id	sid	tid	token	lemma	pos
ejpam-4510	1	1	european	european	PROPN
ejpam-4510	1	2	journal	journal	PROPN
ejpam-4510	1	3	of	of	ADP
ejpam-4510	1	4	pure	pure	ADJ
ejpam-4510	1	5	and	and	CCONJ
ejpam-4510	1	6	applied	apply	VERB
ejpam-4510	1	7	mathematics	mathematic	NOUN
ejpam-4510	1	8	vol	vol	NOUN
ejpam-4510	1	9	.	.	PROPN
ejpam-4510	2	1	15	15	NUM
ejpam-4510	2	2	,	,	PUNCT
ejpam-4510	2	3	no	no	INTJ
ejpam-4510	2	4	.	.	NOUN
ejpam-4510	2	5	4	4	NUM
ejpam-4510	2	6	,	,	PUNCT
ejpam-4510	2	7	2022	2022	NUM
ejpam-4510	2	8	,	,	PUNCT
ejpam-4510	2	9	1521	1521	NUM
ejpam-4510	2	10	-	-	SYM
ejpam-4510	2	11	1535	1535	NUM
ejpam-4510	2	12	issn	issn	PROPN
ejpam-4510	2	13	1307	1307	NUM
ejpam-4510	2	14	-	-	SYM
ejpam-4510	2	15	5543	5543	NUM
ejpam-4510	2	16	–	–	PUNCT
ejpam-4510	2	17	ejpam.com	ejpam.com	X
ejpam-4510	2	18	published	publish	VERB
ejpam-4510	2	19	by	by	ADP
ejpam-4510	2	20	new	new	PROPN
ejpam-4510	2	21	york	york	PROPN
ejpam-4510	2	22	business	business	PROPN
ejpam-4510	2	23	global	global	PROPN
ejpam-4510	2	24	dokdo	dokdo	PROPN
ejpam-4510	2	25	be	be	AUX
ejpam-4510	2	26	-	-	PUNCT
ejpam-4510	2	27	subalgebras	subalgebra	NOUN
ejpam-4510	2	28	and	and	CCONJ
ejpam-4510	2	29	be	be	AUX
ejpam-4510	2	30	-	-	PUNCT
ejpam-4510	2	31	filters	filter	NOUN
ejpam-4510	2	32	of	of	ADP
ejpam-4510	2	33	be	be	AUX
ejpam-4510	2	34	-	-	PUNCT
ejpam-4510	2	35	algebras	algebras	ADJ
ejpam-4510	2	36	young	young	ADJ
ejpam-4510	2	37	bae	bae	PROPN
ejpam-4510	2	38	jun1	jun1	PROPN
ejpam-4510	2	39	,	,	PUNCT
ejpam-4510	2	40	sun	sun	PROPN
ejpam-4510	2	41	shin	shin	PROPN
ejpam-4510	2	42	ahn2,∗	ahn2,∗	PROPN
ejpam-4510	2	43	,	,	PUNCT
ejpam-4510	2	44	eun	eun	PROPN
ejpam-4510	2	45	hwan	hwan	PROPN
ejpam-4510	2	46	roh3	roh3	PROPN
ejpam-4510	2	47	1	1	NUM
ejpam-4510	2	48	department	department	NOUN
ejpam-4510	2	49	of	of	ADP
ejpam-4510	2	50	mathematics	mathematics	PROPN
ejpam-4510	2	51	education	education	NOUN
ejpam-4510	2	52	,	,	PUNCT
ejpam-4510	2	53	gyeongsang	gyeongsang	PROPN
ejpam-4510	2	54	national	national	PROPN
ejpam-4510	2	55	university	university	PROPN
ejpam-4510	2	56	,	,	PUNCT
ejpam-4510	2	57	jinju	jinju	NOUN
ejpam-4510	2	58	52828	52828	NUM
ejpam-4510	2	59	,	,	PUNCT
ejpam-4510	2	60	korea	korea	PROPN
ejpam-4510	2	61	2	2	NUM
ejpam-4510	2	62	department	department	NOUN
ejpam-4510	2	63	of	of	ADP
ejpam-4510	2	64	mathematics	mathematics	PROPN
ejpam-4510	2	65	education	education	NOUN
ejpam-4510	2	66	,	,	PUNCT
ejpam-4510	2	67	dongguk	dongguk	PROPN
ejpam-4510	2	68	university	university	PROPN
ejpam-4510	2	69	,	,	PUNCT
ejpam-4510	2	70	seoul	seoul	PROPN
ejpam-4510	2	71	04620	04620	NUM
ejpam-4510	2	72	,	,	PUNCT
ejpam-4510	2	73	korea	korea	PROPN
ejpam-4510	2	74	3	3	NUM
ejpam-4510	2	75	department	department	PROPN
ejpam-4510	2	76	of	of	ADP
ejpam-4510	2	77	mathematics	mathematics	PROPN
ejpam-4510	2	78	education	education	NOUN
ejpam-4510	2	79	,	,	PUNCT
ejpam-4510	2	80	chinju	chinju	PROPN
ejpam-4510	2	81	national	national	PROPN
ejpam-4510	2	82	university	university	PROPN
ejpam-4510	2	83	of	of	ADP
ejpam-4510	2	84	education	education	NOUN
ejpam-4510	2	85	,	,	PUNCT
ejpam-4510	2	86	jinju	jinju	PROPN
ejpam-4510	2	87	52673	52673	NUM
ejpam-4510	2	88	,	,	PUNCT
ejpam-4510	2	89	korea	korea	PROPN
ejpam-4510	2	90	abstract	abstract	NOUN
ejpam-4510	2	91	.	.	PUNCT
ejpam-4510	3	1	with	with	ADP
ejpam-4510	3	2	the	the	DET
ejpam-4510	3	3	aim	aim	NOUN
ejpam-4510	3	4	of	of	ADP
ejpam-4510	3	5	applying	apply	VERB
ejpam-4510	3	6	the	the	DET
ejpam-4510	3	7	dokdo	dokdo	NOUN
ejpam-4510	3	8	structure	structure	NOUN
ejpam-4510	3	9	to	to	PART
ejpam-4510	3	10	be	be	AUX
ejpam-4510	3	11	-	-	PUNCT
ejpam-4510	3	12	algebra	algebra	NOUN
ejpam-4510	3	13	,	,	PUNCT
ejpam-4510	3	14	the	the	DET
ejpam-4510	3	15	notions	notion	NOUN
ejpam-4510	3	16	of	of	ADP
ejpam-4510	3	17	(	(	PUNCT
ejpam-4510	3	18	weak	weak	ADJ
ejpam-4510	3	19	)	)	PUNCT
ejpam-4510	3	20	dokdo	dokdo	NOUN
ejpam-4510	3	21	be	be	NOUN
ejpam-4510	3	22	-	-	PUNCT
ejpam-4510	3	23	subalgebra	subalgebra	NOUN
ejpam-4510	3	24	and	and	CCONJ
ejpam-4510	3	25	dokdo	dokdo	NOUN
ejpam-4510	3	26	be	be	AUX
ejpam-4510	3	27	-	-	PUNCT
ejpam-4510	3	28	filter	filter	NOUN
ejpam-4510	3	29	are	be	AUX
ejpam-4510	3	30	introduced	introduce	VERB
ejpam-4510	3	31	,	,	PUNCT
ejpam-4510	3	32	and	and	CCONJ
ejpam-4510	3	33	their	their	PRON
ejpam-4510	3	34	properties	property	NOUN
ejpam-4510	3	35	are	be	AUX
ejpam-4510	3	36	investigated	investigate	VERB
ejpam-4510	3	37	.	.	PUNCT
ejpam-4510	4	1	the	the	DET
ejpam-4510	4	2	relationship	relationship	NOUN
ejpam-4510	4	3	between	between	ADP
ejpam-4510	4	4	weak	weak	ADJ
ejpam-4510	4	5	dokdo	dokdo	NOUN
ejpam-4510	4	6	be	be	NOUN
ejpam-4510	4	7	-	-	PUNCT
ejpam-4510	4	8	subalgebra	subalgebra	NOUN
ejpam-4510	4	9	,	,	PUNCT
ejpam-4510	4	10	dokdo	dokdo	PROPN
ejpam-4510	4	11	be	be	NOUN
ejpam-4510	4	12	-	-	PUNCT
ejpam-4510	4	13	subalgebra	subalgebra	NOUN
ejpam-4510	4	14	and	and	CCONJ
ejpam-4510	4	15	dokdo	dokdo	NOUN
ejpam-4510	4	16	be	be	AUX
ejpam-4510	4	17	-	-	PUNCT
ejpam-4510	4	18	filter	filter	NOUN
ejpam-4510	4	19	is	be	AUX
ejpam-4510	4	20	established	establish	VERB
ejpam-4510	4	21	.	.	PUNCT
ejpam-4510	5	1	the	the	DET
ejpam-4510	5	2	conditions	condition	NOUN
ejpam-4510	5	3	under	under	ADP
ejpam-4510	5	4	which	which	PRON
ejpam-4510	5	5	dokdo	dokdo	NOUN
ejpam-4510	5	6	structure	structure	NOUN
ejpam-4510	5	7	can	can	AUX
ejpam-4510	5	8	be	be	AUX
ejpam-4510	5	9	weak	weak	ADJ
ejpam-4510	5	10	dokdo	dokdo	NOUN
ejpam-4510	5	11	be	be	NOUN
ejpam-4510	5	12	-	-	PUNCT
ejpam-4510	5	13	subalgebra	subalgebra	NOUN
ejpam-4510	5	14	and	and	CCONJ
ejpam-4510	5	15	dokdo	dokdo	VERB
ejpam-4510	5	16	be	be	NOUN
ejpam-4510	5	17	-	-	PUNCT
ejpam-4510	5	18	filter	filter	NOUN
ejpam-4510	5	19	,	,	PUNCT
ejpam-4510	5	20	and	and	CCONJ
ejpam-4510	5	21	the	the	DET
ejpam-4510	5	22	condition	condition	NOUN
ejpam-4510	5	23	under	under	ADP
ejpam-4510	5	24	which	which	PRON
ejpam-4510	5	25	weak	weak	ADJ
ejpam-4510	5	26	dokdo	dokdo	NOUN
ejpam-4510	5	27	be	be	NOUN
ejpam-4510	5	28	-	-	PUNCT
ejpam-4510	5	29	subalgebra	subalgebra	NOUN
ejpam-4510	5	30	can	can	AUX
ejpam-4510	5	31	be	be	AUX
ejpam-4510	5	32	dokdo	dokdo	VERB
ejpam-4510	5	33	be	be	AUX
ejpam-4510	5	34	-	-	PUNCT
ejpam-4510	5	35	subalgebra	subalgebra	NOUN
ejpam-4510	5	36	are	be	AUX
ejpam-4510	5	37	explored	explore	VERB
ejpam-4510	5	38	.	.	PUNCT
ejpam-4510	6	1	characterizations	characterization	NOUN
ejpam-4510	6	2	of	of	ADP
ejpam-4510	6	3	dokdo	dokdo	PROPN
ejpam-4510	6	4	be	be	AUX
ejpam-4510	6	5	-	-	PUNCT
ejpam-4510	6	6	filter	filter	NOUN
ejpam-4510	6	7	are	be	AUX
ejpam-4510	6	8	provided	provide	VERB
ejpam-4510	6	9	.	.	PUNCT
ejpam-4510	7	1	2020	2020	NUM
ejpam-4510	7	2	mathematics	mathematic	NOUN
ejpam-4510	7	3	subject	subject	NOUN
ejpam-4510	7	4	classifications	classification	NOUN
ejpam-4510	7	5	:	:	PUNCT
ejpam-4510	7	6	03g25	03g25	NUM
ejpam-4510	7	7	,	,	PUNCT
ejpam-4510	7	8	06f35	06f35	NUM
ejpam-4510	7	9	,	,	PUNCT
ejpam-4510	7	10	08a72	08a72	NOUN
ejpam-4510	7	11	key	key	ADJ
ejpam-4510	7	12	words	word	NOUN
ejpam-4510	7	13	and	and	CCONJ
ejpam-4510	7	14	phrases	phrase	NOUN
ejpam-4510	7	15	:	:	PUNCT
ejpam-4510	7	16	weak	weak	ADJ
ejpam-4510	7	17	dokdo	dokdo	NOUN
ejpam-4510	7	18	be	be	NOUN
ejpam-4510	7	19	-	-	PUNCT
ejpam-4510	7	20	subalgebra	subalgebra	NOUN
ejpam-4510	7	21	,	,	PUNCT
ejpam-4510	7	22	dokdo	dokdo	ADJ
ejpam-4510	7	23	be	be	NOUN
ejpam-4510	7	24	-	-	PUNCT
ejpam-4510	7	25	subalgebra	subalgebra	NOUN
ejpam-4510	7	26	,	,	PUNCT
ejpam-4510	7	27	dokdo	dokdo	PROPN
ejpam-4510	7	28	be	be	NOUN
ejpam-4510	7	29	-	-	PUNCT
ejpam-4510	7	30	filter	filter	NOUN
ejpam-4510	7	31	1	1	NUM
ejpam-4510	7	32	.	.	PUNCT
ejpam-4510	8	1	introduction	introduction	NOUN
ejpam-4510	8	2	soft	soft	ADJ
ejpam-4510	8	3	sets	set	NOUN
ejpam-4510	8	4	and	and	CCONJ
ejpam-4510	8	5	fuzzy	fuzzy	ADJ
ejpam-4510	8	6	sets	set	NOUN
ejpam-4510	8	7	(	(	PUNCT
ejpam-4510	8	8	interval	interval	NOUN
ejpam-4510	8	9	value	value	NOUN
ejpam-4510	8	10	,	,	PUNCT
ejpam-4510	8	11	bipolar	bipolar	ADJ
ejpam-4510	8	12	)	)	PUNCT
ejpam-4510	8	13	are	be	AUX
ejpam-4510	8	14	useful	useful	ADJ
ejpam-4510	8	15	tools	tool	NOUN
ejpam-4510	8	16	for	for	ADP
ejpam-4510	8	17	solving	solve	VERB
ejpam-4510	8	18	the	the	DET
ejpam-4510	8	19	problem	problem	NOUN
ejpam-4510	8	20	of	of	ADP
ejpam-4510	8	21	maintaining	maintain	VERB
ejpam-4510	8	22	uncertainty	uncertainty	NOUN
ejpam-4510	8	23	in	in	ADP
ejpam-4510	8	24	everyday	everyday	ADJ
ejpam-4510	8	25	life	life	NOUN
ejpam-4510	8	26	.	.	PUNCT
ejpam-4510	9	1	fuzzy	fuzzy	ADJ
ejpam-4510	9	2	sets	set	NOUN
ejpam-4510	9	3	are	be	AUX
ejpam-4510	9	4	an	an	DET
ejpam-4510	9	5	extension	extension	NOUN
ejpam-4510	9	6	of	of	ADP
ejpam-4510	9	7	an	an	DET
ejpam-4510	9	8	existing	exist	VERB
ejpam-4510	9	9	set	set	NOUN
ejpam-4510	9	10	using	use	VERB
ejpam-4510	9	11	fuzzy	fuzzy	ADJ
ejpam-4510	9	12	logic	logic	NOUN
ejpam-4510	9	13	,	,	PUNCT
ejpam-4510	9	14	and	and	CCONJ
ejpam-4510	9	15	interval	interval	NOUN
ejpam-4510	9	16	-	-	PUNCT
ejpam-4510	9	17	valued	value	VERB
ejpam-4510	9	18	fuzzy	fuzzy	ADJ
ejpam-4510	9	19	sets	set	NOUN
ejpam-4510	9	20	are	be	AUX
ejpam-4510	9	21	also	also	ADV
ejpam-4510	9	22	an	an	DET
ejpam-4510	9	23	extension	extension	NOUN
ejpam-4510	9	24	of	of	ADP
ejpam-4510	9	25	fuzzy	fuzzy	ADJ
ejpam-4510	9	26	sets	set	NOUN
ejpam-4510	9	27	whose	whose	DET
ejpam-4510	9	28	membership	membership	NOUN
ejpam-4510	9	29	degree	degree	NOUN
ejpam-4510	9	30	range	range	NOUN
ejpam-4510	9	31	is	be	AUX
ejpam-4510	9	32	a	a	DET
ejpam-4510	9	33	subinterval	subinterval	NOUN
ejpam-4510	9	34	of	of	ADP
ejpam-4510	9	35	[	[	X
ejpam-4510	9	36	0	0	NUM
ejpam-4510	9	37	,	,	PUNCT
ejpam-4510	9	38	1	1	NUM
ejpam-4510	9	39	]	]	PUNCT
ejpam-4510	9	40	.	.	PUNCT
ejpam-4510	10	1	as	as	ADP
ejpam-4510	10	2	an	an	DET
ejpam-4510	10	3	extension	extension	NOUN
ejpam-4510	10	4	of	of	ADP
ejpam-4510	10	5	fuzzy	fuzzy	ADJ
ejpam-4510	10	6	sets	set	NOUN
ejpam-4510	10	7	,	,	PUNCT
ejpam-4510	10	8	bipolar	bipolar	ADJ
ejpam-4510	10	9	fuzzy	fuzzy	ADJ
ejpam-4510	10	10	sets	set	NOUN
ejpam-4510	10	11	whose	whose	DET
ejpam-4510	10	12	membership	membership	NOUN
ejpam-4510	10	13	degree	degree	NOUN
ejpam-4510	10	14	range	range	NOUN
ejpam-4510	10	15	is	be	AUX
ejpam-4510	10	16	[	[	X
ejpam-4510	10	17	−1	−1	NOUN
ejpam-4510	10	18	,	,	PUNCT
ejpam-4510	10	19	1	1	NUM
ejpam-4510	10	20	]	]	PUNCT
ejpam-4510	10	21	are	be	AUX
ejpam-4510	10	22	a	a	DET
ejpam-4510	10	23	very	very	ADV
ejpam-4510	10	24	useful	useful	ADJ
ejpam-4510	10	25	tool	tool	NOUN
ejpam-4510	10	26	for	for	ADP
ejpam-4510	10	27	considering	consider	VERB
ejpam-4510	10	28	positive	positive	ADJ
ejpam-4510	10	29	information	information	NOUN
ejpam-4510	10	30	and	and	CCONJ
ejpam-4510	10	31	negative	negative	ADJ
ejpam-4510	10	32	information	information	NOUN
ejpam-4510	10	33	at	at	ADP
ejpam-4510	10	34	the	the	DET
ejpam-4510	10	35	same	same	ADJ
ejpam-4510	10	36	time	time	NOUN
ejpam-4510	10	37	.	.	PUNCT
ejpam-4510	11	1	soft	soft	ADJ
ejpam-4510	11	2	set	set	NOUN
ejpam-4510	11	3	theory	theory	NOUN
ejpam-4510	11	4	is	be	AUX
ejpam-4510	11	5	a	a	DET
ejpam-4510	11	6	generalization	generalization	NOUN
ejpam-4510	11	7	of	of	ADP
ejpam-4510	11	8	fuzzy	fuzzy	ADJ
ejpam-4510	11	9	set	set	NOUN
ejpam-4510	11	10	theory	theory	NOUN
ejpam-4510	11	11	.	.	PUNCT
ejpam-4510	12	1	(	(	PUNCT
ejpam-4510	12	2	bipolar	bipolar	ADJ
ejpam-4510	12	3	,	,	PUNCT
ejpam-4510	12	4	interval	interval	NOUN
ejpam-4510	12	5	-	-	PUNCT
ejpam-4510	12	6	valued	value	VERB
ejpam-4510	12	7	)	)	PUNCT
ejpam-4510	12	8	fuzzy	fuzzy	ADJ
ejpam-4510	12	9	set	set	VERB
ejpam-4510	12	10	theory	theory	NOUN
ejpam-4510	12	11	and	and	CCONJ
ejpam-4510	12	12	soft	soft	ADJ
ejpam-4510	12	13	set	set	NOUN
ejpam-4510	12	14	theory	theory	NOUN
ejpam-4510	12	15	are	be	AUX
ejpam-4510	12	16	good	good	ADJ
ejpam-4510	12	17	mathematical	mathematical	ADJ
ejpam-4510	12	18	tools	tool	NOUN
ejpam-4510	12	19	for	for	ADP
ejpam-4510	12	20	dealing	deal	VERB
ejpam-4510	12	21	with	with	ADP
ejpam-4510	12	22	uncertainty	uncertainty	NOUN
ejpam-4510	12	23	in	in	ADP
ejpam-4510	12	24	a	a	DET
ejpam-4510	12	25	parametric	parametric	ADJ
ejpam-4510	12	26	manner	manner	NOUN
ejpam-4510	12	27	,	,	PUNCT
ejpam-4510	12	28	and	and	CCONJ
ejpam-4510	12	29	have	have	VERB
ejpam-4510	12	30	many	many	ADJ
ejpam-4510	12	31	applications	application	NOUN
ejpam-4510	12	32	in	in	ADP
ejpam-4510	12	33	medical	medical	ADJ
ejpam-4510	12	34	diagnosis	diagnosis	NOUN
ejpam-4510	12	35	and	and	CCONJ
ejpam-4510	12	36	decision	decision	NOUN
ejpam-4510	12	37	making	make	VERB
ejpam-4510	12	38	etc	etc	X
ejpam-4510	12	39	.	.	X
ejpam-4510	13	1	in	in	ADP
ejpam-4510	13	2	the	the	DET
ejpam-4510	13	3	information	information	NOUN
ejpam-4510	13	4	age	age	NOUN
ejpam-4510	13	5	,	,	PUNCT
ejpam-4510	13	6	there	there	PRON
ejpam-4510	13	7	is	be	VERB
ejpam-4510	13	8	a	a	DET
ejpam-4510	13	9	growing	grow	VERB
ejpam-4510	13	10	need	need	NOUN
ejpam-4510	13	11	to	to	PART
ejpam-4510	13	12	use	use	VERB
ejpam-4510	13	13	hybrid	hybrid	ADJ
ejpam-4510	13	14	structures	structure	NOUN
ejpam-4510	13	15	in	in	ADP
ejpam-4510	13	16	various	various	ADJ
ejpam-4510	13	17	fields	field	NOUN
ejpam-4510	13	18	.	.	PUNCT
ejpam-4510	14	1	it	it	PRON
ejpam-4510	14	2	has	have	AUX
ejpam-4510	14	3	become	become	VERB
ejpam-4510	14	4	necessary	necessary	ADJ
ejpam-4510	14	5	to	to	PART
ejpam-4510	14	6	study	study	VERB
ejpam-4510	14	7	hybrid	hybrid	ADJ
ejpam-4510	14	8	structures	structure	NOUN
ejpam-4510	14	9	based	base	VERB
ejpam-4510	14	10	on	on	ADP
ejpam-4510	14	11	logical	logical	ADJ
ejpam-4510	14	12	algebra	algebra	NOUN
ejpam-4510	14	13	to	to	PART
ejpam-4510	14	14	present	present	VERB
ejpam-4510	14	15	the	the	DET
ejpam-4510	14	16	mathematical	mathematical	ADJ
ejpam-4510	14	17	tools	tool	NOUN
ejpam-4510	14	18	needed	need	VERB
ejpam-4510	14	19	to	to	PART
ejpam-4510	14	20	meet	meet	VERB
ejpam-4510	14	21	these	these	DET
ejpam-4510	14	22	needs	need	NOUN
ejpam-4510	14	23	.	.	PUNCT
ejpam-4510	15	1	hybrid	hybrid	ADJ
ejpam-4510	15	2	structures	structure	NOUN
ejpam-4510	15	3	dealing	deal	VERB
ejpam-4510	15	4	with	with	ADP
ejpam-4510	15	5	two	two	NUM
ejpam-4510	15	6	or	or	CCONJ
ejpam-4510	15	7	more	more	ADV
ejpam-4510	15	8	different	different	ADJ
ejpam-4510	15	9	concepts	concept	NOUN
ejpam-4510	15	10	at	at	ADP
ejpam-4510	15	11	the	the	DET
ejpam-4510	15	12	same	same	ADJ
ejpam-4510	15	13	time	time	NOUN
ejpam-4510	15	14	have	have	VERB
ejpam-4510	15	15	the	the	DET
ejpam-4510	15	16	advantage	advantage	NOUN
ejpam-4510	15	17	of	of	ADP
ejpam-4510	15	18	reducing	reduce	VERB
ejpam-4510	15	19	the	the	DET
ejpam-4510	15	20	loss	loss	NOUN
ejpam-4510	15	21	of	of	ADP
ejpam-4510	15	22	∗corresponding	∗corresponde	VERB
ejpam-4510	15	23	author	author	NOUN
ejpam-4510	15	24	.	.	PUNCT
ejpam-4510	16	1	doi	doi	NOUN
ejpam-4510	16	2	:	:	PUNCT
ejpam-4510	16	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4510	https://doi.org/10.29020/nybg.ejpam.v15i4.4510	PROPN
ejpam-4510	16	4	email	email	NOUN
ejpam-4510	16	5	addresses	address	VERB
ejpam-4510	16	6	:	:	PUNCT
ejpam-4510	16	7	skywine@gmail.com	skywine@gmail.com	X
ejpam-4510	16	8	(	(	PUNCT
ejpam-4510	16	9	y.	y.	PROPN
ejpam-4510	16	10	b.	b.	PROPN
ejpam-4510	16	11	jun	jun	PROPN
ejpam-4510	16	12	)	)	PUNCT
ejpam-4510	16	13	,	,	PUNCT
ejpam-4510	16	14	sunshine@dongguk.edu	sunshine@dongguk.edu	PROPN
ejpam-4510	16	15	(	(	PUNCT
ejpam-4510	16	16	s.	s.	PROPN
ejpam-4510	16	17	s.	s.	PROPN
ejpam-4510	16	18	ahn	ahn	PROPN
ejpam-4510	16	19	)	)	PUNCT
ejpam-4510	16	20	,	,	PUNCT
ejpam-4510	16	21	ehroh9988@gmail.com	ehroh9988@gmail.com	X
ejpam-4510	16	22	(	(	PUNCT
ejpam-4510	16	23	e.	e.	PROPN
ejpam-4510	16	24	h.	h.	PROPN
ejpam-4510	16	25	roh	roh	PROPN
ejpam-4510	16	26	)	)	PUNCT
ejpam-4510	16	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4510	16	28	1521	1521	NUM
ejpam-4510	16	29	©	©	ADP
ejpam-4510	16	30	2022	2022	NUM
ejpam-4510	16	31	ejpam	ejpam	VERB
ejpam-4510	16	32	all	all	DET
ejpam-4510	16	33	rights	right	NOUN
ejpam-4510	16	34	reserved	reserve	VERB
ejpam-4510	16	35	.	.	PUNCT
ejpam-4510	17	1	y.	y.	PROPN
ejpam-4510	17	2	b.	b.	PROPN
ejpam-4510	17	3	jun	jun	PROPN
ejpam-4510	17	4	,	,	PUNCT
ejpam-4510	17	5	s.	s.	PROPN
ejpam-4510	17	6	s.	s.	PROPN
ejpam-4510	17	7	ahn	ahn	PROPN
ejpam-4510	17	8	and	and	CCONJ
ejpam-4510	17	9	e.	e.	PROPN
ejpam-4510	17	10	h.	h.	PROPN
ejpam-4510	17	11	roh	roh	PROPN
ejpam-4510	17	12	/	/	SYM
ejpam-4510	17	13	eur	eur	PROPN
ejpam-4510	17	14	.	.	PUNCT
ejpam-4510	18	1	j.	j.	PROPN
ejpam-4510	18	2	pure	pure	PROPN
ejpam-4510	18	3	appl	appl	PROPN
ejpam-4510	18	4	.	.	PROPN
ejpam-4510	18	5	math	math	PROPN
ejpam-4510	18	6	,	,	PUNCT
ejpam-4510	18	7	15	15	NUM
ejpam-4510	18	8	(	(	PUNCT
ejpam-4510	18	9	4	4	NUM
ejpam-4510	18	10	)	)	PUNCT
ejpam-4510	18	11	(	(	PUNCT
ejpam-4510	18	12	2022	2022	NUM
ejpam-4510	18	13	)	)	PUNCT
ejpam-4510	18	14	,	,	PUNCT
ejpam-4510	18	15	1521	1521	NUM
ejpam-4510	18	16	-	-	SYM
ejpam-4510	18	17	1535	1535	NUM
ejpam-4510	18	18	1522	1522	NUM
ejpam-4510	18	19	information	information	NOUN
ejpam-4510	18	20	when	when	SCONJ
ejpam-4510	18	21	addressing	address	VERB
ejpam-4510	18	22	uncertainty	uncertainty	NOUN
ejpam-4510	18	23	issues	issue	NOUN
ejpam-4510	18	24	.	.	PUNCT
ejpam-4510	19	1	in	in	ADP
ejpam-4510	19	2	line	line	NOUN
ejpam-4510	19	3	with	with	ADP
ejpam-4510	19	4	this	this	DET
ejpam-4510	19	5	background	background	NOUN
ejpam-4510	19	6	and	and	CCONJ
ejpam-4510	19	7	need	need	VERB
ejpam-4510	19	8	,	,	PUNCT
ejpam-4510	19	9	jun	jun	PROPN
ejpam-4510	20	1	[	[	X
ejpam-4510	20	2	5	5	NUM
ejpam-4510	20	3	]	]	PUNCT
ejpam-4510	20	4	introduced	introduce	VERB
ejpam-4510	20	5	a	a	DET
ejpam-4510	20	6	new	new	ADJ
ejpam-4510	20	7	type	type	NOUN
ejpam-4510	20	8	of	of	ADP
ejpam-4510	20	9	hybrid	hybrid	ADJ
ejpam-4510	20	10	structure	structure	NOUN
ejpam-4510	20	11	called	call	VERB
ejpam-4510	20	12	dokdo	dokdo	NOUN
ejpam-4510	20	13	structure	structure	NOUN
ejpam-4510	20	14	,	,	PUNCT
ejpam-4510	20	15	where	where	SCONJ
ejpam-4510	20	16	“	"	PUNCT
ejpam-4510	20	17	dokdo	dokdo	PROPN
ejpam-4510	20	18	”	"	PUNCT
ejpam-4510	20	19	is	be	AUX
ejpam-4510	20	20	the	the	DET
ejpam-4510	20	21	name	name	NOUN
ejpam-4510	20	22	of	of	ADP
ejpam-4510	20	23	the	the	DET
ejpam-4510	20	24	most	most	ADV
ejpam-4510	20	25	beautiful	beautiful	ADJ
ejpam-4510	20	26	island	island	NOUN
ejpam-4510	20	27	in	in	ADP
ejpam-4510	20	28	korea	korea	PROPN
ejpam-4510	20	29	,	,	PUNCT
ejpam-4510	20	30	using	use	VERB
ejpam-4510	20	31	the	the	DET
ejpam-4510	20	32	concepts	concept	NOUN
ejpam-4510	20	33	of	of	ADP
ejpam-4510	20	34	bipolar	bipolar	ADJ
ejpam-4510	20	35	fuzzy	fuzzy	ADJ
ejpam-4510	20	36	set	set	NOUN
ejpam-4510	20	37	,	,	PUNCT
ejpam-4510	20	38	soft	soft	ADJ
ejpam-4510	20	39	set	set	NOUN
ejpam-4510	20	40	and	and	CCONJ
ejpam-4510	20	41	interval	interval	NOUN
ejpam-4510	20	42	-	-	PUNCT
ejpam-4510	20	43	valued	value	VERB
ejpam-4510	20	44	fuzzy	fuzzy	ADJ
ejpam-4510	20	45	and	and	CCONJ
ejpam-4510	20	46	first	first	ADV
ejpam-4510	20	47	applied	apply	VERB
ejpam-4510	20	48	it	it	PRON
ejpam-4510	20	49	to	to	ADP
ejpam-4510	20	50	the	the	DET
ejpam-4510	20	51	algebraic	algebraic	ADJ
ejpam-4510	20	52	structure	structure	NOUN
ejpam-4510	20	53	bck	bck	PROPN
ejpam-4510	20	54	/	/	SYM
ejpam-4510	20	55	bcialgebras	bcialgebra	NOUN
ejpam-4510	20	56	(	(	PUNCT
ejpam-4510	20	57	see	see	VERB
ejpam-4510	20	58	[	[	X
ejpam-4510	20	59	5	5	NUM
ejpam-4510	20	60	,	,	PUNCT
ejpam-4510	20	61	6	6	NUM
ejpam-4510	20	62	]	]	NUM
ejpam-4510	20	63	)	)	PUNCT
ejpam-4510	20	64	.	.	PUNCT
ejpam-4510	21	1	in	in	ADP
ejpam-4510	21	2	2007	2007	NUM
ejpam-4510	21	3	,	,	PUNCT
ejpam-4510	21	4	h.	h.	PROPN
ejpam-4510	21	5	s.	s.	PROPN
ejpam-4510	21	6	kim	kim	PROPN
ejpam-4510	21	7	and	and	CCONJ
ejpam-4510	21	8	y.	y.	PROPN
ejpam-4510	21	9	h.	h.	PROPN
ejpam-4510	21	10	kim	kim	PROPN
ejpam-4510	21	11	[	[	X
ejpam-4510	21	12	7	7	X
ejpam-4510	21	13	]	]	PUNCT
ejpam-4510	21	14	introduced	introduce	VERB
ejpam-4510	21	15	the	the	DET
ejpam-4510	21	16	notion	notion	NOUN
ejpam-4510	21	17	of	of	ADP
ejpam-4510	21	18	a	a	DET
ejpam-4510	21	19	be	be	NOUN
ejpam-4510	21	20	-	-	PUNCT
ejpam-4510	21	21	algebra	algebra	NOUN
ejpam-4510	21	22	as	as	ADP
ejpam-4510	21	23	a	a	DET
ejpam-4510	21	24	dualization	dualization	NOUN
ejpam-4510	21	25	of	of	ADP
ejpam-4510	21	26	a	a	DET
ejpam-4510	21	27	generalization	generalization	NOUN
ejpam-4510	21	28	of	of	ADP
ejpam-4510	21	29	a	a	DET
ejpam-4510	21	30	bck	bck	NOUN
ejpam-4510	21	31	-	-	PUNCT
ejpam-4510	21	32	algebra	algebra	NOUN
ejpam-4510	21	33	.	.	PUNCT
ejpam-4510	22	1	they	they	PRON
ejpam-4510	22	2	defined	define	VERB
ejpam-4510	22	3	and	and	CCONJ
ejpam-4510	22	4	studied	study	VERB
ejpam-4510	22	5	the	the	DET
ejpam-4510	22	6	concept	concept	NOUN
ejpam-4510	22	7	of	of	ADP
ejpam-4510	22	8	a	a	DET
ejpam-4510	22	9	filter	filter	NOUN
ejpam-4510	22	10	in	in	ADP
ejpam-4510	22	11	be	be	NOUN
ejpam-4510	22	12	-	-	PUNCT
ejpam-4510	22	13	algebras	algebra	NOUN
ejpam-4510	22	14	.	.	PUNCT
ejpam-4510	23	1	in	in	ADP
ejpam-4510	23	2	[	[	X
ejpam-4510	23	3	1	1	NUM
ejpam-4510	23	4	,	,	PUNCT
ejpam-4510	23	5	11	11	NUM
ejpam-4510	23	6	]	]	PUNCT
ejpam-4510	23	7	,	,	PUNCT
ejpam-4510	23	8	s.	s.	PROPN
ejpam-4510	23	9	s.	s.	PROPN
ejpam-4510	23	10	ahn	ahn	PROPN
ejpam-4510	23	11	et	et	PROPN
ejpam-4510	23	12	al	al	PROPN
ejpam-4510	23	13	.	.	PROPN
ejpam-4510	23	14	and	and	CCONJ
ejpam-4510	23	15	a.	a.	PROPN
ejpam-4510	23	16	rezaei	rezaei	PROPN
ejpam-4510	23	17	et	et	PROPN
ejpam-4510	23	18	al	al	PROPN
ejpam-4510	23	19	.	.	PROPN
ejpam-4510	23	20	studied	study	VERB
ejpam-4510	23	21	fuzzy	fuzzy	ADJ
ejpam-4510	23	22	be	be	NOUN
ejpam-4510	23	23	-	-	PUNCT
ejpam-4510	23	24	algebras	algebra	NOUN
ejpam-4510	23	25	.	.	PUNCT
ejpam-4510	24	1	g.	g.	PROPN
ejpam-4510	24	2	dymek	dymek	PROPN
ejpam-4510	24	3	and	and	CCONJ
ejpam-4510	24	4	a.	a.	PROPN
ejpam-4510	24	5	walendziak	walendziak	PROPN
ejpam-4510	25	1	[	[	X
ejpam-4510	25	2	2	2	NUM
ejpam-4510	25	3	]	]	PUNCT
ejpam-4510	25	4	developed	develop	VERB
ejpam-4510	25	5	the	the	DET
ejpam-4510	25	6	theory	theory	NOUN
ejpam-4510	25	7	of	of	ADP
ejpam-4510	25	8	fuzzy	fuzzy	ADJ
ejpam-4510	25	9	filters	filter	NOUN
ejpam-4510	25	10	in	in	ADP
ejpam-4510	25	11	be	be	AUX
ejpam-4510	25	12	-	-	PUNCT
ejpam-4510	25	13	algebras	algebra	NOUN
ejpam-4510	25	14	.	.	PUNCT
ejpam-4510	26	1	for	for	ADP
ejpam-4510	26	2	the	the	DET
ejpam-4510	26	3	purpose	purpose	NOUN
ejpam-4510	26	4	of	of	ADP
ejpam-4510	26	5	applying	apply	VERB
ejpam-4510	26	6	the	the	DET
ejpam-4510	26	7	dokdo	dokdo	NOUN
ejpam-4510	26	8	structure	structure	NOUN
ejpam-4510	26	9	to	to	PART
ejpam-4510	26	10	be	be	AUX
ejpam-4510	26	11	-	-	PUNCT
ejpam-4510	26	12	algebra	algebra	NOUN
ejpam-4510	26	13	,	,	PUNCT
ejpam-4510	26	14	we	we	PRON
ejpam-4510	26	15	introduce	introduce	VERB
ejpam-4510	26	16	(	(	PUNCT
ejpam-4510	26	17	weak	weak	ADJ
ejpam-4510	26	18	)	)	PUNCT
ejpam-4510	26	19	dokdo	dokdo	NOUN
ejpam-4510	26	20	be	be	NOUN
ejpam-4510	26	21	-	-	PUNCT
ejpam-4510	26	22	subalgebra	subalgebra	NOUN
ejpam-4510	26	23	and	and	CCONJ
ejpam-4510	26	24	dokdo	dokdo	NOUN
ejpam-4510	26	25	be	be	NOUN
ejpam-4510	26	26	-	-	PUNCT
ejpam-4510	26	27	filter	filter	NOUN
ejpam-4510	26	28	and	and	CCONJ
ejpam-4510	26	29	study	study	VERB
ejpam-4510	26	30	its	its	PRON
ejpam-4510	26	31	characteristics	characteristic	NOUN
ejpam-4510	26	32	.	.	PUNCT
ejpam-4510	27	1	we	we	PRON
ejpam-4510	27	2	investigate	investigate	VERB
ejpam-4510	27	3	the	the	DET
ejpam-4510	27	4	relationship	relationship	NOUN
ejpam-4510	27	5	between	between	ADP
ejpam-4510	27	6	weak	weak	ADJ
ejpam-4510	27	7	dokdo	dokdo	NOUN
ejpam-4510	27	8	be	be	NOUN
ejpam-4510	27	9	-	-	PUNCT
ejpam-4510	27	10	subalgebra	subalgebra	NOUN
ejpam-4510	27	11	,	,	PUNCT
ejpam-4510	27	12	dokdo	dokdo	PROPN
ejpam-4510	27	13	be	be	NOUN
ejpam-4510	27	14	-	-	PUNCT
ejpam-4510	27	15	subalgebra	subalgebra	NOUN
ejpam-4510	27	16	and	and	CCONJ
ejpam-4510	27	17	dokdo	dokdo	VERB
ejpam-4510	27	18	be	be	NOUN
ejpam-4510	27	19	-	-	PUNCT
ejpam-4510	27	20	filter	filter	NOUN
ejpam-4510	27	21	.	.	PUNCT
ejpam-4510	28	1	we	we	PRON
ejpam-4510	28	2	explore	explore	VERB
ejpam-4510	28	3	the	the	DET
ejpam-4510	28	4	conditions	condition	NOUN
ejpam-4510	28	5	under	under	ADP
ejpam-4510	28	6	which	which	PRON
ejpam-4510	28	7	dokdo	dokdo	NOUN
ejpam-4510	28	8	structure	structure	NOUN
ejpam-4510	28	9	can	can	AUX
ejpam-4510	28	10	be	be	AUX
ejpam-4510	28	11	weak	weak	ADJ
ejpam-4510	28	12	dokdo	dokdo	NOUN
ejpam-4510	28	13	be	be	NOUN
ejpam-4510	28	14	-	-	PUNCT
ejpam-4510	28	15	subalgebra	subalgebra	NOUN
ejpam-4510	28	16	and	and	CCONJ
ejpam-4510	28	17	dokdo	dokdo	VERB
ejpam-4510	28	18	be	be	NOUN
ejpam-4510	28	19	-	-	PUNCT
ejpam-4510	28	20	filter	filter	NOUN
ejpam-4510	28	21	,	,	PUNCT
ejpam-4510	28	22	and	and	CCONJ
ejpam-4510	28	23	the	the	DET
ejpam-4510	28	24	condition	condition	NOUN
ejpam-4510	28	25	under	under	ADP
ejpam-4510	28	26	which	which	PRON
ejpam-4510	28	27	weak	weak	ADJ
ejpam-4510	28	28	dokdo	dokdo	ADJ
ejpam-4510	28	29	besubalgebra	besubalgebra	NOUN
ejpam-4510	28	30	can	can	AUX
ejpam-4510	28	31	be	be	AUX
ejpam-4510	28	32	dokdo	dokdo	VERB
ejpam-4510	28	33	be	be	NOUN
ejpam-4510	28	34	-	-	PUNCT
ejpam-4510	28	35	subalgebra	subalgebra	NOUN
ejpam-4510	28	36	.	.	PUNCT
ejpam-4510	29	1	we	we	PRON
ejpam-4510	29	2	discuss	discuss	VERB
ejpam-4510	29	3	the	the	DET
ejpam-4510	29	4	characterization	characterization	NOUN
ejpam-4510	29	5	of	of	ADP
ejpam-4510	29	6	dokdo	dokdo	PROPN
ejpam-4510	29	7	befilter	befilter	NOUN
ejpam-4510	29	8	.	.	PUNCT
ejpam-4510	30	1	2	2	X
ejpam-4510	30	2	.	.	NUM
ejpam-4510	30	3	preliminaries	preliminary	NOUN
ejpam-4510	30	4	2.1	2.1	NUM
ejpam-4510	30	5	.	.	PUNCT
ejpam-4510	30	6	basic	basic	ADJ
ejpam-4510	30	7	concepts	concept	NOUN
ejpam-4510	30	8	about	about	ADP
ejpam-4510	30	9	be	be	AUX
ejpam-4510	30	10	-	-	PUNCT
ejpam-4510	30	11	algebras	algebras	X
ejpam-4510	30	12	a	a	DET
ejpam-4510	30	13	be	be	NOUN
ejpam-4510	30	14	-	-	PUNCT
ejpam-4510	30	15	algebra	algebra	NOUN
ejpam-4510	30	16	(	(	PUNCT
ejpam-4510	30	17	see	see	VERB
ejpam-4510	30	18	[	[	X
ejpam-4510	30	19	7	7	NUM
ejpam-4510	30	20	]	]	PUNCT
ejpam-4510	30	21	)	)	PUNCT
ejpam-4510	30	22	is	be	AUX
ejpam-4510	30	23	defined	define	VERB
ejpam-4510	30	24	to	to	PART
ejpam-4510	30	25	be	be	AUX
ejpam-4510	30	26	a	a	DET
ejpam-4510	30	27	set	set	NOUN
ejpam-4510	30	28	x	x	PUNCT
ejpam-4510	30	29	together	together	ADV
ejpam-4510	30	30	with	with	ADP
ejpam-4510	30	31	a	a	DET
ejpam-4510	30	32	binary	binary	ADJ
ejpam-4510	30	33	operation	operation	NOUN
ejpam-4510	30	34	“	"	PUNCT
ejpam-4510	30	35	∗	∗	NOUN
ejpam-4510	30	36	”	"	PUNCT
ejpam-4510	30	37	and	and	CCONJ
ejpam-4510	30	38	a	a	DET
ejpam-4510	30	39	special	special	ADJ
ejpam-4510	30	40	element	element	NOUN
ejpam-4510	30	41	“	"	PUNCT
ejpam-4510	30	42	1	1	NUM
ejpam-4510	30	43	”	"	PUNCT
ejpam-4510	30	44	satisfying	satisfy	VERB
ejpam-4510	30	45	the	the	DET
ejpam-4510	30	46	conditions	condition	NOUN
ejpam-4510	30	47	:	:	PUNCT
ejpam-4510	30	48	(	(	PUNCT
ejpam-4510	30	49	be1	be1	NOUN
ejpam-4510	30	50	)	)	PUNCT
ejpam-4510	30	51	(	(	PUNCT
ejpam-4510	30	52	∀a	∀a	NOUN
ejpam-4510	30	53	∈	∈	NOUN
ejpam-4510	30	54	x	x	NOUN
ejpam-4510	30	55	)	)	PUNCT
ejpam-4510	30	56	(	(	PUNCT
ejpam-4510	30	57	a	a	DET
ejpam-4510	30	58	∗	∗	NOUN
ejpam-4510	30	59	a	a	DET
ejpam-4510	30	60	=	=	NOUN
ejpam-4510	30	61	1	1	NUM
ejpam-4510	30	62	)	)	PUNCT
ejpam-4510	30	63	,	,	PUNCT
ejpam-4510	30	64	(	(	PUNCT
ejpam-4510	30	65	be2	be2	PROPN
ejpam-4510	30	66	)	)	PUNCT
ejpam-4510	30	67	(	(	PUNCT
ejpam-4510	30	68	∀a	∀a	NOUN
ejpam-4510	30	69	∈	∈	NOUN
ejpam-4510	30	70	x	x	NOUN
ejpam-4510	30	71	)	)	PUNCT
ejpam-4510	30	72	(	(	PUNCT
ejpam-4510	30	73	a	a	DET
ejpam-4510	30	74	∗	∗	NOUN
ejpam-4510	30	75	1	1	NUM
ejpam-4510	30	76	=	=	SYM
ejpam-4510	30	77	1	1	NUM
ejpam-4510	30	78	)	)	PUNCT
ejpam-4510	30	79	,	,	PUNCT
ejpam-4510	30	80	(	(	PUNCT
ejpam-4510	30	81	be3	be3	PROPN
ejpam-4510	30	82	)	)	PUNCT
ejpam-4510	30	83	(	(	PUNCT
ejpam-4510	30	84	∀a	∀a	NOUN
ejpam-4510	30	85	∈	∈	NOUN
ejpam-4510	30	86	x	x	NOUN
ejpam-4510	30	87	)	)	PUNCT
ejpam-4510	30	88	(	(	PUNCT
ejpam-4510	30	89	1	1	NUM
ejpam-4510	30	90	∗	∗	NOUN
ejpam-4510	30	91	a	a	DET
ejpam-4510	30	92	=	=	NOUN
ejpam-4510	30	93	a	a	NOUN
ejpam-4510	30	94	)	)	PUNCT
ejpam-4510	30	95	,	,	PUNCT
ejpam-4510	30	96	(	(	PUNCT
ejpam-4510	30	97	be4	be4	NOUN
ejpam-4510	30	98	)	)	PUNCT
ejpam-4510	30	99	(	(	PUNCT
ejpam-4510	30	100	∀a	∀a	X
ejpam-4510	30	101	,	,	PUNCT
ejpam-4510	30	102	b	b	NOUN
ejpam-4510	30	103	,	,	PUNCT
ejpam-4510	30	104	c	c	PROPN
ejpam-4510	30	105	∈	∈	PROPN
ejpam-4510	30	106	x	x	X
ejpam-4510	30	107	)	)	PUNCT
ejpam-4510	30	108	(	(	PUNCT
ejpam-4510	30	109	a	a	DET
ejpam-4510	30	110	∗	∗	NOUN
ejpam-4510	30	111	(	(	PUNCT
ejpam-4510	30	112	b	b	NOUN
ejpam-4510	30	113	∗	∗	NOUN
ejpam-4510	30	114	c	c	NOUN
ejpam-4510	30	115	)	)	PUNCT
ejpam-4510	30	116	=	=	SYM
ejpam-4510	30	117	b	b	NOUN
ejpam-4510	30	118	∗	∗	NOUN
ejpam-4510	30	119	(	(	PUNCT
ejpam-4510	30	120	a	a	DET
ejpam-4510	30	121	∗	∗	NOUN
ejpam-4510	30	122	c	c	NOUN
ejpam-4510	30	123	)	)	PUNCT
ejpam-4510	30	124	)	)	PUNCT
ejpam-4510	30	125	.	.	PUNCT
ejpam-4510	31	1	the	the	DET
ejpam-4510	31	2	order	order	NOUN
ejpam-4510	31	3	relation	relation	NOUN
ejpam-4510	31	4	“	"	PUNCT
ejpam-4510	31	5	≤	≤	NUM
ejpam-4510	31	6	”	"	PUNCT
ejpam-4510	31	7	in	in	ADP
ejpam-4510	31	8	a	a	DET
ejpam-4510	31	9	be	be	NOUN
ejpam-4510	31	10	-	-	PUNCT
ejpam-4510	31	11	algebra	algebra	NOUN
ejpam-4510	31	12	x	x	PUNCT
ejpam-4510	31	13	is	be	AUX
ejpam-4510	31	14	defined	define	VERB
ejpam-4510	31	15	as	as	SCONJ
ejpam-4510	31	16	follows	follow	VERB
ejpam-4510	31	17	:	:	PUNCT
ejpam-4510	31	18	(	(	PUNCT
ejpam-4510	31	19	∀a	∀a	X
ejpam-4510	31	20	,	,	PUNCT
ejpam-4510	31	21	b	b	PROPN
ejpam-4510	31	22	∈	∈	PROPN
ejpam-4510	31	23	x)(a	x)(a	PUNCT
ejpam-4510	32	1	≤	≤	PROPN
ejpam-4510	32	2	b	b	X
ejpam-4510	32	3	⇔	⇔	X
ejpam-4510	32	4	a	a	DET
ejpam-4510	32	5	∗	∗	NOUN
ejpam-4510	32	6	b	b	NOUN
ejpam-4510	32	7	=	=	SYM
ejpam-4510	32	8	1	1	NUM
ejpam-4510	32	9	)	)	PUNCT
ejpam-4510	32	10	.	.	PUNCT
ejpam-4510	33	1	(	(	PUNCT
ejpam-4510	33	2	1	1	X
ejpam-4510	33	3	)	)	PUNCT
ejpam-4510	33	4	every	every	DET
ejpam-4510	33	5	be	be	NOUN
ejpam-4510	33	6	-	-	PUNCT
ejpam-4510	33	7	algebra	algebra	NOUN
ejpam-4510	33	8	x	x	PRON
ejpam-4510	33	9	satisfies	satisfy	VERB
ejpam-4510	33	10	the	the	DET
ejpam-4510	33	11	following	follow	VERB
ejpam-4510	33	12	conditions	condition	NOUN
ejpam-4510	33	13	(	(	PUNCT
ejpam-4510	33	14	see	see	VERB
ejpam-4510	33	15	[	[	X
ejpam-4510	33	16	7	7	NUM
ejpam-4510	33	17	]	]	NUM
ejpam-4510	33	18	):	):	PUNCT
ejpam-4510	33	19	(	(	PUNCT
ejpam-4510	33	20	∀a	∀a	NOUN
ejpam-4510	33	21	,	,	PUNCT
ejpam-4510	33	22	b	b	PROPN
ejpam-4510	33	23	∈	∈	PROPN
ejpam-4510	33	24	x	x	X
ejpam-4510	33	25	)	)	PUNCT
ejpam-4510	33	26	(	(	PUNCT
ejpam-4510	33	27	a	a	DET
ejpam-4510	33	28	∗	∗	NOUN
ejpam-4510	33	29	(	(	PUNCT
ejpam-4510	33	30	b	b	NOUN
ejpam-4510	33	31	∗	∗	X
ejpam-4510	33	32	a	a	NOUN
ejpam-4510	33	33	)	)	PUNCT
ejpam-4510	33	34	=	=	SYM
ejpam-4510	33	35	1	1	NUM
ejpam-4510	33	36	)	)	PUNCT
ejpam-4510	33	37	,	,	PUNCT
ejpam-4510	33	38	(	(	PUNCT
ejpam-4510	33	39	2	2	X
ejpam-4510	33	40	)	)	PUNCT
ejpam-4510	33	41	(	(	PUNCT
ejpam-4510	33	42	∀a	∀a	X
ejpam-4510	33	43	,	,	PUNCT
ejpam-4510	33	44	b	b	PROPN
ejpam-4510	33	45	∈	∈	PROPN
ejpam-4510	33	46	x	x	X
ejpam-4510	33	47	)	)	PUNCT
ejpam-4510	33	48	(	(	PUNCT
ejpam-4510	33	49	a	a	DET
ejpam-4510	33	50	∗	∗	NOUN
ejpam-4510	33	51	(	(	PUNCT
ejpam-4510	33	52	(	(	PUNCT
ejpam-4510	33	53	a	a	DET
ejpam-4510	33	54	∗	∗	NOUN
ejpam-4510	33	55	b	b	NOUN
ejpam-4510	33	56	)	)	PUNCT
ejpam-4510	33	57	∗	∗	PROPN
ejpam-4510	33	58	b	b	NOUN
ejpam-4510	33	59	)	)	PUNCT
ejpam-4510	33	60	=	=	SYM
ejpam-4510	33	61	1	1	NUM
ejpam-4510	33	62	)	)	PUNCT
ejpam-4510	33	63	.	.	PUNCT
ejpam-4510	34	1	(	(	PUNCT
ejpam-4510	34	2	3	3	X
ejpam-4510	34	3	)	)	PUNCT
ejpam-4510	34	4	a	a	DET
ejpam-4510	34	5	be	be	NOUN
ejpam-4510	34	6	-	-	PUNCT
ejpam-4510	34	7	algebra	algebra	NOUN
ejpam-4510	34	8	x	x	PUNCT
ejpam-4510	34	9	is	be	AUX
ejpam-4510	34	10	said	say	VERB
ejpam-4510	34	11	to	to	PART
ejpam-4510	34	12	be	be	AUX
ejpam-4510	34	13	self	self	NOUN
ejpam-4510	34	14	-	-	PUNCT
ejpam-4510	34	15	distributive	distributive	ADJ
ejpam-4510	34	16	(	(	PUNCT
ejpam-4510	34	17	see	see	VERB
ejpam-4510	34	18	[	[	X
ejpam-4510	34	19	7	7	NUM
ejpam-4510	34	20	]	]	PUNCT
ejpam-4510	34	21	)	)	PUNCT
ejpam-4510	34	22	if	if	SCONJ
ejpam-4510	34	23	it	it	PRON
ejpam-4510	34	24	satisfies	satisfy	VERB
ejpam-4510	34	25	:	:	PUNCT
ejpam-4510	34	26	(	(	PUNCT
ejpam-4510	34	27	∀x	∀x	X
ejpam-4510	34	28	,	,	PUNCT
ejpam-4510	34	29	b	b	NOUN
ejpam-4510	34	30	,	,	PUNCT
ejpam-4510	34	31	c	c	PROPN
ejpam-4510	34	32	∈	∈	PROPN
ejpam-4510	34	33	x	x	X
ejpam-4510	34	34	)	)	PUNCT
ejpam-4510	34	35	(	(	PUNCT
ejpam-4510	34	36	x	x	SYM
ejpam-4510	34	37	∗	∗	NOUN
ejpam-4510	34	38	(	(	PUNCT
ejpam-4510	34	39	b	b	NOUN
ejpam-4510	34	40	∗	∗	NOUN
ejpam-4510	34	41	c	c	NOUN
ejpam-4510	34	42	)	)	PUNCT
ejpam-4510	34	43	=	=	SYM
ejpam-4510	35	1	(	(	PUNCT
ejpam-4510	35	2	x	x	NOUN
ejpam-4510	35	3	∗	∗	NUM
ejpam-4510	35	4	b	b	NOUN
ejpam-4510	35	5	)	)	PUNCT
ejpam-4510	35	6	∗	∗	NOUN
ejpam-4510	35	7	(	(	PUNCT
ejpam-4510	35	8	x	x	X
ejpam-4510	35	9	∗	∗	NOUN
ejpam-4510	35	10	c	c	NOUN
ejpam-4510	35	11	)	)	PUNCT
ejpam-4510	35	12	)	)	PUNCT
ejpam-4510	35	13	.	.	PUNCT
ejpam-4510	36	1	(	(	PUNCT
ejpam-4510	36	2	4	4	X
ejpam-4510	36	3	)	)	PUNCT
ejpam-4510	36	4	a	a	DET
ejpam-4510	36	5	subset	subset	NOUN
ejpam-4510	36	6	a	a	PRON
ejpam-4510	36	7	of	of	ADP
ejpam-4510	36	8	a	a	DET
ejpam-4510	36	9	be	be	NOUN
ejpam-4510	36	10	-	-	PUNCT
ejpam-4510	36	11	algebra	algebra	NOUN
ejpam-4510	36	12	x	x	PUNCT
ejpam-4510	36	13	is	be	AUX
ejpam-4510	36	14	called	call	VERB
ejpam-4510	36	15	•	•	ADP
ejpam-4510	36	16	a	a	DET
ejpam-4510	36	17	be	be	NOUN
ejpam-4510	36	18	-	-	PUNCT
ejpam-4510	36	19	subalgebra	subalgebra	NOUN
ejpam-4510	36	20	of	of	ADP
ejpam-4510	36	21	x	x	PART
ejpam-4510	36	22	(	(	PUNCT
ejpam-4510	36	23	see	see	VERB
ejpam-4510	36	24	[	[	X
ejpam-4510	36	25	7	7	NUM
ejpam-4510	36	26	]	]	PUNCT
ejpam-4510	36	27	)	)	PUNCT
ejpam-4510	36	28	if	if	SCONJ
ejpam-4510	36	29	it	it	PRON
ejpam-4510	36	30	satisfies	satisfy	VERB
ejpam-4510	36	31	:	:	PUNCT
ejpam-4510	36	32	(	(	PUNCT
ejpam-4510	36	33	∀a	∀a	NOUN
ejpam-4510	36	34	,	,	PUNCT
ejpam-4510	36	35	b	b	PROPN
ejpam-4510	36	36	∈	∈	PROPN
ejpam-4510	36	37	a)(a	a)(a	NOUN
ejpam-4510	36	38	∗	∗	NOUN
ejpam-4510	36	39	b	b	PROPN
ejpam-4510	36	40	∈	∈	PROPN
ejpam-4510	36	41	a	a	PRON
ejpam-4510	36	42	)	)	PUNCT
ejpam-4510	36	43	,	,	PUNCT
ejpam-4510	36	44	(	(	PUNCT
ejpam-4510	36	45	5	5	X
ejpam-4510	36	46	)	)	PUNCT
ejpam-4510	36	47	y.	y.	PROPN
ejpam-4510	36	48	b.	b.	PROPN
ejpam-4510	36	49	jun	jun	PROPN
ejpam-4510	36	50	,	,	PUNCT
ejpam-4510	36	51	s.	s.	PROPN
ejpam-4510	36	52	s.	s.	PROPN
ejpam-4510	36	53	ahn	ahn	PROPN
ejpam-4510	36	54	and	and	CCONJ
ejpam-4510	36	55	e.	e.	PROPN
ejpam-4510	36	56	h.	h.	PROPN
ejpam-4510	36	57	roh	roh	PROPN
ejpam-4510	36	58	/	/	SYM
