id	sid	tid	token	lemma	pos
ejpam-4872	1	1	european	european	PROPN
ejpam-4872	1	2	journal	journal	PROPN
ejpam-4872	1	3	of	of	ADP
ejpam-4872	1	4	pure	pure	ADJ
ejpam-4872	1	5	and	and	CCONJ
ejpam-4872	1	6	applied	apply	VERB
ejpam-4872	1	7	mathematics	mathematic	NOUN
ejpam-4872	1	8	vol	vol	NOUN
ejpam-4872	1	9	.	.	PUNCT
ejpam-4872	2	1	16	16	NUM
ejpam-4872	2	2	,	,	PUNCT
ejpam-4872	2	3	no	no	INTJ
ejpam-4872	2	4	.	.	NOUN
ejpam-4872	2	5	3	3	NUM
ejpam-4872	2	6	,	,	PUNCT
ejpam-4872	2	7	2023	2023	NUM
ejpam-4872	2	8	,	,	PUNCT
ejpam-4872	2	9	1862	1862	NUM
ejpam-4872	2	10	-	-	SYM
ejpam-4872	2	11	1877	1877	NUM
ejpam-4872	2	12	issn	issn	PROPN
ejpam-4872	2	13	1307	1307	NUM
ejpam-4872	2	14	-	-	SYM
ejpam-4872	2	15	5543	5543	NUM
ejpam-4872	2	16	–	–	PUNCT
ejpam-4872	2	17	ejpam.com	ejpam.com	X
ejpam-4872	2	18	published	publish	VERB
ejpam-4872	2	19	by	by	ADP
ejpam-4872	2	20	new	new	PROPN
ejpam-4872	2	21	york	york	PROPN
ejpam-4872	2	22	business	business	PROPN
ejpam-4872	2	23	global	global	ADJ
ejpam-4872	2	24	dokdo	dokdo	NOUN
ejpam-4872	2	25	filters	filter	NOUN
ejpam-4872	2	26	and	and	CCONJ
ejpam-4872	2	27	deductive	deductive	ADJ
ejpam-4872	2	28	systems	system	NOUN
ejpam-4872	2	29	of	of	ADP
ejpam-4872	2	30	sheffer	sheffer	PROPN
ejpam-4872	2	31	stroke	stroke	PROPN
ejpam-4872	2	32	hilbert	hilbert	PROPN
ejpam-4872	2	33	algebras	algebras	PROPN
ejpam-4872	2	34	sun	sun	PROPN
ejpam-4872	2	35	shin	shin	PROPN
ejpam-4872	2	36	ahn1,∗	ahn1,∗	PROPN
ejpam-4872	2	37	,	,	PUNCT
ejpam-4872	2	38	hee	hee	PROPN
ejpam-4872	2	39	sik	sik	PROPN
ejpam-4872	2	40	kim2	kim2	PROPN
ejpam-4872	2	41	,	,	PUNCT
ejpam-4872	2	42	seok	seok	PROPN
ejpam-4872	2	43	-	-	PUNCT
ejpam-4872	2	44	zun	zun	PROPN
ejpam-4872	2	45	song3	song3	PROPN
ejpam-4872	2	46	,	,	PUNCT
ejpam-4872	2	47	young	young	ADJ
ejpam-4872	2	48	bae	bae	NOUN
ejpam-4872	2	49	jun4	jun4	PROPN
ejpam-4872	2	50	1	1	NUM
ejpam-4872	2	51	department	department	NOUN
ejpam-4872	2	52	of	of	ADP
ejpam-4872	2	53	mathematics	mathematics	PROPN
ejpam-4872	2	54	education	education	NOUN
ejpam-4872	2	55	,	,	PUNCT
ejpam-4872	2	56	dongguk	dongguk	PROPN
ejpam-4872	2	57	university	university	PROPN
ejpam-4872	2	58	,	,	PUNCT
ejpam-4872	2	59	seoul	seoul	PROPN
ejpam-4872	2	60	04620	04620	NUM
ejpam-4872	2	61	,	,	PUNCT
ejpam-4872	2	62	korea	korea	PROPN
ejpam-4872	2	63	2	2	NUM
ejpam-4872	2	64	research	research	NOUN
ejpam-4872	2	65	institute	institute	NOUN
ejpam-4872	2	66	for	for	ADP
ejpam-4872	2	67	natural	natural	ADJ
ejpam-4872	2	68	science	science	NOUN
ejpam-4872	2	69	,	,	PUNCT
ejpam-4872	2	70	department	department	NOUN
ejpam-4872	2	71	of	of	ADP
ejpam-4872	2	72	mathematics	mathematics	PROPN
ejpam-4872	2	73	,	,	PUNCT
ejpam-4872	2	74	hanyang	hanyang	PROPN
ejpam-4872	2	75	university	university	PROPN
ejpam-4872	2	76	,	,	PUNCT
ejpam-4872	2	77	seoul	seoul	PROPN
ejpam-4872	2	78	04763	04763	NUM
ejpam-4872	2	79	,	,	PUNCT
ejpam-4872	2	80	korea	korea	PROPN
ejpam-4872	2	81	3	3	NUM
ejpam-4872	2	82	department	department	PROPN
ejpam-4872	2	83	of	of	ADP
ejpam-4872	2	84	mathematics	mathematics	PROPN
ejpam-4872	2	85	,	,	PUNCT
ejpam-4872	2	86	jeju	jeju	PROPN
ejpam-4872	2	87	national	national	PROPN
ejpam-4872	2	88	university	university	PROPN
ejpam-4872	2	89	,	,	PUNCT
ejpam-4872	2	90	jeju	jeju	PROPN
ejpam-4872	2	91	63243	63243	NUM
ejpam-4872	2	92	,	,	PUNCT
ejpam-4872	2	93	korea	korea	PROPN
ejpam-4872	2	94	4	4	NUM
ejpam-4872	2	95	department	department	PROPN
ejpam-4872	2	96	of	of	ADP
ejpam-4872	2	97	mathematics	mathematics	PROPN
ejpam-4872	2	98	education	education	NOUN
ejpam-4872	2	99	,	,	PUNCT
ejpam-4872	2	100	gyeongsang	gyeongsang	PROPN
ejpam-4872	2	101	national	national	PROPN
ejpam-4872	2	102	university	university	PROPN
ejpam-4872	2	103	,	,	PUNCT
ejpam-4872	2	104	jinju	jinju	NOUN
ejpam-4872	2	105	52828	52828	NUM
ejpam-4872	2	106	,	,	PUNCT
ejpam-4872	2	107	korea	korea	PROPN
ejpam-4872	2	108	abstract	abstract	NOUN
ejpam-4872	2	109	.	.	PUNCT
ejpam-4872	3	1	to	to	PART
ejpam-4872	3	2	investigate	investigate	VERB
ejpam-4872	3	3	the	the	DET
ejpam-4872	3	4	filter	filter	NOUN
ejpam-4872	3	5	and	and	CCONJ
ejpam-4872	3	6	deductive	deductive	ADJ
ejpam-4872	3	7	system	system	NOUN
ejpam-4872	3	8	of	of	ADP
ejpam-4872	3	9	the	the	DET
ejpam-4872	3	10	schaefer	schaefer	PROPN
ejpam-4872	3	11	stroke	stroke	PROPN
ejpam-4872	3	12	hilbert	hilbert	PROPN
ejpam-4872	3	13	algebra	algebra	PROPN
ejpam-4872	3	14	using	use	VERB
ejpam-4872	3	15	the	the	DET
ejpam-4872	3	16	dokdo	dokdo	NOUN
ejpam-4872	3	17	structure	structure	NOUN
ejpam-4872	3	18	,	,	PUNCT
ejpam-4872	3	19	the	the	DET
ejpam-4872	3	20	concept	concept	NOUN
ejpam-4872	3	21	of	of	ADP
ejpam-4872	3	22	dokdo	dokdo	ADJ
ejpam-4872	3	23	filter	filter	NOUN
ejpam-4872	3	24	and	and	CCONJ
ejpam-4872	3	25	dokdo	dokdo	ADJ
ejpam-4872	3	26	deductive	deductive	ADJ
ejpam-4872	3	27	system	system	NOUN
ejpam-4872	3	28	is	be	AUX
ejpam-4872	3	29	defined	define	VERB
ejpam-4872	3	30	,	,	PUNCT
ejpam-4872	3	31	examples	example	NOUN
ejpam-4872	3	32	are	be	AUX
ejpam-4872	3	33	given	give	VERB
ejpam-4872	3	34	,	,	PUNCT
ejpam-4872	3	35	and	and	CCONJ
ejpam-4872	3	36	various	various	ADJ
ejpam-4872	3	37	properties	property	NOUN
ejpam-4872	3	38	are	be	AUX
ejpam-4872	3	39	investigated	investigate	VERB
ejpam-4872	3	40	.	.	PUNCT
ejpam-4872	4	1	the	the	DET
ejpam-4872	4	2	dokdo	dokdo	NOUN
ejpam-4872	4	3	filter	filter	NOUN
ejpam-4872	4	4	is	be	AUX
ejpam-4872	4	5	formed	form	VERB
ejpam-4872	4	6	by	by	ADP
ejpam-4872	4	7	attaching	attach	VERB
ejpam-4872	4	8	appropriate	appropriate	ADJ
ejpam-4872	4	9	conditions	condition	NOUN
ejpam-4872	4	10	to	to	ADP
ejpam-4872	4	11	the	the	DET
ejpam-4872	4	12	given	give	VERB
ejpam-4872	4	13	dokdo	dokdo	NOUN
ejpam-4872	4	14	structure	structure	NOUN
ejpam-4872	4	15	.	.	PUNCT
ejpam-4872	5	1	characterization	characterization	NOUN
ejpam-4872	5	2	of	of	ADP
ejpam-4872	5	3	dokdo	dokdo	ADJ
ejpam-4872	5	4	filter	filter	NOUN
ejpam-4872	5	5	is	be	AUX
ejpam-4872	5	6	studied	study	VERB
ejpam-4872	5	7	.	.	PUNCT
ejpam-4872	6	1	dokdo	dokdo	NOUN
ejpam-4872	6	2	filters	filter	NOUN
ejpam-4872	6	3	related	relate	VERB
ejpam-4872	6	4	to	to	ADP
ejpam-4872	6	5	filters	filter	NOUN
ejpam-4872	6	6	are	be	AUX
ejpam-4872	6	7	constructed	construct	VERB
ejpam-4872	6	8	.	.	PUNCT
ejpam-4872	7	1	dokdo	dokdo	NOUN
ejpam-4872	7	2	filter	filter	NOUN
ejpam-4872	7	3	and	and	CCONJ
ejpam-4872	7	4	dokdo	dokdo	ADJ
ejpam-4872	7	5	deductive	deductive	ADJ
ejpam-4872	7	6	system	system	NOUN
ejpam-4872	7	7	turn	turn	VERB
ejpam-4872	7	8	out	out	ADP
ejpam-4872	7	9	to	to	PART
ejpam-4872	7	10	be	be	AUX
ejpam-4872	7	11	the	the	DET
ejpam-4872	7	12	same	same	ADJ
ejpam-4872	7	13	concept	concept	NOUN
ejpam-4872	7	14	.	.	PUNCT
ejpam-4872	8	1	2020	2020	NUM
ejpam-4872	8	2	mathematics	mathematic	NOUN
ejpam-4872	8	3	subject	subject	NOUN
ejpam-4872	8	4	classifications	classification	NOUN
ejpam-4872	8	5	:	:	PUNCT
ejpam-4872	8	6	03b05	03b05	NUM
ejpam-4872	8	7	,	,	PUNCT
ejpam-4872	8	8	03g25	03g25	NOUN
ejpam-4872	8	9	,	,	PUNCT
ejpam-4872	8	10	06f35	06f35	NUM
ejpam-4872	8	11	,	,	PUNCT
ejpam-4872	8	12	08a72	08a72	NOUN
ejpam-4872	8	13	key	key	ADJ
ejpam-4872	8	14	words	word	NOUN
ejpam-4872	8	15	and	and	CCONJ
ejpam-4872	8	16	phrases	phrase	NOUN
ejpam-4872	8	17	:	:	PUNCT
ejpam-4872	8	18	sheffer	sheffer	NOUN
ejpam-4872	8	19	stroke	stroke	PROPN
ejpam-4872	8	20	hilbert	hilbert	PROPN
ejpam-4872	8	21	algebra	algebra	PROPN
ejpam-4872	8	22	,	,	PUNCT
ejpam-4872	8	23	filter	filter	NOUN
ejpam-4872	8	24	,	,	PUNCT
ejpam-4872	8	25	deductive	deductive	ADJ
ejpam-4872	8	26	system	system	NOUN
ejpam-4872	8	27	,	,	PUNCT
ejpam-4872	8	28	dokdo	dokdo	NOUN
ejpam-4872	8	29	filter	filter	NOUN
ejpam-4872	8	30	,	,	PUNCT
ejpam-4872	8	31	dokdo	dokdo	ADJ
ejpam-4872	8	32	deductive	deductive	ADJ
ejpam-4872	8	33	system	system	NOUN
ejpam-4872	8	34	.	.	PUNCT
ejpam-4872	9	1	1	1	X
ejpam-4872	9	2	.	.	X
ejpam-4872	9	3	introduction	introduction	NOUN
ejpam-4872	9	4	the	the	DET
ejpam-4872	9	5	shaper	shap	ADJ
ejpam-4872	9	6	stroke	stroke	NOUN
ejpam-4872	9	7	represented	represent	VERB
ejpam-4872	9	8	by	by	ADP
ejpam-4872	9	9	the	the	DET
ejpam-4872	9	10	symbol	symbol	NOUN
ejpam-4872	9	11	”	"	PUNCT
ejpam-4872	9	12	|	|	ADV
ejpam-4872	9	13	”	"	PUNCT
ejpam-4872	9	14	is	be	AUX
ejpam-4872	9	15	a	a	DET
ejpam-4872	9	16	logical	logical	ADJ
ejpam-4872	9	17	operation	operation	NOUN
ejpam-4872	9	18	for	for	ADP
ejpam-4872	9	19	two	two	NUM
ejpam-4872	9	20	inputs	input	NOUN
ejpam-4872	9	21	that	that	PRON
ejpam-4872	9	22	produces	produce	VERB
ejpam-4872	9	23	an	an	DET
ejpam-4872	9	24	invalid	invalid	ADJ
ejpam-4872	9	25	result	result	NOUN
ejpam-4872	9	26	only	only	ADV
ejpam-4872	9	27	when	when	SCONJ
ejpam-4872	9	28	both	both	DET
ejpam-4872	9	29	inputs	input	NOUN
ejpam-4872	9	30	are	be	AUX
ejpam-4872	9	31	true	true	ADJ
ejpam-4872	9	32	,	,	PUNCT
ejpam-4872	9	33	as	as	SCONJ
ejpam-4872	9	34	shown	show	VERB
ejpam-4872	9	35	in	in	ADP
ejpam-4872	9	36	table	table	NOUN
ejpam-4872	9	37	1	1	NUM
ejpam-4872	9	38	.	.	PUNCT
ejpam-4872	10	1	the	the	DET
ejpam-4872	10	2	sheffer	sheffer	NOUN
ejpam-4872	10	3	stroke	stroke	NOUN
ejpam-4872	10	4	has	have	AUX
ejpam-4872	10	5	been	be	AUX
ejpam-4872	10	6	applied	apply	VERB
ejpam-4872	10	7	to	to	ADP
ejpam-4872	10	8	several	several	ADJ
ejpam-4872	10	9	algebraic	algebraic	ADJ
ejpam-4872	10	10	structures	structure	NOUN
ejpam-4872	10	11	,	,	PUNCT
ejpam-4872	10	12	for	for	ADP
ejpam-4872	10	13	example	example	NOUN
ejpam-4872	10	14	,	,	PUNCT
ejpam-4872	10	15	boolean	boolean	ADJ
ejpam-4872	10	16	algebra	algebra	NOUN
ejpam-4872	10	17	,	,	PUNCT
ejpam-4872	10	18	mv	mv	PROPN
ejpam-4872	10	19	-	-	NOUN
ejpam-4872	10	20	algebra	algebra	NOUN
ejpam-4872	10	21	,	,	PUNCT
ejpam-4872	10	22	bl	bl	NOUN
ejpam-4872	10	23	-	-	PUNCT
ejpam-4872	10	24	algebra	algebra	NOUN
ejpam-4872	10	25	,	,	PUNCT
ejpam-4872	10	26	bck	bck	NOUN
ejpam-4872	10	27	-	-	PUNCT
ejpam-4872	10	28	algebra	algebra	NOUN
ejpam-4872	10	29	,	,	PUNCT
ejpam-4872	10	30	and	and	CCONJ
ejpam-4872	10	31	ortholattices	ortholattice	NOUN
ejpam-4872	10	32	,	,	PUNCT
ejpam-4872	10	33	etc	etc	X
ejpam-4872	10	34	.	.	X
ejpam-4872	10	35	,	,	PUNCT
ejpam-4872	10	36	and	and	CCONJ
ejpam-4872	10	37	it	it	PRON
ejpam-4872	10	38	is	be	AUX
ejpam-4872	10	39	also	also	ADV
ejpam-4872	10	40	being	be	AUX
ejpam-4872	10	41	dealt	deal	VERB
ejpam-4872	10	42	with	with	ADP
ejpam-4872	10	43	in	in	ADP
ejpam-4872	10	44	the	the	DET
ejpam-4872	10	45	fuzzy	fuzzy	ADJ
ejpam-4872	10	46	environment	environment	NOUN
ejpam-4872	10	47	(	(	PUNCT
ejpam-4872	10	48	see	see	VERB
ejpam-4872	10	49	[	[	X
ejpam-4872	10	50	1	1	NUM
ejpam-4872	10	51	,	,	PUNCT
ejpam-4872	10	52	4	4	NUM
ejpam-4872	10	53	,	,	PUNCT
ejpam-4872	10	54	5	5	NUM
ejpam-4872	10	55	,	,	PUNCT
ejpam-4872	10	56	10–14	10–14	NUM
ejpam-4872	10	57	]	]	PUNCT
ejpam-4872	10	58	)	)	PUNCT
ejpam-4872	10	59	.	.	PUNCT
ejpam-4872	11	1	in	in	ADP
ejpam-4872	11	2	2021	2021	NUM
ejpam-4872	11	3	,	,	PUNCT
ejpam-4872	11	4	oner	oner	NOUN
ejpam-4872	11	5	et	et	PROPN
ejpam-4872	11	6	al	al	PROPN
ejpam-4872	11	7	.	.	PUNCT
ejpam-4872	12	1	[	[	X
ejpam-4872	12	2	12	12	NUM
ejpam-4872	12	3	]	]	PUNCT
ejpam-4872	12	4	applied	apply	VERB
ejpam-4872	12	5	the	the	DET
ejpam-4872	12	6	sheffer	sheffer	NOUN
ejpam-4872	12	7	stroke	stroke	NOUN
ejpam-4872	12	8	to	to	ADP
ejpam-4872	12	9	hilbert	hilbert	PROPN
ejpam-4872	12	10	algebras	algebras	PROPN
ejpam-4872	12	11	.	.	PUNCT
ejpam-4872	13	1	they	they	PRON
ejpam-4872	13	2	introduced	introduce	VERB
ejpam-4872	13	3	sheffer	sheffer	NOUN
ejpam-4872	13	4	stroke	stroke	PROPN
ejpam-4872	13	5	hilbert	hilbert	PROPN
ejpam-4872	13	6	algebra	algebra	PROPN
ejpam-4872	13	7	and	and	CCONJ
ejpam-4872	13	8	investigated	investigate	VERB
ejpam-4872	13	9	several	several	ADJ
ejpam-4872	13	10	properties	property	NOUN
ejpam-4872	13	11	.	.	PUNCT
ejpam-4872	14	1	in	in	ADP
ejpam-4872	14	2	[	[	X
ejpam-4872	14	3	11	11	NUM
ejpam-4872	14	4	]	]	PUNCT
ejpam-4872	14	5	,	,	PUNCT
ejpam-4872	14	6	oner	oner	AUX
ejpam-4872	14	7	et	et	PROPN
ejpam-4872	14	8	al	al	PROPN
ejpam-4872	14	9	.	.	PROPN
ejpam-4872	14	10	introduced	introduce	VERB
ejpam-4872	14	11	the	the	DET
ejpam-4872	14	12	notion	notion	NOUN
ejpam-4872	14	13	of	of	ADP
ejpam-4872	14	14	deductive	deductive	ADJ
ejpam-4872	14	15	system	system	NOUN
ejpam-4872	14	16	and	and	CCONJ
ejpam-4872	14	17	filter	filter	NOUN
ejpam-4872	14	18	of	of	ADP
ejpam-4872	14	19	sheffer	sheffer	PROPN
ejpam-4872	14	20	stroke	stroke	PROPN
ejpam-4872	14	21	hilbert	hilbert	PROPN
ejpam-4872	14	22	algebras	algebras	PROPN
ejpam-4872	14	23	,	,	PUNCT
ejpam-4872	14	24	and	and	CCONJ
ejpam-4872	14	25	dealt	deal	VERB
ejpam-4872	14	26	with	with	ADP
ejpam-4872	14	27	their	their	PRON
ejpam-4872	14	28	fuzzification	fuzzification	NOUN
ejpam-4872	14	29	.	.	PUNCT
ejpam-4872	15	1	the	the	DET
ejpam-4872	15	2	dokdo	dokdo	NOUN
ejpam-4872	15	3	structure	structure	NOUN
ejpam-4872	15	4	,	,	PUNCT
ejpam-4872	15	5	classified	classify	VERB
ejpam-4872	15	6	as	as	ADP
ejpam-4872	15	7	a	a	DET
ejpam-4872	15	8	hybrid	hybrid	ADJ
ejpam-4872	15	9	structure	structure	NOUN
ejpam-4872	15	10	,	,	PUNCT
ejpam-4872	15	11	was	be	AUX
ejpam-4872	15	12	introduced	introduce	VERB
ejpam-4872	15	13	by	by	ADP
ejpam-4872	15	14	jun	jun	PROPN
ejpam-4872	16	1	[	[	X
ejpam-4872	16	2	3	3	NUM
ejpam-4872	16	3	]	]	PUNCT
ejpam-4872	16	4	,	,	PUNCT
ejpam-4872	16	5	and	and	CCONJ
ejpam-4872	16	6	it	it	PRON
ejpam-4872	16	7	consists	consist	VERB
ejpam-4872	16	8	∗corresponding	∗corresponde	VERB
ejpam-4872	16	9	author	author	NOUN
ejpam-4872	16	10	.	.	PUNCT
ejpam-4872	17	1	doi	doi	NOUN
ejpam-4872	17	2	:	:	PUNCT
ejpam-4872	17	3	https://doi.org/10.29020/nybg.ejpam.v16i3.4872	https://doi.org/10.29020/nybg.ejpam.v16i3.4872	NOUN
ejpam-4872	17	4	email	email	NOUN
ejpam-4872	17	5	addresses	address	VERB
ejpam-4872	17	6	:	:	PUNCT
ejpam-4872	18	1	sunshine@dongguk.edu	sunshine@dongguk.edu	PROPN
ejpam-4872	18	2	(	(	PUNCT
ejpam-4872	18	3	s.	s.	PROPN
ejpam-4872	18	4	s.	s.	PROPN
ejpam-4872	18	5	ahn	ahn	PROPN
ejpam-4872	18	6	)	)	PUNCT
ejpam-4872	18	7	,	,	PUNCT
ejpam-4872	18	8	heekim@hanyang.ac.kr	heekim@hanyang.ac.kr	X
ejpam-4872	18	9	(	(	PUNCT
ejpam-4872	18	10	h.	h.	PROPN
ejpam-4872	18	11	s.	s.	PROPN
ejpam-4872	18	12	kim	kim	PROPN
ejpam-4872	18	13	)	)	PUNCT
ejpam-4872	18	14	,	,	PUNCT
ejpam-4872	18	15	szsong@jejunu.ac.kr	szsong@jejunu.ac.kr	NOUN
ejpam-4872	18	16	(	(	PUNCT
ejpam-4872	18	17	s.	s.	PROPN
ejpam-4872	18	18	z.	z.	PROPN
ejpam-4872	18	19	song	song	PROPN
ejpam-4872	18	20	)	)	PUNCT
ejpam-4872	18	21	,	,	PUNCT
ejpam-4872	18	22	skywine@gmail.com	skywine@gmail.com	X
ejpam-4872	18	23	(	(	PUNCT
ejpam-4872	18	24	y.	y.	PROPN
ejpam-4872	18	25	b.	b.	PROPN
ejpam-4872	18	26	jun	jun	PROPN
ejpam-4872	18	27	)	)	PUNCT
ejpam-4872	18	28	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4872	18	29	1862	1862	NUM
ejpam-4872	19	1	©	©	PROPN
ejpam-4872	19	2	2023	2023	NUM
ejpam-4872	19	3	ejpam	ejpam	NOUN
ejpam-4872	19	4	all	all	DET
ejpam-4872	19	5	rights	right	NOUN
ejpam-4872	19	6	reserved	reserve	VERB
ejpam-4872	19	7	.	.	PUNCT
ejpam-4872	20	1	s.	s.	PROPN
ejpam-4872	20	2	s.	s.	PROPN
ejpam-4872	20	3	ahn	ahn	PROPN
ejpam-4872	20	4	et	et	PROPN
ejpam-4872	20	5	al	al	PROPN
ejpam-4872	20	6	.	.	PUNCT
ejpam-4872	20	7	/	/	SYM
ejpam-4872	20	8	eur	eur	PROPN
ejpam-4872	20	9	.	.	PUNCT
ejpam-4872	21	1	j.	j.	PROPN
ejpam-4872	21	2	pure	pure	PROPN
ejpam-4872	21	3	appl	appl	PROPN
ejpam-4872	21	4	.	.	PROPN
ejpam-4872	21	5	math	math	PROPN
ejpam-4872	21	6	,	,	PUNCT
ejpam-4872	21	7	16	16	NUM
ejpam-4872	21	8	(	(	PUNCT
ejpam-4872	21	9	3	3	NUM
ejpam-4872	21	10	)	)	PUNCT
ejpam-4872	21	11	(	(	PUNCT
ejpam-4872	21	12	2023	2023	NUM
ejpam-4872	21	13	)	)	PUNCT
ejpam-4872	21	14	,	,	PUNCT
ejpam-4872	21	15	1862	1862	NUM
ejpam-4872	21	16	-	-	SYM
ejpam-4872	21	17	1877	1877	NUM
ejpam-4872	21	18	1863	1863	NUM
ejpam-4872	21	19	table	table	NOUN
ejpam-4872	21	20	1	1	NUM
ejpam-4872	21	21	:	:	PUNCT
ejpam-4872	21	22	the	the	DET
ejpam-4872	21	23	truth	truth	NOUN
ejpam-4872	21	24	table	table	NOUN
ejpam-4872	21	25	for	for	ADP
ejpam-4872	21	26	the	the	DET
ejpam-4872	21	27	sheffer	sheffer	NOUN
ejpam-4872	21	28	stroke	stroke	NOUN
ejpam-4872	21	29	“	"	PUNCT
ejpam-4872	21	30	|	|	NOUN
ejpam-4872	21	31	”	"	PUNCT
ejpam-4872	21	32	p	p	NOUN
ejpam-4872	21	33	q	q	X
ejpam-4872	21	34	p	p	NOUN
ejpam-4872	21	35	|q	|q	NOUN
ejpam-4872	22	1	f	f	X
ejpam-4872	22	2	f	f	PROPN
ejpam-4872	23	1	t	t	PROPN
ejpam-4872	23	2	f	f	PROPN
ejpam-4872	23	3	t	t	PROPN
ejpam-4872	23	4	t	t	PROPN
ejpam-4872	23	5	t	t	PROPN
ejpam-4872	23	6	f	f	PROPN
ejpam-4872	23	7	t	t	PROPN
ejpam-4872	23	8	t	t	PROPN
ejpam-4872	23	9	t	t	PROPN
ejpam-4872	23	10	f	f	PROPN
ejpam-4872	23	11	of	of	ADP
ejpam-4872	23	12	a	a	DET
ejpam-4872	23	13	combination	combination	NOUN
ejpam-4872	23	14	of	of	ADP
ejpam-4872	23	15	soft	soft	ADJ
ejpam-4872	23	16	set	set	NOUN
ejpam-4872	23	17	,	,	PUNCT
ejpam-4872	23	18	bipolar	bipolar	ADJ
ejpam-4872	23	19	fuzzy	fuzzy	ADJ
ejpam-4872	23	20	set	set	NOUN
ejpam-4872	23	21	,	,	PUNCT
ejpam-4872	23	22	and	and	CCONJ
ejpam-4872	23	23	interval	interval	NOUN
ejpam-4872	23	24	-	-	PUNCT
ejpam-4872	23	25	value	value	NOUN
ejpam-4872	23	26	fuzzy	fuzzy	ADJ
ejpam-4872	23	27	set	set	NOUN
ejpam-4872	23	28	.	.	PUNCT
ejpam-4872	24	1	here	here	ADV
ejpam-4872	24	2	,	,	PUNCT
ejpam-4872	24	3	“	"	PUNCT
ejpam-4872	24	4	dokdo	dokdo	PROPN
ejpam-4872	24	5	”	"	PUNCT
ejpam-4872	24	6	is	be	AUX
ejpam-4872	24	7	the	the	DET
ejpam-4872	24	8	name	name	NOUN
ejpam-4872	24	9	of	of	ADP
ejpam-4872	24	10	korea	korea	PROPN
ejpam-4872	24	11	’s	’s	PART
ejpam-4872	24	12	most	most	ADV
ejpam-4872	24	13	beautiful	beautiful	ADJ
ejpam-4872	24	14	island	island	NOUN
ejpam-4872	24	15	.	.	PUNCT
ejpam-4872	25	1	focusing	focus	VERB
ejpam-4872	25	2	on	on	ADP
ejpam-4872	25	3	examining	examine	VERB
ejpam-4872	25	4	the	the	DET
ejpam-4872	25	5	filter	filter	NOUN
ejpam-4872	25	6	and	and	CCONJ
ejpam-4872	25	7	deductive	deductive	ADJ
ejpam-4872	25	8	system	system	NOUN
ejpam-4872	25	9	of	of	ADP
ejpam-4872	25	10	the	the	DET
ejpam-4872	25	11	sheffer	sheffer	NOUN
ejpam-4872	25	12	stroke	stroke	NOUN
ejpam-4872	25	13	hilbert	hilbert	PROPN
ejpam-4872	25	14	algebra	algebra	PROPN
ejpam-4872	25	15	using	use	VERB
ejpam-4872	25	16	the	the	DET
ejpam-4872	25	17	dokdo	dokdo	NOUN
ejpam-4872	25	18	structure	structure	NOUN
ejpam-4872	25	19	,	,	PUNCT
ejpam-4872	25	20	we	we	PRON
ejpam-4872	25	21	define	define	VERB
ejpam-4872	25	22	the	the	DET
ejpam-4872	25	23	concept	concept	NOUN
ejpam-4872	25	24	of	of	ADP
ejpam-4872	25	25	dokdo	dokdo	ADJ
ejpam-4872	25	26	filter	filter	NOUN
ejpam-4872	25	27	and	and	CCONJ
ejpam-4872	25	28	dokdo	dokdo	ADJ
ejpam-4872	25	29	deductive	deductive	ADJ
ejpam-4872	25	30	system	system	NOUN
ejpam-4872	25	31	,	,	PUNCT
ejpam-4872	25	32	give	give	VERB
ejpam-4872	25	33	examples	example	NOUN
ejpam-4872	25	34	,	,	PUNCT
ejpam-4872	25	35	and	and	CCONJ
ejpam-4872	25	36	then	then	ADV
ejpam-4872	25	37	investigate	investigate	VERB
ejpam-4872	25	38	various	various	ADJ
ejpam-4872	25	39	properties	property	NOUN
ejpam-4872	25	40	.	.	PUNCT
ejpam-4872	26	1	we	we	PRON
ejpam-4872	26	2	form	form	VERB
ejpam-4872	26	3	a	a	DET
ejpam-4872	26	4	dokdo	dokdo	NOUN
ejpam-4872	26	5	filter	filter	NOUN
ejpam-4872	26	6	by	by	ADP
ejpam-4872	26	7	attaching	attach	VERB
ejpam-4872	26	8	appropriate	appropriate	ADJ
ejpam-4872	26	9	conditions	condition	NOUN
ejpam-4872	26	10	to	to	ADP
ejpam-4872	26	11	a	a	DET
ejpam-4872	26	12	given	give	VERB
ejpam-4872	26	13	dokdo	dokdo	NOUN
ejpam-4872	26	14	structure	structure	NOUN
ejpam-4872	26	15	.	.	PUNCT
ejpam-4872	27	1	we	we	PRON
ejpam-4872	27	2	study	study	VERB
ejpam-4872	27	3	characterizations	characterization	NOUN
ejpam-4872	27	4	of	of	ADP
ejpam-4872	27	5	dokdo	dokdo	NOUN
ejpam-4872	27	6	filters	filter	NOUN
ejpam-4872	27	7	.	.	PUNCT
ejpam-4872	28	1	we	we	PRON
ejpam-4872	28	2	construct	construct	VERB
ejpam-4872	28	3	dokdo	dokdo	NOUN
ejpam-4872	28	4	filters	filter	NOUN
ejpam-4872	28	5	that	that	PRON
ejpam-4872	28	6	are	be	AUX
ejpam-4872	28	7	associated	associate	VERB
ejpam-4872	28	8	with	with	ADP
ejpam-4872	28	9	filters	filter	NOUN
ejpam-4872	28	10	.	.	PUNCT
ejpam-4872	29	1	ultimately	ultimately	ADV
ejpam-4872	29	2	,	,	PUNCT
ejpam-4872	29	3	we	we	PRON
ejpam-4872	29	4	show	show	VERB
ejpam-4872	29	5	that	that	SCONJ
ejpam-4872	29	6	dokdo	dokdo	NOUN
ejpam-4872	29	7	filter	filter	NOUN
ejpam-4872	29	8	and	and	CCONJ
ejpam-4872	29	9	dokdo	dokdo	ADJ
ejpam-4872	29	10	deductive	deductive	ADJ
ejpam-4872	29	11	system	system	NOUN
ejpam-4872	29	12	are	be	AUX
ejpam-4872	29	13	a	a	DET
ejpam-4872	29	14	matching	matching	NOUN
ejpam-4872	29	15	concept	concept	NOUN
ejpam-4872	29	16	.	.	PUNCT
ejpam-4872	30	1	2	2	X
ejpam-4872	30	2	.	.	NUM
ejpam-4872	30	3	preliminaries	preliminary	NOUN
ejpam-4872	30	4	2.1	2.1	NUM
ejpam-4872	30	5	.	.	PUNCT
ejpam-4872	31	1	preliminaries	preliminary	NOUN
ejpam-4872	31	2	on	on	ADP
ejpam-4872	31	3	sheffer	sheffer	PROPN
ejpam-4872	31	4	stroke	stroke	PROPN
ejpam-4872	31	5	hilbert	hilbert	PROPN
ejpam-4872	31	6	algebras	algebras	PROPN
ejpam-4872	31	7	definition	definition	NOUN
ejpam-4872	31	8	1	1	NUM
ejpam-4872	31	9	(	(	PUNCT
ejpam-4872	31	10	[	[	X
ejpam-4872	31	11	9	9	NUM
ejpam-4872	31	12	]	]	PUNCT
ejpam-4872	31	13	)	)	PUNCT
ejpam-4872	31	14	.	.	PUNCT
ejpam-4872	32	1	let	let	VERB
ejpam-4872	32	2	a	a	PRON
ejpam-4872	32	3	:	:	PUNCT
ejpam-4872	32	4	=	=	SYM
ejpam-4872	32	5	(	(	PUNCT
ejpam-4872	32	6	a	a	PRON
ejpam-4872	32	7	,	,	PUNCT
ejpam-4872	32	8	|	|	NOUN
ejpam-4872	32	9	)	)	PUNCT
ejpam-4872	32	10	be	be	AUX
ejpam-4872	32	11	a	a	DET
ejpam-4872	32	12	groupoid	groupoid	NOUN
ejpam-4872	32	13	.	.	PUNCT
ejpam-4872	33	1	then	then	ADV
ejpam-4872	33	2	the	the	DET
ejpam-4872	33	3	operation	operation	NOUN
ejpam-4872	33	4	“	"	PUNCT
ejpam-4872	33	5	|	|	ADV
ejpam-4872	33	6	”	"	PUNCT
ejpam-4872	33	7	is	be	AUX
ejpam-4872	33	8	said	say	VERB
ejpam-4872	33	9	to	to	PART
ejpam-4872	33	10	be	be	AUX
ejpam-4872	33	11	sheffer	sheffer	NOUN
ejpam-4872	33	12	stroke	stroke	NOUN
ejpam-4872	33	13	or	or	CCONJ
ejpam-4872	33	14	sheffer	sheffer	VERB
ejpam-4872	33	15	operation	operation	NOUN
ejpam-4872	33	16	if	if	SCONJ
ejpam-4872	33	17	it	it	PRON
ejpam-4872	33	18	satisfies	satisfy	VERB
ejpam-4872	33	19	:	:	PUNCT
ejpam-4872	33	20	(	(	PUNCT
ejpam-4872	33	21	s1	s1	NOUN
ejpam-4872	33	22	)	)	PUNCT
ejpam-4872	33	23	(	(	PUNCT
ejpam-4872	33	24	∀a	∀a	X
ejpam-4872	33	25	,	,	PUNCT
ejpam-4872	33	26	b	b	PROPN
ejpam-4872	33	27	∈	∈	PROPN
ejpam-4872	33	28	a	a	NOUN
ejpam-4872	33	29	)	)	PUNCT
ejpam-4872	33	30	(	(	PUNCT
ejpam-4872	33	31	a|b	a|b	NOUN
ejpam-4872	33	32	=	=	SYM
ejpam-4872	33	33	b|a	b|a	NOUN
ejpam-4872	33	34	)	)	PUNCT
ejpam-4872	33	35	,	,	PUNCT
ejpam-4872	33	36	(	(	PUNCT
ejpam-4872	33	37	s2	s2	PROPN
ejpam-4872	33	38	)	)	PUNCT
ejpam-4872	33	39	(	(	PUNCT
ejpam-4872	33	40	∀a	∀a	X
ejpam-4872	33	41	,	,	PUNCT
ejpam-4872	33	42	b	b	PROPN
ejpam-4872	33	43	∈	∈	PROPN
ejpam-4872	33	44	a	a	NOUN
ejpam-4872	33	45	)	)	PUNCT
ejpam-4872	33	46	(	(	PUNCT
ejpam-4872	33	47	(	(	PUNCT
ejpam-4872	33	48	a|a)|(a|b	a|a)|(a|b	PROPN
ejpam-4872	33	49	)	)	PUNCT
ejpam-4872	33	50	=	=	SYM
ejpam-4872	34	1	a	a	NOUN
ejpam-4872	34	2	)	)	PUNCT
ejpam-4872	34	3	,	,	PUNCT
ejpam-4872	34	4	(	(	PUNCT
ejpam-4872	34	5	s3	s3	PROPN
ejpam-4872	34	6	)	)	PUNCT
ejpam-4872	34	7	(	(	PUNCT
ejpam-4872	34	8	∀a	∀a	X
ejpam-4872	34	9	,	,	PUNCT
ejpam-4872	34	10	b	b	NOUN
ejpam-4872	34	11	,	,	PUNCT
ejpam-4872	34	12	c	c	PROPN
ejpam-4872	34	13	∈	∈	PROPN
ejpam-4872	34	14	a	a	PRON
ejpam-4872	34	15	)	)	PUNCT
ejpam-4872	34	16	(	(	PUNCT
ejpam-4872	34	17	a|((b|c)|(b|c	a|((b|c)|(b|c	NOUN
ejpam-4872	34	18	)	)	PUNCT
ejpam-4872	34	19	)	)	PUNCT
ejpam-4872	35	1	=	=	SYM
ejpam-4872	35	2	(	(	PUNCT
ejpam-4872	35	3	(	(	PUNCT
ejpam-4872	35	4	a|b)|(a|b))|c	a|b)|(a|b))|c	PROPN
ejpam-4872	35	5	)	)	PUNCT
ejpam-4872	35	6	,	,	PUNCT
ejpam-4872	35	7	(	(	PUNCT
ejpam-4872	35	8	s4	s4	PROPN
ejpam-4872	35	9	)	)	PUNCT
ejpam-4872	35	10	(	(	PUNCT
ejpam-4872	35	11	∀a	∀a	X
ejpam-4872	35	12	,	,	PUNCT
ejpam-4872	35	13	b	b	NOUN
ejpam-4872	35	14	,	,	PUNCT
ejpam-4872	35	15	c	c	PROPN
ejpam-4872	35	16	∈	∈	PROPN
ejpam-4872	35	17	a	a	PRON
ejpam-4872	35	18	)	)	PUNCT
ejpam-4872	35	19	(	(	PUNCT
ejpam-4872	35	20	(	(	PUNCT
ejpam-4872	35	21	a|((a|a)|(b|b)))|(a|((a|a)|(b|b	a|((a|a)|(b|b)))|(a|((a|a)|(b|b	NOUN
ejpam-4872	35	22	)	)	PUNCT
ejpam-4872	35	23	)	)	PUNCT
ejpam-4872	35	24	)	)	PUNCT
ejpam-4872	36	1	=	=	PUNCT
ejpam-4872	36	2	a	a	X
ejpam-4872	36	3	)	)	PUNCT
ejpam-4872	36	4	.	.	PUNCT
ejpam-4872	37	1	definition	definition	NOUN
ejpam-4872	37	2	2	2	NUM
ejpam-4872	37	3	(	(	PUNCT
ejpam-4872	37	4	[	[	X
ejpam-4872	37	5	12	12	NUM
ejpam-4872	37	6	]	]	NUM
ejpam-4872	37	7	)	)	PUNCT
ejpam-4872	37	8	.	.	PUNCT
ejpam-4872	38	1	a	a	DET
ejpam-4872	38	2	sheffer	sheffer	NOUN
ejpam-4872	38	3	stroke	stroke	NOUN
ejpam-4872	38	4	hilbert	hilbert	PROPN
ejpam-4872	38	5	algebra	algebra	PROPN
ejpam-4872	38	6	is	be	AUX
ejpam-4872	38	7	a	a	DET
ejpam-4872	38	8	groupoid	groupoid	NOUN
ejpam-4872	38	9	x	x	X
ejpam-4872	38	10	:	:	PUNCT
ejpam-4872	38	11	=	=	SYM
ejpam-4872	38	12	(	(	PUNCT
ejpam-4872	38	13	x	x	NOUN
ejpam-4872	38	14	,	,	PUNCT
ejpam-4872	38	15	|	|	ADV
ejpam-4872	38	16	)	)	PUNCT
ejpam-4872	38	17	with	with	ADP
ejpam-4872	38	18	a	a	DET
ejpam-4872	38	19	sheffer	sheffer	NOUN
ejpam-4872	38	20	stroke	stroke	NOUN
ejpam-4872	38	21	“	"	PUNCT
ejpam-4872	38	22	|	|	ADV
ejpam-4872	38	23	”	"	PUNCT
ejpam-4872	38	24	that	that	PRON
ejpam-4872	38	25	satisfies	satisfy	VERB
ejpam-4872	38	26	:	:	PUNCT
ejpam-4872	38	27	(	(	PUNCT
ejpam-4872	38	28	sh1	sh1	PROPN
ejpam-4872	38	29	)	)	PUNCT
ejpam-4872	38	30	(	(	PUNCT
ejpam-4872	38	31	a|((a)|(a)))|(((b)|((c)|(c)))|((b)|((c)|(c	a|((a)|(a)))|(((b)|((c)|(c)))|((b)|((c)|(c	PROPN
ejpam-4872	38	32	)	)	PUNCT
ejpam-4872	38	33	)	)	PUNCT
ejpam-4872	38	34	)	)	PUNCT
ejpam-4872	38	35	)	)	PUNCT
ejpam-4872	39	1	=	=	SYM
ejpam-4872	39	2	a|(a|a	a|(a|a	PROPN
ejpam-4872	39	3	)	)	PUNCT
ejpam-4872	39	4	,	,	PUNCT
ejpam-4872	39	5	where	where	SCONJ
ejpam-4872	39	6	a	a	DET
ejpam-4872	39	7	:	:	PUNCT
ejpam-4872	39	8	=	=	PUNCT
ejpam-4872	39	9	b|(c|c	b|(c|c	PROPN
ejpam-4872	39	10	)	)	PUNCT
ejpam-4872	39	11	,	,	PUNCT
ejpam-4872	39	12	b	b	X
ejpam-4872	39	13	:	:	PUNCT
ejpam-4872	39	14	=	=	SYM
ejpam-4872	39	15	a|(b|b	a|(b|b	NOUN
ejpam-4872	39	16	)	)	PUNCT
ejpam-4872	39	17	and	and	CCONJ
ejpam-4872	39	18	c	c	NOUN
ejpam-4872	39	19	:	:	PUNCT
ejpam-4872	39	20	=	=	SYM
ejpam-4872	39	21	a|(c|c	a|(c|c	PROPN
ejpam-4872	39	22	)	)	PUNCT
ejpam-4872	39	23	,	,	PUNCT
ejpam-4872	39	24	(	(	PUNCT
ejpam-4872	39	25	sh2	sh2	NOUN
ejpam-4872	39	26	)	)	PUNCT
ejpam-4872	39	27	a|(b|b	a|(b|b	NOUN
ejpam-4872	39	28	)	)	PUNCT
ejpam-4872	39	29	=	=	SYM
ejpam-4872	39	30	b|(a|a	b|(a|a	PROPN
ejpam-4872	39	31	)	)	PUNCT
ejpam-4872	39	32	=	=	SYM
ejpam-4872	39	33	a|(a|a	a|(a|a	PROPN
ejpam-4872	39	34	)	)	PUNCT
ejpam-4872	39	35	⇒	⇒	VERB
ejpam-4872	39	36	a	a	DET
ejpam-4872	39	37	=	=	SYM
ejpam-4872	39	38	b	b	PROPN
ejpam-4872	39	39	for	for	ADP
ejpam-4872	39	40	all	all	DET
ejpam-4872	39	41	a	a	DET
ejpam-4872	39	42	,	,	PUNCT
ejpam-4872	39	43	b	b	NOUN
ejpam-4872	39	44	,	,	PUNCT
ejpam-4872	39	45	c	c	PROPN
ejpam-4872	39	46	∈	∈	PROPN
ejpam-4872	39	47	x.	x.	NOUN
ejpam-4872	39	48	let	let	VERB
ejpam-4872	39	49	x	x	PRON
ejpam-4872	39	50	:	:	PUNCT
ejpam-4872	39	51	=	=	SYM
ejpam-4872	39	52	(	(	PUNCT
ejpam-4872	39	53	x	x	NOUN
ejpam-4872	39	54	,	,	PUNCT
ejpam-4872	39	55	|	|	ADV
ejpam-4872	39	56	)	)	PUNCT
ejpam-4872	39	57	be	be	AUX
ejpam-4872	39	58	a	a	DET
ejpam-4872	39	59	sheffer	sheffer	NOUN
ejpam-4872	39	60	stroke	stroke	NOUN
ejpam-4872	39	61	hilbert	hilbert	PROPN
ejpam-4872	39	62	algebra	algebra	PROPN
ejpam-4872	39	63	.	.	PUNCT
ejpam-4872	40	1	then	then	ADV
ejpam-4872	40	2	the	the	DET
ejpam-4872	40	3	order	order	NOUN
ejpam-4872	40	4	relation	relation	NOUN
ejpam-4872	40	5	“	"	PUNCT
ejpam-4872	40	6	≤x	≤x	PROPN
ejpam-4872	40	7	”	"	PUNCT
ejpam-4872	40	8	on	on	ADP
ejpam-4872	40	9	x	x	PUNCT
ejpam-4872	40	10	is	be	AUX
ejpam-4872	40	11	defined	define	VERB
ejpam-4872	40	12	as	as	SCONJ
ejpam-4872	40	13	follows	follow	VERB
ejpam-4872	40	14	:	:	PUNCT
ejpam-4872	40	15	(	(	PUNCT
ejpam-4872	40	16	∀a	∀a	X
ejpam-4872	40	17	,	,	PUNCT
ejpam-4872	40	18	b	b	PROPN
ejpam-4872	40	19	∈	∈	PROPN
ejpam-4872	40	20	x)(a	x)(a	PUNCT
ejpam-4872	41	1	≤x	≤x	PROPN
ejpam-4872	41	2	b	b	PROPN
ejpam-4872	41	3	⇔	⇔	X
ejpam-4872	41	4	a|(b|b	a|(b|b	PROPN
ejpam-4872	41	5	)	)	PUNCT
ejpam-4872	41	6	=	=	SYM
ejpam-4872	41	7	1	1	NUM
ejpam-4872	41	8	)	)	PUNCT
ejpam-4872	41	9	.	.	PUNCT
ejpam-4872	42	1	(	(	PUNCT
ejpam-4872	42	2	1	1	X
ejpam-4872	42	3	)	)	PUNCT
ejpam-4872	42	4	s.	s.	PROPN
ejpam-4872	42	5	s.	s.	PROPN
ejpam-4872	42	6	ahn	ahn	PROPN
ejpam-4872	42	7	et	et	PROPN
ejpam-4872	42	8	al	al	PROPN
ejpam-4872	42	9	.	.	PUNCT
ejpam-4872	42	10	/	/	SYM
ejpam-4872	42	11	eur	eur	PROPN
ejpam-4872	42	12	.	.	PUNCT
ejpam-4872	43	1	j.	j.	PROPN
ejpam-4872	43	2	pure	pure	PROPN
ejpam-4872	43	3	appl	appl	PROPN
ejpam-4872	43	4	.	.	PROPN
ejpam-4872	43	5	math	math	PROPN
ejpam-4872	43	6	,	,	PUNCT
ejpam-4872	43	7	16	16	NUM
ejpam-4872	43	8	(	(	PUNCT
ejpam-4872	43	9	3	3	NUM
ejpam-4872	43	10	)	)	PUNCT
ejpam-4872	43	11	(	(	PUNCT
ejpam-4872	43	12	2023	2023	NUM
ejpam-4872	43	13	)	)	PUNCT
ejpam-4872	43	14	,	,	PUNCT
ejpam-4872	43	15	1862	1862	NUM
ejpam-4872	43	16	-	-	SYM
ejpam-4872	43	17	1877	1877	NUM
ejpam-4872	43	18	1864	1864	NUM
ejpam-4872	43	19	we	we	PRON
ejpam-4872	43	20	observe	observe	VERB
ejpam-4872	43	21	that	that	SCONJ
ejpam-4872	43	22	the	the	DET
ejpam-4872	43	23	relation	relation	NOUN
ejpam-4872	43	24	“	"	PUNCT
ejpam-4872	43	25	≤x	≤x	PROPN
ejpam-4872	43	26	”	"	PUNCT
ejpam-4872	43	27	is	be	AUX
ejpam-4872	43	28	a	a	DET
ejpam-4872	43	29	partial	partial	ADJ
ejpam-4872	43	30	order	order	NOUN
ejpam-4872	43	31	in	in	ADP
ejpam-4872	43	32	a	a	DET
ejpam-4872	43	33	sheffer	sheffer	NOUN
ejpam-4872	43	34	stroke	stroke	NOUN
ejpam-4872	43	35	hilbert	hilbert	PROPN
ejpam-4872	43	36	algebra	algebra	PROPN
ejpam-4872	43	37	x	x	X
ejpam-4872	43	38	:	:	PUNCT
ejpam-4872	43	39	=	=	SYM
ejpam-4872	43	40	(	(	PUNCT
ejpam-4872	43	41	x	x	NOUN
ejpam-4872	43	42	,	,	PUNCT
ejpam-4872	43	43	|	|	NOUN
ejpam-4872	43	44	)	)	PUNCT
ejpam-4872	43	45	(	(	PUNCT
ejpam-4872	43	46	see	see	VERB
ejpam-4872	43	47	[	[	X
ejpam-4872	43	48	12	12	NUM
ejpam-4872	43	49	]	]	NUM
ejpam-4872	43	50	)	)	PUNCT
ejpam-4872	43	51	.	.	PUNCT
ejpam-4872	44	1	proposition	proposition	NOUN
ejpam-4872	44	2	1	1	NUM
ejpam-4872	44	3	(	(	PUNCT
ejpam-4872	44	4	[	[	X
ejpam-4872	44	5	12	12	NUM
ejpam-4872	44	6	]	]	NUM
ejpam-4872	44	7	)	)	PUNCT
ejpam-4872	44	8	.	.	PUNCT
ejpam-4872	45	1	every	every	DET
ejpam-4872	45	2	sheffer	sheffer	NOUN
ejpam-4872	45	3	stroke	stroke	NOUN
ejpam-4872	45	4	hilbert	hilbert	PROPN
ejpam-4872	45	5	algebra	algebra	PROPN
ejpam-4872	45	6	x	x	X
ejpam-4872	45	7	:	:	PUNCT
ejpam-4872	45	8	=	=	SYM
ejpam-4872	45	9	(	(	PUNCT
ejpam-4872	45	10	x	x	NOUN
ejpam-4872	45	11	,	,	PUNCT
ejpam-4872	45	12	|	|	ADV
ejpam-4872	45	13	)	)	PUNCT
ejpam-4872	45	14	satisfies	satisfie	NOUN
ejpam-4872	45	15	:	:	PUNCT
ejpam-4872	45	16	(	(	PUNCT
ejpam-4872	45	17	∀a	∀a	X
ejpam-4872	45	18	∈	∈	NOUN
ejpam-4872	45	19	x)(a|(a|a	x)(a|(a|a	PUNCT
ejpam-4872	45	20	)	)	PUNCT
ejpam-4872	45	21	=	=	SYM
ejpam-4872	45	22	1	1	NUM
ejpam-4872	45	23	)	)	PUNCT
ejpam-4872	45	24	,	,	PUNCT
ejpam-4872	45	25	(	(	PUNCT
ejpam-4872	45	26	2	2	X
ejpam-4872	45	27	)	)	PUNCT
ejpam-4872	45	28	(	(	PUNCT
ejpam-4872	45	29	∀a	∀a	NOUN
ejpam-4872	45	30	∈	∈	NOUN
ejpam-4872	45	31	x)(a|(1|1	x)(a|(1|1	VERB
ejpam-4872	45	32	)	)	PUNCT
ejpam-4872	45	33	=	=	SYM
ejpam-4872	45	34	1	1	NUM
ejpam-4872	45	35	)	)	PUNCT
ejpam-4872	45	36	,	,	PUNCT
ejpam-4872	45	37	(	(	PUNCT
ejpam-4872	45	38	3	3	X
ejpam-4872	45	39	)	)	PUNCT
ejpam-4872	45	40	(	(	PUNCT
ejpam-4872	45	41	∀a	∀a	NOUN
ejpam-4872	45	42	∈	∈	NOUN
ejpam-4872	45	43	x)(1|(a|a	x)(1|(a|a	PROPN
ejpam-4872	45	44	)	)	PUNCT
ejpam-4872	45	45	=	=	SYM
ejpam-4872	45	46	a	a	X
ejpam-4872	45	47	)	)	PUNCT
ejpam-4872	45	48	,	,	PUNCT
ejpam-4872	45	49	(	(	PUNCT
ejpam-4872	45	50	4	4	NUM
ejpam-4872	45	51	)	)	PUNCT
ejpam-4872	45	52	(	(	PUNCT
ejpam-4872	45	53	∀a	∀a	X
ejpam-4872	45	54	,	,	PUNCT
ejpam-4872	45	55	b	b	PROPN
ejpam-4872	45	56	∈	∈	PROPN
ejpam-4872	45	57	x)(a	x)(a	PUNCT
ejpam-4872	46	1	≤x	≤x	PROPN
ejpam-4872	46	2	b|(a|a	b|(a|a	PROPN
ejpam-4872	46	3	)	)	PUNCT
ejpam-4872	46	4	)	)	PUNCT
ejpam-4872	46	5	,	,	PUNCT
ejpam-4872	46	6	(	(	PUNCT
ejpam-4872	46	7	5	5	X
ejpam-4872	46	8	)	)	PUNCT
ejpam-4872	46	9	(	(	PUNCT
ejpam-4872	46	10	∀a	∀a	X
ejpam-4872	46	11	,	,	PUNCT
ejpam-4872	46	12	b	b	PROPN
ejpam-4872	46	13	∈	∈	PROPN
ejpam-4872	46	14	x)((a|(b|b))|(b|b	x)((a|(b|b))|(b|b	NOUN
ejpam-4872	46	15	)	)	PUNCT
ejpam-4872	46	16	=	=	PRON
ejpam-4872	46	17	(	(	PUNCT
ejpam-4872	46	18	b|(a|a))|(a|a	b|(a|a))|(a|a	PROPN
ejpam-4872	46	19	)	)	PUNCT
ejpam-4872	46	20	)	)	PUNCT
ejpam-4872	46	21	,	,	PUNCT
ejpam-4872	46	22	(	(	PUNCT
ejpam-4872	46	23	6	6	NUM
ejpam-4872	46	24	)	)	PUNCT
ejpam-4872	46	25	(	(	PUNCT
ejpam-4872	46	26	∀a	∀a	X
ejpam-4872	46	27	,	,	PUNCT
ejpam-4872	46	28	b	b	PROPN
ejpam-4872	46	29	∈	∈	PROPN
ejpam-4872	46	30	x	x	X
ejpam-4872	46	31	)	)	PUNCT
ejpam-4872	46	32	(	(	PUNCT
ejpam-4872	46	33	(	(	PUNCT
ejpam-4872	46	34	(	(	PUNCT
ejpam-4872	46	35	a|(b|b))|(b|b))|(b|b	a|(b|b))|(b|b))|(b|b	NOUN
ejpam-4872	46	36	)	)	PUNCT
ejpam-4872	46	37	=	=	SYM
ejpam-4872	46	38	a|(b|b	a|(b|b	NOUN
ejpam-4872	46	39	)	)	PUNCT
ejpam-4872	46	40	)	)	PUNCT
ejpam-4872	46	41	,	,	PUNCT
ejpam-4872	46	42	(	(	PUNCT
ejpam-4872	46	43	7	7	X
ejpam-4872	46	44	)	)	PUNCT
ejpam-4872	46	45	(	(	PUNCT
