id	sid	tid	token	lemma	pos
ejpam-6199	1	1	european	european	PROPN
ejpam-6199	1	2	journal	journal	PROPN
ejpam-6199	1	3	of	of	ADP
ejpam-6199	1	4	pure	pure	ADJ
ejpam-6199	1	5	and	and	CCONJ
ejpam-6199	1	6	applied	applied	ADJ
ejpam-6199	1	7	mathematics	mathematic	NOUN
ejpam-6199	1	8	2025	2025	NUM
ejpam-6199	1	9	,	,	PUNCT
ejpam-6199	1	10	vol	vol	NOUN
ejpam-6199	1	11	.	.	PROPN
ejpam-6199	1	12	18	18	NUM
ejpam-6199	1	13	,	,	PUNCT
ejpam-6199	1	14	issue	issue	NOUN
ejpam-6199	1	15	3	3	NUM
ejpam-6199	1	16	,	,	PUNCT
ejpam-6199	1	17	article	article	NOUN
ejpam-6199	1	18	number	number	NOUN
ejpam-6199	1	19	6199	6199	NUM
ejpam-6199	1	20	issn	issn	VERB
ejpam-6199	1	21	1307	1307	NUM
ejpam-6199	1	22	-	-	SYM
ejpam-6199	1	23	5543	5543	NUM
ejpam-6199	1	24	–	–	PUNCT
ejpam-6199	1	25	ejpam.com	ejpam.com	X
ejpam-6199	1	26	published	publish	VERB
ejpam-6199	1	27	by	by	ADP
ejpam-6199	1	28	new	new	PROPN
ejpam-6199	1	29	york	york	PROPN
ejpam-6199	1	30	business	business	PROPN
ejpam-6199	1	31	global	global	PROPN
ejpam-6199	1	32	sheffer	sheffer	PROPN
ejpam-6199	1	33	stroke	stroke	PROPN
ejpam-6199	1	34	hilbert	hilbert	PROPN
ejpam-6199	1	35	algebras	algebras	PROPN
ejpam-6199	1	36	in	in	ADP
ejpam-6199	1	37	connection	connection	NOUN
ejpam-6199	1	38	with	with	ADP
ejpam-6199	1	39	crossing	cross	VERB
ejpam-6199	1	40	cubic	cubic	ADJ
ejpam-6199	1	41	structures	structure	NOUN
ejpam-6199	1	42	anas	anas	PROPN
ejpam-6199	1	43	al	al	PROPN
ejpam-6199	1	44	-	-	PUNCT
ejpam-6199	1	45	masarwah1,∗	masarwah1,∗	PROPN
ejpam-6199	1	46	,	,	PUNCT
ejpam-6199	1	47	noor	noor	PROPN
ejpam-6199	1	48	bani	bani	PROPN
ejpam-6199	1	49	abd	abd	PROPN
ejpam-6199	1	50	al	al	PROPN
ejpam-6199	1	51	-	-	PROPN
ejpam-6199	1	52	rahman1	rahman1	PROPN
ejpam-6199	1	53	,	,	PUNCT
ejpam-6199	1	54	mohammed	mohammed	PROPN
ejpam-6199	1	55	alqahtani2,∗	alqahtani2,∗	PROPN
ejpam-6199	1	56	,	,	PUNCT
ejpam-6199	1	57	majdoleen	majdoleen	VERB
ejpam-6199	1	58	abuqamar3	abuqamar3	ADJ
ejpam-6199	1	59	1	1	NUM
ejpam-6199	1	60	department	department	NOUN
ejpam-6199	1	61	of	of	ADP
ejpam-6199	1	62	mathematics	mathematic	NOUN
ejpam-6199	1	63	,	,	PUNCT
ejpam-6199	1	64	faculty	faculty	NOUN
ejpam-6199	1	65	of	of	ADP
ejpam-6199	1	66	science	science	NOUN
ejpam-6199	1	67	,	,	PUNCT
ejpam-6199	1	68	ajloun	ajloun	ADJ
ejpam-6199	1	69	national	national	ADJ
ejpam-6199	1	70	university	university	PROPN
ejpam-6199	1	71	,	,	PUNCT
ejpam-6199	1	72	p.	p.	PROPN
ejpam-6199	1	73	o.	o.	PROPN
ejpam-6199	1	74	box	box	PROPN
ejpam-6199	1	75	43	43	NUM
ejpam-6199	1	76	,	,	PUNCT
ejpam-6199	1	77	ajloun	ajloun	ADJ
ejpam-6199	1	78	26810	26810	NUM
ejpam-6199	1	79	,	,	PUNCT
ejpam-6199	1	80	jordan	jordan	PROPN
ejpam-6199	1	81	2	2	NUM
ejpam-6199	1	82	department	department	NOUN
ejpam-6199	1	83	of	of	ADP
ejpam-6199	1	84	basic	basic	ADJ
ejpam-6199	1	85	sciences	science	NOUN
ejpam-6199	1	86	,	,	PUNCT
ejpam-6199	1	87	college	college	NOUN
ejpam-6199	1	88	of	of	ADP
ejpam-6199	1	89	science	science	NOUN
ejpam-6199	1	90	and	and	CCONJ
ejpam-6199	1	91	theoretical	theoretical	ADJ
ejpam-6199	1	92	studies	study	NOUN
ejpam-6199	1	93	,	,	PUNCT
ejpam-6199	1	94	saudi	saudi	ADJ
ejpam-6199	1	95	electronic	electronic	ADJ
ejpam-6199	1	96	university	university	NOUN
ejpam-6199	1	97	,	,	PUNCT
ejpam-6199	1	98	p.o	p.o	PROPN
ejpam-6199	1	99	.	.	PROPN
ejpam-6199	1	100	box	box	PROPN
ejpam-6199	1	101	93499	93499	NUM
ejpam-6199	1	102	,	,	PUNCT
ejpam-6199	1	103	riyadh	riyadh	PROPN
ejpam-6199	1	104	11673	11673	NUM
ejpam-6199	1	105	,	,	PUNCT
ejpam-6199	1	106	saudi	saudi	PROPN
ejpam-6199	1	107	arabia	arabia	PROPN
ejpam-6199	1	108	3	3	NUM
ejpam-6199	1	109	department	department	NOUN
ejpam-6199	1	110	of	of	ADP
ejpam-6199	1	111	mathematics	mathematic	NOUN
ejpam-6199	1	112	,	,	PUNCT
ejpam-6199	1	113	faculty	faculty	NOUN
ejpam-6199	1	114	of	of	ADP
ejpam-6199	1	115	science	science	NOUN
ejpam-6199	1	116	and	and	CCONJ
ejpam-6199	1	117	information	information	NOUN
ejpam-6199	1	118	technology	technology	NOUN
ejpam-6199	1	119	,	,	PUNCT
ejpam-6199	1	120	jadara	jadara	PROPN
ejpam-6199	1	121	university	university	PROPN
ejpam-6199	1	122	,	,	PUNCT
ejpam-6199	1	123	irbid	irbid	VERB
ejpam-6199	1	124	21110	21110	NUM
ejpam-6199	1	125	,	,	PUNCT
ejpam-6199	1	126	jordan	jordan	PROPN
ejpam-6199	1	127	abstract	abstract	PROPN
ejpam-6199	1	128	.	.	PUNCT
ejpam-6199	2	1	the	the	DET
ejpam-6199	2	2	idea	idea	NOUN
ejpam-6199	2	3	of	of	ADP
ejpam-6199	2	4	sheffer	sheffer	PROPN
ejpam-6199	2	5	stroke	stroke	PROPN
ejpam-6199	2	6	hilbert	hilbert	PROPN
ejpam-6199	2	7	algebra	algebra	PROPN
ejpam-6199	2	8	is	be	AUX
ejpam-6199	2	9	studied	study	VERB
ejpam-6199	2	10	from	from	ADP
ejpam-6199	2	11	the	the	DET
ejpam-6199	2	12	perspective	perspective	NOUN
ejpam-6199	2	13	of	of	ADP
ejpam-6199	2	14	the	the	DET
ejpam-6199	2	15	structure	structure	NOUN
ejpam-6199	2	16	of	of	ADP
ejpam-6199	2	17	the	the	DET
ejpam-6199	2	18	cubic	cubic	ADJ
ejpam-6199	2	19	structure	structure	NOUN
ejpam-6199	2	20	.	.	PUNCT
ejpam-6199	3	1	the	the	DET
ejpam-6199	3	2	filter	filter	NOUN
ejpam-6199	3	3	and	and	CCONJ
ejpam-6199	3	4	deductive	deductive	ADJ
ejpam-6199	3	5	system	system	NOUN
ejpam-6199	3	6	of	of	ADP
ejpam-6199	3	7	the	the	DET
ejpam-6199	3	8	sheffer	sheffer	NOUN
ejpam-6199	3	9	stroke	stroke	NOUN
ejpam-6199	3	10	hilbert	hilbert	PROPN
ejpam-6199	3	11	algebra	algebra	PROPN
ejpam-6199	3	12	are	be	AUX
ejpam-6199	3	13	defined	define	VERB
ejpam-6199	3	14	and	and	CCONJ
ejpam-6199	3	15	examined	examine	VERB
ejpam-6199	3	16	through	through	ADP
ejpam-6199	3	17	the	the	DET
ejpam-6199	3	18	crossing	crossing	NOUN
ejpam-6199	3	19	cubic	cubic	ADJ
ejpam-6199	3	20	structure	structure	NOUN
ejpam-6199	3	21	,	,	PUNCT
ejpam-6199	3	22	which	which	PRON
ejpam-6199	3	23	is	be	AUX
ejpam-6199	3	24	an	an	DET
ejpam-6199	3	25	extension	extension	NOUN
ejpam-6199	3	26	of	of	ADP
ejpam-6199	3	27	the	the	DET
ejpam-6199	3	28	fuzziness	fuzziness	NOUN
ejpam-6199	3	29	of	of	ADP
ejpam-6199	3	30	these	these	DET
ejpam-6199	3	31	substructures	substructure	NOUN
ejpam-6199	3	32	,	,	PUNCT
ejpam-6199	3	33	verifying	verify	VERB
ejpam-6199	3	34	their	their	PRON
ejpam-6199	3	35	many	many	ADJ
ejpam-6199	3	36	characteristics	characteristic	NOUN
ejpam-6199	3	37	.	.	PUNCT
ejpam-6199	4	1	moreover	moreover	ADV
ejpam-6199	4	2	,	,	PUNCT
ejpam-6199	4	3	conditions	condition	NOUN
ejpam-6199	4	4	suitable	suitable	ADJ
ejpam-6199	4	5	for	for	ADP
ejpam-6199	4	6	the	the	DET
ejpam-6199	4	7	crossing	crossing	ADJ
ejpam-6199	4	8	cubic	cubic	ADJ
ejpam-6199	4	9	structure	structure	NOUN
ejpam-6199	4	10	are	be	AUX
ejpam-6199	4	11	established	establish	VERB
ejpam-6199	4	12	to	to	PART
ejpam-6199	4	13	be	be	AUX
ejpam-6199	4	14	a	a	DET
ejpam-6199	4	15	crossing	cross	VERB
ejpam-6199	4	16	cubic	cubic	ADJ
ejpam-6199	4	17	filter	filter	NOUN
ejpam-6199	4	18	and	and	CCONJ
ejpam-6199	4	19	several	several	ADJ
ejpam-6199	4	20	characterization	characterization	NOUN
ejpam-6199	4	21	theorems	theorem	NOUN
ejpam-6199	4	22	are	be	AUX
ejpam-6199	4	23	reached	reach	VERB
ejpam-6199	4	24	.	.	PUNCT
ejpam-6199	5	1	accordingly	accordingly	ADV
ejpam-6199	5	2	,	,	PUNCT
ejpam-6199	5	3	the	the	DET
ejpam-6199	5	4	relationship	relationship	NOUN
ejpam-6199	5	5	between	between	ADP
ejpam-6199	5	6	crossing	cross	VERB
ejpam-6199	5	7	cubic	cubic	ADJ
ejpam-6199	5	8	filters	filter	NOUN
ejpam-6199	5	9	and	and	CCONJ
ejpam-6199	5	10	filters	filter	NOUN
ejpam-6199	5	11	of	of	ADP
ejpam-6199	5	12	sheffer	sheffer	PROPN
ejpam-6199	5	13	stroke	stroke	PROPN
ejpam-6199	5	14	hilbert	hilbert	PROPN
ejpam-6199	5	15	algebras	algebras	PROPN
ejpam-6199	5	16	is	be	AUX
ejpam-6199	5	17	explained	explain	VERB
ejpam-6199	5	18	such	such	ADJ
ejpam-6199	5	19	that	that	SCONJ
ejpam-6199	5	20	the	the	DET
ejpam-6199	5	21	crossing	cross	VERB
ejpam-6199	5	22	cubic	cubic	ADJ
ejpam-6199	5	23	deductive	deductive	ADJ
ejpam-6199	5	24	system	system	NOUN
ejpam-6199	5	25	can	can	AUX
ejpam-6199	5	26	handle	handle	VERB
ejpam-6199	5	27	all	all	PRON
ejpam-6199	5	28	of	of	ADP
ejpam-6199	5	29	the	the	DET
ejpam-6199	5	30	results	result	NOUN
ejpam-6199	5	31	for	for	ADP
ejpam-6199	5	32	the	the	DET
ejpam-6199	5	33	crossing	crossing	ADJ
ejpam-6199	5	34	cubic	cubic	ADJ
ejpam-6199	5	35	filter	filter	NOUN
ejpam-6199	5	36	covered	cover	VERB
ejpam-6199	5	37	above	above	ADV
ejpam-6199	5	38	in	in	ADP
ejpam-6199	5	39	the	the	DET
ejpam-6199	5	40	same	same	ADJ
ejpam-6199	5	41	way	way	NOUN
ejpam-6199	5	42	.	.	PUNCT
ejpam-6199	6	1	2020	2020	NUM
ejpam-6199	6	2	mathematics	mathematic	NOUN
ejpam-6199	6	3	subject	subject	NOUN
ejpam-6199	6	4	classifications	classification	NOUN
ejpam-6199	6	5	:	:	PUNCT
ejpam-6199	6	6	03e72	03e72	NUM
ejpam-6199	6	7	,	,	PUNCT
ejpam-6199	6	8	03g25	03g25	NUM
ejpam-6199	6	9	,	,	PUNCT
ejpam-6199	6	10	28e10	28e10	NUM
ejpam-6199	6	11	,	,	PUNCT
ejpam-6199	6	12	03b52	03b52	VERB
ejpam-6199	6	13	key	key	ADJ
ejpam-6199	6	14	words	word	NOUN
ejpam-6199	6	15	and	and	CCONJ
ejpam-6199	6	16	phrases	phrase	NOUN
ejpam-6199	6	17	:	:	PUNCT
ejpam-6199	6	18	sheffer	sheffer	NOUN
ejpam-6199	6	19	stroke	stroke	PROPN
ejpam-6199	6	20	hilbert	hilbert	PROPN
ejpam-6199	6	21	algebras	algebras	PROPN
ejpam-6199	6	22	,	,	PUNCT
ejpam-6199	6	23	filters	filter	NOUN
ejpam-6199	6	24	,	,	PUNCT
ejpam-6199	6	25	deductive	deductive	ADJ
ejpam-6199	6	26	systems	system	NOUN
ejpam-6199	6	27	,	,	PUNCT
ejpam-6199	6	28	crossing	cross	VERB
ejpam-6199	6	29	cubic	cubic	ADJ
ejpam-6199	6	30	filters	filter	NOUN
ejpam-6199	6	31	,	,	PUNCT
ejpam-6199	6	32	crossing	cross	VERB
ejpam-6199	6	33	cubic	cubic	ADJ
ejpam-6199	6	34	deductive	deductive	ADJ
ejpam-6199	6	35	systems	system	NOUN
ejpam-6199	6	36	1	1	NUM
ejpam-6199	6	37	.	.	PUNCT
ejpam-6199	7	1	introduction	introduction	NOUN
ejpam-6199	7	2	in	in	ADP
ejpam-6199	7	3	mathematical	mathematical	ADJ
ejpam-6199	7	4	logic	logic	NOUN
ejpam-6199	7	5	,	,	PUNCT
ejpam-6199	7	6	there	there	PRON
ejpam-6199	7	7	are	be	VERB
ejpam-6199	7	8	certain	certain	ADJ
ejpam-6199	7	9	logical	logical	ADJ
ejpam-6199	7	10	operations	operation	NOUN
ejpam-6199	7	11	such	such	ADJ
ejpam-6199	7	12	that	that	DET
ejpam-6199	7	13	conjunction	conjunction	NOUN
ejpam-6199	7	14	(	(	PUNCT
ejpam-6199	7	15	and	and	CCONJ
ejpam-6199	7	16	)	)	PUNCT
ejpam-6199	7	17	,	,	PUNCT
ejpam-6199	7	18	disjunction	disjunction	NOUN
ejpam-6199	7	19	(	(	PUNCT
ejpam-6199	7	20	or	or	CCONJ
ejpam-6199	7	21	)	)	PUNCT
ejpam-6199	7	22	and	and	CCONJ
ejpam-6199	7	23	negation	negation	NOUN
ejpam-6199	7	24	(	(	PUNCT
ejpam-6199	7	25	not	not	PART
ejpam-6199	7	26	)	)	PUNCT
ejpam-6199	7	27	.	.	PUNCT
ejpam-6199	8	1	these	these	DET
ejpam-6199	8	2	logical	logical	ADJ
ejpam-6199	8	3	operations	operation	NOUN
ejpam-6199	8	4	are	be	AUX
ejpam-6199	8	5	represented	represent	VERB
ejpam-6199	8	6	by	by	ADP
ejpam-6199	8	7	the	the	DET
ejpam-6199	8	8	symbols	symbol	NOUN
ejpam-6199	8	9	“	"	PUNCT
ejpam-6199	8	10	∧	∧	PROPN
ejpam-6199	8	11	”	"	PUNCT
ejpam-6199	8	12	,	,	PUNCT
ejpam-6199	8	13	“	"	PUNCT
ejpam-6199	8	14	∨	∨	NOUN
ejpam-6199	8	15	”	"	PUNCT
ejpam-6199	8	16	and	and	CCONJ
ejpam-6199	8	17	“	"	PUNCT
ejpam-6199	8	18	∼	∼	NOUN
ejpam-6199	8	19	”	"	PUNCT
ejpam-6199	8	20	,	,	PUNCT
ejpam-6199	8	21	respectively	respectively	ADV
ejpam-6199	8	22	.	.	PUNCT
ejpam-6199	9	1	in	in	ADP
ejpam-6199	9	2	a	a	DET
ejpam-6199	9	3	conjunction	conjunction	NOUN
ejpam-6199	9	4	operator	operator	NOUN
ejpam-6199	9	5	,	,	PUNCT
ejpam-6199	9	6	if	if	SCONJ
ejpam-6199	9	7	anyone	anyone	PRON
ejpam-6199	9	8	of	of	ADP
ejpam-6199	9	9	the	the	DET
ejpam-6199	9	10	statement	statement	NOUN
ejpam-6199	9	11	is	be	AUX
ejpam-6199	9	12	false	false	ADJ
ejpam-6199	9	13	,	,	PUNCT
ejpam-6199	9	14	then	then	ADV
ejpam-6199	9	15	the	the	DET
ejpam-6199	9	16	output	output	NOUN
ejpam-6199	9	17	is	be	AUX
ejpam-6199	9	18	false	false	ADJ
ejpam-6199	9	19	.	.	PUNCT
ejpam-6199	10	1	in	in	ADP
ejpam-6199	10	2	a	a	DET
ejpam-6199	10	3	disjunction	disjunction	NOUN
ejpam-6199	10	4	operator	operator	NOUN
ejpam-6199	10	5	,	,	PUNCT
ejpam-6199	10	6	if	if	SCONJ
ejpam-6199	10	7	anyone	anyone	PRON
ejpam-6199	10	8	of	of	ADP
ejpam-6199	10	9	the	the	DET
ejpam-6199	10	10	statements	statement	NOUN
ejpam-6199	10	11	is	be	AUX
ejpam-6199	10	12	true	true	ADJ
ejpam-6199	10	13	,	,	PUNCT
ejpam-6199	10	14	then	then	ADV
ejpam-6199	10	15	the	the	DET
ejpam-6199	10	16	output	output	NOUN
ejpam-6199	10	17	is	be	AUX
ejpam-6199	10	18	true	true	ADJ
ejpam-6199	10	19	.	.	PUNCT
ejpam-6199	11	1	a	a	DET
ejpam-6199	11	2	negation	negation	NOUN
ejpam-6199	11	3	operator	operator	NOUN
ejpam-6199	11	4	gives	give	VERB
ejpam-6199	11	5	the	the	DET
ejpam-6199	11	6	opposite	opposite	ADJ
ejpam-6199	11	7	result	result	NOUN
ejpam-6199	11	8	,	,	PUNCT
ejpam-6199	11	9	i.e.	i.e.	X
ejpam-6199	11	10	,	,	PUNCT
ejpam-6199	11	11	if	if	SCONJ
ejpam-6199	11	12	the	the	DET
ejpam-6199	11	13	input	input	NOUN
ejpam-6199	11	14	is	be	AUX
ejpam-6199	11	15	true	true	ADJ
ejpam-6199	11	16	,	,	PUNCT
ejpam-6199	11	17	then	then	ADV
ejpam-6199	11	18	the	the	DET
ejpam-6199	11	19	output	output	NOUN
ejpam-6199	11	20	is	be	AUX
ejpam-6199	11	21	false	false	ADJ
ejpam-6199	11	22	.	.	PUNCT
ejpam-6199	11	23	table	table	NOUN
ejpam-6199	11	24	1	1	NUM
ejpam-6199	11	25	describes	describe	VERB
ejpam-6199	11	26	the	the	DET
ejpam-6199	11	27	truth	truth	NOUN
ejpam-6199	11	28	table	table	NOUN
ejpam-6199	11	29	for	for	ADP
ejpam-6199	11	30	the	the	DET
ejpam-6199	11	31	conjunction	conjunction	NOUN
ejpam-6199	11	32	“	"	PUNCT
ejpam-6199	11	33	∧	∧	PROPN
ejpam-6199	11	34	”	"	PUNCT
ejpam-6199	11	35	and	and	CCONJ
ejpam-6199	11	36	disjunction	disjunction	NOUN
ejpam-6199	11	37	“	"	PUNCT
ejpam-6199	11	38	∨	∨	NOUN
ejpam-6199	11	39	”	"	PUNCT
ejpam-6199	11	40	operations	operation	NOUN
ejpam-6199	11	41	.	.	PUNCT
ejpam-6199	12	1	∗corresponding	∗corresponde	VERB
ejpam-6199	12	2	author	author	NOUN
ejpam-6199	12	3	.	.	PUNCT
ejpam-6199	13	1	∗corresponding	∗corresponde	VERB
ejpam-6199	13	2	author	author	NOUN
ejpam-6199	13	3	.	.	PUNCT
ejpam-6199	14	1	doi	doi	NOUN
ejpam-6199	14	2	:	:	PUNCT
ejpam-6199	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6199	https://doi.org/10.29020/nybg.ejpam.v18i3.6199	NOUN
ejpam-6199	14	4	email	email	NOUN
ejpam-6199	14	5	addresses	address	NOUN
ejpam-6199	14	6	:	:	PUNCT
ejpam-6199	14	7	anas.almasarwah@anu.edu.jo	anas.almasarwah@anu.edu.jo	PROPN
ejpam-6199	14	8	(	(	PUNCT
ejpam-6199	14	9	a.	a.	PROPN
ejpam-6199	14	10	al	al	PROPN
ejpam-6199	14	11	-	-	PROPN
ejpam-6199	14	12	masarwah	masarwah	NOUN
ejpam-6199	14	13	)	)	PUNCT
ejpam-6199	14	14	,	,	PUNCT
ejpam-6199	14	15	noorbaniabdalrahman@gmail.com	noorbaniabdalrahman@gmail.com	X
ejpam-6199	14	16	(	(	PUNCT
ejpam-6199	14	17	n.	n.	PROPN
ejpam-6199	14	18	bani	bani	PROPN
ejpam-6199	14	19	abd	abd	PROPN
ejpam-6199	14	20	al	al	PROPN
ejpam-6199	14	21	-	-	PUNCT
ejpam-6199	14	22	rahman	rahman	PROPN
ejpam-6199	14	23	)	)	PUNCT
ejpam-6199	14	24	,	,	PUNCT
ejpam-6199	14	25	m.alqahtani@seu.edu.sa	m.alqahtani@seu.edu.sa	PROPN
ejpam-6199	14	26	(	(	PUNCT
ejpam-6199	14	27	m.	m.	NOUN
ejpam-6199	14	28	alqahtani	alqahtani	PROPN
ejpam-6199	14	29	)	)	PUNCT
ejpam-6199	14	30	,	,	PUNCT
ejpam-6199	14	31	mjabuqamar@gmail.com	mjabuqamar@gmail.com	PROPN
ejpam-6199	14	32	(	(	PUNCT
ejpam-6199	14	33	m.	m.	NOUN
ejpam-6199	14	34	abuqamar	abuqamar	PROPN
ejpam-6199	14	35	)	)	PUNCT
ejpam-6199	14	36	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6199	15	1	1	1	NUM
ejpam-6199	15	2	copyright	copyright	NOUN
ejpam-6199	15	3	:	:	PUNCT
ejpam-6199	15	4	©	©	PROPN
ejpam-6199	15	5	2025	2025	NUM
ejpam-6199	15	6	the	the	DET
ejpam-6199	15	7	author(s	author(s	NOUN
ejpam-6199	15	8	)	)	PUNCT
ejpam-6199	15	9	.	.	PUNCT
ejpam-6199	16	1	(	(	PUNCT
ejpam-6199	16	2	cc	cc	NOUN
ejpam-6199	16	3	by	by	ADP
ejpam-6199	16	4	-	-	PUNCT
ejpam-6199	16	5	nc	nc	PROPN
ejpam-6199	16	6	4.0	4.0	NUM
ejpam-6199	16	7	)	)	PUNCT
ejpam-6199	16	8	a.	a.	NOUN
ejpam-6199	16	9	al	al	PROPN
ejpam-6199	16	10	-	-	PROPN
ejpam-6199	16	11	masarwah	masarwah	PROPN
ejpam-6199	16	12	et	et	PROPN
ejpam-6199	16	13	al	al	PROPN
ejpam-6199	16	14	.	.	PUNCT
ejpam-6199	16	15	/	/	SYM
ejpam-6199	16	16	eur	eur	PROPN
ejpam-6199	16	17	.	.	PUNCT
ejpam-6199	17	1	j.	j.	PROPN
ejpam-6199	17	2	pure	pure	PROPN
ejpam-6199	17	3	appl	appl	PROPN
ejpam-6199	17	4	.	.	PROPN
ejpam-6199	17	5	math	math	PROPN
ejpam-6199	17	6	,	,	PUNCT
ejpam-6199	17	7	18	18	NUM
ejpam-6199	17	8	(	(	PUNCT
ejpam-6199	17	9	3	3	NUM
ejpam-6199	17	10	)	)	PUNCT
ejpam-6199	17	11	(	(	PUNCT
ejpam-6199	17	12	2025	2025	NUM
ejpam-6199	17	13	)	)	PUNCT
ejpam-6199	17	14	,	,	PUNCT
ejpam-6199	17	15	6199	6199	NUM
ejpam-6199	17	16	2	2	NUM
ejpam-6199	17	17	of	of	ADP
ejpam-6199	17	18	17	17	NUM
ejpam-6199	17	19	table	table	NOUN
ejpam-6199	17	20	1	1	NUM
ejpam-6199	17	21	:	:	PUNCT
ejpam-6199	17	22	the	the	DET
ejpam-6199	17	23	truth	truth	NOUN
ejpam-6199	17	24	table	table	NOUN
ejpam-6199	17	25	for	for	ADP
ejpam-6199	17	26	the	the	DET
ejpam-6199	17	27	conjunction	conjunction	NOUN
ejpam-6199	17	28	“	"	PUNCT
ejpam-6199	17	29	∧	∧	PROPN
ejpam-6199	17	30	”	"	PUNCT
ejpam-6199	17	31	and	and	CCONJ
ejpam-6199	17	32	disjunction	disjunction	NOUN
ejpam-6199	17	33	“	"	PUNCT
ejpam-6199	17	34	∨	∨	NOUN
ejpam-6199	17	35	”	"	PUNCT
ejpam-6199	17	36	operations	operation	NOUN
ejpam-6199	17	37	.	.	PUNCT
ejpam-6199	18	1	input(a	input(a	NOUN
ejpam-6199	18	2	)	)	PUNCT
ejpam-6199	18	3	input(b	input(b	NOUN
ejpam-6199	18	4	)	)	PUNCT
ejpam-6199	18	5	output(a	output(a	NOUN
ejpam-6199	18	6	∧b	∧b	NOUN
ejpam-6199	18	7	)	)	PUNCT
ejpam-6199	19	1	output(a	output(a	ADP
ejpam-6199	19	2	∨b	∨b	NOUN
ejpam-6199	19	3	)	)	PUNCT
ejpam-6199	19	4	t	t	PROPN
ejpam-6199	19	5	t	t	PROPN
ejpam-6199	19	6	t	t	PROPN
ejpam-6199	19	7	t	t	PROPN
ejpam-6199	19	8	t	t	PROPN
ejpam-6199	20	1	f	f	PROPN
ejpam-6199	20	2	f	f	PROPN
ejpam-6199	21	1	t	t	PROPN
ejpam-6199	22	1	f	f	PROPN
ejpam-6199	22	2	t	t	PROPN
ejpam-6199	23	1	f	f	PROPN
ejpam-6199	23	2	t	t	PROPN
ejpam-6199	23	3	f	f	PROPN
ejpam-6199	23	4	f	f	PROPN
ejpam-6199	23	5	f	f	PROPN
ejpam-6199	23	6	f	f	PROPN
ejpam-6199	23	7	a	a	DET
ejpam-6199	23	8	sheffer	sheffer	NOUN
ejpam-6199	23	9	stroke	stroke	NOUN
ejpam-6199	23	10	,	,	PUNCT
ejpam-6199	23	11	represented	represent	VERB
ejpam-6199	23	12	by	by	ADP
ejpam-6199	23	13	the	the	DET
ejpam-6199	23	14	symbol	symbol	NOUN
ejpam-6199	23	15	“	"	PUNCT
ejpam-6199	23	16	|	|	ADV
ejpam-6199	23	17	”	"	PUNCT
ejpam-6199	23	18	,	,	PUNCT
ejpam-6199	23	19	is	be	AUX
ejpam-6199	23	20	a	a	DET
ejpam-6199	23	21	two	two	NUM
ejpam-6199	23	22	-	-	PUNCT
ejpam-6199	23	23	input	input	NOUN
ejpam-6199	23	24	logical	logical	ADJ
ejpam-6199	23	25	operation	operation	NOUN
ejpam-6199	23	26	that	that	PRON
ejpam-6199	23	27	produces	produce	VERB
ejpam-6199	23	28	an	an	DET
ejpam-6199	23	29	incorrect	incorrect	ADJ
ejpam-6199	23	30	output	output	NOUN
ejpam-6199	23	31	only	only	ADV
ejpam-6199	23	32	when	when	SCONJ
ejpam-6199	23	33	both	both	DET
ejpam-6199	23	34	inputs	input	NOUN
ejpam-6199	23	35	are	be	AUX
ejpam-6199	23	36	true	true	ADJ
ejpam-6199	23	37	i.e.	i.e.	X
ejpam-6199	23	38	,	,	PUNCT
ejpam-6199	23	39	the	the	DET
ejpam-6199	23	40	sheffer	sheffer	NOUN
ejpam-6199	23	41	stroke	stroke	NOUN
ejpam-6199	23	42	operation	operation	NOUN
ejpam-6199	23	43	a	a	DET
ejpam-6199	23	44	|	|	NOUN
ejpam-6199	23	45	b	b	NOUN
ejpam-6199	23	46	is	be	AUX
ejpam-6199	23	47	equivalent	equivalent	ADJ
ejpam-6199	23	48	to	to	ADP
ejpam-6199	23	49	∼	∼	NOUN
ejpam-6199	23	50	(	(	PUNCT
ejpam-6199	23	51	a	a	DET
ejpam-6199	23	52	∧	∧	PROPN
ejpam-6199	23	53	b	b	NOUN
ejpam-6199	23	54	)	)	PUNCT
ejpam-6199	23	55	.	.	PUNCT
ejpam-6199	24	1	table	table	NOUN
ejpam-6199	24	2	2	2	NUM
ejpam-6199	24	3	describes	describe	VERB
ejpam-6199	24	4	the	the	DET
ejpam-6199	24	5	truth	truth	NOUN
ejpam-6199	24	6	table	table	NOUN
ejpam-6199	24	7	for	for	ADP
ejpam-6199	24	8	the	the	DET
ejpam-6199	24	9	sheffer	sheffer	PROPN
ejpam-6199	24	10	stroke	stroke	NOUN
ejpam-6199	24	11	operation	operation	NOUN
ejpam-6199	24	12	“	"	PUNCT
ejpam-6199	24	13	|	|	ADV
ejpam-6199	24	14	”	"	PUNCT
ejpam-6199	24	15	.	.	PUNCT
ejpam-6199	25	1	table	table	NOUN
ejpam-6199	25	2	2	2	NUM
ejpam-6199	25	3	:	:	PUNCT
ejpam-6199	25	4	the	the	DET
ejpam-6199	25	5	truth	truth	NOUN
ejpam-6199	25	6	table	table	NOUN
ejpam-6199	25	7	for	for	ADP
ejpam-6199	25	8	the	the	DET
ejpam-6199	25	9	sheffer	sheffer	NOUN
ejpam-6199	25	10	stroke	stroke	NOUN
ejpam-6199	25	11	“	"	PUNCT
ejpam-6199	25	12	|	|	ADV
ejpam-6199	25	13	”	"	PUNCT
ejpam-6199	25	14	.	.	PUNCT
ejpam-6199	26	1	input(a	input(a	NOUN
ejpam-6199	26	2	)	)	PUNCT
ejpam-6199	26	3	input(b	input(b	NOUN
ejpam-6199	26	4	)	)	PUNCT
ejpam-6199	26	5	output(a	output(a	ADJ
ejpam-6199	26	6	|	|	NOUN
ejpam-6199	26	7	b	b	NOUN
ejpam-6199	26	8	)	)	PUNCT
ejpam-6199	26	9	t	t	PROPN
ejpam-6199	26	10	t	t	PROPN
ejpam-6199	27	1	f	f	PROPN
ejpam-6199	27	2	t	t	PROPN
ejpam-6199	28	1	f	f	PROPN
ejpam-6199	28	2	t	t	PROPN
ejpam-6199	28	3	f	f	PROPN
ejpam-6199	28	4	t	t	PROPN
ejpam-6199	28	5	t	t	PROPN
ejpam-6199	28	6	f	f	PROPN
ejpam-6199	28	7	f	f	PROPN
ejpam-6199	28	8	t	t	PROPN
ejpam-6199	28	9	here	here	ADV
ejpam-6199	28	10	,	,	PUNCT
ejpam-6199	28	11	we	we	PRON
ejpam-6199	28	12	will	will	AUX
ejpam-6199	28	13	make	make	VERB
ejpam-6199	28	14	an	an	DET
ejpam-6199	28	15	example	example	NOUN
ejpam-6199	28	16	on	on	ADP
ejpam-6199	28	17	the	the	DET
ejpam-6199	28	18	truth	truth	NOUN
ejpam-6199	28	19	values	value	NOUN
ejpam-6199	28	20	of	of	ADP
ejpam-6199	28	21	sheffer	sheffer	PROPN
ejpam-6199	28	22	stroke	stroke	NOUN
ejpam-6199	28	23	operation	operation	NOUN
ejpam-6199	28	24	for	for	ADP
ejpam-6199	28	25	the	the	DET
ejpam-6199	28	26	given	give	VERB
ejpam-6199	28	27	two	two	NUM
ejpam-6199	28	28	statements	statement	NOUN
ejpam-6199	28	29	a	a	PRON
ejpam-6199	28	30	and	and	CCONJ
ejpam-6199	28	31	b.	b.	PROPN
ejpam-6199	28	32	consider	consider	VERB
ejpam-6199	28	33	the	the	DET
ejpam-6199	28	34	following	follow	VERB
ejpam-6199	28	35	two	two	NUM
ejpam-6199	28	36	statements	statement	NOUN
ejpam-6199	28	37	:	:	PUNCT
ejpam-6199	28	38	a	a	X
ejpam-6199	28	39	:	:	PUNCT
ejpam-6199	28	40	p	p	NOUN
ejpam-6199	28	41	is	be	AUX
ejpam-6199	28	42	divisible	divisible	ADJ
ejpam-6199	28	43	by	by	ADP
ejpam-6199	28	44	2	2	NUM
ejpam-6199	28	45	,	,	PUNCT
ejpam-6199	28	46	b	b	NOUN
ejpam-6199	28	47	:	:	PUNCT
ejpam-6199	28	48	p	p	PRON
ejpam-6199	28	49	is	be	AUX
ejpam-6199	28	50	divisible	divisible	ADJ
ejpam-6199	28	51	by	by	ADP
ejpam-6199	28	52	3	3	NUM
ejpam-6199	28	53	.	.	PUNCT
ejpam-6199	29	1	then	then	ADV
ejpam-6199	29	2	,	,	PUNCT
ejpam-6199	29	3	the	the	DET
ejpam-6199	29	4	truth	truth	NOUN
ejpam-6199	29	5	table	table	NOUN
ejpam-6199	29	6	of	of	ADP
ejpam-6199	29	7	the	the	DET
ejpam-6199	29	8	sheffer	sheffer	NOUN
ejpam-6199	29	9	stroke	stroke	NOUN
ejpam-6199	29	10	“	"	PUNCT
ejpam-6199	29	11	|	|	ADV
ejpam-6199	29	12	”	"	PUNCT
ejpam-6199	29	13	between	between	ADP
ejpam-6199	29	14	the	the	DET
ejpam-6199	29	15	two	two	NUM
ejpam-6199	29	16	statements	statement	NOUN
ejpam-6199	29	17	a	a	PRON
ejpam-6199	29	18	and	and	CCONJ
ejpam-6199	29	19	b	b	NOUN
ejpam-6199	29	20	is	be	AUX
ejpam-6199	29	21	presented	present	VERB
ejpam-6199	29	22	by	by	ADP
ejpam-6199	29	23	table	table	NOUN
ejpam-6199	29	24	3	3	NUM
ejpam-6199	29	25	.	.	PUNCT
ejpam-6199	29	26	table	table	NOUN
ejpam-6199	29	27	3	3	NUM
ejpam-6199	29	28	:	:	PUNCT
ejpam-6199	29	29	the	the	DET
ejpam-6199	29	30	truth	truth	NOUN
ejpam-6199	29	31	table	table	NOUN
ejpam-6199	29	32	for	for	ADP
ejpam-6199	29	33	the	the	DET
ejpam-6199	29	34	sheffer	sheffer	NOUN
ejpam-6199	29	35	stroke	stroke	NOUN
ejpam-6199	29	36	“	"	PUNCT
ejpam-6199	29	37	|	|	ADV
ejpam-6199	29	38	”	"	PUNCT
ejpam-6199	29	39	.	.	PUNCT
ejpam-6199	30	1	values	value	NOUN
ejpam-6199	30	2	of	of	ADP
ejpam-6199	30	3	p	p	NOUN
ejpam-6199	30	4	a	a	DET
ejpam-6199	30	5	b	b	NOUN
ejpam-6199	30	6	a	a	DET
ejpam-6199	30	7	|	|	NOUN
ejpam-6199	30	8	b	b	NOUN
ejpam-6199	30	9	p	p	NOUN
ejpam-6199	30	10	=	=	NOUN
ejpam-6199	30	11	12	12	NUM
ejpam-6199	30	12	t	t	NOUN
ejpam-6199	30	13	t	t	X
ejpam-6199	31	1	f	f	X
ejpam-6199	31	2	p	p	X
ejpam-6199	31	3	=	=	PROPN
ejpam-6199	31	4	4	4	NUM
ejpam-6199	31	5	t	t	NOUN
ejpam-6199	31	6	f	f	NOUN
ejpam-6199	31	7	t	t	PROPN
ejpam-6199	31	8	p	p	X
ejpam-6199	31	9	=	=	SYM
ejpam-6199	31	10	9	9	NUM
ejpam-6199	31	11	f	f	NOUN
ejpam-6199	31	12	t	t	NOUN
ejpam-6199	31	13	t	t	PROPN
ejpam-6199	31	14	p	p	X
ejpam-6199	31	15	=	=	PROPN
ejpam-6199	31	16	7	7	NUM
ejpam-6199	31	17	f	f	NOUN
ejpam-6199	31	18	f	f	PROPN
ejpam-6199	31	19	t	t	PROPN
ejpam-6199	31	20	sheffer	sheffer	VERB
ejpam-6199	32	1	[	[	X
ejpam-6199	32	2	1	1	X
ejpam-6199	32	3	]	]	PUNCT
ejpam-6199	32	4	used	use	VERB
ejpam-6199	32	5	the	the	DET
ejpam-6199	32	6	sheffer	sheffer	NOUN
ejpam-6199	32	7	stroke	stroke	NOUN
ejpam-6199	32	8	“	"	PUNCT
ejpam-6199	32	9	|	|	ADV
ejpam-6199	32	10	”	"	PUNCT
ejpam-6199	32	11	(	(	PUNCT
ejpam-6199	32	12	the	the	DET
ejpam-6199	32	13	so	so	ADV
ejpam-6199	32	14	-	-	PUNCT
ejpam-6199	32	15	called	call	VERB
ejpam-6199	32	16	sheffer	sheffer	NOUN
ejpam-6199	32	17	operation	operation	NOUN
ejpam-6199	32	18	)	)	PUNCT
ejpam-6199	32	19	in	in	ADP
ejpam-6199	32	20	1913	1913	NUM
ejpam-6199	32	21	as	as	ADP
ejpam-6199	32	22	a	a	DET
ejpam-6199	32	23	fundamental	fundamental	ADJ
ejpam-6199	32	24	axiomatization	axiomatization	NOUN
ejpam-6199	32	25	of	of	ADP
ejpam-6199	32	26	boolean	boolean	ADJ
ejpam-6199	32	27	algebra	algebra	NOUN
ejpam-6199	32	28	and	and	CCONJ
ejpam-6199	32	29	demonstrated	demonstrate	VERB
ejpam-6199	32	30	that	that	SCONJ
ejpam-6199	32	31	all	all	DET
ejpam-6199	32	32	boolean	boolean	ADJ
ejpam-6199	32	33	functions	function	NOUN
ejpam-6199	32	34	may	may	AUX
ejpam-6199	32	35	be	be	AUX
ejpam-6199	32	36	generated	generate	VERB
ejpam-6199	32	37	from	from	ADP
ejpam-6199	32	38	a	a	DET
ejpam-6199	32	39	single	single	ADJ
ejpam-6199	32	40	binary	binary	NOUN
ejpam-6199	32	41	operation	operation	NOUN
ejpam-6199	32	42	,	,	PUNCT
ejpam-6199	32	43	as	as	ADP
ejpam-6199	32	44	term	term	NOUN
ejpam-6199	32	45	operations	operation	NOUN
ejpam-6199	32	46	.	.	PUNCT
ejpam-6199	33	1	after	after	ADP
ejpam-6199	33	2	that	that	PRON
ejpam-6199	33	3	,	,	PUNCT
ejpam-6199	33	4	mccune	mccune	PROPN
ejpam-6199	33	5	et	et	PROPN
ejpam-6199	33	6	al	al	PROPN
ejpam-6199	33	7	.	.	PUNCT
ejpam-6199	34	1	[	[	X
ejpam-6199	34	2	2	2	NUM
ejpam-6199	34	3	]	]	PUNCT
ejpam-6199	34	4	demonstrated	demonstrate	VERB
ejpam-6199	34	5	that	that	SCONJ
ejpam-6199	34	6	this	this	DET
ejpam-6199	34	7	operation	operation	NOUN
ejpam-6199	34	8	can	can	AUX
ejpam-6199	34	9	represent	represent	VERB
ejpam-6199	34	10	any	any	DET
ejpam-6199	34	11	boolean	boolean	ADJ
ejpam-6199	34	12	operation	operation	NOUN
ejpam-6199	34	13	.	.	PUNCT
ejpam-6199	35	1	many	many	ADJ
ejpam-6199	35	2	researchers	researcher	NOUN
ejpam-6199	35	3	were	be	AUX
ejpam-6199	35	4	drawn	draw	VERB
ejpam-6199	35	5	to	to	ADP
ejpam-6199	35	6	this	this	DET
ejpam-6199	35	7	operation	operation	NOUN
ejpam-6199	35	8	since	since	SCONJ
ejpam-6199	35	9	it	it	PRON
ejpam-6199	35	10	is	be	AUX
ejpam-6199	35	11	the	the	DET
ejpam-6199	35	12	only	only	ADJ
ejpam-6199	35	13	way	way	NOUN
ejpam-6199	35	14	to	to	PART
ejpam-6199	35	15	define	define	VERB
ejpam-6199	35	16	any	any	DET
ejpam-6199	35	17	boolean	boolean	ADJ
ejpam-6199	35	18	operation	operation	NOUN
ejpam-6199	35	19	or	or	CCONJ
ejpam-6199	35	20	function	function	NOUN
ejpam-6199	35	21	[	[	X
ejpam-6199	35	22	2	2	NUM
ejpam-6199	35	23	]	]	PUNCT
ejpam-6199	35	24	.	.	PUNCT
ejpam-6199	36	1	as	as	ADP
ejpam-6199	36	2	a	a	DET
ejpam-6199	36	3	result	result	NOUN
ejpam-6199	36	4	,	,	PUNCT
ejpam-6199	36	5	many	many	ADJ
ejpam-6199	36	6	algebraic	algebraic	ADJ
ejpam-6199	36	7	structures	structure	NOUN
ejpam-6199	36	8	,	,	PUNCT
ejpam-6199	36	9	axioms	axiom	NOUN
ejpam-6199	36	10	or	or	CCONJ
ejpam-6199	36	11	formulas	formula	NOUN
ejpam-6199	36	12	,	,	PUNCT
ejpam-6199	36	13	are	be	AUX
ejpam-6199	36	14	reduced	reduce	VERB
ejpam-6199	36	15	.	.	PUNCT
ejpam-6199	37	1	because	because	SCONJ
ejpam-6199	37	2	simple	simple	ADJ
ejpam-6199	37	3	and	and	CCONJ
ejpam-6199	37	4	fewer	few	ADJ
ejpam-6199	37	5	axiom	axiom	NOUN
ejpam-6199	37	6	systems	system	NOUN
ejpam-6199	37	7	are	be	AUX
ejpam-6199	37	8	obtained	obtain	VERB
ejpam-6199	37	9	,	,	PUNCT
ejpam-6199	37	10	it	it	PRON
ejpam-6199	37	11	is	be	AUX
ejpam-6199	37	12	simple	simple	ADJ
ejpam-6199	37	13	to	to	PART
ejpam-6199	37	14	verify	verify	VERB
ejpam-6199	37	15	some	some	DET
ejpam-6199	37	16	attributes	attribute	NOUN
ejpam-6199	37	17	and	and	CCONJ
ejpam-6199	37	18	notations	notation	NOUN
ejpam-6199	37	19	for	for	ADP
ejpam-6199	37	20	a	a	DET
ejpam-6199	37	21	new	new	ADJ
ejpam-6199	37	22	algebraic	algebraic	ADJ
ejpam-6199	37	23	structure	structure	NOUN
ejpam-6199	37	24	.	.	PUNCT
ejpam-6199	38	1	thus	thus	ADV
ejpam-6199	38	2	,	,	PUNCT
ejpam-6199	38	3	many	many	ADJ
ejpam-6199	38	4	scientists	scientist	NOUN
ejpam-6199	38	5	seek	seek	VERB
ejpam-6199	38	6	a.	a.	PROPN
ejpam-6199	38	7	al	al	PROPN
ejpam-6199	38	8	-	-	PROPN
ejpam-6199	38	9	masarwah	masarwah	PROPN
ejpam-6199	38	10	et	et	PROPN
ejpam-6199	38	11	al	al	PROPN
ejpam-6199	38	12	.	.	PUNCT
ejpam-6199	38	13	/	/	SYM
ejpam-6199	38	14	eur	eur	PROPN
ejpam-6199	38	15	.	.	PUNCT
ejpam-6199	39	1	j.	j.	PROPN
ejpam-6199	39	2	pure	pure	PROPN
ejpam-6199	39	3	appl	appl	PROPN
ejpam-6199	39	4	.	.	PROPN
ejpam-6199	39	5	math	math	PROPN
ejpam-6199	39	6	,	,	PUNCT
ejpam-6199	39	7	18	18	NUM
ejpam-6199	39	8	(	(	PUNCT
ejpam-6199	39	9	3	3	NUM
ejpam-6199	39	10	)	)	PUNCT
ejpam-6199	39	11	(	(	PUNCT
ejpam-6199	39	12	2025	2025	NUM
ejpam-6199	39	13	)	)	PUNCT
ejpam-6199	39	14	,	,	PUNCT
ejpam-6199	39	15	6199	6199	NUM
ejpam-6199	39	16	3	3	NUM
ejpam-6199	39	17	of	of	ADP
ejpam-6199	39	18	17	17	NUM
ejpam-6199	39	19	to	to	PART
ejpam-6199	39	20	apply	apply	VERB
ejpam-6199	39	21	such	such	DET
ejpam-6199	39	22	a	a	DET
ejpam-6199	39	23	reduction	reduction	NOUN
ejpam-6199	39	24	to	to	PART
ejpam-6199	39	25	explore	explore	VERB
ejpam-6199	39	26	algebraic	algebraic	ADJ
ejpam-6199	39	27	structures	structure	NOUN
ejpam-6199	39	28	using	use	VERB
ejpam-6199	39	29	the	the	DET
ejpam-6199	39	30	sheffer	sheffer	NOUN
ejpam-6199	39	31	operation	operation	NOUN
ejpam-6199	39	32	such	such	ADJ
ejpam-6199	39	33	as	as	ADP
ejpam-6199	39	34	bg	bg	NOUN
ejpam-6199	39	35	-	-	PUNCT
ejpam-6199	39	36	algebras	algebras	X
ejpam-6199	40	1	[	[	X
ejpam-6199	40	2	3	3	NUM
ejpam-6199	40	3	]	]	PUNCT
ejpam-6199	40	4	,	,	PUNCT
ejpam-6199	40	5	bm	bm	PROPN
ejpam-6199	40	6	-	-	NOUN
ejpam-6199	40	7	algebra	algebra	NOUN
ejpam-6199	40	8	[	[	X
ejpam-6199	40	9	4	4	NUM
ejpam-6199	40	10	]	]	PUNCT
ejpam-6199	40	11	,	,	PUNCT
ejpam-6199	40	12	ortholattices	ortholattice	VERB
ejpam-6199	40	13	[	[	X
ejpam-6199	40	14	5	5	NUM
ejpam-6199	40	15	]	]	PUNCT
ejpam-6199	40	16	,	,	PUNCT
ejpam-6199	40	17	and	and	CCONJ
ejpam-6199	40	18	ink	ink	NOUN
ejpam-6199	40	19	-	-	PUNCT
ejpam-6199	40	20	algebra	algebra	NOUN
ejpam-6199	41	1	[	[	X
ejpam-6199	41	2	6	6	NUM
ejpam-6199	41	3	]	]	PUNCT
ejpam-6199	41	4	,	,	PUNCT
ejpam-6199	41	5	etc	etc	X
ejpam-6199	41	6	.	.	X
ejpam-6199	41	7	henkin	henkin	PROPN
ejpam-6199	42	1	[	[	X
ejpam-6199	42	2	7	7	X
ejpam-6199	42	3	]	]	PUNCT
ejpam-6199	42	4	proposed	propose	VERB
ejpam-6199	42	5	hilbert	hilbert	PROPN
ejpam-6199	42	6	algebras	algebras	PROPN
ejpam-6199	42	7	in	in	ADP
ejpam-6199	42	8	the	the	DET
ejpam-6199	42	9	1950	1950	NUM
ejpam-6199	42	10	’s	’s	NOUN
ejpam-6199	42	11	as	as	ADP
ejpam-6199	42	12	an	an	DET
ejpam-6199	42	13	algebraic	algebraic	ADJ
ejpam-6199	42	14	equivalent	equivalent	NOUN
ejpam-6199	42	15	of	of	ADP
ejpam-6199	42	16	hilbert	hilbert	PROPN
ejpam-6199	42	17	’s	’s	PART
ejpam-6199	42	18	positive	positive	ADJ
ejpam-6199	42	19	implicative	implicative	ADJ
ejpam-6199	42	20	propositional	propositional	ADJ
ejpam-6199	42	21	calculus	calculus	NOUN
ejpam-6199	42	22	[	[	X
ejpam-6199	42	23	8	8	NUM
ejpam-6199	42	24	]	]	PUNCT
ejpam-6199	42	25	,	,	PUNCT
ejpam-6199	42	26	for	for	ADP
ejpam-6199	42	27	use	use	NOUN
ejpam-6199	42	28	in	in	ADP
ejpam-6199	42	29	intuitionistic	intuitionistic	ADJ
ejpam-6199	42	30	and	and	CCONJ
ejpam-6199	42	31	other	other	ADJ
ejpam-6199	42	32	nonclassical	nonclassical	ADJ
ejpam-6199	42	33	logic	logic	NOUN
ejpam-6199	42	34	studies	study	NOUN
ejpam-6199	42	35	.	.	PUNCT
ejpam-6199	43	1	these	these	DET
ejpam-6199	43	2	algebraic	algebraic	ADJ
ejpam-6199	43	3	structures	structure	NOUN
ejpam-6199	43	4	,	,	PUNCT
ejpam-6199	43	5	which	which	PRON
ejpam-6199	43	6	include	include	VERB
ejpam-6199	43	7	the	the	DET
ejpam-6199	43	8	implication	implication	NOUN
ejpam-6199	43	9	and	and	CCONJ
ejpam-6199	43	10	the	the	DET
ejpam-6199	43	11	distinct	distinct	ADJ
ejpam-6199	43	12	element	element	NOUN
ejpam-6199	43	13	1	1	NUM
ejpam-6199	43	14	,	,	PUNCT
ejpam-6199	43	15	can	can	AUX
ejpam-6199	43	16	be	be	AUX
ejpam-6199	43	17	understood	understand	VERB
ejpam-6199	43	18	as	as	ADP
ejpam-6199	43	19	parts	part	NOUN
ejpam-6199	43	20	of	of	ADP
ejpam-6199	43	21	propositional	propositional	ADJ
ejpam-6199	43	22	logic	logic	NOUN
ejpam-6199	43	23	.	.	PUNCT
ejpam-6199	44	1	in	in	ADP
ejpam-6199	44	2	particular	particular	ADJ
ejpam-6199	44	3	,	,	PUNCT
ejpam-6199	44	4	diego	diego	PROPN
ejpam-6199	45	1	[	[	X
ejpam-6199	45	2	9	9	NUM
ejpam-6199	45	3	]	]	PUNCT
ejpam-6199	45	4	analyzed	analyze	VERB
ejpam-6199	45	5	hilbert	hilbert	PROPN
ejpam-6199	45	6	algebras	algebras	PROPN
ejpam-6199	45	7	,	,	PUNCT
ejpam-6199	45	8	including	include	VERB
ejpam-6199	45	9	their	their	PRON
ejpam-6199	45	10	deductive	deductive	ADJ
ejpam-6199	45	11	systems	system	NOUN
ejpam-6199	45	12	and	and	CCONJ
ejpam-6199	45	13	different	different	ADJ
ejpam-6199	45	14	features	feature	NOUN
ejpam-6199	45	15	,	,	PUNCT
ejpam-6199	45	16	and	and	CCONJ
ejpam-6199	45	17	showed	show	VERB
ejpam-6199	45	18	that	that	SCONJ
ejpam-6199	45	19	a	a	DET
ejpam-6199	45	20	variety	variety	NOUN
ejpam-6199	45	21	of	of	ADP
ejpam-6199	45	22	hilbert	hilbert	PROPN
ejpam-6199	45	23	algebras	algebras	PROPN
ejpam-6199	45	24	exist	exist	VERB
ejpam-6199	45	25	.	.	PUNCT
ejpam-6199	46	1	the	the	DET
ejpam-6199	46	2	idea	idea	NOUN
ejpam-6199	46	3	of	of	ADP
ejpam-6199	46	4	a	a	DET
ejpam-6199	46	5	deductive	deductive	ADJ
ejpam-6199	46	6	system	system	NOUN
ejpam-6199	46	7	,	,	PUNCT
ejpam-6199	46	8	also	also	ADV
ejpam-6199	46	9	known	know	VERB
ejpam-6199	46	10	as	as	ADP
ejpam-6199	46	11	implicative	implicative	ADJ
ejpam-6199	46	12	filters	filter	NOUN
ejpam-6199	46	13	,	,	PUNCT
ejpam-6199	46	14	is	be	AUX
ejpam-6199	46	15	crucial	crucial	ADJ
ejpam-6199	46	16	to	to	ADP
ejpam-6199	46	17	the	the	DET
ejpam-6199	46	18	overall	overall	ADJ
ejpam-6199	46	19	development	development	NOUN
ejpam-6199	46	20	of	of	ADP
ejpam-6199	46	21	hilbert	hilbert	PROPN
ejpam-6199	46	22	algebras	algebras	PROPN
ejpam-6199	46	23	because	because	SCONJ
ejpam-6199	46	24	they	they	PRON
ejpam-6199	46	25	can	can	AUX
ejpam-6199	46	26	be	be	AUX
ejpam-6199	46	27	employed	employ	VERB
ejpam-6199	46	28	to	to	PART
ejpam-6199	46	29	symbolize	symbolize	VERB
ejpam-6199	46	30	several	several	ADJ
ejpam-6199	46	31	logical	logical	ADJ
ejpam-6199	46	32	theories	theory	NOUN
ejpam-6199	46	33	.	.	PUNCT
ejpam-6199	47	1	furthermore	furthermore	ADV
ejpam-6199	47	2	,	,	PUNCT
ejpam-6199	47	3	busneag	busneag	NOUN
ejpam-6199	47	4	[	[	X
ejpam-6199	47	5	10	10	NUM
ejpam-6199	47	6	,	,	PUNCT
ejpam-6199	47	7	11	11	NUM
ejpam-6199	47	8	]	]	PUNCT
ejpam-6199	47	9	and	and	CCONJ
ejpam-6199	47	10	jun	jun	PROPN
ejpam-6199	48	1	[	[	X
ejpam-6199	48	2	12	12	NUM
ejpam-6199	48	3	]	]	PUNCT
ejpam-6199	48	4	analyzed	analyze	VERB
ejpam-6199	48	5	hilbert	hilbert	PROPN
ejpam-6199	48	6	algebras	algebras	PROPN
ejpam-6199	48	7	,	,	PUNCT
ejpam-6199	48	8	associated	associated	ADJ
ejpam-6199	48	9	concepts	concept	NOUN
ejpam-6199	48	10	,	,	PUNCT
ejpam-6199	48	11	and	and	CCONJ
ejpam-6199	48	12	deductive	deductive	ADJ
ejpam-6199	48	13	systems	system	NOUN
ejpam-6199	48	14	.	.	PUNCT
ejpam-6199	49	1	the	the	DET
ejpam-6199	49	2	sheffer	sheffer	NOUN
ejpam-6199	49	3	stroke	stroke	NOUN
ejpam-6199	49	4	was	be	AUX
ejpam-6199	49	5	used	use	VERB
ejpam-6199	49	6	in	in	ADP
ejpam-6199	49	7	hilbert	hilbert	PROPN
ejpam-6199	49	8	algebras	algebras	PROPN
ejpam-6199	49	9	by	by	ADP
ejpam-6199	49	10	oner	oner	NOUN
ejpam-6199	49	11	et	et	PROPN
ejpam-6199	49	12	al	al	PROPN
ejpam-6199	49	13	.	.	PROPN
ejpam-6199	49	14	in	in	ADP
ejpam-6199	49	15	2021	2021	NUM
ejpam-6199	49	16	,	,	PUNCT
ejpam-6199	49	17	and	and	CCONJ
ejpam-6199	49	18	they	they	PRON
ejpam-6199	49	19	presented	present	VERB
ejpam-6199	49	20	its	its	PRON
ejpam-6199	49	21	several	several	ADJ
ejpam-6199	49	22	properties	property	NOUN
ejpam-6199	49	23	,	,	PUNCT
ejpam-6199	49	24	deductive	deductive	ADJ
ejpam-6199	49	25	systems	system	NOUN
ejpam-6199	49	26	,	,	PUNCT
ejpam-6199	49	27	and	and	CCONJ
ejpam-6199	49	28	ideals	ideal	NOUN
ejpam-6199	49	29	[	[	X
ejpam-6199	49	30	13	13	NUM
ejpam-6199	49	31	]	]	PUNCT
ejpam-6199	49	32	.	.	PUNCT
ejpam-6199	50	1	fuzzy	fuzzy	ADJ
ejpam-6199	50	2	mathematics	mathematics	PROPN
ejpam-6199	50	3	is	be	AUX
ejpam-6199	50	4	a	a	DET
ejpam-6199	50	5	new	new	ADJ
ejpam-6199	50	6	field	field	NOUN
ejpam-6199	50	7	in	in	ADP
ejpam-6199	50	8	which	which	PRON
ejpam-6199	50	9	ordinary	ordinary	ADJ
ejpam-6199	50	10	notions	notion	NOUN
ejpam-6199	50	11	are	be	AUX
ejpam-6199	50	12	being	be	AUX
ejpam-6199	50	13	transferred	transfer	VERB
ejpam-6199	50	14	to	to	ADP
ejpam-6199	50	15	uncertainty	uncertainty	NOUN
ejpam-6199	50	16	cases	case	NOUN
ejpam-6199	50	17	.	.	PUNCT
ejpam-6199	51	1	zadeh	zadeh	NOUN
ejpam-6199	52	1	[	[	X
ejpam-6199	52	2	14	14	NUM
ejpam-6199	52	3	]	]	PUNCT
ejpam-6199	52	4	adopted	adopt	VERB
ejpam-6199	52	5	the	the	DET
ejpam-6199	52	6	concept	concept	NOUN
ejpam-6199	52	7	of	of	ADP
ejpam-6199	52	8	fuzzy	fuzzy	ADJ
ejpam-6199	52	9	structures	structure	NOUN
ejpam-6199	52	10	through	through	ADP
ejpam-6199	52	11	his	his	PRON
ejpam-6199	52	12	popular	popular	ADJ
ejpam-6199	52	13	paper	paper	NOUN
ejpam-6199	52	14	as	as	ADP
ejpam-6199	52	15	a	a	DET
ejpam-6199	52	16	development	development	NOUN
ejpam-6199	52	17	of	of	ADP
ejpam-6199	52	18	standard	standard	ADJ
ejpam-6199	52	19	structure	structure	NOUN
ejpam-6199	52	20	,	,	PUNCT
ejpam-6199	52	21	which	which	PRON
ejpam-6199	52	22	only	only	ADV
ejpam-6199	52	23	allows	allow	VERB
ejpam-6199	52	24	elements	element	NOUN
ejpam-6199	52	25	to	to	PART
ejpam-6199	52	26	be	be	AUX
ejpam-6199	52	27	fully	fully	ADV
ejpam-6199	52	28	in	in	ADP
ejpam-6199	52	29	or	or	CCONJ
ejpam-6199	52	30	fully	fully	ADV
ejpam-6199	52	31	out	out	ADP
ejpam-6199	52	32	of	of	ADP
ejpam-6199	52	33	a	a	DET
ejpam-6199	52	34	set	set	NOUN
ejpam-6199	52	35	.	.	PUNCT
ejpam-6199	53	1	this	this	DET
ejpam-6199	53	2	concept	concept	NOUN
ejpam-6199	53	3	is	be	AUX
ejpam-6199	53	4	a	a	DET