ejpam-4510	36	59	eur	eur	PROPN
ejpam-4510	36	60	.	.	PUNCT
ejpam-4510	37	1	j.	j.	PROPN
ejpam-4510	37	2	pure	pure	PROPN
ejpam-4510	37	3	appl	appl	PROPN
ejpam-4510	37	4	.	.	PROPN
ejpam-4510	37	5	math	math	PROPN
ejpam-4510	37	6	,	,	PUNCT
ejpam-4510	37	7	15	15	NUM
ejpam-4510	37	8	(	(	PUNCT
ejpam-4510	37	9	4	4	NUM
ejpam-4510	37	10	)	)	PUNCT
ejpam-4510	37	11	(	(	PUNCT
ejpam-4510	37	12	2022	2022	NUM
ejpam-4510	37	13	)	)	PUNCT
ejpam-4510	37	14	,	,	PUNCT
ejpam-4510	37	15	1521	1521	NUM
ejpam-4510	37	16	-	-	SYM
ejpam-4510	37	17	1535	1535	NUM
ejpam-4510	37	18	1523	1523	NUM
ejpam-4510	37	19	•	•	ADP
ejpam-4510	37	20	an	an	DET
ejpam-4510	37	21	n	n	ADV
ejpam-4510	37	22	-	-	ADJ
ejpam-4510	37	23	fold	fold	ADJ
ejpam-4510	37	24	weak	weak	ADJ
ejpam-4510	37	25	be	be	NOUN
ejpam-4510	37	26	-	-	PUNCT
ejpam-4510	37	27	subalgebra	subalgebra	NOUN
ejpam-4510	37	28	of	of	ADP
ejpam-4510	37	29	x	x	PART
ejpam-4510	37	30	(	(	PUNCT
ejpam-4510	37	31	see	see	VERB
ejpam-4510	37	32	[	[	X
ejpam-4510	37	33	4	4	NUM
ejpam-4510	37	34	]	]	PUNCT
ejpam-4510	37	35	)	)	PUNCT
ejpam-4510	37	36	if	if	SCONJ
ejpam-4510	37	37	it	it	PRON
ejpam-4510	37	38	satisfies	satisfy	VERB
ejpam-4510	37	39	:	:	PUNCT
ejpam-4510	37	40	(	(	PUNCT
ejpam-4510	37	41	∀a	∀a	NOUN
ejpam-4510	37	42	,	,	PUNCT
ejpam-4510	37	43	b	b	X
ejpam-4510	37	44	∈	∈	PROPN
ejpam-4510	37	45	a)(an	a)(an	PROPN
ejpam-4510	37	46	∗	∗	NOUN
ejpam-4510	37	47	b	b	PROPN
ejpam-4510	37	48	∈	∈	PROPN
ejpam-4510	37	49	a	a	PRON
ejpam-4510	37	50	)	)	PUNCT
ejpam-4510	37	51	,	,	PUNCT
ejpam-4510	37	52	(	(	PUNCT
ejpam-4510	37	53	6	6	NUM
ejpam-4510	37	54	)	)	PUNCT
ejpam-4510	37	55	where	where	SCONJ
ejpam-4510	37	56	n	n	PRON
ejpam-4510	37	57	is	be	AUX
ejpam-4510	37	58	a	a	DET
ejpam-4510	37	59	natural	natural	ADJ
ejpam-4510	37	60	number	number	NOUN
ejpam-4510	37	61	with	with	ADP
ejpam-4510	37	62	n	n	PRON
ejpam-4510	37	63	≥	≥	NUM
ejpam-4510	37	64	2	2	NUM
ejpam-4510	37	65	and	and	CCONJ
ejpam-4510	37	66	an	an	DET
ejpam-4510	37	67	∗	∗	NOUN
ejpam-4510	37	68	b	b	X
ejpam-4510	37	69	=	=	PUNCT
ejpam-4510	37	70	a	a	DET
ejpam-4510	37	71	∗	∗	NOUN
ejpam-4510	37	72	(	(	PUNCT
ejpam-4510	37	73	a	a	DET
ejpam-4510	37	74	∗	∗	NOUN
ejpam-4510	37	75	(	(	PUNCT
ejpam-4510	37	76	·	·	PUNCT
ejpam-4510	37	77	·	·	PUNCT
ejpam-4510	37	78	·	·	PUNCT
ejpam-4510	37	79	(	(	PUNCT
ejpam-4510	37	80	a	a	DET
ejpam-4510	37	81	∗	∗	NOUN
ejpam-4510	37	82	b	b	NOUN
ejpam-4510	37	83	)	)	PUNCT
ejpam-4510	37	84	·	·	PUNCT
ejpam-4510	37	85	·	·	PUNCT
ejpam-4510	37	86	·	·	PUNCT
ejpam-4510	37	87	)	)	PUNCT
ejpam-4510	37	88	)	)	PUNCT
ejpam-4510	38	1	in	in	ADP
ejpam-4510	38	2	which	which	PRON
ejpam-4510	38	3	a	a	DET
ejpam-4510	38	4	appears	appear	NOUN
ejpam-4510	38	5	n	n	PROPN
ejpam-4510	38	6	times	time	NOUN
ejpam-4510	38	7	.	.	PUNCT
ejpam-4510	39	1	the	the	DET
ejpam-4510	39	2	n	n	ADV
ejpam-4510	39	3	-	-	ADJ
ejpam-4510	39	4	fold	fold	ADJ
ejpam-4510	39	5	weak	weak	ADJ
ejpam-4510	39	6	be	be	NOUN
ejpam-4510	39	7	-	-	PUNCT
ejpam-4510	39	8	subalgebra	subalgebra	NOUN
ejpam-4510	39	9	with	with	ADP
ejpam-4510	39	10	n	n	NOUN
ejpam-4510	39	11	=	=	SYM
ejpam-4510	39	12	2	2	NUM
ejpam-4510	39	13	is	be	AUX
ejpam-4510	39	14	called	call	VERB
ejpam-4510	39	15	a	a	DET
ejpam-4510	39	16	weak	weak	ADJ
ejpam-4510	39	17	be	be	NOUN
ejpam-4510	39	18	-	-	PUNCT
ejpam-4510	39	19	subalgebra	subalgebra	NOUN
ejpam-4510	39	20	.	.	PUNCT
ejpam-4510	40	1	•	•	NUM
ejpam-4510	40	2	a	a	DET
ejpam-4510	40	3	be	be	NOUN
ejpam-4510	40	4	-	-	PUNCT
ejpam-4510	40	5	filter	filter	NOUN
ejpam-4510	40	6	of	of	ADP
ejpam-4510	40	7	x	x	PUNCT
ejpam-4510	40	8	(	(	PUNCT
ejpam-4510	40	9	see	see	VERB
ejpam-4510	40	10	[	[	X
ejpam-4510	40	11	7	7	NUM
ejpam-4510	40	12	]	]	PUNCT
ejpam-4510	40	13	)	)	PUNCT
ejpam-4510	40	14	if	if	SCONJ
ejpam-4510	40	15	it	it	PRON
ejpam-4510	40	16	satisfies	satisfy	VERB
ejpam-4510	40	17	:	:	PUNCT
ejpam-4510	40	18	1	1	NUM
ejpam-4510	40	19	∈	∈	PROPN
ejpam-4510	40	20	a	a	PRON
ejpam-4510	40	21	,	,	PUNCT
ejpam-4510	40	22	(	(	PUNCT
ejpam-4510	40	23	7	7	NUM
ejpam-4510	40	24	)	)	PUNCT
ejpam-4510	40	25	(	(	PUNCT
ejpam-4510	40	26	∀a	∀a	X
ejpam-4510	40	27	,	,	PUNCT
ejpam-4510	40	28	b	b	PROPN
ejpam-4510	40	29	∈	∈	PROPN
ejpam-4510	40	30	x)(a	x)(a	PUNCT
ejpam-4510	41	1	∗	∗	NOUN
ejpam-4510	41	2	b	b	X
ejpam-4510	41	3	∈	∈	PROPN
ejpam-4510	41	4	a	a	PRON
ejpam-4510	41	5	,	,	PUNCT
ejpam-4510	41	6	a	a	DET
ejpam-4510	41	7	∈	∈	PROPN
ejpam-4510	41	8	a	a	DET
ejpam-4510	41	9	⇒	⇒	NOUN
ejpam-4510	41	10	b	b	X
ejpam-4510	41	11	∈	∈	PROPN
ejpam-4510	41	12	a	a	PRON
ejpam-4510	41	13	)	)	PUNCT
ejpam-4510	41	14	.	.	PUNCT
ejpam-4510	42	1	(	(	PUNCT
ejpam-4510	42	2	8)	8)	NUM
ejpam-4510	42	3	2.2	2.2	NUM
ejpam-4510	42	4	.	.	PUNCT
ejpam-4510	42	5	basic	basic	ADJ
ejpam-4510	42	6	concepts	concept	NOUN
ejpam-4510	42	7	about	about	ADP
ejpam-4510	42	8	dokdo	dokdo	NOUN
ejpam-4510	42	9	structures	structure	NOUN
ejpam-4510	42	10	let	let	VERB
ejpam-4510	42	11	x	x	PART
ejpam-4510	42	12	be	be	AUX
ejpam-4510	42	13	a	a	DET
ejpam-4510	42	14	set	set	NOUN
ejpam-4510	42	15	.	.	PUNCT
ejpam-4510	43	1	a	a	DET
ejpam-4510	43	2	bipolar	bipolar	ADJ
ejpam-4510	43	3	fuzzy	fuzzy	ADJ
ejpam-4510	43	4	set	set	NOUN
ejpam-4510	43	5	in	in	ADP
ejpam-4510	43	6	x	x	PROPN
ejpam-4510	43	7	(	(	PUNCT
ejpam-4510	43	8	see	see	VERB
ejpam-4510	43	9	[	[	X
ejpam-4510	43	10	8	8	NUM
ejpam-4510	43	11	]	]	PUNCT
ejpam-4510	43	12	)	)	PUNCT
ejpam-4510	43	13	is	be	AUX
ejpam-4510	43	14	an	an	DET
ejpam-4510	43	15	object	object	NOUN
ejpam-4510	43	16	having	have	VERB
ejpam-4510	43	17	the	the	DET
ejpam-4510	43	18	form	form	NOUN
ejpam-4510	43	19	φ̊	φ̊	X
ejpam-4510	43	20	=	=	PUNCT
ejpam-4510	43	21	{	{	PUNCT
ejpam-4510	43	22	(	(	PUNCT
ejpam-4510	43	23	a	a	PRON
ejpam-4510	43	24	,	,	PUNCT
ejpam-4510	43	25	φ−(a	φ−(a	NOUN
ejpam-4510	43	26	)	)	PUNCT
ejpam-4510	43	27	,	,	PUNCT
ejpam-4510	43	28	φ+(a	φ+(a	NUM
ejpam-4510	43	29	)	)	PUNCT
ejpam-4510	43	30	)	)	PUNCT
ejpam-4510	44	1	|	|	ADV
ejpam-4510	44	2	a	a	DET
ejpam-4510	44	3	∈	∈	NOUN
ejpam-4510	44	4	x	x	PRON
ejpam-4510	44	5	}	}	PUNCT
ejpam-4510	44	6	(	(	PUNCT
ejpam-4510	44	7	9	9	NUM
ejpam-4510	44	8	)	)	PUNCT
ejpam-4510	44	9	where	where	SCONJ
ejpam-4510	44	10	φ−	φ−	PROPN
ejpam-4510	44	11	:	:	PUNCT
ejpam-4510	44	12	x	x	X
ejpam-4510	44	13	→	→	PUNCT
ejpam-4510	45	1	[	[	X
ejpam-4510	45	2	−1	−1	NOUN
ejpam-4510	45	3	,	,	PUNCT
ejpam-4510	45	4	0	0	NUM
ejpam-4510	45	5	]	]	PUNCT
ejpam-4510	45	6	and	and	CCONJ
ejpam-4510	45	7	φ+	φ+	NOUN
ejpam-4510	45	8	:	:	PUNCT
ejpam-4510	45	9	x	x	X
ejpam-4510	45	10	→	→	PUNCT
ejpam-4510	45	11	[	[	X
ejpam-4510	45	12	0	0	NUM
ejpam-4510	45	13	,	,	PUNCT
ejpam-4510	45	14	1	1	NUM
ejpam-4510	45	15	]	]	PUNCT
ejpam-4510	45	16	are	be	AUX
ejpam-4510	45	17	mappings	mapping	NOUN
ejpam-4510	45	18	.	.	PUNCT
ejpam-4510	46	1	the	the	DET
ejpam-4510	46	2	bipolar	bipolar	ADJ
ejpam-4510	46	3	fuzzy	fuzzy	ADJ
ejpam-4510	46	4	set	set	NOUN
ejpam-4510	46	5	which	which	PRON
ejpam-4510	46	6	is	be	AUX
ejpam-4510	46	7	described	describe	VERB
ejpam-4510	46	8	in	in	ADP
ejpam-4510	46	9	(	(	PUNCT
ejpam-4510	46	10	9	9	NUM
ejpam-4510	46	11	)	)	PUNCT
ejpam-4510	46	12	is	be	AUX
ejpam-4510	46	13	simply	simply	ADV
ejpam-4510	46	14	denoted	denote	VERB
ejpam-4510	46	15	by	by	ADP
ejpam-4510	46	16	φ̊	φ̊	PROPN
ejpam-4510	46	17	:	:	PUNCT
ejpam-4510	46	18	=	=	SYM
ejpam-4510	46	19	(	(	PUNCT
ejpam-4510	46	20	x;φ−	x;φ−	PROPN
ejpam-4510	46	21	,	,	PUNCT
ejpam-4510	46	22	φ+	φ+	NOUN
ejpam-4510	46	23	)	)	PUNCT
ejpam-4510	46	24	.	.	PUNCT
ejpam-4510	47	1	a	a	DET
ejpam-4510	47	2	bipolar	bipolar	ADJ
ejpam-4510	47	3	fuzzy	fuzzy	ADJ
ejpam-4510	47	4	set	set	NOUN
ejpam-4510	47	5	can	can	AUX
ejpam-4510	47	6	be	be	AUX
ejpam-4510	47	7	reinterpreted	reinterpret	VERB
ejpam-4510	47	8	as	as	ADP
ejpam-4510	47	9	a	a	DET
ejpam-4510	47	10	function	function	NOUN
ejpam-4510	47	11	:	:	PUNCT
ejpam-4510	47	12	φ̊	φ̊	X
ejpam-4510	47	13	:	:	PUNCT
ejpam-4510	47	14	x	x	X
ejpam-4510	47	15	→	→	PUNCT
ejpam-4510	47	16	[	[	X
ejpam-4510	47	17	−1	−1	NOUN
ejpam-4510	47	18	,	,	PUNCT
ejpam-4510	47	19	0]×	0]×	PROPN
ejpam-4510	48	1	[	[	X
ejpam-4510	48	2	0	0	NUM
ejpam-4510	48	3	,	,	PUNCT
ejpam-4510	48	4	1	1	NUM
ejpam-4510	48	5	]	]	PUNCT
ejpam-4510	48	6	,	,	PUNCT
ejpam-4510	48	7	x	x	SYM
ejpam-4510	48	8	7→	7→	NUM
ejpam-4510	48	9	(	(	PUNCT
ejpam-4510	48	10	φ−(x	φ−(x	PROPN
ejpam-4510	48	11	)	)	PUNCT
ejpam-4510	48	12	,	,	PUNCT
ejpam-4510	48	13	φ+(x	φ+(x	NOUN
ejpam-4510	48	14	)	)	PUNCT
ejpam-4510	48	15	)	)	PUNCT
ejpam-4510	48	16	.	.	PUNCT
ejpam-4510	49	1	let	let	VERB
ejpam-4510	49	2	u	u	PRON
ejpam-4510	49	3	be	be	AUX
ejpam-4510	49	4	an	an	DET
ejpam-4510	49	5	initial	initial	ADJ
ejpam-4510	49	6	universe	universe	NOUN
ejpam-4510	49	7	set	set	VERB
ejpam-4510	49	8	and	and	CCONJ
ejpam-4510	49	9	x	x	PART
ejpam-4510	49	10	be	be	AUX
ejpam-4510	49	11	a	a	DET
ejpam-4510	49	12	set	set	NOUN
ejpam-4510	49	13	of	of	ADP
ejpam-4510	49	14	parameters	parameter	NOUN
ejpam-4510	49	15	.	.	PUNCT
ejpam-4510	50	1	for	for	ADP
ejpam-4510	50	2	any	any	DET
ejpam-4510	50	3	subset	subset	NOUN
ejpam-4510	50	4	a	a	PRON
ejpam-4510	50	5	of	of	ADP
ejpam-4510	50	6	x	x	PRON
ejpam-4510	50	7	,	,	PUNCT
ejpam-4510	50	8	a	a	DET
ejpam-4510	50	9	pair	pair	NOUN
ejpam-4510	50	10	(	(	PUNCT
ejpam-4510	50	11	φs	φs	PROPN
ejpam-4510	50	12	,	,	PUNCT
ejpam-4510	50	13	a	a	PRON
ejpam-4510	50	14	)	)	PUNCT
ejpam-4510	50	15	is	be	AUX
ejpam-4510	50	16	called	call	VERB
ejpam-4510	50	17	a	a	DET
ejpam-4510	50	18	soft	soft	ADJ
ejpam-4510	50	19	set	set	NOUN
ejpam-4510	50	20	over	over	ADP
ejpam-4510	50	21	u	u	NOUN
ejpam-4510	50	22	(	(	PUNCT
ejpam-4510	50	23	see	see	VERB
ejpam-4510	50	24	[	[	X
ejpam-4510	50	25	9	9	NUM
ejpam-4510	50	26	]	]	NUM
ejpam-4510	50	27	)	)	PUNCT
ejpam-4510	50	28	,	,	PUNCT
ejpam-4510	50	29	where	where	SCONJ
ejpam-4510	50	30	φs	φs	ADV
ejpam-4510	50	31	is	be	AUX
ejpam-4510	50	32	a	a	DET
ejpam-4510	50	33	mapping	mapping	NOUN
ejpam-4510	50	34	described	describe	VERB
ejpam-4510	50	35	as	as	ADP
ejpam-4510	50	36	follows	follow	VERB
ejpam-4510	50	37	:	:	PUNCT
ejpam-4510	50	38	φs	φs	ADP
ejpam-4510	50	39	:	:	PUNCT
ejpam-4510	50	40	a	a	DET
ejpam-4510	50	41	→	→	SYM
ejpam-4510	50	42	2u	2u	NOUN
ejpam-4510	50	43	where	where	SCONJ
ejpam-4510	50	44	2u	2u	PROPN
ejpam-4510	50	45	is	be	AUX
ejpam-4510	50	46	the	the	DET
ejpam-4510	50	47	power	power	NOUN
ejpam-4510	50	48	set	set	NOUN
ejpam-4510	50	49	of	of	ADP
ejpam-4510	50	50	u	u	PROPN
ejpam-4510	50	51	.	.	PUNCT
ejpam-4510	51	1	if	if	SCONJ
ejpam-4510	51	2	a	a	DET
ejpam-4510	51	3	=	=	SYM
ejpam-4510	51	4	x	x	NOUN
ejpam-4510	51	5	,	,	PUNCT
ejpam-4510	51	6	the	the	DET
ejpam-4510	51	7	soft	soft	ADJ
ejpam-4510	51	8	set	set	NOUN
ejpam-4510	51	9	(	(	PUNCT
ejpam-4510	51	10	φs	φs	PROPN
ejpam-4510	51	11	,	,	PUNCT
ejpam-4510	51	12	a	a	PRON
ejpam-4510	51	13	)	)	PUNCT
ejpam-4510	51	14	over	over	ADP
ejpam-4510	51	15	u	u	NOUN
ejpam-4510	51	16	is	be	AUX
ejpam-4510	51	17	simply	simply	ADV
ejpam-4510	51	18	denoted	denote	VERB
ejpam-4510	51	19	by	by	ADP
ejpam-4510	51	20	φs	φs	PRON
ejpam-4510	51	21	only	only	ADV
ejpam-4510	51	22	.	.	PUNCT
ejpam-4510	52	1	a	a	DET
ejpam-4510	52	2	mapping	mapping	NOUN
ejpam-4510	52	3	φ̃	φ̃	PROPN
ejpam-4510	52	4	:	:	PUNCT
ejpam-4510	52	5	x	x	X
ejpam-4510	52	6	→	→	PUNCT
ejpam-4510	52	7	[	[	X
ejpam-4510	52	8	[	[	X
ejpam-4510	52	9	0	0	NUM
ejpam-4510	52	10	,	,	PUNCT
ejpam-4510	52	11	1	1	NUM
ejpam-4510	52	12	]	]	PUNCT
ejpam-4510	52	13	]	]	PUNCT
ejpam-4510	52	14	is	be	AUX
ejpam-4510	52	15	called	call	VERB
ejpam-4510	52	16	an	an	DET
ejpam-4510	52	17	interval	interval	NOUN
ejpam-4510	52	18	-	-	PUNCT
ejpam-4510	52	19	valued	value	VERB
ejpam-4510	52	20	fuzzy	fuzzy	ADJ
ejpam-4510	52	21	set	set	NOUN
ejpam-4510	52	22	(	(	PUNCT
ejpam-4510	52	23	briefly	briefly	ADV
ejpam-4510	52	24	,	,	PUNCT
ejpam-4510	52	25	an	an	DET
ejpam-4510	52	26	ivf	ivf	NOUN
ejpam-4510	52	27	set	set	NOUN
ejpam-4510	52	28	)	)	PUNCT
ejpam-4510	52	29	in	in	ADP
ejpam-4510	52	30	x	x	X
ejpam-4510	52	31	(	(	PUNCT
ejpam-4510	52	32	see	see	VERB
ejpam-4510	52	33	[	[	X
ejpam-4510	52	34	3	3	NUM
ejpam-4510	52	35	,	,	PUNCT
ejpam-4510	52	36	12	12	NUM
ejpam-4510	52	37	]	]	PUNCT
ejpam-4510	52	38	)	)	PUNCT
ejpam-4510	53	1	where	where	SCONJ
ejpam-4510	53	2	[	[	X
ejpam-4510	53	3	[	[	X
ejpam-4510	53	4	0	0	NUM
ejpam-4510	53	5	,	,	PUNCT
ejpam-4510	53	6	1	1	NUM
ejpam-4510	53	7	]	]	PUNCT
ejpam-4510	53	8	]	]	X
ejpam-4510	53	9	is	be	AUX
ejpam-4510	53	10	the	the	DET
ejpam-4510	53	11	set	set	NOUN
ejpam-4510	53	12	of	of	ADP
ejpam-4510	53	13	all	all	DET
ejpam-4510	53	14	closed	closed	ADJ
ejpam-4510	53	15	subintervals	subinterval	NOUN
ejpam-4510	53	16	of	of	ADP
ejpam-4510	53	17	[	[	X
ejpam-4510	53	18	0	0	NUM
ejpam-4510	53	19	,	,	PUNCT
ejpam-4510	53	20	1	1	NUM
ejpam-4510	53	21	]	]	PUNCT
ejpam-4510	53	22	,	,	PUNCT
ejpam-4510	53	23	and	and	CCONJ
ejpam-4510	53	24	members	member	NOUN
ejpam-4510	53	25	of	of	ADP
ejpam-4510	53	26	[	[	X
ejpam-4510	53	27	[	[	X
ejpam-4510	53	28	0	0	NUM
ejpam-4510	53	29	,	,	PUNCT
ejpam-4510	53	30	1	1	NUM
ejpam-4510	53	31	]	]	PUNCT
ejpam-4510	53	32	]	]	PUNCT
ejpam-4510	53	33	are	be	AUX
ejpam-4510	53	34	called	call	VERB
ejpam-4510	53	35	interval	interval	NOUN
ejpam-4510	53	36	numbers	number	NOUN
ejpam-4510	53	37	and	and	CCONJ
ejpam-4510	53	38	are	be	AUX
ejpam-4510	53	39	denoted	denote	VERB
ejpam-4510	53	40	by	by	ADP
ejpam-4510	53	41	ã	ã	PROPN
ejpam-4510	53	42	,	,	PUNCT
ejpam-4510	53	43	b̃	b̃	PROPN
ejpam-4510	53	44	,	,	PUNCT
ejpam-4510	53	45	c̃	c̃	PROPN
ejpam-4510	53	46	,	,	PUNCT
ejpam-4510	53	47	etc	etc	X
ejpam-4510	53	48	.	.	X
ejpam-4510	53	49	,	,	PUNCT
ejpam-4510	54	1	where	where	SCONJ
ejpam-4510	54	2	ã	ã	PROPN
ejpam-4510	54	3	=	=	PROPN
ejpam-4510	55	1	[	[	X
ejpam-4510	55	2	a−	a−	PROPN
ejpam-4510	55	3	,	,	PUNCT
ejpam-4510	55	4	a+	a+	ADP
ejpam-4510	55	5	]	]	PUNCT
ejpam-4510	55	6	with	with	ADP
ejpam-4510	55	7	0	0	NUM
ejpam-4510	55	8	≤	≤	NUM
ejpam-4510	55	9	a−	a−	NOUN
ejpam-4510	55	10	≤	≤	NOUN
ejpam-4510	55	11	a+	a+	PUNCT
ejpam-4510	55	12	≤	≤	NUM
ejpam-4510	55	13	1	1	NUM
ejpam-4510	55	14	.	.	PUNCT
ejpam-4510	56	1	for	for	ADP
ejpam-4510	56	2	every	every	DET
ejpam-4510	56	3	two	two	NUM
ejpam-4510	56	4	interval	interval	NOUN
ejpam-4510	56	5	numbers	number	NOUN
ejpam-4510	56	6	ã	ã	PROPN
ejpam-4510	56	7	and	and	CCONJ
ejpam-4510	56	8	b̃	b̃	PROPN
ejpam-4510	56	9	,	,	PUNCT
ejpam-4510	56	10	we	we	PRON
ejpam-4510	56	11	define	define	VERB
ejpam-4510	56	12	ã	ã	PROPN
ejpam-4510	56	13	⪯	⪯	NOUN
ejpam-4510	56	14	b̃	b̃	PROPN
ejpam-4510	56	15	(	(	PUNCT
ejpam-4510	56	16	or	or	CCONJ
ejpam-4510	56	17	b̃	b̃	PROPN
ejpam-4510	56	18	⪰	⪰	NOUN
ejpam-4510	56	19	ã	ã	PROPN
ejpam-4510	56	20	)	)	PUNCT
ejpam-4510	56	21	⇔	⇔	X
ejpam-4510	56	22	a−	a−	PROPN
ejpam-4510	56	23	≤	≤	ADJ
ejpam-4510	56	24	b−	b−	NOUN
ejpam-4510	56	25	,	,	PUNCT
ejpam-4510	56	26	a+	a+	PUNCT
ejpam-4510	56	27	≤	≤	NUM
ejpam-4510	56	28	b+	b+	X
ejpam-4510	56	29	,	,	PUNCT
ejpam-4510	56	30	(	(	PUNCT
ejpam-4510	56	31	10	10	NUM
ejpam-4510	56	32	)	)	PUNCT
ejpam-4510	56	33	ã	ã	PROPN
ejpam-4510	56	34	=	=	SYM
ejpam-4510	56	35	b̃	b̃	PROPN
ejpam-4510	56	36	⇔	⇔	PROPN
ejpam-4510	56	37	ã	ã	PROPN
ejpam-4510	56	38	⪯	⪯	PROPN
ejpam-4510	56	39	b̃	b̃	PROPN
ejpam-4510	56	40	,	,	PUNCT
ejpam-4510	56	41	b̃	b̃	PROPN
ejpam-4510	56	42	⪯	⪯	PROPN
ejpam-4510	56	43	ã	ã	PROPN
ejpam-4510	56	44	,	,	PUNCT
ejpam-4510	56	45	(	(	PUNCT
ejpam-4510	56	46	11	11	NUM
ejpam-4510	56	47	)	)	PUNCT
ejpam-4510	56	48	rmin{ã	rmin{ã	NOUN
ejpam-4510	56	49	,	,	PUNCT
ejpam-4510	56	50	b̃	b̃	PROPN
ejpam-4510	56	51	}	}	PUNCT
ejpam-4510	56	52	=	=	PUNCT
ejpam-4510	57	1	[	[	X
ejpam-4510	57	2	min{a−	min{a−	X
ejpam-4510	57	3	,	,	PUNCT
ejpam-4510	57	4	b−},min{a+	b−},min{a+	NOUN
ejpam-4510	57	5	,	,	PUNCT
ejpam-4510	57	6	b+	b+	X
ejpam-4510	57	7	}	}	PUNCT
ejpam-4510	57	8	]	]	PUNCT
ejpam-4510	57	9	.	.	PUNCT
ejpam-4510	58	1	(	(	PUNCT
ejpam-4510	58	2	12	12	NUM
ejpam-4510	58	3	)	)	PUNCT
ejpam-4510	58	4	let	let	VERB
ejpam-4510	58	5	u	u	PRON
ejpam-4510	58	6	be	be	AUX
ejpam-4510	58	7	an	an	DET
ejpam-4510	58	8	initial	initial	ADJ
ejpam-4510	58	9	universe	universe	NOUN
ejpam-4510	58	10	set	set	VERB
ejpam-4510	58	11	and	and	CCONJ
ejpam-4510	58	12	x	x	ADP
ejpam-4510	58	13	a	a	DET
ejpam-4510	58	14	set	set	NOUN
ejpam-4510	58	15	of	of	ADP
ejpam-4510	58	16	parameters	parameter	NOUN
ejpam-4510	58	17	.	.	PUNCT
ejpam-4510	59	1	a	a	DET
ejpam-4510	59	2	triple	triple	ADJ
ejpam-4510	59	3	dokφ	dokφ	NOUN
ejpam-4510	59	4	:	:	PUNCT
ejpam-4510	59	5	=	=	SYM
ejpam-4510	59	6	(	(	PUNCT
ejpam-4510	59	7	φ̊	φ̊	PROPN
ejpam-4510	59	8	,	,	PUNCT
ejpam-4510	59	9	φs	φs	ADV
ejpam-4510	59	10	,	,	PUNCT
ejpam-4510	59	11	φ̃	φ̃	PROPN
ejpam-4510	59	12	)	)	PUNCT
ejpam-4510	59	13	is	be	AUX
ejpam-4510	59	14	called	call	VERB
ejpam-4510	59	15	a	a	DET
ejpam-4510	59	16	dokdo	dokdo	NOUN
ejpam-4510	59	17	structure	structure	NOUN
ejpam-4510	59	18	(	(	PUNCT
ejpam-4510	59	19	see	see	VERB
ejpam-4510	59	20	[	[	X
ejpam-4510	59	21	5	5	NUM
ejpam-4510	59	22	]	]	PUNCT
ejpam-4510	59	23	)	)	PUNCT
ejpam-4510	59	24	in	in	ADP
ejpam-4510	59	25	(	(	PUNCT
ejpam-4510	59	26	x	x	NOUN
ejpam-4510	59	27	,	,	PUNCT
ejpam-4510	59	28	u	u	NOUN
ejpam-4510	59	29	)	)	PUNCT
ejpam-4510	59	30	if	if	SCONJ
ejpam-4510	59	31	φ̊	φ̊	PRON
ejpam-4510	59	32	:	:	PUNCT
ejpam-4510	59	33	x	x	X
ejpam-4510	60	1	→	→	PUNCT
ejpam-4510	60	2	[	[	X
ejpam-4510	60	3	−1	−1	NOUN
ejpam-4510	60	4	,	,	PUNCT
ejpam-4510	60	5	0	0	NUM
ejpam-4510	60	6	]	]	X
ejpam-4510	60	7	×	×	NOUN
ejpam-4510	61	1	[	[	X
ejpam-4510	61	2	0	0	NUM
ejpam-4510	61	3	,	,	PUNCT
ejpam-4510	61	4	1	1	NUM
ejpam-4510	61	5	]	]	PUNCT
ejpam-4510	61	6	is	be	AUX
ejpam-4510	61	7	a	a	DET
ejpam-4510	61	8	bipolar	bipolar	ADJ
ejpam-4510	61	9	y.	y.	PROPN
ejpam-4510	61	10	b.	b.	PROPN
ejpam-4510	61	11	jun	jun	PROPN
ejpam-4510	61	12	,	,	PUNCT
ejpam-4510	61	13	s.	s.	PROPN
ejpam-4510	61	14	s.	s.	PROPN
ejpam-4510	61	15	ahn	ahn	PROPN
ejpam-4510	61	16	and	and	CCONJ
ejpam-4510	61	17	e.	e.	PROPN
ejpam-4510	61	18	h.	h.	PROPN
ejpam-4510	61	19	roh	roh	PROPN
ejpam-4510	61	20	/	/	SYM
ejpam-4510	61	21	eur	eur	PROPN
ejpam-4510	61	22	.	.	PUNCT
ejpam-4510	62	1	j.	j.	PROPN
ejpam-4510	62	2	pure	pure	PROPN
ejpam-4510	62	3	appl	appl	PROPN
ejpam-4510	62	4	.	.	PROPN
ejpam-4510	62	5	math	math	PROPN
ejpam-4510	62	6	,	,	PUNCT
ejpam-4510	62	7	15	15	NUM
ejpam-4510	62	8	(	(	PUNCT
ejpam-4510	62	9	4	4	NUM
ejpam-4510	62	10	)	)	PUNCT
ejpam-4510	62	11	(	(	PUNCT
ejpam-4510	62	12	2022	2022	NUM
ejpam-4510	62	13	)	)	PUNCT
ejpam-4510	62	14	,	,	PUNCT
ejpam-4510	62	15	1521	1521	NUM
ejpam-4510	62	16	-	-	SYM
ejpam-4510	62	17	1535	1535	NUM
ejpam-4510	62	18	1524	1524	NUM
ejpam-4510	62	19	fuzzy	fuzzy	ADJ
ejpam-4510	62	20	set	set	VERB
ejpam-4510	62	21	in	in	ADP
ejpam-4510	62	22	x	x	NOUN
ejpam-4510	62	23	,	,	PUNCT
ejpam-4510	62	24	φs	φs	ADP
ejpam-4510	62	25	:	:	PUNCT
ejpam-4510	62	26	x	x	X
ejpam-4510	62	27	→	→	SYM
ejpam-4510	62	28	2u	2u	PROPN
ejpam-4510	62	29	is	be	AUX
ejpam-4510	62	30	a	a	DET
ejpam-4510	62	31	soft	soft	ADJ
ejpam-4510	62	32	set	set	NOUN
ejpam-4510	62	33	over	over	ADP
ejpam-4510	62	34	u	u	NOUN
ejpam-4510	62	35	and	and	CCONJ
ejpam-4510	62	36	φ̃	φ̃	PROPN
ejpam-4510	62	37	:	:	PUNCT
ejpam-4510	62	38	x	x	X
ejpam-4510	62	39	→	→	PUNCT
ejpam-4510	62	40	[	[	X
ejpam-4510	62	41	[	[	X
ejpam-4510	62	42	0	0	NUM
ejpam-4510	62	43	,	,	PUNCT
ejpam-4510	62	44	1	1	NUM
ejpam-4510	62	45	]	]	PUNCT
ejpam-4510	62	46	]	]	X
ejpam-4510	62	47	is	be	AUX
ejpam-4510	62	48	an	an	DET
ejpam-4510	62	49	interval	interval	NOUN
ejpam-4510	62	50	-	-	PUNCT
ejpam-4510	62	51	valued	value	VERB
ejpam-4510	62	52	fuzzy	fuzzy	ADJ
ejpam-4510	62	53	set	set	VERB
ejpam-4510	62	54	in	in	ADP
ejpam-4510	62	55	x.	x.	NOUN
ejpam-4510	62	56	the	the	DET
ejpam-4510	62	57	dokdo	dokdo	PROPN
ejpam-4510	62	58	structure	structure	NOUN
ejpam-4510	62	59	dokφ	dokφ	NOUN
ejpam-4510	62	60	:	:	PUNCT
ejpam-4510	62	61	=	=	SYM
ejpam-4510	62	62	(	(	PUNCT
ejpam-4510	62	63	φ̊	φ̊	PROPN
ejpam-4510	62	64	,	,	PUNCT
ejpam-4510	62	65	φs	φs	ADV
ejpam-4510	62	66	,	,	PUNCT
ejpam-4510	62	67	φ̃	φ̃	PROPN
ejpam-4510	62	68	)	)	PUNCT
ejpam-4510	62	69	in	in	ADP
ejpam-4510	62	70	(	(	PUNCT
ejpam-4510	62	71	x	x	NOUN
ejpam-4510	62	72	,	,	PUNCT
ejpam-4510	62	73	u	u	NOUN
ejpam-4510	62	74	)	)	PUNCT
ejpam-4510	62	75	can	can	AUX
ejpam-4510	62	76	be	be	AUX
ejpam-4510	62	77	represented	represent	VERB
ejpam-4510	62	78	as	as	SCONJ
ejpam-4510	62	79	follows	follow	VERB
ejpam-4510	62	80	:	:	PUNCT
ejpam-4510	62	81	dokφ	dokφ	NOUN
ejpam-4510	62	82	:	:	PUNCT
ejpam-4510	62	83	=	=	SYM
ejpam-4510	62	84	(	(	PUNCT
ejpam-4510	62	85	φ̊	φ̊	PROPN
ejpam-4510	62	86	,	,	PUNCT
ejpam-4510	62	87	φs	φs	ADV
ejpam-4510	62	88	,	,	PUNCT
ejpam-4510	62	89	φ̃	φ̃	PROPN
ejpam-4510	62	90	)	)	PUNCT
ejpam-4510	62	91	:	:	PUNCT
ejpam-4510	63	1	x	x	X
ejpam-4510	63	2	→	→	PUNCT
ejpam-4510	63	3	(	(	PUNCT
ejpam-4510	63	4	[	[	X
ejpam-4510	63	5	−1	−1	NOUN
ejpam-4510	63	6	,	,	PUNCT
ejpam-4510	63	7	0]×	0]×	PROPN
ejpam-4510	64	1	[	[	X
ejpam-4510	64	2	0	0	NUM
ejpam-4510	64	3	,	,	PUNCT
ejpam-4510	64	4	1])×	1])×	NOUN
ejpam-4510	64	5	2u	2u	NOUN
ejpam-4510	64	6	×	×	NOUN
ejpam-4510	65	1	[	[	X
ejpam-4510	65	2	[	[	X
ejpam-4510	65	3	0	0	NUM
ejpam-4510	65	4	,	,	PUNCT
ejpam-4510	65	5	1	1	NUM
ejpam-4510	65	6	]	]	PUNCT
ejpam-4510	65	7	]	]	PUNCT
ejpam-4510	65	8	,	,	PUNCT
ejpam-4510	65	9	x	x	SYM
ejpam-4510	65	10	7→	7→	NUM
ejpam-4510	65	11	(	(	PUNCT
ejpam-4510	65	12	φ̊(x	φ̊(x	NOUN
ejpam-4510	65	13	)	)	PUNCT
ejpam-4510	65	14	,	,	PUNCT
ejpam-4510	65	15	φs(x	φs(x	NOUN
ejpam-4510	65	16	)	)	PUNCT
ejpam-4510	65	17	,	,	PUNCT
ejpam-4510	65	18	φ̃(x	φ̃(x	PROPN
ejpam-4510	65	19	)	)	PUNCT
ejpam-4510	65	20	)	)	PUNCT
ejpam-4510	65	21	(	(	PUNCT
ejpam-4510	65	22	13	13	NUM
ejpam-4510	65	23	)	)	PUNCT
ejpam-4510	65	24	where	where	SCONJ
ejpam-4510	65	25	φ̊(x	φ̊(x	NOUN
ejpam-4510	65	26	)	)	PUNCT
ejpam-4510	65	27	=	=	SYM
ejpam-4510	65	28	(	(	PUNCT
ejpam-4510	65	29	φ̊−(x	φ̊−(x	NOUN
ejpam-4510	65	30	)	)	PUNCT
ejpam-4510	65	31	,	,	PUNCT
ejpam-4510	65	32	φ̊+(x	φ̊+(x	NUM
ejpam-4510	65	33	)	)	PUNCT
ejpam-4510	65	34	)	)	PUNCT
ejpam-4510	65	35	and	and	CCONJ
ejpam-4510	65	36	φ̃(x	φ̃(x	PROPN
ejpam-4510	65	37	)	)	PUNCT
ejpam-4510	65	38	=	=	PUNCT
ejpam-4510	66	1	[	[	X
ejpam-4510	66	2	φ̃l(x	φ̃l(x	PROPN
ejpam-4510	66	3	)	)	PUNCT
ejpam-4510	66	4	,	,	PUNCT
ejpam-4510	66	5	φ̃r(x	φ̃r(x	NUM
ejpam-4510	66	6	)	)	PUNCT
ejpam-4510	66	7	]	]	PUNCT
ejpam-4510	66	8	.	.	PUNCT
ejpam-4510	67	1	given	give	VERB
ejpam-4510	67	2	a	a	DET
ejpam-4510	67	3	dokdo	dokdo	NOUN
ejpam-4510	67	4	structure	structure	NOUN
ejpam-4510	67	5	dokφ	dokφ	NOUN
ejpam-4510	67	6	:	:	PUNCT
ejpam-4510	67	7	=	=	SYM
ejpam-4510	67	8	(	(	PUNCT
ejpam-4510	67	9	φ̊	φ̊	PROPN
ejpam-4510	67	10	,	,	PUNCT
ejpam-4510	67	11	φs	φs	ADV
ejpam-4510	67	12	,	,	PUNCT
ejpam-4510	67	13	φ̃	φ̃	PROPN
ejpam-4510	67	14	)	)	PUNCT
ejpam-4510	67	15	in	in	ADP
ejpam-4510	67	16	a	a	DET
ejpam-4510	67	17	dokdo	dokdo	NOUN
ejpam-4510	67	18	universe	universe	NOUN
ejpam-4510	67	19	(	(	PUNCT
ejpam-4510	67	20	x	x	NOUN
ejpam-4510	67	21	,	,	PUNCT
ejpam-4510	67	22	u	u	NOUN
ejpam-4510	67	23	)	)	PUNCT
ejpam-4510	67	24	,	,	PUNCT
ejpam-4510	67	25	we	we	PRON
ejpam-4510	67	26	consider	consider	VERB
ejpam-4510	67	27	the	the	DET
ejpam-4510	67	28	following	follow	VERB
ejpam-4510	67	29	sets	set	NOUN
ejpam-4510	67	30	:	:	PUNCT
ejpam-4510	67	31	φ̊(max	φ̊(max	ADV
ejpam-4510	67	32	,	,	PUNCT
ejpam-4510	67	33	min	min	NOUN
ejpam-4510	67	34	)	)	PUNCT
ejpam-4510	67	35	:	:	PUNCT
ejpam-4510	67	36	=	=	SYM
ejpam-4510	67	37	{	{	PUNCT
ejpam-4510	67	38	x	x	X
ejpam-4510	67	39	(	(	PUNCT
ejpam-4510	67	40	y	y	PROPN
ejpam-4510	67	41	,	,	PUNCT
ejpam-4510	67	42	z	z	NOUN
ejpam-4510	67	43	)	)	PUNCT
ejpam-4510	67	44	∈	∈	PROPN
ejpam-4510	67	45	x	x	PUNCT
ejpam-4510	67	46	x×x	x×x	PROPN
ejpam-4510	67	47	∣∣∣	∣∣∣	ADJ
ejpam-4510	67	48	φ̊−(x	φ̊−(x	NOUN
ejpam-4510	67	49	)	)	PUNCT
ejpam-4510	67	50	≤	≤	NOUN
ejpam-4510	67	51	max{φ̊−(y	max{φ̊−(y	PROPN
ejpam-4510	67	52	)	)	PUNCT
ejpam-4510	67	53	,	,	PUNCT
ejpam-4510	67	54	φ̊−(z	φ̊−(z	NUM
ejpam-4510	67	55	)	)	PUNCT
ejpam-4510	67	56	}	}	PUNCT
ejpam-4510	67	57	φ̊+(x	φ̊+(x	NUM
ejpam-4510	67	58	)	)	PUNCT
ejpam-4510	67	59	≥	≥	NOUN
ejpam-4510	67	60	min{φ̊+(y	min{φ̊+(y	NOUN
ejpam-4510	67	61	)	)	PUNCT
ejpam-4510	67	62	,	,	PUNCT
ejpam-4510	67	63	φ̊+(z	φ̊+(z	NOUN
ejpam-4510	67	64	)	)	PUNCT
ejpam-4510	67	65	}	}	PUNCT
ejpam-4510	67	66	}	}	PUNCT
ejpam-4510	67	67	,	,	PUNCT
ejpam-4510	67	68	φ̊(s,−	φ̊(s,−	PROPN
ejpam-4510	67	69	)	)	PUNCT
ejpam-4510	67	70	:	:	PUNCT
ejpam-4510	68	1	=	=	SYM
ejpam-4510	68	2	{	{	PUNCT
ejpam-4510	68	3	x	x	PUNCT
ejpam-4510	68	4	∈	∈	NOUN
ejpam-4510	68	5	x	x	X
ejpam-4510	68	6	|	|	ADV
ejpam-4510	68	7	φ̊−(x	φ̊−(x	NOUN
ejpam-4510	68	8	)	)	PUNCT
ejpam-4510	68	9	≤	≤	NUM
ejpam-4510	69	1	s	s	X
ejpam-4510	69	2	}	}	PUNCT
ejpam-4510	69	3	,	,	PUNCT
ejpam-4510	69	4	φ̊(t,+	φ̊(t,+	PROPN
ejpam-4510	69	5	)	)	PUNCT
ejpam-4510	69	6	:	:	PUNCT
ejpam-4510	69	7	=	=	SYM
ejpam-4510	69	8	{	{	PUNCT
ejpam-4510	69	9	x	x	PUNCT
ejpam-4510	69	10	∈	∈	PROPN
ejpam-4510	69	11	x	x	X
ejpam-4510	69	12	|	|	ADV
ejpam-4510	69	13	φ̊+(x	φ̊+(x	NUM
ejpam-4510	69	14	)	)	PUNCT
ejpam-4510	69	15	≥	≥	NOUN
ejpam-4510	69	16	t	t	PROPN
ejpam-4510	69	17	}	}	PUNCT
ejpam-4510	69	18	,	,	PUNCT
ejpam-4510	69	19	φ̊(s	φ̊(s	PROPN
ejpam-4510	69	20	,	,	PUNCT
ejpam-4510	69	21	t	t	PROPN
ejpam-4510	69	22	)	)	PUNCT
ejpam-4510	69	23	:	:	PUNCT
ejpam-4510	69	24	=	=	NUM
ejpam-4510	69	25	φ̊(s,−	φ̊(s,−	NOUN
ejpam-4510	69	26	)	)	PUNCT
ejpam-4510	69	27	∩	∩	PROPN
ejpam-4510	69	28	φ̊(t,+	φ̊(t,+	PROPN
ejpam-4510	69	29	)	)	PUNCT
ejpam-4510	69	30	,	,	PUNCT
ejpam-4510	69	31	φs	φs	ADP
ejpam-4510	69	32	α	α	NOUN
ejpam-4510	69	33	:	:	PUNCT
ejpam-4510	69	34	=	=	SYM
ejpam-4510	69	35	{	{	PUNCT
ejpam-4510	69	36	x	x	PUNCT
ejpam-4510	69	37	∈	∈	PROPN
ejpam-4510	69	38	x	x	X
ejpam-4510	69	39	|	|	ADV
ejpam-4510	69	40	φs(x	φs(x	PUNCT
ejpam-4510	69	41	)	)	PUNCT
ejpam-4510	69	42	⊇	⊇	PROPN
ejpam-4510	69	43	α	α	NOUN
ejpam-4510	69	44	}	}	PUNCT
ejpam-4510	69	45	,	,	PUNCT
ejpam-4510	69	46	φ̃ã	φ̃ã	ADV
ejpam-4510	69	47	:	:	PUNCT
ejpam-4510	69	48	=	=	SYM
ejpam-4510	69	49	{	{	PUNCT
ejpam-4510	69	50	x	x	PUNCT
ejpam-4510	69	51	∈	∈	PROPN
ejpam-4510	69	52	x	x	X
ejpam-4510	69	53	|	|	ADV
ejpam-4510	69	54	φ̃(x	φ̃(x	PROPN
ejpam-4510	69	55	)	)	PUNCT
ejpam-4510	69	56	⪰	⪰	NOUN
ejpam-4510	69	57	ã	ã	PROPN
ejpam-4510	69	58	}	}	PUNCT
ejpam-4510	69	59	,	,	PUNCT
ejpam-4510	69	60	where	where	SCONJ
ejpam-4510	69	61	(	(	PUNCT
ejpam-4510	69	62	s	s	X
ejpam-4510	69	63	,	,	PUNCT
ejpam-4510	69	64	t	t	PROPN
ejpam-4510	69	65	)	)	PUNCT
ejpam-4510	69	66	∈	∈	PROPN
ejpam-4510	70	1	[	[	X
ejpam-4510	70	2	−1	−1	NOUN
ejpam-4510	70	3	,	,	PUNCT
ejpam-4510	70	4	0]×	0]×	PROPN
ejpam-4510	71	1	[	[	X
ejpam-4510	71	2	0	0	NUM
ejpam-4510	71	3	,	,	PUNCT
ejpam-4510	71	4	1	1	NUM
ejpam-4510	71	5	]	]	PUNCT
ejpam-4510	71	6	,	,	PUNCT
ejpam-4510	71	7	α	α	PROPN
ejpam-4510	71	8	∈	∈	PROPN
ejpam-4510	71	9	2u	2u	NOUN
ejpam-4510	71	10	and	and	CCONJ
ejpam-4510	71	11	ã	ã	PROPN
ejpam-4510	71	12	=	=	PROPN
ejpam-4510	72	1	[	[	X
ejpam-4510	72	2	al	al	PROPN
ejpam-4510	72	3	,	,	PUNCT
ejpam-4510	72	4	ar	ar	NOUN
ejpam-4510	72	5	]	]	PROPN
ejpam-4510	72	6	.	.	PUNCT
ejpam-4510	73	1	3	3	X
ejpam-4510	73	2	.	.	X
ejpam-4510	73	3	dokdo	dokdo	PROPN
ejpam-4510	73	4	be	be	NOUN
ejpam-4510	73	5	-	-	PUNCT
ejpam-4510	73	6	subalgebras	subalgebras	NOUN
ejpam-4510	73	7	let	let	VERB
ejpam-4510	73	8	u	u	PRON
ejpam-4510	73	9	be	be	AUX
ejpam-4510	73	10	an	an	DET
ejpam-4510	73	11	initial	initial	ADJ
ejpam-4510	73	12	universe	universe	NOUN
ejpam-4510	73	13	set	set	VERB
ejpam-4510	73	14	and	and	CCONJ
ejpam-4510	73	15	x	x	ADP
ejpam-4510	73	16	a	a	DET
ejpam-4510	73	17	set	set	NOUN
ejpam-4510	73	18	of	of	ADP
ejpam-4510	73	19	parameters	parameter	NOUN
ejpam-4510	73	20	.	.	PUNCT
ejpam-4510	74	1	we	we	PRON
ejpam-4510	74	2	say	say	VERB
ejpam-4510	74	3	that	that	SCONJ
ejpam-4510	74	4	the	the	DET
ejpam-4510	74	5	pair	pair	NOUN
ejpam-4510	74	6	(	(	PUNCT
ejpam-4510	74	7	x	x	NOUN
ejpam-4510	74	8	,	,	PUNCT
ejpam-4510	74	9	u	u	NOUN
ejpam-4510	74	10	)	)	PUNCT
ejpam-4510	74	11	is	be	AUX
ejpam-4510	74	12	called	call	VERB
ejpam-4510	74	13	a	a	DET
ejpam-4510	74	14	dokdo	dokdo	NOUN
ejpam-4510	74	15	be	be	NOUN
ejpam-4510	74	16	-	-	PUNCT
ejpam-4510	74	17	universe	universe	NOUN
ejpam-4510	74	18	if	if	SCONJ
ejpam-4510	74	19	x	x	PRON
ejpam-4510	74	20	is	be	AUX
ejpam-4510	74	21	a	a	DET
ejpam-4510	74	22	be	be	NOUN
ejpam-4510	74	23	-	-	PUNCT
ejpam-4510	74	24	algebra	algebra	NOUN
ejpam-4510	74	25	.	.	PUNCT
ejpam-4510	75	1	in	in	ADP
ejpam-4510	75	2	what	what	PRON
ejpam-4510	75	3	follows	follow	VERB
ejpam-4510	75	4	,	,	PUNCT
ejpam-4510	75	5	let	let	VERB
ejpam-4510	75	6	(	(	PUNCT
ejpam-4510	75	7	x	x	NOUN
ejpam-4510	75	8	,	,	PUNCT
ejpam-4510	75	9	u	u	NOUN
ejpam-4510	75	10	)	)	PUNCT
ejpam-4510	75	11	denote	denote	VERB
ejpam-4510	75	12	the	the	DET
ejpam-4510	75	13	dokdo	dokdo	NOUN
ejpam-4510	75	14	be	be	AUX
ejpam-4510	75	15	-	-	PUNCT
ejpam-4510	75	16	universe	universe	NOUN
ejpam-4510	75	17	unless	unless	SCONJ
ejpam-4510	75	18	otherwise	otherwise	ADV
ejpam-4510	75	19	specified	specify	VERB
ejpam-4510	75	20	.	.	PUNCT
ejpam-4510	76	1	definition	definition	NOUN
ejpam-4510	76	2	1	1	NUM
ejpam-4510	76	3	.	.	PUNCT
ejpam-4510	77	1	a	a	DET
ejpam-4510	77	2	dokdo	dokdo	NOUN
ejpam-4510	77	3	structure	structure	NOUN
ejpam-4510	77	4	dokφ	dokφ	NOUN
ejpam-4510	77	5	:	:	PUNCT
ejpam-4510	77	6	=	=	SYM
ejpam-4510	77	7	(	(	PUNCT
ejpam-4510	77	8	φ̊	φ̊	PROPN
ejpam-4510	77	9	,	,	PUNCT
ejpam-4510	77	10	φs	φs	ADV
ejpam-4510	77	11	,	,	PUNCT
ejpam-4510	77	12	φ̃	φ̃	PROPN
ejpam-4510	77	13	)	)	PUNCT
ejpam-4510	77	14	is	be	AUX
ejpam-4510	77	15	called	call	VERB
ejpam-4510	77	16	a	a	DET
ejpam-4510	77	17	dokdo	dokdo	NOUN
ejpam-4510	77	18	be	be	NOUN
ejpam-4510	77	19	-	-	PUNCT
ejpam-4510	77	20	subalgebra	subalgebra	NOUN
ejpam-4510	77	21	of	of	ADP
ejpam-4510	77	22	(	(	PUNCT
ejpam-4510	77	23	x	x	NOUN
ejpam-4510	77	24	,	,	PUNCT
ejpam-4510	77	25	u	u	NOUN
ejpam-4510	77	26	)	)	PUNCT
ejpam-4510	77	27	if	if	SCONJ
ejpam-4510	77	28	it	it	PRON
ejpam-4510	77	29	satisfies	satisfy	VERB
ejpam-4510	77	30	:	:	PUNCT
ejpam-4510	77	31	(	(	PUNCT
ejpam-4510	77	32	∀x	∀x	X
ejpam-4510	77	33	,	,	PUNCT
ejpam-4510	77	34	y	y	PROPN
ejpam-4510	77	35	∈	∈	PROPN
ejpam-4510	77	36	x	x	X
ejpam-4510	77	37	)	)	PUNCT
ejpam-4510	77	38	(	(	PUNCT
ejpam-4510	77	39	x∗y	x∗y	X
ejpam-4510	77	40	(	(	PUNCT
ejpam-4510	77	41	x	x	NOUN
ejpam-4510	77	42	,	,	PUNCT
ejpam-4510	77	43	y	y	PROPN
ejpam-4510	77	44	)	)	PUNCT
ejpam-4510	77	45	∈	∈	PROPN
ejpam-4510	77	46	φ̊(max	φ̊(max	NUM
ejpam-4510	77	47	,	,	PUNCT
ejpam-4510	77	48	min	min	NOUN
ejpam-4510	77	49	)	)	PUNCT
ejpam-4510	77	50	)	)	PUNCT
ejpam-4510	77	51	,	,	PUNCT
ejpam-4510	77	52	(	(	PUNCT
ejpam-4510	77	53	14	14	NUM
ejpam-4510	77	54	)	)	PUNCT
ejpam-4510	77	55	(	(	PUNCT
ejpam-4510	77	56	∀x	∀x	X
ejpam-4510	77	57	,	,	PUNCT
ejpam-4510	77	58	y	y	PROPN
ejpam-4510	77	59	∈	∈	PROPN
ejpam-4510	77	60	x	x	X
ejpam-4510	77	61	)	)	PUNCT
ejpam-4510	77	62	(	(	PUNCT
ejpam-4510	77	63	φs(x	φs(x	X
ejpam-4510	77	64	∗	∗	PROPN
ejpam-4510	77	65	y	y	NOUN
ejpam-4510	77	66	)	)	PUNCT
ejpam-4510	77	67	⊇	⊇	NOUN
ejpam-4510	77	68	φs(x	φs(x	NOUN
ejpam-4510	77	69	)	)	PUNCT
ejpam-4510	77	70	∩	∩	NOUN
ejpam-4510	77	71	φs(y	φs(y	NUM
ejpam-4510	77	72	)	)	PUNCT
ejpam-4510	77	73	)	)	PUNCT
ejpam-4510	77	74	,	,	PUNCT
ejpam-4510	77	75	(	(	PUNCT
ejpam-4510	77	76	15	15	NUM
ejpam-4510	77	77	)	)	PUNCT
ejpam-4510	77	78	(	(	PUNCT
ejpam-4510	77	79	∀x	∀x	X
ejpam-4510	77	80	,	,	PUNCT
ejpam-4510	77	81	y	y	PROPN
ejpam-4510	77	82	∈	∈	PROPN
ejpam-4510	77	83	x	x	X
ejpam-4510	77	84	)	)	PUNCT
ejpam-4510	77	85	(	(	PUNCT
ejpam-4510	77	86	φ̃(x	φ̃(x	PROPN
ejpam-4510	77	87	∗	∗	PROPN
ejpam-4510	77	88	y	y	NOUN
ejpam-4510	77	89	)	)	PUNCT
ejpam-4510	77	90	⪰	⪰	NOUN
ejpam-4510	77	91	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	77	92	)	)	PUNCT
ejpam-4510	77	93	,	,	PUNCT
ejpam-4510	77	94	φ̃(y	φ̃(y	NOUN
ejpam-4510	77	95	)	)	PUNCT
ejpam-4510	77	96	}	}	PUNCT
ejpam-4510	77	97	)	)	PUNCT
ejpam-4510	77	98	.	.	PUNCT
ejpam-4510	78	1	(	(	PUNCT
ejpam-4510	78	2	16	16	NUM
ejpam-4510	78	3	)	)	PUNCT
ejpam-4510	78	4	example	example	NOUN
ejpam-4510	79	1	1	1	NUM
ejpam-4510	79	2	.	.	PUNCT
ejpam-4510	80	1	let	let	VERB
ejpam-4510	80	2	(	(	PUNCT
ejpam-4510	80	3	x	x	NOUN
ejpam-4510	80	4	,	,	PUNCT
ejpam-4510	80	5	u	u	NOUN
ejpam-4510	80	6	)	)	PUNCT
ejpam-4510	80	7	be	be	VERB
ejpam-4510	80	8	a	a	DET
ejpam-4510	80	9	be	be	ADJ
ejpam-4510	80	10	-	-	PUNCT
ejpam-4510	80	11	dokdo	dokdo	ADJ
ejpam-4510	80	12	universe	universe	NOUN
ejpam-4510	80	13	in	in	ADP
ejpam-4510	80	14	which	which	PRON
ejpam-4510	80	15	u	u	NOUN
ejpam-4510	80	16	=	=	PROPN
ejpam-4510	80	17	z	z	PROPN
ejpam-4510	80	18	and	and	CCONJ
ejpam-4510	80	19	x	x	SYM
ejpam-4510	80	20	=	=	PUNCT
ejpam-4510	80	21	{	{	PUNCT
ejpam-4510	80	22	1	1	NUM
ejpam-4510	80	23	,	,	PUNCT
ejpam-4510	80	24	2	2	NUM
ejpam-4510	80	25	,	,	PUNCT
ejpam-4510	80	26	3	3	NUM
ejpam-4510	80	27	,	,	PUNCT
ejpam-4510	80	28	4	4	NUM
ejpam-4510	80	29	,	,	PUNCT
ejpam-4510	80	30	5	5	NUM
ejpam-4510	80	31	,	,	PUNCT
ejpam-4510	80	32	6	6	NUM
ejpam-4510	80	33	}	}	PUNCT
ejpam-4510	80	34	is	be	AUX
ejpam-4510	80	35	a	a	DET
ejpam-4510	80	36	be	be	NOUN
ejpam-4510	80	37	-	-	PUNCT
ejpam-4510	80	38	algebra	algebra	NOUN
ejpam-4510	80	39	(	(	PUNCT
ejpam-4510	80	40	see	see	VERB
ejpam-4510	80	41	[	[	X
ejpam-4510	80	42	1	1	NUM
ejpam-4510	80	43	]	]	PUNCT
ejpam-4510	80	44	)	)	PUNCT
ejpam-4510	80	45	with	with	ADP
ejpam-4510	80	46	a	a	DET
ejpam-4510	80	47	binary	binary	ADJ
ejpam-4510	80	48	operation	operation	NOUN
ejpam-4510	80	49	“	"	PUNCT
ejpam-4510	80	50	∗	∗	NOUN
ejpam-4510	80	51	”	"	PUNCT
ejpam-4510	80	52	given	give	VERB
ejpam-4510	80	53	in	in	ADP
ejpam-4510	80	54	the	the	DET
ejpam-4510	80	55	table	table	NOUN
ejpam-4510	80	56	below	below	ADV
ejpam-4510	80	57	.	.	PUNCT
ejpam-4510	81	1	∗	∗	NOUN
ejpam-4510	81	2	1	1	NUM
ejpam-4510	81	3	2	2	NUM
ejpam-4510	81	4	3	3	NUM
ejpam-4510	81	5	4	4	NUM
ejpam-4510	81	6	5	5	NUM
ejpam-4510	81	7	6	6	NUM
ejpam-4510	81	8	1	1	NUM
ejpam-4510	81	9	1	1	NUM
ejpam-4510	81	10	2	2	NUM
ejpam-4510	81	11	3	3	NUM
ejpam-4510	81	12	4	4	NUM
ejpam-4510	81	13	5	5	NUM
ejpam-4510	81	14	6	6	NUM
ejpam-4510	81	15	2	2	NUM
ejpam-4510	81	16	1	1	NUM
ejpam-4510	81	17	1	1	NUM
ejpam-4510	81	18	2	2	NUM
ejpam-4510	81	19	4	4	NUM
ejpam-4510	81	20	4	4	NUM
ejpam-4510	81	21	5	5	NUM
ejpam-4510	81	22	3	3	NUM
ejpam-4510	81	23	1	1	NUM
ejpam-4510	81	24	1	1	NUM
ejpam-4510	81	25	1	1	NUM
ejpam-4510	81	26	4	4	NUM
ejpam-4510	81	27	4	4	NUM
ejpam-4510	81	28	4	4	NUM
ejpam-4510	81	29	4	4	NUM
ejpam-4510	81	30	1	1	NUM
ejpam-4510	81	31	2	2	NUM
ejpam-4510	81	32	3	3	NUM
ejpam-4510	81	33	1	1	NUM
ejpam-4510	81	34	2	2	NUM
ejpam-4510	81	35	3	3	NUM
ejpam-4510	81	36	5	5	NUM
ejpam-4510	81	37	1	1	NUM
ejpam-4510	81	38	1	1	NUM
ejpam-4510	81	39	2	2	NUM
ejpam-4510	81	40	1	1	NUM
ejpam-4510	81	41	1	1	NUM
ejpam-4510	81	42	2	2	NUM
ejpam-4510	81	43	6	6	NUM
ejpam-4510	81	44	1	1	NUM
ejpam-4510	81	45	1	1	NUM
ejpam-4510	81	46	1	1	NUM
ejpam-4510	81	47	1	1	NUM
ejpam-4510	81	48	1	1	NUM
ejpam-4510	81	49	1	1	NUM
ejpam-4510	81	50	y.	y.	PROPN
ejpam-4510	81	51	b.	b.	PROPN
ejpam-4510	81	52	jun	jun	PROPN
ejpam-4510	81	53	,	,	PUNCT
