id	sid	tid	token	lemma	pos
ejpam-4522	1	1	european	european	PROPN
ejpam-4522	1	2	journal	journal	PROPN
ejpam-4522	1	3	of	of	ADP
ejpam-4522	1	4	pure	pure	ADJ
ejpam-4522	1	5	and	and	CCONJ
ejpam-4522	1	6	applied	apply	VERB
ejpam-4522	1	7	mathematics	mathematic	NOUN
ejpam-4522	1	8	vol	vol	NOUN
ejpam-4522	1	9	.	.	PROPN
ejpam-4522	2	1	15	15	NUM
ejpam-4522	2	2	,	,	PUNCT
ejpam-4522	2	3	no	no	INTJ
ejpam-4522	2	4	.	.	NOUN
ejpam-4522	2	5	4	4	NUM
ejpam-4522	2	6	,	,	PUNCT
ejpam-4522	2	7	2022	2022	NUM
ejpam-4522	2	8	,	,	PUNCT
ejpam-4522	2	9	1498	1498	NUM
ejpam-4522	2	10	-	-	SYM
ejpam-4522	2	11	1511	1511	NUM
ejpam-4522	2	12	issn	issn	PROPN
ejpam-4522	2	13	1307	1307	NUM
ejpam-4522	2	14	-	-	SYM
ejpam-4522	2	15	5543	5543	NUM
ejpam-4522	2	16	–	–	PUNCT
ejpam-4522	2	17	ejpam.com	ejpam.com	X
ejpam-4522	2	18	published	publish	VERB
ejpam-4522	2	19	by	by	ADP
ejpam-4522	2	20	new	new	PROPN
ejpam-4522	2	21	york	york	PROPN
ejpam-4522	2	22	business	business	PROPN
ejpam-4522	2	23	global	global	ADJ
ejpam-4522	2	24	positive	positive	ADJ
ejpam-4522	2	25	implicative	implicative	ADJ
ejpam-4522	2	26	makgeolli	makgeolli	NOUN
ejpam-4522	2	27	ideals	ideal	NOUN
ejpam-4522	2	28	of	of	ADP
ejpam-4522	2	29	bck	bck	NOUN
ejpam-4522	2	30	-	-	PUNCT
ejpam-4522	2	31	algebras	algebras	PROPN
ejpam-4522	2	32	seok	seok	PROPN
ejpam-4522	2	33	-	-	PUNCT
ejpam-4522	2	34	zun	zun	PROPN
ejpam-4522	2	35	song1,∗	song1,∗	NOUN
ejpam-4522	2	36	,	,	PUNCT
ejpam-4522	2	37	mehmet	mehmet	PROPN
ejpam-4522	2	38	ali	ali	PROPN
ejpam-4522	2	39	öztürk2	öztürk2	PROPN
ejpam-4522	2	40	,	,	PUNCT
ejpam-4522	2	41	young	young	ADJ
ejpam-4522	2	42	bae	bae	NOUN
ejpam-4522	2	43	jun3	jun3	PROPN
ejpam-4522	2	44	1	1	NUM
ejpam-4522	2	45	department	department	NOUN
ejpam-4522	2	46	of	of	ADP
ejpam-4522	2	47	mathematics	mathematics	PROPN
ejpam-4522	2	48	,	,	PUNCT
ejpam-4522	2	49	jeju	jeju	PROPN
ejpam-4522	2	50	national	national	PROPN
ejpam-4522	2	51	university	university	PROPN
ejpam-4522	2	52	,	,	PUNCT
ejpam-4522	2	53	jeju	jeju	PROPN
ejpam-4522	2	54	63243	63243	NUM
ejpam-4522	2	55	,	,	PUNCT
ejpam-4522	2	56	korea	korea	PROPN
ejpam-4522	2	57	2	2	NUM
ejpam-4522	2	58	department	department	NOUN
ejpam-4522	2	59	of	of	ADP
ejpam-4522	2	60	mathematics	mathematic	NOUN
ejpam-4522	2	61	,	,	PUNCT
ejpam-4522	2	62	faculty	faculty	NOUN
ejpam-4522	2	63	of	of	ADP
ejpam-4522	2	64	arts	art	NOUN
ejpam-4522	2	65	and	and	CCONJ
ejpam-4522	2	66	sciences	science	NOUN
ejpam-4522	2	67	,	,	PUNCT
ejpam-4522	2	68	adıyaman	adıyaman	NOUN
ejpam-4522	2	69	university	university	NOUN
ejpam-4522	2	70	,	,	PUNCT
ejpam-4522	2	71	02040	02040	NUM
ejpam-4522	2	72	adıyaman	adıyaman	NOUN
ejpam-4522	2	73	,	,	PUNCT
ejpam-4522	2	74	turkiye	turkiye	PROPN
ejpam-4522	2	75	3	3	NUM
ejpam-4522	2	76	department	department	NOUN
ejpam-4522	2	77	of	of	ADP
ejpam-4522	2	78	mathematics	mathematics	PROPN
ejpam-4522	2	79	education	education	NOUN
ejpam-4522	2	80	,	,	PUNCT
ejpam-4522	2	81	gyeongsang	gyeongsang	PROPN
ejpam-4522	2	82	national	national	PROPN
ejpam-4522	2	83	university	university	PROPN
ejpam-4522	2	84	,	,	PUNCT
ejpam-4522	2	85	jinju	jinju	NOUN
ejpam-4522	2	86	52828	52828	NUM
ejpam-4522	2	87	,	,	PUNCT
ejpam-4522	2	88	korea	korea	PROPN
ejpam-4522	2	89	abstract	abstract	NOUN
ejpam-4522	2	90	.	.	PUNCT
ejpam-4522	3	1	the	the	DET
ejpam-4522	3	2	concept	concept	NOUN
ejpam-4522	3	3	of	of	ADP
ejpam-4522	3	4	a	a	DET
ejpam-4522	3	5	positive	positive	ADJ
ejpam-4522	3	6	implicative	implicative	ADJ
ejpam-4522	3	7	makgeolli	makgeolli	NOUN
ejpam-4522	3	8	ideal	ideal	NOUN
ejpam-4522	3	9	in	in	ADP
ejpam-4522	3	10	bck	bck	PROPN
ejpam-4522	3	11	-	-	PUNCT
ejpam-4522	3	12	algebras	algebras	PROPN
ejpam-4522	3	13	is	be	AUX
ejpam-4522	3	14	introduced	introduce	VERB
ejpam-4522	3	15	,	,	PUNCT
ejpam-4522	3	16	and	and	CCONJ
ejpam-4522	3	17	its	its	PRON
ejpam-4522	3	18	properties	property	NOUN
ejpam-4522	3	19	are	be	AUX
ejpam-4522	3	20	investigated	investigate	VERB
ejpam-4522	3	21	.	.	PUNCT
ejpam-4522	4	1	the	the	DET
ejpam-4522	4	2	relationship	relationship	NOUN
ejpam-4522	4	3	between	between	ADP
ejpam-4522	4	4	a	a	DET
ejpam-4522	4	5	makgeolli	makgeolli	NOUN
ejpam-4522	4	6	ideal	ideal	NOUN
ejpam-4522	4	7	and	and	CCONJ
ejpam-4522	4	8	a	a	DET
ejpam-4522	4	9	positive	positive	ADJ
ejpam-4522	4	10	implicative	implicative	ADJ
ejpam-4522	4	11	makgeolli	makgeolli	NOUN
ejpam-4522	4	12	ideal	ideal	NOUN
ejpam-4522	4	13	is	be	AUX
ejpam-4522	4	14	established	establish	VERB
ejpam-4522	4	15	.	.	PUNCT
ejpam-4522	5	1	the	the	DET
ejpam-4522	5	2	conditions	condition	NOUN
ejpam-4522	5	3	under	under	ADP
ejpam-4522	5	4	which	which	PRON
ejpam-4522	5	5	a	a	DET
ejpam-4522	5	6	makgeolli	makgeolli	NOUN
ejpam-4522	5	7	ideal	ideal	NOUN
ejpam-4522	5	8	can	can	AUX
ejpam-4522	5	9	be	be	AUX
ejpam-4522	5	10	a	a	DET
ejpam-4522	5	11	positive	positive	ADJ
ejpam-4522	5	12	implicative	implicative	ADJ
ejpam-4522	5	13	makgeolli	makgeolli	NOUN
ejpam-4522	5	14	ideal	ideal	NOUN
ejpam-4522	5	15	are	be	AUX
ejpam-4522	5	16	explored	explore	VERB
ejpam-4522	5	17	.	.	PUNCT
ejpam-4522	6	1	characterizations	characterization	NOUN
ejpam-4522	6	2	of	of	ADP
ejpam-4522	6	3	a	a	DET
ejpam-4522	6	4	positive	positive	ADJ
ejpam-4522	6	5	implicative	implicative	ADJ
ejpam-4522	6	6	makgeolli	makgeolli	NOUN
ejpam-4522	6	7	ideal	ideal	NOUN
ejpam-4522	6	8	are	be	AUX
ejpam-4522	6	9	discussed	discuss	VERB
ejpam-4522	6	10	,	,	PUNCT
ejpam-4522	6	11	and	and	CCONJ
ejpam-4522	6	12	the	the	DET
ejpam-4522	6	13	extension	extension	NOUN
ejpam-4522	6	14	property	property	NOUN
ejpam-4522	6	15	for	for	ADP
ejpam-4522	6	16	a	a	DET
ejpam-4522	6	17	positive	positive	ADJ
ejpam-4522	6	18	implicative	implicative	ADJ
ejpam-4522	6	19	makgeolli	makgeolli	NOUN
ejpam-4522	6	20	ideal	ideal	NOUN
ejpam-4522	6	21	is	be	AUX
ejpam-4522	6	22	established	establish	VERB
ejpam-4522	6	23	.	.	PUNCT
ejpam-4522	7	1	2020	2020	NUM
ejpam-4522	7	2	mathematics	mathematics	PROPN
ejpam-4522	7	3	subject	subject	NOUN
ejpam-4522	7	4	classifications	classification	NOUN
ejpam-4522	7	5	:	:	PUNCT
ejpam-4522	7	6	03g25	03g25	NUM
ejpam-4522	7	7	,	,	PUNCT
ejpam-4522	7	8	06f35	06f35	NUM
ejpam-4522	7	9	,	,	PUNCT
ejpam-4522	7	10	08a72	08a72	NOUN
ejpam-4522	7	11	key	key	ADJ
ejpam-4522	7	12	words	word	NOUN
ejpam-4522	7	13	and	and	CCONJ
ejpam-4522	7	14	phrases	phrase	NOUN
ejpam-4522	7	15	:	:	PUNCT
ejpam-4522	7	16	bck	bck	VERB
ejpam-4522	7	17	-	-	PUNCT
ejpam-4522	7	18	soft	soft	ADJ
ejpam-4522	7	19	universe	universe	NOUN
ejpam-4522	7	20	,	,	PUNCT
ejpam-4522	7	21	makgeolli	makgeolli	NOUN
ejpam-4522	7	22	structure	structure	NOUN
ejpam-4522	7	23	,	,	PUNCT
ejpam-4522	7	24	makgeolli	makgeolli	PROPN
ejpam-4522	7	25	ideal	ideal	NOUN
ejpam-4522	7	26	,	,	PUNCT
ejpam-4522	7	27	positive	positive	ADJ
ejpam-4522	7	28	implicative	implicative	ADJ
ejpam-4522	7	29	makgeolli	makgeolli	NOUN
ejpam-4522	7	30	ideal	ideal	NOUN
ejpam-4522	7	31	.	.	PUNCT
ejpam-4522	8	1	1	1	X
ejpam-4522	8	2	.	.	X
ejpam-4522	8	3	introduction	introduction	NOUN
ejpam-4522	8	4	many	many	ADJ
ejpam-4522	8	5	problems	problem	NOUN
ejpam-4522	8	6	that	that	PRON
ejpam-4522	8	7	need	need	VERB
ejpam-4522	8	8	to	to	PART
ejpam-4522	8	9	be	be	AUX
ejpam-4522	8	10	solved	solve	VERB
ejpam-4522	8	11	in	in	ADP
ejpam-4522	8	12	the	the	DET
ejpam-4522	8	13	real	real	ADJ
ejpam-4522	8	14	world	world	NOUN
ejpam-4522	8	15	often	often	ADV
ejpam-4522	8	16	involve	involve	VERB
ejpam-4522	8	17	inherently	inherently	ADV
ejpam-4522	8	18	uncertain	uncertain	ADJ
ejpam-4522	8	19	,	,	PUNCT
ejpam-4522	8	20	inaccurate	inaccurate	ADJ
ejpam-4522	8	21	,	,	PUNCT
ejpam-4522	8	22	and	and	CCONJ
ejpam-4522	8	23	ambiguous	ambiguous	ADJ
ejpam-4522	8	24	factors	factor	NOUN
ejpam-4522	8	25	.	.	PUNCT
ejpam-4522	9	1	zadeh	zadeh	NOUN
ejpam-4522	10	1	[	[	X
ejpam-4522	10	2	24	24	NUM
ejpam-4522	10	3	]	]	PUNCT
ejpam-4522	10	4	pointed	point	VERB
ejpam-4522	10	5	out	out	ADP
ejpam-4522	10	6	various	various	ADJ
ejpam-4522	10	7	problems	problem	NOUN
ejpam-4522	10	8	in	in	ADP
ejpam-4522	10	9	system	system	NOUN
ejpam-4522	10	10	identification	identification	NOUN
ejpam-4522	10	11	involve	involve	VERB
ejpam-4522	10	12	characteristics	characteristic	NOUN
ejpam-4522	10	13	which	which	PRON
ejpam-4522	10	14	are	be	AUX
ejpam-4522	10	15	essentially	essentially	ADV
ejpam-4522	10	16	non	non	ADJ
ejpam-4522	10	17	-	-	ADJ
ejpam-4522	10	18	probabilistic	probabilistic	ADJ
ejpam-4522	10	19	in	in	ADP
ejpam-4522	10	20	nature	nature	NOUN
ejpam-4522	10	21	,	,	PUNCT
ejpam-4522	10	22	and	and	CCONJ
ejpam-4522	10	23	he	he	PRON
ejpam-4522	10	24	introduced	introduce	VERB
ejpam-4522	10	25	fuzzy	fuzzy	ADJ
ejpam-4522	10	26	set	set	NOUN
ejpam-4522	10	27	theory	theory	NOUN
ejpam-4522	10	28	as	as	ADP
ejpam-4522	10	29	an	an	DET
ejpam-4522	10	30	alternative	alternative	NOUN
ejpam-4522	10	31	to	to	ADP
ejpam-4522	10	32	probability	probability	NOUN
ejpam-4522	10	33	theory	theory	NOUN
ejpam-4522	10	34	.	.	PUNCT
ejpam-4522	11	1	uncertainty	uncertainty	NOUN
ejpam-4522	11	2	is	be	AUX
ejpam-4522	11	3	an	an	DET
ejpam-4522	11	4	attribute	attribute	NOUN
ejpam-4522	11	5	of	of	ADP
ejpam-4522	11	6	information	information	NOUN
ejpam-4522	11	7	.	.	PUNCT
ejpam-4522	12	1	in	in	ADP
ejpam-4522	12	2	order	order	NOUN
ejpam-4522	12	3	to	to	PART
ejpam-4522	12	4	suggest	suggest	VERB
ejpam-4522	12	5	a	a	DET
ejpam-4522	12	6	more	more	ADV
ejpam-4522	12	7	general	general	ADJ
ejpam-4522	12	8	framework	framework	NOUN
ejpam-4522	12	9	,	,	PUNCT
ejpam-4522	12	10	the	the	DET
ejpam-4522	12	11	approach	approach	NOUN
ejpam-4522	12	12	to	to	ADP
ejpam-4522	12	13	uncertainty	uncertainty	NOUN
ejpam-4522	12	14	is	be	AUX
ejpam-4522	12	15	outlined	outline	VERB
ejpam-4522	12	16	by	by	ADP
ejpam-4522	12	17	zadeh	zadeh	PROPN
ejpam-4522	13	1	[	[	X
ejpam-4522	13	2	25	25	NUM
ejpam-4522	13	3	]	]	PUNCT
ejpam-4522	13	4	.	.	PUNCT
ejpam-4522	14	1	uncertainties	uncertainty	NOUN
ejpam-4522	14	2	ca	can	AUX
ejpam-4522	14	3	n’t	not	PART
ejpam-4522	14	4	be	be	AUX
ejpam-4522	14	5	handled	handle	VERB
ejpam-4522	14	6	using	use	VERB
ejpam-4522	14	7	traditional	traditional	ADJ
ejpam-4522	14	8	mathematical	mathematical	ADJ
ejpam-4522	14	9	tools	tool	NOUN
ejpam-4522	14	10	but	but	CCONJ
ejpam-4522	14	11	may	may	AUX
ejpam-4522	14	12	be	be	AUX
ejpam-4522	14	13	dealt	deal	VERB
ejpam-4522	14	14	with	with	ADP
ejpam-4522	14	15	using	use	VERB
ejpam-4522	14	16	a	a	DET
ejpam-4522	14	17	wide	wide	ADJ
ejpam-4522	14	18	range	range	NOUN
ejpam-4522	14	19	of	of	ADP
ejpam-4522	14	20	existing	exist	VERB
ejpam-4522	14	21	theories	theory	NOUN
ejpam-4522	14	22	such	such	ADJ
ejpam-4522	14	23	as	as	ADP
ejpam-4522	14	24	probability	probability	NOUN
ejpam-4522	14	25	theory	theory	NOUN
ejpam-4522	14	26	,	,	PUNCT
ejpam-4522	14	27	theory	theory	NOUN
ejpam-4522	14	28	of	of	ADP
ejpam-4522	14	29	(	(	PUNCT
ejpam-4522	14	30	intuitionistic	intuitionistic	ADJ
ejpam-4522	14	31	)	)	PUNCT
ejpam-4522	14	32	fuzzy	fuzzy	ADJ
ejpam-4522	14	33	sets	set	NOUN
ejpam-4522	14	34	,	,	PUNCT
ejpam-4522	14	35	theory	theory	NOUN
ejpam-4522	14	36	of	of	ADP
ejpam-4522	14	37	interval	interval	NOUN
ejpam-4522	14	38	mathematics	mathematic	NOUN
ejpam-4522	14	39	,	,	PUNCT
ejpam-4522	14	40	theory	theory	NOUN
ejpam-4522	14	41	of	of	ADP
ejpam-4522	14	42	vague	vague	ADJ
ejpam-4522	14	43	sets	set	NOUN
ejpam-4522	14	44	,	,	PUNCT
ejpam-4522	14	45	and	and	CCONJ
ejpam-4522	14	46	theory	theory	NOUN
ejpam-4522	14	47	of	of	ADP
ejpam-4522	14	48	rough	rough	ADJ
ejpam-4522	14	49	sets	set	NOUN
ejpam-4522	14	50	.	.	PUNCT
ejpam-4522	15	1	but	but	CCONJ
ejpam-4522	15	2	,	,	PUNCT
ejpam-4522	15	3	molodtsov	molodtsov	PROPN
ejpam-4522	15	4	[	[	X
ejpam-4522	15	5	21	21	NUM
ejpam-4522	15	6	]	]	PUNCT
ejpam-4522	15	7	pointed	point	VERB
ejpam-4522	15	8	out	out	ADP
ejpam-4522	15	9	all	all	PRON
ejpam-4522	15	10	of	of	ADP
ejpam-4522	15	11	these	these	DET
ejpam-4522	15	12	theories	theory	NOUN
ejpam-4522	15	13	have	have	VERB
ejpam-4522	15	14	their	their	PRON
ejpam-4522	15	15	own	own	ADJ
ejpam-4522	15	16	difficulties	difficulty	NOUN
ejpam-4522	15	17	.	.	PUNCT
ejpam-4522	16	1	maji	maji	PROPN
ejpam-4522	16	2	et	et	PROPN
ejpam-4522	16	3	al	al	PROPN
ejpam-4522	16	4	.	.	PUNCT
ejpam-4522	17	1	[	[	X
ejpam-4522	17	2	18	18	NUM
ejpam-4522	17	3	]	]	PUNCT
ejpam-4522	17	4	and	and	CCONJ
ejpam-4522	17	5	molodtsov	molodtsov	NOUN
ejpam-4522	17	6	[	[	X
ejpam-4522	17	7	21	21	NUM
ejpam-4522	17	8	]	]	PUNCT
ejpam-4522	17	9	suggested	suggest	VERB
ejpam-4522	17	10	that	that	SCONJ
ejpam-4522	17	11	one	one	NUM
ejpam-4522	17	12	reason	reason	NOUN
ejpam-4522	17	13	for	for	ADP
ejpam-4522	17	14	these	these	DET
ejpam-4522	17	15	difficulties	difficulty	NOUN
ejpam-4522	17	16	may	may	AUX
ejpam-4522	17	17	be	be	AUX
ejpam-4522	17	18	due	due	ADJ
ejpam-4522	17	19	to	to	ADP
ejpam-4522	17	20	the	the	DET
ejpam-4522	17	21	inadequacy	inadequacy	NOUN
ejpam-4522	17	22	of	of	ADP
ejpam-4522	17	23	the	the	DET
ejpam-4522	17	24	parametrization	parametrization	NOUN
ejpam-4522	17	25	tool	tool	NOUN
ejpam-4522	17	26	of	of	ADP
ejpam-4522	17	27	the	the	DET
ejpam-4522	17	28	theory	theory	NOUN
ejpam-4522	17	29	.	.	PUNCT
ejpam-4522	18	1	to	to	PART
ejpam-4522	18	2	overcome	overcome	VERB
ejpam-4522	18	3	these	these	DET
ejpam-4522	18	4	difficulties	difficulty	NOUN
ejpam-4522	18	5	,	,	PUNCT
ejpam-4522	18	6	molodtsov	molodtsov	NOUN
ejpam-4522	18	7	[	[	X
ejpam-4522	18	8	21	21	NUM
ejpam-4522	18	9	]	]	PUNCT
ejpam-4522	18	10	introduced	introduce	VERB
ejpam-4522	18	11	the	the	DET
ejpam-4522	18	12	concept	concept	NOUN
ejpam-4522	18	13	∗corresponding	∗corresponde	VERB
ejpam-4522	18	14	author	author	NOUN
ejpam-4522	18	15	.	.	PUNCT
ejpam-4522	19	1	doi	doi	NOUN
ejpam-4522	19	2	:	:	PUNCT
ejpam-4522	19	3	https://doi.org/10.29020/nybg.ejpam.v15i4.4522	https://doi.org/10.29020/nybg.ejpam.v15i4.4522	ADP
ejpam-4522	19	4	email	email	NOUN
ejpam-4522	19	5	addresses	address	NOUN
ejpam-4522	19	6	:	:	PUNCT
ejpam-4522	19	7	szsong@jejunu.ac.kr	szsong@jejunu.ac.kr	NOUN
ejpam-4522	19	8	(	(	PUNCT
ejpam-4522	19	9	s.	s.	PROPN
ejpam-4522	19	10	z.	z.	PROPN
ejpam-4522	19	11	song	song	PROPN
ejpam-4522	19	12	)	)	PUNCT
ejpam-4522	19	13	,	,	PUNCT
ejpam-4522	19	14	mehaliozturk@gmail.com	mehaliozturk@gmail.com	PROPN
ejpam-4522	19	15	(	(	PUNCT
ejpam-4522	19	16	m.	m.	NOUN
ejpam-4522	19	17	a.	a.	NOUN
ejpam-4522	19	18	öztürk	öztürk	PROPN
ejpam-4522	19	19	)	)	PUNCT
ejpam-4522	19	20	,	,	PUNCT
ejpam-4522	19	21	skywine@gmail.com	skywine@gmail.com	X
ejpam-4522	20	1	(	(	PUNCT
ejpam-4522	20	2	y.	y.	PROPN
ejpam-4522	20	3	b.	b.	PROPN
ejpam-4522	20	4	jun	jun	PROPN
ejpam-4522	20	5	)	)	PUNCT
ejpam-4522	20	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4522	20	7	1498	1498	NUM
ejpam-4522	21	1	©	©	PROPN
ejpam-4522	21	2	2022	2022	NUM
ejpam-4522	21	3	ejpam	ejpam	VERB
ejpam-4522	21	4	all	all	DET
ejpam-4522	21	5	rights	right	NOUN
ejpam-4522	21	6	reserved	reserve	VERB
ejpam-4522	21	7	.	.	PUNCT
ejpam-4522	22	1	s.	s.	PROPN
ejpam-4522	22	2	z.	z.	PROPN
ejpam-4522	22	3	song	song	PROPN
ejpam-4522	22	4	,	,	PUNCT
ejpam-4522	22	5	m.	m.	NOUN
ejpam-4522	22	6	a.	a.	NOUN
ejpam-4522	22	7	öztürk	öztürk	PROPN
ejpam-4522	22	8	,	,	PUNCT
ejpam-4522	22	9	y.	y.	PROPN
ejpam-4522	22	10	b.	b.	PROPN
ejpam-4522	22	11	jun	jun	PROPN
ejpam-4522	22	12	/	/	SYM
ejpam-4522	22	13	eur	eur	PROPN
ejpam-4522	22	14	.	.	PUNCT
ejpam-4522	23	1	j.	j.	PROPN
ejpam-4522	23	2	pure	pure	PROPN
ejpam-4522	23	3	appl	appl	PROPN
ejpam-4522	23	4	.	.	PROPN
ejpam-4522	23	5	math	math	PROPN
ejpam-4522	23	6	,	,	PUNCT
ejpam-4522	23	7	15	15	NUM
ejpam-4522	23	8	(	(	PUNCT
ejpam-4522	23	9	4	4	NUM
ejpam-4522	23	10	)	)	PUNCT
ejpam-4522	23	11	(	(	PUNCT
ejpam-4522	23	12	2022	2022	NUM
ejpam-4522	23	13	)	)	PUNCT
ejpam-4522	23	14	,	,	PUNCT
ejpam-4522	23	15	1498	1498	NUM
ejpam-4522	23	16	-	-	SYM
ejpam-4522	23	17	1511	1511	NUM
ejpam-4522	23	18	1499	1499	NUM
ejpam-4522	23	19	of	of	ADP
ejpam-4522	23	20	soft	soft	ADJ
ejpam-4522	23	21	set	set	NOUN
ejpam-4522	23	22	as	as	ADP
ejpam-4522	23	23	a	a	DET
ejpam-4522	23	24	new	new	ADJ
ejpam-4522	23	25	mathematical	mathematical	ADJ
ejpam-4522	23	26	tool	tool	NOUN
ejpam-4522	23	27	for	for	ADP
ejpam-4522	23	28	dealing	deal	VERB
ejpam-4522	23	29	with	with	ADP
ejpam-4522	23	30	uncertainties	uncertainty	NOUN
ejpam-4522	23	31	that	that	PRON
ejpam-4522	23	32	is	be	AUX
ejpam-4522	23	33	free	free	ADJ
ejpam-4522	23	34	from	from	ADP
ejpam-4522	23	35	the	the	DET
ejpam-4522	23	36	difficulties	difficulty	NOUN
ejpam-4522	23	37	that	that	PRON
ejpam-4522	23	38	have	have	AUX
ejpam-4522	23	39	troubled	trouble	VERB
ejpam-4522	23	40	the	the	DET
ejpam-4522	23	41	usual	usual	ADJ
ejpam-4522	23	42	theoretical	theoretical	ADJ
ejpam-4522	23	43	approaches	approach	NOUN
ejpam-4522	23	44	,	,	PUNCT
ejpam-4522	23	45	and	and	CCONJ
ejpam-4522	23	46	he	he	PRON
ejpam-4522	23	47	pointed	point	VERB
ejpam-4522	23	48	out	out	ADP
ejpam-4522	23	49	several	several	ADJ
ejpam-4522	23	50	directions	direction	NOUN
ejpam-4522	23	51	for	for	ADP
ejpam-4522	23	52	the	the	DET
ejpam-4522	23	53	applications	application	NOUN
ejpam-4522	23	54	of	of	ADP
ejpam-4522	23	55	soft	soft	ADJ
ejpam-4522	23	56	sets	set	NOUN
ejpam-4522	23	57	.	.	PUNCT
ejpam-4522	24	1	globally	globally	ADV
ejpam-4522	24	2	,	,	PUNCT
ejpam-4522	24	3	interest	interest	NOUN
ejpam-4522	24	4	in	in	ADP
ejpam-4522	24	5	soft	soft	ADJ
ejpam-4522	24	6	set	set	NOUN
ejpam-4522	24	7	theory	theory	NOUN
ejpam-4522	24	8	and	and	CCONJ
ejpam-4522	24	9	its	its	PRON
ejpam-4522	24	10	application	application	NOUN
ejpam-4522	24	11	has	have	AUX
ejpam-4522	24	12	been	be	AUX
ejpam-4522	24	13	growing	grow	VERB
ejpam-4522	24	14	rapidly	rapidly	ADV
ejpam-4522	24	15	in	in	ADP
ejpam-4522	24	16	recent	recent	ADJ
ejpam-4522	24	17	years	year	NOUN
ejpam-4522	24	18	.	.	PUNCT
ejpam-4522	25	1	soft	soft	ADJ
ejpam-4522	25	2	set	set	NOUN
ejpam-4522	25	3	theory	theory	NOUN
ejpam-4522	25	4	has	have	AUX
ejpam-4522	25	5	been	be	AUX
ejpam-4522	25	6	applied	apply	VERB
ejpam-4522	25	7	to	to	ADP
ejpam-4522	25	8	algebraic	algebraic	ADJ
ejpam-4522	25	9	structures	structure	NOUN
ejpam-4522	25	10	,	,	PUNCT
ejpam-4522	25	11	for	for	ADP
ejpam-4522	25	12	example	example	NOUN
ejpam-4522	25	13	,	,	PUNCT
ejpam-4522	25	14	groups	group	NOUN
ejpam-4522	25	15	,	,	PUNCT
ejpam-4522	25	16	rings	ring	NOUN
ejpam-4522	25	17	,	,	PUNCT
ejpam-4522	25	18	fields	field	NOUN
ejpam-4522	25	19	and	and	CCONJ
ejpam-4522	25	20	modules	module	NOUN
ejpam-4522	25	21	(	(	PUNCT
ejpam-4522	25	22	see	see	VERB
ejpam-4522	25	23	[	[	X
ejpam-4522	25	24	1	1	NUM
ejpam-4522	25	25	,	,	PUNCT
ejpam-4522	25	26	3–5	3–5	NUM
ejpam-4522	25	27	,	,	PUNCT
ejpam-4522	25	28	14	14	NUM
ejpam-4522	25	29	]	]	PUNCT
ejpam-4522	25	30	)	)	PUNCT
ejpam-4522	25	31	,	,	PUNCT
ejpam-4522	25	32	and	and	CCONJ
ejpam-4522	25	33	bck	bck	VERB
ejpam-4522	25	34	/	/	SYM
ejpam-4522	25	35	bci	bci	NOUN
ejpam-4522	25	36	-	-	PUNCT
ejpam-4522	25	37	algebras	algebras	X
ejpam-4522	25	38	etc	etc	X
ejpam-4522	25	39	.	.	X
ejpam-4522	26	1	(	(	PUNCT
ejpam-4522	26	2	see	see	VERB
ejpam-4522	26	3	[	[	X
ejpam-4522	26	4	9–13	9–13	NOUN
ejpam-4522	26	5	,	,	PUNCT
ejpam-4522	26	6	15–17	15–17	NUM
ejpam-4522	26	7	,	,	PUNCT
ejpam-4522	26	8	22	22	NUM
ejpam-4522	26	9	,	,	PUNCT
ejpam-4522	26	10	23	23	NUM
ejpam-4522	26	11	]	]	PUNCT
ejpam-4522	26	12	)	)	PUNCT
ejpam-4522	26	13	.	.	PUNCT
ejpam-4522	27	1	in	in	ADP
ejpam-4522	27	2	2019	2019	NUM
ejpam-4522	27	3	,	,	PUNCT
ejpam-4522	27	4	ahn	ahn	PROPN
ejpam-4522	27	5	et	et	PROPN
ejpam-4522	27	6	al	al	PROPN
ejpam-4522	27	7	.	.	PUNCT
ejpam-4522	28	1	[	[	X
ejpam-4522	28	2	2	2	X
ejpam-4522	28	3	]	]	PUNCT
ejpam-4522	28	4	introduced	introduce	VERB
ejpam-4522	28	5	the	the	DET
ejpam-4522	28	6	notion	notion	NOUN
ejpam-4522	28	7	of	of	ADP
ejpam-4522	28	8	makgeolli	makgeolli	NOUN
ejpam-4522	28	9	structures	structure	NOUN
ejpam-4522	28	10	as	as	ADP
ejpam-4522	28	11	a	a	DET
ejpam-4522	28	12	hybrid	hybrid	ADJ
ejpam-4522	28	13	structure	structure	NOUN
ejpam-4522	28	14	based	base	VERB
ejpam-4522	28	15	on	on	ADP
ejpam-4522	28	16	fuzzy	fuzzy	ADJ
ejpam-4522	28	17	set	set	VERB
ejpam-4522	28	18	and	and	CCONJ
ejpam-4522	28	19	soft	soft	ADJ
ejpam-4522	28	20	set	set	NOUN
ejpam-4522	28	21	theory	theory	NOUN
ejpam-4522	28	22	,	,	PUNCT
ejpam-4522	28	23	and	and	CCONJ
ejpam-4522	28	24	applied	apply	VERB
ejpam-4522	28	25	it	it	PRON
ejpam-4522	28	26	to	to	PART
ejpam-4522	28	27	bck	bck	VERB
ejpam-4522	28	28	/	/	SYM
ejpam-4522	28	29	bci	bci	NOUN
ejpam-4522	28	30	-	-	PUNCT
ejpam-4522	28	31	algebras	algebras	X
ejpam-4522	28	32	.	.	PUNCT
ejpam-4522	29	1	in	in	ADP
ejpam-4522	29	2	this	this	DET
ejpam-4522	29	3	paper	paper	NOUN
ejpam-4522	29	4	,	,	PUNCT
ejpam-4522	29	5	we	we	PRON
ejpam-4522	29	6	introduce	introduce	VERB
ejpam-4522	29	7	the	the	DET
ejpam-4522	29	8	notion	notion	NOUN
ejpam-4522	29	9	of	of	ADP
ejpam-4522	29	10	a	a	DET
ejpam-4522	29	11	positive	positive	ADJ
ejpam-4522	29	12	implicative	implicative	ADJ
ejpam-4522	29	13	makgeolli	makgeolli	NOUN
ejpam-4522	29	14	ideal	ideal	NOUN
ejpam-4522	29	15	in	in	ADP
ejpam-4522	29	16	bck	bck	PROPN
ejpam-4522	29	17	-	-	PUNCT
ejpam-4522	29	18	algebras	algebras	X
ejpam-4522	29	19	,	,	PUNCT
ejpam-4522	29	20	and	and	CCONJ
ejpam-4522	29	21	investigate	investigate	VERB
ejpam-4522	29	22	its	its	PRON
ejpam-4522	29	23	properties	property	NOUN
ejpam-4522	29	24	.	.	PUNCT
ejpam-4522	30	1	we	we	PRON
ejpam-4522	30	2	establish	establish	VERB
ejpam-4522	30	3	the	the	DET
ejpam-4522	30	4	relationship	relationship	NOUN
ejpam-4522	30	5	between	between	ADP
ejpam-4522	30	6	a	a	DET
ejpam-4522	30	7	makgeolli	makgeolli	NOUN
ejpam-4522	30	8	ideal	ideal	NOUN
ejpam-4522	30	9	and	and	CCONJ
ejpam-4522	30	10	a	a	DET
ejpam-4522	30	11	positive	positive	ADJ
ejpam-4522	30	12	implicative	implicative	ADJ
ejpam-4522	30	13	makgeolli	makgeolli	NOUN
ejpam-4522	30	14	ideal	ideal	NOUN
ejpam-4522	30	15	.	.	PUNCT
ejpam-4522	31	1	we	we	PRON
ejpam-4522	31	2	explore	explore	VERB
ejpam-4522	31	3	the	the	DET
ejpam-4522	31	4	conditions	condition	NOUN
ejpam-4522	31	5	under	under	ADP
ejpam-4522	31	6	which	which	PRON
ejpam-4522	31	7	a	a	DET
ejpam-4522	31	8	makgeolli	makgeolli	NOUN
ejpam-4522	31	9	ideal	ideal	NOUN
ejpam-4522	31	10	can	can	AUX
ejpam-4522	31	11	be	be	AUX
ejpam-4522	31	12	a	a	DET
ejpam-4522	31	13	positive	positive	ADJ
ejpam-4522	31	14	implicative	implicative	ADJ
ejpam-4522	31	15	makgeolli	makgeolli	NOUN
ejpam-4522	31	16	ideal	ideal	NOUN
ejpam-4522	31	17	.	.	PUNCT
ejpam-4522	32	1	we	we	PRON
ejpam-4522	32	2	discusse	discusse	VERB
ejpam-4522	32	3	the	the	DET
ejpam-4522	32	4	characterization	characterization	NOUN
ejpam-4522	32	5	of	of	ADP
ejpam-4522	32	6	positive	positive	ADJ
ejpam-4522	32	7	implicative	implicative	ADJ
ejpam-4522	32	8	makgeolli	makgeolli	NOUN
ejpam-4522	32	9	ideal	ideal	NOUN
ejpam-4522	32	10	,	,	PUNCT
ejpam-4522	32	11	and	and	CCONJ
ejpam-4522	32	12	construct	construct	VERB
ejpam-4522	32	13	the	the	DET
ejpam-4522	32	14	extension	extension	NOUN
ejpam-4522	32	15	property	property	NOUN
ejpam-4522	32	16	for	for	ADP
ejpam-4522	32	17	a	a	DET
ejpam-4522	32	18	positive	positive	ADJ
ejpam-4522	32	19	implicative	implicative	ADJ
ejpam-4522	32	20	makgeolli	makgeolli	NOUN
ejpam-4522	32	21	ideal	ideal	NOUN
ejpam-4522	32	22	.	.	PUNCT
ejpam-4522	33	1	2	2	X
ejpam-4522	33	2	.	.	NUM
ejpam-4522	33	3	preliminaries	preliminary	NOUN
ejpam-4522	33	4	2.1	2.1	NUM
ejpam-4522	33	5	.	.	PUNCT
ejpam-4522	34	1	preliminaries	preliminary	NOUN
ejpam-4522	34	2	on	on	ADP
ejpam-4522	34	3	bck	bck	PROPN
ejpam-4522	34	4	-	-	PUNCT
ejpam-4522	34	5	algebras	algebras	ADJ
ejpam-4522	34	6	bci	bci	PROPN
ejpam-4522	34	7	/	/	SYM
ejpam-4522	34	8	bck	bck	NOUN
ejpam-4522	34	9	-	-	PUNCT
ejpam-4522	34	10	algebra	algebra	NOUN
ejpam-4522	34	11	is	be	AUX
ejpam-4522	34	12	an	an	DET
ejpam-4522	34	13	important	important	ADJ
ejpam-4522	34	14	type	type	NOUN
ejpam-4522	34	15	of	of	ADP
ejpam-4522	34	16	logical	logical	ADJ
ejpam-4522	34	17	algebra	algebra	NOUN
ejpam-4522	34	18	introduced	introduce	VERB
ejpam-4522	34	19	by	by	ADP
ejpam-4522	34	20	k.	k.	PROPN
ejpam-4522	34	21	iséki	iséki	PROPN
ejpam-4522	34	22	(	(	PUNCT
ejpam-4522	34	23	see	see	VERB
ejpam-4522	34	24	[	[	X
ejpam-4522	34	25	7	7	X
ejpam-4522	34	26	]	]	PUNCT
ejpam-4522	34	27	and	and	CCONJ
ejpam-4522	34	28	[	[	X
ejpam-4522	34	29	8	8	NUM
ejpam-4522	34	30	]	]	NUM
ejpam-4522	34	31	)	)	PUNCT
ejpam-4522	34	32	,	,	PUNCT
ejpam-4522	34	33	and	and	CCONJ
ejpam-4522	34	34	it	it	PRON
ejpam-4522	34	35	has	have	AUX
ejpam-4522	34	36	been	be	AUX
ejpam-4522	34	37	extensively	extensively	ADV
ejpam-4522	34	38	investigated	investigate	VERB
ejpam-4522	34	39	by	by	ADP
ejpam-4522	34	40	several	several	ADJ
ejpam-4522	34	41	researchers	researcher	NOUN
ejpam-4522	34	42	.	.	PUNCT
ejpam-4522	35	1	see	see	VERB
ejpam-4522	35	2	the	the	DET
ejpam-4522	35	3	books	book	NOUN
ejpam-4522	35	4	[	[	X
ejpam-4522	35	5	6	6	NUM
ejpam-4522	35	6	,	,	PUNCT
ejpam-4522	35	7	20	20	NUM
ejpam-4522	35	8	]	]	PUNCT
ejpam-4522	35	9	for	for	ADP
ejpam-4522	35	10	further	further	ADJ
ejpam-4522	35	11	information	information	NOUN
ejpam-4522	35	12	regarding	regard	VERB
ejpam-4522	35	13	bci	bci	NOUN
ejpam-4522	35	14	-	-	PUNCT
ejpam-4522	35	15	algebras	algebra	NOUN
ejpam-4522	35	16	and	and	CCONJ
ejpam-4522	35	17	bck	bck	NOUN
ejpam-4522	35	18	-	-	PUNCT
ejpam-4522	35	19	algebras	algebras	PROPN
ejpam-4522	35	20	.	.	PUNCT
ejpam-4522	36	1	in	in	ADP
ejpam-4522	36	2	this	this	DET
ejpam-4522	36	3	section	section	NOUN
ejpam-4522	36	4	,	,	PUNCT
ejpam-4522	36	5	we	we	PRON
ejpam-4522	36	6	recall	recall	VERB
ejpam-4522	36	7	the	the	DET
ejpam-4522	36	8	definitions	definition	NOUN
ejpam-4522	36	9	and	and	CCONJ
ejpam-4522	36	10	basic	basic	ADJ
ejpam-4522	36	11	results	result	NOUN
ejpam-4522	36	12	required	require	VERB
ejpam-4522	36	13	in	in	ADP
ejpam-4522	36	14	this	this	DET
ejpam-4522	36	15	paper	paper	NOUN
ejpam-4522	36	16	.	.	PUNCT
ejpam-4522	37	1	let	let	VERB
ejpam-4522	37	2	x	x	PRON
ejpam-4522	37	3	be	be	AUX
ejpam-4522	37	4	a	a	DET
ejpam-4522	37	5	set	set	NOUN
ejpam-4522	37	6	with	with	ADP
ejpam-4522	37	7	a	a	DET
ejpam-4522	37	8	special	special	ADJ
ejpam-4522	37	9	element	element	NOUN
ejpam-4522	37	10	“	"	PUNCT
ejpam-4522	37	11	0	0	NUM
ejpam-4522	37	12	”	"	PUNCT
ejpam-4522	37	13	and	and	CCONJ
ejpam-4522	37	14	a	a	DET
ejpam-4522	37	15	binary	binary	ADJ
ejpam-4522	37	16	operation	operation	NOUN
ejpam-4522	37	17	“	"	PUNCT
ejpam-4522	37	18	∗	∗	NOUN
ejpam-4522	37	19	”	"	PUNCT
ejpam-4522	37	20	.	.	PUNCT
ejpam-4522	38	1	if	if	SCONJ
ejpam-4522	38	2	it	it	PRON
ejpam-4522	38	3	satisfies	satisfy	VERB
ejpam-4522	38	4	the	the	DET
ejpam-4522	38	5	following	follow	VERB
ejpam-4522	38	6	conditions	condition	NOUN
ejpam-4522	38	7	:	:	PUNCT
ejpam-4522	38	8	(	(	PUNCT
ejpam-4522	38	9	i1	i1	NOUN
ejpam-4522	38	10	)	)	PUNCT
ejpam-4522	38	11	(	(	PUNCT
ejpam-4522	38	12	∀a	∀a	X
ejpam-4522	38	13	,	,	PUNCT
ejpam-4522	38	14	b	b	NOUN
ejpam-4522	38	15	,	,	PUNCT
ejpam-4522	38	16	c	c	PROPN
ejpam-4522	38	17	∈	∈	PROPN
ejpam-4522	38	18	x	x	X
ejpam-4522	38	19	)	)	PUNCT
ejpam-4522	38	20	(	(	PUNCT
ejpam-4522	38	21	(	(	PUNCT
ejpam-4522	38	22	(	(	PUNCT
ejpam-4522	38	23	a	a	DET
ejpam-4522	38	24	∗	∗	NOUN
ejpam-4522	38	25	b	b	NOUN
ejpam-4522	38	26	)	)	PUNCT
ejpam-4522	38	27	∗	∗	NOUN
ejpam-4522	38	28	(	(	PUNCT
ejpam-4522	38	29	a	a	DET
ejpam-4522	38	30	∗	∗	NOUN
ejpam-4522	38	31	c	c	NOUN
ejpam-4522	38	32	)	)	PUNCT
ejpam-4522	38	33	)	)	PUNCT
ejpam-4522	38	34	∗	∗	NOUN
ejpam-4522	38	35	(	(	PUNCT
ejpam-4522	38	36	c	c	NOUN
ejpam-4522	38	37	∗	∗	X
ejpam-4522	38	38	b	b	NOUN
ejpam-4522	38	39	)	)	PUNCT
ejpam-4522	38	40	=	=	SYM
ejpam-4522	38	41	0	0	NUM
ejpam-4522	38	42	)	)	PUNCT
ejpam-4522	38	43	,	,	PUNCT
ejpam-4522	38	44	(	(	PUNCT
ejpam-4522	38	45	i2	i2	PROPN
ejpam-4522	38	46	)	)	PUNCT
ejpam-4522	38	47	(	(	PUNCT
ejpam-4522	38	48	∀a	∀a	X
ejpam-4522	38	49	,	,	PUNCT
ejpam-4522	38	50	b	b	PROPN
ejpam-4522	38	51	∈	∈	PROPN
ejpam-4522	38	52	x	x	X
ejpam-4522	38	53	)	)	PUNCT
ejpam-4522	38	54	(	(	PUNCT
ejpam-4522	38	55	(	(	PUNCT
ejpam-4522	38	56	a	a	DET
ejpam-4522	38	57	∗	∗	NOUN
ejpam-4522	38	58	(	(	PUNCT
ejpam-4522	38	59	a	a	DET
ejpam-4522	38	60	∗	∗	NOUN
ejpam-4522	38	61	b	b	NOUN
ejpam-4522	38	62	)	)	PUNCT
ejpam-4522	38	63	)	)	PUNCT
ejpam-4522	38	64	∗	∗	NOUN
ejpam-4522	38	65	b	b	NOUN
ejpam-4522	38	66	=	=	NOUN
ejpam-4522	38	67	0	0	NUM
ejpam-4522	38	68	)	)	PUNCT
ejpam-4522	38	69	,	,	PUNCT
ejpam-4522	38	70	(	(	PUNCT
ejpam-4522	38	71	i3	i3	NOUN
ejpam-4522	38	72	)	)	PUNCT
ejpam-4522	38	73	(	(	PUNCT
ejpam-4522	38	74	∀a	∀a	NOUN
ejpam-4522	38	75	∈	∈	NOUN
ejpam-4522	38	76	x	x	NOUN
ejpam-4522	38	77	)	)	PUNCT
ejpam-4522	38	78	(	(	PUNCT
ejpam-4522	38	79	a	a	DET
ejpam-4522	38	80	∗	∗	NOUN
ejpam-4522	38	81	a	a	DET
ejpam-4522	38	82	=	=	NOUN
ejpam-4522	38	83	0	0	NUM
ejpam-4522	38	84	)	)	PUNCT
ejpam-4522	38	85	,	,	PUNCT
ejpam-4522	38	86	(	(	PUNCT
ejpam-4522	38	87	i4	i4	PROPN
ejpam-4522	38	88	)	)	PUNCT
ejpam-4522	38	89	(	(	PUNCT
ejpam-4522	38	90	∀a	∀a	X
ejpam-4522	38	91	,	,	PUNCT
ejpam-4522	38	92	b	b	PROPN
ejpam-4522	38	93	∈	∈	PROPN
ejpam-4522	38	94	x	x	X
ejpam-4522	38	95	)	)	PUNCT
ejpam-4522	38	96	(	(	PUNCT
ejpam-4522	38	97	a	a	DET
ejpam-4522	38	98	∗	∗	NOUN
ejpam-4522	38	99	b	b	NOUN
ejpam-4522	38	100	=	=	SYM
ejpam-4522	38	101	0	0	NUM
ejpam-4522	38	102	,	,	PUNCT
ejpam-4522	38	103	b	b	NOUN
ejpam-4522	38	104	∗	∗	NOUN
ejpam-4522	38	105	a	a	DET
ejpam-4522	38	106	=	=	SYM
ejpam-4522	38	107	0	0	PROPN
ejpam-4522	38	108	⇒	⇒	NOUN
ejpam-4522	38	109	a	a	DET
ejpam-4522	38	110	=	=	ADJ
ejpam-4522	38	111	b	b	NOUN
ejpam-4522	38	112	)	)	PUNCT
ejpam-4522	38	113	,	,	PUNCT
ejpam-4522	38	114	(	(	PUNCT
ejpam-4522	38	115	k	k	X
ejpam-4522	38	116	)	)	PUNCT
ejpam-4522	38	117	(	(	PUNCT
ejpam-4522	38	118	∀a	∀a	NOUN
ejpam-4522	38	119	∈	∈	NOUN
ejpam-4522	38	120	x	x	NOUN
ejpam-4522	38	121	)	)	PUNCT
ejpam-4522	38	122	(	(	PUNCT
ejpam-4522	38	123	0	0	NUM
ejpam-4522	38	124	∗	∗	NOUN
ejpam-4522	38	125	a	a	DET
ejpam-4522	38	126	=	=	NOUN
ejpam-4522	38	127	0	0	NUM
ejpam-4522	38	128	)	)	PUNCT
ejpam-4522	38	129	,	,	PUNCT
ejpam-4522	38	130	then	then	ADV
ejpam-4522	38	131	it	it	PRON
ejpam-4522	38	132	is	be	AUX
ejpam-4522	38	133	called	call	VERB
ejpam-4522	38	134	a	a	DET
ejpam-4522	38	135	bck	bck	NOUN
ejpam-4522	38	136	-	-	PUNCT
ejpam-4522	38	137	algebra	algebra	NOUN
ejpam-4522	38	138	,	,	PUNCT
ejpam-4522	38	139	and	and	CCONJ
ejpam-4522	38	140	it	it	PRON
ejpam-4522	38	141	is	be	AUX
ejpam-4522	38	142	denoted	denote	VERB
ejpam-4522	38	143	by	by	ADP
ejpam-4522	38	144	(	(	PUNCT
ejpam-4522	38	145	x	x	NOUN
ejpam-4522	38	146	,	,	PUNCT
ejpam-4522	38	147	∗)0	∗)0	ADJ
ejpam-4522	38	148	.	.	PUNCT
ejpam-4522	39	1	the	the	DET
ejpam-4522	39	2	order	order	NOUN
ejpam-4522	39	3	relation	relation	NOUN
ejpam-4522	39	4	“	"	PUNCT
ejpam-4522	39	5	≤	≤	NUM
ejpam-4522	39	6	”	"	PUNCT
ejpam-4522	39	7	in	in	ADP
ejpam-4522	39	8	a	a	DET
ejpam-4522	39	9	bck	bck	NOUN
ejpam-4522	39	10	-	-	PUNCT
ejpam-4522	39	11	algebra	algebra	NOUN
ejpam-4522	39	12	(	(	PUNCT
ejpam-4522	39	13	x	x	X
ejpam-4522	39	14	,	,	PUNCT
ejpam-4522	39	15	∗)0	∗)0	NUM
ejpam-4522	39	16	is	be	AUX
ejpam-4522	39	17	defined	define	VERB
ejpam-4522	39	18	as	as	SCONJ
ejpam-4522	39	19	follows	follow	VERB
ejpam-4522	39	20	:	:	PUNCT
ejpam-4522	39	21	(	(	PUNCT
ejpam-4522	39	22	∀a	∀a	X
ejpam-4522	39	23	,	,	PUNCT
ejpam-4522	39	24	b	b	PROPN
ejpam-4522	39	25	∈	∈	PROPN
ejpam-4522	39	26	x)(a	x)(a	PUNCT
ejpam-4522	40	1	≤	≤	PROPN
ejpam-4522	40	2	b	b	X
ejpam-4522	40	3	⇔	⇔	X
ejpam-4522	40	4	a	a	DET
ejpam-4522	40	5	∗	∗	NOUN
ejpam-4522	40	6	b	b	NOUN
ejpam-4522	40	7	=	=	NOUN
ejpam-4522	40	8	0	0	NUM
ejpam-4522	40	9	)	)	PUNCT
ejpam-4522	40	10	.	.	PUNCT
ejpam-4522	41	1	(	(	PUNCT
ejpam-4522	41	2	1	1	X
ejpam-4522	41	3	)	)	PUNCT
ejpam-4522	41	4	every	every	DET
ejpam-4522	41	5	bck	bck	NOUN
ejpam-4522	41	6	-	-	PUNCT
ejpam-4522	41	7	algebra	algebra	NOUN
ejpam-4522	41	8	(	(	PUNCT
ejpam-4522	41	9	x	x	X
ejpam-4522	41	10	,	,	PUNCT
ejpam-4522	41	11	∗)0	∗)0	NUM
ejpam-4522	41	12	satisfies	satisfy	VERB
ejpam-4522	41	13	the	the	DET
ejpam-4522	41	14	following	follow	VERB
ejpam-4522	41	15	conditions	condition	NOUN
ejpam-4522	41	16	(	(	PUNCT
ejpam-4522	41	17	see	see	VERB
ejpam-4522	41	18	[	[	X
ejpam-4522	41	19	19	19	NUM
ejpam-4522	41	20	,	,	PUNCT
ejpam-4522	41	21	20	20	NUM
ejpam-4522	41	22	]	]	PUNCT
ejpam-4522	41	23	):	):	PUNCT
ejpam-4522	41	24	(	(	PUNCT
ejpam-4522	41	25	∀a	∀a	NOUN
ejpam-4522	41	26	∈	∈	NOUN
ejpam-4522	41	27	x	x	NOUN
ejpam-4522	41	28	)	)	PUNCT
ejpam-4522	41	29	(	(	PUNCT
ejpam-4522	41	30	a	a	DET
ejpam-4522	41	31	∗	∗	NOUN
ejpam-4522	41	32	0	0	NUM
ejpam-4522	42	1	=	=	SYM
ejpam-4522	42	2	a	a	NOUN
ejpam-4522	42	3	)	)	PUNCT
ejpam-4522	42	4	,	,	PUNCT
ejpam-4522	42	5	(	(	PUNCT
ejpam-4522	42	6	2	2	X
ejpam-4522	42	7	)	)	PUNCT
ejpam-4522	42	8	(	(	PUNCT
ejpam-4522	42	9	∀a	∀a	X
ejpam-4522	42	10	,	,	PUNCT
ejpam-4522	42	11	b	b	NOUN
ejpam-4522	42	12	,	,	PUNCT
ejpam-4522	42	13	c	c	PROPN
ejpam-4522	42	14	∈	∈	PROPN
ejpam-4522	42	15	x	x	X
ejpam-4522	42	16	)	)	PUNCT
ejpam-4522	42	17	(	(	PUNCT
ejpam-4522	42	18	a	a	DET
ejpam-4522	42	19	≤	≤	PROPN
ejpam-4522	42	20	b	b	PROPN
ejpam-4522	42	21	⇒	⇒	NOUN
ejpam-4522	42	22	a	a	DET
ejpam-4522	42	23	∗	∗	NOUN
ejpam-4522	42	24	c	c	NOUN
ejpam-4522	42	25	≤	≤	NUM
ejpam-4522	42	26	b	b	PROPN
ejpam-4522	42	27	∗	∗	NOUN
ejpam-4522	42	28	c	c	NOUN
ejpam-4522	42	29	,	,	PUNCT
ejpam-4522	42	30	c	c	PROPN
ejpam-4522	42	31	∗	∗	X
ejpam-4522	42	32	b	b	PROPN
ejpam-4522	42	33	≤	≤	PROPN
ejpam-4522	42	34	c	c	PROPN
ejpam-4522	42	35	∗	∗	X
ejpam-4522	42	36	a	a	NOUN
ejpam-4522	42	37	)	)	PUNCT
ejpam-4522	42	38	,	,	PUNCT
ejpam-4522	42	39	(	(	PUNCT
ejpam-4522	42	40	3	3	X
ejpam-4522	42	41	)	)	PUNCT
ejpam-4522	42	42	(	(	PUNCT
ejpam-4522	42	43	∀a	∀a	X
ejpam-4522	42	44	,	,	PUNCT
ejpam-4522	42	45	b	b	NOUN
ejpam-4522	42	46	,	,	PUNCT
ejpam-4522	42	47	c	c	PROPN
ejpam-4522	42	48	∈	∈	PROPN
ejpam-4522	42	49	x	x	X
ejpam-4522	42	50	)	)	PUNCT
ejpam-4522	42	51	(	(	PUNCT
ejpam-4522	42	52	(	(	PUNCT
ejpam-4522	42	53	a	a	DET
ejpam-4522	42	54	∗	∗	NOUN
ejpam-4522	42	55	b	b	NOUN
ejpam-4522	42	56	)	)	PUNCT
ejpam-4522	42	57	∗	∗	NOUN
ejpam-4522	42	58	c	c	NOUN
ejpam-4522	43	1	=	=	SYM
ejpam-4522	43	2	(	(	PUNCT
ejpam-4522	43	3	a	a	DET
ejpam-4522	43	4	∗	∗	NOUN
ejpam-4522	43	5	c	c	NOUN
ejpam-4522	43	6	)	)	PUNCT
ejpam-4522	43	7	∗	∗	PROPN
ejpam-4522	43	8	b	b	NOUN
ejpam-4522	43	9	)	)	PUNCT
ejpam-4522	43	10	.	.	PUNCT
ejpam-4522	44	1	(	(	PUNCT
ejpam-4522	44	2	4	4	X
ejpam-4522	44	3	)	)	PUNCT
ejpam-4522	44	4	s.	s.	PROPN
ejpam-4522	44	5	z.	z.	PROPN
ejpam-4522	44	6	song	song	PROPN
ejpam-4522	44	7	,	,	PUNCT
ejpam-4522	44	8	m.	m.	NOUN
ejpam-4522	44	9	a.	a.	NOUN
ejpam-4522	44	10	öztürk	öztürk	PROPN
ejpam-4522	44	11	,	,	PUNCT
ejpam-4522	44	12	y.	y.	PROPN
ejpam-4522	44	13	b.	b.	PROPN
ejpam-4522	44	14	jun	jun	PROPN
ejpam-4522	44	15	/	/	SYM
ejpam-4522	44	16	eur	eur	PROPN
ejpam-4522	44	17	.	.	PUNCT
ejpam-4522	45	1	j.	j.	PROPN
ejpam-4522	45	2	pure	pure	PROPN
ejpam-4522	45	3	appl	appl	PROPN
ejpam-4522	45	4	.	.	PROPN
ejpam-4522	45	5	math	math	PROPN
ejpam-4522	45	6	,	,	PUNCT
ejpam-4522	45	7	15	15	NUM
ejpam-4522	45	8	(	(	PUNCT
ejpam-4522	45	9	4	4	NUM
ejpam-4522	45	10	)	)	PUNCT
ejpam-4522	45	11	(	(	PUNCT
ejpam-4522	45	12	2022	2022	NUM
ejpam-4522	45	13	)	)	PUNCT
ejpam-4522	45	14	,	,	PUNCT
ejpam-4522	45	15	1498	1498	NUM
ejpam-4522	45	16	-	-	SYM
ejpam-4522	45	17	1511	1511	NUM
ejpam-4522	45	18	1500	1500	NUM
ejpam-4522	45	19	a	a	DET
ejpam-4522	45	20	bck	bck	NOUN
ejpam-4522	45	21	-	-	PUNCT
ejpam-4522	45	22	algebra	algebra	NOUN
ejpam-4522	45	23	(	(	PUNCT
ejpam-4522	45	24	x	x	X
ejpam-4522	45	25	,	,	PUNCT
ejpam-4522	45	26	∗)0	∗)0	NUM
ejpam-4522	45	27	is	be	AUX
ejpam-4522	45	28	said	say	VERB
ejpam-4522	45	29	to	to	PART
ejpam-4522	45	30	be	be	AUX
ejpam-4522	45	31	positive	positive	ADJ
ejpam-4522	45	32	implicative	implicative	NOUN
ejpam-4522	45	33	(	(	PUNCT
ejpam-4522	45	34	see	see	VERB
ejpam-4522	45	35	[	[	X
ejpam-4522	45	36	20	20	NUM
ejpam-4522	45	37	]	]	SYM
ejpam-4522	45	38	)	)	PUNCT
ejpam-4522	45	39	if	if	SCONJ
ejpam-4522	45	40	(	(	PUNCT
ejpam-4522	45	41	a	a	DET
ejpam-4522	45	42	∗	∗	NOUN
ejpam-4522	45	43	c	c	NOUN
ejpam-4522	45	44	)	)	PUNCT
ejpam-4522	45	45	∗	∗	NOUN
ejpam-4522	45	46	(	(	PUNCT
ejpam-4522	45	47	b	b	NOUN
ejpam-4522	45	48	∗	∗	NOUN
ejpam-4522	45	49	c	c	NOUN
ejpam-4522	45	50	)	)	PUNCT
ejpam-4522	45	51	=	=	NOUN
ejpam-4522	45	52	(	(	PUNCT
ejpam-4522	45	53	a	a	DET
ejpam-4522	45	54	∗	∗	NOUN
ejpam-4522	45	55	b	b	NOUN
ejpam-4522	45	56	)	)	PUNCT
ejpam-4522	45	57	∗	∗	NOUN
ejpam-4522	45	58	c	c	NOUN
ejpam-4522	45	59	for	for	ADP
ejpam-4522	45	60	all	all	DET
ejpam-4522	45	61	a	a	DET
ejpam-4522	45	62	,	,	PUNCT
ejpam-4522	45	63	b	b	NOUN
ejpam-4522	45	64	,	,	PUNCT
ejpam-4522	45	65	c	c	PROPN
ejpam-4522	45	66	∈	∈	PROPN
ejpam-4522	45	67	x.	x.	NOUN
ejpam-4522	45	68	a	a	DET
ejpam-4522	45	69	subset	subset	NOUN
ejpam-4522	45	70	c	c	NOUN
