts	expert	NOUN
cana-3299	35	29	in	in	ADP
cana-3299	35	30	the	the	DET
cana-3299	35	31	form	form	NOUN
cana-3299	35	32	of	of	ADP
cana-3299	35	33	interval	interval	NOUN
cana-3299	35	34	-	-	PUNCT
cana-3299	35	35	valued	value	VERB
cana-3299	35	36	pythagorean	pythagorean	PROPN
cana-3299	35	37	fuzzy	fuzzy	ADJ
cana-3299	35	38	decision	decision	NOUN
cana-3299	35	39	matrices	matrix	NOUN
cana-3299	35	40	was	be	AUX
cana-3299	35	41	discussed	discuss	VERB
cana-3299	35	42	.	.	PUNCT
cana-3299	36	1	other	other	ADJ
cana-3299	36	2	explorations	exploration	NOUN
cana-3299	36	3	of	of	ADP
cana-3299	36	4	the	the	DET
cana-3299	36	5	theory	theory	NOUN
cana-3299	36	6	of	of	ADP
cana-3299	36	7	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-3299	36	8	’s	’s	PART
cana-3299	36	9	can	can	AUX
cana-3299	36	10	be	be	AUX
cana-3299	36	11	found	find	VERB
cana-3299	36	12	in	in	ADP
cana-3299	36	13	[	[	X
cana-3299	36	14	6	6	NUM
cana-3299	36	15	,	,	PUNCT
cana-3299	36	16	9	9	NUM
cana-3299	36	17	,	,	PUNCT
cana-3299	36	18	13	13	NUM
cana-3299	36	19	,	,	PUNCT
cana-3299	36	20	18	18	NUM
cana-3299	36	21	,	,	PUNCT
cana-3299	36	22	19	19	NUM
cana-3299	36	23	,	,	PUNCT
cana-3299	36	24	25	25	NUM
cana-3299	36	25	,	,	PUNCT
cana-3299	36	26	26	26	NUM
cana-3299	36	27	]	]	PUNCT
cana-3299	36	28	.	.	PUNCT
cana-3299	37	1	saha	saha	PROPN
cana-3299	38	1	[	[	X
cana-3299	38	2	27	27	NUM
cana-3299	38	3	]	]	SYM
cana-3299	38	4	defined	define	VERB
cana-3299	38	5	𝛿-open	𝛿-open	NOUN
cana-3299	38	6	sets	set	NOUN
cana-3299	38	7	in	in	ADP
cana-3299	38	8	topological	topological	ADJ
cana-3299	38	9	spaces	space	NOUN
cana-3299	38	10	.	.	PUNCT
cana-3299	39	1	vadivel	vadivel	VERB
cana-3299	39	2	et	et	PROPN
cana-3299	39	3	al	al	PROPN
cana-3299	39	4	.	.	PUNCT
cana-3299	40	1	[	[	X
cana-3299	40	2	31	31	NUM
cana-3299	40	3	]	]	PUNCT
cana-3299	40	4	introduced	introduce	VERB
cana-3299	40	5	𝛿-open	𝛿-open	NOUN
cana-3299	40	6	sets	set	NOUN
cana-3299	40	7	in	in	ADP
cana-3299	40	8	a	a	DET
cana-3299	40	9	neutrosophic	neutrosophic	ADJ
cana-3299	40	10	topological	topological	ADJ
cana-3299	40	11	space	space	NOUN
cana-3299	40	12	.	.	PUNCT
cana-3299	41	1	the	the	DET
cana-3299	41	2	notion	notion	NOUN
cana-3299	41	3	of	of	ADP
cana-3299	41	4	m	m	NOUN
cana-3299	41	5	-	-	ADJ
cana-3299	41	6	open	open	ADJ
cana-3299	41	7	sets	set	NOUN
cana-3299	41	8	in	in	ADP
cana-3299	41	9	topological	topological	ADJ
cana-3299	41	10	spaces	space	NOUN
cana-3299	41	11	were	be	AUX
cana-3299	41	12	introduced	introduce	VERB
cana-3299	41	13	by	by	ADP
cana-3299	41	14	el	el	NOUN
cana-3299	41	15	-	-	PUNCT
cana-3299	41	16	maghrabi	maghrabi	NOUN
cana-3299	41	17	and	and	CCONJ
cana-3299	41	18	al	al	PROPN
cana-3299	41	19	-	-	PUNCT
cana-3299	41	20	juhani	juhani	PROPN
cana-3299	42	1	[	[	X
cana-3299	42	2	23	23	NUM
cana-3299	42	3	]	]	PUNCT
cana-3299	42	4	in	in	ADP
cana-3299	42	5	2011	2011	NUM
cana-3299	42	6	and	and	CCONJ
cana-3299	42	7	studied	study	VERB
cana-3299	42	8	some	some	PRON
cana-3299	42	9	of	of	ADP
cana-3299	42	10	their	their	PRON
cana-3299	42	11	properties	property	NOUN
cana-3299	42	12	.	.	PUNCT
cana-3299	43	1	the	the	DET
cana-3299	43	2	class	class	NOUN
cana-3299	43	3	of	of	ADP
cana-3299	43	4	sets	set	NOUN
cana-3299	43	5	namely	namely	ADV
cana-3299	43	6	,	,	PUNCT
cana-3299	43	7	𝑀-open	𝑀-open	ADJ
cana-3299	43	8	sets	set	NOUN
cana-3299	43	9	are	be	AUX
cana-3299	43	10	playing	play	VERB
cana-3299	43	11	more	more	ADV
cana-3299	43	12	important	important	ADJ
cana-3299	43	13	role	role	NOUN
cana-3299	43	14	in	in	ADP
cana-3299	43	15	topological	topological	ADJ
cana-3299	43	16	spaces	space	NOUN
cana-3299	43	17	,	,	PUNCT
cana-3299	43	18	because	because	SCONJ
cana-3299	43	19	of	of	ADP
cana-3299	43	20	their	their	PRON
cana-3299	43	21	applications	application	NOUN
cana-3299	43	22	in	in	ADP
cana-3299	43	23	various	various	ADJ
cana-3299	43	24	fields	field	NOUN
cana-3299	43	25	of	of	ADP
cana-3299	43	26	mathematics	mathematic	NOUN
cana-3299	43	27	and	and	CCONJ
cana-3299	43	28	other	other	ADJ
cana-3299	43	29	real	real	ADJ
cana-3299	43	30	fields	field	NOUN
cana-3299	43	31	.	.	PUNCT
cana-3299	44	1	recently	recently	ADV
cana-3299	44	2	,	,	PUNCT
cana-3299	44	3	jeeva	jeeva	PROPN
cana-3299	44	4	et	et	PROPN
cana-3299	44	5	al	al	PROPN
cana-3299	44	6	.	.	PUNCT
cana-3299	45	1	[	[	X
cana-3299	45	2	20	20	NUM
cana-3299	45	3	,	,	PUNCT
cana-3299	45	4	21	21	NUM
cana-3299	45	5	,	,	PUNCT
cana-3299	45	6	22	22	NUM
cana-3299	45	7	]	]	PUNCT
cana-3299	45	8	introduced	introduce	VERB
cana-3299	45	9	neutrosophic	neutrosophic	ADJ
cana-3299	45	10	soft	soft	ADJ
cana-3299	45	11	𝑀-open	𝑀-open	PROPN
cana-3299	45	12	sets	set	NOUN
cana-3299	45	13	in	in	ADP
cana-3299	45	14	neutrosophic	neutrosophic	ADJ
cana-3299	45	15	topological	topological	ADJ
cana-3299	45	16	spaces	space	NOUN
cana-3299	45	17	and	and	CCONJ
cana-3299	45	18	developed	develop	VERB
cana-3299	45	19	the	the	DET
cana-3299	45	20	concepts	concept	NOUN
cana-3299	45	21	of	of	ADP
cana-3299	45	22	neutrosophic	neutrosophic	ADJ
cana-3299	45	23	soft	soft	ADJ
cana-3299	45	24	𝑀-continuity	𝑀-continuity	PROPN
cana-3299	45	25	and	and	CCONJ
cana-3299	45	26	𝑀-irresolute	𝑀-irresolute	PROPN
cana-3299	45	27	maps	map	NOUN
cana-3299	45	28	.	.	PUNCT
cana-3299	46	1	2	2	X
cana-3299	46	2	.	.	X
cana-3299	46	3	preliminaries	preliminary	NOUN
cana-3299	46	4	we	we	PRON
cana-3299	46	5	recall	recall	VERB
cana-3299	46	6	some	some	DET
cana-3299	46	7	basic	basic	ADJ
cana-3299	46	8	notions	notion	NOUN
cana-3299	46	9	of	of	ADP
cana-3299	46	10	fuzzy	fuzzy	ADJ
cana-3299	46	11	sets	set	NOUN
cana-3299	46	12	,	,	PUNCT
cana-3299	46	13	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	46	14	’s	’s	PART
cana-3299	46	15	and	and	CCONJ
cana-3299	46	16	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	46	17	’s	’s	PART
cana-3299	46	18	.	.	PUNCT
cana-3299	47	1	definition	definition	NOUN
cana-3299	47	2	2.1	2.1	NUM
cana-3299	48	1	[	[	SYM
cana-3299	48	2	36	36	NUM
cana-3299	48	3	]	]	PUNCT
cana-3299	48	4	let	let	VERB
cana-3299	48	5	𝑋	𝑋	NOUN
cana-3299	48	6	be	be	AUX
cana-3299	48	7	a	a	DET
cana-3299	48	8	nonempty	nonempty	ADV
cana-3299	48	9	set	set	VERB
cana-3299	48	10	.	.	PUNCT
cana-3299	49	1	a	a	DET
cana-3299	49	2	fuzzy	fuzzy	ADJ
cana-3299	49	3	set	set	VERB
cana-3299	49	4	𝐴	𝐴	PROPN
cana-3299	49	5	in	in	ADP
cana-3299	49	6	𝑋	𝑋	PROPN
cana-3299	49	7	is	be	AUX
cana-3299	49	8	characterized	characterize	VERB
cana-3299	49	9	by	by	ADP
cana-3299	49	10	a	a	DET
cana-3299	49	11	membership	membership	NOUN
cana-3299	49	12	function	function	NOUN
cana-3299	49	13	𝜇𝐴	𝜇𝐴	ADP
cana-3299	49	14	:	:	PUNCT
cana-3299	49	15	𝑋	𝑋	PROPN
cana-3299	49	16	→	→	SYM
cana-3299	50	1	[	[	X
cana-3299	50	2	0,1	0,1	NUM
cana-3299	50	3	]	]	PUNCT
cana-3299	50	4	.	.	PUNCT
cana-3299	51	1	that	that	PRON
cana-3299	51	2	is	be	AUX
cana-3299	51	3	:	:	PUNCT
cana-3299	51	4	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	51	5	)	)	PUNCT
cana-3299	51	6	=	=	NOUN
cana-3299	51	7	{	{	PUNCT
cana-3299	52	1	1	1	NUM
cana-3299	52	2	,	,	PUNCT
cana-3299	52	3	if	if	SCONJ
cana-3299	52	4	𝑥	𝑥	PRON
cana-3299	52	5	∈	∈	PROPN
cana-3299	52	6	𝑋	𝑋	NOUN
cana-3299	52	7	0	0	NUM
cana-3299	52	8	,	,	PUNCT
cana-3299	52	9	if	if	SCONJ
cana-3299	52	10	𝑥	𝑥	PROPN
cana-3299	52	11	∉	∉	X
cana-3299	52	12	𝑋	𝑋	PROPN
cana-3299	52	13	(	(	PUNCT
cana-3299	52	14	0,1	0,1	NUM
cana-3299	52	15	)	)	PUNCT
cana-3299	52	16	if	if	SCONJ
cana-3299	52	17	𝑥	𝑥	NOUN
cana-3299	52	18	ispartlyin	ispartlyin	VERB
cana-3299	52	19	𝑋.	𝑋.	PROPN
cana-3299	52	20	alternatively	alternatively	ADV
cana-3299	52	21	,	,	PUNCT
cana-3299	52	22	a	a	DET
cana-3299	52	23	fuzzy	fuzzy	ADJ
cana-3299	52	24	set	set	VERB
cana-3299	52	25	𝐴	𝐴	PROPN
cana-3299	52	26	in	in	ADP
cana-3299	52	27	𝑋	𝑋	PROPN
cana-3299	52	28	is	be	AUX
cana-3299	52	29	an	an	DET
cana-3299	52	30	object	object	NOUN
cana-3299	52	31	having	have	VERB
cana-3299	52	32	the	the	DET
cana-3299	52	33	form	form	NOUN
cana-3299	52	34	𝐴	𝐴	NOUN
cana-3299	52	35	=	=	PUNCT
cana-3299	52	36	{	{	PUNCT
cana-3299	52	37	<	<	X
cana-3299	52	38	𝑥	𝑥	X
cana-3299	52	39	,	,	PUNCT
cana-3299	52	40	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	52	41	)	)	PUNCT
cana-3299	52	42	>	>	PUNCT
cana-3299	53	1	|𝑥	|𝑥	PROPN
cana-3299	53	2	∈	∈	PROPN
cana-3299	53	3	𝑋	𝑋	PROPN
cana-3299	53	4	}	}	PUNCT
cana-3299	53	5	or	or	CCONJ
cana-3299	53	6	𝐴	𝐴	PROPN
cana-3299	53	7	=	=	PUNCT
cana-3299	53	8	{	{	PUNCT
cana-3299	53	9	⟨	⟨	NOUN
cana-3299	53	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	53	11	)	)	PUNCT
cana-3299	53	12	𝑥	𝑥	DET
cana-3299	53	13	⟩	⟩	NOUN
cana-3299	53	14	|𝑥	|𝑥	NOUN
cana-3299	53	15	∈	∈	PROPN
cana-3299	53	16	𝑋	𝑋	PROPN
cana-3299	53	17	}	}	PUNCT
cana-3299	53	18	,	,	PUNCT
cana-3299	53	19	where	where	SCONJ
cana-3299	53	20	the	the	DET
cana-3299	53	21	function	function	NOUN
cana-3299	53	22	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-3299	53	23	):	):	PUNCT
cana-3299	53	24	𝑋	𝑋	PROPN
cana-3299	53	25	→	→	SYM
cana-3299	53	26	[	[	X
cana-3299	53	27	0,1	0,1	NUM
cana-3299	53	28	]	]	PUNCT
cana-3299	53	29	defines	define	VERB
cana-3299	53	30	the	the	DET
cana-3299	53	31	degree	degree	NOUN
cana-3299	53	32	of	of	ADP
cana-3299	53	33	membership	membership	NOUN
cana-3299	53	34	of	of	ADP
cana-3299	53	35	the	the	DET
cana-3299	53	36	element	element	NOUN
cana-3299	53	37	,	,	PUNCT
cana-3299	53	38	𝑥	𝑥	PROPN
cana-3299	53	39	∈	∈	PROPN
cana-3299	53	40	𝑋.	𝑋.	PROPN
cana-3299	53	41	the	the	PRON
cana-3299	53	42	closer	close	ADV
cana-3299	53	43	the	the	DET
cana-3299	53	44	membership	membership	NOUN
cana-3299	53	45	value	value	NOUN
cana-3299	53	46	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-3299	53	47	)	)	PUNCT
cana-3299	53	48	to	to	ADP
cana-3299	53	49	1	1	NUM
cana-3299	53	50	,	,	PUNCT
cana-3299	53	51	the	the	PRON
cana-3299	53	52	more	more	ADJ
cana-3299	53	53	𝑥	𝑥	NOUN
cana-3299	53	54	belongs	belong	VERB
cana-3299	53	55	to	to	ADP
cana-3299	53	56	𝐴	𝐴	PROPN
cana-3299	53	57	,	,	PUNCT
cana-3299	53	58	where	where	SCONJ
cana-3299	53	59	the	the	DET
cana-3299	53	60	grades	grade	NOUN
cana-3299	53	61	1	1	NUM
cana-3299	53	62	and	and	CCONJ
cana-3299	53	63	0	0	NUM
cana-3299	53	64	represent	represent	VERB
cana-3299	53	65	full	full	ADJ
cana-3299	53	66	membership	membership	NOUN
cana-3299	53	67	and	and	CCONJ
cana-3299	53	68	full	full	ADJ
cana-3299	53	69	nonmembership	nonmembership	NOUN
cana-3299	53	70	.	.	PUNCT
cana-3299	54	1	fuzzy	fuzzy	ADJ
cana-3299	54	2	set	set	NOUN
cana-3299	54	3	is	be	AUX
cana-3299	54	4	a	a	DET
cana-3299	54	5	collection	collection	NOUN
cana-3299	54	6	of	of	ADP
cana-3299	54	7	objects	object	NOUN
cana-3299	54	8	with	with	ADP
cana-3299	54	9	graded	grade	VERB
cana-3299	54	10	membership	membership	NOUN
cana-3299	54	11	,	,	PUNCT
cana-3299	54	12	that	that	ADV
cana-3299	54	13	is	is	ADV
cana-3299	54	14	,	,	PUNCT
cana-3299	54	15	having	have	VERB
cana-3299	54	16	degree	degree	NOUN
cana-3299	54	17	of	of	ADP
cana-3299	54	18	membership	membership	NOUN
cana-3299	54	19	.	.	PUNCT
cana-3299	55	1	fuzzy	fuzzy	ADJ
cana-3299	55	2	set	set	NOUN
cana-3299	55	3	is	be	AUX
cana-3299	55	4	an	an	DET
cana-3299	55	5	extension	extension	NOUN
cana-3299	55	6	of	of	ADP
cana-3299	55	7	the	the	DET
cana-3299	55	8	classical	classical	ADJ
cana-3299	55	9	notion	notion	NOUN
cana-3299	55	10	of	of	ADP
cana-3299	55	11	set	set	NOUN
cana-3299	55	12	.	.	PUNCT
cana-3299	56	1	in	in	ADP
cana-3299	56	2	classical	classical	ADJ
cana-3299	56	3	set	set	NOUN
cana-3299	56	4	theory	theory	NOUN
cana-3299	56	5	,	,	PUNCT
cana-3299	56	6	the	the	DET
cana-3299	56	7	membership	membership	NOUN
cana-3299	56	8	of	of	ADP
cana-3299	56	9	elements	element	NOUN
cana-3299	56	10	in	in	ADP
cana-3299	56	11	a	a	DET
cana-3299	56	12	set	set	NOUN
cana-3299	56	13	is	be	AUX
cana-3299	56	14	assessed	assess	VERB
cana-3299	56	15	in	in	ADP
cana-3299	56	16	a	a	DET
cana-3299	56	17	binary	binary	ADJ
cana-3299	56	18	terms	term	NOUN
cana-3299	56	19	according	accord	VERB
cana-3299	56	20	to	to	ADP
cana-3299	56	21	a	a	DET
cana-3299	56	22	bivalent	bivalent	ADJ
cana-3299	56	23	condition	condition	NOUN
cana-3299	56	24	;	;	PUNCT
cana-3299	56	25	an	an	DET
cana-3299	56	26	element	element	NOUN
cana-3299	56	27	either	either	CCONJ
cana-3299	56	28	belongs	belong	VERB
cana-3299	56	29	or	or	CCONJ
cana-3299	56	30	does	do	AUX
cana-3299	56	31	not	not	PART
cana-3299	56	32	belong	belong	VERB
cana-3299	56	33	to	to	ADP
cana-3299	56	34	the	the	DET
cana-3299	56	35	set	set	NOUN
cana-3299	56	36	.	.	PUNCT
cana-3299	57	1	classical	classical	ADJ
cana-3299	57	2	bivalent	bivalent	ADJ
cana-3299	57	3	sets	set	NOUN
cana-3299	57	4	are	be	AUX
cana-3299	57	5	in	in	ADP
cana-3299	57	6	fuzzy	fuzzy	ADJ
cana-3299	57	7	set	set	NOUN
cana-3299	57	8	theory	theory	NOUN
cana-3299	57	9	called	call	VERB
cana-3299	57	10	crisp	crisp	ADJ
cana-3299	57	11	sets	set	NOUN
cana-3299	57	12	.	.	PUNCT
cana-3299	58	1	fuzzy	fuzzy	ADJ
cana-3299	58	2	sets	set	NOUN
cana-3299	58	3	are	be	AUX
cana-3299	58	4	generalized	generalized	ADJ
cana-3299	58	5	classical	classical	ADJ
cana-3299	58	6	sets	set	NOUN
cana-3299	58	7	,	,	PUNCT
cana-3299	58	8	since	since	SCONJ
cana-3299	58	9	the	the	DET
cana-3299	58	10	indicator	indicator	NOUN
cana-3299	58	11	function	function	NOUN
cana-3299	58	12	of	of	ADP
cana-3299	58	13	classical	classical	ADJ
cana-3299	58	14	sets	set	NOUN
cana-3299	58	15	is	be	AUX
cana-3299	58	16	special	special	ADJ
cana-3299	58	17	cases	case	NOUN
cana-3299	58	18	of	of	ADP
cana-3299	58	19	the	the	DET
cana-3299	58	20	membership	membership	NOUN
cana-3299	58	21	functions	function	NOUN
cana-3299	58	22	of	of	ADP
cana-3299	58	23	fuzzy	fuzzy	ADJ
cana-3299	58	24	sets	set	NOUN
cana-3299	58	25	,	,	PUNCT
cana-3299	58	26	if	if	SCONJ
cana-3299	58	27	the	the	DET
cana-3299	58	28	latter	latter	ADJ
cana-3299	58	29	only	only	ADV
cana-3299	58	30	take	take	VERB
cana-3299	58	31	values	value	NOUN
cana-3299	58	32	0	0	NUM
cana-3299	58	33	or	or	CCONJ
cana-3299	58	34	1	1	NUM
cana-3299	58	35	.	.	X
cana-3299	58	36	fuzzy	fuzzy	ADJ
cana-3299	58	37	sets	set	NOUN
cana-3299	58	38	theory	theory	NOUN
cana-3299	58	39	permits	permit	VERB
cana-3299	58	40	the	the	DET
cana-3299	58	41	gradual	gradual	ADJ
cana-3299	58	42	assessment	assessment	NOUN
cana-3299	58	43	of	of	ADP
cana-3299	58	44	the	the	DET
cana-3299	58	45	membership	membership	NOUN
cana-3299	58	46	of	of	ADP
cana-3299	58	47	element	element	NOUN
cana-3299	58	48	in	in	ADP
cana-3299	58	49	a	a	DET
cana-3299	58	50	set	set	NOUN
cana-3299	58	51	;	;	PUNCT
cana-3299	58	52	this	this	PRON
cana-3299	58	53	is	be	AUX
cana-3299	58	54	described	describe	VERB
cana-3299	58	55	with	with	ADP
cana-3299	58	56	the	the	DET
cana-3299	58	57	aid	aid	NOUN
cana-3299	58	58	of	of	ADP
cana-3299	58	59	a	a	DET
cana-3299	58	60	membership	membership	NOUN
cana-3299	58	61	function	function	NOUN
cana-3299	58	62	valued	value	VERB
cana-3299	58	63	in	in	ADP
cana-3299	58	64	the	the	DET
cana-3299	58	65	real	real	ADJ
cana-3299	58	66	unit	unit	NOUN
cana-3299	58	67	interval	interval	NOUN
cana-3299	58	68	[	[	X
cana-3299	58	69	0,1	0,1	NUM
cana-3299	58	70	]	]	PUNCT
cana-3299	58	71	.	.	PUNCT
cana-3299	59	1	let	let	VERB
cana-3299	59	2	us	we	PRON
cana-3299	59	3	consider	consider	VERB
cana-3299	59	4	two	two	NUM
cana-3299	59	5	examples	example	NOUN
cana-3299	59	6	:	:	PUNCT
cana-3299	59	7	(	(	PUNCT
cana-3299	59	8	i	i	NOUN
cana-3299	59	9	)	)	PUNCT
cana-3299	59	10	all	all	DET
cana-3299	59	11	employees	employee	NOUN
cana-3299	59	12	of	of	ADP
cana-3299	59	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-3299	59	14	who	who	PRON
cana-3299	59	15	are	be	AUX
cana-3299	59	16	over	over	ADP
cana-3299	59	17	1.8𝑚	1.8𝑚	NUM
cana-3299	59	18	in	in	ADP
cana-3299	59	19	height	height	NOUN
cana-3299	59	20	;	;	PUNCT
cana-3299	59	21	(	(	PUNCT
cana-3299	59	22	ii	ii	NOUN
cana-3299	59	23	)	)	PUNCT
cana-3299	59	24	all	all	DET
cana-3299	59	25	employees	employee	NOUN
cana-3299	59	26	of	of	ADP
cana-3299	59	27	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-3299	59	28	who	who	PRON
cana-3299	59	29	are	be	AUX
cana-3299	59	30	tall	tall	ADJ
cana-3299	59	31	.	.	PUNCT
cana-3299	60	1	the	the	DET
cana-3299	60	2	first	first	ADJ
cana-3299	60	3	example	example	NOUN
cana-3299	60	4	is	be	AUX
cana-3299	60	5	a	a	DET
cana-3299	60	6	classical	classical	ADJ
cana-3299	60	7	set	set	NOUN
cana-3299	60	8	with	with	ADP
cana-3299	60	9	a	a	DET
cana-3299	60	10	universe	universe	NOUN
cana-3299	60	11	(	(	PUNCT
cana-3299	60	12	all	all	DET
cana-3299	60	13	𝑋𝑌𝑍	𝑋𝑌𝑍	PROPN
cana-3299	60	14	employees	employee	NOUN
cana-3299	60	15	)	)	PUNCT
cana-3299	60	16	and	and	CCONJ
cana-3299	60	17	a	a	DET
cana-3299	60	18	membership	membership	NOUN
cana-3299	60	19	rule	rule	NOUN
cana-3299	60	20	that	that	PRON
cana-3299	60	21	divides	divide	VERB
cana-3299	60	22	the	the	DET
cana-3299	60	23	universe	universe	NOUN
cana-3299	60	24	into	into	ADP
cana-3299	60	25	members	member	NOUN
cana-3299	60	26	(	(	PUNCT
cana-3299	60	27	those	those	PRON
cana-3299	60	28	over	over	ADP
cana-3299	60	29	1.8𝑚	1.8𝑚	NUM
cana-3299	60	30	)	)	PUNCT
cana-3299	60	31	and	and	CCONJ
cana-3299	60	32	nonmembers	nonmember	NOUN
cana-3299	60	33	.	.	PUNCT
cana-3299	61	1	the	the	DET
cana-3299	61	2	second	second	ADJ
cana-3299	61	3	example	example	NOUN
cana-3299	61	4	is	be	AUX
cana-3299	61	5	a	a	DET
cana-3299	61	6	fuzzy	fuzzy	ADJ
cana-3299	61	7	set	set	NOUN
cana-3299	61	8	,	,	PUNCT
cana-3299	61	9	because	because	SCONJ
cana-3299	61	10	some	some	DET
cana-3299	61	11	employees	employee	NOUN
cana-3299	61	12	are	be	AUX
cana-3299	61	13	definitely	definitely	ADV
cana-3299	61	14	in	in	ADP
cana-3299	61	15	the	the	DET
cana-3299	61	16	set	set	NOUN
cana-3299	61	17	and	and	CCONJ
cana-3299	61	18	some	some	PRON
cana-3299	61	19	are	be	AUX
cana-3299	61	20	definitely	definitely	ADV
cana-3299	61	21	not	not	PART
cana-3299	61	22	in	in	ADP
cana-3299	61	23	the	the	DET
cana-3299	61	24	set	set	NOUN
cana-3299	61	25	,	,	PUNCT
cana-3299	61	26	but	but	CCONJ
cana-3299	61	27	some	some	PRON
cana-3299	61	28	are	be	AUX
cana-3299	61	29	borderline	borderline	NOUN
cana-3299	61	30	.	.	PUNCT
cana-3299	62	1	communications	communication	NOUN
cana-3299	62	2	on	on	ADP
cana-3299	62	3	applied	apply	VERB
cana-3299	62	4	nonlinear	nonlinear	ADJ
cana-3299	62	5	analysis	analysis	NOUN
cana-3299	62	6	issn	issn	NOUN
cana-3299	62	7	:	:	PUNCT
cana-3299	62	8	1074	1074	NUM
cana-3299	62	9	-	-	PUNCT
cana-3299	62	10	133x	133x	NUM
cana-3299	62	11	vol	vol	NOUN
cana-3299	62	12	32	32	NUM
cana-3299	62	13	no	no	NOUN
cana-3299	62	14	.	.	PUNCT
cana-3299	63	1	6s	6s	NUM
cana-3299	63	2	(	(	PUNCT
cana-3299	63	3	2025	2025	NUM
cana-3299	63	4	)	)	PUNCT
cana-3299	63	5	329	329	NUM
cana-3299	63	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	63	7	this	this	DET
cana-3299	63	8	distinction	distinction	NOUN
cana-3299	63	9	between	between	ADP
cana-3299	63	10	the	the	DET
cana-3299	63	11	ins	in	NOUN
cana-3299	63	12	,	,	PUNCT
cana-3299	63	13	the	the	DET
cana-3299	63	14	outs	out	NOUN
cana-3299	63	15	,	,	PUNCT
cana-3299	63	16	and	and	CCONJ
cana-3299	63	17	the	the	DET
cana-3299	63	18	borderline	borderline	NOUN
cana-3299	63	19	is	be	AUX
cana-3299	63	20	made	make	VERB
cana-3299	63	21	more	more	ADV
cana-3299	63	22	exact	exact	ADJ
cana-3299	63	23	by	by	ADP
cana-3299	63	24	the	the	DET
cana-3299	63	25	membership	membership	NOUN
cana-3299	63	26	function	function	NOUN
cana-3299	63	27	,	,	PUNCT
cana-3299	63	28	𝜇.	𝜇.	ADV
cana-3299	63	29	if	if	SCONJ
cana-3299	63	30	we	we	PRON
cana-3299	63	31	return	return	VERB
cana-3299	63	32	to	to	ADP
cana-3299	63	33	our	our	PRON
cana-3299	63	34	second	second	ADJ
cana-3299	63	35	example	example	NOUN
cana-3299	63	36	and	and	CCONJ
cana-3299	63	37	let	let	VERB
cana-3299	63	38	𝐴	𝐴	PROPN
cana-3299	63	39	represent	represent	VERB
cana-3299	63	40	the	the	DET
cana-3299	63	41	fuzzy	fuzzy	ADJ
cana-3299	63	42	set	set	NOUN
cana-3299	63	43	of	of	ADP
cana-3299	63	44	all	all	DET
cana-3299	63	45	tall	tall	ADJ
cana-3299	63	46	employees	employee	NOUN
cana-3299	63	47	and	and	CCONJ
cana-3299	63	48	𝑥	𝑥	PROPN
cana-3299	63	49	represent	represent	VERB
cana-3299	63	50	a	a	DET
cana-3299	63	51	member	member	NOUN
cana-3299	63	52	of	of	ADP
cana-3299	63	53	the	the	DET
cana-3299	63	54	universe	universe	ADJ
cana-3299	63	55	𝑋	𝑋	NOUN
cana-3299	63	56	(	(	PUNCT
cana-3299	63	57	i.e.	i.e.	X
cana-3299	63	58	all	all	DET
cana-3299	63	59	employees	employee	NOUN
cana-3299	63	60	)	)	PUNCT
cana-3299	63	61	,	,	PUNCT
cana-3299	63	62	then	then	ADV
cana-3299	63	63	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	63	64	)	)	PUNCT
cana-3299	63	65	would	would	AUX
cana-3299	63	66	be	be	AUX
cana-3299	63	67	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	63	68	)	)	PUNCT
cana-3299	64	1	=	=	SYM
cana-3299	64	2	1	1	NUM
cana-3299	64	3	if	if	SCONJ
cana-3299	64	4	𝑥	𝑥	PRON
cana-3299	64	5	is	be	AUX
cana-3299	64	6	definitely	definitely	ADV
cana-3299	64	7	tall	tall	ADJ
cana-3299	64	8	or	or	CCONJ
cana-3299	64	9	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	64	10	)	)	PUNCT
cana-3299	64	11	=	=	SYM
cana-3299	64	12	0	0	PUNCT
cana-3299	65	1	if	if	SCONJ
cana-3299	65	2	𝑥	𝑥	PRON
cana-3299	65	3	is	be	AUX
cana-3299	65	4	definitely	definitely	ADV
cana-3299	65	5	not	not	PART
cana-3299	65	6	tall	tall	ADJ
cana-3299	65	7	or	or	CCONJ
cana-3299	65	8	0	0	NUM
cana-3299	65	9	<	<	X
cana-3299	65	10	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-3299	65	11	)	)	PUNCT
cana-3299	65	12	<	<	X
cana-3299	65	13	1	1	NUM
cana-3299	65	14	for	for	ADP
cana-3299	65	15	borderline	borderline	NOUN
cana-3299	65	16	cases	case	NOUN
cana-3299	65	17	.	.	PUNCT
cana-3299	66	1	definition	definition	NOUN
cana-3299	66	2	2.2	2.2	NUM
cana-3299	66	3	[	[	SYM
cana-3299	66	4	1	1	NUM
cana-3299	66	5	,	,	PUNCT
cana-3299	66	6	2	2	NUM
cana-3299	66	7	,	,	PUNCT
cana-3299	66	8	4	4	NUM
cana-3299	66	9	,	,	PUNCT
cana-3299	66	10	5	5	NUM
cana-3299	66	11	]	]	PUNCT
cana-3299	66	12	let	let	VERB
cana-3299	66	13	a	a	DET
cana-3299	66	14	nonempty	nonempty	ADV
cana-3299	66	15	set	set	VERB
cana-3299	66	16	𝑋	𝑋	NOUN
cana-3299	66	17	be	be	AUX
cana-3299	66	18	fixed	fix	VERB
cana-3299	66	19	.	.	PUNCT
cana-3299	67	1	an	an	DET
cana-3299	67	2	𝐼𝐹𝑆	𝐼𝐹𝑆	PROPN
cana-3299	67	3	𝐴	𝐴	PROPN
cana-3299	67	4	in	in	ADP
cana-3299	67	5	𝑋	𝑋	PROPN
cana-3299	67	6	is	be	AUX
cana-3299	67	7	an	an	DET
cana-3299	67	8	object	object	NOUN
cana-3299	67	9	having	have	VERB
cana-3299	67	10	the	the	DET
cana-3299	67	11	form	form	NOUN
cana-3299	67	12	:	:	PUNCT
cana-3299	67	13	𝐴	𝐴	PROPN
cana-3299	67	14	=	=	PUNCT
cana-3299	67	15	{	{	PUNCT
cana-3299	67	16	<	<	X
cana-3299	67	17	𝑥	𝑥	X
cana-3299	67	18	,	,	PUNCT
cana-3299	67	19	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NOUN
cana-3299	67	20	)	)	PUNCT
cana-3299	67	21	,	,	PUNCT
cana-3299	67	22	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-3299	67	23	)	)	PUNCT
cana-3299	67	24	>	>	X
cana-3299	67	25	|𝑥	|𝑥	PROPN
cana-3299	67	26	∈	∈	PROPN
cana-3299	67	27	𝑋	𝑋	PROPN
cana-3299	67	28	}	}	PUNCT
cana-3299	67	29	or	or	CCONJ
cana-3299	67	30	𝐴	𝐴	PROPN
cana-3299	67	31	=	=	PUNCT
cana-3299	67	32	{	{	PUNCT
cana-3299	67	33	⟨	⟨	NOUN
cana-3299	67	34	𝜇𝐴(𝑥),𝜈𝐴(𝑥	𝜇𝐴(𝑥),𝜈𝐴(𝑥	NOUN
cana-3299	67	35	)	)	PUNCT
cana-3299	68	1	𝑥	𝑥	DET
cana-3299	68	2	⟩	⟩	NOUN
cana-3299	68	3	|𝑥	|𝑥	NOUN
cana-3299	68	4	∈	∈	PROPN
cana-3299	68	5	𝑋	𝑋	PROPN
cana-3299	68	6	}	}	PUNCT
cana-3299	68	7	,	,	PUNCT
cana-3299	68	8	where	where	SCONJ
cana-3299	68	9	the	the	DET
cana-3299	68	10	functions	function	NOUN
cana-3299	68	11	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-3299	68	12	):	):	PUNCT
cana-3299	68	13	𝑋	𝑋	PROPN
cana-3299	68	14	→	→	SYM
cana-3299	68	15	[	[	X
cana-3299	68	16	0,1	0,1	NUM
cana-3299	68	17	]	]	PUNCT
cana-3299	68	18	and	and	CCONJ
cana-3299	68	19	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-3299	68	20	):	):	PUNCT
cana-3299	68	21	𝑋	𝑋	PROPN
cana-3299	68	22	→	→	SYM
cana-3299	68	23	[	[	X
cana-3299	68	24	0,1	0,1	NUM
cana-3299	68	25	]	]	PUNCT
cana-3299	68	26	define	define	VERB
cana-3299	68	27	the	the	DET
cana-3299	68	28	degree	degree	NOUN
cana-3299	68	29	of	of	ADP
cana-3299	68	30	membership	membership	NOUN
cana-3299	68	31	and	and	CCONJ
cana-3299	68	32	the	the	DET
cana-3299	68	33	degree	degree	NOUN
cana-3299	68	34	of	of	ADP
cana-3299	68	35	nonmembership	nonmembership	NOUN
cana-3299	68	36	,	,	PUNCT
cana-3299	68	37	respectively	respectively	ADV
cana-3299	68	38	,	,	PUNCT
cana-3299	68	39	of	of	ADP
cana-3299	68	40	the	the	DET
cana-3299	68	41	element	element	NOUN
cana-3299	68	42	𝑥	𝑥	PRON
cana-3299	68	43	∈	∈	PROPN
cana-3299	68	44	𝑋	𝑋	NOUN
cana-3299	68	45	to	to	ADP
cana-3299	68	46	𝐴	𝐴	PROPN
cana-3299	68	47	,	,	PUNCT
cana-3299	68	48	which	which	PRON
cana-3299	68	49	is	be	AUX
cana-3299	68	50	a	a	DET
cana-3299	68	51	subset	subset	NOUN
cana-3299	68	52	of	of	ADP
cana-3299	68	53	𝑋	𝑋	PROPN
cana-3299	68	54	,	,	PUNCT
cana-3299	68	55	and	and	CCONJ
cana-3299	68	56	for	for	ADP
cana-3299	68	57	every	every	DET
cana-3299	68	58	𝑥	𝑥	PRON
cana-3299	68	59	∈	∈	PROPN
cana-3299	68	60	𝑋	𝑋	NOUN
cana-3299	68	61	:	:	PUNCT
cana-3299	68	62	0	0	NUM
cana-3299	68	63	≤	≤	NUM
cana-3299	68	64	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	68	65	)	)	PUNCT
cana-3299	68	66	+	+	NUM
cana-3299	68	67	𝜈𝐴(𝑥	𝜈𝐴(𝑥	X
cana-3299	68	68	)	)	PUNCT
cana-3299	68	69	≤	≤	NUM
cana-3299	68	70	1	1	NUM
cana-3299	68	71	.	.	PUNCT
cana-3299	69	1	for	for	ADP
cana-3299	69	2	each	each	DET
cana-3299	69	3	𝐴	𝐴	PROPN
cana-3299	69	4	in	in	ADP
cana-3299	69	5	𝑋	𝑋	PROPN
cana-3299	69	6	:	:	PUNCT
cana-3299	69	7	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	69	8	)	)	PUNCT
cana-3299	69	9	=	=	SYM
cana-3299	69	10	1	1	NUM
cana-3299	69	11	−	−	NUM
cana-3299	69	12	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	69	13	)	)	PUNCT
cana-3299	69	14	−	−	PROPN
cana-3299	69	15	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-3299	69	16	)	)	PUNCT
cana-3299	69	17	is	be	AUX
cana-3299	69	18	the	the	DET
cana-3299	69	19	intuitionistic	intuitionistic	ADJ
cana-3299	69	20	fuzzy	fuzzy	ADJ
cana-3299	69	21	set	set	VERB
cana-3299	69	22	index	index	NOUN
cana-3299	69	23	or	or	CCONJ
cana-3299	69	24	hesitation	hesitation	NOUN
cana-3299	69	25	margin	margin	NOUN
cana-3299	69	26	of	of	ADP
cana-3299	69	27	𝑥	𝑥	NOUN
cana-3299	69	28	in	in	ADP
cana-3299	69	29	𝑋.	𝑋.	PROPN
cana-3299	69	30	the	the	DET
cana-3299	69	31	hesitation	hesitation	NOUN
cana-3299	69	32	margin	margin	NOUN
cana-3299	69	33	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	69	34	)	)	PUNCT
cana-3299	69	35	is	be	AUX
cana-3299	69	36	the	the	DET
cana-3299	69	37	degree	degree	NOUN
cana-3299	69	38	of	of	ADP
cana-3299	69	39	nondeterminacy	nondeterminacy	NOUN
cana-3299	69	40	of	of	ADP
cana-3299	69	41	𝑥	𝑥	DET
cana-3299	69	42	∈	∈	PROPN
cana-3299	69	43	𝑋	𝑋	NOUN
cana-3299	69	44	to	to	ADP
cana-3299	69	45	the	the	DET
cana-3299	69	46	set	set	ADJ
cana-3299	69	47	𝐴	𝐴	PROPN
cana-3299	69	48	and	and	CCONJ
cana-3299	69	49	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	69	50	)	)	PUNCT
cana-3299	69	51	∈	∈	NOUN
cana-3299	70	1	[	[	X
cana-3299	70	2	0,1	0,1	NUM
cana-3299	70	3	]	]	PUNCT
cana-3299	70	4	.	.	PUNCT
cana-3299	71	1	the	the	DET
cana-3299	71	2	hesitation	hesitation	NOUN
cana-3299	71	3	margin	margin	NOUN
cana-3299	71	4	is	be	AUX
cana-3299	71	5	the	the	DET
cana-3299	71	6	function	function	NOUN
cana-3299	71	7	that	that	PRON
cana-3299	71	8	expresses	express	VERB
cana-3299	71	9	lack	lack	NOUN
cana-3299	71	10	of	of	ADP
cana-3299	71	11	knowledge	knowledge	NOUN
cana-3299	71	12	of	of	ADP
cana-3299	71	13	whether	whether	SCONJ
cana-3299	71	14	𝑥	𝑥	PRON
cana-3299	71	15	∈	∈	PROPN
cana-3299	71	16	𝑋	𝑋	NOUN
cana-3299	71	17	or	or	CCONJ
cana-3299	71	18	𝑥	𝑥	PROPN
cana-3299	71	19	∉	∉	PROPN
cana-3299	71	20	𝑋.	𝑋.	PROPN
cana-3299	71	21	thus	thus	ADV
cana-3299	71	22	:	:	PUNCT
cana-3299	71	23	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	71	24	)	)	PUNCT
cana-3299	71	25	+	+	NUM
cana-3299	71	26	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-3299	71	27	)	)	PUNCT
cana-3299	71	28	+	+	NUM
cana-3299	71	29	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	71	30	)	)	PUNCT
cana-3299	71	31	=	=	SYM
cana-3299	71	32	1	1	X
cana-3299	71	33	.	.	PUNCT
cana-3299	71	34	example	example	NOUN
cana-3299	71	35	2.1	2.1	NUM
cana-3299	71	36	let	let	VERB
cana-3299	71	37	𝑋	𝑋	NOUN
cana-3299	71	38	=	=	SYM
cana-3299	71	39	{	{	PUNCT
cana-3299	71	40	𝑥	𝑥	PROPN
cana-3299	71	41	,	,	PUNCT
cana-3299	71	42	𝑦	𝑦	NOUN
cana-3299	71	43	,	,	PUNCT
cana-3299	71	44	𝑧	𝑧	PRON
cana-3299	71	45	}	}	PUNCT
cana-3299	71	46	be	be	AUX
cana-3299	71	47	a	a	DET
cana-3299	71	48	fixed	fix	VERB
cana-3299	71	49	universe	universe	NOUN
cana-3299	71	50	of	of	ADP
cana-3299	71	51	discourse	discourse	NOUN
cana-3299	71	52	and	and	CCONJ
cana-3299	71	53	𝐴	𝐴	PROPN
cana-3299	71	54	=	=	PUNCT
cana-3299	71	55	{	{	PUNCT
cana-3299	71	56	⟨	⟨	VERB
cana-3299	71	57	0.6,0.1	0.6,0.1	PROPN
cana-3299	71	58	𝑥	𝑥	DET
cana-3299	71	59	⟩	⟩	NOUN
cana-3299	71	60	,	,	PUNCT
cana-3299	71	61	⟨	⟨	VERB
cana-3299	71	62	0.8,0.1	0.8,0.1	PROPN
cana-3299	71	63	𝑦	𝑦	NOUN
cana-3299	71	64	⟩	⟩	NOUN
cana-3299	71	65	,	,	PUNCT
cana-3299	71	66	⟨	⟨	VERB
cana-3299	71	67	0.5,0.3	0.5,0.3	PROPN
cana-3299	71	68	𝑧	𝑧	DET
cana-3299	71	69	⟩	⟩	NOUN
cana-3299	71	70	}	}	PUNCT
cana-3299	71	71	,	,	PUNCT
cana-3299	71	72	be	be	AUX
cana-3299	71	73	the	the	DET
cana-3299	71	74	intuitionistic	intuitionistic	ADJ
cana-3299	71	75	fuzzy	fuzzy	ADJ
cana-3299	71	76	set	set	NOUN
cana-3299	71	77	in	in	ADP
cana-3299	71	78	𝑋.	𝑋.	PROPN
cana-3299	71	79	the	the	DET
cana-3299	71	80	hesitation	hesitation	NOUN
cana-3299	71	81	margins	margin	NOUN
cana-3299	71	82	of	of	ADP
cana-3299	71	83	the	the	DET
cana-3299	71	84	elements	element	NOUN
cana-3299	71	85	𝑥	𝑥	PROPN
cana-3299	71	86	,	,	PUNCT
cana-3299	71	87	𝑦	𝑦	NOUN
cana-3299	71	88	,	,	PUNCT
cana-3299	71	89	𝑧	𝑧	PUNCT
cana-3299	71	90	to	to	ADP
cana-3299	71	91	𝐴	𝐴	PROPN
cana-3299	71	92	are	be	AUX
cana-3299	71	93	as	as	SCONJ
cana-3299	71	94	follows	follow	VERB
cana-3299	71	95	:	:	PUNCT
cana-3299	71	96	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	71	97	)	)	PUNCT
cana-3299	71	98	=	=	SYM
cana-3299	71	99	0.3	0.3	NUM
cana-3299	71	100	,	,	PUNCT
cana-3299	71	101	𝜋𝐴(𝑦	𝜋𝐴(𝑦	PROPN
cana-3299	71	102	)	)	PUNCT
cana-3299	71	103	=	=	SYM
cana-3299	71	104	0.1	0.1	NUM
cana-3299	71	105	and	and	CCONJ
cana-3299	71	106	𝜋𝐴(𝑧	𝜋𝐴(𝑧	NUM
cana-3299	71	107	)	)	PUNCT
cana-3299	71	108	=	=	PUNCT
cana-3299	72	1	0.2	0.2	NUM
cana-3299	72	2	.	.	PUNCT
cana-3299	73	1	definition	definition	NOUN
cana-3299	73	2	2.3	2.3	NUM
cana-3299	74	1	[	[	SYM
cana-3299	74	2	33	33	NUM
cana-3299	74	3	,	,	PUNCT
cana-3299	74	4	34	34	NUM
cana-3299	74	5	,	,	PUNCT
cana-3299	74	6	35	35	NUM
cana-3299	74	7	]	]	PUNCT
cana-3299	74	8	let	let	VERB
cana-3299	74	9	𝑋	𝑋	NOUN
cana-3299	74	10	be	be	AUX
cana-3299	74	11	a	a	DET
cana-3299	74	12	universal	universal	ADJ
cana-3299	74	13	set	set	NOUN
cana-3299	74	14	.	.	PUNCT
cana-3299	75	1	then	then	ADV
cana-3299	75	2	,	,	PUNCT
cana-3299	75	3	a	a	DET
cana-3299	75	4	pythagorean	pythagorean	PROPN
cana-3299	75	5	fuzzy	fuzzy	ADJ
cana-3299	75	6	set	set	PROPN
cana-3299	75	7	𝐴	𝐴	PROPN
cana-3299	75	8	,	,	PUNCT
cana-3299	75	9	which	which	PRON
cana-3299	75	10	is	be	AUX
cana-3299	75	11	a	a	DET
cana-3299	75	12	set	set	NOUN
cana-3299	75	13	of	of	ADP
cana-3299	75	14	ordered	order	VERB
cana-3299	75	15	pairs	pair	NOUN
cana-3299	75	16	over	over	ADP
cana-3299	75	17	𝑋	𝑋	PROPN
cana-3299	75	18	,	,	PUNCT
cana-3299	75	19	is	be	AUX
cana-3299	75	20	defined	define	VERB
cana-3299	75	21	by	by	ADP
cana-3299	75	22	the	the	DET
cana-3299	75	23	following	following	NOUN
cana-3299	75	24	:	:	PUNCT
cana-3299	75	25	𝐴	𝐴	PROPN
cana-3299	75	26	=	=	PUNCT
cana-3299	75	27	{	{	PUNCT
cana-3299	75	28	<	<	X
cana-3299	75	29	𝑥	𝑥	X
cana-3299	75	30	,	,	PUNCT
cana-3299	75	31	𝜇𝐴(𝑥	𝜇𝐴(𝑥	NUM
cana-3299	75	32	)	)	PUNCT
cana-3299	75	33	,	,	PUNCT
cana-3299	75	34	𝜈𝐴(𝑥)|𝑥	𝜈𝐴(𝑥)|𝑥	NOUN
cana-3299	75	35	∈	∈	PROPN
cana-3299	75	36	𝑋	𝑋	PROPN
cana-3299	75	37	}	}	PUNCT
cana-3299	75	38	or	or	CCONJ
cana-3299	75	39	𝐴	𝐴	PROPN
cana-3299	75	40	=	=	PUNCT
cana-3299	75	41	{	{	PUNCT
cana-3299	75	42	⟨	⟨	NOUN
cana-3299	75	43	𝜇𝐴(𝑥),𝜈𝐴(𝑥	𝜇𝐴(𝑥),𝜈𝐴(𝑥	NOUN
cana-3299	75	44	)	)	PUNCT
cana-3299	75	45	𝑥	𝑥	PRON
cana-3299	75	46	⟩	⟩	NOUN
cana-3299	75	47	|𝑥	|𝑥	NOUN
cana-3299	75	48	∈	∈	PROPN
cana-3299	75	49	𝑋	𝑋	PROPN
cana-3299	75	50	}	}	PUNCT
cana-3299	75	51	,	,	PUNCT
cana-3299	75	52	where	where	SCONJ
cana-3299	75	53	the	the	DET
cana-3299	75	54	functions	function	NOUN
cana-3299	75	55	𝜇𝐴(𝑥	𝜇𝐴(𝑥	VERB
cana-3299	75	56	):	):	PUNCT
cana-3299	75	57	𝑋	𝑋	PROPN
cana-3299	75	58	→	→	SYM
cana-3299	75	59	[	[	X
cana-3299	75	60	0,1	0,1	NUM
cana-3299	75	61	]	]	PUNCT
cana-3299	75	62	and	and	CCONJ
cana-3299	75	63	𝜈𝐴(𝑥	𝜈𝐴(𝑥	NUM
cana-3299	75	64	):	):	PUNCT
cana-3299	75	65	𝑋	𝑋	PROPN
cana-3299	75	66	→	→	SYM
cana-3299	75	67	[	[	X
cana-3299	75	68	0,1	0,1	NUM
cana-3299	75	69	]	]	PUNCT
cana-3299	75	70	define	define	VERB
cana-3299	75	71	the	the	DET
cana-3299	75	72	degree	degree	NOUN
cana-3299	75	73	of	of	ADP
cana-3299	75	74	membership	membership	NOUN
cana-3299	75	75	and	and	CCONJ
cana-3299	75	76	the	the	DET
cana-3299	75	77	degree	degree	NOUN
cana-3299	75	78	of	of	ADP
cana-3299	75	79	nonmembership	nonmembership	NOUN
cana-3299	75	80	,	,	PUNCT
cana-3299	75	81	respectively	respectively	ADV
cana-3299	75	82	,	,	PUNCT
cana-3299	75	83	of	of	ADP
cana-3299	75	84	the	the	DET
cana-3299	75	85	element	element	NOUN
cana-3299	75	86	𝑥	𝑥	PRON
cana-3299	75	87	∈	∈	PROPN
cana-3299	75	88	𝑋	𝑋	NOUN
cana-3299	75	89	to	to	ADP
cana-3299	75	90	𝐴	𝐴	PROPN
cana-3299	75	91	,	,	PUNCT
cana-3299	75	92	which	which	PRON
cana-3299	75	93	is	be	AUX
cana-3299	75	94	a	a	DET
cana-3299	75	95	subset	subset	NOUN
cana-3299	75	96	of	of	ADP
cana-3299	75	97	𝑋	𝑋	PROPN
cana-3299	75	98	,	,	PUNCT
cana-3299	75	99	and	and	CCONJ
cana-3299	75	100	for	for	ADP
cana-3299	75	101	every	every	DET
cana-3299	75	102	𝑥	𝑥	PRON
cana-3299	75	103	∈	∈	PROPN
cana-3299	75	104	𝑋	𝑋	PROPN
cana-3299	75	105	,	,	PUNCT
cana-3299	75	106	0	0	NUM
cana-3299	75	107	≤	≤	NUM
cana-3299	75	108	(	(	PUNCT
cana-3299	75	109	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-3299	75	110	+	+	CCONJ
cana-3299	75	111	(	(	PUNCT
cana-3299	75	112	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-3299	75	113	≤	≤	ADV
cana-3299	75	114	1	1	NUM
cana-3299	75	115	.	.	PUNCT
cana-3299	76	1	supposing	suppose	VERB
cana-3299	76	2	(	(	PUNCT
cana-3299	76	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-3299	76	4	+	+	CCONJ
cana-3299	76	5	(	(	PUNCT
cana-3299	76	6	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-3299	76	7	≤	≤	ADV
cana-3299	76	8	1	1	NUM
cana-3299	76	9	,	,	PUNCT
cana-3299	76	10	then	then	ADV
cana-3299	76	11	there	there	PRON
cana-3299	76	12	is	be	VERB
cana-3299	76	13	a	a	DET
cana-3299	76	14	degree	degree	NOUN
cana-3299	76	15	of	of	ADP
cana-3299	76	16	indeterminacy	indeterminacy	NOUN
cana-3299	76	17	of	of	ADP
cana-3299	76	18	𝑥	𝑥	DET
cana-3299	76	19	∈	∈	PROPN
cana-3299	76	20	𝑋	𝑋	NOUN
cana-3299	76	21	to	to	ADP
cana-3299	76	22	𝐴	𝐴	PROPN
cana-3299	76	23	defined	define	VERB
cana-3299	76	24	by	by	ADP
cana-3299	76	25	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	76	26	)	)	PUNCT
cana-3299	76	27	=	=	PUNCT
cana-3299	77	1	√1	√1	ADV
cana-3299	77	2	−	−	PROPN
cana-3299	78	1	[	[	X
cana-3299	78	2	(	(	PUNCT
cana-3299	78	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-3299	78	4	+	+	CCONJ
cana-3299	78	5	(	(	PUNCT
cana-3299	78	6	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	PROPN
cana-3299	78	7	]	]	PUNCT
cana-3299	78	8	and	and	CCONJ
cana-3299	78	9	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	78	10	)	)	PUNCT
cana-3299	78	11	∈	∈	NOUN
cana-3299	79	1	[	[	X
cana-3299	79	2	0,1	0,1	NUM
cana-3299	79	3	]	]	PUNCT
cana-3299	79	4	.	.	PUNCT
cana-3299	80	1	in	in	ADP
cana-3299	80	2	what	what	PRON
cana-3299	80	3	follows	follow	VERB
cana-3299	80	4	,	,	PUNCT
cana-3299	80	5	(	(	PUNCT
cana-3299	80	6	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-3299	80	7	+	+	CCONJ
cana-3299	80	8	(	(	PUNCT
cana-3299	80	9	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-3299	80	10	+	+	CCONJ
cana-3299	80	11	(	(	PUNCT
cana-3299	80	12	𝜋𝐴(𝑥))2	𝜋𝐴(𝑥))2	NOUN
cana-3299	80	13	=	=	SYM
cana-3299	80	14	1	1	X
cana-3299	80	15	.	.	PUNCT
cana-3299	80	16	otherwise	otherwise	ADV
cana-3299	80	17	,	,	PUNCT
cana-3299	80	18	𝜋𝐴(𝑥	𝜋𝐴(𝑥	NUM
cana-3299	80	19	)	)	PUNCT
cana-3299	80	20	=	=	SYM
cana-3299	80	21	0	0	PUNCT
cana-3299	81	1	whenever	whenever	SCONJ
cana-3299	81	2	(	(	PUNCT
cana-3299	81	3	𝜇𝐴(𝑥))2	𝜇𝐴(𝑥))2	NOUN
cana-3299	81	4	+	+	CCONJ
cana-3299	81	5	(	(	PUNCT
cana-3299	81	6	𝜈𝐴(𝑥))2	𝜈𝐴(𝑥))2	NOUN
cana-3299	81	7	=	=	SYM
cana-3299	81	8	1	1	X
cana-3299	81	9	.	.	X
cana-3299	81	10	we	we	PRON
cana-3299	81	11	denote	denote	VERB
cana-3299	81	12	the	the	DET
cana-3299	81	13	set	set	NOUN
cana-3299	81	14	of	of	ADP
cana-3299	81	15	all	all	DET
cana-3299	81	16	𝑃𝐹𝑆	𝑃𝐹𝑆	PROPN
cana-3299	81	17	’s	’s	NOUN
cana-3299	81	18	over	over	ADP
cana-3299	81	19	𝑋	𝑋	PROPN
cana-3299	81	20	by	by	ADP
cana-3299	81	21	𝑝𝑓𝑠(𝑋	𝑝𝑓𝑠(𝑋	PROPN
cana-3299	81	22	)	)	PUNCT
cana-3299	81	23	.	.	PUNCT
cana-3299	82	1	definition	definition	NOUN
cana-3299	82	2	2.4	2.4	NUM
cana-3299	82	3	[	[	SYM
cana-3299	82	4	35	35	NUM
cana-3299	82	5	]	]	PUNCT
cana-3299	82	6	let	let	VERB
cana-3299	82	7	𝐴	𝐴	PROPN
cana-3299	82	8	and	and	CCONJ
cana-3299	82	9	𝐵	𝐵	NOUN
cana-3299	82	10	be	be	AUX
