id	sid	tid	token	lemma	pos
ejpam-6273	1	1	european	european	PROPN
ejpam-6273	1	2	journal	journal	PROPN
ejpam-6273	1	3	of	of	ADP
ejpam-6273	1	4	pure	pure	ADJ
ejpam-6273	1	5	and	and	CCONJ
ejpam-6273	1	6	applied	applied	ADJ
ejpam-6273	1	7	mathematics	mathematic	NOUN
ejpam-6273	1	8	2025	2025	NUM
ejpam-6273	1	9	,	,	PUNCT
ejpam-6273	1	10	vol	vol	NOUN
ejpam-6273	1	11	.	.	PROPN
ejpam-6273	1	12	18	18	NUM
ejpam-6273	1	13	,	,	PUNCT
ejpam-6273	1	14	issue	issue	NOUN
ejpam-6273	1	15	3	3	NUM
ejpam-6273	1	16	,	,	PUNCT
ejpam-6273	1	17	article	article	NOUN
ejpam-6273	1	18	number	number	NOUN
ejpam-6273	1	19	6273	6273	NUM
ejpam-6273	1	20	issn	issn	PROPN
ejpam-6273	1	21	1307	1307	NUM
ejpam-6273	1	22	-	-	SYM
ejpam-6273	1	23	5543	5543	NUM
ejpam-6273	1	24	–	–	PUNCT
ejpam-6273	1	25	ejpam.com	ejpam.com	X
ejpam-6273	1	26	published	publish	VERB
ejpam-6273	1	27	by	by	ADP
ejpam-6273	1	28	new	new	PROPN
ejpam-6273	1	29	york	york	PROPN
ejpam-6273	1	30	business	business	PROPN
ejpam-6273	1	31	global	global	ADJ
ejpam-6273	1	32	hybrid	hybrid	ADJ
ejpam-6273	1	33	ideals	ideal	NOUN
ejpam-6273	1	34	of	of	ADP
ejpam-6273	1	35	a	a	DET
ejpam-6273	1	36	near	near	ADJ
ejpam-6273	1	37	algebra	algebra	PROPN
ejpam-6273	1	38	p.	p.	PROPN
ejpam-6273	1	39	narasimha	narasimha	PROPN
ejpam-6273	1	40	swamy1	swamy1	PROPN
ejpam-6273	1	41	,	,	PUNCT
ejpam-6273	1	42	bhurgula	bhurgula	VERB
ejpam-6273	1	43	harika2	harika2	NOUN
ejpam-6273	1	44	,	,	PUNCT
ejpam-6273	1	45	ravikumar	ravikumar	PROPN
ejpam-6273	1	46	bandaru3	bandaru3	ADJ
ejpam-6273	1	47	,	,	PUNCT
ejpam-6273	1	48	aiyared	aiyare	VERB
ejpam-6273	1	49	iampan4,∗	iampan4,∗	ADJ
ejpam-6273	1	50	1	1	NUM
ejpam-6273	1	51	department	department	NOUN
ejpam-6273	1	52	of	of	ADP
ejpam-6273	1	53	mathematics	mathematic	NOUN
ejpam-6273	1	54	,	,	PUNCT
ejpam-6273	1	55	gitam	gitam	NOUN
ejpam-6273	1	56	deemed	deem	VERB
ejpam-6273	1	57	to	to	PART
ejpam-6273	1	58	be	be	AUX
ejpam-6273	1	59	university	university	NOUN
ejpam-6273	1	60	,	,	PUNCT
ejpam-6273	1	61	hyderabad	hyderabad	PROPN
ejpam-6273	1	62	,	,	PUNCT
ejpam-6273	1	63	telangana-502329	telangana-502329	ADJ
ejpam-6273	1	64	,	,	PUNCT
ejpam-6273	1	65	india	india	PROPN
ejpam-6273	1	66	2	2	NUM
ejpam-6273	1	67	malla	malla	PROPN
ejpam-6273	1	68	reddy	reddy	PROPN
ejpam-6273	1	69	college	college	PROPN
ejpam-6273	1	70	of	of	ADP
ejpam-6273	1	71	engineering	engineering	NOUN
ejpam-6273	1	72	and	and	CCONJ
ejpam-6273	1	73	technology	technology	NOUN
ejpam-6273	1	74	,	,	PUNCT
ejpam-6273	1	75	humanities	humanity	NOUN
ejpam-6273	1	76	and	and	CCONJ
ejpam-6273	1	77	sciences	sciences	PROPN
ejpam-6273	1	78	,	,	PUNCT
ejpam-6273	1	79	hyderabad	hyderabad	PROPN
ejpam-6273	1	80	,	,	PUNCT
ejpam-6273	1	81	telangana-500100	telangana-500100	NOUN
ejpam-6273	1	82	,	,	PUNCT
ejpam-6273	1	83	india	india	PROPN
ejpam-6273	1	84	3	3	NUM
ejpam-6273	1	85	department	department	NOUN
ejpam-6273	1	86	of	of	ADP
ejpam-6273	1	87	mathematics	mathematic	NOUN
ejpam-6273	1	88	,	,	PUNCT
ejpam-6273	1	89	school	school	NOUN
ejpam-6273	1	90	of	of	ADP
ejpam-6273	1	91	advanced	advanced	ADJ
ejpam-6273	1	92	sciences	science	NOUN
ejpam-6273	1	93	,	,	PUNCT
ejpam-6273	1	94	vit	vit	PROPN
ejpam-6273	1	95	-	-	PUNCT
ejpam-6273	1	96	ap	ap	PROPN
ejpam-6273	1	97	university	university	PROPN
ejpam-6273	1	98	,	,	PUNCT
ejpam-6273	1	99	amaravati-522237	amaravati-522237	PROPN
ejpam-6273	1	100	,	,	PUNCT
ejpam-6273	1	101	andhra	andhra	PROPN
ejpam-6273	1	102	pradesh	pradesh	PROPN
ejpam-6273	1	103	,	,	PUNCT
ejpam-6273	1	104	india	india	PROPN
ejpam-6273	1	105	4	4	NUM
ejpam-6273	1	106	department	department	NOUN
ejpam-6273	1	107	of	of	ADP
ejpam-6273	1	108	mathematics	mathematic	NOUN
ejpam-6273	1	109	,	,	PUNCT
ejpam-6273	1	110	school	school	NOUN
ejpam-6273	1	111	of	of	ADP
ejpam-6273	1	112	science	science	NOUN
ejpam-6273	1	113	,	,	PUNCT
ejpam-6273	1	114	university	university	NOUN
ejpam-6273	1	115	of	of	ADP
ejpam-6273	1	116	phayao	phayao	NOUN
ejpam-6273	1	117	,	,	PUNCT
ejpam-6273	1	118	mae	mae	PROPN
ejpam-6273	1	119	ka	ka	PROPN
ejpam-6273	1	120	,	,	PUNCT
ejpam-6273	1	121	mueang	mueang	PROPN
ejpam-6273	1	122	,	,	PUNCT
ejpam-6273	1	123	phayao	phayao	NOUN
ejpam-6273	1	124	56000	56000	NUM
ejpam-6273	1	125	,	,	PUNCT
ejpam-6273	1	126	thailand	thailand	PROPN
ejpam-6273	1	127	abstract	abstract	NOUN
ejpam-6273	1	128	.	.	PUNCT
ejpam-6273	2	1	this	this	DET
ejpam-6273	2	2	study	study	NOUN
ejpam-6273	2	3	aims	aim	VERB
ejpam-6273	2	4	to	to	PART
ejpam-6273	2	5	explore	explore	VERB
ejpam-6273	2	6	hybrid	hybrid	ADJ
ejpam-6273	2	7	ideals	ideal	NOUN
ejpam-6273	2	8	in	in	ADP
ejpam-6273	2	9	a	a	DET
ejpam-6273	2	10	near	near	ADJ
ejpam-6273	2	11	algebra	algebra	NOUN
ejpam-6273	2	12	.	.	PUNCT
ejpam-6273	3	1	it	it	PRON
ejpam-6273	3	2	concludes	conclude	VERB
ejpam-6273	3	3	precise	precise	ADJ
ejpam-6273	3	4	definitions	definition	NOUN
ejpam-6273	3	5	and	and	CCONJ
ejpam-6273	3	6	theorems	theorem	NOUN
ejpam-6273	3	7	regarding	regard	VERB
ejpam-6273	3	8	the	the	DET
ejpam-6273	3	9	hybrid	hybrid	ADJ
ejpam-6273	3	10	ideal	ideal	NOUN
ejpam-6273	3	11	,	,	PUNCT
ejpam-6273	3	12	near	near	ADP
ejpam-6273	3	13	algebra	algebra	PROPN
ejpam-6273	3	14	homomorphism	homomorphism	NOUN
ejpam-6273	3	15	,	,	PUNCT
ejpam-6273	3	16	the	the	DET
ejpam-6273	3	17	cartesian	cartesian	ADJ
ejpam-6273	3	18	product	product	NOUN
ejpam-6273	3	19	of	of	ADP
ejpam-6273	3	20	hybrid	hybrid	ADJ
ejpam-6273	3	21	ideals	ideal	NOUN
ejpam-6273	3	22	,	,	PUNCT
ejpam-6273	3	23	and	and	CCONJ
ejpam-6273	3	24	the	the	DET
ejpam-6273	3	25	coset	coset	NOUN
ejpam-6273	3	26	of	of	ADP
ejpam-6273	3	27	the	the	DET
ejpam-6273	3	28	hybrid	hybrid	ADJ
ejpam-6273	3	29	ideal	ideal	NOUN
ejpam-6273	3	30	within	within	ADP
ejpam-6273	3	31	the	the	DET
ejpam-6273	3	32	context	context	NOUN
ejpam-6273	3	33	of	of	ADP
ejpam-6273	3	34	near	near	ADJ
ejpam-6273	3	35	algebras	algebra	NOUN
ejpam-6273	3	36	.	.	PUNCT
ejpam-6273	4	1	it	it	PRON
ejpam-6273	4	2	is	be	AUX
ejpam-6273	4	3	demonstrated	demonstrate	VERB
ejpam-6273	4	4	that	that	SCONJ
ejpam-6273	4	5	an	an	DET
ejpam-6273	4	6	onto	onto	ADP
ejpam-6273	4	7	homomorphic	homomorphic	ADJ
ejpam-6273	4	8	image	image	NOUN
ejpam-6273	4	9	,	,	PUNCT
ejpam-6273	4	10	and	and	CCONJ
ejpam-6273	4	11	the	the	DET
ejpam-6273	4	12	cartesian	cartesian	ADJ
ejpam-6273	4	13	product	product	NOUN
ejpam-6273	4	14	of	of	ADP
ejpam-6273	4	15	a	a	DET
ejpam-6273	4	16	hybrid	hybrid	ADJ
ejpam-6273	4	17	ideal	ideal	NOUN
ejpam-6273	4	18	of	of	ADP
ejpam-6273	4	19	a	a	DET
ejpam-6273	4	20	near	near	ADJ
ejpam-6273	4	21	algebra	algebra	NOUN
ejpam-6273	4	22	,	,	PUNCT
ejpam-6273	4	23	is	be	AUX
ejpam-6273	4	24	the	the	DET
ejpam-6273	4	25	hybrid	hybrid	ADJ
ejpam-6273	4	26	ideal	ideal	NOUN
ejpam-6273	4	27	of	of	ADP
ejpam-6273	4	28	a	a	DET
ejpam-6273	4	29	near	near	ADJ
ejpam-6273	4	30	algebra	algebra	NOUN
ejpam-6273	4	31	.	.	PUNCT
ejpam-6273	5	1	2020	2020	NUM
ejpam-6273	5	2	mathematics	mathematic	NOUN
ejpam-6273	5	3	subject	subject	NOUN
ejpam-6273	5	4	classifications	classification	NOUN
ejpam-6273	5	5	:	:	PUNCT
ejpam-6273	5	6	16y30	16y30	NUM
ejpam-6273	5	7	,	,	PUNCT
ejpam-6273	5	8	03e72	03e72	NUM
ejpam-6273	5	9	,	,	PUNCT
ejpam-6273	5	10	08a72	08a72	NOUN
ejpam-6273	5	11	key	key	ADJ
ejpam-6273	5	12	words	word	NOUN
ejpam-6273	5	13	and	and	CCONJ
ejpam-6273	5	14	phrases	phrase	NOUN
ejpam-6273	5	15	:	:	PUNCT
ejpam-6273	5	16	hybrid	hybrid	ADJ
ejpam-6273	5	17	structure	structure	NOUN
ejpam-6273	5	18	,	,	PUNCT
ejpam-6273	5	19	near	near	ADP
ejpam-6273	5	20	algebra	algebra	NOUN
ejpam-6273	5	21	,	,	PUNCT
ejpam-6273	5	22	ideal	ideal	ADJ
ejpam-6273	5	23	,	,	PUNCT
ejpam-6273	5	24	hybrid	hybrid	ADJ
ejpam-6273	5	25	field	field	NOUN
ejpam-6273	5	26	1	1	NUM
ejpam-6273	5	27	.	.	PUNCT
ejpam-6273	6	1	introduction	introduction	NOUN
ejpam-6273	6	2	a	a	DET
ejpam-6273	6	3	near	near	ADJ
ejpam-6273	6	4	ring	ring	NOUN
ejpam-6273	6	5	is	be	AUX
ejpam-6273	6	6	an	an	DET
ejpam-6273	6	7	algebraic	algebraic	ADJ
ejpam-6273	6	8	system	system	NOUN
ejpam-6273	6	9	equipped	equip	VERB
ejpam-6273	6	10	with	with	ADP
ejpam-6273	6	11	two	two	NUM
ejpam-6273	6	12	binary	binary	ADJ
ejpam-6273	6	13	operations	operation	NOUN
ejpam-6273	6	14	that	that	PRON
ejpam-6273	6	15	satisfy	satisfy	VERB
ejpam-6273	6	16	all	all	DET
ejpam-6273	6	17	ring	ring	NOUN
ejpam-6273	6	18	axioms	axiom	NOUN
ejpam-6273	6	19	,	,	PUNCT
ejpam-6273	6	20	except	except	SCONJ
ejpam-6273	6	21	possibly	possibly	ADV
ejpam-6273	6	22	one	one	NUM
ejpam-6273	6	23	of	of	ADP
ejpam-6273	6	24	the	the	DET
ejpam-6273	6	25	distributive	distributive	ADJ
ejpam-6273	6	26	laws	law	NOUN
ejpam-6273	6	27	.	.	PUNCT
ejpam-6273	7	1	the	the	DET
ejpam-6273	7	2	concept	concept	NOUN
ejpam-6273	7	3	of	of	ADP
ejpam-6273	7	4	a	a	DET
ejpam-6273	7	5	near	near	ADJ
ejpam-6273	7	6	ring	ring	NOUN
ejpam-6273	7	7	was	be	AUX
ejpam-6273	7	8	first	first	ADV
ejpam-6273	7	9	presented	present	VERB
ejpam-6273	7	10	in	in	ADP
ejpam-6273	7	11	a	a	DET
ejpam-6273	7	12	monograph	monograph	NOUN
ejpam-6273	7	13	by	by	ADP
ejpam-6273	7	14	pilz	pilz	PROPN
ejpam-6273	7	15	[	[	X
ejpam-6273	7	16	1	1	NUM
ejpam-6273	7	17	]	]	PUNCT
ejpam-6273	7	18	.	.	PUNCT
ejpam-6273	8	1	a	a	DET
ejpam-6273	8	2	near	near	ADJ
ejpam-6273	8	3	algebra	algebra	NOUN
ejpam-6273	8	4	is	be	AUX
ejpam-6273	8	5	defined	define	VERB
ejpam-6273	8	6	as	as	ADP
ejpam-6273	8	7	a	a	DET
ejpam-6273	8	8	near	near	ADJ
ejpam-6273	8	9	ring	ring	NOUN
ejpam-6273	8	10	in	in	ADP
ejpam-6273	8	11	which	which	PRON
ejpam-6273	8	12	the	the	DET
ejpam-6273	8	13	right	right	ADJ
ejpam-6273	8	14	scalar	scalar	ADJ
ejpam-6273	8	15	domain	domain	NOUN
ejpam-6273	8	16	is	be	AUX
ejpam-6273	8	17	a	a	DET
ejpam-6273	8	18	field	field	NOUN
ejpam-6273	8	19	,	,	PUNCT
ejpam-6273	8	20	and	and	CCONJ
ejpam-6273	8	21	brown	brown	ADJ
ejpam-6273	9	1	[	[	X
ejpam-6273	9	2	2	2	NUM
ejpam-6273	9	3	]	]	PUNCT
ejpam-6273	9	4	studied	study	VERB
ejpam-6273	9	5	its	its	PRON
ejpam-6273	9	6	foundational	foundational	ADJ
ejpam-6273	9	7	properties	property	NOUN
ejpam-6273	9	8	.	.	PUNCT
ejpam-6273	10	1	according	accord	VERB
ejpam-6273	10	2	to	to	ADP
ejpam-6273	10	3	jordan	jordan	PROPN
ejpam-6273	10	4	,	,	PUNCT
ejpam-6273	10	5	within	within	ADP
ejpam-6273	10	6	the	the	DET
ejpam-6273	10	7	formalism	formalism	NOUN
ejpam-6273	10	8	of	of	ADP
ejpam-6273	10	9	quantum	quantum	ADJ
ejpam-6273	10	10	mechanics	mechanic	NOUN
ejpam-6273	10	11	,	,	PUNCT
ejpam-6273	10	12	the	the	DET
ejpam-6273	10	13	set	set	NOUN
ejpam-6273	10	14	of	of	ADP
ejpam-6273	10	15	operators	operator	NOUN
ejpam-6273	10	16	forms	form	VERB
ejpam-6273	10	17	only	only	ADV
ejpam-6273	10	18	a	a	DET
ejpam-6273	10	19	near	near	ADJ
ejpam-6273	10	20	algebra	algebra	NOUN
ejpam-6273	10	21	,	,	PUNCT
ejpam-6273	10	22	making	make	VERB
ejpam-6273	10	23	the	the	DET
ejpam-6273	10	24	study	study	NOUN
ejpam-6273	10	25	of	of	ADP
ejpam-6273	10	26	such	such	ADJ
ejpam-6273	10	27	structures	structure	NOUN
ejpam-6273	10	28	relevant	relevant	ADJ
ejpam-6273	10	29	not	not	PART
ejpam-6273	10	30	only	only	ADV
ejpam-6273	10	31	for	for	ADP
ejpam-6273	10	32	purely	purely	ADV
ejpam-6273	10	33	axiomatic	axiomatic	ADJ
ejpam-6273	10	34	reasons	reason	NOUN
ejpam-6273	10	35	but	but	CCONJ
ejpam-6273	10	36	also	also	ADV
ejpam-6273	10	37	due	due	ADP
ejpam-6273	10	38	to	to	ADP
ejpam-6273	10	39	their	their	PRON
ejpam-6273	10	40	physical	physical	ADJ
ejpam-6273	10	41	applications	application	NOUN
ejpam-6273	10	42	.	.	PUNCT
ejpam-6273	11	1	in	in	ADP
ejpam-6273	11	2	recent	recent	ADJ
ejpam-6273	11	3	years	year	NOUN
ejpam-6273	11	4	,	,	PUNCT
ejpam-6273	11	5	various	various	ADJ
ejpam-6273	11	6	generalizations	generalization	NOUN
ejpam-6273	11	7	of	of	ADP
ejpam-6273	11	8	classical	classical	ADJ
ejpam-6273	11	9	algebraic	algebraic	ADJ
ejpam-6273	11	10	structures	structure	NOUN
ejpam-6273	11	11	have	have	AUX
ejpam-6273	11	12	emerged	emerge	VERB
ejpam-6273	11	13	,	,	PUNCT
ejpam-6273	11	14	especially	especially	ADV
ejpam-6273	11	15	in	in	ADP
ejpam-6273	11	16	the	the	DET
ejpam-6273	11	17	context	context	NOUN
ejpam-6273	11	18	of	of	ADP
ejpam-6273	11	19	non	non	ADJ
ejpam-6273	11	20	-	-	ADJ
ejpam-6273	11	21	associative	associative	ADJ
ejpam-6273	11	22	algebras	algebra	NOUN
ejpam-6273	11	23	.	.	PUNCT
ejpam-6273	12	1	these	these	PRON
ejpam-6273	12	2	include	include	VERB
ejpam-6273	12	3	alternative	alternative	ADJ
ejpam-6273	12	4	rings	ring	NOUN
ejpam-6273	12	5	,	,	PUNCT
ejpam-6273	12	6	jordan	jordan	PROPN
ejpam-6273	12	7	algebras	algebras	PROPN
ejpam-6273	12	8	and	and	CCONJ
ejpam-6273	12	9	γ	γ	PROPN
ejpam-6273	12	10	-	-	PUNCT
ejpam-6273	12	11	rings	ring	NOUN
ejpam-6273	12	12	serve	serve	VERB
ejpam-6273	12	13	as	as	ADP
ejpam-6273	12	14	fertile	fertile	ADJ
ejpam-6273	12	15	ground	ground	NOUN
ejpam-6273	12	16	for	for	ADP
ejpam-6273	12	17	exploring	explore	VERB
ejpam-6273	12	18	additive	additive	ADJ
ejpam-6273	12	19	and	and	CCONJ
ejpam-6273	12	20	multiplicative	multiplicative	ADJ
ejpam-6273	12	21	mappings	mapping	NOUN
ejpam-6273	12	22	.	.	PUNCT
ejpam-6273	13	1	the	the	DET
ejpam-6273	13	2	behavior	behavior	NOUN
ejpam-6273	13	3	of	of	ADP
ejpam-6273	13	4	such	such	ADJ
ejpam-6273	13	5	mappings	mapping	NOUN
ejpam-6273	13	6	under	under	ADP
ejpam-6273	13	7	weakened	weakened	ADJ
ejpam-6273	13	8	structural	structural	ADJ
ejpam-6273	13	9	assumptions	assumption	NOUN
ejpam-6273	13	10	has	have	AUX
ejpam-6273	13	11	∗corresponding	∗corresponde	VERB
ejpam-6273	13	12	author	author	NOUN
ejpam-6273	13	13	.	.	PUNCT
ejpam-6273	14	1	doi	doi	NOUN
ejpam-6273	14	2	:	:	PUNCT
ejpam-6273	14	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6273	https://doi.org/10.29020/nybg.ejpam.v18i3.6273	ADP
ejpam-6273	14	4	email	email	NOUN
ejpam-6273	14	5	addresses	address	NOUN
ejpam-6273	14	6	:	:	PUNCT
ejpam-6273	14	7	swamy.pasham@gmail.com	swamy.pasham@gmail.com	NUM
ejpam-6273	14	8	(	(	PUNCT
ejpam-6273	14	9	p.	p.	NOUN
ejpam-6273	14	10	narasimha	narasimha	PROPN
ejpam-6273	14	11	swamy	swamy	PROPN
ejpam-6273	14	12	)	)	PUNCT
ejpam-6273	14	13	,	,	PUNCT
ejpam-6273	14	14	harika.burgula84@gmail.com	harika.burgula84@gmail.com	X
ejpam-6273	14	15	(	(	PUNCT
ejpam-6273	14	16	b.	b.	PROPN
ejpam-6273	14	17	harika	harika	PROPN
ejpam-6273	14	18	)	)	PUNCT
ejpam-6273	14	19	,	,	PUNCT
ejpam-6273	14	20	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-6273	14	21	(	(	PUNCT
ejpam-6273	14	22	r.	r.	PROPN
ejpam-6273	14	23	bandaru	bandaru	PROPN
ejpam-6273	14	24	)	)	PUNCT
ejpam-6273	14	25	,	,	PUNCT
ejpam-6273	14	26	aiyared.ia@up.ac.th	aiyared.ia@up.ac.th	NOUN
ejpam-6273	14	27	(	(	PUNCT
ejpam-6273	14	28	a.	a.	NOUN
ejpam-6273	14	29	iampan	iampan	PROPN
ejpam-6273	14	30	)	)	PUNCT
ejpam-6273	14	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6273	15	1	1	1	NUM
ejpam-6273	15	2	copyright	copyright	NOUN
ejpam-6273	15	3	:	:	PUNCT
ejpam-6273	15	4	©	©	PROPN
ejpam-6273	15	5	2025	2025	NUM
ejpam-6273	15	6	the	the	DET
ejpam-6273	15	7	author(s	author(s	NOUN
ejpam-6273	15	8	)	)	PUNCT
ejpam-6273	15	9	.	.	PUNCT
ejpam-6273	16	1	(	(	PUNCT
ejpam-6273	16	2	cc	cc	NOUN
ejpam-6273	16	3	by	by	ADP
ejpam-6273	16	4	-	-	PUNCT
ejpam-6273	16	5	nc	nc	PROPN
ejpam-6273	16	6	4.0	4.0	NUM
ejpam-6273	16	7	)	)	PUNCT
ejpam-6273	16	8	p.	p.	NOUN
ejpam-6273	16	9	n.	n.	PROPN
ejpam-6273	16	10	swamy	swamy	PROPN
ejpam-6273	16	11	et	et	PROPN
ejpam-6273	16	12	al	al	PROPN
ejpam-6273	16	13	.	.	PUNCT
ejpam-6273	16	14	/	/	SYM
ejpam-6273	16	15	eur	eur	PROPN
ejpam-6273	16	16	.	.	PUNCT
ejpam-6273	17	1	j.	j.	PROPN
ejpam-6273	17	2	pure	pure	PROPN
ejpam-6273	17	3	appl	appl	PROPN
ejpam-6273	17	4	.	.	PROPN
ejpam-6273	17	5	math	math	PROPN
ejpam-6273	17	6	,	,	PUNCT
ejpam-6273	17	7	18	18	NUM
ejpam-6273	17	8	(	(	PUNCT
ejpam-6273	17	9	3	3	NUM
ejpam-6273	17	10	)	)	PUNCT
ejpam-6273	17	11	(	(	PUNCT
ejpam-6273	17	12	2025	2025	NUM
ejpam-6273	17	13	)	)	PUNCT
ejpam-6273	17	14	,	,	PUNCT
ejpam-6273	17	15	6273	6273	NUM
ejpam-6273	17	16	2	2	NUM
ejpam-6273	17	17	of	of	ADP
ejpam-6273	17	18	16	16	NUM
ejpam-6273	17	19	been	be	AUX
ejpam-6273	17	20	the	the	DET
ejpam-6273	17	21	subject	subject	NOUN
ejpam-6273	17	22	of	of	ADP
ejpam-6273	17	23	extensive	extensive	ADJ
ejpam-6273	17	24	research	research	NOUN
ejpam-6273	17	25	.	.	PUNCT
ejpam-6273	18	1	notable	notable	ADJ
ejpam-6273	18	2	contributions	contribution	NOUN
ejpam-6273	18	3	include	include	VERB
ejpam-6273	18	4	the	the	DET
ejpam-6273	18	5	investigation	investigation	NOUN
ejpam-6273	18	6	of	of	ADP
ejpam-6273	18	7	n	n	CCONJ
ejpam-6273	18	8	-	-	PUNCT
ejpam-6273	18	9	multiplicative	multiplicative	ADJ
ejpam-6273	18	10	mappings	mapping	NOUN
ejpam-6273	18	11	on	on	ADP
ejpam-6273	18	12	γ	γ	NOUN
ejpam-6273	18	13	-	-	PUNCT
ejpam-6273	18	14	rings	ring	NOUN
ejpam-6273	18	15	[	[	X
ejpam-6273	18	16	3	3	NUM
ejpam-6273	18	17	]	]	PUNCT
ejpam-6273	18	18	,	,	PUNCT
ejpam-6273	18	19	the	the	DET
ejpam-6273	18	20	additivity	additivity	NOUN
ejpam-6273	18	21	of	of	ADP
ejpam-6273	18	22	multiplicative	multiplicative	ADJ
ejpam-6273	18	23	maps	map	NOUN
ejpam-6273	18	24	on	on	ADP
ejpam-6273	18	25	alternative	alternative	ADJ
ejpam-6273	18	26	rings	ring	NOUN
ejpam-6273	18	27	[	[	X
ejpam-6273	18	28	4	4	NUM
ejpam-6273	18	29	]	]	PUNCT
ejpam-6273	18	30	,	,	PUNCT
ejpam-6273	18	31	and	and	CCONJ
ejpam-6273	18	32	additive	additive	ADJ
ejpam-6273	18	33	maps	map	NOUN
ejpam-6273	18	34	preserving	preserve	VERB
ejpam-6273	18	35	generalized	generalize	VERB
ejpam-6273	18	36	inverses	inverse	NOUN
ejpam-6273	18	37	on	on	ADP
ejpam-6273	18	38	alternative	alternative	ADJ
ejpam-6273	18	39	division	division	NOUN
ejpam-6273	18	40	algebras	algebra	VERB
ejpam-6273	19	1	[	[	X
ejpam-6273	19	2	5	5	NUM
ejpam-6273	19	3	]	]	PUNCT
ejpam-6273	19	4	.	.	PUNCT
ejpam-6273	20	1	additionally	additionally	ADV
ejpam-6273	20	2	,	,	PUNCT
ejpam-6273	20	3	breš	breš	PROPN
ejpam-6273	20	4	ar	ar	PROPN
ejpam-6273	20	5	’s	’s	PART
ejpam-6273	20	6	monograph	monograph	NOUN
ejpam-6273	20	7	on	on	ADP
ejpam-6273	20	8	zero	zero	NUM
ejpam-6273	20	9	product	product	NOUN
ejpam-6273	20	10	determined	determine	VERB
ejpam-6273	20	11	algebras	algebra	NOUN
ejpam-6273	20	12	[	[	X
ejpam-6273	20	13	6	6	NUM
ejpam-6273	20	14	]	]	PUNCT
ejpam-6273	20	15	offers	offer	VERB
ejpam-6273	20	16	a	a	DET
ejpam-6273	20	17	comprehensive	comprehensive	ADJ
ejpam-6273	20	18	treatment	treatment	NOUN
ejpam-6273	20	19	of	of	ADP
ejpam-6273	20	20	how	how	SCONJ
ejpam-6273	20	21	structural	structural	ADJ
ejpam-6273	20	22	constraints	constraint	NOUN
ejpam-6273	20	23	influence	influence	VERB
ejpam-6273	20	24	the	the	DET
ejpam-6273	20	25	nature	nature	NOUN
ejpam-6273	20	26	of	of	ADP
ejpam-6273	20	27	linear	linear	PROPN
ejpam-6273	20	28	preservers	preserver	NOUN
ejpam-6273	20	29	and	and	CCONJ
ejpam-6273	20	30	related	related	ADJ
ejpam-6273	20	31	mappings	mapping	NOUN
ejpam-6273	20	32	.	.	PUNCT
ejpam-6273	21	1	in	in	ADP
ejpam-6273	21	2	particular	particular	ADJ
ejpam-6273	21	3	,	,	PUNCT
ejpam-6273	21	4	srinivas	srinivas	PROPN
ejpam-6273	21	5	and	and	CCONJ
ejpam-6273	21	6	narasimha	narasimha	PROPN
ejpam-6273	21	7	swamy	swamy	PROPN
ejpam-6273	22	1	[	[	X
ejpam-6273	22	2	7	7	NUM
ejpam-6273	22	3	]	]	PUNCT
ejpam-6273	22	4	introduced	introduce	VERB
ejpam-6273	22	5	fuzzy	fuzzy	ADJ
ejpam-6273	22	6	near	near	ADP
ejpam-6273	22	7	algebras	algebra	NOUN
ejpam-6273	22	8	over	over	ADP
ejpam-6273	22	9	fuzzy	fuzzy	ADJ
ejpam-6273	22	10	fields	field	NOUN
ejpam-6273	22	11	,	,	PUNCT
ejpam-6273	22	12	defining	define	VERB
ejpam-6273	22	13	fuzzy	fuzzy	ADJ
ejpam-6273	22	14	ideals	ideal	NOUN
ejpam-6273	22	15	and	and	CCONJ
ejpam-6273	22	16	examining	examine	VERB
ejpam-6273	22	17	their	their	PRON
ejpam-6273	22	18	algebraic	algebraic	ADJ
ejpam-6273	22	19	behavior	behavior	NOUN
ejpam-6273	22	20	under	under	ADP
ejpam-6273	22	21	homomorphisms	homomorphism	NOUN
ejpam-6273	22	22	and	and	CCONJ
ejpam-6273	22	23	direct	direct	ADJ
ejpam-6273	22	24	sums	sum	NOUN
ejpam-6273	22	25	.	.	PUNCT
ejpam-6273	23	1	parallel	parallel	ADJ
ejpam-6273	23	2	to	to	ADP
ejpam-6273	23	3	these	these	DET
ejpam-6273	23	4	algebraic	algebraic	ADJ
ejpam-6273	23	5	developments	development	NOUN
ejpam-6273	23	6	,	,	PUNCT
ejpam-6273	23	7	fuzzy	fuzzy	ADJ
ejpam-6273	23	8	set	set	NOUN
ejpam-6273	23	9	theory	theory	NOUN
ejpam-6273	23	10	—	—	PUNCT
ejpam-6273	23	11	pioneered	pioneer	VERB
ejpam-6273	23	12	by	by	ADP
ejpam-6273	23	13	zadeh	zadeh	PROPN
ejpam-6273	24	1	[	[	X
ejpam-6273	24	2	8]—has	8]—has	NUM
ejpam-6273	24	3	evolved	evolve	VERB
ejpam-6273	24	4	into	into	ADP
ejpam-6273	24	5	a	a	DET
ejpam-6273	24	6	robust	robust	ADJ
ejpam-6273	24	7	framework	framework	NOUN
ejpam-6273	24	8	for	for	ADP
ejpam-6273	24	9	dealing	deal	VERB
ejpam-6273	24	10	with	with	ADP
ejpam-6273	24	11	uncertainty	uncertainty	NOUN
ejpam-6273	24	12	in	in	ADP
ejpam-6273	24	13	mathematical	mathematical	ADJ
ejpam-6273	24	14	modeling	modeling	NOUN
ejpam-6273	24	15	.	.	PUNCT
ejpam-6273	25	1	this	this	DET
ejpam-6273	25	2	theory	theory	NOUN
ejpam-6273	25	3	has	have	AUX
ejpam-6273	25	4	found	find	VERB
ejpam-6273	25	5	widespread	widespread	ADJ
ejpam-6273	25	6	applications	application	NOUN
ejpam-6273	25	7	in	in	ADP
ejpam-6273	25	8	engineering	engineering	NOUN
ejpam-6273	25	9	,	,	PUNCT
ejpam-6273	25	10	robotics	robotic	NOUN
ejpam-6273	25	11	,	,	PUNCT
ejpam-6273	25	12	computer	computer	NOUN
ejpam-6273	25	13	science	science	NOUN
ejpam-6273	25	14	,	,	PUNCT
ejpam-6273	25	15	and	and	CCONJ
ejpam-6273	25	16	decision	decision	NOUN
ejpam-6273	25	17	theory	theory	NOUN
ejpam-6273	25	18	.	.	PUNCT
ejpam-6273	26	1	later	late	ADJ
ejpam-6273	26	2	generalizations	generalization	NOUN
ejpam-6273	26	3	,	,	PUNCT
ejpam-6273	26	4	such	such	ADJ
ejpam-6273	26	5	as	as	ADP
ejpam-6273	26	6	hesitant	hesitant	ADJ
ejpam-6273	26	7	fuzzy	fuzzy	ADJ
ejpam-6273	26	8	sets	set	NOUN
ejpam-6273	26	9	[	[	X
ejpam-6273	26	10	9	9	NUM
ejpam-6273	26	11	]	]	PUNCT
ejpam-6273	26	12	,	,	PUNCT
ejpam-6273	26	13	vague	vague	ADJ
ejpam-6273	26	14	sets	set	NOUN
ejpam-6273	26	15	,	,	PUNCT
ejpam-6273	26	16	interval	interval	NOUN
ejpam-6273	26	17	-	-	PUNCT
ejpam-6273	26	18	valued	value	VERB
ejpam-6273	26	19	sets	set	NOUN
ejpam-6273	26	20	,	,	PUNCT
ejpam-6273	26	21	and	and	CCONJ
ejpam-6273	26	22	rough	rough	ADJ
ejpam-6273	26	23	sets	set	NOUN
ejpam-6273	26	24	,	,	PUNCT
ejpam-6273	26	25	have	have	AUX
ejpam-6273	26	26	extended	extend	VERB
ejpam-6273	26	27	this	this	DET
ejpam-6273	26	28	capacity	capacity	NOUN
ejpam-6273	26	29	.	.	PUNCT
ejpam-6273	27	1	to	to	PART
ejpam-6273	27	2	address	address	VERB
ejpam-6273	27	3	the	the	DET
ejpam-6273	27	4	limitations	limitation	NOUN
ejpam-6273	27	5	found	find	VERB
ejpam-6273	27	6	in	in	ADP
ejpam-6273	27	7	these	these	DET
ejpam-6273	27	8	frameworks	framework	NOUN
ejpam-6273	27	9	,	,	PUNCT
ejpam-6273	27	10	molodtsov	molodtsov	NOUN
ejpam-6273	27	11	[	[	X
ejpam-6273	27	12	10	10	NUM
ejpam-6273	27	13	]	]	PUNCT
ejpam-6273	27	14	introduced	introduce	VERB
ejpam-6273	27	15	soft	soft	ADJ
ejpam-6273	27	16	set	set	NOUN
ejpam-6273	27	17	theory	theory	NOUN
ejpam-6273	27	18	,	,	PUNCT
ejpam-6273	27	19	a	a	DET
ejpam-6273	27	20	flexible	flexible	ADJ
ejpam-6273	27	21	tool	tool	NOUN
ejpam-6273	27	22	for	for	ADP
ejpam-6273	27	23	modeling	model	VERB
ejpam-6273	27	24	uncertainty	uncertainty	NOUN
ejpam-6273	27	25	,	,	PUNCT
ejpam-6273	27	26	which	which	PRON
ejpam-6273	27	27	has	have	AUX
ejpam-6273	27	28	since	since	ADV
ejpam-6273	27	29	been	be	AUX
ejpam-6273	27	30	applied	apply	VERB
ejpam-6273	27	31	in	in	ADP
ejpam-6273	27	32	diverse	diverse	ADJ
ejpam-6273	27	33	fields	field	NOUN
ejpam-6273	27	34	,	,	PUNCT
ejpam-6273	27	35	including	include	VERB
ejpam-6273	27	36	game	game	NOUN
ejpam-6273	27	37	theory	theory	NOUN
ejpam-6273	27	38	,	,	PUNCT
ejpam-6273	27	39	integration	integration	NOUN
ejpam-6273	27	40	theory	theory	NOUN
ejpam-6273	27	41	,	,	PUNCT
ejpam-6273	27	42	and	and	CCONJ
ejpam-6273	27	43	operations	operation	NOUN
ejpam-6273	27	44	research	research	NOUN
ejpam-6273	27	45	.	.	PUNCT
ejpam-6273	28	1	to	to	PART
ejpam-6273	28	2	unify	unify	VERB
ejpam-6273	28	3	the	the	DET
ejpam-6273	28	4	strengths	strength	NOUN
ejpam-6273	28	5	of	of	ADP
ejpam-6273	28	6	fuzzy	fuzzy	ADJ
ejpam-6273	28	7	and	and	CCONJ
ejpam-6273	28	8	soft	soft	ADJ
ejpam-6273	28	9	set	set	NOUN
ejpam-6273	28	10	theories	theory	NOUN
ejpam-6273	28	11	,	,	PUNCT
ejpam-6273	28	12	jun	jun	PROPN
ejpam-6273	28	13	et	et	PROPN
ejpam-6273	28	14	al	al	PROPN
ejpam-6273	28	15	.	.	PUNCT
ejpam-6273	29	1	[	[	X
ejpam-6273	29	2	11	11	NUM
ejpam-6273	29	3	]	]	PUNCT
ejpam-6273	29	4	introduced	introduce	VERB
ejpam-6273	29	5	the	the	DET
ejpam-6273	29	6	notion	notion	NOUN
ejpam-6273	29	7	of	of	ADP
ejpam-6273	29	8	hybrid	hybrid	ADJ
ejpam-6273	29	9	structures	structure	NOUN
ejpam-6273	29	10	.	.	PUNCT
ejpam-6273	30	1	these	these	DET
ejpam-6273	30	2	frameworks	framework	NOUN
ejpam-6273	30	3	combine	combine	VERB
ejpam-6273	30	4	multiple	multiple	ADJ
ejpam-6273	30	5	uncertainty	uncertainty	NOUN
ejpam-6273	30	6	paradigms	paradigm	VERB
ejpam-6273	30	7	through	through	ADP
ejpam-6273	30	8	parameterization	parameterization	NOUN
ejpam-6273	30	9	over	over	ADP
ejpam-6273	30	10	a	a	DET
ejpam-6273	30	11	universe	universe	NOUN
ejpam-6273	30	12	set	set	NOUN
ejpam-6273	30	13	,	,	PUNCT
ejpam-6273	30	14	allowing	allow	VERB
ejpam-6273	30	15	for	for	ADP
ejpam-6273	30	16	more	more	ADV
ejpam-6273	30	17	nuanced	nuanced	ADJ
ejpam-6273	30	18	representations	representation	NOUN
ejpam-6273	30	19	.	.	PUNCT
ejpam-6273	31	1	based	base	VERB
ejpam-6273	31	2	on	on	ADP
ejpam-6273	31	3	these	these	DET
ejpam-6273	31	4	ideas	idea	NOUN
ejpam-6273	31	5	,	,	PUNCT
ejpam-6273	31	6	hybrid	hybrid	ADJ
ejpam-6273	31	7	ideals	ideal	NOUN
ejpam-6273	31	8	,	,	PUNCT
ejpam-6273	31	9	hybrid	hybrid	ADJ
ejpam-6273	31	10	fields	field	NOUN
ejpam-6273	31	11	,	,	PUNCT
ejpam-6273	31	12	and	and	CCONJ
ejpam-6273	31	13	hybrid	hybrid	ADJ
ejpam-6273	31	14	subalgebras	subalgebra	NOUN
ejpam-6273	31	15	have	have	AUX
ejpam-6273	31	16	been	be	AUX
ejpam-6273	31	17	defined	define	VERB
ejpam-6273	31	18	and	and	CCONJ
ejpam-6273	31	19	studied	study	VERB
ejpam-6273	31	20	in	in	ADP
ejpam-6273	31	21	[	[	X
ejpam-6273	31	22	12–14	12–14	NUM
ejpam-6273	31	23	]	]	PUNCT
ejpam-6273	31	24	.	.	PUNCT
ejpam-6273	32	1	building	build	VERB
ejpam-6273	32	2	on	on	ADP
ejpam-6273	32	3	this	this	DET
ejpam-6273	32	4	foundation	foundation	NOUN
ejpam-6273	32	5	,	,	PUNCT
ejpam-6273	32	6	bhurgula	bhurgula	VERB
ejpam-6273	32	7	et	et	PROPN
ejpam-6273	32	8	al	al	PROPN
ejpam-6273	32	9	.	.	PUNCT
ejpam-6273	33	1	[	[	X
ejpam-6273	33	2	15	15	NUM
ejpam-6273	33	3	]	]	PUNCT
ejpam-6273	33	4	introduced	introduce	VERB
ejpam-6273	33	5	the	the	DET
ejpam-6273	33	6	concept	concept	NOUN
ejpam-6273	33	7	of	of	ADP
ejpam-6273	33	8	hybrid	hybrid	NOUN
ejpam-6273	33	9	near	near	ADP
ejpam-6273	33	10	algebras	algebra	NOUN
ejpam-6273	33	11	,	,	PUNCT
ejpam-6273	33	12	establishing	establish	VERB
ejpam-6273	33	13	key	key	ADJ
ejpam-6273	33	14	structural	structural	ADJ
ejpam-6273	33	15	properties	property	NOUN
ejpam-6273	33	16	,	,	PUNCT
ejpam-6273	33	17	including	include	VERB
ejpam-6273	33	18	closure	closure	NOUN
ejpam-6273	33	19	under	under	ADP
ejpam-6273	33	20	homomorphisms	homomorphism	NOUN
ejpam-6273	33	21	and	and	CCONJ
ejpam-6273	33	22	cartesian	cartesian	ADJ
ejpam-6273	33	23	products	product	NOUN
ejpam-6273	33	24	.	.	PUNCT
ejpam-6273	34	1	motivated	motivate	VERB
ejpam-6273	34	2	by	by	ADP
ejpam-6273	34	3	these	these	DET
ejpam-6273	34	4	developments	development	NOUN
ejpam-6273	34	5	,	,	PUNCT
ejpam-6273	34	6	this	this	DET
ejpam-6273	34	7	work	work	NOUN
ejpam-6273	34	8	introduces	introduce	VERB
ejpam-6273	34	9	the	the	DET
ejpam-6273	34	10	concept	concept	NOUN
ejpam-6273	34	11	of	of	ADP
ejpam-6273	34	12	hybrid	hybrid	ADJ
ejpam-6273	34	13	ideals	ideal	NOUN
ejpam-6273	34	14	in	in	ADP
ejpam-6273	34	15	near	near	ADJ
ejpam-6273	34	16	algebras	algebra	NOUN
ejpam-6273	34	17	over	over	ADP
ejpam-6273	34	18	hybrid	hybrid	ADJ
ejpam-6273	34	19	fields	field	NOUN
ejpam-6273	34	20	.	.	PUNCT
ejpam-6273	35	1	hybrid	hybrid	ADJ
ejpam-6273	35	2	structures	structure	NOUN
ejpam-6273	35	3	are	be	AUX
ejpam-6273	35	4	then	then	ADV
ejpam-6273	35	5	employed	employ	VERB
ejpam-6273	35	6	to	to	PART
ejpam-6273	35	7	examine	examine	VERB
ejpam-6273	35	8	structural	structural	ADJ
ejpam-6273	35	9	aspects	aspect	NOUN
ejpam-6273	35	10	of	of	ADP
ejpam-6273	35	11	near	near	ADJ
ejpam-6273	35	12	algebras	algebra	NOUN
ejpam-6273	35	13	.	.	PUNCT
ejpam-6273	36	1	throughout	throughout	ADP
ejpam-6273	36	2	this	this	DET
ejpam-6273	36	3	paper	paper	NOUN
ejpam-6273	36	4	,	,	PUNCT
ejpam-6273	36	5	y	y	PROPN
ejpam-6273	36	6	denotes	denote	VERB
ejpam-6273	36	7	a	a	DET
ejpam-6273	36	8	(	(	PUNCT
ejpam-6273	36	9	right	right	NOUN
ejpam-6273	36	10	)	)	PUNCT
ejpam-6273	36	11	near	near	ADP
ejpam-6273	36	12	algebra	algebra	NOUN
ejpam-6273	36	13	over	over	ADP
ejpam-6273	36	14	a	a	DET
ejpam-6273	36	15	field	field	NOUN
ejpam-6273	36	16	l.	l.	NOUN
ejpam-6273	36	17	2	2	NUM
ejpam-6273	36	18	.	.	PUNCT
ejpam-6273	36	19	preliminaries	preliminary	NOUN
ejpam-6273	36	20	this	this	DET
ejpam-6273	36	21	section	section	NOUN
ejpam-6273	36	22	provides	provide	VERB
ejpam-6273	36	23	the	the	DET
ejpam-6273	36	24	necessary	necessary	ADJ
ejpam-6273	36	25	background	background	NOUN
ejpam-6273	36	26	and	and	CCONJ
ejpam-6273	36	27	notational	notational	ADJ
ejpam-6273	36	28	framework	framework	NOUN
ejpam-6273	36	29	for	for	ADP
ejpam-6273	36	30	developing	develop	VERB
ejpam-6273	36	31	hybrid	hybrid	ADJ
ejpam-6273	36	32	ideals	ideal	NOUN
ejpam-6273	36	33	in	in	ADP
ejpam-6273	36	34	near	near	ADP
ejpam-6273	36	35	algebras	algebra	NOUN
ejpam-6273	36	36	.	.	PUNCT
ejpam-6273	37	1	we	we	PRON
ejpam-6273	37	2	begin	begin	VERB
ejpam-6273	37	3	by	by	ADP
ejpam-6273	37	4	recalling	recall	VERB
ejpam-6273	37	5	essential	essential	ADJ
ejpam-6273	37	6	definitions	definition	NOUN
ejpam-6273	37	7	related	relate	VERB