ejpam-4522	45	71	of	of	ADP
ejpam-4522	45	72	a	a	DET
ejpam-4522	45	73	bck	bck	NOUN
ejpam-4522	45	74	-	-	PUNCT
ejpam-4522	45	75	algebra	algebra	NOUN
ejpam-4522	45	76	(	(	PUNCT
ejpam-4522	45	77	x	x	X
ejpam-4522	45	78	,	,	PUNCT
ejpam-4522	45	79	∗)0	∗)0	NUM
ejpam-4522	45	80	is	be	AUX
ejpam-4522	45	81	called	call	VERB
ejpam-4522	45	82	an	an	DET
ejpam-4522	45	83	ideal	ideal	NOUN
ejpam-4522	45	84	of	of	ADP
ejpam-4522	45	85	(	(	PUNCT
ejpam-4522	45	86	x	x	X
ejpam-4522	45	87	,	,	PUNCT
ejpam-4522	45	88	∗)0	∗)0	NUM
ejpam-4522	45	89	(	(	PUNCT
ejpam-4522	45	90	see	see	VERB
ejpam-4522	45	91	[	[	X
ejpam-4522	45	92	6	6	NUM
ejpam-4522	45	93	,	,	PUNCT
ejpam-4522	45	94	20	20	NUM
ejpam-4522	45	95	]	]	PUNCT
ejpam-4522	45	96	)	)	PUNCT
ejpam-4522	45	97	if	if	SCONJ
ejpam-4522	45	98	it	it	PRON
ejpam-4522	45	99	satisfies	satisfy	VERB
ejpam-4522	45	100	:	:	PUNCT
ejpam-4522	45	101	0	0	NUM
ejpam-4522	45	102	∈	∈	PROPN
ejpam-4522	45	103	c	c	NOUN
ejpam-4522	45	104	,	,	PUNCT
ejpam-4522	45	105	(	(	PUNCT
ejpam-4522	45	106	5	5	NUM
ejpam-4522	45	107	)	)	PUNCT
ejpam-4522	45	108	(	(	PUNCT
ejpam-4522	45	109	∀a	∀a	X
ejpam-4522	45	110	,	,	PUNCT
ejpam-4522	45	111	b	b	PROPN
ejpam-4522	45	112	∈	∈	PROPN
ejpam-4522	45	113	x)(a	x)(a	PUNCT
ejpam-4522	46	1	∗	∗	NOUN
ejpam-4522	46	2	b	b	X
ejpam-4522	46	3	∈	∈	PROPN
ejpam-4522	46	4	c	c	X
ejpam-4522	46	5	,	,	PUNCT
ejpam-4522	46	6	b	b	X
ejpam-4522	46	7	∈	∈	PROPN
ejpam-4522	46	8	c	c	NOUN
ejpam-4522	46	9	⇒	⇒	VERB
ejpam-4522	46	10	a	a	DET
ejpam-4522	46	11	∈	∈	PROPN
ejpam-4522	46	12	c	c	NOUN
ejpam-4522	46	13	)	)	PUNCT
ejpam-4522	46	14	.	.	PUNCT
ejpam-4522	47	1	(	(	PUNCT
ejpam-4522	47	2	6	6	X
ejpam-4522	47	3	)	)	PUNCT
ejpam-4522	47	4	a	a	DET
ejpam-4522	47	5	subset	subset	NOUN
ejpam-4522	47	6	c	c	NOUN
ejpam-4522	47	7	of	of	ADP
ejpam-4522	47	8	a	a	DET
ejpam-4522	47	9	bck	bck	NOUN
ejpam-4522	47	10	-	-	PUNCT
ejpam-4522	47	11	algebra	algebra	NOUN
ejpam-4522	47	12	(	(	PUNCT
ejpam-4522	47	13	x	x	X
ejpam-4522	47	14	,	,	PUNCT
ejpam-4522	47	15	∗)0	∗)0	NUM
ejpam-4522	47	16	is	be	AUX
ejpam-4522	47	17	called	call	VERB
ejpam-4522	47	18	a	a	DET
ejpam-4522	47	19	positive	positive	ADJ
ejpam-4522	47	20	implicative	implicative	ADJ
ejpam-4522	47	21	ideal	ideal	NOUN
ejpam-4522	47	22	of	of	ADP
ejpam-4522	47	23	(	(	PUNCT
ejpam-4522	47	24	x	x	X
ejpam-4522	47	25	,	,	PUNCT
ejpam-4522	47	26	∗)0	∗)0	NUM
ejpam-4522	47	27	(	(	PUNCT
ejpam-4522	47	28	see	see	VERB
ejpam-4522	47	29	[	[	X
ejpam-4522	47	30	20	20	NUM
ejpam-4522	47	31	]	]	SYM
ejpam-4522	47	32	)	)	PUNCT
ejpam-4522	47	33	if	if	SCONJ
ejpam-4522	47	34	it	it	PRON
ejpam-4522	47	35	satisfies	satisfy	VERB
ejpam-4522	47	36	(	(	PUNCT
ejpam-4522	47	37	5	5	NUM
ejpam-4522	47	38	)	)	PUNCT
ejpam-4522	47	39	and	and	CCONJ
ejpam-4522	47	40	(	(	PUNCT
ejpam-4522	47	41	∀a	∀a	NOUN
ejpam-4522	47	42	,	,	PUNCT
ejpam-4522	47	43	b	b	NOUN
ejpam-4522	47	44	,	,	PUNCT
ejpam-4522	47	45	c	c	PROPN
ejpam-4522	47	46	∈	∈	PROPN
ejpam-4522	47	47	x)((a	x)((a	PROPN
ejpam-4522	47	48	∗	∗	PROPN
ejpam-4522	47	49	b	b	NOUN
ejpam-4522	47	50	)	)	PUNCT
ejpam-4522	47	51	∗	∗	NOUN
ejpam-4522	47	52	c	c	NOUN
ejpam-4522	47	53	∈	∈	PROPN
ejpam-4522	47	54	c	c	X
ejpam-4522	47	55	,	,	PUNCT
ejpam-4522	47	56	b	b	NOUN
ejpam-4522	47	57	∗	∗	X
ejpam-4522	47	58	c	c	NOUN
ejpam-4522	47	59	∈	∈	PROPN
ejpam-4522	47	60	c	c	PROPN
ejpam-4522	47	61	⇒	⇒	VERB
ejpam-4522	47	62	a	a	DET
ejpam-4522	47	63	∗	∗	NOUN
ejpam-4522	47	64	c	c	NOUN
ejpam-4522	47	65	∈	∈	PROPN
ejpam-4522	47	66	c	c	NOUN
ejpam-4522	47	67	)	)	PUNCT
ejpam-4522	47	68	.	.	PUNCT
ejpam-4522	48	1	(	(	PUNCT
ejpam-4522	48	2	7	7	X
ejpam-4522	48	3	)	)	PUNCT
ejpam-4522	48	4	2.2	2.2	NUM
ejpam-4522	48	5	.	.	PUNCT
ejpam-4522	49	1	preliminaries	preliminary	NOUN
ejpam-4522	49	2	on	on	ADP
ejpam-4522	49	3	makgeolli	makgeolli	NOUN
ejpam-4522	49	4	structures	structure	NOUN
ejpam-4522	49	5	let	let	VERB
ejpam-4522	49	6	x	x	PRON
ejpam-4522	49	7	be	be	AUX
ejpam-4522	49	8	a	a	DET
ejpam-4522	49	9	universal	universal	ADJ
ejpam-4522	49	10	set	set	NOUN
ejpam-4522	49	11	and	and	CCONJ
ejpam-4522	49	12	e	e	X
ejpam-4522	49	13	a	a	DET
ejpam-4522	49	14	set	set	NOUN
ejpam-4522	49	15	of	of	ADP
ejpam-4522	49	16	parameters	parameter	NOUN
ejpam-4522	49	17	.	.	PUNCT
ejpam-4522	50	1	we	we	PRON
ejpam-4522	50	2	say	say	VERB
ejpam-4522	50	3	that	that	SCONJ
ejpam-4522	50	4	the	the	DET
ejpam-4522	50	5	pair	pair	NOUN
ejpam-4522	50	6	(	(	PUNCT
ejpam-4522	50	7	x	x	X
ejpam-4522	50	8	,	,	PUNCT
ejpam-4522	50	9	e	e	NOUN
ejpam-4522	50	10	)	)	PUNCT
ejpam-4522	50	11	is	be	AUX
ejpam-4522	50	12	a	a	DET
ejpam-4522	50	13	soft	soft	ADJ
ejpam-4522	50	14	universe	universe	NOUN
ejpam-4522	50	15	.	.	PUNCT
ejpam-4522	51	1	definition	definition	NOUN
ejpam-4522	51	2	1	1	NUM
ejpam-4522	51	3	(	(	PUNCT
ejpam-4522	51	4	[	[	X
ejpam-4522	51	5	2	2	NUM
ejpam-4522	51	6	]	]	PUNCT
ejpam-4522	51	7	)	)	PUNCT
ejpam-4522	51	8	.	.	PUNCT
ejpam-4522	52	1	let	let	VERB
ejpam-4522	52	2	(	(	PUNCT
ejpam-4522	52	3	x	x	X
ejpam-4522	52	4	,	,	PUNCT
ejpam-4522	52	5	e	e	NOUN
ejpam-4522	52	6	)	)	PUNCT
ejpam-4522	52	7	be	be	AUX
ejpam-4522	52	8	a	a	DET
ejpam-4522	52	9	soft	soft	ADJ
ejpam-4522	52	10	universe	universe	NOUN
ejpam-4522	52	11	and	and	CCONJ
ejpam-4522	52	12	let	let	VERB
ejpam-4522	52	13	c	c	NOUN
ejpam-4522	52	14	and	and	CCONJ
ejpam-4522	52	15	d	d	PROPN
ejpam-4522	52	16	be	be	VERB
ejpam-4522	52	17	subsets	subset	NOUN
ejpam-4522	52	18	of	of	ADP
ejpam-4522	52	19	e.	e.	PROPN
ejpam-4522	52	20	a	a	DET
ejpam-4522	52	21	makgeolli	makgeolli	NOUN
ejpam-4522	52	22	structure	structure	NOUN
ejpam-4522	52	23	on	on	ADP
ejpam-4522	52	24	x	x	SYM
ejpam-4522	52	25	(	(	PUNCT
ejpam-4522	52	26	related	relate	VERB
ejpam-4522	52	27	to	to	ADP
ejpam-4522	52	28	c	c	PROPN
ejpam-4522	52	29	and	and	CCONJ
ejpam-4522	52	30	d	d	X
ejpam-4522	52	31	)	)	PUNCT
ejpam-4522	52	32	is	be	AUX
ejpam-4522	52	33	a	a	DET
ejpam-4522	52	34	structure	structure	NOUN
ejpam-4522	52	35	of	of	ADP
ejpam-4522	52	36	the	the	DET
ejpam-4522	52	37	form	form	NOUN
ejpam-4522	52	38	:	:	PUNCT
ejpam-4522	52	39	m(c	m(c	X
ejpam-4522	52	40	,	,	PUNCT
ejpam-4522	52	41	d	d	X
ejpam-4522	52	42	,	,	PUNCT
ejpam-4522	52	43	x	x	NOUN
ejpam-4522	52	44	)	)	PUNCT
ejpam-4522	52	45	:	:	PUNCT
ejpam-4522	53	1	=	=	PRON
ejpam-4522	53	2	{	{	PUNCT
ejpam-4522	53	3	⟨(a	⟨(a	PROPN
ejpam-4522	53	4	,	,	PUNCT
ejpam-4522	53	5	b	b	NOUN
ejpam-4522	53	6	,	,	PUNCT
ejpam-4522	53	7	x);mc(a	x);mc(a	PROPN
ejpam-4522	53	8	)	)	PUNCT
ejpam-4522	53	9	,	,	PUNCT
ejpam-4522	53	10	gd(b	gd(b	X
ejpam-4522	53	11	)	)	PUNCT
ejpam-4522	53	12	,	,	PUNCT
ejpam-4522	53	13	ξ(x)⟩	ξ(x)⟩	NOUN
ejpam-4522	53	14	|	|	ADV
ejpam-4522	53	15	(	(	PUNCT
ejpam-4522	53	16	a	a	DET
ejpam-4522	53	17	,	,	PUNCT
ejpam-4522	53	18	b	b	NOUN
ejpam-4522	53	19	,	,	PUNCT
ejpam-4522	53	20	x	x	NOUN
ejpam-4522	53	21	)	)	PUNCT
ejpam-4522	53	22	∈	∈	PROPN
ejpam-4522	53	23	c	c	PROPN
ejpam-4522	53	24	×d	×d	NOUN
ejpam-4522	53	25	×x	×x	PROPN
ejpam-4522	53	26	}	}	PUNCT
ejpam-4522	53	27	(	(	PUNCT
ejpam-4522	53	28	8)	8)	NUM
ejpam-4522	53	29	where	where	SCONJ
ejpam-4522	53	30	mc	mc	NOUN
ejpam-4522	53	31	:	:	PUNCT
ejpam-4522	53	32	=	=	SYM
ejpam-4522	53	33	(	(	PUNCT
ejpam-4522	53	34	m	m	PROPN
ejpam-4522	53	35	,	,	PUNCT
ejpam-4522	53	36	c	c	NOUN
ejpam-4522	53	37	)	)	PUNCT
ejpam-4522	53	38	and	and	CCONJ
ejpam-4522	53	39	gd	gd	VERB
ejpam-4522	53	40	:	:	PUNCT
ejpam-4522	53	41	=	=	SYM
ejpam-4522	53	42	(	(	PUNCT
ejpam-4522	53	43	g	g	NOUN
ejpam-4522	53	44	,	,	PUNCT
ejpam-4522	53	45	d	d	NOUN
ejpam-4522	53	46	)	)	PUNCT
ejpam-4522	53	47	are	be	AUX
ejpam-4522	53	48	soft	soft	ADJ
ejpam-4522	53	49	sets	set	NOUN
ejpam-4522	53	50	over	over	ADP
ejpam-4522	53	51	x	x	PUNCT
ejpam-4522	53	52	and	and	CCONJ
ejpam-4522	53	53	ξ	ξ	PROPN
ejpam-4522	53	54	is	be	AUX
ejpam-4522	53	55	a	a	DET
ejpam-4522	53	56	fuzzy	fuzzy	ADJ
ejpam-4522	53	57	set	set	NOUN
ejpam-4522	53	58	in	in	ADP
ejpam-4522	53	59	x.	x.	NOUN
ejpam-4522	53	60	for	for	ADP
ejpam-4522	53	61	the	the	DET
ejpam-4522	53	62	sake	sake	NOUN
ejpam-4522	53	63	of	of	ADP
ejpam-4522	53	64	simplicity	simplicity	NOUN
ejpam-4522	53	65	,	,	PUNCT
ejpam-4522	53	66	the	the	DET
ejpam-4522	53	67	makgeolli	makgeolli	NOUN
ejpam-4522	53	68	structure	structure	NOUN
ejpam-4522	53	69	in	in	ADP
ejpam-4522	53	70	(	(	PUNCT
ejpam-4522	53	71	8)	8)	NUM
ejpam-4522	53	72	will	will	AUX
ejpam-4522	53	73	be	be	AUX
ejpam-4522	53	74	denoted	denote	VERB
ejpam-4522	53	75	by	by	ADP
ejpam-4522	53	76	m(c	m(c	PROPN
ejpam-4522	53	77	,	,	PUNCT
ejpam-4522	53	78	d	d	NOUN
ejpam-4522	53	79	,	,	PUNCT
ejpam-4522	53	80	x	x	NOUN
ejpam-4522	53	81	)	)	PUNCT
ejpam-4522	53	82	=	=	SYM
ejpam-4522	53	83	(	(	PUNCT
ejpam-4522	53	84	mc	mc	PROPN
ejpam-4522	53	85	,	,	PUNCT
ejpam-4522	53	86	gd	gd	PROPN
ejpam-4522	53	87	,	,	PUNCT
ejpam-4522	53	88	ξ	ξ	PROPN
ejpam-4522	53	89	)	)	PUNCT
ejpam-4522	53	90	.	.	PUNCT
ejpam-4522	54	1	the	the	DET
ejpam-4522	54	2	makgeolli	makgeolli	NOUN
ejpam-4522	54	3	structure	structure	NOUN
ejpam-4522	54	4	m(c	m(c	PROPN
ejpam-4522	54	5	,	,	PUNCT
ejpam-4522	54	6	c	c	X
ejpam-4522	54	7	,	,	PUNCT
ejpam-4522	54	8	x	x	NOUN
ejpam-4522	54	9	)	)	PUNCT
ejpam-4522	54	10	=	=	SYM
ejpam-4522	54	11	(	(	PUNCT
ejpam-4522	54	12	mc	mc	PROPN
ejpam-4522	54	13	,	,	PUNCT
ejpam-4522	54	14	gc	gc	PROPN
ejpam-4522	54	15	,	,	PUNCT
ejpam-4522	54	16	ξ	ξ	PROPN
ejpam-4522	54	17	)	)	PUNCT
ejpam-4522	54	18	on	on	ADP
ejpam-4522	54	19	x	x	SYM
ejpam-4522	54	20	related	relate	VERB
ejpam-4522	54	21	to	to	ADP
ejpam-4522	54	22	a	a	DET
ejpam-4522	54	23	subset	subset	NOUN
ejpam-4522	54	24	c	c	NOUN
ejpam-4522	54	25	of	of	ADP
ejpam-4522	54	26	e	e	PROPN
ejpam-4522	54	27	is	be	AUX
ejpam-4522	54	28	simply	simply	ADV
ejpam-4522	54	29	denoted	denote	VERB
ejpam-4522	54	30	by	by	ADP
ejpam-4522	54	31	m(c	m(c	PROPN
ejpam-4522	54	32	,	,	PUNCT
ejpam-4522	54	33	x	x	X
ejpam-4522	54	34	)	)	PUNCT
ejpam-4522	54	35	=	=	SYM
ejpam-4522	54	36	(	(	PUNCT
ejpam-4522	54	37	mc	mc	PROPN
ejpam-4522	54	38	,	,	PUNCT
ejpam-4522	54	39	gc	gc	PROPN
ejpam-4522	54	40	,	,	PUNCT
ejpam-4522	54	41	ξ	ξ	PROPN
ejpam-4522	54	42	)	)	PUNCT
ejpam-4522	54	43	.	.	PUNCT
ejpam-4522	55	1	if	if	SCONJ
ejpam-4522	55	2	c	c	NOUN
ejpam-4522	55	3	=	=	SYM
ejpam-4522	55	4	d	d	PROPN
ejpam-4522	55	5	=	=	SYM
ejpam-4522	55	6	e	e	NOUN
ejpam-4522	55	7	,	,	PUNCT
ejpam-4522	55	8	we	we	PRON
ejpam-4522	55	9	use	use	VERB
ejpam-4522	55	10	the	the	DET
ejpam-4522	55	11	notation	notation	NOUN
ejpam-4522	55	12	m(x	m(x	PROPN
ejpam-4522	55	13	,	,	PUNCT
ejpam-4522	55	14	e	e	NOUN
ejpam-4522	55	15	)	)	PUNCT
ejpam-4522	55	16	:	:	PUNCT
ejpam-4522	56	1	=	=	SYM
ejpam-4522	56	2	(	(	PUNCT
ejpam-4522	56	3	me	i	PRON
ejpam-4522	56	4	,	,	PUNCT
ejpam-4522	56	5	ge	ge	PROPN
ejpam-4522	56	6	,	,	PUNCT
ejpam-4522	56	7	ξ	ξ	PROPN
ejpam-4522	56	8	)	)	PUNCT
ejpam-4522	56	9	as	as	ADP
ejpam-4522	56	10	the	the	DET
ejpam-4522	56	11	makgeolli	makgeolli	NOUN
ejpam-4522	56	12	structure	structure	NOUN
ejpam-4522	56	13	of	of	ADP
ejpam-4522	56	14	(	(	PUNCT
ejpam-4522	56	15	x	x	X
ejpam-4522	56	16	,	,	PUNCT
ejpam-4522	56	17	e	e	NOUN
ejpam-4522	56	18	)	)	PUNCT
ejpam-4522	56	19	.	.	PUNCT
ejpam-4522	57	1	by	by	ADP
ejpam-4522	57	2	a	a	DET
ejpam-4522	57	3	bck	bck	PROPN
ejpam-4522	57	4	/	/	SYM
ejpam-4522	57	5	bci	bci	ADJ
ejpam-4522	57	6	-	-	ADJ
ejpam-4522	57	7	soft	soft	ADJ
ejpam-4522	57	8	universe	universe	NOUN
ejpam-4522	57	9	,	,	PUNCT
ejpam-4522	57	10	we	we	PRON
ejpam-4522	57	11	mean	mean	VERB
ejpam-4522	57	12	a	a	DET
ejpam-4522	57	13	soft	soft	ADJ
ejpam-4522	57	14	universe	universe	NOUN
ejpam-4522	57	15	(	(	PUNCT
ejpam-4522	57	16	x	x	X
ejpam-4522	57	17	,	,	PUNCT
ejpam-4522	57	18	e	e	NOUN
ejpam-4522	57	19	)	)	PUNCT
ejpam-4522	57	20	in	in	ADP
ejpam-4522	57	21	which	which	PRON
ejpam-4522	57	22	x	x	PUNCT
ejpam-4522	57	23	and	and	CCONJ
ejpam-4522	57	24	e	e	NOUN
ejpam-4522	57	25	are	be	AUX
ejpam-4522	57	26	bck	bck	NOUN
ejpam-4522	57	27	/	/	SYM
ejpam-4522	57	28	bci	bci	NOUN
ejpam-4522	57	29	-	-	PUNCT
ejpam-4522	57	30	algebras	algebras	PROPN
ejpam-4522	57	31	with	with	ADP
ejpam-4522	57	32	binary	binary	ADJ
ejpam-4522	57	33	operations	operation	NOUN
ejpam-4522	57	34	“	"	PUNCT
ejpam-4522	57	35	∗	∗	NOUN
ejpam-4522	57	36	”	"	PUNCT
ejpam-4522	57	37	and	and	CCONJ
ejpam-4522	57	38	“	"	PUNCT
ejpam-4522	57	39	↬	↬	PROPN
ejpam-4522	57	40	”	"	PUNCT
ejpam-4522	57	41	,	,	PUNCT
ejpam-4522	57	42	respectively	respectively	ADV
ejpam-4522	57	43	.	.	PUNCT
ejpam-4522	58	1	definition	definition	NOUN
ejpam-4522	58	2	2	2	NUM
ejpam-4522	58	3	(	(	PUNCT
ejpam-4522	58	4	[	[	X
ejpam-4522	58	5	2	2	NUM
ejpam-4522	58	6	]	]	PUNCT
ejpam-4522	58	7	)	)	PUNCT
ejpam-4522	58	8	.	.	PUNCT
ejpam-4522	59	1	let	let	VERB
ejpam-4522	59	2	(	(	PUNCT
ejpam-4522	59	3	x	x	X
ejpam-4522	59	4	,	,	PUNCT
ejpam-4522	59	5	e	e	NOUN
ejpam-4522	59	6	)	)	PUNCT
ejpam-4522	59	7	be	be	AUX
ejpam-4522	59	8	a	a	DET
ejpam-4522	59	9	bck	bck	VERB
ejpam-4522	59	10	/	/	SYM
ejpam-4522	59	11	bci	bci	ADJ
ejpam-4522	59	12	-	-	ADJ
ejpam-4522	59	13	soft	soft	ADJ
ejpam-4522	59	14	universe	universe	NOUN
ejpam-4522	59	15	.	.	PUNCT
ejpam-4522	60	1	a	a	DET
ejpam-4522	60	2	makgeolli	makgeolli	NOUN
ejpam-4522	60	3	structure	structure	NOUN
ejpam-4522	60	4	m(x	m(x	PROPN
ejpam-4522	60	5	,	,	PUNCT
ejpam-4522	60	6	e	e	NOUN
ejpam-4522	60	7	)	)	PUNCT
ejpam-4522	60	8	:	:	PUNCT
ejpam-4522	60	9	=	=	SYM
ejpam-4522	60	10	(	(	PUNCT
ejpam-4522	60	11	me	i	PRON
ejpam-4522	60	12	,	,	PUNCT
ejpam-4522	60	13	ge	ge	PROPN
ejpam-4522	60	14	,	,	PUNCT
ejpam-4522	60	15	ξ	ξ	X
ejpam-4522	60	16	)	)	PUNCT
ejpam-4522	60	17	is	be	AUX
ejpam-4522	60	18	called	call	VERB
ejpam-4522	60	19	a	a	DET
ejpam-4522	60	20	makgeolli	makgeolli	NOUN
ejpam-4522	60	21	ideal	ideal	NOUN
ejpam-4522	60	22	of	of	ADP
ejpam-4522	60	23	(	(	PUNCT
ejpam-4522	60	24	x	x	X
ejpam-4522	60	25	,	,	PUNCT
ejpam-4522	60	26	e	e	NOUN
ejpam-4522	60	27	)	)	PUNCT
ejpam-4522	60	28	if	if	SCONJ
ejpam-4522	60	29	it	it	PRON
ejpam-4522	60	30	satisfies	satisfy	VERB
ejpam-4522	60	31	:	:	PUNCT
ejpam-4522	60	32	{	{	PUNCT
ejpam-4522	60	33	(	(	PUNCT
ejpam-4522	60	34	∀a	∀a	NOUN
ejpam-4522	60	35	∈	∈	NOUN
ejpam-4522	60	36	e	e	NOUN
ejpam-4522	60	37	)	)	PUNCT
ejpam-4522	60	38	(	(	PUNCT
ejpam-4522	60	39	me(0	me(0	PROPN
ejpam-4522	60	40	)	)	PUNCT
ejpam-4522	60	41	⊇	⊇	NOUN
ejpam-4522	60	42	me(a	me(a	NOUN
ejpam-4522	60	43	)	)	PUNCT
ejpam-4522	60	44	,	,	PUNCT
ejpam-4522	60	45	ge(0	ge(0	PROPN
ejpam-4522	60	46	)	)	PUNCT
ejpam-4522	60	47	⊆	⊆	NUM
ejpam-4522	60	48	ge(a	ge(a	NOUN
ejpam-4522	60	49	)	)	PUNCT
ejpam-4522	60	50	)	)	PUNCT
ejpam-4522	60	51	.	.	PUNCT
ejpam-4522	61	1	(	(	PUNCT
ejpam-4522	61	2	∀x	∀x	X
ejpam-4522	61	3	∈	∈	PROPN
ejpam-4522	61	4	x	x	X
ejpam-4522	61	5	)	)	PUNCT
ejpam-4522	61	6	(	(	PUNCT
ejpam-4522	61	7	0	0	NUM
ejpam-4522	61	8	/	/	SYM
ejpam-4522	61	9	ξ(x	ξ(x	NOUN
ejpam-4522	61	10	)	)	PUNCT
ejpam-4522	61	11	∈	∈	PROPN
ejpam-4522	61	12	ξ	ξ	NOUN
ejpam-4522	61	13	)	)	PUNCT
ejpam-4522	61	14	.	.	PUNCT
ejpam-4522	62	1	(	(	PUNCT
ejpam-4522	62	2	9)	9)	NUM
ejpam-4522	62	3	(	(	PUNCT
ejpam-4522	62	4	∀a	∀a	NOUN
ejpam-4522	62	5	,	,	PUNCT
ejpam-4522	62	6	b	b	X
ejpam-4522	62	7	∈	∈	PROPN
ejpam-4522	62	8	e	e	NOUN
ejpam-4522	62	9	)	)	PUNCT
ejpam-4522	62	10	(	(	PUNCT
ejpam-4522	62	11	me(a	me(a	NOUN
ejpam-4522	62	12	)	)	PUNCT
ejpam-4522	62	13	⊇	⊇	NOUN
ejpam-4522	62	14	me(a	me(a	X
ejpam-4522	62	15	↬	↬	PROPN
ejpam-4522	62	16	b	b	X
ejpam-4522	62	17	)	)	PUNCT
ejpam-4522	62	18	∩me(b	∩me(b	ADJ
ejpam-4522	62	19	)	)	PUNCT
ejpam-4522	62	20	ge(a	ge(a	PUNCT
ejpam-4522	62	21	)	)	PUNCT
ejpam-4522	62	22	⊆	⊆	NUM
ejpam-4522	62	23	ge(a	ge(a	PUNCT
ejpam-4522	62	24	↬	↬	PROPN
ejpam-4522	62	25	b	b	X
ejpam-4522	62	26	)	)	PUNCT
ejpam-4522	62	27	∪ge(b	∪ge(b	NOUN
ejpam-4522	62	28	)	)	PUNCT
ejpam-4522	62	29	)	)	PUNCT
ejpam-4522	62	30	.	.	PUNCT
ejpam-4522	63	1	(	(	PUNCT
ejpam-4522	63	2	∀x	∀x	X
ejpam-4522	63	3	,	,	PUNCT
ejpam-4522	63	4	y	y	PROPN
ejpam-4522	63	5	,	,	PUNCT
ejpam-4522	63	6	z	z	PROPN
ejpam-4522	63	7	∈	∈	PROPN
ejpam-4522	63	8	x)(∀t	x)(∀t	PROPN
ejpam-4522	63	9	,	,	PUNCT
ejpam-4522	63	10	r	r	NOUN
ejpam-4522	63	11	∈	∈	PROPN
ejpam-4522	63	12	(	(	PUNCT
ejpam-4522	63	13	0	0	NUM
ejpam-4522	63	14	,	,	PUNCT
ejpam-4522	63	15	1	1	NUM
ejpam-4522	63	16	]	]	NUM
ejpam-4522	63	17	)	)	PUNCT
ejpam-4522	63	18	(	(	PUNCT
ejpam-4522	63	19	{	{	PUNCT
ejpam-4522	63	20	x	x	SYM
ejpam-4522	63	21	∗	∗	VERB
ejpam-4522	63	22	y}/t	y}/t	PROPN
ejpam-4522	63	23	∈	∈	PROPN
ejpam-4522	63	24	ξ	ξ	PROPN
ejpam-4522	63	25	,	,	PUNCT
ejpam-4522	63	26	y	y	PROPN
ejpam-4522	63	27	/	/	SYM
ejpam-4522	63	28	r	r	NOUN
ejpam-4522	63	29	∈	∈	NOUN
ejpam-4522	63	30	ξ	ξ	X
ejpam-4522	63	31	⇒	⇒	NOUN
ejpam-4522	63	32	x	x	SYM
ejpam-4522	63	33	/	/	SYM
ejpam-4522	63	34	min{t	min{t	PROPN
ejpam-4522	63	35	,	,	PUNCT
ejpam-4522	63	36	r	r	NOUN
ejpam-4522	63	37	}	}	PUNCT
ejpam-4522	63	38	∈	∈	PROPN
ejpam-4522	63	39	ξ	ξ	PROPN
ejpam-4522	63	40	)	)	PUNCT
ejpam-4522	63	41	.	.	PUNCT
ejpam-4522	64	1	(	(	PUNCT
ejpam-4522	64	2	10	10	NUM
ejpam-4522	64	3	)	)	PUNCT
ejpam-4522	64	4	lemma	lemma	PROPN
ejpam-4522	64	5	1	1	NUM
ejpam-4522	64	6	(	(	PUNCT
ejpam-4522	64	7	[	[	X
ejpam-4522	64	8	2	2	NUM
ejpam-4522	64	9	]	]	PUNCT
ejpam-4522	64	10	)	)	PUNCT
ejpam-4522	64	11	.	.	PUNCT
ejpam-4522	65	1	let	let	VERB
ejpam-4522	65	2	(	(	PUNCT
ejpam-4522	65	3	x	x	X
ejpam-4522	65	4	,	,	PUNCT
ejpam-4522	65	5	e	e	NOUN
ejpam-4522	65	6	)	)	PUNCT
ejpam-4522	65	7	be	be	AUX
ejpam-4522	65	8	a	a	DET
ejpam-4522	65	9	bck	bck	VERB
ejpam-4522	65	10	/	/	SYM
ejpam-4522	65	11	bci	bci	ADJ
ejpam-4522	65	12	-	-	ADJ
ejpam-4522	65	13	soft	soft	ADJ
ejpam-4522	65	14	universe	universe	NOUN
ejpam-4522	65	15	.	.	PUNCT
ejpam-4522	66	1	every	every	DET
ejpam-4522	66	2	makgeolli	makgeolli	NOUN
ejpam-4522	66	3	ideal	ideal	NOUN
ejpam-4522	66	4	m(x	m(x	PROPN
ejpam-4522	66	5	,	,	PUNCT
ejpam-4522	66	6	e	e	NOUN
ejpam-4522	66	7	)	)	PUNCT
ejpam-4522	66	8	:	:	PUNCT
ejpam-4522	67	1	=	=	SYM
ejpam-4522	67	2	(	(	PUNCT
ejpam-4522	67	3	me	i	PRON
ejpam-4522	67	4	,	,	PUNCT
ejpam-4522	67	5	ge	ge	PROPN
ejpam-4522	67	6	,	,	PUNCT
ejpam-4522	67	7	ξ	ξ	PROPN
ejpam-4522	67	8	)	)	PUNCT
ejpam-4522	67	9	of	of	ADP
ejpam-4522	67	10	(	(	PUNCT
ejpam-4522	67	11	x	x	NOUN
ejpam-4522	67	12	,	,	PUNCT
ejpam-4522	67	13	e	e	NOUN
ejpam-4522	67	14	)	)	PUNCT
ejpam-4522	67	15	satisfies	satisfy	VERB
ejpam-4522	67	16	the	the	DET
ejpam-4522	67	17	following	follow	VERB
ejpam-4522	67	18	assertions	assertion	NOUN
ejpam-4522	67	19	.	.	PUNCT
ejpam-4522	68	1	s.	s.	PROPN
ejpam-4522	68	2	z.	z.	PROPN
ejpam-4522	68	3	song	song	PROPN
ejpam-4522	68	4	,	,	PUNCT
ejpam-4522	68	5	m.	m.	NOUN
ejpam-4522	68	6	a.	a.	NOUN
ejpam-4522	68	7	öztürk	öztürk	PROPN
ejpam-4522	68	8	,	,	PUNCT
ejpam-4522	68	9	y.	y.	PROPN
ejpam-4522	68	10	b.	b.	PROPN
ejpam-4522	68	11	jun	jun	PROPN
ejpam-4522	68	12	/	/	SYM
ejpam-4522	68	13	eur	eur	PROPN
ejpam-4522	68	14	.	.	PUNCT
ejpam-4522	69	1	j.	j.	PROPN
ejpam-4522	69	2	pure	pure	PROPN
ejpam-4522	69	3	appl	appl	PROPN
ejpam-4522	69	4	.	.	PROPN
ejpam-4522	69	5	math	math	PROPN
ejpam-4522	69	6	,	,	PUNCT
ejpam-4522	69	7	15	15	NUM
ejpam-4522	69	8	(	(	PUNCT
ejpam-4522	69	9	4	4	NUM
ejpam-4522	69	10	)	)	PUNCT
ejpam-4522	69	11	(	(	PUNCT
ejpam-4522	69	12	2022	2022	NUM
ejpam-4522	69	13	)	)	PUNCT
ejpam-4522	69	14	,	,	PUNCT
ejpam-4522	69	15	1498	1498	NUM
ejpam-4522	69	16	-	-	SYM
ejpam-4522	69	17	1511	1511	NUM
ejpam-4522	69	18	1501	1501	NUM
ejpam-4522	69	19	(	(	PUNCT
ejpam-4522	69	20	i	i	NOUN
ejpam-4522	69	21	)	)	PUNCT
ejpam-4522	69	22			PUNCT
ejpam-4522	69	23	(	(	PUNCT
ejpam-4522	69	24	∀a	∀a	NOUN
ejpam-4522	69	25	,	,	PUNCT
ejpam-4522	69	26	b	b	X
ejpam-4522	69	27	∈	∈	PROPN
ejpam-4522	69	28	e	e	X
ejpam-4522	69	29	)	)	PUNCT
ejpam-4522	69	30	(	(	PUNCT
ejpam-4522	69	31	a	a	DET
ejpam-4522	69	32	≤	≤	PROPN
ejpam-4522	69	33	b	b	NOUN
ejpam-4522	69	34	⇒	⇒	NOUN
ejpam-4522	69	35	{	{	PUNCT
ejpam-4522	69	36	me(a	me(a	NOUN
ejpam-4522	69	37	)	)	PUNCT
ejpam-4522	69	38	⊇	⊇	NOUN
ejpam-4522	69	39	me(b	me(b	PUNCT
ejpam-4522	69	40	)	)	PUNCT
ejpam-4522	69	41	ge(a	ge(a	NOUN
ejpam-4522	69	42	)	)	PUNCT
ejpam-4522	69	43	⊆	⊆	NUM
ejpam-4522	69	44	ge(b	ge(b	PUNCT
ejpam-4522	69	45	)	)	PUNCT
ejpam-4522	69	46	)	)	PUNCT
ejpam-4522	69	47	.	.	PUNCT
ejpam-4522	70	1	(	(	PUNCT
ejpam-4522	70	2	∀x	∀x	X
ejpam-4522	70	3	,	,	PUNCT
ejpam-4522	70	4	y	y	PROPN
ejpam-4522	70	5	∈	∈	PROPN
ejpam-4522	70	6	x	x	X
ejpam-4522	70	7	)	)	PUNCT
ejpam-4522	70	8	(	(	PUNCT
ejpam-4522	70	9	x	x	X
ejpam-4522	70	10	≤	≤	NOUN
ejpam-4522	70	11	y	y	PROPN
ejpam-4522	70	12	⇒	⇒	PROPN
ejpam-4522	70	13	ξ(x	ξ(x	PROPN
ejpam-4522	70	14	)	)	PUNCT
ejpam-4522	70	15	≥	≥	NOUN
ejpam-4522	70	16	ξ(y	ξ(y	PROPN
ejpam-4522	70	17	∗	∗	NOUN
ejpam-4522	70	18	z	z	PROPN
ejpam-4522	70	19	)	)	PUNCT
ejpam-4522	70	20	)	)	PUNCT
ejpam-4522	70	21	.	.	PUNCT
ejpam-4522	71	1	(	(	PUNCT
ejpam-4522	71	2	ii	ii	NOUN
ejpam-4522	71	3	)	)	PUNCT
ejpam-4522	71	4			PUNCT
ejpam-4522	71	5	(	(	PUNCT
ejpam-4522	71	6	∀a	∀a	X
ejpam-4522	71	7	,	,	PUNCT
ejpam-4522	71	8	b	b	NOUN
ejpam-4522	71	9	,	,	PUNCT
ejpam-4522	71	10	c	c	PROPN
ejpam-4522	71	11	∈	∈	PROPN
ejpam-4522	71	12	e	e	X
ejpam-4522	71	13	)	)	PUNCT
ejpam-4522	71	14	(	(	PUNCT
ejpam-4522	71	15	a	a	DET
ejpam-4522	71	16	↬	↬	PROPN
ejpam-4522	71	17	b	b	PROPN
ejpam-4522	71	18	≤	≤	PROPN
ejpam-4522	71	19	c	c	NOUN
ejpam-4522	71	20	⇒	⇒	NOUN
ejpam-4522	71	21	{	{	PUNCT
ejpam-4522	71	22	me(a	me(a	PROPN
ejpam-4522	71	23	)	)	PUNCT
ejpam-4522	71	24	⊇	⊇	NOUN
ejpam-4522	71	25	me(b	me(b	X
ejpam-4522	71	26	)	)	PUNCT
ejpam-4522	71	27	∩me(c	∩me(c	PROPN
ejpam-4522	71	28	)	)	PUNCT
ejpam-4522	71	29	ge(a	ge(a	NOUN
ejpam-4522	71	30	)	)	PUNCT
ejpam-4522	71	31	⊆	⊆	NUM
ejpam-4522	71	32	ge(b	ge(b	X
ejpam-4522	71	33	)	)	PUNCT
ejpam-4522	71	34	∪ge(c	∪ge(c	NUM
ejpam-4522	71	35	)	)	PUNCT
ejpam-4522	71	36	)	)	PUNCT
ejpam-4522	71	37	.	.	PUNCT
ejpam-4522	72	1	(	(	PUNCT
ejpam-4522	72	2	∀x	∀x	X
ejpam-4522	72	3	,	,	PUNCT
ejpam-4522	72	4	y	y	PROPN
ejpam-4522	72	5	,	,	PUNCT
ejpam-4522	72	6	z	z	NOUN
ejpam-4522	72	7	∈	∈	PROPN
ejpam-4522	72	8	x	x	X
ejpam-4522	72	9	)	)	PUNCT
ejpam-4522	72	10	(	(	PUNCT
ejpam-4522	72	11	x	x	SYM
ejpam-4522	72	12	∗	∗	VERB
ejpam-4522	72	13	y	y	NOUN
ejpam-4522	72	14	≤	≤	PROPN
ejpam-4522	72	15	z	z	NOUN
ejpam-4522	72	16	⇒	⇒	NOUN
ejpam-4522	72	17	ξ(x	ξ(x	PROPN
ejpam-4522	72	18	)	)	PUNCT
ejpam-4522	72	19	≥	≥	NOUN
ejpam-4522	72	20	min{ξ(y	min{ξ(y	PROPN
ejpam-4522	72	21	∗	∗	NOUN
ejpam-4522	72	22	z	z	NOUN
ejpam-4522	72	23	)	)	PUNCT
ejpam-4522	72	24	,	,	PUNCT
ejpam-4522	72	25	ξ(z	ξ(z	PROPN
ejpam-4522	72	26	)	)	PUNCT
ejpam-4522	72	27	}	}	PUNCT
ejpam-4522	72	28	)	)	PUNCT
ejpam-4522	72	29	.	.	PUNCT
ejpam-4522	73	1	let	let	VERB
ejpam-4522	73	2	(	(	PUNCT
ejpam-4522	73	3	x	x	X
ejpam-4522	73	4	,	,	PUNCT
ejpam-4522	73	5	e	e	NOUN
ejpam-4522	73	6	)	)	PUNCT
ejpam-4522	73	7	be	be	AUX
ejpam-4522	73	8	a	a	DET
ejpam-4522	73	9	bck	bck	VERB
ejpam-4522	73	10	/	/	SYM
ejpam-4522	73	11	bci	bci	ADJ
ejpam-4522	73	12	-	-	ADJ
ejpam-4522	73	13	soft	soft	ADJ
ejpam-4522	73	14	universe	universe	NOUN
ejpam-4522	73	15	.	.	PUNCT
ejpam-4522	74	1	given	give	VERB
ejpam-4522	74	2	a	a	DET
ejpam-4522	74	3	makgeolli	makgeolli	NOUN
ejpam-4522	74	4	structure	structure	NOUN
ejpam-4522	74	5	m(x	m(x	PROPN
ejpam-4522	74	6	,	,	PUNCT
ejpam-4522	74	7	e	e	NOUN
ejpam-4522	74	8	)	)	PUNCT
ejpam-4522	74	9	:	:	PUNCT
ejpam-4522	74	10	=	=	SYM
ejpam-4522	74	11	(	(	PUNCT
ejpam-4522	74	12	me	i	PRON
ejpam-4522	74	13	,	,	PUNCT
ejpam-4522	74	14	ge	ge	PROPN
ejpam-4522	74	15	,	,	PUNCT
ejpam-4522	74	16	ξ	ξ	PROPN
ejpam-4522	74	17	)	)	PUNCT
ejpam-4522	74	18	on	on	ADP
ejpam-4522	74	19	(	(	PUNCT
ejpam-4522	74	20	x	x	X
ejpam-4522	74	21	,	,	PUNCT
ejpam-4522	74	22	e	e	NOUN
ejpam-4522	74	23	)	)	PUNCT
ejpam-4522	74	24	,	,	PUNCT
ejpam-4522	74	25	consider	consider	VERB
ejpam-4522	74	26	the	the	DET
ejpam-4522	74	27	following	follow	VERB
ejpam-4522	74	28	sets	set	NOUN
ejpam-4522	74	29	:	:	PUNCT
ejpam-4522	74	30	e(me	e(me	NOUN
ejpam-4522	74	31	;	;	PUNCT
ejpam-4522	74	32	α	α	X
ejpam-4522	74	33	)	)	PUNCT
ejpam-4522	74	34	:	:	PUNCT
ejpam-4522	74	35	=	=	X
ejpam-4522	74	36	{	{	PUNCT
ejpam-4522	74	37	a	a	PRON
ejpam-4522	74	38	∈	∈	PROPN
ejpam-4522	74	39	e	e	NOUN
ejpam-4522	74	40	|	|	ADV
ejpam-4522	74	41	me(a	me(a	NOUN
ejpam-4522	74	42	)	)	PUNCT
ejpam-4522	74	43	⊇	⊇	NOUN
ejpam-4522	74	44	α	α	NOUN
ejpam-4522	74	45	}	}	PUNCT
ejpam-4522	74	46	,	,	PUNCT
ejpam-4522	74	47	e(ge	e(ge	NOUN
ejpam-4522	74	48	;	;	PUNCT
ejpam-4522	74	49	β	β	X
ejpam-4522	74	50	)	)	PUNCT
ejpam-4522	74	51	:	:	PUNCT
ejpam-4522	74	52	=	=	SYM
ejpam-4522	74	53	{	{	PUNCT
ejpam-4522	74	54	b	b	X
ejpam-4522	74	55	∈	∈	PROPN
ejpam-4522	74	56	e	e	NOUN
ejpam-4522	74	57	|	|	ADV
ejpam-4522	74	58	ge(b	ge(b	PUNCT
ejpam-4522	74	59	)	)	PUNCT
ejpam-4522	74	60	⊆	⊆	NUM
ejpam-4522	74	61	β	β	X
ejpam-4522	74	62	}	}	PUNCT
ejpam-4522	74	63	,	,	PUNCT
ejpam-4522	74	64	x	x	X
ejpam-4522	74	65	(	(	PUNCT
ejpam-4522	74	66	ξ	ξ	PROPN
ejpam-4522	74	67	;	;	PUNCT
ejpam-4522	74	68	t	t	PROPN
ejpam-4522	74	69	)	)	PUNCT
ejpam-4522	74	70	:	:	PUNCT
ejpam-4522	75	1	=	=	SYM
ejpam-4522	75	2	{	{	PUNCT
ejpam-4522	75	3	x	x	PUNCT
ejpam-4522	75	4	∈	∈	PROPN
ejpam-4522	75	5	x	x	X
ejpam-4522	75	6	|	|	NOUN
ejpam-4522	75	7	ξ(x	ξ(x	NOUN
ejpam-4522	75	8	)	)	PUNCT
ejpam-4522	75	9	≥	≥	NOUN
ejpam-4522	75	10	t	t	PROPN
ejpam-4522	75	11	}	}	PUNCT
ejpam-4522	75	12	where	where	SCONJ
ejpam-4522	75	13	α	α	NOUN
ejpam-4522	75	14	and	and	CCONJ
ejpam-4522	75	15	β	β	X
ejpam-4522	75	16	are	be	AUX
ejpam-4522	75	17	subsets	subset	NOUN
ejpam-4522	75	18	of	of	ADP
ejpam-4522	75	19	x	x	PUNCT
ejpam-4522	75	20	and	and	CCONJ
ejpam-4522	75	21	t	t	NOUN
ejpam-4522	75	22	∈	∈	PROPN
ejpam-4522	76	1	[	[	X
ejpam-4522	76	2	0	0	NUM
ejpam-4522	76	3	,	,	PUNCT
ejpam-4522	76	4	1	1	NUM
ejpam-4522	76	5	]	]	PUNCT
ejpam-4522	76	6	.	.	PUNCT
ejpam-4522	77	1	3	3	X
ejpam-4522	77	2	.	.	X
ejpam-4522	77	3	positive	positive	ADJ
ejpam-4522	77	4	implicative	implicative	ADJ
ejpam-4522	77	5	makgeolli	makgeolli	NOUN
ejpam-4522	77	6	ideals	ideal	NOUN
ejpam-4522	77	7	in	in	ADP
ejpam-4522	77	8	what	what	PRON
ejpam-4522	77	9	follows	follow	VERB
ejpam-4522	77	10	,	,	PUNCT
ejpam-4522	77	11	let	let	VERB
ejpam-4522	77	12	(	(	PUNCT
ejpam-4522	77	13	x	x	X
ejpam-4522	77	14	,	,	PUNCT
ejpam-4522	77	15	e	e	NOUN
ejpam-4522	77	16	)	)	PUNCT
ejpam-4522	77	17	be	be	AUX
ejpam-4522	77	18	a	a	DET
ejpam-4522	77	19	bck	bck	NOUN
ejpam-4522	77	20	-	-	PUNCT
ejpam-4522	77	21	soft	soft	ADJ
ejpam-4522	77	22	universe	universe	NOUN
ejpam-4522	77	23	unless	unless	SCONJ
ejpam-4522	77	24	otherwise	otherwise	ADV
ejpam-4522	77	25	specified	specify	VERB
ejpam-4522	77	26	.	.	PUNCT
ejpam-4522	78	1	definition	definition	NOUN
ejpam-4522	78	2	3	3	NUM
ejpam-4522	78	3	.	.	PUNCT
ejpam-4522	79	1	a	a	DET
ejpam-4522	79	2	makgeolli	makgeolli	NOUN
ejpam-4522	79	3	structure	structure	NOUN
ejpam-4522	79	4	m(x	m(x	PROPN
ejpam-4522	79	5	,	,	PUNCT
ejpam-4522	79	6	e	e	NOUN
ejpam-4522	79	7	)	)	PUNCT
ejpam-4522	79	8	:	:	PUNCT
ejpam-4522	79	9	=	=	SYM
ejpam-4522	79	10	(	(	PUNCT
ejpam-4522	79	11	me	i	PRON
ejpam-4522	79	12	,	,	PUNCT
ejpam-4522	79	13	ge	ge	PROPN
ejpam-4522	79	14	,	,	PUNCT
ejpam-4522	79	15	ξ	ξ	X
ejpam-4522	79	16	)	)	PUNCT
ejpam-4522	79	17	is	be	AUX
ejpam-4522	79	18	called	call	VERB
ejpam-4522	79	19	a	a	DET
ejpam-4522	79	20	positive	positive	ADJ
ejpam-4522	79	21	implicative	implicative	ADJ
ejpam-4522	79	22	makgeolli	makgeolli	NOUN
ejpam-4522	79	23	ideal	ideal	NOUN
ejpam-4522	79	24	of	of	ADP
ejpam-4522	79	25	(	(	PUNCT
ejpam-4522	79	26	x	x	X
ejpam-4522	79	27	,	,	PUNCT
ejpam-4522	79	28	e	e	NOUN
ejpam-4522	79	29	)	)	PUNCT
ejpam-4522	79	30	if	if	SCONJ
ejpam-4522	79	31	it	it	PRON
ejpam-4522	79	32	satisfies	satisfy	VERB
ejpam-4522	79	33	(	(	PUNCT
ejpam-4522	79	34	9	9	NUM
ejpam-4522	79	35	)	)	PUNCT
ejpam-4522	79	36	and	and	CCONJ
ejpam-4522	79	37	(	(	PUNCT
ejpam-4522	79	38	∀a	∀a	NOUN
ejpam-4522	79	39	,	,	PUNCT
ejpam-4522	79	40	b	b	NOUN
ejpam-4522	79	41	,	,	PUNCT
ejpam-4522	80	1	c	c	PROPN
ejpam-4522	80	2	∈	∈	PROPN
ejpam-4522	80	3	e	e	X
ejpam-4522	80	4	)	)	PUNCT
ejpam-4522	80	5	(	(	PUNCT
ejpam-4522	80	6	me(a	me(a	X
ejpam-4522	80	7	↬	↬	PROPN
ejpam-4522	80	8	c	c	X
ejpam-4522	80	9	)	)	PUNCT
ejpam-4522	80	10	⊇	⊇	PROPN
ejpam-4522	80	11	me((a	me((a	PROPN
ejpam-4522	80	12	↬	↬	PROPN
ejpam-4522	80	13	b	b	X
ejpam-4522	80	14	)	)	PUNCT
ejpam-4522	80	15	↬	↬	PROPN
ejpam-4522	81	1	c	c	X
ejpam-4522	81	2	)	)	PUNCT
ejpam-4522	81	3	∩me(b	∩me(b	ADV
ejpam-4522	81	4	↬	↬	NUM
ejpam-4522	81	5	c	c	X
ejpam-4522	81	6	)	)	PUNCT
ejpam-4522	81	7	ge(a	ge(a	PUNCT
ejpam-4522	81	8	↬	↬	PROPN
ejpam-4522	81	9	c	c	X
ejpam-4522	81	10	)	)	PUNCT
ejpam-4522	81	11	⊆	⊆	NUM
ejpam-4522	81	12	ge((a	ge((a	NOUN
ejpam-4522	81	13	↬	↬	PROPN
ejpam-4522	81	14	b	b	X
ejpam-4522	81	15	)	)	PUNCT
ejpam-4522	81	16	↬	↬	X
ejpam-4522	81	17	c	c	X
ejpam-4522	81	18	)	)	PUNCT
ejpam-4522	81	19	∪ge(b	∪ge(b	ADP
ejpam-4522	81	20	↬	↬	PROPN
ejpam-4522	81	21	c	c	X
ejpam-4522	81	22	)	)	PUNCT
ejpam-4522	81	23	)	)	PUNCT
ejpam-4522	81	24	.	.	PUNCT
ejpam-4522	82	1	(	(	PUNCT
ejpam-4522	82	2	11	11	NUM
ejpam-4522	82	3	)	)	PUNCT
ejpam-4522	82	4	(	(	PUNCT
ejpam-4522	82	5	∀x	∀x	X
ejpam-4522	82	6	,	,	PUNCT
ejpam-4522	82	7	y	y	PROPN
ejpam-4522	82	8	,	,	PUNCT
ejpam-4522	82	9	z	z	PROPN
ejpam-4522	82	10	∈	∈	PROPN
ejpam-4522	82	11	x)(∀t	x)(∀t	PROPN
ejpam-4522	82	12	,	,	PUNCT
ejpam-4522	82	13	r	r	NOUN
ejpam-4522	82	14	∈	∈	PROPN
ejpam-4522	82	15	(	(	PUNCT
ejpam-4522	82	16	0	0	NUM
ejpam-4522	82	17	,	,	PUNCT
ejpam-4522	82	18	1	1	NUM
ejpam-4522	82	19	]	]	NUM
ejpam-4522	82	20	)	)	PUNCT
ejpam-4522	82	21	(	(	PUNCT
ejpam-4522	82	22	{	{	PUNCT
ejpam-4522	82	23	(	(	PUNCT
ejpam-4522	82	24	x	x	NOUN
ejpam-4522	82	25	∗	∗	PROPN
ejpam-4522	82	26	y	y	NOUN
ejpam-4522	82	27	)	)	PUNCT
ejpam-4522	82	28	∗	∗	NOUN
ejpam-4522	83	1	z}/t	z}/t	PROPN
ejpam-4522	83	2	∈	∈	PROPN
ejpam-4522	83	3	ξ	ξ	PROPN
ejpam-4522	83	4	,	,	PUNCT
ejpam-4522	83	5	{	{	PUNCT
ejpam-4522	83	6	y	y	NOUN
ejpam-4522	83	7	∗	∗	NOUN
ejpam-4522	83	8	z}/r	z}/r	PROPN
ejpam-4522	83	9	∈	∈	PROPN
ejpam-4522	83	10	ξ	ξ	X
ejpam-4522	83	11	⇒	⇒	NOUN
ejpam-4522	83	12	{	{	PUNCT
ejpam-4522	83	13	x	x	X
ejpam-4522	83	14	∗	∗	NOUN
ejpam-4522	83	15	z}/min{t	z}/min{t	PROPN
ejpam-4522	83	16	,	,	PUNCT
ejpam-4522	83	17	r	r	NOUN
ejpam-4522	83	18	}	}	PUNCT
ejpam-4522	83	19	∈	∈	PROPN
ejpam-4522	83	20	ξ	ξ	PROPN
ejpam-4522	83	21	)	)	PUNCT
ejpam-4522	83	22	.	.	PUNCT
ejpam-4522	84	1	(	(	PUNCT
ejpam-4522	84	2	12	12	X
ejpam-4522	84	3	)	)	PUNCT
ejpam-4522	84	4	note	note	NOUN
ejpam-4522	84	5	that	that	SCONJ
ejpam-4522	84	6	the	the	DET
ejpam-4522	84	7	condition	condition	NOUN
ejpam-4522	84	8	(	(	PUNCT
ejpam-4522	84	9	12	12	NUM
ejpam-4522	84	10	)	)	PUNCT
ejpam-4522	84	11	is	be	AUX
ejpam-4522	84	12	equivalent	equivalent	ADJ
ejpam-4522	84	13	to	to	ADP
ejpam-4522	84	14	the	the	DET
ejpam-4522	84	15	following	follow	VERB
ejpam-4522	84	16	assertion	assertion	NOUN
ejpam-4522	84	17	.	.	PUNCT
ejpam-4522	85	1	(	(	PUNCT
ejpam-4522	85	2	∀x	∀x	X
ejpam-4522	85	3	,	,	PUNCT
ejpam-4522	85	4	y	y	PROPN
ejpam-4522	85	5	,	,	PUNCT
ejpam-4522	85	6	z	z	NOUN
ejpam-4522	85	7	∈	∈	PROPN
ejpam-4522	85	8	x	x	X
ejpam-4522	85	9	)	)	PUNCT
ejpam-4522	85	10	(	(	PUNCT
ejpam-4522	85	11	ξ(x	ξ(x	NOUN
ejpam-4522	85	12	∗	∗	NOUN
ejpam-4522	85	13	z	z	NOUN
ejpam-4522	85	14	)	)	PUNCT
ejpam-4522	85	15	≥	≥	NOUN
ejpam-4522	85	16	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	85	17	∗	∗	X
ejpam-4522	85	18	y	y	NOUN
ejpam-4522	85	19	)	)	PUNCT
ejpam-4522	85	20	∗	∗	NOUN
ejpam-4522	85	21	z	z	NOUN
ejpam-4522	85	22	)	)	PUNCT
ejpam-4522	85	23	,	,	PUNCT
ejpam-4522	85	24	ξ(y	ξ(y	PROPN
ejpam-4522	85	25	∗	∗	NOUN
ejpam-4522	85	26	z	z	PROPN
ejpam-4522	85	27	)	)	PUNCT
ejpam-4522	85	28	}	}	PUNCT
ejpam-4522	85	29	)	)	PUNCT
ejpam-4522	85	30	.	.	PUNCT
ejpam-4522	86	1	(	(	PUNCT
ejpam-4522	86	2	13	13	NUM
ejpam-4522	86	3	)	)	PUNCT
ejpam-4522	86	4	in	in	ADP
ejpam-4522	86	5	fact	fact	NOUN
ejpam-4522	86	6	,	,	PUNCT
ejpam-4522	86	7	suppose	suppose	VERB
ejpam-4522	86	8	that	that	SCONJ
ejpam-4522	86	9	the	the	DET
ejpam-4522	86	10	condition	condition	NOUN
ejpam-4522	86	11	(	(	PUNCT
ejpam-4522	86	12	12	12	NUM
ejpam-4522	86	13	)	)	PUNCT
ejpam-4522	86	14	is	be	AUX
ejpam-4522	86	15	valid	valid	ADJ
ejpam-4522	86	16	.	.	PUNCT
ejpam-4522	87	1	since	since	SCONJ
ejpam-4522	87	2	{	{	PUNCT
ejpam-4522	87	3	(	(	PUNCT
ejpam-4522	87	4	x	x	NOUN
ejpam-4522	87	5	∗	∗	PROPN
ejpam-4522	87	6	y	y	NOUN
ejpam-4522	87	7	)	)	PUNCT
ejpam-4522	87	8	∗	∗	NOUN
ejpam-4522	87	9	z}/ξ((x	z}/ξ((x	NUM
ejpam-4522	87	10	∗	∗	PROPN
ejpam-4522	87	11	y	y	NOUN
ejpam-4522	87	12	)	)	PUNCT
ejpam-4522	87	13	∗	∗	NOUN
ejpam-4522	87	14	z	z	NOUN
ejpam-4522	87	15	)	)	PUNCT
ejpam-4522	87	16	∈	∈	PROPN
ejpam-4522	87	17	ξ	ξ	PROPN
ejpam-4522	87	18	and	and	CCONJ
ejpam-4522	87	19	{	{	PUNCT
ejpam-4522	87	20	y	y	PROPN
ejpam-4522	87	21	∗	∗	PROPN
ejpam-4522	87	22	z}/ξ(y	z}/ξ(y	PROPN
ejpam-4522	87	23	∗	∗	PROPN
ejpam-4522	87	24	z	z	NOUN
ejpam-4522	87	25	)	)	PUNCT
ejpam-4522	87	26	∈	∈	PROPN
ejpam-4522	87	27	ξ	ξ	PROPN
ejpam-4522	87	28	,	,	PUNCT
ejpam-4522	87	29	it	it	PRON
ejpam-4522	87	30	follows	follow	VERB
ejpam-4522	87	31	from	from	ADP
ejpam-4522	87	32	(	(	PUNCT
ejpam-4522	87	33	12	12	NUM
ejpam-4522	87	34	)	)	PUNCT
ejpam-4522	88	1	that	that	SCONJ
ejpam-4522	88	2	{	{	PUNCT
ejpam-4522	88	3	x	x	SYM
ejpam-4522	88	4	∗	∗	NOUN
ejpam-4522	88	5	z}/min{ξ((x	z}/min{ξ((x	NUM
ejpam-4522	88	6	∗	∗	NOUN
ejpam-4522	88	7	y	y	NOUN
ejpam-4522	88	8	)	)	PUNCT
ejpam-4522	88	9	∗	∗	NOUN
ejpam-4522	88	10	z	z	NOUN
ejpam-4522	88	11	)	)	PUNCT
ejpam-4522	88	12	,	,	PUNCT
ejpam-4522	88	13	ξ(y	ξ(y	PROPN
ejpam-4522	88	14	∗	∗	NOUN
ejpam-4522	88	15	z	z	NOUN
ejpam-4522	88	16	)	)	PUNCT
ejpam-4522	88	17	}	}	PUNCT
ejpam-4522	88	18	∈	∈	PROPN
ejpam-4522	88	19	ξ	ξ	X
ejpam-4522	88	20	.	.	PUNCT
ejpam-4522	89	1	hence	hence	ADV
ejpam-4522	89	2	ξ(x	ξ(x	NOUN
ejpam-4522	89	3	∗	∗	NOUN
ejpam-4522	89	4	z	z	NOUN
ejpam-4522	89	5	)	)	PUNCT
ejpam-4522	89	6	≥	≥	NOUN
ejpam-4522	89	7	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	89	8	∗	∗	X
ejpam-4522	89	9	y	y	NOUN
ejpam-4522	89	10	)	)	PUNCT
ejpam-4522	89	11	∗	∗	NOUN
ejpam-4522	89	12	z	z	NOUN
ejpam-4522	89	13	)	)	PUNCT
ejpam-4522	89	14	,	,	PUNCT
ejpam-4522	89	15	ξ(y	ξ(y	PROPN
ejpam-4522	89	16	∗	∗	NOUN
ejpam-4522	89	17	z	z	PROPN
ejpam-4522	89	18	)	)	PUNCT
ejpam-4522	89	19	}	}	PUNCT
ejpam-4522	89	20	.	.	PUNCT
ejpam-4522	90	1	conversely	conversely	ADV
ejpam-4522	90	2	,	,	PUNCT
ejpam-4522	90	3	assume	assume	VERB
ejpam-4522	90	4	that	that	SCONJ
ejpam-4522	90	5	the	the	DET
ejpam-4522	90	6	condition	condition	NOUN
ejpam-4522	90	7	(	(	PUNCT
ejpam-4522	90	8	13	13	NUM
ejpam-4522	90	9	)	)	PUNCT
ejpam-4522	90	10	is	be	AUX
ejpam-4522	90	11	valid	valid	ADJ
ejpam-4522	90	12	.	.	PUNCT
ejpam-4522	91	1	let	let	VERB
ejpam-4522	91	2	x	x	PRON
ejpam-4522	91	3	,	,	PUNCT
ejpam-4522	91	4	y	y	PROPN
ejpam-4522	91	5	,	,	PUNCT
ejpam-4522	91	6	z	z	NOUN
ejpam-4522	91	7	∈	∈	PROPN
ejpam-4522	91	8	x	x	X
ejpam-4522	91	9	and	and	CCONJ
ejpam-4522	91	10	t	t	PROPN
ejpam-4522	91	11	,	,	PUNCT
ejpam-4522	91	12	r	r	NOUN
ejpam-4522	91	13	∈	∈	PROPN
ejpam-4522	91	14	(	(	PUNCT
ejpam-4522	91	15	0	0	NUM
ejpam-4522	91	16	,	,	PUNCT
ejpam-4522	91	17	1	1	NUM
ejpam-4522	91	18	]	]	PUNCT
ejpam-4522	91	19	be	be	AUX
ejpam-4522	91	20	such	such	ADJ
ejpam-4522	91	21	that	that	SCONJ
ejpam-4522	91	22	{	{	PUNCT
ejpam-4522	91	23	(	(	PUNCT
ejpam-4522	91	24	x	x	NOUN
ejpam-4522	91	25	∗	∗	PROPN
ejpam-4522	91	26	y	y	NOUN
ejpam-4522	91	27	)	)	PUNCT
ejpam-4522	91	28	∗	∗	NOUN
ejpam-4522	91	29	z}/t	z}/t	PROPN
ejpam-4522	91	30	∈	∈	PROPN
ejpam-4522	91	31	ξ	ξ	PROPN
ejpam-4522	91	32	and	and	CCONJ
ejpam-4522	91	33	{	{	PUNCT
ejpam-4522	91	34	y	y	NOUN
ejpam-4522	91	35	∗	∗	NOUN
ejpam-4522	91	36	z}/r	z}/r	PROPN
ejpam-4522	91	37	∈	∈	PROPN
ejpam-4522	91	38	ξ	ξ	X
ejpam-4522	91	39	.	.	PUNCT
ejpam-4522	91	40	then	then	ADV
ejpam-4522	91	41	ξ((x	ξ((x	VERB
ejpam-4522	91	42	∗	∗	PROPN
ejpam-4522	91	43	y	y	NOUN
ejpam-4522	91	44	)	)	PUNCT
ejpam-4522	91	45	∗	∗	NOUN
ejpam-4522	91	46	z	z	NOUN
ejpam-4522	91	47	)	)	PUNCT
ejpam-4522	91	48	≥	≥	NOUN
ejpam-4522	91	49	t	t	NOUN
ejpam-4522	91	50	and	and	CCONJ
ejpam-4522	91	51	ξ(y	ξ(y	PROPN
ejpam-4522	91	52	∗	∗	NOUN
ejpam-4522	91	53	z	z	PROPN
ejpam-4522	91	54	)	)	PUNCT
ejpam-4522	91	55	≥	≥	PROPN
ejpam-4522	91	56	r.	r.	PROPN
ejpam-4522	91	57	it	it	PRON
ejpam-4522	91	58	follows	follow	VERB
ejpam-4522	91	59	from	from	ADP
ejpam-4522	91	60	(	(	PUNCT
ejpam-4522	91	61	13	13	NUM
ejpam-4522	91	62	)	)	PUNCT
ejpam-4522	91	63	that	that	PRON
ejpam-4522	91	64	ξ(x	ξ(x	NOUN
ejpam-4522	91	65	∗	∗	NOUN
ejpam-4522	91	66	z	z	NOUN
ejpam-4522	91	67	)	)	PUNCT
ejpam-4522	91	68	≥	≥	NOUN
ejpam-4522	91	69	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	91	70	∗	∗	X
ejpam-4522	91	71	y	y	NOUN
ejpam-4522	91	72	)	)	PUNCT
ejpam-4522	91	73	∗	∗	NOUN
ejpam-4522	91	74	z	z	NOUN
ejpam-4522	91	75	)	)	PUNCT
ejpam-4522	91	76	,	,	PUNCT
ejpam-4522	91	77	ξ(y	ξ(y	PROPN
ejpam-4522	91	78	∗	∗	NOUN
ejpam-4522	91	79	z	z	NOUN
ejpam-4522	91	80	)	)	PUNCT
ejpam-4522	91	81	}	}	PUNCT