cana-3299	83	1	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	83	2	’s	’s	NOUN
cana-3299	83	3	of	of	ADP
cana-3299	83	4	the	the	DET
cana-3299	83	5	forms	form	NOUN
cana-3299	83	6	𝐴	𝐴	NOUN
cana-3299	83	7	=	=	PUNCT
cana-3299	83	8	{	{	PUNCT
cana-3299	83	9	<	<	X
cana-3299	83	10	𝑎	𝑎	X
cana-3299	83	11	,	,	PUNCT
cana-3299	83	12	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	83	13	)	)	PUNCT
cana-3299	83	14	,	,	PUNCT
cana-3299	83	15	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	83	16	)	)	PUNCT
cana-3299	83	17	>	>	X
cana-3299	83	18	|𝑎	|𝑎	PROPN
cana-3299	84	1	∈	∈	PROPN
cana-3299	84	2	𝑋	𝑋	PROPN
cana-3299	84	3	}	}	PUNCT
cana-3299	84	4	and	and	CCONJ
cana-3299	84	5	𝐵	𝐵	NOUN
cana-3299	84	6	=	=	PUNCT
cana-3299	84	7	{	{	PUNCT
cana-3299	84	8	<	<	X
cana-3299	84	9	𝑎	𝑎	X
cana-3299	84	10	,	,	PUNCT
cana-3299	84	11	𝜆𝐵(𝑎	𝜆𝐵(𝑎	PRON
cana-3299	84	12	)	)	PUNCT
cana-3299	84	13	,	,	PUNCT
cana-3299	84	14	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-3299	84	15	)	)	PUNCT
cana-3299	84	16	>	>	X
cana-3299	84	17	|𝑎	|𝑎	PROPN
cana-3299	85	1	∈	∈	PROPN
cana-3299	85	2	𝑋	𝑋	PROPN
cana-3299	85	3	}	}	PUNCT
cana-3299	85	4	.	.	PUNCT
cana-3299	86	1	then	then	ADV
cana-3299	86	2	1	1	X
cana-3299	86	3	.	.	PUNCT
cana-3299	86	4	𝐴	𝐴	PROPN
cana-3299	86	5	⊆	⊆	NUM
cana-3299	86	6	𝐵	𝐵	PROPN
cana-3299	86	7	if	if	SCONJ
cana-3299	86	8	and	and	CCONJ
cana-3299	86	9	only	only	ADV
cana-3299	86	10	if	if	SCONJ
cana-3299	86	11	𝜆𝐴(𝑎	𝜆𝐴(𝑎	NOUN
cana-3299	86	12	)	)	PUNCT
cana-3299	86	13	≤	≤	NOUN
cana-3299	86	14	𝜆𝐵(𝑎	𝜆𝐵(𝑎	CCONJ
cana-3299	86	15	)	)	PUNCT
cana-3299	86	16	and	and	CCONJ
cana-3299	86	17	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NUM
cana-3299	86	18	)	)	PUNCT
cana-3299	86	19	≥	≥	NOUN
cana-3299	86	20	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-3299	86	21	)	)	PUNCT
cana-3299	86	22	for	for	ADP
cana-3299	86	23	all	all	DET
cana-3299	86	24	𝑎	𝑎	PROPN
cana-3299	86	25	∈	∈	NOUN
cana-3299	86	26	𝑋.	𝑋.	PROPN
cana-3299	86	27	2	2	NUM
cana-3299	86	28	.	.	PUNCT
cana-3299	86	29	𝐴	𝐴	NOUN
cana-3299	86	30	=	=	PROPN
cana-3299	86	31	𝐵	𝐵	PROPN
cana-3299	86	32	if	if	SCONJ
cana-3299	86	33	and	and	CCONJ
cana-3299	86	34	only	only	ADV
cana-3299	86	35	if	if	SCONJ
cana-3299	86	36	𝐴	𝐴	PROPN
cana-3299	86	37	⊆	⊆	NUM
cana-3299	86	38	𝐵	𝐵	NOUN
cana-3299	86	39	and	and	CCONJ
cana-3299	86	40	𝐵	𝐵	NOUN
cana-3299	87	1	⊆	⊆	NUM
cana-3299	87	2	𝐴.	𝐴.	PROPN
cana-3299	87	3	3	3	NUM
cana-3299	87	4	.	.	PUNCT
cana-3299	87	5	�	�	NOUN
cana-3299	87	6	̅	̅	NOUN
cana-3299	87	7	�	�	NOUN
cana-3299	87	8	=	=	SYM
cana-3299	87	9	{	{	PUNCT
cana-3299	87	10	<	<	X
cana-3299	87	11	𝑎	𝑎	NOUN
cana-3299	87	12	,	,	PUNCT
cana-3299	87	13	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-3299	87	14	)	)	PUNCT
cana-3299	87	15	,	,	PUNCT
cana-3299	87	16	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	87	17	)	)	PUNCT
cana-3299	87	18	>	>	X
cana-3299	87	19	|𝑎	|𝑎	PROPN
cana-3299	88	1	∈	∈	PROPN
cana-3299	88	2	𝑋	𝑋	PROPN
cana-3299	88	3	}	}	PUNCT
cana-3299	88	4	.	.	PUNCT
cana-3299	89	1	4	4	X
cana-3299	89	2	.	.	X
cana-3299	89	3	𝐴	𝐴	PROPN
cana-3299	89	4	∩	∩	NOUN
cana-3299	89	5	𝐵	𝐵	NOUN
cana-3299	89	6	=	=	PUNCT
cana-3299	89	7	{	{	PUNCT
cana-3299	89	8	<	<	X
cana-3299	89	9	𝑎	𝑎	X
cana-3299	89	10	,	,	PUNCT
cana-3299	89	11	𝜆𝐴(𝑎	𝜆𝐴(𝑎	NOUN
cana-3299	89	12	)	)	PUNCT
cana-3299	89	13	∧	∧	NOUN
cana-3299	89	14	𝜆𝐵(𝑎	𝜆𝐵(𝑎	NOUN
cana-3299	89	15	)	)	PUNCT
cana-3299	89	16	,	,	PUNCT
cana-3299	89	17	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-3299	89	18	)	)	PUNCT
cana-3299	89	19	∨	∨	NUM
cana-3299	89	20	𝜇𝐵(𝑎	𝜇𝐵(𝑎	NUM
cana-3299	89	21	)	)	PUNCT
cana-3299	89	22	>	>	X
cana-3299	89	23	|𝑎	|𝑎	PROPN
cana-3299	89	24	∈	∈	PROPN
cana-3299	89	25	𝑋	𝑋	PROPN
cana-3299	89	26	}	}	PUNCT
cana-3299	89	27	.	.	PUNCT
cana-3299	90	1	5	5	X
cana-3299	90	2	.	.	X
cana-3299	90	3	𝐴	𝐴	PROPN
cana-3299	90	4	∪	∪	AUX
cana-3299	90	5	𝐵	𝐵	NOUN
cana-3299	90	6	=	=	PUNCT
cana-3299	90	7	{	{	PUNCT
cana-3299	90	8	<	<	X
cana-3299	90	9	𝑎	𝑎	X
cana-3299	90	10	,	,	PUNCT
cana-3299	90	11	𝜆𝐴(𝑎	𝜆𝐴(𝑎	NOUN
cana-3299	90	12	)	)	PUNCT
cana-3299	90	13	∨	∨	NOUN
cana-3299	90	14	𝜆𝐵(𝑎	𝜆𝐵(𝑎	NUM
cana-3299	90	15	)	)	PUNCT
cana-3299	90	16	,	,	PUNCT
cana-3299	90	17	𝜇𝐴(𝑎	𝜇𝐴(𝑎	NOUN
cana-3299	90	18	)	)	PUNCT
cana-3299	90	19	∧	∧	PROPN
cana-3299	90	20	𝜇𝐵(𝑎	𝜇𝐵(𝑎	PROPN
cana-3299	90	21	)	)	PUNCT
cana-3299	90	22	>	>	X
cana-3299	90	23	|𝑎	|𝑎	PROPN
cana-3299	90	24	∈	∈	PROPN
cana-3299	90	25	𝑋	𝑋	PROPN
cana-3299	90	26	}	}	PUNCT
cana-3299	90	27	.	.	PUNCT
cana-3299	91	1	6	6	X
cana-3299	91	2	.	.	X
cana-3299	91	3	0𝑋	0𝑋	NOUN
cana-3299	91	4	=	=	SYM
cana-3299	91	5	{	{	PUNCT
cana-3299	91	6	<	<	X
cana-3299	91	7	𝑎	𝑎	NOUN
cana-3299	91	8	,	,	PUNCT
cana-3299	91	9	0,1	0,1	NUM
cana-3299	91	10	>	>	SYM
cana-3299	91	11	|𝑎	|𝑎	NOUN
cana-3299	92	1	∈	∈	PROPN
cana-3299	92	2	𝑋	𝑋	PROPN
cana-3299	92	3	}	}	PUNCT
cana-3299	92	4	and	and	CCONJ
cana-3299	92	5	1𝑋	1𝑋	NOUN
cana-3299	92	6	=	=	SYM
cana-3299	92	7	{	{	PUNCT
cana-3299	92	8	<	<	X
cana-3299	92	9	𝑎	𝑎	PROPN
cana-3299	92	10	,	,	PUNCT
cana-3299	92	11	1,0	1,0	NUM
cana-3299	92	12	>	>	SYM
cana-3299	92	13	|𝑎	|𝑎	PROPN
cana-3299	92	14	∈	∈	PROPN
cana-3299	92	15	𝑋	𝑋	PROPN
cana-3299	92	16	}	}	PUNCT
cana-3299	92	17	.	.	PUNCT
cana-3299	93	1	7	7	X
cana-3299	93	2	.	.	X
cana-3299	93	3	1̅	1̅	NUM
cana-3299	93	4	=	=	SYM
cana-3299	93	5	0	0	NUM
cana-3299	93	6	and	and	CCONJ
cana-3299	93	7	0̅	0̅	NOUN
cana-3299	93	8	=	=	SYM
cana-3299	93	9	1	1	X
cana-3299	93	10	.	.	PUNCT
cana-3299	94	1	definition	definition	NOUN
cana-3299	94	2	2.5	2.5	NUM
cana-3299	95	1	[	[	X
cana-3299	95	2	24	24	NUM
cana-3299	95	3	]	]	PUNCT
cana-3299	95	4	an	an	DET
cana-3299	95	5	pythagorean	pythagorean	ADJ
cana-3299	95	6	fuzzy	fuzzy	ADJ
cana-3299	95	7	topology	topology	NOUN
cana-3299	95	8	by	by	ADP
cana-3299	95	9	subsets	subset	NOUN
cana-3299	95	10	of	of	ADP
cana-3299	95	11	a	a	DET
cana-3299	95	12	non	non	ADJ
cana-3299	95	13	-	-	ADJ
cana-3299	95	14	empty	empty	ADJ
cana-3299	95	15	set	set	ADJ
cana-3299	95	16	𝑋	𝑋	PROPN
cana-3299	95	17	is	be	AUX
cana-3299	95	18	a	a	DET
cana-3299	95	19	family	family	NOUN
cana-3299	95	20	𝜏	𝜏	X
cana-3299	95	21	of	of	ADP
cana-3299	95	22	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	95	23	’s	’s	AUX
cana-3299	95	24	satisfying	satisfy	VERB
cana-3299	95	25	the	the	DET
cana-3299	95	26	following	follow	VERB
cana-3299	95	27	axioms	axiom	NOUN
cana-3299	95	28	.	.	PUNCT
cana-3299	96	1	1	1	X
cana-3299	96	2	.	.	X
cana-3299	96	3	𝜙	𝜙	X
cana-3299	96	4	,	,	PUNCT
cana-3299	96	5	𝑋	𝑋	PROPN
cana-3299	96	6	∈	∈	PROPN
cana-3299	96	7	𝜏.	𝜏.	NOUN
cana-3299	96	8	2	2	NUM
cana-3299	96	9	.	.	PROPN
cana-3299	96	10	𝐺1	𝐺1	PROPN
cana-3299	96	11	∩	∩	PROPN
cana-3299	96	12	𝐺2	𝐺2	NOUN
cana-3299	96	13	∈	∈	PROPN
cana-3299	96	14	𝜏	𝜏	NOUN
cana-3299	96	15	for	for	ADP
cana-3299	96	16	every	every	DET
cana-3299	96	17	𝐺1	𝐺1	NOUN
cana-3299	96	18	,	,	PUNCT
cana-3299	96	19	𝐺2	𝐺2	NOUN
cana-3299	96	20	∈	∈	PROPN
cana-3299	96	21	𝜏	𝜏	X
cana-3299	96	22	and	and	CCONJ
cana-3299	96	23	communications	communication	NOUN
cana-3299	96	24	on	on	ADP
cana-3299	96	25	applied	apply	VERB
cana-3299	96	26	nonlinear	nonlinear	ADJ
cana-3299	96	27	analysis	analysis	NOUN
cana-3299	96	28	issn	issn	NOUN
cana-3299	96	29	:	:	PUNCT
cana-3299	96	30	1074	1074	NUM
cana-3299	96	31	-	-	PUNCT
cana-3299	96	32	133x	133x	NUM
cana-3299	96	33	vol	vol	NOUN
cana-3299	96	34	32	32	NUM
cana-3299	96	35	no	no	NOUN
cana-3299	96	36	.	.	PUNCT
cana-3299	97	1	6s	6s	NUM
cana-3299	97	2	(	(	PUNCT
cana-3299	97	3	2025	2025	NUM
cana-3299	97	4	)	)	PUNCT
cana-3299	97	5	330	330	NUM
cana-3299	97	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	97	7	3	3	NUM
cana-3299	97	8	.	.	PUNCT
cana-3299	98	1	⋃	⋃	PRON
cana-3299	98	2	𝐺𝑖	𝐺𝑖	VERB
cana-3299	98	3	∈	∈	PRON
cana-3299	98	4	𝜏	𝜏	NOUN
cana-3299	98	5	for	for	ADP
cana-3299	98	6	any	any	DET
cana-3299	98	7	arbitrary	arbitrary	ADJ
cana-3299	98	8	family	family	NOUN
cana-3299	98	9	{	{	PUNCT
cana-3299	98	10	𝐺𝑖|𝑖	𝐺𝑖|𝑖	PROPN
cana-3299	98	11	∈	∈	PROPN
cana-3299	98	12	𝑗	𝑗	NOUN
cana-3299	98	13	}	}	PUNCT
cana-3299	98	14	⊆	⊆	NUM
cana-3299	98	15	𝜏.	𝜏.	AUX
cana-3299	98	16	the	the	DET
cana-3299	98	17	pair	pair	NOUN
cana-3299	98	18	(	(	PUNCT
cana-3299	98	19	𝑋	𝑋	PROPN
cana-3299	98	20	,	,	PUNCT
cana-3299	98	21	𝜏	𝜏	NOUN
cana-3299	98	22	)	)	PUNCT
cana-3299	98	23	is	be	AUX
cana-3299	98	24	called	call	VERB
cana-3299	98	25	an	an	DET
cana-3299	98	26	pythagorean	pythagorean	ADJ
cana-3299	98	27	fuzzy	fuzzy	ADJ
cana-3299	98	28	topological	topological	ADJ
cana-3299	98	29	space	space	NOUN
cana-3299	98	30	(	(	PUNCT
cana-3299	98	31	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	98	32	in	in	ADP
cana-3299	98	33	short	short	ADJ
cana-3299	98	34	)	)	PUNCT
cana-3299	98	35	and	and	CCONJ
cana-3299	98	36	any	any	DET
cana-3299	98	37	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	98	38	𝐺	𝐺	PROPN
cana-3299	98	39	in	in	ADP
cana-3299	98	40	𝜏	𝜏	PROPN
cana-3299	98	41	is	be	AUX
cana-3299	98	42	called	call	VERB
cana-3299	98	43	an	an	DET
cana-3299	98	44	pythagorean	pythagorean	ADJ
cana-3299	98	45	fuzzy	fuzzy	ADJ
cana-3299	98	46	open	open	ADJ
cana-3299	98	47	set	set	NOUN
cana-3299	98	48	(	(	PUNCT
cana-3299	98	49	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	98	50	in	in	ADP
cana-3299	98	51	short	short	ADJ
cana-3299	98	52	)	)	PUNCT
cana-3299	98	53	in	in	ADP
cana-3299	98	54	𝑋.	𝑋.	PROPN
cana-3299	98	55	the	the	DET
cana-3299	98	56	complement	complement	PROPN
cana-3299	98	57	�	�	PROPN
cana-3299	98	58	̅	̅	NOUN
cana-3299	98	59	�	�	NOUN
cana-3299	98	60	of	of	ADP
cana-3299	98	61	an	an	DET
cana-3299	98	62	pythagorean	pythagorean	ADJ
cana-3299	98	63	fuzzy	fuzzy	ADJ
cana-3299	98	64	open	open	ADJ
cana-3299	98	65	set	set	VERB
cana-3299	98	66	𝐴	𝐴	PROPN
cana-3299	98	67	in	in	ADP
cana-3299	98	68	an	an	DET
cana-3299	98	69	𝑝𝑓𝑡𝑠(𝑋	𝑝𝑓𝑡𝑠(𝑋	PROPN
cana-3299	98	70	,	,	PUNCT
cana-3299	98	71	𝜏	𝜏	NOUN
cana-3299	98	72	)	)	PUNCT
cana-3299	98	73	is	be	AUX
cana-3299	98	74	called	call	VERB
cana-3299	98	75	an	an	DET
cana-3299	98	76	pythagorean	pythagorean	ADJ
cana-3299	98	77	fuzzy	fuzzy	NOUN
cana-3299	98	78	closed	close	VERB
cana-3299	98	79	set	set	NOUN
cana-3299	98	80	(	(	PUNCT
cana-3299	98	81	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	98	82	in	in	ADP
cana-3299	98	83	short	short	ADJ
cana-3299	98	84	)	)	PUNCT
cana-3299	98	85	.	.	PUNCT
cana-3299	99	1	definition	definition	NOUN
cana-3299	99	2	2.6	2.6	NUM
cana-3299	100	1	[	[	SYM
cana-3299	100	2	24	24	NUM
cana-3299	100	3	]	]	PUNCT
cana-3299	100	4	let	let	VERB
cana-3299	100	5	(	(	PUNCT
cana-3299	100	6	𝑋	𝑋	NOUN
cana-3299	100	7	,	,	PUNCT
cana-3299	100	8	𝜏	𝜏	NOUN
cana-3299	100	9	)	)	PUNCT
cana-3299	100	10	be	be	VERB
cana-3299	100	11	an	an	DET
cana-3299	100	12	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	100	13	and	and	CCONJ
cana-3299	100	14	𝐴	𝐴	PROPN
cana-3299	100	15	=	=	PUNCT
cana-3299	100	16	{	{	PUNCT
cana-3299	100	17	<	<	X
cana-3299	100	18	𝑎	𝑎	X
cana-3299	100	19	,	,	PUNCT
cana-3299	100	20	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	100	21	)	)	PUNCT
cana-3299	100	22	,	,	PUNCT
cana-3299	100	23	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	100	24	)	)	PUNCT
cana-3299	100	25	>	>	X
cana-3299	100	26	|𝑎	|𝑎	PROPN
cana-3299	101	1	∈	∈	PROPN
cana-3299	101	2	𝑋	𝑋	PROPN
cana-3299	101	3	}	}	PUNCT
cana-3299	101	4	be	be	AUX
cana-3299	101	5	an	an	DET
cana-3299	101	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	101	7	in	in	ADP
cana-3299	101	8	𝑋.	𝑋.	PROPN
cana-3299	101	9	then	then	ADV
cana-3299	101	10	the	the	DET
cana-3299	101	11	interior	interior	NOUN
cana-3299	101	12	and	and	CCONJ
cana-3299	101	13	the	the	DET
cana-3299	101	14	closure	closure	NOUN
cana-3299	101	15	of	of	ADP
cana-3299	101	16	𝐴	𝐴	PROPN
cana-3299	101	17	are	be	AUX
cana-3299	101	18	denoted	denote	VERB
cana-3299	101	19	by	by	ADP
cana-3299	101	20	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	PROPN
cana-3299	101	21	)	)	PUNCT
cana-3299	101	22	and	and	CCONJ
cana-3299	101	23	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NUM
cana-3299	101	24	)	)	PUNCT
cana-3299	101	25	and	and	CCONJ
cana-3299	101	26	are	be	AUX
cana-3299	101	27	defined	define	VERB
cana-3299	101	28	as	as	SCONJ
cana-3299	101	29	follows	follow	VERB
cana-3299	101	30	:	:	PUNCT
cana-3299	101	31	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	X
cana-3299	101	32	)	)	PUNCT
cana-3299	102	1	=	=	NOUN
cana-3299	102	2	∩	∩	NOUN
cana-3299	102	3	{	{	PUNCT
cana-3299	102	4	𝐾|𝐾	𝐾|𝐾	PRON
cana-3299	102	5	𝑖𝑠𝑎𝑛	𝑖𝑠𝑎𝑛	VERB
cana-3299	102	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NUM
cana-3299	102	7	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-3299	102	8	𝐴	𝐴	PROPN
cana-3299	102	9	⊆	⊆	NUM
cana-3299	102	10	𝐾	𝐾	PROPN
cana-3299	102	11	}	}	PUNCT
cana-3299	102	12	and	and	CCONJ
cana-3299	102	13	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	NOUN
cana-3299	102	14	)	)	PUNCT
cana-3299	102	15	=	=	SYM
cana-3299	102	16	∪	∪	X
cana-3299	102	17	{	{	PUNCT
cana-3299	102	18	𝐺|𝐺	𝐺|𝐺	NOUN
cana-3299	102	19	𝑖𝑠𝑎𝑛	𝑖𝑠𝑎𝑛	NOUN
cana-3299	102	20	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	VERB
cana-3299	102	21	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
cana-3299	102	22	𝐺	𝐺	PROPN
cana-3299	102	23	⊆	⊆	NUM
cana-3299	102	24	𝐴	𝐴	PROPN
cana-3299	102	25	}	}	PUNCT
cana-3299	102	26	.	.	PUNCT
cana-3299	103	1	also	also	ADV
cana-3299	103	2	,	,	PUNCT
cana-3299	103	3	it	it	PRON
cana-3299	103	4	can	can	AUX
cana-3299	103	5	be	be	AUX
cana-3299	103	6	established	establish	VERB
cana-3299	103	7	that	that	DET
cana-3299	103	8	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NOUN
cana-3299	103	9	)	)	PUNCT
cana-3299	103	10	is	be	AUX
cana-3299	103	11	an	an	DET
cana-3299	103	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	103	13	and	and	CCONJ
cana-3299	103	14	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	NOUN
cana-3299	103	15	)	)	PUNCT
cana-3299	103	16	is	be	AUX
cana-3299	103	17	an	an	DET
cana-3299	103	18	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	103	19	,	,	PUNCT
cana-3299	103	20	𝐴	𝐴	PROPN
cana-3299	103	21	is	be	AUX
cana-3299	103	22	an	an	DET
cana-3299	103	23	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	103	24	if	if	SCONJ
cana-3299	104	1	and	and	CCONJ
cana-3299	104	2	only	only	ADV
cana-3299	104	3	if	if	SCONJ
cana-3299	104	4	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NUM
cana-3299	104	5	)	)	PUNCT
cana-3299	104	6	=	=	SYM
cana-3299	104	7	𝐴	𝐴	PROPN
cana-3299	104	8	and	and	CCONJ
cana-3299	104	9	𝐴	𝐴	PROPN
cana-3299	104	10	is	be	AUX
cana-3299	104	11	an	an	DET
cana-3299	104	12	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	104	13	if	if	SCONJ
cana-3299	104	14	and	and	CCONJ
cana-3299	104	15	only	only	ADV
cana-3299	104	16	if	if	SCONJ
cana-3299	104	17	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	NOUN
cana-3299	104	18	)	)	PUNCT
cana-3299	104	19	=	=	SYM
cana-3299	105	1	𝐴.	𝐴.	NOUN
cana-3299	105	2	we	we	PRON
cana-3299	105	3	say	say	VERB
cana-3299	105	4	that	that	SCONJ
cana-3299	105	5	𝐴	𝐴	PROPN
cana-3299	105	6	is	be	AUX
cana-3299	105	7	𝑝𝑓-dense	𝑝𝑓-dense	ADJ
cana-3299	105	8	if	if	SCONJ
cana-3299	105	9	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	NUM
cana-3299	105	10	)	)	PUNCT
cana-3299	106	1	=	=	SYM
cana-3299	106	2	𝑋.	𝑋.	PROPN
cana-3299	106	3	lemma	lemma	PROPN
cana-3299	106	4	2.1	2.1	NUM
cana-3299	107	1	[	[	SYM
cana-3299	107	2	30	30	NUM
cana-3299	107	3	]	]	PUNCT
cana-3299	107	4	for	for	ADP
cana-3299	107	5	any	any	DET
cana-3299	107	6	pythagorean	pythagorean	PROPN
cana-3299	107	7	fuzzy	fuzzy	ADJ
cana-3299	107	8	set	set	VERB
cana-3299	107	9	𝐴	𝐴	PROPN
cana-3299	107	10	in	in	ADP
cana-3299	107	11	(	(	PUNCT
cana-3299	107	12	𝑋	𝑋	PROPN
cana-3299	107	13	,	,	PUNCT
cana-3299	107	14	𝜏	𝜏	NOUN
cana-3299	107	15	)	)	PUNCT
cana-3299	107	16	,	,	PUNCT
cana-3299	107	17	we	we	PRON
cana-3299	107	18	have	have	VERB
cana-3299	107	19	𝑋	𝑋	PROPN
cana-3299	107	20	−	−	PROPN
cana-3299	107	21	𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑖𝑛𝑡(𝐴	PROPN
cana-3299	107	22	)	)	PUNCT
cana-3299	107	23	=	=	SYM
cana-3299	107	24	𝑝𝑓𝑐𝑙(𝑋	𝑝𝑓𝑐𝑙(𝑋	PROPN
cana-3299	107	25	−	−	PROPN
cana-3299	107	26	𝐴	𝐴	PROPN
cana-3299	107	27	)	)	PUNCT
cana-3299	107	28	and	and	CCONJ
cana-3299	107	29	𝑋	𝑋	PROPN
cana-3299	107	30	−	−	PROPN
cana-3299	107	31	𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑐𝑙(𝐴	PROPN
cana-3299	107	32	)	)	PUNCT
cana-3299	108	1	=	=	PRON
cana-3299	108	2	𝑝𝑓𝑖𝑛𝑡(𝑋	𝑝𝑓𝑖𝑛𝑡(𝑋	X
cana-3299	108	3	−	−	PROPN
cana-3299	108	4	𝐴	𝐴	PROPN
cana-3299	108	5	)	)	PUNCT
cana-3299	108	6	.	.	PUNCT
cana-3299	109	1	definition	definition	NOUN
cana-3299	109	2	2.7	2.7	NUM
cana-3299	109	3	[	[	SYM
cana-3299	109	4	30	30	NUM
cana-3299	109	5	]	]	X
cana-3299	109	6	let	let	NOUN
cana-3299	109	7	(	(	PUNCT
cana-3299	109	8	𝑋	𝑋	NOUN
cana-3299	109	9	,	,	PUNCT
cana-3299	109	10	𝜏	𝜏	NOUN
cana-3299	109	11	)	)	PUNCT
cana-3299	109	12	be	be	VERB
cana-3299	109	13	an	an	DET
cana-3299	109	14	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	109	15	and	and	CCONJ
cana-3299	109	16	𝐴	𝐴	PROPN
cana-3299	109	17	be	be	VERB
cana-3299	109	18	an	an	DET
cana-3299	109	19	𝑝𝑓𝑠.	𝑝𝑓𝑠.	NOUN
cana-3299	109	20	then	then	ADV
cana-3299	109	21	𝐴	𝐴	PROPN
cana-3299	109	22	is	be	AUX
cana-3299	109	23	said	say	VERB
cana-3299	109	24	to	to	PART
cana-3299	109	25	be	be	AUX
cana-3299	109	26	an	an	DET
cana-3299	109	27	pythagorean	pythagorean	ADJ
cana-3299	109	28	fuzzy	fuzzy	NOUN
cana-3299	109	29	(	(	PUNCT
cana-3299	109	30	i	i	NOUN
cana-3299	109	31	)	)	PUNCT
cana-3299	109	32	regular	regular	ADJ
cana-3299	109	33	open	open	ADJ
cana-3299	109	34	set	set	NOUN
cana-3299	109	35	(	(	PUNCT
cana-3299	109	36	𝑝𝑓𝑟𝑜𝑠	𝑝𝑓𝑟𝑜𝑠	NOUN
cana-3299	109	37	in	in	ADP
cana-3299	109	38	short	short	ADJ
cana-3299	109	39	)	)	PUNCT
cana-3299	109	40	if	if	SCONJ
cana-3299	109	41	𝐴	𝐴	PROPN
cana-3299	109	42	=	=	SYM
cana-3299	109	43	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝑐𝑙(𝐴	PROPN
cana-3299	109	44	)	)	PUNCT
cana-3299	109	45	)	)	PUNCT
cana-3299	109	46	.	.	PUNCT
cana-3299	110	1	(	(	PUNCT
cana-3299	110	2	ii	ii	NOUN
cana-3299	110	3	)	)	PUNCT
cana-3299	110	4	regular	regular	ADJ
cana-3299	110	5	closed	close	VERB
cana-3299	110	6	set	set	NOUN
cana-3299	110	7	(	(	PUNCT
cana-3299	110	8	𝑝𝑓𝑟𝑐𝑠	𝑝𝑓𝑟𝑐𝑠	ADJ
cana-3299	110	9	in	in	ADP
cana-3299	110	10	short	short	ADJ
cana-3299	110	11	)	)	PUNCT
cana-3299	110	12	if	if	SCONJ
cana-3299	110	13	𝐴	𝐴	PROPN
cana-3299	110	14	=	=	SYM
cana-3299	110	15	𝑝𝑓𝑐𝑙(𝑝𝑓𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝑖𝑛𝑡(𝐴	NUM
cana-3299	110	16	)	)	PUNCT
cana-3299	110	17	)	)	PUNCT
cana-3299	110	18	.	.	PUNCT
cana-3299	111	1	by	by	ADP
cana-3299	111	2	lemma	lemma	PROPN
cana-3299	111	3	2.1	2.1	NUM
cana-3299	111	4	,	,	PUNCT
cana-3299	111	5	it	it	PRON
cana-3299	111	6	follows	follow	VERB
cana-3299	111	7	that	that	SCONJ
cana-3299	111	8	𝐴	𝐴	PROPN
cana-3299	111	9	is	be	AUX
cana-3299	111	10	an	an	DET
cana-3299	111	11	𝑝𝑓𝑟𝑜𝑠	𝑝𝑓𝑟𝑜𝑠	NOUN
cana-3299	111	12	iff	iff	PROPN
cana-3299	111	13	�	�	PROPN
cana-3299	111	14	̅	̅	NOUN
cana-3299	111	15	�	�	NOUN
cana-3299	111	16	is	be	AUX
cana-3299	111	17	an	an	DET
cana-3299	111	18	𝑝𝑓𝑟𝑐𝑠.	𝑝𝑓𝑟𝑐𝑠.	ADJ
cana-3299	111	19	definition	definition	NOUN
cana-3299	111	20	2.8	2.8	NUM
cana-3299	111	21	[	[	SYM
cana-3299	111	22	32	32	NUM
cana-3299	111	23	]	]	PUNCT
cana-3299	111	24	let	let	NOUN
cana-3299	111	25	(	(	PUNCT
cana-3299	111	26	𝑋1	𝑋1	PROPN
cana-3299	111	27	,	,	PUNCT
cana-3299	111	28	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	111	29	)	)	PUNCT
cana-3299	111	30	(	(	PUNCT
cana-3299	111	31	or	or	CCONJ
cana-3299	111	32	𝑋1	𝑋1	PROPN
cana-3299	111	33	)	)	PUNCT
cana-3299	111	34	be	be	VERB
cana-3299	111	35	an	an	DET
cana-3299	111	36	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	111	37	and	and	CCONJ
cana-3299	111	38	𝐴	𝐴	PROPN
cana-3299	111	39	=	=	PUNCT
cana-3299	111	40	{	{	PUNCT
cana-3299	111	41	<	<	X
cana-3299	111	42	𝑎	𝑎	X
cana-3299	111	43	,	,	PUNCT
cana-3299	111	44	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	111	45	)	)	PUNCT
cana-3299	111	46	,	,	PUNCT
cana-3299	111	47	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	111	48	)	)	PUNCT
cana-3299	111	49	>	>	X
cana-3299	111	50	|𝑎	|𝑎	PROPN
cana-3299	112	1	∈	∈	PROPN
cana-3299	112	2	𝑋1	𝑋1	PROPN
cana-3299	112	3	}	}	PUNCT
cana-3299	112	4	be	be	AUX
cana-3299	112	5	an	an	DET
cana-3299	112	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	112	7	in	in	ADP
cana-3299	112	8	𝑋1	𝑋1	PROPN
cana-3299	112	9	.	.	PUNCT
cana-3299	113	1	then	then	ADV
cana-3299	113	2	the	the	DET
cana-3299	113	3	(	(	PUNCT
cana-3299	113	4	i	i	NOUN
cana-3299	113	5	)	)	PUNCT
cana-3299	113	6	𝑝𝑓𝛿-interior	𝑝𝑓𝛿-interior	NOUN
cana-3299	113	7	of	of	ADP
cana-3299	113	8	𝐴	𝐴	PROPN
cana-3299	113	9	are	be	AUX
cana-3299	113	10	denoted	denote	VERB
cana-3299	113	11	by	by	ADP
cana-3299	113	12	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	NOUN
cana-3299	113	13	)	)	PUNCT
cana-3299	113	14	and	and	CCONJ
cana-3299	113	15	are	be	AUX
cana-3299	113	16	defined	define	VERB
cana-3299	113	17	as	as	ADP
cana-3299	113	18	follows	follow	NOUN
cana-3299	113	19	.	.	PUNCT
cana-3299	114	1	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	NOUN
cana-3299	114	2	)	)	PUNCT
cana-3299	115	1	=	=	NOUN
cana-3299	115	2	∪	∪	X
cana-3299	115	3	{	{	PUNCT
cana-3299	115	4	𝐺|𝐺	𝐺|𝐺	PROPN
cana-3299	115	5	is	be	AUX
cana-3299	115	6	an	an	DET
cana-3299	115	7	𝑝𝑓𝑟𝑜𝑠	𝑝𝑓𝑟𝑜𝑠	NOUN
cana-3299	115	8	and	and	CCONJ
cana-3299	115	9	𝐺	𝐺	PROPN
cana-3299	115	10	⊆	⊆	NUM
cana-3299	115	11	𝐴	𝐴	PROPN
cana-3299	115	12	}	}	PUNCT
cana-3299	115	13	.	.	PUNCT
cana-3299	116	1	(	(	PUNCT
cana-3299	116	2	ii	ii	NOUN
cana-3299	116	3	)	)	PUNCT
cana-3299	116	4	𝑝𝑓𝛿-closure	𝑝𝑓𝛿-closure	NOUN
cana-3299	116	5	of	of	ADP
cana-3299	116	6	𝐴	𝐴	PROPN
cana-3299	116	7	are	be	AUX
cana-3299	116	8	denoted	denote	VERB
cana-3299	116	9	by	by	ADP
cana-3299	116	10	𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝛿𝑐𝑙(𝐴	NOUN
cana-3299	116	11	)	)	PUNCT
cana-3299	116	12	and	and	CCONJ
cana-3299	116	13	are	be	AUX
cana-3299	116	14	defined	define	VERB
cana-3299	116	15	as	as	ADP
cana-3299	116	16	follows	follow	VERB
cana-3299	116	17	.	.	PUNCT
cana-3299	117	1	𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝛿𝑐𝑙(𝐴	X
cana-3299	117	2	)	)	PUNCT
cana-3299	118	1	=	=	NOUN
cana-3299	118	2	∩	∩	NOUN
cana-3299	118	3	{	{	PUNCT
cana-3299	118	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-3299	118	5	is	be	AUX
cana-3299	118	6	an	an	DET
cana-3299	118	7	𝑝𝑓𝑟𝑐𝑠	𝑝𝑓𝑟𝑐𝑠	NOUN
cana-3299	118	8	and	and	CCONJ
cana-3299	118	9	𝐴	𝐴	PROPN
cana-3299	118	10	⊆	⊆	NUM
cana-3299	118	11	𝐾	𝐾	PROPN
cana-3299	118	12	}	}	PUNCT
cana-3299	118	13	.	.	PUNCT
cana-3299	119	1	definition	definition	NOUN
cana-3299	119	2	2.9	2.9	NUM
cana-3299	120	1	[	[	X
cana-3299	120	2	32	32	NUM
cana-3299	120	3	]	]	PUNCT
cana-3299	120	4	let	let	NOUN
cana-3299	120	5	(	(	PUNCT
cana-3299	120	6	𝑋1	𝑋1	PROPN
cana-3299	120	7	,	,	PUNCT
cana-3299	120	8	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	120	9	)	)	PUNCT
cana-3299	120	10	be	be	AUX
cana-3299	120	11	an	an	DET
cana-3299	120	12	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	120	13	and	and	CCONJ
cana-3299	120	14	𝐴	𝐴	PROPN
cana-3299	120	15	=	=	PUNCT
cana-3299	120	16	{	{	PUNCT
cana-3299	120	17	<	<	X
cana-3299	120	18	𝑎	𝑎	X
cana-3299	120	19	,	,	PUNCT
cana-3299	120	20	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	120	21	)	)	PUNCT
cana-3299	120	22	,	,	PUNCT
cana-3299	120	23	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	120	24	)	)	PUNCT
cana-3299	120	25	>	>	X
cana-3299	120	26	|𝑎	|𝑎	PROPN
cana-3299	121	1	∈	∈	PROPN
cana-3299	121	2	𝑋1	𝑋1	PROPN
cana-3299	121	3	}	}	PUNCT
cana-3299	121	4	be	be	AUX
cana-3299	121	5	an	an	DET
cana-3299	121	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	121	7	in	in	ADP
cana-3299	121	8	𝑋1	𝑋1	PROPN
cana-3299	121	9	.	.	PUNCT
cana-3299	122	1	a	a	DET
cana-3299	122	2	set	set	ADJ
cana-3299	122	3	𝐴	𝐴	PROPN
cana-3299	122	4	is	be	AUX
cana-3299	122	5	said	say	VERB
cana-3299	122	6	to	to	PART
cana-3299	122	7	be	be	AUX
cana-3299	122	8	𝑝𝑓	𝑝𝑓	PRON
cana-3299	122	9	[	[	X
cana-3299	122	10	(	(	PUNCT
cana-3299	122	11	i	i	NOUN
cana-3299	122	12	)	)	PUNCT
cana-3299	122	13	]	]	PUNCT
cana-3299	123	1	1	1	X
cana-3299	123	2	.	.	X
cana-3299	123	3	𝛿-open	𝛿-open	VERB
cana-3299	123	4	set	set	NOUN
cana-3299	123	5	(	(	PUNCT
cana-3299	123	6	briefly	briefly	ADV
cana-3299	123	7	,	,	PUNCT
cana-3299	123	8	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-3299	123	9	)	)	PUNCT
cana-3299	123	10	if	if	SCONJ
cana-3299	123	11	𝐴	𝐴	PROPN
cana-3299	123	12	=	=	SYM
cana-3299	123	13	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	PROPN
cana-3299	123	14	)	)	PUNCT
cana-3299	123	15	,	,	PUNCT
cana-3299	123	16	2	2	X
cana-3299	123	17	.	.	X
cana-3299	123	18	𝛿-pre	𝛿-pre	PROPN
cana-3299	123	19	open	open	ADJ
cana-3299	123	20	set	set	PROPN
cana-3299	123	21	(	(	PUNCT
cana-3299	123	22	briefly	briefly	ADV
cana-3299	123	23	,	,	PUNCT
cana-3299	123	24	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	X
cana-3299	123	25	)	)	PUNCT
cana-3299	123	26	if	if	SCONJ
cana-3299	123	27	𝐴	𝐴	PROPN
cana-3299	123	28	⊆	⊆	NUM
cana-3299	123	29	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	NOUN
cana-3299	123	30	)	)	PUNCT
cana-3299	123	31	)	)	PUNCT
cana-3299	123	32	,	,	PUNCT
cana-3299	123	33	3	3	X
cana-3299	123	34	.	.	X
cana-3299	123	35	𝛿-semi	𝛿-semi	PROPN
cana-3299	123	36	open	open	ADJ
cana-3299	123	37	set	set	NOUN
cana-3299	123	38	(	(	PUNCT
cana-3299	123	39	briefly	briefly	ADV
cana-3299	123	40	,	,	PUNCT
cana-3299	123	41	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	123	42	)	)	PUNCT
cana-3299	124	1	if	if	SCONJ
cana-3299	124	2	𝐴	𝐴	PROPN
cana-3299	124	3	⊆	⊆	NUM
cana-3299	124	4	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	PROPN
cana-3299	124	5	)	)	PUNCT
cana-3299	124	6	)	)	PUNCT
cana-3299	124	7	,	,	PUNCT
cana-3299	124	8	4	4	X
cana-3299	124	9	.	.	X
cana-3299	124	10	𝑒	𝑒	PROPN
cana-3299	124	11	open	open	ADJ
cana-3299	124	12	set	set	NOUN
cana-3299	124	13	(	(	PUNCT
cana-3299	124	14	briefly	briefly	ADV
cana-3299	124	15	,	,	PUNCT
cana-3299	124	16	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	VERB
cana-3299	124	17	)	)	PUNCT
cana-3299	125	1	if	if	SCONJ
cana-3299	125	2	𝐴	𝐴	PROPN
cana-3299	125	3	⊆	⊆	NUM
cana-3299	125	4	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝛿𝑖𝑛𝑡(𝐴	NOUN
cana-3299	125	5	)	)	PUNCT
cana-3299	125	6	)	)	PUNCT
cana-3299	125	7	∪	∪	ADP
cana-3299	125	8	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	PROPN
cana-3299	125	9	)	)	PUNCT
cana-3299	125	10	)	)	PUNCT
cana-3299	125	11	,	,	PUNCT
cana-3299	125	12	5	5	X
cana-3299	125	13	.	.	PUNCT
cana-3299	125	14	𝛿	𝛿	ADJ
cana-3299	125	15	(	(	PUNCT
cana-3299	125	16	resp	resp	NOUN
cana-3299	125	17	.	.	PUNCT
cana-3299	126	1	𝛿-pre	𝛿-pre	PROPN
cana-3299	126	2	,	,	PUNCT
cana-3299	126	3	𝛿-semi	𝛿-semi	VERB
cana-3299	126	4	and	and	CCONJ
cana-3299	126	5	𝑒	𝑒	X
cana-3299	126	6	)	)	PUNCT
cana-3299	126	7	dense	dense	ADJ
cana-3299	126	8	if	if	SCONJ
cana-3299	126	9	𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝛿𝑐𝑙(𝐴	VERB
cana-3299	126	10	)	)	PUNCT
cana-3299	126	11	(	(	PUNCT
cana-3299	126	12	resp	resp	NOUN
cana-3299	126	13	.	.	PUNCT
cana-3299	127	1	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	NUM
cana-3299	127	2	)	)	PUNCT
cana-3299	127	3	,	,	PUNCT
cana-3299	127	4	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-3299	127	5	)	)	PUNCT
cana-3299	127	6	and	and	CCONJ
cana-3299	127	7	𝑝𝑓𝑒𝑐𝑙(𝐴	𝑝𝑓𝑒𝑐𝑙(𝐴	NOUN
cana-3299	127	8	)	)	PUNCT
cana-3299	127	9	)	)	PUNCT
cana-3299	128	1	=	=	SYM
cana-3299	128	2	𝑋1	𝑋1	PROPN
cana-3299	128	3	.	.	PUNCT
cana-3299	129	1	the	the	DET
cana-3299	129	2	complement	complement	NOUN
cana-3299	129	3	of	of	ADP
cana-3299	129	4	an	an	DET
cana-3299	129	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	129	6	(	(	PUNCT
cana-3299	129	7	resp	resp	NOUN
cana-3299	129	8	.	.	PUNCT
cana-3299	130	1	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	X
cana-3299	130	2	,	,	PUNCT
cana-3299	130	3	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	130	4	and	and	CCONJ
cana-3299	130	5	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	130	6	)	)	PUNCT
cana-3299	130	7	is	be	AUX
cana-3299	130	8	called	call	VERB
cana-3299	130	9	an	an	DET
cana-3299	130	10	𝑝𝑓𝛿	𝑝𝑓𝛿	NOUN
cana-3299	130	11	(	(	PUNCT
cana-3299	130	12	resp	resp	NOUN
cana-3299	130	13	.	.	PUNCT
cana-3299	131	1	𝑝𝑓𝛿𝒫	𝑝𝑓𝛿𝒫	ADJ
cana-3299	131	2	,	,	PUNCT
cana-3299	131	3	𝑝𝑓𝛿𝒮	𝑝𝑓𝛿𝒮	X
cana-3299	131	4	and	and	CCONJ
cana-3299	131	5	𝑝𝑓𝑒	𝑝𝑓𝑒	ADJ
cana-3299	131	6	)	)	PUNCT
cana-3299	131	7	closed	close	VERB
cana-3299	131	8	set	set	VERB
cana-3299	131	9	(	(	PUNCT
cana-3299	131	10	briefly	briefly	ADV
cana-3299	131	11	,	,	PUNCT
cana-3299	131	12	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-3299	131	13	(	(	PUNCT
cana-3299	131	14	resp	resp	NOUN
cana-3299	131	15	.	.	PUNCT
cana-3299	132	1	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-3299	132	2	,	,	PUNCT
cana-3299	132	3	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	132	4	and	and	CCONJ
cana-3299	132	5	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	PROPN
cana-3299	132	6	)	)	PUNCT
cana-3299	132	7	)	)	PUNCT
cana-3299	132	8	in	in	ADP
cana-3299	132	9	𝑋1	𝑋1	PROPN
cana-3299	132	10	.	.	PUNCT
cana-3299	133	1	the	the	DET
cana-3299	133	2	family	family	NOUN
cana-3299	133	3	of	of	ADP
cana-3299	133	4	all	all	DET
cana-3299	133	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-3299	133	6	(	(	PUNCT
cana-3299	133	7	resp	resp	NOUN
cana-3299	133	8	.	.	PUNCT
cana-3299	134	1	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-3299	134	2	,	,	PUNCT
cana-3299	134	3	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-3299	134	4	,	,	PUNCT
cana-3299	134	5	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-3299	134	6	,	,	PUNCT
cana-3299	134	7	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	134	8	,	,	PUNCT
cana-3299	134	9	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	134	10	,	,	PUNCT
cana-3299	134	11	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	VERB
cana-3299	134	12	and	and	CCONJ
cana-3299	134	13	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	134	14	)	)	PUNCT
cana-3299	134	15	of	of	ADP
cana-3299	134	16	𝑋1	𝑋1	PROPN
cana-3299	134	17	is	be	AUX
cana-3299	134	18	denoted	denote	VERB
cana-3299	134	19	by	by	ADP
cana-3299	134	20	𝑝𝑓𝛿𝑂𝑆(𝑋1	𝑝𝑓𝛿𝑂𝑆(𝑋1	NOUN
cana-3299	134	21	)	)	PUNCT
cana-3299	134	22	,	,	PUNCT
cana-3299	134	23	(	(	PUNCT
cana-3299	134	24	resp	resp	NOUN
cana-3299	134	25	.	.	PUNCT
cana-3299	134	26	𝑝𝑓𝛿𝐶𝑆(𝑋1	𝑝𝑓𝛿𝐶𝑆(𝑋1	PROPN
cana-3299	134	27	)	)	PUNCT
cana-3299	134	28	,	,	PUNCT
cana-3299	134	29	𝑝𝑓𝛿𝒫𝑂𝑆(𝑋1	𝑝𝑓𝛿𝒫𝑂𝑆(𝑋1	NUM
cana-3299	134	30	)	)	PUNCT
cana-3299	134	31	,	,	PUNCT
cana-3299	134	32	𝑝𝑓𝛿𝒫𝐶𝑆(𝑋1	𝑝𝑓𝛿𝒫𝐶𝑆(𝑋1	NUM
cana-3299	134	33	)	)	PUNCT
cana-3299	134	34	,	,	PUNCT
cana-3299	134	35	𝑝𝑓𝛿𝒮𝑂𝑆(𝑋1	𝑝𝑓𝛿𝒮𝑂𝑆(𝑋1	NUM
cana-3299	134	36	)	)	PUNCT
cana-3299	134	37	,	,	PUNCT
cana-3299	134	38	𝑝𝑓𝛿𝒮𝐶𝑆(𝑋1	𝑝𝑓𝛿𝒮𝐶𝑆(𝑋1	NOUN
cana-3299	134	39	)	)	PUNCT
cana-3299	134	40	,	,	PUNCT
cana-3299	134	41	𝑝𝑓𝑒𝑂𝑆(𝑋1	𝑝𝑓𝑒𝑂𝑆(𝑋1	PROPN
cana-3299	134	42	)	)	PUNCT
cana-3299	134	43	and	and	CCONJ
cana-3299	134	44	𝑝𝑓𝑒𝐶𝑆(𝑋1	𝑝𝑓𝑒𝐶𝑆(𝑋1	NUM
cana-3299	134	45	)	)	PUNCT
cana-3299	134	46	)	)	PUNCT
cana-3299	134	47	.	.	PUNCT
cana-3299	135	1	definition	definition	NOUN
cana-3299	135	2	2.10	2.10	NUM
cana-3299	135	3	[	[	X
cana-3299	135	4	32	32	NUM
cana-3299	135	5	]	]	PUNCT
cana-3299	135	6	let	let	VERB
cana-3299	135	7	(	(	PUNCT
cana-3299	135	8	𝑋	𝑋	NOUN
cana-3299	135	9	,	,	PUNCT
cana-3299	135	10	𝜏	𝜏	NOUN
cana-3299	135	11	)	)	PUNCT
cana-3299	135	12	be	be	VERB
cana-3299	135	13	an	an	DET
cana-3299	135	14	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	135	15	and	and	CCONJ
cana-3299	135	16	𝐴	𝐴	PROPN
cana-3299	135	17	=	=	PUNCT
cana-3299	135	18	{	{	PUNCT
cana-3299	135	19	<	<	X
cana-3299	135	20	𝑎	𝑎	X
cana-3299	135	21	,	,	PUNCT
cana-3299	135	22	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	135	23	)	)	PUNCT
cana-3299	135	24	,	,	PUNCT
cana-3299	135	25	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	135	26	)	)	PUNCT
cana-3299	135	27	>	>	X
cana-3299	135	28	|𝑎	|𝑎	PROPN
cana-3299	136	1	∈	∈	PROPN
cana-3299	136	2	𝑋1	𝑋1	PROPN
cana-3299	136	3	}	}	PUNCT
cana-3299	136	4	be	be	AUX
cana-3299	136	5	an	an	DET
cana-3299	136	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	136	7	in	in	ADP
cana-3299	136	8	𝑋1	𝑋1	PROPN
cana-3299	136	9	.	.	PUNCT
cana-3299	137	1	then	then	ADV
cana-3299	137	2	the	the	DET
cana-3299	137	3	(	(	PUNCT
cana-3299	137	4	i	i	NOUN
cana-3299	137	5	)	)	PUNCT
cana-3299	137	6	𝑝𝑓𝛿-pre	𝑝𝑓𝛿-pre	VERB
cana-3299	137	7	(	(	PUNCT
cana-3299	137	8	resp	resp	NOUN
cana-3299	137	9	.	.	PUNCT
cana-3299	138	1	𝑝𝑓𝛿-semi	𝑝𝑓𝛿-semi	PROPN
cana-3299	138	2	and	and	CCONJ
cana-3299	138	3	𝑝𝑓𝑒)-interior	𝑝𝑓𝑒)-interior	PROPN
cana-3299	138	4	of	of	ADP
cana-3299	138	5	𝐴	𝐴	PROPN
cana-3299	138	6	are	be	AUX
cana-3299	138	7	denoted	denote	VERB
cana-3299	138	8	by	by	ADP
cana-3299	138	9	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	NOUN
cana-3299	138	10	)	)	PUNCT
cana-3299	138	11	(	(	PUNCT
cana-3299	138	12	resp	resp	NOUN
cana-3299	138	13	.	.	PUNCT
cana-3299	139	1	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	PROPN
cana-3299	139	2	)	)	PUNCT
cana-3299	139	3	and	and	CCONJ
cana-3299	139	4	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	NOUN
cana-3299	139	5	)	)	PUNCT
cana-3299	139	6	)	)	PUNCT
cana-3299	140	1	and	and	CCONJ
cana-3299	140	2	are	be	AUX
cana-3299	140	3	defined	define	VERB
cana-3299	140	4	as	as	SCONJ
cana-3299	140	5	follows	follow	VERB
cana-3299	140	6	:	:	PUNCT
cana-3299	140	7	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒫𝑖𝑛𝑡(𝐴	X
cana-3299	140	8	)	)	PUNCT
cana-3299	140	9	(	(	PUNCT
cana-3299	140	10	resp	resp	NOUN
cana-3299	140	11	.	.	PUNCT
cana-3299	141	1	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝛿𝒮𝑖𝑛𝑡(𝐴	PROPN
cana-3299	141	2	)	)	PUNCT
cana-3299	141	3	and	and	CCONJ
cana-3299	141	4	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	𝑝𝑓𝑒𝑖𝑛𝑡(𝐴	X
cana-3299	141	5	)	)	PUNCT
cana-3299	142	1	=	=	NOUN
cana-3299	142	2	∪	∪	X
cana-3299	142	3	{	{	PUNCT
cana-3299	142	4	𝐺|𝐺	𝐺|𝐺	NOUN
cana-3299	142	5	in	in	ADP
cana-3299	142	6	a	a	DET
cana-3299	142	7	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	ADJ
cana-3299	142	8	(	(	PUNCT
cana-3299	142	9	resp	resp	NOUN
cana-3299	142	10	.	.	PUNCT
cana-3299	143	1	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	143	2	and	and	CCONJ
cana-3299	143	3	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	143	4	)	)	PUNCT
cana-3299	143	5	and	and	CCONJ
cana-3299	143	6	𝐺	𝐺	PROPN
cana-3299	143	7	⊆	⊆	NUM
cana-3299	143	8	𝐴	𝐴	PROPN
cana-3299	143	9	}	}	PUNCT
cana-3299	143	10	,	,	PUNCT
cana-3299	143	11	(	(	PUNCT
cana-3299	143	12	ii	ii	NOUN
cana-3299	143	13	)	)	PUNCT
cana-3299	143	14	𝑝𝑓𝛿-pre	𝑝𝑓𝛿-pre	VERB
cana-3299	143	15	(	(	PUNCT
cana-3299	143	16	resp	resp	NOUN
cana-3299	143	17	.	.	PUNCT
cana-3299	144	1	𝑝𝑓𝛿semi	𝑝𝑓𝛿semi	NOUN
cana-3299	144	2	and	and	CCONJ
cana-3299	144	3	𝑝𝑓𝑒)-closure	𝑝𝑓𝑒)-closure	NOUN
cana-3299	144	4	of	of	ADP
cana-3299	144	5	𝐴	𝐴	PROPN
cana-3299	144	6	are	be	AUX
cana-3299	144	7	denoted	denote	VERB
cana-3299	144	8	by	by	ADP
cana-3299	144	9	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	PROPN
cana-3299	144	10	)	)	PUNCT
cana-3299	144	11	(	(	PUNCT
cana-3299	144	12	resp	resp	NOUN
cana-3299	144	13	.	.	PUNCT
cana-3299	145	1	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-3299	145	2	)	)	PUNCT
cana-3299	145	3	and	and	CCONJ
cana-3299	145	4	𝑝𝑓𝑒𝑐𝑙(𝐴	𝑝𝑓𝑒𝑐𝑙(𝐴	NOUN
cana-3299	145	5	)	)	PUNCT
cana-3299	145	6	)	)	PUNCT
cana-3299	146	1	and	and	CCONJ
cana-3299	146	2	are	be	AUX
cana-3299	146	3	defined	define	VERB
cana-3299	146	4	as	as	SCONJ
cana-3299	146	5	follows	follow	VERB
cana-3299	146	6	:	:	PUNCT
cana-3299	146	7	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	𝑝𝑓𝛿𝒫𝑐𝑙(𝐴	NUM
cana-3299	146	8	)	)	PUNCT
cana-3299	146	9	(	(	PUNCT
cana-3299	146	10	resp	resp	NOUN
cana-3299	146	11	.	.	PUNCT
cana-3299	147	1	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	𝑝𝑓𝛿𝒮𝑐𝑙(𝐴	PROPN
cana-3299	147	2	)	)	PUNCT
cana-3299	147	3	and	and	CCONJ
cana-3299	147	4	𝑝𝑓𝑒𝑐𝑙(𝐴	𝑝𝑓𝑒𝑐𝑙(𝐴	NOUN
cana-3299	147	5	)	)	PUNCT
cana-3299	147	6	)	)	PUNCT
cana-3299	148	1	=	=	NOUN
cana-3299	148	2	∩	∩	NOUN
cana-3299	148	3	{	{	PUNCT
cana-3299	148	4	𝐾|𝐾	𝐾|𝐾	NOUN
cana-3299	148	5	is	be	AUX
cana-3299	148	6	an	an	DET
cana-3299	148	7	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	NOUN
cana-3299	148	8	(	(	PUNCT
cana-3299	148	9	resp	resp	NOUN
cana-3299	148	10	.	.	PUNCT
cana-3299	149	1	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	149	2	,	,	PUNCT
cana-3299	149	3	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	PROPN
cana-3299	149	4	)	)	PUNCT
cana-3299	149	5	and	and	CCONJ
cana-3299	149	6	𝐴	𝐴	PROPN
cana-3299	149	7	⊆	⊆	NUM
cana-3299	149	8	𝐾	𝐾	PROPN
cana-3299	149	9	}	}	PUNCT
cana-3299	149	10	.	.	PUNCT
cana-3299	150	1	definition	definition	NOUN
cana-3299	150	2	2.11	2.11	NUM
cana-3299	150	3	[	[	X
cana-3299	150	4	32	32	NUM
cana-3299	150	5	]	]	PUNCT
cana-3299	150	6	let	let	NOUN
cana-3299	150	7	(	(	PUNCT
cana-3299	150	8	𝑋1	𝑋1	PROPN
cana-3299	150	9	,	,	PUNCT
cana-3299	150	10	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	150	11	)	)	PUNCT
cana-3299	150	12	be	be	AUX
cana-3299	150	13	an	an	DET
cana-3299	150	14	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	150	15	and	and	CCONJ
cana-3299	150	16	𝐴	𝐴	PROPN
cana-3299	150	17	=	=	PUNCT
cana-3299	150	18	{	{	PUNCT
cana-3299	150	19	<	<	X
cana-3299	150	20	𝑎	𝑎	X