ejpam-6273	37	8	to	to	ADP
ejpam-6273	37	9	near	near	ADJ
ejpam-6273	37	10	algebras	algebras	PROPN
ejpam-6273	37	11	and	and	CCONJ
ejpam-6273	37	12	hybrid	hybrid	ADJ
ejpam-6273	37	13	structures	structure	NOUN
ejpam-6273	37	14	,	,	PUNCT
ejpam-6273	37	15	including	include	VERB
ejpam-6273	37	16	hybrid	hybrid	ADJ
ejpam-6273	37	17	sets	set	NOUN
ejpam-6273	37	18	,	,	PUNCT
ejpam-6273	37	19	hybrid	hybrid	ADJ
ejpam-6273	37	20	subalgebras	subalgebra	NOUN
ejpam-6273	37	21	,	,	PUNCT
ejpam-6273	37	22	and	and	CCONJ
ejpam-6273	37	23	related	related	ADJ
ejpam-6273	37	24	homomorphisms	homomorphism	NOUN
ejpam-6273	37	25	.	.	PUNCT
ejpam-6273	38	1	these	these	DET
ejpam-6273	38	2	foundational	foundational	ADJ
ejpam-6273	38	3	concepts	concept	NOUN
ejpam-6273	38	4	serve	serve	VERB
ejpam-6273	38	5	as	as	ADP
ejpam-6273	38	6	the	the	DET
ejpam-6273	38	7	basis	basis	NOUN
ejpam-6273	38	8	for	for	ADP
ejpam-6273	38	9	formalizing	formalize	VERB
ejpam-6273	38	10	the	the	DET
ejpam-6273	38	11	hybrid	hybrid	ADJ
ejpam-6273	38	12	ideal	ideal	ADJ
ejpam-6273	38	13	structure	structure	NOUN
ejpam-6273	38	14	introduced	introduce	VERB
ejpam-6273	38	15	in	in	ADP
ejpam-6273	38	16	subsequent	subsequent	ADJ
ejpam-6273	38	17	sections	section	NOUN
ejpam-6273	38	18	.	.	PUNCT
ejpam-6273	39	1	definition	definition	NOUN
ejpam-6273	39	2	1	1	NUM
ejpam-6273	39	3	.	.	PUNCT
ejpam-6273	40	1	[	[	X
ejpam-6273	40	2	1	1	X
ejpam-6273	40	3	]	]	PUNCT
ejpam-6273	40	4	let	let	VERB
ejpam-6273	40	5	u	u	PRON
ejpam-6273	40	6	be	be	AUX
ejpam-6273	40	7	a	a	DET
ejpam-6273	40	8	universal	universal	ADJ
ejpam-6273	40	9	set	set	NOUN
ejpam-6273	40	10	,	,	PUNCT
ejpam-6273	40	11	p	p	X
ejpam-6273	40	12	(	(	PUNCT
ejpam-6273	40	13	u	u	NOUN
ejpam-6273	40	14	)	)	PUNCT
ejpam-6273	40	15	be	be	VERB
ejpam-6273	40	16	the	the	DET
ejpam-6273	40	17	power	power	NOUN
ejpam-6273	40	18	set	set	NOUN
ejpam-6273	40	19	,	,	PUNCT
ejpam-6273	40	20	l	l	X
ejpam-6273	40	21	be	be	VERB
ejpam-6273	40	22	the	the	DET
ejpam-6273	40	23	set	set	NOUN
ejpam-6273	40	24	of	of	ADP
ejpam-6273	40	25	parameters	parameter	NOUN
ejpam-6273	40	26	,	,	PUNCT
ejpam-6273	40	27	and	and	CCONJ
ejpam-6273	40	28	i	i	PRON
ejpam-6273	40	29	be	be	VERB
ejpam-6273	40	30	the	the	DET
ejpam-6273	40	31	unit	unit	NOUN
ejpam-6273	40	32	interval	interval	NOUN
ejpam-6273	40	33	.	.	PUNCT
ejpam-6273	41	1	a	a	DET
ejpam-6273	41	2	mapping	mapping	NOUN
ejpam-6273	41	3	ξ̃λ	ξ̃λ	VERB
ejpam-6273	41	4	:	:	PUNCT
ejpam-6273	41	5	=	=	SYM
ejpam-6273	41	6	(	(	PUNCT
ejpam-6273	41	7	ξ̃	ξ̃	PROPN
ejpam-6273	41	8	,	,	PUNCT
ejpam-6273	41	9	λ	λ	NOUN
ejpam-6273	41	10	)	)	PUNCT
ejpam-6273	41	11	:	:	PUNCT
ejpam-6273	42	1	l	l	X
ejpam-6273	42	2	→	→	PUNCT
ejpam-6273	42	3	p	p	X
ejpam-6273	42	4	(	(	PUNCT
ejpam-6273	42	5	u)×	u)×	X
ejpam-6273	42	6	i	i	NOUN
ejpam-6273	42	7	;	;	PUNCT
ejpam-6273	42	8	q	q	PROPN
ejpam-6273	42	9	7→	7→	NUM
ejpam-6273	42	10	(	(	PUNCT
ejpam-6273	42	11	ξ̃(q	ξ̃(q	PROPN
ejpam-6273	42	12	)	)	PUNCT
ejpam-6273	42	13	,	,	PUNCT
ejpam-6273	42	14	λ(q	λ(q	PROPN
ejpam-6273	42	15	)	)	PUNCT
ejpam-6273	42	16	)	)	PUNCT
ejpam-6273	42	17	,	,	PUNCT
ejpam-6273	42	18	i.e.	i.e.	X
ejpam-6273	42	19	,	,	PUNCT
ejpam-6273	42	20	the	the	DET
ejpam-6273	42	21	image	image	NOUN
ejpam-6273	42	22	of	of	ADP
ejpam-6273	42	23	q	q	NOUN
ejpam-6273	42	24	is	be	AUX
ejpam-6273	42	25	signified	signify	VERB
ejpam-6273	42	26	by	by	ADP
ejpam-6273	42	27	(	(	PUNCT
ejpam-6273	42	28	ξ̃(q	ξ̃(q	PROPN
ejpam-6273	42	29	)	)	PUNCT
ejpam-6273	42	30	,	,	PUNCT
ejpam-6273	42	31	λ(q	λ(q	PROPN
ejpam-6273	42	32	)	)	PUNCT
ejpam-6273	42	33	)	)	PUNCT
ejpam-6273	42	34	is	be	AUX
ejpam-6273	42	35	named	name	VERB
ejpam-6273	42	36	a	a	DET
ejpam-6273	42	37	hybrid	hybrid	ADJ
ejpam-6273	42	38	structure	structure	NOUN
ejpam-6273	42	39	(	(	PUNCT
ejpam-6273	42	40	hs	hs	X
ejpam-6273	42	41	)	)	PUNCT
ejpam-6273	42	42	in	in	ADP
ejpam-6273	42	43	l	l	PROPN
ejpam-6273	42	44	upon	upon	SCONJ
ejpam-6273	42	45	u	u	PROPN
ejpam-6273	42	46	,	,	PUNCT
ejpam-6273	43	1	where	where	SCONJ
ejpam-6273	43	2	ξ̃	ξ̃	NUM
ejpam-6273	43	3	:	:	PUNCT
ejpam-6273	43	4	l	l	X
ejpam-6273	43	5	→	→	PUNCT
ejpam-6273	43	6	p	p	X
ejpam-6273	43	7	(	(	PUNCT
ejpam-6273	43	8	u	u	NOUN
ejpam-6273	43	9	)	)	PUNCT
ejpam-6273	43	10	and	and	CCONJ
ejpam-6273	43	11	λ	λ	X
ejpam-6273	43	12	:	:	PUNCT
ejpam-6273	43	13	l	l	X
ejpam-6273	43	14	→	→	PUNCT
ejpam-6273	43	15	i	i	PRON
ejpam-6273	43	16	are	be	AUX
ejpam-6273	43	17	the	the	DET
ejpam-6273	43	18	mappings	mapping	NOUN
ejpam-6273	43	19	.	.	PUNCT
ejpam-6273	44	1	definition	definition	NOUN
ejpam-6273	44	2	2	2	NUM
ejpam-6273	44	3	.	.	PUNCT
ejpam-6273	45	1	[	[	X
ejpam-6273	45	2	1	1	X
ejpam-6273	45	3	]	]	PUNCT
ejpam-6273	45	4	let	let	VERB
ejpam-6273	45	5	ξ̃λ	ξ̃λ	PRON
ejpam-6273	45	6	be	be	AUX
ejpam-6273	45	7	an	an	DET
ejpam-6273	45	8	hs	hs	NOUN
ejpam-6273	45	9	in	in	ADP
ejpam-6273	45	10	l	l	PROPN
ejpam-6273	45	11	upon	upon	SCONJ
ejpam-6273	45	12	u	u	NOUN
ejpam-6273	45	13	.	.	PUNCT
ejpam-6273	46	1	then	then	ADV
ejpam-6273	46	2	the	the	DET
ejpam-6273	46	3	sets	set	NOUN
ejpam-6273	46	4	ξ̃λ[α	ξ̃λ[α	PROPN
ejpam-6273	46	5	,	,	PUNCT
ejpam-6273	46	6	t	t	X
ejpam-6273	46	7	]	]	X
ejpam-6273	46	8	=	=	X
ejpam-6273	46	9	{	{	PUNCT
ejpam-6273	46	10	q	q	NOUN
ejpam-6273	46	11	∈	∈	PROPN
ejpam-6273	46	12	l	l	NOUN
ejpam-6273	46	13	|	|	NOUN
ejpam-6273	46	14	ξ̃(q	ξ̃(q	PROPN
ejpam-6273	46	15	)	)	PUNCT
ejpam-6273	46	16	⊇	⊇	NOUN
ejpam-6273	46	17	α	α	NOUN
ejpam-6273	46	18	,	,	PUNCT
ejpam-6273	46	19	λ(q	λ(q	PROPN
ejpam-6273	46	20	)	)	PUNCT
ejpam-6273	46	21	≤	≤	NOUN
ejpam-6273	46	22	t	t	PROPN
ejpam-6273	46	23	}	}	PUNCT
ejpam-6273	46	24	,	,	PUNCT
ejpam-6273	46	25	p.	p.	PROPN
ejpam-6273	46	26	n.	n.	PROPN
ejpam-6273	46	27	swamy	swamy	PROPN
ejpam-6273	46	28	et	et	PROPN
ejpam-6273	46	29	al	al	PROPN
ejpam-6273	46	30	.	.	PUNCT
ejpam-6273	46	31	/	/	SYM
ejpam-6273	46	32	eur	eur	PROPN
ejpam-6273	46	33	.	.	PUNCT
ejpam-6273	47	1	j.	j.	PROPN
ejpam-6273	47	2	pure	pure	PROPN
ejpam-6273	47	3	appl	appl	PROPN
ejpam-6273	47	4	.	.	PROPN
ejpam-6273	47	5	math	math	PROPN
ejpam-6273	47	6	,	,	PUNCT
ejpam-6273	47	7	18	18	NUM
ejpam-6273	47	8	(	(	PUNCT
ejpam-6273	47	9	3	3	NUM
ejpam-6273	47	10	)	)	PUNCT
ejpam-6273	47	11	(	(	PUNCT
ejpam-6273	47	12	2025	2025	NUM
ejpam-6273	47	13	)	)	PUNCT
ejpam-6273	47	14	,	,	PUNCT
ejpam-6273	47	15	6273	6273	NUM
ejpam-6273	47	16	3	3	NUM
ejpam-6273	47	17	of	of	ADP
ejpam-6273	47	18	16	16	NUM
ejpam-6273	47	19	ξ̃λ(α	ξ̃λ(α	PROPN
ejpam-6273	47	20	,	,	PUNCT
ejpam-6273	47	21	t	t	PROPN
ejpam-6273	47	22	]	]	X
ejpam-6273	47	23	=	=	X
ejpam-6273	47	24	{	{	PUNCT
ejpam-6273	47	25	q	q	NOUN
ejpam-6273	47	26	∈	∈	PROPN
ejpam-6273	47	27	l	l	NOUN
ejpam-6273	47	28	|	|	NOUN
ejpam-6273	47	29	ξ̃(q	ξ̃(q	PROPN
ejpam-6273	47	30	)	)	PUNCT
ejpam-6273	47	31	⊃	⊃	PROPN
ejpam-6273	47	32	α	α	X
ejpam-6273	47	33	,	,	PUNCT
ejpam-6273	47	34	λ(q	λ(q	PROPN
ejpam-6273	47	35	)	)	PUNCT
ejpam-6273	47	36	≤	≤	NOUN
ejpam-6273	47	37	t	t	PROPN
ejpam-6273	47	38	}	}	PUNCT
ejpam-6273	47	39	,	,	PUNCT
ejpam-6273	47	40	ξ̃λ[α	ξ̃λ[α	PROPN
ejpam-6273	47	41	,	,	PUNCT
ejpam-6273	47	42	t	t	PROPN
ejpam-6273	47	43	)	)	PUNCT
ejpam-6273	47	44	=	=	PRON
ejpam-6273	47	45	{	{	PUNCT
ejpam-6273	47	46	q	q	NOUN
ejpam-6273	47	47	∈	∈	PROPN
ejpam-6273	47	48	l	l	NOUN
ejpam-6273	47	49	|	|	NOUN
ejpam-6273	47	50	ξ̃(q	ξ̃(q	PROPN
ejpam-6273	47	51	)	)	PUNCT
ejpam-6273	47	52	⊇	⊇	NOUN
ejpam-6273	47	53	α	α	NOUN
ejpam-6273	47	54	,	,	PUNCT
ejpam-6273	47	55	λ(q	λ(q	PROPN
ejpam-6273	47	56	)	)	PUNCT
ejpam-6273	47	57	<	<	X
ejpam-6273	47	58	t	t	PROPN
ejpam-6273	47	59	}	}	PUNCT
ejpam-6273	47	60	,	,	PUNCT
ejpam-6273	47	61	ξ̃λ(α	ξ̃λ(α	PROPN
ejpam-6273	47	62	,	,	PUNCT
ejpam-6273	47	63	t	t	PROPN
ejpam-6273	47	64	)	)	PUNCT
ejpam-6273	47	65	=	=	PRON
ejpam-6273	47	66	{	{	PUNCT
ejpam-6273	47	67	q	q	NOUN
ejpam-6273	47	68	∈	∈	PROPN
ejpam-6273	47	69	l	l	NOUN
ejpam-6273	47	70	|	|	NOUN
ejpam-6273	47	71	ξ̃(q	ξ̃(q	PROPN
ejpam-6273	47	72	)	)	PUNCT
ejpam-6273	47	73	⊃	⊃	PROPN
ejpam-6273	47	74	α	α	X
ejpam-6273	47	75	,	,	PUNCT
ejpam-6273	47	76	λ(q	λ(q	PROPN
ejpam-6273	47	77	)	)	PUNCT
ejpam-6273	47	78	<	<	X
ejpam-6273	47	79	t	t	PROPN
ejpam-6273	47	80	}	}	PUNCT
ejpam-6273	47	81	,	,	PUNCT
ejpam-6273	47	82	are	be	AUX
ejpam-6273	47	83	called	call	VERB
ejpam-6273	47	84	the	the	DET
ejpam-6273	47	85	[	[	X
ejpam-6273	47	86	α	α	NOUN
ejpam-6273	47	87	,	,	PUNCT
ejpam-6273	47	88	t]-hybrid	t]-hybrid	VERB
ejpam-6273	47	89	cut	cut	NOUN
ejpam-6273	47	90	(	(	PUNCT
ejpam-6273	47	91	hc	hc	NOUN
ejpam-6273	47	92	)	)	PUNCT
ejpam-6273	47	93	,	,	PUNCT
ejpam-6273	47	94	(	(	PUNCT
ejpam-6273	47	95	α	α	NOUN
ejpam-6273	47	96	,	,	PUNCT
ejpam-6273	47	97	t]-hc	t]-hc	PRON
ejpam-6273	47	98	,	,	PUNCT
ejpam-6273	47	99	[	[	X
ejpam-6273	47	100	α	α	X
ejpam-6273	47	101	,	,	PUNCT
ejpam-6273	47	102	t	t	NOUN
ejpam-6273	47	103	)	)	PUNCT
ejpam-6273	47	104	-hc	-hc	CCONJ
ejpam-6273	47	105	,	,	PUNCT
ejpam-6273	47	106	and	and	CCONJ
ejpam-6273	47	107	(	(	PUNCT
ejpam-6273	47	108	α	α	NOUN
ejpam-6273	47	109	,	,	PUNCT
ejpam-6273	47	110	t)-hc	t)-hc	NOUN
ejpam-6273	47	111	of	of	ADP
ejpam-6273	47	112	ξ̃λ	ξ̃λ	PRON
ejpam-6273	47	113	correspondingly	correspondingly	ADV
ejpam-6273	47	114	,	,	PUNCT
ejpam-6273	47	115	where	where	SCONJ
ejpam-6273	47	116	α	α	PRON
ejpam-6273	47	117	∈	∈	PROPN
ejpam-6273	47	118	p	p	X
ejpam-6273	47	119	(	(	PUNCT
ejpam-6273	47	120	u	u	NOUN
ejpam-6273	47	121	)	)	PUNCT
ejpam-6273	47	122	and	and	CCONJ
ejpam-6273	47	123	t	t	PROPN
ejpam-6273	47	124	∈	∈	PROPN
ejpam-6273	47	125	i.	i.	NOUN
ejpam-6273	47	126	apparently	apparently	ADV
ejpam-6273	47	127	,	,	PUNCT
ejpam-6273	47	128	ξ̃λ(α	ξ̃λ(α	PROPN
ejpam-6273	47	129	,	,	PUNCT
ejpam-6273	47	130	t	t	PROPN
ejpam-6273	47	131	)	)	PUNCT
ejpam-6273	47	132	⊆	⊆	NUM
ejpam-6273	47	133	ξ̃λ(α	ξ̃λ(α	PROPN
ejpam-6273	47	134	,	,	PUNCT
ejpam-6273	47	135	t	t	PROPN
ejpam-6273	47	136	]	]	X
ejpam-6273	47	137	⊆	⊆	NUM
ejpam-6273	47	138	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	47	139	,	,	PUNCT
ejpam-6273	47	140	t	t	PROPN
ejpam-6273	47	141	]	]	PUNCT
ejpam-6273	47	142	and	and	CCONJ
ejpam-6273	47	143	ξ̃λ(α	ξ̃λ(α	PROPN
ejpam-6273	47	144	,	,	PUNCT
ejpam-6273	47	145	t	t	PROPN
ejpam-6273	47	146	)	)	PUNCT
ejpam-6273	47	147	⊆	⊆	NUM
ejpam-6273	47	148	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	47	149	,	,	PUNCT
ejpam-6273	47	150	t	t	PROPN
ejpam-6273	47	151	)	)	PUNCT
ejpam-6273	47	152	⊆	⊆	NUM
ejpam-6273	47	153	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	47	154	,	,	PUNCT
ejpam-6273	47	155	t	t	X
ejpam-6273	47	156	]	]	PUNCT
ejpam-6273	47	157	.	.	PUNCT
ejpam-6273	48	1	definition	definition	NOUN
ejpam-6273	48	2	3	3	NUM
ejpam-6273	48	3	.	.	PUNCT
ejpam-6273	49	1	[	[	X
ejpam-6273	49	2	13	13	NUM
ejpam-6273	49	3	]	]	PUNCT
ejpam-6273	49	4	let	let	AUX
ejpam-6273	49	5	l	l	NOUN
ejpam-6273	49	6	be	be	AUX
ejpam-6273	49	7	a	a	DET
ejpam-6273	49	8	field	field	NOUN
ejpam-6273	49	9	.	.	PUNCT
ejpam-6273	50	1	an	an	DET
ejpam-6273	50	2	hs	hs	PRON
ejpam-6273	50	3	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	50	4	in	in	ADP
ejpam-6273	50	5	l	l	PROPN
ejpam-6273	50	6	upon	upon	SCONJ
ejpam-6273	50	7	u	u	NOUN
ejpam-6273	50	8	is	be	AUX
ejpam-6273	50	9	called	call	VERB
ejpam-6273	50	10	a	a	DET
ejpam-6273	50	11	hybrid	hybrid	ADJ
ejpam-6273	50	12	field	field	NOUN
ejpam-6273	50	13	(	(	PUNCT
ejpam-6273	50	14	hf	hf	NOUN
ejpam-6273	50	15	)	)	PUNCT
ejpam-6273	50	16	of	of	ADP
ejpam-6273	50	17	l	l	NOUN
ejpam-6273	50	18	upon	upon	SCONJ
ejpam-6273	50	19	u	u	NOUN
ejpam-6273	50	20	if	if	SCONJ
ejpam-6273	50	21	the	the	DET
ejpam-6273	50	22	following	follow	VERB
ejpam-6273	50	23	conditions	condition	NOUN
ejpam-6273	50	24	hold	hold	VERB
ejpam-6273	50	25	:	:	PUNCT
ejpam-6273	50	26	(	(	PUNCT
ejpam-6273	50	27	i	i	NOUN
ejpam-6273	50	28	)	)	PUNCT
ejpam-6273	50	29	ξ̃(s+	ξ̃(s+	NOUN
ejpam-6273	50	30	a	a	X
ejpam-6273	50	31	)	)	PUNCT
ejpam-6273	50	32	⊇	⊇	NOUN
ejpam-6273	50	33	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	50	34	)	)	PUNCT
ejpam-6273	50	35	∩	∩	NOUN
ejpam-6273	50	36	ξ̃(a	ξ̃(a	NOUN
ejpam-6273	50	37	)	)	PUNCT
ejpam-6273	50	38	,	,	PUNCT
ejpam-6273	50	39	λ(s+	λ(s+	VERB
ejpam-6273	50	40	a	a	DET
ejpam-6273	50	41	)	)	PUNCT
ejpam-6273	50	42	≤	≤	NUM
ejpam-6273	50	43	∨	∨	NUM
ejpam-6273	50	44	{	{	PUNCT
ejpam-6273	50	45	λ(s	λ(s	PROPN
ejpam-6273	50	46	)	)	PUNCT
ejpam-6273	50	47	,	,	PUNCT
ejpam-6273	50	48	λ(a	λ(a	NOUN
ejpam-6273	50	49	)	)	PUNCT
ejpam-6273	50	50	}	}	PUNCT
ejpam-6273	50	51	,	,	PUNCT
ejpam-6273	50	52	∀s	∀s	PROPN
ejpam-6273	50	53	,	,	PUNCT
ejpam-6273	50	54	a	a	DET
ejpam-6273	50	55	∈	∈	PROPN
ejpam-6273	50	56	l	l	NOUN
ejpam-6273	50	57	(	(	PUNCT
ejpam-6273	50	58	ii	ii	NOUN
ejpam-6273	50	59	)	)	PUNCT
ejpam-6273	50	60	ξ̃(−s	ξ̃(−	NOUN
ejpam-6273	50	61	)	)	PUNCT
ejpam-6273	50	62	⊇	⊇	PROPN
ejpam-6273	50	63	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	50	64	)	)	PUNCT
ejpam-6273	50	65	,	,	PUNCT
ejpam-6273	50	66	λ(−s	λ(−	NOUN
ejpam-6273	50	67	)	)	PUNCT
ejpam-6273	50	68	≤	≤	NUM
ejpam-6273	50	69	λ(s	λ(s	PROPN
ejpam-6273	50	70	)	)	PUNCT
ejpam-6273	50	71	,	,	PUNCT
ejpam-6273	50	72	∀s	∀s	PROPN
ejpam-6273	50	73	∈	∈	PROPN
ejpam-6273	50	74	l	l	X
ejpam-6273	50	75	(	(	PUNCT
ejpam-6273	50	76	iii	iii	NOUN
ejpam-6273	50	77	)	)	PUNCT
ejpam-6273	50	78	ξ̃(sa	ξ̃(sa	NOUN
ejpam-6273	50	79	)	)	PUNCT
ejpam-6273	50	80	⊇	⊇	NOUN
ejpam-6273	50	81	ξ̃(s	ξ̃(s	PROPN
ejpam-6273	50	82	)	)	PUNCT
ejpam-6273	50	83	∩	∩	NOUN
ejpam-6273	50	84	ξ̃(a	ξ̃(a	NOUN
ejpam-6273	50	85	)	)	PUNCT
ejpam-6273	50	86	,	,	PUNCT
ejpam-6273	50	87	λ(sa	λ(sa	NOUN
ejpam-6273	50	88	)	)	PUNCT
ejpam-6273	50	89	≤	≤	NUM
ejpam-6273	50	90	∨	∨	NUM
ejpam-6273	50	91	{	{	PUNCT
ejpam-6273	50	92	λ(s	λ(s	PROPN
ejpam-6273	50	93	)	)	PUNCT
ejpam-6273	50	94	,	,	PUNCT
ejpam-6273	50	95	λ(a)},∀s	λ(a)},∀s	PROPN
ejpam-6273	50	96	,	,	PUNCT
ejpam-6273	50	97	a	a	PRON
ejpam-6273	50	98	∈	∈	PROPN
ejpam-6273	50	99	l	l	NOUN
ejpam-6273	50	100	(	(	PUNCT
ejpam-6273	50	101	iv	iv	X
ejpam-6273	50	102	)	)	PUNCT
ejpam-6273	50	103	s	s	PART
ejpam-6273	50	104	̸=	̸=	PROPN
ejpam-6273	50	105	0	0	NUM
ejpam-6273	50	106	⇒	⇒	PROPN
ejpam-6273	50	107	ξ̃(s−1	ξ̃(s−1	NOUN
ejpam-6273	50	108	)	)	PUNCT
ejpam-6273	50	109	⊇	⊇	NOUN
ejpam-6273	50	110	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	50	111	)	)	PUNCT
ejpam-6273	50	112	,	,	PUNCT
ejpam-6273	50	113	λ(s−1	λ(s−1	PROPN
ejpam-6273	50	114	)	)	PUNCT
ejpam-6273	50	115	≤	≤	NUM
ejpam-6273	50	116	λ(s	λ(s	PROPN
ejpam-6273	50	117	)	)	PUNCT
ejpam-6273	50	118	,	,	PUNCT
ejpam-6273	50	119	∀s	∀s	PROPN
ejpam-6273	50	120	∈	∈	PROPN
ejpam-6273	50	121	l.	l.	PROPN
ejpam-6273	50	122	definition	definition	NOUN
ejpam-6273	50	123	4	4	NUM
ejpam-6273	50	124	.	.	PUNCT
ejpam-6273	51	1	[	[	X
ejpam-6273	51	2	3	3	X
ejpam-6273	51	3	]	]	PUNCT
ejpam-6273	51	4	let	let	VERB
ejpam-6273	51	5	ξ̃λ	ξ̃λ	PRON
ejpam-6273	51	6	be	be	AUX
ejpam-6273	51	7	an	an	DET
ejpam-6273	51	8	hf	hf	NOUN
ejpam-6273	51	9	of	of	ADP
ejpam-6273	51	10	a	a	DET
ejpam-6273	51	11	field	field	NOUN
ejpam-6273	51	12	l	l	NOUN
ejpam-6273	51	13	upon	upon	SCONJ
ejpam-6273	51	14	u	u	PROPN
ejpam-6273	51	15	and	and	CCONJ
ejpam-6273	51	16	y	y	PROPN
ejpam-6273	51	17	be	be	AUX
ejpam-6273	51	18	an	an	DET
ejpam-6273	51	19	na	na	NOUN
ejpam-6273	51	20	over	over	ADP
ejpam-6273	51	21	l.	l.	PROPN
ejpam-6273	51	22	an	an	DET
ejpam-6273	51	23	hs	hs	PROPN
ejpam-6273	51	24	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	51	25	in	in	ADP
ejpam-6273	51	26	y	y	PROPN
ejpam-6273	51	27	upon	upon	SCONJ
ejpam-6273	51	28	u	u	NOUN
ejpam-6273	51	29	is	be	AUX
ejpam-6273	51	30	called	call	VERB
ejpam-6273	51	31	a	a	DET
ejpam-6273	51	32	hybrid	hybrid	NOUN
ejpam-6273	51	33	near	near	ADP
ejpam-6273	51	34	algebra	algebra	PROPN
ejpam-6273	51	35	(	(	PUNCT
ejpam-6273	51	36	hna	hna	PROPN
ejpam-6273	51	37	)	)	PUNCT
ejpam-6273	51	38	upon	upon	SCONJ
ejpam-6273	51	39	hf	hf	PROPN
ejpam-6273	51	40	(	(	PUNCT
ejpam-6273	51	41	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	51	42	,	,	PUNCT
ejpam-6273	51	43	l	l	NOUN
ejpam-6273	51	44	)	)	PUNCT
ejpam-6273	51	45	if	if	SCONJ
ejpam-6273	51	46	the	the	DET
ejpam-6273	51	47	resulting	result	VERB
ejpam-6273	51	48	conditions	condition	NOUN
ejpam-6273	51	49	hold	hold	VERB
ejpam-6273	51	50	:	:	PUNCT
ejpam-6273	51	51	(	(	PUNCT
ejpam-6273	51	52	i	i	NOUN
ejpam-6273	51	53	)	)	PUNCT
ejpam-6273	51	54	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	51	55	+	+	CCONJ
ejpam-6273	51	56	ς	ς	PROPN
ejpam-6273	51	57	)	)	PUNCT
ejpam-6273	51	58	⊇	⊇	PROPN
ejpam-6273	51	59	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	51	60	)	)	PUNCT
ejpam-6273	51	61	∩	∩	PROPN
ejpam-6273	51	62	ϱ̃(ς	ϱ̃(ς	PROPN
ejpam-6273	51	63	)	)	PUNCT
ejpam-6273	51	64	,	,	PUNCT
ejpam-6273	51	65	γ(q	γ(q	PROPN
ejpam-6273	51	66	+	+	CCONJ
ejpam-6273	51	67	ς	ς	NOUN
ejpam-6273	51	68	)	)	PUNCT
ejpam-6273	51	69	≤	≤	NOUN
ejpam-6273	51	70	∨	∨	NUM
ejpam-6273	51	71	{	{	PUNCT
ejpam-6273	51	72	γ(q	γ(q	NOUN
ejpam-6273	51	73	)	)	PUNCT
ejpam-6273	51	74	,	,	PUNCT
ejpam-6273	51	75	γ(ς	γ(ς	NOUN
ejpam-6273	51	76	)	)	PUNCT
ejpam-6273	51	77	}	}	PUNCT
ejpam-6273	51	78	,	,	PUNCT
ejpam-6273	51	79	∀q	∀q	PROPN
ejpam-6273	51	80	,	,	PUNCT
ejpam-6273	51	81	ς	ς	PROPN
ejpam-6273	51	82	∈	∈	PROPN
ejpam-6273	51	83	y	y	PROPN
ejpam-6273	51	84	(	(	PUNCT
ejpam-6273	51	85	ii	ii	NOUN
ejpam-6273	51	86	)	)	PUNCT
ejpam-6273	51	87	ϱ̃(sq	ϱ̃(sq	NOUN
ejpam-6273	51	88	)	)	PUNCT
ejpam-6273	51	89	⊇	⊇	NOUN
ejpam-6273	51	90	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	51	91	)	)	PUNCT
ejpam-6273	51	92	∩	∩	NOUN
ejpam-6273	51	93	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	51	94	)	)	PUNCT
ejpam-6273	51	95	,	,	PUNCT
ejpam-6273	51	96	λ(sq	λ(sq	PROPN
ejpam-6273	51	97	)	)	PUNCT
ejpam-6273	51	98	≤	≤	NOUN
ejpam-6273	51	99	∨	∨	NUM
ejpam-6273	51	100	{	{	PUNCT
ejpam-6273	51	101	λ(s	λ(s	PROPN
ejpam-6273	51	102	)	)	PUNCT
ejpam-6273	51	103	,	,	PUNCT
ejpam-6273	51	104	γ(q)},∀s	γ(q)},∀s	PUNCT
ejpam-6273	51	105	∈	∈	PROPN
ejpam-6273	51	106	l	l	NOUN
ejpam-6273	51	107	,	,	PUNCT
ejpam-6273	51	108	q	q	PROPN
ejpam-6273	51	109	∈	∈	PROPN
ejpam-6273	51	110	y	y	PROPN
ejpam-6273	51	111	(	(	PUNCT
ejpam-6273	51	112	iii	iii	NOUN
ejpam-6273	51	113	)	)	PUNCT
ejpam-6273	51	114	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	51	115	)	)	PUNCT
ejpam-6273	51	116	⊇	⊇	PROPN
ejpam-6273	51	117	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	51	118	)	)	PUNCT
ejpam-6273	51	119	∩	∩	PROPN
ejpam-6273	51	120	ϱ̃(ς	ϱ̃(ς	PROPN
ejpam-6273	51	121	)	)	PUNCT
ejpam-6273	51	122	,	,	PUNCT
ejpam-6273	51	123	γ(qς	γ(qς	NOUN
ejpam-6273	51	124	)	)	PUNCT
ejpam-6273	51	125	≤	≤	NUM
ejpam-6273	51	126	∨	∨	NUM
ejpam-6273	51	127	{	{	PUNCT
ejpam-6273	51	128	γ(q	γ(q	NOUN
ejpam-6273	51	129	)	)	PUNCT
ejpam-6273	51	130	,	,	PUNCT
ejpam-6273	51	131	γ(ς)},∀q	γ(ς)},∀q	PROPN
ejpam-6273	51	132	,	,	PUNCT
ejpam-6273	51	133	ς	ς	PROPN
ejpam-6273	51	134	∈	∈	PROPN
ejpam-6273	51	135	y	y	PROPN
ejpam-6273	51	136	(	(	PUNCT
ejpam-6273	51	137	iv	iv	X
ejpam-6273	51	138	)	)	PUNCT
ejpam-6273	51	139	ξ̃(1	ξ̃(1	NOUN
ejpam-6273	51	140	)	)	PUNCT
ejpam-6273	51	141	⊇	⊇	PROPN
ejpam-6273	51	142	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	51	143	)	)	PUNCT
ejpam-6273	51	144	,	,	PUNCT
ejpam-6273	51	145	λ(1	λ(1	PROPN
ejpam-6273	51	146	)	)	PUNCT
ejpam-6273	51	147	≤	≤	PUNCT
ejpam-6273	52	1	γ(q),∀q	γ(q),∀q	PROPN
ejpam-6273	52	2	∈	∈	PROPN
ejpam-6273	52	3	y	y	PROPN
ejpam-6273	52	4	.	.	PUNCT
ejpam-6273	53	1	definition	definition	NOUN
ejpam-6273	53	2	5	5	NUM
ejpam-6273	53	3	.	.	PUNCT
ejpam-6273	54	1	[	[	X
ejpam-6273	54	2	3	3	X
ejpam-6273	54	3	]	]	PUNCT
ejpam-6273	54	4	let	let	VERB
ejpam-6273	54	5	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	54	6	and	and	CCONJ
ejpam-6273	54	7	h̃µ	h̃µ	NOUN
ejpam-6273	54	8	be	be	AUX
ejpam-6273	54	9	two	two	NUM
ejpam-6273	54	10	hss	hss	NOUN
ejpam-6273	54	11	in	in	ADP
ejpam-6273	54	12	l	l	PROPN
ejpam-6273	54	13	upon	upon	SCONJ
ejpam-6273	54	14	u	u	PROPN
ejpam-6273	54	15	.	.	PUNCT
ejpam-6273	55	1	then	then	ADV
ejpam-6273	55	2	the	the	DET
ejpam-6273	55	3	hybrid	hybrid	ADJ
ejpam-6273	55	4	intersection	intersection	NOUN
ejpam-6273	55	5	of	of	ADP
ejpam-6273	55	6	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	55	7	and	and	CCONJ
ejpam-6273	55	8	h̃µ	h̃µ	NOUN
ejpam-6273	55	9	is	be	AUX
ejpam-6273	55	10	an	an	DET
ejpam-6273	55	11	hs	hs	PROPN
ejpam-6273	55	12	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	55	13	⋒	⋒	PUNCT
ejpam-6273	55	14	h̃µ	h̃µ	NOUN
ejpam-6273	55	15	:	:	PUNCT
ejpam-6273	55	16	l	l	X
ejpam-6273	55	17	→	→	PUNCT
ejpam-6273	55	18	p	p	X
ejpam-6273	55	19	(	(	PUNCT
ejpam-6273	55	20	u)×	u)×	X
ejpam-6273	55	21	i	i	NOUN
ejpam-6273	55	22	;	;	PUNCT
ejpam-6273	55	23	q	q	PROPN
ejpam-6273	55	24	7→	7→	NUM
ejpam-6273	55	25	(	(	PUNCT
ejpam-6273	55	26	(	(	PUNCT
ejpam-6273	55	27	ϱ̃∩̃h̃)(q	ϱ̃∩̃h̃)(q	PROPN
ejpam-6273	55	28	)	)	PUNCT
ejpam-6273	55	29	,	,	PUNCT
ejpam-6273	55	30	(	(	PUNCT
ejpam-6273	55	31	γ	γ	PROPN
ejpam-6273	55	32	∨	∨	NUM
ejpam-6273	55	33	µ)(q)),∀q	µ)(q)),∀q	PROPN
ejpam-6273	55	34	∈	∈	PROPN
ejpam-6273	55	35	l	l	NOUN
ejpam-6273	55	36	,	,	PUNCT
ejpam-6273	55	37	where	where	SCONJ
ejpam-6273	55	38	ϱ̃∩̃h̃	ϱ̃∩̃h̃	NOUN
ejpam-6273	55	39	:	:	PUNCT
ejpam-6273	55	40	l	l	X
ejpam-6273	55	41	→	→	SYM
ejpam-6273	55	42	p	p	X
ejpam-6273	55	43	(	(	PUNCT
ejpam-6273	55	44	u	u	NOUN
ejpam-6273	55	45	)	)	PUNCT
ejpam-6273	55	46	;	;	PUNCT
ejpam-6273	55	47	q	q	PROPN
ejpam-6273	55	48	7→	7→	NUM
ejpam-6273	55	49	ϱ̃(q	ϱ̃(q	ADJ
ejpam-6273	55	50	)	)	PUNCT
ejpam-6273	55	51	∩	∩	NOUN
ejpam-6273	55	52	h̃(q	h̃(q	PROPN
ejpam-6273	55	53	)	)	PUNCT
ejpam-6273	55	54	and	and	CCONJ
ejpam-6273	55	55	γ	γ	PROPN
ejpam-6273	55	56	∨	∨	PROPN
ejpam-6273	55	57	µ	µ	X
ejpam-6273	55	58	:	:	PUNCT
ejpam-6273	55	59	l	l	X
ejpam-6273	55	60	→	→	PUNCT
ejpam-6273	55	61	i	i	NOUN
ejpam-6273	55	62	;	;	PUNCT
ejpam-6273	55	63	q	q	PROPN
ejpam-6273	55	64	7→	7→	NUM
ejpam-6273	55	65	∨{γ(q	∨{γ(q	NOUN
ejpam-6273	55	66	)	)	PUNCT
ejpam-6273	55	67	,	,	PUNCT
ejpam-6273	55	68	µ(q	µ(q	PROPN
ejpam-6273	55	69	)	)	PUNCT
ejpam-6273	55	70	}	}	PUNCT
ejpam-6273	55	71	.	.	PUNCT
ejpam-6273	56	1	3	3	X
ejpam-6273	56	2	.	.	X
ejpam-6273	56	3	hybrid	hybrid	ADJ
ejpam-6273	56	4	ideal	ideal	NOUN
ejpam-6273	56	5	of	of	ADP
ejpam-6273	56	6	a	a	DET
ejpam-6273	56	7	near	near	ADJ
ejpam-6273	56	8	algebra	algebra	NOUN
ejpam-6273	56	9	the	the	DET
ejpam-6273	56	10	hybrid	hybrid	ADJ
ejpam-6273	56	11	ideal	ideal	NOUN
ejpam-6273	56	12	of	of	ADP
ejpam-6273	56	13	a	a	DET
ejpam-6273	56	14	near	near	ADJ
ejpam-6273	56	15	algebra	algebra	NOUN
ejpam-6273	56	16	is	be	AUX
ejpam-6273	56	17	introduced	introduce	VERB
ejpam-6273	56	18	in	in	ADP
ejpam-6273	56	19	this	this	DET
ejpam-6273	56	20	section	section	NOUN
ejpam-6273	56	21	,	,	PUNCT
ejpam-6273	56	22	along	along	ADP
ejpam-6273	56	23	with	with	ADP
ejpam-6273	56	24	some	some	PRON
ejpam-6273	56	25	of	of	ADP
ejpam-6273	56	26	its	its	PRON
ejpam-6273	56	27	features	feature	NOUN
ejpam-6273	56	28	over	over	ADP
ejpam-6273	56	29	the	the	DET
ejpam-6273	56	30	hybrid	hybrid	ADJ
ejpam-6273	56	31	field	field	NOUN
ejpam-6273	56	32	.	.	PUNCT
ejpam-6273	57	1	definition	definition	NOUN
ejpam-6273	57	2	6	6	NUM
ejpam-6273	57	3	.	.	PUNCT
ejpam-6273	58	1	let	let	VERB
ejpam-6273	58	2	ξ̃λ	ξ̃λ	PRON
ejpam-6273	58	3	be	be	AUX
ejpam-6273	58	4	an	an	DET
ejpam-6273	58	5	hf	hf	NOUN
ejpam-6273	58	6	of	of	ADP
ejpam-6273	58	7	a	a	DET
ejpam-6273	58	8	field	field	NOUN
ejpam-6273	58	9	l	l	NOUN
ejpam-6273	58	10	upon	upon	SCONJ
ejpam-6273	58	11	u	u	PROPN
ejpam-6273	58	12	and	and	CCONJ
ejpam-6273	58	13	y	y	PROPN
ejpam-6273	58	14	be	be	AUX
ejpam-6273	58	15	a	a	DET
ejpam-6273	58	16	na	na	NOUN
ejpam-6273	58	17	over	over	ADP
ejpam-6273	58	18	l.	l.	PROPN
ejpam-6273	58	19	an	an	DET
ejpam-6273	58	20	hs	hs	PROPN
ejpam-6273	58	21	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	58	22	in	in	ADP
ejpam-6273	58	23	y	y	PROPN
ejpam-6273	58	24	upon	upon	SCONJ
ejpam-6273	58	25	u	u	NOUN
ejpam-6273	58	26	is	be	AUX
ejpam-6273	58	27	called	call	VERB
ejpam-6273	58	28	a	a	DET
ejpam-6273	58	29	hybrid	hybrid	ADJ
ejpam-6273	58	30	ideal	ideal	NOUN
ejpam-6273	58	31	of	of	ADP
ejpam-6273	58	32	a	a	DET
ejpam-6273	58	33	near	near	ADJ
ejpam-6273	58	34	algebra	algebra	NOUN
ejpam-6273	58	35	(	(	PUNCT
ejpam-6273	58	36	hina	hina	NOUN
ejpam-6273	58	37	)	)	PUNCT
ejpam-6273	58	38	upon	upon	SCONJ
ejpam-6273	58	39	the	the	DET
ejpam-6273	58	40	hf	hf	NOUN
ejpam-6273	58	41	(	(	PUNCT
ejpam-6273	58	42	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	58	43	,	,	PUNCT
ejpam-6273	58	44	l	l	NOUN
ejpam-6273	58	45	)	)	PUNCT
ejpam-6273	59	1	if	if	SCONJ
ejpam-6273	59	2	(	(	PUNCT
ejpam-6273	59	3	i	i	NOUN
ejpam-6273	59	4	)	)	PUNCT
ejpam-6273	59	5	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	59	6	+	+	CCONJ
ejpam-6273	59	7	ς	ς	PROPN
ejpam-6273	59	8	)	)	PUNCT
ejpam-6273	59	9	⊇	⊇	PROPN
ejpam-6273	59	10	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	59	11	)	)	PUNCT
ejpam-6273	59	12	∩	∩	PROPN
ejpam-6273	59	13	ϱ̃(ς	ϱ̃(ς	PROPN
ejpam-6273	59	14	)	)	PUNCT
ejpam-6273	59	15	,	,	PUNCT
ejpam-6273	59	16	γ(q	γ(q	PROPN
ejpam-6273	59	17	+	+	CCONJ
ejpam-6273	59	18	ς	ς	NOUN
ejpam-6273	59	19	)	)	PUNCT
ejpam-6273	59	20	≤	≤	NOUN
ejpam-6273	59	21	∨	∨	NUM
ejpam-6273	59	22	{	{	PUNCT
ejpam-6273	59	23	γ(q	γ(q	NOUN
ejpam-6273	59	24	)	)	PUNCT
ejpam-6273	59	25	,	,	PUNCT
ejpam-6273	59	26	γ(ς	γ(ς	NOUN
ejpam-6273	59	27	)	)	PUNCT
ejpam-6273	59	28	}	}	PUNCT
ejpam-6273	59	29	,	,	PUNCT
ejpam-6273	59	30	∀q	∀q	PROPN
ejpam-6273	59	31	,	,	PUNCT
ejpam-6273	59	32	ς	ς	PROPN
ejpam-6273	59	33	∈	∈	PROPN
ejpam-6273	59	34	y	y	PROPN
ejpam-6273	59	35	(	(	PUNCT
ejpam-6273	59	36	ii	ii	NOUN
ejpam-6273	59	37	)	)	PUNCT
ejpam-6273	59	38	ϱ̃(sq	ϱ̃(sq	NOUN
ejpam-6273	59	39	)	)	PUNCT
ejpam-6273	59	40	⊇	⊇	NOUN
ejpam-6273	59	41	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	59	42	)	)	PUNCT
ejpam-6273	59	43	∩	∩	NOUN
ejpam-6273	59	44	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	59	45	)	)	PUNCT
ejpam-6273	59	46	,	,	PUNCT
ejpam-6273	59	47	λ(sq	λ(sq	PROPN
ejpam-6273	59	48	)	)	PUNCT
ejpam-6273	59	49	≤	≤	NOUN
ejpam-6273	59	50	∨	∨	NUM
ejpam-6273	59	51	{	{	PUNCT
ejpam-6273	59	52	λ(s	λ(s	PROPN
ejpam-6273	59	53	)	)	PUNCT
ejpam-6273	59	54	,	,	PUNCT
ejpam-6273	59	55	γ(q)},∀s	γ(q)},∀s	PUNCT
ejpam-6273	59	56	∈	∈	PROPN
ejpam-6273	59	57	l	l	NOUN
ejpam-6273	59	58	,	,	PUNCT
ejpam-6273	59	59	q	q	PROPN
ejpam-6273	59	60	∈	∈	PROPN
ejpam-6273	59	61	y	y	PROPN
ejpam-6273	59	62	(	(	PUNCT
ejpam-6273	59	63	iii	iii	NOUN
ejpam-6273	59	64	)	)	PUNCT
ejpam-6273	59	65	ξ̃(1	ξ̃(1	NOUN
ejpam-6273	59	66	)	)	PUNCT
ejpam-6273	59	67	⊇	⊇	PROPN
ejpam-6273	59	68	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	59	69	)	)	PUNCT
ejpam-6273	59	70	,	,	PUNCT
ejpam-6273	59	71	λ(1	λ(1	PROPN
ejpam-6273	59	72	)	)	PUNCT
ejpam-6273	59	73	≤	≤	PUNCT
ejpam-6273	60	1	γ(q),∀q	γ(q),∀q	PROPN
ejpam-6273	60	2	∈	∈	PROPN
ejpam-6273	61	1	y	y	PROPN
ejpam-6273	61	2	p.	p.	PROPN
ejpam-6273	61	3	n.	n.	PROPN
ejpam-6273	61	4	swamy	swamy	PROPN
ejpam-6273	61	5	et	et	PROPN
ejpam-6273	61	6	al	al	PROPN
ejpam-6273	61	7	.	.	PUNCT
ejpam-6273	61	8	/	/	SYM
ejpam-6273	61	9	eur	eur	PROPN
ejpam-6273	61	10	.	.	PUNCT
ejpam-6273	62	1	j.	j.	PROPN
ejpam-6273	62	2	pure	pure	PROPN
ejpam-6273	62	3	appl	appl	PROPN
ejpam-6273	62	4	.	.	PROPN
ejpam-6273	62	5	math	math	PROPN
ejpam-6273	62	6	,	,	PUNCT
ejpam-6273	62	7	18	18	NUM
ejpam-6273	62	8	(	(	PUNCT
ejpam-6273	62	9	3	3	NUM
ejpam-6273	62	10	)	)	PUNCT
ejpam-6273	62	11	(	(	PUNCT
ejpam-6273	62	12	2025	2025	NUM
ejpam-6273	62	13	)	)	PUNCT
ejpam-6273	62	14	,	,	PUNCT
ejpam-6273	62	15	6273	6273	NUM
ejpam-6273	62	16	4	4	NUM
ejpam-6273	62	17	of	of	ADP
ejpam-6273	62	18	16	16	NUM
ejpam-6273	62	19	(	(	PUNCT
ejpam-6273	62	20	iv	iv	NOUN
ejpam-6273	62	21	)	)	PUNCT
ejpam-6273	62	22	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	62	23	)	)	PUNCT
ejpam-6273	62	24	⊇	⊇	PROPN
ejpam-6273	62	25	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	62	26	)	)	PUNCT
ejpam-6273	62	27	,	,	PUNCT
ejpam-6273	62	28	γ(qς	γ(qς	NOUN
ejpam-6273	62	29	)	)	PUNCT
ejpam-6273	62	30	≤	≤	NUM
ejpam-6273	62	31	γ(q	γ(q	NOUN
ejpam-6273	62	32	)	)	PUNCT
ejpam-6273	62	33	,	,	PUNCT
ejpam-6273	62	34	∀q	∀q	PROPN
ejpam-6273	62	35	,	,	PUNCT
ejpam-6273	62	36	ς	ς	PROPN
ejpam-6273	62	37	∈	∈	PROPN
ejpam-6273	62	38	y	y	PROPN
ejpam-6273	62	39	(	(	PUNCT
ejpam-6273	62	40	v	v	NOUN
ejpam-6273	62	41	)	)	PUNCT
ejpam-6273	62	42	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	62	43	+	+	PROPN
ejpam-6273	62	44	i)−	i)−	PROPN
ejpam-6273	62	45	ςq	ςq	PROPN
ejpam-6273	62	46	)	)	PUNCT
ejpam-6273	62	47	⊇	⊇	PROPN
ejpam-6273	62	48	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	62	49	)	)	PUNCT
ejpam-6273	62	50	,	,	PUNCT
ejpam-6273	62	51	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	62	52	+	+	PROPN
ejpam-6273	62	53	i)−	i)−	PROPN
ejpam-6273	62	54	ςq	ςq	PROPN
ejpam-6273	62	55	)	)	PUNCT
ejpam-6273	62	56	≤	≤	NOUN
ejpam-6273	63	1	γ(i),∀q	γ(i),∀q	PROPN
ejpam-6273	63	2	,	,	PUNCT
ejpam-6273	63	3	ς	ς	PROPN
ejpam-6273	63	4	,	,	PUNCT
ejpam-6273	63	5	i	i	PROPN
ejpam-6273	63	6	∈	∈	PROPN
ejpam-6273	63	7	y	y	PROPN
ejpam-6273	63	8	,	,	PUNCT
ejpam-6273	63	9	1	1	NUM
ejpam-6273	63	10	is	be	AUX
ejpam-6273	63	11	the	the	DET
ejpam-6273	63	12	unity	unity	NOUN
ejpam-6273	63	13	in	in	ADP
ejpam-6273	63	14	l.	l.	PROPN
ejpam-6273	63	15	if	if	SCONJ
ejpam-6273	63	16	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	63	17	satisfies	satisfy	VERB
ejpam-6273	63	18	(	(	PUNCT
ejpam-6273	63	19	i	i	NOUN
ejpam-6273	63	20	)	)	PUNCT
ejpam-6273	63	21	,	,	PUNCT
ejpam-6273	63	22	(	(	PUNCT
ejpam-6273	63	23	ii	ii	NOUN
ejpam-6273	63	24	)	)	PUNCT
ejpam-6273	63	25	,	,	PUNCT
ejpam-6273	63	26	(	(	PUNCT
ejpam-6273	63	27	iii	iii	NOUN
ejpam-6273	63	28	)	)	PUNCT
ejpam-6273	63	29	and	and	CCONJ
ejpam-6273	63	30	(	(	PUNCT
ejpam-6273	63	31	iv	iv	X
ejpam-6273	63	32	)	)	PUNCT
ejpam-6273	63	33	then	then	ADV
ejpam-6273	63	34	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	63	35	is	be	AUX
ejpam-6273	63	36	called	call	VERB