ejpam-4872	46	46	∀a	∀a	X
ejpam-4872	46	47	,	,	PUNCT
ejpam-4872	46	48	b	b	NOUN
ejpam-4872	46	49	,	,	PUNCT
ejpam-4872	46	50	c	c	PROPN
ejpam-4872	46	51	∈	∈	PROPN
ejpam-4872	46	52	x	x	X
ejpam-4872	46	53	)	)	PUNCT
ejpam-4872	46	54	(	(	PUNCT
ejpam-4872	46	55	a|((b|(c|c))|(b|(c|c	a|((b|(c|c))|(b|(c|c	NOUN
ejpam-4872	46	56	)	)	PUNCT
ejpam-4872	46	57	)	)	PUNCT
ejpam-4872	46	58	)	)	PUNCT
ejpam-4872	47	1	=	=	SYM
ejpam-4872	47	2	b|((a|(c|c))|(a|(c|c	b|((a|(c|c))|(a|(c|c	NOUN
ejpam-4872	47	3	)	)	PUNCT
ejpam-4872	47	4	)	)	PUNCT
ejpam-4872	47	5	)	)	PUNCT
ejpam-4872	47	6	)	)	PUNCT
ejpam-4872	47	7	,	,	PUNCT
ejpam-4872	47	8	(	(	PUNCT
ejpam-4872	47	9	8)	8)	NUM
ejpam-4872	47	10	definition	definition	NOUN
ejpam-4872	47	11	3	3	NUM
ejpam-4872	47	12	(	(	PUNCT
ejpam-4872	47	13	[	[	X
ejpam-4872	47	14	11	11	NUM
ejpam-4872	47	15	]	]	NUM
ejpam-4872	47	16	)	)	PUNCT
ejpam-4872	47	17	.	.	PUNCT
ejpam-4872	48	1	let	let	AUX
ejpam-4872	48	2	(	(	PUNCT
ejpam-4872	48	3	x	x	NOUN
ejpam-4872	48	4	,	,	PUNCT
ejpam-4872	48	5	|	|	ADV
ejpam-4872	48	6	)	)	PUNCT
ejpam-4872	48	7	be	be	AUX
ejpam-4872	48	8	a	a	DET
ejpam-4872	48	9	sheffer	sheffer	NOUN
ejpam-4872	48	10	stroke	stroke	NOUN
ejpam-4872	48	11	hilbert	hilbert	PROPN
ejpam-4872	48	12	algebra	algebra	PROPN
ejpam-4872	48	13	.	.	PUNCT
ejpam-4872	49	1	a	a	DET
ejpam-4872	49	2	subset	subset	NOUN
ejpam-4872	49	3	f	f	NOUN
ejpam-4872	49	4	of	of	ADP
ejpam-4872	49	5	x	x	PROPN
ejpam-4872	49	6	is	be	AUX
ejpam-4872	49	7	called	call	VERB
ejpam-4872	49	8	•	•	ADP
ejpam-4872	49	9	a	a	DET
ejpam-4872	49	10	deductive	deductive	ADJ
ejpam-4872	49	11	system	system	NOUN
ejpam-4872	49	12	of	of	ADP
ejpam-4872	49	13	(	(	PUNCT
ejpam-4872	49	14	x	x	NOUN
ejpam-4872	49	15	,	,	PUNCT
ejpam-4872	49	16	|	|	INTJ
ejpam-4872	49	17	)	)	PUNCT
ejpam-4872	49	18	if	if	SCONJ
ejpam-4872	49	19	it	it	PRON
ejpam-4872	49	20	satisfies	satisfy	VERB
ejpam-4872	49	21	:	:	PUNCT
ejpam-4872	49	22	1	1	NUM
ejpam-4872	49	23	∈	∈	NOUN
ejpam-4872	49	24	f	f	NOUN
ejpam-4872	49	25	,	,	PUNCT
ejpam-4872	49	26	(	(	PUNCT
ejpam-4872	49	27	9	9	NUM
ejpam-4872	49	28	)	)	PUNCT
ejpam-4872	49	29	(	(	PUNCT
ejpam-4872	49	30	∀a	∀a	X
ejpam-4872	49	31	,	,	PUNCT
ejpam-4872	49	32	b	b	PROPN
ejpam-4872	49	33	∈	∈	PROPN
ejpam-4872	49	34	x)(a	x)(a	PUNCT
ejpam-4872	50	1	∈	∈	PROPN
ejpam-4872	50	2	f	f	X
ejpam-4872	50	3	,	,	PUNCT
ejpam-4872	50	4	a|(b|b	a|(b|b	NOUN
ejpam-4872	50	5	)	)	PUNCT
ejpam-4872	50	6	∈	∈	PROPN
ejpam-4872	50	7	f	f	PROPN
ejpam-4872	50	8	⇒	⇒	PROPN
ejpam-4872	50	9	b	b	PROPN
ejpam-4872	50	10	∈	∈	PROPN
ejpam-4872	50	11	f	f	PROPN
ejpam-4872	50	12	)	)	PUNCT
ejpam-4872	50	13	,	,	PUNCT
ejpam-4872	50	14	(	(	PUNCT
ejpam-4872	50	15	10	10	NUM
ejpam-4872	50	16	)	)	PUNCT
ejpam-4872	50	17	•	•	NOUN
ejpam-4872	50	18	a	a	DET
ejpam-4872	50	19	filter	filter	NOUN
ejpam-4872	50	20	of	of	ADP
ejpam-4872	50	21	(	(	PUNCT
ejpam-4872	50	22	x	x	NOUN
ejpam-4872	50	23	,	,	PUNCT
ejpam-4872	50	24	|	|	INTJ
ejpam-4872	50	25	)	)	PUNCT
ejpam-4872	50	26	if	if	SCONJ
ejpam-4872	50	27	it	it	PRON
ejpam-4872	50	28	satisfies	satisfy	VERB
ejpam-4872	50	29	(	(	PUNCT
ejpam-4872	50	30	9	9	NUM
ejpam-4872	50	31	)	)	PUNCT
ejpam-4872	50	32	and	and	CCONJ
ejpam-4872	50	33	(	(	PUNCT
ejpam-4872	50	34	∀a	∀a	NOUN
ejpam-4872	50	35	,	,	PUNCT
ejpam-4872	50	36	b	b	PROPN
ejpam-4872	50	37	∈	∈	PROPN
ejpam-4872	50	38	x)(b	x)(b	PROPN
ejpam-4872	50	39	∈	∈	PROPN
ejpam-4872	50	40	f	f	PROPN
ejpam-4872	50	41	⇒	⇒	PROPN
ejpam-4872	50	42	a|(b|b	a|(b|b	PROPN
ejpam-4872	50	43	)	)	PUNCT
ejpam-4872	50	44	∈	∈	PROPN
ejpam-4872	50	45	f	f	PROPN
ejpam-4872	50	46	)	)	PUNCT
ejpam-4872	50	47	,	,	PUNCT
ejpam-4872	50	48	(	(	PUNCT
ejpam-4872	50	49	11	11	NUM
ejpam-4872	50	50	)	)	PUNCT
ejpam-4872	50	51	(	(	PUNCT
ejpam-4872	50	52	∀a	∀a	X
ejpam-4872	50	53	,	,	PUNCT
ejpam-4872	50	54	b	b	NOUN
ejpam-4872	50	55	,	,	PUNCT
ejpam-4872	50	56	c	c	PROPN
ejpam-4872	50	57	∈	∈	PROPN
ejpam-4872	50	58	x)(b	x)(b	PROPN
ejpam-4872	50	59	,	,	PUNCT
ejpam-4872	50	60	c	c	PROPN
ejpam-4872	50	61	∈	∈	PROPN
ejpam-4872	50	62	f	f	PROPN
ejpam-4872	50	63	⇒	⇒	PROPN
ejpam-4872	50	64	(	(	PUNCT
ejpam-4872	50	65	a|(b|c))|(b|c	a|(b|c))|(b|c	PROPN
ejpam-4872	50	66	)	)	PUNCT
ejpam-4872	50	67	∈	∈	PROPN
ejpam-4872	50	68	f	f	PROPN
ejpam-4872	50	69	)	)	PUNCT
ejpam-4872	50	70	.	.	PUNCT
ejpam-4872	51	1	(	(	PUNCT
ejpam-4872	51	2	12	12	NUM
ejpam-4872	51	3	)	)	PUNCT
ejpam-4872	51	4	2.2	2.2	NUM
ejpam-4872	51	5	.	.	PUNCT
ejpam-4872	51	6	basic	basic	ADJ
ejpam-4872	51	7	concepts	concept	NOUN
ejpam-4872	51	8	about	about	ADP
ejpam-4872	51	9	dokdo	dokdo	NOUN
ejpam-4872	51	10	structure	structure	NOUN
ejpam-4872	51	11	let	let	VERB
ejpam-4872	51	12	x	x	PRON
ejpam-4872	51	13	be	be	AUX
ejpam-4872	51	14	a	a	DET
ejpam-4872	51	15	set	set	NOUN
ejpam-4872	51	16	.	.	PUNCT
ejpam-4872	52	1	a	a	DET
ejpam-4872	52	2	bipolar	bipolar	ADJ
ejpam-4872	52	3	fuzzy	fuzzy	ADJ
ejpam-4872	52	4	set	set	NOUN
ejpam-4872	52	5	in	in	ADP
ejpam-4872	52	6	x	x	PROPN
ejpam-4872	52	7	(	(	PUNCT
ejpam-4872	52	8	see	see	VERB
ejpam-4872	52	9	[	[	X
ejpam-4872	52	10	6	6	NUM
ejpam-4872	52	11	]	]	PUNCT
ejpam-4872	52	12	)	)	PUNCT
ejpam-4872	52	13	is	be	AUX
ejpam-4872	52	14	an	an	DET
ejpam-4872	52	15	object	object	NOUN
ejpam-4872	52	16	of	of	ADP
ejpam-4872	52	17	the	the	DET
ejpam-4872	52	18	following	follow	VERB
ejpam-4872	52	19	type	type	NOUN
ejpam-4872	52	20	f̊	f̊	X
ejpam-4872	52	21	=	=	SYM
ejpam-4872	52	22	{	{	PUNCT
ejpam-4872	52	23	(	(	PUNCT
ejpam-4872	52	24	a	a	PRON
ejpam-4872	52	25	,	,	PUNCT
ejpam-4872	52	26	f̊−(a	f̊−(a	NOUN
ejpam-4872	52	27	)	)	PUNCT
ejpam-4872	52	28	,	,	PUNCT
ejpam-4872	52	29	f̊+(a	f̊+(a	NOUN
ejpam-4872	52	30	)	)	PUNCT
ejpam-4872	52	31	)	)	PUNCT
ejpam-4872	53	1	|	|	ADV
ejpam-4872	53	2	a	a	DET
ejpam-4872	53	3	∈	∈	NOUN
ejpam-4872	53	4	x	x	PRON
ejpam-4872	53	5	}	}	PUNCT
ejpam-4872	53	6	(	(	PUNCT
ejpam-4872	53	7	13	13	NUM
ejpam-4872	53	8	)	)	PUNCT
ejpam-4872	53	9	where	where	SCONJ
ejpam-4872	53	10	f̊−	f̊−	NOUN
ejpam-4872	53	11	:	:	PUNCT
ejpam-4872	54	1	x	x	X
ejpam-4872	55	1	→	→	PUNCT
ejpam-4872	56	1	[	[	X
ejpam-4872	56	2	−1	−1	NOUN
ejpam-4872	56	3	,	,	PUNCT
ejpam-4872	56	4	0	0	NUM
ejpam-4872	56	5	]	]	PUNCT
ejpam-4872	56	6	and	and	CCONJ
ejpam-4872	56	7	f̊+	f̊+	NOUN
ejpam-4872	56	8	:	:	PUNCT
ejpam-4872	57	1	x	x	X
ejpam-4872	57	2	→	→	PUNCT
ejpam-4872	58	1	[	[	X
ejpam-4872	58	2	0	0	NUM
ejpam-4872	58	3	,	,	PUNCT
ejpam-4872	58	4	1	1	NUM
ejpam-4872	58	5	]	]	PUNCT
ejpam-4872	58	6	are	be	AUX
ejpam-4872	58	7	mappings	mapping	NOUN
ejpam-4872	58	8	.	.	PUNCT
ejpam-4872	59	1	the	the	DET
ejpam-4872	59	2	bipolar	bipolar	ADJ
ejpam-4872	59	3	fuzzy	fuzzy	ADJ
ejpam-4872	59	4	set	set	NOUN
ejpam-4872	59	5	which	which	PRON
ejpam-4872	59	6	is	be	AUX
ejpam-4872	59	7	described	describe	VERB
ejpam-4872	59	8	in	in	ADP
ejpam-4872	59	9	(	(	PUNCT
ejpam-4872	59	10	13	13	NUM
ejpam-4872	59	11	)	)	PUNCT
ejpam-4872	59	12	is	be	AUX
ejpam-4872	59	13	simply	simply	ADV
ejpam-4872	59	14	denoted	denote	VERB
ejpam-4872	59	15	by	by	ADP
ejpam-4872	59	16	f̊	f̊	X
ejpam-4872	59	17	:	:	PUNCT
ejpam-4872	59	18	=	=	SYM
ejpam-4872	59	19	(	(	PUNCT
ejpam-4872	59	20	x	x	NOUN
ejpam-4872	59	21	;	;	PUNCT
ejpam-4872	59	22	f̊−	f̊−	NOUN
ejpam-4872	59	23	,	,	PUNCT
ejpam-4872	59	24	f̊+	f̊+	NOUN
ejpam-4872	59	25	)	)	PUNCT
ejpam-4872	59	26	.	.	PUNCT
ejpam-4872	60	1	a	a	DET
ejpam-4872	60	2	bipolar	bipolar	ADJ
ejpam-4872	60	3	fuzzy	fuzzy	ADJ
ejpam-4872	60	4	set	set	NOUN
ejpam-4872	60	5	can	can	AUX
ejpam-4872	60	6	be	be	AUX
ejpam-4872	60	7	reinterpreted	reinterpret	VERB
ejpam-4872	60	8	as	as	ADP
ejpam-4872	60	9	a	a	DET
ejpam-4872	60	10	function	function	NOUN
ejpam-4872	60	11	:	:	PUNCT
ejpam-4872	60	12	f̊	f̊	X
ejpam-4872	60	13	:	:	PUNCT
ejpam-4872	60	14	x	x	X
ejpam-4872	60	15	→	→	PUNCT
ejpam-4872	60	16	[	[	X
ejpam-4872	60	17	−1	−1	NOUN
ejpam-4872	60	18	,	,	PUNCT
ejpam-4872	60	19	0]×	0]×	PROPN
ejpam-4872	61	1	[	[	X
ejpam-4872	61	2	0	0	NUM
ejpam-4872	61	3	,	,	PUNCT
ejpam-4872	61	4	1	1	NUM
ejpam-4872	61	5	]	]	PUNCT
ejpam-4872	61	6	,	,	PUNCT
ejpam-4872	61	7	a	a	DET
ejpam-4872	61	8	7→	7→	PROPN
ejpam-4872	61	9	(	(	PUNCT
ejpam-4872	61	10	f̊−(a	f̊−(a	NOUN
ejpam-4872	61	11	)	)	PUNCT
ejpam-4872	61	12	,	,	PUNCT
ejpam-4872	61	13	f̊+(a	f̊+(a	NOUN
ejpam-4872	61	14	)	)	PUNCT
ejpam-4872	61	15	)	)	PUNCT
ejpam-4872	61	16	.	.	PUNCT
ejpam-4872	62	1	denote	denote	VERB
ejpam-4872	62	2	by	by	ADP
ejpam-4872	62	3	bf	bf	NOUN
ejpam-4872	62	4	(	(	PUNCT
ejpam-4872	62	5	x	x	X
ejpam-4872	62	6	)	)	PUNCT
ejpam-4872	62	7	the	the	DET
ejpam-4872	62	8	set	set	NOUN
ejpam-4872	62	9	of	of	ADP
ejpam-4872	62	10	all	all	DET
ejpam-4872	62	11	bipolar	bipolar	ADJ
ejpam-4872	62	12	fuzzy	fuzzy	ADJ
ejpam-4872	62	13	sets	set	NOUN
ejpam-4872	62	14	in	in	ADP
ejpam-4872	62	15	x.	x.	NOUN
ejpam-4872	62	16	we	we	PRON
ejpam-4872	62	17	define	define	VERB
ejpam-4872	62	18	a	a	DET
ejpam-4872	62	19	binary	binary	ADJ
ejpam-4872	62	20	relation	relation	NOUN
ejpam-4872	62	21	“	"	PUNCT
ejpam-4872	62	22	≤b	≤b	NOUN
ejpam-4872	62	23	”	"	PUNCT
ejpam-4872	62	24	on	on	ADP
ejpam-4872	62	25	bf	bf	NOUN
ejpam-4872	62	26	(	(	PUNCT
ejpam-4872	62	27	x	x	X
ejpam-4872	62	28	)	)	PUNCT
ejpam-4872	62	29	as	as	SCONJ
ejpam-4872	62	30	follows	follow	VERB
ejpam-4872	62	31	:	:	PUNCT
ejpam-4872	62	32	(	(	PUNCT
ejpam-4872	62	33	∀f̊	∀f̊	PROPN
ejpam-4872	62	34	,	,	PUNCT
ejpam-4872	62	35	g̊	g̊	PROPN
ejpam-4872	62	36	∈	∈	NOUN
ejpam-4872	62	37	bf	bf	NOUN
ejpam-4872	62	38	(	(	PUNCT
ejpam-4872	62	39	x	x	NOUN
ejpam-4872	62	40	)	)	PUNCT
ejpam-4872	62	41	)	)	PUNCT
ejpam-4872	62	42	(	(	PUNCT
ejpam-4872	62	43	f̊	f̊	X
ejpam-4872	62	44	≤b	≤b	PROPN
ejpam-4872	62	45	g̊	g̊	PROPN
ejpam-4872	62	46	⇔	⇔	X
ejpam-4872	62	47	{	{	PUNCT
ejpam-4872	62	48	f̊−(a	f̊−(a	NOUN
ejpam-4872	62	49	)	)	PUNCT
ejpam-4872	62	50	≥	≥	NOUN
ejpam-4872	62	51	g̊−(a	g̊−(a	ADV
ejpam-4872	62	52	)	)	PUNCT
ejpam-4872	62	53	f̊+(a	f̊+(a	PROPN
ejpam-4872	62	54	)	)	PUNCT
ejpam-4872	62	55	≤	≤	NUM
ejpam-4872	62	56	g̊+(a	g̊+(a	PROPN
ejpam-4872	62	57	)	)	PUNCT
ejpam-4872	62	58	for	for	ADP
ejpam-4872	62	59	all	all	DET
ejpam-4872	62	60	a	a	DET
ejpam-4872	62	61	∈	∈	NOUN
ejpam-4872	62	62	x	x	PUNCT
ejpam-4872	62	63	)	)	PUNCT
ejpam-4872	62	64	.	.	PUNCT
ejpam-4872	63	1	(	(	PUNCT
ejpam-4872	63	2	14	14	NUM
ejpam-4872	63	3	)	)	PUNCT
ejpam-4872	63	4	then	then	ADV
ejpam-4872	63	5	(	(	PUNCT
ejpam-4872	63	6	bf(x),≤b	bf(x),≤b	PROPN
ejpam-4872	63	7	)	)	PUNCT
ejpam-4872	63	8	is	be	AUX
ejpam-4872	63	9	a	a	DET
ejpam-4872	63	10	poset	poset	NOUN
ejpam-4872	63	11	.	.	PUNCT
ejpam-4872	64	1	s.	s.	PROPN
ejpam-4872	64	2	s.	s.	PROPN
ejpam-4872	64	3	ahn	ahn	PROPN
ejpam-4872	64	4	et	et	PROPN
ejpam-4872	64	5	al	al	PROPN
ejpam-4872	64	6	.	.	PUNCT
ejpam-4872	64	7	/	/	SYM
ejpam-4872	64	8	eur	eur	PROPN
ejpam-4872	64	9	.	.	PUNCT
ejpam-4872	65	1	j.	j.	PROPN
ejpam-4872	65	2	pure	pure	PROPN
ejpam-4872	65	3	appl	appl	PROPN
ejpam-4872	65	4	.	.	PROPN
ejpam-4872	65	5	math	math	PROPN
ejpam-4872	65	6	,	,	PUNCT
ejpam-4872	65	7	16	16	NUM
ejpam-4872	65	8	(	(	PUNCT
ejpam-4872	65	9	3	3	NUM
ejpam-4872	65	10	)	)	PUNCT
ejpam-4872	65	11	(	(	PUNCT
ejpam-4872	65	12	2023	2023	NUM
ejpam-4872	65	13	)	)	PUNCT
ejpam-4872	65	14	,	,	PUNCT
ejpam-4872	65	15	1862	1862	NUM
ejpam-4872	65	16	-	-	SYM
ejpam-4872	65	17	1877	1877	NUM
ejpam-4872	65	18	1865	1865	NUM
ejpam-4872	65	19	let	let	VERB
ejpam-4872	65	20	u	u	PRON
ejpam-4872	65	21	be	be	AUX
ejpam-4872	65	22	an	an	DET
ejpam-4872	65	23	initial	initial	ADJ
ejpam-4872	65	24	universe	universe	NOUN
ejpam-4872	65	25	set	set	VERB
ejpam-4872	65	26	and	and	CCONJ
ejpam-4872	65	27	x	x	PART
ejpam-4872	65	28	be	be	AUX
ejpam-4872	65	29	a	a	DET
ejpam-4872	65	30	set	set	NOUN
ejpam-4872	65	31	of	of	ADP
ejpam-4872	65	32	parameters	parameter	NOUN
ejpam-4872	65	33	.	.	PUNCT
ejpam-4872	66	1	for	for	ADP
ejpam-4872	66	2	any	any	DET
ejpam-4872	66	3	subset	subset	NOUN
ejpam-4872	66	4	a	a	PRON
ejpam-4872	66	5	of	of	ADP
ejpam-4872	66	6	x	x	PRON
ejpam-4872	66	7	,	,	PUNCT
ejpam-4872	66	8	a	a	DET
ejpam-4872	66	9	pair	pair	NOUN
ejpam-4872	66	10	(	(	PUNCT
ejpam-4872	66	11	fs	fs	PROPN
ejpam-4872	66	12	,	,	PUNCT
ejpam-4872	66	13	a	a	PRON
ejpam-4872	66	14	)	)	PUNCT
ejpam-4872	66	15	is	be	AUX
ejpam-4872	66	16	called	call	VERB
ejpam-4872	66	17	a	a	DET
ejpam-4872	66	18	soft	soft	ADJ
ejpam-4872	66	19	set	set	NOUN
ejpam-4872	66	20	over	over	ADP
ejpam-4872	66	21	u	u	NOUN
ejpam-4872	66	22	(	(	PUNCT
ejpam-4872	66	23	see	see	VERB
ejpam-4872	66	24	[	[	X
ejpam-4872	66	25	7	7	NUM
ejpam-4872	66	26	,	,	PUNCT
ejpam-4872	66	27	8	8	NUM
ejpam-4872	66	28	]	]	NUM
ejpam-4872	66	29	)	)	PUNCT
ejpam-4872	66	30	,	,	PUNCT
ejpam-4872	66	31	where	where	SCONJ
ejpam-4872	66	32	fs	fs	PRON
ejpam-4872	66	33	is	be	AUX
ejpam-4872	66	34	a	a	DET
ejpam-4872	66	35	mapping	mapping	NOUN
ejpam-4872	66	36	described	describe	VERB
ejpam-4872	66	37	as	as	SCONJ
ejpam-4872	66	38	follows	follow	VERB
ejpam-4872	66	39	:	:	PUNCT
ejpam-4872	66	40	f	f	PROPN
ejpam-4872	66	41	s	s	PART
ejpam-4872	66	42	:	:	PUNCT
ejpam-4872	66	43	a	a	PRON
ejpam-4872	66	44	→	→	PUNCT
ejpam-4872	66	45	2u	2u	NOUN
ejpam-4872	66	46	where	where	SCONJ
ejpam-4872	66	47	2u	2u	PROPN
ejpam-4872	66	48	is	be	AUX
ejpam-4872	66	49	the	the	DET
ejpam-4872	66	50	power	power	NOUN
ejpam-4872	66	51	set	set	NOUN
ejpam-4872	66	52	of	of	ADP
ejpam-4872	66	53	u	u	PROPN
ejpam-4872	66	54	.	.	PUNCT
ejpam-4872	67	1	if	if	SCONJ
ejpam-4872	67	2	a	a	DET
ejpam-4872	67	3	=	=	SYM
ejpam-4872	67	4	x	x	NOUN
ejpam-4872	67	5	,	,	PUNCT
ejpam-4872	67	6	the	the	DET
ejpam-4872	67	7	soft	soft	ADJ
ejpam-4872	67	8	set	set	NOUN
ejpam-4872	67	9	(	(	PUNCT
ejpam-4872	67	10	fs	fs	PROPN
ejpam-4872	67	11	,	,	PUNCT
ejpam-4872	67	12	a	a	PRON
ejpam-4872	67	13	)	)	PUNCT
ejpam-4872	67	14	over	over	ADP
ejpam-4872	67	15	u	u	NOUN
ejpam-4872	67	16	is	be	AUX
ejpam-4872	67	17	simply	simply	ADV
ejpam-4872	67	18	denoted	denote	VERB
ejpam-4872	67	19	by	by	ADP
ejpam-4872	67	20	fs	f	NOUN
ejpam-4872	67	21	only	only	ADV
ejpam-4872	67	22	.	.	PUNCT
ejpam-4872	68	1	a	a	DET
ejpam-4872	68	2	mapping	mapping	NOUN
ejpam-4872	68	3	f̃	f̃	PROPN
ejpam-4872	68	4	:	:	PUNCT
ejpam-4872	68	5	x	x	X
ejpam-4872	68	6	→	→	PUNCT
ejpam-4872	68	7	[	[	X
ejpam-4872	68	8	[	[	X
ejpam-4872	68	9	0	0	NUM
ejpam-4872	68	10	,	,	PUNCT
ejpam-4872	68	11	1	1	NUM
ejpam-4872	68	12	]	]	PUNCT
ejpam-4872	68	13	]	]	PUNCT
ejpam-4872	68	14	is	be	AUX
ejpam-4872	68	15	called	call	VERB
ejpam-4872	68	16	an	an	DET
ejpam-4872	68	17	interval	interval	NOUN
ejpam-4872	68	18	-	-	PUNCT
ejpam-4872	68	19	valued	value	VERB
ejpam-4872	68	20	fuzzy	fuzzy	ADJ
ejpam-4872	68	21	set	set	NOUN
ejpam-4872	68	22	(	(	PUNCT
ejpam-4872	68	23	briefly	briefly	ADV
ejpam-4872	68	24	,	,	PUNCT
ejpam-4872	68	25	an	an	DET
ejpam-4872	68	26	ivf	ivf	NOUN
ejpam-4872	68	27	set	set	NOUN
ejpam-4872	68	28	)	)	PUNCT
ejpam-4872	68	29	in	in	ADP
ejpam-4872	68	30	x	x	X
ejpam-4872	68	31	(	(	PUNCT
ejpam-4872	68	32	see	see	VERB
ejpam-4872	68	33	[	[	X
ejpam-4872	68	34	2	2	NUM
ejpam-4872	68	35	,	,	PUNCT
ejpam-4872	68	36	15	15	NUM
ejpam-4872	68	37	]	]	PUNCT
ejpam-4872	68	38	)	)	PUNCT
ejpam-4872	68	39	where	where	SCONJ
ejpam-4872	68	40	[	[	X
ejpam-4872	68	41	[	[	X
ejpam-4872	68	42	0	0	NUM
ejpam-4872	68	43	,	,	PUNCT
ejpam-4872	68	44	1	1	NUM
ejpam-4872	68	45	]	]	PUNCT
ejpam-4872	68	46	]	]	X
ejpam-4872	68	47	is	be	AUX
ejpam-4872	68	48	the	the	DET
ejpam-4872	68	49	set	set	NOUN
ejpam-4872	68	50	of	of	ADP
ejpam-4872	68	51	all	all	DET
ejpam-4872	68	52	closed	closed	ADJ
ejpam-4872	68	53	subintervals	subinterval	NOUN
ejpam-4872	68	54	of	of	ADP
ejpam-4872	68	55	[	[	X
ejpam-4872	68	56	0	0	NUM
ejpam-4872	68	57	,	,	PUNCT
ejpam-4872	68	58	1	1	NUM
ejpam-4872	68	59	]	]	PUNCT
ejpam-4872	68	60	,	,	PUNCT
ejpam-4872	68	61	and	and	CCONJ
ejpam-4872	68	62	members	member	NOUN
ejpam-4872	68	63	of	of	ADP
ejpam-4872	68	64	[	[	X
ejpam-4872	68	65	[	[	X
ejpam-4872	68	66	0	0	NUM
ejpam-4872	68	67	,	,	PUNCT
ejpam-4872	68	68	1	1	NUM
ejpam-4872	68	69	]	]	PUNCT
ejpam-4872	68	70	]	]	PUNCT
ejpam-4872	68	71	are	be	AUX
ejpam-4872	68	72	called	call	VERB
ejpam-4872	68	73	interval	interval	NOUN
ejpam-4872	68	74	numbers	number	NOUN
ejpam-4872	68	75	and	and	CCONJ
ejpam-4872	68	76	are	be	AUX
ejpam-4872	68	77	denoted	denote	VERB
ejpam-4872	68	78	by	by	ADP
ejpam-4872	68	79	ã	ã	PROPN
ejpam-4872	68	80	,	,	PUNCT
ejpam-4872	68	81	b̃	b̃	PROPN
ejpam-4872	68	82	,	,	PUNCT
ejpam-4872	68	83	c̃	c̃	PROPN
ejpam-4872	68	84	,	,	PUNCT
ejpam-4872	68	85	etc	etc	X
ejpam-4872	68	86	.	.	X
ejpam-4872	68	87	,	,	PUNCT
ejpam-4872	69	1	where	where	SCONJ
ejpam-4872	69	2	ã	ã	PROPN
ejpam-4872	69	3	=	=	PRON
ejpam-4872	70	1	[	[	X
ejpam-4872	70	2	al	al	PROPN
ejpam-4872	70	3	,	,	PUNCT
ejpam-4872	70	4	ar	ar	NOUN
ejpam-4872	70	5	]	]	X
ejpam-4872	70	6	with	with	ADP
ejpam-4872	70	7	0	0	NUM
ejpam-4872	70	8	≤	≤	NUM
ejpam-4872	70	9	al	al	PROPN
ejpam-4872	70	10	≤	≤	PROPN
ejpam-4872	70	11	ar	ar	NOUN
ejpam-4872	70	12	≤	≤	ADV
ejpam-4872	70	13	1	1	NUM
ejpam-4872	70	14	.	.	PUNCT
ejpam-4872	71	1	for	for	ADP
ejpam-4872	71	2	every	every	DET
ejpam-4872	71	3	two	two	NUM
ejpam-4872	71	4	interval	interval	NOUN
ejpam-4872	71	5	numbers	number	NOUN
ejpam-4872	71	6	ã	ã	PROPN
ejpam-4872	71	7	and	and	CCONJ
ejpam-4872	71	8	b̃	b̃	PROPN
ejpam-4872	71	9	,	,	PUNCT
ejpam-4872	71	10	we	we	PRON
ejpam-4872	71	11	define	define	VERB
ejpam-4872	71	12	ã	ã	PROPN
ejpam-4872	71	13	⊴	⊴	ADP
ejpam-4872	71	14	b̃	b̃	PROPN
ejpam-4872	71	15	(	(	PUNCT
ejpam-4872	71	16	or	or	CCONJ
ejpam-4872	71	17	b̃	b̃	PROPN
ejpam-4872	71	18	⊵	⊵	PROPN
ejpam-4872	71	19	ã	ã	PROPN
ejpam-4872	71	20	)	)	PUNCT
ejpam-4872	71	21	⇔	⇔	PROPN
ejpam-4872	71	22	al	al	PROPN
ejpam-4872	71	23	≤	≤	PROPN
ejpam-4872	71	24	bl	bl	PROPN
ejpam-4872	71	25	,	,	PUNCT
ejpam-4872	71	26	ar	ar	VERB
ejpam-4872	71	27	≤	≤	NUM
ejpam-4872	71	28	br	br	NOUN
ejpam-4872	71	29	,	,	PUNCT
ejpam-4872	71	30	(	(	PUNCT
ejpam-4872	71	31	15	15	X
ejpam-4872	71	32	)	)	PUNCT
ejpam-4872	71	33	ã	ã	PROPN
ejpam-4872	71	34	=	=	SYM
ejpam-4872	71	35	b̃	b̃	PROPN
ejpam-4872	71	36	⇔	⇔	PROPN
ejpam-4872	71	37	ã	ã	PROPN
ejpam-4872	71	38	⊴	⊴	ADP
ejpam-4872	71	39	b̃	b̃	PROPN
ejpam-4872	71	40	,	,	PUNCT
ejpam-4872	71	41	b̃	b̃	PROPN
ejpam-4872	71	42	⊴	⊴	ADP
ejpam-4872	71	43	ã	ã	PROPN
ejpam-4872	71	44	,	,	PUNCT
ejpam-4872	71	45	(	(	PUNCT
ejpam-4872	71	46	16	16	NUM
ejpam-4872	71	47	)	)	PUNCT
ejpam-4872	71	48	rmin{ã	rmin{ã	NOUN
ejpam-4872	71	49	,	,	PUNCT
ejpam-4872	71	50	b̃	b̃	PROPN
ejpam-4872	71	51	}	}	PUNCT
ejpam-4872	71	52	=	=	PUNCT
ejpam-4872	72	1	[	[	X
ejpam-4872	72	2	min{al	min{al	ADJ
ejpam-4872	72	3	,	,	PUNCT
ejpam-4872	72	4	bl},min{ar	bl},min{ar	NOUN
ejpam-4872	72	5	,	,	PUNCT
ejpam-4872	72	6	br	br	NOUN
ejpam-4872	72	7	}	}	PUNCT
ejpam-4872	72	8	]	]	PUNCT
ejpam-4872	72	9	.	.	PUNCT
ejpam-4872	73	1	(	(	PUNCT
ejpam-4872	73	2	17	17	NUM
ejpam-4872	73	3	)	)	PUNCT
ejpam-4872	73	4	let	let	VERB
ejpam-4872	73	5	u	u	PRON
ejpam-4872	73	6	be	be	AUX
ejpam-4872	73	7	an	an	DET
ejpam-4872	73	8	initial	initial	ADJ
ejpam-4872	73	9	universe	universe	NOUN
ejpam-4872	73	10	set	set	VERB
ejpam-4872	73	11	and	and	CCONJ
ejpam-4872	73	12	x	x	ADP
ejpam-4872	73	13	a	a	DET
ejpam-4872	73	14	set	set	NOUN
ejpam-4872	73	15	of	of	ADP
ejpam-4872	73	16	parameters	parameter	NOUN
ejpam-4872	73	17	.	.	PUNCT
ejpam-4872	74	1	a	a	DET
ejpam-4872	74	2	triple	triple	ADJ
ejpam-4872	74	3	dokf	dokf	NOUN
ejpam-4872	74	4	:	:	PUNCT
ejpam-4872	74	5	=	=	SYM
ejpam-4872	74	6	(	(	PUNCT
ejpam-4872	74	7	f̊	f̊	X
ejpam-4872	74	8	,	,	PUNCT
ejpam-4872	74	9	fs	fs	PROPN
ejpam-4872	74	10	,	,	PUNCT
ejpam-4872	74	11	f̃	f̃	PROPN
ejpam-4872	74	12	)	)	PUNCT
ejpam-4872	74	13	is	be	AUX
ejpam-4872	74	14	called	call	VERB
ejpam-4872	74	15	a	a	DET
ejpam-4872	74	16	dokdo	dokdo	NOUN
ejpam-4872	74	17	structure	structure	NOUN
ejpam-4872	74	18	in	in	ADP
ejpam-4872	74	19	(	(	PUNCT
ejpam-4872	74	20	u	u	NOUN
ejpam-4872	74	21	,	,	PUNCT
ejpam-4872	74	22	x	x	X
ejpam-4872	74	23	)	)	PUNCT
ejpam-4872	74	24	(	(	PUNCT
ejpam-4872	74	25	see	see	VERB
ejpam-4872	74	26	[	[	X
ejpam-4872	74	27	3	3	NUM
ejpam-4872	74	28	]	]	PUNCT
ejpam-4872	74	29	)	)	PUNCT
ejpam-4872	74	30	if	if	SCONJ
ejpam-4872	74	31	f̊	f̊	NOUN
ejpam-4872	74	32	:	:	PUNCT
ejpam-4872	74	33	x	x	X
ejpam-4872	74	34	→	→	PUNCT
ejpam-4872	74	35	[	[	X
ejpam-4872	74	36	−1	−1	NOUN
ejpam-4872	74	37	,	,	PUNCT
ejpam-4872	74	38	0	0	NUM
ejpam-4872	74	39	]	]	X
ejpam-4872	74	40	×	×	NOUN
ejpam-4872	74	41	[	[	X
ejpam-4872	74	42	0	0	NUM
ejpam-4872	74	43	,	,	PUNCT
ejpam-4872	74	44	1	1	NUM
ejpam-4872	74	45	]	]	PUNCT
ejpam-4872	74	46	is	be	AUX
ejpam-4872	74	47	a	a	DET
ejpam-4872	74	48	bipolar	bipolar	ADJ
ejpam-4872	74	49	fuzzy	fuzzy	ADJ
ejpam-4872	74	50	set	set	NOUN
ejpam-4872	74	51	in	in	ADP
ejpam-4872	74	52	x	x	PROPN
ejpam-4872	74	53	,	,	PUNCT
ejpam-4872	74	54	fs	fs	ADP
ejpam-4872	74	55	:	:	PUNCT
ejpam-4872	74	56	x	x	X
ejpam-4872	74	57	→	→	SYM
ejpam-4872	74	58	2u	2u	PROPN
ejpam-4872	74	59	is	be	AUX
ejpam-4872	74	60	a	a	DET
ejpam-4872	74	61	soft	soft	ADJ
ejpam-4872	74	62	set	set	NOUN
ejpam-4872	74	63	over	over	ADP
ejpam-4872	74	64	u	u	NOUN
ejpam-4872	74	65	and	and	CCONJ
ejpam-4872	74	66	f̃	f̃	PROPN
ejpam-4872	74	67	:	:	PUNCT
ejpam-4872	74	68	x	x	X
ejpam-4872	74	69	→	→	PUNCT
ejpam-4872	74	70	[	[	X
ejpam-4872	74	71	[	[	X
ejpam-4872	74	72	0	0	NUM
ejpam-4872	74	73	,	,	PUNCT
ejpam-4872	74	74	1	1	NUM
ejpam-4872	74	75	]	]	PUNCT
ejpam-4872	74	76	]	]	X
ejpam-4872	74	77	is	be	AUX
ejpam-4872	74	78	an	an	DET
ejpam-4872	74	79	interval	interval	NOUN
ejpam-4872	74	80	-	-	PUNCT
ejpam-4872	74	81	valued	value	VERB
ejpam-4872	74	82	fuzzy	fuzzy	ADJ
ejpam-4872	74	83	set	set	VERB
ejpam-4872	74	84	in	in	ADP
ejpam-4872	74	85	x.	x.	NOUN
ejpam-4872	74	86	the	the	DET
ejpam-4872	74	87	dokdo	dokdo	PROPN
ejpam-4872	74	88	structure	structure	NOUN
ejpam-4872	74	89	dokf	dokf	NOUN
ejpam-4872	74	90	:	:	PUNCT
ejpam-4872	74	91	=	=	SYM
ejpam-4872	74	92	(	(	PUNCT
ejpam-4872	74	93	f̊	f̊	X
ejpam-4872	74	94	,	,	PUNCT
ejpam-4872	74	95	fs	fs	PROPN
ejpam-4872	74	96	,	,	PUNCT
ejpam-4872	74	97	f̃	f̃	PROPN
ejpam-4872	74	98	)	)	PUNCT
ejpam-4872	74	99	in	in	ADP
ejpam-4872	74	100	(	(	PUNCT
ejpam-4872	74	101	u	u	NOUN
ejpam-4872	74	102	,	,	PUNCT
ejpam-4872	74	103	x	x	X
ejpam-4872	74	104	)	)	PUNCT
ejpam-4872	74	105	can	can	AUX
ejpam-4872	74	106	be	be	AUX
ejpam-4872	74	107	represented	represent	VERB
ejpam-4872	74	108	as	as	SCONJ
ejpam-4872	74	109	follows	follow	VERB
ejpam-4872	74	110	:	:	PUNCT
ejpam-4872	74	111	dokf	dokf	NOUN
ejpam-4872	74	112	:	:	PUNCT
ejpam-4872	74	113	=	=	SYM
ejpam-4872	74	114	(	(	PUNCT
ejpam-4872	74	115	f̊	f̊	X
ejpam-4872	74	116	,	,	PUNCT
ejpam-4872	74	117	f	f	PROPN
ejpam-4872	74	118	s	s	PROPN
ejpam-4872	74	119	,	,	PUNCT
ejpam-4872	74	120	f̃	f̃	PROPN
ejpam-4872	74	121	)	)	PUNCT
ejpam-4872	74	122	:	:	PUNCT
ejpam-4872	74	123	x	x	X
ejpam-4872	74	124	→	→	PUNCT
ejpam-4872	74	125	(	(	PUNCT
ejpam-4872	74	126	[	[	X
ejpam-4872	74	127	−1	−1	NOUN
ejpam-4872	74	128	,	,	PUNCT
ejpam-4872	74	129	0]×	0]×	PROPN
ejpam-4872	75	1	[	[	X
ejpam-4872	75	2	0	0	NUM
ejpam-4872	75	3	,	,	PUNCT
ejpam-4872	75	4	1])×	1])×	NOUN
ejpam-4872	75	5	2u	2u	NOUN
ejpam-4872	75	6	×	×	NOUN
ejpam-4872	76	1	[	[	X
ejpam-4872	76	2	[	[	X
ejpam-4872	76	3	0	0	NUM
ejpam-4872	76	4	,	,	PUNCT
ejpam-4872	76	5	1	1	NUM
ejpam-4872	76	6	]	]	PUNCT
ejpam-4872	76	7	]	]	PUNCT
ejpam-4872	76	8	,	,	PUNCT
ejpam-4872	76	9	x	x	SYM
ejpam-4872	76	10	7→	7→	NUM
ejpam-4872	76	11	(	(	PUNCT
ejpam-4872	76	12	f̊(x	f̊(x	NOUN
ejpam-4872	76	13	)	)	PUNCT
ejpam-4872	76	14	,	,	PUNCT
ejpam-4872	76	15	fs(x	fs(x	NOUN
ejpam-4872	76	16	)	)	PUNCT
ejpam-4872	76	17	,	,	PUNCT
ejpam-4872	76	18	f̃(x	f̃(x	NOUN
ejpam-4872	76	19	)	)	PUNCT
ejpam-4872	76	20	)	)	PUNCT
ejpam-4872	77	1	(	(	PUNCT
ejpam-4872	77	2	18	18	NUM
ejpam-4872	77	3	)	)	PUNCT
ejpam-4872	77	4	where	where	SCONJ
ejpam-4872	77	5	f̊(x	f̊(x	NOUN
ejpam-4872	77	6	)	)	PUNCT
ejpam-4872	77	7	=	=	PUNCT
ejpam-4872	77	8	(	(	PUNCT
ejpam-4872	77	9	f̊−(x	f̊−(x	PROPN
ejpam-4872	77	10	)	)	PUNCT
ejpam-4872	77	11	,	,	PUNCT
ejpam-4872	77	12	f̊+(x	f̊+(x	NUM
ejpam-4872	77	13	)	)	PUNCT
ejpam-4872	77	14	)	)	PUNCT
ejpam-4872	77	15	and	and	CCONJ
ejpam-4872	77	16	f̃(x	f̃(x	PROPN
ejpam-4872	77	17	)	)	PUNCT
ejpam-4872	77	18	=	=	PUNCT
ejpam-4872	78	1	[	[	X
ejpam-4872	78	2	f̃l(x	f̃l(x	X
ejpam-4872	78	3	)	)	PUNCT
ejpam-4872	78	4	,	,	PUNCT
ejpam-4872	78	5	f̃r(x	f̃r(x	X
ejpam-4872	78	6	)	)	PUNCT
ejpam-4872	78	7	]	]	PUNCT
ejpam-4872	78	8	.	.	PUNCT
ejpam-4872	79	1	given	give	VERB
ejpam-4872	79	2	a	a	DET
ejpam-4872	79	3	dokdo	dokdo	NOUN
ejpam-4872	79	4	structure	structure	NOUN
ejpam-4872	79	5	dokf	dokf	NOUN
ejpam-4872	79	6	:	:	PUNCT
ejpam-4872	79	7	=	=	SYM
ejpam-4872	79	8	(	(	PUNCT
ejpam-4872	79	9	f̊	f̊	X
ejpam-4872	79	10	,	,	PUNCT
ejpam-4872	79	11	f	f	PROPN
ejpam-4872	79	12	s	s	PROPN
ejpam-4872	79	13	,	,	PUNCT
ejpam-4872	79	14	f̃	f̃	PROPN
ejpam-4872	79	15	)	)	PUNCT
ejpam-4872	79	16	in	in	ADP
ejpam-4872	79	17	a	a	DET
ejpam-4872	79	18	dokdo	dokdo	NOUN
ejpam-4872	79	19	universe	universe	NOUN
ejpam-4872	79	20	(	(	PUNCT
ejpam-4872	79	21	u	u	NOUN
ejpam-4872	79	22	,	,	PUNCT
ejpam-4872	79	23	x	x	X
ejpam-4872	79	24	)	)	PUNCT
ejpam-4872	79	25	,	,	PUNCT
ejpam-4872	79	26	we	we	PRON
ejpam-4872	79	27	consider	consider	VERB
ejpam-4872	79	28	the	the	DET
ejpam-4872	79	29	following	follow	VERB
ejpam-4872	79	30	sets	set	NOUN
ejpam-4872	79	31	:	:	PUNCT
ejpam-4872	79	32	f̊(m	f̊(m	ADJ
ejpam-4872	79	33	,	,	PUNCT
ejpam-4872	79	34	m	m	PROPN
ejpam-4872	79	35	)	)	PUNCT
ejpam-4872	79	36	:	:	PUNCT
ejpam-4872	79	37	=	=	SYM
ejpam-4872	79	38	{	{	PUNCT
ejpam-4872	79	39	x	x	X
ejpam-4872	79	40	(	(	PUNCT
ejpam-4872	79	41	y	y	PROPN
ejpam-4872	79	42	,	,	PUNCT
ejpam-4872	79	43	z	z	NOUN
ejpam-4872	79	44	)	)	PUNCT
ejpam-4872	79	45	∈	∈	PROPN
ejpam-4872	79	46	x	x	X
ejpam-4872	79	47	x×x	x×x	PROPN
ejpam-4872	79	48	∣∣∣	∣∣∣	ADJ
ejpam-4872	79	49	f̊−(x	f̊−(x	NOUN
ejpam-4872	79	50	)	)	PUNCT
ejpam-4872	79	51	≤	≤	NOUN
ejpam-4872	80	1	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	80	2	)	)	PUNCT
ejpam-4872	80	3	,	,	PUNCT
ejpam-4872	80	4	f̊−(z	f̊−(z	NUM
ejpam-4872	80	5	)	)	PUNCT
ejpam-4872	80	6	}	}	PUNCT
ejpam-4872	80	7	f̊+(x	f̊+(x	NUM
ejpam-4872	80	8	)	)	PUNCT
ejpam-4872	80	9	≥	≥	NOUN
ejpam-4872	80	10	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	80	11	)	)	PUNCT
ejpam-4872	80	12	,	,	PUNCT
ejpam-4872	80	13	f̊+(z	f̊+(z	PROPN
ejpam-4872	80	14	)	)	PUNCT
ejpam-4872	80	15	}	}	PUNCT
ejpam-4872	80	16	}	}	PUNCT
ejpam-4872	80	17	and	and	CCONJ
ejpam-4872	80	18	f̊(t−	f̊(t−	PROPN
ejpam-4872	80	19	)	)	PUNCT
ejpam-4872	80	20	:	:	PUNCT
ejpam-4872	81	1	=	=	SYM
ejpam-4872	81	2	{	{	PUNCT
ejpam-4872	81	3	x	x	PUNCT
ejpam-4872	81	4	∈	∈	PROPN
ejpam-4872	81	5	x	x	X
ejpam-4872	81	6	|	|	ADV
ejpam-4872	81	7	f̊−(x	f̊−(x	NOUN
ejpam-4872	81	8	)	)	PUNCT
ejpam-4872	81	9	≤	≤	NOUN
ejpam-4872	82	1	t−	t−	PROPN
ejpam-4872	82	2	}	}	PUNCT
ejpam-4872	82	3	,	,	PUNCT
ejpam-4872	82	4	f̊(t+	f̊(t+	NUM
ejpam-4872	82	5	)	)	PUNCT
ejpam-4872	82	6	:	:	PUNCT
ejpam-4872	82	7	=	=	SYM
ejpam-4872	82	8	{	{	PUNCT
ejpam-4872	82	9	x	x	PUNCT
ejpam-4872	82	10	∈	∈	PROPN
ejpam-4872	82	11	x	x	X
ejpam-4872	82	12	|	|	ADV
ejpam-4872	82	13	f̊+(x	f̊+(x	NUM
ejpam-4872	82	14	)	)	PUNCT
ejpam-4872	82	15	≥	≥	NOUN
ejpam-4872	82	16	t+	t+	VERB
ejpam-4872	82	17	}	}	PUNCT
ejpam-4872	82	18	,	,	PUNCT
ejpam-4872	82	19	f̊(t−	f̊(t−	PROPN
ejpam-4872	82	20	,	,	PUNCT
ejpam-4872	82	21	t+	t+	NOUN
ejpam-4872	82	22	)	)	PUNCT
ejpam-4872	82	23	:	:	PUNCT
ejpam-4872	82	24	=	=	SYM
ejpam-4872	82	25	f̊(t−	f̊(t−	PROPN
ejpam-4872	82	26	)	)	PUNCT
ejpam-4872	82	27	∩	∩	NOUN
ejpam-4872	82	28	f̊(t+	f̊(t+	NUM
ejpam-4872	82	29	)	)	PUNCT
ejpam-4872	82	30	,	,	PUNCT
ejpam-4872	82	31	fs	fs	ADP
ejpam-4872	82	32	α	α	NOUN
ejpam-4872	82	33	:	:	PUNCT
ejpam-4872	82	34	=	=	SYM
ejpam-4872	82	35	{	{	PUNCT
ejpam-4872	82	36	x	x	PUNCT
ejpam-4872	82	37	∈	∈	PROPN
ejpam-4872	82	38	x	x	X
ejpam-4872	82	39	|	|	NOUN
ejpam-4872	82	40	fs(x	fs(x	NOUN
ejpam-4872	82	41	)	)	PUNCT
ejpam-4872	82	42	⊇	⊇	NOUN
ejpam-4872	82	43	α	α	NOUN
ejpam-4872	82	44	}	}	PUNCT
ejpam-4872	82	45	,	,	PUNCT
ejpam-4872	82	46	f̃ã	f̃ã	NOUN
ejpam-4872	82	47	:	:	PUNCT
ejpam-4872	82	48	=	=	SYM
ejpam-4872	82	49	{	{	PUNCT
ejpam-4872	82	50	x	x	PUNCT
ejpam-4872	82	51	∈	∈	PROPN
ejpam-4872	82	52	x	x	X
ejpam-4872	82	53	|	|	ADV
ejpam-4872	82	54	f̃(x	f̃(x	NOUN
ejpam-4872	82	55	)	)	PUNCT
ejpam-4872	82	56	⊵	⊵	PROPN
ejpam-4872	82	57	ã	ã	PROPN
ejpam-4872	82	58	}	}	PUNCT
ejpam-4872	82	59	,	,	PUNCT
ejpam-4872	82	60	where	where	SCONJ
ejpam-4872	82	61	(	(	PUNCT
ejpam-4872	82	62	t−	t−	NOUN
ejpam-4872	82	63	,	,	PUNCT
ejpam-4872	82	64	t+	t+	ADJ
ejpam-4872	82	65	)	)	PUNCT
ejpam-4872	82	66	∈	∈	PROPN
ejpam-4872	83	1	[	[	X
ejpam-4872	83	2	−1	−1	NOUN
ejpam-4872	83	3	,	,	PUNCT
ejpam-4872	83	4	0]×	0]×	PROPN
ejpam-4872	84	1	[	[	X
ejpam-4872	84	2	0	0	NUM
ejpam-4872	84	3	,	,	PUNCT
ejpam-4872	84	4	1	1	NUM
ejpam-4872	84	5	]	]	PUNCT
ejpam-4872	84	6	,	,	PUNCT
ejpam-4872	84	7	α	α	PROPN
ejpam-4872	84	8	∈	∈	PROPN
ejpam-4872	84	9	2u	2u	NOUN
ejpam-4872	84	10	and	and	CCONJ
ejpam-4872	84	11	ã	ã	PROPN
ejpam-4872	84	12	=	=	PROPN
ejpam-4872	85	1	[	[	X
ejpam-4872	85	2	al	al	PROPN
ejpam-4872	85	3	,	,	PUNCT
ejpam-4872	85	4	ar	ar	PROPN
ejpam-4872	85	5	]	]	PUNCT
ejpam-4872	85	6	.	.	PUNCT
ejpam-4872	86	1	s.	s.	PROPN
ejpam-4872	86	2	s.	s.	PROPN
ejpam-4872	86	3	ahn	ahn	PROPN
ejpam-4872	86	4	et	et	PROPN
ejpam-4872	86	5	al	al	PROPN
ejpam-4872	86	6	.	.	PUNCT
ejpam-4872	86	7	/	/	SYM
ejpam-4872	86	8	eur	eur	PROPN
ejpam-4872	86	9	.	.	PUNCT
ejpam-4872	87	1	j.	j.	PROPN
ejpam-4872	87	2	pure	pure	PROPN
ejpam-4872	87	3	appl	appl	PROPN
ejpam-4872	87	4	.	.	PROPN
ejpam-4872	87	5	math	math	PROPN
ejpam-4872	87	6	,	,	PUNCT
ejpam-4872	87	7	16	16	NUM
ejpam-4872	87	8	(	(	PUNCT
ejpam-4872	87	9	3	3	NUM
ejpam-4872	87	10	)	)	PUNCT
ejpam-4872	87	11	(	(	PUNCT
ejpam-4872	87	12	2023	2023	NUM
ejpam-4872	87	13	)	)	PUNCT
ejpam-4872	87	14	,	,	PUNCT
ejpam-4872	87	15	1862	1862	NUM
ejpam-4872	87	16	-	-	SYM
ejpam-4872	87	17	1877	1877	NUM
ejpam-4872	87	18	1866	1866	NUM
ejpam-4872	87	19	3	3	X
ejpam-4872	87	20	.	.	PUNCT
ejpam-4872	88	1	dokdo	dokdo	NOUN
ejpam-4872	88	2	filters	filter	NOUN
ejpam-4872	88	3	let	let	VERB
ejpam-4872	88	4	u	u	PRON
ejpam-4872	88	5	be	be	AUX
ejpam-4872	88	6	an	an	DET
ejpam-4872	88	7	initial	initial	ADJ
ejpam-4872	88	8	universe	universe	NOUN
ejpam-4872	88	9	set	set	VERB
ejpam-4872	88	10	and	and	CCONJ
ejpam-4872	88	11	x	x	ADP
ejpam-4872	88	12	a	a	DET
ejpam-4872	88	13	set	set	NOUN
ejpam-4872	88	14	of	of	ADP
ejpam-4872	88	15	parameters	parameter	NOUN
ejpam-4872	88	16	.	.	PUNCT
ejpam-4872	89	1	we	we	PRON
ejpam-4872	89	2	say	say	VERB
ejpam-4872	89	3	that	that	SCONJ
ejpam-4872	89	4	the	the	DET
ejpam-4872	89	5	pair	pair	NOUN
ejpam-4872	89	6	(	(	PUNCT
ejpam-4872	89	7	u	u	NOUN
ejpam-4872	89	8	,	,	PUNCT
ejpam-4872	89	9	x	x	X
ejpam-4872	89	10	)	)	PUNCT
ejpam-4872	89	11	is	be	AUX
ejpam-4872	89	12	the	the	DET
ejpam-4872	89	13	ssh	ssh	NOUN
ejpam-4872	89	14	-	-	PUNCT
ejpam-4872	89	15	dokdo	dokdo	ADJ
ejpam-4872	89	16	universe	universe	NOUN
ejpam-4872	89	17	if	if	SCONJ
ejpam-4872	89	18	x	x	PRON
ejpam-4872	89	19	:	:	PUNCT
ejpam-4872	89	20	=	=	SYM
ejpam-4872	89	21	(	(	PUNCT
ejpam-4872	89	22	x	x	NOUN
ejpam-4872	89	23	,	,	PUNCT
ejpam-4872	89	24	|	|	ADV
ejpam-4872	89	25	)	)	PUNCT
ejpam-4872	89	26	is	be	AUX
ejpam-4872	89	27	a	a	DET
ejpam-4872	89	28	sheffer	sheffer	NOUN
ejpam-4872	89	29	stroke	stroke	NOUN
ejpam-4872	89	30	hilbert	hilbert	PROPN
ejpam-4872	89	31	algebra	algebra	PROPN
ejpam-4872	89	32	.	.	PUNCT
ejpam-4872	90	1	in	in	ADP
ejpam-4872	90	2	what	what	PRON
ejpam-4872	90	3	follows	follow	VERB
ejpam-4872	90	4	,	,	PUNCT
ejpam-4872	90	5	let	let	VERB
ejpam-4872	90	6	(	(	PUNCT
ejpam-4872	90	7	u	u	NOUN
ejpam-4872	90	8	,	,	PUNCT
ejpam-4872	90	9	x	x	X
ejpam-4872	90	10	)	)	PUNCT
ejpam-4872	90	11	denote	denote	VERB
ejpam-4872	90	12	the	the	DET
ejpam-4872	90	13	ssh	ssh	NOUN
ejpam-4872	90	14	-	-	PUNCT
ejpam-4872	90	15	dokdo	dokdo	NOUN
ejpam-4872	90	16	universe	universe	NOUN
ejpam-4872	90	17	unless	unless	SCONJ
ejpam-4872	90	18	otherwise	otherwise	ADV
ejpam-4872	90	19	specified	specify	VERB
ejpam-4872	90	20	.	.	PUNCT
ejpam-4872	91	1	definition	definition	NOUN
ejpam-4872	91	2	4	4	NUM
ejpam-4872	91	3	.	.	PUNCT
ejpam-4872	92	1	a	a	DET
ejpam-4872	92	2	dokdo	dokdo	NOUN
ejpam-4872	92	3	structure	structure	NOUN
ejpam-4872	92	4	dokf	dokf	NOUN
ejpam-4872	92	5	:	:	PUNCT
ejpam-4872	92	6	=	=	SYM
ejpam-4872	92	7	(	(	PUNCT
ejpam-4872	92	8	f̊	f̊	X
ejpam-4872	92	9	,	,	PUNCT
ejpam-4872	92	10	fs	fs	PROPN
ejpam-4872	92	11	,	,	PUNCT
ejpam-4872	92	12	f̃	f̃	PROPN
ejpam-4872	92	13	)	)	PUNCT
ejpam-4872	92	14	is	be	AUX
ejpam-4872	92	15	called	call	VERB
ejpam-4872	92	16	a	a	DET
ejpam-4872	92	17	dokdo	dokdo	ADJ
ejpam-4872	92	18	filter	filter	NOUN
ejpam-4872	92	19	of	of	ADP
ejpam-4872	92	20	(	(	PUNCT
ejpam-4872	92	21	u	u	NOUN
ejpam-4872	92	22	,	,	PUNCT
ejpam-4872	92	23	x	x	X
ejpam-4872	92	24	)	)	PUNCT
ejpam-4872	92	25	if	if	SCONJ
ejpam-4872	92	26	it	it	PRON
ejpam-4872	92	27	satisfies	satisfy	VERB
ejpam-4872	92	28	:	:	PUNCT
ejpam-4872	92	29	(	(	PUNCT
ejpam-4872	92	30	∀x	∀x	X
ejpam-4872	92	31	∈	∈	PROPN
ejpam-4872	92	32	x	x	NOUN
ejpam-4872	92	33	)	)	PUNCT
ejpam-4872	92	34	(	(	PUNCT
ejpam-4872	92	35	1	1	NUM
ejpam-4872	92	36	(	(	PUNCT
ejpam-4872	92	37	x	x	NOUN
ejpam-4872	92	38	,	,	PUNCT
ejpam-4872	92	39	x	x	NOUN
ejpam-4872	92	40	)	)	PUNCT
ejpam-4872	92	41	∈	∈	PROPN
ejpam-4872	92	42	f̊(m	f̊(m	PROPN
ejpam-4872	92	43	,	,	PUNCT
ejpam-4872	92	44	m	m	NOUN
ejpam-4872	92	45	)	)	PUNCT
ejpam-4872	92	46	fs(1	fs(1	PROPN
ejpam-4872	92	47	)	)	PUNCT
ejpam-4872	92	48	⊇	⊇	PROPN
ejpam-4872	92	49	fs(x	fs(x	PROPN
ejpam-4872	92	50	)	)	PUNCT
ejpam-4872	92	51	,	,	PUNCT
ejpam-4872	92	52	f̃(1	f̃(1	NOUN
ejpam-4872	92	53	)	)	PUNCT