ejpam-4510	81	54	s.	s.	PROPN
ejpam-4510	81	55	s.	s.	PROPN
ejpam-4510	81	56	ahn	ahn	PROPN
ejpam-4510	81	57	and	and	CCONJ
ejpam-4510	81	58	e.	e.	PROPN
ejpam-4510	81	59	h.	h.	PROPN
ejpam-4510	81	60	roh	roh	PROPN
ejpam-4510	81	61	/	/	SYM
ejpam-4510	81	62	eur	eur	PROPN
ejpam-4510	81	63	.	.	PUNCT
ejpam-4510	82	1	j.	j.	PROPN
ejpam-4510	82	2	pure	pure	PROPN
ejpam-4510	82	3	appl	appl	PROPN
ejpam-4510	82	4	.	.	PROPN
ejpam-4510	82	5	math	math	PROPN
ejpam-4510	82	6	,	,	PUNCT
ejpam-4510	82	7	15	15	NUM
ejpam-4510	82	8	(	(	PUNCT
ejpam-4510	82	9	4	4	NUM
ejpam-4510	82	10	)	)	PUNCT
ejpam-4510	82	11	(	(	PUNCT
ejpam-4510	82	12	2022	2022	NUM
ejpam-4510	82	13	)	)	PUNCT
ejpam-4510	82	14	,	,	PUNCT
ejpam-4510	82	15	1521	1521	NUM
ejpam-4510	82	16	-	-	SYM
ejpam-4510	82	17	1535	1535	NUM
ejpam-4510	82	18	1525	1525	NUM
ejpam-4510	82	19	let	let	VERB
ejpam-4510	82	20	dokφ	dokφ	NOUN
ejpam-4510	82	21	:	:	PUNCT
ejpam-4510	82	22	=	=	SYM
ejpam-4510	82	23	(	(	PUNCT
ejpam-4510	82	24	φ̊	φ̊	PROPN
ejpam-4510	82	25	,	,	PUNCT
ejpam-4510	82	26	φs	φs	ADV
ejpam-4510	82	27	,	,	PUNCT
ejpam-4510	82	28	φ̃	φ̃	PROPN
ejpam-4510	82	29	)	)	PUNCT
ejpam-4510	82	30	be	be	VERB
ejpam-4510	82	31	a	a	DET
ejpam-4510	82	32	dokdo	dokdo	NOUN
ejpam-4510	82	33	structure	structure	NOUN
ejpam-4510	82	34	in	in	ADP
ejpam-4510	82	35	(	(	PUNCT
ejpam-4510	82	36	x	x	X
ejpam-4510	82	37	,	,	PUNCT
ejpam-4510	82	38	u	u	NOUN
ejpam-4510	82	39	=	=	PROPN
ejpam-4510	82	40	z	z	PROPN
ejpam-4510	82	41	)	)	PUNCT
ejpam-4510	82	42	which	which	PRON
ejpam-4510	82	43	is	be	AUX
ejpam-4510	82	44	defined	define	VERB
ejpam-4510	82	45	as	as	SCONJ
ejpam-4510	82	46	follows	follow	VERB
ejpam-4510	82	47	:	:	PUNCT
ejpam-4510	82	48	x	x	SYM
ejpam-4510	82	49	φ̊(x	φ̊(x	NOUN
ejpam-4510	82	50	)	)	PUNCT
ejpam-4510	82	51	φs(x	φs(x	PUNCT
ejpam-4510	82	52	)	)	PUNCT
ejpam-4510	82	53	φ̃(x	φ̃(x	PROPN
ejpam-4510	82	54	)	)	PUNCT
ejpam-4510	82	55	1	1	NUM
ejpam-4510	82	56	(	(	PUNCT
ejpam-4510	82	57	−0.7	−0.7	PROPN
ejpam-4510	82	58	,	,	PUNCT
ejpam-4510	82	59	0.8	0.8	NUM
ejpam-4510	82	60	)	)	PUNCT
ejpam-4510	82	61	2z	2z	NOUN
ejpam-4510	83	1	[	[	X
ejpam-4510	83	2	0.4	0.4	NUM
ejpam-4510	83	3	,	,	PUNCT
ejpam-4510	83	4	0.8	0.8	NUM
ejpam-4510	83	5	]	]	SYM
ejpam-4510	83	6	2	2	NUM
ejpam-4510	83	7	(	(	PUNCT
ejpam-4510	83	8	−0.6	−0.6	PROPN
ejpam-4510	83	9	,	,	PUNCT
ejpam-4510	83	10	0.5	0.5	NUM
ejpam-4510	83	11	)	)	PUNCT
ejpam-4510	83	12	8z	8z	NOUN
ejpam-4510	84	1	[	[	X
ejpam-4510	84	2	0.3	0.3	NUM
ejpam-4510	84	3	,	,	PUNCT
ejpam-4510	84	4	0.6	0.6	NUM
ejpam-4510	84	5	]	]	SYM
ejpam-4510	84	6	3	3	NUM
ejpam-4510	84	7	(	(	PUNCT
ejpam-4510	84	8	−0.3	−0.3	PROPN
ejpam-4510	84	9	,	,	PUNCT
ejpam-4510	84	10	0.2	0.2	NUM
ejpam-4510	84	11	)	)	PUNCT
ejpam-4510	84	12	4z	4z	NOUN
ejpam-4510	85	1	[	[	X
ejpam-4510	85	2	0.1	0.1	NUM
ejpam-4510	85	3	,	,	PUNCT
ejpam-4510	85	4	0.5	0.5	NUM
ejpam-4510	85	5	]	]	SYM
ejpam-4510	85	6	4	4	NUM
ejpam-4510	85	7	(	(	PUNCT
ejpam-4510	85	8	−0.5	−0.5	PROPN
ejpam-4510	85	9	,	,	PUNCT
ejpam-4510	85	10	0.4	0.4	NUM
ejpam-4510	85	11	)	)	PUNCT
ejpam-4510	85	12	8n	8n	NOUN
ejpam-4510	86	1	[	[	X
ejpam-4510	86	2	0.3	0.3	NUM
ejpam-4510	86	3	,	,	PUNCT
ejpam-4510	86	4	0.7	0.7	NUM
ejpam-4510	86	5	]	]	SYM
ejpam-4510	86	6	5	5	NUM
ejpam-4510	86	7	(	(	PUNCT
ejpam-4510	86	8	−0.4	−0.4	NUM
ejpam-4510	86	9	,	,	PUNCT
ejpam-4510	86	10	0.3	0.3	NUM
ejpam-4510	86	11	)	)	PUNCT
ejpam-4510	86	12	16n	16n	NOUN
ejpam-4510	87	1	[	[	X
ejpam-4510	87	2	0.2	0.2	NUM
ejpam-4510	87	3	,	,	PUNCT
ejpam-4510	87	4	0.6	0.6	NUM
ejpam-4510	87	5	]	]	SYM
ejpam-4510	87	6	6	6	NUM
ejpam-4510	87	7	(	(	PUNCT
ejpam-4510	87	8	−0.3	−0.3	PROPN
ejpam-4510	87	9	,	,	PUNCT
ejpam-4510	87	10	0.2	0.2	NUM
ejpam-4510	87	11	)	)	PUNCT
ejpam-4510	87	12	16n	16n	NOUN
ejpam-4510	88	1	[	[	X
ejpam-4510	88	2	0.1	0.1	NUM
ejpam-4510	88	3	,	,	PUNCT
ejpam-4510	88	4	0.5	0.5	NUM
ejpam-4510	88	5	]	]	PUNCT
ejpam-4510	88	6	it	it	PRON
ejpam-4510	88	7	is	be	AUX
ejpam-4510	88	8	routine	routine	ADJ
ejpam-4510	88	9	to	to	PART
ejpam-4510	88	10	verify	verify	VERB
ejpam-4510	88	11	that	that	DET
ejpam-4510	88	12	dokφ	dokφ	NOUN
ejpam-4510	88	13	:	:	PUNCT
ejpam-4510	88	14	=	=	SYM
ejpam-4510	88	15	(	(	PUNCT
ejpam-4510	88	16	φ̊	φ̊	PROPN
ejpam-4510	88	17	,	,	PUNCT
ejpam-4510	88	18	φs	φs	ADV
ejpam-4510	88	19	,	,	PUNCT
ejpam-4510	88	20	φ̃	φ̃	PROPN
ejpam-4510	88	21	)	)	PUNCT
ejpam-4510	88	22	is	be	AUX
ejpam-4510	88	23	a	a	DET
ejpam-4510	88	24	dokdo	dokdo	NOUN
ejpam-4510	88	25	be	be	NOUN
ejpam-4510	88	26	-	-	PUNCT
ejpam-4510	88	27	subalgebra	subalgebra	NOUN
ejpam-4510	88	28	of	of	ADP
ejpam-4510	88	29	(	(	PUNCT
ejpam-4510	88	30	x	x	X
ejpam-4510	88	31	,	,	PUNCT
ejpam-4510	88	32	u	u	NOUN
ejpam-4510	88	33	=	=	PROPN
ejpam-4510	88	34	z	z	PROPN
ejpam-4510	88	35	)	)	PUNCT
ejpam-4510	88	36	.	.	PUNCT
ejpam-4510	89	1	definition	definition	NOUN
ejpam-4510	89	2	2	2	NUM
ejpam-4510	89	3	.	.	PUNCT
ejpam-4510	90	1	a	a	DET
ejpam-4510	90	2	dokdo	dokdo	NOUN
ejpam-4510	90	3	structure	structure	NOUN
ejpam-4510	90	4	dokφ	dokφ	NOUN
ejpam-4510	90	5	:	:	PUNCT
ejpam-4510	90	6	=	=	SYM
ejpam-4510	90	7	(	(	PUNCT
ejpam-4510	90	8	φ̊	φ̊	PROPN
ejpam-4510	90	9	,	,	PUNCT
ejpam-4510	90	10	φs	φs	ADV
ejpam-4510	90	11	,	,	PUNCT
ejpam-4510	90	12	φ̃	φ̃	PROPN
ejpam-4510	90	13	)	)	PUNCT
ejpam-4510	90	14	is	be	AUX
ejpam-4510	90	15	called	call	VERB
ejpam-4510	90	16	a	a	DET
ejpam-4510	90	17	weak	weak	ADJ
ejpam-4510	90	18	dokdo	dokdo	NOUN
ejpam-4510	90	19	be	be	NOUN
ejpam-4510	90	20	-	-	PUNCT
ejpam-4510	90	21	subalgebra	subalgebra	NOUN
ejpam-4510	90	22	of	of	ADP
ejpam-4510	90	23	(	(	PUNCT
ejpam-4510	90	24	x	x	NOUN
ejpam-4510	90	25	,	,	PUNCT
ejpam-4510	90	26	u	u	NOUN
ejpam-4510	90	27	)	)	PUNCT
ejpam-4510	90	28	if	if	SCONJ
ejpam-4510	90	29	it	it	PRON
ejpam-4510	90	30	satisfies	satisfy	VERB
ejpam-4510	90	31	:	:	PUNCT
ejpam-4510	90	32	(	(	PUNCT
ejpam-4510	90	33	∀x	∀x	X
ejpam-4510	90	34	,	,	PUNCT
ejpam-4510	90	35	y	y	PROPN
ejpam-4510	90	36	∈	∈	PROPN
ejpam-4510	90	37	x	x	X
ejpam-4510	90	38	)	)	PUNCT
ejpam-4510	90	39	(	(	PUNCT
ejpam-4510	90	40	x∗(x∗y	x∗(x∗y	NUM
ejpam-4510	90	41	)	)	PUNCT
ejpam-4510	90	42	(	(	PUNCT
ejpam-4510	90	43	x	x	X
ejpam-4510	90	44	,	,	PUNCT
ejpam-4510	90	45	y	y	PROPN
ejpam-4510	90	46	)	)	PUNCT
ejpam-4510	90	47	∈	∈	PROPN
ejpam-4510	90	48	φ̊(max	φ̊(max	NUM
ejpam-4510	90	49	,	,	PUNCT
ejpam-4510	90	50	min	min	NOUN
ejpam-4510	90	51	)	)	PUNCT
ejpam-4510	90	52	)	)	PUNCT
ejpam-4510	90	53	,	,	PUNCT
ejpam-4510	90	54	(	(	PUNCT
ejpam-4510	90	55	17	17	NUM
ejpam-4510	90	56	)	)	PUNCT
ejpam-4510	90	57	(	(	PUNCT
ejpam-4510	90	58	∀x	∀x	X
ejpam-4510	90	59	,	,	PUNCT
ejpam-4510	90	60	y	y	PROPN
ejpam-4510	90	61	∈	∈	PROPN
ejpam-4510	90	62	x	x	X
ejpam-4510	90	63	)	)	PUNCT
ejpam-4510	90	64	(	(	PUNCT
ejpam-4510	90	65	φs(x	φs(x	X
ejpam-4510	90	66	∗	∗	NOUN
ejpam-4510	90	67	(	(	PUNCT
ejpam-4510	90	68	x	x	X
ejpam-4510	90	69	∗	∗	PROPN
ejpam-4510	90	70	y	y	PROPN
ejpam-4510	90	71	)	)	PUNCT
ejpam-4510	90	72	)	)	PUNCT
ejpam-4510	90	73	⊇	⊇	NOUN
ejpam-4510	90	74	φs(x	φs(x	NOUN
ejpam-4510	90	75	)	)	PUNCT
ejpam-4510	90	76	∩	∩	NOUN
ejpam-4510	90	77	φs(y	φs(y	NUM
ejpam-4510	90	78	)	)	PUNCT
ejpam-4510	90	79	)	)	PUNCT
ejpam-4510	90	80	,	,	PUNCT
ejpam-4510	90	81	(	(	PUNCT
ejpam-4510	90	82	18	18	NUM
ejpam-4510	90	83	)	)	PUNCT
ejpam-4510	90	84	(	(	PUNCT
ejpam-4510	90	85	∀x	∀x	X
ejpam-4510	90	86	,	,	PUNCT
ejpam-4510	90	87	y	y	PROPN
ejpam-4510	90	88	∈	∈	PROPN
ejpam-4510	90	89	x	x	X
ejpam-4510	90	90	)	)	PUNCT
ejpam-4510	90	91	(	(	PUNCT
ejpam-4510	90	92	φ̃(x	φ̃(x	PROPN
ejpam-4510	90	93	∗	∗	NOUN
ejpam-4510	90	94	(	(	PUNCT
ejpam-4510	90	95	x	x	X
ejpam-4510	90	96	∗	∗	PROPN
ejpam-4510	90	97	y	y	NOUN
ejpam-4510	90	98	)	)	PUNCT
ejpam-4510	90	99	)	)	PUNCT
ejpam-4510	90	100	⪰	⪰	NOUN
ejpam-4510	90	101	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	90	102	)	)	PUNCT
ejpam-4510	90	103	,	,	PUNCT
ejpam-4510	90	104	φ̃(y	φ̃(y	NOUN
ejpam-4510	90	105	)	)	PUNCT
ejpam-4510	90	106	}	}	PUNCT
ejpam-4510	90	107	)	)	PUNCT
ejpam-4510	90	108	.	.	PUNCT
ejpam-4510	91	1	(	(	PUNCT
ejpam-4510	91	2	19	19	NUM
ejpam-4510	91	3	)	)	PUNCT
ejpam-4510	91	4	example	example	NOUN
ejpam-4510	92	1	2	2	NUM
ejpam-4510	92	2	.	.	X
ejpam-4510	93	1	let	let	VERB
ejpam-4510	93	2	(	(	PUNCT
ejpam-4510	93	3	x	x	NOUN
ejpam-4510	93	4	,	,	PUNCT
ejpam-4510	93	5	u	u	NOUN
ejpam-4510	93	6	)	)	PUNCT
ejpam-4510	93	7	be	be	VERB
ejpam-4510	93	8	a	a	DET
ejpam-4510	93	9	be	be	ADJ
ejpam-4510	93	10	-	-	PUNCT
ejpam-4510	93	11	dokdo	dokdo	ADJ
ejpam-4510	93	12	universe	universe	NOUN
ejpam-4510	93	13	in	in	ADP
ejpam-4510	93	14	which	which	PRON
ejpam-4510	93	15	u	u	NOUN
ejpam-4510	93	16	=	=	PROPN
ejpam-4510	93	17	z	z	PROPN
ejpam-4510	93	18	and	and	CCONJ
ejpam-4510	93	19	x	x	SYM
ejpam-4510	93	20	=	=	PUNCT
ejpam-4510	93	21	{	{	PUNCT
ejpam-4510	93	22	1	1	NUM
ejpam-4510	93	23	,	,	PUNCT
ejpam-4510	93	24	2	2	NUM
ejpam-4510	93	25	,	,	PUNCT
ejpam-4510	93	26	3	3	NUM
ejpam-4510	93	27	,	,	PUNCT
ejpam-4510	93	28	4	4	NUM
ejpam-4510	93	29	}	}	PUNCT
ejpam-4510	93	30	is	be	AUX
ejpam-4510	93	31	a	a	DET
ejpam-4510	93	32	be	be	NOUN
ejpam-4510	93	33	-	-	PUNCT
ejpam-4510	93	34	algebra	algebra	NOUN
ejpam-4510	93	35	(	(	PUNCT
ejpam-4510	93	36	see	see	VERB
ejpam-4510	93	37	[	[	X
ejpam-4510	93	38	10	10	NUM
ejpam-4510	93	39	]	]	PUNCT
ejpam-4510	93	40	)	)	PUNCT
ejpam-4510	93	41	with	with	ADP
ejpam-4510	93	42	a	a	DET
ejpam-4510	93	43	binary	binary	ADJ
ejpam-4510	93	44	operation	operation	NOUN
ejpam-4510	93	45	“	"	PUNCT
ejpam-4510	93	46	∗	∗	NOUN
ejpam-4510	93	47	”	"	PUNCT
ejpam-4510	93	48	given	give	VERB
ejpam-4510	93	49	in	in	ADP
ejpam-4510	93	50	the	the	DET
ejpam-4510	93	51	table	table	NOUN
ejpam-4510	93	52	below	below	ADV
ejpam-4510	93	53	.	.	PUNCT
ejpam-4510	94	1	∗	∗	NOUN
ejpam-4510	94	2	1	1	NUM
ejpam-4510	94	3	2	2	NUM
ejpam-4510	94	4	3	3	NUM
ejpam-4510	94	5	4	4	NUM
ejpam-4510	94	6	1	1	NUM
ejpam-4510	94	7	1	1	NUM
ejpam-4510	94	8	2	2	NUM
ejpam-4510	94	9	3	3	NUM
ejpam-4510	94	10	4	4	NUM
ejpam-4510	94	11	2	2	NUM
ejpam-4510	94	12	1	1	NUM
ejpam-4510	94	13	1	1	NUM
ejpam-4510	94	14	2	2	NUM
ejpam-4510	94	15	2	2	NUM
ejpam-4510	94	16	3	3	NUM
ejpam-4510	94	17	1	1	NUM
ejpam-4510	94	18	1	1	NUM
ejpam-4510	94	19	1	1	NUM
ejpam-4510	94	20	2	2	NUM
ejpam-4510	94	21	4	4	NUM
ejpam-4510	94	22	1	1	NUM
ejpam-4510	94	23	1	1	NUM
ejpam-4510	94	24	2	2	NUM
ejpam-4510	94	25	1	1	NUM
ejpam-4510	94	26	define	define	VERB
ejpam-4510	94	27	a	a	DET
ejpam-4510	94	28	dokdo	dokdo	NOUN
ejpam-4510	94	29	structure	structure	NOUN
ejpam-4510	94	30	dokφ	dokφ	NOUN
ejpam-4510	95	1	:	:	PUNCT
ejpam-4510	95	2	=	=	SYM
ejpam-4510	95	3	(	(	PUNCT
ejpam-4510	95	4	φ̊	φ̊	PROPN
ejpam-4510	95	5	,	,	PUNCT
ejpam-4510	95	6	φs	φs	ADV
ejpam-4510	95	7	,	,	PUNCT
ejpam-4510	95	8	φ̃	φ̃	PROPN
ejpam-4510	95	9	)	)	PUNCT
ejpam-4510	95	10	in	in	ADP
ejpam-4510	95	11	(	(	PUNCT
ejpam-4510	95	12	x	x	NOUN
ejpam-4510	95	13	,	,	PUNCT
ejpam-4510	95	14	u	u	NOUN
ejpam-4510	95	15	)	)	PUNCT
ejpam-4510	95	16	as	as	SCONJ
ejpam-4510	95	17	follows	follow	VERB
ejpam-4510	95	18	:	:	PUNCT
ejpam-4510	95	19	dokφ	dokφ	NOUN
ejpam-4510	95	20	:	:	PUNCT
ejpam-4510	95	21	=	=	SYM
ejpam-4510	95	22	(	(	PUNCT
ejpam-4510	95	23	φ̊	φ̊	PROPN
ejpam-4510	95	24	,	,	PUNCT
ejpam-4510	95	25	φs	φs	ADV
ejpam-4510	95	26	,	,	PUNCT
ejpam-4510	95	27	φ̃	φ̃	PROPN
ejpam-4510	95	28	)	)	PUNCT
ejpam-4510	95	29	:	:	PUNCT
ejpam-4510	95	30	x	x	X
ejpam-4510	95	31	→	→	PUNCT
ejpam-4510	95	32	(	(	PUNCT
ejpam-4510	95	33	[	[	X
ejpam-4510	95	34	−1	−1	NOUN
ejpam-4510	95	35	,	,	PUNCT
ejpam-4510	95	36	0]×	0]×	PROPN
ejpam-4510	96	1	[	[	X
ejpam-4510	96	2	0	0	NUM
ejpam-4510	96	3	,	,	PUNCT
ejpam-4510	96	4	1])×	1])×	NOUN
ejpam-4510	96	5	2u	2u	NOUN
ejpam-4510	96	6	×	×	NOUN
ejpam-4510	97	1	[	[	X
ejpam-4510	97	2	[	[	X
ejpam-4510	97	3	0	0	NUM
ejpam-4510	97	4	,	,	PUNCT
ejpam-4510	97	5	1	1	NUM
ejpam-4510	97	6	]	]	PUNCT
ejpam-4510	97	7	]	]	PUNCT
ejpam-4510	97	8	,	,	PUNCT
ejpam-4510	97	9	x	x	SYM
ejpam-4510	97	10	7→	7→	X
ejpam-4510	97	11	{	{	PUNCT
ejpam-4510	97	12	(	(	PUNCT
ejpam-4510	97	13	(	(	PUNCT
ejpam-4510	97	14	−0.46	−0.46	ADJ
ejpam-4510	97	15	,	,	PUNCT
ejpam-4510	97	16	0.73),z	0.73),z	PROPN
ejpam-4510	97	17	,	,	PUNCT
ejpam-4510	97	18	[	[	X
ejpam-4510	97	19	0.41	0.41	NUM
ejpam-4510	97	20	,	,	PUNCT
ejpam-4510	97	21	0.73	0.73	NUM
ejpam-4510	97	22	]	]	PUNCT
ejpam-4510	97	23	)	)	PUNCT
ejpam-4510	97	24	if	if	SCONJ
ejpam-4510	97	25	x	x	PROPN
ejpam-4510	97	26	=	=	SYM
ejpam-4510	97	27	1	1	NUM
ejpam-4510	97	28	,	,	PUNCT
ejpam-4510	97	29	(	(	PUNCT
ejpam-4510	97	30	(	(	PUNCT
ejpam-4510	97	31	−0.36	−0.36	NOUN
ejpam-4510	97	32	,	,	PUNCT
ejpam-4510	97	33	0.63),n	0.63),n	PROPN
ejpam-4510	97	34	,	,	PUNCT
ejpam-4510	97	35	[	[	X
ejpam-4510	97	36	0.32	0.32	NUM
ejpam-4510	97	37	,	,	PUNCT
ejpam-4510	97	38	0.64	0.64	NUM
ejpam-4510	97	39	]	]	PUNCT
ejpam-4510	97	40	)	)	PUNCT
ejpam-4510	97	41	otherwise	otherwise	ADV
ejpam-4510	97	42	.	.	PUNCT
ejpam-4510	98	1	it	it	PRON
ejpam-4510	98	2	is	be	AUX
ejpam-4510	98	3	routine	routine	ADJ
ejpam-4510	98	4	to	to	PART
ejpam-4510	98	5	check	check	VERB
ejpam-4510	98	6	that	that	DET
ejpam-4510	98	7	dokφ	dokφ	NOUN
ejpam-4510	98	8	:	:	PUNCT
ejpam-4510	98	9	=	=	SYM
ejpam-4510	98	10	(	(	PUNCT
ejpam-4510	98	11	φ̊	φ̊	PROPN
ejpam-4510	98	12	,	,	PUNCT
ejpam-4510	98	13	φs	φs	ADV
ejpam-4510	98	14	,	,	PUNCT
ejpam-4510	98	15	φ̃	φ̃	PROPN
ejpam-4510	98	16	)	)	PUNCT
ejpam-4510	98	17	is	be	AUX
ejpam-4510	98	18	a	a	DET
ejpam-4510	98	19	weak	weak	ADJ
ejpam-4510	98	20	dokdo	dokdo	NOUN
ejpam-4510	98	21	be	be	NOUN
ejpam-4510	98	22	-	-	PUNCT
ejpam-4510	98	23	subalgebra	subalgebra	NOUN
ejpam-4510	98	24	of	of	ADP
ejpam-4510	98	25	(	(	PUNCT
ejpam-4510	98	26	x	x	NOUN
ejpam-4510	98	27	,	,	PUNCT
ejpam-4510	98	28	u	u	NOUN
ejpam-4510	98	29	)	)	PUNCT
ejpam-4510	98	30	.	.	PUNCT
ejpam-4510	99	1	lemma	lemma	PROPN
ejpam-4510	99	2	1	1	NUM
ejpam-4510	99	3	.	.	PUNCT
ejpam-4510	100	1	every	every	DET
ejpam-4510	100	2	dokdo	dokdo	NOUN
ejpam-4510	100	3	be	be	AUX
ejpam-4510	100	4	-	-	PUNCT
ejpam-4510	100	5	subalgebra	subalgebra	NOUN
ejpam-4510	100	6	is	be	AUX
ejpam-4510	100	7	a	a	DET
ejpam-4510	100	8	weak	weak	ADJ
ejpam-4510	100	9	dokdo	dokdo	NOUN
ejpam-4510	100	10	be	be	NOUN
ejpam-4510	100	11	-	-	PUNCT
ejpam-4510	100	12	subalgebra	subalgebra	NOUN
ejpam-4510	100	13	.	.	PUNCT
ejpam-4510	101	1	proof	proof	NOUN
ejpam-4510	101	2	.	.	PUNCT
ejpam-4510	102	1	the	the	DET
ejpam-4510	102	2	proof	proof	NOUN
ejpam-4510	102	3	is	be	AUX
ejpam-4510	102	4	straightforward	straightforward	ADJ
ejpam-4510	102	5	.	.	PUNCT
ejpam-4510	103	1	the	the	DET
ejpam-4510	103	2	converse	converse	NOUN
ejpam-4510	103	3	of	of	ADP
ejpam-4510	103	4	lemma	lemma	PROPN
ejpam-4510	103	5	1	1	NUM
ejpam-4510	103	6	may	may	AUX
ejpam-4510	103	7	not	not	PART
ejpam-4510	103	8	be	be	AUX
ejpam-4510	103	9	true	true	ADJ
ejpam-4510	103	10	as	as	SCONJ
ejpam-4510	103	11	seen	see	VERB
ejpam-4510	103	12	in	in	ADP
ejpam-4510	103	13	the	the	DET
ejpam-4510	103	14	following	follow	VERB
ejpam-4510	103	15	example	example	NOUN
ejpam-4510	103	16	.	.	PUNCT
ejpam-4510	104	1	example	example	NOUN
ejpam-4510	105	1	3	3	X
ejpam-4510	105	2	.	.	PUNCT
ejpam-4510	106	1	let	let	AUX
ejpam-4510	106	2	(	(	PUNCT
ejpam-4510	106	3	x	x	NOUN
ejpam-4510	106	4	,	,	PUNCT
ejpam-4510	106	5	u	u	NOUN
ejpam-4510	106	6	)	)	PUNCT
ejpam-4510	106	7	be	be	VERB
ejpam-4510	106	8	a	a	DET
ejpam-4510	106	9	be	be	ADJ
ejpam-4510	106	10	-	-	PUNCT
ejpam-4510	106	11	dokdo	dokdo	ADJ
ejpam-4510	106	12	universe	universe	NOUN
ejpam-4510	106	13	in	in	ADP
ejpam-4510	106	14	which	which	PRON
ejpam-4510	106	15	u	u	NOUN
ejpam-4510	106	16	=	=	PROPN
ejpam-4510	106	17	z	z	PROPN
ejpam-4510	106	18	and	and	CCONJ
ejpam-4510	106	19	x	x	SYM
ejpam-4510	106	20	=	=	PUNCT
ejpam-4510	106	21	{	{	PUNCT
ejpam-4510	106	22	1	1	NUM
ejpam-4510	106	23	,	,	PUNCT
ejpam-4510	106	24	2	2	NUM
ejpam-4510	106	25	,	,	PUNCT
ejpam-4510	106	26	3	3	NUM
ejpam-4510	106	27	,	,	PUNCT
ejpam-4510	106	28	4	4	NUM
ejpam-4510	106	29	}	}	PUNCT
ejpam-4510	106	30	is	be	AUX
ejpam-4510	106	31	a	a	DET
ejpam-4510	106	32	be	be	NOUN
ejpam-4510	106	33	-	-	PUNCT
ejpam-4510	106	34	algebra	algebra	NOUN
ejpam-4510	106	35	(	(	PUNCT
ejpam-4510	106	36	see	see	VERB
ejpam-4510	106	37	[	[	X
ejpam-4510	106	38	10	10	NUM
ejpam-4510	106	39	]	]	PUNCT
ejpam-4510	106	40	)	)	PUNCT
ejpam-4510	106	41	with	with	ADP
ejpam-4510	106	42	a	a	DET
ejpam-4510	106	43	binary	binary	ADJ
ejpam-4510	106	44	operation	operation	NOUN
ejpam-4510	106	45	“	"	PUNCT
ejpam-4510	106	46	∗	∗	NOUN
ejpam-4510	106	47	”	"	PUNCT
ejpam-4510	106	48	given	give	VERB
ejpam-4510	106	49	in	in	ADP
ejpam-4510	106	50	the	the	DET
ejpam-4510	106	51	table	table	NOUN
ejpam-4510	106	52	below	below	ADV
ejpam-4510	106	53	.	.	PUNCT
ejpam-4510	107	1	y.	y.	PROPN
ejpam-4510	107	2	b.	b.	PROPN
ejpam-4510	107	3	jun	jun	PROPN
ejpam-4510	107	4	,	,	PUNCT
ejpam-4510	107	5	s.	s.	PROPN
ejpam-4510	107	6	s.	s.	PROPN
ejpam-4510	107	7	ahn	ahn	PROPN
ejpam-4510	107	8	and	and	CCONJ
ejpam-4510	107	9	e.	e.	PROPN
ejpam-4510	107	10	h.	h.	PROPN
ejpam-4510	107	11	roh	roh	PROPN
ejpam-4510	107	12	/	/	SYM
ejpam-4510	107	13	eur	eur	PROPN
ejpam-4510	107	14	.	.	PUNCT
ejpam-4510	108	1	j.	j.	PROPN
ejpam-4510	108	2	pure	pure	PROPN
ejpam-4510	108	3	appl	appl	PROPN
ejpam-4510	108	4	.	.	PROPN
ejpam-4510	108	5	math	math	PROPN
ejpam-4510	108	6	,	,	PUNCT
ejpam-4510	108	7	15	15	NUM
ejpam-4510	108	8	(	(	PUNCT
ejpam-4510	108	9	4	4	NUM
ejpam-4510	108	10	)	)	PUNCT
ejpam-4510	108	11	(	(	PUNCT
ejpam-4510	108	12	2022	2022	NUM
ejpam-4510	108	13	)	)	PUNCT
ejpam-4510	108	14	,	,	PUNCT
ejpam-4510	108	15	1521	1521	NUM
ejpam-4510	108	16	-	-	SYM
ejpam-4510	108	17	1535	1535	NUM
ejpam-4510	108	18	1526	1526	NUM
ejpam-4510	108	19	∗	∗	NOUN
ejpam-4510	108	20	1	1	NUM
ejpam-4510	108	21	2	2	NUM
ejpam-4510	108	22	3	3	NUM
ejpam-4510	108	23	4	4	NUM
ejpam-4510	108	24	1	1	NUM
ejpam-4510	108	25	1	1	NUM
ejpam-4510	108	26	2	2	NUM
ejpam-4510	108	27	3	3	NUM
ejpam-4510	108	28	4	4	NUM
ejpam-4510	108	29	2	2	NUM
ejpam-4510	108	30	1	1	NUM
ejpam-4510	108	31	1	1	NUM
ejpam-4510	108	32	4	4	NUM
ejpam-4510	108	33	3	3	NUM
ejpam-4510	108	34	3	3	NUM
ejpam-4510	108	35	1	1	NUM
ejpam-4510	108	36	4	4	NUM
ejpam-4510	108	37	1	1	NUM
ejpam-4510	108	38	2	2	NUM
ejpam-4510	108	39	4	4	NUM
ejpam-4510	108	40	1	1	NUM
ejpam-4510	108	41	3	3	NUM
ejpam-4510	108	42	2	2	NUM
ejpam-4510	108	43	1	1	NUM
ejpam-4510	108	44	define	define	VERB
ejpam-4510	108	45	a	a	DET
ejpam-4510	108	46	dokdo	dokdo	NOUN
ejpam-4510	108	47	structure	structure	NOUN
ejpam-4510	108	48	dokφ	dokφ	NOUN
ejpam-4510	108	49	:	:	PUNCT
ejpam-4510	108	50	=	=	SYM
ejpam-4510	108	51	(	(	PUNCT
ejpam-4510	108	52	φ̊	φ̊	PROPN
ejpam-4510	108	53	,	,	PUNCT
ejpam-4510	108	54	φs	φs	ADV
ejpam-4510	108	55	,	,	PUNCT
ejpam-4510	108	56	φ̃	φ̃	PROPN
ejpam-4510	108	57	)	)	PUNCT
ejpam-4510	108	58	in	in	ADP
ejpam-4510	108	59	(	(	PUNCT
ejpam-4510	108	60	x	x	NOUN
ejpam-4510	108	61	,	,	PUNCT
ejpam-4510	108	62	u	u	NOUN
ejpam-4510	108	63	)	)	PUNCT
ejpam-4510	108	64	as	as	SCONJ
ejpam-4510	108	65	follows	follow	VERB
ejpam-4510	108	66	:	:	PUNCT
ejpam-4510	108	67	dokφ	dokφ	NOUN
ejpam-4510	108	68	:	:	PUNCT
ejpam-4510	108	69	=	=	SYM
ejpam-4510	108	70	(	(	PUNCT
ejpam-4510	108	71	φ̊	φ̊	PROPN
ejpam-4510	108	72	,	,	PUNCT
ejpam-4510	108	73	φs	φs	ADV
ejpam-4510	108	74	,	,	PUNCT
ejpam-4510	108	75	φ̃	φ̃	PROPN
ejpam-4510	108	76	)	)	PUNCT
ejpam-4510	108	77	:	:	PUNCT
ejpam-4510	109	1	x	x	X
ejpam-4510	109	2	→	→	PUNCT
ejpam-4510	109	3	(	(	PUNCT
ejpam-4510	109	4	[	[	X
ejpam-4510	109	5	−1	−1	NOUN
ejpam-4510	109	6	,	,	PUNCT
ejpam-4510	109	7	0]×	0]×	PROPN
ejpam-4510	110	1	[	[	X
ejpam-4510	110	2	0	0	NUM
ejpam-4510	110	3	,	,	PUNCT
ejpam-4510	110	4	1])×	1])×	NOUN
ejpam-4510	110	5	2u	2u	NOUN
ejpam-4510	110	6	×	×	NOUN
ejpam-4510	111	1	[	[	X
ejpam-4510	111	2	[	[	X
ejpam-4510	111	3	0	0	NUM
ejpam-4510	111	4	,	,	PUNCT
ejpam-4510	111	5	1	1	NUM
ejpam-4510	111	6	]	]	PUNCT
ejpam-4510	111	7	]	]	PUNCT
ejpam-4510	111	8	,	,	PUNCT
ejpam-4510	111	9	x	x	SYM
ejpam-4510	111	10	7→	7→	NUM
ejpam-4510	111	11			PUNCT
ejpam-4510	111	12	(	(	PUNCT
ejpam-4510	111	13	(	(	PUNCT
ejpam-4510	111	14	−0.46	−0.46	ADJ
ejpam-4510	111	15	,	,	PUNCT
ejpam-4510	111	16	0.73),z	0.73),z	PROPN
ejpam-4510	111	17	,	,	PUNCT
ejpam-4510	111	18	[	[	X
ejpam-4510	111	19	0.41	0.41	NUM
ejpam-4510	111	20	,	,	PUNCT
ejpam-4510	111	21	0.73	0.73	NUM
ejpam-4510	111	22	]	]	PUNCT
ejpam-4510	111	23	)	)	PUNCT
ejpam-4510	111	24	if	if	SCONJ
ejpam-4510	111	25	x	x	PROPN
ejpam-4510	111	26	=	=	SYM
ejpam-4510	111	27	1	1	NUM
ejpam-4510	111	28	,	,	PUNCT
ejpam-4510	111	29	(	(	PUNCT
ejpam-4510	111	30	(	(	PUNCT
ejpam-4510	111	31	−0.36	−0.36	NOUN
ejpam-4510	111	32	,	,	PUNCT
ejpam-4510	111	33	0.63	0.63	NUM
ejpam-4510	111	34	)	)	PUNCT
ejpam-4510	111	35	,	,	PUNCT
ejpam-4510	111	36	2z	2z	NUM
ejpam-4510	111	37	,	,	PUNCT
ejpam-4510	111	38	[	[	X
ejpam-4510	111	39	0.32	0.32	NUM
ejpam-4510	111	40	,	,	PUNCT
ejpam-4510	111	41	0.64	0.64	NUM
ejpam-4510	111	42	]	]	PUNCT
ejpam-4510	111	43	)	)	PUNCT
ejpam-4510	111	44	if	if	SCONJ
ejpam-4510	111	45	x	x	PUNCT
ejpam-4510	111	46	∈	∈	PROPN
ejpam-4510	111	47	{	{	PUNCT
ejpam-4510	111	48	2	2	NUM
ejpam-4510	111	49	,	,	PUNCT
ejpam-4510	111	50	4	4	NUM
ejpam-4510	111	51	}	}	PUNCT
ejpam-4510	111	52	,	,	PUNCT
ejpam-4510	111	53	(	(	PUNCT
ejpam-4510	111	54	(	(	PUNCT
ejpam-4510	111	55	−0.27	−0.27	INTJ
ejpam-4510	111	56	,	,	PUNCT
ejpam-4510	111	57	0.58	0.58	NUM
ejpam-4510	111	58	)	)	PUNCT
ejpam-4510	111	59	,	,	PUNCT
ejpam-4510	111	60	2n	2n	NUM
ejpam-4510	111	61	,	,	PUNCT
ejpam-4510	111	62	[	[	X
ejpam-4510	111	63	0.29	0.29	NUM
ejpam-4510	111	64	,	,	PUNCT
ejpam-4510	111	65	0.59	0.59	NUM
ejpam-4510	111	66	]	]	PUNCT
ejpam-4510	111	67	)	)	PUNCT
ejpam-4510	111	68	if	if	SCONJ
ejpam-4510	111	69	x	x	PROPN
ejpam-4510	111	70	=	=	NOUN
ejpam-4510	111	71	3	3	X
ejpam-4510	111	72	.	.	PUNCT
ejpam-4510	112	1	it	it	PRON
ejpam-4510	112	2	is	be	AUX
ejpam-4510	112	3	routine	routine	ADJ
ejpam-4510	112	4	to	to	PART
ejpam-4510	112	5	check	check	VERB
ejpam-4510	112	6	that	that	DET
ejpam-4510	112	7	dokφ	dokφ	NOUN
ejpam-4510	112	8	:	:	PUNCT
ejpam-4510	112	9	=	=	SYM
ejpam-4510	112	10	(	(	PUNCT
ejpam-4510	112	11	φ̊	φ̊	PROPN
ejpam-4510	112	12	,	,	PUNCT
ejpam-4510	112	13	φs	φs	ADV
ejpam-4510	112	14	,	,	PUNCT
ejpam-4510	112	15	φ̃	φ̃	PROPN
ejpam-4510	112	16	)	)	PUNCT
ejpam-4510	112	17	is	be	AUX
ejpam-4510	112	18	a	a	DET
ejpam-4510	112	19	weak	weak	ADJ
ejpam-4510	112	20	dokdo	dokdo	NOUN
ejpam-4510	112	21	be	be	NOUN
ejpam-4510	112	22	-	-	PUNCT
ejpam-4510	112	23	subalgebra	subalgebra	NOUN
ejpam-4510	112	24	of	of	ADP
ejpam-4510	112	25	(	(	PUNCT
ejpam-4510	112	26	x	x	NOUN
ejpam-4510	112	27	,	,	PUNCT
ejpam-4510	112	28	u	u	NOUN
ejpam-4510	112	29	)	)	PUNCT
ejpam-4510	112	30	.	.	PUNCT
ejpam-4510	113	1	but	but	CCONJ
ejpam-4510	113	2	it	it	PRON
ejpam-4510	113	3	is	be	AUX
ejpam-4510	113	4	not	not	PART
ejpam-4510	113	5	a	a	DET
ejpam-4510	113	6	dokdo	dokdo	NOUN
ejpam-4510	113	7	be	be	NOUN
ejpam-4510	113	8	-	-	PUNCT
ejpam-4510	113	9	subalgebra	subalgebra	NOUN
ejpam-4510	113	10	of	of	ADP
ejpam-4510	113	11	(	(	PUNCT
ejpam-4510	113	12	x	x	NOUN
ejpam-4510	113	13	,	,	PUNCT
ejpam-4510	113	14	u	u	NOUN
ejpam-4510	113	15	)	)	PUNCT
ejpam-4510	113	16	since	since	SCONJ
ejpam-4510	113	17	2∗4	2∗4	NUM
ejpam-4510	113	18	(	(	PUNCT
ejpam-4510	113	19	2,4	2,4	NUM
ejpam-4510	113	20	)	)	PUNCT
ejpam-4510	113	21	=	=	SYM
ejpam-4510	113	22	3	3	NUM
ejpam-4510	113	23	(	(	PUNCT
ejpam-4510	113	24	2,4	2,4	NUM
ejpam-4510	113	25	)	)	PUNCT
ejpam-4510	113	26	/∈	/∈	PUNCT
ejpam-4510	114	1	φ̊(max	φ̊(max	ADV
ejpam-4510	114	2	,	,	PUNCT
ejpam-4510	114	3	min	min	NOUN
ejpam-4510	114	4	)	)	PUNCT
ejpam-4510	114	5	,	,	PUNCT
ejpam-4510	114	6	φs(2∗4	φs(2∗4	PROPN
ejpam-4510	114	7	)	)	PUNCT
ejpam-4510	114	8	=	=	SYM
ejpam-4510	114	9	φs(3	φs(3	NOUN
ejpam-4510	114	10	)	)	PUNCT
ejpam-4510	114	11	=	=	SYM
ejpam-4510	114	12	2n	2n	NUM
ejpam-4510	115	1	⊉	⊉	PROPN
ejpam-4510	115	2	2z	2z	NUM
ejpam-4510	115	3	=	=	PUNCT
ejpam-4510	115	4	φs(2	φs(2	NOUN
ejpam-4510	115	5	)	)	PUNCT
ejpam-4510	115	6	∩	∩	ADJ
ejpam-4510	115	7	φs(4	φs(4	NOUN
ejpam-4510	115	8	)	)	PUNCT
ejpam-4510	115	9	,	,	PUNCT
ejpam-4510	115	10	or	or	CCONJ
ejpam-4510	115	11	φ̃(2	φ̃(2	VERB
ejpam-4510	115	12	∗	∗	NOUN
ejpam-4510	115	13	4	4	NUM
ejpam-4510	115	14	)	)	PUNCT
ejpam-4510	115	15	=	=	PUNCT
ejpam-4510	115	16	φ̃(3	φ̃(3	NOUN
ejpam-4510	115	17	)	)	PUNCT
ejpam-4510	115	18	=	=	PUNCT
ejpam-4510	116	1	[	[	X
ejpam-4510	116	2	0.29	0.29	NUM
ejpam-4510	116	3	,	,	PUNCT
ejpam-4510	116	4	0.59	0.59	NUM
ejpam-4510	116	5	]	]	PUNCT
ejpam-4510	116	6	⪰̸	⪰̸	PUNCT
ejpam-4510	117	1	[	[	X
ejpam-4510	117	2	0.32	0.32	NUM
ejpam-4510	117	3	,	,	PUNCT
ejpam-4510	117	4	0.64	0.64	NUM
ejpam-4510	117	5	]	]	PUNCT
ejpam-4510	117	6	=	=	SYM
ejpam-4510	117	7	rmin{φ̃(2	rmin{φ̃(2	PROPN
ejpam-4510	117	8	)	)	PUNCT
ejpam-4510	117	9	,	,	PUNCT
ejpam-4510	117	10	φ̃(4	φ̃(4	NOUN
ejpam-4510	117	11	)	)	PUNCT
ejpam-4510	117	12	}	}	PUNCT
ejpam-4510	117	13	.	.	PUNCT
ejpam-4510	118	1	we	we	PRON
ejpam-4510	118	2	explore	explore	VERB
ejpam-4510	118	3	the	the	DET
ejpam-4510	118	4	conditions	condition	NOUN
ejpam-4510	118	5	under	under	ADP
ejpam-4510	118	6	which	which	PRON
ejpam-4510	118	7	the	the	DET
ejpam-4510	118	8	converse	converse	NOUN
ejpam-4510	118	9	of	of	ADP
ejpam-4510	118	10	lemma	lemma	PROPN
ejpam-4510	118	11	1	1	NUM
ejpam-4510	118	12	becomes	become	VERB
ejpam-4510	118	13	true	true	ADJ
ejpam-4510	118	14	.	.	PUNCT
ejpam-4510	119	1	theorem	theorem	NOUN
ejpam-4510	119	2	1	1	NUM
ejpam-4510	119	3	.	.	PUNCT
ejpam-4510	120	1	if	if	SCONJ
ejpam-4510	120	2	a	a	DET
ejpam-4510	120	3	weak	weak	ADJ
ejpam-4510	120	4	dokdo	dokdo	NOUN
ejpam-4510	120	5	be	be	NOUN
ejpam-4510	120	6	-	-	PUNCT
ejpam-4510	120	7	subalgebra	subalgebra	ADJ
ejpam-4510	120	8	dokφ	dokφ	NOUN
ejpam-4510	120	9	:	:	PUNCT
ejpam-4510	120	10	=	=	SYM
ejpam-4510	120	11	(	(	PUNCT
ejpam-4510	120	12	φ̊	φ̊	PROPN
ejpam-4510	120	13	,	,	PUNCT
ejpam-4510	120	14	φs	φs	ADV
ejpam-4510	120	15	,	,	PUNCT
ejpam-4510	120	16	φ̃	φ̃	PROPN
ejpam-4510	120	17	)	)	PUNCT
ejpam-4510	120	18	of	of	ADP
ejpam-4510	120	19	(	(	PUNCT
ejpam-4510	120	20	x	x	NOUN
ejpam-4510	120	21	,	,	PUNCT
ejpam-4510	120	22	u	u	NOUN
ejpam-4510	120	23	)	)	PUNCT
ejpam-4510	120	24	satisfies	satisfie	NOUN
ejpam-4510	120	25	:	:	PUNCT
ejpam-4510	120	26	(	(	PUNCT
ejpam-4510	120	27	∀x	∀x	X
ejpam-4510	120	28	,	,	PUNCT
ejpam-4510	120	29	y	y	PROPN
ejpam-4510	120	30	∈	∈	PROPN
ejpam-4510	120	31	x	x	X
ejpam-4510	120	32	)	)	PUNCT
ejpam-4510	121	1			PROPN
ejpam-4510	121	2	x∗y	x∗y	X
ejpam-4510	121	3	(	(	PUNCT
ejpam-4510	121	4	x∗(x∗y	x∗(x∗y	NUM
ejpam-4510	121	5	)	)	PUNCT
ejpam-4510	121	6	,	,	PUNCT
ejpam-4510	121	7	x∗(x∗y	x∗(x∗y	NUM
ejpam-4510	121	8	)	)	PUNCT
ejpam-4510	121	9	)	)	PUNCT
ejpam-4510	122	1	∈	∈	PROPN
ejpam-4510	123	1	φ̊(max	φ̊(max	NUM
ejpam-4510	123	2	,	,	PUNCT
ejpam-4510	123	3	min	min	NOUN
ejpam-4510	123	4	)	)	PUNCT
ejpam-4510	123	5	,	,	PUNCT
ejpam-4510	123	6	φs(x	φs(x	PUNCT
ejpam-4510	123	7	∗	∗	X
ejpam-4510	123	8	y	y	NOUN
ejpam-4510	123	9	)	)	PUNCT
ejpam-4510	123	10	⊇	⊇	NOUN
ejpam-4510	123	11	φs(x	φs(x	PUNCT
ejpam-4510	123	12	∗	∗	NOUN
ejpam-4510	123	13	(	(	PUNCT
ejpam-4510	123	14	x	x	X
ejpam-4510	123	15	∗	∗	PROPN
ejpam-4510	123	16	y	y	PROPN
ejpam-4510	123	17	)	)	PUNCT
ejpam-4510	123	18	)	)	PUNCT
ejpam-4510	124	1	,	,	PUNCT
ejpam-4510	124	2	φ̃(x	φ̃(x	PROPN
ejpam-4510	124	3	∗	∗	NOUN
ejpam-4510	124	4	y	y	NOUN
ejpam-4510	124	5	)	)	PUNCT
ejpam-4510	124	6	⪰	⪰	NOUN
ejpam-4510	124	7	φ̃(x	φ̃(x	PROPN
ejpam-4510	124	8	∗	∗	NOUN
ejpam-4510	124	9	(	(	PUNCT
ejpam-4510	124	10	x	x	X
ejpam-4510	124	11	∗	∗	PROPN
ejpam-4510	124	12	y	y	PROPN
ejpam-4510	124	13	)	)	PUNCT
ejpam-4510	124	14	)	)	PUNCT
ejpam-4510	125	1			PROPN
ejpam-4510	125	2	,	,	PUNCT
ejpam-4510	125	3	(	(	PUNCT
ejpam-4510	125	4	20	20	NUM
ejpam-4510	125	5	)	)	PUNCT
ejpam-4510	125	6	then	then	ADV
ejpam-4510	125	7	dokφ	dokφ	VERB
ejpam-4510	125	8	:	:	PUNCT
ejpam-4510	125	9	=	=	SYM
ejpam-4510	125	10	(	(	PUNCT
ejpam-4510	125	11	φ̊	φ̊	PROPN
ejpam-4510	125	12	,	,	PUNCT
ejpam-4510	125	13	φs	φs	ADV
ejpam-4510	125	14	,	,	PUNCT
ejpam-4510	125	15	φ̃	φ̃	PROPN
ejpam-4510	125	16	)	)	PUNCT
ejpam-4510	125	17	is	be	AUX
ejpam-4510	125	18	a	a	DET
ejpam-4510	125	19	dokdo	dokdo	NOUN
ejpam-4510	125	20	be	be	NOUN
ejpam-4510	125	21	-	-	PUNCT
ejpam-4510	125	22	subalgebra	subalgebra	NOUN
ejpam-4510	125	23	of	of	ADP
ejpam-4510	125	24	(	(	PUNCT
ejpam-4510	125	25	x	x	NOUN
ejpam-4510	125	26	,	,	PUNCT
ejpam-4510	125	27	u	u	NOUN
ejpam-4510	125	28	)	)	PUNCT
ejpam-4510	125	29	.	.	PUNCT
ejpam-4510	126	1	proof	proof	NOUN
ejpam-4510	126	2	.	.	PUNCT
ejpam-4510	127	1	for	for	ADP
ejpam-4510	127	2	every	every	DET
ejpam-4510	127	3	x	x	NOUN
ejpam-4510	127	4	,	,	PUNCT
ejpam-4510	127	5	y	y	PROPN
ejpam-4510	127	6	∈	∈	PROPN
ejpam-4510	127	7	x	x	X
ejpam-4510	127	8	,	,	PUNCT
ejpam-4510	127	9	we	we	PRON
ejpam-4510	127	10	have	have	VERB
ejpam-4510	127	11	φ̊−(x	φ̊−(x	NOUN
ejpam-4510	127	12	∗	∗	PROPN
ejpam-4510	127	13	y	y	NOUN
ejpam-4510	127	14	)	)	PUNCT
ejpam-4510	127	15	≤	≤	NOUN
ejpam-4510	127	16	φ̊−(x	φ̊−(x	X
ejpam-4510	127	17	∗	∗	NOUN
ejpam-4510	127	18	(	(	PUNCT
ejpam-4510	127	19	x	x	X
ejpam-4510	127	20	∗	∗	PROPN
ejpam-4510	127	21	y	y	PROPN
ejpam-4510	127	22	)	)	PUNCT
ejpam-4510	127	23	)	)	PUNCT
ejpam-4510	127	24	≤	≤	NOUN
ejpam-4510	128	1	max{φ̊−(x	max{φ̊−(x	NUM
ejpam-4510	128	2	)	)	PUNCT
ejpam-4510	128	3	,	,	PUNCT
ejpam-4510	128	4	φ̊−(y	φ̊−(y	NOUN
ejpam-4510	128	5	)	)	PUNCT
ejpam-4510	128	6	}	}	PUNCT
ejpam-4510	128	7	and	and	CCONJ
ejpam-4510	128	8	φ̊+(x	φ̊+(x	PROPN
ejpam-4510	128	9	∗	∗	PROPN
ejpam-4510	128	10	y	y	NOUN
ejpam-4510	128	11	)	)	PUNCT
ejpam-4510	128	12	≥	≥	NOUN
ejpam-4510	128	13	φ̊+(x	φ̊+(x	PROPN
ejpam-4510	128	14	∗	∗	NOUN
ejpam-4510	128	15	(	(	PUNCT
ejpam-4510	128	16	x	x	X
ejpam-4510	128	17	∗	∗	PROPN
ejpam-4510	128	18	y	y	PROPN
ejpam-4510	128	19	)	)	PUNCT
ejpam-4510	128	20	)	)	PUNCT
ejpam-4510	128	21	≥	≥	PROPN
ejpam-4510	128	22	min{φ̊+(x	min{φ̊+(x	NUM
ejpam-4510	128	23	)	)	PUNCT
ejpam-4510	128	24	,	,	PUNCT
ejpam-4510	128	25	φ̊+(y	φ̊+(y	NOUN
ejpam-4510	128	26	)	)	PUNCT
ejpam-4510	128	27	}	}	PUNCT
ejpam-4510	128	28	.	.	PUNCT
ejpam-4510	129	1	hence	hence	ADV
ejpam-4510	129	2	x∗y	x∗y	X
ejpam-4510	129	3	(	(	PUNCT
ejpam-4510	129	4	x	x	NOUN
ejpam-4510	129	5	,	,	PUNCT
ejpam-4510	129	6	y	y	NOUN
ejpam-4510	129	7	)	)	PUNCT
ejpam-4510	129	8	∈	∈	PROPN
ejpam-4510	129	9	φ̊(max	φ̊(max	NUM
ejpam-4510	129	10	,	,	PUNCT
ejpam-4510	129	11	min	min	NOUN
ejpam-4510	129	12	)	)	PUNCT
ejpam-4510	129	13	.	.	PUNCT
ejpam-4510	130	1	also	also	ADV
ejpam-4510	130	2	,	,	PUNCT
ejpam-4510	130	3	φs(x∗y	φs(x∗y	NUM
ejpam-4510	130	4	)	)	PUNCT
ejpam-4510	130	5	⊇	⊇	PROPN
ejpam-4510	130	6	φs(x∗	φs(x∗	NOUN
ejpam-4510	130	7	(	(	PUNCT
ejpam-4510	130	8	x∗y	x∗y	X
ejpam-4510	130	9	)	)	PUNCT
ejpam-4510	130	10	)	)	PUNCT
ejpam-4510	130	11	⊇	⊇	PROPN
ejpam-4510	130	12	φs(x)∩φs(y	φs(x)∩φs(y	PROPN
ejpam-4510	130	13	)	)	PUNCT
ejpam-4510	130	14	and	and	CCONJ
ejpam-4510	130	15	φ̃(x∗y	φ̃(x∗y	X
ejpam-4510	130	16	)	)	PUNCT
ejpam-4510	130	17	⪰	⪰	NOUN
ejpam-4510	130	18	φ̃(x∗	φ̃(x∗	PROPN
ejpam-4510	130	19	(	(	PUNCT
ejpam-4510	130	20	x∗y	x∗y	X
ejpam-4510	130	21	)	)	PUNCT
ejpam-4510	130	22	)	)	PUNCT
ejpam-4510	130	23	⪰	⪰	NOUN
ejpam-4510	130	24	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	130	25	)	)	PUNCT
ejpam-4510	130	26	,	,	PUNCT
ejpam-4510	130	27	φ̃(y	φ̃(y	NOUN
ejpam-4510	130	28	)	)	PUNCT
ejpam-4510	130	29	}	}	PUNCT
ejpam-4510	130	30	.	.	PUNCT
ejpam-4510	131	1	therefore	therefore	ADV
ejpam-4510	131	2	dokφ	dokφ	NOUN
ejpam-4510	131	3	:	:	PUNCT
ejpam-4510	131	4	=	=	SYM
ejpam-4510	131	5	(	(	PUNCT
ejpam-4510	131	6	φ̊	φ̊	PROPN
ejpam-4510	131	7	,	,	PUNCT
ejpam-4510	131	8	φs	φs	ADV
ejpam-4510	131	9	,	,	PUNCT
ejpam-4510	131	10	φ̃	φ̃	PROPN
ejpam-4510	131	11	)	)	PUNCT
ejpam-4510	131	12	is	be	AUX
ejpam-4510	131	13	a	a	DET
ejpam-4510	131	14	dokdo	dokdo	NOUN
ejpam-4510	131	15	be	be	NOUN
ejpam-4510	131	16	-	-	PUNCT
ejpam-4510	131	17	subalgebra	subalgebra	NOUN
ejpam-4510	131	18	of	of	ADP
ejpam-4510	131	19	(	(	PUNCT
ejpam-4510	131	20	x	x	NOUN
ejpam-4510	131	21	,	,	PUNCT
ejpam-4510	131	22	u	u	NOUN
ejpam-4510	131	23	)	)	PUNCT
ejpam-4510	131	24	.	.	PUNCT
ejpam-4510	132	1	proposition	proposition	NOUN
ejpam-4510	132	2	1	1	NUM
ejpam-4510	132	3	.	.	PUNCT
ejpam-4510	133	1	if	if	SCONJ
ejpam-4510	133	2	dokφ	dokφ	NOUN
ejpam-4510	133	3	:	:	PUNCT
ejpam-4510	133	4	=	=	SYM
ejpam-4510	133	5	(	(	PUNCT
ejpam-4510	133	6	φ̊	φ̊	PROPN
ejpam-4510	133	7	,	,	PUNCT
ejpam-4510	133	8	φs	φs	ADV
ejpam-4510	133	9	,	,	PUNCT
ejpam-4510	133	10	φ̃	φ̃	PROPN
ejpam-4510	133	11	)	)	PUNCT
ejpam-4510	133	12	is	be	AUX
ejpam-4510	133	13	a	a	DET
ejpam-4510	133	14	weak	weak	ADJ
ejpam-4510	133	15	dokdo	dokdo	NOUN
ejpam-4510	133	16	be	be	NOUN
ejpam-4510	133	17	-	-	PUNCT
ejpam-4510	133	18	subalgebra	subalgebra	NOUN
ejpam-4510	133	19	of	of	ADP
ejpam-4510	133	20	(	(	PUNCT
ejpam-4510	133	21	x	x	NOUN
ejpam-4510	133	22	,	,	PUNCT
ejpam-4510	133	23	u	u	NOUN
ejpam-4510	133	24	)	)	PUNCT
ejpam-4510	133	25	,	,	PUNCT
ejpam-4510	133	26	then	then	ADV
ejpam-4510	133	27	(	(	PUNCT
ejpam-4510	133	28	i	i	NOUN
ejpam-4510	133	29	)	)	PUNCT
ejpam-4510	133	30	φ−(1	φ−(1	PROPN
ejpam-4510	133	31	)	)	PUNCT
ejpam-4510	133	32	is	be	AUX
ejpam-4510	133	33	a	a	DET
ejpam-4510	133	34	lower	low	ADJ
ejpam-4510	133	35	bound	bind	VERB
ejpam-4510	133	36	of	of	ADP
ejpam-4510	133	37	{	{	PUNCT
ejpam-4510	133	38	φ−(x	φ−(x	PROPN
ejpam-4510	133	39	)	)	PUNCT
ejpam-4510	134	1	|	|	ADV
ejpam-4510	134	2	x	x	SYM
ejpam-4510	134	3	∈	∈	NOUN
ejpam-4510	134	4	x	x	X
ejpam-4510	134	5	}	}	PUNCT
ejpam-4510	134	6	,	,	PUNCT
ejpam-4510	134	7	(	(	PUNCT
ejpam-4510	134	8	ii	ii	NOUN
ejpam-4510	134	9	)	)	PUNCT
ejpam-4510	134	10	φ+(1	φ+(1	NOUN
ejpam-4510	134	11	)	)	PUNCT
ejpam-4510	134	12	is	be	AUX
ejpam-4510	134	13	an	an	DET
ejpam-4510	134	14	upper	upper	ADJ
ejpam-4510	134	15	bound	bind	VERB
ejpam-4510	134	16	of	of	ADP
ejpam-4510	134	17	{	{	PUNCT
ejpam-4510	134	18	φ−(x	φ−(x	PROPN
ejpam-4510	134	19	)	)	PUNCT
ejpam-4510	135	1	|	|	ADV
ejpam-4510	135	2	x	x	SYM
ejpam-4510	135	3	∈	∈	NOUN
ejpam-4510	135	4	x	x	X
ejpam-4510	135	5	}	}	PUNCT
ejpam-4510	135	6	,	,	PUNCT
ejpam-4510	135	7	(	(	PUNCT
ejpam-4510	135	8	iii	iii	X
ejpam-4510	135	9	)	)	PUNCT
ejpam-4510	135	10	(	(	PUNCT
ejpam-4510	135	11	∀x	∀x	X
ejpam-4510	135	12	∈	∈	PROPN
ejpam-4510	135	13	x	x	X
ejpam-4510	135	14	)	)	PUNCT
ejpam-4510	135	15	(	(	PUNCT
ejpam-4510	135	16	φs(1	φs(1	PROPN
ejpam-4510	135	17	)	)	PUNCT
ejpam-4510	135	18	⊇	⊇	NOUN
ejpam-4510	135	19	φs(x	φs(x	PROPN
ejpam-4510	135	20	)	)	PUNCT
ejpam-4510	135	21	,	,	PUNCT
ejpam-4510	135	22	φ̃(1	φ̃(1	NOUN
ejpam-4510	135	23	)	)	PUNCT
ejpam-4510	135	24	⪰	⪰	NOUN
ejpam-4510	135	25	φ̃(x	φ̃(x	PROPN
ejpam-4510	135	26	)	)	PUNCT
ejpam-4510	135	27	)	)	PUNCT
ejpam-4510	135	28	.	.	PUNCT
ejpam-4510	136	1	y.	y.	PROPN
ejpam-4510	136	2	b.	b.	PROPN
ejpam-4510	136	3	jun	jun	PROPN
ejpam-4510	136	4	,	,	PUNCT
ejpam-4510	136	5	s.	s.	PROPN
ejpam-4510	136	6	s.	s.	PROPN
ejpam-4510	136	7	ahn	ahn	PROPN
ejpam-4510	136	8	and	and	CCONJ
ejpam-4510	136	9	e.	e.	PROPN
ejpam-4510	136	10	h.	h.	PROPN
ejpam-4510	136	11	roh	roh	PROPN
ejpam-4510	136	12	/	/	SYM