cana-3299	150	21	,	,	PUNCT
cana-3299	150	22	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	150	23	)	)	PUNCT
cana-3299	150	24	,	,	PUNCT
cana-3299	150	25	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	150	26	)	)	PUNCT
cana-3299	150	27	>	>	X
cana-3299	150	28	|𝑎	|𝑎	PROPN
cana-3299	151	1	∈	∈	PROPN
cana-3299	151	2	𝑋1	𝑋1	PROPN
cana-3299	151	3	}	}	PUNCT
cana-3299	151	4	be	be	AUX
cana-3299	151	5	an	an	DET
cana-3299	151	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	151	7	in	in	ADP
cana-3299	151	8	𝑋1	𝑋1	PROPN
cana-3299	151	9	.	.	PUNCT
cana-3299	152	1	a	a	DET
cana-3299	152	2	set	set	ADJ
cana-3299	152	3	𝐴	𝐴	PROPN
cana-3299	152	4	is	be	AUX
cana-3299	152	5	said	say	VERB
cana-3299	152	6	to	to	PART
cana-3299	152	7	be	be	AUX
cana-3299	152	8	𝑝𝑓	𝑝𝑓	PRON
cana-3299	152	9	communications	communication	NOUN
cana-3299	152	10	on	on	ADP
cana-3299	152	11	applied	apply	VERB
cana-3299	152	12	nonlinear	nonlinear	ADJ
cana-3299	152	13	analysis	analysis	NOUN
cana-3299	152	14	issn	issn	NOUN
cana-3299	152	15	:	:	PUNCT
cana-3299	152	16	1074	1074	NUM
cana-3299	152	17	-	-	PUNCT
cana-3299	152	18	133x	133x	NUM
cana-3299	152	19	vol	vol	NOUN
cana-3299	152	20	32	32	NUM
cana-3299	152	21	no	no	NOUN
cana-3299	152	22	.	.	PUNCT
cana-3299	153	1	6s	6s	NUM
cana-3299	153	2	(	(	PUNCT
cana-3299	153	3	2025	2025	NUM
cana-3299	153	4	)	)	PUNCT
cana-3299	153	5	331	331	NUM
cana-3299	153	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	153	7	1	1	NUM
cana-3299	153	8	.	.	PUNCT
cana-3299	153	9	𝜃-interior	𝜃-interior	NOUN
cana-3299	153	10	of	of	ADP
cana-3299	153	11	𝐴	𝐴	PROPN
cana-3299	153	12	(	(	PUNCT
cana-3299	153	13	briefly	briefly	ADV
cana-3299	153	14	,	,	PUNCT
cana-3299	153	15	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	PROPN
cana-3299	153	16	)	)	PUNCT
cana-3299	153	17	)	)	PUNCT
cana-3299	153	18	is	be	AUX
cana-3299	153	19	defined	define	VERB
cana-3299	153	20	by	by	ADP
cana-3299	153	21	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-3299	153	22	)	)	PUNCT
cana-3299	154	1	=	=	SYM
cana-3299	154	2	∪	∪	X
cana-3299	154	3	{	{	PUNCT
cana-3299	154	4	𝑝𝑓𝑖𝑛𝑡(𝐵	𝑝𝑓𝑖𝑛𝑡(𝐵	NOUN
cana-3299	154	5	):	):	PUNCT
cana-3299	154	6	𝐵	𝐵	PROPN
cana-3299	154	7	⊆	⊆	NUM
cana-3299	154	8	𝐴	𝐴	PROPN
cana-3299	154	9	&	&	CCONJ
cana-3299	154	10	𝐵	𝐵	PROPN
cana-3299	154	11	isa	isa	VERB
cana-3299	154	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	154	13	in	in	ADP
cana-3299	154	14	𝑋1	𝑋1	PROPN
cana-3299	154	15	}	}	PUNCT
cana-3299	154	16	.	.	PUNCT
cana-3299	155	1	2	2	X
cana-3299	155	2	.	.	X
cana-3299	155	3	𝜃-open	𝜃-open	NOUN
cana-3299	155	4	set	set	NOUN
cana-3299	155	5	(	(	PUNCT
cana-3299	155	6	briefly	briefly	ADV
cana-3299	155	7	,	,	PUNCT
cana-3299	155	8	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	155	9	)	)	PUNCT
cana-3299	155	10	if	if	SCONJ
cana-3299	155	11	𝐴	𝐴	PROPN
cana-3299	155	12	=	=	SYM
cana-3299	155	13	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	PROPN
cana-3299	155	14	)	)	PUNCT
cana-3299	155	15	.	.	PUNCT
cana-3299	156	1	3	3	X
cana-3299	156	2	.	.	X
cana-3299	156	3	𝜃	𝜃	PRON
cana-3299	156	4	-semi	-semi	VERB
cana-3299	156	5	open	open	ADJ
cana-3299	156	6	set	set	NOUN
cana-3299	156	7	(	(	PUNCT
cana-3299	156	8	briefly	briefly	ADV
cana-3299	156	9	,	,	PUNCT
cana-3299	156	10	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	156	11	)	)	PUNCT
cana-3299	156	12	if	if	SCONJ
cana-3299	156	13	𝐴	𝐴	PROPN
cana-3299	156	14	⊆	⊆	NUM
cana-3299	156	15	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-3299	156	16	)	)	PUNCT
cana-3299	156	17	)	)	PUNCT
cana-3299	156	18	.	.	PUNCT
cana-3299	157	1	4	4	X
cana-3299	157	2	.	.	X
cana-3299	158	1	𝑀-open	𝑀-open	ADJ
cana-3299	158	2	set	set	NOUN
cana-3299	158	3	(	(	PUNCT
cana-3299	158	4	briefly	briefly	ADV
cana-3299	158	5	,	,	PUNCT
cana-3299	158	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	158	7	)	)	PUNCT
cana-3299	158	8	if	if	SCONJ
cana-3299	158	9	𝐴	𝐴	PROPN
cana-3299	158	10	⊆	⊆	NUM
cana-3299	158	11	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝑐𝑙(𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-3299	158	12	)	)	PUNCT
cana-3299	158	13	)	)	PUNCT
cana-3299	158	14	∪	∪	ADP
cana-3299	158	15	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	𝑝𝑓𝑖𝑛𝑡(𝑝𝑓𝛿𝑐𝑙(𝐴	PROPN
cana-3299	158	16	)	)	PUNCT
cana-3299	158	17	)	)	PUNCT
cana-3299	158	18	.	.	PUNCT
cana-3299	159	1	the	the	DET
cana-3299	159	2	complement	complement	NOUN
cana-3299	159	3	of	of	ADP
cana-3299	159	4	a	a	DET
cana-3299	159	5	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	159	6	(	(	PUNCT
cana-3299	159	7	resp	resp	NOUN
cana-3299	159	8	.	.	PUNCT
cana-3299	160	1	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	PROPN
cana-3299	160	2	&	&	CCONJ
cana-3299	160	3	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	160	4	)	)	PUNCT
cana-3299	160	5	is	be	AUX
cana-3299	160	6	called	call	VERB
cana-3299	160	7	an	an	DET
cana-3299	160	8	𝑝𝑓𝑀	𝑝𝑓𝑀	NOUN
cana-3299	160	9	(	(	PUNCT
cana-3299	160	10	resp	resp	NOUN
cana-3299	160	11	.	.	PUNCT
cana-3299	161	1	𝑝𝑓𝜃	𝑝𝑓𝜃	PROPN
cana-3299	161	2	&	&	CCONJ
cana-3299	161	3	𝑝𝑓𝜃𝒮	𝑝𝑓𝜃𝒮	NOUN
cana-3299	161	4	)	)	PUNCT
cana-3299	161	5	closed	closed	ADJ
cana-3299	161	6	set	set	NOUN
cana-3299	161	7	(	(	PUNCT
cana-3299	161	8	briefly	briefly	ADV
cana-3299	161	9	,	,	PUNCT
cana-3299	161	10	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	PROPN
cana-3299	161	11	(	(	PUNCT
cana-3299	161	12	resp	resp	NOUN
cana-3299	161	13	.	.	PUNCT
cana-3299	161	14	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	PROPN
cana-3299	161	15	&	&	CCONJ
cana-3299	161	16	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NUM
cana-3299	161	17	)	)	PUNCT
cana-3299	161	18	)	)	PUNCT
cana-3299	161	19	in	in	ADP
cana-3299	161	20	𝑋1	𝑋1	PROPN
cana-3299	161	21	.	.	PUNCT
cana-3299	162	1	the	the	DET
cana-3299	162	2	family	family	NOUN
cana-3299	162	3	of	of	ADP
cana-3299	162	4	all	all	DET
cana-3299	162	5	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	162	6	(	(	PUNCT
cana-3299	162	7	resp	resp	NOUN
cana-3299	162	8	.	.	PUNCT
cana-3299	163	1	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	PROPN
cana-3299	163	2	,	,	PUNCT
cana-3299	163	3	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	163	4	,	,	PUNCT
cana-3299	163	5	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-3299	163	6	,	,	PUNCT
cana-3299	163	7	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	163	8	and	and	CCONJ
cana-3299	163	9	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NUM
cana-3299	163	10	)	)	PUNCT
cana-3299	163	11	of	of	ADP
cana-3299	163	12	𝑋1	𝑋1	PROPN
cana-3299	163	13	is	be	AUX
cana-3299	163	14	denoted	denote	VERB
cana-3299	163	15	by	by	ADP
cana-3299	163	16	𝑝𝑓𝜃𝑂𝑆(𝑋1	𝑝𝑓𝜃𝑂𝑆(𝑋1	NOUN
cana-3299	163	17	)	)	PUNCT
cana-3299	163	18	,	,	PUNCT
cana-3299	163	19	(	(	PUNCT
cana-3299	163	20	resp	resp	NOUN
cana-3299	163	21	.	.	PUNCT
cana-3299	164	1	𝑝𝑓𝜃𝐶𝑆(𝑋1	𝑝𝑓𝜃𝐶𝑆(𝑋1	PROPN
cana-3299	164	2	)	)	PUNCT
cana-3299	164	3	,	,	PUNCT
cana-3299	164	4	𝑝𝑓𝜃𝒮𝑂𝑆(𝑋1	𝑝𝑓𝜃𝒮𝑂𝑆(𝑋1	NUM
cana-3299	164	5	)	)	PUNCT
cana-3299	164	6	,	,	PUNCT
cana-3299	164	7	𝑝𝑓𝜃𝒮𝐶𝑆(𝑋1	𝑝𝑓𝜃𝒮𝐶𝑆(𝑋1	NUM
cana-3299	164	8	)	)	PUNCT
cana-3299	164	9	,	,	PUNCT
cana-3299	164	10	𝑝𝑓𝑀𝑂𝑆(𝑋1	𝑝𝑓𝑀𝑂𝑆(𝑋1	NUM
cana-3299	164	11	)	)	PUNCT
cana-3299	164	12	and	and	CCONJ
cana-3299	164	13	𝑝𝑓𝑀𝐶𝑆(𝑋1	𝑝𝑓𝑀𝐶𝑆(𝑋1	NUM
cana-3299	164	14	)	)	PUNCT
cana-3299	164	15	)	)	PUNCT
cana-3299	164	16	.	.	PUNCT
cana-3299	165	1	definition	definition	NOUN
cana-3299	165	2	2.12	2.12	NUM
cana-3299	165	3	[	[	X
cana-3299	165	4	32	32	NUM
cana-3299	165	5	]	]	PUNCT
cana-3299	165	6	let	let	NOUN
cana-3299	165	7	(	(	PUNCT
cana-3299	165	8	𝑋1	𝑋1	PROPN
cana-3299	165	9	,	,	PUNCT
cana-3299	165	10	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	165	11	)	)	PUNCT
cana-3299	165	12	be	be	AUX
cana-3299	165	13	an	an	DET
cana-3299	165	14	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	165	15	and	and	CCONJ
cana-3299	165	16	𝐴	𝐴	PROPN
cana-3299	165	17	=	=	PUNCT
cana-3299	165	18	{	{	PUNCT
cana-3299	165	19	<	<	X
cana-3299	165	20	𝑎	𝑎	X
cana-3299	165	21	,	,	PUNCT
cana-3299	165	22	𝜆𝐴(𝑎	𝜆𝐴(𝑎	PROPN
cana-3299	165	23	)	)	PUNCT
cana-3299	165	24	,	,	PUNCT
cana-3299	165	25	𝜇𝐴(𝑎	𝜇𝐴(𝑎	PROPN
cana-3299	165	26	)	)	PUNCT
cana-3299	165	27	>	>	X
cana-3299	165	28	|𝑎	|𝑎	PROPN
cana-3299	166	1	∈	∈	PROPN
cana-3299	166	2	𝑋1	𝑋1	PROPN
cana-3299	166	3	}	}	PUNCT
cana-3299	166	4	be	be	AUX
cana-3299	166	5	an	an	DET
cana-3299	166	6	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	166	7	in	in	ADP
cana-3299	166	8	𝑋1	𝑋1	PROPN
cana-3299	166	9	.	.	PUNCT
cana-3299	167	1	then	then	ADV
cana-3299	167	2	the	the	DET
cana-3299	167	3	𝑝𝑓	𝑝𝑓	PROPN
cana-3299	167	4	1	1	NUM
cana-3299	167	5	.	.	PUNCT
cana-3299	167	6	𝑀	𝑀	PROPN
cana-3299	167	7	(	(	PUNCT
cana-3299	167	8	resp	resp	PROPN
cana-3299	167	9	.	.	PUNCT
cana-3299	168	1	𝑝𝑓𝜃-semi	𝑝𝑓𝜃-semi	ADJ
cana-3299	168	2	)	)	PUNCT
cana-3299	168	3	-interior	-interior	NOUN
cana-3299	168	4	of	of	ADP
cana-3299	168	5	𝐴	𝐴	PROPN
cana-3299	168	6	(	(	PUNCT
cana-3299	168	7	briefly	briefly	ADV
cana-3299	168	8	,	,	PUNCT
cana-3299	168	9	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	NUM
cana-3299	168	10	)	)	PUNCT
cana-3299	168	11	(	(	PUNCT
cana-3299	168	12	resp	resp	NOUN
cana-3299	168	13	.	.	PUNCT
cana-3299	169	1	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	NOUN
cana-3299	169	2	)	)	PUNCT
cana-3299	169	3	)	)	PUNCT
cana-3299	170	1	is	be	AUX
cana-3299	170	2	defined	define	VERB
cana-3299	170	3	by	by	ADP
cana-3299	170	4	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	𝑝𝑓𝑀𝑖𝑛𝑡(𝐴	NUM
cana-3299	170	5	)	)	PUNCT
cana-3299	170	6	(	(	PUNCT
cana-3299	170	7	resp	resp	NOUN
cana-3299	170	8	.	.	PUNCT
cana-3299	171	1	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝑖𝑛𝑡(𝐴	NOUN
cana-3299	171	2	)	)	PUNCT
cana-3299	171	3	and	and	CCONJ
cana-3299	171	4	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	𝑝𝑓𝜃𝒮𝑖𝑛𝑡(𝐴	NOUN
cana-3299	171	5	)	)	PUNCT
cana-3299	171	6	)	)	PUNCT
cana-3299	172	1	=	=	SYM
cana-3299	172	2	∪	∪	X
cana-3299	172	3	{	{	PUNCT
cana-3299	172	4	𝐵	𝐵	NOUN
cana-3299	172	5	:	:	PUNCT
cana-3299	172	6	𝐵	𝐵	PROPN
cana-3299	172	7	⊆	⊆	NUM
cana-3299	172	8	𝐴	𝐴	PROPN
cana-3299	172	9	and	and	CCONJ
cana-3299	172	10	𝐵	𝐵	PROPN
cana-3299	172	11	is	be	AUX
cana-3299	172	12	a	a	DET
cana-3299	172	13	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	172	14	(	(	PUNCT
cana-3299	172	15	resp	resp	NOUN
cana-3299	172	16	.	.	PUNCT
cana-3299	173	1	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	173	2	)	)	PUNCT
cana-3299	174	1	in	in	ADP
cana-3299	174	2	𝑋1	𝑋1	PROPN
cana-3299	174	3	}	}	PUNCT
cana-3299	174	4	.	.	PUNCT
cana-3299	175	1	2	2	X
cana-3299	175	2	.	.	X
cana-3299	175	3	𝑀	𝑀	PROPN
cana-3299	175	4	(	(	PUNCT
cana-3299	175	5	resp	resp	PROPN
cana-3299	175	6	.	.	PUNCT
cana-3299	176	1	𝜃-semi	𝜃-semi	NOUN
cana-3299	176	2	)	)	PUNCT
cana-3299	176	3	-closure	-closure	NOUN
cana-3299	176	4	of	of	ADP
cana-3299	176	5	𝐴	𝐴	PROPN
cana-3299	176	6	(	(	PUNCT
cana-3299	176	7	briefly	briefly	ADV
cana-3299	176	8	,	,	PUNCT
cana-3299	176	9	𝑝𝑓𝑀𝑐𝑙(𝐴	𝑝𝑓𝑀𝑐𝑙(𝐴	INTJ
cana-3299	176	10	)	)	PUNCT
cana-3299	176	11	(	(	PUNCT
cana-3299	176	12	resp	resp	NOUN
cana-3299	176	13	.	.	PUNCT
cana-3299	177	1	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	NUM
cana-3299	177	2	)	)	PUNCT
cana-3299	177	3	)	)	PUNCT
cana-3299	177	4	is	be	AUX
cana-3299	177	5	defined	define	VERB
cana-3299	177	6	by	by	ADP
cana-3299	177	7	𝑝𝑓𝑀𝑐𝑙(𝐴	𝑝𝑓𝑀𝑐𝑙(𝐴	NOUN
cana-3299	177	8	)	)	PUNCT
cana-3299	177	9	(	(	PUNCT
cana-3299	177	10	resp	resp	NOUN
cana-3299	177	11	.	.	PUNCT
cana-3299	178	1	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	𝑝𝑓𝜃𝒮𝑐𝑙(𝐴	NUM
cana-3299	178	2	)	)	PUNCT
cana-3299	178	3	)	)	PUNCT
cana-3299	179	1	=	=	NOUN
cana-3299	179	2	∩	∩	X
cana-3299	179	3	{	{	PUNCT
cana-3299	179	4	𝐵	𝐵	NOUN
cana-3299	179	5	:	:	PUNCT
cana-3299	179	6	𝐴	𝐴	PROPN
cana-3299	179	7	⊆	⊆	NUM
cana-3299	179	8	𝐵	𝐵	PROPN
cana-3299	179	9	and	and	CCONJ
cana-3299	179	10	𝐴	𝐴	PROPN
cana-3299	179	11	is	be	AUX
cana-3299	179	12	a	a	DET
cana-3299	179	13	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	179	14	(	(	PUNCT
cana-3299	179	15	resp	resp	NOUN
cana-3299	179	16	.	.	PUNCT
cana-3299	180	1	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NUM
cana-3299	180	2	)	)	PUNCT
cana-3299	181	1	in	in	ADP
cana-3299	181	2	𝑋1	𝑋1	PROPN
cana-3299	181	3	}	}	PUNCT
cana-3299	181	4	.	.	PUNCT
cana-3299	182	1	definition	definition	NOUN
cana-3299	182	2	2.13	2.13	NUM
cana-3299	182	3	let	let	VERB
cana-3299	182	4	(	(	PUNCT
cana-3299	182	5	𝑋1	𝑋1	PROPN
cana-3299	182	6	,	,	PUNCT
cana-3299	182	7	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	182	8	)	)	PUNCT
cana-3299	182	9	and	and	CCONJ
cana-3299	182	10	(	(	PUNCT
cana-3299	182	11	𝑋2	𝑋2	PROPN
cana-3299	182	12	,	,	PUNCT
cana-3299	182	13	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	182	14	)	)	PUNCT
cana-3299	182	15	be	be	VERB
cana-3299	182	16	any	any	DET
cana-3299	182	17	two	two	NUM
cana-3299	182	18	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	182	19	’s	’s	PART
cana-3299	182	20	.	.	PUNCT
cana-3299	183	1	a	a	DET
cana-3299	183	2	mapping	mapping	NOUN
cana-3299	183	3	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	183	4	:	:	PUNCT
cana-3299	183	5	(	(	PUNCT
cana-3299	183	6	𝑋1	𝑋1	PROPN
cana-3299	183	7	,	,	PUNCT
cana-3299	183	8	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	183	9	)	)	PUNCT
cana-3299	183	10	→	→	PUNCT
cana-3299	183	11	(	(	PUNCT
cana-3299	183	12	𝑋2	𝑋2	PROPN
cana-3299	183	13	,	,	PUNCT
cana-3299	183	14	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	183	15	)	)	PUNCT
cana-3299	183	16	is	be	AUX
cana-3299	183	17	said	say	VERB
cana-3299	183	18	to	to	PART
cana-3299	183	19	be	be	AUX
cana-3299	183	20	a	a	DET
cana-3299	183	21	pythagorean	pythagorean	ADJ
cana-3299	183	22	fuzzy	fuzzy	NOUN
cana-3299	183	23	(	(	PUNCT
cana-3299	183	24	resp	resp	NOUN
cana-3299	183	25	.	.	PUNCT
cana-3299	184	1	𝛿	𝛿	ADJ
cana-3299	184	2	,	,	PUNCT
cana-3299	184	3	𝛿𝒫	𝛿𝒫	NOUN
cana-3299	184	4	,	,	PUNCT
cana-3299	184	5	𝛿𝒮	𝛿𝒮	NOUN
cana-3299	184	6	,	,	PUNCT
cana-3299	184	7	𝑒	𝑒	NOUN
cana-3299	184	8	,	,	PUNCT
cana-3299	184	9	𝜃	𝜃	NOUN
cana-3299	184	10	,	,	PUNCT
cana-3299	184	11	𝜃𝒮	𝜃𝒮	ADJ
cana-3299	184	12	and	and	CCONJ
cana-3299	184	13	𝑀	𝑀	PROPN
cana-3299	184	14	)	)	PUNCT
cana-3299	184	15	-continuous	-continuous	ADJ
cana-3299	184	16	(	(	PUNCT
cana-3299	184	17	briefly	briefly	ADV
cana-3299	184	18	,	,	PUNCT
cana-3299	184	19	𝑝𝑓𝐶𝑡𝑠	𝑝𝑓𝐶𝑡𝑠	PROPN
cana-3299	184	20	(	(	PUNCT
cana-3299	184	21	resp	resp	NOUN
cana-3299	184	22	.	.	PUNCT
cana-3299	185	1	𝑝𝑓𝛿𝐶𝑡𝑠	𝑝𝑓𝛿𝐶𝑡𝑠	PROPN
cana-3299	185	2	,	,	PUNCT
cana-3299	185	3	𝑝𝑓𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝛿𝒫𝐶𝑡𝑠	PROPN
cana-3299	185	4	,	,	PUNCT
cana-3299	185	5	𝑝𝑓𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝛿𝒮𝐶𝑡𝑠	PROPN
cana-3299	185	6	,	,	PUNCT
cana-3299	185	7	𝑝𝑓𝑒𝐶𝑡𝑠	𝑝𝑓𝑒𝐶𝑡𝑠	NOUN
cana-3299	185	8	,	,	PUNCT
cana-3299	185	9	𝑝𝑓𝜃𝐶𝑡𝑠	𝑝𝑓𝜃𝐶𝑡𝑠	NOUN
cana-3299	185	10	,	,	PUNCT
cana-3299	185	11	𝑝𝑓𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝜃𝒮𝐶𝑡𝑠	PROPN
cana-3299	185	12	and	and	CCONJ
cana-3299	185	13	𝑝𝑓𝑀𝐶𝑡𝑠	𝑝𝑓𝑀𝐶𝑡𝑠	PROPN
cana-3299	185	14	)	)	PUNCT
cana-3299	185	15	)	)	PUNCT
cana-3299	186	1	if	if	SCONJ
cana-3299	186	2	the	the	DET
cana-3299	186	3	inverse	inverse	ADJ
cana-3299	186	4	image	image	NOUN
cana-3299	186	5	of	of	ADP
cana-3299	186	6	every	every	DET
cana-3299	186	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	186	8	in	in	ADP
cana-3299	186	9	(	(	PUNCT
cana-3299	186	10	𝑋2	𝑋2	PROPN
cana-3299	186	11	,	,	PUNCT
cana-3299	186	12	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	186	13	)	)	PUNCT
cana-3299	186	14	is	be	AUX
cana-3299	186	15	a	a	DET
cana-3299	186	16	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	186	17	(	(	PUNCT
cana-3299	186	18	resp	resp	NOUN
cana-3299	186	19	.	.	PUNCT
cana-3299	187	1	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-3299	187	2	,	,	PUNCT
cana-3299	187	3	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-3299	187	4	,	,	PUNCT
cana-3299	187	5	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	187	6	,	,	PUNCT
cana-3299	187	7	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	187	8	,	,	PUNCT
cana-3299	187	9	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	187	10	,	,	PUNCT
cana-3299	187	11	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	187	12	and	and	CCONJ
cana-3299	187	13	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	187	14	)	)	PUNCT
cana-3299	187	15	in	in	ADP
cana-3299	187	16	(	(	PUNCT
cana-3299	187	17	𝑋1	𝑋1	PROPN
cana-3299	187	18	,	,	PUNCT
cana-3299	187	19	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	187	20	)	)	PUNCT
cana-3299	187	21	.	.	PUNCT
cana-3299	188	1	3	3	NUM
cana-3299	188	2	pythagorean	pythagorean	PROPN
cana-3299	188	3	fuzzy	fuzzy	ADJ
cana-3299	188	4	contra	contra	PROPN
cana-3299	188	5	𝑴-continuous	𝑴-continuous	PROPN
cana-3299	188	6	maps	map	NOUN
cana-3299	188	7	definition	definition	NOUN
cana-3299	188	8	3.1	3.1	NUM
cana-3299	188	9	let	let	NOUN
cana-3299	188	10	(	(	PUNCT
cana-3299	188	11	𝑋1	𝑋1	PROPN
cana-3299	188	12	,	,	PUNCT
cana-3299	188	13	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	188	14	)	)	PUNCT
cana-3299	188	15	and	and	CCONJ
cana-3299	188	16	(	(	PUNCT
cana-3299	188	17	𝑋2	𝑋2	PROPN
cana-3299	188	18	,	,	PUNCT
cana-3299	188	19	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	188	20	)	)	PUNCT
cana-3299	188	21	be	be	VERB
cana-3299	188	22	any	any	DET
cana-3299	188	23	two	two	NUM
cana-3299	188	24	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	188	25	’s	’s	PART
cana-3299	188	26	.	.	PUNCT
cana-3299	189	1	a	a	DET
cana-3299	189	2	mapping	mapping	NOUN
cana-3299	189	3	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	189	4	:	:	PUNCT
cana-3299	189	5	(	(	PUNCT
cana-3299	189	6	𝑋1	𝑋1	PROPN
cana-3299	189	7	,	,	PUNCT
cana-3299	189	8	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	189	9	)	)	PUNCT
cana-3299	189	10	→	→	PUNCT
cana-3299	189	11	(	(	PUNCT
cana-3299	189	12	𝑋2	𝑋2	PROPN
cana-3299	189	13	,	,	PUNCT
cana-3299	189	14	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	189	15	)	)	PUNCT
cana-3299	189	16	is	be	AUX
cana-3299	189	17	said	say	VERB
cana-3299	189	18	to	to	PART
cana-3299	189	19	be	be	AUX
cana-3299	189	20	a	a	DET
cana-3299	189	21	pythagorean	pythagorean	ADJ
cana-3299	189	22	fuzzy	fuzzy	ADJ
cana-3299	189	23	contra	contra	PROPN
cana-3299	189	24	(	(	PUNCT
cana-3299	189	25	resp	resp	NOUN
cana-3299	189	26	.	.	PUNCT
cana-3299	190	1	𝛿	𝛿	ADJ
cana-3299	190	2	,	,	PUNCT
cana-3299	190	3	𝛿𝒫	𝛿𝒫	NOUN
cana-3299	190	4	,	,	PUNCT
cana-3299	190	5	𝛿𝒮	𝛿𝒮	NOUN
cana-3299	190	6	,	,	PUNCT
cana-3299	190	7	𝑒	𝑒	NOUN
cana-3299	190	8	,	,	PUNCT
cana-3299	190	9	𝜃	𝜃	NOUN
cana-3299	190	10	,	,	PUNCT
cana-3299	190	11	𝜃𝒮	𝜃𝒮	ADJ
cana-3299	190	12	and	and	CCONJ
cana-3299	190	13	𝑀	𝑀	PROPN
cana-3299	190	14	)	)	PUNCT
cana-3299	190	15	-continuous	-continuous	ADJ
cana-3299	190	16	(	(	PUNCT
cana-3299	190	17	briefly	briefly	ADV
cana-3299	190	18	,	,	PUNCT
cana-3299	190	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	190	20	(	(	PUNCT
cana-3299	190	21	resp	resp	NOUN
cana-3299	190	22	.	.	PUNCT
cana-3299	191	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PUNCT
cana-3299	191	2	,	,	PUNCT
cana-3299	191	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	191	4	,	,	PUNCT
cana-3299	191	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	191	6	,	,	PUNCT
cana-3299	191	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PRON
cana-3299	191	8	,	,	PUNCT
cana-3299	191	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	PRON
cana-3299	191	10	,	,	PUNCT
cana-3299	191	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	191	12	and	and	CCONJ
cana-3299	191	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	191	14	)	)	PUNCT
cana-3299	191	15	)	)	PUNCT
cana-3299	191	16	if	if	SCONJ
cana-3299	191	17	the	the	DET
cana-3299	191	18	inverse	inverse	ADJ
cana-3299	191	19	image	image	NOUN
cana-3299	191	20	of	of	ADP
cana-3299	191	21	every	every	DET
cana-3299	191	22	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	191	23	in	in	ADP
cana-3299	191	24	(	(	PUNCT
cana-3299	191	25	𝑋2	𝑋2	PROPN
cana-3299	191	26	,	,	PUNCT
cana-3299	191	27	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	191	28	)	)	PUNCT
cana-3299	191	29	is	be	AUX
cana-3299	191	30	a	a	DET
cana-3299	191	31	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	191	32	(	(	PUNCT
cana-3299	191	33	resp	resp	NOUN
cana-3299	191	34	.	.	PUNCT
cana-3299	191	35	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-3299	191	36	,	,	PUNCT
cana-3299	191	37	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-3299	191	38	,	,	PUNCT
cana-3299	191	39	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	191	40	,	,	PUNCT
cana-3299	191	41	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	PROPN
cana-3299	191	42	,	,	PUNCT
cana-3299	191	43	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	191	44	,	,	PUNCT
cana-3299	191	45	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-3299	191	46	and	and	CCONJ
cana-3299	191	47	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NUM
cana-3299	191	48	)	)	PUNCT
cana-3299	191	49	in	in	ADP
cana-3299	191	50	(	(	PUNCT
cana-3299	191	51	𝑋1	𝑋1	PROPN
cana-3299	191	52	,	,	PUNCT
cana-3299	191	53	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	191	54	)	)	PUNCT
cana-3299	191	55	.	.	PUNCT
cana-3299	192	1	proposition	proposition	NOUN
cana-3299	192	2	3.1	3.1	NUM
cana-3299	192	3	let	let	NOUN
cana-3299	192	4	(	(	PUNCT
cana-3299	192	5	𝑋1	𝑋1	PROPN
cana-3299	192	6	,	,	PUNCT
cana-3299	192	7	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	192	8	)	)	PUNCT
cana-3299	192	9	&	&	CCONJ
cana-3299	192	10	(	(	PUNCT
cana-3299	192	11	𝑋2	𝑋2	PROPN
cana-3299	192	12	,	,	PUNCT
cana-3299	192	13	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	192	14	)	)	PUNCT
cana-3299	192	15	be	be	VERB
cana-3299	192	16	a	a	DET
cana-3299	192	17	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	192	18	’s	’s	PART
cana-3299	192	19	.	.	PUNCT
cana-3299	193	1	let	let	VERB
cana-3299	193	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	193	3	:	:	PUNCT
cana-3299	193	4	(	(	PUNCT
cana-3299	193	5	𝑋1	𝑋1	PROPN
cana-3299	193	6	,	,	PUNCT
cana-3299	193	7	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	193	8	)	)	PUNCT
cana-3299	193	9	→	→	PUNCT
cana-3299	193	10	(	(	PUNCT
cana-3299	193	11	𝑋2	𝑋2	PROPN
cana-3299	193	12	,	,	PUNCT
cana-3299	193	13	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	193	14	)	)	PUNCT
cana-3299	193	15	be	be	AUX
cana-3299	193	16	a	a	DET
cana-3299	193	17	mapping	mapping	NOUN
cana-3299	193	18	.	.	PUNCT
cana-3299	194	1	then	then	ADV
cana-3299	194	2	the	the	DET
cana-3299	194	3	following	following	ADJ
cana-3299	194	4	statements	statement	NOUN
cana-3299	194	5	are	be	AUX
cana-3299	194	6	hold	hold	ADJ
cana-3299	194	7	for	for	ADP
cana-3299	194	8	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	194	9	,	,	PUNCT
cana-3299	194	10	but	but	CCONJ
cana-3299	194	11	not	not	PART
cana-3299	194	12	conversely	conversely	ADV
cana-3299	194	13	.	.	PUNCT
cana-3299	195	1	1	1	X
cana-3299	195	2	.	.	X
cana-3299	196	1	every	every	DET
cana-3299	196	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NOUN
cana-3299	196	3	is	be	AUX
cana-3299	196	4	a	a	DET
cana-3299	196	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	NOUN
cana-3299	196	6	2	2	NUM
cana-3299	196	7	.	.	X
cana-3299	197	1	every	every	DET
cana-3299	197	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NOUN
cana-3299	197	3	is	be	AUX
cana-3299	197	4	a	a	DET
cana-3299	197	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠.	PROPN
cana-3299	197	6	3	3	NUM
cana-3299	197	7	.	.	PUNCT
cana-3299	198	1	every	every	DET
cana-3299	198	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	198	3	is	be	AUX
cana-3299	198	4	a	a	DET
cana-3299	198	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	PROPN
cana-3299	198	6	4	4	NUM
cana-3299	198	7	.	.	PUNCT
cana-3299	199	1	every	every	DET
cana-3299	199	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-3299	199	3	is	be	AUX
cana-3299	199	4	a	a	DET
cana-3299	199	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	NOUN
cana-3299	199	6	5	5	NUM
cana-3299	199	7	.	.	PUNCT
cana-3299	200	1	every	every	DET
cana-3299	200	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-3299	200	3	is	be	AUX
cana-3299	200	4	a	a	DET
cana-3299	200	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-3299	200	6	6	6	NUM
cana-3299	200	7	.	.	PUNCT
cana-3299	201	1	every	every	DET
cana-3299	201	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	201	3	is	be	AUX
cana-3299	201	4	a	a	DET
cana-3299	201	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	NOUN
cana-3299	201	6	7	7	NUM
cana-3299	201	7	.	.	PUNCT
cana-3299	202	1	every	every	DET
cana-3299	202	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	202	3	is	be	AUX
cana-3299	202	4	a	a	DET
cana-3299	202	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	PROPN
cana-3299	202	6	8	8	NUM
cana-3299	202	7	.	.	PUNCT
cana-3299	203	1	every	every	DET
cana-3299	203	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	203	3	is	be	AUX
cana-3299	203	4	a	a	DET
cana-3299	203	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	NOUN
cana-3299	203	6	9	9	NUM
cana-3299	203	7	.	.	PUNCT
cana-3299	204	1	every	every	DET
cana-3299	204	2	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NOUN
cana-3299	204	3	is	be	AUX
cana-3299	204	4	a	a	DET
cana-3299	204	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	NOUN
cana-3299	204	6	communications	communication	NOUN
cana-3299	204	7	on	on	ADP
cana-3299	204	8	applied	apply	VERB
cana-3299	204	9	nonlinear	nonlinear	ADJ
cana-3299	204	10	analysis	analysis	NOUN
cana-3299	204	11	issn	issn	NOUN
cana-3299	204	12	:	:	PUNCT
cana-3299	204	13	1074	1074	NUM
cana-3299	204	14	-	-	PUNCT
cana-3299	204	15	133x	133x	NUM
cana-3299	204	16	vol	vol	NOUN
cana-3299	204	17	32	32	NUM
cana-3299	204	18	no	no	NOUN
cana-3299	204	19	.	.	PUNCT
cana-3299	205	1	6s	6s	NUM
cana-3299	205	2	(	(	PUNCT
cana-3299	205	3	2025	2025	NUM
cana-3299	205	4	)	)	PUNCT
cana-3299	205	5	332	332	NUM
cana-3299	206	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	206	2	proof	proof	NOUN
cana-3299	206	3	.	.	PUNCT
cana-3299	207	1	1	1	X
cana-3299	207	2	.	.	X
cana-3299	207	3	let	let	VERB
cana-3299	207	4	𝐵	𝐵	PRON
cana-3299	207	5	be	be	AUX
cana-3299	207	6	a	a	DET
cana-3299	207	7	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	207	8	in	in	ADP
cana-3299	207	9	(	(	PUNCT
cana-3299	207	10	𝑋2	𝑋2	ADJ
cana-3299	207	11	,	,	PUNCT
cana-3299	207	12	ψ𝑃	ψ𝑃	NOUN
cana-3299	207	13	)	)	PUNCT
cana-3299	207	14	.	.	PUNCT
cana-3299	208	1	since	since	SCONJ
cana-3299	208	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	208	3	is	be	AUX
cana-3299	208	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	208	5	,	,	PUNCT
cana-3299	208	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	208	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	208	8	)	)	PUNCT
cana-3299	208	9	is	be	AUX
cana-3299	208	10	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	208	11	in	in	ADP
cana-3299	208	12	(	(	PUNCT
cana-3299	208	13	𝑋1	𝑋1	NOUN
cana-3299	208	14	,	,	PUNCT
cana-3299	208	15	γ𝑃	γ𝑃	NOUN
cana-3299	208	16	)	)	PUNCT
cana-3299	208	17	.	.	PUNCT
cana-3299	209	1	since	since	SCONJ
cana-3299	209	2	every	every	DET
cana-3299	209	3	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	209	4	is	be	AUX
cana-3299	209	5	a	a	DET
cana-3299	209	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	209	7	,	,	PUNCT
cana-3299	209	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	209	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	209	10	)	)	PUNCT
cana-3299	209	11	is	be	AUX
cana-3299	209	12	a	a	DET
cana-3299	209	13	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	209	14	in	in	ADP
cana-3299	209	15	(	(	PUNCT
cana-3299	209	16	𝑋1	𝑋1	NOUN
cana-3299	209	17	,	,	PUNCT
cana-3299	209	18	γ𝑃	γ𝑃	NOUN
cana-3299	209	19	)	)	PUNCT
cana-3299	209	20	.	.	PUNCT
cana-3299	210	1	hence	hence	ADV
cana-3299	210	2	,	,	PUNCT
cana-3299	210	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	210	4	is	be	AUX
cana-3299	210	5	a	a	DET
cana-3299	210	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	NOUN
cana-3299	210	7	2	2	NUM
cana-3299	210	8	.	.	PUNCT
cana-3299	211	1	let	let	VERB
cana-3299	211	2	𝐵	𝐵	PRON
cana-3299	211	3	be	be	AUX
cana-3299	211	4	a	a	DET
cana-3299	211	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	211	6	in	in	ADP
cana-3299	211	7	(	(	PUNCT
cana-3299	211	8	𝑋2	𝑋2	ADJ
cana-3299	211	9	,	,	PUNCT
cana-3299	211	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	211	11	)	)	PUNCT
cana-3299	211	12	.	.	PUNCT
cana-3299	212	1	since	since	SCONJ
cana-3299	212	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	212	3	is	be	AUX
cana-3299	212	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	212	5	,	,	PUNCT
cana-3299	212	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	212	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	212	8	)	)	PUNCT
cana-3299	212	9	is	be	AUX
cana-3299	212	10	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	212	11	in	in	ADP
cana-3299	212	12	(	(	PUNCT
cana-3299	212	13	𝑋1	𝑋1	NOUN
cana-3299	212	14	,	,	PUNCT
cana-3299	212	15	γ𝑃	γ𝑃	NOUN
cana-3299	212	16	)	)	PUNCT
cana-3299	212	17	.	.	PUNCT
cana-3299	213	1	since	since	SCONJ
cana-3299	213	2	every	every	DET
cana-3299	213	3	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	213	4	is	be	AUX
cana-3299	213	5	a	a	DET
cana-3299	213	6	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NOUN
cana-3299	213	7	,	,	PUNCT
cana-3299	213	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	213	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	213	10	)	)	PUNCT
cana-3299	213	11	is	be	AUX
cana-3299	213	12	a	a	DET
cana-3299	213	13	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	213	14	in	in	ADP
cana-3299	213	15	(	(	PUNCT
cana-3299	213	16	𝑋1	𝑋1	NOUN
cana-3299	213	17	,	,	PUNCT
cana-3299	213	18	γ𝑃	γ𝑃	NOUN
cana-3299	213	19	)	)	PUNCT
cana-3299	213	20	.	.	PUNCT
cana-3299	214	1	hence	hence	ADV
cana-3299	214	2	,	,	PUNCT
cana-3299	214	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	214	4	is	be	AUX
cana-3299	214	5	a	a	DET
cana-3299	214	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠.	PROPN
cana-3299	214	7	3	3	NUM
cana-3299	214	8	.	.	PUNCT
cana-3299	215	1	let	let	VERB
cana-3299	215	2	𝐵	𝐵	PRON
cana-3299	215	3	be	be	AUX
cana-3299	215	4	a	a	DET
cana-3299	215	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	215	6	in	in	ADP
cana-3299	215	7	(	(	PUNCT
cana-3299	215	8	𝑋2	𝑋2	ADJ
cana-3299	215	9	,	,	PUNCT
cana-3299	215	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	215	11	)	)	PUNCT
cana-3299	215	12	.	.	PUNCT
cana-3299	216	1	since	since	SCONJ
cana-3299	216	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	216	3	is	be	AUX
cana-3299	216	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	216	5	,	,	PUNCT
cana-3299	216	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	216	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	216	8	)	)	PUNCT
cana-3299	216	9	is	be	AUX
cana-3299	216	10	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-3299	216	11	in	in	ADP
cana-3299	216	12	(	(	PUNCT
cana-3299	216	13	𝑋1	𝑋1	NOUN
cana-3299	216	14	,	,	PUNCT
cana-3299	216	15	γ𝑃	γ𝑃	NOUN
cana-3299	216	16	)	)	PUNCT
cana-3299	216	17	.	.	PUNCT
cana-3299	217	1	since	since	SCONJ
cana-3299	217	2	every	every	DET
cana-3299	217	3	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-3299	217	4	is	be	AUX
cana-3299	217	5	a	a	DET
cana-3299	217	6	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	217	7	,	,	PUNCT
cana-3299	217	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	217	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	217	10	)	)	PUNCT
cana-3299	217	11	is	be	AUX
cana-3299	217	12	a	a	DET
cana-3299	217	13	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	217	14	in	in	ADP
cana-3299	217	15	(	(	PUNCT
cana-3299	217	16	𝑋1	𝑋1	NOUN
cana-3299	217	17	,	,	PUNCT
cana-3299	217	18	γ𝑃	γ𝑃	NOUN
cana-3299	217	19	)	)	PUNCT
cana-3299	217	20	.	.	PUNCT
cana-3299	218	1	hence	hence	ADV
cana-3299	218	2	,	,	PUNCT
cana-3299	218	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	218	4	is	be	AUX
cana-3299	218	5	a	a	DET
cana-3299	218	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	PROPN
cana-3299	218	7	4	4	NUM
cana-3299	218	8	.	.	PUNCT
cana-3299	219	1	let	let	VERB
cana-3299	219	2	𝐵	𝐵	PRON
cana-3299	219	3	be	be	AUX
cana-3299	219	4	a	a	DET
cana-3299	219	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	219	6	in	in	ADP
cana-3299	219	7	(	(	PUNCT
cana-3299	219	8	𝑋2	𝑋2	ADJ
cana-3299	219	9	,	,	PUNCT
cana-3299	219	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	219	11	)	)	PUNCT
cana-3299	219	12	.	.	PUNCT
cana-3299	220	1	since	since	SCONJ
cana-3299	220	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	220	3	is	be	AUX
cana-3299	220	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-3299	220	5	,	,	PUNCT
cana-3299	220	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	220	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	220	8	)	)	PUNCT
cana-3299	220	9	is	be	AUX
cana-3299	220	10	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-3299	220	11	in	in	ADP
cana-3299	220	12	(	(	PUNCT
cana-3299	220	13	𝑋1	𝑋1	NOUN
cana-3299	220	14	,	,	PUNCT
cana-3299	220	15	γ𝑃	γ𝑃	NOUN
cana-3299	220	16	)	)	PUNCT
cana-3299	220	17	.	.	PUNCT
cana-3299	221	1	since	since	SCONJ
cana-3299	221	2	every	every	DET
cana-3299	221	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	NOUN
cana-3299	221	4	is	be	AUX
cana-3299	221	5	a	a	DET
cana-3299	221	6	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	221	7	,	,	PUNCT
cana-3299	221	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	221	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	221	10	)	)	PUNCT
cana-3299	221	11	is	be	AUX
cana-3299	221	12	a	a	DET
cana-3299	221	13	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	221	14	in	in	ADP
cana-3299	221	15	(	(	PUNCT
cana-3299	221	16	𝑋1	𝑋1	NOUN
cana-3299	221	17	,	,	PUNCT
cana-3299	221	18	γ𝑃	γ𝑃	NOUN
cana-3299	221	19	)	)	PUNCT
cana-3299	221	20	.	.	PUNCT
cana-3299	222	1	hence	hence	ADV
cana-3299	222	2	,	,	PUNCT
cana-3299	222	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	222	4	is	be	AUX
cana-3299	222	5	a	a	DET
cana-3299	222	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠.	NOUN
cana-3299	222	7	5	5	NUM
cana-3299	222	8	.	.	PUNCT
cana-3299	223	1	let	let	VERB
cana-3299	223	2	𝐵	𝐵	PRON
cana-3299	223	3	be	be	AUX
cana-3299	223	4	a	a	DET
cana-3299	223	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	223	6	in	in	ADP
cana-3299	223	7	(	(	PUNCT
cana-3299	223	8	𝑋2	𝑋2	ADJ
cana-3299	223	9	,	,	PUNCT
cana-3299	223	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	223	11	)	)	PUNCT
cana-3299	223	12	.	.	PUNCT
cana-3299	224	1	since	since	SCONJ
cana-3299	224	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	224	3	is	be	AUX
cana-3299	224	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-3299	224	5	,	,	PUNCT
cana-3299	224	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	224	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	224	8	)	)	PUNCT
cana-3299	224	9	is	be	AUX
cana-3299	224	10	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-3299	224	11	in	in	ADP
cana-3299	224	12	(	(	PUNCT
cana-3299	224	13	𝑋1	𝑋1	NOUN
cana-3299	224	14	,	,	PUNCT
cana-3299	224	15	γ𝑃	γ𝑃	NOUN
cana-3299	224	16	)	)	PUNCT
cana-3299	224	17	.	.	PUNCT
cana-3299	225	1	since	since	SCONJ
cana-3299	225	2	every	every	DET
cana-3299	225	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	NOUN
cana-3299	225	4	is	be	AUX
cana-3299	225	5	a	a	DET
cana-3299	225	6	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	NOUN
cana-3299	225	7	,	,	PUNCT
cana-3299	225	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	225	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	225	10	)	)	PUNCT
cana-3299	225	11	is	be	AUX
cana-3299	225	12	a	a	DET
cana-3299	225	13	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-3299	225	14	in	in	ADP
cana-3299	225	15	(	(	PUNCT
cana-3299	225	16	𝑋1	𝑋1	NOUN
cana-3299	225	17	,	,	PUNCT
cana-3299	225	18	γ𝑃	γ𝑃	NOUN
cana-3299	225	19	)	)	PUNCT
cana-3299	225	20	.	.	PUNCT
cana-3299	226	1	hence	hence	ADV
cana-3299	226	2	,	,	PUNCT
cana-3299	226	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	226	4	is	be	AUX
cana-3299	226	5	a	a	DET
cana-3299	226	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠.	PROPN
cana-3299	226	7	6	6	NUM
cana-3299	226	8	.	.	PUNCT
cana-3299	227	1	let	let	VERB
cana-3299	227	2	𝐵	𝐵	PRON
cana-3299	227	3	be	be	AUX
cana-3299	227	4	a	a	DET
cana-3299	227	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	227	6	in	in	ADP
cana-3299	227	7	(	(	PUNCT
cana-3299	227	8	𝑋2	𝑋2	ADJ
cana-3299	227	9	,	,	PUNCT
cana-3299	227	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	227	11	)	)	PUNCT
cana-3299	227	12	.	.	PUNCT
cana-3299	228	1	since	since	SCONJ
cana-3299	228	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	228	3	is	be	AUX
cana-3299	228	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	228	5	,	,	PUNCT
cana-3299	228	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	228	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	228	8	)	)	PUNCT
cana-3299	228	9	is	be	AUX