ejpam-4872	92	54	⊵	⊵	PROPN
ejpam-4872	92	55	f̃(x	f̃(x	PROPN
ejpam-4872	92	56	)	)	PUNCT
ejpam-4872	92	57	)	)	PUNCT
ejpam-4872	92	58	,	,	PUNCT
ejpam-4872	92	59	(	(	PUNCT
ejpam-4872	92	60	19	19	NUM
ejpam-4872	92	61	)	)	PUNCT
ejpam-4872	92	62	(	(	PUNCT
ejpam-4872	92	63	∀x	∀x	X
ejpam-4872	92	64	,	,	PUNCT
ejpam-4872	92	65	y	y	PROPN
ejpam-4872	92	66	∈	∈	PROPN
ejpam-4872	92	67	x	x	NOUN
ejpam-4872	92	68	)	)	PUNCT
ejpam-4872	92	69			NOUN
ejpam-4872	92	70	x|(y|y	x|(y|y	PROPN
ejpam-4872	92	71	)	)	PUNCT
ejpam-4872	92	72	(	(	PUNCT
ejpam-4872	92	73	y	y	PROPN
ejpam-4872	92	74	,	,	PUNCT
ejpam-4872	92	75	y	y	NOUN
ejpam-4872	92	76	)	)	PUNCT
ejpam-4872	92	77	∈	∈	PROPN
ejpam-4872	92	78	f̊(m	f̊(m	PROPN
ejpam-4872	92	79	,	,	PUNCT
ejpam-4872	92	80	m	m	NOUN
ejpam-4872	92	81	)	)	PUNCT
ejpam-4872	92	82	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	92	83	)	)	PUNCT
ejpam-4872	92	84	)	)	PUNCT
ejpam-4872	93	1	⊇	⊇	PROPN
ejpam-4872	93	2	f	f	PROPN
ejpam-4872	93	3	s(y	s(y	PROPN
ejpam-4872	93	4	)	)	PUNCT
ejpam-4872	93	5	f̃(x|(y|y	f̃(x|(y|y	ADJ
ejpam-4872	93	6	)	)	PUNCT
ejpam-4872	93	7	)	)	PUNCT
ejpam-4872	93	8	⊵	⊵	ADJ
ejpam-4872	93	9	f̃(y	f̃(y	NOUN
ejpam-4872	93	10	)	)	PUNCT
ejpam-4872	93	11			NOUN
ejpam-4872	93	12	,	,	PUNCT
ejpam-4872	93	13	(	(	PUNCT
ejpam-4872	93	14	20	20	NUM
ejpam-4872	93	15	)	)	PUNCT
ejpam-4872	93	16	(	(	PUNCT
ejpam-4872	93	17	∀x	∀x	X
ejpam-4872	93	18	,	,	PUNCT
ejpam-4872	93	19	y	y	PROPN
ejpam-4872	93	20	,	,	PUNCT
ejpam-4872	93	21	z	z	NOUN
ejpam-4872	93	22	∈	∈	PROPN
ejpam-4872	93	23	x	x	NOUN
ejpam-4872	93	24	)	)	PUNCT
ejpam-4872	93	25			X
ejpam-4872	93	26	(	(	PUNCT
ejpam-4872	93	27	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	93	28	)	)	PUNCT
ejpam-4872	93	29	(	(	PUNCT
ejpam-4872	93	30	y	y	NOUN
ejpam-4872	93	31	,	,	PUNCT
ejpam-4872	93	32	z	z	NOUN
ejpam-4872	93	33	)	)	PUNCT
ejpam-4872	93	34	∈	∈	PROPN
ejpam-4872	93	35	f̊(m	f̊(m	PROPN
ejpam-4872	93	36	,	,	PUNCT
ejpam-4872	93	37	m	m	NOUN
ejpam-4872	93	38	)	)	PUNCT
ejpam-4872	93	39	fs((x|(y|z))|(y|z	fs((x|(y|z))|(y|z	ADJ
ejpam-4872	93	40	)	)	PUNCT
ejpam-4872	93	41	)	)	PUNCT
ejpam-4872	93	42	⊇	⊇	PROPN
ejpam-4872	93	43	f	f	PROPN
ejpam-4872	93	44	s(y	s(y	PROPN
ejpam-4872	93	45	)	)	PUNCT
ejpam-4872	93	46	∩	∩	NOUN
ejpam-4872	93	47	fs(z	fs(z	NUM
ejpam-4872	93	48	)	)	PUNCT
ejpam-4872	93	49	f̃((x|(y|z))|(y|z	f̃((x|(y|z))|(y|z	PROPN
ejpam-4872	93	50	)	)	PUNCT
ejpam-4872	93	51	)	)	PUNCT
ejpam-4872	93	52	⊵	⊵	PROPN
ejpam-4872	93	53	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	93	54	)	)	PUNCT
ejpam-4872	93	55	,	,	PUNCT
ejpam-4872	93	56	f̃(z	f̃(z	PROPN
ejpam-4872	93	57	)	)	PUNCT
ejpam-4872	93	58	}	}	PUNCT
ejpam-4872	93	59			PROPN
ejpam-4872	93	60	.	.	PUNCT
ejpam-4872	94	1	(	(	PUNCT
ejpam-4872	94	2	21	21	NUM
ejpam-4872	94	3	)	)	PUNCT
ejpam-4872	94	4	example	example	NOUN
ejpam-4872	94	5	1	1	NUM
ejpam-4872	94	6	.	.	X
ejpam-4872	94	7	consider	consider	VERB
ejpam-4872	94	8	a	a	DET
ejpam-4872	94	9	set	set	NOUN
ejpam-4872	94	10	x	x	X
ejpam-4872	94	11	=	=	SYM
ejpam-4872	94	12	{	{	PUNCT
ejpam-4872	94	13	0	0	NUM
ejpam-4872	94	14	,	,	PUNCT
ejpam-4872	94	15	1	1	NUM
ejpam-4872	94	16	,	,	PUNCT
ejpam-4872	94	17	2	2	NUM
ejpam-4872	94	18	,	,	PUNCT
ejpam-4872	94	19	3	3	NUM
ejpam-4872	94	20	,	,	PUNCT
ejpam-4872	94	21	4	4	NUM
ejpam-4872	94	22	,	,	PUNCT
ejpam-4872	94	23	5	5	NUM
ejpam-4872	94	24	,	,	PUNCT
ejpam-4872	94	25	6	6	NUM
ejpam-4872	94	26	,	,	PUNCT
ejpam-4872	94	27	7	7	NUM
ejpam-4872	94	28	}	}	PUNCT
ejpam-4872	94	29	.	.	PUNCT
ejpam-4872	95	1	the	the	DET
ejpam-4872	95	2	hasse	hasse	PROPN
ejpam-4872	95	3	diagram	diagram	NOUN
ejpam-4872	95	4	and	and	CCONJ
ejpam-4872	95	5	the	the	DET
ejpam-4872	95	6	sheffer	sheffer	NOUN
ejpam-4872	95	7	stroke	stroke	NOUN
ejpam-4872	95	8	“	"	PUNCT
ejpam-4872	95	9	|	|	ADV
ejpam-4872	95	10	”	"	PUNCT
ejpam-4872	95	11	on	on	ADP
ejpam-4872	95	12	x	x	PART
ejpam-4872	95	13	are	be	AUX
ejpam-4872	95	14	given	give	VERB
ejpam-4872	95	15	by	by	ADP
ejpam-4872	95	16	figure	figure	NOUN
ejpam-4872	95	17	1	1	NUM
ejpam-4872	95	18	and	and	CCONJ
ejpam-4872	95	19	table	table	NOUN
ejpam-4872	95	20	2	2	NUM
ejpam-4872	95	21	,	,	PUNCT
ejpam-4872	95	22	respectively	respectively	ADV
ejpam-4872	95	23	.	.	PUNCT
ejpam-4872	96	1	figure	figure	NOUN
ejpam-4872	96	2	1	1	NUM
ejpam-4872	96	3	:	:	PUNCT
ejpam-4872	96	4	hasse	hasse	NOUN
ejpam-4872	96	5	diagram	diagram	NOUN
ejpam-4872	96	6	r	r	NOUN
ejpam-4872	96	7	r	r	NOUN
ejpam-4872	96	8	r	r	NOUN
ejpam-4872	96	9	r	r	NOUN
ejpam-4872	96	10	r	r	NOUN
ejpam-4872	96	11	r	r	NOUN
ejpam-4872	96	12	r	r	NOUN
ejpam-4872	96	13	r	r	NOUN
ejpam-4872	96	14	0	0	NUM
ejpam-4872	96	15	2	2	NUM
ejpam-4872	96	16	5	5	NUM
ejpam-4872	96	17	3	3	NUM
ejpam-4872	96	18	6	6	NUM
ejpam-4872	96	19	4	4	NUM
ejpam-4872	96	20	7	7	NUM
ejpam-4872	96	21	1	1	NUM
ejpam-4872	96	22	�	�	PROPN
ejpam-4872	96	23	�	�	PROPN
ejpam-4872	96	24	�	�	PROPN
ejpam-4872	96	25	�	�	PROPN
ejpam-4872	96	26	�	�	PROPN
ejpam-4872	96	27	hh	hh	PROPN
ejpam-4872	97	1	hhh	hhh	PROPN
ejpam-4872	97	2	�	�	PROPN
ejpam-4872	97	3	�	�	PROPN
ejpam-4872	97	4	�	�	PROPN
ejpam-4872	97	5	�	�	PROPN
ejpam-4872	97	6	�	�	PROPN
ejpam-4872	97	7	hhh	hhh	PROPN
ejpam-4872	97	8	hh	hh	PROPN
ejpam-4872	97	9	�	�	PROPN
ejpam-4872	97	10	�	�	PROPN
ejpam-4872	97	11	�	�	PROPN
ejpam-4872	97	12	�	�	PROPN
ejpam-4872	97	13	�	�	PROPN
ejpam-4872	97	14	�	�	PROPN
ejpam-4872	97	15	�	�	PROPN
ejpam-4872	97	16	�	�	PROPN
ejpam-4872	97	17	�	�	PROPN
ejpam-4872	97	18	�	�	PROPN
ejpam-4872	97	19	hhh	hhh	PROPN
ejpam-4872	97	20	hh	hh	PROPN
ejpam-4872	97	21	h	h	NOUN
ejpam-4872	97	22	hhh	hhh	INTJ
ejpam-4872	97	23	h	h	NOUN
ejpam-4872	97	24	then	then	ADV
ejpam-4872	97	25	x	x	X
ejpam-4872	97	26	:	:	PUNCT
ejpam-4872	97	27	=	=	SYM
ejpam-4872	97	28	(	(	PUNCT
ejpam-4872	97	29	x	x	NOUN
ejpam-4872	97	30	,	,	PUNCT
ejpam-4872	97	31	|	|	ADV
ejpam-4872	97	32	)	)	PUNCT
ejpam-4872	97	33	is	be	AUX
ejpam-4872	97	34	a	a	DET
ejpam-4872	97	35	sheffer	sheffer	NOUN
ejpam-4872	97	36	stroke	stroke	NOUN
ejpam-4872	97	37	hilbert	hilbert	PROPN
ejpam-4872	97	38	algebra	algebra	PROPN
ejpam-4872	97	39	(	(	PUNCT
ejpam-4872	97	40	see	see	VERB
ejpam-4872	97	41	[	[	X
ejpam-4872	97	42	12	12	NUM
ejpam-4872	97	43	]	]	PUNCT
ejpam-4872	97	44	)	)	PUNCT
ejpam-4872	97	45	.	.	PUNCT
ejpam-4872	98	1	let	let	VERB
ejpam-4872	98	2	dokf	dokf	VERB
ejpam-4872	98	3	:	:	PUNCT
ejpam-4872	98	4	=	=	SYM
ejpam-4872	98	5	(	(	PUNCT
ejpam-4872	98	6	f̊	f̊	X
ejpam-4872	98	7	,	,	PUNCT
ejpam-4872	98	8	fs	fs	PROPN
ejpam-4872	98	9	,	,	PUNCT
ejpam-4872	98	10	f̃	f̃	PROPN
ejpam-4872	98	11	)	)	PUNCT
ejpam-4872	98	12	be	be	VERB
ejpam-4872	98	13	a	a	DET
ejpam-4872	98	14	dokdo	dokdo	NOUN
ejpam-4872	98	15	structure	structure	NOUN
ejpam-4872	98	16	in	in	ADP
ejpam-4872	98	17	(	(	PUNCT
ejpam-4872	98	18	x	x	X
ejpam-4872	98	19	,	,	PUNCT
ejpam-4872	98	20	u	u	NOUN
ejpam-4872	98	21	=	=	PROPN
ejpam-4872	98	22	z	z	PROPN
ejpam-4872	98	23	)	)	PUNCT
ejpam-4872	98	24	which	which	PRON
ejpam-4872	98	25	is	be	AUX
ejpam-4872	98	26	given	give	VERB
ejpam-4872	98	27	by	by	ADP
ejpam-4872	98	28	table	table	NOUN
ejpam-4872	98	29	3	3	NUM
ejpam-4872	98	30	.	.	PUNCT
ejpam-4872	99	1	it	it	PRON
ejpam-4872	99	2	is	be	AUX
ejpam-4872	99	3	routine	routine	ADJ
ejpam-4872	99	4	to	to	PART
ejpam-4872	99	5	verify	verify	VERB
ejpam-4872	99	6	that	that	DET
ejpam-4872	99	7	dokf	dokf	NOUN
ejpam-4872	99	8	:	:	PUNCT
ejpam-4872	99	9	=	=	SYM
ejpam-4872	99	10	(	(	PUNCT
ejpam-4872	99	11	f̊	f̊	X
ejpam-4872	99	12	,	,	PUNCT
ejpam-4872	99	13	f	f	PROPN
ejpam-4872	99	14	s	s	PROPN
ejpam-4872	99	15	,	,	PUNCT
ejpam-4872	99	16	f̃	f̃	PROPN
ejpam-4872	99	17	)	)	PUNCT
ejpam-4872	99	18	is	be	AUX
ejpam-4872	99	19	a	a	DET
ejpam-4872	99	20	dokdo	dokdo	ADJ
ejpam-4872	99	21	filter	filter	NOUN
ejpam-4872	99	22	of	of	ADP
ejpam-4872	99	23	(	(	PUNCT
ejpam-4872	99	24	u	u	NOUN
ejpam-4872	99	25	=	=	PROPN
ejpam-4872	99	26	z	z	PROPN
ejpam-4872	99	27	,	,	PUNCT
ejpam-4872	99	28	x	x	PROPN
ejpam-4872	99	29	)	)	PUNCT
ejpam-4872	99	30	.	.	PUNCT
ejpam-4872	100	1	proposition	proposition	NOUN
ejpam-4872	100	2	2	2	NUM
ejpam-4872	100	3	.	.	PUNCT
ejpam-4872	101	1	every	every	DET
ejpam-4872	101	2	dokdo	dokdo	NOUN
ejpam-4872	101	3	filter	filter	NOUN
ejpam-4872	101	4	dokf	dokf	NOUN
ejpam-4872	101	5	:	:	PUNCT
ejpam-4872	101	6	=	=	SYM
ejpam-4872	101	7	(	(	PUNCT
ejpam-4872	101	8	f̊	f̊	X
ejpam-4872	101	9	,	,	PUNCT
ejpam-4872	101	10	f	f	PROPN
ejpam-4872	101	11	s	s	PROPN
ejpam-4872	101	12	,	,	PUNCT
ejpam-4872	101	13	f̃	f̃	PROPN
ejpam-4872	101	14	)	)	PUNCT
ejpam-4872	101	15	of	of	ADP
ejpam-4872	101	16	(	(	PUNCT
ejpam-4872	101	17	u	u	NOUN
ejpam-4872	101	18	,	,	PUNCT
ejpam-4872	101	19	x	x	X
ejpam-4872	101	20	)	)	PUNCT
ejpam-4872	101	21	satisfies	satisfie	NOUN
ejpam-4872	101	22	:	:	PUNCT
ejpam-4872	101	23	(	(	PUNCT
ejpam-4872	101	24	∀x	∀x	X
ejpam-4872	101	25	,	,	PUNCT
ejpam-4872	101	26	y	y	PROPN
ejpam-4872	101	27	∈	∈	PROPN
ejpam-4872	101	28	x	x	NOUN
ejpam-4872	101	29	)	)	PUNCT
ejpam-4872	101	30			X
ejpam-4872	101	31	(	(	PUNCT
ejpam-4872	101	32	x|(y|y))|(y|y	x|(y|y))|(y|y	PROPN
ejpam-4872	101	33	)	)	PUNCT
ejpam-4872	101	34	(	(	PUNCT
ejpam-4872	101	35	x	x	X
ejpam-4872	101	36	,	,	PUNCT
ejpam-4872	101	37	x	x	NOUN
ejpam-4872	101	38	)	)	PUNCT
ejpam-4872	101	39	∈	∈	PROPN
ejpam-4872	101	40	f̊(m	f̊(m	PROPN
ejpam-4872	101	41	,	,	PUNCT
ejpam-4872	101	42	m	m	NOUN
ejpam-4872	101	43	)	)	PUNCT
ejpam-4872	101	44	fs((x|(y|y))|(y|y	fs((x|(y|y))|(y|y	NUM
ejpam-4872	101	45	)	)	PUNCT
ejpam-4872	101	46	)	)	PUNCT
ejpam-4872	101	47	⊇	⊇	PROPN
ejpam-4872	101	48	f	f	PROPN
ejpam-4872	101	49	s(x	s(x	PROPN
ejpam-4872	101	50	)	)	PUNCT
ejpam-4872	101	51	f̃((x|(y|y))|(y|y	f̃((x|(y|y))|(y|y	NUM
ejpam-4872	101	52	)	)	PUNCT
ejpam-4872	101	53	)	)	PUNCT
ejpam-4872	101	54	⊵	⊵	PROPN
ejpam-4872	101	55	f̃(x	f̃(x	PROPN
ejpam-4872	101	56	)	)	PUNCT
ejpam-4872	101	57			NOUN
ejpam-4872	101	58	,	,	PUNCT
ejpam-4872	101	59	(	(	PUNCT
ejpam-4872	101	60	22	22	NUM
ejpam-4872	101	61	)	)	PUNCT
ejpam-4872	101	62	(	(	PUNCT
ejpam-4872	101	63	∀x	∀x	X
ejpam-4872	101	64	,	,	PUNCT
ejpam-4872	101	65	y	y	PROPN
ejpam-4872	101	66	∈	∈	PROPN
ejpam-4872	101	67	x	x	NOUN
ejpam-4872	101	68	)	)	PUNCT
ejpam-4872	101	69			NOUN
ejpam-4872	101	70	x	x	PUNCT
ejpam-4872	101	71	≤x	≤x	PROPN
ejpam-4872	101	72	y	y	PROPN
ejpam-4872	101	73	⇒	⇒	VERB
ejpam-4872	101	74			PROPN
ejpam-4872	101	75	y	y	PROPN
ejpam-4872	101	76	(	(	PUNCT
ejpam-4872	101	77	x	x	X
ejpam-4872	101	78	,	,	PUNCT
ejpam-4872	101	79	x	x	NOUN
ejpam-4872	101	80	)	)	PUNCT
ejpam-4872	101	81	∈	∈	PROPN
ejpam-4872	101	82	f̊(m	f̊(m	PROPN
ejpam-4872	101	83	,	,	PUNCT
ejpam-4872	101	84	m	m	NOUN
ejpam-4872	101	85	)	)	PUNCT
ejpam-4872	101	86	fs(x	fs(x	NOUN
ejpam-4872	101	87	)	)	PUNCT
ejpam-4872	101	88	⊆	⊆	NUM
ejpam-4872	101	89	fs(y	fs(y	ADJ
ejpam-4872	101	90	)	)	PUNCT
ejpam-4872	101	91	f̃(x	f̃(x	NOUN
ejpam-4872	101	92	)	)	PUNCT
ejpam-4872	101	93	⊴	⊴	ADP
ejpam-4872	101	94	f̃(y	f̃(y	ADJ
ejpam-4872	101	95	)	)	PUNCT
ejpam-4872	101	96			PROPN
ejpam-4872	101	97	.	.	PUNCT
ejpam-4872	102	1	(	(	PUNCT
ejpam-4872	102	2	23	23	NUM
ejpam-4872	102	3	)	)	PUNCT
ejpam-4872	102	4	s.	s.	PROPN
ejpam-4872	102	5	s.	s.	PROPN
ejpam-4872	102	6	ahn	ahn	PROPN
ejpam-4872	102	7	et	et	PROPN
ejpam-4872	102	8	al	al	PROPN
ejpam-4872	102	9	.	.	PUNCT
ejpam-4872	102	10	/	/	SYM
ejpam-4872	102	11	eur	eur	PROPN
ejpam-4872	102	12	.	.	PUNCT
ejpam-4872	103	1	j.	j.	PROPN
ejpam-4872	103	2	pure	pure	PROPN
ejpam-4872	103	3	appl	appl	PROPN
ejpam-4872	103	4	.	.	PROPN
ejpam-4872	103	5	math	math	PROPN
ejpam-4872	103	6	,	,	PUNCT
ejpam-4872	103	7	16	16	NUM
ejpam-4872	103	8	(	(	PUNCT
ejpam-4872	103	9	3	3	NUM
ejpam-4872	103	10	)	)	PUNCT
ejpam-4872	103	11	(	(	PUNCT
ejpam-4872	103	12	2023	2023	NUM
ejpam-4872	103	13	)	)	PUNCT
ejpam-4872	103	14	,	,	PUNCT
ejpam-4872	103	15	1862	1862	NUM
ejpam-4872	103	16	-	-	SYM
ejpam-4872	103	17	1877	1877	NUM
ejpam-4872	103	18	1867	1867	NUM
ejpam-4872	103	19	table	table	NOUN
ejpam-4872	103	20	2	2	NUM
ejpam-4872	103	21	:	:	PUNCT
ejpam-4872	103	22	cayley	cayley	ADJ
ejpam-4872	103	23	table	table	NOUN
ejpam-4872	103	24	for	for	ADP
ejpam-4872	103	25	the	the	DET
ejpam-4872	103	26	sheffer	sheffer	NOUN
ejpam-4872	103	27	stroke	stroke	NOUN
ejpam-4872	103	28	“	"	PUNCT
ejpam-4872	103	29	|	|	ADV
ejpam-4872	103	30	”	"	PUNCT
ejpam-4872	103	31	|	|	ADV
ejpam-4872	103	32	0	0	NUM
ejpam-4872	103	33	2	2	NUM
ejpam-4872	103	34	3	3	NUM
ejpam-4872	103	35	4	4	NUM
ejpam-4872	103	36	5	5	NUM
ejpam-4872	103	37	6	6	NUM
ejpam-4872	103	38	7	7	NUM
ejpam-4872	103	39	1	1	NUM
ejpam-4872	103	40	0	0	NUM
ejpam-4872	103	41	1	1	NUM
ejpam-4872	103	42	1	1	NUM
ejpam-4872	103	43	1	1	NUM
ejpam-4872	103	44	1	1	NUM
ejpam-4872	103	45	1	1	NUM
ejpam-4872	103	46	1	1	NUM
ejpam-4872	103	47	1	1	NUM
ejpam-4872	103	48	1	1	NUM
ejpam-4872	103	49	2	2	NUM
ejpam-4872	103	50	1	1	NUM
ejpam-4872	103	51	7	7	NUM
ejpam-4872	103	52	1	1	NUM
ejpam-4872	103	53	1	1	NUM
ejpam-4872	103	54	7	7	NUM
ejpam-4872	103	55	7	7	NUM
ejpam-4872	103	56	1	1	NUM
ejpam-4872	103	57	7	7	NUM
ejpam-4872	103	58	3	3	NUM
ejpam-4872	103	59	1	1	NUM
ejpam-4872	103	60	1	1	NUM
ejpam-4872	103	61	6	6	NUM
ejpam-4872	103	62	1	1	NUM
ejpam-4872	103	63	6	6	NUM
ejpam-4872	103	64	1	1	NUM
ejpam-4872	103	65	6	6	NUM
ejpam-4872	103	66	6	6	NUM
ejpam-4872	103	67	4	4	NUM
ejpam-4872	103	68	1	1	NUM
ejpam-4872	103	69	1	1	NUM
ejpam-4872	103	70	1	1	NUM
ejpam-4872	103	71	5	5	NUM
ejpam-4872	103	72	1	1	NUM
ejpam-4872	103	73	5	5	NUM
ejpam-4872	103	74	5	5	NUM
ejpam-4872	103	75	5	5	NUM
ejpam-4872	103	76	5	5	NUM
ejpam-4872	103	77	1	1	NUM
ejpam-4872	103	78	7	7	NUM
ejpam-4872	103	79	6	6	NUM
ejpam-4872	103	80	1	1	NUM
ejpam-4872	103	81	4	4	NUM
ejpam-4872	103	82	7	7	NUM
ejpam-4872	103	83	6	6	NUM
ejpam-4872	103	84	4	4	NUM
ejpam-4872	103	85	6	6	NUM
ejpam-4872	103	86	1	1	NUM
ejpam-4872	103	87	7	7	NUM
ejpam-4872	103	88	1	1	NUM
ejpam-4872	103	89	5	5	NUM
ejpam-4872	103	90	7	7	NUM
ejpam-4872	103	91	3	3	NUM
ejpam-4872	103	92	5	5	NUM
ejpam-4872	103	93	3	3	NUM
ejpam-4872	103	94	7	7	NUM
ejpam-4872	103	95	1	1	NUM
ejpam-4872	103	96	1	1	NUM
ejpam-4872	103	97	6	6	NUM
ejpam-4872	103	98	5	5	NUM
ejpam-4872	103	99	6	6	NUM
ejpam-4872	103	100	5	5	NUM
ejpam-4872	103	101	2	2	NUM
ejpam-4872	103	102	2	2	NUM
ejpam-4872	103	103	1	1	NUM
ejpam-4872	103	104	1	1	NUM
ejpam-4872	103	105	7	7	NUM
ejpam-4872	103	106	6	6	NUM
ejpam-4872	103	107	5	5	NUM
ejpam-4872	103	108	4	4	NUM
ejpam-4872	103	109	3	3	NUM
ejpam-4872	103	110	2	2	NUM
ejpam-4872	103	111	0	0	NUM
ejpam-4872	103	112	table	table	NOUN
ejpam-4872	103	113	3	3	NUM
ejpam-4872	103	114	:	:	PUNCT
ejpam-4872	103	115	tabular	tabular	PROPN
ejpam-4872	103	116	representation	representation	NOUN
ejpam-4872	103	117	of	of	ADP
ejpam-4872	103	118	dokf	dokf	NOUN
ejpam-4872	103	119	:	:	PUNCT
ejpam-4872	103	120	=	=	SYM
ejpam-4872	103	121	(	(	PUNCT
ejpam-4872	103	122	f̊	f̊	X
ejpam-4872	103	123	,	,	PUNCT
ejpam-4872	103	124	fs	fs	PROPN
ejpam-4872	103	125	,	,	PUNCT
ejpam-4872	103	126	f̃	f̃	PROPN
ejpam-4872	103	127	)	)	PUNCT
ejpam-4872	103	128	x	x	PUNCT
ejpam-4872	103	129	f̊(x	f̊(x	NOUN
ejpam-4872	103	130	)	)	PUNCT
ejpam-4872	103	131	fs(x	fs(x	NOUN
ejpam-4872	103	132	)	)	PUNCT
ejpam-4872	103	133	f̃(x	f̃(x	NOUN
ejpam-4872	103	134	)	)	PUNCT
ejpam-4872	103	135	0	0	NUM
ejpam-4872	104	1	(	(	PUNCT
ejpam-4872	104	2	−0.41	−0.41	NOUN
ejpam-4872	104	3	,	,	PUNCT
ejpam-4872	104	4	0.48	0.48	NUM
ejpam-4872	104	5	)	)	PUNCT
ejpam-4872	104	6	16n	16n	NOUN
ejpam-4872	105	1	[	[	X
ejpam-4872	105	2	0.28	0.28	NUM
ejpam-4872	105	3	,	,	PUNCT
ejpam-4872	105	4	0.65	0.65	NUM
ejpam-4872	105	5	]	]	SYM
ejpam-4872	105	6	2	2	NUM
ejpam-4872	105	7	(	(	PUNCT
ejpam-4872	105	8	−0.55	−0.55	NOUN
ejpam-4872	105	9	,	,	PUNCT
ejpam-4872	105	10	0.67	0.67	NUM
ejpam-4872	105	11	)	)	PUNCT
ejpam-4872	105	12	16n	16n	NOUN
ejpam-4872	106	1	[	[	X
ejpam-4872	106	2	0.28	0.28	NUM
ejpam-4872	106	3	,	,	PUNCT
ejpam-4872	106	4	0.65	0.65	NUM
ejpam-4872	106	5	]	]	SYM
ejpam-4872	106	6	3	3	NUM
ejpam-4872	106	7	(	(	PUNCT
ejpam-4872	106	8	−0.41	−0.41	NOUN
ejpam-4872	106	9	,	,	PUNCT
ejpam-4872	106	10	0.48	0.48	NUM
ejpam-4872	106	11	)	)	PUNCT
ejpam-4872	106	12	8n	8n	NOUN
ejpam-4872	107	1	[	[	X
ejpam-4872	107	2	0.28	0.28	NUM
ejpam-4872	107	3	,	,	PUNCT
ejpam-4872	107	4	0.65	0.65	NUM
ejpam-4872	107	5	]	]	SYM
ejpam-4872	107	6	4	4	NUM
ejpam-4872	107	7	(	(	PUNCT
ejpam-4872	107	8	−0.41	−0.41	NOUN
ejpam-4872	107	9	,	,	PUNCT
ejpam-4872	107	10	0.48	0.48	NUM
ejpam-4872	107	11	)	)	PUNCT
ejpam-4872	107	12	16n	16n	NOUN
ejpam-4872	108	1	[	[	X
ejpam-4872	108	2	0.32	0.32	NUM
ejpam-4872	108	3	,	,	PUNCT
ejpam-4872	108	4	0.73	0.73	NUM
ejpam-4872	108	5	]	]	SYM
ejpam-4872	108	6	5	5	NUM
ejpam-4872	108	7	(	(	PUNCT
ejpam-4872	108	8	−0.63	−0.63	INTJ
ejpam-4872	108	9	,	,	PUNCT
ejpam-4872	108	10	0.78	0.78	NUM
ejpam-4872	108	11	)	)	PUNCT
ejpam-4872	108	12	8n	8n	NOUN
ejpam-4872	109	1	[	[	X
ejpam-4872	109	2	0.28	0.28	NUM
ejpam-4872	109	3	,	,	PUNCT
ejpam-4872	109	4	0.65	0.65	NUM
ejpam-4872	109	5	]	]	SYM
ejpam-4872	109	6	6	6	NUM
ejpam-4872	109	7	(	(	PUNCT
ejpam-4872	109	8	−0.55	−0.55	NOUN
ejpam-4872	109	9	,	,	PUNCT
ejpam-4872	109	10	0.67	0.67	NUM
ejpam-4872	109	11	)	)	PUNCT
ejpam-4872	109	12	16n	16n	NOUN
ejpam-4872	110	1	[	[	X
ejpam-4872	110	2	0.38	0.38	NUM
ejpam-4872	110	3	,	,	PUNCT
ejpam-4872	110	4	0.76	0.76	NUM
ejpam-4872	110	5	]	]	SYM
ejpam-4872	110	6	7	7	NUM
ejpam-4872	110	7	(	(	PUNCT
ejpam-4872	110	8	−0.41	−0.41	NOUN
ejpam-4872	110	9	,	,	PUNCT
ejpam-4872	110	10	0.48	0.48	NUM
ejpam-4872	110	11	)	)	PUNCT
ejpam-4872	110	12	4n	4n	NOUN
ejpam-4872	111	1	[	[	X
ejpam-4872	111	2	0.32	0.32	NUM
ejpam-4872	111	3	,	,	PUNCT
ejpam-4872	111	4	0.73	0.73	NUM
ejpam-4872	111	5	]	]	SYM
ejpam-4872	111	6	1	1	NUM
ejpam-4872	111	7	(	(	PUNCT
ejpam-4872	111	8	−0.71	−0.71	ADV
ejpam-4872	111	9	,	,	PUNCT
ejpam-4872	111	10	0.82	0.82	NUM
ejpam-4872	111	11	)	)	PUNCT
ejpam-4872	111	12	2n	2n	NUM
ejpam-4872	112	1	[	[	X
ejpam-4872	112	2	0.42	0.42	NUM
ejpam-4872	112	3	,	,	PUNCT
ejpam-4872	112	4	0.91	0.91	NUM
ejpam-4872	112	5	]	]	PUNCT
ejpam-4872	112	6	proof	proof	NOUN
ejpam-4872	112	7	.	.	PUNCT
ejpam-4872	113	1	let	let	VERB
ejpam-4872	113	2	dokf	dokf	VERB
ejpam-4872	113	3	:	:	PUNCT
ejpam-4872	113	4	=	=	SYM
ejpam-4872	113	5	(	(	PUNCT
ejpam-4872	113	6	f̊	f̊	X
ejpam-4872	113	7	,	,	PUNCT
ejpam-4872	113	8	fs	fs	PROPN
ejpam-4872	113	9	,	,	PUNCT
ejpam-4872	113	10	f̃	f̃	PROPN
ejpam-4872	113	11	)	)	PUNCT
ejpam-4872	113	12	be	be	VERB
ejpam-4872	113	13	a	a	DET
ejpam-4872	113	14	dokdo	dokdo	NOUN
ejpam-4872	113	15	filter	filter	NOUN
ejpam-4872	113	16	of	of	ADP
ejpam-4872	113	17	(	(	PUNCT
ejpam-4872	113	18	u	u	NOUN
ejpam-4872	113	19	,	,	PUNCT
ejpam-4872	113	20	x	x	PROPN
ejpam-4872	113	21	)	)	PUNCT
ejpam-4872	113	22	.	.	PUNCT
ejpam-4872	114	1	then	then	ADV
ejpam-4872	114	2	f̊−((x|(y|y))|(y|y	f̊−((x|(y|y))|(y|y	ADJ
ejpam-4872	114	3	)	)	PUNCT
ejpam-4872	114	4	)	)	PUNCT
ejpam-4872	115	1	=	=	SYM
ejpam-4872	115	2	f̊−((y|(x|x))|(x|x	f̊−((y|(x|x))|(x|x	X
ejpam-4872	115	3	)	)	PUNCT
ejpam-4872	115	4	)	)	PUNCT
ejpam-4872	116	1	≤	≤	PUNCT
ejpam-4872	117	1	max{f̊−(x	max{f̊−(x	PROPN
ejpam-4872	117	2	)	)	PUNCT
ejpam-4872	117	3	,	,	PUNCT
ejpam-4872	117	4	f̊−(x	f̊−(x	NOUN
ejpam-4872	117	5	)	)	PUNCT
ejpam-4872	117	6	}	}	PUNCT
ejpam-4872	117	7	=	=	SYM
ejpam-4872	117	8	f̊−(x	f̊−(x	NOUN
ejpam-4872	117	9	)	)	PUNCT
ejpam-4872	117	10	,	,	PUNCT
ejpam-4872	117	11	and	and	CCONJ
ejpam-4872	117	12	f̊+((x|(y|y))|(y|y	f̊+((x|(y|y))|(y|y	ADJ
ejpam-4872	117	13	)	)	PUNCT
ejpam-4872	117	14	)	)	PUNCT
ejpam-4872	118	1	=	=	PUNCT
ejpam-4872	118	2	f̊+((y|(x|x))|(x|x	f̊+((y|(x|x))|(x|x	PROPN
ejpam-4872	118	3	)	)	PUNCT
ejpam-4872	118	4	)	)	PUNCT
ejpam-4872	118	5	≥	≥	X
ejpam-4872	118	6	min{f̊+(x	min{f̊+(x	PROPN
ejpam-4872	118	7	)	)	PUNCT
ejpam-4872	118	8	,	,	PUNCT
ejpam-4872	118	9	f̊+(x	f̊+(x	NUM
ejpam-4872	118	10	)	)	PUNCT
ejpam-4872	118	11	}	}	PUNCT
ejpam-4872	118	12	=	=	SYM
ejpam-4872	118	13	f̊+(x	f̊+(x	X
ejpam-4872	118	14	)	)	PUNCT
ejpam-4872	118	15	by	by	ADP
ejpam-4872	118	16	(	(	PUNCT
ejpam-4872	118	17	6	6	NUM
ejpam-4872	118	18	)	)	PUNCT
ejpam-4872	118	19	and	and	CCONJ
ejpam-4872	118	20	(	(	PUNCT
ejpam-4872	118	21	21	21	NUM
ejpam-4872	118	22	)	)	PUNCT
ejpam-4872	118	23	,	,	PUNCT
ejpam-4872	118	24	that	that	ADV
ejpam-4872	118	25	is	is	ADV
ejpam-4872	118	26	,	,	PUNCT
ejpam-4872	118	27	(	(	PUNCT
ejpam-4872	118	28	x|(y|y))|(y|y	x|(y|y))|(y|y	PROPN
ejpam-4872	118	29	)	)	PUNCT
ejpam-4872	118	30	(	(	PUNCT
ejpam-4872	118	31	x	x	X
ejpam-4872	118	32	,	,	PUNCT
ejpam-4872	118	33	x	x	NOUN
ejpam-4872	118	34	)	)	PUNCT
ejpam-4872	118	35	∈	∈	PROPN
ejpam-4872	118	36	f̊(m	f̊(m	PROPN
ejpam-4872	118	37	,	,	PUNCT
ejpam-4872	118	38	m	m	PROPN
ejpam-4872	118	39	)	)	PUNCT
ejpam-4872	118	40	for	for	ADP
ejpam-4872	118	41	all	all	DET
ejpam-4872	118	42	x	x	NOUN
ejpam-4872	118	43	,	,	PUNCT
ejpam-4872	118	44	y	y	PROPN
ejpam-4872	118	45	∈	∈	PROPN
ejpam-4872	118	46	x.	x.	NOUN
ejpam-4872	119	1	also	also	ADV
ejpam-4872	119	2	,	,	PUNCT
ejpam-4872	119	3	we	we	PRON
ejpam-4872	119	4	have	have	AUX
ejpam-4872	119	5	fs((x|(y|y))|(y|y	fs((x|(y|y))|(y|y	VERB
ejpam-4872	119	6	)	)	PUNCT
ejpam-4872	119	7	)	)	PUNCT
ejpam-4872	120	1	=	=	PUNCT
ejpam-4872	120	2	f	f	X
ejpam-4872	120	3	s((y|(x|x))|(x|x	s((y|(x|x))|(x|x	NOUN
ejpam-4872	120	4	)	)	PUNCT
ejpam-4872	120	5	)	)	PUNCT
ejpam-4872	120	6	⊇	⊇	PROPN
ejpam-4872	120	7	fs(x	fs(x	NOUN
ejpam-4872	120	8	)	)	PUNCT
ejpam-4872	120	9	∩	∩	NOUN
ejpam-4872	120	10	fs(x	fs(x	NOUN
ejpam-4872	120	11	)	)	PUNCT
ejpam-4872	120	12	=	=	SYM
ejpam-4872	120	13	f	f	X
ejpam-4872	120	14	s(x	s(x	PROPN
ejpam-4872	120	15	)	)	PUNCT
ejpam-4872	120	16	and	and	CCONJ
ejpam-4872	120	17	f̃((x|(y|y))|(y|y	f̃((x|(y|y))|(y|y	NUM
ejpam-4872	120	18	)	)	PUNCT
ejpam-4872	120	19	)	)	PUNCT
ejpam-4872	121	1	=	=	SYM
ejpam-4872	121	2	f̃((y|(x|x))|(x|x	f̃((y|(x|x))|(x|x	NOUN
ejpam-4872	121	3	)	)	PUNCT
ejpam-4872	121	4	)	)	PUNCT
ejpam-4872	122	1	⊵	⊵	PROPN
ejpam-4872	122	2	rmin{f̃(x	rmin{f̃(x	NOUN
ejpam-4872	122	3	)	)	PUNCT
ejpam-4872	122	4	,	,	PUNCT
ejpam-4872	122	5	f̃(x	f̃(x	NOUN
ejpam-4872	122	6	)	)	PUNCT
ejpam-4872	122	7	}	}	PUNCT
ejpam-4872	122	8	=	=	SYM
ejpam-4872	122	9	f̃(x	f̃(x	PROPN
ejpam-4872	122	10	)	)	PUNCT
ejpam-4872	122	11	for	for	ADP
ejpam-4872	122	12	all	all	DET
ejpam-4872	122	13	x	x	NOUN
ejpam-4872	122	14	,	,	PUNCT
ejpam-4872	122	15	y	y	PROPN
ejpam-4872	122	16	∈	∈	PROPN
ejpam-4872	122	17	x.	x.	NOUN
ejpam-4872	123	1	therefore	therefore	ADV
ejpam-4872	123	2	(	(	PUNCT
ejpam-4872	123	3	22	22	NUM
ejpam-4872	123	4	)	)	PUNCT
ejpam-4872	123	5	is	be	AUX
ejpam-4872	123	6	valid	valid	ADJ
ejpam-4872	123	7	.	.	PUNCT
ejpam-4872	124	1	let	let	VERB
ejpam-4872	124	2	x	x	PRON
ejpam-4872	124	3	,	,	PUNCT
ejpam-4872	124	4	y	y	PROPN
ejpam-4872	124	5	∈	∈	PROPN
ejpam-4872	124	6	x	x	AUX
ejpam-4872	124	7	be	be	AUX
ejpam-4872	124	8	such	such	ADJ
ejpam-4872	124	9	that	that	SCONJ
ejpam-4872	124	10	x	x	SYM
ejpam-4872	124	11	≤x	≤x	PROPN
ejpam-4872	124	12	y.	y.	PROPN
ejpam-4872	124	13	then	then	ADV
ejpam-4872	124	14	x|(y|y	x|(y|y	PROPN
ejpam-4872	124	15	)	)	PUNCT
ejpam-4872	125	1	=	=	SYM
ejpam-4872	125	2	1	1	NUM
ejpam-4872	125	3	by	by	ADP
ejpam-4872	125	4	(	(	PUNCT
ejpam-4872	125	5	1	1	NUM
ejpam-4872	125	6	)	)	PUNCT
ejpam-4872	125	7	.	.	PUNCT
ejpam-4872	126	1	using	use	VERB
ejpam-4872	126	2	(	(	PUNCT
ejpam-4872	126	3	4	4	NUM
ejpam-4872	126	4	)	)	PUNCT
ejpam-4872	126	5	and	and	CCONJ
ejpam-4872	126	6	(	(	PUNCT
ejpam-4872	126	7	22	22	NUM
ejpam-4872	126	8	)	)	PUNCT
ejpam-4872	126	9	,	,	PUNCT
ejpam-4872	126	10	we	we	PRON
ejpam-4872	126	11	have	have	VERB
ejpam-4872	126	12	f̊−(y	f̊−(y	VERB
ejpam-4872	126	13	)	)	PUNCT
ejpam-4872	127	1	=	=	SYM
ejpam-4872	127	2	f̊−(1|(y|y	f̊−(1|(y|y	ADJ
ejpam-4872	127	3	)	)	PUNCT
ejpam-4872	127	4	)	)	PUNCT
ejpam-4872	128	1	=	=	SYM
ejpam-4872	128	2	f̊−((x|(y|y))|(y|y	f̊−((x|(y|y))|(y|y	ADJ
ejpam-4872	128	3	)	)	PUNCT
ejpam-4872	128	4	)	)	PUNCT
ejpam-4872	128	5	≤	≤	NUM
ejpam-4872	128	6	f̊−(x	f̊−(x	NOUN
ejpam-4872	128	7	)	)	PUNCT
ejpam-4872	128	8	,	,	PUNCT
ejpam-4872	128	9	s.	s.	PROPN
ejpam-4872	128	10	s.	s.	PROPN
ejpam-4872	128	11	ahn	ahn	PROPN
ejpam-4872	128	12	et	et	PROPN
ejpam-4872	128	13	al	al	PROPN
ejpam-4872	128	14	.	.	PUNCT
ejpam-4872	128	15	/	/	SYM
ejpam-4872	128	16	eur	eur	PROPN
ejpam-4872	128	17	.	.	PUNCT
ejpam-4872	129	1	j.	j.	PROPN
ejpam-4872	129	2	pure	pure	PROPN
ejpam-4872	129	3	appl	appl	PROPN
ejpam-4872	129	4	.	.	PROPN
ejpam-4872	129	5	math	math	PROPN
ejpam-4872	129	6	,	,	PUNCT
ejpam-4872	129	7	16	16	NUM
ejpam-4872	129	8	(	(	PUNCT
ejpam-4872	129	9	3	3	NUM
ejpam-4872	129	10	)	)	PUNCT
ejpam-4872	129	11	(	(	PUNCT
ejpam-4872	129	12	2023	2023	NUM
ejpam-4872	129	13	)	)	PUNCT
ejpam-4872	129	14	,	,	PUNCT
ejpam-4872	129	15	1862	1862	NUM
ejpam-4872	129	16	-	-	SYM
ejpam-4872	129	17	1877	1877	NUM
ejpam-4872	129	18	1868	1868	NUM
ejpam-4872	129	19	f̊+(y	f̊+(y	NOUN
ejpam-4872	129	20	)	)	PUNCT
ejpam-4872	129	21	=	=	SYM
ejpam-4872	130	1	f̊+(1|(y|y	f̊+(1|(y|y	ADJ
ejpam-4872	130	2	)	)	PUNCT
ejpam-4872	130	3	)	)	PUNCT
ejpam-4872	131	1	=	=	PUNCT
ejpam-4872	131	2	f̊+((x|(y|y))|(y|y	f̊+((x|(y|y))|(y|y	ADJ
ejpam-4872	131	3	)	)	PUNCT
ejpam-4872	131	4	)	)	PUNCT
ejpam-4872	131	5	≥	≥	NOUN
ejpam-4872	131	6	f̊+(x	f̊+(x	NUM
ejpam-4872	131	7	)	)	PUNCT
ejpam-4872	131	8	,	,	PUNCT
ejpam-4872	131	9	which	which	PRON
ejpam-4872	131	10	shows	show	VERB
ejpam-4872	131	11	that	that	SCONJ
ejpam-4872	131	12	y	y	PROPN
ejpam-4872	131	13	(	(	PUNCT
ejpam-4872	131	14	x	x	X
ejpam-4872	131	15	,	,	PUNCT
ejpam-4872	131	16	x	x	NOUN
ejpam-4872	131	17	)	)	PUNCT
ejpam-4872	131	18	∈	∈	PROPN
ejpam-4872	131	19	f̊(m	f̊(m	PROPN
ejpam-4872	131	20	,	,	PUNCT
ejpam-4872	131	21	m	m	PROPN
ejpam-4872	131	22	)	)	PUNCT
ejpam-4872	131	23	.	.	PUNCT
ejpam-4872	132	1	also	also	ADV
ejpam-4872	132	2	we	we	PRON
ejpam-4872	132	3	get	get	VERB
ejpam-4872	132	4	fs(x	fs(x	NOUN
ejpam-4872	132	5	)	)	PUNCT
ejpam-4872	133	1	⊆	⊆	NUM
ejpam-4872	133	2	fs((x|(y|y))|(y|y	fs((x|(y|y))|(y|y	NUM
ejpam-4872	133	3	)	)	PUNCT
ejpam-4872	133	4	)	)	PUNCT
ejpam-4872	134	1	=	=	PUNCT
ejpam-4872	134	2	fs(1|(y|y	fs(1|(y|y	NUM
ejpam-4872	134	3	)	)	PUNCT
ejpam-4872	134	4	)	)	PUNCT
ejpam-4872	135	1	=	=	SYM
ejpam-4872	135	2	fs(y	fs(y	X
ejpam-4872	135	3	)	)	PUNCT
ejpam-4872	135	4	and	and	CCONJ
ejpam-4872	135	5	f̃(x	f̃(x	PROPN
ejpam-4872	135	6	)	)	PUNCT
ejpam-4872	135	7	⊴	⊴	ADP
ejpam-4872	135	8	f̃((x|(y|y))|(y|y	f̃((x|(y|y))|(y|y	NUM
ejpam-4872	135	9	)	)	PUNCT
ejpam-4872	135	10	)	)	PUNCT
ejpam-4872	136	1	=	=	SYM
ejpam-4872	136	2	f̃(1|(y|y	f̃(1|(y|y	ADJ
ejpam-4872	136	3	)	)	PUNCT
ejpam-4872	136	4	)	)	PUNCT
ejpam-4872	137	1	=	=	PUNCT
ejpam-4872	137	2	f̃(y	f̃(y	NOUN
ejpam-4872	137	3	)	)	PUNCT
ejpam-4872	137	4	.	.	PUNCT
ejpam-4872	138	1	we	we	PRON
ejpam-4872	138	2	have	have	VERB
ejpam-4872	138	3	a	a	DET
ejpam-4872	138	4	question	question	NOUN
ejpam-4872	138	5	:	:	PUNCT
ejpam-4872	138	6	if	if	SCONJ
ejpam-4872	138	7	a	a	DET
ejpam-4872	138	8	dokdo	dokdo	NOUN
ejpam-4872	138	9	structure	structure	NOUN
ejpam-4872	138	10	dokf	dokf	NOUN
ejpam-4872	138	11	:	:	PUNCT
ejpam-4872	138	12	=	=	SYM
ejpam-4872	138	13	(	(	PUNCT
ejpam-4872	138	14	f̊	f̊	X
ejpam-4872	138	15	,	,	PUNCT
ejpam-4872	138	16	fs	fs	PROPN
ejpam-4872	138	17	,	,	PUNCT
ejpam-4872	138	18	f̃	f̃	PROPN
ejpam-4872	138	19	)	)	PUNCT
ejpam-4872	138	20	in	in	ADP
ejpam-4872	138	21	(	(	PUNCT
ejpam-4872	138	22	u	u	NOUN
ejpam-4872	138	23	,	,	PUNCT
ejpam-4872	138	24	x	x	X
ejpam-4872	138	25	)	)	PUNCT
ejpam-4872	138	26	satisfies	satisfy	VERB
ejpam-4872	138	27	the	the	DET
ejpam-4872	138	28	condition	condition	NOUN
ejpam-4872	138	29	(	(	PUNCT
ejpam-4872	138	30	23	23	NUM
ejpam-4872	138	31	)	)	PUNCT
ejpam-4872	138	32	then	then	ADV
ejpam-4872	138	33	is	be	AUX
ejpam-4872	138	34	it	it	PRON
ejpam-4872	138	35	a	a	DET
ejpam-4872	138	36	dokdo	dokdo	NOUN
ejpam-4872	138	37	filter	filter	NOUN
ejpam-4872	138	38	of	of	ADP
ejpam-4872	138	39	(	(	PUNCT
ejpam-4872	138	40	u	u	NOUN
ejpam-4872	138	41	,	,	PUNCT
ejpam-4872	138	42	x	x	PROPN
ejpam-4872	138	43	)	)	PUNCT
ejpam-4872	138	44	?	?	PUNCT
ejpam-4872	139	1	the	the	DET
ejpam-4872	139	2	example	example	NOUN
ejpam-4872	139	3	below	below	ADV
ejpam-4872	139	4	provides	provide	VERB
ejpam-4872	139	5	a	a	DET
ejpam-4872	139	6	negative	negative	ADJ
ejpam-4872	139	7	answer	answer	NOUN
ejpam-4872	139	8	to	to	ADP
ejpam-4872	139	9	the	the	DET
ejpam-4872	139	10	question	question	NOUN
ejpam-4872	139	11	.	.	PUNCT
ejpam-4872	140	1	example	example	NOUN
ejpam-4872	140	2	2	2	NUM
ejpam-4872	140	3	.	.	X
ejpam-4872	141	1	consider	consider	VERB
ejpam-4872	141	2	a	a	DET
ejpam-4872	141	3	set	set	NOUN
ejpam-4872	141	4	x	x	X
ejpam-4872	141	5	=	=	SYM
ejpam-4872	141	6	{	{	PUNCT
ejpam-4872	141	7	0	0	NUM
ejpam-4872	141	8	,	,	PUNCT
ejpam-4872	141	9	1	1	NUM
ejpam-4872	141	10	,	,	PUNCT
ejpam-4872	141	11	2	2	NUM
ejpam-4872	141	12	,	,	PUNCT
ejpam-4872	141	13	3	3	NUM
ejpam-4872	141	14	}	}	PUNCT
ejpam-4872	141	15	.	.	PUNCT
ejpam-4872	142	1	the	the	DET
ejpam-4872	142	2	hasse	hasse	PROPN
ejpam-4872	142	3	diagram	diagram	NOUN
ejpam-4872	142	4	and	and	CCONJ
ejpam-4872	142	5	the	the	DET
ejpam-4872	142	6	sheffer	sheffer	NOUN
ejpam-4872	142	7	stroke	stroke	NOUN
ejpam-4872	142	8	“	"	PUNCT
ejpam-4872	142	9	|	|	ADV
ejpam-4872	142	10	”	"	PUNCT
ejpam-4872	142	11	on	on	ADP
ejpam-4872	142	12	x	x	PART
ejpam-4872	142	13	are	be	AUX
ejpam-4872	142	14	given	give	VERB
ejpam-4872	142	15	by	by	ADP
ejpam-4872	142	16	figure	figure	NOUN
ejpam-4872	142	17	2	2	NUM
ejpam-4872	142	18	and	and	CCONJ
ejpam-4872	142	19	table	table	NOUN
ejpam-4872	142	20	4	4	NUM
ejpam-4872	142	21	,	,	PUNCT
ejpam-4872	142	22	respectively	respectively	ADV
ejpam-4872	142	23	.	.	PUNCT
ejpam-4872	143	1	figure	figure	NOUN
ejpam-4872	143	2	2	2	NUM
ejpam-4872	143	3	:	:	PUNCT
ejpam-4872	143	4	hasse	hasse	PROPN
ejpam-4872	143	5	diagram	diagram	PROPN
ejpam-4872	143	6	rr	rr	PROPN
ejpam-4872	143	7	rr	rr	PROPN
ejpam-4872	143	8	0	0	NUM
ejpam-4872	143	9	2	2	NUM
ejpam-4872	143	10	3	3	NUM
ejpam-4872	143	11	1	1	NUM
ejpam-4872	143	12	�	�	PROPN
ejpam-4872	143	13	�	�	PROPN
ejpam-4872	143	14	a	a	DET
ejpam-4872	143	15	a	a	DET
ejpam-4872	143	16	�	�	PROPN
ejpam-4872	143	17	�	�	PROPN
ejpam-4872	143	18	a	a	DET
ejpam-4872	143	19	a	a	DET
ejpam-4872	143	20	table	table	NOUN
ejpam-4872	143	21	4	4	NUM
ejpam-4872	143	22	:	:	PUNCT
ejpam-4872	143	23	cayley	cayley	ADJ
ejpam-4872	143	24	table	table	NOUN
ejpam-4872	143	25	for	for	ADP
ejpam-4872	143	26	the	the	DET
ejpam-4872	143	27	sheffer	sheffer	NOUN
ejpam-4872	143	28	stroke	stroke	NOUN
ejpam-4872	143	29	“	"	PUNCT
ejpam-4872	143	30	|	|	ADV
ejpam-4872	143	31	”	"	PUNCT
ejpam-4872	143	32	|	|	ADV
ejpam-4872	143	33	1	1	NUM
ejpam-4872	143	34	2	2	NUM
ejpam-4872	143	35	3	3	NUM
ejpam-4872	143	36	0	0	NUM
ejpam-4872	143	37	1	1	NUM
ejpam-4872	143	38	0	0	NUM
ejpam-4872	143	39	3	3	NUM
ejpam-4872	143	40	2	2	NUM
ejpam-4872	143	41	1	1	NUM
ejpam-4872	143	42	2	2	NUM
ejpam-4872	143	43	3	3	NUM
ejpam-4872	143	44	3	3	NUM
ejpam-4872	143	45	1	1	NUM
ejpam-4872	143	46	1	1	NUM
ejpam-4872	143	47	3	3	NUM
ejpam-4872	143	48	2	2	NUM
ejpam-4872	143	49	1	1	NUM
ejpam-4872	143	50	2	2	NUM
ejpam-4872	143	51	1	1	NUM
ejpam-4872	143	52	0	0	NUM
ejpam-4872	143	53	1	1	NUM
ejpam-4872	143	54	1	1	NUM
ejpam-4872	143	55	1	1	NUM
ejpam-4872	143	56	1	1	NUM
ejpam-4872	143	57	then	then	ADV
ejpam-4872	143	58	x	x	X
ejpam-4872	143	59	:	:	PUNCT
ejpam-4872	143	60	=	=	SYM
ejpam-4872	143	61	(	(	PUNCT
ejpam-4872	143	62	x	x	NOUN
ejpam-4872	143	63	,	,	PUNCT
ejpam-4872	143	64	|	|	ADV
ejpam-4872	143	65	)	)	PUNCT
ejpam-4872	143	66	is	be	AUX
ejpam-4872	143	67	a	a	DET
ejpam-4872	143	68	sheffer	sheffer	NOUN
ejpam-4872	143	69	stroke	stroke	NOUN
ejpam-4872	143	70	hilbert	hilbert	PROPN
ejpam-4872	143	71	algebra	algebra	PROPN
ejpam-4872	143	72	(	(	PUNCT
ejpam-4872	143	73	see	see	VERB
ejpam-4872	143	74	[	[	X
ejpam-4872	143	75	12	12	NUM
ejpam-4872	143	76	]	]	PUNCT
ejpam-4872	143	77	)	)	PUNCT
ejpam-4872	143	78	.	.	PUNCT
ejpam-4872	144	1	let	let	VERB
ejpam-4872	144	2	dokf	dokf	VERB
ejpam-4872	144	3	:	:	PUNCT
ejpam-4872	144	4	=	=	SYM
ejpam-4872	144	5	(	(	PUNCT
ejpam-4872	144	6	f̊	f̊	X
ejpam-4872	144	7	,	,	PUNCT
ejpam-4872	144	8	fs	fs	PROPN
ejpam-4872	144	9	,	,	PUNCT
ejpam-4872	144	10	f̃	f̃	PROPN
ejpam-4872	144	11	)	)	PUNCT
ejpam-4872	144	12	be	be	VERB
ejpam-4872	144	13	a	a	DET
ejpam-4872	144	14	dokdo	dokdo	NOUN
ejpam-4872	144	15	structure	structure	NOUN
ejpam-4872	144	16	in	in	ADP
ejpam-4872	144	17	(	(	PUNCT
ejpam-4872	144	18	u	u	NOUN
ejpam-4872	144	19	=	=	PROPN
ejpam-4872	144	20	z	z	PROPN
ejpam-4872	144	21	,	,	PUNCT
ejpam-4872	144	22	x	x	X
ejpam-4872	144	23	)	)	PUNCT
ejpam-4872	144	24	which	which	PRON
ejpam-4872	144	25	is	be	AUX
ejpam-4872	144	26	given	give	VERB
ejpam-4872	144	27	by	by	ADP
ejpam-4872	144	28	table	table	NOUN
ejpam-4872	144	29	5	5	NUM
ejpam-4872	144	30	.	.	PUNCT
ejpam-4872	144	31	table	table	NOUN
ejpam-4872	144	32	5	5	NUM
ejpam-4872	144	33	:	:	PUNCT
ejpam-4872	144	34	tabular	tabular	PROPN
ejpam-4872	144	35	representation	representation	NOUN
ejpam-4872	144	36	of	of	ADP
ejpam-4872	144	37	dokf	dokf	NOUN
ejpam-4872	144	38	:	:	PUNCT
ejpam-4872	144	39	=	=	SYM
ejpam-4872	144	40	(	(	PUNCT
ejpam-4872	144	41	f̊	f̊	X
ejpam-4872	144	42	,	,	PUNCT
ejpam-4872	144	43	fs	fs	PROPN
ejpam-4872	144	44	,	,	PUNCT
ejpam-4872	144	45	f̃	f̃	PROPN
ejpam-4872	144	46	)	)	PUNCT
ejpam-4872	144	47	x	x	PUNCT
ejpam-4872	144	48	f̊(x	f̊(x	NOUN
ejpam-4872	144	49	)	)	PUNCT
ejpam-4872	144	50	fs(x	fs(x	NOUN
ejpam-4872	144	51	)	)	PUNCT
ejpam-4872	144	52	f̃(x	f̃(x	NOUN
ejpam-4872	144	53	)	)	PUNCT
ejpam-4872	144	54	0	0	NUM
ejpam-4872	145	1	(	(	PUNCT
ejpam-4872	145	2	−0.13	−0.13	NOUN
ejpam-4872	145	3	,	,	PUNCT