ejpam-4510	136	13	eur	eur	PROPN
ejpam-4510	136	14	.	.	PUNCT
ejpam-4510	137	1	j.	j.	PROPN
ejpam-4510	137	2	pure	pure	PROPN
ejpam-4510	137	3	appl	appl	PROPN
ejpam-4510	137	4	.	.	PROPN
ejpam-4510	137	5	math	math	PROPN
ejpam-4510	137	6	,	,	PUNCT
ejpam-4510	137	7	15	15	NUM
ejpam-4510	137	8	(	(	PUNCT
ejpam-4510	137	9	4	4	NUM
ejpam-4510	137	10	)	)	PUNCT
ejpam-4510	137	11	(	(	PUNCT
ejpam-4510	137	12	2022	2022	NUM
ejpam-4510	137	13	)	)	PUNCT
ejpam-4510	137	14	,	,	PUNCT
ejpam-4510	137	15	1521	1521	NUM
ejpam-4510	137	16	-	-	SYM
ejpam-4510	137	17	1535	1535	NUM
ejpam-4510	137	18	1527	1527	NUM
ejpam-4510	137	19	proof	proof	NOUN
ejpam-4510	137	20	.	.	PUNCT
ejpam-4510	138	1	let	let	VERB
ejpam-4510	138	2	dokφ	dokφ	NOUN
ejpam-4510	138	3	:	:	PUNCT
ejpam-4510	138	4	=	=	SYM
ejpam-4510	138	5	(	(	PUNCT
ejpam-4510	138	6	φ̊	φ̊	PROPN
ejpam-4510	138	7	,	,	PUNCT
ejpam-4510	138	8	φs	φs	ADV
ejpam-4510	138	9	,	,	PUNCT
ejpam-4510	138	10	φ̃	φ̃	PROPN
ejpam-4510	138	11	)	)	PUNCT
ejpam-4510	138	12	be	be	VERB
ejpam-4510	138	13	a	a	DET
ejpam-4510	138	14	weak	weak	ADJ
ejpam-4510	138	15	dokdo	dokdo	NOUN
ejpam-4510	138	16	be	be	NOUN
ejpam-4510	138	17	-	-	PUNCT
ejpam-4510	138	18	subalgebra	subalgebra	NOUN
ejpam-4510	138	19	of	of	ADP
ejpam-4510	138	20	(	(	PUNCT
ejpam-4510	138	21	x	x	NOUN
ejpam-4510	138	22	,	,	PUNCT
ejpam-4510	138	23	u	u	NOUN
ejpam-4510	138	24	)	)	PUNCT
ejpam-4510	138	25	.	.	PUNCT
ejpam-4510	139	1	for	for	ADP
ejpam-4510	139	2	every	every	DET
ejpam-4510	139	3	x	x	SYM
ejpam-4510	139	4	∈	∈	PROPN
ejpam-4510	139	5	x	x	NOUN
ejpam-4510	139	6	,	,	PUNCT
ejpam-4510	139	7	if	if	SCONJ
ejpam-4510	139	8	we	we	PRON
ejpam-4510	139	9	use	use	VERB
ejpam-4510	139	10	(	(	PUNCT
ejpam-4510	139	11	be1	be1	NOUN
ejpam-4510	139	12	)	)	PUNCT
ejpam-4510	139	13	and	and	CCONJ
ejpam-4510	139	14	(	(	PUNCT
ejpam-4510	139	15	be2	be2	PROPN
ejpam-4510	139	16	)	)	PUNCT
ejpam-4510	139	17	,	,	PUNCT
ejpam-4510	139	18	then	then	ADV
ejpam-4510	139	19	1	1	NUM
ejpam-4510	139	20	(	(	PUNCT
ejpam-4510	139	21	x	x	NOUN
ejpam-4510	139	22	,	,	PUNCT
ejpam-4510	139	23	x	x	X
ejpam-4510	139	24	)	)	PUNCT
ejpam-4510	139	25	=	=	SYM
ejpam-4510	139	26	x∗(x∗x	x∗(x∗x	NUM
ejpam-4510	139	27	)	)	PUNCT
ejpam-4510	139	28	(	(	PUNCT
ejpam-4510	139	29	x	x	X
ejpam-4510	139	30	,	,	PUNCT
ejpam-4510	139	31	x	x	NOUN
ejpam-4510	139	32	)	)	PUNCT
ejpam-4510	139	33	∈	∈	PROPN
ejpam-4510	139	34	φ̊(max	φ̊(max	NUM
ejpam-4510	139	35	,	,	PUNCT
ejpam-4510	139	36	min	min	NOUN
ejpam-4510	139	37	)	)	PUNCT
ejpam-4510	139	38	which	which	PRON
ejpam-4510	139	39	implies	imply	VERB
ejpam-4510	139	40	that	that	SCONJ
ejpam-4510	139	41	φ−(1	φ−(1	NOUN
ejpam-4510	139	42	)	)	PUNCT
ejpam-4510	139	43	≤	≤	NUM
ejpam-4510	139	44	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	139	45	)	)	PUNCT
ejpam-4510	139	46	,	,	PUNCT
ejpam-4510	139	47	φ−(x	φ−(x	PROPN
ejpam-4510	139	48	)	)	PUNCT
ejpam-4510	139	49	}	}	PUNCT
ejpam-4510	139	50	=	=	SYM
ejpam-4510	139	51	φ−(x	φ−(x	PROPN
ejpam-4510	139	52	)	)	PUNCT
ejpam-4510	139	53	and	and	CCONJ
ejpam-4510	139	54	φ+(1	φ+(1	NOUN
ejpam-4510	139	55	)	)	PUNCT
ejpam-4510	139	56	≥	≥	NOUN
ejpam-4510	139	57	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	139	58	)	)	PUNCT
ejpam-4510	139	59	,	,	PUNCT
ejpam-4510	139	60	φ+(x	φ+(x	NOUN
ejpam-4510	139	61	)	)	PUNCT
ejpam-4510	139	62	}	}	PUNCT
ejpam-4510	139	63	=	=	SYM
ejpam-4510	139	64	φ+(x	φ+(x	X
ejpam-4510	139	65	)	)	PUNCT
ejpam-4510	139	66	.	.	PUNCT
ejpam-4510	140	1	hence	hence	ADV
ejpam-4510	140	2	(	(	PUNCT
ejpam-4510	140	3	i	i	NOUN
ejpam-4510	140	4	)	)	PUNCT
ejpam-4510	140	5	and	and	CCONJ
ejpam-4510	140	6	(	(	PUNCT
ejpam-4510	140	7	ii	ii	NOUN
ejpam-4510	140	8	)	)	PUNCT
ejpam-4510	140	9	are	be	AUX
ejpam-4510	140	10	valid	valid	ADJ
ejpam-4510	140	11	.	.	PUNCT
ejpam-4510	141	1	also	also	ADV
ejpam-4510	141	2	,	,	PUNCT
ejpam-4510	141	3	φs(1	φs(1	PROPN
ejpam-4510	141	4	)	)	PUNCT
ejpam-4510	141	5	=	=	NOUN
ejpam-4510	141	6	φs(x	φs(x	X
ejpam-4510	141	7	∗	∗	NOUN
ejpam-4510	141	8	(	(	PUNCT
ejpam-4510	141	9	x	x	X
ejpam-4510	141	10	∗	∗	NOUN
ejpam-4510	141	11	x	x	NOUN
ejpam-4510	141	12	)	)	PUNCT
ejpam-4510	141	13	)	)	PUNCT
ejpam-4510	141	14	⊇	⊇	NOUN
ejpam-4510	141	15	φs(x	φs(x	NOUN
ejpam-4510	141	16	)	)	PUNCT
ejpam-4510	141	17	∩	∩	NOUN
ejpam-4510	141	18	φs(x	φs(x	PRON
ejpam-4510	141	19	)	)	PUNCT
ejpam-4510	141	20	=	=	SYM
ejpam-4510	141	21	φs(x	φs(x	X
ejpam-4510	141	22	)	)	PUNCT
ejpam-4510	141	23	and	and	CCONJ
ejpam-4510	141	24	φ̃(1	φ̃(1	NOUN
ejpam-4510	141	25	)	)	PUNCT
ejpam-4510	141	26	=	=	SYM
ejpam-4510	142	1	φ̃(x	φ̃(x	PROPN
ejpam-4510	142	2	∗	∗	NOUN
ejpam-4510	142	3	(	(	PUNCT
ejpam-4510	142	4	x	x	X
ejpam-4510	142	5	∗	∗	NOUN
ejpam-4510	142	6	x	x	NOUN
ejpam-4510	142	7	)	)	PUNCT
ejpam-4510	142	8	)	)	PUNCT
ejpam-4510	142	9	⪰	⪰	NOUN
ejpam-4510	142	10	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	142	11	)	)	PUNCT
ejpam-4510	142	12	,	,	PUNCT
ejpam-4510	142	13	φ̃(x	φ̃(x	PROPN
ejpam-4510	142	14	)	)	PUNCT
ejpam-4510	142	15	}	}	PUNCT
ejpam-4510	142	16	=	=	SYM
ejpam-4510	142	17	φ̃(x	φ̃(x	PROPN
ejpam-4510	142	18	)	)	PUNCT
ejpam-4510	142	19	.	.	PUNCT
ejpam-4510	143	1	the	the	DET
ejpam-4510	143	2	combination	combination	NOUN
ejpam-4510	143	3	of	of	ADP
ejpam-4510	143	4	lemma	lemma	PROPN
ejpam-4510	143	5	1	1	NUM
ejpam-4510	143	6	and	and	CCONJ
ejpam-4510	143	7	proposition	proposition	NOUN
ejpam-4510	143	8	1	1	NUM
ejpam-4510	143	9	leads	lead	VERB
ejpam-4510	143	10	to	to	ADP
ejpam-4510	143	11	the	the	DET
ejpam-4510	143	12	following	follow	VERB
ejpam-4510	143	13	corollary	corollary	NOUN
ejpam-4510	143	14	.	.	PUNCT
ejpam-4510	144	1	corollary	corollary	ADJ
ejpam-4510	144	2	1	1	NUM
ejpam-4510	144	3	.	.	PUNCT
ejpam-4510	145	1	if	if	SCONJ
ejpam-4510	145	2	dokφ	dokφ	NOUN
ejpam-4510	145	3	:	:	PUNCT
ejpam-4510	145	4	=	=	SYM
ejpam-4510	145	5	(	(	PUNCT
ejpam-4510	145	6	φ̊	φ̊	PROPN
ejpam-4510	145	7	,	,	PUNCT
ejpam-4510	145	8	φs	φs	ADV
ejpam-4510	145	9	,	,	PUNCT
ejpam-4510	145	10	φ̃	φ̃	PROPN
ejpam-4510	145	11	)	)	PUNCT
ejpam-4510	145	12	is	be	AUX
ejpam-4510	145	13	a	a	DET
ejpam-4510	145	14	dokdo	dokdo	NOUN
ejpam-4510	145	15	be	be	NOUN
ejpam-4510	145	16	-	-	PUNCT
ejpam-4510	145	17	subalgebra	subalgebra	NOUN
ejpam-4510	145	18	of	of	ADP
ejpam-4510	145	19	(	(	PUNCT
ejpam-4510	145	20	x	x	NOUN
ejpam-4510	145	21	,	,	PUNCT
ejpam-4510	145	22	u	u	NOUN
ejpam-4510	145	23	)	)	PUNCT
ejpam-4510	145	24	,	,	PUNCT
ejpam-4510	145	25	then	then	ADV
ejpam-4510	145	26	the	the	DET
ejpam-4510	145	27	results	result	NOUN
ejpam-4510	145	28	(	(	PUNCT
ejpam-4510	145	29	i	i	NOUN
ejpam-4510	145	30	)	)	PUNCT
ejpam-4510	145	31	,	,	PUNCT
ejpam-4510	145	32	(	(	PUNCT
ejpam-4510	145	33	ii	ii	NOUN
ejpam-4510	145	34	)	)	PUNCT
ejpam-4510	145	35	,	,	PUNCT
ejpam-4510	145	36	and	and	CCONJ
ejpam-4510	145	37	(	(	PUNCT
ejpam-4510	145	38	iii	iii	NOUN
ejpam-4510	145	39	)	)	PUNCT
ejpam-4510	145	40	in	in	ADP
ejpam-4510	145	41	proposition	proposition	NOUN
ejpam-4510	145	42	1	1	NUM
ejpam-4510	145	43	are	be	AUX
ejpam-4510	145	44	valid	valid	ADJ
ejpam-4510	145	45	.	.	PUNCT
ejpam-4510	146	1	proposition	proposition	NOUN
ejpam-4510	146	2	2	2	NUM
ejpam-4510	146	3	.	.	PUNCT
ejpam-4510	147	1	every	every	DET
ejpam-4510	147	2	weak	weak	ADJ
ejpam-4510	147	3	dokdo	dokdo	NOUN
ejpam-4510	147	4	be	be	NOUN
ejpam-4510	147	5	-	-	PUNCT
ejpam-4510	147	6	subalgebra	subalgebra	ADJ
ejpam-4510	147	7	dokφ	dokφ	NOUN
ejpam-4510	147	8	:	:	PUNCT
ejpam-4510	147	9	=	=	SYM
ejpam-4510	147	10	(	(	PUNCT
ejpam-4510	147	11	φ̊	φ̊	PROPN
ejpam-4510	147	12	,	,	PUNCT
ejpam-4510	147	13	φs	φs	ADV
ejpam-4510	147	14	,	,	PUNCT
ejpam-4510	147	15	φ̃	φ̃	PROPN
ejpam-4510	147	16	)	)	PUNCT
ejpam-4510	147	17	of	of	ADP
ejpam-4510	147	18	(	(	PUNCT
ejpam-4510	147	19	x	x	NOUN
ejpam-4510	147	20	,	,	PUNCT
ejpam-4510	147	21	u	u	NOUN
ejpam-4510	147	22	)	)	PUNCT
ejpam-4510	147	23	satisfies	satisfie	NOUN
ejpam-4510	147	24	:	:	PUNCT
ejpam-4510	147	25	(	(	PUNCT
ejpam-4510	147	26	∀x	∀x	X
ejpam-4510	147	27	,	,	PUNCT
ejpam-4510	147	28	y	y	PROPN
ejpam-4510	147	29	∈	∈	PROPN
ejpam-4510	147	30	x	x	X
ejpam-4510	147	31	)	)	PUNCT
ejpam-4510	147	32	(	(	PUNCT
ejpam-4510	147	33	y	y	PROPN
ejpam-4510	147	34	(	(	PUNCT
ejpam-4510	147	35	y∗(y∗x),y∗(y∗x	y∗(y∗x),y∗(y∗x	PROPN
ejpam-4510	147	36	)	)	PUNCT
ejpam-4510	147	37	)	)	PUNCT
ejpam-4510	148	1	∈	∈	PROPN
ejpam-4510	148	2	φ̊(max	φ̊(max	NUM
ejpam-4510	148	3	,	,	PUNCT
ejpam-4510	148	4	min	min	NOUN
ejpam-4510	148	5	)	)	PUNCT
ejpam-4510	148	6	⇒	⇒	NOUN
ejpam-4510	148	7	{	{	PUNCT
ejpam-4510	148	8	φ−(y	φ−(y	PROPN
ejpam-4510	148	9	)	)	PUNCT
ejpam-4510	148	10	=	=	SYM
ejpam-4510	148	11	φ−(1	φ−(1	PROPN
ejpam-4510	148	12	)	)	PUNCT
ejpam-4510	148	13	φ+(y	φ+(y	NUM
ejpam-4510	148	14	)	)	PUNCT
ejpam-4510	148	15	=	=	SYM
ejpam-4510	148	16	φ+(1	φ+(1	NOUN
ejpam-4510	148	17	)	)	PUNCT
ejpam-4510	148	18	)	)	PUNCT
ejpam-4510	148	19	,	,	PUNCT
ejpam-4510	148	20	(	(	PUNCT
ejpam-4510	148	21	21	21	NUM
ejpam-4510	148	22	)	)	PUNCT
ejpam-4510	148	23	(	(	PUNCT
ejpam-4510	148	24	∀x	∀x	X
ejpam-4510	148	25	,	,	PUNCT
ejpam-4510	148	26	y	y	PROPN
ejpam-4510	148	27	∈	∈	PROPN
ejpam-4510	148	28	x	x	X
ejpam-4510	148	29	)	)	PUNCT
ejpam-4510	148	30	(	(	PUNCT
ejpam-4510	148	31	φs(y	φs(y	NUM
ejpam-4510	148	32	)	)	PUNCT
ejpam-4510	148	33	⊇	⊇	NOUN
ejpam-4510	148	34	φs(y	φs(y	ADJ
ejpam-4510	148	35	∗	∗	NOUN
ejpam-4510	148	36	(	(	PUNCT
ejpam-4510	148	37	y	y	PROPN
ejpam-4510	148	38	∗	∗	NOUN
ejpam-4510	148	39	x	x	NOUN
ejpam-4510	148	40	)	)	PUNCT
ejpam-4510	148	41	)	)	PUNCT
ejpam-4510	148	42	⇒	⇒	NOUN
ejpam-4510	148	43	φs(y	φs(y	NUM
ejpam-4510	148	44	)	)	PUNCT
ejpam-4510	148	45	=	=	SYM
ejpam-4510	148	46	φs(1	φs(1	PROPN
ejpam-4510	148	47	)	)	PUNCT
ejpam-4510	148	48	)	)	PUNCT
ejpam-4510	148	49	,	,	PUNCT
ejpam-4510	148	50	(	(	PUNCT
ejpam-4510	148	51	22	22	NUM
ejpam-4510	148	52	)	)	PUNCT
ejpam-4510	148	53	(	(	PUNCT
ejpam-4510	148	54	∀x	∀x	X
ejpam-4510	148	55	,	,	PUNCT
ejpam-4510	148	56	y	y	PROPN
ejpam-4510	148	57	∈	∈	PROPN
ejpam-4510	148	58	x	x	X
ejpam-4510	148	59	)	)	PUNCT
ejpam-4510	148	60	(	(	PUNCT
ejpam-4510	148	61	φ̃(y	φ̃(y	NOUN
ejpam-4510	148	62	)	)	PUNCT
ejpam-4510	148	63	⪰	⪰	NOUN
ejpam-4510	148	64	φ̃(y	φ̃(y	ADJ
ejpam-4510	148	65	∗	∗	NOUN
ejpam-4510	148	66	(	(	PUNCT
ejpam-4510	148	67	y	y	PROPN
ejpam-4510	148	68	∗	∗	NOUN
ejpam-4510	148	69	x	x	NOUN
ejpam-4510	148	70	)	)	PUNCT
ejpam-4510	148	71	)	)	PUNCT
ejpam-4510	148	72	⇒	⇒	NOUN
ejpam-4510	148	73	φ̃(y	φ̃(y	PROPN
ejpam-4510	148	74	)	)	PUNCT
ejpam-4510	148	75	=	=	SYM
ejpam-4510	148	76	φ̃(1	φ̃(1	NOUN
ejpam-4510	148	77	)	)	PUNCT
ejpam-4510	148	78	)	)	PUNCT
ejpam-4510	148	79	.	.	PUNCT
ejpam-4510	149	1	(	(	PUNCT
ejpam-4510	149	2	23	23	X
ejpam-4510	149	3	)	)	PUNCT
ejpam-4510	149	4	proof	proof	NOUN
ejpam-4510	149	5	.	.	PUNCT
ejpam-4510	150	1	assume	assume	VERB
ejpam-4510	151	1	that	that	SCONJ
ejpam-4510	151	2	y	y	PROPN
ejpam-4510	151	3	(	(	PUNCT
ejpam-4510	151	4	y∗(y∗x),y∗(y∗x	y∗(y∗x),y∗(y∗x	PROPN
ejpam-4510	151	5	)	)	PUNCT
ejpam-4510	151	6	)	)	PUNCT
ejpam-4510	151	7	∈	∈	PROPN
ejpam-4510	152	1	φ̊(max	φ̊(max	NUM
ejpam-4510	152	2	,	,	PUNCT
ejpam-4510	152	3	min	min	NOUN
ejpam-4510	152	4	)	)	PUNCT
ejpam-4510	152	5	,	,	PUNCT
ejpam-4510	152	6	φs(y	φs(y	NUM
ejpam-4510	152	7	)	)	PUNCT
ejpam-4510	152	8	⊇	⊇	NOUN
ejpam-4510	152	9	φs(y	φs(y	ADJ
ejpam-4510	152	10	∗	∗	NOUN
ejpam-4510	152	11	(	(	PUNCT
ejpam-4510	152	12	y	y	PROPN
ejpam-4510	152	13	∗	∗	NOUN
ejpam-4510	152	14	x	x	NOUN
ejpam-4510	152	15	)	)	PUNCT
ejpam-4510	152	16	)	)	PUNCT
ejpam-4510	152	17	and	and	CCONJ
ejpam-4510	152	18	φ̃(y	φ̃(y	NOUN
ejpam-4510	152	19	)	)	PUNCT
ejpam-4510	152	20	⪰	⪰	NOUN
ejpam-4510	152	21	φ̃(y∗(y∗x	φ̃(y∗(y∗x	NOUN
ejpam-4510	152	22	)	)	PUNCT
ejpam-4510	152	23	)	)	PUNCT
ejpam-4510	152	24	for	for	ADP
ejpam-4510	152	25	all	all	DET
ejpam-4510	152	26	x	x	NOUN
ejpam-4510	152	27	,	,	PUNCT
ejpam-4510	152	28	y	y	PROPN
ejpam-4510	152	29	∈	∈	PROPN
ejpam-4510	152	30	x.	x.	NOUN
ejpam-4510	153	1	if	if	SCONJ
ejpam-4510	153	2	we	we	PRON
ejpam-4510	153	3	take	take	VERB
ejpam-4510	153	4	x	x	NOUN
ejpam-4510	153	5	=	=	SYM
ejpam-4510	153	6	1	1	NUM
ejpam-4510	153	7	and	and	CCONJ
ejpam-4510	153	8	use	use	NOUN
ejpam-4510	153	9	(	(	PUNCT
ejpam-4510	153	10	be2	be2	PROPN
ejpam-4510	153	11	)	)	PUNCT
ejpam-4510	153	12	,	,	PUNCT
ejpam-4510	153	13	then	then	ADV
ejpam-4510	153	14	y	y	PROPN
ejpam-4510	153	15	(	(	PUNCT
ejpam-4510	153	16	1,1	1,1	NUM
ejpam-4510	153	17	)	)	PUNCT
ejpam-4510	154	1	=	=	SYM
ejpam-4510	154	2	y	y	PROPN
ejpam-4510	154	3	(	(	PUNCT
ejpam-4510	154	4	y∗(y∗1),y∗(y∗1	y∗(y∗1),y∗(y∗1	PROPN
ejpam-4510	154	5	)	)	PUNCT
ejpam-4510	154	6	)	)	PUNCT
ejpam-4510	155	1	∈	∈	PROPN
ejpam-4510	156	1	φ̊(max	φ̊(max	NUM
ejpam-4510	156	2	,	,	PUNCT
ejpam-4510	156	3	min	min	NOUN
ejpam-4510	156	4	)	)	PUNCT
ejpam-4510	156	5	,	,	PUNCT
ejpam-4510	156	6	φs(y	φs(y	NUM
ejpam-4510	156	7	)	)	PUNCT
ejpam-4510	156	8	⊇	⊇	NOUN
ejpam-4510	156	9	φs(y	φs(y	ADJ
ejpam-4510	156	10	∗	∗	NOUN
ejpam-4510	156	11	(	(	PUNCT
ejpam-4510	156	12	y	y	PROPN
ejpam-4510	156	13	∗	∗	PROPN
ejpam-4510	156	14	1	1	NUM
ejpam-4510	156	15	)	)	PUNCT
ejpam-4510	156	16	)	)	PUNCT
ejpam-4510	156	17	=	=	SYM
ejpam-4510	156	18	φs(1	φs(1	PROPN
ejpam-4510	156	19	)	)	PUNCT
ejpam-4510	156	20	and	and	CCONJ
ejpam-4510	156	21	φ̃(y	φ̃(y	NOUN
ejpam-4510	156	22	)	)	PUNCT
ejpam-4510	156	23	⪰	⪰	NOUN
ejpam-4510	156	24	φ̃(y	φ̃(y	ADJ
ejpam-4510	156	25	∗	∗	NOUN
ejpam-4510	156	26	(	(	PUNCT
ejpam-4510	156	27	y	y	PROPN
ejpam-4510	156	28	∗	∗	PROPN
ejpam-4510	156	29	1	1	NUM
ejpam-4510	156	30	)	)	PUNCT
ejpam-4510	156	31	)	)	PUNCT
ejpam-4510	157	1	=	=	SYM
ejpam-4510	157	2	φ̃(1	φ̃(1	NOUN
ejpam-4510	157	3	)	)	PUNCT
ejpam-4510	157	4	.	.	PUNCT
ejpam-4510	158	1	the	the	DET
ejpam-4510	158	2	combination	combination	NOUN
ejpam-4510	158	3	of	of	ADP
ejpam-4510	158	4	these	these	PRON
ejpam-4510	158	5	and	and	CCONJ
ejpam-4510	158	6	proposition	proposition	NOUN
ejpam-4510	158	7	1	1	NUM
ejpam-4510	158	8	leads	lead	VERB
ejpam-4510	158	9	to	to	ADP
ejpam-4510	158	10	φ−(y	φ−(y	NOUN
ejpam-4510	158	11	)	)	PUNCT
ejpam-4510	158	12	=	=	SYM
ejpam-4510	158	13	φ−(1	φ−(1	PROPN
ejpam-4510	158	14	)	)	PUNCT
ejpam-4510	158	15	,	,	PUNCT
ejpam-4510	158	16	φ+(y	φ+(y	CCONJ
ejpam-4510	158	17	)	)	PUNCT
ejpam-4510	158	18	=	=	SYM
ejpam-4510	158	19	φ+(1	φ+(1	NOUN
ejpam-4510	158	20	)	)	PUNCT
ejpam-4510	158	21	,	,	PUNCT
ejpam-4510	158	22	φs(y	φs(y	NUM
ejpam-4510	158	23	)	)	PUNCT
ejpam-4510	158	24	=	=	SYM
ejpam-4510	158	25	φs(1	φs(1	PROPN
ejpam-4510	158	26	)	)	PUNCT
ejpam-4510	158	27	and	and	CCONJ
ejpam-4510	158	28	φ̃(y	φ̃(y	NOUN
ejpam-4510	158	29	)	)	PUNCT
ejpam-4510	158	30	=	=	SYM
ejpam-4510	158	31	φ̃(1	φ̃(1	NOUN
ejpam-4510	158	32	)	)	PUNCT
ejpam-4510	158	33	.	.	PUNCT
ejpam-4510	159	1	corollary	corollary	ADJ
ejpam-4510	159	2	2	2	NUM
ejpam-4510	159	3	.	.	PUNCT
ejpam-4510	160	1	every	every	DET
ejpam-4510	160	2	dokdo	dokdo	NOUN
ejpam-4510	160	3	be	be	AUX
ejpam-4510	160	4	-	-	PUNCT
ejpam-4510	160	5	subalgebra	subalgebra	ADJ
ejpam-4510	160	6	dokφ	dokφ	NOUN
ejpam-4510	160	7	:	:	PUNCT
ejpam-4510	160	8	=	=	SYM
ejpam-4510	160	9	(	(	PUNCT
ejpam-4510	160	10	φ̊	φ̊	PROPN
ejpam-4510	160	11	,	,	PUNCT
ejpam-4510	160	12	φs	φs	ADV
ejpam-4510	160	13	,	,	PUNCT
ejpam-4510	160	14	φ̃	φ̃	PROPN
ejpam-4510	160	15	)	)	PUNCT
ejpam-4510	160	16	of	of	ADP
ejpam-4510	160	17	(	(	PUNCT
ejpam-4510	160	18	x	x	NOUN
ejpam-4510	160	19	,	,	PUNCT
ejpam-4510	160	20	u	u	NOUN
ejpam-4510	160	21	)	)	PUNCT
ejpam-4510	160	22	satisfies	satisfie	NOUN
ejpam-4510	160	23	(	(	PUNCT
ejpam-4510	160	24	21	21	NUM
ejpam-4510	160	25	)	)	PUNCT
ejpam-4510	160	26	,	,	PUNCT
ejpam-4510	160	27	(	(	PUNCT
ejpam-4510	160	28	22	22	NUM
ejpam-4510	160	29	)	)	PUNCT
ejpam-4510	160	30	and	and	CCONJ
ejpam-4510	160	31	(	(	PUNCT
ejpam-4510	160	32	23	23	NUM
ejpam-4510	160	33	)	)	PUNCT
ejpam-4510	160	34	.	.	PUNCT
ejpam-4510	161	1	theorem	theorem	NOUN
ejpam-4510	161	2	2	2	NUM
ejpam-4510	161	3	.	.	PUNCT
ejpam-4510	162	1	if	if	SCONJ
ejpam-4510	162	2	dokφ	dokφ	NOUN
ejpam-4510	162	3	:	:	PUNCT
ejpam-4510	162	4	=	=	SYM
ejpam-4510	162	5	(	(	PUNCT
ejpam-4510	162	6	φ̊	φ̊	PROPN
ejpam-4510	162	7	,	,	PUNCT
ejpam-4510	162	8	φs	φs	ADV
ejpam-4510	162	9	,	,	PUNCT
ejpam-4510	162	10	φ̃	φ̃	PROPN
ejpam-4510	162	11	)	)	PUNCT
ejpam-4510	162	12	is	be	AUX
ejpam-4510	162	13	a	a	DET
ejpam-4510	162	14	weak	weak	ADJ
ejpam-4510	162	15	dokdo	dokdo	NOUN
ejpam-4510	162	16	be	be	NOUN
ejpam-4510	162	17	-	-	PUNCT
ejpam-4510	162	18	subalgebra	subalgebra	NOUN
ejpam-4510	162	19	of	of	ADP
ejpam-4510	162	20	(	(	PUNCT
ejpam-4510	162	21	x	x	NOUN
ejpam-4510	162	22	,	,	PUNCT
ejpam-4510	162	23	u	u	NOUN
ejpam-4510	162	24	)	)	PUNCT
ejpam-4510	162	25	,	,	PUNCT
ejpam-4510	162	26	then	then	ADV
ejpam-4510	162	27	the	the	DET
ejpam-4510	162	28	nonempty	nonempty	NOUN
ejpam-4510	162	29	sets	set	VERB
ejpam-4510	162	30	φ̊(s	φ̊(s	PROPN
ejpam-4510	162	31	,	,	PUNCT
ejpam-4510	162	32	t	t	PROPN
ejpam-4510	162	33	)	)	PUNCT
ejpam-4510	162	34	,	,	PUNCT
ejpam-4510	162	35	φs	φs	ADP
ejpam-4510	162	36	α	α	NOUN
ejpam-4510	162	37	and	and	CCONJ
ejpam-4510	162	38	φ̃ã	φ̃ã	NOUN
ejpam-4510	162	39	are	be	AUX
ejpam-4510	162	40	weak	weak	ADJ
ejpam-4510	162	41	be	be	NOUN
ejpam-4510	162	42	-	-	PUNCT
ejpam-4510	162	43	subalgebras	subalgebra	NOUN
ejpam-4510	162	44	of	of	ADP
ejpam-4510	162	45	x	x	PUNCT
ejpam-4510	162	46	for	for	ADP
ejpam-4510	162	47	all	all	DET
ejpam-4510	162	48	(	(	PUNCT
ejpam-4510	162	49	s	s	PROPN
ejpam-4510	162	50	,	,	PUNCT
ejpam-4510	162	51	t	t	PROPN
ejpam-4510	162	52	)	)	PUNCT
ejpam-4510	162	53	∈	∈	PROPN
ejpam-4510	163	1	[	[	X
ejpam-4510	163	2	−1	−1	NOUN
ejpam-4510	163	3	,	,	PUNCT
ejpam-4510	163	4	0	0	NUM
ejpam-4510	163	5	]	]	X
ejpam-4510	163	6	×	×	NOUN
ejpam-4510	164	1	[	[	X
ejpam-4510	164	2	0	0	NUM
ejpam-4510	164	3	,	,	PUNCT
ejpam-4510	164	4	1	1	NUM
ejpam-4510	164	5	]	]	PUNCT
ejpam-4510	164	6	,	,	PUNCT
ejpam-4510	164	7	α	α	PROPN
ejpam-4510	164	8	∈	∈	PROPN
ejpam-4510	164	9	2u	2u	NOUN
ejpam-4510	164	10	and	and	CCONJ
ejpam-4510	164	11	ã	ã	PROPN
ejpam-4510	164	12	=	=	PUNCT
ejpam-4510	165	1	[	[	X
ejpam-4510	165	2	a−	a−	PROPN
ejpam-4510	165	3	,	,	PUNCT
ejpam-4510	165	4	a+	a+	ADP
ejpam-4510	165	5	]	]	PUNCT
ejpam-4510	165	6	.	.	PUNCT
ejpam-4510	166	1	proof	proof	NOUN
ejpam-4510	166	2	.	.	PUNCT
ejpam-4510	167	1	let	let	VERB
ejpam-4510	167	2	(	(	PUNCT
ejpam-4510	167	3	s	s	X
ejpam-4510	167	4	,	,	PUNCT
ejpam-4510	167	5	t	t	PROPN
ejpam-4510	167	6	)	)	PUNCT
ejpam-4510	167	7	∈	∈	PROPN
ejpam-4510	168	1	[	[	X
ejpam-4510	168	2	−1	−1	NOUN
ejpam-4510	168	3	,	,	PUNCT
ejpam-4510	168	4	0]×	0]×	PROPN
ejpam-4510	169	1	[	[	X
ejpam-4510	169	2	0	0	NUM
ejpam-4510	169	3	,	,	PUNCT
ejpam-4510	169	4	1	1	NUM
ejpam-4510	169	5	]	]	PUNCT
ejpam-4510	169	6	,	,	PUNCT
ejpam-4510	169	7	α	α	PROPN
ejpam-4510	169	8	∈	∈	PROPN
ejpam-4510	169	9	2u	2u	NOUN
ejpam-4510	169	10	and	and	CCONJ
ejpam-4510	169	11	ã	ã	PROPN
ejpam-4510	169	12	=	=	PUNCT
ejpam-4510	170	1	[	[	X
ejpam-4510	170	2	a−	a−	PROPN
ejpam-4510	170	3	,	,	PUNCT
ejpam-4510	170	4	a+	a+	ADP
ejpam-4510	170	5	]	]	PUNCT
ejpam-4510	170	6	be	be	AUX
ejpam-4510	170	7	such	such	ADJ
ejpam-4510	170	8	that	that	SCONJ
ejpam-4510	170	9	φ̊(s	φ̊(s	PROPN
ejpam-4510	170	10	,	,	PUNCT
ejpam-4510	170	11	t	t	PROPN
ejpam-4510	170	12	)	)	PUNCT
ejpam-4510	170	13	,	,	PUNCT
ejpam-4510	170	14	φs	φs	ADP
ejpam-4510	170	15	α	α	NOUN
ejpam-4510	170	16	and	and	CCONJ
ejpam-4510	170	17	φ̃ã	φ̃ã	NOUN
ejpam-4510	170	18	are	be	AUX
ejpam-4510	170	19	nonempty	nonempty	ADJ
ejpam-4510	170	20	.	.	PUNCT
ejpam-4510	171	1	let	let	VERB
ejpam-4510	171	2	x	x	PRON
ejpam-4510	171	3	,	,	PUNCT
ejpam-4510	171	4	y	y	PROPN
ejpam-4510	171	5	∈	∈	PROPN
ejpam-4510	171	6	φ̊(s	φ̊(s	PROPN
ejpam-4510	171	7	,	,	PUNCT
ejpam-4510	171	8	t	t	PROPN
ejpam-4510	171	9	)	)	PUNCT
ejpam-4510	171	10	∩	∩	NOUN
ejpam-4510	171	11	φs	φs	ADP
ejpam-4510	171	12	α	α	PROPN
ejpam-4510	171	13	∩	∩	ADJ
ejpam-4510	171	14	φ̃ã.	φ̃ã.	NOUN
ejpam-4510	171	15	then	then	ADV
ejpam-4510	171	16	φ−(x	φ−(x	PROPN
ejpam-4510	171	17	)	)	PUNCT
ejpam-4510	171	18	≤	≤	PROPN
ejpam-4510	171	19	s	s	PROPN
ejpam-4510	171	20	,	,	PUNCT
ejpam-4510	171	21	φ−(y	φ−(y	PROPN
ejpam-4510	171	22	)	)	PUNCT
ejpam-4510	171	23	≤	≤	PROPN
ejpam-4510	171	24	s	s	PROPN
ejpam-4510	171	25	,	,	PUNCT
ejpam-4510	171	26	φ+(x	φ+(x	NOUN
ejpam-4510	171	27	)	)	PUNCT
ejpam-4510	171	28	≥	≥	PROPN
ejpam-4510	171	29	t	t	PROPN
ejpam-4510	171	30	,	,	PUNCT
ejpam-4510	171	31	φ+(y	φ+(y	NUM
ejpam-4510	171	32	)	)	PUNCT
ejpam-4510	171	33	≥	≥	PROPN
ejpam-4510	171	34	t	t	PROPN
ejpam-4510	171	35	,	,	PUNCT
ejpam-4510	171	36	φs(x	φs(x	PUNCT
ejpam-4510	171	37	)	)	PUNCT
ejpam-4510	171	38	⊇	⊇	NOUN
ejpam-4510	171	39	α	α	NOUN
ejpam-4510	171	40	,	,	PUNCT
ejpam-4510	171	41	φs(y	φs(y	NUM
ejpam-4510	171	42	)	)	PUNCT
ejpam-4510	171	43	⊇	⊇	NOUN
ejpam-4510	171	44	α	α	NOUN
ejpam-4510	171	45	,	,	PUNCT
ejpam-4510	171	46	φ̃(x	φ̃(x	PROPN
ejpam-4510	171	47	)	)	PUNCT
ejpam-4510	171	48	⪰	⪰	VERB
ejpam-4510	171	49	ã	ã	PROPN
ejpam-4510	171	50	and	and	CCONJ
ejpam-4510	171	51	φ̃(y	φ̃(y	NOUN
ejpam-4510	171	52	)	)	PUNCT
ejpam-4510	171	53	⪰	⪰	NOUN
ejpam-4510	171	54	ã.	ã.	NOUN
ejpam-4510	171	55	hence	hence	ADV
ejpam-4510	171	56	φ−(x	φ−(x	PROPN
ejpam-4510	171	57	∗	∗	NOUN
ejpam-4510	171	58	(	(	PUNCT
ejpam-4510	171	59	x	x	X
ejpam-4510	171	60	∗	∗	PROPN
ejpam-4510	171	61	y	y	PROPN
ejpam-4510	171	62	)	)	PUNCT
ejpam-4510	171	63	)	)	PUNCT
ejpam-4510	172	1	≤	≤	NUM
ejpam-4510	172	2	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	172	3	)	)	PUNCT
ejpam-4510	172	4	,	,	PUNCT
ejpam-4510	172	5	φ−(y	φ−(y	PROPN
ejpam-4510	172	6	)	)	PUNCT
ejpam-4510	172	7	}	}	PUNCT
ejpam-4510	172	8	≤	≤	NUM
ejpam-4510	172	9	s	s	PROPN
ejpam-4510	172	10	,	,	PUNCT
ejpam-4510	172	11	φ+(x	φ+(x	NOUN
ejpam-4510	172	12	∗	∗	NOUN
ejpam-4510	172	13	(	(	PUNCT
ejpam-4510	172	14	x	x	X
ejpam-4510	172	15	∗	∗	PROPN
ejpam-4510	172	16	y	y	PROPN
ejpam-4510	172	17	)	)	PUNCT
ejpam-4510	172	18	)	)	PUNCT
ejpam-4510	172	19	≥	≥	NOUN
ejpam-4510	172	20	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	172	21	)	)	PUNCT
ejpam-4510	172	22	,	,	PUNCT
ejpam-4510	172	23	φ+(y	φ+(y	CCONJ
ejpam-4510	172	24	)	)	PUNCT
ejpam-4510	172	25	}	}	PUNCT
ejpam-4510	172	26	≥	≥	PROPN
ejpam-4510	172	27	t	t	PROPN
ejpam-4510	172	28	,	,	PUNCT
ejpam-4510	172	29	and	and	CCONJ
ejpam-4510	172	30	so	so	ADV
ejpam-4510	172	31	x	x	VERB
ejpam-4510	172	32	∗	∗	NOUN
ejpam-4510	172	33	(	(	PUNCT
ejpam-4510	172	34	x	x	X
ejpam-4510	172	35	∗	∗	PROPN
ejpam-4510	172	36	y	y	NOUN
ejpam-4510	172	37	)	)	PUNCT
ejpam-4510	172	38	∈	∈	PROPN
ejpam-4510	172	39	φ̊(s	φ̊(s	PROPN
ejpam-4510	172	40	,	,	PUNCT
ejpam-4510	172	41	t	t	PROPN
ejpam-4510	172	42	)	)	PUNCT
ejpam-4510	172	43	.	.	PUNCT
ejpam-4510	173	1	also	also	ADV
ejpam-4510	173	2	we	we	PRON
ejpam-4510	173	3	have	have	VERB
ejpam-4510	173	4	φs(x	φs(x	PUNCT
ejpam-4510	173	5	∗	∗	NOUN
ejpam-4510	173	6	(	(	PUNCT
ejpam-4510	173	7	x	x	X
ejpam-4510	173	8	∗	∗	PROPN
ejpam-4510	173	9	y	y	PROPN
ejpam-4510	173	10	)	)	PUNCT
ejpam-4510	173	11	)	)	PUNCT
ejpam-4510	174	1	⊇	⊇	NOUN
ejpam-4510	174	2	φs(x	φs(x	NOUN
ejpam-4510	174	3	)	)	PUNCT
ejpam-4510	174	4	∩	∩	NOUN
ejpam-4510	174	5	φs(y	φs(y	NUM
ejpam-4510	174	6	)	)	PUNCT
ejpam-4510	174	7	⊇	⊇	PROPN
ejpam-4510	174	8	α	α	PROPN
ejpam-4510	174	9	and	and	CCONJ
ejpam-4510	174	10	φ̃(x	φ̃(x	PROPN
ejpam-4510	174	11	∗	∗	NOUN
ejpam-4510	174	12	(	(	PUNCT
ejpam-4510	174	13	x	x	X
ejpam-4510	174	14	∗	∗	PROPN
ejpam-4510	174	15	y	y	NOUN
ejpam-4510	174	16	)	)	PUNCT
ejpam-4510	174	17	)	)	PUNCT
ejpam-4510	174	18	⪰	⪰	NOUN
ejpam-4510	174	19	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	174	20	)	)	PUNCT
ejpam-4510	174	21	,	,	PUNCT
ejpam-4510	174	22	φ̃(y	φ̃(y	NOUN
ejpam-4510	174	23	)	)	PUNCT
ejpam-4510	174	24	}	}	PUNCT
ejpam-4510	174	25	⪰	⪰	NOUN
ejpam-4510	174	26	ã	ã	PROPN
ejpam-4510	174	27	,	,	PUNCT
ejpam-4510	174	28	that	that	ADV
ejpam-4510	174	29	is	is	ADV
ejpam-4510	174	30	,	,	PUNCT
ejpam-4510	174	31	x	x	SYM
ejpam-4510	174	32	∗	∗	NOUN
ejpam-4510	174	33	(	(	PUNCT
ejpam-4510	174	34	x	x	X
ejpam-4510	174	35	∗	∗	PROPN
ejpam-4510	174	36	y	y	NOUN
ejpam-4510	174	37	)	)	PUNCT
ejpam-4510	174	38	∈	∈	PROPN
ejpam-4510	174	39	φs	φs	ADP
ejpam-4510	174	40	α	α	NOUN
ejpam-4510	174	41	and	and	CCONJ
ejpam-4510	174	42	x	x	SYM
ejpam-4510	174	43	∗	∗	NOUN
ejpam-4510	174	44	(	(	PUNCT
ejpam-4510	174	45	x	x	X
ejpam-4510	174	46	∗	∗	PROPN
ejpam-4510	174	47	y	y	NOUN
ejpam-4510	174	48	)	)	PUNCT
ejpam-4510	174	49	∈	∈	PROPN
ejpam-4510	174	50	φ̃ã.	φ̃ã.	NOUN
ejpam-4510	174	51	therefore	therefore	ADV
ejpam-4510	174	52	φ̊(s	φ̊(s	PROPN
ejpam-4510	174	53	,	,	PUNCT
ejpam-4510	174	54	t	t	PROPN
ejpam-4510	174	55	)	)	PUNCT
ejpam-4510	174	56	,	,	PUNCT
ejpam-4510	174	57	φs	φs	ADP
ejpam-4510	174	58	α	α	NOUN
ejpam-4510	174	59	and	and	CCONJ
ejpam-4510	174	60	φ̃ã	φ̃ã	NOUN
ejpam-4510	174	61	are	be	AUX
ejpam-4510	174	62	weak	weak	ADJ
ejpam-4510	174	63	be	be	NOUN
ejpam-4510	174	64	-	-	PUNCT
ejpam-4510	174	65	subalgebras	subalgebra	NOUN
ejpam-4510	174	66	of	of	ADP
ejpam-4510	174	67	x.	x.	PROPN
ejpam-4510	174	68	y.	y.	PROPN
ejpam-4510	174	69	b.	b.	PROPN
ejpam-4510	174	70	jun	jun	PROPN
ejpam-4510	174	71	,	,	PUNCT
ejpam-4510	174	72	s.	s.	PROPN
ejpam-4510	174	73	s.	s.	PROPN
ejpam-4510	174	74	ahn	ahn	PROPN
ejpam-4510	174	75	and	and	CCONJ
ejpam-4510	174	76	e.	e.	PROPN
ejpam-4510	174	77	h.	h.	PROPN
ejpam-4510	174	78	roh	roh	PROPN
ejpam-4510	174	79	/	/	SYM
ejpam-4510	174	80	eur	eur	PROPN
ejpam-4510	174	81	.	.	PUNCT
ejpam-4510	175	1	j.	j.	PROPN
ejpam-4510	175	2	pure	pure	PROPN
ejpam-4510	175	3	appl	appl	PROPN
ejpam-4510	175	4	.	.	PROPN
ejpam-4510	175	5	math	math	PROPN
ejpam-4510	175	6	,	,	PUNCT
ejpam-4510	175	7	15	15	NUM
ejpam-4510	175	8	(	(	PUNCT
ejpam-4510	175	9	4	4	NUM
ejpam-4510	175	10	)	)	PUNCT
ejpam-4510	175	11	(	(	PUNCT
ejpam-4510	175	12	2022	2022	NUM
ejpam-4510	175	13	)	)	PUNCT
ejpam-4510	175	14	,	,	PUNCT
ejpam-4510	175	15	1521	1521	NUM
ejpam-4510	175	16	-	-	SYM
ejpam-4510	175	17	1535	1535	NUM
ejpam-4510	175	18	1528	1528	NUM
ejpam-4510	175	19	corollary	corollary	NOUN
ejpam-4510	175	20	3	3	NUM
ejpam-4510	175	21	.	.	PUNCT
ejpam-4510	176	1	if	if	SCONJ
ejpam-4510	176	2	dokφ	dokφ	NOUN
ejpam-4510	176	3	:	:	PUNCT
ejpam-4510	176	4	=	=	SYM
ejpam-4510	176	5	(	(	PUNCT
ejpam-4510	176	6	φ̊	φ̊	PROPN
ejpam-4510	176	7	,	,	PUNCT
ejpam-4510	176	8	φs	φs	ADV
ejpam-4510	176	9	,	,	PUNCT
ejpam-4510	176	10	φ̃	φ̃	PROPN
ejpam-4510	176	11	)	)	PUNCT
ejpam-4510	176	12	is	be	AUX
ejpam-4510	176	13	a	a	DET
ejpam-4510	176	14	dokdo	dokdo	NOUN
ejpam-4510	176	15	be	be	NOUN
ejpam-4510	176	16	-	-	PUNCT
ejpam-4510	176	17	subalgebra	subalgebra	NOUN
ejpam-4510	176	18	of	of	ADP
ejpam-4510	176	19	(	(	PUNCT
ejpam-4510	176	20	x	x	NOUN
ejpam-4510	176	21	,	,	PUNCT
ejpam-4510	176	22	u	u	NOUN
ejpam-4510	176	23	)	)	PUNCT
ejpam-4510	176	24	,	,	PUNCT
ejpam-4510	176	25	then	then	ADV
ejpam-4510	176	26	the	the	DET
ejpam-4510	176	27	nonempty	nonempty	NOUN
ejpam-4510	176	28	sets	set	VERB
ejpam-4510	176	29	φ̊(s	φ̊(s	PROPN
ejpam-4510	176	30	,	,	PUNCT
ejpam-4510	176	31	t	t	PROPN
ejpam-4510	176	32	)	)	PUNCT
ejpam-4510	176	33	,	,	PUNCT
ejpam-4510	176	34	φs	φs	ADP
ejpam-4510	176	35	α	α	NOUN
ejpam-4510	176	36	and	and	CCONJ
ejpam-4510	176	37	φ̃ã	φ̃ã	NOUN
ejpam-4510	176	38	are	be	AUX
ejpam-4510	176	39	weak	weak	ADJ
ejpam-4510	176	40	be	be	NOUN
ejpam-4510	176	41	-	-	PUNCT
ejpam-4510	176	42	subalgebras	subalgebra	NOUN
ejpam-4510	176	43	of	of	ADP
ejpam-4510	176	44	x	x	PUNCT
ejpam-4510	176	45	for	for	ADP
ejpam-4510	176	46	all	all	DET
ejpam-4510	176	47	(	(	PUNCT
ejpam-4510	176	48	s	s	PROPN
ejpam-4510	176	49	,	,	PUNCT
ejpam-4510	176	50	t	t	PROPN
ejpam-4510	176	51	)	)	PUNCT
ejpam-4510	176	52	∈	∈	PROPN
ejpam-4510	177	1	[	[	X
ejpam-4510	177	2	−1	−1	NOUN
ejpam-4510	177	3	,	,	PUNCT
ejpam-4510	177	4	0	0	NUM
ejpam-4510	177	5	]	]	X
ejpam-4510	177	6	×	×	NOUN
ejpam-4510	178	1	[	[	X
ejpam-4510	178	2	0	0	NUM
ejpam-4510	178	3	,	,	PUNCT
ejpam-4510	178	4	1	1	NUM
ejpam-4510	178	5	]	]	PUNCT
ejpam-4510	178	6	,	,	PUNCT
ejpam-4510	178	7	α	α	PROPN
ejpam-4510	178	8	∈	∈	PROPN
ejpam-4510	178	9	2u	2u	NOUN
ejpam-4510	178	10	and	and	CCONJ
ejpam-4510	178	11	ã	ã	PROPN
ejpam-4510	178	12	=	=	PUNCT
ejpam-4510	179	1	[	[	X
ejpam-4510	179	2	a−	a−	PROPN
ejpam-4510	179	3	,	,	PUNCT
ejpam-4510	179	4	a+	a+	ADP
ejpam-4510	179	5	]	]	PUNCT
ejpam-4510	179	6	.	.	PUNCT
ejpam-4510	180	1	the	the	DET
ejpam-4510	180	2	following	follow	VERB
ejpam-4510	180	3	example	example	NOUN
ejpam-4510	180	4	shows	show	VERB
ejpam-4510	180	5	that	that	SCONJ
ejpam-4510	180	6	the	the	DET
ejpam-4510	180	7	converse	converse	NOUN
ejpam-4510	180	8	of	of	ADP
ejpam-4510	180	9	theorem	theorem	ADJ
ejpam-4510	180	10	2	2	NUM
ejpam-4510	180	11	may	may	AUX
ejpam-4510	180	12	not	not	PART
ejpam-4510	180	13	be	be	AUX
ejpam-4510	180	14	true	true	ADJ
ejpam-4510	180	15	.	.	PUNCT
ejpam-4510	181	1	example	example	NOUN
ejpam-4510	182	1	4	4	X
ejpam-4510	182	2	.	.	PUNCT
ejpam-4510	183	1	let	let	AUX
ejpam-4510	183	2	(	(	PUNCT
ejpam-4510	183	3	x	x	NOUN
ejpam-4510	183	4	,	,	PUNCT
ejpam-4510	183	5	u	u	NOUN
ejpam-4510	183	6	)	)	PUNCT
ejpam-4510	183	7	be	be	VERB
ejpam-4510	183	8	the	the	DET
ejpam-4510	183	9	be	be	ADJ
ejpam-4510	183	10	-	-	PUNCT
ejpam-4510	183	11	dokdo	dokdo	ADJ
ejpam-4510	183	12	universe	universe	NOUN
ejpam-4510	183	13	in	in	ADP
ejpam-4510	183	14	example	example	NOUN
ejpam-4510	183	15	1	1	NUM
ejpam-4510	183	16	.	.	X
ejpam-4510	184	1	define	define	VERB
ejpam-4510	184	2	a	a	DET
ejpam-4510	184	3	dokdo	dokdo	ADJ
ejpam-4510	184	4	structure	structure	NOUN
ejpam-4510	184	5	dokφ	dokφ	NOUN
ejpam-4510	185	1	:	:	PUNCT
ejpam-4510	185	2	=	=	SYM
ejpam-4510	185	3	(	(	PUNCT
ejpam-4510	185	4	φ̊	φ̊	PROPN
ejpam-4510	185	5	,	,	PUNCT
ejpam-4510	185	6	φs	φs	ADV
ejpam-4510	185	7	,	,	PUNCT
ejpam-4510	185	8	φ̃	φ̃	PROPN
ejpam-4510	185	9	)	)	PUNCT
ejpam-4510	185	10	in	in	ADP
ejpam-4510	185	11	(	(	PUNCT
ejpam-4510	185	12	x	x	NOUN
ejpam-4510	185	13	,	,	PUNCT
ejpam-4510	185	14	u	u	NOUN
ejpam-4510	185	15	)	)	PUNCT
ejpam-4510	185	16	as	as	SCONJ
ejpam-4510	185	17	follows	follow	VERB
ejpam-4510	185	18	:	:	PUNCT
ejpam-4510	185	19	dokφ	dokφ	NOUN
ejpam-4510	185	20	:	:	PUNCT
ejpam-4510	185	21	=	=	SYM
ejpam-4510	185	22	(	(	PUNCT
ejpam-4510	185	23	φ̊	φ̊	PROPN
ejpam-4510	185	24	,	,	PUNCT
ejpam-4510	185	25	φs	φs	ADV
ejpam-4510	185	26	,	,	PUNCT
ejpam-4510	185	27	φ̃	φ̃	PROPN
ejpam-4510	185	28	)	)	PUNCT
ejpam-4510	185	29	:	:	PUNCT
ejpam-4510	185	30	x	x	X
ejpam-4510	185	31	→	→	PUNCT
ejpam-4510	185	32	(	(	PUNCT
ejpam-4510	185	33	[	[	X
ejpam-4510	185	34	−1	−1	NOUN
ejpam-4510	185	35	,	,	PUNCT
ejpam-4510	185	36	0]×	0]×	PROPN
ejpam-4510	186	1	[	[	X
ejpam-4510	186	2	0	0	NUM
ejpam-4510	186	3	,	,	PUNCT
ejpam-4510	186	4	1])×	1])×	NOUN
ejpam-4510	186	5	2u	2u	NOUN
ejpam-4510	186	6	×	×	NOUN
ejpam-4510	187	1	[	[	X
ejpam-4510	187	2	[	[	X
ejpam-4510	187	3	0	0	NUM
ejpam-4510	187	4	,	,	PUNCT
ejpam-4510	187	5	1	1	NUM
ejpam-4510	187	6	]	]	PUNCT
ejpam-4510	187	7	]	]	PUNCT
ejpam-4510	187	8	,	,	PUNCT
ejpam-4510	187	9	x	x	SYM
ejpam-4510	187	10	7→	7→	NUM
ejpam-4510	187	11			NUM
ejpam-4510	187	12	(	(	PUNCT
ejpam-4510	187	13	(	(	PUNCT
ejpam-4510	187	14	−0.85	−0.85	INTJ
ejpam-4510	187	15	,	,	PUNCT
ejpam-4510	187	16	0.71	0.71	NUM
ejpam-4510	187	17	)	)	PUNCT
ejpam-4510	187	18	,	,	PUNCT
ejpam-4510	187	19	z	z	X
ejpam-4510	187	20	,	,	PUNCT
ejpam-4510	187	21	[	[	X
ejpam-4510	187	22	0.42	0.42	NUM
ejpam-4510	187	23	,	,	PUNCT
ejpam-4510	187	24	0.76	0.76	NUM
ejpam-4510	187	25	]	]	PUNCT
ejpam-4510	187	26	)	)	PUNCT
ejpam-4510	187	27	if	if	SCONJ
ejpam-4510	187	28	x	x	PROPN
ejpam-4510	187	29	=	=	SYM
ejpam-4510	187	30	1	1	NUM
ejpam-4510	187	31	,	,	PUNCT
ejpam-4510	187	32	(	(	PUNCT
ejpam-4510	187	33	(	(	PUNCT
ejpam-4510	187	34	−0.66	−0.66	NOUN
ejpam-4510	187	35	,	,	PUNCT
ejpam-4510	187	36	0.53	0.53	NUM
ejpam-4510	187	37	)	)	PUNCT
ejpam-4510	187	38	,	,	PUNCT
ejpam-4510	187	39	4z	4z	NOUN
ejpam-4510	187	40	,	,	PUNCT
ejpam-4510	187	41	[	[	X
ejpam-4510	187	42	0.29	0.29	NUM
ejpam-4510	187	43	,	,	PUNCT
ejpam-4510	187	44	0.58	0.58	NUM
ejpam-4510	187	45	]	]	PUNCT
ejpam-4510	187	46	)	)	PUNCT
ejpam-4510	187	47	if	if	SCONJ
ejpam-4510	187	48	x	x	PROPN
ejpam-4510	187	49	=	=	SYM
ejpam-4510	187	50	2	2	NUM
ejpam-4510	187	51	,	,	PUNCT
ejpam-4510	187	52	(	(	PUNCT
ejpam-4510	187	53	(	(	PUNCT
ejpam-4510	187	54	−0.44	−0.44	NOUN
ejpam-4510	187	55	,	,	PUNCT
ejpam-4510	187	56	0.57	0.57	NUM
ejpam-4510	187	57	)	)	PUNCT
ejpam-4510	187	58	,	,	PUNCT
ejpam-4510	187	59	4z	4z	NOUN
ejpam-4510	187	60	,	,	PUNCT
ejpam-4510	187	61	[	[	X
ejpam-4510	187	62	0.29	0.29	NUM
ejpam-4510	187	63	,	,	PUNCT
ejpam-4510	187	64	0.58	0.58	NUM
ejpam-4510	187	65	]	]	PUNCT
ejpam-4510	187	66	)	)	PUNCT
ejpam-4510	187	67	if	if	SCONJ
ejpam-4510	187	68	x	x	PROPN
ejpam-4510	187	69	=	=	SYM
ejpam-4510	187	70	3	3	NUM
ejpam-4510	187	71	,	,	PUNCT
ejpam-4510	187	72	(	(	PUNCT
ejpam-4510	187	73	(	(	PUNCT
ejpam-4510	187	74	−0.44	−0.44	NOUN
ejpam-4510	187	75	,	,	PUNCT
ejpam-4510	187	76	0.53	0.53	NUM
ejpam-4510	187	77	)	)	PUNCT
ejpam-4510	187	78	,	,	PUNCT
ejpam-4510	187	79	4z	4z	NOUN
ejpam-4510	187	80	,	,	PUNCT
ejpam-4510	187	81	[	[	X
ejpam-4510	187	82	0.29	0.29	NUM
ejpam-4510	187	83	,	,	PUNCT
ejpam-4510	187	84	0.58	0.58	NUM
ejpam-4510	187	85	]	]	PUNCT
ejpam-4510	187	86	)	)	PUNCT
ejpam-4510	187	87	if	if	SCONJ
ejpam-4510	187	88	x	x	PROPN
ejpam-4510	187	89	=	=	SYM
ejpam-4510	187	90	4	4	NUM
ejpam-4510	187	91	,	,	PUNCT
ejpam-4510	187	92	(	(	PUNCT
ejpam-4510	187	93	(	(	PUNCT
ejpam-4510	187	94	−0.44	−0.44	NOUN
ejpam-4510	187	95	,	,	PUNCT
ejpam-4510	187	96	0.53	0.53	NUM
ejpam-4510	187	97	)	)	PUNCT
ejpam-4510	187	98	,	,	PUNCT
ejpam-4510	187	99	4z	4z	NOUN
ejpam-4510	187	100	,	,	PUNCT
ejpam-4510	187	101	[	[	X
ejpam-4510	187	102	0.29	0.29	NUM
ejpam-4510	187	103	,	,	PUNCT
ejpam-4510	187	104	0.58	0.58	NUM
ejpam-4510	187	105	]	]	PUNCT
ejpam-4510	187	106	)	)	PUNCT
ejpam-4510	187	107	if	if	SCONJ
ejpam-4510	187	108	x	x	PROPN
ejpam-4510	187	109	=	=	SYM
ejpam-4510	187	110	5	5	NUM
ejpam-4510	187	111	,	,	PUNCT
ejpam-4510	187	112	(	(	PUNCT
ejpam-4510	187	113	(	(	PUNCT
ejpam-4510	187	114	−0.72	−0.72	PROPN
ejpam-4510	187	115	,	,	PUNCT
ejpam-4510	187	116	0.68	0.68	NUM
ejpam-4510	187	117	)	)	PUNCT
ejpam-4510	187	118	,	,	PUNCT
ejpam-4510	187	119	2z	2z	NUM
ejpam-4510	187	120	,	,	PUNCT
ejpam-4510	187	121	[	[	X
ejpam-4510	187	122	0.33	0.33	NUM
ejpam-4510	187	123	,	,	PUNCT
ejpam-4510	187	124	0.72	0.72	NUM
ejpam-4510	187	125	]	]	PUNCT
ejpam-4510	187	126	)	)	PUNCT
ejpam-4510	187	127	if	if	SCONJ
ejpam-4510	187	128	x	x	PROPN
ejpam-4510	187	129	=	=	SYM
ejpam-4510	187	130	6	6	NUM
ejpam-4510	187	131	.	.	PUNCT
ejpam-4510	188	1	it	it	PRON
ejpam-4510	188	2	is	be	AUX
ejpam-4510	188	3	routine	routine	ADJ
ejpam-4510	188	4	to	to	PART
ejpam-4510	188	5	verify	verify	VERB
ejpam-4510	188	6	that	that	SCONJ
ejpam-4510	188	7	the	the	DET
ejpam-4510	188	8	nonempty	nonempty	NOUN
ejpam-4510	188	9	sets	set	VERB
ejpam-4510	188	10	φ̊(s	φ̊(s	PROPN
ejpam-4510	188	11	,	,	PUNCT
ejpam-4510	188	12	t	t	PROPN
ejpam-4510	188	13	)	)	PUNCT
ejpam-4510	188	14	,	,	PUNCT
ejpam-4510	188	15	φs	φs	ADP
ejpam-4510	188	16	α	α	NOUN
ejpam-4510	188	17	and	and	CCONJ
ejpam-4510	188	18	φ̃ã	φ̃ã	NOUN
ejpam-4510	188	19	are	be	AUX
ejpam-4510	188	20	weak	weak	ADJ