ejpam-6199	53	5	significant	significant	ADJ
ejpam-6199	53	6	mathematical	mathematical	ADJ
ejpam-6199	53	7	framework	framework	NOUN
ejpam-6199	53	8	for	for	ADP
ejpam-6199	53	9	dealing	deal	VERB
ejpam-6199	53	10	with	with	ADP
ejpam-6199	53	11	uncertainty	uncertainty	NOUN
ejpam-6199	53	12	and	and	CCONJ
ejpam-6199	53	13	ambiguity	ambiguity	NOUN
ejpam-6199	53	14	in	in	ADP
ejpam-6199	53	15	data	data	PROPN
ejpam-6199	53	16	.	.	PUNCT
ejpam-6199	54	1	zadeh	zadeh	NOUN
ejpam-6199	55	1	[	[	X
ejpam-6199	55	2	15	15	NUM
ejpam-6199	55	3	]	]	PUNCT
ejpam-6199	55	4	made	make	VERB
ejpam-6199	55	5	an	an	DET
ejpam-6199	55	6	extension	extension	NOUN
ejpam-6199	55	7	of	of	ADP
ejpam-6199	55	8	the	the	DET
ejpam-6199	55	9	theory	theory	NOUN
ejpam-6199	55	10	of	of	ADP
ejpam-6199	55	11	fuzziness	fuzziness	NOUN
ejpam-6199	55	12	concept	concept	NOUN
ejpam-6199	55	13	by	by	ADP
ejpam-6199	55	14	an	an	DET
ejpam-6199	55	15	interval	interval	NOUN
ejpam-6199	55	16	-	-	PUNCT
ejpam-6199	55	17	valued	value	VERB
ejpam-6199	55	18	fuzziness	fuzziness	NOUN
ejpam-6199	55	19	concept	concept	NOUN
ejpam-6199	55	20	.	.	PUNCT
ejpam-6199	56	1	as	as	ADP
ejpam-6199	56	2	another	another	DET
ejpam-6199	56	3	extension	extension	NOUN
ejpam-6199	56	4	of	of	ADP
ejpam-6199	56	5	uncertainty	uncertainty	NOUN
ejpam-6199	56	6	sets	set	NOUN
ejpam-6199	56	7	,	,	PUNCT
ejpam-6199	56	8	zhang	zhang	PROPN
ejpam-6199	57	1	[	[	X
ejpam-6199	57	2	16	16	NUM
ejpam-6199	57	3	]	]	PUNCT
ejpam-6199	57	4	presented	present	VERB
ejpam-6199	57	5	the	the	DET
ejpam-6199	57	6	notion	notion	NOUN
ejpam-6199	57	7	bipolar	bipolar	ADJ
ejpam-6199	57	8	fuzzy	fuzzy	ADJ
ejpam-6199	57	9	sets	set	NOUN
ejpam-6199	57	10	as	as	ADP
ejpam-6199	57	11	a	a	DET
ejpam-6199	57	12	very	very	ADV
ejpam-6199	57	13	useful	useful	ADJ
ejpam-6199	57	14	tool	tool	NOUN
ejpam-6199	57	15	for	for	ADP
ejpam-6199	57	16	considering	consider	VERB
ejpam-6199	57	17	positive	positive	ADJ
ejpam-6199	57	18	and	and	CCONJ
ejpam-6199	57	19	negative	negative	ADJ
ejpam-6199	57	20	data	datum	NOUN
ejpam-6199	57	21	at	at	ADP
ejpam-6199	57	22	the	the	DET
ejpam-6199	57	23	same	same	ADJ
ejpam-6199	57	24	time	time	NOUN
ejpam-6199	57	25	.	.	PUNCT
ejpam-6199	58	1	by	by	AUX
ejpam-6199	58	2	ignore	ignore	VERB
ejpam-6199	58	3	the	the	DET
ejpam-6199	58	4	positive	positive	ADJ
ejpam-6199	58	5	part	part	NOUN
ejpam-6199	58	6	of	of	ADP
ejpam-6199	58	7	a	a	DET
ejpam-6199	58	8	bipolar	bipolar	ADJ
ejpam-6199	58	9	uncertainty	uncertainty	NOUN
ejpam-6199	58	10	set	set	NOUN
ejpam-6199	58	11	,	,	PUNCT
ejpam-6199	58	12	jun	jun	PROPN
ejpam-6199	58	13	et	et	PROPN
ejpam-6199	58	14	al	al	PROPN
ejpam-6199	58	15	.	.	PUNCT
ejpam-6199	59	1	[	[	X
ejpam-6199	59	2	17	17	NUM
ejpam-6199	59	3	]	]	PUNCT
ejpam-6199	59	4	proposed	propose	VERB
ejpam-6199	59	5	a	a	DET
ejpam-6199	59	6	new	new	ADJ
ejpam-6199	59	7	concept	concept	NOUN
ejpam-6199	59	8	,	,	PUNCT
ejpam-6199	59	9	namely	namely	ADV
ejpam-6199	59	10	n	n	CCONJ
ejpam-6199	59	11	-	-	PUNCT
ejpam-6199	59	12	structures	structure	NOUN
ejpam-6199	59	13	.	.	PUNCT
ejpam-6199	60	1	after	after	ADP
ejpam-6199	60	2	that	that	PRON
ejpam-6199	60	3	,	,	PUNCT
ejpam-6199	60	4	there	there	PRON
ejpam-6199	60	5	were	be	VERB
ejpam-6199	60	6	many	many	ADJ
ejpam-6199	60	7	extensions	extension	NOUN
ejpam-6199	60	8	of	of	ADP
ejpam-6199	60	9	fuzziness	fuzziness	NOUN
ejpam-6199	60	10	structures	structure	NOUN
ejpam-6199	60	11	,	,	PUNCT
ejpam-6199	60	12	such	such	ADJ
ejpam-6199	60	13	as	as	ADP
ejpam-6199	60	14	the	the	DET
ejpam-6199	60	15	intuitionistic	intuitionistic	ADJ
ejpam-6199	60	16	fuzzy	fuzzy	ADJ
ejpam-6199	60	17	,	,	PUNCT
ejpam-6199	60	18	neutrosophic	neutrosophic	ADJ
ejpam-6199	60	19	set	set	NOUN
ejpam-6199	60	20	and	and	CCONJ
ejpam-6199	60	21	lukasiewicz	lukasiewicz	ADJ
ejpam-6199	60	22	fuzzy	fuzzy	ADJ
ejpam-6199	60	23	set	set	NOUN
ejpam-6199	60	24	,	,	PUNCT
ejpam-6199	60	25	see	see	VERB
ejpam-6199	60	26	[	[	X
ejpam-6199	60	27	18–20	18–20	NUM
ejpam-6199	60	28	]	]	PUNCT
ejpam-6199	60	29	.	.	PUNCT
ejpam-6199	61	1	by	by	ADP
ejpam-6199	61	2	incorporating	incorporate	VERB
ejpam-6199	61	3	the	the	DET
ejpam-6199	61	4	concept	concept	NOUN
ejpam-6199	61	5	of	of	ADP
ejpam-6199	61	6	interval	interval	NOUN
ejpam-6199	61	7	-	-	PUNCT
ejpam-6199	61	8	valued	value	VERB
ejpam-6199	61	9	fuzziness	fuzziness	NOUN
ejpam-6199	61	10	sets	set	NOUN
ejpam-6199	61	11	with	with	ADP
ejpam-6199	61	12	n	n	DET
ejpam-6199	61	13	-structures	-structure	NOUN
ejpam-6199	61	14	,	,	PUNCT
ejpam-6199	61	15	which	which	PRON
ejpam-6199	61	16	creates	create	VERB
ejpam-6199	61	17	an	an	DET
ejpam-6199	61	18	expansion	expansion	NOUN
ejpam-6199	61	19	of	of	ADP
ejpam-6199	61	20	a	a	DET
ejpam-6199	61	21	bipolar	bipolar	ADV
ejpam-6199	61	22	-	-	PUNCT
ejpam-6199	61	23	valued	value	VERB
ejpam-6199	61	24	fuzziness	fuzziness	NOUN
ejpam-6199	61	25	set	set	VERB
ejpam-6199	61	26	to	to	PART
ejpam-6199	61	27	produce	produce	VERB
ejpam-6199	61	28	the	the	DET
ejpam-6199	61	29	thought	thought	NOUN
ejpam-6199	61	30	of	of	ADP
ejpam-6199	61	31	crossing	cross	VERB
ejpam-6199	61	32	cubic	cubic	ADJ
ejpam-6199	61	33	structures	structure	NOUN
ejpam-6199	61	34	[	[	X
ejpam-6199	61	35	21	21	NUM
ejpam-6199	61	36	]	]	PUNCT
ejpam-6199	61	37	,	,	PUNCT
ejpam-6199	61	38	that	that	PRON
ejpam-6199	61	39	floated	float	VERB
ejpam-6199	61	40	for	for	ADP
ejpam-6199	61	41	the	the	DET
ejpam-6199	61	42	first	first	ADJ
ejpam-6199	61	43	time	time	NOUN
ejpam-6199	61	44	in	in	ADP
ejpam-6199	61	45	2021	2021	NUM
ejpam-6199	61	46	by	by	ADP
ejpam-6199	61	47	jun	jun	PROPN
ejpam-6199	61	48	and	and	CCONJ
ejpam-6199	61	49	song	song	NOUN
ejpam-6199	61	50	[	[	X
ejpam-6199	61	51	22	22	NUM
ejpam-6199	61	52	]	]	PUNCT
ejpam-6199	61	53	,	,	PUNCT
ejpam-6199	61	54	where	where	SCONJ
ejpam-6199	61	55	they	they	PRON
ejpam-6199	61	56	applied	apply	VERB
ejpam-6199	61	57	it	it	PRON
ejpam-6199	61	58	to	to	PART
ejpam-6199	61	59	bck	bck	VERB
ejpam-6199	61	60	/	/	SYM
ejpam-6199	61	61	bci	bci	NOUN
ejpam-6199	61	62	-	-	NOUN
ejpam-6199	61	63	algebra	algebra	NOUN
ejpam-6199	61	64	.	.	PUNCT
ejpam-6199	62	1	additionally	additionally	ADV
ejpam-6199	62	2	,	,	PUNCT
ejpam-6199	62	3	ozturk	ozturk	PROPN
ejpam-6199	62	4	et	et	PROPN
ejpam-6199	62	5	al	al	PROPN
ejpam-6199	62	6	.	.	PUNCT
ejpam-6199	63	1	[	[	X
ejpam-6199	63	2	23	23	NUM
ejpam-6199	63	3	]	]	PUNCT
ejpam-6199	63	4	developed	develop	VERB
ejpam-6199	63	5	the	the	DET
ejpam-6199	63	6	concept	concept	NOUN
ejpam-6199	63	7	of	of	ADP
ejpam-6199	63	8	crossing	cross	VERB
ejpam-6199	63	9	cubic	cubic	ADV
ejpam-6199	63	10	on	on	ADP
ejpam-6199	63	11	semigroup	semigroup	ADJ
ejpam-6199	63	12	structures	structure	NOUN
ejpam-6199	63	13	,	,	PUNCT
ejpam-6199	63	14	and	and	CCONJ
ejpam-6199	63	15	commutative	commutative	ADJ
ejpam-6199	63	16	ideal	ideal	NOUN
ejpam-6199	63	17	in	in	ADP
ejpam-6199	63	18	bck	bck	PROPN
ejpam-6199	63	19	-	-	PUNCT
ejpam-6199	63	20	algebras	algebras	PROPN
ejpam-6199	63	21	.	.	PUNCT
ejpam-6199	64	1	al	al	PROPN
ejpam-6199	64	2	-	-	PROPN
ejpam-6199	64	3	masarwah	masarwah	PROPN
ejpam-6199	64	4	et	et	PROPN
ejpam-6199	64	5	al	al	PROPN
ejpam-6199	64	6	.	.	PUNCT
ejpam-6199	65	1	[	[	X
ejpam-6199	65	2	24	24	NUM
ejpam-6199	65	3	]	]	PUNCT
ejpam-6199	65	4	established	establish	VERB
ejpam-6199	65	5	the	the	DET
ejpam-6199	65	6	idea	idea	NOUN
ejpam-6199	65	7	of	of	ADP
ejpam-6199	65	8	crossing	cross	VERB
ejpam-6199	65	9	cubic	cubic	ADJ
ejpam-6199	65	10	lie	lie	NOUN
ejpam-6199	65	11	subalgebra	subalgebra	NOUN
ejpam-6199	65	12	in	in	ADP
ejpam-6199	65	13	the	the	DET
ejpam-6199	65	14	context	context	NOUN
ejpam-6199	65	15	of	of	ADP
ejpam-6199	65	16	lie	lie	NOUN
ejpam-6199	65	17	algebras	algebra	NOUN
ejpam-6199	65	18	.	.	PUNCT
ejpam-6199	66	1	they	they	PRON
ejpam-6199	66	2	utilized	utilize	VERB
ejpam-6199	66	3	the	the	DET
ejpam-6199	66	4	notions	notion	NOUN
ejpam-6199	66	5	of	of	ADP
ejpam-6199	66	6	lie	lie	NOUN
ejpam-6199	66	7	ideals	ideal	NOUN
ejpam-6199	66	8	,	,	PUNCT
ejpam-6199	66	9	homomorphisms	homomorphism	NOUN
ejpam-6199	66	10	and	and	CCONJ
ejpam-6199	66	11	some	some	DET
ejpam-6199	66	12	fundamental	fundamental	ADJ
ejpam-6199	66	13	properties	property	NOUN
ejpam-6199	66	14	of	of	ADP
ejpam-6199	66	15	lie	lie	NOUN
ejpam-6199	66	16	algebras	algebra	NOUN
ejpam-6199	66	17	.	.	PUNCT
ejpam-6199	67	1	in	in	ADP
ejpam-6199	67	2	the	the	DET
ejpam-6199	67	3	fuzzification	fuzzification	NOUN
ejpam-6199	67	4	of	of	ADP
ejpam-6199	67	5	the	the	DET
ejpam-6199	67	6	sheffer	sheffer	NOUN
ejpam-6199	67	7	stroke	stroke	PROPN
ejpam-6199	67	8	hilbert	hilbert	PROPN
ejpam-6199	67	9	algebras	algebras	PROPN
ejpam-6199	67	10	,	,	PUNCT
ejpam-6199	67	11	the	the	DET
ejpam-6199	67	12	concept	concept	NOUN
ejpam-6199	67	13	of	of	ADP
ejpam-6199	67	14	fuzzy	fuzzy	ADJ
ejpam-6199	67	15	(	(	PUNCT
ejpam-6199	67	16	uncertainty	uncertainty	NOUN
ejpam-6199	67	17	)	)	PUNCT
ejpam-6199	67	18	sets	set	NOUN
ejpam-6199	67	19	was	be	AUX
ejpam-6199	67	20	connected	connect	VERB
ejpam-6199	67	21	with	with	ADP
ejpam-6199	67	22	a	a	DET
ejpam-6199	67	23	filter	filter	NOUN
ejpam-6199	67	24	and	and	CCONJ
ejpam-6199	67	25	a	a	DET
ejpam-6199	67	26	deductive	deductive	ADJ
ejpam-6199	67	27	system	system	NOUN
ejpam-6199	67	28	of	of	ADP
ejpam-6199	67	29	sheffer	sheffer	PROPN
ejpam-6199	67	30	stroke	stroke	PROPN
ejpam-6199	67	31	hilbert	hilbert	PROPN
ejpam-6199	67	32	algebra	algebra	PROPN
ejpam-6199	67	33	by	by	ADP
ejpam-6199	67	34	oner	oner	NOUN
ejpam-6199	67	35	et	et	PROPN
ejpam-6199	67	36	al	al	PROPN
ejpam-6199	67	37	.	.	PUNCT
ejpam-6199	68	1	[	[	X
ejpam-6199	68	2	25	25	NUM
ejpam-6199	68	3	]	]	PUNCT
ejpam-6199	68	4	.	.	PUNCT
ejpam-6199	69	1	vasuki	vasuki	PROPN
ejpam-6199	69	2	et	et	PROPN
ejpam-6199	69	3	al	al	PROPN
ejpam-6199	69	4	.	.	PUNCT
ejpam-6199	70	1	[	[	X
ejpam-6199	70	2	26	26	NUM
ejpam-6199	70	3	]	]	PUNCT
ejpam-6199	70	4	presented	present	VERB
ejpam-6199	70	5	the	the	DET
ejpam-6199	70	6	concept	concept	NOUN
ejpam-6199	70	7	of	of	ADP
ejpam-6199	70	8	anti	anti	ADJ
ejpam-6199	70	9	-	-	ADJ
ejpam-6199	70	10	q	q	ADJ
ejpam-6199	70	11	-	-	PUNCT
ejpam-6199	70	12	fuzzy	fuzzy	ADJ
ejpam-6199	70	13	deductive	deductive	ADJ
ejpam-6199	70	14	systems	system	NOUN
ejpam-6199	70	15	of	of	ADP
ejpam-6199	70	16	hilbert	hilbert	PROPN
ejpam-6199	70	17	algebras	algebras	PROPN
ejpam-6199	70	18	and	and	CCONJ
ejpam-6199	70	19	proved	prove	VERB
ejpam-6199	70	20	some	some	DET
ejpam-6199	70	21	results	result	NOUN
ejpam-6199	70	22	.	.	PUNCT
ejpam-6199	71	1	in	in	ADP
ejpam-6199	71	2	the	the	DET
ejpam-6199	71	3	connection	connection	NOUN
ejpam-6199	71	4	between	between	ADP
ejpam-6199	71	5	intuitionistic	intuitionistic	ADJ
ejpam-6199	71	6	fuzzy	fuzzy	ADJ
ejpam-6199	71	7	sets	set	NOUN
ejpam-6199	71	8	and	and	CCONJ
ejpam-6199	71	9	sheffer	sheffer	PROPN
ejpam-6199	71	10	stroke	stroke	PROPN
ejpam-6199	71	11	hilbert	hilbert	PROPN
ejpam-6199	71	12	algebras	algebras	PROPN
ejpam-6199	71	13	,	,	PUNCT
ejpam-6199	71	14	saeid	saeid	PROPN
ejpam-6199	71	15	et	et	PROPN
ejpam-6199	71	16	al	al	PROPN
ejpam-6199	71	17	.	.	PUNCT
ejpam-6199	72	1	[	[	X
ejpam-6199	72	2	27	27	NUM
ejpam-6199	72	3	]	]	PUNCT
ejpam-6199	72	4	implemented	implement	VERB
ejpam-6199	72	5	the	the	DET
ejpam-6199	72	6	concept	concept	NOUN
ejpam-6199	72	7	of	of	ADP
ejpam-6199	72	8	intuitionistic	intuitionistic	ADJ
ejpam-6199	72	9	fuzzy	fuzzy	ADJ
ejpam-6199	72	10	deductive	deductive	ADJ
ejpam-6199	72	11	system	system	NOUN
ejpam-6199	72	12	and	and	CCONJ
ejpam-6199	72	13	intuitionistic	intuitionistic	ADJ
ejpam-6199	72	14	fuzzy	fuzzy	ADJ
ejpam-6199	72	15	filter	filter	NOUN
ejpam-6199	72	16	in	in	ADP
ejpam-6199	72	17	sheffer	sheffer	PROPN
ejpam-6199	72	18	stroke	stroke	PROPN
ejpam-6199	72	19	hilbert	hilbert	PROPN
ejpam-6199	72	20	algebras	algebras	PROPN
ejpam-6199	72	21	,	,	PUNCT
ejpam-6199	72	22	and	and	CCONJ
ejpam-6199	72	23	investigated	investigate	VERB
ejpam-6199	72	24	some	some	PRON
ejpam-6199	72	25	of	of	ADP
ejpam-6199	72	26	its	its	PRON
ejpam-6199	72	27	features	feature	NOUN
ejpam-6199	72	28	.	.	PUNCT
ejpam-6199	73	1	oner	oner	NOUN
ejpam-6199	73	2	et	et	PROPN
ejpam-6199	73	3	al	al	PROPN
ejpam-6199	73	4	.	.	PUNCT
ejpam-6199	74	1	[	[	X
ejpam-6199	74	2	28	28	NUM
ejpam-6199	74	3	]	]	PUNCT
ejpam-6199	74	4	studied	study	VERB
ejpam-6199	74	5	the	the	DET
ejpam-6199	74	6	idea	idea	NOUN
ejpam-6199	74	7	of	of	ADP
ejpam-6199	74	8	sheffer	sheffer	PROPN
ejpam-6199	74	9	stroke	stroke	PROPN
ejpam-6199	74	10	hilbert	hilbert	PROPN
ejpam-6199	74	11	algebras	algebras	PROPN
ejpam-6199	74	12	via	via	ADP
ejpam-6199	74	13	neutrosophic	neutrosophic	ADJ
ejpam-6199	74	14	n	n	CCONJ
ejpam-6199	74	15	-	-	PUNCT
ejpam-6199	74	16	structures	structure	NOUN
ejpam-6199	74	17	.	.	PUNCT
ejpam-6199	75	1	they	they	PRON
ejpam-6199	75	2	discussed	discuss	VERB
ejpam-6199	75	3	neutrosophic	neutrosophic	ADJ
ejpam-6199	75	4	n	n	CCONJ
ejpam-6199	75	5	-	-	PUNCT
ejpam-6199	75	6	subalgebras	subalgebras	PROPN
ejpam-6199	75	7	and	and	CCONJ
ejpam-6199	75	8	neutrosophic	neutrosophic	ADJ
ejpam-6199	75	9	n	n	CCONJ
ejpam-6199	75	10	-	-	PUNCT
ejpam-6199	75	11	ideals	ideal	NOUN
ejpam-6199	75	12	in	in	ADP
ejpam-6199	75	13	sheffer	sheffer	PROPN
ejpam-6199	75	14	stroke	stroke	PROPN
ejpam-6199	75	15	hilbert	hilbert	PROPN
ejpam-6199	75	16	algebras	algebras	PROPN
ejpam-6199	75	17	.	.	PUNCT
ejpam-6199	76	1	concentrating	concentrate	VERB
ejpam-6199	76	2	on	on	ADP
ejpam-6199	76	3	exploring	explore	VERB
ejpam-6199	76	4	the	the	DET
ejpam-6199	76	5	filter	filter	NOUN
ejpam-6199	76	6	and	and	CCONJ
ejpam-6199	76	7	deductive	deductive	ADJ
ejpam-6199	76	8	system	system	NOUN
ejpam-6199	76	9	of	of	ADP
ejpam-6199	76	10	the	the	DET
ejpam-6199	76	11	sheffer	sheffer	NOUN
ejpam-6199	76	12	stroke	stroke	NOUN
ejpam-6199	76	13	hilbert	hilbert	PROPN
ejpam-6199	76	14	algebra	algebra	PROPN
ejpam-6199	76	15	using	use	VERB
ejpam-6199	76	16	the	the	DET
ejpam-6199	76	17	crossing	crossing	NOUN
ejpam-6199	76	18	cubic	cubic	ADJ
ejpam-6199	76	19	structure	structure	NOUN
ejpam-6199	76	20	,	,	PUNCT
ejpam-6199	76	21	we	we	PRON
ejpam-6199	76	22	propose	propose	VERB
ejpam-6199	76	23	the	the	DET
ejpam-6199	76	24	idea	idea	NOUN
ejpam-6199	76	25	of	of	ADP
ejpam-6199	76	26	crossing	cross	VERB
ejpam-6199	76	27	cubic	cubic	ADJ
ejpam-6199	76	28	filter	filter	NOUN
ejpam-6199	76	29	and	and	CCONJ
ejpam-6199	76	30	a.	a.	PROPN
ejpam-6199	76	31	al	al	PROPN
ejpam-6199	76	32	-	-	PROPN
ejpam-6199	76	33	masarwah	masarwah	PROPN
ejpam-6199	76	34	et	et	PROPN
ejpam-6199	76	35	al	al	PROPN
ejpam-6199	76	36	.	.	PUNCT
ejpam-6199	76	37	/	/	SYM
ejpam-6199	76	38	eur	eur	PROPN
ejpam-6199	76	39	.	.	PUNCT
ejpam-6199	77	1	j.	j.	PROPN
ejpam-6199	77	2	pure	pure	PROPN
ejpam-6199	77	3	appl	appl	PROPN
ejpam-6199	77	4	.	.	PROPN
ejpam-6199	77	5	math	math	PROPN
ejpam-6199	77	6	,	,	PUNCT
ejpam-6199	77	7	18	18	NUM
ejpam-6199	77	8	(	(	PUNCT
ejpam-6199	77	9	3	3	NUM
ejpam-6199	77	10	)	)	PUNCT
ejpam-6199	77	11	(	(	PUNCT
ejpam-6199	77	12	2025	2025	NUM
ejpam-6199	77	13	)	)	PUNCT
ejpam-6199	77	14	,	,	PUNCT
ejpam-6199	77	15	6199	6199	NUM
ejpam-6199	77	16	4	4	NUM
ejpam-6199	77	17	of	of	ADP
ejpam-6199	77	18	17	17	NUM
ejpam-6199	77	19	crossing	cross	VERB
ejpam-6199	77	20	cubic	cubic	ADJ
ejpam-6199	77	21	deductive	deductive	ADJ
ejpam-6199	77	22	system	system	NOUN
ejpam-6199	77	23	,	,	PUNCT
ejpam-6199	77	24	give	give	VERB
ejpam-6199	77	25	examples	example	NOUN
ejpam-6199	77	26	,	,	PUNCT
ejpam-6199	77	27	and	and	CCONJ
ejpam-6199	77	28	then	then	ADV
ejpam-6199	77	29	discuss	discuss	VERB
ejpam-6199	77	30	certain	certain	ADJ
ejpam-6199	77	31	features	feature	NOUN
ejpam-6199	77	32	.	.	PUNCT
ejpam-6199	78	1	we	we	PRON
ejpam-6199	78	2	create	create	VERB
ejpam-6199	78	3	a	a	DET
ejpam-6199	78	4	crossing	cross	VERB
ejpam-6199	78	5	cubic	cubic	ADJ
ejpam-6199	78	6	filter	filter	NOUN
ejpam-6199	78	7	by	by	ADP
ejpam-6199	78	8	applying	apply	VERB
ejpam-6199	78	9	appropriate	appropriate	ADJ
ejpam-6199	78	10	conditions	condition	NOUN
ejpam-6199	78	11	to	to	ADP
ejpam-6199	78	12	a	a	DET
ejpam-6199	78	13	specific	specific	ADJ
ejpam-6199	78	14	crossing	crossing	NOUN
ejpam-6199	78	15	cubic	cubic	ADJ
ejpam-6199	78	16	structure	structure	NOUN
ejpam-6199	78	17	.	.	PUNCT
ejpam-6199	79	1	we	we	PRON
ejpam-6199	79	2	study	study	VERB
ejpam-6199	79	3	characterizations	characterization	NOUN
ejpam-6199	79	4	of	of	ADP
ejpam-6199	79	5	crossing	cross	VERB
ejpam-6199	79	6	cubic	cubic	ADJ
ejpam-6199	79	7	filters	filter	NOUN
ejpam-6199	79	8	.	.	PUNCT
ejpam-6199	80	1	we	we	PRON
ejpam-6199	80	2	construct	construct	VERB
ejpam-6199	80	3	crossing	cross	VERB
ejpam-6199	80	4	cubic	cubic	ADJ
ejpam-6199	80	5	filters	filter	NOUN
ejpam-6199	80	6	that	that	PRON
ejpam-6199	80	7	are	be	AUX
ejpam-6199	80	8	associated	associate	VERB
ejpam-6199	80	9	with	with	ADP
ejpam-6199	80	10	filters	filter	NOUN
ejpam-6199	80	11	.	.	PUNCT
ejpam-6199	81	1	eventually	eventually	ADV
ejpam-6199	81	2	,	,	PUNCT
ejpam-6199	81	3	we	we	PRON
ejpam-6199	81	4	prove	prove	VERB
ejpam-6199	81	5	that	that	SCONJ
ejpam-6199	81	6	crossing	cross	VERB
ejpam-6199	81	7	cubic	cubic	ADJ
ejpam-6199	81	8	deductive	deductive	ADJ
ejpam-6199	81	9	system	system	NOUN
ejpam-6199	81	10	and	and	CCONJ
ejpam-6199	81	11	crossing	cross	VERB
ejpam-6199	81	12	cubic	cubic	ADJ
ejpam-6199	81	13	filter	filter	NOUN
ejpam-6199	81	14	are	be	AUX
ejpam-6199	81	15	a	a	DET
ejpam-6199	81	16	complementary	complementary	ADJ
ejpam-6199	81	17	notion	notion	NOUN
ejpam-6199	81	18	.	.	PUNCT
ejpam-6199	82	1	2	2	X
ejpam-6199	82	2	.	.	X
ejpam-6199	82	3	preliminaries	preliminary	NOUN
ejpam-6199	82	4	this	this	DET
ejpam-6199	82	5	section	section	NOUN
ejpam-6199	82	6	covers	cover	VERB
ejpam-6199	82	7	some	some	DET
ejpam-6199	82	8	fundamental	fundamental	ADJ
ejpam-6199	82	9	definitions	definition	NOUN
ejpam-6199	82	10	and	and	CCONJ
ejpam-6199	82	11	results	result	NOUN
ejpam-6199	82	12	of	of	ADP
ejpam-6199	82	13	sheffer	sheffer	PROPN
ejpam-6199	82	14	stroke	stroke	PROPN
ejpam-6199	82	15	hilbert	hilbert	PROPN
ejpam-6199	82	16	algebras	algebras	PROPN
ejpam-6199	82	17	,	,	PUNCT
ejpam-6199	82	18	filters	filter	NOUN
ejpam-6199	82	19	,	,	PUNCT
ejpam-6199	82	20	deductive	deductive	ADJ
ejpam-6199	82	21	systems	system	NOUN
ejpam-6199	82	22	,	,	PUNCT
ejpam-6199	82	23	crossing	cross	VERB
ejpam-6199	82	24	cubic	cubic	ADJ
ejpam-6199	82	25	structures	structure	NOUN
ejpam-6199	82	26	,	,	PUNCT
ejpam-6199	82	27	and	and	CCONJ
ejpam-6199	82	28	some	some	DET
ejpam-6199	82	29	results	result	NOUN
ejpam-6199	82	30	that	that	PRON
ejpam-6199	82	31	will	will	AUX
ejpam-6199	82	32	be	be	AUX
ejpam-6199	82	33	utilized	utilize	VERB
ejpam-6199	82	34	throughout	throughout	ADP
ejpam-6199	82	35	the	the	DET
ejpam-6199	82	36	study	study	NOUN
ejpam-6199	82	37	.	.	PUNCT
ejpam-6199	83	1	definition	definition	NOUN
ejpam-6199	83	2	1	1	NUM
ejpam-6199	83	3	(	(	PUNCT
ejpam-6199	83	4	[	[	X
ejpam-6199	83	5	1	1	NUM
ejpam-6199	83	6	]	]	NUM
ejpam-6199	83	7	)	)	PUNCT
ejpam-6199	83	8	.	.	PUNCT
ejpam-6199	84	1	a	a	DET
ejpam-6199	84	2	groupoid	groupoid	PROPN
ejpam-6199	84	3	is	be	AUX
ejpam-6199	84	4	denoted	denote	VERB
ejpam-6199	84	5	by	by	ADP
ejpam-6199	84	6	φ	φ	NUM
ejpam-6199	84	7	◦	◦	NOUN
ejpam-6199	84	8	:	:	PUNCT
ejpam-6199	84	9	=	=	SYM
ejpam-6199	84	10	(	(	PUNCT
ejpam-6199	84	11	φ	φ	NOUN
ejpam-6199	84	12	,	,	PUNCT
ejpam-6199	84	13	|	|	NOUN
ejpam-6199	84	14	)	)	PUNCT
ejpam-6199	84	15	.	.	PUNCT
ejpam-6199	85	1	then	then	ADV
ejpam-6199	85	2	,	,	PUNCT
ejpam-6199	85	3	the	the	DET
ejpam-6199	85	4	operation	operation	NOUN
ejpam-6199	85	5	“	"	PUNCT
ejpam-6199	85	6	|	|	ADV
ejpam-6199	85	7	”	"	PUNCT
ejpam-6199	85	8	is	be	AUX
ejpam-6199	85	9	called	call	VERB
ejpam-6199	85	10	a	a	DET
ejpam-6199	85	11	sheffer	sheffer	NOUN
ejpam-6199	85	12	stroke	stroke	NOUN
ejpam-6199	85	13	(	(	PUNCT
ejpam-6199	85	14	sheffer	sheffer	NOUN
ejpam-6199	85	15	operation	operation	NOUN
ejpam-6199	85	16	)	)	PUNCT
ejpam-6199	85	17	if	if	SCONJ
ejpam-6199	85	18	the	the	DET
ejpam-6199	85	19	following	follow	VERB
ejpam-6199	85	20	identities	identity	NOUN
ejpam-6199	85	21	hold	hold	VERB
ejpam-6199	85	22	:	:	PUNCT
ejpam-6199	85	23	∀n	∀n	NUM
ejpam-6199	85	24	,	,	PUNCT
ejpam-6199	85	25	v	v	PROPN
ejpam-6199	85	26	,	,	PUNCT
ejpam-6199	85	27	w,∈	w,∈	PROPN
ejpam-6199	85	28	φ	φ	NOUN
ejpam-6199	85	29	,	,	PUNCT
ejpam-6199	85	30	(	(	PUNCT
ejpam-6199	85	31	1	1	NUM
ejpam-6199	85	32	)	)	PUNCT
ejpam-6199	85	33	n	n	NOUN
ejpam-6199	85	34	|	|	ADV
ejpam-6199	85	35	v	v	NOUN
ejpam-6199	85	36	=	=	SYM
ejpam-6199	85	37	v	v	NOUN
ejpam-6199	85	38	|	|	NOUN
ejpam-6199	85	39	n	n	CCONJ
ejpam-6199	85	40	;	;	PUNCT
ejpam-6199	85	41	(	(	PUNCT
ejpam-6199	85	42	2	2	X
ejpam-6199	85	43	)	)	PUNCT
ejpam-6199	85	44	(	(	PUNCT
ejpam-6199	85	45	n	n	CCONJ
ejpam-6199	85	46	|	|	ADV
ejpam-6199	85	47	n	n	CCONJ
ejpam-6199	85	48	)	)	PUNCT
ejpam-6199	86	1	|	|	ADV
ejpam-6199	86	2	(	(	PUNCT
ejpam-6199	86	3	n	n	CCONJ
ejpam-6199	86	4	|	|	ADV
ejpam-6199	86	5	v	v	NOUN
ejpam-6199	86	6	)	)	PUNCT
ejpam-6199	86	7	=	=	SYM
ejpam-6199	86	8	n	n	CCONJ
ejpam-6199	86	9	;	;	PUNCT
ejpam-6199	86	10	(	(	PUNCT
ejpam-6199	86	11	3	3	X
ejpam-6199	86	12	)	)	PUNCT
ejpam-6199	86	13	n	n	NOUN
ejpam-6199	87	1	|	|	ADV
ejpam-6199	87	2	(	(	PUNCT
ejpam-6199	87	3	(	(	PUNCT
ejpam-6199	87	4	v	v	INTJ
ejpam-6199	87	5	|	|	ADV
ejpam-6199	87	6	w	w	NOUN
ejpam-6199	87	7	)	)	PUNCT
ejpam-6199	87	8	|	|	ADV
ejpam-6199	87	9	(	(	PUNCT
ejpam-6199	87	10	v	v	NOUN
ejpam-6199	87	11	|	|	ADV
ejpam-6199	87	12	w	w	NOUN
ejpam-6199	87	13	)	)	PUNCT
ejpam-6199	87	14	)	)	PUNCT
ejpam-6199	88	1	=	=	SYM
ejpam-6199	88	2	(	(	PUNCT
ejpam-6199	88	3	(	(	PUNCT
ejpam-6199	88	4	n	n	CCONJ
ejpam-6199	88	5	|	|	ADV
ejpam-6199	88	6	v	v	NOUN
ejpam-6199	88	7	)	)	PUNCT
ejpam-6199	89	1	|	|	ADV
ejpam-6199	89	2	(	(	PUNCT
ejpam-6199	89	3	n	n	CCONJ
ejpam-6199	89	4	|	|	ADV
ejpam-6199	89	5	v	v	NOUN
ejpam-6199	89	6	)	)	PUNCT
ejpam-6199	89	7	)	)	PUNCT
ejpam-6199	90	1	|	|	ADV
ejpam-6199	90	2	w	w	NOUN
ejpam-6199	90	3	;	;	PUNCT
ejpam-6199	90	4	(	(	PUNCT
ejpam-6199	90	5	4	4	NUM
ejpam-6199	90	6	)	)	PUNCT
ejpam-6199	90	7	(	(	PUNCT
ejpam-6199	90	8	n	n	CCONJ
ejpam-6199	90	9	|	|	ADV
ejpam-6199	90	10	(	(	PUNCT
ejpam-6199	90	11	(	(	PUNCT
ejpam-6199	90	12	n	n	CCONJ
ejpam-6199	90	13	|	|	ADV
ejpam-6199	90	14	n	n	CCONJ
ejpam-6199	90	15	)	)	PUNCT
ejpam-6199	91	1	|	|	ADV
ejpam-6199	91	2	(	(	PUNCT
ejpam-6199	91	3	v	v	NOUN
ejpam-6199	91	4	|	|	ADV
ejpam-6199	91	5	v	v	NOUN
ejpam-6199	91	6	)	)	PUNCT
ejpam-6199	91	7	)	)	PUNCT
ejpam-6199	91	8	)	)	PUNCT
ejpam-6199	92	1	|	|	ADV
ejpam-6199	92	2	(	(	PUNCT
ejpam-6199	92	3	n	n	CCONJ
ejpam-6199	92	4	|	|	ADV
ejpam-6199	92	5	(	(	PUNCT
ejpam-6199	92	6	(	(	PUNCT
ejpam-6199	92	7	n	n	CCONJ
ejpam-6199	92	8	|	|	ADV
ejpam-6199	92	9	n	n	CCONJ
ejpam-6199	92	10	)	)	PUNCT
ejpam-6199	92	11	|	|	ADV
ejpam-6199	92	12	(	(	PUNCT
ejpam-6199	92	13	v	v	NOUN
ejpam-6199	92	14	|	|	ADV
ejpam-6199	92	15	v	v	NOUN
ejpam-6199	92	16	)	)	PUNCT
ejpam-6199	92	17	)	)	PUNCT
ejpam-6199	92	18	)	)	PUNCT
ejpam-6199	93	1	=	=	PUNCT
ejpam-6199	93	2	n.	n.	NOUN
ejpam-6199	93	3	definition	definition	NOUN
ejpam-6199	93	4	2	2	NUM
ejpam-6199	93	5	(	(	PUNCT
ejpam-6199	93	6	[	[	X
ejpam-6199	93	7	13	13	NUM
ejpam-6199	93	8	]	]	NUM
ejpam-6199	93	9	)	)	PUNCT
ejpam-6199	93	10	.	.	PUNCT
ejpam-6199	94	1	a	a	DET
ejpam-6199	94	2	sheffer	sheffer	NOUN
ejpam-6199	94	3	stroke	stroke	NOUN
ejpam-6199	94	4	hilbert	hilbert	PROPN
ejpam-6199	94	5	algebra	algebra	PROPN
ejpam-6199	94	6	with	with	ADP
ejpam-6199	94	7	a	a	DET
ejpam-6199	94	8	sheffer	sheffer	NOUN
ejpam-6199	94	9	stroke	stroke	NOUN
ejpam-6199	94	10	“	"	PUNCT
ejpam-6199	94	11	|	|	ADV
ejpam-6199	94	12	”	"	PUNCT
ejpam-6199	94	13	is	be	AUX
ejpam-6199	94	14	a	a	DET
ejpam-6199	94	15	groupoid	groupoid	NOUN
ejpam-6199	94	16	ϑ	ϑ	NOUN
ejpam-6199	94	17	◦	◦	NOUN
ejpam-6199	94	18	:	:	PUNCT
ejpam-6199	94	19	=	=	SYM
ejpam-6199	94	20	(	(	PUNCT
ejpam-6199	94	21	ϑ	ϑ	X
ejpam-6199	94	22	,	,	PUNCT
ejpam-6199	94	23	|	|	NOUN
ejpam-6199	94	24	)	)	PUNCT
ejpam-6199	94	25	that	that	PRON
ejpam-6199	94	26	satisfies	satisfy	VERB
ejpam-6199	94	27	the	the	DET
ejpam-6199	94	28	axioms	axiom	NOUN
ejpam-6199	94	29	,	,	PUNCT
ejpam-6199	94	30	∀n	∀n	NUM
ejpam-6199	94	31	,	,	PUNCT
ejpam-6199	94	32	v	v	NOUN
ejpam-6199	94	33	,	,	PUNCT
ejpam-6199	94	34	w	w	PROPN
ejpam-6199	94	35	∈	∈	PROPN
ejpam-6199	95	1	ϑ	ϑ	X
ejpam-6199	96	1	:	:	PUNCT
ejpam-6199	97	1	(	(	PUNCT
ejpam-6199	97	2	1	1	X
ejpam-6199	97	3	)	)	PUNCT
ejpam-6199	97	4	(	(	PUNCT
ejpam-6199	97	5	n	n	CCONJ
ejpam-6199	97	6	|	|	ADV
ejpam-6199	97	7	(	(	PUNCT
ejpam-6199	97	8	(	(	PUNCT
ejpam-6199	97	9	x	x	X
ejpam-6199	97	10	)	)	PUNCT
ejpam-6199	98	1	|	|	ADV
ejpam-6199	98	2	(	(	PUNCT
ejpam-6199	98	3	x	x	NOUN
ejpam-6199	98	4	)	)	PUNCT
ejpam-6199	98	5	)	)	PUNCT
ejpam-6199	98	6	)	)	PUNCT
ejpam-6199	99	1	|	|	ADV
ejpam-6199	99	2	(	(	PUNCT
ejpam-6199	99	3	(	(	PUNCT
ejpam-6199	99	4	(	(	PUNCT
ejpam-6199	99	5	y	y	NOUN
ejpam-6199	99	6	)	)	PUNCT
ejpam-6199	99	7	|	|	ADV
ejpam-6199	99	8	(	(	PUNCT
ejpam-6199	99	9	(	(	PUNCT
ejpam-6199	99	10	z	z	NOUN
ejpam-6199	99	11	)	)	PUNCT
ejpam-6199	99	12	|	|	ADV
ejpam-6199	99	13	(	(	PUNCT
ejpam-6199	99	14	z	z	NOUN
ejpam-6199	99	15	)	)	PUNCT
ejpam-6199	99	16	)	)	PUNCT
ejpam-6199	99	17	)	)	PUNCT
ejpam-6199	100	1	|	|	ADV
ejpam-6199	100	2	(	(	PUNCT
ejpam-6199	100	3	(	(	PUNCT
ejpam-6199	100	4	y	y	PROPN
ejpam-6199	100	5	)	)	PUNCT
ejpam-6199	100	6	|	|	ADV
ejpam-6199	100	7	(	(	PUNCT
ejpam-6199	100	8	(	(	PUNCT
ejpam-6199	100	9	z	z	NOUN
ejpam-6199	100	10	)	)	PUNCT
ejpam-6199	100	11	|	|	ADV
ejpam-6199	100	12	(	(	PUNCT
ejpam-6199	100	13	z	z	NOUN
ejpam-6199	100	14	)	)	PUNCT
ejpam-6199	100	15	)	)	PUNCT
ejpam-6199	100	16	)	)	PUNCT
ejpam-6199	100	17	)	)	PUNCT
ejpam-6199	101	1	=	=	SYM
ejpam-6199	101	2	n	n	CCONJ
ejpam-6199	102	1	|	|	ADV
ejpam-6199	102	2	(	(	PUNCT
ejpam-6199	102	3	n	n	CCONJ
ejpam-6199	102	4	|	|	ADV
ejpam-6199	102	5	n	n	CCONJ
ejpam-6199	102	6	)	)	PUNCT
ejpam-6199	102	7	,	,	PUNCT
ejpam-6199	102	8	where	where	SCONJ
ejpam-6199	102	9	x	x	X
ejpam-6199	102	10	:	:	PUNCT
ejpam-6199	102	11	=	=	SYM
ejpam-6199	102	12	v	v	NUM
ejpam-6199	102	13	|	|	INTJ
ejpam-6199	102	14	(	(	PUNCT
ejpam-6199	102	15	w	w	PROPN
ejpam-6199	102	16	|	|	ADV
ejpam-6199	102	17	w	w	NOUN
ejpam-6199	102	18	)	)	PUNCT
ejpam-6199	102	19	,	,	PUNCT
ejpam-6199	102	20	y	y	PROPN
ejpam-6199	102	21	:	:	PUNCT
ejpam-6199	102	22	=	=	SYM
ejpam-6199	102	23	n	n	CCONJ
ejpam-6199	103	1	|	|	ADV
ejpam-6199	103	2	(	(	PUNCT
ejpam-6199	103	3	v	v	NOUN
ejpam-6199	103	4	|	|	NOUN
ejpam-6199	103	5	v	v	NOUN
ejpam-6199	103	6	)	)	PUNCT
ejpam-6199	103	7	and	and	CCONJ
ejpam-6199	103	8	z	z	NOUN
ejpam-6199	103	9	:	:	PUNCT
ejpam-6199	103	10	=	=	SYM
ejpam-6199	103	11	n	n	CCONJ
ejpam-6199	104	1	|	|	ADV
ejpam-6199	104	2	(	(	PUNCT
ejpam-6199	104	3	w	w	PROPN
ejpam-6199	104	4	|	|	ADV
ejpam-6199	104	5	w	w	NOUN
ejpam-6199	104	6	)	)	PUNCT
ejpam-6199	104	7	;	;	PUNCT
ejpam-6199	104	8	(	(	PUNCT
ejpam-6199	104	9	2	2	X
ejpam-6199	104	10	)	)	PUNCT
ejpam-6199	104	11	n	n	NOUN
ejpam-6199	104	12	|	|	ADV
ejpam-6199	104	13	(	(	PUNCT
ejpam-6199	104	14	v	v	NOUN
ejpam-6199	104	15	|	|	NOUN
ejpam-6199	104	16	v	v	NOUN
ejpam-6199	104	17	)	)	PUNCT
ejpam-6199	104	18	=	=	SYM
ejpam-6199	105	1	v	v	ADP
ejpam-6199	105	2	|	|	NOUN
ejpam-6199	105	3	(	(	PUNCT
ejpam-6199	105	4	n	n	CCONJ
ejpam-6199	105	5	|	|	ADV
ejpam-6199	105	6	n	n	CCONJ
ejpam-6199	105	7	)	)	PUNCT
ejpam-6199	105	8	=	=	SYM
ejpam-6199	106	1	n	n	CCONJ
ejpam-6199	107	1	|	|	ADV
ejpam-6199	107	2	(	(	PUNCT
ejpam-6199	107	3	n	n	CCONJ
ejpam-6199	107	4	|	|	ADV
ejpam-6199	107	5	n	n	CCONJ
ejpam-6199	107	6	)	)	PUNCT
ejpam-6199	107	7	⇒	⇒	NOUN
ejpam-6199	107	8	n	n	NOUN
ejpam-6199	107	9	=	=	PUNCT
ejpam-6199	107	10	v.	v.	PROPN
ejpam-6199	107	11	for	for	ADP
ejpam-6199	107	12	a	a	DET
ejpam-6199	107	13	sheffer	sheffer	NOUN
ejpam-6199	107	14	stroke	stroke	NOUN
ejpam-6199	107	15	hilbert	hilbert	PROPN
ejpam-6199	107	16	algebra	algebra	PROPN
ejpam-6199	107	17	ϑ	ϑ	ADP
ejpam-6199	107	18	◦	◦	NOUN
ejpam-6199	107	19	:	:	PUNCT
ejpam-6199	107	20	=	=	SYM
ejpam-6199	107	21	(	(	PUNCT
ejpam-6199	107	22	ϑ	ϑ	X
ejpam-6199	107	23	,	,	PUNCT
ejpam-6199	107	24	|	|	NOUN
ejpam-6199	107	25	)	)	PUNCT
ejpam-6199	107	26	,	,	PUNCT
ejpam-6199	107	27	see[13	see[13	PROPN
ejpam-6199	107	28	]	]	X
ejpam-6199	107	29	a	a	DET
ejpam-6199	107	30	relation	relation	NOUN
ejpam-6199	107	31	“	"	PUNCT
ejpam-6199	107	32	≤	≤	NUM
ejpam-6199	107	33	”	"	PUNCT
ejpam-6199	107	34	,	,	PUNCT
ejpam-6199	107	35	which	which	PRON
ejpam-6199	107	36	is	be	AUX
ejpam-6199	107	37	a	a	DET
ejpam-6199	107	38	partial	partial	ADJ
ejpam-6199	107	39	order	order	NOUN
ejpam-6199	107	40	on	on	ADP
ejpam-6199	107	41	ϑ	ϑ	NOUN
ejpam-6199	107	42	,	,	PUNCT
ejpam-6199	107	43	is	be	AUX
ejpam-6199	107	44	defined	define	VERB
ejpam-6199	107	45	as	as	ADP
ejpam-6199	107	46	(	(	PUNCT
ejpam-6199	107	47	a)(n	a)(n	PROPN
ejpam-6199	107	48	≤	≤	PROPN
ejpam-6199	107	49	v	v	ADP
ejpam-6199	107	50	⇔	⇔	PROPN
ejpam-6199	107	51	n	n	CCONJ
ejpam-6199	108	1	|	|	ADV
ejpam-6199	108	2	(	(	PUNCT
ejpam-6199	108	3	v	v	NOUN
ejpam-6199	108	4	|	|	NOUN
ejpam-6199	108	5	v	v	NOUN
ejpam-6199	108	6	)	)	PUNCT
ejpam-6199	108	7	=	=	SYM
ejpam-6199	108	8	1	1	NUM
ejpam-6199	108	9	,	,	PUNCT
ejpam-6199	108	10	∀n	∀n	NUM
ejpam-6199	108	11	,	,	PUNCT
ejpam-6199	108	12	v	v	NOUN
ejpam-6199	108	13	∈	∈	PROPN
ejpam-6199	108	14	ϑ	ϑ	NOUN
ejpam-6199	108	15	)	)	PUNCT
ejpam-6199	108	16	.	.	PUNCT
ejpam-6199	109	1	proposition	proposition	NOUN
ejpam-6199	109	2	1	1	NUM
ejpam-6199	109	3	(	(	PUNCT
ejpam-6199	109	4	[	[	X
ejpam-6199	109	5	13	13	NUM
ejpam-6199	109	6	]	]	NUM
ejpam-6199	109	7	)	)	PUNCT
ejpam-6199	109	8	.	.	PUNCT
ejpam-6199	110	1	if	if	SCONJ
ejpam-6199	110	2	ϑ	ϑ	VERB
ejpam-6199	110	3	◦	◦	NOUN
ejpam-6199	110	4	:	:	PUNCT
ejpam-6199	110	5	=	=	SYM
ejpam-6199	110	6	(	(	PUNCT
ejpam-6199	110	7	ϑ	ϑ	X
ejpam-6199	110	8	,	,	PUNCT
ejpam-6199	110	9	|	|	NOUN
ejpam-6199	110	10	)	)	PUNCT
ejpam-6199	110	11	is	be	AUX
ejpam-6199	110	12	a	a	DET
ejpam-6199	110	13	sheffer	sheffer	NOUN
ejpam-6199	110	14	stroke	stroke	NOUN
ejpam-6199	110	15	hilbert	hilbert	PROPN
ejpam-6199	110	16	algebra	algebra	PROPN
ejpam-6199	110	17	,	,	PUNCT
ejpam-6199	110	18	then	then	ADV
ejpam-6199	110	19	ϑ	ϑ	X
ejpam-6199	110	20	satisfies	satisfie	NOUN
ejpam-6199	110	21	:	:	PUNCT
ejpam-6199	110	22	∀n	∀n	NUM
ejpam-6199	110	23	,	,	PUNCT
ejpam-6199	110	24	v	v	NOUN
ejpam-6199	110	25	,	,	PUNCT
ejpam-6199	110	26	w	w	PROPN
ejpam-6199	110	27	∈	∈	PROPN
ejpam-6199	110	28	ϑ	ϑ	X
ejpam-6199	110	29	,	,	PUNCT
ejpam-6199	110	30	(	(	PUNCT
ejpam-6199	110	31	1	1	NUM
ejpam-6199	110	32	)	)	PUNCT
ejpam-6199	110	33	n	n	NOUN
ejpam-6199	111	1	|	|	ADV
ejpam-6199	111	2	(	(	PUNCT
ejpam-6199	111	3	n	n	CCONJ
ejpam-6199	111	4	|	|	ADV
ejpam-6199	111	5	n	n	CCONJ
ejpam-6199	111	6	)	)	PUNCT
ejpam-6199	111	7	=	=	SYM
ejpam-6199	111	8	1	1	NUM
ejpam-6199	111	9	;	;	PUNCT
ejpam-6199	111	10	(	(	PUNCT
ejpam-6199	111	11	2	2	X
ejpam-6199	111	12	)	)	PUNCT
ejpam-6199	111	13	n	n	NOUN
ejpam-6199	111	14	|	|	ADV
ejpam-6199	111	15	(	(	PUNCT
ejpam-6199	111	16	1	1	NUM
ejpam-6199	111	17	|	|	ADV
ejpam-6199	111	18	1	1	NUM
ejpam-6199	111	19	)	)	PUNCT
ejpam-6199	111	20	=	=	SYM
ejpam-6199	111	21	1	1	NUM
ejpam-6199	111	22	;	;	PUNCT
ejpam-6199	111	23	(	(	PUNCT
ejpam-6199	111	24	3	3	X
ejpam-6199	111	25	)	)	PUNCT
ejpam-6199	111	26	1	1	NUM
ejpam-6199	112	1	|	|	ADV
ejpam-6199	112	2	(	(	PUNCT
ejpam-6199	112	3	n	n	CCONJ
ejpam-6199	112	4	|	|	ADV
ejpam-6199	112	5	n	n	CCONJ
ejpam-6199	112	6	)	)	PUNCT
ejpam-6199	112	7	=	=	SYM
ejpam-6199	112	8	n	n	CCONJ
ejpam-6199	112	9	;	;	PUNCT
ejpam-6199	112	10	(	(	PUNCT
ejpam-6199	112	11	4	4	X
ejpam-6199	112	12	)	)	PUNCT
ejpam-6199	112	13	n	n	PRON
ejpam-6199	112	14	≤	≤	NOUN
ejpam-6199	112	15	v	v	ADP
ejpam-6199	113	1	|	|	NOUN
ejpam-6199	114	1	(	(	PUNCT
ejpam-6199	114	2	n	n	NOUN
ejpam-6199	114	3	|	|	ADV
ejpam-6199	114	4	n	n	CCONJ
ejpam-6199	114	5	)	)	PUNCT
ejpam-6199	114	6	;	;	PUNCT
ejpam-6199	114	7	(	(	PUNCT
ejpam-6199	114	8	5	5	X
ejpam-6199	114	9	)	)	PUNCT
ejpam-6199	114	10	(	(	PUNCT
ejpam-6199	114	11	n	n	CCONJ
ejpam-6199	114	12	|	|	ADV
ejpam-6199	114	13	(	(	PUNCT
ejpam-6199	114	14	v	v	NOUN
ejpam-6199	114	15	|	|	ADV
ejpam-6199	114	16	v	v	NOUN
ejpam-6199	114	17	)	)	PUNCT
ejpam-6199	114	18	)	)	PUNCT
ejpam-6199	115	1	|	|	ADV
ejpam-6199	115	2	(	(	PUNCT
ejpam-6199	115	3	v	v	NOUN
ejpam-6199	115	4	|	|	NOUN
ejpam-6199	115	5	v	v	NOUN
ejpam-6199	115	6	)	)	PUNCT
ejpam-6199	115	7	=	=	SYM
ejpam-6199	115	8	(	(	PUNCT
ejpam-6199	115	9	v	v	NUM
ejpam-6199	115	10	|	|	ADV
ejpam-6199	115	11	(	(	PUNCT
ejpam-6199	115	12	n	n	CCONJ
ejpam-6199	115	13	|	|	ADV
ejpam-6199	115	14	n	n	CCONJ
ejpam-6199	115	15	)	)	PUNCT
ejpam-6199	115	16	)	)	PUNCT
ejpam-6199	116	1	|	|	ADV
ejpam-6199	116	2	(	(	PUNCT
ejpam-6199	116	3	n	n	CCONJ
ejpam-6199	116	4	|	|	ADV
ejpam-6199	116	5	n	n	CCONJ
ejpam-6199	116	6	)	)	PUNCT
ejpam-6199	116	7	;	;	PUNCT
ejpam-6199	116	8	a.	a.	PROPN
ejpam-6199	116	9	al	al	PROPN
ejpam-6199	116	10	-	-	PROPN
ejpam-6199	116	11	masarwah	masarwah	PROPN
ejpam-6199	116	12	et	et	PROPN
ejpam-6199	116	13	al	al	PROPN
ejpam-6199	116	14	.	.	PUNCT
ejpam-6199	116	15	/	/	SYM
ejpam-6199	116	16	eur	eur	PROPN
ejpam-6199	116	17	.	.	PUNCT
ejpam-6199	117	1	j.	j.	PROPN
ejpam-6199	117	2	pure	pure	PROPN
ejpam-6199	117	3	appl	appl	PROPN
ejpam-6199	117	4	.	.	PROPN
ejpam-6199	117	5	math	math	PROPN
ejpam-6199	117	6	,	,	PUNCT
ejpam-6199	117	7	18	18	NUM
ejpam-6199	117	8	(	(	PUNCT
ejpam-6199	117	9	3	3	NUM
ejpam-6199	117	10	)	)	PUNCT
ejpam-6199	117	11	(	(	PUNCT
ejpam-6199	117	12	2025	2025	NUM
ejpam-6199	117	13	)	)	PUNCT
ejpam-6199	117	14	,	,	PUNCT
ejpam-6199	117	15	6199	6199	NUM
ejpam-6199	117	16	5	5	NUM
ejpam-6199	117	17	of	of	ADP
ejpam-6199	117	18	17	17	NUM
ejpam-6199	117	19	(	(	PUNCT
ejpam-6199	117	20	6	6	NUM
ejpam-6199	117	21	)	)	PUNCT
ejpam-6199	117	22	(	(	PUNCT
ejpam-6199	117	23	(	(	PUNCT
ejpam-6199	117	24	n	n	CCONJ
ejpam-6199	117	25	|	|	ADV
ejpam-6199	117	26	(	(	PUNCT
ejpam-6199	117	27	v	v	NOUN
ejpam-6199	117	28	|	|	ADV
ejpam-6199	117	29	v	v	NOUN
ejpam-6199	117	30	)	)	PUNCT
ejpam-6199	117	31	)	)	PUNCT
ejpam-6199	118	1	|	|	ADV
ejpam-6199	118	2	(	(	PUNCT
ejpam-6199	118	3	v	v	NOUN
ejpam-6199	118	4	|	|	ADV
ejpam-6199	118	5	v	v	NOUN
ejpam-6199	118	6	)	)	PUNCT
ejpam-6199	118	7	)	)	PUNCT
ejpam-6199	119	1	|	|	ADV
ejpam-6199	119	2	(	(	PUNCT
ejpam-6199	119	3	v	v	NOUN
ejpam-6199	119	4	|	|	NOUN
ejpam-6199	119	5	v	v	NOUN
ejpam-6199	119	6	)	)	PUNCT
ejpam-6199	119	7	=	=	SYM
ejpam-6199	119	8	n	n	CCONJ
ejpam-6199	119	9	|	|	ADV
ejpam-6199	119	10	(	(	PUNCT
ejpam-6199	119	11	v	v	NOUN
ejpam-6199	119	12	|	|	ADV
ejpam-6199	119	13	v	v	NOUN
ejpam-6199	119	14	)	)	PUNCT
ejpam-6199	119	15	;	;	PUNCT
ejpam-6199	119	16	(	(	PUNCT
ejpam-6199	119	17	7	7	X
ejpam-6199	119	18	)	)	PUNCT
ejpam-6199	119	19	n	n	NOUN
ejpam-6199	119	20	|	|	ADV
ejpam-6199	119	21	(	(	PUNCT
ejpam-6199	119	22	(	(	PUNCT
ejpam-6199	119	23	v	v	X
ejpam-6199	119	24	|	|	ADV
ejpam-6199	119	25	(	(	PUNCT
ejpam-6199	119	26	w	w	PROPN
ejpam-6199	119	27	|	|	ADV
ejpam-6199	119	28	w	w	NOUN
ejpam-6199	119	29	)	)	PUNCT
ejpam-6199	119	30	)	)	PUNCT
ejpam-6199	120	1	|	|	ADV
ejpam-6199	120	2	(	(	PUNCT
ejpam-6199	120	3	v	v	NOUN
ejpam-6199	120	4	|	|	ADV
ejpam-6199	120	5	(	(	PUNCT
ejpam-6199	120	6	w	w	PROPN
ejpam-6199	120	7	|	|	ADV
ejpam-6199	120	8	w	w	NOUN
ejpam-6199	120	9	)	)	PUNCT
ejpam-6199	120	10	)	)	PUNCT
ejpam-6199	120	11	)	)	PUNCT
ejpam-6199	121	1	=	=	PUNCT
ejpam-6199	121	2	v	v	ADP
ejpam-6199	121	3	|	|	INTJ
ejpam-6199	121	4	(	(	PUNCT
ejpam-6199	121	5	(	(	PUNCT
ejpam-6199	121	6	n	n	CCONJ
ejpam-6199	121	7	|	|	ADV
ejpam-6199	121	8	(	(	PUNCT
ejpam-6199	121	9	w	w	PROPN
ejpam-6199	121	10	|	|	ADV
ejpam-6199	121	11	w	w	NOUN
ejpam-6199	121	12	)	)	PUNCT
ejpam-6199	121	13	)	)	PUNCT
ejpam-6199	122	1	|	|	ADV
ejpam-6199	122	2	(	(	PUNCT
ejpam-6199	122	3	n	n	CCONJ
ejpam-6199	122	4	|	|	ADV
ejpam-6199	122	5	(	(	PUNCT
ejpam-6199	122	6	w	w	PROPN
ejpam-6199	122	7	|	|	ADV
ejpam-6199	122	8	w	w	NOUN
ejpam-6199	122	9	)	)	PUNCT
ejpam-6199	122	10	)	)	PUNCT
ejpam-6199	122	11	)	)	PUNCT
ejpam-6199	122	12	.	.	PUNCT
ejpam-6199	123	1	definition	definition	NOUN
ejpam-6199	123	2	3	3	NUM
ejpam-6199	123	3	(	(	PUNCT
ejpam-6199	123	4	[	[	X
ejpam-6199	123	5	25	25	NUM
ejpam-6199	123	6	]	]	PUNCT
ejpam-6199	123	7	)	)	PUNCT
ejpam-6199	123	8	.	.	PUNCT
ejpam-6199	124	1	a	a	DET
ejpam-6199	124	2	subset	subset	NOUN
ejpam-6199	124	3	ψ	ψ	NOUN
ejpam-6199	124	4	of	of	ADP
ejpam-6199	124	5	a	a	DET
ejpam-6199	124	6	sheffer	sheffer	NOUN
ejpam-6199	124	7	stroke	stroke	NOUN
ejpam-6199	124	8	hilbert	hilbert	PROPN
ejpam-6199	124	9	algebra	algebra	PROPN
ejpam-6199	124	10	ϑ	ϑ	ADP
ejpam-6199	124	11	◦	◦	NOUN
ejpam-6199	124	12	:	:	PUNCT
ejpam-6199	124	13	=	=	SYM
ejpam-6199	124	14	(	(	PUNCT
ejpam-6199	124	15	ϑ	ϑ	X
ejpam-6199	124	16	,	,	PUNCT
ejpam-6199	124	17	|	|	NOUN
ejpam-6199	124	18	)	)	PUNCT
ejpam-6199	124	19	is	be	AUX
ejpam-6199	124	20	called	call	VERB
ejpam-6199	124	21	a	a	DET
ejpam-6199	124	22	filter	filter	NOUN
ejpam-6199	124	23	of	of	ADP
ejpam-6199	124	24	ϑ	ϑ	NOUN
ejpam-6199	124	25	if	if	SCONJ
ejpam-6199	124	26	the	the	DET
ejpam-6199	124	27	conditions	condition	NOUN
ejpam-6199	124	28	are	be	AUX
ejpam-6199	124	29	satisfied	satisfied	ADJ
ejpam-6199	124	30	:	:	PUNCT
ejpam-6199	124	31	∀n	∀n	NUM
ejpam-6199	124	32	,	,	PUNCT
ejpam-6199	124	33	v	v	NOUN
ejpam-6199	124	34	,	,	PUNCT
ejpam-6199	124	35	w	w	PROPN
ejpam-6199	124	36	∈	∈	PROPN
ejpam-6199	124	37	ϑ	ϑ	X
ejpam-6199	124	38	(	(	PUNCT
ejpam-6199	124	39	1	1	NUM
ejpam-6199	124	40	)	)	SYM
ejpam-6199	124	41	1	1	NUM
ejpam-6199	124	42	∈	∈	PROPN
ejpam-6199	124	43	ψ	ψ	NOUN
ejpam-6199	124	44	;	;	PUNCT
ejpam-6199	124	45	(	(	PUNCT
ejpam-6199	124	46	2	2	X
ejpam-6199	124	47	)	)	PUNCT
ejpam-6199	124	48	v	v	ADP
ejpam-6199	124	49	∈	∈	NOUN
ejpam-6199	124	50	ψ	ψ	NOUN
ejpam-6199	124	51	⇒	⇒	NOUN
ejpam-6199	125	1	n	n	CCONJ
ejpam-6199	125	2	|	|	ADV
ejpam-6199	125	3	(	(	PUNCT
ejpam-6199	125	4	v	v	NOUN
ejpam-6199	125	5	|	|	ADV
ejpam-6199	125	6	v	v	NOUN
ejpam-6199	125	7	)	)	PUNCT
ejpam-6199	125	8	∈	∈	PROPN
ejpam-6199	125	9	ψ	ψ	NOUN
ejpam-6199	125	10	;	;	PUNCT
ejpam-6199	125	11	(	(	PUNCT
ejpam-6199	125	12	3	3	X
ejpam-6199	125	13	)	)	PUNCT
ejpam-6199	125	14	v	v	NOUN
ejpam-6199	125	15	,	,	PUNCT
ejpam-6199	125	16	w	w	PROPN
ejpam-6199	125	17	∈	∈	PROPN
ejpam-6199	125	18	ψ	ψ	ADP
ejpam-6199	125	19	⇒	⇒	NOUN
ejpam-6199	125	20	(	(	PUNCT
ejpam-6199	125	21	n	n	CCONJ
ejpam-6199	125	22	|	|	ADV
ejpam-6199	125	23	(	(	PUNCT
ejpam-6199	125	24	v	v	NOUN
ejpam-6199	125	25	|	|	ADV
ejpam-6199	125	26	w	w	NOUN
ejpam-6199	125	27	)	)	PUNCT
ejpam-6199	125	28	)	)	PUNCT
ejpam-6199	126	1	|	|	ADV
ejpam-6199	126	2	(	(	PUNCT
ejpam-6199	126	3	v	v	NOUN
ejpam-6199	126	4	|	|	ADV
ejpam-6199	126	5	w	w	NOUN
ejpam-6199	126	6	)	)	PUNCT
ejpam-6199	126	7	∈	∈	PROPN
ejpam-6199	126	8	ψ	ψ	NOUN
ejpam-6199	126	9	.	.	PUNCT