ejpam-4872	145	4	0.10	0.10	NUM
ejpam-4872	145	5	)	)	PUNCT
ejpam-4872	145	6	8n	8n	NOUN
ejpam-4872	145	7	[	[	X
ejpam-4872	145	8	0.29	0.29	NUM
ejpam-4872	145	9	,	,	PUNCT
ejpam-4872	145	10	0.63	0.63	NUM
ejpam-4872	145	11	]	]	SYM
ejpam-4872	145	12	2	2	NUM
ejpam-4872	145	13	(	(	PUNCT
ejpam-4872	145	14	−0.38	−0.38	PROPN
ejpam-4872	145	15	,	,	PUNCT
ejpam-4872	145	16	0.17	0.17	NUM
ejpam-4872	145	17	)	)	PUNCT
ejpam-4872	145	18	4n	4n	NOUN
ejpam-4872	146	1	[	[	X
ejpam-4872	146	2	0.32	0.32	NUM
ejpam-4872	146	3	,	,	PUNCT
ejpam-4872	146	4	0.67	0.67	NUM
ejpam-4872	146	5	]	]	SYM
ejpam-4872	146	6	3	3	NUM
ejpam-4872	146	7	(	(	PUNCT
ejpam-4872	146	8	−0.55	−0.55	NOUN
ejpam-4872	146	9	,	,	PUNCT
ejpam-4872	146	10	0.29	0.29	NUM
ejpam-4872	146	11	)	)	PUNCT
ejpam-4872	146	12	4z	4z	NOUN
ejpam-4872	147	1	[	[	X
ejpam-4872	147	2	0.36	0.36	NUM
ejpam-4872	147	3	,	,	PUNCT
ejpam-4872	147	4	0.75	0.75	NUM
ejpam-4872	147	5	]	]	SYM
ejpam-4872	147	6	1	1	NUM
ejpam-4872	147	7	(	(	PUNCT
ejpam-4872	147	8	−0.82	−0.82	PROPN
ejpam-4872	147	9	,	,	PUNCT
ejpam-4872	147	10	0.63	0.63	NUM
ejpam-4872	147	11	)	)	PUNCT
ejpam-4872	147	12	2z	2z	NOUN
ejpam-4872	148	1	[	[	X
ejpam-4872	148	2	0.47	0.47	NUM
ejpam-4872	148	3	,	,	PUNCT
ejpam-4872	148	4	0.89	0.89	NUM
ejpam-4872	148	5	]	]	PUNCT
ejpam-4872	148	6	s.	s.	PROPN
ejpam-4872	148	7	s.	s.	PROPN
ejpam-4872	148	8	ahn	ahn	PROPN
ejpam-4872	148	9	et	et	PROPN
ejpam-4872	148	10	al	al	PROPN
ejpam-4872	148	11	.	.	PUNCT
ejpam-4872	148	12	/	/	SYM
ejpam-4872	148	13	eur	eur	PROPN
ejpam-4872	148	14	.	.	PUNCT
ejpam-4872	149	1	j.	j.	PROPN
ejpam-4872	149	2	pure	pure	PROPN
ejpam-4872	149	3	appl	appl	PROPN
ejpam-4872	149	4	.	.	PROPN
ejpam-4872	149	5	math	math	PROPN
ejpam-4872	149	6	,	,	PUNCT
ejpam-4872	149	7	16	16	NUM
ejpam-4872	149	8	(	(	PUNCT
ejpam-4872	149	9	3	3	NUM
ejpam-4872	149	10	)	)	PUNCT
ejpam-4872	149	11	(	(	PUNCT
ejpam-4872	149	12	2023	2023	NUM
ejpam-4872	149	13	)	)	PUNCT
ejpam-4872	149	14	,	,	PUNCT
ejpam-4872	149	15	1862	1862	NUM
ejpam-4872	149	16	-	-	SYM
ejpam-4872	149	17	1877	1877	NUM
ejpam-4872	149	18	1869	1869	NUM
ejpam-4872	149	19	it	it	PRON
ejpam-4872	149	20	is	be	AUX
ejpam-4872	149	21	routine	routine	ADJ
ejpam-4872	149	22	to	to	PART
ejpam-4872	149	23	check	check	VERB
ejpam-4872	149	24	that	that	DET
ejpam-4872	149	25	dokf	dokf	NOUN
ejpam-4872	149	26	:	:	PUNCT
ejpam-4872	149	27	=	=	SYM
ejpam-4872	149	28	(	(	PUNCT
ejpam-4872	149	29	f̊	f̊	X
ejpam-4872	149	30	,	,	PUNCT
ejpam-4872	149	31	fs	fs	PROPN
ejpam-4872	149	32	,	,	PUNCT
ejpam-4872	149	33	f̃	f̃	PROPN
ejpam-4872	149	34	)	)	PUNCT
ejpam-4872	149	35	in	in	ADP
ejpam-4872	149	36	(	(	PUNCT
ejpam-4872	149	37	u	u	NOUN
ejpam-4872	149	38	,	,	PUNCT
ejpam-4872	149	39	x	x	X
ejpam-4872	149	40	)	)	PUNCT
ejpam-4872	149	41	satisfies	satisfy	VERB
ejpam-4872	149	42	the	the	DET
ejpam-4872	149	43	condition	condition	NOUN
ejpam-4872	149	44	(	(	PUNCT
ejpam-4872	149	45	23	23	NUM
ejpam-4872	149	46	)	)	PUNCT
ejpam-4872	149	47	.	.	PUNCT
ejpam-4872	150	1	but	but	CCONJ
ejpam-4872	150	2	it	it	PRON
ejpam-4872	150	3	is	be	AUX
ejpam-4872	150	4	not	not	PART
ejpam-4872	150	5	a	a	DET
ejpam-4872	150	6	dokdo	dokdo	NOUN
ejpam-4872	150	7	filter	filter	NOUN
ejpam-4872	150	8	of	of	ADP
ejpam-4872	150	9	(	(	PUNCT
ejpam-4872	150	10	u	u	NOUN
ejpam-4872	150	11	=	=	PROPN
ejpam-4872	150	12	z	z	PROPN
ejpam-4872	150	13	,	,	PUNCT
ejpam-4872	150	14	x	x	NOUN
ejpam-4872	150	15	)	)	PUNCT
ejpam-4872	150	16	since	since	SCONJ
ejpam-4872	150	17	(	(	PUNCT
ejpam-4872	150	18	0|(2|3))|(2|3	0|(2|3))|(2|3	NUM
ejpam-4872	150	19	)	)	PUNCT
ejpam-4872	150	20	(	(	PUNCT
ejpam-4872	150	21	2,3	2,3	NUM
ejpam-4872	150	22	)	)	PUNCT
ejpam-4872	150	23	=	=	SYM
ejpam-4872	150	24	0	0	NUM
ejpam-4872	150	25	(	(	PUNCT
ejpam-4872	150	26	2,3	2,3	NUM
ejpam-4872	150	27	)	)	PUNCT
ejpam-4872	150	28	/∈	/∈	PUNCT
ejpam-4872	151	1	f̊(m	f̊(m	ADJ
ejpam-4872	151	2	,	,	PUNCT
ejpam-4872	151	3	m	m	PROPN
ejpam-4872	151	4	)	)	PUNCT
ejpam-4872	151	5	,	,	PUNCT
ejpam-4872	151	6	fs((0|(2|3))|(2|3	fs((0|(2|3))|(2|3	PROPN
ejpam-4872	151	7	)	)	PUNCT
ejpam-4872	151	8	)	)	PUNCT
ejpam-4872	152	1	=	=	PUNCT
ejpam-4872	152	2	fs(0	fs(0	NOUN
ejpam-4872	152	3	)	)	PUNCT
ejpam-4872	152	4	=	=	NOUN
ejpam-4872	152	5	8n	8n	NOUN
ejpam-4872	152	6	⊊	⊊	VERB
ejpam-4872	152	7	4n	4n	NOUN
ejpam-4872	152	8	=	=	SYM
ejpam-4872	152	9	fs(2	fs(2	NOUN
ejpam-4872	152	10	)	)	PUNCT
ejpam-4872	152	11	∩	∩	NOUN
ejpam-4872	152	12	f	f	PROPN
ejpam-4872	152	13	s(3	s(3	PROPN
ejpam-4872	152	14	)	)	PUNCT
ejpam-4872	152	15	or	or	CCONJ
ejpam-4872	152	16	f̃((0|(2|3))|(2|3	f̃((0|(2|3))|(2|3	NOUN
ejpam-4872	152	17	)	)	PUNCT
ejpam-4872	152	18	)	)	PUNCT
ejpam-4872	152	19	=	=	SYM
ejpam-4872	152	20	f̃(0	f̃(0	NOUN
ejpam-4872	152	21	)	)	PUNCT
ejpam-4872	152	22	=	=	PUNCT
ejpam-4872	153	1	[	[	X
ejpam-4872	153	2	0.29	0.29	NUM
ejpam-4872	153	3	,	,	PUNCT
ejpam-4872	153	4	0.63	0.63	NUM
ejpam-4872	153	5	]	]	PUNCT
ejpam-4872	153	6	̸⊵	̸⊵	NOUN
ejpam-4872	153	7	[	[	X
ejpam-4872	153	8	0.32	0.32	NUM
ejpam-4872	153	9	,	,	PUNCT
ejpam-4872	153	10	0.67	0.67	NUM
ejpam-4872	153	11	]	]	X
ejpam-4872	153	12	=	=	PUNCT
ejpam-4872	153	13	rmin{f̃(2	rmin{f̃(2	PROPN
ejpam-4872	153	14	)	)	PUNCT
ejpam-4872	153	15	,	,	PUNCT
ejpam-4872	153	16	f̃(3	f̃(3	NOUN
ejpam-4872	153	17	)	)	PUNCT
ejpam-4872	153	18	}	}	PUNCT
ejpam-4872	153	19	.	.	PUNCT
ejpam-4872	154	1	we	we	PRON
ejpam-4872	154	2	provide	provide	VERB
ejpam-4872	154	3	conditions	condition	NOUN
ejpam-4872	154	4	for	for	SCONJ
ejpam-4872	154	5	the	the	DET
ejpam-4872	154	6	dokdo	dokdo	NOUN
ejpam-4872	154	7	structure	structure	NOUN
ejpam-4872	154	8	to	to	PART
ejpam-4872	154	9	be	be	AUX
ejpam-4872	154	10	the	the	DET
ejpam-4872	154	11	dokdo	dokdo	NOUN
ejpam-4872	154	12	filter	filter	NOUN
ejpam-4872	154	13	.	.	PUNCT
ejpam-4872	155	1	theorem	theorem	NOUN
ejpam-4872	155	2	1	1	NUM
ejpam-4872	155	3	.	.	PUNCT
ejpam-4872	156	1	let	let	VERB
ejpam-4872	156	2	dokf	dokf	VERB
ejpam-4872	156	3	:	:	PUNCT
ejpam-4872	156	4	=	=	SYM
ejpam-4872	156	5	(	(	PUNCT
ejpam-4872	156	6	f̊	f̊	X
ejpam-4872	156	7	,	,	PUNCT
ejpam-4872	156	8	f	f	PROPN
ejpam-4872	156	9	s	s	PROPN
ejpam-4872	156	10	,	,	PUNCT
ejpam-4872	156	11	f̃	f̃	PROPN
ejpam-4872	156	12	)	)	PUNCT
ejpam-4872	156	13	be	be	VERB
ejpam-4872	156	14	a	a	DET
ejpam-4872	156	15	dokdo	dokdo	NOUN
ejpam-4872	156	16	structure	structure	NOUN
ejpam-4872	156	17	in	in	ADP
ejpam-4872	156	18	(	(	PUNCT
ejpam-4872	156	19	u	u	NOUN
ejpam-4872	156	20	,	,	PUNCT
ejpam-4872	156	21	x	x	NOUN
ejpam-4872	156	22	)	)	PUNCT
ejpam-4872	156	23	.	.	PUNCT
ejpam-4872	157	1	then	then	ADV
ejpam-4872	157	2	it	it	PRON
ejpam-4872	157	3	is	be	AUX
ejpam-4872	157	4	dokdo	dokdo	NOUN
ejpam-4872	157	5	filter	filter	NOUN
ejpam-4872	157	6	of	of	ADP
ejpam-4872	157	7	(	(	PUNCT
ejpam-4872	157	8	u	u	NOUN
ejpam-4872	157	9	,	,	PUNCT
ejpam-4872	157	10	x	x	NOUN
ejpam-4872	157	11	)	)	PUNCT
ejpam-4872	157	12	if	if	SCONJ
ejpam-4872	158	1	and	and	CCONJ
ejpam-4872	158	2	only	only	ADV
ejpam-4872	158	3	if	if	SCONJ
ejpam-4872	158	4	it	it	PRON
ejpam-4872	158	5	satisfies	satisfy	VERB
ejpam-4872	158	6	the	the	DET
ejpam-4872	158	7	condition	condition	NOUN
ejpam-4872	158	8	(	(	PUNCT
ejpam-4872	158	9	23	23	NUM
ejpam-4872	158	10	)	)	PUNCT
ejpam-4872	158	11	and	and	CCONJ
ejpam-4872	158	12	(	(	PUNCT
ejpam-4872	158	13	∀x	∀x	X
ejpam-4872	158	14	,	,	PUNCT
ejpam-4872	158	15	y	y	PROPN
ejpam-4872	158	16	∈	∈	PROPN
ejpam-4872	158	17	x	x	NOUN
ejpam-4872	158	18	)	)	PUNCT
ejpam-4872	158	19			X
ejpam-4872	158	20	(	(	PUNCT
ejpam-4872	158	21	x|y)|(x|y	x|y)|(x|y	ADV
ejpam-4872	158	22	)	)	PUNCT
ejpam-4872	158	23	(	(	PUNCT
ejpam-4872	158	24	x	x	X
ejpam-4872	158	25	,	,	PUNCT
ejpam-4872	158	26	y	y	NOUN
ejpam-4872	158	27	)	)	PUNCT
ejpam-4872	158	28	∈	∈	PROPN
ejpam-4872	158	29	f̊(m	f̊(m	PROPN
ejpam-4872	158	30	,	,	PUNCT
ejpam-4872	158	31	m	m	PROPN
ejpam-4872	158	32	)	)	PUNCT
ejpam-4872	158	33	,	,	PUNCT
ejpam-4872	158	34	fs((x|y)|(x|y	fs((x|y)|(x|y	NOUN
ejpam-4872	158	35	)	)	PUNCT
ejpam-4872	158	36	)	)	PUNCT
ejpam-4872	158	37	⊇	⊇	PROPN
ejpam-4872	158	38	f	f	PROPN
ejpam-4872	158	39	s(x	s(x	PROPN
ejpam-4872	158	40	)	)	PUNCT
ejpam-4872	158	41	∩	∩	NOUN
ejpam-4872	158	42	fs(y	fs(y	NUM
ejpam-4872	158	43	)	)	PUNCT
ejpam-4872	158	44	,	,	PUNCT
ejpam-4872	158	45	f̃((x|y)|(x|y	f̃((x|y)|(x|y	PROPN
ejpam-4872	158	46	)	)	PUNCT
ejpam-4872	158	47	)	)	PUNCT
ejpam-4872	158	48	⊵	⊵	PROPN
ejpam-4872	158	49	rmin{f̃(x	rmin{f̃(x	NOUN
ejpam-4872	158	50	)	)	PUNCT
ejpam-4872	158	51	,	,	PUNCT
ejpam-4872	158	52	f̃(y	f̃(y	NOUN
ejpam-4872	158	53	)	)	PUNCT
ejpam-4872	158	54	}	}	PUNCT
ejpam-4872	158	55			PROPN
ejpam-4872	158	56	.	.	PUNCT
ejpam-4872	159	1	(	(	PUNCT
ejpam-4872	159	2	24	24	NUM
ejpam-4872	159	3	)	)	PUNCT
ejpam-4872	159	4	proof	proof	NOUN
ejpam-4872	159	5	.	.	PUNCT
ejpam-4872	160	1	let	let	VERB
ejpam-4872	160	2	dokf	dokf	VERB
ejpam-4872	160	3	:	:	PUNCT
ejpam-4872	160	4	=	=	SYM
ejpam-4872	160	5	(	(	PUNCT
ejpam-4872	160	6	f̊	f̊	X
ejpam-4872	160	7	,	,	PUNCT
ejpam-4872	160	8	fs	fs	PROPN
ejpam-4872	160	9	,	,	PUNCT
ejpam-4872	160	10	f̃	f̃	PROPN
ejpam-4872	160	11	)	)	PUNCT
ejpam-4872	160	12	be	be	VERB
ejpam-4872	160	13	a	a	DET
ejpam-4872	160	14	dokdo	dokdo	NOUN
ejpam-4872	160	15	filter	filter	NOUN
ejpam-4872	160	16	of	of	ADP
ejpam-4872	160	17	(	(	PUNCT
ejpam-4872	160	18	u	u	NOUN
ejpam-4872	160	19	,	,	PUNCT
ejpam-4872	160	20	x	x	NOUN
ejpam-4872	160	21	)	)	PUNCT
ejpam-4872	160	22	.	.	PUNCT
ejpam-4872	161	1	the	the	DET
ejpam-4872	161	2	condition	condition	NOUN
ejpam-4872	161	3	(	(	PUNCT
ejpam-4872	161	4	23	23	NUM
ejpam-4872	161	5	)	)	PUNCT
ejpam-4872	161	6	is	be	AUX
ejpam-4872	161	7	valid	valid	ADJ
ejpam-4872	161	8	by	by	ADP
ejpam-4872	161	9	proposition	proposition	NOUN
ejpam-4872	161	10	2	2	NUM
ejpam-4872	161	11	.	.	PUNCT
ejpam-4872	162	1	since	since	SCONJ
ejpam-4872	162	2	(	(	PUNCT
ejpam-4872	162	3	(	(	PUNCT
ejpam-4872	162	4	1|1)|(x|y))|(x|y	1|1)|(x|y))|(x|y	NUM
ejpam-4872	162	5	)	)	PUNCT
ejpam-4872	162	6	(	(	PUNCT
ejpam-4872	162	7	s1	s1	NOUN
ejpam-4872	162	8	)	)	PUNCT
ejpam-4872	162	9	=	=	SYM
ejpam-4872	162	10	(	(	PUNCT
ejpam-4872	162	11	(	(	PUNCT
ejpam-4872	162	12	x|y)|(1|1))|(x|y	x|y)|(1|1))|(x|y	NUM
ejpam-4872	162	13	)	)	PUNCT
ejpam-4872	162	14	(	(	PUNCT
ejpam-4872	162	15	3	3	X
ejpam-4872	162	16	)	)	PUNCT
ejpam-4872	162	17	=	=	SYM
ejpam-4872	162	18	1|(x|y	1|(x|y	NUM
ejpam-4872	162	19	)	)	PUNCT
ejpam-4872	162	20	(	(	PUNCT
ejpam-4872	162	21	s2	s2	PROPN
ejpam-4872	162	22	)	)	PUNCT
ejpam-4872	162	23	=	=	SYM
ejpam-4872	162	24	1|(((x|y)|(x|y))|((x|y)|(x|y	1|(((x|y)|(x|y))|((x|y)|(x|y	NUM
ejpam-4872	162	25	)	)	PUNCT
ejpam-4872	162	26	)	)	PUNCT
ejpam-4872	162	27	)	)	PUNCT
ejpam-4872	163	1	(	(	PUNCT
ejpam-4872	163	2	4	4	X
ejpam-4872	163	3	)	)	PUNCT
ejpam-4872	163	4	=	=	SYM
ejpam-4872	163	5	(	(	PUNCT
ejpam-4872	163	6	x|y)|(x|y	x|y)|(x|y	ADJ
ejpam-4872	163	7	)	)	PUNCT
ejpam-4872	163	8	for	for	ADP
ejpam-4872	163	9	all	all	DET
ejpam-4872	163	10	x	x	NOUN
ejpam-4872	163	11	,	,	PUNCT
ejpam-4872	163	12	y	y	PROPN
ejpam-4872	163	13	∈	∈	PROPN
ejpam-4872	163	14	x	x	AUX
ejpam-4872	163	15	,	,	PUNCT
ejpam-4872	163	16	it	it	PRON
ejpam-4872	163	17	follows	follow	VERB
ejpam-4872	163	18	from	from	ADP
ejpam-4872	163	19	(	(	PUNCT
ejpam-4872	163	20	21	21	NUM
ejpam-4872	163	21	)	)	PUNCT
ejpam-4872	163	22	that	that	SCONJ
ejpam-4872	163	23	(	(	PUNCT
ejpam-4872	163	24	x|y)|(x|y	x|y)|(x|y	ADV
ejpam-4872	163	25	)	)	PUNCT
ejpam-4872	163	26	(	(	PUNCT
ejpam-4872	163	27	x	x	X
ejpam-4872	163	28	,	,	PUNCT
ejpam-4872	163	29	y	y	NOUN
ejpam-4872	163	30	)	)	PUNCT
ejpam-4872	163	31	=	=	SYM
ejpam-4872	163	32	(	(	PUNCT
ejpam-4872	163	33	(	(	PUNCT
ejpam-4872	163	34	1|1)|(x|y))|(x|y	1|1)|(x|y))|(x|y	NUM
ejpam-4872	163	35	)	)	PUNCT
ejpam-4872	163	36	(	(	PUNCT
ejpam-4872	163	37	x	x	X
ejpam-4872	163	38	,	,	PUNCT
ejpam-4872	163	39	y	y	NOUN
ejpam-4872	163	40	)	)	PUNCT
ejpam-4872	163	41	∈	∈	PROPN
ejpam-4872	163	42	f̊(m	f̊(m	PROPN
ejpam-4872	163	43	,	,	PUNCT
ejpam-4872	163	44	m	m	PROPN
ejpam-4872	163	45	)	)	PUNCT
ejpam-4872	163	46	,	,	PUNCT
ejpam-4872	163	47	fs((x|y)|(x|y	fs((x|y)|(x|y	NOUN
ejpam-4872	163	48	)	)	PUNCT
ejpam-4872	163	49	)	)	PUNCT
ejpam-4872	164	1	=	=	SYM
ejpam-4872	164	2	f	f	X
ejpam-4872	164	3	s(((1|1)|(x|y))|(x|y	s(((1|1)|(x|y))|(x|y	PROPN
ejpam-4872	164	4	)	)	PUNCT
ejpam-4872	164	5	)	)	PUNCT
ejpam-4872	164	6	⊇	⊇	PROPN
ejpam-4872	164	7	fs(x	fs(x	NOUN
ejpam-4872	164	8	)	)	PUNCT
ejpam-4872	164	9	∩	∩	NOUN
ejpam-4872	164	10	fs(y	fs(y	NUM
ejpam-4872	164	11	)	)	PUNCT
ejpam-4872	164	12	}	}	PUNCT
ejpam-4872	164	13	and	and	CCONJ
ejpam-4872	164	14	f̃((x|y)|(x|y	f̃((x|y)|(x|y	NUM
ejpam-4872	164	15	)	)	PUNCT
ejpam-4872	164	16	)	)	PUNCT
ejpam-4872	165	1	=	=	SYM
ejpam-4872	165	2	f̃(((1|1)|(x|y))|(x|y	f̃(((1|1)|(x|y))|(x|y	X
ejpam-4872	165	3	)	)	PUNCT
ejpam-4872	165	4	)	)	PUNCT
ejpam-4872	166	1	⊵	⊵	PROPN
ejpam-4872	166	2	rmin{f̃(x	rmin{f̃(x	NOUN
ejpam-4872	166	3	)	)	PUNCT
ejpam-4872	166	4	,	,	PUNCT
ejpam-4872	166	5	f̃(y	f̃(y	NOUN
ejpam-4872	166	6	)	)	PUNCT
ejpam-4872	166	7	}	}	PUNCT
ejpam-4872	166	8	for	for	ADP
ejpam-4872	166	9	all	all	DET
ejpam-4872	166	10	x	x	NOUN
ejpam-4872	166	11	,	,	PUNCT
ejpam-4872	166	12	y	y	PROPN
ejpam-4872	166	13	∈	∈	PROPN
ejpam-4872	166	14	x.	x.	NOUN
ejpam-4872	166	15	conversely	conversely	ADV
ejpam-4872	166	16	,	,	PUNCT
ejpam-4872	166	17	suppose	suppose	VERB
ejpam-4872	166	18	that	that	SCONJ
ejpam-4872	166	19	a	a	DET
ejpam-4872	166	20	dokdo	dokdo	NOUN
ejpam-4872	166	21	structure	structure	NOUN
ejpam-4872	166	22	dokf	dokf	NOUN
ejpam-4872	166	23	:	:	PUNCT
ejpam-4872	166	24	=	=	SYM
ejpam-4872	166	25	(	(	PUNCT
ejpam-4872	166	26	f̊	f̊	X
ejpam-4872	166	27	,	,	PUNCT
ejpam-4872	166	28	fs	fs	PROPN
ejpam-4872	166	29	,	,	PUNCT
ejpam-4872	166	30	f̃	f̃	PROPN
ejpam-4872	166	31	)	)	PUNCT
ejpam-4872	166	32	satisfies	satisfy	VERB
ejpam-4872	166	33	the	the	DET
ejpam-4872	166	34	conditions	condition	NOUN
ejpam-4872	166	35	(	(	PUNCT
ejpam-4872	166	36	23	23	NUM
ejpam-4872	166	37	)	)	PUNCT
ejpam-4872	166	38	and	and	CCONJ
ejpam-4872	166	39	(	(	PUNCT
ejpam-4872	166	40	24	24	NUM
ejpam-4872	166	41	)	)	PUNCT
ejpam-4872	166	42	.	.	PUNCT
ejpam-4872	167	1	since	since	SCONJ
ejpam-4872	167	2	x	x	NUM
ejpam-4872	167	3	≤x	≤x	PROPN
ejpam-4872	167	4	1	1	NUM
ejpam-4872	167	5	for	for	ADP
ejpam-4872	167	6	all	all	DET
ejpam-4872	167	7	x	x	SYM
ejpam-4872	167	8	∈	∈	PROPN
ejpam-4872	167	9	x	x	NOUN
ejpam-4872	167	10	,	,	PUNCT
ejpam-4872	167	11	we	we	PRON
ejpam-4872	167	12	have	have	VERB
ejpam-4872	167	13	1	1	NUM
ejpam-4872	167	14	(	(	PUNCT
ejpam-4872	167	15	x	x	NOUN
ejpam-4872	167	16	,	,	PUNCT
ejpam-4872	167	17	x	x	NOUN
ejpam-4872	167	18	)	)	PUNCT
ejpam-4872	167	19	∈	∈	PROPN
ejpam-4872	167	20	f̊(m	f̊(m	PROPN
ejpam-4872	167	21	,	,	PUNCT
ejpam-4872	167	22	m	m	PROPN
ejpam-4872	167	23	)	)	PUNCT
ejpam-4872	167	24	,	,	PUNCT
ejpam-4872	167	25	fs(x	fs(x	NOUN
ejpam-4872	167	26	)	)	PUNCT
ejpam-4872	167	27	⊆	⊆	NUM
ejpam-4872	167	28	fs(1	fs(1	PROPN
ejpam-4872	167	29	)	)	PUNCT
ejpam-4872	167	30	,	,	PUNCT
ejpam-4872	167	31	and	and	CCONJ
ejpam-4872	167	32	f̃(x	f̃(x	PROPN
ejpam-4872	167	33	)	)	PUNCT
ejpam-4872	167	34	⊴	⊴	ADP
ejpam-4872	167	35	f̃(1	f̃(1	NOUN
ejpam-4872	167	36	)	)	PUNCT
ejpam-4872	167	37	by	by	ADP
ejpam-4872	167	38	(	(	PUNCT
ejpam-4872	167	39	23	23	NUM
ejpam-4872	167	40	)	)	PUNCT
ejpam-4872	167	41	.	.	PUNCT
ejpam-4872	168	1	since	since	SCONJ
ejpam-4872	168	2	y	y	PROPN
ejpam-4872	168	3	≤x	≤x	PROPN
ejpam-4872	168	4	x|(y|y	x|(y|y	PROPN
ejpam-4872	168	5	)	)	PUNCT
ejpam-4872	168	6	for	for	ADP
ejpam-4872	168	7	all	all	DET
ejpam-4872	168	8	x	x	NOUN
ejpam-4872	168	9	,	,	PUNCT
ejpam-4872	168	10	y	y	PROPN
ejpam-4872	168	11	∈	∈	PROPN
ejpam-4872	168	12	x	x	X
ejpam-4872	168	13	,	,	PUNCT
ejpam-4872	168	14	we	we	PRON
ejpam-4872	168	15	have	have	VERB
ejpam-4872	168	16	x|(y|y	x|(y|y	PROPN
ejpam-4872	168	17	)	)	PUNCT
ejpam-4872	168	18	(	(	PUNCT
ejpam-4872	168	19	y	y	PROPN
ejpam-4872	168	20	,	,	PUNCT
ejpam-4872	168	21	y	y	NOUN
ejpam-4872	168	22	)	)	PUNCT
ejpam-4872	168	23	∈	∈	PROPN
ejpam-4872	168	24	f̊(m	f̊(m	PROPN
ejpam-4872	168	25	,	,	PUNCT
ejpam-4872	168	26	m	m	PROPN
ejpam-4872	168	27	)	)	PUNCT
ejpam-4872	168	28	,	,	PUNCT
ejpam-4872	168	29	fs(y	fs(y	NOUN
ejpam-4872	168	30	)	)	PUNCT
ejpam-4872	168	31	⊆	⊆	NUM
ejpam-4872	168	32	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	168	33	)	)	PUNCT
ejpam-4872	168	34	)	)	PUNCT
ejpam-4872	168	35	,	,	PUNCT
ejpam-4872	168	36	and	and	CCONJ
ejpam-4872	168	37	f̃(y	f̃(y	NOUN
ejpam-4872	168	38	)	)	PUNCT
ejpam-4872	168	39	⊴	⊴	ADP
ejpam-4872	168	40	f̃(x|(y|y	f̃(x|(y|y	ADJ
ejpam-4872	168	41	)	)	PUNCT
ejpam-4872	168	42	)	)	PUNCT
ejpam-4872	168	43	by	by	ADP
ejpam-4872	168	44	(	(	PUNCT
ejpam-4872	168	45	23	23	NUM
ejpam-4872	168	46	)	)	PUNCT
ejpam-4872	168	47	.	.	PUNCT
ejpam-4872	169	1	in	in	ADP
ejpam-4872	169	2	(	(	PUNCT
ejpam-4872	169	3	5	5	NUM
ejpam-4872	169	4	)	)	PUNCT
ejpam-4872	169	5	,	,	PUNCT
ejpam-4872	169	6	if	if	SCONJ
ejpam-4872	169	7	we	we	PRON
ejpam-4872	169	8	replace	replace	VERB
ejpam-4872	169	9	a	a	PRON
ejpam-4872	169	10	and	and	CCONJ
ejpam-4872	169	11	b	b	NOUN
ejpam-4872	169	12	with	with	ADP
ejpam-4872	169	13	(	(	PUNCT
ejpam-4872	169	14	y|z)|(y|z	y|z)|(y|z	PROPN
ejpam-4872	169	15	)	)	PUNCT
ejpam-4872	169	16	and	and	CCONJ
ejpam-4872	169	17	x|(y|z	x|(y|z	PROPN
ejpam-4872	169	18	)	)	PUNCT
ejpam-4872	169	19	,	,	PUNCT
ejpam-4872	169	20	respectively	respectively	ADV
ejpam-4872	169	21	,	,	PUNCT
ejpam-4872	169	22	and	and	CCONJ
ejpam-4872	169	23	use	use	NOUN
ejpam-4872	169	24	(	(	PUNCT
ejpam-4872	169	25	s2	s2	PROPN
ejpam-4872	169	26	)	)	PUNCT
ejpam-4872	169	27	,	,	PUNCT
ejpam-4872	169	28	then	then	ADV
ejpam-4872	169	29	(	(	PUNCT
ejpam-4872	169	30	y|z)|(y|z	y|z)|(y|z	PROPN
ejpam-4872	169	31	)	)	PUNCT
ejpam-4872	169	32	≤x	≤x	PROPN
ejpam-4872	169	33	(	(	PUNCT
ejpam-4872	169	34	x|(y|z))|(((y|z)|(y|z))|((y|z)|(y|z	x|(y|z))|(((y|z)|(y|z))|((y|z)|(y|z	PROPN
ejpam-4872	169	35	)	)	PUNCT
ejpam-4872	169	36	)	)	PUNCT
ejpam-4872	169	37	)	)	PUNCT
ejpam-4872	170	1	=	=	PRON
ejpam-4872	170	2	(	(	PUNCT
ejpam-4872	170	3	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	170	4	)	)	PUNCT
ejpam-4872	170	5	for	for	ADP
ejpam-4872	170	6	all	all	DET
ejpam-4872	170	7	x	x	NOUN
ejpam-4872	170	8	,	,	PUNCT
ejpam-4872	170	9	y	y	PROPN
ejpam-4872	170	10	,	,	PUNCT
ejpam-4872	170	11	z	z	NOUN
ejpam-4872	170	12	∈	∈	NOUN
ejpam-4872	170	13	x.	x.	NOUN
ejpam-4872	170	14	using	use	VERB
ejpam-4872	170	15	(	(	PUNCT
ejpam-4872	170	16	23	23	NUM
ejpam-4872	170	17	)	)	PUNCT
ejpam-4872	170	18	and	and	CCONJ
ejpam-4872	170	19	(	(	PUNCT
ejpam-4872	170	20	24	24	NUM
ejpam-4872	170	21	)	)	PUNCT
ejpam-4872	170	22	,	,	PUNCT
ejpam-4872	170	23	we	we	PRON
ejpam-4872	170	24	have	have	VERB
ejpam-4872	170	25	(	(	PUNCT
ejpam-4872	170	26	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	170	27	)	)	PUNCT
ejpam-4872	170	28	(	(	PUNCT
ejpam-4872	170	29	(	(	PUNCT
ejpam-4872	170	30	y|z)|(y|z),(y|z)|(y|z	y|z)|(y|z),(y|z)|(y|z	NOUN
ejpam-4872	170	31	)	)	PUNCT
ejpam-4872	170	32	)	)	PUNCT
ejpam-4872	171	1	∈	∈	PROPN
ejpam-4872	171	2	f̊(m	f̊(m	PROPN
ejpam-4872	171	3	,	,	PUNCT
ejpam-4872	171	4	m	m	PROPN
ejpam-4872	171	5	)	)	PUNCT
ejpam-4872	171	6	,	,	PUNCT
ejpam-4872	171	7	s.	s.	PROPN
ejpam-4872	171	8	s.	s.	PROPN
ejpam-4872	171	9	ahn	ahn	PROPN
ejpam-4872	171	10	et	et	PROPN
ejpam-4872	171	11	al	al	PROPN
ejpam-4872	171	12	.	.	PUNCT
ejpam-4872	171	13	/	/	SYM
ejpam-4872	171	14	eur	eur	PROPN
ejpam-4872	171	15	.	.	PUNCT
ejpam-4872	172	1	j.	j.	PROPN
ejpam-4872	172	2	pure	pure	PROPN
ejpam-4872	172	3	appl	appl	PROPN
ejpam-4872	172	4	.	.	PROPN
ejpam-4872	172	5	math	math	PROPN
ejpam-4872	172	6	,	,	PUNCT
ejpam-4872	172	7	16	16	NUM
ejpam-4872	172	8	(	(	PUNCT
ejpam-4872	172	9	3	3	NUM
ejpam-4872	172	10	)	)	PUNCT
ejpam-4872	172	11	(	(	PUNCT
ejpam-4872	172	12	2023	2023	NUM
ejpam-4872	172	13	)	)	PUNCT
ejpam-4872	172	14	,	,	PUNCT
ejpam-4872	172	15	1862	1862	NUM
ejpam-4872	172	16	-	-	SYM
ejpam-4872	172	17	1877	1877	NUM
ejpam-4872	172	18	1870	1870	NUM
ejpam-4872	172	19	and	and	CCONJ
ejpam-4872	172	20	so	so	ADV
ejpam-4872	172	21	max{f−(y	max{f−(y	PROPN
ejpam-4872	172	22	)	)	PUNCT
ejpam-4872	172	23	,	,	PUNCT
ejpam-4872	172	24	f−(z	f−(z	PROPN
ejpam-4872	172	25	)	)	PUNCT
ejpam-4872	172	26	}	}	PUNCT
ejpam-4872	172	27	≥	≥	PROPN
ejpam-4872	172	28	f−((y|z)|(y|z	f−((y|z)|(y|z	PROPN
ejpam-4872	172	29	)	)	PUNCT
ejpam-4872	172	30	)	)	PUNCT
ejpam-4872	172	31	≥	≥	PROPN
ejpam-4872	172	32	f−((x|(y|z))|(y|z	f−((x|(y|z))|(y|z	NOUN
ejpam-4872	172	33	)	)	PUNCT
ejpam-4872	172	34	)	)	PUNCT
ejpam-4872	172	35	and	and	CCONJ
ejpam-4872	172	36	min{f+(y	min{f+(y	NOUN
ejpam-4872	172	37	)	)	PUNCT
ejpam-4872	172	38	,	,	PUNCT
ejpam-4872	172	39	f+(z	f+(z	NUM
ejpam-4872	172	40	)	)	PUNCT
ejpam-4872	172	41	}	}	PUNCT
ejpam-4872	172	42	≤	≤	ADJ
ejpam-4872	172	43	f+((y|z)|(y|z	f+((y|z)|(y|z	PROPN
ejpam-4872	172	44	)	)	PUNCT
ejpam-4872	172	45	)	)	PUNCT
ejpam-4872	172	46	≤	≤	NOUN
ejpam-4872	172	47	f+((x|(y|z))|(y|z	f+((x|(y|z))|(y|z	NOUN
ejpam-4872	172	48	)	)	PUNCT
ejpam-4872	172	49	)	)	PUNCT
ejpam-4872	172	50	.	.	PUNCT
ejpam-4872	173	1	hence	hence	ADV
ejpam-4872	173	2	(	(	PUNCT
ejpam-4872	173	3	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	173	4	)	)	PUNCT
ejpam-4872	173	5	(	(	PUNCT
ejpam-4872	173	6	y	y	NOUN
ejpam-4872	173	7	,	,	PUNCT
ejpam-4872	173	8	z	z	NOUN
ejpam-4872	173	9	)	)	PUNCT
ejpam-4872	173	10	∈	∈	PROPN
ejpam-4872	173	11	f̊(m	f̊(m	PROPN
ejpam-4872	173	12	,	,	PUNCT
ejpam-4872	173	13	m	m	PROPN
ejpam-4872	173	14	)	)	PUNCT
ejpam-4872	173	15	.	.	PUNCT
ejpam-4872	174	1	also	also	ADV
ejpam-4872	174	2	,	,	PUNCT
ejpam-4872	174	3	we	we	PRON
ejpam-4872	174	4	have	have	VERB
ejpam-4872	174	5	fs(y	fs(y	NOUN
ejpam-4872	174	6	)	)	PUNCT
ejpam-4872	174	7	∩	∩	NOUN
ejpam-4872	174	8	fs(z	fs(z	NUM
ejpam-4872	174	9	)	)	PUNCT
ejpam-4872	174	10	⊆	⊆	NUM
ejpam-4872	174	11	fs((y|z)|(y|z	fs((y|z)|(y|z	NOUN
ejpam-4872	174	12	)	)	PUNCT
ejpam-4872	174	13	)	)	PUNCT
ejpam-4872	175	1	⊆	⊆	NUM
ejpam-4872	175	2	fs((x|(y|z))|(y|z	fs((x|(y|z))|(y|z	NOUN
ejpam-4872	175	3	)	)	PUNCT
ejpam-4872	175	4	)	)	PUNCT
ejpam-4872	175	5	and	and	CCONJ
ejpam-4872	175	6	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	175	7	)	)	PUNCT
ejpam-4872	175	8	,	,	PUNCT
ejpam-4872	175	9	f̃(z	f̃(z	PROPN
ejpam-4872	175	10	)	)	PUNCT
ejpam-4872	175	11	}	}	PUNCT
ejpam-4872	175	12	⊴	⊴	ADP
ejpam-4872	175	13	f̃((y|z)|(y|z	f̃((y|z)|(y|z	PROPN
ejpam-4872	175	14	)	)	PUNCT
ejpam-4872	175	15	)	)	PUNCT
ejpam-4872	175	16	⊴	⊴	ADP
ejpam-4872	175	17	f̃((x|(y|z))|(y|z	f̃((x|(y|z))|(y|z	PROPN
ejpam-4872	175	18	)	)	PUNCT
ejpam-4872	175	19	)	)	PUNCT
ejpam-4872	175	20	.	.	PUNCT
ejpam-4872	176	1	therefore	therefore	ADV
ejpam-4872	176	2	,	,	PUNCT
ejpam-4872	176	3	dokf	dokf	NOUN
ejpam-4872	176	4	:	:	PUNCT
ejpam-4872	176	5	=	=	SYM
ejpam-4872	176	6	(	(	PUNCT
ejpam-4872	176	7	f̊	f̊	X
ejpam-4872	176	8	,	,	PUNCT
ejpam-4872	176	9	fs	fs	PROPN
ejpam-4872	176	10	,	,	PUNCT
ejpam-4872	176	11	f̃	f̃	PROPN
ejpam-4872	176	12	)	)	PUNCT
ejpam-4872	176	13	is	be	AUX
ejpam-4872	176	14	a	a	DET
ejpam-4872	176	15	dokdo	dokdo	ADJ
ejpam-4872	176	16	filter	filter	NOUN
ejpam-4872	176	17	of	of	ADP
ejpam-4872	176	18	(	(	PUNCT
ejpam-4872	176	19	u	u	NOUN
ejpam-4872	176	20	,	,	PUNCT
ejpam-4872	176	21	x	x	NOUN
ejpam-4872	176	22	)	)	PUNCT
ejpam-4872	176	23	.	.	PUNCT
ejpam-4872	177	1	theorem	theorem	NOUN
ejpam-4872	177	2	2	2	NUM
ejpam-4872	177	3	.	.	PUNCT
ejpam-4872	178	1	if	if	SCONJ
ejpam-4872	178	2	dokf	dokf	NOUN
ejpam-4872	178	3	:	:	PUNCT
ejpam-4872	178	4	=	=	SYM
ejpam-4872	178	5	(	(	PUNCT
ejpam-4872	178	6	f̊	f̊	X
ejpam-4872	178	7	,	,	PUNCT
ejpam-4872	178	8	f	f	PROPN
ejpam-4872	178	9	s	s	PROPN
ejpam-4872	178	10	,	,	PUNCT
ejpam-4872	178	11	f̃	f̃	PROPN
ejpam-4872	178	12	)	)	PUNCT
ejpam-4872	178	13	is	be	AUX
ejpam-4872	178	14	a	a	DET
ejpam-4872	178	15	dokdo	dokdo	ADJ
ejpam-4872	178	16	filter	filter	NOUN
ejpam-4872	178	17	of	of	ADP
ejpam-4872	178	18	(	(	PUNCT
ejpam-4872	178	19	u	u	NOUN
ejpam-4872	178	20	,	,	PUNCT
ejpam-4872	178	21	x	x	NOUN
ejpam-4872	178	22	)	)	PUNCT
ejpam-4872	178	23	,	,	PUNCT
ejpam-4872	178	24	then	then	ADV
ejpam-4872	178	25	the	the	DET
ejpam-4872	178	26	sets	set	NOUN
ejpam-4872	178	27	f̊(t−	f̊(t−	PROPN
ejpam-4872	178	28	,	,	PUNCT
ejpam-4872	178	29	t+	t+	NOUN
ejpam-4872	178	30	)	)	PUNCT
ejpam-4872	178	31	,	,	PUNCT
ejpam-4872	178	32	fs	fs	ADP
ejpam-4872	178	33	α	α	NOUN
ejpam-4872	178	34	and	and	CCONJ
ejpam-4872	178	35	f̃ã	f̃ã	NOUN
ejpam-4872	178	36	are	be	AUX
ejpam-4872	178	37	filters	filter	NOUN
ejpam-4872	178	38	of	of	ADP
ejpam-4872	178	39	x	x	PRON
ejpam-4872	178	40	:	:	PUNCT
ejpam-4872	178	41	=	=	SYM
ejpam-4872	178	42	(	(	PUNCT
ejpam-4872	178	43	x	x	NOUN
ejpam-4872	178	44	,	,	PUNCT
ejpam-4872	178	45	|	|	INTJ
ejpam-4872	178	46	)	)	PUNCT
ejpam-4872	178	47	whenever	whenever	SCONJ
ejpam-4872	178	48	they	they	PRON
ejpam-4872	178	49	are	be	AUX
ejpam-4872	178	50	nonempty	nonempty	ADJ
ejpam-4872	178	51	for	for	ADP
ejpam-4872	178	52	all	all	DET
ejpam-4872	178	53	(	(	PUNCT
ejpam-4872	178	54	t−	t−	PROPN
ejpam-4872	178	55	,	,	PUNCT
ejpam-4872	178	56	t+	t+	ADJ
ejpam-4872	178	57	)	)	PUNCT
ejpam-4872	178	58	∈	∈	PROPN
ejpam-4872	179	1	[	[	X
ejpam-4872	179	2	−1	−1	NOUN
ejpam-4872	179	3	,	,	PUNCT
ejpam-4872	179	4	0	0	NUM
ejpam-4872	179	5	]	]	X
ejpam-4872	179	6	×	×	NOUN
ejpam-4872	180	1	[	[	X
ejpam-4872	180	2	0	0	NUM
ejpam-4872	180	3	,	,	PUNCT
ejpam-4872	180	4	1	1	NUM
ejpam-4872	180	5	]	]	PUNCT
ejpam-4872	180	6	,	,	PUNCT
ejpam-4872	180	7	α	α	PROPN
ejpam-4872	180	8	∈	∈	PROPN
ejpam-4872	180	9	2u	2u	NOUN
ejpam-4872	180	10	and	and	CCONJ
ejpam-4872	180	11	ã	ã	PROPN
ejpam-4872	180	12	=	=	PROPN
ejpam-4872	181	1	[	[	X
ejpam-4872	181	2	al	al	PROPN
ejpam-4872	181	3	,	,	PUNCT
ejpam-4872	181	4	ar	ar	NOUN
ejpam-4872	181	5	]	]	PUNCT
ejpam-4872	181	6	.	.	PUNCT
ejpam-4872	182	1	proof	proof	NOUN
ejpam-4872	182	2	.	.	PUNCT
ejpam-4872	183	1	assume	assume	VERB
ejpam-4872	183	2	that	that	SCONJ
ejpam-4872	183	3	dokf	dokf	NOUN
ejpam-4872	183	4	:	:	PUNCT
ejpam-4872	183	5	=	=	SYM
ejpam-4872	183	6	(	(	PUNCT
ejpam-4872	183	7	f̊	f̊	X
ejpam-4872	183	8	,	,	PUNCT
ejpam-4872	183	9	f	f	PROPN
ejpam-4872	183	10	s	s	PROPN
ejpam-4872	183	11	,	,	PUNCT
ejpam-4872	183	12	f̃	f̃	PROPN
ejpam-4872	183	13	)	)	PUNCT
ejpam-4872	183	14	is	be	AUX
ejpam-4872	183	15	a	a	DET
ejpam-4872	183	16	dokdo	dokdo	ADJ
ejpam-4872	183	17	filter	filter	NOUN
ejpam-4872	183	18	of	of	ADP
ejpam-4872	183	19	(	(	PUNCT
ejpam-4872	183	20	u	u	NOUN
ejpam-4872	183	21	,	,	PUNCT
ejpam-4872	183	22	x	x	X
ejpam-4872	183	23	)	)	PUNCT
ejpam-4872	183	24	and	and	CCONJ
ejpam-4872	183	25	let	let	VERB
ejpam-4872	183	26	(	(	PUNCT
ejpam-4872	183	27	t−	t−	NOUN
ejpam-4872	183	28	,	,	PUNCT
ejpam-4872	183	29	t+	t+	ADJ
ejpam-4872	183	30	)	)	PUNCT
ejpam-4872	183	31	∈	∈	PROPN
ejpam-4872	184	1	[	[	X
ejpam-4872	184	2	−1	−1	NOUN
ejpam-4872	184	3	,	,	PUNCT
ejpam-4872	184	4	0]×	0]×	PROPN
ejpam-4872	185	1	[	[	X
ejpam-4872	185	2	0	0	NUM
ejpam-4872	185	3	,	,	PUNCT
ejpam-4872	185	4	1	1	NUM
ejpam-4872	185	5	]	]	PUNCT
ejpam-4872	185	6	,	,	PUNCT
ejpam-4872	185	7	α	α	PROPN
ejpam-4872	185	8	∈	∈	PROPN
ejpam-4872	185	9	2u	2u	NOUN
ejpam-4872	185	10	and	and	CCONJ
ejpam-4872	185	11	ã	ã	PROPN
ejpam-4872	185	12	=	=	PROPN
ejpam-4872	186	1	[	[	X
ejpam-4872	186	2	al	al	PROPN
ejpam-4872	186	3	,	,	PUNCT
ejpam-4872	186	4	ar	ar	PROPN
ejpam-4872	186	5	]	]	PUNCT
ejpam-4872	186	6	be	be	AUX
ejpam-4872	186	7	such	such	ADJ
ejpam-4872	186	8	that	that	PRON
ejpam-4872	186	9	f̊(t−	f̊(t−	PROPN
ejpam-4872	186	10	,	,	PUNCT
ejpam-4872	186	11	t+	t+	NOUN
ejpam-4872	186	12	)	)	PUNCT
ejpam-4872	186	13	,	,	PUNCT
ejpam-4872	186	14	fs	fs	ADP
ejpam-4872	186	15	α	α	NOUN
ejpam-4872	186	16	and	and	CCONJ
ejpam-4872	186	17	f̃ã	f̃ã	NOUN
ejpam-4872	186	18	are	be	AUX
ejpam-4872	186	19	nonempty	nonempty	ADJ
ejpam-4872	186	20	.	.	PUNCT
ejpam-4872	187	1	it	it	PRON
ejpam-4872	187	2	is	be	AUX
ejpam-4872	187	3	clear	clear	ADJ
ejpam-4872	187	4	that	that	SCONJ
ejpam-4872	187	5	1	1	NUM
ejpam-4872	187	6	∈	∈	PROPN
ejpam-4872	187	7	f̊(t−	f̊(t−	PROPN
ejpam-4872	187	8	,	,	PUNCT
ejpam-4872	187	9	t+	t+	NOUN
ejpam-4872	187	10	)	)	PUNCT
ejpam-4872	187	11	∩	∩	NOUN
ejpam-4872	187	12	fs	fs	ADP
ejpam-4872	187	13	α	α	NOUN
ejpam-4872	187	14	∩	∩	NOUN
ejpam-4872	187	15	f̃ã	f̃ã	NOUN
ejpam-4872	187	16	by	by	ADP
ejpam-4872	187	17	(	(	PUNCT
ejpam-4872	187	18	19	19	NUM
ejpam-4872	187	19	)	)	PUNCT
ejpam-4872	187	20	.	.	PUNCT
ejpam-4872	188	1	let	let	VERB
ejpam-4872	188	2	x	x	PUNCT
ejpam-4872	188	3	∈	∈	PROPN
ejpam-4872	188	4	x	x	X
ejpam-4872	188	5	and	and	CCONJ
ejpam-4872	188	6	y	y	PROPN
ejpam-4872	188	7	∈	∈	PROPN
ejpam-4872	188	8	f̊(t−	f̊(t−	PROPN
ejpam-4872	188	9	,	,	PUNCT
ejpam-4872	188	10	t+	t+	NOUN
ejpam-4872	188	11	)	)	PUNCT
ejpam-4872	188	12	∩	∩	NOUN
ejpam-4872	188	13	fs	fs	ADP
ejpam-4872	188	14	α	α	PROPN
ejpam-4872	188	15	∩	∩	ADJ
ejpam-4872	188	16	f̃ã.	f̃ã.	NOUN
ejpam-4872	188	17	then	then	ADV
ejpam-4872	188	18	f̊−(y	f̊−(y	X
ejpam-4872	188	19	)	)	PUNCT
ejpam-4872	189	1	≤	≤	NOUN
ejpam-4872	189	2	t−	t−	PROPN
ejpam-4872	189	3	,	,	PUNCT
ejpam-4872	189	4	f̊+(y	f̊+(y	NOUN
ejpam-4872	189	5	)	)	PUNCT
ejpam-4872	189	6	≥	≥	NOUN
ejpam-4872	189	7	t+	t+	VERB
ejpam-4872	189	8	,	,	PUNCT
ejpam-4872	189	9	fs(y	fs(y	NUM
ejpam-4872	189	10	)	)	PUNCT
ejpam-4872	189	11	⊇	⊇	NOUN
ejpam-4872	189	12	α	α	NOUN
ejpam-4872	189	13	,	,	PUNCT
ejpam-4872	189	14	and	and	CCONJ
ejpam-4872	189	15	f̃(y	f̃(y	ADJ
ejpam-4872	189	16	)	)	PUNCT
ejpam-4872	189	17	⊵	⊵	PROPN
ejpam-4872	189	18	ã.	ã.	NOUN
ejpam-4872	189	19	using	use	VERB
ejpam-4872	189	20	(	(	PUNCT
ejpam-4872	189	21	20	20	NUM
ejpam-4872	189	22	)	)	PUNCT
ejpam-4872	189	23	,	,	PUNCT
ejpam-4872	189	24	we	we	PRON
ejpam-4872	189	25	have	have	VERB
ejpam-4872	189	26	f̊−(x|(y|y	f̊−(x|(y|y	PROPN
ejpam-4872	189	27	)	)	PUNCT
ejpam-4872	189	28	)	)	PUNCT
ejpam-4872	189	29	≤	≤	NOUN
ejpam-4872	189	30	f̊−(y	f̊−(y	X
ejpam-4872	189	31	)	)	PUNCT
ejpam-4872	190	1	≤	≤	NOUN
ejpam-4872	190	2	t−	t−	PROPN
ejpam-4872	190	3	and	and	CCONJ
ejpam-4872	190	4	f̊+(x|(y|y	f̊+(x|(y|y	NUM
ejpam-4872	190	5	)	)	PUNCT
ejpam-4872	190	6	)	)	PUNCT
ejpam-4872	190	7	≥	≥	NOUN
ejpam-4872	190	8	f̊+(y	f̊+(y	VERB
ejpam-4872	190	9	)	)	PUNCT
ejpam-4872	190	10	≥	≥	NOUN
ejpam-4872	190	11	t+	t+	VERB
ejpam-4872	190	12	,	,	PUNCT
ejpam-4872	190	13	that	that	ADV
ejpam-4872	190	14	is	is	ADV
ejpam-4872	190	15	,	,	PUNCT
ejpam-4872	190	16	x|(y|y	x|(y|y	PROPN
ejpam-4872	190	17	)	)	PUNCT
ejpam-4872	190	18	∈	∈	PROPN
ejpam-4872	190	19	f̊(t−	f̊(t−	PROPN
ejpam-4872	190	20	,	,	PUNCT
ejpam-4872	190	21	t+	t+	NOUN
ejpam-4872	190	22	)	)	PUNCT
ejpam-4872	190	23	.	.	PUNCT
ejpam-4872	191	1	also	also	ADV
ejpam-4872	191	2	,	,	PUNCT
ejpam-4872	191	3	we	we	PRON
ejpam-4872	191	4	obtain	obtain	VERB
ejpam-4872	191	5	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	191	6	)	)	PUNCT
ejpam-4872	191	7	)	)	PUNCT
ejpam-4872	192	1	⊇	⊇	PROPN
ejpam-4872	192	2	fs(y	fs(y	X
ejpam-4872	192	3	)	)	PUNCT
ejpam-4872	192	4	⊇	⊇	NOUN
ejpam-4872	192	5	α	α	NOUN
ejpam-4872	192	6	and	and	CCONJ
ejpam-4872	192	7	f̃(x|(y|y	f̃(x|(y|y	ADJ
ejpam-4872	192	8	)	)	PUNCT
ejpam-4872	192	9	)	)	PUNCT
ejpam-4872	192	10	⊵	⊵	ADJ
ejpam-4872	192	11	f̃(y	f̃(y	NOUN
ejpam-4872	192	12	)	)	PUNCT
ejpam-4872	192	13	⊵	⊵	PROPN
ejpam-4872	192	14	ã.	ã.	PROPN
ejpam-4872	192	15	hence	hence	ADV
ejpam-4872	192	16	x|(y|y	x|(y|y	PROPN
ejpam-4872	192	17	)	)	PUNCT
ejpam-4872	192	18	∈	∈	PROPN
ejpam-4872	192	19	f	f	PROPN
ejpam-4872	192	20	s	s	PROPN
ejpam-4872	192	21	α	α	PROPN
ejpam-4872	192	22	∩	∩	ADJ
ejpam-4872	192	23	f̃ã.	f̃ã.	NOUN
ejpam-4872	192	24	let	let	VERB
ejpam-4872	192	25	x	x	SYM
ejpam-4872	192	26	∈	∈	PROPN
ejpam-4872	192	27	x	x	X
ejpam-4872	192	28	and	and	CCONJ
ejpam-4872	192	29	y	y	PROPN
ejpam-4872	192	30	,	,	PUNCT
ejpam-4872	192	31	z	z	PROPN
ejpam-4872	192	32	∈	∈	PROPN
ejpam-4872	192	33	f̊(t−	f̊(t−	PROPN
ejpam-4872	192	34	,	,	PUNCT
ejpam-4872	192	35	t+	t+	NOUN
ejpam-4872	192	36	)	)	PUNCT
ejpam-4872	192	37	∩	∩	NOUN
ejpam-4872	192	38	fs	fs	ADP
ejpam-4872	192	39	α	α	PROPN
ejpam-4872	192	40	∩	∩	ADJ
ejpam-4872	192	41	f̃ã.	f̃ã.	NOUN
ejpam-4872	192	42	then	then	ADV
ejpam-4872	192	43	f̊−(y	f̊−(y	X
ejpam-4872	192	44	)	)	PUNCT
ejpam-4872	192	45	≤	≤	NOUN
ejpam-4872	192	46	t−	t−	PROPN
ejpam-4872	192	47	,	,	PUNCT
ejpam-4872	192	48	f̊+(y	f̊+(y	NOUN
ejpam-4872	192	49	)	)	PUNCT
ejpam-4872	192	50	≥	≥	NOUN
ejpam-4872	192	51	t+	t+	PROPN
ejpam-4872	192	52	,	,	PUNCT
ejpam-4872	192	53	f	f	PROPN
ejpam-4872	192	54	s(y	s(y	PROPN
ejpam-4872	192	55	)	)	PUNCT
ejpam-4872	192	56	⊇	⊇	NOUN
ejpam-4872	192	57	α	α	NOUN
ejpam-4872	192	58	,	,	PUNCT
ejpam-4872	192	59	f̃(y	f̃(y	ADJ
ejpam-4872	192	60	)	)	PUNCT
ejpam-4872	192	61	⊵	⊵	PROPN
ejpam-4872	192	62	ã	ã	PROPN
ejpam-4872	192	63	,	,	PUNCT
ejpam-4872	192	64	f̊−(z	f̊−(z	NOUN
ejpam-4872	192	65	)	)	PUNCT
ejpam-4872	192	66	≤	≤	NOUN
ejpam-4872	192	67	t−	t−	PROPN
ejpam-4872	192	68	,	,	PUNCT
ejpam-4872	192	69	f̊+(z	f̊+(z	PROPN
ejpam-4872	192	70	)	)	PUNCT
ejpam-4872	192	71	≥	≥	NOUN
ejpam-4872	192	72	t+	t+	PROPN
ejpam-4872	192	73	,	,	PUNCT
ejpam-4872	192	74	f	f	PROPN
ejpam-4872	192	75	s(z	s(z	PROPN
ejpam-4872	192	76	)	)	PUNCT
ejpam-4872	192	77	⊇	⊇	NOUN
ejpam-4872	192	78	α	α	NOUN
ejpam-4872	192	79	,	,	PUNCT
ejpam-4872	192	80	and	and	CCONJ
ejpam-4872	192	81	f̃(z	f̃(z	PROPN
ejpam-4872	192	82	)	)	PUNCT
ejpam-4872	192	83	⊵	⊵	PROPN
ejpam-4872	192	84	ã.	ã.	PROPN
ejpam-4872	192	85	it	it	PRON
ejpam-4872	192	86	follows	follow	VERB
ejpam-4872	192	87	from	from	ADP
ejpam-4872	192	88	(	(	PUNCT
ejpam-4872	192	89	21	21	NUM
ejpam-4872	192	90	)	)	PUNCT
ejpam-4872	192	91	that	that	DET
ejpam-4872	192	92	f̊−((x|(y|z))|(y|z	f̊−((x|(y|z))|(y|z	ADJ
