id	sid	tid	token	lemma	pos
ejpam-5705	1	1	european	european	PROPN
ejpam-5705	1	2	journal	journal	PROPN
ejpam-5705	1	3	of	of	ADP
ejpam-5705	1	4	pure	pure	ADJ
ejpam-5705	1	5	and	and	CCONJ
ejpam-5705	1	6	applied	applied	ADJ
ejpam-5705	1	7	mathematics	mathematic	NOUN
ejpam-5705	1	8	2025	2025	NUM
ejpam-5705	1	9	,	,	PUNCT
ejpam-5705	1	10	vol	vol	NOUN
ejpam-5705	1	11	.	.	PROPN
ejpam-5705	1	12	18	18	NUM
ejpam-5705	1	13	,	,	PUNCT
ejpam-5705	1	14	issue	issue	NOUN
ejpam-5705	1	15	2	2	NUM
ejpam-5705	1	16	,	,	PUNCT
ejpam-5705	1	17	article	article	NOUN
ejpam-5705	1	18	number	number	NOUN
ejpam-5705	1	19	5705	5705	NUM
ejpam-5705	1	20	issn	issn	PROPN
ejpam-5705	1	21	1307	1307	NUM
ejpam-5705	1	22	-	-	SYM
ejpam-5705	1	23	5543	5543	NUM
ejpam-5705	1	24	–	–	PUNCT
ejpam-5705	1	25	ejpam.com	ejpam.com	X
ejpam-5705	1	26	published	publish	VERB
ejpam-5705	1	27	by	by	ADP
ejpam-5705	1	28	new	new	PROPN
ejpam-5705	1	29	york	york	PROPN
ejpam-5705	1	30	business	business	PROPN
ejpam-5705	1	31	global	global	ADJ
ejpam-5705	1	32	•-paradistributive	•-paradistributive	PROPN
ejpam-5705	1	33	latticoids	latticoids	PROPN
ejpam-5705	1	34	ravikumar	ravikumar	PROPN
ejpam-5705	1	35	bandaru1	bandaru1	PROPN
ejpam-5705	1	36	,	,	PUNCT
ejpam-5705	1	37	suryavardhani	suryavardhani	PROPN
ejpam-5705	1	38	ajjarapu2	ajjarapu2	PROPN
ejpam-5705	1	39	,	,	PUNCT
ejpam-5705	1	40	rafi	rafi	PROPN
ejpam-5705	1	41	noorbhasha3	noorbhasha3	PROPN
ejpam-5705	1	42	,	,	PUNCT
ejpam-5705	1	43	rahul	rahul	PROPN
ejpam-5705	1	44	shukla3,∗	shukla3,∗	PROPN
ejpam-5705	1	45	1	1	NUM
ejpam-5705	1	46	department	department	NOUN
ejpam-5705	1	47	of	of	ADP
ejpam-5705	1	48	mathematics	mathematic	NOUN
ejpam-5705	1	49	,	,	PUNCT
ejpam-5705	1	50	school	school	NOUN
ejpam-5705	1	51	of	of	ADP
ejpam-5705	1	52	advanced	advanced	ADJ
ejpam-5705	1	53	sciences	science	NOUN
ejpam-5705	1	54	,	,	PUNCT
ejpam-5705	1	55	vit	vit	PROPN
ejpam-5705	1	56	-	-	PUNCT
ejpam-5705	1	57	ap	ap	PROPN
ejpam-5705	1	58	university	university	PROPN
ejpam-5705	1	59	,	,	PUNCT
ejpam-5705	1	60	andhra	andhra	PROPN
ejpam-5705	1	61	pradesh-522237	pradesh-522237	NOUN
ejpam-5705	1	62	,	,	PUNCT
ejpam-5705	1	63	india	india	PROPN
ejpam-5705	1	64	2	2	NUM
ejpam-5705	1	65	department	department	NOUN
ejpam-5705	1	66	of	of	ADP
ejpam-5705	1	67	mathematics	mathematic	NOUN
ejpam-5705	1	68	,	,	PUNCT
ejpam-5705	1	69	gitam	gitam	NOUN
ejpam-5705	1	70	deemed	deem	VERB
ejpam-5705	1	71	to	to	PART
ejpam-5705	1	72	be	be	AUX
ejpam-5705	1	73	university	university	NOUN
ejpam-5705	1	74	,	,	PUNCT
ejpam-5705	1	75	hyderabad	hyderabad	PROPN
ejpam-5705	1	76	campus	campus	NOUN
ejpam-5705	1	77	,	,	PUNCT
ejpam-5705	1	78	telangana-502329	telangana-502329	ADJ
ejpam-5705	1	79	,	,	PUNCT
ejpam-5705	1	80	india	india	PROPN
ejpam-5705	1	81	3	3	NUM
ejpam-5705	1	82	department	department	NOUN
ejpam-5705	1	83	of	of	ADP
ejpam-5705	1	84	mathematics	mathematic	NOUN
ejpam-5705	1	85	,	,	PUNCT
ejpam-5705	1	86	bapatla	bapatla	VERB
ejpam-5705	1	87	engineering	engineering	NOUN
ejpam-5705	1	88	college	college	NOUN
ejpam-5705	1	89	,	,	PUNCT
ejpam-5705	1	90	bapatla	bapatla	NOUN
ejpam-5705	1	91	,	,	PUNCT
ejpam-5705	1	92	andhra	andhra	PROPN
ejpam-5705	1	93	pradesh-522	pradesh-522	PROPN
ejpam-5705	1	94	102	102	NUM
ejpam-5705	1	95	,	,	PUNCT
ejpam-5705	1	96	india	india	PROPN
ejpam-5705	1	97	4	4	NUM
ejpam-5705	1	98	department	department	PROPN
ejpam-5705	1	99	of	of	ADP
ejpam-5705	1	100	mathematical	mathematical	ADJ
ejpam-5705	1	101	sciences	sciences	PROPN
ejpam-5705	1	102	and	and	CCONJ
ejpam-5705	1	103	computing	computing	NOUN
ejpam-5705	1	104	,	,	PUNCT
ejpam-5705	1	105	walter	walter	PROPN
ejpam-5705	1	106	sisulu	sisulu	PROPN
ejpam-5705	1	107	university	university	PROPN
ejpam-5705	1	108	,	,	PUNCT
ejpam-5705	1	109	mthatha	mthatha	NOUN
ejpam-5705	1	110	5117	5117	NUM
ejpam-5705	1	111	,	,	PUNCT
ejpam-5705	1	112	south	south	PROPN
ejpam-5705	1	113	africa	africa	PROPN
ejpam-5705	1	114	abstract	abstract	PROPN
ejpam-5705	1	115	.	.	PUNCT
ejpam-5705	2	1	in	in	ADP
ejpam-5705	2	2	this	this	DET
ejpam-5705	2	3	paper	paper	NOUN
ejpam-5705	2	4	,	,	PUNCT
ejpam-5705	2	5	we	we	PRON
ejpam-5705	2	6	introduce	introduce	VERB
ejpam-5705	2	7	the	the	DET
ejpam-5705	2	8	notion	notion	NOUN
ejpam-5705	2	9	of	of	ADP
ejpam-5705	2	10	a	a	DET
ejpam-5705	2	11	new	new	ADJ
ejpam-5705	2	12	class	class	NOUN
ejpam-5705	2	13	of	of	ADP
ejpam-5705	2	14	paradistributive	paradistributive	ADJ
ejpam-5705	2	15	latticoids	latticoid	NOUN
ejpam-5705	2	16	termed	term	VERB
ejpam-5705	2	17	•-pdls	•-pdls	NOUN
ejpam-5705	2	18	and	and	CCONJ
ejpam-5705	2	19	investigate	investigate	VERB
ejpam-5705	2	20	its	its	PRON
ejpam-5705	2	21	properties	property	NOUN
ejpam-5705	2	22	.	.	PUNCT
ejpam-5705	3	1	in	in	ADP
ejpam-5705	3	2	addition	addition	NOUN
ejpam-5705	3	3	,	,	PUNCT
ejpam-5705	3	4	we	we	PRON
ejpam-5705	3	5	prove	prove	VERB
ejpam-5705	3	6	that	that	SCONJ
ejpam-5705	3	7	a	a	DET
ejpam-5705	3	8	paradistributive	paradistributive	ADJ
ejpam-5705	3	9	latticoid(pdl	latticoid(pdl	NOUN
ejpam-5705	3	10	)	)	PUNCT
ejpam-5705	3	11	v	v	NOUN
ejpam-5705	3	12	is	be	AUX