ejpam-6199	126	10	definition	definition	NOUN
ejpam-6199	126	11	4	4	NUM
ejpam-6199	126	12	(	(	PUNCT
ejpam-6199	126	13	[	[	X
ejpam-6199	126	14	13	13	NUM
ejpam-6199	126	15	]	]	NUM
ejpam-6199	126	16	)	)	PUNCT
ejpam-6199	126	17	.	.	PUNCT
ejpam-6199	127	1	a	a	DET
ejpam-6199	127	2	subset	subset	NOUN
ejpam-6199	127	3	ψ	ψ	NOUN
ejpam-6199	127	4	of	of	ADP
ejpam-6199	127	5	a	a	DET
ejpam-6199	127	6	sheffer	sheffer	NOUN
ejpam-6199	127	7	stroke	stroke	NOUN
ejpam-6199	127	8	hilbert	hilbert	PROPN
ejpam-6199	127	9	algebra	algebra	PROPN
ejpam-6199	127	10	ϑ	ϑ	ADP
ejpam-6199	127	11	◦	◦	NOUN
ejpam-6199	127	12	:	:	PUNCT
ejpam-6199	127	13	=	=	SYM
ejpam-6199	127	14	(	(	PUNCT
ejpam-6199	127	15	ϑ	ϑ	X
ejpam-6199	127	16	,	,	PUNCT
ejpam-6199	127	17	|	|	NOUN
ejpam-6199	127	18	)	)	PUNCT
ejpam-6199	127	19	is	be	AUX
ejpam-6199	127	20	called	call	VERB
ejpam-6199	127	21	a	a	DET
ejpam-6199	127	22	deductive	deductive	ADJ
ejpam-6199	127	23	system	system	NOUN
ejpam-6199	127	24	of	of	ADP
ejpam-6199	127	25	ϑ	ϑ	PRON
ejpam-6199	127	26	if	if	SCONJ
ejpam-6199	127	27	the	the	DET
ejpam-6199	127	28	conditions	condition	NOUN
ejpam-6199	127	29	are	be	AUX
ejpam-6199	127	30	satisfied	satisfied	ADJ
ejpam-6199	127	31	:	:	PUNCT
ejpam-6199	127	32	∀n	∀n	NUM
ejpam-6199	127	33	,	,	PUNCT
ejpam-6199	127	34	v	v	ADP
ejpam-6199	127	35	∈	∈	PROPN
ejpam-6199	127	36	ϑ	ϑ	X
ejpam-6199	127	37	(	(	PUNCT
ejpam-6199	127	38	1	1	NUM
ejpam-6199	127	39	)	)	SYM
ejpam-6199	127	40	1	1	NUM
ejpam-6199	127	41	∈	∈	PROPN
ejpam-6199	127	42	ψ	ψ	NOUN
ejpam-6199	127	43	;	;	PUNCT
ejpam-6199	127	44	(	(	PUNCT
ejpam-6199	127	45	2	2	X
ejpam-6199	127	46	)	)	PUNCT
ejpam-6199	127	47	n	n	PRON
ejpam-6199	127	48	∈	∈	PROPN
ejpam-6199	127	49	ψ	ψ	NOUN
ejpam-6199	127	50	,	,	PUNCT
ejpam-6199	127	51	n	n	CCONJ
ejpam-6199	127	52	|	|	ADV
ejpam-6199	127	53	(	(	PUNCT
ejpam-6199	127	54	v	v	NOUN
ejpam-6199	127	55	|	|	ADV
ejpam-6199	127	56	v	v	NOUN
ejpam-6199	127	57	)	)	PUNCT
ejpam-6199	127	58	∈	∈	PROPN
ejpam-6199	127	59	ψ	ψ	ADP
ejpam-6199	127	60	⇒	⇒	NOUN
ejpam-6199	127	61	v	v	ADP
ejpam-6199	127	62	∈	∈	PROPN
ejpam-6199	127	63	ψ	ψ	NOUN
ejpam-6199	127	64	.	.	PUNCT
ejpam-6199	128	1	definition	definition	NOUN
ejpam-6199	128	2	5	5	NUM
ejpam-6199	128	3	(	(	PUNCT
ejpam-6199	128	4	[	[	X
ejpam-6199	128	5	15	15	NUM
ejpam-6199	128	6	]	]	NUM
ejpam-6199	128	7	)	)	PUNCT
ejpam-6199	128	8	.	.	PUNCT
ejpam-6199	129	1	let	let	VERB
ejpam-6199	129	2	ϑ	ϑ	X
ejpam-6199	129	3	̸=	̸=	PROPN
ejpam-6199	129	4	ϕ	ϕ	NOUN
ejpam-6199	129	5	be	be	AUX
ejpam-6199	129	6	a	a	DET
ejpam-6199	129	7	set	set	NOUN
ejpam-6199	129	8	.	.	PUNCT
ejpam-6199	130	1	an	an	DET
ejpam-6199	130	2	interval	interval	NOUN
ejpam-6199	130	3	valued	value	VERB
ejpam-6199	130	4	fuzzy	fuzzy	ADJ
ejpam-6199	130	5	set	set	VERB
ejpam-6199	130	6	on	on	ADP
ejpam-6199	130	7	ϑ	ϑ	PROPN
ejpam-6199	130	8	is	be	AUX
ejpam-6199	130	9	an	an	DET
ejpam-6199	130	10	object	object	NOUN
ejpam-6199	130	11	of	of	ADP
ejpam-6199	130	12	the	the	DET
ejpam-6199	130	13	following	follow	VERB
ejpam-6199	130	14	form	form	NOUN
ejpam-6199	130	15	:	:	PUNCT
ejpam-6199	130	16	υ̃π	υ̃π	PROPN
ejpam-6199	131	1	=	=	SYM
ejpam-6199	131	2	{	{	PUNCT
ejpam-6199	131	3	(	(	PUNCT
ejpam-6199	131	4	n	n	CCONJ
ejpam-6199	131	5	,	,	PUNCT
ejpam-6199	131	6	∓	∓	PROPN
ejpam-6199	131	7	υπ	υπ	PROPN
ejpam-6199	131	8	(	(	PUNCT
ejpam-6199	131	9	n	n	CCONJ
ejpam-6199	131	10	)	)	PUNCT
ejpam-6199	131	11	)	)	PUNCT
ejpam-6199	131	12	:	:	PUNCT
ejpam-6199	132	1	n	n	X
ejpam-6199	132	2	∈	∈	PROPN
ejpam-6199	132	3	ϑ	ϑ	NOUN
ejpam-6199	132	4	}	}	PUNCT
ejpam-6199	132	5	=	=	SYM
ejpam-6199	132	6	{	{	PUNCT
ejpam-6199	132	7	(	(	PUNCT
ejpam-6199	132	8	n	n	X
ejpam-6199	132	9	,	,	PUNCT
ejpam-6199	132	10	[	[	X
ejpam-6199	132	11	υ−	υ−	PROPN
ejpam-6199	132	12	π(n),υ+	π(n),υ+	NOUN
ejpam-6199	132	13	π(n	π(n	PROPN
ejpam-6199	132	14	)	)	PUNCT
ejpam-6199	132	15	]	]	PUNCT
ejpam-6199	132	16	)	)	PUNCT
ejpam-6199	132	17	:	:	PUNCT
ejpam-6199	133	1	n	n	X
ejpam-6199	133	2	∈	∈	PROPN
ejpam-6199	133	3	ϑ	ϑ	NOUN
ejpam-6199	133	4	}	}	PUNCT
ejpam-6199	133	5	,	,	PUNCT
ejpam-6199	133	6	where	where	SCONJ
ejpam-6199	133	7	∓	∓	PROPN
ejpam-6199	133	8	υπ	υπ	PROPN
ejpam-6199	133	9	:	:	PUNCT
ejpam-6199	133	10	ϑ	ϑ	X
ejpam-6199	133	11	→	→	SYM
ejpam-6199	133	12	i[0	i[0	PROPN
ejpam-6199	133	13	,	,	PUNCT
ejpam-6199	133	14	1	1	NUM
ejpam-6199	133	15	]	]	PUNCT
ejpam-6199	133	16	is	be	AUX
ejpam-6199	133	17	a	a	DET
ejpam-6199	133	18	function	function	NOUN
ejpam-6199	133	19	and	and	CCONJ
ejpam-6199	133	20	i[0	i[0	PROPN
ejpam-6199	133	21	,	,	PUNCT
ejpam-6199	133	22	1	1	NUM
ejpam-6199	133	23	]	]	PUNCT
ejpam-6199	133	24	denotes	denote	VERB
ejpam-6199	133	25	the	the	DET
ejpam-6199	133	26	set	set	NOUN
ejpam-6199	133	27	containing	contain	VERB
ejpam-6199	133	28	every	every	DET
ejpam-6199	133	29	closed	closed	ADJ
ejpam-6199	133	30	subinterval	subinterval	NOUN
ejpam-6199	133	31	of	of	ADP
ejpam-6199	133	32	[	[	X
ejpam-6199	133	33	0	0	NUM
ejpam-6199	133	34	,	,	PUNCT
ejpam-6199	133	35	1	1	NUM
ejpam-6199	133	36	]	]	PUNCT
ejpam-6199	133	37	.	.	PUNCT
ejpam-6199	134	1	the	the	DET
ejpam-6199	134	2	members	member	NOUN
ejpam-6199	134	3	of	of	ADP
ejpam-6199	134	4	i[0	i[0	PROPN
ejpam-6199	134	5	,	,	PUNCT
ejpam-6199	134	6	1	1	NUM
ejpam-6199	134	7	]	]	PUNCT
ejpam-6199	134	8	are	be	AUX
ejpam-6199	134	9	called	call	VERB
ejpam-6199	134	10	interval	interval	NOUN
ejpam-6199	134	11	numbers	number	NOUN
ejpam-6199	134	12	.	.	PUNCT
ejpam-6199	135	1	if	if	SCONJ
ejpam-6199	135	2	we	we	PRON
ejpam-6199	135	3	take	take	VERB
ejpam-6199	135	4	an	an	DET
ejpam-6199	135	5	interval	interval	NOUN
ejpam-6199	135	6	number	number	NOUN
ejpam-6199	135	7	υ̃	υ̃	PROPN
ejpam-6199	135	8	=	=	PROPN
ejpam-6199	136	1	[	[	X
ejpam-6199	136	2	υ−	υ−	PROPN
ejpam-6199	136	3	,	,	PUNCT
ejpam-6199	136	4	υ+	υ+	X
ejpam-6199	136	5	]	]	X
ejpam-6199	136	6	∈	∈	PROPN
ejpam-6199	136	7	i[0	i[0	PROPN
ejpam-6199	136	8	,	,	PUNCT
ejpam-6199	136	9	1	1	NUM
ejpam-6199	136	10	]	]	PUNCT
ejpam-6199	136	11	,	,	PUNCT
ejpam-6199	136	12	then	then	ADV
ejpam-6199	136	13	0	0	NUM
ejpam-6199	136	14	≤	≤	NUM
ejpam-6199	136	15	υ−	υ−	PROPN
ejpam-6199	136	16	≤	≤	NUM
ejpam-6199	136	17	υ+	υ+	X
ejpam-6199	136	18	≤	≤	NUM
ejpam-6199	136	19	1	1	NUM
ejpam-6199	136	20	.	.	PUNCT
ejpam-6199	137	1	for	for	ADP
ejpam-6199	137	2	each	each	DET
ejpam-6199	137	3	two	two	NUM
ejpam-6199	137	4	interval	interval	NOUN
ejpam-6199	137	5	numbers	number	NOUN
ejpam-6199	137	6	υ̃	υ̃	PROPN
ejpam-6199	137	7	=	=	PROPN
ejpam-6199	138	1	[	[	X
ejpam-6199	138	2	υ−	υ−	PROPN
ejpam-6199	138	3	,	,	PUNCT
ejpam-6199	138	4	υ+	υ+	X
ejpam-6199	138	5	]	]	X
ejpam-6199	138	6	and	and	CCONJ
ejpam-6199	138	7	σ̃	σ̃	PROPN
ejpam-6199	138	8	=	=	PUNCT
ejpam-6199	139	1	[	[	X
ejpam-6199	139	2	σ−	σ−	NOUN
ejpam-6199	139	3	,	,	PUNCT
ejpam-6199	139	4	σ+	σ+	X
ejpam-6199	139	5	]	]	X
ejpam-6199	139	6	in	in	ADP
ejpam-6199	139	7	i[0	i[0	PROPN
ejpam-6199	139	8	,	,	PUNCT
ejpam-6199	139	9	1	1	NUM
ejpam-6199	139	10	]	]	PUNCT
ejpam-6199	139	11	,	,	PUNCT
ejpam-6199	139	12	we	we	PRON
ejpam-6199	139	13	define	define	VERB
ejpam-6199	139	14	(	(	PUNCT
ejpam-6199	139	15	1	1	X
ejpam-6199	139	16	)	)	PUNCT
ejpam-6199	139	17	υ̃	υ̃	PROPN
ejpam-6199	139	18	⪯	⪯	NOUN
ejpam-6199	139	19	σ̃	σ̃	NOUN
ejpam-6199	139	20	(	(	PUNCT
ejpam-6199	139	21	or	or	CCONJ
ejpam-6199	139	22	σ̃	σ̃	PROPN
ejpam-6199	139	23	⪰	⪰	NOUN
ejpam-6199	139	24	υ̃	υ̃	PROPN
ejpam-6199	139	25	)	)	PUNCT
ejpam-6199	139	26	⇔	⇔	PROPN
ejpam-6199	139	27	υ−	υ−	PROPN
ejpam-6199	139	28	≤	≤	PROPN
ejpam-6199	139	29	σ−	σ−	PROPN
ejpam-6199	139	30	,	,	PUNCT
ejpam-6199	139	31	υ+	υ+	X
ejpam-6199	139	32	≤	≤	NOUN
ejpam-6199	139	33	σ+	σ+	X
ejpam-6199	139	34	;	;	PUNCT
ejpam-6199	139	35	(	(	PUNCT
ejpam-6199	139	36	2	2	X
ejpam-6199	139	37	)	)	PUNCT
ejpam-6199	139	38	υ̃	υ̃	PROPN
ejpam-6199	139	39	=	=	SYM
ejpam-6199	140	1	σ̃	σ̃	PROPN
ejpam-6199	140	2	⇔	⇔	PROPN
ejpam-6199	140	3	υ̃	υ̃	PROPN
ejpam-6199	140	4	⪯	⪯	NOUN
ejpam-6199	140	5	σ̃	σ̃	PROPN
ejpam-6199	140	6	and	and	CCONJ
ejpam-6199	140	7	σ̃	σ̃	PROPN
ejpam-6199	140	8	⪯	⪯	NOUN
ejpam-6199	140	9	υ̃	υ̃	PROPN
ejpam-6199	140	10	;	;	PUNCT
ejpam-6199	140	11	(	(	PUNCT
ejpam-6199	140	12	3	3	X
ejpam-6199	140	13	)	)	PUNCT
ejpam-6199	140	14	m̃in{υ̃	m̃in{υ̃	PROPN
ejpam-6199	140	15	,	,	PUNCT
ejpam-6199	140	16	σ̃	σ̃	NOUN
ejpam-6199	140	17	}	}	PUNCT
ejpam-6199	140	18	=	=	PUNCT
ejpam-6199	141	1	[	[	X
ejpam-6199	141	2	min{υ−	min{υ−	PROPN
ejpam-6199	141	3	,	,	PUNCT
ejpam-6199	141	4	σ−},min{υ+	σ−},min{υ+	NOUN
ejpam-6199	141	5	,	,	PUNCT
ejpam-6199	141	6	σ+	σ+	PROPN
ejpam-6199	141	7	}	}	PUNCT
ejpam-6199	141	8	]	]	PUNCT
ejpam-6199	141	9	.	.	PUNCT
ejpam-6199	142	1	definition	definition	NOUN
ejpam-6199	142	2	6	6	NUM
ejpam-6199	142	3	(	(	PUNCT
ejpam-6199	142	4	[	[	X
ejpam-6199	142	5	17	17	NUM
ejpam-6199	142	6	]	]	NUM
ejpam-6199	142	7	)	)	PUNCT
ejpam-6199	142	8	.	.	PUNCT
ejpam-6199	143	1	an	an	DET
ejpam-6199	143	2	n	n	NOUN
ejpam-6199	143	3	-	-	PUNCT
ejpam-6199	143	4	structure	structure	NOUN
ejpam-6199	143	5	ϖπ	ϖπ	NOUN
ejpam-6199	143	6	of	of	ADP
ejpam-6199	143	7	ϑ	ϑ	PROPN
ejpam-6199	143	8	is	be	AUX
ejpam-6199	143	9	an	an	DET
ejpam-6199	143	10	object	object	NOUN
ejpam-6199	143	11	of	of	ADP
ejpam-6199	143	12	the	the	DET
ejpam-6199	143	13	following	follow	VERB
ejpam-6199	143	14	form	form	NOUN
ejpam-6199	143	15	:	:	PUNCT
ejpam-6199	143	16	ϖπ	ϖπ	NOUN
ejpam-6199	143	17	=	=	SYM
ejpam-6199	143	18	{	{	PUNCT
ejpam-6199	143	19	(	(	PUNCT
ejpam-6199	143	20	n	n	CCONJ
ejpam-6199	143	21	,	,	PUNCT
ejpam-6199	143	22	ϖ−(n	ϖ−(n	PROPN
ejpam-6199	143	23	)	)	PUNCT
ejpam-6199	143	24	)	)	PUNCT
ejpam-6199	143	25	:	:	PUNCT
ejpam-6199	144	1	n	n	X
ejpam-6199	144	2	∈	∈	PROPN
ejpam-6199	144	3	ϑ	ϑ	NOUN
ejpam-6199	144	4	}	}	PUNCT
ejpam-6199	144	5	,	,	PUNCT
ejpam-6199	144	6	where	where	SCONJ
ejpam-6199	144	7	ϖ−	ϖ−	NOUN
ejpam-6199	144	8	:	:	PUNCT
ejpam-6199	144	9	ϑ	ϑ	X
ejpam-6199	144	10	→	→	X
ejpam-6199	144	11	[	[	X
ejpam-6199	144	12	−1	−1	NOUN
ejpam-6199	144	13	,	,	PUNCT
ejpam-6199	144	14	0	0	NUM
ejpam-6199	144	15	]	]	PUNCT
ejpam-6199	144	16	.	.	PUNCT
ejpam-6199	145	1	definition	definition	NOUN
ejpam-6199	145	2	7	7	NUM
ejpam-6199	145	3	(	(	PUNCT
ejpam-6199	145	4	[	[	X
ejpam-6199	145	5	21	21	NUM
ejpam-6199	145	6	]	]	PUNCT
ejpam-6199	145	7	)	)	PUNCT
ejpam-6199	145	8	.	.	PUNCT
ejpam-6199	146	1	let	let	VERB
ejpam-6199	146	2	ϑ	ϑ	X
ejpam-6199	146	3	̸=	̸=	PROPN
ejpam-6199	146	4	ϕ	ϕ	NOUN
ejpam-6199	146	5	be	be	AUX
ejpam-6199	146	6	a	a	DET
ejpam-6199	146	7	set	set	NOUN
ejpam-6199	146	8	.	.	PUNCT
ejpam-6199	147	1	a	a	DET
ejpam-6199	147	2	crossing	cross	VERB
ejpam-6199	147	3	cubic	cubic	ADJ
ejpam-6199	147	4	structure	structure	NOUN
ejpam-6199	147	5	of	of	ADP
ejpam-6199	147	6	ϑ	ϑ	PROPN
ejpam-6199	147	7	is	be	AUX
ejpam-6199	147	8	an	an	DET
ejpam-6199	147	9	object	object	NOUN
ejpam-6199	147	10	having	have	VERB
ejpam-6199	147	11	the	the	DET
ejpam-6199	147	12	following	follow	VERB
ejpam-6199	147	13	form	form	NOUN
ejpam-6199	147	14	:	:	PUNCT
ejpam-6199	147	15	π	π	X
ejpam-6199	147	16	=	=	PRON
ejpam-6199	147	17	{	{	PUNCT
ejpam-6199	147	18	(	(	PUNCT
ejpam-6199	147	19	n	n	X
ejpam-6199	147	20	,	,	PUNCT
ejpam-6199	147	21	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	147	22	)	)	PUNCT
ejpam-6199	147	23	,	,	PUNCT
ejpam-6199	147	24	ϖπ(n	ϖπ(n	NOUN
ejpam-6199	147	25	)	)	PUNCT
ejpam-6199	147	26	)	)	PUNCT
ejpam-6199	148	1	|	|	ADV
ejpam-6199	148	2	n	n	PRON
ejpam-6199	148	3	∈	∈	PROPN
ejpam-6199	148	4	ϑ	ϑ	NOUN
ejpam-6199	148	5	}	}	PUNCT
ejpam-6199	148	6	,	,	PUNCT
ejpam-6199	148	7	a.	a.	PROPN
ejpam-6199	148	8	al	al	PROPN
ejpam-6199	148	9	-	-	PROPN
ejpam-6199	148	10	masarwah	masarwah	PROPN
ejpam-6199	148	11	et	et	PROPN
ejpam-6199	148	12	al	al	PROPN
ejpam-6199	148	13	.	.	PUNCT
ejpam-6199	148	14	/	/	SYM
ejpam-6199	148	15	eur	eur	PROPN
ejpam-6199	148	16	.	.	PUNCT
ejpam-6199	149	1	j.	j.	PROPN
ejpam-6199	149	2	pure	pure	PROPN
ejpam-6199	149	3	appl	appl	PROPN
ejpam-6199	149	4	.	.	PROPN
ejpam-6199	149	5	math	math	PROPN
ejpam-6199	149	6	,	,	PUNCT
ejpam-6199	149	7	18	18	NUM
ejpam-6199	149	8	(	(	PUNCT
ejpam-6199	149	9	3	3	NUM
ejpam-6199	149	10	)	)	PUNCT
ejpam-6199	149	11	(	(	PUNCT
ejpam-6199	149	12	2025	2025	NUM
ejpam-6199	149	13	)	)	PUNCT
ejpam-6199	149	14	,	,	PUNCT
ejpam-6199	149	15	6199	6199	NUM
ejpam-6199	149	16	6	6	NUM
ejpam-6199	149	17	of	of	ADP
ejpam-6199	149	18	17	17	NUM
ejpam-6199	149	19	where	where	SCONJ
ejpam-6199	149	20	υ̃π	υ̃π	ADJ
ejpam-6199	150	1	=	=	PUNCT
ejpam-6199	151	1	[	[	X
ejpam-6199	151	2	υ−	υ−	PROPN
ejpam-6199	151	3	π	π	PROPN
ejpam-6199	151	4	,	,	PUNCT
ejpam-6199	151	5	υ	υ	PROPN
ejpam-6199	151	6	+	+	X
ejpam-6199	151	7	π	π	NOUN
ejpam-6199	151	8	]	]	X
ejpam-6199	151	9	:	:	PUNCT
ejpam-6199	151	10	ϑ	ϑ	X
ejpam-6199	151	11	→	→	SYM
ejpam-6199	151	12	i[0	i[0	PROPN
ejpam-6199	151	13	,	,	PUNCT
ejpam-6199	151	14	1	1	NUM
ejpam-6199	151	15	]	]	PUNCT
ejpam-6199	151	16	is	be	AUX
ejpam-6199	151	17	an	an	DET
ejpam-6199	151	18	interval	interval	NOUN
ejpam-6199	151	19	valued	value	VERB
ejpam-6199	151	20	fuzzy	fuzzy	ADJ
ejpam-6199	151	21	set	set	VERB
ejpam-6199	151	22	on	on	ADP
ejpam-6199	151	23	ϑ	ϑ	PROPN
ejpam-6199	151	24	and	and	CCONJ
ejpam-6199	151	25	ϖπ	ϖπ	INTJ
ejpam-6199	151	26	:	:	PUNCT
ejpam-6199	151	27	ϑ	ϑ	X
ejpam-6199	151	28	→	→	X
ejpam-6199	151	29	[	[	X
ejpam-6199	151	30	−1	−1	NOUN
ejpam-6199	151	31	,	,	PUNCT
ejpam-6199	151	32	0	0	NUM
ejpam-6199	151	33	]	]	PUNCT
ejpam-6199	151	34	is	be	AUX
ejpam-6199	151	35	an	an	DET
ejpam-6199	151	36	n	n	NOUN
ejpam-6199	151	37	-	-	PUNCT
ejpam-6199	151	38	structure	structure	NOUN
ejpam-6199	151	39	on	on	ADP
ejpam-6199	151	40	ϑ.	ϑ.	NOUN
ejpam-6199	151	41	for	for	ADP
ejpam-6199	151	42	the	the	DET
ejpam-6199	151	43	purpose	purpose	NOUN
ejpam-6199	151	44	of	of	ADP
ejpam-6199	151	45	simplicity	simplicity	NOUN
ejpam-6199	151	46	,	,	PUNCT
ejpam-6199	151	47	we	we	PRON
ejpam-6199	151	48	will	will	AUX
ejpam-6199	151	49	employ	employ	VERB
ejpam-6199	151	50	the	the	DET
ejpam-6199	151	51	symbol	symbol	NOUN
ejpam-6199	151	52	π	π	NOUN
ejpam-6199	151	53	=	=	SYM
ejpam-6199	151	54	(	(	PUNCT
ejpam-6199	151	55	υ̃π	υ̃π	PROPN
ejpam-6199	151	56	,	,	PUNCT
ejpam-6199	151	57	ϖπ	ϖπ	NOUN
ejpam-6199	151	58	)	)	PUNCT
ejpam-6199	151	59	for	for	ADP
ejpam-6199	151	60	the	the	DET
ejpam-6199	151	61	crossing	crossing	NOUN
ejpam-6199	151	62	cubic	cubic	ADJ
ejpam-6199	151	63	structure	structure	NOUN
ejpam-6199	151	64	π	π	PROPN
ejpam-6199	151	65	=	=	PRON
ejpam-6199	151	66	{	{	PUNCT
ejpam-6199	151	67	(	(	PUNCT
ejpam-6199	151	68	n	n	X
ejpam-6199	151	69	,	,	PUNCT
ejpam-6199	151	70	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	151	71	)	)	PUNCT
ejpam-6199	151	72	,	,	PUNCT
ejpam-6199	151	73	ϖπ(n	ϖπ(n	NOUN
ejpam-6199	151	74	)	)	PUNCT
ejpam-6199	151	75	)	)	PUNCT
ejpam-6199	152	1	|	|	ADV
ejpam-6199	152	2	n	n	PRON
ejpam-6199	152	3	∈	∈	PROPN
ejpam-6199	152	4	ϑ	ϑ	NOUN
ejpam-6199	152	5	}	}	PUNCT
ejpam-6199	152	6	.	.	PUNCT
ejpam-6199	153	1	definition	definition	NOUN
ejpam-6199	153	2	8	8	NUM
ejpam-6199	153	3	(	(	PUNCT
ejpam-6199	153	4	[	[	X
ejpam-6199	153	5	21	21	NUM
ejpam-6199	153	6	]	]	PUNCT
ejpam-6199	153	7	)	)	PUNCT
ejpam-6199	153	8	.	.	PUNCT
ejpam-6199	154	1	let	let	VERB
ejpam-6199	154	2	π	π	PROPN
ejpam-6199	154	3	=	=	SYM
ejpam-6199	154	4	(	(	PUNCT
ejpam-6199	154	5	υ̃π	υ̃π	PROPN
ejpam-6199	154	6	,	,	PUNCT
ejpam-6199	154	7	ϖπ	ϖπ	NOUN
ejpam-6199	154	8	)	)	PUNCT
ejpam-6199	154	9	be	be	AUX
ejpam-6199	154	10	a	a	DET
ejpam-6199	154	11	crossing	cross	VERB
ejpam-6199	154	12	cubic	cubic	ADJ
ejpam-6199	154	13	structure	structure	NOUN
ejpam-6199	154	14	over	over	ADP
ejpam-6199	154	15	ϑ.	ϑ.	NOUN
ejpam-6199	154	16	then	then	ADV
ejpam-6199	154	17	,	,	PUNCT
ejpam-6199	154	18	(	(	PUNCT
ejpam-6199	154	19	τ̃	τ̃	PROPN
ejpam-6199	154	20	,	,	PUNCT
ejpam-6199	154	21	κ)-level	κ)-level	NOUN
ejpam-6199	154	22	of	of	ADP
ejpam-6199	154	23	π	π	PROPN
ejpam-6199	154	24	=	=	SYM
ejpam-6199	154	25	(	(	PUNCT
ejpam-6199	154	26	υ̃π	υ̃π	PROPN
ejpam-6199	154	27	,	,	PUNCT
ejpam-6199	154	28	ϖπ	ϖπ	NOUN
ejpam-6199	154	29	)	)	PUNCT
ejpam-6199	154	30	is	be	AUX
ejpam-6199	154	31	the	the	DET
ejpam-6199	154	32	crisp	crisp	ADJ
ejpam-6199	154	33	set	set	NOUN
ejpam-6199	154	34	in	in	ADP
ejpam-6199	154	35	ϑ	ϑ	NOUN
ejpam-6199	154	36	denoted	denote	VERB
ejpam-6199	154	37	by	by	ADP
ejpam-6199	154	38	γ	γ	PROPN
ejpam-6199	154	39	(	(	PUNCT
ejpam-6199	154	40	υ̃π	υ̃π	PROPN
ejpam-6199	154	41	;	;	PUNCT
ejpam-6199	154	42	(	(	PUNCT
ejpam-6199	154	43	τ̃	τ̃	PROPN
ejpam-6199	154	44	,	,	PUNCT
ejpam-6199	154	45	κ	κ	NOUN
ejpam-6199	154	46	)	)	PUNCT
ejpam-6199	154	47	)	)	PUNCT
ejpam-6199	154	48	and	and	CCONJ
ejpam-6199	154	49	is	be	AUX
ejpam-6199	154	50	defined	define	VERB
ejpam-6199	154	51	as	as	ADP
ejpam-6199	154	52	γ	γ	X
ejpam-6199	154	53	(	(	PUNCT
ejpam-6199	154	54	υ̃π	υ̃π	PROPN
ejpam-6199	154	55	;	;	PUNCT
ejpam-6199	154	56	(	(	PUNCT
ejpam-6199	154	57	τ̃	τ̃	PROPN
ejpam-6199	154	58	,	,	PUNCT
ejpam-6199	154	59	κ	κ	NOUN
ejpam-6199	154	60	)	)	PUNCT
ejpam-6199	154	61	)	)	PUNCT
ejpam-6199	155	1	=	=	PRON
ejpam-6199	155	2	{	{	PUNCT
ejpam-6199	155	3	n	n	PRON
ejpam-6199	155	4	∈	∈	PROPN
ejpam-6199	155	5	ϑ	ϑ	X
ejpam-6199	155	6	|	|	ADV
ejpam-6199	155	7	υ̃π(n	υ̃π(n	NOUN
ejpam-6199	155	8	)	)	PUNCT
ejpam-6199	155	9	⪰	⪰	NOUN
ejpam-6199	155	10	τ̃	τ̃	PROPN
ejpam-6199	155	11	,	,	PUNCT
ejpam-6199	155	12	ϖπ(n	ϖπ(n	NUM
ejpam-6199	155	13	)	)	PUNCT
ejpam-6199	155	14	≤	≤	NUM
ejpam-6199	155	15	κ	κ	NOUN
ejpam-6199	155	16	}	}	PUNCT
ejpam-6199	155	17	,	,	PUNCT
ejpam-6199	155	18	where	where	SCONJ
ejpam-6199	155	19	τ̃	τ̃	PROPN
ejpam-6199	155	20	∈	∈	PROPN
ejpam-6199	155	21	i[0	i[0	PROPN
ejpam-6199	155	22	,	,	PUNCT
ejpam-6199	155	23	1	1	NUM
ejpam-6199	155	24	]	]	PUNCT
ejpam-6199	155	25	and	and	CCONJ
ejpam-6199	155	26	κ	κ	ADP
ejpam-6199	155	27	∈	∈	PROPN
ejpam-6199	156	1	[	[	X
ejpam-6199	156	2	−1	−1	NOUN
ejpam-6199	156	3	,	,	PUNCT
ejpam-6199	156	4	0	0	NUM
ejpam-6199	156	5	]	]	PUNCT
ejpam-6199	156	6	.	.	PUNCT
ejpam-6199	157	1	for	for	ADP
ejpam-6199	157	2	τ̃	τ̃	PROPN
ejpam-6199	157	3	∈	∈	PROPN
ejpam-6199	157	4	i[0	i[0	PROPN
ejpam-6199	157	5	,	,	PUNCT
ejpam-6199	157	6	1	1	NUM
ejpam-6199	157	7	]	]	PUNCT
ejpam-6199	157	8	and	and	CCONJ
ejpam-6199	157	9	κ	κ	ADP
ejpam-6199	157	10	∈	∈	PROPN
ejpam-6199	157	11	[	[	X
ejpam-6199	157	12	−1	−1	NOUN
ejpam-6199	157	13	,	,	PUNCT
ejpam-6199	157	14	0	0	NUM
ejpam-6199	157	15	]	]	PUNCT
ejpam-6199	157	16	.	.	PUNCT
ejpam-6199	158	1	the	the	DET
ejpam-6199	158	2	τ̃	τ̃	PROPN
ejpam-6199	158	3	-level	-level	NOUN
ejpam-6199	158	4	γ	γ	X
ejpam-6199	158	5	(	(	PUNCT
ejpam-6199	158	6	υ̃π	υ̃π	PROPN
ejpam-6199	158	7	;	;	PUNCT
ejpam-6199	158	8	τ̃	τ̃	X
ejpam-6199	158	9	)	)	PUNCT
ejpam-6199	158	10	and	and	CCONJ
ejpam-6199	158	11	κ	κ	NOUN
ejpam-6199	158	12	-	-	PUNCT
ejpam-6199	158	13	level	level	NOUN
ejpam-6199	158	14	γ	γ	NOUN
ejpam-6199	158	15	(	(	PUNCT
ejpam-6199	158	16	ϖω;κ	ϖω;κ	NUM
ejpam-6199	158	17	)	)	PUNCT
ejpam-6199	158	18	subsets	subset	NOUN
ejpam-6199	158	19	of	of	ADP
ejpam-6199	158	20	∏	∏	PROPN
ejpam-6199	158	21	can	can	AUX
ejpam-6199	158	22	be	be	AUX
ejpam-6199	158	23	defined	define	VERB
ejpam-6199	158	24	as	as	ADP
ejpam-6199	158	25	:	:	PUNCT
ejpam-6199	158	26	γ	γ	X
ejpam-6199	158	27	(	(	PUNCT
ejpam-6199	158	28	υ̃π	υ̃π	PROPN
ejpam-6199	158	29	;	;	PUNCT
ejpam-6199	158	30	τ̃	τ̃	X
ejpam-6199	158	31	)	)	PUNCT
ejpam-6199	159	1	=	=	PRON
ejpam-6199	159	2	{	{	PUNCT
ejpam-6199	159	3	n	n	PRON
ejpam-6199	159	4	∈	∈	PROPN
ejpam-6199	159	5	ϑ	ϑ	X
ejpam-6199	159	6	|	|	ADV
ejpam-6199	159	7	υ̃π(n	υ̃π(n	NOUN
ejpam-6199	159	8	)	)	PUNCT
ejpam-6199	159	9	⪰	⪰	NOUN
ejpam-6199	159	10	τ̃	τ̃	PROPN
ejpam-6199	159	11	}	}	PUNCT
ejpam-6199	159	12	and	and	CCONJ
ejpam-6199	159	13	γ	γ	X
ejpam-6199	159	14	(	(	PUNCT
ejpam-6199	159	15	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	159	16	)	)	PUNCT
ejpam-6199	159	17	=	=	PRON
ejpam-6199	159	18	{	{	PUNCT
ejpam-6199	159	19	n	n	PRON
ejpam-6199	159	20	∈	∈	PROPN
ejpam-6199	159	21	ϑ	ϑ	X
ejpam-6199	159	22	|	|	NOUN
ejpam-6199	159	23	ϖπ(n	ϖπ(n	NOUN
ejpam-6199	159	24	)	)	PUNCT
ejpam-6199	159	25	≤	≤	NUM
ejpam-6199	159	26	κ	κ	NOUN
ejpam-6199	159	27	}	}	PUNCT
ejpam-6199	159	28	.	.	PUNCT
ejpam-6199	160	1	3	3	X
ejpam-6199	160	2	.	.	X
ejpam-6199	160	3	crossing	cross	VERB
ejpam-6199	160	4	cubic	cubic	ADJ
ejpam-6199	160	5	filters	filter	NOUN
ejpam-6199	160	6	here	here	ADV
ejpam-6199	160	7	,	,	PUNCT
ejpam-6199	160	8	we	we	PRON
ejpam-6199	160	9	present	present	VERB
ejpam-6199	160	10	the	the	DET
ejpam-6199	160	11	idea	idea	NOUN
ejpam-6199	160	12	of	of	ADP
ejpam-6199	160	13	crossing	cross	VERB
ejpam-6199	160	14	cubic	cubic	ADJ
ejpam-6199	160	15	filters	filter	NOUN
ejpam-6199	160	16	.	.	PUNCT
ejpam-6199	161	1	then	then	ADV
ejpam-6199	161	2	,	,	PUNCT
ejpam-6199	161	3	we	we	PRON
ejpam-6199	161	4	study	study	VERB
ejpam-6199	161	5	certain	certain	ADJ
ejpam-6199	161	6	characterizations	characterization	NOUN
ejpam-6199	161	7	of	of	ADP
ejpam-6199	161	8	it	it	PRON
ejpam-6199	161	9	.	.	PUNCT
ejpam-6199	162	1	also	also	ADV
ejpam-6199	162	2	,	,	PUNCT
ejpam-6199	162	3	we	we	PRON
ejpam-6199	162	4	discuss	discuss	VERB
ejpam-6199	162	5	a	a	DET
ejpam-6199	162	6	relation	relation	NOUN
ejpam-6199	162	7	between	between	ADP
ejpam-6199	162	8	a	a	DET
ejpam-6199	162	9	crossing	cross	VERB
ejpam-6199	162	10	cubic	cubic	ADJ
ejpam-6199	162	11	filter	filter	NOUN
ejpam-6199	162	12	and	and	CCONJ
ejpam-6199	162	13	a	a	DET
ejpam-6199	162	14	crisp	crisp	ADJ
ejpam-6199	162	15	filter	filter	NOUN
ejpam-6199	162	16	.	.	PUNCT
ejpam-6199	163	1	definition	definition	NOUN
ejpam-6199	163	2	9	9	NUM
ejpam-6199	163	3	.	.	PUNCT
ejpam-6199	164	1	a	a	DET
ejpam-6199	164	2	crossing	cross	VERB
ejpam-6199	164	3	cubic	cubic	ADJ
ejpam-6199	164	4	structure	structure	NOUN
ejpam-6199	164	5	π	π	PROPN
ejpam-6199	164	6	=	=	SYM
ejpam-6199	164	7	(	(	PUNCT
ejpam-6199	164	8	υ̃π	υ̃π	PROPN
ejpam-6199	164	9	,	,	PUNCT
ejpam-6199	164	10	ϖπ	ϖπ	NOUN
ejpam-6199	164	11	)	)	PUNCT
ejpam-6199	164	12	over	over	ADP
ejpam-6199	164	13	ϑ	ϑ	PROPN
ejpam-6199	164	14	is	be	AUX
ejpam-6199	164	15	called	call	VERB
ejpam-6199	164	16	a	a	DET
ejpam-6199	164	17	crossing	cross	VERB
ejpam-6199	164	18	cubic	cubic	ADJ
ejpam-6199	164	19	filter	filter	NOUN
ejpam-6199	164	20	of	of	ADP
ejpam-6199	164	21	ϑ	ϑ	PRON
ejpam-6199	164	22	if	if	SCONJ
ejpam-6199	164	23	it	it	PRON
ejpam-6199	164	24	satisfies	satisfy	VERB
ejpam-6199	164	25	the	the	DET
ejpam-6199	164	26	conditions	condition	NOUN
ejpam-6199	164	27	:	:	PUNCT
ejpam-6199	164	28	∀n	∀n	NUM
ejpam-6199	164	29	,	,	PUNCT
ejpam-6199	164	30	v	v	NOUN
ejpam-6199	164	31	,	,	PUNCT
ejpam-6199	164	32	w	w	PROPN
ejpam-6199	164	33	∈	∈	PROPN
ejpam-6199	164	34	ϑ	ϑ	X
ejpam-6199	164	35	,	,	PUNCT
ejpam-6199	164	36	(	(	PUNCT
ejpam-6199	164	37	i	i	NOUN
ejpam-6199	164	38	)	)	PUNCT
ejpam-6199	164	39	(	(	PUNCT
ejpam-6199	164	40	∀n	∀n	NUM
ejpam-6199	164	41	∈	∈	PROPN
ejpam-6199	164	42	ϑ	ϑ	NOUN
ejpam-6199	164	43	)	)	PUNCT
ejpam-6199	164	44	(	(	PUNCT
ejpam-6199	164	45	υ̃π(1	υ̃π(1	PROPN
ejpam-6199	164	46	)	)	PUNCT
ejpam-6199	164	47	⪰	⪰	NOUN
ejpam-6199	164	48	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	164	49	)	)	PUNCT
ejpam-6199	164	50	,	,	PUNCT
ejpam-6199	164	51	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	164	52	)	)	PUNCT
ejpam-6199	164	53	≤	≤	NOUN
ejpam-6199	164	54	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	164	55	)	)	PUNCT
ejpam-6199	164	56	)	)	PUNCT
ejpam-6199	165	1	;	;	PUNCT
ejpam-6199	165	2	(	(	PUNCT
ejpam-6199	165	3	ii	ii	NOUN
ejpam-6199	165	4	)	)	PUNCT
ejpam-6199	165	5	(	(	PUNCT
ejpam-6199	165	6	∀n	∀n	X
ejpam-6199	165	7	,	,	PUNCT
ejpam-6199	165	8	v	v	NOUN
ejpam-6199	165	9	∈	∈	PROPN
ejpam-6199	165	10	ϑ	ϑ	NOUN
ejpam-6199	165	11	)	)	PUNCT
ejpam-6199	165	12	(	(	PUNCT
ejpam-6199	165	13	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	165	14	|	|	ADV
ejpam-6199	165	15	(	(	PUNCT
ejpam-6199	165	16	v	v	NOUN
ejpam-6199	165	17	|	|	ADV
ejpam-6199	165	18	v	v	NOUN
ejpam-6199	165	19	)	)	PUNCT
ejpam-6199	165	20	)	)	PUNCT
ejpam-6199	165	21	⪰	⪰	NOUN
ejpam-6199	165	22	υ̃π(v	υ̃π(v	NOUN
ejpam-6199	165	23	)	)	PUNCT
ejpam-6199	165	24	,	,	PUNCT
ejpam-6199	165	25	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	166	1	|	|	ADV
ejpam-6199	166	2	(	(	PUNCT
ejpam-6199	166	3	v	v	NOUN
ejpam-6199	166	4	|	|	ADV
ejpam-6199	166	5	v	v	NOUN
ejpam-6199	166	6	)	)	PUNCT
ejpam-6199	166	7	)	)	PUNCT
ejpam-6199	166	8	≤	≤	NOUN
ejpam-6199	166	9	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	166	10	)	)	PUNCT
ejpam-6199	166	11	)	)	PUNCT
ejpam-6199	167	1	;	;	PUNCT
ejpam-6199	167	2	(	(	PUNCT
ejpam-6199	167	3	iii	iii	X
ejpam-6199	167	4	)	)	PUNCT
ejpam-6199	167	5	(	(	PUNCT
ejpam-6199	167	6	∀n	∀n	X
ejpam-6199	167	7	,	,	PUNCT
ejpam-6199	167	8	v	v	NOUN
ejpam-6199	167	9	,	,	PUNCT
ejpam-6199	167	10	w	w	PROPN
ejpam-6199	167	11	∈	∈	PROPN
ejpam-6199	167	12	ϑ	ϑ	NOUN
ejpam-6199	167	13	)	)	PUNCT
ejpam-6199	167	14	(	(	PUNCT
ejpam-6199	167	15	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	168	1	|	|	ADV
ejpam-6199	168	2	(	(	PUNCT
ejpam-6199	168	3	v	v	NOUN
ejpam-6199	168	4	|	|	ADV
ejpam-6199	168	5	w	w	NOUN
ejpam-6199	168	6	)	)	PUNCT
ejpam-6199	168	7	)	)	PUNCT
ejpam-6199	169	1	|	|	ADV
ejpam-6199	169	2	(	(	PUNCT
ejpam-6199	169	3	v	v	NOUN
ejpam-6199	169	4	|	|	ADV
ejpam-6199	169	5	w	w	NOUN
ejpam-6199	169	6	)	)	PUNCT
ejpam-6199	169	7	)	)	PUNCT
ejpam-6199	169	8	⪰	⪰	NOUN
ejpam-6199	169	9	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	169	10	)	)	PUNCT
ejpam-6199	169	11	,	,	PUNCT
ejpam-6199	169	12	υ̃π(w	υ̃π(w	NOUN
ejpam-6199	169	13	)	)	PUNCT
ejpam-6199	169	14	}	}	PUNCT
ejpam-6199	169	15	,	,	PUNCT
ejpam-6199	169	16	ϖπ((n	ϖπ((n	PROPN
ejpam-6199	169	17	|	|	ADV
ejpam-6199	169	18	(	(	PUNCT
ejpam-6199	169	19	v	v	NOUN
ejpam-6199	169	20	|	|	ADV
ejpam-6199	169	21	w	w	NOUN
ejpam-6199	169	22	)	)	PUNCT
ejpam-6199	169	23	)	)	PUNCT
ejpam-6199	170	1	|	|	ADV
ejpam-6199	170	2	(	(	PUNCT
ejpam-6199	170	3	v	v	NOUN
ejpam-6199	170	4	|	|	ADV
ejpam-6199	170	5	w	w	NOUN
ejpam-6199	170	6	)	)	PUNCT
ejpam-6199	170	7	)	)	PUNCT
ejpam-6199	170	8	≤	≤	NUM
ejpam-6199	170	9	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	170	10	)	)	PUNCT
ejpam-6199	170	11	,	,	PUNCT
ejpam-6199	170	12	ϖπ(w	ϖπ(w	ADJ
ejpam-6199	170	13	)	)	PUNCT
ejpam-6199	170	14	}	}	PUNCT
ejpam-6199	170	15	)	)	PUNCT
ejpam-6199	170	16	.	.	PUNCT
ejpam-6199	171	1	example	example	NOUN
ejpam-6199	172	1	1	1	X
ejpam-6199	172	2	.	.	PUNCT
ejpam-6199	172	3	let	let	VERB
ejpam-6199	172	4	ϑ	ϑ	X
ejpam-6199	172	5	=	=	X
ejpam-6199	172	6	{	{	PUNCT
ejpam-6199	172	7	0	0	NUM
ejpam-6199	172	8	,	,	PUNCT
ejpam-6199	172	9	1	1	NUM
ejpam-6199	172	10	,	,	PUNCT
ejpam-6199	172	11	2ϑ	2ϑ	NUM
ejpam-6199	172	12	,	,	PUNCT
ejpam-6199	172	13	3ϑ	3ϑ	NUM
ejpam-6199	172	14	,	,	PUNCT
ejpam-6199	172	15	4ϑ	4ϑ	NUM
ejpam-6199	172	16	,	,	PUNCT
ejpam-6199	172	17	5ϑ	5ϑ	NUM
ejpam-6199	172	18	,	,	PUNCT
ejpam-6199	172	19	6ϑ	6ϑ	NOUN
ejpam-6199	172	20	,	,	PUNCT
ejpam-6199	172	21	7ϑ	7ϑ	NUM
ejpam-6199	172	22	}	}	PUNCT
ejpam-6199	172	23	be	be	AUX
ejpam-6199	172	24	a	a	DET
ejpam-6199	172	25	set	set	NOUN
ejpam-6199	172	26	.	.	PUNCT
ejpam-6199	173	1	the	the	DET
ejpam-6199	173	2	hasse	hasse	PROPN
ejpam-6199	173	3	diagram	diagram	PROPN
ejpam-6199	173	4	and	and	CCONJ
ejpam-6199	173	5	sheffer	sheffer	PROPN
ejpam-6199	173	6	stroke	stroke	NOUN
ejpam-6199	173	7	“	"	PUNCT
ejpam-6199	173	8	|	|	ADV
ejpam-6199	173	9	”	"	PUNCT
ejpam-6199	173	10	on	on	ADP
ejpam-6199	173	11	ϑ	ϑ	PRON
ejpam-6199	173	12	,	,	PUNCT
ejpam-6199	173	13	which	which	PRON
ejpam-6199	173	14	are	be	AUX
ejpam-6199	173	15	shown	show	VERB
ejpam-6199	173	16	in	in	ADP
ejpam-6199	173	17	figure	figure	NOUN
ejpam-6199	173	18	1	1	NUM
ejpam-6199	173	19	and	and	CCONJ
ejpam-6199	173	20	table	table	NOUN
ejpam-6199	173	21	4	4	NUM
ejpam-6199	173	22	,	,	PUNCT
ejpam-6199	173	23	respectively	respectively	ADV
ejpam-6199	173	24	.	.	PUNCT
ejpam-6199	174	1	a.	a.	PROPN
ejpam-6199	174	2	al	al	PROPN
ejpam-6199	174	3	-	-	PROPN
ejpam-6199	174	4	masarwah	masarwah	PROPN
ejpam-6199	174	5	et	et	PROPN
ejpam-6199	174	6	al	al	PROPN
ejpam-6199	174	7	.	.	PUNCT
ejpam-6199	174	8	/	/	SYM
ejpam-6199	174	9	eur	eur	PROPN
ejpam-6199	174	10	.	.	PUNCT
ejpam-6199	175	1	j.	j.	PROPN
ejpam-6199	175	2	pure	pure	PROPN
ejpam-6199	175	3	appl	appl	PROPN
ejpam-6199	175	4	.	.	PROPN
ejpam-6199	175	5	math	math	PROPN
ejpam-6199	175	6	,	,	PUNCT
ejpam-6199	175	7	18	18	NUM
ejpam-6199	175	8	(	(	PUNCT
ejpam-6199	175	9	3	3	NUM
ejpam-6199	175	10	)	)	PUNCT
ejpam-6199	175	11	(	(	PUNCT
ejpam-6199	175	12	2025	2025	NUM
ejpam-6199	175	13	)	)	PUNCT
ejpam-6199	175	14	,	,	PUNCT
ejpam-6199	175	15	6199	6199	NUM
ejpam-6199	175	16	7	7	NUM
ejpam-6199	175	17	of	of	ADP
ejpam-6199	175	18	17	17	NUM
ejpam-6199	175	19	figure	figure	NOUN
ejpam-6199	175	20	1	1	NUM
ejpam-6199	175	21	:	:	PUNCT
ejpam-6199	175	22	hasse	hasse	NOUN
ejpam-6199	175	23	diagram	diagram	NOUN
ejpam-6199	175	24	table	table	NOUN
ejpam-6199	175	25	4	4	NUM
ejpam-6199	175	26	:	:	PUNCT
ejpam-6199	175	27	cayley	cayley	ADJ
ejpam-6199	175	28	table	table	NOUN
ejpam-6199	175	29	for	for	ADP
ejpam-6199	175	30	the	the	DET
ejpam-6199	175	31	sheffer	sheffer	NOUN
ejpam-6199	175	32	stroke	stroke	NOUN
ejpam-6199	175	33	“	"	PUNCT
ejpam-6199	175	34	|	|	ADV
ejpam-6199	175	35	”	"	PUNCT
ejpam-6199	176	1	|	|	ADV
ejpam-6199	176	2	0	0	NUM
ejpam-6199	177	1	2ϑ	2ϑ	NUM
ejpam-6199	177	2	3ϑ	3ϑ	NUM
ejpam-6199	177	3	4ϑ	4ϑ	NUM
ejpam-6199	178	1	5ϑ	5ϑ	NUM
ejpam-6199	178	2	6ϑ	6ϑ	NOUN
ejpam-6199	178	3	7ϑ	7ϑ	NOUN
ejpam-6199	178	4	1	1	NUM
ejpam-6199	178	5	0	0	NUM
ejpam-6199	178	6	1	1	NUM
ejpam-6199	178	7	1	1	NUM
ejpam-6199	178	8	1	1	NUM
ejpam-6199	178	9	1	1	NUM
ejpam-6199	178	10	1	1	NUM
ejpam-6199	178	11	1	1	NUM
ejpam-6199	178	12	1	1	NUM
ejpam-6199	178	13	1	1	NUM
ejpam-6199	178	14	2ϑ	2ϑ	NUM
ejpam-6199	178	15	1	1	NUM
ejpam-6199	178	16	7ϑ	7ϑ	NUM
ejpam-6199	178	17	1	1	NUM
ejpam-6199	178	18	1	1	NUM
ejpam-6199	178	19	7ϑ	7ϑ	NUM
ejpam-6199	178	20	7ϑ	7ϑ	NOUN
ejpam-6199	178	21	1	1	NUM
ejpam-6199	178	22	7ϑ	7ϑ	NUM
ejpam-6199	178	23	3ϑ	3ϑ	NUM
ejpam-6199	178	24	1	1	NUM
ejpam-6199	178	25	1	1	NUM
ejpam-6199	178	26	6ϑ	6ϑ	NOUN
ejpam-6199	178	27	1	1	NUM
ejpam-6199	178	28	6ϑ	6ϑ	NOUN
ejpam-6199	178	29	1	1	NUM
ejpam-6199	178	30	6ϑ	6ϑ	NOUN
ejpam-6199	178	31	6ϑ	6ϑ	NOUN
ejpam-6199	178	32	4ϑ	4ϑ	NOUN
ejpam-6199	178	33	1	1	NUM
ejpam-6199	178	34	1	1	NUM
ejpam-6199	178	35	1	1	NUM
ejpam-6199	178	36	5ϑ	5ϑ	NUM
ejpam-6199	178	37	1	1	NUM
ejpam-6199	178	38	5ϑ	5ϑ	NUM
ejpam-6199	178	39	5ϑ	5ϑ	NUM
ejpam-6199	179	1	5ϑ	5ϑ	NUM
ejpam-6199	179	2	5ϑ	5ϑ	NUM
ejpam-6199	179	3	1	1	NUM
ejpam-6199	179	4	7ϑ	7ϑ	NUM
ejpam-6199	179	5	6ϑ	6ϑ	NOUN
ejpam-6199	179	6	1	1	NUM
ejpam-6199	179	7	4ϑ	4ϑ	NUM
ejpam-6199	179	8	7ϑ	7ϑ	NUM
ejpam-6199	179	9	6ϑ	6ϑ	VERB
ejpam-6199	179	10	4ϑ	4ϑ	PRON
ejpam-6199	179	11	6ϑ	6ϑ	NOUN
ejpam-6199	179	12	1	1	NUM
ejpam-6199	179	13	7ϑ	7ϑ	NUM
ejpam-6199	179	14	1	1	NUM
ejpam-6199	179	15	5ϑ	5ϑ	NUM
ejpam-6199	179	16	7ϑ	7ϑ	NOUN
ejpam-6199	179	17	3ϑ	3ϑ	NUM
ejpam-6199	179	18	5ϑ	5ϑ	NUM
ejpam-6199	179	19	3ϑ	3ϑ	NUM
ejpam-6199	179	20	7ϑ	7ϑ	NUM
ejpam-6199	179	21	1	1	NUM
ejpam-6199	179	22	1	1	NUM
ejpam-6199	179	23	6ϑ	6ϑ	NOUN
ejpam-6199	179	24	5ϑ	5ϑ	NUM
ejpam-6199	179	25	6ϑ	6ϑ	NOUN
ejpam-6199	179	26	5ϑ	5ϑ	NUM
ejpam-6199	179	27	2ϑ	2ϑ	NUM
ejpam-6199	179	28	2ϑ	2ϑ	NUM
ejpam-6199	179	29	1	1	NUM
ejpam-6199	179	30	1	1	NUM
ejpam-6199	179	31	7ϑ	7ϑ	NUM
ejpam-6199	179	32	6ϑ	6ϑ	VERB
ejpam-6199	179	33	5ϑ	5ϑ	NUM
ejpam-6199	179	34	4ϑ	4ϑ	NOUN
ejpam-6199	179	35	3ϑ	3ϑ	NUM
ejpam-6199	179	36	2ϑ	2ϑ	NUM
ejpam-6199	179	37	0	0	PUNCT
ejpam-6199	180	1	then	then	ADV
ejpam-6199	180	2	,	,	PUNCT
ejpam-6199	180	3	ϑ	ϑ	VERB
ejpam-6199	180	4	◦	◦	NOUN
ejpam-6199	180	5	:	:	PUNCT
ejpam-6199	180	6	=	=	SYM
ejpam-6199	180	7	(	(	PUNCT
ejpam-6199	180	8	ϑ	ϑ	X
ejpam-6199	180	9	,	,	PUNCT
ejpam-6199	180	10	|	|	NOUN
ejpam-6199	180	11	)	)	PUNCT
ejpam-6199	180	12	is	be	AUX
ejpam-6199	180	13	a	a	DET
ejpam-6199	180	14	sheffer	sheffer	NOUN
ejpam-6199	180	15	stroke	stroke	NOUN
ejpam-6199	180	16	hilbert	hilbert	PROPN
ejpam-6199	180	17	algebra	algebra	PROPN
ejpam-6199	180	18	(	(	PUNCT
ejpam-6199	180	19	see	see	VERB
ejpam-6199	180	20	[	[	X
ejpam-6199	180	21	13	13	NUM
ejpam-6199	180	22	]	]	NUM
ejpam-6199	180	23	)	)	PUNCT
ejpam-6199	180	24	.	.	PUNCT
ejpam-6199	181	1	let	let	VERB
ejpam-6199	181	2	π	π	PROPN
ejpam-6199	181	3	=	=	SYM
ejpam-6199	181	4	(	(	PUNCT
ejpam-6199	181	5	υ̃π	υ̃π	PROPN
ejpam-6199	181	6	,	,	PUNCT
ejpam-6199	181	7	ϖπ	ϖπ	NOUN
ejpam-6199	181	8	)	)	PUNCT
ejpam-6199	181	9	be	be	AUX
ejpam-6199	181	10	a	a	DET
ejpam-6199	181	11	crossing	cross	VERB
ejpam-6199	181	12	cubic	cubic	ADJ
ejpam-6199	181	13	structure	structure	NOUN
ejpam-6199	181	14	in	in	ADP
ejpam-6199	181	15	ϑ	ϑ	PRON
ejpam-6199	181	16	,	,	PUNCT
ejpam-6199	181	17	which	which	PRON
ejpam-6199	181	18	is	be	AUX
ejpam-6199	181	19	shown	show	VERB
ejpam-6199	181	20	in	in	ADP
ejpam-6199	181	21	table	table	NOUN
ejpam-6199	181	22	5	5	NUM
ejpam-6199	181	23	.	.	PUNCT
ejpam-6199	181	24	table	table	NOUN
ejpam-6199	181	25	5	5	NUM
ejpam-6199	181	26	:	:	PUNCT
ejpam-6199	181	27	π	π	X
ejpam-6199	181	28	=	=	SYM
ejpam-6199	181	29	(	(	PUNCT
ejpam-6199	181	30	υ̃π	υ̃π	PROPN
ejpam-6199	181	31	,	,	PUNCT
ejpam-6199	181	32	ϖπ	ϖπ	NOUN
ejpam-6199	181	33	)	)	PUNCT
ejpam-6199	181	34	is	be	AUX
ejpam-6199	181	35	represented	represent	VERB
ejpam-6199	181	36	tabularly	tabularly	ADV
ejpam-6199	181	37	ϑ	ϑ	X
ejpam-6199	181	38	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	181	39	)	)	PUNCT
ejpam-6199	182	1	ϖπ(n	ϖπ(n	ADP
ejpam-6199	182	2	)	)	PUNCT
ejpam-6199	182	3	0	0	PUNCT
ejpam-6199	183	1	[	[	X
ejpam-6199	183	2	0.28	0.28	NUM
ejpam-6199	183	3	,	,	PUNCT
ejpam-6199	183	4	0.65	0.65	NUM
ejpam-6199	183	5	]	]	PUNCT
ejpam-6199	183	6	-0.41	-0.41	NUM
ejpam-6199	183	7	2ϑ	2ϑ	NUM
ejpam-6199	184	1	[	[	X
ejpam-6199	184	2	0.28	0.28	NUM
ejpam-6199	184	3	,	,	PUNCT
ejpam-6199	184	4	0.65	0.65	NUM
ejpam-6199	184	5	]	]	PUNCT
ejpam-6199	184	6	-0.55	-0.55	NUM
ejpam-6199	184	7	3ϑ	3ϑ	NUM
ejpam-6199	185	1	[	[	X
ejpam-6199	185	2	0.28	0.28	NUM
ejpam-6199	185	3	,	,	PUNCT
ejpam-6199	185	4	0.65	0.65	NUM
ejpam-6199	185	5	]	]	PUNCT
ejpam-6199	186	1	-0.41	-0.41	NUM
ejpam-6199	186	2	4ϑ	4ϑ	NUM
ejpam-6199	187	1	[	[	X
ejpam-6199	187	2	0.32	0.32	NUM
ejpam-6199	187	3	,	,	PUNCT
ejpam-6199	187	4	0.73	0.73	NUM
ejpam-6199	187	5	]	]	PUNCT
ejpam-6199	188	1	-0.41	-0.41	NUM
ejpam-6199	188	2	5ϑ	5ϑ	NUM
ejpam-6199	189	1	[	[	X
ejpam-6199	189	2	0.28	0.28	NUM
ejpam-6199	189	3	,	,	PUNCT
ejpam-6199	189	4	0.65	0.65	NUM
ejpam-6199	189	5	]	]	PUNCT
ejpam-6199	189	6	-0.63	-0.63	NUM
ejpam-6199	189	7	6ϑ	6ϑ	X
ejpam-6199	190	1	[	[	X
ejpam-6199	190	2	0.38	0.38	NUM
ejpam-6199	190	3	,	,	PUNCT
ejpam-6199	190	4	0.76	0.76	NUM
ejpam-6199	190	5	]	]	PUNCT
ejpam-6199	190	6	-0.55	-0.55	NUM
ejpam-6199	190	7	7ϑ	7ϑ	NOUN
ejpam-6199	191	1	[	[	X
ejpam-6199	191	2	0.32	0.32	NUM
ejpam-6199	191	3	,	,	PUNCT
ejpam-6199	191	4	0.73	0.73	NUM
ejpam-6199	191	5	]	]	PUNCT
ejpam-6199	192	1	-0.41	-0.41	CCONJ
ejpam-6199	192	2	1	1	NUM
ejpam-6199	193	1	[	[	X
ejpam-6199	193	2	0.42	0.42	NUM
ejpam-6199	193	3	,	,	PUNCT
ejpam-6199	193	4	0.91	0.91	NUM
ejpam-6199	193	5	]	]	PUNCT
ejpam-6199	193	6	-0.71	-0.71	NOUN
ejpam-6199	193	7	it	it	PRON
ejpam-6199	193	8	is	be	AUX
ejpam-6199	193	9	customary	customary	ADJ
ejpam-6199	193	10	to	to	PART
ejpam-6199	193	11	check	check	VERB
ejpam-6199	193	12	that	that	PRON
ejpam-6199	193	13	π	π	PROPN
ejpam-6199	193	14	=	=	PRON
ejpam-6199	193	15	(	(	PUNCT
ejpam-6199	193	16	υ̃π	υ̃π	PROPN
ejpam-6199	193	17	,	,	PUNCT
ejpam-6199	193	18	ϖπ	ϖπ	NOUN
ejpam-6199	193	19	)	)	PUNCT
ejpam-6199	193	20	is	be	AUX
ejpam-6199	193	21	a	a	DET
ejpam-6199	193	22	crossing	cross	VERB
ejpam-6199	193	23	cubic	cubic	ADJ
ejpam-6199	193	24	filter	filter	NOUN
ejpam-6199	193	25	of	of	ADP
ejpam-6199	193	26	ϑ.	ϑ.	NOUN
ejpam-6199	193	27	proposition	proposition	NOUN
ejpam-6199	193	28	2	2	NUM
ejpam-6199	193	29	.	.	PUNCT
ejpam-6199	194	1	every	every	DET
ejpam-6199	194	2	crossing	cross	VERB
ejpam-6199	194	3	cubic	cubic	ADJ
ejpam-6199	194	4	filter	filter	NOUN
ejpam-6199	194	5	π	π	X
ejpam-6199	194	6	=	=	SYM
ejpam-6199	194	7	(	(	PUNCT
ejpam-6199	194	8	υ̃π	υ̃π	PROPN
ejpam-6199	194	9	,	,	PUNCT
ejpam-6199	194	10	ϖπ	ϖπ	NOUN
ejpam-6199	194	11	)	)	PUNCT
ejpam-6199	194	12	of	of	ADP
ejpam-6199	194	13	ϑ	ϑ	ADJ
ejpam-6199	194	14	satisfies	satisfie	NOUN
ejpam-6199	194	15	:	:	PUNCT
ejpam-6199	194	16	(	(	PUNCT
ejpam-6199	194	17	i	i	NOUN
ejpam-6199	194	18	)	)	PUNCT
ejpam-6199	194	19	(	(	PUNCT
ejpam-6199	194	20	∀n	∀n	X
ejpam-6199	194	21	,	,	PUNCT
ejpam-6199	194	22	v	v	NOUN
ejpam-6199	194	23	∈	∈	PROPN
ejpam-6199	194	24	ϑ	ϑ	NOUN
ejpam-6199	194	25	)	)	PUNCT
ejpam-6199	194	26	(	(	PUNCT
ejpam-6199	194	27	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	194	28	|	|	ADV
ejpam-6199	194	29	(	(	PUNCT
ejpam-6199	194	30	v	v	NOUN
ejpam-6199	194	31	|	|	ADV
ejpam-6199	194	32	v	v	NOUN
ejpam-6199	194	33	)	)	PUNCT
ejpam-6199	194	34	)	)	PUNCT
ejpam-6199	195	1	|	|	ADV
ejpam-6199	195	2	(	(	PUNCT
ejpam-6199	195	3	v	v	NOUN
ejpam-6199	195	4	|	|	ADV
ejpam-6199	195	5	v	v	NOUN
ejpam-6199	195	6	)	)	PUNCT
ejpam-6199	195	7	)	)	PUNCT
ejpam-6199	195	8	⪰	⪰	NOUN
ejpam-6199	195	9	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	195	10	)	)	PUNCT
ejpam-6199	195	11	,	,	PUNCT
ejpam-6199	195	12	ϖπ((n	ϖπ((n	PROPN
ejpam-6199	196	1	|	|	ADV
ejpam-6199	196	2	(	(	PUNCT
ejpam-6199	196	3	v	v	NOUN
ejpam-6199	196	4	|	|	ADV
ejpam-6199	196	5	v	v	NOUN
ejpam-6199	196	6	)	)	PUNCT
ejpam-6199	196	7	)	)	PUNCT
ejpam-6199	197	1	|	|	ADV
ejpam-6199	197	2	(	(	PUNCT
ejpam-6199	197	3	v	v	NOUN
ejpam-6199	197	4	|	|	ADV
ejpam-6199	197	5	v	v	NOUN
ejpam-6199	197	6	)	)	PUNCT
ejpam-6199	197	7	)	)	PUNCT
ejpam-6199	197	8	≤	≤	NOUN
ejpam-6199	197	9	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	197	10	)	)	PUNCT
ejpam-6199	197	11	)	)	PUNCT
ejpam-6199	197	12	;	;	PUNCT
ejpam-6199	197	13	a.	a.	PROPN
ejpam-6199	197	14	al	al	PROPN
ejpam-6199	197	15	-	-	PROPN
ejpam-6199	197	16	masarwah	masarwah	PROPN
ejpam-6199	197	17	et	et	PROPN
ejpam-6199	197	18	al	al	PROPN
ejpam-6199	197	19	.	.	PUNCT
ejpam-6199	197	20	/	/	SYM
ejpam-6199	197	21	eur	eur	PROPN
ejpam-6199	197	22	.	.	PUNCT
ejpam-6199	198	1	j.	j.	PROPN
ejpam-6199	198	2	pure	pure	PROPN
ejpam-6199	198	3	appl	appl	PROPN
ejpam-6199	198	4	.	.	PROPN
ejpam-6199	198	5	math	math	PROPN
ejpam-6199	198	6	,	,	PUNCT
ejpam-6199	198	7	18	18	NUM
ejpam-6199	198	8	(	(	PUNCT
ejpam-6199	198	9	3	3	NUM
ejpam-6199	198	10	)	)	PUNCT
ejpam-6199	198	11	(	(	PUNCT
ejpam-6199	198	12	2025	2025	NUM
ejpam-6199	198	13	)	)	PUNCT
ejpam-6199	198	14	,	,	PUNCT
ejpam-6199	198	15	6199	6199	NUM
ejpam-6199	198	16	8	8	NUM
ejpam-6199	198	17	of	of	ADP
ejpam-6199	198	18	17	17	NUM
ejpam-6199	198	19	(	(	PUNCT
ejpam-6199	198	20	ii	ii	NOUN
ejpam-6199	198	21	)	)	PUNCT
ejpam-6199	198	22	(	(	PUNCT
ejpam-6199	198	23	∀n	∀n	X
ejpam-6199	198	24	,	,	PUNCT
ejpam-6199	198	25	v	v	NOUN
ejpam-6199	198	26	∈	∈	PROPN