ejpam-4872	192	93	)	)	PUNCT
ejpam-4872	192	94	)	)	PUNCT
ejpam-4872	192	95	≤	≤	NOUN
ejpam-4872	193	1	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	193	2	)	)	PUNCT
ejpam-4872	193	3	,	,	PUNCT
ejpam-4872	193	4	f̊−(z	f̊−(z	NUM
ejpam-4872	193	5	)	)	PUNCT
ejpam-4872	193	6	}	}	PUNCT
ejpam-4872	193	7	≤	≤	NOUN
ejpam-4872	193	8	t−	t−	PROPN
ejpam-4872	193	9	,	,	PUNCT
ejpam-4872	193	10	f̊+((x|(y|z))|(y|z	f̊+((x|(y|z))|(y|z	NUM
ejpam-4872	193	11	)	)	PUNCT
ejpam-4872	193	12	)	)	PUNCT
ejpam-4872	193	13	≥	≥	NOUN
ejpam-4872	193	14	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	193	15	)	)	PUNCT
ejpam-4872	193	16	,	,	PUNCT
ejpam-4872	193	17	f̊+(z	f̊+(z	PROPN
ejpam-4872	193	18	)	)	PUNCT
ejpam-4872	193	19	}	}	PUNCT
ejpam-4872	193	20	≥	≥	NUM
ejpam-4872	193	21	t+	t+	VERB
ejpam-4872	193	22	,	,	PUNCT
ejpam-4872	193	23	i.e.	i.e.	X
ejpam-4872	193	24	,	,	PUNCT
ejpam-4872	193	25	(	(	PUNCT
ejpam-4872	193	26	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	193	27	)	)	PUNCT
ejpam-4872	193	28	∈	∈	PROPN
ejpam-4872	193	29	f̊(t−	f̊(t−	PROPN
ejpam-4872	193	30	,	,	PUNCT
ejpam-4872	193	31	t+	t+	NOUN
ejpam-4872	193	32	)	)	PUNCT
ejpam-4872	193	33	.	.	PUNCT
ejpam-4872	194	1	also	also	ADV
ejpam-4872	194	2	,	,	PUNCT
ejpam-4872	194	3	f	f	PROPN
ejpam-4872	194	4	s((x|(y|z))|(y|z	s((x|(y|z))|(y|z	PROPN
ejpam-4872	194	5	)	)	PUNCT
ejpam-4872	194	6	)	)	PUNCT
ejpam-4872	195	1	⊇	⊇	PROPN
ejpam-4872	195	2	fs(y	fs(y	ADJ
ejpam-4872	195	3	)	)	PUNCT
ejpam-4872	195	4	∩	∩	NOUN
ejpam-4872	195	5	fs(z	fs(z	NUM
ejpam-4872	195	6	)	)	PUNCT
ejpam-4872	195	7	⊇	⊇	NOUN
ejpam-4872	195	8	α	α	PROPN
ejpam-4872	195	9	and	and	CCONJ
ejpam-4872	195	10	f̃((x|(y|z))|(y|z	f̃((x|(y|z))|(y|z	PROPN
ejpam-4872	195	11	)	)	PUNCT
ejpam-4872	195	12	)	)	PUNCT
ejpam-4872	195	13	⊵	⊵	PROPN
ejpam-4872	195	14	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	195	15	)	)	PUNCT
ejpam-4872	195	16	,	,	PUNCT
ejpam-4872	195	17	f̃(z	f̃(z	PROPN
ejpam-4872	195	18	)	)	PUNCT
ejpam-4872	195	19	}	}	PUNCT
ejpam-4872	195	20	⊵	⊵	PROPN
ejpam-4872	195	21	ã.	ã.	PROPN
ejpam-4872	195	22	thus	thus	ADV
ejpam-4872	195	23	(	(	PUNCT
ejpam-4872	195	24	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	195	25	)	)	PUNCT
ejpam-4872	195	26	∈	∈	PROPN
ejpam-4872	195	27	fs	fs	ADP
ejpam-4872	195	28	α	α	PROPN
ejpam-4872	195	29	∩	∩	ADJ
ejpam-4872	195	30	f̃ã.	f̃ã.	NOUN
ejpam-4872	195	31	therefore	therefore	ADV
ejpam-4872	195	32	,	,	PUNCT
ejpam-4872	195	33	f̊(t	f̊(t	PUNCT
ejpam-4872	195	34	−	−	NOUN
ejpam-4872	195	35	,	,	PUNCT
ejpam-4872	195	36	t+	t+	NOUN
ejpam-4872	195	37	)	)	PUNCT
ejpam-4872	195	38	,	,	PUNCT
ejpam-4872	195	39	fs	fs	ADP
ejpam-4872	195	40	α	α	NOUN
ejpam-4872	195	41	and	and	CCONJ
ejpam-4872	195	42	f̃ã	f̃ã	NOUN
ejpam-4872	195	43	are	be	AUX
ejpam-4872	195	44	filters	filter	NOUN
ejpam-4872	195	45	of	of	ADP
ejpam-4872	195	46	x	x	PRON
ejpam-4872	195	47	:	:	PUNCT
ejpam-4872	195	48	=	=	SYM
ejpam-4872	195	49	(	(	PUNCT
ejpam-4872	195	50	x	x	NOUN
ejpam-4872	195	51	,	,	PUNCT
ejpam-4872	195	52	|	|	NOUN
ejpam-4872	195	53	)	)	PUNCT
ejpam-4872	195	54	.	.	PUNCT
ejpam-4872	196	1	the	the	DET
ejpam-4872	196	2	example	example	NOUN
ejpam-4872	196	3	below	below	ADP
ejpam-4872	196	4	shows	show	VERB
ejpam-4872	196	5	that	that	SCONJ
ejpam-4872	196	6	the	the	DET
ejpam-4872	196	7	converse	converse	NOUN
ejpam-4872	196	8	of	of	ADP
ejpam-4872	196	9	theorem	theorem	ADJ
ejpam-4872	196	10	2	2	NUM
ejpam-4872	196	11	may	may	AUX
ejpam-4872	196	12	not	not	PART
ejpam-4872	196	13	be	be	AUX
ejpam-4872	196	14	true	true	ADJ
ejpam-4872	196	15	.	.	PUNCT
ejpam-4872	197	1	example	example	NOUN
ejpam-4872	198	1	3	3	X
ejpam-4872	198	2	.	.	X
ejpam-4872	198	3	consider	consider	VERB
ejpam-4872	198	4	the	the	DET
ejpam-4872	198	5	sheffer	sheffer	NOUN
ejpam-4872	198	6	stroke	stroke	NOUN
ejpam-4872	198	7	hilbert	hilbert	PROPN
ejpam-4872	198	8	algebra	algebra	PROPN
ejpam-4872	198	9	x	x	X
ejpam-4872	198	10	:	:	PUNCT
ejpam-4872	198	11	=	=	SYM
ejpam-4872	198	12	(	(	PUNCT
ejpam-4872	198	13	x	x	NOUN
ejpam-4872	198	14	,	,	PUNCT
ejpam-4872	198	15	|	|	ADV
ejpam-4872	198	16	)	)	PUNCT
ejpam-4872	198	17	in	in	ADP
ejpam-4872	198	18	example	example	NOUN
ejpam-4872	198	19	1	1	NUM
ejpam-4872	198	20	and	and	CCONJ
ejpam-4872	198	21	let	let	VERB
ejpam-4872	198	22	dokf	dokf	VERB
ejpam-4872	198	23	:	:	PUNCT
ejpam-4872	198	24	=	=	SYM
ejpam-4872	198	25	(	(	PUNCT
ejpam-4872	198	26	f̊	f̊	X
ejpam-4872	198	27	,	,	PUNCT
ejpam-4872	198	28	f	f	PROPN
ejpam-4872	198	29	s	s	PROPN
ejpam-4872	198	30	,	,	PUNCT
ejpam-4872	198	31	f̃	f̃	PROPN
ejpam-4872	198	32	)	)	PUNCT
ejpam-4872	198	33	be	be	VERB
ejpam-4872	198	34	a	a	DET
ejpam-4872	198	35	dokdo	dokdo	NOUN
ejpam-4872	198	36	structure	structure	NOUN
ejpam-4872	198	37	in	in	ADP
ejpam-4872	198	38	(	(	PUNCT
ejpam-4872	198	39	x	x	X
ejpam-4872	198	40	,	,	PUNCT
ejpam-4872	198	41	u	u	NOUN
ejpam-4872	198	42	=	=	PROPN
ejpam-4872	198	43	z	z	PROPN
ejpam-4872	198	44	)	)	PUNCT
ejpam-4872	198	45	which	which	PRON
ejpam-4872	198	46	is	be	AUX
ejpam-4872	198	47	given	give	VERB
ejpam-4872	198	48	by	by	ADP
ejpam-4872	198	49	table	table	NOUN
ejpam-4872	198	50	6	6	NUM
ejpam-4872	198	51	.	.	PUNCT
ejpam-4872	199	1	it	it	PRON
ejpam-4872	199	2	is	be	AUX
ejpam-4872	199	3	routine	routine	ADJ
ejpam-4872	199	4	to	to	PART
ejpam-4872	199	5	verify	verify	VERB
ejpam-4872	199	6	that	that	SCONJ
ejpam-4872	199	7	the	the	DET
ejpam-4872	199	8	nonempty	nonempty	NOUN
ejpam-4872	199	9	sets	set	VERB
ejpam-4872	199	10	f̊(t−	f̊(t−	PROPN
ejpam-4872	199	11	,	,	PUNCT
ejpam-4872	199	12	t+	t+	NOUN
ejpam-4872	199	13	)	)	PUNCT
ejpam-4872	199	14	,	,	PUNCT
ejpam-4872	199	15	fs	fs	ADP
ejpam-4872	199	16	α	α	NOUN
ejpam-4872	199	17	and	and	CCONJ
ejpam-4872	199	18	f̃ã	f̃ã	NOUN
ejpam-4872	199	19	are	be	AUX
ejpam-4872	199	20	filters	filter	NOUN
ejpam-4872	199	21	of	of	ADP
ejpam-4872	199	22	x	x	PRON
ejpam-4872	199	23	:	:	PUNCT
ejpam-4872	199	24	=	=	SYM
ejpam-4872	199	25	(	(	PUNCT
ejpam-4872	199	26	x	x	NOUN
ejpam-4872	199	27	,	,	PUNCT
ejpam-4872	199	28	|	|	ADV
ejpam-4872	199	29	)	)	PUNCT
ejpam-4872	199	30	for	for	ADP
ejpam-4872	199	31	all	all	DET
ejpam-4872	199	32	(	(	PUNCT
ejpam-4872	199	33	t−	t−	PROPN
ejpam-4872	199	34	,	,	PUNCT
ejpam-4872	199	35	t+	t+	ADJ
ejpam-4872	199	36	)	)	PUNCT
ejpam-4872	199	37	∈	∈	PROPN
ejpam-4872	200	1	[	[	X
ejpam-4872	200	2	−1	−1	NOUN
ejpam-4872	200	3	,	,	PUNCT
ejpam-4872	200	4	0]×	0]×	PROPN
ejpam-4872	201	1	[	[	X
ejpam-4872	201	2	0	0	NUM
ejpam-4872	201	3	,	,	PUNCT
ejpam-4872	201	4	1	1	NUM
ejpam-4872	201	5	]	]	PUNCT
ejpam-4872	201	6	,	,	PUNCT
ejpam-4872	201	7	α	α	PROPN
ejpam-4872	201	8	∈	∈	PROPN
ejpam-4872	201	9	2u	2u	NOUN
ejpam-4872	201	10	and	and	CCONJ
ejpam-4872	201	11	ã	ã	PROPN
ejpam-4872	201	12	=	=	PROPN
ejpam-4872	202	1	[	[	X
ejpam-4872	202	2	al	al	PROPN
ejpam-4872	202	3	,	,	PUNCT
ejpam-4872	202	4	ar	ar	NOUN
ejpam-4872	202	5	]	]	PUNCT
ejpam-4872	202	6	.	.	PUNCT
ejpam-4872	203	1	but	but	CCONJ
ejpam-4872	203	2	dokf	dokf	VERB
ejpam-4872	203	3	:	:	PUNCT
ejpam-4872	203	4	=	=	SYM
ejpam-4872	203	5	(	(	PUNCT
ejpam-4872	203	6	f̊	f̊	X
ejpam-4872	203	7	,	,	PUNCT
ejpam-4872	203	8	f	f	PROPN
ejpam-4872	203	9	s	s	PROPN
ejpam-4872	203	10	,	,	PUNCT
ejpam-4872	203	11	f̃	f̃	PROPN
ejpam-4872	203	12	)	)	PUNCT
ejpam-4872	203	13	is	be	AUX
ejpam-4872	203	14	not	not	PART
ejpam-4872	203	15	a	a	DET
ejpam-4872	203	16	dokdo	dokdo	NOUN
ejpam-4872	203	17	filter	filter	NOUN
ejpam-4872	203	18	of	of	ADP
ejpam-4872	203	19	(	(	PUNCT
ejpam-4872	203	20	u	u	NOUN
ejpam-4872	203	21	,	,	PUNCT
ejpam-4872	203	22	x	x	NOUN
ejpam-4872	203	23	)	)	PUNCT
ejpam-4872	203	24	since	since	SCONJ
ejpam-4872	203	25	2|(4|4	2|(4|4	NUM
ejpam-4872	203	26	)	)	PUNCT
ejpam-4872	203	27	(	(	PUNCT
ejpam-4872	203	28	4,4	4,4	NUM
ejpam-4872	203	29	)	)	PUNCT
ejpam-4872	203	30	=	=	SYM
ejpam-4872	203	31	7	7	NUM
ejpam-4872	203	32	(	(	PUNCT
ejpam-4872	203	33	4,4	4,4	NUM
ejpam-4872	203	34	)	)	PUNCT
ejpam-4872	203	35	/∈	/∈	PUNCT
ejpam-4872	204	1	f̊(m	f̊(m	ADJ
ejpam-4872	204	2	,	,	PUNCT
ejpam-4872	204	3	m	m	PROPN
ejpam-4872	204	4	)	)	PUNCT
ejpam-4872	204	5	.	.	PUNCT
ejpam-4872	205	1	we	we	PRON
ejpam-4872	205	2	provide	provide	VERB
ejpam-4872	205	3	conditions	condition	NOUN
ejpam-4872	205	4	for	for	SCONJ
ejpam-4872	205	5	a	a	DET
ejpam-4872	205	6	dokdo	dokdo	NOUN
ejpam-4872	205	7	structure	structure	NOUN
ejpam-4872	205	8	to	to	PART
ejpam-4872	205	9	be	be	AUX
ejpam-4872	205	10	a	a	DET
ejpam-4872	205	11	dokdo	dokdo	NOUN
ejpam-4872	205	12	filter	filter	NOUN
ejpam-4872	205	13	.	.	PUNCT
ejpam-4872	206	1	theorem	theorem	NOUN
ejpam-4872	206	2	3	3	NUM
ejpam-4872	206	3	.	.	PUNCT
ejpam-4872	206	4	given	give	VERB
ejpam-4872	206	5	a	a	DET
ejpam-4872	206	6	dokdo	dokdo	NOUN
ejpam-4872	206	7	stucture	stucture	NOUN
ejpam-4872	206	8	dokf	dokf	NOUN
ejpam-4872	206	9	:	:	PUNCT
ejpam-4872	206	10	=	=	SYM
ejpam-4872	206	11	(	(	PUNCT
ejpam-4872	206	12	f̊	f̊	X
ejpam-4872	206	13	,	,	PUNCT
ejpam-4872	206	14	fs	fs	PROPN
ejpam-4872	206	15	,	,	PUNCT
ejpam-4872	206	16	f̃	f̃	PROPN
ejpam-4872	206	17	)	)	PUNCT
ejpam-4872	206	18	in	in	ADP
ejpam-4872	206	19	(	(	PUNCT
ejpam-4872	206	20	u	u	NOUN
ejpam-4872	206	21	,	,	PUNCT
ejpam-4872	206	22	x	x	NOUN
ejpam-4872	206	23	)	)	PUNCT
ejpam-4872	206	24	,	,	PUNCT
ejpam-4872	206	25	if	if	SCONJ
ejpam-4872	206	26	the	the	DET
ejpam-4872	206	27	nonempty	nonempty	NOUN
ejpam-4872	206	28	sets	set	VERB
ejpam-4872	206	29	f̊(t−	f̊(t−	PROPN
ejpam-4872	206	30	)	)	PUNCT
ejpam-4872	206	31	,	,	PUNCT
ejpam-4872	206	32	f̊(t+	f̊(t+	NUM
ejpam-4872	206	33	)	)	PUNCT
ejpam-4872	206	34	,	,	PUNCT
ejpam-4872	206	35	fs	fs	ADP
ejpam-4872	206	36	α	α	NOUN
ejpam-4872	206	37	and	and	CCONJ
ejpam-4872	206	38	f̃ã	f̃ã	NOUN
ejpam-4872	206	39	are	be	AUX
ejpam-4872	206	40	filters	filter	NOUN
ejpam-4872	206	41	of	of	ADP
ejpam-4872	206	42	x	x	PRON
ejpam-4872	206	43	:	:	PUNCT
ejpam-4872	206	44	=	=	SYM
ejpam-4872	206	45	(	(	PUNCT
ejpam-4872	206	46	x	x	NOUN
ejpam-4872	206	47	,	,	PUNCT
ejpam-4872	206	48	|	|	ADV
ejpam-4872	206	49	)	)	PUNCT
ejpam-4872	206	50	for	for	ADP
ejpam-4872	206	51	all	all	DET
ejpam-4872	206	52	(	(	PUNCT
ejpam-4872	206	53	t−	t−	PROPN
ejpam-4872	206	54	,	,	PUNCT
ejpam-4872	206	55	t+	t+	ADJ
ejpam-4872	206	56	)	)	PUNCT
ejpam-4872	206	57	∈	∈	PROPN
ejpam-4872	207	1	[	[	X
ejpam-4872	207	2	−1	−1	NOUN
ejpam-4872	207	3	,	,	PUNCT
ejpam-4872	207	4	0]×	0]×	PROPN
ejpam-4872	208	1	[	[	X
ejpam-4872	208	2	0	0	NUM
ejpam-4872	208	3	,	,	PUNCT
ejpam-4872	208	4	1	1	NUM
ejpam-4872	208	5	]	]	PUNCT
ejpam-4872	208	6	,	,	PUNCT
ejpam-4872	208	7	α	α	PROPN
ejpam-4872	208	8	∈	∈	PROPN
ejpam-4872	208	9	2u	2u	NOUN
ejpam-4872	208	10	and	and	CCONJ
ejpam-4872	208	11	ã	ã	PROPN
ejpam-4872	208	12	=	=	PROPN
ejpam-4872	209	1	[	[	X
ejpam-4872	209	2	al	al	PROPN
ejpam-4872	209	3	,	,	PUNCT
ejpam-4872	209	4	ar	ar	PROPN
ejpam-4872	209	5	]	]	PROPN
ejpam-4872	209	6	,	,	PUNCT
ejpam-4872	209	7	then	then	ADV
ejpam-4872	209	8	dokf	dokf	VERB
ejpam-4872	209	9	:	:	PUNCT
ejpam-4872	209	10	=	=	SYM
ejpam-4872	209	11	(	(	PUNCT
ejpam-4872	209	12	f̊	f̊	X
ejpam-4872	209	13	,	,	PUNCT
ejpam-4872	209	14	f	f	PROPN
ejpam-4872	209	15	s	s	PROPN
ejpam-4872	209	16	,	,	PUNCT
ejpam-4872	209	17	f̃	f̃	PROPN
ejpam-4872	209	18	)	)	PUNCT
ejpam-4872	209	19	is	be	AUX
ejpam-4872	209	20	a	a	DET
ejpam-4872	209	21	dokdo	dokdo	ADJ
ejpam-4872	209	22	filter	filter	NOUN
ejpam-4872	209	23	of	of	ADP
ejpam-4872	209	24	(	(	PUNCT
ejpam-4872	209	25	u	u	NOUN
ejpam-4872	209	26	,	,	PUNCT
ejpam-4872	209	27	x	x	NOUN
ejpam-4872	209	28	)	)	PUNCT
ejpam-4872	209	29	.	.	PUNCT
ejpam-4872	210	1	s.	s.	PROPN
ejpam-4872	210	2	s.	s.	PROPN
ejpam-4872	210	3	ahn	ahn	PROPN
ejpam-4872	210	4	et	et	PROPN
ejpam-4872	210	5	al	al	PROPN
ejpam-4872	210	6	.	.	PUNCT
ejpam-4872	210	7	/	/	SYM
ejpam-4872	210	8	eur	eur	PROPN
ejpam-4872	210	9	.	.	PUNCT
ejpam-4872	211	1	j.	j.	PROPN
ejpam-4872	211	2	pure	pure	PROPN
ejpam-4872	211	3	appl	appl	PROPN
ejpam-4872	211	4	.	.	PROPN
ejpam-4872	211	5	math	math	PROPN
ejpam-4872	211	6	,	,	PUNCT
ejpam-4872	211	7	16	16	NUM
ejpam-4872	211	8	(	(	PUNCT
ejpam-4872	211	9	3	3	NUM
ejpam-4872	211	10	)	)	PUNCT
ejpam-4872	211	11	(	(	PUNCT
ejpam-4872	211	12	2023	2023	NUM
ejpam-4872	211	13	)	)	PUNCT
ejpam-4872	211	14	,	,	PUNCT
ejpam-4872	211	15	1862	1862	NUM
ejpam-4872	211	16	-	-	SYM
ejpam-4872	211	17	1877	1877	NUM
ejpam-4872	211	18	1871	1871	NUM
ejpam-4872	211	19	table	table	NOUN
ejpam-4872	211	20	6	6	NUM
ejpam-4872	211	21	:	:	PUNCT
ejpam-4872	211	22	tabular	tabular	PROPN
ejpam-4872	211	23	representation	representation	NOUN
ejpam-4872	211	24	of	of	ADP
ejpam-4872	211	25	dokf	dokf	NOUN
ejpam-4872	211	26	:	:	PUNCT
ejpam-4872	211	27	=	=	SYM
ejpam-4872	211	28	(	(	PUNCT
ejpam-4872	211	29	f̊	f̊	X
ejpam-4872	211	30	,	,	PUNCT
ejpam-4872	211	31	fs	fs	PROPN
ejpam-4872	211	32	,	,	PUNCT
ejpam-4872	211	33	f̃	f̃	PROPN
ejpam-4872	211	34	)	)	PUNCT
ejpam-4872	211	35	x	x	PUNCT
ejpam-4872	211	36	f̊(x	f̊(x	NOUN
ejpam-4872	211	37	)	)	PUNCT
ejpam-4872	211	38	fs(x	fs(x	NOUN
ejpam-4872	211	39	)	)	PUNCT
ejpam-4872	211	40	f̃(x	f̃(x	NOUN
ejpam-4872	211	41	)	)	PUNCT
ejpam-4872	211	42	0	0	NUM
ejpam-4872	212	1	(	(	PUNCT
ejpam-4872	212	2	−0.37	−0.37	NOUN
ejpam-4872	212	3	,	,	PUNCT
ejpam-4872	212	4	0.48	0.48	NUM
ejpam-4872	212	5	)	)	PUNCT
ejpam-4872	212	6	8n	8n	NOUN
ejpam-4872	212	7	[	[	X
ejpam-4872	212	8	0.26	0.26	NUM
ejpam-4872	212	9	,	,	PUNCT
ejpam-4872	212	10	0.62	0.62	NUM
ejpam-4872	212	11	]	]	SYM
ejpam-4872	212	12	2	2	NUM
ejpam-4872	212	13	(	(	PUNCT
ejpam-4872	212	14	−0.37	−0.37	PROPN
ejpam-4872	212	15	,	,	PUNCT
ejpam-4872	212	16	0.67	0.67	NUM
ejpam-4872	212	17	)	)	PUNCT
ejpam-4872	212	18	8n	8n	NOUN
ejpam-4872	213	1	[	[	X
ejpam-4872	213	2	0.26	0.26	NUM
ejpam-4872	213	3	,	,	PUNCT
ejpam-4872	213	4	0.62	0.62	NUM
ejpam-4872	213	5	]	]	SYM
ejpam-4872	213	6	3	3	NUM
ejpam-4872	213	7	(	(	PUNCT
ejpam-4872	213	8	−0.37	−0.37	PROPN
ejpam-4872	213	9	,	,	PUNCT
ejpam-4872	213	10	0.48	0.48	NUM
ejpam-4872	213	11	)	)	PUNCT
ejpam-4872	213	12	8z	8z	NOUN
ejpam-4872	214	1	[	[	X
ejpam-4872	214	2	0.26	0.26	NUM
ejpam-4872	214	3	,	,	PUNCT
ejpam-4872	214	4	0.62	0.62	NUM
ejpam-4872	214	5	]	]	SYM
ejpam-4872	214	6	4	4	NUM
ejpam-4872	214	7	(	(	PUNCT
ejpam-4872	214	8	−0.55	−0.55	NOUN
ejpam-4872	214	9	,	,	PUNCT
ejpam-4872	214	10	0.48	0.48	NUM
ejpam-4872	214	11	)	)	PUNCT
ejpam-4872	214	12	8n	8n	NOUN
ejpam-4872	214	13	[	[	X
ejpam-4872	214	14	0.31	0.31	NUM
ejpam-4872	214	15	,	,	PUNCT
ejpam-4872	214	16	0.70	0.70	NUM
ejpam-4872	214	17	]	]	SYM
ejpam-4872	214	18	5	5	NUM
ejpam-4872	214	19	(	(	PUNCT
ejpam-4872	214	20	−0.63	−0.63	INTJ
ejpam-4872	214	21	,	,	PUNCT
ejpam-4872	214	22	0.78	0.78	NUM
ejpam-4872	214	23	)	)	PUNCT
ejpam-4872	214	24	8z	8z	NOUN
ejpam-4872	215	1	[	[	X
ejpam-4872	215	2	0.26	0.26	NUM
ejpam-4872	215	3	,	,	PUNCT
ejpam-4872	215	4	0.62	0.62	NUM
ejpam-4872	215	5	]	]	SYM
ejpam-4872	215	6	6	6	NUM
ejpam-4872	215	7	(	(	PUNCT
ejpam-4872	215	8	−0.55	−0.55	NOUN
ejpam-4872	215	9	,	,	PUNCT
ejpam-4872	215	10	0.48	0.48	NUM
ejpam-4872	215	11	)	)	PUNCT
ejpam-4872	215	12	8n	8n	NOUN
ejpam-4872	215	13	[	[	X
ejpam-4872	215	14	0.36	0.36	NUM
ejpam-4872	215	15	,	,	PUNCT
ejpam-4872	215	16	0.73	0.73	NUM
ejpam-4872	215	17	]	]	PUNCT
ejpam-4872	215	18	7	7	NUM
ejpam-4872	215	19	(	(	PUNCT
ejpam-4872	215	20	−0.37	−0.37	NOUN
ejpam-4872	215	21	,	,	PUNCT
ejpam-4872	215	22	0.48	0.48	NUM
ejpam-4872	215	23	)	)	PUNCT
ejpam-4872	215	24	4z	4z	NOUN
ejpam-4872	216	1	[	[	X
ejpam-4872	216	2	0.32	0.32	NUM
ejpam-4872	216	3	,	,	PUNCT
ejpam-4872	216	4	0.70	0.70	NUM
ejpam-4872	216	5	]	]	SYM
ejpam-4872	216	6	1	1	NUM
ejpam-4872	216	7	(	(	PUNCT
ejpam-4872	216	8	−0.71	−0.71	ADV
ejpam-4872	216	9	,	,	PUNCT
ejpam-4872	216	10	0.82	0.82	NUM
ejpam-4872	216	11	)	)	PUNCT
ejpam-4872	216	12	2z	2z	NOUN
ejpam-4872	217	1	[	[	X
ejpam-4872	217	2	0.41	0.41	NUM
ejpam-4872	217	3	,	,	PUNCT
ejpam-4872	217	4	0.88	0.88	NUM
ejpam-4872	217	5	]	]	PUNCT
ejpam-4872	217	6	proof	proof	NOUN
ejpam-4872	217	7	.	.	PUNCT
ejpam-4872	218	1	assume	assume	VERB
ejpam-4872	218	2	that	that	SCONJ
ejpam-4872	218	3	f̊(t−	f̊(t−	PROPN
ejpam-4872	218	4	)	)	PUNCT
ejpam-4872	218	5	,	,	PUNCT
ejpam-4872	218	6	f̊(t+	f̊(t+	NUM
ejpam-4872	218	7	)	)	PUNCT
ejpam-4872	218	8	,	,	PUNCT
ejpam-4872	218	9	fs	fs	ADP
ejpam-4872	218	10	α	α	NOUN
ejpam-4872	218	11	and	and	CCONJ
ejpam-4872	218	12	f̃ã	f̃ã	NOUN
ejpam-4872	218	13	are	be	AUX
ejpam-4872	218	14	nonempty	nonempty	ADJ
ejpam-4872	218	15	filters	filter	NOUN
ejpam-4872	218	16	of	of	ADP
ejpam-4872	218	17	x	x	PRON
ejpam-4872	218	18	:	:	PUNCT
ejpam-4872	218	19	=	=	SYM
ejpam-4872	218	20	(	(	PUNCT
ejpam-4872	218	21	x	x	NOUN
ejpam-4872	218	22	,	,	PUNCT
ejpam-4872	218	23	|	|	ADV
ejpam-4872	218	24	)	)	PUNCT
ejpam-4872	218	25	for	for	ADP
ejpam-4872	218	26	all	all	DET
ejpam-4872	218	27	(	(	PUNCT
ejpam-4872	218	28	t−	t−	PROPN
ejpam-4872	218	29	,	,	PUNCT
ejpam-4872	218	30	t+	t+	ADJ
ejpam-4872	218	31	)	)	PUNCT
ejpam-4872	218	32	∈	∈	PROPN
ejpam-4872	219	1	[	[	X
ejpam-4872	219	2	−1	−1	NOUN
ejpam-4872	219	3	,	,	PUNCT
ejpam-4872	219	4	0	0	NUM
ejpam-4872	219	5	]	]	X
ejpam-4872	219	6	×	×	NOUN
ejpam-4872	220	1	[	[	X
ejpam-4872	220	2	0	0	NUM
ejpam-4872	220	3	,	,	PUNCT
ejpam-4872	220	4	1	1	NUM
ejpam-4872	220	5	]	]	PUNCT
ejpam-4872	220	6	,	,	PUNCT
ejpam-4872	220	7	α	α	PROPN
ejpam-4872	220	8	∈	∈	PROPN
ejpam-4872	220	9	2u	2u	NOUN
ejpam-4872	220	10	and	and	CCONJ
ejpam-4872	220	11	ã	ã	PROPN
ejpam-4872	220	12	=	=	PROPN
ejpam-4872	221	1	[	[	X
ejpam-4872	221	2	al	al	PROPN
ejpam-4872	221	3	,	,	PUNCT
ejpam-4872	221	4	ar	ar	NOUN
ejpam-4872	221	5	]	]	X
ejpam-4872	221	6	.	.	PUNCT
ejpam-4872	222	1	if	if	SCONJ
ejpam-4872	222	2	there	there	PRON
ejpam-4872	222	3	is	be	VERB
ejpam-4872	222	4	a	a	DET
ejpam-4872	222	5	∈	∈	NOUN
ejpam-4872	222	6	x	x	PUNCT
ejpam-4872	222	7	such	such	ADJ
ejpam-4872	222	8	that	that	SCONJ
ejpam-4872	222	9	1	1	NUM
ejpam-4872	222	10	(	(	PUNCT
ejpam-4872	222	11	a	a	PRON
ejpam-4872	222	12	,	,	PUNCT
ejpam-4872	222	13	a	a	NOUN
ejpam-4872	222	14	)	)	PUNCT
ejpam-4872	222	15	/∈	/∈	PUNCT
ejpam-4872	223	1	f̊(m	f̊(m	ADJ
ejpam-4872	223	2	,	,	PUNCT
ejpam-4872	223	3	m	m	PROPN
ejpam-4872	223	4	)	)	PUNCT
ejpam-4872	223	5	,	,	PUNCT
ejpam-4872	223	6	then	then	ADV
ejpam-4872	223	7	f̊−(1	f̊−(1	NOUN
ejpam-4872	223	8	)	)	PUNCT
ejpam-4872	223	9	>	>	X
ejpam-4872	223	10	f̊−(a	f̊−(a	NOUN
ejpam-4872	223	11	)	)	PUNCT
ejpam-4872	223	12	or	or	CCONJ
ejpam-4872	223	13	f̊+(1	f̊+(1	NOUN
ejpam-4872	223	14	)	)	PUNCT
ejpam-4872	223	15	<	<	X
ejpam-4872	223	16	f̊+(a	f̊+(a	PROPN
ejpam-4872	223	17	)	)	PUNCT
ejpam-4872	223	18	.	.	PUNCT
ejpam-4872	224	1	hence	hence	ADV
ejpam-4872	224	2	a	a	DET
ejpam-4872	224	3	∈	∈	PROPN
ejpam-4872	224	4	f̊(f̊−(a	f̊(f̊−(a	NOUN
ejpam-4872	224	5	)	)	PUNCT
ejpam-4872	224	6	)	)	PUNCT
ejpam-4872	224	7	∩	∩	ADJ
ejpam-4872	224	8	f̊(f̊+(a	f̊(f̊+(a	ADJ
ejpam-4872	224	9	)	)	PUNCT
ejpam-4872	224	10	)	)	PUNCT
ejpam-4872	224	11	and	and	CCONJ
ejpam-4872	224	12	1	1	NUM
ejpam-4872	224	13	/∈	/∈	INTJ
ejpam-4872	224	14	f̊(f̊−(a	f̊(f̊−(a	ADJ
ejpam-4872	224	15	)	)	PUNCT
ejpam-4872	224	16	)	)	PUNCT
ejpam-4872	224	17	∩	∩	ADJ
ejpam-4872	224	18	f̊(f̊+(a	f̊(f̊+(a	ADJ
ejpam-4872	224	19	)	)	PUNCT
ejpam-4872	224	20	)	)	PUNCT
ejpam-4872	224	21	,	,	PUNCT
ejpam-4872	224	22	a	a	DET
ejpam-4872	224	23	contradiction	contradiction	NOUN
ejpam-4872	224	24	.	.	PUNCT
ejpam-4872	225	1	thus	thus	ADV
ejpam-4872	225	2	1	1	NUM
ejpam-4872	225	3	(	(	PUNCT
ejpam-4872	225	4	x	x	NOUN
ejpam-4872	225	5	,	,	PUNCT
ejpam-4872	225	6	x	x	NOUN
ejpam-4872	225	7	)	)	PUNCT
ejpam-4872	225	8	∈	∈	PROPN
ejpam-4872	225	9	f̊(m	f̊(m	PROPN
ejpam-4872	225	10	,	,	PUNCT
ejpam-4872	225	11	m	m	PROPN
ejpam-4872	225	12	)	)	PUNCT
ejpam-4872	225	13	for	for	ADP
ejpam-4872	225	14	all	all	PRON
ejpam-4872	225	15	x	x	SYM
ejpam-4872	225	16	∈	∈	NOUN
ejpam-4872	225	17	x.	x.	NOUN
ejpam-4872	225	18	let	let	VERB
ejpam-4872	225	19	x	x	PRON
ejpam-4872	225	20	,	,	PUNCT
ejpam-4872	225	21	a	a	DET
ejpam-4872	225	22	∈	∈	NOUN
ejpam-4872	225	23	x	x	AUX
ejpam-4872	225	24	be	be	AUX
ejpam-4872	225	25	such	such	ADJ
ejpam-4872	225	26	that	that	DET
ejpam-4872	225	27	fs(x	fs(x	NOUN
ejpam-4872	225	28	)	)	PUNCT
ejpam-4872	225	29	=	=	SYM
ejpam-4872	225	30	α	α	PROPN
ejpam-4872	225	31	and	and	CCONJ
ejpam-4872	225	32	f̃(a	f̃(a	NOUN
ejpam-4872	225	33	)	)	PUNCT
ejpam-4872	226	1	=	=	PUNCT
ejpam-4872	226	2	ã.	ã.	NOUN
ejpam-4872	226	3	then	then	ADV
ejpam-4872	226	4	(	(	PUNCT
ejpam-4872	226	5	x	x	X
ejpam-4872	226	6	,	,	PUNCT
ejpam-4872	226	7	a	a	PRON
ejpam-4872	226	8	)	)	PUNCT
ejpam-4872	226	9	∈	∈	NOUN
ejpam-4872	226	10	fs	fs	ADP
ejpam-4872	226	11	α	α	DET
ejpam-4872	226	12	×	×	NOUN
ejpam-4872	226	13	f̃ã	f̃ã	NOUN
ejpam-4872	226	14	,	,	PUNCT
ejpam-4872	226	15	i.e.	i.e.	X
ejpam-4872	226	16	,	,	PUNCT
ejpam-4872	226	17	f	f	PROPN
ejpam-4872	226	18	s	s	PROPN
ejpam-4872	226	19	α	α	PROPN
ejpam-4872	226	20	̸=	̸=	PROPN
ejpam-4872	226	21	∅	∅	NOUN
ejpam-4872	226	22	̸=	̸=	PROPN
ejpam-4872	226	23	f̃ã	f̃ã	NOUN
ejpam-4872	226	24	,	,	PUNCT
ejpam-4872	226	25	and	and	CCONJ
ejpam-4872	226	26	so	so	ADV
ejpam-4872	226	27	1	1	NUM
ejpam-4872	226	28	∈	∈	NOUN
ejpam-4872	226	29	fs	fs	ADP
ejpam-4872	226	30	α	α	PROPN
ejpam-4872	226	31	∩	∩	ADJ
ejpam-4872	226	32	f̃ã.	f̃ã.	NOUN
ejpam-4872	226	33	hence	hence	ADV
ejpam-4872	226	34	f	f	PROPN
ejpam-4872	226	35	s(1	s(1	PROPN
ejpam-4872	226	36	)	)	PUNCT
ejpam-4872	226	37	⊇	⊇	PROPN
ejpam-4872	226	38	α	α	NOUN
ejpam-4872	226	39	=	=	SYM
ejpam-4872	226	40	fs(x	fs(x	PROPN
ejpam-4872	226	41	)	)	PUNCT
ejpam-4872	226	42	and	and	CCONJ
ejpam-4872	226	43	f̃(1	f̃(1	NOUN
ejpam-4872	226	44	)	)	PUNCT
ejpam-4872	226	45	⊵	⊵	NOUN
ejpam-4872	226	46	ã	ã	PROPN
ejpam-4872	226	47	=	=	PUNCT
ejpam-4872	226	48	f̃(a	f̃(a	PROPN
ejpam-4872	226	49	)	)	PUNCT
ejpam-4872	226	50	.	.	PUNCT
ejpam-4872	227	1	if	if	SCONJ
ejpam-4872	227	2	there	there	PRON
ejpam-4872	227	3	are	be	VERB
ejpam-4872	227	4	a	a	DET
ejpam-4872	227	5	,	,	PUNCT
ejpam-4872	227	6	b	b	X
ejpam-4872	227	7	∈	∈	PROPN
ejpam-4872	227	8	x	x	PUNCT
ejpam-4872	227	9	such	such	ADJ
ejpam-4872	227	10	that	that	SCONJ
ejpam-4872	227	11	a|(b|b	a|(b|b	NOUN
ejpam-4872	227	12	)	)	PUNCT
ejpam-4872	227	13	(	(	PUNCT
ejpam-4872	227	14	b	b	X
ejpam-4872	227	15	,	,	PUNCT
ejpam-4872	227	16	b	b	NOUN
ejpam-4872	227	17	)	)	PUNCT
ejpam-4872	227	18	/∈	/∈	PUNCT
ejpam-4872	228	1	f̊(m	f̊(m	ADJ
ejpam-4872	228	2	,	,	PUNCT
ejpam-4872	228	3	m	m	PROPN
ejpam-4872	228	4	)	)	PUNCT
ejpam-4872	228	5	,	,	PUNCT
ejpam-4872	228	6	then	then	ADV
ejpam-4872	228	7	f̊−(a|(b|b	f̊−(a|(b|b	NOUN
ejpam-4872	228	8	)	)	PUNCT
ejpam-4872	228	9	)	)	PUNCT
ejpam-4872	228	10	>	>	PUNCT
ejpam-4872	228	11	f̊−(b	f̊−(b	NOUN
ejpam-4872	228	12	)	)	PUNCT
ejpam-4872	228	13	or	or	CCONJ
ejpam-4872	228	14	f̊+(a|(b|b	f̊+(a|(b|b	NOUN
ejpam-4872	228	15	)	)	PUNCT
ejpam-4872	228	16	)	)	PUNCT
ejpam-4872	229	1	<	<	X
ejpam-4872	229	2	f̊+(b	f̊+(b	NOUN
ejpam-4872	229	3	)	)	PUNCT
ejpam-4872	229	4	.	.	PUNCT
ejpam-4872	230	1	it	it	PRON
ejpam-4872	230	2	follows	follow	VERB
ejpam-4872	230	3	that	that	SCONJ
ejpam-4872	230	4	b	b	PROPN
ejpam-4872	230	5	∈	∈	PROPN
ejpam-4872	230	6	f̊(f̊−(b	f̊(f̊−(b	NOUN
ejpam-4872	230	7	)	)	PUNCT
ejpam-4872	230	8	)	)	PUNCT
ejpam-4872	230	9	∩	∩	NOUN
ejpam-4872	230	10	f̊(f̊+(b	f̊(f̊+(b	NOUN
ejpam-4872	230	11	)	)	PUNCT
ejpam-4872	230	12	)	)	PUNCT
ejpam-4872	230	13	and	and	CCONJ
ejpam-4872	230	14	a|(b|b	a|(b|b	PROPN
ejpam-4872	230	15	)	)	PUNCT
ejpam-4872	230	16	/∈	/∈	PUNCT
ejpam-4872	230	17	f̊(f̊−(b	f̊(f̊−(b	NOUN
ejpam-4872	230	18	)	)	PUNCT
ejpam-4872	230	19	)	)	PUNCT
ejpam-4872	230	20	∩	∩	NOUN
ejpam-4872	230	21	f̊(f̊+(b	f̊(f̊+(b	NOUN
ejpam-4872	230	22	)	)	PUNCT
ejpam-4872	230	23	)	)	PUNCT
ejpam-4872	230	24	,	,	PUNCT
ejpam-4872	230	25	a	a	DET
ejpam-4872	230	26	contradiction	contradiction	NOUN
ejpam-4872	230	27	.	.	PUNCT
ejpam-4872	231	1	hence	hence	ADV
ejpam-4872	231	2	x|(y|y	x|(y|y	PROPN
ejpam-4872	231	3	)	)	PUNCT
ejpam-4872	231	4	(	(	PUNCT
ejpam-4872	231	5	y	y	PROPN
ejpam-4872	231	6	,	,	PUNCT
ejpam-4872	231	7	y	y	NOUN
ejpam-4872	231	8	)	)	PUNCT
ejpam-4872	231	9	∈	∈	PROPN
ejpam-4872	231	10	f̊(m	f̊(m	PROPN
ejpam-4872	231	11	,	,	PUNCT
ejpam-4872	231	12	m	m	PROPN
ejpam-4872	231	13	)	)	PUNCT
ejpam-4872	231	14	for	for	ADP
ejpam-4872	231	15	all	all	DET
ejpam-4872	231	16	x	x	NOUN
ejpam-4872	231	17	,	,	PUNCT
ejpam-4872	231	18	y	y	PROPN
ejpam-4872	231	19	∈	∈	PROPN
ejpam-4872	231	20	x.	x.	NOUN
ejpam-4872	231	21	let	let	VERB
ejpam-4872	231	22	y	y	NOUN
ejpam-4872	231	23	,	,	PUNCT
ejpam-4872	231	24	b	b	PROPN
ejpam-4872	231	25	∈	∈	PROPN
ejpam-4872	231	26	x	x	AUX
ejpam-4872	231	27	be	be	AUX
ejpam-4872	231	28	such	such	ADJ
ejpam-4872	231	29	that	that	SCONJ
ejpam-4872	231	30	f	f	PROPN
ejpam-4872	231	31	s(y	s(y	PROPN
ejpam-4872	231	32	)	)	PUNCT
ejpam-4872	232	1	=	=	SYM
ejpam-4872	232	2	α	α	PROPN
ejpam-4872	232	3	and	and	CCONJ
ejpam-4872	232	4	f̃(b	f̃(b	NOUN
ejpam-4872	232	5	)	)	PUNCT
ejpam-4872	233	1	=	=	PUNCT
ejpam-4872	233	2	ã.	ã.	NOUN
ejpam-4872	233	3	then	then	ADV
ejpam-4872	233	4	(	(	PUNCT
ejpam-4872	233	5	y	y	PROPN
ejpam-4872	233	6	,	,	PUNCT
ejpam-4872	233	7	b	b	NOUN
ejpam-4872	233	8	)	)	PUNCT
ejpam-4872	233	9	∈	∈	PROPN
ejpam-4872	233	10	f	f	X
ejpam-4872	233	11	s	s	NOUN
ejpam-4872	233	12	α	α	PRON
ejpam-4872	233	13	×	×	NOUN
ejpam-4872	233	14	f̃ã	f̃ã	NOUN
ejpam-4872	233	15	,	,	PUNCT
ejpam-4872	233	16	which	which	PRON
ejpam-4872	233	17	implies	imply	VERB
ejpam-4872	233	18	that	that	SCONJ
ejpam-4872	233	19	(	(	PUNCT
ejpam-4872	233	20	x|(y|y	x|(y|y	PROPN
ejpam-4872	233	21	)	)	PUNCT
ejpam-4872	233	22	,	,	PUNCT
ejpam-4872	233	23	a|(b|b	a|(b|b	NOUN
ejpam-4872	233	24	)	)	PUNCT
ejpam-4872	233	25	)	)	PUNCT
ejpam-4872	234	1	∈	∈	NOUN
ejpam-4872	234	2	fs	fs	ADP
ejpam-4872	234	3	α	α	DET
ejpam-4872	234	4	×	×	NOUN
ejpam-4872	234	5	f̃ã	f̃ã	NOUN
ejpam-4872	234	6	for	for	ADP
ejpam-4872	234	7	all	all	DET
ejpam-4872	234	8	x	x	NOUN
ejpam-4872	234	9	,	,	PUNCT
ejpam-4872	234	10	a	a	DET
ejpam-4872	234	11	∈	∈	NOUN
ejpam-4872	234	12	x.	x.	NOUN
ejpam-4872	234	13	hence	hence	ADV
ejpam-4872	234	14	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	234	15	)	)	PUNCT
ejpam-4872	234	16	)	)	PUNCT
ejpam-4872	234	17	⊇	⊇	PROPN
ejpam-4872	234	18	α	α	NOUN
ejpam-4872	234	19	=	=	SYM
ejpam-4872	234	20	fs(y	fs(y	X
ejpam-4872	234	21	)	)	PUNCT
ejpam-4872	234	22	and	and	CCONJ
ejpam-4872	234	23	f̃(a|(b|b	f̃(a|(b|b	NOUN
ejpam-4872	234	24	)	)	PUNCT
ejpam-4872	234	25	)	)	PUNCT
ejpam-4872	235	1	⊵	⊵	PROPN
ejpam-4872	235	2	ã	ã	PROPN
ejpam-4872	235	3	=	=	SYM
ejpam-4872	235	4	f̃(b	f̃(b	PROPN
ejpam-4872	235	5	)	)	PUNCT
ejpam-4872	235	6	.	.	PUNCT
ejpam-4872	236	1	if	if	SCONJ
ejpam-4872	236	2	there	there	PRON
ejpam-4872	236	3	are	be	VERB
ejpam-4872	236	4	a	a	DET
ejpam-4872	236	5	,	,	PUNCT
ejpam-4872	236	6	b	b	NOUN
ejpam-4872	236	7	,	,	PUNCT
ejpam-4872	236	8	c	c	PROPN
ejpam-4872	236	9	∈	∈	PROPN
ejpam-4872	236	10	x	x	PUNCT
ejpam-4872	236	11	such	such	ADJ
ejpam-4872	236	12	that	that	PRON
ejpam-4872	236	13	(	(	PUNCT
ejpam-4872	236	14	a|(b|c))|(b|c	a|(b|c))|(b|c	PROPN
ejpam-4872	236	15	)	)	PUNCT
ejpam-4872	236	16	(	(	PUNCT
ejpam-4872	236	17	b	b	X
ejpam-4872	236	18	,	,	PUNCT
ejpam-4872	236	19	c	c	NOUN
ejpam-4872	236	20	)	)	PUNCT
ejpam-4872	236	21	/∈	/∈	PUNCT
ejpam-4872	237	1	f̊(m	f̊(m	ADJ
ejpam-4872	237	2	,	,	PUNCT
ejpam-4872	237	3	m	m	PROPN
ejpam-4872	237	4	)	)	PUNCT
ejpam-4872	237	5	,	,	PUNCT
ejpam-4872	237	6	then	then	ADV
ejpam-4872	237	7	f̊−((a|(b|c))|(b|c	f̊−((a|(b|c))|(b|c	NOUN
ejpam-4872	237	8	)	)	PUNCT
ejpam-4872	237	9	)	)	PUNCT
ejpam-4872	237	10	>	>	PUNCT
ejpam-4872	238	1	max{f̊−(b	max{f̊−(b	PROPN
ejpam-4872	238	2	)	)	PUNCT
ejpam-4872	238	3	,	,	PUNCT
ejpam-4872	238	4	f̊−(c	f̊−(c	VERB
ejpam-4872	238	5	)	)	PUNCT
ejpam-4872	238	6	}	}	PUNCT
ejpam-4872	238	7	or	or	CCONJ
ejpam-4872	238	8	f̊+((a|(b|c))|(b|c	f̊+((a|(b|c))|(b|c	PROPN
ejpam-4872	238	9	)	)	PUNCT
ejpam-4872	238	10	)	)	PUNCT
ejpam-4872	238	11	<	<	X
ejpam-4872	238	12	min{f̊+(b	min{f̊+(b	NOUN
ejpam-4872	238	13	)	)	PUNCT
ejpam-4872	238	14	,	,	PUNCT
ejpam-4872	238	15	f̊+(c	f̊+(c	PROPN
ejpam-4872	238	16	)	)	PUNCT
ejpam-4872	238	17	}	}	PUNCT
ejpam-4872	238	18	.	.	PUNCT
ejpam-4872	239	1	if	if	SCONJ
ejpam-4872	239	2	we	we	PRON
ejpam-4872	239	3	take	take	VERB
ejpam-4872	239	4	t−	t−	PROPN
ejpam-4872	239	5	:	:	PUNCT
ejpam-4872	239	6	=	=	SYM
ejpam-4872	239	7	max{f̊−(b	max{f̊−(b	PROPN
ejpam-4872	239	8	)	)	PUNCT
ejpam-4872	239	9	,	,	PUNCT
ejpam-4872	239	10	f̊−(c	f̊−(c	VERB
ejpam-4872	239	11	)	)	PUNCT
ejpam-4872	239	12	}	}	PUNCT
ejpam-4872	239	13	and	and	CCONJ
ejpam-4872	239	14	t+	t+	NOUN
ejpam-4872	239	15	:	:	PUNCT
ejpam-4872	239	16	=	=	PUNCT
ejpam-4872	239	17	min{f̊+(b	min{f̊+(b	NOUN
ejpam-4872	239	18	)	)	PUNCT
ejpam-4872	239	19	,	,	PUNCT
ejpam-4872	239	20	f̊+(c	f̊+(c	PROPN
ejpam-4872	239	21	)	)	PUNCT
ejpam-4872	239	22	}	}	PUNCT
ejpam-4872	239	23	,	,	PUNCT
ejpam-4872	239	24	then	then	ADV
ejpam-4872	239	25	b	b	X
ejpam-4872	239	26	,	,	PUNCT
ejpam-4872	239	27	c	c	PROPN
ejpam-4872	239	28	∈	∈	PROPN
ejpam-4872	239	29	f̊(t−	f̊(t−	PROPN
ejpam-4872	239	30	)	)	PUNCT
ejpam-4872	239	31	∩	∩	NOUN
ejpam-4872	239	32	f̊(t+	f̊(t+	NUM
ejpam-4872	239	33	)	)	PUNCT
ejpam-4872	239	34	and	and	CCONJ
ejpam-4872	239	35	(	(	PUNCT
ejpam-4872	239	36	a|(b|c))|(b|c	a|(b|c))|(b|c	PROPN
ejpam-4872	239	37	)	)	PUNCT
ejpam-4872	239	38	/∈	/∈	PUNCT
ejpam-4872	240	1	f̊(t−	f̊(t−	NOUN
ejpam-4872	240	2	)	)	PUNCT
ejpam-4872	240	3	∩	∩	NOUN
ejpam-4872	240	4	f̊(t+	f̊(t+	NUM
ejpam-4872	240	5	)	)	PUNCT
ejpam-4872	240	6	.	.	PUNCT
ejpam-4872	241	1	this	this	PRON
ejpam-4872	241	2	is	be	AUX
ejpam-4872	241	3	a	a	DET
ejpam-4872	241	4	contradiction	contradiction	NOUN
ejpam-4872	241	5	,	,	PUNCT
ejpam-4872	241	6	and	and	CCONJ
ejpam-4872	241	7	thus	thus	ADV
ejpam-4872	241	8	(	(	PUNCT
ejpam-4872	241	9	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	241	10	)	)	PUNCT
ejpam-4872	241	11	(	(	PUNCT
ejpam-4872	241	12	y	y	NOUN
ejpam-4872	241	13	,	,	PUNCT
ejpam-4872	241	14	z	z	NOUN
ejpam-4872	241	15	)	)	PUNCT
ejpam-4872	241	16	∈	∈	PROPN
ejpam-4872	241	17	f̊(m	f̊(m	PROPN
ejpam-4872	241	18	,	,	PUNCT
ejpam-4872	241	19	m	m	PROPN
ejpam-4872	241	20	)	)	PUNCT
ejpam-4872	241	21	for	for	ADP
ejpam-4872	241	22	all	all	DET
ejpam-4872	241	23	x	x	NOUN
ejpam-4872	241	24	,	,	PUNCT
ejpam-4872	241	25	y	y	PROPN
ejpam-4872	241	26	,	,	PUNCT
ejpam-4872	241	27	z	z	PROPN
ejpam-4872	241	28	∈	∈	PROPN
ejpam-4872	241	29	x.	x.	NOUN
ejpam-4872	241	30	let	let	VERB
ejpam-4872	241	31	(	(	PUNCT
ejpam-4872	241	32	x	x	X
ejpam-4872	241	33	,	,	PUNCT
ejpam-4872	241	34	a	a	PRON
ejpam-4872	241	35	)	)	PUNCT
ejpam-4872	241	36	,	,	PUNCT
ejpam-4872	241	37	(	(	PUNCT
ejpam-4872	241	38	y	y	PROPN
ejpam-4872	241	39	,	,	PUNCT
ejpam-4872	241	40	b	b	NOUN
ejpam-4872	241	41	)	)	PUNCT
ejpam-4872	241	42	,	,	PUNCT
ejpam-4872	241	43	(	(	PUNCT
ejpam-4872	241	44	z	z	X
ejpam-4872	241	45	,	,	PUNCT
ejpam-4872	241	46	c	c	NOUN
ejpam-4872	241	47	)	)	PUNCT
ejpam-4872	241	48	∈	∈	NOUN
ejpam-4872	242	1	x	x	SYM
ejpam-4872	242	2	×	×	NOUN
ejpam-4872	242	3	x	x	VERB
ejpam-4872	242	4	be	be	AUX
ejpam-4872	242	5	such	such	ADJ
ejpam-4872	242	6	that	that	SCONJ
ejpam-4872	242	7	fs(y	fs(y	NOUN
ejpam-4872	242	8	)	)	PUNCT
ejpam-4872	242	9	∩	∩	NOUN
ejpam-4872	242	10	fs(z	fs(z	NUM
ejpam-4872	242	11	)	)	PUNCT
ejpam-4872	242	12	=	=	SYM
ejpam-4872	242	13	α	α	NOUN
ejpam-4872	242	14	and	and	CCONJ
ejpam-4872	242	15	rmin{f̃(b	rmin{f̃(b	NOUN
ejpam-4872	242	16	)	)	PUNCT
ejpam-4872	242	17	,	,	PUNCT
ejpam-4872	242	18	f̃(c	f̃(c	NOUN
ejpam-4872	242	19	)	)	PUNCT
ejpam-4872	242	20	}	}	PUNCT
ejpam-4872	243	1	=	=	PUNCT
ejpam-4872	243	2	ã.	ã.	PROPN
ejpam-4872	243	3	then	then	ADV
ejpam-4872	243	4	y	y	PROPN
ejpam-4872	243	5	,	,	PUNCT
ejpam-4872	243	6	z	z	PROPN
ejpam-4872	243	7	∈	∈	PROPN
ejpam-4872	243	8	fs	fs	ADP
ejpam-4872	243	9	α	α	PROPN
ejpam-4872	243	10	and	and	CCONJ
ejpam-4872	243	11	b	b	NOUN
ejpam-4872	243	12	,	,	PUNCT
ejpam-4872	243	13	c	c	PROPN
ejpam-4872	243	14	∈	∈	PROPN
ejpam-4872	243	15	f̃ã.	f̃ã.	NOUN
ejpam-4872	243	16	it	it	PRON
ejpam-4872	243	17	follows	follow	VERB
ejpam-4872	244	1	that	that	SCONJ
ejpam-4872	244	2	(	(	PUNCT
ejpam-4872	244	3	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	244	4	)	)	PUNCT
ejpam-4872	244	5	∈	∈	PROPN
ejpam-4872	244	6	f	f	PROPN
ejpam-4872	244	7	s	s	PROPN
ejpam-4872	244	8	α	α	NOUN
ejpam-4872	244	9	and	and	CCONJ
ejpam-4872	244	10	(	(	PUNCT
ejpam-4872	244	11	a|(b|c))|(b|c	a|(b|c))|(b|c	NOUN
ejpam-4872	244	12	)	)	PUNCT
ejpam-4872	244	13	∈	∈	NOUN
ejpam-4872	244	14	f̃ã.	f̃ã.	NOUN
ejpam-4872	244	15	therefore	therefore	ADV
ejpam-4872	244	16	fs((x|(y|z))|(y|z	fs((x|(y|z))|(y|z	ADJ
ejpam-4872	244	17	)	)	PUNCT
ejpam-4872	244	18	)	)	PUNCT
ejpam-4872	244	19	⊇	⊇	PROPN
ejpam-4872	244	20	α	α	NOUN
ejpam-4872	244	21	=	=	SYM
ejpam-4872	244	22	fs(y	fs(y	NOUN
ejpam-4872	244	23	)	)	PUNCT
ejpam-4872	244	24	∩	∩	NOUN
ejpam-4872	244	25	fs(z	fs(z	NUM
ejpam-4872	244	26	)	)	PUNCT
ejpam-4872	244	27	and	and	CCONJ
ejpam-4872	244	28	f̃((a|(b|c))|(b|c	f̃((a|(b|c))|(b|c	NOUN
ejpam-4872	244	29	)	)	PUNCT
ejpam-4872	244	30	)	)	PUNCT
ejpam-4872	245	1	⊵	⊵	PROPN
ejpam-4872	245	2	ã	ã	PROPN
ejpam-4872	245	3	=	=	PUNCT
ejpam-4872	245	4	rmin{f̃(b	rmin{f̃(b	NOUN
ejpam-4872	245	5	)	)	PUNCT
ejpam-4872	245	6	,	,	PUNCT
ejpam-4872	245	7	f̃(c	f̃(c	PROPN
ejpam-4872	245	8	)	)	PUNCT
ejpam-4872	245	9	}	}	PUNCT
ejpam-4872	245	10	.	.	PUNCT
ejpam-4872	246	1	consequently	consequently	ADV
ejpam-4872	246	2	,	,	PUNCT
ejpam-4872	246	3	dokf	dokf	NOUN
ejpam-4872	246	4	:	:	PUNCT
ejpam-4872	246	5	=	=	SYM
ejpam-4872	246	6	(	(	PUNCT
ejpam-4872	246	7	f̊	f̊	X
ejpam-4872	246	8	,	,	PUNCT
ejpam-4872	246	9	fs	fs	PROPN
ejpam-4872	246	10	,	,	PUNCT
ejpam-4872	246	11	f̃	f̃	PROPN
ejpam-4872	246	12	)	)	PUNCT
ejpam-4872	246	13	is	be	AUX