ejpam-4522	91	82	≥	≥	NOUN
ejpam-4522	91	83	min{t	min{t	PROPN
ejpam-4522	91	84	,	,	PUNCT
ejpam-4522	91	85	r	r	NOUN
ejpam-4522	91	86	}	}	PUNCT
ejpam-4522	91	87	,	,	PUNCT
ejpam-4522	91	88	that	that	ADV
ejpam-4522	91	89	is	is	ADV
ejpam-4522	91	90	,	,	PUNCT
ejpam-4522	91	91	{	{	PUNCT
ejpam-4522	91	92	x	x	X
ejpam-4522	91	93	∗	∗	NOUN
ejpam-4522	91	94	z}/min{t	z}/min{t	PROPN
ejpam-4522	91	95	,	,	PUNCT
ejpam-4522	91	96	r	r	NOUN
ejpam-4522	91	97	}	}	PUNCT
ejpam-4522	91	98	∈	∈	PROPN
ejpam-4522	91	99	ξ	ξ	PROPN
ejpam-4522	91	100	.	.	PUNCT
ejpam-4522	91	101	example	example	NOUN
ejpam-4522	92	1	1	1	NUM
ejpam-4522	92	2	.	.	X
ejpam-4522	92	3	consider	consider	VERB
ejpam-4522	92	4	a	a	DET
ejpam-4522	92	5	bck	bck	VERB
ejpam-4522	92	6	-	-	PUNCT
ejpam-4522	92	7	soft	soft	ADJ
ejpam-4522	92	8	universe	universe	NOUN
ejpam-4522	92	9	(	(	PUNCT
ejpam-4522	92	10	x	x	X
ejpam-4522	92	11	,	,	PUNCT
ejpam-4522	92	12	e	e	NOUN
ejpam-4522	92	13	)	)	PUNCT
ejpam-4522	92	14	in	in	ADP
ejpam-4522	92	15	which	which	PRON
ejpam-4522	92	16	x	x	SYM
ejpam-4522	92	17	:	:	PUNCT
ejpam-4522	92	18	=	=	SYM
ejpam-4522	92	19	{	{	PUNCT
ejpam-4522	92	20	0	0	NUM
ejpam-4522	92	21	,	,	PUNCT
ejpam-4522	92	22	1	1	NUM
ejpam-4522	92	23	,	,	PUNCT
ejpam-4522	92	24	2	2	NUM
ejpam-4522	92	25	,	,	PUNCT
ejpam-4522	92	26	3	3	NUM
ejpam-4522	92	27	,	,	PUNCT
ejpam-4522	92	28	4	4	NUM
ejpam-4522	92	29	}	}	PUNCT
ejpam-4522	92	30	and	and	CCONJ
ejpam-4522	92	31	e	e	NOUN
ejpam-4522	92	32	:	:	PUNCT
ejpam-4522	92	33	=	=	SYM
ejpam-4522	92	34	{	{	PUNCT
ejpam-4522	92	35	0	0	NUM
ejpam-4522	92	36	,	,	PUNCT
ejpam-4522	92	37	1	1	NUM
ejpam-4522	92	38	,	,	PUNCT
ejpam-4522	92	39	2	2	NUM
ejpam-4522	92	40	,	,	PUNCT
ejpam-4522	92	41	3	3	NUM
ejpam-4522	92	42	}	}	PUNCT
ejpam-4522	92	43	with	with	ADP
ejpam-4522	92	44	binary	binary	ADJ
ejpam-4522	92	45	operations	operation	NOUN
ejpam-4522	92	46	“	"	PUNCT
ejpam-4522	92	47	∗	∗	NOUN
ejpam-4522	92	48	”	"	PUNCT
ejpam-4522	92	49	and	and	CCONJ
ejpam-4522	92	50	“	"	PUNCT
ejpam-4522	92	51	↬	↬	PROPN
ejpam-4522	92	52	”	"	PUNCT
ejpam-4522	92	53	,	,	PUNCT
ejpam-4522	92	54	respectively	respectively	ADV
ejpam-4522	92	55	,	,	PUNCT
ejpam-4522	92	56	given	give	VERB
ejpam-4522	92	57	by	by	ADP
ejpam-4522	92	58	table	table	NOUN
ejpam-4522	92	59	1	1	NUM
ejpam-4522	92	60	.	.	PUNCT
ejpam-4522	93	1	let	let	VERB
ejpam-4522	93	2	m(x	m(x	PROPN
ejpam-4522	93	3	,	,	PUNCT
ejpam-4522	93	4	e	e	NOUN
ejpam-4522	93	5	)	)	PUNCT
ejpam-4522	93	6	:	:	PUNCT
ejpam-4522	94	1	=	=	SYM
ejpam-4522	94	2	(	(	PUNCT
ejpam-4522	94	3	me	i	PRON
ejpam-4522	94	4	,	,	PUNCT
ejpam-4522	94	5	ge	ge	PROPN
ejpam-4522	94	6	,	,	PUNCT
ejpam-4522	94	7	ξ	ξ	X
ejpam-4522	94	8	)	)	PUNCT
ejpam-4522	94	9	be	be	VERB
ejpam-4522	94	10	a	a	DET
ejpam-4522	94	11	makgeolli	makgeolli	NOUN
ejpam-4522	94	12	structure	structure	NOUN
ejpam-4522	94	13	on	on	ADP
ejpam-4522	94	14	(	(	PUNCT
ejpam-4522	94	15	x	x	X
ejpam-4522	94	16	,	,	PUNCT
ejpam-4522	94	17	e	e	NOUN
ejpam-4522	94	18	)	)	PUNCT
ejpam-4522	94	19	defined	define	VERB
ejpam-4522	94	20	as	as	SCONJ
ejpam-4522	94	21	follows	follow	VERB
ejpam-4522	94	22	:	:	PUNCT
ejpam-4522	94	23	(	(	PUNCT
ejpam-4522	94	24	me	i	PRON
ejpam-4522	94	25	,	,	PUNCT
ejpam-4522	94	26	ge	ge	PROPN
ejpam-4522	94	27	)	)	PUNCT
ejpam-4522	94	28	:	:	PUNCT
ejpam-4522	95	1	e	e	X
ejpam-4522	95	2	→	→	SYM
ejpam-4522	95	3	p(x)×	p(x)×	PROPN
ejpam-4522	95	4	p(x	p(x	PROPN
ejpam-4522	95	5	)	)	PUNCT
ejpam-4522	95	6	,	,	PUNCT
ejpam-4522	95	7	x	x	X
ejpam-4522	95	8	7→	7→	NUM
ejpam-4522	95	9			NUM
ejpam-4522	95	10	(	(	PUNCT
ejpam-4522	95	11	x	x	X
ejpam-4522	95	12	,	,	PUNCT
ejpam-4522	95	13	{	{	PUNCT
ejpam-4522	95	14	2	2	NUM
ejpam-4522	95	15	}	}	PUNCT
ejpam-4522	95	16	)	)	PUNCT
ejpam-4522	95	17	if	if	SCONJ
ejpam-4522	95	18	x	x	PROPN
ejpam-4522	95	19	=	=	SYM
ejpam-4522	95	20	0	0	NUM
ejpam-4522	95	21	,	,	PUNCT
ejpam-4522	95	22	(	(	PUNCT
ejpam-4522	95	23	{	{	PUNCT
ejpam-4522	95	24	0	0	NUM
ejpam-4522	95	25	,	,	PUNCT
ejpam-4522	95	26	1	1	NUM
ejpam-4522	95	27	,	,	PUNCT
ejpam-4522	95	28	3	3	NUM
ejpam-4522	95	29	,	,	PUNCT
ejpam-4522	95	30	4	4	NUM
ejpam-4522	95	31	}	}	PUNCT
ejpam-4522	95	32	,	,	PUNCT
ejpam-4522	95	33	{	{	PUNCT
ejpam-4522	95	34	0	0	NUM
ejpam-4522	95	35	,	,	PUNCT
ejpam-4522	95	36	2	2	NUM
ejpam-4522	95	37	}	}	PUNCT
ejpam-4522	95	38	)	)	PUNCT
ejpam-4522	95	39	if	if	SCONJ
ejpam-4522	95	40	x	x	SYM
ejpam-4522	95	41	=	=	SYM
ejpam-4522	95	42	1	1	NUM
ejpam-4522	95	43	,	,	PUNCT
ejpam-4522	95	44	(	(	PUNCT
ejpam-4522	95	45	{	{	PUNCT
ejpam-4522	95	46	1	1	NUM
ejpam-4522	95	47	,	,	PUNCT
ejpam-4522	95	48	3	3	NUM
ejpam-4522	95	49	,	,	PUNCT
ejpam-4522	95	50	4	4	NUM
ejpam-4522	95	51	}	}	PUNCT
ejpam-4522	95	52	,	,	PUNCT
ejpam-4522	95	53	x	x	X
ejpam-4522	95	54	)	)	PUNCT
ejpam-4522	95	55	if	if	SCONJ
ejpam-4522	95	56	x	x	PROPN
ejpam-4522	95	57	=	=	SYM
ejpam-4522	95	58	2	2	NUM
ejpam-4522	95	59	,	,	PUNCT
ejpam-4522	95	60	(	(	PUNCT
ejpam-4522	95	61	{	{	PUNCT
ejpam-4522	95	62	1	1	NUM
ejpam-4522	95	63	,	,	PUNCT
ejpam-4522	95	64	4	4	NUM
ejpam-4522	95	65	}	}	PUNCT
ejpam-4522	95	66	,	,	PUNCT
ejpam-4522	95	67	{	{	PUNCT
ejpam-4522	95	68	0	0	NUM
ejpam-4522	95	69	,	,	PUNCT
ejpam-4522	95	70	2	2	NUM
ejpam-4522	95	71	,	,	PUNCT
ejpam-4522	95	72	3	3	NUM
ejpam-4522	95	73	}	}	PUNCT
ejpam-4522	95	74	)	)	PUNCT
ejpam-4522	95	75	if	if	SCONJ
ejpam-4522	95	76	x	x	PROPN
ejpam-4522	95	77	=	=	SYM
ejpam-4522	95	78	3	3	NUM
ejpam-4522	95	79	,	,	PUNCT
ejpam-4522	96	1	s.	s.	PROPN
ejpam-4522	96	2	z.	z.	PROPN
ejpam-4522	96	3	song	song	PROPN
ejpam-4522	96	4	,	,	PUNCT
ejpam-4522	96	5	m.	m.	NOUN
ejpam-4522	96	6	a.	a.	NOUN
ejpam-4522	96	7	öztürk	öztürk	PROPN
ejpam-4522	96	8	,	,	PUNCT
ejpam-4522	96	9	y.	y.	PROPN
ejpam-4522	96	10	b.	b.	PROPN
ejpam-4522	96	11	jun	jun	PROPN
ejpam-4522	96	12	/	/	SYM
ejpam-4522	96	13	eur	eur	PROPN
ejpam-4522	96	14	.	.	PUNCT
ejpam-4522	97	1	j.	j.	PROPN
ejpam-4522	97	2	pure	pure	PROPN
ejpam-4522	97	3	appl	appl	PROPN
ejpam-4522	97	4	.	.	PROPN
ejpam-4522	97	5	math	math	PROPN
ejpam-4522	97	6	,	,	PUNCT
ejpam-4522	97	7	15	15	NUM
ejpam-4522	97	8	(	(	PUNCT
ejpam-4522	97	9	4	4	NUM
ejpam-4522	97	10	)	)	PUNCT
ejpam-4522	97	11	(	(	PUNCT
ejpam-4522	97	12	2022	2022	NUM
ejpam-4522	97	13	)	)	PUNCT
ejpam-4522	97	14	,	,	PUNCT
ejpam-4522	97	15	1498	1498	NUM
ejpam-4522	97	16	-	-	SYM
ejpam-4522	97	17	1511	1511	NUM
ejpam-4522	97	18	1502	1502	NUM
ejpam-4522	97	19	table	table	NOUN
ejpam-4522	97	20	1	1	NUM
ejpam-4522	97	21	:	:	PUNCT
ejpam-4522	97	22	cayley	cayley	ADJ
ejpam-4522	97	23	table	table	NOUN
ejpam-4522	97	24	for	for	ADP
ejpam-4522	97	25	the	the	DET
ejpam-4522	97	26	binary	binary	ADJ
ejpam-4522	97	27	operations	operation	NOUN
ejpam-4522	97	28	“	"	PUNCT
ejpam-4522	97	29	↬	↬	PROPN
ejpam-4522	97	30	”	"	PUNCT
ejpam-4522	97	31	∗	∗	NOUN
ejpam-4522	97	32	0	0	NUM
ejpam-4522	97	33	1	1	NUM
ejpam-4522	97	34	2	2	NUM
ejpam-4522	97	35	3	3	NUM
ejpam-4522	97	36	4	4	NUM
ejpam-4522	97	37	0	0	NUM
ejpam-4522	97	38	0	0	NUM
ejpam-4522	97	39	0	0	NUM
ejpam-4522	97	40	0	0	NUM
ejpam-4522	97	41	0	0	NUM
ejpam-4522	97	42	0	0	NUM
ejpam-4522	97	43	1	1	NUM
ejpam-4522	97	44	1	1	NUM
ejpam-4522	97	45	0	0	NUM
ejpam-4522	97	46	0	0	NUM
ejpam-4522	97	47	0	0	NUM
ejpam-4522	97	48	0	0	NUM
ejpam-4522	97	49	2	2	NUM
ejpam-4522	97	50	2	2	NUM
ejpam-4522	97	51	2	2	NUM
ejpam-4522	97	52	0	0	NUM
ejpam-4522	97	53	2	2	NUM
ejpam-4522	97	54	2	2	NUM
ejpam-4522	97	55	3	3	NUM
ejpam-4522	97	56	3	3	NUM
ejpam-4522	97	57	3	3	NUM
ejpam-4522	97	58	3	3	NUM
ejpam-4522	97	59	0	0	NUM
ejpam-4522	97	60	3	3	NUM
ejpam-4522	97	61	4	4	NUM
ejpam-4522	97	62	4	4	NUM
ejpam-4522	97	63	4	4	NUM
ejpam-4522	97	64	4	4	NUM
ejpam-4522	97	65	4	4	NUM
ejpam-4522	97	66	0	0	NUM
ejpam-4522	97	67	↬	↬	NOUN
ejpam-4522	97	68	0	0	NUM
ejpam-4522	98	1	1	1	NUM
ejpam-4522	98	2	2	2	NUM
ejpam-4522	98	3	3	3	NUM
ejpam-4522	98	4	0	0	NUM
ejpam-4522	98	5	0	0	NUM
ejpam-4522	98	6	0	0	NUM
ejpam-4522	98	7	0	0	NUM
ejpam-4522	98	8	0	0	NUM
ejpam-4522	98	9	1	1	NUM
ejpam-4522	98	10	1	1	NUM
ejpam-4522	98	11	0	0	NUM
ejpam-4522	98	12	0	0	NUM
ejpam-4522	98	13	0	0	NUM
ejpam-4522	98	14	2	2	NUM
ejpam-4522	98	15	2	2	NUM
ejpam-4522	98	16	2	2	NUM
ejpam-4522	98	17	0	0	NUM
ejpam-4522	98	18	2	2	NUM
ejpam-4522	98	19	3	3	NUM
ejpam-4522	98	20	3	3	NUM
ejpam-4522	98	21	3	3	NUM
ejpam-4522	98	22	3	3	NUM
ejpam-4522	98	23	0	0	SYM
ejpam-4522	98	24	ξ	ξ	PRON
ejpam-4522	98	25	:	:	PUNCT
ejpam-4522	98	26	x	x	SYM
ejpam-4522	98	27	→	→	SYM
ejpam-4522	99	1	[	[	X
ejpam-4522	99	2	0	0	NUM
ejpam-4522	99	3	,	,	PUNCT
ejpam-4522	99	4	1	1	NUM
ejpam-4522	99	5	]	]	PUNCT
ejpam-4522	99	6	,	,	PUNCT
ejpam-4522	99	7	y	y	PROPN
ejpam-4522	99	8	7→	7→	PROPN
ejpam-4522	99	9			NOUN
ejpam-4522	99	10	0.78	0.78	NUM
ejpam-4522	99	11	if	if	SCONJ
ejpam-4522	99	12	y	y	NOUN
ejpam-4522	99	13	=	=	SYM
ejpam-4522	99	14	0	0	PROPN
ejpam-4522	99	15	,	,	PUNCT
ejpam-4522	99	16	0.63	0.63	NUM
ejpam-4522	99	17	if	if	SCONJ
ejpam-4522	99	18	y	y	PROPN
ejpam-4522	99	19	=	=	SYM
ejpam-4522	99	20	1	1	NUM
ejpam-4522	99	21	,	,	PUNCT
ejpam-4522	99	22	0.51	0.51	NUM
ejpam-4522	99	23	if	if	SCONJ
ejpam-4522	99	24	y	y	PROPN
ejpam-4522	99	25	=	=	SYM
ejpam-4522	99	26	2	2	NUM
ejpam-4522	99	27	,	,	PUNCT
ejpam-4522	99	28	0.44	0.44	NUM
ejpam-4522	99	29	if	if	SCONJ
ejpam-4522	99	30	y	y	PROPN
ejpam-4522	99	31	=	=	SYM
ejpam-4522	99	32	3	3	NUM
ejpam-4522	99	33	,	,	PUNCT
ejpam-4522	99	34	0.59	0.59	NUM
ejpam-4522	100	1	if	if	SCONJ
ejpam-4522	100	2	y	y	PROPN
ejpam-4522	100	3	=	=	NOUN
ejpam-4522	100	4	4	4	X
ejpam-4522	100	5	.	.	PUNCT
ejpam-4522	101	1	it	it	PRON
ejpam-4522	101	2	is	be	AUX
ejpam-4522	101	3	routine	routine	ADJ
ejpam-4522	101	4	to	to	PART
ejpam-4522	101	5	verify	verify	VERB
ejpam-4522	101	6	that	that	SCONJ
ejpam-4522	101	7	m(x	m(x	PROPN
ejpam-4522	101	8	,	,	PUNCT
ejpam-4522	101	9	e	e	NOUN
ejpam-4522	101	10	)	)	PUNCT
ejpam-4522	101	11	:	:	PUNCT
ejpam-4522	101	12	=	=	SYM
ejpam-4522	101	13	(	(	PUNCT
ejpam-4522	101	14	me	i	PRON
ejpam-4522	101	15	,	,	PUNCT
ejpam-4522	101	16	ge	ge	PROPN
ejpam-4522	101	17	,	,	PUNCT
ejpam-4522	101	18	ξ	ξ	X
ejpam-4522	101	19	)	)	PUNCT
ejpam-4522	101	20	is	be	AUX
ejpam-4522	101	21	a	a	DET
ejpam-4522	101	22	positive	positive	ADJ
ejpam-4522	101	23	implicative	implicative	ADJ
ejpam-4522	101	24	makgeolli	makgeolli	NOUN
ejpam-4522	101	25	ideal	ideal	NOUN
ejpam-4522	101	26	of	of	ADP
ejpam-4522	101	27	(	(	PUNCT
ejpam-4522	101	28	x	x	X
ejpam-4522	101	29	,	,	PUNCT
ejpam-4522	101	30	e	e	NOUN
ejpam-4522	101	31	)	)	PUNCT
ejpam-4522	101	32	.	.	PUNCT
ejpam-4522	102	1	proposition	proposition	NOUN
ejpam-4522	102	2	1	1	NUM
ejpam-4522	102	3	.	.	PUNCT
ejpam-4522	103	1	every	every	DET
ejpam-4522	103	2	positive	positive	ADJ
ejpam-4522	103	3	implicative	implicative	ADJ
ejpam-4522	103	4	makgeolli	makgeolli	NOUN
ejpam-4522	103	5	ideal	ideal	NOUN
ejpam-4522	103	6	m(x	m(x	PROPN
ejpam-4522	103	7	,	,	PUNCT
ejpam-4522	103	8	e	e	NOUN
ejpam-4522	103	9	)	)	PUNCT
ejpam-4522	103	10	:	:	PUNCT
ejpam-4522	104	1	=	=	SYM
ejpam-4522	104	2	(	(	PUNCT
ejpam-4522	104	3	me	i	PRON
ejpam-4522	104	4	,	,	PUNCT
ejpam-4522	104	5	ge	ge	PROPN
ejpam-4522	104	6	,	,	PUNCT
ejpam-4522	104	7	ξ	ξ	PROPN
ejpam-4522	104	8	)	)	PUNCT
ejpam-4522	104	9	of	of	ADP
ejpam-4522	104	10	(	(	PUNCT
ejpam-4522	104	11	x	x	NOUN
ejpam-4522	104	12	,	,	PUNCT
ejpam-4522	104	13	e	e	NOUN
ejpam-4522	104	14	)	)	PUNCT
ejpam-4522	104	15	satisfies	satisfie	NOUN
ejpam-4522	104	16	:	:	PUNCT
ejpam-4522	104	17			PRON
ejpam-4522	104	18	(	(	PUNCT
ejpam-4522	104	19	∀a	∀a	X
ejpam-4522	104	20	,	,	PUNCT
ejpam-4522	104	21	b	b	X
ejpam-4522	104	22	∈	∈	PROPN
ejpam-4522	104	23	e	e	NOUN
ejpam-4522	104	24	)	)	PUNCT
ejpam-4522	104	25	(	(	PUNCT
ejpam-4522	104	26	me(a	me(a	X
ejpam-4522	104	27	↬	↬	PROPN
ejpam-4522	104	28	b	b	X
ejpam-4522	104	29	)	)	PUNCT
ejpam-4522	104	30	⊇	⊇	PROPN
ejpam-4522	104	31	me((a	me((a	PROPN
ejpam-4522	104	32	↬	↬	PROPN
ejpam-4522	104	33	b	b	X
ejpam-4522	104	34	)	)	PUNCT
ejpam-4522	104	35	↬	↬	PROPN
ejpam-4522	104	36	b	b	X
ejpam-4522	104	37	)	)	PUNCT
ejpam-4522	104	38	ge(a	ge(a	PUNCT
ejpam-4522	104	39	↬	↬	PROPN
ejpam-4522	104	40	b	b	X
ejpam-4522	104	41	)	)	PUNCT
ejpam-4522	104	42	⊆	⊆	NUM
ejpam-4522	104	43	ge((a	ge((a	NOUN
ejpam-4522	104	44	↬	↬	PROPN
ejpam-4522	104	45	b	b	NOUN
ejpam-4522	104	46	)	)	PUNCT
ejpam-4522	104	47	↬	↬	PROPN
ejpam-4522	104	48	b	b	X
ejpam-4522	104	49	)	)	PUNCT
ejpam-4522	104	50	)	)	PUNCT
ejpam-4522	104	51	,	,	PUNCT
ejpam-4522	104	52	(	(	PUNCT
ejpam-4522	104	53	∀x	∀x	X
ejpam-4522	104	54	,	,	PUNCT
ejpam-4522	104	55	y	y	PROPN
ejpam-4522	104	56	∈	∈	PROPN
ejpam-4522	104	57	x	x	X
ejpam-4522	104	58	)	)	PUNCT
ejpam-4522	104	59	(	(	PUNCT
ejpam-4522	104	60	ξ((x	ξ((x	NOUN
ejpam-4522	104	61	∗	∗	PROPN
ejpam-4522	104	62	y	y	NOUN
ejpam-4522	104	63	)	)	PUNCT
ejpam-4522	104	64	≥	≥	NOUN
ejpam-4522	104	65	ξ((x	ξ((x	PROPN
ejpam-4522	104	66	∗	∗	PROPN
ejpam-4522	104	67	y	y	NOUN
ejpam-4522	104	68	)	)	PUNCT
ejpam-4522	104	69	∗	∗	PROPN
ejpam-4522	104	70	y	y	PROPN
ejpam-4522	104	71	)	)	PUNCT
ejpam-4522	104	72	)	)	PUNCT
ejpam-4522	104	73	.	.	PUNCT
ejpam-4522	105	1	(	(	PUNCT
ejpam-4522	105	2	14	14	NUM
ejpam-4522	105	3	)	)	PUNCT
ejpam-4522	105	4	proof	proof	NOUN
ejpam-4522	105	5	.	.	PUNCT
ejpam-4522	106	1	if	if	SCONJ
ejpam-4522	106	2	we	we	PRON
ejpam-4522	106	3	replace	replace	VERB
ejpam-4522	106	4	c	c	NOUN
ejpam-4522	106	5	and	and	CCONJ
ejpam-4522	106	6	z	z	NOUN
ejpam-4522	106	7	with	with	ADP
ejpam-4522	106	8	b	b	PROPN
ejpam-4522	106	9	and	and	CCONJ
ejpam-4522	106	10	y	y	PROPN
ejpam-4522	106	11	in	in	ADP
ejpam-4522	106	12	(	(	PUNCT
ejpam-4522	106	13	11	11	NUM
ejpam-4522	106	14	)	)	PUNCT
ejpam-4522	106	15	and	and	CCONJ
ejpam-4522	106	16	(	(	PUNCT
ejpam-4522	106	17	12	12	NUM
ejpam-4522	106	18	)	)	PUNCT
ejpam-4522	106	19	,	,	PUNCT
ejpam-4522	106	20	respectively	respectively	ADV
ejpam-4522	106	21	,	,	PUNCT
ejpam-4522	106	22	and	and	CCONJ
ejpam-4522	106	23	use	use	NOUN
ejpam-4522	106	24	(	(	PUNCT
ejpam-4522	106	25	i3	i3	NOUN
ejpam-4522	106	26	)	)	PUNCT
ejpam-4522	106	27	and	and	CCONJ
ejpam-4522	106	28	(	(	PUNCT
ejpam-4522	106	29	9	9	NUM
ejpam-4522	106	30	)	)	PUNCT
ejpam-4522	106	31	,	,	PUNCT
ejpam-4522	106	32	then	then	ADV
ejpam-4522	106	33	we	we	PRON
ejpam-4522	106	34	have	have	VERB
ejpam-4522	106	35	(	(	PUNCT
ejpam-4522	106	36	14	14	NUM
ejpam-4522	106	37	)	)	PUNCT
ejpam-4522	106	38	.	.	PUNCT
ejpam-4522	107	1	we	we	PRON
ejpam-4522	107	2	discuss	discuss	VERB
ejpam-4522	107	3	the	the	DET
ejpam-4522	107	4	relationship	relationship	NOUN
ejpam-4522	107	5	between	between	ADP
ejpam-4522	107	6	positive	positive	ADJ
ejpam-4522	107	7	implicative	implicative	ADJ
ejpam-4522	107	8	makgeolli	makgeolli	NOUN
ejpam-4522	107	9	ideal	ideal	NOUN
ejpam-4522	107	10	and	and	CCONJ
ejpam-4522	107	11	makgeolli	makgeolli	PROPN
ejpam-4522	107	12	ideal	ideal	ADJ
ejpam-4522	107	13	.	.	PUNCT
ejpam-4522	108	1	theorem	theorem	VERB
ejpam-4522	108	2	1	1	NUM
ejpam-4522	108	3	.	.	PUNCT
ejpam-4522	109	1	every	every	DET
ejpam-4522	109	2	positive	positive	ADJ
ejpam-4522	109	3	implicative	implicative	ADJ
ejpam-4522	109	4	makgeolli	makgeolli	NOUN
ejpam-4522	109	5	ideal	ideal	NOUN
ejpam-4522	109	6	is	be	AUX
ejpam-4522	109	7	a	a	DET
ejpam-4522	109	8	makgeolli	makgeolli	NOUN
ejpam-4522	109	9	ideal	ideal	NOUN
ejpam-4522	109	10	.	.	PUNCT
ejpam-4522	110	1	proof	proof	NOUN
ejpam-4522	110	2	.	.	PUNCT
ejpam-4522	111	1	let	let	VERB
ejpam-4522	111	2	m(x	m(x	PROPN
ejpam-4522	111	3	,	,	PUNCT
ejpam-4522	111	4	e	e	NOUN
ejpam-4522	111	5	)	)	PUNCT
ejpam-4522	111	6	:	:	PUNCT
ejpam-4522	112	1	=	=	SYM
ejpam-4522	112	2	(	(	PUNCT
ejpam-4522	112	3	me	i	PRON
ejpam-4522	112	4	,	,	PUNCT
ejpam-4522	112	5	ge	ge	PROPN
ejpam-4522	112	6	,	,	PUNCT
ejpam-4522	112	7	ξ	ξ	X
ejpam-4522	112	8	)	)	PUNCT
ejpam-4522	112	9	be	be	VERB
ejpam-4522	112	10	a	a	DET
ejpam-4522	112	11	positive	positive	ADJ
ejpam-4522	112	12	implicative	implicative	ADJ
ejpam-4522	112	13	makgeolli	makgeolli	NOUN
ejpam-4522	112	14	ideal	ideal	NOUN
ejpam-4522	112	15	of	of	ADP
ejpam-4522	112	16	(	(	PUNCT
ejpam-4522	112	17	x	x	X
ejpam-4522	112	18	,	,	PUNCT
ejpam-4522	112	19	e	e	NOUN
ejpam-4522	112	20	)	)	PUNCT
ejpam-4522	112	21	.	.	PUNCT
ejpam-4522	113	1	if	if	SCONJ
ejpam-4522	113	2	we	we	PRON
ejpam-4522	113	3	replace	replace	VERB
ejpam-4522	113	4	c	c	NOUN
ejpam-4522	113	5	and	and	CCONJ
ejpam-4522	113	6	z	z	NOUN
ejpam-4522	113	7	with	with	ADP
ejpam-4522	113	8	0	0	NUM
ejpam-4522	113	9	in	in	ADP
ejpam-4522	113	10	(	(	PUNCT
ejpam-4522	113	11	11	11	NUM
ejpam-4522	113	12	)	)	PUNCT
ejpam-4522	113	13	and	and	CCONJ
ejpam-4522	113	14	(	(	PUNCT
ejpam-4522	113	15	12	12	NUM
ejpam-4522	113	16	)	)	PUNCT
ejpam-4522	113	17	,	,	PUNCT
ejpam-4522	113	18	then	then	ADV
ejpam-4522	113	19	we	we	PRON
ejpam-4522	113	20	can	can	AUX
ejpam-4522	113	21	get	get	VERB
ejpam-4522	113	22	(	(	PUNCT
ejpam-4522	113	23	10	10	NUM
ejpam-4522	113	24	)	)	PUNCT
ejpam-4522	113	25	.	.	PUNCT
ejpam-4522	114	1	hence	hence	ADV
ejpam-4522	114	2	m(x	m(x	PROPN
ejpam-4522	114	3	,	,	PUNCT
ejpam-4522	114	4	e	e	NOUN
ejpam-4522	114	5	)	)	PUNCT
ejpam-4522	114	6	:	:	PUNCT
ejpam-4522	115	1	=	=	SYM
ejpam-4522	115	2	(	(	PUNCT
ejpam-4522	115	3	me	i	PRON
ejpam-4522	115	4	,	,	PUNCT
ejpam-4522	115	5	ge	ge	PROPN
ejpam-4522	115	6	,	,	PUNCT
ejpam-4522	115	7	ξ	ξ	X
ejpam-4522	115	8	)	)	PUNCT
ejpam-4522	115	9	is	be	AUX
ejpam-4522	115	10	a	a	DET
ejpam-4522	115	11	makgeolli	makgeolli	NOUN
ejpam-4522	115	12	ideal	ideal	NOUN
ejpam-4522	115	13	of	of	ADP
ejpam-4522	115	14	(	(	PUNCT
ejpam-4522	115	15	x	x	X
ejpam-4522	115	16	,	,	PUNCT
ejpam-4522	115	17	e	e	NOUN
ejpam-4522	115	18	)	)	PUNCT
ejpam-4522	115	19	.	.	PUNCT
ejpam-4522	116	1	the	the	DET
ejpam-4522	116	2	following	follow	VERB
ejpam-4522	116	3	example	example	NOUN
ejpam-4522	116	4	shows	show	VERB
ejpam-4522	116	5	that	that	SCONJ
ejpam-4522	116	6	the	the	DET
ejpam-4522	116	7	converse	converse	NOUN
ejpam-4522	116	8	of	of	ADP
ejpam-4522	116	9	theorem	theorem	NOUN
ejpam-4522	116	10	1	1	NUM
ejpam-4522	116	11	may	may	AUX
ejpam-4522	116	12	not	not	PART
ejpam-4522	116	13	be	be	AUX
ejpam-4522	116	14	true	true	ADJ
ejpam-4522	116	15	.	.	PUNCT
ejpam-4522	117	1	example	example	NOUN
ejpam-4522	117	2	2	2	NUM
ejpam-4522	117	3	.	.	X
ejpam-4522	117	4	consider	consider	VERB
ejpam-4522	117	5	a	a	DET
ejpam-4522	117	6	bck	bck	VERB
ejpam-4522	117	7	-	-	PUNCT
ejpam-4522	117	8	soft	soft	ADJ
ejpam-4522	117	9	universe	universe	NOUN
ejpam-4522	117	10	(	(	PUNCT
ejpam-4522	117	11	x	x	X
ejpam-4522	117	12	,	,	PUNCT
ejpam-4522	117	13	e	e	NOUN
ejpam-4522	117	14	)	)	PUNCT
ejpam-4522	117	15	in	in	ADP
ejpam-4522	117	16	which	which	PRON
ejpam-4522	117	17	x	x	SYM
ejpam-4522	117	18	:	:	PUNCT
ejpam-4522	117	19	=	=	SYM
ejpam-4522	117	20	{	{	PUNCT
ejpam-4522	117	21	0	0	NUM
ejpam-4522	117	22	,	,	PUNCT
ejpam-4522	117	23	1	1	NUM
ejpam-4522	117	24	,	,	PUNCT
ejpam-4522	117	25	2	2	NUM
ejpam-4522	117	26	,	,	PUNCT
ejpam-4522	117	27	3	3	NUM
ejpam-4522	117	28	,	,	PUNCT
ejpam-4522	117	29	4	4	NUM
ejpam-4522	117	30	}	}	PUNCT
ejpam-4522	117	31	and	and	CCONJ
ejpam-4522	117	32	e	e	NOUN
ejpam-4522	117	33	:	:	PUNCT
ejpam-4522	117	34	=	=	SYM
ejpam-4522	117	35	{	{	PUNCT
ejpam-4522	117	36	0	0	NUM
ejpam-4522	117	37	,	,	PUNCT
ejpam-4522	117	38	1	1	NUM
ejpam-4522	117	39	,	,	PUNCT
ejpam-4522	117	40	2	2	NUM
ejpam-4522	117	41	,	,	PUNCT
ejpam-4522	117	42	3	3	NUM
ejpam-4522	117	43	}	}	PUNCT
ejpam-4522	117	44	with	with	ADP
ejpam-4522	117	45	binary	binary	ADJ
ejpam-4522	117	46	operations	operation	NOUN
ejpam-4522	117	47	“	"	PUNCT
ejpam-4522	117	48	∗	∗	NOUN
ejpam-4522	117	49	”	"	PUNCT
ejpam-4522	117	50	and	and	CCONJ
ejpam-4522	117	51	“	"	PUNCT
ejpam-4522	117	52	↬	↬	PROPN
ejpam-4522	117	53	”	"	PUNCT
ejpam-4522	117	54	,	,	PUNCT
ejpam-4522	117	55	respectively	respectively	ADV
ejpam-4522	117	56	,	,	PUNCT
ejpam-4522	117	57	given	give	VERB
ejpam-4522	117	58	by	by	ADP
ejpam-4522	117	59	table	table	NOUN
ejpam-4522	117	60	2	2	NUM
ejpam-4522	117	61	.	.	PUNCT
ejpam-4522	118	1	let	let	VERB
ejpam-4522	118	2	m(x	m(x	PROPN
ejpam-4522	118	3	,	,	PUNCT
ejpam-4522	118	4	e	e	NOUN
ejpam-4522	118	5	)	)	PUNCT
ejpam-4522	118	6	:	:	PUNCT
ejpam-4522	119	1	=	=	SYM
ejpam-4522	119	2	(	(	PUNCT
ejpam-4522	119	3	me	i	PRON
ejpam-4522	119	4	,	,	PUNCT
ejpam-4522	119	5	ge	ge	PROPN
ejpam-4522	119	6	,	,	PUNCT
ejpam-4522	119	7	ξ	ξ	X
ejpam-4522	119	8	)	)	PUNCT
ejpam-4522	119	9	be	be	VERB
ejpam-4522	119	10	a	a	DET
ejpam-4522	119	11	makgeolli	makgeolli	NOUN
ejpam-4522	119	12	structure	structure	NOUN
ejpam-4522	119	13	on	on	ADP
ejpam-4522	119	14	(	(	PUNCT
ejpam-4522	119	15	x	x	X
ejpam-4522	119	16	,	,	PUNCT
ejpam-4522	119	17	e	e	NOUN
ejpam-4522	119	18	)	)	PUNCT
ejpam-4522	119	19	defined	define	VERB
ejpam-4522	119	20	as	as	SCONJ
ejpam-4522	119	21	follows	follow	VERB
ejpam-4522	119	22	:	:	PUNCT
ejpam-4522	119	23	(	(	PUNCT
ejpam-4522	119	24	me	i	PRON
ejpam-4522	119	25	,	,	PUNCT
ejpam-4522	119	26	ge	ge	PROPN
ejpam-4522	119	27	)	)	PUNCT
ejpam-4522	119	28	:	:	PUNCT
ejpam-4522	120	1	e	e	X
ejpam-4522	120	2	→	→	SYM
ejpam-4522	120	3	p(x)×	p(x)×	PROPN
ejpam-4522	120	4	p(x	p(x	PROPN
ejpam-4522	120	5	)	)	PUNCT
ejpam-4522	120	6	,	,	PUNCT
ejpam-4522	120	7	x	x	X
ejpam-4522	120	8	7→	7→	NUM
ejpam-4522	120	9			NUM
ejpam-4522	120	10	(	(	PUNCT
ejpam-4522	120	11	x	x	X
ejpam-4522	120	12	,	,	PUNCT
ejpam-4522	120	13	{	{	PUNCT
ejpam-4522	120	14	2	2	NUM
ejpam-4522	120	15	,	,	PUNCT
ejpam-4522	120	16	4	4	NUM
ejpam-4522	120	17	}	}	PUNCT
ejpam-4522	120	18	)	)	PUNCT
ejpam-4522	120	19	if	if	SCONJ
ejpam-4522	120	20	x	x	PROPN
ejpam-4522	120	21	=	=	SYM
ejpam-4522	120	22	0	0	NUM
ejpam-4522	120	23	,	,	PUNCT
ejpam-4522	120	24	(	(	PUNCT
ejpam-4522	120	25	{	{	PUNCT
ejpam-4522	120	26	1	1	NUM
ejpam-4522	120	27	,	,	PUNCT
ejpam-4522	120	28	3	3	NUM
ejpam-4522	120	29	}	}	PUNCT
ejpam-4522	120	30	,	,	PUNCT
ejpam-4522	120	31	{	{	PUNCT
ejpam-4522	120	32	0	0	NUM
ejpam-4522	120	33	,	,	PUNCT
ejpam-4522	120	34	1	1	NUM
ejpam-4522	120	35	,	,	PUNCT
ejpam-4522	120	36	2	2	NUM
ejpam-4522	120	37	,	,	PUNCT
ejpam-4522	120	38	4	4	NUM
ejpam-4522	120	39	}	}	PUNCT
ejpam-4522	120	40	)	)	PUNCT
ejpam-4522	120	41	if	if	SCONJ
ejpam-4522	120	42	x	x	SYM
ejpam-4522	120	43	=	=	SYM
ejpam-4522	120	44	1	1	NUM
ejpam-4522	120	45	,	,	PUNCT
ejpam-4522	120	46	(	(	PUNCT
ejpam-4522	120	47	{	{	PUNCT
ejpam-4522	120	48	1	1	NUM
ejpam-4522	120	49	,	,	PUNCT
ejpam-4522	120	50	3	3	NUM
ejpam-4522	120	51	}	}	PUNCT
ejpam-4522	120	52	,	,	PUNCT
ejpam-4522	120	53	{	{	PUNCT
ejpam-4522	120	54	0	0	NUM
ejpam-4522	120	55	,	,	PUNCT
ejpam-4522	120	56	1	1	NUM
ejpam-4522	120	57	,	,	PUNCT
ejpam-4522	120	58	2	2	NUM
ejpam-4522	120	59	,	,	PUNCT
ejpam-4522	120	60	4	4	NUM
ejpam-4522	120	61	}	}	PUNCT
ejpam-4522	120	62	)	)	PUNCT
ejpam-4522	120	63	if	if	SCONJ
ejpam-4522	120	64	x	x	PROPN
ejpam-4522	120	65	=	=	SYM
ejpam-4522	120	66	2	2	NUM
ejpam-4522	120	67	,	,	PUNCT
ejpam-4522	120	68	(	(	PUNCT
ejpam-4522	120	69	{	{	PUNCT
ejpam-4522	120	70	0	0	NUM
ejpam-4522	120	71	,	,	PUNCT
ejpam-4522	120	72	1	1	NUM
ejpam-4522	120	73	,	,	PUNCT
ejpam-4522	120	74	3	3	NUM
ejpam-4522	120	75	,	,	PUNCT
ejpam-4522	120	76	4	4	NUM
ejpam-4522	120	77	}	}	PUNCT
ejpam-4522	120	78	,	,	PUNCT
ejpam-4522	120	79	{	{	PUNCT
ejpam-4522	120	80	0	0	NUM
ejpam-4522	120	81	,	,	PUNCT
ejpam-4522	120	82	2	2	NUM
ejpam-4522	120	83	,	,	PUNCT
ejpam-4522	120	84	4	4	NUM
ejpam-4522	120	85	}	}	PUNCT
ejpam-4522	120	86	)	)	PUNCT
ejpam-4522	120	87	if	if	SCONJ
ejpam-4522	120	88	x	x	PROPN
ejpam-4522	120	89	=	=	SYM
ejpam-4522	120	90	3	3	NUM
ejpam-4522	120	91	,	,	PUNCT
ejpam-4522	121	1	s.	s.	PROPN
ejpam-4522	121	2	z.	z.	PROPN
ejpam-4522	121	3	song	song	PROPN
ejpam-4522	121	4	,	,	PUNCT
ejpam-4522	121	5	m.	m.	NOUN
ejpam-4522	121	6	a.	a.	NOUN
ejpam-4522	121	7	öztürk	öztürk	PROPN
ejpam-4522	121	8	,	,	PUNCT
ejpam-4522	121	9	y.	y.	PROPN
ejpam-4522	121	10	b.	b.	PROPN
ejpam-4522	121	11	jun	jun	PROPN
ejpam-4522	121	12	/	/	SYM
ejpam-4522	121	13	eur	eur	PROPN
ejpam-4522	121	14	.	.	PUNCT
ejpam-4522	122	1	j.	j.	PROPN
ejpam-4522	122	2	pure	pure	PROPN
ejpam-4522	122	3	appl	appl	PROPN
ejpam-4522	122	4	.	.	PROPN
ejpam-4522	122	5	math	math	PROPN
ejpam-4522	122	6	,	,	PUNCT
ejpam-4522	122	7	15	15	NUM
ejpam-4522	122	8	(	(	PUNCT
ejpam-4522	122	9	4	4	NUM
ejpam-4522	122	10	)	)	PUNCT
ejpam-4522	122	11	(	(	PUNCT
ejpam-4522	122	12	2022	2022	NUM
ejpam-4522	122	13	)	)	PUNCT
ejpam-4522	122	14	,	,	PUNCT
ejpam-4522	122	15	1498	1498	NUM
ejpam-4522	122	16	-	-	SYM
ejpam-4522	122	17	1511	1511	NUM
ejpam-4522	122	18	1503	1503	NUM
ejpam-4522	122	19	table	table	NOUN
ejpam-4522	122	20	2	2	NUM
ejpam-4522	122	21	:	:	PUNCT
ejpam-4522	122	22	cayley	cayley	ADJ
ejpam-4522	122	23	table	table	NOUN
ejpam-4522	122	24	for	for	ADP
ejpam-4522	122	25	the	the	DET
ejpam-4522	122	26	binary	binary	ADJ
ejpam-4522	122	27	operations	operation	NOUN
ejpam-4522	122	28	“	"	PUNCT
ejpam-4522	122	29	↬	↬	PROPN
ejpam-4522	122	30	”	"	PUNCT
ejpam-4522	122	31	∗	∗	NOUN
ejpam-4522	122	32	0	0	NUM
ejpam-4522	122	33	1	1	NUM
ejpam-4522	122	34	2	2	NUM
ejpam-4522	122	35	3	3	NUM
ejpam-4522	122	36	4	4	NUM
ejpam-4522	122	37	0	0	NUM
ejpam-4522	122	38	0	0	NUM
ejpam-4522	122	39	0	0	NUM
ejpam-4522	122	40	0	0	NUM
ejpam-4522	122	41	0	0	NUM
ejpam-4522	122	42	0	0	NUM
ejpam-4522	122	43	1	1	NUM
ejpam-4522	122	44	1	1	NUM
ejpam-4522	122	45	0	0	NUM
ejpam-4522	122	46	1	1	NUM
ejpam-4522	122	47	0	0	NUM
ejpam-4522	122	48	1	1	NUM
ejpam-4522	122	49	2	2	NUM
ejpam-4522	122	50	2	2	NUM
ejpam-4522	122	51	2	2	NUM
ejpam-4522	122	52	0	0	NUM
ejpam-4522	122	53	2	2	NUM
ejpam-4522	122	54	0	0	NUM
ejpam-4522	122	55	3	3	NUM
ejpam-4522	122	56	3	3	NUM
ejpam-4522	122	57	1	1	NUM
ejpam-4522	122	58	3	3	NUM
ejpam-4522	122	59	0	0	NUM
ejpam-4522	122	60	3	3	NUM
ejpam-4522	122	61	4	4	NUM
ejpam-4522	122	62	4	4	NUM
ejpam-4522	122	63	4	4	NUM
ejpam-4522	122	64	4	4	NUM
ejpam-4522	122	65	4	4	NUM
ejpam-4522	122	66	0	0	NUM
ejpam-4522	122	67	↬	↬	NOUN
ejpam-4522	122	68	0	0	NUM
ejpam-4522	123	1	1	1	NUM
ejpam-4522	123	2	2	2	NUM
ejpam-4522	123	3	3	3	NUM
ejpam-4522	123	4	0	0	NUM
ejpam-4522	123	5	0	0	NUM
ejpam-4522	123	6	0	0	NUM
ejpam-4522	123	7	0	0	NUM
ejpam-4522	123	8	0	0	NUM
ejpam-4522	123	9	1	1	NUM
ejpam-4522	123	10	1	1	NUM
ejpam-4522	123	11	0	0	NUM
ejpam-4522	123	12	0	0	NUM
ejpam-4522	123	13	1	1	NUM
ejpam-4522	123	14	2	2	NUM
ejpam-4522	123	15	2	2	NUM
ejpam-4522	123	16	1	1	NUM
ejpam-4522	123	17	0	0	NUM
ejpam-4522	123	18	2	2	NUM
ejpam-4522	123	19	3	3	NUM
ejpam-4522	123	20	3	3	NUM
ejpam-4522	123	21	3	3	NUM
ejpam-4522	123	22	3	3	NUM
ejpam-4522	123	23	0	0	SYM
ejpam-4522	123	24	ξ	ξ	PRON
ejpam-4522	123	25	:	:	PUNCT
ejpam-4522	123	26	x	x	SYM
ejpam-4522	123	27	→	→	SYM
ejpam-4522	124	1	[	[	X
ejpam-4522	124	2	0	0	NUM
ejpam-4522	124	3	,	,	PUNCT
ejpam-4522	124	4	1	1	NUM
ejpam-4522	124	5	]	]	PUNCT
ejpam-4522	124	6	,	,	PUNCT
ejpam-4522	124	7	y	y	PROPN
ejpam-4522	124	8	7→	7→	PROPN
ejpam-4522	124	9			NOUN
ejpam-4522	124	10	0.83	0.83	NUM
ejpam-4522	124	11	if	if	SCONJ
ejpam-4522	124	12	y	y	NOUN
ejpam-4522	124	13	=	=	SYM
ejpam-4522	124	14	0	0	NUM
ejpam-4522	124	15	,	,	PUNCT
ejpam-4522	124	16	0.52	0.52	NUM
ejpam-4522	124	17	if	if	SCONJ
ejpam-4522	124	18	y	y	PROPN
ejpam-4522	124	19	=	=	SYM
ejpam-4522	124	20	1	1	NUM
ejpam-4522	124	21	,	,	PUNCT
ejpam-4522	124	22	0.77	0.77	NUM
ejpam-4522	124	23	if	if	SCONJ
ejpam-4522	124	24	y	y	PROPN
ejpam-4522	124	25	=	=	SYM
ejpam-4522	124	26	2	2	NUM
ejpam-4522	124	27	,	,	PUNCT
ejpam-4522	124	28	0.52	0.52	NUM
ejpam-4522	124	29	if	if	SCONJ
ejpam-4522	124	30	y	y	PROPN
ejpam-4522	124	31	=	=	SYM
ejpam-4522	124	32	3	3	NUM
ejpam-4522	124	33	,	,	PUNCT
ejpam-4522	124	34	0.69	0.69	NUM
ejpam-4522	125	1	if	if	SCONJ
ejpam-4522	125	2	y	y	NOUN
ejpam-4522	125	3	=	=	NOUN
ejpam-4522	125	4	4	4	X
ejpam-4522	125	5	.	.	PUNCT
ejpam-4522	126	1	it	it	PRON
ejpam-4522	126	2	is	be	AUX
ejpam-4522	126	3	routine	routine	ADJ
ejpam-4522	126	4	to	to	PART
ejpam-4522	126	5	check	check	VERB
ejpam-4522	126	6	that	that	SCONJ
ejpam-4522	126	7	m(x	m(x	PROPN
ejpam-4522	126	8	,	,	PUNCT
ejpam-4522	126	9	e	e	NOUN
ejpam-4522	126	10	)	)	PUNCT
ejpam-4522	126	11	:	:	PUNCT
ejpam-4522	127	1	=	=	SYM
ejpam-4522	127	2	(	(	PUNCT
ejpam-4522	127	3	me	i	PRON
ejpam-4522	127	4	,	,	PUNCT
ejpam-4522	127	5	ge	ge	PROPN
ejpam-4522	127	6	,	,	PUNCT
ejpam-4522	127	7	ξ	ξ	X
ejpam-4522	127	8	)	)	PUNCT
ejpam-4522	127	9	is	be	AUX
ejpam-4522	127	10	a	a	DET
ejpam-4522	127	11	makgeolli	makgeolli	NOUN
ejpam-4522	127	12	ideal	ideal	NOUN
ejpam-4522	127	13	of	of	ADP
ejpam-4522	127	14	(	(	PUNCT
ejpam-4522	127	15	x	x	X
ejpam-4522	127	16	,	,	PUNCT
ejpam-4522	127	17	e	e	NOUN
ejpam-4522	127	18	)	)	PUNCT
ejpam-4522	127	19	.	.	PUNCT
ejpam-4522	128	1	but	but	CCONJ
ejpam-4522	128	2	it	it	PRON
ejpam-4522	128	3	is	be	AUX
ejpam-4522	128	4	not	not	PART
ejpam-4522	128	5	a	a	DET
ejpam-4522	128	6	positive	positive	ADJ
ejpam-4522	128	7	implicative	implicative	ADJ
ejpam-4522	128	8	makgeolli	makgeolli	NOUN
ejpam-4522	128	9	ideal	ideal	NOUN
ejpam-4522	128	10	of	of	ADP
ejpam-4522	128	11	(	(	PUNCT
ejpam-4522	128	12	x	x	X
ejpam-4522	128	13	,	,	PUNCT
ejpam-4522	128	14	e	e	NOUN
ejpam-4522	128	15	)	)	PUNCT
ejpam-4522	128	16	since	since	SCONJ
ejpam-4522	128	17	ge(2	ge(2	NOUN
ejpam-4522	128	18	↬	↬	PROPN
ejpam-4522	128	19	1	1	NUM
ejpam-4522	128	20	)	)	PUNCT
ejpam-4522	128	21	=	=	SYM
ejpam-4522	128	22	ge(1	ge(1	NOUN
ejpam-4522	128	23	)	)	PUNCT
ejpam-4522	128	24	=	=	SYM
ejpam-4522	128	25	{	{	PUNCT
ejpam-4522	128	26	0	0	NUM
ejpam-4522	128	27	,	,	PUNCT
ejpam-4522	128	28	1	1	NUM
ejpam-4522	128	29	,	,	PUNCT
ejpam-4522	128	30	2	2	NUM
ejpam-4522	128	31	,	,	PUNCT
ejpam-4522	128	32	4	4	NUM
ejpam-4522	128	33	}	}	PUNCT
ejpam-4522	128	34	⊈	⊈	PROPN
ejpam-4522	128	35	{	{	PUNCT
ejpam-4522	128	36	2	2	NUM
ejpam-4522	128	37	,	,	PUNCT
ejpam-4522	128	38	4	4	NUM
ejpam-4522	128	39	}	}	PUNCT
ejpam-4522	128	40	=	=	SYM
ejpam-4522	128	41	ge((2	ge((2	NOUN
ejpam-4522	128	42	↬	↬	PROPN
ejpam-4522	128	43	1	1	NUM
ejpam-4522	128	44	)	)	PUNCT
ejpam-4522	128	45	↬	↬	PROPN
ejpam-4522	128	46	1	1	NUM
ejpam-4522	128	47	)	)	PUNCT
ejpam-4522	128	48	∪	∪	ADP
ejpam-4522	128	49	ge(1	ge(1	PROPN
ejpam-4522	128	50	↬	↬	PROPN
ejpam-4522	128	51	1	1	NUM
ejpam-4522	128	52	)	)	PUNCT
ejpam-4522	128	53	or	or	CCONJ
ejpam-4522	128	54	{	{	PUNCT
ejpam-4522	128	55	(	(	PUNCT
ejpam-4522	128	56	3	3	NUM
ejpam-4522	128	57	∗	∗	NOUN
ejpam-4522	128	58	1	1	NUM
ejpam-4522	128	59	)	)	PUNCT
ejpam-4522	128	60	∗	∗	NOUN
ejpam-4522	128	61	1}/0.76	1}/0.76	PROPN
ejpam-4522	128	62	=	=	PUNCT
ejpam-4522	129	1	0/0.76	0/0.76	PROPN
ejpam-4522	129	2	∈	∈	PROPN
ejpam-4522	129	3	ξ	ξ	PROPN
ejpam-4522	129	4	and	and	CCONJ
ejpam-4522	129	5	{	{	PUNCT
ejpam-4522	129	6	1	1	NUM
ejpam-4522	129	7	∗	∗	NOUN
ejpam-4522	129	8	1}/0.79	1}/0.79	PROPN
ejpam-4522	129	9	=	=	SYM
ejpam-4522	129	10	0/0.79	0/0.79	NUM
ejpam-4522	129	11	∈	∈	PROPN
ejpam-4522	129	12	ξ	ξ	NOUN
ejpam-4522	129	13	,	,	PUNCT
ejpam-4522	129	14	but	but	CCONJ
ejpam-4522	129	15	{	{	PUNCT
ejpam-4522	129	16	3	3	NUM
ejpam-4522	129	17	∗	∗	NOUN
ejpam-4522	129	18	1}/min{0.76	1}/min{0.76	NUM
ejpam-4522	129	19	,	,	PUNCT
ejpam-4522	129	20	0.79	0.79	NUM
ejpam-4522	129	21	}	}	PUNCT
ejpam-4522	129	22	=	=	PROPN
ejpam-4522	129	23	1/0.76	1/0.76	NUM
ejpam-4522	129	24	/∈	/∈	PUNCT
ejpam-4522	130	1	ξ	ξ	X
ejpam-4522	130	2	.	.	PUNCT
ejpam-4522	131	1	we	we	PRON
ejpam-4522	131	2	explore	explore	VERB
ejpam-4522	131	3	the	the	DET
ejpam-4522	131	4	conditions	condition	NOUN
ejpam-4522	131	5	under	under	ADP
ejpam-4522	131	6	which	which	PRON
ejpam-4522	131	7	the	the	DET
ejpam-4522	131	8	converse	converse	NOUN
ejpam-4522	131	9	of	of	ADP
ejpam-4522	131	10	theorem	theorem	NOUN
ejpam-4522	131	11	1	1	NUM
ejpam-4522	131	12	can	can	AUX
ejpam-4522	131	13	be	be	AUX
ejpam-4522	131	14	established	establish	VERB
ejpam-4522	131	15	.	.	PUNCT
ejpam-4522	132	1	theorem	theorem	NOUN
ejpam-4522	132	2	2	2	NUM
ejpam-4522	132	3	.	.	PUNCT
ejpam-4522	132	4	in	in	ADP
ejpam-4522	132	5	a	a	DET
ejpam-4522	132	6	bck	bck	NOUN
ejpam-4522	132	7	-	-	PUNCT
ejpam-4522	132	8	soft	soft	ADJ
ejpam-4522	132	9	universe	universe	NOUN
ejpam-4522	132	10	(	(	PUNCT
ejpam-4522	132	11	x	x	X
ejpam-4522	132	12	,	,	PUNCT
ejpam-4522	132	13	e	e	NOUN
ejpam-4522	132	14	)	)	PUNCT
ejpam-4522	132	15	in	in	ADP
ejpam-4522	132	16	which	which	PRON
ejpam-4522	132	17	x	x	PUNCT
ejpam-4522	132	18	and	and	CCONJ
ejpam-4522	132	19	e	e	NOUN
ejpam-4522	132	20	are	be	AUX
ejpam-4522	132	21	positive	positive	ADJ
ejpam-4522	132	22	implicative	implicative	ADJ
ejpam-4522	132	23	bck	bck	NOUN
ejpam-4522	132	24	-	-	PUNCT
ejpam-4522	132	25	algebras	algebras	PROPN
ejpam-4522	132	26	,	,	PUNCT
ejpam-4522	132	27	every	every	DET
ejpam-4522	132	28	makgeolli	makgeolli	NOUN
ejpam-4522	132	29	ideal	ideal	NOUN
ejpam-4522	132	30	is	be	AUX
ejpam-4522	132	31	a	a	DET
ejpam-4522	132	32	positive	positive	ADJ
ejpam-4522	132	33	implicative	implicative	ADJ
ejpam-4522	132	34	makgeolli	makgeolli	NOUN
ejpam-4522	132	35	ideal	ideal	NOUN
ejpam-4522	132	36	.	.	PUNCT
ejpam-4522	133	1	proof	proof	NOUN
ejpam-4522	133	2	.	.	PUNCT
ejpam-4522	134	1	straightforward	straightforward	ADJ
ejpam-4522	134	2	.	.	PUNCT
ejpam-4522	135	1	theorem	theorem	NOUN
ejpam-4522	135	2	3	3	NUM
ejpam-4522	135	3	.	.	PUNCT
ejpam-4522	136	1	if	if	SCONJ
ejpam-4522	136	2	a	a	DET
ejpam-4522	136	3	makgeolli	makgeolli	NOUN
ejpam-4522	136	4	ideal	ideal	NOUN
ejpam-4522	136	5	m(x	m(x	PROPN
ejpam-4522	136	6	,	,	PUNCT
ejpam-4522	136	7	e	e	NOUN
ejpam-4522	136	8	)	)	PUNCT
ejpam-4522	136	9	:	:	PUNCT
ejpam-4522	137	1	=	=	SYM
ejpam-4522	137	2	(	(	PUNCT
ejpam-4522	137	3	me	i	PRON
ejpam-4522	137	4	,	,	PUNCT
ejpam-4522	137	5	ge	ge	PROPN
ejpam-4522	137	6	,	,	PUNCT
ejpam-4522	137	7	ξ	ξ	PROPN
ejpam-4522	137	8	)	)	PUNCT
ejpam-4522	137	9	of	of	ADP
ejpam-4522	137	10	(	(	PUNCT
ejpam-4522	137	11	x	x	NOUN
ejpam-4522	137	12	,	,	PUNCT
ejpam-4522	137	13	e	e	NOUN
ejpam-4522	137	14	)	)	PUNCT
ejpam-4522	137	15	satisfies	satisfy	VERB
ejpam-4522	137	16	the	the	DET
ejpam-4522	137	17	condition	condition	NOUN
ejpam-4522	137	18	(	(	PUNCT
ejpam-4522	137	19	14	14	NUM
ejpam-4522	137	20	)	)	PUNCT
ejpam-4522	137	21	,	,	PUNCT
ejpam-4522	137	22	then	then	ADV
ejpam-4522	137	23	it	it	PRON
ejpam-4522	137	24	is	be	AUX
ejpam-4522	137	25	a	a	DET
ejpam-4522	137	26	positive	positive	ADJ
ejpam-4522	137	27	implicative	implicative	ADJ
ejpam-4522	137	28	makgeolli	makgeolli	NOUN
ejpam-4522	137	29	ideal	ideal	NOUN
ejpam-4522	137	30	of	of	ADP
ejpam-4522	137	31	(	(	PUNCT
ejpam-4522	137	32	x	x	X
ejpam-4522	137	33	,	,	PUNCT
ejpam-4522	137	34	e	e	NOUN
ejpam-4522	137	35	)	)	PUNCT
ejpam-4522	137	36	.	.	PUNCT
ejpam-4522	138	1	proof	proof	NOUN
ejpam-4522	138	2	.	.	PUNCT
ejpam-4522	139	1	let	let	VERB
ejpam-4522	139	2	m(x	m(x	PROPN
ejpam-4522	139	3	,	,	PUNCT
ejpam-4522	139	4	e	e	NOUN
ejpam-4522	139	5	)	)	PUNCT
ejpam-4522	139	6	:	:	PUNCT
ejpam-4522	140	1	=	=	SYM
ejpam-4522	140	2	(	(	PUNCT
ejpam-4522	140	3	me	i	PRON
ejpam-4522	140	4	,	,	PUNCT
ejpam-4522	140	5	ge	ge	PROPN
ejpam-4522	140	6	,	,	PUNCT
ejpam-4522	140	7	ξ	ξ	X
ejpam-4522	140	8	)	)	PUNCT
ejpam-4522	140	9	be	be	VERB
ejpam-4522	140	10	a	a	DET
ejpam-4522	140	11	makgeolli	makgeolli	NOUN
ejpam-4522	140	12	ideal	ideal	NOUN
ejpam-4522	140	13	of	of	ADP
ejpam-4522	140	14	(	(	PUNCT
ejpam-4522	140	15	x	x	X
ejpam-4522	140	16	,	,	PUNCT
ejpam-4522	140	17	e	e	NOUN
ejpam-4522	140	18	)	)	PUNCT
ejpam-4522	140	19	that	that	PRON
ejpam-4522	140	20	satisfies	satisfy	VERB
ejpam-4522	140	21	the	the	DET
ejpam-4522	140	22	condition	condition	NOUN
ejpam-4522	140	23	(	(	PUNCT
ejpam-4522	140	24	14	14	NUM
ejpam-4522	140	25	)	)	PUNCT
ejpam-4522	140	26	.	.	PUNCT
ejpam-4522	141	1	the	the	DET
ejpam-4522	141	2	combination	combination	NOUN
ejpam-4522	141	3	of	of	ADP
ejpam-4522	141	4	(	(	PUNCT
ejpam-4522	141	5	i1	i1	PROPN
ejpam-4522	141	6	)	)	PUNCT
ejpam-4522	141	7	and	and	CCONJ
ejpam-4522	141	8	(	(	PUNCT
ejpam-4522	141	9	4	4	X
ejpam-4522	141	10	)	)	PUNCT
ejpam-4522	141	11	derive	derive	NOUN
ejpam-4522	141	12	(	(	PUNCT
ejpam-4522	141	13	(	(	PUNCT
ejpam-4522	141	14	a	a	DET
ejpam-4522	141	15	↬	↬	PROPN
ejpam-4522	141	16	c	c	NOUN
ejpam-4522	141	17	)	)	PUNCT
ejpam-4522	141	18	↬	↬	X
ejpam-4522	141	19	c	c	X
ejpam-4522	141	20	)	)	PUNCT
ejpam-4522	141	21	↬	↬	NOUN
ejpam-4522	141	22	(	(	PUNCT
ejpam-4522	141	23	b	b	X
ejpam-4522	141	24	↬	↬	NUM
ejpam-4522	141	25	c	c	NOUN
ejpam-4522	141	26	)	)	PUNCT
ejpam-4522	141	27	≤	≤	NOUN
ejpam-4522	141	28	(	(	PUNCT
ejpam-4522	141	29	a	a	DET
ejpam-4522	141	30	↬	↬	PROPN
ejpam-4522	141	31	c	c	NOUN
ejpam-4522	141	32	)	)	PUNCT
ejpam-4522	141	33	↬	↬	PROPN
ejpam-4522	142	1	b	b	X
ejpam-4522	143	1	=	=	SYM
ejpam-4522	144	1	(	(	PUNCT
ejpam-4522	144	2	a	a	DET
ejpam-4522	144	3	↬	↬	PROPN
ejpam-4522	144	4	b	b	NOUN
ejpam-4522	144	5	)	)	PUNCT
ejpam-4522	144	6	↬	↬	PROPN
ejpam-4522	144	7	c	c	PROPN
ejpam-4522	144	8	and	and	CCONJ
ejpam-4522	144	9	(	(	PUNCT
ejpam-4522	144	10	(	(	PUNCT
ejpam-4522	144	11	x	x	SYM
ejpam-4522	144	12	∗	∗	PROPN
ejpam-4522	144	13	z	z	NOUN
ejpam-4522	144	14	)	)	PUNCT
ejpam-4522	144	15	∗	∗	PROPN
ejpam-4522	144	16	z	z	NOUN