ejpam-5705	3	13	a	a	DET
ejpam-5705	3	14	•-pdl	•-pdl	PUNCT
ejpam-5705	3	15	iff	iff	PROPN
ejpam-5705	3	16	v	v	PROPN
ejpam-5705	3	17	/	/	SYM
ejpam-5705	3	18	θ	θ	PROPN
ejpam-5705	3	19	is	be	AUX
ejpam-5705	3	20	a	a	DET
ejpam-5705	3	21	boolean	boolean	ADJ
ejpam-5705	3	22	algebra	algebra	NOUN
ejpam-5705	3	23	with	with	ADP
ejpam-5705	3	24	a	a	DET
ejpam-5705	3	25	minimal	minimal	ADJ
ejpam-5705	3	26	element	element	NOUN
ejpam-5705	3	27	,	,	PUNCT
ejpam-5705	3	28	where	where	SCONJ
ejpam-5705	3	29	θ	θ	PROPN
ejpam-5705	3	30	=	=	SYM
ejpam-5705	3	31	{	{	PUNCT
ejpam-5705	3	32	(	(	PUNCT
ejpam-5705	3	33	℘	℘	NOUN
ejpam-5705	3	34	,	,	PUNCT
ejpam-5705	3	35	ℏ	ℏ	NOUN
ejpam-5705	3	36	)	)	PUNCT
ejpam-5705	3	37	∈	∈	PROPN
ejpam-5705	4	1	v	v	ADP
ejpam-5705	4	2	×	×	NOUN
ejpam-5705	4	3	v	v	INTJ
ejpam-5705	5	1	|	|	NOUN
ejpam-5705	6	1	[	[	X
ejpam-5705	6	2	℘]•	℘]•	PROPN
ejpam-5705	6	3	=	=	PUNCT
ejpam-5705	6	4	[	[	X
ejpam-5705	6	5	ℏ]•	ℏ]•	NOUN
ejpam-5705	6	6	}	}	PUNCT
ejpam-5705	6	7	is	be	AUX
ejpam-5705	6	8	a	a	DET
ejpam-5705	6	9	congruence	congruence	NOUN
ejpam-5705	6	10	relation	relation	NOUN
ejpam-5705	6	11	on	on	ADP
ejpam-5705	6	12	v	v	NUM
ejpam-5705	6	13	.	.	PUNCT
ejpam-5705	7	1	further	far	ADV
ejpam-5705	7	2	,	,	PUNCT
ejpam-5705	7	3	we	we	PRON
ejpam-5705	7	4	explore	explore	VERB
ejpam-5705	7	5	the	the	DET
ejpam-5705	7	6	concept	concept	NOUN
ejpam-5705	7	7	of	of	ADP
ejpam-5705	7	8	dense	dense	ADJ
ejpam-5705	7	9	elements	element	NOUN
ejpam-5705	7	10	in	in	ADP
ejpam-5705	7	11	a	a	DET
ejpam-5705	7	12	pdl	pdl	NOUN
ejpam-5705	7	13	and	and	CCONJ
ejpam-5705	7	14	characterize	characterize	VERB
ejpam-5705	7	15	•-pdl	•-pdl	PUNCT
ejpam-5705	7	16	in	in	ADP
ejpam-5705	7	17	terms	term	NOUN
ejpam-5705	7	18	of	of	ADP
ejpam-5705	7	19	dense	dense	ADJ
ejpam-5705	7	20	elements	element	NOUN
ejpam-5705	7	21	.	.	PUNCT
ejpam-5705	8	1	also	also	ADV
ejpam-5705	8	2	,	,	PUNCT
ejpam-5705	8	3	we	we	PRON
ejpam-5705	8	4	introduce	introduce	VERB
ejpam-5705	8	5	the	the	DET
ejpam-5705	8	6	notion	notion	NOUN
ejpam-5705	8	7	of	of	ADP
ejpam-5705	8	8	a	a	DET
ejpam-5705	8	9	disjunctive	disjunctive	ADJ
ejpam-5705	8	10	pdl	pdl	NOUN
ejpam-5705	8	11	and	and	CCONJ
ejpam-5705	8	12	we	we	PRON
ejpam-5705	8	13	give	give	VERB
ejpam-5705	8	14	equivalent	equivalent	ADJ
ejpam-5705	8	15	conditions	condition	NOUN
ejpam-5705	8	16	for	for	SCONJ
ejpam-5705	8	17	a	a	PRON
ejpam-5705	8	18	•-pdl	•-pdl	PUNCT
ejpam-5705	8	19	to	to	PART
ejpam-5705	8	20	be	be	AUX
ejpam-5705	8	21	a	a	DET
ejpam-5705	8	22	disjunctive	disjunctive	ADJ
ejpam-5705	8	23	pdl	pdl	NOUN
ejpam-5705	8	24	.	.	PROPN
ejpam-5705	8	25	2020	2020	NUM
ejpam-5705	8	26	mathematics	mathematic	NOUN
ejpam-5705	8	27	subject	subject	NOUN
ejpam-5705	8	28	classifications	classification	NOUN
ejpam-5705	8	29	:	:	PUNCT
ejpam-5705	8	30	06d99	06d99	NUM
ejpam-5705	8	31	key	key	ADJ
ejpam-5705	8	32	words	word	NOUN
ejpam-5705	8	33	and	and	CCONJ
ejpam-5705	8	34	phrases	phrase	NOUN
ejpam-5705	8	35	:	:	PUNCT
ejpam-5705	8	36	•-pdl	•-pdl	ADJ
ejpam-5705	8	37	,	,	PUNCT
ejpam-5705	8	38	congruence	congruence	PROPN
ejpam-5705	8	39	relation	relation	PROPN
ejpam-5705	8	40	,	,	PUNCT
ejpam-5705	8	41	boolean	boolean	ADJ
ejpam-5705	8	42	algebra	algebra	NOUN
ejpam-5705	8	43	,	,	PUNCT
ejpam-5705	8	44	dense	dense	ADJ
ejpam-5705	8	45	element	element	NOUN
ejpam-5705	8	46	,	,	PUNCT
ejpam-5705	8	47	disjunctive	disjunctive	ADJ
ejpam-5705	8	48	pdl	pdl	PROPN
ejpam-5705	8	49	1	1	NUM
ejpam-5705	8	50	.	.	PUNCT
ejpam-5705	9	1	introduction	introduction	NOUN
ejpam-5705	9	2	a	a	DET
ejpam-5705	9	3	variety	variety	NOUN
ejpam-5705	9	4	of	of	ADP
ejpam-5705	9	5	generalisations	generalisation	NOUN
ejpam-5705	9	6	have	have	AUX
ejpam-5705	9	7	emerged	emerge	VERB
ejpam-5705	9	8	as	as	ADP
ejpam-5705	9	9	a	a	DET
ejpam-5705	9	10	result	result	NOUN
ejpam-5705	9	11	of	of	ADP
ejpam-5705	9	12	booles	boole	NOUN
ejpam-5705	9	13	’	'	PUNCT
ejpam-5705	9	14	axiomatization	axiomatization	NOUN
ejpam-5705	9	15	of	of	ADP
ejpam-5705	9	16	two	two	NUM
ejpam-5705	9	17	valued	value	VERB
ejpam-5705	9	18	propositional	propositional	ADJ
ejpam-5705	9	19	calculus	calculus	NOUN
ejpam-5705	9	20	as	as	ADP
ejpam-5705	9	21	a	a	DET
ejpam-5705	9	22	boolean	boolean	ADJ
ejpam-5705	9	23	algebra	algebra	NOUN
ejpam-5705	9	24	,	,	PUNCT
ejpam-5705	9	25	both	both	PRON
ejpam-5705	9	26	ring	re	VERB
ejpam-5705	9	27	theoretically	theoretically	ADV
ejpam-5705	9	28	and	and	CCONJ
ejpam-5705	9	29	lattice	lattice	VERB
ejpam-5705	9	30	theoretically	theoretically	ADV
ejpam-5705	9	31	.	.	PUNCT
ejpam-5705	10	1	tarski	tarski	ADJ
ejpam-5705	10	2	,	,	PUNCT
ejpam-5705	10	3	moisil	moisil	NOUN
ejpam-5705	10	4	and	and	CCONJ
ejpam-5705	10	5	others	other	NOUN
ejpam-5705	10	6	studied	study	VERB
ejpam-5705	10	7	filters	filter	NOUN
ejpam-5705	10	8	in	in	ADP
ejpam-5705	10	9	lattices	lattice	NOUN
ejpam-5705	10	10	,	,	PUNCT
ejpam-5705	10	11	and	and	CCONJ
ejpam-5705	10	12	many	many	ADJ
ejpam-5705	10	13	of	of	ADP
ejpam-5705	10	14	their	their	PRON
ejpam-5705	10	15	findings	finding	NOUN
ejpam-5705	10	16	are	be	AUX
ejpam-5705	10	17	found	find	VERB
ejpam-5705	10	18	in	in	ADP