ejpam-4872	246	14	a	a	DET
ejpam-4872	246	15	dokdo	dokdo	ADJ
ejpam-4872	246	16	filter	filter	NOUN
ejpam-4872	246	17	of	of	ADP
ejpam-4872	246	18	(	(	PUNCT
ejpam-4872	246	19	u	u	NOUN
ejpam-4872	246	20	,	,	PUNCT
ejpam-4872	246	21	x	x	NOUN
ejpam-4872	246	22	)	)	PUNCT
ejpam-4872	246	23	.	.	PUNCT
ejpam-4872	247	1	theorem	theorem	ADJ
ejpam-4872	247	2	4	4	NUM
ejpam-4872	247	3	.	.	PUNCT
ejpam-4872	247	4	given	give	VERB
ejpam-4872	247	5	a	a	DET
ejpam-4872	247	6	nonempty	nonempty	ADJ
ejpam-4872	247	7	subset	subset	VERB
ejpam-4872	247	8	f	f	PROPN
ejpam-4872	247	9	of	of	ADP
ejpam-4872	247	10	x	x	PRON
ejpam-4872	247	11	,	,	PUNCT
ejpam-4872	247	12	let	let	VERB
ejpam-4872	247	13	dokff	dokff	VERB
ejpam-4872	247	14	:	:	PUNCT
ejpam-4872	247	15	=	=	SYM
ejpam-4872	247	16	(	(	PUNCT
ejpam-4872	247	17	f̊f	f̊f	PROPN
ejpam-4872	247	18	,	,	PUNCT
ejpam-4872	247	19	f	f	PROPN
ejpam-4872	247	20	s	s	PROPN
ejpam-4872	247	21	f	f	PROPN
ejpam-4872	247	22	,	,	PUNCT
ejpam-4872	247	23	f̃f	f̃f	PROPN
ejpam-4872	247	24	)	)	PUNCT
ejpam-4872	247	25	be	be	AUX
ejpam-4872	247	26	a	a	DET
ejpam-4872	247	27	dokdo	dokdo	NOUN
ejpam-4872	247	28	structure	structure	NOUN
ejpam-4872	247	29	in	in	ADP
ejpam-4872	247	30	(	(	PUNCT
ejpam-4872	247	31	u	u	NOUN
ejpam-4872	247	32	,	,	PUNCT
ejpam-4872	247	33	x	x	NOUN
ejpam-4872	247	34	)	)	PUNCT
ejpam-4872	247	35	defined	define	VERB
ejpam-4872	247	36	by	by	ADP
ejpam-4872	247	37	dokff	dokff	NOUN
ejpam-4872	247	38	:	:	PUNCT
ejpam-4872	247	39	=	=	SYM
ejpam-4872	247	40	(	(	PUNCT
ejpam-4872	247	41	f̊f	f̊f	PROPN
ejpam-4872	247	42	,	,	PUNCT
ejpam-4872	247	43	f	f	PROPN
ejpam-4872	247	44	s	s	PROPN
ejpam-4872	247	45	f	f	PROPN
ejpam-4872	247	46	,	,	PUNCT
ejpam-4872	247	47	f̃f	f̃f	PROPN
ejpam-4872	247	48	)	)	PUNCT
ejpam-4872	247	49	:	:	PUNCT
ejpam-4872	248	1	x	x	X
ejpam-4872	248	2	→	→	PUNCT
ejpam-4872	248	3	(	(	PUNCT
ejpam-4872	248	4	[	[	X
ejpam-4872	248	5	−1	−1	NOUN
ejpam-4872	248	6	,	,	PUNCT
ejpam-4872	248	7	0]×	0]×	PROPN
ejpam-4872	249	1	[	[	X
ejpam-4872	249	2	0	0	NUM
ejpam-4872	249	3	,	,	PUNCT
ejpam-4872	249	4	1])×	1])×	NOUN
ejpam-4872	249	5	2u	2u	NOUN
ejpam-4872	249	6	×	×	NOUN
ejpam-4872	250	1	[	[	X
ejpam-4872	250	2	[	[	X
ejpam-4872	250	3	0	0	NUM
ejpam-4872	250	4	,	,	PUNCT
ejpam-4872	250	5	1	1	NUM
ejpam-4872	250	6	]	]	PUNCT
ejpam-4872	250	7	]	]	PUNCT
ejpam-4872	250	8	,	,	PUNCT
ejpam-4872	250	9	x	x	SYM
ejpam-4872	250	10	7→	7→	X
ejpam-4872	250	11	{	{	PUNCT
ejpam-4872	250	12	(	(	PUNCT
ejpam-4872	250	13	(	(	PUNCT
ejpam-4872	250	14	t−	t−	NOUN
ejpam-4872	250	15	,	,	PUNCT
ejpam-4872	250	16	t+	t+	NOUN
ejpam-4872	250	17	)	)	PUNCT
ejpam-4872	250	18	,	,	PUNCT
ejpam-4872	250	19	α	α	PROPN
ejpam-4872	250	20	,	,	PUNCT
ejpam-4872	250	21	ã	ã	PROPN
ejpam-4872	250	22	)	)	PUNCT
ejpam-4872	250	23	if	if	SCONJ
ejpam-4872	250	24	x	x	SYM
ejpam-4872	250	25	∈	∈	PROPN
ejpam-4872	250	26	f	f	AUX
ejpam-4872	250	27	,	,	PUNCT
ejpam-4872	250	28	(	(	PUNCT
ejpam-4872	250	29	(	(	PUNCT
ejpam-4872	250	30	0	0	NUM
ejpam-4872	250	31	,	,	PUNCT
ejpam-4872	250	32	0	0	NUM
ejpam-4872	250	33	)	)	PUNCT
ejpam-4872	250	34	,	,	PUNCT
ejpam-4872	250	35	∅	∅	NOUN
ejpam-4872	250	36	,	,	PUNCT
ejpam-4872	250	37	0̃	0̃	PROPN
ejpam-4872	250	38	)	)	PUNCT
ejpam-4872	250	39	otherwise	otherwise	ADV
ejpam-4872	250	40	,	,	PUNCT
ejpam-4872	250	41	(	(	PUNCT
ejpam-4872	250	42	25	25	NUM
ejpam-4872	250	43	)	)	PUNCT
ejpam-4872	250	44	s.	s.	PROPN
ejpam-4872	250	45	s.	s.	PROPN
ejpam-4872	250	46	ahn	ahn	PROPN
ejpam-4872	250	47	et	et	PROPN
ejpam-4872	250	48	al	al	PROPN
ejpam-4872	250	49	.	.	PUNCT
ejpam-4872	250	50	/	/	SYM
ejpam-4872	250	51	eur	eur	PROPN
ejpam-4872	250	52	.	.	PUNCT
ejpam-4872	251	1	j.	j.	PROPN
ejpam-4872	251	2	pure	pure	PROPN
ejpam-4872	251	3	appl	appl	PROPN
ejpam-4872	251	4	.	.	PROPN
ejpam-4872	251	5	math	math	PROPN
ejpam-4872	251	6	,	,	PUNCT
ejpam-4872	251	7	16	16	NUM
ejpam-4872	251	8	(	(	PUNCT
ejpam-4872	251	9	3	3	NUM
ejpam-4872	251	10	)	)	PUNCT
ejpam-4872	251	11	(	(	PUNCT
ejpam-4872	251	12	2023	2023	NUM
ejpam-4872	251	13	)	)	PUNCT
ejpam-4872	251	14	,	,	PUNCT
ejpam-4872	251	15	1862	1862	NUM
ejpam-4872	251	16	-	-	SYM
ejpam-4872	251	17	1877	1877	NUM
ejpam-4872	251	18	1872	1872	NUM
ejpam-4872	251	19	where	where	SCONJ
ejpam-4872	251	20	t−	t−	PROPN
ejpam-4872	251	21	̸=	̸=	PROPN
ejpam-4872	251	22	0	0	NUM
ejpam-4872	251	23	̸=	̸=	PROPN
ejpam-4872	251	24	t+	t+	VERB
ejpam-4872	251	25	,	,	PUNCT
ejpam-4872	251	26	α	α	PROPN
ejpam-4872	251	27	̸=	̸=	PROPN
ejpam-4872	251	28	∅	∅	NOUN
ejpam-4872	251	29	and	and	CCONJ
ejpam-4872	251	30	ã	ã	PROPN
ejpam-4872	251	31	̸=	̸=	PROPN
ejpam-4872	251	32	0̃	0̃	NOUN
ejpam-4872	251	33	:	:	PUNCT
ejpam-4872	251	34	=	=	PUNCT
ejpam-4872	252	1	[	[	X
ejpam-4872	252	2	0	0	NUM
ejpam-4872	252	3	,	,	PUNCT
ejpam-4872	252	4	0	0	NUM
ejpam-4872	252	5	]	]	PUNCT
ejpam-4872	252	6	.	.	PUNCT
ejpam-4872	253	1	then	then	ADV
ejpam-4872	253	2	dokff	dokff	VERB
ejpam-4872	253	3	:	:	PUNCT
ejpam-4872	253	4	=	=	SYM
ejpam-4872	253	5	(	(	PUNCT
ejpam-4872	253	6	f̊f	f̊f	PROPN
ejpam-4872	253	7	,	,	PUNCT
ejpam-4872	253	8	f	f	PROPN
ejpam-4872	253	9	s	s	PROPN
ejpam-4872	253	10	f	f	PROPN
ejpam-4872	253	11	,	,	PUNCT
ejpam-4872	253	12	f̃f	f̃f	PROPN
ejpam-4872	253	13	)	)	PUNCT
ejpam-4872	253	14	is	be	AUX
ejpam-4872	253	15	a	a	DET
ejpam-4872	253	16	dokdo	dokdo	ADJ
ejpam-4872	253	17	filter	filter	NOUN
ejpam-4872	253	18	of	of	ADP
ejpam-4872	253	19	(	(	PUNCT
ejpam-4872	253	20	u	u	NOUN
ejpam-4872	253	21	,	,	PUNCT
ejpam-4872	253	22	x	x	NOUN
ejpam-4872	253	23	)	)	PUNCT
ejpam-4872	254	1	if	if	SCONJ
ejpam-4872	254	2	and	and	CCONJ
ejpam-4872	254	3	only	only	ADV
ejpam-4872	254	4	if	if	SCONJ
ejpam-4872	254	5	f	f	PROPN
ejpam-4872	254	6	is	be	AUX
ejpam-4872	254	7	a	a	DET
ejpam-4872	254	8	filter	filter	NOUN
ejpam-4872	254	9	of	of	ADP
ejpam-4872	254	10	x	x	NOUN
ejpam-4872	254	11	:	:	PUNCT
ejpam-4872	254	12	=	=	SYM
ejpam-4872	254	13	(	(	PUNCT
ejpam-4872	254	14	x	x	NOUN
ejpam-4872	254	15	,	,	PUNCT
ejpam-4872	254	16	|	|	NOUN
ejpam-4872	254	17	)	)	PUNCT
ejpam-4872	254	18	.	.	PUNCT
ejpam-4872	255	1	moreover	moreover	ADV
ejpam-4872	255	2	,	,	PUNCT
ejpam-4872	255	3	we	we	PRON
ejpam-4872	255	4	have	have	VERB
ejpam-4872	255	5	f	f	NOUN
ejpam-4872	255	6	=	=	SYM
ejpam-4872	255	7	xff	xff	PROPN
ejpam-4872	255	8	:	:	PUNCT
ejpam-4872	256	1	=	=	SYM
ejpam-4872	256	2	{	{	PUNCT
ejpam-4872	256	3	x	x	SYM
ejpam-4872	256	4	∈	∈	PROPN
ejpam-4872	256	5	x	x	SYM
ejpam-4872	256	6	|	|	ADV
ejpam-4872	256	7	f̊f	f̊f	PROPN
ejpam-4872	256	8	(	(	PUNCT
ejpam-4872	256	9	x	x	NOUN
ejpam-4872	256	10	)	)	PUNCT
ejpam-4872	256	11	=	=	SYM
ejpam-4872	256	12	f̊f	f̊f	PROPN
ejpam-4872	256	13	(	(	PUNCT
ejpam-4872	256	14	1	1	NUM
ejpam-4872	256	15	)	)	PUNCT
ejpam-4872	256	16	,	,	PUNCT
ejpam-4872	256	17	f	f	PROPN
ejpam-4872	256	18	s	s	PROPN
ejpam-4872	256	19	f	f	X
ejpam-4872	256	20	(	(	PUNCT
ejpam-4872	256	21	x	x	NOUN
ejpam-4872	256	22	)	)	PUNCT
ejpam-4872	256	23	=	=	SYM
ejpam-4872	256	24	fs	fs	PART
ejpam-4872	256	25	f	f	X
ejpam-4872	256	26	(	(	PUNCT
ejpam-4872	256	27	1	1	NUM
ejpam-4872	256	28	)	)	PUNCT
ejpam-4872	256	29	,	,	PUNCT
ejpam-4872	256	30	f̃f	f̃f	PROPN
ejpam-4872	256	31	(	(	PUNCT
ejpam-4872	256	32	x	x	X
ejpam-4872	256	33	)	)	PUNCT
ejpam-4872	256	34	=	=	SYM
ejpam-4872	256	35	f̃f	f̃f	PROPN
ejpam-4872	256	36	(	(	PUNCT
ejpam-4872	256	37	1	1	NUM
ejpam-4872	256	38	)	)	PUNCT
ejpam-4872	256	39	}	}	PUNCT
ejpam-4872	256	40	.	.	PUNCT
ejpam-4872	257	1	proof	proof	NOUN
ejpam-4872	257	2	.	.	PUNCT
ejpam-4872	258	1	assume	assume	VERB
ejpam-4872	258	2	that	that	SCONJ
ejpam-4872	258	3	dokff	dokff	NOUN
ejpam-4872	258	4	:	:	PUNCT
ejpam-4872	258	5	=	=	SYM
ejpam-4872	258	6	(	(	PUNCT
ejpam-4872	258	7	f̊f	f̊f	PROPN
ejpam-4872	258	8	,	,	PUNCT
ejpam-4872	258	9	f	f	PROPN
ejpam-4872	258	10	s	s	PROPN
ejpam-4872	258	11	f	f	PROPN
ejpam-4872	258	12	,	,	PUNCT
ejpam-4872	258	13	f̃f	f̃f	PROPN
ejpam-4872	258	14	)	)	PUNCT
ejpam-4872	258	15	is	be	AUX
ejpam-4872	258	16	a	a	DET
ejpam-4872	258	17	dokdo	dokdo	ADJ
ejpam-4872	258	18	filter	filter	NOUN
ejpam-4872	258	19	of	of	ADP
ejpam-4872	258	20	(	(	PUNCT
ejpam-4872	258	21	u	u	NOUN
ejpam-4872	258	22	,	,	PUNCT
ejpam-4872	258	23	x	x	NOUN
ejpam-4872	258	24	)	)	PUNCT
ejpam-4872	258	25	.	.	PUNCT
ejpam-4872	259	1	then	then	ADV
ejpam-4872	259	2	dokff	dokff	INTJ
ejpam-4872	259	3	(	(	PUNCT
ejpam-4872	259	4	1	1	NUM
ejpam-4872	259	5	)	)	PUNCT
ejpam-4872	259	6	=	=	SYM
ejpam-4872	259	7	(	(	PUNCT
ejpam-4872	259	8	(	(	PUNCT
ejpam-4872	259	9	t−	t−	NOUN
ejpam-4872	259	10	,	,	PUNCT
ejpam-4872	259	11	t+	t+	NOUN
ejpam-4872	259	12	)	)	PUNCT
ejpam-4872	259	13	,	,	PUNCT
ejpam-4872	259	14	α	α	PROPN
ejpam-4872	259	15	,	,	PUNCT
ejpam-4872	259	16	ã	ã	PROPN
ejpam-4872	259	17	)	)	PUNCT
ejpam-4872	259	18	by	by	ADP
ejpam-4872	259	19	(	(	PUNCT
ejpam-4872	259	20	19	19	NUM
ejpam-4872	259	21	)	)	PUNCT
ejpam-4872	259	22	,	,	PUNCT
ejpam-4872	259	23	and	and	CCONJ
ejpam-4872	259	24	so	so	ADV
ejpam-4872	259	25	1	1	NUM
ejpam-4872	259	26	∈	∈	PROPN
ejpam-4872	259	27	f	f	X
ejpam-4872	259	28	.	.	PUNCT
ejpam-4872	260	1	let	let	VERB
ejpam-4872	260	2	x	x	PRON
ejpam-4872	260	3	,	,	PUNCT
ejpam-4872	260	4	y	y	PROPN
ejpam-4872	260	5	∈	∈	PROPN
ejpam-4872	260	6	x	x	AUX
ejpam-4872	260	7	be	be	AUX
ejpam-4872	260	8	such	such	ADJ
ejpam-4872	260	9	that	that	SCONJ
ejpam-4872	260	10	y	y	PROPN
ejpam-4872	260	11	∈	∈	PROPN
ejpam-4872	260	12	f	f	PROPN
ejpam-4872	260	13	.	.	PUNCT
ejpam-4872	261	1	then	then	ADV
ejpam-4872	261	2	f̊−	f̊−	PROPN
ejpam-4872	261	3	f	f	PROPN
ejpam-4872	261	4	(	(	PUNCT
ejpam-4872	261	5	y	y	NOUN
ejpam-4872	261	6	)	)	PUNCT
ejpam-4872	261	7	=	=	SYM
ejpam-4872	261	8	t−	t−	PROPN
ejpam-4872	261	9	,	,	PUNCT
ejpam-4872	261	10	f̊+	f̊+	NUM
ejpam-4872	261	11	f	f	PROPN
ejpam-4872	261	12	(	(	PUNCT
ejpam-4872	261	13	y	y	NOUN
ejpam-4872	261	14	)	)	PUNCT
ejpam-4872	261	15	=	=	SYM
ejpam-4872	262	1	t+	t+	PROPN
ejpam-4872	262	2	,	,	PUNCT
ejpam-4872	262	3	f	f	PROPN
ejpam-4872	262	4	s	s	PROPN
ejpam-4872	262	5	f	f	PROPN
ejpam-4872	262	6	(	(	PUNCT
ejpam-4872	262	7	y	y	NOUN
ejpam-4872	262	8	)	)	PUNCT
ejpam-4872	262	9	=	=	SYM
ejpam-4872	262	10	α	α	NOUN
ejpam-4872	262	11	,	,	PUNCT
ejpam-4872	262	12	and	and	CCONJ
ejpam-4872	262	13	f̃f	f̃f	PROPN
ejpam-4872	262	14	(	(	PUNCT
ejpam-4872	262	15	y	y	NOUN
ejpam-4872	262	16	)	)	PUNCT
ejpam-4872	262	17	=	=	VERB
ejpam-4872	263	1	ã.	ã.	NOUN
ejpam-4872	263	2	it	it	PRON
ejpam-4872	263	3	follows	follow	VERB
ejpam-4872	263	4	from	from	ADP
ejpam-4872	263	5	(	(	PUNCT
ejpam-4872	263	6	20	20	NUM
ejpam-4872	263	7	)	)	PUNCT
ejpam-4872	264	1	that	that	PRON
ejpam-4872	264	2	f̊−	f̊−	PRON
ejpam-4872	264	3	f	f	X
ejpam-4872	264	4	(	(	PUNCT
ejpam-4872	264	5	x|(y|y	x|(y|y	PROPN
ejpam-4872	264	6	)	)	PUNCT
ejpam-4872	264	7	)	)	PUNCT
ejpam-4872	264	8	≤	≤	NUM
ejpam-4872	264	9	f̊−	f̊−	NUM
ejpam-4872	264	10	f	f	PROPN
ejpam-4872	264	11	(	(	PUNCT
ejpam-4872	264	12	y	y	NOUN
ejpam-4872	264	13	)	)	PUNCT
ejpam-4872	264	14	=	=	SYM
ejpam-4872	264	15	t−	t−	PROPN
ejpam-4872	264	16	,	,	PUNCT
ejpam-4872	264	17	f̊+	f̊+	NUM
ejpam-4872	264	18	f	f	X
ejpam-4872	264	19	(	(	PUNCT
ejpam-4872	264	20	x|(y|y	x|(y|y	PROPN
ejpam-4872	264	21	)	)	PUNCT
ejpam-4872	264	22	)	)	PUNCT
ejpam-4872	264	23	≥	≥	AUX
ejpam-4872	264	24	f̊+	f̊+	NOUN
ejpam-4872	264	25	f	f	PROPN
ejpam-4872	264	26	(	(	PUNCT
ejpam-4872	264	27	y	y	NOUN
ejpam-4872	264	28	)	)	PUNCT
ejpam-4872	264	29	=	=	SYM
ejpam-4872	265	1	t+	t+	PROPN
ejpam-4872	265	2	,	,	PUNCT
ejpam-4872	265	3	fs	fs	ADP
ejpam-4872	265	4	f	f	PROPN
ejpam-4872	265	5	(	(	PUNCT
ejpam-4872	265	6	x|(y|y	x|(y|y	PROPN
ejpam-4872	265	7	)	)	PUNCT
ejpam-4872	265	8	)	)	PUNCT
ejpam-4872	266	1	⊇	⊇	PROPN
ejpam-4872	266	2	fs	fs	ADP
ejpam-4872	266	3	f	f	PROPN
ejpam-4872	266	4	(	(	PUNCT
ejpam-4872	266	5	y	y	NOUN
ejpam-4872	266	6	)	)	PUNCT
ejpam-4872	266	7	=	=	SYM
ejpam-4872	266	8	α	α	PROPN
ejpam-4872	266	9	and	and	CCONJ
ejpam-4872	266	10	f̃f	f̃f	PROPN
ejpam-4872	266	11	(	(	PUNCT
ejpam-4872	266	12	x|(y|y	x|(y|y	PROPN
ejpam-4872	266	13	)	)	PUNCT
ejpam-4872	266	14	)	)	PUNCT
ejpam-4872	267	1	⊵	⊵	PROPN
ejpam-4872	267	2	f̃f	f̃f	PROPN
ejpam-4872	267	3	(	(	PUNCT
ejpam-4872	267	4	y	y	NOUN
ejpam-4872	267	5	)	)	PUNCT
ejpam-4872	267	6	=	=	SYM
ejpam-4872	267	7	ã.	ã.	NOUN
ejpam-4872	267	8	hence	hence	ADV
ejpam-4872	267	9	f̊f	f̊f	PROPN
ejpam-4872	267	10	(	(	PUNCT
ejpam-4872	267	11	x|(y|y	x|(y|y	PROPN
ejpam-4872	267	12	)	)	PUNCT
ejpam-4872	267	13	)	)	PUNCT
ejpam-4872	268	1	=	=	SYM
ejpam-4872	268	2	(	(	PUNCT
ejpam-4872	268	3	t−	t−	PROPN
ejpam-4872	268	4	,	,	PUNCT
ejpam-4872	268	5	t+	t+	NOUN
ejpam-4872	268	6	)	)	PUNCT
ejpam-4872	268	7	,	,	PUNCT
ejpam-4872	268	8	f	f	PROPN
ejpam-4872	268	9	s	s	PROPN
ejpam-4872	268	10	f	f	X
ejpam-4872	268	11	(	(	PUNCT
ejpam-4872	268	12	x|(y|y	x|(y|y	PROPN
ejpam-4872	268	13	)	)	PUNCT
ejpam-4872	268	14	)	)	PUNCT
ejpam-4872	269	1	=	=	SYM
ejpam-4872	269	2	α	α	PROPN
ejpam-4872	269	3	and	and	CCONJ
ejpam-4872	269	4	f̃f	f̃f	PROPN
ejpam-4872	269	5	(	(	PUNCT
ejpam-4872	269	6	x|(y|y	x|(y|y	PROPN
ejpam-4872	269	7	)	)	PUNCT
ejpam-4872	269	8	)	)	PUNCT
ejpam-4872	270	1	=	=	PUNCT
ejpam-4872	270	2	ã.	ã.	NOUN
ejpam-4872	270	3	this	this	PRON
ejpam-4872	270	4	shows	show	VERB
ejpam-4872	270	5	that	that	SCONJ
ejpam-4872	270	6	x|(y|y	x|(y|y	PROPN
ejpam-4872	270	7	)	)	PUNCT
ejpam-4872	270	8	∈	∈	PROPN
ejpam-4872	270	9	f	f	X
ejpam-4872	270	10	.	.	PUNCT
ejpam-4872	271	1	let	let	VERB
ejpam-4872	271	2	y	y	PRON
ejpam-4872	271	3	,	,	PUNCT
ejpam-4872	272	1	z	z	PROPN
ejpam-4872	272	2	∈	∈	PROPN
ejpam-4872	272	3	f	f	X
ejpam-4872	272	4	.	.	PUNCT
ejpam-4872	273	1	then	then	ADV
ejpam-4872	273	2	f̊−	f̊−	PROPN
ejpam-4872	273	3	f	f	PROPN
ejpam-4872	273	4	(	(	PUNCT
ejpam-4872	273	5	y	y	NOUN
ejpam-4872	273	6	)	)	PUNCT
ejpam-4872	273	7	=	=	PUNCT
ejpam-4872	274	1	t−	t−	PROPN
ejpam-4872	274	2	=	=	SYM
ejpam-4872	274	3	f̊−	f̊−	NOUN
ejpam-4872	274	4	f	f	X
ejpam-4872	274	5	(	(	PUNCT
ejpam-4872	274	6	z	z	NOUN
ejpam-4872	274	7	)	)	PUNCT
ejpam-4872	274	8	,	,	PUNCT
ejpam-4872	274	9	f̊+	f̊+	PROPN
ejpam-4872	274	10	f	f	PROPN
ejpam-4872	274	11	(	(	PUNCT
ejpam-4872	274	12	y	y	NOUN
ejpam-4872	274	13	)	)	PUNCT
ejpam-4872	274	14	=	=	VERB
ejpam-4872	274	15	t+	t+	PUNCT
ejpam-4872	274	16	=	=	SYM
ejpam-4872	274	17	f̊+	f̊+	NUM
ejpam-4872	274	18	f	f	X
ejpam-4872	274	19	(	(	PUNCT
ejpam-4872	274	20	z	z	NOUN
ejpam-4872	274	21	)	)	PUNCT
ejpam-4872	274	22	,	,	PUNCT
ejpam-4872	274	23	f	f	PROPN
ejpam-4872	274	24	s	s	PROPN
ejpam-4872	274	25	f	f	X
ejpam-4872	274	26	(	(	PUNCT
ejpam-4872	274	27	y	y	NOUN
ejpam-4872	274	28	)	)	PUNCT
ejpam-4872	274	29	=	=	SYM
ejpam-4872	275	1	α	α	X
ejpam-4872	275	2	=	=	PUNCT
ejpam-4872	275	3	fs	fs	PROPN
ejpam-4872	275	4	f	f	X
ejpam-4872	275	5	(	(	PUNCT
ejpam-4872	275	6	z	z	NOUN
ejpam-4872	275	7	)	)	PUNCT
ejpam-4872	275	8	,	,	PUNCT
ejpam-4872	275	9	and	and	CCONJ
ejpam-4872	275	10	f̃f	f̃f	PROPN
ejpam-4872	275	11	(	(	PUNCT
ejpam-4872	275	12	y	y	NOUN
ejpam-4872	275	13	)	)	PUNCT
ejpam-4872	275	14	=	=	SYM
ejpam-4872	276	1	ã	ã	PROPN
ejpam-4872	276	2	=	=	SYM
ejpam-4872	276	3	f̃f	f̃f	PROPN
ejpam-4872	276	4	(	(	PUNCT
ejpam-4872	276	5	z	z	NOUN
ejpam-4872	276	6	)	)	PUNCT
ejpam-4872	276	7	.	.	PUNCT
ejpam-4872	277	1	using	use	VERB
ejpam-4872	277	2	(	(	PUNCT
ejpam-4872	277	3	21	21	NUM
ejpam-4872	277	4	)	)	PUNCT
ejpam-4872	277	5	,	,	PUNCT
ejpam-4872	277	6	we	we	PRON
ejpam-4872	277	7	have	have	VERB
ejpam-4872	277	8	f̊−	f̊−	NUM
ejpam-4872	277	9	f	f	PROPN
ejpam-4872	277	10	(	(	PUNCT
ejpam-4872	277	11	(	(	PUNCT
ejpam-4872	277	12	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	277	13	)	)	PUNCT
ejpam-4872	277	14	)	)	PUNCT
ejpam-4872	277	15	≤	≤	NOUN
ejpam-4872	278	1	max{f̊−	max{f̊−	X
ejpam-4872	278	2	f	f	X
ejpam-4872	278	3	(	(	PUNCT
ejpam-4872	278	4	y	y	PROPN
ejpam-4872	278	5	)	)	PUNCT
ejpam-4872	278	6	,	,	PUNCT
ejpam-4872	278	7	f̊−	f̊−	PRON
ejpam-4872	278	8	f	f	X
ejpam-4872	278	9	(	(	PUNCT
ejpam-4872	278	10	z	z	NOUN
ejpam-4872	278	11	)	)	PUNCT
ejpam-4872	278	12	}	}	PUNCT
ejpam-4872	278	13	=	=	SYM
ejpam-4872	278	14	t−	t−	PROPN
ejpam-4872	278	15	,	,	PUNCT
ejpam-4872	278	16	f̊+	f̊+	NUM
ejpam-4872	278	17	f	f	X
ejpam-4872	278	18	(	(	PUNCT
ejpam-4872	278	19	(	(	PUNCT
ejpam-4872	278	20	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	278	21	)	)	PUNCT
ejpam-4872	278	22	)	)	PUNCT
ejpam-4872	278	23	≥	≥	X
ejpam-4872	278	24	min{f̊+	min{f̊+	NOUN
ejpam-4872	278	25	f	f	X
ejpam-4872	278	26	(	(	PUNCT
ejpam-4872	278	27	y	y	PROPN
ejpam-4872	278	28	)	)	PUNCT
ejpam-4872	278	29	,	,	PUNCT
ejpam-4872	278	30	f̊+	f̊+	PROPN
ejpam-4872	278	31	f	f	X
ejpam-4872	278	32	(	(	PUNCT
ejpam-4872	278	33	z	z	NOUN
ejpam-4872	278	34	)	)	PUNCT
ejpam-4872	278	35	}	}	PUNCT
ejpam-4872	278	36	=	=	SYM
ejpam-4872	279	1	t+	t+	VERB
ejpam-4872	279	2	,	,	PUNCT
ejpam-4872	279	3	fs	fs	ADP
ejpam-4872	279	4	f	f	PROPN
ejpam-4872	279	5	(	(	PUNCT
ejpam-4872	279	6	(	(	PUNCT
ejpam-4872	279	7	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	279	8	)	)	PUNCT
ejpam-4872	279	9	)	)	PUNCT
ejpam-4872	280	1	⊇	⊇	PROPN
ejpam-4872	280	2	fs	fs	ADP
ejpam-4872	280	3	f	f	PROPN
ejpam-4872	280	4	(	(	PUNCT
ejpam-4872	280	5	y)∩fs	y)∩fs	PROPN
ejpam-4872	280	6	f	f	PROPN
ejpam-4872	280	7	(	(	PUNCT
ejpam-4872	280	8	z	z	NOUN
ejpam-4872	280	9	)	)	PUNCT
ejpam-4872	280	10	=	=	SYM
ejpam-4872	280	11	α	α	PROPN
ejpam-4872	280	12	and	and	CCONJ
ejpam-4872	280	13	f̃f	f̃f	PROPN
ejpam-4872	280	14	(	(	PUNCT
ejpam-4872	280	15	(	(	PUNCT
ejpam-4872	280	16	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	280	17	)	)	PUNCT
ejpam-4872	280	18	)	)	PUNCT
ejpam-4872	281	1	⊵	⊵	PROPN
ejpam-4872	281	2	rmin{f̃f	rmin{f̃f	PROPN
ejpam-4872	281	3	(	(	PUNCT
ejpam-4872	281	4	y	y	NOUN
ejpam-4872	281	5	)	)	PUNCT
ejpam-4872	281	6	,	,	PUNCT
ejpam-4872	281	7	f̃f	f̃f	PROPN
ejpam-4872	281	8	(	(	PUNCT
ejpam-4872	281	9	z	z	NOUN
ejpam-4872	281	10	)	)	PUNCT
ejpam-4872	281	11	}	}	PUNCT
ejpam-4872	282	1	=	=	PUNCT
ejpam-4872	282	2	ã.	ã.	NOUN
ejpam-4872	282	3	it	it	PRON
ejpam-4872	282	4	follows	follow	VERB
ejpam-4872	282	5	that	that	SCONJ
ejpam-4872	282	6	f̊f	f̊f	PROPN
ejpam-4872	282	7	(	(	PUNCT
ejpam-4872	282	8	(	(	PUNCT
ejpam-4872	282	9	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	282	10	)	)	PUNCT
ejpam-4872	282	11	)	)	PUNCT
ejpam-4872	283	1	=	=	SYM
ejpam-4872	283	2	(	(	PUNCT
ejpam-4872	283	3	t−	t−	PROPN
ejpam-4872	283	4	,	,	PUNCT
ejpam-4872	283	5	t+	t+	NOUN
ejpam-4872	283	6	)	)	PUNCT
ejpam-4872	283	7	,	,	PUNCT
ejpam-4872	283	8	f	f	PROPN
ejpam-4872	283	9	s	s	PROPN
ejpam-4872	283	10	f	f	X
ejpam-4872	283	11	(	(	PUNCT
ejpam-4872	283	12	(	(	PUNCT
ejpam-4872	283	13	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	283	14	)	)	PUNCT
ejpam-4872	283	15	)	)	PUNCT
ejpam-4872	284	1	=	=	SYM
ejpam-4872	284	2	α	α	PROPN
ejpam-4872	284	3	and	and	CCONJ
ejpam-4872	284	4	f̃f	f̃f	PROPN
ejpam-4872	284	5	(	(	PUNCT
ejpam-4872	284	6	(	(	PUNCT
ejpam-4872	284	7	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	284	8	)	)	PUNCT
ejpam-4872	284	9	)	)	PUNCT
ejpam-4872	285	1	=	=	PUNCT
ejpam-4872	285	2	ã.	ã.	NOUN
ejpam-4872	285	3	hence	hence	ADV
ejpam-4872	285	4	(	(	PUNCT
ejpam-4872	285	5	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	285	6	)	)	PUNCT
ejpam-4872	285	7	∈	∈	PROPN
ejpam-4872	286	1	f	f	PROPN
ejpam-4872	286	2	.	.	PUNCT
ejpam-4872	287	1	therefore	therefore	ADV
ejpam-4872	287	2	f	f	PROPN
ejpam-4872	287	3	is	be	AUX
ejpam-4872	287	4	a	a	DET
ejpam-4872	287	5	filter	filter	NOUN
ejpam-4872	287	6	of	of	ADP
ejpam-4872	287	7	x	x	NOUN
ejpam-4872	287	8	:	:	PUNCT
ejpam-4872	287	9	=	=	SYM
ejpam-4872	287	10	(	(	PUNCT
ejpam-4872	287	11	x	x	NOUN
ejpam-4872	287	12	,	,	PUNCT
ejpam-4872	287	13	|	|	NOUN
ejpam-4872	287	14	)	)	PUNCT
ejpam-4872	287	15	.	.	PUNCT
ejpam-4872	288	1	conversely	conversely	ADV
ejpam-4872	288	2	,	,	PUNCT
ejpam-4872	288	3	let	let	VERB
ejpam-4872	288	4	f	f	PRON
ejpam-4872	288	5	be	be	AUX
ejpam-4872	288	6	a	a	DET
ejpam-4872	288	7	filter	filter	NOUN
ejpam-4872	288	8	of	of	ADP
ejpam-4872	288	9	x	x	NOUN
ejpam-4872	288	10	:	:	PUNCT
ejpam-4872	288	11	=	=	SYM
ejpam-4872	288	12	(	(	PUNCT
ejpam-4872	288	13	x	x	NOUN
ejpam-4872	288	14	,	,	PUNCT
ejpam-4872	288	15	|	|	NOUN
ejpam-4872	288	16	)	)	PUNCT
ejpam-4872	288	17	.	.	PUNCT
ejpam-4872	289	1	since	since	SCONJ
ejpam-4872	289	2	1	1	NUM
ejpam-4872	289	3	∈	∈	PROPN
ejpam-4872	289	4	f	f	NOUN
ejpam-4872	289	5	,	,	PUNCT
ejpam-4872	289	6	we	we	PRON
ejpam-4872	289	7	have	have	VERB
ejpam-4872	289	8	f̊−(1	f̊−(1	NOUN
ejpam-4872	289	9	)	)	PUNCT
ejpam-4872	290	1	=	=	SYM
ejpam-4872	290	2	t−	t−	PROPN
ejpam-4872	290	3	≤	≤	NOUN
ejpam-4872	290	4	f̊−(x	f̊−(x	NOUN
ejpam-4872	290	5	)	)	PUNCT
ejpam-4872	290	6	and	and	CCONJ
ejpam-4872	290	7	f̊+(1	f̊+(1	NOUN
ejpam-4872	290	8	)	)	PUNCT
ejpam-4872	290	9	=	=	PUNCT
ejpam-4872	290	10	t+	t+	PUNCT
ejpam-4872	290	11	≥	≥	NOUN
ejpam-4872	290	12	f̊+(x	f̊+(x	NUM
ejpam-4872	290	13	)	)	PUNCT
ejpam-4872	290	14	,	,	PUNCT
ejpam-4872	290	15	and	and	CCONJ
ejpam-4872	290	16	so	so	ADV
ejpam-4872	290	17	1	1	NUM
ejpam-4872	290	18	(	(	PUNCT
ejpam-4872	290	19	x	x	NOUN
ejpam-4872	290	20	,	,	PUNCT
ejpam-4872	290	21	x	x	NOUN
ejpam-4872	290	22	)	)	PUNCT
ejpam-4872	290	23	∈	∈	PROPN
ejpam-4872	290	24	f̊(m	f̊(m	PROPN
ejpam-4872	290	25	,	,	PUNCT
ejpam-4872	290	26	m	m	PROPN
ejpam-4872	290	27	)	)	PUNCT
ejpam-4872	290	28	for	for	ADP
ejpam-4872	290	29	all	all	DET
ejpam-4872	290	30	x	x	SYM
ejpam-4872	290	31	∈	∈	ADJ
ejpam-4872	290	32	x.	x.	NOUN
ejpam-4872	290	33	also	also	ADV
ejpam-4872	290	34	fs(1	fs(1	PROPN
ejpam-4872	290	35	)	)	PUNCT
ejpam-4872	290	36	=	=	PUNCT
ejpam-4872	291	1	α	α	PROPN
ejpam-4872	291	2	⊇	⊇	PROPN
ejpam-4872	291	3	fs(x	fs(x	PROPN
ejpam-4872	291	4	)	)	PUNCT
ejpam-4872	291	5	and	and	CCONJ
ejpam-4872	291	6	f̃(1	f̃(1	NOUN
ejpam-4872	291	7	)	)	PUNCT
ejpam-4872	291	8	=	=	PUNCT
ejpam-4872	292	1	ã	ã	PROPN
ejpam-4872	292	2	⊵	⊵	PROPN
ejpam-4872	292	3	f̃(x	f̃(x	PROPN
ejpam-4872	292	4	)	)	PUNCT
ejpam-4872	292	5	for	for	ADP
ejpam-4872	292	6	all	all	PRON
ejpam-4872	292	7	x	x	SYM
ejpam-4872	292	8	∈	∈	NOUN
ejpam-4872	292	9	x.	x.	NOUN
ejpam-4872	292	10	let	let	VERB
ejpam-4872	292	11	x	x	PRON
ejpam-4872	292	12	,	,	PUNCT
ejpam-4872	292	13	y	y	PROPN
ejpam-4872	292	14	∈	∈	PROPN
ejpam-4872	292	15	x.	x.	NOUN
ejpam-4872	293	1	if	if	SCONJ
ejpam-4872	293	2	y	y	PROPN
ejpam-4872	293	3	∈	∈	PROPN
ejpam-4872	293	4	f	f	PROPN
ejpam-4872	293	5	,	,	PUNCT
ejpam-4872	293	6	then	then	ADV
ejpam-4872	293	7	x|(y|y	x|(y|y	PROPN
ejpam-4872	293	8	)	)	PUNCT
ejpam-4872	293	9	∈	∈	PROPN
ejpam-4872	293	10	f	f	PROPN
ejpam-4872	293	11	,	,	PUNCT
ejpam-4872	293	12	and	and	CCONJ
ejpam-4872	293	13	thus	thus	ADV
ejpam-4872	293	14	f̊−(x|(y|y	f̊−(x|(y|y	NUM
ejpam-4872	293	15	)	)	PUNCT
ejpam-4872	293	16	)	)	PUNCT
ejpam-4872	294	1	=	=	PUNCT
ejpam-4872	295	1	t−	t−	PROPN
ejpam-4872	295	2	=	=	SYM
ejpam-4872	295	3	f̊−(y	f̊−(y	X
ejpam-4872	295	4	)	)	PUNCT
ejpam-4872	295	5	and	and	CCONJ
ejpam-4872	295	6	f̊+(x|(y|y	f̊+(x|(y|y	NUM
ejpam-4872	295	7	)	)	PUNCT
ejpam-4872	295	8	)	)	PUNCT
ejpam-4872	296	1	=	=	SYM
ejpam-4872	296	2	t+	t+	NOUN
ejpam-4872	296	3	=	=	SYM
ejpam-4872	296	4	f̊+(y	f̊+(y	X
ejpam-4872	296	5	)	)	PUNCT
ejpam-4872	296	6	.	.	PUNCT
ejpam-4872	297	1	hence	hence	ADV
ejpam-4872	297	2	x|(y|y	x|(y|y	PROPN
ejpam-4872	297	3	)	)	PUNCT
ejpam-4872	297	4	(	(	PUNCT
ejpam-4872	297	5	y	y	PROPN
ejpam-4872	297	6	,	,	PUNCT
ejpam-4872	297	7	y	y	NOUN
ejpam-4872	297	8	)	)	PUNCT
ejpam-4872	297	9	∈	∈	PROPN
ejpam-4872	297	10	f̊(m	f̊(m	PROPN
ejpam-4872	297	11	,	,	PUNCT
ejpam-4872	297	12	m	m	PROPN
ejpam-4872	297	13	)	)	PUNCT
ejpam-4872	297	14	.	.	PUNCT
ejpam-4872	298	1	also	also	ADV
ejpam-4872	298	2	we	we	PRON
ejpam-4872	298	3	get	get	VERB
ejpam-4872	298	4	fs(x|(y|y	fs(x|(y|y	NOUN
ejpam-4872	298	5	)	)	PUNCT
ejpam-4872	298	6	)	)	PUNCT
ejpam-4872	299	1	=	=	SYM
ejpam-4872	299	2	α	α	NOUN
ejpam-4872	299	3	=	=	SYM
ejpam-4872	299	4	fs(y	fs(y	X
ejpam-4872	299	5	)	)	PUNCT
ejpam-4872	299	6	and	and	CCONJ
ejpam-4872	299	7	f̃(x|(y|y	f̃(x|(y|y	ADJ
ejpam-4872	299	8	)	)	PUNCT
ejpam-4872	299	9	)	)	PUNCT
ejpam-4872	300	1	=	=	PUNCT
ejpam-4872	300	2	ã	ã	PROPN
ejpam-4872	300	3	=	=	SYM
ejpam-4872	300	4	f̃(y	f̃(y	NOUN
ejpam-4872	300	5	)	)	PUNCT
ejpam-4872	300	6	.	.	PUNCT
ejpam-4872	301	1	if	if	SCONJ
ejpam-4872	301	2	y	y	PROPN
ejpam-4872	301	3	/∈	/∈	PROPN
ejpam-4872	302	1	f	f	PROPN
ejpam-4872	302	2	,	,	PUNCT
ejpam-4872	302	3	then	then	ADV
ejpam-4872	302	4	it	it	PRON
ejpam-4872	302	5	is	be	AUX
ejpam-4872	302	6	clear	clear	ADJ
ejpam-4872	302	7	that	that	SCONJ
ejpam-4872	302	8	x|(y|y	x|(y|y	PROPN
ejpam-4872	302	9	)	)	PUNCT
ejpam-4872	302	10	(	(	PUNCT
ejpam-4872	302	11	y	y	PROPN
ejpam-4872	302	12	,	,	PUNCT
ejpam-4872	302	13	y	y	NOUN
ejpam-4872	302	14	)	)	PUNCT
ejpam-4872	302	15	∈	∈	PROPN
ejpam-4872	302	16	f̊(m	f̊(m	PROPN
ejpam-4872	302	17	,	,	PUNCT
ejpam-4872	302	18	m	m	PROPN
ejpam-4872	302	19	)	)	PUNCT
ejpam-4872	302	20	,	,	PUNCT
ejpam-4872	302	21	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	302	22	)	)	PUNCT
ejpam-4872	302	23	)	)	PUNCT
ejpam-4872	303	1	⊇	⊇	PROPN
ejpam-4872	303	2	f	f	PROPN
ejpam-4872	303	3	s(y	s(y	PROPN
ejpam-4872	303	4	)	)	PUNCT
ejpam-4872	303	5	and	and	CCONJ
ejpam-4872	303	6	f̃(x|(y|y	f̃(x|(y|y	ADJ
ejpam-4872	303	7	)	)	PUNCT
ejpam-4872	303	8	)	)	PUNCT
ejpam-4872	303	9	⊵	⊵	ADJ
ejpam-4872	303	10	f̃(y	f̃(y	NOUN
ejpam-4872	303	11	)	)	PUNCT
ejpam-4872	303	12	.	.	PUNCT
ejpam-4872	304	1	let	let	VERB
ejpam-4872	304	2	x	x	PRON
ejpam-4872	304	3	,	,	PUNCT
ejpam-4872	304	4	y	y	PROPN
ejpam-4872	304	5	,	,	PUNCT
ejpam-4872	304	6	z	z	NOUN
ejpam-4872	304	7	∈	∈	PROPN
ejpam-4872	304	8	x.	x.	NOUN
ejpam-4872	305	1	it	it	PRON
ejpam-4872	305	2	is	be	AUX
ejpam-4872	305	3	obvious	obvious	ADJ
ejpam-4872	305	4	that	that	SCONJ
ejpam-4872	305	5	if	if	SCONJ
ejpam-4872	305	6	y	y	PROPN
ejpam-4872	305	7	/∈	/∈	PUNCT
ejpam-4872	305	8	f	f	PROPN
ejpam-4872	305	9	or	or	CCONJ
ejpam-4872	305	10	z	z	PROPN
ejpam-4872	305	11	/∈	/∈	PUNCT
ejpam-4872	305	12	f	f	PROPN
ejpam-4872	305	13	,	,	PUNCT
ejpam-4872	305	14	(	(	PUNCT
ejpam-4872	305	15	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	305	16	)	)	PUNCT
ejpam-4872	305	17	(	(	PUNCT
ejpam-4872	305	18	y	y	NOUN
ejpam-4872	305	19	,	,	PUNCT
ejpam-4872	305	20	z	z	NOUN
ejpam-4872	305	21	)	)	PUNCT
ejpam-4872	305	22	∈	∈	PROPN
ejpam-4872	305	23	f̊(m	f̊(m	PROPN
ejpam-4872	305	24	,	,	PUNCT
ejpam-4872	305	25	m	m	PROPN
ejpam-4872	305	26	)	)	PUNCT
ejpam-4872	305	27	,	,	PUNCT
ejpam-4872	305	28	fs((x|(y|z))|(y|z	fs((x|(y|z))|(y|z	NOUN
ejpam-4872	305	29	)	)	PUNCT
ejpam-4872	305	30	)	)	PUNCT
ejpam-4872	305	31	⊇	⊇	PROPN
ejpam-4872	305	32	fs(y)∩	fs(y)∩	NOUN
ejpam-4872	305	33	fs(z	fs(z	NUM
ejpam-4872	305	34	)	)	PUNCT
ejpam-4872	305	35	and	and	CCONJ
ejpam-4872	305	36	f̃((x|(y|z))|(y|z	f̃((x|(y|z))|(y|z	PROPN
ejpam-4872	305	37	)	)	PUNCT
ejpam-4872	305	38	)	)	PUNCT
ejpam-4872	305	39	⊵	⊵	PROPN
ejpam-4872	305	40	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	305	41	)	)	PUNCT
ejpam-4872	305	42	,	,	PUNCT
ejpam-4872	305	43	f̃(z	f̃(z	PROPN
ejpam-4872	305	44	)	)	PUNCT
ejpam-4872	305	45	.	.	PUNCT
ejpam-4872	306	1	suppose	suppose	VERB
ejpam-4872	306	2	that	that	SCONJ
ejpam-4872	306	3	y	y	PROPN
ejpam-4872	306	4	,	,	PUNCT
ejpam-4872	306	5	z	z	PROPN
ejpam-4872	306	6	∈	∈	PROPN
ejpam-4872	306	7	f	f	X
ejpam-4872	306	8	.	.	PUNCT
ejpam-4872	307	1	then	then	ADV
ejpam-4872	307	2	(	(	PUNCT
ejpam-4872	307	3	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	307	4	)	)	PUNCT
ejpam-4872	307	5	∈	∈	PROPN
ejpam-4872	307	6	f	f	X
ejpam-4872	307	7	.	.	PUNCT
ejpam-4872	308	1	thus	thus	ADV
ejpam-4872	308	2	f̊−((x|(y|z))|(y|z	f̊−((x|(y|z))|(y|z	NOUN
ejpam-4872	308	3	)	)	PUNCT
ejpam-4872	308	4	)	)	PUNCT
ejpam-4872	309	1	=	=	PUNCT
ejpam-4872	309	2	t−	t−	PROPN
ejpam-4872	309	3	=	=	SYM
ejpam-4872	310	1	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	310	2	)	)	PUNCT
ejpam-4872	310	3	,	,	PUNCT
ejpam-4872	310	4	f̊−(z	f̊−(z	NOUN
ejpam-4872	310	5	)	)	PUNCT
ejpam-4872	310	6	}	}	PUNCT
ejpam-4872	310	7	and	and	CCONJ
ejpam-4872	310	8	f̊+((x|(y|z))|(y|z	f̊+((x|(y|z))|(y|z	NUM
ejpam-4872	310	9	)	)	PUNCT
ejpam-4872	310	10	)	)	PUNCT
ejpam-4872	311	1	=	=	PUNCT
ejpam-4872	311	2	t+	t+	PUNCT
ejpam-4872	311	3	=	=	NOUN
ejpam-4872	311	4	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	311	5	)	)	PUNCT
ejpam-4872	311	6	,	,	PUNCT
ejpam-4872	311	7	f̊+(z	f̊+(z	PROPN
ejpam-4872	311	8	)	)	PUNCT
ejpam-4872	311	9	}	}	PUNCT
ejpam-4872	311	10	.	.	PUNCT
ejpam-4872	312	1	hence	hence	ADV
ejpam-4872	312	2	(	(	PUNCT
ejpam-4872	312	3	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	312	4	)	)	PUNCT
ejpam-4872	312	5	(	(	PUNCT
ejpam-4872	312	6	y	y	NOUN
ejpam-4872	312	7	,	,	PUNCT
ejpam-4872	312	8	z	z	NOUN
ejpam-4872	312	9	)	)	PUNCT
ejpam-4872	312	10	∈	∈	PROPN
ejpam-4872	312	11	f̊(m	f̊(m	PROPN
ejpam-4872	312	12	,	,	PUNCT
ejpam-4872	312	13	m	m	PROPN
ejpam-4872	312	14	)	)	PUNCT
ejpam-4872	312	15	.	.	PUNCT
ejpam-4872	313	1	also	also	ADV
ejpam-4872	313	2	we	we	PRON
ejpam-4872	313	3	get	get	VERB
ejpam-4872	313	4	fs((x|(y|z))|(y|z	fs((x|(y|z))|(y|z	NOUN
ejpam-4872	313	5	)	)	PUNCT
ejpam-4872	313	6	)	)	PUNCT
ejpam-4872	314	1	=	=	SYM
ejpam-4872	314	2	α	α	X
ejpam-4872	314	3	=	=	SYM
ejpam-4872	314	4	fs(y)∩	fs(y)∩	NOUN
ejpam-4872	314	5	fs(z	fs(z	NUM
ejpam-4872	314	6	)	)	PUNCT
ejpam-4872	314	7	and	and	CCONJ
ejpam-4872	314	8	f̃((x|(y|z))|(y|z	f̃((x|(y|z))|(y|z	PROPN
ejpam-4872	314	9	)	)	PUNCT
ejpam-4872	314	10	)	)	PUNCT
ejpam-4872	315	1	=	=	PUNCT
ejpam-4872	315	2	ã	ã	PROPN
ejpam-4872	315	3	=	=	PUNCT
ejpam-4872	315	4	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	315	5	)	)	PUNCT
ejpam-4872	315	6	,	,	PUNCT
ejpam-4872	315	7	f̃(z	f̃(z	PROPN
ejpam-4872	315	8	)	)	PUNCT
ejpam-4872	315	9	}	}	PUNCT
ejpam-4872	315	10	.	.	PUNCT
ejpam-4872	316	1	consequently	consequently	ADV
ejpam-4872	316	2	,	,	PUNCT
ejpam-4872	316	3	dokff	dokff	INTJ
ejpam-4872	316	4	:	:	PUNCT
ejpam-4872	316	5	=	=	SYM
ejpam-4872	316	6	(	(	PUNCT
ejpam-4872	316	7	f̊f	f̊f	PROPN
ejpam-4872	316	8	,	,	PUNCT
ejpam-4872	316	9	fs	fs	ADP
ejpam-4872	316	10	f	f	PROPN
ejpam-4872	316	11	,	,	PUNCT
ejpam-4872	316	12	f̃f	f̃f	PROPN
ejpam-4872	316	13	)	)	PUNCT
ejpam-4872	316	14	is	be	AUX
ejpam-4872	316	15	a	a	DET
ejpam-4872	316	16	dokdo	dokdo	ADJ
ejpam-4872	316	17	filter	filter	NOUN
ejpam-4872	316	18	of	of	ADP
ejpam-4872	316	19	(	(	PUNCT
ejpam-4872	316	20	u	u	NOUN
ejpam-4872	316	21	,	,	PUNCT
ejpam-4872	316	22	x	x	NOUN
ejpam-4872	316	23	)	)	PUNCT
ejpam-4872	316	24	.	.	PUNCT
ejpam-4872	317	1	since	since	SCONJ
ejpam-4872	317	2	f	f	PROPN
ejpam-4872	317	3	is	be	AUX
ejpam-4872	317	4	a	a	DET
ejpam-4872	317	5	filter	filter	NOUN
ejpam-4872	317	6	of	of	ADP
ejpam-4872	317	7	x	x	NOUN
ejpam-4872	317	8	:	:	PUNCT
ejpam-4872	317	9	=	=	SYM
ejpam-4872	317	10	(	(	PUNCT
ejpam-4872	317	11	x	x	NOUN
ejpam-4872	317	12	,	,	PUNCT
ejpam-4872	317	13	|	|	NOUN
ejpam-4872	317	14	)	)	PUNCT
ejpam-4872	317	15	,	,	PUNCT
ejpam-4872	317	16	we	we	PRON
ejpam-4872	317	17	get	get	VERB
ejpam-4872	317	18	xff	xff	PROPN
ejpam-4872	317	19	=	=	PUNCT
ejpam-4872	317	20	{	{	PUNCT
ejpam-4872	317	21	x	x	PUNCT
ejpam-4872	317	22	∈	∈	PROPN
ejpam-4872	317	23	x	x	SYM
ejpam-4872	317	24	|	|	ADV
ejpam-4872	317	25	f̊f	f̊f	PROPN
ejpam-4872	317	26	(	(	PUNCT
ejpam-4872	317	27	x	x	NOUN
ejpam-4872	317	28	)	)	PUNCT
ejpam-4872	317	29	=	=	SYM
ejpam-4872	317	30	f̊f	f̊f	PROPN
ejpam-4872	317	31	(	(	PUNCT
ejpam-4872	317	32	1	1	NUM
ejpam-4872	317	33	)	)	PUNCT
ejpam-4872	317	34	,	,	PUNCT
ejpam-4872	318	1	f	f	PROPN
ejpam-4872	318	2	s	s	PROPN
ejpam-4872	318	3	f	f	X
ejpam-4872	318	4	(	(	PUNCT
ejpam-4872	318	5	x	x	NOUN
ejpam-4872	318	6	)	)	PUNCT
ejpam-4872	318	7	=	=	SYM
ejpam-4872	318	8	fs	fs	PART
ejpam-4872	318	9	f	f	X
ejpam-4872	318	10	(	(	PUNCT
ejpam-4872	318	11	1	1	NUM
ejpam-4872	318	12	)	)	PUNCT
ejpam-4872	318	13	,	,	PUNCT
ejpam-4872	318	14	f̃f	f̃f	PROPN
ejpam-4872	318	15	(	(	PUNCT
ejpam-4872	318	16	x	x	X
ejpam-4872	318	17	)	)	PUNCT
ejpam-4872	318	18	=	=	SYM
ejpam-4872	318	19	f̃f	f̃f	PROPN
ejpam-4872	318	20	(	(	PUNCT
ejpam-4872	318	21	1	1	NUM
ejpam-4872	318	22	)	)	PUNCT
ejpam-4872	318	23	}	}	PUNCT
ejpam-4872	318	24	=	=	SYM
ejpam-4872	318	25	{	{	PUNCT
ejpam-4872	318	26	x	x	PUNCT
ejpam-4872	318	27	∈	∈	PROPN
ejpam-4872	318	28	x	x	SYM
ejpam-4872	318	29	|	|	ADV
ejpam-4872	318	30	f̊f	f̊f	PROPN
ejpam-4872	318	31	(	(	PUNCT
ejpam-4872	318	32	x	x	NOUN
ejpam-4872	318	33	)	)	PUNCT
ejpam-4872	318	34	=	=	SYM
ejpam-4872	318	35	(	(	PUNCT
ejpam-4872	318	36	t−	t−	PROPN
ejpam-4872	318	37	,	,	PUNCT
ejpam-4872	318	38	t+	t+	NOUN
ejpam-4872	318	39	)	)	PUNCT
ejpam-4872	318	40	,	,	PUNCT
ejpam-4872	318	41	f	f	PROPN
ejpam-4872	318	42	s	s	PROPN
ejpam-4872	318	43	f	f	X
ejpam-4872	318	44	(	(	PUNCT
ejpam-4872	318	45	x	x	NOUN
ejpam-4872	318	46	)	)	PUNCT
ejpam-4872	318	47	=	=	SYM
ejpam-4872	318	48	α	α	PROPN
ejpam-4872	318	49	,	,	PUNCT
ejpam-4872	318	50	f̃f	f̃f	PROPN
ejpam-4872	318	51	(	(	PUNCT
ejpam-4872	318	52	x	x	NOUN
ejpam-4872	318	53	)	)	PUNCT
ejpam-4872	318	54	=	=	SYM
ejpam-4872	318	55	ã	ã	PROPN
ejpam-4872	318	56	}	}	PUNCT
ejpam-4872	318	57	=	=	SYM
ejpam-4872	318	58	{	{	PUNCT
ejpam-4872	318	59	x	x	PUNCT
ejpam-4872	318	60	∈	∈	NOUN
ejpam-4872	318	61	x	x	PUNCT
ejpam-4872	318	62	|	|	ADV
ejpam-4872	318	63	x	x	SYM
ejpam-4872	318	64	∈	∈	PROPN
ejpam-4872	318	65	f	f	X
ejpam-4872	318	66	}	}	PUNCT
ejpam-4872	318	67	=	=	NOUN
ejpam-4872	318	68	f.	f.	NOUN
ejpam-4872	319	1	this	this	PRON
ejpam-4872	319	2	completes	complete	VERB
ejpam-4872	319	3	the	the	DET
ejpam-4872	319	4	proof	proof	NOUN
ejpam-4872	319	5	.	.	PUNCT
ejpam-4872	320	1	s.	s.	PROPN
ejpam-4872	320	2	s.	s.	PROPN
ejpam-4872	320	3	ahn	ahn	PROPN
ejpam-4872	320	4	et	et	PROPN
ejpam-4872	320	5	al	al	PROPN
ejpam-4872	320	6	.	.	PUNCT
ejpam-4872	320	7	/	/	SYM
ejpam-4872	320	8	eur	eur	PROPN