ejpam-4510	188	21	be	be	NOUN
ejpam-4510	188	22	-	-	PUNCT
ejpam-4510	188	23	subalgebras	subalgebra	NOUN
ejpam-4510	188	24	of	of	ADP
ejpam-4510	188	25	x	x	PUNCT
ejpam-4510	188	26	for	for	ADP
ejpam-4510	188	27	all	all	DET
ejpam-4510	188	28	(	(	PUNCT
ejpam-4510	188	29	s	s	PROPN
ejpam-4510	188	30	,	,	PUNCT
ejpam-4510	188	31	t	t	PROPN
ejpam-4510	188	32	)	)	PUNCT
ejpam-4510	188	33	∈	∈	PROPN
ejpam-4510	189	1	[	[	X
ejpam-4510	189	2	−1	−1	NOUN
ejpam-4510	189	3	,	,	PUNCT
ejpam-4510	189	4	0	0	NUM
ejpam-4510	189	5	]	]	X
ejpam-4510	189	6	×	×	NOUN
ejpam-4510	190	1	[	[	X
ejpam-4510	190	2	0	0	NUM
ejpam-4510	190	3	,	,	PUNCT
ejpam-4510	190	4	1	1	NUM
ejpam-4510	190	5	]	]	PUNCT
ejpam-4510	190	6	,	,	PUNCT
ejpam-4510	190	7	α	α	PROPN
ejpam-4510	190	8	∈	∈	PROPN
ejpam-4510	190	9	2u	2u	NOUN
ejpam-4510	190	10	and	and	CCONJ
ejpam-4510	190	11	ã	ã	PROPN
ejpam-4510	190	12	=	=	PUNCT
ejpam-4510	191	1	[	[	X
ejpam-4510	191	2	a−	a−	PROPN
ejpam-4510	191	3	,	,	PUNCT
ejpam-4510	191	4	a+	a+	PRON
ejpam-4510	191	5	]	]	PUNCT
ejpam-4510	191	6	.	.	PUNCT
ejpam-4510	192	1	but	but	CCONJ
ejpam-4510	192	2	dokφ	dokφ	NOUN
ejpam-4510	192	3	:	:	PUNCT
ejpam-4510	193	1	=	=	SYM
ejpam-4510	193	2	(	(	PUNCT
ejpam-4510	193	3	φ̊	φ̊	PROPN
ejpam-4510	193	4	,	,	PUNCT
ejpam-4510	193	5	φs	φs	ADV
ejpam-4510	193	6	,	,	PUNCT
ejpam-4510	193	7	φ̃	φ̃	PROPN
ejpam-4510	193	8	)	)	PUNCT
ejpam-4510	193	9	is	be	AUX
ejpam-4510	193	10	not	not	PART
ejpam-4510	193	11	a	a	DET
ejpam-4510	193	12	weak	weak	ADJ
ejpam-4510	193	13	dokdo	dokdo	NOUN
ejpam-4510	193	14	be	be	NOUN
ejpam-4510	193	15	-	-	PUNCT
ejpam-4510	193	16	subalgebra	subalgebra	NOUN
ejpam-4510	193	17	of	of	ADP
ejpam-4510	193	18	(	(	PUNCT
ejpam-4510	193	19	x	x	NOUN
ejpam-4510	193	20	,	,	PUNCT
ejpam-4510	193	21	u	u	NOUN
ejpam-4510	193	22	)	)	PUNCT
ejpam-4510	193	23	because	because	SCONJ
ejpam-4510	193	24	of	of	ADP
ejpam-4510	193	25	2∗(2∗6	2∗(2∗6	NUM
ejpam-4510	193	26	)	)	PUNCT
ejpam-4510	193	27	(	(	PUNCT
ejpam-4510	193	28	2,6	2,6	NUM
ejpam-4510	193	29	)	)	PUNCT
ejpam-4510	193	30	=	=	SYM
ejpam-4510	193	31	4	4	NUM
ejpam-4510	193	32	(	(	PUNCT
ejpam-4510	193	33	2,6	2,6	NUM
ejpam-4510	193	34	)	)	PUNCT
ejpam-4510	193	35	/∈	/∈	PUNCT
ejpam-4510	194	1	φ̊(max	φ̊(max	ADV
ejpam-4510	194	2	,	,	PUNCT
ejpam-4510	194	3	min	min	NOUN
ejpam-4510	194	4	)	)	PUNCT
ejpam-4510	194	5	.	.	PUNCT
ejpam-4510	195	1	we	we	PRON
ejpam-4510	195	2	provide	provide	VERB
ejpam-4510	195	3	conditions	condition	NOUN
ejpam-4510	195	4	for	for	SCONJ
ejpam-4510	195	5	a	a	DET
ejpam-4510	195	6	dokdo	dokdo	NOUN
ejpam-4510	195	7	structure	structure	NOUN
ejpam-4510	195	8	to	to	PART
ejpam-4510	195	9	be	be	AUX
ejpam-4510	195	10	a	a	DET
ejpam-4510	195	11	weak	weak	ADJ
ejpam-4510	195	12	dokdo	dokdo	NOUN
ejpam-4510	195	13	be	be	NOUN
ejpam-4510	195	14	-	-	PUNCT
ejpam-4510	195	15	subalgebra	subalgebra	NOUN
ejpam-4510	195	16	.	.	PUNCT
ejpam-4510	196	1	theorem	theorem	NOUN
ejpam-4510	196	2	3	3	NUM
ejpam-4510	196	3	.	.	PUNCT
ejpam-4510	196	4	given	give	VERB
ejpam-4510	196	5	a	a	DET
ejpam-4510	196	6	dokdo	dokdo	NOUN
ejpam-4510	196	7	structure	structure	NOUN
ejpam-4510	196	8	dokφ	dokφ	NOUN
ejpam-4510	196	9	:	:	PUNCT
ejpam-4510	197	1	=	=	SYM
ejpam-4510	197	2	(	(	PUNCT
ejpam-4510	197	3	φ̊	φ̊	PROPN
ejpam-4510	197	4	,	,	PUNCT
ejpam-4510	197	5	φs	φs	ADV
ejpam-4510	197	6	,	,	PUNCT
ejpam-4510	197	7	φ̃	φ̃	PROPN
ejpam-4510	197	8	)	)	PUNCT
ejpam-4510	197	9	in	in	ADP
ejpam-4510	197	10	(	(	PUNCT
ejpam-4510	197	11	x	x	NOUN
ejpam-4510	197	12	,	,	PUNCT
ejpam-4510	197	13	u	u	NOUN
ejpam-4510	197	14	)	)	PUNCT
ejpam-4510	197	15	,	,	PUNCT
ejpam-4510	197	16	if	if	SCONJ
ejpam-4510	197	17	the	the	DET
ejpam-4510	197	18	nonempty	nonempty	NOUN
ejpam-4510	197	19	sets	set	VERB
ejpam-4510	197	20	φ̊(s,−	φ̊(s,−	NUM
ejpam-4510	197	21	)	)	PUNCT
ejpam-4510	197	22	,	,	PUNCT
ejpam-4510	197	23	φ̊(t,+	φ̊(t,+	PROPN
ejpam-4510	197	24	)	)	PUNCT
ejpam-4510	197	25	,	,	PUNCT
ejpam-4510	197	26	φs	φs	ADP
ejpam-4510	197	27	α	α	NOUN
ejpam-4510	197	28	and	and	CCONJ
ejpam-4510	197	29	φ̃ã	φ̃ã	NOUN
ejpam-4510	197	30	are	be	AUX
ejpam-4510	197	31	weak	weak	ADJ
ejpam-4510	197	32	be	be	NOUN
ejpam-4510	197	33	-	-	PUNCT
ejpam-4510	197	34	subalgebras	subalgebra	NOUN
ejpam-4510	197	35	of	of	ADP
ejpam-4510	197	36	x	x	PUNCT
ejpam-4510	197	37	for	for	ADP
ejpam-4510	197	38	all	all	DET
ejpam-4510	197	39	(	(	PUNCT
ejpam-4510	197	40	s	s	PROPN
ejpam-4510	197	41	,	,	PUNCT
ejpam-4510	197	42	t	t	PROPN
ejpam-4510	197	43	)	)	PUNCT
ejpam-4510	197	44	∈	∈	PROPN
ejpam-4510	198	1	[	[	X
ejpam-4510	198	2	−1	−1	NOUN
ejpam-4510	198	3	,	,	PUNCT
ejpam-4510	198	4	0	0	NUM
ejpam-4510	198	5	]	]	X
ejpam-4510	198	6	×	×	NOUN
ejpam-4510	199	1	[	[	X
ejpam-4510	199	2	0	0	NUM
ejpam-4510	199	3	,	,	PUNCT
ejpam-4510	199	4	1	1	NUM
ejpam-4510	199	5	]	]	PUNCT
ejpam-4510	199	6	,	,	PUNCT
ejpam-4510	199	7	α	α	PROPN
ejpam-4510	199	8	∈	∈	PROPN
ejpam-4510	199	9	2u	2u	NOUN
ejpam-4510	199	10	and	and	CCONJ
ejpam-4510	199	11	ã	ã	PROPN
ejpam-4510	199	12	=	=	PUNCT
ejpam-4510	200	1	[	[	X
ejpam-4510	200	2	a−	a−	PROPN
ejpam-4510	200	3	,	,	PUNCT
ejpam-4510	200	4	a+	a+	ADP
ejpam-4510	200	5	]	]	PUNCT
ejpam-4510	200	6	,	,	PUNCT
ejpam-4510	200	7	then	then	ADV
ejpam-4510	200	8	dokφ	dokφ	VERB
ejpam-4510	200	9	:	:	PUNCT
ejpam-4510	200	10	=	=	SYM
ejpam-4510	200	11	(	(	PUNCT
ejpam-4510	200	12	φ̊	φ̊	PROPN
ejpam-4510	200	13	,	,	PUNCT
ejpam-4510	200	14	φs	φs	ADV
ejpam-4510	200	15	,	,	PUNCT
ejpam-4510	200	16	φ̃	φ̃	PROPN
ejpam-4510	200	17	)	)	PUNCT
ejpam-4510	200	18	is	be	AUX
ejpam-4510	200	19	a	a	DET
ejpam-4510	200	20	weak	weak	ADJ
ejpam-4510	200	21	dokdo	dokdo	NOUN
ejpam-4510	200	22	be	be	NOUN
ejpam-4510	200	23	-	-	PUNCT
ejpam-4510	200	24	subalgebra	subalgebra	NOUN
ejpam-4510	200	25	of	of	ADP
ejpam-4510	200	26	(	(	PUNCT
ejpam-4510	200	27	x	x	NOUN
ejpam-4510	200	28	,	,	PUNCT
ejpam-4510	200	29	u	u	NOUN
ejpam-4510	200	30	)	)	PUNCT
ejpam-4510	200	31	.	.	PUNCT
ejpam-4510	201	1	proof	proof	NOUN
ejpam-4510	201	2	.	.	PUNCT
ejpam-4510	202	1	assume	assume	VERB
ejpam-4510	202	2	that	that	SCONJ
ejpam-4510	202	3	φ̊(s,−	φ̊(s,−	PROPN
ejpam-4510	202	4	)	)	PUNCT
ejpam-4510	202	5	,	,	PUNCT
ejpam-4510	202	6	φ̊(t,+	φ̊(t,+	PROPN
ejpam-4510	202	7	)	)	PUNCT
ejpam-4510	202	8	,	,	PUNCT
ejpam-4510	202	9	φs	φs	ADP
ejpam-4510	202	10	α	α	NOUN
ejpam-4510	202	11	and	and	CCONJ
ejpam-4510	202	12	φ̃ã	φ̃ã	NOUN
ejpam-4510	202	13	are	be	AUX
ejpam-4510	202	14	nonempty	nonempty	X
ejpam-4510	202	15	weak	weak	ADJ
ejpam-4510	202	16	be	be	NOUN
ejpam-4510	202	17	-	-	PUNCT
ejpam-4510	202	18	subalgebras	subalgebra	NOUN
ejpam-4510	202	19	of	of	ADP
ejpam-4510	202	20	x	x	PUNCT
ejpam-4510	202	21	for	for	ADP
ejpam-4510	202	22	all	all	DET
ejpam-4510	202	23	(	(	PUNCT
ejpam-4510	202	24	s	s	PROPN
ejpam-4510	202	25	,	,	PUNCT
ejpam-4510	202	26	t	t	PROPN
ejpam-4510	202	27	)	)	PUNCT
ejpam-4510	202	28	∈	∈	PROPN
ejpam-4510	203	1	[	[	X
ejpam-4510	203	2	−1	−1	NOUN
ejpam-4510	203	3	,	,	PUNCT
ejpam-4510	203	4	0	0	NUM
ejpam-4510	203	5	]	]	X
ejpam-4510	203	6	×	×	NOUN
ejpam-4510	204	1	[	[	X
ejpam-4510	204	2	0	0	NUM
ejpam-4510	204	3	,	,	PUNCT
ejpam-4510	204	4	1	1	NUM
ejpam-4510	204	5	]	]	PUNCT
ejpam-4510	204	6	,	,	PUNCT
ejpam-4510	204	7	α	α	PROPN
ejpam-4510	204	8	∈	∈	PROPN
ejpam-4510	204	9	2u	2u	NOUN
ejpam-4510	204	10	and	and	CCONJ
ejpam-4510	204	11	ã	ã	PROPN
ejpam-4510	204	12	=	=	PUNCT
ejpam-4510	205	1	[	[	X
ejpam-4510	205	2	a−	a−	PROPN
ejpam-4510	205	3	,	,	PUNCT
ejpam-4510	205	4	a+	a+	ADP
ejpam-4510	205	5	]	]	PUNCT
ejpam-4510	205	6	.	.	PUNCT
ejpam-4510	206	1	if	if	SCONJ
ejpam-4510	206	2	there	there	PRON
ejpam-4510	206	3	exist	exist	VERB
ejpam-4510	206	4	x	x	NOUN
ejpam-4510	206	5	,	,	PUNCT
ejpam-4510	206	6	y	y	PROPN
ejpam-4510	206	7	∈	∈	PROPN
ejpam-4510	206	8	x	x	PUNCT
ejpam-4510	206	9	such	such	ADJ
ejpam-4510	206	10	that	that	SCONJ
ejpam-4510	206	11	x∗(x∗y	x∗(x∗y	NUM
ejpam-4510	206	12	)	)	PUNCT
ejpam-4510	206	13	(	(	PUNCT
ejpam-4510	206	14	x	x	X
ejpam-4510	206	15	,	,	PUNCT
ejpam-4510	206	16	y	y	PROPN
ejpam-4510	206	17	)	)	PUNCT
ejpam-4510	206	18	/∈	/∈	PUNCT
ejpam-4510	207	1	φ̊(max	φ̊(max	ADV
ejpam-4510	207	2	,	,	PUNCT
ejpam-4510	207	3	min	min	NOUN
ejpam-4510	207	4	)	)	PUNCT
ejpam-4510	207	5	,	,	PUNCT
ejpam-4510	207	6	then	then	ADV
ejpam-4510	207	7	φ−(x	φ−(x	PROPN
ejpam-4510	207	8	∗	∗	NOUN
ejpam-4510	207	9	(	(	PUNCT
ejpam-4510	207	10	x	x	X
ejpam-4510	207	11	∗	∗	PROPN
ejpam-4510	207	12	y	y	PROPN
ejpam-4510	207	13	)	)	PUNCT
ejpam-4510	207	14	)	)	PUNCT
ejpam-4510	207	15	>	>	X
ejpam-4510	208	1	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	208	2	)	)	PUNCT
ejpam-4510	208	3	,	,	PUNCT
ejpam-4510	208	4	φ−(y	φ−(y	PROPN
ejpam-4510	208	5	)	)	PUNCT
ejpam-4510	208	6	}	}	PUNCT
ejpam-4510	208	7	or	or	CCONJ
ejpam-4510	208	8	φ+(x	φ+(x	NOUN
ejpam-4510	208	9	∗	∗	NOUN
ejpam-4510	208	10	(	(	PUNCT
ejpam-4510	208	11	x	x	X
ejpam-4510	208	12	∗	∗	PROPN
ejpam-4510	208	13	y	y	PROPN
ejpam-4510	208	14	)	)	PUNCT
ejpam-4510	208	15	)	)	PUNCT
ejpam-4510	208	16	<	<	X
ejpam-4510	209	1	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	209	2	)	)	PUNCT
ejpam-4510	209	3	,	,	PUNCT
ejpam-4510	209	4	φ+(y	φ+(y	PUNCT
ejpam-4510	209	5	)	)	PUNCT
ejpam-4510	209	6	}	}	PUNCT
ejpam-4510	209	7	.	.	PUNCT
ejpam-4510	210	1	it	it	PRON
ejpam-4510	210	2	follows	follow	VERB
ejpam-4510	210	3	that	that	SCONJ
ejpam-4510	210	4	x	x	SYM
ejpam-4510	210	5	,	,	PUNCT
ejpam-4510	210	6	y	y	PROPN
ejpam-4510	210	7	∈	∈	PROPN
ejpam-4510	210	8	φ̊(s,−	φ̊(s,−	PROPN
ejpam-4510	210	9	)	)	PUNCT
ejpam-4510	210	10	∩	∩	PROPN
ejpam-4510	210	11	φ̊(t,+	φ̊(t,+	PROPN
ejpam-4510	210	12	)	)	PUNCT
ejpam-4510	210	13	,	,	PUNCT
ejpam-4510	210	14	x	x	X
ejpam-4510	210	15	∗	∗	NOUN
ejpam-4510	210	16	(	(	PUNCT
ejpam-4510	210	17	x	x	X
ejpam-4510	210	18	∗	∗	PROPN
ejpam-4510	210	19	y	y	PROPN
ejpam-4510	210	20	)	)	PUNCT
ejpam-4510	210	21	/∈	/∈	PUNCT
ejpam-4510	210	22	φ̊(s,−	φ̊(s,−	PROPN
ejpam-4510	210	23	)	)	PUNCT
ejpam-4510	210	24	and	and	CCONJ
ejpam-4510	210	25	x	x	PUNCT
ejpam-4510	210	26	∗	∗	NOUN
ejpam-4510	210	27	(	(	PUNCT
ejpam-4510	210	28	x	x	X
ejpam-4510	210	29	∗	∗	PROPN
ejpam-4510	210	30	y	y	NOUN
ejpam-4510	210	31	)	)	PUNCT
ejpam-4510	210	32	/∈	/∈	PUNCT
ejpam-4510	211	1	φ̊(t,+	φ̊(t,+	PROPN
ejpam-4510	211	2	)	)	PUNCT
ejpam-4510	211	3	for	for	ADP
ejpam-4510	211	4	s	s	PRON
ejpam-4510	211	5	:	:	PUNCT
ejpam-4510	211	6	=	=	SYM
ejpam-4510	211	7	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	211	8	)	)	PUNCT
ejpam-4510	211	9	,	,	PUNCT
ejpam-4510	211	10	φ−(y	φ−(y	PROPN
ejpam-4510	211	11	)	)	PUNCT
ejpam-4510	211	12	}	}	PUNCT
ejpam-4510	211	13	and	and	CCONJ
ejpam-4510	211	14	t	t	X
ejpam-4510	211	15	:	:	PUNCT
ejpam-4510	211	16	=	=	SYM
ejpam-4510	211	17	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	211	18	)	)	PUNCT
ejpam-4510	211	19	,	,	PUNCT
ejpam-4510	211	20	φ+(y	φ+(y	PUNCT
ejpam-4510	211	21	)	)	PUNCT
ejpam-4510	211	22	}	}	PUNCT
ejpam-4510	211	23	.	.	PUNCT
ejpam-4510	212	1	this	this	PRON
ejpam-4510	212	2	is	be	AUX
ejpam-4510	212	3	a	a	DET
ejpam-4510	212	4	contradiction	contradiction	NOUN
ejpam-4510	212	5	,	,	PUNCT
ejpam-4510	212	6	and	and	CCONJ
ejpam-4510	212	7	thus	thus	ADV
ejpam-4510	212	8	x∗(x∗y	x∗(x∗y	NUM
ejpam-4510	212	9	)	)	PUNCT
ejpam-4510	212	10	(	(	PUNCT
ejpam-4510	212	11	x	x	X
ejpam-4510	212	12	,	,	PUNCT
ejpam-4510	212	13	y	y	PROPN
ejpam-4510	212	14	)	)	PUNCT
ejpam-4510	212	15	∈	∈	PROPN
ejpam-4510	212	16	φ̊(max	φ̊(max	NUM
ejpam-4510	212	17	,	,	PUNCT
ejpam-4510	212	18	min	min	NOUN
ejpam-4510	212	19	)	)	PUNCT
ejpam-4510	212	20	for	for	ADP
ejpam-4510	212	21	all	all	DET
ejpam-4510	212	22	x	x	NOUN
ejpam-4510	212	23	,	,	PUNCT
ejpam-4510	212	24	y	y	PROPN
ejpam-4510	212	25	∈	∈	PROPN
ejpam-4510	212	26	x.	x.	NOUN
ejpam-4510	212	27	for	for	SCONJ
ejpam-4510	212	28	every	every	DET
ejpam-4510	212	29	x	x	PROPN
ejpam-4510	212	30	,	,	PUNCT
ejpam-4510	212	31	y	y	PROPN
ejpam-4510	212	32	∈	∈	PROPN
ejpam-4510	212	33	x	x	AUX
ejpam-4510	212	34	,	,	PUNCT
ejpam-4510	212	35	let	let	VERB
ejpam-4510	212	36	φs(x	φs(x	PUNCT
ejpam-4510	212	37	)	)	PUNCT
ejpam-4510	213	1	=	=	PUNCT
ejpam-4510	213	2	αx	αx	PROPN
ejpam-4510	213	3	,	,	PUNCT
ejpam-4510	213	4	φ	φ	PROPN
ejpam-4510	213	5	s(y	s(y	PROPN
ejpam-4510	213	6	)	)	PUNCT
ejpam-4510	213	7	=	=	SYM
ejpam-4510	213	8	αy	αy	NOUN
ejpam-4510	213	9	,	,	PUNCT
ejpam-4510	213	10	φ̃(x	φ̃(x	PROPN
ejpam-4510	213	11	)	)	PUNCT
ejpam-4510	213	12	=	=	SYM
ejpam-4510	213	13	ã	ã	PROPN
ejpam-4510	213	14	and	and	CCONJ
ejpam-4510	213	15	φ̃(y	φ̃(y	NOUN
ejpam-4510	213	16	)	)	PUNCT
ejpam-4510	213	17	=	=	PUNCT
ejpam-4510	213	18	b̃.	b̃.	NOUN
ejpam-4510	213	19	if	if	SCONJ
ejpam-4510	213	20	we	we	PRON
ejpam-4510	213	21	take	take	VERB
ejpam-4510	213	22	α	α	NOUN
ejpam-4510	213	23	:	:	PUNCT
ejpam-4510	213	24	=	=	SYM
ejpam-4510	213	25	αx	αx	ADP
ejpam-4510	213	26	∩	∩	X
ejpam-4510	213	27	αy	αy	NOUN
ejpam-4510	213	28	and	and	CCONJ
ejpam-4510	213	29	c̃	c̃	PROPN
ejpam-4510	213	30	:	:	PUNCT
ejpam-4510	213	31	=	=	SYM
ejpam-4510	213	32	rmin{ã	rmin{ã	NOUN
ejpam-4510	213	33	,	,	PUNCT
ejpam-4510	213	34	b̃	b̃	PROPN
ejpam-4510	213	35	}	}	PUNCT
ejpam-4510	213	36	,	,	PUNCT
ejpam-4510	213	37	then	then	ADV
ejpam-4510	213	38	x	x	X
ejpam-4510	213	39	,	,	PUNCT
ejpam-4510	213	40	y	y	PROPN
ejpam-4510	213	41	∈	∈	PROPN
ejpam-4510	213	42	φs	φs	ADP
ejpam-4510	213	43	α	α	NOUN
ejpam-4510	213	44	∩	∩	NOUN
ejpam-4510	213	45	φ̃c̃	φ̃c̃	NOUN
ejpam-4510	213	46	and	and	CCONJ
ejpam-4510	213	47	so	so	ADV
ejpam-4510	213	48	x	x	SYM
ejpam-4510	213	49	∗	∗	NOUN
ejpam-4510	213	50	(	(	PUNCT
ejpam-4510	213	51	x	x	X
ejpam-4510	213	52	∗	∗	PROPN
ejpam-4510	213	53	y	y	NOUN
ejpam-4510	213	54	)	)	PUNCT
ejpam-4510	213	55	∈	∈	PROPN
ejpam-4510	213	56	φs	φs	ADP
ejpam-4510	213	57	α	α	PROPN
ejpam-4510	213	58	∩	∩	ADJ
ejpam-4510	213	59	φ̃c̃.	φ̃c̃.	NOUN
ejpam-4510	213	60	hence	hence	ADV
ejpam-4510	213	61	φs(x	φs(x	PUNCT
ejpam-4510	213	62	∗	∗	NOUN
ejpam-4510	213	63	(	(	PUNCT
ejpam-4510	213	64	x	x	X
ejpam-4510	213	65	∗	∗	PROPN
ejpam-4510	213	66	y	y	PROPN
ejpam-4510	213	67	)	)	PUNCT
ejpam-4510	213	68	)	)	PUNCT
ejpam-4510	213	69	⊇	⊇	PROPN
ejpam-4510	213	70	α	α	NOUN
ejpam-4510	213	71	=	=	PUNCT
ejpam-4510	213	72	αx	αx	NOUN
ejpam-4510	213	73	∩	∩	ADJ
ejpam-4510	213	74	αy	αy	NOUN
ejpam-4510	213	75	=	=	SYM
ejpam-4510	213	76	φs(x	φs(x	X
ejpam-4510	213	77	)	)	PUNCT
ejpam-4510	213	78	∩	∩	NOUN
ejpam-4510	213	79	φs(y	φs(y	NUM
ejpam-4510	213	80	)	)	PUNCT
ejpam-4510	213	81	and	and	CCONJ
ejpam-4510	213	82	φ̃(x	φ̃(x	PROPN
ejpam-4510	213	83	∗	∗	NOUN
ejpam-4510	213	84	(	(	PUNCT
ejpam-4510	213	85	x	x	X
ejpam-4510	213	86	∗	∗	PROPN
ejpam-4510	213	87	y	y	NOUN
ejpam-4510	213	88	)	)	PUNCT
ejpam-4510	213	89	)	)	PUNCT
ejpam-4510	213	90	⪰	⪰	NOUN
ejpam-4510	213	91	c̃	c̃	PROPN
ejpam-4510	213	92	=	=	SYM
ejpam-4510	213	93	rmin{ã	rmin{ã	PROPN
ejpam-4510	213	94	,	,	PUNCT
ejpam-4510	213	95	b̃	b̃	PROPN
ejpam-4510	213	96	}	}	PUNCT
ejpam-4510	213	97	=	=	SYM
ejpam-4510	213	98	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	213	99	)	)	PUNCT
ejpam-4510	213	100	,	,	PUNCT
ejpam-4510	213	101	φ̃(y	φ̃(y	NOUN
ejpam-4510	213	102	)	)	PUNCT
ejpam-4510	213	103	}	}	PUNCT
ejpam-4510	213	104	.	.	PUNCT
ejpam-4510	214	1	therefore	therefore	ADV
ejpam-4510	214	2	dokφ	dokφ	NOUN
ejpam-4510	214	3	:	:	PUNCT
ejpam-4510	214	4	=	=	SYM
ejpam-4510	214	5	(	(	PUNCT
ejpam-4510	214	6	φ̊	φ̊	PROPN
ejpam-4510	214	7	,	,	PUNCT
ejpam-4510	214	8	φs	φs	ADV
ejpam-4510	214	9	,	,	PUNCT
ejpam-4510	214	10	φ̃	φ̃	PROPN
ejpam-4510	214	11	)	)	PUNCT
ejpam-4510	214	12	is	be	AUX
ejpam-4510	214	13	a	a	DET
ejpam-4510	214	14	weak	weak	ADJ
ejpam-4510	214	15	dokdo	dokdo	NOUN
ejpam-4510	214	16	be	be	NOUN
ejpam-4510	214	17	-	-	PUNCT
ejpam-4510	214	18	subalgebra	subalgebra	NOUN
ejpam-4510	214	19	of	of	ADP
ejpam-4510	214	20	(	(	PUNCT
ejpam-4510	214	21	x	x	NOUN
ejpam-4510	214	22	,	,	PUNCT
ejpam-4510	214	23	u	u	NOUN
ejpam-4510	214	24	)	)	PUNCT
ejpam-4510	214	25	.	.	PUNCT
ejpam-4510	215	1	y.	y.	PROPN
ejpam-4510	215	2	b.	b.	PROPN
ejpam-4510	215	3	jun	jun	PROPN
ejpam-4510	215	4	,	,	PUNCT
ejpam-4510	215	5	s.	s.	PROPN
ejpam-4510	215	6	s.	s.	PROPN
ejpam-4510	215	7	ahn	ahn	PROPN
ejpam-4510	215	8	and	and	CCONJ
ejpam-4510	215	9	e.	e.	PROPN
ejpam-4510	215	10	h.	h.	PROPN
ejpam-4510	215	11	roh	roh	PROPN
ejpam-4510	215	12	/	/	SYM
ejpam-4510	215	13	eur	eur	PROPN
ejpam-4510	215	14	.	.	PUNCT
ejpam-4510	216	1	j.	j.	PROPN
ejpam-4510	216	2	pure	pure	PROPN
ejpam-4510	216	3	appl	appl	PROPN
ejpam-4510	216	4	.	.	PROPN
ejpam-4510	216	5	math	math	PROPN
ejpam-4510	216	6	,	,	PUNCT
ejpam-4510	216	7	15	15	NUM
ejpam-4510	216	8	(	(	PUNCT
ejpam-4510	216	9	4	4	NUM
ejpam-4510	216	10	)	)	PUNCT
ejpam-4510	216	11	(	(	PUNCT
ejpam-4510	216	12	2022	2022	NUM
ejpam-4510	216	13	)	)	PUNCT
ejpam-4510	216	14	,	,	PUNCT
ejpam-4510	216	15	1521	1521	NUM
ejpam-4510	216	16	-	-	SYM
ejpam-4510	216	17	1535	1535	NUM
ejpam-4510	216	18	1529	1529	NUM
ejpam-4510	216	19	4	4	NUM
ejpam-4510	216	20	.	.	PUNCT
ejpam-4510	217	1	dokdo	dokdo	PROPN
ejpam-4510	217	2	be	be	NOUN
ejpam-4510	217	3	-	-	PUNCT
ejpam-4510	217	4	filters	filter	NOUN
ejpam-4510	217	5	definition	definition	NOUN
ejpam-4510	217	6	3	3	NUM
ejpam-4510	217	7	.	.	PUNCT
ejpam-4510	218	1	a	a	DET
ejpam-4510	218	2	dokdo	dokdo	NOUN
ejpam-4510	218	3	structure	structure	NOUN
ejpam-4510	218	4	dokφ	dokφ	NOUN
ejpam-4510	218	5	:	:	PUNCT
ejpam-4510	218	6	=	=	SYM
ejpam-4510	218	7	(	(	PUNCT
ejpam-4510	218	8	φ̊	φ̊	PROPN
ejpam-4510	218	9	,	,	PUNCT
ejpam-4510	218	10	φs	φs	ADV
ejpam-4510	218	11	,	,	PUNCT
ejpam-4510	218	12	φ̃	φ̃	PROPN
ejpam-4510	218	13	)	)	PUNCT
ejpam-4510	218	14	in	in	ADP
ejpam-4510	218	15	(	(	PUNCT
ejpam-4510	218	16	x	x	NOUN
ejpam-4510	218	17	,	,	PUNCT
ejpam-4510	218	18	u	u	NOUN
ejpam-4510	218	19	)	)	PUNCT
ejpam-4510	218	20	is	be	AUX
ejpam-4510	218	21	called	call	VERB
ejpam-4510	218	22	a	a	DET
ejpam-4510	218	23	dokdo	dokdo	NOUN
ejpam-4510	218	24	be	be	NOUN
ejpam-4510	218	25	-	-	PUNCT
ejpam-4510	218	26	filter	filter	NOUN
ejpam-4510	218	27	of	of	ADP
ejpam-4510	218	28	(	(	PUNCT
ejpam-4510	218	29	x	x	NOUN
ejpam-4510	218	30	,	,	PUNCT
ejpam-4510	218	31	u	u	NOUN
ejpam-4510	218	32	)	)	PUNCT
ejpam-4510	218	33	if	if	SCONJ
ejpam-4510	218	34	it	it	PRON
ejpam-4510	218	35	satisfies	satisfy	VERB
ejpam-4510	218	36	:	:	PUNCT
ejpam-4510	218	37	(	(	PUNCT
ejpam-4510	218	38	∀x	∀x	X
ejpam-4510	218	39	∈	∈	PROPN
ejpam-4510	218	40	x	x	NOUN
ejpam-4510	218	41	)	)	PUNCT
ejpam-4510	218	42	(	(	PUNCT
ejpam-4510	218	43	1	1	NUM
ejpam-4510	218	44	(	(	PUNCT
ejpam-4510	218	45	x	x	NOUN
ejpam-4510	218	46	,	,	PUNCT
ejpam-4510	218	47	x	x	NOUN
ejpam-4510	218	48	)	)	PUNCT
ejpam-4510	218	49	∈	∈	PROPN
ejpam-4510	218	50	φ̊(max	φ̊(max	NUM
ejpam-4510	218	51	,	,	PUNCT
ejpam-4510	218	52	min	min	NOUN
ejpam-4510	218	53	)	)	PUNCT
ejpam-4510	218	54	,	,	PUNCT
ejpam-4510	218	55	φs(1	φs(1	PROPN
ejpam-4510	218	56	)	)	PUNCT
ejpam-4510	218	57	⊇	⊇	NOUN
ejpam-4510	218	58	φs(x	φs(x	PROPN
ejpam-4510	218	59	)	)	PUNCT
ejpam-4510	218	60	,	,	PUNCT
ejpam-4510	218	61	φ̃(1	φ̃(1	NOUN
ejpam-4510	218	62	)	)	PUNCT
ejpam-4510	218	63	⪰	⪰	NOUN
ejpam-4510	218	64	φ̃(x	φ̃(x	PROPN
ejpam-4510	218	65	)	)	PUNCT
ejpam-4510	218	66	)	)	PUNCT
ejpam-4510	218	67	,	,	PUNCT
ejpam-4510	218	68	(	(	PUNCT
ejpam-4510	218	69	24	24	NUM
ejpam-4510	218	70	)	)	PUNCT
ejpam-4510	218	71	(	(	PUNCT
ejpam-4510	218	72	∀x	∀x	X
ejpam-4510	218	73	,	,	PUNCT
ejpam-4510	218	74	y	y	PROPN
ejpam-4510	218	75	∈	∈	PROPN
ejpam-4510	218	76	x	x	X
ejpam-4510	218	77	)	)	PUNCT
ejpam-4510	218	78			PROPN
ejpam-4510	218	79	y	y	PROPN
ejpam-4510	218	80	(	(	PUNCT
ejpam-4510	218	81	x	x	X
ejpam-4510	218	82	,	,	PUNCT
ejpam-4510	218	83	x∗y	x∗y	NUM
ejpam-4510	218	84	)	)	PUNCT
ejpam-4510	218	85	∈	∈	PROPN
ejpam-4510	218	86	φ̊(max	φ̊(max	NUM
ejpam-4510	218	87	,	,	PUNCT
ejpam-4510	218	88	min	min	NOUN
ejpam-4510	218	89	)	)	PUNCT
ejpam-4510	218	90	,	,	PUNCT
ejpam-4510	218	91	φs(y	φs(y	NUM
ejpam-4510	218	92	)	)	PUNCT
ejpam-4510	218	93	⊇	⊇	NOUN
ejpam-4510	218	94	φs(x	φs(x	NOUN
ejpam-4510	218	95	)	)	PUNCT
ejpam-4510	218	96	∩	∩	NOUN
ejpam-4510	218	97	φs(x	φs(x	PART
ejpam-4510	218	98	∗	∗	PROPN
ejpam-4510	218	99	y	y	PROPN
ejpam-4510	218	100	)	)	PUNCT
ejpam-4510	218	101	,	,	PUNCT
ejpam-4510	218	102	φ̃(y	φ̃(y	NOUN
ejpam-4510	218	103	)	)	PUNCT
ejpam-4510	218	104	⪰	⪰	NOUN
ejpam-4510	218	105	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	218	106	)	)	PUNCT
ejpam-4510	218	107	,	,	PUNCT
ejpam-4510	218	108	φ̃(x	φ̃(x	PROPN
ejpam-4510	218	109	∗	∗	PROPN
ejpam-4510	218	110	y	y	PROPN
ejpam-4510	218	111	)	)	PUNCT
ejpam-4510	218	112	}	}	PUNCT
ejpam-4510	218	113			PROPN
ejpam-4510	218	114	.	.	PUNCT
ejpam-4510	219	1	(	(	PUNCT
ejpam-4510	219	2	25	25	NUM
ejpam-4510	219	3	)	)	PUNCT
ejpam-4510	219	4	example	example	NOUN
ejpam-4510	219	5	5	5	NUM
ejpam-4510	219	6	.	.	PUNCT
ejpam-4510	220	1	let	let	VERB
ejpam-4510	220	2	(	(	PUNCT
ejpam-4510	220	3	x	x	NOUN
ejpam-4510	220	4	,	,	PUNCT
ejpam-4510	220	5	u	u	NOUN
ejpam-4510	220	6	)	)	PUNCT
ejpam-4510	220	7	be	be	VERB
ejpam-4510	220	8	a	a	DET
ejpam-4510	220	9	be	be	ADJ
ejpam-4510	220	10	-	-	PUNCT
ejpam-4510	220	11	dokdo	dokdo	ADJ
ejpam-4510	220	12	universe	universe	NOUN
ejpam-4510	220	13	in	in	ADP
ejpam-4510	220	14	which	which	PRON
ejpam-4510	220	15	u	u	NOUN
ejpam-4510	220	16	=	=	PUNCT
ejpam-4510	220	17	n	n	PROPN
ejpam-4510	220	18	and	and	CCONJ
ejpam-4510	220	19	x	x	X
ejpam-4510	220	20	=	=	PUNCT
ejpam-4510	220	21	{	{	PUNCT
ejpam-4510	220	22	1	1	NUM
ejpam-4510	220	23	,	,	PUNCT
ejpam-4510	220	24	2	2	NUM
ejpam-4510	220	25	,	,	PUNCT
ejpam-4510	220	26	3	3	NUM
ejpam-4510	220	27	,	,	PUNCT
ejpam-4510	220	28	4	4	NUM
ejpam-4510	220	29	,	,	PUNCT
ejpam-4510	220	30	5	5	NUM
ejpam-4510	220	31	}	}	PUNCT
ejpam-4510	220	32	is	be	AUX
ejpam-4510	220	33	a	a	DET
ejpam-4510	220	34	be	be	NOUN
ejpam-4510	220	35	-	-	PUNCT
ejpam-4510	220	36	algebra	algebra	NOUN
ejpam-4510	220	37	(	(	PUNCT
ejpam-4510	220	38	see	see	VERB
ejpam-4510	220	39	[	[	X
ejpam-4510	220	40	7	7	NUM
ejpam-4510	220	41	]	]	PUNCT
ejpam-4510	220	42	)	)	PUNCT
ejpam-4510	220	43	with	with	ADP
ejpam-4510	220	44	a	a	DET
ejpam-4510	220	45	binary	binary	ADJ
ejpam-4510	220	46	operation	operation	NOUN
ejpam-4510	220	47	“	"	PUNCT
ejpam-4510	220	48	∗	∗	NOUN
ejpam-4510	220	49	”	"	PUNCT
ejpam-4510	220	50	given	give	VERB
ejpam-4510	220	51	in	in	ADP
ejpam-4510	220	52	the	the	DET
ejpam-4510	220	53	table	table	NOUN
ejpam-4510	220	54	below	below	ADV
ejpam-4510	220	55	.	.	PUNCT
ejpam-4510	221	1	∗	∗	NOUN
ejpam-4510	221	2	1	1	NUM
ejpam-4510	221	3	2	2	NUM
ejpam-4510	221	4	3	3	NUM
ejpam-4510	221	5	4	4	NUM
ejpam-4510	221	6	5	5	NUM
ejpam-4510	221	7	1	1	NUM
ejpam-4510	221	8	1	1	NUM
ejpam-4510	221	9	2	2	NUM
ejpam-4510	221	10	3	3	NUM
ejpam-4510	221	11	4	4	NUM
ejpam-4510	221	12	5	5	NUM
ejpam-4510	221	13	2	2	NUM
ejpam-4510	221	14	1	1	NUM
ejpam-4510	221	15	1	1	NUM
ejpam-4510	221	16	3	3	NUM
ejpam-4510	221	17	4	4	NUM
ejpam-4510	221	18	5	5	NUM
ejpam-4510	221	19	3	3	NUM
ejpam-4510	221	20	1	1	NUM
ejpam-4510	221	21	2	2	NUM
ejpam-4510	221	22	1	1	NUM
ejpam-4510	221	23	4	4	NUM
ejpam-4510	221	24	4	4	NUM
ejpam-4510	221	25	4	4	NUM
ejpam-4510	221	26	1	1	NUM
ejpam-4510	221	27	1	1	NUM
ejpam-4510	221	28	3	3	NUM
ejpam-4510	221	29	1	1	NUM
ejpam-4510	221	30	3	3	NUM
ejpam-4510	221	31	5	5	NUM
ejpam-4510	221	32	1	1	NUM
ejpam-4510	221	33	1	1	NUM
ejpam-4510	221	34	1	1	NUM
ejpam-4510	221	35	1	1	NUM
ejpam-4510	221	36	1	1	NUM
ejpam-4510	221	37	let	let	VERB
ejpam-4510	221	38	dokφ	dokφ	NOUN
ejpam-4510	221	39	:	:	PUNCT
ejpam-4510	221	40	=	=	SYM
ejpam-4510	221	41	(	(	PUNCT
ejpam-4510	221	42	φ̊	φ̊	PROPN
ejpam-4510	221	43	,	,	PUNCT
ejpam-4510	221	44	φs	φs	ADV
ejpam-4510	221	45	,	,	PUNCT
ejpam-4510	221	46	φ̃	φ̃	PROPN
ejpam-4510	221	47	)	)	PUNCT
ejpam-4510	221	48	be	be	VERB
ejpam-4510	221	49	a	a	DET
ejpam-4510	221	50	dokdo	dokdo	NOUN
ejpam-4510	221	51	structure	structure	NOUN
ejpam-4510	221	52	in	in	ADP
ejpam-4510	221	53	(	(	PUNCT
ejpam-4510	221	54	x	x	NOUN
ejpam-4510	221	55	,	,	PUNCT
ejpam-4510	221	56	u	u	NOUN
ejpam-4510	221	57	=	=	NOUN
ejpam-4510	221	58	n	n	CCONJ
ejpam-4510	221	59	)	)	PUNCT
ejpam-4510	221	60	given	give	VERB
ejpam-4510	221	61	in	in	ADP
ejpam-4510	221	62	the	the	DET
ejpam-4510	221	63	table	table	NOUN
ejpam-4510	221	64	below	below	ADV
ejpam-4510	221	65	.	.	PUNCT
ejpam-4510	222	1	x	x	PUNCT
ejpam-4510	222	2	φ̊(x	φ̊(x	NOUN
ejpam-4510	222	3	)	)	PUNCT
ejpam-4510	222	4	φs(x	φs(x	PUNCT
ejpam-4510	222	5	)	)	PUNCT
ejpam-4510	222	6	φ̃(x	φ̃(x	PROPN
ejpam-4510	222	7	)	)	PUNCT
ejpam-4510	222	8	1	1	NUM
ejpam-4510	222	9	(	(	PUNCT
ejpam-4510	222	10	−0.6	−0.6	PROPN
ejpam-4510	222	11	,	,	PUNCT
ejpam-4510	222	12	0.8	0.8	NUM
ejpam-4510	222	13	)	)	PUNCT
ejpam-4510	222	14	2n	2n	NUM
ejpam-4510	223	1	[	[	X
ejpam-4510	223	2	0.4	0.4	NUM
ejpam-4510	223	3	,	,	PUNCT
ejpam-4510	223	4	0.9	0.9	NUM
ejpam-4510	223	5	]	]	SYM
ejpam-4510	223	6	2	2	NUM
ejpam-4510	223	7	(	(	PUNCT
ejpam-4510	223	8	−0.6	−0.6	PROPN
ejpam-4510	223	9	,	,	PUNCT
ejpam-4510	223	10	0.8	0.8	NUM
ejpam-4510	223	11	)	)	PUNCT
ejpam-4510	223	12	2n	2n	NUM
ejpam-4510	224	1	[	[	X
ejpam-4510	224	2	0.4	0.4	NUM
ejpam-4510	224	3	,	,	PUNCT
ejpam-4510	224	4	0.9	0.9	NUM
ejpam-4510	224	5	]	]	SYM
ejpam-4510	224	6	3	3	NUM
ejpam-4510	224	7	(	(	PUNCT
ejpam-4510	224	8	−0.3	−0.3	PROPN
ejpam-4510	224	9	,	,	PUNCT
ejpam-4510	224	10	0.6	0.6	NUM
ejpam-4510	224	11	)	)	PUNCT
ejpam-4510	224	12	4n	4n	NOUN
ejpam-4510	224	13	[	[	X
ejpam-4510	224	14	0.2	0.2	NUM
ejpam-4510	224	15	,	,	PUNCT
ejpam-4510	224	16	0.5	0.5	NUM
ejpam-4510	224	17	]	]	SYM
ejpam-4510	224	18	4	4	NUM
ejpam-4510	224	19	(	(	PUNCT
ejpam-4510	224	20	−0.5	−0.5	PROPN
ejpam-4510	224	21	,	,	PUNCT
ejpam-4510	224	22	0.4	0.4	NUM
ejpam-4510	224	23	)	)	PUNCT
ejpam-4510	224	24	8n	8n	NOUN
ejpam-4510	225	1	[	[	X
ejpam-4510	225	2	0.3	0.3	NUM
ejpam-4510	225	3	,	,	PUNCT
ejpam-4510	225	4	0.7	0.7	NUM
ejpam-4510	225	5	]	]	SYM
ejpam-4510	225	6	5	5	NUM
ejpam-4510	225	7	(	(	PUNCT
ejpam-4510	225	8	−0.3	−0.3	PROPN
ejpam-4510	225	9	,	,	PUNCT
ejpam-4510	225	10	0.4	0.4	NUM
ejpam-4510	225	11	)	)	PUNCT
ejpam-4510	225	12	8n	8n	NOUN
ejpam-4510	226	1	[	[	X
ejpam-4510	226	2	0.2	0.2	NUM
ejpam-4510	226	3	,	,	PUNCT
ejpam-4510	226	4	0.5	0.5	NUM
ejpam-4510	226	5	]	]	PUNCT
ejpam-4510	226	6	through	through	ADP
ejpam-4510	226	7	routine	routine	ADJ
ejpam-4510	226	8	calculations	calculation	NOUN
ejpam-4510	226	9	,	,	PUNCT
ejpam-4510	226	10	we	we	PRON
ejpam-4510	226	11	can	can	AUX
ejpam-4510	226	12	confirm	confirm	VERB
ejpam-4510	226	13	that	that	DET
ejpam-4510	226	14	dokφ	dokφ	NOUN
ejpam-4510	226	15	:	:	PUNCT
ejpam-4510	226	16	=	=	SYM
ejpam-4510	226	17	(	(	PUNCT
ejpam-4510	226	18	φ̊	φ̊	PROPN
ejpam-4510	226	19	,	,	PUNCT
ejpam-4510	226	20	φs	φs	ADV
ejpam-4510	226	21	,	,	PUNCT
ejpam-4510	226	22	φ̃	φ̃	PROPN
ejpam-4510	226	23	)	)	PUNCT
ejpam-4510	226	24	in	in	ADP
ejpam-4510	226	25	(	(	PUNCT
ejpam-4510	226	26	x	x	NOUN
ejpam-4510	226	27	,	,	PUNCT
ejpam-4510	226	28	u	u	NOUN
ejpam-4510	226	29	)	)	PUNCT
ejpam-4510	226	30	is	be	AUX
ejpam-4510	226	31	a	a	DET
ejpam-4510	226	32	dokdo	dokdo	NOUN
ejpam-4510	226	33	be	be	NOUN
ejpam-4510	226	34	-	-	PUNCT
ejpam-4510	226	35	filter	filter	NOUN
ejpam-4510	226	36	of	of	ADP
ejpam-4510	226	37	(	(	PUNCT
ejpam-4510	226	38	x	x	NOUN
ejpam-4510	226	39	,	,	PUNCT
ejpam-4510	226	40	u	u	NOUN
ejpam-4510	226	41	=	=	NOUN
ejpam-4510	226	42	n	n	CCONJ
ejpam-4510	226	43	)	)	PUNCT
ejpam-4510	226	44	.	.	PUNCT
ejpam-4510	227	1	proposition	proposition	NOUN
ejpam-4510	227	2	3	3	NUM
ejpam-4510	227	3	.	.	PUNCT
ejpam-4510	228	1	every	every	DET
ejpam-4510	228	2	dokdo	dokdo	NOUN
ejpam-4510	228	3	be	be	AUX
ejpam-4510	228	4	-	-	PUNCT
ejpam-4510	228	5	filter	filter	NOUN
ejpam-4510	228	6	dokφ	dokφ	NOUN
ejpam-4510	228	7	:	:	PUNCT
ejpam-4510	228	8	=	=	SYM
ejpam-4510	228	9	(	(	PUNCT
ejpam-4510	228	10	φ̊	φ̊	PROPN
ejpam-4510	228	11	,	,	PUNCT
ejpam-4510	228	12	φs	φs	ADV
ejpam-4510	228	13	,	,	PUNCT
ejpam-4510	228	14	φ̃	φ̃	PROPN
ejpam-4510	228	15	)	)	PUNCT
ejpam-4510	228	16	of	of	ADP
ejpam-4510	228	17	(	(	PUNCT
ejpam-4510	228	18	x	x	NOUN
ejpam-4510	228	19	,	,	PUNCT
ejpam-4510	228	20	u	u	NOUN
ejpam-4510	228	21	)	)	PUNCT
ejpam-4510	228	22	satisfies	satisfie	NOUN
ejpam-4510	228	23	:	:	PUNCT
ejpam-4510	228	24	(	(	PUNCT
ejpam-4510	228	25	∀x	∀x	X
ejpam-4510	228	26	,	,	PUNCT
ejpam-4510	228	27	y	y	PROPN
ejpam-4510	228	28	∈	∈	PROPN
ejpam-4510	228	29	x	x	X
ejpam-4510	228	30	)	)	PUNCT
ejpam-4510	228	31	(	(	PUNCT
ejpam-4510	228	32	x	x	SYM
ejpam-4510	228	33	≤	≤	NOUN
ejpam-4510	228	34	y	y	PROPN
ejpam-4510	228	35	⇒	⇒	NOUN
ejpam-4510	228	36	{	{	PUNCT
ejpam-4510	228	37	y	y	PROPN
ejpam-4510	228	38	(	(	PUNCT
ejpam-4510	228	39	x	x	NOUN
ejpam-4510	228	40	,	,	PUNCT
ejpam-4510	228	41	x	x	NOUN
ejpam-4510	228	42	)	)	PUNCT
ejpam-4510	228	43	∈	∈	PROPN
ejpam-4510	228	44	φ̊(max	φ̊(max	NUM
ejpam-4510	228	45	,	,	PUNCT
ejpam-4510	228	46	min	min	NOUN
ejpam-4510	228	47	)	)	PUNCT
ejpam-4510	228	48	φs(y	φs(y	NUM
ejpam-4510	228	49	)	)	PUNCT
ejpam-4510	228	50	⊇	⊇	NOUN
ejpam-4510	228	51	φs(x	φs(x	PRON
ejpam-4510	228	52	)	)	PUNCT
ejpam-4510	228	53	,	,	PUNCT
ejpam-4510	228	54	φ̃(y	φ̃(y	NOUN
ejpam-4510	228	55	)	)	PUNCT
ejpam-4510	228	56	⪰	⪰	NOUN
ejpam-4510	228	57	φ̃(x	φ̃(x	PROPN
ejpam-4510	228	58	)	)	PUNCT
ejpam-4510	228	59	)	)	PUNCT
ejpam-4510	228	60	,	,	PUNCT
ejpam-4510	228	61	(	(	PUNCT
ejpam-4510	228	62	26	26	NUM
ejpam-4510	228	63	)	)	PUNCT
ejpam-4510	228	64	(	(	PUNCT
ejpam-4510	228	65	∀x	∀x	X
ejpam-4510	228	66	,	,	PUNCT
ejpam-4510	228	67	y	y	PROPN
ejpam-4510	228	68	,	,	PUNCT
ejpam-4510	228	69	z	z	NOUN
ejpam-4510	228	70	∈	∈	PROPN
ejpam-4510	228	71	x	x	NOUN
ejpam-4510	228	72	)	)	PUNCT
ejpam-4510	228	73	x	x	ADP
ejpam-4510	228	74	≤	≤	NUM
ejpam-4510	228	75	y	y	PROPN
ejpam-4510	228	76	∗	∗	NOUN
ejpam-4510	228	77	z	z	PROPN
ejpam-4510	228	78	⇒	⇒	PROPN
ejpam-4510	228	79			PUNCT
ejpam-4510	228	80	z	z	NOUN
ejpam-4510	228	81	(	(	PUNCT
ejpam-4510	228	82	x	x	NOUN
ejpam-4510	228	83	,	,	PUNCT
ejpam-4510	228	84	y	y	PROPN
ejpam-4510	228	85	)	)	PUNCT
ejpam-4510	228	86	∈	∈	PROPN
ejpam-4510	228	87	φ̊(max	φ̊(max	NUM
ejpam-4510	228	88	,	,	PUNCT
ejpam-4510	228	89	min	min	NOUN
ejpam-4510	228	90	)	)	PUNCT
ejpam-4510	228	91	φs(z	φs(z	NUM
ejpam-4510	228	92	)	)	PUNCT
ejpam-4510	228	93	⊇	⊇	NOUN
ejpam-4510	228	94	φs(x	φs(x	NOUN
ejpam-4510	228	95	)	)	PUNCT
ejpam-4510	228	96	∩	∩	NOUN
ejpam-4510	228	97	φs(y	φs(y	NUM
ejpam-4510	228	98	)	)	PUNCT
ejpam-4510	229	1	φ̃(z	φ̃(z	ADJ
ejpam-4510	229	2	)	)	PUNCT
ejpam-4510	229	3	⪰	⪰	NOUN
ejpam-4510	229	4	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	229	5	)	)	PUNCT
ejpam-4510	229	6	,	,	PUNCT
ejpam-4510	229	7	φ̃(y	φ̃(y	NOUN
ejpam-4510	229	8	)	)	PUNCT
ejpam-4510	229	9	}	}	PUNCT
ejpam-4510	229	10			PROPN
ejpam-4510	229	11	,	,	PUNCT
ejpam-4510	229	12	(	(	PUNCT
ejpam-4510	229	13	27	27	NUM
ejpam-4510	229	14	)	)	PUNCT
ejpam-4510	229	15	(	(	PUNCT
ejpam-4510	229	16	∀x	∀x	X
ejpam-4510	229	17	,	,	PUNCT
ejpam-4510	229	18	y	y	PROPN
ejpam-4510	229	19	∈	∈	PROPN
ejpam-4510	229	20	x	x	X
ejpam-4510	229	21	)	)	PUNCT
ejpam-4510	229	22			PROPN
ejpam-4510	229	23	y∗x	y∗x	NUM
ejpam-4510	229	24	(	(	PUNCT
ejpam-4510	229	25	1	1	NUM
ejpam-4510	229	26	,	,	PUNCT
ejpam-4510	229	27	1	1	NUM
ejpam-4510	229	28	)	)	PUNCT
ejpam-4510	229	29	∈	∈	NOUN
ejpam-4510	230	1	φ̊(max	φ̊(max	NUM
ejpam-4510	230	2	,	,	PUNCT
ejpam-4510	230	3	min	min	NOUN
ejpam-4510	230	4	)	)	PUNCT
ejpam-4510	230	5	,	,	PUNCT
ejpam-4510	230	6	φs(y	φs(y	NOUN
ejpam-4510	230	7	∗	∗	NOUN
ejpam-4510	230	8	x	x	NOUN
ejpam-4510	230	9	)	)	PUNCT
ejpam-4510	230	10	=	=	SYM
ejpam-4510	230	11	φs(1	φs(1	PROPN
ejpam-4510	230	12	)	)	PUNCT
ejpam-4510	230	13	,	,	PUNCT
ejpam-4510	230	14	φ̃(y	φ̃(y	ADJ
ejpam-4510	230	15	∗	∗	NOUN
ejpam-4510	230	16	x	x	NOUN
ejpam-4510	230	17	)	)	PUNCT
ejpam-4510	230	18	=	=	SYM
ejpam-4510	230	19	φ̃(1	φ̃(1	NOUN
ejpam-4510	230	20	)	)	PUNCT
ejpam-4510	230	21			PROPN
ejpam-4510	230	22	⇒	⇒	NOUN
ejpam-4510	230	23			PUNCT
ejpam-4510	230	24	x	x	SYM
ejpam-4510	230	25	(	(	PUNCT
ejpam-4510	230	26	y	y	PROPN
ejpam-4510	230	27	,	,	PUNCT
ejpam-4510	230	28	y	y	NOUN
ejpam-4510	230	29	)	)	PUNCT
ejpam-4510	230	30	∈	∈	PROPN
ejpam-4510	230	31	φ̊(max	φ̊(max	NUM
ejpam-4510	230	32	,	,	PUNCT
ejpam-4510	230	33	min	min	NOUN
ejpam-4510	230	34	)	)	PUNCT
ejpam-4510	230	35	φs(x	φs(x	PUNCT
ejpam-4510	230	36	)	)	PUNCT
ejpam-4510	230	37	⊇	⊇	NOUN
ejpam-4510	230	38	φs(y	φs(y	NUM
ejpam-4510	230	39	)	)	PUNCT
ejpam-4510	230	40	,	,	PUNCT
ejpam-4510	230	41	φ̃(x	φ̃(x	PROPN
ejpam-4510	230	42	)	)	PUNCT
ejpam-4510	230	43	⪰	⪰	NOUN
ejpam-4510	230	44	φ̃(y	φ̃(y	NOUN
ejpam-4510	230	45	)	)	PUNCT
ejpam-4510	230	46			PROPN
ejpam-4510	230	47	.	.	PUNCT
ejpam-4510	231	1	(	(	PUNCT
ejpam-4510	231	2	28	28	X
ejpam-4510	231	3	)	)	PUNCT
ejpam-4510	231	4	y.	y.	PROPN
ejpam-4510	231	5	b.	b.	PROPN
ejpam-4510	231	6	jun	jun	PROPN
ejpam-4510	231	7	,	,	PUNCT
ejpam-4510	231	8	s.	s.	PROPN
ejpam-4510	231	9	s.	s.	PROPN
ejpam-4510	231	10	ahn	ahn	PROPN
ejpam-4510	231	11	and	and	CCONJ
ejpam-4510	231	12	e.	e.	PROPN
ejpam-4510	231	13	h.	h.	PROPN
ejpam-4510	231	14	roh	roh	PROPN
ejpam-4510	231	15	/	/	SYM
ejpam-4510	231	16	eur	eur	PROPN
ejpam-4510	231	17	.	.	PUNCT
ejpam-4510	232	1	j.	j.	PROPN
ejpam-4510	232	2	pure	pure	PROPN
ejpam-4510	232	3	appl	appl	PROPN
ejpam-4510	232	4	.	.	PROPN
ejpam-4510	232	5	math	math	PROPN
ejpam-4510	232	6	,	,	PUNCT
ejpam-4510	232	7	15	15	NUM
ejpam-4510	232	8	(	(	PUNCT
ejpam-4510	232	9	4	4	NUM
ejpam-4510	232	10	)	)	PUNCT
ejpam-4510	232	11	(	(	PUNCT
ejpam-4510	232	12	2022	2022	NUM
ejpam-4510	232	13	)	)	PUNCT
ejpam-4510	232	14	,	,	PUNCT
ejpam-4510	232	15	1521	1521	NUM
ejpam-4510	232	16	-	-	SYM
ejpam-4510	232	17	1535	1535	NUM
ejpam-4510	232	18	1530	1530	NUM
ejpam-4510	232	19	proof	proof	NOUN
ejpam-4510	232	20	.	.	PUNCT
ejpam-4510	233	1	if	if	SCONJ
ejpam-4510	233	2	x	x	PROPN
ejpam-4510	233	3	≤	≤	NOUN
ejpam-4510	233	4	y	y	NOUN
ejpam-4510	233	5	,	,	PUNCT
ejpam-4510	233	6	then	then	ADV
ejpam-4510	233	7	x	x	X
ejpam-4510	233	8	∗	∗	NOUN
ejpam-4510	233	9	y	y	NOUN
ejpam-4510	233	10	=	=	SYM
ejpam-4510	233	11	1	1	NUM
ejpam-4510	233	12	and	and	CCONJ
ejpam-4510	233	13	so	so	ADV
ejpam-4510	233	14	(	(	PUNCT
ejpam-4510	233	15	26	26	NUM
ejpam-4510	233	16	)	)	PUNCT
ejpam-4510	233	17	is	be	AUX
ejpam-4510	233	18	derived	derive	VERB
ejpam-4510	233	19	from	from	ADP
ejpam-4510	233	20	the	the	DET
ejpam-4510	233	21	definition	definition	NOUN
ejpam-4510	233	22	of	of	ADP
ejpam-4510	233	23	dokdo	dokdo	PROPN
ejpam-4510	233	24	be	be	NOUN
ejpam-4510	233	25	-	-	PUNCT
ejpam-4510	233	26	filter	filter	NOUN
ejpam-4510	233	27	.	.	PUNCT
ejpam-4510	234	1	let	let	VERB
ejpam-4510	234	2	x	x	PRON
ejpam-4510	234	3	,	,	PUNCT
ejpam-4510	234	4	y	y	PROPN
ejpam-4510	234	5	,	,	PUNCT
ejpam-4510	234	6	z	z	NOUN
ejpam-4510	234	7	∈	∈	PROPN
ejpam-4510	234	8	x	x	AUX
ejpam-4510	234	9	be	be	AUX
ejpam-4510	234	10	such	such	ADJ
ejpam-4510	234	11	that	that	SCONJ
ejpam-4510	234	12	x	x	X
ejpam-4510	234	13	≤	≤	NUM
ejpam-4510	234	14	y	y	PROPN
ejpam-4510	234	15	∗	∗	NOUN
ejpam-4510	234	16	z.	z.	PROPN
ejpam-4510	235	1	then	then	ADV
ejpam-4510	235	2	x	x	X
ejpam-4510	235	3	∗	∗	NOUN
ejpam-4510	235	4	(	(	PUNCT
ejpam-4510	235	5	y	y	PROPN
ejpam-4510	235	6	∗	∗	PROPN
ejpam-4510	235	7	z	z	NOUN
ejpam-4510	235	8	)	)	PUNCT
ejpam-4510	235	9	=	=	SYM