ejpam-5705	10	19	birkhoff	birkhoff	NOUN
ejpam-5705	10	20	’s	’s	PART
ejpam-5705	10	21	lattice	lattice	PROPN
ejpam-5705	10	22	theory[1	theory[1	PROPN
ejpam-5705	10	23	]	]	PUNCT
ejpam-5705	10	24	.	.	PUNCT
ejpam-5705	11	1	the	the	DET
ejpam-5705	11	2	thought	thought	NOUN
ejpam-5705	11	3	of	of	ADP
ejpam-5705	11	4	an	an	DET
ejpam-5705	11	5	almost	almost	ADV
ejpam-5705	11	6	distributive	distributive	ADJ
ejpam-5705	11	7	lattice	lattice	NOUN
ejpam-5705	11	8	(	(	PUNCT
ejpam-5705	11	9	adl	adl	PROPN
ejpam-5705	11	10	)	)	PUNCT
ejpam-5705	11	11	was	be	AUX
ejpam-5705	11	12	developed	develop	VERB
ejpam-5705	11	13	by	by	ADP
ejpam-5705	11	14	swamy	swamy	NOUN
ejpam-5705	11	15	and	and	CCONJ
ejpam-5705	11	16	rao[2	rao[2	NOUN
ejpam-5705	11	17	]	]	PUNCT
ejpam-5705	11	18	as	as	ADP
ejpam-5705	11	19	a	a	DET
ejpam-5705	11	20	common	common	ADJ
ejpam-5705	11	21	abstraction	abstraction	NOUN
ejpam-5705	11	22	of	of	ADP
ejpam-5705	11	23	multiple	multiple	ADJ
ejpam-5705	11	24	existing	exist	VERB
ejpam-5705	11	25	ring	ring	NOUN
ejpam-5705	11	26	theoretic	theoretic	NOUN
ejpam-5705	11	27	generalisations	generalisation	NOUN
ejpam-5705	11	28	of	of	ADP
ejpam-5705	11	29	a	a	DET
ejpam-5705	11	30	boolean	boolean	ADJ
ejpam-5705	11	31	algebra	algebra	NOUN
ejpam-5705	11	32	on	on	ADP
ejpam-5705	11	33	one	one	NUM
ejpam-5705	11	34	hand	hand	NOUN
ejpam-5705	11	35	and	and	CCONJ
ejpam-5705	11	36	the	the	DET
ejpam-5705	11	37	class	class	NOUN
ejpam-5705	11	38	of	of	ADP
ejpam-5705	11	39	distributive	distributive	ADJ
ejpam-5705	11	40	lattices	lattice	NOUN
ejpam-5705	11	41	on	on	ADP
ejpam-5705	11	42	the	the	DET
ejpam-5705	11	43	other	other	ADJ
ejpam-5705	11	44	.	.	PUNCT
ejpam-5705	12	1	they	they	PRON
ejpam-5705	12	2	developed	develop	VERB
ejpam-5705	12	3	ideals	ideal	NOUN
ejpam-5705	12	4	and	and	CCONJ
ejpam-5705	12	5	filters	filter	NOUN
ejpam-5705	12	6	in	in	ADP
ejpam-5705	12	7	an	an	DET
ejpam-5705	12	8	adl	adl	NOUN
ejpam-5705	12	9	and	and	CCONJ
ejpam-5705	12	10	showed	show	VERB
ejpam-5705	12	11	that	that	SCONJ
ejpam-5705	12	12	the	the	DET
ejpam-5705	12	13	set	set	NOUN
ejpam-5705	12	14	of	of	ADP
ejpam-5705	12	15	all	all	DET
ejpam-5705	12	16	filters	filter	NOUN
ejpam-5705	12	17	in	in	ADP
ejpam-5705	12	18	an	an	DET
ejpam-5705	12	19	adl	adl	NOUN
ejpam-5705	12	20	forms	form	NOUN
ejpam-5705	12	21	a	a	DET
ejpam-5705	12	22	distributive	distributive	ADJ
ejpam-5705	12	23	lattice	lattice	NOUN
ejpam-5705	12	24	.	.	PUNCT
ejpam-5705	13	1	they	they	PRON
ejpam-5705	13	2	also	also	ADV
ejpam-5705	13	3	devised	devise	VERB
ejpam-5705	13	4	a	a	DET
ejpam-5705	13	5	set	set	NOUN
ejpam-5705	13	6	of	of	ADP
ejpam-5705	13	7	∗corresponding	∗corresponde	VERB
ejpam-5705	13	8	author	author	NOUN
ejpam-5705	13	9	.	.	PUNCT
ejpam-5705	14	1	doi	doi	NOUN
ejpam-5705	14	2	:	:	PUNCT
ejpam-5705	14	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5705	https://doi.org/10.29020/nybg.ejpam.v18i2.5705	PROPN
ejpam-5705	14	4	email	email	NOUN
ejpam-5705	14	5	addresses	address	NOUN
ejpam-5705	14	6	:	:	PUNCT
ejpam-5705	15	1	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-5705	15	2	(	(	PUNCT
ejpam-5705	15	3	r.	r.	PROPN
ejpam-5705	15	4	bandaru	bandaru	PROPN
ejpam-5705	15	5	)	)	PUNCT
ejpam-5705	15	6	,	,	PUNCT
ejpam-5705	15	7	syerrapr@gitam.in	syerrapr@gitam.in	PROPN
ejpam-5705	15	8	(	(	PUNCT
ejpam-5705	15	9	s.	s.	PROPN
ejpam-5705	15	10	ajjarapu	ajjarapu	PROPN
ejpam-5705	15	11	)	)	PUNCT
ejpam-5705	15	12	,	,	PUNCT
ejpam-5705	15	13	rafimaths@gmail.com	rafimaths@gmail.com	X
ejpam-5705	15	14	(	(	PUNCT
ejpam-5705	15	15	r.	r.	PROPN
ejpam-5705	15	16	noorbhasha	noorbhasha	PROPN
ejpam-5705	15	17	)	)	PUNCT
ejpam-5705	15	18	,	,	PUNCT
ejpam-5705	15	19	rshukla@wsu.ac.za	rshukla@wsu.ac.za	NOUN
ejpam-5705	15	20	(	(	PUNCT
ejpam-5705	15	21	r.	r.	NOUN
ejpam-5705	15	22	shukla	shukla	PROPN
ejpam-5705	15	23	)	)	PUNCT
ejpam-5705	15	24	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5705	16	1	1	1	NUM
ejpam-5705	16	2	copyright	copyright	NOUN
ejpam-5705	16	3	:	:	PUNCT
ejpam-5705	16	4	©	©	PROPN
ejpam-5705	16	5	2025	2025	NUM
ejpam-5705	16	6	the	the	DET
ejpam-5705	16	7	author(s	author(s	NOUN
ejpam-5705	16	8	)	)	PUNCT
ejpam-5705	16	9	.	.	PUNCT
ejpam-5705	17	1	(	(	PUNCT
ejpam-5705	17	2	cc	cc	NOUN
ejpam-5705	17	3	by	by	ADP
ejpam-5705	17	4	-	-	PUNCT
ejpam-5705	17	5	nc	nc	PROPN
ejpam-5705	17	6	4.0	4.0	NUM
ejpam-5705	17	7	)	)	PUNCT
ejpam-5705	17	8	r.	r.	PROPN
ejpam-5705	17	9	bandaru	bandaru	PROPN
ejpam-5705	17	10	et	et	PROPN
ejpam-5705	17	11	al	al	PROPN
ejpam-5705	17	12	.	.	PUNCT
ejpam-5705	17	13	/	/	SYM
ejpam-5705	17	14	eur	eur	PROPN
ejpam-5705	17	15	.	.	PUNCT
ejpam-5705	18	1	j.	j.	PROPN
ejpam-5705	18	2	pure	pure	PROPN
ejpam-5705	18	3	appl	appl	PROPN
ejpam-5705	18	4	.	.	PROPN
ejpam-5705	18	5	math	math	PROPN
ejpam-5705	18	6	,	,	PUNCT
ejpam-5705	18	7	18	18	NUM
ejpam-5705	18	8	(	(	PUNCT
ejpam-5705	18	9	2	2	NUM
ejpam-5705	18	10	)	)	PUNCT
ejpam-5705	18	11	(	(	PUNCT
ejpam-5705	18	12	2025	2025	NUM
ejpam-5705	18	13	)	)	PUNCT
ejpam-5705	18	14	,	,	PUNCT
ejpam-5705	18	15	5705	5705	NUM
ejpam-5705	18	16	2	2	NUM
ejpam-5705	18	17	of	of	ADP