ejpam-4522	144	17	)	)	PUNCT
ejpam-4522	144	18	∗	∗	NOUN
ejpam-4522	144	19	(	(	PUNCT
ejpam-4522	144	20	y	y	PROPN
ejpam-4522	144	21	∗	∗	PROPN
ejpam-4522	144	22	z	z	PROPN
ejpam-4522	144	23	)	)	PUNCT
ejpam-4522	144	24	≤	≤	NOUN
ejpam-4522	144	25	(	(	PUNCT
ejpam-4522	144	26	x	x	X
ejpam-4522	144	27	∗	∗	PROPN
ejpam-4522	144	28	z	z	NOUN
ejpam-4522	144	29	)	)	PUNCT
ejpam-4522	144	30	∗	∗	NOUN
ejpam-4522	144	31	y	y	NOUN
ejpam-4522	144	32	=	=	SYM
ejpam-4522	144	33	(	(	PUNCT
ejpam-4522	144	34	x	x	X
ejpam-4522	144	35	∗	∗	PROPN
ejpam-4522	144	36	y	y	NOUN
ejpam-4522	144	37	)	)	PUNCT
ejpam-4522	144	38	∗	∗	NOUN
ejpam-4522	144	39	z	z	NOUN
ejpam-4522	144	40	for	for	ADP
ejpam-4522	144	41	all	all	DET
ejpam-4522	144	42	a	a	DET
ejpam-4522	144	43	,	,	PUNCT
ejpam-4522	144	44	b	b	NOUN
ejpam-4522	144	45	,	,	PUNCT
ejpam-4522	144	46	c	c	PROPN
ejpam-4522	144	47	∈	∈	PROPN
ejpam-4522	144	48	e	e	PROPN
ejpam-4522	144	49	and	and	CCONJ
ejpam-4522	144	50	x	x	PROPN
ejpam-4522	144	51	,	,	PUNCT
ejpam-4522	144	52	y	y	PROPN
ejpam-4522	144	53	,	,	PUNCT
ejpam-4522	144	54	z	z	NOUN
ejpam-4522	144	55	∈	∈	PROPN
ejpam-4522	144	56	x	x	X
ejpam-4522	144	57	,	,	PUNCT
ejpam-4522	144	58	and	and	CCONJ
ejpam-4522	144	59	so	so	ADV
ejpam-4522	144	60	me(((a	me(((a	DET
ejpam-4522	144	61	↬	↬	X
ejpam-4522	144	62	c	c	X
ejpam-4522	144	63	)	)	PUNCT
ejpam-4522	144	64	↬	↬	X
ejpam-4522	144	65	c	c	X
ejpam-4522	144	66	)	)	PUNCT
ejpam-4522	144	67	↬	↬	NOUN
ejpam-4522	144	68	(	(	PUNCT
ejpam-4522	144	69	b	b	X
ejpam-4522	144	70	↬	↬	PROPN
ejpam-4522	144	71	c	c	NOUN
ejpam-4522	144	72	)	)	PUNCT
ejpam-4522	144	73	)	)	PUNCT
ejpam-4522	145	1	⊇	⊇	PROPN
ejpam-4522	145	2	me((a	me((a	PROPN
ejpam-4522	145	3	↬	↬	PROPN
ejpam-4522	145	4	b	b	X
ejpam-4522	145	5	)	)	PUNCT
ejpam-4522	145	6	↬	↬	PROPN
ejpam-4522	145	7	c	c	NOUN
ejpam-4522	145	8	)	)	PUNCT
ejpam-4522	145	9	,	,	PUNCT
ejpam-4522	145	10	ge(((a	ge(((a	NUM
ejpam-4522	145	11	↬	↬	PROPN
ejpam-4522	145	12	c	c	X
ejpam-4522	145	13	)	)	PUNCT
ejpam-4522	145	14	↬	↬	X
ejpam-4522	145	15	c	c	X
ejpam-4522	145	16	)	)	PUNCT
ejpam-4522	145	17	↬	↬	NOUN
ejpam-4522	145	18	(	(	PUNCT
ejpam-4522	145	19	b	b	X
ejpam-4522	145	20	↬	↬	PROPN
ejpam-4522	145	21	c	c	NOUN
ejpam-4522	145	22	)	)	PUNCT
ejpam-4522	145	23	)	)	PUNCT
ejpam-4522	146	1	⊆	⊆	NUM
ejpam-4522	146	2	ge((a	ge((a	NOUN
ejpam-4522	146	3	↬	↬	PROPN
ejpam-4522	146	4	b	b	NOUN
ejpam-4522	146	5	)	)	PUNCT
ejpam-4522	146	6	↬	↬	PROPN
ejpam-4522	146	7	c	c	X
ejpam-4522	146	8	)	)	PUNCT
ejpam-4522	146	9	,	,	PUNCT
ejpam-4522	146	10	ξ(((x	ξ(((x	PROPN
ejpam-4522	146	11	∗	∗	NOUN
ejpam-4522	146	12	z	z	NOUN
ejpam-4522	146	13	)	)	PUNCT
ejpam-4522	146	14	∗	∗	NOUN
ejpam-4522	146	15	z	z	NOUN
ejpam-4522	146	16	)	)	PUNCT
ejpam-4522	146	17	∗	∗	NOUN
ejpam-4522	146	18	(	(	PUNCT
ejpam-4522	146	19	y	y	PROPN
ejpam-4522	146	20	∗	∗	PROPN
ejpam-4522	146	21	z	z	NOUN
ejpam-4522	146	22	)	)	PUNCT
ejpam-4522	146	23	)	)	PUNCT
ejpam-4522	146	24	≥	≥	PRON
ejpam-4522	146	25	ξ((x	ξ((x	PROPN
ejpam-4522	146	26	∗	∗	PROPN
ejpam-4522	146	27	y	y	NOUN
ejpam-4522	146	28	)	)	PUNCT
ejpam-4522	146	29	∗	∗	NOUN
ejpam-4522	146	30	z	z	NOUN
ejpam-4522	146	31	)	)	PUNCT
ejpam-4522	146	32	by	by	ADP
ejpam-4522	146	33	lemma	lemma	PROPN
ejpam-4522	146	34	1(i	1(i	NUM
ejpam-4522	146	35	)	)	PUNCT
ejpam-4522	146	36	.	.	PUNCT
ejpam-4522	147	1	it	it	PRON
ejpam-4522	147	2	follows	follow	VERB
ejpam-4522	147	3	from	from	ADP
ejpam-4522	147	4	(	(	PUNCT
ejpam-4522	147	5	10	10	NUM
ejpam-4522	147	6	)	)	PUNCT
ejpam-4522	147	7	and	and	CCONJ
ejpam-4522	147	8	(	(	PUNCT
ejpam-4522	147	9	14	14	NUM
ejpam-4522	147	10	)	)	PUNCT
ejpam-4522	147	11	that	that	PRON
ejpam-4522	147	12	me(a	me(a	PRON
ejpam-4522	147	13	↬	↬	PROPN
ejpam-4522	147	14	c	c	X
ejpam-4522	147	15	)	)	PUNCT
ejpam-4522	147	16	⊇	⊇	PROPN
ejpam-4522	147	17	me((a	me((a	PROPN
ejpam-4522	147	18	↬	↬	PROPN
ejpam-4522	147	19	c	c	PROPN
ejpam-4522	147	20	)	)	PUNCT
ejpam-4522	147	21	↬	↬	X
ejpam-4522	147	22	c	c	X
ejpam-4522	147	23	)	)	PUNCT
ejpam-4522	147	24	⊇	⊇	NOUN
ejpam-4522	147	25	me(((a	me(((a	X
ejpam-4522	147	26	↬	↬	X
ejpam-4522	147	27	c	c	X
ejpam-4522	147	28	)	)	PUNCT
ejpam-4522	147	29	↬	↬	X
ejpam-4522	147	30	c	c	X
ejpam-4522	147	31	)	)	PUNCT
ejpam-4522	147	32	↬	↬	NOUN
ejpam-4522	148	1	(	(	PUNCT
ejpam-4522	148	2	b	b	X
ejpam-4522	148	3	↬	↬	PROPN
ejpam-4522	148	4	c	c	NOUN
ejpam-4522	148	5	)	)	PUNCT
ejpam-4522	148	6	)	)	PUNCT
ejpam-4522	149	1	∩me(b	∩me(b	ADV
ejpam-4522	149	2	↬	↬	NUM
ejpam-4522	149	3	c	c	X
ejpam-4522	149	4	)	)	PUNCT
ejpam-4522	149	5	s.	s.	PROPN
ejpam-4522	149	6	z.	z.	PROPN
ejpam-4522	149	7	song	song	PROPN
ejpam-4522	149	8	,	,	PUNCT
ejpam-4522	149	9	m.	m.	NOUN
ejpam-4522	149	10	a.	a.	NOUN
ejpam-4522	149	11	öztürk	öztürk	PROPN
ejpam-4522	149	12	,	,	PUNCT
ejpam-4522	149	13	y.	y.	PROPN
ejpam-4522	149	14	b.	b.	PROPN
ejpam-4522	149	15	jun	jun	PROPN
ejpam-4522	149	16	/	/	SYM
ejpam-4522	149	17	eur	eur	PROPN
ejpam-4522	149	18	.	.	PUNCT
ejpam-4522	150	1	j.	j.	PROPN
ejpam-4522	150	2	pure	pure	PROPN
ejpam-4522	150	3	appl	appl	PROPN
ejpam-4522	150	4	.	.	PROPN
ejpam-4522	150	5	math	math	PROPN
ejpam-4522	150	6	,	,	PUNCT
ejpam-4522	150	7	15	15	NUM
ejpam-4522	150	8	(	(	PUNCT
ejpam-4522	150	9	4	4	NUM
ejpam-4522	150	10	)	)	PUNCT
ejpam-4522	150	11	(	(	PUNCT
ejpam-4522	150	12	2022	2022	NUM
ejpam-4522	150	13	)	)	PUNCT
ejpam-4522	150	14	,	,	PUNCT
ejpam-4522	150	15	1498	1498	NUM
ejpam-4522	150	16	-	-	SYM
ejpam-4522	150	17	1511	1511	NUM
ejpam-4522	150	18	1504	1504	NUM
ejpam-4522	150	19	⊇	⊇	PROPN
ejpam-4522	150	20	me((a	me((a	PROPN
ejpam-4522	150	21	↬	↬	PROPN
ejpam-4522	150	22	b	b	X
ejpam-4522	150	23	)	)	PUNCT
ejpam-4522	150	24	↬	↬	PROPN
ejpam-4522	151	1	c	c	X
ejpam-4522	151	2	)	)	PUNCT
ejpam-4522	151	3	∩me(b	∩me(b	ADV
ejpam-4522	151	4	↬	↬	PROPN
ejpam-4522	151	5	c	c	X
ejpam-4522	151	6	)	)	PUNCT
ejpam-4522	151	7	,	,	PUNCT
ejpam-4522	151	8	ge(a	ge(a	PRON
ejpam-4522	151	9	↬	↬	PROPN
ejpam-4522	151	10	c	c	X
ejpam-4522	151	11	)	)	PUNCT
ejpam-4522	151	12	⊆	⊆	NUM
ejpam-4522	151	13	ge((a	ge((a	NOUN
ejpam-4522	151	14	↬	↬	X
ejpam-4522	151	15	c	c	NOUN
ejpam-4522	151	16	)	)	PUNCT
ejpam-4522	151	17	↬	↬	X
ejpam-4522	152	1	c	c	X
ejpam-4522	152	2	)	)	PUNCT
ejpam-4522	153	1	⊆	⊆	NUM
ejpam-4522	153	2	ge(((a	ge(((a	NUM
ejpam-4522	153	3	↬	↬	PROPN
ejpam-4522	153	4	c	c	NOUN
ejpam-4522	153	5	)	)	PUNCT
ejpam-4522	153	6	↬	↬	X
ejpam-4522	154	1	c	c	X
ejpam-4522	154	2	)	)	PUNCT
ejpam-4522	154	3	↬	↬	NOUN
ejpam-4522	154	4	(	(	PUNCT
ejpam-4522	154	5	b	b	X
ejpam-4522	154	6	↬	↬	PROPN
ejpam-4522	154	7	c	c	NOUN
ejpam-4522	154	8	)	)	PUNCT
ejpam-4522	154	9	)	)	PUNCT
ejpam-4522	154	10	∪ge(b	∪ge(b	CCONJ
ejpam-4522	154	11	↬	↬	PROPN
ejpam-4522	154	12	c	c	X
ejpam-4522	154	13	)	)	PUNCT
ejpam-4522	154	14	⊆	⊆	NUM
ejpam-4522	154	15	ge((a	ge((a	NOUN
ejpam-4522	154	16	↬	↬	PROPN
ejpam-4522	154	17	b	b	X
ejpam-4522	154	18	)	)	PUNCT
ejpam-4522	154	19	↬	↬	X
ejpam-4522	154	20	c	c	X
ejpam-4522	154	21	)	)	PUNCT
ejpam-4522	154	22	∪ge(b	∪ge(b	ADP
ejpam-4522	154	23	↬	↬	PROPN
ejpam-4522	154	24	c	c	X
ejpam-4522	154	25	)	)	PUNCT
ejpam-4522	154	26	,	,	PUNCT
ejpam-4522	154	27	and	and	CCONJ
ejpam-4522	154	28	ξ(x	ξ(x	NOUN
ejpam-4522	154	29	∗	∗	NOUN
ejpam-4522	154	30	z	z	NOUN
ejpam-4522	154	31	)	)	PUNCT
ejpam-4522	154	32	≥	≥	NOUN
ejpam-4522	154	33	ξ((x	ξ((x	NOUN
ejpam-4522	154	34	∗	∗	PROPN
ejpam-4522	154	35	z	z	NOUN
ejpam-4522	154	36	)	)	PUNCT
ejpam-4522	154	37	∗	∗	NOUN
ejpam-4522	154	38	z	z	NOUN
ejpam-4522	154	39	)	)	PUNCT
ejpam-4522	154	40	≥	≥	NOUN
ejpam-4522	154	41	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	154	42	∗	∗	NOUN
ejpam-4522	154	43	z	z	NOUN
ejpam-4522	154	44	)	)	PUNCT
ejpam-4522	154	45	∗	∗	NOUN
ejpam-4522	154	46	z	z	NOUN
ejpam-4522	154	47	)	)	PUNCT
ejpam-4522	154	48	∗	∗	NOUN
ejpam-4522	154	49	(	(	PUNCT
ejpam-4522	154	50	y	y	PROPN
ejpam-4522	154	51	∗	∗	PROPN
ejpam-4522	154	52	z	z	PROPN
ejpam-4522	154	53	)	)	PUNCT
ejpam-4522	154	54	)	)	PUNCT
ejpam-4522	154	55	,	,	PUNCT
ejpam-4522	154	56	ξ(y	ξ(y	PROPN
ejpam-4522	154	57	∗	∗	NOUN
ejpam-4522	154	58	z	z	NOUN
ejpam-4522	154	59	)	)	PUNCT
ejpam-4522	154	60	}	}	PUNCT
ejpam-4522	154	61	≥	≥	NUM
ejpam-4522	154	62	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	154	63	∗	∗	X
ejpam-4522	154	64	y	y	NOUN
ejpam-4522	154	65	)	)	PUNCT
ejpam-4522	154	66	∗	∗	NOUN
ejpam-4522	154	67	z	z	NOUN
ejpam-4522	154	68	)	)	PUNCT
ejpam-4522	154	69	,	,	PUNCT
ejpam-4522	154	70	ξ(y	ξ(y	PROPN
ejpam-4522	154	71	∗	∗	NOUN
ejpam-4522	154	72	z	z	PROPN
ejpam-4522	154	73	)	)	PUNCT
ejpam-4522	154	74	}	}	PUNCT
ejpam-4522	154	75	.	.	PUNCT
ejpam-4522	155	1	hence	hence	ADV
ejpam-4522	155	2	m(x	m(x	PROPN
ejpam-4522	155	3	,	,	PUNCT
ejpam-4522	155	4	e	e	NOUN
ejpam-4522	155	5	)	)	PUNCT
ejpam-4522	155	6	:	:	PUNCT
ejpam-4522	156	1	=	=	SYM
ejpam-4522	156	2	(	(	PUNCT
ejpam-4522	156	3	me	i	PRON
ejpam-4522	156	4	,	,	PUNCT
ejpam-4522	156	5	ge	ge	PROPN
ejpam-4522	156	6	,	,	PUNCT
ejpam-4522	156	7	ξ	ξ	X
ejpam-4522	156	8	)	)	PUNCT
ejpam-4522	156	9	is	be	AUX
ejpam-4522	156	10	a	a	DET
ejpam-4522	156	11	positive	positive	ADJ
ejpam-4522	156	12	implicative	implicative	ADJ
ejpam-4522	156	13	makgeolli	makgeolli	NOUN
ejpam-4522	156	14	ideal	ideal	NOUN
ejpam-4522	156	15	of	of	ADP
ejpam-4522	156	16	(	(	PUNCT
ejpam-4522	156	17	x	x	X
ejpam-4522	156	18	,	,	PUNCT
ejpam-4522	156	19	e	e	NOUN
ejpam-4522	156	20	)	)	PUNCT
ejpam-4522	156	21	.	.	PUNCT
ejpam-4522	157	1	theorem	theorem	ADJ
ejpam-4522	157	2	4	4	NUM
ejpam-4522	157	3	.	.	PUNCT
ejpam-4522	158	1	a	a	DET
ejpam-4522	158	2	makgeolli	makgeolli	NOUN
ejpam-4522	158	3	structure	structure	NOUN
ejpam-4522	158	4	m(x	m(x	PROPN
ejpam-4522	158	5	,	,	PUNCT
ejpam-4522	158	6	e	e	NOUN
ejpam-4522	158	7	)	)	PUNCT
ejpam-4522	158	8	:	:	PUNCT
ejpam-4522	158	9	=	=	SYM
ejpam-4522	158	10	(	(	PUNCT
ejpam-4522	158	11	me	i	PRON
ejpam-4522	158	12	,	,	PUNCT
ejpam-4522	158	13	ge	ge	PROPN
ejpam-4522	158	14	,	,	PUNCT
ejpam-4522	158	15	ξ	ξ	PROPN
ejpam-4522	158	16	)	)	PUNCT
ejpam-4522	158	17	on	on	ADP
ejpam-4522	158	18	(	(	PUNCT
ejpam-4522	158	19	x	x	X
ejpam-4522	158	20	,	,	PUNCT
ejpam-4522	158	21	e	e	NOUN
ejpam-4522	158	22	)	)	PUNCT
ejpam-4522	158	23	is	be	AUX
ejpam-4522	158	24	a	a	DET
ejpam-4522	158	25	positive	positive	ADJ
ejpam-4522	158	26	implicative	implicative	ADJ
ejpam-4522	158	27	makgeolli	makgeolli	NOUN
ejpam-4522	158	28	ideal	ideal	NOUN
ejpam-4522	158	29	of	of	ADP
ejpam-4522	158	30	(	(	PUNCT
ejpam-4522	158	31	x	x	X
ejpam-4522	158	32	,	,	PUNCT
ejpam-4522	158	33	e	e	NOUN
ejpam-4522	158	34	)	)	PUNCT
ejpam-4522	159	1	if	if	SCONJ
ejpam-4522	160	1	and	and	CCONJ
ejpam-4522	160	2	only	only	ADV
ejpam-4522	160	3	if	if	SCONJ
ejpam-4522	160	4	it	it	PRON
ejpam-4522	160	5	is	be	AUX
ejpam-4522	160	6	a	a	DET
ejpam-4522	160	7	makgeolli	makgeolli	NOUN
ejpam-4522	160	8	ideal	ideal	NOUN
ejpam-4522	160	9	of	of	ADP
ejpam-4522	160	10	(	(	PUNCT
ejpam-4522	160	11	x	x	X
ejpam-4522	160	12	,	,	PUNCT
ejpam-4522	160	13	e	e	NOUN
ejpam-4522	160	14	)	)	PUNCT
ejpam-4522	160	15	that	that	PRON
ejpam-4522	160	16	satisfies	satisfy	VERB
ejpam-4522	160	17	the	the	DET
ejpam-4522	160	18	following	follow	VERB
ejpam-4522	160	19	condition.	condition.	PROPN
ejpam-4522	160	20	(	(	PUNCT
ejpam-4522	160	21	∀a	∀a	X
ejpam-4522	160	22	,	,	PUNCT
ejpam-4522	160	23	b	b	NOUN
ejpam-4522	160	24	,	,	PUNCT
ejpam-4522	160	25	c	c	PROPN
ejpam-4522	160	26	∈	∈	PROPN
ejpam-4522	160	27	e	e	X
ejpam-4522	160	28	)	)	PUNCT
ejpam-4522	160	29	(	(	PUNCT
ejpam-4522	160	30	me((a	me((a	X
ejpam-4522	160	31	↬	↬	PROPN
ejpam-4522	160	32	c	c	NOUN
ejpam-4522	160	33	)	)	PUNCT
ejpam-4522	160	34	↬	↬	NOUN
ejpam-4522	160	35	(	(	PUNCT
ejpam-4522	160	36	b	b	X
ejpam-4522	160	37	↬	↬	PROPN
ejpam-4522	160	38	c	c	NOUN
ejpam-4522	160	39	)	)	PUNCT
ejpam-4522	160	40	)	)	PUNCT
ejpam-4522	161	1	⊇	⊇	PROPN
ejpam-4522	161	2	me((a	me((a	PROPN
ejpam-4522	161	3	↬	↬	PROPN
ejpam-4522	161	4	b	b	X
ejpam-4522	161	5	)	)	PUNCT
ejpam-4522	161	6	↬	↬	PROPN
ejpam-4522	161	7	c	c	X
ejpam-4522	161	8	)	)	PUNCT
ejpam-4522	161	9	ge((a	ge((a	NOUN
ejpam-4522	161	10	↬	↬	X
ejpam-4522	161	11	c	c	NOUN
ejpam-4522	161	12	)	)	PUNCT
ejpam-4522	161	13	↬	↬	NOUN
ejpam-4522	161	14	(	(	PUNCT
ejpam-4522	161	15	b	b	X
ejpam-4522	161	16	↬	↬	PROPN
ejpam-4522	161	17	c	c	NOUN
ejpam-4522	161	18	)	)	PUNCT
ejpam-4522	161	19	)	)	PUNCT
ejpam-4522	162	1	⊆	⊆	NUM
ejpam-4522	162	2	ge((a	ge((a	NOUN
ejpam-4522	162	3	↬	↬	PROPN
ejpam-4522	162	4	b	b	X
ejpam-4522	162	5	)	)	PUNCT
ejpam-4522	162	6	↬	↬	PROPN
ejpam-4522	162	7	c	c	NOUN
ejpam-4522	162	8	)	)	PUNCT
ejpam-4522	162	9	)	)	PUNCT
ejpam-4522	162	10	,	,	PUNCT
ejpam-4522	162	11	(	(	PUNCT
ejpam-4522	162	12	∀x	∀x	X
ejpam-4522	162	13	,	,	PUNCT
ejpam-4522	162	14	y	y	PROPN
ejpam-4522	162	15	,	,	PUNCT
ejpam-4522	162	16	z	z	NOUN
ejpam-4522	162	17	∈	∈	PROPN
ejpam-4522	162	18	x	x	X
ejpam-4522	162	19	)	)	PUNCT
ejpam-4522	162	20	(	(	PUNCT
ejpam-4522	162	21	ξ((x	ξ((x	NOUN
ejpam-4522	162	22	∗	∗	PROPN
ejpam-4522	162	23	z	z	NOUN
ejpam-4522	162	24	)	)	PUNCT
ejpam-4522	162	25	∗	∗	NOUN
ejpam-4522	162	26	(	(	PUNCT
ejpam-4522	162	27	y	y	PROPN
ejpam-4522	162	28	∗	∗	PROPN
ejpam-4522	162	29	z	z	NOUN
ejpam-4522	162	30	)	)	PUNCT
ejpam-4522	162	31	)	)	PUNCT
ejpam-4522	162	32	≥	≥	X
ejpam-4522	162	33	ξ(((x	ξ(((x	VERB
ejpam-4522	162	34	∗	∗	NOUN
ejpam-4522	162	35	y	y	NOUN
ejpam-4522	162	36	)	)	PUNCT
ejpam-4522	162	37	∗	∗	NOUN
ejpam-4522	162	38	z	z	NOUN
ejpam-4522	162	39	)	)	PUNCT
ejpam-4522	162	40	)	)	PUNCT
ejpam-4522	162	41	.	.	PUNCT
ejpam-4522	163	1	(	(	PUNCT
ejpam-4522	163	2	15	15	X
ejpam-4522	163	3	)	)	PUNCT
ejpam-4522	163	4	proof	proof	NOUN
ejpam-4522	163	5	.	.	PUNCT
ejpam-4522	164	1	let	let	VERB
ejpam-4522	164	2	m(x	m(x	PROPN
ejpam-4522	164	3	,	,	PUNCT
ejpam-4522	164	4	e	e	NOUN
ejpam-4522	164	5	)	)	PUNCT
ejpam-4522	164	6	:	:	PUNCT
ejpam-4522	165	1	=	=	SYM
ejpam-4522	165	2	(	(	PUNCT
ejpam-4522	165	3	me	i	PRON
ejpam-4522	165	4	,	,	PUNCT
ejpam-4522	165	5	ge	ge	PROPN
ejpam-4522	165	6	,	,	PUNCT
ejpam-4522	165	7	ξ	ξ	X
ejpam-4522	165	8	)	)	PUNCT
ejpam-4522	165	9	be	be	VERB
ejpam-4522	165	10	a	a	DET
ejpam-4522	165	11	makgeolli	makgeolli	NOUN
ejpam-4522	165	12	ideal	ideal	NOUN
ejpam-4522	165	13	of	of	ADP
ejpam-4522	165	14	(	(	PUNCT
ejpam-4522	165	15	x	x	X
ejpam-4522	165	16	,	,	PUNCT
ejpam-4522	165	17	e	e	NOUN
ejpam-4522	165	18	)	)	PUNCT
ejpam-4522	165	19	that	that	PRON
ejpam-4522	165	20	satisfies	satisfie	NOUN
ejpam-4522	165	21	(	(	PUNCT
ejpam-4522	165	22	15	15	NUM
ejpam-4522	165	23	)	)	PUNCT
ejpam-4522	165	24	.	.	PUNCT
ejpam-4522	166	1	if	if	SCONJ
ejpam-4522	166	2	we	we	PRON
ejpam-4522	166	3	put	put	VERB
ejpam-4522	166	4	b	b	NOUN
ejpam-4522	166	5	:	:	PUNCT
ejpam-4522	166	6	=	=	SYM
ejpam-4522	166	7	c	c	PROPN
ejpam-4522	166	8	and	and	CCONJ
ejpam-4522	166	9	y	y	PROPN
ejpam-4522	167	1	:	:	PUNCT
ejpam-4522	167	2	=	=	SYM
ejpam-4522	167	3	z	z	X
ejpam-4522	167	4	in	in	ADP
ejpam-4522	167	5	(	(	PUNCT
ejpam-4522	167	6	15	15	NUM
ejpam-4522	167	7	)	)	PUNCT
ejpam-4522	167	8	,	,	PUNCT
ejpam-4522	167	9	then	then	ADV
ejpam-4522	167	10	me(a	me(a	NUM
ejpam-4522	167	11	↬	↬	PROPN
ejpam-4522	167	12	c	c	X
ejpam-4522	167	13	)	)	PUNCT
ejpam-4522	167	14	=	=	SYM
ejpam-4522	167	15	me((a	me((a	PROPN
ejpam-4522	167	16	↬	↬	PROPN
ejpam-4522	167	17	c	c	NOUN
ejpam-4522	167	18	)	)	PUNCT
ejpam-4522	167	19	↬	↬	NOUN
ejpam-4522	167	20	0	0	NUM
ejpam-4522	167	21	)	)	PUNCT
ejpam-4522	167	22	=	=	SYM
ejpam-4522	167	23	me((a	me((a	PROPN
ejpam-4522	167	24	↬	↬	PROPN
ejpam-4522	167	25	c	c	X
ejpam-4522	167	26	)	)	PUNCT
ejpam-4522	167	27	↬	↬	NOUN
ejpam-4522	167	28	(	(	PUNCT
ejpam-4522	167	29	c	c	X
ejpam-4522	167	30	↬	↬	PROPN
ejpam-4522	167	31	c	c	NOUN
ejpam-4522	167	32	)	)	PUNCT
ejpam-4522	167	33	)	)	PUNCT
ejpam-4522	167	34	⊇	⊇	PROPN
ejpam-4522	167	35	me((a	me((a	PROPN
ejpam-4522	167	36	↬	↬	PROPN
ejpam-4522	167	37	c	c	PROPN
ejpam-4522	167	38	)	)	PUNCT
ejpam-4522	167	39	↬	↬	PROPN
ejpam-4522	167	40	c	c	X
ejpam-4522	167	41	)	)	PUNCT
ejpam-4522	167	42	,	,	PUNCT
ejpam-4522	167	43	ge(a	ge(a	PRON
ejpam-4522	167	44	↬	↬	PROPN
ejpam-4522	167	45	c	c	X
ejpam-4522	167	46	)	)	PUNCT
ejpam-4522	167	47	=	=	VERB
ejpam-4522	167	48	ge((a	ge((a	NOUN
ejpam-4522	167	49	↬	↬	X
ejpam-4522	167	50	c	c	NOUN
ejpam-4522	167	51	)	)	PUNCT
ejpam-4522	167	52	↬	↬	X
ejpam-4522	167	53	0	0	NUM
ejpam-4522	167	54	)	)	PUNCT
ejpam-4522	167	55	=	=	VERB
ejpam-4522	167	56	ge((a	ge((a	NOUN
ejpam-4522	167	57	↬	↬	X
ejpam-4522	167	58	c	c	X
ejpam-4522	167	59	)	)	PUNCT
ejpam-4522	167	60	↬	↬	NOUN
ejpam-4522	168	1	(	(	PUNCT
ejpam-4522	168	2	c	c	X
ejpam-4522	168	3	↬	↬	PROPN
ejpam-4522	168	4	c	c	NOUN
ejpam-4522	168	5	)	)	PUNCT
ejpam-4522	168	6	)	)	PUNCT
ejpam-4522	169	1	⊆	⊆	NUM
ejpam-4522	169	2	ge((a	ge((a	NOUN
ejpam-4522	169	3	↬	↬	X
ejpam-4522	169	4	c	c	NOUN
ejpam-4522	169	5	)	)	PUNCT
ejpam-4522	169	6	↬	↬	PROPN
ejpam-4522	169	7	c	c	NOUN
ejpam-4522	169	8	)	)	PUNCT
ejpam-4522	169	9	,	,	PUNCT
ejpam-4522	169	10	ξ(x	ξ(x	NOUN
ejpam-4522	169	11	∗	∗	NOUN
ejpam-4522	169	12	z	z	NOUN
ejpam-4522	169	13	)	)	PUNCT
ejpam-4522	169	14	=	=	SYM
ejpam-4522	169	15	ξ((x	ξ((x	NOUN
ejpam-4522	169	16	∗	∗	NOUN
ejpam-4522	169	17	z	z	NOUN
ejpam-4522	169	18	)	)	PUNCT
ejpam-4522	169	19	∗	∗	NOUN
ejpam-4522	169	20	0	0	NUM
ejpam-4522	169	21	)	)	PUNCT
ejpam-4522	169	22	=	=	SYM
ejpam-4522	169	23	ξ((x	ξ((x	NOUN
ejpam-4522	169	24	∗	∗	NOUN
ejpam-4522	169	25	z	z	NOUN
ejpam-4522	169	26	)	)	PUNCT
ejpam-4522	169	27	∗	∗	NOUN
ejpam-4522	169	28	(	(	PUNCT
ejpam-4522	169	29	z	z	NOUN
ejpam-4522	169	30	∗	∗	PROPN
ejpam-4522	169	31	z	z	NOUN
ejpam-4522	169	32	)	)	PUNCT
ejpam-4522	169	33	)	)	PUNCT
ejpam-4522	169	34	≥	≥	PRON
ejpam-4522	169	35	ξ((x	ξ((x	VERB
ejpam-4522	169	36	∗	∗	PROPN
ejpam-4522	169	37	z	z	NOUN
ejpam-4522	169	38	)	)	PUNCT
ejpam-4522	169	39	∗	∗	NOUN
ejpam-4522	169	40	z	z	NOUN
ejpam-4522	169	41	)	)	PUNCT
ejpam-4522	169	42	for	for	ADP
ejpam-4522	169	43	all	all	DET
ejpam-4522	169	44	a	a	PRON
ejpam-4522	169	45	,	,	PUNCT
ejpam-4522	169	46	c	c	PROPN
ejpam-4522	169	47	∈	∈	PROPN
ejpam-4522	169	48	e	e	PROPN
ejpam-4522	169	49	and	and	CCONJ
ejpam-4522	169	50	x	x	NOUN
ejpam-4522	169	51	,	,	PUNCT
ejpam-4522	169	52	z	z	NOUN
ejpam-4522	169	53	∈	∈	PROPN
ejpam-4522	169	54	x	x	PUNCT
ejpam-4522	169	55	by	by	ADP
ejpam-4522	169	56	(	(	PUNCT
ejpam-4522	169	57	i3	i3	NOUN
ejpam-4522	169	58	)	)	PUNCT
ejpam-4522	169	59	and	and	CCONJ
ejpam-4522	169	60	(	(	PUNCT
ejpam-4522	169	61	2	2	NUM
ejpam-4522	169	62	)	)	PUNCT
ejpam-4522	169	63	.	.	PUNCT
ejpam-4522	170	1	it	it	PRON
ejpam-4522	170	2	follows	follow	VERB
ejpam-4522	170	3	from	from	ADP
ejpam-4522	170	4	theorem	theorem	ADJ
ejpam-4522	170	5	3	3	NUM
ejpam-4522	170	6	that	that	SCONJ
ejpam-4522	170	7	m(x	m(x	PROPN
ejpam-4522	170	8	,	,	PUNCT
ejpam-4522	170	9	e	e	NOUN
ejpam-4522	170	10	)	)	PUNCT
ejpam-4522	170	11	:	:	PUNCT
ejpam-4522	171	1	=	=	SYM
ejpam-4522	171	2	(	(	PUNCT
ejpam-4522	171	3	me	i	PRON
ejpam-4522	171	4	,	,	PUNCT
ejpam-4522	171	5	ge	ge	PROPN
ejpam-4522	171	6	,	,	PUNCT
ejpam-4522	171	7	ξ	ξ	X
ejpam-4522	171	8	)	)	PUNCT
ejpam-4522	171	9	is	be	AUX
ejpam-4522	171	10	a	a	DET
ejpam-4522	171	11	positive	positive	ADJ
ejpam-4522	171	12	implicative	implicative	ADJ
ejpam-4522	171	13	makgeolli	makgeolli	NOUN
ejpam-4522	171	14	ideal	ideal	NOUN
ejpam-4522	171	15	of	of	ADP
ejpam-4522	171	16	(	(	PUNCT
ejpam-4522	171	17	x	x	X
ejpam-4522	171	18	,	,	PUNCT
ejpam-4522	171	19	e	e	NOUN
ejpam-4522	171	20	)	)	PUNCT
ejpam-4522	171	21	.	.	PUNCT
ejpam-4522	172	1	conversely	conversely	ADV
ejpam-4522	172	2	,	,	PUNCT
ejpam-4522	172	3	assume	assume	VERB
ejpam-4522	172	4	that	that	SCONJ
ejpam-4522	172	5	m(x	m(x	PROPN
ejpam-4522	172	6	,	,	PUNCT
ejpam-4522	172	7	e	e	NOUN
ejpam-4522	172	8	)	)	PUNCT
ejpam-4522	172	9	:	:	PUNCT
ejpam-4522	173	1	=	=	SYM
ejpam-4522	173	2	(	(	PUNCT
ejpam-4522	173	3	me	i	PRON
ejpam-4522	173	4	,	,	PUNCT
ejpam-4522	173	5	ge	ge	PROPN
ejpam-4522	173	6	,	,	PUNCT
ejpam-4522	173	7	ξ	ξ	X
ejpam-4522	173	8	)	)	PUNCT
ejpam-4522	173	9	is	be	AUX
ejpam-4522	173	10	a	a	DET
ejpam-4522	173	11	positive	positive	ADJ
ejpam-4522	173	12	implicative	implicative	ADJ
ejpam-4522	173	13	makgeolli	makgeolli	NOUN
ejpam-4522	173	14	ideal	ideal	NOUN
ejpam-4522	173	15	of	of	ADP
ejpam-4522	173	16	(	(	PUNCT
ejpam-4522	173	17	x	x	X
ejpam-4522	173	18	,	,	PUNCT
ejpam-4522	173	19	e	e	NOUN
ejpam-4522	173	20	)	)	PUNCT
ejpam-4522	173	21	.	.	PUNCT
ejpam-4522	174	1	then	then	ADV
ejpam-4522	174	2	it	it	PRON
ejpam-4522	174	3	is	be	AUX
ejpam-4522	174	4	a	a	DET
ejpam-4522	174	5	makgeolli	makgeolli	NOUN
ejpam-4522	174	6	ideal	ideal	NOUN
ejpam-4522	174	7	of	of	ADP
ejpam-4522	174	8	(	(	PUNCT
ejpam-4522	174	9	x	x	X
ejpam-4522	174	10	,	,	PUNCT
ejpam-4522	174	11	e	e	NOUN
ejpam-4522	174	12	)	)	PUNCT
ejpam-4522	174	13	by	by	ADP
ejpam-4522	174	14	theorem	theorem	NOUN
ejpam-4522	174	15	1	1	NUM
ejpam-4522	174	16	.	.	PUNCT
ejpam-4522	175	1	since	since	SCONJ
ejpam-4522	175	2	(	(	PUNCT
ejpam-4522	175	3	(	(	PUNCT
ejpam-4522	175	4	a	a	DET
ejpam-4522	175	5	↬	↬	PROPN
ejpam-4522	175	6	(	(	PUNCT
ejpam-4522	175	7	b	b	NOUN
ejpam-4522	175	8	↬	↬	PROPN
ejpam-4522	175	9	c	c	NOUN
ejpam-4522	175	10	)	)	PUNCT
ejpam-4522	175	11	)	)	PUNCT
ejpam-4522	175	12	↬	↬	PROPN
ejpam-4522	175	13	c	c	X
ejpam-4522	175	14	)	)	PUNCT
ejpam-4522	175	15	↬	↬	NOUN
ejpam-4522	175	16	c	c	X
ejpam-4522	176	1	=	=	SYM
ejpam-4522	176	2	(	(	PUNCT
ejpam-4522	176	3	(	(	PUNCT
ejpam-4522	176	4	a	a	DET
ejpam-4522	176	5	↬	↬	PROPN
ejpam-4522	176	6	c	c	NOUN
ejpam-4522	176	7	)	)	PUNCT
ejpam-4522	176	8	↬	↬	NOUN
ejpam-4522	176	9	(	(	PUNCT
ejpam-4522	176	10	b	b	X
ejpam-4522	176	11	↬	↬	PROPN
ejpam-4522	176	12	c	c	NOUN
ejpam-4522	176	13	)	)	PUNCT
ejpam-4522	176	14	)	)	PUNCT
ejpam-4522	177	1	↬	↬	PROPN
ejpam-4522	177	2	c	c	NOUN
ejpam-4522	177	3	≤	≤	NUM
ejpam-4522	177	4	(	(	PUNCT
ejpam-4522	177	5	a	a	DET
ejpam-4522	177	6	↬	↬	PROPN
ejpam-4522	177	7	b	b	NOUN
ejpam-4522	177	8	)	)	PUNCT
ejpam-4522	177	9	↬	↬	PROPN
ejpam-4522	177	10	c	c	NOUN
ejpam-4522	177	11	and	and	CCONJ
ejpam-4522	177	12	(	(	PUNCT
ejpam-4522	177	13	(	(	PUNCT
ejpam-4522	177	14	x∗	x∗	X
ejpam-4522	177	15	(	(	PUNCT
ejpam-4522	177	16	y	y	PROPN
ejpam-4522	177	17	∗z))∗z)∗z	∗z))∗z)∗z	PROPN
ejpam-4522	177	18	=	=	PUNCT
ejpam-4522	177	19	(	(	PUNCT
ejpam-4522	177	20	(	(	PUNCT
ejpam-4522	177	21	x∗z)∗	x∗z)∗	PROPN
ejpam-4522	177	22	(	(	PUNCT
ejpam-4522	177	23	y	y	PROPN
ejpam-4522	177	24	∗z))∗z	∗z))∗z	PROPN
ejpam-4522	177	25	≤	≤	PROPN
ejpam-4522	177	26	(	(	PUNCT
ejpam-4522	177	27	x∗y)∗z	x∗y)∗z	NOUN
ejpam-4522	177	28	for	for	ADP
ejpam-4522	177	29	all	all	DET
ejpam-4522	177	30	a	a	DET
ejpam-4522	177	31	,	,	PUNCT
ejpam-4522	177	32	b	b	NOUN
ejpam-4522	177	33	,	,	PUNCT
ejpam-4522	177	34	c	c	PROPN
ejpam-4522	177	35	∈	∈	PROPN
ejpam-4522	177	36	e	e	PROPN
ejpam-4522	177	37	and	and	CCONJ
ejpam-4522	177	38	x	x	PROPN
ejpam-4522	177	39	,	,	PUNCT
ejpam-4522	177	40	y	y	PROPN
ejpam-4522	177	41	,	,	PUNCT
ejpam-4522	177	42	z	z	PROPN
ejpam-4522	177	43	∈	∈	PROPN
ejpam-4522	178	1	x	x	X
ejpam-4522	178	2	,	,	PUNCT
ejpam-4522	178	3	we	we	PRON
ejpam-4522	178	4	have	have	VERB
ejpam-4522	178	5	me((a	me((a	PROPN
ejpam-4522	178	6	↬	↬	PROPN
ejpam-4522	178	7	c	c	PROPN
ejpam-4522	178	8	)	)	PUNCT
ejpam-4522	178	9	↬	↬	NOUN
ejpam-4522	179	1	(	(	PUNCT
ejpam-4522	179	2	b	b	X
ejpam-4522	179	3	↬	↬	PROPN
ejpam-4522	179	4	c	c	NOUN
ejpam-4522	179	5	)	)	PUNCT
ejpam-4522	179	6	)	)	PUNCT
ejpam-4522	180	1	=	=	SYM
ejpam-4522	180	2	me((a	me((a	PROPN
ejpam-4522	180	3	↬	↬	PROPN
ejpam-4522	180	4	(	(	PUNCT
ejpam-4522	180	5	b	b	NOUN
ejpam-4522	180	6	↬	↬	PROPN
ejpam-4522	180	7	c	c	NOUN
ejpam-4522	180	8	)	)	PUNCT
ejpam-4522	180	9	)	)	PUNCT
ejpam-4522	180	10	↬	↬	PROPN
ejpam-4522	180	11	c	c	X
ejpam-4522	180	12	)	)	PUNCT
ejpam-4522	180	13	⊇	⊇	NOUN
ejpam-4522	180	14	me(((a	me(((a	X
ejpam-4522	180	15	↬	↬	X
ejpam-4522	181	1	(	(	PUNCT
ejpam-4522	181	2	b	b	NOUN
ejpam-4522	181	3	↬	↬	PROPN
ejpam-4522	181	4	c	c	NOUN
ejpam-4522	181	5	)	)	PUNCT
ejpam-4522	181	6	)	)	PUNCT
ejpam-4522	181	7	↬	↬	PROPN
ejpam-4522	182	1	c	c	X
ejpam-4522	182	2	)	)	PUNCT
ejpam-4522	182	3	↬	↬	X
ejpam-4522	182	4	c	c	X
ejpam-4522	182	5	)	)	PUNCT
ejpam-4522	182	6	⊇	⊇	PROPN
ejpam-4522	182	7	me((a	me((a	PROPN
ejpam-4522	182	8	↬	↬	PROPN
ejpam-4522	182	9	b	b	X
ejpam-4522	182	10	)	)	PUNCT
ejpam-4522	182	11	↬	↬	PROPN
ejpam-4522	182	12	c	c	NOUN
ejpam-4522	182	13	)	)	PUNCT
ejpam-4522	182	14	,	,	PUNCT
ejpam-4522	182	15	ge((a	ge((a	NOUN
ejpam-4522	182	16	↬	↬	PROPN
ejpam-4522	182	17	c	c	X
ejpam-4522	182	18	)	)	PUNCT
ejpam-4522	182	19	↬	↬	NOUN
ejpam-4522	183	1	(	(	PUNCT
ejpam-4522	183	2	b	b	X
ejpam-4522	183	3	↬	↬	PROPN
ejpam-4522	183	4	c	c	NOUN
ejpam-4522	183	5	)	)	PUNCT
ejpam-4522	183	6	)	)	PUNCT
ejpam-4522	184	1	=	=	PRON
ejpam-4522	184	2	ge((a	ge((a	ADJ
ejpam-4522	184	3	↬	↬	PROPN
ejpam-4522	184	4	(	(	PUNCT
ejpam-4522	184	5	b	b	NOUN
ejpam-4522	184	6	↬	↬	PROPN
ejpam-4522	184	7	c	c	NOUN
ejpam-4522	184	8	)	)	PUNCT
ejpam-4522	184	9	)	)	PUNCT
ejpam-4522	184	10	↬	↬	PROPN
ejpam-4522	184	11	c	c	X
ejpam-4522	184	12	)	)	PUNCT
ejpam-4522	184	13	s.	s.	PROPN
ejpam-4522	184	14	z.	z.	PROPN
ejpam-4522	184	15	song	song	PROPN
ejpam-4522	184	16	,	,	PUNCT
ejpam-4522	184	17	m.	m.	NOUN
ejpam-4522	184	18	a.	a.	NOUN
ejpam-4522	184	19	öztürk	öztürk	PROPN
ejpam-4522	184	20	,	,	PUNCT
ejpam-4522	184	21	y.	y.	PROPN
ejpam-4522	184	22	b.	b.	PROPN
ejpam-4522	184	23	jun	jun	PROPN
ejpam-4522	184	24	/	/	SYM
ejpam-4522	184	25	eur	eur	PROPN
ejpam-4522	184	26	.	.	PUNCT
ejpam-4522	185	1	j.	j.	PROPN
ejpam-4522	185	2	pure	pure	PROPN
ejpam-4522	185	3	appl	appl	PROPN
ejpam-4522	185	4	.	.	PROPN
ejpam-4522	185	5	math	math	PROPN
ejpam-4522	185	6	,	,	PUNCT
ejpam-4522	185	7	15	15	NUM
ejpam-4522	185	8	(	(	PUNCT
ejpam-4522	185	9	4	4	NUM
ejpam-4522	185	10	)	)	PUNCT
ejpam-4522	185	11	(	(	PUNCT
ejpam-4522	185	12	2022	2022	NUM
ejpam-4522	185	13	)	)	PUNCT
ejpam-4522	185	14	,	,	PUNCT
ejpam-4522	185	15	1498	1498	NUM
ejpam-4522	185	16	-	-	SYM
ejpam-4522	185	17	1511	1511	NUM
ejpam-4522	185	18	1505	1505	NUM
ejpam-4522	185	19	⊆	⊆	NUM
ejpam-4522	185	20	ge(((a	ge(((a	NUM
ejpam-4522	185	21	↬	↬	PROPN
ejpam-4522	185	22	(	(	PUNCT
ejpam-4522	185	23	b	b	NOUN
ejpam-4522	185	24	↬	↬	PROPN
ejpam-4522	185	25	c	c	NOUN
ejpam-4522	185	26	)	)	PUNCT
ejpam-4522	185	27	)	)	PUNCT
ejpam-4522	185	28	↬	↬	PROPN
ejpam-4522	186	1	c	c	X
ejpam-4522	186	2	)	)	PUNCT
ejpam-4522	186	3	↬	↬	X
ejpam-4522	186	4	c	c	X
ejpam-4522	186	5	)	)	PUNCT
ejpam-4522	186	6	⊆	⊆	NUM
ejpam-4522	186	7	ge((a	ge((a	NOUN
ejpam-4522	186	8	↬	↬	PROPN
ejpam-4522	186	9	b	b	NOUN
ejpam-4522	186	10	)	)	PUNCT
ejpam-4522	186	11	↬	↬	PROPN
ejpam-4522	186	12	c	c	NOUN
ejpam-4522	186	13	)	)	PUNCT
ejpam-4522	186	14	,	,	PUNCT
ejpam-4522	186	15	and	and	CCONJ
ejpam-4522	186	16	ξ((x	ξ((x	VERB
ejpam-4522	186	17	∗	∗	PROPN
ejpam-4522	186	18	z	z	NOUN
ejpam-4522	186	19	)	)	PUNCT
ejpam-4522	186	20	∗	∗	NOUN
ejpam-4522	186	21	(	(	PUNCT
ejpam-4522	186	22	y	y	PROPN
ejpam-4522	186	23	∗	∗	PROPN
ejpam-4522	186	24	z	z	NOUN
ejpam-4522	186	25	)	)	PUNCT
ejpam-4522	186	26	)	)	PUNCT
ejpam-4522	187	1	=	=	SYM
ejpam-4522	187	2	ξ((x	ξ((x	NOUN
ejpam-4522	187	3	∗	∗	NOUN
ejpam-4522	187	4	(	(	PUNCT
ejpam-4522	187	5	y	y	PROPN
ejpam-4522	187	6	∗	∗	PROPN
ejpam-4522	187	7	z	z	NOUN
ejpam-4522	187	8	)	)	PUNCT
ejpam-4522	187	9	)	)	PUNCT
ejpam-4522	187	10	∗	∗	PROPN
ejpam-4522	187	11	z	z	NOUN
ejpam-4522	187	12	)	)	PUNCT
ejpam-4522	187	13	≥	≥	NOUN
ejpam-4522	187	14	ξ(((x	ξ(((x	PROPN
ejpam-4522	187	15	∗	∗	NOUN
ejpam-4522	187	16	(	(	PUNCT
ejpam-4522	187	17	y	y	PROPN
ejpam-4522	187	18	∗	∗	PROPN
ejpam-4522	187	19	z	z	NOUN
ejpam-4522	187	20	)	)	PUNCT
ejpam-4522	187	21	)	)	PUNCT
ejpam-4522	187	22	∗	∗	PROPN
ejpam-4522	187	23	z	z	NOUN
ejpam-4522	187	24	)	)	PUNCT
ejpam-4522	187	25	∗	∗	NOUN
ejpam-4522	187	26	z	z	NOUN
ejpam-4522	187	27	)	)	PUNCT
ejpam-4522	187	28	≥	≥	NOUN
ejpam-4522	187	29	ξ((x	ξ((x	PROPN
ejpam-4522	187	30	∗	∗	PROPN
ejpam-4522	187	31	y	y	NOUN
ejpam-4522	187	32	)	)	PUNCT
ejpam-4522	187	33	∗	∗	NOUN
ejpam-4522	187	34	z	z	NOUN
ejpam-4522	187	35	)	)	PUNCT
ejpam-4522	187	36	by	by	ADP
ejpam-4522	187	37	(	(	PUNCT
ejpam-4522	187	38	4	4	NUM
ejpam-4522	187	39	)	)	PUNCT
ejpam-4522	187	40	,	,	PUNCT
ejpam-4522	187	41	lemma	lemma	PROPN
ejpam-4522	187	42	1(i	1(i	NUM
ejpam-4522	187	43	)	)	PUNCT
ejpam-4522	187	44	and	and	CCONJ
ejpam-4522	187	45	proposition	proposition	NOUN
ejpam-4522	187	46	1	1	NUM
ejpam-4522	187	47	.	.	PUNCT
ejpam-4522	188	1	hence	hence	ADV
ejpam-4522	188	2	(	(	PUNCT
ejpam-4522	188	3	15	15	NUM
ejpam-4522	188	4	)	)	PUNCT
ejpam-4522	188	5	is	be	AUX
ejpam-4522	188	6	valid	valid	ADJ
ejpam-4522	188	7	.	.	PUNCT
ejpam-4522	189	1	theorem	theorem	ADJ
ejpam-4522	189	2	5	5	NUM
ejpam-4522	189	3	.	.	PUNCT
ejpam-4522	190	1	a	a	DET
ejpam-4522	190	2	makgeolli	makgeolli	NOUN
ejpam-4522	190	3	structure	structure	NOUN
ejpam-4522	190	4	m(x	m(x	PROPN
ejpam-4522	190	5	,	,	PUNCT
ejpam-4522	190	6	e	e	NOUN
ejpam-4522	190	7	)	)	PUNCT
ejpam-4522	190	8	:	:	PUNCT
ejpam-4522	190	9	=	=	SYM
ejpam-4522	190	10	(	(	PUNCT
ejpam-4522	190	11	me	i	PRON
ejpam-4522	190	12	,	,	PUNCT
ejpam-4522	190	13	ge	ge	PROPN
ejpam-4522	190	14	,	,	PUNCT
ejpam-4522	190	15	ξ	ξ	PROPN
ejpam-4522	190	16	)	)	PUNCT
ejpam-4522	190	17	on	on	ADP
ejpam-4522	190	18	(	(	PUNCT
ejpam-4522	190	19	x	x	X
ejpam-4522	190	20	,	,	PUNCT
ejpam-4522	190	21	e	e	NOUN
ejpam-4522	190	22	)	)	PUNCT
ejpam-4522	190	23	is	be	AUX
ejpam-4522	190	24	a	a	DET
ejpam-4522	190	25	positive	positive	ADJ
ejpam-4522	190	26	implicative	implicative	ADJ
ejpam-4522	190	27	makgeolli	makgeolli	NOUN
ejpam-4522	190	28	ideal	ideal	NOUN
ejpam-4522	190	29	of	of	ADP
ejpam-4522	190	30	(	(	PUNCT
ejpam-4522	190	31	x	x	X
ejpam-4522	190	32	,	,	PUNCT
ejpam-4522	190	33	e	e	NOUN
ejpam-4522	190	34	)	)	PUNCT
ejpam-4522	191	1	if	if	SCONJ
ejpam-4522	192	1	and	and	CCONJ
ejpam-4522	192	2	only	only	ADV
ejpam-4522	192	3	if	if	SCONJ
ejpam-4522	192	4	it	it	PRON
ejpam-4522	192	5	satisfies	satisfy	VERB
ejpam-4522	192	6	(	(	PUNCT
ejpam-4522	192	7	9	9	NUM
ejpam-4522	192	8	)	)	PUNCT
ejpam-4522	192	9	and	and	NOUN
ejpam-4522	192	10	(	(	PUNCT
ejpam-4522	192	11	∀a	∀a	X
ejpam-4522	192	12	,	,	PUNCT
ejpam-4522	192	13	b	b	NOUN
ejpam-4522	192	14	,	,	PUNCT
ejpam-4522	192	15	c	c	PROPN
ejpam-4522	192	16	∈	∈	PROPN
ejpam-4522	192	17	e	e	X
ejpam-4522	192	18	)	)	PUNCT
ejpam-4522	192	19	(	(	PUNCT
ejpam-4522	192	20	me(a	me(a	X
ejpam-4522	192	21	↬	↬	PROPN
ejpam-4522	192	22	b	b	X
ejpam-4522	192	23	)	)	PUNCT
ejpam-4522	192	24	⊇	⊇	NOUN
ejpam-4522	192	25	me(((a	me(((a	PROPN
ejpam-4522	192	26	↬	↬	PROPN
ejpam-4522	192	27	b	b	X
ejpam-4522	192	28	)	)	PUNCT
ejpam-4522	192	29	↬	↬	PROPN
ejpam-4522	192	30	b	b	X
ejpam-4522	192	31	)	)	PUNCT
ejpam-4522	192	32	↬	↬	X
ejpam-4522	192	33	c	c	X
ejpam-4522	192	34	)	)	PUNCT
ejpam-4522	192	35	∩me(c	∩me(c	PROPN
ejpam-4522	192	36	)	)	PUNCT
ejpam-4522	192	37	ge(a	ge(a	PUNCT
ejpam-4522	192	38	↬	↬	PROPN
ejpam-4522	192	39	b	b	X
ejpam-4522	192	40	)	)	PUNCT
ejpam-4522	192	41	⊆	⊆	NUM
ejpam-4522	192	42	ge(((a	ge(((a	NUM
ejpam-4522	192	43	↬	↬	PROPN
ejpam-4522	192	44	b	b	NOUN
ejpam-4522	192	45	)	)	PUNCT
ejpam-4522	192	46	↬	↬	PROPN
ejpam-4522	192	47	b	b	X
ejpam-4522	192	48	)	)	PUNCT
ejpam-4522	192	49	↬	↬	PROPN
ejpam-4522	192	50	c	c	X
ejpam-4522	192	51	)	)	PUNCT
ejpam-4522	192	52	∪ge(c	∪ge(c	NUM
ejpam-4522	192	53	)	)	PUNCT
ejpam-4522	192	54	)	)	PUNCT
ejpam-4522	192	55	,	,	PUNCT
ejpam-4522	192	56	(	(	PUNCT
ejpam-4522	192	57	∀x	∀x	X
ejpam-4522	192	58	,	,	PUNCT
ejpam-4522	192	59	y	y	PROPN
ejpam-4522	192	60	,	,	PUNCT
ejpam-4522	192	61	z	z	NOUN
ejpam-4522	192	62	∈	∈	PROPN
ejpam-4522	192	63	x	x	X
ejpam-4522	192	64	)	)	PUNCT
ejpam-4522	192	65	(	(	PUNCT
ejpam-4522	192	66	ξ(x	ξ(x	NOUN
ejpam-4522	192	67	∗	∗	NOUN
ejpam-4522	192	68	y	y	NOUN
ejpam-4522	192	69	)	)	PUNCT
ejpam-4522	192	70	≥	≥	NOUN
ejpam-4522	192	71	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	192	72	∗	∗	PROPN
ejpam-4522	192	73	y	y	PROPN
ejpam-4522	192	74	)	)	PUNCT
ejpam-4522	192	75	∗	∗	PROPN
ejpam-4522	192	76	y	y	NOUN
ejpam-4522	192	77	)	)	PUNCT
ejpam-4522	192	78	∗	∗	NOUN
ejpam-4522	192	79	z	z	NOUN
ejpam-4522	192	80	)	)	PUNCT
ejpam-4522	192	81	,	,	PUNCT
ejpam-4522	192	82	ξ(z	ξ(z	PROPN
ejpam-4522	192	83	)	)	PUNCT
ejpam-4522	192	84	}	}	PUNCT
ejpam-4522	192	85	)	)	PUNCT
ejpam-4522	192	86	.	.	PUNCT
ejpam-4522	193	1	(	(	PUNCT
ejpam-4522	193	2	16	16	X
ejpam-4522	193	3	)	)	PUNCT
ejpam-4522	193	4	proof	proof	NOUN
ejpam-4522	193	5	.	.	PUNCT
ejpam-4522	194	1	let	let	VERB
ejpam-4522	194	2	m(x	m(x	PROPN
ejpam-4522	194	3	,	,	PUNCT
ejpam-4522	194	4	e	e	NOUN
ejpam-4522	194	5	)	)	PUNCT
ejpam-4522	194	6	:	:	PUNCT
ejpam-4522	195	1	=	=	SYM
ejpam-4522	195	2	(	(	PUNCT
ejpam-4522	195	3	me	i	PRON
ejpam-4522	195	4	,	,	PUNCT
ejpam-4522	195	5	ge	ge	PROPN
ejpam-4522	195	6	,	,	PUNCT
ejpam-4522	195	7	ξ	ξ	X
ejpam-4522	195	8	)	)	PUNCT
ejpam-4522	195	9	be	be	VERB
ejpam-4522	195	10	a	a	DET
ejpam-4522	195	11	positive	positive	ADJ
ejpam-4522	195	12	implicative	implicative	ADJ
ejpam-4522	195	13	makgeolli	makgeolli	NOUN
ejpam-4522	195	14	ideal	ideal	NOUN
ejpam-4522	195	15	of	of	ADP
ejpam-4522	195	16	(	(	PUNCT
ejpam-4522	195	17	x	x	X
ejpam-4522	195	18	,	,	PUNCT
ejpam-4522	195	19	e	e	NOUN
ejpam-4522	195	20	)	)	PUNCT
ejpam-4522	195	21	.	.	PUNCT
ejpam-4522	196	1	then	then	ADV
ejpam-4522	196	2	it	it	PRON
ejpam-4522	196	3	is	be	AUX
ejpam-4522	196	4	a	a	DET
ejpam-4522	196	5	makgeolli	makgeolli	NOUN
ejpam-4522	196	6	ideal	ideal	NOUN
ejpam-4522	196	7	of	of	ADP
ejpam-4522	196	8	(	(	PUNCT
ejpam-4522	196	9	x	x	X
ejpam-4522	196	10	,	,	PUNCT
ejpam-4522	196	11	e	e	NOUN
ejpam-4522	196	12	)	)	PUNCT
ejpam-4522	196	13	by	by	ADP
ejpam-4522	196	14	theorem	theorem	NOUN
ejpam-4522	196	15	1	1	NUM
ejpam-4522	196	16	,	,	PUNCT
ejpam-4522	196	17	and	and	CCONJ
ejpam-4522	196	18	so	so	ADV
ejpam-4522	196	19	the	the	DET
ejpam-4522	196	20	condition	condition	NOUN
ejpam-4522	196	21	(	(	PUNCT
ejpam-4522	196	22	9	9	NUM
ejpam-4522	196	23	)	)	PUNCT
ejpam-4522	196	24	is	be	AUX
ejpam-4522	196	25	valid	valid	ADJ
ejpam-4522	196	26	.	.	PUNCT
ejpam-4522	197	1	using	use	VERB
ejpam-4522	197	2	(	(	PUNCT
ejpam-4522	197	3	i3	i3	NOUN
ejpam-4522	197	4	)	)	PUNCT
ejpam-4522	197	5	,	,	PUNCT
ejpam-4522	197	6	(	(	PUNCT
ejpam-4522	197	7	2	2	NUM
ejpam-4522	197	8	)	)	PUNCT
ejpam-4522	197	9	,	,	PUNCT
ejpam-4522	197	10	(	(	PUNCT
ejpam-4522	197	11	4	4	NUM
ejpam-4522	197	12	)	)	PUNCT
ejpam-4522	197	13	,	,	PUNCT
ejpam-4522	197	14	(	(	PUNCT
ejpam-4522	197	15	10	10	NUM
ejpam-4522	197	16	)	)	PUNCT
ejpam-4522	197	17	and	and	CCONJ
ejpam-4522	197	18	(	(	PUNCT
ejpam-4522	197	19	15	15	NUM
ejpam-4522	197	20	)	)	PUNCT
ejpam-4522	197	21	,	,	PUNCT
ejpam-4522	197	22	we	we	PRON
ejpam-4522	197	23	get	get	VERB
ejpam-4522	197	24	me(a	me(a	DET
ejpam-4522	197	25	↬	↬	PROPN
ejpam-4522	197	26	b	b	X
ejpam-4522	197	27	)	)	PUNCT
ejpam-4522	197	28	⊇	⊇	PROPN
ejpam-4522	197	29	me((a	me((a	PROPN
ejpam-4522	197	30	↬	↬	PROPN
ejpam-4522	197	31	b	b	X
ejpam-4522	197	32	)	)	PUNCT
ejpam-4522	197	33	↬	↬	X
ejpam-4522	197	34	c	c	X
ejpam-4522	197	35	)	)	PUNCT
ejpam-4522	197	36	∩me(c	∩me(c	PROPN
ejpam-4522	197	37	)	)	PUNCT
ejpam-4522	197	38	=	=	PUNCT
ejpam-4522	198	1	me(((a	me(((a	NOUN
ejpam-4522	198	2	↬	↬	X
ejpam-4522	198	3	c	c	X
ejpam-4522	198	4	)	)	PUNCT
ejpam-4522	198	5	↬	↬	PROPN
ejpam-4522	198	6	b	b	X
ejpam-4522	198	7	)	)	PUNCT
ejpam-4522	198	8	↬	↬	PROPN
ejpam-4522	199	1	(	(	PUNCT
ejpam-4522	199	2	b	b	PROPN
ejpam-4522	199	3	↬	↬	PROPN
ejpam-4522	199	4	b	b	NOUN
ejpam-4522	199	5	)	)	PUNCT
ejpam-4522	199	6	)	)	PUNCT
ejpam-4522	199	7	∩me(c	∩me(c	PROPN
ejpam-4522	199	8	)	)	PUNCT
ejpam-4522	199	9	⊇	⊇	NOUN
ejpam-4522	199	10	me(((a	me(((a	X
ejpam-4522	199	11	↬	↬	X
ejpam-4522	199	12	c	c	X
ejpam-4522	199	13	)	)	PUNCT
ejpam-4522	199	14	↬	↬	PROPN
ejpam-4522	199	15	b	b	X
ejpam-4522	199	16	)	)	PUNCT
ejpam-4522	199	17	↬	↬	PROPN
ejpam-4522	199	18	b	b	X
ejpam-4522	199	19	)	)	PUNCT
ejpam-4522	199	20	∩me(c	∩me(c	PROPN
ejpam-4522	199	21	)	)	PUNCT
ejpam-4522	199	22	=	=	PUNCT
ejpam-4522	200	1	me(((a	me(((a	NOUN
ejpam-4522	200	2	↬	↬	PROPN
ejpam-4522	200	3	b	b	X
ejpam-4522	200	4	)	)	PUNCT
ejpam-4522	200	5	↬	↬	PROPN
ejpam-4522	200	6	b	b	X
ejpam-4522	200	7	)	)	PUNCT
ejpam-4522	200	8	↬	↬	X
ejpam-4522	200	9	c	c	X
ejpam-4522	200	10	)	)	PUNCT
ejpam-4522	200	11	∩me(c	∩me(c	PROPN
ejpam-4522	200	12	)	)	PUNCT
ejpam-4522	200	13	,	,	PUNCT
ejpam-4522	200	14	ge(a	ge(a	PRON
ejpam-4522	200	15	↬	↬	PROPN
ejpam-4522	200	16	b	b	X
ejpam-4522	200	17	)	)	PUNCT
ejpam-4522	200	18	⊆	⊆	NUM
ejpam-4522	200	19	ge((a	ge((a	NOUN
ejpam-4522	200	20	↬	↬	PROPN
ejpam-4522	200	21	b	b	X
ejpam-4522	200	22	)	)	PUNCT
ejpam-4522	200	23	↬	↬	X
ejpam-4522	200	24	c	c	X
ejpam-4522	200	25	)	)	PUNCT
ejpam-4522	200	26	∪me(c	∪me(c	ADV
ejpam-4522	200	27	)	)	PUNCT
ejpam-4522	200	28	=	=	SYM
ejpam-4522	201	1	ge(((a	ge(((a	PROPN
ejpam-4522	201	2	↬	↬	NUM
ejpam-4522	201	3	c	c	NOUN
ejpam-4522	201	4	)	)	PUNCT
ejpam-4522	201	5	↬	↬	PROPN
ejpam-4522	201	6	b	b	X
ejpam-4522	201	7	)	)	PUNCT
ejpam-4522	201	8	↬	↬	PROPN
ejpam-4522	201	9	(	(	PUNCT