ejpam-6273	63	37	a	a	DET
ejpam-6273	63	38	right	right	ADJ
ejpam-6273	63	39	hina	hina	NOUN
ejpam-6273	63	40	of	of	ADP
ejpam-6273	63	41	y	y	PROPN
ejpam-6273	63	42	.	.	PUNCT
ejpam-6273	64	1	if	if	SCONJ
ejpam-6273	64	2	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	64	3	satisfies	satisfy	VERB
ejpam-6273	64	4	(	(	PUNCT
ejpam-6273	64	5	i	i	NOUN
ejpam-6273	64	6	)	)	PUNCT
ejpam-6273	64	7	,	,	PUNCT
ejpam-6273	64	8	(	(	PUNCT
ejpam-6273	64	9	ii	ii	NOUN
ejpam-6273	64	10	)	)	PUNCT
ejpam-6273	64	11	,	,	PUNCT
ejpam-6273	64	12	(	(	PUNCT
ejpam-6273	64	13	iii	iii	NOUN
ejpam-6273	64	14	)	)	PUNCT
ejpam-6273	64	15	and	and	CCONJ
ejpam-6273	64	16	(	(	PUNCT
ejpam-6273	64	17	v	v	NOUN
ejpam-6273	64	18	)	)	PUNCT
ejpam-6273	64	19	then	then	ADV
ejpam-6273	64	20	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	64	21	is	be	AUX
ejpam-6273	64	22	called	call	VERB
ejpam-6273	64	23	a	a	DET
ejpam-6273	64	24	left	left	ADJ
ejpam-6273	64	25	hina	hina	NOUN
ejpam-6273	64	26	of	of	ADP
ejpam-6273	64	27	y	y	PROPN
ejpam-6273	64	28	.	.	PUNCT
ejpam-6273	64	29	example	example	NOUN
ejpam-6273	65	1	1	1	NUM
ejpam-6273	65	2	.	.	PUNCT
ejpam-6273	65	3	let	let	VERB
ejpam-6273	65	4	l	l	NOUN
ejpam-6273	65	5	=	=	SYM
ejpam-6273	65	6	z2	z2	PROPN
ejpam-6273	65	7	=	=	SYM
ejpam-6273	65	8	{	{	PUNCT
ejpam-6273	65	9	0	0	NUM
ejpam-6273	65	10	,	,	PUNCT
ejpam-6273	65	11	1}⊕2,⊗2	1}⊕2,⊗2	NUM
ejpam-6273	65	12	be	be	AUX
ejpam-6273	65	13	a	a	DET
ejpam-6273	65	14	field	field	NOUN
ejpam-6273	65	15	.	.	PUNCT
ejpam-6273	66	1	the	the	DET
ejpam-6273	66	2	hs	hs	PROPN
ejpam-6273	66	3	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	66	4	in	in	ADP
ejpam-6273	66	5	l	l	PROPN
ejpam-6273	66	6	upon	upon	SCONJ
ejpam-6273	66	7	u	u	NOUN
ejpam-6273	66	8	=	=	NOUN
ejpam-6273	66	9	{	{	PUNCT
ejpam-6273	66	10	u1	u1	NOUN
ejpam-6273	66	11	,	,	PUNCT
ejpam-6273	66	12	u2	u2	NOUN
ejpam-6273	66	13	,	,	PUNCT
ejpam-6273	66	14	u3	u3	PROPN
ejpam-6273	66	15	,	,	PUNCT
ejpam-6273	66	16	u4	u4	PROPN
ejpam-6273	66	17	,	,	PUNCT
ejpam-6273	66	18	u5	u5	PROPN
ejpam-6273	66	19	}	}	PUNCT
ejpam-6273	66	20	is	be	AUX
ejpam-6273	66	21	given	give	VERB
ejpam-6273	66	22	by	by	ADP
ejpam-6273	66	23	l	l	NOUN
ejpam-6273	66	24	ξ̃	ξ̃	PROPN
ejpam-6273	66	25	λ	λ	PROPN
ejpam-6273	66	26	0	0	NUM
ejpam-6273	66	27	{	{	PUNCT
ejpam-6273	66	28	u1	u1	NOUN
ejpam-6273	66	29	,	,	PUNCT
ejpam-6273	66	30	u2	u2	NOUN
ejpam-6273	66	31	,	,	PUNCT
ejpam-6273	66	32	u3	u3	NOUN
ejpam-6273	66	33	,	,	PUNCT
ejpam-6273	66	34	u4	u4	PROPN
ejpam-6273	66	35	}	}	PUNCT
ejpam-6273	66	36	0.4	0.4	NUM
ejpam-6273	66	37	1	1	NUM
ejpam-6273	66	38	{	{	PUNCT
ejpam-6273	66	39	u3	u3	PROPN
ejpam-6273	66	40	,	,	PUNCT
ejpam-6273	66	41	u4	u4	PROPN
ejpam-6273	66	42	,	,	PUNCT
ejpam-6273	66	43	u5	u5	PROPN
ejpam-6273	66	44	}	}	PUNCT
ejpam-6273	66	45	0.5	0.5	NUM
ejpam-6273	66	46	then	then	ADV
ejpam-6273	66	47	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	66	48	is	be	AUX
ejpam-6273	66	49	an	an	DET
ejpam-6273	66	50	hf	hf	NOUN
ejpam-6273	66	51	in	in	ADP
ejpam-6273	66	52	l	l	PROPN
ejpam-6273	66	53	upon	upon	SCONJ
ejpam-6273	66	54	u	u	NOUN
ejpam-6273	66	55	.	.	PUNCT
ejpam-6273	67	1	let	let	VERB
ejpam-6273	67	2	y	y	PROPN
ejpam-6273	67	3	=	=	PUNCT
ejpam-6273	67	4	{	{	PUNCT
ejpam-6273	67	5	0	0	PROPN
ejpam-6273	67	6	,	,	PUNCT
ejpam-6273	67	7	a3	a3	NOUN
ejpam-6273	67	8	,	,	PUNCT
ejpam-6273	67	9	b3	b3	PROPN
ejpam-6273	67	10	,	,	PUNCT
ejpam-6273	67	11	c3	c3	PROPN
ejpam-6273	67	12	}	}	PUNCT
ejpam-6273	67	13	be	be	VERB
ejpam-6273	67	14	a	a	DET
ejpam-6273	67	15	set	set	NOUN
ejpam-6273	67	16	with	with	ADP
ejpam-6273	67	17	two	two	NUM
ejpam-6273	67	18	binary	binary	ADJ
ejpam-6273	67	19	operations	operation	NOUN
ejpam-6273	67	20	+	+	CCONJ
ejpam-6273	67	21	by	by	ADP
ejpam-6273	67	22	+	+	SYM
ejpam-6273	67	23	0	0	NUM
ejpam-6273	67	24	a3	a3	NOUN
ejpam-6273	67	25	b3	b3	PROPN
ejpam-6273	67	26	c3	c3	NOUN
ejpam-6273	67	27	0	0	NUM
ejpam-6273	67	28	0	0	NUM
ejpam-6273	67	29	a3	a3	NOUN
ejpam-6273	67	30	b3	b3	PROPN
ejpam-6273	67	31	c3	c3	PROPN
ejpam-6273	67	32	a3	a3	PROPN
ejpam-6273	67	33	a3	a3	PROPN
ejpam-6273	67	34	0	0	NUM
ejpam-6273	68	1	c3	c3	PROPN
ejpam-6273	68	2	b3	b3	PROPN
ejpam-6273	68	3	b3	b3	PROPN
ejpam-6273	68	4	b3	b3	PROPN
ejpam-6273	68	5	c3	c3	NOUN
ejpam-6273	68	6	0	0	NUM
ejpam-6273	68	7	a3	a3	PROPN
ejpam-6273	68	8	c3	c3	PROPN
ejpam-6273	68	9	c3	c3	PROPN
ejpam-6273	68	10	b3	b3	PROPN
ejpam-6273	68	11	a3	a3	NOUN
ejpam-6273	68	12	0	0	NUM
ejpam-6273	68	13	.	.	PUNCT
ejpam-6273	68	14	0	0	NUM
ejpam-6273	68	15	a3	a3	NOUN
ejpam-6273	68	16	b3	b3	PROPN
ejpam-6273	68	17	c3	c3	X
ejpam-6273	68	18	0	0	NUM
ejpam-6273	68	19	0	0	NUM
ejpam-6273	68	20	0	0	NUM
ejpam-6273	68	21	0	0	SYM
ejpam-6273	68	22	0	0	NUM
ejpam-6273	68	23	a3	a3	NOUN
ejpam-6273	68	24	a3	a3	PROPN
ejpam-6273	68	25	a3	a3	PROPN
ejpam-6273	68	26	a3	a3	PROPN
ejpam-6273	68	27	a3	a3	PROPN
ejpam-6273	68	28	b3	b3	PROPN
ejpam-6273	68	29	b3	b3	PROPN
ejpam-6273	68	30	b3	b3	PROPN
ejpam-6273	68	31	b3	b3	PROPN
ejpam-6273	68	32	b3	b3	PROPN
ejpam-6273	68	33	c3	c3	PROPN
ejpam-6273	68	34	c3	c3	PROPN
ejpam-6273	68	35	c3	c3	PROPN
ejpam-6273	68	36	c3	c3	PROPN
ejpam-6273	68	37	c3	c3	PROPN
ejpam-6273	68	38	clearly	clearly	ADV
ejpam-6273	68	39	,	,	PUNCT
ejpam-6273	68	40	y	y	PROPN
ejpam-6273	68	41	forms	form	VERB
ejpam-6273	68	42	an	an	DET
ejpam-6273	68	43	na	na	NOUN
ejpam-6273	68	44	over	over	ADP
ejpam-6273	68	45	l.	l.	PROPN
ejpam-6273	68	46	the	the	DET
ejpam-6273	68	47	hs	hs	PROPN
ejpam-6273	68	48	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	68	49	in	in	ADP
ejpam-6273	68	50	y	y	PROPN
ejpam-6273	68	51	upon	upon	SCONJ
ejpam-6273	68	52	u	u	NOUN
ejpam-6273	68	53	=	=	NOUN
ejpam-6273	68	54	{	{	PUNCT
ejpam-6273	68	55	u1	u1	NOUN
ejpam-6273	68	56	,	,	PUNCT
ejpam-6273	68	57	u2	u2	NOUN
ejpam-6273	68	58	,	,	PUNCT
ejpam-6273	68	59	u3	u3	PROPN
ejpam-6273	68	60	,	,	PUNCT
ejpam-6273	68	61	u4	u4	PROPN
ejpam-6273	68	62	,	,	PUNCT
ejpam-6273	68	63	u5	u5	PROPN
ejpam-6273	68	64	}	}	PUNCT
ejpam-6273	68	65	is	be	AUX
ejpam-6273	68	66	given	give	VERB
ejpam-6273	68	67	as	as	SCONJ
ejpam-6273	68	68	follows	follow	VERB
ejpam-6273	68	69	:	:	PUNCT
ejpam-6273	68	70	y	y	PROPN
ejpam-6273	68	71	ϱ̃	ϱ̃	PROPN
ejpam-6273	68	72	γ	γ	X
ejpam-6273	68	73	0	0	NUM
ejpam-6273	68	74	{	{	PUNCT
ejpam-6273	68	75	u1	u1	PROPN
ejpam-6273	68	76	,	,	PUNCT
ejpam-6273	68	77	u4	u4	PROPN
ejpam-6273	68	78	,	,	PUNCT
ejpam-6273	68	79	u5	u5	PROPN
ejpam-6273	68	80	}	}	PUNCT
ejpam-6273	68	81	0.5	0.5	NUM
ejpam-6273	68	82	a3	a3	NOUN
ejpam-6273	68	83	{	{	PUNCT
ejpam-6273	68	84	u1	u1	NOUN
ejpam-6273	68	85	,	,	PUNCT
ejpam-6273	68	86	u2	u2	PROPN
ejpam-6273	68	87	}	}	PUNCT
ejpam-6273	68	88	0.6	0.6	NUM
ejpam-6273	68	89	b3	b3	PROPN
ejpam-6273	68	90	{	{	PUNCT
ejpam-6273	68	91	u1	u1	NOUN
ejpam-6273	68	92	,	,	PUNCT
ejpam-6273	68	93	u3	u3	PROPN
ejpam-6273	68	94	,	,	PUNCT
ejpam-6273	68	95	u4	u4	PROPN
ejpam-6273	68	96	}	}	PUNCT
ejpam-6273	68	97	0.8	0.8	NUM
ejpam-6273	68	98	c3	c3	PROPN
ejpam-6273	68	99	{	{	PUNCT
ejpam-6273	68	100	u1	u1	PROPN
ejpam-6273	68	101	,	,	PUNCT
ejpam-6273	68	102	u4	u4	PROPN
ejpam-6273	68	103	}	}	PUNCT
ejpam-6273	68	104	0.9	0.9	NUM
ejpam-6273	68	105	therefore	therefore	ADV
ejpam-6273	68	106	,	,	PUNCT
ejpam-6273	68	107	(	(	PUNCT
ejpam-6273	68	108	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	68	109	,	,	PUNCT
ejpam-6273	68	110	y	y	PROPN
ejpam-6273	68	111	)	)	PUNCT
ejpam-6273	68	112	is	be	AUX
ejpam-6273	68	113	an	an	DET
ejpam-6273	68	114	hina	hina	NOUN
ejpam-6273	68	115	upon	upon	SCONJ
ejpam-6273	68	116	(	(	PUNCT
ejpam-6273	68	117	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	68	118	,	,	PUNCT
ejpam-6273	68	119	l	l	NOUN
ejpam-6273	68	120	)	)	PUNCT
ejpam-6273	68	121	.	.	PUNCT
ejpam-6273	69	1	theorem	theorem	NOUN
ejpam-6273	69	2	1	1	NUM
ejpam-6273	69	3	.	.	PUNCT
ejpam-6273	69	4	(	(	PUNCT
ejpam-6273	69	5	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	69	6	,	,	PUNCT
ejpam-6273	69	7	y	y	PROPN
ejpam-6273	69	8	)	)	PUNCT
ejpam-6273	69	9	is	be	AUX
ejpam-6273	69	10	an	an	DET
ejpam-6273	69	11	hina	hina	NOUN
ejpam-6273	69	12	upon	upon	SCONJ
ejpam-6273	69	13	an	an	DET
ejpam-6273	69	14	hf	hf	NOUN
ejpam-6273	69	15	(	(	PUNCT
ejpam-6273	69	16	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	69	17	,	,	PUNCT
ejpam-6273	69	18	l	l	NOUN
ejpam-6273	69	19	)	)	PUNCT
ejpam-6273	69	20	if	if	SCONJ
ejpam-6273	69	21	and	and	CCONJ
ejpam-6273	69	22	only	only	ADV
ejpam-6273	69	23	if	if	SCONJ
ejpam-6273	69	24	nonempty	nonempty	ADV
ejpam-6273	69	25	set	set	VERB
ejpam-6273	69	26	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	70	1	[	[	X
ejpam-6273	70	2	α	α	X
ejpam-6273	70	3	,	,	PUNCT
ejpam-6273	70	4	t	t	PROPN
ejpam-6273	70	5	]	]	PUNCT
ejpam-6273	70	6	is	be	AUX
ejpam-6273	70	7	an	an	DET
ejpam-6273	70	8	ideal	ideal	NOUN
ejpam-6273	70	9	of	of	ADP
ejpam-6273	70	10	y	y	PROPN
ejpam-6273	70	11	upon	upon	SCONJ
ejpam-6273	70	12	the	the	DET
ejpam-6273	70	13	field	field	NOUN
ejpam-6273	70	14	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	70	15	,	,	PUNCT
ejpam-6273	70	16	t],∀t	t],∀t	X
ejpam-6273	70	17	∈	∈	PROPN
ejpam-6273	71	1	[	[	X
ejpam-6273	71	2	0	0	NUM
ejpam-6273	71	3	,	,	PUNCT
ejpam-6273	71	4	1	1	NUM
ejpam-6273	71	5	]	]	PUNCT
ejpam-6273	71	6	,	,	PUNCT
ejpam-6273	71	7	α	α	PROPN
ejpam-6273	71	8	∈	∈	PROPN
ejpam-6273	71	9	p	p	X
ejpam-6273	71	10	(	(	PUNCT
ejpam-6273	71	11	u	u	NOUN
ejpam-6273	71	12	)	)	PUNCT
ejpam-6273	71	13	.	.	PUNCT
ejpam-6273	72	1	proof	proof	NOUN
ejpam-6273	72	2	.	.	PUNCT
ejpam-6273	73	1	let	let	VERB
ejpam-6273	73	2	t	t	PROPN
ejpam-6273	73	3	∈	∈	PROPN
ejpam-6273	74	1	[	[	X
ejpam-6273	74	2	0	0	NUM
ejpam-6273	74	3	,	,	PUNCT
ejpam-6273	74	4	1	1	NUM
ejpam-6273	74	5	]	]	PUNCT
ejpam-6273	74	6	be	be	AUX
ejpam-6273	74	7	such	such	ADJ
ejpam-6273	74	8	that	that	SCONJ
ejpam-6273	74	9	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	75	1	[	[	X
ejpam-6273	75	2	α	α	X
ejpam-6273	75	3	,	,	PUNCT
ejpam-6273	75	4	t	t	PROPN
ejpam-6273	75	5	]	]	X
ejpam-6273	75	6	̸=	̸=	PROPN
ejpam-6273	75	7	∅	∅	NOUN
ejpam-6273	75	8	and	and	CCONJ
ejpam-6273	75	9	q	q	NOUN
ejpam-6273	75	10	,	,	PUNCT
ejpam-6273	75	11	ς	ς	PROPN
ejpam-6273	75	12	∈	∈	PROPN
ejpam-6273	75	13	ϱ̃γ	ϱ̃γ	PUNCT
ejpam-6273	76	1	[	[	X
ejpam-6273	76	2	α	α	X
ejpam-6273	76	3	,	,	PUNCT
ejpam-6273	76	4	t	t	PROPN
ejpam-6273	76	5	]	]	PUNCT
ejpam-6273	76	6	,	,	PUNCT
ejpam-6273	76	7	s	s	PROPN
ejpam-6273	76	8	∈	∈	PROPN
ejpam-6273	76	9	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	76	10	,	,	PUNCT
ejpam-6273	76	11	t	t	X
ejpam-6273	76	12	]	]	PUNCT
ejpam-6273	76	13	.	.	PUNCT
ejpam-6273	77	1	then	then	ADV
ejpam-6273	77	2	q	q	X
ejpam-6273	77	3	,	,	PUNCT
ejpam-6273	77	4	ς	ς	PROPN
ejpam-6273	77	5	∈	∈	PROPN
ejpam-6273	77	6	y	y	PROPN
ejpam-6273	77	7	,	,	PUNCT
ejpam-6273	77	8	s	s	PROPN
ejpam-6273	77	9	∈	∈	PROPN
ejpam-6273	77	10	l	l	NOUN
ejpam-6273	77	11	and	and	CCONJ
ejpam-6273	77	12	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	77	13	)	)	PUNCT
ejpam-6273	77	14	⊇	⊇	NOUN
ejpam-6273	77	15	α	α	NOUN
ejpam-6273	77	16	,	,	PUNCT
ejpam-6273	77	17	γ(q	γ(q	PROPN
ejpam-6273	77	18	)	)	PUNCT
ejpam-6273	77	19	≤	≤	NOUN
ejpam-6273	77	20	t	t	PROPN
ejpam-6273	77	21	,	,	PUNCT
ejpam-6273	77	22	ϱ̃(ς	ϱ̃(ς	PROPN
ejpam-6273	77	23	)	)	PUNCT
ejpam-6273	77	24	⊇	⊇	NOUN
ejpam-6273	77	25	α	α	NOUN
ejpam-6273	77	26	,	,	PUNCT
ejpam-6273	77	27	γ(ς	γ(ς	NOUN
ejpam-6273	77	28	)	)	PUNCT
ejpam-6273	77	29	≤	≤	NOUN
ejpam-6273	77	30	t	t	PROPN
ejpam-6273	77	31	,	,	PUNCT
ejpam-6273	77	32	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	77	33	)	)	PUNCT
ejpam-6273	77	34	⊇	⊇	NOUN
ejpam-6273	77	35	α	α	NOUN
ejpam-6273	77	36	,	,	PUNCT
ejpam-6273	77	37	λ(s	λ(s	PROPN
ejpam-6273	77	38	)	)	PUNCT
ejpam-6273	77	39	≤	≤	NOUN
ejpam-6273	77	40	t	t	PROPN
ejpam-6273	77	41	,	,	PUNCT
ejpam-6273	77	42	so	so	SCONJ
ejpam-6273	77	43	that	that	SCONJ
ejpam-6273	77	44	q−ς	q−ς	ADJ
ejpam-6273	77	45	∈	∈	PROPN
ejpam-6273	77	46	y	y	NOUN
ejpam-6273	77	47	and	and	CCONJ
ejpam-6273	77	48	sq	sq	PROPN
ejpam-6273	77	49	∈	∈	PROPN
ejpam-6273	77	50	y	y	PROPN
ejpam-6273	77	51	.	.	PUNCT
ejpam-6273	78	1	also	also	ADV
ejpam-6273	78	2	,	,	PUNCT
ejpam-6273	78	3	ϱ̃(q−ς	ϱ̃(q−ς	X
ejpam-6273	78	4	)	)	PUNCT
ejpam-6273	78	5	⊇	⊇	PROPN
ejpam-6273	78	6	ϱ̃(q)∩ϱ̃(ς	ϱ̃(q)∩ϱ̃(ς	PROPN
ejpam-6273	78	7	)	)	PUNCT
ejpam-6273	78	8	⊇	⊇	PROPN
ejpam-6273	78	9	α∩α	α∩α	NUM
ejpam-6273	78	10	=	=	SYM
ejpam-6273	78	11	α	α	PROPN
ejpam-6273	78	12	and	and	CCONJ
ejpam-6273	78	13	γ(q−ς	γ(q−ς	NOUN
ejpam-6273	78	14	)	)	PUNCT
ejpam-6273	78	15	≤	≤	NOUN
ejpam-6273	78	16	∨	∨	NUM
ejpam-6273	78	17	{	{	PUNCT
ejpam-6273	78	18	γ(q	γ(q	NOUN
ejpam-6273	78	19	)	)	PUNCT
ejpam-6273	78	20	,	,	PUNCT
ejpam-6273	78	21	γ(ς	γ(ς	NOUN
ejpam-6273	78	22	)	)	PUNCT
ejpam-6273	78	23	}	}	PUNCT
ejpam-6273	78	24	≤	≤	NUM
ejpam-6273	78	25	∨	∨	NUM
ejpam-6273	78	26	{	{	PUNCT
ejpam-6273	78	27	t	t	PROPN
ejpam-6273	78	28	,	,	PUNCT
ejpam-6273	78	29	t	t	PROPN
ejpam-6273	78	30	}	}	PUNCT
ejpam-6273	78	31	=	=	PUNCT
ejpam-6273	78	32	t.	t.	PROPN
ejpam-6273	78	33	p.	p.	PROPN
ejpam-6273	78	34	n.	n.	PROPN
ejpam-6273	78	35	swamy	swamy	PROPN
ejpam-6273	78	36	et	et	PROPN
ejpam-6273	78	37	al	al	PROPN
ejpam-6273	78	38	.	.	PUNCT
ejpam-6273	78	39	/	/	SYM
ejpam-6273	78	40	eur	eur	PROPN
ejpam-6273	78	41	.	.	PUNCT
ejpam-6273	79	1	j.	j.	PROPN
ejpam-6273	79	2	pure	pure	PROPN
ejpam-6273	79	3	appl	appl	PROPN
ejpam-6273	79	4	.	.	PROPN
ejpam-6273	79	5	math	math	PROPN
ejpam-6273	79	6	,	,	PUNCT
ejpam-6273	79	7	18	18	NUM
ejpam-6273	79	8	(	(	PUNCT
ejpam-6273	79	9	3	3	NUM
ejpam-6273	79	10	)	)	PUNCT
ejpam-6273	79	11	(	(	PUNCT
ejpam-6273	79	12	2025	2025	NUM
ejpam-6273	79	13	)	)	PUNCT
ejpam-6273	79	14	,	,	PUNCT
ejpam-6273	79	15	6273	6273	NUM
ejpam-6273	79	16	5	5	NUM
ejpam-6273	79	17	of	of	ADP
ejpam-6273	79	18	16	16	NUM
ejpam-6273	79	19	also	also	ADV
ejpam-6273	79	20	,	,	PUNCT
ejpam-6273	79	21	ϱ̃(sq	ϱ̃(sq	NOUN
ejpam-6273	79	22	)	)	PUNCT
ejpam-6273	79	23	⊇	⊇	NOUN
ejpam-6273	79	24	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	79	25	)	)	PUNCT
ejpam-6273	79	26	∩	∩	ADJ
ejpam-6273	79	27	ϱ̃(q	ϱ̃(q	ADJ
ejpam-6273	79	28	)	)	PUNCT
ejpam-6273	79	29	⊇	⊇	NOUN
ejpam-6273	79	30	α	α	PROPN
ejpam-6273	79	31	∩	∩	ADJ
ejpam-6273	79	32	α	α	NOUN
ejpam-6273	79	33	=	=	SYM
ejpam-6273	79	34	α	α	PROPN
ejpam-6273	79	35	and	and	CCONJ
ejpam-6273	79	36	γ(sq	γ(sq	PROPN
ejpam-6273	79	37	)	)	PUNCT
ejpam-6273	79	38	≤	≤	NUM
ejpam-6273	79	39	∨	∨	NUM
ejpam-6273	79	40	{	{	PUNCT
ejpam-6273	79	41	λ(s	λ(s	PROPN
ejpam-6273	79	42	)	)	PUNCT
ejpam-6273	79	43	,	,	PUNCT
ejpam-6273	79	44	γ(q	γ(q	PROPN
ejpam-6273	79	45	)	)	PUNCT
ejpam-6273	79	46	}	}	PUNCT
ejpam-6273	79	47	≤	≤	NUM
ejpam-6273	79	48	∨	∨	NUM
ejpam-6273	79	49	{	{	PUNCT
ejpam-6273	79	50	t	t	PROPN
ejpam-6273	79	51	,	,	PUNCT
ejpam-6273	79	52	t	t	PROPN
ejpam-6273	79	53	}	}	PUNCT
ejpam-6273	79	54	=	=	SYM
ejpam-6273	79	55	t.	t.	NOUN
ejpam-6273	79	56	thus	thus	ADV
ejpam-6273	79	57	,	,	PUNCT
ejpam-6273	79	58	q	q	PROPN
ejpam-6273	79	59	−	−	PROPN
ejpam-6273	79	60	ς	ς	PROPN
ejpam-6273	79	61	∈	∈	PROPN
ejpam-6273	79	62	ϱ̃γ	ϱ̃γ	PUNCT
ejpam-6273	80	1	[	[	X
ejpam-6273	80	2	α	α	X
ejpam-6273	80	3	,	,	PUNCT
ejpam-6273	80	4	t	t	PROPN
ejpam-6273	80	5	]	]	PUNCT
ejpam-6273	80	6	and	and	CCONJ
ejpam-6273	80	7	sq	sq	PROPN
ejpam-6273	80	8	∈	∈	PROPN
ejpam-6273	80	9	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	81	1	[	[	X
ejpam-6273	81	2	α	α	X
ejpam-6273	81	3	,	,	PUNCT
ejpam-6273	81	4	t	t	PROPN
ejpam-6273	81	5	]	]	PUNCT
ejpam-6273	81	6	.	.	PUNCT
ejpam-6273	82	1	hence	hence	ADV
ejpam-6273	82	2	,	,	PUNCT
ejpam-6273	82	3	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	83	1	[	[	X
ejpam-6273	83	2	α	α	X
ejpam-6273	83	3	,	,	PUNCT
ejpam-6273	83	4	t	t	PROPN
ejpam-6273	83	5	]	]	PUNCT
ejpam-6273	83	6	is	be	AUX
ejpam-6273	83	7	a	a	DET
ejpam-6273	83	8	subspace	subspace	NOUN
ejpam-6273	83	9	of	of	ADP
ejpam-6273	83	10	the	the	DET
ejpam-6273	83	11	linear	linear	ADJ
ejpam-6273	83	12	space	space	NOUN
ejpam-6273	83	13	y	y	NOUN
ejpam-6273	83	14	over	over	ADP
ejpam-6273	83	15	a	a	DET
ejpam-6273	83	16	field	field	NOUN
ejpam-6273	83	17	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	83	18	,	,	PUNCT
ejpam-6273	83	19	t	t	X
ejpam-6273	83	20	]	]	PUNCT
ejpam-6273	83	21	.	.	PUNCT
ejpam-6273	84	1	suppose	suppose	VERB
ejpam-6273	84	2	that	that	SCONJ
ejpam-6273	84	3	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	84	4	,	,	PUNCT
ejpam-6273	84	5	t	t	X
ejpam-6273	84	6	]	]	X
ejpam-6273	84	7	̸=	̸=	PROPN
ejpam-6273	84	8	∅.	∅.	ADV
ejpam-6273	84	9	we	we	PRON
ejpam-6273	84	10	know	know	VERB
ejpam-6273	84	11	that	that	SCONJ
ejpam-6273	84	12	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	84	13	,	,	PUNCT
ejpam-6273	84	14	t	t	PROPN
ejpam-6273	84	15	]	]	PUNCT
ejpam-6273	84	16	is	be	AUX
ejpam-6273	84	17	a	a	DET
ejpam-6273	84	18	subfield	subfield	NOUN
ejpam-6273	84	19	of	of	ADP
ejpam-6273	84	20	l.	l.	PROPN
ejpam-6273	84	21	let	let	VERB
ejpam-6273	84	22	q	q	PROPN
ejpam-6273	84	23	∈	∈	PROPN
ejpam-6273	84	24	y	y	PROPN
ejpam-6273	84	25	,	,	PUNCT
ejpam-6273	84	26	i	i	PRON
ejpam-6273	84	27	∈	∈	PROPN
ejpam-6273	84	28	ϱ̃γ	ϱ̃γ	PUNCT
ejpam-6273	85	1	[	[	X
ejpam-6273	85	2	α	α	X
ejpam-6273	85	3	,	,	PUNCT
ejpam-6273	85	4	t	t	PROPN
ejpam-6273	85	5	]	]	PUNCT
ejpam-6273	85	6	.	.	PUNCT
ejpam-6273	86	1	then	then	ADV
ejpam-6273	86	2	i	i	PRON
ejpam-6273	86	3	∈	∈	PROPN
ejpam-6273	86	4	y	y	PROPN
ejpam-6273	86	5	and	and	CCONJ
ejpam-6273	86	6	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	86	7	)	)	PUNCT
ejpam-6273	86	8	⊇	⊇	NOUN
ejpam-6273	86	9	α	α	NOUN
ejpam-6273	86	10	,	,	PUNCT
ejpam-6273	86	11	γ(i	γ(i	NOUN
ejpam-6273	86	12	)	)	PUNCT
ejpam-6273	86	13	≤	≤	NOUN
ejpam-6273	87	1	t.	t.	PROPN
ejpam-6273	87	2	thus	thus	ADV
ejpam-6273	87	3	,	,	PUNCT
ejpam-6273	87	4	i	i	PRON
ejpam-6273	87	5	,	,	PUNCT
ejpam-6273	87	6	q	q	PROPN
ejpam-6273	87	7	∈	∈	PROPN
ejpam-6273	87	8	y	y	PROPN
ejpam-6273	87	9	,	,	PUNCT
ejpam-6273	87	10	iq	iq	PROPN
ejpam-6273	87	11	∈	∈	PROPN
ejpam-6273	87	12	y	y	PROPN
ejpam-6273	87	13	and	and	CCONJ
ejpam-6273	87	14	ϱ̃(iq	ϱ̃(iq	VERB
ejpam-6273	87	15	)	)	PUNCT
ejpam-6273	87	16	⊇	⊇	PROPN
ejpam-6273	87	17	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	87	18	)	)	PUNCT
ejpam-6273	87	19	⊇	⊇	NOUN
ejpam-6273	87	20	α	α	NOUN
ejpam-6273	87	21	,	,	PUNCT
ejpam-6273	87	22	γ(iq	γ(iq	PROPN
ejpam-6273	87	23	)	)	PUNCT
ejpam-6273	87	24	≤	≤	NUM
ejpam-6273	87	25	γ(i	γ(i	NOUN
ejpam-6273	87	26	)	)	PUNCT
ejpam-6273	87	27	≤	≤	NOUN
ejpam-6273	88	1	t.	t.	PROPN
ejpam-6273	88	2	thus	thus	ADV
ejpam-6273	88	3	,	,	PUNCT
ejpam-6273	88	4	iq	iq	PROPN
ejpam-6273	88	5	∈	∈	PROPN
ejpam-6273	88	6	ϱ̃γ	ϱ̃γ	PUNCT
ejpam-6273	89	1	[	[	X
ejpam-6273	89	2	α	α	X
ejpam-6273	89	3	,	,	PUNCT
ejpam-6273	89	4	t	t	PROPN
ejpam-6273	89	5	]	]	PUNCT
ejpam-6273	89	6	.	.	PUNCT
ejpam-6273	90	1	let	let	VERB
ejpam-6273	90	2	q	q	X
ejpam-6273	90	3	,	,	PUNCT
ejpam-6273	90	4	ς	ς	PROPN
ejpam-6273	90	5	∈	∈	PROPN
ejpam-6273	90	6	y	y	PROPN
ejpam-6273	90	7	,	,	PUNCT
ejpam-6273	90	8	i	i	PRON
ejpam-6273	90	9	∈	∈	PROPN
ejpam-6273	90	10	ϱ̃γ	ϱ̃γ	PUNCT
ejpam-6273	91	1	[	[	X
ejpam-6273	91	2	α	α	X
ejpam-6273	91	3	,	,	PUNCT
ejpam-6273	91	4	t	t	PROPN
ejpam-6273	91	5	]	]	PUNCT
ejpam-6273	91	6	.	.	PUNCT
ejpam-6273	92	1	then	then	ADV
ejpam-6273	92	2	i	i	PRON
ejpam-6273	92	3	∈	∈	PROPN
ejpam-6273	92	4	y	y	PROPN
ejpam-6273	92	5	and	and	CCONJ
ejpam-6273	92	6	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	92	7	)	)	PUNCT
ejpam-6273	92	8	⊇	⊇	NOUN
ejpam-6273	92	9	α	α	NOUN
ejpam-6273	92	10	,	,	PUNCT
ejpam-6273	92	11	γ(i	γ(i	NOUN
ejpam-6273	92	12	)	)	PUNCT
ejpam-6273	92	13	≤	≤	NOUN
ejpam-6273	93	1	t.	t.	PROPN
ejpam-6273	93	2	thus	thus	ADV
ejpam-6273	93	3	,	,	PUNCT
ejpam-6273	93	4	i	i	PRON
ejpam-6273	93	5	,	,	PUNCT
ejpam-6273	93	6	q	q	X
ejpam-6273	93	7	,	,	PUNCT
ejpam-6273	93	8	ς	ς	PROPN
ejpam-6273	93	9	∈	∈	PROPN
ejpam-6273	93	10	y	y	PROPN
ejpam-6273	93	11	,	,	PUNCT
ejpam-6273	93	12	ς(q	ς(q	PROPN
ejpam-6273	93	13	+	+	NUM
ejpam-6273	93	14	i	i	NOUN
ejpam-6273	93	15	)	)	PUNCT
ejpam-6273	94	1	−	−	PROPN
ejpam-6273	94	2	ςq	ςq	ADP
ejpam-6273	94	3	∈	∈	PROPN
ejpam-6273	94	4	y	y	PROPN
ejpam-6273	94	5	and	and	CCONJ
ejpam-6273	94	6	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	94	7	+	+	PROPN
ejpam-6273	94	8	i	i	NOUN
ejpam-6273	94	9	)	)	PUNCT
ejpam-6273	95	1	−	−	PROPN
ejpam-6273	95	2	ςq	ςq	NOUN
ejpam-6273	95	3	)	)	PUNCT
ejpam-6273	95	4	⊇	⊇	PROPN
ejpam-6273	95	5	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	95	6	)	)	PUNCT
ejpam-6273	95	7	⊇	⊇	NOUN
ejpam-6273	95	8	α	α	NOUN
ejpam-6273	95	9	,	,	PUNCT
ejpam-6273	95	10	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	95	11	+	+	PROPN
ejpam-6273	95	12	i	i	NOUN
ejpam-6273	95	13	)	)	PUNCT
ejpam-6273	96	1	−	−	ADP
ejpam-6273	96	2	ςq	ςq	NOUN
ejpam-6273	96	3	)	)	PUNCT
ejpam-6273	96	4	≤	≤	NUM
ejpam-6273	96	5	γ(i	γ(i	NOUN
ejpam-6273	96	6	)	)	PUNCT
ejpam-6273	96	7	≤	≤	NOUN
ejpam-6273	96	8	t.	t.	PROPN
ejpam-6273	96	9	thus	thus	ADV
ejpam-6273	96	10	,	,	PUNCT
ejpam-6273	96	11	ς(q	ς(q	PROPN
ejpam-6273	96	12	+	+	NUM
ejpam-6273	96	13	i	i	NOUN
ejpam-6273	96	14	)	)	PUNCT
ejpam-6273	97	1	−	−	PROPN
ejpam-6273	97	2	ςq	ςq	ADP
ejpam-6273	97	3	∈	∈	NOUN
ejpam-6273	97	4	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	98	1	[	[	X
ejpam-6273	98	2	α	α	X
ejpam-6273	98	3	,	,	PUNCT
ejpam-6273	98	4	t	t	PROPN
ejpam-6273	98	5	]	]	PUNCT
ejpam-6273	98	6	.	.	PUNCT
ejpam-6273	99	1	hence	hence	ADV
ejpam-6273	99	2	,	,	PUNCT
ejpam-6273	99	3	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	100	1	[	[	X
ejpam-6273	100	2	α	α	X
ejpam-6273	100	3	,	,	PUNCT
ejpam-6273	100	4	t	t	PROPN
ejpam-6273	100	5	]	]	PUNCT
ejpam-6273	100	6	is	be	AUX
ejpam-6273	100	7	an	an	DET
ejpam-6273	100	8	ideal	ideal	NOUN
ejpam-6273	100	9	of	of	ADP
ejpam-6273	100	10	y	y	PROPN
ejpam-6273	100	11	over	over	ADP
ejpam-6273	100	12	a	a	DET
ejpam-6273	100	13	field	field	NOUN
ejpam-6273	100	14	ξ̃λ[α	ξ̃λ[α	NOUN
ejpam-6273	100	15	,	,	PUNCT
ejpam-6273	100	16	t	t	X
ejpam-6273	100	17	]	]	PUNCT
ejpam-6273	100	18	.	.	PUNCT
ejpam-6273	101	1	conversely	conversely	ADV
ejpam-6273	101	2	,	,	PUNCT
ejpam-6273	101	3	suppose	suppose	VERB
ejpam-6273	101	4	that	that	SCONJ
ejpam-6273	101	5	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	101	6	[	[	X
ejpam-6273	101	7	α	α	X
ejpam-6273	101	8	,	,	PUNCT
ejpam-6273	101	9	t	t	PROPN
ejpam-6273	101	10	]	]	X
ejpam-6273	101	11	̸=	̸=	PROPN
ejpam-6273	101	12	∅	∅	NOUN
ejpam-6273	101	13	is	be	AUX
ejpam-6273	101	14	an	an	DET
ejpam-6273	101	15	ideal	ideal	NOUN
ejpam-6273	101	16	of	of	ADP
ejpam-6273	101	17	y	y	PROPN
ejpam-6273	101	18	.	.	PUNCT
ejpam-6273	102	1	since	since	SCONJ
ejpam-6273	102	2	(	(	PUNCT
ejpam-6273	102	3	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	102	4	,	,	PUNCT
ejpam-6273	102	5	y	y	PROPN
ejpam-6273	102	6	)	)	PUNCT
ejpam-6273	102	7	is	be	AUX
ejpam-6273	102	8	an	an	DET
ejpam-6273	102	9	hna	hna	PROPN
ejpam-6273	102	10	upon	upon	SCONJ
ejpam-6273	102	11	(	(	PUNCT
ejpam-6273	102	12	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	102	13	,	,	PUNCT
ejpam-6273	102	14	l	l	NOUN
ejpam-6273	102	15	)	)	PUNCT
ejpam-6273	102	16	,	,	PUNCT
ejpam-6273	102	17	the	the	DET
ejpam-6273	102	18	first	first	ADJ
ejpam-6273	102	19	three	three	NUM
ejpam-6273	102	20	conditions	condition	NOUN
ejpam-6273	102	21	of	of	ADP
ejpam-6273	102	22	hina	hina	NOUN
ejpam-6273	102	23	holds	hold	VERB
ejpam-6273	102	24	directly	directly	ADV
ejpam-6273	102	25	.	.	PUNCT
ejpam-6273	103	1	if	if	SCONJ
ejpam-6273	103	2	possible	possible	ADJ
ejpam-6273	103	3	,	,	PUNCT
ejpam-6273	103	4	suppose	suppose	VERB
ejpam-6273	103	5	that	that	SCONJ
ejpam-6273	103	6	there	there	PRON
ejpam-6273	103	7	exists	exist	VERB
ejpam-6273	103	8	q	q	X
ejpam-6273	103	9	,	,	PUNCT
ejpam-6273	103	10	ς	ς	PROPN
ejpam-6273	103	11	∈	∈	PROPN
ejpam-6273	103	12	y	y	PROPN
ejpam-6273	103	13	such	such	ADJ
ejpam-6273	103	14	that	that	DET
ejpam-6273	103	15	ϱ̃(qς	ϱ̃(qς	NOUN
ejpam-6273	103	16	)	)	PUNCT
ejpam-6273	104	1	⊆	⊆	NUM
ejpam-6273	104	2	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	104	3	)	)	PUNCT
ejpam-6273	104	4	,	,	PUNCT
ejpam-6273	104	5	γ(qς	γ(qς	NOUN
ejpam-6273	104	6	)	)	PUNCT
ejpam-6273	104	7	≥	≥	NOUN
ejpam-6273	104	8	γ(q	γ(q	NOUN
ejpam-6273	104	9	)	)	PUNCT
ejpam-6273	104	10	.	.	PUNCT
ejpam-6273	105	1	put	put	VERB
ejpam-6273	105	2	u1	u1	NOUN
ejpam-6273	105	3	=	=	NOUN
ejpam-6273	105	4	1	1	NUM
ejpam-6273	105	5	2{ϱ̃(qς	2{ϱ̃(qς	NUM
ejpam-6273	105	6	)	)	PUNCT
ejpam-6273	106	1	+	+	CCONJ
ejpam-6273	107	1	ϱ̃(q	ϱ̃(q	ADJ
ejpam-6273	107	2	)	)	PUNCT
ejpam-6273	107	3	}	}	PUNCT
ejpam-6273	107	4	,	,	PUNCT
ejpam-6273	107	5	v1	v1	NOUN
ejpam-6273	107	6	=	=	SYM
ejpam-6273	107	7	1	1	NUM
ejpam-6273	107	8	2{γ(qς	2{γ(qς	NUM
ejpam-6273	107	9	)	)	PUNCT
ejpam-6273	107	10	+	+	NUM
ejpam-6273	107	11	γ(q	γ(q	NOUN
ejpam-6273	107	12	)	)	PUNCT
ejpam-6273	107	13	}	}	PUNCT
ejpam-6273	107	14	.	.	PUNCT
ejpam-6273	108	1	then	then	ADV
ejpam-6273	108	2	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	108	3	)	)	PUNCT
ejpam-6273	108	4	⊂	⊂	PROPN
ejpam-6273	108	5	u1	u1	PROPN
ejpam-6273	108	6	⊂	⊂	PROPN
ejpam-6273	108	7	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	108	8	)	)	PUNCT
ejpam-6273	108	9	and	and	CCONJ
ejpam-6273	108	10	γ(qς	γ(qς	NOUN
ejpam-6273	108	11	)	)	PUNCT
ejpam-6273	108	12	>	>	X
ejpam-6273	109	1	v1	v1	PROPN
ejpam-6273	109	2	>	>	X
ejpam-6273	109	3	γ(q	γ(q	NOUN
ejpam-6273	109	4	)	)	PUNCT
ejpam-6273	109	5	.	.	PUNCT
ejpam-6273	110	1	hence	hence	ADV
ejpam-6273	110	2	,	,	PUNCT
ejpam-6273	110	3	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	110	4	)	)	PUNCT
ejpam-6273	110	5	⊂	⊂	PROPN
ejpam-6273	110	6	u1	u1	PROPN
ejpam-6273	110	7	,	,	PUNCT
ejpam-6273	110	8	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	110	9	)	)	PUNCT
ejpam-6273	110	10	⊃	⊃	PROPN
ejpam-6273	110	11	u1	u1	NOUN
ejpam-6273	110	12	and	and	CCONJ
ejpam-6273	110	13	γ(qς	γ(qς	NOUN
ejpam-6273	110	14	)	)	PUNCT
ejpam-6273	110	15	>	>	X
ejpam-6273	110	16	v1	v1	PROPN
ejpam-6273	110	17	,	,	PUNCT
ejpam-6273	110	18	γ(q	γ(q	NOUN
ejpam-6273	110	19	)	)	PUNCT
ejpam-6273	110	20	<	<	X
ejpam-6273	110	21	v1	v1	NOUN
ejpam-6273	110	22	.	.	PUNCT
ejpam-6273	111	1	since	since	SCONJ
ejpam-6273	111	2	q	q	PROPN
ejpam-6273	111	3	,	,	PUNCT
ejpam-6273	111	4	ς	ς	PROPN
ejpam-6273	111	5	∈	∈	PROPN
ejpam-6273	111	6	y	y	PROPN
ejpam-6273	111	7	,	,	PUNCT
ejpam-6273	111	8	we	we	PRON
ejpam-6273	111	9	have	have	VERB
ejpam-6273	111	10	qς	qς	ADP
ejpam-6273	111	11	∈	∈	PROPN
ejpam-6273	111	12	y	y	PROPN
ejpam-6273	111	13	.	.	PUNCT
ejpam-6273	112	1	thus	thus	ADV
ejpam-6273	112	2	,	,	PUNCT
ejpam-6273	112	3	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	112	4	)	)	PUNCT
ejpam-6273	112	5	⊂	⊂	PROPN
ejpam-6273	112	6	u1	u1	PROPN
ejpam-6273	112	7	,	,	PUNCT
ejpam-6273	112	8	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	112	9	)	)	PUNCT
ejpam-6273	112	10	⊃	⊃	PROPN
ejpam-6273	112	11	u1	u1	NOUN
ejpam-6273	112	12	and	and	CCONJ
ejpam-6273	112	13	γ(qς	γ(qς	NOUN
ejpam-6273	112	14	)	)	PUNCT
ejpam-6273	112	15	>	>	X
ejpam-6273	112	16	v1	v1	PROPN
ejpam-6273	112	17	,	,	PUNCT
ejpam-6273	112	18	γ(q	γ(q	NOUN
ejpam-6273	112	19	)	)	PUNCT
ejpam-6273	112	20	<	<	X
ejpam-6273	112	21	v1	v1	NOUN
ejpam-6273	112	22	.	.	PUNCT
ejpam-6273	113	1	therefore	therefore	ADV
ejpam-6273	113	2	,	,	PUNCT
ejpam-6273	113	3	qς	qς	NOUN
ejpam-6273	113	4	/∈	/∈	PUNCT
ejpam-6273	113	5	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	114	1	[	[	X
ejpam-6273	114	2	u1	u1	NOUN
ejpam-6273	114	3	,	,	PUNCT
ejpam-6273	114	4	t	t	PROPN
ejpam-6273	114	5	]	]	PUNCT
ejpam-6273	114	6	∩	∩	ADJ
ejpam-6273	114	7	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	115	1	[	[	X
ejpam-6273	115	2	v1	v1	NOUN
ejpam-6273	115	3	,	,	PUNCT
ejpam-6273	115	4	t	t	PROPN
ejpam-6273	115	5	]	]	PUNCT
ejpam-6273	115	6	,	,	PUNCT
ejpam-6273	115	7	q	q	PROPN
ejpam-6273	115	8	∈	∈	NOUN
ejpam-6273	115	9	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	116	1	[	[	X
ejpam-6273	116	2	u1	u1	NOUN
ejpam-6273	116	3	,	,	PUNCT
ejpam-6273	116	4	t	t	PROPN
ejpam-6273	116	5	]	]	PUNCT
ejpam-6273	116	6	∩	∩	ADJ
ejpam-6273	116	7	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	117	1	[	[	X
ejpam-6273	117	2	v1	v1	NOUN
ejpam-6273	117	3	,	,	PUNCT
ejpam-6273	117	4	t	t	X
ejpam-6273	117	5	]	]	PUNCT
ejpam-6273	117	6	,	,	PUNCT
ejpam-6273	117	7	∀ς	∀ς	PROPN
ejpam-6273	117	8	∈	∈	PROPN
ejpam-6273	117	9	y	y	PROPN
ejpam-6273	117	10	,	,	PUNCT
ejpam-6273	117	11	which	which	PRON
ejpam-6273	117	12	is	be	AUX
ejpam-6273	117	13	a	a	DET
ejpam-6273	117	14	contradiction	contradiction	NOUN
ejpam-6273	117	15	.	.	PUNCT
ejpam-6273	118	1	hence	hence	ADV
ejpam-6273	118	2	,	,	PUNCT
ejpam-6273	118	3	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	118	4	)	)	PUNCT
ejpam-6273	118	5	⊇	⊇	PROPN
ejpam-6273	118	6	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	118	7	)	)	PUNCT
ejpam-6273	118	8	,	,	PUNCT
ejpam-6273	118	9	γ(qς	γ(qς	NOUN
ejpam-6273	118	10	)	)	PUNCT
ejpam-6273	118	11	≤	≤	NUM
ejpam-6273	118	12	γ(q	γ(q	NOUN
ejpam-6273	118	13	)	)	PUNCT
ejpam-6273	118	14	.	.	PUNCT
ejpam-6273	119	1	if	if	SCONJ
ejpam-6273	119	2	possible	possible	ADJ
ejpam-6273	119	3	,	,	PUNCT
ejpam-6273	119	4	presume	presume	VERB
ejpam-6273	119	5	that	that	SCONJ
ejpam-6273	119	6	there	there	PRON
ejpam-6273	119	7	exists	exist	VERB
ejpam-6273	119	8	i	i	PRON
ejpam-6273	119	9	,	,	PUNCT
ejpam-6273	119	10	q	q	X
ejpam-6273	119	11	,	,	PUNCT
ejpam-6273	119	12	ς	ς	PROPN
ejpam-6273	119	13	∈	∈	PROPN
ejpam-6273	119	14	y	y	PROPN
ejpam-6273	119	15	such	such	ADJ
ejpam-6273	119	16	that	that	SCONJ
ejpam-6273	119	17	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	119	18	+	+	NUM
ejpam-6273	119	19	i	i	NOUN
ejpam-6273	119	20	)	)	PUNCT
ejpam-6273	119	21	−	−	PROPN
ejpam-6273	119	22	ςq	ςq	NOUN
ejpam-6273	119	23	)	)	PUNCT
ejpam-6273	119	24	⊆	⊆	NUM
ejpam-6273	119	25	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	119	26	)	)	PUNCT
ejpam-6273	119	27	,	,	PUNCT
ejpam-6273	119	28	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	119	29	+	+	PROPN