ejpam-5705	18	18	13	13	NUM
ejpam-5705	18	19	identities	identity	NOUN
ejpam-5705	18	20	to	to	PART
ejpam-5705	18	21	ensure	ensure	VERB
ejpam-5705	18	22	that	that	SCONJ
ejpam-5705	18	23	the	the	DET
ejpam-5705	18	24	lattice	lattice	NOUN
ejpam-5705	18	25	of	of	ADP
ejpam-5705	18	26	all	all	DET
ejpam-5705	18	27	filters	filter	NOUN
ejpam-5705	18	28	in	in	ADP
ejpam-5705	18	29	an	an	DET
ejpam-5705	18	30	adl	adl	NOUN
ejpam-5705	18	31	becomes	become	VERB
ejpam-5705	18	32	a	a	DET
ejpam-5705	18	33	complete	complete	ADJ
ejpam-5705	18	34	lattice	lattice	NOUN
ejpam-5705	18	35	.	.	PUNCT
ejpam-5705	19	1	g.nanaji	g.nanaji	PROPN
ejpam-5705	19	2	rao	rao	NOUN
ejpam-5705	19	3	and	and	CCONJ
ejpam-5705	19	4	habtamu	habtamu	VERB
ejpam-5705	19	5	tiruneh	tiruneh	PROPN
ejpam-5705	19	6	alemu[3	alemu[3	NUM
ejpam-5705	19	7	,	,	PUNCT
ejpam-5705	19	8	4	4	NUM
ejpam-5705	19	9	]	]	PUNCT
ejpam-5705	19	10	developed	develop	VERB
ejpam-5705	19	11	the	the	DET
ejpam-5705	19	12	hypothesis	hypothesis	NOUN
ejpam-5705	19	13	of	of	ADP
ejpam-5705	19	14	almost	almost	ADV
ejpam-5705	19	15	lattice	lattice	NOUN
ejpam-5705	19	16	(	(	PUNCT
ejpam-5705	19	17	al	al	PROPN
ejpam-5705	19	18	)	)	PUNCT
ejpam-5705	19	19	as	as	ADP
ejpam-5705	19	20	a	a	DET
ejpam-5705	19	21	common	common	ADJ
ejpam-5705	19	22	abstraction	abstraction	NOUN
ejpam-5705	19	23	of	of	ADP
ejpam-5705	19	24	all	all	DET
ejpam-5705	19	25	lattice	lattice	ADJ
ejpam-5705	19	26	-	-	PUNCT
ejpam-5705	19	27	theoretic	theoretic	ADJ
ejpam-5705	19	28	generalisations	generalisation	NOUN
ejpam-5705	19	29	of	of	ADP
ejpam-5705	19	30	boolean	boolean	ADJ
ejpam-5705	19	31	algebra	algebra	NOUN
ejpam-5705	19	32	,	,	PUNCT
ejpam-5705	19	33	such	such	ADJ
ejpam-5705	19	34	as	as	ADP
ejpam-5705	19	35	distributive	distributive	ADJ
ejpam-5705	19	36	lattices	lattice	NOUN
ejpam-5705	19	37	,	,	PUNCT
ejpam-5705	19	38	almost	almost	ADV
ejpam-5705	19	39	distributive	distributive	ADJ
ejpam-5705	19	40	lattices	lattice	NOUN
ejpam-5705	19	41	,	,	PUNCT
ejpam-5705	19	42	and	and	CCONJ
ejpam-5705	19	43	lattices	lattice	NOUN
ejpam-5705	19	44	.	.	PUNCT
ejpam-5705	20	1	distributive	distributive	ADJ
ejpam-5705	20	2	pseudo	pseudo	NOUN
ejpam-5705	20	3	-	-	ADJ
ejpam-5705	20	4	complemented	complement	VERB
ejpam-5705	20	5	lattices[5	lattices[5	PROPN
ejpam-5705	20	6	]	]	PUNCT
ejpam-5705	20	7	form	form	NOUN
ejpam-5705	20	8	an	an	DET
ejpam-5705	20	9	extensively	extensively	ADV
ejpam-5705	20	10	studied	study	VERB
ejpam-5705	20	11	class	class	NOUN
ejpam-5705	20	12	of	of	ADP
ejpam-5705	20	13	distributive	distributive	ADJ
ejpam-5705	20	14	lattices	lattice	NOUN
ejpam-5705	20	15	.	.	PUNCT
ejpam-5705	21	1	examples	example	NOUN
ejpam-5705	21	2	are	be	AUX
ejpam-5705	21	3	the	the	DET
ejpam-5705	21	4	lattice	lattice	NOUN
ejpam-5705	21	5	of	of	ADP
ejpam-5705	21	6	all	all	DET
ejpam-5705	21	7	open	open	ADJ
ejpam-5705	21	8	sets	set	NOUN
ejpam-5705	21	9	of	of	ADP
ejpam-5705	21	10	a	a	DET
ejpam-5705	21	11	topological	topological	ADJ
ejpam-5705	21	12	space	space	NOUN
ejpam-5705	21	13	,	,	PUNCT
ejpam-5705	21	14	the	the	DET
ejpam-5705	21	15	lattice	lattice	NOUN
ejpam-5705	21	16	of	of	ADP
ejpam-5705	21	17	all	all	DET
ejpam-5705	21	18	ideals	ideal	NOUN
ejpam-5705	21	19	of	of	ADP
ejpam-5705	21	20	a	a	DET
ejpam-5705	21	21	distributive	distributive	ADJ
ejpam-5705	21	22	lattice	lattice	NOUN
ejpam-5705	21	23	with	with	ADP
ejpam-5705	21	24	zero	zero	NUM
ejpam-5705	21	25	and	and	CCONJ
ejpam-5705	21	26	the	the	DET
ejpam-5705	21	27	lattice	lattice	NOUN
ejpam-5705	21	28	of	of	ADP
ejpam-5705	21	29	all	all	DET
ejpam-5705	21	30	congruences	congruence	NOUN
ejpam-5705	21	31	of	of	ADP
ejpam-5705	21	32	an	an	DET
ejpam-5705	21	33	arbitrary	arbitrary	ADJ
ejpam-5705	21	34	lattice	lattice	NOUN
ejpam-5705	21	35	.	.	PUNCT
ejpam-5705	22	1	lattice	lattice	PROPN
ejpam-5705	22	2	which	which	PRON
ejpam-5705	22	3	are	be	AUX
ejpam-5705	22	4	just	just	ADV
ejpam-5705	22	5	pseudo	pseudo	NOUN
ejpam-5705	22	6	-	-	VERB
ejpam-5705	22	7	complemented	complement	VERB
ejpam-5705	22	8	have	have	AUX
ejpam-5705	22	9	been	be	AUX
ejpam-5705	22	10	studied	study	VERB
ejpam-5705	22	11	in	in	ADP
ejpam-5705	22	12	detail	detail	NOUN
ejpam-5705	22	13	,	,	PUNCT
ejpam-5705	22	14	however	however	ADV
ejpam-5705	22	15	,	,	PUNCT
ejpam-5705	22	16	the	the	DET
ejpam-5705	22	17	most	most	ADV
ejpam-5705	22	18	interesting	interesting	ADJ
ejpam-5705	22	19	results	result	NOUN
ejpam-5705	22	20	require	require	VERB
ejpam-5705	22	21	at	at	ADP
ejpam-5705	22	22	least	least	ADJ
ejpam-5705	22	23	the	the	DET
ejpam-5705	22	24	assumption	assumption	NOUN
ejpam-5705	22	25	of	of	ADP
ejpam-5705	22	26	modularity	modularity	NOUN
ejpam-5705	22	27	,	,	PUNCT
ejpam-5705	22	28	sometimes	sometimes	ADV
ejpam-5705	22	29	distributivity	distributivity	NOUN
ejpam-5705	22	30	.	.	PUNCT
ejpam-5705	23	1	with	with	ADP
ejpam-5705	23	2	this	this	DET
ejpam-5705	23	3	motivation	motivation	NOUN
ejpam-5705	23	4	,	,	PUNCT
ejpam-5705	23	5	bandaru	bandaru	NOUN
ejpam-5705	23	6	et	et	NOUN
ejpam-5705	23	7	al.[6	al.[6	PROPN
ejpam-5705	23	8	]	]	PUNCT
ejpam-5705	23	9	introduced	introduce	VERB