ejpam-6199	198	27	ϑ	ϑ	NOUN
ejpam-6199	198	28	)	)	PUNCT
ejpam-6199	198	29	(	(	PUNCT
ejpam-6199	198	30	n	n	ADV
ejpam-6199	198	31	≤	≤	X
ejpam-6199	198	32	v	v	ADP
ejpam-6199	198	33	⇒	⇒	NOUN
ejpam-6199	198	34	{	{	PUNCT
ejpam-6199	198	35	υ̃π(v	υ̃π(v	PROPN
ejpam-6199	198	36	)	)	PUNCT
ejpam-6199	198	37	⪰	⪰	NOUN
ejpam-6199	198	38	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	198	39	)	)	PUNCT
ejpam-6199	198	40	,	,	PUNCT
ejpam-6199	198	41	ϖπ(v	ϖπ(v	ADP
ejpam-6199	198	42	)	)	PUNCT
ejpam-6199	198	43	≤	≤	NOUN
ejpam-6199	198	44	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	198	45	)	)	PUNCT
ejpam-6199	198	46	)	)	PUNCT
ejpam-6199	198	47	.	.	PUNCT
ejpam-6199	199	1	proof	proof	NOUN
ejpam-6199	199	2	.	.	PUNCT
ejpam-6199	200	1	let	let	VERB
ejpam-6199	200	2	π	π	PROPN
ejpam-6199	200	3	=	=	SYM
ejpam-6199	200	4	(	(	PUNCT
ejpam-6199	200	5	υ̃π	υ̃π	PROPN
ejpam-6199	200	6	,	,	PUNCT
ejpam-6199	200	7	ϖπ	ϖπ	NOUN
ejpam-6199	200	8	)	)	PUNCT
ejpam-6199	200	9	be	be	AUX
ejpam-6199	200	10	a	a	DET
ejpam-6199	200	11	crossing	cross	VERB
ejpam-6199	200	12	cubic	cubic	ADJ
ejpam-6199	200	13	filter	filter	NOUN
ejpam-6199	200	14	of	of	ADP
ejpam-6199	200	15	ϑ.	ϑ.	NOUN
ejpam-6199	200	16	then	then	ADV
ejpam-6199	200	17	,	,	PUNCT
ejpam-6199	200	18	by	by	ADP
ejpam-6199	200	19	using	use	VERB
ejpam-6199	200	20	(	(	PUNCT
ejpam-6199	200	21	5	5	NUM
ejpam-6199	200	22	)	)	PUNCT
ejpam-6199	200	23	of	of	ADP
ejpam-6199	200	24	proposition	proposition	NOUN
ejpam-6199	200	25	1	1	NUM
ejpam-6199	200	26	and	and	CCONJ
ejpam-6199	200	27	(	(	PUNCT
ejpam-6199	200	28	iii	iii	NOUN
ejpam-6199	200	29	)	)	PUNCT
ejpam-6199	200	30	of	of	ADP
ejpam-6199	200	31	definition	definition	NOUN
ejpam-6199	200	32	9	9	NUM
ejpam-6199	200	33	,	,	PUNCT
ejpam-6199	200	34	∀n	∀n	NUM
ejpam-6199	200	35	,	,	PUNCT
ejpam-6199	200	36	v	v	ADP
ejpam-6199	200	37	∈	∈	PROPN
ejpam-6199	200	38	ϑ	ϑ	X
ejpam-6199	200	39	,	,	PUNCT
ejpam-6199	200	40	we	we	PRON
ejpam-6199	200	41	have	have	VERB
ejpam-6199	200	42	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	201	1	|	|	ADV
ejpam-6199	201	2	(	(	PUNCT
ejpam-6199	201	3	v	v	NOUN
ejpam-6199	201	4	|	|	ADV
ejpam-6199	201	5	v	v	NOUN
ejpam-6199	201	6	)	)	PUNCT
ejpam-6199	201	7	)	)	PUNCT
ejpam-6199	202	1	|	|	ADV
ejpam-6199	202	2	(	(	PUNCT
ejpam-6199	202	3	v	v	NOUN
ejpam-6199	202	4	|	|	ADV
ejpam-6199	202	5	v	v	NOUN
ejpam-6199	202	6	)	)	PUNCT
ejpam-6199	202	7	)	)	PUNCT
ejpam-6199	203	1	=	=	SYM
ejpam-6199	203	2	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	203	3	|	|	ADV
ejpam-6199	203	4	(	(	PUNCT
ejpam-6199	203	5	n	n	CCONJ
ejpam-6199	203	6	|	|	ADV
ejpam-6199	203	7	n	n	CCONJ
ejpam-6199	203	8	)	)	PUNCT
ejpam-6199	203	9	)	)	PUNCT
ejpam-6199	204	1	|	|	ADV
ejpam-6199	204	2	(	(	PUNCT
ejpam-6199	204	3	n	n	CCONJ
ejpam-6199	204	4	|	|	ADV
ejpam-6199	204	5	n	n	CCONJ
ejpam-6199	204	6	)	)	PUNCT
ejpam-6199	204	7	)	)	PUNCT
ejpam-6199	204	8	⪰	⪰	NOUN
ejpam-6199	204	9	m̃in{υ̃π(n	m̃in{υ̃π(n	PROPN
ejpam-6199	204	10	)	)	PUNCT
ejpam-6199	204	11	,	,	PUNCT
ejpam-6199	204	12	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	204	13	)	)	PUNCT
ejpam-6199	204	14	}	}	PUNCT
ejpam-6199	205	1	=	=	SYM
ejpam-6199	205	2	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	205	3	)	)	PUNCT
ejpam-6199	205	4	and	and	CCONJ
ejpam-6199	205	5	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	206	1	|	|	ADV
ejpam-6199	206	2	(	(	PUNCT
ejpam-6199	206	3	v	v	NOUN
ejpam-6199	206	4	|	|	ADV
ejpam-6199	206	5	v	v	NOUN
ejpam-6199	206	6	)	)	PUNCT
ejpam-6199	206	7	)	)	PUNCT
ejpam-6199	207	1	|	|	ADV
ejpam-6199	207	2	(	(	PUNCT
ejpam-6199	207	3	v	v	NOUN
ejpam-6199	207	4	|	|	ADV
ejpam-6199	207	5	v	v	NOUN
ejpam-6199	207	6	)	)	PUNCT
ejpam-6199	207	7	)	)	PUNCT
ejpam-6199	208	1	=	=	SYM
ejpam-6199	208	2	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	208	3	|	|	ADV
ejpam-6199	208	4	(	(	PUNCT
ejpam-6199	208	5	n	n	CCONJ
ejpam-6199	208	6	|	|	ADV
ejpam-6199	208	7	n	n	CCONJ
ejpam-6199	208	8	)	)	PUNCT
ejpam-6199	208	9	)	)	PUNCT
ejpam-6199	209	1	|	|	ADV
ejpam-6199	209	2	(	(	PUNCT
ejpam-6199	209	3	n	n	CCONJ
ejpam-6199	209	4	|	|	ADV
ejpam-6199	209	5	n	n	CCONJ
ejpam-6199	209	6	)	)	PUNCT
ejpam-6199	209	7	)	)	PUNCT
ejpam-6199	209	8	≤	≤	NUM
ejpam-6199	209	9	max{ϖπ(n	max{ϖπ(n	PROPN
ejpam-6199	209	10	)	)	PUNCT
ejpam-6199	209	11	,	,	PUNCT
ejpam-6199	209	12	ϖπ(n	ϖπ(n	NOUN
ejpam-6199	209	13	)	)	PUNCT
ejpam-6199	209	14	}	}	PUNCT
ejpam-6199	209	15	=	=	SYM
ejpam-6199	209	16	ϖπ(n	ϖπ(n	PROPN
ejpam-6199	209	17	)	)	PUNCT
ejpam-6199	209	18	.	.	PUNCT
ejpam-6199	210	1	therefore	therefore	ADV
ejpam-6199	210	2	,	,	PUNCT
ejpam-6199	210	3	the	the	DET
ejpam-6199	210	4	proof	proof	NOUN
ejpam-6199	210	5	of	of	ADP
ejpam-6199	210	6	(	(	PUNCT
ejpam-6199	210	7	i	i	NOUN
ejpam-6199	210	8	)	)	PUNCT
ejpam-6199	210	9	is	be	AUX
ejpam-6199	210	10	completed	complete	VERB
ejpam-6199	210	11	.	.	PUNCT
ejpam-6199	211	1	now	now	ADV
ejpam-6199	211	2	,	,	PUNCT
ejpam-6199	211	3	let	let	VERB
ejpam-6199	211	4	n	n	CCONJ
ejpam-6199	211	5	,	,	PUNCT
ejpam-6199	211	6	v	v	ADP
ejpam-6199	211	7	∈	∈	PRON
ejpam-6199	211	8	ϑ	ϑ	PART
ejpam-6199	211	9	be	be	AUX
ejpam-6199	211	10	such	such	ADJ
ejpam-6199	211	11	that	that	SCONJ
ejpam-6199	211	12	n	n	NOUN
ejpam-6199	211	13	≤	≤	NOUN
ejpam-6199	212	1	v.	v.	CCONJ
ejpam-6199	212	2	then	then	ADV
ejpam-6199	212	3	n	n	CCONJ
ejpam-6199	213	1	|	|	ADV
ejpam-6199	213	2	(	(	PUNCT
ejpam-6199	213	3	v	v	NOUN
ejpam-6199	213	4	|	|	NOUN
ejpam-6199	213	5	v	v	NOUN
ejpam-6199	213	6	)	)	PUNCT
ejpam-6199	213	7	=	=	SYM
ejpam-6199	213	8	1	1	NUM
ejpam-6199	213	9	by	by	ADP
ejpam-6199	213	10	condition	condition	NOUN
ejpam-6199	213	11	(	(	PUNCT
ejpam-6199	213	12	a	a	NOUN
ejpam-6199	213	13	)	)	PUNCT
ejpam-6199	213	14	.	.	PUNCT
ejpam-6199	214	1	using	use	VERB
ejpam-6199	214	2	(	(	PUNCT
ejpam-6199	214	3	3	3	NUM
ejpam-6199	214	4	)	)	PUNCT
ejpam-6199	214	5	of	of	ADP
ejpam-6199	214	6	proposition	proposition	NOUN
ejpam-6199	214	7	1	1	NUM
ejpam-6199	214	8	and	and	CCONJ
ejpam-6199	214	9	(	(	PUNCT
ejpam-6199	214	10	i	i	NOUN
ejpam-6199	214	11	)	)	PUNCT
ejpam-6199	214	12	of	of	ADP
ejpam-6199	214	13	proposition	proposition	NOUN
ejpam-6199	214	14	2	2	NUM
ejpam-6199	214	15	,	,	PUNCT
ejpam-6199	214	16	we	we	PRON
ejpam-6199	214	17	have	have	VERB
ejpam-6199	214	18	υ̃π(v	υ̃π(v	NOUN
ejpam-6199	214	19	)	)	PUNCT
ejpam-6199	214	20	=	=	SYM
ejpam-6199	215	1	υ̃π(1	υ̃π(1	PROPN
ejpam-6199	215	2	|	|	ADV
ejpam-6199	215	3	(	(	PUNCT
ejpam-6199	215	4	v	v	NOUN
ejpam-6199	215	5	|	|	ADV
ejpam-6199	215	6	v	v	NOUN
ejpam-6199	215	7	)	)	PUNCT
ejpam-6199	215	8	)	)	PUNCT
ejpam-6199	216	1	=	=	SYM
ejpam-6199	216	2	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	217	1	|	|	ADV
ejpam-6199	217	2	(	(	PUNCT
ejpam-6199	217	3	v	v	NOUN
ejpam-6199	217	4	|	|	ADV
ejpam-6199	217	5	v	v	NOUN
ejpam-6199	217	6	)	)	PUNCT
ejpam-6199	217	7	)	)	PUNCT
ejpam-6199	218	1	|	|	ADV
ejpam-6199	218	2	(	(	PUNCT
ejpam-6199	218	3	v	v	NOUN
ejpam-6199	218	4	|	|	ADV
ejpam-6199	218	5	v	v	NOUN
ejpam-6199	218	6	)	)	PUNCT
ejpam-6199	218	7	)	)	PUNCT
ejpam-6199	218	8	⪰	⪰	NOUN
ejpam-6199	218	9	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	218	10	)	)	PUNCT
ejpam-6199	218	11	and	and	CCONJ
ejpam-6199	218	12	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	218	13	)	)	PUNCT
ejpam-6199	219	1	=	=	SYM
ejpam-6199	220	1	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	220	2	|	|	ADV
ejpam-6199	220	3	(	(	PUNCT
ejpam-6199	220	4	v	v	NOUN
ejpam-6199	220	5	|	|	ADV
ejpam-6199	220	6	v	v	NOUN
ejpam-6199	220	7	)	)	PUNCT
ejpam-6199	220	8	)	)	PUNCT
ejpam-6199	221	1	=	=	SYM
ejpam-6199	221	2	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	221	3	|	|	NOUN
ejpam-6199	221	4	(	(	PUNCT
ejpam-6199	221	5	v	v	NOUN
ejpam-6199	221	6	|	|	ADV
ejpam-6199	221	7	v	v	NOUN
ejpam-6199	221	8	)	)	PUNCT
ejpam-6199	221	9	)	)	PUNCT
ejpam-6199	222	1	|	|	ADV
ejpam-6199	222	2	(	(	PUNCT
ejpam-6199	222	3	v	v	NOUN
ejpam-6199	222	4	|	|	ADV
ejpam-6199	222	5	v	v	NOUN
ejpam-6199	222	6	)	)	PUNCT
ejpam-6199	222	7	)	)	PUNCT
ejpam-6199	222	8	≤	≤	NOUN
ejpam-6199	222	9	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	222	10	)	)	PUNCT
ejpam-6199	222	11	.	.	PUNCT
ejpam-6199	223	1	this	this	PRON
ejpam-6199	223	2	completes	complete	VERB
ejpam-6199	223	3	the	the	DET
ejpam-6199	223	4	proof	proof	NOUN
ejpam-6199	223	5	of	of	ADP
ejpam-6199	223	6	(	(	PUNCT
ejpam-6199	223	7	ii	ii	NOUN
ejpam-6199	223	8	)	)	PUNCT
ejpam-6199	223	9	.	.	PUNCT
ejpam-6199	224	1	next	next	ADJ
ejpam-6199	224	2	example	example	NOUN
ejpam-6199	224	3	illustrates	illustrate	VERB
ejpam-6199	224	4	that	that	SCONJ
ejpam-6199	224	5	if	if	SCONJ
ejpam-6199	224	6	a	a	DET
ejpam-6199	224	7	crossing	cross	VERB
ejpam-6199	224	8	cubic	cubic	ADJ
ejpam-6199	224	9	structure	structure	NOUN
ejpam-6199	224	10	π	π	PROPN
ejpam-6199	224	11	=	=	SYM
ejpam-6199	224	12	(	(	PUNCT
ejpam-6199	224	13	υ̃π	υ̃π	PROPN
ejpam-6199	224	14	,	,	PUNCT
ejpam-6199	224	15	ϖπ	ϖπ	NOUN
ejpam-6199	224	16	)	)	PUNCT
ejpam-6199	224	17	satisfies	satisfy	VERB
ejpam-6199	224	18	condition	condition	NOUN
ejpam-6199	224	19	(	(	PUNCT
ejpam-6199	224	20	ii	ii	NOUN
ejpam-6199	224	21	)	)	PUNCT
ejpam-6199	224	22	of	of	ADP
ejpam-6199	224	23	proposition	proposition	NOUN
ejpam-6199	224	24	2	2	NUM
ejpam-6199	224	25	,	,	PUNCT
ejpam-6199	224	26	then	then	ADV
ejpam-6199	224	27	it	it	PRON
ejpam-6199	224	28	is	be	AUX
ejpam-6199	224	29	not	not	PART
ejpam-6199	224	30	enough	enough	ADJ
ejpam-6199	224	31	for	for	ADP
ejpam-6199	224	32	a	a	DET
ejpam-6199	224	33	crossing	cross	VERB
ejpam-6199	224	34	cubic	cubic	ADJ
ejpam-6199	224	35	filter	filter	NOUN
ejpam-6199	224	36	of	of	ADP
ejpam-6199	224	37	ϑ.	ϑ.	NOUN
ejpam-6199	224	38	example	example	NOUN
ejpam-6199	225	1	2	2	X
ejpam-6199	225	2	.	.	PUNCT
ejpam-6199	225	3	let	let	VERB
ejpam-6199	225	4	ϑ	ϑ	X
ejpam-6199	225	5	=	=	X
ejpam-6199	225	6	{	{	PUNCT
ejpam-6199	225	7	0	0	NUM
ejpam-6199	225	8	,	,	PUNCT
ejpam-6199	225	9	1	1	NUM
ejpam-6199	225	10	,	,	PUNCT
ejpam-6199	225	11	2ϑ	2ϑ	NUM
ejpam-6199	225	12	,	,	PUNCT
ejpam-6199	225	13	3ϑ	3ϑ	NUM
ejpam-6199	225	14	}	}	PUNCT
ejpam-6199	225	15	be	be	AUX
ejpam-6199	225	16	a	a	DET
ejpam-6199	225	17	set	set	NOUN
ejpam-6199	225	18	.	.	PUNCT
ejpam-6199	226	1	the	the	DET
ejpam-6199	226	2	hasse	hasse	PROPN
ejpam-6199	226	3	diagram	diagram	PROPN
ejpam-6199	226	4	and	and	CCONJ
ejpam-6199	226	5	sheffer	sheffer	PROPN
ejpam-6199	226	6	stroke	stroke	NOUN
ejpam-6199	226	7	“	"	PUNCT
ejpam-6199	226	8	|	|	ADV
ejpam-6199	226	9	”	"	PUNCT
ejpam-6199	226	10	on	on	ADP
ejpam-6199	226	11	ϑ	ϑ	PRON
ejpam-6199	226	12	,	,	PUNCT
ejpam-6199	226	13	which	which	PRON
ejpam-6199	226	14	are	be	AUX
ejpam-6199	226	15	shown	show	VERB
ejpam-6199	226	16	in	in	ADP
ejpam-6199	226	17	figure	figure	NOUN
ejpam-6199	226	18	2	2	NUM
ejpam-6199	226	19	and	and	CCONJ
ejpam-6199	226	20	table	table	NOUN
ejpam-6199	226	21	6	6	NUM
ejpam-6199	226	22	,	,	PUNCT
ejpam-6199	226	23	respectively	respectively	ADV
ejpam-6199	226	24	.	.	PUNCT
ejpam-6199	226	25	figure	figure	NOUN
ejpam-6199	226	26	2	2	NUM
ejpam-6199	226	27	:	:	PUNCT
ejpam-6199	226	28	hasse	hasse	PROPN
ejpam-6199	226	29	diagram	diagram	PROPN
ejpam-6199	226	30	a.	a.	PROPN
ejpam-6199	226	31	al	al	PROPN
ejpam-6199	226	32	-	-	PROPN
ejpam-6199	226	33	masarwah	masarwah	PROPN
ejpam-6199	226	34	et	et	PROPN
ejpam-6199	226	35	al	al	PROPN
ejpam-6199	226	36	.	.	PUNCT
ejpam-6199	226	37	/	/	SYM
ejpam-6199	226	38	eur	eur	PROPN
ejpam-6199	226	39	.	.	PUNCT
ejpam-6199	227	1	j.	j.	PROPN
ejpam-6199	227	2	pure	pure	PROPN
ejpam-6199	227	3	appl	appl	PROPN
ejpam-6199	227	4	.	.	PROPN
ejpam-6199	227	5	math	math	PROPN
ejpam-6199	227	6	,	,	PUNCT
ejpam-6199	227	7	18	18	NUM
ejpam-6199	227	8	(	(	PUNCT
ejpam-6199	227	9	3	3	NUM
ejpam-6199	227	10	)	)	PUNCT
ejpam-6199	227	11	(	(	PUNCT
ejpam-6199	227	12	2025	2025	NUM
ejpam-6199	227	13	)	)	PUNCT
ejpam-6199	227	14	,	,	PUNCT
ejpam-6199	227	15	6199	6199	NUM
ejpam-6199	227	16	9	9	NUM
ejpam-6199	227	17	of	of	ADP
ejpam-6199	227	18	17	17	NUM
ejpam-6199	227	19	table	table	NOUN
ejpam-6199	227	20	6	6	NUM
ejpam-6199	227	21	:	:	PUNCT
ejpam-6199	227	22	cayley	cayley	ADJ
ejpam-6199	227	23	table	table	NOUN
ejpam-6199	227	24	for	for	ADP
ejpam-6199	227	25	the	the	DET
ejpam-6199	227	26	sheffer	sheffer	NOUN
ejpam-6199	227	27	stroke	stroke	NOUN
ejpam-6199	227	28	“	"	PUNCT
ejpam-6199	227	29	|	|	ADV
ejpam-6199	227	30	”	"	PUNCT
ejpam-6199	228	1	|	|	ADV
ejpam-6199	228	2	1	1	NUM
ejpam-6199	228	3	2ϑ	2ϑ	NUM
ejpam-6199	228	4	3ϑ	3ϑ	NUM
ejpam-6199	228	5	0	0	NUM
ejpam-6199	229	1	1	1	NUM
ejpam-6199	229	2	0	0	NUM
ejpam-6199	229	3	3ϑ	3ϑ	NUM
ejpam-6199	229	4	2ϑ	2ϑ	NUM
ejpam-6199	229	5	1	1	NUM
ejpam-6199	229	6	2ϑ	2ϑ	NUM
ejpam-6199	229	7	3ϑ	3ϑ	NUM
ejpam-6199	229	8	3ϑ	3ϑ	NUM
ejpam-6199	229	9	1	1	NUM
ejpam-6199	229	10	1	1	NUM
ejpam-6199	229	11	3ϑ	3ϑ	NUM
ejpam-6199	229	12	2ϑ	2ϑ	NUM
ejpam-6199	229	13	1	1	NUM
ejpam-6199	229	14	2ϑ	2ϑ	NUM
ejpam-6199	229	15	1	1	NUM
ejpam-6199	229	16	0	0	NUM
ejpam-6199	229	17	1	1	NUM
ejpam-6199	229	18	1	1	NUM
ejpam-6199	229	19	1	1	NUM
ejpam-6199	229	20	1	1	NUM
ejpam-6199	229	21	then	then	ADV
ejpam-6199	229	22	,	,	PUNCT
ejpam-6199	229	23	ϑ	ϑ	VERB
ejpam-6199	229	24	◦	◦	NOUN
ejpam-6199	229	25	:	:	PUNCT
ejpam-6199	229	26	=	=	SYM
ejpam-6199	229	27	(	(	PUNCT
ejpam-6199	229	28	ϑ	ϑ	X
ejpam-6199	229	29	,	,	PUNCT
ejpam-6199	229	30	|	|	NOUN
ejpam-6199	229	31	)	)	PUNCT
ejpam-6199	229	32	is	be	AUX
ejpam-6199	229	33	a	a	DET
ejpam-6199	229	34	sheffer	sheffer	NOUN
ejpam-6199	229	35	stroke	stroke	NOUN
ejpam-6199	229	36	hilbert	hilbert	PROPN
ejpam-6199	229	37	algebra	algebra	PROPN
ejpam-6199	229	38	(	(	PUNCT
ejpam-6199	229	39	see	see	VERB
ejpam-6199	229	40	[	[	X
ejpam-6199	229	41	13	13	NUM
ejpam-6199	229	42	]	]	NUM
ejpam-6199	229	43	)	)	PUNCT
ejpam-6199	229	44	.	.	PUNCT
ejpam-6199	230	1	let	let	VERB
ejpam-6199	230	2	π	π	PROPN
ejpam-6199	230	3	=	=	SYM
ejpam-6199	230	4	(	(	PUNCT
ejpam-6199	230	5	υ̃π	υ̃π	PROPN
ejpam-6199	230	6	,	,	PUNCT
ejpam-6199	230	7	ϖπ	ϖπ	NOUN
ejpam-6199	230	8	)	)	PUNCT
ejpam-6199	230	9	be	be	AUX
ejpam-6199	230	10	a	a	DET
ejpam-6199	230	11	crossing	cross	VERB
ejpam-6199	230	12	cubic	cubic	ADJ
ejpam-6199	230	13	structure	structure	NOUN
ejpam-6199	230	14	in	in	ADP
ejpam-6199	230	15	ϑ	ϑ	NOUN
ejpam-6199	230	16	which	which	PRON
ejpam-6199	230	17	is	be	AUX
ejpam-6199	230	18	shown	show	VERB
ejpam-6199	230	19	in	in	ADP
ejpam-6199	230	20	table	table	NOUN
ejpam-6199	230	21	7	7	NUM
ejpam-6199	230	22	.	.	PUNCT
ejpam-6199	230	23	table	table	NOUN
ejpam-6199	230	24	7	7	NUM
ejpam-6199	230	25	:	:	PUNCT
ejpam-6199	230	26	π	π	X
ejpam-6199	230	27	=	=	SYM
ejpam-6199	230	28	(	(	PUNCT
ejpam-6199	230	29	υ̃π	υ̃π	PROPN
ejpam-6199	230	30	,	,	PUNCT
ejpam-6199	230	31	ϖπ	ϖπ	NOUN
ejpam-6199	230	32	)	)	PUNCT
ejpam-6199	230	33	is	be	AUX
ejpam-6199	230	34	represented	represent	VERB
ejpam-6199	230	35	tabularly	tabularly	ADV
ejpam-6199	230	36	ϑ	ϑ	X
ejpam-6199	230	37	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	230	38	)	)	PUNCT
ejpam-6199	231	1	ϖπ(n	ϖπ(n	ADP
ejpam-6199	231	2	)	)	PUNCT
ejpam-6199	231	3	0	0	PUNCT
ejpam-6199	232	1	[	[	X
ejpam-6199	232	2	0.29,0.63	0.29,0.63	X
ejpam-6199	232	3	]	]	X
ejpam-6199	232	4	-0.13	-0.13	NUM
ejpam-6199	232	5	2ϑ	2ϑ	NUM
ejpam-6199	233	1	[	[	X
ejpam-6199	233	2	0.32,0.67	0.32,0.67	X
ejpam-6199	233	3	]	]	X
ejpam-6199	233	4	-0.38	-0.38	VERB
ejpam-6199	233	5	3ϑ	3ϑ	NUM
ejpam-6199	234	1	[	[	X
ejpam-6199	234	2	0.36,0.75	0.36,0.75	X
ejpam-6199	234	3	]	]	X
ejpam-6199	234	4	-0.55	-0.55	NOUN
ejpam-6199	234	5	1	1	NUM
ejpam-6199	235	1	[	[	NOUN
ejpam-6199	235	2	0.47,0.89	0.47,0.89	X
ejpam-6199	235	3	]	]	X
ejpam-6199	235	4	-0.82	-0.82	NUM
ejpam-6199	235	5	it	it	PRON
ejpam-6199	235	6	is	be	AUX
ejpam-6199	235	7	customary	customary	ADJ
ejpam-6199	235	8	to	to	PART
ejpam-6199	235	9	check	check	VERB
ejpam-6199	235	10	that	that	DET
ejpam-6199	235	11	π	π	PROPN
ejpam-6199	235	12	=	=	PRON
ejpam-6199	235	13	(	(	PUNCT
ejpam-6199	235	14	υ̃π	υ̃π	PROPN
ejpam-6199	235	15	,	,	PUNCT
ejpam-6199	235	16	ϖπ	ϖπ	NOUN
ejpam-6199	235	17	)	)	PUNCT
ejpam-6199	235	18	in	in	ADP
ejpam-6199	235	19	ϑ	ϑ	PRON
ejpam-6199	235	20	satisfies	satisfie	NOUN
ejpam-6199	235	21	condition	condition	NOUN
ejpam-6199	235	22	(	(	PUNCT
ejpam-6199	235	23	ii	ii	NOUN
ejpam-6199	235	24	)	)	PUNCT
ejpam-6199	235	25	of	of	ADP
ejpam-6199	235	26	proposition	proposition	NOUN
ejpam-6199	235	27	2	2	NUM
ejpam-6199	235	28	,	,	PUNCT
ejpam-6199	235	29	but	but	CCONJ
ejpam-6199	235	30	it	it	PRON
ejpam-6199	235	31	is	be	AUX
ejpam-6199	235	32	not	not	PART
ejpam-6199	235	33	a	a	DET
ejpam-6199	235	34	crossing	cross	VERB
ejpam-6199	235	35	cubic	cubic	ADJ
ejpam-6199	235	36	filter	filter	NOUN
ejpam-6199	235	37	of	of	ADP
ejpam-6199	235	38	ϑ	ϑ	PRON
ejpam-6199	235	39	since	since	SCONJ
ejpam-6199	236	1	υ̃π((0	υ̃π((0	ADP
ejpam-6199	237	1	|	|	INTJ
ejpam-6199	237	2	(	(	PUNCT
ejpam-6199	237	3	2ϑ	2ϑ	NUM
ejpam-6199	237	4	|	|	NOUN
ejpam-6199	237	5	3ϑ	3ϑ	NUM
ejpam-6199	237	6	)	)	PUNCT
ejpam-6199	237	7	)	)	PUNCT
ejpam-6199	238	1	|	|	CCONJ
ejpam-6199	238	2	(	(	PUNCT
ejpam-6199	238	3	2ϑ	2ϑ	NUM
ejpam-6199	238	4	|	|	NOUN
ejpam-6199	238	5	3ϑ	3ϑ	NUM
ejpam-6199	238	6	)	)	PUNCT
ejpam-6199	238	7	)	)	PUNCT
ejpam-6199	239	1	=	=	PUNCT
ejpam-6199	239	2	υ̃π(0	υ̃π(0	NUM
ejpam-6199	239	3	)	)	PUNCT
ejpam-6199	239	4	=	=	PUNCT
ejpam-6199	240	1	[	[	X
ejpam-6199	240	2	0.29	0.29	NUM
ejpam-6199	240	3	,	,	PUNCT
ejpam-6199	240	4	0.63	0.63	NUM
ejpam-6199	240	5	]	]	PUNCT
ejpam-6199	240	6	⪰̸	⪰̸	PUNCT
ejpam-6199	240	7	[	[	X
ejpam-6199	240	8	0.32	0.32	NUM
ejpam-6199	240	9	,	,	PUNCT
ejpam-6199	240	10	0.67	0.67	NUM
ejpam-6199	240	11	]	]	PUNCT
ejpam-6199	240	12	=	=	PUNCT
ejpam-6199	240	13	m̃in{υ̃π(2ϑ	m̃in{υ̃π(2ϑ	PROPN
ejpam-6199	240	14	)	)	PUNCT
ejpam-6199	240	15	,	,	PUNCT
ejpam-6199	240	16	υ̃π(3ϑ	υ̃π(3ϑ	NUM
ejpam-6199	240	17	)	)	PUNCT
ejpam-6199	240	18	}	}	PUNCT
ejpam-6199	240	19	or	or	CCONJ
ejpam-6199	240	20	ϖπ((0	ϖπ((0	PUNCT
ejpam-6199	241	1	|	|	ADV
ejpam-6199	241	2	(	(	PUNCT
ejpam-6199	241	3	2ϑ	2ϑ	NUM
ejpam-6199	241	4	|	|	NOUN
ejpam-6199	241	5	3ϑ	3ϑ	NUM
ejpam-6199	241	6	)	)	PUNCT
ejpam-6199	241	7	)	)	PUNCT
ejpam-6199	242	1	|	|	CCONJ
ejpam-6199	242	2	(	(	PUNCT
ejpam-6199	242	3	2ϑ	2ϑ	NUM
ejpam-6199	242	4	|	|	NOUN
ejpam-6199	242	5	3ϑ	3ϑ	NUM
ejpam-6199	242	6	)	)	PUNCT
ejpam-6199	242	7	)	)	PUNCT
ejpam-6199	243	1	=	=	PUNCT
ejpam-6199	243	2	ϖπ(0	ϖπ(0	NOUN
ejpam-6199	243	3	)	)	PUNCT
ejpam-6199	243	4	=	=	PUNCT
ejpam-6199	244	1	−0.13	−0.13	NUM
ejpam-6199	244	2	⩽̸	⩽̸	NOUN
ejpam-6199	244	3	−0.38	−0.38	PROPN
ejpam-6199	244	4	=	=	PUNCT
ejpam-6199	244	5	max{ϖπ(2ϑ	max{ϖπ(2ϑ	PROPN
ejpam-6199	244	6	)	)	PUNCT
ejpam-6199	244	7	,	,	PUNCT
ejpam-6199	244	8	ϖπ(3ϑ	ϖπ(3ϑ	NUM
ejpam-6199	244	9	)	)	PUNCT
ejpam-6199	244	10	}	}	PUNCT
ejpam-6199	244	11	.	.	PUNCT
ejpam-6199	245	1	next	next	ADV
ejpam-6199	245	2	,	,	PUNCT
ejpam-6199	245	3	we	we	PRON
ejpam-6199	245	4	propose	propose	VERB
ejpam-6199	245	5	conditions	condition	NOUN
ejpam-6199	245	6	under	under	ADP
ejpam-6199	245	7	which	which	PRON
ejpam-6199	245	8	a	a	DET
ejpam-6199	245	9	crossing	cross	VERB
ejpam-6199	245	10	cubic	cubic	ADJ
ejpam-6199	245	11	structure	structure	NOUN
ejpam-6199	245	12	π	π	PROPN
ejpam-6199	245	13	=	=	SYM
ejpam-6199	245	14	(	(	PUNCT
ejpam-6199	245	15	υ̃π	υ̃π	PROPN
ejpam-6199	245	16	,	,	PUNCT
ejpam-6199	245	17	ϖπ	ϖπ	NOUN
ejpam-6199	245	18	)	)	PUNCT
ejpam-6199	245	19	is	be	AUX
ejpam-6199	245	20	a	a	DET
ejpam-6199	245	21	crossing	cross	VERB
ejpam-6199	245	22	cubic	cubic	ADJ
ejpam-6199	245	23	filter	filter	NOUN
ejpam-6199	245	24	of	of	ADP
ejpam-6199	245	25	ϑ.	ϑ.	NOUN
ejpam-6199	245	26	theorem	theorem	VERB
ejpam-6199	245	27	1	1	X
ejpam-6199	245	28	.	.	PUNCT
ejpam-6199	246	1	let	let	VERB
ejpam-6199	246	2	π	π	PROPN
ejpam-6199	246	3	=	=	SYM
ejpam-6199	246	4	(	(	PUNCT
ejpam-6199	246	5	υ̃π	υ̃π	PROPN
ejpam-6199	246	6	,	,	PUNCT
ejpam-6199	246	7	ϖπ	ϖπ	NOUN
ejpam-6199	246	8	)	)	PUNCT
ejpam-6199	246	9	be	be	AUX
ejpam-6199	246	10	a	a	DET
ejpam-6199	246	11	crossing	cross	VERB
ejpam-6199	246	12	cubic	cubic	ADJ
ejpam-6199	246	13	structure	structure	NOUN
ejpam-6199	246	14	in	in	ADP
ejpam-6199	246	15	ϑ.	ϑ.	NOUN
ejpam-6199	246	16	then	then	ADV
ejpam-6199	246	17	,	,	PUNCT
ejpam-6199	246	18	π	π	PROPN
ejpam-6199	246	19	=	=	SYM
ejpam-6199	246	20	(	(	PUNCT
ejpam-6199	246	21	υ̃π	υ̃π	PROPN
ejpam-6199	246	22	,	,	PUNCT
ejpam-6199	246	23	ϖπ	ϖπ	NOUN
ejpam-6199	246	24	)	)	PUNCT
ejpam-6199	246	25	is	be	AUX
ejpam-6199	246	26	a	a	DET
ejpam-6199	246	27	crossing	cross	VERB
ejpam-6199	246	28	cubic	cubic	ADJ
ejpam-6199	246	29	filter	filter	NOUN
ejpam-6199	246	30	of	of	ADP
ejpam-6199	246	31	ϑ	ϑ	NOUN
ejpam-6199	246	32	if	if	SCONJ
ejpam-6199	247	1	and	and	CCONJ
ejpam-6199	247	2	only	only	ADV
ejpam-6199	247	3	if	if	SCONJ
ejpam-6199	247	4	it	it	PRON
ejpam-6199	247	5	satisfies	satisfy	VERB
ejpam-6199	247	6	(	(	PUNCT
ejpam-6199	247	7	ii	ii	NOUN
ejpam-6199	247	8	)	)	PUNCT
ejpam-6199	247	9	of	of	ADP
ejpam-6199	247	10	proposition	proposition	NOUN
ejpam-6199	247	11	2	2	NUM
ejpam-6199	247	12	and	and	CCONJ
ejpam-6199	247	13	condition	condition	NOUN
ejpam-6199	247	14	(	(	PUNCT
ejpam-6199	247	15	b	b	NOUN
ejpam-6199	247	16	)	)	PUNCT
ejpam-6199	247	17	,	,	PUNCT
ejpam-6199	248	1	where	where	SCONJ
ejpam-6199	248	2	(	(	PUNCT
ejpam-6199	248	3	b	b	NOUN
ejpam-6199	248	4	)	)	PUNCT
ejpam-6199	248	5	(	(	PUNCT
ejpam-6199	248	6	∀n	∀n	X
ejpam-6199	248	7	,	,	PUNCT
ejpam-6199	248	8	v	v	NOUN
ejpam-6199	248	9	∈	∈	PROPN
ejpam-6199	248	10	ϑ	ϑ	NOUN
ejpam-6199	248	11	)	)	PUNCT
ejpam-6199	248	12	(	(	PUNCT
ejpam-6199	248	13	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	248	14	|	|	ADV
ejpam-6199	248	15	v	v	NOUN
ejpam-6199	248	16	)	)	PUNCT
ejpam-6199	248	17	|	|	ADV
ejpam-6199	248	18	(	(	PUNCT
ejpam-6199	248	19	n	n	CCONJ
ejpam-6199	248	20	|	|	ADV
ejpam-6199	248	21	v	v	NOUN
ejpam-6199	248	22	)	)	PUNCT
ejpam-6199	248	23	)	)	PUNCT
ejpam-6199	248	24	⪰	⪰	NOUN
ejpam-6199	248	25	m̃in{υ̃π(n	m̃in{υ̃π(n	PROPN
ejpam-6199	248	26	)	)	PUNCT
ejpam-6199	248	27	,	,	PUNCT
ejpam-6199	248	28	υ̃π(v	υ̃π(v	NUM
ejpam-6199	248	29	)	)	PUNCT
ejpam-6199	248	30	}	}	PUNCT
ejpam-6199	248	31	,	,	PUNCT
ejpam-6199	248	32	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	248	33	|	|	CCONJ
ejpam-6199	248	34	v	v	NOUN
ejpam-6199	248	35	)	)	PUNCT
ejpam-6199	249	1	|	|	ADV
ejpam-6199	249	2	(	(	PUNCT
ejpam-6199	249	3	n	n	CCONJ
ejpam-6199	249	4	|	|	ADV
ejpam-6199	249	5	v	v	NOUN
ejpam-6199	249	6	)	)	PUNCT
ejpam-6199	249	7	)	)	PUNCT
ejpam-6199	250	1	≤	≤	NUM
ejpam-6199	250	2	max{ϖπ(n	max{ϖπ(n	PROPN
ejpam-6199	250	3	)	)	PUNCT
ejpam-6199	250	4	,	,	PUNCT
ejpam-6199	250	5	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	250	6	)	)	PUNCT
ejpam-6199	250	7	}	}	PUNCT
ejpam-6199	250	8	)	)	PUNCT
ejpam-6199	250	9	.	.	PUNCT
ejpam-6199	251	1	proof	proof	NOUN
ejpam-6199	251	2	.	.	PUNCT
ejpam-6199	252	1	let	let	VERB
ejpam-6199	252	2	π	π	PROPN
ejpam-6199	252	3	=	=	SYM
ejpam-6199	252	4	(	(	PUNCT
ejpam-6199	252	5	υ̃π	υ̃π	PROPN
ejpam-6199	252	6	,	,	PUNCT
ejpam-6199	252	7	ϖπ	ϖπ	NOUN
ejpam-6199	252	8	)	)	PUNCT
ejpam-6199	252	9	be	be	AUX
ejpam-6199	252	10	a	a	DET
ejpam-6199	252	11	crossing	cross	VERB
ejpam-6199	252	12	cubic	cubic	ADJ
ejpam-6199	252	13	filter	filter	NOUN
ejpam-6199	252	14	of	of	ADP
ejpam-6199	252	15	ϑ.	ϑ.	NOUN
ejpam-6199	252	16	proposition	proposition	NOUN
ejpam-6199	252	17	2	2	NUM
ejpam-6199	252	18	establishes	establish	VERB
ejpam-6199	252	19	the	the	DET
ejpam-6199	252	20	validity	validity	NOUN
ejpam-6199	252	21	of	of	ADP
ejpam-6199	252	22	condition	condition	NOUN
ejpam-6199	252	23	(	(	PUNCT
ejpam-6199	252	24	ii	ii	NOUN
ejpam-6199	252	25	)	)	PUNCT
ejpam-6199	252	26	.	.	PUNCT
ejpam-6199	253	1	now	now	ADV
ejpam-6199	253	2	,	,	PUNCT
ejpam-6199	253	3	using	use	VERB
ejpam-6199	253	4	(	(	PUNCT
ejpam-6199	253	5	1	1	NUM
ejpam-6199	253	6	)	)	PUNCT
ejpam-6199	253	7	and	and	CCONJ
ejpam-6199	253	8	(	(	PUNCT
ejpam-6199	253	9	2	2	X
ejpam-6199	253	10	)	)	PUNCT
ejpam-6199	253	11	of	of	ADP
ejpam-6199	253	12	definition	definition	NOUN
ejpam-6199	253	13	1	1	NUM
ejpam-6199	253	14	,	,	PUNCT
ejpam-6199	253	15	as	as	ADV
ejpam-6199	253	16	well	well	ADV
ejpam-6199	253	17	as	as	ADP
ejpam-6199	253	18	(	(	PUNCT
ejpam-6199	253	19	2	2	NUM
ejpam-6199	253	20	)	)	PUNCT
ejpam-6199	253	21	and	and	CCONJ
ejpam-6199	253	22	(	(	PUNCT
ejpam-6199	253	23	3	3	X
ejpam-6199	253	24	)	)	PUNCT
ejpam-6199	253	25	of	of	ADP
ejpam-6199	253	26	proposition	proposition	NOUN
ejpam-6199	253	27	1	1	NUM
ejpam-6199	253	28	,	,	PUNCT
ejpam-6199	253	29	we	we	PRON
ejpam-6199	253	30	get	get	VERB
ejpam-6199	253	31	(	(	PUNCT
ejpam-6199	253	32	(	(	PUNCT
ejpam-6199	253	33	1	1	NUM
ejpam-6199	253	34	|	|	ADV
ejpam-6199	253	35	1	1	X
ejpam-6199	253	36	)	)	PUNCT
ejpam-6199	254	1	|	|	ADV
ejpam-6199	254	2	(	(	PUNCT
ejpam-6199	254	3	n	n	CCONJ
ejpam-6199	254	4	|	|	ADV
ejpam-6199	254	5	v	v	NOUN
ejpam-6199	254	6	)	)	PUNCT
ejpam-6199	254	7	)	)	PUNCT
ejpam-6199	255	1	|	|	ADV
ejpam-6199	255	2	(	(	PUNCT
ejpam-6199	255	3	n	n	CCONJ
ejpam-6199	255	4	|	|	ADV
ejpam-6199	255	5	v	v	NOUN
ejpam-6199	255	6	)	)	PUNCT
ejpam-6199	255	7	=	=	SYM
ejpam-6199	255	8	(	(	PUNCT
ejpam-6199	255	9	(	(	PUNCT
ejpam-6199	255	10	n	n	CCONJ
ejpam-6199	255	11	|	|	ADV
ejpam-6199	255	12	v	v	NOUN
ejpam-6199	255	13	)	)	PUNCT
ejpam-6199	255	14	|	|	ADV
ejpam-6199	255	15	(	(	PUNCT
ejpam-6199	255	16	1	1	NUM
ejpam-6199	255	17	|	|	ADV
ejpam-6199	255	18	1	1	NUM
ejpam-6199	255	19	)	)	PUNCT
ejpam-6199	255	20	)	)	PUNCT
ejpam-6199	256	1	|	|	ADV
ejpam-6199	256	2	(	(	PUNCT
ejpam-6199	256	3	n	n	CCONJ
ejpam-6199	256	4	|	|	ADV
ejpam-6199	256	5	v	v	NOUN
ejpam-6199	256	6	)	)	PUNCT
ejpam-6199	256	7	=	=	SYM
ejpam-6199	256	8	1	1	NUM
ejpam-6199	257	1	|	|	ADV
ejpam-6199	257	2	(	(	PUNCT
ejpam-6199	257	3	n	n	CCONJ
ejpam-6199	257	4	|	|	ADV
ejpam-6199	257	5	v	v	NOUN
ejpam-6199	257	6	)	)	PUNCT
ejpam-6199	258	1	=	=	SYM
ejpam-6199	258	2	1	1	NUM
ejpam-6199	258	3	|	|	ADV
ejpam-6199	258	4	(	(	PUNCT
ejpam-6199	258	5	(	(	PUNCT
ejpam-6199	258	6	(	(	PUNCT
ejpam-6199	258	7	n	n	CCONJ
ejpam-6199	258	8	|	|	ADV
ejpam-6199	258	9	v	v	NOUN
ejpam-6199	258	10	)	)	PUNCT
ejpam-6199	259	1	|	|	ADV
ejpam-6199	259	2	(	(	PUNCT
ejpam-6199	259	3	n	n	CCONJ
ejpam-6199	259	4	|	|	ADV
ejpam-6199	259	5	v	v	NOUN
ejpam-6199	259	6	)	)	PUNCT
ejpam-6199	259	7	)	)	PUNCT
ejpam-6199	260	1	|	|	ADV
ejpam-6199	260	2	(	(	PUNCT
ejpam-6199	260	3	(	(	PUNCT
ejpam-6199	260	4	n	n	CCONJ
ejpam-6199	260	5	|	|	ADV
ejpam-6199	260	6	v	v	NOUN
ejpam-6199	260	7	)	)	PUNCT
ejpam-6199	260	8	|	|	ADV
ejpam-6199	260	9	(	(	PUNCT
ejpam-6199	260	10	n	n	CCONJ
ejpam-6199	260	11	|	|	ADV
ejpam-6199	260	12	v	v	NOUN
ejpam-6199	260	13	)	)	PUNCT
ejpam-6199	260	14	)	)	PUNCT
ejpam-6199	260	15	)	)	PUNCT
ejpam-6199	261	1	=	=	PUNCT
ejpam-6199	261	2	(	(	PUNCT
ejpam-6199	261	3	n	n	CCONJ
ejpam-6199	261	4	|	|	ADV
ejpam-6199	261	5	v	v	NOUN
ejpam-6199	261	6	)	)	PUNCT
ejpam-6199	262	1	|	|	ADV
ejpam-6199	262	2	(	(	PUNCT
ejpam-6199	262	3	n	n	CCONJ
ejpam-6199	262	4	|	|	ADV
ejpam-6199	262	5	v	v	NOUN
ejpam-6199	262	6	)	)	PUNCT
ejpam-6199	262	7	a.	a.	PROPN
ejpam-6199	262	8	al	al	PROPN
ejpam-6199	262	9	-	-	PROPN
ejpam-6199	262	10	masarwah	masarwah	PROPN
ejpam-6199	262	11	et	et	PROPN
ejpam-6199	262	12	al	al	PROPN
ejpam-6199	262	13	.	.	PUNCT
ejpam-6199	262	14	/	/	SYM
ejpam-6199	262	15	eur	eur	PROPN
ejpam-6199	262	16	.	.	PUNCT
ejpam-6199	263	1	j.	j.	PROPN
ejpam-6199	263	2	pure	pure	PROPN
ejpam-6199	263	3	appl	appl	PROPN
ejpam-6199	263	4	.	.	PROPN
ejpam-6199	263	5	math	math	PROPN
ejpam-6199	263	6	,	,	PUNCT
ejpam-6199	263	7	18	18	NUM
ejpam-6199	263	8	(	(	PUNCT
ejpam-6199	263	9	3	3	NUM
ejpam-6199	263	10	)	)	PUNCT
ejpam-6199	263	11	(	(	PUNCT
ejpam-6199	263	12	2025	2025	NUM
ejpam-6199	263	13	)	)	PUNCT
ejpam-6199	263	14	,	,	PUNCT
ejpam-6199	263	15	6199	6199	NUM
ejpam-6199	263	16	10	10	NUM
ejpam-6199	263	17	of	of	ADP
ejpam-6199	263	18	17	17	NUM
ejpam-6199	263	19	∀n	∀n	NOUN
ejpam-6199	263	20	,	,	PUNCT
ejpam-6199	263	21	v	v	ADP
ejpam-6199	263	22	∈	∈	PROPN
ejpam-6199	263	23	ϑ	ϑ	X
ejpam-6199	263	24	,	,	PUNCT
ejpam-6199	263	25	it	it	PRON
ejpam-6199	263	26	follows	follow	VERB
ejpam-6199	263	27	from	from	ADP
ejpam-6199	263	28	(	(	PUNCT
ejpam-6199	263	29	iii	iii	NOUN
ejpam-6199	263	30	)	)	PUNCT
ejpam-6199	263	31	of	of	ADP
ejpam-6199	263	32	definition	definition	NOUN
ejpam-6199	263	33	9	9	NUM
ejpam-6199	263	34	that	that	DET
ejpam-6199	263	35	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	263	36	|	|	ADV
ejpam-6199	263	37	v	v	NOUN
ejpam-6199	263	38	)	)	PUNCT
ejpam-6199	264	1	|	|	ADV
ejpam-6199	264	2	(	(	PUNCT
ejpam-6199	264	3	n	n	CCONJ
ejpam-6199	264	4	|	|	ADV
ejpam-6199	264	5	v	v	NOUN
ejpam-6199	264	6	)	)	PUNCT
ejpam-6199	264	7	)	)	PUNCT
ejpam-6199	265	1	=	=	PUNCT
ejpam-6199	266	1	υ̃π(((1	υ̃π(((1	PROPN
ejpam-6199	266	2	|	|	ADV
ejpam-6199	266	3	1	1	NUM
ejpam-6199	266	4	)	)	PUNCT
ejpam-6199	266	5	|	|	ADV
ejpam-6199	266	6	(	(	PUNCT
ejpam-6199	266	7	n	n	CCONJ
ejpam-6199	266	8	|	|	ADV
ejpam-6199	266	9	v	v	NOUN
ejpam-6199	266	10	)	)	PUNCT
ejpam-6199	266	11	)	)	PUNCT
ejpam-6199	267	1	|	|	ADV
ejpam-6199	267	2	(	(	PUNCT
ejpam-6199	267	3	n	n	CCONJ
ejpam-6199	267	4	|	|	ADV
ejpam-6199	267	5	v	v	NOUN
ejpam-6199	267	6	)	)	PUNCT
ejpam-6199	267	7	)	)	PUNCT
ejpam-6199	267	8	⪰	⪰	NOUN
ejpam-6199	267	9	m̃in{υ̃π(n	m̃in{υ̃π(n	PROPN
ejpam-6199	267	10	)	)	PUNCT
ejpam-6199	267	11	,	,	PUNCT
ejpam-6199	267	12	υ̃π(v	υ̃π(v	NUM
ejpam-6199	267	13	)	)	PUNCT
ejpam-6199	267	14	}	}	PUNCT
ejpam-6199	267	15	and	and	CCONJ
ejpam-6199	267	16	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	267	17	|	|	ADV
ejpam-6199	267	18	v	v	NOUN
ejpam-6199	267	19	)	)	PUNCT
ejpam-6199	267	20	|	|	ADV
ejpam-6199	267	21	(	(	PUNCT
ejpam-6199	267	22	n	n	CCONJ
ejpam-6199	267	23	|	|	ADV
ejpam-6199	267	24	v	v	NOUN
ejpam-6199	267	25	)	)	PUNCT
ejpam-6199	267	26	)	)	PUNCT
ejpam-6199	268	1	=	=	PUNCT
ejpam-6199	268	2	ϖπ(((1	ϖπ(((1	PROPN
ejpam-6199	268	3	|	|	ADV
ejpam-6199	268	4	1	1	X
ejpam-6199	268	5	)	)	PUNCT
ejpam-6199	269	1	|	|	ADV
ejpam-6199	269	2	(	(	PUNCT
ejpam-6199	269	3	n	n	CCONJ
ejpam-6199	269	4	|	|	ADV
ejpam-6199	269	5	v	v	NOUN
ejpam-6199	269	6	)	)	PUNCT
ejpam-6199	269	7	)	)	PUNCT
ejpam-6199	270	1	|	|	ADV
ejpam-6199	270	2	(	(	PUNCT
ejpam-6199	270	3	n	n	CCONJ
ejpam-6199	270	4	|	|	ADV
ejpam-6199	270	5	v	v	NOUN
ejpam-6199	270	6	)	)	PUNCT
ejpam-6199	270	7	)	)	PUNCT
ejpam-6199	270	8	≤	≤	NUM
ejpam-6199	270	9	max{ϖπ(n	max{ϖπ(n	PROPN
ejpam-6199	270	10	)	)	PUNCT
ejpam-6199	270	11	,	,	PUNCT
ejpam-6199	270	12	ϖπ(v	ϖπ(v	ADP
ejpam-6199	270	13	)	)	PUNCT
ejpam-6199	270	14	}	}	PUNCT
ejpam-6199	270	15	.	.	PUNCT
ejpam-6199	271	1	in	in	ADP
ejpam-6199	271	2	contrast	contrast	NOUN
ejpam-6199	271	3	,	,	PUNCT
ejpam-6199	271	4	let	let	VERB
ejpam-6199	271	5	us	we	PRON
ejpam-6199	271	6	assume	assume	VERB
ejpam-6199	271	7	that	that	SCONJ
ejpam-6199	271	8	a	a	DET
ejpam-6199	271	9	crossing	cross	VERB
ejpam-6199	271	10	cubic	cubic	ADJ
ejpam-6199	271	11	structure	structure	NOUN
ejpam-6199	271	12	π	π	PROPN
ejpam-6199	271	13	=	=	SYM
ejpam-6199	271	14	(	(	PUNCT
ejpam-6199	271	15	υ̃π	υ̃π	PROPN
ejpam-6199	271	16	,	,	PUNCT
ejpam-6199	271	17	ϖπ	ϖπ	NOUN
ejpam-6199	271	18	)	)	PUNCT
ejpam-6199	271	19	satisfies	satisfie	NOUN
ejpam-6199	271	20	(	(	PUNCT
ejpam-6199	271	21	ii	ii	NOUN
ejpam-6199	271	22	)	)	PUNCT
ejpam-6199	271	23	of	of	ADP
ejpam-6199	271	24	proposition	proposition	NOUN
ejpam-6199	271	25	2	2	NUM
ejpam-6199	271	26	and	and	CCONJ
ejpam-6199	271	27	the	the	DET
ejpam-6199	271	28	condition	condition	NOUN
ejpam-6199	271	29	(	(	PUNCT
ejpam-6199	271	30	b	b	NOUN
ejpam-6199	271	31	)	)	PUNCT
ejpam-6199	271	32	.	.	PUNCT
ejpam-6199	272	1	since	since	SCONJ
ejpam-6199	272	2	n	n	ADV
ejpam-6199	272	3	≤	≤	NUM
ejpam-6199	272	4	1	1	NUM
ejpam-6199	272	5	and	and	CCONJ
ejpam-6199	272	6	v	v	ADP
ejpam-6199	272	7	≤	≤	NOUN
ejpam-6199	273	1	n	n	CCONJ
ejpam-6199	273	2	|	|	ADV
ejpam-6199	273	3	(	(	PUNCT
ejpam-6199	273	4	v	v	NOUN
ejpam-6199	273	5	|	|	ADV
ejpam-6199	273	6	v)∀n	v)∀n	ADV
ejpam-6199	273	7	,	,	PUNCT
ejpam-6199	273	8	v	v	ADP
ejpam-6199	273	9	∈	∈	PROPN
ejpam-6199	273	10	ϑ	ϑ	NOUN
ejpam-6199	273	11	,	,	PUNCT
ejpam-6199	273	12	using	use	VERB
ejpam-6199	273	13	(	(	PUNCT
ejpam-6199	273	14	ii	ii	NOUN
ejpam-6199	273	15	)	)	PUNCT
ejpam-6199	273	16	of	of	ADP
ejpam-6199	273	17	proposition	proposition	NOUN
ejpam-6199	273	18	2	2	NUM
ejpam-6199	273	19	,	,	PUNCT
ejpam-6199	273	20	we	we	PRON
ejpam-6199	273	21	have	have	AUX
ejpam-6199	273	22	(	(	PUNCT
ejpam-6199	273	23	∀n	∀n	X
ejpam-6199	273	24	,	,	PUNCT
ejpam-6199	273	25	v	v	NOUN
ejpam-6199	273	26	∈	∈	PROPN
ejpam-6199	273	27	ϑ	ϑ	NOUN
ejpam-6199	273	28	)	)	PUNCT
ejpam-6199	273	29	(	(	PUNCT
ejpam-6199	273	30	υ̃π(1	υ̃π(1	PROPN
ejpam-6199	273	31	)	)	PUNCT
ejpam-6199	273	32	⪰	⪰	NOUN
ejpam-6199	273	33	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	273	34	)	)	PUNCT
ejpam-6199	273	35	,	,	PUNCT
ejpam-6199	273	36	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	273	37	)	)	PUNCT
ejpam-6199	273	38	≤	≤	NOUN
ejpam-6199	273	39	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	273	40	)	)	PUNCT
ejpam-6199	273	41	)	)	PUNCT
ejpam-6199	274	1	and	and	CCONJ
ejpam-6199	274	2	(	(	PUNCT
ejpam-6199	274	3	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	274	4	|	|	ADV
ejpam-6199	274	5	(	(	PUNCT
ejpam-6199	274	6	v	v	NOUN
ejpam-6199	274	7	|	|	ADV
ejpam-6199	274	8	v	v	NOUN
ejpam-6199	274	9	)	)	PUNCT
ejpam-6199	274	10	)	)	PUNCT
ejpam-6199	274	11	⪰	⪰	NOUN
ejpam-6199	274	12	υ̃π(v	υ̃π(v	NOUN
ejpam-6199	274	13	)	)	PUNCT
ejpam-6199	274	14	,	,	PUNCT
ejpam-6199	274	15	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	275	1	|	|	ADV
ejpam-6199	275	2	(	(	PUNCT
ejpam-6199	275	3	v	v	NOUN
ejpam-6199	275	4	|	|	ADV
ejpam-6199	275	5	v	v	NOUN
ejpam-6199	275	6	)	)	PUNCT
ejpam-6199	275	7	)	)	PUNCT
ejpam-6199	276	1	≤	≤	NOUN
ejpam-6199	276	2	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	276	3	)	)	PUNCT
ejpam-6199	276	4	)	)	PUNCT
ejpam-6199	276	5	,	,	PUNCT
ejpam-6199	276	6	respectively	respectively	ADV
ejpam-6199	276	7	.	.	PUNCT
ejpam-6199	277	1	in	in	ADP
ejpam-6199	277	2	(	(	PUNCT
ejpam-6199	277	3	4	4	NUM
ejpam-6199	277	4	)	)	PUNCT
ejpam-6199	277	5	of	of	ADP
ejpam-6199	277	6	proposition	proposition	NOUN
ejpam-6199	277	7	1	1	NUM
ejpam-6199	277	8	,	,	PUNCT
ejpam-6199	277	9	if	if	SCONJ
ejpam-6199	277	10	n	n	ADV
ejpam-6199	277	11	=	=	SYM
ejpam-6199	277	12	(	(	PUNCT
ejpam-6199	277	13	v	v	INTJ
ejpam-6199	277	14	|	|	ADV
ejpam-6199	277	15	w	w	NOUN
ejpam-6199	277	16	)	)	PUNCT
ejpam-6199	277	17	|	|	ADV
ejpam-6199	277	18	(	(	PUNCT
ejpam-6199	277	19	v	v	NOUN
ejpam-6199	277	20	|	|	ADV
ejpam-6199	277	21	w	w	NOUN
ejpam-6199	277	22	)	)	PUNCT
ejpam-6199	277	23	and	and	CCONJ
ejpam-6199	277	24	v	v	NOUN
ejpam-6199	277	25	=	=	SYM
ejpam-6199	277	26	n	n	NOUN
ejpam-6199	278	1	|	|	ADV
ejpam-6199	279	1	(	(	PUNCT
ejpam-6199	279	2	v	v	NOUN
ejpam-6199	279	3	|	|	ADV
ejpam-6199	279	4	w	w	NOUN
ejpam-6199	279	5	)	)	PUNCT
ejpam-6199	279	6	,	,	PUNCT
ejpam-6199	279	7	and	and	CCONJ
ejpam-6199	279	8	use	use	NOUN
ejpam-6199	279	9	(	(	PUNCT
ejpam-6199	279	10	2	2	NUM
ejpam-6199	279	11	)	)	PUNCT
ejpam-6199	279	12	of	of	ADP
ejpam-6199	279	13	definition	definition	NOUN
ejpam-6199	279	14	1	1	NUM
ejpam-6199	279	15	,	,	PUNCT
ejpam-6199	279	16	then	then	ADV
ejpam-6199	279	17	∀n	∀n	NUM
ejpam-6199	279	18	,	,	PUNCT
ejpam-6199	279	19	v	v	NOUN
ejpam-6199	279	20	,	,	PUNCT
ejpam-6199	279	21	w	w	PROPN
ejpam-6199	279	22	∈	∈	PROPN
ejpam-6199	279	23	ϑ	ϑ	X
ejpam-6199	279	24	,	,	PUNCT
ejpam-6199	279	25	(	(	PUNCT
ejpam-6199	279	26	v	v	ADP
ejpam-6199	279	27	|	|	ADV
ejpam-6199	279	28	w	w	NOUN
ejpam-6199	279	29	)	)	PUNCT
ejpam-6199	280	1	|	|	ADV
ejpam-6199	280	2	(	(	PUNCT
ejpam-6199	280	3	v	v	NOUN
ejpam-6199	280	4	|	|	ADV
ejpam-6199	280	5	w	w	NOUN
ejpam-6199	280	6	)	)	PUNCT
ejpam-6199	280	7	≤	≤	NOUN
ejpam-6199	280	8	(	(	PUNCT
ejpam-6199	280	9	n	n	CCONJ
ejpam-6199	280	10	|	|	ADV
ejpam-6199	280	11	(	(	PUNCT
ejpam-6199	280	12	v	v	NOUN
ejpam-6199	280	13	|	|	ADV
ejpam-6199	280	14	w	w	NOUN
ejpam-6199	280	15	)	)	PUNCT
ejpam-6199	280	16	)	)	PUNCT
ejpam-6199	281	1	|	|	ADV
ejpam-6199	281	2	(	(	PUNCT
ejpam-6199	281	3	(	(	PUNCT
ejpam-6199	281	4	(	(	PUNCT
ejpam-6199	281	5	v	v	NOUN
ejpam-6199	281	6	|	|	ADV
ejpam-6199	281	7	w	w	NOUN
ejpam-6199	281	8	)	)	PUNCT
ejpam-6199	281	9	|	|	ADV
ejpam-6199	281	10	(	(	PUNCT
ejpam-6199	281	11	v	v	NOUN
ejpam-6199	281	12	|	|	ADV
ejpam-6199	281	13	w	w	NOUN
ejpam-6199	281	14	)	)	PUNCT
ejpam-6199	281	15	)	)	PUNCT
ejpam-6199	282	1	|	|	ADV
ejpam-6199	282	2	(	(	PUNCT
ejpam-6199	282	3	(	(	PUNCT
ejpam-6199	282	4	v	v	INTJ
ejpam-6199	282	5	|	|	ADV
ejpam-6199	282	6	w	w	NOUN
ejpam-6199	282	7	)	)	PUNCT
ejpam-6199	282	8	|	|	ADV
ejpam-6199	282	9	(	(	PUNCT
ejpam-6199	282	10	v	v	NOUN
ejpam-6199	282	11	|	|	ADV
ejpam-6199	282	12	w	w	NOUN
ejpam-6199	282	13	)	)	PUNCT
ejpam-6199	282	14	)	)	PUNCT
ejpam-6199	282	15	)	)	PUNCT
ejpam-6199	283	1	=	=	PUNCT
ejpam-6199	283	2	(	(	PUNCT
ejpam-6199	283	3	n	n	CCONJ
ejpam-6199	283	4	|	|	ADV
ejpam-6199	283	5	(	(	PUNCT
ejpam-6199	283	6	v	v	NOUN
ejpam-6199	283	7	|	|	ADV
ejpam-6199	283	8	w	w	NOUN
ejpam-6199	283	9	)	)	PUNCT
ejpam-6199	283	10	)	)	PUNCT
ejpam-6199	284	1	|	|	ADV
ejpam-6199	284	2	(	(	PUNCT
ejpam-6199	284	3	v	v	NOUN
ejpam-6199	284	4	|	|	ADV
ejpam-6199	284	5	w	w	NOUN
ejpam-6199	284	6	)	)	PUNCT
ejpam-6199	284	7	.	.	PUNCT
ejpam-6199	285	1	using	use	VERB
ejpam-6199	285	2	(	(	PUNCT
ejpam-6199	285	3	ii	ii	NOUN
ejpam-6199	285	4	)	)	PUNCT
ejpam-6199	285	5	of	of	ADP
ejpam-6199	285	6	proposition	proposition	NOUN
ejpam-6199	285	7	2	2	NUM
ejpam-6199	285	8	and	and	CCONJ
ejpam-6199	285	9	the	the	DET
ejpam-6199	285	10	condition	condition	NOUN
ejpam-6199	285	11	(	(	PUNCT
ejpam-6199	285	12	b	b	NOUN
ejpam-6199	285	13	)	)	PUNCT
ejpam-6199	285	14	,	,	PUNCT
ejpam-6199	285	15	we	we	PRON
ejpam-6199	285	16	have	have	VERB
ejpam-6199	285	17	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	286	1	|	|	ADV
ejpam-6199	286	2	(	(	PUNCT
ejpam-6199	286	3	v	v	NOUN
ejpam-6199	286	4	|	|	ADV
ejpam-6199	286	5	w	w	NOUN
ejpam-6199	286	6	)	)	PUNCT
ejpam-6199	286	7	)	)	PUNCT
ejpam-6199	287	1	|	|	ADV
ejpam-6199	287	2	(	(	PUNCT
ejpam-6199	287	3	v	v	NOUN
ejpam-6199	287	4	|	|	ADV
ejpam-6199	287	5	w	w	NOUN
ejpam-6199	287	6	)	)	PUNCT
ejpam-6199	287	7	)	)	PUNCT
ejpam-6199	287	8	⪰	⪰	NOUN
ejpam-6199	287	9	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	287	10	|	|	CCONJ
ejpam-6199	287	11	w	w	NOUN
ejpam-6199	287	12	)	)	PUNCT
ejpam-6199	287	13	|	|	ADV
ejpam-6199	287	14	(	(	PUNCT
ejpam-6199	287	15	v	v	NOUN
ejpam-6199	287	16	|	|	ADV
ejpam-6199	287	17	w	w	NOUN
ejpam-6199	287	18	)	)	PUNCT
ejpam-6199	287	19	)	)	PUNCT
ejpam-6199	287	20	⪰	⪰	NOUN
ejpam-6199	287	21	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	287	22	)	)	PUNCT
ejpam-6199	287	23	,	,	PUNCT
ejpam-6199	287	24	υ̃π(w	υ̃π(w	ADJ
ejpam-6199	287	25	)	)	PUNCT
ejpam-6199	287	26	}	}	PUNCT