ejpam-4510	235	10	1	1	NUM
ejpam-4510	235	11	,	,	PUNCT
ejpam-4510	235	12	and	and	CCONJ
ejpam-4510	235	13	so	so	ADV
ejpam-4510	235	14	φ−(z	φ−(z	ADJ
ejpam-4510	235	15	)	)	PUNCT
ejpam-4510	235	16	≤	≤	NOUN
ejpam-4510	236	1	max{φ−(y	max{φ−(y	NOUN
ejpam-4510	236	2	)	)	PUNCT
ejpam-4510	237	1	,	,	PUNCT
ejpam-4510	237	2	φ−(y	φ−(y	PROPN
ejpam-4510	237	3	∗	∗	VERB
ejpam-4510	237	4	z	z	NOUN
ejpam-4510	237	5	)	)	PUNCT
ejpam-4510	237	6	}	}	PUNCT
ejpam-4510	237	7	≤	≤	NUM
ejpam-4510	237	8	max{φ−(y),max{φ−(x	max{φ−(y),max{φ−(x	NOUN
ejpam-4510	237	9	)	)	PUNCT
ejpam-4510	237	10	,	,	PUNCT
ejpam-4510	237	11	φ−(x	φ−(x	PROPN
ejpam-4510	237	12	∗	∗	NOUN
ejpam-4510	237	13	(	(	PUNCT
ejpam-4510	237	14	y	y	PROPN
ejpam-4510	237	15	∗	∗	PROPN
ejpam-4510	237	16	z	z	PROPN
ejpam-4510	237	17	)	)	PUNCT
ejpam-4510	237	18	)	)	PUNCT
ejpam-4510	237	19	}	}	PUNCT
ejpam-4510	237	20	}	}	PUNCT
ejpam-4510	237	21	=	=	SYM
ejpam-4510	237	22	max{φ−(y),max{φ−(x	max{φ−(y),max{φ−(x	NOUN
ejpam-4510	237	23	)	)	PUNCT
ejpam-4510	237	24	,	,	PUNCT
ejpam-4510	237	25	φ−(1	φ−(1	NOUN
ejpam-4510	237	26	)	)	PUNCT
ejpam-4510	237	27	}	}	PUNCT
ejpam-4510	237	28	}	}	PUNCT
ejpam-4510	237	29	=	=	SYM
ejpam-4510	237	30	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	237	31	)	)	PUNCT
ejpam-4510	237	32	,	,	PUNCT
ejpam-4510	237	33	φ−(y	φ−(y	PROPN
ejpam-4510	237	34	)	)	PUNCT
ejpam-4510	237	35	}	}	PUNCT
ejpam-4510	237	36	and	and	CCONJ
ejpam-4510	237	37	φ+(z	φ+(z	DET
ejpam-4510	237	38	)	)	PUNCT
ejpam-4510	237	39	≥	≥	NOUN
ejpam-4510	237	40	min{φ+(y	min{φ+(y	NOUN
ejpam-4510	237	41	)	)	PUNCT
ejpam-4510	237	42	,	,	PUNCT
ejpam-4510	237	43	φ+(y	φ+(y	CCONJ
ejpam-4510	237	44	∗	∗	PROPN
ejpam-4510	237	45	z	z	NOUN
ejpam-4510	237	46	)	)	PUNCT
ejpam-4510	237	47	}	}	PUNCT
ejpam-4510	237	48	≥	≥	NOUN
ejpam-4510	237	49	min{φ+(y),min{φ+(x	min{φ+(y),min{φ+(x	NOUN
ejpam-4510	237	50	)	)	PUNCT
ejpam-4510	237	51	,	,	PUNCT
ejpam-4510	237	52	φ+(x	φ+(x	NOUN
ejpam-4510	237	53	∗	∗	NOUN
ejpam-4510	237	54	(	(	PUNCT
ejpam-4510	237	55	y	y	PROPN
ejpam-4510	237	56	∗	∗	PROPN
ejpam-4510	237	57	z	z	PROPN
ejpam-4510	237	58	)	)	PUNCT
ejpam-4510	237	59	)	)	PUNCT
ejpam-4510	237	60	}	}	PUNCT
ejpam-4510	237	61	}	}	PUNCT
ejpam-4510	237	62	=	=	SYM
ejpam-4510	237	63	min{φ+(y),min{φ+(x	min{φ+(y),min{φ+(x	NOUN
ejpam-4510	237	64	)	)	PUNCT
ejpam-4510	237	65	,	,	PUNCT
ejpam-4510	237	66	φ+(1	φ+(1	NOUN
ejpam-4510	237	67	)	)	PUNCT
ejpam-4510	237	68	}	}	PUNCT
ejpam-4510	237	69	}	}	PUNCT
ejpam-4510	237	70	=	=	SYM
ejpam-4510	237	71	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	237	72	)	)	PUNCT
ejpam-4510	237	73	,	,	PUNCT
ejpam-4510	237	74	φ+(y	φ+(y	CCONJ
ejpam-4510	237	75	)	)	PUNCT
ejpam-4510	237	76	}	}	PUNCT
ejpam-4510	237	77	,	,	PUNCT
ejpam-4510	237	78	that	that	ADV
ejpam-4510	237	79	is	be	AUX
ejpam-4510	237	80	,	,	PUNCT
ejpam-4510	237	81	z	z	PROPN
ejpam-4510	237	82	(	(	PUNCT
ejpam-4510	237	83	x	x	NOUN
ejpam-4510	237	84	,	,	PUNCT
ejpam-4510	237	85	y	y	PROPN
ejpam-4510	237	86	)	)	PUNCT
ejpam-4510	237	87	∈	∈	PROPN
ejpam-4510	238	1	φ̊(max	φ̊(max	NUM
ejpam-4510	238	2	,	,	PUNCT
ejpam-4510	238	3	min	min	NOUN
ejpam-4510	238	4	)	)	PUNCT
ejpam-4510	238	5	.	.	PUNCT
ejpam-4510	239	1	also	also	ADV
ejpam-4510	239	2	,	,	PUNCT
ejpam-4510	239	3	we	we	PRON
ejpam-4510	239	4	have	have	VERB
ejpam-4510	239	5	φs(z	φs(z	ADV
ejpam-4510	239	6	)	)	PUNCT
ejpam-4510	239	7	⊇	⊇	X
ejpam-4510	239	8	φs(y	φs(y	NUM
ejpam-4510	239	9	)	)	PUNCT
ejpam-4510	239	10	∩	∩	NOUN
ejpam-4510	239	11	φs(y	φs(y	PART
ejpam-4510	239	12	∗	∗	NOUN
ejpam-4510	239	13	z	z	NOUN
ejpam-4510	239	14	)	)	PUNCT
ejpam-4510	239	15	⊇	⊇	NOUN
ejpam-4510	239	16	φs(y	φs(y	NUM
ejpam-4510	239	17	)	)	PUNCT
ejpam-4510	239	18	∩	∩	NOUN
ejpam-4510	239	19	(	(	PUNCT
ejpam-4510	239	20	φs(x	φs(x	NOUN
ejpam-4510	239	21	)	)	PUNCT
ejpam-4510	239	22	∩	∩	NOUN
ejpam-4510	239	23	φs(x	φs(x	PART
ejpam-4510	239	24	∗	∗	NOUN
ejpam-4510	239	25	(	(	PUNCT
ejpam-4510	239	26	y	y	PROPN
ejpam-4510	239	27	∗	∗	PROPN
ejpam-4510	239	28	z	z	PROPN
ejpam-4510	239	29	)	)	PUNCT
ejpam-4510	239	30	)	)	PUNCT
ejpam-4510	239	31	)	)	PUNCT
ejpam-4510	240	1	=	=	SYM
ejpam-4510	240	2	φs(y	φs(y	X
ejpam-4510	240	3	)	)	PUNCT
ejpam-4510	240	4	∩	∩	NOUN
ejpam-4510	240	5	(	(	PUNCT
ejpam-4510	240	6	φs(x	φs(x	NOUN
ejpam-4510	240	7	)	)	PUNCT
ejpam-4510	240	8	∩	∩	PROPN
ejpam-4510	240	9	φs(1	φs(1	PROPN
ejpam-4510	240	10	)	)	PUNCT
ejpam-4510	240	11	)	)	PUNCT
ejpam-4510	240	12	=	=	SYM
ejpam-4510	240	13	φs(y	φs(y	X
ejpam-4510	240	14	)	)	PUNCT
ejpam-4510	240	15	∩	∩	NOUN
ejpam-4510	240	16	φs(x	φs(x	PRON
ejpam-4510	240	17	)	)	PUNCT
ejpam-4510	240	18	and	and	CCONJ
ejpam-4510	240	19	φ̃(z	φ̃(z	PROPN
ejpam-4510	240	20	)	)	PUNCT
ejpam-4510	240	21	⪰	⪰	NOUN
ejpam-4510	240	22	rmin{φ̃(y	rmin{φ̃(y	NOUN
ejpam-4510	240	23	)	)	PUNCT
ejpam-4510	240	24	,	,	PUNCT
ejpam-4510	240	25	φ̃(y	φ̃(y	ADJ
ejpam-4510	240	26	∗	∗	NOUN
ejpam-4510	240	27	z	z	NOUN
ejpam-4510	240	28	)	)	PUNCT
ejpam-4510	240	29	}	}	PUNCT
ejpam-4510	240	30	⪰	⪰	NOUN
ejpam-4510	240	31	rmin{φ̃(y	rmin{φ̃(y	NOUN
ejpam-4510	240	32	)	)	PUNCT
ejpam-4510	240	33	,	,	PUNCT
ejpam-4510	240	34	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	240	35	)	)	PUNCT
ejpam-4510	240	36	,	,	PUNCT
ejpam-4510	240	37	φ̃(x	φ̃(x	PROPN
ejpam-4510	240	38	∗	∗	NOUN
ejpam-4510	240	39	(	(	PUNCT
ejpam-4510	240	40	y	y	PROPN
ejpam-4510	240	41	∗	∗	PROPN
ejpam-4510	240	42	z	z	PROPN
ejpam-4510	240	43	)	)	PUNCT
ejpam-4510	240	44	)	)	PUNCT
ejpam-4510	240	45	}	}	PUNCT
ejpam-4510	240	46	}	}	PUNCT
ejpam-4510	240	47	=	=	SYM
ejpam-4510	240	48	rmin{φ̃(y	rmin{φ̃(y	X
ejpam-4510	240	49	)	)	PUNCT
ejpam-4510	240	50	,	,	PUNCT
ejpam-4510	240	51	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	240	52	)	)	PUNCT
ejpam-4510	240	53	,	,	PUNCT
ejpam-4510	240	54	φ̃(1	φ̃(1	NOUN
ejpam-4510	240	55	)	)	PUNCT
ejpam-4510	240	56	}	}	PUNCT
ejpam-4510	240	57	}	}	PUNCT
ejpam-4510	240	58	=	=	SYM
ejpam-4510	240	59	rmin{φ̃(y	rmin{φ̃(y	ADV
ejpam-4510	240	60	)	)	PUNCT
ejpam-4510	240	61	,	,	PUNCT
ejpam-4510	240	62	φ̃(x	φ̃(x	PROPN
ejpam-4510	240	63	)	)	PUNCT
ejpam-4510	240	64	}	}	PUNCT
ejpam-4510	240	65	.	.	PUNCT
ejpam-4510	241	1	let	let	VERB
ejpam-4510	241	2	x	x	PRON
ejpam-4510	241	3	,	,	PUNCT
ejpam-4510	241	4	y	y	PROPN
ejpam-4510	241	5	∈	∈	PROPN
ejpam-4510	241	6	x	x	AUX
ejpam-4510	241	7	be	be	AUX
ejpam-4510	241	8	such	such	ADJ
ejpam-4510	241	9	that	that	SCONJ
ejpam-4510	241	10	y∗x	y∗x	ADJ
ejpam-4510	241	11	(	(	PUNCT
ejpam-4510	241	12	1	1	NUM
ejpam-4510	241	13	,	,	PUNCT
ejpam-4510	241	14	1	1	NUM
ejpam-4510	241	15	)	)	PUNCT
ejpam-4510	241	16	∈	∈	NOUN
ejpam-4510	241	17	φ̊(max	φ̊(max	NUM
ejpam-4510	241	18	,	,	PUNCT
ejpam-4510	241	19	min	min	NOUN
ejpam-4510	241	20	)	)	PUNCT
ejpam-4510	241	21	,	,	PUNCT
ejpam-4510	241	22	φs(y	φs(y	NOUN
ejpam-4510	241	23	∗	∗	NOUN
ejpam-4510	241	24	x	x	NOUN
ejpam-4510	241	25	)	)	PUNCT
ejpam-4510	241	26	=	=	SYM
ejpam-4510	241	27	φs(1	φs(1	PROPN
ejpam-4510	241	28	)	)	PUNCT
ejpam-4510	241	29	and	and	CCONJ
ejpam-4510	241	30	φ̃(y	φ̃(y	PROPN
ejpam-4510	241	31	∗	∗	NOUN
ejpam-4510	241	32	x	x	NOUN
ejpam-4510	241	33	)	)	PUNCT
ejpam-4510	241	34	=	=	SYM
ejpam-4510	241	35	φ̃(1	φ̃(1	NOUN
ejpam-4510	241	36	)	)	PUNCT
ejpam-4510	241	37	.	.	PUNCT
ejpam-4510	242	1	it	it	PRON
ejpam-4510	242	2	follows	follow	VERB
ejpam-4510	242	3	that	that	SCONJ
ejpam-4510	242	4	φ−(x	φ−(x	PROPN
ejpam-4510	242	5	)	)	PUNCT
ejpam-4510	242	6	≤	≤	NOUN
ejpam-4510	242	7	max{φ−(y	max{φ−(y	NOUN
ejpam-4510	242	8	)	)	PUNCT
ejpam-4510	242	9	,	,	PUNCT
ejpam-4510	242	10	φ−(y	φ−(y	PROPN
ejpam-4510	242	11	∗	∗	NOUN
ejpam-4510	242	12	x	x	NOUN
ejpam-4510	242	13	)	)	PUNCT
ejpam-4510	242	14	}	}	PUNCT
ejpam-4510	242	15	≤	≤	NUM
ejpam-4510	242	16	max{φ−(y	max{φ−(y	NOUN
ejpam-4510	242	17	)	)	PUNCT
ejpam-4510	242	18	,	,	PUNCT
ejpam-4510	242	19	φ−(1	φ−(1	NOUN
ejpam-4510	242	20	)	)	PUNCT
ejpam-4510	242	21	}	}	PUNCT
ejpam-4510	242	22	=	=	SYM
ejpam-4510	242	23	φ−(y	φ−(y	PROPN
ejpam-4510	242	24	)	)	PUNCT
ejpam-4510	242	25	and	and	CCONJ
ejpam-4510	242	26	φ+(x	φ+(x	NOUN
ejpam-4510	242	27	)	)	PUNCT
ejpam-4510	242	28	≥	≥	NOUN
ejpam-4510	242	29	min{φ+(y	min{φ+(y	NOUN
ejpam-4510	242	30	)	)	PUNCT
ejpam-4510	242	31	,	,	PUNCT
ejpam-4510	242	32	φ+(y	φ+(y	CCONJ
ejpam-4510	242	33	∗	∗	NOUN
ejpam-4510	242	34	x	x	NOUN
ejpam-4510	242	35	)	)	PUNCT
ejpam-4510	242	36	}	}	PUNCT
ejpam-4510	242	37	≥	≥	NOUN
ejpam-4510	242	38	min{φ+(y	min{φ+(y	NOUN
ejpam-4510	242	39	)	)	PUNCT
ejpam-4510	242	40	,	,	PUNCT
ejpam-4510	242	41	φ+(1	φ+(1	NOUN
ejpam-4510	242	42	)	)	PUNCT
ejpam-4510	242	43	}	}	PUNCT
ejpam-4510	242	44	=	=	SYM
ejpam-4510	242	45	φ+(y	φ+(y	PUNCT
ejpam-4510	242	46	)	)	PUNCT
ejpam-4510	242	47	,	,	PUNCT
ejpam-4510	242	48	that	that	ADV
ejpam-4510	242	49	is	is	ADV
ejpam-4510	242	50	,	,	PUNCT
ejpam-4510	242	51	x	x	SYM
ejpam-4510	242	52	(	(	PUNCT
ejpam-4510	242	53	y	y	PROPN
ejpam-4510	242	54	,	,	PUNCT
ejpam-4510	242	55	y	y	NOUN
ejpam-4510	242	56	)	)	PUNCT
ejpam-4510	242	57	∈	∈	PROPN
ejpam-4510	242	58	φ̊(max	φ̊(max	NUM
ejpam-4510	242	59	,	,	PUNCT
ejpam-4510	242	60	min	min	NOUN
ejpam-4510	242	61	)	)	PUNCT
ejpam-4510	242	62	.	.	PUNCT
ejpam-4510	243	1	also	also	ADV
ejpam-4510	243	2	,	,	PUNCT
ejpam-4510	243	3	we	we	PRON
ejpam-4510	243	4	get	get	VERB
ejpam-4510	243	5	φs(x	φs(x	PRON
ejpam-4510	243	6	)	)	PUNCT
ejpam-4510	243	7	⊇	⊇	NOUN
ejpam-4510	243	8	φs(y	φs(y	NUM
ejpam-4510	243	9	)	)	PUNCT
ejpam-4510	243	10	∩	∩	NOUN
ejpam-4510	243	11	φs(y	φs(y	PART
ejpam-4510	243	12	∗	∗	NOUN
ejpam-4510	243	13	x	x	NOUN
ejpam-4510	243	14	)	)	PUNCT
ejpam-4510	243	15	=	=	SYM
ejpam-4510	243	16	φs(y	φs(y	X
ejpam-4510	243	17	)	)	PUNCT
ejpam-4510	243	18	∩	∩	NOUN
ejpam-4510	243	19	φs(1	φs(1	PROPN
ejpam-4510	243	20	)	)	PUNCT
ejpam-4510	243	21	=	=	NOUN
ejpam-4510	243	22	φs(y	φs(y	NUM
ejpam-4510	243	23	)	)	PUNCT
ejpam-4510	243	24	and	and	CCONJ
ejpam-4510	243	25	φ̃(x	φ̃(x	PROPN
ejpam-4510	243	26	)	)	PUNCT
ejpam-4510	243	27	⪰	⪰	NOUN
ejpam-4510	243	28	rmin{φ̃(y	rmin{φ̃(y	NOUN
ejpam-4510	243	29	)	)	PUNCT
ejpam-4510	243	30	,	,	PUNCT
ejpam-4510	243	31	φ̃(y	φ̃(y	ADJ
ejpam-4510	243	32	∗	∗	NOUN
ejpam-4510	243	33	x	x	NOUN
ejpam-4510	243	34	)	)	PUNCT
ejpam-4510	243	35	}	}	PUNCT
ejpam-4510	243	36	=	=	SYM
ejpam-4510	243	37	rmin{φ̃(y	rmin{φ̃(y	X
ejpam-4510	243	38	)	)	PUNCT
ejpam-4510	243	39	,	,	PUNCT
ejpam-4510	243	40	φ̃(1	φ̃(1	NOUN
ejpam-4510	243	41	)	)	PUNCT
ejpam-4510	243	42	}	}	PUNCT
ejpam-4510	243	43	=	=	SYM
ejpam-4510	243	44	φ̃(y	φ̃(y	NOUN
ejpam-4510	243	45	)	)	PUNCT
ejpam-4510	243	46	.	.	PUNCT
ejpam-4510	244	1	this	this	PRON
ejpam-4510	244	2	completes	complete	VERB
ejpam-4510	244	3	the	the	DET
ejpam-4510	244	4	proof	proof	NOUN
ejpam-4510	244	5	.	.	PUNCT
ejpam-4510	245	1	theorem	theorem	ADJ
ejpam-4510	245	2	4	4	NUM
ejpam-4510	245	3	.	.	PUNCT
ejpam-4510	246	1	every	every	DET
ejpam-4510	246	2	dokdo	dokdo	NOUN
ejpam-4510	246	3	be	be	AUX
ejpam-4510	246	4	-	-	PUNCT
ejpam-4510	246	5	filter	filter	NOUN
ejpam-4510	246	6	is	be	AUX
ejpam-4510	246	7	a	a	DET
ejpam-4510	246	8	(	(	PUNCT
ejpam-4510	246	9	weak	weak	ADJ
ejpam-4510	246	10	)	)	PUNCT
ejpam-4510	246	11	dokdo	dokdo	NOUN
ejpam-4510	246	12	be	be	NOUN
ejpam-4510	246	13	-	-	PUNCT
ejpam-4510	246	14	subalgebra	subalgebra	NOUN
ejpam-4510	246	15	.	.	PUNCT
ejpam-4510	247	1	y.	y.	PROPN
ejpam-4510	247	2	b.	b.	PROPN
ejpam-4510	247	3	jun	jun	PROPN
ejpam-4510	247	4	,	,	PUNCT
ejpam-4510	247	5	s.	s.	PROPN
ejpam-4510	247	6	s.	s.	PROPN
ejpam-4510	247	7	ahn	ahn	PROPN
ejpam-4510	247	8	and	and	CCONJ
ejpam-4510	247	9	e.	e.	PROPN
ejpam-4510	247	10	h.	h.	PROPN
ejpam-4510	247	11	roh	roh	PROPN
ejpam-4510	247	12	/	/	SYM
ejpam-4510	247	13	eur	eur	PROPN
ejpam-4510	247	14	.	.	PUNCT
ejpam-4510	248	1	j.	j.	PROPN
ejpam-4510	248	2	pure	pure	PROPN
ejpam-4510	248	3	appl	appl	PROPN
ejpam-4510	248	4	.	.	PROPN
ejpam-4510	248	5	math	math	PROPN
ejpam-4510	248	6	,	,	PUNCT
ejpam-4510	248	7	15	15	NUM
ejpam-4510	248	8	(	(	PUNCT
ejpam-4510	248	9	4	4	NUM
ejpam-4510	248	10	)	)	PUNCT
ejpam-4510	248	11	(	(	PUNCT
ejpam-4510	248	12	2022	2022	NUM
ejpam-4510	248	13	)	)	PUNCT
ejpam-4510	248	14	,	,	PUNCT
ejpam-4510	248	15	1521	1521	NUM
ejpam-4510	248	16	-	-	SYM
ejpam-4510	248	17	1535	1535	NUM
ejpam-4510	248	18	1531	1531	NUM
ejpam-4510	248	19	proof	proof	NOUN
ejpam-4510	248	20	.	.	PUNCT
ejpam-4510	249	1	let	let	VERB
ejpam-4510	249	2	dokφ	dokφ	NOUN
ejpam-4510	249	3	:	:	PUNCT
ejpam-4510	249	4	=	=	SYM
ejpam-4510	249	5	(	(	PUNCT
ejpam-4510	249	6	φ̊	φ̊	PROPN
ejpam-4510	249	7	,	,	PUNCT
ejpam-4510	249	8	φs	φs	ADV
ejpam-4510	249	9	,	,	PUNCT
ejpam-4510	249	10	φ̃	φ̃	PROPN
ejpam-4510	249	11	)	)	PUNCT
ejpam-4510	249	12	be	be	VERB
ejpam-4510	249	13	a	a	DET
ejpam-4510	249	14	dokdo	dokdo	NOUN
ejpam-4510	249	15	be	be	NOUN
ejpam-4510	249	16	-	-	PUNCT
ejpam-4510	249	17	filter	filter	NOUN
ejpam-4510	249	18	of	of	ADP
ejpam-4510	249	19	(	(	PUNCT
ejpam-4510	249	20	x	x	NOUN
ejpam-4510	249	21	,	,	PUNCT
ejpam-4510	249	22	u	u	NOUN
ejpam-4510	249	23	)	)	PUNCT
ejpam-4510	249	24	.	.	PUNCT
ejpam-4510	250	1	since	since	SCONJ
ejpam-4510	250	2	x	x	PROPN
ejpam-4510	250	3	≤	≤	NUM
ejpam-4510	250	4	y	y	PROPN
ejpam-4510	250	5	∗	∗	NOUN
ejpam-4510	250	6	x	x	PUNCT
ejpam-4510	250	7	for	for	ADP
ejpam-4510	250	8	all	all	DET
ejpam-4510	250	9	x	x	NOUN
ejpam-4510	250	10	,	,	PUNCT
ejpam-4510	250	11	y	y	PROPN
ejpam-4510	250	12	∈	∈	PROPN
ejpam-4510	250	13	x	x	X
ejpam-4510	250	14	,	,	PUNCT
ejpam-4510	250	15	we	we	PRON
ejpam-4510	250	16	have	have	VERB
ejpam-4510	250	17	y∗x	y∗x	NUM
ejpam-4510	250	18	(	(	PUNCT
ejpam-4510	250	19	x	x	X
ejpam-4510	250	20	,	,	PUNCT
ejpam-4510	250	21	x	x	NOUN
ejpam-4510	250	22	)	)	PUNCT
ejpam-4510	250	23	∈	∈	PROPN
ejpam-4510	251	1	φ̊(max	φ̊(max	NUM
ejpam-4510	251	2	,	,	PUNCT
ejpam-4510	251	3	min	min	NOUN
ejpam-4510	251	4	)	)	PUNCT
ejpam-4510	251	5	,	,	PUNCT
ejpam-4510	251	6	φs(y	φs(y	NOUN
ejpam-4510	251	7	∗	∗	NOUN
ejpam-4510	251	8	x	x	NOUN
ejpam-4510	251	9	)	)	PUNCT
ejpam-4510	251	10	⊇	⊇	NOUN
ejpam-4510	251	11	φs(x	φs(x	PRON
ejpam-4510	251	12	)	)	PUNCT
ejpam-4510	251	13	,	,	PUNCT
ejpam-4510	251	14	and	and	CCONJ
ejpam-4510	251	15	φ̃(y	φ̃(y	PROPN
ejpam-4510	251	16	∗	∗	NOUN
ejpam-4510	251	17	x	x	NOUN
ejpam-4510	251	18	)	)	PUNCT
ejpam-4510	251	19	⪰	⪰	ADP
ejpam-4510	251	20	φ̃(x	φ̃(x	PROPN
ejpam-4510	251	21	)	)	PUNCT
ejpam-4510	251	22	by	by	ADP
ejpam-4510	251	23	(	(	PUNCT
ejpam-4510	251	24	26	26	NUM
ejpam-4510	251	25	)	)	PUNCT
ejpam-4510	251	26	.	.	PUNCT
ejpam-4510	252	1	it	it	PRON
ejpam-4510	252	2	follows	follow	VERB
ejpam-4510	252	3	from	from	ADP
ejpam-4510	252	4	(	(	PUNCT
ejpam-4510	252	5	25	25	NUM
ejpam-4510	252	6	)	)	PUNCT
ejpam-4510	252	7	that	that	PRON
ejpam-4510	252	8	φ−(y	φ−(y	PROPN
ejpam-4510	252	9	∗	∗	NOUN
ejpam-4510	252	10	x	x	NOUN
ejpam-4510	252	11	)	)	PUNCT
ejpam-4510	252	12	≤	≤	NUM
ejpam-4510	252	13	φ−(x	φ−(x	PROPN
ejpam-4510	252	14	)	)	PUNCT
ejpam-4510	252	15	≤	≤	NOUN
ejpam-4510	253	1	max{φ−(y	max{φ−(y	NOUN
ejpam-4510	253	2	)	)	PUNCT
ejpam-4510	253	3	,	,	PUNCT
ejpam-4510	253	4	φ−(y	φ−(y	PROPN
ejpam-4510	253	5	∗	∗	NOUN
ejpam-4510	253	6	x	x	NOUN
ejpam-4510	253	7	)	)	PUNCT
ejpam-4510	253	8	}	}	PUNCT
ejpam-4510	253	9	≤	≤	NUM
ejpam-4510	253	10	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	253	11	)	)	PUNCT
ejpam-4510	253	12	,	,	PUNCT
ejpam-4510	253	13	φ−(y	φ−(y	PROPN
ejpam-4510	253	14	)	)	PUNCT
ejpam-4510	253	15	}	}	PUNCT
ejpam-4510	253	16	,	,	PUNCT
ejpam-4510	253	17	φ+(y	φ+(y	CCONJ
ejpam-4510	253	18	∗	∗	NOUN
ejpam-4510	253	19	x	x	NOUN
ejpam-4510	253	20	)	)	PUNCT
ejpam-4510	253	21	≥	≥	X
ejpam-4510	253	22	φ+(x	φ+(x	X
ejpam-4510	253	23	)	)	PUNCT
ejpam-4510	253	24	≥	≥	NOUN
ejpam-4510	253	25	min{φ+(y	min{φ+(y	NOUN
ejpam-4510	253	26	)	)	PUNCT
ejpam-4510	253	27	,	,	PUNCT
ejpam-4510	253	28	φ+(y	φ+(y	CCONJ
ejpam-4510	253	29	∗	∗	NOUN
ejpam-4510	253	30	x	x	NOUN
ejpam-4510	253	31	)	)	PUNCT
ejpam-4510	253	32	}	}	PUNCT
ejpam-4510	253	33	≥	≥	NOUN
ejpam-4510	253	34	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	253	35	)	)	PUNCT
ejpam-4510	253	36	,	,	PUNCT
ejpam-4510	253	37	φ+(y	φ+(y	CCONJ
ejpam-4510	253	38	)	)	PUNCT
ejpam-4510	253	39	}	}	PUNCT
ejpam-4510	253	40	,	,	PUNCT
ejpam-4510	253	41	φs(y	φs(y	NOUN
ejpam-4510	253	42	∗	∗	NOUN
ejpam-4510	253	43	x	x	NOUN
ejpam-4510	253	44	)	)	PUNCT
ejpam-4510	253	45	⊇	⊇	NOUN
ejpam-4510	253	46	φs(x	φs(x	NOUN
ejpam-4510	253	47	)	)	PUNCT
ejpam-4510	253	48	⊇	⊇	NOUN
ejpam-4510	253	49	φs(y	φs(y	NUM
ejpam-4510	253	50	)	)	PUNCT
ejpam-4510	253	51	∩	∩	NOUN
ejpam-4510	253	52	φs(y	φs(y	PART
ejpam-4510	253	53	∗	∗	NOUN
ejpam-4510	253	54	x	x	NOUN
ejpam-4510	253	55	)	)	PUNCT
ejpam-4510	253	56	⊇	⊇	NOUN
ejpam-4510	253	57	φs(x	φs(x	NOUN
ejpam-4510	253	58	)	)	PUNCT
ejpam-4510	253	59	∩	∩	NOUN
ejpam-4510	253	60	φs(y	φs(y	NUM
ejpam-4510	253	61	)	)	PUNCT
ejpam-4510	253	62	,	,	PUNCT
ejpam-4510	253	63	φ̃(y	φ̃(y	ADJ
ejpam-4510	253	64	∗	∗	NOUN
ejpam-4510	253	65	x	x	NOUN
ejpam-4510	253	66	)	)	PUNCT
ejpam-4510	253	67	⪰	⪰	NOUN
ejpam-4510	253	68	φ̃(x	φ̃(x	PROPN
ejpam-4510	253	69	)	)	PUNCT
ejpam-4510	253	70	⪰	⪰	NOUN
ejpam-4510	253	71	rmin{φ̃(y	rmin{φ̃(y	NOUN
ejpam-4510	253	72	)	)	PUNCT
ejpam-4510	253	73	,	,	PUNCT
ejpam-4510	253	74	φ̃(y	φ̃(y	ADJ
ejpam-4510	253	75	∗	∗	NOUN
ejpam-4510	253	76	x	x	NOUN
ejpam-4510	253	77	)	)	PUNCT
ejpam-4510	253	78	}	}	PUNCT
ejpam-4510	253	79	⪰	⪰	NOUN
ejpam-4510	253	80	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	253	81	)	)	PUNCT
ejpam-4510	253	82	,	,	PUNCT
ejpam-4510	253	83	φ̃(y	φ̃(y	NOUN
ejpam-4510	253	84	)	)	PUNCT
ejpam-4510	253	85	}	}	PUNCT
ejpam-4510	253	86	.	.	PUNCT
ejpam-4510	254	1	therefore	therefore	ADV
ejpam-4510	254	2	dokφ	dokφ	NOUN
ejpam-4510	254	3	:	:	PUNCT
ejpam-4510	254	4	=	=	SYM
ejpam-4510	254	5	(	(	PUNCT
ejpam-4510	254	6	φ̊	φ̊	PROPN
ejpam-4510	254	7	,	,	PUNCT
ejpam-4510	254	8	φs	φs	ADV
ejpam-4510	254	9	,	,	PUNCT
ejpam-4510	254	10	φ̃	φ̃	PROPN
ejpam-4510	254	11	)	)	PUNCT
ejpam-4510	254	12	is	be	AUX
ejpam-4510	254	13	a	a	DET
ejpam-4510	254	14	dokdo	dokdo	NOUN
ejpam-4510	254	15	be	be	NOUN
ejpam-4510	254	16	-	-	PUNCT
ejpam-4510	254	17	subalgebra	subalgebra	NOUN
ejpam-4510	254	18	,	,	PUNCT
ejpam-4510	254	19	and	and	CCONJ
ejpam-4510	254	20	hence	hence	ADV
ejpam-4510	254	21	a	a	DET
ejpam-4510	254	22	weak	weak	ADJ
ejpam-4510	254	23	dokdo	dokdo	ADJ
ejpam-4510	254	24	besubalgebra	besubalgebra	NOUN
ejpam-4510	254	25	of	of	ADP
ejpam-4510	254	26	(	(	PUNCT
ejpam-4510	254	27	x	x	NOUN
ejpam-4510	254	28	,	,	PUNCT
ejpam-4510	254	29	u	u	NOUN
ejpam-4510	254	30	)	)	PUNCT
ejpam-4510	254	31	.	.	PUNCT
ejpam-4510	255	1	the	the	DET
ejpam-4510	255	2	converse	converse	NOUN
ejpam-4510	255	3	of	of	ADP
ejpam-4510	255	4	theorem	theorem	NOUN
ejpam-4510	255	5	4	4	NUM
ejpam-4510	255	6	may	may	AUX
ejpam-4510	255	7	not	not	PART
ejpam-4510	255	8	be	be	AUX
ejpam-4510	255	9	true	true	ADJ
ejpam-4510	255	10	as	as	SCONJ
ejpam-4510	255	11	seen	see	VERB
ejpam-4510	255	12	in	in	ADP
ejpam-4510	255	13	the	the	DET
ejpam-4510	255	14	following	follow	VERB
ejpam-4510	255	15	example	example	NOUN
ejpam-4510	255	16	.	.	PUNCT
ejpam-4510	256	1	example	example	NOUN
ejpam-4510	256	2	6	6	NUM
ejpam-4510	256	3	.	.	PUNCT
ejpam-4510	257	1	(	(	PUNCT
ejpam-4510	257	2	i	i	NOUN
ejpam-4510	257	3	)	)	PUNCT
ejpam-4510	257	4	let	let	VERB
ejpam-4510	257	5	dokφ	dokφ	NOUN
ejpam-4510	257	6	:	:	PUNCT
ejpam-4510	257	7	=	=	SYM
ejpam-4510	257	8	(	(	PUNCT
ejpam-4510	257	9	φ̊	φ̊	PROPN
ejpam-4510	257	10	,	,	PUNCT
ejpam-4510	257	11	φs	φs	ADV
ejpam-4510	257	12	,	,	PUNCT
ejpam-4510	257	13	φ̃	φ̃	PROPN
ejpam-4510	257	14	)	)	PUNCT
ejpam-4510	257	15	be	be	VERB
ejpam-4510	257	16	the	the	DET
ejpam-4510	257	17	dokdo	dokdo	NOUN
ejpam-4510	257	18	be	be	NOUN
ejpam-4510	257	19	-	-	PUNCT
ejpam-4510	257	20	subalgebra	subalgebra	NOUN
ejpam-4510	257	21	of	of	ADP
ejpam-4510	257	22	(	(	PUNCT
ejpam-4510	257	23	x	x	NOUN
ejpam-4510	257	24	,	,	PUNCT
ejpam-4510	257	25	u	u	NOUN
ejpam-4510	257	26	)	)	PUNCT
ejpam-4510	257	27	which	which	PRON
ejpam-4510	257	28	is	be	AUX
ejpam-4510	257	29	described	describe	VERB
ejpam-4510	257	30	in	in	ADP
ejpam-4510	257	31	example	example	NOUN
ejpam-4510	257	32	1	1	X
ejpam-4510	257	33	.	.	PUNCT
ejpam-4510	258	1	it	it	PRON
ejpam-4510	258	2	is	be	AUX
ejpam-4510	258	3	not	not	PART
ejpam-4510	258	4	a	a	DET
ejpam-4510	258	5	dokdo	dokdo	NOUN
ejpam-4510	258	6	be	be	NOUN
ejpam-4510	258	7	-	-	PUNCT
ejpam-4510	258	8	filter	filter	NOUN
ejpam-4510	258	9	of	of	ADP
ejpam-4510	258	10	(	(	PUNCT
ejpam-4510	258	11	x	x	NOUN
ejpam-4510	258	12	,	,	PUNCT
ejpam-4510	258	13	u	u	NOUN
ejpam-4510	258	14	)	)	PUNCT
ejpam-4510	258	15	since	since	SCONJ
ejpam-4510	258	16	φs(5	φs(5	NOUN
ejpam-4510	258	17	)	)	PUNCT
ejpam-4510	258	18	=	=	SYM
ejpam-4510	258	19	16n	16n	NUM
ejpam-4510	258	20	⊉	⊉	NOUN
ejpam-4510	258	21	8n	8n	NOUN
ejpam-4510	258	22	=	=	SYM
ejpam-4510	258	23	φs(2	φs(2	NOUN
ejpam-4510	258	24	)	)	PUNCT
ejpam-4510	258	25	∩	∩	NOUN
ejpam-4510	258	26	φs(2	φs(2	NOUN
ejpam-4510	258	27	∗	∗	X
ejpam-4510	258	28	5	5	NUM
ejpam-4510	258	29	)	)	PUNCT
ejpam-4510	258	30	or	or	CCONJ
ejpam-4510	258	31	3	3	NUM
ejpam-4510	258	32	(	(	PUNCT
ejpam-4510	258	33	5,5∗3	5,5∗3	NUM
ejpam-4510	258	34	)	)	PUNCT
ejpam-4510	258	35	=	=	SYM
ejpam-4510	258	36	3	3	NUM
ejpam-4510	258	37	(	(	PUNCT
ejpam-4510	258	38	5,2	5,2	NUM
ejpam-4510	258	39	)	)	PUNCT
ejpam-4510	258	40	/∈	/∈	PUNCT
ejpam-4510	259	1	φ̊(max	φ̊(max	ADV
ejpam-4510	259	2	,	,	PUNCT
ejpam-4510	259	3	min	min	NOUN
ejpam-4510	259	4	)	)	PUNCT
ejpam-4510	259	5	.	.	PUNCT
ejpam-4510	260	1	(	(	PUNCT
ejpam-4510	260	2	ii	ii	NOUN
ejpam-4510	260	3	)	)	PUNCT
ejpam-4510	260	4	let	let	VERB
ejpam-4510	260	5	dokφ	dokφ	NOUN
ejpam-4510	260	6	:	:	PUNCT
ejpam-4510	260	7	=	=	SYM
ejpam-4510	260	8	(	(	PUNCT
ejpam-4510	260	9	φ̊	φ̊	PROPN
ejpam-4510	260	10	,	,	PUNCT
ejpam-4510	260	11	φs	φs	ADV
ejpam-4510	260	12	,	,	PUNCT
ejpam-4510	260	13	φ̃	φ̃	PROPN
ejpam-4510	260	14	)	)	PUNCT
ejpam-4510	260	15	be	be	VERB
ejpam-4510	260	16	the	the	DET
ejpam-4510	260	17	weak	weak	ADJ
ejpam-4510	260	18	dokdo	dokdo	NOUN
ejpam-4510	260	19	be	be	NOUN
ejpam-4510	260	20	-	-	PUNCT
ejpam-4510	260	21	subalgebra	subalgebra	NOUN
ejpam-4510	260	22	of	of	ADP
ejpam-4510	260	23	(	(	PUNCT
ejpam-4510	260	24	x	x	NOUN
ejpam-4510	260	25	,	,	PUNCT
ejpam-4510	260	26	u	u	NOUN
ejpam-4510	260	27	)	)	PUNCT
ejpam-4510	260	28	which	which	PRON
ejpam-4510	260	29	is	be	AUX
ejpam-4510	260	30	described	describe	VERB
ejpam-4510	260	31	in	in	ADP
ejpam-4510	260	32	example	example	NOUN
ejpam-4510	261	1	3	3	X
ejpam-4510	261	2	.	.	PUNCT
ejpam-4510	262	1	it	it	PRON
ejpam-4510	262	2	is	be	AUX
ejpam-4510	262	3	not	not	PART
ejpam-4510	262	4	a	a	DET
ejpam-4510	262	5	dokdo	dokdo	NOUN
ejpam-4510	262	6	be	be	NOUN
ejpam-4510	262	7	-	-	PUNCT
ejpam-4510	262	8	filter	filter	NOUN
ejpam-4510	262	9	of	of	ADP
ejpam-4510	262	10	(	(	PUNCT
ejpam-4510	262	11	x	x	NOUN
ejpam-4510	262	12	,	,	PUNCT
ejpam-4510	262	13	u	u	NOUN
ejpam-4510	262	14	)	)	PUNCT
ejpam-4510	262	15	since	since	SCONJ
ejpam-4510	262	16	3	3	NUM
ejpam-4510	262	17	(	(	PUNCT
ejpam-4510	262	18	2,2∗3	2,2∗3	NUM
ejpam-4510	262	19	)	)	PUNCT
ejpam-4510	262	20	=	=	SYM
ejpam-4510	262	21	3	3	NUM
ejpam-4510	262	22	(	(	PUNCT
ejpam-4510	262	23	2,4	2,4	NUM
ejpam-4510	262	24	)	)	PUNCT
ejpam-4510	262	25	/∈	/∈	PUNCT
ejpam-4510	263	1	φ̊(max	φ̊(max	ADV
ejpam-4510	263	2	,	,	PUNCT
ejpam-4510	263	3	min	min	NOUN
ejpam-4510	263	4	)	)	PUNCT
ejpam-4510	263	5	or	or	CCONJ
ejpam-4510	263	6	φ̃(3	φ̃(3	NOUN
ejpam-4510	263	7	)	)	PUNCT
ejpam-4510	263	8	=	=	PUNCT
ejpam-4510	264	1	[	[	X
ejpam-4510	264	2	0.29	0.29	NUM
ejpam-4510	264	3	,	,	PUNCT
ejpam-4510	264	4	0.59	0.59	NUM
ejpam-4510	264	5	]	]	PUNCT
ejpam-4510	264	6	⪰̸	⪰̸	PUNCT
ejpam-4510	265	1	[	[	X
ejpam-4510	265	2	0.32	0.32	NUM
ejpam-4510	265	3	,	,	PUNCT
ejpam-4510	265	4	0.64	0.64	NUM
ejpam-4510	265	5	]	]	PUNCT
ejpam-4510	265	6	=	=	SYM
ejpam-4510	265	7	rmin{φ̃(2	rmin{φ̃(2	PROPN
ejpam-4510	265	8	)	)	PUNCT
ejpam-4510	265	9	,	,	PUNCT
ejpam-4510	265	10	φ̃(2	φ̃(2	VERB
ejpam-4510	265	11	∗	∗	NOUN
ejpam-4510	265	12	3	3	NUM
ejpam-4510	265	13	)	)	PUNCT
ejpam-4510	265	14	}	}	PUNCT
ejpam-4510	265	15	.	.	PUNCT
ejpam-4510	266	1	proposition	proposition	NOUN
ejpam-4510	266	2	4	4	NUM
ejpam-4510	266	3	.	.	PUNCT
ejpam-4510	267	1	let	let	AUX
ejpam-4510	267	2	(	(	PUNCT
ejpam-4510	267	3	x	x	NOUN
ejpam-4510	267	4	,	,	PUNCT
ejpam-4510	267	5	u	u	NOUN
ejpam-4510	267	6	)	)	PUNCT
ejpam-4510	267	7	be	be	VERB
ejpam-4510	267	8	a	a	DET
ejpam-4510	267	9	dokdo	dokdo	NOUN
ejpam-4510	267	10	be	be	NOUN
ejpam-4510	267	11	-	-	PUNCT
ejpam-4510	267	12	universe	universe	NOUN
ejpam-4510	267	13	in	in	ADP
ejpam-4510	267	14	which	which	PRON
ejpam-4510	267	15	x	x	PRON
ejpam-4510	267	16	is	be	AUX
ejpam-4510	267	17	a	a	DET
ejpam-4510	267	18	self	self	NOUN
ejpam-4510	267	19	-	-	PUNCT
ejpam-4510	267	20	distributive	distributive	ADJ
ejpam-4510	267	21	bealgebra	bealgebra	NOUN
ejpam-4510	267	22	.	.	PUNCT
ejpam-4510	268	1	if	if	SCONJ
ejpam-4510	268	2	dokφ	dokφ	NOUN
ejpam-4510	268	3	:	:	PUNCT
ejpam-4510	268	4	=	=	SYM
ejpam-4510	268	5	(	(	PUNCT
ejpam-4510	268	6	φ̊	φ̊	PROPN
ejpam-4510	268	7	,	,	PUNCT
ejpam-4510	268	8	φs	φs	ADV
ejpam-4510	268	9	,	,	PUNCT
ejpam-4510	268	10	φ̃	φ̃	PROPN
ejpam-4510	268	11	)	)	PUNCT
ejpam-4510	268	12	is	be	AUX
ejpam-4510	268	13	a	a	DET
ejpam-4510	268	14	dokdo	dokdo	NOUN
ejpam-4510	268	15	be	be	NOUN
ejpam-4510	268	16	-	-	PUNCT
ejpam-4510	268	17	filter	filter	NOUN
ejpam-4510	268	18	of	of	ADP
ejpam-4510	268	19	(	(	PUNCT
ejpam-4510	268	20	x	x	NOUN
ejpam-4510	268	21	,	,	PUNCT
ejpam-4510	268	22	u	u	NOUN
ejpam-4510	268	23	)	)	PUNCT
ejpam-4510	268	24	,	,	PUNCT
ejpam-4510	268	25	then	then	ADV
ejpam-4510	268	26	the	the	DET
ejpam-4510	268	27	next	next	ADJ
ejpam-4510	268	28	assertions	assertion	NOUN
ejpam-4510	268	29	are	be	AUX
ejpam-4510	268	30	equivalent	equivalent	ADJ
ejpam-4510	268	31	.	.	PUNCT
ejpam-4510	269	1	(	(	PUNCT
ejpam-4510	269	2	∀x	∀x	X
ejpam-4510	269	3	,	,	PUNCT
ejpam-4510	269	4	y	y	PROPN
ejpam-4510	269	5	∈	∈	PROPN
ejpam-4510	269	6	x	x	X
ejpam-4510	269	7	)	)	PUNCT
ejpam-4510	269	8			PROPN
ejpam-4510	269	9	y∗x	y∗x	NUM
ejpam-4510	269	10	(	(	PUNCT
ejpam-4510	269	11	y∗(y∗x	y∗(y∗x	PROPN
ejpam-4510	269	12	)	)	PUNCT
ejpam-4510	269	13	,	,	PUNCT
ejpam-4510	269	14	y∗(y∗x	y∗(y∗x	PROPN
ejpam-4510	269	15	)	)	PUNCT
ejpam-4510	269	16	)	)	PUNCT
ejpam-4510	269	17	∈	∈	PROPN
ejpam-4510	270	1	φ̊(max	φ̊(max	NUM
ejpam-4510	270	2	,	,	PUNCT
ejpam-4510	270	3	min	min	NOUN
ejpam-4510	270	4	)	)	PUNCT
ejpam-4510	270	5	,	,	PUNCT
ejpam-4510	270	6	φs(y	φs(y	NOUN
ejpam-4510	270	7	∗	∗	NOUN
ejpam-4510	270	8	x	x	NOUN
ejpam-4510	270	9	)	)	PUNCT
ejpam-4510	270	10	⊇	⊇	PROPN
ejpam-4510	270	11	φs(y	φs(y	ADJ
ejpam-4510	270	12	∗	∗	NOUN
ejpam-4510	270	13	(	(	PUNCT
ejpam-4510	270	14	y	y	PROPN
ejpam-4510	270	15	∗	∗	NOUN
ejpam-4510	270	16	x	x	NOUN
ejpam-4510	270	17	)	)	PUNCT
ejpam-4510	270	18	)	)	PUNCT
ejpam-4510	270	19	,	,	PUNCT
ejpam-4510	270	20	φ̃(y	φ̃(y	ADJ
ejpam-4510	270	21	∗	∗	NOUN
ejpam-4510	270	22	x	x	NOUN
ejpam-4510	270	23	)	)	PUNCT
ejpam-4510	270	24	⪰	⪰	NOUN
ejpam-4510	270	25	φ̃(y	φ̃(y	ADJ
ejpam-4510	270	26	∗	∗	NOUN
ejpam-4510	270	27	(	(	PUNCT
ejpam-4510	270	28	y	y	PROPN
ejpam-4510	270	29	∗	∗	NOUN
ejpam-4510	270	30	x	x	NOUN
ejpam-4510	270	31	)	)	PUNCT
ejpam-4510	270	32	)	)	PUNCT
ejpam-4510	271	1			PROPN
ejpam-4510	271	2	.	.	PUNCT
ejpam-4510	272	1	(	(	PUNCT
ejpam-4510	272	2	29	29	NUM
ejpam-4510	272	3	)	)	PUNCT
ejpam-4510	272	4	(	(	PUNCT
ejpam-4510	272	5	∀x	∀x	X
ejpam-4510	272	6	,	,	PUNCT
ejpam-4510	272	7	y	y	PROPN
ejpam-4510	272	8	,	,	PUNCT
ejpam-4510	272	9	z	z	NOUN
ejpam-4510	272	10	∈	∈	PROPN
ejpam-4510	272	11	x	x	NOUN
ejpam-4510	272	12	)	)	PUNCT
ejpam-4510	272	13			X
ejpam-4510	272	14	(	(	PUNCT
ejpam-4510	272	15	z∗y)∗(z∗x	z∗y)∗(z∗x	PROPN
ejpam-4510	272	16	)	)	PUNCT
ejpam-4510	272	17	(	(	PUNCT
ejpam-4510	272	18	z∗(y∗x	z∗(y∗x	NUM
ejpam-4510	272	19	)	)	PUNCT
ejpam-4510	272	20	,	,	PUNCT
ejpam-4510	272	21	z∗(y∗x	z∗(y∗x	NUM
ejpam-4510	272	22	)	)	PUNCT
ejpam-4510	272	23	)	)	PUNCT
ejpam-4510	272	24	∈	∈	PROPN
ejpam-4510	273	1	φ̊(max	φ̊(max	NUM
ejpam-4510	273	2	,	,	PUNCT
ejpam-4510	273	3	min	min	NOUN
ejpam-4510	273	4	)	)	PUNCT
ejpam-4510	273	5	,	,	PUNCT
ejpam-4510	273	6	φs((z	φs((z	PROPN
ejpam-4510	273	7	∗	∗	PROPN
ejpam-4510	273	8	y	y	PROPN
ejpam-4510	273	9	)	)	PUNCT
ejpam-4510	273	10	∗	∗	NOUN
ejpam-4510	273	11	(	(	PUNCT
ejpam-4510	273	12	z	z	NOUN
ejpam-4510	273	13	∗	∗	NOUN
ejpam-4510	273	14	x	x	NOUN
ejpam-4510	273	15	)	)	PUNCT
ejpam-4510	273	16	)	)	PUNCT
ejpam-4510	273	17	⊇	⊇	NOUN
ejpam-4510	273	18	φs(z	φs(z	X
ejpam-4510	273	19	∗	∗	NOUN
ejpam-4510	273	20	(	(	PUNCT
ejpam-4510	273	21	y	y	PROPN
ejpam-4510	273	22	∗	∗	NOUN
ejpam-4510	273	23	x	x	NOUN
ejpam-4510	273	24	)	)	PUNCT
ejpam-4510	273	25	)	)	PUNCT
ejpam-4510	273	26	,	,	PUNCT
ejpam-4510	273	27	φ̃((z	φ̃((z	NOUN
ejpam-4510	273	28	∗	∗	PROPN
ejpam-4510	273	29	y	y	NOUN
ejpam-4510	273	30	)	)	PUNCT
ejpam-4510	273	31	∗	∗	NOUN
ejpam-4510	273	32	(	(	PUNCT
ejpam-4510	273	33	z	z	NOUN
ejpam-4510	273	34	∗	∗	NOUN
ejpam-4510	273	35	x	x	NOUN
ejpam-4510	273	36	)	)	PUNCT
ejpam-4510	273	37	)	)	PUNCT
ejpam-4510	273	38	⪰	⪰	VERB
ejpam-4510	273	39	φ̃(z	φ̃(z	PROPN
ejpam-4510	273	40	∗	∗	NOUN
ejpam-4510	273	41	(	(	PUNCT
ejpam-4510	273	42	y	y	PROPN
ejpam-4510	273	43	∗	∗	NOUN
ejpam-4510	273	44	x	x	NOUN
ejpam-4510	273	45	)	)	PUNCT
ejpam-4510	273	46	)	)	PUNCT
ejpam-4510	273	47			PROPN
ejpam-4510	273	48	.	.	PUNCT
ejpam-4510	274	1	(	(	PUNCT
ejpam-4510	274	2	30	30	X
ejpam-4510	274	3	)	)	PUNCT
ejpam-4510	274	4	proof	proof	NOUN
ejpam-4510	274	5	.	.	PUNCT
ejpam-4510	275	1	let	let	VERB
ejpam-4510	275	2	x	x	PRON
ejpam-4510	275	3	,	,	PUNCT
ejpam-4510	275	4	y	y	PROPN
ejpam-4510	275	5	,	,	PUNCT
ejpam-4510	275	6	z	z	NOUN
ejpam-4510	275	7	∈	∈	PROPN
ejpam-4510	275	8	x.	x.	NOUN
ejpam-4510	275	9	since	since	SCONJ
ejpam-4510	275	10	x	x	PROPN
ejpam-4510	275	11	is	be	AUX
ejpam-4510	275	12	self	self	NOUN
ejpam-4510	275	13	-	-	PUNCT
ejpam-4510	275	14	distributive	distributive	ADJ
ejpam-4510	275	15	,	,	PUNCT
ejpam-4510	275	16	we	we	PRON
ejpam-4510	275	17	have	have	VERB
ejpam-4510	275	18	z	z	NOUN
ejpam-4510	275	19	∗	∗	NOUN
ejpam-4510	275	20	(	(	PUNCT
ejpam-4510	275	21	y	y	PROPN
ejpam-4510	275	22	∗	∗	X
ejpam-4510	275	23	x	x	NOUN
ejpam-4510	275	24	)	)	PUNCT
ejpam-4510	275	25	≤	≤	NUM
ejpam-4510	275	26	z	z	NOUN
ejpam-4510	275	27	∗	∗	NOUN
ejpam-4510	275	28	(	(	PUNCT
ejpam-4510	275	29	(	(	PUNCT
ejpam-4510	275	30	z	z	NOUN
ejpam-4510	275	31	∗	∗	PROPN
ejpam-4510	275	32	y	y	PROPN
ejpam-4510	275	33	)	)	PUNCT
ejpam-4510	275	34	∗	∗	NOUN
ejpam-4510	275	35	(	(	PUNCT
ejpam-4510	275	36	z	z	NOUN
ejpam-4510	275	37	∗	∗	NOUN
ejpam-4510	275	38	x	x	NOUN
ejpam-4510	275	39	)	)	PUNCT
ejpam-4510	275	40	)	)	PUNCT
ejpam-4510	276	1	=	=	SYM
ejpam-4510	276	2	z	z	NOUN
ejpam-4510	276	3	∗	∗	NOUN
ejpam-4510	276	4	(	(	PUNCT
ejpam-4510	276	5	z	z	NOUN
ejpam-4510	276	6	∗	∗	NOUN
ejpam-4510	276	7	(	(	PUNCT
ejpam-4510	276	8	(	(	PUNCT
ejpam-4510	276	9	z	z	NOUN
ejpam-4510	276	10	∗	∗	PROPN
ejpam-4510	276	11	y	y	PROPN
ejpam-4510	276	12	)	)	PUNCT
ejpam-4510	276	13	∗	∗	NOUN
ejpam-4510	276	14	x	x	NOUN
ejpam-4510	276	15	)	)	PUNCT
ejpam-4510	276	16	)	)	PUNCT
ejpam-4510	276	17	.	.	PUNCT
ejpam-4510	277	1	assume	assume	VERB
ejpam-4510	277	2	that	that	SCONJ
ejpam-4510	277	3	(	(	PUNCT
ejpam-4510	277	4	29	29	NUM
ejpam-4510	277	5	)	)	PUNCT
ejpam-4510	277	6	is	be	AUX
ejpam-4510	277	7	valid	valid	ADJ
ejpam-4510	277	8	.	.	PUNCT
ejpam-4510	278	1	using	use	VERB
ejpam-4510	278	2	(	(	PUNCT
ejpam-4510	278	3	be4	be4	NOUN
ejpam-4510	278	4	)	)	PUNCT
ejpam-4510	278	5	,	,	PUNCT
ejpam-4510	278	6	(	(	PUNCT
ejpam-4510	278	7	26	26	NUM
ejpam-4510	278	8	)	)	PUNCT
ejpam-4510	278	9	and	and	CCONJ
ejpam-4510	278	10	(	(	PUNCT
ejpam-4510	278	11	29	29	NUM
ejpam-4510	278	12	)	)	PUNCT
ejpam-4510	278	13	,	,	PUNCT
ejpam-4510	278	14	we	we	PRON
ejpam-4510	278	15	have	have	VERB
ejpam-4510	278	16	φ−((z	φ−((z	PROPN
ejpam-4510	278	17	∗	∗	NOUN
ejpam-4510	278	18	y	y	NOUN
ejpam-4510	278	19	)	)	PUNCT
ejpam-4510	278	20	∗	∗	NOUN
ejpam-4510	278	21	(	(	PUNCT
ejpam-4510	278	22	z	z	NOUN
ejpam-4510	278	23	∗	∗	NOUN
ejpam-4510	278	24	x	x	NOUN
ejpam-4510	278	25	)	)	PUNCT
ejpam-4510	278	26	)	)	PUNCT
ejpam-4510	279	1	=	=	PUNCT
ejpam-4510	280	1	φ−(z	φ−(z	NOUN
ejpam-4510	280	2	∗	∗	NOUN
ejpam-4510	280	3	(	(	PUNCT
ejpam-4510	280	4	(	(	PUNCT
ejpam-4510	280	5	z	z	NOUN
ejpam-4510	280	6	∗	∗	PROPN
ejpam-4510	280	7	y	y	PROPN
ejpam-4510	280	8	)	)	PUNCT
ejpam-4510	280	9	∗	∗	NOUN
ejpam-4510	280	10	x	x	NOUN
ejpam-4510	280	11	)	)	PUNCT
ejpam-4510	280	12	)	)	PUNCT
ejpam-4510	280	13	≤	≤	NOUN
ejpam-4510	281	1	φ−(z	φ−(z	ADJ
ejpam-4510	281	2	∗	∗	NOUN
ejpam-4510	281	3	(	(	PUNCT
ejpam-4510	281	4	z	z	NOUN
ejpam-4510	281	5	∗	∗	NOUN
ejpam-4510	281	6	(	(	PUNCT
ejpam-4510	281	7	(	(	PUNCT
ejpam-4510	281	8	z	z	NOUN
ejpam-4510	281	9	∗	∗	PROPN
ejpam-4510	281	10	y	y	PROPN
ejpam-4510	281	11	)	)	PUNCT
ejpam-4510	281	12	∗	∗	NOUN
ejpam-4510	281	13	x	x	NOUN
ejpam-4510	281	14	)	)	PUNCT
ejpam-4510	281	15	)	)	PUNCT
ejpam-4510	281	16	)	)	PUNCT
ejpam-4510	281	17	≤	≤	NOUN
ejpam-4510	282	1	φ−(z	φ−(z	ADJ
ejpam-4510	282	2	∗	∗	NOUN
ejpam-4510	282	3	(	(	PUNCT
ejpam-4510	282	4	y	y	PROPN
ejpam-4510	282	5	∗	∗	NOUN
ejpam-4510	282	6	x	x	NOUN
ejpam-4510	282	7	)	)	PUNCT
ejpam-4510	282	8	)	)	PUNCT
ejpam-4510	282	9	and	and	CCONJ
ejpam-4510	282	10	φ+((z	φ+((z	VERB
ejpam-4510	282	11	∗	∗	PROPN
ejpam-4510	282	12	y	y	NOUN
ejpam-4510	282	13	)	)	PUNCT
ejpam-4510	282	14	∗	∗	NOUN
ejpam-4510	282	15	(	(	PUNCT
ejpam-4510	282	16	z	z	NOUN
ejpam-4510	282	17	∗	∗	NOUN
ejpam-4510	282	18	x	x	NOUN
ejpam-4510	282	19	)	)	PUNCT
ejpam-4510	282	20	)	)	PUNCT
ejpam-4510	283	1	=	=	SYM
ejpam-4510	283	2	φ+(z	φ+(z	NOUN
ejpam-4510	283	3	∗	∗	NOUN
ejpam-4510	283	4	(	(	PUNCT
ejpam-4510	283	5	(	(	PUNCT
ejpam-4510	283	6	z	z	NOUN
ejpam-4510	283	7	∗	∗	PROPN
ejpam-4510	283	8	y	y	PROPN
ejpam-4510	283	9	)	)	PUNCT
ejpam-4510	283	10	∗	∗	NOUN
ejpam-4510	283	11	x	x	NOUN
ejpam-4510	283	12	)	)	PUNCT
ejpam-4510	283	13	)	)	PUNCT
ejpam-4510	284	1	y.	y.	PROPN
ejpam-4510	284	2	b.	b.	PROPN
ejpam-4510	284	3	jun	jun	PROPN
ejpam-4510	284	4	,	,	PUNCT
ejpam-4510	284	5	s.	s.	PROPN
ejpam-4510	284	6	s.	s.	PROPN
ejpam-4510	284	7	ahn	ahn	PROPN
ejpam-4510	284	8	and	and	CCONJ
ejpam-4510	284	9	e.	e.	PROPN
ejpam-4510	284	10	h.	h.	PROPN
ejpam-4510	284	11	roh	roh	PROPN
ejpam-4510	284	12	/	/	SYM
ejpam-4510	284	13	eur	eur	PROPN
ejpam-4510	284	14	.	.	PUNCT
ejpam-4510	285	1	j.	j.	PROPN
ejpam-4510	285	2	pure	pure	PROPN
ejpam-4510	285	3	appl	appl	PROPN
ejpam-4510	285	4	.	.	PROPN
ejpam-4510	285	5	math	math	PROPN
ejpam-4510	285	6	,	,	PUNCT
ejpam-4510	285	7	15	15	NUM
ejpam-4510	285	8	(	(	PUNCT
ejpam-4510	285	9	4	4	NUM
ejpam-4510	285	10	)	)	PUNCT
ejpam-4510	285	11	(	(	PUNCT
ejpam-4510	285	12	2022	2022	NUM
ejpam-4510	285	13	)	)	PUNCT
ejpam-4510	285	14	,	,	PUNCT
ejpam-4510	285	15	1521	1521	NUM
ejpam-4510	285	16	-	-	SYM
ejpam-4510	285	17	1535	1535	NUM
ejpam-4510	285	18	1532	1532	NUM
ejpam-4510	285	19	≥	≥	NOUN
ejpam-4510	285	20	φ+(z	φ+(z	X
ejpam-4510	285	21	∗	∗	NOUN
ejpam-4510	285	22	(	(	PUNCT
ejpam-4510	285	23	z	z	NOUN
ejpam-4510	285	24	∗	∗	NOUN
ejpam-4510	285	25	(	(	PUNCT
ejpam-4510	285	26	(	(	PUNCT
ejpam-4510	285	27	z	z	NOUN
ejpam-4510	285	28	∗	∗	PROPN