ejpam-5705	23	10	the	the	DET
ejpam-5705	23	11	notion	notion	NOUN
ejpam-5705	23	12	of	of	ADP
ejpam-5705	23	13	paradistributive	paradistributive	ADJ
ejpam-5705	23	14	latticoid	latticoid	NOUN
ejpam-5705	23	15	and	and	CCONJ
ejpam-5705	23	16	studied	study	VERB
ejpam-5705	23	17	its	its	PRON
ejpam-5705	23	18	important	important	ADJ
ejpam-5705	23	19	properties	property	NOUN
ejpam-5705	23	20	.	.	PUNCT
ejpam-5705	24	1	also	also	ADV
ejpam-5705	24	2	,	,	PUNCT
ejpam-5705	24	3	authors	author	NOUN
ejpam-5705	24	4	given	give	VERB
ejpam-5705	24	5	its	its	PRON
ejpam-5705	24	6	subdirect	subdirect	NOUN
ejpam-5705	24	7	representation	representation	NOUN
ejpam-5705	24	8	.	.	PUNCT
ejpam-5705	25	1	later	later	ADV
ejpam-5705	25	2	,	,	PUNCT
ejpam-5705	25	3	ajjarapu	ajjarapu	PROPN
ejpam-5705	25	4	et	et	NOUN
ejpam-5705	25	5	al.[7	al.[7	PROPN
ejpam-5705	25	6	]	]	PUNCT
ejpam-5705	25	7	introduced	introduce	VERB
ejpam-5705	25	8	the	the	DET
ejpam-5705	25	9	concept	concept	NOUN
ejpam-5705	25	10	of	of	ADP
ejpam-5705	25	11	parapseudo	parapseudo	NOUN
ejpam-5705	25	12	-	-	NOUN
ejpam-5705	25	13	complementation	complementation	NOUN
ejpam-5705	25	14	on	on	ADP
ejpam-5705	25	15	a	a	DET
ejpam-5705	25	16	paradistributive	paradistributive	ADJ
ejpam-5705	25	17	latticoid	latticoid	NOUN
ejpam-5705	25	18	and	and	CCONJ
ejpam-5705	25	19	its	its	PRON
ejpam-5705	25	20	characterisations	characterisation	NOUN
ejpam-5705	25	21	are	be	AUX
ejpam-5705	25	22	given	give	VERB
ejpam-5705	25	23	.	.	PUNCT
ejpam-5705	26	1	later	later	ADV
ejpam-5705	26	2	,	,	PUNCT
ejpam-5705	26	3	bandaru	bandaru	PROPN
ejpam-5705	26	4	et	et	PROPN
ejpam-5705	26	5	al	al	PROPN
ejpam-5705	26	6	.	.	PUNCT
ejpam-5705	27	1	[	[	X
ejpam-5705	27	2	8	8	NUM
ejpam-5705	27	3	]	]	PUNCT
ejpam-5705	27	4	introduced	introduce	VERB
ejpam-5705	27	5	the	the	DET
ejpam-5705	27	6	concept	concept	NOUN
ejpam-5705	27	7	of	of	ADP
ejpam-5705	27	8	a	a	DET
ejpam-5705	27	9	normal	normal	ADJ
ejpam-5705	27	10	paradistributive	paradistributive	ADJ
ejpam-5705	27	11	latticoid	latticoid	NOUN
ejpam-5705	27	12	and	and	CCONJ
ejpam-5705	27	13	characterized	characterize	VERB
ejpam-5705	27	14	in	in	ADP
ejpam-5705	27	15	terms	term	NOUN
ejpam-5705	27	16	of	of	ADP
ejpam-5705	27	17	the	the	DET
ejpam-5705	27	18	prime	prime	ADJ
ejpam-5705	27	19	filters	filter	NOUN
ejpam-5705	27	20	and	and	CCONJ
ejpam-5705	27	21	minimal	minimal	ADJ
ejpam-5705	27	22	prime	prime	ADJ
ejpam-5705	27	23	filters	filter	NOUN
ejpam-5705	27	24	.	.	PUNCT
ejpam-5705	28	1	also	also	ADV
ejpam-5705	28	2	,	,	PUNCT
ejpam-5705	28	3	ajjarapu	ajjarapu	PROPN
ejpam-5705	28	4	et	et	PROPN
ejpam-5705	28	5	al	al	PROPN
ejpam-5705	28	6	.	.	PUNCT
ejpam-5705	29	1	[	[	X
ejpam-5705	29	2	9	9	NUM
ejpam-5705	29	3	]	]	PUNCT
ejpam-5705	29	4	studied	study	VERB
ejpam-5705	29	5	topological	topological	ADJ
ejpam-5705	29	6	properties	property	NOUN
ejpam-5705	29	7	of	of	ADP
ejpam-5705	29	8	(	(	PUNCT
ejpam-5705	29	9	minimal	minimal	ADJ
ejpam-5705	29	10	)	)	PUNCT
ejpam-5705	29	11	prime	prime	ADJ
ejpam-5705	29	12	filters	filter	NOUN
ejpam-5705	29	13	in	in	ADP
ejpam-5705	29	14	a	a	DET
ejpam-5705	29	15	paradistributive	paradistributive	ADJ
ejpam-5705	29	16	latticoid	latticoid	NOUN
ejpam-5705	29	17	.	.	PUNCT
ejpam-5705	30	1	the	the	DET
ejpam-5705	30	2	main	main	ADJ
ejpam-5705	30	3	purpose	purpose	NOUN
ejpam-5705	30	4	of	of	ADP
ejpam-5705	30	5	this	this	DET
ejpam-5705	30	6	paper	paper	NOUN
ejpam-5705	30	7	is	be	AUX
ejpam-5705	30	8	to	to	PART
ejpam-5705	30	9	introduce	introduce	VERB
ejpam-5705	30	10	the	the	DET
ejpam-5705	30	11	concept	concept	NOUN
ejpam-5705	30	12	of	of	ADP
ejpam-5705	30	13	•-pdl	•-pdl	X
ejpam-5705	30	14	.	.	PUNCT
ejpam-5705	31	1	in	in	ADP
ejpam-5705	31	2	section	section	NOUN
ejpam-5705	31	3	1	1	NUM
ejpam-5705	31	4	,	,	PUNCT
ejpam-5705	31	5	basic	basic	ADJ
ejpam-5705	31	6	introduction	introduction	NOUN
ejpam-5705	31	7	is	be	AUX
ejpam-5705	31	8	given	give	VERB
ejpam-5705	31	9	,	,	PUNCT
ejpam-5705	31	10	in	in	ADP
ejpam-5705	31	11	continuation	continuation	NOUN
ejpam-5705	31	12	to	to	ADP
ejpam-5705	31	13	this	this	PRON
ejpam-5705	31	14	in	in	ADP
ejpam-5705	31	15	section	section	NOUN
ejpam-5705	31	16	2	2	NUM
ejpam-5705	31	17	,	,	PUNCT
ejpam-5705	31	18	preliminaries	preliminary	NOUN
ejpam-5705	31	19	related	relate	VERB
ejpam-5705	31	20	to	to	ADP
ejpam-5705	31	21	this	this	DET
ejpam-5705	31	22	topic	topic	NOUN
ejpam-5705	31	23	are	be	AUX
ejpam-5705	31	24	mentioned	mention	VERB
ejpam-5705	31	25	.	.	PUNCT
ejpam-5705	32	1	further	far	ADV
ejpam-5705	32	2	,	,	PUNCT
ejpam-5705	32	3	in	in	ADP
ejpam-5705	32	4	section	section	NOUN
ejpam-5705	32	5	3	3	NUM
ejpam-5705	32	6	,	,	PUNCT
ejpam-5705	32	7	we	we	PRON
ejpam-5705	32	8	discuss	discuss	VERB
ejpam-5705	32	9	the	the	DET
ejpam-5705	32	10	basic	basic	ADJ
ejpam-5705	32	11	definition	definition	NOUN
ejpam-5705	32	12	of	of	ADP
ejpam-5705	32	13	•-pdl	•-pdl	PUNCT
ejpam-5705	32	14	and	and	CCONJ
ejpam-5705	32	15	study	study	VERB
ejpam-5705	32	16	various	various	ADJ
ejpam-5705	32	17	results	result	NOUN
ejpam-5705	32	18	associated	associate	VERB