ejpam-6199	287	27	and	and	CCONJ
ejpam-6199	287	28	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	288	1	|	|	ADV
ejpam-6199	288	2	(	(	PUNCT
ejpam-6199	288	3	v	v	NOUN
ejpam-6199	288	4	|	|	ADV
ejpam-6199	288	5	w	w	NOUN
ejpam-6199	288	6	)	)	PUNCT
ejpam-6199	288	7	)	)	PUNCT
ejpam-6199	289	1	|	|	ADV
ejpam-6199	289	2	(	(	PUNCT
ejpam-6199	289	3	v	v	NOUN
ejpam-6199	289	4	|	|	ADV
ejpam-6199	289	5	w	w	NOUN
ejpam-6199	289	6	)	)	PUNCT
ejpam-6199	289	7	)	)	PUNCT
ejpam-6199	289	8	≤	≤	NUM
ejpam-6199	289	9	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	289	10	|	|	PROPN
ejpam-6199	289	11	w	w	NOUN
ejpam-6199	289	12	)	)	PUNCT
ejpam-6199	289	13	|	|	ADV
ejpam-6199	289	14	(	(	PUNCT
ejpam-6199	289	15	v	v	NOUN
ejpam-6199	289	16	|	|	ADV
ejpam-6199	289	17	w	w	NOUN
ejpam-6199	289	18	)	)	PUNCT
ejpam-6199	289	19	)	)	PUNCT
ejpam-6199	289	20	≤	≤	NUM
ejpam-6199	289	21	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	289	22	)	)	PUNCT
ejpam-6199	289	23	,	,	PUNCT
ejpam-6199	289	24	ϖπ(w	ϖπ(w	ADP
ejpam-6199	289	25	)	)	PUNCT
ejpam-6199	289	26	}	}	PUNCT
ejpam-6199	289	27	.	.	PUNCT
ejpam-6199	290	1	therefore	therefore	ADV
ejpam-6199	290	2	,	,	PUNCT
ejpam-6199	290	3	π	π	PROPN
ejpam-6199	290	4	=	=	PRON
ejpam-6199	290	5	(	(	PUNCT
ejpam-6199	290	6	υ̃π	υ̃π	PROPN
ejpam-6199	290	7	,	,	PUNCT
ejpam-6199	290	8	ϖπ	ϖπ	NOUN
ejpam-6199	290	9	)	)	PUNCT
ejpam-6199	290	10	is	be	AUX
ejpam-6199	290	11	a	a	DET
ejpam-6199	290	12	crossing	cross	VERB
ejpam-6199	290	13	cubic	cubic	ADJ
ejpam-6199	290	14	filter	filter	NOUN
ejpam-6199	290	15	of	of	ADP
ejpam-6199	290	16	ϑ.	ϑ.	NOUN
ejpam-6199	290	17	theorem	theorem	VERB
ejpam-6199	290	18	2	2	X
ejpam-6199	290	19	.	.	PUNCT
ejpam-6199	291	1	if	if	SCONJ
ejpam-6199	291	2	π	π	PROPN
ejpam-6199	291	3	=	=	PRON
ejpam-6199	291	4	(	(	PUNCT
ejpam-6199	291	5	υ̃π	υ̃π	PROPN
ejpam-6199	291	6	,	,	PUNCT
ejpam-6199	291	7	ϖπ	ϖπ	NOUN
ejpam-6199	291	8	)	)	PUNCT
ejpam-6199	291	9	is	be	AUX
ejpam-6199	291	10	a	a	DET
ejpam-6199	291	11	crossing	cross	VERB
ejpam-6199	291	12	cubic	cubic	ADJ
ejpam-6199	291	13	filter	filter	NOUN
ejpam-6199	291	14	of	of	ADP
ejpam-6199	291	15	ϑ	ϑ	NOUN
ejpam-6199	291	16	,	,	PUNCT
ejpam-6199	291	17	then	then	ADV
ejpam-6199	291	18	the	the	DET
ejpam-6199	291	19	nonempty	nonempty	NOUN
ejpam-6199	291	20	sets	set	VERB
ejpam-6199	291	21	ξ	ξ	PROPN
ejpam-6199	291	22	(	(	PUNCT
ejpam-6199	291	23	υ̃π	υ̃π	PROPN
ejpam-6199	291	24	;	;	PUNCT
ejpam-6199	291	25	τ̃	τ̃	X
ejpam-6199	291	26	)	)	PUNCT
ejpam-6199	291	27	and	and	CCONJ
ejpam-6199	291	28	ξ	ξ	PROPN
ejpam-6199	291	29	(	(	PUNCT
ejpam-6199	291	30	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	291	31	)	)	PUNCT
ejpam-6199	291	32	are	be	AUX
ejpam-6199	291	33	filters	filter	NOUN
ejpam-6199	291	34	of	of	ADP
ejpam-6199	291	35	ϑ	ϑ	NOUN
ejpam-6199	291	36	,	,	PUNCT
ejpam-6199	291	37	for	for	ADP
ejpam-6199	291	38	all	all	PRON
ejpam-6199	291	39	τ̃	τ̃	PROPN
ejpam-6199	292	1	=	=	PUNCT
ejpam-6199	293	1	[	[	X
ejpam-6199	293	2	τ−	τ−	PROPN
ejpam-6199	293	3	,	,	PUNCT
ejpam-6199	293	4	τ+	τ+	PRON
ejpam-6199	293	5	]	]	X
ejpam-6199	293	6	∈	∈	PROPN
ejpam-6199	293	7	i[0	i[0	PROPN
ejpam-6199	293	8	,	,	PUNCT
ejpam-6199	293	9	1	1	NUM
ejpam-6199	293	10	]	]	PUNCT
ejpam-6199	293	11	and	and	CCONJ
ejpam-6199	293	12	κ	κ	ADP
ejpam-6199	293	13	∈	∈	PROPN
ejpam-6199	294	1	[	[	X
ejpam-6199	294	2	−1	−1	NOUN
ejpam-6199	294	3	,	,	PUNCT
ejpam-6199	294	4	0	0	NUM
ejpam-6199	294	5	]	]	PUNCT
ejpam-6199	294	6	.	.	PUNCT
ejpam-6199	295	1	proof	proof	NOUN
ejpam-6199	295	2	.	.	PUNCT
ejpam-6199	296	1	suppose	suppose	VERB
ejpam-6199	296	2	that	that	SCONJ
ejpam-6199	296	3	π	π	PROPN
ejpam-6199	296	4	=	=	PRON
ejpam-6199	296	5	(	(	PUNCT
ejpam-6199	296	6	υ̃π	υ̃π	PROPN
ejpam-6199	296	7	,	,	PUNCT
ejpam-6199	296	8	ϖπ	ϖπ	NOUN
ejpam-6199	296	9	)	)	PUNCT
ejpam-6199	296	10	is	be	AUX
ejpam-6199	296	11	a	a	DET
ejpam-6199	296	12	crossing	cross	VERB
ejpam-6199	296	13	cubic	cubic	ADJ
ejpam-6199	296	14	filter	filter	NOUN
ejpam-6199	296	15	of	of	ADP
ejpam-6199	296	16	ϑ.	ϑ.	NOUN
ejpam-6199	296	17	let	let	VERB
ejpam-6199	296	18	τ̃	τ̃	PROPN
ejpam-6199	296	19	=	=	PUNCT
ejpam-6199	297	1	[	[	X
ejpam-6199	297	2	τ−	τ−	PROPN
ejpam-6199	297	3	,	,	PUNCT
ejpam-6199	297	4	τ+	τ+	PRON
ejpam-6199	297	5	]	]	X
ejpam-6199	297	6	∈	∈	PROPN
ejpam-6199	297	7	i[0	i[0	PROPN
ejpam-6199	297	8	,	,	PUNCT
ejpam-6199	297	9	1	1	NUM
ejpam-6199	297	10	]	]	PUNCT
ejpam-6199	297	11	and	and	CCONJ
ejpam-6199	297	12	κ	κ	PROPN
ejpam-6199	297	13	∈	∈	PROPN
ejpam-6199	298	1	[	[	X
ejpam-6199	298	2	-1	-1	X
ejpam-6199	298	3	,	,	PUNCT
ejpam-6199	298	4	0	0	NUM
ejpam-6199	298	5	]	]	PUNCT
ejpam-6199	298	6	be	be	VERB
ejpam-6199	298	7	such	such	ADJ
ejpam-6199	298	8	that	that	SCONJ
ejpam-6199	298	9	ξ	ξ	PROPN
ejpam-6199	298	10	(	(	PUNCT
ejpam-6199	298	11	υ̃π	υ̃π	PROPN
ejpam-6199	298	12	;	;	PUNCT
ejpam-6199	298	13	τ̃	τ̃	X
ejpam-6199	298	14	)	)	PUNCT
ejpam-6199	298	15	and	and	CCONJ
ejpam-6199	298	16	ξ	ξ	PROPN
ejpam-6199	298	17	(	(	PUNCT
ejpam-6199	298	18	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	298	19	)	)	PUNCT
ejpam-6199	298	20	are	be	AUX
ejpam-6199	298	21	nonempty	nonempty	ADJ
ejpam-6199	298	22	.	.	PUNCT
ejpam-6199	299	1	clearly	clearly	ADV
ejpam-6199	299	2	,	,	PUNCT
ejpam-6199	299	3	1	1	NUM
ejpam-6199	299	4	∈	∈	PROPN
ejpam-6199	299	5	ξ	ξ	X
ejpam-6199	299	6	(	(	PUNCT
ejpam-6199	299	7	υ̃π	υ̃π	PROPN
ejpam-6199	299	8	;	;	PUNCT
ejpam-6199	299	9	τ̃	τ̃	X
ejpam-6199	299	10	)	)	PUNCT
ejpam-6199	299	11	∩	∩	X
ejpam-6199	299	12	ξ	ξ	PROPN
ejpam-6199	299	13	(	(	PUNCT
ejpam-6199	299	14	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	299	15	)	)	PUNCT
ejpam-6199	299	16	by	by	ADP
ejpam-6199	299	17	(	(	PUNCT
ejpam-6199	299	18	i	i	NOUN
ejpam-6199	299	19	)	)	PUNCT
ejpam-6199	299	20	of	of	ADP
ejpam-6199	299	21	definition	definition	NOUN
ejpam-6199	299	22	9	9	NUM
ejpam-6199	299	23	.	.	PUNCT
ejpam-6199	300	1	let	let	VERB
ejpam-6199	300	2	n	n	PRON
ejpam-6199	300	3	∈	∈	PROPN
ejpam-6199	300	4	ϑ	ϑ	X
ejpam-6199	300	5	and	and	CCONJ
ejpam-6199	300	6	v	v	ADP
ejpam-6199	300	7	∈	∈	PROPN
ejpam-6199	300	8	ξ	ξ	X
ejpam-6199	300	9	(	(	PUNCT
ejpam-6199	300	10	υ̃π	υ̃π	PROPN
ejpam-6199	300	11	;	;	PUNCT
ejpam-6199	300	12	τ̃	τ̃	X
ejpam-6199	300	13	)	)	PUNCT
ejpam-6199	300	14	∩	∩	X
ejpam-6199	300	15	ξ	ξ	PROPN
ejpam-6199	300	16	(	(	PUNCT
ejpam-6199	300	17	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	300	18	)	)	PUNCT
ejpam-6199	300	19	.	.	PUNCT
ejpam-6199	301	1	then	then	ADV
ejpam-6199	301	2	,	,	PUNCT
ejpam-6199	301	3	υ̃π(v	υ̃π(v	X
ejpam-6199	301	4	)	)	PUNCT
ejpam-6199	301	5	⪰	⪰	NOUN
ejpam-6199	301	6	τ̃	τ̃	PROPN
ejpam-6199	301	7	and	and	CCONJ
ejpam-6199	301	8	ϖφ(v	ϖφ(v	NOUN
ejpam-6199	301	9	)	)	PUNCT
ejpam-6199	301	10	≤	≤	NUM
ejpam-6199	301	11	κ	κ	NOUN
ejpam-6199	301	12	.	.	PUNCT
ejpam-6199	302	1	using	use	VERB
ejpam-6199	302	2	(	(	PUNCT
ejpam-6199	302	3	ii	ii	NOUN
ejpam-6199	302	4	)	)	PUNCT
ejpam-6199	302	5	of	of	ADP
ejpam-6199	302	6	definition	definition	NOUN
ejpam-6199	302	7	9	9	NUM
ejpam-6199	302	8	,	,	PUNCT
ejpam-6199	302	9	we	we	PRON
ejpam-6199	302	10	have	have	VERB
ejpam-6199	302	11	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	303	1	|	|	ADV
ejpam-6199	303	2	(	(	PUNCT
ejpam-6199	303	3	v	v	NOUN
ejpam-6199	303	4	|	|	ADV
ejpam-6199	303	5	v	v	NOUN
ejpam-6199	303	6	)	)	PUNCT
ejpam-6199	303	7	)	)	PUNCT
ejpam-6199	304	1	⪰	⪰	VERB
ejpam-6199	304	2	υ̃π(v	υ̃π(v	NOUN
ejpam-6199	304	3	)	)	PUNCT
ejpam-6199	304	4	⪰	⪰	NOUN
ejpam-6199	304	5	τ̃	τ̃	PROPN
ejpam-6199	304	6	and	and	CCONJ
ejpam-6199	304	7	ϖπ(n	ϖπ(n	NOUN
ejpam-6199	305	1	|	|	ADV
ejpam-6199	305	2	(	(	PUNCT
ejpam-6199	305	3	v	v	NOUN
ejpam-6199	305	4	|	|	ADV
ejpam-6199	305	5	v	v	NOUN
ejpam-6199	305	6	)	)	PUNCT
ejpam-6199	305	7	)	)	PUNCT
ejpam-6199	305	8	≤	≤	NOUN
ejpam-6199	305	9	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	305	10	)	)	PUNCT
ejpam-6199	305	11	≤	≤	NUM
ejpam-6199	305	12	κ	κ	NOUN
ejpam-6199	305	13	.	.	PUNCT
ejpam-6199	306	1	hence	hence	ADV
ejpam-6199	306	2	,	,	PUNCT
ejpam-6199	306	3	n	n	CCONJ
ejpam-6199	306	4	|	|	ADV
ejpam-6199	306	5	(	(	PUNCT
ejpam-6199	306	6	v	v	NOUN
ejpam-6199	306	7	|	|	ADV
ejpam-6199	306	8	v	v	NOUN
ejpam-6199	306	9	)	)	PUNCT
ejpam-6199	306	10	∈	∈	PROPN
ejpam-6199	306	11	ξ	ξ	PROPN
ejpam-6199	306	12	(	(	PUNCT
ejpam-6199	306	13	υ̃π	υ̃π	PROPN
ejpam-6199	306	14	;	;	PUNCT
ejpam-6199	306	15	τ̃	τ̃	X
ejpam-6199	306	16	)	)	PUNCT
ejpam-6199	306	17	∩	∩	X
ejpam-6199	306	18	ξ	ξ	PROPN
ejpam-6199	306	19	(	(	PUNCT
ejpam-6199	306	20	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	306	21	)	)	PUNCT
ejpam-6199	306	22	.	.	PUNCT
ejpam-6199	307	1	let	let	VERB
ejpam-6199	307	2	n	n	PRON
ejpam-6199	307	3	∈	∈	PROPN
ejpam-6199	307	4	ϑ	ϑ	X
ejpam-6199	307	5	and	and	CCONJ
ejpam-6199	307	6	v	v	NOUN
ejpam-6199	307	7	,	,	PUNCT
ejpam-6199	307	8	w	w	PROPN
ejpam-6199	307	9	∈	∈	PROPN
ejpam-6199	307	10	ξ	ξ	X
ejpam-6199	307	11	(	(	PUNCT
ejpam-6199	307	12	υ̃π	υ̃π	PROPN
ejpam-6199	307	13	;	;	PUNCT
ejpam-6199	307	14	τ̃	τ̃	X
ejpam-6199	307	15	)	)	PUNCT
ejpam-6199	307	16	∩ξ	∩ξ	NOUN
ejpam-6199	308	1	(	(	PUNCT
ejpam-6199	308	2	ϖπ;κ	ϖπ;κ	ADP
ejpam-6199	308	3	)	)	PUNCT
ejpam-6199	308	4	.	.	PUNCT
ejpam-6199	309	1	then	then	ADV
ejpam-6199	309	2	υ̃π(v	υ̃π(v	X
ejpam-6199	309	3	)	)	PUNCT
ejpam-6199	309	4	⪰	⪰	NOUN
ejpam-6199	309	5	τ̃	τ̃	PROPN
ejpam-6199	309	6	,	,	PUNCT
ejpam-6199	309	7	ϖπ(v	ϖπ(v	ADJ
ejpam-6199	309	8	)	)	PUNCT
ejpam-6199	309	9	≤	≤	NUM
ejpam-6199	309	10	κ	κ	NOUN
ejpam-6199	309	11	,	,	PUNCT
ejpam-6199	309	12	υ̃π(w	υ̃π(w	ADJ
ejpam-6199	309	13	)	)	PUNCT
ejpam-6199	309	14	⪰	⪰	NOUN
ejpam-6199	309	15	τ̃	τ̃	PROPN
ejpam-6199	309	16	and	and	CCONJ
ejpam-6199	309	17	ϖπ(w	ϖπ(w	NOUN
ejpam-6199	309	18	)	)	PUNCT
ejpam-6199	309	19	≤	≤	NUM
ejpam-6199	309	20	κ	κ	NOUN
ejpam-6199	309	21	.	.	PUNCT
ejpam-6199	310	1	it	it	PRON
ejpam-6199	310	2	follows	follow	VERB
ejpam-6199	310	3	from	from	ADP
ejpam-6199	310	4	(	(	PUNCT
ejpam-6199	310	5	iii	iii	NOUN
ejpam-6199	310	6	)	)	PUNCT
ejpam-6199	310	7	of	of	ADP
ejpam-6199	310	8	definition	definition	NOUN
ejpam-6199	310	9	9	9	NUM
ejpam-6199	310	10	that	that	DET
ejpam-6199	310	11	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	311	1	|	|	ADV
ejpam-6199	311	2	(	(	PUNCT
ejpam-6199	311	3	v	v	NOUN
ejpam-6199	311	4	|	|	ADV
ejpam-6199	311	5	w	w	NOUN
ejpam-6199	311	6	)	)	PUNCT
ejpam-6199	311	7	)	)	PUNCT
ejpam-6199	312	1	|	|	ADV
ejpam-6199	312	2	(	(	PUNCT
ejpam-6199	312	3	v	v	NOUN
ejpam-6199	312	4	|	|	ADV
ejpam-6199	312	5	w	w	NOUN
ejpam-6199	312	6	)	)	PUNCT
ejpam-6199	312	7	)	)	PUNCT
ejpam-6199	312	8	⪰	⪰	NOUN
ejpam-6199	312	9	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	312	10	)	)	PUNCT
ejpam-6199	312	11	,	,	PUNCT
ejpam-6199	312	12	υ̃(w	υ̃(w	NOUN
ejpam-6199	312	13	)	)	PUNCT
ejpam-6199	312	14	}	}	PUNCT
ejpam-6199	312	15	⪰	⪰	VERB
ejpam-6199	312	16	τ̃	τ̃	PROPN
ejpam-6199	312	17	a.	a.	PROPN
ejpam-6199	312	18	al	al	PROPN
ejpam-6199	312	19	-	-	PROPN
ejpam-6199	312	20	masarwah	masarwah	PROPN
ejpam-6199	312	21	et	et	PROPN
ejpam-6199	312	22	al	al	PROPN
ejpam-6199	312	23	.	.	PUNCT
ejpam-6199	312	24	/	/	SYM
ejpam-6199	312	25	eur	eur	PROPN
ejpam-6199	312	26	.	.	PUNCT
ejpam-6199	313	1	j.	j.	PROPN
ejpam-6199	313	2	pure	pure	PROPN
ejpam-6199	313	3	appl	appl	PROPN
ejpam-6199	313	4	.	.	PROPN
ejpam-6199	313	5	math	math	PROPN
ejpam-6199	313	6	,	,	PUNCT
ejpam-6199	313	7	18	18	NUM
ejpam-6199	313	8	(	(	PUNCT
ejpam-6199	313	9	3	3	NUM
ejpam-6199	313	10	)	)	PUNCT
ejpam-6199	313	11	(	(	PUNCT
ejpam-6199	313	12	2025	2025	NUM
ejpam-6199	313	13	)	)	PUNCT
ejpam-6199	313	14	,	,	PUNCT
ejpam-6199	313	15	6199	6199	NUM
ejpam-6199	313	16	11	11	NUM
ejpam-6199	313	17	of	of	ADP
ejpam-6199	313	18	17	17	NUM
ejpam-6199	313	19	and	and	CCONJ
ejpam-6199	313	20	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	314	1	|	|	ADV
ejpam-6199	314	2	(	(	PUNCT
ejpam-6199	314	3	v	v	NOUN
ejpam-6199	314	4	|	|	ADV
ejpam-6199	314	5	w	w	NOUN
ejpam-6199	314	6	)	)	PUNCT
ejpam-6199	314	7	)	)	PUNCT
ejpam-6199	315	1	|	|	ADV
ejpam-6199	315	2	(	(	PUNCT
ejpam-6199	315	3	v	v	NOUN
ejpam-6199	315	4	|	|	ADV
ejpam-6199	315	5	w	w	NOUN
ejpam-6199	315	6	)	)	PUNCT
ejpam-6199	315	7	)	)	PUNCT
ejpam-6199	315	8	≤	≤	NUM
ejpam-6199	315	9	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	315	10	)	)	PUNCT
ejpam-6199	315	11	,	,	PUNCT
ejpam-6199	315	12	ϖπ(w	ϖπ(w	ADJ
ejpam-6199	315	13	)	)	PUNCT
ejpam-6199	315	14	}	}	PUNCT
ejpam-6199	315	15	≤	≤	NUM
ejpam-6199	315	16	κ	κ	NOUN
ejpam-6199	315	17	.	.	PUNCT
ejpam-6199	316	1	thus	thus	ADV
ejpam-6199	316	2	,	,	PUNCT
ejpam-6199	316	3	(	(	PUNCT
ejpam-6199	316	4	n	n	CCONJ
ejpam-6199	316	5	|	|	ADV
ejpam-6199	316	6	(	(	PUNCT
ejpam-6199	316	7	v	v	NOUN
ejpam-6199	316	8	|	|	ADV
ejpam-6199	316	9	w	w	NOUN
ejpam-6199	316	10	)	)	PUNCT
ejpam-6199	316	11	)	)	PUNCT
ejpam-6199	317	1	|	|	ADV
ejpam-6199	317	2	(	(	PUNCT
ejpam-6199	317	3	v	v	NOUN
ejpam-6199	317	4	|	|	ADV
ejpam-6199	317	5	w	w	NOUN
ejpam-6199	317	6	)	)	PUNCT
ejpam-6199	317	7	∈	∈	PROPN
ejpam-6199	318	1	ξ	ξ	PROPN
ejpam-6199	318	2	(	(	PUNCT
ejpam-6199	318	3	υ̃π	υ̃π	PROPN
ejpam-6199	318	4	;	;	PUNCT
ejpam-6199	318	5	τ̃	τ̃	X
ejpam-6199	318	6	)	)	PUNCT
ejpam-6199	318	7	∩	∩	X
ejpam-6199	318	8	ξ	ξ	PROPN
ejpam-6199	318	9	(	(	PUNCT
ejpam-6199	318	10	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	318	11	)	)	PUNCT
ejpam-6199	318	12	.	.	PUNCT
ejpam-6199	319	1	therefore	therefore	ADV
ejpam-6199	319	2	,	,	PUNCT
ejpam-6199	319	3	ξ	ξ	PROPN
ejpam-6199	319	4	(	(	PUNCT
ejpam-6199	319	5	υ̃π	υ̃π	PROPN
ejpam-6199	319	6	;	;	PUNCT
ejpam-6199	319	7	τ̃	τ̃	X
ejpam-6199	319	8	)	)	PUNCT
ejpam-6199	319	9	and	and	CCONJ
ejpam-6199	319	10	ξ	ξ	PROPN
ejpam-6199	319	11	(	(	PUNCT
ejpam-6199	319	12	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	319	13	)	)	PUNCT
ejpam-6199	319	14	are	be	AUX
ejpam-6199	319	15	filters	filter	NOUN
ejpam-6199	319	16	of	of	ADP
ejpam-6199	319	17	ϑ.	ϑ.	NOUN
ejpam-6199	319	18	theorem	theorem	VERB
ejpam-6199	319	19	3	3	X
ejpam-6199	319	20	.	.	PUNCT
ejpam-6199	319	21	given	give	VERB
ejpam-6199	319	22	a	a	DET
ejpam-6199	319	23	crossing	cross	VERB
ejpam-6199	319	24	cubic	cubic	ADJ
ejpam-6199	319	25	structure	structure	NOUN
ejpam-6199	319	26	π	π	PROPN
ejpam-6199	319	27	=	=	SYM
ejpam-6199	319	28	(	(	PUNCT
ejpam-6199	319	29	υ̃π	υ̃π	PROPN
ejpam-6199	319	30	,	,	PUNCT
ejpam-6199	319	31	ϖπ	ϖπ	NOUN
ejpam-6199	319	32	)	)	PUNCT
ejpam-6199	319	33	in	in	ADP
ejpam-6199	319	34	ϑ.	ϑ.	NOUN
ejpam-6199	319	35	if	if	SCONJ
ejpam-6199	319	36	the	the	DET
ejpam-6199	319	37	nonempty	nonempty	NOUN
ejpam-6199	319	38	sets	set	VERB
ejpam-6199	319	39	ξ	ξ	PROPN
ejpam-6199	319	40	(	(	PUNCT
ejpam-6199	319	41	υ̃π	υ̃π	PROPN
ejpam-6199	319	42	;	;	PUNCT
ejpam-6199	319	43	τ̃	τ̃	X
ejpam-6199	319	44	)	)	PUNCT
ejpam-6199	319	45	and	and	CCONJ
ejpam-6199	319	46	ξ	ξ	PROPN
ejpam-6199	319	47	(	(	PUNCT
ejpam-6199	319	48	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	319	49	)	)	PUNCT
ejpam-6199	319	50	are	be	AUX
ejpam-6199	319	51	filters	filter	NOUN
ejpam-6199	319	52	of	of	ADP
ejpam-6199	319	53	ϑ	ϑ	NOUN
ejpam-6199	319	54	for	for	ADP
ejpam-6199	319	55	all	all	PRON
ejpam-6199	319	56	τ̃	τ̃	PROPN
ejpam-6199	320	1	=	=	PUNCT
ejpam-6199	321	1	[	[	X
ejpam-6199	321	2	τ−	τ−	PROPN
ejpam-6199	321	3	,	,	PUNCT
ejpam-6199	321	4	τ+	τ+	PRON
ejpam-6199	321	5	]	]	X
ejpam-6199	321	6	∈	∈	PROPN
ejpam-6199	321	7	i[0	i[0	PROPN
ejpam-6199	321	8	,	,	PUNCT
ejpam-6199	321	9	1	1	NUM
ejpam-6199	321	10	]	]	PUNCT
ejpam-6199	321	11	and	and	CCONJ
ejpam-6199	321	12	κ	κ	ADP
ejpam-6199	321	13	∈	∈	PROPN
ejpam-6199	322	1	[	[	X
ejpam-6199	322	2	−1	−1	NOUN
ejpam-6199	322	3	,	,	PUNCT
ejpam-6199	322	4	0	0	NUM
ejpam-6199	322	5	]	]	PUNCT
ejpam-6199	322	6	,	,	PUNCT
ejpam-6199	322	7	then	then	ADV
ejpam-6199	322	8	π	π	PROPN
ejpam-6199	322	9	=	=	SYM
ejpam-6199	322	10	(	(	PUNCT
ejpam-6199	322	11	υ̃π	υ̃π	PROPN
ejpam-6199	322	12	,	,	PUNCT
ejpam-6199	322	13	ϖπ	ϖπ	NOUN
ejpam-6199	322	14	)	)	PUNCT
ejpam-6199	322	15	is	be	AUX
ejpam-6199	322	16	a	a	DET
ejpam-6199	322	17	crossing	cross	VERB
ejpam-6199	322	18	cubic	cubic	ADJ
ejpam-6199	322	19	filter	filter	NOUN
ejpam-6199	322	20	of	of	ADP
ejpam-6199	322	21	ϑ.	ϑ.	NOUN
ejpam-6199	322	22	proof	proof	NOUN
ejpam-6199	322	23	.	.	PUNCT
ejpam-6199	323	1	assume	assume	VERB
ejpam-6199	323	2	that	that	SCONJ
ejpam-6199	323	3	ξ	ξ	PROPN
ejpam-6199	323	4	(	(	PUNCT
ejpam-6199	323	5	υ̃π	υ̃π	PROPN
ejpam-6199	323	6	;	;	PUNCT
ejpam-6199	323	7	τ̃	τ̃	X
ejpam-6199	323	8	)	)	PUNCT
ejpam-6199	323	9	and	and	CCONJ
ejpam-6199	323	10	ξ	ξ	PROPN
ejpam-6199	323	11	(	(	PUNCT
ejpam-6199	323	12	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	323	13	)	)	PUNCT
ejpam-6199	323	14	are	be	AUX
ejpam-6199	323	15	nonempty	nonempty	ADJ
ejpam-6199	323	16	filters	filter	NOUN
ejpam-6199	323	17	of	of	ADP
ejpam-6199	323	18	ϑ	ϑ	NOUN
ejpam-6199	323	19	for	for	ADP
ejpam-6199	323	20	all	all	PRON
ejpam-6199	323	21	τ̃	τ̃	PROPN
ejpam-6199	324	1	=	=	PUNCT
ejpam-6199	325	1	[	[	X
ejpam-6199	325	2	τ−	τ−	PROPN
ejpam-6199	325	3	,	,	PUNCT
ejpam-6199	325	4	τ+	τ+	PRON
ejpam-6199	325	5	]	]	X
ejpam-6199	325	6	∈	∈	PROPN
ejpam-6199	325	7	i[0	i[0	PROPN
ejpam-6199	325	8	,	,	PUNCT
ejpam-6199	325	9	1	1	NUM
ejpam-6199	325	10	]	]	PUNCT
ejpam-6199	325	11	and	and	CCONJ
ejpam-6199	325	12	κ	κ	ADP
ejpam-6199	325	13	∈	∈	PROPN
ejpam-6199	326	1	[	[	X
ejpam-6199	326	2	−1	−1	NOUN
ejpam-6199	326	3	,	,	PUNCT
ejpam-6199	326	4	0	0	NUM
ejpam-6199	326	5	]	]	PUNCT
ejpam-6199	326	6	.	.	PUNCT
ejpam-6199	327	1	let	let	VERB
ejpam-6199	327	2	n	n	PRON
ejpam-6199	327	3	∈	∈	PROPN
ejpam-6199	327	4	ϑ	ϑ	PART
ejpam-6199	327	5	be	be	AUX
ejpam-6199	327	6	such	such	ADJ
ejpam-6199	327	7	that	that	SCONJ
ejpam-6199	327	8	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	327	9	)	)	PUNCT
ejpam-6199	328	1	=	=	PUNCT
ejpam-6199	328	2	τ̃	τ̃	PROPN
ejpam-6199	328	3	.	.	PUNCT
ejpam-6199	329	1	then	then	ADV
ejpam-6199	329	2	,	,	PUNCT
ejpam-6199	329	3	n	n	PROPN
ejpam-6199	329	4	∈	∈	PROPN
ejpam-6199	329	5	ξ	ξ	X
ejpam-6199	329	6	(	(	PUNCT
ejpam-6199	329	7	υ̃π	υ̃π	PROPN
ejpam-6199	329	8	;	;	PUNCT
ejpam-6199	329	9	τ̃	τ̃	X
ejpam-6199	329	10	)	)	PUNCT
ejpam-6199	329	11	i.e.	i.e.	X
ejpam-6199	329	12	,	,	PUNCT
ejpam-6199	329	13	ξ	ξ	PROPN
ejpam-6199	329	14	(	(	PUNCT
ejpam-6199	329	15	υ̃π	υ̃π	PROPN
ejpam-6199	329	16	;	;	PUNCT
ejpam-6199	329	17	τ̃	τ̃	X
ejpam-6199	329	18	)	)	PUNCT
ejpam-6199	329	19	̸=	̸=	PROPN
ejpam-6199	329	20	ϕ	ϕ	NOUN
ejpam-6199	329	21	,	,	PUNCT
ejpam-6199	329	22	and	and	CCONJ
ejpam-6199	329	23	so	so	ADV
ejpam-6199	329	24	1	1	NUM
ejpam-6199	329	25	∈	∈	NOUN
ejpam-6199	329	26	ξ	ξ	X
ejpam-6199	329	27	(	(	PUNCT
ejpam-6199	329	28	υ̃π	υ̃π	PROPN
ejpam-6199	329	29	;	;	PUNCT
ejpam-6199	329	30	τ̃	τ̃	PROPN
ejpam-6199	329	31	)	)	PUNCT
ejpam-6199	329	32	.	.	PUNCT
ejpam-6199	330	1	hence	hence	ADV
ejpam-6199	330	2	,	,	PUNCT
ejpam-6199	330	3	υ̃π(1	υ̃π(1	PROPN
ejpam-6199	330	4	)	)	PUNCT
ejpam-6199	330	5	⪰	⪰	NOUN
ejpam-6199	330	6	τ̃	τ̃	PROPN
ejpam-6199	330	7	=	=	SYM
ejpam-6199	330	8	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	330	9	)	)	PUNCT
ejpam-6199	330	10	.	.	PUNCT
ejpam-6199	331	1	if	if	SCONJ
ejpam-6199	331	2	there	there	PRON
ejpam-6199	331	3	is	be	VERB
ejpam-6199	331	4	n	n	DET
ejpam-6199	331	5	∈	∈	NOUN
ejpam-6199	331	6	ϑ	ϑ	NOUN
ejpam-6199	331	7	such	such	ADJ
ejpam-6199	331	8	that	that	SCONJ
ejpam-6199	331	9	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	331	10	)	)	PUNCT
ejpam-6199	331	11	≰	≰	PROPN
ejpam-6199	331	12	ϖπ(n	ϖπ(n	ADJ
ejpam-6199	331	13	)	)	PUNCT
ejpam-6199	331	14	,	,	PUNCT
ejpam-6199	331	15	then	then	ADV
ejpam-6199	331	16	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	331	17	)	)	PUNCT
ejpam-6199	331	18	>	>	X
ejpam-6199	331	19	ϖπ(n	ϖπ(n	PROPN
ejpam-6199	331	20	)	)	PUNCT
ejpam-6199	331	21	.	.	PUNCT
ejpam-6199	332	1	hence	hence	ADV
ejpam-6199	332	2	,	,	PUNCT
ejpam-6199	332	3	n	n	PROPN
ejpam-6199	332	4	∈	∈	PROPN
ejpam-6199	332	5	ξ	ξ	PROPN
ejpam-6199	332	6	(	(	PUNCT
ejpam-6199	332	7	ϖπ;ϖπ(n	ϖπ;ϖπ(n	NOUN
ejpam-6199	332	8	)	)	PUNCT
ejpam-6199	332	9	)	)	PUNCT
ejpam-6199	332	10	and	and	CCONJ
ejpam-6199	332	11	1	1	NUM
ejpam-6199	332	12	/∈	/∈	SYM
ejpam-6199	332	13	ξ	ξ	PROPN
ejpam-6199	332	14	(	(	PUNCT
ejpam-6199	332	15	ϖπ;ϖπ(n	ϖπ;ϖπ(n	NOUN
ejpam-6199	332	16	)	)	PUNCT
ejpam-6199	332	17	)	)	PUNCT
ejpam-6199	332	18	,	,	PUNCT
ejpam-6199	332	19	a	a	DET
ejpam-6199	332	20	contradiction	contradiction	NOUN
ejpam-6199	332	21	.	.	PUNCT
ejpam-6199	333	1	let	let	VERB
ejpam-6199	333	2	v	v	PRON
ejpam-6199	333	3	∈	∈	PROPN
ejpam-6199	333	4	ϑ	ϑ	PART
ejpam-6199	333	5	be	be	AUX
ejpam-6199	333	6	such	such	ADJ
ejpam-6199	333	7	that	that	SCONJ
ejpam-6199	333	8	υ̃π(v	υ̃π(v	NOUN
ejpam-6199	333	9	)	)	PUNCT
ejpam-6199	333	10	=	=	SYM
ejpam-6199	334	1	τ̃	τ̃	PROPN
ejpam-6199	334	2	.	.	PUNCT
ejpam-6199	335	1	then	then	ADV
ejpam-6199	335	2	,	,	PUNCT
ejpam-6199	335	3	v	v	X
ejpam-6199	335	4	∈	∈	PROPN
ejpam-6199	335	5	ξ	ξ	X
ejpam-6199	335	6	(	(	PUNCT
ejpam-6199	335	7	υ̃π	υ̃π	PROPN
ejpam-6199	335	8	;	;	PUNCT
ejpam-6199	335	9	τ̃	τ̃	X
ejpam-6199	335	10	)	)	PUNCT
ejpam-6199	335	11	,	,	PUNCT
ejpam-6199	335	12	which	which	PRON
ejpam-6199	335	13	implies	imply	VERB
ejpam-6199	335	14	that	that	SCONJ
ejpam-6199	335	15	n	n	CCONJ
ejpam-6199	335	16	|	|	ADV
ejpam-6199	335	17	(	(	PUNCT
ejpam-6199	335	18	v	v	NOUN
ejpam-6199	335	19	|	|	ADV
ejpam-6199	335	20	v	v	NOUN
ejpam-6199	335	21	)	)	PUNCT
ejpam-6199	335	22	∈	∈	PROPN
ejpam-6199	335	23	ξ	ξ	PROPN
ejpam-6199	335	24	(	(	PUNCT
ejpam-6199	335	25	υ̃π	υ̃π	PROPN
ejpam-6199	335	26	;	;	PUNCT
ejpam-6199	335	27	τ̃	τ̃	X
ejpam-6199	335	28	)	)	PUNCT
ejpam-6199	335	29	∀n	∀n	NUM
ejpam-6199	336	1	∈	∈	PROPN
ejpam-6199	336	2	ϑ.	ϑ.	NOUN
ejpam-6199	336	3	hence	hence	ADV
ejpam-6199	336	4	,	,	PUNCT
ejpam-6199	336	5	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	336	6	|	|	ADV
ejpam-6199	336	7	(	(	PUNCT
ejpam-6199	336	8	v	v	NOUN
ejpam-6199	336	9	|	|	ADV
ejpam-6199	336	10	v	v	NOUN
ejpam-6199	336	11	)	)	PUNCT
ejpam-6199	336	12	)	)	PUNCT
ejpam-6199	336	13	⪰	⪰	VERB
ejpam-6199	336	14	τ̃	τ̃	PROPN
ejpam-6199	336	15	=	=	PUNCT
ejpam-6199	336	16	υ̃π(v	υ̃π(v	PROPN
ejpam-6199	336	17	)	)	PUNCT
ejpam-6199	336	18	.	.	PUNCT
ejpam-6199	337	1	if	if	SCONJ
ejpam-6199	337	2	there	there	PRON
ejpam-6199	337	3	are	be	VERB
ejpam-6199	337	4	n	n	PRON
ejpam-6199	337	5	,	,	PUNCT
ejpam-6199	337	6	v	v	NOUN
ejpam-6199	337	7	∈	∈	PRON
ejpam-6199	337	8	ϑ	ϑ	NOUN
ejpam-6199	337	9	such	such	ADJ
ejpam-6199	337	10	that	that	PRON
ejpam-6199	337	11	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	338	1	|	|	ADV
ejpam-6199	338	2	(	(	PUNCT
ejpam-6199	338	3	v	v	NOUN
ejpam-6199	338	4	|	|	ADV
ejpam-6199	338	5	v	v	NOUN
ejpam-6199	338	6	)	)	PUNCT
ejpam-6199	338	7	)	)	PUNCT
ejpam-6199	339	1	≰	≰	PROPN
ejpam-6199	339	2	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	339	3	)	)	PUNCT
ejpam-6199	339	4	,	,	PUNCT
ejpam-6199	339	5	then	then	ADV
ejpam-6199	339	6	ϖπ(n	ϖπ(n	ADV
ejpam-6199	340	1	|	|	ADV
ejpam-6199	340	2	(	(	PUNCT
ejpam-6199	340	3	v	v	NOUN
ejpam-6199	340	4	|	|	ADV
ejpam-6199	340	5	v	v	NOUN
ejpam-6199	340	6	)	)	PUNCT
ejpam-6199	340	7	)	)	PUNCT
ejpam-6199	340	8	>	>	PUNCT
ejpam-6199	340	9	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	340	10	)	)	PUNCT
ejpam-6199	340	11	.	.	PUNCT
ejpam-6199	341	1	it	it	PRON
ejpam-6199	341	2	follows	follow	VERB
ejpam-6199	341	3	that	that	SCONJ
ejpam-6199	341	4	v	v	NUM
ejpam-6199	341	5	∈	∈	PROPN
ejpam-6199	341	6	ξ	ξ	X
ejpam-6199	341	7	(	(	PUNCT
ejpam-6199	341	8	ϖπ;ϖπ(v	ϖπ;ϖπ(v	NUM
ejpam-6199	341	9	)	)	PUNCT
ejpam-6199	341	10	)	)	PUNCT
ejpam-6199	341	11	and	and	CCONJ
ejpam-6199	341	12	n	n	PRON
ejpam-6199	341	13	|	|	ADV
ejpam-6199	341	14	(	(	PUNCT
ejpam-6199	341	15	v	v	NOUN
ejpam-6199	341	16	|	|	NOUN
ejpam-6199	341	17	v	v	NOUN
ejpam-6199	341	18	)	)	PUNCT
ejpam-6199	341	19	/∈	/∈	PUNCT
ejpam-6199	342	1	ξ	ξ	PROPN
ejpam-6199	342	2	(	(	PUNCT
ejpam-6199	342	3	ϖπ;ϖπ(v	ϖπ;ϖπ(v	NUM
ejpam-6199	342	4	)	)	PUNCT
ejpam-6199	342	5	)	)	PUNCT
ejpam-6199	342	6	,	,	PUNCT
ejpam-6199	342	7	a	a	DET
ejpam-6199	342	8	contradiction	contradiction	NOUN
ejpam-6199	342	9	.	.	PUNCT
ejpam-6199	343	1	let	let	VERB
ejpam-6199	343	2	n	n	CCONJ
ejpam-6199	343	3	,	,	PUNCT
ejpam-6199	343	4	v	v	NOUN
ejpam-6199	343	5	,	,	PUNCT
ejpam-6199	343	6	w	w	PROPN
ejpam-6199	343	7	∈	∈	PROPN
ejpam-6199	343	8	ϑ	ϑ	PART
ejpam-6199	343	9	be	be	AUX
ejpam-6199	343	10	such	such	ADJ
ejpam-6199	343	11	that	that	SCONJ
ejpam-6199	343	12	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	343	13	)	)	PUNCT
ejpam-6199	343	14	,	,	PUNCT
ejpam-6199	343	15	υ̃π(w	υ̃π(w	NOUN
ejpam-6199	343	16	)	)	PUNCT
ejpam-6199	343	17	}	}	PUNCT
ejpam-6199	344	1	=	=	SYM
ejpam-6199	344	2	τ̃	τ̃	PROPN
ejpam-6199	344	3	.	.	PUNCT
ejpam-6199	345	1	then	then	ADV
ejpam-6199	345	2	v	v	ADP
ejpam-6199	345	3	,	,	PUNCT
ejpam-6199	345	4	w	w	PROPN
ejpam-6199	345	5	∈	∈	PROPN
ejpam-6199	345	6	ξ	ξ	X
ejpam-6199	345	7	(	(	PUNCT
ejpam-6199	345	8	υ̃π	υ̃π	PROPN
ejpam-6199	345	9	;	;	PUNCT
ejpam-6199	345	10	τ̃	τ̃	PROPN
ejpam-6199	345	11	)	)	PUNCT
ejpam-6199	345	12	.	.	PUNCT
ejpam-6199	346	1	it	it	PRON
ejpam-6199	346	2	follows	follow	VERB
ejpam-6199	346	3	that	that	PRON
ejpam-6199	346	4	(	(	PUNCT
ejpam-6199	346	5	n	n	CCONJ
ejpam-6199	346	6	|	|	ADV
ejpam-6199	346	7	(	(	PUNCT
ejpam-6199	346	8	v	v	NOUN
ejpam-6199	346	9	|	|	ADV
ejpam-6199	346	10	w	w	NOUN
ejpam-6199	346	11	)	)	PUNCT
ejpam-6199	346	12	)	)	PUNCT
ejpam-6199	347	1	|	|	ADV
ejpam-6199	347	2	(	(	PUNCT
ejpam-6199	347	3	v	v	NOUN
ejpam-6199	347	4	|	|	ADV
ejpam-6199	347	5	w	w	NOUN
ejpam-6199	347	6	)	)	PUNCT
ejpam-6199	347	7	∈	∈	PROPN
ejpam-6199	348	1	ξ	ξ	PROPN
ejpam-6199	348	2	(	(	PUNCT
ejpam-6199	348	3	υ̃π	υ̃π	PROPN
ejpam-6199	348	4	;	;	PUNCT
ejpam-6199	348	5	τ̃	τ̃	PROPN
ejpam-6199	348	6	)	)	PUNCT
ejpam-6199	348	7	.	.	PUNCT
ejpam-6199	349	1	therefore	therefore	ADV
ejpam-6199	349	2	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	350	1	|	|	ADV
ejpam-6199	350	2	(	(	PUNCT
ejpam-6199	350	3	v	v	NOUN
ejpam-6199	350	4	|	|	ADV
ejpam-6199	350	5	w	w	NOUN
ejpam-6199	350	6	)	)	PUNCT
ejpam-6199	350	7	)	)	PUNCT
ejpam-6199	351	1	|	|	ADV
ejpam-6199	351	2	(	(	PUNCT
ejpam-6199	351	3	v	v	NOUN
ejpam-6199	351	4	|	|	ADV
ejpam-6199	351	5	w	w	NOUN
ejpam-6199	351	6	)	)	PUNCT
ejpam-6199	351	7	)	)	PUNCT
ejpam-6199	351	8	⪰	⪰	VERB
ejpam-6199	351	9	τ̃	τ̃	PROPN
ejpam-6199	351	10	=	=	SYM
ejpam-6199	351	11	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	351	12	)	)	PUNCT
ejpam-6199	351	13	,	,	PUNCT
ejpam-6199	351	14	υ̃π(w	υ̃π(w	NOUN
ejpam-6199	351	15	)	)	PUNCT
ejpam-6199	351	16	}	}	PUNCT
ejpam-6199	351	17	.	.	PUNCT
ejpam-6199	352	1	if	if	SCONJ
ejpam-6199	352	2	there	there	PRON
ejpam-6199	352	3	are	be	VERB
ejpam-6199	352	4	n	n	CCONJ
ejpam-6199	352	5	,	,	PUNCT
ejpam-6199	352	6	v	v	NOUN
ejpam-6199	352	7	,	,	PUNCT
ejpam-6199	352	8	w	w	PROPN
ejpam-6199	352	9	∈	∈	PROPN
ejpam-6199	352	10	ϑ	ϑ	NOUN
ejpam-6199	352	11	such	such	ADJ
ejpam-6199	352	12	that	that	DET
ejpam-6199	352	13	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	353	1	|	|	ADV
ejpam-6199	353	2	(	(	PUNCT
ejpam-6199	353	3	v	v	NOUN
ejpam-6199	353	4	|	|	ADV
ejpam-6199	353	5	w	w	NOUN
ejpam-6199	353	6	)	)	PUNCT
ejpam-6199	353	7	)	)	PUNCT
ejpam-6199	354	1	|	|	ADV
ejpam-6199	354	2	(	(	PUNCT
ejpam-6199	354	3	v	v	NOUN
ejpam-6199	354	4	|	|	ADV
ejpam-6199	354	5	w	w	NOUN
ejpam-6199	354	6	)	)	PUNCT
ejpam-6199	354	7	)	)	PUNCT
ejpam-6199	354	8	≰	≰	PROPN
ejpam-6199	354	9	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	354	10	)	)	PUNCT
ejpam-6199	354	11	,	,	PUNCT
ejpam-6199	354	12	ϖπ(w	ϖπ(w	ADP
ejpam-6199	354	13	)	)	PUNCT
ejpam-6199	354	14	}	}	PUNCT
ejpam-6199	354	15	,	,	PUNCT
ejpam-6199	354	16	then	then	ADV
ejpam-6199	354	17	ϖπ((n	ϖπ((n	PROPN
ejpam-6199	354	18	|	|	ADV
ejpam-6199	354	19	(	(	PUNCT
ejpam-6199	354	20	v	v	NOUN
ejpam-6199	354	21	|	|	ADV
ejpam-6199	354	22	w	w	NOUN
ejpam-6199	354	23	)	)	PUNCT
ejpam-6199	354	24	)	)	PUNCT
ejpam-6199	355	1	|	|	ADV
ejpam-6199	355	2	(	(	PUNCT
ejpam-6199	355	3	v	v	NOUN
ejpam-6199	355	4	|	|	ADV
ejpam-6199	355	5	w	w	NOUN
ejpam-6199	355	6	)	)	PUNCT
ejpam-6199	355	7	)	)	PUNCT
ejpam-6199	355	8	>	>	X
ejpam-6199	356	1	max{ϖπ(v	max{ϖπ(v	PROPN
ejpam-6199	356	2	)	)	PUNCT
ejpam-6199	356	3	,	,	PUNCT
ejpam-6199	356	4	ϖπ(w	ϖπ(w	ADP
ejpam-6199	356	5	)	)	PUNCT
ejpam-6199	356	6	}	}	PUNCT
ejpam-6199	356	7	.	.	PUNCT
ejpam-6199	357	1	if	if	SCONJ
ejpam-6199	357	2	we	we	PRON
ejpam-6199	357	3	take	take	VERB
ejpam-6199	357	4	κ	κ	NOUN
ejpam-6199	357	5	:	:	PUNCT
ejpam-6199	357	6	=	=	SYM
ejpam-6199	357	7	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	357	8	)	)	PUNCT
ejpam-6199	357	9	,	,	PUNCT
ejpam-6199	357	10	ϖπ(w	ϖπ(w	ADP
ejpam-6199	357	11	)	)	PUNCT
ejpam-6199	357	12	}	}	PUNCT
ejpam-6199	357	13	,	,	PUNCT
ejpam-6199	357	14	then	then	ADV
ejpam-6199	357	15	v	v	NOUN
ejpam-6199	357	16	,	,	PUNCT
ejpam-6199	357	17	w	w	PROPN
ejpam-6199	357	18	∈	∈	PROPN
ejpam-6199	357	19	ξ	ξ	PROPN
ejpam-6199	357	20	(	(	PUNCT
ejpam-6199	357	21	ϖπ;κ	ϖπ;κ	PUNCT
ejpam-6199	357	22	)	)	PUNCT
ejpam-6199	357	23	and	and	CCONJ
ejpam-6199	357	24	(	(	PUNCT
ejpam-6199	357	25	n	n	CCONJ
ejpam-6199	357	26	|	|	ADV
ejpam-6199	357	27	(	(	PUNCT
ejpam-6199	357	28	v	v	NOUN
ejpam-6199	357	29	|	|	ADV
ejpam-6199	357	30	w	w	NOUN
ejpam-6199	357	31	)	)	PUNCT
ejpam-6199	357	32	)	)	PUNCT
ejpam-6199	358	1	|	|	ADV
ejpam-6199	358	2	(	(	PUNCT
ejpam-6199	358	3	v	v	NOUN
ejpam-6199	358	4	|	|	ADV
ejpam-6199	358	5	w	w	NOUN
ejpam-6199	358	6	)	)	PUNCT
ejpam-6199	358	7	/∈	/∈	PUNCT
ejpam-6199	359	1	ξ	ξ	PROPN
ejpam-6199	359	2	(	(	PUNCT
ejpam-6199	359	3	ϖπ;κ	ϖπ;κ	NOUN
ejpam-6199	359	4	)	)	PUNCT
ejpam-6199	359	5	.	.	PUNCT
ejpam-6199	360	1	this	this	PRON
ejpam-6199	360	2	is	be	AUX
ejpam-6199	360	3	a	a	DET
ejpam-6199	360	4	contradiction	contradiction	NOUN
ejpam-6199	360	5	.	.	PUNCT
ejpam-6199	361	1	consequently	consequently	ADV
ejpam-6199	361	2	,	,	PUNCT
ejpam-6199	361	3	π	π	PROPN
ejpam-6199	361	4	=	=	SYM
ejpam-6199	361	5	(	(	PUNCT
ejpam-6199	361	6	υ̃π	υ̃π	PROPN
ejpam-6199	361	7	,	,	PUNCT
ejpam-6199	361	8	ϖπ	ϖπ	NOUN
ejpam-6199	361	9	)	)	PUNCT
ejpam-6199	361	10	is	be	AUX
ejpam-6199	361	11	a	a	DET
ejpam-6199	361	12	crossing	cross	VERB
ejpam-6199	361	13	cubic	cubic	ADJ
ejpam-6199	361	14	filter	filter	NOUN
ejpam-6199	361	15	of	of	ADP
ejpam-6199	361	16	ϑ.	ϑ.	NOUN
ejpam-6199	361	17	theorem	theorem	VERB
ejpam-6199	361	18	4	4	NUM
ejpam-6199	361	19	.	.	PUNCT
ejpam-6199	361	20	given	give	VERB
ejpam-6199	361	21	a	a	DET
ejpam-6199	361	22	nonempty	nonempty	ADJ
ejpam-6199	361	23	subset	subset	NOUN
ejpam-6199	361	24	ψ	ψ	X
ejpam-6199	361	25	of	of	ADP
ejpam-6199	361	26	ϑ	ϑ	PRON
ejpam-6199	361	27	,	,	PUNCT
ejpam-6199	361	28	let	let	VERB
ejpam-6199	361	29	πψ	πψ	ADP
ejpam-6199	361	30	=	=	SYM
ejpam-6199	361	31	(	(	PUNCT
ejpam-6199	361	32	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	361	33	,	,	PUNCT
ejpam-6199	361	34	ϖπψ	ϖπψ	PROPN
ejpam-6199	361	35	)	)	PUNCT
ejpam-6199	361	36	be	be	AUX
ejpam-6199	361	37	a	a	DET
ejpam-6199	361	38	crossing	cross	VERB
ejpam-6199	361	39	cubic	cubic	ADJ
ejpam-6199	361	40	structure	structure	NOUN
ejpam-6199	361	41	in	in	ADP
ejpam-6199	361	42	ϑ	ϑ	PROPN
ejpam-6199	361	43	defined	define	VERB
ejpam-6199	361	44	by	by	ADP
ejpam-6199	361	45	πψ	πψ	ADP
ejpam-6199	361	46	=	=	SYM
ejpam-6199	361	47	(	(	PUNCT
ejpam-6199	361	48	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	361	49	,	,	PUNCT
ejpam-6199	361	50	ϖπψ	ϖπψ	PROPN
ejpam-6199	361	51	)	)	PUNCT
ejpam-6199	361	52	:	:	PUNCT
ejpam-6199	361	53	ϑ	ϑ	X
ejpam-6199	361	54	→	→	SYM
ejpam-6199	361	55	i[0	i[0	PROPN
ejpam-6199	361	56	,	,	PUNCT
ejpam-6199	361	57	1	1	NUM
ejpam-6199	361	58	]	]	SYM
ejpam-6199	361	59	×	×	NOUN
ejpam-6199	362	1	[	[	X
ejpam-6199	362	2	−1	−1	NOUN
ejpam-6199	362	3	,	,	PUNCT
ejpam-6199	362	4	0	0	NUM
ejpam-6199	362	5	]	]	PUNCT
ejpam-6199	362	6	,	,	PUNCT
ejpam-6199	362	7	n	n	PROPN
ejpam-6199	362	8	7→	7→	NUM
ejpam-6199	362	9	{	{	PUNCT
ejpam-6199	362	10	(	(	PUNCT
ejpam-6199	362	11	τ̃	τ̃	PROPN
ejpam-6199	362	12	,	,	PUNCT
ejpam-6199	362	13	κ	κ	NOUN
ejpam-6199	362	14	)	)	PUNCT
ejpam-6199	362	15	if	if	SCONJ
ejpam-6199	362	16	n	n	PRON
ejpam-6199	362	17	∈	∈	PROPN
ejpam-6199	362	18	ψ	ψ	NOUN
ejpam-6199	362	19	,	,	PUNCT
ejpam-6199	362	20	(	(	PUNCT
ejpam-6199	362	21	α̃	α̃	PROPN
ejpam-6199	362	22	,	,	PUNCT
ejpam-6199	362	23	β	β	NOUN
ejpam-6199	362	24	)	)	PUNCT
ejpam-6199	362	25	otherwise	otherwise	ADV
ejpam-6199	362	26	,	,	PUNCT
ejpam-6199	362	27	where	where	SCONJ
ejpam-6199	362	28	(	(	PUNCT
ejpam-6199	362	29	τ̃	τ̃	PROPN
ejpam-6199	362	30	,	,	PUNCT
ejpam-6199	362	31	κ	κ	NOUN
ejpam-6199	362	32	)	)	PUNCT
ejpam-6199	362	33	,	,	PUNCT
ejpam-6199	362	34	(	(	PUNCT
ejpam-6199	362	35	α̃	α̃	PROPN
ejpam-6199	362	36	,	,	PUNCT
ejpam-6199	362	37	β	β	X
ejpam-6199	362	38	)	)	PUNCT
ejpam-6199	362	39	∈	∈	PROPN
ejpam-6199	362	40	i[0	i[0	PROPN
ejpam-6199	362	41	,	,	PUNCT
ejpam-6199	362	42	1]×	1]×	NUM
ejpam-6199	363	1	[	[	X
ejpam-6199	363	2	−1	−1	NOUN
ejpam-6199	363	3	,	,	PUNCT
ejpam-6199	363	4	0	0	NUM
ejpam-6199	363	5	]	]	PUNCT
ejpam-6199	363	6	such	such	ADJ
ejpam-6199	363	7	that	that	SCONJ
ejpam-6199	363	8	τ̃	τ̃	PROPN
ejpam-6199	363	9	≻	≻	PROPN
ejpam-6199	363	10	α̃	α̃	PROPN
ejpam-6199	363	11	and	and	CCONJ
ejpam-6199	363	12	κ	κ	X
ejpam-6199	363	13	<	<	X
ejpam-6199	363	14	β	β	NOUN
ejpam-6199	363	15	.	.	PUNCT
ejpam-6199	364	1	then	then	ADV
ejpam-6199	364	2	,	,	PUNCT
ejpam-6199	364	3	πψ	πψ	ADP
ejpam-6199	364	4	=	=	SYM
ejpam-6199	364	5	(	(	PUNCT
ejpam-6199	364	6	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	364	7	,	,	PUNCT
ejpam-6199	364	8	ϖπψ	ϖπψ	PROPN
ejpam-6199	364	9	)	)	PUNCT
ejpam-6199	364	10	is	be	AUX
ejpam-6199	364	11	a	a	DET
ejpam-6199	364	12	crossing	cross	VERB
ejpam-6199	364	13	cubic	cubic	ADJ
ejpam-6199	364	14	filter	filter	NOUN
ejpam-6199	364	15	of	of	ADP
ejpam-6199	364	16	ϑ	ϑ	NOUN
ejpam-6199	364	17	if	if	SCONJ
ejpam-6199	365	1	and	and	CCONJ
ejpam-6199	365	2	only	only	ADV
ejpam-6199	365	3	if	if	SCONJ
ejpam-6199	365	4	ψ	ψ	NOUN
ejpam-6199	365	5	is	be	AUX
ejpam-6199	365	6	a	a	DET
ejpam-6199	365	7	filter	filter	NOUN
ejpam-6199	365	8	of	of	ADP
ejpam-6199	365	9	ϑ.	ϑ.	NOUN
ejpam-6199	365	10	also	also	ADV
ejpam-6199	365	11	,	,	PUNCT
ejpam-6199	365	12	ψ	ψ	X
ejpam-6199	365	13	=	=	X
ejpam-6199	365	14	ϑπψ	ϑπψ	X
ejpam-6199	365	15	,	,	PUNCT
ejpam-6199	365	16	where	where	SCONJ
ejpam-6199	365	17	ϑπψ	ϑπψ	VERB
ejpam-6199	365	18	=	=	SYM
ejpam-6199	365	19	{	{	PUNCT
ejpam-6199	365	20	n	n	ADP
ejpam-6199	365	21	∈	∈	PROPN
ejpam-6199	365	22	ϑ	ϑ	X
ejpam-6199	365	23	|	|	ADV
ejpam-6199	365	24	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	365	25	(	(	PUNCT
ejpam-6199	365	26	n	n	CCONJ
ejpam-6199	365	27	)	)	PUNCT
ejpam-6199	366	1	=	=	SYM
ejpam-6199	366	2	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	366	3	(	(	PUNCT
ejpam-6199	366	4	1	1	NUM
ejpam-6199	366	5	)	)	PUNCT
ejpam-6199	366	6	,	,	PUNCT
ejpam-6199	366	7	and	and	CCONJ
ejpam-6199	366	8	ϖπψ	ϖπψ	NOUN
ejpam-6199	366	9	(	(	PUNCT
ejpam-6199	366	10	n	n	CCONJ
ejpam-6199	366	11	)	)	PUNCT
ejpam-6199	366	12	=	=	NOUN
ejpam-6199	366	13	ϖπψ	ϖπψ	X
ejpam-6199	366	14	(	(	PUNCT
ejpam-6199	366	15	1	1	NUM
ejpam-6199	366	16	)	)	PUNCT
ejpam-6199	366	17	}	}	PUNCT
ejpam-6199	366	18	.	.	PUNCT
ejpam-6199	367	1	a.	a.	PROPN
ejpam-6199	367	2	al	al	PROPN
ejpam-6199	367	3	-	-	PROPN
ejpam-6199	367	4	masarwah	masarwah	PROPN
ejpam-6199	367	5	et	et	PROPN
ejpam-6199	367	6	al	al	PROPN
ejpam-6199	367	7	.	.	PUNCT
ejpam-6199	367	8	/	/	SYM
ejpam-6199	367	9	eur	eur	PROPN
ejpam-6199	367	10	.	.	PUNCT
ejpam-6199	368	1	j.	j.	PROPN
ejpam-6199	368	2	pure	pure	PROPN
ejpam-6199	368	3	appl	appl	PROPN
ejpam-6199	368	4	.	.	PROPN
ejpam-6199	368	5	math	math	PROPN
ejpam-6199	368	6	,	,	PUNCT
ejpam-6199	368	7	18	18	NUM
ejpam-6199	368	8	(	(	PUNCT
ejpam-6199	368	9	3	3	NUM
ejpam-6199	368	10	)	)	PUNCT
ejpam-6199	368	11	(	(	PUNCT
ejpam-6199	368	12	2025	2025	NUM
ejpam-6199	368	13	)	)	PUNCT
ejpam-6199	368	14	,	,	PUNCT
ejpam-6199	368	15	6199	6199	NUM
ejpam-6199	368	16	12	12	NUM
ejpam-6199	368	17	of	of	ADP
ejpam-6199	368	18	17	17	NUM
ejpam-6199	368	19	proof	proof	NOUN
ejpam-6199	368	20	.	.	PUNCT
ejpam-6199	369	1	assume	assume	VERB
ejpam-6199	369	2	that	that	SCONJ
ejpam-6199	369	3	πψ	πψ	ADP
ejpam-6199	369	4	=	=	SYM
ejpam-6199	369	5	(	(	PUNCT
ejpam-6199	369	6	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	369	7	,	,	PUNCT
ejpam-6199	369	8	ϖπψ	ϖπψ	PROPN
ejpam-6199	369	9	)	)	PUNCT
ejpam-6199	369	10	is	be	AUX
ejpam-6199	369	11	a	a	DET
ejpam-6199	369	12	crossing	cross	VERB
ejpam-6199	369	13	cubic	cubic	ADJ
ejpam-6199	369	14	filter	filter	NOUN
ejpam-6199	369	15	of	of	ADP
ejpam-6199	369	16	ϑ.	ϑ.	NOUN
ejpam-6199	369	17	then	then	ADV
ejpam-6199	369	18	,	,	PUNCT
ejpam-6199	369	19	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	369	20	(	(	PUNCT
ejpam-6199	369	21	1	1	NUM
ejpam-6199	369	22	)	)	PUNCT
ejpam-6199	369	23	=	=	SYM
ejpam-6199	369	24	τ̃	τ̃	PROPN
ejpam-6199	369	25	and	and	CCONJ
ejpam-6199	369	26	ϖπψ	ϖπψ	NOUN
ejpam-6199	369	27	(	(	PUNCT
ejpam-6199	369	28	1	1	X
ejpam-6199	369	29	)	)	PUNCT
ejpam-6199	369	30	=	=	SYM
ejpam-6199	369	31	κ	κ	X
ejpam-6199	369	32	by	by	X
ejpam-6199	369	33	(	(	PUNCT
ejpam-6199	369	34	i	i	NOUN
ejpam-6199	369	35	)	)	PUNCT
ejpam-6199	369	36	of	of	ADP
ejpam-6199	369	37	definition	definition	NOUN
ejpam-6199	369	38	9	9	NUM
ejpam-6199	369	39	,	,	PUNCT
ejpam-6199	369	40	and	and	CCONJ
ejpam-6199	369	41	so	so	ADV
ejpam-6199	369	42	1	1	NUM
ejpam-6199	369	43	∈	∈	PROPN
ejpam-6199	369	44	ψ	ψ	NOUN
ejpam-6199	369	45	.	.	PUNCT
ejpam-6199	370	1	let	let	VERB
ejpam-6199	370	2	n	n	CCONJ
ejpam-6199	370	3	,	,	PUNCT
ejpam-6199	370	4	v	v	ADP
ejpam-6199	370	5	∈	∈	PRON
ejpam-6199	370	6	ϑ	ϑ	PART
ejpam-6199	370	7	be	be	AUX
ejpam-6199	370	8	such	such	ADJ
ejpam-6199	370	9	that	that	SCONJ
ejpam-6199	370	10	v	v	NUM
ejpam-6199	370	11	∈	∈	PROPN
ejpam-6199	370	12	ψ	ψ	NOUN
ejpam-6199	370	13	.	.	PUNCT
ejpam-6199	371	1	then	then	ADV
ejpam-6199	371	2	,	,	PUNCT
ejpam-6199	371	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	371	4	(	(	PUNCT
ejpam-6199	371	5	v	v	NOUN
ejpam-6199	371	6	)	)	PUNCT
ejpam-6199	371	7	=	=	SYM
ejpam-6199	371	8	τ̃	τ̃	PROPN
ejpam-6199	371	9	and	and	CCONJ
ejpam-6199	371	10	ϖπψ	ϖπψ	NOUN
ejpam-6199	371	11	(	(	PUNCT
ejpam-6199	371	12	v	v	NOUN
ejpam-6199	371	13	)	)	PUNCT
ejpam-6199	371	14	=	=	SYM
ejpam-6199	371	15	κ	κ	X
ejpam-6199	371	16	.	.	PUNCT
ejpam-6199	372	1	it	it	PRON
ejpam-6199	372	2	follows	follow	VERB
ejpam-6199	372	3	from	from	ADP
ejpam-6199	372	4	(	(	PUNCT
ejpam-6199	372	5	ii	ii	NOUN
ejpam-6199	372	6	)	)	PUNCT
ejpam-6199	372	7	of	of	ADP
ejpam-6199	372	8	definition	definition	NOUN
ejpam-6199	372	9	9	9	NUM
ejpam-6199	372	10	that	that	SCONJ
ejpam-6199	372	11	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	372	12	(	(	PUNCT
ejpam-6199	372	13	n	n	CCONJ
ejpam-6199	372	14	|	|	ADV
ejpam-6199	372	15	(	(	PUNCT
ejpam-6199	372	16	v	v	NOUN
ejpam-6199	372	17	|	|	ADV