cana-3299	228	10	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	228	11	in	in	ADP
cana-3299	228	12	(	(	PUNCT
cana-3299	228	13	𝑋1	𝑋1	NOUN
cana-3299	228	14	,	,	PUNCT
cana-3299	228	15	γ𝑃	γ𝑃	NOUN
cana-3299	228	16	)	)	PUNCT
cana-3299	228	17	.	.	PUNCT
cana-3299	229	1	since	since	SCONJ
cana-3299	229	2	every	every	DET
cana-3299	229	3	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	NOUN
cana-3299	229	4	is	be	AUX
cana-3299	229	5	a	a	DET
cana-3299	229	6	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	229	7	,	,	PUNCT
cana-3299	229	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	229	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	229	10	)	)	PUNCT
cana-3299	229	11	is	be	AUX
cana-3299	229	12	a	a	DET
cana-3299	229	13	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	229	14	in	in	ADP
cana-3299	229	15	(	(	PUNCT
cana-3299	229	16	𝑋1	𝑋1	NOUN
cana-3299	229	17	,	,	PUNCT
cana-3299	229	18	γ𝑃	γ𝑃	NOUN
cana-3299	229	19	)	)	PUNCT
cana-3299	229	20	.	.	PUNCT
cana-3299	230	1	hence	hence	ADV
cana-3299	230	2	,	,	PUNCT
cana-3299	230	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	230	4	is	be	AUX
cana-3299	230	5	a	a	DET
cana-3299	230	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	NOUN
cana-3299	230	7	7	7	NUM
cana-3299	230	8	.	.	PUNCT
cana-3299	231	1	let	let	VERB
cana-3299	231	2	𝐵	𝐵	PRON
cana-3299	231	3	be	be	AUX
cana-3299	231	4	a	a	DET
cana-3299	231	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	231	6	in	in	ADP
cana-3299	231	7	(	(	PUNCT
cana-3299	231	8	𝑋2	𝑋2	ADJ
cana-3299	231	9	,	,	PUNCT
cana-3299	231	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	231	11	)	)	PUNCT
cana-3299	231	12	.	.	PUNCT
cana-3299	232	1	since	since	SCONJ
cana-3299	232	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	232	3	is	be	AUX
cana-3299	232	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	232	5	,	,	PUNCT
cana-3299	232	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	232	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	232	8	)	)	PUNCT
cana-3299	232	9	is	be	AUX
cana-3299	232	10	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-3299	232	11	in	in	ADP
cana-3299	232	12	(	(	PUNCT
cana-3299	232	13	𝑋1	𝑋1	NOUN
cana-3299	232	14	,	,	PUNCT
cana-3299	232	15	γ𝑃	γ𝑃	NOUN
cana-3299	232	16	)	)	PUNCT
cana-3299	232	17	.	.	PUNCT
cana-3299	233	1	since	since	SCONJ
cana-3299	233	2	every	every	DET
cana-3299	233	3	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-3299	233	4	is	be	AUX
cana-3299	233	5	a	a	DET
cana-3299	233	6	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	233	7	,	,	PUNCT
cana-3299	233	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	233	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	233	10	)	)	PUNCT
cana-3299	233	11	is	be	AUX
cana-3299	233	12	a	a	DET
cana-3299	233	13	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	233	14	in	in	ADP
cana-3299	233	15	(	(	PUNCT
cana-3299	233	16	𝑋1	𝑋1	NOUN
cana-3299	233	17	,	,	PUNCT
cana-3299	233	18	γ𝑃	γ𝑃	NOUN
cana-3299	233	19	)	)	PUNCT
cana-3299	233	20	.	.	PUNCT
cana-3299	234	1	hence	hence	ADV
cana-3299	234	2	,	,	PUNCT
cana-3299	234	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	234	4	is	be	AUX
cana-3299	234	5	a	a	DET
cana-3299	234	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	PROPN
cana-3299	234	7	8	8	NUM
cana-3299	234	8	.	.	PUNCT
cana-3299	235	1	let	let	VERB
cana-3299	235	2	𝐵	𝐵	PRON
cana-3299	235	3	be	be	AUX
cana-3299	235	4	a	a	DET
cana-3299	235	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	235	6	in	in	ADP
cana-3299	235	7	(	(	PUNCT
cana-3299	235	8	𝑋2	𝑋2	ADJ
cana-3299	235	9	,	,	PUNCT
cana-3299	235	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	235	11	)	)	PUNCT
cana-3299	235	12	.	.	PUNCT
cana-3299	236	1	since	since	SCONJ
cana-3299	236	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	236	3	is	be	AUX
cana-3299	236	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	236	5	,	,	PUNCT
cana-3299	236	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	236	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	236	8	)	)	PUNCT
cana-3299	236	9	is	be	AUX
cana-3299	236	10	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	236	11	in	in	ADP
cana-3299	236	12	(	(	PUNCT
cana-3299	236	13	𝑋1	𝑋1	NOUN
cana-3299	236	14	,	,	PUNCT
cana-3299	236	15	γ𝑃	γ𝑃	NOUN
cana-3299	236	16	)	)	PUNCT
cana-3299	236	17	.	.	PUNCT
cana-3299	237	1	since	since	SCONJ
cana-3299	237	2	every	every	DET
cana-3299	237	3	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	237	4	is	be	AUX
cana-3299	237	5	a	a	DET
cana-3299	237	6	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	237	7	,	,	PUNCT
cana-3299	237	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	237	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	237	10	)	)	PUNCT
cana-3299	237	11	is	be	AUX
cana-3299	237	12	a	a	DET
cana-3299	237	13	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	237	14	in	in	ADP
cana-3299	237	15	(	(	PUNCT
cana-3299	237	16	𝑋1	𝑋1	NOUN
cana-3299	237	17	,	,	PUNCT
cana-3299	237	18	γ𝑃	γ𝑃	NOUN
cana-3299	237	19	)	)	PUNCT
cana-3299	237	20	.	.	PUNCT
cana-3299	238	1	hence	hence	ADV
cana-3299	238	2	,	,	PUNCT
cana-3299	238	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	238	4	is	be	AUX
cana-3299	238	5	a	a	DET
cana-3299	238	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠.	NOUN
cana-3299	238	7	9	9	NUM
cana-3299	238	8	.	.	PUNCT
cana-3299	239	1	let	let	VERB
cana-3299	239	2	𝐵	𝐵	PRON
cana-3299	239	3	be	be	AUX
cana-3299	239	4	a	a	DET
cana-3299	239	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	239	6	in	in	ADP
cana-3299	239	7	(	(	PUNCT
cana-3299	239	8	𝑋2	𝑋2	ADJ
cana-3299	239	9	,	,	PUNCT
cana-3299	239	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	239	11	)	)	PUNCT
cana-3299	239	12	.	.	PUNCT
cana-3299	240	1	since	since	SCONJ
cana-3299	240	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	240	3	is	be	AUX
cana-3299	240	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-3299	240	5	,	,	PUNCT
cana-3299	240	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	240	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	240	8	)	)	PUNCT
cana-3299	240	9	is	be	AUX
cana-3299	240	10	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-3299	240	11	in	in	ADP
cana-3299	240	12	(	(	PUNCT
cana-3299	240	13	𝑋1	𝑋1	NOUN
cana-3299	240	14	,	,	PUNCT
cana-3299	240	15	γ𝑃	γ𝑃	NOUN
cana-3299	240	16	)	)	PUNCT
cana-3299	240	17	.	.	PUNCT
cana-3299	241	1	since	since	SCONJ
cana-3299	241	2	every	every	DET
cana-3299	241	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	NOUN
cana-3299	241	4	is	be	AUX
cana-3299	241	5	a	a	DET
cana-3299	241	6	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	241	7	,	,	PUNCT
cana-3299	241	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	241	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	241	10	)	)	PUNCT
cana-3299	241	11	is	be	AUX
cana-3299	241	12	a	a	DET
cana-3299	241	13	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	241	14	in	in	ADP
cana-3299	241	15	(	(	PUNCT
cana-3299	241	16	𝑋1	𝑋1	NOUN
cana-3299	241	17	,	,	PUNCT
cana-3299	241	18	γ𝑃	γ𝑃	NOUN
cana-3299	241	19	)	)	PUNCT
cana-3299	241	20	.	.	PUNCT
cana-3299	242	1	hence	hence	ADV
cana-3299	242	2	,	,	PUNCT
cana-3299	242	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	242	4	is	be	AUX
cana-3299	242	5	a	a	DET
cana-3299	242	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	NOUN
cana-3299	242	7	remark	remark	NOUN
cana-3299	242	8	3.1	3.1	NUM
cana-3299	242	9	we	we	PRON
cana-3299	242	10	obtain	obtain	VERB
cana-3299	242	11	the	the	DET
cana-3299	242	12	following	follow	VERB
cana-3299	242	13	diagram	diagram	NOUN
cana-3299	242	14	from	from	ADP
cana-3299	242	15	the	the	DET
cana-3299	242	16	results	result	NOUN
cana-3299	242	17	are	be	AUX
cana-3299	242	18	discussed	discuss	VERB
cana-3299	242	19	above	above	ADV
cana-3299	242	20	.	.	PUNCT
cana-3299	243	1	note	note	NOUN
cana-3299	243	2	:	:	PUNCT
cana-3299	243	3	𝐴	𝐴	PROPN
cana-3299	243	4	→	→	SYM
cana-3299	243	5	𝐵	𝐵	PROPN
cana-3299	243	6	denotes	denote	NOUN
cana-3299	243	7	𝐴	𝐴	PROPN
cana-3299	243	8	implies	imply	VERB
cana-3299	243	9	𝐵	𝐵	PROPN
cana-3299	243	10	,	,	PUNCT
cana-3299	243	11	but	but	CCONJ
cana-3299	243	12	not	not	PART
cana-3299	243	13	conversely	conversely	ADV
cana-3299	243	14	.	.	PUNCT
cana-3299	244	1	example	example	NOUN
cana-3299	244	2	3.1	3.1	NUM
cana-3299	244	3	let	let	VERB
cana-3299	244	4	𝑋1	𝑋1	NOUN
cana-3299	244	5	=	=	SYM
cana-3299	244	6	𝑋2	𝑋2	VERB
cana-3299	244	7	=	=	PUNCT
cana-3299	244	8	{	{	PUNCT
cana-3299	244	9	𝑥1	𝑥1	NOUN
cana-3299	244	10	,	,	PUNCT
cana-3299	244	11	𝑥2	𝑥2	NOUN
cana-3299	244	12	}	}	PUNCT
cana-3299	244	13	and	and	CCONJ
cana-3299	244	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	244	15	’s	’s	PART
cana-3299	244	16	𝐴1	𝐴1	PROPN
cana-3299	244	17	,	,	PUNCT
cana-3299	244	18	𝐴2	𝐴2	PROPN
cana-3299	244	19	,	,	PUNCT
cana-3299	244	20	𝐴3	𝐴3	PROPN
cana-3299	244	21	&	&	CCONJ
cana-3299	244	22	𝐴4	𝐴4	PROPN
cana-3299	244	23	in	in	ADP
cana-3299	244	24	𝑋1	𝑋1	PROPN
cana-3299	244	25	and	and	CCONJ
cana-3299	244	26	𝐵1	𝐵1	PROPN
cana-3299	244	27	,	,	PUNCT
cana-3299	244	28	𝐵2	𝐵2	NOUN
cana-3299	244	29	,	,	PUNCT
cana-3299	244	30	𝐵3	𝐵3	PROPN
cana-3299	244	31	&	&	CCONJ
cana-3299	244	32	𝐵4	𝐵4	PROPN
cana-3299	244	33	in	in	ADP
cana-3299	244	34	𝑋2	𝑋2	PROPN
cana-3299	244	35	are	be	AUX
cana-3299	244	36	defined	define	VERB
cana-3299	244	37	as	as	ADP
cana-3299	244	38	,	,	PUNCT
cana-3299	244	39	𝐴1	𝐴1	PROPN
cana-3299	244	40	=	=	SYM
cana-3299	244	41	{	{	PUNCT
cana-3299	244	42	<	<	X
cana-3299	244	43	𝑥1	𝑥1	PROPN
cana-3299	244	44	,	,	PUNCT
cana-3299	244	45	0.20,0.80	0.20,0.80	NOUN
cana-3299	244	46	>	>	X
cana-3299	244	47	,	,	PUNCT
cana-3299	244	48	<	<	X
cana-3299	244	49	𝑥2	𝑥2	NOUN
cana-3299	244	50	,	,	PUNCT
cana-3299	244	51	0.40,0.60	0.40,0.60	NUM
cana-3299	244	52	>	>	PUNCT
cana-3299	244	53	}	}	PUNCT
cana-3299	244	54	𝐴2	𝐴2	PROPN
cana-3299	244	55	=	=	SYM
cana-3299	244	56	{	{	PUNCT
cana-3299	244	57	<	<	X
cana-3299	244	58	𝑥1	𝑥1	PROPN
cana-3299	244	59	,	,	PUNCT
cana-3299	244	60	0.10,0.90	0.10,0.90	NUM
cana-3299	244	61	>	>	X
cana-3299	244	62	,	,	PUNCT
cana-3299	244	63	<	<	X
cana-3299	244	64	𝑥2	𝑥2	NOUN
cana-3299	244	65	,	,	PUNCT
cana-3299	244	66	0.30,0.70	0.30,0.70	PRON
cana-3299	244	67	>	>	PUNCT
cana-3299	244	68	}	}	PUNCT
cana-3299	244	69	communications	communication	NOUN
cana-3299	244	70	on	on	ADP
cana-3299	244	71	applied	apply	VERB
cana-3299	244	72	nonlinear	nonlinear	ADJ
cana-3299	244	73	analysis	analysis	NOUN
cana-3299	244	74	issn	issn	NOUN
cana-3299	244	75	:	:	PUNCT
cana-3299	244	76	1074	1074	NUM
cana-3299	244	77	-	-	PUNCT
cana-3299	244	78	133x	133x	NUM
cana-3299	244	79	vol	vol	NOUN
cana-3299	244	80	32	32	NUM
cana-3299	244	81	no	no	NOUN
cana-3299	244	82	.	.	PUNCT
cana-3299	245	1	6s	6s	NUM
cana-3299	245	2	(	(	PUNCT
cana-3299	245	3	2025	2025	NUM
cana-3299	245	4	)	)	PUNCT
cana-3299	245	5	333	333	NUM
cana-3299	245	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	245	7	𝐴3	𝐴3	PROPN
cana-3299	245	8	=	=	SYM
cana-3299	245	9	{	{	PUNCT
cana-3299	245	10	<	<	X
cana-3299	245	11	𝑥1	𝑥1	PROPN
cana-3299	245	12	,	,	PUNCT
cana-3299	245	13	0.90,0.10	0.90,0.10	NOUN
cana-3299	245	14	>	>	X
cana-3299	245	15	,	,	PUNCT
cana-3299	245	16	<	<	X
cana-3299	245	17	𝑥2	𝑥2	NOUN
cana-3299	245	18	,	,	PUNCT
cana-3299	245	19	0.70,0.30	0.70,0.30	NOUN
cana-3299	245	20	>	>	PUNCT
cana-3299	245	21	}	}	PUNCT
cana-3299	245	22	𝐴4	𝐴4	PROPN
cana-3299	245	23	=	=	PUNCT
cana-3299	245	24	{	{	PUNCT
cana-3299	245	25	<	<	X
cana-3299	245	26	𝑥1	𝑥1	PROPN
cana-3299	245	27	,	,	PUNCT
cana-3299	245	28	0.20,0.80	0.20,0.80	NOUN
cana-3299	245	29	>	>	X
cana-3299	245	30	,	,	PUNCT
cana-3299	245	31	<	<	X
cana-3299	245	32	𝑥2	𝑥2	NOUN
cana-3299	245	33	,	,	PUNCT
cana-3299	245	34	0.30,0.70	0.30,0.70	PRON
cana-3299	245	35	>	>	PUNCT
cana-3299	245	36	}	}	PUNCT
cana-3299	245	37	𝐵1	𝐵1	NOUN
cana-3299	245	38	=	=	PUNCT
cana-3299	245	39	{	{	PUNCT
cana-3299	245	40	<	<	X
cana-3299	245	41	𝑥1	𝑥1	PROPN
cana-3299	245	42	,	,	PUNCT
cana-3299	245	43	0.80,0.20	0.80,0.20	X
cana-3299	245	44	>	>	X
cana-3299	245	45	,	,	PUNCT
cana-3299	245	46	<	<	X
cana-3299	245	47	𝑥2	𝑥2	NOUN
cana-3299	245	48	,	,	PUNCT
cana-3299	245	49	0.60,0.40	0.60,0.40	X
cana-3299	245	50	>	>	PUNCT
cana-3299	245	51	}	}	PUNCT
cana-3299	245	52	𝐵2	𝐵2	NOUN
cana-3299	245	53	=	=	SYM
cana-3299	245	54	{	{	PUNCT
cana-3299	245	55	<	<	X
cana-3299	245	56	𝑥1	𝑥1	PROPN
cana-3299	245	57	,	,	PUNCT
cana-3299	245	58	0.90,0.10	0.90,0.10	NOUN
cana-3299	245	59	>	>	X
cana-3299	245	60	,	,	PUNCT
cana-3299	245	61	<	<	X
cana-3299	245	62	𝑥2	𝑥2	NOUN
cana-3299	245	63	,	,	PUNCT
cana-3299	245	64	0.70,0.30	0.70,0.30	NOUN
cana-3299	245	65	>	>	PUNCT
cana-3299	245	66	}	}	PUNCT
cana-3299	245	67	𝐵3	𝐵3	NOUN
cana-3299	245	68	=	=	PUNCT
cana-3299	245	69	{	{	PUNCT
cana-3299	245	70	<	<	X
cana-3299	245	71	𝑥1	𝑥1	PROPN
cana-3299	245	72	,	,	PUNCT
cana-3299	245	73	0.10,0.90	0.10,0.90	NUM
cana-3299	245	74	>	>	X
cana-3299	245	75	,	,	PUNCT
cana-3299	245	76	<	<	X
cana-3299	245	77	𝑥2	𝑥2	NOUN
cana-3299	245	78	,	,	PUNCT
cana-3299	245	79	0.30,0.70	0.30,0.70	PRON
cana-3299	245	80	>	>	PUNCT
cana-3299	245	81	}	}	PUNCT
cana-3299	245	82	𝐵4	𝐵4	NOUN
cana-3299	245	83	=	=	SYM
cana-3299	245	84	{	{	PUNCT
cana-3299	245	85	<	<	X
cana-3299	245	86	𝑥1	𝑥1	PROPN
cana-3299	245	87	,	,	PUNCT
cana-3299	245	88	0.80,0.20	0.80,0.20	X
cana-3299	245	89	>	>	X
cana-3299	245	90	,	,	PUNCT
cana-3299	245	91	<	<	X
cana-3299	245	92	𝑥2	𝑥2	NOUN
cana-3299	245	93	,	,	PUNCT
cana-3299	245	94	0.70,0.30	0.70,0.30	NOUN
cana-3299	245	95	>	>	PUNCT
cana-3299	245	96	}	}	PUNCT
cana-3299	245	97	.	.	PUNCT
cana-3299	246	1	then	then	ADV
cana-3299	246	2	,	,	PUNCT
cana-3299	246	3	we	we	PRON
cana-3299	246	4	have	have	VERB
cana-3299	246	5	γ𝑃	γ𝑃	ADJ
cana-3299	246	6	=	=	PUNCT
cana-3299	246	7	{	{	PUNCT
cana-3299	246	8	0𝑋	0𝑋	PROPN
cana-3299	246	9	,	,	PUNCT
cana-3299	246	10	1𝑋	1𝑋	PROPN
cana-3299	246	11	,	,	PUNCT
cana-3299	246	12	𝐴1	𝐴1	PROPN
cana-3299	246	13	,	,	PUNCT
cana-3299	246	14	𝐴2	𝐴2	PROPN
cana-3299	246	15	,	,	PUNCT
cana-3299	246	16	𝐴3	𝐴3	PROPN
cana-3299	246	17	,	,	PUNCT
cana-3299	246	18	𝐴4	𝐴4	PROPN
cana-3299	246	19	}	}	PUNCT
cana-3299	246	20	and	and	CCONJ
cana-3299	246	21	ψ𝑃	ψ𝑃	PROPN
cana-3299	246	22	=	=	SYM
cana-3299	246	23	{	{	PUNCT
cana-3299	246	24	0𝑋	0𝑋	PROPN
cana-3299	246	25	,	,	PUNCT
cana-3299	246	26	1𝑋	1𝑋	PROPN
cana-3299	246	27	,	,	PUNCT
cana-3299	246	28	𝐵1	𝐵1	PROPN
cana-3299	246	29	,	,	PUNCT
cana-3299	246	30	𝐵2	𝐵2	NOUN
cana-3299	246	31	,	,	PUNCT
cana-3299	246	32	𝐵3	𝐵3	PROPN
cana-3299	246	33	,	,	PUNCT
cana-3299	246	34	𝐵4	𝐵4	NOUN
cana-3299	246	35	}	}	PUNCT
cana-3299	246	36	.	.	PUNCT
cana-3299	247	1	let	let	VERB
cana-3299	247	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	247	3	:	:	PUNCT
cana-3299	247	4	(	(	PUNCT
cana-3299	247	5	𝑋1	𝑋1	NOUN
cana-3299	247	6	,	,	PUNCT
cana-3299	247	7	γ𝑃	γ𝑃	NOUN
cana-3299	247	8	)	)	PUNCT
cana-3299	247	9	→	→	SYM
cana-3299	247	10	(	(	PUNCT
cana-3299	247	11	𝑋2	𝑋2	ADJ
cana-3299	247	12	,	,	PUNCT
cana-3299	247	13	ψ𝑃	ψ𝑃	NOUN
cana-3299	247	14	)	)	PUNCT
cana-3299	247	15	be	be	VERB
cana-3299	247	16	an	an	DET
cana-3299	247	17	identity	identity	NOUN
cana-3299	247	18	mapping	mapping	NOUN
cana-3299	247	19	.	.	PUNCT
cana-3299	248	1	then	then	ADV
cana-3299	248	2	,	,	PUNCT
cana-3299	248	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	248	4	is	be	AUX
cana-3299	248	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	248	6	but	but	CCONJ
cana-3299	248	7	not	not	PART
cana-3299	248	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	248	9	,	,	PUNCT
cana-3299	248	10	because	because	SCONJ
cana-3299	248	11	the	the	DET
cana-3299	248	12	set	set	NOUN
cana-3299	248	13	𝐵1	𝐵1	NOUN
cana-3299	248	14	is	be	AUX
cana-3299	248	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	248	16	in	in	ADP
cana-3299	248	17	𝑋2	𝑋2	ADJ
cana-3299	248	18	but	but	CCONJ
cana-3299	248	19	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	248	20	−1(𝐵1	−1(𝐵1	VERB
cana-3299	248	21	)	)	PUNCT
cana-3299	249	1	=	=	NOUN
cana-3299	249	2	𝐵1	𝐵1	NOUN
cana-3299	249	3	is	be	AUX
cana-3299	249	4	not	not	PART
cana-3299	249	5	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	249	6	in	in	ADP
cana-3299	249	7	𝑋1	𝑋1	PROPN
cana-3299	249	8	.	.	PUNCT
cana-3299	249	9	example	example	NOUN
cana-3299	249	10	3.2	3.2	NUM
cana-3299	249	11	let	let	VERB
cana-3299	249	12	𝑋1	𝑋1	NOUN
cana-3299	249	13	=	=	SYM
cana-3299	249	14	𝑋2	𝑋2	VERB
cana-3299	249	15	=	=	PUNCT
cana-3299	249	16	{	{	PUNCT
cana-3299	249	17	𝑥1	𝑥1	NOUN
cana-3299	249	18	,	,	PUNCT
cana-3299	249	19	𝑥2	𝑥2	NOUN
cana-3299	249	20	}	}	PUNCT
cana-3299	249	21	and	and	CCONJ
cana-3299	249	22	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	249	23	’s	’s	PART
cana-3299	249	24	𝐴1	𝐴1	PROPN
cana-3299	249	25	,	,	PUNCT
cana-3299	249	26	𝐴2	𝐴2	PROPN
cana-3299	249	27	,	,	PUNCT
cana-3299	249	28	𝐴3	𝐴3	PROPN
cana-3299	249	29	,	,	PUNCT
cana-3299	249	30	𝐴4	𝐴4	PROPN
cana-3299	249	31	in	in	ADP
cana-3299	249	32	𝑋1	𝑋1	PROPN
cana-3299	249	33	&	&	CCONJ
cana-3299	249	34	𝐵1	𝐵1	PROPN
cana-3299	249	35	in	in	ADP
cana-3299	249	36	𝑋2	𝑋2	PROPN
cana-3299	249	37	are	be	AUX
cana-3299	249	38	defined	define	VERB
cana-3299	249	39	as	as	ADP
cana-3299	249	40	,	,	PUNCT
cana-3299	249	41	𝐴1	𝐴1	PROPN
cana-3299	249	42	=	=	SYM
cana-3299	249	43	{	{	PUNCT
cana-3299	249	44	<	<	X
cana-3299	249	45	𝑥1	𝑥1	PROPN
cana-3299	249	46	,	,	PUNCT
cana-3299	249	47	0.20,0.80	0.20,0.80	NOUN
cana-3299	249	48	>	>	X
cana-3299	249	49	,	,	PUNCT
cana-3299	249	50	<	<	X
cana-3299	249	51	𝑥2	𝑥2	NOUN
cana-3299	249	52	,	,	PUNCT
cana-3299	249	53	0.40,0.60	0.40,0.60	NUM
cana-3299	249	54	>	>	PUNCT
cana-3299	249	55	}	}	PUNCT
cana-3299	249	56	𝐴2	𝐴2	PROPN
cana-3299	249	57	=	=	SYM
cana-3299	249	58	{	{	PUNCT
cana-3299	249	59	<	<	X
cana-3299	249	60	𝑥1	𝑥1	PROPN
cana-3299	249	61	,	,	PUNCT
cana-3299	249	62	0.10,0.90	0.10,0.90	NUM
cana-3299	249	63	>	>	X
cana-3299	249	64	,	,	PUNCT
cana-3299	249	65	<	<	X
cana-3299	249	66	𝑥2	𝑥2	NOUN
cana-3299	249	67	,	,	PUNCT
cana-3299	249	68	0.30,0.70	0.30,0.70	PRON
cana-3299	249	69	>	>	PUNCT
cana-3299	249	70	}	}	PUNCT
cana-3299	249	71	𝐴3	𝐴3	PROPN
cana-3299	249	72	=	=	SYM
cana-3299	249	73	{	{	PUNCT
cana-3299	249	74	<	<	X
cana-3299	249	75	𝑥1	𝑥1	PROPN
cana-3299	249	76	,	,	PUNCT
cana-3299	249	77	0.90,0.10	0.90,0.10	NOUN
cana-3299	249	78	>	>	X
cana-3299	249	79	,	,	PUNCT
cana-3299	249	80	<	<	X
cana-3299	249	81	𝑥2	𝑥2	NOUN
cana-3299	249	82	,	,	PUNCT
cana-3299	249	83	0.70,0.30	0.70,0.30	NOUN
cana-3299	249	84	>	>	PUNCT
cana-3299	249	85	}	}	PUNCT
cana-3299	249	86	𝐴4	𝐴4	PROPN
cana-3299	249	87	=	=	PUNCT
cana-3299	249	88	{	{	PUNCT
cana-3299	249	89	<	<	X
cana-3299	249	90	𝑥1	𝑥1	PROPN
cana-3299	249	91	,	,	PUNCT
cana-3299	249	92	0.20,0.80	0.20,0.80	NOUN
cana-3299	249	93	>	>	X
cana-3299	249	94	,	,	PUNCT
cana-3299	249	95	<	<	X
cana-3299	249	96	𝑥2	𝑥2	NOUN
cana-3299	249	97	,	,	PUNCT
cana-3299	249	98	0.30,0.70	0.30,0.70	PRON
cana-3299	249	99	>	>	PUNCT
cana-3299	249	100	}	}	PUNCT
cana-3299	249	101	𝐵1	𝐵1	NOUN
cana-3299	249	102	=	=	PUNCT
cana-3299	249	103	{	{	PUNCT
cana-3299	249	104	<	<	X
cana-3299	249	105	𝑥1	𝑥1	PROPN
cana-3299	249	106	,	,	PUNCT
cana-3299	249	107	0.20,0.80	0.20,0.80	NOUN
cana-3299	249	108	>	>	X
cana-3299	249	109	,	,	PUNCT
cana-3299	249	110	<	<	X
cana-3299	249	111	𝑥2	𝑥2	NOUN
cana-3299	249	112	,	,	PUNCT
cana-3299	249	113	0.40,0.60	0.40,0.60	NUM
cana-3299	249	114	>	>	PUNCT
cana-3299	249	115	}	}	PUNCT
cana-3299	249	116	here	here	ADV
cana-3299	249	117	,	,	PUNCT
cana-3299	249	118	we	we	PRON
cana-3299	249	119	have	have	VERB
cana-3299	249	120	γ𝑃	γ𝑃	ADJ
cana-3299	249	121	=	=	PUNCT
cana-3299	249	122	{	{	PUNCT
cana-3299	249	123	0𝑋	0𝑋	PROPN
cana-3299	249	124	,	,	PUNCT
cana-3299	249	125	1𝑋	1𝑋	PROPN
cana-3299	249	126	,	,	PUNCT
cana-3299	249	127	𝐴1	𝐴1	PROPN
cana-3299	249	128	,	,	PUNCT
cana-3299	249	129	𝐴2	𝐴2	PROPN
cana-3299	249	130	,	,	PUNCT
cana-3299	249	131	𝐴3	𝐴3	PROPN
cana-3299	249	132	,	,	PUNCT
cana-3299	249	133	𝐴4	𝐴4	PROPN
cana-3299	249	134	}	}	PUNCT
cana-3299	249	135	and	and	CCONJ
cana-3299	249	136	ψ𝑃	ψ𝑃	PROPN
cana-3299	249	137	=	=	SYM
cana-3299	249	138	{	{	PUNCT
cana-3299	249	139	0𝑋	0𝑋	PROPN
cana-3299	249	140	,	,	PUNCT
cana-3299	249	141	1𝑋	1𝑋	PROPN
cana-3299	249	142	,	,	PUNCT
cana-3299	249	143	𝐵1	𝐵1	PROPN
cana-3299	249	144	}	}	PUNCT
cana-3299	249	145	.	.	PUNCT
cana-3299	250	1	let	let	VERB
cana-3299	250	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	250	3	:	:	PUNCT
cana-3299	250	4	(	(	PUNCT
cana-3299	250	5	𝑋1	𝑋1	NOUN
cana-3299	250	6	,	,	PUNCT
cana-3299	250	7	γ𝑃	γ𝑃	NOUN
cana-3299	250	8	)	)	PUNCT
cana-3299	250	9	→	→	SYM
cana-3299	250	10	(	(	PUNCT
cana-3299	250	11	𝑋2	𝑋2	ADJ
cana-3299	250	12	,	,	PUNCT
cana-3299	250	13	ψ𝑃	ψ𝑃	NOUN
cana-3299	250	14	)	)	PUNCT
cana-3299	250	15	be	be	VERB
cana-3299	250	16	an	an	DET
cana-3299	250	17	identity	identity	NOUN
cana-3299	250	18	mapping	mapping	NOUN
cana-3299	250	19	.	.	PUNCT
cana-3299	251	1	then	then	ADV
cana-3299	251	2	,	,	PUNCT
cana-3299	251	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	251	4	is	be	AUX
cana-3299	251	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	251	6	(	(	PUNCT
cana-3299	251	7	resp	resp	NOUN
cana-3299	251	8	.	.	PUNCT
cana-3299	251	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	251	10	)	)	PUNCT
cana-3299	251	11	but	but	CCONJ
cana-3299	251	12	not	not	PART
cana-3299	251	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	PROPN
cana-3299	251	14	(	(	PUNCT
cana-3299	251	15	resp	resp	NOUN
cana-3299	251	16	.	.	PUNCT
cana-3299	252	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	X
cana-3299	252	2	)	)	PUNCT
cana-3299	252	3	,	,	PUNCT
cana-3299	252	4	because	because	SCONJ
cana-3299	252	5	the	the	DET
cana-3299	252	6	set	set	NOUN
cana-3299	252	7	𝐵1	𝐵1	NOUN
cana-3299	252	8	is	be	AUX
cana-3299	252	9	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	252	10	in	in	ADP
cana-3299	252	11	𝑋2	𝑋2	ADJ
cana-3299	252	12	but	but	CCONJ
cana-3299	252	13	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	252	14	−1(𝐵1	−1(𝐵1	VERB
cana-3299	252	15	)	)	PUNCT
cana-3299	252	16	=	=	NOUN
cana-3299	252	17	𝐵1	𝐵1	NOUN
cana-3299	252	18	is	be	AUX
cana-3299	252	19	not	not	PART
cana-3299	252	20	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	252	21	(	(	PUNCT
cana-3299	252	22	resp	resp	NOUN
cana-3299	252	23	.	.	PUNCT
cana-3299	253	1	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-3299	253	2	)	)	PUNCT
cana-3299	253	3	in	in	ADP
cana-3299	253	4	𝑋1	𝑋1	PROPN
cana-3299	253	5	.	.	PUNCT
cana-3299	254	1	example	example	NOUN
cana-3299	254	2	3.3	3.3	NUM
cana-3299	254	3	let	let	VERB
cana-3299	254	4	𝑋1	𝑋1	NOUN
cana-3299	254	5	=	=	SYM
cana-3299	254	6	𝑋2	𝑋2	VERB
cana-3299	254	7	=	=	PUNCT
cana-3299	254	8	{	{	PUNCT
cana-3299	254	9	𝑥1	𝑥1	NOUN
cana-3299	254	10	,	,	PUNCT
cana-3299	254	11	𝑥2	𝑥2	NOUN
cana-3299	254	12	}	}	PUNCT
cana-3299	254	13	and	and	CCONJ
cana-3299	254	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	254	15	’s	’s	PART
cana-3299	254	16	𝐴1	𝐴1	PROPN
cana-3299	254	17	,	,	PUNCT
cana-3299	254	18	𝐴2	𝐴2	PROPN
cana-3299	254	19	,	,	PUNCT
cana-3299	254	20	𝐴3	𝐴3	PROPN
cana-3299	254	21	,	,	PUNCT
cana-3299	254	22	𝐴4	𝐴4	PROPN
cana-3299	254	23	in	in	ADP
cana-3299	254	24	𝑋1	𝑋1	PROPN
cana-3299	254	25	&	&	CCONJ
cana-3299	254	26	𝐵1	𝐵1	PROPN
cana-3299	254	27	in	in	ADP
cana-3299	254	28	𝑋2	𝑋2	PROPN
cana-3299	254	29	are	be	AUX
cana-3299	254	30	defined	define	VERB
cana-3299	254	31	as	as	ADP
cana-3299	254	32	,	,	PUNCT
cana-3299	254	33	𝐴1	𝐴1	PROPN
cana-3299	254	34	=	=	SYM
cana-3299	254	35	{	{	PUNCT
cana-3299	254	36	<	<	X
cana-3299	254	37	𝑥1	𝑥1	PROPN
cana-3299	254	38	,	,	PUNCT
cana-3299	254	39	0.20,0.80	0.20,0.80	NOUN
cana-3299	254	40	>	>	X
cana-3299	254	41	,	,	PUNCT
cana-3299	254	42	<	<	X
cana-3299	254	43	𝑥2	𝑥2	NOUN
cana-3299	254	44	,	,	PUNCT
cana-3299	254	45	0.40,0.60	0.40,0.60	NUM
cana-3299	254	46	>	>	PUNCT
cana-3299	254	47	}	}	PUNCT
cana-3299	254	48	𝐴2	𝐴2	PROPN
cana-3299	254	49	=	=	SYM
cana-3299	254	50	{	{	PUNCT
cana-3299	254	51	<	<	X
cana-3299	254	52	𝑥1	𝑥1	PROPN
cana-3299	254	53	,	,	PUNCT
cana-3299	254	54	0.10,0.90	0.10,0.90	NUM
cana-3299	254	55	>	>	X
cana-3299	254	56	,	,	PUNCT
cana-3299	254	57	<	<	X
cana-3299	254	58	𝑥2	𝑥2	NOUN
cana-3299	254	59	,	,	PUNCT
cana-3299	254	60	0.30,0.70	0.30,0.70	PRON
cana-3299	254	61	>	>	PUNCT
cana-3299	254	62	}	}	PUNCT
cana-3299	254	63	𝐴3	𝐴3	PROPN
cana-3299	255	1	=	=	SYM
cana-3299	255	2	{	{	PUNCT
cana-3299	255	3	<	<	X
cana-3299	255	4	𝑥1	𝑥1	PROPN
cana-3299	255	5	,	,	PUNCT
cana-3299	255	6	0.90,0.10	0.90,0.10	NOUN
cana-3299	255	7	>	>	X
cana-3299	255	8	,	,	PUNCT
cana-3299	255	9	<	<	X
cana-3299	255	10	𝑥2	𝑥2	NOUN
cana-3299	255	11	,	,	PUNCT
cana-3299	255	12	0.70,0.30	0.70,0.30	NOUN
cana-3299	255	13	>	>	PUNCT
cana-3299	255	14	}	}	PUNCT
cana-3299	255	15	𝐴4	𝐴4	PROPN
cana-3299	255	16	=	=	PUNCT
cana-3299	255	17	{	{	PUNCT
cana-3299	255	18	<	<	X
cana-3299	255	19	𝑥1	𝑥1	PROPN
cana-3299	255	20	,	,	PUNCT
cana-3299	255	21	0.20,0.80	0.20,0.80	NOUN
cana-3299	255	22	>	>	X
cana-3299	255	23	,	,	PUNCT
cana-3299	255	24	<	<	X
cana-3299	255	25	𝑥2	𝑥2	NOUN
cana-3299	255	26	,	,	PUNCT
cana-3299	255	27	0.30,0.70	0.30,0.70	PRON
cana-3299	255	28	>	>	PUNCT
cana-3299	255	29	}	}	PUNCT
cana-3299	255	30	𝐵1	𝐵1	NOUN
cana-3299	255	31	=	=	PUNCT
cana-3299	255	32	{	{	PUNCT
cana-3299	255	33	<	<	X
cana-3299	255	34	𝑥1	𝑥1	PROPN
cana-3299	255	35	,	,	PUNCT
cana-3299	255	36	0.80,0.20	0.80,0.20	X
cana-3299	255	37	>	>	X
cana-3299	255	38	,	,	PUNCT
cana-3299	255	39	<	<	X
cana-3299	255	40	𝑥2	𝑥2	NOUN
cana-3299	255	41	,	,	PUNCT
cana-3299	255	42	0.60,0.40	0.60,0.40	X
cana-3299	255	43	>	>	PUNCT
cana-3299	255	44	}	}	PUNCT
cana-3299	255	45	.	.	PUNCT
cana-3299	256	1	here	here	ADV
cana-3299	256	2	,	,	PUNCT
cana-3299	256	3	we	we	PRON
cana-3299	256	4	have	have	VERB
cana-3299	256	5	γ𝑃	γ𝑃	ADJ
cana-3299	256	6	=	=	PUNCT
cana-3299	256	7	{	{	PUNCT
cana-3299	256	8	0𝑋	0𝑋	PROPN
cana-3299	256	9	,	,	PUNCT
cana-3299	256	10	1𝑋	1𝑋	PROPN
cana-3299	256	11	,	,	PUNCT
cana-3299	256	12	𝐴1	𝐴1	PROPN
cana-3299	256	13	,	,	PUNCT
cana-3299	256	14	𝐴2	𝐴2	PROPN
cana-3299	256	15	,	,	PUNCT
cana-3299	256	16	𝐴3	𝐴3	PROPN
cana-3299	256	17	,	,	PUNCT
cana-3299	256	18	𝐴4	𝐴4	PROPN
cana-3299	256	19	}	}	PUNCT
cana-3299	256	20	and	and	CCONJ
cana-3299	256	21	ψ𝑃	ψ𝑃	PROPN
cana-3299	256	22	=	=	SYM
cana-3299	256	23	{	{	PUNCT
cana-3299	256	24	0𝑋	0𝑋	PROPN
cana-3299	256	25	,	,	PUNCT
cana-3299	256	26	1𝑋	1𝑋	PROPN
cana-3299	256	27	,	,	PUNCT
cana-3299	256	28	𝐵1	𝐵1	PROPN
cana-3299	256	29	}	}	PUNCT
cana-3299	256	30	.	.	PUNCT
cana-3299	257	1	let	let	VERB
cana-3299	257	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	257	3	:	:	PUNCT
cana-3299	257	4	(	(	PUNCT
cana-3299	257	5	𝑋1	𝑋1	NOUN
cana-3299	257	6	,	,	PUNCT
cana-3299	257	7	γ𝑃	γ𝑃	NOUN
cana-3299	257	8	)	)	PUNCT
cana-3299	257	9	→	→	SYM
cana-3299	257	10	(	(	PUNCT
cana-3299	257	11	𝑋2	𝑋2	ADJ
cana-3299	257	12	,	,	PUNCT
cana-3299	257	13	ψ𝑃	ψ𝑃	NOUN
cana-3299	257	14	)	)	PUNCT
cana-3299	257	15	be	be	VERB
cana-3299	257	16	an	an	DET
cana-3299	257	17	identity	identity	NOUN
cana-3299	257	18	mapping	mapping	NOUN
cana-3299	257	19	.	.	PUNCT
cana-3299	258	1	then	then	ADV
cana-3299	258	2	,	,	PUNCT
cana-3299	258	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	258	4	is	be	AUX
cana-3299	258	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	258	6	but	but	CCONJ
cana-3299	258	7	not	not	PART
cana-3299	258	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	258	9	,	,	PUNCT
cana-3299	258	10	because	because	SCONJ
cana-3299	258	11	the	the	DET
cana-3299	258	12	set	set	NOUN
cana-3299	258	13	𝐵1	𝐵1	NOUN
cana-3299	258	14	is	be	AUX
cana-3299	258	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	258	16	in	in	ADP
cana-3299	258	17	𝑋2	𝑋2	ADJ
cana-3299	258	18	but	but	CCONJ
cana-3299	258	19	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	258	20	−1(𝐵1	−1(𝐵1	VERB
cana-3299	258	21	)	)	PUNCT
cana-3299	259	1	=	=	NOUN
cana-3299	259	2	𝐵1	𝐵1	NOUN
cana-3299	259	3	is	be	AUX
cana-3299	259	4	not	not	PART
cana-3299	259	5	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-3299	259	6	in	in	ADP
cana-3299	259	7	𝑋1	𝑋1	PROPN
cana-3299	259	8	.	.	PUNCT
cana-3299	260	1	example	example	NOUN
cana-3299	260	2	3.4	3.4	NUM
cana-3299	260	3	let	let	VERB
cana-3299	260	4	𝑋1	𝑋1	NOUN
cana-3299	260	5	=	=	SYM
cana-3299	260	6	𝑋2	𝑋2	VERB
cana-3299	260	7	=	=	PUNCT
cana-3299	260	8	{	{	PUNCT
cana-3299	260	9	𝑥1	𝑥1	NOUN
cana-3299	260	10	,	,	PUNCT
cana-3299	260	11	𝑥2	𝑥2	NOUN
cana-3299	260	12	}	}	PUNCT
cana-3299	260	13	and	and	CCONJ
cana-3299	260	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	260	15	’s	’s	PART
cana-3299	260	16	𝐴1	𝐴1	PROPN
cana-3299	260	17	,	,	PUNCT
cana-3299	260	18	𝐴2	𝐴2	PROPN
cana-3299	260	19	,	,	PUNCT
cana-3299	260	20	𝐴3	𝐴3	PROPN
cana-3299	260	21	,	,	PUNCT
cana-3299	260	22	𝐴4	𝐴4	PROPN
cana-3299	260	23	in	in	ADP
cana-3299	260	24	𝑋1	𝑋1	PROPN
cana-3299	260	25	&	&	CCONJ
cana-3299	260	26	𝐵1	𝐵1	PROPN
cana-3299	260	27	in	in	ADP
cana-3299	260	28	𝑋2	𝑋2	PROPN
cana-3299	260	29	are	be	AUX
cana-3299	260	30	defined	define	VERB
cana-3299	260	31	as	as	ADP
cana-3299	260	32	,	,	PUNCT
cana-3299	260	33	𝐴1	𝐴1	PROPN
cana-3299	260	34	=	=	SYM
cana-3299	260	35	{	{	PUNCT
cana-3299	260	36	<	<	X
cana-3299	260	37	𝑥1	𝑥1	PROPN
cana-3299	260	38	,	,	PUNCT
cana-3299	260	39	0.20,0.80	0.20,0.80	NOUN
cana-3299	260	40	>	>	X
cana-3299	260	41	,	,	PUNCT
cana-3299	260	42	<	<	X
cana-3299	260	43	𝑥2	𝑥2	NOUN
cana-3299	260	44	,	,	PUNCT
cana-3299	260	45	0.40,0.60	0.40,0.60	NUM
cana-3299	260	46	>	>	PUNCT
cana-3299	260	47	}	}	PUNCT
cana-3299	260	48	𝐴2	𝐴2	PROPN
cana-3299	260	49	=	=	SYM
cana-3299	260	50	{	{	PUNCT
cana-3299	260	51	<	<	X
cana-3299	260	52	𝑥1	𝑥1	PROPN
cana-3299	260	53	,	,	PUNCT
cana-3299	260	54	0.10,0.90	0.10,0.90	NUM
cana-3299	260	55	>	>	X
cana-3299	260	56	,	,	PUNCT
cana-3299	260	57	<	<	X
cana-3299	260	58	𝑥2	𝑥2	NOUN
cana-3299	260	59	,	,	PUNCT
cana-3299	260	60	0.30,0.70	0.30,0.70	PRON
cana-3299	260	61	>	>	PUNCT
cana-3299	260	62	}	}	PUNCT
cana-3299	260	63	𝐴3	𝐴3	PROPN
cana-3299	261	1	=	=	SYM
cana-3299	261	2	{	{	PUNCT
cana-3299	261	3	<	<	X
cana-3299	261	4	𝑥1	𝑥1	PROPN
cana-3299	261	5	,	,	PUNCT
cana-3299	261	6	0.90,0.10	0.90,0.10	NOUN
cana-3299	261	7	>	>	X
cana-3299	261	8	,	,	PUNCT
cana-3299	261	9	<	<	X
cana-3299	261	10	𝑥2	𝑥2	NOUN
cana-3299	261	11	,	,	PUNCT
cana-3299	261	12	0.70,0.30	0.70,0.30	NOUN
cana-3299	261	13	>	>	PUNCT
cana-3299	261	14	}	}	PUNCT
cana-3299	261	15	𝐴4	𝐴4	PROPN
cana-3299	261	16	=	=	PUNCT
cana-3299	261	17	{	{	PUNCT
cana-3299	261	18	<	<	X
cana-3299	261	19	𝑥1	𝑥1	PROPN
cana-3299	261	20	,	,	PUNCT
cana-3299	261	21	0.20,0.80	0.20,0.80	NOUN
cana-3299	261	22	>	>	X
cana-3299	261	23	,	,	PUNCT
cana-3299	261	24	<	<	X
cana-3299	261	25	𝑥2	𝑥2	NOUN
cana-3299	261	26	,	,	PUNCT
cana-3299	261	27	0.30,0.70	0.30,0.70	PRON
cana-3299	261	28	>	>	PUNCT
cana-3299	261	29	}	}	PUNCT
cana-3299	261	30	𝐵1	𝐵1	NOUN
cana-3299	261	31	=	=	PUNCT
cana-3299	261	32	{	{	PUNCT
cana-3299	261	33	<	<	X
cana-3299	261	34	𝑥1	𝑥1	PROPN
cana-3299	261	35	,	,	PUNCT
cana-3299	261	36	0.20,0.40	0.20,0.40	X
cana-3299	261	37	>	>	X
cana-3299	261	38	,	,	PUNCT
cana-3299	261	39	<	<	X
cana-3299	261	40	𝑥2	𝑥2	NOUN
cana-3299	261	41	,	,	PUNCT
cana-3299	261	42	0.40,0.40	0.40,0.40	NOUN
cana-3299	261	43	>	>	X
cana-3299	261	44	}	}	PUNCT
cana-3299	261	45	communications	communication	NOUN
cana-3299	261	46	on	on	ADP
cana-3299	261	47	applied	apply	VERB
cana-3299	261	48	nonlinear	nonlinear	ADJ
cana-3299	261	49	analysis	analysis	NOUN
cana-3299	261	50	issn	issn	NOUN
cana-3299	261	51	:	:	PUNCT
cana-3299	261	52	1074	1074	NUM
cana-3299	261	53	-	-	PUNCT
cana-3299	261	54	133x	133x	NUM
cana-3299	261	55	vol	vol	NOUN
cana-3299	261	56	32	32	NUM
cana-3299	261	57	no	no	NOUN
cana-3299	261	58	.	.	PUNCT
cana-3299	262	1	6s	6s	NUM
cana-3299	262	2	(	(	PUNCT
cana-3299	262	3	2025	2025	NUM
cana-3299	262	4	)	)	PUNCT
cana-3299	262	5	334	334	NUM
cana-3299	262	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	263	1	now	now	ADV
cana-3299	263	2	,	,	PUNCT
cana-3299	263	3	we	we	PRON
cana-3299	263	4	have	have	VERB
cana-3299	263	5	γ𝑃	γ𝑃	ADJ
cana-3299	263	6	=	=	PUNCT
cana-3299	263	7	{	{	PUNCT
cana-3299	263	8	0𝑋	0𝑋	PROPN
cana-3299	263	9	,	,	PUNCT
cana-3299	263	10	1𝑋	1𝑋	PROPN
cana-3299	263	11	,	,	PUNCT
cana-3299	263	12	𝐴1	𝐴1	PROPN
cana-3299	263	13	,	,	PUNCT
cana-3299	263	14	𝐴2	𝐴2	PROPN
cana-3299	263	15	,	,	PUNCT
cana-3299	263	16	𝐴3	𝐴3	PROPN
cana-3299	263	17	,	,	PUNCT
cana-3299	263	18	𝐴4	𝐴4	PROPN
cana-3299	263	19	}	}	PUNCT
cana-3299	263	20	and	and	CCONJ
cana-3299	263	21	ψ𝑃	ψ𝑃	PROPN
cana-3299	263	22	=	=	SYM
cana-3299	263	23	{	{	PUNCT
cana-3299	263	24	0𝑋	0𝑋	PROPN
cana-3299	263	25	,	,	PUNCT
cana-3299	263	26	1𝑋	1𝑋	PROPN
cana-3299	263	27	,	,	PUNCT
cana-3299	263	28	𝐵1	𝐵1	PROPN
cana-3299	263	29	}	}	PUNCT
cana-3299	263	30	.	.	PUNCT
cana-3299	264	1	let	let	VERB
cana-3299	264	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	264	3	:	:	PUNCT
cana-3299	264	4	(	(	PUNCT
cana-3299	264	5	𝑋1	𝑋1	NOUN
cana-3299	264	6	,	,	PUNCT
cana-3299	264	7	γ𝑃	γ𝑃	NOUN
cana-3299	264	8	)	)	PUNCT
cana-3299	264	9	→	→	SYM
cana-3299	264	10	(	(	PUNCT
cana-3299	264	11	𝑋2	𝑋2	ADJ
cana-3299	264	12	,	,	PUNCT
cana-3299	264	13	ψ𝑃	ψ𝑃	NOUN
cana-3299	264	14	)	)	PUNCT
cana-3299	264	15	be	be	VERB
cana-3299	264	16	an	an	DET
cana-3299	264	17	identity	identity	NOUN
cana-3299	264	18	mapping	mapping	NOUN
cana-3299	264	19	.	.	PUNCT
cana-3299	265	1	then	then	ADV
cana-3299	265	2	,	,	PUNCT
cana-3299	265	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	265	4	is	be	AUX
cana-3299	265	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PROPN
cana-3299	265	6	but	but	CCONJ
cana-3299	265	7	not	not	PART
cana-3299	265	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	265	9	,	,	PUNCT
cana-3299	265	10	because	because	SCONJ
cana-3299	265	11	the	the	DET
cana-3299	265	12	set	set	NOUN
cana-3299	265	13	𝐵1	𝐵1	NOUN
cana-3299	265	14	is	be	AUX
cana-3299	265	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	265	16	in	in	ADP
cana-3299	265	17	𝑋2	𝑋2	ADJ
cana-3299	265	18	but	but	CCONJ
cana-3299	265	19	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	265	20	−1(𝐵1	−1(𝐵1	VERB
cana-3299	265	21	)	)	PUNCT
cana-3299	266	1	=	=	NOUN
cana-3299	266	2	𝐵1	𝐵1	NOUN
cana-3299	266	3	is	be	AUX
cana-3299	266	4	not	not	PART
cana-3299	266	5	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	266	6	in	in	ADP
cana-3299	266	7	𝑋1	𝑋1	PROPN
cana-3299	266	8	.	.	PUNCT
cana-3299	267	1	example	example	NOUN
cana-3299	267	2	3.5	3.5	NUM
cana-3299	267	3	let	let	VERB
cana-3299	267	4	𝑋1	𝑋1	NOUN
cana-3299	267	5	=	=	SYM
cana-3299	267	6	𝑋2	𝑋2	VERB
cana-3299	267	7	=	=	PUNCT
cana-3299	267	8	{	{	PUNCT
cana-3299	267	9	𝑥1	𝑥1	NOUN
cana-3299	267	10	,	,	PUNCT
cana-3299	267	11	𝑥2	𝑥2	NOUN
cana-3299	267	12	}	}	PUNCT
cana-3299	267	13	and	and	CCONJ
cana-3299	267	14	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	267	15	’s	’s	PART
cana-3299	267	16	𝐴1	𝐴1	PROPN
cana-3299	267	17	,	,	PUNCT
cana-3299	267	18	𝐴2	𝐴2	PROPN
cana-3299	267	19	,	,	PUNCT
cana-3299	267	20	𝐴3	𝐴3	PROPN
cana-3299	267	21	,	,	PUNCT
cana-3299	267	22	𝐴4	𝐴4	PROPN
cana-3299	267	23	in	in	ADP
cana-3299	267	24	𝑋1	𝑋1	PROPN
cana-3299	267	25	&	&	CCONJ
cana-3299	267	26	𝐵1	𝐵1	PROPN
cana-3299	267	27	in	in	ADP
cana-3299	267	28	𝑋2	𝑋2	PROPN
cana-3299	267	29	are	be	AUX
cana-3299	267	30	defined	define	VERB
cana-3299	267	31	as	as	ADP
cana-3299	267	32	,	,	PUNCT
cana-3299	267	33	𝐴1	𝐴1	PROPN
cana-3299	267	34	=	=	SYM
cana-3299	267	35	{	{	PUNCT
cana-3299	267	36	<	<	X
cana-3299	267	37	𝑥1	𝑥1	PROPN
cana-3299	267	38	,	,	PUNCT
cana-3299	267	39	0.20,0.80	0.20,0.80	NOUN
cana-3299	267	40	>	>	X
cana-3299	267	41	,	,	PUNCT
cana-3299	267	42	<	<	X
cana-3299	267	43	𝑥2	𝑥2	NOUN
cana-3299	267	44	,	,	PUNCT
cana-3299	267	45	0.40,0.60	0.40,0.60	NUM
cana-3299	267	46	>	>	PUNCT
cana-3299	267	47	}	}	PUNCT
cana-3299	267	48	𝐴2	𝐴2	PROPN
cana-3299	267	49	=	=	SYM
cana-3299	267	50	{	{	PUNCT
cana-3299	267	51	<	<	X
cana-3299	267	52	𝑥1	𝑥1	PROPN
cana-3299	267	53	,	,	PUNCT
cana-3299	267	54	0.10,0.90	0.10,0.90	NUM
cana-3299	267	55	>	>	X
cana-3299	267	56	,	,	PUNCT
cana-3299	267	57	<	<	X
cana-3299	267	58	𝑥2	𝑥2	NOUN
cana-3299	267	59	,	,	PUNCT
cana-3299	267	60	0.30,0.70	0.30,0.70	PRON
cana-3299	267	61	>	>	PUNCT
cana-3299	267	62	}	}	PUNCT
cana-3299	267	63	𝐴3	𝐴3	PROPN
cana-3299	268	1	=	=	SYM
cana-3299	268	2	{	{	PUNCT
cana-3299	268	3	<	<	X
cana-3299	268	4	𝑥1	𝑥1	PROPN
cana-3299	268	5	,	,	PUNCT
cana-3299	268	6	0.90,0.10	0.90,0.10	NOUN
cana-3299	268	7	>	>	X
cana-3299	268	8	,	,	PUNCT
cana-3299	268	9	<	<	X
cana-3299	268	10	𝑥2	𝑥2	NOUN
cana-3299	268	11	,	,	PUNCT
cana-3299	268	12	0.70,0.30	0.70,0.30	NOUN
cana-3299	268	13	>	>	PUNCT
cana-3299	268	14	}	}	PUNCT
cana-3299	268	15	𝐴4	𝐴4	PROPN
cana-3299	268	16	=	=	PUNCT
cana-3299	268	17	{	{	PUNCT
cana-3299	268	18	<	<	X
cana-3299	268	19	𝑥1	𝑥1	PROPN
cana-3299	268	20	,	,	PUNCT
cana-3299	268	21	0.20,0.80	0.20,0.80	NOUN
cana-3299	268	22	>	>	X
cana-3299	268	23	,	,	PUNCT
cana-3299	268	24	<	<	X
cana-3299	268	25	𝑥2	𝑥2	NOUN
cana-3299	268	26	,	,	PUNCT
cana-3299	268	27	0.30,0.70	0.30,0.70	PRON
cana-3299	268	28	>	>	PUNCT
cana-3299	268	29	}	}	PUNCT
cana-3299	268	30	𝐵1	𝐵1	NOUN
cana-3299	268	31	=	=	PUNCT
cana-3299	268	32	{	{	PUNCT
cana-3299	268	33	<	<	X
cana-3299	268	34	𝑥1	𝑥1	PROPN
cana-3299	268	35	,	,	PUNCT
cana-3299	268	36	0.80,0.20	0.80,0.20	X
cana-3299	268	37	>	>	X
cana-3299	268	38	,	,	PUNCT
cana-3299	268	39	<	<	X