ejpam-4872	320	9	.	.	PUNCT
ejpam-4872	321	1	j.	j.	PROPN
ejpam-4872	321	2	pure	pure	PROPN
ejpam-4872	321	3	appl	appl	PROPN
ejpam-4872	321	4	.	.	PROPN
ejpam-4872	321	5	math	math	PROPN
ejpam-4872	321	6	,	,	PUNCT
ejpam-4872	321	7	16	16	NUM
ejpam-4872	321	8	(	(	PUNCT
ejpam-4872	321	9	3	3	NUM
ejpam-4872	321	10	)	)	PUNCT
ejpam-4872	321	11	(	(	PUNCT
ejpam-4872	321	12	2023	2023	NUM
ejpam-4872	321	13	)	)	PUNCT
ejpam-4872	321	14	,	,	PUNCT
ejpam-4872	321	15	1862	1862	NUM
ejpam-4872	321	16	-	-	SYM
ejpam-4872	321	17	1877	1877	NUM
ejpam-4872	321	18	1873	1873	NUM
ejpam-4872	321	19	definition	definition	NOUN
ejpam-4872	321	20	5	5	NUM
ejpam-4872	321	21	.	.	PUNCT
ejpam-4872	322	1	a	a	DET
ejpam-4872	322	2	dokdo	dokdo	NOUN
ejpam-4872	322	3	structure	structure	NOUN
ejpam-4872	322	4	dokf	dokf	NOUN
ejpam-4872	322	5	:	:	PUNCT
ejpam-4872	322	6	=	=	SYM
ejpam-4872	322	7	(	(	PUNCT
ejpam-4872	322	8	f̊	f̊	X
ejpam-4872	322	9	,	,	PUNCT
ejpam-4872	322	10	fs	fs	PROPN
ejpam-4872	322	11	,	,	PUNCT
ejpam-4872	322	12	f̃	f̃	PROPN
ejpam-4872	322	13	)	)	PUNCT
ejpam-4872	322	14	is	be	AUX
ejpam-4872	322	15	called	call	VERB
ejpam-4872	322	16	a	a	DET
ejpam-4872	322	17	dokdo	dokdo	ADJ
ejpam-4872	322	18	deductive	deductive	ADJ
ejpam-4872	322	19	system	system	NOUN
ejpam-4872	322	20	of	of	ADP
ejpam-4872	322	21	(	(	PUNCT
ejpam-4872	322	22	u	u	NOUN
ejpam-4872	322	23	,	,	PUNCT
ejpam-4872	322	24	x	x	X
ejpam-4872	322	25	)	)	PUNCT
ejpam-4872	322	26	if	if	SCONJ
ejpam-4872	322	27	it	it	PRON
ejpam-4872	322	28	satisfies	satisfy	VERB
ejpam-4872	322	29	(	(	PUNCT
ejpam-4872	322	30	19	19	NUM
ejpam-4872	322	31	)	)	PUNCT
ejpam-4872	322	32	and	and	CCONJ
ejpam-4872	322	33	(	(	PUNCT
ejpam-4872	322	34	∀x	∀x	X
ejpam-4872	322	35	,	,	PUNCT
ejpam-4872	322	36	y	y	PROPN
ejpam-4872	322	37	∈	∈	PROPN
ejpam-4872	322	38	x	x	NOUN
ejpam-4872	322	39	)	)	PUNCT
ejpam-4872	322	40			PROPN
ejpam-4872	322	41	y	y	PROPN
ejpam-4872	322	42	(	(	PUNCT
ejpam-4872	322	43	x	x	X
ejpam-4872	322	44	,	,	PUNCT
ejpam-4872	322	45	x|(y|y	x|(y|y	PROPN
ejpam-4872	322	46	)	)	PUNCT
ejpam-4872	322	47	)	)	PUNCT
ejpam-4872	323	1	∈	∈	PROPN
ejpam-4872	323	2	f̊(m	f̊(m	PROPN
ejpam-4872	323	3	,	,	PUNCT
ejpam-4872	323	4	m	m	PROPN
ejpam-4872	323	5	)	)	PUNCT
ejpam-4872	323	6	,	,	PUNCT
ejpam-4872	323	7	fs(y	fs(y	ADJ
ejpam-4872	323	8	)	)	PUNCT
ejpam-4872	323	9	⊇	⊇	NOUN
ejpam-4872	323	10	fs(x	fs(x	NOUN
ejpam-4872	323	11	)	)	PUNCT
ejpam-4872	323	12	∩	∩	NOUN
ejpam-4872	323	13	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	323	14	)	)	PUNCT
ejpam-4872	323	15	)	)	PUNCT
ejpam-4872	323	16	,	,	PUNCT
ejpam-4872	323	17	f̃(y	f̃(y	ADJ
ejpam-4872	323	18	)	)	PUNCT
ejpam-4872	323	19	⊵	⊵	ADJ
ejpam-4872	323	20	rmin{f̃(x	rmin{f̃(x	NOUN
ejpam-4872	323	21	)	)	PUNCT
ejpam-4872	323	22	,	,	PUNCT
ejpam-4872	323	23	f̃(x|(y|y	f̃(x|(y|y	PROPN
ejpam-4872	323	24	)	)	PUNCT
ejpam-4872	323	25	)	)	PUNCT
ejpam-4872	323	26	}	}	PUNCT
ejpam-4872	323	27			PROPN
ejpam-4872	323	28	.	.	PUNCT
ejpam-4872	324	1	(	(	PUNCT
ejpam-4872	324	2	26	26	NUM
ejpam-4872	324	3	)	)	PUNCT
ejpam-4872	324	4	example	example	NOUN
ejpam-4872	324	5	4	4	NUM
ejpam-4872	324	6	.	.	PUNCT
ejpam-4872	324	7	consider	consider	VERB
ejpam-4872	324	8	the	the	DET
ejpam-4872	324	9	sheffer	sheffer	NOUN
ejpam-4872	324	10	stroke	stroke	NOUN
ejpam-4872	324	11	hilbert	hilbert	PROPN
ejpam-4872	324	12	algebra	algebra	PROPN
ejpam-4872	324	13	x	x	X
ejpam-4872	324	14	:	:	PUNCT
ejpam-4872	324	15	=	=	SYM
ejpam-4872	324	16	(	(	PUNCT
ejpam-4872	324	17	x	x	NOUN
ejpam-4872	324	18	,	,	PUNCT
ejpam-4872	324	19	|	|	ADV
ejpam-4872	324	20	)	)	PUNCT
ejpam-4872	324	21	in	in	ADP
ejpam-4872	324	22	example	example	NOUN
ejpam-4872	324	23	1	1	NUM
ejpam-4872	324	24	and	and	CCONJ
ejpam-4872	324	25	let	let	VERB
ejpam-4872	324	26	dokf	dokf	VERB
ejpam-4872	324	27	:	:	PUNCT
ejpam-4872	324	28	=	=	SYM
ejpam-4872	324	29	(	(	PUNCT
ejpam-4872	324	30	f̊	f̊	X
ejpam-4872	324	31	,	,	PUNCT
ejpam-4872	324	32	f	f	PROPN
ejpam-4872	324	33	s	s	PROPN
ejpam-4872	324	34	,	,	PUNCT
ejpam-4872	324	35	f̃	f̃	PROPN
ejpam-4872	324	36	)	)	PUNCT
ejpam-4872	324	37	be	be	VERB
ejpam-4872	324	38	a	a	DET
ejpam-4872	324	39	dokdo	dokdo	NOUN
ejpam-4872	324	40	structure	structure	NOUN
ejpam-4872	324	41	in	in	ADP
ejpam-4872	324	42	(	(	PUNCT
ejpam-4872	324	43	x	x	X
ejpam-4872	324	44	,	,	PUNCT
ejpam-4872	324	45	u	u	NOUN
ejpam-4872	324	46	=	=	PROPN
ejpam-4872	324	47	z	z	PROPN
ejpam-4872	324	48	)	)	PUNCT
ejpam-4872	324	49	which	which	PRON
ejpam-4872	324	50	is	be	AUX
ejpam-4872	324	51	given	give	VERB
ejpam-4872	324	52	by	by	ADP
ejpam-4872	324	53	table	table	NOUN
ejpam-4872	324	54	7	7	NUM
ejpam-4872	324	55	.	.	PUNCT
ejpam-4872	324	56	table	table	NOUN
ejpam-4872	324	57	7	7	NUM
ejpam-4872	324	58	:	:	PUNCT
ejpam-4872	324	59	tabular	tabular	PROPN
ejpam-4872	324	60	representation	representation	NOUN
ejpam-4872	324	61	of	of	ADP
ejpam-4872	324	62	dokf	dokf	NOUN
ejpam-4872	324	63	:	:	PUNCT
ejpam-4872	324	64	=	=	SYM
ejpam-4872	324	65	(	(	PUNCT
ejpam-4872	324	66	f̊	f̊	X
ejpam-4872	324	67	,	,	PUNCT
ejpam-4872	324	68	fs	fs	PROPN
ejpam-4872	324	69	,	,	PUNCT
ejpam-4872	324	70	f̃	f̃	PROPN
ejpam-4872	324	71	)	)	PUNCT
ejpam-4872	324	72	x	x	PUNCT
ejpam-4872	324	73	f̊(x	f̊(x	NOUN
ejpam-4872	324	74	)	)	PUNCT
ejpam-4872	324	75	fs(x	fs(x	NOUN
ejpam-4872	324	76	)	)	PUNCT
ejpam-4872	324	77	f̃(x	f̃(x	NOUN
ejpam-4872	324	78	)	)	PUNCT
ejpam-4872	324	79	0	0	NUM
ejpam-4872	325	1	(	(	PUNCT
ejpam-4872	325	2	−0.37	−0.37	NOUN
ejpam-4872	325	3	,	,	PUNCT
ejpam-4872	325	4	0.48	0.48	NUM
ejpam-4872	325	5	)	)	PUNCT
ejpam-4872	325	6	8n	8n	NOUN
ejpam-4872	325	7	[	[	X
ejpam-4872	325	8	0.19	0.19	NUM
ejpam-4872	325	9	,	,	PUNCT
ejpam-4872	325	10	0.54	0.54	NUM
ejpam-4872	325	11	]	]	SYM
ejpam-4872	325	12	2	2	NUM
ejpam-4872	325	13	(	(	PUNCT
ejpam-4872	325	14	−0.57	−0.57	ADV
ejpam-4872	325	15	,	,	PUNCT
ejpam-4872	325	16	0.67	0.67	NUM
ejpam-4872	325	17	)	)	PUNCT
ejpam-4872	325	18	4n	4n	NOUN
ejpam-4872	326	1	[	[	X
ejpam-4872	326	2	0.24	0.24	NUM
ejpam-4872	326	3	,	,	PUNCT
ejpam-4872	326	4	0.62	0.62	NUM
ejpam-4872	326	5	]	]	SYM
ejpam-4872	326	6	3	3	NUM
ejpam-4872	326	7	(	(	PUNCT
ejpam-4872	326	8	−0.37	−0.37	PROPN
ejpam-4872	326	9	,	,	PUNCT
ejpam-4872	326	10	0.48	0.48	NUM
ejpam-4872	326	11	)	)	PUNCT
ejpam-4872	326	12	8z	8z	NOUN
ejpam-4872	327	1	[	[	X
ejpam-4872	327	2	0.19	0.19	NUM
ejpam-4872	327	3	,	,	PUNCT
ejpam-4872	327	4	0.54	0.54	NUM
ejpam-4872	327	5	]	]	SYM
ejpam-4872	327	6	4	4	NUM
ejpam-4872	327	7	(	(	PUNCT
ejpam-4872	327	8	−0.37	−0.37	NOUN
ejpam-4872	327	9	,	,	PUNCT
ejpam-4872	327	10	0.48	0.48	NUM
ejpam-4872	327	11	)	)	PUNCT
ejpam-4872	327	12	8n	8n	NOUN
ejpam-4872	327	13	[	[	X
ejpam-4872	327	14	0.19	0.19	NUM
ejpam-4872	327	15	,	,	PUNCT
ejpam-4872	327	16	0.54	0.54	NUM
ejpam-4872	327	17	]	]	SYM
ejpam-4872	327	18	5	5	NUM
ejpam-4872	327	19	(	(	PUNCT
ejpam-4872	327	20	−0.61	−0.61	NOUN
ejpam-4872	327	21	,	,	PUNCT
ejpam-4872	327	22	0.72	0.72	NUM
ejpam-4872	327	23	)	)	PUNCT
ejpam-4872	327	24	4z	4z	NOUN
ejpam-4872	328	1	[	[	X
ejpam-4872	328	2	0.26	0.26	NUM
ejpam-4872	328	3	,	,	PUNCT
ejpam-4872	328	4	0.63	0.63	NUM
ejpam-4872	328	5	]	]	SYM
ejpam-4872	328	6	6	6	NUM
ejpam-4872	328	7	(	(	PUNCT
ejpam-4872	328	8	−0.57	−0.57	ADV
ejpam-4872	328	9	,	,	PUNCT
ejpam-4872	328	10	0.67	0.67	NUM
ejpam-4872	328	11	)	)	PUNCT
ejpam-4872	328	12	4n	4n	NOUN
ejpam-4872	329	1	[	[	X
ejpam-4872	329	2	0.24	0.24	NUM
ejpam-4872	329	3	,	,	PUNCT
ejpam-4872	329	4	0.62	0.62	NUM
ejpam-4872	329	5	]	]	SYM
ejpam-4872	329	6	7	7	NUM
ejpam-4872	329	7	(	(	PUNCT
ejpam-4872	329	8	−0.37	−0.37	NOUN
ejpam-4872	329	9	,	,	PUNCT
ejpam-4872	329	10	0.48	0.48	NUM
ejpam-4872	329	11	)	)	PUNCT
ejpam-4872	329	12	8n	8n	NOUN
ejpam-4872	329	13	[	[	X
ejpam-4872	329	14	0.19	0.19	NUM
ejpam-4872	329	15	,	,	PUNCT
ejpam-4872	329	16	0.54	0.54	NUM
ejpam-4872	329	17	]	]	SYM
ejpam-4872	329	18	1	1	NUM
ejpam-4872	329	19	(	(	PUNCT
ejpam-4872	329	20	−0.69	−0.69	NOUN
ejpam-4872	329	21	,	,	PUNCT
ejpam-4872	329	22	0.79	0.79	NUM
ejpam-4872	329	23	)	)	PUNCT
ejpam-4872	329	24	2z	2z	NOUN
ejpam-4872	330	1	[	[	X
ejpam-4872	330	2	0.41	0.41	NUM
ejpam-4872	330	3	,	,	PUNCT
ejpam-4872	330	4	0.87	0.87	NUM
ejpam-4872	330	5	]	]	PUNCT
ejpam-4872	330	6	it	it	PRON
ejpam-4872	330	7	is	be	AUX
ejpam-4872	330	8	routine	routine	ADJ
ejpam-4872	330	9	to	to	PART
ejpam-4872	330	10	verify	verify	VERB
ejpam-4872	330	11	that	that	DET
ejpam-4872	330	12	dokf	dokf	NOUN
ejpam-4872	330	13	:	:	PUNCT
ejpam-4872	330	14	=	=	SYM
ejpam-4872	330	15	(	(	PUNCT
ejpam-4872	330	16	f̊	f̊	X
ejpam-4872	330	17	,	,	PUNCT
ejpam-4872	330	18	f	f	PROPN
ejpam-4872	330	19	s	s	PROPN
ejpam-4872	330	20	,	,	PUNCT
ejpam-4872	330	21	f̃	f̃	PROPN
ejpam-4872	330	22	)	)	PUNCT
ejpam-4872	330	23	is	be	AUX
ejpam-4872	330	24	a	a	DET
ejpam-4872	330	25	dokdo	dokdo	ADJ
ejpam-4872	330	26	deductive	deductive	ADJ
ejpam-4872	330	27	system	system	NOUN
ejpam-4872	330	28	of	of	ADP
ejpam-4872	330	29	(	(	PUNCT
ejpam-4872	330	30	x	x	X
ejpam-4872	330	31	,	,	PUNCT
ejpam-4872	330	32	u	u	NOUN
ejpam-4872	330	33	=	=	PROPN
ejpam-4872	330	34	z	z	PROPN
ejpam-4872	330	35	)	)	PUNCT
ejpam-4872	330	36	.	.	PUNCT
ejpam-4872	331	1	theorem	theorem	ADJ
ejpam-4872	331	2	5	5	NUM
ejpam-4872	331	3	.	.	PUNCT
ejpam-4872	331	4	a	a	DET
ejpam-4872	331	5	dokdo	dokdo	NOUN
ejpam-4872	331	6	structure	structure	NOUN
ejpam-4872	331	7	dokf	dokf	NOUN
ejpam-4872	331	8	:	:	PUNCT
ejpam-4872	331	9	=	=	SYM
ejpam-4872	331	10	(	(	PUNCT
ejpam-4872	331	11	f̊	f̊	X
ejpam-4872	331	12	,	,	PUNCT
ejpam-4872	331	13	fs	fs	PROPN
ejpam-4872	331	14	,	,	PUNCT
ejpam-4872	331	15	f̃	f̃	PROPN
ejpam-4872	331	16	)	)	PUNCT
ejpam-4872	331	17	in	in	ADP
ejpam-4872	331	18	(	(	PUNCT
ejpam-4872	331	19	x	x	NOUN
ejpam-4872	331	20	,	,	PUNCT
ejpam-4872	331	21	u	u	NOUN
ejpam-4872	331	22	)	)	PUNCT
ejpam-4872	331	23	is	be	AUX
ejpam-4872	331	24	a	a	DET
ejpam-4872	331	25	dokdo	dokdo	ADJ
ejpam-4872	331	26	deductive	deductive	ADJ
ejpam-4872	331	27	system	system	NOUN
ejpam-4872	331	28	of	of	ADP
ejpam-4872	331	29	(	(	PUNCT
ejpam-4872	331	30	x	x	NOUN
ejpam-4872	331	31	,	,	PUNCT
ejpam-4872	331	32	u	u	NOUN
ejpam-4872	331	33	)	)	PUNCT
ejpam-4872	331	34	if	if	SCONJ
ejpam-4872	331	35	and	and	CCONJ
ejpam-4872	331	36	only	only	ADV
ejpam-4872	331	37	if	if	SCONJ
ejpam-4872	331	38	it	it	PRON
ejpam-4872	331	39	is	be	AUX
ejpam-4872	331	40	a	a	DET
ejpam-4872	331	41	dokdo	dokdo	ADJ
ejpam-4872	331	42	filter	filter	NOUN
ejpam-4872	331	43	of	of	ADP
ejpam-4872	331	44	(	(	PUNCT
ejpam-4872	331	45	x	x	NOUN
ejpam-4872	331	46	,	,	PUNCT
ejpam-4872	331	47	u	u	NOUN
ejpam-4872	331	48	)	)	PUNCT
ejpam-4872	331	49	.	.	PUNCT
ejpam-4872	332	1	proof	proof	NOUN
ejpam-4872	332	2	.	.	PUNCT
ejpam-4872	333	1	assume	assume	VERB
ejpam-4872	333	2	that	that	SCONJ
ejpam-4872	333	3	dokf	dokf	NOUN
ejpam-4872	333	4	:	:	PUNCT
ejpam-4872	333	5	=	=	SYM
ejpam-4872	333	6	(	(	PUNCT
ejpam-4872	333	7	f̊	f̊	X
ejpam-4872	333	8	,	,	PUNCT
ejpam-4872	333	9	fs	fs	PROPN
ejpam-4872	333	10	,	,	PUNCT
ejpam-4872	333	11	f̃	f̃	PROPN
ejpam-4872	333	12	)	)	PUNCT
ejpam-4872	333	13	is	be	AUX
ejpam-4872	333	14	a	a	DET
ejpam-4872	333	15	dokdo	dokdo	ADJ
ejpam-4872	333	16	deductive	deductive	ADJ
ejpam-4872	333	17	system	system	NOUN
ejpam-4872	333	18	of	of	ADP
ejpam-4872	333	19	(	(	PUNCT
ejpam-4872	333	20	x	x	NOUN
ejpam-4872	333	21	,	,	PUNCT
ejpam-4872	333	22	u	u	NOUN
ejpam-4872	333	23	)	)	PUNCT
ejpam-4872	333	24	and	and	CCONJ
ejpam-4872	333	25	let	let	VERB
ejpam-4872	333	26	x	x	PRON
ejpam-4872	333	27	,	,	PUNCT
ejpam-4872	333	28	y	y	PROPN
ejpam-4872	333	29	,	,	PUNCT
ejpam-4872	333	30	z	z	NOUN
ejpam-4872	333	31	∈	∈	NOUN
ejpam-4872	333	32	x.	x.	NOUN
ejpam-4872	333	33	using	use	VERB
ejpam-4872	333	34	(	(	PUNCT
ejpam-4872	333	35	1	1	NUM
ejpam-4872	333	36	)	)	PUNCT
ejpam-4872	333	37	and	and	CCONJ
ejpam-4872	333	38	(	(	PUNCT
ejpam-4872	333	39	5	5	X
ejpam-4872	333	40	)	)	PUNCT
ejpam-4872	333	41	induces	induce	VERB
ejpam-4872	333	42	y|((x|(y|y))|(x|(y|y	y|((x|(y|y))|(x|(y|y	NOUN
ejpam-4872	333	43	)	)	PUNCT
ejpam-4872	333	44	)	)	PUNCT
ejpam-4872	333	45	)	)	PUNCT
ejpam-4872	334	1	=	=	PUNCT
ejpam-4872	334	2	1	1	X
ejpam-4872	334	3	.	.	PUNCT
ejpam-4872	335	1	it	it	PRON
ejpam-4872	335	2	follows	follow	VERB
ejpam-4872	335	3	from	from	ADP
ejpam-4872	335	4	(	(	PUNCT
ejpam-4872	335	5	19	19	NUM
ejpam-4872	335	6	)	)	PUNCT
ejpam-4872	335	7	and	and	CCONJ
ejpam-4872	335	8	(	(	PUNCT
ejpam-4872	335	9	26	26	NUM
ejpam-4872	335	10	)	)	PUNCT
ejpam-4872	335	11	that	that	PRON
ejpam-4872	335	12	f̊−(x|(y|y	f̊−(x|(y|y	PROPN
ejpam-4872	335	13	)	)	PUNCT
ejpam-4872	335	14	)	)	PUNCT
ejpam-4872	335	15	≤	≤	NOUN
ejpam-4872	336	1	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	336	2	)	)	PUNCT
ejpam-4872	336	3	,	,	PUNCT
ejpam-4872	336	4	f̊−(y|((x|(y|y))|(x|(y|y	f̊−(y|((x|(y|y))|(x|(y|y	NOUN
ejpam-4872	336	5	)	)	PUNCT
ejpam-4872	336	6	)	)	PUNCT
ejpam-4872	336	7	)	)	PUNCT
ejpam-4872	336	8	)	)	PUNCT
ejpam-4872	336	9	}	}	PUNCT
ejpam-4872	337	1	=	=	SYM
ejpam-4872	337	2	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	337	3	)	)	PUNCT
ejpam-4872	337	4	,	,	PUNCT
ejpam-4872	337	5	f̊−(1	f̊−(1	NOUN
ejpam-4872	337	6	)	)	PUNCT
ejpam-4872	337	7	}	}	PUNCT
ejpam-4872	337	8	=	=	SYM
ejpam-4872	337	9	f̊−(y	f̊−(y	X
ejpam-4872	337	10	)	)	PUNCT
ejpam-4872	337	11	,	,	PUNCT
ejpam-4872	337	12	f̊+(x|(y|y	f̊+(x|(y|y	NUM
ejpam-4872	337	13	)	)	PUNCT
ejpam-4872	337	14	)	)	PUNCT
ejpam-4872	337	15	≥	≥	NOUN
ejpam-4872	337	16	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	337	17	)	)	PUNCT
ejpam-4872	337	18	,	,	PUNCT
ejpam-4872	337	19	f̊+(y|((x|(y|y))|(x|(y|y	f̊+(y|((x|(y|y))|(x|(y|y	ADJ
ejpam-4872	337	20	)	)	PUNCT
ejpam-4872	337	21	)	)	PUNCT
ejpam-4872	337	22	)	)	PUNCT
ejpam-4872	337	23	)	)	PUNCT
ejpam-4872	337	24	}	}	PUNCT
ejpam-4872	337	25	=	=	SYM
ejpam-4872	337	26	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	337	27	)	)	PUNCT
ejpam-4872	337	28	,	,	PUNCT
ejpam-4872	337	29	f̊+(1	f̊+(1	NOUN
ejpam-4872	337	30	)	)	PUNCT
ejpam-4872	337	31	}	}	PUNCT
ejpam-4872	337	32	=	=	SYM
ejpam-4872	337	33	f̊+(y	f̊+(y	X
ejpam-4872	337	34	)	)	PUNCT
ejpam-4872	337	35	,	,	PUNCT
ejpam-4872	337	36	that	that	ADV
ejpam-4872	337	37	is	is	ADV
ejpam-4872	337	38	,	,	PUNCT
ejpam-4872	337	39	x|(y|y	x|(y|y	PROPN
ejpam-4872	337	40	)	)	PUNCT
ejpam-4872	337	41	(	(	PUNCT
ejpam-4872	337	42	y	y	PROPN
ejpam-4872	337	43	,	,	PUNCT
ejpam-4872	337	44	y	y	NOUN
ejpam-4872	337	45	)	)	PUNCT
ejpam-4872	337	46	∈	∈	PROPN
ejpam-4872	337	47	f̊(m	f̊(m	PROPN
ejpam-4872	337	48	,	,	PUNCT
ejpam-4872	337	49	m	m	PROPN
ejpam-4872	337	50	)	)	PUNCT
ejpam-4872	337	51	,	,	PUNCT
ejpam-4872	337	52	and	and	CCONJ
ejpam-4872	337	53	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	337	54	)	)	PUNCT
ejpam-4872	337	55	)	)	PUNCT
ejpam-4872	337	56	⊇	⊇	PROPN
ejpam-4872	337	57	fs(y	fs(y	ADJ
ejpam-4872	337	58	)	)	PUNCT
ejpam-4872	337	59	∩	∩	PROPN
ejpam-4872	337	60	f	f	PROPN
ejpam-4872	337	61	s(y|((x|(y|y))|(x|(y|y	s(y|((x|(y|y))|(x|(y|y	X
ejpam-4872	337	62	)	)	PUNCT
ejpam-4872	337	63	)	)	PUNCT
ejpam-4872	337	64	)	)	PUNCT
ejpam-4872	337	65	)	)	PUNCT
ejpam-4872	338	1	=	=	PUNCT
ejpam-4872	338	2	f	f	PROPN
ejpam-4872	338	3	s(y	s(y	PROPN
ejpam-4872	338	4	)	)	PUNCT
ejpam-4872	338	5	∩	∩	PROPN
ejpam-4872	338	6	fs(1	fs(1	PROPN
ejpam-4872	338	7	)	)	PUNCT
ejpam-4872	338	8	}	}	PUNCT
ejpam-4872	338	9	=	=	SYM
ejpam-4872	338	10	fs(y	fs(y	X
ejpam-4872	338	11	)	)	PUNCT
ejpam-4872	338	12	s.	s.	PROPN
ejpam-4872	338	13	s.	s.	PROPN
ejpam-4872	338	14	ahn	ahn	PROPN
ejpam-4872	338	15	et	et	PROPN
ejpam-4872	338	16	al	al	PROPN
ejpam-4872	338	17	.	.	PUNCT
ejpam-4872	338	18	/	/	SYM
ejpam-4872	338	19	eur	eur	PROPN
ejpam-4872	338	20	.	.	PUNCT
ejpam-4872	339	1	j.	j.	PROPN
ejpam-4872	339	2	pure	pure	PROPN
ejpam-4872	339	3	appl	appl	PROPN
ejpam-4872	339	4	.	.	PROPN
ejpam-4872	339	5	math	math	PROPN
ejpam-4872	339	6	,	,	PUNCT
ejpam-4872	339	7	16	16	NUM
ejpam-4872	339	8	(	(	PUNCT
ejpam-4872	339	9	3	3	NUM
ejpam-4872	339	10	)	)	PUNCT
ejpam-4872	339	11	(	(	PUNCT
ejpam-4872	339	12	2023	2023	NUM
ejpam-4872	339	13	)	)	PUNCT
ejpam-4872	339	14	,	,	PUNCT
ejpam-4872	339	15	1862	1862	NUM
ejpam-4872	339	16	-	-	SYM
ejpam-4872	339	17	1877	1877	NUM
ejpam-4872	339	18	1874	1874	NUM
ejpam-4872	339	19	and	and	CCONJ
ejpam-4872	339	20	f̃(x|(y|y	f̃(x|(y|y	ADJ
ejpam-4872	339	21	)	)	PUNCT
ejpam-4872	339	22	)	)	PUNCT
ejpam-4872	339	23	⊵	⊵	PROPN
ejpam-4872	339	24	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	339	25	)	)	PUNCT
ejpam-4872	339	26	,	,	PUNCT
ejpam-4872	339	27	f̃(y|((x|(y|y))|(x|(y|y	f̃(y|((x|(y|y))|(x|(y|y	NOUN
ejpam-4872	339	28	)	)	PUNCT
ejpam-4872	339	29	)	)	PUNCT
ejpam-4872	339	30	)	)	PUNCT
ejpam-4872	339	31	)	)	PUNCT
ejpam-4872	339	32	}	}	PUNCT
ejpam-4872	339	33	=	=	SYM
ejpam-4872	339	34	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	339	35	)	)	PUNCT
ejpam-4872	339	36	,	,	PUNCT
ejpam-4872	339	37	f̃(1	f̃(1	NOUN
ejpam-4872	339	38	)	)	PUNCT
ejpam-4872	339	39	}	}	PUNCT
ejpam-4872	339	40	=	=	SYM
ejpam-4872	339	41	f̃(y	f̃(y	NOUN
ejpam-4872	339	42	)	)	PUNCT
ejpam-4872	339	43	.	.	PUNCT
ejpam-4872	340	1	note	note	VERB
ejpam-4872	340	2	that	that	SCONJ
ejpam-4872	340	3	y|(((y|z)|z)|((y|z)|z	y|(((y|z)|z)|((y|z)|z	NOUN
ejpam-4872	340	4	)	)	PUNCT
ejpam-4872	340	5	)	)	PUNCT
ejpam-4872	341	1	=	=	SYM
ejpam-4872	341	2	y|(((y|z)|((z|z)|(z|z)))|((y|z)|((z|z)|(z|z	y|(((y|z)|((z|z)|(z|z)))|((y|z)|((z|z)|(z|z	NOUN
ejpam-4872	341	3	)	)	PUNCT
ejpam-4872	341	4	)	)	PUNCT
ejpam-4872	341	5	)	)	PUNCT
ejpam-4872	341	6	)	)	PUNCT
ejpam-4872	342	1	=	=	PRON
ejpam-4872	342	2	(	(	PUNCT
ejpam-4872	342	3	y|z)|((y|((z|z)|(z|z)))|(y|((z|z)|(z|z	y|z)|((y|((z|z)|(z|z)))|(y|((z|z)|(z|z	NUM
ejpam-4872	342	4	)	)	PUNCT
ejpam-4872	342	5	)	)	PUNCT
ejpam-4872	342	6	)	)	PUNCT
ejpam-4872	342	7	)	)	PUNCT
ejpam-4872	343	1	=	=	PUNCT
ejpam-4872	343	2	(	(	PUNCT
ejpam-4872	343	3	y|z)|((y|z)|(y|z	y|z)|((y|z)|(y|z	NOUN
ejpam-4872	343	4	)	)	PUNCT
ejpam-4872	343	5	)	)	PUNCT
ejpam-4872	344	1	=	=	SYM
ejpam-4872	344	2	1	1	X
ejpam-4872	344	3	by	by	ADP
ejpam-4872	344	4	(	(	PUNCT
ejpam-4872	344	5	s2	s2	PROPN
ejpam-4872	344	6	)	)	PUNCT
ejpam-4872	344	7	,	,	PUNCT
ejpam-4872	344	8	(	(	PUNCT
ejpam-4872	344	9	2	2	X
ejpam-4872	344	10	)	)	PUNCT
ejpam-4872	344	11	and	and	CCONJ
ejpam-4872	344	12	(	(	PUNCT
ejpam-4872	344	13	8)	8)	NUM
ejpam-4872	344	14	.	.	PUNCT
ejpam-4872	344	15	using	use	VERB
ejpam-4872	344	16	(	(	PUNCT
ejpam-4872	344	17	19	19	NUM
ejpam-4872	344	18	)	)	PUNCT
ejpam-4872	344	19	and	and	CCONJ
ejpam-4872	344	20	(	(	PUNCT
ejpam-4872	344	21	26	26	NUM
ejpam-4872	344	22	)	)	PUNCT
ejpam-4872	344	23	,	,	PUNCT
ejpam-4872	344	24	we	we	PRON
ejpam-4872	344	25	have	have	VERB
ejpam-4872	344	26	f̊−((y|z)|z	f̊−((y|z)|z	NOUN
ejpam-4872	344	27	)	)	PUNCT
ejpam-4872	344	28	≤	≤	NOUN
ejpam-4872	345	1	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	345	2	)	)	PUNCT
ejpam-4872	345	3	,	,	PUNCT
ejpam-4872	345	4	f̊−(y|(((y|z)|z)|((y|z)|z	f̊−(y|(((y|z)|z)|((y|z)|z	NOUN
ejpam-4872	345	5	)	)	PUNCT
ejpam-4872	345	6	)	)	PUNCT
ejpam-4872	345	7	)	)	PUNCT
ejpam-4872	345	8	}	}	PUNCT
ejpam-4872	346	1	=	=	SYM
ejpam-4872	346	2	max{f̊−(y	max{f̊−(y	NOUN
ejpam-4872	346	3	)	)	PUNCT
ejpam-4872	346	4	,	,	PUNCT
ejpam-4872	346	5	f̊−(1	f̊−(1	NOUN
ejpam-4872	346	6	)	)	PUNCT
ejpam-4872	346	7	}	}	PUNCT
ejpam-4872	346	8	=	=	SYM
ejpam-4872	346	9	f̊−(y	f̊−(y	X
ejpam-4872	346	10	)	)	PUNCT
ejpam-4872	346	11	,	,	PUNCT
ejpam-4872	346	12	f̊+((y|z)|z	f̊+((y|z)|z	NOUN
ejpam-4872	346	13	)	)	PUNCT
ejpam-4872	346	14	≥	≥	NOUN
ejpam-4872	346	15	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	346	16	)	)	PUNCT
ejpam-4872	346	17	,	,	PUNCT
ejpam-4872	346	18	f̊+(y|(((y|z)|z)|((y|z)|z	f̊+(y|(((y|z)|z)|((y|z)|z	NOUN
ejpam-4872	346	19	)	)	PUNCT
ejpam-4872	346	20	)	)	PUNCT
ejpam-4872	346	21	)	)	PUNCT
ejpam-4872	346	22	}	}	PUNCT
ejpam-4872	346	23	=	=	SYM
ejpam-4872	346	24	min{f̊+(y	min{f̊+(y	NOUN
ejpam-4872	346	25	)	)	PUNCT
ejpam-4872	346	26	,	,	PUNCT
ejpam-4872	346	27	f̊+(1	f̊+(1	NOUN
ejpam-4872	346	28	)	)	PUNCT
ejpam-4872	346	29	}	}	PUNCT
ejpam-4872	346	30	=	=	SYM
ejpam-4872	346	31	f̊+(y	f̊+(y	X
ejpam-4872	346	32	)	)	PUNCT
ejpam-4872	346	33	,	,	PUNCT
ejpam-4872	346	34	fs((y|z)|z	fs((y|z)|z	PROPN
ejpam-4872	346	35	)	)	PUNCT
ejpam-4872	346	36	⊇	⊇	PROPN
ejpam-4872	346	37	fs(y	fs(y	ADJ
ejpam-4872	346	38	)	)	PUNCT
ejpam-4872	346	39	∩	∩	ADJ
ejpam-4872	346	40	fs(y|(((y|z)|z)|((y|z)|z	fs(y|(((y|z)|z)|((y|z)|z	NOUN
ejpam-4872	346	41	)	)	PUNCT
ejpam-4872	346	42	)	)	PUNCT
ejpam-4872	346	43	)	)	PUNCT
ejpam-4872	347	1	=	=	SYM
ejpam-4872	347	2	f	f	PROPN
ejpam-4872	347	3	s(y	s(y	PROPN
ejpam-4872	347	4	)	)	PUNCT
ejpam-4872	347	5	∩	∩	PROPN
ejpam-4872	347	6	fs(1	fs(1	PROPN
ejpam-4872	347	7	)	)	PUNCT
ejpam-4872	347	8	}	}	PUNCT
ejpam-4872	347	9	=	=	SYM
ejpam-4872	347	10	fs(y	fs(y	X
ejpam-4872	347	11	)	)	PUNCT
ejpam-4872	347	12	,	,	PUNCT
ejpam-4872	347	13	and	and	CCONJ
ejpam-4872	347	14	f̃((y|z)|z	f̃((y|z)|z	NOUN
ejpam-4872	347	15	)	)	PUNCT
ejpam-4872	347	16	⊵	⊵	PROPN
ejpam-4872	347	17	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	347	18	)	)	PUNCT
ejpam-4872	347	19	,	,	PUNCT
ejpam-4872	347	20	f̃(y|(((y|z)|z)|((y|z)|z	f̃(y|(((y|z)|z)|((y|z)|z	NOUN
ejpam-4872	347	21	)	)	PUNCT
ejpam-4872	347	22	)	)	PUNCT
ejpam-4872	347	23	)	)	PUNCT
ejpam-4872	347	24	}	}	PUNCT
ejpam-4872	347	25	=	=	SYM
ejpam-4872	347	26	rmin{f̃(y	rmin{f̃(y	PROPN
ejpam-4872	347	27	)	)	PUNCT
ejpam-4872	347	28	,	,	PUNCT
ejpam-4872	347	29	f̃(1	f̃(1	NOUN
ejpam-4872	347	30	)	)	PUNCT
ejpam-4872	347	31	}	}	PUNCT
ejpam-4872	347	32	=	=	SYM
ejpam-4872	347	33	f̃(y	f̃(y	NOUN
ejpam-4872	347	34	)	)	PUNCT
ejpam-4872	347	35	.	.	PUNCT
ejpam-4872	348	1	since	since	SCONJ
ejpam-4872	348	2	z|(((y|z)|(y|z))|((y|z)|(y|z	z|(((y|z)|(y|z))|((y|z)|(y|z	PROPN
ejpam-4872	348	3	)	)	PUNCT
ejpam-4872	348	4	)	)	PUNCT
ejpam-4872	348	5	)	)	PUNCT
ejpam-4872	348	6	(	(	PUNCT
ejpam-4872	348	7	s2	s2	PROPN
ejpam-4872	348	8	)	)	PUNCT
ejpam-4872	348	9	=	=	SYM
ejpam-4872	348	10	z|(y|z	z|(y|z	PROPN
ejpam-4872	348	11	)	)	PUNCT
ejpam-4872	348	12	(	(	PUNCT
ejpam-4872	348	13	s1	s1	NOUN
ejpam-4872	348	14	)	)	PUNCT
ejpam-4872	348	15	=	=	SYM
ejpam-4872	348	16	(	(	PUNCT
ejpam-4872	348	17	y|z)|z	y|z)|z	PROPN
ejpam-4872	348	18	,	,	PUNCT
ejpam-4872	348	19	we	we	PRON
ejpam-4872	348	20	obtain	obtain	VERB
ejpam-4872	348	21	f̊−((y|z)|(y|z	f̊−((y|z)|(y|z	NOUN
ejpam-4872	348	22	)	)	PUNCT
ejpam-4872	348	23	)	)	PUNCT
ejpam-4872	348	24	≤	≤	NUM
ejpam-4872	349	1	max{f̊−(z	max{f̊−(z	NUM
ejpam-4872	349	2	)	)	PUNCT
ejpam-4872	349	3	,	,	PUNCT
ejpam-4872	349	4	f̊−(z|(((y|z)|(y|z))|((y|z)|(y|z	f̊−(z|(((y|z)|(y|z))|((y|z)|(y|z	PROPN
ejpam-4872	349	5	)	)	PUNCT
ejpam-4872	349	6	)	)	PUNCT
ejpam-4872	349	7	)	)	PUNCT
ejpam-4872	349	8	)	)	PUNCT
ejpam-4872	349	9	}	}	PUNCT
ejpam-4872	350	1	=	=	SYM
ejpam-4872	350	2	max{f̊−(z	max{f̊−(z	NUM
ejpam-4872	350	3	)	)	PUNCT
ejpam-4872	350	4	,	,	PUNCT
ejpam-4872	350	5	f̊−((y|z)|z	f̊−((y|z)|z	NOUN
ejpam-4872	350	6	)	)	PUNCT
ejpam-4872	350	7	}	}	PUNCT
ejpam-4872	350	8	≤	≤	NUM
ejpam-4872	351	1	max{f̊−(z	max{f̊−(z	NUM
ejpam-4872	351	2	)	)	PUNCT
ejpam-4872	351	3	,	,	PUNCT
ejpam-4872	351	4	f̊−(y	f̊−(y	NOUN
ejpam-4872	351	5	)	)	PUNCT
ejpam-4872	351	6	}	}	PUNCT
ejpam-4872	351	7	,	,	PUNCT
ejpam-4872	351	8	f̊+((y|z)|(y|z	f̊+((y|z)|(y|z	NOUN
ejpam-4872	351	9	)	)	PUNCT
ejpam-4872	351	10	)	)	PUNCT
ejpam-4872	351	11	≥	≥	NOUN
ejpam-4872	351	12	min{f̊+(z	min{f̊+(z	NOUN
ejpam-4872	351	13	)	)	PUNCT
ejpam-4872	351	14	,	,	PUNCT
ejpam-4872	351	15	f̊+(z|(((y|z)|(y|z))|((y|z)|(y|z	f̊+(z|(((y|z)|(y|z))|((y|z)|(y|z	NOUN
ejpam-4872	351	16	)	)	PUNCT
ejpam-4872	351	17	)	)	PUNCT
ejpam-4872	351	18	)	)	PUNCT
ejpam-4872	351	19	)	)	PUNCT
ejpam-4872	351	20	}	}	PUNCT
ejpam-4872	352	1	=	=	SYM
ejpam-4872	352	2	min{f̊+(z	min{f̊+(z	NOUN
ejpam-4872	352	3	)	)	PUNCT
ejpam-4872	352	4	,	,	PUNCT
ejpam-4872	352	5	f̊+((y|z)|z	f̊+((y|z)|z	NOUN
ejpam-4872	352	6	)	)	PUNCT
ejpam-4872	352	7	}	}	PUNCT
ejpam-4872	352	8	≥	≥	X
ejpam-4872	352	9	min{f̊+(z	min{f̊+(z	NOUN
ejpam-4872	352	10	)	)	PUNCT
ejpam-4872	352	11	,	,	PUNCT
ejpam-4872	352	12	f̊+(y	f̊+(y	NOUN
ejpam-4872	352	13	)	)	PUNCT
ejpam-4872	352	14	}	}	PUNCT
ejpam-4872	352	15	,	,	PUNCT
ejpam-4872	352	16	fs((y|z)|(y|z	fs((y|z)|(y|z	NOUN
ejpam-4872	352	17	)	)	PUNCT
ejpam-4872	352	18	)	)	PUNCT
ejpam-4872	353	1	⊇	⊇	PROPN
ejpam-4872	353	2	fs(z	fs(z	NUM
ejpam-4872	353	3	)	)	PUNCT
ejpam-4872	353	4	∩	∩	NOUN
ejpam-4872	353	5	fs(z|(((y|z)|(y|z))|((y|z)|(y|z	fs(z|(((y|z)|(y|z))|((y|z)|(y|z	NOUN
ejpam-4872	353	6	)	)	PUNCT
ejpam-4872	353	7	)	)	PUNCT
ejpam-4872	353	8	)	)	PUNCT
ejpam-4872	353	9	)	)	PUNCT
ejpam-4872	354	1	=	=	SYM
ejpam-4872	354	2	fs(z	fs(z	X
ejpam-4872	354	3	)	)	PUNCT
ejpam-4872	354	4	∩	∩	ADJ
ejpam-4872	354	5	fs((y|z)|z	fs((y|z)|z	NOUN
ejpam-4872	354	6	)	)	PUNCT
ejpam-4872	354	7	}	}	PUNCT
ejpam-4872	354	8	⊇	⊇	PROPN
ejpam-4872	354	9	f	f	PROPN
ejpam-4872	354	10	s(z	s(z	PROPN
ejpam-4872	354	11	)	)	PUNCT
ejpam-4872	354	12	∩	∩	NOUN
ejpam-4872	354	13	fs(y	fs(y	NUM
ejpam-4872	354	14	)	)	PUNCT
ejpam-4872	354	15	}	}	PUNCT
ejpam-4872	354	16	,	,	PUNCT
ejpam-4872	354	17	and	and	CCONJ
ejpam-4872	354	18	f̃((y|z)|(y|z	f̃((y|z)|(y|z	PROPN
ejpam-4872	354	19	)	)	PUNCT
ejpam-4872	354	20	)	)	PUNCT
ejpam-4872	355	1	⊵	⊵	PROPN
ejpam-4872	355	2	rmin{f̃(z	rmin{f̃(z	PROPN
ejpam-4872	355	3	)	)	PUNCT
ejpam-4872	355	4	,	,	PUNCT
ejpam-4872	355	5	f̃(z|(((y|z)|(y|z))|((y|z)|(y|z	f̃(z|(((y|z)|(y|z))|((y|z)|(y|z	NOUN
ejpam-4872	355	6	)	)	PUNCT
ejpam-4872	355	7	)	)	PUNCT
ejpam-4872	355	8	)	)	PUNCT
ejpam-4872	355	9	)	)	PUNCT
ejpam-4872	355	10	}	}	PUNCT
ejpam-4872	356	1	=	=	SYM
ejpam-4872	356	2	rmin{f̃(z	rmin{f̃(z	PROPN
ejpam-4872	356	3	)	)	PUNCT
ejpam-4872	356	4	,	,	PUNCT
ejpam-4872	356	5	f̃((y|z)|z	f̃((y|z)|z	NOUN
ejpam-4872	356	6	)	)	PUNCT
ejpam-4872	356	7	}	}	PUNCT
ejpam-4872	356	8	⊵	⊵	PROPN
ejpam-4872	356	9	rmin{f̃(z	rmin{f̃(z	NOUN
ejpam-4872	356	10	)	)	PUNCT
ejpam-4872	356	11	,	,	PUNCT
ejpam-4872	356	12	f̃(y	f̃(y	NOUN
ejpam-4872	356	13	)	)	PUNCT
ejpam-4872	356	14	}	}	PUNCT
ejpam-4872	356	15	.	.	PUNCT
ejpam-4872	357	1	therefore	therefore	ADV
ejpam-4872	357	2	f̊−((x|(y|z))|(y|z	f̊−((x|(y|z))|(y|z	NOUN
ejpam-4872	357	3	)	)	PUNCT
ejpam-4872	357	4	)	)	PUNCT
ejpam-4872	358	1	=	=	PUNCT
ejpam-4872	358	2	f̊−((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	f̊−((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	PROPN
ejpam-4872	358	3	)	)	PUNCT
ejpam-4872	358	4	)	)	PUNCT
ejpam-4872	358	5	)	)	PUNCT
ejpam-4872	358	6	)	)	PUNCT
ejpam-4872	359	1	≤	≤	NOUN
ejpam-4872	359	2	f̊−((y|z)|(y|z	f̊−((y|z)|(y|z	PROPN
ejpam-4872	359	3	)	)	PUNCT
ejpam-4872	359	4	)	)	PUNCT
ejpam-4872	359	5	≤	≤	NUM
ejpam-4872	360	1	max{f̊−(z	max{f̊−(z	NUM
ejpam-4872	360	2	)	)	PUNCT
ejpam-4872	360	3	,	,	PUNCT
ejpam-4872	360	4	f̊−(y	f̊−(y	NUM
ejpam-4872	360	5	)	)	PUNCT
ejpam-4872	360	6	}	}	PUNCT
ejpam-4872	360	7	s.	s.	PROPN
ejpam-4872	360	8	s.	s.	PROPN
ejpam-4872	360	9	ahn	ahn	PROPN
ejpam-4872	360	10	et	et	PROPN
ejpam-4872	360	11	al	al	PROPN
ejpam-4872	360	12	.	.	PUNCT
ejpam-4872	360	13	/	/	SYM
ejpam-4872	360	14	eur	eur	PROPN
ejpam-4872	360	15	.	.	PUNCT
ejpam-4872	361	1	j.	j.	PROPN
ejpam-4872	361	2	pure	pure	PROPN
ejpam-4872	361	3	appl	appl	PROPN
ejpam-4872	361	4	.	.	PROPN
ejpam-4872	361	5	math	math	PROPN
ejpam-4872	361	6	,	,	PUNCT
ejpam-4872	361	7	16	16	NUM
ejpam-4872	361	8	(	(	PUNCT
ejpam-4872	361	9	3	3	NUM
ejpam-4872	361	10	)	)	PUNCT
ejpam-4872	361	11	(	(	PUNCT
ejpam-4872	361	12	2023	2023	NUM
ejpam-4872	361	13	)	)	PUNCT
ejpam-4872	361	14	,	,	PUNCT
ejpam-4872	361	15	1862	1862	NUM
ejpam-4872	361	16	-	-	SYM
ejpam-4872	361	17	1877	1877	NUM
ejpam-4872	361	18	1875	1875	NUM
ejpam-4872	361	19	and	and	CCONJ
ejpam-4872	361	20	f̊+((x|(y|z))|(y|z	f̊+((x|(y|z))|(y|z	NOUN
ejpam-4872	361	21	)	)	PUNCT
ejpam-4872	361	22	)	)	PUNCT
ejpam-4872	362	1	=	=	SYM
ejpam-4872	362	2	f̊+((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	f̊+((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	PROPN
ejpam-4872	362	3	)	)	PUNCT
ejpam-4872	362	4	)	)	PUNCT
ejpam-4872	362	5	)	)	PUNCT
ejpam-4872	362	6	)	)	PUNCT
ejpam-4872	362	7	≥	≥	NOUN
ejpam-4872	362	8	f̊+((y|z)|(y|z	f̊+((y|z)|(y|z	NOUN
ejpam-4872	362	9	)	)	PUNCT
ejpam-4872	362	10	)	)	PUNCT
ejpam-4872	362	11	≥	≥	NOUN
ejpam-4872	362	12	min{f̊+(z	min{f̊+(z	NOUN
ejpam-4872	362	13	)	)	PUNCT
ejpam-4872	362	14	,	,	PUNCT
ejpam-4872	362	15	f̊+(y	f̊+(y	NOUN
ejpam-4872	362	16	)	)	PUNCT
ejpam-4872	362	17	}	}	PUNCT
ejpam-4872	362	18	,	,	PUNCT
ejpam-4872	362	19	that	that	ADV
ejpam-4872	362	20	is	is	ADV
ejpam-4872	362	21	,	,	PUNCT
ejpam-4872	362	22	(	(	PUNCT
ejpam-4872	362	23	x|(y|z))|(y|z	x|(y|z))|(y|z	PROPN
ejpam-4872	362	24	)	)	PUNCT
ejpam-4872	362	25	(	(	PUNCT
ejpam-4872	362	26	y	y	NOUN
ejpam-4872	362	27	,	,	PUNCT
ejpam-4872	362	28	z	z	NOUN
ejpam-4872	362	29	)	)	PUNCT
ejpam-4872	362	30	∈	∈	PROPN
ejpam-4872	362	31	f̊(m	f̊(m	PROPN
ejpam-4872	362	32	,	,	PUNCT
ejpam-4872	362	33	m	m	PROPN
ejpam-4872	362	34	)	)	PUNCT
ejpam-4872	362	35	,	,	PUNCT
ejpam-4872	362	36	and	and	CCONJ
ejpam-4872	362	37	fs((x|(y|z))|(y|z	fs((x|(y|z))|(y|z	NOUN
ejpam-4872	362	38	)	)	PUNCT
ejpam-4872	362	39	)	)	PUNCT
ejpam-4872	362	40	=	=	PUNCT
ejpam-4872	362	41	fs((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	fs((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	PROPN
ejpam-4872	362	42	)	)	PUNCT
ejpam-4872	362	43	)	)	PUNCT
ejpam-4872	362	44	)	)	PUNCT
ejpam-4872	362	45	)	)	PUNCT
ejpam-4872	363	1	⊇	⊇	PROPN
ejpam-4872	363	2	fs((y|z)|(y|z	fs((y|z)|(y|z	NOUN
ejpam-4872	363	3	)	)	PUNCT
ejpam-4872	363	4	)	)	PUNCT
ejpam-4872	363	5	⊇	⊇	PROPN
ejpam-4872	363	6	fs(z	fs(z	NUM
ejpam-4872	363	7	)	)	PUNCT
ejpam-4872	363	8	∩	∩	NOUN
ejpam-4872	363	9	fs(y	fs(y	NUM
ejpam-4872	363	10	)	)	PUNCT
ejpam-4872	363	11	,	,	PUNCT
ejpam-4872	363	12	and	and	CCONJ
ejpam-4872	363	13	f̃((x|(y|z))|(y|z	f̃((x|(y|z))|(y|z	PROPN
ejpam-4872	363	14	)	)	PUNCT
ejpam-4872	363	15	)	)	PUNCT
ejpam-4872	364	1	=	=	SYM
ejpam-4872	364	2	f̃((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	f̃((x|(((y|z)|(y|z))|((y|z)|(y|z))))|(((y|z)|(y|z))|((y|z)|(y|z	NOUN
ejpam-4872	364	3	)	)	PUNCT
ejpam-4872	364	4	)	)	PUNCT
ejpam-4872	364	5	)	)	PUNCT
ejpam-4872	364	6	)	)	PUNCT
ejpam-4872	365	1	⊵	⊵	PROPN
ejpam-4872	365	2	f̃((y|z)|(y|z	f̃((y|z)|(y|z	PROPN
ejpam-4872	365	3	)	)	PUNCT
ejpam-4872	365	4	)	)	PUNCT
ejpam-4872	366	1	⊵	⊵	PROPN
ejpam-4872	366	2	rmin{f̃(z	rmin{f̃(z	PROPN
ejpam-4872	366	3	)	)	PUNCT
ejpam-4872	366	4	,	,	PUNCT
ejpam-4872	366	5	f̃(y	f̃(y	NOUN
ejpam-4872	366	6	)	)	PUNCT
ejpam-4872	366	7	}	}	PUNCT
ejpam-4872	366	8	.	.	PUNCT
ejpam-4872	367	1	consequently	consequently	ADV
ejpam-4872	367	2	,	,	PUNCT
ejpam-4872	367	3	dokf	dokf	NOUN
ejpam-4872	367	4	:	:	PUNCT
ejpam-4872	367	5	=	=	SYM
ejpam-4872	367	6	(	(	PUNCT
ejpam-4872	367	7	f̊	f̊	X
ejpam-4872	367	8	,	,	PUNCT
ejpam-4872	367	9	fs	fs	PROPN
ejpam-4872	367	10	,	,	PUNCT
ejpam-4872	367	11	f̃	f̃	PROPN
ejpam-4872	367	12	)	)	PUNCT
ejpam-4872	367	13	is	be	AUX
ejpam-4872	367	14	a	a	DET
ejpam-4872	367	15	dokdo	dokdo	ADJ
ejpam-4872	367	16	filter	filter	NOUN
ejpam-4872	367	17	of	of	ADP
ejpam-4872	367	18	(	(	PUNCT
ejpam-4872	367	19	x	x	NOUN
ejpam-4872	367	20	,	,	PUNCT
ejpam-4872	367	21	u	u	NOUN
ejpam-4872	367	22	)	)	PUNCT
ejpam-4872	367	23	.	.	PUNCT
ejpam-4872	368	1	conversely	conversely	ADV
ejpam-4872	368	2	,	,	PUNCT
ejpam-4872	368	3	suppose	suppose	VERB
ejpam-4872	368	4	that	that	SCONJ
ejpam-4872	368	5	dokf	dokf	NOUN
ejpam-4872	368	6	:	:	PUNCT
ejpam-4872	368	7	=	=	SYM
ejpam-4872	368	8	(	(	PUNCT
ejpam-4872	368	9	f̊	f̊	X
ejpam-4872	368	10	,	,	PUNCT
ejpam-4872	368	11	f	f	PROPN
ejpam-4872	368	12	s	s	PROPN
ejpam-4872	368	13	,	,	PUNCT
ejpam-4872	368	14	f̃	f̃	PROPN
ejpam-4872	368	15	)	)	PUNCT
ejpam-4872	368	16	is	be	AUX
ejpam-4872	368	17	a	a	DET
ejpam-4872	368	18	dokdo	dokdo	ADJ
ejpam-4872	368	19	filter	filter	NOUN
ejpam-4872	368	20	of	of	ADP
ejpam-4872	368	21	(	(	PUNCT
ejpam-4872	368	22	x	x	NOUN
ejpam-4872	368	23	,	,	PUNCT
ejpam-4872	368	24	u	u	NOUN
ejpam-4872	368	25	)	)	PUNCT
ejpam-4872	368	26	.	.	PUNCT
ejpam-4872	369	1	for	for	ADP
ejpam-4872	369	2	every	every	DET
ejpam-4872	369	3	x	x	NOUN
ejpam-4872	369	4	,	,	PUNCT
ejpam-4872	369	5	y	y	PROPN
ejpam-4872	369	6	∈	∈	PROPN
ejpam-4872	369	7	x	x	X
ejpam-4872	369	8	,	,	PUNCT
ejpam-4872	369	9	we	we	PRON
ejpam-4872	369	10	have	have	VERB
ejpam-4872	369	11	y	y	NOUN
ejpam-4872	369	12	=	=	SYM
ejpam-4872	369	13	(	(	PUNCT
ejpam-4872	369	14	(	(	PUNCT
ejpam-4872	369	15	x|x)|(1|1))|(y|y	x|x)|(1|1))|(y|y	PROPN
ejpam-4872	369	16	)	)	PUNCT
ejpam-4872	370	1	=	=	PRON
ejpam-4872	370	2	(	(	PUNCT
ejpam-4872	370	3	(	(	PUNCT
ejpam-4872	370	4	x|x)|((y|(y|y))|(y|(y|y))))|(y|y	x|x)|((y|(y|y))|(y|(y|y))))|(y|y	PROPN
ejpam-4872	370	5	)	)	PUNCT
ejpam-4872	370	6	=	=	SYM
ejpam-4872	370	7	(	(	PUNCT
ejpam-4872	370	8	(	(	PUNCT
ejpam-4872	370	9	(	(	PUNCT
ejpam-4872	370	10	(	(	PUNCT
ejpam-4872	370	11	x|x)|y)|((x|x)|y))|(y|y))|(y|y	x|x)|y)|((x|x)|y))|(y|y))|(y|y	ADJ
ejpam-4872	370	12	)	)	PUNCT
ejpam-4872	370	13	=	=	PUNCT
ejpam-4872	370	14	(	(	PUNCT
ejpam-4872	370	15	y|((x|x)|y))|((x|x)|y	y|((x|x)|y))|((x|x)|y	NUM
ejpam-4872	370	16	)	)	PUNCT
ejpam-4872	370	17	=	=	SYM
ejpam-4872	370	18	(	(	PUNCT
ejpam-4872	370	19	(	(	PUNCT
ejpam-4872	370	20	(	(	PUNCT
ejpam-4872	370	21	(	(	PUNCT
ejpam-4872	370	22	x|x)|y)|y)|y)|(((x|x)|y)|y	x|x)|y)|y)|y)|(((x|x)|y)|y	PROPN
ejpam-4872	370	23	)	)	PUNCT
ejpam-4872	370	24	=	=	PUNCT
ejpam-4872	370	25	(	(	PUNCT
ejpam-4872	370	26	y|(x|(x|(y|y))))|(x|(x|(y|y	y|(x|(x|(y|y))))|(x|(x|(y|y	NUM
ejpam-4872	370	27	)	)	PUNCT
ejpam-4872	370	28	)	)	PUNCT
ejpam-4872	370	29	)	)	PUNCT
ejpam-4872	371	1	by	by	ADP
ejpam-4872	371	2	(	(	PUNCT