ejpam-6199	372	18	v	v	NOUN
ejpam-6199	372	19	)	)	PUNCT
ejpam-6199	372	20	)	)	PUNCT
ejpam-6199	373	1	⪰	⪰	ADP
ejpam-6199	373	2	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	373	3	(	(	PUNCT
ejpam-6199	373	4	v	v	NOUN
ejpam-6199	373	5	)	)	PUNCT
ejpam-6199	373	6	=	=	SYM
ejpam-6199	373	7	τ̃	τ̃	PROPN
ejpam-6199	373	8	and	and	CCONJ
ejpam-6199	373	9	ϖπψ	ϖπψ	NOUN
ejpam-6199	373	10	(	(	PUNCT
ejpam-6199	373	11	n	n	CCONJ
ejpam-6199	373	12	|	|	ADV
ejpam-6199	373	13	(	(	PUNCT
ejpam-6199	373	14	v	v	NOUN
ejpam-6199	373	15	|	|	ADV
ejpam-6199	373	16	v	v	NOUN
ejpam-6199	373	17	)	)	PUNCT
ejpam-6199	373	18	)	)	PUNCT
ejpam-6199	374	1	≤	≤	NUM
ejpam-6199	374	2	ϖπψ	ϖπψ	NOUN
ejpam-6199	374	3	(	(	PUNCT
ejpam-6199	374	4	v	v	NOUN
ejpam-6199	374	5	)	)	PUNCT
ejpam-6199	374	6	=	=	SYM
ejpam-6199	374	7	κ	κ	X
ejpam-6199	374	8	.	.	PUNCT
ejpam-6199	374	9	hence	hence	ADV
ejpam-6199	374	10	,	,	PUNCT
ejpam-6199	374	11	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	374	12	(	(	PUNCT
ejpam-6199	374	13	n	n	NUM
ejpam-6199	374	14	|	|	ADV
ejpam-6199	374	15	(	(	PUNCT
ejpam-6199	374	16	v	v	NOUN
ejpam-6199	374	17	|	|	ADV
ejpam-6199	374	18	v	v	NOUN
ejpam-6199	374	19	)	)	PUNCT
ejpam-6199	374	20	)	)	PUNCT
ejpam-6199	374	21	=	=	SYM
ejpam-6199	374	22	τ̃	τ̃	PROPN
ejpam-6199	374	23	and	and	CCONJ
ejpam-6199	374	24	ϖπψ	ϖπψ	NOUN
ejpam-6199	374	25	(	(	PUNCT
ejpam-6199	374	26	n	n	CCONJ
ejpam-6199	374	27	|	|	ADV
ejpam-6199	374	28	(	(	PUNCT
ejpam-6199	374	29	v	v	NOUN
ejpam-6199	374	30	|	|	ADV
ejpam-6199	374	31	v	v	NOUN
ejpam-6199	374	32	)	)	PUNCT
ejpam-6199	374	33	)	)	PUNCT
ejpam-6199	375	1	=	=	SYM
ejpam-6199	375	2	κ	κ	X
ejpam-6199	375	3	.	.	PUNCT
ejpam-6199	376	1	this	this	PRON
ejpam-6199	376	2	illustrates	illustrate	VERB
ejpam-6199	376	3	that	that	SCONJ
ejpam-6199	376	4	n	n	CCONJ
ejpam-6199	376	5	|	|	ADV
ejpam-6199	376	6	(	(	PUNCT
ejpam-6199	376	7	v	v	NOUN
ejpam-6199	376	8	|	|	ADV
ejpam-6199	376	9	v	v	NOUN
ejpam-6199	376	10	)	)	PUNCT
ejpam-6199	376	11	∈	∈	PROPN
ejpam-6199	376	12	ψ	ψ	X
ejpam-6199	376	13	.	.	PUNCT
ejpam-6199	377	1	let	let	VERB
ejpam-6199	377	2	v	v	NOUN
ejpam-6199	377	3	,	,	PUNCT
ejpam-6199	377	4	w	w	PROPN
ejpam-6199	377	5	∈	∈	PROPN
ejpam-6199	377	6	ψ	ψ	NOUN
ejpam-6199	377	7	.	.	PUNCT
ejpam-6199	378	1	then	then	ADV
ejpam-6199	378	2	,	,	PUNCT
ejpam-6199	378	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	378	4	(	(	PUNCT
ejpam-6199	378	5	v	v	NOUN
ejpam-6199	378	6	)	)	PUNCT
ejpam-6199	378	7	=	=	PUNCT
ejpam-6199	378	8	τ̃	τ̃	PROPN
ejpam-6199	378	9	=	=	SYM
ejpam-6199	379	1	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	379	2	(	(	PUNCT
ejpam-6199	379	3	w	w	NOUN
ejpam-6199	379	4	)	)	PUNCT
ejpam-6199	379	5	and	and	CCONJ
ejpam-6199	379	6	ϖπψ	ϖπψ	NOUN
ejpam-6199	379	7	(	(	PUNCT
ejpam-6199	379	8	v	v	NOUN
ejpam-6199	379	9	)	)	PUNCT
ejpam-6199	379	10	=	=	SYM
ejpam-6199	379	11	κ	κ	X
ejpam-6199	379	12	=	=	VERB
ejpam-6199	379	13	ϖπψ	ϖπψ	X
ejpam-6199	379	14	(	(	PUNCT
ejpam-6199	379	15	w	w	NOUN
ejpam-6199	379	16	)	)	PUNCT
ejpam-6199	379	17	.	.	PUNCT
ejpam-6199	380	1	using	use	VERB
ejpam-6199	380	2	(	(	PUNCT
ejpam-6199	380	3	iii	iii	NOUN
ejpam-6199	380	4	)	)	PUNCT
ejpam-6199	380	5	of	of	ADP
ejpam-6199	380	6	definition	definition	NOUN
ejpam-6199	380	7	9	9	NUM
ejpam-6199	380	8	and	and	CCONJ
ejpam-6199	380	9	for	for	ADP
ejpam-6199	380	10	n	n	PRON
ejpam-6199	380	11	∈	∈	PROPN
ejpam-6199	380	12	ϑ	ϑ	X
ejpam-6199	380	13	,	,	PUNCT
ejpam-6199	380	14	we	we	PRON
ejpam-6199	380	15	have	have	VERB
ejpam-6199	380	16	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	380	17	(	(	PUNCT
ejpam-6199	380	18	(	(	PUNCT
ejpam-6199	380	19	n	n	CCONJ
ejpam-6199	380	20	|	|	ADV
ejpam-6199	380	21	(	(	PUNCT
ejpam-6199	380	22	v	v	NOUN
ejpam-6199	380	23	|	|	ADV
ejpam-6199	380	24	w	w	NOUN
ejpam-6199	380	25	)	)	PUNCT
ejpam-6199	380	26	)	)	PUNCT
ejpam-6199	381	1	|	|	ADV
ejpam-6199	381	2	(	(	PUNCT
ejpam-6199	381	3	v	v	NOUN
ejpam-6199	381	4	|	|	ADV
ejpam-6199	381	5	w	w	NOUN
ejpam-6199	381	6	)	)	PUNCT
ejpam-6199	381	7	)	)	PUNCT
ejpam-6199	381	8	⪰	⪰	NOUN
ejpam-6199	381	9	m̃in{υ̃πψ	m̃in{υ̃πψ	PROPN
ejpam-6199	381	10	(	(	PUNCT
ejpam-6199	381	11	v	v	NOUN
ejpam-6199	381	12	)	)	PUNCT
ejpam-6199	381	13	,	,	PUNCT
ejpam-6199	381	14	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	381	15	(	(	PUNCT
ejpam-6199	381	16	w	w	NOUN
ejpam-6199	381	17	)	)	PUNCT
ejpam-6199	381	18	}	}	PUNCT
ejpam-6199	381	19	=	=	SYM
ejpam-6199	381	20	τ̃	τ̃	PROPN
ejpam-6199	381	21	and	and	CCONJ
ejpam-6199	381	22	ϖπψ	ϖπψ	NOUN
ejpam-6199	381	23	(	(	PUNCT
ejpam-6199	381	24	(	(	PUNCT
ejpam-6199	381	25	n	n	CCONJ
ejpam-6199	381	26	|	|	ADV
ejpam-6199	381	27	(	(	PUNCT
ejpam-6199	381	28	v	v	NOUN
ejpam-6199	381	29	|	|	ADV
ejpam-6199	381	30	w	w	NOUN
ejpam-6199	381	31	)	)	PUNCT
ejpam-6199	381	32	)	)	PUNCT
ejpam-6199	382	1	|	|	ADV
ejpam-6199	382	2	(	(	PUNCT
ejpam-6199	382	3	v	v	NOUN
ejpam-6199	382	4	|	|	ADV
ejpam-6199	382	5	w	w	NOUN
ejpam-6199	382	6	)	)	PUNCT
ejpam-6199	382	7	)	)	PUNCT
ejpam-6199	382	8	≤	≤	NUM
ejpam-6199	382	9	max{ϖπψ	max{ϖπψ	NOUN
ejpam-6199	382	10	(	(	PUNCT
ejpam-6199	382	11	v	v	NOUN
ejpam-6199	382	12	)	)	PUNCT
ejpam-6199	382	13	,	,	PUNCT
ejpam-6199	382	14	ϖπψ	ϖπψ	X
ejpam-6199	382	15	(	(	PUNCT
ejpam-6199	382	16	w	w	NOUN
ejpam-6199	382	17	)	)	PUNCT
ejpam-6199	382	18	}	}	PUNCT
ejpam-6199	382	19	=	=	SYM
ejpam-6199	382	20	κ	κ	X
ejpam-6199	382	21	.	.	PUNCT
ejpam-6199	383	1	it	it	PRON
ejpam-6199	383	2	follows	follow	VERB
ejpam-6199	383	3	that	that	SCONJ
ejpam-6199	383	4	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	383	5	(	(	PUNCT
ejpam-6199	383	6	(	(	PUNCT
ejpam-6199	383	7	n	n	CCONJ
ejpam-6199	383	8	|	|	ADV
ejpam-6199	383	9	(	(	PUNCT
ejpam-6199	383	10	v	v	NOUN
ejpam-6199	383	11	|	|	ADV
ejpam-6199	383	12	w	w	NOUN
ejpam-6199	383	13	)	)	PUNCT
ejpam-6199	383	14	)	)	PUNCT
ejpam-6199	384	1	|	|	ADV
ejpam-6199	384	2	(	(	PUNCT
ejpam-6199	384	3	v	v	NOUN
ejpam-6199	384	4	|	|	ADV
ejpam-6199	384	5	w	w	NOUN
ejpam-6199	384	6	)	)	PUNCT
ejpam-6199	384	7	)	)	PUNCT
ejpam-6199	385	1	=	=	SYM
ejpam-6199	386	1	τ̃	τ̃	PROPN
ejpam-6199	386	2	and	and	CCONJ
ejpam-6199	386	3	ϖπψ	ϖπψ	NOUN
ejpam-6199	386	4	(	(	PUNCT
ejpam-6199	386	5	(	(	PUNCT
ejpam-6199	386	6	n	n	CCONJ
ejpam-6199	386	7	|	|	ADV
ejpam-6199	386	8	(	(	PUNCT
ejpam-6199	386	9	v	v	NOUN
ejpam-6199	386	10	|	|	ADV
ejpam-6199	386	11	w	w	NOUN
ejpam-6199	386	12	)	)	PUNCT
ejpam-6199	386	13	)	)	PUNCT
ejpam-6199	387	1	|	|	ADV
ejpam-6199	387	2	(	(	PUNCT
ejpam-6199	387	3	v	v	NOUN
ejpam-6199	387	4	|	|	ADV
ejpam-6199	387	5	w	w	NOUN
ejpam-6199	387	6	)	)	PUNCT
ejpam-6199	387	7	)	)	PUNCT
ejpam-6199	388	1	=	=	SYM
ejpam-6199	388	2	κ	κ	X
ejpam-6199	388	3	.	.	PUNCT
ejpam-6199	389	1	hence	hence	ADV
ejpam-6199	389	2	,	,	PUNCT
ejpam-6199	389	3	(	(	PUNCT
ejpam-6199	389	4	n	n	CCONJ
ejpam-6199	389	5	|	|	ADV
ejpam-6199	389	6	(	(	PUNCT
ejpam-6199	389	7	v	v	NOUN
ejpam-6199	389	8	|	|	ADV
ejpam-6199	389	9	w	w	NOUN
ejpam-6199	389	10	)	)	PUNCT
ejpam-6199	389	11	)	)	PUNCT
ejpam-6199	390	1	|	|	ADV
ejpam-6199	390	2	(	(	PUNCT
ejpam-6199	390	3	v	v	NOUN
ejpam-6199	390	4	|	|	ADV
ejpam-6199	390	5	w	w	NOUN
ejpam-6199	390	6	)	)	PUNCT
ejpam-6199	390	7	∈	∈	PROPN
ejpam-6199	391	1	ψ	ψ	NOUN
ejpam-6199	391	2	.	.	PUNCT
ejpam-6199	391	3	therefore	therefore	ADV
ejpam-6199	391	4	,	,	PUNCT
ejpam-6199	391	5	ψ	ψ	X
ejpam-6199	391	6	is	be	AUX
ejpam-6199	391	7	a	a	DET
ejpam-6199	391	8	filter	filter	NOUN
ejpam-6199	391	9	of	of	ADP
ejpam-6199	391	10	ϑ.	ϑ.	NOUN
ejpam-6199	391	11	conversely	conversely	ADV
ejpam-6199	391	12	,	,	PUNCT
ejpam-6199	391	13	let	let	VERB
ejpam-6199	391	14	ψ	ψ	PART
ejpam-6199	391	15	be	be	AUX
ejpam-6199	391	16	a	a	DET
ejpam-6199	391	17	filter	filter	NOUN
ejpam-6199	391	18	of	of	ADP
ejpam-6199	391	19	ϑ.	ϑ.	NOUN
ejpam-6199	391	20	since	since	SCONJ
ejpam-6199	391	21	1	1	NUM
ejpam-6199	391	22	∈	∈	PROPN
ejpam-6199	391	23	ψ	ψ	NOUN
ejpam-6199	391	24	,	,	PUNCT
ejpam-6199	391	25	we	we	PRON
ejpam-6199	391	26	have	have	VERB
ejpam-6199	391	27	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	391	28	(	(	PUNCT
ejpam-6199	391	29	1	1	NUM
ejpam-6199	391	30	)	)	PUNCT
ejpam-6199	391	31	=	=	SYM
ejpam-6199	391	32	τ̃	τ̃	NOUN
ejpam-6199	391	33	⪰	⪰	NOUN
ejpam-6199	391	34	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	391	35	(	(	PUNCT
ejpam-6199	391	36	n	n	CCONJ
ejpam-6199	391	37	)	)	PUNCT
ejpam-6199	391	38	and	and	CCONJ
ejpam-6199	391	39	ϖπψ	ϖπψ	NOUN
ejpam-6199	391	40	(	(	PUNCT
ejpam-6199	391	41	1	1	X
ejpam-6199	391	42	)	)	PUNCT
ejpam-6199	391	43	=	=	SYM
ejpam-6199	392	1	κ	κ	X
ejpam-6199	392	2	≤	≤	NUM
ejpam-6199	392	3	ϖπψ	ϖπψ	NOUN
ejpam-6199	392	4	(	(	PUNCT
ejpam-6199	392	5	n	n	CCONJ
ejpam-6199	392	6	)	)	PUNCT
ejpam-6199	392	7	for	for	ADP
ejpam-6199	392	8	all	all	DET
ejpam-6199	392	9	n	n	PRON
ejpam-6199	392	10	∈	∈	NOUN
ejpam-6199	392	11	ϑ.	ϑ.	NOUN
ejpam-6199	392	12	let	let	VERB
ejpam-6199	392	13	n	n	CCONJ
ejpam-6199	392	14	,	,	PUNCT
ejpam-6199	392	15	v	v	NOUN
ejpam-6199	392	16	∈	∈	NOUN
ejpam-6199	392	17	ϑ.	ϑ.	NOUN
ejpam-6199	392	18	then	then	ADV
ejpam-6199	392	19	,	,	PUNCT
ejpam-6199	392	20	we	we	PRON
ejpam-6199	392	21	have	have	VERB
ejpam-6199	392	22	two	two	NUM
ejpam-6199	392	23	cases	case	NOUN
ejpam-6199	392	24	:	:	PUNCT
ejpam-6199	392	25	case(1	case(1	NUM
ejpam-6199	392	26	)	)	PUNCT
ejpam-6199	392	27	.	.	PUNCT
ejpam-6199	393	1	if	if	SCONJ
ejpam-6199	393	2	v	v	NUM
ejpam-6199	393	3	∈	∈	PROPN
ejpam-6199	393	4	ψ	ψ	NOUN
ejpam-6199	393	5	,	,	PUNCT
ejpam-6199	393	6	then	then	ADV
ejpam-6199	393	7	n	n	CCONJ
ejpam-6199	393	8	|	|	ADV
ejpam-6199	393	9	(	(	PUNCT
ejpam-6199	393	10	v	v	NOUN
ejpam-6199	393	11	|	|	ADV
ejpam-6199	393	12	v	v	NOUN
ejpam-6199	393	13	)	)	PUNCT
ejpam-6199	393	14	∈	∈	NOUN
ejpam-6199	393	15	ψ	ψ	NOUN
ejpam-6199	393	16	and	and	CCONJ
ejpam-6199	393	17	thus	thus	ADV
ejpam-6199	393	18	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	393	19	(	(	PUNCT
ejpam-6199	393	20	n	n	NUM
ejpam-6199	394	1	|	|	ADV
ejpam-6199	394	2	(	(	PUNCT
ejpam-6199	394	3	v	v	NOUN
ejpam-6199	394	4	|	|	ADV
ejpam-6199	394	5	v	v	NOUN
ejpam-6199	394	6	)	)	PUNCT
ejpam-6199	394	7	)	)	PUNCT
ejpam-6199	395	1	=	=	PUNCT
ejpam-6199	395	2	τ̃	τ̃	PROPN
ejpam-6199	396	1	=	=	SYM
ejpam-6199	396	2	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	396	3	(	(	PUNCT
ejpam-6199	396	4	v	v	NOUN
ejpam-6199	396	5	)	)	PUNCT
ejpam-6199	396	6	and	and	CCONJ
ejpam-6199	396	7	ϖπψ	ϖπψ	NOUN
ejpam-6199	396	8	(	(	PUNCT
ejpam-6199	396	9	n	n	CCONJ
ejpam-6199	396	10	|	|	ADV
ejpam-6199	396	11	(	(	PUNCT
ejpam-6199	396	12	v	v	NOUN
ejpam-6199	396	13	|	|	ADV
ejpam-6199	396	14	v	v	NOUN
ejpam-6199	396	15	)	)	PUNCT
ejpam-6199	396	16	)	)	PUNCT
ejpam-6199	397	1	=	=	PUNCT
ejpam-6199	397	2	κ	κ	X
ejpam-6199	397	3	=	=	VERB
ejpam-6199	397	4	ϖπψ	ϖπψ	X
ejpam-6199	397	5	(	(	PUNCT
ejpam-6199	397	6	v	v	NOUN
ejpam-6199	397	7	)	)	PUNCT
ejpam-6199	397	8	.	.	PUNCT
ejpam-6199	398	1	case(2	case(2	NOUN
ejpam-6199	398	2	)	)	PUNCT
ejpam-6199	398	3	.	.	PUNCT
ejpam-6199	399	1	if	if	SCONJ
ejpam-6199	399	2	v	v	NUM
ejpam-6199	399	3	/∈	/∈	PUNCT
ejpam-6199	400	1	ψ	ψ	NOUN
ejpam-6199	400	2	,	,	PUNCT
ejpam-6199	400	3	then	then	ADV
ejpam-6199	400	4	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	400	5	(	(	PUNCT
ejpam-6199	400	6	v	v	NOUN
ejpam-6199	400	7	)	)	PUNCT
ejpam-6199	400	8	=	=	SYM
ejpam-6199	400	9	α̃	α̃	PROPN
ejpam-6199	400	10	and	and	CCONJ
ejpam-6199	400	11	ϖπψ	ϖπψ	NOUN
ejpam-6199	400	12	(	(	PUNCT
ejpam-6199	400	13	v	v	NOUN
ejpam-6199	400	14	)	)	PUNCT
ejpam-6199	400	15	=	=	SYM
ejpam-6199	401	1	β	β	X
ejpam-6199	401	2	.	.	PUNCT
ejpam-6199	402	1	hence	hence	ADV
ejpam-6199	402	2	,	,	PUNCT
ejpam-6199	402	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	402	4	(	(	PUNCT
ejpam-6199	402	5	n	n	NUM
ejpam-6199	402	6	|	|	ADV
ejpam-6199	402	7	(	(	PUNCT
ejpam-6199	402	8	v	v	NOUN
ejpam-6199	402	9	|	|	ADV
ejpam-6199	402	10	v	v	NOUN
ejpam-6199	402	11	)	)	PUNCT
ejpam-6199	402	12	)	)	PUNCT
ejpam-6199	402	13	⪰	⪰	ADP
ejpam-6199	402	14	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	402	15	(	(	PUNCT
ejpam-6199	402	16	v	v	NOUN
ejpam-6199	402	17	)	)	PUNCT
ejpam-6199	402	18	and	and	CCONJ
ejpam-6199	402	19	ϖπψ	ϖπψ	NOUN
ejpam-6199	402	20	(	(	PUNCT
ejpam-6199	402	21	n	n	CCONJ
ejpam-6199	402	22	|	|	ADV
ejpam-6199	402	23	(	(	PUNCT
ejpam-6199	402	24	v	v	NOUN
ejpam-6199	402	25	|	|	ADV
ejpam-6199	402	26	v	v	NOUN
ejpam-6199	402	27	)	)	PUNCT
ejpam-6199	402	28	)	)	PUNCT
ejpam-6199	402	29	≤	≤	NUM
ejpam-6199	402	30	ϖπψ	ϖπψ	NOUN
ejpam-6199	402	31	(	(	PUNCT
ejpam-6199	402	32	v	v	NOUN
ejpam-6199	402	33	)	)	PUNCT
ejpam-6199	402	34	.	.	PUNCT
ejpam-6199	403	1	moreover	moreover	ADV
ejpam-6199	403	2	,	,	PUNCT
ejpam-6199	403	3	let	let	VERB
ejpam-6199	403	4	n	n	CCONJ
ejpam-6199	403	5	,	,	PUNCT
ejpam-6199	403	6	v	v	NOUN
ejpam-6199	403	7	,	,	PUNCT
ejpam-6199	403	8	w	w	PROPN
ejpam-6199	403	9	∈	∈	PROPN
ejpam-6199	403	10	ϑ.	ϑ.	NOUN
ejpam-6199	403	11	then	then	ADV
ejpam-6199	403	12	,	,	PUNCT
ejpam-6199	403	13	we	we	PRON
ejpam-6199	403	14	have	have	VERB
ejpam-6199	403	15	the	the	DET
ejpam-6199	403	16	following	follow	VERB
ejpam-6199	403	17	cases	case	NOUN
ejpam-6199	403	18	:	:	PUNCT
ejpam-6199	403	19	case(1	case(1	NUM
ejpam-6199	403	20	)	)	PUNCT
ejpam-6199	403	21	.	.	PUNCT
ejpam-6199	404	1	if	if	SCONJ
ejpam-6199	404	2	v	v	X
ejpam-6199	404	3	,	,	PUNCT
ejpam-6199	404	4	w	w	PROPN
ejpam-6199	404	5	∈	∈	PROPN
ejpam-6199	404	6	ψ	ψ	NOUN
ejpam-6199	404	7	.	.	PUNCT
ejpam-6199	405	1	then	then	ADV
ejpam-6199	405	2	,	,	PUNCT
ejpam-6199	405	3	(	(	PUNCT
ejpam-6199	405	4	n	n	CCONJ
ejpam-6199	405	5	|	|	ADV
ejpam-6199	405	6	(	(	PUNCT
ejpam-6199	405	7	v	v	NOUN
ejpam-6199	405	8	|	|	ADV
ejpam-6199	405	9	w	w	NOUN
ejpam-6199	405	10	)	)	PUNCT
ejpam-6199	405	11	)	)	PUNCT
ejpam-6199	406	1	|	|	ADV
ejpam-6199	406	2	(	(	PUNCT
ejpam-6199	406	3	v	v	NOUN
ejpam-6199	406	4	|	|	ADV
ejpam-6199	406	5	w	w	NOUN
ejpam-6199	406	6	)	)	PUNCT
ejpam-6199	406	7	∈	∈	PROPN
ejpam-6199	406	8	ψ	ψ	NOUN
ejpam-6199	406	9	.	.	PUNCT
ejpam-6199	407	1	thus	thus	ADV
ejpam-6199	407	2	,	,	PUNCT
ejpam-6199	407	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	407	4	(	(	PUNCT
ejpam-6199	407	5	(	(	PUNCT
ejpam-6199	407	6	n	n	CCONJ
ejpam-6199	407	7	|	|	ADV
ejpam-6199	407	8	(	(	PUNCT
ejpam-6199	407	9	v	v	NOUN
ejpam-6199	407	10	|	|	ADV
ejpam-6199	407	11	w	w	NOUN
ejpam-6199	407	12	)	)	PUNCT
ejpam-6199	407	13	)	)	PUNCT
ejpam-6199	407	14	|	|	ADV
ejpam-6199	407	15	(	(	PUNCT
ejpam-6199	407	16	v	v	NOUN
ejpam-6199	407	17	|	|	ADV
ejpam-6199	407	18	w	w	NOUN
ejpam-6199	407	19	)	)	PUNCT
ejpam-6199	407	20	)	)	PUNCT
ejpam-6199	408	1	=	=	PUNCT
ejpam-6199	408	2	τ̃	τ̃	PUNCT
ejpam-6199	409	1	=	=	SYM
ejpam-6199	409	2	m̃in{υ̃πψ	m̃in{υ̃πψ	PROPN
ejpam-6199	409	3	(	(	PUNCT
ejpam-6199	409	4	v	v	NOUN
ejpam-6199	409	5	)	)	PUNCT
ejpam-6199	409	6	,	,	PUNCT
ejpam-6199	409	7	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	409	8	(	(	PUNCT
ejpam-6199	409	9	w	w	NOUN
ejpam-6199	409	10	)	)	PUNCT
ejpam-6199	409	11	}	}	PUNCT
ejpam-6199	409	12	and	and	CCONJ
ejpam-6199	409	13	ϖπψ	ϖπψ	NOUN
ejpam-6199	409	14	(	(	PUNCT
ejpam-6199	409	15	(	(	PUNCT
ejpam-6199	409	16	n	n	CCONJ
ejpam-6199	409	17	|	|	ADV
ejpam-6199	409	18	(	(	PUNCT
ejpam-6199	409	19	v	v	NOUN
ejpam-6199	409	20	|	|	ADV
ejpam-6199	409	21	w	w	NOUN
ejpam-6199	409	22	)	)	PUNCT
ejpam-6199	409	23	)	)	PUNCT
ejpam-6199	410	1	|	|	ADV
ejpam-6199	410	2	(	(	PUNCT
ejpam-6199	410	3	v	v	NOUN
ejpam-6199	410	4	|	|	ADV
ejpam-6199	410	5	w	w	NOUN
ejpam-6199	410	6	)	)	PUNCT
ejpam-6199	410	7	)	)	PUNCT
ejpam-6199	411	1	=	=	PUNCT
ejpam-6199	411	2	κ	κ	NOUN
ejpam-6199	411	3	=	=	SYM
ejpam-6199	411	4	max{ϖπψ	max{ϖπψ	PROPN
ejpam-6199	411	5	(	(	PUNCT
ejpam-6199	411	6	v	v	NOUN
ejpam-6199	411	7	)	)	PUNCT
ejpam-6199	411	8	,	,	PUNCT
ejpam-6199	411	9	ϖπψ	ϖπψ	X
ejpam-6199	411	10	(	(	PUNCT
ejpam-6199	411	11	w	w	NOUN
ejpam-6199	411	12	)	)	PUNCT
ejpam-6199	411	13	}	}	PUNCT
ejpam-6199	411	14	.	.	PUNCT
ejpam-6199	412	1	case(2	case(2	NOUN
ejpam-6199	412	2	)	)	PUNCT
ejpam-6199	412	3	.	.	PUNCT
ejpam-6199	413	1	if	if	SCONJ
ejpam-6199	413	2	v	v	X
ejpam-6199	413	3	,	,	PUNCT
ejpam-6199	413	4	w	w	NOUN
ejpam-6199	413	5	/∈	/∈	PUNCT
ejpam-6199	414	1	ψ	ψ	X
ejpam-6199	414	2	.	.	PUNCT
ejpam-6199	415	1	then	then	ADV
ejpam-6199	415	2	,	,	PUNCT
ejpam-6199	415	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	415	4	(	(	PUNCT
ejpam-6199	415	5	(	(	PUNCT
ejpam-6199	415	6	n	n	CCONJ
ejpam-6199	415	7	|	|	ADV
ejpam-6199	415	8	(	(	PUNCT
ejpam-6199	415	9	v	v	NOUN
ejpam-6199	415	10	|	|	ADV
ejpam-6199	415	11	w	w	NOUN
ejpam-6199	415	12	)	)	PUNCT
ejpam-6199	415	13	)	)	PUNCT
ejpam-6199	415	14	|	|	ADV
ejpam-6199	415	15	(	(	PUNCT
ejpam-6199	415	16	v	v	NOUN
ejpam-6199	415	17	|	|	ADV
ejpam-6199	415	18	w	w	NOUN
ejpam-6199	415	19	)	)	PUNCT
ejpam-6199	415	20	)	)	PUNCT
ejpam-6199	415	21	⪰	⪰	NOUN
ejpam-6199	415	22	m̃in{υ̃πψ	m̃in{υ̃πψ	PROPN
ejpam-6199	415	23	(	(	PUNCT
ejpam-6199	415	24	v	v	NOUN
ejpam-6199	415	25	)	)	PUNCT
ejpam-6199	415	26	,	,	PUNCT
ejpam-6199	415	27	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	415	28	(	(	PUNCT
ejpam-6199	415	29	w	w	NOUN
ejpam-6199	415	30	)	)	PUNCT
ejpam-6199	415	31	}	}	PUNCT
ejpam-6199	415	32	=	=	SYM
ejpam-6199	415	33	α̃	α̃	PROPN
ejpam-6199	415	34	and	and	CCONJ
ejpam-6199	415	35	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	415	36	|	|	ADV
ejpam-6199	415	37	(	(	PUNCT
ejpam-6199	415	38	v	v	NOUN
ejpam-6199	415	39	|	|	ADV
ejpam-6199	415	40	w	w	NOUN
ejpam-6199	415	41	)	)	PUNCT
ejpam-6199	415	42	)	)	PUNCT
ejpam-6199	416	1	|	|	ADV
ejpam-6199	416	2	(	(	PUNCT
ejpam-6199	416	3	v	v	NOUN
ejpam-6199	416	4	|	|	ADV
ejpam-6199	416	5	w	w	NOUN
ejpam-6199	416	6	)	)	PUNCT
ejpam-6199	416	7	)	)	PUNCT
ejpam-6199	416	8	≤	≤	NUM
ejpam-6199	416	9	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	416	10	)	)	PUNCT
ejpam-6199	416	11	,	,	PUNCT
ejpam-6199	416	12	ϖπ(w	ϖπ(w	ADV
ejpam-6199	416	13	)	)	PUNCT
ejpam-6199	416	14	}	}	PUNCT
ejpam-6199	416	15	=	=	SYM
ejpam-6199	416	16	β	β	X
ejpam-6199	416	17	.	.	PUNCT
ejpam-6199	416	18	case(3	case(3	NOUN
ejpam-6199	416	19	)	)	PUNCT
ejpam-6199	416	20	.	.	PUNCT
ejpam-6199	417	1	if	if	SCONJ
ejpam-6199	417	2	v	v	NUM
ejpam-6199	417	3	∈	∈	NOUN
ejpam-6199	417	4	ψ	ψ	NOUN
ejpam-6199	417	5	and	and	CCONJ
ejpam-6199	417	6	w	w	PROPN
ejpam-6199	417	7	/∈	/∈	PUNCT
ejpam-6199	418	1	ψ	ψ	NOUN
ejpam-6199	418	2	,	,	PUNCT
ejpam-6199	418	3	then	then	ADV
ejpam-6199	418	4	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	418	5	(	(	PUNCT
ejpam-6199	418	6	v	v	NOUN
ejpam-6199	418	7	)	)	PUNCT
ejpam-6199	418	8	=	=	SYM
ejpam-6199	418	9	τ̃	τ̃	PROPN
ejpam-6199	418	10	,	,	PUNCT
ejpam-6199	418	11	ϖπψ	ϖπψ	X
ejpam-6199	418	12	(	(	PUNCT
ejpam-6199	418	13	v	v	NOUN
ejpam-6199	418	14	)	)	PUNCT
ejpam-6199	418	15	=	=	SYM
ejpam-6199	418	16	κ	κ	NOUN
ejpam-6199	418	17	,	,	PUNCT
ejpam-6199	418	18	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	418	19	(	(	PUNCT
ejpam-6199	418	20	w	w	NOUN
ejpam-6199	418	21	)	)	PUNCT
ejpam-6199	418	22	=	=	SYM
ejpam-6199	418	23	α̃	α̃	PROPN
ejpam-6199	418	24	and	and	CCONJ
ejpam-6199	418	25	ϖπψ	ϖπψ	NOUN
ejpam-6199	418	26	(	(	PUNCT
ejpam-6199	418	27	w	w	NOUN
ejpam-6199	418	28	)	)	PUNCT
ejpam-6199	418	29	=	=	SYM
ejpam-6199	419	1	β	β	X
ejpam-6199	419	2	.	.	PUNCT
ejpam-6199	420	1	so	so	ADV
ejpam-6199	420	2	,	,	PUNCT
ejpam-6199	420	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	420	4	(	(	PUNCT
ejpam-6199	420	5	(	(	PUNCT
ejpam-6199	420	6	n	n	CCONJ
ejpam-6199	420	7	|	|	ADV
ejpam-6199	420	8	(	(	PUNCT
ejpam-6199	420	9	v	v	NOUN
ejpam-6199	420	10	|	|	ADV
ejpam-6199	420	11	w	w	NOUN
ejpam-6199	420	12	)	)	PUNCT
ejpam-6199	420	13	)	)	PUNCT
ejpam-6199	421	1	|	|	ADV
ejpam-6199	421	2	(	(	PUNCT
ejpam-6199	421	3	v	v	NOUN
ejpam-6199	421	4	|	|	ADV
ejpam-6199	421	5	w	w	NOUN
ejpam-6199	421	6	)	)	PUNCT
ejpam-6199	421	7	)	)	PUNCT
ejpam-6199	421	8	⪰	⪰	NOUN
ejpam-6199	421	9	m̃in{υ̃πψ	m̃in{υ̃πψ	PROPN
ejpam-6199	421	10	(	(	PUNCT
ejpam-6199	421	11	v	v	NOUN
ejpam-6199	421	12	)	)	PUNCT
ejpam-6199	421	13	,	,	PUNCT
ejpam-6199	421	14	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	421	15	(	(	PUNCT
ejpam-6199	421	16	w	w	NOUN
ejpam-6199	421	17	)	)	PUNCT
ejpam-6199	421	18	}	}	PUNCT
ejpam-6199	421	19	=	=	SYM
ejpam-6199	421	20	α̃	α̃	PROPN
ejpam-6199	421	21	and	and	CCONJ
ejpam-6199	421	22	ϖπψ	ϖπψ	NOUN
ejpam-6199	421	23	(	(	PUNCT
ejpam-6199	421	24	(	(	PUNCT
ejpam-6199	421	25	n	n	CCONJ
ejpam-6199	421	26	|	|	ADV
ejpam-6199	421	27	(	(	PUNCT
ejpam-6199	421	28	v	v	NOUN
ejpam-6199	421	29	|	|	ADV
ejpam-6199	421	30	w	w	NOUN
ejpam-6199	421	31	)	)	PUNCT
ejpam-6199	421	32	)	)	PUNCT
ejpam-6199	422	1	|	|	ADV
ejpam-6199	422	2	(	(	PUNCT
ejpam-6199	422	3	v	v	NOUN
ejpam-6199	422	4	|	|	ADV
ejpam-6199	422	5	w	w	NOUN
ejpam-6199	422	6	)	)	PUNCT
ejpam-6199	422	7	)	)	PUNCT
ejpam-6199	422	8	≤	≤	NUM
ejpam-6199	422	9	max{ϖπψ	max{ϖπψ	NOUN
ejpam-6199	422	10	(	(	PUNCT
ejpam-6199	422	11	v	v	NOUN
ejpam-6199	422	12	)	)	PUNCT
ejpam-6199	422	13	,	,	PUNCT
ejpam-6199	422	14	ϖπψ	ϖπψ	X
ejpam-6199	422	15	(	(	PUNCT
ejpam-6199	422	16	w	w	NOUN
ejpam-6199	422	17	)	)	PUNCT
ejpam-6199	422	18	}	}	PUNCT
ejpam-6199	422	19	=	=	SYM
ejpam-6199	422	20	β	β	X
ejpam-6199	422	21	.	.	PUNCT
ejpam-6199	422	22	a.	a.	PROPN
ejpam-6199	422	23	al	al	PROPN
ejpam-6199	422	24	-	-	PROPN
ejpam-6199	422	25	masarwah	masarwah	PROPN
ejpam-6199	422	26	et	et	PROPN
ejpam-6199	422	27	al	al	PROPN
ejpam-6199	422	28	.	.	PUNCT
ejpam-6199	422	29	/	/	SYM
ejpam-6199	422	30	eur	eur	PROPN
ejpam-6199	422	31	.	.	PUNCT
ejpam-6199	423	1	j.	j.	PROPN
ejpam-6199	423	2	pure	pure	PROPN
ejpam-6199	423	3	appl	appl	PROPN
ejpam-6199	423	4	.	.	PROPN
ejpam-6199	423	5	math	math	PROPN
ejpam-6199	423	6	,	,	PUNCT
ejpam-6199	423	7	18	18	NUM
ejpam-6199	423	8	(	(	PUNCT
ejpam-6199	423	9	3	3	NUM
ejpam-6199	423	10	)	)	PUNCT
ejpam-6199	423	11	(	(	PUNCT
ejpam-6199	423	12	2025	2025	NUM
ejpam-6199	423	13	)	)	PUNCT
ejpam-6199	423	14	,	,	PUNCT
ejpam-6199	423	15	6199	6199	NUM
ejpam-6199	423	16	13	13	NUM
ejpam-6199	423	17	of	of	ADP
ejpam-6199	423	18	17	17	NUM
ejpam-6199	423	19	case(4	case(4	PROPN
ejpam-6199	423	20	)	)	PUNCT
ejpam-6199	423	21	.	.	PUNCT
ejpam-6199	424	1	if	if	SCONJ
ejpam-6199	424	2	v	v	NUM
ejpam-6199	424	3	/∈	/∈	NOUN
ejpam-6199	424	4	ψ	ψ	NOUN
ejpam-6199	424	5	and	and	CCONJ
ejpam-6199	424	6	w	w	PROPN
ejpam-6199	424	7	∈	∈	PROPN
ejpam-6199	424	8	ψ	ψ	NOUN
ejpam-6199	424	9	,	,	PUNCT
ejpam-6199	424	10	then	then	ADV
ejpam-6199	424	11	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	424	12	(	(	PUNCT
ejpam-6199	424	13	v	v	NOUN
ejpam-6199	424	14	)	)	PUNCT
ejpam-6199	424	15	=	=	PUNCT
ejpam-6199	424	16	α̃,ϖπψ	α̃,ϖπψ	PROPN
ejpam-6199	424	17	(	(	PUNCT
ejpam-6199	424	18	v	v	NOUN
ejpam-6199	424	19	)	)	PUNCT
ejpam-6199	424	20	=	=	SYM
ejpam-6199	424	21	β	β	X
ejpam-6199	424	22	,	,	PUNCT
ejpam-6199	424	23	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	424	24	(	(	PUNCT
ejpam-6199	424	25	w	w	NOUN
ejpam-6199	424	26	)	)	PUNCT
ejpam-6199	424	27	=	=	SYM
ejpam-6199	424	28	τ̃	τ̃	PROPN
ejpam-6199	424	29	and	and	CCONJ
ejpam-6199	424	30	ϖπψ	ϖπψ	NOUN
ejpam-6199	424	31	(	(	PUNCT
ejpam-6199	424	32	w	w	NOUN
ejpam-6199	424	33	)	)	PUNCT
ejpam-6199	424	34	=	=	SYM
ejpam-6199	424	35	κ	κ	X
ejpam-6199	424	36	.	.	PUNCT
ejpam-6199	425	1	so	so	ADV
ejpam-6199	425	2	,	,	PUNCT
ejpam-6199	425	3	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	425	4	(	(	PUNCT
ejpam-6199	425	5	(	(	PUNCT
ejpam-6199	425	6	n	n	CCONJ
ejpam-6199	425	7	|	|	ADV
ejpam-6199	425	8	(	(	PUNCT
ejpam-6199	425	9	v	v	NOUN
ejpam-6199	425	10	|	|	ADV
ejpam-6199	425	11	w	w	NOUN
ejpam-6199	425	12	)	)	PUNCT
ejpam-6199	425	13	)	)	PUNCT
ejpam-6199	426	1	|	|	ADV
ejpam-6199	426	2	(	(	PUNCT
ejpam-6199	426	3	v	v	NOUN
ejpam-6199	426	4	|	|	ADV
ejpam-6199	426	5	w	w	NOUN
ejpam-6199	426	6	)	)	PUNCT
ejpam-6199	426	7	)	)	PUNCT
ejpam-6199	426	8	⪰	⪰	NOUN
ejpam-6199	426	9	m̃in{υ̃πψ	m̃in{υ̃πψ	PROPN
ejpam-6199	426	10	(	(	PUNCT
ejpam-6199	426	11	v	v	NOUN
ejpam-6199	426	12	)	)	PUNCT
ejpam-6199	426	13	,	,	PUNCT
ejpam-6199	426	14	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	426	15	(	(	PUNCT
ejpam-6199	426	16	w	w	NOUN
ejpam-6199	426	17	)	)	PUNCT
ejpam-6199	426	18	}	}	PUNCT
ejpam-6199	426	19	=	=	SYM
ejpam-6199	426	20	α̃	α̃	PROPN
ejpam-6199	426	21	and	and	CCONJ
ejpam-6199	426	22	ϖπψ	ϖπψ	NOUN
ejpam-6199	426	23	(	(	PUNCT
ejpam-6199	426	24	(	(	PUNCT
ejpam-6199	426	25	n	n	CCONJ
ejpam-6199	426	26	|	|	ADV
ejpam-6199	426	27	(	(	PUNCT
ejpam-6199	426	28	v	v	NOUN
ejpam-6199	426	29	|	|	ADV
ejpam-6199	426	30	w	w	NOUN
ejpam-6199	426	31	)	)	PUNCT
ejpam-6199	426	32	)	)	PUNCT
ejpam-6199	427	1	|	|	ADV
ejpam-6199	427	2	(	(	PUNCT
ejpam-6199	427	3	v	v	NOUN
ejpam-6199	427	4	|	|	ADV
ejpam-6199	427	5	w	w	NOUN
ejpam-6199	427	6	)	)	PUNCT
ejpam-6199	427	7	)	)	PUNCT
ejpam-6199	427	8	≤	≤	NUM
ejpam-6199	427	9	max{ϖπψ	max{ϖπψ	NOUN
ejpam-6199	427	10	(	(	PUNCT
ejpam-6199	427	11	v	v	NOUN
ejpam-6199	427	12	)	)	PUNCT
ejpam-6199	427	13	,	,	PUNCT
ejpam-6199	427	14	ϖπψ	ϖπψ	X
ejpam-6199	427	15	(	(	PUNCT
ejpam-6199	427	16	w	w	NOUN
ejpam-6199	427	17	)	)	PUNCT
ejpam-6199	427	18	}	}	PUNCT
ejpam-6199	427	19	=	=	SYM
ejpam-6199	427	20	β	β	X
ejpam-6199	427	21	.	.	PUNCT
ejpam-6199	428	1	hence	hence	ADV
ejpam-6199	428	2	,	,	PUNCT
ejpam-6199	428	3	πψ	πψ	ADP
ejpam-6199	428	4	=	=	SYM
ejpam-6199	428	5	(	(	PUNCT
ejpam-6199	428	6	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	428	7	,	,	PUNCT
ejpam-6199	428	8	ϖπψ	ϖπψ	PROPN
ejpam-6199	428	9	)	)	PUNCT
ejpam-6199	428	10	is	be	AUX
ejpam-6199	428	11	a	a	DET
ejpam-6199	428	12	crossing	cross	VERB
ejpam-6199	428	13	cubic	cubic	ADJ
ejpam-6199	428	14	filter	filter	NOUN
ejpam-6199	428	15	of	of	ADP
ejpam-6199	428	16	ϑ.	ϑ.	NOUN
ejpam-6199	428	17	since	since	SCONJ
ejpam-6199	428	18	ψ	ψ	NOUN
ejpam-6199	428	19	is	be	AUX
ejpam-6199	428	20	a	a	DET
ejpam-6199	428	21	filter	filter	NOUN
ejpam-6199	428	22	of	of	ADP
ejpam-6199	428	23	ϑ	ϑ	X
ejpam-6199	428	24	,	,	PUNCT
ejpam-6199	428	25	we	we	PRON
ejpam-6199	428	26	get	get	VERB
ejpam-6199	428	27	ϑπψ	ϑπψ	NOUN
ejpam-6199	428	28	=	=	SYM
ejpam-6199	428	29	{	{	PUNCT
ejpam-6199	428	30	n	n	ADP
ejpam-6199	428	31	∈	∈	PROPN
ejpam-6199	428	32	ϑ	ϑ	X
ejpam-6199	428	33	|	|	ADV
ejpam-6199	428	34	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	428	35	(	(	PUNCT
ejpam-6199	428	36	n	n	CCONJ
ejpam-6199	428	37	)	)	PUNCT
ejpam-6199	428	38	=	=	SYM
ejpam-6199	429	1	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	429	2	(	(	PUNCT
ejpam-6199	429	3	1	1	NUM
ejpam-6199	429	4	)	)	PUNCT
ejpam-6199	429	5	,	,	PUNCT
ejpam-6199	429	6	and	and	CCONJ
ejpam-6199	429	7	ϖπψ	ϖπψ	NOUN
ejpam-6199	429	8	(	(	PUNCT
ejpam-6199	429	9	n	n	CCONJ
ejpam-6199	429	10	)	)	PUNCT
ejpam-6199	429	11	=	=	NOUN
ejpam-6199	429	12	ϖπψ	ϖπψ	X
ejpam-6199	429	13	(	(	PUNCT
ejpam-6199	429	14	1	1	NUM
ejpam-6199	429	15	)	)	PUNCT
ejpam-6199	429	16	}	}	PUNCT
ejpam-6199	429	17	=	=	SYM
ejpam-6199	429	18	{	{	PUNCT
ejpam-6199	429	19	n	n	PRON
ejpam-6199	429	20	∈	∈	PROPN
ejpam-6199	429	21	ϑ	ϑ	X
ejpam-6199	429	22	|	|	ADV
ejpam-6199	429	23	υ̃πψ	υ̃πψ	PROPN
ejpam-6199	429	24	(	(	PUNCT
ejpam-6199	429	25	n	n	CCONJ
ejpam-6199	429	26	)	)	PUNCT
ejpam-6199	429	27	=	=	SYM
ejpam-6199	429	28	τ̃	τ̃	PROPN
ejpam-6199	429	29	,	,	PUNCT
ejpam-6199	429	30	and	and	CCONJ
ejpam-6199	429	31	ϖπψ	ϖπψ	NOUN
ejpam-6199	429	32	(	(	PUNCT
ejpam-6199	429	33	n	n	CCONJ
ejpam-6199	429	34	)	)	PUNCT
ejpam-6199	429	35	=	=	SYM
ejpam-6199	429	36	κ	κ	X
ejpam-6199	429	37	}	}	PUNCT
ejpam-6199	429	38	=	=	SYM
ejpam-6199	429	39	{	{	PUNCT
ejpam-6199	429	40	n	n	X
ejpam-6199	429	41	∈	∈	VERB
ejpam-6199	429	42	ϑ|n	ϑ|n	ADV
ejpam-6199	429	43	∈	∈	NOUN
ejpam-6199	429	44	ψ	ψ	NOUN
ejpam-6199	429	45	}	}	PUNCT
ejpam-6199	429	46	=	=	SYM
ejpam-6199	429	47	ψ	ψ	NOUN
ejpam-6199	429	48	.	.	NOUN
ejpam-6199	429	49	4	4	X
ejpam-6199	429	50	.	.	X
ejpam-6199	429	51	crossing	cross	VERB
ejpam-6199	429	52	cubic	cubic	ADJ
ejpam-6199	429	53	deductive	deductive	ADJ
ejpam-6199	429	54	systems	system	NOUN
ejpam-6199	429	55	here	here	ADV
ejpam-6199	429	56	,	,	PUNCT
ejpam-6199	429	57	we	we	PRON
ejpam-6199	429	58	present	present	VERB
ejpam-6199	429	59	the	the	DET
ejpam-6199	429	60	idea	idea	NOUN
ejpam-6199	429	61	of	of	ADP
ejpam-6199	429	62	crossing	cross	VERB
ejpam-6199	429	63	cubic	cubic	ADJ
ejpam-6199	429	64	deductive	deductive	ADJ
ejpam-6199	429	65	system	system	NOUN
ejpam-6199	429	66	and	and	CCONJ
ejpam-6199	429	67	give	give	VERB
ejpam-6199	429	68	an	an	DET
ejpam-6199	429	69	example	example	NOUN
ejpam-6199	429	70	on	on	ADP
ejpam-6199	429	71	it	it	PRON
ejpam-6199	429	72	.	.	PUNCT
ejpam-6199	430	1	then	then	ADV
ejpam-6199	430	2	,	,	PUNCT
ejpam-6199	430	3	we	we	PRON
ejpam-6199	430	4	prove	prove	VERB
ejpam-6199	430	5	that	that	SCONJ
ejpam-6199	430	6	a	a	DET
ejpam-6199	430	7	crossing	cross	VERB
ejpam-6199	430	8	cubic	cubic	ADJ
ejpam-6199	430	9	deductive	deductive	ADJ
ejpam-6199	430	10	system	system	NOUN
ejpam-6199	430	11	and	and	CCONJ
ejpam-6199	430	12	a	a	DET
ejpam-6199	430	13	crossing	cross	VERB
ejpam-6199	430	14	cubic	cubic	ADJ
ejpam-6199	430	15	filter	filter	NOUN
ejpam-6199	430	16	are	be	AUX
ejpam-6199	430	17	a	a	DET
ejpam-6199	430	18	complementary	complementary	ADJ
ejpam-6199	430	19	notion	notion	NOUN
ejpam-6199	430	20	.	.	PUNCT
ejpam-6199	431	1	definition	definition	NOUN
ejpam-6199	431	2	10	10	NUM
ejpam-6199	431	3	.	.	PUNCT
ejpam-6199	432	1	a	a	DET
ejpam-6199	432	2	crossing	cross	VERB
ejpam-6199	432	3	cubic	cubic	ADJ
ejpam-6199	432	4	structure	structure	NOUN
ejpam-6199	432	5	π	π	PROPN
ejpam-6199	432	6	=	=	SYM
ejpam-6199	432	7	(	(	PUNCT
ejpam-6199	432	8	υ̃π	υ̃π	PROPN
ejpam-6199	432	9	,	,	PUNCT
ejpam-6199	432	10	ϖπ	ϖπ	NOUN
ejpam-6199	432	11	)	)	PUNCT
ejpam-6199	432	12	is	be	AUX
ejpam-6199	432	13	called	call	VERB
ejpam-6199	432	14	a	a	DET
ejpam-6199	432	15	crossing	cross	VERB
ejpam-6199	432	16	cubic	cubic	ADJ
ejpam-6199	432	17	deductive	deductive	ADJ
ejpam-6199	432	18	system	system	NOUN
ejpam-6199	432	19	of	of	ADP
ejpam-6199	432	20	ϑ	ϑ	PRON
ejpam-6199	432	21	if	if	SCONJ
ejpam-6199	432	22	it	it	PRON
ejpam-6199	432	23	satisfies	satisfy	VERB
ejpam-6199	432	24	(	(	PUNCT
ejpam-6199	432	25	i	i	NOUN
ejpam-6199	432	26	)	)	PUNCT
ejpam-6199	432	27	of	of	ADP
ejpam-6199	432	28	definition	definition	NOUN
ejpam-6199	432	29	9	9	NUM
ejpam-6199	432	30	and	and	CCONJ
ejpam-6199	432	31	the	the	DET
ejpam-6199	432	32	condition	condition	NOUN
ejpam-6199	432	33	(	(	PUNCT
ejpam-6199	432	34	c	c	NOUN
ejpam-6199	432	35	)	)	PUNCT
ejpam-6199	432	36	,	,	PUNCT
ejpam-6199	432	37	where	where	SCONJ
ejpam-6199	432	38	(	(	PUNCT
ejpam-6199	432	39	c	c	NOUN
ejpam-6199	432	40	)	)	PUNCT
ejpam-6199	432	41	(	(	PUNCT
ejpam-6199	432	42	∀n	∀n	X
ejpam-6199	432	43	,	,	PUNCT
ejpam-6199	432	44	v	v	NOUN
ejpam-6199	432	45	∈	∈	PROPN
ejpam-6199	432	46	ϑ	ϑ	NOUN
ejpam-6199	432	47	)	)	PUNCT
ejpam-6199	432	48	(	(	PUNCT
ejpam-6199	432	49	υ̃π(v	υ̃π(v	NUM
ejpam-6199	432	50	)	)	PUNCT
ejpam-6199	432	51	⪰	⪰	NOUN
ejpam-6199	432	52	m̃in{υ̃π(n	m̃in{υ̃π(n	PROPN
ejpam-6199	432	53	)	)	PUNCT
ejpam-6199	432	54	,	,	PUNCT
ejpam-6199	432	55	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	432	56	|	|	ADV
ejpam-6199	432	57	(	(	PUNCT
ejpam-6199	432	58	v	v	NOUN
ejpam-6199	432	59	|	|	ADV
ejpam-6199	432	60	v	v	NOUN
ejpam-6199	432	61	)	)	PUNCT
ejpam-6199	432	62	)	)	PUNCT
ejpam-6199	432	63	}	}	PUNCT
ejpam-6199	432	64	,	,	PUNCT
ejpam-6199	432	65	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	432	66	)	)	PUNCT
ejpam-6199	432	67	≤	≤	NUM
ejpam-6199	432	68	max{ϖπ(n	max{ϖπ(n	PROPN
ejpam-6199	432	69	)	)	PUNCT
ejpam-6199	432	70	,	,	PUNCT
ejpam-6199	432	71	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	433	1	|	|	ADV
ejpam-6199	433	2	(	(	PUNCT
ejpam-6199	433	3	v	v	NOUN
ejpam-6199	433	4	|	|	ADV
ejpam-6199	433	5	v	v	NOUN
ejpam-6199	433	6	)	)	PUNCT
ejpam-6199	433	7	)	)	PUNCT
ejpam-6199	433	8	}	}	PUNCT
ejpam-6199	433	9	)	)	PUNCT
ejpam-6199	433	10	.	.	PUNCT
ejpam-6199	434	1	example	example	NOUN
ejpam-6199	435	1	3	3	X
ejpam-6199	435	2	.	.	X
ejpam-6199	435	3	consider	consider	VERB
ejpam-6199	435	4	the	the	DET
ejpam-6199	435	5	sheffer	sheffer	NOUN
ejpam-6199	435	6	stroke	stroke	NOUN
ejpam-6199	435	7	hilbert	hilbert	PROPN
ejpam-6199	435	8	algebra	algebra	PROPN
ejpam-6199	435	9	ϑ	ϑ	ADP
ejpam-6199	435	10	◦	◦	NOUN
ejpam-6199	435	11	:	:	PUNCT
ejpam-6199	435	12	=	=	SYM
ejpam-6199	435	13	(	(	PUNCT
ejpam-6199	435	14	ϑ	ϑ	X
ejpam-6199	435	15	,	,	PUNCT
ejpam-6199	435	16	|	|	INTJ
ejpam-6199	435	17	)	)	PUNCT
ejpam-6199	435	18	in	in	ADP
ejpam-6199	435	19	example	example	NOUN
ejpam-6199	435	20	1	1	NUM
ejpam-6199	435	21	and	and	CCONJ
ejpam-6199	435	22	let	let	VERB
ejpam-6199	435	23	π	π	PROPN
ejpam-6199	435	24	=	=	SYM
ejpam-6199	435	25	(	(	PUNCT
ejpam-6199	435	26	υ̃π	υ̃π	PROPN
ejpam-6199	435	27	,	,	PUNCT
ejpam-6199	435	28	ϖπ	ϖπ	NOUN
ejpam-6199	435	29	)	)	PUNCT
ejpam-6199	435	30	be	be	AUX
ejpam-6199	435	31	a	a	DET
ejpam-6199	435	32	crossing	cross	VERB
ejpam-6199	435	33	cubic	cubic	ADJ
ejpam-6199	435	34	structure	structure	NOUN
ejpam-6199	435	35	in	in	ADP
ejpam-6199	435	36	ϑ	ϑ	PRON
ejpam-6199	435	37	,	,	PUNCT
ejpam-6199	435	38	which	which	PRON
ejpam-6199	435	39	is	be	AUX
ejpam-6199	435	40	displayed	display	VERB
ejpam-6199	435	41	in	in	ADP
ejpam-6199	435	42	table	table	NOUN
ejpam-6199	435	43	8	8	NUM
ejpam-6199	435	44	.	.	PUNCT
ejpam-6199	435	45	table	table	NOUN
ejpam-6199	435	46	8	8	NUM
ejpam-6199	435	47	:	:	PUNCT
ejpam-6199	435	48	π	π	X
ejpam-6199	435	49	=	=	SYM
ejpam-6199	435	50	(	(	PUNCT
ejpam-6199	435	51	υ̃π	υ̃π	PROPN
ejpam-6199	435	52	,	,	PUNCT
ejpam-6199	435	53	ϖπ	ϖπ	NOUN
ejpam-6199	435	54	)	)	PUNCT
ejpam-6199	435	55	is	be	AUX
ejpam-6199	435	56	represented	represent	VERB
ejpam-6199	435	57	tabularly	tabularly	ADV
ejpam-6199	435	58	ϑ	ϑ	X
ejpam-6199	435	59	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	435	60	)	)	PUNCT
ejpam-6199	436	1	ϖπ(n	ϖπ(n	ADP
ejpam-6199	436	2	)	)	PUNCT
ejpam-6199	436	3	0	0	PUNCT
ejpam-6199	437	1	[	[	X
ejpam-6199	437	2	0.19	0.19	NUM
ejpam-6199	437	3	,	,	PUNCT
ejpam-6199	437	4	0.54	0.54	NUM
ejpam-6199	437	5	]	]	PUNCT
ejpam-6199	437	6	-0.37	-0.37	NUM
ejpam-6199	437	7	2ϑ	2ϑ	NUM
ejpam-6199	438	1	[	[	X
ejpam-6199	438	2	0.24	0.24	NUM
ejpam-6199	438	3	,	,	PUNCT
ejpam-6199	438	4	0.62	0.62	NUM
ejpam-6199	438	5	]	]	PUNCT
ejpam-6199	438	6	-0.57	-0.57	X
ejpam-6199	439	1	3ϑ	3ϑ	NUM
ejpam-6199	440	1	[	[	X
ejpam-6199	440	2	0.19	0.19	NUM
ejpam-6199	440	3	,	,	PUNCT
ejpam-6199	440	4	0.54	0.54	NUM
ejpam-6199	440	5	]	]	PUNCT
ejpam-6199	440	6	-0.37	-0.37	NUM
ejpam-6199	440	7	4ϑ	4ϑ	NOUN
ejpam-6199	441	1	[	[	X
ejpam-6199	441	2	0.19	0.19	NUM
ejpam-6199	441	3	,	,	PUNCT
ejpam-6199	441	4	0.54	0.54	NUM
ejpam-6199	441	5	]	]	PUNCT
ejpam-6199	441	6	-0.37	-0.37	NUM
ejpam-6199	441	7	5ϑ	5ϑ	NUM
ejpam-6199	441	8	[	[	X
ejpam-6199	441	9	0.26	0.26	NUM
ejpam-6199	441	10	,	,	PUNCT
ejpam-6199	441	11	0.63	0.63	NUM
ejpam-6199	441	12	]	]	X
ejpam-6199	441	13	-0.61	-0.61	NOUN
ejpam-6199	441	14	6ϑ	6ϑ	NOUN
ejpam-6199	442	1	[	[	X
ejpam-6199	442	2	0.24	0.24	NUM
ejpam-6199	442	3	,	,	PUNCT
ejpam-6199	442	4	0.62	0.62	NUM
ejpam-6199	442	5	]	]	PUNCT
ejpam-6199	442	6	-0.57	-0.57	NOUN
ejpam-6199	443	1	7ϑ	7ϑ	NOUN
ejpam-6199	444	1	[	[	X
ejpam-6199	444	2	0.19	0.19	NUM
ejpam-6199	444	3	,	,	PUNCT
ejpam-6199	444	4	0.54	0.54	NUM
ejpam-6199	444	5	]	]	PUNCT
ejpam-6199	444	6	-0.37	-0.37	NUM
ejpam-6199	444	7	1	1	NUM
ejpam-6199	444	8	[	[	X
ejpam-6199	444	9	0.41	0.41	NUM
ejpam-6199	444	10	,	,	PUNCT
ejpam-6199	444	11	0.87	0.87	NUM
ejpam-6199	444	12	]	]	PUNCT
ejpam-6199	444	13	-0.69	-0.69	NOUN
ejpam-6199	444	14	it	it	PRON
ejpam-6199	444	15	is	be	AUX
ejpam-6199	444	16	routine	routine	ADJ
ejpam-6199	444	17	to	to	PART
ejpam-6199	444	18	check	check	VERB
ejpam-6199	444	19	that	that	PRON
ejpam-6199	444	20	π	π	PROPN
ejpam-6199	444	21	=	=	PRON
ejpam-6199	444	22	(	(	PUNCT
ejpam-6199	444	23	υ̃π	υ̃π	PROPN
ejpam-6199	444	24	,	,	PUNCT
ejpam-6199	444	25	ϖπ	ϖπ	NOUN
ejpam-6199	444	26	)	)	PUNCT
ejpam-6199	444	27	is	be	AUX
ejpam-6199	444	28	a	a	DET
ejpam-6199	444	29	crossing	cross	VERB
ejpam-6199	444	30	cubic	cubic	ADJ
ejpam-6199	444	31	deductive	deductive	ADJ
ejpam-6199	444	32	system	system	NOUN
ejpam-6199	444	33	of	of	ADP
ejpam-6199	444	34	ϑ.	ϑ.	PROPN
ejpam-6199	444	35	a.	a.	PROPN
ejpam-6199	444	36	al	al	PROPN
ejpam-6199	444	37	-	-	PROPN
ejpam-6199	444	38	masarwah	masarwah	PROPN
ejpam-6199	444	39	et	et	PROPN
ejpam-6199	444	40	al	al	PROPN
ejpam-6199	444	41	.	.	PUNCT
ejpam-6199	444	42	/	/	SYM
ejpam-6199	444	43	eur	eur	PROPN
ejpam-6199	444	44	.	.	PUNCT
ejpam-6199	445	1	j.	j.	PROPN
ejpam-6199	445	2	pure	pure	PROPN
ejpam-6199	445	3	appl	appl	PROPN
ejpam-6199	445	4	.	.	PROPN
ejpam-6199	445	5	math	math	PROPN
ejpam-6199	445	6	,	,	PUNCT
ejpam-6199	445	7	18	18	NUM
ejpam-6199	445	8	(	(	PUNCT
ejpam-6199	445	9	3	3	NUM
ejpam-6199	445	10	)	)	PUNCT
ejpam-6199	445	11	(	(	PUNCT
ejpam-6199	445	12	2025	2025	NUM
ejpam-6199	445	13	)	)	PUNCT
ejpam-6199	445	14	,	,	PUNCT
ejpam-6199	445	15	6199	6199	NUM
ejpam-6199	445	16	14	14	NUM
ejpam-6199	445	17	of	of	ADP
ejpam-6199	445	18	17	17	NUM
ejpam-6199	445	19	next	next	ADJ
ejpam-6199	445	20	theorem	theorem	NOUN
ejpam-6199	445	21	proves	prove	VERB
ejpam-6199	445	22	that	that	SCONJ
ejpam-6199	445	23	a	a	DET
ejpam-6199	445	24	crossing	cross	VERB
ejpam-6199	445	25	cubic	cubic	ADJ
ejpam-6199	445	26	deductive	deductive	ADJ
ejpam-6199	445	27	system	system	NOUN
ejpam-6199	445	28	and	and	CCONJ
ejpam-6199	445	29	a	a	DET
ejpam-6199	445	30	crossing	cross	VERB
ejpam-6199	445	31	cubic	cubic	ADJ
ejpam-6199	445	32	filter	filter	NOUN
ejpam-6199	445	33	are	be	AUX
ejpam-6199	445	34	a	a	DET
ejpam-6199	445	35	complementary	complementary	ADJ
ejpam-6199	445	36	notion	notion	NOUN
ejpam-6199	445	37	.	.	PUNCT
ejpam-6199	446	1	theorem	theorem	NOUN
ejpam-6199	446	2	5	5	NUM
ejpam-6199	446	3	.	.	PUNCT
ejpam-6199	446	4	a	a	DET
ejpam-6199	446	5	crossing	cross	VERB
ejpam-6199	446	6	cubic	cubic	ADJ
ejpam-6199	446	7	structure	structure	NOUN
ejpam-6199	446	8	π	π	PROPN
ejpam-6199	446	9	=	=	SYM
ejpam-6199	446	10	(	(	PUNCT
ejpam-6199	446	11	υ̃π	υ̃π	PROPN
ejpam-6199	446	12	,	,	PUNCT
ejpam-6199	446	13	ϖπ	ϖπ	NOUN
ejpam-6199	446	14	)	)	PUNCT
ejpam-6199	446	15	in	in	ADP
ejpam-6199	446	16	ϑ	ϑ	PROPN
ejpam-6199	446	17	is	be	AUX
ejpam-6199	446	18	a	a	DET
ejpam-6199	446	19	crossing	cross	VERB
ejpam-6199	446	20	cubic	cubic	ADJ
ejpam-6199	446	21	deductive	deductive	ADJ
ejpam-6199	446	22	system	system	NOUN
ejpam-6199	446	23	of	of	ADP
ejpam-6199	446	24	ϑ	ϑ	PRON
ejpam-6199	446	25	if	if	SCONJ
ejpam-6199	446	26	and	and	CCONJ
ejpam-6199	446	27	only	only	ADV
ejpam-6199	446	28	if	if	SCONJ
ejpam-6199	446	29	it	it	PRON
ejpam-6199	446	30	is	be	AUX
ejpam-6199	446	31	a	a	DET
ejpam-6199	446	32	crossing	cross	VERB
ejpam-6199	446	33	cubic	cubic	ADJ
ejpam-6199	446	34	filter	filter	NOUN
ejpam-6199	446	35	of	of	ADP
ejpam-6199	446	36	ϑ.	ϑ.	NOUN
ejpam-6199	446	37	proof	proof	NOUN