ejpam-6273	119	30	i)−	i)−	PROPN
ejpam-6273	119	31	ςq	ςq	PROPN
ejpam-6273	119	32	)	)	PUNCT
ejpam-6273	119	33	≥	≥	NOUN
ejpam-6273	119	34	γ(i	γ(i	NOUN
ejpam-6273	119	35	)	)	PUNCT
ejpam-6273	119	36	.	.	PUNCT
ejpam-6273	120	1	put	put	VERB
ejpam-6273	120	2	u2	u2	NOUN
ejpam-6273	120	3	=	=	NOUN
ejpam-6273	120	4	1	1	NUM
ejpam-6273	120	5	2{ϱ̃(ς(q+	2{ϱ̃(ς(q+	NUM
ejpam-6273	120	6	i)−	i)−	PROPN
ejpam-6273	120	7	ςq	ςq	PROPN
ejpam-6273	120	8	)	)	PUNCT
ejpam-6273	120	9	+	+	CCONJ
ejpam-6273	120	10	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	120	11	)	)	PUNCT
ejpam-6273	120	12	}	}	PUNCT
ejpam-6273	120	13	,	,	PUNCT
ejpam-6273	120	14	v2	v2	PROPN
ejpam-6273	120	15	=	=	SYM
ejpam-6273	120	16	1	1	NUM
ejpam-6273	120	17	2{γ(ς(q+	2{γ(ς(q+	NUM
ejpam-6273	120	18	i)−	i)−	PROPN
ejpam-6273	120	19	ςq	ςq	PROPN
ejpam-6273	120	20	)	)	PUNCT
ejpam-6273	120	21	+	+	CCONJ
ejpam-6273	120	22	γ(i	γ(i	NOUN
ejpam-6273	120	23	)	)	PUNCT
ejpam-6273	120	24	}	}	PUNCT
ejpam-6273	120	25	.	.	PUNCT
ejpam-6273	121	1	then	then	ADV
ejpam-6273	121	2	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	121	3	+	+	PROPN
ejpam-6273	121	4	i	i	NOUN
ejpam-6273	121	5	)	)	PUNCT
ejpam-6273	122	1	−	−	PROPN
ejpam-6273	122	2	ςq	ςq	NOUN
ejpam-6273	122	3	)	)	PUNCT
ejpam-6273	122	4	⊂	⊂	PROPN
ejpam-6273	122	5	u2	u2	PROPN
ejpam-6273	122	6	⊂	⊂	PROPN
ejpam-6273	122	7	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	122	8	)	)	PUNCT
ejpam-6273	122	9	and	and	CCONJ
ejpam-6273	122	10	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	122	11	+	+	CCONJ
ejpam-6273	122	12	i	i	NOUN
ejpam-6273	122	13	)	)	PUNCT
ejpam-6273	123	1	−	−	PROPN
ejpam-6273	123	2	ςq	ςq	NOUN
ejpam-6273	123	3	)	)	PUNCT
ejpam-6273	123	4	>	>	PUNCT
ejpam-6273	124	1	v2	v2	PROPN
ejpam-6273	124	2	>	>	X
ejpam-6273	124	3	γ(i	γ(i	NOUN
ejpam-6273	124	4	)	)	PUNCT
ejpam-6273	124	5	.	.	PUNCT
ejpam-6273	125	1	hence	hence	ADV
ejpam-6273	125	2	,	,	PUNCT
ejpam-6273	125	3	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	125	4	+	+	NUM
ejpam-6273	125	5	i	i	NOUN
ejpam-6273	125	6	)	)	PUNCT
ejpam-6273	125	7	−	−	PROPN
ejpam-6273	125	8	ςq	ςq	NOUN
ejpam-6273	125	9	)	)	PUNCT
ejpam-6273	125	10	⊂	⊂	PROPN
ejpam-6273	125	11	u2	u2	PROPN
ejpam-6273	125	12	,	,	PUNCT
ejpam-6273	125	13	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	125	14	)	)	PUNCT
ejpam-6273	125	15	⊃	⊃	PROPN
ejpam-6273	125	16	u2	u2	NOUN
ejpam-6273	125	17	and	and	CCONJ
ejpam-6273	125	18	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	125	19	+	+	CCONJ
ejpam-6273	125	20	i	i	NOUN
ejpam-6273	125	21	)	)	PUNCT
ejpam-6273	126	1	−	−	PROPN
ejpam-6273	126	2	ςq	ςq	NOUN
ejpam-6273	126	3	)	)	PUNCT
ejpam-6273	126	4	>	>	PUNCT
ejpam-6273	127	1	v2	v2	PROPN
ejpam-6273	127	2	,	,	PUNCT
ejpam-6273	127	3	γ(i	γ(i	NOUN
ejpam-6273	127	4	)	)	PUNCT
ejpam-6273	127	5	<	<	X
ejpam-6273	127	6	v2	v2	PROPN
ejpam-6273	127	7	.	.	PUNCT
ejpam-6273	128	1	since	since	SCONJ
ejpam-6273	128	2	i	i	PRON
ejpam-6273	128	3	,	,	PUNCT
ejpam-6273	128	4	q	q	X
ejpam-6273	128	5	,	,	PUNCT
ejpam-6273	128	6	ς	ς	PROPN
ejpam-6273	128	7	∈	∈	PROPN
ejpam-6273	128	8	y	y	PROPN
ejpam-6273	128	9	,	,	PUNCT
ejpam-6273	128	10	ς(q	ς(q	PROPN
ejpam-6273	128	11	+	+	NUM
ejpam-6273	128	12	i	i	NOUN
ejpam-6273	128	13	)	)	PUNCT
ejpam-6273	129	1	−	−	PROPN
ejpam-6273	129	2	ςq	ςq	ADP
ejpam-6273	129	3	∈	∈	PROPN
ejpam-6273	129	4	y	y	PROPN
ejpam-6273	129	5	.	.	PUNCT
ejpam-6273	130	1	thus	thus	ADV
ejpam-6273	130	2	,	,	PUNCT
ejpam-6273	130	3	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	130	4	+	+	NUM
ejpam-6273	130	5	i	i	NOUN
ejpam-6273	130	6	)	)	PUNCT
ejpam-6273	130	7	−	−	PROPN
ejpam-6273	130	8	ςq	ςq	NOUN
ejpam-6273	130	9	)	)	PUNCT
ejpam-6273	130	10	⊂	⊂	PROPN
ejpam-6273	130	11	u2	u2	PROPN
ejpam-6273	130	12	,	,	PUNCT
ejpam-6273	130	13	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	130	14	)	)	PUNCT
ejpam-6273	130	15	⊃	⊃	PROPN
ejpam-6273	130	16	u2	u2	NOUN
ejpam-6273	130	17	and	and	CCONJ
ejpam-6273	130	18	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	130	19	+	+	CCONJ
ejpam-6273	130	20	i	i	NOUN
ejpam-6273	130	21	)	)	PUNCT
ejpam-6273	131	1	−	−	PROPN
ejpam-6273	131	2	ςq	ςq	NOUN
ejpam-6273	131	3	)	)	PUNCT
ejpam-6273	131	4	>	>	PUNCT
ejpam-6273	132	1	v2	v2	PROPN
ejpam-6273	132	2	,	,	PUNCT
ejpam-6273	132	3	γ(i	γ(i	NOUN
ejpam-6273	132	4	)	)	PUNCT
ejpam-6273	132	5	<	<	X
ejpam-6273	132	6	v2	v2	PROPN
ejpam-6273	132	7	.	.	PUNCT
ejpam-6273	133	1	therefore	therefore	ADV
ejpam-6273	133	2	,	,	PUNCT
ejpam-6273	133	3	ς(q	ς(q	PROPN
ejpam-6273	133	4	+	+	NUM
ejpam-6273	133	5	i	i	NOUN
ejpam-6273	133	6	)	)	PUNCT
ejpam-6273	133	7	−	−	PROPN
ejpam-6273	133	8	ςq	ςq	NOUN
ejpam-6273	133	9	/∈	/∈	NOUN
ejpam-6273	133	10	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	134	1	[	[	X
ejpam-6273	134	2	u2	u2	PROPN
ejpam-6273	134	3	,	,	PUNCT
ejpam-6273	134	4	t	t	PROPN
ejpam-6273	134	5	]	]	PUNCT
ejpam-6273	134	6	∩	∩	ADJ
ejpam-6273	134	7	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	135	1	[	[	X
ejpam-6273	135	2	v2	v2	X
ejpam-6273	135	3	,	,	PUNCT
ejpam-6273	135	4	t	t	PROPN
ejpam-6273	135	5	]	]	PUNCT
ejpam-6273	135	6	,	,	PUNCT
ejpam-6273	135	7	i	i	PRON
ejpam-6273	135	8	∈	∈	VERB
ejpam-6273	135	9	ϱ̃γ	ϱ̃γ	PUNCT
ejpam-6273	136	1	[	[	X
ejpam-6273	136	2	u2	u2	NOUN
ejpam-6273	136	3	,	,	PUNCT
ejpam-6273	136	4	t	t	PROPN
ejpam-6273	136	5	]	]	PUNCT
ejpam-6273	136	6	∩	∩	ADJ
ejpam-6273	136	7	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	137	1	[	[	X
ejpam-6273	137	2	v2	v2	X
ejpam-6273	137	3	,	,	PUNCT
ejpam-6273	137	4	t	t	PROPN
ejpam-6273	137	5	]	]	PUNCT
ejpam-6273	137	6	,	,	PUNCT
ejpam-6273	137	7	which	which	PRON
ejpam-6273	137	8	is	be	AUX
ejpam-6273	137	9	a	a	DET
ejpam-6273	137	10	contradiction	contradiction	NOUN
ejpam-6273	137	11	.	.	PUNCT
ejpam-6273	138	1	thus	thus	ADV
ejpam-6273	138	2	,	,	PUNCT
ejpam-6273	138	3	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	138	4	+	+	PROPN
ejpam-6273	138	5	i)−	i)−	PROPN
ejpam-6273	138	6	ςq	ςq	PROPN
ejpam-6273	138	7	)	)	PUNCT
ejpam-6273	138	8	⊇	⊇	PROPN
ejpam-6273	138	9	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	138	10	)	)	PUNCT
ejpam-6273	138	11	,	,	PUNCT
ejpam-6273	138	12	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	138	13	+	+	PROPN
ejpam-6273	138	14	i)−	i)−	PROPN
ejpam-6273	138	15	ςq	ςq	PROPN
ejpam-6273	138	16	)	)	PUNCT
ejpam-6273	138	17	≤	≤	NUM
ejpam-6273	138	18	γ(i	γ(i	NOUN
ejpam-6273	138	19	)	)	PUNCT
ejpam-6273	138	20	.	.	PUNCT
ejpam-6273	139	1	hence	hence	ADV
ejpam-6273	139	2	,	,	PUNCT
ejpam-6273	139	3	(	(	PUNCT
ejpam-6273	139	4	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	139	5	,	,	PUNCT
ejpam-6273	139	6	y	y	PROPN
ejpam-6273	139	7	)	)	PUNCT
ejpam-6273	139	8	is	be	AUX
ejpam-6273	139	9	an	an	DET
ejpam-6273	139	10	hina	hina	NOUN
ejpam-6273	139	11	upon	upon	SCONJ
ejpam-6273	139	12	(	(	PUNCT
ejpam-6273	139	13	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	139	14	,	,	PUNCT
ejpam-6273	139	15	l	l	NOUN
ejpam-6273	139	16	)	)	PUNCT
ejpam-6273	139	17	.	.	PUNCT
ejpam-6273	140	1	theorem	theorem	NOUN
ejpam-6273	140	2	2	2	NUM
ejpam-6273	140	3	.	.	PUNCT
ejpam-6273	140	4	let	let	VERB
ejpam-6273	140	5	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	140	6	and	and	CCONJ
ejpam-6273	140	7	h̃µ	h̃µ	NOUN
ejpam-6273	140	8	be	be	AUX
ejpam-6273	140	9	two	two	NUM
ejpam-6273	140	10	hinas	hina	NOUN
ejpam-6273	140	11	of	of	ADP
ejpam-6273	140	12	y	y	PROPN
ejpam-6273	140	13	upon	upon	SCONJ
ejpam-6273	140	14	an	an	DET
ejpam-6273	140	15	hf	hf	NOUN
ejpam-6273	140	16	(	(	PUNCT
ejpam-6273	140	17	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	140	18	,	,	PUNCT
ejpam-6273	140	19	l	l	NOUN
ejpam-6273	140	20	)	)	PUNCT
ejpam-6273	140	21	.	.	PUNCT
ejpam-6273	141	1	then	then	ADV
ejpam-6273	141	2	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	141	3	⋒	⋒	PUNCT
ejpam-6273	141	4	h̃µ	h̃µ	PROPN
ejpam-6273	141	5	is	be	AUX
ejpam-6273	141	6	an	an	DET
ejpam-6273	141	7	hina	hina	NOUN
ejpam-6273	141	8	of	of	ADP
ejpam-6273	141	9	y	y	PROPN
ejpam-6273	141	10	upon	upon	SCONJ
ejpam-6273	141	11	an	an	DET
ejpam-6273	141	12	hf	hf	NOUN
ejpam-6273	141	13	(	(	PUNCT
ejpam-6273	141	14	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	141	15	,	,	PUNCT
ejpam-6273	141	16	l	l	NOUN
ejpam-6273	141	17	)	)	PUNCT
ejpam-6273	141	18	.	.	PUNCT
ejpam-6273	142	1	proof	proof	NOUN
ejpam-6273	142	2	.	.	PUNCT
ejpam-6273	143	1	we	we	PRON
ejpam-6273	143	2	know	know	VERB
ejpam-6273	143	3	that	that	SCONJ
ejpam-6273	143	4	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	143	5	⋒	⋒	PUNCT
ejpam-6273	143	6	h̃µ	h̃µ	PROPN
ejpam-6273	143	7	is	be	AUX
ejpam-6273	143	8	an	an	DET
ejpam-6273	143	9	hna	hna	NOUN
ejpam-6273	143	10	of	of	ADP
ejpam-6273	143	11	y	y	PROPN
ejpam-6273	143	12	upon	upon	SCONJ
ejpam-6273	143	13	an	an	DET
ejpam-6273	143	14	hf	hf	NOUN
ejpam-6273	143	15	ξ̃	ξ̃	PROPN
ejpam-6273	143	16	of	of	ADP
ejpam-6273	143	17	l.	l.	PROPN
ejpam-6273	143	18	let	let	VERB
ejpam-6273	143	19	q	q	PRON
ejpam-6273	143	20	,	,	PUNCT
ejpam-6273	143	21	ς	ς	PROPN
ejpam-6273	143	22	,	,	PUNCT
ejpam-6273	143	23	i	i	PRON
ejpam-6273	143	24	∈	∈	PROPN
ejpam-6273	144	1	y	y	INTJ
ejpam-6273	144	2	.	.	PUNCT
ejpam-6273	145	1	then	then	ADV
ejpam-6273	145	2	(	(	PUNCT
ejpam-6273	145	3	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	145	4	⋒	⋒	PUNCT
ejpam-6273	145	5	h̃µ)(qς	h̃µ)(qς	X
ejpam-6273	145	6	)	)	PUNCT
ejpam-6273	145	7	=	=	PUNCT
ejpam-6273	145	8	(	(	PUNCT
ejpam-6273	145	9	ϱ̃∩̃h̃)(qς	ϱ̃∩̃h̃)(qς	NOUN
ejpam-6273	145	10	)	)	PUNCT
ejpam-6273	145	11	=	=	SYM
ejpam-6273	145	12	ϱ̃(qς)∩̃h̃(qς	ϱ̃(qς)∩̃h̃(qς	NOUN
ejpam-6273	145	13	)	)	PUNCT
ejpam-6273	145	14	⊇	⊇	NOUN
ejpam-6273	145	15	(	(	PUNCT
ejpam-6273	145	16	ϱ̃(q)∩̃(h̃(q	ϱ̃(q)∩̃(h̃(q	PROPN
ejpam-6273	145	17	)	)	PUNCT
ejpam-6273	145	18	)	)	PUNCT
ejpam-6273	146	1	=	=	SYM
ejpam-6273	146	2	(	(	PUNCT
ejpam-6273	146	3	ϱ̃	ϱ̃	PROPN
ejpam-6273	146	4	∩	∩	NOUN
ejpam-6273	146	5	h̃)(q	h̃)(q	NOUN
ejpam-6273	146	6	)	)	PUNCT
ejpam-6273	146	7	,	,	PUNCT
ejpam-6273	146	8	(	(	PUNCT
ejpam-6273	146	9	γ	γ	PROPN
ejpam-6273	146	10	∨	∨	X
ejpam-6273	146	11	µ)(qς	µ)(qς	NUM
ejpam-6273	146	12	)	)	PUNCT
ejpam-6273	146	13	=	=	SYM
ejpam-6273	146	14	∨{γ(qς	∨{γ(qς	X
ejpam-6273	146	15	)	)	PUNCT
ejpam-6273	146	16	,	,	PUNCT
ejpam-6273	146	17	µ(qς	µ(qς	NOUN
ejpam-6273	146	18	)	)	PUNCT
ejpam-6273	146	19	}	}	PUNCT
ejpam-6273	146	20	≤	≤	NUM
ejpam-6273	146	21	∨{γ(q	∨{γ(q	NOUN
ejpam-6273	146	22	)	)	PUNCT
ejpam-6273	146	23	,	,	PUNCT
ejpam-6273	146	24	µ(q	µ(q	PROPN
ejpam-6273	146	25	)	)	PUNCT
ejpam-6273	146	26	}	}	PUNCT
ejpam-6273	146	27	=	=	SYM
ejpam-6273	146	28	(	(	PUNCT
ejpam-6273	146	29	γ	γ	X
ejpam-6273	146	30	∨	∨	NUM
ejpam-6273	146	31	µ)(q	µ)(q	NUM
ejpam-6273	146	32	)	)	PUNCT
ejpam-6273	146	33	,	,	PUNCT
ejpam-6273	146	34	(	(	PUNCT
ejpam-6273	146	35	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	146	36	⋒	⋒	X
ejpam-6273	146	37	h̃µ)(ς(q	h̃µ)(ς(q	PRON
ejpam-6273	146	38	+	+	PROPN
ejpam-6273	146	39	i)−	i)−	PROPN
ejpam-6273	146	40	ςq	ςq	PROPN
ejpam-6273	146	41	)	)	PUNCT
ejpam-6273	146	42	=	=	SYM
ejpam-6273	146	43	(	(	PUNCT
ejpam-6273	146	44	ϱ̃∩̃h̃)(ς(q	ϱ̃∩̃h̃)(ς(q	PROPN
ejpam-6273	146	45	+	+	PROPN
ejpam-6273	146	46	i)−	i)−	PROPN
ejpam-6273	146	47	ςq	ςq	PROPN
ejpam-6273	146	48	)	)	PUNCT
ejpam-6273	146	49	=	=	SYM
ejpam-6273	146	50	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	146	51	+	+	CCONJ
ejpam-6273	146	52	i)−	i)−	PROPN
ejpam-6273	146	53	ςq)∩̃h̃(ς(q	ςq)∩̃h̃(ς(q	NOUN
ejpam-6273	146	54	+	+	PUNCT
ejpam-6273	146	55	i)−	i)−	PROPN
ejpam-6273	146	56	ςq	ςq	PROPN
ejpam-6273	146	57	)	)	PUNCT
ejpam-6273	146	58	⊇	⊇	NOUN
ejpam-6273	146	59	(	(	PUNCT
ejpam-6273	146	60	ϱ̃(i)∩̃(h̃(i	ϱ̃(i)∩̃(h̃(i	NOUN
ejpam-6273	146	61	)	)	PUNCT
ejpam-6273	146	62	)	)	PUNCT
ejpam-6273	147	1	p.	p.	NOUN
ejpam-6273	147	2	n.	n.	PROPN
ejpam-6273	147	3	swamy	swamy	PROPN
ejpam-6273	147	4	et	et	PROPN
ejpam-6273	147	5	al	al	PROPN
ejpam-6273	147	6	.	.	PUNCT
ejpam-6273	147	7	/	/	SYM
ejpam-6273	147	8	eur	eur	PROPN
ejpam-6273	147	9	.	.	PUNCT
ejpam-6273	148	1	j.	j.	PROPN
ejpam-6273	148	2	pure	pure	PROPN
ejpam-6273	148	3	appl	appl	PROPN
ejpam-6273	148	4	.	.	PROPN
ejpam-6273	148	5	math	math	PROPN
ejpam-6273	148	6	,	,	PUNCT
ejpam-6273	148	7	18	18	NUM
ejpam-6273	148	8	(	(	PUNCT
ejpam-6273	148	9	3	3	NUM
ejpam-6273	148	10	)	)	PUNCT
ejpam-6273	148	11	(	(	PUNCT
ejpam-6273	148	12	2025	2025	NUM
ejpam-6273	148	13	)	)	PUNCT
ejpam-6273	148	14	,	,	PUNCT
ejpam-6273	148	15	6273	6273	NUM
ejpam-6273	148	16	6	6	NUM
ejpam-6273	148	17	of	of	ADP
ejpam-6273	148	18	16	16	NUM
ejpam-6273	148	19	=	=	SYM
ejpam-6273	148	20	(	(	PUNCT
ejpam-6273	148	21	ϱ̃	ϱ̃	PROPN
ejpam-6273	148	22	∩	∩	NOUN
ejpam-6273	148	23	h̃)(i	h̃)(i	NOUN
ejpam-6273	148	24	)	)	PUNCT
ejpam-6273	148	25	,	,	PUNCT
ejpam-6273	148	26	and	and	CCONJ
ejpam-6273	148	27	(	(	PUNCT
ejpam-6273	148	28	γ	γ	PROPN
ejpam-6273	148	29	∨	∨	NUM
ejpam-6273	148	30	µ)(ς(q	µ)(ς(q	PUNCT
ejpam-6273	148	31	+	+	PROPN
ejpam-6273	148	32	i)−	i)−	PROPN
ejpam-6273	148	33	ςq	ςq	PROPN
ejpam-6273	148	34	)	)	PUNCT
ejpam-6273	148	35	=	=	PUNCT
ejpam-6273	149	1	∨{γ(ς(q	∨{γ(ς(q	PROPN
ejpam-6273	149	2	+	+	PUNCT
ejpam-6273	149	3	i)−	i)−	PROPN
ejpam-6273	149	4	ςq	ςq	PROPN
ejpam-6273	149	5	)	)	PUNCT
ejpam-6273	150	1	,	,	PUNCT
ejpam-6273	150	2	µ(ς(q	µ(ς(q	NOUN
ejpam-6273	150	3	+	+	PROPN
ejpam-6273	150	4	i)−	i)−	PROPN
ejpam-6273	150	5	ςq	ςq	PROPN
ejpam-6273	150	6	)	)	PUNCT
ejpam-6273	150	7	}	}	PUNCT
ejpam-6273	150	8	≤	≤	NUM
ejpam-6273	150	9	∨{γ(i	∨{γ(i	NOUN
ejpam-6273	150	10	)	)	PUNCT
ejpam-6273	150	11	,	,	PUNCT
ejpam-6273	150	12	µ(i	µ(i	PROPN
ejpam-6273	150	13	)	)	PUNCT
ejpam-6273	150	14	}	}	PUNCT
ejpam-6273	150	15	=	=	SYM
ejpam-6273	150	16	(	(	PUNCT
ejpam-6273	150	17	γ	γ	X
ejpam-6273	150	18	∨	∨	NUM
ejpam-6273	150	19	µ)(i	µ)(i	NUM
ejpam-6273	150	20	)	)	PUNCT
ejpam-6273	150	21	.	.	PUNCT
ejpam-6273	151	1	definition	definition	NOUN
ejpam-6273	151	2	7	7	NUM
ejpam-6273	151	3	.	.	PUNCT
ejpam-6273	152	1	let	let	VERB
ejpam-6273	152	2	y	y	PRON
ejpam-6273	152	3	and	and	CCONJ
ejpam-6273	152	4	y	y	PROPN
ejpam-6273	152	5	′	′	NUM
ejpam-6273	152	6	be	be	AUX
ejpam-6273	152	7	two	two	NUM
ejpam-6273	152	8	nas	nas	NOUN
ejpam-6273	152	9	and	and	CCONJ
ejpam-6273	152	10	ω	ω	NUM
ejpam-6273	153	1	:	:	PUNCT
ejpam-6273	154	1	y	y	PROPN
ejpam-6273	154	2	→	→	SYM
ejpam-6273	154	3	y	y	PROPN
ejpam-6273	154	4	′	′	NOUN
ejpam-6273	154	5	be	be	AUX
ejpam-6273	154	6	a	a	DET
ejpam-6273	154	7	mapping	mapping	NOUN
ejpam-6273	154	8	.	.	PUNCT
ejpam-6273	155	1	then	then	ADV
ejpam-6273	155	2	:	:	PUNCT
ejpam-6273	155	3	(	(	PUNCT
ejpam-6273	155	4	i	i	NOUN
ejpam-6273	155	5	)	)	PUNCT
ejpam-6273	155	6	if	if	SCONJ
ejpam-6273	155	7	h̃µ	h̃µ	ADJ
ejpam-6273	155	8	is	be	AUX
ejpam-6273	155	9	an	an	DET
ejpam-6273	155	10	hs	hs	PROPN
ejpam-6273	155	11	of	of	ADP
ejpam-6273	155	12	y	y	PROPN
ejpam-6273	155	13	′	′	NUM
ejpam-6273	155	14	,	,	PUNCT
ejpam-6273	155	15	then	then	ADV
ejpam-6273	155	16	the	the	DET
ejpam-6273	155	17	preimage	preimage	NOUN
ejpam-6273	155	18	of	of	ADP
ejpam-6273	155	19	h̃µ	h̃µ	NOUN
ejpam-6273	155	20	under	under	ADP
ejpam-6273	155	21	ω	ω	PROPN
ejpam-6273	155	22	is	be	AUX
ejpam-6273	155	23	the	the	DET
ejpam-6273	155	24	hs	hs	PROPN
ejpam-6273	155	25	in	in	ADP
ejpam-6273	155	26	y	y	PROPN
ejpam-6273	155	27	upon	upon	SCONJ
ejpam-6273	155	28	u	u	NOUN
ejpam-6273	155	29	demarcated	demarcate	VERB
ejpam-6273	155	30	by	by	ADP
ejpam-6273	155	31	ω−1(h̃µ)(q	ω−1(h̃µ)(q	PROPN
ejpam-6273	155	32	)	)	PUNCT
ejpam-6273	156	1	=	=	PRON
ejpam-6273	156	2	(	(	PUNCT
ejpam-6273	156	3	ω−1(h̃)(q	ω−1(h̃)(q	PROPN
ejpam-6273	156	4	)	)	PUNCT
ejpam-6273	156	5	,	,	PUNCT
ejpam-6273	156	6	ω−1(µ)(q	ω−1(µ)(q	PROPN
ejpam-6273	156	7	)	)	PUNCT
ejpam-6273	156	8	)	)	PUNCT
ejpam-6273	157	1	=	=	SYM
ejpam-6273	157	2	(	(	PUNCT
ejpam-6273	157	3	h̃(ω)(q	h̃(ω)(q	PROPN
ejpam-6273	157	4	)	)	PUNCT
ejpam-6273	157	5	,	,	PUNCT
ejpam-6273	157	6	µ(ω)(q	µ(ω)(q	ADJ
ejpam-6273	157	7	)	)	PUNCT
ejpam-6273	157	8	)	)	PUNCT
ejpam-6273	157	9	,	,	PUNCT
ejpam-6273	157	10	∀q	∀q	PROPN
ejpam-6273	157	11	∈	∈	PROPN
ejpam-6273	157	12	y	y	PROPN
ejpam-6273	157	13	.	.	PUNCT
ejpam-6273	158	1	(	(	PUNCT
ejpam-6273	158	2	ii	ii	NOUN
ejpam-6273	158	3	)	)	PUNCT
ejpam-6273	158	4	if	if	SCONJ
ejpam-6273	158	5	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	158	6	is	be	AUX
ejpam-6273	158	7	an	an	DET
ejpam-6273	158	8	hs	hs	PROPN
ejpam-6273	158	9	of	of	ADP
ejpam-6273	158	10	y	y	PROPN
ejpam-6273	158	11	,	,	PUNCT
ejpam-6273	158	12	then	then	ADV
ejpam-6273	158	13	the	the	DET
ejpam-6273	158	14	image	image	NOUN
ejpam-6273	158	15	of	of	ADP
ejpam-6273	158	16	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	158	17	under	under	ADP
ejpam-6273	158	18	ω	ω	PROPN
ejpam-6273	158	19	is	be	AUX
ejpam-6273	158	20	the	the	DET
ejpam-6273	158	21	hs	hs	PROPN
ejpam-6273	158	22	in	in	ADP
ejpam-6273	158	23	y	y	PROPN
ejpam-6273	158	24	′	′	NUM
ejpam-6273	158	25	upon	upon	SCONJ
ejpam-6273	158	26	u	u	NOUN
ejpam-6273	158	27	demarcated	demarcate	VERB
ejpam-6273	158	28	by	by	ADP
ejpam-6273	158	29	ω(ϱ̃)(ς	ω(ϱ̃)(ς	NUM
ejpam-6273	158	30	)	)	PUNCT
ejpam-6273	158	31	=	=	PUNCT
ejpam-6273	158	32			PUNCT
ejpam-6273	158	33	⋃	⋃	NOUN
ejpam-6273	158	34	q∈ω−1(ς	q∈ω−1(ς	NOUN
ejpam-6273	158	35	)	)	PUNCT
ejpam-6273	158	36	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	158	37	)	)	PUNCT
ejpam-6273	158	38	,	,	PUNCT
ejpam-6273	158	39	if	if	SCONJ
ejpam-6273	158	40	ω−1(ς	ω−1(ς	PROPN
ejpam-6273	158	41	)	)	PUNCT
ejpam-6273	158	42	̸=	̸=	PROPN
ejpam-6273	158	43	∅	∅	NOUN
ejpam-6273	158	44	0	0	NUM
ejpam-6273	158	45	,	,	PUNCT
ejpam-6273	158	46	otherwise	otherwise	ADV
ejpam-6273	158	47	ω(γ)(ς	ω(γ)(ς	NUM
ejpam-6273	158	48	)	)	PUNCT
ejpam-6273	158	49	=	=	SYM
ejpam-6273	158	50			PUNCT
ejpam-6273	158	51	∧	∧	PROPN
ejpam-6273	158	52	q∈ω−1(ς	q∈ω−1(ς	NOUN
ejpam-6273	158	53	)	)	PUNCT
ejpam-6273	158	54	γ(q	γ(q	NOUN
ejpam-6273	158	55	)	)	PUNCT
ejpam-6273	158	56	,	,	PUNCT
ejpam-6273	158	57	if	if	SCONJ
ejpam-6273	158	58	ω−1(ς	ω−1(ς	PROPN
ejpam-6273	158	59	)	)	PUNCT
ejpam-6273	158	60	̸=	̸=	PROPN
ejpam-6273	158	61	∅	∅	ADP
ejpam-6273	158	62	1	1	NUM
ejpam-6273	158	63	,	,	PUNCT
ejpam-6273	158	64	otherwise	otherwise	ADV
ejpam-6273	158	65	for	for	ADP
ejpam-6273	158	66	every	every	DET
ejpam-6273	158	67	ς	ς	PROPN
ejpam-6273	158	68	∈	∈	PROPN
ejpam-6273	158	69	y	y	PROPN
ejpam-6273	158	70	.	.	PUNCT
ejpam-6273	159	1	theorem	theorem	NOUN
ejpam-6273	159	2	3	3	X
ejpam-6273	159	3	.	.	PUNCT
ejpam-6273	160	1	let	let	VERB
ejpam-6273	160	2	y	y	PRON
ejpam-6273	160	3	and	and	CCONJ
ejpam-6273	160	4	y	y	PROPN
ejpam-6273	160	5	′	′	NUM
ejpam-6273	160	6	be	be	AUX
ejpam-6273	160	7	two	two	NUM
ejpam-6273	160	8	near	near	ADP
ejpam-6273	160	9	algebras	algebra	NOUN
ejpam-6273	160	10	upon	upon	SCONJ
ejpam-6273	160	11	a	a	DET
ejpam-6273	160	12	field	field	NOUN
ejpam-6273	160	13	l	l	NOUN
ejpam-6273	160	14	and	and	CCONJ
ejpam-6273	160	15	ω	ω	NUM
ejpam-6273	160	16	:	:	PUNCT
ejpam-6273	160	17	y	y	PROPN
ejpam-6273	160	18	→	→	SYM
ejpam-6273	160	19	y	y	PROPN
ejpam-6273	160	20	′	′	NOUN
ejpam-6273	160	21	be	be	AUX
ejpam-6273	160	22	an	an	DET
ejpam-6273	160	23	onto	onto	NOUN
ejpam-6273	160	24	near	near	ADJ
ejpam-6273	160	25	algebra	algebra	PROPN
ejpam-6273	160	26	homomorphism	homomorphism	NOUN
ejpam-6273	160	27	.	.	PUNCT
ejpam-6273	161	1	if	if	SCONJ
ejpam-6273	161	2	(	(	PUNCT
ejpam-6273	161	3	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	161	4	,	,	PUNCT
ejpam-6273	161	5	y	y	PROPN
ejpam-6273	161	6	)	)	PUNCT
ejpam-6273	161	7	is	be	AUX
ejpam-6273	161	8	an	an	DET
ejpam-6273	161	9	hina	hina	NOUN
ejpam-6273	161	10	upon	upon	SCONJ
ejpam-6273	161	11	an	an	DET
ejpam-6273	161	12	hf	hf	NOUN
ejpam-6273	161	13	(	(	PUNCT
ejpam-6273	161	14	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	161	15	,	,	PUNCT
ejpam-6273	161	16	l	l	NOUN
ejpam-6273	161	17	)	)	PUNCT
ejpam-6273	161	18	,	,	PUNCT
ejpam-6273	161	19	then	then	ADV
ejpam-6273	161	20	(	(	PUNCT
ejpam-6273	161	21	ω(ϱ̃γ	ω(ϱ̃γ	NUM
ejpam-6273	161	22	)	)	PUNCT
ejpam-6273	161	23	,	,	PUNCT
ejpam-6273	161	24	y	y	PROPN
ejpam-6273	161	25	′	′	NUM
ejpam-6273	161	26	)	)	PUNCT
ejpam-6273	161	27	is	be	AUX
ejpam-6273	161	28	an	an	DET
ejpam-6273	161	29	hina	hina	NOUN
ejpam-6273	161	30	upon	upon	SCONJ
ejpam-6273	161	31	(	(	PUNCT
ejpam-6273	161	32	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	161	33	,	,	PUNCT
ejpam-6273	161	34	l	l	NOUN
ejpam-6273	161	35	)	)	PUNCT
ejpam-6273	161	36	.	.	PUNCT
ejpam-6273	162	1	proof	proof	NOUN
ejpam-6273	162	2	.	.	PUNCT
ejpam-6273	163	1	let	let	VERB
ejpam-6273	163	2	q	q	X
ejpam-6273	163	3	,	,	PUNCT
ejpam-6273	163	4	ς	ς	PROPN
ejpam-6273	163	5	∈	∈	PROPN
ejpam-6273	163	6	y	y	NOUN
ejpam-6273	163	7	′	′	NUM
ejpam-6273	163	8	.	.	PUNCT
ejpam-6273	164	1	then	then	ADV
ejpam-6273	164	2	{	{	PUNCT
ejpam-6273	164	3	r	r	NOUN
ejpam-6273	164	4	|	|	ADV
ejpam-6273	164	5	r	r	NOUN
ejpam-6273	164	6	∈	∈	NOUN
ejpam-6273	164	7	ω−1(q	ω−1(q	PROPN
ejpam-6273	164	8	+	+	CCONJ
ejpam-6273	164	9	ς	ς	NOUN
ejpam-6273	164	10	)	)	PUNCT
ejpam-6273	164	11	}	}	PUNCT
ejpam-6273	164	12	⊇	⊇	X
ejpam-6273	164	13	{	{	PUNCT
ejpam-6273	164	14	d+	d+	NOUN
ejpam-6273	164	15	t	t	NOUN
ejpam-6273	165	1	|	|	NOUN
ejpam-6273	165	2	d	d	PROPN
ejpam-6273	165	3	∈	∈	PROPN
ejpam-6273	165	4	ω−1(q	ω−1(q	PROPN
ejpam-6273	165	5	)	)	PUNCT
ejpam-6273	165	6	and	and	CCONJ
ejpam-6273	165	7	t	t	PROPN
ejpam-6273	165	8	∈	∈	PROPN
ejpam-6273	165	9	ω−1(ς	ω−1(ς	PROPN
ejpam-6273	165	10	)	)	PUNCT
ejpam-6273	165	11	}	}	PUNCT
ejpam-6273	165	12	and	and	CCONJ
ejpam-6273	165	13	{	{	PUNCT
ejpam-6273	165	14	r	r	NOUN
ejpam-6273	165	15	|	|	ADV
ejpam-6273	165	16	r	r	NOUN
ejpam-6273	165	17	∈	∈	PROPN
ejpam-6273	165	18	ω−1(qς	ω−1(qς	PROPN
ejpam-6273	165	19	)	)	PUNCT
ejpam-6273	165	20	}	}	PUNCT
ejpam-6273	165	21	⊇	⊇	NOUN
ejpam-6273	165	22	{	{	PUNCT
ejpam-6273	165	23	dt	dt	NOUN
ejpam-6273	166	1	|	|	NOUN
ejpam-6273	166	2	d	d	PROPN
ejpam-6273	166	3	∈	∈	PROPN
ejpam-6273	166	4	ω−1(q	ω−1(q	PROPN
ejpam-6273	166	5	)	)	PUNCT
ejpam-6273	166	6	and	and	CCONJ
ejpam-6273	166	7	t	t	PROPN
ejpam-6273	166	8	∈	∈	PROPN
ejpam-6273	166	9	ω−1(ς	ω−1(ς	PROPN
ejpam-6273	166	10	)	)	PUNCT
ejpam-6273	166	11	}	}	PUNCT
ejpam-6273	166	12	.	.	PUNCT
ejpam-6273	167	1	if	if	SCONJ
ejpam-6273	167	2	ω−1(q	ω−1(q	NUM
ejpam-6273	167	3	)	)	PUNCT
ejpam-6273	167	4	̸=	̸=	PROPN
ejpam-6273	167	5	∅	∅	NOUN
ejpam-6273	167	6	and	and	CCONJ
ejpam-6273	167	7	ω−1(ς	ω−1(ς	PROPN
ejpam-6273	167	8	)	)	PUNCT
ejpam-6273	167	9	̸=	̸=	PROPN
ejpam-6273	167	10	∅	∅	NOUN
ejpam-6273	167	11	,	,	PUNCT
ejpam-6273	167	12	then	then	ADV
ejpam-6273	167	13	ω−1(qς	ω−1(qς	PROPN
ejpam-6273	167	14	)	)	PUNCT
ejpam-6273	167	15	̸=	̸=	PROPN
ejpam-6273	167	16	∅.	∅.	ADP
ejpam-6273	167	17	(	(	PUNCT
ejpam-6273	167	18	i	i	NOUN
ejpam-6273	167	19	)	)	PUNCT
ejpam-6273	167	20	for	for	ADP
ejpam-6273	167	21	all	all	DET
ejpam-6273	167	22	q	q	PROPN
ejpam-6273	167	23	,	,	PUNCT
ejpam-6273	167	24	ς	ς	PROPN
ejpam-6273	167	25	∈	∈	PROPN
ejpam-6273	167	26	y	y	PROPN
ejpam-6273	167	27	′∃	′∃	PROPN
ejpam-6273	167	28	d	d	PROPN
ejpam-6273	167	29	,	,	PUNCT
ejpam-6273	167	30	t	t	PROPN
ejpam-6273	167	31	∈	∈	PROPN
ejpam-6273	168	1	y	y	PROPN
ejpam-6273	168	2	such	such	ADJ
ejpam-6273	168	3	that	that	DET
ejpam-6273	168	4	q	q	NOUN
ejpam-6273	168	5	=	=	SYM
ejpam-6273	168	6	ω(d	ω(d	NOUN
ejpam-6273	168	7	)	)	PUNCT
ejpam-6273	168	8	,	,	PUNCT
ejpam-6273	168	9	ς	ς	PROPN
ejpam-6273	168	10	=	=	SYM
ejpam-6273	168	11	ω(t	ω(t	NOUN
ejpam-6273	168	12	)	)	PUNCT
ejpam-6273	168	13	,	,	PUNCT
ejpam-6273	168	14	ω(ϱ̃)(q	ω(ϱ̃)(q	PUNCT
ejpam-6273	169	1	+	+	CCONJ
ejpam-6273	169	2	ς	ς	X
ejpam-6273	169	3	)	)	PUNCT
ejpam-6273	169	4	=	=	NOUN
ejpam-6273	169	5	⋃	⋃	NOUN
ejpam-6273	169	6	r∈ω−1(q+ς	r∈ω−1(q+ς	ADJ
ejpam-6273	169	7	)	)	PUNCT
ejpam-6273	169	8	ϱ̃(r	ϱ̃(r	PROPN
ejpam-6273	169	9	)	)	PUNCT
ejpam-6273	169	10	⊇	⊇	NOUN
ejpam-6273	169	11	⋃	⋃	PROPN
ejpam-6273	169	12	d∈ω−1(q),t∈ω−1(ς	d∈ω−1(q),t∈ω−1(ς	PROPN
ejpam-6273	169	13	)	)	PUNCT
ejpam-6273	169	14	ϱ̃(d+	ϱ̃(d+	PROPN
ejpam-6273	169	15	t	t	PROPN
ejpam-6273	169	16	)	)	PUNCT
ejpam-6273	169	17	⊇	⊇	NOUN
ejpam-6273	169	18	⋃	⋃	PROPN
ejpam-6273	169	19	d∈ω−1(q),t∈ω−1(ς	d∈ω−1(q),t∈ω−1(ς	ADJ
ejpam-6273	169	20	)	)	PUNCT
ejpam-6273	169	21	ϱ̃(d	ϱ̃(d	ADJ
ejpam-6273	169	22	)	)	PUNCT
ejpam-6273	169	23	∩	∩	NOUN
ejpam-6273	169	24	ϱ̃(t	ϱ̃(t	PROPN
ejpam-6273	169	25	)	)	PUNCT
ejpam-6273	169	26	=	=	PRON
ejpam-6273	169	27	(	(	PUNCT
ejpam-6273	169	28	⋃	⋃	NOUN
ejpam-6273	169	29	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	169	30	)	)	PUNCT
ejpam-6273	169	31	ϱ̃(d	ϱ̃(d	NOUN
ejpam-6273	169	32	)	)	PUNCT
ejpam-6273	169	33	)	)	PUNCT
ejpam-6273	170	1	∩	∩	NOUN
ejpam-6273	170	2	(	(	PUNCT
ejpam-6273	170	3	⋃	⋃	PROPN
ejpam-6273	170	4	t∈ω−1(ς	t∈ω−1(ς	NOUN
ejpam-6273	170	5	)	)	PUNCT
ejpam-6273	170	6	ϱ̃(t	ϱ̃(t	PROPN
ejpam-6273	170	7	)	)	PUNCT
ejpam-6273	170	8	)	)	PUNCT
ejpam-6273	171	1	p.	p.	NOUN
ejpam-6273	171	2	n.	n.	PROPN
ejpam-6273	171	3	swamy	swamy	PROPN
ejpam-6273	171	4	et	et	PROPN
ejpam-6273	171	5	al	al	PROPN
ejpam-6273	171	6	.	.	PUNCT
ejpam-6273	171	7	/	/	SYM
ejpam-6273	171	8	eur	eur	PROPN
ejpam-6273	171	9	.	.	PUNCT
ejpam-6273	172	1	j.	j.	PROPN
ejpam-6273	172	2	pure	pure	PROPN
ejpam-6273	172	3	appl	appl	PROPN
ejpam-6273	172	4	.	.	PROPN
ejpam-6273	172	5	math	math	PROPN
ejpam-6273	172	6	,	,	PUNCT
ejpam-6273	172	7	18	18	NUM
ejpam-6273	172	8	(	(	PUNCT
ejpam-6273	172	9	3	3	NUM
ejpam-6273	172	10	)	)	PUNCT
ejpam-6273	172	11	(	(	PUNCT
ejpam-6273	172	12	2025	2025	NUM
ejpam-6273	172	13	)	)	PUNCT
ejpam-6273	172	14	,	,	PUNCT
ejpam-6273	172	15	6273	6273	NUM
ejpam-6273	172	16	7	7	NUM
ejpam-6273	172	17	of	of	ADP
ejpam-6273	172	18	16	16	NUM
ejpam-6273	172	19	=	=	SYM
ejpam-6273	172	20	(	(	PUNCT
ejpam-6273	172	21	ω(ϱ̃)(q	ω(ϱ̃)(q	NOUN
ejpam-6273	172	22	)	)	PUNCT
ejpam-6273	172	23	)	)	PUNCT
ejpam-6273	172	24	∩	∩	NOUN
ejpam-6273	172	25	(	(	PUNCT
ejpam-6273	172	26	ω(ϱ̃)(ς	ω(ϱ̃)(ς	NUM
ejpam-6273	172	27	)	)	PUNCT
ejpam-6273	172	28	)	)	PUNCT
ejpam-6273	172	29	and	and	CCONJ
ejpam-6273	172	30	ω(γ)(q	ω(γ)(q	NUM
ejpam-6273	172	31	+	+	CCONJ
ejpam-6273	172	32	ς	ς	X
ejpam-6273	172	33	)	)	PUNCT
ejpam-6273	172	34	=	=	SYM
ejpam-6273	172	35	∧	∧	NOUN
ejpam-6273	172	36	r∈ω−1(q+ς	r∈ω−1(q+ς	ADJ
ejpam-6273	172	37	)	)	PUNCT
ejpam-6273	172	38	γ(r	γ(r	PROPN
ejpam-6273	172	39	)	)	PUNCT
ejpam-6273	172	40	≤	≤	NUM
ejpam-6273	173	1	∧	∧	PROPN
ejpam-6273	173	2	d∈ω−1(q),t∈ω−1(ς	d∈ω−1(q),t∈ω−1(ς	PROPN
ejpam-6273	173	3	)	)	PUNCT
ejpam-6273	173	4	γ(d+	γ(d+	PROPN
ejpam-6273	173	5	t	t	PROPN
ejpam-6273	173	6	)	)	PUNCT
ejpam-6273	173	7	≤	≤	NUM
ejpam-6273	173	8	∧	∧	PROPN
ejpam-6273	173	9	d∈ω−1(q),t∈ω−1(ς	d∈ω−1(q),t∈ω−1(ς	PROPN
ejpam-6273	173	10	)	)	PUNCT
ejpam-6273	173	11	(	(	PUNCT
ejpam-6273	173	12	∨{γ(d	∨{γ(d	NOUN
ejpam-6273	173	13	)	)	PUNCT
ejpam-6273	173	14	,	,	PUNCT
ejpam-6273	173	15	γ(d	γ(d	PROPN
ejpam-6273	173	16	)	)	PUNCT
ejpam-6273	173	17	}	}	PUNCT
ejpam-6273	173	18	)	)	PUNCT
ejpam-6273	174	1	=	=	SYM
ejpam-6273	174	2	∨	∨	X
ejpam-6273	174	3	{	{	PUNCT
ejpam-6273	174	4	∧	∧	PROPN
ejpam-6273	174	5	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	174	6	)	)	PUNCT
ejpam-6273	174	7	γ(d	γ(d	PROPN
ejpam-6273	174	8	)	)	PUNCT
ejpam-6273	174	9	,	,	PUNCT
ejpam-6273	174	10	∧	∧	PROPN
ejpam-6273	174	11	t∈ω−1(ς	t∈ω−1(ς	PROPN
ejpam-6273	174	12	)	)	PUNCT
ejpam-6273	174	13	γ(t	γ(t	NOUN
ejpam-6273	174	14	)	)	PUNCT
ejpam-6273	174	15	}	}	PUNCT
ejpam-6273	174	16	=	=	SYM
ejpam-6273	174	17	∨{ω(γ)(q	∨{ω(γ)(q	PROPN
ejpam-6273	174	18	)	)	PUNCT
ejpam-6273	174	19	,	,	PUNCT
ejpam-6273	174	20	ω(γ)(ς	ω(γ)(ς	NUM
ejpam-6273	174	21	)	)	PUNCT
ejpam-6273	174	22	}	}	PUNCT
ejpam-6273	174	23	.	.	PUNCT
ejpam-6273	175	1	(	(	PUNCT
ejpam-6273	175	2	ii	ii	NOUN
ejpam-6273	175	3	)	)	PUNCT
ejpam-6273	175	4	let	let	VERB
ejpam-6273	175	5	s	s	PRON
ejpam-6273	175	6	∈	∈	PROPN
ejpam-6273	175	7	l.	l.	NOUN
ejpam-6273	175	8	then	then	ADV
ejpam-6273	175	9	ω(ϱ̃)(sq	ω(ϱ̃)(sq	PROPN
ejpam-6273	175	10	)	)	PUNCT
ejpam-6273	175	11	=	=	SYM
ejpam-6273	175	12	⋃	⋃	NOUN
ejpam-6273	175	13	r∈ω−1(sq	r∈ω−1(sq	NOUN
ejpam-6273	175	14	)	)	PUNCT
ejpam-6273	175	15	ϱ̃(r	ϱ̃(r	PROPN
ejpam-6273	175	16	)	)	PUNCT
ejpam-6273	175	17	⊇	⊇	NOUN
ejpam-6273	175	18	⋃	⋃	NOUN
ejpam-6273	175	19	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	175	20	)	)	PUNCT
ejpam-6273	175	21	ϱ̃(sd	ϱ̃(sd	NOUN
ejpam-6273	175	22	)	)	PUNCT
ejpam-6273	175	23	⊇	⊇	NOUN
ejpam-6273	175	24	⋃	⋃	NOUN
ejpam-6273	175	25	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	175	26	)	)	PUNCT
ejpam-6273	175	27	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	175	28	)	)	PUNCT
ejpam-6273	175	29	∩	∩	NOUN
ejpam-6273	175	30	ϱ̃(d	ϱ̃(d	NOUN
ejpam-6273	175	31	)	)	PUNCT
ejpam-6273	175	32	=	=	SYM
ejpam-6273	175	33	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	175	34	)	)	PUNCT
ejpam-6273	175	35	∩	∩	NOUN
ejpam-6273	175	36	(	(	PUNCT
ejpam-6273	175	37	⋃	⋃	NOUN
ejpam-6273	175	38	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	175	39	)	)	PUNCT
ejpam-6273	175	40	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	175	41	)	)	PUNCT
ejpam-6273	175	42	)	)	PUNCT
ejpam-6273	176	1	=	=	SYM
ejpam-6273	176	2	ξ̃(s	ξ̃(s	NOUN
ejpam-6273	176	3	)	)	PUNCT
ejpam-6273	176	4	∩	∩	NOUN
ejpam-6273	176	5	ω(ϱ̃)(q	ω(ϱ̃)(q	NUM
ejpam-6273	176	6	)	)	PUNCT
ejpam-6273	176	7	and	and	CCONJ
ejpam-6273	176	8	ω(γ)(sq	ω(γ)(sq	NUM
ejpam-6273	176	9	)	)	PUNCT
ejpam-6273	176	10	=	=	SYM
ejpam-6273	177	1	∧	∧	NOUN
ejpam-6273	177	2	r∈ω−1(sq	r∈ω−1(sq	NOUN
ejpam-6273	177	3	)	)	PUNCT
ejpam-6273	177	4	γ(r	γ(r	PROPN
ejpam-6273	177	5	)	)	PUNCT
ejpam-6273	177	6	≤	≤	NUM
ejpam-6273	177	7	∧	∧	PROPN
ejpam-6273	177	8	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	177	9	)	)	PUNCT
ejpam-6273	177	10	γ(sd	γ(sd	PROPN
ejpam-6273	177	11	)	)	PUNCT
ejpam-6273	177	12	≤	≤	NUM
ejpam-6273	177	13	∧	∧	PROPN
ejpam-6273	177	14	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	177	15	)	)	PUNCT
ejpam-6273	177	16	(	(	PUNCT
ejpam-6273	177	17	∨	∨	X
ejpam-6273	177	18	{	{	PUNCT
ejpam-6273	177	19	λ(s	λ(s	PROPN