ejpam-4872	371	3	s1	s1	NOUN
ejpam-4872	371	4	)	)	PUNCT
ejpam-4872	371	5	,	,	PUNCT
ejpam-4872	371	6	(	(	PUNCT
ejpam-4872	371	7	s2	s2	PROPN
ejpam-4872	371	8	)	)	PUNCT
ejpam-4872	371	9	,	,	PUNCT
ejpam-4872	371	10	(	(	PUNCT
ejpam-4872	371	11	s3	s3	PROPN
ejpam-4872	371	12	)	)	PUNCT
ejpam-4872	371	13	,	,	PUNCT
ejpam-4872	371	14	(	(	PUNCT
ejpam-4872	371	15	2	2	NUM
ejpam-4872	371	16	)	)	PUNCT
ejpam-4872	371	17	,	,	PUNCT
ejpam-4872	371	18	(	(	PUNCT
ejpam-4872	371	19	3	3	NUM
ejpam-4872	371	20	)	)	PUNCT
ejpam-4872	371	21	,	,	PUNCT
ejpam-4872	371	22	(	(	PUNCT
ejpam-4872	371	23	4	4	X
ejpam-4872	371	24	)	)	PUNCT
ejpam-4872	371	25	(	(	PUNCT
ejpam-4872	371	26	6	6	NUM
ejpam-4872	371	27	)	)	PUNCT
ejpam-4872	371	28	and	and	CCONJ
ejpam-4872	371	29	(	(	PUNCT
ejpam-4872	371	30	7	7	NUM
ejpam-4872	371	31	)	)	PUNCT
ejpam-4872	371	32	.	.	PUNCT
ejpam-4872	372	1	it	it	PRON
ejpam-4872	372	2	follows	follow	VERB
ejpam-4872	372	3	from	from	ADP
ejpam-4872	372	4	(	(	PUNCT
ejpam-4872	372	5	21	21	NUM
ejpam-4872	372	6	)	)	PUNCT
ejpam-4872	372	7	that	that	SCONJ
ejpam-4872	372	8	f̊−(y	f̊−(y	VERB
ejpam-4872	372	9	)	)	PUNCT
ejpam-4872	373	1	=	=	SYM
ejpam-4872	373	2	f̊−((y|(x|(x|(y|y))))|(x|(x|(y|y	f̊−((y|(x|(x|(y|y))))|(x|(x|(y|y	NOUN
ejpam-4872	373	3	)	)	PUNCT
ejpam-4872	373	4	)	)	PUNCT
ejpam-4872	373	5	)	)	PUNCT
ejpam-4872	373	6	)	)	PUNCT
ejpam-4872	374	1	≤	≤	PUNCT
ejpam-4872	375	1	max{f̊−(x	max{f̊−(x	PROPN
ejpam-4872	375	2	)	)	PUNCT
ejpam-4872	375	3	,	,	PUNCT
ejpam-4872	375	4	f̊−(x|(y|y	f̊−(x|(y|y	PROPN
ejpam-4872	375	5	)	)	PUNCT
ejpam-4872	375	6	)	)	PUNCT
ejpam-4872	375	7	}	}	PUNCT
ejpam-4872	375	8	,	,	PUNCT
ejpam-4872	375	9	f̊+(y	f̊+(y	NOUN
ejpam-4872	375	10	)	)	PUNCT
ejpam-4872	375	11	=	=	SYM
ejpam-4872	375	12	f̊+((y|(x|(x|(y|y))))|(x|(x|(y|y	f̊+((y|(x|(x|(y|y))))|(x|(x|(y|y	PROPN
ejpam-4872	375	13	)	)	PUNCT
ejpam-4872	375	14	)	)	PUNCT
ejpam-4872	375	15	)	)	PUNCT
ejpam-4872	375	16	)	)	PUNCT
ejpam-4872	375	17	≥	≥	X
ejpam-4872	375	18	min{f̊+(x	min{f̊+(x	PROPN
ejpam-4872	375	19	)	)	PUNCT
ejpam-4872	375	20	,	,	PUNCT
ejpam-4872	375	21	f̊+(x|(y|y	f̊+(x|(y|y	NOUN
ejpam-4872	375	22	)	)	PUNCT
ejpam-4872	375	23	)	)	PUNCT
ejpam-4872	375	24	}	}	PUNCT
ejpam-4872	375	25	,	,	PUNCT
ejpam-4872	375	26	that	that	ADV
ejpam-4872	375	27	is	is	ADV
ejpam-4872	375	28	,	,	PUNCT
ejpam-4872	375	29	y	y	PROPN
ejpam-4872	375	30	(	(	PUNCT
ejpam-4872	375	31	x	x	X
ejpam-4872	375	32	,	,	PUNCT
ejpam-4872	375	33	x|(y|y	x|(y|y	PROPN
ejpam-4872	375	34	)	)	PUNCT
ejpam-4872	375	35	)	)	PUNCT
ejpam-4872	376	1	∈	∈	PROPN
ejpam-4872	376	2	f̊(m	f̊(m	PROPN
ejpam-4872	376	3	,	,	PUNCT
ejpam-4872	376	4	m	m	PROPN
ejpam-4872	376	5	)	)	PUNCT
ejpam-4872	376	6	,	,	PUNCT
ejpam-4872	376	7	and	and	CCONJ
ejpam-4872	376	8	fs(y	fs(y	NUM
ejpam-4872	376	9	)	)	PUNCT
ejpam-4872	376	10	=	=	SYM
ejpam-4872	377	1	fs((y|(x|(x|(y|y))))|(x|(x|(y|y	fs((y|(x|(x|(y|y))))|(x|(x|(y|y	ADJ
ejpam-4872	377	2	)	)	PUNCT
ejpam-4872	377	3	)	)	PUNCT
ejpam-4872	377	4	)	)	PUNCT
ejpam-4872	377	5	)	)	PUNCT
ejpam-4872	377	6	⊇	⊇	PROPN
ejpam-4872	377	7	fs(x	fs(x	NOUN
ejpam-4872	377	8	)	)	PUNCT
ejpam-4872	377	9	∩	∩	NOUN
ejpam-4872	377	10	fs(x|(y|y	fs(x|(y|y	PROPN
ejpam-4872	377	11	)	)	PUNCT
ejpam-4872	377	12	)	)	PUNCT
ejpam-4872	377	13	,	,	PUNCT
ejpam-4872	377	14	and	and	CCONJ
ejpam-4872	377	15	f̃(y	f̃(y	ADJ
ejpam-4872	377	16	)	)	PUNCT
ejpam-4872	377	17	=	=	SYM
ejpam-4872	377	18	f̃((y|(x|(x|(y|y))))|(x|(x|(y|y	f̃((y|(x|(x|(y|y))))|(x|(x|(y|y	NOUN
ejpam-4872	377	19	)	)	PUNCT
ejpam-4872	377	20	)	)	PUNCT
ejpam-4872	377	21	)	)	PUNCT
ejpam-4872	377	22	)	)	PUNCT
ejpam-4872	378	1	⊵	⊵	PROPN
ejpam-4872	378	2	rmin{f̃(x	rmin{f̃(x	NOUN
ejpam-4872	378	3	)	)	PUNCT
ejpam-4872	378	4	,	,	PUNCT
ejpam-4872	378	5	f̃(x|(y|y	f̃(x|(y|y	PROPN
ejpam-4872	378	6	)	)	PUNCT
ejpam-4872	378	7	)	)	PUNCT
ejpam-4872	378	8	}	}	PUNCT
ejpam-4872	378	9	.	.	PUNCT
ejpam-4872	379	1	therefore	therefore	ADV
ejpam-4872	379	2	dokf	dokf	VERB
ejpam-4872	379	3	:	:	PUNCT
ejpam-4872	379	4	=	=	SYM
ejpam-4872	379	5	(	(	PUNCT
ejpam-4872	379	6	f̊	f̊	X
ejpam-4872	379	7	,	,	PUNCT
ejpam-4872	379	8	fs	fs	PROPN
ejpam-4872	379	9	,	,	PUNCT
ejpam-4872	379	10	f̃	f̃	PROPN
ejpam-4872	379	11	)	)	PUNCT
ejpam-4872	379	12	is	be	AUX
ejpam-4872	379	13	a	a	DET
ejpam-4872	379	14	dokdo	dokdo	ADJ
ejpam-4872	379	15	deductive	deductive	ADJ
ejpam-4872	379	16	system	system	NOUN
ejpam-4872	379	17	of	of	ADP
ejpam-4872	379	18	(	(	PUNCT
ejpam-4872	379	19	x	x	NOUN
ejpam-4872	379	20	,	,	PUNCT
ejpam-4872	379	21	u	u	NOUN
ejpam-4872	379	22	)	)	PUNCT
ejpam-4872	379	23	.	.	PUNCT
ejpam-4872	380	1	remark	remark	PROPN
ejpam-4872	380	2	1	1	NUM
ejpam-4872	380	3	.	.	PUNCT
ejpam-4872	380	4	by	by	ADP
ejpam-4872	380	5	theorem	theorem	NOUN
ejpam-4872	380	6	5	5	NUM
ejpam-4872	380	7	,	,	PUNCT
ejpam-4872	380	8	it	it	PRON
ejpam-4872	380	9	can	can	AUX
ejpam-4872	380	10	be	be	AUX
ejpam-4872	380	11	seen	see	VERB
ejpam-4872	380	12	that	that	SCONJ
ejpam-4872	380	13	all	all	DET
ejpam-4872	380	14	the	the	DET
ejpam-4872	380	15	results	result	NOUN
ejpam-4872	380	16	for	for	ADP
ejpam-4872	380	17	the	the	DET
ejpam-4872	380	18	dokdo	dokdo	NOUN
ejpam-4872	380	19	filter	filter	NOUN
ejpam-4872	380	20	covered	cover	VERB
ejpam-4872	380	21	above	above	ADV
ejpam-4872	380	22	can	can	AUX
ejpam-4872	380	23	be	be	AUX
ejpam-4872	380	24	handled	handle	VERB
ejpam-4872	380	25	in	in	ADP
ejpam-4872	380	26	the	the	DET
ejpam-4872	380	27	same	same	ADJ
ejpam-4872	380	28	way	way	NOUN
ejpam-4872	380	29	using	use	VERB
ejpam-4872	380	30	the	the	DET
ejpam-4872	380	31	dokdo	dokdo	ADJ
ejpam-4872	380	32	deductive	deductive	ADJ
ejpam-4872	380	33	system	system	NOUN
ejpam-4872	380	34	.	.	PUNCT
ejpam-4872	381	1	references	reference	NOUN
ejpam-4872	381	2	1876	1876	NUM
ejpam-4872	381	3	4	4	NUM
ejpam-4872	381	4	.	.	PUNCT
ejpam-4872	381	5	conclusion	conclusion	VERB
ejpam-4872	381	6	the	the	DET
ejpam-4872	381	7	dokdo	dokdo	NOUN
ejpam-4872	381	8	structure	structure	NOUN
ejpam-4872	381	9	dokf	dokf	NOUN
ejpam-4872	381	10	:	:	PUNCT
ejpam-4872	382	1	=	=	SYM
ejpam-4872	382	2	(	(	PUNCT
ejpam-4872	382	3	f̊	f̊	X
ejpam-4872	382	4	,	,	PUNCT
ejpam-4872	382	5	f	f	PROPN
ejpam-4872	382	6	s	s	PROPN
ejpam-4872	382	7	,	,	PUNCT
ejpam-4872	382	8	f̃	f̃	PROPN
ejpam-4872	382	9	)	)	PUNCT
ejpam-4872	382	10	in	in	ADP
ejpam-4872	382	11	a	a	DET
ejpam-4872	382	12	set	set	NOUN
ejpam-4872	382	13	x	x	PUNCT
ejpam-4872	382	14	consists	consist	VERB
ejpam-4872	382	15	of	of	ADP
ejpam-4872	382	16	a	a	DET
ejpam-4872	382	17	combination	combination	NOUN
ejpam-4872	382	18	of	of	ADP
ejpam-4872	382	19	soft	soft	ADJ
ejpam-4872	382	20	set	set	NOUN
ejpam-4872	382	21	,	,	PUNCT
ejpam-4872	382	22	bipolar	bipolar	ADJ
ejpam-4872	382	23	fuzzy	fuzzy	ADJ
ejpam-4872	382	24	set	set	NOUN
ejpam-4872	382	25	,	,	PUNCT
ejpam-4872	382	26	and	and	CCONJ
ejpam-4872	382	27	interval	interval	NOUN
ejpam-4872	382	28	-	-	PUNCT
ejpam-4872	382	29	value	value	NOUN
ejpam-4872	382	30	fuzzy	fuzzy	ADJ
ejpam-4872	382	31	set	set	NOUN
ejpam-4872	382	32	,	,	PUNCT
ejpam-4872	382	33	and	and	CCONJ
ejpam-4872	382	34	it	it	PRON
ejpam-4872	382	35	can	can	AUX
ejpam-4872	382	36	be	be	AUX
ejpam-4872	382	37	shaped	shape	VERB
ejpam-4872	382	38	into	into	ADP
ejpam-4872	382	39	a	a	DET
ejpam-4872	382	40	pentagon	pentagon	PROPN
ejpam-4872	382	41	as	as	SCONJ
ejpam-4872	382	42	shown	show	VERB
ejpam-4872	382	43	in	in	ADP
ejpam-4872	382	44	the	the	DET
ejpam-4872	382	45	figure	figure	NOUN
ejpam-4872	382	46	below	below	ADV
ejpam-4872	382	47	.	.	PUNCT
ejpam-4872	383	1	r	r	NOUN
ejpam-4872	383	2	r	r	NOUN
ejpam-4872	383	3	r	r	NOUN
ejpam-4872	383	4	r	r	NOUN
ejpam-4872	383	5	r	r	NOUN
ejpam-4872	383	6	2x	2x	NUM
ejpam-4872	384	1	[	[	X
ejpam-4872	384	2	−1	−1	NOUN
ejpam-4872	384	3	,	,	PUNCT
ejpam-4872	384	4	0	0	NUM
ejpam-4872	384	5	]	]	PUNCT
ejpam-4872	384	6	x	x	PUNCT
ejpam-4872	385	1	[	[	X
ejpam-4872	385	2	0	0	NUM
ejpam-4872	385	3	,	,	PUNCT
ejpam-4872	385	4	1	1	NUM
ejpam-4872	385	5	]	]	PART
ejpam-4872	385	6	�	�	PROPN
ejpam-4872	385	7	�	�	PROPN
ejpam-4872	385	8	�	�	PROPN
ejpam-4872	385	9	�	�	PROPN
ejpam-4872	385	10	�	�	PROPN
ejpam-4872	385	11	�	�	PROPN
ejpam-4872	385	12	q	q	PROPN
ejpam-4872	385	13	q	q	X
ejpam-4872	385	14	q	q	X
ejpam-4872	385	15	q	q	X
ejpam-4872	385	16	q	q	X
ejpam-4872	385	17	q	q	PROPN
ejpam-4872	385	18	b	b	PROPN
ejpam-4872	385	19	b	b	PROPN
ejpam-4872	385	20	b	b	PROPN
ejpam-4872	385	21	b	b	PROPN
ejpam-4872	385	22	b	b	PROPN
ejpam-4872	385	23	bb	bb	INTJ
ejpam-4872	385	24	�	�	PROPN
ejpam-4872	385	25	�	�	PROPN
ejpam-4872	385	26	�	�	PROPN
ejpam-4872	385	27	�	�	PROPN
ejpam-4872	385	28	�	�	PROPN
ejpam-4872	385	29	�	�	PROPN
ejpam-4872	385	30	�	�	PROPN
ejpam-4872	386	1	[	[	X
ejpam-4872	386	2	[	[	X
ejpam-4872	386	3	0	0	NUM
ejpam-4872	386	4	,	,	PUNCT
ejpam-4872	386	5	1	1	NUM
ejpam-4872	386	6	]	]	PUNCT
ejpam-4872	386	7	]	]	X
ejpam-4872	386	8	�	�	PROPN
ejpam-4872	386	9	�	�	PROPN
ejpam-4872	386	10	�	�	PROPN
ejpam-4872	386	11	�	�	PROPN
ejpam-4872	386	12	1f+	1f+	NUM
ejpam-4872	386	13	ppppi	ppppi	NOUN
ejpam-4872	386	14	f−	f−	PROPN
ejpam-4872	386	15	?	?	PUNCT
ejpam-4872	387	1	f̃	f̃	PROPN
ejpam-4872	387	2	6	6	NUM
ejpam-4872	387	3	fs	fs	ADP
ejpam-4872	387	4	where	where	SCONJ
ejpam-4872	387	5	fs	fs	PROPN
ejpam-4872	387	6	is	be	AUX
ejpam-4872	387	7	a	a	DET
ejpam-4872	387	8	soft	soft	ADJ
ejpam-4872	387	9	set	set	NOUN
ejpam-4872	387	10	of	of	ADP
ejpam-4872	387	11	x	x	PROPN
ejpam-4872	387	12	,	,	PUNCT
ejpam-4872	387	13	f̊	f̊	X
ejpam-4872	387	14	:	:	PUNCT
ejpam-4872	387	15	=	=	SYM
ejpam-4872	387	16	(	(	PUNCT
ejpam-4872	387	17	x	x	X
ejpam-4872	387	18	;	;	PUNCT
ejpam-4872	387	19	f−	f−	PROPN
ejpam-4872	387	20	,	,	PUNCT
ejpam-4872	387	21	f+	f+	PROPN
ejpam-4872	387	22	)	)	PUNCT
ejpam-4872	387	23	is	be	AUX
ejpam-4872	387	24	a	a	DET
ejpam-4872	387	25	bipolar	bipolar	ADJ
ejpam-4872	387	26	fuzzy	fuzzy	ADJ
ejpam-4872	387	27	set	set	NOUN
ejpam-4872	387	28	in	in	ADP
ejpam-4872	387	29	x	x	NOUN
ejpam-4872	387	30	,	,	PUNCT
ejpam-4872	387	31	and	and	CCONJ
ejpam-4872	387	32	f̃	f̃	PROPN
ejpam-4872	387	33	:	:	PUNCT
ejpam-4872	388	1	x	x	X
ejpam-4872	388	2	→	→	PUNCT
ejpam-4872	388	3	[	[	X
ejpam-4872	388	4	[	[	X
ejpam-4872	388	5	0	0	NUM
ejpam-4872	388	6	,	,	PUNCT
ejpam-4872	388	7	1	1	NUM
ejpam-4872	388	8	]	]	PUNCT
ejpam-4872	388	9	]	]	X
ejpam-4872	388	10	is	be	AUX
ejpam-4872	388	11	an	an	DET
ejpam-4872	388	12	interval	interval	NOUN
ejpam-4872	388	13	-	-	PUNCT
ejpam-4872	388	14	valued	value	VERB
ejpam-4872	388	15	fuzzy	fuzzy	ADJ
ejpam-4872	388	16	set	set	VERB
ejpam-4872	388	17	in	in	ADP
ejpam-4872	388	18	x.	x.	NOUN
ejpam-4872	389	1	what	what	PRON
ejpam-4872	389	2	this	this	DET
ejpam-4872	389	3	paper	paper	NOUN
ejpam-4872	389	4	intends	intend	VERB
ejpam-4872	389	5	to	to	PART
ejpam-4872	389	6	do	do	VERB
ejpam-4872	389	7	is	be	AUX
ejpam-4872	389	8	look	look	VERB
ejpam-4872	389	9	at	at	ADP
ejpam-4872	389	10	filters	filter	NOUN
ejpam-4872	389	11	and	and	CCONJ
ejpam-4872	389	12	deductive	deductive	ADJ
ejpam-4872	389	13	systems	system	NOUN
ejpam-4872	389	14	in	in	ADP
ejpam-4872	389	15	sheffer	sheffer	PROPN
ejpam-4872	389	16	stroke	stroke	PROPN
ejpam-4872	389	17	hilbert	hilbert	PROPN
ejpam-4872	389	18	algebras	algebras	PROPN
ejpam-4872	389	19	using	use	VERB
ejpam-4872	389	20	the	the	DET
ejpam-4872	389	21	dokdo	dokdo	NOUN
ejpam-4872	389	22	structure	structure	NOUN
ejpam-4872	389	23	.	.	PUNCT
ejpam-4872	390	1	we	we	PRON
ejpam-4872	390	2	defined	define	VERB
ejpam-4872	390	3	the	the	DET
ejpam-4872	390	4	concept	concept	NOUN
ejpam-4872	390	5	of	of	ADP
ejpam-4872	390	6	dokdo	dokdo	ADJ
ejpam-4872	390	7	filter	filter	NOUN
ejpam-4872	390	8	and	and	CCONJ
ejpam-4872	390	9	dokdo	dokdo	ADJ
ejpam-4872	390	10	deductive	deductive	ADJ
ejpam-4872	390	11	system	system	NOUN
ejpam-4872	390	12	,	,	PUNCT
ejpam-4872	390	13	and	and	CCONJ
ejpam-4872	390	14	investigated	investigate	VERB
ejpam-4872	390	15	several	several	ADJ
ejpam-4872	390	16	properties	property	NOUN
ejpam-4872	390	17	.	.	PUNCT
ejpam-4872	391	1	we	we	PRON
ejpam-4872	391	2	formed	form	VERB
ejpam-4872	391	3	a	a	DET
ejpam-4872	391	4	dokdo	dokdo	NOUN
ejpam-4872	391	5	filter	filter	NOUN
ejpam-4872	391	6	by	by	ADP
ejpam-4872	391	7	attaching	attach	VERB
ejpam-4872	391	8	appropriate	appropriate	ADJ
ejpam-4872	391	9	conditions	condition	NOUN
ejpam-4872	391	10	to	to	ADP
ejpam-4872	391	11	a	a	DET
ejpam-4872	391	12	given	give	VERB
ejpam-4872	391	13	dokdo	dokdo	NOUN
ejpam-4872	391	14	structure	structure	NOUN
ejpam-4872	391	15	.	.	PUNCT
ejpam-4872	392	1	we	we	PRON
ejpam-4872	392	2	studied	study	VERB
ejpam-4872	392	3	characterizations	characterization	NOUN
ejpam-4872	392	4	of	of	ADP
ejpam-4872	392	5	dokdo	dokdo	NOUN
ejpam-4872	392	6	filters	filter	NOUN
ejpam-4872	392	7	.	.	PUNCT
ejpam-4872	393	1	we	we	PRON
ejpam-4872	393	2	constructed	construct	VERB
ejpam-4872	393	3	dokdo	dokdo	NOUN
ejpam-4872	393	4	filters	filter	NOUN
ejpam-4872	393	5	that	that	PRON
ejpam-4872	393	6	are	be	AUX
ejpam-4872	393	7	associated	associate	VERB
ejpam-4872	393	8	with	with	ADP
ejpam-4872	393	9	filters	filter	NOUN
ejpam-4872	393	10	.	.	PUNCT
ejpam-4872	394	1	finally	finally	ADV
ejpam-4872	394	2	,	,	PUNCT
ejpam-4872	394	3	we	we	PRON
ejpam-4872	394	4	showed	show	VERB
ejpam-4872	394	5	that	that	SCONJ
ejpam-4872	394	6	the	the	DET
ejpam-4872	394	7	dokdo	dokdo	NOUN
ejpam-4872	394	8	filter	filter	NOUN
ejpam-4872	394	9	is	be	AUX
ejpam-4872	394	10	consistent	consistent	ADJ
ejpam-4872	394	11	with	with	ADP
ejpam-4872	394	12	the	the	DET
ejpam-4872	394	13	dokdo	dokdo	ADJ
ejpam-4872	394	14	deductive	deductive	ADJ
ejpam-4872	394	15	system	system	NOUN
ejpam-4872	394	16	,	,	PUNCT
ejpam-4872	394	17	which	which	PRON
ejpam-4872	394	18	means	mean	VERB
ejpam-4872	394	19	that	that	SCONJ
ejpam-4872	394	20	all	all	DET
ejpam-4872	394	21	the	the	DET
ejpam-4872	394	22	results	result	NOUN
ejpam-4872	394	23	covered	cover	VERB
ejpam-4872	394	24	using	use	VERB
ejpam-4872	394	25	the	the	DET
ejpam-4872	394	26	dokdo	dokdo	NOUN
ejpam-4872	394	27	filter	filter	NOUN
ejpam-4872	394	28	can	can	AUX
ejpam-4872	394	29	be	be	AUX
ejpam-4872	394	30	treated	treat	VERB
ejpam-4872	394	31	using	use	VERB
ejpam-4872	394	32	dokdo	dokdo	ADJ
ejpam-4872	394	33	deductive	deductive	ADJ
ejpam-4872	394	34	system	system	NOUN
ejpam-4872	394	35	.	.	PUNCT
ejpam-4872	395	1	as	as	ADP
ejpam-4872	395	2	an	an	DET
ejpam-4872	395	3	application	application	NOUN
ejpam-4872	395	4	of	of	ADP
ejpam-4872	395	5	the	the	DET
ejpam-4872	395	6	dokdo	dokdo	NOUN
ejpam-4872	395	7	structure	structure	NOUN
ejpam-4872	395	8	in	in	ADP
ejpam-4872	395	9	the	the	DET
ejpam-4872	395	10	future	future	NOUN
ejpam-4872	395	11	,	,	PUNCT
ejpam-4872	395	12	we	we	PRON
ejpam-4872	395	13	will	will	AUX
ejpam-4872	395	14	apply	apply	VERB
ejpam-4872	395	15	it	it	PRON
ejpam-4872	395	16	to	to	ADP
ejpam-4872	395	17	other	other	ADJ
ejpam-4872	395	18	logical	logical	ADJ
ejpam-4872	395	19	algebras	algebra	NOUN
ejpam-4872	395	20	such	such	ADJ
ejpam-4872	395	21	as	as	ADP
ejpam-4872	395	22	bl	bl	NOUN
ejpam-4872	395	23	-	-	PUNCT
ejpam-4872	395	24	algebras	algebras	PROPN
ejpam-4872	395	25	,	,	PUNCT
ejpam-4872	395	26	mtl	mtl	PROPN
ejpam-4872	395	27	-	-	PUNCT
ejpam-4872	395	28	algebras	algebras	PROPN
ejpam-4872	395	29	,	,	PUNCT
ejpam-4872	395	30	hoops	hoop	NOUN
ejpam-4872	395	31	,	,	PUNCT
ejpam-4872	395	32	sheffer	sheffer	NOUN
ejpam-4872	395	33	stroke	stroke	PROPN
ejpam-4872	395	34	hilbert	hilbert	PROPN
ejpam-4872	395	35	algebras	algebras	PROPN
ejpam-4872	395	36	,	,	PUNCT
ejpam-4872	395	37	sheffer	sheffer	NOUN
ejpam-4872	395	38	stroke	stroke	NOUN
ejpam-4872	395	39	be	be	AUX
ejpam-4872	395	40	-	-	PUNCT
ejpam-4872	395	41	algebras	algebras	X
ejpam-4872	395	42	,	,	PUNCT
ejpam-4872	395	43	etc	etc	X
ejpam-4872	395	44	.	.	X
ejpam-4872	395	45	based	base	VERB
ejpam-4872	395	46	on	on	ADP
ejpam-4872	395	47	these	these	DET
ejpam-4872	395	48	studies	study	NOUN
ejpam-4872	395	49	,	,	PUNCT
ejpam-4872	395	50	we	we	PRON
ejpam-4872	395	51	think	think	VERB
ejpam-4872	395	52	the	the	DET
ejpam-4872	395	53	possibility	possibility	NOUN
ejpam-4872	395	54	of	of	ADP
ejpam-4872	395	55	application	application	NOUN
ejpam-4872	395	56	to	to	ADP
ejpam-4872	395	57	decision	decision	NOUN
ejpam-4872	395	58	-	-	PUNCT
ejpam-4872	395	59	making	make	VERB
ejpam-4872	395	60	theory	theory	NOUN
ejpam-4872	395	61	,	,	PUNCT
ejpam-4872	395	62	pattern	pattern	NOUN
ejpam-4872	395	63	recognition	recognition	NOUN
ejpam-4872	395	64	,	,	PUNCT
ejpam-4872	395	65	and	and	CCONJ
ejpam-4872	395	66	medical	medical	ADJ
ejpam-4872	395	67	diagnosis	diagnosis	NOUN
ejpam-4872	395	68	systems	system	NOUN
ejpam-4872	395	69	,	,	PUNCT
ejpam-4872	395	70	etc	etc	X
ejpam-4872	395	71	.	.	X
ejpam-4872	395	72	will	will	AUX
ejpam-4872	395	73	open	open	VERB
ejpam-4872	395	74	up	up	ADP
ejpam-4872	395	75	.	.	PUNCT
ejpam-4872	396	1	acknowledgements	acknowledgement	NOUN
ejpam-4872	396	2	the	the	DET
ejpam-4872	396	3	authors	author	NOUN
ejpam-4872	396	4	wish	wish	VERB
ejpam-4872	396	5	to	to	PART
ejpam-4872	396	6	thank	thank	VERB
ejpam-4872	396	7	the	the	DET
ejpam-4872	396	8	anonymous	anonymous	ADJ
ejpam-4872	396	9	reviewers	reviewer	NOUN
ejpam-4872	396	10	for	for	ADP
ejpam-4872	396	11	their	their	PRON
ejpam-4872	396	12	valuable	valuable	ADJ
ejpam-4872	396	13	suggestions	suggestion	NOUN
ejpam-4872	396	14	.	.	PUNCT
ejpam-4872	397	1	the	the	DET
ejpam-4872	397	2	3rd	3rd	ADJ
ejpam-4872	397	3	author	author	NOUN
ejpam-4872	397	4	(	(	PUNCT
ejpam-4872	397	5	s.	s.	PROPN
ejpam-4872	397	6	z.	z.	PROPN
ejpam-4872	397	7	song	song	PROPN
ejpam-4872	397	8	)	)	PUNCT
ejpam-4872	397	9	was	be	AUX
ejpam-4872	397	10	partially	partially	ADV
ejpam-4872	397	11	supported	support	VERB
ejpam-4872	397	12	by	by	ADP
ejpam-4872	397	13	basic	basic	ADJ
ejpam-4872	397	14	science	science	NOUN
ejpam-4872	397	15	research	research	NOUN
ejpam-4872	397	16	program	program	NOUN
ejpam-4872	397	17	through	through	ADP
ejpam-4872	397	18	the	the	DET
ejpam-4872	397	19	national	national	PROPN
ejpam-4872	397	20	research	research	PROPN
ejpam-4872	397	21	foundation	foundation	PROPN
ejpam-4872	397	22	of	of	ADP
ejpam-4872	397	23	korea	korea	PROPN
ejpam-4872	397	24	(	(	PUNCT
ejpam-4872	397	25	nrf	nrf	NOUN
ejpam-4872	397	26	)	)	PUNCT
ejpam-4872	397	27	funded	fund	VERB
ejpam-4872	397	28	by	by	ADP
ejpam-4872	397	29	the	the	DET
ejpam-4872	397	30	ministry	ministry	PROPN
ejpam-4872	397	31	of	of	ADP
ejpam-4872	397	32	education	education	PROPN
ejpam-4872	397	33	[	[	X
ejpam-4872	397	34	grant	grant	NOUN
ejpam-4872	397	35	number	number	NOUN
ejpam-4872	397	36	2016r1d1a1b02006812	2016r1d1a1b02006812	NUM
ejpam-4872	397	37	]	]	PUNCT
ejpam-4872	397	38	.	.	PUNCT
ejpam-4872	398	1	references	reference	NOUN
ejpam-4872	398	2	[	[	X
ejpam-4872	398	3	1	1	NUM
ejpam-4872	398	4	]	]	PUNCT
ejpam-4872	398	5	i.	i.	NOUN
ejpam-4872	398	6	chajad	chajad	PROPN
ejpam-4872	398	7	.	.	PUNCT
ejpam-4872	399	1	sheffer	sheffer	PROPN
ejpam-4872	399	2	operation	operation	NOUN
ejpam-4872	399	3	in	in	ADP
ejpam-4872	399	4	ortholattices	ortholattice	NOUN
ejpam-4872	399	5	.	.	PUNCT
ejpam-4872	400	1	acta	acta	PROPN
ejpam-4872	400	2	univ	univ	PROPN
ejpam-4872	400	3	.	.	PUNCT
ejpam-4872	401	1	palack	palack	NOUN
ejpam-4872	401	2	.	.	PUNCT
ejpam-4872	402	1	olomuc	olomuc	PROPN
ejpam-4872	402	2	.	.	PUNCT
ejpam-4872	403	1	fac	fac	PROPN
ejpam-4872	403	2	.	.	PUNCT
ejpam-4872	404	1	rerum	rerum	PROPN
ejpam-4872	404	2	natur	natur	PROPN
ejpam-4872	404	3	.	.	PUNCT
ejpam-4872	405	1	math	math	NOUN
ejpam-4872	405	2	.	.	PUNCT
ejpam-4872	405	3	,	,	PUNCT
ejpam-4872	405	4	44(1):19–23	44(1):19–23	NUM
ejpam-4872	405	5	,	,	PUNCT
ejpam-4872	405	6	2005	2005	NUM
ejpam-4872	405	7	.	.	PUNCT
ejpam-4872	406	1	[	[	X
ejpam-4872	406	2	2	2	NUM
ejpam-4872	406	3	]	]	PUNCT
ejpam-4872	406	4	m.	m.	NOUN
ejpam-4872	406	5	b.	b.	PROPN
ejpam-4872	406	6	gorzalczany	gorzalczany	NOUN
ejpam-4872	406	7	.	.	PUNCT
ejpam-4872	407	1	a	a	DET
ejpam-4872	407	2	method	method	NOUN
ejpam-4872	407	3	of	of	ADP
ejpam-4872	407	4	inference	inference	NOUN
ejpam-4872	407	5	in	in	ADP
ejpam-4872	407	6	approximate	approximate	ADJ
ejpam-4872	407	7	reasoning	reasoning	NOUN
ejpam-4872	407	8	based	base	VERB
ejpam-4872	407	9	on	on	ADP
ejpam-4872	407	10	intervalvalued	intervalvalue	VERB
ejpam-4872	407	11	fuzzy	fuzzy	ADJ
ejpam-4872	407	12	sets	set	NOUN
ejpam-4872	407	13	.	.	PUNCT
ejpam-4872	408	1	fuzzy	fuzzy	ADJ
ejpam-4872	408	2	sets	set	NOUN
ejpam-4872	408	3	and	and	CCONJ
ejpam-4872	408	4	systems	system	NOUN
ejpam-4872	408	5	,	,	PUNCT
ejpam-4872	408	6	21:1–17	21:1–17	NUM
ejpam-4872	408	7	,	,	PUNCT
ejpam-4872	408	8	1987	1987	NUM
ejpam-4872	408	9	.	.	PUNCT
ejpam-4872	409	1	references	reference	NOUN
ejpam-4872	409	2	1877	1877	NUM
ejpam-4872	410	1	[	[	X
ejpam-4872	410	2	3	3	NUM
ejpam-4872	410	3	]	]	X
ejpam-4872	410	4	y.	y.	PROPN
ejpam-4872	410	5	b.	b.	PROPN
ejpam-4872	410	6	jun	jun	PROPN
ejpam-4872	410	7	.	.	PROPN
ejpam-4872	410	8	dokdo	dokdo	PROPN
ejpam-4872	410	9	structure	structure	NOUN
ejpam-4872	410	10	and	and	CCONJ
ejpam-4872	410	11	its	its	PRON
ejpam-4872	410	12	application	application	NOUN
ejpam-4872	410	13	in	in	ADP
ejpam-4872	410	14	bck	bck	PROPN
ejpam-4872	410	15	/	/	SYM
ejpam-4872	410	16	bci	bci	NOUN
ejpam-4872	410	17	-	-	PUNCT
ejpam-4872	410	18	algebras	algebras	X
ejpam-4872	410	19	.	.	PUNCT
ejpam-4872	411	1	twms	twms	PROPN
ejpam-4872	411	2	j.	j.	PROPN
ejpam-4872	411	3	pure	pure	PROPN
ejpam-4872	411	4	appl	appl	PROPN
ejpam-4872	411	5	.	.	PUNCT
ejpam-4872	411	6	math	math	PROPN
ejpam-4872	411	7	.	.	PUNCT
ejpam-4872	412	1	(	(	PUNCT
ejpam-4872	412	2	in	in	ADP
ejpam-4872	412	3	press	press	NOUN
ejpam-4872	412	4	)	)	PUNCT
ejpam-4872	412	5	.	.	PUNCT
ejpam-4872	413	1	[	[	X
ejpam-4872	413	2	4	4	X
ejpam-4872	413	3	]	]	PUNCT
ejpam-4872	413	4	t.	t.	PROPN
ejpam-4872	413	5	katican	katican	PROPN
ejpam-4872	413	6	.	.	PUNCT
ejpam-4872	413	7	branchesm	branchesm	VERB
ejpam-4872	413	8	and	and	CCONJ
ejpam-4872	413	9	obstinate	obstinate	VERB
ejpam-4872	413	10	sbe	sbe	NOUN
ejpam-4872	413	11	-	-	PUNCT
ejpam-4872	413	12	filters	filter	NOUN
ejpam-4872	413	13	of	of	ADP
ejpam-4872	413	14	sheffer	sheffer	NOUN
ejpam-4872	413	15	stroke	stroke	NOUN
ejpam-4872	413	16	be	be	AUX
ejpam-4872	413	17	-	-	PUNCT
ejpam-4872	413	18	algebras	algebra	NOUN
ejpam-4872	413	19	.	.	PUNCT
ejpam-4872	414	1	bull	bull	NOUN
ejpam-4872	414	2	.	.	PUNCT
ejpam-4872	415	1	int	int	NOUN
ejpam-4872	415	2	.	.	PUNCT
ejpam-4872	416	1	math	math	NOUN
ejpam-4872	416	2	.	.	PUNCT
ejpam-4872	417	1	virtual	virtual	ADJ
ejpam-4872	417	2	inst	inst	PROPN
ejpam-4872	417	3	.	.	PROPN
ejpam-4872	417	4	,	,	PUNCT
ejpam-4872	417	5	12(1):41–50	12(1):41–50	NUM
ejpam-4872	417	6	,	,	PUNCT
ejpam-4872	417	7	2002	2002	NUM
ejpam-4872	417	8	.	.	PUNCT
ejpam-4872	418	1	[	[	X
ejpam-4872	418	2	5	5	X
ejpam-4872	418	3	]	]	PUNCT
ejpam-4872	418	4	v.	v.	CCONJ
ejpam-4872	418	5	kozarkiewicz	kozarkiewicz	PROPN
ejpam-4872	418	6	and	and	CCONJ
ejpam-4872	418	7	a.	a.	PROPN
ejpam-4872	418	8	grabowski	grabowski	PROPN
ejpam-4872	418	9	.	.	PUNCT
ejpam-4872	419	1	axiomatization	axiomatization	NOUN
ejpam-4872	419	2	of	of	ADP
ejpam-4872	419	3	boolean	boolean	ADJ
ejpam-4872	419	4	algebras	algebra	NOUN
ejpam-4872	419	5	based	base	VERB
ejpam-4872	419	6	on	on	ADP
ejpam-4872	419	7	sheffer	sheffer	PROPN
ejpam-4872	419	8	stroke	stroke	PROPN
ejpam-4872	419	9	.	.	PUNCT
ejpam-4872	420	1	formalized	formalize	VERB
ejpam-4872	420	2	mathematics	mathematic	NOUN
ejpam-4872	420	3	,	,	PUNCT
ejpam-4872	420	4	12(3):355–361	12(3):355–361	NUM
ejpam-4872	420	5	,	,	PUNCT
ejpam-4872	420	6	2004	2004	NUM
ejpam-4872	420	7	.	.	PUNCT
ejpam-4872	421	1	[	[	X
ejpam-4872	421	2	6	6	NUM
ejpam-4872	421	3	]	]	PUNCT
ejpam-4872	421	4	k.	k.	PROPN
ejpam-4872	421	5	m.	m.	PROPN
ejpam-4872	421	6	lee	lee	PROPN
ejpam-4872	421	7	.	.	PUNCT
ejpam-4872	422	1	bipolar	bipolar	ADJ
ejpam-4872	422	2	-	-	PUNCT
ejpam-4872	422	3	valued	value	VERB
ejpam-4872	422	4	fuzzy	fuzzy	ADJ
ejpam-4872	422	5	sets	set	NOUN
ejpam-4872	422	6	and	and	CCONJ
ejpam-4872	422	7	their	their	PRON
ejpam-4872	422	8	operations	operation	NOUN
ejpam-4872	422	9	.	.	PUNCT
ejpam-4872	423	1	proc	proc	NOUN
ejpam-4872	423	2	.	.	PUNCT
ejpam-4872	424	1	int	int	NOUN
ejpam-4872	424	2	.	.	PUNCT
ejpam-4872	424	3	conf	conf	PROPN
ejpam-4872	424	4	.	.	PUNCT
ejpam-4872	425	1	on	on	ADP
ejpam-4872	425	2	intelligent	intelligent	ADJ
ejpam-4872	425	3	technologies	technology	NOUN
ejpam-4872	425	4	,	,	PUNCT
ejpam-4872	425	5	pages	page	NOUN
ejpam-4872	425	6	307–312	307–312	NUM
ejpam-4872	425	7	,	,	PUNCT
ejpam-4872	425	8	2000	2000	NUM
ejpam-4872	425	9	.	.	PUNCT
ejpam-4872	426	1	[	[	X
ejpam-4872	426	2	7	7	X
ejpam-4872	426	3	]	]	X
ejpam-4872	426	4	d.	d.	PROPN
ejpam-4872	426	5	molodtsov	molodtsov	PROPN
ejpam-4872	426	6	.	.	PUNCT
ejpam-4872	427	1	soft	soft	ADJ
ejpam-4872	427	2	set	set	NOUN
ejpam-4872	427	3	theory	theory	NOUN
ejpam-4872	427	4	–	–	PUNCT
ejpam-4872	427	5	first	first	ADJ
ejpam-4872	427	6	results	result	NOUN
ejpam-4872	427	7	.	.	PUNCT
ejpam-4872	428	1	comput	comput	NOUN
ejpam-4872	428	2	.	.	PUNCT
ejpam-4872	429	1	math	math	NOUN
ejpam-4872	429	2	.	.	PUNCT
ejpam-4872	430	1	appl	appl	PROPN
ejpam-4872	430	2	.	.	PROPN
ejpam-4872	430	3	,	,	PUNCT
ejpam-4872	430	4	37:19–31	37:19–31	PROPN
ejpam-4872	430	5	,	,	PUNCT
ejpam-4872	430	6	1999	1999	NUM
ejpam-4872	430	7	.	.	PUNCT
ejpam-4872	431	1	[	[	X
ejpam-4872	431	2	8	8	NUM
ejpam-4872	431	3	]	]	PUNCT
ejpam-4872	432	1	r.	r.	PROPN
ejpam-4872	432	2	biswas	biswas	PROPN
ejpam-4872	433	1	p.	p.	PROPN
ejpam-4872	433	2	k.	k.	PROPN
ejpam-4872	434	1	maji	maji	PROPN
ejpam-4872	434	2	and	and	CCONJ
ejpam-4872	434	3	a.	a.	PROPN
ejpam-4872	434	4	r.	r.	PROPN
ejpam-4872	434	5	roy	roy	PROPN
ejpam-4872	434	6	.	.	PROPN
ejpam-4872	434	7	soft	soft	ADJ
ejpam-4872	434	8	set	set	PROPN
ejpam-4872	434	9	theory	theory	NOUN
ejpam-4872	434	10	.	.	PUNCT
ejpam-4872	435	1	comput	comput	NOUN
ejpam-4872	435	2	.	.	PUNCT
ejpam-4872	436	1	math	math	NOUN
ejpam-4872	436	2	.	.	PUNCT
ejpam-4872	437	1	appl	appl	PROPN
ejpam-4872	437	2	.	.	PROPN
ejpam-4872	437	3	,	,	PUNCT
ejpam-4872	437	4	45:555	45:555	NUM
ejpam-4872	437	5	–	–	PUNCT
ejpam-4872	437	6	562	562	NUM
ejpam-4872	437	7	,	,	PUNCT
ejpam-4872	437	8	2003	2003	NUM
ejpam-4872	437	9	.	.	PUNCT
ejpam-4872	438	1	[	[	X
ejpam-4872	438	2	9	9	NUM
ejpam-4872	438	3	]	]	X
ejpam-4872	438	4	h.	h.	PROPN
ejpam-4872	438	5	m.	m.	PROPN
ejpam-4872	438	6	sheffer	sheffer	PROPN
ejpam-4872	438	7	.	.	PUNCT
ejpam-4872	439	1	a	a	DET
ejpam-4872	439	2	set	set	NOUN
ejpam-4872	439	3	of	of	ADP
ejpam-4872	439	4	five	five	NUM
ejpam-4872	439	5	independent	independent	ADJ
ejpam-4872	439	6	postulates	postulate	NOUN
ejpam-4872	439	7	for	for	ADP
ejpam-4872	439	8	boolean	boolean	ADJ
ejpam-4872	439	9	algebras	algebra	NOUN
ejpam-4872	439	10	.	.	PUNCT
ejpam-4872	440	1	trans	trans	PROPN
ejpam-4872	440	2	.	.	PUNCT
ejpam-4872	441	1	amer	amer	PROPN
ejpam-4872	441	2	.	.	PUNCT
ejpam-4872	441	3	math	math	PROPN
ejpam-4872	441	4	.	.	PUNCT
ejpam-4872	442	1	soc	soc	PROPN
ejpam-4872	442	2	.	.	PUNCT
ejpam-4872	442	3	,	,	PUNCT
ejpam-4872	442	4	14(4):481–488	14(4):481–488	NUM
ejpam-4872	442	5	,	,	PUNCT
ejpam-4872	442	6	1913	1913	NUM
ejpam-4872	442	7	.	.	PUNCT
ejpam-4872	443	1	[	[	X
ejpam-4872	443	2	10	10	NUM
ejpam-4872	443	3	]	]	PUNCT
ejpam-4872	443	4	a.	a.	NOUN
ejpam-4872	443	5	borumand	borumand	PROPN
ejpam-4872	443	6	saeid	saeid	PROPN
ejpam-4872	443	7	t.	t.	PROPN
ejpam-4872	443	8	oner	oner	NOUN
ejpam-4872	443	9	,	,	PUNCT
ejpam-4872	443	10	t.	t.	PROPN
ejpam-4872	443	11	katican	katican	PROPN
ejpam-4872	443	12	and	and	CCONJ
ejpam-4872	443	13	m.	m.	NOUN
ejpam-4872	443	14	terziler	terziler	PROPN
ejpam-4872	443	15	.	.	PUNCT
ejpam-4872	444	1	filters	filter	NOUN
ejpam-4872	444	2	of	of	ADP
ejpam-4872	444	3	strong	strong	ADJ
ejpam-4872	444	4	sheffer	sheffer	NOUN
ejpam-4872	444	5	stroke	stroke	NOUN
ejpam-4872	444	6	non	non	ADJ
ejpam-4872	444	7	-	-	ADJ
ejpam-4872	444	8	associative	associative	ADJ
ejpam-4872	444	9	mv	mv	NOUN
ejpam-4872	444	10	-	-	PUNCT
ejpam-4872	444	11	algebras	algebra	NOUN
ejpam-4872	444	12	.	.	PUNCT
ejpam-4872	445	1	an	an	PRON
ejpam-4872	445	2	.	.	PUNCT
ejpam-4872	446	1	şt	şt	PROPN
ejpam-4872	446	2	.	.	PROPN
ejpam-4872	446	3	univ	univ	PROPN
ejpam-4872	446	4	.	.	PUNCT
ejpam-4872	447	1	ovidius	ovidius	PROPN
ejpam-4872	447	2	constanţa	constanţa	NOUN
ejpam-4872	447	3	,	,	PUNCT
ejpam-4872	447	4	29(1):143–164	29(1):143–164	NOUN
ejpam-4872	447	5	,	,	PUNCT
ejpam-4872	447	6	2021	2021	NUM
ejpam-4872	447	7	.	.	PUNCT
ejpam-4872	448	1	[	[	X
ejpam-4872	448	2	11	11	NUM
ejpam-4872	448	3	]	]	PUNCT
ejpam-4872	448	4	t.	t.	PROPN
ejpam-4872	448	5	katican	katican	PROPN
ejpam-4872	448	6	t.	t.	PROPN
ejpam-4872	448	7	oner	oner	PROPN
ejpam-4872	448	8	and	and	CCONJ
ejpam-4872	448	9	a.	a.	PROPN
ejpam-4872	448	10	borumand	borumand	PROPN
ejpam-4872	448	11	saeid	saeid	PROPN
ejpam-4872	448	12	.	.	PUNCT
ejpam-4872	449	1	fuzzy	fuzzy	ADJ
ejpam-4872	449	2	filters	filter	NOUN
ejpam-4872	449	3	of	of	ADP
ejpam-4872	449	4	sheffer	sheffer	PROPN
ejpam-4872	449	5	stroke	stroke	PROPN
ejpam-4872	449	6	hilbert	hilbert	PROPN
ejpam-4872	449	7	algebras	algebras	PROPN
ejpam-4872	449	8	.	.	PUNCT
ejpam-4872	450	1	j.	j.	PROPN
ejpam-4872	450	2	intell	intell	PROPN
ejpam-4872	450	3	.	.	PUNCT
ejpam-4872	451	1	fuzzy	fuzzy	ADJ
ejpam-4872	451	2	systems	system	NOUN
ejpam-4872	451	3	,	,	PUNCT
ejpam-4872	451	4	40(1):759–772	40(1):759–772	NOUN
ejpam-4872	451	5	,	,	PUNCT
ejpam-4872	451	6	2021	2021	NUM
ejpam-4872	451	7	.	.	PUNCT
ejpam-4872	452	1	[	[	X
ejpam-4872	452	2	12	12	NUM
ejpam-4872	452	3	]	]	PUNCT
ejpam-4872	452	4	t.	t.	PROPN
ejpam-4872	452	5	katican	katican	PROPN
ejpam-4872	452	6	t.	t.	PROPN
ejpam-4872	452	7	oner	oner	PROPN
ejpam-4872	452	8	and	and	CCONJ
ejpam-4872	452	9	a.	a.	PROPN
ejpam-4872	452	10	borumand	borumand	PROPN
ejpam-4872	452	11	saeid	saeid	PROPN
ejpam-4872	452	12	.	.	PUNCT
ejpam-4872	453	1	relation	relation	NOUN
ejpam-4872	453	2	between	between	ADP
ejpam-4872	453	3	sheffer	sheffer	PROPN
ejpam-4872	453	4	stroke	stroke	PROPN
ejpam-4872	453	5	and	and	CCONJ
ejpam-4872	453	6	hilbert	hilbert	PROPN
ejpam-4872	453	7	algebras	algebras	PROPN
ejpam-4872	453	8	.	.	PUNCT
ejpam-4872	453	9	categories	category	NOUN
ejpam-4872	453	10	and	and	CCONJ
ejpam-4872	453	11	general	general	ADJ
ejpam-4872	453	12	algebraic	algebraic	ADJ
ejpam-4872	453	13	structures	structure	NOUN
ejpam-4872	453	14	with	with	ADP
ejpam-4872	453	15	applications	application	NOUN
ejpam-4872	453	16	,	,	PUNCT
ejpam-4872	453	17	14(1):245–268	14(1):245–268	NUM
ejpam-4872	453	18	,	,	PUNCT
ejpam-4872	453	19	2021	2021	NUM
ejpam-4872	453	20	.	.	PUNCT
ejpam-4872	454	1	[	[	X
ejpam-4872	454	2	13	13	NUM
ejpam-4872	454	3	]	]	PUNCT
ejpam-4872	454	4	t.	t.	PROPN
ejpam-4872	454	5	katican	katican	PROPN
ejpam-4872	454	6	t.	t.	PROPN
ejpam-4872	454	7	oner	oner	PROPN
ejpam-4872	454	8	and	and	CCONJ
ejpam-4872	454	9	a.	a.	PROPN
ejpam-4872	454	10	borumand	borumand	PROPN
ejpam-4872	454	11	saeid	saeid	PROPN
ejpam-4872	454	12	.	.	PUNCT
ejpam-4872	454	13	bl	bl	VERB
ejpam-4872	454	14	-	-	PUNCT
ejpam-4872	454	15	algebras	algebras	PROPN
ejpam-4872	454	16	defined	define	VERB
ejpam-4872	454	17	by	by	ADP
ejpam-4872	454	18	an	an	DET
ejpam-4872	454	19	operator	operator	NOUN
ejpam-4872	454	20	.	.	PUNCT
ejpam-4872	455	1	honam	honam	PROPN
ejpam-4872	455	2	math	math	PROPN
ejpam-4872	455	3	.	.	PUNCT
ejpam-4872	456	1	j.	j.	PROPN
ejpam-4872	456	2	,	,	PUNCT
ejpam-4872	456	3	44(2):18–31	44(2):18–31	NUM
ejpam-4872	456	4	,	,	PUNCT
ejpam-4872	456	5	2022	2022	NUM
ejpam-4872	456	6	.	.	PUNCT
ejpam-4872	457	1	[	[	X
ejpam-4872	457	2	14	14	NUM
ejpam-4872	457	3	]	]	PUNCT
ejpam-4872	457	4	t.	t.	PROPN
ejpam-4872	457	5	katican	katican	PROPN
ejpam-4872	457	6	t.	t.	PROPN
ejpam-4872	457	7	oner	oner	PROPN
ejpam-4872	457	8	and	and	CCONJ
ejpam-4872	457	9	a.	a.	PROPN
ejpam-4872	457	10	borumand	borumand	PROPN
ejpam-4872	457	11	saeid	saeid	PROPN
ejpam-4872	457	12	.	.	PUNCT
ejpam-4872	458	1	class	class	NOUN
ejpam-4872	458	2	of	of	ADP
ejpam-4872	458	3	sheffer	sheffer	PROPN
ejpam-4872	458	4	stroke	stroke	NOUN
ejpam-4872	458	5	bck	bck	PROPN
ejpam-4872	458	6	-	-	PUNCT
ejpam-4872	458	7	algebras	algebras	PROPN
ejpam-4872	458	8	.	.	PUNCT
ejpam-4872	459	1	an	an	PRON
ejpam-4872	459	2	.	.	PUNCT
ejpam-4872	460	1	şt	şt	PROPN
ejpam-4872	460	2	.	.	PROPN
ejpam-4872	460	3	univ	univ	PROPN
ejpam-4872	460	4	.	.	PUNCT
ejpam-4872	461	1	ovidius	ovidius	PROPN
ejpam-4872	461	2	constanţa	constanţa	PROPN
ejpam-4872	461	3	,	,	PUNCT
ejpam-4872	461	4	30(1):247–269	30(1):247–269	NOUN
ejpam-4872	461	5	,	,	PUNCT
ejpam-4872	461	6	2022	2022	NUM
ejpam-4872	461	7	.	.	PUNCT
ejpam-4872	462	1	[	[	X
ejpam-4872	462	2	15	15	NUM
ejpam-4872	462	3	]	]	X
ejpam-4872	462	4	l.	l.	PROPN
ejpam-4872	462	5	a.	a.	PROPN
ejpam-4872	462	6	zadeh	zadeh	PROPN
ejpam-4872	462	7	.	.	PUNCT
ejpam-4872	463	1	the	the	DET
ejpam-4872	463	2	concept	concept	NOUN
ejpam-4872	463	3	of	of	ADP
ejpam-4872	463	4	a	a	DET
ejpam-4872	463	5	linguistic	linguistic	ADJ
ejpam-4872	463	6	variable	variable	NOUN
ejpam-4872	463	7	and	and	CCONJ
ejpam-4872	463	8	its	its	PRON
ejpam-4872	463	9	application	application	NOUN
ejpam-4872	463	10	to	to	PART
ejpam-4872	463	11	approximate	approximate	ADJ
ejpam-4872	463	12	reasoning	reasoning	NOUN
ejpam-4872	463	13	.	.	PUNCT
ejpam-4872	464	1	inform	inform	NOUN
ejpam-4872	464	2	.	.	PUNCT
ejpam-4872	465	1	sci	sci	PROPN
ejpam-4872	465	2	.	.	PROPN
ejpam-4872	465	3	,	,	PUNCT
ejpam-4872	465	4	8:199–249	8:199–249	NUM
ejpam-4872	465	5	,	,	PUNCT
ejpam-4872	465	6	1975	1975	NUM
ejpam-4872	465	7	.	.	PUNCT