ejpam-5705	32	19	to	to	ADP
ejpam-5705	32	20	the	the	DET
ejpam-5705	32	21	concept	concept	NOUN
ejpam-5705	32	22	,	,	PUNCT
ejpam-5705	32	23	connecting	connect	VERB
ejpam-5705	32	24	the	the	DET
ejpam-5705	32	25	results	result	NOUN
ejpam-5705	32	26	to	to	ADP
ejpam-5705	32	27	boolean	boolean	ADJ
ejpam-5705	32	28	algebra	algebra	NOUN
ejpam-5705	32	29	.	.	PUNCT
ejpam-5705	33	1	later	later	ADV
ejpam-5705	33	2	,	,	PUNCT
ejpam-5705	33	3	in	in	ADP
ejpam-5705	33	4	section	section	NOUN
ejpam-5705	33	5	4	4	NUM
ejpam-5705	33	6	,	,	PUNCT
ejpam-5705	33	7	we	we	PRON
ejpam-5705	33	8	discuss	discuss	VERB
ejpam-5705	33	9	the	the	DET
ejpam-5705	33	10	definition	definition	NOUN
ejpam-5705	33	11	of	of	ADP
ejpam-5705	33	12	dense	dense	ADJ
ejpam-5705	33	13	elements	element	NOUN
ejpam-5705	33	14	,	,	PUNCT
ejpam-5705	33	15	and	and	CCONJ
ejpam-5705	33	16	prove	prove	VERB
ejpam-5705	33	17	certain	certain	ADJ
ejpam-5705	33	18	characterization	characterization	NOUN
ejpam-5705	33	19	theorems	theorem	NOUN
ejpam-5705	33	20	for	for	ADP
ejpam-5705	33	21	dense	dense	ADJ
ejpam-5705	33	22	elements	element	NOUN
ejpam-5705	33	23	.	.	PUNCT
ejpam-5705	34	1	we	we	PRON
ejpam-5705	34	2	conclude	conclude	VERB
ejpam-5705	34	3	this	this	DET
ejpam-5705	34	4	section	section	NOUN
ejpam-5705	34	5	by	by	ADP
ejpam-5705	34	6	introducing	introduce	VERB
ejpam-5705	34	7	disjunctive	disjunctive	ADJ
ejpam-5705	34	8	pdl	pdl	NOUN
ejpam-5705	34	9	and	and	CCONJ
ejpam-5705	34	10	provide	provide	VERB
ejpam-5705	34	11	results	result	NOUN
ejpam-5705	34	12	related	relate	VERB
ejpam-5705	34	13	to	to	ADP
ejpam-5705	34	14	disjunctive	disjunctive	ADJ
ejpam-5705	34	15	and	and	CCONJ
ejpam-5705	34	16	boolean	boolean	ADJ
ejpam-5705	34	17	algebra	algebra	NOUN
ejpam-5705	34	18	.	.	PUNCT
ejpam-5705	35	1	2	2	X
ejpam-5705	35	2	.	.	X
ejpam-5705	35	3	preliminaries	preliminary	NOUN
ejpam-5705	35	4	first	first	ADV
ejpam-5705	35	5	we	we	PRON
ejpam-5705	35	6	recall	recall	VERB
ejpam-5705	35	7	the	the	DET
ejpam-5705	35	8	necessary	necessary	ADJ
ejpam-5705	35	9	definitions	definition	NOUN
ejpam-5705	35	10	and	and	CCONJ
ejpam-5705	35	11	results	result	NOUN
ejpam-5705	35	12	from	from	ADP
ejpam-5705	35	13	[	[	X
ejpam-5705	35	14	6	6	NUM
ejpam-5705	35	15	]	]	PUNCT
ejpam-5705	35	16	.	.	PUNCT
ejpam-5705	36	1	definition	definition	NOUN
ejpam-5705	36	2	1	1	NUM
ejpam-5705	36	3	(	(	PUNCT
ejpam-5705	36	4	[	[	X
ejpam-5705	36	5	6	6	NUM
ejpam-5705	36	6	]	]	NUM
ejpam-5705	36	7	)	)	PUNCT
ejpam-5705	36	8	.	.	PUNCT
ejpam-5705	37	1	an	an	DET
ejpam-5705	37	2	algebra	algebra	NOUN
ejpam-5705	37	3	(	(	PUNCT
ejpam-5705	37	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	37	5	,	,	PUNCT
ejpam-5705	37	6	1	1	NUM
ejpam-5705	37	7	)	)	PUNCT
ejpam-5705	37	8	of	of	ADP
ejpam-5705	37	9	type	type	NOUN
ejpam-5705	37	10	(	(	PUNCT
ejpam-5705	37	11	2,2,0	2,2,0	NOUN
ejpam-5705	37	12	)	)	PUNCT
ejpam-5705	37	13	is	be	AUX
ejpam-5705	37	14	called	call	VERB
ejpam-5705	37	15	a	a	DET
ejpam-5705	37	16	paradistributive	paradistributive	ADJ
ejpam-5705	37	17	latticoid	latticoid	NOUN
ejpam-5705	37	18	,	,	PUNCT
ejpam-5705	37	19	abbreviated	abbreviate	VERB
ejpam-5705	37	20	as	as	ADP
ejpam-5705	37	21	pdl	pdl	NOUN
ejpam-5705	37	22	,	,	PUNCT
ejpam-5705	37	23	if	if	SCONJ
ejpam-5705	37	24	it	it	PRON
ejpam-5705	37	25	assures	assure	VERB
ejpam-5705	37	26	the	the	DET
ejpam-5705	37	27	subsequent	subsequent	ADJ
ejpam-5705	37	28	axioms	axiom	NOUN
ejpam-5705	37	29	:	:	PUNCT
ejpam-5705	37	30	(	(	PUNCT
ejpam-5705	37	31	ld∨	ld∨	NOUN
ejpam-5705	37	32	)	)	PUNCT
ejpam-5705	37	33	∂1	∂1	ADV
ejpam-5705	37	34	∨	∨	NUM
ejpam-5705	37	35	(	(	PUNCT
ejpam-5705	37	36	∂2	∂2	PROPN
ejpam-5705	37	37	∧	∧	PROPN
ejpam-5705	37	38	∂3	∂3	NUM
ejpam-5705	37	39	)	)	PUNCT
ejpam-5705	38	1	=	=	SYM
ejpam-5705	38	2	(	(	PUNCT
ejpam-5705	38	3	∂1	∂1	PROPN
ejpam-5705	38	4	∨	∨	NUM
ejpam-5705	38	5	∂2	∂2	NOUN
ejpam-5705	38	6	)	)	PUNCT
ejpam-5705	38	7	∧	∧	NOUN
ejpam-5705	38	8	(	(	PUNCT
ejpam-5705	38	9	∂1	∂1	ADJ
ejpam-5705	38	10	∨	∨	NUM
ejpam-5705	38	11	∂3	∂3	NUM
ejpam-5705	38	12	)	)	PUNCT
ejpam-5705	38	13	,	,	PUNCT
ejpam-5705	38	14	(	(	PUNCT
ejpam-5705	38	15	rd∨	rd∨	X
ejpam-5705	38	16	)	)	PUNCT
ejpam-5705	38	17	(	(	PUNCT
ejpam-5705	38	18	∂1	∂1	X
ejpam-5705	38	19	∧	∧	PROPN
ejpam-5705	38	20	∂2	∂2	PROPN
ejpam-5705	38	21	)	)	PUNCT
ejpam-5705	38	22	∨	∨	NOUN
ejpam-5705	38	23	∂3	∂3	NOUN
ejpam-5705	38	24	=	=	PUNCT
ejpam-5705	38	25	(	(	PUNCT
ejpam-5705	38	26	∂1	∂1	ADJ
ejpam-5705	38	27	∨	∨	NUM
ejpam-5705	38	28	∂3	∂3	NOUN
ejpam-5705	38	29	)	)	PUNCT
ejpam-5705	39	1	∧	∧	NOUN
ejpam-5705	39	2	(	(	PUNCT
ejpam-5705	39	3	∂2	∂2	PROPN
ejpam-5705	39	4	∨	∨	NUM
ejpam-5705	39	5	∂3	∂3	NUM
ejpam-5705	39	6	)	)	PUNCT
ejpam-5705	39	7	,	,	PUNCT
ejpam-5705	39	8	(	(	PUNCT
ejpam-5705	39	9	l1	l1	PROPN
ejpam-5705	39	10	)	)	PUNCT
ejpam-5705	39	11	(	(	PUNCT
ejpam-5705	39	12	∂1	∂1	PROPN
ejpam-5705	39	13	∨	∨	NUM
ejpam-5705	39	14	∂2	∂2	NOUN
ejpam-5705	39	15	)	)	PUNCT
ejpam-5705	39	16	∧	∧	NOUN
ejpam-5705	39	17	∂2	∂2	NOUN
ejpam-5705	39	18	=	=	SYM
ejpam-5705	39	19	∂2	∂2	NOUN
ejpam-5705	39	20	,	,	PUNCT
ejpam-5705	39	21	(	(	PUNCT