ejpam-4522	201	10	b	b	PROPN
ejpam-4522	201	11	↬	↬	PROPN
ejpam-4522	201	12	b	b	NOUN
ejpam-4522	201	13	)	)	PUNCT
ejpam-4522	201	14	)	)	PUNCT
ejpam-4522	202	1	∪ge(c	∪ge(c	CCONJ
ejpam-4522	202	2	)	)	PUNCT
ejpam-4522	202	3	⊆	⊆	NUM
ejpam-4522	202	4	ge(((a	ge(((a	NUM
ejpam-4522	202	5	↬	↬	PROPN
ejpam-4522	202	6	c	c	NOUN
ejpam-4522	202	7	)	)	PUNCT
ejpam-4522	202	8	↬	↬	PROPN
ejpam-4522	203	1	b	b	X
ejpam-4522	203	2	)	)	PUNCT
ejpam-4522	203	3	↬	↬	PROPN
ejpam-4522	203	4	b	b	X
ejpam-4522	203	5	)	)	PUNCT
ejpam-4522	203	6	∪ge(c	∪ge(c	NUM
ejpam-4522	203	7	)	)	PUNCT
ejpam-4522	203	8	=	=	SYM
ejpam-4522	203	9	ge(((a	ge(((a	PROPN
ejpam-4522	203	10	↬	↬	PROPN
ejpam-4522	203	11	b	b	X
ejpam-4522	203	12	)	)	PUNCT
ejpam-4522	203	13	↬	↬	PROPN
ejpam-4522	203	14	b	b	X
ejpam-4522	203	15	)	)	PUNCT
ejpam-4522	203	16	↬	↬	PROPN
ejpam-4522	203	17	c	c	X
ejpam-4522	203	18	)	)	PUNCT
ejpam-4522	203	19	∪ge(c	∪ge(c	NUM
ejpam-4522	203	20	)	)	PUNCT
ejpam-4522	203	21	and	and	CCONJ
ejpam-4522	203	22	ξ(x	ξ(x	PROPN
ejpam-4522	203	23	∗	∗	X
ejpam-4522	203	24	y	y	PROPN
ejpam-4522	203	25	)	)	PUNCT
ejpam-4522	203	26	≥	≥	NOUN
ejpam-4522	203	27	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	203	28	∗	∗	X
ejpam-4522	203	29	y	y	NOUN
ejpam-4522	203	30	)	)	PUNCT
ejpam-4522	203	31	∗	∗	NOUN
ejpam-4522	203	32	z	z	NOUN
ejpam-4522	203	33	)	)	PUNCT
ejpam-4522	203	34	,	,	PUNCT
ejpam-4522	203	35	ξ(z	ξ(z	PROPN
ejpam-4522	203	36	)	)	PUNCT
ejpam-4522	203	37	}	}	PUNCT
ejpam-4522	203	38	=	=	SYM
ejpam-4522	203	39	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	203	40	∗	∗	NOUN
ejpam-4522	203	41	z	z	NOUN
ejpam-4522	203	42	)	)	PUNCT
ejpam-4522	203	43	∗	∗	PROPN
ejpam-4522	203	44	y	y	NOUN
ejpam-4522	203	45	)	)	PUNCT
ejpam-4522	203	46	∗	∗	NOUN
ejpam-4522	203	47	(	(	PUNCT
ejpam-4522	203	48	y	y	PROPN
ejpam-4522	203	49	∗	∗	PROPN
ejpam-4522	203	50	y	y	PROPN
ejpam-4522	203	51	)	)	PUNCT
ejpam-4522	203	52	)	)	PUNCT
ejpam-4522	203	53	,	,	PUNCT
ejpam-4522	203	54	ξ(z	ξ(z	PROPN
ejpam-4522	203	55	)	)	PUNCT
ejpam-4522	203	56	}	}	PUNCT
ejpam-4522	203	57	≥	≥	NOUN
ejpam-4522	203	58	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	203	59	∗	∗	NOUN
ejpam-4522	203	60	z	z	NOUN
ejpam-4522	203	61	)	)	PUNCT
ejpam-4522	203	62	∗	∗	PROPN
ejpam-4522	203	63	y	y	PROPN
ejpam-4522	203	64	)	)	PUNCT
ejpam-4522	203	65	∗	∗	PROPN
ejpam-4522	203	66	y	y	PROPN
ejpam-4522	203	67	)	)	PUNCT
ejpam-4522	203	68	,	,	PUNCT
ejpam-4522	203	69	ξ(z	ξ(z	PROPN
ejpam-4522	203	70	)	)	PUNCT
ejpam-4522	203	71	}	}	PUNCT
ejpam-4522	203	72	=	=	SYM
ejpam-4522	203	73	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	203	74	∗	∗	NOUN
ejpam-4522	203	75	y	y	NOUN
ejpam-4522	203	76	)	)	PUNCT
ejpam-4522	203	77	∗	∗	PROPN
ejpam-4522	203	78	y	y	NOUN
ejpam-4522	203	79	)	)	PUNCT
ejpam-4522	203	80	∗	∗	NOUN
ejpam-4522	203	81	z	z	NOUN
ejpam-4522	203	82	)	)	PUNCT
ejpam-4522	203	83	,	,	PUNCT
ejpam-4522	203	84	ξ(z	ξ(z	PROPN
ejpam-4522	203	85	)	)	PUNCT
ejpam-4522	203	86	}	}	PUNCT
ejpam-4522	203	87	for	for	ADP
ejpam-4522	203	88	all	all	DET
ejpam-4522	203	89	a	a	DET
ejpam-4522	203	90	,	,	PUNCT
ejpam-4522	203	91	b	b	NOUN
ejpam-4522	203	92	,	,	PUNCT
ejpam-4522	203	93	c	c	PROPN
ejpam-4522	203	94	∈	∈	PROPN
ejpam-4522	203	95	e	e	PROPN
ejpam-4522	203	96	and	and	CCONJ
ejpam-4522	203	97	x	x	PROPN
ejpam-4522	203	98	,	,	PUNCT
ejpam-4522	203	99	y	y	PROPN
ejpam-4522	203	100	,	,	PUNCT
ejpam-4522	203	101	z	z	PROPN
ejpam-4522	203	102	∈	∈	PROPN
ejpam-4522	203	103	x.	x.	NOUN
ejpam-4522	204	1	therefore	therefore	ADV
ejpam-4522	204	2	(	(	PUNCT
ejpam-4522	204	3	16	16	NUM
ejpam-4522	204	4	)	)	PUNCT
ejpam-4522	204	5	is	be	AUX
ejpam-4522	204	6	valid	valid	ADJ
ejpam-4522	204	7	.	.	PUNCT
ejpam-4522	205	1	conversely	conversely	ADV
ejpam-4522	205	2	,	,	PUNCT
ejpam-4522	205	3	assume	assume	VERB
ejpam-4522	205	4	that	that	SCONJ
ejpam-4522	205	5	m(x	m(x	PROPN
ejpam-4522	205	6	,	,	PUNCT
ejpam-4522	205	7	e	e	NOUN
ejpam-4522	205	8	)	)	PUNCT
ejpam-4522	205	9	:	:	PUNCT
ejpam-4522	206	1	=	=	SYM
ejpam-4522	206	2	(	(	PUNCT
ejpam-4522	206	3	me	i	PRON
ejpam-4522	206	4	,	,	PUNCT
ejpam-4522	206	5	ge	ge	PROPN
ejpam-4522	206	6	,	,	PUNCT
ejpam-4522	206	7	ξ	ξ	X
ejpam-4522	206	8	)	)	PUNCT
ejpam-4522	206	9	satisfies	satisfie	NOUN
ejpam-4522	206	10	(	(	PUNCT
ejpam-4522	206	11	9	9	NUM
ejpam-4522	206	12	)	)	PUNCT
ejpam-4522	206	13	and	and	CCONJ
ejpam-4522	206	14	(	(	PUNCT
ejpam-4522	206	15	16	16	NUM
ejpam-4522	206	16	)	)	PUNCT
ejpam-4522	206	17	.	.	PUNCT
ejpam-4522	207	1	then	then	ADV
ejpam-4522	207	2	me(a	me(a	NOUN
ejpam-4522	207	3	)	)	PUNCT
ejpam-4522	207	4	=	=	NOUN
ejpam-4522	207	5	me(a	me(a	X
ejpam-4522	207	6	↬	↬	PROPN
ejpam-4522	207	7	0	0	NUM
ejpam-4522	207	8	)	)	PUNCT
ejpam-4522	207	9	⊇	⊇	NOUN
ejpam-4522	207	10	me(((a	me(((a	X
ejpam-4522	207	11	↬	↬	X
ejpam-4522	207	12	0	0	NUM
ejpam-4522	207	13	)	)	PUNCT
ejpam-4522	207	14	↬	↬	NOUN
ejpam-4522	207	15	0	0	NUM
ejpam-4522	207	16	)	)	PUNCT
ejpam-4522	207	17	↬	↬	X
ejpam-4522	207	18	c	c	X
ejpam-4522	207	19	)	)	PUNCT
ejpam-4522	207	20	∩me(c	∩me(c	PROPN
ejpam-4522	207	21	)	)	PUNCT
ejpam-4522	208	1	=	=	NOUN
ejpam-4522	208	2	me(a	me(a	X
ejpam-4522	208	3	↬	↬	PROPN
ejpam-4522	208	4	c	c	X
ejpam-4522	208	5	)	)	PUNCT
ejpam-4522	208	6	∩me(c	∩me(c	PROPN
ejpam-4522	208	7	)	)	PUNCT
ejpam-4522	208	8	,	,	PUNCT
ejpam-4522	208	9	ge(a	ge(a	NOUN
ejpam-4522	208	10	)	)	PUNCT
ejpam-4522	208	11	=	=	NOUN
ejpam-4522	208	12	ge(a	ge(a	PRON
ejpam-4522	208	13	↬	↬	PROPN
ejpam-4522	208	14	0	0	NUM
ejpam-4522	208	15	)	)	PUNCT
ejpam-4522	208	16	⊆	⊆	NUM
ejpam-4522	208	17	ge(((a	ge(((a	NUM
ejpam-4522	208	18	↬	↬	PROPN
ejpam-4522	208	19	0	0	NUM
ejpam-4522	208	20	)	)	PUNCT
ejpam-4522	208	21	↬	↬	NOUN
ejpam-4522	208	22	0	0	NUM
ejpam-4522	208	23	)	)	PUNCT
ejpam-4522	208	24	↬	↬	X
ejpam-4522	208	25	c	c	X
ejpam-4522	208	26	)	)	PUNCT
ejpam-4522	208	27	∪ge(c	∪ge(c	NUM
ejpam-4522	208	28	)	)	PUNCT
ejpam-4522	209	1	=	=	NOUN
ejpam-4522	209	2	ge(a	ge(a	NOUN
ejpam-4522	209	3	↬	↬	PROPN
ejpam-4522	209	4	c	c	X
ejpam-4522	209	5	)	)	PUNCT
ejpam-4522	209	6	∪ge(c	∪ge(c	NUM
ejpam-4522	209	7	)	)	PUNCT
ejpam-4522	209	8	,	,	PUNCT
ejpam-4522	209	9	and	and	CCONJ
ejpam-4522	209	10	ξ(x	ξ(x	NOUN
ejpam-4522	209	11	)	)	PUNCT
ejpam-4522	209	12	=	=	SYM
ejpam-4522	209	13	ξ(x	ξ(x	NOUN
ejpam-4522	209	14	∗	∗	NOUN
ejpam-4522	209	15	0	0	NUM
ejpam-4522	209	16	)	)	PUNCT
ejpam-4522	209	17	≥	≥	NOUN
ejpam-4522	209	18	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	209	19	∗	∗	NOUN
ejpam-4522	209	20	0	0	NUM
ejpam-4522	209	21	)	)	PUNCT
ejpam-4522	209	22	∗	∗	NOUN
ejpam-4522	209	23	0	0	NUM
ejpam-4522	209	24	)	)	PUNCT
ejpam-4522	209	25	∗	∗	NOUN
ejpam-4522	209	26	z	z	NOUN
ejpam-4522	209	27	)	)	PUNCT
ejpam-4522	209	28	,	,	PUNCT
ejpam-4522	209	29	ξ(z	ξ(z	PROPN
ejpam-4522	209	30	)	)	PUNCT
ejpam-4522	209	31	}	}	PUNCT
ejpam-4522	209	32	=	=	SYM
ejpam-4522	209	33	min{ξ(x	min{ξ(x	PROPN
ejpam-4522	209	34	∗	∗	NOUN
ejpam-4522	209	35	z	z	NOUN
ejpam-4522	209	36	)	)	PUNCT
ejpam-4522	209	37	,	,	PUNCT
ejpam-4522	209	38	ξ(z	ξ(z	PROPN
ejpam-4522	209	39	)	)	PUNCT
ejpam-4522	209	40	}	}	PUNCT
ejpam-4522	209	41	for	for	ADP
ejpam-4522	209	42	all	all	DET
ejpam-4522	209	43	a	a	PRON
ejpam-4522	209	44	,	,	PUNCT
ejpam-4522	209	45	c	c	PROPN
ejpam-4522	209	46	∈	∈	PROPN
ejpam-4522	209	47	e	e	PROPN
ejpam-4522	209	48	and	and	CCONJ
ejpam-4522	209	49	x	x	NOUN
ejpam-4522	209	50	,	,	PUNCT
ejpam-4522	209	51	z	z	PROPN
ejpam-4522	209	52	∈	∈	NOUN
ejpam-4522	209	53	x.	x.	NOUN
ejpam-4522	209	54	hence	hence	ADV
ejpam-4522	209	55	m(x	m(x	PROPN
ejpam-4522	209	56	,	,	PUNCT
ejpam-4522	209	57	e	e	NOUN
ejpam-4522	209	58	)	)	PUNCT
ejpam-4522	209	59	:	:	PUNCT
ejpam-4522	209	60	=	=	SYM
ejpam-4522	209	61	(	(	PUNCT
ejpam-4522	209	62	me	i	PRON
ejpam-4522	209	63	,	,	PUNCT
ejpam-4522	209	64	ge	ge	PROPN
ejpam-4522	209	65	,	,	PUNCT
ejpam-4522	209	66	ξ	ξ	X
ejpam-4522	209	67	)	)	PUNCT
ejpam-4522	209	68	is	be	AUX
ejpam-4522	209	69	a	a	DET
ejpam-4522	209	70	makgeolli	makgeolli	NOUN
ejpam-4522	209	71	ideal	ideal	NOUN
ejpam-4522	209	72	of	of	ADP
ejpam-4522	209	73	(	(	PUNCT
ejpam-4522	209	74	x	x	X
ejpam-4522	209	75	,	,	PUNCT
ejpam-4522	209	76	e	e	NOUN
ejpam-4522	209	77	)	)	PUNCT
ejpam-4522	209	78	.	.	PUNCT
ejpam-4522	210	1	if	if	SCONJ
ejpam-4522	210	2	we	we	PRON
ejpam-4522	210	3	put	put	VERB
ejpam-4522	210	4	c	c	NOUN
ejpam-4522	210	5	=	=	SYM
ejpam-4522	210	6	0	0	PUNCT
ejpam-4522	211	1	=	=	SYM
ejpam-4522	211	2	z	z	NOUN
ejpam-4522	211	3	in	in	ADP
ejpam-4522	211	4	(	(	PUNCT
ejpam-4522	211	5	16	16	NUM
ejpam-4522	211	6	)	)	PUNCT
ejpam-4522	211	7	and	and	CCONJ
ejpam-4522	211	8	use	use	NOUN
ejpam-4522	211	9	(	(	PUNCT
ejpam-4522	211	10	2	2	NUM
ejpam-4522	211	11	)	)	PUNCT
ejpam-4522	211	12	,	,	PUNCT
ejpam-4522	211	13	then	then	ADV
ejpam-4522	211	14	me(a	me(a	NUM
ejpam-4522	211	15	↬	↬	PROPN
ejpam-4522	211	16	b	b	X
ejpam-4522	211	17	)	)	PUNCT
ejpam-4522	211	18	⊇	⊇	NOUN
ejpam-4522	211	19	me(((a	me(((a	PROPN
ejpam-4522	211	20	↬	↬	PROPN
ejpam-4522	211	21	b	b	X
ejpam-4522	211	22	)	)	PUNCT
ejpam-4522	211	23	↬	↬	PROPN
ejpam-4522	211	24	b	b	X
ejpam-4522	211	25	)	)	PUNCT
ejpam-4522	211	26	↬	↬	PROPN
ejpam-4522	211	27	0	0	NUM
ejpam-4522	211	28	)	)	PUNCT
ejpam-4522	211	29	∩me(0	∩me(0	PROPN
ejpam-4522	211	30	)	)	PUNCT
ejpam-4522	211	31	s.	s.	PROPN
ejpam-4522	211	32	z.	z.	PROPN
ejpam-4522	211	33	song	song	PROPN
ejpam-4522	211	34	,	,	PUNCT
ejpam-4522	211	35	m.	m.	NOUN
ejpam-4522	211	36	a.	a.	NOUN
ejpam-4522	211	37	öztürk	öztürk	PROPN
ejpam-4522	211	38	,	,	PUNCT
ejpam-4522	211	39	y.	y.	PROPN
ejpam-4522	211	40	b.	b.	PROPN
ejpam-4522	211	41	jun	jun	PROPN
ejpam-4522	211	42	/	/	SYM
ejpam-4522	211	43	eur	eur	PROPN
ejpam-4522	211	44	.	.	PUNCT
ejpam-4522	212	1	j.	j.	PROPN
ejpam-4522	212	2	pure	pure	PROPN
ejpam-4522	212	3	appl	appl	PROPN
ejpam-4522	212	4	.	.	PROPN
ejpam-4522	212	5	math	math	PROPN
ejpam-4522	212	6	,	,	PUNCT
ejpam-4522	212	7	15	15	NUM
ejpam-4522	212	8	(	(	PUNCT
ejpam-4522	212	9	4	4	NUM
ejpam-4522	212	10	)	)	PUNCT
ejpam-4522	212	11	(	(	PUNCT
ejpam-4522	212	12	2022	2022	NUM
ejpam-4522	212	13	)	)	PUNCT
ejpam-4522	212	14	,	,	PUNCT
ejpam-4522	212	15	1498	1498	NUM
ejpam-4522	212	16	-	-	SYM
ejpam-4522	212	17	1511	1511	NUM
ejpam-4522	212	18	1506	1506	NUM
ejpam-4522	212	19	=	=	SYM
ejpam-4522	212	20	me((a	me((a	PROPN
ejpam-4522	212	21	↬	↬	PROPN
ejpam-4522	212	22	b	b	X
ejpam-4522	212	23	)	)	PUNCT
ejpam-4522	212	24	↬	↬	PROPN
ejpam-4522	212	25	b	b	X
ejpam-4522	212	26	)	)	PUNCT
ejpam-4522	212	27	∩me(0	∩me(0	NOUN
ejpam-4522	212	28	)	)	PUNCT
ejpam-4522	212	29	=	=	SYM
ejpam-4522	212	30	me((a	me((a	PROPN
ejpam-4522	212	31	↬	↬	PROPN
ejpam-4522	212	32	b	b	X
ejpam-4522	212	33	)	)	PUNCT
ejpam-4522	212	34	↬	↬	PROPN
ejpam-4522	212	35	b	b	X
ejpam-4522	212	36	)	)	PUNCT
ejpam-4522	212	37	,	,	PUNCT
ejpam-4522	212	38	ge(a	ge(a	PRON
ejpam-4522	212	39	↬	↬	PROPN
ejpam-4522	212	40	b	b	X
ejpam-4522	212	41	)	)	PUNCT
ejpam-4522	212	42	⊆	⊆	NUM
ejpam-4522	212	43	ge(((a	ge(((a	NUM
ejpam-4522	212	44	↬	↬	PROPN
ejpam-4522	212	45	b	b	NOUN
ejpam-4522	212	46	)	)	PUNCT
ejpam-4522	212	47	↬	↬	PROPN
ejpam-4522	212	48	b	b	X
ejpam-4522	212	49	)	)	PUNCT
ejpam-4522	212	50	↬	↬	PROPN
ejpam-4522	212	51	0	0	NUM
ejpam-4522	212	52	)	)	PUNCT
ejpam-4522	212	53	∪ge(0	∪ge(0	PROPN
ejpam-4522	212	54	)	)	PUNCT
ejpam-4522	212	55	=	=	SYM
ejpam-4522	213	1	ge((a	ge((a	NOUN
ejpam-4522	213	2	↬	↬	PROPN
ejpam-4522	213	3	b	b	X
ejpam-4522	213	4	)	)	PUNCT
ejpam-4522	213	5	↬	↬	PROPN
ejpam-4522	213	6	b	b	X
ejpam-4522	213	7	)	)	PUNCT
ejpam-4522	213	8	∪ge(0	∪ge(0	PROPN
ejpam-4522	213	9	)	)	PUNCT
ejpam-4522	213	10	=	=	SYM
ejpam-4522	214	1	ge((a	ge((a	NOUN
ejpam-4522	214	2	↬	↬	PROPN
ejpam-4522	214	3	b	b	X
ejpam-4522	214	4	)	)	PUNCT
ejpam-4522	214	5	↬	↬	PROPN
ejpam-4522	214	6	b	b	X
ejpam-4522	214	7	)	)	PUNCT
ejpam-4522	214	8	and	and	CCONJ
ejpam-4522	214	9	ξ(x	ξ(x	PROPN
ejpam-4522	214	10	∗	∗	X
ejpam-4522	214	11	y	y	PROPN
ejpam-4522	214	12	)	)	PUNCT
ejpam-4522	214	13	≥	≥	NOUN
ejpam-4522	214	14	min{ξ(((x	min{ξ(((x	NOUN
ejpam-4522	214	15	∗	∗	PROPN
ejpam-4522	214	16	y	y	PROPN
ejpam-4522	214	17	)	)	PUNCT
ejpam-4522	214	18	∗	∗	PROPN
ejpam-4522	214	19	y	y	PROPN
ejpam-4522	214	20	)	)	PUNCT
ejpam-4522	214	21	∗	∗	NOUN
ejpam-4522	214	22	0	0	NUM
ejpam-4522	214	23	)	)	PUNCT
ejpam-4522	214	24	,	,	PUNCT
ejpam-4522	214	25	ξ(0	ξ(0	NOUN
ejpam-4522	214	26	)	)	PUNCT
ejpam-4522	214	27	}	}	PUNCT
ejpam-4522	214	28	=	=	SYM
ejpam-4522	214	29	min{ξ((x	min{ξ((x	X
ejpam-4522	214	30	∗	∗	X
ejpam-4522	214	31	y	y	NOUN
ejpam-4522	214	32	)	)	PUNCT
ejpam-4522	214	33	∗	∗	PROPN
ejpam-4522	214	34	y	y	PROPN
ejpam-4522	214	35	)	)	PUNCT
ejpam-4522	214	36	,	,	PUNCT
ejpam-4522	214	37	ξ(0	ξ(0	NOUN
ejpam-4522	214	38	)	)	PUNCT
ejpam-4522	214	39	}	}	PUNCT
ejpam-4522	214	40	=	=	SYM
ejpam-4522	214	41	ξ((x	ξ((x	NOUN
ejpam-4522	214	42	∗	∗	NOUN
ejpam-4522	214	43	y	y	NOUN
ejpam-4522	214	44	)	)	PUNCT
ejpam-4522	214	45	∗	∗	PROPN
ejpam-4522	214	46	y	y	PROPN
ejpam-4522	214	47	)	)	PUNCT
ejpam-4522	214	48	for	for	ADP
ejpam-4522	214	49	all	all	DET
ejpam-4522	214	50	a	a	DET
ejpam-4522	214	51	,	,	PUNCT
ejpam-4522	214	52	b	b	X
ejpam-4522	214	53	∈	∈	PROPN
ejpam-4522	214	54	e	e	X
ejpam-4522	214	55	and	and	CCONJ
ejpam-4522	214	56	x	x	NOUN
ejpam-4522	214	57	,	,	PUNCT
ejpam-4522	214	58	y	y	PROPN
ejpam-4522	214	59	∈	∈	PROPN
ejpam-4522	214	60	x.	x.	NOUN
ejpam-4522	214	61	therefore	therefore	ADV
ejpam-4522	214	62	m(x	m(x	PROPN
ejpam-4522	214	63	,	,	PUNCT
ejpam-4522	214	64	e	e	NOUN
ejpam-4522	214	65	)	)	PUNCT
ejpam-4522	214	66	:	:	PUNCT
ejpam-4522	215	1	=	=	SYM
ejpam-4522	215	2	(	(	PUNCT
ejpam-4522	215	3	me	i	PRON
ejpam-4522	215	4	,	,	PUNCT
ejpam-4522	215	5	ge	ge	PROPN
ejpam-4522	215	6	,	,	PUNCT
ejpam-4522	215	7	ξ	ξ	X
ejpam-4522	215	8	)	)	PUNCT
ejpam-4522	215	9	is	be	AUX
ejpam-4522	215	10	a	a	DET
ejpam-4522	215	11	positive	positive	ADJ
ejpam-4522	215	12	implicative	implicative	ADJ
ejpam-4522	215	13	makgeolli	makgeolli	NOUN
ejpam-4522	215	14	ideal	ideal	NOUN
ejpam-4522	215	15	of	of	ADP
ejpam-4522	215	16	(	(	PUNCT
ejpam-4522	215	17	x	x	X
ejpam-4522	215	18	,	,	PUNCT
ejpam-4522	215	19	e	e	NOUN
ejpam-4522	215	20	)	)	PUNCT
ejpam-4522	215	21	by	by	ADP
ejpam-4522	215	22	theorem	theorem	NOUN
ejpam-4522	215	23	3	3	NUM
ejpam-4522	215	24	.	.	PUNCT
ejpam-4522	215	25	lemma	lemma	PROPN
ejpam-4522	215	26	2	2	NUM
ejpam-4522	215	27	.	.	PUNCT
ejpam-4522	216	1	if	if	SCONJ
ejpam-4522	216	2	a	a	DET
ejpam-4522	216	3	makgeolli	makgeolli	NOUN
ejpam-4522	216	4	structure	structure	NOUN
ejpam-4522	216	5	m(x	m(x	PROPN
ejpam-4522	216	6	,	,	PUNCT
ejpam-4522	216	7	e	e	NOUN
ejpam-4522	216	8	)	)	PUNCT
ejpam-4522	216	9	:	:	PUNCT
ejpam-4522	216	10	=	=	SYM
ejpam-4522	216	11	(	(	PUNCT
ejpam-4522	216	12	me	i	PRON
ejpam-4522	216	13	,	,	PUNCT
ejpam-4522	216	14	ge	ge	PROPN
ejpam-4522	216	15	,	,	PUNCT
ejpam-4522	216	16	ξ	ξ	PROPN
ejpam-4522	216	17	)	)	PUNCT
ejpam-4522	216	18	on	on	ADP
ejpam-4522	216	19	(	(	PUNCT
ejpam-4522	216	20	x	x	X
ejpam-4522	216	21	,	,	PUNCT
ejpam-4522	216	22	e	e	NOUN
ejpam-4522	216	23	)	)	PUNCT
ejpam-4522	216	24	satisfies	satisfy	VERB
ejpam-4522	216	25	the	the	DET
ejpam-4522	216	26	assertion	assertion	NOUN
ejpam-4522	216	27	(	(	PUNCT
ejpam-4522	216	28	ii	ii	NOUN
ejpam-4522	216	29	)	)	PUNCT
ejpam-4522	216	30	in	in	ADP
ejpam-4522	216	31	lemma	lemma	PROPN
ejpam-4522	216	32	1	1	NUM
ejpam-4522	216	33	,	,	PUNCT
ejpam-4522	216	34	then	then	ADV
ejpam-4522	216	35	it	it	PRON
ejpam-4522	216	36	is	be	AUX
ejpam-4522	216	37	a	a	DET
ejpam-4522	216	38	makgeolli	makgeolli	NOUN
ejpam-4522	216	39	ideal	ideal	NOUN
ejpam-4522	216	40	of	of	ADP
ejpam-4522	216	41	(	(	PUNCT
ejpam-4522	216	42	x	x	X
ejpam-4522	216	43	,	,	PUNCT
ejpam-4522	216	44	e	e	NOUN
ejpam-4522	216	45	)	)	PUNCT
ejpam-4522	216	46	.	.	PUNCT
ejpam-4522	217	1	proof	proof	NOUN
ejpam-4522	217	2	.	.	PUNCT
ejpam-4522	218	1	since	since	SCONJ
ejpam-4522	218	2	0	0	NUM
ejpam-4522	218	3	↬	↬	PROPN
ejpam-4522	218	4	a	a	DET
ejpam-4522	218	5	≤	≤	PROPN
ejpam-4522	218	6	a	a	DET
ejpam-4522	218	7	and	and	CCONJ
ejpam-4522	218	8	0	0	NUM
ejpam-4522	218	9	∗	∗	NOUN
ejpam-4522	218	10	x	x	SYM
ejpam-4522	218	11	≤	≤	NUM
ejpam-4522	218	12	x	x	PUNCT
ejpam-4522	218	13	for	for	ADP
ejpam-4522	218	14	all	all	DET
ejpam-4522	218	15	a	a	DET
ejpam-4522	218	16	∈	∈	NOUN
ejpam-4522	218	17	e	e	NOUN
ejpam-4522	218	18	and	and	CCONJ
ejpam-4522	218	19	x	x	SYM
ejpam-4522	218	20	∈	∈	NOUN
ejpam-4522	218	21	x	x	X
ejpam-4522	218	22	,	,	PUNCT
ejpam-4522	218	23	we	we	PRON
ejpam-4522	218	24	have	have	VERB
ejpam-4522	218	25	me(0	me(0	PROPN
ejpam-4522	218	26	)	)	PUNCT
ejpam-4522	218	27	⊇	⊇	NOUN
ejpam-4522	218	28	me(a)∩me(a	me(a)∩me(a	PROPN
ejpam-4522	218	29	)	)	PUNCT
ejpam-4522	218	30	=	=	SYM
ejpam-4522	218	31	me(a	me(a	NOUN
ejpam-4522	218	32	)	)	PUNCT
ejpam-4522	218	33	,	,	PUNCT
ejpam-4522	218	34	ge(0	ge(0	PROPN
ejpam-4522	218	35	)	)	PUNCT
ejpam-4522	218	36	⊆	⊆	NUM
ejpam-4522	218	37	ge(a)∪ge(a	ge(a)∪ge(a	NOUN
ejpam-4522	218	38	)	)	PUNCT
ejpam-4522	218	39	=	=	PUNCT
ejpam-4522	218	40	ge(a	ge(a	X
ejpam-4522	218	41	)	)	PUNCT
ejpam-4522	218	42	,	,	PUNCT
ejpam-4522	218	43	and	and	CCONJ
ejpam-4522	218	44	ξ(0	ξ(0	PROPN
ejpam-4522	218	45	)	)	PUNCT
ejpam-4522	218	46	≥	≥	NOUN
ejpam-4522	218	47	min{ξ(x	min{ξ(x	NUM
ejpam-4522	218	48	)	)	PUNCT
ejpam-4522	218	49	,	,	PUNCT
ejpam-4522	218	50	ξ(x	ξ(x	NOUN
ejpam-4522	218	51	)	)	PUNCT
ejpam-4522	218	52	}	}	PUNCT
ejpam-4522	218	53	=	=	SYM
ejpam-4522	218	54	ξ(x	ξ(x	NOUN
ejpam-4522	218	55	)	)	PUNCT
ejpam-4522	218	56	,	,	PUNCT
ejpam-4522	218	57	i.e.	i.e.	X
ejpam-4522	218	58	,	,	PUNCT
ejpam-4522	218	59	0	0	NUM
ejpam-4522	218	60	/	/	SYM
ejpam-4522	218	61	ξ(x	ξ(x	NOUN
ejpam-4522	218	62	)	)	PUNCT
ejpam-4522	218	63	∈	∈	PROPN
ejpam-4522	218	64	ξ	ξ	X
ejpam-4522	218	65	by	by	ADP
ejpam-4522	218	66	the	the	DET
ejpam-4522	218	67	condition	condition	NOUN
ejpam-4522	218	68	(	(	PUNCT
ejpam-4522	218	69	ii	ii	NOUN
ejpam-4522	218	70	)	)	PUNCT
ejpam-4522	218	71	in	in	ADP
ejpam-4522	218	72	lemma	lemma	PROPN
ejpam-4522	218	73	1	1	NUM
ejpam-4522	218	74	.	.	PUNCT
ejpam-4522	219	1	since	since	SCONJ
ejpam-4522	219	2	a	a	DET
ejpam-4522	219	3	↬	↬	NOUN
ejpam-4522	219	4	(	(	PUNCT
ejpam-4522	219	5	a	a	DET
ejpam-4522	219	6	↬	↬	PROPN
ejpam-4522	219	7	b	b	NOUN
ejpam-4522	219	8	)	)	PUNCT
ejpam-4522	219	9	≤	≤	NUM
ejpam-4522	219	10	b	b	PROPN
ejpam-4522	219	11	and	and	CCONJ
ejpam-4522	219	12	x∗(x∗y	x∗(x∗y	NUM
ejpam-4522	219	13	)	)	PUNCT
ejpam-4522	219	14	≤	≤	NUM
ejpam-4522	219	15	y	y	PROPN
ejpam-4522	219	16	for	for	ADP
ejpam-4522	219	17	all	all	DET
ejpam-4522	219	18	a	a	DET
ejpam-4522	219	19	,	,	PUNCT
ejpam-4522	219	20	b	b	X
ejpam-4522	219	21	∈	∈	PROPN
ejpam-4522	219	22	e	e	X
ejpam-4522	219	23	and	and	CCONJ
ejpam-4522	219	24	x	x	NOUN
ejpam-4522	219	25	,	,	PUNCT
ejpam-4522	219	26	y	y	PROPN
ejpam-4522	219	27	∈	∈	PROPN
ejpam-4522	219	28	x	x	AUX
ejpam-4522	219	29	,	,	PUNCT
ejpam-4522	219	30	it	it	PRON
ejpam-4522	219	31	follows	follow	VERB
ejpam-4522	219	32	from	from	ADP
ejpam-4522	219	33	the	the	DET
ejpam-4522	219	34	condition	condition	NOUN
ejpam-4522	219	35	(	(	PUNCT
ejpam-4522	219	36	ii	ii	NOUN
ejpam-4522	219	37	)	)	PUNCT
ejpam-4522	219	38	in	in	ADP
ejpam-4522	219	39	lemma	lemma	PROPN
ejpam-4522	219	40	1	1	NUM
ejpam-4522	219	41	that	that	SCONJ
ejpam-4522	219	42	me(a	me(a	NOUN
ejpam-4522	219	43	)	)	PUNCT
ejpam-4522	219	44	⊇	⊇	NOUN
ejpam-4522	219	45	me(a	me(a	X
ejpam-4522	219	46	↬	↬	PROPN
ejpam-4522	219	47	b)∩me(b	b)∩me(b	PROPN
ejpam-4522	219	48	)	)	PUNCT
ejpam-4522	219	49	,	,	PUNCT
ejpam-4522	219	50	ge(a	ge(a	NOUN
ejpam-4522	219	51	)	)	PUNCT
ejpam-4522	219	52	⊆	⊆	NUM
ejpam-4522	219	53	ge(a	ge(a	PUNCT
ejpam-4522	219	54	↬	↬	PROPN
ejpam-4522	219	55	b)∪ge(b	b)∪ge(b	PROPN
ejpam-4522	219	56	)	)	PUNCT
ejpam-4522	219	57	,	,	PUNCT
ejpam-4522	219	58	and	and	CCONJ
ejpam-4522	219	59	ξ(x	ξ(x	NOUN
ejpam-4522	219	60	)	)	PUNCT
ejpam-4522	219	61	≥	≥	NOUN
ejpam-4522	219	62	min{ξ(x∗y	min{ξ(x∗y	NOUN
ejpam-4522	219	63	)	)	PUNCT
ejpam-4522	219	64	,	,	PUNCT
ejpam-4522	219	65	ξ(y	ξ(y	PROPN
ejpam-4522	219	66	)	)	PUNCT
ejpam-4522	219	67	}	}	PUNCT
ejpam-4522	219	68	for	for	ADP
ejpam-4522	219	69	all	all	DET
ejpam-4522	219	70	a	a	DET
ejpam-4522	219	71	,	,	PUNCT
ejpam-4522	219	72	b	b	X
ejpam-4522	219	73	∈	∈	PROPN
ejpam-4522	219	74	e	e	X
ejpam-4522	219	75	and	and	CCONJ
ejpam-4522	219	76	x	x	NOUN
ejpam-4522	219	77	,	,	PUNCT
ejpam-4522	219	78	y	y	PROPN
ejpam-4522	219	79	∈	∈	PROPN
ejpam-4522	219	80	x.	x.	NOUN
ejpam-4522	219	81	consequently	consequently	ADV
ejpam-4522	219	82	,	,	PUNCT
ejpam-4522	219	83	m(x	m(x	PROPN
ejpam-4522	219	84	,	,	PUNCT
ejpam-4522	219	85	e	e	NOUN
ejpam-4522	219	86	)	)	PUNCT
ejpam-4522	219	87	:	:	PUNCT
ejpam-4522	220	1	=	=	SYM
ejpam-4522	220	2	(	(	PUNCT
ejpam-4522	220	3	me	i	PRON
ejpam-4522	220	4	,	,	PUNCT
ejpam-4522	220	5	ge	ge	PROPN
ejpam-4522	220	6	,	,	PUNCT
ejpam-4522	220	7	ξ	ξ	X
ejpam-4522	220	8	)	)	PUNCT
ejpam-4522	220	9	is	be	AUX
ejpam-4522	220	10	a	a	DET
ejpam-4522	220	11	makgeolli	makgeolli	NOUN
ejpam-4522	220	12	ideal	ideal	NOUN
ejpam-4522	220	13	of	of	ADP
ejpam-4522	220	14	(	(	PUNCT
ejpam-4522	220	15	x	x	X
ejpam-4522	220	16	,	,	PUNCT
ejpam-4522	220	17	e	e	NOUN
ejpam-4522	220	18	)	)	PUNCT
ejpam-4522	220	19	.	.	PUNCT
ejpam-4522	221	1	the	the	DET
ejpam-4522	221	2	next	next	ADJ
ejpam-4522	221	3	corollary	corollary	NOUN
ejpam-4522	221	4	is	be	AUX
ejpam-4522	221	5	derived	derive	VERB
ejpam-4522	221	6	by	by	ADP
ejpam-4522	221	7	the	the	DET
ejpam-4522	221	8	combination	combination	NOUN
ejpam-4522	221	9	of	of	ADP
ejpam-4522	221	10	theorem	theorem	ADJ
ejpam-4522	221	11	4	4	NUM
ejpam-4522	221	12	and	and	CCONJ
ejpam-4522	221	13	lemma	lemma	PROPN
ejpam-4522	221	14	2	2	NUM
ejpam-4522	221	15	.	.	PUNCT
ejpam-4522	221	16	corollary	corollary	ADJ
ejpam-4522	221	17	1	1	NUM
ejpam-4522	221	18	.	.	PUNCT
ejpam-4522	222	1	if	if	SCONJ
ejpam-4522	222	2	a	a	DET
ejpam-4522	222	3	makgeolli	makgeolli	NOUN
ejpam-4522	222	4	structure	structure	NOUN
ejpam-4522	222	5	m(x	m(x	PROPN
ejpam-4522	222	6	,	,	PUNCT
ejpam-4522	222	7	e	e	NOUN
ejpam-4522	222	8	)	)	PUNCT
ejpam-4522	222	9	:	:	PUNCT
ejpam-4522	222	10	=	=	SYM
ejpam-4522	222	11	(	(	PUNCT
ejpam-4522	222	12	me	i	PRON
ejpam-4522	222	13	,	,	PUNCT
ejpam-4522	222	14	ge	ge	PROPN
ejpam-4522	222	15	,	,	PUNCT
ejpam-4522	222	16	ξ	ξ	PROPN
ejpam-4522	222	17	)	)	PUNCT
ejpam-4522	222	18	on	on	ADP
ejpam-4522	222	19	(	(	PUNCT
ejpam-4522	222	20	x	x	X
ejpam-4522	222	21	,	,	PUNCT
ejpam-4522	222	22	e	e	NOUN
ejpam-4522	222	23	)	)	PUNCT
ejpam-4522	222	24	satisfies	satisfie	NOUN
ejpam-4522	222	25	(	(	PUNCT
ejpam-4522	222	26	15	15	NUM
ejpam-4522	222	27	)	)	PUNCT
ejpam-4522	222	28	and	and	CCONJ
ejpam-4522	222	29	the	the	DET
ejpam-4522	222	30	assertion	assertion	NOUN
ejpam-4522	222	31	(	(	PUNCT
ejpam-4522	222	32	ii	ii	NOUN
ejpam-4522	222	33	)	)	PUNCT
ejpam-4522	222	34	in	in	ADP
ejpam-4522	222	35	lemma	lemma	PROPN
ejpam-4522	222	36	1	1	NUM
ejpam-4522	222	37	,	,	PUNCT
ejpam-4522	222	38	then	then	ADV
ejpam-4522	222	39	m(x	m(x	PROPN
ejpam-4522	222	40	,	,	PUNCT
ejpam-4522	222	41	e	e	NOUN
ejpam-4522	222	42	)	)	PUNCT
ejpam-4522	222	43	:	:	PUNCT
ejpam-4522	222	44	=	=	SYM
ejpam-4522	222	45	(	(	PUNCT
ejpam-4522	222	46	me	i	PRON
ejpam-4522	222	47	,	,	PUNCT
ejpam-4522	222	48	ge	ge	PROPN
ejpam-4522	222	49	,	,	PUNCT
ejpam-4522	222	50	ξ	ξ	X
ejpam-4522	222	51	)	)	PUNCT
ejpam-4522	222	52	is	be	AUX
ejpam-4522	222	53	a	a	DET
ejpam-4522	222	54	positive	positive	ADJ
ejpam-4522	222	55	implicative	implicative	ADJ
ejpam-4522	222	56	makgeolli	makgeolli	NOUN
ejpam-4522	222	57	ideal	ideal	NOUN
ejpam-4522	222	58	of	of	ADP
ejpam-4522	222	59	(	(	PUNCT
ejpam-4522	222	60	x	x	X
ejpam-4522	222	61	,	,	PUNCT
ejpam-4522	222	62	e	e	NOUN
ejpam-4522	222	63	)	)	PUNCT
ejpam-4522	222	64	.	.	PUNCT
ejpam-4522	223	1	theorem	theorem	VERB
ejpam-4522	223	2	6	6	NUM
ejpam-4522	223	3	.	.	PUNCT
ejpam-4522	224	1	a	a	DET
ejpam-4522	224	2	makgeolli	makgeolli	NOUN
ejpam-4522	224	3	structure	structure	NOUN
ejpam-4522	224	4	m(x	m(x	PROPN
ejpam-4522	224	5	,	,	PUNCT
ejpam-4522	224	6	e	e	NOUN
ejpam-4522	224	7	)	)	PUNCT
ejpam-4522	224	8	:	:	PUNCT
ejpam-4522	224	9	=	=	SYM
ejpam-4522	224	10	(	(	PUNCT
ejpam-4522	224	11	me	i	PRON
ejpam-4522	224	12	,	,	PUNCT
ejpam-4522	224	13	ge	ge	PROPN
ejpam-4522	224	14	,	,	PUNCT
ejpam-4522	224	15	ξ	ξ	PROPN
ejpam-4522	224	16	)	)	PUNCT
ejpam-4522	224	17	on	on	ADP
ejpam-4522	224	18	(	(	PUNCT
ejpam-4522	224	19	x	x	X
ejpam-4522	224	20	,	,	PUNCT
ejpam-4522	224	21	e	e	NOUN
ejpam-4522	224	22	)	)	PUNCT
ejpam-4522	224	23	is	be	AUX
ejpam-4522	224	24	a	a	DET
ejpam-4522	224	25	positive	positive	ADJ
ejpam-4522	224	26	implicative	implicative	ADJ
ejpam-4522	224	27	makgeolli	makgeolli	NOUN
ejpam-4522	224	28	ideal	ideal	NOUN
ejpam-4522	224	29	of	of	ADP
ejpam-4522	224	30	(	(	PUNCT
ejpam-4522	224	31	x	x	X
ejpam-4522	224	32	,	,	PUNCT
ejpam-4522	224	33	e	e	NOUN
ejpam-4522	224	34	)	)	PUNCT
ejpam-4522	225	1	if	if	SCONJ
ejpam-4522	226	1	and	and	CCONJ
ejpam-4522	226	2	only	only	ADV
ejpam-4522	226	3	if	if	SCONJ
ejpam-4522	226	4	it	it	PRON
ejpam-4522	226	5	satisfies:	satisfies:	X
ejpam-4522	226	6	(	(	PUNCT
ejpam-4522	226	7	∀a	∀a	X
ejpam-4522	226	8	,	,	PUNCT
ejpam-4522	226	9	b	b	NOUN
ejpam-4522	226	10	,	,	PUNCT
ejpam-4522	226	11	x	x	X
ejpam-4522	226	12	,	,	PUNCT
ejpam-4522	226	13	y	y	PROPN
ejpam-4522	226	14	∈	∈	PROPN
ejpam-4522	226	15	e	e	X
ejpam-4522	226	16	)	)	PUNCT
ejpam-4522	226	17			PROPN
ejpam-4522	226	18	(	(	PUNCT
ejpam-4522	226	19	(	(	PUNCT
ejpam-4522	226	20	a	a	DET
ejpam-4522	226	21	↬	↬	PROPN
ejpam-4522	226	22	b	b	NOUN
ejpam-4522	226	23	)	)	PUNCT
ejpam-4522	226	24	↬	↬	PROPN
ejpam-4522	226	25	b	b	X
ejpam-4522	226	26	)	)	PUNCT
ejpam-4522	226	27	↬	↬	NOUN
ejpam-4522	226	28	x	x	X
ejpam-4522	226	29	≤	≤	NUM
ejpam-4522	226	30	y	y	PROPN
ejpam-4522	226	31	⇒	⇒	NOUN
ejpam-4522	226	32	{	{	PUNCT
ejpam-4522	226	33	me(a	me(a	PROPN
ejpam-4522	226	34	↬	↬	PROPN
ejpam-4522	226	35	b	b	X
ejpam-4522	226	36	)	)	PUNCT
ejpam-4522	226	37	⊇	⊇	NOUN
ejpam-4522	226	38	me(x	me(x	X
ejpam-4522	226	39	)	)	PUNCT
ejpam-4522	226	40	∩me(y	∩me(y	PROPN
ejpam-4522	226	41	)	)	PUNCT
ejpam-4522	226	42	ge(a	ge(a	PUNCT
ejpam-4522	226	43	↬	↬	PROPN
ejpam-4522	226	44	b	b	X
ejpam-4522	226	45	)	)	PUNCT
ejpam-4522	226	46	⊆	⊆	NUM
ejpam-4522	226	47	ge(x	ge(x	X
ejpam-4522	226	48	)	)	PUNCT
ejpam-4522	226	49	∪ge(y	∪ge(y	PROPN
ejpam-4522	226	50	)	)	PUNCT
ejpam-4522	226	51			PROPN
ejpam-4522	226	52	.	.	PUNCT
ejpam-4522	227	1	(	(	PUNCT
ejpam-4522	227	2	∀x	∀x	X
ejpam-4522	227	3	,	,	PUNCT
ejpam-4522	227	4	y	y	PROPN
ejpam-4522	227	5	,	,	PUNCT
ejpam-4522	227	6	a	a	PRON
ejpam-4522	227	7	,	,	PUNCT
ejpam-4522	227	8	b	b	PROPN
ejpam-4522	227	9	∈	∈	PROPN
ejpam-4522	227	10	x	x	X
ejpam-4522	227	11	)	)	PUNCT
ejpam-4522	227	12	(	(	PUNCT
ejpam-4522	227	13	(	(	PUNCT
ejpam-4522	227	14	(	(	PUNCT
ejpam-4522	227	15	x	x	SYM
ejpam-4522	227	16	∗	∗	PROPN
ejpam-4522	227	17	y	y	NOUN
ejpam-4522	227	18	)	)	PUNCT
ejpam-4522	227	19	∗	∗	PROPN
ejpam-4522	227	20	y	y	PROPN
ejpam-4522	227	21	)	)	PUNCT
ejpam-4522	227	22	∗	∗	VERB
ejpam-4522	227	23	a	a	DET
ejpam-4522	227	24	≤	≤	NUM
ejpam-4522	227	25	b	b	NOUN
ejpam-4522	227	26	⇒	⇒	NOUN
ejpam-4522	227	27	ξ(x	ξ(x	PROPN
ejpam-4522	227	28	∗	∗	X
ejpam-4522	227	29	y	y	PROPN
ejpam-4522	227	30	)	)	PUNCT
ejpam-4522	227	31	≥	≥	NOUN
ejpam-4522	227	32	min{ξ(a	min{ξ(a	NUM
ejpam-4522	227	33	)	)	PUNCT
ejpam-4522	227	34	,	,	PUNCT
ejpam-4522	227	35	ξ(b	ξ(b	NOUN
ejpam-4522	227	36	)	)	PUNCT
ejpam-4522	227	37	}	}	PUNCT
ejpam-4522	227	38	)	)	PUNCT
ejpam-4522	227	39	.	.	PUNCT
ejpam-4522	228	1	(	(	PUNCT
ejpam-4522	228	2	17	17	NUM
ejpam-4522	228	3	)	)	PUNCT
ejpam-4522	228	4	proof	proof	NOUN
ejpam-4522	228	5	.	.	PUNCT
ejpam-4522	229	1	assume	assume	VERB
ejpam-4522	229	2	that	that	SCONJ
ejpam-4522	229	3	m(x	m(x	PROPN
ejpam-4522	229	4	,	,	PUNCT
ejpam-4522	229	5	e	e	NOUN
ejpam-4522	229	6	)	)	PUNCT
ejpam-4522	229	7	:	:	PUNCT
ejpam-4522	229	8	=	=	SYM
ejpam-4522	229	9	(	(	PUNCT
ejpam-4522	229	10	me	i	PRON
ejpam-4522	229	11	,	,	PUNCT
ejpam-4522	229	12	ge	ge	PROPN
ejpam-4522	229	13	,	,	PUNCT
ejpam-4522	229	14	ξ	ξ	X
ejpam-4522	229	15	)	)	PUNCT
ejpam-4522	229	16	is	be	AUX
ejpam-4522	229	17	a	a	DET
ejpam-4522	229	18	positive	positive	ADJ
ejpam-4522	229	19	implicative	implicative	ADJ
ejpam-4522	229	20	makgeolli	makgeolli	NOUN
ejpam-4522	229	21	ideal	ideal	NOUN
ejpam-4522	229	22	of	of	ADP
ejpam-4522	229	23	(	(	PUNCT
ejpam-4522	229	24	x	x	X
ejpam-4522	229	25	,	,	PUNCT
ejpam-4522	229	26	e	e	NOUN
ejpam-4522	229	27	)	)	PUNCT
ejpam-4522	229	28	.	.	PUNCT
ejpam-4522	230	1	then	then	ADV
ejpam-4522	230	2	it	it	PRON
ejpam-4522	230	3	is	be	AUX
ejpam-4522	230	4	a	a	DET
ejpam-4522	230	5	makgeolli	makgeolli	NOUN
ejpam-4522	230	6	ideal	ideal	NOUN
ejpam-4522	230	7	of	of	ADP
ejpam-4522	230	8	(	(	PUNCT
ejpam-4522	230	9	x	x	X
ejpam-4522	230	10	,	,	PUNCT
ejpam-4522	230	11	e	e	NOUN
ejpam-4522	230	12	)	)	PUNCT
ejpam-4522	230	13	.	.	PUNCT
ejpam-4522	231	1	let	let	VERB
ejpam-4522	231	2	a	a	DET
ejpam-4522	231	3	,	,	PUNCT
ejpam-4522	231	4	b	b	NOUN
ejpam-4522	231	5	,	,	PUNCT
ejpam-4522	231	6	x	x	X
ejpam-4522	231	7	,	,	PUNCT
ejpam-4522	231	8	y	y	PROPN
ejpam-4522	231	9	∈	∈	PROPN
ejpam-4522	231	10	e	e	PROPN
ejpam-4522	231	11	and	and	CCONJ
ejpam-4522	231	12	x	x	PROPN
ejpam-4522	231	13	,	,	PUNCT
ejpam-4522	231	14	y	y	PROPN
ejpam-4522	231	15	,	,	PUNCT
ejpam-4522	231	16	a	a	PRON
ejpam-4522	231	17	,	,	PUNCT
ejpam-4522	231	18	b	b	X
ejpam-4522	231	19	∈	∈	PROPN
ejpam-4522	231	20	x	x	AUX
ejpam-4522	231	21	be	be	AUX
ejpam-4522	231	22	such	such	ADJ
ejpam-4522	231	23	that	that	SCONJ
ejpam-4522	231	24	(	(	PUNCT
ejpam-4522	231	25	(	(	PUNCT
ejpam-4522	231	26	a	a	DET
ejpam-4522	231	27	↬	↬	PROPN
ejpam-4522	231	28	b	b	NOUN
ejpam-4522	231	29	)	)	PUNCT
ejpam-4522	231	30	↬	↬	PROPN
ejpam-4522	231	31	b	b	X
ejpam-4522	231	32	)	)	PUNCT
ejpam-4522	231	33	↬	↬	NOUN
ejpam-4522	231	34	x	x	PUNCT
ejpam-4522	231	35	≤	≤	NUM
ejpam-4522	231	36	y	y	PROPN
ejpam-4522	231	37	and	and	CCONJ
ejpam-4522	231	38	(	(	PUNCT
ejpam-4522	231	39	(	(	PUNCT
ejpam-4522	231	40	x	x	SYM
ejpam-4522	231	41	∗	∗	PROPN
ejpam-4522	231	42	y	y	NOUN
ejpam-4522	231	43	)	)	PUNCT
ejpam-4522	231	44	∗	∗	PROPN
ejpam-4522	231	45	y	y	PROPN
ejpam-4522	231	46	)	)	PUNCT
ejpam-4522	231	47	∗	∗	VERB
ejpam-4522	231	48	a	a	DET
ejpam-4522	231	49	≤	≤	PROPN
ejpam-4522	231	50	b.	b.	PROPN
ejpam-4522	231	51	then	then	ADV
ejpam-4522	231	52	me(a	me(a	NUM
ejpam-4522	231	53	↬	↬	PROPN
ejpam-4522	231	54	b	b	X
ejpam-4522	231	55	)	)	PUNCT
ejpam-4522	231	56	⊇	⊇	PROPN
ejpam-4522	231	57	me((a	me((a	PROPN
ejpam-4522	231	58	↬	↬	PROPN
ejpam-4522	231	59	b	b	X
ejpam-4522	231	60	)	)	PUNCT
ejpam-4522	231	61	↬	↬	PROPN
ejpam-4522	231	62	b	b	X
ejpam-4522	231	63	)	)	PUNCT
ejpam-4522	231	64	⊇	⊇	NOUN
ejpam-4522	231	65	me(x	me(x	X
ejpam-4522	231	66	)	)	PUNCT
ejpam-4522	231	67	∩me(y	∩me(y	PROPN
ejpam-4522	231	68	)	)	PUNCT
ejpam-4522	231	69	,	,	PUNCT
ejpam-4522	231	70	ge(a	ge(a	PRON
ejpam-4522	231	71	↬	↬	PROPN
ejpam-4522	231	72	b	b	X
ejpam-4522	231	73	)	)	PUNCT
ejpam-4522	231	74	⊆	⊆	NUM
ejpam-4522	231	75	ge((a	ge((a	NOUN
ejpam-4522	231	76	↬	↬	PROPN
ejpam-4522	231	77	b	b	NOUN
ejpam-4522	231	78	)	)	PUNCT
ejpam-4522	231	79	↬	↬	PROPN
ejpam-4522	231	80	b	b	X
ejpam-4522	231	81	)	)	PUNCT
ejpam-4522	231	82	⊆	⊆	NUM
ejpam-4522	231	83	ge(x	ge(x	X
ejpam-4522	231	84	)	)	PUNCT
ejpam-4522	231	85	∪ge(y	∪ge(y	PROPN
ejpam-4522	231	86	)	)	PUNCT
ejpam-4522	231	87	,	,	PUNCT
ejpam-4522	231	88	ξ(x	ξ(x	PROPN
ejpam-4522	231	89	∗	∗	NOUN
ejpam-4522	231	90	y	y	PROPN
ejpam-4522	231	91	)	)	PUNCT
ejpam-4522	231	92	≥	≥	NOUN
ejpam-4522	231	93	ξ((x	ξ((x	PROPN
ejpam-4522	231	94	∗	∗	PROPN
ejpam-4522	231	95	y	y	NOUN
ejpam-4522	231	96	)	)	PUNCT
ejpam-4522	231	97	∗	∗	PROPN
ejpam-4522	231	98	y	y	PROPN
ejpam-4522	231	99	)	)	PUNCT
ejpam-4522	231	100	≥	≥	NOUN
ejpam-4522	231	101	min{ξ(a	min{ξ(a	NUM
ejpam-4522	231	102	)	)	PUNCT
ejpam-4522	231	103	,	,	PUNCT
ejpam-4522	231	104	ξ(b	ξ(b	NOUN
ejpam-4522	231	105	)	)	PUNCT
ejpam-4522	231	106	}	}	PUNCT
ejpam-4522	231	107	by	by	ADP
ejpam-4522	231	108	proposition	proposition	NOUN
ejpam-4522	231	109	1	1	NUM
ejpam-4522	231	110	and	and	CCONJ
ejpam-4522	231	111	the	the	DET
ejpam-4522	231	112	assertion	assertion	NOUN
ejpam-4522	231	113	(	(	PUNCT
ejpam-4522	231	114	ii	ii	NOUN
ejpam-4522	231	115	)	)	PUNCT
ejpam-4522	231	116	in	in	ADP
ejpam-4522	231	117	lemma	lemma	PROPN
ejpam-4522	231	118	1	1	NUM
ejpam-4522	231	119	.	.	PUNCT
ejpam-4522	232	1	conversely	conversely	ADV
ejpam-4522	232	2	,	,	PUNCT
ejpam-4522	232	3	letm(x	letm(x	NOUN
ejpam-4522	232	4	,	,	PUNCT
ejpam-4522	232	5	e	e	NOUN
ejpam-4522	232	6	)	)	PUNCT
ejpam-4522	232	7	:	:	PUNCT
ejpam-4522	233	1	=	=	SYM
ejpam-4522	233	2	(	(	PUNCT
ejpam-4522	233	3	me	i	PRON
ejpam-4522	233	4	,	,	PUNCT
ejpam-4522	233	5	ge	ge	PROPN
ejpam-4522	233	6	,	,	PUNCT
ejpam-4522	233	7	ξ	ξ	X
ejpam-4522	233	8	)	)	PUNCT
ejpam-4522	233	9	be	be	VERB
ejpam-4522	233	10	a	a	DET
ejpam-4522	233	11	makgeolli	makgeolli	NOUN
ejpam-4522	233	12	structure	structure	NOUN
ejpam-4522	233	13	on	on	ADP
ejpam-4522	233	14	(	(	PUNCT
ejpam-4522	233	15	x	x	X
ejpam-4522	233	16	,	,	PUNCT
ejpam-4522	233	17	e	e	NOUN
ejpam-4522	233	18	)	)	PUNCT
ejpam-4522	233	19	that	that	PRON
ejpam-4522	233	20	satisfies	satisfie	NOUN
ejpam-4522	233	21	(	(	PUNCT
ejpam-4522	233	22	17	17	NUM
ejpam-4522	233	23	)	)	PUNCT
ejpam-4522	233	24	.	.	PUNCT
ejpam-4522	234	1	let	let	VERB
ejpam-4522	234	2	a	a	DET
ejpam-4522	234	3	,	,	PUNCT
ejpam-4522	234	4	b	b	NOUN
ejpam-4522	234	5	,	,	PUNCT
ejpam-4522	234	6	c	c	PROPN
ejpam-4522	234	7	∈	∈	PROPN
ejpam-4522	234	8	e	e	PROPN
ejpam-4522	234	9	and	and	CCONJ
ejpam-4522	234	10	x	x	PROPN
ejpam-4522	234	11	,	,	PUNCT
ejpam-4522	234	12	y	y	PROPN
ejpam-4522	234	13	,	,	PUNCT
ejpam-4522	234	14	z	z	NOUN
ejpam-4522	234	15	∈	∈	PROPN
ejpam-4522	234	16	x	x	AUX
ejpam-4522	234	17	be	be	AUX
ejpam-4522	234	18	such	such	ADJ
ejpam-4522	234	19	that	that	SCONJ
ejpam-4522	234	20	a	a	DET
ejpam-4522	234	21	↬	↬	PROPN
ejpam-4522	234	22	b	b	PROPN
ejpam-4522	234	23	≤	≤	NUM
ejpam-4522	234	24	c	c	PROPN
ejpam-4522	234	25	and	and	CCONJ
ejpam-4522	234	26	x	x	PROPN
ejpam-4522	234	27	∗	∗	NOUN
ejpam-4522	234	28	y	y	PROPN
ejpam-4522	234	29	≤	≤	PROPN
ejpam-4522	234	30	z.	z.	PROPN
ejpam-4522	235	1	then	then	ADV
ejpam-4522	235	2	(	(	PUNCT
ejpam-4522	235	3	(	(	PUNCT
ejpam-4522	235	4	a	a	DET
ejpam-4522	235	5	↬	↬	PROPN
ejpam-4522	235	6	s.	s.	PROPN
ejpam-4522	235	7	z.	z.	PROPN
ejpam-4522	235	8	song	song	PROPN
ejpam-4522	235	9	,	,	PUNCT
ejpam-4522	235	10	m.	m.	NOUN
ejpam-4522	235	11	a.	a.	NOUN
ejpam-4522	235	12	öztürk	öztürk	PROPN
ejpam-4522	235	13	,	,	PUNCT
ejpam-4522	235	14	y.	y.	PROPN
ejpam-4522	235	15	b.	b.	PROPN
ejpam-4522	235	16	jun	jun	PROPN
ejpam-4522	235	17	/	/	SYM
ejpam-4522	235	18	eur	eur	PROPN
ejpam-4522	235	19	.	.	PUNCT
ejpam-4522	236	1	j.	j.	PROPN
ejpam-4522	236	2	pure	pure	PROPN
ejpam-4522	236	3	appl	appl	PROPN
ejpam-4522	236	4	.	.	PROPN
ejpam-4522	236	5	math	math	PROPN
ejpam-4522	236	6	,	,	PUNCT
ejpam-4522	236	7	15	15	NUM
ejpam-4522	236	8	(	(	PUNCT
ejpam-4522	236	9	4	4	NUM
ejpam-4522	236	10	)	)	PUNCT
ejpam-4522	236	11	(	(	PUNCT
ejpam-4522	236	12	2022	2022	NUM
ejpam-4522	236	13	)	)	PUNCT
ejpam-4522	236	14	,	,	PUNCT
ejpam-4522	236	15	1498	1498	NUM
ejpam-4522	236	16	-	-	SYM
ejpam-4522	236	17	1511	1511	NUM
ejpam-4522	236	18	1507	1507	NUM
ejpam-4522	236	19	0	0	NUM
ejpam-4522	236	20	)	)	PUNCT
ejpam-4522	236	21	↬	↬	NOUN
ejpam-4522	236	22	0	0	NUM
ejpam-4522	236	23	)	)	PUNCT
ejpam-4522	236	24	↬	↬	PROPN
ejpam-4522	236	25	b	b	X
ejpam-4522	236	26	≤	≤	NUM
ejpam-4522	236	27	c	c	PROPN
ejpam-4522	236	28	and	and	CCONJ
ejpam-4522	236	29	(	(	PUNCT
ejpam-4522	236	30	(	(	PUNCT
ejpam-4522	236	31	x	x	NOUN
ejpam-4522	236	32	∗	∗	NOUN
ejpam-4522	236	33	0	0	NUM
ejpam-4522	236	34	)	)	PUNCT
ejpam-4522	236	35	∗	∗	NOUN
ejpam-4522	236	36	0	0	NUM
ejpam-4522	236	37	)	)	PUNCT
ejpam-4522	236	38	∗	∗	NOUN
ejpam-4522	236	39	y	y	PROPN
ejpam-4522	236	40	≤	≤	PROPN
ejpam-4522	237	1	z	z	NOUN
ejpam-4522	237	2	,	,	PUNCT
ejpam-4522	237	3	and	and	CCONJ
ejpam-4522	237	4	so	so	ADV
ejpam-4522	237	5	me(a	me(a	ADJ
ejpam-4522	237	6	)	)	PUNCT
ejpam-4522	237	7	=	=	NOUN
ejpam-4522	237	8	me(a	me(a	X
ejpam-4522	237	9	↬	↬	PROPN
ejpam-4522	237	10	0	0	NUM
ejpam-4522	237	11	)	)	PUNCT
ejpam-4522	237	12	⊇	⊇	NOUN
ejpam-4522	237	13	me(b	me(b	X
ejpam-4522	237	14	)	)	PUNCT
ejpam-4522	237	15	∩me(c	∩me(c	PROPN
ejpam-4522	237	16	)	)	PUNCT
ejpam-4522	237	17	,	,	PUNCT
ejpam-4522	237	18	ge(a	ge(a	NOUN
ejpam-4522	237	19	)	)	PUNCT
ejpam-4522	237	20	=	=	NOUN
ejpam-4522	237	21	ge(a	ge(a	PRON
ejpam-4522	237	22	↬	↬	PROPN
ejpam-4522	237	23	0	0	NUM
ejpam-4522	237	24	)	)	PUNCT
ejpam-4522	237	25	⊆	⊆	NUM
ejpam-4522	237	26	ge(b	ge(b	X
ejpam-4522	237	27	)	)	PUNCT
ejpam-4522	237	28	∪	∪	ADP
ejpam-4522	237	29	ge(c	ge(c	NUM
ejpam-4522	237	30	)	)	PUNCT
ejpam-4522	237	31	and	and	CCONJ
ejpam-4522	237	32	ξ(x	ξ(x	NOUN
ejpam-4522	237	33	)	)	PUNCT
ejpam-4522	238	1	=	=	SYM
ejpam-4522	238	2	ξ(x	ξ(x	NOUN