ejpam-6273	177	20	)	)	PUNCT
ejpam-6273	177	21	,	,	PUNCT
ejpam-6273	177	22	γ(d	γ(d	PROPN
ejpam-6273	177	23	)	)	PUNCT
ejpam-6273	177	24	}	}	PUNCT
ejpam-6273	177	25	)	)	PUNCT
ejpam-6273	178	1	=	=	SYM
ejpam-6273	178	2	∨	∨	X
ejpam-6273	178	3	{	{	PUNCT
ejpam-6273	178	4	λ(s	λ(s	PROPN
ejpam-6273	178	5	)	)	PUNCT
ejpam-6273	178	6	,	,	PUNCT
ejpam-6273	178	7	∧	∧	PROPN
ejpam-6273	178	8	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	178	9	)	)	PUNCT
ejpam-6273	178	10	γ(d	γ(d	PROPN
ejpam-6273	178	11	)	)	PUNCT
ejpam-6273	178	12	}	}	PUNCT
ejpam-6273	178	13	=	=	SYM
ejpam-6273	178	14	∨	∨	X
ejpam-6273	178	15	{	{	PUNCT
ejpam-6273	178	16	λ(s	λ(s	PROPN
ejpam-6273	178	17	)	)	PUNCT
ejpam-6273	178	18	,	,	PUNCT
ejpam-6273	178	19	ω(γ)(q	ω(γ)(q	NUM
ejpam-6273	178	20	)	)	PUNCT
ejpam-6273	178	21	}	}	PUNCT
ejpam-6273	178	22	.	.	PUNCT
ejpam-6273	179	1	(	(	PUNCT
ejpam-6273	179	2	iii	iii	X
ejpam-6273	179	3	)	)	PUNCT
ejpam-6273	179	4	ξ̃(1	ξ̃(1	NOUN
ejpam-6273	179	5	)	)	PUNCT
ejpam-6273	179	6	⊇	⊇	NOUN
ejpam-6273	179	7	ω(ϱ̃)(q	ω(ϱ̃)(q	NUM
ejpam-6273	179	8	)	)	PUNCT
ejpam-6273	179	9	and	and	CCONJ
ejpam-6273	179	10	λ(1	λ(1	PROPN
ejpam-6273	179	11	)	)	PUNCT
ejpam-6273	179	12	≤	≤	NUM
ejpam-6273	179	13	ω(γ)(q),∀q	ω(γ)(q),∀q	PUNCT
ejpam-6273	179	14	∈	∈	PROPN
ejpam-6273	179	15	y	y	NOUN
ejpam-6273	179	16	′	′	NUM
ejpam-6273	179	17	.	.	PUNCT
ejpam-6273	180	1	p.	p.	NOUN
ejpam-6273	180	2	n.	n.	PROPN
ejpam-6273	180	3	swamy	swamy	PROPN
ejpam-6273	180	4	et	et	PROPN
ejpam-6273	180	5	al	al	PROPN
ejpam-6273	180	6	.	.	PUNCT
ejpam-6273	180	7	/	/	SYM
ejpam-6273	180	8	eur	eur	PROPN
ejpam-6273	180	9	.	.	PUNCT
ejpam-6273	181	1	j.	j.	PROPN
ejpam-6273	181	2	pure	pure	PROPN
ejpam-6273	181	3	appl	appl	PROPN
ejpam-6273	181	4	.	.	PROPN
ejpam-6273	181	5	math	math	PROPN
ejpam-6273	181	6	,	,	PUNCT
ejpam-6273	181	7	18	18	NUM
ejpam-6273	181	8	(	(	PUNCT
ejpam-6273	181	9	3	3	NUM
ejpam-6273	181	10	)	)	PUNCT
ejpam-6273	181	11	(	(	PUNCT
ejpam-6273	181	12	2025	2025	NUM
ejpam-6273	181	13	)	)	PUNCT
ejpam-6273	181	14	,	,	PUNCT
ejpam-6273	181	15	6273	6273	NUM
ejpam-6273	181	16	8	8	NUM
ejpam-6273	181	17	of	of	ADP
ejpam-6273	181	18	16	16	NUM
ejpam-6273	181	19	(	(	PUNCT
ejpam-6273	181	20	iv	iv	NOUN
ejpam-6273	181	21	)	)	PUNCT
ejpam-6273	181	22	ω(ϱ̃)(qς	ω(ϱ̃)(qς	NUM
ejpam-6273	181	23	)	)	PUNCT
ejpam-6273	182	1	=	=	SYM
ejpam-6273	182	2	⋃	⋃	NOUN
ejpam-6273	182	3	r∈ω−1(qς	r∈ω−1(qς	NOUN
ejpam-6273	182	4	)	)	PUNCT
ejpam-6273	182	5	ϱ̃(r	ϱ̃(r	PROPN
ejpam-6273	182	6	)	)	PUNCT
ejpam-6273	182	7	⊇	⊇	NOUN
ejpam-6273	182	8	⋃	⋃	PROPN
ejpam-6273	182	9	d∈ω−1(q),t∈ω−1(ς	d∈ω−1(q),t∈ω−1(ς	PROPN
ejpam-6273	182	10	)	)	PUNCT
ejpam-6273	182	11	ϱ̃(dt	ϱ̃(dt	PROPN
ejpam-6273	182	12	)	)	PUNCT
ejpam-6273	182	13	⊇	⊇	NOUN
ejpam-6273	182	14	⋃	⋃	NOUN
ejpam-6273	182	15	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	182	16	)	)	PUNCT
ejpam-6273	182	17	ϱ̃(d	ϱ̃(d	NOUN
ejpam-6273	182	18	)	)	PUNCT
ejpam-6273	182	19	=	=	SYM
ejpam-6273	182	20	(	(	PUNCT
ejpam-6273	182	21	ω(ϱ̃)(q	ω(ϱ̃)(q	NOUN
ejpam-6273	182	22	)	)	PUNCT
ejpam-6273	182	23	)	)	PUNCT
ejpam-6273	182	24	and	and	CCONJ
ejpam-6273	182	25	ω(γ)(qς	ω(γ)(qς	NUM
ejpam-6273	182	26	)	)	PUNCT
ejpam-6273	182	27	=	=	SYM
ejpam-6273	182	28	∧	∧	PROPN
ejpam-6273	182	29	r∈ω−1(qς	r∈ω−1(qς	NOUN
ejpam-6273	182	30	)	)	PUNCT
ejpam-6273	182	31	γ(r	γ(r	PROPN
ejpam-6273	182	32	)	)	PUNCT
ejpam-6273	182	33	≤	≤	NUM
ejpam-6273	182	34	∧	∧	PROPN
ejpam-6273	182	35	d∈ω−1(q),t∈ω−1(ς	d∈ω−1(q),t∈ω−1(ς	PROPN
ejpam-6273	182	36	)	)	PUNCT
ejpam-6273	182	37	γ(dt	γ(dt	PROPN
ejpam-6273	182	38	)	)	PUNCT
ejpam-6273	182	39	≤	≤	NUM
ejpam-6273	182	40	∧	∧	PROPN
ejpam-6273	182	41	d∈ω−1(q	d∈ω−1(q	NOUN
ejpam-6273	182	42	)	)	PUNCT
ejpam-6273	182	43	γ(d	γ(d	PROPN
ejpam-6273	182	44	)	)	PUNCT
ejpam-6273	182	45	=	=	PUNCT
ejpam-6273	183	1	ω(γ)(q	ω(γ)(q	NUM
ejpam-6273	183	2	)	)	PUNCT
ejpam-6273	183	3	.	.	PUNCT
ejpam-6273	184	1	(	(	PUNCT
ejpam-6273	184	2	v	v	X
ejpam-6273	184	3	)	)	PUNCT
ejpam-6273	184	4	let	let	VERB
ejpam-6273	184	5	q	q	PRON
ejpam-6273	184	6	,	,	PUNCT
ejpam-6273	184	7	ς	ς	PROPN
ejpam-6273	184	8	,	,	PUNCT
ejpam-6273	185	1	i	i	PRON
ejpam-6273	185	2	∈	∈	VERB
ejpam-6273	186	1	y	y	NOUN
ejpam-6273	186	2	′	′	NUM
ejpam-6273	186	3	.	.	PUNCT
ejpam-6273	187	1	then	then	ADV
ejpam-6273	187	2	there	there	PRON
ejpam-6273	187	3	exist	exist	VERB
ejpam-6273	187	4	d	d	PROPN
ejpam-6273	187	5	,	,	PUNCT
ejpam-6273	187	6	t	t	PROPN
ejpam-6273	187	7	,	,	PUNCT
ejpam-6273	187	8	m	m	PROPN
ejpam-6273	187	9	∈	∈	NOUN
ejpam-6273	187	10	y	y	NOUN
ejpam-6273	187	11	such	such	ADJ
ejpam-6273	187	12	that	that	DET
ejpam-6273	187	13	q	q	NOUN
ejpam-6273	187	14	=	=	SYM
ejpam-6273	187	15	ω(d	ω(d	NOUN
ejpam-6273	187	16	)	)	PUNCT
ejpam-6273	187	17	,	,	PUNCT
ejpam-6273	187	18	ς	ς	PROPN
ejpam-6273	187	19	=	=	SYM
ejpam-6273	187	20	ω(t	ω(t	NOUN
ejpam-6273	187	21	)	)	PUNCT
ejpam-6273	187	22	,	,	PUNCT
ejpam-6273	187	23	and	and	CCONJ
ejpam-6273	187	24	i	i	PRON
ejpam-6273	187	25	=	=	SYM
ejpam-6273	187	26	ω(m	ω(m	NOUN
ejpam-6273	187	27	)	)	PUNCT
ejpam-6273	187	28	.	.	PUNCT
ejpam-6273	188	1	thus	thus	ADV
ejpam-6273	188	2	,	,	PUNCT
ejpam-6273	188	3	ω(ϱ̃)(ς(q	ω(ϱ̃)(ς(q	NOUN
ejpam-6273	188	4	+	+	PUNCT
ejpam-6273	188	5	i)−	i)−	PROPN
ejpam-6273	188	6	ςq	ςq	PROPN
ejpam-6273	188	7	)	)	PUNCT
ejpam-6273	188	8	=	=	PUNCT
ejpam-6273	188	9	⋃	⋃	NOUN
ejpam-6273	188	10	r∈ω−1(ς(q+i)−ςq	r∈ω−1(ς(q+i)−ςq	NOUN
ejpam-6273	188	11	)	)	PUNCT
ejpam-6273	188	12	ϱ̃(r	ϱ̃(r	PROPN
ejpam-6273	188	13	)	)	PUNCT
ejpam-6273	188	14	⊇	⊇	NOUN
ejpam-6273	188	15	⋃	⋃	PROPN
ejpam-6273	188	16	d∈ω−1(q),t∈ω−1(ς),m∈ω−1(i	d∈ω−1(q),t∈ω−1(ς),m∈ω−1(i	PROPN
ejpam-6273	188	17	)	)	PUNCT
ejpam-6273	188	18	ϱ̃(t(d+m)−	ϱ̃(t(d+m)−	NOUN
ejpam-6273	188	19	td	td	NOUN
ejpam-6273	188	20	)	)	PUNCT
ejpam-6273	188	21	⊇	⊇	NOUN
ejpam-6273	188	22	⋃	⋃	PROPN
ejpam-6273	188	23	m∈ω−1(i	m∈ω−1(i	NOUN
ejpam-6273	188	24	)	)	PUNCT
ejpam-6273	188	25	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	188	26	)	)	PUNCT
ejpam-6273	188	27	=	=	PUNCT
ejpam-6273	188	28	(	(	PUNCT
ejpam-6273	188	29	ω(ϱ̃)(i	ω(ϱ̃)(i	NUM
ejpam-6273	188	30	)	)	PUNCT
ejpam-6273	188	31	)	)	PUNCT
ejpam-6273	188	32	and	and	CCONJ
ejpam-6273	188	33	ω(γ)(ς(q	ω(γ)(ς(q	PRON
ejpam-6273	188	34	+	+	CCONJ
ejpam-6273	188	35	i)−	i)−	PROPN
ejpam-6273	188	36	ςq	ςq	PROPN
ejpam-6273	188	37	)	)	PUNCT
ejpam-6273	188	38	=	=	SYM
ejpam-6273	188	39	∧	∧	NOUN
ejpam-6273	188	40	r∈ω−1(ς(q+i)−ςq	r∈ω−1(ς(q+i)−ςq	NOUN
ejpam-6273	188	41	)	)	PUNCT
ejpam-6273	188	42	γ(r	γ(r	PROPN
ejpam-6273	188	43	)	)	PUNCT
ejpam-6273	188	44	≤	≤	NUM
ejpam-6273	189	1	∧	∧	PROPN
ejpam-6273	189	2	d∈ω−1(q),t∈ω−1(ς),m∈ω−1(i	d∈ω−1(q),t∈ω−1(ς),m∈ω−1(i	PROPN
ejpam-6273	189	3	)	)	PUNCT
ejpam-6273	189	4	γ(t(d+m)−	γ(t(d+m)−	VERB
ejpam-6273	189	5	td	td	NOUN
ejpam-6273	189	6	)	)	PUNCT
ejpam-6273	189	7	≤	≤	NOUN
ejpam-6273	189	8	∧	∧	PROPN
ejpam-6273	189	9	m∈ω−1(i	m∈ω−1(i	NOUN
ejpam-6273	189	10	)	)	PUNCT
ejpam-6273	189	11	γ(i	γ(i	NOUN
ejpam-6273	189	12	)	)	PUNCT
ejpam-6273	190	1	p.	p.	NOUN
ejpam-6273	190	2	n.	n.	PROPN
ejpam-6273	190	3	swamy	swamy	PROPN
ejpam-6273	190	4	et	et	PROPN
ejpam-6273	190	5	al	al	PROPN
ejpam-6273	190	6	.	.	PUNCT
ejpam-6273	190	7	/	/	SYM
ejpam-6273	190	8	eur	eur	PROPN
ejpam-6273	190	9	.	.	PUNCT
ejpam-6273	191	1	j.	j.	PROPN
ejpam-6273	191	2	pure	pure	PROPN
ejpam-6273	191	3	appl	appl	PROPN
ejpam-6273	191	4	.	.	PROPN
ejpam-6273	191	5	math	math	PROPN
ejpam-6273	191	6	,	,	PUNCT
ejpam-6273	191	7	18	18	NUM
ejpam-6273	191	8	(	(	PUNCT
ejpam-6273	191	9	3	3	NUM
ejpam-6273	191	10	)	)	PUNCT
ejpam-6273	191	11	(	(	PUNCT
ejpam-6273	191	12	2025	2025	NUM
ejpam-6273	191	13	)	)	PUNCT
ejpam-6273	191	14	,	,	PUNCT
ejpam-6273	191	15	6273	6273	NUM
ejpam-6273	191	16	9	9	NUM
ejpam-6273	191	17	of	of	ADP
ejpam-6273	191	18	16	16	NUM
ejpam-6273	191	19	=	=	SYM
ejpam-6273	191	20	ω(γ)(i	ω(γ)(i	NUM
ejpam-6273	191	21	)	)	PUNCT
ejpam-6273	191	22	.	.	PUNCT
ejpam-6273	192	1	hence	hence	ADV
ejpam-6273	192	2	,	,	PUNCT
ejpam-6273	192	3	(	(	PUNCT
ejpam-6273	192	4	ω(ϱ̃γ	ω(ϱ̃γ	ADV
ejpam-6273	192	5	)	)	PUNCT
ejpam-6273	192	6	,	,	PUNCT
ejpam-6273	192	7	y	y	PROPN
ejpam-6273	192	8	′	′	NUM
ejpam-6273	192	9	)	)	PUNCT
ejpam-6273	192	10	is	be	AUX
ejpam-6273	192	11	an	an	DET
ejpam-6273	192	12	hina	hina	NOUN
ejpam-6273	192	13	upon	upon	SCONJ
ejpam-6273	192	14	(	(	PUNCT
ejpam-6273	192	15	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	192	16	,	,	PUNCT
ejpam-6273	192	17	l	l	NOUN
ejpam-6273	192	18	)	)	PUNCT
ejpam-6273	192	19	.	.	PUNCT
ejpam-6273	193	1	theorem	theorem	ADJ
ejpam-6273	193	2	4	4	NUM
ejpam-6273	193	3	.	.	PUNCT
ejpam-6273	194	1	let	let	VERB
ejpam-6273	194	2	y	y	PRON
ejpam-6273	194	3	and	and	CCONJ
ejpam-6273	194	4	y	y	PROPN
ejpam-6273	194	5	′	′	NUM
ejpam-6273	194	6	be	be	AUX
ejpam-6273	194	7	two	two	NUM
ejpam-6273	194	8	near	near	ADP
ejpam-6273	194	9	algebras	algebra	NOUN
ejpam-6273	194	10	upon	upon	SCONJ
ejpam-6273	194	11	a	a	DET
ejpam-6273	194	12	field	field	NOUN
ejpam-6273	194	13	l	l	NOUN
ejpam-6273	194	14	and	and	CCONJ
ejpam-6273	194	15	ω	ω	NUM
ejpam-6273	194	16	:	:	PUNCT
ejpam-6273	194	17	y	y	PROPN
ejpam-6273	194	18	→	→	SYM
ejpam-6273	194	19	y	y	PROPN
ejpam-6273	194	20	′	′	NOUN
ejpam-6273	194	21	be	be	AUX
ejpam-6273	194	22	an	an	DET
ejpam-6273	194	23	onto	onto	NOUN
ejpam-6273	194	24	near	near	ADJ
ejpam-6273	194	25	algebra	algebra	PROPN
ejpam-6273	194	26	homomorphism	homomorphism	NOUN
ejpam-6273	194	27	.	.	PUNCT
ejpam-6273	195	1	if	if	SCONJ
ejpam-6273	195	2	h̃µ	h̃µ	ADJ
ejpam-6273	195	3	is	be	AUX
ejpam-6273	195	4	an	an	DET
ejpam-6273	195	5	hina	hina	NOUN
ejpam-6273	195	6	in	in	ADP
ejpam-6273	195	7	y	y	PROPN
ejpam-6273	195	8	′	′	NUM
ejpam-6273	195	9	upon	upon	SCONJ
ejpam-6273	195	10	(	(	PUNCT
ejpam-6273	195	11	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	195	12	,	,	PUNCT
ejpam-6273	195	13	l	l	NOUN
ejpam-6273	195	14	)	)	PUNCT
ejpam-6273	195	15	,	,	PUNCT
ejpam-6273	195	16	then	then	ADV
ejpam-6273	195	17	ω−1(h̃µ	ω−1(h̃µ	NUM
ejpam-6273	195	18	)	)	PUNCT
ejpam-6273	195	19	=	=	SYM
ejpam-6273	195	20	(	(	PUNCT
ejpam-6273	195	21	ω−1(h̃	ω−1(h̃	NOUN
ejpam-6273	195	22	)	)	PUNCT
ejpam-6273	195	23	,	,	PUNCT
ejpam-6273	195	24	ω−1(µ	ω−1(µ	PROPN
ejpam-6273	195	25	)	)	PUNCT
ejpam-6273	195	26	)	)	PUNCT
ejpam-6273	195	27	is	be	AUX
ejpam-6273	195	28	an	an	DET
ejpam-6273	195	29	hina	hina	NOUN
ejpam-6273	195	30	in	in	ADP
ejpam-6273	195	31	y	y	PROPN
ejpam-6273	195	32	upon	upon	SCONJ
ejpam-6273	195	33	(	(	PUNCT
ejpam-6273	195	34	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	195	35	,	,	PUNCT
ejpam-6273	195	36	l	l	NOUN
ejpam-6273	195	37	)	)	PUNCT
ejpam-6273	195	38	.	.	PUNCT
ejpam-6273	196	1	proof	proof	NOUN
ejpam-6273	196	2	.	.	PUNCT
ejpam-6273	197	1	let	let	VERB
ejpam-6273	197	2	q	q	PRON
ejpam-6273	197	3	,	,	PUNCT
ejpam-6273	197	4	ς	ς	PROPN
ejpam-6273	197	5	,	,	PUNCT
ejpam-6273	197	6	i	i	PRON
ejpam-6273	197	7	∈	∈	PROPN
ejpam-6273	198	1	y	y	INTJ
ejpam-6273	198	2	.	.	PUNCT
ejpam-6273	199	1	then	then	ADV
ejpam-6273	199	2	(	(	PUNCT
ejpam-6273	199	3	i	i	NOUN
ejpam-6273	199	4	)	)	PUNCT
ejpam-6273	199	5	ω−1(h̃)(qς	ω−1(h̃)(qς	PROPN
ejpam-6273	199	6	)	)	PUNCT
ejpam-6273	199	7	=	=	SYM
ejpam-6273	199	8	h̃(ω(qς	h̃(ω(qς	NOUN
ejpam-6273	199	9	)	)	PUNCT
ejpam-6273	199	10	)	)	PUNCT
ejpam-6273	200	1	=	=	SYM
ejpam-6273	200	2	h̃(ω(q)ω(ς	h̃(ω(q)ω(ς	PROPN
ejpam-6273	200	3	)	)	PUNCT
ejpam-6273	200	4	)	)	PUNCT
ejpam-6273	201	1	⊇	⊇	PROPN
ejpam-6273	201	2	h̃(ω(q	h̃(ω(q	NUM
ejpam-6273	201	3	)	)	PUNCT
ejpam-6273	201	4	)	)	PUNCT
ejpam-6273	201	5	=	=	SYM
ejpam-6273	201	6	ω−1(h̃)(q	ω−1(h̃)(q	PROPN
ejpam-6273	201	7	)	)	PUNCT
ejpam-6273	201	8	and	and	CCONJ
ejpam-6273	201	9	ω−1(µ)(qς	ω−1(µ)(qς	PROPN
ejpam-6273	201	10	)	)	PUNCT
ejpam-6273	201	11	=	=	SYM
ejpam-6273	201	12	µ(ω(qς	µ(ω(qς	NOUN
ejpam-6273	201	13	)	)	PUNCT
ejpam-6273	201	14	)	)	PUNCT
ejpam-6273	202	1	=	=	SYM
ejpam-6273	202	2	µ(ω(q)ω(ς	µ(ω(q)ω(ς	NOUN
ejpam-6273	202	3	)	)	PUNCT
ejpam-6273	202	4	)	)	PUNCT
ejpam-6273	203	1	≤	≤	PROPN
ejpam-6273	203	2	µ(ω(q	µ(ω(q	PROPN
ejpam-6273	203	3	)	)	PUNCT
ejpam-6273	203	4	)	)	PUNCT
ejpam-6273	204	1	=	=	PUNCT
ejpam-6273	204	2	ω−1(µ)(q	ω−1(µ)(q	PROPN
ejpam-6273	204	3	)	)	PUNCT
ejpam-6273	204	4	.	.	PUNCT
ejpam-6273	205	1	(	(	PUNCT
ejpam-6273	205	2	ii	ii	NOUN
ejpam-6273	205	3	)	)	PUNCT
ejpam-6273	205	4	ω−1(h̃)(ς(q	ω−1(h̃)(ς(q	PROPN
ejpam-6273	206	1	+	+	NUM
ejpam-6273	206	2	i	i	NOUN
ejpam-6273	206	3	)	)	PUNCT
ejpam-6273	206	4	−	−	PROPN
ejpam-6273	206	5	ςq	ςq	NOUN
ejpam-6273	206	6	)	)	PUNCT
ejpam-6273	206	7	=	=	SYM
ejpam-6273	206	8	h̃(ω(ς(q	h̃(ω(ς(q	NUM
ejpam-6273	206	9	+	+	CCONJ
ejpam-6273	206	10	i	i	NOUN
ejpam-6273	206	11	)	)	PUNCT
ejpam-6273	206	12	−	−	PROPN
ejpam-6273	206	13	ςq	ςq	NOUN
ejpam-6273	206	14	)	)	PUNCT
ejpam-6273	206	15	)	)	PUNCT
ejpam-6273	207	1	=	=	SYM
ejpam-6273	207	2	h̃(ω(ς)(ω(q	h̃(ω(ς)(ω(q	X
ejpam-6273	207	3	)	)	PUNCT
ejpam-6273	208	1	+	+	CCONJ
ejpam-6273	208	2	ω(i	ω(i	PROPN
ejpam-6273	208	3	)	)	PUNCT
ejpam-6273	208	4	)	)	PUNCT
ejpam-6273	209	1	−	−	PROPN
ejpam-6273	209	2	ω(q)ω(ς	ω(q)ω(ς	NUM
ejpam-6273	209	3	)	)	PUNCT
ejpam-6273	209	4	)	)	PUNCT
ejpam-6273	210	1	⊇	⊇	PROPN
ejpam-6273	210	2	h̃(ω(i	h̃(ω(i	PROPN
ejpam-6273	210	3	)	)	PUNCT
ejpam-6273	210	4	)	)	PUNCT
ejpam-6273	211	1	=	=	SYM
ejpam-6273	211	2	ω−1(h̃)(i	ω−1(h̃)(i	PROPN
ejpam-6273	211	3	)	)	PUNCT
ejpam-6273	211	4	and	and	CCONJ
ejpam-6273	211	5	ω−1(µ)(ς(q	ω−1(µ)(ς(q	PRON
ejpam-6273	211	6	+	+	NUM
ejpam-6273	211	7	i	i	NOUN
ejpam-6273	211	8	)	)	PUNCT
ejpam-6273	212	1	−	−	PROPN
ejpam-6273	212	2	ςq	ςq	NOUN
ejpam-6273	212	3	)	)	PUNCT
ejpam-6273	212	4	=	=	PUNCT
ejpam-6273	213	1	µ(ω(ς(q	µ(ω(ς(q	PROPN
ejpam-6273	213	2	+	+	NUM
ejpam-6273	213	3	i	i	NOUN
ejpam-6273	213	4	)	)	PUNCT
ejpam-6273	214	1	−	−	PROPN
ejpam-6273	214	2	ςq	ςq	NOUN
ejpam-6273	214	3	)	)	PUNCT
ejpam-6273	214	4	)	)	PUNCT
ejpam-6273	215	1	=	=	SYM
ejpam-6273	215	2	µ(ω(ς)(ω(q	µ(ω(ς)(ω(q	X
ejpam-6273	215	3	)	)	PUNCT
ejpam-6273	215	4	+	+	CCONJ
ejpam-6273	215	5	ω(i))−	ω(i))−	ADP
ejpam-6273	215	6	ω(q)ω(ς	ω(q)ω(ς	NUM
ejpam-6273	215	7	)	)	PUNCT
ejpam-6273	215	8	)	)	PUNCT
ejpam-6273	215	9	≤	≤	PROPN
ejpam-6273	215	10	µ(ω(i	µ(ω(i	NOUN
ejpam-6273	215	11	)	)	PUNCT
ejpam-6273	215	12	)	)	PUNCT
ejpam-6273	216	1	=	=	SYM
ejpam-6273	216	2	ω−1(µ)(i	ω−1(µ)(i	PROPN
ejpam-6273	216	3	)	)	PUNCT
ejpam-6273	216	4	.	.	PUNCT
ejpam-6273	217	1	therefore	therefore	ADV
ejpam-6273	217	2	,	,	PUNCT
ejpam-6273	217	3	ω−1(h̃µ	ω−1(h̃µ	PUNCT
ejpam-6273	217	4	)	)	PUNCT
ejpam-6273	217	5	=	=	SYM
ejpam-6273	217	6	(	(	PUNCT
ejpam-6273	217	7	ω−1(h̃	ω−1(h̃	NOUN
ejpam-6273	217	8	)	)	PUNCT
ejpam-6273	217	9	,	,	PUNCT
ejpam-6273	217	10	ω−1(µ	ω−1(µ	PROPN
ejpam-6273	217	11	)	)	PUNCT
ejpam-6273	217	12	)	)	PUNCT
ejpam-6273	217	13	is	be	AUX
ejpam-6273	217	14	an	an	DET
ejpam-6273	217	15	hina	hina	NOUN
ejpam-6273	217	16	in	in	ADP
ejpam-6273	217	17	y	y	PROPN
ejpam-6273	217	18	upon	upon	SCONJ
ejpam-6273	217	19	(	(	PUNCT
ejpam-6273	217	20	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	217	21	,	,	PUNCT
ejpam-6273	217	22	l	l	NOUN
ejpam-6273	217	23	)	)	PUNCT
ejpam-6273	217	24	.	.	PUNCT
ejpam-6273	218	1	theorem	theorem	NOUN
ejpam-6273	218	2	5	5	NUM
ejpam-6273	218	3	.	.	PUNCT
ejpam-6273	219	1	let	let	VERB
ejpam-6273	219	2	y	y	PRON
ejpam-6273	219	3	and	and	CCONJ
ejpam-6273	219	4	y	y	PROPN
ejpam-6273	219	5	′	′	NUM
ejpam-6273	219	6	be	be	AUX
ejpam-6273	219	7	two	two	NUM
ejpam-6273	219	8	near	near	ADP
ejpam-6273	219	9	algebras	algebra	NOUN
ejpam-6273	219	10	upon	upon	SCONJ
ejpam-6273	219	11	a	a	DET
ejpam-6273	219	12	field	field	NOUN
ejpam-6273	219	13	l	l	NOUN
ejpam-6273	219	14	and	and	CCONJ
ejpam-6273	219	15	ω	ω	NUM
ejpam-6273	219	16	:	:	PUNCT
ejpam-6273	219	17	y	y	PROPN
ejpam-6273	219	18	→	→	SYM
ejpam-6273	219	19	y	y	PROPN
ejpam-6273	219	20	′	′	NOUN
ejpam-6273	219	21	be	be	AUX
ejpam-6273	219	22	an	an	DET
ejpam-6273	219	23	onto	onto	NOUN
ejpam-6273	219	24	near	near	ADJ
ejpam-6273	219	25	algebra	algebra	PROPN
ejpam-6273	219	26	homomorphism	homomorphism	NOUN
ejpam-6273	219	27	.	.	PUNCT
ejpam-6273	220	1	if	if	SCONJ
ejpam-6273	220	2	h̃µ	h̃µ	ADJ
ejpam-6273	220	3	is	be	AUX
ejpam-6273	220	4	an	an	DET
ejpam-6273	220	5	hina	hina	NOUN
ejpam-6273	220	6	in	in	ADP
ejpam-6273	220	7	y	y	PROPN
ejpam-6273	220	8	′	′	NUM
ejpam-6273	220	9	upon	upon	SCONJ
ejpam-6273	220	10	(	(	PUNCT
ejpam-6273	220	11	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	220	12	,	,	PUNCT
ejpam-6273	220	13	l	l	NOUN
ejpam-6273	220	14	)	)	PUNCT
ejpam-6273	220	15	,	,	PUNCT
ejpam-6273	220	16	then	then	ADV
ejpam-6273	220	17	ω−1(h̃µ	ω−1(h̃µ	NUM
ejpam-6273	220	18	)	)	PUNCT
ejpam-6273	220	19	=	=	SYM
ejpam-6273	220	20	(	(	PUNCT
ejpam-6273	220	21	ω−1(h̃	ω−1(h̃	NOUN
ejpam-6273	220	22	)	)	PUNCT
ejpam-6273	220	23	,	,	PUNCT
ejpam-6273	220	24	ω−1(µ	ω−1(µ	PROPN
ejpam-6273	220	25	)	)	PUNCT
ejpam-6273	220	26	)	)	PUNCT
ejpam-6273	220	27	is	be	AUX
ejpam-6273	220	28	an	an	DET
ejpam-6273	220	29	hina	hina	NOUN
ejpam-6273	220	30	in	in	ADP
ejpam-6273	220	31	y	y	PROPN
ejpam-6273	220	32	upon	upon	SCONJ
ejpam-6273	220	33	(	(	PUNCT
ejpam-6273	220	34	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	220	35	,	,	PUNCT
ejpam-6273	220	36	l	l	NOUN
ejpam-6273	220	37	)	)	PUNCT
ejpam-6273	220	38	.	.	PUNCT
ejpam-6273	221	1	proof	proof	NOUN
ejpam-6273	221	2	.	.	PUNCT
ejpam-6273	222	1	let	let	VERB
ejpam-6273	222	2	q	q	PRON
ejpam-6273	222	3	,	,	PUNCT
ejpam-6273	222	4	ς	ς	PROPN
ejpam-6273	222	5	,	,	PUNCT
ejpam-6273	222	6	i	i	PRON
ejpam-6273	222	7	∈	∈	PROPN
ejpam-6273	223	1	y	y	INTJ
ejpam-6273	223	2	.	.	PUNCT
ejpam-6273	224	1	then	then	ADV
ejpam-6273	224	2	(	(	PUNCT
ejpam-6273	224	3	i	i	NOUN
ejpam-6273	224	4	)	)	PUNCT
ejpam-6273	224	5	ω−1(h̃)(qς	ω−1(h̃)(qς	PROPN
ejpam-6273	224	6	)	)	PUNCT
ejpam-6273	224	7	=	=	SYM
ejpam-6273	224	8	h̃(ω(qς	h̃(ω(qς	NOUN
ejpam-6273	224	9	)	)	PUNCT
ejpam-6273	224	10	)	)	PUNCT
ejpam-6273	225	1	=	=	SYM
ejpam-6273	225	2	h̃(ω(q)ω(ς	h̃(ω(q)ω(ς	PROPN
ejpam-6273	225	3	)	)	PUNCT
ejpam-6273	225	4	)	)	PUNCT
ejpam-6273	226	1	⊇	⊇	PROPN
ejpam-6273	226	2	h̃(ω(q	h̃(ω(q	NUM
ejpam-6273	226	3	)	)	PUNCT
ejpam-6273	226	4	)	)	PUNCT
ejpam-6273	226	5	=	=	SYM
ejpam-6273	226	6	ω−1(h̃)(q	ω−1(h̃)(q	PROPN
ejpam-6273	226	7	)	)	PUNCT
ejpam-6273	226	8	and	and	CCONJ
ejpam-6273	226	9	ω−1(µ)(qς	ω−1(µ)(qς	PROPN
ejpam-6273	226	10	)	)	PUNCT
ejpam-6273	226	11	=	=	SYM
ejpam-6273	226	12	µ(ω(qς	µ(ω(qς	NOUN
ejpam-6273	226	13	)	)	PUNCT
ejpam-6273	226	14	)	)	PUNCT
ejpam-6273	227	1	=	=	SYM
ejpam-6273	227	2	µ(ω(q)ω(ς	µ(ω(q)ω(ς	NOUN
ejpam-6273	227	3	)	)	PUNCT
ejpam-6273	227	4	)	)	PUNCT
ejpam-6273	228	1	≤	≤	PROPN
ejpam-6273	228	2	µ(ω(q	µ(ω(q	PROPN
ejpam-6273	228	3	)	)	PUNCT
ejpam-6273	228	4	)	)	PUNCT
ejpam-6273	229	1	=	=	PUNCT
ejpam-6273	229	2	ω−1(µ)(q	ω−1(µ)(q	PROPN
ejpam-6273	229	3	)	)	PUNCT
ejpam-6273	229	4	.	.	PUNCT
ejpam-6273	230	1	(	(	PUNCT
ejpam-6273	230	2	ii	ii	NOUN
ejpam-6273	230	3	)	)	PUNCT
ejpam-6273	230	4	ω−1(h̃)(ς(q	ω−1(h̃)(ς(q	PROPN
ejpam-6273	231	1	+	+	NUM
ejpam-6273	231	2	i	i	NOUN
ejpam-6273	231	3	)	)	PUNCT
ejpam-6273	231	4	−	−	PROPN
ejpam-6273	231	5	ςq	ςq	NOUN
ejpam-6273	231	6	)	)	PUNCT
ejpam-6273	231	7	=	=	SYM
ejpam-6273	231	8	h̃(ω(ς(q	h̃(ω(ς(q	NUM
ejpam-6273	231	9	+	+	CCONJ
ejpam-6273	231	10	i	i	NOUN
ejpam-6273	231	11	)	)	PUNCT
ejpam-6273	231	12	−	−	PROPN
ejpam-6273	231	13	ςq	ςq	NOUN
ejpam-6273	231	14	)	)	PUNCT
ejpam-6273	231	15	)	)	PUNCT
ejpam-6273	232	1	=	=	SYM
ejpam-6273	232	2	h̃(ω(ς)(ω(q	h̃(ω(ς)(ω(q	X
ejpam-6273	232	3	)	)	PUNCT
ejpam-6273	233	1	+	+	CCONJ
ejpam-6273	233	2	ω(i	ω(i	PROPN
ejpam-6273	233	3	)	)	PUNCT
ejpam-6273	233	4	)	)	PUNCT
ejpam-6273	234	1	−	−	PROPN
ejpam-6273	234	2	ω(q)ω(ς	ω(q)ω(ς	NUM
ejpam-6273	234	3	)	)	PUNCT
ejpam-6273	234	4	)	)	PUNCT
ejpam-6273	235	1	⊇	⊇	PROPN
ejpam-6273	235	2	h̃(ω(i	h̃(ω(i	PROPN
ejpam-6273	235	3	)	)	PUNCT
ejpam-6273	235	4	)	)	PUNCT
ejpam-6273	236	1	=	=	SYM
ejpam-6273	236	2	ω−1(h̃)(i	ω−1(h̃)(i	PROPN
ejpam-6273	236	3	)	)	PUNCT
ejpam-6273	236	4	and	and	CCONJ
ejpam-6273	236	5	ω−1(µ)(ς(q	ω−1(µ)(ς(q	PRON
ejpam-6273	236	6	+	+	NUM
ejpam-6273	236	7	i	i	NOUN
ejpam-6273	236	8	)	)	PUNCT
ejpam-6273	237	1	−	−	PROPN
ejpam-6273	237	2	ςq	ςq	NOUN
ejpam-6273	237	3	)	)	PUNCT
ejpam-6273	237	4	=	=	PUNCT
ejpam-6273	238	1	µ(ω(ς(q	µ(ω(ς(q	PROPN
ejpam-6273	238	2	+	+	NUM
ejpam-6273	238	3	i	i	NOUN
ejpam-6273	238	4	)	)	PUNCT
ejpam-6273	239	1	−	−	PROPN
ejpam-6273	239	2	ςq	ςq	NOUN
ejpam-6273	239	3	)	)	PUNCT
ejpam-6273	239	4	)	)	PUNCT
ejpam-6273	240	1	=	=	SYM
ejpam-6273	240	2	µ(ω(ς)(ω(q	µ(ω(ς)(ω(q	X
ejpam-6273	240	3	)	)	PUNCT
ejpam-6273	240	4	+	+	CCONJ
ejpam-6273	240	5	ω(i))−	ω(i))−	ADP
ejpam-6273	240	6	ω(q)ω(ς	ω(q)ω(ς	NUM
ejpam-6273	240	7	)	)	PUNCT
ejpam-6273	240	8	)	)	PUNCT
ejpam-6273	240	9	≤	≤	PROPN
ejpam-6273	240	10	µ(ω(i	µ(ω(i	NOUN
ejpam-6273	240	11	)	)	PUNCT
ejpam-6273	240	12	)	)	PUNCT
ejpam-6273	241	1	=	=	SYM
ejpam-6273	241	2	ω−1(µ)(i	ω−1(µ)(i	PROPN
ejpam-6273	241	3	)	)	PUNCT
ejpam-6273	241	4	.	.	PUNCT
ejpam-6273	242	1	therefore	therefore	ADV
ejpam-6273	242	2	,	,	PUNCT
ejpam-6273	242	3	ω−1(h̃µ	ω−1(h̃µ	PUNCT
ejpam-6273	242	4	)	)	PUNCT
ejpam-6273	242	5	=	=	SYM
ejpam-6273	242	6	(	(	PUNCT
ejpam-6273	242	7	ω−1(h̃	ω−1(h̃	NOUN
ejpam-6273	242	8	)	)	PUNCT
ejpam-6273	242	9	,	,	PUNCT
ejpam-6273	242	10	ω−1(µ	ω−1(µ	PROPN
ejpam-6273	242	11	)	)	PUNCT
ejpam-6273	242	12	)	)	PUNCT
ejpam-6273	242	13	is	be	AUX
ejpam-6273	242	14	an	an	DET
ejpam-6273	242	15	hina	hina	NOUN
ejpam-6273	242	16	in	in	ADP
ejpam-6273	242	17	y	y	PROPN
ejpam-6273	242	18	upon	upon	SCONJ
ejpam-6273	242	19	(	(	PUNCT
ejpam-6273	242	20	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	242	21	,	,	PUNCT
ejpam-6273	242	22	l	l	NOUN
ejpam-6273	242	23	)	)	PUNCT
ejpam-6273	242	24	.	.	PUNCT
ejpam-6273	243	1	definition	definition	NOUN
ejpam-6273	243	2	8	8	NUM
ejpam-6273	243	3	.	.	PUNCT
ejpam-6273	244	1	let	let	VERB
ejpam-6273	244	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	244	3	and	and	CCONJ
ejpam-6273	244	4	h̃µ	h̃µ	NOUN
ejpam-6273	244	5	be	be	AUX
ejpam-6273	244	6	two	two	NUM
ejpam-6273	244	7	hybrid	hybrid	ADJ
ejpam-6273	244	8	structures	structure	NOUN
ejpam-6273	244	9	of	of	ADP
ejpam-6273	244	10	near	near	ADJ
ejpam-6273	244	11	algebras	algebras	PROPN
ejpam-6273	244	12	y	y	PROPN
ejpam-6273	244	13	and	and	CCONJ
ejpam-6273	244	14	y	y	PROPN
ejpam-6273	244	15	′	′	VERB
ejpam-6273	244	16	over	over	ADP
ejpam-6273	244	17	l	l	NOUN
ejpam-6273	244	18	,	,	PUNCT
ejpam-6273	244	19	respectively	respectively	ADV
ejpam-6273	244	20	.	.	PUNCT
ejpam-6273	245	1	then	then	ADV
ejpam-6273	245	2	the	the	DET
ejpam-6273	245	3	cartesian	cartesian	ADJ
ejpam-6273	245	4	product	product	NOUN
ejpam-6273	245	5	of	of	ADP
ejpam-6273	245	6	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	245	7	and	and	CCONJ
ejpam-6273	245	8	h̃µ	h̃µ	NOUN
ejpam-6273	245	9	is	be	AUX
ejpam-6273	245	10	denoted	denote	VERB
ejpam-6273	245	11	by	by	ADP
ejpam-6273	245	12	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	245	13	×	×	NOUN
ejpam-6273	245	14	h̃µ	h̃µ	ADV
ejpam-6273	245	15	,	,	PUNCT
ejpam-6273	245	16	is	be	AUX
ejpam-6273	245	17	defined	define	VERB
ejpam-6273	245	18	to	to	PART
ejpam-6273	245	19	be	be	AUX
ejpam-6273	245	20	a	a	DET
ejpam-6273	245	21	hybrid	hybrid	ADJ
ejpam-6273	245	22	structure	structure	NOUN
ejpam-6273	246	1	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	246	2	×	×	VERB
ejpam-6273	246	3	h̃µ	h̃µ	NOUN
ejpam-6273	246	4	:	:	PUNCT
ejpam-6273	247	1	y	y	PROPN
ejpam-6273	247	2	×	×	NOUN
ejpam-6273	247	3	y	y	NOUN
ejpam-6273	247	4	′	′	NUM
ejpam-6273	248	1	→	→	PUNCT
ejpam-6273	248	2	p	p	X
ejpam-6273	248	3	(	(	PUNCT
ejpam-6273	248	4	u	u	NOUN
ejpam-6273	248	5	)	)	PUNCT
ejpam-6273	248	6	×	×	PROPN
ejpam-6273	248	7	i	i	PRON
ejpam-6273	248	8	;	;	PUNCT
ejpam-6273	248	9	(	(	PUNCT
ejpam-6273	248	10	q	q	X
ejpam-6273	248	11	,	,	PUNCT
ejpam-6273	248	12	q	q	NOUN
ejpam-6273	248	13	′	′	NOUN
ejpam-6273	248	14	)	)	PUNCT
ejpam-6273	248	15	7→	7→	NUM
ejpam-6273	248	16	(	(	PUNCT
ejpam-6273	248	17	(	(	PUNCT
ejpam-6273	248	18	ϱ̃	ϱ̃	NOUN
ejpam-6273	248	19	×	×	NOUN
ejpam-6273	248	20	h̃)(q	h̃)(q	NOUN
ejpam-6273	248	21	,	,	PUNCT
ejpam-6273	248	22	q	q	PROPN
ejpam-6273	248	23	′	′	NOUN
ejpam-6273	248	24	)	)	PUNCT
ejpam-6273	248	25	,	,	PUNCT
ejpam-6273	248	26	(	(	PUNCT
ejpam-6273	248	27	γ	γ	X
ejpam-6273	248	28	×	×	NOUN
ejpam-6273	248	29	µ)(q	µ)(q	ADJ
ejpam-6273	248	30	,	,	PUNCT
ejpam-6273	248	31	q	q	NOUN
ejpam-6273	248	32	′	′	NOUN
ejpam-6273	248	33	)	)	PUNCT
ejpam-6273	248	34	)	)	PUNCT
ejpam-6273	248	35	,	,	PUNCT
ejpam-6273	248	36	∀(q	∀(q	PROPN
ejpam-6273	248	37	,	,	PUNCT
ejpam-6273	248	38	q′	q′	NOUN
ejpam-6273	248	39	)	)	PUNCT
ejpam-6273	249	1	∈	∈	PROPN
ejpam-6273	250	1	y	y	NOUN
ejpam-6273	250	2	×	×	NOUN
ejpam-6273	250	3	y	y	NOUN
ejpam-6273	250	4	′	′	NOUN
ejpam-6273	250	5	,	,	PUNCT
ejpam-6273	250	6	where	where	SCONJ
ejpam-6273	250	7	ϱ̃	ϱ̃	PROPN
ejpam-6273	250	8	×	×	NOUN
ejpam-6273	250	9	h̃	h̃	PROPN
ejpam-6273	250	10	:	:	PUNCT
ejpam-6273	251	1	y	y	PROPN
ejpam-6273	251	2	×	×	NOUN
ejpam-6273	251	3	y	y	NOUN
ejpam-6273	251	4	′	′	NUM
ejpam-6273	251	5	→	→	PUNCT
ejpam-6273	251	6	p	p	X
ejpam-6273	251	7	(	(	PUNCT
ejpam-6273	251	8	u	u	NOUN
ejpam-6273	251	9	)	)	PUNCT
ejpam-6273	251	10	;	;	PUNCT
ejpam-6273	251	11	(	(	PUNCT
ejpam-6273	251	12	q	q	X
ejpam-6273	251	13	,	,	PUNCT
ejpam-6273	251	14	q	q	NOUN
ejpam-6273	251	15	′	′	NOUN
ejpam-6273	251	16	)	)	PUNCT
ejpam-6273	251	17	7→	7→	NUM
ejpam-6273	251	18	ϱ̃(q	ϱ̃(q	ADJ
ejpam-6273	251	19	)	)	PUNCT
ejpam-6273	251	20	∩	∩	NOUN
ejpam-6273	251	21	h̃(q	h̃(q	PROPN
ejpam-6273	251	22	′	′	NUM
ejpam-6273	251	23	)	)	PUNCT
ejpam-6273	251	24	and	and	CCONJ
ejpam-6273	251	25	γ	γ	X
ejpam-6273	251	26	×	×	PROPN
ejpam-6273	251	27	µ	µ	X
ejpam-6273	251	28	:	:	PUNCT
ejpam-6273	251	29	y	y	PROPN
ejpam-6273	251	30	×	×	NOUN
ejpam-6273	251	31	y	y	NOUN
ejpam-6273	251	32	′	′	NUM
ejpam-6273	251	33	→	→	PUNCT
ejpam-6273	251	34	i	i	NOUN
ejpam-6273	251	35	;	;	PUNCT
ejpam-6273	251	36	(	(	PUNCT
ejpam-6273	251	37	q	q	X
ejpam-6273	251	38	,	,	PUNCT
ejpam-6273	251	39	q	q	NOUN
ejpam-6273	251	40	′	′	NOUN
ejpam-6273	251	41	)	)	PUNCT
ejpam-6273	252	1	7→	7→	NUM
ejpam-6273	252	2	∨	∨	NUM
ejpam-6273	252	3	{	{	PUNCT
ejpam-6273	252	4	γ(q	γ(q	NOUN
ejpam-6273	252	5	)	)	PUNCT
ejpam-6273	252	6	,	,	PUNCT
ejpam-6273	252	7	µ(q′	µ(q′	PROPN
ejpam-6273	252	8	)	)	PUNCT
ejpam-6273	252	9	}	}	PUNCT
ejpam-6273	252	10	.	.	PUNCT
ejpam-6273	253	1	theorem	theorem	NOUN
ejpam-6273	253	2	6	6	NUM
ejpam-6273	253	3	.	.	PUNCT
ejpam-6273	254	1	let	let	VERB
ejpam-6273	254	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	254	3	and	and	CCONJ
ejpam-6273	254	4	h̃µ	h̃µ	NOUN
ejpam-6273	254	5	be	be	AUX
ejpam-6273	254	6	two	two	NUM
ejpam-6273	254	7	hinas	hina	NOUN
ejpam-6273	254	8	of	of	ADP
ejpam-6273	254	9	y	y	PROPN
ejpam-6273	254	10	and	and	CCONJ
ejpam-6273	254	11	y	y	PROPN
ejpam-6273	254	12	′	′	VERB
ejpam-6273	254	13	upon	upon	SCONJ
ejpam-6273	254	14	an	an	DET
ejpam-6273	254	15	hf	hf	NOUN
ejpam-6273	254	16	(	(	PUNCT
ejpam-6273	254	17	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	254	18	,	,	PUNCT
ejpam-6273	254	19	l	l	NOUN
ejpam-6273	254	20	)	)	PUNCT
ejpam-6273	254	21	.	.	PUNCT
ejpam-6273	255	1	then	then	ADV
ejpam-6273	255	2	ϱ̃γ×	ϱ̃γ×	PROPN
ejpam-6273	255	3	h̃µ	h̃µ	ADV
ejpam-6273	255	4	is	be	AUX
ejpam-6273	255	5	an	an	DET
ejpam-6273	255	6	hina	hina	NOUN
ejpam-6273	255	7	of	of	ADP
ejpam-6273	255	8	y	y	PROPN
ejpam-6273	256	1	×	×	PROPN
ejpam-6273	256	2	y	y	NOUN
ejpam-6273	256	3	′	′	NUM
ejpam-6273	256	4	upon	upon	SCONJ
ejpam-6273	256	5	(	(	PUNCT
ejpam-6273	256	6	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	256	7	,	,	PUNCT
ejpam-6273	256	8	l	l	NOUN
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ejpam-6273	290	42	µ(q′	µ(q′	PROPN
ejpam-6273	290	43	)	)	PUNCT
ejpam-6273	290	44	}	}	PUNCT
ejpam-6273	290	45	}	}	PUNCT
ejpam-6273	290	46	=	=	SYM
ejpam-6273	290	47	∨	∨	X
ejpam-6273	290	48	{	{	PUNCT
ejpam-6273	290	49	λ(s	λ(s	PROPN
ejpam-6273	290	50	)	)	PUNCT
ejpam-6273	290	51	,	,	PUNCT
ejpam-6273	290	52	(	(	PUNCT
ejpam-6273	290	53	γ	γ	X
ejpam-6273	290	54	×	×	NOUN
ejpam-6273	290	55	µ)(q	µ)(q	ADJ
ejpam-6273	290	56	,	,	PUNCT
ejpam-6273	290	57	q	q	NOUN
ejpam-6273	290	58	′	′	NOUN
ejpam-6273	290	59	)	)	PUNCT
ejpam-6273	290	60	}	}	PUNCT
ejpam-6273	290	61	.	.	PUNCT
ejpam-6273	291	1	(	(	PUNCT
ejpam-6273	291	2	iii	iii	X
ejpam-6273	291	3	)	)	PUNCT
ejpam-6273	291	4	let	let	VERB
ejpam-6273	291	5	1	1	NUM
ejpam-6273	291	6	be	be	AUX
ejpam-6273	291	7	the	the	DET
ejpam-6273	291	8	unity	unity	NOUN
ejpam-6273	291	9	in	in	ADP
ejpam-6273	291	10	l.	l.	PROPN
ejpam-6273	291	11	since	since	SCONJ
ejpam-6273	291	12	(	(	PUNCT
ejpam-6273	291	13	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	291	14	,	,	PUNCT
ejpam-6273	291	15	y	y	PROPN
ejpam-6273	291	16	)	)	PUNCT
ejpam-6273	291	17	and	and	CCONJ
ejpam-6273	291	18	(	(	PUNCT
ejpam-6273	291	19	h̃µ	h̃µ	INTJ
ejpam-6273	291	20	,	,	PUNCT
ejpam-6273	291	21	y	y	PROPN
ejpam-6273	291	22	′	′	NUM
ejpam-6273	291	23	)	)	PUNCT
ejpam-6273	291	24	are	be	AUX
ejpam-6273	291	25	hinas	hina	NOUN
ejpam-6273	291	26	over	over	ADP
ejpam-6273	291	27	hf	hf	PROPN
ejpam-6273	291	28	(	(	PUNCT
ejpam-6273	291	29	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	291	30	,	,	PUNCT
ejpam-6273	291	31	l	l	NOUN
ejpam-6273	291	32	)	)	PUNCT
ejpam-6273	291	33	,	,	PUNCT
ejpam-6273	291	34	we	we	PRON
ejpam-6273	291	35	have	have	VERB
ejpam-6273	291	36	ξ̃(1	ξ̃(1	NOUN
ejpam-6273	291	37	)	)	PUNCT
ejpam-6273	291	38	⊇	⊇	PROPN
ejpam-6273	291	39	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	291	40	)	)	PUNCT
ejpam-6273	291	41	,	,	PUNCT
ejpam-6273	291	42	∀q	∀q	PROPN
ejpam-6273	291	43	∈	∈	PROPN
ejpam-6273	291	44	y	y	PROPN
ejpam-6273	291	45	,	,	PUNCT
ejpam-6273	291	46	λ(1	λ(1	PROPN
ejpam-6273	291	47	)	)	PUNCT
ejpam-6273	291	48	≤	≤	NUM
ejpam-6273	291	49	γ(q	γ(q	NOUN
ejpam-6273	291	50	)	)	PUNCT
ejpam-6273	291	51	and	and	CCONJ
ejpam-6273	291	52	ξ̃(1	ξ̃(1	NOUN
ejpam-6273	291	53	)	)	PUNCT
ejpam-6273	291	54	⊇	⊇	NOUN
ejpam-6273	291	55	h̃(q	h̃(q	PROPN
ejpam-6273	291	56	′	′	NUM