ejpam-6199	446	38	.	.	PUNCT
ejpam-6199	447	1	assume	assume	VERB
ejpam-6199	447	2	that	that	SCONJ
ejpam-6199	447	3	π	π	PROPN
ejpam-6199	447	4	=	=	PRON
ejpam-6199	447	5	(	(	PUNCT
ejpam-6199	447	6	υ̃π	υ̃π	PROPN
ejpam-6199	447	7	,	,	PUNCT
ejpam-6199	447	8	ϖπ	ϖπ	NOUN
ejpam-6199	447	9	)	)	PUNCT
ejpam-6199	447	10	is	be	AUX
ejpam-6199	447	11	a	a	DET
ejpam-6199	447	12	crossing	cross	VERB
ejpam-6199	447	13	cubic	cubic	ADJ
ejpam-6199	447	14	deductive	deductive	ADJ
ejpam-6199	447	15	system	system	NOUN
ejpam-6199	447	16	of	of	ADP
ejpam-6199	447	17	ϑ	ϑ	NOUN
ejpam-6199	447	18	and	and	CCONJ
ejpam-6199	447	19	let	let	VERB
ejpam-6199	447	20	n	n	CCONJ
ejpam-6199	447	21	,	,	PUNCT
ejpam-6199	447	22	v	v	NOUN
ejpam-6199	447	23	,	,	PUNCT
ejpam-6199	447	24	w	w	PROPN
ejpam-6199	447	25	∈	∈	PROPN
ejpam-6199	447	26	ϑ.	ϑ.	NOUN
ejpam-6199	447	27	using	use	VERB
ejpam-6199	447	28	the	the	DET
ejpam-6199	447	29	condition	condition	NOUN
ejpam-6199	447	30	(	(	PUNCT
ejpam-6199	447	31	a	a	X
ejpam-6199	447	32	)	)	PUNCT
ejpam-6199	447	33	and	and	CCONJ
ejpam-6199	447	34	(	(	PUNCT
ejpam-6199	447	35	4	4	X
ejpam-6199	447	36	)	)	PUNCT
ejpam-6199	447	37	of	of	ADP
ejpam-6199	447	38	proposition	proposition	NOUN
ejpam-6199	447	39	1	1	NUM
ejpam-6199	447	40	induces	induce	VERB
ejpam-6199	447	41	v	v	ADP
ejpam-6199	447	42	|	|	NOUN
ejpam-6199	447	43	(	(	PUNCT
ejpam-6199	447	44	(	(	PUNCT
ejpam-6199	447	45	n	n	CCONJ
ejpam-6199	447	46	|	|	ADV
ejpam-6199	447	47	(	(	PUNCT
ejpam-6199	447	48	v	v	NOUN
ejpam-6199	447	49	|	|	ADV
ejpam-6199	447	50	v	v	NOUN
ejpam-6199	447	51	)	)	PUNCT
ejpam-6199	447	52	)	)	PUNCT
ejpam-6199	448	1	|	|	ADV
ejpam-6199	448	2	(	(	PUNCT
ejpam-6199	448	3	n	n	CCONJ
ejpam-6199	448	4	|	|	ADV
ejpam-6199	448	5	(	(	PUNCT
ejpam-6199	448	6	v	v	NOUN
ejpam-6199	448	7	|	|	ADV
ejpam-6199	448	8	v	v	NOUN
ejpam-6199	448	9	)	)	PUNCT
ejpam-6199	448	10	)	)	PUNCT
ejpam-6199	448	11	)	)	PUNCT
ejpam-6199	449	1	=	=	PUNCT
ejpam-6199	450	1	1	1	X
ejpam-6199	450	2	.	.	PUNCT
ejpam-6199	451	1	it	it	PRON
ejpam-6199	451	2	follows	follow	VERB
ejpam-6199	451	3	from	from	ADP
ejpam-6199	451	4	(	(	PUNCT
ejpam-6199	451	5	i	i	NOUN
ejpam-6199	451	6	)	)	PUNCT
ejpam-6199	451	7	of	of	ADP
ejpam-6199	451	8	definition	definition	NOUN
ejpam-6199	451	9	9	9	NUM
ejpam-6199	451	10	and	and	CCONJ
ejpam-6199	451	11	the	the	DET
ejpam-6199	451	12	condition	condition	NOUN
ejpam-6199	451	13	(	(	PUNCT
ejpam-6199	451	14	c	c	NOUN
ejpam-6199	451	15	)	)	PUNCT
ejpam-6199	451	16	that	that	PRON
ejpam-6199	451	17	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	452	1	|	|	ADV
ejpam-6199	452	2	(	(	PUNCT
ejpam-6199	452	3	v	v	NOUN
ejpam-6199	452	4	|	|	ADV
ejpam-6199	452	5	v	v	NOUN
ejpam-6199	452	6	)	)	PUNCT
ejpam-6199	452	7	)	)	PUNCT
ejpam-6199	453	1	⪰	⪰	NOUN
ejpam-6199	453	2	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	453	3	)	)	PUNCT
ejpam-6199	453	4	,	,	PUNCT
ejpam-6199	453	5	υ̃π(v	υ̃π(v	NUM
ejpam-6199	453	6	|	|	ADV
ejpam-6199	453	7	(	(	PUNCT
ejpam-6199	453	8	(	(	PUNCT
ejpam-6199	453	9	n	n	CCONJ
ejpam-6199	453	10	|	|	ADV
ejpam-6199	453	11	(	(	PUNCT
ejpam-6199	453	12	v	v	NOUN
ejpam-6199	453	13	|	|	ADV
ejpam-6199	453	14	v	v	NOUN
ejpam-6199	453	15	)	)	PUNCT
ejpam-6199	453	16	)	)	PUNCT
ejpam-6199	454	1	|	|	ADV
ejpam-6199	454	2	(	(	PUNCT
ejpam-6199	454	3	n	n	CCONJ
ejpam-6199	454	4	|	|	ADV
ejpam-6199	454	5	(	(	PUNCT
ejpam-6199	454	6	v	v	NOUN
ejpam-6199	454	7	|	|	ADV
ejpam-6199	454	8	v	v	NOUN
ejpam-6199	454	9	)	)	PUNCT
ejpam-6199	454	10	)	)	PUNCT
ejpam-6199	454	11	)	)	PUNCT
ejpam-6199	454	12	)	)	PUNCT
ejpam-6199	454	13	}	}	PUNCT
ejpam-6199	455	1	=	=	SYM
ejpam-6199	455	2	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	455	3	)	)	PUNCT
ejpam-6199	455	4	,	,	PUNCT
ejpam-6199	455	5	υ̃π(1	υ̃π(1	NOUN
ejpam-6199	455	6	)	)	PUNCT
ejpam-6199	455	7	}	}	PUNCT
ejpam-6199	455	8	=	=	SYM
ejpam-6199	455	9	υ̃π(v	υ̃π(v	NUM
ejpam-6199	455	10	)	)	PUNCT
ejpam-6199	455	11	and	and	CCONJ
ejpam-6199	455	12	ϖπ(n	ϖπ(n	ADV
ejpam-6199	456	1	|	|	ADV
ejpam-6199	456	2	(	(	PUNCT
ejpam-6199	456	3	v	v	NOUN
ejpam-6199	456	4	|	|	ADV
ejpam-6199	456	5	v	v	NOUN
ejpam-6199	456	6	)	)	PUNCT
ejpam-6199	456	7	)	)	PUNCT
ejpam-6199	457	1	≤	≤	NUM
ejpam-6199	457	2	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	457	3	)	)	PUNCT
ejpam-6199	457	4	,	,	PUNCT
ejpam-6199	457	5	ϖπ(v	ϖπ(v	PUNCT
ejpam-6199	457	6	|	|	ADV
ejpam-6199	457	7	(	(	PUNCT
ejpam-6199	457	8	(	(	PUNCT
ejpam-6199	457	9	n	n	CCONJ
ejpam-6199	457	10	|	|	ADV
ejpam-6199	457	11	(	(	PUNCT
ejpam-6199	457	12	v	v	NOUN
ejpam-6199	457	13	|	|	ADV
ejpam-6199	457	14	v	v	NOUN
ejpam-6199	457	15	)	)	PUNCT
ejpam-6199	457	16	)	)	PUNCT
ejpam-6199	458	1	|	|	ADV
ejpam-6199	458	2	(	(	PUNCT
ejpam-6199	458	3	n	n	CCONJ
ejpam-6199	458	4	|	|	ADV
ejpam-6199	458	5	(	(	PUNCT
ejpam-6199	458	6	v	v	NOUN
ejpam-6199	458	7	|	|	ADV
ejpam-6199	458	8	v	v	NOUN
ejpam-6199	458	9	)	)	PUNCT
ejpam-6199	458	10	)	)	PUNCT
ejpam-6199	458	11	)	)	PUNCT
ejpam-6199	458	12	)	)	PUNCT
ejpam-6199	458	13	}	}	PUNCT
ejpam-6199	458	14	=	=	SYM
ejpam-6199	458	15	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	458	16	)	)	PUNCT
ejpam-6199	458	17	,	,	PUNCT
ejpam-6199	458	18	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	458	19	)	)	PUNCT
ejpam-6199	458	20	}	}	PUNCT
ejpam-6199	458	21	=	=	SYM
ejpam-6199	458	22	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	458	23	)	)	PUNCT
ejpam-6199	458	24	.	.	PUNCT
ejpam-6199	459	1	note	note	VERB
ejpam-6199	459	2	that	that	SCONJ
ejpam-6199	459	3	by	by	ADP
ejpam-6199	459	4	(	(	PUNCT
ejpam-6199	459	5	2	2	NUM
ejpam-6199	459	6	)	)	PUNCT
ejpam-6199	459	7	of	of	ADP
ejpam-6199	459	8	definition	definition	NOUN
ejpam-6199	459	9	1	1	NUM
ejpam-6199	459	10	,	,	PUNCT
ejpam-6199	459	11	(	(	PUNCT
ejpam-6199	459	12	1	1	NUM
ejpam-6199	459	13	)	)	PUNCT
ejpam-6199	459	14	and	and	CCONJ
ejpam-6199	459	15	(	(	PUNCT
ejpam-6199	459	16	7	7	X
ejpam-6199	459	17	)	)	PUNCT
ejpam-6199	459	18	of	of	ADP
ejpam-6199	459	19	proposition	proposition	NOUN
ejpam-6199	459	20	1	1	NUM
ejpam-6199	459	21	,	,	PUNCT
ejpam-6199	459	22	we	we	PRON
ejpam-6199	459	23	have	have	VERB
ejpam-6199	459	24	v	v	NUM
ejpam-6199	459	25	|	|	ADV
ejpam-6199	459	26	(	(	PUNCT
ejpam-6199	459	27	(	(	PUNCT
ejpam-6199	459	28	(	(	PUNCT
ejpam-6199	459	29	v	v	NOUN
ejpam-6199	459	30	|	|	ADV
ejpam-6199	459	31	w	w	NOUN
ejpam-6199	459	32	)	)	PUNCT
ejpam-6199	459	33	|	|	ADV
ejpam-6199	459	34	w	w	NOUN
ejpam-6199	459	35	)	)	PUNCT
ejpam-6199	460	1	|	|	ADV
ejpam-6199	460	2	(	(	PUNCT
ejpam-6199	460	3	(	(	PUNCT
ejpam-6199	460	4	v	v	INTJ
ejpam-6199	460	5	|	|	ADV
ejpam-6199	460	6	w	w	NOUN
ejpam-6199	460	7	)	)	PUNCT
ejpam-6199	460	8	|	|	ADV
ejpam-6199	460	9	w	w	NOUN
ejpam-6199	460	10	)	)	PUNCT
ejpam-6199	460	11	)	)	PUNCT
ejpam-6199	461	1	=	=	PUNCT
ejpam-6199	461	2	v	v	ADP
ejpam-6199	461	3	|	|	INTJ
ejpam-6199	461	4	(	(	PUNCT
ejpam-6199	461	5	(	(	PUNCT
ejpam-6199	461	6	(	(	PUNCT
ejpam-6199	461	7	v	v	NOUN
ejpam-6199	461	8	|	|	ADV
ejpam-6199	461	9	w	w	NOUN
ejpam-6199	461	10	)	)	PUNCT
ejpam-6199	462	1	|	|	ADV
ejpam-6199	462	2	(	(	PUNCT
ejpam-6199	462	3	(	(	PUNCT
ejpam-6199	462	4	w	w	PROPN
ejpam-6199	462	5	|	|	ADV
ejpam-6199	462	6	w	w	NOUN
ejpam-6199	462	7	)	)	PUNCT
ejpam-6199	463	1	|	|	ADV
ejpam-6199	463	2	(	(	PUNCT
ejpam-6199	463	3	w	w	PROPN
ejpam-6199	463	4	|	|	ADV
ejpam-6199	463	5	w	w	NOUN
ejpam-6199	463	6	)	)	PUNCT
ejpam-6199	463	7	)	)	PUNCT
ejpam-6199	463	8	)	)	PUNCT
ejpam-6199	464	1	|	|	ADV
ejpam-6199	464	2	(	(	PUNCT
ejpam-6199	464	3	(	(	PUNCT
ejpam-6199	464	4	v	v	INTJ
ejpam-6199	464	5	|	|	ADV
ejpam-6199	464	6	w	w	NOUN
ejpam-6199	464	7	)	)	PUNCT
ejpam-6199	464	8	|	|	ADV
ejpam-6199	464	9	(	(	PUNCT
ejpam-6199	464	10	(	(	PUNCT
ejpam-6199	464	11	w	w	PROPN
ejpam-6199	464	12	|	|	ADV
ejpam-6199	464	13	w	w	NOUN
ejpam-6199	464	14	)	)	PUNCT
ejpam-6199	464	15	|	|	ADV
ejpam-6199	464	16	(	(	PUNCT
ejpam-6199	464	17	w	w	PROPN
ejpam-6199	464	18	|	|	ADV
ejpam-6199	464	19	w	w	NOUN
ejpam-6199	464	20	)	)	PUNCT
ejpam-6199	464	21	)	)	PUNCT
ejpam-6199	464	22	)	)	PUNCT
ejpam-6199	464	23	)	)	PUNCT
ejpam-6199	465	1	=	=	PRON
ejpam-6199	465	2	(	(	PUNCT
ejpam-6199	465	3	v	v	INTJ
ejpam-6199	465	4	|	|	ADV
ejpam-6199	465	5	w	w	NOUN
ejpam-6199	465	6	)	)	PUNCT
ejpam-6199	465	7	|	|	ADV
ejpam-6199	465	8	(	(	PUNCT
ejpam-6199	465	9	(	(	PUNCT
ejpam-6199	465	10	v	v	X
ejpam-6199	465	11	|	|	ADV
ejpam-6199	465	12	(	(	PUNCT
ejpam-6199	465	13	(	(	PUNCT
ejpam-6199	465	14	w	w	PROPN
ejpam-6199	465	15	|	|	ADV
ejpam-6199	465	16	w	w	NOUN
ejpam-6199	465	17	)	)	PUNCT
ejpam-6199	466	1	|	|	ADV
ejpam-6199	466	2	(	(	PUNCT
ejpam-6199	466	3	w	w	PROPN
ejpam-6199	466	4	|	|	ADV
ejpam-6199	466	5	w	w	NOUN
ejpam-6199	466	6	)	)	PUNCT
ejpam-6199	466	7	)	)	PUNCT
ejpam-6199	466	8	)	)	PUNCT
ejpam-6199	467	1	|	|	ADV
ejpam-6199	467	2	(	(	PUNCT
ejpam-6199	467	3	v	v	NOUN
ejpam-6199	467	4	|	|	ADV
ejpam-6199	467	5	(	(	PUNCT
ejpam-6199	467	6	(	(	PUNCT
ejpam-6199	467	7	w	w	PROPN
ejpam-6199	467	8	|	|	ADV
ejpam-6199	467	9	w	w	NOUN
ejpam-6199	467	10	)	)	PUNCT
ejpam-6199	467	11	|	|	ADV
ejpam-6199	467	12	(	(	PUNCT
ejpam-6199	467	13	w	w	PROPN
ejpam-6199	467	14	|	|	ADV
ejpam-6199	467	15	w	w	NOUN
ejpam-6199	467	16	)	)	PUNCT
ejpam-6199	467	17	)	)	PUNCT
ejpam-6199	467	18	)	)	PUNCT
ejpam-6199	467	19	)	)	PUNCT
ejpam-6199	468	1	=	=	PRON
ejpam-6199	468	2	(	(	PUNCT
ejpam-6199	468	3	v	v	INTJ
ejpam-6199	468	4	|	|	ADV
ejpam-6199	468	5	w	w	NOUN
ejpam-6199	468	6	)	)	PUNCT
ejpam-6199	468	7	|	|	ADV
ejpam-6199	468	8	(	(	PUNCT
ejpam-6199	468	9	(	(	PUNCT
ejpam-6199	468	10	v	v	INTJ
ejpam-6199	468	11	|	|	ADV
ejpam-6199	468	12	w	w	NOUN
ejpam-6199	468	13	)	)	PUNCT
ejpam-6199	468	14	|	|	ADV
ejpam-6199	468	15	(	(	PUNCT
ejpam-6199	468	16	v	v	NOUN
ejpam-6199	468	17	|	|	ADV
ejpam-6199	468	18	w	w	NOUN
ejpam-6199	468	19	)	)	PUNCT
ejpam-6199	468	20	)	)	PUNCT
ejpam-6199	468	21	=	=	SYM
ejpam-6199	469	1	1	1	X
ejpam-6199	469	2	.	.	X
ejpam-6199	469	3	using	use	VERB
ejpam-6199	469	4	(	(	PUNCT
ejpam-6199	469	5	i	i	NOUN
ejpam-6199	469	6	)	)	PUNCT
ejpam-6199	469	7	of	of	ADP
ejpam-6199	469	8	definition	definition	NOUN
ejpam-6199	469	9	9	9	NUM
ejpam-6199	469	10	and	and	CCONJ
ejpam-6199	469	11	the	the	DET
ejpam-6199	469	12	condition	condition	NOUN
ejpam-6199	469	13	(	(	PUNCT
ejpam-6199	469	14	c	c	NOUN
ejpam-6199	469	15	)	)	PUNCT
ejpam-6199	469	16	,	,	PUNCT
ejpam-6199	469	17	we	we	PRON
ejpam-6199	469	18	get	get	VERB
ejpam-6199	469	19	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	469	20	|	|	ADV
ejpam-6199	469	21	w	w	NOUN
ejpam-6199	469	22	)	)	PUNCT
ejpam-6199	469	23	|	|	ADV
ejpam-6199	469	24	w	w	NOUN
ejpam-6199	469	25	)	)	PUNCT
ejpam-6199	469	26	⪰	⪰	NOUN
ejpam-6199	469	27	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	469	28	)	)	PUNCT
ejpam-6199	469	29	,	,	PUNCT
ejpam-6199	469	30	υ̃π(v	υ̃π(v	NUM
ejpam-6199	469	31	|	|	ADV
ejpam-6199	469	32	(	(	PUNCT
ejpam-6199	469	33	(	(	PUNCT
ejpam-6199	469	34	(	(	PUNCT
ejpam-6199	469	35	v	v	NOUN
ejpam-6199	469	36	|	|	ADV
ejpam-6199	469	37	w	w	NOUN
ejpam-6199	469	38	)	)	PUNCT
ejpam-6199	469	39	|	|	ADV
ejpam-6199	469	40	w	w	NOUN
ejpam-6199	469	41	)	)	PUNCT
ejpam-6199	470	1	|	|	ADV
ejpam-6199	470	2	(	(	PUNCT
ejpam-6199	470	3	(	(	PUNCT
ejpam-6199	470	4	v	v	INTJ
ejpam-6199	470	5	|	|	ADV
ejpam-6199	470	6	w	w	NOUN
ejpam-6199	470	7	)	)	PUNCT
ejpam-6199	470	8	|	|	ADV
ejpam-6199	470	9	w	w	NOUN
ejpam-6199	470	10	)	)	PUNCT
ejpam-6199	470	11	)	)	PUNCT
ejpam-6199	470	12	)	)	PUNCT
ejpam-6199	470	13	}	}	PUNCT
ejpam-6199	471	1	=	=	SYM
ejpam-6199	471	2	m̃in{υ̃π(v	m̃in{υ̃π(v	NOUN
ejpam-6199	471	3	)	)	PUNCT
ejpam-6199	471	4	,	,	PUNCT
ejpam-6199	471	5	υ̃π(1	υ̃π(1	NOUN
ejpam-6199	471	6	)	)	PUNCT
ejpam-6199	471	7	}	}	PUNCT
ejpam-6199	471	8	=	=	SYM
ejpam-6199	471	9	υ̃π(v	υ̃π(v	NUM
ejpam-6199	471	10	)	)	PUNCT
ejpam-6199	471	11	and	and	CCONJ
ejpam-6199	471	12	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	471	13	|	|	ADV
ejpam-6199	471	14	w	w	NOUN
ejpam-6199	471	15	)	)	PUNCT
ejpam-6199	471	16	|	|	ADV
ejpam-6199	471	17	w	w	NOUN
ejpam-6199	471	18	)	)	PUNCT
ejpam-6199	471	19	≤	≤	NOUN
ejpam-6199	471	20	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	471	21	)	)	PUNCT
ejpam-6199	471	22	,	,	PUNCT
ejpam-6199	471	23	ϖπ(v	ϖπ(v	PUNCT
ejpam-6199	472	1	|	|	ADV
ejpam-6199	472	2	(	(	PUNCT
ejpam-6199	472	3	(	(	PUNCT
ejpam-6199	472	4	(	(	PUNCT
ejpam-6199	472	5	v	v	NOUN
ejpam-6199	472	6	|	|	ADV
ejpam-6199	472	7	w	w	NOUN
ejpam-6199	472	8	)	)	PUNCT
ejpam-6199	472	9	|	|	ADV
ejpam-6199	472	10	w	w	NOUN
ejpam-6199	472	11	)	)	PUNCT
ejpam-6199	472	12	|	|	ADV
ejpam-6199	472	13	(	(	PUNCT
ejpam-6199	472	14	(	(	PUNCT
ejpam-6199	472	15	v	v	INTJ
ejpam-6199	472	16	|	|	ADV
ejpam-6199	472	17	w	w	NOUN
ejpam-6199	472	18	)	)	PUNCT
ejpam-6199	472	19	|	|	ADV
ejpam-6199	472	20	w	w	NOUN
ejpam-6199	472	21	)	)	PUNCT
ejpam-6199	472	22	)	)	PUNCT
ejpam-6199	472	23	)	)	PUNCT
ejpam-6199	473	1	}	}	PUNCT
ejpam-6199	473	2	=	=	SYM
ejpam-6199	473	3	max{ϖπ(v	max{ϖπ(v	NOUN
ejpam-6199	473	4	)	)	PUNCT
ejpam-6199	473	5	,	,	PUNCT
ejpam-6199	473	6	ϖπ(1	ϖπ(1	NOUN
ejpam-6199	473	7	)	)	PUNCT
ejpam-6199	473	8	}	}	PUNCT
ejpam-6199	473	9	=	=	SYM
ejpam-6199	473	10	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	473	11	)	)	PUNCT
ejpam-6199	473	12	.	.	PUNCT
ejpam-6199	474	1	since	since	SCONJ
ejpam-6199	474	2	by	by	ADP
ejpam-6199	474	3	(	(	PUNCT
ejpam-6199	474	4	1	1	NUM
ejpam-6199	474	5	)	)	PUNCT
ejpam-6199	474	6	and	and	CCONJ
ejpam-6199	474	7	(	(	PUNCT
ejpam-6199	474	8	2	2	X
ejpam-6199	474	9	)	)	PUNCT
ejpam-6199	474	10	of	of	ADP
ejpam-6199	474	11	definition	definition	NOUN
ejpam-6199	474	12	1	1	NUM
ejpam-6199	474	13	,	,	PUNCT
ejpam-6199	474	14	we	we	PRON
ejpam-6199	474	15	get	get	VERB
ejpam-6199	474	16	w	w	ADP
ejpam-6199	475	1	|	|	NOUN
ejpam-6199	475	2	(	(	PUNCT
ejpam-6199	475	3	(	(	PUNCT
ejpam-6199	475	4	(	(	PUNCT
ejpam-6199	475	5	v	v	NOUN
ejpam-6199	475	6	|	|	ADV
ejpam-6199	475	7	w	w	NOUN
ejpam-6199	475	8	)	)	PUNCT
ejpam-6199	476	1	|	|	ADV
ejpam-6199	476	2	(	(	PUNCT
ejpam-6199	476	3	v	v	NOUN
ejpam-6199	476	4	|	|	ADV
ejpam-6199	476	5	w	w	NOUN
ejpam-6199	476	6	)	)	PUNCT
ejpam-6199	476	7	)	)	PUNCT
ejpam-6199	477	1	|	|	ADV
ejpam-6199	477	2	(	(	PUNCT
ejpam-6199	477	3	(	(	PUNCT
ejpam-6199	477	4	v	v	INTJ
ejpam-6199	477	5	|	|	ADV
ejpam-6199	477	6	w	w	NOUN
ejpam-6199	477	7	)	)	PUNCT
ejpam-6199	477	8	|	|	ADV
ejpam-6199	477	9	(	(	PUNCT
ejpam-6199	477	10	v	v	NOUN
ejpam-6199	477	11	|	|	ADV
ejpam-6199	477	12	w	w	NOUN
ejpam-6199	477	13	)	)	PUNCT
ejpam-6199	477	14	)	)	PUNCT
ejpam-6199	477	15	)	)	PUNCT
ejpam-6199	478	1	=	=	PUNCT
ejpam-6199	479	1	w	w	X
ejpam-6199	479	2	|	|	ADV
ejpam-6199	479	3	(	(	PUNCT
ejpam-6199	479	4	v	v	NOUN
ejpam-6199	479	5	|	|	ADV
ejpam-6199	479	6	w	w	NOUN
ejpam-6199	479	7	)	)	PUNCT
ejpam-6199	479	8	=	=	SYM
ejpam-6199	479	9	(	(	PUNCT
ejpam-6199	479	10	v	v	INTJ
ejpam-6199	479	11	|	|	ADV
ejpam-6199	479	12	w	w	NOUN
ejpam-6199	479	13	)	)	PUNCT
ejpam-6199	479	14	|	|	ADV
ejpam-6199	479	15	w.	w.	PROPN
ejpam-6199	479	16	then	then	ADV
ejpam-6199	479	17	,	,	PUNCT
ejpam-6199	479	18	we	we	PRON
ejpam-6199	479	19	obtain	obtain	VERB
ejpam-6199	479	20	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	479	21	|	|	ADV
ejpam-6199	479	22	w	w	NOUN
ejpam-6199	479	23	)	)	PUNCT
ejpam-6199	480	1	|	|	ADV
ejpam-6199	480	2	(	(	PUNCT
ejpam-6199	480	3	v	v	NOUN
ejpam-6199	480	4	|	|	ADV
ejpam-6199	480	5	w	w	NOUN
ejpam-6199	480	6	)	)	PUNCT
ejpam-6199	480	7	)	)	PUNCT
ejpam-6199	480	8	⪰	⪰	NOUN
ejpam-6199	480	9	m̃in{υ̃π(w	m̃in{υ̃π(w	PROPN
ejpam-6199	480	10	)	)	PUNCT
ejpam-6199	480	11	,	,	PUNCT
ejpam-6199	480	12	υ̃π(w	υ̃π(w	PUNCT
ejpam-6199	481	1	|	|	ADV
ejpam-6199	481	2	(	(	PUNCT
ejpam-6199	481	3	(	(	PUNCT
ejpam-6199	481	4	(	(	PUNCT
ejpam-6199	481	5	v	v	NOUN
ejpam-6199	481	6	|	|	ADV
ejpam-6199	481	7	w	w	NOUN
ejpam-6199	481	8	)	)	PUNCT
ejpam-6199	481	9	|	|	ADV
ejpam-6199	481	10	(	(	PUNCT
ejpam-6199	481	11	v	v	NOUN
ejpam-6199	481	12	|	|	ADV
ejpam-6199	481	13	w	w	NOUN
ejpam-6199	481	14	)	)	PUNCT
ejpam-6199	481	15	)	)	PUNCT
ejpam-6199	482	1	|	|	ADV
ejpam-6199	482	2	(	(	PUNCT
ejpam-6199	482	3	(	(	PUNCT
ejpam-6199	482	4	v	v	INTJ
ejpam-6199	482	5	|	|	ADV
ejpam-6199	482	6	w	w	NOUN
ejpam-6199	482	7	)	)	PUNCT
ejpam-6199	482	8	|	|	ADV
ejpam-6199	482	9	(	(	PUNCT
ejpam-6199	482	10	v	v	NOUN
ejpam-6199	482	11	|	|	ADV
ejpam-6199	482	12	w	w	NOUN
ejpam-6199	482	13	)	)	PUNCT
ejpam-6199	482	14	)	)	PUNCT
ejpam-6199	482	15	)	)	PUNCT
ejpam-6199	482	16	)	)	PUNCT
ejpam-6199	482	17	}	}	PUNCT
ejpam-6199	483	1	=	=	SYM
ejpam-6199	483	2	m̃in{υ̃π(w	m̃in{υ̃π(w	ADJ
ejpam-6199	483	3	)	)	PUNCT
ejpam-6199	483	4	,	,	PUNCT
ejpam-6199	483	5	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	483	6	|	|	CCONJ
ejpam-6199	483	7	w	w	PROPN
ejpam-6199	483	8	)	)	PUNCT
ejpam-6199	483	9	|	|	ADV
ejpam-6199	483	10	w	w	NOUN
ejpam-6199	483	11	)	)	PUNCT
ejpam-6199	483	12	}	}	PUNCT
ejpam-6199	483	13	⪰	⪰	VERB
ejpam-6199	483	14	m̃in{υ̃π(w	m̃in{υ̃π(w	PROPN
ejpam-6199	483	15	)	)	PUNCT
ejpam-6199	483	16	,	,	PUNCT
ejpam-6199	483	17	υ̃π(v	υ̃π(v	NUM
ejpam-6199	483	18	)	)	PUNCT
ejpam-6199	483	19	}	}	PUNCT
ejpam-6199	483	20	a.	a.	PROPN
ejpam-6199	483	21	al	al	PROPN
ejpam-6199	483	22	-	-	PROPN
ejpam-6199	483	23	masarwah	masarwah	PROPN
ejpam-6199	483	24	et	et	PROPN
ejpam-6199	483	25	al	al	PROPN
ejpam-6199	483	26	.	.	PUNCT
ejpam-6199	483	27	/	/	SYM
ejpam-6199	483	28	eur	eur	PROPN
ejpam-6199	483	29	.	.	PUNCT
ejpam-6199	484	1	j.	j.	PROPN
ejpam-6199	484	2	pure	pure	PROPN
ejpam-6199	484	3	appl	appl	PROPN
ejpam-6199	484	4	.	.	PROPN
ejpam-6199	484	5	math	math	PROPN
ejpam-6199	484	6	,	,	PUNCT
ejpam-6199	484	7	18	18	NUM
ejpam-6199	484	8	(	(	PUNCT
ejpam-6199	484	9	3	3	NUM
ejpam-6199	484	10	)	)	PUNCT
ejpam-6199	484	11	(	(	PUNCT
ejpam-6199	484	12	2025	2025	NUM
ejpam-6199	484	13	)	)	PUNCT
ejpam-6199	484	14	,	,	PUNCT
ejpam-6199	484	15	6199	6199	NUM
ejpam-6199	484	16	15	15	NUM
ejpam-6199	484	17	of	of	ADP
ejpam-6199	484	18	17	17	NUM
ejpam-6199	484	19	and	and	CCONJ
ejpam-6199	484	20	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	484	21	|	|	ADV
ejpam-6199	484	22	w	w	NOUN
ejpam-6199	484	23	)	)	PUNCT
ejpam-6199	485	1	|	|	ADV
ejpam-6199	485	2	(	(	PUNCT
ejpam-6199	485	3	v	v	NOUN
ejpam-6199	485	4	|	|	ADV
ejpam-6199	485	5	w	w	NOUN
ejpam-6199	485	6	)	)	PUNCT
ejpam-6199	485	7	)	)	PUNCT
ejpam-6199	486	1	≤	≤	NOUN
ejpam-6199	486	2	max{ϖπ(w	max{ϖπ(w	NOUN
ejpam-6199	486	3	)	)	PUNCT
ejpam-6199	486	4	,	,	PUNCT
ejpam-6199	486	5	ϖπ(w	ϖπ(w	PUNCT
ejpam-6199	486	6	|	|	ADV
ejpam-6199	486	7	(	(	PUNCT
ejpam-6199	486	8	(	(	PUNCT
ejpam-6199	486	9	(	(	PUNCT
ejpam-6199	486	10	v	v	NOUN
ejpam-6199	486	11	|	|	ADV
ejpam-6199	486	12	w	w	NOUN
ejpam-6199	486	13	)	)	PUNCT
ejpam-6199	486	14	|	|	ADV
ejpam-6199	486	15	(	(	PUNCT
ejpam-6199	486	16	v	v	NOUN
ejpam-6199	486	17	|	|	ADV
ejpam-6199	486	18	w	w	NOUN
ejpam-6199	486	19	)	)	PUNCT
ejpam-6199	486	20	)	)	PUNCT
ejpam-6199	487	1	|	|	ADV
ejpam-6199	487	2	(	(	PUNCT
ejpam-6199	487	3	(	(	PUNCT
ejpam-6199	487	4	v	v	INTJ
ejpam-6199	487	5	|	|	ADV
ejpam-6199	487	6	w	w	NOUN
ejpam-6199	487	7	)	)	PUNCT
ejpam-6199	487	8	|	|	ADV
ejpam-6199	487	9	(	(	PUNCT
ejpam-6199	487	10	v	v	NOUN
ejpam-6199	487	11	|	|	ADV
ejpam-6199	487	12	w	w	NOUN
ejpam-6199	487	13	)	)	PUNCT
ejpam-6199	487	14	)	)	PUNCT
ejpam-6199	487	15	)	)	PUNCT
ejpam-6199	487	16	)	)	PUNCT
ejpam-6199	487	17	}	}	PUNCT
ejpam-6199	488	1	=	=	SYM
ejpam-6199	488	2	max{ϖπ(w	max{ϖπ(w	X
ejpam-6199	488	3	)	)	PUNCT
ejpam-6199	488	4	,	,	PUNCT
ejpam-6199	488	5	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	488	6	|	|	ADV
ejpam-6199	488	7	w	w	NOUN
ejpam-6199	488	8	)	)	PUNCT
ejpam-6199	488	9	|	|	ADV
ejpam-6199	488	10	w	w	NOUN
ejpam-6199	488	11	)	)	PUNCT
ejpam-6199	488	12	}	}	PUNCT
ejpam-6199	488	13	≤	≤	NOUN
ejpam-6199	488	14	max{ϖπ(w	max{ϖπ(w	NOUN
ejpam-6199	488	15	)	)	PUNCT
ejpam-6199	488	16	,	,	PUNCT
ejpam-6199	488	17	ϖπ(v	ϖπ(v	ADP
ejpam-6199	488	18	)	)	PUNCT
ejpam-6199	488	19	}	}	PUNCT
ejpam-6199	488	20	.	.	PUNCT
ejpam-6199	489	1	therefore	therefore	ADV
ejpam-6199	489	2	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	489	3	|	|	ADV
ejpam-6199	489	4	(	(	PUNCT
ejpam-6199	489	5	v	v	NOUN
ejpam-6199	489	6	|	|	ADV
ejpam-6199	489	7	w	w	NOUN
ejpam-6199	489	8	)	)	PUNCT
ejpam-6199	489	9	)	)	PUNCT
ejpam-6199	490	1	|	|	ADV
ejpam-6199	490	2	(	(	PUNCT
ejpam-6199	490	3	v	v	NOUN
ejpam-6199	490	4	|	|	ADV
ejpam-6199	490	5	w	w	NOUN
ejpam-6199	490	6	)	)	PUNCT
ejpam-6199	490	7	)	)	PUNCT
ejpam-6199	491	1	=	=	SYM
ejpam-6199	491	2	υ̃π((n	υ̃π((n	NOUN
ejpam-6199	492	1	|	|	ADV
ejpam-6199	492	2	(	(	PUNCT
ejpam-6199	492	3	(	(	PUNCT
ejpam-6199	492	4	(	(	PUNCT
ejpam-6199	492	5	v	v	NOUN
ejpam-6199	492	6	|	|	ADV
ejpam-6199	492	7	w	w	NOUN
ejpam-6199	492	8	)	)	PUNCT
ejpam-6199	492	9	|	|	ADV
ejpam-6199	492	10	(	(	PUNCT
ejpam-6199	492	11	v	v	NOUN
ejpam-6199	492	12	|	|	ADV
ejpam-6199	492	13	w	w	NOUN
ejpam-6199	492	14	)	)	PUNCT
ejpam-6199	492	15	)	)	PUNCT
ejpam-6199	493	1	|	|	ADV
ejpam-6199	493	2	(	(	PUNCT
ejpam-6199	493	3	(	(	PUNCT
ejpam-6199	493	4	v	v	INTJ
ejpam-6199	493	5	|	|	ADV
ejpam-6199	493	6	w	w	NOUN
ejpam-6199	493	7	)	)	PUNCT
ejpam-6199	493	8	|	|	ADV
ejpam-6199	493	9	(	(	PUNCT
ejpam-6199	493	10	v	v	NOUN
ejpam-6199	493	11	|	|	ADV
ejpam-6199	493	12	w	w	NOUN
ejpam-6199	493	13	)	)	PUNCT
ejpam-6199	493	14	)	)	PUNCT
ejpam-6199	493	15	)	)	PUNCT
ejpam-6199	493	16	)	)	PUNCT
ejpam-6199	494	1	|	|	ADV
ejpam-6199	494	2	(	(	PUNCT
ejpam-6199	494	3	(	(	PUNCT
ejpam-6199	494	4	(	(	PUNCT
ejpam-6199	494	5	v	v	NOUN
ejpam-6199	494	6	|	|	ADV
ejpam-6199	494	7	w	w	NOUN
ejpam-6199	494	8	)	)	PUNCT
ejpam-6199	494	9	|	|	ADV
ejpam-6199	494	10	(	(	PUNCT
ejpam-6199	494	11	v	v	NOUN
ejpam-6199	494	12	|	|	ADV
ejpam-6199	494	13	w	w	NOUN
ejpam-6199	494	14	)	)	PUNCT
ejpam-6199	494	15	)	)	PUNCT
ejpam-6199	495	1	|	|	ADV
ejpam-6199	495	2	(	(	PUNCT
ejpam-6199	495	3	(	(	PUNCT
ejpam-6199	495	4	v	v	INTJ
ejpam-6199	495	5	|	|	ADV
ejpam-6199	495	6	w	w	NOUN
ejpam-6199	495	7	)	)	PUNCT
ejpam-6199	495	8	|	|	ADV
ejpam-6199	495	9	(	(	PUNCT
ejpam-6199	495	10	v	v	NOUN
ejpam-6199	495	11	|	|	ADV
ejpam-6199	495	12	w	w	NOUN
ejpam-6199	495	13	)	)	PUNCT
ejpam-6199	495	14	)	)	PUNCT
ejpam-6199	495	15	)	)	PUNCT
ejpam-6199	495	16	)	)	PUNCT
ejpam-6199	495	17	⪰	⪰	NOUN
ejpam-6199	495	18	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	495	19	|	|	CCONJ
ejpam-6199	495	20	w	w	NOUN
ejpam-6199	495	21	)	)	PUNCT
ejpam-6199	495	22	|	|	ADV
ejpam-6199	495	23	(	(	PUNCT
ejpam-6199	495	24	v	v	NOUN
ejpam-6199	495	25	|	|	ADV
ejpam-6199	495	26	w	w	NOUN
ejpam-6199	495	27	)	)	PUNCT
ejpam-6199	495	28	)	)	PUNCT
ejpam-6199	495	29	⪰	⪰	NOUN
ejpam-6199	495	30	m̃in{υ̃π(w	m̃in{υ̃π(w	PROPN
ejpam-6199	495	31	)	)	PUNCT
ejpam-6199	495	32	,	,	PUNCT
ejpam-6199	495	33	υ̃π(v	υ̃π(v	NUM
ejpam-6199	495	34	)	)	PUNCT
ejpam-6199	495	35	}	}	PUNCT
ejpam-6199	495	36	and	and	CCONJ
ejpam-6199	495	37	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	496	1	|	|	ADV
ejpam-6199	496	2	(	(	PUNCT
ejpam-6199	496	3	v	v	NOUN
ejpam-6199	496	4	|	|	ADV
ejpam-6199	496	5	w	w	NOUN
ejpam-6199	496	6	)	)	PUNCT
ejpam-6199	496	7	)	)	PUNCT
ejpam-6199	497	1	|	|	ADV
ejpam-6199	497	2	(	(	PUNCT
ejpam-6199	497	3	v	v	NOUN
ejpam-6199	497	4	|	|	ADV
ejpam-6199	497	5	w	w	NOUN
ejpam-6199	497	6	)	)	PUNCT
ejpam-6199	497	7	)	)	PUNCT
ejpam-6199	498	1	=	=	SYM
ejpam-6199	498	2	ϖπ((n	ϖπ((n	NOUN
ejpam-6199	498	3	|	|	ADV
ejpam-6199	498	4	(	(	PUNCT
ejpam-6199	498	5	(	(	PUNCT
ejpam-6199	498	6	(	(	PUNCT
ejpam-6199	498	7	v	v	NOUN
ejpam-6199	498	8	|	|	ADV
ejpam-6199	498	9	w	w	NOUN
ejpam-6199	498	10	)	)	PUNCT
ejpam-6199	498	11	|	|	ADV
ejpam-6199	498	12	(	(	PUNCT
ejpam-6199	498	13	v	v	NOUN
ejpam-6199	498	14	|	|	ADV
ejpam-6199	498	15	w	w	NOUN
ejpam-6199	498	16	)	)	PUNCT
ejpam-6199	498	17	)	)	PUNCT
ejpam-6199	499	1	|	|	ADV
ejpam-6199	499	2	(	(	PUNCT
ejpam-6199	499	3	(	(	PUNCT
ejpam-6199	499	4	v	v	INTJ
ejpam-6199	499	5	|	|	ADV
ejpam-6199	499	6	w	w	NOUN
ejpam-6199	499	7	)	)	PUNCT
ejpam-6199	499	8	|	|	ADV
ejpam-6199	499	9	(	(	PUNCT
ejpam-6199	499	10	v	v	NOUN
ejpam-6199	499	11	|	|	ADV
ejpam-6199	499	12	w	w	NOUN
ejpam-6199	499	13	)	)	PUNCT
ejpam-6199	499	14	)	)	PUNCT
ejpam-6199	499	15	)	)	PUNCT
ejpam-6199	499	16	)	)	PUNCT
ejpam-6199	500	1	|	|	ADV
ejpam-6199	500	2	(	(	PUNCT
ejpam-6199	500	3	(	(	PUNCT
ejpam-6199	500	4	(	(	PUNCT
ejpam-6199	500	5	v	v	NOUN
ejpam-6199	500	6	|	|	ADV
ejpam-6199	500	7	w	w	NOUN
ejpam-6199	500	8	)	)	PUNCT
ejpam-6199	500	9	|	|	ADV
ejpam-6199	500	10	(	(	PUNCT
ejpam-6199	500	11	v	v	NOUN
ejpam-6199	500	12	|	|	ADV
ejpam-6199	500	13	w	w	NOUN
ejpam-6199	500	14	)	)	PUNCT
ejpam-6199	500	15	)	)	PUNCT
ejpam-6199	501	1	|	|	ADV
ejpam-6199	501	2	(	(	PUNCT
ejpam-6199	501	3	(	(	PUNCT
ejpam-6199	501	4	v	v	INTJ
ejpam-6199	501	5	|	|	ADV
ejpam-6199	501	6	w	w	NOUN
ejpam-6199	501	7	)	)	PUNCT
ejpam-6199	501	8	|	|	ADV
ejpam-6199	501	9	(	(	PUNCT
ejpam-6199	501	10	v	v	NOUN
ejpam-6199	501	11	|	|	ADV
ejpam-6199	501	12	w	w	NOUN
ejpam-6199	501	13	)	)	PUNCT
ejpam-6199	501	14	)	)	PUNCT
ejpam-6199	501	15	)	)	PUNCT
ejpam-6199	501	16	)	)	PUNCT
ejpam-6199	501	17	≤	≤	NUM
ejpam-6199	501	18	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	501	19	|	|	PROPN
ejpam-6199	501	20	w	w	NOUN
ejpam-6199	501	21	)	)	PUNCT
ejpam-6199	501	22	|	|	ADV
ejpam-6199	501	23	(	(	PUNCT
ejpam-6199	501	24	v	v	NOUN
ejpam-6199	501	25	|	|	ADV
ejpam-6199	501	26	w	w	NOUN
ejpam-6199	501	27	)	)	PUNCT
ejpam-6199	501	28	)	)	PUNCT
ejpam-6199	502	1	≤	≤	NOUN
ejpam-6199	502	2	max{ϖπ(w	max{ϖπ(w	NOUN
ejpam-6199	502	3	)	)	PUNCT
ejpam-6199	502	4	,	,	PUNCT
ejpam-6199	502	5	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	502	6	)	)	PUNCT
ejpam-6199	502	7	}	}	PUNCT
ejpam-6199	502	8	consequently	consequently	ADV
ejpam-6199	502	9	,	,	PUNCT
ejpam-6199	502	10	π	π	PROPN
ejpam-6199	502	11	=	=	SYM
ejpam-6199	502	12	(	(	PUNCT
ejpam-6199	502	13	υ̃π	υ̃π	PROPN
ejpam-6199	502	14	,	,	PUNCT
ejpam-6199	502	15	ϖπ	ϖπ	NOUN
ejpam-6199	502	16	)	)	PUNCT
ejpam-6199	502	17	is	be	AUX
ejpam-6199	502	18	a	a	DET
ejpam-6199	502	19	crossing	cross	VERB
ejpam-6199	502	20	cubic	cubic	ADJ
ejpam-6199	502	21	filter	filter	NOUN
ejpam-6199	502	22	of	of	ADP
ejpam-6199	502	23	ϑ.	ϑ.	NOUN
ejpam-6199	502	24	conversely	conversely	ADV
ejpam-6199	502	25	,	,	PUNCT
ejpam-6199	502	26	suppose	suppose	VERB
ejpam-6199	502	27	that	that	SCONJ
ejpam-6199	502	28	π	π	PROPN
ejpam-6199	502	29	=	=	PRON
ejpam-6199	502	30	(	(	PUNCT
ejpam-6199	502	31	υ̃π	υ̃π	PROPN
ejpam-6199	502	32	,	,	PUNCT
ejpam-6199	502	33	ϖπ	ϖπ	NOUN
ejpam-6199	502	34	)	)	PUNCT
ejpam-6199	502	35	is	be	AUX
ejpam-6199	502	36	a	a	DET
ejpam-6199	502	37	crossing	cross	VERB
ejpam-6199	502	38	cubic	cubic	ADJ
ejpam-6199	502	39	filter	filter	NOUN
ejpam-6199	502	40	of	of	ADP
ejpam-6199	502	41	ϑ.	ϑ.	NOUN
ejpam-6199	502	42	by	by	ADP
ejpam-6199	502	43	(	(	PUNCT
ejpam-6199	502	44	1	1	NUM
ejpam-6199	502	45	)	)	PUNCT
ejpam-6199	502	46	,	,	PUNCT
ejpam-6199	502	47	(	(	PUNCT
ejpam-6199	502	48	2	2	X
ejpam-6199	502	49	)	)	PUNCT
ejpam-6199	502	50	and	and	CCONJ
ejpam-6199	502	51	(	(	PUNCT
ejpam-6199	502	52	3	3	X
ejpam-6199	502	53	)	)	PUNCT
ejpam-6199	502	54	of	of	ADP
ejpam-6199	502	55	definition	definition	NOUN
ejpam-6199	502	56	1	1	NUM
ejpam-6199	502	57	;	;	PUNCT
ejpam-6199	502	58	and	and	CCONJ
ejpam-6199	502	59	(	(	PUNCT
ejpam-6199	502	60	1	1	NUM
ejpam-6199	502	61	)	)	PUNCT
ejpam-6199	502	62	,	,	PUNCT
ejpam-6199	502	63	(	(	PUNCT
ejpam-6199	502	64	2	2	NUM
ejpam-6199	502	65	)	)	PUNCT
ejpam-6199	502	66	,	,	PUNCT
ejpam-6199	502	67	(	(	PUNCT
ejpam-6199	502	68	3	3	NUM
ejpam-6199	502	69	)	)	PUNCT
ejpam-6199	502	70	,	,	PUNCT
ejpam-6199	502	71	(	(	PUNCT
ejpam-6199	502	72	5	5	NUM
ejpam-6199	502	73	)	)	PUNCT
ejpam-6199	502	74	and	and	CCONJ
ejpam-6199	502	75	(	(	PUNCT
ejpam-6199	502	76	6	6	NUM
ejpam-6199	502	77	)	)	PUNCT
ejpam-6199	502	78	of	of	ADP
ejpam-6199	502	79	proposition	proposition	NOUN
ejpam-6199	502	80	1	1	NUM
ejpam-6199	502	81	,	,	PUNCT
ejpam-6199	502	82	and	and	CCONJ
ejpam-6199	502	83	for	for	ADP
ejpam-6199	502	84	every	every	DET
ejpam-6199	502	85	n	n	CCONJ
ejpam-6199	502	86	,	,	PUNCT
ejpam-6199	502	87	v	v	NOUN
ejpam-6199	502	88	∈	∈	PROPN
ejpam-6199	502	89	ϑ	ϑ	X
ejpam-6199	502	90	,	,	PUNCT
ejpam-6199	502	91	we	we	PRON
ejpam-6199	502	92	have	have	VERB
ejpam-6199	502	93	v	v	NOUN
ejpam-6199	502	94	=	=	SYM
ejpam-6199	502	95	(	(	PUNCT
ejpam-6199	502	96	(	(	PUNCT
ejpam-6199	502	97	n	n	CCONJ
ejpam-6199	502	98	|	|	ADV
ejpam-6199	502	99	n	n	CCONJ
ejpam-6199	502	100	)	)	PUNCT
ejpam-6199	503	1	|	|	CCONJ
ejpam-6199	503	2	(	(	PUNCT
ejpam-6199	503	3	1	1	NUM
ejpam-6199	503	4	|	|	ADV
ejpam-6199	503	5	1	1	NUM
ejpam-6199	503	6	)	)	PUNCT
ejpam-6199	503	7	)	)	PUNCT
ejpam-6199	504	1	|	|	ADV
ejpam-6199	504	2	(	(	PUNCT
ejpam-6199	504	3	v	v	NOUN
ejpam-6199	504	4	|	|	NOUN
ejpam-6199	504	5	v	v	NOUN
ejpam-6199	504	6	)	)	PUNCT
ejpam-6199	504	7	=	=	SYM
ejpam-6199	504	8	(	(	PUNCT
ejpam-6199	504	9	(	(	PUNCT
ejpam-6199	504	10	n	n	CCONJ
ejpam-6199	504	11	|	|	ADV
ejpam-6199	504	12	n	n	CCONJ
ejpam-6199	504	13	)	)	PUNCT
ejpam-6199	504	14	|	|	ADV
ejpam-6199	504	15	(	(	PUNCT
ejpam-6199	504	16	(	(	PUNCT
ejpam-6199	504	17	v	v	X
ejpam-6199	504	18	|	|	ADV
ejpam-6199	504	19	(	(	PUNCT
ejpam-6199	504	20	v	v	NOUN
ejpam-6199	504	21	|	|	ADV
ejpam-6199	504	22	v	v	NOUN
ejpam-6199	504	23	)	)	PUNCT
ejpam-6199	504	24	)	)	PUNCT
ejpam-6199	505	1	|	|	ADV
ejpam-6199	505	2	(	(	PUNCT
ejpam-6199	505	3	v	v	NOUN
ejpam-6199	505	4	|	|	ADV
ejpam-6199	505	5	(	(	PUNCT
ejpam-6199	505	6	v	v	NOUN
ejpam-6199	505	7	|	|	ADV
ejpam-6199	505	8	v	v	NOUN
ejpam-6199	505	9	)	)	PUNCT
ejpam-6199	505	10	)	)	PUNCT
ejpam-6199	505	11	)	)	PUNCT
ejpam-6199	505	12	)	)	PUNCT
ejpam-6199	506	1	|	|	ADV
ejpam-6199	506	2	(	(	PUNCT
ejpam-6199	506	3	v	v	NOUN
ejpam-6199	506	4	|	|	NOUN
ejpam-6199	506	5	v	v	NOUN
ejpam-6199	506	6	)	)	PUNCT
ejpam-6199	506	7	=	=	SYM
ejpam-6199	506	8	(	(	PUNCT
ejpam-6199	506	9	(	(	PUNCT
ejpam-6199	506	10	(	(	PUNCT
ejpam-6199	506	11	(	(	PUNCT
ejpam-6199	506	12	n	n	CCONJ
ejpam-6199	506	13	|	|	NOUN
ejpam-6199	506	14	n	n	CCONJ
ejpam-6199	506	15	)	)	PUNCT
ejpam-6199	506	16	|	|	ADV
ejpam-6199	506	17	v	v	NOUN
ejpam-6199	506	18	)	)	PUNCT
ejpam-6199	506	19	|	|	ADV
ejpam-6199	506	20	(	(	PUNCT
ejpam-6199	506	21	(	(	PUNCT
ejpam-6199	506	22	n	n	CCONJ
ejpam-6199	506	23	|	|	ADV
ejpam-6199	506	24	n	n	CCONJ
ejpam-6199	506	25	)	)	PUNCT
ejpam-6199	506	26	|	|	ADV
ejpam-6199	506	27	v	v	NOUN
ejpam-6199	506	28	)	)	PUNCT
ejpam-6199	506	29	)	)	PUNCT
ejpam-6199	507	1	|	|	ADV
ejpam-6199	507	2	(	(	PUNCT
ejpam-6199	507	3	v	v	NOUN
ejpam-6199	507	4	|	|	ADV
ejpam-6199	507	5	v	v	NOUN
ejpam-6199	507	6	)	)	PUNCT
ejpam-6199	507	7	)	)	PUNCT
ejpam-6199	508	1	|	|	ADV
ejpam-6199	508	2	(	(	PUNCT
ejpam-6199	508	3	v	v	NOUN
ejpam-6199	508	4	|	|	NOUN
ejpam-6199	508	5	v	v	NOUN
ejpam-6199	508	6	)	)	PUNCT
ejpam-6199	508	7	=	=	SYM
ejpam-6199	508	8	(	(	PUNCT
ejpam-6199	508	9	v	v	NUM
ejpam-6199	508	10	|	|	ADV
ejpam-6199	508	11	(	(	PUNCT
ejpam-6199	508	12	(	(	PUNCT
ejpam-6199	508	13	n	n	CCONJ
ejpam-6199	508	14	|	|	ADV
ejpam-6199	508	15	n	n	CCONJ
ejpam-6199	508	16	)	)	PUNCT
ejpam-6199	508	17	|	|	ADV
ejpam-6199	508	18	v	v	NOUN
ejpam-6199	508	19	)	)	PUNCT
ejpam-6199	508	20	)	)	PUNCT
ejpam-6199	509	1	|	|	ADV
ejpam-6199	509	2	(	(	PUNCT
ejpam-6199	509	3	(	(	PUNCT
ejpam-6199	509	4	n	n	CCONJ
ejpam-6199	509	5	|	|	ADV
ejpam-6199	509	6	n	n	CCONJ
ejpam-6199	509	7	)	)	PUNCT
ejpam-6199	509	8	|	|	ADV
ejpam-6199	509	9	v	v	NOUN
ejpam-6199	509	10	)	)	PUNCT
ejpam-6199	509	11	=	=	SYM
ejpam-6199	509	12	(	(	PUNCT
ejpam-6199	509	13	(	(	PUNCT
ejpam-6199	509	14	(	(	PUNCT
ejpam-6199	509	15	(	(	PUNCT
ejpam-6199	509	16	n	n	CCONJ
ejpam-6199	509	17	|	|	NOUN
ejpam-6199	509	18	n	n	CCONJ
ejpam-6199	509	19	)	)	PUNCT
ejpam-6199	509	20	|	|	ADV
ejpam-6199	509	21	v	v	NOUN
ejpam-6199	509	22	)	)	PUNCT
ejpam-6199	509	23	|	|	ADV
ejpam-6199	509	24	v	v	NOUN
ejpam-6199	509	25	)	)	PUNCT
ejpam-6199	509	26	|	|	ADV
ejpam-6199	509	27	v	v	NOUN
ejpam-6199	509	28	)	)	PUNCT
ejpam-6199	509	29	|	|	ADV
ejpam-6199	509	30	(	(	PUNCT
ejpam-6199	509	31	(	(	PUNCT
ejpam-6199	509	32	(	(	PUNCT
ejpam-6199	509	33	n	n	CCONJ
ejpam-6199	509	34	|	|	NOUN
ejpam-6199	509	35	n	n	CCONJ
ejpam-6199	509	36	)	)	PUNCT
ejpam-6199	509	37	|	|	ADV
ejpam-6199	509	38	v	v	NOUN
ejpam-6199	509	39	)	)	PUNCT
ejpam-6199	509	40	|	|	ADV
ejpam-6199	509	41	v	v	NOUN
ejpam-6199	509	42	)	)	PUNCT
ejpam-6199	509	43	=	=	SYM
ejpam-6199	509	44	(	(	PUNCT
ejpam-6199	509	45	v	v	NUM
ejpam-6199	509	46	|	|	ADV
ejpam-6199	509	47	(	(	PUNCT
ejpam-6199	509	48	n	n	CCONJ
ejpam-6199	509	49	|	|	ADV
ejpam-6199	509	50	(	(	PUNCT
ejpam-6199	509	51	n	n	CCONJ
ejpam-6199	509	52	|	|	ADV
ejpam-6199	509	53	(	(	PUNCT
ejpam-6199	509	54	v	v	NOUN
ejpam-6199	509	55	|	|	ADV
ejpam-6199	509	56	v	v	NOUN
ejpam-6199	509	57	)	)	PUNCT
ejpam-6199	509	58	)	)	PUNCT
ejpam-6199	509	59	)	)	PUNCT
ejpam-6199	509	60	)	)	PUNCT
ejpam-6199	510	1	|	|	ADV
ejpam-6199	510	2	(	(	PUNCT
ejpam-6199	510	3	n	n	CCONJ
ejpam-6199	510	4	|	|	ADV
ejpam-6199	510	5	(	(	PUNCT
ejpam-6199	510	6	n	n	CCONJ
ejpam-6199	510	7	|	|	ADV
ejpam-6199	510	8	(	(	PUNCT
ejpam-6199	510	9	v	v	NOUN
ejpam-6199	510	10	|	|	ADV
ejpam-6199	510	11	v	v	NOUN
ejpam-6199	510	12	)	)	PUNCT
ejpam-6199	510	13	)	)	PUNCT
ejpam-6199	510	14	)	)	PUNCT
ejpam-6199	510	15	.	.	PUNCT
ejpam-6199	511	1	it	it	PRON
ejpam-6199	511	2	follows	follow	VERB
ejpam-6199	511	3	from	from	ADP
ejpam-6199	511	4	(	(	PUNCT
ejpam-6199	511	5	iii	iii	NOUN
ejpam-6199	511	6	)	)	PUNCT
ejpam-6199	511	7	of	of	ADP
ejpam-6199	511	8	definition	definition	NOUN
ejpam-6199	511	9	9	9	NUM
ejpam-6199	511	10	that	that	SCONJ
ejpam-6199	511	11	υ̃π(v	υ̃π(v	X
ejpam-6199	511	12	)	)	PUNCT
ejpam-6199	511	13	=	=	SYM
ejpam-6199	511	14	υ̃π((v	υ̃π((v	NOUN
ejpam-6199	511	15	|	|	ADV
ejpam-6199	511	16	(	(	PUNCT
ejpam-6199	511	17	n	n	CCONJ
ejpam-6199	511	18	|	|	ADV
ejpam-6199	511	19	(	(	PUNCT
ejpam-6199	511	20	n	n	CCONJ
ejpam-6199	511	21	|	|	ADV
ejpam-6199	511	22	(	(	PUNCT
ejpam-6199	511	23	v	v	NOUN
ejpam-6199	511	24	|	|	ADV
ejpam-6199	511	25	v	v	NOUN
ejpam-6199	511	26	)	)	PUNCT
ejpam-6199	511	27	)	)	PUNCT
ejpam-6199	511	28	)	)	PUNCT
ejpam-6199	511	29	)	)	PUNCT
ejpam-6199	512	1	|	|	ADV
ejpam-6199	512	2	(	(	PUNCT
ejpam-6199	512	3	n	n	CCONJ
ejpam-6199	512	4	|	|	ADV
ejpam-6199	512	5	(	(	PUNCT
ejpam-6199	512	6	n	n	CCONJ
ejpam-6199	512	7	|	|	ADV
ejpam-6199	512	8	(	(	PUNCT
ejpam-6199	512	9	v	v	NOUN
ejpam-6199	512	10	|	|	ADV
ejpam-6199	512	11	v	v	NOUN
ejpam-6199	512	12	)	)	PUNCT
ejpam-6199	512	13	)	)	PUNCT
ejpam-6199	512	14	)	)	PUNCT
ejpam-6199	512	15	)	)	PUNCT
ejpam-6199	513	1	⪰	⪰	NOUN
ejpam-6199	513	2	m̃in{υ̃π(n	m̃in{υ̃π(n	PROPN
ejpam-6199	513	3	)	)	PUNCT
ejpam-6199	513	4	,	,	PUNCT
ejpam-6199	513	5	υ̃π(n	υ̃π(n	PROPN
ejpam-6199	514	1	|	|	ADV
ejpam-6199	514	2	(	(	PUNCT
ejpam-6199	514	3	v	v	NOUN
ejpam-6199	514	4	|	|	ADV
ejpam-6199	514	5	v	v	NOUN
ejpam-6199	514	6	)	)	PUNCT
ejpam-6199	514	7	)	)	PUNCT
ejpam-6199	514	8	}	}	PUNCT
ejpam-6199	514	9	and	and	CCONJ
ejpam-6199	514	10	ϖπ(v	ϖπ(v	NOUN
ejpam-6199	514	11	)	)	PUNCT
ejpam-6199	514	12	=	=	SYM
ejpam-6199	514	13	ϖπ((v	ϖπ((v	NOUN
ejpam-6199	514	14	|	|	ADV
ejpam-6199	514	15	(	(	PUNCT
ejpam-6199	514	16	n	n	CCONJ
ejpam-6199	515	1	|	|	ADV
ejpam-6199	515	2	(	(	PUNCT
ejpam-6199	515	3	n	n	CCONJ
ejpam-6199	515	4	|	|	ADV
ejpam-6199	515	5	(	(	PUNCT
ejpam-6199	515	6	v	v	NOUN
ejpam-6199	515	7	|	|	ADV
ejpam-6199	515	8	v	v	NOUN
ejpam-6199	515	9	)	)	PUNCT
ejpam-6199	515	10	)	)	PUNCT
ejpam-6199	515	11	)	)	PUNCT
ejpam-6199	515	12	)	)	PUNCT
ejpam-6199	516	1	|	|	ADV
ejpam-6199	516	2	(	(	PUNCT
ejpam-6199	516	3	n	n	CCONJ
ejpam-6199	516	4	|	|	ADV
ejpam-6199	516	5	(	(	PUNCT
ejpam-6199	516	6	n	n	CCONJ
ejpam-6199	516	7	|	|	ADV
ejpam-6199	516	8	(	(	PUNCT
ejpam-6199	516	9	v	v	NOUN
ejpam-6199	516	10	|	|	ADV
ejpam-6199	516	11	v	v	NOUN
ejpam-6199	516	12	)	)	PUNCT
ejpam-6199	516	13	)	)	PUNCT
ejpam-6199	516	14	)	)	PUNCT
ejpam-6199	516	15	)	)	PUNCT
ejpam-6199	517	1	≤	≤	NUM
ejpam-6199	517	2	max{ϖπ(n	max{ϖπ(n	PROPN
ejpam-6199	517	3	)	)	PUNCT
ejpam-6199	517	4	,	,	PUNCT
ejpam-6199	517	5	ϖπ(n	ϖπ(n	PUNCT
ejpam-6199	518	1	|	|	ADV
ejpam-6199	518	2	(	(	PUNCT
ejpam-6199	518	3	v	v	NOUN
ejpam-6199	518	4	|	|	ADV
ejpam-6199	518	5	v	v	NOUN
ejpam-6199	518	6	)	)	PUNCT
ejpam-6199	518	7	)	)	PUNCT
ejpam-6199	518	8	}	}	PUNCT
ejpam-6199	518	9	.	.	PUNCT
ejpam-6199	519	1	therefore	therefore	ADV
ejpam-6199	519	2	π	π	PROPN
ejpam-6199	519	3	=	=	SYM
ejpam-6199	519	4	(	(	PUNCT
ejpam-6199	519	5	υ̃π	υ̃π	PROPN
ejpam-6199	519	6	,	,	PUNCT
ejpam-6199	519	7	ϖπ	ϖπ	NOUN
ejpam-6199	519	8	)	)	PUNCT
ejpam-6199	519	9	is	be	AUX
ejpam-6199	519	10	a	a	DET
ejpam-6199	519	11	crossing	cross	VERB
ejpam-6199	519	12	cubic	cubic	ADJ
ejpam-6199	519	13	deductive	deductive	ADJ
ejpam-6199	519	14	system	system	NOUN
ejpam-6199	519	15	of	of	ADP
ejpam-6199	519	16	ϑ.	ϑ.	NOUN
ejpam-6199	519	17	remark	remark	VERB
ejpam-6199	519	18	1	1	NUM
ejpam-6199	519	19	.	.	PUNCT
ejpam-6199	519	20	by	by	ADP
ejpam-6199	519	21	theorem	theorem	NOUN
ejpam-6199	519	22	5	5	NUM
ejpam-6199	519	23	,	,	PUNCT
ejpam-6199	519	24	the	the	DET
ejpam-6199	519	25	crossing	cross	VERB
ejpam-6199	519	26	cubic	cubic	ADJ
ejpam-6199	519	27	deductive	deductive	ADJ
ejpam-6199	519	28	system	system	NOUN
ejpam-6199	519	29	can	can	AUX
ejpam-6199	519	30	handle	handle	VERB
ejpam-6199	519	31	all	all	PRON
ejpam-6199	519	32	of	of	ADP
ejpam-6199	519	33	the	the	DET
ejpam-6199	519	34	results	result	NOUN
ejpam-6199	519	35	for	for	ADP
ejpam-6199	519	36	the	the	DET
ejpam-6199	519	37	crossing	crossing	ADJ
ejpam-6199	519	38	cubic	cubic	ADJ
ejpam-6199	519	39	filter	filter	NOUN
ejpam-6199	519	40	covered	cover	VERB
ejpam-6199	519	41	above	above	ADV
ejpam-6199	519	42	in	in	ADP
ejpam-6199	519	43	the	the	DET
ejpam-6199	519	44	same	same	ADJ
ejpam-6199	519	45	way	way	NOUN
ejpam-6199	519	46	.	.	PUNCT
ejpam-6199	520	1	a.	a.	PROPN
ejpam-6199	520	2	al	al	PROPN
ejpam-6199	520	3	-	-	PROPN
ejpam-6199	520	4	masarwah	masarwah	PROPN
ejpam-6199	520	5	et	et	PROPN
ejpam-6199	520	6	al	al	PROPN
ejpam-6199	520	7	.	.	PUNCT
ejpam-6199	520	8	/	/	SYM
ejpam-6199	520	9	eur	eur	PROPN
ejpam-6199	520	10	.	.	PUNCT
ejpam-6199	521	1	j.	j.	PROPN
ejpam-6199	521	2	pure	pure	PROPN
ejpam-6199	521	3	appl	appl	PROPN
ejpam-6199	521	4	.	.	PROPN
ejpam-6199	521	5	math	math	PROPN
ejpam-6199	521	6	,	,	PUNCT
ejpam-6199	521	7	18	18	NUM
ejpam-6199	521	8	(	(	PUNCT
ejpam-6199	521	9	3	3	NUM
ejpam-6199	521	10	)	)	PUNCT
ejpam-6199	521	11	(	(	PUNCT
ejpam-6199	521	12	2025	2025	NUM
ejpam-6199	521	13	)	)	PUNCT
ejpam-6199	521	14	,	,	PUNCT
ejpam-6199	521	15	6199	6199	NUM
ejpam-6199	521	16	16	16	NUM
ejpam-6199	521	17	of	of	ADP
ejpam-6199	521	18	17	17	NUM
ejpam-6199	521	19	5	5	NUM
ejpam-6199	521	20	.	.	PUNCT
ejpam-6199	521	21	conclusion	conclusion	VERB
ejpam-6199	521	22	the	the	DET
ejpam-6199	521	23	crossing	cross	VERB
ejpam-6199	521	24	cubic	cubic	ADJ
ejpam-6199	521	25	structure	structure	NOUN
ejpam-6199	521	26	creates	create	VERB
ejpam-6199	521	27	new	new	ADJ