ejpam-5705	39	22	l2	l2	NOUN
ejpam-5705	39	23	)	)	PUNCT
ejpam-5705	39	24	(	(	PUNCT
ejpam-5705	39	25	∂1	∂1	PROPN
ejpam-5705	39	26	∨	∨	NUM
ejpam-5705	39	27	∂2	∂2	NOUN
ejpam-5705	39	28	)	)	PUNCT
ejpam-5705	39	29	∧	∧	NOUN
ejpam-5705	39	30	∂1	∂1	ADJ
ejpam-5705	39	31	=	=	SYM
ejpam-5705	39	32	∂1	∂1	ADJ
ejpam-5705	39	33	,	,	PUNCT
ejpam-5705	39	34	(	(	PUNCT
ejpam-5705	39	35	l3	l3	NOUN
ejpam-5705	39	36	)	)	PUNCT
ejpam-5705	39	37	∂1	∂1	NOUN
ejpam-5705	39	38	∨	∨	X
ejpam-5705	39	39	(	(	PUNCT
ejpam-5705	39	40	∂1	∂1	PROPN
ejpam-5705	39	41	∧	∧	PROPN
ejpam-5705	39	42	∂2	∂2	NOUN
ejpam-5705	39	43	)	)	PUNCT
ejpam-5705	39	44	=	=	SYM
ejpam-5705	40	1	∂1	∂1	ADJ
ejpam-5705	40	2	,	,	PUNCT
ejpam-5705	40	3	(	(	PUNCT
ejpam-5705	40	4	i1	i1	PROPN
ejpam-5705	40	5	)	)	PUNCT
ejpam-5705	40	6	∂1	∂1	PROPN
ejpam-5705	40	7	∨	∨	NUM
ejpam-5705	40	8	1	1	NUM
ejpam-5705	40	9	=	=	SYM
ejpam-5705	40	10	1	1	NUM
ejpam-5705	40	11	,	,	PUNCT
ejpam-5705	40	12	for	for	ADP
ejpam-5705	40	13	any	any	DET
ejpam-5705	40	14	∂1	∂1	ADJ
ejpam-5705	40	15	,	,	PUNCT
ejpam-5705	40	16	∂2	∂2	PROPN
ejpam-5705	40	17	,	,	PUNCT
ejpam-5705	40	18	∂3	∂3	NOUN
ejpam-5705	40	19	∈	∈	PROPN
ejpam-5705	40	20	v	v	NOUN
ejpam-5705	40	21	.	.	PUNCT
ejpam-5705	41	1	for	for	ADP
ejpam-5705	41	2	any	any	DET
ejpam-5705	41	3	∂1	∂1	ADJ
ejpam-5705	41	4	,	,	PUNCT
ejpam-5705	41	5	∂2	∂2	PROPN
ejpam-5705	41	6	∈	∈	PROPN
ejpam-5705	41	7	v	v	NOUN
ejpam-5705	41	8	,	,	PUNCT
ejpam-5705	41	9	we	we	PRON
ejpam-5705	41	10	say	say	VERB
ejpam-5705	41	11	that	that	SCONJ
ejpam-5705	41	12	∂1	∂1	ADJ
ejpam-5705	41	13	is	be	AUX
ejpam-5705	41	14	less	less	ADJ
ejpam-5705	41	15	than	than	ADP
ejpam-5705	41	16	or	or	CCONJ
ejpam-5705	41	17	equal	equal	ADJ
ejpam-5705	41	18	to	to	ADP
ejpam-5705	41	19	∂2	∂2	NOUN
ejpam-5705	41	20	and	and	CCONJ
ejpam-5705	41	21	write	write	VERB
ejpam-5705	41	22	∂1	∂1	ADJ
ejpam-5705	41	23	≤	≤	ADJ
ejpam-5705	41	24	∂2	∂2	NOUN
ejpam-5705	41	25	if	if	SCONJ
ejpam-5705	41	26	∂1	∂1	ADJ
ejpam-5705	41	27	∧	∧	PROPN
ejpam-5705	41	28	∂2	∂2	NOUN
ejpam-5705	41	29	=	=	SYM
ejpam-5705	41	30	∂1	∂1	ADJ
ejpam-5705	41	31	or	or	CCONJ
ejpam-5705	41	32	equivalently	equivalently	ADV
ejpam-5705	41	33	∂1	∂1	ADJ
ejpam-5705	41	34	∨	∨	NUM
ejpam-5705	41	35	∂2	∂2	NOUN
ejpam-5705	41	36	=	=	SYM
ejpam-5705	41	37	∂2	∂2	NOUN
ejpam-5705	41	38	and	and	CCONJ
ejpam-5705	41	39	it	it	PRON
ejpam-5705	41	40	can	can	AUX
ejpam-5705	41	41	be	be	AUX
ejpam-5705	41	42	easily	easily	ADV
ejpam-5705	41	43	observed	observe	VERB
ejpam-5705	41	44	that	that	SCONJ
ejpam-5705	41	45	≤	≤	NUM
ejpam-5705	41	46	is	be	AUX
ejpam-5705	41	47	a	a	DET
ejpam-5705	41	48	partial	partial	ADJ
ejpam-5705	41	49	order	order	NOUN
ejpam-5705	41	50	on	on	ADP
ejpam-5705	41	51	v	v	NOUN
ejpam-5705	41	52	.	.	PUNCT
ejpam-5705	42	1	we	we	PRON
ejpam-5705	42	2	can	can	AUX
ejpam-5705	42	3	observe	observe	VERB
ejpam-5705	42	4	that	that	SCONJ
ejpam-5705	42	5	,	,	PUNCT
ejpam-5705	42	6	the	the	DET
ejpam-5705	42	7	element	element	NOUN
ejpam-5705	42	8	1	1	NUM
ejpam-5705	42	9	,	,	PUNCT
ejpam-5705	42	10	in	in	ADP
ejpam-5705	42	11	definition	definition	NOUN
ejpam-5705	42	12	1	1	NUM
ejpam-5705	42	13	,	,	PUNCT
ejpam-5705	42	14	is	be	AUX
ejpam-5705	42	15	the	the	DET
ejpam-5705	42	16	greatest	great	ADJ
ejpam-5705	42	17	element	element	NOUN
ejpam-5705	42	18	with	with	ADP
ejpam-5705	42	19	respect	respect	NOUN
ejpam-5705	42	20	to	to	ADP
ejpam-5705	42	21	the	the	DET
ejpam-5705	42	22	partial	partial	ADJ
ejpam-5705	42	23	ordering	ordering	NOUN
ejpam-5705	42	24	≤.	≤.	PROPN
ejpam-5705	42	25	example	example	NOUN
ejpam-5705	42	26	1	1	NUM
ejpam-5705	42	27	(	(	PUNCT
ejpam-5705	42	28	[	[	X
ejpam-5705	42	29	6	6	NUM
ejpam-5705	42	30	]	]	PUNCT
ejpam-5705	42	31	)	)	PUNCT
ejpam-5705	42	32	.	.	PUNCT
ejpam-5705	43	1	let	let	VERB
ejpam-5705	43	2	v	v	PART
ejpam-5705	43	3	be	be	AUX
ejpam-5705	43	4	a	a	DET
ejpam-5705	43	5	non	non	ADJ
ejpam-5705	43	6	-	-	ADJ
ejpam-5705	43	7	empty	empty	ADJ
ejpam-5705	43	8	set	set	NOUN
ejpam-5705	43	9	.	.	PUNCT
ejpam-5705	44	1	fix	fix	VERB
ejpam-5705	44	2	some	some	DET
ejpam-5705	44	3	element	element	NOUN
ejpam-5705	44	4	g	g	PROPN
ejpam-5705	44	5	∈	∈	PROPN
ejpam-5705	44	6	v	v	NOUN
ejpam-5705	44	7	.	.	PUNCT
ejpam-5705	45	1	then	then	ADV
ejpam-5705	45	2	,	,	PUNCT
ejpam-5705	45	3	for	for	ADP
ejpam-5705	45	4	any	any	DET
ejpam-5705	45	5	r.	r.	PROPN
ejpam-5705	45	6	bandaru	bandaru	PROPN
ejpam-5705	45	7	et	et	PROPN
ejpam-5705	45	8	al	al	PROPN
ejpam-5705	45	9	.	.	PUNCT
ejpam-5705	45	10	/	/	SYM
ejpam-5705	45	11	eur	eur	PROPN
ejpam-5705	45	12	.	.	PUNCT
ejpam-5705	46	1	j.	j.	PROPN
ejpam-5705	46	2	pure	pure	PROPN
ejpam-5705	46	3	appl	appl	PROPN
ejpam-5705	46	4	.	.	PROPN
ejpam-5705	46	5	math	math	PROPN
ejpam-5705	46	6	,	,	PUNCT
ejpam-5705	46	7	18	18	NUM
ejpam-5705	46	8	(	(	PUNCT
ejpam-5705	46	9	2	2	NUM
ejpam-5705	46	10	)	)	PUNCT
ejpam-5705	46	11	(	(	PUNCT
ejpam-5705	46	12	2025	2025	NUM
ejpam-5705	46	13	)	)	PUNCT
ejpam-5705	46	14	,	,	PUNCT
ejpam-5705	46	15	5705	5705	NUM
ejpam-5705	46	16	3	3	NUM
ejpam-5705	46	17	of	of	ADP
ejpam-5705	46	18	13	13	NUM
ejpam-5705	46	19	℘	℘	NOUN
ejpam-5705	46	20	,	,	PUNCT