cana-3299	268	40	𝑥2	𝑥2	NOUN
cana-3299	268	41	,	,	PUNCT
cana-3299	268	42	0.70,0.30	0.70,0.30	NOUN
cana-3299	268	43	>	>	PUNCT
cana-3299	268	44	}	}	PUNCT
cana-3299	268	45	now	now	ADV
cana-3299	268	46	,	,	PUNCT
cana-3299	268	47	we	we	PRON
cana-3299	268	48	have	have	VERB
cana-3299	268	49	γ𝑃	γ𝑃	ADJ
cana-3299	268	50	=	=	PUNCT
cana-3299	268	51	{	{	PUNCT
cana-3299	268	52	0𝑋	0𝑋	PROPN
cana-3299	268	53	,	,	PUNCT
cana-3299	268	54	1𝑋	1𝑋	PROPN
cana-3299	268	55	,	,	PUNCT
cana-3299	268	56	𝐴1	𝐴1	PROPN
cana-3299	268	57	,	,	PUNCT
cana-3299	268	58	𝐴2	𝐴2	PROPN
cana-3299	268	59	,	,	PUNCT
cana-3299	268	60	𝐴3	𝐴3	PROPN
cana-3299	268	61	,	,	PUNCT
cana-3299	268	62	𝐴4	𝐴4	PROPN
cana-3299	268	63	}	}	PUNCT
cana-3299	268	64	and	and	CCONJ
cana-3299	268	65	ψ𝑃	ψ𝑃	PROPN
cana-3299	268	66	=	=	SYM
cana-3299	268	67	{	{	PUNCT
cana-3299	268	68	0𝑋	0𝑋	PROPN
cana-3299	268	69	,	,	PUNCT
cana-3299	268	70	1𝑋	1𝑋	PROPN
cana-3299	268	71	,	,	PUNCT
cana-3299	268	72	𝐵1	𝐵1	PROPN
cana-3299	268	73	}	}	PUNCT
cana-3299	268	74	.	.	PUNCT
cana-3299	269	1	let	let	VERB
cana-3299	269	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	269	3	:	:	PUNCT
cana-3299	269	4	(	(	PUNCT
cana-3299	269	5	𝑋1	𝑋1	NOUN
cana-3299	269	6	,	,	PUNCT
cana-3299	269	7	γ𝑃	γ𝑃	NOUN
cana-3299	269	8	)	)	PUNCT
cana-3299	269	9	→	→	SYM
cana-3299	269	10	(	(	PUNCT
cana-3299	269	11	𝑋2	𝑋2	ADJ
cana-3299	269	12	,	,	PUNCT
cana-3299	269	13	ψ𝑃	ψ𝑃	NOUN
cana-3299	269	14	)	)	PUNCT
cana-3299	269	15	be	be	VERB
cana-3299	269	16	an	an	DET
cana-3299	269	17	identity	identity	NOUN
cana-3299	269	18	mapping	mapping	NOUN
cana-3299	269	19	.	.	PUNCT
cana-3299	270	1	then	then	ADV
cana-3299	270	2	,	,	PUNCT
cana-3299	270	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	270	4	is	be	AUX
cana-3299	270	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	270	6	(	(	PUNCT
cana-3299	270	7	resp	resp	NOUN
cana-3299	270	8	.	.	PUNCT
cana-3299	271	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PRON
cana-3299	271	2	and	and	CCONJ
cana-3299	271	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	271	4	)	)	PUNCT
cana-3299	271	5	but	but	CCONJ
cana-3299	271	6	not	not	PART
cana-3299	271	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	ADJ
cana-3299	271	8	(	(	PUNCT
cana-3299	271	9	resp	resp	NOUN
cana-3299	271	10	.	.	PUNCT
cana-3299	271	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	271	12	and	and	CCONJ
cana-3299	271	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	NUM
cana-3299	271	14	)	)	PUNCT
cana-3299	271	15	,	,	PUNCT
cana-3299	271	16	because	because	SCONJ
cana-3299	271	17	the	the	DET
cana-3299	271	18	set	set	NOUN
cana-3299	271	19	𝐵1	𝐵1	NOUN
cana-3299	271	20	is	be	AUX
cana-3299	271	21	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	271	22	in	in	ADP
cana-3299	271	23	𝑋2	𝑋2	ADJ
cana-3299	271	24	but	but	CCONJ
cana-3299	271	25	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	271	26	−1(𝐵1	−1(𝐵1	VERB
cana-3299	271	27	)	)	PUNCT
cana-3299	272	1	=	=	NOUN
cana-3299	272	2	𝐵1	𝐵1	NOUN
cana-3299	272	3	is	be	AUX
cana-3299	272	4	not	not	PART
cana-3299	272	5	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-3299	272	6	(	(	PUNCT
cana-3299	272	7	resp	resp	NOUN
cana-3299	272	8	.	.	PUNCT
cana-3299	273	1	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	273	2	and	and	CCONJ
cana-3299	273	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-3299	273	4	)	)	PUNCT
cana-3299	273	5	in	in	ADP
cana-3299	273	6	𝑋1	𝑋1	PROPN
cana-3299	273	7	.	.	PUNCT
cana-3299	273	8	example	example	NOUN
cana-3299	273	9	3.6	3.6	NUM
cana-3299	273	10	let	let	VERB
cana-3299	273	11	𝑋1	𝑋1	NOUN
cana-3299	273	12	=	=	SYM
cana-3299	273	13	𝑋2	𝑋2	VERB
cana-3299	273	14	=	=	PUNCT
cana-3299	273	15	{	{	PUNCT
cana-3299	273	16	𝑥1	𝑥1	NOUN
cana-3299	273	17	,	,	PUNCT
cana-3299	273	18	𝑥2	𝑥2	NOUN
cana-3299	273	19	}	}	PUNCT
cana-3299	273	20	and	and	CCONJ
cana-3299	273	21	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	273	22	’s	’s	PART
cana-3299	273	23	𝐴1	𝐴1	PROPN
cana-3299	273	24	,	,	PUNCT
cana-3299	273	25	𝐴2	𝐴2	PROPN
cana-3299	273	26	,	,	PUNCT
cana-3299	273	27	𝐴3	𝐴3	PROPN
cana-3299	273	28	,	,	PUNCT
cana-3299	273	29	𝐴4	𝐴4	PROPN
cana-3299	273	30	in	in	ADP
cana-3299	273	31	𝑋1	𝑋1	PROPN
cana-3299	273	32	&	&	CCONJ
cana-3299	273	33	𝐵1	𝐵1	PROPN
cana-3299	273	34	in	in	ADP
cana-3299	273	35	𝑋2	𝑋2	PROPN
cana-3299	273	36	are	be	AUX
cana-3299	273	37	defined	define	VERB
cana-3299	273	38	as	as	ADP
cana-3299	273	39	,	,	PUNCT
cana-3299	273	40	𝐴1	𝐴1	PROPN
cana-3299	273	41	=	=	SYM
cana-3299	273	42	{	{	PUNCT
cana-3299	273	43	<	<	X
cana-3299	273	44	𝑥1	𝑥1	PROPN
cana-3299	273	45	,	,	PUNCT
cana-3299	273	46	0.20,0.80	0.20,0.80	NOUN
cana-3299	273	47	>	>	X
cana-3299	273	48	,	,	PUNCT
cana-3299	273	49	<	<	X
cana-3299	273	50	𝑥2	𝑥2	NOUN
cana-3299	273	51	,	,	PUNCT
cana-3299	273	52	0.40,0.60	0.40,0.60	NUM
cana-3299	273	53	>	>	PUNCT
cana-3299	273	54	}	}	PUNCT
cana-3299	273	55	𝐴2	𝐴2	PROPN
cana-3299	273	56	=	=	SYM
cana-3299	273	57	{	{	PUNCT
cana-3299	273	58	<	<	X
cana-3299	273	59	𝑥1	𝑥1	PROPN
cana-3299	273	60	,	,	PUNCT
cana-3299	273	61	0.10,0.90	0.10,0.90	NUM
cana-3299	273	62	>	>	X
cana-3299	273	63	,	,	PUNCT
cana-3299	273	64	<	<	X
cana-3299	273	65	𝑥2	𝑥2	NOUN
cana-3299	273	66	,	,	PUNCT
cana-3299	273	67	0.30,0.70	0.30,0.70	PRON
cana-3299	273	68	>	>	PUNCT
cana-3299	273	69	}	}	PUNCT
cana-3299	273	70	𝐴3	𝐴3	PROPN
cana-3299	274	1	=	=	SYM
cana-3299	274	2	{	{	PUNCT
cana-3299	274	3	<	<	X
cana-3299	274	4	𝑥1	𝑥1	PROPN
cana-3299	274	5	,	,	PUNCT
cana-3299	274	6	0.90,0.10	0.90,0.10	NOUN
cana-3299	274	7	>	>	X
cana-3299	274	8	,	,	PUNCT
cana-3299	274	9	<	<	X
cana-3299	274	10	𝑥2	𝑥2	NOUN
cana-3299	274	11	,	,	PUNCT
cana-3299	274	12	0.70,0.30	0.70,0.30	NOUN
cana-3299	274	13	>	>	PUNCT
cana-3299	274	14	}	}	PUNCT
cana-3299	274	15	𝐴4	𝐴4	PROPN
cana-3299	274	16	=	=	PUNCT
cana-3299	274	17	{	{	PUNCT
cana-3299	274	18	<	<	X
cana-3299	274	19	𝑥1	𝑥1	PROPN
cana-3299	274	20	,	,	PUNCT
cana-3299	274	21	0.20,0.80	0.20,0.80	NOUN
cana-3299	274	22	>	>	X
cana-3299	274	23	,	,	PUNCT
cana-3299	274	24	<	<	X
cana-3299	274	25	𝑥2	𝑥2	NOUN
cana-3299	274	26	,	,	PUNCT
cana-3299	274	27	0.30,0.70	0.30,0.70	PRON
cana-3299	274	28	>	>	PUNCT
cana-3299	274	29	}	}	PUNCT
cana-3299	274	30	𝐵1	𝐵1	NOUN
cana-3299	274	31	=	=	PUNCT
cana-3299	274	32	{	{	PUNCT
cana-3299	274	33	<	<	X
cana-3299	274	34	𝑥1	𝑥1	PROPN
cana-3299	274	35	,	,	PUNCT
cana-3299	274	36	0.20,0.80	0.20,0.80	NOUN
cana-3299	274	37	>	>	X
cana-3299	274	38	,	,	PUNCT
cana-3299	274	39	<	<	X
cana-3299	274	40	𝑥2	𝑥2	NOUN
cana-3299	274	41	,	,	PUNCT
cana-3299	274	42	0.30,0.60	0.30,0.60	PROPN
cana-3299	274	43	>	>	X
cana-3299	274	44	}	}	PUNCT
cana-3299	274	45	now	now	ADV
cana-3299	274	46	,	,	PUNCT
cana-3299	274	47	we	we	PRON
cana-3299	274	48	have	have	VERB
cana-3299	274	49	γ𝑃	γ𝑃	ADJ
cana-3299	274	50	=	=	PUNCT
cana-3299	274	51	{	{	PUNCT
cana-3299	274	52	0𝑋	0𝑋	PROPN
cana-3299	274	53	,	,	PUNCT
cana-3299	274	54	1𝑋	1𝑋	PROPN
cana-3299	274	55	,	,	PUNCT
cana-3299	274	56	𝐴1	𝐴1	PROPN
cana-3299	274	57	,	,	PUNCT
cana-3299	274	58	𝐴2	𝐴2	PROPN
cana-3299	274	59	,	,	PUNCT
cana-3299	274	60	𝐴3	𝐴3	PROPN
cana-3299	274	61	,	,	PUNCT
cana-3299	274	62	𝐴4	𝐴4	PROPN
cana-3299	274	63	}	}	PUNCT
cana-3299	274	64	and	and	CCONJ
cana-3299	274	65	ψ𝑃	ψ𝑃	PROPN
cana-3299	274	66	=	=	SYM
cana-3299	274	67	{	{	PUNCT
cana-3299	274	68	0𝑋	0𝑋	PROPN
cana-3299	274	69	,	,	PUNCT
cana-3299	274	70	1𝑋	1𝑋	PROPN
cana-3299	274	71	,	,	PUNCT
cana-3299	274	72	𝐵1	𝐵1	PROPN
cana-3299	274	73	}	}	PUNCT
cana-3299	274	74	.	.	PUNCT
cana-3299	275	1	let	let	VERB
cana-3299	275	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	275	3	:	:	PUNCT
cana-3299	275	4	(	(	PUNCT
cana-3299	275	5	𝑋1	𝑋1	NOUN
cana-3299	275	6	,	,	PUNCT
cana-3299	275	7	γ𝑃	γ𝑃	NOUN
cana-3299	275	8	)	)	PUNCT
cana-3299	275	9	→	→	SYM
cana-3299	275	10	(	(	PUNCT
cana-3299	275	11	𝑋2	𝑋2	ADJ
cana-3299	275	12	,	,	PUNCT
cana-3299	275	13	ψ𝑃	ψ𝑃	NOUN
cana-3299	275	14	)	)	PUNCT
cana-3299	275	15	be	be	VERB
cana-3299	275	16	an	an	DET
cana-3299	275	17	identity	identity	NOUN
cana-3299	275	18	mapping	mapping	NOUN
cana-3299	275	19	.	.	PUNCT
cana-3299	276	1	then	then	ADV
cana-3299	276	2	,	,	PUNCT
cana-3299	276	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	276	4	is	be	AUX
cana-3299	276	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	276	6	but	but	CCONJ
cana-3299	276	7	not	not	PART
cana-3299	276	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	276	9	,	,	PUNCT
cana-3299	276	10	because	because	SCONJ
cana-3299	276	11	the	the	DET
cana-3299	276	12	set	set	NOUN
cana-3299	276	13	𝐵1	𝐵1	NOUN
cana-3299	276	14	is	be	AUX
cana-3299	276	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	276	16	in	in	ADP
cana-3299	276	17	𝑋2	𝑋2	ADJ
cana-3299	276	18	but	but	CCONJ
cana-3299	276	19	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	276	20	−1(𝐵1	−1(𝐵1	VERB
cana-3299	276	21	)	)	PUNCT
cana-3299	277	1	=	=	NOUN
cana-3299	277	2	𝐵1	𝐵1	NOUN
cana-3299	277	3	is	be	AUX
cana-3299	277	4	not	not	PART
cana-3299	277	5	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-3299	277	6	in	in	ADP
cana-3299	277	7	𝑋1	𝑋1	PROPN
cana-3299	277	8	.	.	PUNCT
cana-3299	278	1	theorem	theorem	VERB
cana-3299	278	2	3.1	3.1	NUM
cana-3299	278	3	a	a	DET
cana-3299	278	4	map	map	NOUN
cana-3299	278	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	278	6	:	:	PUNCT
cana-3299	278	7	(	(	PUNCT
cana-3299	278	8	𝑋1	𝑋1	PROPN
cana-3299	278	9	,	,	PUNCT
cana-3299	278	10	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	278	11	)	)	PUNCT
cana-3299	278	12	→	→	PUNCT
cana-3299	278	13	(	(	PUNCT
cana-3299	278	14	𝑋2	𝑋2	PROPN
cana-3299	278	15	,	,	PUNCT
cana-3299	278	16	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	278	17	)	)	PUNCT
cana-3299	278	18	is	be	AUX
cana-3299	278	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	278	20	(	(	PUNCT
cana-3299	278	21	resp	resp	NOUN
cana-3299	278	22	.	.	PUNCT
cana-3299	279	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NUM
cana-3299	279	2	,	,	PUNCT
cana-3299	279	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-3299	279	4	,	,	PUNCT
cana-3299	279	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	279	6	,	,	PUNCT
cana-3299	279	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	279	8	,	,	PUNCT
cana-3299	279	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	279	10	,	,	PUNCT
cana-3299	279	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PRON
cana-3299	279	12	and	and	CCONJ
cana-3299	279	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	279	14	)	)	PUNCT
cana-3299	280	1	iff	iff	VERB
cana-3299	280	2	the	the	DET
cana-3299	280	3	inverse	inverse	ADJ
cana-3299	280	4	image	image	NOUN
cana-3299	280	5	of	of	ADP
cana-3299	280	6	each	each	DET
cana-3299	280	7	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	280	8	in	in	ADP
cana-3299	280	9	(	(	PUNCT
cana-3299	280	10	𝑋2	𝑋2	PROPN
cana-3299	280	11	,	,	PUNCT
cana-3299	280	12	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	280	13	)	)	PUNCT
cana-3299	280	14	is	be	AUX
cana-3299	280	15	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	280	16	(	(	PUNCT
cana-3299	280	17	resp	resp	NOUN
cana-3299	280	18	.	.	PUNCT
cana-3299	281	1	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	PROPN
cana-3299	281	2	,	,	PUNCT
cana-3299	281	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-3299	281	4	,	,	PUNCT
cana-3299	281	5	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	281	6	,	,	PUNCT
cana-3299	281	7	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-3299	281	8	,	,	PUNCT
cana-3299	281	9	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	281	10	,	,	PUNCT
cana-3299	281	11	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	281	12	and	and	CCONJ
cana-3299	281	13	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	281	14	)	)	PUNCT
cana-3299	281	15	in	in	ADP
cana-3299	281	16	(	(	PUNCT
cana-3299	281	17	𝑋1	𝑋1	PROPN
cana-3299	281	18	,	,	PUNCT
cana-3299	281	19	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	281	20	)	)	PUNCT
cana-3299	281	21	.	.	PUNCT
cana-3299	282	1	proof	proof	NOUN
cana-3299	282	2	.	.	PUNCT
cana-3299	283	1	let	let	VERB
cana-3299	283	2	𝐵	𝐵	PRON
cana-3299	283	3	be	be	AUX
cana-3299	283	4	a	a	DET
cana-3299	283	5	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	283	6	in	in	ADP
cana-3299	283	7	(	(	PUNCT
cana-3299	283	8	𝑋2	𝑋2	ADJ
cana-3299	283	9	,	,	PUNCT
cana-3299	283	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	283	11	)	)	PUNCT
cana-3299	283	12	.	.	PUNCT
cana-3299	284	1	this	this	PRON
cana-3299	284	2	implies	imply	VERB
cana-3299	284	3	𝐵𝑐	𝐵𝑐	PROPN
cana-3299	284	4	is	be	AUX
cana-3299	284	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	284	6	in	in	ADP
cana-3299	284	7	(	(	PUNCT
cana-3299	284	8	𝑋2	𝑋2	ADJ
cana-3299	284	9	,	,	PUNCT
cana-3299	284	10	ψ𝑃	ψ𝑃	NOUN
cana-3299	284	11	)	)	PUNCT
cana-3299	284	12	.	.	PUNCT
cana-3299	285	1	since	since	SCONJ
cana-3299	285	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	285	3	is	be	AUX
cana-3299	285	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	285	5	,	,	PUNCT
cana-3299	285	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	285	7	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-3299	285	8	)	)	PUNCT
cana-3299	285	9	is	be	AUX
cana-3299	285	10	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	285	11	in	in	ADP
cana-3299	285	12	(	(	PUNCT
cana-3299	285	13	𝑋1	𝑋1	NOUN
cana-3299	285	14	,	,	PUNCT
cana-3299	285	15	γ𝑃	γ𝑃	NOUN
cana-3299	285	16	)	)	PUNCT
cana-3299	285	17	.	.	PUNCT
cana-3299	286	1	since	since	SCONJ
cana-3299	286	2	,	,	PUNCT
cana-3299	286	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	286	4	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-3299	286	5	)	)	PUNCT
cana-3299	287	1	=	=	PRON
cana-3299	288	1	(	(	PUNCT
cana-3299	288	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	288	3	−1(𝐵))𝑐	−1(𝐵))𝑐	PROPN
cana-3299	288	4	,	,	PUNCT
cana-3299	288	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	288	6	−1(𝐵	−1(𝐵	NOUN
cana-3299	288	7	)	)	PUNCT
cana-3299	288	8	is	be	AUX
cana-3299	288	9	a	a	DET
cana-3299	288	10	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	288	11	in	in	ADP
cana-3299	288	12	(	(	PUNCT
cana-3299	288	13	𝑋1	𝑋1	NOUN
cana-3299	288	14	,	,	PUNCT
cana-3299	288	15	γ𝑃	γ𝑃	NOUN
cana-3299	288	16	)	)	PUNCT
cana-3299	288	17	.	.	PUNCT
cana-3299	289	1	conversely	conversely	ADV
cana-3299	289	2	,	,	PUNCT
cana-3299	289	3	let	let	VERB
cana-3299	289	4	𝐵	𝐵	PRON
cana-3299	289	5	be	be	AUX
cana-3299	289	6	a	a	DET
cana-3299	289	7	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	289	8	in	in	ADP
cana-3299	289	9	(	(	PUNCT
cana-3299	289	10	𝑋2	𝑋2	ADJ
cana-3299	289	11	,	,	PUNCT
cana-3299	289	12	ψ𝑃	ψ𝑃	NOUN
cana-3299	289	13	)	)	PUNCT
cana-3299	289	14	.	.	PUNCT
cana-3299	290	1	then	then	ADV
cana-3299	290	2	,	,	PUNCT
cana-3299	290	3	𝐵𝑐	𝐵𝑐	PROPN
cana-3299	290	4	is	be	AUX
cana-3299	290	5	a	a	DET
cana-3299	290	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	290	7	in	in	ADP
cana-3299	290	8	(	(	PUNCT
cana-3299	290	9	𝑋2	𝑋2	ADJ
cana-3299	290	10	,	,	PUNCT
cana-3299	290	11	ψ𝑃	ψ𝑃	NOUN
cana-3299	290	12	)	)	PUNCT
cana-3299	290	13	.	.	PUNCT
cana-3299	291	1	by	by	ADP
cana-3299	291	2	hypothesis	hypothesis	NOUN
cana-3299	291	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	291	4	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-3299	291	5	)	)	PUNCT
cana-3299	291	6	is	be	AUX
cana-3299	291	7	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	291	8	in	in	ADP
cana-3299	291	9	(	(	PUNCT
cana-3299	291	10	𝑋1	𝑋1	NOUN
cana-3299	291	11	,	,	PUNCT
cana-3299	291	12	γ𝑃	γ𝑃	NOUN
cana-3299	291	13	)	)	PUNCT
cana-3299	291	14	.	.	PUNCT
cana-3299	292	1	since	since	SCONJ
cana-3299	292	2	,	,	PUNCT
cana-3299	292	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	292	4	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-3299	292	5	)	)	PUNCT
cana-3299	293	1	=	=	PRON
cana-3299	294	1	(	(	PUNCT
cana-3299	294	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	294	3	−1(𝐵))𝑐	−1(𝐵))𝑐	PROPN
cana-3299	294	4	,	,	PUNCT
cana-3299	294	5	(	(	PUNCT
cana-3299	294	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	294	7	−1(𝐵))𝑐	−1(𝐵))𝑐	PRON
cana-3299	294	8	is	be	AUX
cana-3299	294	9	a	a	DET
cana-3299	294	10	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	294	11	in	in	ADP
cana-3299	294	12	(	(	PUNCT
cana-3299	294	13	𝑋1	𝑋1	NOUN
cana-3299	294	14	,	,	PUNCT
cana-3299	294	15	γ𝑃	γ𝑃	NOUN
cana-3299	294	16	)	)	PUNCT
cana-3299	294	17	.	.	PUNCT
cana-3299	295	1	therefore	therefore	ADV
cana-3299	295	2	,	,	PUNCT
cana-3299	295	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	295	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	295	5	)	)	PUNCT
cana-3299	295	6	is	be	AUX
cana-3299	295	7	a	a	DET
cana-3299	295	8	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	295	9	in	in	ADP
cana-3299	295	10	(	(	PUNCT
cana-3299	295	11	𝑋1	𝑋1	NOUN
cana-3299	295	12	,	,	PUNCT
cana-3299	295	13	γ𝑃	γ𝑃	NOUN
cana-3299	295	14	)	)	PUNCT
cana-3299	295	15	.	.	PUNCT
cana-3299	296	1	hence	hence	ADV
cana-3299	296	2	,	,	PUNCT
cana-3299	296	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	296	4	is	be	AUX
cana-3299	296	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	PROPN
cana-3299	296	6	the	the	DET
cana-3299	296	7	proof	proof	NOUN
cana-3299	296	8	of	of	ADP
cana-3299	296	9	other	other	ADJ
cana-3299	296	10	cases	case	NOUN
cana-3299	296	11	are	be	AUX
cana-3299	296	12	similar	similar	ADJ
cana-3299	296	13	definition	definition	NOUN
cana-3299	296	14	3.2	3.2	NUM
cana-3299	296	15	a	a	DET
cana-3299	296	16	𝑝𝑓𝑡𝑠	𝑝𝑓𝑡𝑠	NOUN
cana-3299	296	17	(	(	PUNCT
cana-3299	296	18	𝑋1	𝑋1	PROPN
cana-3299	296	19	,	,	PUNCT
cana-3299	296	20	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	296	21	)	)	PUNCT
cana-3299	296	22	is	be	AUX
cana-3299	296	23	said	say	VERB
cana-3299	296	24	to	to	PART
cana-3299	296	25	be	be	AUX
cana-3299	296	26	a	a	DET
cana-3299	296	27	pythagorean	pythagorean	ADJ
cana-3299	296	28	fuzzy	fuzzy	ADJ
cana-3299	296	29	𝑀𝑈1/2	𝑀𝑈1/2	ADJ
cana-3299	296	30	(	(	PUNCT
cana-3299	296	31	resp.𝑝𝑓𝛿𝒮𝑈1/2	resp.𝑝𝑓𝛿𝒮𝑈1/2	ADJ
cana-3299	296	32	,	,	PUNCT
cana-3299	296	33	𝑝𝑓𝛿𝒫𝑈1/2	𝑝𝑓𝛿𝒫𝑈1/2	ADJ
cana-3299	296	34	,	,	PUNCT
cana-3299	296	35	𝑝𝑓𝜃𝑈1/2	𝑝𝑓𝜃𝑈1/2	PROPN
cana-3299	296	36	,	,	PUNCT
cana-3299	296	37	𝑝𝑓𝑒𝑈1/2	𝑝𝑓𝑒𝑈1/2	ADJ
cana-3299	296	38	and	and	CCONJ
cana-3299	296	39	𝑝𝑓𝜃𝒮𝑈1/2	𝑝𝑓𝜃𝒮𝑈1/2	ADJ
cana-3299	296	40	)	)	PUNCT
cana-3299	296	41	-space	-space	NOUN
cana-3299	296	42	,	,	PUNCT
cana-3299	296	43	if	if	SCONJ
cana-3299	296	44	every	every	DET
cana-3299	296	45	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	296	46	(	(	PUNCT
cana-3299	296	47	resp	resp	NOUN
cana-3299	296	48	.	.	PUNCT
cana-3299	297	1	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	297	2	,	,	PUNCT
cana-3299	297	3	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PRON
cana-3299	297	4	,	,	PUNCT
cana-3299	297	5	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	297	6	,	,	PUNCT
cana-3299	297	7	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	297	8	and	and	CCONJ
cana-3299	297	9	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	PROPN
cana-3299	297	10	)	)	PUNCT
cana-3299	297	11	in	in	ADP
cana-3299	297	12	𝑋1	𝑋1	PROPN
cana-3299	297	13	is	be	AUX
cana-3299	297	14	a	a	DET
cana-3299	297	15	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	297	16	in	in	ADP
cana-3299	297	17	𝑋1	𝑋1	PROPN
cana-3299	297	18	.	.	PUNCT
cana-3299	298	1	theorem	theorem	ADJ
cana-3299	298	2	3.2	3.2	NUM
cana-3299	298	3	let	let	VERB
cana-3299	298	4	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	298	5	:	:	PUNCT
cana-3299	298	6	(	(	PUNCT
cana-3299	298	7	𝑋1	𝑋1	PROPN
cana-3299	298	8	,	,	PUNCT
cana-3299	298	9	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	298	10	)	)	PUNCT
cana-3299	298	11	→	→	PUNCT
cana-3299	298	12	(	(	PUNCT
cana-3299	298	13	𝑋2	𝑋2	PROPN
cana-3299	298	14	,	,	PUNCT
cana-3299	298	15	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	298	16	)	)	PUNCT
cana-3299	298	17	be	be	AUX
cana-3299	298	18	a	a	DET
cana-3299	298	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	298	20	(	(	PUNCT
cana-3299	298	21	resp	resp	NOUN
cana-3299	298	22	.	.	PUNCT
cana-3299	299	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	299	2	,	,	PUNCT
cana-3299	299	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	299	4	,	,	PUNCT
cana-3299	299	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	299	6	,	,	PUNCT
cana-3299	299	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PRON
cana-3299	299	8	and	and	CCONJ
cana-3299	299	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	299	10	)	)	PUNCT
cana-3299	299	11	,	,	PUNCT
cana-3299	299	12	then	then	ADV
cana-3299	299	13	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	299	14	is	be	AUX
cana-3299	299	15	a	a	DET
cana-3299	299	16	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	299	17	if	if	SCONJ
cana-3299	299	18	𝑋1	𝑋1	PROPN
cana-3299	299	19	is	be	AUX
cana-3299	299	20	a	a	DET
cana-3299	299	21	𝑝𝑓𝑀𝑈1/2	𝑝𝑓𝑀𝑈1/2	NOUN
cana-3299	299	22	)	)	PUNCT
cana-3299	299	23	(	(	PUNCT
cana-3299	299	24	resp	resp	NOUN
cana-3299	299	25	.	.	PUNCT
cana-3299	299	26	𝑝𝑓𝛿𝒮𝑈1/2	𝑝𝑓𝛿𝒮𝑈1/2	PROPN
cana-3299	299	27	,	,	PUNCT
cana-3299	299	28	𝑝𝑓𝛿𝒫𝑈1/2	𝑝𝑓𝛿𝒫𝑈1/2	NOUN
cana-3299	299	29	,	,	PUNCT
cana-3299	299	30	𝑝𝑓𝜃𝑈1/2	𝑝𝑓𝜃𝑈1/2	PROPN
cana-3299	299	31	,	,	PUNCT
cana-3299	299	32	𝑝𝑓𝑒𝑈1/2	𝑝𝑓𝑒𝑈1/2	ADJ
cana-3299	299	33	and	and	CCONJ
cana-3299	299	34	𝑝𝑓𝜃𝒮𝑈1/2	𝑝𝑓𝜃𝒮𝑈1/2	ADJ
cana-3299	299	35	)	)	PUNCT
cana-3299	299	36	-space	-space	NOUN
cana-3299	299	37	.	.	PUNCT
cana-3299	300	1	communications	communication	NOUN
cana-3299	300	2	on	on	ADP
cana-3299	300	3	applied	apply	VERB
cana-3299	300	4	nonlinear	nonlinear	ADJ
cana-3299	300	5	analysis	analysis	NOUN
cana-3299	300	6	issn	issn	NOUN
cana-3299	300	7	:	:	PUNCT
cana-3299	300	8	1074	1074	NUM
cana-3299	300	9	-	-	PUNCT
cana-3299	300	10	133x	133x	NUM
cana-3299	300	11	vol	vol	NOUN
cana-3299	300	12	32	32	NUM
cana-3299	300	13	no	no	NOUN
cana-3299	300	14	.	.	PUNCT
cana-3299	301	1	6s	6s	NUM
cana-3299	301	2	(	(	PUNCT
cana-3299	301	3	2025	2025	NUM
cana-3299	301	4	)	)	PUNCT
cana-3299	301	5	335	335	NUM
cana-3299	302	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	302	2	proof	proof	NOUN
cana-3299	302	3	.	.	PUNCT
cana-3299	303	1	let	let	VERB
cana-3299	303	2	𝐵	𝐵	PRON
cana-3299	303	3	be	be	AUX
cana-3299	303	4	a	a	DET
cana-3299	303	5	𝑃𝑓𝑜𝑠	𝑃𝑓𝑜𝑠	PROPN
cana-3299	303	6	in	in	ADP
cana-3299	303	7	𝑋2	𝑋2	PROPN
cana-3299	303	8	.	.	PUNCT
cana-3299	304	1	then	then	ADV
cana-3299	304	2	,	,	PUNCT
cana-3299	304	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	304	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	304	5	)	)	PUNCT
cana-3299	304	6	is	be	AUX
cana-3299	304	7	a	a	DET
cana-3299	304	8	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	304	9	in	in	ADP
cana-3299	304	10	𝑋1	𝑋1	PROPN
cana-3299	304	11	,	,	PUNCT
cana-3299	304	12	by	by	ADP
cana-3299	304	13	hypothesis	hypothesis	NOUN
cana-3299	304	14	.	.	PUNCT
cana-3299	305	1	since	since	SCONJ
cana-3299	305	2	𝑋1	𝑋1	PROPN
cana-3299	305	3	is	be	AUX
cana-3299	305	4	a	a	DET
cana-3299	305	5	𝑝𝑓𝑀𝑈1/2space	𝑝𝑓𝑀𝑈1/2space	PROPN
cana-3299	305	6	,	,	PUNCT
cana-3299	305	7	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	305	8	−1(𝐵	−1(𝐵	NOUN
cana-3299	305	9	)	)	PUNCT
cana-3299	305	10	is	be	AUX
cana-3299	305	11	a	a	DET
cana-3299	305	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	305	13	in	in	ADP
cana-3299	305	14	𝑋1	𝑋1	PROPN
cana-3299	305	15	.	.	PUNCT
cana-3299	306	1	hence	hence	ADV
cana-3299	306	2	,	,	PUNCT
cana-3299	306	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	306	4	is	be	AUX
cana-3299	306	5	a	a	DET
cana-3299	306	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠.	NOUN
cana-3299	306	7	the	the	DET
cana-3299	306	8	proof	proof	NOUN
cana-3299	306	9	of	of	ADP
cana-3299	306	10	other	other	ADJ
cana-3299	306	11	cases	case	NOUN
cana-3299	306	12	are	be	AUX
cana-3299	306	13	similar	similar	ADJ
cana-3299	306	14	.	.	PUNCT
cana-3299	307	1	theorem	theorem	VERB
cana-3299	307	2	3.3	3.3	NUM
cana-3299	307	3	let	let	VERB
cana-3299	307	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	307	5	:	:	PUNCT
cana-3299	307	6	(	(	PUNCT
cana-3299	307	7	𝑋1	𝑋1	PROPN
cana-3299	307	8	,	,	PUNCT
cana-3299	307	9	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	307	10	)	)	PUNCT
cana-3299	307	11	→	→	PUNCT
cana-3299	307	12	(	(	PUNCT
cana-3299	307	13	𝑋2	𝑋2	PROPN
cana-3299	307	14	,	,	PUNCT
cana-3299	307	15	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	307	16	)	)	PUNCT
cana-3299	307	17	be	be	VERB
cana-3299	307	18	a	a	DET
cana-3299	307	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	307	20	map	map	NOUN
cana-3299	307	21	and	and	CCONJ
cana-3299	307	22	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	307	23	:	:	PUNCT
cana-3299	307	24	(	(	PUNCT
cana-3299	307	25	𝑋2	𝑋2	PROPN
cana-3299	307	26	,	,	PUNCT
cana-3299	307	27	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	307	28	)	)	PUNCT
cana-3299	307	29	→	→	SYM
cana-3299	307	30	(	(	PUNCT
cana-3299	307	31	𝑋3	𝑋3	NOUN
cana-3299	307	32	,	,	PUNCT
cana-3299	307	33	𝛷𝑃	𝛷𝑃	PROPN
cana-3299	307	34	)	)	PUNCT
cana-3299	307	35	be	be	VERB
cana-3299	307	36	a	a	DET
cana-3299	307	37	𝑝𝑓𝐶𝑡𝑠	𝑝𝑓𝐶𝑡𝑠	NOUN
cana-3299	307	38	,	,	PUNCT
cana-3299	307	39	then	then	ADV
cana-3299	307	40	𝑔𝑃	𝑔𝑃	ADP
cana-3299	307	41	∘	∘	PROPN
cana-3299	307	42	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	307	43	:	:	PUNCT
cana-3299	307	44	(	(	PUNCT
cana-3299	307	45	𝑋1	𝑋1	PROPN
cana-3299	307	46	,	,	PUNCT
cana-3299	307	47	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	307	48	)	)	PUNCT
cana-3299	307	49	→	→	SYM
cana-3299	307	50	(	(	PUNCT
cana-3299	307	51	𝑋3	𝑋3	NOUN
cana-3299	307	52	,	,	PUNCT
cana-3299	307	53	𝛷𝑃	𝛷𝑃	PROPN
cana-3299	307	54	)	)	PUNCT
cana-3299	307	55	is	be	AUX
cana-3299	307	56	a	a	DET
cana-3299	307	57	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠.	PROPN
cana-3299	307	58	proof	proof	NOUN
cana-3299	307	59	.	.	PUNCT
cana-3299	308	1	let	let	VERB
cana-3299	308	2	𝐾	𝐾	PRON
cana-3299	308	3	be	be	AUX
cana-3299	308	4	a	a	DET
cana-3299	308	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	308	6	in	in	ADP
cana-3299	308	7	𝑋3	𝑋3	NOUN
cana-3299	308	8	.	.	PUNCT
cana-3299	309	1	then	then	ADV
cana-3299	309	2	,	,	PUNCT
cana-3299	309	3	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	309	4	−1(𝐾	−1(𝐾	NOUN
cana-3299	309	5	)	)	PUNCT
cana-3299	309	6	is	be	AUX
cana-3299	309	7	a	a	DET
cana-3299	309	8	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	309	9	in	in	ADP
cana-3299	309	10	𝑋2	𝑋2	ADJ
cana-3299	309	11	,	,	PUNCT
cana-3299	309	12	by	by	ADP
cana-3299	309	13	hypothesis	hypothesis	NOUN
cana-3299	309	14	.	.	PUNCT
cana-3299	310	1	since	since	SCONJ
cana-3299	310	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	310	3	is	be	AUX
cana-3299	310	4	a	a	DET
cana-3299	310	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	310	6	map	map	NOUN
cana-3299	310	7	,	,	PUNCT
cana-3299	310	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	310	9	−1(𝑔𝑃	−1(𝑔𝑃	NOUN
cana-3299	310	10	−1(𝐾	−1(𝐾	NOUN
cana-3299	310	11	)	)	PUNCT
cana-3299	310	12	)	)	PUNCT
cana-3299	310	13	is	be	AUX
cana-3299	310	14	a	a	DET
cana-3299	310	15	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	310	16	in	in	ADP
cana-3299	310	17	𝑋1	𝑋1	PROPN
cana-3299	310	18	.	.	PUNCT
cana-3299	311	1	hence	hence	ADV
cana-3299	311	2	𝑔𝑃	𝑔𝑃	VERB
cana-3299	311	3	∘	∘	PROPN
cana-3299	311	4	𝑓𝑃	𝑓𝑃	PROPN
cana-3299	311	5	is	be	AUX
cana-3299	311	6	a	a	DET
cana-3299	311	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	311	8	map	map	NOUN
cana-3299	311	9	.	.	PUNCT
cana-3299	312	1	the	the	DET
cana-3299	312	2	proof	proof	NOUN
cana-3299	312	3	of	of	ADP
cana-3299	312	4	other	other	ADJ
cana-3299	312	5	cases	case	NOUN
cana-3299	312	6	are	be	AUX
cana-3299	312	7	similar	similar	ADJ
cana-3299	312	8	.	.	PUNCT
cana-3299	313	1	theorem	theorem	VERB
cana-3299	313	2	3.4	3.4	NUM
cana-3299	313	3	let	let	VERB
cana-3299	313	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	313	5	:	:	PUNCT
cana-3299	313	6	(	(	PUNCT
cana-3299	313	7	𝑋1	𝑋1	PROPN
cana-3299	313	8	,	,	PUNCT
cana-3299	313	9	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	313	10	)	)	PUNCT
cana-3299	313	11	→	→	PUNCT
cana-3299	313	12	(	(	PUNCT
cana-3299	313	13	𝑋2	𝑋2	PROPN
cana-3299	313	14	,	,	PUNCT
cana-3299	313	15	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	313	16	)	)	PUNCT
cana-3299	313	17	be	be	VERB
cana-3299	313	18	a	a	DET
cana-3299	313	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	313	20	map	map	NOUN
cana-3299	313	21	.	.	PUNCT
cana-3299	314	1	then	then	ADV
cana-3299	314	2	,	,	PUNCT
cana-3299	314	3	the	the	DET
cana-3299	314	4	following	follow	VERB
cana-3299	314	5	conditions	condition	NOUN
cana-3299	314	6	are	be	AUX
cana-3299	314	7	hold	hold	ADJ
cana-3299	314	8	.	.	PUNCT
cana-3299	315	1	1	1	X
cana-3299	315	2	.	.	X
cana-3299	315	3	ℎ𝑃(𝑝𝑓𝑀𝑐𝑙(𝐴	ℎ𝑃(𝑝𝑓𝑀𝑐𝑙(𝐴	ADJ
cana-3299	315	4	)	)	PUNCT
cana-3299	315	5	)	)	PUNCT
cana-3299	315	6	≥	≥	NOUN
cana-3299	315	7	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(𝐴	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(𝐴	NUM
cana-3299	315	8	)	)	PUNCT
cana-3299	315	9	)	)	PUNCT
cana-3299	315	10	,	,	PUNCT
cana-3299	315	11	for	for	ADP
cana-3299	315	12	all	all	DET
cana-3299	315	13	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	315	14	𝐴	𝐴	PROPN
cana-3299	315	15	in	in	ADP
cana-3299	315	16	𝑋1	𝑋1	PROPN
cana-3299	315	17	.	.	PUNCT
cana-3299	316	1	2	2	NUM
cana-3299	316	2	.	.	X
cana-3299	316	3	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃	ADJ
cana-3299	316	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	316	5	)	)	PUNCT
cana-3299	316	6	)	)	PUNCT
cana-3299	317	1	≥	≥	NOUN
cana-3299	317	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	317	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	NUM
cana-3299	317	4	)	)	PUNCT
cana-3299	317	5	)	)	PUNCT
cana-3299	318	1	,	,	PUNCT
cana-3299	318	2	for	for	ADP
cana-3299	318	3	all	all	DET
cana-3299	318	4	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	PROPN
cana-3299	318	5	𝐵	𝐵	NOUN
cana-3299	318	6	in	in	ADP
cana-3299	318	7	𝑋2	𝑋2	ADJ
cana-3299	318	8	.	.	PUNCT
cana-3299	319	1	proof	proof	NOUN
cana-3299	319	2	.	.	PUNCT
cana-3299	320	1	1	1	X
cana-3299	320	2	.	.	X
cana-3299	320	3	since	since	SCONJ
cana-3299	320	4	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃(𝐴	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃(𝐴	PROPN
cana-3299	320	5	)	)	PUNCT
cana-3299	320	6	)	)	PUNCT
cana-3299	320	7	is	be	AUX
cana-3299	320	8	a	a	DET
cana-3299	320	9	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	320	10	in	in	ADP
cana-3299	320	11	𝑋2	𝑋2	ADJ
cana-3299	320	12	and	and	CCONJ
cana-3299	320	13	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	320	14	is	be	AUX
cana-3299	320	15	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	320	16	,	,	PUNCT
cana-3299	320	17	then	then	ADV
cana-3299	320	18	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	320	19	−1(𝑝𝑓𝑀𝑐𝑙(ℎ𝑃(𝐴	−1(𝑝𝑓𝑀𝑐𝑙(ℎ𝑃(𝐴	PROPN
cana-3299	320	20	)	)	PUNCT
cana-3299	320	21	)	)	PUNCT
cana-3299	320	22	)	)	PUNCT
cana-3299	321	1	is	be	AUX
cana-3299	321	2	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	321	3	in	in	ADP
cana-3299	321	4	𝑋1	𝑋1	PROPN
cana-3299	321	5	.	.	PUNCT
cana-3299	322	1	now	now	ADV
cana-3299	322	2	,	,	PUNCT
cana-3299	322	3	since	since	SCONJ
cana-3299	322	4	𝐴	𝐴	PROPN
cana-3299	322	5	≥	≥	PRON
cana-3299	322	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	322	7	−1(𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(𝐴	−1(𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(𝐴	PROPN
cana-3299	322	8	)	)	PUNCT
cana-3299	322	9	)	)	PUNCT
cana-3299	322	10	)	)	PUNCT
cana-3299	322	11	,	,	PUNCT
cana-3299	322	12	𝑝𝑓𝑀𝑐𝑙(𝐴	𝑝𝑓𝑀𝑐𝑙(𝐴	X
cana-3299	322	13	)	)	PUNCT
cana-3299	322	14	≥	≥	NOUN
cana-3299	322	15	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	322	16	−1(𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐴	−1(𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃(𝐴	NOUN
cana-3299	322	17	)	)	PUNCT
cana-3299	322	18	)	)	PUNCT
cana-3299	322	19	)	)	PUNCT
cana-3299	322	20	.	.	PUNCT
cana-3299	323	1	therefore	therefore	ADV
cana-3299	323	2	,	,	PUNCT
cana-3299	323	3	ℎ𝑃(𝑝𝑓𝑀𝑐𝑙(𝐴	ℎ𝑃(𝑝𝑓𝑀𝑐𝑙(𝐴	PROPN
cana-3299	323	4	)	)	PUNCT
cana-3299	323	5	)	)	PUNCT
cana-3299	323	6	≥	≥	NOUN
cana-3299	323	7	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(𝐴	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(𝐴	NUM
cana-3299	323	8	)	)	PUNCT
cana-3299	323	9	)	)	PUNCT
cana-3299	323	10	.	.	PUNCT
cana-3299	324	1	2	2	X
cana-3299	324	2	.	.	PUNCT
cana-3299	324	3	by	by	ADP
cana-3299	324	4	replacing	replace	VERB
cana-3299	324	5	𝐴	𝐴	PROPN
cana-3299	324	6	with	with	ADP
cana-3299	324	7	𝐵	𝐵	NOUN
cana-3299	324	8	in	in	ADP
cana-3299	324	9	(	(	PUNCT
cana-3299	324	10	i	i	NOUN
cana-3299	324	11	)	)	PUNCT
cana-3299	324	12	,	,	PUNCT
cana-3299	324	13	we	we	PRON
cana-3299	324	14	obtain	obtain	VERB
cana-3299	324	15	ℎ𝑃(𝑝𝑓𝑀𝑐𝑙(ℎ𝑃	ℎ𝑃(𝑝𝑓𝑀𝑐𝑙(ℎ𝑃	NOUN
cana-3299	324	16	−1(𝐵	−1(𝐵	NOUN
cana-3299	324	17	)	)	PUNCT
cana-3299	324	18	)	)	PUNCT
cana-3299	324	19	)	)	PUNCT
cana-3299	325	1	≥	≥	PROPN
cana-3299	325	2	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(ℎ𝑃	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃(ℎ𝑃	ADJ
cana-3299	325	3	−1(𝐵	−1(𝐵	NOUN
cana-3299	325	4	)	)	PUNCT
cana-3299	325	5	)	)	PUNCT
cana-3299	325	6	)	)	PUNCT
cana-3299	325	7	≥	≥	PROPN
cana-3299	325	8	𝑝𝑓𝑖𝑛𝑡(𝐵	𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	325	9	)	)	PUNCT
cana-3299	325	10	.	.	PUNCT
cana-3299	326	1	hence	hence	ADV
cana-3299	326	2	,	,	PUNCT
cana-3299	326	3	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃	𝑝𝑓𝑀𝑐𝑙(ℎ𝑃	ADJ
cana-3299	326	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	326	5	)	)	PUNCT
cana-3299	326	6	)	)	PUNCT
cana-3299	327	1	≥	≥	NOUN
cana-3299	327	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	327	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	NUM
cana-3299	327	4	)	)	PUNCT
cana-3299	327	5	)	)	PUNCT
cana-3299	327	6	.	.	PUNCT
cana-3299	328	1	remark	remark	VERB
cana-3299	328	2	3.2	3.2	NUM
cana-3299	328	3	theorems	theorem	NOUN
cana-3299	328	4	3.3	3.3	NUM
cana-3299	328	5	and	and	CCONJ
cana-3299	328	6	3.4	3.4	NUM
cana-3299	328	7	are	be	AUX
cana-3299	328	8	true	true	ADJ
cana-3299	328	9	for	for	ADP
cana-3299	328	10	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-3299	328	11	,	,	PUNCT
cana-3299	328	12	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	328	13	,	,	PUNCT
cana-3299	328	14	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	328	15	,	,	PUNCT
cana-3299	328	16	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	328	17	,	,	PUNCT
cana-3299	328	18	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PROPN
cana-3299	328	19	and	and	CCONJ
cana-3299	328	20	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠.	PROPN
cana-3299	328	21	4	4	NUM
cana-3299	328	22	pythagorean	pythagorean	NOUN
cana-3299	328	23	fuzzy	fuzzy	ADJ
cana-3299	328	24	contra	contra	PROPN
cana-3299	328	25	𝑴	𝑴	PROPN
cana-3299	328	26	-irresolute	-irresolute	PROPN
cana-3299	328	27	maps	map	NOUN
cana-3299	328	28	in	in	ADP
cana-3299	328	29	𝒑𝒇𝒕𝒔	𝒑𝒇𝒕𝒔	NOUN
cana-3299	328	30	in	in	ADP
cana-3299	328	31	this	this	DET
cana-3299	328	32	section	section	NOUN
cana-3299	328	33	,	,	PUNCT
cana-3299	328	34	we	we	PRON
cana-3299	328	35	introduce	introduce	VERB
cana-3299	328	36	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	328	37	(	(	PUNCT
cana-3299	328	38	resp	resp	NOUN
cana-3299	328	39	.	.	PUNCT
cana-3299	329	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-3299	329	2	,	,	PUNCT
cana-3299	329	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-3299	329	4	,	,	PUNCT
cana-3299	329	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	329	6	,	,	PUNCT
cana-3299	329	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	329	8	,	,	PUNCT
cana-3299	329	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	329	10	,	,	PUNCT
cana-3299	329	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	329	12	and	and	CCONJ
cana-3299	329	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	329	14	)	)	PUNCT
cana-3299	329	15	maps	map	NOUN
cana-3299	329	16	and	and	CCONJ
cana-3299	329	17	study	study	VERB
cana-3299	329	18	some	some	PRON
cana-3299	329	19	of	of	ADP
cana-3299	329	20	its	its	PRON
cana-3299	329	21	characterizations	characterization	NOUN
cana-3299	329	22	.	.	PUNCT
cana-3299	330	1	definition	definition	NOUN
cana-3299	330	2	4.1	4.1	NUM
cana-3299	330	3	a	a	DET
cana-3299	330	4	map	map	NOUN
cana-3299	330	5	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	330	6	:	:	PUNCT
cana-3299	330	7	(	(	PUNCT
cana-3299	330	8	𝑋1	𝑋1	PROPN
cana-3299	330	9	,	,	PUNCT
cana-3299	330	10	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	330	11	)	)	PUNCT
cana-3299	330	12	→	→	PUNCT
cana-3299	330	13	(	(	PUNCT
cana-3299	330	14	𝑋2	𝑋2	PROPN
cana-3299	330	15	,	,	PUNCT
cana-3299	330	16	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	330	17	)	)	PUNCT
cana-3299	330	18	is	be	AUX
cana-3299	330	19	called	call	VERB
cana-3299	330	20	a	a	DET
cana-3299	330	21	pythagorean	pythagorean	ADJ
cana-3299	330	22	fuzzy	fuzzy	ADJ
cana-3299	330	23	contra	contra	PROPN
cana-3299	330	24	𝑀	𝑀	PROPN
cana-3299	330	25	(	(	PUNCT
cana-3299	330	26	resp	resp	PROPN
cana-3299	330	27	.	.	PUNCT
cana-3299	331	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎	PROPN