ejpam-4510	285	29	y	y	PROPN
ejpam-4510	285	30	)	)	PUNCT
ejpam-4510	285	31	∗	∗	NOUN
ejpam-4510	285	32	x	x	NOUN
ejpam-4510	285	33	)	)	PUNCT
ejpam-4510	285	34	)	)	PUNCT
ejpam-4510	285	35	)	)	PUNCT
ejpam-4510	286	1	≥	≥	X
ejpam-4510	286	2	φ+(z	φ+(z	X
ejpam-4510	286	3	∗	∗	NOUN
ejpam-4510	286	4	(	(	PUNCT
ejpam-4510	286	5	y	y	PROPN
ejpam-4510	286	6	∗	∗	NOUN
ejpam-4510	286	7	x	x	NOUN
ejpam-4510	286	8	)	)	PUNCT
ejpam-4510	286	9	)	)	PUNCT
ejpam-4510	286	10	,	,	PUNCT
ejpam-4510	286	11	that	that	ADV
ejpam-4510	286	12	is	is	ADV
ejpam-4510	286	13	,	,	PUNCT
ejpam-4510	286	14	(	(	PUNCT
ejpam-4510	286	15	z∗y)∗(z∗x	z∗y)∗(z∗x	PROPN
ejpam-4510	286	16	)	)	PUNCT
ejpam-4510	286	17	(	(	PUNCT
ejpam-4510	286	18	z∗(y∗x	z∗(y∗x	NUM
ejpam-4510	286	19	)	)	PUNCT
ejpam-4510	286	20	,	,	PUNCT
ejpam-4510	286	21	z∗(y∗x	z∗(y∗x	NUM
ejpam-4510	286	22	)	)	PUNCT
ejpam-4510	286	23	)	)	PUNCT
ejpam-4510	287	1	∈	∈	PROPN
ejpam-4510	287	2	φ̊(max	φ̊(max	NUM
ejpam-4510	287	3	,	,	PUNCT
ejpam-4510	287	4	min	min	NOUN
ejpam-4510	287	5	)	)	PUNCT
ejpam-4510	287	6	.	.	PUNCT
ejpam-4510	288	1	also	also	ADV
ejpam-4510	288	2	,	,	PUNCT
ejpam-4510	288	3	we	we	PRON
ejpam-4510	288	4	have	have	VERB
ejpam-4510	288	5	φs((z	φs((z	PROPN
ejpam-4510	288	6	∗	∗	NOUN
ejpam-4510	288	7	y	y	NOUN
ejpam-4510	288	8	)	)	PUNCT
ejpam-4510	288	9	∗	∗	NOUN
ejpam-4510	288	10	(	(	PUNCT
ejpam-4510	288	11	z	z	NOUN
ejpam-4510	288	12	∗	∗	NOUN
ejpam-4510	288	13	x	x	NOUN
ejpam-4510	288	14	)	)	PUNCT
ejpam-4510	288	15	)	)	PUNCT
ejpam-4510	289	1	=	=	SYM
ejpam-4510	289	2	φs(z	φs(z	X
ejpam-4510	289	3	∗	∗	NOUN
ejpam-4510	289	4	(	(	PUNCT
ejpam-4510	289	5	(	(	PUNCT
ejpam-4510	289	6	z	z	NOUN
ejpam-4510	289	7	∗	∗	PROPN
ejpam-4510	289	8	y	y	PROPN
ejpam-4510	289	9	)	)	PUNCT
ejpam-4510	289	10	∗	∗	NOUN
ejpam-4510	289	11	x	x	NOUN
ejpam-4510	289	12	)	)	PUNCT
ejpam-4510	289	13	)	)	PUNCT
ejpam-4510	289	14	⊇	⊇	NOUN
ejpam-4510	289	15	φs(z	φs(z	X
ejpam-4510	289	16	∗	∗	NOUN
ejpam-4510	289	17	(	(	PUNCT
ejpam-4510	289	18	z	z	NOUN
ejpam-4510	289	19	∗	∗	NOUN
ejpam-4510	289	20	(	(	PUNCT
ejpam-4510	289	21	(	(	PUNCT
ejpam-4510	289	22	z	z	NOUN
ejpam-4510	289	23	∗	∗	PROPN
ejpam-4510	289	24	y	y	PROPN
ejpam-4510	289	25	)	)	PUNCT
ejpam-4510	289	26	∗	∗	NOUN
ejpam-4510	289	27	x	x	NOUN
ejpam-4510	289	28	)	)	PUNCT
ejpam-4510	289	29	)	)	PUNCT
ejpam-4510	289	30	)	)	PUNCT
ejpam-4510	290	1	⊇	⊇	NOUN
ejpam-4510	290	2	φs(z	φs(z	X
ejpam-4510	290	3	∗	∗	NOUN
ejpam-4510	290	4	(	(	PUNCT
ejpam-4510	290	5	y	y	PROPN
ejpam-4510	290	6	∗	∗	NOUN
ejpam-4510	290	7	x	x	NOUN
ejpam-4510	290	8	)	)	PUNCT
ejpam-4510	290	9	)	)	PUNCT
ejpam-4510	290	10	,	,	PUNCT
ejpam-4510	290	11	and	and	CCONJ
ejpam-4510	290	12	φ̃((z	φ̃((z	NOUN
ejpam-4510	290	13	∗	∗	PROPN
ejpam-4510	290	14	y	y	NOUN
ejpam-4510	290	15	)	)	PUNCT
ejpam-4510	290	16	∗	∗	NOUN
ejpam-4510	290	17	(	(	PUNCT
ejpam-4510	290	18	z	z	NOUN
ejpam-4510	290	19	∗	∗	NOUN
ejpam-4510	290	20	x	x	NOUN
ejpam-4510	290	21	)	)	PUNCT
ejpam-4510	290	22	)	)	PUNCT
ejpam-4510	291	1	=	=	SYM
ejpam-4510	292	1	φ̃(z	φ̃(z	PROPN
ejpam-4510	292	2	∗	∗	NOUN
ejpam-4510	292	3	(	(	PUNCT
ejpam-4510	292	4	(	(	PUNCT
ejpam-4510	292	5	z	z	NOUN
ejpam-4510	292	6	∗	∗	PROPN
ejpam-4510	292	7	y	y	PROPN
ejpam-4510	292	8	)	)	PUNCT
ejpam-4510	292	9	∗	∗	NOUN
ejpam-4510	292	10	x	x	NOUN
ejpam-4510	292	11	)	)	PUNCT
ejpam-4510	292	12	)	)	PUNCT
ejpam-4510	292	13	⪰	⪰	VERB
ejpam-4510	292	14	φ̃(z	φ̃(z	DET
ejpam-4510	292	15	∗	∗	NOUN
ejpam-4510	292	16	(	(	PUNCT
ejpam-4510	292	17	z	z	NOUN
ejpam-4510	292	18	∗	∗	NOUN
ejpam-4510	292	19	(	(	PUNCT
ejpam-4510	292	20	(	(	PUNCT
ejpam-4510	292	21	z	z	NOUN
ejpam-4510	292	22	∗	∗	PROPN
ejpam-4510	292	23	y	y	PROPN
ejpam-4510	292	24	)	)	PUNCT
ejpam-4510	292	25	∗	∗	NOUN
ejpam-4510	292	26	x	x	NOUN
ejpam-4510	292	27	)	)	PUNCT
ejpam-4510	292	28	)	)	PUNCT
ejpam-4510	292	29	)	)	PUNCT
ejpam-4510	292	30	⪰	⪰	VERB
ejpam-4510	292	31	φ̃(z	φ̃(z	PROPN
ejpam-4510	292	32	∗	∗	NOUN
ejpam-4510	292	33	(	(	PUNCT
ejpam-4510	292	34	y	y	PROPN
ejpam-4510	292	35	∗	∗	NOUN
ejpam-4510	292	36	x	x	NOUN
ejpam-4510	292	37	)	)	PUNCT
ejpam-4510	292	38	)	)	PUNCT
ejpam-4510	292	39	.	.	PUNCT
ejpam-4510	293	1	conversely	conversely	ADV
ejpam-4510	293	2	,	,	PUNCT
ejpam-4510	293	3	suppose	suppose	VERB
ejpam-4510	293	4	that	that	SCONJ
ejpam-4510	293	5	(	(	PUNCT
ejpam-4510	293	6	30	30	NUM
ejpam-4510	293	7	)	)	PUNCT
ejpam-4510	293	8	is	be	AUX
ejpam-4510	293	9	valid	valid	ADJ
ejpam-4510	293	10	.	.	PUNCT
ejpam-4510	294	1	if	if	SCONJ
ejpam-4510	294	2	we	we	PRON
ejpam-4510	294	3	put	put	VERB
ejpam-4510	294	4	y	y	NOUN
ejpam-4510	294	5	:	:	PUNCT
ejpam-4510	294	6	=	=	SYM
ejpam-4510	294	7	z	z	X
ejpam-4510	294	8	in	in	ADP
ejpam-4510	294	9	(	(	PUNCT
ejpam-4510	294	10	30	30	NUM
ejpam-4510	294	11	)	)	PUNCT
ejpam-4510	294	12	and	and	CCONJ
ejpam-4510	294	13	use	use	NOUN
ejpam-4510	294	14	(	(	PUNCT
ejpam-4510	294	15	be1	be1	NOUN
ejpam-4510	294	16	)	)	PUNCT
ejpam-4510	294	17	and	and	CCONJ
ejpam-4510	294	18	(	(	PUNCT
ejpam-4510	294	19	be3	be3	PROPN
ejpam-4510	294	20	)	)	PUNCT
ejpam-4510	294	21	,	,	PUNCT
ejpam-4510	294	22	then	then	ADV
ejpam-4510	294	23	z∗x	z∗x	NUM
ejpam-4510	294	24	(	(	PUNCT
ejpam-4510	294	25	z∗(z∗x	z∗(z∗x	NOUN
ejpam-4510	294	26	)	)	PUNCT
ejpam-4510	294	27	,	,	PUNCT
ejpam-4510	294	28	z∗(z∗x	z∗(z∗x	NOUN
ejpam-4510	294	29	)	)	PUNCT
ejpam-4510	294	30	)	)	PUNCT
ejpam-4510	295	1	=	=	SYM
ejpam-4510	295	2	1∗(z∗x	1∗(z∗x	PROPN
ejpam-4510	295	3	)	)	PUNCT
ejpam-4510	295	4	(	(	PUNCT
ejpam-4510	295	5	z∗(z∗x	z∗(z∗x	NOUN
ejpam-4510	295	6	)	)	PUNCT
ejpam-4510	295	7	,	,	PUNCT
ejpam-4510	295	8	z∗(z∗x	z∗(z∗x	NOUN
ejpam-4510	295	9	)	)	PUNCT
ejpam-4510	295	10	)	)	PUNCT
ejpam-4510	296	1	=	=	SYM
ejpam-4510	296	2	(	(	PUNCT
ejpam-4510	296	3	z∗z)∗(z∗x	z∗z)∗(z∗x	PROPN
ejpam-4510	296	4	)	)	PUNCT
ejpam-4510	296	5	(	(	PUNCT
ejpam-4510	296	6	z∗(z∗x	z∗(z∗x	NOUN
ejpam-4510	296	7	)	)	PUNCT
ejpam-4510	296	8	,	,	PUNCT
ejpam-4510	296	9	z∗(z∗x	z∗(z∗x	NOUN
ejpam-4510	296	10	)	)	PUNCT
ejpam-4510	296	11	)	)	PUNCT
ejpam-4510	297	1	∈	∈	PROPN
ejpam-4510	297	2	φ̊(max	φ̊(max	NUM
ejpam-4510	297	3	,	,	PUNCT
ejpam-4510	297	4	min	min	NOUN
ejpam-4510	297	5	)	)	PUNCT
ejpam-4510	297	6	,	,	PUNCT
ejpam-4510	297	7	φs(z	φs(z	X
ejpam-4510	297	8	∗	∗	NOUN
ejpam-4510	297	9	x	x	NOUN
ejpam-4510	297	10	)	)	PUNCT
ejpam-4510	297	11	=	=	SYM
ejpam-4510	297	12	φs(1	φs(1	PROPN
ejpam-4510	297	13	∗	∗	NOUN
ejpam-4510	297	14	(	(	PUNCT
ejpam-4510	297	15	z	z	NOUN
ejpam-4510	297	16	∗	∗	NOUN
ejpam-4510	297	17	x	x	NOUN
ejpam-4510	297	18	)	)	PUNCT
ejpam-4510	297	19	)	)	PUNCT
ejpam-4510	297	20	=	=	SYM
ejpam-4510	298	1	φs((z	φs((z	PROPN
ejpam-4510	298	2	∗	∗	X
ejpam-4510	298	3	z	z	NOUN
ejpam-4510	298	4	)	)	PUNCT
ejpam-4510	298	5	∗	∗	NOUN
ejpam-4510	298	6	(	(	PUNCT
ejpam-4510	298	7	z	z	NOUN
ejpam-4510	298	8	∗	∗	NOUN
ejpam-4510	298	9	x	x	NOUN
ejpam-4510	298	10	)	)	PUNCT
ejpam-4510	298	11	)	)	PUNCT
ejpam-4510	298	12	⊇	⊇	NOUN
ejpam-4510	298	13	φs(z	φs(z	X
ejpam-4510	298	14	∗	∗	NOUN
ejpam-4510	298	15	(	(	PUNCT
ejpam-4510	298	16	z	z	NOUN
ejpam-4510	298	17	∗	∗	NOUN
ejpam-4510	298	18	x	x	NOUN
ejpam-4510	298	19	)	)	PUNCT
ejpam-4510	298	20	)	)	PUNCT
ejpam-4510	298	21	and	and	CCONJ
ejpam-4510	298	22	φ̃(z	φ̃(z	DET
ejpam-4510	298	23	∗	∗	NOUN
ejpam-4510	298	24	x	x	NOUN
ejpam-4510	298	25	)	)	PUNCT
ejpam-4510	298	26	=	=	PUNCT
ejpam-4510	298	27	φ̃(1	φ̃(1	NOUN
ejpam-4510	298	28	∗	∗	NOUN
ejpam-4510	298	29	(	(	PUNCT
ejpam-4510	298	30	z	z	NOUN
ejpam-4510	298	31	∗	∗	NOUN
ejpam-4510	298	32	x	x	NOUN
ejpam-4510	298	33	)	)	PUNCT
ejpam-4510	298	34	)	)	PUNCT
ejpam-4510	299	1	=	=	SYM
ejpam-4510	299	2	φ̃((z	φ̃((z	NOUN
ejpam-4510	299	3	∗	∗	NOUN
ejpam-4510	299	4	z	z	NOUN
ejpam-4510	299	5	)	)	PUNCT
ejpam-4510	299	6	∗	∗	NOUN
ejpam-4510	299	7	(	(	PUNCT
ejpam-4510	299	8	z	z	NOUN
ejpam-4510	299	9	∗	∗	NOUN
ejpam-4510	299	10	x	x	NOUN
ejpam-4510	299	11	)	)	PUNCT
ejpam-4510	299	12	)	)	PUNCT
ejpam-4510	299	13	⪰	⪰	VERB
ejpam-4510	299	14	φ̃(z	φ̃(z	DET
ejpam-4510	299	15	∗	∗	NOUN
ejpam-4510	299	16	(	(	PUNCT
ejpam-4510	299	17	z	z	NOUN
ejpam-4510	299	18	∗	∗	NOUN
ejpam-4510	299	19	x	x	NOUN
ejpam-4510	299	20	)	)	PUNCT
ejpam-4510	299	21	)	)	PUNCT
ejpam-4510	299	22	.	.	PUNCT
ejpam-4510	300	1	this	this	PRON
ejpam-4510	300	2	proves	prove	VERB
ejpam-4510	300	3	(	(	PUNCT
ejpam-4510	300	4	29	29	NUM
ejpam-4510	300	5	)	)	PUNCT
ejpam-4510	300	6	.	.	PUNCT
ejpam-4510	301	1	proposition	proposition	NOUN
ejpam-4510	301	2	5	5	NUM
ejpam-4510	301	3	.	.	PUNCT
ejpam-4510	302	1	let	let	VERB
ejpam-4510	302	2	(	(	PUNCT
ejpam-4510	302	3	x	x	NOUN
ejpam-4510	302	4	,	,	PUNCT
ejpam-4510	302	5	u	u	NOUN
ejpam-4510	302	6	)	)	PUNCT
ejpam-4510	302	7	be	be	VERB
ejpam-4510	302	8	a	a	DET
ejpam-4510	302	9	dokdo	dokdo	NOUN
ejpam-4510	302	10	be	be	NOUN
ejpam-4510	302	11	-	-	PUNCT
ejpam-4510	302	12	universe	universe	NOUN
ejpam-4510	302	13	in	in	ADP
ejpam-4510	302	14	which	which	PRON
ejpam-4510	302	15	x	x	PRON
ejpam-4510	302	16	is	be	AUX
ejpam-4510	302	17	a	a	DET
ejpam-4510	302	18	self	self	NOUN
ejpam-4510	302	19	-	-	PUNCT
ejpam-4510	302	20	distributive	distributive	ADJ
ejpam-4510	302	21	be	be	NOUN
ejpam-4510	302	22	-	-	PUNCT
ejpam-4510	302	23	algebra	algebra	NOUN
ejpam-4510	302	24	.	.	PUNCT
ejpam-4510	303	1	then	then	ADV
ejpam-4510	303	2	every	every	DET
ejpam-4510	303	3	dokdo	dokdo	NOUN
ejpam-4510	303	4	be	be	AUX
ejpam-4510	303	5	-	-	PUNCT
ejpam-4510	303	6	filter	filter	NOUN
ejpam-4510	303	7	dokφ	dokφ	NOUN
ejpam-4510	303	8	:	:	PUNCT
ejpam-4510	303	9	=	=	SYM
ejpam-4510	303	10	(	(	PUNCT
ejpam-4510	303	11	φ̊	φ̊	PROPN
ejpam-4510	303	12	,	,	PUNCT
ejpam-4510	303	13	φs	φs	ADV
ejpam-4510	303	14	,	,	PUNCT
ejpam-4510	303	15	φ̃	φ̃	PROPN
ejpam-4510	303	16	)	)	PUNCT
ejpam-4510	303	17	of	of	ADP
ejpam-4510	303	18	(	(	PUNCT
ejpam-4510	303	19	x	x	NOUN
ejpam-4510	303	20	,	,	PUNCT
ejpam-4510	303	21	u	u	NOUN
ejpam-4510	303	22	)	)	PUNCT
ejpam-4510	303	23	satisfies	satisfie	NOUN
ejpam-4510	303	24	:	:	PUNCT
ejpam-4510	303	25	(	(	PUNCT
ejpam-4510	303	26	∀x	∀x	X
ejpam-4510	303	27	,	,	PUNCT
ejpam-4510	303	28	y	y	PROPN
ejpam-4510	303	29	,	,	PUNCT
ejpam-4510	303	30	z	z	NOUN
ejpam-4510	303	31	∈	∈	PROPN
ejpam-4510	303	32	x	x	X
ejpam-4510	303	33	)	)	PUNCT
ejpam-4510	303	34			PROPN
ejpam-4510	303	35	y∗x	y∗x	NUM
ejpam-4510	303	36	(	(	PUNCT
ejpam-4510	303	37	y∗z	y∗z	PROPN
ejpam-4510	303	38	,	,	PUNCT
ejpam-4510	303	39	z∗x	z∗x	NUM
ejpam-4510	303	40	)	)	PUNCT
ejpam-4510	303	41	∈	∈	PROPN
ejpam-4510	303	42	φ̊(max	φ̊(max	NUM
ejpam-4510	303	43	,	,	PUNCT
ejpam-4510	303	44	min	min	NOUN
ejpam-4510	303	45	)	)	PUNCT
ejpam-4510	303	46	,	,	PUNCT
ejpam-4510	303	47	φs(y	φs(y	NOUN
ejpam-4510	303	48	∗	∗	NOUN
ejpam-4510	303	49	x	x	NOUN
ejpam-4510	303	50	)	)	PUNCT
ejpam-4510	303	51	⊇	⊇	PROPN
ejpam-4510	303	52	φs(y	φs(y	X
ejpam-4510	303	53	∗	∗	X
ejpam-4510	303	54	z	z	NOUN
ejpam-4510	303	55	)	)	PUNCT
ejpam-4510	303	56	∩	∩	NOUN
ejpam-4510	303	57	φs(z	φs(z	X
ejpam-4510	303	58	∗	∗	NOUN
ejpam-4510	303	59	x	x	NOUN
ejpam-4510	303	60	)	)	PUNCT
ejpam-4510	303	61	,	,	PUNCT
ejpam-4510	303	62	φ̃(y	φ̃(y	ADJ
ejpam-4510	303	63	∗	∗	NOUN
ejpam-4510	303	64	x	x	NOUN
ejpam-4510	303	65	)	)	PUNCT
ejpam-4510	303	66	⪰	⪰	NOUN
ejpam-4510	303	67	rmin{φ̃(y	rmin{φ̃(y	ADP
ejpam-4510	303	68	∗	∗	NOUN
ejpam-4510	303	69	z	z	NOUN
ejpam-4510	303	70	)	)	PUNCT
ejpam-4510	303	71	,	,	PUNCT
ejpam-4510	303	72	φ̃(z	φ̃(z	PROPN
ejpam-4510	303	73	∗	∗	NOUN
ejpam-4510	303	74	x	x	NOUN
ejpam-4510	303	75	)	)	PUNCT
ejpam-4510	303	76	}	}	PUNCT
ejpam-4510	303	77			PROPN
ejpam-4510	303	78	.	.	PUNCT
ejpam-4510	304	1	(	(	PUNCT
ejpam-4510	304	2	31	31	NUM
ejpam-4510	304	3	)	)	PUNCT
ejpam-4510	304	4	proof	proof	NOUN
ejpam-4510	304	5	.	.	PUNCT
ejpam-4510	305	1	using	use	VERB
ejpam-4510	305	2	(	(	PUNCT
ejpam-4510	305	3	be1	be1	NOUN
ejpam-4510	305	4	)	)	PUNCT
ejpam-4510	305	5	,	,	PUNCT
ejpam-4510	305	6	(	(	PUNCT
ejpam-4510	305	7	be2	be2	PROPN
ejpam-4510	305	8	)	)	PUNCT
ejpam-4510	305	9	,	,	PUNCT
ejpam-4510	305	10	(	(	PUNCT
ejpam-4510	305	11	be4	be4	NOUN
ejpam-4510	305	12	)	)	PUNCT
ejpam-4510	305	13	and	and	CCONJ
ejpam-4510	305	14	(	(	PUNCT
ejpam-4510	305	15	4	4	NUM
ejpam-4510	305	16	)	)	PUNCT
ejpam-4510	305	17	,	,	PUNCT
ejpam-4510	305	18	we	we	PRON
ejpam-4510	305	19	have	have	VERB
ejpam-4510	305	20	y	y	PROPN
ejpam-4510	305	21	∗	∗	NOUN
ejpam-4510	305	22	z	z	NOUN
ejpam-4510	305	23	≤	≤	NUM
ejpam-4510	305	24	(	(	PUNCT
ejpam-4510	305	25	z	z	NOUN
ejpam-4510	305	26	∗	∗	X
ejpam-4510	305	27	x	x	NOUN
ejpam-4510	305	28	)	)	PUNCT
ejpam-4510	305	29	∗	∗	NOUN
ejpam-4510	305	30	(	(	PUNCT
ejpam-4510	305	31	y	y	PROPN
ejpam-4510	305	32	∗	∗	X
ejpam-4510	305	33	x	x	NOUN
ejpam-4510	305	34	)	)	PUNCT
ejpam-4510	305	35	for	for	ADP
ejpam-4510	305	36	all	all	DET
ejpam-4510	305	37	x	x	NOUN
ejpam-4510	305	38	,	,	PUNCT
ejpam-4510	305	39	y	y	PROPN
ejpam-4510	305	40	,	,	PUNCT
ejpam-4510	305	41	z	z	NOUN
ejpam-4510	305	42	∈	∈	NOUN
ejpam-4510	305	43	x.	x.	NOUN
ejpam-4510	305	44	hence	hence	ADV
ejpam-4510	305	45	(	(	PUNCT
ejpam-4510	305	46	31	31	NUM
ejpam-4510	305	47	)	)	PUNCT
ejpam-4510	305	48	is	be	AUX
ejpam-4510	305	49	derived	derive	VERB
ejpam-4510	305	50	from	from	ADP
ejpam-4510	305	51	(	(	PUNCT
ejpam-4510	305	52	27	27	NUM
ejpam-4510	305	53	)	)	PUNCT
ejpam-4510	305	54	.	.	PUNCT
ejpam-4510	306	1	theorem	theorem	ADJ
ejpam-4510	306	2	5	5	NUM
ejpam-4510	306	3	.	.	PUNCT
ejpam-4510	307	1	if	if	SCONJ
ejpam-4510	307	2	a	a	DET
ejpam-4510	307	3	dokdo	dokdo	NOUN
ejpam-4510	307	4	structure	structure	NOUN
ejpam-4510	307	5	dokφ	dokφ	NOUN
ejpam-4510	307	6	:	:	PUNCT
ejpam-4510	307	7	=	=	SYM
ejpam-4510	307	8	(	(	PUNCT
ejpam-4510	307	9	φ̊	φ̊	PROPN
ejpam-4510	307	10	,	,	PUNCT
ejpam-4510	307	11	φs	φs	ADV
ejpam-4510	307	12	,	,	PUNCT
ejpam-4510	307	13	φ̃	φ̃	PROPN
ejpam-4510	307	14	)	)	PUNCT
ejpam-4510	307	15	in	in	ADP
ejpam-4510	307	16	(	(	PUNCT
ejpam-4510	307	17	x	x	NOUN
ejpam-4510	307	18	,	,	PUNCT
ejpam-4510	307	19	u	u	NOUN
ejpam-4510	307	20	)	)	PUNCT
ejpam-4510	307	21	satisfies	satisfie	NOUN
ejpam-4510	307	22	(	(	PUNCT
ejpam-4510	307	23	27	27	NUM
ejpam-4510	307	24	)	)	PUNCT
ejpam-4510	307	25	,	,	PUNCT
ejpam-4510	307	26	then	then	ADV
ejpam-4510	307	27	it	it	PRON
ejpam-4510	307	28	is	be	AUX
ejpam-4510	307	29	a	a	DET
ejpam-4510	307	30	dokdo	dokdo	NOUN
ejpam-4510	307	31	be	be	NOUN
ejpam-4510	307	32	-	-	PUNCT
ejpam-4510	307	33	filter	filter	NOUN
ejpam-4510	307	34	of	of	ADP
ejpam-4510	307	35	(	(	PUNCT
ejpam-4510	307	36	x	x	NOUN
ejpam-4510	307	37	,	,	PUNCT
ejpam-4510	307	38	u	u	NOUN
ejpam-4510	307	39	)	)	PUNCT
ejpam-4510	307	40	.	.	PUNCT
ejpam-4510	308	1	proof	proof	NOUN
ejpam-4510	308	2	.	.	PUNCT
ejpam-4510	309	1	since	since	SCONJ
ejpam-4510	309	2	x	x	PROPN
ejpam-4510	309	3	≤	≤	NUM
ejpam-4510	309	4	x	x	PUNCT
ejpam-4510	309	5	∗	∗	NOUN
ejpam-4510	309	6	1	1	NUM
ejpam-4510	309	7	for	for	ADP
ejpam-4510	309	8	all	all	DET
ejpam-4510	309	9	x	x	SYM
ejpam-4510	309	10	∈	∈	PROPN
ejpam-4510	309	11	x	x	NOUN
ejpam-4510	309	12	,	,	PUNCT
ejpam-4510	309	13	we	we	PRON
ejpam-4510	309	14	have	have	VERB
ejpam-4510	309	15	1	1	NUM
ejpam-4510	309	16	(	(	PUNCT
ejpam-4510	309	17	x	x	NOUN
ejpam-4510	309	18	,	,	PUNCT
ejpam-4510	309	19	x	x	NOUN
ejpam-4510	309	20	)	)	PUNCT
ejpam-4510	309	21	∈	∈	PROPN
ejpam-4510	309	22	φ̊(max	φ̊(max	NUM
ejpam-4510	309	23	,	,	PUNCT
ejpam-4510	309	24	min	min	NOUN
ejpam-4510	309	25	)	)	PUNCT
ejpam-4510	309	26	,	,	PUNCT
ejpam-4510	309	27	φs(1	φs(1	PROPN
ejpam-4510	309	28	)	)	PUNCT
ejpam-4510	309	29	⊇	⊇	NOUN
ejpam-4510	309	30	φs(x	φs(x	PRON
ejpam-4510	309	31	)	)	PUNCT
ejpam-4510	309	32	,	,	PUNCT
ejpam-4510	309	33	and	and	CCONJ
ejpam-4510	309	34	φ̃(1	φ̃(1	NOUN
ejpam-4510	309	35	)	)	PUNCT
ejpam-4510	309	36	⪰	⪰	NOUN
ejpam-4510	309	37	φ̃(x	φ̃(x	PROPN
ejpam-4510	309	38	)	)	PUNCT
ejpam-4510	309	39	by	by	ADP
ejpam-4510	309	40	(	(	PUNCT
ejpam-4510	309	41	27	27	NUM
ejpam-4510	309	42	)	)	PUNCT
ejpam-4510	309	43	.	.	PUNCT
ejpam-4510	310	1	since	since	SCONJ
ejpam-4510	310	2	x	x	PROPN
ejpam-4510	310	3	∗	∗	VERB
ejpam-4510	310	4	y	y	NOUN
ejpam-4510	310	5	≤	≤	NUM
ejpam-4510	310	6	x	x	PUNCT
ejpam-4510	310	7	∗	∗	NOUN
ejpam-4510	310	8	y	y	PROPN
ejpam-4510	310	9	for	for	ADP
ejpam-4510	310	10	all	all	DET
ejpam-4510	310	11	x	x	NOUN
ejpam-4510	310	12	,	,	PUNCT
ejpam-4510	310	13	y	y	PROPN
ejpam-4510	310	14	∈	∈	PROPN
ejpam-4510	310	15	x	x	AUX
ejpam-4510	310	16	,	,	PUNCT
ejpam-4510	310	17	it	it	PRON
ejpam-4510	310	18	follows	follow	VERB
ejpam-4510	310	19	from	from	ADP
ejpam-4510	310	20	(	(	PUNCT
ejpam-4510	310	21	27	27	NUM
ejpam-4510	310	22	)	)	PUNCT
ejpam-4510	311	1	that	that	SCONJ
ejpam-4510	311	2	y	y	PROPN
ejpam-4510	311	3	(	(	PUNCT
ejpam-4510	311	4	x	x	X
ejpam-4510	311	5	,	,	PUNCT
ejpam-4510	311	6	x∗y	x∗y	NUM
ejpam-4510	311	7	)	)	PUNCT
ejpam-4510	311	8	∈	∈	PROPN
ejpam-4510	311	9	φ̊(max	φ̊(max	NUM
ejpam-4510	311	10	,	,	PUNCT
ejpam-4510	311	11	min	min	NOUN
ejpam-4510	311	12	)	)	PUNCT
ejpam-4510	311	13	,	,	PUNCT
ejpam-4510	311	14	φs(y	φs(y	NUM
ejpam-4510	311	15	)	)	PUNCT
ejpam-4510	311	16	⊇	⊇	NOUN
ejpam-4510	311	17	φs(x	φs(x	NOUN
ejpam-4510	311	18	)	)	PUNCT
ejpam-4510	311	19	∩	∩	NOUN
ejpam-4510	311	20	φs(x	φs(x	PART
ejpam-4510	311	21	∗	∗	PROPN
ejpam-4510	311	22	y	y	PROPN
ejpam-4510	311	23	)	)	PUNCT
ejpam-4510	311	24	,	,	PUNCT
ejpam-4510	311	25	and	and	CCONJ
ejpam-4510	311	26	φ̃(y	φ̃(y	NOUN
ejpam-4510	311	27	)	)	PUNCT
ejpam-4510	311	28	⪰	⪰	NOUN
ejpam-4510	311	29	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	311	30	)	)	PUNCT
ejpam-4510	311	31	,	,	PUNCT
ejpam-4510	311	32	φ̃(x	φ̃(x	PROPN
ejpam-4510	311	33	∗	∗	PROPN
ejpam-4510	311	34	y	y	PROPN
ejpam-4510	311	35	)	)	PUNCT
ejpam-4510	311	36	}	}	PUNCT
ejpam-4510	311	37	.	.	PUNCT
ejpam-4510	312	1	so	so	ADV
ejpam-4510	312	2	,	,	PUNCT
ejpam-4510	312	3	dokφ	dokφ	NOUN
ejpam-4510	312	4	:	:	PUNCT
ejpam-4510	312	5	=	=	SYM
ejpam-4510	312	6	(	(	PUNCT
ejpam-4510	312	7	φ̊	φ̊	PROPN
ejpam-4510	312	8	,	,	PUNCT
ejpam-4510	312	9	φs	φs	ADV
ejpam-4510	312	10	,	,	PUNCT
ejpam-4510	312	11	φ̃	φ̃	PROPN
ejpam-4510	312	12	)	)	PUNCT
ejpam-4510	312	13	is	be	AUX
ejpam-4510	312	14	a	a	DET
ejpam-4510	312	15	dokdo	dokdo	NOUN
ejpam-4510	312	16	be	be	NOUN
ejpam-4510	312	17	-	-	PUNCT
ejpam-4510	312	18	filter	filter	NOUN
ejpam-4510	312	19	of	of	ADP
ejpam-4510	312	20	(	(	PUNCT
ejpam-4510	312	21	x	x	NOUN
ejpam-4510	312	22	,	,	PUNCT
ejpam-4510	312	23	u	u	NOUN
ejpam-4510	312	24	)	)	PUNCT
ejpam-4510	312	25	.	.	PUNCT
ejpam-4510	313	1	corollary	corollary	ADJ
ejpam-4510	313	2	4	4	NUM
ejpam-4510	313	3	.	.	PUNCT
ejpam-4510	314	1	if	if	SCONJ
ejpam-4510	314	2	a	a	DET
ejpam-4510	314	3	dokdo	dokdo	NOUN
ejpam-4510	314	4	structure	structure	NOUN
ejpam-4510	314	5	dokφ	dokφ	NOUN
ejpam-4510	314	6	:	:	PUNCT
ejpam-4510	314	7	=	=	SYM
ejpam-4510	314	8	(	(	PUNCT
ejpam-4510	314	9	φ̊	φ̊	PROPN
ejpam-4510	314	10	,	,	PUNCT
ejpam-4510	314	11	φs	φs	ADV
ejpam-4510	314	12	,	,	PUNCT
ejpam-4510	314	13	φ̃	φ̃	PROPN
ejpam-4510	314	14	)	)	PUNCT
ejpam-4510	314	15	in	in	ADP
ejpam-4510	314	16	(	(	PUNCT
ejpam-4510	314	17	x	x	NOUN
ejpam-4510	314	18	,	,	PUNCT
ejpam-4510	314	19	u	u	NOUN
ejpam-4510	314	20	)	)	PUNCT
ejpam-4510	314	21	satisfies	satisfie	NOUN
ejpam-4510	314	22	(	(	PUNCT
ejpam-4510	314	23	27	27	NUM
ejpam-4510	314	24	)	)	PUNCT
ejpam-4510	314	25	,	,	PUNCT
ejpam-4510	314	26	then	then	ADV
ejpam-4510	314	27	it	it	PRON
ejpam-4510	314	28	is	be	AUX
ejpam-4510	314	29	a	a	DET
ejpam-4510	314	30	(	(	PUNCT
ejpam-4510	314	31	weak	weak	ADJ
ejpam-4510	314	32	)	)	PUNCT
ejpam-4510	314	33	dokdo	dokdo	NOUN
ejpam-4510	314	34	be	be	NOUN
ejpam-4510	314	35	-	-	PUNCT
ejpam-4510	314	36	subalgebra	subalgebra	NOUN
ejpam-4510	314	37	of	of	ADP
ejpam-4510	314	38	(	(	PUNCT
ejpam-4510	314	39	x	x	NOUN
ejpam-4510	314	40	,	,	PUNCT
ejpam-4510	314	41	u	u	NOUN
ejpam-4510	314	42	)	)	PUNCT
ejpam-4510	314	43	.	.	PUNCT
ejpam-4510	315	1	y.	y.	PROPN
ejpam-4510	315	2	b.	b.	PROPN
ejpam-4510	315	3	jun	jun	PROPN
ejpam-4510	315	4	,	,	PUNCT
ejpam-4510	315	5	s.	s.	PROPN
ejpam-4510	315	6	s.	s.	PROPN
ejpam-4510	315	7	ahn	ahn	PROPN
ejpam-4510	315	8	and	and	CCONJ
ejpam-4510	315	9	e.	e.	PROPN
ejpam-4510	315	10	h.	h.	PROPN
ejpam-4510	315	11	roh	roh	PROPN
ejpam-4510	315	12	/	/	SYM
ejpam-4510	315	13	eur	eur	PROPN
ejpam-4510	315	14	.	.	PUNCT
ejpam-4510	316	1	j.	j.	PROPN
ejpam-4510	316	2	pure	pure	PROPN
ejpam-4510	316	3	appl	appl	PROPN
ejpam-4510	316	4	.	.	PROPN
ejpam-4510	316	5	math	math	PROPN
ejpam-4510	316	6	,	,	PUNCT
ejpam-4510	316	7	15	15	NUM
ejpam-4510	316	8	(	(	PUNCT
ejpam-4510	316	9	4	4	NUM
ejpam-4510	316	10	)	)	PUNCT
ejpam-4510	316	11	(	(	PUNCT
ejpam-4510	316	12	2022	2022	NUM
ejpam-4510	316	13	)	)	PUNCT
ejpam-4510	316	14	,	,	PUNCT
ejpam-4510	316	15	1521	1521	NUM
ejpam-4510	316	16	-	-	SYM
ejpam-4510	316	17	1535	1535	NUM
ejpam-4510	316	18	1533	1533	NUM
ejpam-4510	316	19	theorem	theorem	NOUN
ejpam-4510	316	20	6	6	NUM
ejpam-4510	316	21	.	.	PUNCT
ejpam-4510	317	1	a	a	DET
ejpam-4510	317	2	dokdo	dokdo	ADJ
ejpam-4510	317	3	structure	structure	NOUN
ejpam-4510	317	4	dokφ	dokφ	NOUN
ejpam-4510	317	5	:	:	PUNCT
ejpam-4510	317	6	=	=	SYM
ejpam-4510	317	7	(	(	PUNCT
ejpam-4510	317	8	φ̊	φ̊	PROPN
ejpam-4510	317	9	,	,	PUNCT
ejpam-4510	317	10	φs	φs	ADV
ejpam-4510	317	11	,	,	PUNCT
ejpam-4510	317	12	φ̃	φ̃	PROPN
ejpam-4510	317	13	)	)	PUNCT
ejpam-4510	317	14	in	in	ADP
ejpam-4510	317	15	(	(	PUNCT
ejpam-4510	317	16	x	x	NOUN
ejpam-4510	317	17	,	,	PUNCT
ejpam-4510	317	18	u	u	NOUN
ejpam-4510	317	19	)	)	PUNCT
ejpam-4510	317	20	is	be	AUX
ejpam-4510	317	21	a	a	DET
ejpam-4510	317	22	dokdo	dokdo	NOUN
ejpam-4510	317	23	be	be	NOUN
ejpam-4510	317	24	-	-	PUNCT
ejpam-4510	317	25	filter	filter	NOUN
ejpam-4510	317	26	of	of	ADP
ejpam-4510	317	27	(	(	PUNCT
ejpam-4510	317	28	x	x	NOUN
ejpam-4510	317	29	,	,	PUNCT
ejpam-4510	317	30	u	u	NOUN
ejpam-4510	317	31	)	)	PUNCT
ejpam-4510	317	32	if	if	SCONJ
ejpam-4510	318	1	and	and	CCONJ
ejpam-4510	318	2	only	only	ADV
ejpam-4510	318	3	if	if	SCONJ
ejpam-4510	318	4	it	it	PRON
ejpam-4510	318	5	satisfies	satisfy	VERB
ejpam-4510	318	6	(	(	PUNCT
ejpam-4510	318	7	24	24	NUM
ejpam-4510	318	8	)	)	PUNCT
ejpam-4510	318	9	and	and	CCONJ
ejpam-4510	318	10	(	(	PUNCT
ejpam-4510	318	11	∀x	∀x	NUM
ejpam-4510	318	12	,	,	PUNCT
ejpam-4510	318	13	y	y	PROPN
ejpam-4510	318	14	,	,	PUNCT
ejpam-4510	318	15	z	z	NOUN
ejpam-4510	318	16	∈	∈	PROPN
ejpam-4510	318	17	x	x	X
ejpam-4510	318	18	)	)	PUNCT
ejpam-4510	318	19			PROPN
ejpam-4510	318	20	x∗z	x∗z	PROPN
ejpam-4510	318	21	(	(	PUNCT
ejpam-4510	318	22	x∗(y∗z	x∗(y∗z	PROPN
ejpam-4510	318	23	)	)	PUNCT
ejpam-4510	318	24	,	,	PUNCT
ejpam-4510	318	25	y	y	X
ejpam-4510	318	26	)	)	PUNCT
ejpam-4510	318	27	∈	∈	PROPN
ejpam-4510	319	1	φ̊(max	φ̊(max	NUM
ejpam-4510	319	2	,	,	PUNCT
ejpam-4510	319	3	min	min	NOUN
ejpam-4510	319	4	)	)	PUNCT
ejpam-4510	319	5	,	,	PUNCT
ejpam-4510	319	6	φs(x	φs(x	PUNCT
ejpam-4510	319	7	∗	∗	PROPN
ejpam-4510	319	8	z	z	NOUN
ejpam-4510	319	9	)	)	PUNCT
ejpam-4510	319	10	⊇	⊇	NOUN
ejpam-4510	319	11	φs(x	φs(x	PUNCT
ejpam-4510	319	12	∗	∗	NOUN
ejpam-4510	319	13	(	(	PUNCT
ejpam-4510	319	14	y	y	PROPN
ejpam-4510	319	15	∗	∗	PROPN
ejpam-4510	319	16	z	z	NOUN
ejpam-4510	319	17	)	)	PUNCT
ejpam-4510	319	18	)	)	PUNCT
ejpam-4510	319	19	∩	∩	NOUN
ejpam-4510	319	20	φs(y	φs(y	NUM
ejpam-4510	319	21	)	)	PUNCT
ejpam-4510	319	22	,	,	PUNCT
ejpam-4510	319	23	φ̃(x	φ̃(x	PROPN
ejpam-4510	319	24	∗	∗	NOUN
ejpam-4510	319	25	z	z	NOUN
ejpam-4510	319	26	)	)	PUNCT
ejpam-4510	319	27	⪰	⪰	NOUN
ejpam-4510	319	28	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	319	29	∗	∗	NOUN
ejpam-4510	319	30	(	(	PUNCT
ejpam-4510	319	31	y	y	PROPN
ejpam-4510	319	32	∗	∗	PROPN
ejpam-4510	319	33	z	z	PROPN
ejpam-4510	319	34	)	)	PUNCT
ejpam-4510	319	35	)	)	PUNCT
ejpam-4510	319	36	,	,	PUNCT
ejpam-4510	319	37	φ̃(y	φ̃(y	NOUN
ejpam-4510	319	38	)	)	PUNCT
ejpam-4510	319	39	}	}	PUNCT
ejpam-4510	319	40			PROPN
ejpam-4510	319	41	.	.	PUNCT
ejpam-4510	320	1	(	(	PUNCT
ejpam-4510	320	2	32	32	NUM
ejpam-4510	320	3	)	)	PUNCT
ejpam-4510	320	4	proof	proof	NOUN
ejpam-4510	320	5	.	.	PUNCT
ejpam-4510	321	1	assume	assume	VERB
ejpam-4510	321	2	that	that	SCONJ
ejpam-4510	321	3	dokφ	dokφ	NOUN
ejpam-4510	321	4	:	:	PUNCT
ejpam-4510	321	5	=	=	SYM
ejpam-4510	321	6	(	(	PUNCT
ejpam-4510	321	7	φ̊	φ̊	PROPN
ejpam-4510	321	8	,	,	PUNCT
ejpam-4510	321	9	φs	φs	ADV
ejpam-4510	321	10	,	,	PUNCT
ejpam-4510	321	11	φ̃	φ̃	PROPN
ejpam-4510	321	12	)	)	PUNCT
ejpam-4510	321	13	is	be	AUX
ejpam-4510	321	14	a	a	DET
ejpam-4510	321	15	dokdo	dokdo	NOUN
ejpam-4510	321	16	be	be	NOUN
ejpam-4510	321	17	-	-	PUNCT
ejpam-4510	321	18	filter	filter	NOUN
ejpam-4510	321	19	of	of	ADP
ejpam-4510	321	20	(	(	PUNCT
ejpam-4510	321	21	x	x	NOUN
ejpam-4510	321	22	,	,	PUNCT
ejpam-4510	321	23	u	u	NOUN
ejpam-4510	321	24	)	)	PUNCT
ejpam-4510	321	25	and	and	CCONJ
ejpam-4510	321	26	let	let	VERB
ejpam-4510	321	27	x	x	PRON
ejpam-4510	321	28	,	,	PUNCT
ejpam-4510	321	29	y	y	PROPN
ejpam-4510	321	30	,	,	PUNCT
ejpam-4510	321	31	z	z	PROPN
ejpam-4510	321	32	∈	∈	PROPN
ejpam-4510	321	33	x.	x.	NOUN
ejpam-4510	322	1	then	then	ADV
ejpam-4510	322	2	φ−(x	φ−(x	PROPN
ejpam-4510	322	3	∗	∗	PROPN
ejpam-4510	322	4	z	z	PROPN
ejpam-4510	322	5	)	)	PUNCT
ejpam-4510	322	6	≤	≤	NOUN
ejpam-4510	322	7	max{φ−(y	max{φ−(y	NOUN
ejpam-4510	322	8	)	)	PUNCT
ejpam-4510	322	9	,	,	PUNCT
ejpam-4510	322	10	φ−(y	φ−(y	PROPN
ejpam-4510	322	11	∗	∗	VERB
ejpam-4510	322	12	(	(	PUNCT
ejpam-4510	322	13	x	x	X
ejpam-4510	322	14	∗	∗	PROPN
ejpam-4510	322	15	z	z	NOUN
ejpam-4510	322	16	)	)	PUNCT
ejpam-4510	322	17	)	)	PUNCT
ejpam-4510	322	18	}	}	PUNCT
ejpam-4510	322	19	=	=	SYM
ejpam-4510	322	20	max{φ−(y	max{φ−(y	PROPN
ejpam-4510	322	21	)	)	PUNCT
ejpam-4510	322	22	,	,	PUNCT
ejpam-4510	322	23	φ−(x	φ−(x	PROPN
ejpam-4510	322	24	∗	∗	X
ejpam-4510	322	25	(	(	PUNCT
ejpam-4510	322	26	y	y	PROPN
ejpam-4510	322	27	∗	∗	PROPN
ejpam-4510	322	28	z	z	PROPN
ejpam-4510	322	29	)	)	PUNCT
ejpam-4510	322	30	)	)	PUNCT
ejpam-4510	322	31	}	}	PUNCT
ejpam-4510	322	32	and	and	CCONJ
ejpam-4510	322	33	φ+(x∗z	φ+(x∗z	NUM
ejpam-4510	322	34	)	)	PUNCT
ejpam-4510	322	35	≥	≥	NOUN
ejpam-4510	322	36	min{φ+(y	min{φ+(y	NOUN
ejpam-4510	322	37	)	)	PUNCT
ejpam-4510	322	38	,	,	PUNCT
ejpam-4510	322	39	φ+(y	φ+(y	CCONJ
ejpam-4510	322	40	∗	∗	NOUN
ejpam-4510	322	41	(	(	PUNCT
ejpam-4510	322	42	x∗z	x∗z	NOUN
ejpam-4510	322	43	)	)	PUNCT
ejpam-4510	322	44	)	)	PUNCT
ejpam-4510	322	45	}	}	PUNCT
ejpam-4510	322	46	=	=	SYM
ejpam-4510	322	47	min{φ+(y	min{φ+(y	NOUN
ejpam-4510	322	48	)	)	PUNCT
ejpam-4510	322	49	,	,	PUNCT
ejpam-4510	322	50	φ+(x∗	φ+(x∗	PROPN
ejpam-4510	322	51	(	(	PUNCT
ejpam-4510	322	52	y	y	PROPN
ejpam-4510	322	53	∗z	∗z	PROPN
ejpam-4510	322	54	)	)	PUNCT
ejpam-4510	322	55	)	)	PUNCT
ejpam-4510	322	56	}	}	PUNCT
ejpam-4510	322	57	,	,	PUNCT
ejpam-4510	322	58	that	that	ADV
ejpam-4510	322	59	is	be	AUX
ejpam-4510	322	60	,	,	PUNCT
ejpam-4510	322	61	x∗z	x∗z	PUNCT
ejpam-4510	322	62	(	(	PUNCT
ejpam-4510	322	63	x∗(y∗z	x∗(y∗z	PROPN
ejpam-4510	322	64	)	)	PUNCT
ejpam-4510	322	65	,	,	PUNCT
ejpam-4510	322	66	y	y	X
ejpam-4510	322	67	)	)	PUNCT
ejpam-4510	322	68	∈	∈	PROPN
ejpam-4510	323	1	φ̊(max	φ̊(max	NUM
ejpam-4510	323	2	,	,	PUNCT
ejpam-4510	323	3	min	min	NOUN
ejpam-4510	323	4	)	)	PUNCT
ejpam-4510	323	5	.	.	PUNCT
ejpam-4510	324	1	also	also	ADV
ejpam-4510	324	2	,	,	PUNCT
ejpam-4510	324	3	we	we	PRON
ejpam-4510	324	4	have	have	VERB
ejpam-4510	324	5	φs(x	φs(x	NOUN
ejpam-4510	324	6	∗	∗	NOUN
ejpam-4510	324	7	z	z	NOUN
ejpam-4510	324	8	)	)	PUNCT
ejpam-4510	324	9	⊇	⊇	NOUN
ejpam-4510	324	10	φs(y	φs(y	NUM
ejpam-4510	324	11	)	)	PUNCT
ejpam-4510	324	12	∩	∩	NOUN
ejpam-4510	324	13	φs(y	φs(y	PART
ejpam-4510	324	14	∗	∗	NOUN
ejpam-4510	324	15	(	(	PUNCT
ejpam-4510	324	16	x	x	X
ejpam-4510	324	17	∗	∗	PROPN
ejpam-4510	324	18	z	z	NOUN
ejpam-4510	324	19	)	)	PUNCT
ejpam-4510	324	20	)	)	PUNCT
ejpam-4510	324	21	=	=	SYM
ejpam-4510	325	1	φs(y	φs(y	X
ejpam-4510	325	2	)	)	PUNCT
ejpam-4510	326	1	∩	∩	NOUN
ejpam-4510	326	2	φs(x	φs(x	PART
ejpam-4510	326	3	∗	∗	NOUN
ejpam-4510	326	4	(	(	PUNCT
ejpam-4510	326	5	y	y	PROPN
ejpam-4510	326	6	∗	∗	PROPN
ejpam-4510	326	7	z	z	NOUN
ejpam-4510	326	8	)	)	PUNCT
ejpam-4510	326	9	)	)	PUNCT
ejpam-4510	326	10	and	and	CCONJ
ejpam-4510	326	11	φ̃(x	φ̃(x	PROPN
ejpam-4510	326	12	∗	∗	NOUN
ejpam-4510	326	13	z	z	NOUN
ejpam-4510	326	14	)	)	PUNCT
ejpam-4510	326	15	⪰	⪰	NOUN
ejpam-4510	326	16	rmin{φ̃(y	rmin{φ̃(y	NOUN
ejpam-4510	326	17	)	)	PUNCT
ejpam-4510	326	18	,	,	PUNCT
ejpam-4510	326	19	φ̃(y	φ̃(y	ADJ
ejpam-4510	326	20	∗	∗	NOUN
ejpam-4510	326	21	(	(	PUNCT
ejpam-4510	326	22	x	x	X
ejpam-4510	326	23	∗	∗	PROPN
ejpam-4510	326	24	z	z	NOUN
ejpam-4510	326	25	)	)	PUNCT
ejpam-4510	326	26	)	)	PUNCT
ejpam-4510	326	27	}	}	PUNCT
ejpam-4510	327	1	=	=	SYM
ejpam-4510	327	2	rmin{φ̃(y	rmin{φ̃(y	X
ejpam-4510	327	3	)	)	PUNCT
ejpam-4510	327	4	,	,	PUNCT
ejpam-4510	327	5	φ̃(x	φ̃(x	PROPN
ejpam-4510	327	6	∗	∗	NOUN
ejpam-4510	327	7	(	(	PUNCT
ejpam-4510	327	8	y	y	PROPN
ejpam-4510	327	9	∗	∗	PROPN
ejpam-4510	327	10	z	z	PROPN
ejpam-4510	327	11	)	)	PUNCT
ejpam-4510	327	12	)	)	PUNCT
ejpam-4510	327	13	}	}	PUNCT
ejpam-4510	327	14	.	.	PUNCT
ejpam-4510	328	1	conversely	conversely	ADV
ejpam-4510	328	2	,	,	PUNCT
ejpam-4510	328	3	suppose	suppose	VERB
ejpam-4510	328	4	that	that	SCONJ
ejpam-4510	328	5	dokφ	dokφ	NOUN
ejpam-4510	328	6	:	:	PUNCT
ejpam-4510	328	7	=	=	SYM
ejpam-4510	328	8	(	(	PUNCT
ejpam-4510	328	9	φ̊	φ̊	PROPN
ejpam-4510	328	10	,	,	PUNCT
ejpam-4510	328	11	φs	φs	ADV
ejpam-4510	328	12	,	,	PUNCT
ejpam-4510	328	13	φ̃	φ̃	PROPN
ejpam-4510	328	14	)	)	PUNCT
ejpam-4510	328	15	satisfies	satisfie	NOUN
ejpam-4510	328	16	(	(	PUNCT
ejpam-4510	328	17	24	24	NUM
ejpam-4510	328	18	)	)	PUNCT
ejpam-4510	328	19	and	and	CCONJ
ejpam-4510	328	20	(	(	PUNCT
ejpam-4510	328	21	32	32	NUM
ejpam-4510	328	22	)	)	PUNCT
ejpam-4510	328	23	.	.	PUNCT
ejpam-4510	329	1	if	if	SCONJ
ejpam-4510	329	2	we	we	PRON
ejpam-4510	329	3	put	put	VERB
ejpam-4510	329	4	x	x	PUNCT
ejpam-4510	329	5	=	=	SYM
ejpam-4510	329	6	1	1	NUM
ejpam-4510	329	7	in	in	ADP
ejpam-4510	329	8	(	(	PUNCT
ejpam-4510	329	9	32	32	NUM
ejpam-4510	329	10	)	)	PUNCT
ejpam-4510	329	11	and	and	CCONJ
ejpam-4510	329	12	use	use	NOUN
ejpam-4510	329	13	(	(	PUNCT
ejpam-4510	329	14	be3	be3	PROPN
ejpam-4510	329	15	)	)	PUNCT
ejpam-4510	329	16	,	,	PUNCT
ejpam-4510	329	17	then	then	ADV
ejpam-4510	329	18	we	we	PRON
ejpam-4510	329	19	get	get	VERB
ejpam-4510	329	20	z	z	NOUN
ejpam-4510	329	21	(	(	PUNCT
ejpam-4510	329	22	y∗z	y∗z	PROPN
ejpam-4510	329	23	,	,	PUNCT
ejpam-4510	329	24	y	y	NOUN
ejpam-4510	329	25	)	)	PUNCT
ejpam-4510	329	26	=	=	SYM
ejpam-4510	330	1	1∗z	1∗z	NUM
ejpam-4510	330	2	(	(	PUNCT
ejpam-4510	330	3	1∗(y∗z	1∗(y∗z	NUM
ejpam-4510	330	4	)	)	PUNCT
ejpam-4510	330	5	,	,	PUNCT
ejpam-4510	330	6	y	y	X
ejpam-4510	330	7	)	)	PUNCT
ejpam-4510	330	8	∈	∈	PROPN
ejpam-4510	331	1	φ̊(max	φ̊(max	NUM
ejpam-4510	331	2	,	,	PUNCT
ejpam-4510	331	3	min	min	NOUN
ejpam-4510	331	4	)	)	PUNCT
ejpam-4510	331	5	,	,	PUNCT
ejpam-4510	331	6	φs(z	φs(z	NOUN
ejpam-4510	331	7	)	)	PUNCT
ejpam-4510	331	8	=	=	SYM
ejpam-4510	331	9	φs(1	φs(1	PROPN
ejpam-4510	331	10	∗	∗	NOUN
ejpam-4510	331	11	z	z	PROPN
ejpam-4510	331	12	)	)	PUNCT
ejpam-4510	331	13	⊇	⊇	PROPN
ejpam-4510	331	14	φs(1	φs(1	PROPN
ejpam-4510	331	15	∗	∗	NOUN
ejpam-4510	331	16	(	(	PUNCT
ejpam-4510	331	17	y	y	PROPN
ejpam-4510	331	18	∗	∗	PROPN
ejpam-4510	331	19	z	z	NOUN
ejpam-4510	331	20	)	)	PUNCT
ejpam-4510	331	21	)	)	PUNCT
ejpam-4510	331	22	∩	∩	NOUN
ejpam-4510	331	23	φs(y	φs(y	NUM
ejpam-4510	331	24	)	)	PUNCT
ejpam-4510	331	25	=	=	SYM
ejpam-4510	331	26	φs(y	φs(y	NOUN
ejpam-4510	331	27	∗	∗	X
ejpam-4510	331	28	z	z	NOUN
ejpam-4510	331	29	)	)	PUNCT
ejpam-4510	331	30	∩	∩	NOUN
ejpam-4510	331	31	φs(y	φs(y	NUM
ejpam-4510	331	32	)	)	PUNCT
ejpam-4510	331	33	and	and	CCONJ
ejpam-4510	331	34	φ̃(z	φ̃(z	NUM
ejpam-4510	331	35	)	)	PUNCT
ejpam-4510	331	36	=	=	NOUN
ejpam-4510	331	37	φ̃(1	φ̃(1	NOUN
ejpam-4510	331	38	∗	∗	NOUN
ejpam-4510	331	39	z	z	NOUN
ejpam-4510	331	40	)	)	PUNCT
ejpam-4510	331	41	⪰	⪰	NOUN
ejpam-4510	331	42	rmin{φ̃(1	rmin{φ̃(1	PROPN
ejpam-4510	331	43	∗	∗	NOUN
ejpam-4510	331	44	(	(	PUNCT
ejpam-4510	331	45	y	y	PROPN
ejpam-4510	331	46	∗	∗	PROPN
ejpam-4510	331	47	z	z	PROPN
ejpam-4510	331	48	)	)	PUNCT
ejpam-4510	331	49	)	)	PUNCT
ejpam-4510	331	50	,	,	PUNCT
ejpam-4510	331	51	φ̃(y	φ̃(y	NOUN
ejpam-4510	331	52	)	)	PUNCT
ejpam-4510	331	53	}	}	PUNCT
ejpam-4510	331	54	=	=	SYM
ejpam-4510	331	55	rmin{φ̃(y	rmin{φ̃(y	ADJ
ejpam-4510	331	56	∗	∗	NOUN
ejpam-4510	331	57	z	z	NOUN
ejpam-4510	331	58	)	)	PUNCT
ejpam-4510	331	59	,	,	PUNCT
ejpam-4510	331	60	φ̃(y	φ̃(y	NOUN
ejpam-4510	331	61	)	)	PUNCT
ejpam-4510	331	62	}	}	PUNCT
ejpam-4510	331	63	for	for	ADP
ejpam-4510	331	64	all	all	DET
ejpam-4510	331	65	y	y	PROPN
ejpam-4510	331	66	,	,	PUNCT
ejpam-4510	331	67	z	z	PROPN
ejpam-4510	331	68	∈	∈	PROPN
ejpam-4510	331	69	x.	x.	NOUN
ejpam-4510	331	70	therefore	therefore	ADV
ejpam-4510	331	71	dokφ	dokφ	VERB
ejpam-4510	331	72	:	:	PUNCT
ejpam-4510	331	73	=	=	SYM
ejpam-4510	331	74	(	(	PUNCT
ejpam-4510	331	75	φ̊	φ̊	PROPN
ejpam-4510	331	76	,	,	PUNCT
ejpam-4510	331	77	φs	φs	ADV
ejpam-4510	331	78	,	,	PUNCT
ejpam-4510	331	79	φ̃	φ̃	PROPN
ejpam-4510	331	80	)	)	PUNCT
ejpam-4510	331	81	is	be	AUX
ejpam-4510	331	82	a	a	DET
ejpam-4510	331	83	dokdo	dokdo	NOUN
ejpam-4510	331	84	be	be	NOUN
ejpam-4510	331	85	-	-	PUNCT
ejpam-4510	331	86	filter	filter	NOUN
ejpam-4510	331	87	of	of	ADP
ejpam-4510	331	88	(	(	PUNCT
ejpam-4510	331	89	x	x	NOUN
ejpam-4510	331	90	,	,	PUNCT
ejpam-4510	331	91	u	u	NOUN
ejpam-4510	331	92	)	)	PUNCT
ejpam-4510	331	93	.	.	PUNCT
ejpam-4510	332	1	theorem	theorem	VERB
ejpam-4510	332	2	7	7	NUM
ejpam-4510	332	3	.	.	PUNCT
ejpam-4510	332	4	a	a	DET
ejpam-4510	332	5	dokdo	dokdo	ADJ
ejpam-4510	332	6	structure	structure	NOUN
ejpam-4510	332	7	dokφ	dokφ	NOUN
ejpam-4510	332	8	:	:	PUNCT
ejpam-4510	333	1	=	=	SYM
ejpam-4510	333	2	(	(	PUNCT
ejpam-4510	333	3	φ̊	φ̊	PROPN
ejpam-4510	333	4	,	,	PUNCT
ejpam-4510	333	5	φs	φs	ADV
ejpam-4510	333	6	,	,	PUNCT
ejpam-4510	333	7	φ̃	φ̃	PROPN
ejpam-4510	333	8	)	)	PUNCT
ejpam-4510	333	9	in	in	ADP
ejpam-4510	333	10	(	(	PUNCT
ejpam-4510	333	11	x	x	NOUN
ejpam-4510	333	12	,	,	PUNCT
ejpam-4510	333	13	u	u	NOUN
ejpam-4510	333	14	)	)	PUNCT
ejpam-4510	333	15	is	be	AUX
ejpam-4510	333	16	a	a	DET
ejpam-4510	333	17	dokdo	dokdo	NOUN
ejpam-4510	333	18	be	be	NOUN
ejpam-4510	333	19	-	-	PUNCT
ejpam-4510	333	20	filter	filter	NOUN
ejpam-4510	333	21	of	of	ADP
ejpam-4510	333	22	(	(	PUNCT
ejpam-4510	333	23	x	x	NOUN
ejpam-4510	333	24	,	,	PUNCT
ejpam-4510	333	25	u	u	NOUN
ejpam-4510	333	26	)	)	PUNCT
ejpam-4510	333	27	if	if	SCONJ
ejpam-4510	333	28	and	and	CCONJ
ejpam-4510	333	29	only	only	ADV
ejpam-4510	333	30	if	if	SCONJ
ejpam-4510	333	31	it	it	PRON
ejpam-4510	333	32	satisfies	satisfy	VERB
ejpam-4510	333	33	:	:	PUNCT
ejpam-4510	333	34	(	(	PUNCT
ejpam-4510	333	35	∀x	∀x	X
ejpam-4510	333	36	,	,	PUNCT
ejpam-4510	333	37	y	y	PROPN
ejpam-4510	333	38	∈	∈	PROPN
ejpam-4510	333	39	x	x	X
ejpam-4510	333	40	)	)	PUNCT
ejpam-4510	333	41			PROPN
ejpam-4510	333	42	y∗x	y∗x	ADV
ejpam-4510	333	43	(	(	PUNCT
ejpam-4510	333	44	x	x	NOUN
ejpam-4510	333	45	,	,	PUNCT
ejpam-4510	333	46	x	x	SYM
ejpam-4510	333	47	)	)	PUNCT
ejpam-4510	333	48	∈	∈	PROPN
ejpam-4510	333	49	φ̊(max	φ̊(max	NUM
ejpam-4510	333	50	,	,	PUNCT
ejpam-4510	333	51	min	min	NOUN