ejpam-6273	291	57	)	)	PUNCT
ejpam-6273	291	58	,	,	PUNCT
ejpam-6273	291	59	∀q′	∀q′	PROPN
ejpam-6273	291	60	∈	∈	PROPN
ejpam-6273	291	61	y	y	NOUN
ejpam-6273	291	62	′	′	NOUN
ejpam-6273	291	63	,	,	PUNCT
ejpam-6273	291	64	λ(1	λ(1	PROPN
ejpam-6273	291	65	)	)	PUNCT
ejpam-6273	291	66	≤	≤	NOUN
ejpam-6273	291	67	µ(q	µ(q	ADP
ejpam-6273	291	68	′	′	NOUN
ejpam-6273	291	69	)	)	PUNCT
ejpam-6273	291	70	.	.	PUNCT
ejpam-6273	292	1	then	then	ADV
ejpam-6273	292	2	ξ̃(1	ξ̃(1	NUM
ejpam-6273	292	3	)	)	PUNCT
ejpam-6273	292	4	⊇	⊇	PROPN
ejpam-6273	292	5	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	292	6	)	)	PUNCT
ejpam-6273	292	7	∩	∩	NOUN
ejpam-6273	292	8	h̃(q	h̃(q	PROPN
ejpam-6273	292	9	′	′	NUM
ejpam-6273	292	10	)	)	PUNCT
ejpam-6273	293	1	=	=	SYM
ejpam-6273	293	2	(	(	PUNCT
ejpam-6273	293	3	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	293	4	h̃)(q	h̃)(q	NOUN
ejpam-6273	293	5	,	,	PUNCT
ejpam-6273	293	6	q	q	NOUN
ejpam-6273	293	7	′	′	NOUN
ejpam-6273	293	8	)	)	PUNCT
ejpam-6273	293	9	and	and	CCONJ
ejpam-6273	293	10	λ(1	λ(1	PROPN
ejpam-6273	293	11	)	)	PUNCT
ejpam-6273	293	12	≤	≤	NOUN
ejpam-6273	293	13	∨	∨	NUM
ejpam-6273	293	14	{	{	PUNCT
ejpam-6273	293	15	γ(q	γ(q	NOUN
ejpam-6273	293	16	)	)	PUNCT
ejpam-6273	293	17	,	,	PUNCT
ejpam-6273	293	18	µ(q′	µ(q′	PROPN
ejpam-6273	293	19	)	)	PUNCT
ejpam-6273	293	20	}	}	PUNCT
ejpam-6273	293	21	=	=	SYM
ejpam-6273	293	22	(	(	PUNCT
ejpam-6273	293	23	γ	γ	X
ejpam-6273	293	24	×	×	NOUN
ejpam-6273	293	25	µ)(q	µ)(q	ADJ
ejpam-6273	293	26	,	,	PUNCT
ejpam-6273	293	27	q	q	NOUN
ejpam-6273	293	28	′	′	NOUN
ejpam-6273	293	29	)	)	PUNCT
ejpam-6273	293	30	.	.	PUNCT
ejpam-6273	294	1	(	(	PUNCT
ejpam-6273	294	2	iv	iv	X
ejpam-6273	294	3	)	)	PUNCT
ejpam-6273	294	4	(	(	PUNCT
ejpam-6273	294	5	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	294	6	h̃)[(q	h̃)[(q	PROPN
ejpam-6273	294	7	,	,	PUNCT
ejpam-6273	294	8	q	q	NOUN
ejpam-6273	294	9	′	′	NOUN
ejpam-6273	294	10	)	)	PUNCT
ejpam-6273	294	11	(	(	PUNCT
ejpam-6273	294	12	ς	ς	PROPN
ejpam-6273	294	13	,	,	PUNCT
ejpam-6273	294	14	ς	ς	PROPN
ejpam-6273	294	15	′	′	NUM
ejpam-6273	294	16	)	)	PUNCT
ejpam-6273	294	17	]	]	PUNCT
ejpam-6273	295	1	=	=	PUNCT
ejpam-6273	295	2	(	(	PUNCT
ejpam-6273	295	3	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	295	4	h̃)(qς	h̃)(qς	NOUN
ejpam-6273	295	5	,	,	PUNCT
ejpam-6273	295	6	q	q	NOUN
ejpam-6273	295	7	′	′	NUM
ejpam-6273	295	8	ς	ς	NOUN
ejpam-6273	295	9	′	′	NUM
ejpam-6273	295	10	)	)	PUNCT
ejpam-6273	296	1	=	=	SYM
ejpam-6273	296	2	ϱ̃(qς	ϱ̃(qς	ADJ
ejpam-6273	296	3	)	)	PUNCT
ejpam-6273	296	4	∩	∩	NOUN
ejpam-6273	296	5	h̃(q	h̃(q	PROPN
ejpam-6273	296	6	′	′	NUM
ejpam-6273	296	7	ς	ς	PROPN
ejpam-6273	296	8	′	′	NUM
ejpam-6273	296	9	)	)	PUNCT
ejpam-6273	296	10	⊇	⊇	PROPN
ejpam-6273	296	11	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	296	12	)	)	PUNCT
ejpam-6273	296	13	∩	∩	NOUN
ejpam-6273	296	14	h̃(q	h̃(q	PROPN
ejpam-6273	296	15	′	′	NUM
ejpam-6273	296	16	)	)	PUNCT
ejpam-6273	297	1	=	=	SYM
ejpam-6273	297	2	(	(	PUNCT
ejpam-6273	297	3	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	297	4	h̃)(q	h̃)(q	NOUN
ejpam-6273	297	5	,	,	PUNCT
ejpam-6273	297	6	q	q	NOUN
ejpam-6273	297	7	′	′	NOUN
ejpam-6273	297	8	)	)	PUNCT
ejpam-6273	297	9	and	and	CCONJ
ejpam-6273	297	10	(	(	PUNCT
ejpam-6273	297	11	γ	γ	X
ejpam-6273	297	12	×	×	PROPN
ejpam-6273	297	13	µ)[(q	µ)[(q	NOUN
ejpam-6273	297	14	,	,	PUNCT
ejpam-6273	297	15	q	q	NOUN
ejpam-6273	297	16	′	′	NOUN
ejpam-6273	297	17	)	)	PUNCT
ejpam-6273	297	18	(	(	PUNCT
ejpam-6273	297	19	ς	ς	PROPN
ejpam-6273	297	20	,	,	PUNCT
ejpam-6273	297	21	ς	ς	PROPN
ejpam-6273	297	22	′	′	NUM
ejpam-6273	297	23	)	)	PUNCT
ejpam-6273	297	24	]	]	PUNCT
ejpam-6273	298	1	=	=	PUNCT
ejpam-6273	298	2	(	(	PUNCT
ejpam-6273	298	3	γ	γ	X
ejpam-6273	298	4	×	×	PROPN
ejpam-6273	298	5	µ)(qς	µ)(qς	NUM
ejpam-6273	298	6	,	,	PUNCT
ejpam-6273	298	7	q	q	NOUN
ejpam-6273	299	1	′	′	NUM
ejpam-6273	299	2	ς	ς	NOUN
ejpam-6273	299	3	′	′	NUM
ejpam-6273	299	4	)	)	PUNCT
ejpam-6273	300	1	p.	p.	NOUN
ejpam-6273	300	2	n.	n.	PROPN
ejpam-6273	300	3	swamy	swamy	PROPN
ejpam-6273	300	4	et	et	PROPN
ejpam-6273	300	5	al	al	PROPN
ejpam-6273	300	6	.	.	PUNCT
ejpam-6273	300	7	/	/	SYM
ejpam-6273	300	8	eur	eur	PROPN
ejpam-6273	300	9	.	.	PUNCT
ejpam-6273	301	1	j.	j.	PROPN
ejpam-6273	301	2	pure	pure	PROPN
ejpam-6273	301	3	appl	appl	PROPN
ejpam-6273	301	4	.	.	PROPN
ejpam-6273	301	5	math	math	PROPN
ejpam-6273	301	6	,	,	PUNCT
ejpam-6273	301	7	18	18	NUM
ejpam-6273	301	8	(	(	PUNCT
ejpam-6273	301	9	3	3	NUM
ejpam-6273	301	10	)	)	PUNCT
ejpam-6273	301	11	(	(	PUNCT
ejpam-6273	301	12	2025	2025	NUM
ejpam-6273	301	13	)	)	PUNCT
ejpam-6273	301	14	,	,	PUNCT
ejpam-6273	301	15	6273	6273	NUM
ejpam-6273	301	16	11	11	NUM
ejpam-6273	301	17	of	of	ADP
ejpam-6273	301	18	16	16	NUM
ejpam-6273	301	19	=	=	SYM
ejpam-6273	301	20	∨	∨	NUM
ejpam-6273	301	21	{	{	PUNCT
ejpam-6273	301	22	γ(qς	γ(qς	NOUN
ejpam-6273	301	23	)	)	PUNCT
ejpam-6273	301	24	,	,	PUNCT
ejpam-6273	301	25	µ(q′	µ(q′	PROPN
ejpam-6273	301	26	ς	ς	PROPN
ejpam-6273	301	27	′	′	NUM
ejpam-6273	301	28	)	)	PUNCT
ejpam-6273	301	29	}	}	PUNCT
ejpam-6273	301	30	≤	≤	NUM
ejpam-6273	301	31	∨	∨	NUM
ejpam-6273	301	32	{	{	PUNCT
ejpam-6273	301	33	γ(q	γ(q	NOUN
ejpam-6273	301	34	)	)	PUNCT
ejpam-6273	301	35	,	,	PUNCT
ejpam-6273	301	36	µ(q′	µ(q′	PROPN
ejpam-6273	301	37	)	)	PUNCT
ejpam-6273	301	38	}	}	PUNCT
ejpam-6273	301	39	=	=	SYM
ejpam-6273	301	40	(	(	PUNCT
ejpam-6273	301	41	γ	γ	X
ejpam-6273	301	42	×	×	NOUN
ejpam-6273	301	43	µ)(q	µ)(q	ADJ
ejpam-6273	301	44	,	,	PUNCT
ejpam-6273	301	45	q	q	NOUN
ejpam-6273	301	46	′	′	NOUN
ejpam-6273	301	47	)	)	PUNCT
ejpam-6273	301	48	.	.	PUNCT
ejpam-6273	302	1	(	(	PUNCT
ejpam-6273	302	2	v	v	NOUN
ejpam-6273	302	3	)	)	PUNCT
ejpam-6273	302	4	(	(	PUNCT
ejpam-6273	302	5	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	302	6	h̃)[(ς	h̃)[(ς	PROPN
ejpam-6273	302	7	,	,	PUNCT
ejpam-6273	302	8	ς	ς	PROPN
ejpam-6273	302	9	′	′	NOUN
ejpam-6273	302	10	)	)	PUNCT
ejpam-6273	302	11	(	(	PUNCT
ejpam-6273	302	12	(	(	PUNCT
ejpam-6273	302	13	q	q	NOUN
ejpam-6273	302	14	,	,	PUNCT
ejpam-6273	302	15	q	q	NOUN
ejpam-6273	302	16	′	′	NOUN
ejpam-6273	302	17	)	)	PUNCT
ejpam-6273	303	1	+	+	CCONJ
ejpam-6273	303	2	(	(	PUNCT
ejpam-6273	303	3	i	i	PRON
ejpam-6273	303	4	,	,	PUNCT
ejpam-6273	303	5	i	i	PRON
ejpam-6273	303	6	′	′	NUM
ejpam-6273	303	7	)	)	PUNCT
ejpam-6273	303	8	)	)	PUNCT
ejpam-6273	303	9	−	−	PROPN
ejpam-6273	304	1	(	(	PUNCT
ejpam-6273	304	2	ς	ς	PROPN
ejpam-6273	304	3	,	,	PUNCT
ejpam-6273	304	4	ς	ς	PROPN
ejpam-6273	304	5	′	′	NUM
ejpam-6273	304	6	)	)	PUNCT
ejpam-6273	304	7	(	(	PUNCT
ejpam-6273	304	8	q	q	X
ejpam-6273	304	9	,	,	PUNCT
ejpam-6273	304	10	q	q	NOUN
ejpam-6273	304	11	′	′	ADP
ejpam-6273	304	12	]	]	PUNCT
ejpam-6273	304	13	=	=	PUNCT
ejpam-6273	304	14	(	(	PUNCT
ejpam-6273	304	15	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	304	16	h̃)[(ς	h̃)[(ς	PROPN
ejpam-6273	304	17	,	,	PUNCT
ejpam-6273	304	18	ς	ς	PROPN
ejpam-6273	304	19	′	′	NOUN
ejpam-6273	304	20	)	)	PUNCT
ejpam-6273	304	21	(	(	PUNCT
ejpam-6273	304	22	q	q	PROPN
ejpam-6273	305	1	+	+	CCONJ
ejpam-6273	305	2	i	i	NOUN
ejpam-6273	305	3	,	,	PUNCT
ejpam-6273	305	4	q	q	NOUN
ejpam-6273	306	1	′	′	INTJ
ejpam-6273	307	1	+	+	CCONJ
ejpam-6273	307	2	i	i	PRON
ejpam-6273	307	3	′	′	VERB
ejpam-6273	307	4	)	)	PUNCT
ejpam-6273	308	1	−	−	PROPN
ejpam-6273	308	2	(	(	PUNCT
ejpam-6273	308	3	ςq	ςq	NOUN
ejpam-6273	308	4	,	,	PUNCT
ejpam-6273	308	5	ς	ς	PROPN
ejpam-6273	308	6	′	′	NOUN
ejpam-6273	308	7	q	q	NOUN
ejpam-6273	308	8	′	′	NUM
ejpam-6273	308	9	)	)	PUNCT
ejpam-6273	308	10	]	]	PUNCT
ejpam-6273	309	1	=	=	PUNCT
ejpam-6273	309	2	(	(	PUNCT
ejpam-6273	309	3	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	309	4	h̃)[(ς(q	h̃)[(ς(q	VERB
ejpam-6273	309	5	+	+	CCONJ
ejpam-6273	309	6	i	i	NOUN
ejpam-6273	309	7	)	)	PUNCT
ejpam-6273	309	8	,	,	PUNCT
ejpam-6273	309	9	ς	ς	PROPN
ejpam-6273	309	10	′	′	NUM
ejpam-6273	309	11	(	(	PUNCT
ejpam-6273	309	12	q	q	NOUN
ejpam-6273	309	13	′	′	NUM
ejpam-6273	310	1	+	+	CCONJ
ejpam-6273	310	2	i	i	PRON
ejpam-6273	310	3	′	′	NUM
ejpam-6273	310	4	)	)	PUNCT
ejpam-6273	310	5	)	)	PUNCT
ejpam-6273	311	1	−	−	PROPN
ejpam-6273	311	2	(	(	PUNCT
ejpam-6273	311	3	ςq	ςq	NOUN
ejpam-6273	311	4	,	,	PUNCT
ejpam-6273	311	5	ς	ς	PROPN
ejpam-6273	311	6	′	′	NOUN
ejpam-6273	311	7	q	q	NOUN
ejpam-6273	311	8	′	′	NUM
ejpam-6273	311	9	)	)	PUNCT
ejpam-6273	311	10	]	]	PUNCT
ejpam-6273	312	1	=	=	PUNCT
ejpam-6273	312	2	(	(	PUNCT
ejpam-6273	312	3	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	312	4	h̃)[(ς(q	h̃)[(ς(q	VERB
ejpam-6273	312	5	+	+	CCONJ
ejpam-6273	312	6	i)−	i)−	PROPN
ejpam-6273	312	7	ςq	ςq	PROPN
ejpam-6273	312	8	,	,	PUNCT
ejpam-6273	312	9	ς	ς	PROPN
ejpam-6273	312	10	′	′	NUM
ejpam-6273	312	11	(	(	PUNCT
ejpam-6273	312	12	q	q	NOUN
ejpam-6273	312	13	′	′	NUM
ejpam-6273	313	1	+	+	CCONJ
ejpam-6273	313	2	i	i	PRON
ejpam-6273	313	3	′	′	NUM
ejpam-6273	313	4	)	)	PUNCT
ejpam-6273	313	5	)	)	PUNCT
ejpam-6273	314	1	−	−	PROPN
ejpam-6273	315	1	ς	ς	PROPN
ejpam-6273	315	2	′	′	NUM
ejpam-6273	315	3	q	q	NOUN
ejpam-6273	315	4	′	′	NUM
ejpam-6273	315	5	)	)	PUNCT
ejpam-6273	315	6	]	]	PUNCT
ejpam-6273	316	1	=	=	PUNCT
ejpam-6273	316	2	ϱ̃(ς(q	ϱ̃(ς(q	PROPN
ejpam-6273	316	3	+	+	CCONJ
ejpam-6273	316	4	i)−	i)−	PROPN
ejpam-6273	316	5	ςq	ςq	PROPN
ejpam-6273	316	6	)	)	PUNCT
ejpam-6273	316	7	∩	∩	ADJ
ejpam-6273	316	8	h̃(ς	h̃(ς	ADJ
ejpam-6273	316	9	′	′	NUM
ejpam-6273	316	10	(	(	PUNCT
ejpam-6273	316	11	q	q	NOUN
ejpam-6273	317	1	′	′	NUM
ejpam-6273	318	1	+	+	CCONJ
ejpam-6273	318	2	i	i	PRON
ejpam-6273	318	3	′	′	NUM
ejpam-6273	318	4	)	)	PUNCT
ejpam-6273	318	5	)	)	PUNCT
ejpam-6273	319	1	−	−	PROPN
ejpam-6273	320	1	ς	ς	PROPN
ejpam-6273	320	2	′	′	NUM
ejpam-6273	320	3	q	q	NOUN
ejpam-6273	320	4	′	′	NOUN
ejpam-6273	320	5	)	)	PUNCT
ejpam-6273	320	6	⊇	⊇	PROPN
ejpam-6273	320	7	ϱ̃(i	ϱ̃(i	PROPN
ejpam-6273	320	8	)	)	PUNCT
ejpam-6273	320	9	∩	∩	NOUN
ejpam-6273	320	10	h̃(i	h̃(i	NOUN
ejpam-6273	320	11	′	′	NUM
ejpam-6273	320	12	)	)	PUNCT
ejpam-6273	321	1	=	=	PUNCT
ejpam-6273	321	2	(	(	PUNCT
ejpam-6273	321	3	ϱ̃×	ϱ̃×	PROPN
ejpam-6273	321	4	h̃)(i	h̃)(i	PROPN
ejpam-6273	321	5	,	,	PUNCT
ejpam-6273	321	6	i	i	PRON
ejpam-6273	321	7	′	′	VERB
ejpam-6273	321	8	)	)	PUNCT
ejpam-6273	321	9	and	and	CCONJ
ejpam-6273	321	10	(	(	PUNCT
ejpam-6273	321	11	γ	γ	X
ejpam-6273	321	12	×	×	PROPN
ejpam-6273	321	13	µ)[(ς	µ)[(ς	PROPN
ejpam-6273	321	14	,	,	PUNCT
ejpam-6273	321	15	ς	ς	PROPN
ejpam-6273	321	16	′	′	NOUN
ejpam-6273	321	17	)	)	PUNCT
ejpam-6273	321	18	(	(	PUNCT
ejpam-6273	321	19	(	(	PUNCT
ejpam-6273	321	20	q	q	NOUN
ejpam-6273	321	21	,	,	PUNCT
ejpam-6273	321	22	q	q	NOUN
ejpam-6273	321	23	′	′	NOUN
ejpam-6273	321	24	)	)	PUNCT
ejpam-6273	322	1	+	+	CCONJ
ejpam-6273	322	2	(	(	PUNCT
ejpam-6273	322	3	i	i	PRON
ejpam-6273	322	4	,	,	PUNCT
ejpam-6273	322	5	i	i	PRON
ejpam-6273	322	6	′	′	NUM
ejpam-6273	322	7	)	)	PUNCT
ejpam-6273	322	8	)	)	PUNCT
ejpam-6273	322	9	−	−	PROPN
ejpam-6273	323	1	(	(	PUNCT
ejpam-6273	323	2	ς	ς	PROPN
ejpam-6273	323	3	,	,	PUNCT
ejpam-6273	323	4	ς	ς	PROPN
ejpam-6273	323	5	′	′	NUM
ejpam-6273	323	6	)	)	PUNCT
ejpam-6273	323	7	(	(	PUNCT
ejpam-6273	323	8	q	q	X
ejpam-6273	323	9	,	,	PUNCT
ejpam-6273	323	10	q	q	NOUN
ejpam-6273	323	11	′	′	ADP
ejpam-6273	323	12	]	]	PUNCT
ejpam-6273	324	1	=	=	PUNCT
ejpam-6273	324	2	(	(	PUNCT
ejpam-6273	324	3	γ	γ	X
ejpam-6273	324	4	×	×	PROPN
ejpam-6273	324	5	µ)[(ς	µ)[(ς	PROPN
ejpam-6273	324	6	,	,	PUNCT
ejpam-6273	324	7	ς	ς	PROPN
ejpam-6273	324	8	′	′	NOUN
ejpam-6273	324	9	)	)	PUNCT
ejpam-6273	324	10	(	(	PUNCT
ejpam-6273	324	11	q	q	PROPN
ejpam-6273	325	1	+	+	CCONJ
ejpam-6273	325	2	i	i	NOUN
ejpam-6273	325	3	,	,	PUNCT
ejpam-6273	325	4	q	q	NOUN
ejpam-6273	326	1	′	′	INTJ
ejpam-6273	327	1	+	+	CCONJ
ejpam-6273	327	2	i	i	PRON
ejpam-6273	327	3	′	′	VERB
ejpam-6273	327	4	)	)	PUNCT
ejpam-6273	328	1	−	−	PROPN
ejpam-6273	328	2	(	(	PUNCT
ejpam-6273	328	3	ςq	ςq	NOUN
ejpam-6273	328	4	,	,	PUNCT
ejpam-6273	328	5	ς	ς	PROPN
ejpam-6273	328	6	′	′	NOUN
ejpam-6273	328	7	q	q	NOUN
ejpam-6273	328	8	′	′	NUM
ejpam-6273	328	9	)	)	PUNCT
ejpam-6273	328	10	]	]	PUNCT
ejpam-6273	329	1	=	=	PUNCT
ejpam-6273	329	2	(	(	PUNCT
ejpam-6273	329	3	γ	γ	X
ejpam-6273	329	4	×	×	PROPN
ejpam-6273	329	5	µ)[(ς(q	µ)[(ς(q	X
ejpam-6273	329	6	+	+	X
ejpam-6273	329	7	i	i	NOUN
ejpam-6273	329	8	)	)	PUNCT
ejpam-6273	329	9	,	,	PUNCT
ejpam-6273	329	10	ς	ς	PROPN
ejpam-6273	329	11	′	′	NUM
ejpam-6273	329	12	(	(	PUNCT
ejpam-6273	329	13	q	q	NOUN
ejpam-6273	329	14	′	′	NUM
ejpam-6273	330	1	+	+	CCONJ
ejpam-6273	330	2	i	i	PRON
ejpam-6273	330	3	′	′	NUM
ejpam-6273	330	4	)	)	PUNCT
ejpam-6273	330	5	)	)	PUNCT
ejpam-6273	331	1	−	−	PROPN
ejpam-6273	331	2	(	(	PUNCT
ejpam-6273	331	3	ςq	ςq	NOUN
ejpam-6273	331	4	,	,	PUNCT
ejpam-6273	331	5	ς	ς	PROPN
ejpam-6273	331	6	′	′	NOUN
ejpam-6273	331	7	q	q	NOUN
ejpam-6273	331	8	′	′	NUM
ejpam-6273	331	9	)	)	PUNCT
ejpam-6273	331	10	]	]	PUNCT
ejpam-6273	332	1	=	=	PUNCT
ejpam-6273	332	2	(	(	PUNCT
ejpam-6273	332	3	γ	γ	X
ejpam-6273	332	4	×	×	PROPN
ejpam-6273	332	5	µ)[(ς(q	µ)[(ς(q	X
ejpam-6273	332	6	+	+	PROPN
ejpam-6273	332	7	i)−	i)−	PROPN
ejpam-6273	332	8	ςq	ςq	PROPN
ejpam-6273	332	9	,	,	PUNCT
ejpam-6273	332	10	ς	ς	PROPN
ejpam-6273	332	11	′	′	NUM
ejpam-6273	332	12	(	(	PUNCT
ejpam-6273	332	13	q	q	NOUN
ejpam-6273	332	14	′	′	NUM
ejpam-6273	333	1	+	+	CCONJ
ejpam-6273	333	2	i	i	PRON
ejpam-6273	333	3	′	′	NUM
ejpam-6273	333	4	)	)	PUNCT
ejpam-6273	333	5	)	)	PUNCT
ejpam-6273	334	1	−	−	PROPN
ejpam-6273	335	1	ς	ς	PROPN
ejpam-6273	335	2	′	′	NUM
ejpam-6273	335	3	q	q	NOUN
ejpam-6273	335	4	′	′	NUM
ejpam-6273	335	5	)	)	PUNCT
ejpam-6273	335	6	]	]	PUNCT
ejpam-6273	336	1	=	=	PUNCT
ejpam-6273	336	2	γ(ς(q	γ(ς(q	PROPN
ejpam-6273	336	3	+	+	CCONJ
ejpam-6273	336	4	i)−	i)−	PROPN
ejpam-6273	336	5	ςq	ςq	PROPN
ejpam-6273	336	6	)	)	PUNCT
ejpam-6273	336	7	∩	∩	NOUN
ejpam-6273	336	8	µ(ς	µ(ς	PROPN
ejpam-6273	336	9	′	′	NUM
ejpam-6273	336	10	(	(	PUNCT
ejpam-6273	336	11	q	q	NOUN
ejpam-6273	336	12	′	′	NUM
ejpam-6273	337	1	+	+	CCONJ
ejpam-6273	337	2	i	i	PRON
ejpam-6273	337	3	′	′	NUM
ejpam-6273	337	4	)	)	PUNCT
ejpam-6273	337	5	)	)	PUNCT
ejpam-6273	338	1	−	−	PROPN
ejpam-6273	339	1	ς	ς	PROPN
ejpam-6273	339	2	′	′	NUM
ejpam-6273	339	3	q	q	NOUN
ejpam-6273	339	4	′	′	NUM
ejpam-6273	339	5	)	)	PUNCT
ejpam-6273	339	6	≤	≤	NUM
ejpam-6273	339	7	γ(i	γ(i	NOUN
ejpam-6273	339	8	)	)	PUNCT
ejpam-6273	339	9	∩	∩	NOUN
ejpam-6273	339	10	µ(i	µ(i	PROPN
ejpam-6273	339	11	′	′	NUM
ejpam-6273	339	12	)	)	PUNCT
ejpam-6273	340	1	=	=	PUNCT
ejpam-6273	340	2	(	(	PUNCT
ejpam-6273	340	3	γ	γ	X
ejpam-6273	340	4	×	×	NOUN
ejpam-6273	340	5	µ)(i	µ)(i	NUM
ejpam-6273	340	6	,	,	PUNCT
ejpam-6273	340	7	i	i	PRON
ejpam-6273	340	8	′	′	NUM
ejpam-6273	340	9	)	)	PUNCT
ejpam-6273	340	10	.	.	PUNCT
ejpam-6273	341	1	hence	hence	ADV
ejpam-6273	341	2	,	,	PUNCT
ejpam-6273	341	3	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	341	4	×	×	VERB
ejpam-6273	341	5	h̃µ	h̃µ	ADJ
ejpam-6273	341	6	is	be	AUX
ejpam-6273	341	7	an	an	DET
ejpam-6273	341	8	hina	hina	NOUN
ejpam-6273	341	9	of	of	ADP
ejpam-6273	341	10	y	y	PROPN
ejpam-6273	342	1	×	×	PROPN
ejpam-6273	342	2	y	y	NOUN
ejpam-6273	342	3	′	′	NUM
ejpam-6273	342	4	upon	upon	SCONJ
ejpam-6273	342	5	(	(	PUNCT
ejpam-6273	342	6	ξ̃λ	ξ̃λ	PROPN
ejpam-6273	342	7	,	,	PUNCT
ejpam-6273	342	8	l	l	NOUN
ejpam-6273	342	9	)	)	PUNCT
ejpam-6273	342	10	.	.	PUNCT
ejpam-6273	343	1	definition	definition	NOUN
ejpam-6273	343	2	9	9	NUM
ejpam-6273	343	3	.	.	PUNCT
ejpam-6273	344	1	let	let	VERB
ejpam-6273	344	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	344	3	be	be	AUX
ejpam-6273	344	4	an	an	DET
ejpam-6273	344	5	hina	hina	NOUN
ejpam-6273	344	6	of	of	ADP
ejpam-6273	344	7	y	y	PROPN
ejpam-6273	344	8	upon	upon	SCONJ
ejpam-6273	344	9	u	u	NOUN
ejpam-6273	344	10	and	and	CCONJ
ejpam-6273	344	11	ς	ς	PROPN
ejpam-6273	344	12	∈	∈	PROPN
ejpam-6273	344	13	y	y	PROPN
ejpam-6273	344	14	.	.	PUNCT
ejpam-6273	345	1	then	then	ADV
ejpam-6273	345	2	the	the	DET
ejpam-6273	345	3	hybrid	hybrid	ADJ
ejpam-6273	345	4	coset	coset	NOUN
ejpam-6273	345	5	(	(	PUNCT
ejpam-6273	345	6	or	or	CCONJ
ejpam-6273	345	7	coset	coset	VERB
ejpam-6273	345	8	)	)	PUNCT
ejpam-6273	345	9	of	of	ADP
ejpam-6273	345	10	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	345	11	is	be	AUX
ejpam-6273	345	12	denoted	denote	VERB
ejpam-6273	345	13	by	by	ADP
ejpam-6273	345	14	ς	ς	PROPN
ejpam-6273	345	15	+	+	NOUN
ejpam-6273	345	16	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	345	17	and	and	CCONJ
ejpam-6273	345	18	is	be	AUX
ejpam-6273	345	19	defined	define	VERB
ejpam-6273	345	20	by	by	ADP
ejpam-6273	345	21	(	(	PUNCT
ejpam-6273	345	22	ς	ς	PROPN
ejpam-6273	345	23	+	+	NOUN
ejpam-6273	345	24	ϱ̃)(q	ϱ̃)(q	NOUN
ejpam-6273	345	25	)	)	PUNCT
ejpam-6273	346	1	=	=	PUNCT
ejpam-6273	346	2	ϱ̃(q	ϱ̃(q	ADJ
ejpam-6273	346	3	−	−	PROPN
ejpam-6273	346	4	ς	ς	PROPN
ejpam-6273	346	5	)	)	PUNCT
ejpam-6273	346	6	and	and	CCONJ
ejpam-6273	346	7	(	(	PUNCT
ejpam-6273	346	8	ς	ς	PROPN
ejpam-6273	346	9	+	+	NOUN
ejpam-6273	346	10	γ)(q	γ)(q	NUM
ejpam-6273	346	11	)	)	PUNCT
ejpam-6273	347	1	=	=	SYM
ejpam-6273	347	2	γ(q	γ(q	PROPN
ejpam-6273	348	1	−	−	PROPN
ejpam-6273	348	2	ς),∀q	ς),∀q	NOUN
ejpam-6273	348	3	∈	∈	PROPN
ejpam-6273	348	4	y	y	PROPN
ejpam-6273	348	5	.	.	PUNCT
ejpam-6273	349	1	theorem	theorem	VERB
ejpam-6273	349	2	7	7	NUM
ejpam-6273	349	3	.	.	PUNCT
ejpam-6273	350	1	let	let	VERB
ejpam-6273	350	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	350	3	be	be	AUX
ejpam-6273	350	4	an	an	DET
ejpam-6273	350	5	hina	hina	NOUN
ejpam-6273	350	6	of	of	ADP
ejpam-6273	350	7	y	y	PROPN
ejpam-6273	350	8	upon	upon	SCONJ
ejpam-6273	350	9	u	u	PROPN
ejpam-6273	350	10	and	and	CCONJ
ejpam-6273	350	11	q	q	NOUN
ejpam-6273	350	12	,	,	PUNCT
ejpam-6273	350	13	ς	ς	PROPN
ejpam-6273	350	14	∈	∈	PROPN
ejpam-6273	350	15	y	y	PROPN
ejpam-6273	350	16	.	.	PUNCT
ejpam-6273	351	1	then	then	ADV
ejpam-6273	351	2	q	q	X
ejpam-6273	352	1	+	+	NUM
ejpam-6273	352	2	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	352	3	=	=	SYM
ejpam-6273	353	1	ς	ς	PROPN
ejpam-6273	353	2	+	+	NOUN
ejpam-6273	353	3	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	353	4	if	if	SCONJ
ejpam-6273	353	5	and	and	CCONJ
ejpam-6273	353	6	only	only	ADV
ejpam-6273	353	7	if	if	SCONJ
ejpam-6273	353	8	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	353	9	−	−	PROPN
ejpam-6273	353	10	ς	ς	PROPN
ejpam-6273	353	11	)	)	PUNCT
ejpam-6273	353	12	=	=	SYM
ejpam-6273	353	13	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	353	14	)	)	PUNCT
ejpam-6273	353	15	and	and	CCONJ
ejpam-6273	353	16	γ(q	γ(q	PROPN
ejpam-6273	354	1	−	−	PROPN
ejpam-6273	354	2	ς	ς	NOUN
ejpam-6273	354	3	)	)	PUNCT
ejpam-6273	354	4	=	=	SYM
ejpam-6273	354	5	γ(0	γ(0	PROPN
ejpam-6273	354	6	)	)	PUNCT
ejpam-6273	354	7	.	.	PUNCT
ejpam-6273	355	1	proof	proof	NOUN
ejpam-6273	355	2	.	.	PUNCT
ejpam-6273	356	1	let	let	VERB
ejpam-6273	356	2	q	q	X
ejpam-6273	356	3	,	,	PUNCT
ejpam-6273	356	4	ς	ς	PROPN
ejpam-6273	356	5	∈	∈	PROPN
ejpam-6273	356	6	y	y	PROPN
ejpam-6273	356	7	.	.	PUNCT
ejpam-6273	357	1	suppose	suppose	VERB
ejpam-6273	357	2	that	that	SCONJ
ejpam-6273	357	3	q	q	PROPN
ejpam-6273	358	1	+	+	NUM
ejpam-6273	358	2	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	358	3	=	=	SYM
ejpam-6273	358	4	ς	ς	PROPN
ejpam-6273	358	5	+	+	NUM
ejpam-6273	358	6	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	358	7	.	.	PUNCT
ejpam-6273	359	1	then	then	ADV
ejpam-6273	359	2	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	359	3	−	−	PROPN
ejpam-6273	359	4	ς	ς	PROPN
ejpam-6273	359	5	)	)	PUNCT
ejpam-6273	359	6	=	=	SYM
ejpam-6273	359	7	(	(	PUNCT
ejpam-6273	359	8	ς	ς	NOUN
ejpam-6273	359	9	+	+	CCONJ
ejpam-6273	359	10	ϱ̃)(q	ϱ̃)(q	NOUN
ejpam-6273	359	11	)	)	PUNCT
ejpam-6273	359	12	=	=	SYM
ejpam-6273	360	1	(	(	PUNCT
ejpam-6273	360	2	q	q	NOUN
ejpam-6273	360	3	+	+	CCONJ
ejpam-6273	360	4	ϱ̃)(q	ϱ̃)(q	NOUN
ejpam-6273	360	5	)	)	PUNCT
ejpam-6273	361	1	=	=	PUNCT
ejpam-6273	361	2	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	361	3	−	−	PROPN
ejpam-6273	361	4	q	q	NOUN
ejpam-6273	361	5	)	)	PUNCT
ejpam-6273	361	6	=	=	SYM
ejpam-6273	361	7	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	361	8	)	)	PUNCT
ejpam-6273	361	9	and	and	CCONJ
ejpam-6273	361	10	γ(q	γ(q	PROPN
ejpam-6273	361	11	−	−	PROPN
ejpam-6273	361	12	ς	ς	NOUN
ejpam-6273	361	13	)	)	PUNCT
ejpam-6273	361	14	=	=	PUNCT
ejpam-6273	361	15	(	(	PUNCT
ejpam-6273	361	16	ς	ς	PROPN
ejpam-6273	361	17	+	+	NOUN
ejpam-6273	361	18	γ)(q	γ)(q	NUM
ejpam-6273	361	19	)	)	PUNCT
ejpam-6273	361	20	=	=	PUNCT
ejpam-6273	361	21	(	(	PUNCT
ejpam-6273	361	22	q	q	X
ejpam-6273	361	23	+	+	NUM
ejpam-6273	361	24	γ)(q	γ)(q	NUM
ejpam-6273	361	25	)	)	PUNCT
ejpam-6273	361	26	=	=	SYM
ejpam-6273	361	27	γ(q	γ(q	NOUN
ejpam-6273	362	1	−	−	NOUN
ejpam-6273	362	2	q	q	NOUN
ejpam-6273	362	3	)	)	PUNCT
ejpam-6273	362	4	=	=	SYM
ejpam-6273	362	5	γ(0	γ(0	PROPN
ejpam-6273	362	6	)	)	PUNCT
ejpam-6273	362	7	.	.	PUNCT
ejpam-6273	363	1	conversely	conversely	ADV
ejpam-6273	363	2	,	,	PUNCT
ejpam-6273	363	3	suppose	suppose	VERB
ejpam-6273	363	4	that	that	SCONJ
ejpam-6273	363	5	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	363	6	−	−	PROPN
ejpam-6273	363	7	ς	ς	PROPN
ejpam-6273	363	8	)	)	PUNCT
ejpam-6273	363	9	=	=	SYM
ejpam-6273	363	10	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	363	11	)	)	PUNCT
ejpam-6273	363	12	and	and	CCONJ
ejpam-6273	363	13	γ(q	γ(q	PROPN
ejpam-6273	363	14	−	−	PROPN
ejpam-6273	363	15	ς	ς	NOUN
ejpam-6273	363	16	)	)	PUNCT
ejpam-6273	363	17	=	=	SYM
ejpam-6273	363	18	γ(0	γ(0	PROPN
ejpam-6273	363	19	)	)	PUNCT
ejpam-6273	363	20	.	.	PUNCT
ejpam-6273	364	1	for	for	ADP
ejpam-6273	364	2	every	every	DET
ejpam-6273	364	3	κ	κ	PROPN
ejpam-6273	364	4	∈	∈	PROPN
ejpam-6273	364	5	y	y	PROPN
ejpam-6273	364	6	,	,	PUNCT
ejpam-6273	364	7	we	we	PRON
ejpam-6273	364	8	have	have	VERB
ejpam-6273	364	9	(	(	PUNCT
ejpam-6273	364	10	q	q	SYM
ejpam-6273	364	11	+	+	NUM
ejpam-6273	364	12	ϱ̃)(κ	ϱ̃)(κ	NOUN
ejpam-6273	364	13	)	)	PUNCT
ejpam-6273	364	14	=	=	SYM
ejpam-6273	364	15	ϱ̃(κ−	ϱ̃(κ−	PART
ejpam-6273	364	16	q	q	NOUN
ejpam-6273	364	17	)	)	PUNCT
ejpam-6273	364	18	=	=	SYM
ejpam-6273	364	19	ϱ̃(κ−	ϱ̃(κ−	ADP
ejpam-6273	364	20	ς	ς	PROPN
ejpam-6273	365	1	+	+	PROPN
ejpam-6273	365	2	ς	ς	PROPN
ejpam-6273	365	3	−	−	NOUN
ejpam-6273	365	4	q	q	NOUN
ejpam-6273	365	5	)	)	PUNCT
ejpam-6273	365	6	=	=	SYM
ejpam-6273	365	7	ϱ̃[(κ−	ϱ̃[(κ−	NOUN
ejpam-6273	365	8	ς	ς	NOUN
ejpam-6273	365	9	)	)	PUNCT
ejpam-6273	365	10	+	+	CCONJ
ejpam-6273	365	11	(	(	PUNCT
ejpam-6273	365	12	ς	ς	PROPN
ejpam-6273	365	13	−	−	PROPN
ejpam-6273	365	14	q	q	NOUN
ejpam-6273	365	15	)	)	PUNCT
ejpam-6273	365	16	]	]	PUNCT
ejpam-6273	365	17	⊇	⊇	PROPN
ejpam-6273	365	18	ϱ̃(κ−	ϱ̃(κ−	NOUN
ejpam-6273	365	19	ς	ς	NOUN
ejpam-6273	365	20	)	)	PUNCT
ejpam-6273	365	21	∩	∩	PROPN
ejpam-6273	365	22	ϱ̃(ς	ϱ̃(ς	PROPN
ejpam-6273	365	23	−	−	PROPN
ejpam-6273	365	24	q	q	NOUN
ejpam-6273	365	25	)	)	PUNCT
ejpam-6273	365	26	=	=	SYM
ejpam-6273	365	27	ϱ̃(κ−	ϱ̃(κ−	ADP
ejpam-6273	365	28	ς	ς	NOUN
ejpam-6273	365	29	)	)	PUNCT
ejpam-6273	365	30	∩	∩	ADJ
ejpam-6273	365	31	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	365	32	−	−	PROPN
ejpam-6273	365	33	ς	ς	NOUN
ejpam-6273	365	34	)	)	PUNCT
ejpam-6273	365	35	=	=	SYM
ejpam-6273	365	36	ϱ̃(κ−	ϱ̃(κ−	ADP
ejpam-6273	365	37	ς	ς	NOUN
ejpam-6273	365	38	)	)	PUNCT
ejpam-6273	365	39	∩	∩	NOUN
ejpam-6273	365	40	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	365	41	)	)	PUNCT
ejpam-6273	365	42	p.	p.	PROPN
ejpam-6273	365	43	n.	n.	PROPN
ejpam-6273	365	44	swamy	swamy	PROPN
ejpam-6273	365	45	et	et	PROPN
ejpam-6273	365	46	al	al	PROPN
ejpam-6273	365	47	.	.	PUNCT
ejpam-6273	365	48	/	/	SYM
ejpam-6273	365	49	eur	eur	PROPN
ejpam-6273	365	50	.	.	PUNCT
ejpam-6273	366	1	j.	j.	PROPN
ejpam-6273	366	2	pure	pure	PROPN
ejpam-6273	366	3	appl	appl	PROPN
ejpam-6273	366	4	.	.	PROPN
ejpam-6273	366	5	math	math	PROPN
ejpam-6273	366	6	,	,	PUNCT
ejpam-6273	366	7	18	18	NUM
ejpam-6273	366	8	(	(	PUNCT
ejpam-6273	366	9	3	3	NUM
ejpam-6273	366	10	)	)	PUNCT
ejpam-6273	366	11	(	(	PUNCT
ejpam-6273	366	12	2025	2025	NUM
ejpam-6273	366	13	)	)	PUNCT
ejpam-6273	366	14	,	,	PUNCT
ejpam-6273	366	15	6273	6273	NUM
ejpam-6273	366	16	12	12	NUM
ejpam-6273	366	17	of	of	ADP
ejpam-6273	366	18	16	16	NUM
ejpam-6273	366	19	=	=	SYM
ejpam-6273	366	20	ϱ̃(κ−	ϱ̃(κ−	NOUN
ejpam-6273	366	21	ς	ς	NOUN
ejpam-6273	366	22	)	)	PUNCT
ejpam-6273	366	23	=	=	SYM
ejpam-6273	366	24	(	(	PUNCT
ejpam-6273	366	25	ς	ς	PROPN
ejpam-6273	366	26	+	+	X
ejpam-6273	366	27	ϱ̃)(κ	ϱ̃)(κ	NOUN
ejpam-6273	366	28	)	)	PUNCT
ejpam-6273	366	29	and	and	CCONJ
ejpam-6273	366	30	(	(	PUNCT
ejpam-6273	366	31	q	q	X
ejpam-6273	366	32	+	+	CCONJ
ejpam-6273	366	33	γ)(κ	γ)(κ	NOUN
ejpam-6273	366	34	)	)	PUNCT
ejpam-6273	366	35	=	=	SYM
ejpam-6273	366	36	γ(κ−	γ(κ−	PROPN
ejpam-6273	366	37	q	q	NOUN
ejpam-6273	366	38	)	)	PUNCT
ejpam-6273	366	39	=	=	SYM
ejpam-6273	366	40	γ(κ−	γ(κ−	PROPN
ejpam-6273	366	41	ς	ς	PROPN
ejpam-6273	366	42	+	+	NOUN
ejpam-6273	366	43	ς	ς	PROPN
ejpam-6273	366	44	−	−	NOUN
ejpam-6273	366	45	q	q	NOUN
ejpam-6273	366	46	)	)	PUNCT
ejpam-6273	366	47	=	=	SYM
ejpam-6273	366	48	γ[(κ−	γ[(κ−	ADP
ejpam-6273	366	49	ς	ς	NOUN
ejpam-6273	366	50	)	)	PUNCT
ejpam-6273	367	1	+	+	CCONJ
ejpam-6273	367	2	(	(	PUNCT
ejpam-6273	367	3	ς	ς	PROPN
ejpam-6273	367	4	−	−	PROPN
ejpam-6273	367	5	q	q	NOUN
ejpam-6273	367	6	)	)	PUNCT
ejpam-6273	367	7	]	]	PUNCT
ejpam-6273	367	8	≤	≤	NUM
ejpam-6273	367	9	∨	∨	NUM
ejpam-6273	367	10	{	{	PUNCT
ejpam-6273	367	11	γ(κ−	γ(κ−	PROPN
ejpam-6273	367	12	ς	ς	PROPN
ejpam-6273	367	13	)	)	PUNCT
ejpam-6273	367	14	,	,	PUNCT
ejpam-6273	367	15	γ(ς	γ(ς	PUNCT
ejpam-6273	367	16	−	−	PROPN
ejpam-6273	367	17	q	q	X
ejpam-6273	367	18	)	)	PUNCT
ejpam-6273	367	19	}	}	PUNCT
ejpam-6273	367	20	=	=	SYM
ejpam-6273	367	21	∨	∨	X
ejpam-6273	367	22	{	{	PUNCT
ejpam-6273	367	23	γ(κ−	γ(κ−	PROPN
ejpam-6273	367	24	ς	ς	PROPN
ejpam-6273	367	25	)	)	PUNCT
ejpam-6273	367	26	,	,	PUNCT
ejpam-6273	367	27	γ(q	γ(q	PROPN
ejpam-6273	367	28	−	−	PROPN
ejpam-6273	367	29	ς	ς	NOUN
ejpam-6273	367	30	)	)	PUNCT
ejpam-6273	367	31	}	}	PUNCT
ejpam-6273	368	1	=	=	SYM
ejpam-6273	368	2	∨	∨	X
ejpam-6273	368	3	{	{	PUNCT
ejpam-6273	368	4	γ(κ−	γ(κ−	PROPN
ejpam-6273	368	5	ς	ς	PROPN
ejpam-6273	368	6	)	)	PUNCT
ejpam-6273	368	7	,	,	PUNCT
ejpam-6273	368	8	γ(0	γ(0	PROPN
ejpam-6273	368	9	)	)	PUNCT
ejpam-6273	368	10	}	}	PUNCT
ejpam-6273	368	11	=	=	SYM
ejpam-6273	368	12	γ(κ−	γ(κ−	PROPN
ejpam-6273	368	13	ς	ς	NOUN
ejpam-6273	368	14	)	)	PUNCT
ejpam-6273	368	15	=	=	SYM
ejpam-6273	368	16	(	(	PUNCT
ejpam-6273	368	17	ς	ς	X
ejpam-6273	368	18	+	+	NOUN
ejpam-6273	368	19	γ)(κ	γ)(κ	NOUN
ejpam-6273	368	20	)	)	PUNCT
ejpam-6273	368	21	.	.	PUNCT
ejpam-6273	369	1	thus	thus	ADV
ejpam-6273	369	2	,	,	PUNCT
ejpam-6273	369	3	q	q	X
ejpam-6273	369	4	+	+	PUNCT
ejpam-6273	369	5	ϱ̃	ϱ̃	PROPN
ejpam-6273	369	6	⊇	⊇	NOUN
ejpam-6273	369	7	ς	ς	PROPN
ejpam-6273	369	8	+	+	PROPN
ejpam-6273	369	9	ϱ̃	ϱ̃	PROPN
ejpam-6273	369	10	and	and	CCONJ
ejpam-6273	369	11	q	q	NOUN
ejpam-6273	369	12	+	+	CCONJ
ejpam-6273	369	13	γ	γ	X
ejpam-6273	369	14	=	=	SYM
ejpam-6273	369	15	ς	ς	PROPN
ejpam-6273	369	16	+	+	X
ejpam-6273	369	17	γ	γ	X
ejpam-6273	369	18	.	.	PROPN
ejpam-6273	369	19	now	now	ADV
ejpam-6273	369	20	,	,	PUNCT
ejpam-6273	369	21	(	(	PUNCT
ejpam-6273	369	22	ς	ς	PROPN
ejpam-6273	369	23	+	+	X
ejpam-6273	369	24	ϱ̃)(κ	ϱ̃)(κ	NOUN
ejpam-6273	369	25	)	)	PUNCT
ejpam-6273	369	26	=	=	SYM
ejpam-6273	369	27	ϱ̃(κ−	ϱ̃(κ−	ADP
ejpam-6273	369	28	ς	ς	NOUN
ejpam-6273	369	29	)	)	PUNCT
ejpam-6273	369	30	=	=	SYM
ejpam-6273	369	31	ϱ̃(κ−	ϱ̃(κ−	PART
ejpam-6273	369	32	q	q	NOUN
ejpam-6273	370	1	+	+	NOUN
ejpam-6273	370	2	q	q	NOUN
ejpam-6273	370	3	−	−	PROPN
ejpam-6273	370	4	ς	ς	NOUN
ejpam-6273	370	5	)	)	PUNCT
ejpam-6273	370	6	=	=	SYM
ejpam-6273	370	7	ϱ̃[(κ−	ϱ̃[(κ−	NOUN
ejpam-6273	370	8	q	q	NOUN
ejpam-6273	370	9	)	)	PUNCT
ejpam-6273	371	1	+	+	CCONJ
ejpam-6273	371	2	(	(	PUNCT
ejpam-6273	371	3	q	q	NOUN
ejpam-6273	371	4	−	−	PROPN
ejpam-6273	371	5	ς	ς	PROPN
ejpam-6273	371	6	)	)	PUNCT
ejpam-6273	371	7	]	]	PUNCT
ejpam-6273	371	8	⊇	⊇	PROPN
ejpam-6273	371	9	ϱ̃(κ−	ϱ̃(κ−	NOUN
ejpam-6273	371	10	q	q	NOUN
ejpam-6273	371	11	)	)	PUNCT
ejpam-6273	371	12	∩	∩	NOUN
ejpam-6273	371	13	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	371	14	−	−	PROPN
ejpam-6273	371	15	ς	ς	PROPN
ejpam-6273	371	16	)	)	PUNCT
ejpam-6273	371	17	=	=	SYM
ejpam-6273	371	18	ϱ̃(κ−	ϱ̃(κ−	NOUN
ejpam-6273	371	19	q	q	ADJ
ejpam-6273	371	20	)	)	PUNCT
ejpam-6273	371	21	∩	∩	NOUN
ejpam-6273	371	22	ϱ̃(0	ϱ̃(0	NOUN
ejpam-6273	371	23	)	)	PUNCT
ejpam-6273	371	24	=	=	SYM
ejpam-6273	371	25	ϱ̃(κ−	ϱ̃(κ−	PART
ejpam-6273	371	26	q	q	NOUN
ejpam-6273	371	27	)	)	PUNCT
ejpam-6273	371	28	=	=	SYM
ejpam-6273	371	29	(	(	PUNCT
ejpam-6273	371	30	q	q	X
ejpam-6273	371	31	+	+	NUM
ejpam-6273	371	32	ϱ̃)(κ	ϱ̃)(κ	NOUN
ejpam-6273	371	33	)	)	PUNCT
ejpam-6273	371	34	and	and	CCONJ
ejpam-6273	371	35	(	(	PUNCT
ejpam-6273	371	36	ς	ς	PROPN
ejpam-6273	371	37	+	+	X
ejpam-6273	371	38	γ)(κ	γ)(κ	NOUN
ejpam-6273	371	39	)	)	PUNCT
ejpam-6273	371	40	=	=	SYM
ejpam-6273	371	41	γ(κ−	γ(κ−	PROPN
ejpam-6273	371	42	ς	ς	NOUN
ejpam-6273	371	43	)	)	PUNCT
ejpam-6273	371	44	=	=	SYM
ejpam-6273	371	45	γ(κ−	γ(κ−	PROPN
ejpam-6273	371	46	q	q	NOUN
ejpam-6273	372	1	+	+	CCONJ
ejpam-6273	372	2	q	q	ADJ
ejpam-6273	372	3	−	−	PROPN
ejpam-6273	372	4	ς	ς	NOUN
ejpam-6273	372	5	)	)	PUNCT
ejpam-6273	372	6	=	=	NOUN
ejpam-6273	372	7	γ[(κ−	γ[(κ−	NOUN
ejpam-6273	372	8	q	q	X
ejpam-6273	372	9	)	)	PUNCT
ejpam-6273	372	10	+	+	CCONJ
ejpam-6273	372	11	(	(	PUNCT
ejpam-6273	372	12	q	q	NOUN
ejpam-6273	372	13	−	−	PROPN
ejpam-6273	372	14	ς	ς	NOUN
ejpam-6273	372	15	)	)	PUNCT
ejpam-6273	372	16	]	]	PUNCT
ejpam-6273	372	17	≤	≤	NUM
ejpam-6273	372	18	∨	∨	NUM
ejpam-6273	372	19	{	{	PUNCT
ejpam-6273	372	20	γ(κ−	γ(κ−	PROPN
ejpam-6273	372	21	q	q	NOUN
ejpam-6273	372	22	)	)	PUNCT
ejpam-6273	372	23	,	,	PUNCT
ejpam-6273	372	24	γ(q	γ(q	PROPN
ejpam-6273	372	25	−	−	PROPN
ejpam-6273	372	26	ς	ς	NOUN