ejpam-4522	238	3	∗	∗	NOUN
ejpam-4522	238	4	0	0	NUM
ejpam-4522	238	5	)	)	PUNCT
ejpam-4522	238	6	≥	≥	NOUN
ejpam-4522	238	7	min{ξ(y	min{ξ(y	PROPN
ejpam-4522	238	8	)	)	PUNCT
ejpam-4522	238	9	,	,	PUNCT
ejpam-4522	238	10	ξ(z	ξ(z	PROPN
ejpam-4522	238	11	)	)	PUNCT
ejpam-4522	238	12	}	}	PUNCT
ejpam-4522	238	13	by	by	ADP
ejpam-4522	238	14	(	(	PUNCT
ejpam-4522	238	15	2	2	NUM
ejpam-4522	238	16	)	)	PUNCT
ejpam-4522	238	17	and	and	CCONJ
ejpam-4522	238	18	(	(	PUNCT
ejpam-4522	238	19	17	17	NUM
ejpam-4522	238	20	)	)	PUNCT
ejpam-4522	238	21	.	.	PUNCT
ejpam-4522	239	1	hence	hence	ADV
ejpam-4522	239	2	m(x	m(x	PROPN
ejpam-4522	239	3	,	,	PUNCT
ejpam-4522	239	4	e	e	NOUN
ejpam-4522	239	5	)	)	PUNCT
ejpam-4522	239	6	:	:	PUNCT
ejpam-4522	240	1	=	=	SYM
ejpam-4522	240	2	(	(	PUNCT
ejpam-4522	240	3	me	i	PRON
ejpam-4522	240	4	,	,	PUNCT
ejpam-4522	240	5	ge	ge	PROPN
ejpam-4522	240	6	,	,	PUNCT
ejpam-4522	240	7	ξ	ξ	X
ejpam-4522	240	8	)	)	PUNCT
ejpam-4522	240	9	is	be	AUX
ejpam-4522	240	10	a	a	DET
ejpam-4522	240	11	makgeolli	makgeolli	NOUN
ejpam-4522	240	12	ideal	ideal	NOUN
ejpam-4522	240	13	of	of	ADP
ejpam-4522	240	14	(	(	PUNCT
ejpam-4522	240	15	x	x	X
ejpam-4522	240	16	,	,	PUNCT
ejpam-4522	240	17	e	e	NOUN
ejpam-4522	240	18	)	)	PUNCT
ejpam-4522	240	19	by	by	ADP
ejpam-4522	240	20	lemma	lemma	PROPN
ejpam-4522	240	21	2	2	NUM
ejpam-4522	240	22	.	.	PUNCT
ejpam-4522	241	1	since	since	SCONJ
ejpam-4522	241	2	(	(	PUNCT
ejpam-4522	241	3	(	(	PUNCT
ejpam-4522	241	4	(	(	PUNCT
ejpam-4522	241	5	a	a	DET
ejpam-4522	241	6	↬	↬	PROPN
ejpam-4522	241	7	b	b	NOUN
ejpam-4522	241	8	)	)	PUNCT
ejpam-4522	241	9	↬	↬	PROPN
ejpam-4522	241	10	b	b	X
ejpam-4522	241	11	)	)	PUNCT
ejpam-4522	241	12	↬	↬	NOUN
ejpam-4522	241	13	(	(	PUNCT
ejpam-4522	241	14	(	(	PUNCT
ejpam-4522	241	15	a	a	DET
ejpam-4522	241	16	↬	↬	PROPN
ejpam-4522	241	17	b	b	NOUN
ejpam-4522	241	18	)	)	PUNCT
ejpam-4522	241	19	↬	↬	PROPN
ejpam-4522	241	20	b	b	X
ejpam-4522	241	21	)	)	PUNCT
ejpam-4522	241	22	)	)	PUNCT
ejpam-4522	241	23	↬	↬	NOUN
ejpam-4522	241	24	0	0	NUM
ejpam-4522	242	1	=	=	SYM
ejpam-4522	242	2	0	0	NUM
ejpam-4522	243	1	and	and	CCONJ
ejpam-4522	243	2	(	(	PUNCT
ejpam-4522	243	3	(	(	PUNCT
ejpam-4522	243	4	(	(	PUNCT
ejpam-4522	243	5	x	x	SYM
ejpam-4522	243	6	∗	∗	PROPN
ejpam-4522	243	7	y	y	NOUN
ejpam-4522	243	8	)	)	PUNCT
ejpam-4522	243	9	∗	∗	PROPN
ejpam-4522	243	10	y	y	NOUN
ejpam-4522	243	11	)	)	PUNCT
ejpam-4522	243	12	∗	∗	NOUN
ejpam-4522	243	13	(	(	PUNCT
ejpam-4522	243	14	(	(	PUNCT
ejpam-4522	243	15	x	x	SYM
ejpam-4522	243	16	∗	∗	PROPN
ejpam-4522	243	17	y	y	NOUN
ejpam-4522	243	18	)	)	PUNCT
ejpam-4522	243	19	∗	∗	PROPN
ejpam-4522	243	20	y	y	PROPN
ejpam-4522	243	21	)	)	PUNCT
ejpam-4522	243	22	)	)	PUNCT
ejpam-4522	243	23	∗	∗	NOUN
ejpam-4522	243	24	0	0	NUM
ejpam-4522	244	1	=	=	SYM
ejpam-4522	244	2	0	0	NUM
ejpam-4522	244	3	for	for	ADP
ejpam-4522	244	4	all	all	DET
ejpam-4522	244	5	a	a	DET
ejpam-4522	244	6	,	,	PUNCT
ejpam-4522	244	7	b	b	X
ejpam-4522	244	8	∈	∈	PROPN
ejpam-4522	244	9	e	e	X
ejpam-4522	244	10	and	and	CCONJ
ejpam-4522	244	11	x	x	NOUN
ejpam-4522	244	12	,	,	PUNCT
ejpam-4522	244	13	y	y	PROPN
ejpam-4522	244	14	∈	∈	PROPN
ejpam-4522	244	15	x	x	AUX
ejpam-4522	244	16	,	,	PUNCT
ejpam-4522	244	17	it	it	PRON
ejpam-4522	244	18	follows	follow	VERB
ejpam-4522	244	19	from	from	ADP
ejpam-4522	244	20	(	(	PUNCT
ejpam-4522	244	21	9	9	NUM
ejpam-4522	244	22	)	)	PUNCT
ejpam-4522	244	23	and	and	CCONJ
ejpam-4522	244	24	(	(	PUNCT
ejpam-4522	244	25	17	17	NUM
ejpam-4522	244	26	)	)	PUNCT
ejpam-4522	245	1	that	that	PRON
ejpam-4522	245	2	me(a	me(a	PRON
ejpam-4522	245	3	↬	↬	PROPN
ejpam-4522	245	4	b	b	X
ejpam-4522	245	5	)	)	PUNCT
ejpam-4522	245	6	⊇	⊇	PROPN
ejpam-4522	245	7	me((a	me((a	PROPN
ejpam-4522	245	8	↬	↬	PROPN
ejpam-4522	245	9	b	b	X
ejpam-4522	245	10	)	)	PUNCT
ejpam-4522	245	11	↬	↬	PROPN
ejpam-4522	245	12	b	b	X
ejpam-4522	245	13	)	)	PUNCT
ejpam-4522	245	14	∩me(0	∩me(0	NOUN
ejpam-4522	245	15	)	)	PUNCT
ejpam-4522	245	16	=	=	SYM
ejpam-4522	245	17	me((a	me((a	PROPN
ejpam-4522	245	18	↬	↬	PROPN
ejpam-4522	245	19	b	b	X
ejpam-4522	245	20	)	)	PUNCT
ejpam-4522	245	21	↬	↬	PROPN
ejpam-4522	245	22	b	b	X
ejpam-4522	245	23	)	)	PUNCT
ejpam-4522	245	24	,	,	PUNCT
ejpam-4522	245	25	ge(a	ge(a	PRON
ejpam-4522	245	26	↬	↬	PROPN
ejpam-4522	245	27	b	b	X
ejpam-4522	245	28	)	)	PUNCT
ejpam-4522	245	29	⊆	⊆	NUM
ejpam-4522	245	30	ge((a	ge((a	NOUN
ejpam-4522	245	31	↬	↬	PROPN
ejpam-4522	245	32	b	b	NOUN
ejpam-4522	245	33	)	)	PUNCT
ejpam-4522	245	34	↬	↬	PROPN
ejpam-4522	245	35	b	b	X
ejpam-4522	245	36	)	)	PUNCT
ejpam-4522	245	37	∪ge(0	∪ge(0	PROPN
ejpam-4522	245	38	)	)	PUNCT
ejpam-4522	245	39	=	=	SYM
ejpam-4522	246	1	ge((a	ge((a	NOUN
ejpam-4522	246	2	↬	↬	PROPN
ejpam-4522	246	3	b	b	X
ejpam-4522	246	4	)	)	PUNCT
ejpam-4522	246	5	↬	↬	PROPN
ejpam-4522	246	6	b	b	X
ejpam-4522	246	7	)	)	PUNCT
ejpam-4522	246	8	,	,	PUNCT
ejpam-4522	246	9	ξ(x	ξ(x	PROPN
ejpam-4522	246	10	∗	∗	NOUN
ejpam-4522	246	11	y	y	PROPN
ejpam-4522	246	12	)	)	PUNCT
ejpam-4522	246	13	≥	≥	NOUN
ejpam-4522	246	14	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	246	15	∗	∗	X
ejpam-4522	246	16	y	y	NOUN
ejpam-4522	246	17	)	)	PUNCT
ejpam-4522	246	18	∗	∗	PROPN
ejpam-4522	246	19	y	y	PROPN
ejpam-4522	246	20	)	)	PUNCT
ejpam-4522	246	21	,	,	PUNCT
ejpam-4522	246	22	ξ(0	ξ(0	NOUN
ejpam-4522	246	23	)	)	PUNCT
ejpam-4522	246	24	}	}	PUNCT
ejpam-4522	246	25	=	=	SYM
ejpam-4522	246	26	ξ((x	ξ((x	NOUN
ejpam-4522	246	27	∗	∗	NOUN
ejpam-4522	246	28	y	y	NOUN
ejpam-4522	246	29	)	)	PUNCT
ejpam-4522	246	30	∗	∗	PROPN
ejpam-4522	246	31	y	y	PROPN
ejpam-4522	246	32	)	)	PUNCT
ejpam-4522	246	33	.	.	PUNCT
ejpam-4522	247	1	consequently	consequently	ADV
ejpam-4522	247	2	,	,	PUNCT
ejpam-4522	247	3	m(x	m(x	PROPN
ejpam-4522	247	4	,	,	PUNCT
ejpam-4522	247	5	e	e	NOUN
ejpam-4522	247	6	)	)	PUNCT
ejpam-4522	247	7	:	:	PUNCT
ejpam-4522	248	1	=	=	SYM
ejpam-4522	248	2	(	(	PUNCT
ejpam-4522	248	3	me	i	PRON
ejpam-4522	248	4	,	,	PUNCT
ejpam-4522	248	5	ge	ge	PROPN
ejpam-4522	248	6	,	,	PUNCT
ejpam-4522	248	7	ξ	ξ	X
ejpam-4522	248	8	)	)	PUNCT
ejpam-4522	248	9	is	be	AUX
ejpam-4522	248	10	a	a	DET
ejpam-4522	248	11	positive	positive	ADJ
ejpam-4522	248	12	implicative	implicative	ADJ
ejpam-4522	248	13	makgeolli	makgeolli	NOUN
ejpam-4522	248	14	ideal	ideal	NOUN
ejpam-4522	248	15	of	of	ADP
ejpam-4522	248	16	(	(	PUNCT
ejpam-4522	248	17	x	x	X
ejpam-4522	248	18	,	,	PUNCT
ejpam-4522	248	19	e	e	NOUN
ejpam-4522	248	20	)	)	PUNCT
ejpam-4522	248	21	by	by	ADP
ejpam-4522	248	22	theorem	theorem	ADJ
ejpam-4522	248	23	3	3	NUM
ejpam-4522	248	24	.	.	PUNCT
ejpam-4522	248	25	theorem	theorem	VERB
ejpam-4522	248	26	7	7	NUM
ejpam-4522	248	27	.	.	PUNCT
ejpam-4522	248	28	a	a	DET
ejpam-4522	248	29	makgeolli	makgeolli	NOUN
ejpam-4522	248	30	structure	structure	NOUN
ejpam-4522	248	31	m(x	m(x	PROPN
ejpam-4522	248	32	,	,	PUNCT
ejpam-4522	248	33	e	e	NOUN
ejpam-4522	248	34	)	)	PUNCT
ejpam-4522	248	35	:	:	PUNCT
ejpam-4522	248	36	=	=	SYM
ejpam-4522	248	37	(	(	PUNCT
ejpam-4522	248	38	me	i	PRON
ejpam-4522	248	39	,	,	PUNCT
ejpam-4522	248	40	ge	ge	PROPN
ejpam-4522	248	41	,	,	PUNCT
ejpam-4522	248	42	ξ	ξ	PROPN
ejpam-4522	248	43	)	)	PUNCT
ejpam-4522	248	44	on	on	ADP
ejpam-4522	248	45	(	(	PUNCT
ejpam-4522	248	46	x	x	X
ejpam-4522	248	47	,	,	PUNCT
ejpam-4522	248	48	e	e	NOUN
ejpam-4522	248	49	)	)	PUNCT
ejpam-4522	248	50	is	be	AUX
ejpam-4522	248	51	a	a	DET
ejpam-4522	248	52	positive	positive	ADJ
ejpam-4522	248	53	implicative	implicative	ADJ
ejpam-4522	248	54	makgeolli	makgeolli	NOUN
ejpam-4522	248	55	ideal	ideal	NOUN
ejpam-4522	248	56	of	of	ADP
ejpam-4522	248	57	(	(	PUNCT
ejpam-4522	248	58	x	x	X
ejpam-4522	248	59	,	,	PUNCT
ejpam-4522	248	60	e	e	NOUN
ejpam-4522	248	61	)	)	PUNCT
ejpam-4522	248	62	if	if	SCONJ
ejpam-4522	248	63	and	and	CCONJ
ejpam-4522	248	64	only	only	ADV
ejpam-4522	248	65	if	if	SCONJ
ejpam-4522	248	66	it	it	PRON
ejpam-4522	248	67	satisfies:	satisfies:	VERB
ejpam-4522	248	68	(	(	PUNCT
ejpam-4522	248	69	∀a	∀a	X
ejpam-4522	248	70	,	,	PUNCT
ejpam-4522	248	71	b	b	X
ejpam-4522	248	72	,	,	PUNCT
ejpam-4522	248	73	c	c	NOUN
ejpam-4522	248	74	,	,	PUNCT
ejpam-4522	248	75	x	x	X
ejpam-4522	248	76	,	,	PUNCT
ejpam-4522	248	77	y	y	PROPN
ejpam-4522	248	78	∈	∈	PROPN
ejpam-4522	248	79	e	e	X
ejpam-4522	248	80	)	)	PUNCT
ejpam-4522	248	81			PROPN
ejpam-4522	248	82	(	(	PUNCT
ejpam-4522	248	83	(	(	PUNCT
ejpam-4522	248	84	a	a	DET
ejpam-4522	248	85	↬	↬	PROPN
ejpam-4522	248	86	b	b	NOUN
ejpam-4522	248	87	)	)	PUNCT
ejpam-4522	248	88	↬	↬	PROPN
ejpam-4522	248	89	c	c	X
ejpam-4522	248	90	)	)	PUNCT
ejpam-4522	248	91	↬	↬	NOUN
ejpam-4522	249	1	x	x	X
ejpam-4522	249	2	≤	≤	NUM
ejpam-4522	249	3	y	y	PROPN
ejpam-4522	249	4	⇒	⇒	PROPN
ejpam-4522	249	5	{	{	PUNCT
ejpam-4522	249	6	me((a	me((a	PROPN
ejpam-4522	249	7	↬	↬	PROPN
ejpam-4522	249	8	c	c	NOUN
ejpam-4522	249	9	)	)	PUNCT
ejpam-4522	249	10	↬	↬	NOUN
ejpam-4522	249	11	(	(	PUNCT
ejpam-4522	249	12	b	b	X
ejpam-4522	249	13	↬	↬	PROPN
ejpam-4522	249	14	c	c	NOUN
ejpam-4522	249	15	)	)	PUNCT
ejpam-4522	249	16	)	)	PUNCT
ejpam-4522	249	17	⊇	⊇	NOUN
ejpam-4522	249	18	me(x	me(x	X
ejpam-4522	249	19	)	)	PUNCT
ejpam-4522	249	20	∩me(y	∩me(y	PROPN
ejpam-4522	249	21	)	)	PUNCT
ejpam-4522	249	22	ge((a	ge((a	NOUN
ejpam-4522	249	23	↬	↬	PROPN
ejpam-4522	249	24	c	c	NOUN
ejpam-4522	249	25	)	)	PUNCT
ejpam-4522	249	26	↬	↬	NOUN
ejpam-4522	249	27	(	(	PUNCT
ejpam-4522	249	28	b	b	X
ejpam-4522	249	29	↬	↬	PROPN
ejpam-4522	249	30	c	c	NOUN
ejpam-4522	249	31	)	)	PUNCT
ejpam-4522	249	32	)	)	PUNCT
ejpam-4522	250	1	⊆	⊆	NUM
ejpam-4522	250	2	ge(x	ge(x	X
ejpam-4522	250	3	)	)	PUNCT
ejpam-4522	250	4	∪ge(y	∪ge(y	PROPN
ejpam-4522	250	5	)	)	PUNCT
ejpam-4522	250	6			PROPN
ejpam-4522	250	7	.	.	PUNCT
ejpam-4522	251	1	(	(	PUNCT
ejpam-4522	251	2	∀x	∀x	X
ejpam-4522	251	3	,	,	PUNCT
ejpam-4522	251	4	y	y	PROPN
ejpam-4522	251	5	,	,	PUNCT
ejpam-4522	251	6	z	z	PROPN
ejpam-4522	251	7	,	,	PUNCT
ejpam-4522	251	8	a	a	PRON
ejpam-4522	251	9	,	,	PUNCT
ejpam-4522	251	10	b	b	X
ejpam-4522	251	11	∈	∈	PROPN
ejpam-4522	251	12	x	x	X
ejpam-4522	251	13	)	)	PUNCT
ejpam-4522	251	14	(	(	PUNCT
ejpam-4522	251	15	(	(	PUNCT
ejpam-4522	251	16	(	(	PUNCT
ejpam-4522	251	17	x	x	SYM
ejpam-4522	251	18	∗	∗	PROPN
ejpam-4522	251	19	y	y	NOUN
ejpam-4522	251	20	)	)	PUNCT
ejpam-4522	251	21	∗	∗	NOUN
ejpam-4522	251	22	z	z	NOUN
ejpam-4522	251	23	)	)	PUNCT
ejpam-4522	251	24	∗	∗	NOUN
ejpam-4522	251	25	a	a	DET
ejpam-4522	251	26	≤	≤	NUM
ejpam-4522	251	27	b	b	NOUN
ejpam-4522	251	28	⇒	⇒	NOUN
ejpam-4522	251	29	ξ((x	ξ((x	PROPN
ejpam-4522	251	30	∗	∗	PROPN
ejpam-4522	251	31	z	z	NOUN
ejpam-4522	251	32	)	)	PUNCT
ejpam-4522	251	33	∗	∗	NOUN
ejpam-4522	251	34	(	(	PUNCT
ejpam-4522	251	35	y	y	PROPN
ejpam-4522	251	36	∗	∗	PROPN
ejpam-4522	251	37	z	z	NOUN
ejpam-4522	251	38	)	)	PUNCT
ejpam-4522	251	39	)	)	PUNCT
ejpam-4522	251	40	≥	≥	NOUN
ejpam-4522	251	41	min{ξ(a	min{ξ(a	NUM
ejpam-4522	251	42	)	)	PUNCT
ejpam-4522	251	43	,	,	PUNCT
ejpam-4522	251	44	ξ(b	ξ(b	NOUN
ejpam-4522	251	45	)	)	PUNCT
ejpam-4522	251	46	}	}	PUNCT
ejpam-4522	251	47	)	)	PUNCT
ejpam-4522	251	48	.	.	PUNCT
ejpam-4522	252	1	(	(	PUNCT
ejpam-4522	252	2	18	18	NUM
ejpam-4522	252	3	)	)	PUNCT
ejpam-4522	252	4	proof	proof	NOUN
ejpam-4522	252	5	.	.	PUNCT
ejpam-4522	253	1	assume	assume	VERB
ejpam-4522	253	2	that	that	SCONJ
ejpam-4522	253	3	m(x	m(x	PROPN
ejpam-4522	253	4	,	,	PUNCT
ejpam-4522	253	5	e	e	NOUN
ejpam-4522	253	6	)	)	PUNCT
ejpam-4522	253	7	:	:	PUNCT
ejpam-4522	253	8	=	=	SYM
ejpam-4522	253	9	(	(	PUNCT
ejpam-4522	253	10	me	i	PRON
ejpam-4522	253	11	,	,	PUNCT
ejpam-4522	253	12	ge	ge	PROPN
ejpam-4522	253	13	,	,	PUNCT
ejpam-4522	253	14	ξ	ξ	X
ejpam-4522	253	15	)	)	PUNCT
ejpam-4522	253	16	is	be	AUX
ejpam-4522	253	17	a	a	DET
ejpam-4522	253	18	positive	positive	ADJ
ejpam-4522	253	19	implicative	implicative	ADJ
ejpam-4522	253	20	makgeolli	makgeolli	NOUN
ejpam-4522	253	21	ideal	ideal	NOUN
ejpam-4522	253	22	of	of	ADP
ejpam-4522	253	23	(	(	PUNCT
ejpam-4522	253	24	x	x	X
ejpam-4522	253	25	,	,	PUNCT
ejpam-4522	253	26	e	e	NOUN
ejpam-4522	253	27	)	)	PUNCT
ejpam-4522	253	28	.	.	PUNCT
ejpam-4522	254	1	then	then	ADV
ejpam-4522	254	2	it	it	PRON
ejpam-4522	254	3	is	be	AUX
ejpam-4522	254	4	a	a	DET
ejpam-4522	254	5	makgeolli	makgeolli	NOUN
ejpam-4522	254	6	ideal	ideal	NOUN
ejpam-4522	254	7	of	of	ADP
ejpam-4522	254	8	(	(	PUNCT
ejpam-4522	254	9	x	x	X
ejpam-4522	254	10	,	,	PUNCT
ejpam-4522	254	11	e	e	NOUN
ejpam-4522	254	12	)	)	PUNCT
ejpam-4522	254	13	(	(	PUNCT
ejpam-4522	254	14	see	see	VERB
ejpam-4522	254	15	theorem	theorem	NOUN
ejpam-4522	254	16	1	1	NUM
ejpam-4522	254	17	)	)	PUNCT
ejpam-4522	254	18	.	.	PUNCT
ejpam-4522	255	1	let	let	VERB
ejpam-4522	255	2	(	(	PUNCT
ejpam-4522	255	3	(	(	PUNCT
ejpam-4522	255	4	a	a	DET
ejpam-4522	255	5	↬	↬	PROPN
ejpam-4522	255	6	b	b	NOUN
ejpam-4522	255	7	)	)	PUNCT
ejpam-4522	255	8	↬	↬	PROPN
ejpam-4522	255	9	c	c	X
ejpam-4522	255	10	)	)	PUNCT
ejpam-4522	255	11	↬	↬	NOUN
ejpam-4522	255	12	x	x	PUNCT
ejpam-4522	255	13	≤	≤	NUM
ejpam-4522	255	14	y	y	NOUN
ejpam-4522	255	15	for	for	ADP
ejpam-4522	255	16	all	all	DET
ejpam-4522	255	17	a	a	DET
ejpam-4522	255	18	,	,	PUNCT
ejpam-4522	255	19	b	b	NOUN
ejpam-4522	255	20	,	,	PUNCT
ejpam-4522	255	21	c	c	NOUN
ejpam-4522	255	22	,	,	PUNCT
ejpam-4522	255	23	x	x	X
ejpam-4522	255	24	,	,	PUNCT
ejpam-4522	255	25	y	y	PROPN
ejpam-4522	255	26	∈	∈	PROPN
ejpam-4522	255	27	e	e	NOUN
ejpam-4522	255	28	,	,	PUNCT
ejpam-4522	255	29	and	and	CCONJ
ejpam-4522	255	30	let	let	VERB
ejpam-4522	255	31	(	(	PUNCT
ejpam-4522	255	32	(	(	PUNCT
ejpam-4522	255	33	x	x	SYM
ejpam-4522	255	34	∗	∗	PROPN
ejpam-4522	255	35	y	y	NOUN
ejpam-4522	255	36	)	)	PUNCT
ejpam-4522	255	37	∗	∗	NOUN
ejpam-4522	255	38	z	z	NOUN
ejpam-4522	255	39	)	)	PUNCT
ejpam-4522	255	40	∗	∗	NOUN
ejpam-4522	255	41	a	a	DET
ejpam-4522	255	42	≤	≤	NUM
ejpam-4522	255	43	b	b	NOUN
ejpam-4522	255	44	for	for	ADP
ejpam-4522	255	45	all	all	DET
ejpam-4522	255	46	x	x	NOUN
ejpam-4522	255	47	,	,	PUNCT
ejpam-4522	255	48	y	y	PROPN
ejpam-4522	255	49	,	,	PUNCT
ejpam-4522	255	50	z	z	PROPN
ejpam-4522	255	51	,	,	PUNCT
ejpam-4522	255	52	a	a	PRON
ejpam-4522	255	53	,	,	PUNCT
ejpam-4522	255	54	b	b	X
ejpam-4522	255	55	∈	∈	PROPN
ejpam-4522	255	56	x.	x.	NOUN
ejpam-4522	256	1	the	the	DET
ejpam-4522	256	2	combination	combination	NOUN
ejpam-4522	256	3	of	of	ADP
ejpam-4522	256	4	the	the	DET
ejpam-4522	256	5	assertion	assertion	NOUN
ejpam-4522	256	6	(	(	PUNCT
ejpam-4522	256	7	ii	ii	NOUN
ejpam-4522	256	8	)	)	PUNCT
ejpam-4522	256	9	in	in	ADP
ejpam-4522	256	10	lemma	lemma	PROPN
ejpam-4522	256	11	1	1	NUM
ejpam-4522	256	12	and	and	CCONJ
ejpam-4522	256	13	theorem	theorem	VERB
ejpam-4522	256	14	4	4	NUM
ejpam-4522	256	15	leads	lead	VERB
ejpam-4522	256	16	to	to	ADP
ejpam-4522	256	17	me((a	me((a	PROPN
ejpam-4522	256	18	↬	↬	PROPN
ejpam-4522	256	19	c	c	X
ejpam-4522	256	20	)	)	PUNCT
ejpam-4522	256	21	↬	↬	NOUN
ejpam-4522	257	1	(	(	PUNCT
ejpam-4522	257	2	b	b	X
ejpam-4522	257	3	↬	↬	PROPN
ejpam-4522	257	4	c	c	NOUN
ejpam-4522	257	5	)	)	PUNCT
ejpam-4522	257	6	)	)	PUNCT
ejpam-4522	257	7	⊇	⊇	PROPN
ejpam-4522	257	8	me((a	me((a	PROPN
ejpam-4522	257	9	↬	↬	PROPN
ejpam-4522	257	10	b	b	X
ejpam-4522	257	11	)	)	PUNCT
ejpam-4522	257	12	↬	↬	X
ejpam-4522	257	13	c	c	X
ejpam-4522	257	14	)	)	PUNCT
ejpam-4522	257	15	⊇	⊇	NOUN
ejpam-4522	257	16	me(x	me(x	X
ejpam-4522	257	17	)	)	PUNCT
ejpam-4522	257	18	∩me(y	∩me(y	PROPN
ejpam-4522	257	19	)	)	PUNCT
ejpam-4522	257	20	,	,	PUNCT
ejpam-4522	257	21	ge((a	ge((a	NOUN
ejpam-4522	257	22	↬	↬	PROPN
ejpam-4522	257	23	c	c	X
ejpam-4522	257	24	)	)	PUNCT
ejpam-4522	257	25	↬	↬	NOUN
ejpam-4522	258	1	(	(	PUNCT
ejpam-4522	258	2	b	b	X
ejpam-4522	258	3	↬	↬	PROPN
ejpam-4522	258	4	c	c	NOUN
ejpam-4522	258	5	)	)	PUNCT
ejpam-4522	258	6	)	)	PUNCT
ejpam-4522	259	1	⊆	⊆	NUM
ejpam-4522	259	2	ge((a	ge((a	NOUN
ejpam-4522	259	3	↬	↬	PROPN
ejpam-4522	259	4	b	b	X
ejpam-4522	259	5	)	)	PUNCT
ejpam-4522	259	6	↬	↬	X
ejpam-4522	259	7	c	c	X
ejpam-4522	259	8	)	)	PUNCT
ejpam-4522	259	9	⊆	⊆	NUM
ejpam-4522	259	10	ge(x	ge(x	X
ejpam-4522	259	11	)	)	PUNCT
ejpam-4522	259	12	∪ge(y	∪ge(y	PROPN
ejpam-4522	259	13	)	)	PUNCT
ejpam-4522	259	14	,	,	PUNCT
ejpam-4522	259	15	ξ((x	ξ((x	VERB
ejpam-4522	259	16	∗	∗	PROPN
ejpam-4522	259	17	z	z	NOUN
ejpam-4522	259	18	)	)	PUNCT
ejpam-4522	259	19	∗	∗	NOUN
ejpam-4522	259	20	(	(	PUNCT
ejpam-4522	259	21	y	y	PROPN
ejpam-4522	259	22	∗	∗	PROPN
ejpam-4522	259	23	z	z	NOUN
ejpam-4522	259	24	)	)	PUNCT
ejpam-4522	259	25	)	)	PUNCT
ejpam-4522	259	26	≥	≥	PRON
ejpam-4522	259	27	ξ((x	ξ((x	PROPN
ejpam-4522	259	28	∗	∗	PROPN
ejpam-4522	259	29	y	y	NOUN
ejpam-4522	259	30	)	)	PUNCT
ejpam-4522	259	31	∗	∗	NOUN
ejpam-4522	259	32	z	z	NOUN
ejpam-4522	259	33	)	)	PUNCT
ejpam-4522	259	34	≥	≥	NOUN
ejpam-4522	259	35	min{ξ(a	min{ξ(a	NUM
ejpam-4522	259	36	)	)	PUNCT
ejpam-4522	259	37	,	,	PUNCT
ejpam-4522	259	38	ξ(b	ξ(b	NOUN
ejpam-4522	259	39	)	)	PUNCT
ejpam-4522	259	40	}	}	PUNCT
ejpam-4522	259	41	.	.	PUNCT
ejpam-4522	260	1	conversely	conversely	ADV
ejpam-4522	260	2	,	,	PUNCT
ejpam-4522	260	3	letm(x	letm(x	NOUN
ejpam-4522	260	4	,	,	PUNCT
ejpam-4522	260	5	e	e	NOUN
ejpam-4522	260	6	)	)	PUNCT
ejpam-4522	260	7	:	:	PUNCT
ejpam-4522	261	1	=	=	SYM
ejpam-4522	261	2	(	(	PUNCT
ejpam-4522	261	3	me	i	PRON
ejpam-4522	261	4	,	,	PUNCT
ejpam-4522	261	5	ge	ge	PROPN
ejpam-4522	261	6	,	,	PUNCT
ejpam-4522	261	7	ξ	ξ	X
ejpam-4522	261	8	)	)	PUNCT
ejpam-4522	261	9	be	be	VERB
ejpam-4522	261	10	a	a	DET
ejpam-4522	261	11	makgeolli	makgeolli	NOUN
ejpam-4522	261	12	structure	structure	NOUN
ejpam-4522	261	13	on	on	ADP
ejpam-4522	261	14	(	(	PUNCT
ejpam-4522	261	15	x	x	X
ejpam-4522	261	16	,	,	PUNCT
ejpam-4522	261	17	e	e	NOUN
ejpam-4522	261	18	)	)	PUNCT
ejpam-4522	261	19	that	that	PRON
ejpam-4522	261	20	satisfies	satisfie	NOUN
ejpam-4522	261	21	(	(	PUNCT
ejpam-4522	261	22	18	18	NUM
ejpam-4522	261	23	)	)	PUNCT
ejpam-4522	261	24	.	.	PUNCT
ejpam-4522	262	1	let	let	VERB
ejpam-4522	262	2	a	a	DET
ejpam-4522	262	3	,	,	PUNCT
ejpam-4522	262	4	b	b	NOUN
ejpam-4522	262	5	,	,	PUNCT
ejpam-4522	262	6	x	x	X
ejpam-4522	262	7	,	,	PUNCT
ejpam-4522	262	8	y	y	PROPN
ejpam-4522	262	9	∈	∈	PROPN
ejpam-4522	262	10	e	e	NOUN
ejpam-4522	262	11	be	be	VERB
ejpam-4522	262	12	such	such	ADJ
ejpam-4522	262	13	that	that	SCONJ
ejpam-4522	262	14	(	(	PUNCT
ejpam-4522	262	15	(	(	PUNCT
ejpam-4522	262	16	a	a	DET
ejpam-4522	262	17	↬	↬	PROPN
ejpam-4522	262	18	b	b	NOUN
ejpam-4522	262	19	)	)	PUNCT
ejpam-4522	262	20	↬	↬	PROPN
ejpam-4522	262	21	b	b	X
ejpam-4522	262	22	)	)	PUNCT
ejpam-4522	262	23	↬	↬	NOUN
ejpam-4522	262	24	x	x	PUNCT
ejpam-4522	262	25	≤	≤	NUM
ejpam-4522	262	26	y	y	PROPN
ejpam-4522	262	27	,	,	PUNCT
ejpam-4522	262	28	and	and	CCONJ
ejpam-4522	262	29	let	let	VERB
ejpam-4522	262	30	x	x	PRON
ejpam-4522	262	31	,	,	PUNCT
ejpam-4522	262	32	y	y	PROPN
ejpam-4522	262	33	,	,	PUNCT
ejpam-4522	262	34	a	a	PRON
ejpam-4522	262	35	,	,	PUNCT
ejpam-4522	262	36	b	b	X
ejpam-4522	262	37	∈	∈	PROPN
ejpam-4522	262	38	x	x	AUX
ejpam-4522	262	39	be	be	AUX
ejpam-4522	262	40	such	such	ADJ
ejpam-4522	262	41	that	that	SCONJ
ejpam-4522	262	42	(	(	PUNCT
ejpam-4522	262	43	(	(	PUNCT
ejpam-4522	262	44	x	x	SYM
ejpam-4522	262	45	∗	∗	PROPN
ejpam-4522	262	46	y	y	NOUN
ejpam-4522	262	47	)	)	PUNCT
ejpam-4522	262	48	∗	∗	PROPN
ejpam-4522	262	49	y	y	PROPN
ejpam-4522	262	50	)	)	PUNCT
ejpam-4522	262	51	∗	∗	VERB
ejpam-4522	262	52	a	a	DET
ejpam-4522	262	53	≤	≤	PROPN
ejpam-4522	262	54	b.	b.	NOUN
ejpam-4522	262	55	using	use	VERB
ejpam-4522	262	56	(	(	PUNCT
ejpam-4522	262	57	i3	i3	NOUN
ejpam-4522	262	58	)	)	PUNCT
ejpam-4522	262	59	,	,	PUNCT
ejpam-4522	262	60	(	(	PUNCT
ejpam-4522	262	61	2	2	X
ejpam-4522	262	62	)	)	PUNCT
ejpam-4522	262	63	and	and	CCONJ
ejpam-4522	262	64	(	(	PUNCT
ejpam-4522	262	65	18	18	NUM
ejpam-4522	262	66	)	)	PUNCT
ejpam-4522	262	67	,	,	PUNCT
ejpam-4522	262	68	we	we	PRON
ejpam-4522	262	69	have	have	VERB
ejpam-4522	262	70	me(a	me(a	NOUN
ejpam-4522	262	71	↬	↬	PROPN
ejpam-4522	262	72	b	b	X
ejpam-4522	262	73	)	)	PUNCT
ejpam-4522	262	74	=	=	SYM
ejpam-4522	262	75	me((a	me((a	PROPN
ejpam-4522	262	76	↬	↬	PROPN
ejpam-4522	262	77	b	b	X
ejpam-4522	262	78	)	)	PUNCT
ejpam-4522	262	79	↬	↬	PROPN
ejpam-4522	262	80	(	(	PUNCT
ejpam-4522	262	81	b	b	PROPN
ejpam-4522	262	82	↬	↬	PROPN
ejpam-4522	262	83	b	b	NOUN
ejpam-4522	262	84	)	)	PUNCT
ejpam-4522	262	85	)	)	PUNCT
ejpam-4522	262	86	⊇	⊇	NOUN
ejpam-4522	262	87	me(x	me(x	X
ejpam-4522	262	88	)	)	PUNCT
ejpam-4522	262	89	∩me(y	∩me(y	PROPN
ejpam-4522	262	90	)	)	PUNCT
ejpam-4522	262	91	,	,	PUNCT
ejpam-4522	262	92	ge(a	ge(a	PRON
ejpam-4522	262	93	↬	↬	PROPN
ejpam-4522	262	94	b	b	X
ejpam-4522	262	95	)	)	PUNCT
ejpam-4522	262	96	=	=	VERB
ejpam-4522	263	1	ge((a	ge((a	NOUN
ejpam-4522	263	2	↬	↬	PROPN
ejpam-4522	263	3	b	b	X
ejpam-4522	263	4	)	)	PUNCT
ejpam-4522	263	5	↬	↬	PROPN
ejpam-4522	264	1	(	(	PUNCT
ejpam-4522	264	2	b	b	PROPN
ejpam-4522	264	3	↬	↬	PROPN
ejpam-4522	264	4	b	b	NOUN
ejpam-4522	264	5	)	)	PUNCT
ejpam-4522	264	6	)	)	PUNCT
ejpam-4522	264	7	⊆	⊆	NUM
ejpam-4522	264	8	ge(x	ge(x	X
ejpam-4522	264	9	)	)	PUNCT
ejpam-4522	264	10	∪ge(y	∪ge(y	PROPN
ejpam-4522	264	11	)	)	PUNCT
ejpam-4522	264	12	,	,	PUNCT
ejpam-4522	264	13	ξ(x	ξ(x	PROPN
ejpam-4522	264	14	∗	∗	NOUN
ejpam-4522	264	15	y	y	NOUN
ejpam-4522	264	16	)	)	PUNCT
ejpam-4522	264	17	=	=	SYM
ejpam-4522	264	18	ξ((x	ξ((x	NOUN
ejpam-4522	264	19	∗	∗	NOUN
ejpam-4522	264	20	y	y	NOUN
ejpam-4522	264	21	)	)	PUNCT
ejpam-4522	264	22	∗	∗	NOUN
ejpam-4522	264	23	(	(	PUNCT
ejpam-4522	264	24	y	y	PROPN
ejpam-4522	264	25	∗	∗	PROPN
ejpam-4522	264	26	y	y	PROPN
ejpam-4522	264	27	)	)	PUNCT
ejpam-4522	264	28	)	)	PUNCT
ejpam-4522	264	29	≥	≥	NOUN
ejpam-4522	264	30	min{ξ(a	min{ξ(a	NUM
ejpam-4522	264	31	)	)	PUNCT
ejpam-4522	264	32	,	,	PUNCT
ejpam-4522	264	33	ξ(b	ξ(b	NOUN
ejpam-4522	264	34	)	)	PUNCT
ejpam-4522	264	35	}	}	PUNCT
ejpam-4522	264	36	.	.	PUNCT
ejpam-4522	265	1	it	it	PRON
ejpam-4522	265	2	follows	follow	VERB
ejpam-4522	265	3	from	from	ADP
ejpam-4522	265	4	theorem	theorem	NOUN
ejpam-4522	265	5	6	6	NUM
ejpam-4522	265	6	that	that	SCONJ
ejpam-4522	265	7	m(x	m(x	PROPN
ejpam-4522	265	8	,	,	PUNCT
ejpam-4522	265	9	e	e	NOUN
ejpam-4522	265	10	)	)	PUNCT
ejpam-4522	265	11	:	:	PUNCT
ejpam-4522	266	1	=	=	SYM
ejpam-4522	266	2	(	(	PUNCT
ejpam-4522	266	3	me	i	PRON
ejpam-4522	266	4	,	,	PUNCT
ejpam-4522	266	5	ge	ge	PROPN
ejpam-4522	266	6	,	,	PUNCT
ejpam-4522	266	7	ξ	ξ	X
ejpam-4522	266	8	)	)	PUNCT
ejpam-4522	266	9	is	be	AUX
ejpam-4522	266	10	a	a	DET
ejpam-4522	266	11	positive	positive	ADJ
ejpam-4522	266	12	implicative	implicative	ADJ
ejpam-4522	266	13	makgeolli	makgeolli	NOUN
ejpam-4522	266	14	ideal	ideal	NOUN
ejpam-4522	266	15	of	of	ADP
ejpam-4522	266	16	(	(	PUNCT
ejpam-4522	266	17	x	x	X
ejpam-4522	266	18	,	,	PUNCT
ejpam-4522	266	19	e	e	NOUN
ejpam-4522	266	20	)	)	PUNCT
ejpam-4522	266	21	.	.	PUNCT
ejpam-4522	267	1	theorem	theorem	ADJ
ejpam-4522	267	2	8	8	NUM
ejpam-4522	267	3	.	.	PUNCT
ejpam-4522	268	1	a	a	DET
ejpam-4522	268	2	makgeolli	makgeolli	NOUN
ejpam-4522	268	3	structure	structure	NOUN
ejpam-4522	268	4	m(x	m(x	PROPN
ejpam-4522	268	5	,	,	PUNCT
ejpam-4522	268	6	e	e	NOUN
ejpam-4522	268	7	)	)	PUNCT
ejpam-4522	268	8	:	:	PUNCT
ejpam-4522	268	9	=	=	SYM
ejpam-4522	268	10	(	(	PUNCT
ejpam-4522	268	11	me	i	PRON
ejpam-4522	268	12	,	,	PUNCT
ejpam-4522	268	13	ge	ge	PROPN
ejpam-4522	268	14	,	,	PUNCT
ejpam-4522	268	15	ξ	ξ	PROPN
ejpam-4522	268	16	)	)	PUNCT
ejpam-4522	268	17	on	on	ADP
ejpam-4522	268	18	(	(	PUNCT
ejpam-4522	268	19	x	x	X
ejpam-4522	268	20	,	,	PUNCT
ejpam-4522	268	21	e	e	NOUN
ejpam-4522	268	22	)	)	PUNCT
ejpam-4522	268	23	is	be	AUX
ejpam-4522	268	24	a	a	DET
ejpam-4522	268	25	positive	positive	ADJ
ejpam-4522	268	26	implicative	implicative	ADJ
ejpam-4522	268	27	makgeolli	makgeolli	NOUN
ejpam-4522	268	28	ideal	ideal	NOUN
ejpam-4522	268	29	of	of	ADP
ejpam-4522	268	30	(	(	PUNCT
ejpam-4522	268	31	x	x	X
ejpam-4522	268	32	,	,	PUNCT
ejpam-4522	268	33	e	e	NOUN
ejpam-4522	268	34	)	)	PUNCT
ejpam-4522	269	1	if	if	SCONJ
ejpam-4522	270	1	and	and	CCONJ
ejpam-4522	270	2	only	only	ADV
ejpam-4522	270	3	if	if	SCONJ
ejpam-4522	270	4	the	the	PRON
ejpam-4522	270	5	sets	set	VERB
ejpam-4522	270	6	e(me	e(me	NOUN
ejpam-4522	270	7	;	;	PUNCT
ejpam-4522	270	8	α	α	X
ejpam-4522	270	9	)	)	PUNCT
ejpam-4522	270	10	and	and	CCONJ
ejpam-4522	270	11	e(ge	e(ge	NOUN
ejpam-4522	270	12	;	;	PUNCT
ejpam-4522	270	13	β	β	X
ejpam-4522	270	14	)	)	PUNCT
ejpam-4522	270	15	are	be	AUX
ejpam-4522	270	16	positive	positive	ADJ
ejpam-4522	270	17	implicative	implicative	ADJ
ejpam-4522	270	18	ideals	ideal	NOUN
ejpam-4522	270	19	of	of	ADP
ejpam-4522	270	20	e	e	NOUN
ejpam-4522	270	21	,	,	PUNCT
ejpam-4522	270	22	and	and	CCONJ
ejpam-4522	270	23	the	the	DET
ejpam-4522	270	24	set	set	NOUN
ejpam-4522	270	25	x	x	SYM
ejpam-4522	270	26	(	(	PUNCT
ejpam-4522	270	27	ξ	ξ	PROPN
ejpam-4522	270	28	;	;	PUNCT
ejpam-4522	270	29	t	t	PROPN
ejpam-4522	270	30	)	)	PUNCT
ejpam-4522	270	31	is	be	AUX
ejpam-4522	270	32	a	a	DET
ejpam-4522	270	33	positive	positive	ADJ
ejpam-4522	270	34	implicative	implicative	ADJ
ejpam-4522	270	35	ideal	ideal	NOUN
ejpam-4522	270	36	of	of	ADP
ejpam-4522	270	37	x	x	PUNCT
ejpam-4522	270	38	for	for	ADP
ejpam-4522	270	39	all	all	DET
ejpam-4522	270	40	α	α	NOUN
ejpam-4522	270	41	,	,	PUNCT
ejpam-4522	270	42	β	β	X
ejpam-4522	270	43	∈	∈	PROPN
ejpam-4522	270	44	p(x	p(x	PROPN
ejpam-4522	270	45	)	)	PUNCT
ejpam-4522	270	46	and	and	CCONJ
ejpam-4522	270	47	t	t	NOUN
ejpam-4522	270	48	∈	∈	PROPN
ejpam-4522	271	1	[	[	X
ejpam-4522	271	2	0	0	NUM
ejpam-4522	271	3	,	,	PUNCT
ejpam-4522	271	4	1	1	NUM
ejpam-4522	271	5	]	]	PUNCT
ejpam-4522	271	6	.	.	PUNCT
ejpam-4522	272	1	s.	s.	PROPN
ejpam-4522	272	2	z.	z.	PROPN
ejpam-4522	272	3	song	song	PROPN
ejpam-4522	272	4	,	,	PUNCT
ejpam-4522	272	5	m.	m.	NOUN
ejpam-4522	272	6	a.	a.	NOUN
ejpam-4522	272	7	öztürk	öztürk	PROPN
ejpam-4522	272	8	,	,	PUNCT
ejpam-4522	272	9	y.	y.	PROPN
ejpam-4522	272	10	b.	b.	PROPN
ejpam-4522	272	11	jun	jun	PROPN
ejpam-4522	272	12	/	/	SYM
ejpam-4522	272	13	eur	eur	PROPN
ejpam-4522	272	14	.	.	PUNCT
ejpam-4522	273	1	j.	j.	PROPN
ejpam-4522	273	2	pure	pure	PROPN
ejpam-4522	273	3	appl	appl	PROPN
ejpam-4522	273	4	.	.	PROPN
ejpam-4522	273	5	math	math	PROPN
ejpam-4522	273	6	,	,	PUNCT
ejpam-4522	273	7	15	15	NUM
ejpam-4522	273	8	(	(	PUNCT
ejpam-4522	273	9	4	4	NUM
ejpam-4522	273	10	)	)	PUNCT
ejpam-4522	273	11	(	(	PUNCT
ejpam-4522	273	12	2022	2022	NUM
ejpam-4522	273	13	)	)	PUNCT
ejpam-4522	273	14	,	,	PUNCT
ejpam-4522	273	15	1498	1498	NUM
ejpam-4522	273	16	-	-	SYM
ejpam-4522	273	17	1511	1511	NUM
ejpam-4522	273	18	1508	1508	NUM
ejpam-4522	273	19	proof	proof	NOUN
ejpam-4522	273	20	.	.	PUNCT
ejpam-4522	274	1	assume	assume	VERB
ejpam-4522	274	2	that	that	SCONJ
ejpam-4522	274	3	m(x	m(x	PROPN
ejpam-4522	274	4	,	,	PUNCT
ejpam-4522	274	5	e	e	NOUN
ejpam-4522	274	6	)	)	PUNCT
ejpam-4522	274	7	:	:	PUNCT
ejpam-4522	274	8	=	=	SYM
ejpam-4522	274	9	(	(	PUNCT
ejpam-4522	274	10	me	i	PRON
ejpam-4522	274	11	,	,	PUNCT
ejpam-4522	274	12	ge	ge	PROPN
ejpam-4522	274	13	,	,	PUNCT
ejpam-4522	274	14	ξ	ξ	X
ejpam-4522	274	15	)	)	PUNCT
ejpam-4522	274	16	is	be	AUX
ejpam-4522	274	17	a	a	DET
ejpam-4522	274	18	positive	positive	ADJ
ejpam-4522	274	19	implicative	implicative	ADJ
ejpam-4522	274	20	makgeolli	makgeolli	NOUN
ejpam-4522	274	21	ideal	ideal	NOUN
ejpam-4522	274	22	of	of	ADP
ejpam-4522	274	23	(	(	PUNCT
ejpam-4522	274	24	x	x	X
ejpam-4522	274	25	,	,	PUNCT
ejpam-4522	274	26	e	e	NOUN
ejpam-4522	274	27	)	)	PUNCT
ejpam-4522	274	28	.	.	PUNCT
ejpam-4522	275	1	it	it	PRON
ejpam-4522	275	2	is	be	AUX
ejpam-4522	275	3	clear	clear	ADJ
ejpam-4522	275	4	that	that	SCONJ
ejpam-4522	275	5	0	0	NUM
ejpam-4522	275	6	∈	∈	PROPN
ejpam-4522	275	7	e(me	e(me	NOUN
ejpam-4522	275	8	;	;	PUNCT
ejpam-4522	275	9	α	α	X
ejpam-4522	275	10	)	)	PUNCT
ejpam-4522	275	11	∩	∩	ADJ
ejpam-4522	275	12	e(ge	e(ge	NOUN
ejpam-4522	275	13	;	;	PUNCT
ejpam-4522	275	14	β	β	X
ejpam-4522	275	15	)	)	PUNCT
ejpam-4522	275	16	∩	∩	NOUN
ejpam-4522	275	17	x	x	SYM
ejpam-4522	275	18	(	(	PUNCT
ejpam-4522	275	19	ξ	ξ	PROPN
ejpam-4522	275	20	;	;	PUNCT
ejpam-4522	275	21	t	t	X
ejpam-4522	275	22	)	)	PUNCT
ejpam-4522	275	23	for	for	ADP
ejpam-4522	275	24	all	all	DET
ejpam-4522	275	25	α	α	NOUN
ejpam-4522	275	26	,	,	PUNCT
ejpam-4522	275	27	β	β	X
ejpam-4522	275	28	∈	∈	PROPN
ejpam-4522	275	29	p(x	p(x	PROPN
ejpam-4522	275	30	)	)	PUNCT
ejpam-4522	275	31	and	and	CCONJ
ejpam-4522	275	32	t	t	NOUN
ejpam-4522	275	33	∈	∈	PROPN
ejpam-4522	276	1	[	[	X
ejpam-4522	276	2	0	0	NUM
ejpam-4522	276	3	,	,	PUNCT
ejpam-4522	276	4	1	1	NUM
ejpam-4522	276	5	]	]	PUNCT
ejpam-4522	276	6	.	.	PUNCT
ejpam-4522	277	1	let	let	VERB
ejpam-4522	277	2	a	a	DET
ejpam-4522	277	3	,	,	PUNCT
ejpam-4522	277	4	b	b	NOUN
ejpam-4522	277	5	,	,	PUNCT
ejpam-4522	277	6	c	c	PROPN
ejpam-4522	277	7	∈	∈	PROPN
ejpam-4522	277	8	e	e	NOUN
ejpam-4522	277	9	be	be	VERB
ejpam-4522	277	10	such	such	ADJ
ejpam-4522	277	11	that	that	SCONJ
ejpam-4522	277	12	(	(	PUNCT
ejpam-4522	277	13	a	a	DET
ejpam-4522	277	14	↬	↬	PROPN
ejpam-4522	277	15	b	b	NOUN
ejpam-4522	277	16	)	)	PUNCT
ejpam-4522	277	17	↬	↬	VERB
ejpam-4522	277	18	c	c	PROPN
ejpam-4522	277	19	∈	∈	PROPN
ejpam-4522	277	20	e(me	e(me	NOUN
ejpam-4522	277	21	;	;	PUNCT
ejpam-4522	277	22	α	α	X
ejpam-4522	277	23	)	)	PUNCT
ejpam-4522	277	24	∩	∩	ADJ
ejpam-4522	277	25	e(ge	e(ge	NOUN
ejpam-4522	277	26	;	;	PUNCT
ejpam-4522	277	27	β	β	X
ejpam-4522	277	28	)	)	PUNCT
ejpam-4522	277	29	and	and	CCONJ
ejpam-4522	277	30	b	b	X
ejpam-4522	277	31	↬	↬	X
ejpam-4522	277	32	c	c	PROPN
ejpam-4522	277	33	∈	∈	PROPN
ejpam-4522	277	34	e(me	e(me	NOUN
ejpam-4522	277	35	;	;	PUNCT
ejpam-4522	277	36	α	α	X
ejpam-4522	277	37	)	)	PUNCT
ejpam-4522	277	38	∩	∩	ADJ
ejpam-4522	277	39	e(ge	e(ge	NOUN
ejpam-4522	277	40	;	;	PUNCT
ejpam-4522	277	41	β	β	X
ejpam-4522	277	42	)	)	PUNCT
ejpam-4522	277	43	.	.	PUNCT
ejpam-4522	278	1	then	then	ADV
ejpam-4522	278	2	me(a	me(a	NUM
ejpam-4522	278	3	↬	↬	PROPN
ejpam-4522	278	4	c	c	X
ejpam-4522	278	5	)	)	PUNCT
ejpam-4522	278	6	⊇	⊇	PROPN
ejpam-4522	278	7	me((a	me((a	PROPN
ejpam-4522	278	8	↬	↬	PROPN
ejpam-4522	278	9	b	b	X
ejpam-4522	278	10	)	)	PUNCT
ejpam-4522	278	11	↬	↬	PROPN
ejpam-4522	278	12	c	c	X
ejpam-4522	278	13	)	)	PUNCT
ejpam-4522	278	14	∩me(b	∩me(b	ADV
ejpam-4522	278	15	↬	↬	NUM
ejpam-4522	278	16	c	c	X
ejpam-4522	278	17	)	)	PUNCT
ejpam-4522	278	18	⊇	⊇	NOUN
ejpam-4522	278	19	α	α	NOUN
ejpam-4522	278	20	,	,	PUNCT
ejpam-4522	278	21	ge(a	ge(a	ADJ
ejpam-4522	278	22	↬	↬	PROPN
ejpam-4522	278	23	c	c	X
ejpam-4522	278	24	)	)	PUNCT
ejpam-4522	278	25	⊆	⊆	NUM
ejpam-4522	278	26	ge((a	ge((a	NOUN
ejpam-4522	278	27	↬	↬	PROPN
ejpam-4522	278	28	b	b	X
ejpam-4522	278	29	)	)	PUNCT
ejpam-4522	278	30	↬	↬	X
ejpam-4522	278	31	c	c	X
ejpam-4522	278	32	)	)	PUNCT
ejpam-4522	278	33	∪ge(b	∪ge(b	ADP
ejpam-4522	278	34	↬	↬	PROPN
ejpam-4522	278	35	c	c	X
ejpam-4522	278	36	)	)	PUNCT
ejpam-4522	278	37	⊆	⊆	NUM
ejpam-4522	278	38	β	β	NOUN
ejpam-4522	278	39	,	,	PUNCT
ejpam-4522	278	40	and	and	CCONJ
ejpam-4522	278	41	so	so	ADV
ejpam-4522	278	42	a	a	DET
ejpam-4522	278	43	↬	↬	PROPN
ejpam-4522	278	44	c	c	NOUN
ejpam-4522	278	45	∈	∈	PROPN
ejpam-4522	278	46	e(me	e(me	NOUN
ejpam-4522	278	47	;	;	PUNCT
ejpam-4522	278	48	α)∩e(ge	α)∩e(ge	NUM
ejpam-4522	278	49	;	;	PUNCT
ejpam-4522	278	50	β	β	X
ejpam-4522	278	51	)	)	PUNCT
ejpam-4522	278	52	.	.	PUNCT
ejpam-4522	279	1	let	let	VERB
ejpam-4522	279	2	x	x	PRON
ejpam-4522	279	3	,	,	PUNCT
ejpam-4522	279	4	y	y	PROPN
ejpam-4522	279	5	,	,	PUNCT
ejpam-4522	279	6	z	z	NOUN
ejpam-4522	279	7	∈	∈	PROPN
ejpam-4522	279	8	x	x	AUX
ejpam-4522	279	9	be	be	AUX
ejpam-4522	279	10	such	such	ADJ
ejpam-4522	279	11	that	that	SCONJ
ejpam-4522	279	12	(	(	PUNCT
ejpam-4522	279	13	x	x	SYM
ejpam-4522	279	14	∗	∗	PROPN
ejpam-4522	279	15	y	y	NOUN
ejpam-4522	279	16	)	)	PUNCT
ejpam-4522	279	17	∗	∗	NOUN
ejpam-4522	279	18	z	z	NOUN
ejpam-4522	279	19	∈	∈	PROPN
ejpam-4522	279	20	x	x	SYM
ejpam-4522	279	21	(	(	PUNCT
ejpam-4522	279	22	ξ	ξ	PROPN
ejpam-4522	279	23	;	;	PUNCT
ejpam-4522	279	24	t	t	PROPN
ejpam-4522	279	25	)	)	PUNCT
ejpam-4522	279	26	and	and	CCONJ
ejpam-4522	279	27	y	y	PROPN
ejpam-4522	279	28	∗	∗	NOUN
ejpam-4522	279	29	z	z	NOUN
ejpam-4522	279	30	∈	∈	PROPN
ejpam-4522	279	31	x	x	SYM
ejpam-4522	279	32	(	(	PUNCT
ejpam-4522	279	33	ξ	ξ	PROPN
ejpam-4522	279	34	;	;	PUNCT
ejpam-4522	279	35	t	t	PROPN
ejpam-4522	279	36	)	)	PUNCT
ejpam-4522	279	37	.	.	PUNCT
ejpam-4522	280	1	then	then	ADV
ejpam-4522	280	2	ξ(x	ξ(x	NOUN
ejpam-4522	280	3	∗	∗	NOUN
ejpam-4522	280	4	z	z	NOUN
ejpam-4522	280	5	)	)	PUNCT
ejpam-4522	280	6	≥	≥	NOUN
ejpam-4522	280	7	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	280	8	∗	∗	X
ejpam-4522	280	9	y	y	NOUN
ejpam-4522	280	10	)	)	PUNCT
ejpam-4522	280	11	∗	∗	NOUN
ejpam-4522	280	12	z	z	NOUN
ejpam-4522	280	13	)	)	PUNCT
ejpam-4522	280	14	,	,	PUNCT
ejpam-4522	280	15	ξ(y	ξ(y	PROPN
ejpam-4522	280	16	∗	∗	NOUN
ejpam-4522	280	17	z	z	NOUN
ejpam-4522	280	18	)	)	PUNCT
ejpam-4522	280	19	}	}	PUNCT
ejpam-4522	280	20	≥	≥	PROPN
ejpam-4522	280	21	t	t	PROPN
ejpam-4522	280	22	,	,	PUNCT
ejpam-4522	280	23	and	and	CCONJ
ejpam-4522	280	24	thus	thus	ADV
ejpam-4522	280	25	x	x	ADP
ejpam-4522	280	26	∗	∗	NOUN
ejpam-4522	280	27	z	z	NOUN
ejpam-4522	280	28	∈	∈	PROPN
ejpam-4522	280	29	x	x	SYM
ejpam-4522	280	30	(	(	PUNCT
ejpam-4522	280	31	ξ	ξ	PROPN
ejpam-4522	280	32	;	;	PUNCT
ejpam-4522	280	33	t	t	PROPN
ejpam-4522	280	34	)	)	PUNCT
ejpam-4522	280	35	.	.	PUNCT
ejpam-4522	281	1	therefore	therefore	ADV
ejpam-4522	281	2	e(me	e(me	X
ejpam-4522	281	3	;	;	PUNCT
ejpam-4522	281	4	α	α	X
ejpam-4522	281	5	)	)	PUNCT
ejpam-4522	281	6	and	and	CCONJ
ejpam-4522	281	7	e(ge	e(ge	NOUN
ejpam-4522	281	8	;	;	PUNCT
ejpam-4522	281	9	β	β	X
ejpam-4522	281	10	)	)	PUNCT
ejpam-4522	281	11	are	be	AUX
ejpam-4522	281	12	positive	positive	ADJ
ejpam-4522	281	13	implicative	implicative	ADJ
ejpam-4522	281	14	ideals	ideal	NOUN
ejpam-4522	281	15	of	of	ADP
ejpam-4522	281	16	e	e	NOUN
ejpam-4522	281	17	,	,	PUNCT
ejpam-4522	281	18	and	and	CCONJ
ejpam-4522	281	19	x	x	X
ejpam-4522	281	20	(	(	PUNCT
ejpam-4522	281	21	ξ	ξ	PROPN
ejpam-4522	281	22	;	;	PUNCT
ejpam-4522	281	23	t	t	PROPN
ejpam-4522	281	24	)	)	PUNCT
ejpam-4522	281	25	is	be	AUX
ejpam-4522	281	26	a	a	DET
ejpam-4522	281	27	positive	positive	ADJ
ejpam-4522	281	28	implicative	implicative	ADJ
ejpam-4522	281	29	ideal	ideal	NOUN
ejpam-4522	281	30	of	of	ADP
ejpam-4522	281	31	x	x	PUNCT
ejpam-4522	281	32	for	for	ADP
ejpam-4522	281	33	all	all	DET
ejpam-4522	281	34	α	α	NOUN
ejpam-4522	281	35	,	,	PUNCT
ejpam-4522	281	36	β	β	X
ejpam-4522	281	37	∈	∈	PROPN
ejpam-4522	281	38	p(x	p(x	PROPN
ejpam-4522	281	39	)	)	PUNCT
ejpam-4522	281	40	and	and	CCONJ
ejpam-4522	281	41	t	t	NOUN
ejpam-4522	281	42	∈	∈	PROPN
ejpam-4522	282	1	[	[	X
ejpam-4522	282	2	0	0	NUM
ejpam-4522	282	3	,	,	PUNCT
ejpam-4522	282	4	1	1	NUM
ejpam-4522	282	5	]	]	PUNCT
ejpam-4522	282	6	.	.	PUNCT
ejpam-4522	283	1	conversely	conversely	ADV
ejpam-4522	283	2	,	,	PUNCT
ejpam-4522	283	3	suppose	suppose	VERB
ejpam-4522	283	4	that	that	SCONJ
ejpam-4522	283	5	e(me	e(me	NOUN
ejpam-4522	283	6	;	;	PUNCT
ejpam-4522	283	7	α	α	X
ejpam-4522	283	8	)	)	PUNCT
ejpam-4522	283	9	and	and	CCONJ
ejpam-4522	283	10	e(ge	e(ge	NOUN
ejpam-4522	283	11	;	;	PUNCT
ejpam-4522	283	12	β	β	X
ejpam-4522	283	13	)	)	PUNCT
ejpam-4522	283	14	are	be	AUX
ejpam-4522	283	15	positive	positive	ADJ
ejpam-4522	283	16	implicative	implicative	ADJ
ejpam-4522	283	17	ideals	ideal	NOUN
ejpam-4522	283	18	of	of	ADP
ejpam-4522	283	19	e	e	NOUN
ejpam-4522	283	20	,	,	PUNCT
ejpam-4522	283	21	and	and	CCONJ
ejpam-4522	283	22	x	x	X
ejpam-4522	283	23	(	(	PUNCT
ejpam-4522	283	24	ξ	ξ	PROPN
ejpam-4522	283	25	;	;	PUNCT
ejpam-4522	283	26	t	t	PROPN
ejpam-4522	283	27	)	)	PUNCT
ejpam-4522	283	28	is	be	AUX
ejpam-4522	283	29	a	a	DET
ejpam-4522	283	30	positive	positive	ADJ
ejpam-4522	283	31	implicative	implicative	ADJ
ejpam-4522	283	32	ideal	ideal	NOUN
ejpam-4522	283	33	of	of	ADP
ejpam-4522	283	34	x	x	PUNCT
ejpam-4522	283	35	for	for	ADP
ejpam-4522	283	36	all	all	DET
ejpam-4522	283	37	α	α	NOUN
ejpam-4522	283	38	,	,	PUNCT
ejpam-4522	283	39	β	β	X
ejpam-4522	283	40	∈	∈	PROPN
ejpam-4522	283	41	p(x	p(x	PROPN
ejpam-4522	283	42	)	)	PUNCT
ejpam-4522	283	43	and	and	CCONJ
ejpam-4522	283	44	t	t	NOUN
ejpam-4522	283	45	∈	∈	PROPN
ejpam-4522	284	1	[	[	X
ejpam-4522	284	2	0	0	NUM
ejpam-4522	284	3	,	,	PUNCT
ejpam-4522	284	4	1	1	NUM
ejpam-4522	284	5	]	]	PUNCT
ejpam-4522	284	6	.	.	PUNCT
ejpam-4522	285	1	then	then	ADV
ejpam-4522	285	2	e(me	e(me	NOUN
ejpam-4522	285	3	;	;	PUNCT
ejpam-4522	285	4	α	α	X
ejpam-4522	285	5	)	)	PUNCT
ejpam-4522	285	6	and	and	CCONJ
ejpam-4522	285	7	e(ge	e(ge	NOUN
ejpam-4522	285	8	;	;	PUNCT
ejpam-4522	285	9	β	β	X
ejpam-4522	285	10	)	)	PUNCT
ejpam-4522	285	11	are	be	AUX
ejpam-4522	285	12	subalgebras	subalgebra	NOUN
ejpam-4522	285	13	of	of	ADP
ejpam-4522	285	14	e	e	NOUN
ejpam-4522	285	15	,	,	PUNCT
ejpam-4522	285	16	and	and	CCONJ
ejpam-4522	285	17	x	x	X