cana-3299	331	2	,	,	PUNCT
cana-3299	331	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿	PROPN
cana-3299	331	4	,	,	PUNCT
cana-3299	331	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮	PROPN
cana-3299	331	6	,	,	PUNCT
cana-3299	331	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫	PROPN
cana-3299	331	8	,	,	PUNCT
cana-3299	331	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃	NOUN
cana-3299	331	10	,	,	PUNCT
cana-3299	331	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒	NOUN
cana-3299	331	12	and	and	CCONJ
cana-3299	331	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮	PROPN
cana-3299	331	14	)	)	PUNCT
cana-3299	331	15	irresolute	irresolute	NOUN
cana-3299	331	16	(	(	PUNCT
cana-3299	331	17	briefly	briefly	ADV
cana-3299	331	18	,	,	PUNCT
cana-3299	331	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	331	20	(	(	PUNCT
cana-3299	331	21	resp	resp	NOUN
cana-3299	331	22	.	.	PUNCT
cana-3299	332	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-3299	332	2	,	,	PUNCT
cana-3299	332	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-3299	332	4	,	,	PUNCT
cana-3299	332	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	332	6	,	,	PUNCT
cana-3299	332	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	332	8	,	,	PUNCT
cana-3299	332	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	332	10	,	,	PUNCT
cana-3299	332	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	332	12	and	and	CCONJ
cana-3299	332	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	332	14	)	)	PUNCT
cana-3299	332	15	)	)	PUNCT
cana-3299	332	16	map	map	NOUN
cana-3299	332	17	if	if	SCONJ
cana-3299	332	18	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	332	19	−1(𝐵	−1(𝐵	NOUN
cana-3299	332	20	)	)	PUNCT
cana-3299	332	21	is	be	AUX
cana-3299	332	22	a	a	DET
cana-3299	332	23	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	332	24	(	(	PUNCT
cana-3299	332	25	resp	resp	NOUN
cana-3299	332	26	.	.	PUNCT
cana-3299	333	1	𝑝𝑓𝒮𝑐𝑠	𝑝𝑓𝒮𝑐𝑠	NOUN
cana-3299	333	2	,	,	PUNCT
cana-3299	333	3	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	PROPN
cana-3299	333	4	,	,	PUNCT
cana-3299	333	5	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	333	6	,	,	PUNCT
cana-3299	333	7	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PROPN
cana-3299	333	8	,	,	PUNCT
cana-3299	333	9	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	333	10	,	,	PUNCT
cana-3299	333	11	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	333	12	and	and	CCONJ
cana-3299	333	13	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	NUM
cana-3299	333	14	)	)	PUNCT
cana-3299	334	1	in	in	ADP
cana-3299	334	2	(	(	PUNCT
cana-3299	334	3	𝑋1	𝑋1	PROPN
cana-3299	334	4	,	,	PUNCT
cana-3299	334	5	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	334	6	)	)	PUNCT
cana-3299	334	7	for	for	ADP
cana-3299	334	8	every	every	DET
cana-3299	334	9	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADJ
cana-3299	334	10	(	(	PUNCT
cana-3299	334	11	resp	resp	NOUN
cana-3299	334	12	.	.	PUNCT
cana-3299	334	13	𝑝𝑓𝒮𝑜𝑠	𝑝𝑓𝒮𝑜𝑠	PROPN
cana-3299	334	14	,	,	PUNCT
cana-3299	334	15	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	PROPN
cana-3299	334	16	,	,	PUNCT
cana-3299	334	17	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	334	18	,	,	PUNCT
cana-3299	334	19	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	PROPN
cana-3299	334	20	,	,	PUNCT
cana-3299	334	21	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	334	22	,	,	PUNCT
cana-3299	334	23	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	334	24	and	and	CCONJ
cana-3299	334	25	𝑝𝑓𝜃𝒮𝑜𝑠	𝑝𝑓𝜃𝒮𝑜𝑠	ADJ
cana-3299	334	26	)	)	PUNCT
cana-3299	334	27	𝐵	𝐵	NOUN
cana-3299	334	28	of	of	ADP
cana-3299	334	29	(	(	PUNCT
cana-3299	334	30	𝑋2	𝑋2	PROPN
cana-3299	334	31	,	,	PUNCT
cana-3299	334	32	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	334	33	)	)	PUNCT
cana-3299	334	34	.	.	PUNCT
cana-3299	335	1	theorem	theorem	VERB
cana-3299	335	2	4.1	4.1	NUM
cana-3299	335	3	let	let	VERB
cana-3299	335	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	335	5	:	:	PUNCT
cana-3299	335	6	(	(	PUNCT
cana-3299	335	7	𝑋1	𝑋1	PROPN
cana-3299	335	8	,	,	PUNCT
cana-3299	335	9	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	335	10	)	)	PUNCT
cana-3299	335	11	→	→	PUNCT
cana-3299	335	12	(	(	PUNCT
cana-3299	335	13	𝑋2	𝑋2	PROPN
cana-3299	335	14	,	,	PUNCT
cana-3299	335	15	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	335	16	)	)	PUNCT
cana-3299	335	17	be	be	AUX
cana-3299	335	18	a	a	DET
cana-3299	335	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-3299	335	20	(	(	PUNCT
cana-3299	335	21	resp	resp	NOUN
cana-3299	335	22	.	.	PUNCT
cana-3299	336	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	336	2	,	,	PUNCT
cana-3299	336	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NOUN
cana-3299	336	4	,	,	PUNCT
cana-3299	336	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	336	6	,	,	PUNCT
cana-3299	336	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	336	8	,	,	PUNCT
cana-3299	336	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	336	10	,	,	PUNCT
cana-3299	336	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	336	12	and	and	CCONJ
cana-3299	336	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	336	14	)	)	PUNCT
cana-3299	336	15	,	,	PUNCT
cana-3299	336	16	then	then	ADV
cana-3299	336	17	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	336	18	is	be	AUX
cana-3299	336	19	a	a	DET
cana-3299	336	20	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	NOUN
cana-3299	336	21	(	(	PUNCT
cana-3299	336	22	resp	resp	NOUN
cana-3299	336	23	.	.	PUNCT
cana-3299	337	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	PROPN
cana-3299	337	2	,	,	PUNCT
cana-3299	337	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NUM
cana-3299	337	4	,	,	PUNCT
cana-3299	337	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	337	6	,	,	PUNCT
cana-3299	337	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	337	8	,	,	PUNCT
cana-3299	337	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	NUM
cana-3299	337	10	,	,	PUNCT
cana-3299	337	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PRON
cana-3299	337	12	and	and	CCONJ
cana-3299	337	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	337	14	)	)	PUNCT
cana-3299	337	15	map	map	NOUN
cana-3299	337	16	.	.	PUNCT
cana-3299	338	1	but	but	CCONJ
cana-3299	338	2	not	not	PART
cana-3299	338	3	conversely	conversely	ADV
cana-3299	338	4	.	.	PUNCT
cana-3299	339	1	proof	proof	NOUN
cana-3299	339	2	.	.	PUNCT
cana-3299	340	1	(	(	PUNCT
cana-3299	340	2	i	i	NOUN
cana-3299	340	3	)	)	PUNCT
cana-3299	340	4	let	let	VERB
cana-3299	340	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	340	6	be	be	AUX
cana-3299	340	7	a	a	DET
cana-3299	340	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-3299	340	9	map	map	NOUN
cana-3299	340	10	.	.	PUNCT
cana-3299	341	1	let	let	VERB
cana-3299	341	2	𝐵	𝐵	PRON
cana-3299	341	3	be	be	AUX
cana-3299	341	4	any	any	DET
cana-3299	341	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	341	6	in	in	ADP
cana-3299	341	7	𝑋2	𝑋2	PROPN
cana-3299	341	8	.	.	PUNCT
cana-3299	342	1	since	since	SCONJ
cana-3299	342	2	every	every	DET
cana-3299	342	3	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	342	4	is	be	AUX
cana-3299	342	5	a	a	DET
cana-3299	342	6	𝑝𝑓𝒮𝑜𝑠	𝑝𝑓𝒮𝑜𝑠	NOUN
cana-3299	342	7	,	,	PUNCT
cana-3299	342	8	𝐵	𝐵	NOUN
cana-3299	342	9	is	be	AUX
cana-3299	342	10	a	a	DET
cana-3299	342	11	𝑝𝑓𝒮𝑜𝑠	𝑝𝑓𝒮𝑜𝑠	PROPN
cana-3299	342	12	in	in	ADP
cana-3299	342	13	𝑋2	𝑋2	PROPN
cana-3299	342	14	.	.	PUNCT
cana-3299	343	1	by	by	ADP
cana-3299	343	2	hypothesis	hypothesis	NOUN
cana-3299	343	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	343	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	343	5	)	)	PUNCT
cana-3299	343	6	is	be	AUX
cana-3299	343	7	a	a	DET
cana-3299	343	8	𝑝𝑓𝒮𝑐𝑠	𝑝𝑓𝒮𝑐𝑠	NOUN
cana-3299	343	9	in	in	ADP
cana-3299	343	10	𝑋1	𝑋1	PROPN
cana-3299	343	11	.	.	PUNCT
cana-3299	344	1	hence	hence	ADV
cana-3299	344	2	,	,	PUNCT
cana-3299	344	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	344	4	is	be	AUX
cana-3299	344	5	a	a	DET
cana-3299	344	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	NOUN
cana-3299	344	7	map	map	NOUN
cana-3299	344	8	.	.	PUNCT
cana-3299	345	1	(	(	PUNCT
cana-3299	345	2	ii	ii	NOUN
cana-3299	345	3	)	)	PUNCT
cana-3299	345	4	let	let	VERB
cana-3299	345	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	345	6	be	be	AUX
cana-3299	345	7	a	a	DET
cana-3299	345	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	345	9	map	map	NOUN
cana-3299	345	10	.	.	PUNCT
cana-3299	346	1	let	let	VERB
cana-3299	346	2	𝐵	𝐵	PRON
cana-3299	346	3	be	be	AUX
cana-3299	346	4	any	any	DET
cana-3299	346	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	346	6	in	in	ADP
cana-3299	346	7	𝑋2	𝑋2	PROPN
cana-3299	346	8	.	.	PUNCT
cana-3299	347	1	since	since	SCONJ
cana-3299	347	2	every	every	DET
cana-3299	347	3	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	347	4	is	be	AUX
cana-3299	347	5	a	a	DET
cana-3299	347	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	347	7	,	,	PUNCT
cana-3299	347	8	𝐵	𝐵	NOUN
cana-3299	347	9	is	be	AUX
cana-3299	347	10	a	a	DET
cana-3299	347	11	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	347	12	in	in	ADP
cana-3299	347	13	𝑋2	𝑋2	PROPN
cana-3299	347	14	.	.	PUNCT
cana-3299	348	1	by	by	ADP
cana-3299	348	2	hypothesis	hypothesis	NOUN
cana-3299	348	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	348	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	348	5	)	)	PUNCT
cana-3299	348	6	is	be	AUX
cana-3299	348	7	a	a	DET
cana-3299	348	8	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	348	9	in	in	ADP
cana-3299	348	10	𝑋1	𝑋1	PROPN
cana-3299	348	11	.	.	PUNCT
cana-3299	349	1	hence	hence	ADV
cana-3299	349	2	,	,	PUNCT
cana-3299	349	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	349	4	is	be	AUX
cana-3299	349	5	a	a	DET
cana-3299	349	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	349	7	map	map	NOUN
cana-3299	349	8	.	.	PUNCT
cana-3299	350	1	(	(	PUNCT
cana-3299	350	2	iii	iii	X
cana-3299	350	3	)	)	PUNCT
cana-3299	350	4	let	let	VERB
cana-3299	350	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	350	6	be	be	AUX
cana-3299	350	7	a	a	DET
cana-3299	350	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NOUN
cana-3299	350	9	map	map	NOUN
cana-3299	350	10	.	.	PUNCT
cana-3299	351	1	let	let	VERB
cana-3299	351	2	𝐵	𝐵	PRON
cana-3299	351	3	be	be	AUX
cana-3299	351	4	any	any	DET
cana-3299	351	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	351	6	in	in	ADP
cana-3299	351	7	𝑋2	𝑋2	PROPN
cana-3299	351	8	.	.	PUNCT
cana-3299	352	1	since	since	SCONJ
cana-3299	352	2	every	every	DET
cana-3299	352	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	352	4	is	be	AUX
cana-3299	352	5	a	a	DET
cana-3299	352	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	352	7	,	,	PUNCT
cana-3299	352	8	𝐵	𝐵	NOUN
cana-3299	352	9	is	be	AUX
cana-3299	352	10	a	a	DET
cana-3299	352	11	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	352	12	in	in	ADP
cana-3299	352	13	𝑋2	𝑋2	PROPN
cana-3299	352	14	.	.	PUNCT
cana-3299	353	1	by	by	ADP
cana-3299	353	2	hypothesis	hypothesis	NOUN
cana-3299	353	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	353	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	353	5	)	)	PUNCT
cana-3299	353	6	is	be	AUX
cana-3299	353	7	a	a	DET
cana-3299	353	8	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	353	9	in	in	ADP
cana-3299	353	10	𝑋1	𝑋1	PROPN
cana-3299	353	11	.	.	PUNCT
cana-3299	354	1	hence	hence	ADV
cana-3299	354	2	,	,	PUNCT
cana-3299	354	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	354	4	is	be	AUX
cana-3299	354	5	a	a	DET
cana-3299	354	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	354	7	map	map	NOUN
cana-3299	354	8	.	.	PUNCT
cana-3299	355	1	communications	communication	NOUN
cana-3299	355	2	on	on	ADP
cana-3299	355	3	applied	apply	VERB
cana-3299	355	4	nonlinear	nonlinear	ADJ
cana-3299	355	5	analysis	analysis	NOUN
cana-3299	355	6	issn	issn	NOUN
cana-3299	355	7	:	:	PUNCT
cana-3299	355	8	1074	1074	NUM
cana-3299	355	9	-	-	PUNCT
cana-3299	355	10	133x	133x	NUM
cana-3299	355	11	vol	vol	NOUN
cana-3299	355	12	32	32	NUM
cana-3299	355	13	no	no	NOUN
cana-3299	355	14	.	.	PUNCT
cana-3299	356	1	6s	6s	NUM
cana-3299	356	2	(	(	PUNCT
cana-3299	356	3	2025	2025	NUM
cana-3299	356	4	)	)	PUNCT
cana-3299	356	5	336	336	NUM
cana-3299	356	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	356	7	(	(	PUNCT
cana-3299	356	8	iv	iv	X
cana-3299	356	9	)	)	PUNCT
cana-3299	356	10	let	let	VERB
cana-3299	356	11	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	356	12	be	be	AUX
cana-3299	356	13	a	a	DET
cana-3299	356	14	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	ADJ
cana-3299	356	15	map	map	NOUN
cana-3299	356	16	.	.	PUNCT
cana-3299	357	1	let	let	VERB
cana-3299	357	2	𝐵	𝐵	PRON
cana-3299	357	3	be	be	AUX
cana-3299	357	4	any	any	DET
cana-3299	357	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	357	6	in	in	ADP
cana-3299	357	7	𝑋2	𝑋2	PROPN
cana-3299	357	8	.	.	PUNCT
cana-3299	358	1	since	since	SCONJ
cana-3299	358	2	every	every	DET
cana-3299	358	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	358	4	is	be	AUX
cana-3299	358	5	a	a	DET
cana-3299	358	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	358	7	,	,	PUNCT
cana-3299	358	8	𝐵	𝐵	NOUN
cana-3299	358	9	is	be	AUX
cana-3299	358	10	a	a	DET
cana-3299	358	11	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	358	12	in	in	ADP
cana-3299	358	13	𝑋2	𝑋2	PROPN
cana-3299	358	14	.	.	PUNCT
cana-3299	359	1	by	by	ADP
cana-3299	359	2	hypothesis	hypothesis	NOUN
cana-3299	359	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	359	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	359	5	)	)	PUNCT
cana-3299	359	6	is	be	AUX
cana-3299	359	7	a	a	DET
cana-3299	359	8	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	NOUN
cana-3299	359	9	in	in	ADP
cana-3299	359	10	𝑋1	𝑋1	PROPN
cana-3299	359	11	.	.	PUNCT
cana-3299	360	1	hence	hence	ADV
cana-3299	360	2	,	,	PUNCT
cana-3299	360	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	360	4	is	be	AUX
cana-3299	360	5	a	a	DET
cana-3299	360	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	360	7	map	map	NOUN
cana-3299	360	8	.	.	PUNCT
cana-3299	361	1	(	(	PUNCT
cana-3299	361	2	v	v	NOUN
cana-3299	361	3	)	)	PUNCT
cana-3299	361	4	let	let	VERB
cana-3299	361	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	361	6	be	be	AUX
cana-3299	361	7	a	a	DET
cana-3299	361	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	361	9	map	map	NOUN
cana-3299	361	10	.	.	PUNCT
cana-3299	362	1	let	let	VERB
cana-3299	362	2	𝐵	𝐵	PRON
cana-3299	362	3	be	be	AUX
cana-3299	362	4	any	any	DET
cana-3299	362	5	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	362	6	in	in	ADP
cana-3299	362	7	𝑋2	𝑋2	PROPN
cana-3299	362	8	.	.	PUNCT
cana-3299	363	1	since	since	SCONJ
cana-3299	363	2	every	every	DET
cana-3299	363	3	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	363	4	is	be	AUX
cana-3299	363	5	a	a	DET
cana-3299	363	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	363	7	,	,	PUNCT
cana-3299	363	8	𝐵	𝐵	NOUN
cana-3299	363	9	is	be	AUX
cana-3299	363	10	a	a	DET
cana-3299	363	11	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	363	12	in	in	ADP
cana-3299	363	13	𝑋2	𝑋2	PROPN
cana-3299	363	14	.	.	PUNCT
cana-3299	364	1	by	by	ADP
cana-3299	364	2	hypothesis	hypothesis	NOUN
cana-3299	364	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	364	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	364	5	)	)	PUNCT
cana-3299	364	6	is	be	AUX
cana-3299	364	7	a	a	DET
cana-3299	364	8	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	NOUN
cana-3299	364	9	in	in	ADP
cana-3299	364	10	𝑋1	𝑋1	PROPN
cana-3299	364	11	.	.	PUNCT
cana-3299	365	1	hence	hence	ADV
cana-3299	365	2	,	,	PUNCT
cana-3299	365	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	365	4	is	be	AUX
cana-3299	365	5	a	a	DET
cana-3299	365	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	365	7	map	map	NOUN
cana-3299	365	8	.	.	PUNCT
cana-3299	366	1	(	(	PUNCT
cana-3299	366	2	vi	vi	X
cana-3299	366	3	)	)	PUNCT
cana-3299	366	4	let	let	VERB
cana-3299	366	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	366	6	be	be	AUX
cana-3299	366	7	a	a	DET
cana-3299	366	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	ADJ
cana-3299	366	9	map	map	NOUN
cana-3299	366	10	.	.	PUNCT
cana-3299	367	1	let	let	VERB
cana-3299	367	2	𝐵	𝐵	PRON
cana-3299	367	3	be	be	AUX
cana-3299	367	4	any	any	DET
cana-3299	367	5	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	367	6	in	in	ADP
cana-3299	367	7	𝑋2	𝑋2	PROPN
cana-3299	367	8	.	.	PUNCT
cana-3299	368	1	since	since	SCONJ
cana-3299	368	2	every	every	DET
cana-3299	368	3	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	368	4	is	be	AUX
cana-3299	368	5	a	a	DET
cana-3299	368	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	368	7	,	,	PUNCT
cana-3299	368	8	𝐵	𝐵	NOUN
cana-3299	368	9	is	be	AUX
cana-3299	368	10	a	a	DET
cana-3299	368	11	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	368	12	in	in	ADP
cana-3299	368	13	𝑋2	𝑋2	PROPN
cana-3299	368	14	.	.	PUNCT
cana-3299	369	1	by	by	ADP
cana-3299	369	2	hypothesis	hypothesis	NOUN
cana-3299	369	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	369	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	369	5	)	)	PUNCT
cana-3299	369	6	is	be	AUX
cana-3299	369	7	a	a	DET
cana-3299	369	8	𝑝𝑓𝜃𝑐𝑠	𝑝𝑓𝜃𝑐𝑠	NOUN
cana-3299	369	9	in	in	ADP
cana-3299	369	10	𝑋1	𝑋1	PROPN
cana-3299	369	11	.	.	PUNCT
cana-3299	370	1	hence	hence	ADV
cana-3299	370	2	,	,	PUNCT
cana-3299	370	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	370	4	is	be	AUX
cana-3299	370	5	a	a	DET
cana-3299	370	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	PROPN
cana-3299	370	7	map	map	NOUN
cana-3299	370	8	.	.	PUNCT
cana-3299	371	1	(	(	PUNCT
cana-3299	371	2	vii	vii	PROPN
cana-3299	371	3	)	)	PUNCT
cana-3299	371	4	let	let	VERB
cana-3299	371	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	371	6	be	be	AUX
cana-3299	371	7	a	a	DET
cana-3299	371	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	371	9	map	map	NOUN
cana-3299	371	10	.	.	PUNCT
cana-3299	372	1	let	let	VERB
cana-3299	372	2	𝐵	𝐵	PRON
cana-3299	372	3	be	be	AUX
cana-3299	372	4	any	any	DET
cana-3299	372	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	372	6	in	in	ADP
cana-3299	372	7	𝑋2	𝑋2	PROPN
cana-3299	372	8	.	.	PUNCT
cana-3299	373	1	since	since	SCONJ
cana-3299	373	2	every	every	DET
cana-3299	373	3	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	373	4	is	be	AUX
cana-3299	373	5	a	a	DET
cana-3299	373	6	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	373	7	,	,	PUNCT
cana-3299	373	8	𝐵	𝐵	NOUN
cana-3299	373	9	is	be	AUX
cana-3299	373	10	a	a	DET
cana-3299	373	11	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	373	12	in	in	ADP
cana-3299	373	13	𝑋2	𝑋2	PROPN
cana-3299	373	14	.	.	PUNCT
cana-3299	374	1	by	by	ADP
cana-3299	374	2	hypothesis	hypothesis	NOUN
cana-3299	374	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	374	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	374	5	)	)	PUNCT
cana-3299	374	6	is	be	AUX
cana-3299	374	7	a	a	DET
cana-3299	374	8	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	NOUN
cana-3299	374	9	in	in	ADP
cana-3299	374	10	𝑋1	𝑋1	PROPN
cana-3299	374	11	.	.	PUNCT
cana-3299	375	1	hence	hence	ADV
cana-3299	375	2	,	,	PUNCT
cana-3299	375	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	375	4	is	be	AUX
cana-3299	375	5	a	a	DET
cana-3299	375	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PROPN
cana-3299	375	7	map	map	NOUN
cana-3299	375	8	.	.	PUNCT
cana-3299	376	1	(	(	PUNCT
cana-3299	376	2	viii	viii	NOUN
cana-3299	376	3	)	)	PUNCT
cana-3299	376	4	let	let	VERB
cana-3299	376	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	376	6	be	be	AUX
cana-3299	376	7	a	a	DET
cana-3299	376	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	376	9	map	map	NOUN
cana-3299	376	10	.	.	PUNCT
cana-3299	377	1	let	let	VERB
cana-3299	377	2	𝐵	𝐵	PRON
cana-3299	377	3	be	be	AUX
cana-3299	377	4	any	any	DET
cana-3299	377	5	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	377	6	in	in	ADP
cana-3299	377	7	𝑋2	𝑋2	PROPN
cana-3299	377	8	.	.	PUNCT
cana-3299	378	1	since	since	SCONJ
cana-3299	378	2	every	every	DET
cana-3299	378	3	𝑝𝑓𝜃𝑜𝑠	𝑝𝑓𝜃𝑜𝑠	NOUN
cana-3299	378	4	is	be	AUX
cana-3299	378	5	a	a	DET
cana-3299	378	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	ADJ
cana-3299	378	7	,	,	PUNCT
cana-3299	378	8	𝐵	𝐵	NOUN
cana-3299	378	9	is	be	AUX
cana-3299	378	10	a	a	DET
cana-3299	378	11	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	378	12	in	in	ADP
cana-3299	378	13	𝑋2	𝑋2	PROPN
cana-3299	378	14	.	.	PUNCT
cana-3299	379	1	by	by	ADP
cana-3299	379	2	hypothesis	hypothesis	NOUN
cana-3299	379	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	379	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	379	5	)	)	PUNCT
cana-3299	379	6	is	be	AUX
cana-3299	379	7	a	a	DET
cana-3299	379	8	𝑝𝑓𝜃𝒮𝑐𝑠	𝑝𝑓𝜃𝒮𝑐𝑠	PROPN
cana-3299	379	9	in	in	ADP
cana-3299	379	10	𝑋1	𝑋1	PROPN
cana-3299	379	11	.	.	PUNCT
cana-3299	380	1	hence	hence	ADV
cana-3299	380	2	,	,	PUNCT
cana-3299	380	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	380	4	is	be	AUX
cana-3299	380	5	a	a	DET
cana-3299	380	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	380	7	map	map	NOUN
cana-3299	380	8	.	.	PUNCT
cana-3299	381	1	example	example	NOUN
cana-3299	381	2	4.1	4.1	NUM
cana-3299	381	3	let	let	VERB
cana-3299	381	4	𝑋	𝑋	PROPN
cana-3299	381	5	=	=	SYM
cana-3299	381	6	{	{	PUNCT
cana-3299	381	7	𝑥1	𝑥1	NOUN
cana-3299	381	8	,	,	PUNCT
cana-3299	381	9	𝑥2	𝑥2	NOUN
cana-3299	381	10	}	}	PUNCT
cana-3299	381	11	=	=	SYM
cana-3299	381	12	𝑌	𝑌	PROPN
cana-3299	381	13	=	=	SYM
cana-3299	381	14	{	{	PUNCT
cana-3299	381	15	𝑦1	𝑦1	PROPN
cana-3299	381	16	,	,	PUNCT
cana-3299	381	17	𝑦2	𝑦2	NOUN
cana-3299	381	18	}	}	PUNCT
cana-3299	381	19	and	and	CCONJ
cana-3299	381	20	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	381	21	’s	’s	PART
cana-3299	381	22	𝐴1	𝐴1	PROPN
cana-3299	381	23	,	,	PUNCT
cana-3299	381	24	𝐴2	𝐴2	PROPN
cana-3299	381	25	,	,	PUNCT
cana-3299	381	26	𝐴3	𝐴3	PROPN
cana-3299	381	27	&	&	CCONJ
cana-3299	381	28	𝐴4	𝐴4	PROPN
cana-3299	381	29	in	in	ADP
cana-3299	381	30	𝑋	𝑋	PROPN
cana-3299	381	31	and	and	CCONJ
cana-3299	381	32	𝐵1	𝐵1	PROPN
cana-3299	381	33	&	&	CCONJ
cana-3299	381	34	𝐵2	𝐵2	PROPN
cana-3299	381	35	in	in	ADP
cana-3299	381	36	𝑌	𝑌	PROPN
cana-3299	381	37	are	be	AUX
cana-3299	381	38	defined	define	VERB
cana-3299	381	39	as	as	ADP
cana-3299	381	40	,	,	PUNCT
cana-3299	381	41	𝐴1	𝐴1	PROPN
cana-3299	381	42	=	=	SYM
cana-3299	381	43	{	{	PUNCT
cana-3299	381	44	<	<	X
cana-3299	381	45	𝑥1	𝑥1	PROPN
cana-3299	381	46	,	,	PUNCT
cana-3299	381	47	0.20,0.80	0.20,0.80	NOUN
cana-3299	381	48	>	>	X
cana-3299	381	49	,	,	PUNCT
cana-3299	381	50	<	<	X
cana-3299	381	51	𝑥2	𝑥2	NOUN
cana-3299	381	52	,	,	PUNCT
cana-3299	381	53	0.40,0.60	0.40,0.60	NUM
cana-3299	381	54	>	>	PUNCT
cana-3299	381	55	}	}	PUNCT
cana-3299	381	56	𝐴2	𝐴2	PROPN
cana-3299	381	57	=	=	SYM
cana-3299	381	58	{	{	PUNCT
cana-3299	381	59	<	<	X
cana-3299	381	60	𝑥1	𝑥1	PROPN
cana-3299	381	61	,	,	PUNCT
cana-3299	381	62	0.10,0.90	0.10,0.90	NUM
cana-3299	381	63	>	>	X
cana-3299	381	64	,	,	PUNCT
cana-3299	381	65	<	<	X
cana-3299	381	66	𝑥2	𝑥2	NOUN
cana-3299	381	67	,	,	PUNCT
cana-3299	381	68	0.30,0.70	0.30,0.70	PRON
cana-3299	381	69	>	>	PUNCT
cana-3299	381	70	}	}	PUNCT
cana-3299	381	71	𝐴3	𝐴3	PROPN
cana-3299	382	1	=	=	SYM
cana-3299	382	2	{	{	PUNCT
cana-3299	382	3	<	<	X
cana-3299	382	4	𝑥1	𝑥1	PROPN
cana-3299	382	5	,	,	PUNCT
cana-3299	382	6	0.90,0.10	0.90,0.10	NOUN
cana-3299	382	7	>	>	X
cana-3299	382	8	,	,	PUNCT
cana-3299	382	9	<	<	X
cana-3299	382	10	𝑥2	𝑥2	NOUN
cana-3299	382	11	,	,	PUNCT
cana-3299	382	12	0.70,0.30	0.70,0.30	NOUN
cana-3299	382	13	>	>	PUNCT
cana-3299	382	14	}	}	PUNCT
cana-3299	382	15	𝐴4	𝐴4	PROPN
cana-3299	382	16	=	=	PUNCT
cana-3299	382	17	{	{	PUNCT
cana-3299	382	18	<	<	X
cana-3299	382	19	𝑥1	𝑥1	PROPN
cana-3299	382	20	,	,	PUNCT
cana-3299	382	21	0.20,0.80	0.20,0.80	NOUN
cana-3299	382	22	>	>	X
cana-3299	382	23	,	,	PUNCT
cana-3299	382	24	<	<	X
cana-3299	382	25	𝑥2	𝑥2	NOUN
cana-3299	382	26	,	,	PUNCT
cana-3299	382	27	0.30,0.70	0.30,0.70	PRON
cana-3299	382	28	>	>	PUNCT
cana-3299	382	29	}	}	PUNCT
cana-3299	382	30	𝐵1	𝐵1	NOUN
cana-3299	382	31	=	=	PUNCT
cana-3299	382	32	{	{	PUNCT
cana-3299	382	33	<	<	X
cana-3299	382	34	𝑦1	𝑦1	PROPN
cana-3299	382	35	,	,	PUNCT
cana-3299	382	36	0.10,0.90	0.10,0.90	NUM
cana-3299	382	37	>	>	X
cana-3299	382	38	,	,	PUNCT
cana-3299	382	39	<	<	X
cana-3299	382	40	𝑦2	𝑦2	PROPN
cana-3299	382	41	,	,	PUNCT
cana-3299	382	42	0.30,0.70	0.30,0.70	PRON
cana-3299	382	43	>	>	PUNCT
cana-3299	382	44	}	}	PUNCT
cana-3299	382	45	𝐵2	𝐵2	NOUN
cana-3299	382	46	=	=	SYM
cana-3299	382	47	{	{	PUNCT
cana-3299	382	48	<	<	X
cana-3299	382	49	𝑦1	𝑦1	PROPN
cana-3299	382	50	,	,	PUNCT
cana-3299	382	51	0.20,0.40	0.20,0.40	X
cana-3299	382	52	>	>	X
cana-3299	382	53	,	,	PUNCT
cana-3299	382	54	<	<	X
cana-3299	382	55	𝑦2	𝑦2	PROPN
cana-3299	382	56	,	,	PUNCT
cana-3299	382	57	0.40,0.40	0.40,0.40	NOUN
cana-3299	382	58	>	>	PUNCT
cana-3299	382	59	}	}	PUNCT
cana-3299	382	60	.	.	PUNCT
cana-3299	383	1	here	here	ADV
cana-3299	383	2	,	,	PUNCT
cana-3299	383	3	𝜏1	𝜏1	NOUN
cana-3299	383	4	=	=	PUNCT
cana-3299	383	5	{	{	PUNCT
cana-3299	383	6	0𝑃	0𝑃	PROPN
cana-3299	383	7	,	,	PUNCT
cana-3299	383	8	1𝑃	1𝑃	NOUN
cana-3299	383	9	,	,	PUNCT
cana-3299	383	10	𝐴1	𝐴1	PROPN
cana-3299	383	11	,	,	PUNCT
cana-3299	383	12	𝐴2	𝐴2	PROPN
cana-3299	383	13	,	,	PUNCT
cana-3299	383	14	𝐴3	𝐴3	PROPN
cana-3299	383	15	,	,	PUNCT
cana-3299	383	16	𝐴4	𝐴4	PROPN
cana-3299	383	17	}	}	PUNCT
cana-3299	383	18	,	,	PUNCT
cana-3299	383	19	𝜏2	𝜏2	PROPN
cana-3299	383	20	=	=	SYM
cana-3299	383	21	{	{	PUNCT
cana-3299	383	22	0𝑃	0𝑃	PROPN
cana-3299	383	23	,	,	PUNCT
cana-3299	383	24	1𝑃	1𝑃	NOUN
cana-3299	383	25	,	,	PUNCT
cana-3299	383	26	𝐵1	𝐵1	NOUN
cana-3299	383	27	}	}	PUNCT
cana-3299	383	28	,	,	PUNCT
cana-3299	383	29	𝜏3	𝜏3	NOUN
cana-3299	383	30	=	=	SYM
cana-3299	383	31	{	{	PUNCT
cana-3299	383	32	0𝑃	0𝑃	PROPN
cana-3299	383	33	,	,	PUNCT
cana-3299	383	34	1𝑃	1𝑃	NOUN
cana-3299	383	35	,	,	PUNCT
cana-3299	383	36	𝐴2	𝐴2	PROPN
cana-3299	383	37	𝑐	𝑐	PROPN
cana-3299	383	38	}	}	PUNCT
cana-3299	383	39	,	,	PUNCT
cana-3299	383	40	𝜏4	𝜏4	PROPN
cana-3299	383	41	=	=	SYM
cana-3299	383	42	{	{	PUNCT
cana-3299	383	43	0𝑃	0𝑃	PROPN
cana-3299	383	44	,	,	PUNCT
cana-3299	383	45	1𝑃	1𝑃	NOUN
cana-3299	383	46	,	,	PUNCT
cana-3299	383	47	𝐴4	𝐴4	PROPN
cana-3299	383	48	𝑐	𝑐	NOUN
cana-3299	383	49	}	}	PUNCT
cana-3299	383	50	and	and	CCONJ
cana-3299	383	51	𝜏5	𝜏5	PROPN
cana-3299	383	52	=	=	SYM
cana-3299	383	53	{	{	PUNCT
cana-3299	383	54	0𝑃	0𝑃	PROPN
cana-3299	383	55	,	,	PUNCT
cana-3299	383	56	1𝑃	1𝑃	NOUN
cana-3299	383	57	,	,	PUNCT
cana-3299	383	58	𝐴2	𝐴2	PROPN
cana-3299	383	59	𝑐	𝑐	PROPN
cana-3299	383	60	,	,	PUNCT
cana-3299	383	61	𝐴3	𝐴3	PROPN
cana-3299	383	62	𝑐	𝑐	PROPN
cana-3299	383	63	}	}	PUNCT
cana-3299	383	64	.	.	PUNCT
cana-3299	384	1	(	(	PUNCT
cana-3299	384	2	i	i	NOUN
cana-3299	384	3	)	)	PUNCT
cana-3299	384	4	let	let	VERB
cana-3299	384	5	𝑓1	𝑓1	ADJ
cana-3299	384	6	:	:	PUNCT
cana-3299	384	7	(	(	PUNCT
cana-3299	384	8	𝑋	𝑋	PROPN
cana-3299	384	9	,	,	PUNCT
cana-3299	384	10	𝜏1	𝜏1	NOUN
cana-3299	384	11	)	)	PUNCT
cana-3299	384	12	→	→	SYM
cana-3299	384	13	(	(	PUNCT
cana-3299	384	14	𝑌	𝑌	PROPN
cana-3299	384	15	,	,	PUNCT
cana-3299	384	16	𝜏2	𝜏2	PROPN
cana-3299	384	17	)	)	PUNCT
cana-3299	384	18	be	be	VERB
cana-3299	384	19	an	an	DET
cana-3299	384	20	identity	identity	NOUN
cana-3299	384	21	mapping	mapping	NOUN
cana-3299	384	22	.	.	PUNCT
cana-3299	385	1	then	then	ADV
cana-3299	385	2	,	,	PUNCT
cana-3299	385	3	𝑓1	𝑓1	PROPN
cana-3299	385	4	is	be	AUX
cana-3299	385	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	385	6	but	but	CCONJ
cana-3299	385	7	not	not	PART
cana-3299	385	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	385	9	,	,	PUNCT
cana-3299	385	10	because	because	SCONJ
cana-3299	385	11	the	the	DET
cana-3299	385	12	set	set	NOUN
cana-3299	385	13	𝐵2	𝐵2	NOUN
cana-3299	385	14	is	be	AUX
cana-3299	385	15	a	a	DET
cana-3299	385	16	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	385	17	in	in	ADP
cana-3299	385	18	𝑌	𝑌	PROPN
cana-3299	385	19	but	but	CCONJ
cana-3299	385	20	𝑓−1(𝐵2	𝑓−1(𝐵2	NUM
cana-3299	385	21	)	)	PUNCT
cana-3299	386	1	=	=	PUNCT
cana-3299	386	2	𝐵2	𝐵2	NOUN
cana-3299	386	3	is	be	AUX
cana-3299	386	4	not	not	PART
cana-3299	386	5	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	386	6	in	in	ADP
cana-3299	386	7	𝑋.	𝑋.	PROPN
cana-3299	386	8	(	(	PUNCT
cana-3299	386	9	ii	ii	NOUN
cana-3299	386	10	)	)	PUNCT
cana-3299	386	11	let	let	VERB
cana-3299	386	12	𝑓2	𝑓2	NOUN
cana-3299	386	13	:	:	PUNCT
cana-3299	386	14	(	(	PUNCT
cana-3299	386	15	𝑋	𝑋	PROPN
cana-3299	386	16	,	,	PUNCT
cana-3299	386	17	𝜏1	𝜏1	NOUN
cana-3299	386	18	)	)	PUNCT
cana-3299	386	19	→	→	SYM
cana-3299	386	20	(	(	PUNCT
cana-3299	386	21	𝑌	𝑌	PROPN
cana-3299	386	22	,	,	PUNCT
cana-3299	386	23	𝜏3	𝜏3	NOUN
cana-3299	386	24	)	)	PUNCT
cana-3299	386	25	be	be	VERB
cana-3299	386	26	an	an	DET
cana-3299	386	27	identity	identity	NOUN
cana-3299	386	28	mapping	mapping	NOUN
cana-3299	386	29	.	.	PUNCT
cana-3299	387	1	then	then	ADV
cana-3299	387	2	,	,	PUNCT
cana-3299	387	3	𝑓2	𝑓2	PROPN
cana-3299	387	4	is	be	AUX
cana-3299	387	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝒮𝐶𝑡𝑠	NOUN
cana-3299	387	6	but	but	CCONJ
cana-3299	387	7	not	not	PART
cana-3299	387	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐼𝑟𝑟	PROPN
cana-3299	387	9	,	,	PUNCT
cana-3299	387	10	because	because	SCONJ
cana-3299	387	11	the	the	DET
cana-3299	387	12	set	set	NOUN
cana-3299	387	13	𝐴2	𝐴2	PROPN
cana-3299	387	14	𝑐	𝑐	PROPN
cana-3299	387	15	is	be	AUX
cana-3299	387	16	a	a	DET
cana-3299	387	17	𝑝𝑓𝒮𝑜𝑠	𝑝𝑓𝒮𝑜𝑠	NOUN
cana-3299	387	18	in	in	ADP
cana-3299	387	19	𝑌	𝑌	PROPN
cana-3299	387	20	but	but	CCONJ
cana-3299	387	21	𝑓2	𝑓2	PROPN
cana-3299	387	22	−1(𝐴2	−1(𝐴2	NOUN
cana-3299	387	23	𝑐	𝑐	NOUN
cana-3299	387	24	)	)	PUNCT
cana-3299	387	25	=	=	PUNCT
cana-3299	388	1	𝐴2	𝐴2	PROPN
cana-3299	388	2	𝑐	𝑐	PROPN
cana-3299	388	3	is	be	AUX
cana-3299	388	4	not	not	PART
cana-3299	388	5	𝑝𝑓𝒮𝑐𝑠	𝑝𝑓𝒮𝑐𝑠	NOUN
cana-3299	388	6	in	in	ADP
cana-3299	388	7	𝑋.	𝑋.	PROPN
cana-3299	388	8	(	(	PUNCT
cana-3299	388	9	iii	iii	NOUN
cana-3299	388	10	)	)	PUNCT
cana-3299	388	11	let	let	VERB
cana-3299	388	12	𝑓3	𝑓3	PROPN
cana-3299	388	13	:	:	PUNCT
cana-3299	388	14	(	(	PUNCT
cana-3299	388	15	𝑋	𝑋	PROPN
cana-3299	388	16	,	,	PUNCT
cana-3299	388	17	𝜏1	𝜏1	NOUN
cana-3299	388	18	)	)	PUNCT
cana-3299	388	19	→	→	SYM
cana-3299	388	20	(	(	PUNCT
cana-3299	388	21	𝑌	𝑌	PROPN
cana-3299	388	22	,	,	PUNCT
cana-3299	388	23	𝜏4	𝜏4	NOUN
cana-3299	388	24	)	)	PUNCT
cana-3299	388	25	be	be	AUX
cana-3299	388	26	an	an	DET
cana-3299	388	27	identity	identity	NOUN
cana-3299	388	28	mapping	mapping	NOUN
cana-3299	388	29	.	.	PUNCT
cana-3299	389	1	then	then	ADV
cana-3299	389	2	,	,	PUNCT
cana-3299	389	3	𝑓3	𝑓3	NOUN
cana-3299	389	4	is	be	AUX
cana-3299	389	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	389	6	(	(	PUNCT
cana-3299	389	7	resp	resp	NOUN
cana-3299	389	8	.	.	PUNCT
cana-3299	389	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	389	10	)	)	PUNCT
cana-3299	389	11	but	but	CCONJ
cana-3299	389	12	not	not	PART
cana-3299	389	13	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	PROPN
cana-3299	389	14	(	(	PUNCT
cana-3299	389	15	resp	resp	NOUN
cana-3299	389	16	.	.	PUNCT
cana-3299	390	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	ADJ
cana-3299	390	2	)	)	PUNCT
cana-3299	390	3	,	,	PUNCT
cana-3299	390	4	because	because	SCONJ
cana-3299	390	5	the	the	DET
cana-3299	390	6	set	set	NOUN
cana-3299	390	7	𝐴4	𝐴4	PROPN
cana-3299	390	8	𝑐	𝑐	PROPN
cana-3299	390	9	is	be	AUX
cana-3299	390	10	a	a	DET
cana-3299	390	11	𝑝𝑓𝛿𝑜𝑠	𝑝𝑓𝛿𝑜𝑠	NOUN
cana-3299	390	12	(	(	PUNCT
cana-3299	390	13	resp	resp	NOUN
cana-3299	390	14	.	.	PUNCT
cana-3299	391	1	𝑝𝑓𝛿𝒮𝑜𝑠	𝑝𝑓𝛿𝒮𝑜𝑠	PROPN
cana-3299	391	2	)	)	PUNCT
cana-3299	391	3	in	in	ADP
cana-3299	391	4	𝑌	𝑌	PROPN
cana-3299	391	5	but	but	CCONJ
cana-3299	391	6	𝑓3	𝑓3	PROPN
cana-3299	391	7	−1(𝐴4	−1(𝐴4	NOUN
cana-3299	391	8	𝑐	𝑐	NOUN
cana-3299	391	9	)	)	PUNCT
cana-3299	391	10	=	=	VERB
cana-3299	392	1	𝐴4	𝐴4	PROPN
cana-3299	392	2	𝑐	𝑐	PROPN
cana-3299	392	3	is	be	AUX
cana-3299	392	4	not	not	PART
cana-3299	392	5	𝑝𝑓𝛿𝑐𝑠	𝑝𝑓𝛿𝑐𝑠	VERB
cana-3299	392	6	(	(	PUNCT
cana-3299	392	7	resp	resp	NOUN
cana-3299	392	8	.	.	PUNCT
cana-3299	393	1	𝑝𝑓𝛿𝒮𝑐𝑠	𝑝𝑓𝛿𝒮𝑐𝑠	PROPN
cana-3299	393	2	)	)	PUNCT
cana-3299	394	1	in	in	ADP
cana-3299	394	2	𝑋.	𝑋.	PROPN
cana-3299	394	3	(	(	PUNCT
cana-3299	394	4	iv	iv	X
cana-3299	394	5	)	)	PUNCT
cana-3299	394	6	let	let	VERB
cana-3299	394	7	𝑓4	𝑓4	NOUN
cana-3299	394	8	:	:	PUNCT
cana-3299	394	9	(	(	PUNCT
cana-3299	394	10	𝑋	𝑋	PROPN
cana-3299	394	11	,	,	PUNCT
cana-3299	394	12	𝜏1	𝜏1	NOUN
cana-3299	394	13	)	)	PUNCT
cana-3299	394	14	→	→	SYM
cana-3299	394	15	(	(	PUNCT
cana-3299	394	16	𝑌	𝑌	PROPN
cana-3299	394	17	,	,	PUNCT
cana-3299	394	18	𝜏5	𝜏5	PROPN
cana-3299	394	19	)	)	PUNCT
cana-3299	394	20	be	be	AUX
cana-3299	394	21	an	an	DET
cana-3299	394	22	identity	identity	NOUN
cana-3299	394	23	mapping	mapping	NOUN
cana-3299	394	24	.	.	PUNCT
cana-3299	395	1	then	then	ADV
cana-3299	395	2	,	,	PUNCT
cana-3299	395	3	𝑓4	𝑓4	PROPN
cana-3299	395	4	is	be	AUX
cana-3299	395	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	395	6	but	but	CCONJ
cana-3299	395	7	not	not	PART
cana-3299	395	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	395	9	,	,	PUNCT
cana-3299	395	10	because	because	SCONJ
cana-3299	395	11	the	the	DET
cana-3299	395	12	set	set	NOUN
cana-3299	395	13	𝐴1	𝐴1	PROPN
cana-3299	395	14	is	be	AUX
cana-3299	395	15	a	a	DET
cana-3299	395	16	𝑝𝑓𝛿𝒫𝑜𝑠	𝑝𝑓𝛿𝒫𝑜𝑠	NOUN
cana-3299	395	17	in	in	ADP
cana-3299	395	18	𝑌	𝑌	PROPN
cana-3299	395	19	but	but	CCONJ
cana-3299	395	20	𝑓4	𝑓4	PROPN
cana-3299	395	21	−1(𝐴1	−1(𝐴1	NOUN
cana-3299	395	22	)	)	PUNCT
cana-3299	396	1	=	=	PUNCT
cana-3299	396	2	𝐴1	𝐴1	PROPN
cana-3299	396	3	is	be	AUX
cana-3299	396	4	not	not	PART
cana-3299	396	5	𝑝𝑓𝛿𝒫𝑐𝑠	𝑝𝑓𝛿𝒫𝑐𝑠	PRON
cana-3299	396	6	in	in	ADP
cana-3299	396	7	𝑋.	𝑋.	PROPN
cana-3299	396	8	example	example	NOUN
cana-3299	396	9	4.2	4.2	NUM
cana-3299	396	10	let	let	VERB
cana-3299	396	11	𝑋	𝑋	PROPN
cana-3299	396	12	=	=	SYM
cana-3299	396	13	{	{	PUNCT
cana-3299	396	14	𝑥1	𝑥1	NOUN
cana-3299	396	15	,	,	PUNCT
cana-3299	396	16	𝑥2	𝑥2	NOUN
cana-3299	396	17	}	}	PUNCT
cana-3299	396	18	=	=	SYM
cana-3299	396	19	𝑌	𝑌	PROPN
cana-3299	396	20	=	=	SYM
cana-3299	396	21	{	{	PUNCT
cana-3299	396	22	𝑦1	𝑦1	PROPN
cana-3299	396	23	,	,	PUNCT
cana-3299	396	24	𝑦2	𝑦2	NOUN
cana-3299	396	25	}	}	PUNCT
cana-3299	396	26	and	and	CCONJ
cana-3299	396	27	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	396	28	’s	’s	PART
cana-3299	396	29	𝐴1	𝐴1	PROPN
cana-3299	396	30	,	,	PUNCT
cana-3299	396	31	𝐴2	𝐴2	PROPN
cana-3299	396	32	,	,	PUNCT
cana-3299	396	33	𝐴3	𝐴3	PROPN
cana-3299	396	34	,	,	PUNCT
cana-3299	396	35	𝐴4	𝐴4	PROPN
cana-3299	396	36	&	&	CCONJ
cana-3299	396	37	𝐴5	𝐴5	PROPN
cana-3299	396	38	in	in	ADP
cana-3299	396	39	𝑋	𝑋	PROPN
cana-3299	396	40	are	be	AUX
cana-3299	396	41	defined	define	VERB
cana-3299	396	42	as	as	ADP
cana-3299	396	43	,	,	PUNCT
cana-3299	396	44	𝐴1	𝐴1	PROPN
cana-3299	396	45	=	=	SYM
cana-3299	396	46	{	{	PUNCT
cana-3299	396	47	<	<	X
cana-3299	396	48	𝑥1	𝑥1	PROPN
cana-3299	396	49	,	,	PUNCT
cana-3299	396	50	0.20,0.80	0.20,0.80	NOUN
cana-3299	396	51	>	>	X
cana-3299	396	52	,	,	PUNCT
cana-3299	396	53	<	<	X
cana-3299	396	54	𝑥2	𝑥2	NOUN
cana-3299	396	55	,	,	PUNCT
cana-3299	396	56	0.40,0.60	0.40,0.60	NUM
cana-3299	396	57	>	>	PUNCT
cana-3299	396	58	}	}	PUNCT
cana-3299	396	59	𝐴2	𝐴2	PROPN
cana-3299	396	60	=	=	SYM
cana-3299	396	61	{	{	PUNCT
cana-3299	396	62	<	<	X
cana-3299	396	63	𝑥1	𝑥1	PROPN
cana-3299	396	64	,	,	PUNCT
cana-3299	396	65	0.10,0.90	0.10,0.90	NUM
cana-3299	396	66	>	>	X
cana-3299	396	67	,	,	PUNCT
cana-3299	396	68	<	<	X
cana-3299	396	69	𝑥2	𝑥2	NOUN
cana-3299	396	70	,	,	PUNCT
cana-3299	396	71	0.30,0.70	0.30,0.70	PRON
cana-3299	396	72	>	>	PUNCT
cana-3299	396	73	}	}	PUNCT
cana-3299	396	74	𝐴3	𝐴3	PROPN
cana-3299	396	75	=	=	SYM
cana-3299	396	76	{	{	PUNCT
cana-3299	396	77	<	<	X
cana-3299	396	78	𝑥1	𝑥1	PROPN
cana-3299	396	79	,	,	PUNCT
cana-3299	396	80	0.90,0.10	0.90,0.10	NOUN
cana-3299	396	81	>	>	X
cana-3299	396	82	,	,	PUNCT
cana-3299	396	83	<	<	X
cana-3299	396	84	𝑥2	𝑥2	NOUN
cana-3299	396	85	,	,	PUNCT
cana-3299	396	86	0.70,0.30	0.70,0.30	NOUN
cana-3299	396	87	>	>	PUNCT
cana-3299	396	88	}	}	PUNCT
cana-3299	396	89	𝐴4	𝐴4	PROPN
cana-3299	396	90	=	=	PUNCT
cana-3299	396	91	{	{	PUNCT
cana-3299	396	92	<	<	X
cana-3299	396	93	𝑥1	𝑥1	PROPN
cana-3299	396	94	,	,	PUNCT
cana-3299	396	95	0.20,0.80	0.20,0.80	NOUN
cana-3299	396	96	>	>	X
cana-3299	396	97	,	,	PUNCT
cana-3299	396	98	<	<	X
cana-3299	396	99	𝑥2	𝑥2	NOUN
cana-3299	396	100	,	,	PUNCT
cana-3299	396	101	0.30,0.70	0.30,0.70	PRON
cana-3299	396	102	>	>	PUNCT
cana-3299	396	103	}	}	PUNCT
cana-3299	396	104	𝐴5	𝐴5	NOUN
cana-3299	396	105	=	=	PUNCT
cana-3299	396	106	{	{	PUNCT
cana-3299	396	107	<	<	X
cana-3299	396	108	𝑥1	𝑥1	PROPN
cana-3299	396	109	,	,	PUNCT
cana-3299	396	110	0.10,0.90	0.10,0.90	NUM
cana-3299	396	111	>	>	X
cana-3299	396	112	,	,	PUNCT
cana-3299	396	113	<	<	X