ejpam-6273	372	27	)	)	PUNCT
ejpam-6273	372	28	}	}	PUNCT
ejpam-6273	372	29	=	=	SYM
ejpam-6273	372	30	∨	∨	X
ejpam-6273	372	31	{	{	PUNCT
ejpam-6273	372	32	γ(κ−	γ(κ−	PROPN
ejpam-6273	372	33	q	q	NOUN
ejpam-6273	372	34	)	)	PUNCT
ejpam-6273	372	35	,	,	PUNCT
ejpam-6273	372	36	γ(0	γ(0	PROPN
ejpam-6273	372	37	)	)	PUNCT
ejpam-6273	372	38	}	}	PUNCT
ejpam-6273	372	39	=	=	SYM
ejpam-6273	372	40	γ(κ−	γ(κ−	NOUN
ejpam-6273	372	41	q	q	NOUN
ejpam-6273	372	42	)	)	PUNCT
ejpam-6273	372	43	=	=	SYM
ejpam-6273	372	44	(	(	PUNCT
ejpam-6273	372	45	q	q	NOUN
ejpam-6273	372	46	+	+	NUM
ejpam-6273	372	47	γ)(κ	γ)(κ	NOUN
ejpam-6273	372	48	)	)	PUNCT
ejpam-6273	372	49	.	.	PUNCT
ejpam-6273	373	1	thus	thus	ADV
ejpam-6273	373	2	,	,	PUNCT
ejpam-6273	373	3	ς	ς	PROPN
ejpam-6273	373	4	+	+	PUNCT
ejpam-6273	373	5	ϱ̃	ϱ̃	PROPN
ejpam-6273	373	6	⊇	⊇	NOUN
ejpam-6273	373	7	q	q	NOUN
ejpam-6273	373	8	+	+	CCONJ
ejpam-6273	373	9	ϱ̃	ϱ̃	PROPN
ejpam-6273	373	10	and	and	CCONJ
ejpam-6273	373	11	ς	ς	PROPN
ejpam-6273	373	12	+	+	CCONJ
ejpam-6273	373	13	γ	γ	X
ejpam-6273	373	14	=	=	SYM
ejpam-6273	373	15	q	q	PROPN
ejpam-6273	374	1	+	+	X
ejpam-6273	374	2	γ	γ	X
ejpam-6273	374	3	.	.	PROPN
ejpam-6273	374	4	hence	hence	ADV
ejpam-6273	374	5	,	,	PUNCT
ejpam-6273	374	6	q	q	X
ejpam-6273	374	7	+	+	PUNCT
ejpam-6273	374	8	ϱ̃	ϱ̃	NOUN
ejpam-6273	374	9	=	=	SYM
ejpam-6273	374	10	ς	ς	PROPN
ejpam-6273	374	11	+	+	PROPN
ejpam-6273	374	12	ϱ̃	ϱ̃	PROPN
ejpam-6273	374	13	and	and	CCONJ
ejpam-6273	374	14	q	q	NOUN
ejpam-6273	374	15	+	+	CCONJ
ejpam-6273	374	16	γ	γ	X
ejpam-6273	374	17	=	=	SYM
ejpam-6273	374	18	ς	ς	PROPN
ejpam-6273	374	19	+	+	PROPN
ejpam-6273	374	20	γ	γ	PROPN
ejpam-6273	374	21	.	.	PROPN
ejpam-6273	374	22	theorem	theorem	NOUN
ejpam-6273	374	23	8	8	NUM
ejpam-6273	374	24	.	.	PUNCT
ejpam-6273	375	1	let	let	VERB
ejpam-6273	375	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	375	3	be	be	AUX
ejpam-6273	375	4	an	an	DET
ejpam-6273	375	5	hina	hina	NOUN
ejpam-6273	375	6	of	of	ADP
ejpam-6273	375	7	y	y	PROPN
ejpam-6273	375	8	upon	upon	SCONJ
ejpam-6273	375	9	u	u	PROPN
ejpam-6273	375	10	.	.	PUNCT
ejpam-6273	376	1	then	then	ADV
ejpam-6273	376	2	the	the	DET
ejpam-6273	376	3	following	follow	VERB
ejpam-6273	376	4	two	two	NUM
ejpam-6273	376	5	statements	statement	NOUN
ejpam-6273	376	6	hold	hold	VERB
ejpam-6273	376	7	:	:	PUNCT
ejpam-6273	376	8	(	(	PUNCT
ejpam-6273	376	9	i	i	NOUN
ejpam-6273	376	10	)	)	PUNCT
ejpam-6273	376	11	if	if	SCONJ
ejpam-6273	376	12	q+	q+	ADP
ejpam-6273	376	13	ϱ̃	ϱ̃	PROPN
ejpam-6273	376	14	=	=	SYM
ejpam-6273	376	15	p+	p+	PROPN
ejpam-6273	376	16	ϱ̃	ϱ̃	PROPN
ejpam-6273	376	17	,	,	PUNCT
ejpam-6273	376	18	ς	ς	PROPN
ejpam-6273	376	19	+	+	PUNCT
ejpam-6273	376	20	ϱ̃	ϱ̃	PROPN
ejpam-6273	376	21	=	=	SYM
ejpam-6273	376	22	m+	m+	NUM
ejpam-6273	377	1	ϱ̃	ϱ̃	PROPN
ejpam-6273	377	2	,	,	PUNCT
ejpam-6273	377	3	then	then	ADV
ejpam-6273	377	4	(	(	PUNCT
ejpam-6273	377	5	q+	q+	ADP
ejpam-6273	377	6	ς	ς	NOUN
ejpam-6273	377	7	)	)	PUNCT
ejpam-6273	378	1	+	+	CCONJ
ejpam-6273	378	2	ϱ̃	ϱ̃	NUM
ejpam-6273	378	3	=	=	SYM
ejpam-6273	378	4	(	(	PUNCT
ejpam-6273	378	5	p+m	p+m	NOUN
ejpam-6273	378	6	)	)	PUNCT
ejpam-6273	378	7	+	+	CCONJ
ejpam-6273	378	8	ϱ̃	ϱ̃	NOUN
ejpam-6273	378	9	,	,	PUNCT
ejpam-6273	378	10	qς	qς	ADP
ejpam-6273	378	11	+	+	SYM
ejpam-6273	378	12	ϱ̃	ϱ̃	PROPN
ejpam-6273	378	13	=	=	PUNCT
ejpam-6273	378	14	pm+	pm+	NOUN
ejpam-6273	378	15	ϱ̃	ϱ̃	NUM
ejpam-6273	378	16	,	,	PUNCT
ejpam-6273	378	17	and	and	CCONJ
ejpam-6273	378	18	if	if	SCONJ
ejpam-6273	378	19	q	q	X
ejpam-6273	378	20	+	+	NUM
ejpam-6273	378	21	γ	γ	X
ejpam-6273	378	22	=	=	SYM
ejpam-6273	378	23	p+	p+	PROPN
ejpam-6273	378	24	γ	γ	X
ejpam-6273	378	25	,	,	PUNCT
ejpam-6273	378	26	ς	ς	PROPN
ejpam-6273	378	27	+	+	CCONJ
ejpam-6273	378	28	γ	γ	X
ejpam-6273	378	29	=	=	SYM
ejpam-6273	378	30	m+	m+	NUM
ejpam-6273	378	31	γ	γ	NOUN
ejpam-6273	378	32	,	,	PUNCT
ejpam-6273	378	33	then	then	ADV
ejpam-6273	378	34	(	(	PUNCT
ejpam-6273	378	35	q	q	PROPN
ejpam-6273	378	36	+	+	CCONJ
ejpam-6273	378	37	ς	ς	NOUN
ejpam-6273	378	38	)	)	PUNCT
ejpam-6273	378	39	+	+	CCONJ
ejpam-6273	378	40	γ	γ	X
ejpam-6273	378	41	=	=	SYM
ejpam-6273	378	42	(	(	PUNCT
ejpam-6273	378	43	p+m	p+m	NOUN
ejpam-6273	378	44	)	)	PUNCT
ejpam-6273	378	45	+	+	CCONJ
ejpam-6273	378	46	γ	γ	X
ejpam-6273	378	47	,	,	PUNCT
ejpam-6273	378	48	qς	qς	ADP
ejpam-6273	378	49	+	+	CCONJ
ejpam-6273	378	50	γ	γ	X
ejpam-6273	378	51	=	=	SYM
ejpam-6273	378	52	pm+	pm+	PROPN
ejpam-6273	378	53	γ	γ	PROPN
ejpam-6273	378	54	p.	p.	PROPN
ejpam-6273	378	55	n.	n.	PROPN
ejpam-6273	378	56	swamy	swamy	PROPN
ejpam-6273	378	57	et	et	PROPN
ejpam-6273	378	58	al	al	PROPN
ejpam-6273	378	59	.	.	PUNCT
ejpam-6273	378	60	/	/	SYM
ejpam-6273	378	61	eur	eur	PROPN
ejpam-6273	378	62	.	.	PUNCT
ejpam-6273	379	1	j.	j.	PROPN
ejpam-6273	379	2	pure	pure	PROPN
ejpam-6273	379	3	appl	appl	PROPN
ejpam-6273	379	4	.	.	PROPN
ejpam-6273	379	5	math	math	PROPN
ejpam-6273	379	6	,	,	PUNCT
ejpam-6273	379	7	18	18	NUM
ejpam-6273	379	8	(	(	PUNCT
ejpam-6273	379	9	3	3	NUM
ejpam-6273	379	10	)	)	PUNCT
ejpam-6273	379	11	(	(	PUNCT
ejpam-6273	379	12	2025	2025	NUM
ejpam-6273	379	13	)	)	PUNCT
ejpam-6273	379	14	,	,	PUNCT
ejpam-6273	379	15	6273	6273	NUM
ejpam-6273	379	16	13	13	NUM
ejpam-6273	379	17	of	of	ADP
ejpam-6273	379	18	16	16	NUM
ejpam-6273	379	19	(	(	PUNCT
ejpam-6273	379	20	ii	ii	NOUN
ejpam-6273	379	21	)	)	PUNCT
ejpam-6273	379	22	if	if	SCONJ
ejpam-6273	379	23	q	q	NOUN
ejpam-6273	379	24	+	+	PUNCT
ejpam-6273	379	25	ϱ̃	ϱ̃	PROPN
ejpam-6273	379	26	=	=	SYM
ejpam-6273	379	27	p+	p+	PROPN
ejpam-6273	379	28	ϱ̃	ϱ̃	PROPN
ejpam-6273	379	29	,	,	PUNCT
ejpam-6273	379	30	then	then	ADV
ejpam-6273	379	31	sq	sq	PROPN
ejpam-6273	379	32	+	+	NUM
ejpam-6273	379	33	ϱ̃	ϱ̃	NOUN
ejpam-6273	379	34	=	=	SYM
ejpam-6273	379	35	sp+	sp+	ADJ
ejpam-6273	379	36	ϱ̃	ϱ̃	PROPN
ejpam-6273	379	37	,	,	PUNCT
ejpam-6273	379	38	and	and	CCONJ
ejpam-6273	379	39	if	if	SCONJ
ejpam-6273	379	40	q	q	X
ejpam-6273	380	1	+	+	NUM
ejpam-6273	380	2	γ	γ	X
ejpam-6273	380	3	=	=	SYM
ejpam-6273	380	4	p+	p+	PROPN
ejpam-6273	380	5	γ	γ	X
ejpam-6273	380	6	,	,	PUNCT
ejpam-6273	380	7	then	then	ADV
ejpam-6273	380	8	sq	sq	PROPN
ejpam-6273	380	9	+	+	CCONJ
ejpam-6273	380	10	γ	γ	X
ejpam-6273	380	11	=	=	SYM
ejpam-6273	380	12	sp+	sp+	ADV
ejpam-6273	380	13	γ	γ	NOUN
ejpam-6273	380	14	for	for	ADP
ejpam-6273	380	15	all	all	DET
ejpam-6273	380	16	q	q	PROPN
ejpam-6273	380	17	,	,	PUNCT
ejpam-6273	380	18	ς	ς	PROPN
ejpam-6273	380	19	,	,	PUNCT
ejpam-6273	380	20	p	p	X
ejpam-6273	380	21	,	,	PUNCT
ejpam-6273	380	22	m	m	PROPN
ejpam-6273	380	23	∈	∈	PROPN
ejpam-6273	380	24	y	y	NOUN
ejpam-6273	380	25	and	and	CCONJ
ejpam-6273	380	26	s	s	PROPN
ejpam-6273	380	27	∈	∈	PROPN
ejpam-6273	380	28	l.	l.	NOUN
ejpam-6273	380	29	proof	proof	NOUN
ejpam-6273	380	30	.	.	PUNCT
ejpam-6273	381	1	(	(	PUNCT
ejpam-6273	381	2	i	i	NOUN
ejpam-6273	381	3	)	)	PUNCT
ejpam-6273	381	4	suppose	suppose	VERB
ejpam-6273	381	5	that	that	SCONJ
ejpam-6273	381	6	q+	q+	ADP
ejpam-6273	381	7	ϱ̃	ϱ̃	PROPN
ejpam-6273	381	8	=	=	SYM
ejpam-6273	381	9	p+	p+	PROPN
ejpam-6273	381	10	ϱ̃	ϱ̃	PROPN
ejpam-6273	381	11	,	,	PUNCT
ejpam-6273	381	12	ς	ς	PROPN
ejpam-6273	381	13	+	+	PUNCT
ejpam-6273	381	14	ϱ̃	ϱ̃	PROPN
ejpam-6273	381	15	=	=	SYM
ejpam-6273	381	16	m+	m+	NUM
ejpam-6273	381	17	ϱ̃	ϱ̃	PROPN
ejpam-6273	381	18	and	and	CCONJ
ejpam-6273	381	19	q+	q+	NOUN
ejpam-6273	381	20	γ	γ	X
ejpam-6273	381	21	=	=	PROPN
ejpam-6273	381	22	p+	p+	PROPN
ejpam-6273	381	23	γ	γ	X
ejpam-6273	381	24	,	,	PUNCT
ejpam-6273	381	25	ς	ς	PROPN
ejpam-6273	381	26	+	+	CCONJ
ejpam-6273	381	27	γ	γ	X
ejpam-6273	381	28	=	=	SYM
ejpam-6273	381	29	m+	m+	NUM
ejpam-6273	381	30	γ	γ	PROPN
ejpam-6273	381	31	.	.	PROPN
ejpam-6273	381	32	then	then	ADV
ejpam-6273	381	33	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	381	34	−	−	PROPN
ejpam-6273	381	35	p	p	X
ejpam-6273	381	36	)	)	PUNCT
ejpam-6273	381	37	=	=	SYM
ejpam-6273	381	38	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	381	39	)	)	PUNCT
ejpam-6273	381	40	,	,	PUNCT
ejpam-6273	381	41	ϱ̃(ς	ϱ̃(ς	NOUN
ejpam-6273	381	42	−m	−m	NOUN
ejpam-6273	381	43	)	)	PUNCT
ejpam-6273	381	44	=	=	SYM
ejpam-6273	381	45	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	381	46	)	)	PUNCT
ejpam-6273	381	47	and	and	CCONJ
ejpam-6273	381	48	γ(q	γ(q	PROPN
ejpam-6273	381	49	−	−	PROPN
ejpam-6273	381	50	p	p	NOUN
ejpam-6273	381	51	)	)	PUNCT
ejpam-6273	381	52	=	=	SYM
ejpam-6273	381	53	γ(0	γ(0	PROPN
ejpam-6273	381	54	)	)	PUNCT
ejpam-6273	381	55	,	,	PUNCT
ejpam-6273	381	56	γ(ς	γ(ς	NOUN
ejpam-6273	381	57	−m	−m	NOUN
ejpam-6273	381	58	)	)	PUNCT
ejpam-6273	381	59	=	=	SYM
ejpam-6273	381	60	γ(0	γ(0	PROPN
ejpam-6273	381	61	)	)	PUNCT
ejpam-6273	381	62	.	.	PUNCT
ejpam-6273	382	1	consider	consider	VERB
ejpam-6273	382	2	,	,	PUNCT
ejpam-6273	382	3	ϱ̃[(q	ϱ̃[(q	PROPN
ejpam-6273	382	4	+	+	PROPN
ejpam-6273	382	5	ς)−	ς)−	PROPN
ejpam-6273	382	6	(	(	PUNCT
ejpam-6273	382	7	p+m	p+m	NOUN
ejpam-6273	382	8	)	)	PUNCT
ejpam-6273	382	9	]	]	PUNCT
ejpam-6273	383	1	=	=	PUNCT
ejpam-6273	383	2	ϱ̃[(q	ϱ̃[(q	PRON
ejpam-6273	383	3	−	−	PROPN
ejpam-6273	383	4	p	p	NOUN
ejpam-6273	383	5	)	)	PUNCT
ejpam-6273	383	6	+	+	CCONJ
ejpam-6273	383	7	(	(	PUNCT
ejpam-6273	383	8	ς	ς	PROPN
ejpam-6273	383	9	−m	−m	NOUN
ejpam-6273	383	10	)	)	PUNCT
ejpam-6273	383	11	]	]	PUNCT
ejpam-6273	384	1	⊇	⊇	PROPN
ejpam-6273	384	2	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	384	3	−	−	PROPN
ejpam-6273	384	4	p	p	X
ejpam-6273	384	5	)	)	PUNCT
ejpam-6273	384	6	∩	∩	ADJ
ejpam-6273	384	7	ϱ̃(ς	ϱ̃(ς	NOUN
ejpam-6273	384	8	−m	−m	NOUN
ejpam-6273	384	9	)	)	PUNCT
ejpam-6273	384	10	=	=	SYM
ejpam-6273	384	11	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	384	12	)	)	PUNCT
ejpam-6273	384	13	∩	∩	NOUN
ejpam-6273	384	14	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	384	15	)	)	PUNCT
ejpam-6273	384	16	=	=	SYM
ejpam-6273	384	17	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	384	18	)	)	PUNCT
ejpam-6273	384	19	and	and	CCONJ
ejpam-6273	384	20	γ[(q	γ[(q	PROPN
ejpam-6273	384	21	+	+	CCONJ
ejpam-6273	384	22	ς	ς	PROPN
ejpam-6273	384	23	)	)	PUNCT
ejpam-6273	384	24	−	−	PROPN
ejpam-6273	385	1	(	(	PUNCT
ejpam-6273	385	2	p	p	X
ejpam-6273	385	3	+	+	NOUN
ejpam-6273	385	4	m	m	NOUN
ejpam-6273	385	5	)	)	PUNCT
ejpam-6273	385	6	]	]	PUNCT
ejpam-6273	386	1	=	=	SYM
ejpam-6273	386	2	γ[(q	γ[(q	NOUN
ejpam-6273	386	3	−	−	PROPN
ejpam-6273	386	4	p	p	NOUN
ejpam-6273	386	5	)	)	PUNCT
ejpam-6273	386	6	+	+	CCONJ
ejpam-6273	386	7	(	(	PUNCT
ejpam-6273	386	8	ς	ς	PROPN
ejpam-6273	386	9	−m	−m	NOUN
ejpam-6273	386	10	)	)	PUNCT
ejpam-6273	386	11	]	]	PUNCT
ejpam-6273	386	12	≤	≤	NUM
ejpam-6273	386	13	∨	∨	NUM
ejpam-6273	386	14	{	{	PUNCT
ejpam-6273	386	15	γ(q	γ(q	PROPN
ejpam-6273	386	16	−	−	PROPN
ejpam-6273	386	17	p	p	NOUN
ejpam-6273	386	18	)	)	PUNCT
ejpam-6273	386	19	,	,	PUNCT
ejpam-6273	386	20	γ(ς	γ(ς	NOUN
ejpam-6273	386	21	−m	−m	NOUN
ejpam-6273	386	22	)	)	PUNCT
ejpam-6273	386	23	}	}	PUNCT
ejpam-6273	386	24	=	=	SYM
ejpam-6273	386	25	∨	∨	X
ejpam-6273	386	26	{	{	PUNCT
ejpam-6273	386	27	γ(0	γ(0	PROPN
ejpam-6273	386	28	)	)	PUNCT
ejpam-6273	386	29	,	,	PUNCT
ejpam-6273	386	30	γ(0	γ(0	PROPN
ejpam-6273	386	31	)	)	PUNCT
ejpam-6273	386	32	}	}	PUNCT
ejpam-6273	386	33	=	=	SYM
ejpam-6273	386	34	γ(0	γ(0	PROPN
ejpam-6273	386	35	)	)	PUNCT
ejpam-6273	386	36	.	.	PUNCT
ejpam-6273	387	1	but	but	CCONJ
ejpam-6273	387	2	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	387	3	)	)	PUNCT
ejpam-6273	387	4	⊇	⊇	PROPN
ejpam-6273	387	5	ϱ̃[(q	ϱ̃[(q	PROPN
ejpam-6273	387	6	+	+	PROPN
ejpam-6273	387	7	ς	ς	PROPN
ejpam-6273	387	8	)	)	PUNCT
ejpam-6273	387	9	−	−	PROPN
ejpam-6273	388	1	(	(	PUNCT
ejpam-6273	388	2	p	p	X
ejpam-6273	388	3	+	+	NOUN
ejpam-6273	388	4	m	m	NOUN
ejpam-6273	388	5	)	)	PUNCT
ejpam-6273	388	6	]	]	PUNCT
ejpam-6273	388	7	and	and	CCONJ
ejpam-6273	388	8	γ(0	γ(0	PROPN
ejpam-6273	388	9	)	)	PUNCT
ejpam-6273	388	10	≤	≤	NOUN
ejpam-6273	388	11	γ[(q	γ[(q	NOUN
ejpam-6273	388	12	+	+	CCONJ
ejpam-6273	388	13	ς	ς	PROPN
ejpam-6273	388	14	)	)	PUNCT
ejpam-6273	389	1	−	−	PROPN
ejpam-6273	390	1	(	(	PUNCT
ejpam-6273	390	2	p	p	X
ejpam-6273	390	3	+	+	NOUN
ejpam-6273	390	4	m	m	NOUN
ejpam-6273	390	5	)	)	PUNCT
ejpam-6273	390	6	]	]	PUNCT
ejpam-6273	390	7	.	.	PUNCT
ejpam-6273	391	1	therefore	therefore	ADV
ejpam-6273	391	2	,	,	PUNCT
ejpam-6273	391	3	ϱ̃[(q+	ϱ̃[(q+	PROPN
ejpam-6273	391	4	ς)−	ς)−	PROPN
ejpam-6273	391	5	(	(	PUNCT
ejpam-6273	391	6	p+m	p+m	NOUN
ejpam-6273	391	7	)	)	PUNCT
ejpam-6273	391	8	]	]	PUNCT
ejpam-6273	392	1	=	=	SYM
ejpam-6273	392	2	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	392	3	)	)	PUNCT
ejpam-6273	392	4	and	and	CCONJ
ejpam-6273	392	5	γ[(q+	γ[(q+	PROPN
ejpam-6273	392	6	ς)−	ς)−	PROPN
ejpam-6273	392	7	(	(	PUNCT
ejpam-6273	392	8	p+m	p+m	NOUN
ejpam-6273	392	9	)	)	PUNCT
ejpam-6273	392	10	]	]	PUNCT
ejpam-6273	392	11	=	=	PUNCT
ejpam-6273	392	12	γ(0	γ(0	PROPN
ejpam-6273	392	13	)	)	PUNCT
ejpam-6273	392	14	.	.	PUNCT
ejpam-6273	393	1	thus	thus	ADV
ejpam-6273	393	2	,	,	PUNCT
ejpam-6273	393	3	(	(	PUNCT
ejpam-6273	393	4	q+	q+	ADP
ejpam-6273	393	5	ς)+	ς)+	NUM
ejpam-6273	393	6	ϱ̃	ϱ̃	NUM
ejpam-6273	393	7	=	=	PUNCT
ejpam-6273	393	8	(	(	PUNCT
ejpam-6273	393	9	p+m)+	p+m)+	NOUN
ejpam-6273	393	10	ϱ̃	ϱ̃	NUM
ejpam-6273	393	11	and	and	CCONJ
ejpam-6273	393	12	(	(	PUNCT
ejpam-6273	393	13	q	q	PROPN
ejpam-6273	393	14	+	+	CCONJ
ejpam-6273	393	15	ς	ς	NOUN
ejpam-6273	393	16	)	)	PUNCT
ejpam-6273	393	17	+	+	CCONJ
ejpam-6273	393	18	γ	γ	X
ejpam-6273	393	19	=	=	SYM
ejpam-6273	393	20	(	(	PUNCT
ejpam-6273	393	21	p+m	p+m	NOUN
ejpam-6273	393	22	)	)	PUNCT
ejpam-6273	393	23	+	+	CCONJ
ejpam-6273	393	24	γ	γ	X
ejpam-6273	393	25	.	.	PROPN
ejpam-6273	393	26	again	again	ADV
ejpam-6273	393	27	,	,	PUNCT
ejpam-6273	393	28	ϱ̃[qς	ϱ̃[qς	NOUN
ejpam-6273	393	29	−	−	PROPN
ejpam-6273	393	30	pm	pm	NOUN
ejpam-6273	393	31	]	]	X
ejpam-6273	393	32	=	=	SYM
ejpam-6273	393	33	ϱ̃[pm−	ϱ̃[pm−	PROPN
ejpam-6273	393	34	qς	qς	PROPN
ejpam-6273	393	35	]	]	X
ejpam-6273	393	36	=	=	SYM
ejpam-6273	393	37	ϱ̃(pm−	ϱ̃(pm−	PROPN
ejpam-6273	393	38	qm+	qm+	ADJ
ejpam-6273	393	39	qm−	qm−	PUNCT
ejpam-6273	393	40	qς	qς	PROPN
ejpam-6273	393	41	)	)	PUNCT
ejpam-6273	393	42	=	=	NOUN
ejpam-6273	393	43	ϱ̃[(p−	ϱ̃[(p−	VERB
ejpam-6273	393	44	q)m+	q)m+	ADJ
ejpam-6273	393	45	q(ς	q(ς	NOUN
ejpam-6273	393	46	+	+	CCONJ
ejpam-6273	393	47	(	(	PUNCT
ejpam-6273	393	48	−ς	−ς	ADJ
ejpam-6273	393	49	+	+	ADJ
ejpam-6273	393	50	m))−	m))−	NOUN
ejpam-6273	393	51	qς	qς	NOUN
ejpam-6273	393	52	)	)	PUNCT
ejpam-6273	393	53	]	]	PUNCT
ejpam-6273	393	54	⊇	⊇	NOUN
ejpam-6273	393	55	ϱ̃((p−	ϱ̃((p−	X
ejpam-6273	393	56	q)m	q)m	NOUN
ejpam-6273	393	57	)	)	PUNCT
ejpam-6273	393	58	∩	∩	NOUN
ejpam-6273	393	59	ϱ̃(q(ς	ϱ̃(q(ς	PROPN
ejpam-6273	393	60	+	+	CCONJ
ejpam-6273	393	61	(	(	PUNCT
ejpam-6273	393	62	−ς	−ς	ADJ
ejpam-6273	393	63	+	+	ADJ
ejpam-6273	393	64	m))−	m))−	VERB
ejpam-6273	393	65	qς	qς	NOUN
ejpam-6273	393	66	)	)	PUNCT
ejpam-6273	393	67	=	=	PUNCT
ejpam-6273	393	68	ϱ̃(p−	ϱ̃(p−	VERB
ejpam-6273	393	69	q	q	NOUN
ejpam-6273	393	70	)	)	PUNCT
ejpam-6273	393	71	∩	∩	ADJ
ejpam-6273	393	72	ϱ̃(ς	ϱ̃(ς	NOUN
ejpam-6273	393	73	−m	−m	NOUN
ejpam-6273	393	74	)	)	PUNCT
ejpam-6273	393	75	=	=	SYM
ejpam-6273	393	76	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	393	77	)	)	PUNCT
ejpam-6273	393	78	∩	∩	NOUN
ejpam-6273	393	79	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	393	80	)	)	PUNCT
ejpam-6273	393	81	=	=	SYM
ejpam-6273	393	82	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	393	83	)	)	PUNCT
ejpam-6273	393	84	and	and	CCONJ
ejpam-6273	393	85	γ[qς	γ[qς	PRON
ejpam-6273	393	86	−	−	PROPN
ejpam-6273	393	87	pm	pm	NOUN
ejpam-6273	393	88	]	]	X
ejpam-6273	393	89	=	=	SYM
ejpam-6273	393	90	γ[pm−	γ[pm−	PROPN
ejpam-6273	393	91	qς	qς	PROPN
ejpam-6273	393	92	]	]	X
ejpam-6273	393	93	=	=	PUNCT
ejpam-6273	393	94	γ(pm−	γ(pm−	NUM
ejpam-6273	393	95	qm+	qm+	ADJ
ejpam-6273	393	96	qm−	qm−	NUM
ejpam-6273	393	97	qς	qς	PROPN
ejpam-6273	393	98	)	)	PUNCT
ejpam-6273	393	99	=	=	PUNCT
ejpam-6273	393	100	γ[(p−	γ[(p−	VERB
ejpam-6273	393	101	q)m+	q)m+	ADJ
ejpam-6273	393	102	q(ς	q(ς	NOUN
ejpam-6273	393	103	+	+	CCONJ
ejpam-6273	393	104	(	(	PUNCT
ejpam-6273	393	105	−ς	−ς	ADJ
ejpam-6273	393	106	+	+	ADJ
ejpam-6273	393	107	m))−	m))−	VERB
ejpam-6273	393	108	qς	qς	NOUN
ejpam-6273	393	109	]	]	X
ejpam-6273	393	110	≤	≤	NUM
ejpam-6273	393	111	∨	∨	NUM
ejpam-6273	393	112	{	{	PUNCT
ejpam-6273	393	113	γ((p−	γ((p−	X
ejpam-6273	393	114	q)m	q)m	NOUN
ejpam-6273	393	115	)	)	PUNCT
ejpam-6273	393	116	,	,	PUNCT
ejpam-6273	393	117	γ(q(ς	γ(q(ς	NUM
ejpam-6273	393	118	+	+	CCONJ
ejpam-6273	393	119	(	(	PUNCT
ejpam-6273	393	120	−ς	−ς	ADJ
ejpam-6273	393	121	+	+	ADJ
ejpam-6273	393	122	m))−	m))−	VERB
ejpam-6273	393	123	qς	qς	NOUN
ejpam-6273	393	124	)	)	PUNCT
ejpam-6273	393	125	}	}	PUNCT
ejpam-6273	393	126	≤	≤	NUM
ejpam-6273	393	127	∨	∨	NUM
ejpam-6273	393	128	{	{	PUNCT
ejpam-6273	393	129	γ(p−	γ(p−	X
ejpam-6273	393	130	q	q	NOUN
ejpam-6273	393	131	)	)	PUNCT
ejpam-6273	393	132	,	,	PUNCT
ejpam-6273	393	133	γ(ς	γ(ς	NOUN
ejpam-6273	393	134	−m	−m	NOUN
ejpam-6273	393	135	)	)	PUNCT
ejpam-6273	393	136	}	}	PUNCT
ejpam-6273	393	137	=	=	SYM
ejpam-6273	393	138	∨	∨	X
ejpam-6273	393	139	{	{	PUNCT
ejpam-6273	393	140	γ(0	γ(0	PROPN
ejpam-6273	393	141	)	)	PUNCT
ejpam-6273	393	142	,	,	PUNCT
ejpam-6273	393	143	γ(0	γ(0	PROPN
ejpam-6273	393	144	)	)	PUNCT
ejpam-6273	393	145	}	}	PUNCT
ejpam-6273	393	146	=	=	SYM
ejpam-6273	393	147	γ(0	γ(0	PROPN
ejpam-6273	393	148	)	)	PUNCT
ejpam-6273	393	149	.	.	PUNCT
ejpam-6273	394	1	but	but	CCONJ
ejpam-6273	394	2	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	394	3	)	)	PUNCT
ejpam-6273	394	4	⊇	⊇	PROPN
ejpam-6273	394	5	ϱ̃[(qς	ϱ̃[(qς	NOUN
ejpam-6273	394	6	)	)	PUNCT
ejpam-6273	394	7	−	−	PROPN
ejpam-6273	394	8	(	(	PUNCT
ejpam-6273	394	9	pm	pm	NOUN
ejpam-6273	394	10	)	)	PUNCT
ejpam-6273	394	11	]	]	PUNCT
ejpam-6273	394	12	and	and	CCONJ
ejpam-6273	394	13	γ(0	γ(0	PROPN
ejpam-6273	394	14	)	)	PUNCT
ejpam-6273	394	15	≤	≤	NUM
ejpam-6273	394	16	γ[(qς	γ[(qς	NOUN
ejpam-6273	394	17	)	)	PUNCT
ejpam-6273	394	18	−	−	PROPN
ejpam-6273	394	19	(	(	PUNCT
ejpam-6273	394	20	pm	pm	NOUN
ejpam-6273	394	21	)	)	PUNCT
ejpam-6273	394	22	]	]	PUNCT
ejpam-6273	394	23	.	.	PUNCT
ejpam-6273	395	1	therefore	therefore	ADV
ejpam-6273	395	2	,	,	PUNCT
ejpam-6273	395	3	ϱ̃[qς	ϱ̃[qς	NOUN
ejpam-6273	395	4	−	−	PROPN
ejpam-6273	395	5	pm	pm	NOUN
ejpam-6273	395	6	]	]	X
ejpam-6273	395	7	=	=	SYM
ejpam-6273	395	8	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	395	9	)	)	PUNCT
ejpam-6273	395	10	and	and	CCONJ
ejpam-6273	395	11	γ[qς	γ[qς	PRON
ejpam-6273	395	12	−	−	PROPN
ejpam-6273	395	13	pm	pm	NOUN
ejpam-6273	395	14	]	]	X
ejpam-6273	395	15	=	=	SYM
ejpam-6273	395	16	γ(0	γ(0	PROPN
ejpam-6273	395	17	)	)	PUNCT
ejpam-6273	395	18	.	.	PUNCT
ejpam-6273	396	1	thus	thus	ADV
ejpam-6273	396	2	,	,	PUNCT
ejpam-6273	396	3	qς	qς	ADP
ejpam-6273	396	4	+	+	SYM
ejpam-6273	396	5	ϱ̃	ϱ̃	PROPN
ejpam-6273	396	6	=	=	PUNCT
ejpam-6273	396	7	pm+	pm+	NOUN
ejpam-6273	396	8	ϱ̃	ϱ̃	NUM
ejpam-6273	396	9	and	and	CCONJ
ejpam-6273	396	10	qς	qς	PROPN
ejpam-6273	396	11	+	+	PROPN
ejpam-6273	396	12	γ	γ	X
ejpam-6273	396	13	=	=	SYM
ejpam-6273	396	14	pm+	pm+	PROPN
ejpam-6273	396	15	γ	γ	X
ejpam-6273	396	16	.	.	PROPN
ejpam-6273	396	17	(	(	PUNCT
ejpam-6273	396	18	ii	ii	NOUN
ejpam-6273	396	19	)	)	PUNCT
ejpam-6273	396	20	suppose	suppose	VERB
ejpam-6273	396	21	that	that	SCONJ
ejpam-6273	396	22	q	q	PROPN
ejpam-6273	397	1	+	+	PUNCT
ejpam-6273	397	2	ϱ̃	ϱ̃	NOUN
ejpam-6273	397	3	=	=	PUNCT
ejpam-6273	397	4	p	p	NOUN
ejpam-6273	397	5	+	+	X
ejpam-6273	397	6	ϱ̃	ϱ̃	PROPN
ejpam-6273	397	7	and	and	CCONJ
ejpam-6273	397	8	q	q	NOUN
ejpam-6273	397	9	+	+	CCONJ
ejpam-6273	397	10	γ	γ	X
ejpam-6273	397	11	=	=	SYM
ejpam-6273	397	12	p	p	PROPN
ejpam-6273	397	13	+	+	X
ejpam-6273	397	14	γ	γ	X
ejpam-6273	397	15	.	.	PROPN
ejpam-6273	398	1	then	then	ADV
ejpam-6273	398	2	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	398	3	−	−	PROPN
ejpam-6273	399	1	p	p	X
ejpam-6273	399	2	)	)	PUNCT
ejpam-6273	399	3	=	=	SYM
ejpam-6273	399	4	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	399	5	)	)	PUNCT
ejpam-6273	399	6	and	and	CCONJ
ejpam-6273	399	7	γ(q	γ(q	PROPN
ejpam-6273	399	8	−	−	PROPN
ejpam-6273	399	9	p	p	NOUN
ejpam-6273	399	10	)	)	PUNCT
ejpam-6273	399	11	=	=	SYM
ejpam-6273	399	12	γ(0	γ(0	PROPN
ejpam-6273	399	13	)	)	PUNCT
ejpam-6273	399	14	.	.	PUNCT
ejpam-6273	400	1	now	now	ADV
ejpam-6273	400	2	,	,	PUNCT
ejpam-6273	400	3	ϱ̃(sq	ϱ̃(sq	NOUN
ejpam-6273	400	4	−	−	PROPN
ejpam-6273	400	5	sp	sp	NOUN
ejpam-6273	400	6	)	)	PUNCT
ejpam-6273	400	7	=	=	SYM
ejpam-6273	400	8	ϱ̃(s(q	ϱ̃(s(q	PROPN
ejpam-6273	400	9	−	−	PROPN
ejpam-6273	400	10	p	p	NOUN
ejpam-6273	400	11	)	)	PUNCT
ejpam-6273	400	12	)	)	PUNCT
ejpam-6273	401	1	⊇	⊇	PROPN
ejpam-6273	401	2	ϱ̃(q	ϱ̃(q	PROPN
ejpam-6273	401	3	−	−	PROPN
ejpam-6273	401	4	p	p	X
ejpam-6273	401	5	)	)	PUNCT
ejpam-6273	401	6	=	=	SYM
ejpam-6273	401	7	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	401	8	)	)	PUNCT
ejpam-6273	401	9	and	and	CCONJ
ejpam-6273	401	10	γ(sq	γ(sq	PROPN
ejpam-6273	401	11	−	−	PROPN
ejpam-6273	401	12	sp	sp	NOUN
ejpam-6273	401	13	)	)	PUNCT
ejpam-6273	401	14	=	=	SYM
ejpam-6273	401	15	γ(s(q	γ(s(q	VERB
ejpam-6273	401	16	−	−	PROPN
ejpam-6273	401	17	p	p	NOUN
ejpam-6273	401	18	)	)	PUNCT
ejpam-6273	401	19	)	)	PUNCT
ejpam-6273	402	1	≤	≤	NUM
ejpam-6273	402	2	γ(q	γ(q	PROPN
ejpam-6273	402	3	−	−	NOUN
ejpam-6273	402	4	p	p	NOUN
ejpam-6273	402	5	)	)	PUNCT
ejpam-6273	402	6	=	=	SYM
ejpam-6273	402	7	γ(0	γ(0	PROPN
ejpam-6273	402	8	)	)	PUNCT
ejpam-6273	402	9	.	.	PUNCT
ejpam-6273	403	1	but	but	CCONJ
ejpam-6273	403	2	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	403	3	)	)	PUNCT
ejpam-6273	403	4	⊇	⊇	PROPN
ejpam-6273	403	5	ϱ̃(sq	ϱ̃(sq	NOUN
ejpam-6273	403	6	−	−	PROPN
ejpam-6273	403	7	sp	sp	NOUN
ejpam-6273	403	8	)	)	PUNCT
ejpam-6273	403	9	and	and	CCONJ
ejpam-6273	403	10	γ(0	γ(0	PROPN
ejpam-6273	403	11	)	)	PUNCT
ejpam-6273	403	12	≤	≤	NUM
ejpam-6273	403	13	γ(sq	γ(sq	PROPN
ejpam-6273	403	14	−	−	PROPN
ejpam-6273	403	15	sp	sp	NOUN
ejpam-6273	403	16	)	)	PUNCT
ejpam-6273	403	17	.	.	PUNCT
ejpam-6273	404	1	therefore	therefore	ADV
ejpam-6273	404	2	,	,	PUNCT
ejpam-6273	404	3	ϱ̃(sq	ϱ̃(sq	NOUN
ejpam-6273	404	4	−	−	PROPN
ejpam-6273	404	5	sp	sp	NOUN
ejpam-6273	404	6	)	)	PUNCT
ejpam-6273	404	7	=	=	SYM
ejpam-6273	404	8	ϱ̃(0	ϱ̃(0	PROPN
ejpam-6273	404	9	)	)	PUNCT
ejpam-6273	404	10	and	and	CCONJ
ejpam-6273	404	11	γ(sq	γ(sq	PROPN
ejpam-6273	404	12	−	−	PROPN
ejpam-6273	404	13	sp	sp	NOUN
ejpam-6273	404	14	)	)	PUNCT
ejpam-6273	404	15	=	=	SYM
ejpam-6273	404	16	γ(0	γ(0	PROPN
ejpam-6273	404	17	)	)	PUNCT
ejpam-6273	404	18	.	.	PUNCT
ejpam-6273	405	1	thus	thus	ADV
ejpam-6273	405	2	,	,	PUNCT
ejpam-6273	405	3	sq	sq	PROPN
ejpam-6273	405	4	+	+	NUM
ejpam-6273	405	5	ϱ̃	ϱ̃	NOUN
ejpam-6273	405	6	=	=	SYM
ejpam-6273	405	7	sp+	sp+	ADV
ejpam-6273	405	8	ϱ̃	ϱ̃	PROPN
ejpam-6273	405	9	and	and	CCONJ
ejpam-6273	405	10	sq	sq	PROPN
ejpam-6273	405	11	+	+	CCONJ
ejpam-6273	405	12	γ	γ	X
ejpam-6273	405	13	=	=	SYM
ejpam-6273	405	14	sp+	sp+	ADV
ejpam-6273	405	15	γ	γ	PROPN
ejpam-6273	405	16	.	.	PROPN
ejpam-6273	405	17	definition	definition	NOUN
ejpam-6273	405	18	10	10	NUM
ejpam-6273	405	19	.	.	PUNCT
ejpam-6273	406	1	let	let	VERB
ejpam-6273	406	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	406	3	be	be	AUX
ejpam-6273	406	4	an	an	DET
ejpam-6273	406	5	hina	hina	NOUN
ejpam-6273	406	6	of	of	ADP
ejpam-6273	406	7	y	y	PROPN
ejpam-6273	406	8	upon	upon	SCONJ
ejpam-6273	406	9	u	u	PROPN
ejpam-6273	406	10	.	.	PUNCT
ejpam-6273	407	1	then	then	ADV
ejpam-6273	407	2	the	the	DET
ejpam-6273	407	3	set	set	NOUN
ejpam-6273	407	4	of	of	ADP
ejpam-6273	407	5	all	all	DET
ejpam-6273	407	6	cosets	coset	NOUN
ejpam-6273	407	7	of	of	ADP
ejpam-6273	407	8	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	407	9	is	be	AUX
ejpam-6273	407	10	y/ϱ̃γ	y/ϱ̃γ	PROPN
ejpam-6273	407	11	=	=	PUNCT
ejpam-6273	407	12	{	{	PUNCT
ejpam-6273	407	13	ς	ς	PROPN
ejpam-6273	407	14	+	+	NOUN
ejpam-6273	407	15	ϱ̃γ	ϱ̃γ	NOUN
ejpam-6273	407	16	|	|	ADV
ejpam-6273	407	17	ς	ς	PROPN
ejpam-6273	407	18	∈	∈	PROPN
ejpam-6273	407	19	y	y	PROPN
ejpam-6273	407	20	}	}	PUNCT
ejpam-6273	407	21	,	,	PUNCT
ejpam-6273	407	22	where	where	SCONJ
ejpam-6273	407	23	y/ϱ̃	y/ϱ̃	PROPN
ejpam-6273	407	24	=	=	SYM
ejpam-6273	407	25	{	{	PUNCT
ejpam-6273	407	26	ς	ς	PROPN
ejpam-6273	407	27	+	+	PUNCT
ejpam-6273	407	28	ϱ̃	ϱ̃	PROPN
ejpam-6273	407	29	|	|	ADV
ejpam-6273	407	30	ς	ς	PROPN
ejpam-6273	407	31	∈	∈	PROPN
ejpam-6273	407	32	y	y	PROPN
ejpam-6273	407	33	}	}	PUNCT
ejpam-6273	407	34	and	and	CCONJ
ejpam-6273	407	35	y	y	PROPN
ejpam-6273	407	36	/	/	SYM
ejpam-6273	407	37	γ	γ	X
ejpam-6273	407	38	=	=	X
ejpam-6273	407	39	{	{	PUNCT
ejpam-6273	407	40	ς	ς	PROPN
ejpam-6273	407	41	+	+	X
ejpam-6273	407	42	γ	γ	PROPN
ejpam-6273	407	43	|	|	ADV
ejpam-6273	407	44	ς	ς	PROPN
ejpam-6273	407	45	∈	∈	PROPN
ejpam-6273	407	46	y	y	PROPN
ejpam-6273	407	47	}	}	PUNCT
ejpam-6273	407	48	.	.	PUNCT
ejpam-6273	408	1	p.	p.	NOUN
ejpam-6273	408	2	n.	n.	PROPN
ejpam-6273	408	3	swamy	swamy	PROPN
ejpam-6273	408	4	et	et	PROPN
ejpam-6273	408	5	al	al	PROPN
ejpam-6273	408	6	.	.	PUNCT
ejpam-6273	408	7	/	/	SYM
ejpam-6273	408	8	eur	eur	PROPN
ejpam-6273	408	9	.	.	PUNCT
ejpam-6273	409	1	j.	j.	PROPN
ejpam-6273	409	2	pure	pure	PROPN
ejpam-6273	409	3	appl	appl	PROPN
ejpam-6273	409	4	.	.	PROPN
ejpam-6273	409	5	math	math	PROPN
ejpam-6273	409	6	,	,	PUNCT
ejpam-6273	409	7	18	18	NUM
ejpam-6273	409	8	(	(	PUNCT
ejpam-6273	409	9	3	3	NUM
ejpam-6273	409	10	)	)	PUNCT
ejpam-6273	409	11	(	(	PUNCT
ejpam-6273	409	12	2025	2025	NUM
ejpam-6273	409	13	)	)	PUNCT
ejpam-6273	409	14	,	,	PUNCT
ejpam-6273	409	15	6273	6273	NUM
ejpam-6273	409	16	14	14	NUM
ejpam-6273	409	17	of	of	ADP
ejpam-6273	409	18	16	16	NUM
ejpam-6273	409	19	theorem	theorem	NOUN
ejpam-6273	409	20	9	9	NUM
ejpam-6273	409	21	.	.	PUNCT
ejpam-6273	410	1	let	let	VERB
ejpam-6273	410	2	ϱ̃γ	ϱ̃γ	PROPN
ejpam-6273	410	3	be	be	AUX
ejpam-6273	410	4	an	an	DET
ejpam-6273	410	5	hina	hina	NOUN
ejpam-6273	410	6	of	of	ADP
ejpam-6273	410	7	y	y	PROPN
ejpam-6273	410	8	upon	upon	SCONJ
ejpam-6273	410	9	u	u	PROPN
ejpam-6273	410	10	.	.	PUNCT
ejpam-6273	411	1	then	then	ADV
ejpam-6273	411	2	y/ϱ̃γ	y/ϱ̃γ	PROPN
ejpam-6273	411	3	is	be	AUX
ejpam-6273	411	4	a	a	DET
ejpam-6273	411	5	near	near	ADJ
ejpam-6273	411	6	algebra	algebra	NOUN
ejpam-6273	411	7	with	with	ADP
ejpam-6273	411	8	respect	respect	NOUN
ejpam-6273	411	9	to	to	ADP
ejpam-6273	411	10	the	the	DET
ejpam-6273	411	11	operations	operation	NOUN
ejpam-6273	411	12	defined	define	VERB
ejpam-6273	411	13	by	by	ADP
ejpam-6273	411	14	(	(	PUNCT
ejpam-6273	411	15	q	q	PROPN
ejpam-6273	411	16	+	+	NUM
ejpam-6273	411	17	ϱ̃	ϱ̃	NOUN
ejpam-6273	411	18	)	)	PUNCT
ejpam-6273	412	1	+	+	CCONJ
ejpam-6273	412	2	(	(	PUNCT
ejpam-6273	412	3	ς	ς	PROPN
ejpam-6273	412	4	+	+	X
ejpam-6273	412	5	ϱ̃	ϱ̃	PROPN
ejpam-6273	412	6	)	)	PUNCT
ejpam-6273	413	1	=	=	PUNCT
ejpam-6273	413	2	(	(	PUNCT
ejpam-6273	413	3	q	q	PROPN
ejpam-6273	413	4	+	+	NUM
ejpam-6273	413	5	ς	ς	NOUN
ejpam-6273	413	6	)	)	PUNCT
ejpam-6273	414	1	+	+	CCONJ
ejpam-6273	414	2	ϱ̃	ϱ̃	PROPN
ejpam-6273	414	3	(	(	PUNCT
ejpam-6273	414	4	q	q	NOUN
ejpam-6273	414	5	+	+	NUM
ejpam-6273	414	6	ϱ̃)(ς	ϱ̃)(ς	X
ejpam-6273	414	7	+	+	X
ejpam-6273	414	8	ϱ̃	ϱ̃	NUM
ejpam-6273	414	9	)	)	PUNCT
ejpam-6273	414	10	=	=	PRON
ejpam-6273	414	11	qς	qς	PROPN
ejpam-6273	414	12	+	+	NUM
ejpam-6273	414	13	ϱ̃	ϱ̃	PROPN
ejpam-6273	414	14	s(q	s(q	NOUN
ejpam-6273	414	15	+	+	CCONJ
ejpam-6273	414	16	ϱ̃	ϱ̃	NUM
ejpam-6273	414	17	)	)	PUNCT
ejpam-6273	414	18	=	=	PUNCT
ejpam-6273	414	19	sq	sq	PROPN
ejpam-6273	414	20	+	+	NUM
ejpam-6273	414	21	ϱ̃	ϱ̃	PROPN
ejpam-6273	414	22	(	(	PUNCT
ejpam-6273	414	23	q	q	NOUN
ejpam-6273	414	24	+	+	NUM
ejpam-6273	414	25	γ	γ	X
ejpam-6273	414	26	)	)	PUNCT
ejpam-6273	414	27	+	+	CCONJ
ejpam-6273	414	28	(	(	PUNCT
ejpam-6273	414	29	ς	ς	PROPN
ejpam-6273	414	30	+	+	X
ejpam-6273	414	31	γ	γ	X
ejpam-6273	414	32	)	)	PUNCT
ejpam-6273	414	33	=	=	PUNCT
ejpam-6273	414	34	(	(	PUNCT
ejpam-6273	414	35	q	q	PROPN
ejpam-6273	414	36	+	+	NUM
ejpam-6273	414	37	ς	ς	NOUN
ejpam-6273	414	38	)	)	PUNCT
ejpam-6273	414	39	+	+	CCONJ
ejpam-6273	414	40	γ	γ	X
ejpam-6273	414	41	(	(	PUNCT
ejpam-6273	414	42	q	q	PROPN
ejpam-6273	414	43	+	+	NUM
ejpam-6273	414	44	γ)(ς	γ)(ς	PROPN
ejpam-6273	414	45	+	+	CCONJ
ejpam-6273	414	46	γ	γ	X
ejpam-6273	414	47	)	)	PUNCT
ejpam-6273	414	48	=	=	PRON
ejpam-6273	414	49	qς	qς	PROPN
ejpam-6273	414	50	+	+	NUM
ejpam-6273	414	51	γ	γ	X
ejpam-6273	414	52	s(q	s(q	PROPN
ejpam-6273	414	53	+	+	CCONJ
ejpam-6273	414	54	γ	γ	X
ejpam-6273	414	55	)	)	PUNCT
ejpam-6273	414	56	=	=	SYM
ejpam-6273	414	57	sq	sq	PROPN
ejpam-6273	414	58	+	+	CCONJ
ejpam-6273	414	59	γ	γ	NOUN
ejpam-6273	414	60	for	for	ADP
ejpam-6273	414	61	all	all	DET
ejpam-6273	414	62	q	q	PROPN
ejpam-6273	414	63	,	,	PUNCT
ejpam-6273	414	64	ς	ς	PROPN
ejpam-6273	414	65	∈	∈	PROPN
ejpam-6273	414	66	y	y	PROPN
ejpam-6273	414	67	and	and	CCONJ
ejpam-6273	414	68	s	s	PROPN
ejpam-6273	414	69	∈	∈	PROPN
ejpam-6273	414	70	l.	l.	NOUN
ejpam-6273	414	71	proof	proof	PROPN
ejpam-6273	414	72	.	.	PUNCT
ejpam-6273	415	1	a	a	DET
ejpam-6273	415	2	direct	direct	ADJ
ejpam-6273	415	3	verification	verification	NOUN
ejpam-6273	415	4	shows	show	VERB
ejpam-6273	415	5	that	that	SCONJ
ejpam-6273	415	6	y/ϱ̃γ	y/ϱ̃γ	PROPN
ejpam-6273	415	7	is	be	AUX
ejpam-6273	415	8	a	a	DET
ejpam-6273	415	9	linear	linear	ADJ
ejpam-6273	415	10	space	space	NOUN
ejpam-6273	415	11	.	.	PUNCT
ejpam-6273	416	1	let	let	VERB
ejpam-6273	416	2	q+ϱ̃	q+ϱ̃	PROPN
ejpam-6273	416	3	,	,	PUNCT
ejpam-6273	416	4	ς+ϱ̃	ς+ϱ̃	PROPN
ejpam-6273	416	5	,	,	PUNCT
ejpam-6273	416	6	j+ϱ̃	j+ϱ̃	PROPN
ejpam-6273	416	7	∈	∈	PROPN
ejpam-6273	417	1	y/ϱ̃	y/ϱ̃	PROPN
ejpam-6273	417	2	and	and	CCONJ
ejpam-6273	417	3	q	q	PROPN
ejpam-6273	418	1	+	+	CCONJ
ejpam-6273	418	2	γ	γ	X
ejpam-6273	418	3	,	,	PUNCT
ejpam-6273	418	4	ς	ς	PROPN
ejpam-6273	418	5	+	+	X
ejpam-6273	418	6	γ	γ	X
ejpam-6273	418	7	,	,	PUNCT