ejpam-4522	285	18	(	(	PUNCT
ejpam-4522	285	19	ξ	ξ	PROPN
ejpam-4522	285	20	;	;	PUNCT
ejpam-4522	285	21	t	t	PROPN
ejpam-4522	285	22	)	)	PUNCT
ejpam-4522	285	23	is	be	AUX
ejpam-4522	285	24	a	a	DET
ejpam-4522	285	25	subalgebra	subalgebra	NOUN
ejpam-4522	285	26	of	of	ADP
ejpam-4522	285	27	x.	x.	NOUN
ejpam-4522	285	28	let	let	VERB
ejpam-4522	285	29	(	(	PUNCT
ejpam-4522	285	30	a1	a1	NOUN
ejpam-4522	285	31	,	,	PUNCT
ejpam-4522	285	32	b1	b1	NOUN
ejpam-4522	285	33	,	,	PUNCT
ejpam-4522	285	34	x1	x1	PROPN
ejpam-4522	285	35	)	)	PUNCT
ejpam-4522	285	36	,	,	PUNCT
ejpam-4522	286	1	(	(	PUNCT
ejpam-4522	286	2	a2	a2	PROPN
ejpam-4522	286	3	,	,	PUNCT
ejpam-4522	286	4	b2	b2	NOUN
ejpam-4522	286	5	,	,	PUNCT
ejpam-4522	286	6	x2	x2	PROPN
ejpam-4522	286	7	)	)	PUNCT
ejpam-4522	286	8	∈	∈	PROPN
ejpam-4522	286	9	e	e	NOUN
ejpam-4522	286	10	×	×	PROPN
ejpam-4522	286	11	e	e	PROPN
ejpam-4522	286	12	×x	×x	AUX
ejpam-4522	286	13	be	be	AUX
ejpam-4522	286	14	such	such	ADJ
ejpam-4522	286	15	that	that	SCONJ
ejpam-4522	286	16	m(x	m(x	PROPN
ejpam-4522	286	17	,	,	PUNCT
ejpam-4522	286	18	e)(a1	e)(a1	NOUN
ejpam-4522	286	19	,	,	PUNCT
ejpam-4522	286	20	b1	b1	NOUN
ejpam-4522	286	21	,	,	PUNCT
ejpam-4522	286	22	x1	x1	PROPN
ejpam-4522	286	23	)	)	PUNCT
ejpam-4522	286	24	:	:	PUNCT
ejpam-4522	286	25	=	=	SYM
ejpam-4522	286	26	(	(	PUNCT
ejpam-4522	286	27	me(a1	me(a1	NOUN
ejpam-4522	286	28	)	)	PUNCT
ejpam-4522	286	29	,	,	PUNCT
ejpam-4522	286	30	ge(b1	ge(b1	NOUN
ejpam-4522	286	31	)	)	PUNCT
ejpam-4522	286	32	,	,	PUNCT
ejpam-4522	286	33	ξ(x1	ξ(x1	NOUN
ejpam-4522	286	34	)	)	PUNCT
ejpam-4522	286	35	)	)	PUNCT
ejpam-4522	287	1	=	=	SYM
ejpam-4522	287	2	(	(	PUNCT
ejpam-4522	287	3	α1	α1	PROPN
ejpam-4522	287	4	,	,	PUNCT
ejpam-4522	287	5	β1	β1	PROPN
ejpam-4522	287	6	,	,	PUNCT
ejpam-4522	287	7	t1	t1	NOUN
ejpam-4522	287	8	)	)	PUNCT
ejpam-4522	287	9	and	and	CCONJ
ejpam-4522	287	10	m(x	m(x	PROPN
ejpam-4522	287	11	,	,	PUNCT
ejpam-4522	287	12	e)(a2	e)(a2	PROPN
ejpam-4522	287	13	,	,	PUNCT
ejpam-4522	287	14	b2	b2	NOUN
ejpam-4522	287	15	,	,	PUNCT
ejpam-4522	287	16	x2	x2	PROPN
ejpam-4522	287	17	)	)	PUNCT
ejpam-4522	287	18	:	:	PUNCT
ejpam-4522	287	19	=	=	SYM
ejpam-4522	287	20	(	(	PUNCT
ejpam-4522	287	21	me(a2	me(a2	NOUN
ejpam-4522	287	22	)	)	PUNCT
ejpam-4522	287	23	,	,	PUNCT
ejpam-4522	287	24	ge(b2	ge(b2	NOUN
ejpam-4522	287	25	)	)	PUNCT
ejpam-4522	287	26	,	,	PUNCT
ejpam-4522	287	27	ξ(x2	ξ(x2	NOUN
ejpam-4522	287	28	)	)	PUNCT
ejpam-4522	287	29	)	)	PUNCT
ejpam-4522	288	1	=	=	SYM
ejpam-4522	288	2	(	(	PUNCT
ejpam-4522	288	3	α2	α2	ADJ
ejpam-4522	288	4	,	,	PUNCT
ejpam-4522	288	5	β2	β2	NOUN
ejpam-4522	288	6	,	,	PUNCT
ejpam-4522	288	7	t2	t2	NOUN
ejpam-4522	288	8	)	)	PUNCT
ejpam-4522	288	9	.	.	PUNCT
ejpam-4522	289	1	if	if	SCONJ
ejpam-4522	289	2	we	we	PRON
ejpam-4522	289	3	take	take	VERB
ejpam-4522	289	4	(	(	PUNCT
ejpam-4522	289	5	α	α	NOUN
ejpam-4522	289	6	,	,	PUNCT
ejpam-4522	289	7	β	β	X
ejpam-4522	289	8	,	,	PUNCT
ejpam-4522	289	9	t	t	PROPN
ejpam-4522	289	10	)	)	PUNCT
ejpam-4522	289	11	:	:	PUNCT
ejpam-4522	290	1	=	=	SYM
ejpam-4522	290	2	(	(	PUNCT
ejpam-4522	290	3	α1∩α2	α1∩α2	PROPN
ejpam-4522	290	4	,	,	PUNCT
ejpam-4522	290	5	β1∪β2,min{t1	β1∪β2,min{t1	NOUN
ejpam-4522	290	6	,	,	PUNCT
ejpam-4522	290	7	t2	t2	NOUN
ejpam-4522	290	8	}	}	PUNCT
ejpam-4522	290	9	)	)	PUNCT
ejpam-4522	290	10	,	,	PUNCT
ejpam-4522	290	11	then	then	ADV
ejpam-4522	290	12	a1	a1	PROPN
ejpam-4522	290	13	,	,	PUNCT
ejpam-4522	290	14	a2	a2	PROPN
ejpam-4522	290	15	∈	∈	PROPN
ejpam-4522	290	16	e(me	e(me	PROPN
ejpam-4522	290	17	;	;	PUNCT
ejpam-4522	290	18	α	α	X
ejpam-4522	290	19	)	)	PUNCT
ejpam-4522	290	20	,	,	PUNCT
ejpam-4522	290	21	b1	b1	NOUN
ejpam-4522	290	22	,	,	PUNCT
ejpam-4522	290	23	b2	b2	NOUN
ejpam-4522	290	24	∈	∈	NOUN
ejpam-4522	290	25	e(ge	e(ge	NOUN
ejpam-4522	290	26	;	;	PUNCT
ejpam-4522	290	27	β	β	X
ejpam-4522	290	28	)	)	PUNCT
ejpam-4522	290	29	and	and	CCONJ
ejpam-4522	290	30	x1	x1	NUM
ejpam-4522	290	31	,	,	PUNCT
ejpam-4522	290	32	x2	x2	PROPN
ejpam-4522	290	33	∈	∈	PROPN
ejpam-4522	290	34	x	x	X
ejpam-4522	290	35	(	(	PUNCT
ejpam-4522	290	36	ξ	ξ	PROPN
ejpam-4522	290	37	;	;	PUNCT
ejpam-4522	290	38	t	t	NUM
ejpam-4522	290	39	)	)	PUNCT
ejpam-4522	290	40	.	.	PUNCT
ejpam-4522	291	1	hence	hence	ADV
ejpam-4522	291	2	a1	a1	VERB
ejpam-4522	291	3	↬	↬	PROPN
ejpam-4522	291	4	a2	a2	PROPN
ejpam-4522	291	5	∈	∈	PROPN
ejpam-4522	291	6	e(me	e(me	PROPN
ejpam-4522	291	7	;	;	PUNCT
ejpam-4522	291	8	α	α	X
ejpam-4522	291	9	)	)	PUNCT
ejpam-4522	291	10	,	,	PUNCT
ejpam-4522	291	11	b1	b1	PROPN
ejpam-4522	291	12	↬	↬	PROPN
ejpam-4522	291	13	b2	b2	NOUN
ejpam-4522	291	14	∈	∈	NOUN
ejpam-4522	291	15	e(ge	e(ge	NOUN
ejpam-4522	291	16	;	;	PUNCT
ejpam-4522	291	17	β	β	X
ejpam-4522	291	18	)	)	PUNCT
ejpam-4522	291	19	and	and	CCONJ
ejpam-4522	291	20	x1∗x2	x1∗x2	SYM
ejpam-4522	291	21	∈	∈	PROPN
ejpam-4522	291	22	x	x	X
ejpam-4522	291	23	(	(	PUNCT
ejpam-4522	291	24	ξ	ξ	PROPN
ejpam-4522	291	25	;	;	PUNCT
ejpam-4522	291	26	t	t	NUM
ejpam-4522	291	27	)	)	PUNCT
ejpam-4522	291	28	.	.	PUNCT
ejpam-4522	292	1	if	if	SCONJ
ejpam-4522	292	2	we	we	PRON
ejpam-4522	292	3	put	put	VERB
ejpam-4522	292	4	a1	a1	NOUN
ejpam-4522	292	5	=	=	NOUN
ejpam-4522	292	6	a2	a2	PROPN
ejpam-4522	292	7	,	,	PUNCT
ejpam-4522	292	8	b1	b1	NOUN
ejpam-4522	292	9	=	=	SYM
ejpam-4522	292	10	b2	b2	NOUN
ejpam-4522	292	11	,	,	PUNCT
ejpam-4522	292	12	and	and	CCONJ
ejpam-4522	292	13	x1	x1	PROPN
ejpam-4522	292	14	=	=	SYM
ejpam-4522	292	15	x2	x2	PROPN
ejpam-4522	292	16	,	,	PUNCT
ejpam-4522	292	17	then	then	ADV
ejpam-4522	292	18	0	0	NUM
ejpam-4522	292	19	∈	∈	PROPN
ejpam-4522	292	20	e(me	e(me	NOUN
ejpam-4522	292	21	;	;	PUNCT
ejpam-4522	292	22	α	α	X
ejpam-4522	292	23	)	)	PUNCT
ejpam-4522	292	24	∩	∩	ADJ
ejpam-4522	292	25	e(ge	e(ge	NOUN
ejpam-4522	292	26	;	;	PUNCT
ejpam-4522	292	27	β	β	X
ejpam-4522	292	28	)	)	PUNCT
ejpam-4522	292	29	∩	∩	NOUN
ejpam-4522	292	30	x	x	SYM
ejpam-4522	292	31	(	(	PUNCT
ejpam-4522	292	32	ξ	ξ	PROPN
ejpam-4522	292	33	;	;	PUNCT
ejpam-4522	292	34	t	t	PROPN
ejpam-4522	292	35	)	)	PUNCT
ejpam-4522	292	36	,	,	PUNCT
ejpam-4522	292	37	and	and	CCONJ
ejpam-4522	292	38	so	so	ADV
ejpam-4522	292	39	me(0	me(0	PROPN
ejpam-4522	292	40	)	)	PUNCT
ejpam-4522	292	41	⊇	⊇	NOUN
ejpam-4522	292	42	α	α	NOUN
ejpam-4522	292	43	=	=	SYM
ejpam-4522	292	44	me(a	me(a	NOUN
ejpam-4522	292	45	)	)	PUNCT
ejpam-4522	292	46	,	,	PUNCT
ejpam-4522	292	47	ge(0	ge(0	PROPN
ejpam-4522	292	48	)	)	PUNCT
ejpam-4522	292	49	⊆	⊆	NUM
ejpam-4522	292	50	ge(b	ge(b	X
ejpam-4522	292	51	)	)	PUNCT
ejpam-4522	292	52	and	and	CCONJ
ejpam-4522	292	53	ξ(0	ξ(0	PROPN
ejpam-4522	292	54	)	)	PUNCT
ejpam-4522	292	55	≥	≥	NOUN
ejpam-4522	292	56	ξ(x	ξ(x	NOUN
ejpam-4522	292	57	)	)	PUNCT
ejpam-4522	292	58	for	for	ADP
ejpam-4522	292	59	all	all	DET
ejpam-4522	292	60	(	(	PUNCT
ejpam-4522	292	61	a	a	PRON
ejpam-4522	292	62	,	,	PUNCT
ejpam-4522	292	63	b	b	NOUN
ejpam-4522	292	64	,	,	PUNCT
ejpam-4522	292	65	x	x	NOUN
ejpam-4522	292	66	)	)	PUNCT
ejpam-4522	292	67	∈	∈	PROPN
ejpam-4522	292	68	e	e	AUX
ejpam-4522	292	69	×	×	NOUN
ejpam-4522	292	70	e	e	X
ejpam-4522	292	71	×	×	NOUN
ejpam-4522	292	72	x.	x.	NOUN
ejpam-4522	292	73	let	let	VERB
ejpam-4522	292	74	a	a	DET
ejpam-4522	292	75	,	,	PUNCT
ejpam-4522	292	76	b	b	NOUN
ejpam-4522	292	77	,	,	PUNCT
ejpam-4522	292	78	c	c	PROPN
ejpam-4522	292	79	∈	∈	PROPN
ejpam-4522	292	80	e	e	PROPN
ejpam-4522	292	81	and	and	CCONJ
ejpam-4522	292	82	x	x	PROPN
ejpam-4522	292	83	,	,	PUNCT
ejpam-4522	292	84	y	y	PROPN
ejpam-4522	292	85	,	,	PUNCT
ejpam-4522	292	86	z	z	NOUN
ejpam-4522	292	87	∈	∈	PROPN
ejpam-4522	292	88	x	x	AUX
ejpam-4522	292	89	be	be	AUX
ejpam-4522	292	90	such	such	ADJ
ejpam-4522	292	91	that	that	PRON
ejpam-4522	292	92	me((a	me((a	PROPN
ejpam-4522	292	93	↬	↬	PROPN
ejpam-4522	292	94	b	b	X
ejpam-4522	292	95	)	)	PUNCT
ejpam-4522	292	96	↬	↬	X
ejpam-4522	292	97	c	c	X
ejpam-4522	292	98	)	)	PUNCT
ejpam-4522	292	99	=	=	SYM
ejpam-4522	292	100	α1	α1	PROPN
ejpam-4522	292	101	,	,	PUNCT
ejpam-4522	292	102	me(b	me(b	PUNCT
ejpam-4522	292	103	↬	↬	X
ejpam-4522	292	104	c	c	X
ejpam-4522	292	105	)	)	PUNCT
ejpam-4522	292	106	=	=	SYM
ejpam-4522	292	107	α2	α2	PROPN
ejpam-4522	292	108	ge((a	ge((a	NOUN
ejpam-4522	292	109	↬	↬	PROPN
ejpam-4522	292	110	b	b	X
ejpam-4522	292	111	)	)	PUNCT
ejpam-4522	292	112	↬	↬	X
ejpam-4522	293	1	c	c	X
ejpam-4522	293	2	)	)	PUNCT
ejpam-4522	293	3	=	=	SYM
ejpam-4522	293	4	β1	β1	PROPN
ejpam-4522	293	5	,	,	PUNCT
ejpam-4522	293	6	ge(b	ge(b	PUNCT
ejpam-4522	293	7	↬	↬	X
ejpam-4522	293	8	c	c	X
ejpam-4522	293	9	)	)	PUNCT
ejpam-4522	294	1	=	=	VERB
ejpam-4522	294	2	β2	β2	VERB
ejpam-4522	294	3	,	,	PUNCT
ejpam-4522	294	4	ξ((x	ξ((x	NOUN
ejpam-4522	294	5	∗	∗	PROPN
ejpam-4522	294	6	y	y	NOUN
ejpam-4522	294	7	)	)	PUNCT
ejpam-4522	294	8	∗	∗	NOUN
ejpam-4522	294	9	z	z	NOUN
ejpam-4522	294	10	)	)	PUNCT
ejpam-4522	294	11	=	=	SYM
ejpam-4522	294	12	t1	t1	NOUN
ejpam-4522	294	13	,	,	PUNCT
ejpam-4522	294	14	and	and	CCONJ
ejpam-4522	294	15	ξ(y	ξ(y	PROPN
ejpam-4522	294	16	∗	∗	NOUN
ejpam-4522	294	17	z	z	NOUN
ejpam-4522	294	18	)	)	PUNCT
ejpam-4522	294	19	=	=	SYM
ejpam-4522	294	20	t2	t2	NOUN
ejpam-4522	294	21	.	.	PUNCT
ejpam-4522	295	1	if	if	SCONJ
ejpam-4522	295	2	we	we	PRON
ejpam-4522	295	3	take	take	VERB
ejpam-4522	295	4	α	α	NOUN
ejpam-4522	295	5	=	=	SYM
ejpam-4522	295	6	α1	α1	PROPN
ejpam-4522	295	7	∩	∩	NOUN
ejpam-4522	295	8	α2	α2	PROPN
ejpam-4522	295	9	,	,	PUNCT
ejpam-4522	295	10	β	β	X
ejpam-4522	295	11	=	=	SYM
ejpam-4522	295	12	β1	β1	PROPN
ejpam-4522	295	13	∪	∪	ADP
ejpam-4522	295	14	β2	β2	PROPN
ejpam-4522	295	15	and	and	CCONJ
ejpam-4522	295	16	t	t	NOUN
ejpam-4522	295	17	=	=	PUNCT
ejpam-4522	295	18	min{t1	min{t1	NOUN
ejpam-4522	295	19	,	,	PUNCT
ejpam-4522	295	20	t2	t2	NOUN
ejpam-4522	295	21	}	}	PUNCT
ejpam-4522	295	22	,	,	PUNCT
ejpam-4522	295	23	then	then	ADV
ejpam-4522	295	24	(	(	PUNCT
ejpam-4522	295	25	a	a	DET
ejpam-4522	295	26	↬	↬	PROPN
ejpam-4522	295	27	b	b	NOUN
ejpam-4522	295	28	)	)	PUNCT
ejpam-4522	295	29	↬	↬	VERB
ejpam-4522	295	30	c	c	PROPN
ejpam-4522	295	31	∈	∈	PROPN
ejpam-4522	295	32	e(me	e(me	NOUN
ejpam-4522	295	33	;	;	PUNCT
ejpam-4522	295	34	α	α	X
ejpam-4522	295	35	)	)	PUNCT
ejpam-4522	295	36	,	,	PUNCT
ejpam-4522	295	37	b	b	X
ejpam-4522	295	38	↬	↬	PROPN
ejpam-4522	295	39	c	c	PROPN
ejpam-4522	295	40	∈	∈	PROPN
ejpam-4522	295	41	e(me	e(me	NOUN
ejpam-4522	295	42	;	;	PUNCT
ejpam-4522	295	43	α	α	X
ejpam-4522	295	44	)	)	PUNCT
ejpam-4522	295	45	,	,	PUNCT
ejpam-4522	295	46	(	(	PUNCT
ejpam-4522	295	47	a	a	DET
ejpam-4522	295	48	↬	↬	PROPN
ejpam-4522	295	49	b	b	NOUN
ejpam-4522	295	50	)	)	PUNCT
ejpam-4522	295	51	↬	↬	VERB
ejpam-4522	295	52	c	c	NOUN
ejpam-4522	295	53	∈	∈	PROPN
ejpam-4522	295	54	e(ge	e(ge	PROPN
ejpam-4522	295	55	;	;	PUNCT
ejpam-4522	295	56	α	α	X
ejpam-4522	295	57	)	)	PUNCT
ejpam-4522	295	58	,	,	PUNCT
ejpam-4522	295	59	b	b	X
ejpam-4522	295	60	↬	↬	PROPN
ejpam-4522	295	61	c	c	PROPN
ejpam-4522	295	62	∈	∈	PROPN
ejpam-4522	295	63	e(ge	e(ge	PROPN
ejpam-4522	295	64	;	;	PUNCT
ejpam-4522	295	65	α	α	X
ejpam-4522	295	66	)	)	PUNCT
ejpam-4522	295	67	,	,	PUNCT
ejpam-4522	295	68	(	(	PUNCT
ejpam-4522	295	69	x	x	X
ejpam-4522	295	70	∗	∗	PROPN
ejpam-4522	295	71	y	y	NOUN
ejpam-4522	295	72	)	)	PUNCT
ejpam-4522	295	73	∗	∗	NOUN
ejpam-4522	295	74	z	z	NOUN
ejpam-4522	295	75	∈	∈	PROPN
ejpam-4522	295	76	x	x	SYM
ejpam-4522	295	77	(	(	PUNCT
ejpam-4522	295	78	ξ	ξ	PROPN
ejpam-4522	295	79	;	;	PUNCT
ejpam-4522	295	80	t	t	PROPN
ejpam-4522	295	81	)	)	PUNCT
ejpam-4522	295	82	,	,	PUNCT
ejpam-4522	295	83	and	and	CCONJ
ejpam-4522	295	84	y	y	PROPN
ejpam-4522	295	85	∗	∗	NOUN
ejpam-4522	295	86	z	z	NOUN
ejpam-4522	295	87	∈	∈	PROPN
ejpam-4522	295	88	x	x	SYM
ejpam-4522	295	89	(	(	PUNCT
ejpam-4522	295	90	ξ	ξ	PROPN
ejpam-4522	295	91	;	;	PUNCT
ejpam-4522	295	92	t	t	NUM
ejpam-4522	295	93	)	)	PUNCT
ejpam-4522	295	94	.	.	PUNCT
ejpam-4522	296	1	it	it	PRON
ejpam-4522	296	2	follows	follow	VERB
ejpam-4522	296	3	that	that	SCONJ
ejpam-4522	296	4	a	a	DET
ejpam-4522	296	5	↬	↬	PROPN
ejpam-4522	296	6	c	c	NOUN
ejpam-4522	296	7	∈	∈	PROPN
ejpam-4522	296	8	e(me	e(me	NOUN
ejpam-4522	296	9	;	;	PUNCT
ejpam-4522	296	10	α	α	X
ejpam-4522	296	11	)	)	PUNCT
ejpam-4522	296	12	∩	∩	ADJ
ejpam-4522	296	13	e(ge	e(ge	NOUN
ejpam-4522	296	14	;	;	PUNCT
ejpam-4522	296	15	α	α	X
ejpam-4522	296	16	)	)	PUNCT
ejpam-4522	296	17	and	and	CCONJ
ejpam-4522	296	18	x	x	SYM
ejpam-4522	296	19	∗	∗	NOUN
ejpam-4522	296	20	z	z	NOUN
ejpam-4522	296	21	∈	∈	PROPN
ejpam-4522	296	22	x	x	SYM
ejpam-4522	296	23	(	(	PUNCT
ejpam-4522	296	24	ξ	ξ	PROPN
ejpam-4522	296	25	;	;	PUNCT
ejpam-4522	296	26	t	t	NUM
ejpam-4522	296	27	)	)	PUNCT
ejpam-4522	296	28	.	.	PUNCT
ejpam-4522	297	1	hence	hence	ADV
ejpam-4522	297	2	me(a	me(a	NUM
ejpam-4522	297	3	↬	↬	PROPN
ejpam-4522	297	4	c	c	X
ejpam-4522	297	5	)	)	PUNCT
ejpam-4522	297	6	⊇	⊇	NOUN
ejpam-4522	297	7	α	α	NOUN
ejpam-4522	297	8	=	=	SYM
ejpam-4522	297	9	α1	α1	PROPN
ejpam-4522	297	10	∩	∩	ADJ
ejpam-4522	297	11	α2	α2	NOUN
ejpam-4522	297	12	=	=	SYM
ejpam-4522	297	13	me((a	me((a	PROPN
ejpam-4522	297	14	↬	↬	PROPN
ejpam-4522	297	15	b	b	X
ejpam-4522	297	16	)	)	PUNCT
ejpam-4522	297	17	↬	↬	PROPN
ejpam-4522	297	18	c	c	X
ejpam-4522	297	19	)	)	PUNCT
ejpam-4522	297	20	∩me(b	∩me(b	ADV
ejpam-4522	297	21	↬	↬	PROPN
ejpam-4522	297	22	c	c	X
ejpam-4522	297	23	)	)	PUNCT
ejpam-4522	297	24	,	,	PUNCT
ejpam-4522	297	25	ge(a	ge(a	DET
ejpam-4522	297	26	↬	↬	PROPN
ejpam-4522	297	27	c	c	X
ejpam-4522	297	28	)	)	PUNCT
ejpam-4522	297	29	⊆	⊆	NUM
ejpam-4522	297	30	β	β	X
ejpam-4522	297	31	=	=	SYM
ejpam-4522	297	32	β1	β1	PROPN
ejpam-4522	297	33	∪	∪	ADP
ejpam-4522	297	34	β2	β2	PROPN
ejpam-4522	297	35	=	=	SYM
ejpam-4522	297	36	ge((a	ge((a	NOUN
ejpam-4522	297	37	↬	↬	PROPN
ejpam-4522	297	38	b	b	X
ejpam-4522	297	39	)	)	PUNCT
ejpam-4522	297	40	↬	↬	X
ejpam-4522	298	1	c	c	X
ejpam-4522	298	2	)	)	PUNCT
ejpam-4522	298	3	∪ge(b	∪ge(b	ADP
ejpam-4522	298	4	↬	↬	PROPN
ejpam-4522	298	5	c	c	X
ejpam-4522	298	6	)	)	PUNCT
ejpam-4522	298	7	,	,	PUNCT
ejpam-4522	298	8	ξ(x	ξ(x	NOUN
ejpam-4522	298	9	∗	∗	NOUN
ejpam-4522	298	10	z	z	NOUN
ejpam-4522	298	11	)	)	PUNCT
ejpam-4522	298	12	≥	≥	NOUN
ejpam-4522	298	13	t	t	NOUN
ejpam-4522	298	14	=	=	PUNCT
ejpam-4522	298	15	min{t1	min{t1	NOUN
ejpam-4522	298	16	,	,	PUNCT
ejpam-4522	298	17	t2	t2	NOUN
ejpam-4522	298	18	}	}	PUNCT
ejpam-4522	298	19	=	=	SYM
ejpam-4522	298	20	min{ξ((x	min{ξ((x	NOUN
ejpam-4522	298	21	∗	∗	X
ejpam-4522	298	22	y	y	NOUN
ejpam-4522	298	23	)	)	PUNCT
ejpam-4522	298	24	∗	∗	NOUN
ejpam-4522	298	25	z	z	NOUN
ejpam-4522	298	26	)	)	PUNCT
ejpam-4522	298	27	,	,	PUNCT
ejpam-4522	298	28	ξ(y	ξ(y	PROPN
ejpam-4522	298	29	∗	∗	NOUN
ejpam-4522	298	30	z	z	PROPN
ejpam-4522	298	31	)	)	PUNCT
ejpam-4522	298	32	}	}	PUNCT
ejpam-4522	298	33	.	.	PUNCT
ejpam-4522	299	1	therefore	therefore	ADV
ejpam-4522	299	2	m(x	m(x	PROPN
ejpam-4522	299	3	,	,	PUNCT
ejpam-4522	299	4	e	e	NOUN
ejpam-4522	299	5	)	)	PUNCT
ejpam-4522	299	6	:	:	PUNCT
ejpam-4522	300	1	=	=	SYM
ejpam-4522	300	2	(	(	PUNCT
ejpam-4522	300	3	me	i	PRON
ejpam-4522	300	4	,	,	PUNCT
ejpam-4522	300	5	ge	ge	PROPN
ejpam-4522	300	6	,	,	PUNCT
ejpam-4522	300	7	ξ	ξ	X
ejpam-4522	300	8	)	)	PUNCT
ejpam-4522	300	9	is	be	AUX
ejpam-4522	300	10	a	a	DET
ejpam-4522	300	11	positive	positive	ADJ
ejpam-4522	300	12	implicative	implicative	ADJ
ejpam-4522	300	13	makgeolli	makgeolli	NOUN
ejpam-4522	300	14	ideal	ideal	NOUN
ejpam-4522	300	15	of	of	ADP
ejpam-4522	300	16	(	(	PUNCT
ejpam-4522	300	17	x	x	X
ejpam-4522	300	18	,	,	PUNCT
ejpam-4522	300	19	e	e	NOUN
ejpam-4522	300	20	)	)	PUNCT
ejpam-4522	300	21	.	.	PUNCT
ejpam-4522	301	1	note	note	VERB
ejpam-4522	301	2	that	that	SCONJ
ejpam-4522	301	3	a	a	DET
ejpam-4522	301	4	makgeolli	makgeolli	NOUN
ejpam-4522	301	5	ideal	ideal	NOUN
ejpam-4522	301	6	might	might	AUX
ejpam-4522	301	7	not	not	PART
ejpam-4522	301	8	be	be	AUX
ejpam-4522	301	9	a	a	DET
ejpam-4522	301	10	positive	positive	ADJ
ejpam-4522	301	11	implicative	implicative	ADJ
ejpam-4522	301	12	makgeolli	makgeolli	NOUN
ejpam-4522	301	13	ideal	ideal	NOUN
ejpam-4522	301	14	(	(	PUNCT
ejpam-4522	301	15	see	see	VERB
ejpam-4522	301	16	example	example	NOUN
ejpam-4522	301	17	2	2	NUM
ejpam-4522	301	18	)	)	PUNCT
ejpam-4522	301	19	.	.	PUNCT
ejpam-4522	302	1	but	but	CCONJ
ejpam-4522	302	2	we	we	PRON
ejpam-4522	302	3	have	have	VERB
ejpam-4522	302	4	the	the	DET
ejpam-4522	302	5	following	follow	VERB
ejpam-4522	302	6	extension	extension	NOUN
ejpam-4522	302	7	property	property	NOUN
ejpam-4522	302	8	for	for	ADP
ejpam-4522	302	9	a	a	DET
ejpam-4522	302	10	positive	positive	ADJ
ejpam-4522	302	11	implicative	implicative	ADJ
ejpam-4522	302	12	makgeolli	makgeolli	NOUN
ejpam-4522	302	13	ideal	ideal	NOUN
ejpam-4522	302	14	.	.	PUNCT
ejpam-4522	303	1	theorem	theorem	VERB
ejpam-4522	303	2	9	9	NUM
ejpam-4522	303	3	.	.	PUNCT
ejpam-4522	304	1	let	let	VERB
ejpam-4522	304	2	m(x	m(x	PROPN
ejpam-4522	304	3	,	,	PUNCT
ejpam-4522	304	4	e	e	NOUN
ejpam-4522	304	5	)	)	PUNCT
ejpam-4522	304	6	:	:	PUNCT
ejpam-4522	305	1	=	=	SYM
ejpam-4522	305	2	(	(	PUNCT
ejpam-4522	305	3	me	i	PRON
ejpam-4522	305	4	,	,	PUNCT
ejpam-4522	305	5	ge	ge	PROPN
ejpam-4522	305	6	,	,	PUNCT
ejpam-4522	305	7	ξ	ξ	PROPN
ejpam-4522	305	8	)	)	PUNCT
ejpam-4522	305	9	and	and	CCONJ
ejpam-4522	305	10	n(x	n(x	PROPN
ejpam-4522	305	11	,	,	PUNCT
ejpam-4522	305	12	e	e	NOUN
ejpam-4522	305	13	)	)	PUNCT
ejpam-4522	305	14	:	:	PUNCT
ejpam-4522	305	15	=	=	SYM
ejpam-4522	305	16	(	(	PUNCT
ejpam-4522	305	17	ne	ne	INTJ
ejpam-4522	305	18	,	,	PUNCT
ejpam-4522	305	19	he	he	PRON
ejpam-4522	305	20	,	,	PUNCT
ejpam-4522	305	21	η	η	PROPN
ejpam-4522	305	22	)	)	PUNCT
ejpam-4522	305	23	be	be	VERB
ejpam-4522	305	24	makgeolli	makgeolli	NOUN
ejpam-4522	305	25	ideals	ideal	NOUN
ejpam-4522	305	26	of	of	ADP
ejpam-4522	305	27	(	(	PUNCT
ejpam-4522	305	28	x	x	X
ejpam-4522	305	29	,	,	PUNCT
ejpam-4522	305	30	e	e	NOUN
ejpam-4522	305	31	)	)	PUNCT
ejpam-4522	305	32	such	such	ADJ
ejpam-4522	305	33	that	that	SCONJ
ejpam-4522	305	34	me(0	me(0	PROPN
ejpam-4522	305	35	)	)	PUNCT
ejpam-4522	305	36	=	=	SYM
ejpam-4522	305	37	ne(0	ne(0	NOUN
ejpam-4522	305	38	)	)	PUNCT
ejpam-4522	305	39	,	,	PUNCT
ejpam-4522	305	40	ge(0	ge(0	PROPN
ejpam-4522	305	41	)	)	PUNCT
ejpam-4522	305	42	=	=	PUNCT
ejpam-4522	305	43	he(0	he(0	PROPN
ejpam-4522	305	44	)	)	PUNCT
ejpam-4522	305	45	,	,	PUNCT
ejpam-4522	305	46	ξ(0	ξ(0	NOUN
ejpam-4522	305	47	)	)	PUNCT
ejpam-4522	305	48	=	=	SYM
ejpam-4522	305	49	η(0	η(0	PROPN
ejpam-4522	305	50	)	)	PUNCT
ejpam-4522	305	51	,	,	PUNCT
ejpam-4522	305	52	me(a	me(a	NOUN
ejpam-4522	305	53	)	)	PUNCT
ejpam-4522	305	54	⊆	⊆	NUM
ejpam-4522	305	55	ne(a	ne(a	NOUN
ejpam-4522	305	56	)	)	PUNCT
ejpam-4522	305	57	,	,	PUNCT
ejpam-4522	305	58	ge(b	ge(b	X
ejpam-4522	305	59	)	)	PUNCT
ejpam-4522	305	60	⊇	⊇	NOUN
ejpam-4522	305	61	he(b	he(b	NOUN
ejpam-4522	305	62	)	)	PUNCT
ejpam-4522	305	63	and	and	CCONJ
ejpam-4522	305	64	ξ(x	ξ(x	NOUN
ejpam-4522	305	65	)	)	PUNCT
ejpam-4522	305	66	≤	≤	NOUN
ejpam-4522	305	67	η(x	η(x	NOUN
ejpam-4522	305	68	)	)	PUNCT
ejpam-4522	305	69	for	for	ADP
ejpam-4522	305	70	all	all	PRON
ejpam-4522	305	71	(	(	PUNCT
ejpam-4522	305	72	a	a	PRON
ejpam-4522	305	73	,	,	PUNCT
ejpam-4522	305	74	b	b	NOUN
ejpam-4522	305	75	,	,	PUNCT
ejpam-4522	305	76	x	x	NOUN
ejpam-4522	305	77	)	)	PUNCT
ejpam-4522	305	78	∈	∈	PROPN
ejpam-4522	305	79	e	e	X
ejpam-4522	305	80	×e	×e	X
ejpam-4522	305	81	×x	×x	PROPN
ejpam-4522	305	82	.	.	PUNCT
ejpam-4522	306	1	if	if	SCONJ
ejpam-4522	306	2	m(x	m(x	PROPN
ejpam-4522	306	3	,	,	PUNCT
ejpam-4522	306	4	e	e	NOUN
ejpam-4522	306	5	)	)	PUNCT
ejpam-4522	306	6	:	:	PUNCT
ejpam-4522	306	7	=	=	SYM
ejpam-4522	306	8	(	(	PUNCT
ejpam-4522	306	9	me	i	PRON
ejpam-4522	306	10	,	,	PUNCT
ejpam-4522	306	11	ge	ge	PROPN
ejpam-4522	306	12	,	,	PUNCT
ejpam-4522	306	13	ξ	ξ	X
ejpam-4522	306	14	)	)	PUNCT
ejpam-4522	306	15	is	be	AUX
ejpam-4522	306	16	a	a	DET
ejpam-4522	306	17	positive	positive	ADJ
ejpam-4522	306	18	implicative	implicative	ADJ
ejpam-4522	306	19	makgeolli	makgeolli	NOUN
ejpam-4522	306	20	ideal	ideal	NOUN
ejpam-4522	306	21	of	of	ADP
ejpam-4522	306	22	(	(	PUNCT
ejpam-4522	306	23	x	x	X
ejpam-4522	306	24	,	,	PUNCT
ejpam-4522	306	25	e	e	NOUN
ejpam-4522	306	26	)	)	PUNCT
ejpam-4522	306	27	,	,	PUNCT
ejpam-4522	306	28	then	then	ADV
ejpam-4522	306	29	so	so	ADV
ejpam-4522	306	30	is	be	AUX
ejpam-4522	306	31	n(x	n(x	X
ejpam-4522	306	32	,	,	PUNCT
ejpam-4522	306	33	e	e	NOUN
ejpam-4522	306	34	)	)	PUNCT
ejpam-4522	306	35	:	:	PUNCT
ejpam-4522	307	1	=	=	SYM
ejpam-4522	307	2	(	(	PUNCT
ejpam-4522	307	3	ne	ne	INTJ
ejpam-4522	307	4	,	,	PUNCT
ejpam-4522	307	5	he	he	PRON
ejpam-4522	307	6	,	,	PUNCT
ejpam-4522	307	7	η	η	PROPN
ejpam-4522	307	8	)	)	PUNCT
ejpam-4522	307	9	.	.	PUNCT
ejpam-4522	308	1	proof	proof	NOUN
ejpam-4522	308	2	.	.	PUNCT
ejpam-4522	309	1	assume	assume	VERB
ejpam-4522	309	2	that	that	SCONJ
ejpam-4522	309	3	m(x	m(x	PROPN
ejpam-4522	309	4	,	,	PUNCT
ejpam-4522	309	5	e	e	NOUN
ejpam-4522	309	6	)	)	PUNCT
ejpam-4522	309	7	:	:	PUNCT
ejpam-4522	309	8	=	=	SYM
ejpam-4522	309	9	(	(	PUNCT
ejpam-4522	309	10	me	i	PRON
ejpam-4522	309	11	,	,	PUNCT
ejpam-4522	309	12	ge	ge	PROPN
ejpam-4522	309	13	,	,	PUNCT
ejpam-4522	309	14	ξ	ξ	X
ejpam-4522	309	15	)	)	PUNCT
ejpam-4522	309	16	is	be	AUX
ejpam-4522	309	17	a	a	DET
ejpam-4522	309	18	positive	positive	ADJ
ejpam-4522	309	19	implicative	implicative	ADJ
ejpam-4522	309	20	makgeolli	makgeolli	NOUN
ejpam-4522	309	21	ideal	ideal	NOUN
ejpam-4522	309	22	of	of	ADP
ejpam-4522	309	23	(	(	PUNCT
ejpam-4522	309	24	x	x	X
ejpam-4522	309	25	,	,	PUNCT
ejpam-4522	309	26	e	e	NOUN
ejpam-4522	309	27	)	)	PUNCT
ejpam-4522	309	28	.	.	PUNCT
ejpam-4522	310	1	using	use	VERB
ejpam-4522	310	2	(	(	PUNCT
ejpam-4522	310	3	i3	i3	NOUN
ejpam-4522	310	4	)	)	PUNCT
ejpam-4522	310	5	,	,	PUNCT
ejpam-4522	310	6	(	(	PUNCT
ejpam-4522	310	7	4	4	NUM
ejpam-4522	310	8	)	)	PUNCT
ejpam-4522	310	9	,	,	PUNCT
ejpam-4522	310	10	theorem	theorem	VERB
ejpam-4522	310	11	4	4	NUM
ejpam-4522	310	12	and	and	CCONJ
ejpam-4522	310	13	the	the	DET
ejpam-4522	310	14	given	give	VERB
ejpam-4522	310	15	assumption	assumption	NOUN
ejpam-4522	310	16	,	,	PUNCT
ejpam-4522	310	17	we	we	PRON
ejpam-4522	310	18	have	have	VERB
ejpam-4522	310	19	ne(0	ne(0	NOUN
ejpam-4522	310	20	)	)	PUNCT
ejpam-4522	310	21	=	=	SYM
ejpam-4522	310	22	me(0	me(0	PROPN
ejpam-4522	310	23	)	)	PUNCT
ejpam-4522	310	24	=	=	PUNCT
ejpam-4522	311	1	me(((a	me(((a	NOUN
ejpam-4522	311	2	↬	↬	PROPN
ejpam-4522	311	3	b	b	X
ejpam-4522	311	4	)	)	PUNCT
ejpam-4522	311	5	↬	↬	PROPN
ejpam-4522	311	6	c	c	X
ejpam-4522	311	7	)	)	PUNCT
ejpam-4522	311	8	↬	↬	NOUN
ejpam-4522	311	9	(	(	PUNCT
ejpam-4522	311	10	(	(	PUNCT
ejpam-4522	311	11	a	a	DET
ejpam-4522	311	12	↬	↬	PROPN
ejpam-4522	311	13	b	b	NOUN
ejpam-4522	311	14	)	)	PUNCT
ejpam-4522	311	15	↬	↬	PROPN
ejpam-4522	311	16	c	c	NOUN
ejpam-4522	311	17	)	)	PUNCT
ejpam-4522	311	18	)	)	PUNCT
ejpam-4522	312	1	s.	s.	PROPN
ejpam-4522	312	2	z.	z.	PROPN
ejpam-4522	312	3	song	song	PROPN
ejpam-4522	312	4	,	,	PUNCT
ejpam-4522	312	5	m.	m.	NOUN
ejpam-4522	312	6	a.	a.	NOUN
ejpam-4522	312	7	öztürk	öztürk	PROPN
ejpam-4522	312	8	,	,	PUNCT
ejpam-4522	312	9	y.	y.	PROPN
ejpam-4522	312	10	b.	b.	PROPN
ejpam-4522	312	11	jun	jun	PROPN
ejpam-4522	312	12	/	/	SYM
ejpam-4522	312	13	eur	eur	PROPN
ejpam-4522	312	14	.	.	PUNCT
ejpam-4522	313	1	j.	j.	PROPN
ejpam-4522	313	2	pure	pure	PROPN
ejpam-4522	313	3	appl	appl	PROPN
ejpam-4522	313	4	.	.	PROPN
ejpam-4522	313	5	math	math	PROPN
ejpam-4522	313	6	,	,	PUNCT
ejpam-4522	313	7	15	15	NUM
ejpam-4522	313	8	(	(	PUNCT
ejpam-4522	313	9	4	4	NUM
ejpam-4522	313	10	)	)	PUNCT
ejpam-4522	313	11	(	(	PUNCT
ejpam-4522	313	12	2022	2022	NUM
ejpam-4522	313	13	)	)	PUNCT
ejpam-4522	313	14	,	,	PUNCT
ejpam-4522	313	15	1498	1498	NUM
ejpam-4522	313	16	-	-	SYM
ejpam-4522	313	17	1511	1511	NUM
ejpam-4522	313	18	1509	1509	NUM
ejpam-4522	313	19	=	=	SYM
ejpam-4522	313	20	me(((a	me(((a	X
ejpam-4522	313	21	↬	↬	PROPN
ejpam-4522	313	22	b	b	X
ejpam-4522	313	23	)	)	PUNCT
ejpam-4522	313	24	↬	↬	NOUN
ejpam-4522	313	25	(	(	PUNCT
ejpam-4522	313	26	(	(	PUNCT
ejpam-4522	313	27	a	a	DET
ejpam-4522	313	28	↬	↬	PROPN
ejpam-4522	313	29	b	b	NOUN
ejpam-4522	313	30	)	)	PUNCT
ejpam-4522	313	31	↬	↬	PROPN
ejpam-4522	313	32	c	c	NOUN
ejpam-4522	313	33	)	)	PUNCT
ejpam-4522	313	34	)	)	PUNCT
ejpam-4522	313	35	↬	↬	PROPN
ejpam-4522	313	36	c	c	X
ejpam-4522	313	37	)	)	PUNCT
ejpam-4522	313	38	=	=	PUNCT
ejpam-4522	314	1	me(((a	me(((a	NOUN
ejpam-4522	314	2	↬	↬	PROPN
ejpam-4522	314	3	(	(	PUNCT
ejpam-4522	314	4	(	(	PUNCT
ejpam-4522	314	5	a	a	DET
ejpam-4522	314	6	↬	↬	PROPN
ejpam-4522	314	7	b	b	NOUN
ejpam-4522	314	8	)	)	PUNCT
ejpam-4522	314	9	↬	↬	PROPN
ejpam-4522	314	10	c	c	NOUN
ejpam-4522	314	11	)	)	PUNCT
ejpam-4522	314	12	)	)	PUNCT
ejpam-4522	314	13	↬	↬	PROPN
ejpam-4522	315	1	b	b	X
ejpam-4522	315	2	)	)	PUNCT
ejpam-4522	315	3	↬	↬	X
ejpam-4522	315	4	c	c	X
ejpam-4522	315	5	)	)	PUNCT
ejpam-4522	315	6	⊆	⊆	NUM
ejpam-4522	315	7	me(((a	me(((a	X
ejpam-4522	315	8	↬	↬	X
ejpam-4522	315	9	(	(	PUNCT
ejpam-4522	315	10	(	(	PUNCT
ejpam-4522	315	11	a	a	DET
ejpam-4522	315	12	↬	↬	PROPN
ejpam-4522	315	13	b	b	NOUN
ejpam-4522	315	14	)	)	PUNCT
ejpam-4522	315	15	↬	↬	PROPN
ejpam-4522	315	16	c	c	NOUN
ejpam-4522	315	17	)	)	PUNCT
ejpam-4522	315	18	)	)	PUNCT
ejpam-4522	315	19	↬	↬	PROPN
ejpam-4522	316	1	c	c	X
ejpam-4522	316	2	)	)	PUNCT
ejpam-4522	316	3	↬	↬	NOUN
ejpam-4522	316	4	(	(	PUNCT
ejpam-4522	316	5	b	b	X
ejpam-4522	316	6	↬	↬	PROPN
ejpam-4522	316	7	c	c	NOUN
ejpam-4522	316	8	)	)	PUNCT
ejpam-4522	316	9	)	)	PUNCT
ejpam-4522	317	1	⊆	⊆	NUM
ejpam-4522	317	2	ne(((a	ne(((a	NUM
ejpam-4522	317	3	↬	↬	X
ejpam-4522	317	4	(	(	PUNCT
ejpam-4522	317	5	(	(	PUNCT
ejpam-4522	317	6	a	a	DET
ejpam-4522	317	7	↬	↬	PROPN
ejpam-4522	317	8	b	b	NOUN
ejpam-4522	317	9	)	)	PUNCT
ejpam-4522	317	10	↬	↬	PROPN
ejpam-4522	317	11	c	c	NOUN
ejpam-4522	317	12	)	)	PUNCT
ejpam-4522	317	13	)	)	PUNCT
ejpam-4522	317	14	↬	↬	PROPN
ejpam-4522	317	15	c	c	X
ejpam-4522	317	16	)	)	PUNCT
ejpam-4522	317	17	↬	↬	NOUN
ejpam-4522	317	18	(	(	PUNCT
ejpam-4522	317	19	b	b	X
ejpam-4522	317	20	↬	↬	PROPN
ejpam-4522	317	21	c	c	NOUN
ejpam-4522	317	22	)	)	PUNCT
ejpam-4522	317	23	)	)	PUNCT
ejpam-4522	318	1	=	=	SYM
ejpam-4522	318	2	ne(((a	ne(((a	NUM
ejpam-4522	318	3	↬	↬	X
ejpam-4522	318	4	c	c	X
ejpam-4522	318	5	)	)	PUNCT
ejpam-4522	318	6	↬	↬	NOUN
ejpam-4522	318	7	(	(	PUNCT
ejpam-4522	318	8	(	(	PUNCT
ejpam-4522	318	9	a	a	DET
ejpam-4522	318	10	↬	↬	PROPN
ejpam-4522	318	11	b	b	NOUN
ejpam-4522	318	12	)	)	PUNCT
ejpam-4522	318	13	↬	↬	PROPN
ejpam-4522	318	14	c	c	NOUN
ejpam-4522	318	15	)	)	PUNCT
ejpam-4522	318	16	)	)	PUNCT
ejpam-4522	319	1	↬	↬	PROPN
ejpam-4522	319	2	(	(	PUNCT
ejpam-4522	319	3	b	b	X
ejpam-4522	319	4	↬	↬	PROPN
ejpam-4522	319	5	c	c	NOUN
ejpam-4522	319	6	)	)	PUNCT
ejpam-4522	319	7	)	)	PUNCT
ejpam-4522	320	1	=	=	SYM
ejpam-4522	320	2	ne(((a	ne(((a	NUM
ejpam-4522	320	3	↬	↬	X
ejpam-4522	320	4	c	c	X
ejpam-4522	320	5	)	)	PUNCT
ejpam-4522	320	6	↬	↬	NOUN
ejpam-4522	320	7	(	(	PUNCT
ejpam-4522	320	8	b	b	X
ejpam-4522	320	9	↬	↬	PROPN
ejpam-4522	320	10	c	c	NOUN
ejpam-4522	320	11	)	)	PUNCT
ejpam-4522	320	12	)	)	PUNCT
ejpam-4522	321	1	↬	↬	PROPN
ejpam-4522	321	2	(	(	PUNCT
ejpam-4522	321	3	(	(	PUNCT
ejpam-4522	321	4	a	a	DET
ejpam-4522	321	5	↬	↬	PROPN
ejpam-4522	321	6	b	b	NOUN
ejpam-4522	321	7	)	)	PUNCT
ejpam-4522	321	8	↬	↬	PROPN
ejpam-4522	321	9	c	c	NOUN
ejpam-4522	321	10	)	)	PUNCT
ejpam-4522	321	11	)	)	PUNCT
ejpam-4522	321	12	,	,	PUNCT
ejpam-4522	321	13	he(0	he(0	PROPN
ejpam-4522	321	14	)	)	PUNCT
ejpam-4522	321	15	=	=	SYM
ejpam-4522	321	16	ge(0	ge(0	PROPN
ejpam-4522	321	17	)	)	PUNCT
ejpam-4522	321	18	=	=	SYM
ejpam-4522	321	19	ge(((a	ge(((a	PROPN
ejpam-4522	321	20	↬	↬	PROPN
ejpam-4522	321	21	b	b	X
ejpam-4522	321	22	)	)	PUNCT
ejpam-4522	321	23	↬	↬	PROPN
ejpam-4522	322	1	c	c	X
ejpam-4522	322	2	)	)	PUNCT
ejpam-4522	322	3	↬	↬	NOUN
ejpam-4522	322	4	(	(	PUNCT
ejpam-4522	322	5	(	(	PUNCT
ejpam-4522	322	6	a	a	DET
ejpam-4522	322	7	↬	↬	PROPN
ejpam-4522	322	8	b	b	NOUN
ejpam-4522	322	9	)	)	PUNCT
ejpam-4522	322	10	↬	↬	PROPN
ejpam-4522	322	11	c	c	NOUN
ejpam-4522	322	12	)	)	PUNCT
ejpam-4522	322	13	)	)	PUNCT
ejpam-4522	323	1	=	=	SYM
ejpam-4522	323	2	ge(((a	ge(((a	PROPN
ejpam-4522	323	3	↬	↬	PROPN
ejpam-4522	323	4	b	b	X
ejpam-4522	323	5	)	)	PUNCT
ejpam-4522	323	6	↬	↬	NOUN
ejpam-4522	323	7	(	(	PUNCT
ejpam-4522	323	8	(	(	PUNCT
ejpam-4522	323	9	a	a	DET
ejpam-4522	323	10	↬	↬	PROPN
ejpam-4522	323	11	b	b	NOUN
ejpam-4522	323	12	)	)	PUNCT
ejpam-4522	323	13	↬	↬	PROPN
ejpam-4522	323	14	c	c	NOUN
ejpam-4522	323	15	)	)	PUNCT
ejpam-4522	323	16	)	)	PUNCT
ejpam-4522	323	17	↬	↬	PROPN
ejpam-4522	323	18	c	c	X
ejpam-4522	323	19	)	)	PUNCT
ejpam-4522	323	20	=	=	SYM
ejpam-4522	323	21	ge(((a	ge(((a	PROPN
ejpam-4522	323	22	↬	↬	PROPN
ejpam-4522	323	23	(	(	PUNCT
ejpam-4522	323	24	(	(	PUNCT
ejpam-4522	323	25	a	a	DET
ejpam-4522	323	26	↬	↬	PROPN
ejpam-4522	323	27	b	b	NOUN
ejpam-4522	323	28	)	)	PUNCT
ejpam-4522	323	29	↬	↬	PROPN
ejpam-4522	323	30	c	c	NOUN
ejpam-4522	323	31	)	)	PUNCT
ejpam-4522	323	32	)	)	PUNCT
ejpam-4522	323	33	↬	↬	PROPN
ejpam-4522	324	1	b	b	X
ejpam-4522	324	2	)	)	PUNCT
ejpam-4522	324	3	↬	↬	X
ejpam-4522	324	4	c	c	X
ejpam-4522	324	5	)	)	PUNCT
ejpam-4522	324	6	⊇	⊇	PROPN
ejpam-4522	324	7	ge(((a	ge(((a	PROPN
ejpam-4522	324	8	↬	↬	PROPN
ejpam-4522	324	9	(	(	PUNCT
ejpam-4522	324	10	(	(	PUNCT
ejpam-4522	324	11	a	a	DET
ejpam-4522	324	12	↬	↬	PROPN
ejpam-4522	324	13	b	b	NOUN
ejpam-4522	324	14	)	)	PUNCT
ejpam-4522	324	15	↬	↬	PROPN
ejpam-4522	324	16	c	c	NOUN
ejpam-4522	324	17	)	)	PUNCT
ejpam-4522	324	18	)	)	PUNCT
ejpam-4522	324	19	↬	↬	PROPN
ejpam-4522	324	20	c	c	X
ejpam-4522	324	21	)	)	PUNCT
ejpam-4522	324	22	↬	↬	NOUN
ejpam-4522	324	23	(	(	PUNCT
ejpam-4522	324	24	b	b	X
ejpam-4522	324	25	↬	↬	PROPN
ejpam-4522	324	26	c	c	NOUN
ejpam-4522	324	27	)	)	PUNCT
ejpam-4522	324	28	)	)	PUNCT
ejpam-4522	325	1	⊇	⊇	NOUN
ejpam-4522	325	2	he(((a	he(((a	PRON
ejpam-4522	325	3	↬	↬	PROPN
ejpam-4522	325	4	(	(	PUNCT
ejpam-4522	325	5	(	(	PUNCT
ejpam-4522	325	6	a	a	DET
ejpam-4522	325	7	↬	↬	PROPN
ejpam-4522	325	8	b	b	NOUN
ejpam-4522	325	9	)	)	PUNCT
ejpam-4522	325	10	↬	↬	PROPN
ejpam-4522	325	11	c	c	NOUN
ejpam-4522	325	12	)	)	PUNCT
ejpam-4522	325	13	)	)	PUNCT
ejpam-4522	325	14	↬	↬	PROPN
ejpam-4522	325	15	c	c	X
ejpam-4522	325	16	)	)	PUNCT
ejpam-4522	325	17	↬	↬	NOUN
ejpam-4522	325	18	(	(	PUNCT
ejpam-4522	325	19	b	b	X
ejpam-4522	325	20	↬	↬	PROPN
ejpam-4522	325	21	c	c	NOUN
ejpam-4522	325	22	)	)	PUNCT
ejpam-4522	325	23	)	)	PUNCT
ejpam-4522	326	1	=	=	PUNCT
ejpam-4522	326	2	he(((a	he(((a	PROPN
ejpam-4522	326	3	↬	↬	PROPN
ejpam-4522	326	4	c	c	X
ejpam-4522	326	5	)	)	PUNCT
ejpam-4522	326	6	↬	↬	NOUN
ejpam-4522	326	7	(	(	PUNCT
ejpam-4522	326	8	(	(	PUNCT
ejpam-4522	326	9	a	a	DET
ejpam-4522	326	10	↬	↬	PROPN
ejpam-4522	326	11	b	b	NOUN
ejpam-4522	326	12	)	)	PUNCT
ejpam-4522	326	13	↬	↬	PROPN
ejpam-4522	326	14	c	c	NOUN
ejpam-4522	326	15	)	)	PUNCT
ejpam-4522	326	16	)	)	PUNCT
ejpam-4522	326	17	↬	↬	PROPN
ejpam-4522	326	18	(	(	PUNCT
ejpam-4522	326	19	b	b	X
ejpam-4522	326	20	↬	↬	PROPN
ejpam-4522	326	21	c	c	NOUN
ejpam-4522	326	22	)	)	PUNCT
ejpam-4522	326	23	)	)	PUNCT
ejpam-4522	327	1	=	=	PUNCT
ejpam-4522	327	2	he(((a	he(((a	PROPN
ejpam-4522	327	3	↬	↬	PROPN
ejpam-4522	327	4	c	c	X
ejpam-4522	327	5	)	)	PUNCT
ejpam-4522	327	6	↬	↬	NOUN
ejpam-4522	328	1	(	(	PUNCT
ejpam-4522	328	2	b	b	X
ejpam-4522	328	3	↬	↬	PROPN
ejpam-4522	328	4	c	c	NOUN
ejpam-4522	328	5	)	)	PUNCT
ejpam-4522	328	6	)	)	PUNCT
ejpam-4522	329	1	↬	↬	PROPN
ejpam-4522	329	2	(	(	PUNCT
ejpam-4522	329	3	(	(	PUNCT
ejpam-4522	329	4	a	a	DET
ejpam-4522	329	5	↬	↬	PROPN
ejpam-4522	329	6	b	b	NOUN
ejpam-4522	329	7	)	)	PUNCT
ejpam-4522	329	8	↬	↬	PROPN
ejpam-4522	329	9	c	c	NOUN
ejpam-4522	329	10	)	)	PUNCT
ejpam-4522	329	11	)	)	PUNCT
ejpam-4522	329	12	and	and	CCONJ
ejpam-4522	329	13	η(0	η(0	PROPN
ejpam-4522	329	14	)	)	PUNCT
ejpam-4522	330	1	=	=	SYM
ejpam-4522	330	2	ξ(0	ξ(0	X
ejpam-4522	330	3	)	)	PUNCT
ejpam-4522	330	4	=	=	PUNCT
ejpam-4522	331	1	ξ(((x	ξ(((x	PROPN
ejpam-4522	331	2	∗	∗	NOUN
ejpam-4522	331	3	y	y	NOUN
ejpam-4522	331	4	)	)	PUNCT
ejpam-4522	331	5	∗	∗	PROPN
ejpam-4522	331	6	z	z	NOUN
ejpam-4522	331	7	)	)	PUNCT
ejpam-4522	331	8	∗	∗	NOUN
ejpam-4522	331	9	(	(	PUNCT
ejpam-4522	331	10	(	(	PUNCT
ejpam-4522	331	11	x	x	SYM
ejpam-4522	331	12	∗	∗	PROPN
ejpam-4522	331	13	y	y	NOUN
ejpam-4522	331	14	)	)	PUNCT
ejpam-4522	331	15	∗	∗	NOUN
ejpam-4522	331	16	z	z	NOUN
ejpam-4522	331	17	)	)	PUNCT
ejpam-4522	331	18	)	)	PUNCT
ejpam-4522	332	1	=	=	PUNCT
ejpam-4522	332	2	ξ(((x	ξ(((x	PROPN
ejpam-4522	332	3	∗	∗	NOUN
ejpam-4522	332	4	y	y	NOUN
ejpam-4522	332	5	)	)	PUNCT
ejpam-4522	332	6	∗	∗	NOUN
ejpam-4522	332	7	(	(	PUNCT
ejpam-4522	332	8	(	(	PUNCT
ejpam-4522	332	9	x	x	SYM
ejpam-4522	332	10	∗	∗	PROPN
ejpam-4522	332	11	y	y	NOUN
ejpam-4522	332	12	)	)	PUNCT
ejpam-4522	332	13	∗	∗	NOUN
ejpam-4522	332	14	z	z	NOUN
ejpam-4522	332	15	)	)	PUNCT
ejpam-4522	332	16	)	)	PUNCT
ejpam-4522	332	17	∗	∗	NOUN
ejpam-4522	332	18	z	z	NOUN
ejpam-4522	332	19	)	)	PUNCT
ejpam-4522	332	20	=	=	SYM
ejpam-4522	333	1	ξ(((x	ξ(((x	PROPN
ejpam-4522	333	2	∗	∗	NOUN
ejpam-4522	333	3	(	(	PUNCT
ejpam-4522	333	4	(	(	PUNCT
ejpam-4522	333	5	x	x	SYM
ejpam-4522	333	6	∗	∗	PROPN
ejpam-4522	333	7	y	y	NOUN
ejpam-4522	333	8	)	)	PUNCT
ejpam-4522	333	9	∗	∗	NOUN
ejpam-4522	333	10	z	z	NOUN
ejpam-4522	333	11	)	)	PUNCT
ejpam-4522	333	12	)	)	PUNCT
ejpam-4522	333	13	∗	∗	PROPN
ejpam-4522	333	14	y	y	NOUN
ejpam-4522	333	15	)	)	PUNCT
ejpam-4522	333	16	∗	∗	NOUN
ejpam-4522	333	17	z	z	NOUN
ejpam-4522	333	18	)	)	PUNCT
ejpam-4522	333	19	≤	≤	PUNCT
ejpam-4522	334	1	ξ(((x	ξ(((x	PROPN
ejpam-4522	334	2	∗	∗	NOUN
ejpam-4522	334	3	(	(	PUNCT
ejpam-4522	334	4	(	(	PUNCT
ejpam-4522	334	5	x	x	SYM
ejpam-4522	334	6	∗	∗	PROPN
ejpam-4522	334	7	y	y	NOUN
ejpam-4522	334	8	)	)	PUNCT
ejpam-4522	334	9	∗	∗	NOUN
ejpam-4522	334	10	z	z	NOUN
ejpam-4522	334	11	)	)	PUNCT
ejpam-4522	334	12	)	)	PUNCT
ejpam-4522	335	1	∗	∗	PROPN
ejpam-4522	335	2	z	z	NOUN
ejpam-4522	335	3	)	)	PUNCT
ejpam-4522	335	4	∗	∗	NOUN
ejpam-4522	335	5	(	(	PUNCT
ejpam-4522	335	6	y	y	PROPN
ejpam-4522	335	7	∗	∗	PROPN
ejpam-4522	335	8	z	z	NOUN
ejpam-4522	335	9	)	)	PUNCT
ejpam-4522	335	10	)	)	PUNCT
ejpam-4522	336	1	≤	≤	NUM
ejpam-4522	336	2	η(((x	η(((x	PROPN
ejpam-4522	336	3	∗	∗	NOUN
ejpam-4522	336	4	(	(	PUNCT
ejpam-4522	336	5	(	(	PUNCT
ejpam-4522	336	6	x	x	SYM
ejpam-4522	336	7	∗	∗	PROPN
ejpam-4522	336	8	y	y	NOUN
ejpam-4522	336	9	)	)	PUNCT
ejpam-4522	336	10	∗	∗	NOUN
ejpam-4522	336	11	z	z	NOUN
ejpam-4522	336	12	)	)	PUNCT
ejpam-4522	336	13	)	)	PUNCT
ejpam-4522	336	14	∗	∗	PROPN
ejpam-4522	336	15	z	z	NOUN
ejpam-4522	336	16	)	)	PUNCT
ejpam-4522	336	17	∗	∗	NOUN
ejpam-4522	336	18	(	(	PUNCT
ejpam-4522	336	19	y	y	PROPN
ejpam-4522	336	20	∗	∗	PROPN
ejpam-4522	336	21	z	z	NOUN
ejpam-4522	336	22	)	)	PUNCT
ejpam-4522	336	23	)	)	PUNCT
ejpam-4522	337	1	=	=	PUNCT
ejpam-4522	337	2	η(((x	η(((x	PROPN
ejpam-4522	337	3	∗	∗	NOUN
ejpam-4522	337	4	z	z	NOUN
ejpam-4522	337	5	)	)	PUNCT
ejpam-4522	337	6	∗	∗	NOUN
ejpam-4522	337	7	(	(	PUNCT
ejpam-4522	337	8	(	(	PUNCT
ejpam-4522	337	9	x	x	SYM
ejpam-4522	337	10	∗	∗	PROPN
ejpam-4522	337	11	y	y	NOUN
ejpam-4522	337	12	)	)	PUNCT
ejpam-4522	337	13	∗	∗	NOUN
ejpam-4522	337	14	z	z	NOUN
ejpam-4522	337	15	)	)	PUNCT
ejpam-4522	337	16	)	)	PUNCT
ejpam-4522	337	17	∗	∗	NOUN
ejpam-4522	337	18	(	(	PUNCT
ejpam-4522	337	19	y	y	PROPN
ejpam-4522	337	20	∗	∗	PROPN
ejpam-4522	337	21	z	z	NOUN
ejpam-4522	337	22	)	)	PUNCT
ejpam-4522	337	23	)	)	PUNCT
ejpam-4522	338	1	=	=	PUNCT
ejpam-4522	338	2	η(((x	η(((x	PROPN
ejpam-4522	338	3	∗	∗	NOUN
ejpam-4522	338	4	z	z	NOUN
ejpam-4522	338	5	)	)	PUNCT
ejpam-4522	338	6	∗	∗	NOUN
ejpam-4522	338	7	(	(	PUNCT
ejpam-4522	338	8	y	y	PROPN
ejpam-4522	338	9	∗	∗	PROPN
ejpam-4522	338	10	z	z	NOUN
ejpam-4522	338	11	)	)	PUNCT
ejpam-4522	338	12	)	)	PUNCT
ejpam-4522	338	13	∗	∗	NOUN
ejpam-4522	338	14	(	(	PUNCT
ejpam-4522	338	15	(	(	PUNCT
ejpam-4522	338	16	x	x	SYM
ejpam-4522	338	17	∗	∗	PROPN
ejpam-4522	338	18	y	y	NOUN
ejpam-4522	338	19	)	)	PUNCT
ejpam-4522	338	20	∗	∗	NOUN
ejpam-4522	338	21	z	z	NOUN
ejpam-4522	338	22	)	)	PUNCT
ejpam-4522	338	23	)	)	PUNCT
ejpam-4522	338	24	.	.	PUNCT
ejpam-4522	339	1	it	it	PRON
ejpam-4522	339	2	follows	follow	VERB
ejpam-4522	339	3	from	from	ADP
ejpam-4522	339	4	(	(	PUNCT
ejpam-4522	339	5	9	9	NUM
ejpam-4522	339	6	)	)	PUNCT
ejpam-4522	339	7	and	and	CCONJ
ejpam-4522	339	8	(	(	PUNCT
ejpam-4522	339	9	10	10	NUM
ejpam-4522	339	10	)	)	PUNCT
ejpam-4522	339	11	that	that	SCONJ
ejpam-4522	339	12	ne((a	ne((a	NOUN
ejpam-4522	339	13	↬	↬	VERB
ejpam-4522	339	14	c	c	X
ejpam-4522	339	15	)	)	PUNCT
ejpam-4522	339	16	↬	↬	NOUN
ejpam-4522	340	1	(	(	PUNCT
ejpam-4522	340	2	b	b	X
ejpam-4522	340	3	↬	↬	PROPN
ejpam-4522	340	4	c	c	NOUN
ejpam-4522	340	5	)	)	PUNCT
ejpam-4522	340	6	)	)	PUNCT
ejpam-4522	340	7	⊇	⊇	PROPN
ejpam-4522	340	8	ne(((a	ne(((a	X
ejpam-4522	340	9	↬	↬	X
ejpam-4522	340	10	c	c	X
ejpam-4522	340	11	)	)	PUNCT