ejpam-4510	333	52	)	)	PUNCT
ejpam-4510	333	53	,	,	PUNCT
ejpam-4510	333	54	φs(y	φs(y	NOUN
ejpam-4510	333	55	∗	∗	NOUN
ejpam-4510	333	56	x	x	NOUN
ejpam-4510	333	57	)	)	PUNCT
ejpam-4510	333	58	⊇	⊇	NOUN
ejpam-4510	333	59	φs(x	φs(x	PRON
ejpam-4510	333	60	)	)	PUNCT
ejpam-4510	333	61	,	,	PUNCT
ejpam-4510	333	62	φ̃(y	φ̃(y	ADJ
ejpam-4510	333	63	∗	∗	NOUN
ejpam-4510	333	64	x	x	NOUN
ejpam-4510	333	65	)	)	PUNCT
ejpam-4510	333	66	⪰	⪰	NOUN
ejpam-4510	333	67	φ̃(x	φ̃(x	PROPN
ejpam-4510	333	68	)	)	PUNCT
ejpam-4510	333	69			PROPN
ejpam-4510	333	70	,	,	PUNCT
ejpam-4510	333	71	(	(	PUNCT
ejpam-4510	333	72	33	33	NUM
ejpam-4510	333	73	)	)	PUNCT
ejpam-4510	333	74	(	(	PUNCT
ejpam-4510	333	75	∀x	∀x	X
ejpam-4510	333	76	,	,	PUNCT
ejpam-4510	333	77	y	y	PROPN
ejpam-4510	333	78	,	,	PUNCT
ejpam-4510	333	79	a	a	PRON
ejpam-4510	333	80	,	,	PUNCT
ejpam-4510	333	81	b	b	X
ejpam-4510	333	82	∈	∈	PROPN
ejpam-4510	333	83	x	x	NOUN
ejpam-4510	333	84	)	)	PUNCT
ejpam-4510	333	85			X
ejpam-4510	333	86	(	(	PUNCT
ejpam-4510	333	87	a∗(b∗x))∗x	a∗(b∗x))∗x	X
ejpam-4510	333	88	(	(	PUNCT
ejpam-4510	333	89	a	a	PRON
ejpam-4510	333	90	,	,	PUNCT
ejpam-4510	333	91	b	b	NOUN
ejpam-4510	333	92	)	)	PUNCT
ejpam-4510	333	93	∈	∈	PROPN
ejpam-4510	333	94	φ̊(max	φ̊(max	NUM
ejpam-4510	333	95	,	,	PUNCT
ejpam-4510	333	96	min	min	NOUN
ejpam-4510	333	97	)	)	PUNCT
ejpam-4510	333	98	,	,	PUNCT
ejpam-4510	333	99	φs((a	φs((a	PROPN
ejpam-4510	333	100	∗	∗	PROPN
ejpam-4510	333	101	(	(	PUNCT
ejpam-4510	333	102	b	b	NOUN
ejpam-4510	333	103	∗	∗	NOUN
ejpam-4510	333	104	x	x	NOUN
ejpam-4510	333	105	)	)	PUNCT
ejpam-4510	333	106	)	)	PUNCT
ejpam-4510	333	107	∗	∗	NOUN
ejpam-4510	333	108	x	x	X
ejpam-4510	333	109	)	)	PUNCT
ejpam-4510	333	110	⊇	⊇	NOUN
ejpam-4510	333	111	φs(a	φs(a	NUM
ejpam-4510	333	112	)	)	PUNCT
ejpam-4510	333	113	∩	∩	NOUN
ejpam-4510	333	114	φs(b	φs(b	NOUN
ejpam-4510	333	115	)	)	PUNCT
ejpam-4510	333	116	,	,	PUNCT
ejpam-4510	333	117	φ̃((a	φ̃((a	NOUN
ejpam-4510	333	118	∗	∗	NOUN
ejpam-4510	333	119	(	(	PUNCT
ejpam-4510	333	120	b	b	NOUN
ejpam-4510	333	121	∗	∗	NOUN
ejpam-4510	333	122	x	x	NOUN
ejpam-4510	333	123	)	)	PUNCT
ejpam-4510	333	124	)	)	PUNCT
ejpam-4510	333	125	∗	∗	NOUN
ejpam-4510	333	126	x	x	NOUN
ejpam-4510	333	127	)	)	PUNCT
ejpam-4510	333	128	⪰	⪰	NOUN
ejpam-4510	333	129	rmin{φ̃(a	rmin{φ̃(a	NOUN
ejpam-4510	333	130	)	)	PUNCT
ejpam-4510	333	131	,	,	PUNCT
ejpam-4510	333	132	φ̃(b	φ̃(b	NOUN
ejpam-4510	333	133	)	)	PUNCT
ejpam-4510	333	134	}	}	PUNCT
ejpam-4510	333	135			PROPN
ejpam-4510	333	136	.	.	PUNCT
ejpam-4510	334	1	(	(	PUNCT
ejpam-4510	334	2	34	34	NUM
ejpam-4510	334	3	)	)	PUNCT
ejpam-4510	334	4	proof	proof	NOUN
ejpam-4510	334	5	.	.	PUNCT
ejpam-4510	335	1	assume	assume	VERB
ejpam-4510	335	2	thatdokφ	thatdokφ	NOUN
ejpam-4510	335	3	:	:	PUNCT
ejpam-4510	335	4	=	=	SYM
ejpam-4510	335	5	(	(	PUNCT
ejpam-4510	335	6	φ̊	φ̊	PROPN
ejpam-4510	335	7	,	,	PUNCT
ejpam-4510	335	8	φs	φs	ADV
ejpam-4510	335	9	,	,	PUNCT
ejpam-4510	335	10	φ̃	φ̃	PROPN
ejpam-4510	335	11	)	)	PUNCT
ejpam-4510	335	12	is	be	AUX
ejpam-4510	335	13	a	a	DET
ejpam-4510	335	14	dokdo	dokdo	NOUN
ejpam-4510	335	15	be	be	NOUN
ejpam-4510	335	16	-	-	PUNCT
ejpam-4510	335	17	filter	filter	NOUN
ejpam-4510	335	18	of	of	ADP
ejpam-4510	335	19	(	(	PUNCT
ejpam-4510	335	20	x	x	NOUN
ejpam-4510	335	21	,	,	PUNCT
ejpam-4510	335	22	u	u	NOUN
ejpam-4510	335	23	)	)	PUNCT
ejpam-4510	335	24	and	and	CCONJ
ejpam-4510	335	25	let	let	VERB
ejpam-4510	335	26	x	x	PRON
ejpam-4510	335	27	,	,	PUNCT
ejpam-4510	335	28	y	y	PROPN
ejpam-4510	335	29	,	,	PUNCT
ejpam-4510	335	30	a	a	DET
ejpam-4510	335	31	,	,	PUNCT
ejpam-4510	335	32	b	b	X
ejpam-4510	335	33	∈	∈	PROPN
ejpam-4510	335	34	x.	x.	NOUN
ejpam-4510	335	35	then	then	ADV
ejpam-4510	335	36	φ−(y	φ−(y	PROPN
ejpam-4510	335	37	∗	∗	NOUN
ejpam-4510	335	38	x	x	NOUN
ejpam-4510	335	39	)	)	PUNCT
ejpam-4510	335	40	≤	≤	NUM
ejpam-4510	335	41	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	335	42	)	)	PUNCT
ejpam-4510	335	43	,	,	PUNCT
ejpam-4510	336	1	φ−(x	φ−(x	PROPN
ejpam-4510	336	2	∗	∗	NOUN
ejpam-4510	336	3	(	(	PUNCT
ejpam-4510	336	4	y	y	PROPN
ejpam-4510	336	5	∗	∗	NOUN
ejpam-4510	336	6	x	x	NOUN
ejpam-4510	336	7	)	)	PUNCT
ejpam-4510	336	8	)	)	PUNCT
ejpam-4510	336	9	}	}	PUNCT
ejpam-4510	336	10	=	=	SYM
ejpam-4510	336	11	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	336	12	)	)	PUNCT
ejpam-4510	336	13	,	,	PUNCT
ejpam-4510	336	14	φ−(1	φ−(1	NOUN
ejpam-4510	336	15	)	)	PUNCT
ejpam-4510	336	16	}	}	PUNCT
ejpam-4510	336	17	=	=	SYM
ejpam-4510	336	18	φ−(x	φ−(x	PROPN
ejpam-4510	336	19	)	)	PUNCT
ejpam-4510	336	20	and	and	CCONJ
ejpam-4510	336	21	φ+(y	φ+(y	X
ejpam-4510	336	22	∗	∗	NOUN
ejpam-4510	336	23	x	x	NOUN
ejpam-4510	336	24	)	)	PUNCT
ejpam-4510	336	25	≥	≥	NOUN
ejpam-4510	336	26	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	336	27	)	)	PUNCT
ejpam-4510	336	28	,	,	PUNCT
ejpam-4510	336	29	φ+(x	φ+(x	NOUN
ejpam-4510	336	30	∗	∗	NOUN
ejpam-4510	336	31	(	(	PUNCT
ejpam-4510	336	32	y	y	PROPN
ejpam-4510	336	33	∗	∗	NOUN
ejpam-4510	336	34	x	x	NOUN
ejpam-4510	336	35	)	)	PUNCT
ejpam-4510	336	36	)	)	PUNCT
ejpam-4510	336	37	}	}	PUNCT
ejpam-4510	336	38	=	=	SYM
ejpam-4510	336	39	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	336	40	)	)	PUNCT
ejpam-4510	336	41	,	,	PUNCT
ejpam-4510	336	42	φ+(1	φ+(1	NOUN
ejpam-4510	336	43	)	)	PUNCT
ejpam-4510	336	44	}	}	PUNCT
ejpam-4510	336	45	=	=	SYM
ejpam-4510	336	46	φ+(x	φ+(x	X
ejpam-4510	336	47	)	)	PUNCT
ejpam-4510	336	48	,	,	PUNCT
ejpam-4510	336	49	that	that	ADV
ejpam-4510	336	50	is	is	ADV
ejpam-4510	336	51	,	,	PUNCT
ejpam-4510	336	52	y∗x	y∗x	PRON
ejpam-4510	336	53	(	(	PUNCT
ejpam-4510	336	54	x	x	X
ejpam-4510	336	55	,	,	PUNCT
ejpam-4510	336	56	x	x	SYM
ejpam-4510	336	57	)	)	PUNCT
ejpam-4510	336	58	∈	∈	PROPN
ejpam-4510	337	1	φ̊(max	φ̊(max	ADJ
ejpam-4510	337	2	,	,	PUNCT
ejpam-4510	337	3	min	min	NOUN
ejpam-4510	337	4	)	)	PUNCT
ejpam-4510	337	5	.	.	PUNCT
ejpam-4510	338	1	also	also	ADV
ejpam-4510	338	2	,	,	PUNCT
ejpam-4510	338	3	we	we	PRON
ejpam-4510	338	4	obtain	obtain	VERB
ejpam-4510	338	5	φs(y	φs(y	ADJ
ejpam-4510	338	6	∗	∗	NOUN
ejpam-4510	338	7	x	x	NOUN
ejpam-4510	338	8	)	)	PUNCT
ejpam-4510	338	9	⊇	⊇	NOUN
ejpam-4510	338	10	φs(x	φs(x	NOUN
ejpam-4510	338	11	)	)	PUNCT
ejpam-4510	338	12	∩	∩	NOUN
ejpam-4510	338	13	φs(x	φs(x	PART
ejpam-4510	338	14	∗	∗	NOUN
ejpam-4510	338	15	(	(	PUNCT
ejpam-4510	338	16	y	y	PROPN
ejpam-4510	338	17	∗	∗	NOUN
ejpam-4510	338	18	x	x	NOUN
ejpam-4510	338	19	)	)	PUNCT
ejpam-4510	338	20	)	)	PUNCT
ejpam-4510	339	1	=	=	SYM
ejpam-4510	339	2	φs(x	φs(x	X
ejpam-4510	339	3	)	)	PUNCT
ejpam-4510	339	4	∩	∩	NOUN
ejpam-4510	339	5	φs(1	φs(1	PROPN
ejpam-4510	339	6	)	)	PUNCT
ejpam-4510	339	7	=	=	SYM
ejpam-4510	339	8	φs(x	φs(x	X
ejpam-4510	339	9	)	)	PUNCT
ejpam-4510	339	10	references	reference	NOUN
ejpam-4510	339	11	1534	1534	NUM
ejpam-4510	339	12	and	and	CCONJ
ejpam-4510	339	13	φ̃(y	φ̃(y	PROPN
ejpam-4510	339	14	∗	∗	NOUN
ejpam-4510	339	15	x	x	NOUN
ejpam-4510	339	16	)	)	PUNCT
ejpam-4510	339	17	⪰	⪰	NOUN
ejpam-4510	339	18	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	339	19	)	)	PUNCT
ejpam-4510	339	20	,	,	PUNCT
ejpam-4510	339	21	φ̃(x	φ̃(x	PROPN
ejpam-4510	339	22	∗	∗	NOUN
ejpam-4510	339	23	(	(	PUNCT
ejpam-4510	339	24	y	y	PROPN
ejpam-4510	339	25	∗	∗	NOUN
ejpam-4510	339	26	x	x	NOUN
ejpam-4510	339	27	)	)	PUNCT
ejpam-4510	339	28	)	)	PUNCT
ejpam-4510	339	29	}	}	PUNCT
ejpam-4510	339	30	=	=	SYM
ejpam-4510	339	31	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	339	32	)	)	PUNCT
ejpam-4510	339	33	,	,	PUNCT
ejpam-4510	339	34	φ̃(1	φ̃(1	NOUN
ejpam-4510	339	35	)	)	PUNCT
ejpam-4510	339	36	}	}	PUNCT
ejpam-4510	339	37	=	=	SYM
ejpam-4510	339	38	φ̃(x	φ̃(x	PROPN
ejpam-4510	339	39	)	)	PUNCT
ejpam-4510	339	40	.	.	PUNCT
ejpam-4510	340	1	hence	hence	ADV
ejpam-4510	340	2	(	(	PUNCT
ejpam-4510	340	3	33	33	NUM
ejpam-4510	340	4	)	)	PUNCT
ejpam-4510	340	5	is	be	AUX
ejpam-4510	340	6	valid	valid	ADJ
ejpam-4510	340	7	.	.	PUNCT
ejpam-4510	341	1	the	the	DET
ejpam-4510	341	2	following	follow	VERB
ejpam-4510	341	3	facts	fact	NOUN
ejpam-4510	341	4	can	can	AUX
ejpam-4510	341	5	be	be	AUX
ejpam-4510	341	6	obtained	obtain	VERB
ejpam-4510	341	7	by	by	ADP
ejpam-4510	341	8	using	use	VERB
ejpam-4510	341	9	(	(	PUNCT
ejpam-4510	341	10	3	3	NUM
ejpam-4510	341	11	)	)	PUNCT
ejpam-4510	341	12	,	,	PUNCT
ejpam-4510	341	13	(	(	PUNCT
ejpam-4510	341	14	26	26	NUM
ejpam-4510	341	15	)	)	PUNCT
ejpam-4510	341	16	,	,	PUNCT
ejpam-4510	341	17	and	and	CCONJ
ejpam-4510	341	18	theorem	theorem	VERB
ejpam-4510	341	19	6	6	NUM
ejpam-4510	341	20	.	.	PUNCT
ejpam-4510	342	1	φ−((a	φ−((a	NOUN
ejpam-4510	342	2	∗	∗	NOUN
ejpam-4510	342	3	(	(	PUNCT
ejpam-4510	342	4	b	b	NOUN
ejpam-4510	342	5	∗	∗	NOUN
ejpam-4510	342	6	x	x	NOUN
ejpam-4510	342	7	)	)	PUNCT
ejpam-4510	342	8	)	)	PUNCT
ejpam-4510	342	9	∗	∗	NOUN
ejpam-4510	342	10	x	x	NOUN
ejpam-4510	342	11	)	)	PUNCT
ejpam-4510	342	12	≤	≤	NUM
ejpam-4510	342	13	max{φ−((a	max{φ−((a	NOUN
ejpam-4510	342	14	∗	∗	NOUN
ejpam-4510	342	15	(	(	PUNCT
ejpam-4510	342	16	b	b	NOUN
ejpam-4510	342	17	∗	∗	NOUN
ejpam-4510	342	18	x	x	NOUN
ejpam-4510	342	19	)	)	PUNCT
ejpam-4510	342	20	)	)	PUNCT
ejpam-4510	342	21	∗	∗	NOUN
ejpam-4510	342	22	(	(	PUNCT
ejpam-4510	342	23	b	b	NOUN
ejpam-4510	342	24	∗	∗	NOUN
ejpam-4510	342	25	x	x	NOUN
ejpam-4510	342	26	)	)	PUNCT
ejpam-4510	342	27	)	)	PUNCT
ejpam-4510	342	28	,	,	PUNCT
ejpam-4510	342	29	φ−(b	φ−(b	PROPN
ejpam-4510	342	30	)	)	PUNCT
ejpam-4510	342	31	}	}	PUNCT
ejpam-4510	342	32	≤	≤	NUM
ejpam-4510	342	33	max{φ−(a	max{φ−(a	NOUN
ejpam-4510	342	34	)	)	PUNCT
ejpam-4510	342	35	,	,	PUNCT
ejpam-4510	342	36	φ−(b	φ−(b	PROPN
ejpam-4510	342	37	)	)	PUNCT
ejpam-4510	342	38	}	}	PUNCT
ejpam-4510	342	39	,	,	PUNCT
ejpam-4510	342	40	φ+((a	φ+((a	CCONJ
ejpam-4510	342	41	∗	∗	NOUN
ejpam-4510	342	42	(	(	PUNCT
ejpam-4510	342	43	b	b	NOUN
ejpam-4510	342	44	∗	∗	NOUN
ejpam-4510	342	45	x	x	NOUN
ejpam-4510	342	46	)	)	PUNCT
ejpam-4510	342	47	)	)	PUNCT
ejpam-4510	342	48	∗	∗	NOUN
ejpam-4510	342	49	x	x	NOUN
ejpam-4510	342	50	)	)	PUNCT
ejpam-4510	342	51	≥	≥	NOUN
ejpam-4510	342	52	min{φ+((a	min{φ+((a	NOUN
ejpam-4510	343	1	∗	∗	NOUN
ejpam-4510	344	1	(	(	PUNCT
ejpam-4510	344	2	b	b	NOUN
ejpam-4510	344	3	∗	∗	NOUN
ejpam-4510	344	4	x	x	NOUN
ejpam-4510	344	5	)	)	PUNCT
ejpam-4510	344	6	)	)	PUNCT
ejpam-4510	345	1	∗	∗	NOUN
ejpam-4510	345	2	(	(	PUNCT
ejpam-4510	345	3	b	b	NOUN
ejpam-4510	345	4	∗	∗	NOUN
ejpam-4510	345	5	x	x	NOUN
ejpam-4510	345	6	)	)	PUNCT
ejpam-4510	345	7	)	)	PUNCT
ejpam-4510	345	8	,	,	PUNCT
ejpam-4510	345	9	φ+(b	φ+(b	NOUN
ejpam-4510	345	10	)	)	PUNCT
ejpam-4510	345	11	}	}	PUNCT
ejpam-4510	345	12	≥	≥	NOUN
ejpam-4510	345	13	min{φ+(a	min{φ+(a	PROPN
ejpam-4510	345	14	)	)	PUNCT
ejpam-4510	345	15	,	,	PUNCT
ejpam-4510	345	16	φ+(b	φ+(b	NOUN
ejpam-4510	345	17	)	)	PUNCT
ejpam-4510	345	18	}	}	PUNCT
ejpam-4510	345	19	,	,	PUNCT
ejpam-4510	345	20	φs((a	φs((a	PROPN
ejpam-4510	345	21	∗	∗	PROPN
ejpam-4510	345	22	(	(	PUNCT
ejpam-4510	345	23	b	b	NOUN
ejpam-4510	345	24	∗	∗	NOUN
ejpam-4510	345	25	x	x	NOUN
ejpam-4510	345	26	)	)	PUNCT
ejpam-4510	345	27	)	)	PUNCT
ejpam-4510	345	28	∗	∗	NOUN
ejpam-4510	345	29	x	x	X
ejpam-4510	345	30	)	)	PUNCT
ejpam-4510	345	31	⊇	⊇	PROPN
ejpam-4510	345	32	φs((a	φs((a	PROPN
ejpam-4510	345	33	∗	∗	PROPN
ejpam-4510	345	34	(	(	PUNCT
ejpam-4510	345	35	b	b	NOUN
ejpam-4510	345	36	∗	∗	NOUN
ejpam-4510	345	37	x	x	NOUN
ejpam-4510	345	38	)	)	PUNCT
ejpam-4510	345	39	)	)	PUNCT
ejpam-4510	345	40	∗	∗	NOUN
ejpam-4510	345	41	(	(	PUNCT
ejpam-4510	345	42	b	b	NOUN
ejpam-4510	345	43	∗	∗	NOUN
ejpam-4510	345	44	x	x	NOUN
ejpam-4510	345	45	)	)	PUNCT
ejpam-4510	345	46	)	)	PUNCT
ejpam-4510	345	47	∩	∩	NOUN
ejpam-4510	345	48	φs(b	φs(b	NOUN
ejpam-4510	345	49	)	)	PUNCT
ejpam-4510	345	50	⊇	⊇	NOUN
ejpam-4510	345	51	φs(a	φs(a	NUM
ejpam-4510	345	52	)	)	PUNCT
ejpam-4510	345	53	∩	∩	NOUN
ejpam-4510	345	54	φs(b	φs(b	NOUN
ejpam-4510	345	55	)	)	PUNCT
ejpam-4510	345	56	,	,	PUNCT
ejpam-4510	345	57	φ̃((a	φ̃((a	NOUN
ejpam-4510	345	58	∗	∗	NOUN
ejpam-4510	345	59	(	(	PUNCT
ejpam-4510	345	60	b	b	NOUN
ejpam-4510	345	61	∗	∗	NOUN
ejpam-4510	345	62	x	x	NOUN
ejpam-4510	345	63	)	)	PUNCT
ejpam-4510	345	64	)	)	PUNCT
ejpam-4510	345	65	∗	∗	NOUN
ejpam-4510	345	66	x	x	NOUN
ejpam-4510	345	67	)	)	PUNCT
ejpam-4510	345	68	⪰	⪰	NOUN
ejpam-4510	345	69	rmin{φ̃((a	rmin{φ̃((a	NOUN
ejpam-4510	345	70	∗	∗	NOUN
ejpam-4510	345	71	(	(	PUNCT
ejpam-4510	345	72	b	b	NOUN
ejpam-4510	345	73	∗	∗	NOUN
ejpam-4510	345	74	x	x	NOUN
ejpam-4510	345	75	)	)	PUNCT
ejpam-4510	345	76	)	)	PUNCT
ejpam-4510	345	77	∗	∗	NOUN
ejpam-4510	345	78	(	(	PUNCT
ejpam-4510	345	79	b	b	NOUN
ejpam-4510	345	80	∗	∗	NOUN
ejpam-4510	345	81	x	x	NOUN
ejpam-4510	345	82	)	)	PUNCT
ejpam-4510	345	83	)	)	PUNCT
ejpam-4510	345	84	,	,	PUNCT
ejpam-4510	345	85	φ̃(b	φ̃(b	NOUN
ejpam-4510	345	86	)	)	PUNCT
ejpam-4510	345	87	}	}	PUNCT
ejpam-4510	345	88	⪰	⪰	NOUN
ejpam-4510	345	89	rmin{φ̃(a	rmin{φ̃(a	NOUN
ejpam-4510	345	90	)	)	PUNCT
ejpam-4510	345	91	,	,	PUNCT
ejpam-4510	345	92	φ̃(b	φ̃(b	NOUN
ejpam-4510	345	93	)	)	PUNCT
ejpam-4510	345	94	}	}	PUNCT
ejpam-4510	345	95	.	.	PUNCT
ejpam-4510	346	1	thus	thus	ADV
ejpam-4510	346	2	(	(	PUNCT
ejpam-4510	346	3	34	34	NUM
ejpam-4510	346	4	)	)	PUNCT
ejpam-4510	346	5	is	be	AUX
ejpam-4510	346	6	valid	valid	ADJ
ejpam-4510	346	7	.	.	PUNCT
ejpam-4510	347	1	conversely	conversely	ADV
ejpam-4510	347	2	,	,	PUNCT
ejpam-4510	347	3	suppose	suppose	VERB
ejpam-4510	347	4	that	that	SCONJ
ejpam-4510	347	5	dokφ	dokφ	NOUN
ejpam-4510	347	6	:	:	PUNCT
ejpam-4510	347	7	=	=	SYM
ejpam-4510	347	8	(	(	PUNCT
ejpam-4510	347	9	φ̊	φ̊	PROPN
ejpam-4510	347	10	,	,	PUNCT
ejpam-4510	347	11	φs	φs	ADV
ejpam-4510	347	12	,	,	PUNCT
ejpam-4510	347	13	φ̃	φ̃	PROPN
ejpam-4510	347	14	)	)	PUNCT
ejpam-4510	347	15	satisfies	satisfie	NOUN
ejpam-4510	347	16	(	(	PUNCT
ejpam-4510	347	17	33	33	NUM
ejpam-4510	347	18	)	)	PUNCT
ejpam-4510	347	19	and	and	CCONJ
ejpam-4510	347	20	(	(	PUNCT
ejpam-4510	347	21	34	34	NUM
ejpam-4510	347	22	)	)	PUNCT
ejpam-4510	347	23	.	.	PUNCT
ejpam-4510	348	1	if	if	SCONJ
ejpam-4510	348	2	we	we	PRON
ejpam-4510	348	3	take	take	VERB
ejpam-4510	348	4	y	y	NOUN
ejpam-4510	348	5	=	=	PUNCT
ejpam-4510	349	1	x	x	PROPN
ejpam-4510	349	2	in	in	ADP
ejpam-4510	349	3	(	(	PUNCT
ejpam-4510	349	4	33	33	NUM
ejpam-4510	349	5	)	)	PUNCT
ejpam-4510	349	6	and	and	CCONJ
ejpam-4510	349	7	use	use	NOUN
ejpam-4510	349	8	(	(	PUNCT
ejpam-4510	349	9	be1	be1	NOUN
ejpam-4510	349	10	)	)	PUNCT
ejpam-4510	349	11	,	,	PUNCT
ejpam-4510	349	12	then	then	ADV
ejpam-4510	349	13	1	1	NUM
ejpam-4510	349	14	(	(	PUNCT
ejpam-4510	349	15	x	x	NOUN
ejpam-4510	349	16	,	,	PUNCT
ejpam-4510	349	17	x	x	X
ejpam-4510	349	18	)	)	PUNCT
ejpam-4510	349	19	=	=	SYM
ejpam-4510	349	20	x∗x	x∗x	PUNCT
ejpam-4510	349	21	(	(	PUNCT
ejpam-4510	349	22	x	x	X
ejpam-4510	349	23	,	,	PUNCT
ejpam-4510	349	24	x	x	SYM
ejpam-4510	349	25	)	)	PUNCT
ejpam-4510	349	26	∈	∈	PROPN
ejpam-4510	349	27	φ̊(max	φ̊(max	NUM
ejpam-4510	349	28	,	,	PUNCT
ejpam-4510	349	29	min	min	NOUN
ejpam-4510	349	30	)	)	PUNCT
ejpam-4510	349	31	,	,	PUNCT
ejpam-4510	349	32	φs(1	φs(1	PROPN
ejpam-4510	349	33	)	)	PUNCT
ejpam-4510	349	34	=	=	NOUN
ejpam-4510	349	35	φs(x	φs(x	X
ejpam-4510	349	36	∗	∗	NOUN
ejpam-4510	349	37	x	x	SYM
ejpam-4510	349	38	)	)	PUNCT
ejpam-4510	349	39	⊇	⊇	NOUN
ejpam-4510	349	40	φs(x	φs(x	PRON
ejpam-4510	349	41	)	)	PUNCT
ejpam-4510	349	42	,	,	PUNCT
ejpam-4510	349	43	and	and	CCONJ
ejpam-4510	349	44	φ̃(1	φ̃(1	NOUN
ejpam-4510	349	45	)	)	PUNCT
ejpam-4510	349	46	=	=	SYM
ejpam-4510	349	47	φ̃(x	φ̃(x	PROPN
ejpam-4510	349	48	∗	∗	NOUN
ejpam-4510	349	49	x	x	NOUN
ejpam-4510	349	50	)	)	PUNCT
ejpam-4510	349	51	⪰	⪰	NOUN
ejpam-4510	349	52	φ̃(x	φ̃(x	PROPN
ejpam-4510	349	53	)	)	PUNCT
ejpam-4510	349	54	for	for	ADP
ejpam-4510	349	55	all	all	PRON
ejpam-4510	349	56	x	x	SYM
ejpam-4510	349	57	∈	∈	NOUN
ejpam-4510	349	58	x.	x.	NOUN
ejpam-4510	349	59	using	use	VERB
ejpam-4510	349	60	(	(	PUNCT
ejpam-4510	349	61	be1	be1	NOUN
ejpam-4510	349	62	)	)	PUNCT
ejpam-4510	349	63	,	,	PUNCT
ejpam-4510	349	64	(	(	PUNCT
ejpam-4510	349	65	be3	be3	PROPN
ejpam-4510	349	66	)	)	PUNCT
ejpam-4510	349	67	and	and	CCONJ
ejpam-4510	349	68	(	(	PUNCT
ejpam-4510	349	69	34	34	NUM
ejpam-4510	349	70	)	)	PUNCT
ejpam-4510	349	71	,	,	PUNCT
ejpam-4510	349	72	we	we	PRON
ejpam-4510	349	73	have	have	VERB
ejpam-4510	349	74	φ−(y	φ−(y	NOUN
ejpam-4510	349	75	)	)	PUNCT
ejpam-4510	350	1	=	=	SYM
ejpam-4510	350	2	φ−(1	φ−(1	NOUN
ejpam-4510	350	3	∗	∗	NOUN
ejpam-4510	350	4	y	y	NOUN
ejpam-4510	350	5	)	)	PUNCT
ejpam-4510	351	1	=	=	PUNCT
ejpam-4510	352	1	φ−(((x	φ−(((x	CCONJ
ejpam-4510	352	2	∗	∗	NOUN
ejpam-4510	352	3	y	y	NOUN
ejpam-4510	352	4	)	)	PUNCT
ejpam-4510	352	5	∗	∗	NOUN
ejpam-4510	352	6	(	(	PUNCT
ejpam-4510	352	7	x	x	X
ejpam-4510	352	8	∗	∗	PROPN
ejpam-4510	352	9	y	y	PROPN
ejpam-4510	352	10	)	)	PUNCT
ejpam-4510	352	11	)	)	PUNCT
ejpam-4510	352	12	∗	∗	PROPN
ejpam-4510	352	13	y	y	NOUN
ejpam-4510	352	14	)	)	PUNCT
ejpam-4510	352	15	≤	≤	NOUN
ejpam-4510	352	16	max{φ−(x	max{φ−(x	PROPN
ejpam-4510	352	17	∗	∗	PROPN
ejpam-4510	352	18	y	y	PROPN
ejpam-4510	352	19	)	)	PUNCT
ejpam-4510	352	20	,	,	PUNCT
ejpam-4510	352	21	φ−(x	φ−(x	PROPN
ejpam-4510	352	22	)	)	PUNCT
ejpam-4510	352	23	}	}	PUNCT
ejpam-4510	352	24	,	,	PUNCT
ejpam-4510	352	25	φ+(y	φ+(y	CCONJ
ejpam-4510	352	26	)	)	PUNCT
ejpam-4510	352	27	=	=	SYM
ejpam-4510	352	28	φ+(1	φ+(1	NOUN
ejpam-4510	352	29	∗	∗	NOUN
ejpam-4510	352	30	y	y	NOUN
ejpam-4510	352	31	)	)	PUNCT
ejpam-4510	353	1	=	=	PUNCT
ejpam-4510	353	2	φ+(((x	φ+(((x	NOUN
ejpam-4510	353	3	∗	∗	X
ejpam-4510	353	4	y	y	NOUN
ejpam-4510	353	5	)	)	PUNCT
ejpam-4510	353	6	∗	∗	NOUN
ejpam-4510	353	7	(	(	PUNCT
ejpam-4510	353	8	x	x	X
ejpam-4510	353	9	∗	∗	PROPN
ejpam-4510	353	10	y	y	PROPN
ejpam-4510	353	11	)	)	PUNCT
ejpam-4510	353	12	)	)	PUNCT
ejpam-4510	353	13	∗	∗	PROPN
ejpam-4510	353	14	y	y	PROPN
ejpam-4510	353	15	)	)	PUNCT
ejpam-4510	353	16	≥	≥	NOUN
ejpam-4510	354	1	min{φ+(x	min{φ+(x	PROPN
ejpam-4510	354	2	∗	∗	X
ejpam-4510	354	3	y	y	NOUN
ejpam-4510	354	4	)	)	PUNCT
ejpam-4510	354	5	,	,	PUNCT
ejpam-4510	354	6	φ+(x	φ+(x	NOUN
ejpam-4510	354	7	)	)	PUNCT
ejpam-4510	354	8	}	}	PUNCT
ejpam-4510	354	9	,	,	PUNCT
ejpam-4510	354	10	φs(y	φs(y	NUM
ejpam-4510	354	11	)	)	PUNCT
ejpam-4510	355	1	=	=	SYM
ejpam-4510	355	2	φs(1	φs(1	PROPN
ejpam-4510	355	3	∗	∗	NOUN
ejpam-4510	355	4	y	y	NOUN
ejpam-4510	355	5	)	)	PUNCT
ejpam-4510	356	1	=	=	SYM
ejpam-4510	356	2	φs(((x	φs(((x	PROPN
ejpam-4510	356	3	∗	∗	PROPN
ejpam-4510	356	4	y	y	NOUN
ejpam-4510	356	5	)	)	PUNCT
ejpam-4510	356	6	∗	∗	NOUN
ejpam-4510	356	7	(	(	PUNCT
ejpam-4510	356	8	x	x	X
ejpam-4510	356	9	∗	∗	PROPN
ejpam-4510	356	10	y	y	PROPN
ejpam-4510	356	11	)	)	PUNCT
ejpam-4510	356	12	)	)	PUNCT
ejpam-4510	357	1	∗	∗	PROPN
ejpam-4510	357	2	y	y	NOUN
ejpam-4510	357	3	)	)	PUNCT
ejpam-4510	357	4	⊇	⊇	NOUN
ejpam-4510	357	5	φs(x	φs(x	PUNCT
ejpam-4510	357	6	∗	∗	PROPN
ejpam-4510	357	7	y	y	NOUN
ejpam-4510	357	8	)	)	PUNCT
ejpam-4510	357	9	∩	∩	NOUN
ejpam-4510	357	10	φs(x	φs(x	NUM
ejpam-4510	357	11	)	)	PUNCT
ejpam-4510	357	12	,	,	PUNCT
ejpam-4510	357	13	φ̃(y	φ̃(y	NOUN
ejpam-4510	357	14	)	)	PUNCT
ejpam-4510	357	15	=	=	SYM
ejpam-4510	357	16	φ̃(1	φ̃(1	NOUN
ejpam-4510	357	17	∗	∗	X
ejpam-4510	357	18	y	y	PROPN
ejpam-4510	357	19	)	)	PUNCT
ejpam-4510	357	20	=	=	SYM
ejpam-4510	358	1	φ̃(((x	φ̃(((x	X
ejpam-4510	358	2	∗	∗	NOUN
ejpam-4510	358	3	y	y	NOUN
ejpam-4510	358	4	)	)	PUNCT
ejpam-4510	358	5	∗	∗	NOUN
ejpam-4510	358	6	(	(	PUNCT
ejpam-4510	358	7	x	x	X
ejpam-4510	358	8	∗	∗	PROPN
ejpam-4510	358	9	y	y	PROPN
ejpam-4510	358	10	)	)	PUNCT
ejpam-4510	358	11	)	)	PUNCT
ejpam-4510	358	12	∗	∗	PROPN
ejpam-4510	358	13	y	y	NOUN
ejpam-4510	358	14	)	)	PUNCT
ejpam-4510	358	15	⪰	⪰	NOUN
ejpam-4510	358	16	rmin{φ̃(x	rmin{φ̃(x	NOUN
ejpam-4510	358	17	∗	∗	PROPN
ejpam-4510	358	18	y	y	PROPN
ejpam-4510	358	19	)	)	PUNCT
ejpam-4510	358	20	,	,	PUNCT
ejpam-4510	358	21	φ̃(x	φ̃(x	PROPN
ejpam-4510	358	22	)	)	PUNCT
ejpam-4510	358	23	}	}	PUNCT
ejpam-4510	358	24	.	.	PUNCT
ejpam-4510	359	1	consequently	consequently	ADV
ejpam-4510	359	2	,	,	PUNCT
ejpam-4510	359	3	dokφ	dokφ	NOUN
ejpam-4510	359	4	:	:	PUNCT
ejpam-4510	359	5	=	=	SYM
ejpam-4510	359	6	(	(	PUNCT
ejpam-4510	359	7	φ̊	φ̊	PROPN
ejpam-4510	359	8	,	,	PUNCT
ejpam-4510	359	9	φs	φs	ADV
ejpam-4510	359	10	,	,	PUNCT
ejpam-4510	359	11	φ̃	φ̃	PROPN
ejpam-4510	359	12	)	)	PUNCT
ejpam-4510	359	13	is	be	AUX
ejpam-4510	359	14	a	a	DET
ejpam-4510	359	15	dokdo	dokdo	NOUN
ejpam-4510	359	16	be	be	NOUN
ejpam-4510	359	17	-	-	PUNCT
ejpam-4510	359	18	filter	filter	NOUN
ejpam-4510	359	19	of	of	ADP
ejpam-4510	359	20	(	(	PUNCT
ejpam-4510	359	21	x	x	NOUN
ejpam-4510	359	22	,	,	PUNCT
ejpam-4510	359	23	u	u	NOUN
ejpam-4510	359	24	)	)	PUNCT
ejpam-4510	359	25	.	.	PUNCT
ejpam-4510	360	1	5	5	X
ejpam-4510	360	2	.	.	X
ejpam-4510	360	3	conclusion	conclusion	NOUN
ejpam-4510	360	4	to	to	PART
ejpam-4510	360	5	apply	apply	VERB
ejpam-4510	360	6	the	the	DET
ejpam-4510	360	7	dokdo	dokdo	NOUN
ejpam-4510	360	8	structure	structure	NOUN
ejpam-4510	360	9	to	to	PART
ejpam-4510	360	10	be	be	AUX
ejpam-4510	360	11	-	-	PUNCT
ejpam-4510	360	12	algebra	algebra	NOUN
ejpam-4510	360	13	,	,	PUNCT
ejpam-4510	360	14	we	we	PRON
ejpam-4510	360	15	introduced	introduce	VERB
ejpam-4510	360	16	(	(	PUNCT
ejpam-4510	360	17	weak	weak	ADJ
ejpam-4510	360	18	)	)	PUNCT
ejpam-4510	360	19	dokdo	dokdo	NOUN
ejpam-4510	360	20	be	be	NOUN
ejpam-4510	360	21	-	-	PUNCT
ejpam-4510	360	22	subalgebra	subalgebra	NOUN
ejpam-4510	360	23	and	and	CCONJ
ejpam-4510	360	24	dokdo	dokdo	NOUN
ejpam-4510	360	25	be	be	NOUN
ejpam-4510	360	26	-	-	PUNCT
ejpam-4510	360	27	filter	filter	NOUN
ejpam-4510	360	28	and	and	CCONJ
ejpam-4510	360	29	study	study	VERB
ejpam-4510	360	30	its	its	PRON
ejpam-4510	360	31	characteristics	characteristic	NOUN
ejpam-4510	360	32	.	.	PUNCT
ejpam-4510	361	1	we	we	PRON
ejpam-4510	361	2	investigated	investigate	VERB
ejpam-4510	361	3	the	the	DET
ejpam-4510	361	4	relationship	relationship	NOUN
ejpam-4510	361	5	between	between	ADP
ejpam-4510	361	6	weak	weak	ADJ
ejpam-4510	361	7	dokdo	dokdo	NOUN
ejpam-4510	361	8	be	be	NOUN
ejpam-4510	361	9	-	-	PUNCT
ejpam-4510	361	10	subalgebra	subalgebra	NOUN
ejpam-4510	361	11	,	,	PUNCT
ejpam-4510	361	12	dokdo	dokdo	PROPN
ejpam-4510	361	13	be	be	NOUN
ejpam-4510	361	14	-	-	PUNCT
ejpam-4510	361	15	subalgebra	subalgebra	NOUN
ejpam-4510	361	16	and	and	CCONJ
ejpam-4510	361	17	dokdo	dokdo	VERB
ejpam-4510	361	18	be	be	NOUN
ejpam-4510	361	19	-	-	PUNCT
ejpam-4510	361	20	filter	filter	NOUN
ejpam-4510	361	21	.	.	PUNCT
ejpam-4510	362	1	we	we	PRON
ejpam-4510	362	2	explored	explore	VERB
ejpam-4510	362	3	the	the	DET
ejpam-4510	362	4	conditions	condition	NOUN
ejpam-4510	362	5	under	under	ADP
ejpam-4510	362	6	which	which	PRON
ejpam-4510	362	7	dokdo	dokdo	NOUN
ejpam-4510	362	8	structure	structure	NOUN
ejpam-4510	362	9	can	can	AUX
ejpam-4510	362	10	be	be	AUX
ejpam-4510	362	11	weak	weak	ADJ
ejpam-4510	362	12	dokdo	dokdo	NOUN
ejpam-4510	362	13	be	be	NOUN
ejpam-4510	362	14	-	-	PUNCT
ejpam-4510	362	15	subalgebra	subalgebra	NOUN
ejpam-4510	362	16	and	and	CCONJ
ejpam-4510	362	17	dokdo	dokdo	VERB
ejpam-4510	362	18	be	be	NOUN
ejpam-4510	362	19	-	-	PUNCT
ejpam-4510	362	20	filter	filter	NOUN
ejpam-4510	362	21	,	,	PUNCT
ejpam-4510	362	22	and	and	CCONJ
ejpam-4510	362	23	the	the	DET
ejpam-4510	362	24	condition	condition	NOUN
ejpam-4510	362	25	under	under	ADP
ejpam-4510	362	26	which	which	PRON
ejpam-4510	362	27	weak	weak	ADJ
ejpam-4510	362	28	dokdo	dokdo	NOUN
ejpam-4510	362	29	be	be	NOUN
ejpam-4510	362	30	-	-	PUNCT
ejpam-4510	362	31	subalgebra	subalgebra	NOUN
ejpam-4510	362	32	can	can	AUX
ejpam-4510	362	33	be	be	AUX
ejpam-4510	362	34	dokdo	dokdo	VERB
ejpam-4510	362	35	be	be	NOUN
ejpam-4510	362	36	-	-	PUNCT
ejpam-4510	362	37	subalgebra	subalgebra	NOUN
ejpam-4510	362	38	.	.	PUNCT
ejpam-4510	363	1	we	we	PRON
ejpam-4510	363	2	discussed	discuss	VERB
ejpam-4510	363	3	the	the	DET
ejpam-4510	363	4	characterization	characterization	NOUN
ejpam-4510	363	5	of	of	ADP
ejpam-4510	363	6	dokdo	dokdo	NOUN
ejpam-4510	363	7	be	be	NOUN
ejpam-4510	363	8	-	-	PUNCT
ejpam-4510	363	9	filter	filter	NOUN
ejpam-4510	363	10	.	.	PUNCT
ejpam-4510	364	1	acknowledgements	acknowledgement	NOUN
ejpam-4510	364	2	the	the	DET
ejpam-4510	364	3	authors	author	NOUN
ejpam-4510	364	4	wish	wish	VERB
ejpam-4510	364	5	to	to	PART
ejpam-4510	364	6	thank	thank	VERB
ejpam-4510	364	7	the	the	DET
ejpam-4510	364	8	anonymous	anonymous	ADJ
ejpam-4510	364	9	reviewers	reviewer	NOUN
ejpam-4510	364	10	for	for	ADP
ejpam-4510	364	11	their	their	PRON
ejpam-4510	364	12	valuable	valuable	ADJ
ejpam-4510	364	13	suggestions	suggestion	NOUN
ejpam-4510	364	14	.	.	PUNCT
ejpam-4510	365	1	references	reference	NOUN
ejpam-4510	365	2	[	[	X
ejpam-4510	365	3	1	1	X
ejpam-4510	365	4	]	]	PUNCT
ejpam-4510	365	5	s.	s.	PROPN
ejpam-4510	365	6	s.	s.	PROPN
ejpam-4510	365	7	ahn	ahn	PROPN
ejpam-4510	365	8	,	,	PUNCT
ejpam-4510	365	9	y.	y.	PROPN
ejpam-4510	365	10	h.	h.	PROPN
ejpam-4510	365	11	kim	kim	PROPN
ejpam-4510	365	12	,	,	PUNCT
ejpam-4510	365	13	and	and	CCONJ
ejpam-4510	365	14	k.	k.	PROPN
ejpam-4510	365	15	s.	s.	PROPN
ejpam-4510	366	1	so	so	ADV
ejpam-4510	366	2	.	.	PUNCT
ejpam-4510	367	1	fuzzy	fuzzy	ADJ
ejpam-4510	367	2	be	be	AUX
ejpam-4510	367	3	-	-	PUNCT
ejpam-4510	367	4	algebras	algebras	X
ejpam-4510	367	5	.	.	PUNCT
ejpam-4510	368	1	j.	j.	PROPN
ejpam-4510	368	2	appl	appl	PROPN
ejpam-4510	368	3	.	.	PROPN
ejpam-4510	368	4	math	math	PROPN
ejpam-4510	368	5	.	.	PUNCT
ejpam-4510	369	1	informatics	informatic	NOUN
ejpam-4510	369	2	,	,	PUNCT
ejpam-4510	369	3	29:1049–1057	29:1049–1057	PROPN
ejpam-4510	369	4	,	,	PUNCT
ejpam-4510	369	5	2011	2011	NUM
ejpam-4510	369	6	.	.	PUNCT
ejpam-4510	370	1	[	[	X
ejpam-4510	370	2	2	2	NUM
ejpam-4510	370	3	]	]	SYM
ejpam-4510	370	4	g.dymek	g.dymek	NOUN
ejpam-4510	370	5	and	and	CCONJ
ejpam-4510	370	6	a.	a.	PROPN
ejpam-4510	370	7	walendiziak	walendiziak	PROPN
ejpam-4510	370	8	.	.	PUNCT
ejpam-4510	371	1	fuzzy	fuzzy	ADJ
ejpam-4510	371	2	filters	filter	NOUN
ejpam-4510	371	3	of	of	ADP
ejpam-4510	371	4	be	be	NOUN
ejpam-4510	371	5	-	-	PUNCT
ejpam-4510	371	6	algebras	algebra	NOUN
ejpam-4510	371	7	.	.	PUNCT
ejpam-4510	372	1	math	math	NOUN
ejpam-4510	372	2	.	.	PUNCT
ejpam-4510	373	1	slovaca	slovaca	PROPN
ejpam-4510	373	2	,	,	PUNCT
ejpam-4510	373	3	63:935	63:935	NUM
ejpam-4510	373	4	–	–	PUNCT
ejpam-4510	373	5	946	946	NUM
ejpam-4510	373	6	,	,	PUNCT
ejpam-4510	373	7	2013	2013	NUM
ejpam-4510	373	8	.	.	PUNCT
ejpam-4510	374	1	references	reference	NOUN
ejpam-4510	374	2	1535	1535	NUM
ejpam-4510	374	3	[	[	X
ejpam-4510	374	4	3	3	NUM
ejpam-4510	374	5	]	]	PUNCT
ejpam-4510	374	6	m.	m.	NOUN
ejpam-4510	374	7	b.	b.	PROPN
ejpam-4510	374	8	gorzalczany	gorzalczany	NOUN
ejpam-4510	374	9	.	.	PUNCT
ejpam-4510	375	1	a	a	DET
ejpam-4510	375	2	method	method	NOUN
ejpam-4510	375	3	of	of	ADP
ejpam-4510	375	4	inference	inference	NOUN
ejpam-4510	375	5	in	in	ADP
ejpam-4510	375	6	approximate	approximate	ADJ
ejpam-4510	375	7	reasoning	reasoning	NOUN
ejpam-4510	375	8	based	base	VERB
ejpam-4510	375	9	on	on	ADP
ejpam-4510	375	10	intervalvalued	intervalvalue	VERB
ejpam-4510	375	11	fuzzy	fuzzy	ADJ
ejpam-4510	375	12	sets	set	NOUN
ejpam-4510	375	13	.	.	PUNCT
ejpam-4510	376	1	fuzzy	fuzzy	ADJ
ejpam-4510	376	2	sets	set	NOUN
ejpam-4510	376	3	and	and	CCONJ
ejpam-4510	376	4	systems	system	NOUN
ejpam-4510	376	5	,	,	PUNCT
ejpam-4510	376	6	21:1–17	21:1–17	NUM
ejpam-4510	376	7	,	,	PUNCT
ejpam-4510	376	8	1987	1987	NUM
ejpam-4510	376	9	.	.	PUNCT
ejpam-4510	377	1	[	[	X
ejpam-4510	377	2	4	4	X
ejpam-4510	377	3	]	]	X
ejpam-4510	377	4	y.	y.	PROPN
ejpam-4510	377	5	huang	huang	PROPN
ejpam-4510	377	6	.	.	PUNCT
ejpam-4510	378	1	bci	bci	PROPN
ejpam-4510	378	2	-	-	PUNCT
ejpam-4510	378	3	algebras	algebras	PROPN
ejpam-4510	378	4	.	.	PUNCT
ejpam-4510	379	1	science	science	PROPN
ejpam-4510	379	2	press	press	PROPN
ejpam-4510	379	3	,	,	PUNCT
ejpam-4510	379	4	beijing	beijing	PROPN
ejpam-4510	379	5	,	,	PUNCT
ejpam-4510	379	6	china	china	PROPN
ejpam-4510	379	7	,	,	PUNCT
ejpam-4510	379	8	2006	2006	NUM
ejpam-4510	379	9	.	.	PUNCT
ejpam-4510	380	1	[	[	X
ejpam-4510	380	2	5	5	X
ejpam-4510	380	3	]	]	X
ejpam-4510	380	4	y.	y.	PROPN
ejpam-4510	380	5	b.	b.	PROPN
ejpam-4510	380	6	jun	jun	PROPN
ejpam-4510	380	7	.	.	PROPN
ejpam-4510	380	8	dokdo	dokdo	PROPN
ejpam-4510	380	9	structure	structure	NOUN
ejpam-4510	380	10	and	and	CCONJ
ejpam-4510	380	11	its	its	PRON
ejpam-4510	380	12	application	application	NOUN
ejpam-4510	380	13	in	in	ADP
ejpam-4510	380	14	bck	bck	PROPN
ejpam-4510	380	15	/	/	SYM
ejpam-4510	380	16	bci	bci	NOUN
ejpam-4510	380	17	-	-	PUNCT
ejpam-4510	380	18	algebras	algebras	X
ejpam-4510	380	19	.	.	PUNCT
ejpam-4510	381	1	twms	twms	PROPN
ejpam-4510	381	2	j.	j.	PROPN
ejpam-4510	381	3	pure	pure	PROPN
ejpam-4510	381	4	appl	appl	PROPN
ejpam-4510	381	5	.	.	PROPN
ejpam-4510	381	6	math.(submitted	math.(submitte	VERB
ejpam-4510	381	7	)	)	PUNCT
ejpam-4510	381	8	.	.	PUNCT
ejpam-4510	382	1	[	[	X
ejpam-4510	382	2	6	6	NUM
ejpam-4510	382	3	]	]	X
ejpam-4510	382	4	y.	y.	PROPN
ejpam-4510	382	5	b.	b.	PROPN
ejpam-4510	382	6	jun	jun	PROPN
ejpam-4510	382	7	.	.	PROPN
ejpam-4510	382	8	implicative	implicative	ADJ
ejpam-4510	382	9	ideals	ideal	NOUN
ejpam-4510	382	10	of	of	ADP
ejpam-4510	382	11	bck	bck	NOUN
ejpam-4510	382	12	-	-	PUNCT
ejpam-4510	382	13	algebras	algebras	PROPN
ejpam-4510	382	14	based	base	VERB
ejpam-4510	382	15	on	on	ADP
ejpam-4510	382	16	dokdo	dokdo	PROPN
ejpam-4510	382	17	structure	structure	NOUN
ejpam-4510	382	18	.	.	PUNCT
ejpam-4510	383	1	journal	journal	NOUN
ejpam-4510	383	2	of	of	ADP
ejpam-4510	383	3	algebraic	algebraic	PROPN
ejpam-4510	383	4	hyperstructures	hyperstructure	NOUN
ejpam-4510	383	5	and	and	CCONJ
ejpam-4510	383	6	logical	logical	ADJ
ejpam-4510	383	7	algebras	algebra	NOUN
ejpam-4510	383	8	,	,	PUNCT
ejpam-4510	383	9	3(3):33–43	3(3):33–43	NUM
ejpam-4510	383	10	,	,	PUNCT
ejpam-4510	383	11	2022	2022	NUM
ejpam-4510	383	12	.	.	PUNCT
ejpam-4510	384	1	[	[	X
ejpam-4510	384	2	7	7	X
ejpam-4510	384	3	]	]	PUNCT
ejpam-4510	384	4	h.	h.	PROPN
ejpam-4510	384	5	s.	s.	PROPN
ejpam-4510	384	6	kim	kim	PROPN
ejpam-4510	384	7	and	and	CCONJ
ejpam-4510	384	8	y.	y.	PROPN
ejpam-4510	384	9	h.	h.	PROPN
ejpam-4510	384	10	kim	kim	PROPN
ejpam-4510	384	11	.	.	PUNCT
ejpam-4510	385	1	on	on	ADP
ejpam-4510	385	2	be	be	AUX
ejpam-4510	385	3	-	-	PUNCT
ejpam-4510	385	4	algebras	algebra	NOUN
ejpam-4510	385	5	.	.	PUNCT
ejpam-4510	385	6	sci	sci	PROPN
ejpam-4510	385	7	.	.	PROPN
ejpam-4510	385	8	math	math	PROPN
ejpam-4510	385	9	.	.	PUNCT
ejpam-4510	386	1	jpn	jpn	PROPN
ejpam-4510	386	2	.	.	PROPN
ejpam-4510	386	3	,	,	PUNCT
ejpam-4510	386	4	66:113–116	66:113–116	PROPN
ejpam-4510	386	5	,	,	PUNCT
ejpam-4510	386	6	2007	2007	NUM
ejpam-4510	386	7	.	.	PUNCT
ejpam-4510	387	1	[	[	X
ejpam-4510	387	2	8	8	NUM
ejpam-4510	387	3	]	]	PUNCT
ejpam-4510	387	4	k.	k.	PROPN
ejpam-4510	387	5	m.	m.	PROPN
ejpam-4510	387	6	lee	lee	PROPN
ejpam-4510	387	7	.	.	PUNCT
ejpam-4510	388	1	bipolar	bipolar	ADJ
ejpam-4510	388	2	-	-	PUNCT
ejpam-4510	388	3	valued	value	VERB
ejpam-4510	388	4	fuzzy	fuzzy	ADJ
ejpam-4510	388	5	sets	set	NOUN
ejpam-4510	388	6	and	and	CCONJ
ejpam-4510	388	7	their	their	PRON
ejpam-4510	388	8	operations	operation	NOUN
ejpam-4510	388	9	.	.	PUNCT
ejpam-4510	389	1	proc	proc	NOUN
ejpam-4510	389	2	.	.	PUNCT
ejpam-4510	390	1	int	int	NOUN
ejpam-4510	390	2	.	.	PUNCT
ejpam-4510	390	3	conf	conf	PROPN
ejpam-4510	390	4	.	.	PUNCT
ejpam-4510	391	1	on	on	ADP
ejpam-4510	391	2	intelligent	intelligent	ADJ
ejpam-4510	391	3	technologies	technology	NOUN
ejpam-4510	391	4	,	,	PUNCT
ejpam-4510	391	5	bangkok	bangkok	PROPN
ejpam-4510	391	6	,	,	PUNCT
ejpam-4510	391	7	thailand	thailand	PROPN
ejpam-4510	391	8	,	,	PUNCT
ejpam-4510	391	9	2000	2000	NUM
ejpam-4510	391	10	.	.	PUNCT
ejpam-4510	392	1	[	[	X
ejpam-4510	392	2	9	9	NUM
ejpam-4510	392	3	]	]	PUNCT
ejpam-4510	392	4	d.	d.	PROPN
ejpam-4510	392	5	molodtsov	molodtsov	PROPN
ejpam-4510	392	6	.	.	PUNCT
ejpam-4510	393	1	soft	soft	ADJ
ejpam-4510	393	2	set	set	NOUN
ejpam-4510	393	3	theory	theory	NOUN
ejpam-4510	393	4	–	–	PUNCT
ejpam-4510	393	5	first	first	ADJ
ejpam-4510	393	6	results	result	NOUN
ejpam-4510	393	7	.	.	PUNCT
ejpam-4510	394	1	comput	comput	NOUN
ejpam-4510	394	2	.	.	PUNCT
ejpam-4510	395	1	math	math	NOUN
ejpam-4510	395	2	.	.	PUNCT
ejpam-4510	396	1	appl	appl	PROPN
ejpam-4510	396	2	.	.	PROPN
ejpam-4510	396	3	,	,	PUNCT
ejpam-4510	396	4	37:19–31	37:19–31	PROPN
ejpam-4510	396	5	,	,	PUNCT
ejpam-4510	396	6	1999	1999	NUM
ejpam-4510	396	7	.	.	PUNCT
ejpam-4510	397	1	[	[	X
ejpam-4510	397	2	10	10	NUM
ejpam-4510	397	3	]	]	X
ejpam-4510	397	4	s.	s.	PROPN
ejpam-4510	397	5	r.	r.	PROPN
ejpam-4510	397	6	mukkamala	mukkamala	PROPN
ejpam-4510	397	7	.	.	PUNCT
ejpam-4510	398	1	a	a	DET
ejpam-4510	398	2	course	course	NOUN
ejpam-4510	398	3	in	in	ADP
ejpam-4510	398	4	be	be	NOUN
ejpam-4510	398	5	-	-	PUNCT
ejpam-4510	398	6	algebras	algebra	NOUN
ejpam-4510	398	7	.	.	PUNCT
ejpam-4510	399	1	springer	springer	NOUN
ejpam-4510	399	2	nature	nature	PROPN
ejpam-4510	399	3	singapor	singapor	PROPN
ejpam-4510	399	4	pte	pte	PROPN
ejpam-4510	399	5	ltd	ltd	PROPN
ejpam-4510	399	6	.	.	PROPN
ejpam-4510	399	7	,	,	PUNCT
ejpam-4510	399	8	2018	2018	NUM
ejpam-4510	399	9	.	.	PUNCT
ejpam-4510	400	1	[	[	X
ejpam-4510	400	2	11	11	NUM
ejpam-4510	400	3	]	]	PUNCT
ejpam-4510	400	4	a.	a.	NOUN
ejpam-4510	400	5	rezaei	rezaei	PROPN
ejpam-4510	400	6	and	and	CCONJ
ejpam-4510	400	7	a.	a.	PROPN
ejpam-4510	400	8	borumand	borumand	PROPN
ejpam-4510	400	9	saeid	saeid	PROPN
ejpam-4510	400	10	.	.	PUNCT
ejpam-4510	401	1	on	on	ADP
ejpam-4510	401	2	fuzzy	fuzzy	ADJ
ejpam-4510	401	3	subalgebras	subalgebra	NOUN
ejpam-4510	401	4	of	of	ADP
ejpam-4510	401	5	be	be	AUX
ejpam-4510	401	6	-	-	PUNCT
ejpam-4510	401	7	algebras	algebra	NOUN
ejpam-4510	401	8	.	.	PUNCT
ejpam-4510	401	9	afr	afr	PROPN
ejpam-4510	401	10	.	.	PUNCT
ejpam-4510	402	1	mat	mat	PROPN
ejpam-4510	402	2	.	.	PROPN
ejpam-4510	402	3	,	,	PUNCT
ejpam-4510	402	4	22:115–127	22:115–127	PROPN
ejpam-4510	402	5	,	,	PUNCT
ejpam-4510	402	6	2011	2011	NUM
ejpam-4510	402	7	.	.	PUNCT
ejpam-4510	403	1	[	[	X
ejpam-4510	403	2	12	12	NUM
ejpam-4510	403	3	]	]	PUNCT
ejpam-4510	403	4	l.	l.	PROPN
ejpam-4510	403	5	a.	a.	PROPN
ejpam-4510	403	6	zadeh	zadeh	PROPN
ejpam-4510	403	7	.	.	PUNCT
ejpam-4510	404	1	the	the	DET
ejpam-4510	404	2	concept	concept	NOUN
ejpam-4510	404	3	of	of	ADP
ejpam-4510	404	4	a	a	DET
ejpam-4510	404	5	linguistic	linguistic	ADJ
ejpam-4510	404	6	variable	variable	NOUN
ejpam-4510	404	7	and	and	CCONJ
ejpam-4510	404	8	its	its	PRON
ejpam-4510	404	9	application	application	NOUN
ejpam-4510	404	10	to	to	PART
ejpam-4510	404	11	approximate	approximate	ADJ
ejpam-4510	404	12	reasoning	reasoning	NOUN
ejpam-4510	404	13	-	-	PUNCT
ejpam-4510	404	14	i.	i.	NOUN
ejpam-4510	404	15	inform	inform	NOUN
ejpam-4510	404	16	.	.	PUNCT
ejpam-4510	405	1	sci	sci	PROPN
ejpam-4510	405	2	.	.	PROPN
ejpam-4510	405	3	,	,	PUNCT
ejpam-4510	405	4	8:199–249	8:199–249	NUM
ejpam-4510	405	5	,	,	PUNCT
ejpam-4510	405	6	1975	1975	NUM
ejpam-4510	405	7	.	.	PUNCT