ejpam-6199	521	28	opportunities	opportunity	NOUN
ejpam-6199	521	29	to	to	PART
ejpam-6199	521	30	introduce	introduce	VERB
ejpam-6199	521	31	new	new	ADJ
ejpam-6199	521	32	tools	tool	NOUN
ejpam-6199	521	33	,	,	PUNCT
ejpam-6199	521	34	allowing	allow	VERB
ejpam-6199	521	35	experiments	experiment	NOUN
ejpam-6199	521	36	and	and	CCONJ
ejpam-6199	521	37	studies	study	NOUN
ejpam-6199	521	38	that	that	PRON
ejpam-6199	521	39	were	be	AUX
ejpam-6199	521	40	previously	previously	ADV
ejpam-6199	521	41	not	not	PART
ejpam-6199	521	42	possible	possible	ADJ
ejpam-6199	521	43	through	through	ADP
ejpam-6199	521	44	broad	broad	ADJ
ejpam-6199	521	45	applications	application	NOUN
ejpam-6199	521	46	in	in	ADP
ejpam-6199	521	47	various	various	ADJ
ejpam-6199	521	48	fields	field	NOUN
ejpam-6199	521	49	.	.	PUNCT
ejpam-6199	522	1	combining	combine	VERB
ejpam-6199	522	2	the	the	DET
ejpam-6199	522	3	interval	interval	NOUN
ejpam-6199	522	4	-	-	PUNCT
ejpam-6199	522	5	value	value	NOUN
ejpam-6199	522	6	fuzzy	fuzzy	ADJ
ejpam-6199	522	7	set	set	NOUN
ejpam-6199	522	8	and	and	CCONJ
ejpam-6199	522	9	n	n	CCONJ
ejpam-6199	522	10	-	-	PUNCT
ejpam-6199	522	11	structure	structure	NOUN
ejpam-6199	522	12	leads	lead	VERB
ejpam-6199	522	13	to	to	ADP
ejpam-6199	522	14	acquiring	acquire	VERB
ejpam-6199	522	15	the	the	DET
ejpam-6199	522	16	crossing	crossing	NOUN
ejpam-6199	522	17	cubic	cubic	ADJ
ejpam-6199	522	18	structure	structure	NOUN
ejpam-6199	522	19	.	.	PUNCT
ejpam-6199	523	1	we	we	PRON
ejpam-6199	523	2	utilized	utilize	VERB
ejpam-6199	523	3	the	the	DET
ejpam-6199	523	4	crossing	crossing	NOUN
ejpam-6199	523	5	cubic	cubic	ADJ
ejpam-6199	523	6	structure	structure	NOUN
ejpam-6199	523	7	on	on	ADP
ejpam-6199	523	8	filters	filter	NOUN
ejpam-6199	523	9	and	and	CCONJ
ejpam-6199	523	10	deductive	deductive	ADJ
ejpam-6199	523	11	systems	system	NOUN
ejpam-6199	523	12	in	in	ADP
ejpam-6199	523	13	sheffer	sheffer	PROPN
ejpam-6199	523	14	stroke	stroke	PROPN
ejpam-6199	523	15	hilbert	hilbert	PROPN
ejpam-6199	523	16	algebras	algebras	PROPN
ejpam-6199	523	17	.	.	PUNCT
ejpam-6199	524	1	also	also	ADV
ejpam-6199	524	2	,	,	PUNCT
ejpam-6199	524	3	we	we	PRON
ejpam-6199	524	4	defined	define	VERB
ejpam-6199	524	5	the	the	DET
ejpam-6199	524	6	notions	notion	NOUN
ejpam-6199	524	7	of	of	ADP
ejpam-6199	524	8	the	the	DET
ejpam-6199	524	9	crossing	crossing	ADJ
ejpam-6199	524	10	cubic	cubic	ADJ
ejpam-6199	524	11	filter	filter	NOUN
ejpam-6199	524	12	and	and	CCONJ
ejpam-6199	524	13	crossing	cross	VERB
ejpam-6199	524	14	cubic	cubic	ADJ
ejpam-6199	524	15	deductive	deductive	ADJ
ejpam-6199	524	16	system	system	NOUN
ejpam-6199	524	17	.	.	PUNCT
ejpam-6199	525	1	then	then	ADV
ejpam-6199	525	2	,	,	PUNCT
ejpam-6199	525	3	we	we	PRON
ejpam-6199	525	4	verified	verify	VERB
ejpam-6199	525	5	many	many	ADJ
ejpam-6199	525	6	characteristics	characteristic	NOUN
ejpam-6199	525	7	of	of	ADP
ejpam-6199	525	8	these	these	DET
ejpam-6199	525	9	notions	notion	NOUN
ejpam-6199	525	10	.	.	PUNCT
ejpam-6199	526	1	we	we	PRON
ejpam-6199	526	2	established	establish	VERB
ejpam-6199	526	3	conditions	condition	NOUN
ejpam-6199	526	4	suitable	suitable	ADJ
ejpam-6199	526	5	for	for	SCONJ
ejpam-6199	526	6	the	the	DET
ejpam-6199	526	7	crossing	crossing	ADJ
ejpam-6199	526	8	cubic	cubic	ADJ
ejpam-6199	526	9	structure	structure	NOUN
ejpam-6199	526	10	to	to	PART
ejpam-6199	526	11	be	be	AUX
ejpam-6199	526	12	a	a	DET
ejpam-6199	526	13	crossing	cross	VERB
ejpam-6199	526	14	cubic	cubic	ADJ
ejpam-6199	526	15	filter	filter	NOUN
ejpam-6199	526	16	.	.	PUNCT
ejpam-6199	527	1	the	the	DET
ejpam-6199	527	2	crossing	cross	VERB
ejpam-6199	527	3	cubic	cubic	ADJ
ejpam-6199	527	4	filters	filter	NOUN
ejpam-6199	527	5	also	also	ADV
ejpam-6199	527	6	received	receive	VERB
ejpam-6199	527	7	further	further	ADJ
ejpam-6199	527	8	characterization	characterization	NOUN
ejpam-6199	527	9	theorems	theorem	NOUN
ejpam-6199	527	10	.	.	PUNCT
ejpam-6199	528	1	to	to	PART
ejpam-6199	528	2	create	create	VERB
ejpam-6199	528	3	a	a	DET
ejpam-6199	528	4	relationship	relationship	NOUN
ejpam-6199	528	5	between	between	ADP
ejpam-6199	528	6	crossing	cross	VERB
ejpam-6199	528	7	cubic	cubic	ADJ
ejpam-6199	528	8	filters	filter	NOUN
ejpam-6199	528	9	and	and	CCONJ
ejpam-6199	528	10	filters	filter	NOUN
ejpam-6199	528	11	,	,	PUNCT
ejpam-6199	528	12	we	we	PRON
ejpam-6199	528	13	generated	generate	VERB
ejpam-6199	528	14	crossing	cross	VERB
ejpam-6199	528	15	cubic	cubic	ADJ
ejpam-6199	528	16	filters	filter	NOUN
ejpam-6199	528	17	that	that	PRON
ejpam-6199	528	18	are	be	AUX
ejpam-6199	528	19	related	relate	VERB
ejpam-6199	528	20	with	with	ADP
ejpam-6199	528	21	filters	filter	NOUN
ejpam-6199	528	22	.	.	PUNCT
ejpam-6199	529	1	we	we	PRON
ejpam-6199	529	2	demonstrated	demonstrate	VERB
ejpam-6199	529	3	that	that	SCONJ
ejpam-6199	529	4	the	the	DET
ejpam-6199	529	5	crossing	cross	VERB
ejpam-6199	529	6	cubic	cubic	ADJ
ejpam-6199	529	7	deductive	deductive	ADJ
ejpam-6199	529	8	system	system	NOUN
ejpam-6199	529	9	can	can	AUX
ejpam-6199	529	10	handle	handle	VERB
ejpam-6199	529	11	all	all	PRON
ejpam-6199	529	12	of	of	ADP
ejpam-6199	529	13	the	the	DET
ejpam-6199	529	14	results	result	NOUN
ejpam-6199	529	15	for	for	ADP
ejpam-6199	529	16	the	the	DET
ejpam-6199	529	17	crossing	crossing	ADJ
ejpam-6199	529	18	cubic	cubic	ADJ
ejpam-6199	529	19	filter	filter	NOUN
ejpam-6199	529	20	in	in	ADP
ejpam-6199	529	21	the	the	DET
ejpam-6199	529	22	same	same	ADJ
ejpam-6199	529	23	way	way	NOUN
ejpam-6199	529	24	.	.	PUNCT
ejpam-6199	530	1	this	this	DET
ejpam-6199	530	2	work	work	NOUN
ejpam-6199	530	3	is	be	AUX
ejpam-6199	530	4	designed	design	VERB
ejpam-6199	530	5	to	to	PART
ejpam-6199	530	6	stimulate	stimulate	VERB
ejpam-6199	530	7	more	more	ADJ
ejpam-6199	530	8	research	research	NOUN
ejpam-6199	530	9	on	on	ADP
ejpam-6199	530	10	crossing	cross	VERB
ejpam-6199	530	11	cubic	cubic	ADJ
ejpam-6199	530	12	structures	structure	NOUN
ejpam-6199	530	13	,	,	PUNCT
ejpam-6199	530	14	resulting	result	VERB
ejpam-6199	530	15	in	in	ADP
ejpam-6199	530	16	fresh	fresh	ADJ
ejpam-6199	530	17	and	and	CCONJ
ejpam-6199	530	18	unfamiliar	unfamiliar	ADJ
ejpam-6199	530	19	findings	finding	NOUN
ejpam-6199	530	20	.	.	PUNCT
ejpam-6199	531	1	this	this	PRON
ejpam-6199	531	2	opens	open	VERB
ejpam-6199	531	3	up	up	ADP
ejpam-6199	531	4	possibilities	possibility	NOUN
ejpam-6199	531	5	for	for	ADP
ejpam-6199	531	6	additional	additional	ADJ
ejpam-6199	531	7	research	research	NOUN
ejpam-6199	531	8	and	and	CCONJ
ejpam-6199	531	9	applications	application	NOUN
ejpam-6199	531	10	.	.	PUNCT
ejpam-6199	532	1	the	the	DET
ejpam-6199	532	2	concept	concept	NOUN
ejpam-6199	532	3	of	of	ADP
ejpam-6199	532	4	crossing	cross	VERB
ejpam-6199	532	5	cubic	cubic	ADJ
ejpam-6199	532	6	structures	structure	NOUN
ejpam-6199	532	7	can	can	AUX
ejpam-6199	532	8	be	be	AUX
ejpam-6199	532	9	applied	apply	VERB
ejpam-6199	532	10	in	in	ADP
ejpam-6199	532	11	the	the	DET
ejpam-6199	532	12	future	future	NOUN
ejpam-6199	532	13	.	.	PUNCT
ejpam-6199	533	1	their	their	PRON
ejpam-6199	533	2	application	application	NOUN
ejpam-6199	533	3	extends	extend	VERB
ejpam-6199	533	4	to	to	ADP
ejpam-6199	533	5	numerous	numerous	ADJ
ejpam-6199	533	6	algebraic	algebraic	ADJ
ejpam-6199	533	7	structures	structure	NOUN
ejpam-6199	533	8	such	such	ADJ
ejpam-6199	533	9	as	as	ADP
ejpam-6199	533	10	pi	pi	NOUN
ejpam-6199	533	11	-	-	PUNCT
ejpam-6199	533	12	algebras	algebras	ADV
ejpam-6199	533	13	,	,	PUNCT
ejpam-6199	533	14	lie	lie	NOUN
ejpam-6199	533	15	algebras	algebra	NOUN
ejpam-6199	533	16	,	,	PUNCT
ejpam-6199	533	17	lattices	lattice	NOUN
ejpam-6199	533	18	,	,	PUNCT
ejpam-6199	533	19	bck	bck	PROPN
ejpam-6199	533	20	/	/	SYM
ejpam-6199	533	21	bci	bci	NOUN
ejpam-6199	533	22	-	-	PUNCT
ejpam-6199	533	23	algebras	algebra	NOUN
ejpam-6199	533	24	,	,	PUNCT
ejpam-6199	533	25	hopf	hopf	ADJ
ejpam-6199	533	26	algebras	algebras	X
ejpam-6199	533	27	,	,	PUNCT
ejpam-6199	533	28	etc	etc	X
ejpam-6199	533	29	.	.	X
ejpam-6199	534	1	in	in	ADP
ejpam-6199	534	2	addition	addition	NOUN
ejpam-6199	534	3	,	,	PUNCT
ejpam-6199	534	4	we	we	PRON
ejpam-6199	534	5	believe	believe	VERB
ejpam-6199	534	6	that	that	SCONJ
ejpam-6199	534	7	the	the	DET
ejpam-6199	534	8	potential	potential	NOUN
ejpam-6199	534	9	of	of	ADP
ejpam-6199	534	10	this	this	DET
ejpam-6199	534	11	work	work	NOUN
ejpam-6199	534	12	will	will	AUX
ejpam-6199	534	13	be	be	AUX
ejpam-6199	534	14	used	use	VERB
ejpam-6199	534	15	in	in	ADP
ejpam-6199	534	16	database	database	NOUN
ejpam-6199	534	17	theory	theory	NOUN
ejpam-6199	534	18	,	,	PUNCT
ejpam-6199	534	19	probability	probability	NOUN
ejpam-6199	534	20	theory	theory	NOUN
ejpam-6199	534	21	,	,	PUNCT
ejpam-6199	534	22	and	and	CCONJ
ejpam-6199	534	23	other	other	ADJ
ejpam-6199	534	24	fields	field	NOUN
ejpam-6199	534	25	.	.	PUNCT
ejpam-6199	535	1	references	reference	NOUN
ejpam-6199	535	2	[	[	X
ejpam-6199	535	3	1	1	NUM
ejpam-6199	535	4	]	]	PUNCT
ejpam-6199	535	5	h.	h.	PROPN
ejpam-6199	535	6	m.	m.	PROPN
ejpam-6199	535	7	sheffer	sheffer	PROPN
ejpam-6199	535	8	.	.	PUNCT
ejpam-6199	536	1	a	a	DET
ejpam-6199	536	2	set	set	NOUN
ejpam-6199	536	3	of	of	ADP
ejpam-6199	536	4	five	five	NUM
ejpam-6199	536	5	independent	independent	ADJ
ejpam-6199	536	6	postulates	postulate	NOUN
ejpam-6199	536	7	for	for	ADP
ejpam-6199	536	8	boolean	boolean	ADJ
ejpam-6199	536	9	algebras	algebra	NOUN
ejpam-6199	536	10	,	,	PUNCT
ejpam-6199	536	11	with	with	ADP
ejpam-6199	536	12	application	application	NOUN
ejpam-6199	536	13	to	to	ADP
ejpam-6199	536	14	logical	logical	ADJ
ejpam-6199	536	15	constants	constant	NOUN
ejpam-6199	536	16	.	.	PUNCT
ejpam-6199	537	1	transactions	transaction	NOUN
ejpam-6199	537	2	of	of	ADP
ejpam-6199	537	3	the	the	DET
ejpam-6199	537	4	american	american	PROPN
ejpam-6199	537	5	mathematical	mathematical	PROPN
ejpam-6199	537	6	society	society	NOUN
ejpam-6199	537	7	,	,	PUNCT
ejpam-6199	537	8	14(4):481–488	14(4):481–488	NUM
ejpam-6199	537	9	,	,	PUNCT
ejpam-6199	537	10	1913	1913	NUM
ejpam-6199	537	11	.	.	PUNCT
ejpam-6199	538	1	[	[	X
ejpam-6199	538	2	2	2	NUM
ejpam-6199	538	3	]	]	PUNCT
ejpam-6199	538	4	w.	w.	PROPN
ejpam-6199	538	5	mccune	mccune	PROPN
ejpam-6199	538	6	,	,	PUNCT
ejpam-6199	538	7	r.	r.	PROPN
ejpam-6199	538	8	veroff	veroff	PROPN
ejpam-6199	538	9	,	,	PUNCT
ejpam-6199	538	10	b.	b.	PROPN
ejpam-6199	538	11	fitelson	fitelson	PROPN
ejpam-6199	538	12	,	,	PUNCT
ejpam-6199	538	13	k.	k.	PROPN
ejpam-6199	538	14	harris	harris	PROPN
ejpam-6199	538	15	,	,	PUNCT
ejpam-6199	538	16	a.	a.	NOUN
ejpam-6199	538	17	feist	feist	PROPN
ejpam-6199	538	18	,	,	PUNCT
ejpam-6199	538	19	and	and	CCONJ
ejpam-6199	538	20	l.	l.	PROPN
ejpam-6199	538	21	wos	wos	PROPN
ejpam-6199	538	22	.	.	PUNCT
ejpam-6199	538	23	short	short	ADJ
ejpam-6199	538	24	single	single	ADJ
ejpam-6199	538	25	axioms	axiom	NOUN
ejpam-6199	538	26	for	for	ADP
ejpam-6199	538	27	boolean	boolean	ADJ
ejpam-6199	538	28	algebra	algebra	NOUN
ejpam-6199	538	29	.	.	PUNCT
ejpam-6199	539	1	journal	journal	NOUN
ejpam-6199	539	2	of	of	ADP
ejpam-6199	539	3	automated	automate	VERB
ejpam-6199	539	4	reasoning	reasoning	NOUN
ejpam-6199	539	5	,	,	PUNCT
ejpam-6199	539	6	29(1):1–16	29(1):1–16	PROPN
ejpam-6199	539	7	,	,	PUNCT
ejpam-6199	539	8	2002	2002	NUM
ejpam-6199	539	9	.	.	PUNCT
ejpam-6199	540	1	[	[	X
ejpam-6199	540	2	3	3	X
ejpam-6199	540	3	]	]	PUNCT
ejpam-6199	540	4	t.	t.	NOUN
ejpam-6199	540	5	oner	oner	NOUN
ejpam-6199	540	6	,	,	PUNCT
ejpam-6199	540	7	t.	t.	PROPN
ejpam-6199	540	8	kalkan	kalkan	PROPN
ejpam-6199	540	9	,	,	PUNCT
ejpam-6199	540	10	and	and	CCONJ
ejpam-6199	540	11	n.	n.	PROPN
ejpam-6199	540	12	k.	k.	PROPN
ejpam-6199	540	13	gursoy	gursoy	PROPN
ejpam-6199	540	14	.	.	PUNCT
ejpam-6199	541	1	sheffer	sheffer	PROPN
ejpam-6199	541	2	stroke	stroke	PROPN
ejpam-6199	541	3	bg	bg	PROPN
ejpam-6199	541	4	-	-	PUNCT
ejpam-6199	541	5	algebras	algebras	PROPN
ejpam-6199	541	6	.	.	PUNCT
ejpam-6199	542	1	international	international	ADJ
ejpam-6199	542	2	journal	journal	PROPN
ejpam-6199	542	3	of	of	ADP
ejpam-6199	542	4	maps	map	NOUN
ejpam-6199	542	5	in	in	ADP
ejpam-6199	542	6	mathematics	mathematic	NOUN
ejpam-6199	542	7	,	,	PUNCT
ejpam-6199	542	8	4(1):27–39	4(1):27–39	NUM
ejpam-6199	542	9	,	,	PUNCT
ejpam-6199	542	10	2021	2021	NUM
ejpam-6199	542	11	.	.	PUNCT
ejpam-6199	543	1	[	[	X
ejpam-6199	543	2	4	4	X
ejpam-6199	543	3	]	]	PUNCT
ejpam-6199	543	4	t.	t.	NOUN
ejpam-6199	543	5	oner	oner	NOUN
ejpam-6199	543	6	,	,	PUNCT
ejpam-6199	543	7	t.	t.	PROPN
ejpam-6199	543	8	kalkan	kalkan	PROPN
ejpam-6199	543	9	,	,	PUNCT
ejpam-6199	543	10	a.	a.	PROPN
ejpam-6199	543	11	hamal	hamal	ADJ
ejpam-6199	543	12	,	,	PUNCT
ejpam-6199	543	13	and	and	CCONJ
ejpam-6199	543	14	m.	m.	NOUN
ejpam-6199	543	15	kibar	kibar	PROPN
ejpam-6199	543	16	.	.	PUNCT
ejpam-6199	544	1	sheffer	sheffer	PROPN
ejpam-6199	544	2	stroke	stroke	PROPN
ejpam-6199	544	3	bm	bm	PROPN
ejpam-6199	544	4	-	-	PUNCT
ejpam-6199	544	5	algebras	algebras	PROPN
ejpam-6199	544	6	and	and	CCONJ
ejpam-6199	544	7	related	related	ADJ
ejpam-6199	544	8	algebras	algebra	NOUN
ejpam-6199	544	9	.	.	PUNCT
ejpam-6199	545	1	journal	journal	PROPN
ejpam-6199	545	2	of	of	ADP
ejpam-6199	545	3	international	international	PROPN
ejpam-6199	545	4	mathematical	mathematical	ADJ
ejpam-6199	545	5	virtual	virtual	PROPN
ejpam-6199	545	6	institute	institute	NOUN
ejpam-6199	545	7	,	,	PUNCT
ejpam-6199	545	8	12(1):87–102	12(1):87–102	NUM
ejpam-6199	545	9	,	,	PUNCT
ejpam-6199	545	10	2022	2022	NUM
ejpam-6199	545	11	.	.	PUNCT
ejpam-6199	546	1	[	[	X
ejpam-6199	546	2	5	5	NUM
ejpam-6199	546	3	]	]	PUNCT
ejpam-6199	546	4	i.	i.	NOUN
ejpam-6199	546	5	chajda	chajda	PROPN
ejpam-6199	546	6	.	.	PUNCT
ejpam-6199	547	1	sheffer	sheffer	PROPN
ejpam-6199	547	2	operation	operation	NOUN
ejpam-6199	547	3	in	in	ADP
ejpam-6199	547	4	ortholattices	ortholattice	NOUN
ejpam-6199	547	5	.	.	PUNCT
ejpam-6199	548	1	acta	acta	PROPN
ejpam-6199	548	2	universitatis	universitatis	PROPN
ejpam-6199	548	3	palackianae	palackianae	VERB
ejpam-6199	548	4	olomucensis	olomucensis	NOUN
ejpam-6199	548	5	.	.	PUNCT
ejpam-6199	549	1	facultas	facultas	PROPN
ejpam-6199	549	2	rerum	rerum	PROPN
ejpam-6199	549	3	naturalium	naturalium	PROPN
ejpam-6199	549	4	.	.	PUNCT
ejpam-6199	550	1	mathematica	mathematica	PROPN
ejpam-6199	550	2	,	,	PUNCT
ejpam-6199	550	3	44(1):19–23	44(1):19–23	NUM
ejpam-6199	550	4	,	,	PUNCT
ejpam-6199	550	5	2005	2005	NUM
ejpam-6199	550	6	.	.	PUNCT
ejpam-6199	551	1	[	[	X
ejpam-6199	551	2	6	6	NUM
ejpam-6199	551	3	]	]	PUNCT
ejpam-6199	551	4	t.	t.	NOUN
ejpam-6199	551	5	oner	oner	NOUN
ejpam-6199	551	6	,	,	PUNCT
ejpam-6199	551	7	t.	t.	PROPN
ejpam-6199	551	8	kalkan	kalkan	PROPN
ejpam-6199	551	9	,	,	PUNCT
ejpam-6199	551	10	and	and	CCONJ
ejpam-6199	551	11	s.	s.	PROPN
ejpam-6199	551	12	a.	a.	PROPN
ejpam-6199	551	13	ozbal	ozbal	PROPN
ejpam-6199	551	14	.	.	PUNCT
ejpam-6199	552	1	sheffer	sheffer	PROPN
ejpam-6199	552	2	stroke	stroke	PROPN
ejpam-6199	552	3	ink	ink	PROPN
ejpam-6199	552	4	-	-	PUNCT
ejpam-6199	552	5	algebras	algebras	PROPN
ejpam-6199	552	6	.	.	PUNCT
ejpam-6199	553	1	journal	journal	PROPN
ejpam-6199	553	2	of	of	ADP
ejpam-6199	553	3	international	international	PROPN
ejpam-6199	553	4	mathematical	mathematical	ADJ
ejpam-6199	553	5	virtual	virtual	PROPN
ejpam-6199	553	6	institute	institute	NOUN
ejpam-6199	553	7	,	,	PUNCT
ejpam-6199	553	8	13(1):1–16	13(1):1–16	NUM
ejpam-6199	553	9	,	,	PUNCT
ejpam-6199	553	10	2023	2023	NUM
ejpam-6199	553	11	.	.	PUNCT
ejpam-6199	554	1	[	[	X
ejpam-6199	554	2	7	7	X
ejpam-6199	554	3	]	]	X
ejpam-6199	554	4	l.	l.	PROPN
ejpam-6199	554	5	henkin	henkin	PROPN
ejpam-6199	554	6	.	.	PUNCT
ejpam-6199	555	1	an	an	DET
ejpam-6199	555	2	algebraic	algebraic	ADJ
ejpam-6199	555	3	characterization	characterization	NOUN
ejpam-6199	555	4	of	of	ADP
ejpam-6199	555	5	quantifiers	quantifier	NOUN
ejpam-6199	555	6	.	.	PUNCT
ejpam-6199	556	1	fundamenta	fundamenta	PROPN
ejpam-6199	556	2	mathematicae	mathematicae	PROPN
ejpam-6199	556	3	,	,	PUNCT
ejpam-6199	556	4	37(1):63–74	37(1):63–74	NUM
ejpam-6199	556	5	,	,	PUNCT
ejpam-6199	556	6	1950	1950	NUM
ejpam-6199	556	7	.	.	PUNCT
ejpam-6199	557	1	[	[	X
ejpam-6199	557	2	8	8	X
ejpam-6199	557	3	]	]	X
ejpam-6199	557	4	h.	h.	PROPN
ejpam-6199	557	5	rasiowa	rasiowa	PROPN
ejpam-6199	557	6	.	.	PUNCT
ejpam-6199	558	1	an	an	DET
ejpam-6199	558	2	algebraic	algebraic	ADJ
ejpam-6199	558	3	approach	approach	NOUN
ejpam-6199	558	4	to	to	ADP
ejpam-6199	558	5	non	non	ADJ
ejpam-6199	558	6	-	-	ADJ
ejpam-6199	558	7	classical	classical	ADJ
ejpam-6199	558	8	logics	logic	NOUN
ejpam-6199	558	9	,	,	PUNCT
ejpam-6199	558	10	volume	volume	NOUN
ejpam-6199	558	11	78	78	NUM
ejpam-6199	558	12	of	of	ADP
ejpam-6199	558	13	studies	study	NOUN
ejpam-6199	558	14	in	in	ADP
ejpam-6199	558	15	logic	logic	NOUN
ejpam-6199	558	16	and	and	CCONJ
ejpam-6199	558	17	the	the	DET
ejpam-6199	558	18	foundations	foundation	NOUN
ejpam-6199	558	19	of	of	ADP
ejpam-6199	558	20	mathematics	mathematic	NOUN
ejpam-6199	558	21	.	.	PUNCT
ejpam-6199	559	1	north	north	NOUN
ejpam-6199	559	2	-	-	PUNCT
ejpam-6199	559	3	holland	holland	PROPN
ejpam-6199	559	4	,	,	PUNCT
ejpam-6199	559	5	amsterdam	amsterdam	PROPN
ejpam-6199	559	6	,	,	PUNCT
ejpam-6199	559	7	1974	1974	NUM
ejpam-6199	559	8	.	.	PUNCT
ejpam-6199	560	1	[	[	X
ejpam-6199	560	2	9	9	NUM
ejpam-6199	560	3	]	]	SYM
ejpam-6199	560	4	a.	a.	NOUN
ejpam-6199	560	5	diego	diego	PROPN
ejpam-6199	560	6	.	.	PUNCT
ejpam-6199	561	1	sur	sur	PROPN
ejpam-6199	561	2	les	les	PROPN
ejpam-6199	561	3	algèbres	algèbre	NOUN
ejpam-6199	561	4	de	de	X
ejpam-6199	561	5	hilbert	hilbert	NOUN
ejpam-6199	561	6	,	,	PUNCT
ejpam-6199	561	7	volume	volume	NOUN
ejpam-6199	561	8	21	21	NUM
ejpam-6199	561	9	of	of	ADP
ejpam-6199	561	10	collection	collection	NOUN
ejpam-6199	561	11	de	de	X
ejpam-6199	561	12	logique	logique	X
ejpam-6199	561	13	mathématique	mathématique	PROPN
ejpam-6199	561	14	,	,	PUNCT
ejpam-6199	561	15	série	série	PROPN
ejpam-6199	561	16	a.	a.	PROPN
ejpam-6199	561	17	hermann	hermann	PROPN
ejpam-6199	561	18	,	,	PUNCT
ejpam-6199	561	19	1966	1966	NUM
ejpam-6199	561	20	.	.	PUNCT
ejpam-6199	562	1	[	[	X
ejpam-6199	562	2	10	10	NUM
ejpam-6199	562	3	]	]	X
ejpam-6199	562	4	d.	d.	PROPN
ejpam-6199	562	5	busneag	busneag	PROPN
ejpam-6199	562	6	.	.	PUNCT
ejpam-6199	563	1	a	a	DET
ejpam-6199	563	2	note	note	NOUN
ejpam-6199	563	3	on	on	ADP
ejpam-6199	563	4	deductive	deductive	ADJ
ejpam-6199	563	5	systems	system	NOUN
ejpam-6199	563	6	of	of	ADP
ejpam-6199	563	7	a	a	DET
ejpam-6199	563	8	hilbert	hilbert	NOUN
ejpam-6199	563	9	algebra	algebra	NOUN
ejpam-6199	563	10	.	.	PUNCT
ejpam-6199	564	1	kobe	kobe	PROPN
ejpam-6199	564	2	journal	journal	PROPN
ejpam-6199	564	3	of	of	ADP
ejpam-6199	564	4	mathematics	mathematics	PROPN
ejpam-6199	564	5	,	,	PUNCT
ejpam-6199	564	6	2:29–35	2:29–35	NUM
ejpam-6199	564	7	,	,	PUNCT
ejpam-6199	564	8	1985	1985	NUM
ejpam-6199	564	9	.	.	PUNCT
ejpam-6199	565	1	a.	a.	PROPN
ejpam-6199	565	2	al	al	PROPN
ejpam-6199	565	3	-	-	PROPN
ejpam-6199	565	4	masarwah	masarwah	PROPN
ejpam-6199	565	5	et	et	PROPN
ejpam-6199	565	6	al	al	PROPN
ejpam-6199	565	7	.	.	PUNCT
ejpam-6199	565	8	/	/	SYM
ejpam-6199	565	9	eur	eur	PROPN
ejpam-6199	565	10	.	.	PUNCT
ejpam-6199	566	1	j.	j.	PROPN
ejpam-6199	566	2	pure	pure	PROPN
ejpam-6199	566	3	appl	appl	PROPN
ejpam-6199	566	4	.	.	PROPN
ejpam-6199	566	5	math	math	PROPN
ejpam-6199	566	6	,	,	PUNCT
ejpam-6199	566	7	18	18	NUM
ejpam-6199	566	8	(	(	PUNCT
ejpam-6199	566	9	3	3	NUM
ejpam-6199	566	10	)	)	PUNCT
ejpam-6199	566	11	(	(	PUNCT
ejpam-6199	566	12	2025	2025	NUM
ejpam-6199	566	13	)	)	PUNCT
ejpam-6199	566	14	,	,	PUNCT
ejpam-6199	566	15	6199	6199	NUM
ejpam-6199	566	16	17	17	NUM
ejpam-6199	566	17	of	of	ADP
ejpam-6199	566	18	17	17	NUM
ejpam-6199	566	19	[	[	SYM
ejpam-6199	566	20	11	11	NUM
ejpam-6199	566	21	]	]	X
ejpam-6199	566	22	d.	d.	PROPN
ejpam-6199	566	23	busneag	busneag	PROPN
ejpam-6199	566	24	.	.	PUNCT
ejpam-6199	567	1	hilbert	hilbert	PROPN
ejpam-6199	567	2	algebras	algebras	PROPN
ejpam-6199	567	3	of	of	ADP
ejpam-6199	567	4	fractions	fraction	NOUN
ejpam-6199	567	5	and	and	CCONJ
ejpam-6199	567	6	maximal	maximal	ADJ
ejpam-6199	567	7	hilbert	hilbert	NOUN
ejpam-6199	567	8	algebras	algebra	NOUN
ejpam-6199	567	9	of	of	ADP
ejpam-6199	567	10	quotients	quotient	NOUN
ejpam-6199	567	11	.	.	PUNCT
ejpam-6199	568	1	kobe	kobe	PROPN
ejpam-6199	568	2	journal	journal	PROPN
ejpam-6199	568	3	of	of	ADP
ejpam-6199	568	4	mathematics	mathematic	NOUN
ejpam-6199	568	5	,	,	PUNCT
ejpam-6199	568	6	5(2):132–136	5(2):132–136	NOUN
ejpam-6199	568	7	,	,	PUNCT
ejpam-6199	568	8	1988	1988	NUM
ejpam-6199	568	9	.	.	PUNCT
ejpam-6199	569	1	[	[	X
ejpam-6199	569	2	12	12	NUM
ejpam-6199	569	3	]	]	X
ejpam-6199	569	4	y.	y.	PROPN
ejpam-6199	569	5	b.	b.	PROPN
ejpam-6199	569	6	jun	jun	PROPN
ejpam-6199	569	7	.	.	PROPN
ejpam-6199	569	8	deductive	deductive	ADJ
ejpam-6199	569	9	systems	system	NOUN
ejpam-6199	569	10	of	of	ADP
ejpam-6199	569	11	hilbert	hilbert	PROPN
ejpam-6199	569	12	algebra	algebra	PROPN
ejpam-6199	569	13	.	.	PUNCT
ejpam-6199	570	1	mathematica	mathematica	PROPN
ejpam-6199	570	2	japonica	japonica	PROPN
ejpam-6199	570	3	,	,	PUNCT
ejpam-6199	570	4	43(1):51–54	43(1):51–54	NUM
ejpam-6199	570	5	,	,	PUNCT
ejpam-6199	570	6	1996	1996	NUM
ejpam-6199	570	7	.	.	PUNCT
ejpam-6199	571	1	[	[	X
ejpam-6199	571	2	13	13	NUM
ejpam-6199	571	3	]	]	PUNCT
ejpam-6199	571	4	t.	t.	NOUN
ejpam-6199	571	5	oner	oner	NOUN
ejpam-6199	571	6	,	,	PUNCT
ejpam-6199	571	7	t.	t.	PROPN
ejpam-6199	571	8	katican	katican	PROPN
ejpam-6199	571	9	,	,	PUNCT
ejpam-6199	571	10	and	and	CCONJ
ejpam-6199	571	11	a.	a.	PROPN
ejpam-6199	571	12	borumand	borumand	PROPN
ejpam-6199	571	13	saeid	saeid	PROPN
ejpam-6199	571	14	.	.	PUNCT
ejpam-6199	572	1	relation	relation	NOUN
ejpam-6199	572	2	between	between	ADP
ejpam-6199	572	3	sheffer	sheffer	PROPN
ejpam-6199	572	4	stroke	stroke	PROPN
ejpam-6199	572	5	and	and	CCONJ
ejpam-6199	572	6	hilbert	hilbert	PROPN
ejpam-6199	572	7	algebras	algebras	PROPN
ejpam-6199	572	8	.	.	PUNCT
ejpam-6199	572	9	categories	category	NOUN
ejpam-6199	572	10	and	and	CCONJ
ejpam-6199	572	11	general	general	ADJ
ejpam-6199	572	12	algebraic	algebraic	ADJ
ejpam-6199	572	13	structures	structure	NOUN
ejpam-6199	572	14	with	with	ADP
ejpam-6199	572	15	applications	application	NOUN
ejpam-6199	572	16	,	,	PUNCT
ejpam-6199	572	17	14(1):245–268	14(1):245–268	NUM
ejpam-6199	572	18	,	,	PUNCT
ejpam-6199	572	19	2021	2021	NUM
ejpam-6199	572	20	.	.	PUNCT
ejpam-6199	573	1	[	[	X
ejpam-6199	573	2	14	14	NUM
ejpam-6199	573	3	]	]	X
ejpam-6199	573	4	l.	l.	PROPN
ejpam-6199	573	5	a.	a.	PROPN
ejpam-6199	573	6	zadeh	zadeh	PROPN
ejpam-6199	573	7	.	.	PUNCT
ejpam-6199	573	8	fuzzy	fuzzy	ADJ
ejpam-6199	573	9	sets	set	NOUN
ejpam-6199	573	10	.	.	PUNCT
ejpam-6199	574	1	information	information	NOUN
ejpam-6199	574	2	and	and	CCONJ
ejpam-6199	574	3	control	control	NOUN
ejpam-6199	574	4	,	,	PUNCT
ejpam-6199	574	5	8(3):338–353	8(3):338–353	NUM
ejpam-6199	574	6	,	,	PUNCT
ejpam-6199	574	7	1965	1965	NUM
ejpam-6199	574	8	.	.	PUNCT
ejpam-6199	575	1	[	[	X
ejpam-6199	575	2	15	15	NUM
ejpam-6199	575	3	]	]	X
ejpam-6199	575	4	l.	l.	PROPN
ejpam-6199	575	5	a.	a.	PROPN
ejpam-6199	575	6	zadeh	zadeh	PROPN
ejpam-6199	575	7	.	.	PUNCT
ejpam-6199	576	1	the	the	DET
ejpam-6199	576	2	concept	concept	NOUN
ejpam-6199	576	3	of	of	ADP
ejpam-6199	576	4	a	a	DET
ejpam-6199	576	5	linguistic	linguistic	ADJ
ejpam-6199	576	6	variable	variable	NOUN
ejpam-6199	576	7	and	and	CCONJ
ejpam-6199	576	8	its	its	PRON
ejpam-6199	576	9	application	application	NOUN
ejpam-6199	576	10	to	to	PART
ejpam-6199	576	11	approximate	approximate	ADJ
ejpam-6199	576	12	reasoning	reasoning	NOUN
ejpam-6199	576	13	–	–	PUNCT
ejpam-6199	576	14	i.	i.	PROPN
ejpam-6199	576	15	information	information	PROPN
ejpam-6199	576	16	sciences	sciences	PROPN
ejpam-6199	576	17	,	,	PUNCT
ejpam-6199	576	18	8(3):199–249	8(3):199–249	NUM
ejpam-6199	576	19	,	,	PUNCT
ejpam-6199	576	20	1975	1975	NUM
ejpam-6199	576	21	.	.	PUNCT
ejpam-6199	577	1	[	[	X
ejpam-6199	577	2	16	16	NUM
ejpam-6199	577	3	]	]	PUNCT
ejpam-6199	577	4	w.-r	w.-r	PROPN
ejpam-6199	577	5	.	.	PUNCT
ejpam-6199	578	1	zhang	zhang	PROPN
ejpam-6199	578	2	.	.	PUNCT
ejpam-6199	578	3	bipolar	bipolar	ADJ
ejpam-6199	578	4	fuzzy	fuzzy	ADJ
ejpam-6199	578	5	sets	set	NOUN
ejpam-6199	578	6	and	and	CCONJ
ejpam-6199	578	7	relations	relation	NOUN
ejpam-6199	578	8	:	:	PUNCT
ejpam-6199	578	9	a	a	DET
ejpam-6199	578	10	computational	computational	ADJ
ejpam-6199	578	11	framework	framework	NOUN
ejpam-6199	578	12	for	for	ADP
ejpam-6199	578	13	cognitive	cognitive	ADJ
ejpam-6199	578	14	modeling	modeling	NOUN
ejpam-6199	578	15	and	and	CCONJ
ejpam-6199	578	16	multiagent	multiagent	ADJ
ejpam-6199	578	17	decision	decision	NOUN
ejpam-6199	578	18	analysis	analysis	NOUN
ejpam-6199	578	19	.	.	PUNCT
ejpam-6199	579	1	in	in	ADP
ejpam-6199	579	2	proceedings	proceeding	NOUN
ejpam-6199	579	3	of	of	ADP
ejpam-6199	579	4	the	the	DET
ejpam-6199	579	5	fuzzy	fuzzy	ADJ
ejpam-6199	579	6	information	information	NOUN
ejpam-6199	579	7	processing	processing	NOUN
ejpam-6199	579	8	society	society	NOUN
ejpam-6199	579	9	biannual	biannual	ADJ
ejpam-6199	579	10	conference	conference	NOUN
ejpam-6199	579	11	,	,	PUNCT
ejpam-6199	579	12	pages	page	NOUN
ejpam-6199	579	13	305–309	305–309	NUM
ejpam-6199	579	14	,	,	PUNCT
ejpam-6199	579	15	san	san	PROPN
ejpam-6199	579	16	antonio	antonio	PROPN
ejpam-6199	579	17	,	,	PUNCT
ejpam-6199	579	18	tx	tx	PROPN
ejpam-6199	579	19	,	,	PUNCT
ejpam-6199	579	20	usa	usa	PROPN
ejpam-6199	579	21	,	,	PUNCT
ejpam-6199	579	22	december	december	PROPN
ejpam-6199	579	23	1994	1994	NUM
ejpam-6199	579	24	.	.	PUNCT
ejpam-6199	580	1	[	[	X
ejpam-6199	580	2	17	17	NUM
ejpam-6199	580	3	]	]	X
ejpam-6199	580	4	y.	y.	PROPN
ejpam-6199	580	5	b.	b.	PROPN
ejpam-6199	580	6	jun	jun	PROPN
ejpam-6199	580	7	,	,	PUNCT
ejpam-6199	580	8	k.	k.	PROPN
ejpam-6199	580	9	j.	j.	PROPN
ejpam-6199	580	10	lee	lee	PROPN
ejpam-6199	580	11	,	,	PUNCT
ejpam-6199	580	12	and	and	CCONJ
ejpam-6199	580	13	s.	s.	PROPN
ejpam-6199	580	14	z.	z.	PROPN
ejpam-6199	580	15	song	song	PROPN
ejpam-6199	580	16	.	.	PUNCT
ejpam-6199	581	1	n	n	CCONJ
ejpam-6199	581	2	-	-	PUNCT
ejpam-6199	581	3	ideals	ideal	NOUN
ejpam-6199	581	4	of	of	ADP
ejpam-6199	581	5	bck	bck	PROPN
ejpam-6199	581	6	/	/	SYM
ejpam-6199	581	7	bci	bci	NOUN
ejpam-6199	581	8	-	-	PUNCT
ejpam-6199	581	9	algebras	algebras	PROPN
ejpam-6199	581	10	.	.	PUNCT
ejpam-6199	582	1	journal	journal	PROPN
ejpam-6199	582	2	of	of	ADP
ejpam-6199	582	3	the	the	DET
ejpam-6199	582	4	chungcheong	chungcheong	PROPN
ejpam-6199	582	5	mathematical	mathematical	ADJ
ejpam-6199	582	6	society	society	NOUN
ejpam-6199	582	7	,	,	PUNCT
ejpam-6199	582	8	22(3):417–437	22(3):417–437	NUM
ejpam-6199	582	9	,	,	PUNCT
ejpam-6199	582	10	2009	2009	NUM
ejpam-6199	582	11	.	.	PUNCT
ejpam-6199	583	1	[	[	X
ejpam-6199	583	2	18	18	NUM
ejpam-6199	583	3	]	]	PUNCT
ejpam-6199	583	4	k.	k.	PROPN
ejpam-6199	583	5	t.	t.	PROPN
ejpam-6199	583	6	atanassov	atanassov	PROPN
ejpam-6199	583	7	.	.	PUNCT
ejpam-6199	584	1	intuitionistic	intuitionistic	ADJ
ejpam-6199	584	2	fuzzy	fuzzy	ADJ
ejpam-6199	584	3	sets	set	NOUN
ejpam-6199	584	4	.	.	PUNCT
ejpam-6199	585	1	fuzzy	fuzzy	ADJ
ejpam-6199	585	2	sets	set	NOUN
ejpam-6199	585	3	and	and	CCONJ
ejpam-6199	585	4	systems	system	NOUN
ejpam-6199	585	5	,	,	PUNCT
ejpam-6199	585	6	20(1):87–96	20(1):87–96	NUM
ejpam-6199	585	7	,	,	PUNCT
ejpam-6199	585	8	1986	1986	NUM
ejpam-6199	585	9	.	.	PUNCT
ejpam-6199	586	1	[	[	X
ejpam-6199	586	2	19	19	NUM
ejpam-6199	586	3	]	]	X
ejpam-6199	586	4	f.	f.	PROPN
ejpam-6199	586	5	smarandache	smarandache	PROPN
ejpam-6199	586	6	.	.	PUNCT
ejpam-6199	587	1	neutrosophy	neutrosophy	NOUN
ejpam-6199	587	2	:	:	PUNCT
ejpam-6199	587	3	neutrosophic	neutrosophic	ADJ
ejpam-6199	587	4	probability	probability	NOUN
ejpam-6199	587	5	,	,	PUNCT
ejpam-6199	587	6	set	set	NOUN
ejpam-6199	587	7	,	,	PUNCT
ejpam-6199	587	8	and	and	CCONJ
ejpam-6199	587	9	logic	logic	NOUN
ejpam-6199	587	10	:	:	PUNCT
ejpam-6199	587	11	analytic	analytic	ADJ
ejpam-6199	587	12	synthesis	synthesis	NOUN
ejpam-6199	587	13	and	and	CCONJ
ejpam-6199	587	14	synthetic	synthetic	ADJ
ejpam-6199	587	15	analysis	analysis	NOUN
ejpam-6199	587	16	.	.	PUNCT
ejpam-6199	588	1	american	american	ADJ
ejpam-6199	588	2	research	research	PROPN
ejpam-6199	588	3	press	press	PROPN
ejpam-6199	588	4	,	,	PUNCT
ejpam-6199	588	5	rehoboth	rehoboth	PROPN
ejpam-6199	588	6	,	,	PUNCT
ejpam-6199	588	7	nm	nm	PROPN
ejpam-6199	588	8	,	,	PUNCT
ejpam-6199	588	9	usa	usa	PROPN
ejpam-6199	588	10	,	,	PUNCT
ejpam-6199	588	11	1998	1998	NUM
ejpam-6199	588	12	.	.	PUNCT
ejpam-6199	589	1	[	[	X
ejpam-6199	589	2	20	20	NUM
ejpam-6199	589	3	]	]	X
ejpam-6199	589	4	y.	y.	PROPN
ejpam-6199	589	5	b.	b.	PROPN
ejpam-6199	589	6	jun	jun	PROPN
ejpam-6199	589	7	.	.	PROPN
ejpam-6199	589	8	lukasiewicz	lukasiewicz	ADJ
ejpam-6199	589	9	fuzzy	fuzzy	ADJ
ejpam-6199	589	10	subalgebras	subalgebras	PROPN
ejpam-6199	589	11	in	in	ADP
ejpam-6199	589	12	bck	bck	PROPN
ejpam-6199	589	13	-	-	PUNCT
ejpam-6199	589	14	algebras	algebras	PROPN
ejpam-6199	589	15	and	and	CCONJ
ejpam-6199	589	16	bci	bci	NOUN
ejpam-6199	589	17	-	-	PUNCT
ejpam-6199	589	18	algebras	algebra	NOUN
ejpam-6199	589	19	.	.	PUNCT
ejpam-6199	590	1	annals	annal	NOUN
ejpam-6199	590	2	of	of	ADP
ejpam-6199	590	3	fuzzy	fuzzy	ADJ
ejpam-6199	590	4	mathematics	mathematic	NOUN
ejpam-6199	590	5	and	and	CCONJ
ejpam-6199	590	6	informatics	informatic	NOUN
ejpam-6199	590	7	,	,	PUNCT
ejpam-6199	590	8	23(2):213–223	23(2):213–223	PROPN
ejpam-6199	590	9	,	,	PUNCT
ejpam-6199	590	10	2022	2022	NUM
ejpam-6199	590	11	.	.	PUNCT
ejpam-6199	591	1	[	[	X
ejpam-6199	591	2	21	21	NUM
ejpam-6199	591	3	]	]	X
ejpam-6199	591	4	y.	y.	PROPN
ejpam-6199	591	5	b.	b.	PROPN
ejpam-6199	591	6	jun	jun	PROPN
ejpam-6199	591	7	,	,	PUNCT
ejpam-6199	591	8	k.	k.	PROPN
ejpam-6199	591	9	hur	hur	PROPN
ejpam-6199	591	10	,	,	PUNCT
ejpam-6199	591	11	j.	j.	PROPN
ejpam-6199	591	12	g.	g.	PROPN
ejpam-6199	591	13	lee	lee	PROPN
ejpam-6199	591	14	,	,	PUNCT
ejpam-6199	591	15	and	and	CCONJ
ejpam-6199	591	16	j.	j.	PROPN
ejpam-6199	591	17	kim	kim	PROPN
ejpam-6199	591	18	.	.	PUNCT
ejpam-6199	592	1	crossing	cross	VERB
ejpam-6199	592	2	cubic	cubic	ADJ
ejpam-6199	592	3	structures	structure	NOUN
ejpam-6199	592	4	as	as	ADP
ejpam-6199	592	5	an	an	DET
ejpam-6199	592	6	extension	extension	NOUN
ejpam-6199	592	7	of	of	ADP
ejpam-6199	592	8	bipolar	bipolar	ADJ
ejpam-6199	592	9	fuzzy	fuzzy	ADJ
ejpam-6199	592	10	sets	set	NOUN
ejpam-6199	592	11	.	.	PUNCT
ejpam-6199	593	1	annals	annal	NOUN
ejpam-6199	593	2	of	of	ADP
ejpam-6199	593	3	fuzzy	fuzzy	ADJ
ejpam-6199	593	4	mathematics	mathematic	NOUN
ejpam-6199	593	5	and	and	CCONJ
ejpam-6199	593	6	informatics	informatic	NOUN
ejpam-6199	593	7	,	,	PUNCT
ejpam-6199	593	8	22(1):1–15	22(1):1–15	NUM
ejpam-6199	593	9	,	,	PUNCT
ejpam-6199	593	10	2021	2021	NUM
ejpam-6199	593	11	.	.	PUNCT
ejpam-6199	594	1	[	[	X
ejpam-6199	594	2	22	22	NUM
ejpam-6199	594	3	]	]	X
ejpam-6199	594	4	y.	y.	PROPN
ejpam-6199	594	5	b.	b.	PROPN
ejpam-6199	594	6	jun	jun	PROPN
ejpam-6199	594	7	and	and	CCONJ
ejpam-6199	594	8	s.	s.	PROPN
ejpam-6199	594	9	z.	z.	PROPN
ejpam-6199	594	10	song	song	PROPN
ejpam-6199	594	11	.	.	PUNCT
ejpam-6199	595	1	crossing	cross	VERB
ejpam-6199	595	2	cubic	cubic	ADJ
ejpam-6199	595	3	ideals	ideal	NOUN
ejpam-6199	595	4	of	of	ADP
ejpam-6199	595	5	bck	bck	PROPN
ejpam-6199	595	6	/	/	SYM
ejpam-6199	595	7	bci	bci	NOUN
ejpam-6199	595	8	-	-	PUNCT
ejpam-6199	595	9	algebras	algebras	PROPN
ejpam-6199	595	10	.	.	PUNCT
ejpam-6199	596	1	journal	journal	PROPN
ejpam-6199	596	2	of	of	ADP
ejpam-6199	596	3	algebraic	algebraic	PROPN
ejpam-6199	596	4	hyperstructures	hyperstructure	NOUN
ejpam-6199	596	5	and	and	CCONJ
ejpam-6199	596	6	logical	logical	ADJ
ejpam-6199	596	7	algebras	algebra	NOUN
ejpam-6199	596	8	,	,	PUNCT
ejpam-6199	596	9	2(1):17–31	2(1):17–31	NUM
ejpam-6199	596	10	,	,	PUNCT
ejpam-6199	596	11	2021	2021	NUM
ejpam-6199	596	12	.	.	PUNCT
ejpam-6199	597	1	[	[	X
ejpam-6199	597	2	23	23	NUM
ejpam-6199	597	3	]	]	PUNCT
ejpam-6199	597	4	m.	m.	NOUN
ejpam-6199	597	5	a.	a.	NOUN
ejpam-6199	597	6	oztürk	oztürk	PROPN
ejpam-6199	597	7	,	,	PUNCT
ejpam-6199	597	8	d.	d.	PROPN
ejpam-6199	597	9	yılmaz	yılmaz	PROPN
ejpam-6199	597	10	,	,	PUNCT
ejpam-6199	597	11	and	and	CCONJ
ejpam-6199	597	12	y.	y.	PROPN
ejpam-6199	597	13	b.	b.	PROPN
ejpam-6199	597	14	jun	jun	PROPN
ejpam-6199	597	15	.	.	PROPN
ejpam-6199	598	1	semigroup	semigroup	PROPN
ejpam-6199	598	2	structures	structure	NOUN
ejpam-6199	598	3	and	and	CCONJ
ejpam-6199	598	4	commutative	commutative	ADJ
ejpam-6199	598	5	ideals	ideal	NOUN
ejpam-6199	598	6	of	of	ADP
ejpam-6199	598	7	bck	bck	NOUN
ejpam-6199	598	8	-	-	PUNCT
ejpam-6199	598	9	algebras	algebras	PROPN
ejpam-6199	598	10	based	base	VERB
ejpam-6199	598	11	on	on	ADP
ejpam-6199	598	12	crossing	cross	VERB
ejpam-6199	598	13	cubic	cubic	ADJ
ejpam-6199	598	14	set	set	NOUN
ejpam-6199	598	15	structures	structure	NOUN
ejpam-6199	598	16	.	.	PUNCT
ejpam-6199	599	1	axioms	axiom	NOUN
ejpam-6199	599	2	,	,	PUNCT
ejpam-6199	599	3	11(1):25	11(1):25	NUM
ejpam-6199	599	4	,	,	PUNCT
ejpam-6199	599	5	2022	2022	NUM
ejpam-6199	599	6	.	.	PUNCT
ejpam-6199	600	1	[	[	X
ejpam-6199	600	2	24	24	NUM
ejpam-6199	600	3	]	]	PUNCT
ejpam-6199	600	4	a.	a.	PROPN
ejpam-6199	600	5	al	al	PROPN
ejpam-6199	600	6	-	-	PROPN
ejpam-6199	600	7	masarwah	masarwah	PROPN
ejpam-6199	600	8	,	,	PUNCT
ejpam-6199	600	9	n.	n.	PROPN
ejpam-6199	600	10	kdaisat	kdaisat	PROPN
ejpam-6199	600	11	,	,	PUNCT
ejpam-6199	600	12	m.	m.	NOUN
ejpam-6199	600	13	abuqamar	abuqamar	PROPN
ejpam-6199	600	14	,	,	PUNCT
ejpam-6199	600	15	and	and	CCONJ
ejpam-6199	600	16	k.	k.	PROPN
ejpam-6199	600	17	alsager	alsager	PROPN
ejpam-6199	600	18	.	.	PUNCT
ejpam-6199	601	1	crossing	cross	VERB
ejpam-6199	601	2	cubic	cubic	ADJ
ejpam-6199	601	3	lie	lie	NOUN
ejpam-6199	601	4	algebras	algebra	NOUN
ejpam-6199	601	5	.	.	PUNCT
ejpam-6199	602	1	aims	aim	VERB
ejpam-6199	602	2	mathematics	mathematic	NOUN
ejpam-6199	602	3	,	,	PUNCT
ejpam-6199	602	4	9(8):22112–22129	9(8):22112–22129	NUM
ejpam-6199	602	5	,	,	PUNCT
ejpam-6199	602	6	2024	2024	NUM
ejpam-6199	602	7	.	.	PUNCT
ejpam-6199	603	1	[	[	X
ejpam-6199	603	2	25	25	NUM
ejpam-6199	603	3	]	]	PUNCT
ejpam-6199	603	4	t.	t.	NOUN
ejpam-6199	603	5	oner	oner	NOUN
ejpam-6199	603	6	,	,	PUNCT
ejpam-6199	603	7	t.	t.	PROPN
ejpam-6199	603	8	katican	katican	PROPN
ejpam-6199	603	9	,	,	PUNCT
ejpam-6199	603	10	and	and	CCONJ
ejpam-6199	603	11	a.	a.	PROPN
ejpam-6199	603	12	b.	b.	PROPN
ejpam-6199	603	13	saeid	saeid	PROPN
ejpam-6199	603	14	.	.	PUNCT
ejpam-6199	604	1	fuzzy	fuzzy	ADJ
ejpam-6199	604	2	filters	filter	NOUN
ejpam-6199	604	3	of	of	ADP
ejpam-6199	604	4	sheffer	sheffer	PROPN
ejpam-6199	604	5	stroke	stroke	PROPN
ejpam-6199	604	6	hilbert	hilbert	PROPN
ejpam-6199	604	7	algebras	algebras	PROPN
ejpam-6199	604	8	.	.	PUNCT
ejpam-6199	605	1	journal	journal	PROPN
ejpam-6199	605	2	of	of	ADP
ejpam-6199	605	3	intelligent	intelligent	ADJ
ejpam-6199	605	4	fuzzy	fuzzy	ADJ
ejpam-6199	605	5	systems	system	NOUN
ejpam-6199	605	6	,	,	PUNCT
ejpam-6199	605	7	40(1):759–772	40(1):759–772	NOUN
ejpam-6199	605	8	,	,	PUNCT
ejpam-6199	605	9	2021	2021	NUM
ejpam-6199	605	10	.	.	PUNCT
ejpam-6199	606	1	[	[	X
ejpam-6199	606	2	26	26	NUM
ejpam-6199	606	3	]	]	PUNCT
ejpam-6199	606	4	m.	m.	NOUN
ejpam-6199	606	5	vasuki	vasuki	PROPN
ejpam-6199	606	6	,	,	PUNCT
ejpam-6199	606	7	p.	p.	PROPN
ejpam-6199	606	8	senthil	senthil	PROPN
ejpam-6199	606	9	kumar	kumar	PROPN
ejpam-6199	606	10	,	,	PUNCT
ejpam-6199	606	11	and	and	CCONJ
ejpam-6199	606	12	n.	n.	PROPN
ejpam-6199	606	13	rajesh	rajesh	PROPN
ejpam-6199	606	14	.	.	PUNCT
ejpam-6199	607	1	on	on	ADP
ejpam-6199	607	2	anti	anti	ADJ
ejpam-6199	607	3	-	-	ADJ
ejpam-6199	607	4	q	q	ADJ
ejpam-6199	607	5	-	-	PUNCT
ejpam-6199	607	6	fuzzy	fuzzy	ADJ
ejpam-6199	607	7	deductive	deductive	ADJ
ejpam-6199	607	8	systems	system	NOUN
ejpam-6199	607	9	of	of	ADP
ejpam-6199	607	10	hilbert	hilbert	PROPN
ejpam-6199	607	11	algebras	algebras	PROPN
ejpam-6199	607	12	.	.	PUNCT
ejpam-6199	608	1	international	international	ADJ
ejpam-6199	608	2	journal	journal	NOUN
ejpam-6199	608	3	of	of	ADP
ejpam-6199	608	4	analysis	analysis	NOUN
ejpam-6199	608	5	and	and	CCONJ
ejpam-6199	608	6	applications	application	NOUN
ejpam-6199	608	7	,	,	PUNCT
ejpam-6199	608	8	21:42	21:42	NUM
ejpam-6199	608	9	,	,	PUNCT
ejpam-6199	608	10	2023	2023	NUM
ejpam-6199	608	11	.	.	PUNCT
ejpam-6199	609	1	[	[	X
ejpam-6199	609	2	27	27	NUM
ejpam-6199	609	3	]	]	PUNCT
ejpam-6199	609	4	a.	a.	PROPN
ejpam-6199	609	5	b.	b.	PROPN
ejpam-6199	609	6	saeid	saeid	PROPN
ejpam-6199	609	7	,	,	PUNCT
ejpam-6199	609	8	t.	t.	PROPN
ejpam-6199	609	9	oner	oner	NOUN
ejpam-6199	609	10	,	,	PUNCT
ejpam-6199	609	11	and	and	CCONJ
ejpam-6199	609	12	y.	y.	PROPN
ejpam-6199	609	13	b.	b.	PROPN
ejpam-6199	609	14	jun	jun	PROPN
ejpam-6199	609	15	.	.	PROPN
ejpam-6199	610	1	intuitionistic	intuitionistic	ADJ
ejpam-6199	610	2	fuzzy	fuzzy	ADJ
ejpam-6199	610	3	filters	filter	NOUN
ejpam-6199	610	4	in	in	ADP
ejpam-6199	610	5	sheffer	sheffer	PROPN
ejpam-6199	610	6	stroke	stroke	PROPN
ejpam-6199	610	7	hilbert	hilbert	PROPN
ejpam-6199	610	8	algebras	algebras	PROPN
ejpam-6199	610	9	.	.	PUNCT
ejpam-6199	611	1	journal	journal	PROPN
ejpam-6199	611	2	of	of	ADP
ejpam-6199	611	3	mathematical	mathematical	ADJ
ejpam-6199	611	4	extension	extension	NOUN
ejpam-6199	611	5	,	,	PUNCT
ejpam-6199	611	6	18(10):1–20	18(10):1–20	NUM
ejpam-6199	611	7	,	,	PUNCT
ejpam-6199	611	8	2024	2024	NUM
ejpam-6199	611	9	.	.	PUNCT
ejpam-6199	612	1	[	[	X
ejpam-6199	612	2	28	28	NUM
ejpam-6199	612	3	]	]	X
ejpam-6199	612	4	t.	t.	NOUN
ejpam-6199	612	5	oner	oner	NOUN
ejpam-6199	612	6	,	,	PUNCT
ejpam-6199	612	7	t.	t.	PROPN
ejpam-6199	612	8	katican	katican	PROPN
ejpam-6199	612	9	,	,	PUNCT
ejpam-6199	612	10	and	and	CCONJ
ejpam-6199	612	11	a.	a.	PROPN
ejpam-6199	612	12	b.	b.	PROPN
ejpam-6199	612	13	saeid	saeid	PROPN
ejpam-6199	612	14	.	.	PUNCT
ejpam-6199	613	1	neutrosophic	neutrosophic	PROPN
ejpam-6199	613	2	n	n	CCONJ
ejpam-6199	613	3	-	-	PUNCT
ejpam-6199	613	4	structures	structure	NOUN
ejpam-6199	613	5	on	on	ADP
ejpam-6199	613	6	sheffer	sheffer	PROPN
ejpam-6199	613	7	stroke	stroke	PROPN
ejpam-6199	613	8	hilbert	hilbert	PROPN
ejpam-6199	613	9	algebras	algebras	PROPN
ejpam-6199	613	10	.	.	PUNCT
ejpam-6199	613	11	neutrosophic	neutrosophic	ADJ
ejpam-6199	613	12	sets	set	NOUN
ejpam-6199	613	13	and	and	CCONJ
ejpam-6199	613	14	systems	system	NOUN
ejpam-6199	613	15	,	,	PUNCT
ejpam-6199	613	16	42:221–238	42:221–238	NUM
ejpam-6199	613	17	,	,	PUNCT
ejpam-6199	613	18	2021	2021	NUM
ejpam-6199	613	19	.	.	PUNCT