ejpam-4522	340	12	↬	↬	NOUN
ejpam-4522	340	13	(	(	PUNCT
ejpam-4522	340	14	b	b	X
ejpam-4522	340	15	↬	↬	PROPN
ejpam-4522	340	16	c	c	NOUN
ejpam-4522	340	17	)	)	PUNCT
ejpam-4522	340	18	)	)	PUNCT
ejpam-4522	341	1	↬	↬	PROPN
ejpam-4522	341	2	(	(	PUNCT
ejpam-4522	341	3	(	(	PUNCT
ejpam-4522	341	4	a	a	DET
ejpam-4522	341	5	↬	↬	PROPN
ejpam-4522	341	6	b	b	NOUN
ejpam-4522	341	7	)	)	PUNCT
ejpam-4522	341	8	↬	↬	PROPN
ejpam-4522	341	9	c	c	NOUN
ejpam-4522	341	10	)	)	PUNCT
ejpam-4522	341	11	)	)	PUNCT
ejpam-4522	342	1	∩ne((a	∩ne((a	PROPN
ejpam-4522	342	2	↬	↬	PROPN
ejpam-4522	343	1	b	b	X
ejpam-4522	343	2	)	)	PUNCT
ejpam-4522	343	3	↬	↬	X
ejpam-4522	343	4	c	c	X
ejpam-4522	343	5	)	)	PUNCT
ejpam-4522	343	6	⊇	⊇	PROPN
ejpam-4522	343	7	ne(0	ne(0	NOUN
ejpam-4522	343	8	)	)	PUNCT
ejpam-4522	343	9	∩ne((a	∩ne((a	PROPN
ejpam-4522	343	10	↬	↬	PROPN
ejpam-4522	344	1	b	b	X
ejpam-4522	344	2	)	)	PUNCT
ejpam-4522	344	3	↬	↬	X
ejpam-4522	344	4	c	c	X
ejpam-4522	344	5	)	)	PUNCT
ejpam-4522	344	6	=	=	SYM
ejpam-4522	344	7	ne((a	ne((a	NOUN
ejpam-4522	344	8	↬	↬	PROPN
ejpam-4522	344	9	b	b	X
ejpam-4522	344	10	)	)	PUNCT
ejpam-4522	344	11	↬	↬	PROPN
ejpam-4522	344	12	c	c	X
ejpam-4522	344	13	)	)	PUNCT
ejpam-4522	344	14	,	,	PUNCT
ejpam-4522	344	15	he((a	he((a	NOUN
ejpam-4522	344	16	↬	↬	PROPN
ejpam-4522	344	17	c	c	X
ejpam-4522	344	18	)	)	PUNCT
ejpam-4522	344	19	↬	↬	NOUN
ejpam-4522	344	20	(	(	PUNCT
ejpam-4522	344	21	b	b	X
ejpam-4522	344	22	↬	↬	PROPN
ejpam-4522	344	23	c	c	NOUN
ejpam-4522	344	24	)	)	PUNCT
ejpam-4522	344	25	)	)	PUNCT
ejpam-4522	345	1	⊆	⊆	NUM
ejpam-4522	345	2	he(((a	he(((a	ADP
ejpam-4522	345	3	↬	↬	PROPN
ejpam-4522	345	4	c	c	X
ejpam-4522	345	5	)	)	PUNCT
ejpam-4522	345	6	↬	↬	NOUN
ejpam-4522	345	7	(	(	PUNCT
ejpam-4522	345	8	b	b	X
ejpam-4522	345	9	↬	↬	PROPN
ejpam-4522	345	10	c	c	NOUN
ejpam-4522	345	11	)	)	PUNCT
ejpam-4522	345	12	)	)	PUNCT
ejpam-4522	345	13	↬	↬	PROPN
ejpam-4522	345	14	(	(	PUNCT
ejpam-4522	345	15	(	(	PUNCT
ejpam-4522	345	16	a	a	DET
ejpam-4522	345	17	↬	↬	PROPN
ejpam-4522	345	18	b	b	NOUN
ejpam-4522	345	19	)	)	PUNCT
ejpam-4522	345	20	↬	↬	PROPN
ejpam-4522	345	21	c	c	NOUN
ejpam-4522	345	22	)	)	PUNCT
ejpam-4522	345	23	)	)	PUNCT
ejpam-4522	346	1	∪he((a	∪he((a	PROPN
ejpam-4522	346	2	↬	↬	PROPN
ejpam-4522	346	3	b	b	X
ejpam-4522	346	4	)	)	PUNCT
ejpam-4522	346	5	↬	↬	X
ejpam-4522	346	6	c	c	X
ejpam-4522	346	7	)	)	PUNCT
ejpam-4522	346	8	⊆	⊆	NUM
ejpam-4522	346	9	he(0	he(0	PROPN
ejpam-4522	346	10	)	)	PUNCT
ejpam-4522	346	11	∪he((a	∪he((a	PROPN
ejpam-4522	346	12	↬	↬	PROPN
ejpam-4522	346	13	b	b	X
ejpam-4522	346	14	)	)	PUNCT
ejpam-4522	346	15	↬	↬	X
ejpam-4522	347	1	c	c	X
ejpam-4522	347	2	)	)	PUNCT
ejpam-4522	347	3	=	=	PUNCT
ejpam-4522	347	4	he((a	he((a	NOUN
ejpam-4522	347	5	↬	↬	PROPN
ejpam-4522	347	6	b	b	X
ejpam-4522	347	7	)	)	PUNCT
ejpam-4522	347	8	↬	↬	PROPN
ejpam-4522	347	9	c	c	NOUN
ejpam-4522	347	10	)	)	PUNCT
ejpam-4522	347	11	,	,	PUNCT
ejpam-4522	347	12	and	and	CCONJ
ejpam-4522	347	13	η((x	η((x	NOUN
ejpam-4522	347	14	∗	∗	NOUN
ejpam-4522	347	15	z	z	NOUN
ejpam-4522	347	16	)	)	PUNCT
ejpam-4522	347	17	∗	∗	NOUN
ejpam-4522	347	18	(	(	PUNCT
ejpam-4522	347	19	y	y	PROPN
ejpam-4522	347	20	∗	∗	PROPN
ejpam-4522	347	21	z	z	NOUN
ejpam-4522	347	22	)	)	PUNCT
ejpam-4522	347	23	)	)	PUNCT
ejpam-4522	347	24	≥	≥	X
ejpam-4522	348	1	min{η(((x	min{η(((x	NOUN
ejpam-4522	348	2	∗	∗	PROPN
ejpam-4522	348	3	z	z	NOUN
ejpam-4522	348	4	)	)	PUNCT
ejpam-4522	348	5	∗	∗	NOUN
ejpam-4522	348	6	(	(	PUNCT
ejpam-4522	348	7	y	y	PROPN
ejpam-4522	348	8	∗	∗	PROPN
ejpam-4522	348	9	z	z	NOUN
ejpam-4522	348	10	)	)	PUNCT
ejpam-4522	348	11	)	)	PUNCT
ejpam-4522	348	12	∗	∗	NOUN
ejpam-4522	348	13	(	(	PUNCT
ejpam-4522	348	14	(	(	PUNCT
ejpam-4522	348	15	x	x	SYM
ejpam-4522	348	16	∗	∗	PROPN
ejpam-4522	348	17	y	y	NOUN
ejpam-4522	348	18	)	)	PUNCT
ejpam-4522	348	19	∗	∗	NOUN
ejpam-4522	348	20	z	z	NOUN
ejpam-4522	348	21	)	)	PUNCT
ejpam-4522	348	22	)	)	PUNCT
ejpam-4522	348	23	,	,	PUNCT
ejpam-4522	348	24	η((x	η((x	NOUN
ejpam-4522	348	25	∗	∗	NOUN
ejpam-4522	348	26	y	y	NOUN
ejpam-4522	348	27	)	)	PUNCT
ejpam-4522	348	28	∗	∗	NOUN
ejpam-4522	348	29	z	z	NOUN
ejpam-4522	348	30	)	)	PUNCT
ejpam-4522	348	31	}	}	PUNCT
ejpam-4522	348	32	references	reference	NOUN
ejpam-4522	348	33	1510	1510	NUM
ejpam-4522	348	34	≥	≥	NUM
ejpam-4522	348	35	min{η(0	min{η(0	NOUN
ejpam-4522	348	36	)	)	PUNCT
ejpam-4522	348	37	,	,	PUNCT
ejpam-4522	348	38	η((x	η((x	NOUN
ejpam-4522	348	39	∗	∗	NOUN
ejpam-4522	348	40	y	y	NOUN
ejpam-4522	348	41	)	)	PUNCT
ejpam-4522	348	42	∗	∗	NOUN
ejpam-4522	348	43	z	z	NOUN
ejpam-4522	348	44	)	)	PUNCT
ejpam-4522	348	45	}	}	PUNCT
ejpam-4522	349	1	=	=	SYM
ejpam-4522	349	2	η((x	η((x	NOUN
ejpam-4522	349	3	∗	∗	NOUN
ejpam-4522	349	4	y	y	NOUN
ejpam-4522	349	5	)	)	PUNCT
ejpam-4522	349	6	∗	∗	NOUN
ejpam-4522	349	7	z	z	NOUN
ejpam-4522	349	8	)	)	PUNCT
ejpam-4522	349	9	for	for	ADP
ejpam-4522	349	10	all	all	DET
ejpam-4522	349	11	a	a	DET
ejpam-4522	349	12	,	,	PUNCT
ejpam-4522	349	13	b	b	NOUN
ejpam-4522	349	14	,	,	PUNCT
ejpam-4522	349	15	c	c	PROPN
ejpam-4522	349	16	∈	∈	PROPN
ejpam-4522	349	17	e	e	PROPN
ejpam-4522	349	18	and	and	CCONJ
ejpam-4522	349	19	x	x	PROPN
ejpam-4522	349	20	,	,	PUNCT
ejpam-4522	349	21	y	y	PROPN
ejpam-4522	349	22	,	,	PUNCT
ejpam-4522	349	23	z	z	PROPN
ejpam-4522	349	24	∈	∈	PROPN
ejpam-4522	349	25	x.	x.	NOUN
ejpam-4522	349	26	therefore	therefore	ADV
ejpam-4522	349	27	n(x	n(x	PROPN
ejpam-4522	349	28	,	,	PUNCT
ejpam-4522	349	29	e	e	NOUN
ejpam-4522	349	30	)	)	PUNCT
ejpam-4522	349	31	:	:	PUNCT
ejpam-4522	349	32	=	=	SYM
ejpam-4522	349	33	(	(	PUNCT
ejpam-4522	349	34	ne	ne	INTJ
ejpam-4522	349	35	,	,	PUNCT
ejpam-4522	349	36	he	he	PRON
ejpam-4522	349	37	,	,	PUNCT
ejpam-4522	349	38	η	η	PROPN
ejpam-4522	349	39	)	)	PUNCT
ejpam-4522	349	40	is	be	AUX
ejpam-4522	349	41	a	a	DET
ejpam-4522	349	42	positive	positive	ADJ
ejpam-4522	349	43	implicative	implicative	ADJ
ejpam-4522	349	44	makgeolli	makgeolli	NOUN
ejpam-4522	349	45	ideal	ideal	NOUN
ejpam-4522	349	46	of	of	ADP
ejpam-4522	349	47	(	(	PUNCT
ejpam-4522	349	48	x	x	X
ejpam-4522	349	49	,	,	PUNCT
ejpam-4522	349	50	e	e	NOUN
ejpam-4522	349	51	)	)	PUNCT
ejpam-4522	349	52	by	by	ADP
ejpam-4522	349	53	theorem	theorem	NOUN
ejpam-4522	349	54	4	4	NUM
ejpam-4522	349	55	.	.	NOUN
ejpam-4522	349	56	4	4	NUM
ejpam-4522	349	57	.	.	PUNCT
ejpam-4522	349	58	conclusions	conclusion	NOUN
ejpam-4522	349	59	a	a	DET
ejpam-4522	349	60	fuzzy	fuzzy	ADJ
ejpam-4522	349	61	set	set	NOUN
ejpam-4522	349	62	is	be	AUX
ejpam-4522	349	63	an	an	DET
ejpam-4522	349	64	extension	extension	NOUN
ejpam-4522	349	65	of	of	ADP
ejpam-4522	349	66	an	an	DET
ejpam-4522	349	67	existing	exist	VERB
ejpam-4522	349	68	set	set	NOUN
ejpam-4522	349	69	using	use	VERB
ejpam-4522	349	70	fuzzy	fuzzy	ADJ
ejpam-4522	349	71	logic	logic	NOUN
ejpam-4522	349	72	.	.	PUNCT
ejpam-4522	350	1	soft	soft	ADJ
ejpam-4522	350	2	set	set	NOUN
ejpam-4522	350	3	theory	theory	NOUN
ejpam-4522	350	4	is	be	AUX
ejpam-4522	350	5	a	a	DET
ejpam-4522	350	6	generalization	generalization	NOUN
ejpam-4522	350	7	of	of	ADP
ejpam-4522	350	8	fuzzy	fuzzy	ADJ
ejpam-4522	350	9	set	set	NOUN
ejpam-4522	350	10	theory	theory	NOUN
ejpam-4522	350	11	.	.	PUNCT
ejpam-4522	351	1	fuzzy	fuzzy	ADJ
ejpam-4522	351	2	and	and	CCONJ
ejpam-4522	351	3	soft	soft	ADJ
ejpam-4522	351	4	set	set	NOUN
ejpam-4522	351	5	theory	theory	NOUN
ejpam-4522	351	6	are	be	AUX
ejpam-4522	351	7	good	good	ADJ
ejpam-4522	351	8	mathematical	mathematical	ADJ
ejpam-4522	351	9	tools	tool	NOUN
ejpam-4522	351	10	for	for	ADP
ejpam-4522	351	11	dealing	deal	VERB
ejpam-4522	351	12	with	with	ADP
ejpam-4522	351	13	uncertainty	uncertainty	NOUN
ejpam-4522	351	14	in	in	ADP
ejpam-4522	351	15	a	a	DET
ejpam-4522	351	16	parametric	parametric	ADJ
ejpam-4522	351	17	manner	manner	NOUN
ejpam-4522	351	18	.	.	PUNCT
ejpam-4522	352	1	ahn	ahn	PROPN
ejpam-4522	352	2	et	et	PROPN
ejpam-4522	352	3	al	al	PROPN
ejpam-4522	352	4	.	.	PUNCT
ejpam-4522	353	1	[	[	X
ejpam-4522	353	2	2	2	X
ejpam-4522	353	3	]	]	PUNCT
ejpam-4522	353	4	introduced	introduce	VERB
ejpam-4522	353	5	the	the	DET
ejpam-4522	353	6	concept	concept	NOUN
ejpam-4522	353	7	of	of	ADP
ejpam-4522	353	8	makgeolli	makgeolli	NOUN
ejpam-4522	353	9	structures	structure	NOUN
ejpam-4522	353	10	as	as	ADP
ejpam-4522	353	11	a	a	DET
ejpam-4522	353	12	hybrid	hybrid	ADJ
ejpam-4522	353	13	structure	structure	NOUN
ejpam-4522	353	14	using	use	VERB
ejpam-4522	353	15	fuzzy	fuzzy	ADJ
ejpam-4522	353	16	and	and	CCONJ
ejpam-4522	353	17	soft	soft	ADJ
ejpam-4522	353	18	set	set	NOUN
ejpam-4522	353	19	theory	theory	NOUN
ejpam-4522	353	20	,	,	PUNCT
ejpam-4522	353	21	and	and	CCONJ
ejpam-4522	353	22	applied	apply	VERB
ejpam-4522	353	23	it	it	PRON
ejpam-4522	353	24	to	to	PART
ejpam-4522	353	25	bck	bck	VERB
ejpam-4522	353	26	/	/	SYM
ejpam-4522	353	27	bci	bci	NOUN
ejpam-4522	353	28	-	-	PUNCT
ejpam-4522	353	29	algebras	algebras	X
ejpam-4522	353	30	.	.	PUNCT
ejpam-4522	354	1	in	in	ADP
ejpam-4522	354	2	this	this	DET
ejpam-4522	354	3	article	article	NOUN
ejpam-4522	354	4	,	,	PUNCT
ejpam-4522	354	5	we	we	PRON
ejpam-4522	354	6	introduced	introduce	VERB
ejpam-4522	354	7	the	the	DET
ejpam-4522	354	8	notion	notion	NOUN
ejpam-4522	354	9	of	of	ADP
ejpam-4522	354	10	a	a	DET
ejpam-4522	354	11	positive	positive	ADJ
ejpam-4522	354	12	implicative	implicative	ADJ
ejpam-4522	354	13	makgeolli	makgeolli	NOUN
ejpam-4522	354	14	ideal	ideal	NOUN
ejpam-4522	354	15	in	in	ADP
ejpam-4522	354	16	bck	bck	PROPN
ejpam-4522	354	17	-	-	PUNCT
ejpam-4522	354	18	algebras	algebras	X
ejpam-4522	354	19	,	,	PUNCT
ejpam-4522	354	20	and	and	CCONJ
ejpam-4522	354	21	investigated	investigate	VERB
ejpam-4522	354	22	its	its	PRON
ejpam-4522	354	23	properties	property	NOUN
ejpam-4522	354	24	.	.	PUNCT
ejpam-4522	355	1	we	we	PRON
ejpam-4522	355	2	established	establish	VERB
ejpam-4522	355	3	the	the	DET
ejpam-4522	355	4	relationship	relationship	NOUN
ejpam-4522	355	5	between	between	ADP
ejpam-4522	355	6	makgeolli	makgeolli	NOUN
ejpam-4522	355	7	ideal	ideal	NOUN
ejpam-4522	355	8	and	and	CCONJ
ejpam-4522	355	9	positive	positive	ADJ
ejpam-4522	355	10	implicative	implicative	ADJ
ejpam-4522	355	11	makgeolli	makgeolli	NOUN
ejpam-4522	355	12	ideal	ideal	NOUN
ejpam-4522	355	13	,	,	PUNCT
ejpam-4522	355	14	and	and	CCONJ
ejpam-4522	355	15	explored	explore	VERB
ejpam-4522	355	16	the	the	DET
ejpam-4522	355	17	conditions	condition	NOUN
ejpam-4522	355	18	under	under	ADP
ejpam-4522	355	19	which	which	PRON
ejpam-4522	355	20	makgeolli	makgeolli	NOUN
ejpam-4522	355	21	ideal	ideal	NOUN
ejpam-4522	355	22	can	can	AUX
ejpam-4522	355	23	be	be	AUX
ejpam-4522	355	24	positive	positive	ADJ
ejpam-4522	355	25	implicative	implicative	ADJ
ejpam-4522	355	26	makgeolli	makgeolli	NOUN
ejpam-4522	355	27	ideal	ideal	NOUN
ejpam-4522	355	28	.	.	PUNCT
ejpam-4522	356	1	we	we	PRON
ejpam-4522	356	2	discussed	discuss	VERB
ejpam-4522	356	3	the	the	DET
ejpam-4522	356	4	characterization	characterization	NOUN
ejpam-4522	356	5	of	of	ADP
ejpam-4522	356	6	positive	positive	ADJ
ejpam-4522	356	7	implicative	implicative	ADJ
ejpam-4522	356	8	makgeolli	makgeolli	NOUN
ejpam-4522	356	9	ideal	ideal	NOUN
ejpam-4522	356	10	,	,	PUNCT
ejpam-4522	356	11	and	and	CCONJ
ejpam-4522	356	12	constructed	construct	VERB
ejpam-4522	356	13	the	the	DET
ejpam-4522	356	14	extension	extension	NOUN
ejpam-4522	356	15	property	property	NOUN
ejpam-4522	356	16	for	for	ADP
ejpam-4522	356	17	a	a	DET
ejpam-4522	356	18	positive	positive	ADJ
ejpam-4522	356	19	implicative	implicative	ADJ
ejpam-4522	356	20	makgeolli	makgeolli	NOUN
ejpam-4522	356	21	ideal	ideal	NOUN
ejpam-4522	356	22	.	.	PUNCT
ejpam-4522	357	1	acknowledgements	acknowledgement	VERB
ejpam-4522	357	2	the	the	DET
ejpam-4522	357	3	author	author	NOUN
ejpam-4522	357	4	,	,	PUNCT
ejpam-4522	357	5	seok	seok	PROPN
ejpam-4522	357	6	-	-	PUNCT
ejpam-4522	357	7	zun	zun	NOUN
ejpam-4522	357	8	song	song	NOUN
ejpam-4522	357	9	,	,	PUNCT
ejpam-4522	357	10	was	be	AUX
ejpam-4522	357	11	supported	support	VERB
ejpam-4522	357	12	by	by	ADP
ejpam-4522	357	13	basic	basic	ADJ
ejpam-4522	357	14	science	science	NOUN
ejpam-4522	357	15	research	research	NOUN
ejpam-4522	357	16	program	program	NOUN
ejpam-4522	357	17	through	through	ADP
ejpam-4522	357	18	the	the	DET
ejpam-4522	357	19	national	national	PROPN
ejpam-4522	357	20	research	research	PROPN
ejpam-4522	357	21	foundation	foundation	PROPN
ejpam-4522	357	22	of	of	ADP
ejpam-4522	357	23	korea	korea	PROPN
ejpam-4522	357	24	(	(	PUNCT
ejpam-4522	357	25	nrf	nrf	NOUN
ejpam-4522	357	26	)	)	PUNCT
ejpam-4522	357	27	funded	fund	VERB
ejpam-4522	357	28	by	by	ADP
ejpam-4522	357	29	the	the	DET
ejpam-4522	357	30	ministry	ministry	PROPN
ejpam-4522	357	31	of	of	ADP
ejpam-4522	357	32	education	education	PROPN
ejpam-4522	357	33	(	(	PUNCT
ejpam-4522	357	34	no	no	INTJ
ejpam-4522	357	35	.	.	NOUN
ejpam-4522	357	36	2016r1d1a1b02006812	2016r1d1a1b02006812	NUM
ejpam-4522	357	37	)	)	PUNCT
ejpam-4522	357	38	.	.	PUNCT
ejpam-4522	358	1	the	the	DET
ejpam-4522	358	2	authors	author	NOUN
ejpam-4522	358	3	wish	wish	VERB
ejpam-4522	358	4	to	to	PART
ejpam-4522	358	5	thank	thank	VERB
ejpam-4522	358	6	the	the	DET
ejpam-4522	358	7	anonymous	anonymous	ADJ
ejpam-4522	358	8	reviewers	reviewer	NOUN
ejpam-4522	358	9	for	for	ADP
ejpam-4522	358	10	their	their	PRON
ejpam-4522	358	11	valuable	valuable	ADJ
ejpam-4522	358	12	suggestions	suggestion	NOUN
ejpam-4522	358	13	.	.	PUNCT
ejpam-4522	359	1	references	reference	NOUN
ejpam-4522	359	2	[	[	X
ejpam-4522	359	3	1	1	NUM
ejpam-4522	359	4	]	]	X
ejpam-4522	359	5	u.	u.	NOUN
ejpam-4522	359	6	acar	acar	PROPN
ejpam-4522	359	7	,	,	PUNCT
ejpam-4522	359	8	f.	f.	PROPN
ejpam-4522	359	9	koyuncu	koyuncu	PROPN
ejpam-4522	359	10	,	,	PUNCT
ejpam-4522	359	11	and	and	CCONJ
ejpam-4522	359	12	b.	b.	PROPN
ejpam-4522	359	13	tanay	tanay	PROPN
ejpam-4522	359	14	.	.	PUNCT
ejpam-4522	360	1	soft	soft	ADJ
ejpam-4522	360	2	sets	set	NOUN
ejpam-4522	360	3	and	and	CCONJ
ejpam-4522	360	4	soft	soft	ADJ
ejpam-4522	360	5	rings	ring	NOUN
ejpam-4522	360	6	,	,	PUNCT
ejpam-4522	360	7	2010	2010	NUM
ejpam-4522	360	8	.	.	PUNCT
ejpam-4522	361	1	[	[	X
ejpam-4522	361	2	2	2	X
ejpam-4522	361	3	]	]	PUNCT
ejpam-4522	361	4	s.	s.	PROPN
ejpam-4522	361	5	s.	s.	PROPN
ejpam-4522	361	6	ahn	ahn	PROPN
ejpam-4522	361	7	,	,	PUNCT
ejpam-4522	361	8	s.	s.	PROPN
ejpam-4522	361	9	z.	z.	PROPN
ejpam-4522	361	10	song	song	PROPN
ejpam-4522	361	11	,	,	PUNCT
ejpam-4522	361	12	y.	y.	PROPN
ejpam-4522	361	13	b.	b.	PROPN
ejpam-4522	361	14	jun	jun	PROPN
ejpam-4522	361	15	,	,	PUNCT
ejpam-4522	361	16	and	and	CCONJ
ejpam-4522	361	17	h.	h.	PROPN
ejpam-4522	361	18	s.	s.	PROPN
ejpam-4522	361	19	kim	kim	PROPN
ejpam-4522	361	20	.	.	PUNCT
ejpam-4522	362	1	makgeolli	makgeolli	PROPN
ejpam-4522	362	2	structures	structure	NOUN
ejpam-4522	362	3	and	and	CCONJ
ejpam-4522	362	4	its	its	PRON
ejpam-4522	362	5	application	application	NOUN
ejpam-4522	362	6	in	in	ADP
ejpam-4522	362	7	bck	bck	PROPN
ejpam-4522	362	8	/	/	SYM
ejpam-4522	362	9	bci	bci	NOUN
ejpam-4522	362	10	-	-	PUNCT
ejpam-4522	362	11	algebras	algebra	NOUN
ejpam-4522	362	12	.	.	PUNCT
ejpam-4522	363	1	mathematics	mathematic	NOUN
ejpam-4522	363	2	,	,	PUNCT
ejpam-4522	363	3	7(784	7(784	NUM
ejpam-4522	363	4	)	)	PUNCT
ejpam-4522	363	5	,	,	PUNCT
ejpam-4522	363	6	2019	2019	NUM
ejpam-4522	363	7	.	.	PUNCT
ejpam-4522	364	1	[	[	X
ejpam-4522	364	2	3	3	X
ejpam-4522	364	3	]	]	PUNCT
ejpam-4522	364	4	h.	h.	PROPN
ejpam-4522	364	5	aktaş	aktaş	PROPN
ejpam-4522	364	6	and	and	CCONJ
ejpam-4522	364	7	n.	n.	PROPN
ejpam-4522	364	8	çağman	çağman	PROPN
ejpam-4522	364	9	.	.	PUNCT
ejpam-4522	364	10	soft	soft	ADJ
ejpam-4522	364	11	sets	set	NOUN
ejpam-4522	364	12	and	and	CCONJ
ejpam-4522	364	13	soft	soft	ADJ
ejpam-4522	364	14	groups	group	NOUN
ejpam-4522	364	15	.	.	PUNCT
ejpam-4522	365	1	inform	inform	NOUN
ejpam-4522	365	2	.	.	PUNCT
ejpam-4522	366	1	sci	sci	PROPN
ejpam-4522	366	2	.	.	PROPN
ejpam-4522	366	3	,	,	PUNCT
ejpam-4522	366	4	177:2726–2735	177:2726–2735	NUM
ejpam-4522	366	5	,	,	PUNCT
ejpam-4522	366	6	2007	2007	NUM
ejpam-4522	366	7	.	.	PUNCT
ejpam-4522	367	1	[	[	X
ejpam-4522	367	2	4	4	NUM
ejpam-4522	367	3	]	]	PUNCT
ejpam-4522	367	4	a.	a.	NOUN
ejpam-4522	367	5	o.	o.	NOUN
ejpam-4522	367	6	atagün	atagün	PROPN
ejpam-4522	367	7	and	and	CCONJ
ejpam-4522	367	8	a.	a.	NOUN
ejpam-4522	367	9	sezgin	sezgin	PROPN
ejpam-4522	367	10	.	.	PUNCT
ejpam-4522	368	1	soft	soft	ADJ
ejpam-4522	368	2	substructures	substructure	NOUN
ejpam-4522	368	3	of	of	ADP
ejpam-4522	368	4	rings	ring	NOUN
ejpam-4522	368	5	,	,	PUNCT
ejpam-4522	368	6	fields	field	NOUN
ejpam-4522	368	7	and	and	CCONJ
ejpam-4522	368	8	modules	module	NOUN
ejpam-4522	368	9	.	.	PUNCT
ejpam-4522	369	1	comput	comput	NOUN
ejpam-4522	369	2	.	.	PUNCT
ejpam-4522	370	1	math	math	NOUN
ejpam-4522	370	2	.	.	PUNCT
ejpam-4522	371	1	appl	appl	PROPN
ejpam-4522	371	2	.	.	PROPN
ejpam-4522	372	1	,	,	PUNCT
ejpam-4522	372	2	61:592–601	61:592–601	PROPN
ejpam-4522	372	3	,	,	PUNCT
ejpam-4522	372	4	2011	2011	NUM
ejpam-4522	372	5	.	.	PUNCT
ejpam-4522	373	1	[	[	X
ejpam-4522	373	2	5	5	X
ejpam-4522	373	3	]	]	PUNCT
ejpam-4522	373	4	f.	f.	PROPN
ejpam-4522	373	5	feng	feng	PROPN
ejpam-4522	373	6	,	,	PUNCT
ejpam-4522	373	7	y.	y.	PROPN
ejpam-4522	373	8	b.	b.	PROPN
ejpam-4522	373	9	jun	jun	PROPN
ejpam-4522	373	10	,	,	PUNCT
ejpam-4522	373	11	and	and	CCONJ
ejpam-4522	373	12	x.	x.	PROPN
ejpam-4522	373	13	zhao	zhao	PROPN
ejpam-4522	373	14	.	.	PUNCT
ejpam-4522	373	15	soft	soft	ADJ
ejpam-4522	373	16	semirings	semiring	NOUN
ejpam-4522	373	17	.	.	PUNCT
ejpam-4522	374	1	comput	comput	PROPN
ejpam-4522	374	2	.	.	PUNCT
ejpam-4522	375	1	math	math	NOUN
ejpam-4522	375	2	.	.	PUNCT
ejpam-4522	376	1	appl	appl	PROPN
ejpam-4522	376	2	.	.	PROPN
ejpam-4522	376	3	,	,	PUNCT
ejpam-4522	376	4	56:2621–2628	56:2621–2628	NUM
ejpam-4522	376	5	,	,	PUNCT
ejpam-4522	376	6	2008	2008	NUM
ejpam-4522	376	7	.	.	PUNCT
ejpam-4522	377	1	[	[	X
ejpam-4522	377	2	6	6	NUM
ejpam-4522	377	3	]	]	X
ejpam-4522	377	4	y.	y.	PROPN
ejpam-4522	377	5	s.	s.	PROPN
ejpam-4522	377	6	huang	huang	PROPN
ejpam-4522	377	7	.	.	PUNCT
ejpam-4522	378	1	bci	bci	PROPN
ejpam-4522	378	2	-	-	NOUN
ejpam-4522	378	3	algebra	algebra	NOUN
ejpam-4522	378	4	.	.	PUNCT
ejpam-4522	379	1	science	science	NOUN
ejpam-4522	379	2	press	press	PROPN
ejpam-4522	379	3	,	,	PUNCT
ejpam-4522	379	4	beijing	beijing	PROPN
ejpam-4522	379	5	,	,	PUNCT
ejpam-4522	379	6	china	china	PROPN
ejpam-4522	379	7	,	,	PUNCT
ejpam-4522	379	8	2006	2006	NUM
ejpam-4522	379	9	.	.	PUNCT
ejpam-4522	380	1	[	[	X
ejpam-4522	380	2	7	7	X
ejpam-4522	380	3	]	]	X
ejpam-4522	380	4	k.	k.	PROPN
ejpam-4522	380	5	iséki	iséki	PROPN
ejpam-4522	380	6	.	.	PROPN
ejpam-4522	380	7	on	on	ADP
ejpam-4522	380	8	bci	bci	NOUN
ejpam-4522	380	9	-	-	PUNCT
ejpam-4522	380	10	algebras	algebra	NOUN
ejpam-4522	380	11	.	.	PUNCT
ejpam-4522	380	12	math	math	NOUN
ejpam-4522	380	13	.	.	PUNCT
ejpam-4522	381	1	seminar	seminar	NOUN
ejpam-4522	381	2	notes	note	NOUN
ejpam-4522	381	3	,	,	PUNCT
ejpam-4522	381	4	8:125–130	8:125–130	NOUN
ejpam-4522	381	5	,	,	PUNCT
ejpam-4522	381	6	1980	1980	NUM
ejpam-4522	381	7	.	.	PUNCT
ejpam-4522	382	1	references	reference	NOUN
ejpam-4522	382	2	1511	1511	NUM
ejpam-4522	383	1	[	[	X
ejpam-4522	383	2	8	8	NUM
ejpam-4522	383	3	]	]	X
ejpam-4522	383	4	k.	k.	PROPN
ejpam-4522	383	5	iséki	iséki	PROPN
ejpam-4522	383	6	and	and	CCONJ
ejpam-4522	383	7	s.	s.	PROPN
ejpam-4522	383	8	tanaka	tanaka	PROPN
ejpam-4522	383	9	.	.	PUNCT
ejpam-4522	384	1	an	an	DET
ejpam-4522	384	2	introduction	introduction	NOUN
ejpam-4522	384	3	to	to	ADP
ejpam-4522	384	4	the	the	DET
ejpam-4522	384	5	theory	theory	NOUN
ejpam-4522	384	6	of	of	ADP
ejpam-4522	384	7	bck	bck	PROPN
ejpam-4522	384	8	-	-	PUNCT
ejpam-4522	384	9	algebras	algebras	PROPN
ejpam-4522	384	10	.	.	PUNCT
ejpam-4522	385	1	math	math	PROPN
ejpam-4522	385	2	.	.	PUNCT
ejpam-4522	386	1	japon	japon	PROPN
ejpam-4522	386	2	.	.	PROPN
ejpam-4522	386	3	,	,	PUNCT
ejpam-4522	386	4	23:1–26	23:1–26	NUM
ejpam-4522	386	5	,	,	PUNCT
ejpam-4522	386	6	1978	1978	NUM
ejpam-4522	386	7	.	.	PUNCT
ejpam-4522	387	1	[	[	X
ejpam-4522	387	2	9	9	NUM
ejpam-4522	387	3	]	]	X
ejpam-4522	387	4	y.	y.	PROPN
ejpam-4522	387	5	b.	b.	PROPN
ejpam-4522	387	6	jun	jun	PROPN
ejpam-4522	387	7	.	.	PROPN
ejpam-4522	387	8	soft	soft	ADJ
ejpam-4522	387	9	bck	bck	PROPN
ejpam-4522	387	10	/	/	SYM
ejpam-4522	387	11	bci	bci	NOUN
ejpam-4522	387	12	-	-	PUNCT
ejpam-4522	387	13	algebras	algebra	NOUN
ejpam-4522	387	14	.	.	PUNCT
ejpam-4522	388	1	comput	comput	PROPN
ejpam-4522	388	2	.	.	PUNCT
ejpam-4522	389	1	math	math	NOUN
ejpam-4522	389	2	.	.	PUNCT
ejpam-4522	390	1	appl	appl	PROPN
ejpam-4522	390	2	.	.	PROPN
ejpam-4522	390	3	,	,	PUNCT
ejpam-4522	390	4	56:1408–1413	56:1408–1413	NUM
ejpam-4522	390	5	,	,	PUNCT
ejpam-4522	390	6	2008	2008	NUM
ejpam-4522	390	7	.	.	PUNCT
ejpam-4522	391	1	[	[	X
ejpam-4522	391	2	10	10	NUM
ejpam-4522	391	3	]	]	X
ejpam-4522	391	4	y.	y.	PROPN
ejpam-4522	391	5	b.	b.	PROPN
ejpam-4522	391	6	jun	jun	PROPN
ejpam-4522	391	7	.	.	PROPN
ejpam-4522	392	1	union	union	PROPN
ejpam-4522	392	2	soft	soft	ADJ
ejpam-4522	392	3	sets	set	NOUN
ejpam-4522	392	4	with	with	ADP
ejpam-4522	392	5	applications	application	NOUN
ejpam-4522	392	6	in	in	ADP
ejpam-4522	392	7	bck	bck	PROPN
ejpam-4522	392	8	/	/	SYM
ejpam-4522	392	9	bci	bci	NOUN
ejpam-4522	392	10	-	-	PUNCT
ejpam-4522	392	11	algebras	algebra	NOUN
ejpam-4522	392	12	.	.	PUNCT
ejpam-4522	393	1	bull	bull	NOUN
ejpam-4522	393	2	.	.	PUNCT
ejpam-4522	394	1	korean	korean	ADJ
ejpam-4522	394	2	math	math	PROPN
ejpam-4522	394	3	.	.	PUNCT
ejpam-4522	395	1	soc	soc	PROPN
ejpam-4522	395	2	.	.	PUNCT
ejpam-4522	395	3	,	,	PUNCT
ejpam-4522	395	4	50(6):1937–1956	50(6):1937–1956	NUM
ejpam-4522	395	5	,	,	PUNCT
ejpam-4522	395	6	2013	2013	NUM
ejpam-4522	395	7	.	.	PUNCT
ejpam-4522	396	1	[	[	X
ejpam-4522	396	2	11	11	NUM
ejpam-4522	396	3	]	]	X
ejpam-4522	396	4	y.	y.	PROPN
ejpam-4522	396	5	b.	b.	PROPN
ejpam-4522	396	6	jun	jun	PROPN
ejpam-4522	396	7	,	,	PUNCT
ejpam-4522	396	8	h.	h.	PROPN
ejpam-4522	396	9	s.	s.	PROPN
ejpam-4522	396	10	kim	kim	PROPN
ejpam-4522	396	11	,	,	PUNCT
ejpam-4522	396	12	and	and	CCONJ
ejpam-4522	396	13	j.	j.	PROPN
ejpam-4522	396	14	neggers	neggers	PROPN
ejpam-4522	396	15	.	.	PUNCT
ejpam-4522	397	1	pseudo	pseudo	NOUN
ejpam-4522	397	2	d	d	NOUN
ejpam-4522	397	3	-	-	PUNCT
ejpam-4522	397	4	algebras	algebras	X
ejpam-4522	397	5	.	.	PUNCT
ejpam-4522	398	1	inform	inform	NOUN
ejpam-4522	398	2	.	.	PUNCT
ejpam-4522	399	1	sci	sci	PROPN
ejpam-4522	399	2	.	.	PROPN
ejpam-4522	399	3	,	,	PUNCT
ejpam-4522	399	4	179:1751–1759	179:1751–1759	NUM
ejpam-4522	399	5	,	,	PUNCT
ejpam-4522	399	6	2009	2009	NUM
ejpam-4522	399	7	.	.	PUNCT
ejpam-4522	400	1	[	[	X
ejpam-4522	400	2	12	12	NUM
ejpam-4522	400	3	]	]	X
ejpam-4522	400	4	y.	y.	PROPN
ejpam-4522	400	5	b.	b.	PROPN
ejpam-4522	400	6	jun	jun	PROPN
ejpam-4522	400	7	,	,	PUNCT
ejpam-4522	400	8	k.	k.	PROPN
ejpam-4522	400	9	j.	j.	PROPN
ejpam-4522	400	10	lee	lee	PROPN
ejpam-4522	400	11	,	,	PUNCT
ejpam-4522	400	12	and	and	CCONJ
ejpam-4522	400	13	m.	m.	PROPN
ejpam-4522	400	14	s.	s.	PROPN
ejpam-4522	400	15	kang	kang	PROPN
ejpam-4522	400	16	.	.	PUNCT
ejpam-4522	401	1	soft	soft	ADJ
ejpam-4522	401	2	set	set	ADJ
ejpam-4522	401	3	theory	theory	NOUN
ejpam-4522	401	4	applied	apply	VERB
ejpam-4522	401	5	to	to	ADP
ejpam-4522	401	6	ideals	ideal	NOUN
ejpam-4522	401	7	in	in	ADP
ejpam-4522	401	8	d	d	NOUN
ejpam-4522	401	9	-	-	PUNCT
ejpam-4522	401	10	algebras	algebra	NOUN
ejpam-4522	401	11	.	.	PUNCT
ejpam-4522	402	1	comput	comput	NOUN
ejpam-4522	402	2	.	.	PUNCT
ejpam-4522	403	1	math	math	NOUN
ejpam-4522	403	2	.	.	PUNCT
ejpam-4522	404	1	appl	appl	PROPN
ejpam-4522	404	2	.	.	PROPN
ejpam-4522	404	3	,	,	PUNCT
ejpam-4522	405	1	57:367–378	57:367–378	NUM
ejpam-4522	405	2	,	,	PUNCT
ejpam-4522	405	3	2009	2009	NUM
ejpam-4522	405	4	.	.	PUNCT
ejpam-4522	406	1	[	[	X
ejpam-4522	406	2	13	13	NUM
ejpam-4522	406	3	]	]	X
ejpam-4522	406	4	y.	y.	PROPN
ejpam-4522	406	5	b.	b.	PROPN
ejpam-4522	406	6	jun	jun	PROPN
ejpam-4522	406	7	,	,	PUNCT
ejpam-4522	406	8	k.	k.	PROPN
ejpam-4522	406	9	j.	j.	PROPN
ejpam-4522	406	10	lee	lee	PROPN
ejpam-4522	406	11	,	,	PUNCT
ejpam-4522	406	12	and	and	CCONJ
ejpam-4522	406	13	m.	m.	PROPN
ejpam-4522	406	14	s.	s.	PROPN
ejpam-4522	406	15	kang	kang	PROPN
ejpam-4522	406	16	.	.	PUNCT
ejpam-4522	407	1	intersectional	intersectional	ADJ
ejpam-4522	407	2	soft	soft	ADJ
ejpam-4522	407	3	sets	set	NOUN
ejpam-4522	407	4	and	and	CCONJ
ejpam-4522	407	5	applications	application	NOUN
ejpam-4522	407	6	to	to	PART
ejpam-4522	407	7	bck	bck	VERB
ejpam-4522	407	8	/	/	SYM
ejpam-4522	407	9	bci	bci	NOUN
ejpam-4522	407	10	-	-	PUNCT
ejpam-4522	407	11	algebras	algebra	NOUN
ejpam-4522	407	12	.	.	PUNCT
ejpam-4522	408	1	commun	commun	PROPN
ejpam-4522	408	2	.	.	PUNCT
ejpam-4522	409	1	korean	korean	ADJ
ejpam-4522	409	2	math	math	PROPN
ejpam-4522	409	3	.	.	PUNCT
ejpam-4522	410	1	soc	soc	PROPN
ejpam-4522	410	2	.	.	PUNCT
ejpam-4522	410	3	,	,	PUNCT
ejpam-4522	410	4	28(1):11–24	28(1):11–24	NUM
ejpam-4522	410	5	,	,	PUNCT
ejpam-4522	410	6	2013	2013	NUM
ejpam-4522	410	7	.	.	PUNCT
ejpam-4522	411	1	[	[	X
ejpam-4522	411	2	14	14	NUM
ejpam-4522	411	3	]	]	X
ejpam-4522	411	4	y.	y.	PROPN
ejpam-4522	411	5	b.	b.	PROPN
ejpam-4522	411	6	jun	jun	PROPN
ejpam-4522	411	7	,	,	PUNCT
ejpam-4522	411	8	k.	k.	PROPN
ejpam-4522	411	9	j.	j.	PROPN
ejpam-4522	411	10	lee	lee	PROPN
ejpam-4522	411	11	,	,	PUNCT
ejpam-4522	411	12	and	and	CCONJ
ejpam-4522	411	13	a.	a.	PROPN
ejpam-4522	411	14	khan	khan	PROPN
ejpam-4522	411	15	.	.	PUNCT
ejpam-4522	412	1	soft	soft	ADJ
ejpam-4522	412	2	ordered	order	VERB
ejpam-4522	412	3	semigroups	semigroup	NOUN
ejpam-4522	412	4	.	.	PUNCT
ejpam-4522	413	1	math	math	NOUN
ejpam-4522	413	2	.	.	PUNCT
ejpam-4522	414	1	logic	logic	PROPN
ejpam-4522	414	2	q.	q.	PROPN
ejpam-4522	414	3	,	,	PUNCT
ejpam-4522	414	4	56:42–50	56:42–50	NUM
ejpam-4522	414	5	,	,	PUNCT
ejpam-4522	414	6	2010	2010	NUM
ejpam-4522	414	7	.	.	PUNCT
ejpam-4522	415	1	[	[	X
ejpam-4522	415	2	15	15	NUM
ejpam-4522	415	3	]	]	X
ejpam-4522	415	4	y.	y.	PROPN
ejpam-4522	415	5	b.	b.	PROPN
ejpam-4522	415	6	jun	jun	PROPN
ejpam-4522	415	7	,	,	PUNCT
ejpam-4522	415	8	k.	k.	PROPN
ejpam-4522	415	9	j.	j.	PROPN
ejpam-4522	415	10	lee	lee	PROPN
ejpam-4522	415	11	,	,	PUNCT
ejpam-4522	415	12	and	and	CCONJ
ejpam-4522	415	13	e.	e.	PROPN
ejpam-4522	415	14	h.	h.	PROPN
ejpam-4522	415	15	roh	roh	PROPN
ejpam-4522	415	16	.	.	PUNCT
ejpam-4522	416	1	intersectional	intersectional	ADJ
ejpam-4522	416	2	soft	soft	ADJ
ejpam-4522	416	3	bck	bck	NOUN
ejpam-4522	416	4	/	/	SYM
ejpam-4522	416	5	bci	bci	NOUN
ejpam-4522	416	6	-	-	NOUN
ejpam-4522	416	7	ideals	ideal	NOUN
ejpam-4522	416	8	.	.	PUNCT
ejpam-4522	417	1	ann	ann	PROPN
ejpam-4522	417	2	.	.	PUNCT
ejpam-4522	417	3	fuzzy	fuzzy	ADJ
ejpam-4522	417	4	math	math	NOUN
ejpam-4522	417	5	.	.	PUNCT
ejpam-4522	418	1	inform	inform	NOUN
ejpam-4522	418	2	.	.	PUNCT
ejpam-4522	418	3	,	,	PUNCT
ejpam-4522	418	4	4(1):1–7	4(1):1–7	NOUN
ejpam-4522	418	5	,	,	PUNCT
ejpam-4522	418	6	2012	2012	NUM
ejpam-4522	418	7	.	.	PUNCT
ejpam-4522	419	1	[	[	X
ejpam-4522	419	2	16	16	NUM
ejpam-4522	419	3	]	]	X
ejpam-4522	419	4	y.	y.	PROPN
ejpam-4522	419	5	b.	b.	PROPN
ejpam-4522	419	6	jun	jun	PROPN
ejpam-4522	419	7	,	,	PUNCT
ejpam-4522	419	8	k.	k.	PROPN
ejpam-4522	419	9	j.	j.	PROPN
ejpam-4522	419	10	lee	lee	PROPN
ejpam-4522	419	11	,	,	PUNCT
ejpam-4522	419	12	and	and	CCONJ
ejpam-4522	419	13	j.	j.	PROPN
ejpam-4522	419	14	zhan	zhan	PROPN
ejpam-4522	419	15	.	.	PUNCT
ejpam-4522	420	1	soft	soft	ADJ
ejpam-4522	420	2	p	p	NOUN
ejpam-4522	420	3	-	-	PUNCT
ejpam-4522	420	4	ideals	ideal	NOUN
ejpam-4522	420	5	of	of	ADP
ejpam-4522	420	6	soft	soft	ADJ
ejpam-4522	420	7	bci	bci	NOUN
ejpam-4522	420	8	-	-	PUNCT
ejpam-4522	420	9	algebras	algebra	NOUN
ejpam-4522	420	10	.	.	PUNCT
ejpam-4522	421	1	comput	comput	PROPN
ejpam-4522	421	2	.	.	PUNCT
ejpam-4522	422	1	math	math	NOUN
ejpam-4522	422	2	.	.	PUNCT
ejpam-4522	423	1	appl	appl	PROPN
ejpam-4522	423	2	.	.	PROPN
ejpam-4522	423	3	,	,	PUNCT
ejpam-4522	424	1	58:2060–2068	58:2060–2068	NUM
ejpam-4522	424	2	,	,	PUNCT
ejpam-4522	424	3	2009	2009	NUM
ejpam-4522	424	4	.	.	PUNCT
ejpam-4522	425	1	[	[	X
ejpam-4522	425	2	17	17	NUM
ejpam-4522	425	3	]	]	X
ejpam-4522	425	4	y.	y.	PROPN
ejpam-4522	425	5	b.	b.	PROPN
ejpam-4522	425	6	jun	jun	PROPN
ejpam-4522	425	7	and	and	CCONJ
ejpam-4522	425	8	c.	c.	PROPN
ejpam-4522	425	9	h.	h.	PROPN
ejpam-4522	425	10	park	park	PROPN
ejpam-4522	425	11	.	.	PUNCT
ejpam-4522	426	1	applications	application	NOUN
ejpam-4522	426	2	of	of	ADP
ejpam-4522	426	3	soft	soft	ADJ
ejpam-4522	426	4	sets	set	NOUN
ejpam-4522	426	5	in	in	ADP
ejpam-4522	426	6	ideal	ideal	ADJ
ejpam-4522	426	7	theory	theory	NOUN
ejpam-4522	426	8	of	of	ADP
ejpam-4522	426	9	bck	bck	PROPN
ejpam-4522	426	10	/	/	SYM
ejpam-4522	426	11	bci	bci	NOUN
ejpam-4522	426	12	-	-	PUNCT
ejpam-4522	426	13	algebras	algebra	NOUN
ejpam-4522	426	14	.	.	PUNCT
ejpam-4522	427	1	inform	inform	NOUN
ejpam-4522	427	2	.	.	PUNCT
ejpam-4522	428	1	sci	sci	PROPN
ejpam-4522	428	2	.	.	PROPN
ejpam-4522	428	3	,	,	PUNCT
ejpam-4522	428	4	178:2466–2475	178:2466–2475	PROPN
ejpam-4522	428	5	,	,	PUNCT
ejpam-4522	428	6	2008	2008	NUM
ejpam-4522	428	7	.	.	PUNCT
ejpam-4522	429	1	[	[	X
ejpam-4522	429	2	18	18	NUM
ejpam-4522	429	3	]	]	PUNCT
ejpam-4522	429	4	p.	p.	PROPN
ejpam-4522	429	5	k.	k.	PROPN
ejpam-4522	429	6	maji	maji	PROPN
ejpam-4522	429	7	,	,	PUNCT
ejpam-4522	429	8	a.	a.	PROPN
ejpam-4522	429	9	r.	r.	PROPN
ejpam-4522	429	10	roy	roy	PROPN
ejpam-4522	429	11	,	,	PUNCT
ejpam-4522	429	12	and	and	CCONJ
ejpam-4522	429	13	r.	r.	PROPN
ejpam-4522	429	14	biswas	biswas	PROPN
ejpam-4522	429	15	.	.	PUNCT
ejpam-4522	430	1	an	an	DET
ejpam-4522	430	2	application	application	NOUN
ejpam-4522	430	3	of	of	ADP
ejpam-4522	430	4	soft	soft	ADJ
ejpam-4522	430	5	sets	set	NOUN
ejpam-4522	430	6	in	in	ADP
ejpam-4522	430	7	a	a	DET
ejpam-4522	430	8	decision	decision	NOUN
ejpam-4522	430	9	making	make	VERB
ejpam-4522	430	10	problem	problem	NOUN
ejpam-4522	430	11	.	.	PUNCT
ejpam-4522	431	1	comput	comput	NOUN
ejpam-4522	431	2	.	.	PUNCT
ejpam-4522	432	1	math	math	NOUN
ejpam-4522	432	2	.	.	PUNCT
ejpam-4522	433	1	appl	appl	PROPN
ejpam-4522	433	2	.	.	PROPN
ejpam-4522	433	3	,	,	PUNCT
ejpam-4522	433	4	44:1077–1083	44:1077–1083	PROPN
ejpam-4522	433	5	,	,	PUNCT
ejpam-4522	433	6	2002	2002	NUM
ejpam-4522	433	7	.	.	PUNCT
ejpam-4522	434	1	[	[	X
ejpam-4522	434	2	19	19	NUM
ejpam-4522	434	3	]	]	PUNCT
ejpam-4522	434	4	j.	j.	PROPN
ejpam-4522	434	5	meng	meng	PROPN
ejpam-4522	434	6	.	.	PUNCT
ejpam-4522	435	1	on	on	ADP
ejpam-4522	435	2	ideals	ideal	NOUN
ejpam-4522	435	3	in	in	ADP
ejpam-4522	435	4	bck	bck	NOUN
ejpam-4522	435	5	-	-	PUNCT
ejpam-4522	435	6	algebras	algebras	PROPN
ejpam-4522	435	7	.	.	PUNCT
ejpam-4522	435	8	math	math	PROPN
ejpam-4522	435	9	.	.	PUNCT
ejpam-4522	436	1	japon	japon	PROPN
ejpam-4522	436	2	.	.	PUNCT
ejpam-4522	437	1	,	,	PUNCT
ejpam-4522	437	2	40(1):143–154	40(1):143–154	PROPN
ejpam-4522	437	3	,	,	PUNCT
ejpam-4522	437	4	1994	1994	NUM
ejpam-4522	437	5	.	.	PUNCT
ejpam-4522	438	1	[	[	X
ejpam-4522	438	2	20	20	NUM
ejpam-4522	438	3	]	]	PUNCT
ejpam-4522	438	4	j.	j.	PROPN
ejpam-4522	438	5	meng	meng	PROPN
ejpam-4522	438	6	and	and	CCONJ
ejpam-4522	438	7	y.	y.	PROPN
ejpam-4522	438	8	b.	b.	PROPN
ejpam-4522	439	1	jun	jun	PROPN
ejpam-4522	439	2	.	.	PUNCT
ejpam-4522	440	1	bck	bck	PROPN
ejpam-4522	440	2	-	-	PUNCT
ejpam-4522	440	3	algebras	algebras	PROPN
ejpam-4522	440	4	.	.	PUNCT
ejpam-4522	441	1	kyungmoon	kyungmoon	PROPN
ejpam-4522	441	2	sa	sa	PROPN
ejpam-4522	441	3	co.	co.	PROPN
ejpam-4522	441	4	,	,	PUNCT
ejpam-4522	441	5	seoul	seoul	PROPN
ejpam-4522	441	6	,	,	PUNCT
ejpam-4522	441	7	korea	korea	PROPN
ejpam-4522	441	8	,	,	PUNCT
ejpam-4522	441	9	1994	1994	NUM
ejpam-4522	441	10	.	.	PUNCT
ejpam-4522	442	1	[	[	X
ejpam-4522	442	2	21	21	NUM
ejpam-4522	442	3	]	]	X
ejpam-4522	442	4	d.	d.	PROPN
ejpam-4522	442	5	molodtsov	molodtsov	PROPN
ejpam-4522	442	6	.	.	PUNCT
ejpam-4522	443	1	soft	soft	ADJ
ejpam-4522	443	2	set	set	ADJ
ejpam-4522	443	3	theory	theory	NOUN
ejpam-4522	443	4	first	first	ADJ
ejpam-4522	443	5	results	result	NOUN
ejpam-4522	443	6	.	.	PUNCT
ejpam-4522	444	1	comput	comput	NOUN
ejpam-4522	444	2	.	.	PUNCT
ejpam-4522	445	1	math	math	NOUN
ejpam-4522	445	2	.	.	PUNCT
ejpam-4522	446	1	appl	appl	PROPN
ejpam-4522	446	2	.	.	PROPN
ejpam-4522	446	3	,	,	PUNCT
ejpam-4522	446	4	37:19–31	37:19–31	PROPN
ejpam-4522	446	5	,	,	PUNCT
ejpam-4522	446	6	1999	1999	NUM
ejpam-4522	446	7	.	.	PUNCT
ejpam-4522	447	1	[	[	X
ejpam-4522	447	2	22	22	NUM
ejpam-4522	447	3	]	]	X
ejpam-4522	447	4	c.	c.	PROPN
ejpam-4522	447	5	h.	h.	PROPN
ejpam-4522	447	6	park	park	PROPN
ejpam-4522	447	7	,	,	PUNCT
ejpam-4522	447	8	y.	y.	PROPN
ejpam-4522	447	9	b.	b.	PROPN
ejpam-4522	447	10	jun	jun	PROPN
ejpam-4522	447	11	,	,	PUNCT
ejpam-4522	447	12	and	and	CCONJ
ejpam-4522	447	13	m.	m.	NOUN
ejpam-4522	447	14	a.	a.	NOUN
ejpam-4522	447	15	öztürk	öztürk	PROPN
ejpam-4522	447	16	.	.	PUNCT
ejpam-4522	448	1	soft	soft	ADJ
ejpam-4522	448	2	ws	ws	NOUN
ejpam-4522	448	3	-	-	PUNCT
ejpam-4522	448	4	algebras	algebras	PROPN
ejpam-4522	448	5	.	.	PUNCT
ejpam-4522	449	1	commun	commun	PROPN
ejpam-4522	449	2	.	.	PUNCT
ejpam-4522	450	1	korean	korean	ADJ
ejpam-4522	450	2	math	math	PROPN
ejpam-4522	450	3	.	.	PUNCT
ejpam-4522	451	1	soc	soc	PROPN
ejpam-4522	451	2	.	.	PUNCT
ejpam-4522	451	3	,	,	PUNCT
ejpam-4522	452	1	23:313–324	23:313–324	NUM
ejpam-4522	452	2	,	,	PUNCT
ejpam-4522	452	3	2008	2008	NUM
ejpam-4522	452	4	.	.	PUNCT
ejpam-4522	453	1	[	[	X
ejpam-4522	453	2	23	23	NUM
ejpam-4522	453	3	]	]	PUNCT
ejpam-4522	453	4	s.	s.	PROPN
ejpam-4522	453	5	z.	z.	PROPN
ejpam-4522	453	6	song	song	PROPN
ejpam-4522	453	7	,	,	PUNCT
ejpam-4522	453	8	k.	k.	PROPN
ejpam-4522	453	9	j.	j.	PROPN
ejpam-4522	453	10	lee	lee	PROPN
ejpam-4522	453	11	,	,	PUNCT
ejpam-4522	453	12	and	and	CCONJ
ejpam-4522	453	13	y.	y.	PROPN
ejpam-4522	453	14	b.	b.	PROPN
ejpam-4522	453	15	jun	jun	PROPN
ejpam-4522	453	16	.	.	PROPN
ejpam-4522	453	17	intersectional	intersectional	ADJ
ejpam-4522	453	18	soft	soft	ADJ
ejpam-4522	453	19	sets	set	NOUN
ejpam-4522	453	20	applied	apply	VERB
ejpam-4522	453	21	to	to	ADP
ejpam-4522	453	22	subalgebras	subalgebras	PROPN
ejpam-4522	453	23	/	/	SYM
ejpam-4522	453	24	ideals	ideal	NOUN
ejpam-4522	453	25	in	in	ADP
ejpam-4522	453	26	bck	bck	PROPN
ejpam-4522	453	27	/	/	SYM
ejpam-4522	453	28	bci	bci	NOUN
ejpam-4522	453	29	-	-	PUNCT
ejpam-4522	453	30	algebras	algebra	NOUN
ejpam-4522	453	31	.	.	PUNCT
ejpam-4522	454	1	adv	adv	PROPN
ejpam-4522	454	2	.	.	PUNCT
ejpam-4522	454	3	stud	stud	PROPN
ejpam-4522	454	4	.	.	PUNCT
ejpam-4522	455	1	contemp	contemp	NOUN
ejpam-4522	455	2	.	.	PUNCT
ejpam-4522	456	1	math	math	NOUN
ejpam-4522	456	2	.	.	PUNCT
ejpam-4522	457	1	(	(	PUNCT
ejpam-4522	457	2	kyungshang	kyungshang	PROPN
ejpam-4522	457	3	)	)	PUNCT
ejpam-4522	457	4	,	,	PUNCT
ejpam-4522	457	5	23(3):509–524	23(3):509–524	PROPN
ejpam-4522	457	6	,	,	PUNCT
ejpam-4522	457	7	2013	2013	NUM
ejpam-4522	457	8	.	.	PUNCT
ejpam-4522	458	1	[	[	X
ejpam-4522	458	2	24	24	NUM
ejpam-4522	458	3	]	]	PUNCT
ejpam-4522	458	4	l.	l.	PROPN
ejpam-4522	458	5	a.	a.	PROPN
ejpam-4522	458	6	zadeh	zadeh	PROPN
ejpam-4522	458	7	.	.	PUNCT
ejpam-4522	459	1	from	from	ADP
ejpam-4522	459	2	circuit	circuit	NOUN
ejpam-4522	459	3	theory	theory	NOUN
ejpam-4522	459	4	to	to	ADP
ejpam-4522	459	5	system	system	NOUN
ejpam-4522	459	6	theory	theory	NOUN
ejpam-4522	459	7	.	.	PUNCT
ejpam-4522	460	1	proc	proc	PROPN
ejpam-4522	460	2	.	.	PUNCT
ejpam-4522	461	1	inst	inst	PROPN
ejpam-4522	461	2	.	.	PUNCT
ejpam-4522	461	3	radio	radio	PROPN
ejpam-4522	461	4	eng	eng	PROPN
ejpam-4522	461	5	.	.	PROPN
ejpam-4522	461	6	,	,	PUNCT
ejpam-4522	461	7	50:856	50:856	NUM
ejpam-4522	461	8	–	–	PUNCT
ejpam-4522	461	9	865	865	NUM
ejpam-4522	461	10	,	,	PUNCT
ejpam-4522	461	11	1962	1962	NUM
ejpam-4522	461	12	.	.	PUNCT
ejpam-4522	462	1	[	[	X
ejpam-4522	462	2	25	25	NUM
ejpam-4522	462	3	]	]	PUNCT
ejpam-4522	462	4	l.	l.	PROPN
ejpam-4522	462	5	a.	a.	PROPN
ejpam-4522	462	6	zadeh	zadeh	PROPN
ejpam-4522	462	7	.	.	PUNCT
ejpam-4522	463	1	toward	toward	ADP
ejpam-4522	463	2	a	a	DET
ejpam-4522	463	3	generalized	generalized	ADJ
ejpam-4522	463	4	theory	theory	NOUN
ejpam-4522	463	5	of	of	ADP
ejpam-4522	463	6	uncertainty	uncertainty	NOUN
ejpam-4522	463	7	(	(	PUNCT
ejpam-4522	463	8	gtu	gtu	NOUN
ejpam-4522	463	9	)	)	PUNCT
ejpam-4522	463	10	an	an	DET
ejpam-4522	463	11	outline	outline	NOUN
ejpam-4522	463	12	.	.	PUNCT
ejpam-4522	464	1	inform	inform	NOUN
ejpam-4522	464	2	.	.	PUNCT
ejpam-4522	465	1	sci	sci	PROPN
ejpam-4522	465	2	.	.	PROPN
ejpam-4522	465	3	,	,	PUNCT
ejpam-4522	465	4	172:1–40	172:1–40	NUM
ejpam-4522	465	5	,	,	PUNCT
ejpam-4522	465	6	2005	2005	NUM
ejpam-4522	465	7	.	.	PUNCT