cana-3299	396	114	𝑥2	𝑥2	NOUN
cana-3299	396	115	,	,	PUNCT
cana-3299	396	116	0.30,0.60	0.30,0.60	PROPN
cana-3299	396	117	>	>	X
cana-3299	396	118	}	}	PUNCT
cana-3299	396	119	.	.	PUNCT
cana-3299	397	1	here	here	ADV
cana-3299	397	2	,	,	PUNCT
cana-3299	397	3	𝜏1	𝜏1	NOUN
cana-3299	397	4	=	=	PUNCT
cana-3299	397	5	{	{	PUNCT
cana-3299	397	6	0𝑃	0𝑃	PROPN
cana-3299	397	7	,	,	PUNCT
cana-3299	397	8	1𝑃	1𝑃	NOUN
cana-3299	397	9	,	,	PUNCT
cana-3299	397	10	𝐴2	𝐴2	PROPN
cana-3299	397	11	,	,	PUNCT
cana-3299	397	12	𝐴4	𝐴4	PROPN
cana-3299	397	13	}	}	PUNCT
cana-3299	397	14	,	,	PUNCT
cana-3299	397	15	𝜏2	𝜏2	PROPN
cana-3299	397	16	=	=	SYM
cana-3299	397	17	{	{	PUNCT
cana-3299	397	18	0𝑃	0𝑃	PROPN
cana-3299	397	19	,	,	PUNCT
cana-3299	397	20	1𝑃	1𝑃	PROPN
cana-3299	397	21	,	,	PUNCT
cana-3299	397	22	𝐴1	𝐴1	PROPN
cana-3299	397	23	𝑐	𝑐	PROPN
cana-3299	397	24	,	,	PUNCT
cana-3299	397	25	𝐴2	𝐴2	PROPN
cana-3299	397	26	𝑐	𝑐	PROPN
cana-3299	397	27	,	,	PUNCT
cana-3299	397	28	𝐴3	𝐴3	PROPN
cana-3299	397	29	𝑐	𝑐	PROPN
cana-3299	397	30	,	,	PUNCT
cana-3299	397	31	𝐴4	𝐴4	PROPN
cana-3299	397	32	𝑐	𝑐	PROPN
cana-3299	397	33	}	}	PUNCT
cana-3299	397	34	.	.	PUNCT
cana-3299	398	1	let	let	VERB
cana-3299	398	2	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	398	3	:	:	PUNCT
cana-3299	398	4	(	(	PUNCT
cana-3299	398	5	𝑋	𝑋	PROPN
cana-3299	398	6	,	,	PUNCT
cana-3299	398	7	𝜏1	𝜏1	NOUN
cana-3299	398	8	)	)	PUNCT
cana-3299	398	9	→	→	SYM
cana-3299	398	10	(	(	PUNCT
cana-3299	398	11	𝑌	𝑌	PROPN
cana-3299	398	12	,	,	PUNCT
cana-3299	398	13	𝜏2	𝜏2	PROPN
cana-3299	398	14	)	)	PUNCT
cana-3299	398	15	be	be	VERB
cana-3299	398	16	an	an	DET
cana-3299	398	17	identity	identity	NOUN
cana-3299	398	18	mapping	mapping	NOUN
cana-3299	398	19	.	.	PUNCT
cana-3299	399	1	then	then	ADV
cana-3299	399	2	,	,	PUNCT
cana-3299	399	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	399	4	is	be	AUX
cana-3299	399	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PROPN
cana-3299	399	6	but	but	CCONJ
cana-3299	399	7	not	not	PART
cana-3299	399	8	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	ADJ
cana-3299	399	9	,	,	PUNCT
cana-3299	399	10	because	because	SCONJ
cana-3299	399	11	the	the	DET
cana-3299	399	12	set	set	NOUN
cana-3299	399	13	𝐴5	𝐴5	PROPN
cana-3299	399	14	𝑐	𝑐	PROPN
cana-3299	399	15	is	be	AUX
cana-3299	399	16	a	a	DET
cana-3299	399	17	𝑝𝑓𝑒𝑜𝑠	𝑝𝑓𝑒𝑜𝑠	NOUN
cana-3299	399	18	in	in	ADP
cana-3299	399	19	𝑌	𝑌	PROPN
cana-3299	399	20	but	but	CCONJ
cana-3299	399	21	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	399	22	−1(𝐴5	−1(𝐴5	PROPN
cana-3299	399	23	𝑐	𝑐	PROPN
cana-3299	399	24	)	)	PUNCT
cana-3299	399	25	=	=	PUNCT
cana-3299	400	1	𝐴5	𝐴5	PROPN
cana-3299	400	2	𝑐	𝑐	PROPN
cana-3299	400	3	is	be	AUX
cana-3299	400	4	not	not	PART
cana-3299	400	5	𝑝𝑓𝑒𝑐𝑠	𝑝𝑓𝑒𝑐𝑠	VERB
cana-3299	400	6	in	in	ADP
cana-3299	400	7	𝑋.	𝑋.	PROPN
cana-3299	400	8	communications	communication	NOUN
cana-3299	400	9	on	on	ADP
cana-3299	400	10	applied	apply	VERB
cana-3299	400	11	nonlinear	nonlinear	ADJ
cana-3299	400	12	analysis	analysis	NOUN
cana-3299	400	13	issn	issn	NOUN
cana-3299	400	14	:	:	PUNCT
cana-3299	400	15	1074	1074	NUM
cana-3299	400	16	-	-	PUNCT
cana-3299	400	17	133x	133x	NUM
cana-3299	400	18	vol	vol	NOUN
cana-3299	400	19	32	32	NUM
cana-3299	400	20	no	no	NOUN
cana-3299	400	21	.	.	PUNCT
cana-3299	401	1	6s	6s	NUM
cana-3299	401	2	(	(	PUNCT
cana-3299	401	3	2025	2025	NUM
cana-3299	401	4	)	)	PUNCT
cana-3299	401	5	337	337	NUM
cana-3299	401	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	401	7	theorem	theorem	VERB
cana-3299	401	8	4.2	4.2	NUM
cana-3299	401	9	let	let	VERB
cana-3299	401	10	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	401	11	:	:	PUNCT
cana-3299	401	12	(	(	PUNCT
cana-3299	401	13	𝑋1	𝑋1	PROPN
cana-3299	401	14	,	,	PUNCT
cana-3299	401	15	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	401	16	)	)	PUNCT
cana-3299	401	17	→	→	PUNCT
cana-3299	401	18	(	(	PUNCT
cana-3299	401	19	𝑋2	𝑋2	PROPN
cana-3299	401	20	,	,	PUNCT
cana-3299	401	21	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	401	22	)	)	PUNCT
cana-3299	401	23	be	be	AUX
cana-3299	401	24	a	a	DET
cana-3299	401	25	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	401	26	(	(	PUNCT
cana-3299	401	27	resp	resp	NOUN
cana-3299	401	28	.	.	PUNCT
cana-3299	402	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NOUN
cana-3299	402	2	,	,	PUNCT
cana-3299	402	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	402	4	,	,	PUNCT
cana-3299	402	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	402	6	,	,	PUNCT
cana-3299	402	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	402	8	,	,	PUNCT
cana-3299	402	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	402	10	and	and	CCONJ
cana-3299	402	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	402	12	)	)	PUNCT
cana-3299	402	13	,	,	PUNCT
cana-3299	402	14	then	then	ADV
cana-3299	402	15	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	402	16	is	be	AUX
cana-3299	402	17	a	a	DET
cana-3299	402	18	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	402	19	map	map	NOUN
cana-3299	402	20	if	if	SCONJ
cana-3299	402	21	𝑋1	𝑋1	PROPN
cana-3299	402	22	is	be	AUX
cana-3299	402	23	a	a	DET
cana-3299	402	24	𝑝𝑓𝑀𝑈1/2	𝑝𝑓𝑀𝑈1/2	PROPN
cana-3299	402	25	(	(	PUNCT
cana-3299	402	26	resp	resp	NOUN
cana-3299	402	27	.	.	PUNCT
cana-3299	403	1	𝑝𝑓𝛿𝑈1/2	𝑝𝑓𝛿𝑈1/2	PROPN
cana-3299	403	2	,	,	PUNCT
cana-3299	403	3	𝑝𝑓𝛿𝒮𝑈1/2	𝑝𝑓𝛿𝒮𝑈1/2	NOUN
cana-3299	403	4	,	,	PUNCT
cana-3299	403	5	𝑝𝑓𝛿𝒫𝑈1/2	𝑝𝑓𝛿𝒫𝑈1/2	NOUN
cana-3299	403	6	,	,	PUNCT
cana-3299	403	7	𝑝𝑓𝜃𝑈1/2	𝑝𝑓𝜃𝑈1/2	PROPN
cana-3299	403	8	,	,	PUNCT
cana-3299	403	9	𝑝𝑓𝑒𝑈1/2	𝑝𝑓𝑒𝑈1/2	ADJ
cana-3299	403	10	and	and	CCONJ
cana-3299	403	11	𝑝𝑓𝜃𝒮𝑈1/2	𝑝𝑓𝜃𝒮𝑈1/2	ADJ
cana-3299	403	12	)	)	PUNCT
cana-3299	403	13	-space	-space	NOUN
cana-3299	403	14	.	.	PUNCT
cana-3299	404	1	proof	proof	NOUN
cana-3299	404	2	.	.	PUNCT
cana-3299	405	1	let	let	VERB
cana-3299	405	2	𝐵	𝐵	PRON
cana-3299	405	3	be	be	AUX
cana-3299	405	4	a	a	DET
cana-3299	405	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	405	6	in	in	ADP
cana-3299	405	7	𝑋2	𝑋2	PROPN
cana-3299	405	8	.	.	PUNCT
cana-3299	406	1	then	then	ADV
cana-3299	406	2	,	,	PUNCT
cana-3299	406	3	𝐵	𝐵	NOUN
cana-3299	406	4	is	be	AUX
cana-3299	406	5	a	a	DET
cana-3299	406	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	406	7	in	in	ADP
cana-3299	406	8	𝑋2	𝑋2	PROPN
cana-3299	406	9	.	.	PUNCT
cana-3299	407	1	therefore	therefore	ADV
cana-3299	407	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	407	3	−1(𝐵	−1(𝐵	NOUN
cana-3299	407	4	)	)	PUNCT
cana-3299	407	5	is	be	AUX
cana-3299	407	6	a	a	DET
cana-3299	407	7	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	407	8	in	in	ADP
cana-3299	407	9	𝑋1	𝑋1	PROPN
cana-3299	407	10	,	,	PUNCT
cana-3299	407	11	by	by	ADP
cana-3299	407	12	hypothesis	hypothesis	NOUN
cana-3299	407	13	.	.	PUNCT
cana-3299	408	1	since	since	SCONJ
cana-3299	408	2	𝑋1	𝑋1	PROPN
cana-3299	408	3	is	be	AUX
cana-3299	408	4	a	a	DET
cana-3299	408	5	𝑝𝑓𝑀𝑈1/2	𝑝𝑓𝑀𝑈1/2	ADJ
cana-3299	408	6	-space	-space	NOUN
cana-3299	408	7	,	,	PUNCT
cana-3299	408	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	408	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	408	10	)	)	PUNCT
cana-3299	408	11	is	be	AUX
cana-3299	408	12	a	a	DET
cana-3299	408	13	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	408	14	in	in	ADP
cana-3299	408	15	𝑋1	𝑋1	PROPN
cana-3299	408	16	.	.	PUNCT
cana-3299	409	1	hence	hence	ADV
cana-3299	409	2	,	,	PUNCT
cana-3299	409	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	409	4	is	be	AUX
cana-3299	409	5	a	a	DET
cana-3299	409	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝐶𝑡𝑠	PROPN
cana-3299	409	7	map	map	NOUN
cana-3299	409	8	.	.	PUNCT
cana-3299	410	1	the	the	DET
cana-3299	410	2	proof	proof	NOUN
cana-3299	410	3	of	of	ADP
cana-3299	410	4	other	other	ADJ
cana-3299	410	5	cases	case	NOUN
cana-3299	410	6	is	be	AUX
cana-3299	410	7	similar	similar	ADJ
cana-3299	410	8	.	.	PUNCT
cana-3299	411	1	theorem	theorem	VERB
cana-3299	411	2	4.3	4.3	NUM
cana-3299	411	3	let	let	VERB
cana-3299	411	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	411	5	:	:	PUNCT
cana-3299	411	6	(	(	PUNCT
cana-3299	411	7	𝑋1	𝑋1	PROPN
cana-3299	411	8	,	,	PUNCT
cana-3299	411	9	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	411	10	)	)	PUNCT
cana-3299	411	11	→	→	PUNCT
cana-3299	411	12	(	(	PUNCT
cana-3299	411	13	𝑋2	𝑋2	PROPN
cana-3299	411	14	,	,	PUNCT
cana-3299	411	15	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	411	16	)	)	PUNCT
cana-3299	411	17	and	and	CCONJ
cana-3299	411	18	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	411	19	:	:	PUNCT
cana-3299	411	20	(	(	PUNCT
cana-3299	411	21	𝑋2	𝑋2	PROPN
cana-3299	411	22	,	,	PUNCT
cana-3299	411	23	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	411	24	)	)	PUNCT
cana-3299	411	25	→	→	SYM
cana-3299	411	26	(	(	PUNCT
cana-3299	411	27	𝑋3	𝑋3	NOUN
cana-3299	411	28	,	,	PUNCT
cana-3299	411	29	𝛷𝑃	𝛷𝑃	PROPN
cana-3299	411	30	)	)	PUNCT
cana-3299	411	31	be	be	VERB
cana-3299	411	32	a	a	DET
cana-3299	411	33	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	411	34	(	(	PUNCT
cana-3299	411	35	resp	resp	NOUN
cana-3299	411	36	.	.	PUNCT
cana-3299	412	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NOUN
cana-3299	412	2	,	,	PUNCT
cana-3299	412	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	412	4	,	,	PUNCT
cana-3299	412	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	412	6	,	,	PUNCT
cana-3299	412	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	412	8	,	,	PUNCT
cana-3299	412	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	412	10	and	and	CCONJ
cana-3299	412	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	412	12	)	)	PUNCT
cana-3299	412	13	maps	map	NOUN
cana-3299	412	14	,	,	PUNCT
cana-3299	412	15	then	then	ADV
cana-3299	412	16	𝑔𝑃	𝑔𝑃	ADP
cana-3299	412	17	∘	∘	PROPN
cana-3299	412	18	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	412	19	:	:	PUNCT
cana-3299	412	20	(	(	PUNCT
cana-3299	412	21	𝑋1	𝑋1	PROPN
cana-3299	412	22	,	,	PUNCT
cana-3299	412	23	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	412	24	)	)	PUNCT
cana-3299	412	25	→	→	SYM
cana-3299	412	26	(	(	PUNCT
cana-3299	412	27	𝑋3	𝑋3	NOUN
cana-3299	412	28	,	,	PUNCT
cana-3299	412	29	𝛷𝑃	𝛷𝑃	PROPN
cana-3299	412	30	)	)	PUNCT
cana-3299	412	31	is	be	AUX
cana-3299	412	32	a	a	DET
cana-3299	412	33	𝑝𝑓𝑀𝐼𝑟𝑟	𝑝𝑓𝑀𝐼𝑟𝑟	PROPN
cana-3299	412	34	(	(	PUNCT
cana-3299	412	35	resp	resp	NOUN
cana-3299	412	36	.	.	PUNCT
cana-3299	413	1	𝑝𝑓𝛿𝐼𝑟𝑟	𝑝𝑓𝛿𝐼𝑟𝑟	PROPN
cana-3299	413	2	,	,	PUNCT
cana-3299	413	3	𝑝𝑓𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	413	4	,	,	PUNCT
cana-3299	413	5	𝑝𝑓𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	413	6	,	,	PUNCT
cana-3299	413	7	𝑝𝑓𝜃𝐼𝑟𝑟	𝑝𝑓𝜃𝐼𝑟𝑟	NOUN
cana-3299	413	8	,	,	PUNCT
cana-3299	413	9	𝑝𝑓𝑒𝐼𝑟𝑟	𝑝𝑓𝑒𝐼𝑟𝑟	NOUN
cana-3299	413	10	and	and	CCONJ
cana-3299	413	11	𝑝𝑓𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	413	12	)	)	PUNCT
cana-3299	413	13	map	map	NOUN
cana-3299	413	14	.	.	PUNCT
cana-3299	414	1	proof	proof	NOUN
cana-3299	414	2	.	.	PUNCT
cana-3299	415	1	let	let	VERB
cana-3299	415	2	𝐾	𝐾	PRON
cana-3299	415	3	be	be	AUX
cana-3299	415	4	a	a	DET
cana-3299	415	5	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	415	6	in	in	ADP
cana-3299	415	7	𝑋3	𝑋3	NOUN
cana-3299	415	8	.	.	PUNCT
cana-3299	416	1	then	then	ADV
cana-3299	416	2	,	,	PUNCT
cana-3299	416	3	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	416	4	−1(𝐾	−1(𝐾	NOUN
cana-3299	416	5	)	)	PUNCT
cana-3299	416	6	is	be	AUX
cana-3299	416	7	a	a	DET
cana-3299	416	8	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	416	9	in	in	ADP
cana-3299	416	10	𝑋2	𝑋2	PROPN
cana-3299	416	11	.	.	PUNCT
cana-3299	417	1	since	since	SCONJ
cana-3299	417	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	417	3	is	be	AUX
cana-3299	417	4	a	a	DET
cana-3299	417	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	417	6	map	map	NOUN
cana-3299	417	7	,	,	PUNCT
cana-3299	417	8	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	417	9	−1(𝑔𝑃	−1(𝑔𝑃	NOUN
cana-3299	417	10	−1(𝐾	−1(𝐾	NOUN
cana-3299	417	11	)	)	PUNCT
cana-3299	417	12	)	)	PUNCT
cana-3299	417	13	is	be	AUX
cana-3299	417	14	a	a	DET
cana-3299	417	15	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	417	16	in	in	ADP
cana-3299	417	17	𝑋1	𝑋1	PROPN
cana-3299	417	18	.	.	PUNCT
cana-3299	418	1	hence	hence	ADV
cana-3299	418	2	𝑔𝑃	𝑔𝑃	VERB
cana-3299	418	3	∘	∘	PROPN
cana-3299	418	4	𝑓𝑃	𝑓𝑃	PROPN
cana-3299	418	5	is	be	AUX
cana-3299	418	6	a	a	DET
cana-3299	418	7	𝑝𝑓𝑀𝐼𝑟𝑟	𝑝𝑓𝑀𝐼𝑟𝑟	PROPN
cana-3299	418	8	map	map	NOUN
cana-3299	418	9	.	.	PUNCT
cana-3299	419	1	the	the	DET
cana-3299	419	2	proof	proof	NOUN
cana-3299	419	3	of	of	ADP
cana-3299	419	4	other	other	ADJ
cana-3299	419	5	cases	case	NOUN
cana-3299	419	6	is	be	AUX
cana-3299	419	7	similar	similar	ADJ
cana-3299	419	8	.	.	PUNCT
cana-3299	420	1	theorem	theorem	VERB
cana-3299	420	2	4.4	4.4	NUM
cana-3299	420	3	let	let	VERB
cana-3299	420	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	420	5	:	:	PUNCT
cana-3299	420	6	(	(	PUNCT
cana-3299	420	7	𝑋1	𝑋1	PROPN
cana-3299	420	8	,	,	PUNCT
cana-3299	420	9	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	420	10	)	)	PUNCT
cana-3299	420	11	→	→	PUNCT
cana-3299	420	12	(	(	PUNCT
cana-3299	420	13	𝑋2	𝑋2	PROPN
cana-3299	420	14	,	,	PUNCT
cana-3299	420	15	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	420	16	)	)	PUNCT
cana-3299	420	17	be	be	AUX
cana-3299	420	18	a	a	DET
cana-3299	420	19	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	420	20	(	(	PUNCT
cana-3299	420	21	resp	resp	NOUN
cana-3299	420	22	.	.	PUNCT
cana-3299	421	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NOUN
cana-3299	421	2	,	,	PUNCT
cana-3299	421	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	PROPN
cana-3299	421	4	,	,	PUNCT
cana-3299	421	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	421	6	,	,	PUNCT
cana-3299	421	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	421	8	,	,	PUNCT
cana-3299	421	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	421	10	and	and	CCONJ
cana-3299	421	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟	PROPN
cana-3299	421	12	)	)	PUNCT
cana-3299	421	13	map	map	NOUN
cana-3299	421	14	and	and	CCONJ
cana-3299	421	15	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	421	16	:	:	PUNCT
cana-3299	421	17	(	(	PUNCT
cana-3299	421	18	𝑋2	𝑋2	PROPN
cana-3299	421	19	,	,	PUNCT
cana-3299	421	20	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	421	21	)	)	PUNCT
cana-3299	421	22	→	→	SYM
cana-3299	421	23	(	(	PUNCT
cana-3299	421	24	𝑋3	𝑋3	NOUN
cana-3299	421	25	,	,	PUNCT
cana-3299	421	26	𝛷𝑃	𝛷𝑃	PROPN
cana-3299	421	27	)	)	PUNCT
cana-3299	421	28	be	be	VERB
cana-3299	421	29	a	a	DET
cana-3299	421	30	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	421	31	(	(	PUNCT
cana-3299	421	32	resp	resp	NOUN
cana-3299	421	33	.	.	PUNCT
cana-3299	422	1	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐶𝑡𝑠	PRON
cana-3299	422	2	,	,	PUNCT
cana-3299	422	3	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐶𝑡𝑠	NOUN
cana-3299	422	4	,	,	PUNCT
cana-3299	422	5	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐶𝑡𝑠	NOUN
cana-3299	422	6	,	,	PUNCT
cana-3299	422	7	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐶𝑡𝑠	NUM
cana-3299	422	8	,	,	PUNCT
cana-3299	422	9	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐶𝑡𝑠	PROPN
cana-3299	422	10	and	and	CCONJ
cana-3299	422	11	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐶𝑡𝑠	NOUN
cana-3299	422	12	)	)	PUNCT
cana-3299	422	13	map	map	NOUN
cana-3299	422	14	,	,	PUNCT
cana-3299	422	15	then	then	ADV
cana-3299	422	16	𝑔𝑃	𝑔𝑃	ADP
cana-3299	422	17	∘	∘	PROPN
cana-3299	422	18	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	422	19	:	:	PUNCT
cana-3299	422	20	(	(	PUNCT
cana-3299	422	21	𝑋	𝑋	PROPN
cana-3299	422	22	,	,	PUNCT
cana-3299	422	23	𝜏1	𝜏1	NOUN
cana-3299	422	24	)	)	PUNCT
cana-3299	422	25	→	→	SYM
cana-3299	422	26	(	(	PUNCT
cana-3299	422	27	𝑍	𝑍	NOUN
cana-3299	422	28	,	,	PUNCT
cana-3299	422	29	𝜏3	𝜏3	NOUN
cana-3299	422	30	)	)	PUNCT
cana-3299	422	31	is	be	AUX
cana-3299	422	32	a	a	DET
cana-3299	422	33	𝑝𝑓𝑀𝐶𝑡𝑠	𝑝𝑓𝑀𝐶𝑡𝑠	PROPN
cana-3299	422	34	(	(	PUNCT
cana-3299	422	35	resp	resp	NOUN
cana-3299	422	36	.	.	PUNCT
cana-3299	423	1	𝑝𝑓𝛿𝐶𝑡𝑠	𝑝𝑓𝛿𝐶𝑡𝑠	PROPN
cana-3299	423	2	,	,	PUNCT
cana-3299	423	3	𝑝𝑓𝛿𝒮𝐶𝑡𝑠	𝑝𝑓𝛿𝒮𝐶𝑡𝑠	PROPN
cana-3299	423	4	,	,	PUNCT
cana-3299	423	5	𝑝𝑓𝛿𝒫𝐶𝑡𝑠	𝑝𝑓𝛿𝒫𝐶𝑡𝑠	PROPN
cana-3299	423	6	,	,	PUNCT
cana-3299	423	7	𝑝𝑓𝜃𝐶𝑡𝑠	𝑝𝑓𝜃𝐶𝑡𝑠	NOUN
cana-3299	423	8	,	,	PUNCT
cana-3299	423	9	𝑝𝑓𝑒𝐶𝑡𝑠	𝑝𝑓𝑒𝐶𝑡𝑠	PROPN
cana-3299	423	10	and	and	CCONJ
cana-3299	423	11	𝑝𝑓𝜃𝒮𝐶𝑡𝑠	𝑝𝑓𝜃𝒮𝐶𝑡𝑠	PROPN
cana-3299	423	12	)	)	PUNCT
cana-3299	423	13	map	map	NOUN
cana-3299	423	14	.	.	PUNCT
cana-3299	424	1	proof	proof	NOUN
cana-3299	424	2	.	.	PUNCT
cana-3299	425	1	let	let	VERB
cana-3299	425	2	𝐾	𝐾	PRON
cana-3299	425	3	be	be	AUX
cana-3299	425	4	a	a	DET
cana-3299	425	5	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	425	6	in	in	ADP
cana-3299	425	7	𝑋3	𝑋3	NOUN
cana-3299	425	8	.	.	PUNCT
cana-3299	426	1	then	then	ADV
cana-3299	426	2	,	,	PUNCT
cana-3299	426	3	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	426	4	−1(𝐾	−1(𝐾	NOUN
cana-3299	426	5	)	)	PUNCT
cana-3299	426	6	is	be	AUX
cana-3299	426	7	a	a	DET
cana-3299	426	8	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	426	9	in	in	ADP
cana-3299	426	10	𝑋2	𝑋2	PROPN
cana-3299	426	11	.	.	PUNCT
cana-3299	427	1	since	since	SCONJ
cana-3299	427	2	,	,	PUNCT
cana-3299	427	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	427	4	is	be	AUX
cana-3299	427	5	a	a	DET
cana-3299	427	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	427	7	,	,	PUNCT
cana-3299	427	8	ℎ𝑃	ℎ𝑃	ADJ
cana-3299	427	9	−1(𝑔𝑃	−1(𝑔𝑃	NOUN
cana-3299	427	10	−1(𝐾	−1(𝐾	NOUN
cana-3299	427	11	)	)	PUNCT
cana-3299	427	12	)	)	PUNCT
cana-3299	428	1	is	be	AUX
cana-3299	428	2	a	a	DET
cana-3299	428	3	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	428	4	in	in	ADP
cana-3299	428	5	𝑋1	𝑋1	PROPN
cana-3299	428	6	.	.	PUNCT
cana-3299	429	1	hence	hence	ADV
cana-3299	429	2	,	,	PUNCT
cana-3299	429	3	𝑔𝑃	𝑔𝑃	ADJ
cana-3299	429	4	∘	∘	PROPN
cana-3299	429	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	429	6	is	be	AUX
cana-3299	429	7	a	a	DET
cana-3299	429	8	𝑝𝑓𝑀𝐶𝑡𝑠	𝑝𝑓𝑀𝐶𝑡𝑠	PROPN
cana-3299	429	9	map	map	NOUN
cana-3299	429	10	.	.	PUNCT
cana-3299	430	1	the	the	DET
cana-3299	430	2	proof	proof	NOUN
cana-3299	430	3	of	of	ADP
cana-3299	430	4	other	other	ADJ
cana-3299	430	5	cases	case	NOUN
cana-3299	430	6	is	be	AUX
cana-3299	430	7	similar	similar	ADJ
cana-3299	430	8	.	.	PUNCT
cana-3299	431	1	theorem	theorem	VERB
cana-3299	431	2	4.5	4.5	NUM
cana-3299	431	3	let	let	VERB
cana-3299	431	4	a	a	DET
cana-3299	431	5	map	map	NOUN
cana-3299	431	6	ℎ𝑃	ℎ𝑃	NOUN
cana-3299	431	7	:	:	PUNCT
cana-3299	431	8	(	(	PUNCT
cana-3299	431	9	𝑋1	𝑋1	PROPN
cana-3299	431	10	,	,	PUNCT
cana-3299	431	11	𝛤𝑃	𝛤𝑃	PROPN
cana-3299	431	12	)	)	PUNCT
cana-3299	431	13	→	→	PUNCT
cana-3299	431	14	(	(	PUNCT
cana-3299	431	15	𝑋2	𝑋2	PROPN
cana-3299	431	16	,	,	PUNCT
cana-3299	431	17	𝛹𝑃	𝛹𝑃	PROPN
cana-3299	431	18	)	)	PUNCT
cana-3299	431	19	.	.	PUNCT
cana-3299	432	1	then	then	ADV
cana-3299	432	2	the	the	DET
cana-3299	432	3	following	follow	VERB
cana-3299	432	4	conditions	condition	NOUN
cana-3299	432	5	are	be	AUX
cana-3299	432	6	equivalent	equivalent	ADJ
cana-3299	432	7	if	if	SCONJ
cana-3299	432	8	𝑋1	𝑋1	PROPN
cana-3299	432	9	and	and	CCONJ
cana-3299	432	10	𝑋2	𝑋2	VERB
cana-3299	432	11	are	be	AUX
cana-3299	432	12	𝑝𝑓𝑀𝑈1/2	𝑝𝑓𝑀𝑈1/2	PROPN
cana-3299	432	13	-spaces	-space	NOUN
cana-3299	432	14	.	.	PUNCT
cana-3299	433	1	1	1	X
cana-3299	433	2	.	.	X
cana-3299	434	1	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	434	2	is	be	AUX
cana-3299	434	3	a	a	DET
cana-3299	434	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	434	5	map	map	NOUN
cana-3299	434	6	.	.	PUNCT
cana-3299	435	1	2	2	X
cana-3299	435	2	.	.	X
cana-3299	435	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	435	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	435	5	)	)	PUNCT
cana-3299	435	6	is	be	AUX
cana-3299	435	7	a	a	DET
cana-3299	435	8	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	435	9	in	in	ADP
cana-3299	435	10	𝑋1	𝑋1	PROPN
cana-3299	435	11	,	,	PUNCT
cana-3299	435	12	for	for	ADP
cana-3299	435	13	each	each	DET
cana-3299	435	14	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	435	15	𝐵	𝐵	NOUN
cana-3299	435	16	in	in	ADP
cana-3299	435	17	𝑋2	𝑋2	ADJ
cana-3299	435	18	.	.	PUNCT
cana-3299	436	1	3	3	X
cana-3299	436	2	.	.	X
cana-3299	436	3	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-3299	436	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	436	5	)	)	PUNCT
cana-3299	436	6	)	)	PUNCT
cana-3299	437	1	⊇	⊇	PROPN
cana-3299	437	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	437	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	437	4	)	)	PUNCT
cana-3299	437	5	)	)	PUNCT
cana-3299	437	6	,	,	PUNCT
cana-3299	437	7	for	for	ADP
cana-3299	437	8	each	each	DET
cana-3299	437	9	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	437	10	𝐵	𝐵	PROPN
cana-3299	437	11	of	of	ADP
cana-3299	437	12	𝑋2	𝑋2	ADJ
cana-3299	437	13	.	.	PUNCT
cana-3299	438	1	proof	proof	NOUN
cana-3299	438	2	.	.	PUNCT
cana-3299	439	1	(	(	PUNCT
cana-3299	439	2	i	i	NOUN
cana-3299	439	3	)	)	PUNCT
cana-3299	439	4	→	→	SYM
cana-3299	439	5	(	(	PUNCT
cana-3299	439	6	ii	ii	NOUN
cana-3299	439	7	):	):	PUNCT
cana-3299	439	8	let	let	VERB
cana-3299	439	9	𝐵	𝐵	PRON
cana-3299	439	10	be	be	AUX
cana-3299	439	11	any	any	DET
cana-3299	439	12	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	439	13	in	in	ADP
cana-3299	439	14	𝑋2	𝑋2	PROPN
cana-3299	439	15	.	.	PUNCT
cana-3299	440	1	then	then	ADV
cana-3299	440	2	,	,	PUNCT
cana-3299	440	3	𝐵𝑐	𝐵𝑐	PROPN
cana-3299	440	4	is	be	AUX
cana-3299	440	5	a	a	DET
cana-3299	440	6	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	440	7	in	in	ADP
cana-3299	440	8	𝑋2	𝑋2	PROPN
cana-3299	440	9	.	.	PUNCT
cana-3299	441	1	since	since	SCONJ
cana-3299	441	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	441	3	is	be	AUX
cana-3299	441	4	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	441	5	,	,	PUNCT
cana-3299	441	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	441	7	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-3299	441	8	)	)	PUNCT
cana-3299	441	9	is	be	AUX
cana-3299	441	10	a	a	DET
cana-3299	441	11	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	441	12	in	in	ADP
cana-3299	441	13	𝑋1	𝑋1	PROPN
cana-3299	441	14	.	.	PUNCT
cana-3299	442	1	but	but	CCONJ
cana-3299	442	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	442	3	−1(𝐵𝑐	−1(𝐵𝑐	PROPN
cana-3299	442	4	)	)	PUNCT
cana-3299	443	1	=	=	PRON
cana-3299	444	1	(	(	PUNCT
cana-3299	444	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	444	3	−1(𝐵))𝑐.	−1(𝐵))𝑐.	PROPN
cana-3299	444	4	therefore	therefore	ADV
cana-3299	444	5	,	,	PUNCT
cana-3299	444	6	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	444	7	−1(𝐵	−1(𝐵	NOUN
cana-3299	444	8	)	)	PUNCT
cana-3299	444	9	is	be	AUX
cana-3299	444	10	a	a	DET
cana-3299	444	11	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	444	12	in	in	ADP
cana-3299	444	13	𝑋1	𝑋1	PROPN
cana-3299	444	14	.	.	PUNCT
cana-3299	445	1	(	(	PUNCT
cana-3299	445	2	ii	ii	NOUN
cana-3299	445	3	)	)	PUNCT
cana-3299	445	4	→	→	SYM
cana-3299	445	5	(	(	PUNCT
cana-3299	445	6	iii	iii	NOUN
cana-3299	445	7	)	)	PUNCT
cana-3299	445	8	:	:	PUNCT
cana-3299	445	9	let	let	VERB
cana-3299	445	10	𝐵	𝐵	PRON
cana-3299	445	11	be	be	AUX
cana-3299	445	12	any	any	DET
cana-3299	445	13	𝑝𝑓𝑠	𝑝𝑓𝑠	PROPN
cana-3299	445	14	in	in	ADP
cana-3299	445	15	𝑋2	𝑋2	PROPN
cana-3299	445	16	and	and	CCONJ
cana-3299	445	17	𝑝𝑓𝑖𝑛𝑡(𝐵	𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	445	18	)	)	PUNCT
cana-3299	445	19	≤	≤	NOUN
cana-3299	445	20	𝐵.	𝐵.	PROPN
cana-3299	445	21	then	then	ADV
cana-3299	445	22	,	,	PUNCT
cana-3299	445	23	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	445	24	−1(𝑝𝑓𝑐𝑙(𝐵))ℎ𝑃	−1(𝑝𝑓𝑐𝑙(𝐵))ℎ𝑃	NOUN
cana-3299	445	25	−1(𝐵	−1(𝐵	NOUN
cana-3299	445	26	)	)	PUNCT
cana-3299	445	27	≤	≤	NOUN
cana-3299	446	1	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	446	2	−1(𝐵	−1(𝐵	NOUN
cana-3299	446	3	)	)	PUNCT
cana-3299	446	4	.	.	PUNCT
cana-3299	447	1	since	since	SCONJ
cana-3299	447	2	𝑝𝑓𝑖𝑛𝑡(𝐵	𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	447	3	)	)	PUNCT
cana-3299	447	4	is	be	AUX
cana-3299	447	5	a	a	DET
cana-3299	447	6	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	447	7	in	in	ADP
cana-3299	447	8	𝑋2	𝑋2	ADJ
cana-3299	447	9	,	,	PUNCT
cana-3299	447	10	𝑝𝑓𝑖𝑛𝑡(𝐵	𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	447	11	)	)	PUNCT
cana-3299	447	12	is	be	AUX
cana-3299	447	13	a	a	DET
cana-3299	447	14	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	447	15	in	in	ADP
cana-3299	447	16	𝑋2	𝑋2	PROPN
cana-3299	447	17	.	.	PUNCT
cana-3299	448	1	therefore	therefore	ADV
cana-3299	448	2	,	,	PUNCT
cana-3299	448	3	(	(	PUNCT
cana-3299	448	4	𝑝𝑓𝑖𝑛𝑡(𝐵))𝑐	𝑝𝑓𝑖𝑛𝑡(𝐵))𝑐	PROPN
cana-3299	448	5	is	be	AUX
cana-3299	448	6	a	a	DET
cana-3299	448	7	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	448	8	in	in	ADP
cana-3299	448	9	𝑋2	𝑋2	PROPN
cana-3299	448	10	.	.	PUNCT
cana-3299	449	1	by	by	ADP
cana-3299	449	2	hypothesis	hypothesis	NOUN
cana-3299	449	3	,	,	PUNCT
cana-3299	449	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	449	5	−1((𝑝𝑓𝑖𝑛𝑡(𝐵))𝑐	−1((𝑝𝑓𝑖𝑛𝑡(𝐵))𝑐	NOUN
cana-3299	449	6	)	)	PUNCT
cana-3299	449	7	is	be	AUX
cana-3299	449	8	a	a	DET
cana-3299	449	9	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	449	10	in	in	ADP
cana-3299	449	11	𝑋1	𝑋1	PROPN
cana-3299	449	12	.	.	PUNCT
cana-3299	450	1	since	since	SCONJ
cana-3299	450	2	,	,	PUNCT
cana-3299	450	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	450	4	−1((𝑝𝑓𝑖𝑛𝑡(𝐵))𝑐	−1((𝑝𝑓𝑖𝑛𝑡(𝐵))𝑐	NOUN
cana-3299	450	5	)	)	PUNCT
cana-3299	450	6	=	=	SYM
cana-3299	451	1	(	(	PUNCT
cana-3299	451	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	451	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵)))𝑐	−1(𝑝𝑓𝑖𝑛𝑡(𝐵)))𝑐	PROPN
cana-3299	451	4	,	,	PUNCT
cana-3299	451	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	451	6	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	NUM
cana-3299	451	7	)	)	PUNCT
cana-3299	451	8	)	)	PUNCT
cana-3299	451	9	is	be	AUX
cana-3299	451	10	a	a	DET
cana-3299	451	11	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	451	12	in	in	ADP
cana-3299	451	13	𝑋1	𝑋1	PROPN
cana-3299	451	14	.	.	PUNCT
cana-3299	452	1	since	since	SCONJ
cana-3299	452	2	,	,	PUNCT
cana-3299	452	3	𝑋1	𝑋1	PROPN
cana-3299	452	4	is	be	AUX
cana-3299	452	5	a	a	DET
cana-3299	452	6	𝑝𝑓𝑀𝑈1/2	𝑝𝑓𝑀𝑈1/2	ADJ
cana-3299	452	7	-space	-space	NOUN
cana-3299	452	8	,	,	PUNCT
cana-3299	452	9	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	452	10	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	NUM
cana-3299	452	11	)	)	PUNCT
cana-3299	452	12	)	)	PUNCT
cana-3299	453	1	is	be	AUX
cana-3299	453	2	a	a	DET
cana-3299	453	3	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	453	4	in	in	ADP
cana-3299	453	5	𝑋1	𝑋1	PROPN
cana-3299	453	6	.	.	PUNCT
cana-3299	454	1	hence	hence	ADV
cana-3299	454	2	,	,	PUNCT
cana-3299	454	3	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-3299	454	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	454	5	)	)	PUNCT
cana-3299	454	6	)	)	PUNCT
cana-3299	455	1	⊇	⊇	PROPN
cana-3299	455	2	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-3299	455	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	NUM
cana-3299	455	4	)	)	PUNCT
cana-3299	455	5	)	)	PUNCT
cana-3299	455	6	)	)	PUNCT
cana-3299	456	1	=	=	PUNCT
cana-3299	456	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	456	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	456	4	)	)	PUNCT
cana-3299	456	5	)	)	PUNCT
cana-3299	456	6	.	.	PUNCT
cana-3299	457	1	that	that	PRON
cana-3299	457	2	is	be	AUX
cana-3299	457	3	,	,	PUNCT
cana-3299	457	4	𝑝𝑓𝑐𝑙(ℎ𝑃	𝑝𝑓𝑐𝑙(ℎ𝑃	NOUN
cana-3299	457	5	−1(𝐵	−1(𝐵	NOUN
cana-3299	457	6	)	)	PUNCT
cana-3299	457	7	)	)	PUNCT
cana-3299	458	1	⊇	⊇	PROPN
cana-3299	458	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	458	3	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	−1(𝑝𝑓𝑖𝑛𝑡(𝐵	PROPN
cana-3299	458	4	)	)	PUNCT
cana-3299	458	5	)	)	PUNCT
cana-3299	458	6	.	.	PUNCT
cana-3299	459	1	(	(	PUNCT
cana-3299	459	2	iii	iii	NOUN
cana-3299	459	3	)	)	PUNCT
cana-3299	459	4	→	→	SYM
cana-3299	459	5	(	(	PUNCT
cana-3299	459	6	i	i	NOUN
cana-3299	459	7	)	)	PUNCT
cana-3299	459	8	:	:	PUNCT
cana-3299	459	9	let	let	VERB
cana-3299	459	10	𝐵	𝐵	PRON
cana-3299	459	11	be	be	AUX
cana-3299	459	12	any	any	DET
cana-3299	459	13	𝑝𝑓𝑀𝑐𝑠	𝑝𝑓𝑀𝑐𝑠	NOUN
cana-3299	459	14	in	in	ADP
cana-3299	459	15	𝑋2	𝑋2	PROPN
cana-3299	459	16	.	.	PUNCT
cana-3299	460	1	since	since	SCONJ
cana-3299	460	2	𝑋2	𝑋2	PROPN
cana-3299	460	3	is	be	AUX
cana-3299	460	4	a	a	DET
cana-3299	460	5	𝑝𝑓𝑀𝑈1/2	𝑝𝑓𝑀𝑈1/2	ADJ
cana-3299	460	6	-	-	PUNCT
cana-3299	460	7	space	space	NOUN
cana-3299	460	8	,	,	PUNCT
cana-3299	460	9	𝐵	𝐵	NOUN
cana-3299	460	10	is	be	AUX
cana-3299	460	11	a	a	DET
cana-3299	460	12	𝑝𝑓𝑐𝑠	𝑝𝑓𝑐𝑠	NOUN
cana-3299	460	13	in	in	ADP
cana-3299	460	14	𝑋2	𝑋2	ADJ
cana-3299	460	15	and	and	CCONJ
cana-3299	460	16	𝑝𝑓𝑐𝑙(𝐵	𝑝𝑓𝑐𝑙(𝐵	PUNCT
cana-3299	460	17	)	)	PUNCT
cana-3299	461	1	=	=	SYM
cana-3299	461	2	𝐵.	𝐵.	PROPN
cana-3299	461	3	hence	hence	ADV
cana-3299	461	4	,	,	PUNCT
cana-3299	461	5	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	461	6	−1(𝐵	−1(𝐵	NOUN
cana-3299	461	7	)	)	PUNCT
cana-3299	462	1	=	=	SYM
cana-3299	462	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	462	3	−1(𝑝𝑓𝑀𝑐𝑙(𝐵	−1(𝑝𝑓𝑀𝑐𝑙(𝐵	X
cana-3299	462	4	)	)	PUNCT
cana-3299	462	5	)	)	PUNCT
cana-3299	463	1	⊇	⊇	PROPN
cana-3299	463	2	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃	𝑝𝑓𝑀𝑖𝑛𝑡(ℎ𝑃	ADJ
cana-3299	463	3	−1(𝐵	−1(𝐵	NOUN
cana-3299	463	4	)	)	PUNCT
cana-3299	463	5	)	)	PUNCT
cana-3299	463	6	.	.	PUNCT
cana-3299	464	1	but	but	CCONJ
cana-3299	464	2	clearly	clearly	ADV
cana-3299	464	3	,	,	PUNCT
cana-3299	464	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	464	5	−1(𝐵	−1(𝐵	NOUN
cana-3299	464	6	)	)	PUNCT
cana-3299	464	7	⊇	⊇	PROPN
cana-3299	464	8	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	PROPN
cana-3299	464	9	−1(𝐵	−1(𝐵	NOUN
cana-3299	464	10	)	)	PUNCT
cana-3299	464	11	)	)	PUNCT
cana-3299	464	12	.	.	PUNCT
cana-3299	465	1	therefore	therefore	ADV
cana-3299	465	2	,	,	PUNCT
cana-3299	465	3	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	𝑝𝑓𝑖𝑛𝑡(ℎ𝑃	NOUN
cana-3299	465	4	−1(𝐵	−1(𝐵	NOUN
cana-3299	465	5	)	)	PUNCT
cana-3299	465	6	)	)	PUNCT
cana-3299	466	1	=	=	PUNCT
cana-3299	466	2	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	466	3	−1(𝐵	−1(𝐵	NOUN
cana-3299	466	4	)	)	PUNCT
cana-3299	466	5	.	.	PUNCT
cana-3299	467	1	this	this	PRON
cana-3299	467	2	implies	imply	VERB
cana-3299	467	3	,	,	PUNCT
cana-3299	467	4	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	467	5	−1(𝐵	−1(𝐵	NOUN
cana-3299	467	6	)	)	PUNCT
cana-3299	467	7	is	be	AUX
cana-3299	467	8	a	a	DET
cana-3299	467	9	𝑝𝑓𝑜𝑠	𝑝𝑓𝑜𝑠	NOUN
cana-3299	467	10	and	and	CCONJ
cana-3299	467	11	hence	hence	ADV
cana-3299	467	12	,	,	PUNCT
cana-3299	467	13	it	it	PRON
cana-3299	467	14	is	be	AUX
cana-3299	467	15	a	a	DET
cana-3299	467	16	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	NOUN
cana-3299	467	17	in	in	ADP
cana-3299	467	18	𝑋1	𝑋1	PROPN
cana-3299	467	19	.	.	PUNCT
cana-3299	468	1	thus	thus	ADV
cana-3299	468	2	,	,	PUNCT
cana-3299	468	3	ℎ𝑃	ℎ𝑃	PROPN
cana-3299	468	4	is	be	AUX
cana-3299	468	5	a	a	DET
cana-3299	468	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐼𝑟𝑟	ADJ
cana-3299	468	7	map	map	NOUN
cana-3299	468	8	.	.	PUNCT
cana-3299	469	1	communications	communication	NOUN
cana-3299	469	2	on	on	ADP
cana-3299	469	3	applied	apply	VERB
cana-3299	469	4	nonlinear	nonlinear	ADJ
cana-3299	469	5	analysis	analysis	NOUN
cana-3299	469	6	issn	issn	NOUN
cana-3299	469	7	:	:	PUNCT
cana-3299	469	8	1074	1074	NUM
cana-3299	469	9	-	-	PUNCT
cana-3299	469	10	133x	133x	NUM
cana-3299	469	11	vol	vol	NOUN
cana-3299	469	12	32	32	NUM
cana-3299	469	13	no	no	NOUN
cana-3299	469	14	.	.	PUNCT
cana-3299	470	1	6s	6s	NUM
cana-3299	470	2	(	(	PUNCT
cana-3299	470	3	2025	2025	NUM
cana-3299	470	4	)	)	PUNCT
cana-3299	470	5	338	338	NUM
cana-3299	470	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	470	7	remark	remark	NOUN
cana-3299	470	8	4.1	4.1	NUM
cana-3299	470	9	theorem	theorem	NOUN
cana-3299	470	10	4.5	4.5	NUM
cana-3299	470	11	is	be	AUX
cana-3299	470	12	true	true	ADJ
cana-3299	470	13	for	for	ADP
cana-3299	470	14	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝐼𝑟𝑟	NOUN
cana-3299	470	15	,	,	PUNCT
cana-3299	470	16	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒮𝐼𝑟𝑟	ADJ
cana-3299	470	17	,	,	PUNCT
cana-3299	470	18	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝛿𝒫𝐼𝑟𝑟	PROPN
cana-3299	470	19	,	,	PUNCT
cana-3299	470	20	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝐼𝑟𝑟	PROPN
cana-3299	470	21	,	,	PUNCT
cana-3299	470	22	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑒𝐼𝑟𝑟	PROPN
cana-3299	470	23	and	and	CCONJ
cana-3299	470	24	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟.	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝜃𝒮𝐼𝑟𝑟.	VERB
cana-3299	470	25	5	5	NUM
cana-3299	470	26	conclusion	conclusion	NOUN
cana-3299	470	27	in	in	ADP
cana-3299	470	28	this	this	DET
cana-3299	470	29	paper	paper	NOUN
cana-3299	470	30	,	,	PUNCT
cana-3299	470	31	using	use	VERB
cana-3299	470	32	𝑝𝑓𝑀𝑜𝑠	𝑝𝑓𝑀𝑜𝑠	ADV
cana-3299	470	33	we	we	PRON
cana-3299	470	34	have	have	AUX
cana-3299	470	35	defined	define	VERB
cana-3299	470	36	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀𝐶𝑡𝑠	NOUN
cana-3299	470	37	map	map	NOUN
cana-3299	470	38	and	and	CCONJ
cana-3299	470	39	analyzed	analyze	VERB
cana-3299	470	40	its	its	PRON
cana-3299	470	41	properties	property	NOUN
cana-3299	470	42	.	.	PUNCT
cana-3299	471	1	after	after	ADP
cana-3299	471	2	that	that	PRON
cana-3299	471	3	we	we	PRON
cana-3299	471	4	have	have	AUX
cana-3299	471	5	defined	define	VERB
cana-3299	471	6	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀-irresolute	𝑝𝑓𝑐𝑜𝑛𝑡𝑟𝑎𝑀-irresolute	NOUN
cana-3299	471	7	maps	map	NOUN
cana-3299	471	8	.	.	PUNCT
cana-3299	472	1	in	in	ADP
cana-3299	472	2	future	future	NOUN
cana-3299	472	3	,	,	PUNCT
cana-3299	472	4	these	these	DET
cana-3299	472	5	concepts	concept	NOUN
cana-3299	472	6	can	can	AUX
cana-3299	472	7	be	be	AUX
cana-3299	472	8	extended	extend	VERB
cana-3299	472	9	to	to	ADP
cana-3299	472	10	some	some	DET
cana-3299	472	11	mathematical	mathematical	ADJ
cana-3299	472	12	applications	application	NOUN
cana-3299	472	13	.	.	PUNCT
cana-3299	473	1	references	reference	NOUN
cana-3299	473	2	[	[	X
cana-3299	473	3	1	1	NUM
cana-3299	473	4	]	]	PUNCT
cana-3299	473	5	k.	k.	PROPN
cana-3299	473	6	t.	t.	PROPN
cana-3299	473	7	atanassov	atanassov	PROPN
cana-3299	473	8	(	(	PUNCT
cana-3299	473	9	1983	1983	NUM
cana-3299	473	10	)	)	PUNCT
cana-3299	473	11	,	,	PUNCT
cana-3299	473	12	intuitionistic	intuitionistic	ADJ
cana-3299	473	13	fuzzy	fuzzy	ADJ
cana-3299	473	14	sets	set	NOUN
cana-3299	473	15	,	,	PUNCT
cana-3299	473	16	vii	vii	PROPN
cana-3299	473	17	itkrâ€	itkrâ€	PROPN
cana-3299	473	18	™	™	PROPN
cana-3299	473	19	s	s	PART
cana-3299	473	20	session	session	NOUN
cana-3299	473	21	,	,	PUNCT
cana-3299	473	22	sofia	sofia	PROPN
cana-3299	473	23	.	.	PUNCT
cana-3299	474	1	[	[	X
cana-3299	474	2	2	2	X
cana-3299	474	3	]	]	PUNCT
cana-3299	474	4	k.	k.	PROPN
cana-3299	474	5	t.	t.	PROPN
cana-3299	474	6	atanassov	atanassov	PROPN
cana-3299	474	7	(	(	PUNCT
cana-3299	474	8	1986	1986	NUM
cana-3299	474	9	)	)	PUNCT
cana-3299	474	10	,	,	PUNCT
cana-3299	474	11	intuitionistic	intuitionistic	ADJ
cana-3299	474	12	fuzzy	fuzzy	ADJ
cana-3299	474	13	sets	set	NOUN
cana-3299	474	14	,	,	PUNCT
cana-3299	474	15	fuzzy	fuzzy	ADJ
cana-3299	474	16	sets	set	NOUN
cana-3299	474	17	syst	syst	NOUN
cana-3299	474	18	.	.	PUNCT
cana-3299	475	1	20	20	NUM
cana-3299	475	2	,	,	PUNCT
cana-3299	475	3	87	87	NUM
cana-3299	475	4	-	-	SYM
cana-3299	475	5	96	96	NUM
cana-3299	475	6	.	.	PUNCT
cana-3299	476	1	[	[	X
cana-3299	476	2	3	3	X
cana-3299	476	3	]	]	PUNCT
cana-3299	476	4	k.	k.	PROPN
cana-3299	476	5	t.	t.	PROPN
cana-3299	476	6	atanassov	atanassov	PROPN
cana-3299	476	7	(	(	PUNCT
cana-3299	476	8	1989	1989	NUM
cana-3299	476	9	)	)	PUNCT
cana-3299	476	10	,	,	PUNCT
cana-3299	476	11	geometrical	geometrical	ADJ
cana-3299	476	12	interpretation	interpretation	NOUN
cana-3299	476	13	of	of	ADP
cana-3299	476	14	the	the	DET
cana-3299	476	15	elements	element	NOUN
cana-3299	476	16	of	of	ADP
cana-3299	476	17	the	the	DET
cana-3299	476	18	intuitionistic	intuitionistic	ADJ
cana-3299	476	19	fuzzy	fuzzy	ADJ
cana-3299	476	20	objects	object	NOUN
cana-3299	476	21	,	,	PUNCT
cana-3299	476	22	preprint	preprint	NOUN
cana-3299	476	23	immfais-1	immfais-1	NOUN
cana-3299	476	24	-	-	SYM
cana-3299	476	25	89	89	NUM
cana-3299	476	26	,	,	PUNCT
cana-3299	476	27	sofia	sofia	NOUN
cana-3299	476	28	.	.	PUNCT
cana-3299	477	1	[	[	X
cana-3299	477	2	4	4	X
cana-3299	477	3	]	]	PUNCT
cana-3299	477	4	k.	k.	PROPN
cana-3299	477	5	t.	t.	PROPN
cana-3299	477	6	atanassov	atanassov	PROPN
cana-3299	477	7	(	(	PUNCT
cana-3299	477	8	1999	1999	NUM
cana-3299	477	9	)	)	PUNCT
cana-3299	477	10	,	,	PUNCT
cana-3299	477	11	intuitionistic	intuitionistic	ADJ
cana-3299	477	12	fuzzy	fuzzy	ADJ
cana-3299	477	13	sets	set	NOUN
cana-3299	477	14	:	:	PUNCT
cana-3299	477	15	theory	theory	NOUN
cana-3299	477	16	and	and	CCONJ