ejpam-6273	418	8	j	j	PROPN
ejpam-6273	418	9	+	+	CCONJ
ejpam-6273	418	10	γ	γ	PROPN
ejpam-6273	418	11	∈	∈	PROPN
ejpam-6273	418	12	y	y	PROPN
ejpam-6273	418	13	/	/	SYM
ejpam-6273	418	14	γ	γ	PROPN
ejpam-6273	418	15	,	,	PUNCT
ejpam-6273	418	16	where	where	SCONJ
ejpam-6273	418	17	q	q	X
ejpam-6273	418	18	,	,	PUNCT
ejpam-6273	418	19	ς	ς	PROPN
ejpam-6273	418	20	,	,	PUNCT
ejpam-6273	418	21	j	j	PROPN
ejpam-6273	418	22	∈	∈	PROPN
ejpam-6273	418	23	y	y	PROPN
ejpam-6273	418	24	.	.	PUNCT
ejpam-6273	419	1	then	then	ADV
ejpam-6273	419	2	[	[	X
ejpam-6273	419	3	(	(	PUNCT
ejpam-6273	419	4	q	q	NOUN
ejpam-6273	419	5	+	+	NUM
ejpam-6273	419	6	ϱ̃)(ς	ϱ̃)(ς	NOUN
ejpam-6273	419	7	+	+	NUM
ejpam-6273	419	8	ϱ̃)](j	ϱ̃)](j	NOUN
ejpam-6273	419	9	+	+	CCONJ
ejpam-6273	419	10	ϱ̃	ϱ̃	NUM
ejpam-6273	419	11	)	)	PUNCT
ejpam-6273	419	12	=	=	PUNCT
ejpam-6273	419	13	(	(	PUNCT
ejpam-6273	419	14	qς	qς	ADP
ejpam-6273	419	15	+	+	ADJ
ejpam-6273	419	16	ϱ̃)(j	ϱ̃)(j	NOUN
ejpam-6273	419	17	+	+	X
ejpam-6273	419	18	ϱ̃	ϱ̃	NUM
ejpam-6273	419	19	)	)	PUNCT
ejpam-6273	419	20	=	=	PUNCT
ejpam-6273	419	21	(	(	PUNCT
ejpam-6273	419	22	qς)j	qς)j	PROPN
ejpam-6273	420	1	+	+	NUM
ejpam-6273	420	2	ϱ̃	ϱ̃	PROPN
ejpam-6273	420	3	=	=	SYM
ejpam-6273	420	4	(	(	PUNCT
ejpam-6273	420	5	q	q	NOUN
ejpam-6273	420	6	+	+	PUNCT
ejpam-6273	420	7	ϱ̃)[(ς	ϱ̃)[(ς	NOUN
ejpam-6273	420	8	+	+	CCONJ
ejpam-6273	420	9	ϱ̃)(j	ϱ̃)(j	NOUN
ejpam-6273	420	10	+	+	X
ejpam-6273	420	11	ϱ̃	ϱ̃	PROPN
ejpam-6273	420	12	)	)	PUNCT
ejpam-6273	420	13	]	]	PUNCT
ejpam-6273	420	14	and	and	CCONJ
ejpam-6273	420	15	[	[	X
ejpam-6273	420	16	(	(	PUNCT
ejpam-6273	420	17	q	q	X
ejpam-6273	420	18	+	+	NUM
ejpam-6273	420	19	γ)(ς	γ)(ς	PROPN
ejpam-6273	420	20	+	+	CCONJ
ejpam-6273	420	21	γ)](j	γ)](j	NOUN
ejpam-6273	420	22	+	+	CCONJ
ejpam-6273	420	23	γ	γ	X
ejpam-6273	420	24	)	)	PUNCT
ejpam-6273	420	25	=	=	PUNCT
ejpam-6273	420	26	(	(	PUNCT
ejpam-6273	420	27	qς	qς	PROPN
ejpam-6273	420	28	+	+	SYM
ejpam-6273	420	29	γ)(j	γ)(j	VERB
ejpam-6273	420	30	+	+	CCONJ
ejpam-6273	420	31	γ	γ	X
ejpam-6273	420	32	)	)	PUNCT
ejpam-6273	420	33	=	=	PUNCT
ejpam-6273	420	34	(	(	PUNCT
ejpam-6273	420	35	qς)j	qς)j	PROPN
ejpam-6273	420	36	+	+	CCONJ
ejpam-6273	420	37	γ	γ	X
ejpam-6273	420	38	=	=	SYM
ejpam-6273	420	39	(	(	PUNCT
ejpam-6273	420	40	q	q	PROPN
ejpam-6273	420	41	+	+	CCONJ
ejpam-6273	420	42	γ)[(ς	γ)[(ς	NUM
ejpam-6273	420	43	+	+	NUM
ejpam-6273	420	44	γ)(j	γ)(j	NUM
ejpam-6273	420	45	+	+	CCONJ
ejpam-6273	420	46	γ	γ	X
ejpam-6273	420	47	)	)	PUNCT
ejpam-6273	420	48	]	]	PUNCT
ejpam-6273	420	49	.	.	PUNCT
ejpam-6273	421	1	this	this	PRON
ejpam-6273	421	2	shows	show	VERB
ejpam-6273	421	3	that	that	SCONJ
ejpam-6273	421	4	y/ϱ̃γ	y/ϱ̃γ	PROPN
ejpam-6273	421	5	is	be	AUX
ejpam-6273	421	6	a	a	DET
ejpam-6273	421	7	semigroup	semigroup	NOUN
ejpam-6273	421	8	under	under	ADP
ejpam-6273	421	9	multiplication	multiplication	NOUN
ejpam-6273	421	10	.	.	PUNCT
ejpam-6273	422	1	consider	consider	VERB
ejpam-6273	422	2	,	,	PUNCT
ejpam-6273	422	3	[	[	X
ejpam-6273	422	4	(	(	PUNCT
ejpam-6273	422	5	q	q	X
ejpam-6273	422	6	+	+	NUM
ejpam-6273	422	7	ϱ̃	ϱ̃	NOUN
ejpam-6273	422	8	)	)	PUNCT
ejpam-6273	423	1	+	+	CCONJ
ejpam-6273	423	2	(	(	PUNCT
ejpam-6273	423	3	ς	ς	PROPN
ejpam-6273	423	4	+	+	NOUN
ejpam-6273	423	5	ϱ̃)](j	ϱ̃)](j	NOUN
ejpam-6273	423	6	+	+	CCONJ
ejpam-6273	423	7	ϱ̃	ϱ̃	NUM
ejpam-6273	423	8	)	)	PUNCT
ejpam-6273	424	1	=	=	SYM
ejpam-6273	424	2	(	(	PUNCT
ejpam-6273	424	3	(	(	PUNCT
ejpam-6273	424	4	q	q	NOUN
ejpam-6273	424	5	+	+	CCONJ
ejpam-6273	424	6	ς	ς	NOUN
ejpam-6273	424	7	)	)	PUNCT
ejpam-6273	424	8	+	+	NUM
ejpam-6273	424	9	ϱ̃)(j	ϱ̃)(j	NOUN
ejpam-6273	424	10	+	+	X
ejpam-6273	424	11	ϱ̃	ϱ̃	NUM
ejpam-6273	424	12	)	)	PUNCT
ejpam-6273	424	13	=	=	PUNCT
ejpam-6273	424	14	(	(	PUNCT
ejpam-6273	424	15	q	q	NOUN
ejpam-6273	424	16	+	+	NUM
ejpam-6273	424	17	ς)j	ς)j	NOUN
ejpam-6273	424	18	+	+	PUNCT
ejpam-6273	424	19	ϱ̃	ϱ̃	PROPN
ejpam-6273	424	20	=	=	SYM
ejpam-6273	424	21	(	(	PUNCT
ejpam-6273	424	22	qj	qj	PROPN
ejpam-6273	424	23	+	+	CCONJ
ejpam-6273	424	24	ςj	ςj	ADJ
ejpam-6273	424	25	)	)	PUNCT
ejpam-6273	424	26	+	+	CCONJ
ejpam-6273	424	27	ϱ̃	ϱ̃	NOUN
ejpam-6273	424	28	=	=	SYM
ejpam-6273	424	29	(	(	PUNCT
ejpam-6273	424	30	qj	qj	PROPN
ejpam-6273	424	31	+	+	CCONJ
ejpam-6273	424	32	ϱ̃	ϱ̃	PROPN
ejpam-6273	424	33	)	)	PUNCT
ejpam-6273	424	34	+	+	CCONJ
ejpam-6273	424	35	(	(	PUNCT
ejpam-6273	424	36	ςj	ςj	ADP
ejpam-6273	424	37	+	+	X
ejpam-6273	424	38	ϱ̃	ϱ̃	NOUN
ejpam-6273	424	39	)	)	PUNCT
ejpam-6273	424	40	=	=	PUNCT
ejpam-6273	424	41	(	(	PUNCT
ejpam-6273	424	42	q	q	NOUN
ejpam-6273	424	43	+	+	NUM
ejpam-6273	424	44	ϱ̃)(j	ϱ̃)(j	NOUN
ejpam-6273	424	45	+	+	X
ejpam-6273	424	46	ϱ̃	ϱ̃	NUM
ejpam-6273	424	47	)	)	PUNCT
ejpam-6273	425	1	+	+	CCONJ
ejpam-6273	425	2	(	(	PUNCT
ejpam-6273	425	3	ς	ς	PROPN
ejpam-6273	425	4	+	+	X
ejpam-6273	425	5	ϱ̃)(j	ϱ̃)(j	NOUN
ejpam-6273	425	6	+	+	X
ejpam-6273	425	7	ϱ̃	ϱ̃	NOUN
ejpam-6273	425	8	)	)	PUNCT
ejpam-6273	425	9	and	and	CCONJ
ejpam-6273	426	1	[	[	X
ejpam-6273	426	2	(	(	PUNCT
ejpam-6273	426	3	q	q	NOUN
ejpam-6273	426	4	+	+	X
ejpam-6273	426	5	γ	γ	X
ejpam-6273	426	6	)	)	PUNCT
ejpam-6273	426	7	+	+	CCONJ
ejpam-6273	426	8	(	(	PUNCT
ejpam-6273	426	9	ς	ς	PROPN
ejpam-6273	426	10	+	+	X
ejpam-6273	426	11	γ)](j	γ)](j	NOUN
ejpam-6273	426	12	+	+	CCONJ
ejpam-6273	426	13	γ	γ	X
ejpam-6273	426	14	)	)	PUNCT
ejpam-6273	426	15	=	=	SYM
ejpam-6273	426	16	(	(	PUNCT
ejpam-6273	426	17	(	(	PUNCT
ejpam-6273	426	18	q	q	NOUN
ejpam-6273	426	19	+	+	CCONJ
ejpam-6273	426	20	ς	ς	NOUN
ejpam-6273	426	21	)	)	PUNCT
ejpam-6273	426	22	+	+	NUM
ejpam-6273	426	23	γ)(j	γ)(j	NUM
ejpam-6273	426	24	+	+	CCONJ
ejpam-6273	426	25	γ	γ	X
ejpam-6273	426	26	)	)	PUNCT
ejpam-6273	426	27	=	=	NOUN
ejpam-6273	426	28	(	(	PUNCT
ejpam-6273	426	29	q	q	NOUN
ejpam-6273	426	30	+	+	NUM
ejpam-6273	426	31	ς)j	ς)j	NOUN
ejpam-6273	426	32	+	+	CCONJ
ejpam-6273	426	33	γ	γ	X
ejpam-6273	426	34	=	=	SYM
ejpam-6273	426	35	(	(	PUNCT
ejpam-6273	426	36	qj	qj	PROPN
ejpam-6273	426	37	+	+	CCONJ
ejpam-6273	426	38	ςj	ςj	PROPN
ejpam-6273	426	39	)	)	PUNCT
ejpam-6273	426	40	+	+	CCONJ
ejpam-6273	426	41	γ	γ	X
ejpam-6273	426	42	=	=	SYM
ejpam-6273	426	43	(	(	PUNCT
ejpam-6273	426	44	qj	qj	PROPN
ejpam-6273	426	45	+	+	CCONJ
ejpam-6273	426	46	γ	γ	X
ejpam-6273	426	47	)	)	PUNCT
ejpam-6273	426	48	+	+	CCONJ
ejpam-6273	426	49	(	(	PUNCT
ejpam-6273	426	50	ςj	ςj	ADP
ejpam-6273	426	51	+	+	CCONJ
ejpam-6273	426	52	γ	γ	X
ejpam-6273	426	53	)	)	PUNCT
ejpam-6273	426	54	=	=	PUNCT
ejpam-6273	426	55	(	(	PUNCT
ejpam-6273	426	56	q	q	PROPN
ejpam-6273	426	57	+	+	PUNCT
ejpam-6273	426	58	γ)(j	γ)(j	NUM
ejpam-6273	426	59	+	+	CCONJ
ejpam-6273	426	60	γ	γ	X
ejpam-6273	426	61	)	)	PUNCT
ejpam-6273	426	62	+	+	CCONJ
ejpam-6273	426	63	(	(	PUNCT
ejpam-6273	426	64	ς	ς	PROPN
ejpam-6273	426	65	+	+	X
ejpam-6273	426	66	γ)(j	γ)(j	VERB
ejpam-6273	426	67	+	+	CCONJ
ejpam-6273	426	68	γ	γ	X
ejpam-6273	426	69	)	)	PUNCT
ejpam-6273	426	70	.	.	PUNCT
ejpam-6273	427	1	let	let	VERB
ejpam-6273	427	2	s	s	PRON
ejpam-6273	427	3	∈	∈	PROPN
ejpam-6273	427	4	l.	l.	NOUN
ejpam-6273	427	5	then	then	ADV
ejpam-6273	427	6	p.	p.	PROPN
ejpam-6273	427	7	n.	n.	PROPN
ejpam-6273	427	8	swamy	swamy	PROPN
ejpam-6273	427	9	et	et	PROPN
ejpam-6273	427	10	al	al	PROPN
ejpam-6273	427	11	.	.	PUNCT
ejpam-6273	427	12	/	/	SYM
ejpam-6273	427	13	eur	eur	PROPN
ejpam-6273	427	14	.	.	PUNCT
ejpam-6273	428	1	j.	j.	PROPN
ejpam-6273	428	2	pure	pure	PROPN
ejpam-6273	428	3	appl	appl	PROPN
ejpam-6273	428	4	.	.	PROPN
ejpam-6273	428	5	math	math	PROPN
ejpam-6273	428	6	,	,	PUNCT
ejpam-6273	428	7	18	18	NUM
ejpam-6273	428	8	(	(	PUNCT
ejpam-6273	428	9	3	3	NUM
ejpam-6273	428	10	)	)	PUNCT
ejpam-6273	428	11	(	(	PUNCT
ejpam-6273	428	12	2025	2025	NUM
ejpam-6273	428	13	)	)	PUNCT
ejpam-6273	428	14	,	,	PUNCT
ejpam-6273	428	15	6273	6273	NUM
ejpam-6273	428	16	15	15	NUM
ejpam-6273	428	17	of	of	ADP
ejpam-6273	428	18	16	16	NUM
ejpam-6273	428	19	(	(	PUNCT
ejpam-6273	428	20	s(q	s(q	PROPN
ejpam-6273	428	21	+	+	CCONJ
ejpam-6273	428	22	ϱ̃))(ς	ϱ̃))(ς	NOUN
ejpam-6273	428	23	+	+	PUNCT
ejpam-6273	428	24	ϱ̃	ϱ̃	NUM
ejpam-6273	428	25	)	)	PUNCT
ejpam-6273	428	26	=	=	SYM
ejpam-6273	428	27	(	(	PUNCT
ejpam-6273	428	28	sq	sq	INTJ
ejpam-6273	428	29	+	+	NUM
ejpam-6273	428	30	ϱ̃)(ς	ϱ̃)(ς	NOUN
ejpam-6273	428	31	+	+	X
ejpam-6273	428	32	ϱ̃	ϱ̃	NUM
ejpam-6273	428	33	)	)	PUNCT
ejpam-6273	428	34	=	=	SYM
ejpam-6273	428	35	(	(	PUNCT
ejpam-6273	428	36	sq)ς	sq)ς	PROPN
ejpam-6273	428	37	+	+	PROPN
ejpam-6273	428	38	ϱ̃	ϱ̃	PROPN
ejpam-6273	428	39	=	=	SYM
ejpam-6273	428	40	s(qς	s(qς	PROPN
ejpam-6273	428	41	)	)	PUNCT
ejpam-6273	429	1	+	+	CCONJ
ejpam-6273	429	2	ϱ̃	ϱ̃	PROPN
ejpam-6273	429	3	=	=	SYM
ejpam-6273	429	4	s(qς	s(qς	NOUN
ejpam-6273	429	5	+	+	CCONJ
ejpam-6273	429	6	ϱ̃	ϱ̃	PROPN
ejpam-6273	429	7	)	)	PUNCT
ejpam-6273	429	8	=	=	SYM
ejpam-6273	429	9	s((q	s((q	NOUN
ejpam-6273	429	10	+	+	CCONJ
ejpam-6273	429	11	ϱ̃)(ς	ϱ̃)(ς	X
ejpam-6273	429	12	+	+	X
ejpam-6273	429	13	ϱ̃	ϱ̃	PROPN
ejpam-6273	429	14	)	)	PUNCT
ejpam-6273	429	15	)	)	PUNCT
ejpam-6273	429	16	and	and	CCONJ
ejpam-6273	429	17	(	(	PUNCT
ejpam-6273	429	18	s(q	s(q	PROPN
ejpam-6273	429	19	+	+	CCONJ
ejpam-6273	429	20	γ))(ς	γ))(ς	PROPN
ejpam-6273	429	21	+	+	CCONJ
ejpam-6273	429	22	γ	γ	X
ejpam-6273	429	23	)	)	PUNCT
ejpam-6273	429	24	=	=	SYM
ejpam-6273	429	25	(	(	PUNCT
ejpam-6273	429	26	sq	sq	INTJ
ejpam-6273	429	27	+	+	NUM
ejpam-6273	429	28	γ)(ς	γ)(ς	PROPN
ejpam-6273	429	29	+	+	CCONJ
ejpam-6273	429	30	γ	γ	X
ejpam-6273	429	31	)	)	PUNCT
ejpam-6273	429	32	=	=	SYM
ejpam-6273	429	33	(	(	PUNCT
ejpam-6273	429	34	sq)ς	sq)ς	PROPN
ejpam-6273	429	35	+	+	CCONJ
ejpam-6273	429	36	γ	γ	X
ejpam-6273	429	37	=	=	SYM
ejpam-6273	429	38	s(qς	s(qς	PROPN
ejpam-6273	429	39	)	)	PUNCT
ejpam-6273	430	1	+	+	CCONJ
ejpam-6273	430	2	γ	γ	X
ejpam-6273	430	3	=	=	SYM
ejpam-6273	430	4	s(qς	s(qς	PROPN
ejpam-6273	430	5	+	+	CCONJ
ejpam-6273	430	6	γ	γ	X
ejpam-6273	430	7	)	)	PUNCT
ejpam-6273	430	8	=	=	NOUN
ejpam-6273	430	9	s((q	s((q	NOUN
ejpam-6273	430	10	+	+	CCONJ
ejpam-6273	430	11	γ)(ς	γ)(ς	PROPN
ejpam-6273	430	12	+	+	CCONJ
ejpam-6273	430	13	γ	γ	NOUN
ejpam-6273	430	14	)	)	PUNCT
ejpam-6273	430	15	)	)	PUNCT
ejpam-6273	430	16	.	.	PUNCT
ejpam-6273	431	1	hence	hence	ADV
ejpam-6273	431	2	,	,	PUNCT
ejpam-6273	431	3	y/ϱ̃γ	y/ϱ̃γ	PROPN
ejpam-6273	431	4	is	be	AUX
ejpam-6273	431	5	a	a	DET
ejpam-6273	431	6	near	near	ADJ
ejpam-6273	431	7	algebra	algebra	NOUN
ejpam-6273	431	8	over	over	ADP
ejpam-6273	431	9	l.	l.	PROPN
ejpam-6273	431	10	4	4	NUM
ejpam-6273	431	11	.	.	PUNCT
ejpam-6273	431	12	conclusion	conclusion	NOUN
ejpam-6273	431	13	in	in	ADP
ejpam-6273	431	14	this	this	DET
ejpam-6273	431	15	work	work	NOUN
ejpam-6273	431	16	,	,	PUNCT
ejpam-6273	431	17	we	we	PRON
ejpam-6273	431	18	combined	combine	VERB
ejpam-6273	431	19	soft	soft	ADJ
ejpam-6273	431	20	sets	set	NOUN
ejpam-6273	431	21	and	and	CCONJ
ejpam-6273	431	22	fuzzy	fuzzy	ADJ
ejpam-6273	431	23	sets	set	NOUN
ejpam-6273	431	24	in	in	ADP
ejpam-6273	431	25	near	near	ADJ
ejpam-6273	431	26	algebras	algebra	NOUN
ejpam-6273	431	27	,	,	PUNCT
ejpam-6273	431	28	thereby	thereby	ADV
ejpam-6273	431	29	developing	develop	VERB
ejpam-6273	431	30	a	a	DET
ejpam-6273	431	31	novel	novel	ADJ
ejpam-6273	431	32	structure	structure	NOUN
ejpam-6273	431	33	of	of	ADP
ejpam-6273	431	34	hybrid	hybrid	ADJ
ejpam-6273	431	35	ideals	ideal	NOUN
ejpam-6273	431	36	.	.	PUNCT
ejpam-6273	432	1	this	this	DET
ejpam-6273	432	2	manuscript	manuscript	NOUN
ejpam-6273	432	3	provided	provide	VERB
ejpam-6273	432	4	an	an	DET
ejpam-6273	432	5	in	in	ADP
ejpam-6273	432	6	-	-	PUNCT
ejpam-6273	432	7	depth	depth	NOUN
ejpam-6273	432	8	exploration	exploration	NOUN
ejpam-6273	432	9	of	of	ADP
ejpam-6273	432	10	hybrid	hybrid	ADJ
ejpam-6273	432	11	ideals	ideal	NOUN
ejpam-6273	432	12	within	within	ADP
ejpam-6273	432	13	a	a	DET
ejpam-6273	432	14	near	near	ADJ
ejpam-6273	432	15	algebra	algebra	NOUN
ejpam-6273	432	16	,	,	PUNCT
ejpam-6273	432	17	elucidating	elucidate	VERB
ejpam-6273	432	18	their	their	PRON
ejpam-6273	432	19	unique	unique	ADJ
ejpam-6273	432	20	properties	property	NOUN
ejpam-6273	432	21	through	through	ADP
ejpam-6273	432	22	a	a	DET
ejpam-6273	432	23	systematic	systematic	ADJ
ejpam-6273	432	24	investigation	investigation	NOUN
ejpam-6273	432	25	.	.	PUNCT
ejpam-6273	433	1	theoretical	theoretical	ADJ
ejpam-6273	433	2	findings	finding	NOUN
ejpam-6273	433	3	were	be	AUX
ejpam-6273	433	4	substantiated	substantiate	VERB
ejpam-6273	433	5	with	with	ADP
ejpam-6273	433	6	illustrative	illustrative	ADJ
ejpam-6273	433	7	examples	example	NOUN
ejpam-6273	433	8	.	.	PUNCT
ejpam-6273	434	1	we	we	PRON
ejpam-6273	434	2	also	also	ADV
ejpam-6273	434	3	introduced	introduce	VERB
ejpam-6273	434	4	the	the	DET
ejpam-6273	434	5	notions	notion	NOUN
ejpam-6273	434	6	of	of	ADP
ejpam-6273	434	7	hina	hina	PROPN
ejpam-6273	434	8	homomorphism	homomorphism	PROPN
ejpam-6273	434	9	,	,	PUNCT
ejpam-6273	434	10	the	the	DET
ejpam-6273	434	11	cartesian	cartesian	ADJ
ejpam-6273	434	12	product	product	NOUN
ejpam-6273	434	13	of	of	ADP
ejpam-6273	434	14	hina	hina	NOUN
ejpam-6273	434	15	,	,	PUNCT
ejpam-6273	434	16	and	and	CCONJ
ejpam-6273	434	17	the	the	DET
ejpam-6273	434	18	coset	coset	NOUN
ejpam-6273	434	19	of	of	ADP
ejpam-6273	434	20	hina	hina	NOUN
ejpam-6273	434	21	.	.	PUNCT
ejpam-6273	435	1	future	future	ADJ
ejpam-6273	435	2	research	research	NOUN
ejpam-6273	435	3	can	can	AUX
ejpam-6273	435	4	be	be	AUX
ejpam-6273	435	5	extended	extend	VERB
ejpam-6273	435	6	to	to	PART
ejpam-6273	435	7	investigate	investigate	VERB
ejpam-6273	435	8	the	the	DET
ejpam-6273	435	9	hybrid	hybrid	ADJ
ejpam-6273	435	10	gamma	gamma	NOUN
ejpam-6273	435	11	near	near	ADP
ejpam-6273	435	12	algebra	algebra	PROPN
ejpam-6273	435	13	,	,	PUNCT
ejpam-6273	435	14	the	the	DET
ejpam-6273	435	15	hybrid	hybrid	ADJ
ejpam-6273	435	16	ideal	ideal	NOUN
ejpam-6273	435	17	of	of	ADP
ejpam-6273	435	18	a	a	DET
ejpam-6273	435	19	gamma	gamma	NOUN
ejpam-6273	435	20	near	near	ADP
ejpam-6273	435	21	algebra	algebra	PROPN
ejpam-6273	435	22	,	,	PUNCT
ejpam-6273	435	23	and	and	CCONJ
ejpam-6273	435	24	explore	explore	VERB
ejpam-6273	435	25	the	the	DET
ejpam-6273	435	26	concept	concept	NOUN
ejpam-6273	435	27	of	of	ADP
ejpam-6273	435	28	hybrid	hybrid	NOUN
ejpam-6273	435	29	near	near	ADP
ejpam-6273	435	30	algebra	algebra	NOUN
ejpam-6273	435	31	on	on	ADP
ejpam-6273	435	32	anti	anti	ADJ
ejpam-6273	435	33	-	-	ADJ
ejpam-6273	435	34	fuzzy	fuzzy	ADJ
ejpam-6273	435	35	sets	set	NOUN
ejpam-6273	435	36	.	.	PUNCT
ejpam-6273	436	1	acknowledgements	acknowledgement	NOUN
ejpam-6273	436	2	this	this	DET
ejpam-6273	436	3	research	research	NOUN
ejpam-6273	436	4	was	be	AUX
ejpam-6273	436	5	supported	support	VERB
ejpam-6273	436	6	by	by	ADP
ejpam-6273	436	7	university	university	NOUN
ejpam-6273	436	8	of	of	ADP
ejpam-6273	436	9	phayao	phayao	NOUN
ejpam-6273	436	10	and	and	CCONJ
ejpam-6273	436	11	thailand	thailand	PROPN
ejpam-6273	436	12	science	science	PROPN
ejpam-6273	436	13	research	research	PROPN
ejpam-6273	436	14	and	and	CCONJ
ejpam-6273	436	15	innovation	innovation	NOUN
ejpam-6273	436	16	fund	fund	NOUN
ejpam-6273	436	17	(	(	PUNCT
ejpam-6273	436	18	fundamental	fundamental	ADJ
ejpam-6273	436	19	fund	fund	NOUN
ejpam-6273	436	20	2025	2025	NUM
ejpam-6273	436	21	,	,	PUNCT
ejpam-6273	436	22	grant	grant	VERB
ejpam-6273	436	23	no	no	NOUN
ejpam-6273	436	24	.	.	PROPN
ejpam-6273	437	1	5027/2567	5027/2567	NUM
ejpam-6273	437	2	)	)	PUNCT
ejpam-6273	437	3	.	.	PUNCT
ejpam-6273	438	1	references	reference	NOUN
ejpam-6273	438	2	[	[	X
ejpam-6273	438	3	1	1	NUM
ejpam-6273	438	4	]	]	X
ejpam-6273	438	5	g.	g.	PROPN
ejpam-6273	438	6	pilz	pilz	PROPN
ejpam-6273	438	7	.	.	PUNCT
ejpam-6273	439	1	near	near	ADP
ejpam-6273	439	2	-	-	PUNCT
ejpam-6273	439	3	ring	ring	NOUN
ejpam-6273	439	4	:	:	PUNCT
ejpam-6273	439	5	the	the	DET
ejpam-6273	439	6	theory	theory	NOUN
ejpam-6273	439	7	and	and	CCONJ
ejpam-6273	439	8	its	its	PRON
ejpam-6273	439	9	applications	application	NOUN
ejpam-6273	439	10	.	.	PUNCT
ejpam-6273	440	1	north	north	NOUN
ejpam-6273	440	2	holland	holland	PROPN
ejpam-6273	440	3	publishers	publisher	NOUN
ejpam-6273	440	4	,	,	PUNCT
ejpam-6273	440	5	amsterdam	amsterdam	PROPN
ejpam-6273	440	6	,	,	PUNCT
ejpam-6273	440	7	1983	1983	NUM
ejpam-6273	440	8	.	.	PUNCT
ejpam-6273	441	1	[	[	X
ejpam-6273	441	2	2	2	X
ejpam-6273	441	3	]	]	PUNCT
ejpam-6273	441	4	h.	h.	PROPN
ejpam-6273	441	5	brown	brown	PROPN
ejpam-6273	441	6	.	.	PUNCT
ejpam-6273	442	1	near	near	ADP
ejpam-6273	442	2	algebras	algebras	PROPN
ejpam-6273	442	3	.	.	PUNCT
ejpam-6273	442	4	illinois	illinois	PROPN
ejpam-6273	442	5	journal	journal	PROPN
ejpam-6273	442	6	of	of	ADP
ejpam-6273	442	7	mathematics	mathematic	NOUN
ejpam-6273	442	8	,	,	PUNCT
ejpam-6273	442	9	12:215–227	12:215–227	PROPN
ejpam-6273	442	10	,	,	PUNCT
ejpam-6273	442	11	1968	1968	NUM
ejpam-6273	442	12	.	.	PUNCT
ejpam-6273	443	1	[	[	X
ejpam-6273	443	2	3	3	NUM
ejpam-6273	443	3	]	]	PUNCT
ejpam-6273	443	4	a.	a.	NOUN
ejpam-6273	443	5	j.	j.	PROPN
ejpam-6273	443	6	de	de	PROPN
ejpam-6273	443	7	oliveira	oliveira	PROPN
ejpam-6273	443	8	andrade	andrade	PROPN
ejpam-6273	443	9	,	,	PUNCT
ejpam-6273	443	10	g.	g.	PROPN
ejpam-6273	443	11	c.	c.	PROPN
ejpam-6273	443	12	de	de	PROPN
ejpam-6273	443	13	moraes	moraes	PROPN
ejpam-6273	443	14	,	,	PUNCT
ejpam-6273	443	15	r.	r.	PROPN
ejpam-6273	443	16	n.	n.	PROPN
ejpam-6273	443	17	ferreira	ferreira	PROPN
ejpam-6273	443	18	,	,	PUNCT
ejpam-6273	443	19	and	and	CCONJ
ejpam-6273	443	20	b.	b.	PROPN
ejpam-6273	443	21	l.	l.	PROPN
ejpam-6273	443	22	m.	m.	PROPN
ejpam-6273	443	23	ferreira	ferreira	PROPN
ejpam-6273	443	24	.	.	PUNCT
ejpam-6273	444	1	additivity	additivity	NOUN
ejpam-6273	444	2	of	of	ADP
ejpam-6273	444	3	n	n	CCONJ
ejpam-6273	444	4	-	-	PUNCT
ejpam-6273	444	5	multiplicative	multiplicative	ADJ
ejpam-6273	444	6	mappings	mapping	NOUN
ejpam-6273	444	7	of	of	ADP
ejpam-6273	444	8	gamma	gamma	NOUN
ejpam-6273	444	9	rings	ring	NOUN
ejpam-6273	444	10	.	.	PUNCT
ejpam-6273	445	1	afrika	afrika	PROPN
ejpam-6273	445	2	matematika	matematika	PROPN
ejpam-6273	445	3	,	,	PUNCT
ejpam-6273	445	4	32:1563	32:1563	NUM
ejpam-6273	445	5	–	–	PUNCT
ejpam-6273	445	6	1571	1571	NUM
ejpam-6273	445	7	,	,	PUNCT
ejpam-6273	445	8	2021	2021	NUM
ejpam-6273	445	9	.	.	PUNCT
ejpam-6273	446	1	p.	p.	NOUN
ejpam-6273	446	2	n.	n.	PROPN
ejpam-6273	446	3	swamy	swamy	PROPN
ejpam-6273	446	4	et	et	PROPN
ejpam-6273	446	5	al	al	PROPN
ejpam-6273	446	6	.	.	PUNCT
ejpam-6273	446	7	/	/	SYM
ejpam-6273	446	8	eur	eur	PROPN
ejpam-6273	446	9	.	.	PUNCT
ejpam-6273	447	1	j.	j.	PROPN
ejpam-6273	447	2	pure	pure	PROPN
ejpam-6273	447	3	appl	appl	PROPN
ejpam-6273	447	4	.	.	PROPN
ejpam-6273	447	5	math	math	PROPN
ejpam-6273	447	6	,	,	PUNCT
ejpam-6273	447	7	18	18	NUM
ejpam-6273	447	8	(	(	PUNCT
ejpam-6273	447	9	3	3	NUM
ejpam-6273	447	10	)	)	PUNCT
ejpam-6273	447	11	(	(	PUNCT
ejpam-6273	447	12	2025	2025	NUM
ejpam-6273	447	13	)	)	PUNCT
ejpam-6273	447	14	,	,	PUNCT
ejpam-6273	447	15	6273	6273	NUM
ejpam-6273	447	16	16	16	NUM
ejpam-6273	447	17	of	of	ADP
ejpam-6273	447	18	16	16	NUM
ejpam-6273	448	1	[	[	X
ejpam-6273	448	2	4	4	NUM
ejpam-6273	448	3	]	]	PUNCT
ejpam-6273	448	4	j.	j.	PROPN
ejpam-6273	448	5	c.	c.	PROPN
ejpam-6273	448	6	da	da	PROPN
ejpam-6273	448	7	motta	motta	PROPN
ejpam-6273	448	8	ferreira	ferreira	PROPN
ejpam-6273	448	9	and	and	CCONJ
ejpam-6273	448	10	b.	b.	PROPN
ejpam-6273	448	11	l.	l.	PROPN
ejpam-6273	448	12	m.	m.	PROPN
ejpam-6273	448	13	ferreira	ferreira	PROPN
ejpam-6273	448	14	.	.	PUNCT
ejpam-6273	449	1	additivity	additivity	NOUN
ejpam-6273	449	2	of	of	ADP
ejpam-6273	449	3	n	n	CCONJ
ejpam-6273	449	4	-	-	PUNCT
ejpam-6273	449	5	multiplicative	multiplicative	ADJ
ejpam-6273	449	6	maps	map	NOUN
ejpam-6273	449	7	on	on	ADP
ejpam-6273	449	8	alternative	alternative	ADJ
ejpam-6273	449	9	rings	ring	NOUN
ejpam-6273	449	10	.	.	PUNCT
ejpam-6273	450	1	communications	communication	NOUN
ejpam-6273	450	2	in	in	ADP
ejpam-6273	450	3	algebra	algebra	NOUN
ejpam-6273	450	4	,	,	PUNCT
ejpam-6273	450	5	44:1557–1568	44:1557–1568	NUM
ejpam-6273	450	6	,	,	PUNCT
ejpam-6273	450	7	2016	2016	NUM
ejpam-6273	450	8	.	.	PUNCT
ejpam-6273	451	1	[	[	X
ejpam-6273	451	2	5	5	NUM
ejpam-6273	451	3	]	]	PUNCT
ejpam-6273	451	4	b.	b.	PROPN
ejpam-6273	451	5	l.	l.	PROPN
ejpam-6273	451	6	m.	m.	PROPN
ejpam-6273	451	7	ferreira	ferreira	PROPN
ejpam-6273	451	8	and	and	CCONJ
ejpam-6273	451	9	h.	h.	PROPN
ejpam-6273	451	10	julius	julius	PROPN
ejpam-6273	451	11	.	.	PUNCT
ejpam-6273	452	1	additive	additive	NOUN
ejpam-6273	452	2	maps	map	NOUN
ejpam-6273	452	3	preserving	preserve	VERB
ejpam-6273	452	4	(	(	PUNCT
ejpam-6273	452	5	generalized	generalized	ADJ
ejpam-6273	452	6	)	)	PUNCT
ejpam-6273	452	7	inverses	inverse	NOUN
ejpam-6273	452	8	on	on	ADP
ejpam-6273	452	9	alternative	alternative	ADJ
ejpam-6273	452	10	division	division	NOUN
ejpam-6273	452	11	algebras	algebra	NOUN
ejpam-6273	452	12	.	.	PUNCT
ejpam-6273	453	1	european	european	PROPN
ejpam-6273	453	2	journal	journal	PROPN
ejpam-6273	453	3	of	of	ADP
ejpam-6273	453	4	mathematics	mathematic	NOUN
ejpam-6273	453	5	,	,	PUNCT
ejpam-6273	453	6	10:51	10:51	NUM
ejpam-6273	453	7	,	,	PUNCT
ejpam-6273	453	8	2024	2024	NUM
ejpam-6273	453	9	.	.	PUNCT
ejpam-6273	454	1	[	[	X
ejpam-6273	454	2	6	6	NUM
ejpam-6273	454	3	]	]	PUNCT
ejpam-6273	454	4	m.	m.	NOUN
ejpam-6273	454	5	brešar	brešar	PROPN
ejpam-6273	454	6	.	.	PUNCT
ejpam-6273	455	1	zero	zero	NUM
ejpam-6273	455	2	product	product	NOUN
ejpam-6273	455	3	determined	determine	VERB
ejpam-6273	455	4	algebras	algebra	NOUN
ejpam-6273	455	5	.	.	PUNCT
ejpam-6273	455	6	birkhäuser	birkhäuser	PROPN
ejpam-6273	455	7	cham	cham	PROPN
ejpam-6273	455	8	,	,	PUNCT
ejpam-6273	455	9	frontiers	frontier	NOUN
ejpam-6273	455	10	in	in	ADP
ejpam-6273	455	11	mathematics	mathematic	NOUN
ejpam-6273	455	12	series	series	PROPN
ejpam-6273	455	13	,	,	PUNCT
ejpam-6273	455	14	switzerland	switzerland	PROPN
ejpam-6273	455	15	,	,	PUNCT
ejpam-6273	455	16	2021	2021	NUM
ejpam-6273	455	17	.	.	PUNCT
ejpam-6273	456	1	[	[	X
ejpam-6273	456	2	7	7	X
ejpam-6273	456	3	]	]	PUNCT
ejpam-6273	456	4	t.	t.	PROPN
ejpam-6273	456	5	srinivas	srinivas	PROPN
ejpam-6273	456	6	and	and	CCONJ
ejpam-6273	456	7	p.	p.	PROPN
ejpam-6273	456	8	narasimha	narasimha	PROPN
ejpam-6273	456	9	swamy	swamy	PROPN
ejpam-6273	456	10	.	.	PUNCT
ejpam-6273	457	1	a	a	DET
ejpam-6273	457	2	note	note	NOUN
ejpam-6273	457	3	on	on	ADP
ejpam-6273	457	4	fuzzy	fuzzy	ADJ
ejpam-6273	457	5	near	near	NOUN
ejpam-6273	457	6	-	-	PUNCT
ejpam-6273	457	7	algebras	algebras	PROPN
ejpam-6273	457	8	.	.	PUNCT
ejpam-6273	458	1	international	international	ADJ
ejpam-6273	458	2	journal	journal	PROPN
ejpam-6273	458	3	of	of	ADP
ejpam-6273	458	4	algebra	algebra	PROPN
ejpam-6273	458	5	,	,	PUNCT
ejpam-6273	458	6	5(22):1085–1098	5(22):1085–1098	NUM
ejpam-6273	458	7	,	,	PUNCT
ejpam-6273	458	8	2011	2011	NUM
ejpam-6273	458	9	.	.	PUNCT
ejpam-6273	459	1	[	[	X
ejpam-6273	459	2	8	8	NUM
ejpam-6273	459	3	]	]	X
ejpam-6273	459	4	l.	l.	PROPN
ejpam-6273	459	5	a.	a.	PROPN
ejpam-6273	459	6	zadeh	zadeh	PROPN
ejpam-6273	459	7	.	.	PUNCT
ejpam-6273	459	8	fuzzy	fuzzy	ADJ
ejpam-6273	459	9	sets	set	NOUN
ejpam-6273	459	10	.	.	PUNCT
ejpam-6273	460	1	information	information	NOUN
ejpam-6273	460	2	and	and	CCONJ
ejpam-6273	460	3	control	control	NOUN
ejpam-6273	460	4	,	,	PUNCT
ejpam-6273	460	5	8(3):338–353	8(3):338–353	NUM
ejpam-6273	460	6	,	,	PUNCT
ejpam-6273	460	7	1965	1965	NUM
ejpam-6273	460	8	.	.	PUNCT
ejpam-6273	461	1	[	[	X
ejpam-6273	461	2	9	9	NUM
ejpam-6273	461	3	]	]	X
ejpam-6273	461	4	v.	v.	CCONJ
ejpam-6273	461	5	torra	torra	PROPN
ejpam-6273	461	6	.	.	PUNCT
ejpam-6273	462	1	hesitant	hesitant	ADJ
ejpam-6273	462	2	fuzzy	fuzzy	ADJ
ejpam-6273	462	3	sets	set	NOUN
ejpam-6273	462	4	.	.	PUNCT
ejpam-6273	463	1	international	international	ADJ
ejpam-6273	463	2	journal	journal	NOUN
ejpam-6273	463	3	of	of	ADP
ejpam-6273	463	4	intelligent	intelligent	ADJ
ejpam-6273	463	5	systems	system	NOUN
ejpam-6273	463	6	,	,	PUNCT
ejpam-6273	463	7	25:529	25:529	NUM
ejpam-6273	463	8	–	–	PUNCT
ejpam-6273	463	9	539	539	NUM
ejpam-6273	463	10	,	,	PUNCT
ejpam-6273	463	11	2010	2010	NUM
ejpam-6273	463	12	.	.	PUNCT
ejpam-6273	464	1	[	[	X
ejpam-6273	464	2	10	10	NUM
ejpam-6273	464	3	]	]	X
ejpam-6273	464	4	d.	d.	PROPN
ejpam-6273	464	5	molodtsov	molodtsov	PROPN
ejpam-6273	464	6	.	.	PUNCT
ejpam-6273	465	1	soft	soft	ADJ
ejpam-6273	465	2	set	set	NOUN
ejpam-6273	465	3	theory	theory	NOUN
ejpam-6273	465	4	—	—	PUNCT
ejpam-6273	465	5	first	first	ADJ
ejpam-6273	465	6	results	result	NOUN
ejpam-6273	465	7	.	.	PUNCT
ejpam-6273	466	1	computers	computer	NOUN
ejpam-6273	466	2	and	and	CCONJ
ejpam-6273	466	3	mathematics	mathematic	NOUN
ejpam-6273	466	4	with	with	ADP
ejpam-6273	466	5	applications	application	NOUN
ejpam-6273	466	6	,	,	PUNCT
ejpam-6273	466	7	37:19–31	37:19–31	NUM
ejpam-6273	466	8	,	,	PUNCT
ejpam-6273	466	9	1999	1999	NUM
ejpam-6273	466	10	.	.	PUNCT
ejpam-6273	467	1	[	[	X
ejpam-6273	467	2	11	11	NUM
ejpam-6273	467	3	]	]	X
ejpam-6273	467	4	y.	y.	PROPN
ejpam-6273	467	5	b.	b.	PROPN
ejpam-6273	467	6	jun	jun	PROPN
ejpam-6273	467	7	,	,	PUNCT
ejpam-6273	467	8	s.	s.	PROPN
ejpam-6273	467	9	z.	z.	PROPN
ejpam-6273	467	10	song	song	PROPN
ejpam-6273	467	11	,	,	PUNCT
ejpam-6273	467	12	and	and	CCONJ
ejpam-6273	467	13	g.	g.	PROPN
ejpam-6273	467	14	muhiuddin	muhiuddin	PROPN
ejpam-6273	467	15	.	.	PUNCT
ejpam-6273	468	1	hybrid	hybrid	ADJ
ejpam-6273	468	2	structures	structure	NOUN
ejpam-6273	468	3	and	and	CCONJ
ejpam-6273	468	4	applications	application	NOUN
ejpam-6273	468	5	.	.	PUNCT
ejpam-6273	469	1	annals	annal	NOUN
ejpam-6273	469	2	of	of	ADP
ejpam-6273	469	3	communications	communication	NOUN
ejpam-6273	469	4	in	in	ADP
ejpam-6273	469	5	mathematics	mathematic	NOUN
ejpam-6273	469	6	,	,	PUNCT
ejpam-6273	469	7	1(1):11–25	1(1):11–25	NUM
ejpam-6273	469	8	,	,	PUNCT
ejpam-6273	469	9	2018	2018	NUM
ejpam-6273	469	10	.	.	PUNCT
ejpam-6273	470	1	[	[	X
ejpam-6273	470	2	12	12	NUM
ejpam-6273	470	3	]	]	X
ejpam-6273	470	4	s.	s.	PROPN
ejpam-6273	470	5	anis	anis	PROPN
ejpam-6273	470	6	,	,	PUNCT
ejpam-6273	470	7	m.	m.	NOUN
ejpam-6273	470	8	khan	khan	PROPN
ejpam-6273	470	9	,	,	PUNCT
ejpam-6273	470	10	and	and	CCONJ
ejpam-6273	470	11	y.	y.	PROPN
ejpam-6273	470	12	b.	b.	PROPN
ejpam-6273	470	13	jun	jun	PROPN
ejpam-6273	470	14	.	.	PROPN
ejpam-6273	470	15	hybrid	hybrid	ADJ
ejpam-6273	470	16	ideals	ideal	NOUN
ejpam-6273	470	17	in	in	ADP
ejpam-6273	470	18	semigroups	semigroup	NOUN
ejpam-6273	470	19	.	.	PUNCT
ejpam-6273	471	1	cogent	cogent	NOUN
ejpam-6273	471	2	mathematics	mathematic	NOUN
ejpam-6273	471	3	,	,	PUNCT
ejpam-6273	471	4	4:1352117	4:1352117	NUM
ejpam-6273	471	5	,	,	PUNCT
ejpam-6273	471	6	2017	2017	NUM
ejpam-6273	471	7	.	.	PUNCT
ejpam-6273	472	1	[	[	X
ejpam-6273	472	2	13	13	NUM
ejpam-6273	472	3	]	]	PUNCT
ejpam-6273	472	4	m.	m.	NOUN
ejpam-6273	472	5	himaya	himaya	PROPN
ejpam-6273	472	6	jaleela	jaleela	PROPN
ejpam-6273	472	7	begum	begum	PROPN
ejpam-6273	472	8	and	and	CCONJ
ejpam-6273	472	9	g.	g.	PROPN
ejpam-6273	472	10	rama	rama	PROPN
ejpam-6273	472	11	.	.	PUNCT
ejpam-6273	473	1	hybrid	hybrid	ADJ
ejpam-6273	473	2	fuzzy	fuzzy	ADJ
ejpam-6273	473	3	bi	bi	NOUN
ejpam-6273	473	4	-	-	NOUN
ejpam-6273	473	5	ideals	ideal	NOUN
ejpam-6273	473	6	in	in	ADP
ejpam-6273	473	7	near	near	ADJ
ejpam-6273	473	8	-	-	PUNCT
ejpam-6273	473	9	rings	ring	NOUN
ejpam-6273	473	10	.	.	PUNCT
ejpam-6273	474	1	turkish	turkish	ADJ
ejpam-6273	474	2	journal	journal	NOUN
ejpam-6273	474	3	of	of	ADP
ejpam-6273	474	4	computer	computer	NOUN
ejpam-6273	474	5	and	and	CCONJ
ejpam-6273	474	6	mathematics	mathematic	NOUN
ejpam-6273	474	7	education	education	NOUN
ejpam-6273	474	8	,	,	PUNCT
ejpam-6273	474	9	12(7):3291–3295	12(7):3291–3295	NUM
ejpam-6273	474	10	,	,	PUNCT
ejpam-6273	474	11	2021	2021	NUM
ejpam-6273	474	12	.	.	PUNCT
ejpam-6273	475	1	[	[	X
ejpam-6273	475	2	14	14	NUM
ejpam-6273	475	3	]	]	PUNCT
ejpam-6273	475	4	b.	b.	PROPN
ejpam-6273	475	5	elavarasan	elavarasan	PROPN
ejpam-6273	475	6	,	,	PUNCT
ejpam-6273	475	7	g.	g.	PROPN
ejpam-6273	475	8	muhiuddin	muhiuddin	PROPN
ejpam-6273	475	9	,	,	PUNCT
ejpam-6273	475	10	k.	k.	PROPN
ejpam-6273	475	11	porselvi	porselvi	PROPN
ejpam-6273	475	12	,	,	PUNCT
ejpam-6273	475	13	and	and	CCONJ
ejpam-6273	475	14	y.	y.	PROPN
ejpam-6273	475	15	b.	b.	PROPN
ejpam-6273	475	16	jun	jun	PROPN
ejpam-6273	475	17	.	.	PROPN
ejpam-6273	475	18	hybrid	hybrid	ADJ
ejpam-6273	475	19	structures	structure	NOUN
ejpam-6273	475	20	applied	apply	VERB
ejpam-6273	475	21	to	to	ADP
ejpam-6273	475	22	ideals	ideal	NOUN
ejpam-6273	475	23	in	in	ADP
ejpam-6273	475	24	near	near	ADJ
ejpam-6273	475	25	-	-	PUNCT
ejpam-6273	475	26	rings	ring	NOUN
ejpam-6273	475	27	.	.	PUNCT
ejpam-6273	476	1	complex	complex	ADJ
ejpam-6273	476	2	and	and	CCONJ
ejpam-6273	476	3	intelligent	intelligent	ADJ
ejpam-6273	476	4	systems	system	NOUN
ejpam-6273	476	5	,	,	PUNCT
ejpam-6273	476	6	7:1489–1498	7:1489–1498	NUM
ejpam-6273	476	7	,	,	PUNCT
ejpam-6273	476	8	2021	2021	NUM
ejpam-6273	476	9	.	.	PUNCT
ejpam-6273	477	1	[	[	X
ejpam-6273	477	2	15	15	NUM
ejpam-6273	477	3	]	]	X
ejpam-6273	477	4	h.	h.	PROPN
ejpam-6273	477	5	bhurgula	bhurgula	PROPN
ejpam-6273	477	6	,	,	PUNCT
ejpam-6273	477	7	n.s	n.s	PROPN
ejpam-6273	477	8	.	.	PROPN
ejpam-6273	477	9	pasham	pasham	PROPN
ejpam-6273	477	10	,	,	PUNCT
ejpam-6273	477	11	r.	r.	PROPN
ejpam-6273	477	12	bandaru	bandaru	PROPN
ejpam-6273	477	13	,	,	PUNCT
ejpam-6273	477	14	and	and	CCONJ
ejpam-6273	477	15	a.	a.	PROPN
ejpam-6273	477	16	s.	s.	PROPN
ejpam-6273	477	17	alali	alali	PROPN
ejpam-6273	477	18	.	.	PUNCT
ejpam-6273	478	1	hybrid	hybrid	NOUN
ejpam-6273	478	2	near	near	ADP
ejpam-6273	478	3	algebra	algebra	PROPN
ejpam-6273	478	4	.	.	PUNCT
ejpam-6273	479	1	axioms	axiom	NOUN
ejpam-6273	479	2	,	,	PUNCT
ejpam-6273	479	3	12:877	12:877	NUM
ejpam-6273	479	4	,	,	PUNCT
ejpam-6273	479	5	2023	2023	NUM
ejpam-6273	479	6	.	.	PUNCT