cana-3299	477	17	applications	application	NOUN
cana-3299	477	18	,	,	PUNCT
cana-3299	477	19	physica	physica	NOUN
cana-3299	477	20	,	,	PUNCT
cana-3299	477	21	heidelberg	heidelberg	NOUN
cana-3299	477	22	.	.	PUNCT
cana-3299	478	1	[	[	X
cana-3299	478	2	5	5	X
cana-3299	478	3	]	]	PUNCT
cana-3299	478	4	k.	k.	PROPN
cana-3299	478	5	t.	t.	PROPN
cana-3299	478	6	atanassov	atanassov	PROPN
cana-3299	478	7	(	(	PUNCT
cana-3299	478	8	2012	2012	NUM
cana-3299	478	9	)	)	PUNCT
cana-3299	478	10	,	,	PUNCT
cana-3299	478	11	on	on	ADP
cana-3299	478	12	intuitionistic	intuitionistic	ADJ
cana-3299	478	13	fuzzy	fuzzy	ADJ
cana-3299	478	14	sets	set	NOUN
cana-3299	478	15	theory	theory	NOUN
cana-3299	478	16	,	,	PUNCT
cana-3299	478	17	springer	springer	NOUN
cana-3299	478	18	,	,	PUNCT
cana-3299	478	19	berlin	berlin	PROPN
cana-3299	478	20	.	.	PUNCT
cana-3299	479	1	[	[	X
cana-3299	479	2	6	6	NUM
cana-3299	479	3	]	]	X
cana-3299	479	4	g.	g.	PROPN
cana-3299	479	5	beliakov	beliakov	PROPN
cana-3299	479	6	and	and	CCONJ
cana-3299	479	7	s.	s.	PROPN
cana-3299	479	8	james	james	PROPN
cana-3299	479	9	(	(	PUNCT
cana-3299	479	10	2014	2014	NUM
cana-3299	479	11	)	)	PUNCT
cana-3299	479	12	,	,	PUNCT
cana-3299	479	13	averaging	average	VERB
cana-3299	479	14	aggregation	aggregation	NOUN
cana-3299	479	15	functions	function	NOUN
cana-3299	479	16	for	for	ADP
cana-3299	479	17	preferences	preference	NOUN
cana-3299	479	18	expressed	express	VERB
cana-3299	479	19	as	as	ADP
cana-3299	479	20	pythagorean	pythagorean	PROPN
cana-3299	479	21	membership	membership	NOUN
cana-3299	479	22	grades	grade	NOUN
cana-3299	479	23	and	and	CCONJ
cana-3299	479	24	fuzzy	fuzzy	ADJ
cana-3299	479	25	orthopairs	orthopair	NOUN
cana-3299	479	26	,	,	PUNCT
cana-3299	479	27	in	in	ADP
cana-3299	479	28	:	:	PUNCT
cana-3299	479	29	proceedings	proceeding	NOUN
cana-3299	479	30	of	of	ADP
cana-3299	479	31	the	the	DET
cana-3299	479	32	ieee	ieee	NOUN
cana-3299	479	33	international	international	PROPN
cana-3299	479	34	conference	conference	NOUN
cana-3299	479	35	on	on	ADP
cana-3299	479	36	fuzzy	fuzzy	ADJ
cana-3299	479	37	systems	system	NOUN
cana-3299	479	38	(	(	PUNCT
cana-3299	479	39	fuzz	fuzz	NOUN
cana-3299	479	40	-	-	PUNCT
cana-3299	479	41	ieee	ieee	NOUN
cana-3299	479	42	)	)	PUNCT
cana-3299	479	43	,	,	PUNCT
cana-3299	479	44	298	298	NUM
cana-3299	479	45	-	-	SYM
cana-3299	479	46	305	305	NUM
cana-3299	479	47	.	.	PUNCT
cana-3299	480	1	[	[	X
cana-3299	480	2	7	7	X
cana-3299	480	3	]	]	X
cana-3299	480	4	b.	b.	PROPN
cana-3299	480	5	davvaz	davvaz	PROPN
cana-3299	480	6	and	and	CCONJ
cana-3299	480	7	e.	e.	PROPN
cana-3299	480	8	h.	h.	PROPN
cana-3299	480	9	sadrabadi	sadrabadi	PROPN
cana-3299	480	10	(	(	PUNCT
cana-3299	480	11	2016	2016	NUM
cana-3299	480	12	)	)	PUNCT
cana-3299	480	13	,	,	PUNCT
cana-3299	480	14	an	an	DET
cana-3299	480	15	application	application	NOUN
cana-3299	480	16	of	of	ADP
cana-3299	480	17	intuitionistic	intuitionistic	ADJ
cana-3299	480	18	fuzzy	fuzzy	ADJ
cana-3299	480	19	sets	set	NOUN
cana-3299	480	20	in	in	ADP
cana-3299	480	21	medicine	medicine	NOUN
cana-3299	480	22	,	,	PUNCT
cana-3299	480	23	int	int	NOUN
cana-3299	480	24	.	.	PUNCT
cana-3299	481	1	j.	j.	PROPN
cana-3299	481	2	biomath	biomath	PROPN
cana-3299	481	3	9	9	NUM
cana-3299	481	4	,	,	PUNCT
cana-3299	481	5	(	(	PUNCT
cana-3299	481	6	3	3	NUM
cana-3299	481	7	)	)	PUNCT
cana-3299	481	8	1650037	1650037	NUM
cana-3299	481	9	.	.	PUNCT
cana-3299	482	1	[	[	X
cana-3299	482	2	8	8	NUM
cana-3299	482	3	]	]	PUNCT
cana-3299	482	4	s.	s.	PROPN
cana-3299	482	5	k.	k.	PROPN
cana-3299	482	6	de	de	PROPN
cana-3299	482	7	,	,	PUNCT
cana-3299	482	8	r.	r.	PROPN
cana-3299	482	9	biswas	biswas	PROPN
cana-3299	482	10	and	and	CCONJ
cana-3299	482	11	a.	a.	PROPN
cana-3299	482	12	r.	r.	PROPN
cana-3299	482	13	roy	roy	PROPN
cana-3299	482	14	(	(	PUNCT
cana-3299	482	15	2001	2001	NUM
cana-3299	482	16	)	)	PUNCT
cana-3299	482	17	,	,	PUNCT
cana-3299	482	18	an	an	DET
cana-3299	482	19	application	application	NOUN
cana-3299	482	20	of	of	ADP
cana-3299	482	21	intuitionistic	intuitionistic	ADJ
cana-3299	482	22	fuzzy	fuzzy	ADJ
cana-3299	482	23	sets	set	NOUN
cana-3299	482	24	in	in	ADP
cana-3299	482	25	medical	medical	ADJ
cana-3299	482	26	diagnosis	diagnosis	NOUN
cana-3299	482	27	,	,	PUNCT
cana-3299	482	28	fuzzy	fuzzy	ADJ
cana-3299	482	29	sets	set	VERB
cana-3299	482	30	syst	syst	NOUN
cana-3299	482	31	.	.	PUNCT
cana-3299	482	32	117	117	NUM
cana-3299	482	33	(	(	PUNCT
cana-3299	482	34	2	2	NUM
cana-3299	482	35	)	)	PUNCT
cana-3299	482	36	,	,	PUNCT
cana-3299	482	37	209	209	NUM
cana-3299	482	38	-	-	SYM
cana-3299	482	39	213	213	NUM
cana-3299	482	40	.	.	PUNCT
cana-3299	483	1	[	[	X
cana-3299	483	2	9	9	NUM
cana-3299	483	3	]	]	PUNCT
cana-3299	483	4	s.	s.	PROPN
cana-3299	483	5	dick	dick	PROPN
cana-3299	483	6	,	,	PUNCT
cana-3299	483	7	r.	r.	PROPN
cana-3299	483	8	r.	r.	PROPN
cana-3299	483	9	yager	yager	PROPN
cana-3299	483	10	and	and	CCONJ
cana-3299	483	11	o.	o.	PROPN
cana-3299	483	12	yazdanbakhsh	yazdanbakhsh	PROPN
cana-3299	483	13	(	(	PUNCT
cana-3299	483	14	2016	2016	NUM
cana-3299	483	15	)	)	PUNCT
cana-3299	483	16	,	,	PUNCT
cana-3299	483	17	on	on	ADP
cana-3299	483	18	pythagorean	pythagorean	PROPN
cana-3299	483	19	and	and	CCONJ
cana-3299	483	20	complex	complex	ADJ
cana-3299	483	21	fuzzy	fuzzy	ADJ
cana-3299	483	22	set	set	NOUN
cana-3299	483	23	operations	operation	NOUN
cana-3299	483	24	.	.	PUNCT
cana-3299	484	1	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-3299	484	2	trans	trans	PROPN
cana-3299	484	3	fuzzy	fuzzy	ADJ
cana-3299	484	4	syst	syst	PROPN
cana-3299	484	5	.	.	PUNCT
cana-3299	485	1	24	24	NUM
cana-3299	485	2	(	(	PUNCT
cana-3299	485	3	5	5	NUM
cana-3299	485	4	)	)	PUNCT
cana-3299	485	5	,	,	PUNCT
cana-3299	485	6	1009	1009	NUM
cana-3299	485	7	-	-	SYM
cana-3299	485	8	1021	1021	NUM
cana-3299	485	9	.	.	PUNCT
cana-3299	486	1	[	[	X
cana-3299	486	2	10	10	NUM
cana-3299	486	3	]	]	X
cana-3299	486	4	p.	p.	NOUN
cana-3299	486	5	a.	a.	NOUN
cana-3299	486	6	ejegwa	ejegwa	PROPN
cana-3299	486	7	,	,	PUNCT
cana-3299	486	8	a.	a.	PROPN
cana-3299	486	9	j.	j.	PROPN
cana-3299	486	10	akubo	akubo	PROPN
cana-3299	486	11	and	and	CCONJ
cana-3299	486	12	o.	o.	PROPN
cana-3299	486	13	m.	m.	PROPN
cana-3299	486	14	joshua	joshua	PROPN
cana-3299	486	15	(	(	PUNCT
cana-3299	486	16	2014	2014	NUM
cana-3299	486	17	)	)	PUNCT
cana-3299	486	18	,	,	PUNCT
cana-3299	486	19	intuitionistic	intuitionistic	ADJ
cana-3299	486	20	fuzzzy	fuzzzy	ADJ
cana-3299	486	21	sets	set	NOUN
cana-3299	486	22	in	in	ADP
cana-3299	486	23	career	career	NOUN
cana-3299	486	24	determination	determination	NOUN
cana-3299	486	25	,	,	PUNCT
cana-3299	486	26	j	j	PROPN
cana-3299	486	27	info	info	NOUN
cana-3299	486	28	comput	comput	NOUN
cana-3299	486	29	.	.	PUNCT
cana-3299	487	1	sci	sci	PROPN
cana-3299	487	2	.	.	PROPN
cana-3299	487	3	9	9	NUM
cana-3299	487	4	(	(	PUNCT
cana-3299	487	5	4	4	NUM
cana-3299	487	6	)	)	PUNCT
cana-3299	487	7	,	,	PUNCT
cana-3299	487	8	285	285	NUM
cana-3299	487	9	-	-	SYM
cana-3299	487	10	288	288	NUM
cana-3299	487	11	.	.	PUNCT
cana-3299	488	1	[	[	X
cana-3299	488	2	11	11	NUM
cana-3299	488	3	]	]	PUNCT
cana-3299	488	4	p.	p.	NOUN
cana-3299	488	5	a.	a.	NOUN
cana-3299	488	6	ejegwa	ejegwa	PROPN
cana-3299	488	7	(	(	PUNCT
cana-3299	488	8	2015	2015	NUM
cana-3299	488	9	)	)	PUNCT
cana-3299	488	10	,	,	PUNCT
cana-3299	488	11	intuitionistic	intuitionistic	ADJ
cana-3299	488	12	fuzzy	fuzzy	ADJ
cana-3299	488	13	sets	set	NOUN
cana-3299	488	14	approach	approach	NOUN
cana-3299	488	15	in	in	ADP
cana-3299	488	16	appointment	appointment	NOUN
cana-3299	488	17	of	of	ADP
cana-3299	488	18	positions	position	NOUN
cana-3299	488	19	in	in	ADP
cana-3299	488	20	an	an	DET
cana-3299	488	21	organization	organization	NOUN
cana-3299	488	22	via	via	ADP
cana-3299	488	23	max–min–max	max–min–max	NOUN
cana-3299	488	24	rule	rule	NOUN
cana-3299	488	25	,	,	PUNCT
cana-3299	488	26	glob	glob	NOUN
cana-3299	488	27	.	.	PUNCT
cana-3299	489	1	j	j	PROPN
cana-3299	489	2	sci	sci	PROPN
cana-3299	489	3	.	.	PROPN
cana-3299	490	1	front	front	PROPN
cana-3299	490	2	res	res	PROPN
cana-3299	490	3	f	f	PROPN
cana-3299	490	4	math	math	PROPN
cana-3299	490	5	.	.	PUNCT
cana-3299	491	1	decis	decis	PROPN
cana-3299	491	2	.	.	PUNCT
cana-3299	492	1	sci	sci	PROPN
cana-3299	492	2	.	.	PROPN
cana-3299	492	3	15	15	NUM
cana-3299	492	4	(	(	PUNCT
cana-3299	492	5	6	6	NUM
cana-3299	492	6	)	)	PUNCT
cana-3299	492	7	,	,	PUNCT
cana-3299	492	8	1	1	NUM
cana-3299	492	9	-	-	SYM
cana-3299	492	10	6	6	NUM
cana-3299	492	11	.	.	PUNCT
cana-3299	493	1	[	[	X
cana-3299	493	2	12	12	NUM
cana-3299	493	3	]	]	X
cana-3299	493	4	p.	p.	NOUN
cana-3299	493	5	a.	a.	NOUN
cana-3299	493	6	ejegwa	ejegwa	PROPN
cana-3299	493	7	and	and	CCONJ
cana-3299	493	8	e.	e.	PROPN
cana-3299	493	9	s.	s.	PROPN
cana-3299	493	10	modom	modom	PROPN
cana-3299	493	11	(	(	PUNCT
cana-3299	493	12	2015	2015	NUM
cana-3299	493	13	)	)	PUNCT
cana-3299	493	14	,	,	PUNCT
cana-3299	493	15	diagnosis	diagnosis	NOUN
cana-3299	493	16	of	of	ADP
cana-3299	493	17	viral	viral	ADJ
cana-3299	493	18	hepatitis	hepatitis	NOUN
cana-3299	493	19	using	use	VERB
cana-3299	493	20	new	new	ADJ
cana-3299	493	21	distance	distance	NOUN
cana-3299	493	22	measure	measure	NOUN
cana-3299	493	23	of	of	ADP
cana-3299	493	24	intuitionistic	intuitionistic	ADJ
cana-3299	493	25	fuzzy	fuzzy	ADJ
cana-3299	493	26	sets	set	NOUN
cana-3299	493	27	,	,	PUNCT
cana-3299	493	28	int	int	NOUN
cana-3299	493	29	.	.	PUNCT
cana-3299	494	1	j.	j.	PROPN
cana-3299	494	2	fuzzy	fuzzy	PROPN
cana-3299	494	3	math	math	PROPN
cana-3299	494	4	.	.	PUNCT
cana-3299	495	1	arch	arch	NOUN
cana-3299	495	2	.	.	PUNCT
cana-3299	496	1	8	8	NUM
cana-3299	496	2	(	(	PUNCT
cana-3299	496	3	1	1	NUM
cana-3299	496	4	)	)	PUNCT
cana-3299	496	5	,	,	PUNCT
cana-3299	496	6	1	1	NUM
cana-3299	496	7	-	-	SYM
cana-3299	496	8	7	7	NUM
cana-3299	496	9	.	.	PUNCT
cana-3299	497	1	[	[	X
cana-3299	497	2	13	13	NUM
cana-3299	497	3	]	]	PUNCT
cana-3299	497	4	p.	p.	NOUN
cana-3299	497	5	a.	a.	NOUN
cana-3299	497	6	ejegwa	ejegwa	PROPN
cana-3299	497	7	(	(	PUNCT
cana-3299	497	8	2018	2018	NUM
cana-3299	497	9	)	)	PUNCT
cana-3299	497	10	,	,	PUNCT
cana-3299	497	11	distance	distance	NOUN
cana-3299	497	12	and	and	CCONJ
cana-3299	497	13	similarity	similarity	NOUN
cana-3299	497	14	measures	measure	NOUN
cana-3299	497	15	of	of	ADP
cana-3299	497	16	pythagorean	pythagorean	ADJ
cana-3299	497	17	fuzzy	fuzzy	ADJ
cana-3299	497	18	sets	set	NOUN
cana-3299	497	19	,	,	PUNCT
cana-3299	497	20	granul	granul	ADJ
cana-3299	497	21	comput	comput	NOUN
cana-3299	497	22	.	.	PUNCT
cana-3299	498	1	https://doi.org/10.1007/s41066-018-00149-z	https://doi.org/10.1007/s41066-018-00149-z	PROPN
cana-3299	498	2	.	.	PUNCT
cana-3299	499	1	[	[	X
cana-3299	499	2	14	14	NUM
cana-3299	499	3	]	]	X
cana-3299	499	4	h.	h.	PROPN
cana-3299	499	5	garg	garg	PROPN
cana-3299	499	6	(	(	PUNCT
cana-3299	499	7	2017	2017	NUM
cana-3299	499	8	)	)	PUNCT
cana-3299	499	9	,	,	PUNCT
cana-3299	499	10	a	a	DET
cana-3299	499	11	new	new	ADJ
cana-3299	499	12	improved	improve	VERB
cana-3299	499	13	score	score	NOUN
cana-3299	499	14	function	function	NOUN
cana-3299	499	15	of	of	ADP
cana-3299	499	16	an	an	DET
cana-3299	499	17	interval	interval	NOUN
cana-3299	499	18	-	-	PUNCT
cana-3299	499	19	valued	value	VERB
cana-3299	499	20	pythagorean	pythagorean	PROPN
cana-3299	499	21	fuzzy	fuzzy	PROPN
cana-3299	499	22	set	set	VERB
cana-3299	499	23	based	base	VERB
cana-3299	499	24	topsis	topsis	NOUN
cana-3299	499	25	method	method	NOUN
cana-3299	499	26	,	,	PUNCT
cana-3299	499	27	int	int	NOUN
cana-3299	499	28	.	.	PUNCT
cana-3299	500	1	j	j	PROPN
cana-3299	500	2	uncertain	uncertain	ADJ
cana-3299	500	3	quantif	quantif	PROPN
cana-3299	500	4	7	7	NUM
cana-3299	500	5	(	(	PUNCT
cana-3299	500	6	5	5	NUM
cana-3299	500	7	)	)	PUNCT
cana-3299	500	8	,	,	PUNCT
cana-3299	500	9	463	463	NUM
cana-3299	500	10	-	-	SYM
cana-3299	500	11	474	474	NUM
cana-3299	500	12	.	.	PUNCT
cana-3299	501	1	[	[	X
cana-3299	501	2	15	15	NUM
cana-3299	501	3	]	]	X
cana-3299	501	4	h.	h.	PROPN
cana-3299	501	5	garg	garg	PROPN
cana-3299	501	6	and	and	CCONJ
cana-3299	501	7	s.	s.	PROPN
cana-3299	501	8	singh	singh	PROPN
cana-3299	501	9	(	(	PUNCT
cana-3299	501	10	2018	2018	NUM
cana-3299	501	11	)	)	PUNCT
cana-3299	501	12	,	,	PUNCT
cana-3299	501	13	a	a	DET
cana-3299	501	14	novel	novel	ADJ
cana-3299	501	15	triangular	triangular	NOUN
cana-3299	501	16	interval	interval	NOUN
cana-3299	501	17	type-2	type-2	NUM
cana-3299	501	18	intuitionistic	intuitionistic	ADJ
cana-3299	501	19	fuzzy	fuzzy	ADJ
cana-3299	501	20	set	set	NOUN
cana-3299	501	21	and	and	CCONJ
cana-3299	501	22	their	their	PRON
cana-3299	501	23	aggregation	aggregation	NOUN
cana-3299	501	24	operators	operator	NOUN
cana-3299	501	25	,	,	PUNCT
cana-3299	501	26	iran	iran	PROPN
cana-3299	501	27	j	j	PROPN
cana-3299	501	28	fuzzy	fuzzy	PROPN
cana-3299	501	29	syst	syst	PROPN
cana-3299	501	30	.	.	PUNCT
cana-3299	502	1	15	15	NUM
cana-3299	502	2	(	(	PUNCT
cana-3299	502	3	5	5	NUM
cana-3299	502	4	)	)	PUNCT
cana-3299	502	5	,	,	PUNCT
cana-3299	502	6	69	69	NUM
cana-3299	502	7	-	-	SYM
cana-3299	502	8	93	93	NUM
cana-3299	502	9	.	.	PUNCT
cana-3299	503	1	[	[	X
cana-3299	503	2	16	16	NUM
cana-3299	503	3	]	]	X
cana-3299	503	4	h.	h.	PROPN
cana-3299	503	5	garg	garg	PROPN
cana-3299	503	6	and	and	CCONJ
cana-3299	503	7	k.	k.	PROPN
cana-3299	503	8	kumar	kumar	PROPN
cana-3299	503	9	(	(	PUNCT
cana-3299	503	10	2018	2018	NUM
cana-3299	503	11	)	)	PUNCT
cana-3299	503	12	,	,	PUNCT
cana-3299	503	13	distance	distance	NOUN
cana-3299	503	14	measures	measure	NOUN
cana-3299	503	15	for	for	ADP
cana-3299	503	16	connection	connection	NOUN
cana-3299	503	17	number	number	NOUN
cana-3299	503	18	sets	set	NOUN
cana-3299	503	19	based	base	VERB
cana-3299	503	20	on	on	ADP
cana-3299	503	21	set	set	VERB
cana-3299	503	22	pair	pair	NOUN
cana-3299	503	23	analysis	analysis	NOUN
cana-3299	503	24	and	and	CCONJ
cana-3299	503	25	its	its	PRON
cana-3299	503	26	applications	application	NOUN
cana-3299	503	27	to	to	PART
cana-3299	503	28	decision	decision	VERB
cana-3299	503	29	making	making	NOUN
cana-3299	503	30	process	process	NOUN
cana-3299	503	31	,	,	PUNCT
cana-3299	503	32	appl.intell	appl.intell	ADP
cana-3299	503	33	48	48	NUM
cana-3299	503	34	(	(	PUNCT
cana-3299	503	35	10	10	NUM
cana-3299	503	36	)	)	PUNCT
cana-3299	503	37	,	,	PUNCT
cana-3299	503	38	3346	3346	NUM
cana-3299	503	39	-	-	SYM
cana-3299	503	40	3359	3359	NUM
cana-3299	503	41	.	.	PUNCT
cana-3299	504	1	[	[	X
cana-3299	504	2	17	17	NUM
cana-3299	504	3	]	]	X
cana-3299	504	4	h.	h.	PROPN
cana-3299	504	5	garg	garg	PROPN
cana-3299	504	6	and	and	CCONJ
cana-3299	504	7	k.	k.	PROPN
cana-3299	504	8	kumar	kumar	PROPN
cana-3299	504	9	(	(	PUNCT
cana-3299	504	10	2018	2018	NUM
cana-3299	504	11	)	)	PUNCT
cana-3299	504	12	,	,	PUNCT
cana-3299	504	13	an	an	DET
cana-3299	504	14	advance	advance	NOUN
cana-3299	504	15	study	study	NOUN
cana-3299	504	16	on	on	ADP
cana-3299	504	17	the	the	DET
cana-3299	504	18	similarity	similarity	NOUN
cana-3299	504	19	measures	measure	NOUN
cana-3299	504	20	of	of	ADP
cana-3299	504	21	intuitionistic	intuitionistic	ADJ
cana-3299	504	22	fuzzy	fuzzy	ADJ
cana-3299	504	23	sets	set	NOUN
cana-3299	504	24	based	base	VERB
cana-3299	504	25	on	on	ADP
cana-3299	504	26	the	the	DET
cana-3299	504	27	set	set	VERB
cana-3299	504	28	pair	pair	NOUN
cana-3299	504	29	analysis	analysis	NOUN
cana-3299	504	30	theory	theory	NOUN
cana-3299	504	31	and	and	CCONJ
cana-3299	504	32	their	their	PRON
cana-3299	504	33	application	application	NOUN
cana-3299	504	34	in	in	ADP
cana-3299	504	35	decision	decision	NOUN
cana-3299	504	36	making	making	NOUN
cana-3299	504	37	,	,	PUNCT
cana-3299	504	38	soft	soft	ADJ
cana-3299	504	39	comput	comput	NOUN
cana-3299	504	40	.	.	PUNCT
cana-3299	505	1	22	22	NUM
cana-3299	505	2	(	(	PUNCT
cana-3299	505	3	15	15	NUM
cana-3299	505	4	)	)	PUNCT
cana-3299	505	5	,	,	PUNCT
cana-3299	505	6	4959	4959	NUM
cana-3299	505	7	-	-	SYM
cana-3299	505	8	4970	4970	NUM
cana-3299	505	9	.	.	PUNCT
cana-3299	506	1	[	[	X
cana-3299	506	2	18	18	NUM
cana-3299	506	3	]	]	PUNCT
cana-3299	506	4	x.	x.	NOUN
cana-3299	506	5	j.	j.	PROPN
cana-3299	506	6	gou	gou	PROPN
cana-3299	506	7	,	,	PUNCT
cana-3299	506	8	z.	z.	PROPN
cana-3299	506	9	s.	s.	PROPN
cana-3299	506	10	xu	xu	PROPN
cana-3299	506	11	and	and	CCONJ
cana-3299	506	12	p.	p.	PROPN
cana-3299	506	13	j.	j.	PROPN
cana-3299	506	14	ren	ren	PROPN
cana-3299	506	15	(	(	PUNCT
cana-3299	506	16	2016	2016	NUM
cana-3299	506	17	)	)	PUNCT
cana-3299	506	18	,	,	PUNCT
cana-3299	506	19	the	the	DET
cana-3299	506	20	properties	property	NOUN
cana-3299	506	21	of	of	ADP
cana-3299	506	22	continuous	continuous	ADJ
cana-3299	506	23	pyhagorean	pyhagorean	NOUN
cana-3299	506	24	fuzzy	fuzzy	ADJ
cana-3299	506	25	information	information	NOUN
cana-3299	506	26	,	,	PUNCT
cana-3299	506	27	int	int	NOUN
cana-3299	506	28	.	.	PUNCT
cana-3299	507	1	j	j	PROPN
cana-3299	507	2	intell	intell	PROPN
cana-3299	507	3	.	.	PUNCT
cana-3299	508	1	syst	syst	PROPN
cana-3299	508	2	.	.	PUNCT
cana-3299	509	1	31	31	NUM
cana-3299	509	2	(	(	PUNCT
cana-3299	509	3	5	5	NUM
cana-3299	509	4	)	)	PUNCT
cana-3299	509	5	,	,	PUNCT
cana-3299	509	6	401	401	NUM
cana-3299	509	7	-	-	SYM
cana-3299	509	8	424	424	NUM
cana-3299	509	9	.	.	PUNCT
cana-3299	510	1	[	[	X
cana-3299	510	2	19	19	NUM
cana-3299	510	3	]	]	PUNCT
cana-3299	510	4	x.	x.	NOUN
cana-3299	510	5	he	he	PRON
cana-3299	510	6	,	,	PUNCT
cana-3299	510	7	y.	y.	PROPN
cana-3299	510	8	du	du	PROPN
cana-3299	510	9	and	and	CCONJ
cana-3299	510	10	w.	w.	PROPN
cana-3299	510	11	liu	liu	PROPN
cana-3299	510	12	(	(	PUNCT
cana-3299	510	13	2016	2016	NUM
cana-3299	510	14	)	)	PUNCT
cana-3299	510	15	,	,	PUNCT
cana-3299	510	16	pythagorean	pythagorean	VERB
cana-3299	510	17	fuzzy	fuzzy	ADJ
cana-3299	510	18	power	power	PROPN
cana-3299	510	19	average	average	ADJ
cana-3299	510	20	operators	operator	NOUN
cana-3299	510	21	,	,	PUNCT
cana-3299	510	22	fuzzy	fuzzy	ADJ
cana-3299	510	23	syst	syst	NOUN
cana-3299	510	24	.	.	PUNCT
cana-3299	510	25	math	math	NOUN
cana-3299	510	26	.	.	PUNCT
cana-3299	511	1	30	30	NUM
cana-3299	511	2	(	(	PUNCT
cana-3299	511	3	6	6	NUM
cana-3299	511	4	)	)	PUNCT
cana-3299	511	5	,	,	PUNCT
cana-3299	511	6	116	116	NUM
cana-3299	511	7	-	-	SYM
cana-3299	511	8	124	124	NUM
cana-3299	511	9	.	.	PUNCT
cana-3299	512	1	[	[	X
cana-3299	512	2	20	20	NUM
cana-3299	512	3	]	]	X
cana-3299	512	4	d.	d.	PROPN
cana-3299	512	5	jeeva	jeeva	PROPN
cana-3299	512	6	,	,	PUNCT
cana-3299	512	7	d.sivakumar	d.sivakumar	NOUN
cana-3299	512	8	and	and	CCONJ
cana-3299	512	9	a.	a.	NOUN
cana-3299	512	10	vadivel	vadivel	NOUN
cana-3299	512	11	(	(	PUNCT
cana-3299	512	12	2023	2023	NUM
cana-3299	512	13	)	)	PUNCT
cana-3299	512	14	,	,	PUNCT
cana-3299	512	15	contra	contra	PROPN
cana-3299	512	16	𝑀-continuous	𝑀-continuous	ADJ
cana-3299	512	17	maps	map	NOUN
cana-3299	512	18	in	in	ADP
cana-3299	512	19	neutrosophic	neutrosophic	ADJ
cana-3299	512	20	soft	soft	ADJ
cana-3299	512	21	topological	topological	ADJ
cana-3299	512	22	spaces	space	NOUN
cana-3299	512	23	,	,	PUNCT
cana-3299	512	24	ijns	ijns	PROPN
cana-3299	512	25	,	,	PUNCT
cana-3299	512	26	20	20	NUM
cana-3299	512	27	(	(	PUNCT
cana-3299	512	28	3	3	NUM
cana-3299	512	29	)	)	PUNCT
cana-3299	512	30	,	,	PUNCT
cana-3299	512	31	98	98	NUM
cana-3299	512	32	-	-	SYM
cana-3299	512	33	106	106	NUM
cana-3299	512	34	.	.	PUNCT
cana-3299	513	1	[	[	X
cana-3299	513	2	21	21	NUM
cana-3299	513	3	]	]	X
cana-3299	513	4	d.	d.	PROPN
cana-3299	513	5	jeeva	jeeva	PROPN
cana-3299	513	6	,	,	PUNCT
cana-3299	513	7	a.	a.	NOUN
cana-3299	513	8	vadivel	vadivel	NOUN
cana-3299	513	9	and	and	CCONJ
cana-3299	513	10	d.	d.	PROPN
cana-3299	513	11	sivakumar	sivakumar	PROPN
cana-3299	513	12	(	(	PUNCT
cana-3299	513	13	2023	2023	NUM
cana-3299	513	14	)	)	PUNCT
cana-3299	513	15	,	,	PUNCT
cana-3299	513	16	𝑀-continuous	𝑀-continuous	PROPN
cana-3299	513	17	and	and	CCONJ
cana-3299	513	18	𝑀-irresolute	𝑀-irresolute	PROPN
cana-3299	513	19	maps	map	NOUN
cana-3299	513	20	in	in	ADP
cana-3299	513	21	neutrosophic	neutrosophic	ADJ
cana-3299	513	22	soft	soft	ADJ
cana-3299	513	23	topological	topological	ADJ
cana-3299	513	24	spaces	space	NOUN
cana-3299	513	25	,	,	PUNCT
cana-3299	513	26	aip	aip	PROPN
cana-3299	513	27	conference	conference	NOUN
cana-3299	513	28	proceedings	proceeding	NOUN
cana-3299	513	29	,	,	PUNCT
cana-3299	513	30	2852	2852	NUM
cana-3299	513	31	,	,	PUNCT
cana-3299	513	32	150001	150001	NUM
cana-3299	513	33	.	.	PUNCT
cana-3299	514	1	[	[	X
cana-3299	514	2	22	22	NUM
cana-3299	514	3	]	]	X
cana-3299	514	4	d.	d.	PROPN
cana-3299	514	5	jeeva	jeeva	PROPN
cana-3299	514	6	,	,	PUNCT
cana-3299	514	7	a.	a.	NOUN
cana-3299	514	8	vadivel	vadivel	NOUN
cana-3299	514	9	and	and	CCONJ
cana-3299	514	10	d.	d.	PROPN
cana-3299	514	11	sivakumar	sivakumar	PROPN
cana-3299	514	12	(	(	PUNCT
cana-3299	514	13	2023	2023	NUM
cana-3299	514	14	)	)	PUNCT
cana-3299	514	15	,	,	PUNCT
cana-3299	514	16	maps	map	NOUN
cana-3299	514	17	and	and	CCONJ
cana-3299	514	18	homeomorphisms	homeomorphism	NOUN
cana-3299	514	19	via	via	ADP
cana-3299	514	20	𝑀-open	𝑀-open	PROPN
cana-3299	514	21	sets	set	NOUN
cana-3299	514	22	in	in	ADP
cana-3299	514	23	neutrosophic	neutrosophic	ADJ
cana-3299	514	24	soft	soft	ADJ
cana-3299	514	25	topological	topological	ADJ
cana-3299	514	26	spaces	space	NOUN
cana-3299	514	27	,	,	PUNCT
cana-3299	514	28	south	south	PROPN
cana-3299	514	29	east	east	PROPN
cana-3299	514	30	asian	asian	PROPN
cana-3299	514	31	j.	j.	PROPN
cana-3299	514	32	of	of	ADP
cana-3299	514	33	mathematics	mathematics	PROPN
cana-3299	514	34	and	and	CCONJ
cana-3299	514	35	mathematical	mathematical	ADJ
cana-3299	514	36	sciences	science	NOUN
cana-3299	514	37	19	19	NUM
cana-3299	514	38	(	(	PUNCT
cana-3299	514	39	1	1	NUM
cana-3299	514	40	)	)	PUNCT
cana-3299	514	41	(	(	PUNCT
cana-3299	514	42	2023	2023	NUM
cana-3299	514	43	)	)	PUNCT
cana-3299	514	44	,	,	PUNCT
cana-3299	514	45	367	367	NUM
cana-3299	514	46	-	-	SYM
cana-3299	514	47	384	384	NUM
cana-3299	514	48	.	.	PUNCT
cana-3299	515	1	[	[	X
cana-3299	515	2	23	23	NUM
cana-3299	515	3	]	]	PUNCT
cana-3299	515	4	a.	a.	PROPN
cana-3299	515	5	i.	i.	PROPN
cana-3299	515	6	el	el	PROPN
cana-3299	515	7	-	-	PUNCT
cana-3299	515	8	maghrabi	maghrabi	NOUN
cana-3299	515	9	and	and	CCONJ
cana-3299	515	10	m.	m.	NOUN
cana-3299	515	11	a.	a.	PROPN
cana-3299	515	12	al	al	PROPN
cana-3299	515	13	-	-	PUNCT
cana-3299	515	14	juhani	juhani	PROPN
cana-3299	515	15	,	,	PUNCT
cana-3299	515	16	𝑀open	𝑀open	NOUN
cana-3299	515	17	sets	set	NOUN
cana-3299	515	18	in	in	ADP
cana-3299	515	19	topological	topological	ADJ
cana-3299	515	20	spaces	space	NOUN
cana-3299	515	21	,	,	PUNCT
cana-3299	515	22	pioneer	pioneer	PROPN
cana-3299	515	23	j.	j.	PROPN
cana-3299	515	24	math	math	PROPN
cana-3299	515	25	.	.	PUNCT
cana-3299	516	1	sci	sci	PROPN
cana-3299	516	2	.	.	PROPN
cana-3299	516	3	,	,	PUNCT
cana-3299	516	4	4	4	NUM
cana-3299	516	5	(	(	PUNCT
cana-3299	516	6	2	2	NUM
cana-3299	516	7	)	)	PUNCT
cana-3299	516	8	(	(	PUNCT
cana-3299	516	9	2011	2011	NUM
cana-3299	516	10	)	)	PUNCT
cana-3299	516	11	,	,	PUNCT
cana-3299	516	12	213230	213230	NUM
cana-3299	516	13	.	.	PUNCT
cana-3299	517	1	[	[	X
cana-3299	517	2	24	24	NUM
cana-3299	517	3	]	]	X
cana-3299	517	4	murat	murat	PROPN
cana-3299	517	5	olgun	olgun	PROPN
cana-3299	517	6	,	,	PUNCT
cana-3299	517	7	mehmet	mehmet	PROPN
cana-3299	517	8	unver	unver	PROPN
cana-3299	517	9	and	and	CCONJ
cana-3299	517	10	seyhmus	seyhmus	VERB
cana-3299	517	11	yardimci	yardimci	PROPN
cana-3299	517	12	(	(	PUNCT
cana-3299	517	13	2019	2019	NUM
cana-3299	517	14	)	)	PUNCT
cana-3299	517	15	,	,	PUNCT
cana-3299	517	16	pythagorean	pythagorean	PROPN
cana-3299	517	17	fuzzy	fuzzy	ADJ
cana-3299	517	18	topological	topological	ADJ
cana-3299	517	19	spaces	space	NOUN
cana-3299	517	20	,	,	PUNCT
cana-3299	517	21	complex	complex	ADJ
cana-3299	517	22	&	&	CCONJ
cana-3299	517	23	intelligent	intelligent	ADJ
cana-3299	517	24	systems	system	NOUN
cana-3299	517	25	.	.	PUNCT
cana-3299	518	1	https://doi.org/10.1007/s40747019-0095-2	https://doi.org/10.1007/s40747019-0095-2	PROPN
cana-3299	518	2	.	.	PUNCT
cana-3299	519	1	[	[	X
cana-3299	519	2	25	25	NUM
cana-3299	519	3	]	]	PUNCT
cana-3299	519	4	x.	x.	NOUN
cana-3299	519	5	peng	peng	PROPN
cana-3299	519	6	and	and	CCONJ
cana-3299	519	7	y.	y.	PROPN
cana-3299	519	8	yang	yang	PROPN
cana-3299	519	9	(	(	PUNCT
cana-3299	519	10	2015	2015	NUM
cana-3299	519	11	)	)	PUNCT
cana-3299	519	12	,	,	PUNCT
cana-3299	519	13	some	some	PRON
cana-3299	519	14	results	result	VERB
cana-3299	519	15	for	for	ADP
cana-3299	519	16	pythagorean	pythagorean	ADJ
cana-3299	519	17	fuzzy	fuzzy	ADJ
cana-3299	519	18	sets	set	NOUN
cana-3299	519	19	,	,	PUNCT
cana-3299	519	20	int	int	NOUN
cana-3299	519	21	.	.	PUNCT
cana-3299	520	1	j	j	PROPN
cana-3299	520	2	intell	intell	PROPN
cana-3299	520	3	syst	syst	PROPN
cana-3299	520	4	.	.	PUNCT
cana-3299	521	1	30	30	NUM
cana-3299	521	2	,	,	PUNCT
cana-3299	521	3	1133	1133	NUM
cana-3299	521	4	-	-	SYM
cana-3299	521	5	1160	1160	NUM
cana-3299	521	6	.	.	PUNCT
cana-3299	522	1	[	[	X
cana-3299	522	2	26	26	NUM
cana-3299	522	3	]	]	PUNCT
cana-3299	522	4	x.	x.	NOUN
cana-3299	522	5	peng	peng	PROPN
cana-3299	522	6	and	and	CCONJ
cana-3299	522	7	g.	g.	PROPN
cana-3299	522	8	selvachandran	selvachandran	PROPN
cana-3299	522	9	(	(	PUNCT
cana-3299	522	10	2017	2017	NUM
cana-3299	522	11	)	)	PUNCT
cana-3299	522	12	,	,	PUNCT
cana-3299	522	13	pythagorean	pythagorean	PROPN
cana-3299	522	14	fuzzy	fuzzy	PROPN
cana-3299	522	15	set	set	VERB
cana-3299	522	16	state	state	NOUN
cana-3299	522	17	of	of	ADP
cana-3299	522	18	the	the	DET
cana-3299	522	19	art	art	NOUN
cana-3299	522	20	and	and	CCONJ
cana-3299	522	21	future	future	ADJ
cana-3299	522	22	directions	direction	NOUN
cana-3299	522	23	,	,	PUNCT
cana-3299	522	24	artif	artif	PROPN
cana-3299	522	25	intell	intell	PROPN
cana-3299	522	26	rev	rev	VERB
cana-3299	522	27	.	.	PUNCT
cana-3299	522	28	https://doi.org/10.1007/s10462-017-9596-9	https://doi.org/10.1007/s10462-017-9596-9	PROPN
cana-3299	522	29	.	.	PUNCT
cana-3299	523	1	https://doi.org/10.1007/s40747communications	https://doi.org/10.1007/s40747communication	NOUN
cana-3299	523	2	on	on	ADP
cana-3299	523	3	applied	apply	VERB
cana-3299	523	4	nonlinear	nonlinear	ADJ
cana-3299	523	5	analysis	analysis	NOUN
cana-3299	523	6	issn	issn	NOUN
cana-3299	523	7	:	:	PUNCT
cana-3299	523	8	1074	1074	NUM
cana-3299	523	9	-	-	PUNCT
cana-3299	523	10	133x	133x	NUM
cana-3299	523	11	vol	vol	NOUN
cana-3299	523	12	32	32	NUM
cana-3299	523	13	no	no	NOUN
cana-3299	523	14	.	.	PUNCT
cana-3299	524	1	6s	6s	NUM
cana-3299	524	2	(	(	PUNCT
cana-3299	524	3	2025	2025	NUM
cana-3299	524	4	)	)	PUNCT
cana-3299	524	5	339	339	NUM
cana-3299	524	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-3299	525	1	[	[	X
cana-3299	525	2	27	27	NUM
cana-3299	525	3	]	]	X
cana-3299	525	4	supriti	supriti	PROPN
cana-3299	525	5	saha	saha	PROPN
cana-3299	525	6	,	,	PUNCT
cana-3299	525	7	fuzzy	fuzzy	ADJ
cana-3299	525	8	𝛿-continuous	𝛿-continuous	ADJ
cana-3299	525	9	mappings	mapping	NOUN
cana-3299	525	10	,	,	PUNCT
cana-3299	525	11	journal	journal	NOUN
cana-3299	525	12	of	of	ADP
cana-3299	525	13	mathematical	mathematical	ADJ
cana-3299	525	14	analysis	analysis	NOUN
cana-3299	525	15	and	and	CCONJ
cana-3299	525	16	applications	application	NOUN
cana-3299	525	17	,	,	PUNCT
cana-3299	525	18	126	126	NUM
cana-3299	525	19	(	(	PUNCT
cana-3299	525	20	1987	1987	NUM
cana-3299	525	21	)	)	PUNCT
cana-3299	525	22	,	,	PUNCT
cana-3299	525	23	130142	130142	NUM
cana-3299	525	24	.	.	PUNCT
cana-3299	526	1	[	[	X
cana-3299	526	2	28	28	NUM
cana-3299	526	3	]	]	X
cana-3299	526	4	e.	e.	PROPN
cana-3299	526	5	szmidt	szmidt	PROPN
cana-3299	526	6	and	and	CCONJ
cana-3299	526	7	j.	j.	PROPN
cana-3299	526	8	kacprzyk	kacprzyk	PROPN
cana-3299	526	9	(	(	PUNCT
cana-3299	526	10	2001	2001	NUM
cana-3299	526	11	)	)	PUNCT
cana-3299	526	12	,	,	PUNCT
cana-3299	526	13	intuitionistic	intuitionistic	ADJ
cana-3299	526	14	fuzzy	fuzzy	ADJ
cana-3299	526	15	sets	set	NOUN
cana-3299	526	16	in	in	ADP
cana-3299	526	17	some	some	DET
cana-3299	526	18	medical	medical	ADJ
cana-3299	526	19	applications	application	NOUN
cana-3299	526	20	,	,	PUNCT
cana-3299	526	21	note	note	VERB
cana-3299	526	22	ifs	ifs	PROPN
cana-3299	526	23	7	7	NUM
cana-3299	526	24	(	(	PUNCT
cana-3299	526	25	4	4	NUM
cana-3299	526	26	)	)	PUNCT
cana-3299	526	27	,	,	PUNCT
cana-3299	526	28	58	58	NUM
cana-3299	526	29	-	-	SYM
cana-3299	526	30	64	64	NUM
cana-3299	526	31	.	.	PUNCT
cana-3299	527	1	[	[	X
cana-3299	527	2	29	29	NUM
cana-3299	527	3	]	]	PUNCT
cana-3299	527	4	e.	e.	PROPN
cana-3299	527	5	szmidt	szmidt	PROPN
cana-3299	527	6	and	and	CCONJ
cana-3299	527	7	j.	j.	PROPN
cana-3299	527	8	kacprzyk	kacprzyk	PROPN
cana-3299	527	9	(	(	PUNCT
cana-3299	527	10	2004	2004	NUM
cana-3299	527	11	)	)	PUNCT
cana-3299	527	12	,	,	PUNCT
cana-3299	527	13	medical	medical	ADJ
cana-3299	527	14	diagnostic	diagnostic	ADJ
cana-3299	527	15	reasoning	reasoning	NOUN
cana-3299	527	16	using	use	VERB
cana-3299	527	17	a	a	DET
cana-3299	527	18	similarity	similarity	NOUN
cana-3299	527	19	measure	measure	NOUN
cana-3299	527	20	for	for	ADP
cana-3299	527	21	intuitionistic	intuitionistic	ADJ
cana-3299	527	22	fuzzy	fuzzy	ADJ
cana-3299	527	23	sets	set	NOUN
cana-3299	527	24	,	,	PUNCT
cana-3299	527	25	note	note	VERB
cana-3299	527	26	ifs	ifs	PROPN
cana-3299	527	27	10	10	NUM
cana-3299	527	28	(	(	PUNCT
cana-3299	527	29	4	4	NUM
cana-3299	527	30	)	)	PUNCT
cana-3299	527	31	,	,	PUNCT
cana-3299	527	32	61	61	NUM
cana-3299	527	33	-	-	SYM
cana-3299	527	34	69	69	NUM
cana-3299	527	35	.	.	PUNCT
cana-3299	528	1	[	[	X
cana-3299	528	2	30	30	NUM
cana-3299	528	3	]	]	X
cana-3299	528	4	m.	m.	NOUN
cana-3299	528	5	udhaya	udhaya	PROPN
cana-3299	528	6	shalini	shalini	PROPN
cana-3299	528	7	and	and	CCONJ
cana-3299	528	8	a.	a.	PROPN
cana-3299	528	9	stanis	stanis	PROPN
cana-3299	528	10	arul	arul	PROPN
cana-3299	528	11	mary	mary	PROPN
cana-3299	528	12	(	(	PUNCT
cana-3299	528	13	2022	2022	NUM
cana-3299	528	14	)	)	PUNCT
cana-3299	528	15	,	,	PUNCT
cana-3299	528	16	generalized	generalize	VERB
cana-3299	528	17	pre	pre	ADJ
cana-3299	528	18	-	-	ADJ
cana-3299	528	19	closed	closed	ADJ
cana-3299	528	20	sets	set	NOUN
cana-3299	528	21	in	in	ADP
cana-3299	528	22	pythagorean	pythagorean	PROPN
cana-3299	528	23	fuzzy	fuzzy	ADJ
cana-3299	528	24	topological	topological	ADJ
cana-3299	528	25	spaces	space	NOUN
cana-3299	528	26	,	,	PUNCT
cana-3299	528	27	international	international	ADJ
cana-3299	528	28	journal	journal	NOUN
cana-3299	528	29	of	of	ADP
cana-3299	528	30	creative	creative	ADJ
cana-3299	528	31	research	research	NOUN
cana-3299	528	32	thoughts	thought	NOUN
cana-3299	528	33	(	(	PUNCT
cana-3299	528	34	ijcrt	ijcrt	NOUN
cana-3299	528	35	)	)	PUNCT
cana-3299	528	36	,	,	PUNCT
cana-3299	528	37	10	10	NUM
cana-3299	528	38	(	(	PUNCT
cana-3299	528	39	30	30	NUM
cana-3299	528	40	)	)	PUNCT
cana-3299	528	41	,	,	PUNCT
cana-3299	528	42	e142	e142	PROPN
cana-3299	528	43	-	-	PUNCT
cana-3299	528	44	e147	e147	PROPN
cana-3299	528	45	.	.	PUNCT
cana-3299	529	1	[	[	X
cana-3299	529	2	31	31	NUM
cana-3299	529	3	]	]	PUNCT
cana-3299	529	4	a.	a.	NOUN
cana-3299	529	5	vadivel	vadivel	NOUN
cana-3299	529	6	,	,	PUNCT
cana-3299	529	7	m.	m.	NOUN
cana-3299	529	8	seenivasan	seenivasan	NOUN
cana-3299	529	9	and	and	CCONJ
cana-3299	529	10	c.	c.	PROPN
cana-3299	529	11	john	john	PROPN
cana-3299	529	12	sundar	sundar	PROPN
cana-3299	529	13	,	,	PUNCT
cana-3299	529	14	an	an	DET
cana-3299	529	15	introduction	introduction	NOUN
cana-3299	529	16	to	to	PART
cana-3299	529	17	𝛿-open	𝛿-open	VERB
cana-3299	529	18	sets	set	NOUN
cana-3299	529	19	in	in	ADP
cana-3299	529	20	a	a	DET
cana-3299	529	21	neutrosophic	neutrosophic	ADJ
cana-3299	529	22	topological	topological	ADJ
cana-3299	529	23	spaces	space	NOUN
cana-3299	529	24	,	,	PUNCT
cana-3299	529	25	journal	journal	NOUN
cana-3299	529	26	of	of	ADP
cana-3299	529	27	physics	physics	PROPN
cana-3299	529	28	:	:	PUNCT
cana-3299	529	29	conference	conference	NOUN
cana-3299	529	30	series	series	NOUN
cana-3299	529	31	,	,	PUNCT
cana-3299	529	32	1724	1724	NUM
cana-3299	529	33	(	(	PUNCT
cana-3299	529	34	2021	2021	NUM
cana-3299	529	35	)	)	PUNCT
cana-3299	529	36	,	,	PUNCT
cana-3299	529	37	012011	012011	NUM
cana-3299	529	38	.	.	PUNCT
cana-3299	530	1	[	[	X
cana-3299	530	2	32	32	NUM
cana-3299	530	3	]	]	PUNCT
cana-3299	530	4	b.	b.	PROPN
cana-3299	530	5	vijayalakshmi	vijayalakshmi	NOUN
cana-3299	530	6	,	,	PUNCT
cana-3299	530	7	m.	m.	NOUN
cana-3299	530	8	ramalakshmi	ramalakshmi	NOUN
cana-3299	530	9	,	,	PUNCT
cana-3299	530	10	a.	a.	NOUN
cana-3299	530	11	vadivel	vadivel	NOUN
cana-3299	530	12	and	and	CCONJ
cana-3299	530	13	g.	g.	PROPN
cana-3299	530	14	saravanakumar	saravanakumar	PROPN
cana-3299	530	15	,	,	PUNCT
cana-3299	530	16	more	more	ADJ
cana-3299	530	17	on	on	ADP
cana-3299	530	18	maps	map	NOUN
cana-3299	530	19	and	and	CCONJ
cana-3299	530	20	its	its	PRON
cana-3299	530	21	application	application	NOUN
cana-3299	530	22	in	in	ADP
cana-3299	530	23	pythagorean	pythagorean	PROPN
cana-3299	530	24	fuzzy	fuzzy	ADJ
cana-3299	530	25	topological	topological	ADJ
cana-3299	530	26	spaces	space	NOUN
cana-3299	530	27	,	,	PUNCT
cana-3299	530	28	nanotechnology	nanotechnology	NOUN
cana-3299	530	29	perceptions	perception	NOUN
cana-3299	530	30	.	.	PUNCT
cana-3299	531	1	20(s14	20(s14	X
cana-3299	531	2	)	)	PUNCT
cana-3299	531	3	2024,1601	2024,1601	NOUN
cana-3299	531	4	-	-	SYM
cana-3299	531	5	1615	1615	NUM
cana-3299	531	6	.	.	PUNCT
cana-3299	532	1	[	[	X
cana-3299	532	2	33	33	NUM
cana-3299	532	3	]	]	PUNCT
cana-3299	532	4	r.	r.	PROPN
cana-3299	532	5	r.	r.	PROPN
cana-3299	532	6	yager	yager	PROPN
cana-3299	532	7	(	(	PUNCT
cana-3299	532	8	2013	2013	NUM
cana-3299	532	9	)	)	PUNCT
cana-3299	532	10	,	,	PUNCT
cana-3299	532	11	pythagorean	pythagorean	PROPN
cana-3299	532	12	membership	membership	NOUN
cana-3299	532	13	grades	grade	NOUN
cana-3299	532	14	in	in	ADP
cana-3299	532	15	multicriteria	multicriteria	PROPN
cana-3299	532	16	decision	decision	NOUN
cana-3299	532	17	making	making	NOUN
cana-3299	532	18	,	,	PUNCT
cana-3299	532	19	in	in	ADP
cana-3299	532	20	:	:	PUNCT
cana-3299	532	21	technical	technical	ADJ
cana-3299	532	22	report	report	NOUN
cana-3299	532	23	𝑀𝐼𝐼3301	𝑀𝐼𝐼3301	PROPN
cana-3299	532	24	.	.	PUNCT
cana-3299	533	1	machine	machine	NOUN
cana-3299	533	2	intelligence	intelligence	PROPN
cana-3299	533	3	institute	institute	PROPN
cana-3299	533	4	,	,	PUNCT
cana-3299	533	5	iona	iona	PROPN
cana-3299	533	6	college	college	PROPN
cana-3299	533	7	,	,	PUNCT
cana-3299	533	8	new	new	ADJ
cana-3299	533	9	rochelle	rochelle	NOUN
cana-3299	533	10	.	.	PUNCT
cana-3299	534	1	[	[	X
cana-3299	534	2	34	34	NUM
cana-3299	534	3	]	]	X
cana-3299	534	4	r.	r.	PROPN
cana-3299	534	5	r.	r.	PROPN
cana-3299	534	6	yager	yager	PROPN
cana-3299	534	7	(	(	PUNCT
cana-3299	534	8	2013	2013	NUM
cana-3299	534	9	)	)	PUNCT
cana-3299	534	10	,	,	PUNCT
cana-3299	534	11	pythagorean	pythagorean	PROPN
cana-3299	534	12	fuzzy	fuzzy	ADJ
cana-3299	534	13	subsets	subset	NOUN
cana-3299	534	14	,	,	PUNCT
cana-3299	534	15	in	in	ADP
cana-3299	534	16	:	:	PUNCT
cana-3299	534	17	proceedings	proceeding	NOUN
cana-3299	534	18	of	of	ADP
cana-3299	534	19	the	the	DET
cana-3299	534	20	joint	joint	ADJ
cana-3299	534	21	𝐼𝐹𝑆𝐴	𝐼𝐹𝑆𝐴	PROPN
cana-3299	534	22	world	world	PROPN
cana-3299	534	23	congress	congress	PROPN
cana-3299	534	24	𝑁𝐴𝐹𝐼𝑃𝑆	𝑁𝐴𝐹𝐼𝑃𝑆	PROPN
cana-3299	534	25	annual	annual	ADJ
cana-3299	534	26	meeting	meeting	NOUN
cana-3299	534	27	,	,	PUNCT
cana-3299	534	28	57	57	NUM
cana-3299	534	29	-	-	SYM
cana-3299	534	30	61	61	NUM
cana-3299	534	31	.	.	PUNCT
cana-3299	535	1	[	[	X
cana-3299	535	2	35	35	NUM
cana-3299	535	3	]	]	X
cana-3299	535	4	r.	r.	PROPN
cana-3299	535	5	r.	r.	PROPN
cana-3299	535	6	yager	yager	PROPN
cana-3299	535	7	(	(	PUNCT
cana-3299	535	8	2014	2014	NUM
cana-3299	535	9	)	)	PUNCT
cana-3299	535	10	,	,	PUNCT
cana-3299	535	11	pythagorean	pythagorean	PROPN
cana-3299	535	12	membership	membership	NOUN
cana-3299	535	13	grades	grade	NOUN
cana-3299	535	14	in	in	ADP
cana-3299	535	15	multicriteria	multicriteria	PROPN
cana-3299	535	16	decision	decision	NOUN
cana-3299	535	17	making	making	NOUN
cana-3299	535	18	,	,	PUNCT
cana-3299	535	19	𝐼𝐸𝐸𝐸	𝐼𝐸𝐸𝐸	PROPN
cana-3299	535	20	trans	trans	PROPN
cana-3299	535	21	fuzzy	fuzzy	PROPN
cana-3299	535	22	syst	syst	PROPN
cana-3299	535	23	.	.	PUNCT
cana-3299	536	1	22	22	NUM
cana-3299	536	2	(	(	PUNCT
cana-3299	536	3	4	4	NUM
cana-3299	536	4	)	)	PUNCT
cana-3299	536	5	,	,	PUNCT
cana-3299	536	6	958	958	NUM
cana-3299	536	7	-	-	SYM
cana-3299	536	8	965	965	NUM
cana-3299	536	9	.	.	PUNCT
cana-3299	537	1	[	[	X
cana-3299	537	2	36	36	NUM
cana-3299	537	3	]	]	X
cana-3299	537	4	l.	l.	PROPN
cana-3299	537	5	a.	a.	PROPN
cana-3299	537	6	zadeh	zadeh	PROPN
cana-3299	537	7	(	(	PUNCT
cana-3299	537	8	1965	1965	NUM
cana-3299	537	9	)	)	PUNCT
cana-3299	537	10	,	,	PUNCT
cana-3299	537	11	fuzzy	fuzzy	ADJ
cana-3299	537	12	sets	set	NOUN
cana-3299	537	13	,	,	PUNCT
cana-3299	537	14	inf	inf	PROPN
cana-3299	537	15	.	.	PROPN
cana-3299	537	16	control	control	PROPN
cana-3299	537	17	,	,	PUNCT
cana-3299	537	18	8	8	NUM
cana-3299	537	19	,	,	PUNCT
cana-3299	537	20	338	338	NUM
cana-3299	537	21	-	-	SYM
cana-3299	537	22	353	353	NUM
cana-3299	537	23	.	.	PUNCT