ejpam-5705	46	21	ℏ	ℏ	PROPN
ejpam-5705	46	22	∈	∈	NOUN
ejpam-5705	46	23	v	v	AUX
ejpam-5705	46	24	define	define	VERB
ejpam-5705	46	25	∨	∨	NOUN
ejpam-5705	46	26	and	and	CCONJ
ejpam-5705	46	27	∧	∧	NOUN
ejpam-5705	46	28	on	on	ADP
ejpam-5705	46	29	v	v	NUM
ejpam-5705	46	30	by	by	ADP
ejpam-5705	46	31	℘	℘	PROPN
ejpam-5705	46	32	∨	∨	NUM
ejpam-5705	46	33	ℏ	ℏ	NOUN
ejpam-5705	46	34	=	=	PUNCT
ejpam-5705	46	35	{	{	PUNCT
ejpam-5705	46	36	℘	℘	PROPN
ejpam-5705	46	37	ℏ	ℏ	PROPN
ejpam-5705	46	38	̸=	̸=	PROPN
ejpam-5705	46	39	g	g	NOUN
ejpam-5705	46	40	g	g	PROPN
ejpam-5705	46	41	ℏ	ℏ	PROPN
ejpam-5705	46	42	=	=	SYM
ejpam-5705	46	43	g	g	NOUN
ejpam-5705	46	44	and	and	CCONJ
ejpam-5705	46	45	℘	℘	VERB
ejpam-5705	46	46	∧	∧	PROPN
ejpam-5705	46	47	ℏ	ℏ	NOUN
ejpam-5705	46	48	=	=	PUNCT
ejpam-5705	46	49	{	{	PUNCT
ejpam-5705	47	1	ℏ	ℏ	PROPN
ejpam-5705	47	2	ℏ	ℏ	NOUN
ejpam-5705	47	3	̸=	̸=	PROPN
ejpam-5705	47	4	g	g	PROPN
ejpam-5705	47	5	℘	℘	NUM
ejpam-5705	47	6	ℏ	ℏ	NOUN
ejpam-5705	47	7	=	=	SYM
ejpam-5705	47	8	g	g	PROPN
ejpam-5705	47	9	then	then	ADV
ejpam-5705	47	10	(	(	PUNCT
ejpam-5705	47	11	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	47	12	,	,	PUNCT
ejpam-5705	47	13	g	g	NOUN
ejpam-5705	47	14	)	)	PUNCT
ejpam-5705	47	15	is	be	AUX
ejpam-5705	47	16	a	a	DET
ejpam-5705	47	17	disconnected	disconnected	ADJ
ejpam-5705	47	18	pdl	pdl	NOUN
ejpam-5705	47	19	with	with	ADP
ejpam-5705	47	20	g	g	PROPN
ejpam-5705	47	21	as	as	ADP
ejpam-5705	47	22	its	its	PRON
ejpam-5705	47	23	greatest	great	ADJ
ejpam-5705	47	24	element	element	NOUN
ejpam-5705	47	25	.	.	PUNCT
ejpam-5705	48	1	according	accord	VERB
ejpam-5705	48	2	to	to	ADP
ejpam-5705	48	3	lemma	lemma	PROPN
ejpam-5705	48	4	7	7	NUM
ejpam-5705	48	5	,	,	PUNCT
ejpam-5705	48	6	theorem	theorem	ADJ
ejpam-5705	48	7	1	1	NUM
ejpam-5705	48	8	,	,	PUNCT
ejpam-5705	48	9	lemma	lemma	PROPN
ejpam-5705	48	10	8	8	NUM
ejpam-5705	48	11	,	,	PUNCT
ejpam-5705	48	12	theorem	theorem	VERB
ejpam-5705	48	13	4	4	NUM
ejpam-5705	48	14	,	,	PUNCT
ejpam-5705	48	15	corollary	corollary	ADJ
ejpam-5705	48	16	8	8	NUM
ejpam-5705	48	17	,	,	PUNCT
ejpam-5705	48	18	lemma	lemma	PROPN
ejpam-5705	48	19	9	9	NUM
ejpam-5705	48	20	and	and	CCONJ
ejpam-5705	48	21	lemma	lemma	PROPN
ejpam-5705	48	22	10	10	NUM
ejpam-5705	48	23	of	of	ADP
ejpam-5705	48	24	[	[	X
ejpam-5705	48	25	6	6	NUM
ejpam-5705	48	26	]	]	PUNCT
ejpam-5705	48	27	,	,	PUNCT
ejpam-5705	48	28	the	the	DET
ejpam-5705	48	29	following	follow	VERB
ejpam-5705	48	30	lemma	lemma	PROPN
ejpam-5705	48	31	holds	hold	VERB
ejpam-5705	48	32	.	.	PUNCT
ejpam-5705	49	1	lemma	lemma	PROPN
ejpam-5705	49	2	1	1	NUM
ejpam-5705	49	3	(	(	PUNCT
ejpam-5705	49	4	[	[	X
ejpam-5705	49	5	6	6	NUM
ejpam-5705	49	6	]	]	PUNCT
ejpam-5705	49	7	)	)	PUNCT
ejpam-5705	49	8	.	.	PUNCT
ejpam-5705	50	1	let	let	AUX
ejpam-5705	50	2	(	(	PUNCT
ejpam-5705	50	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	50	4	,	,	PUNCT
ejpam-5705	50	5	1	1	NUM
ejpam-5705	50	6	)	)	PUNCT
ejpam-5705	50	7	be	be	AUX
ejpam-5705	50	8	a	a	DET
ejpam-5705	50	9	pdl	pdl	NOUN
ejpam-5705	50	10	.	.	PUNCT
ejpam-5705	51	1	then	then	ADV
ejpam-5705	51	2	for	for	ADP
ejpam-5705	51	3	any	any	DET
ejpam-5705	51	4	∂1	∂1	ADJ
ejpam-5705	51	5	,	,	PUNCT
ejpam-5705	51	6	∂2	∂2	PROPN
ejpam-5705	51	7	,	,	PUNCT
ejpam-5705	51	8	∂3	∂3	PROPN
ejpam-5705	51	9	,	,	PUNCT
ejpam-5705	51	10	∂4	∂4	PROPN
ejpam-5705	51	11	∈	∈	PROPN
ejpam-5705	51	12	v	v	NOUN
ejpam-5705	51	13	,	,	PUNCT
ejpam-5705	51	14	we	we	PRON
ejpam-5705	51	15	have	have	VERB
ejpam-5705	51	16	the	the	DET
ejpam-5705	51	17	following	following	NOUN
ejpam-5705	51	18	:	:	PUNCT
ejpam-5705	51	19	(	(	PUNCT
ejpam-5705	51	20	1	1	X
ejpam-5705	51	21	)	)	SYM
ejpam-5705	51	22	1	1	NUM
ejpam-5705	51	23	∧	∧	PROPN
ejpam-5705	51	24	∂1	∂1	ADJ
ejpam-5705	51	25	=	=	SYM
ejpam-5705	51	26	∂1	∂1	ADJ
ejpam-5705	51	27	,	,	PUNCT
ejpam-5705	51	28	(	(	PUNCT
ejpam-5705	51	29	2	2	X
ejpam-5705	51	30	)	)	PUNCT
ejpam-5705	51	31	∂1	∂1	NOUN
ejpam-5705	51	32	∧	∧	PROPN
ejpam-5705	51	33	1	1	NUM
ejpam-5705	51	34	=	=	SYM
ejpam-5705	51	35	∂1	∂1	ADJ
ejpam-5705	51	36	,	,	PUNCT
ejpam-5705	51	37	(	(	PUNCT
ejpam-5705	51	38	3	3	NUM
ejpam-5705	51	39	)	)	PUNCT
ejpam-5705	51	40	1	1	NUM
ejpam-5705	51	41	∨	∨	NUM
ejpam-5705	51	42	∂1	∂1	NOUN
ejpam-5705	51	43	=	=	SYM
ejpam-5705	51	44	1	1	NUM
ejpam-5705	51	45	,	,	PUNCT
ejpam-5705	51	46	(	(	PUNCT
ejpam-5705	51	47	4	4	NUM
ejpam-5705	51	48	)	)	PUNCT
ejpam-5705	51	49	(	(	PUNCT
ejpam-5705	51	50	∂1	∂1	PROPN
ejpam-5705	51	51	∨	∨	NUM
ejpam-5705	51	52	∂2	∂2	NOUN
ejpam-5705	51	53	)	)	PUNCT
ejpam-5705	51	54	∧	∧	NOUN
ejpam-5705	51	55	∂3	∂3	NOUN
ejpam-5705	51	56	=	=	SYM
ejpam-5705	51	57	(	(	PUNCT
ejpam-5705	51	58	∂1	∂1	X
ejpam-5705	51	59	∧	∧	PROPN
ejpam-5705	51	60	∂3	∂3	NUM
ejpam-5705	51	61	)	)	PUNCT
ejpam-5705	51	62	∨	∨	PROPN
ejpam-5705	51	63	(	(	PUNCT
ejpam-5705	51	64	∂2	∂2	PROPN
ejpam-5705	51	65	∧	∧	PROPN
ejpam-5705	51	66	∂3	∂3	NUM
ejpam-5705	51	67	)	)	PUNCT
ejpam-5705	51	68	,	,	PUNCT
ejpam-5705	51	69	(	(	PUNCT
ejpam-5705	51	70	5	5	X
ejpam-5705	51	71	)	)	PUNCT
ejpam-5705	51	72	∂1	∂1	ADJ
ejpam-5705	51	73	∨	∨	NOUN
ejpam-5705	51	74	(	(	PUNCT
ejpam-5705	51	75	∂2	∂2	PROPN
ejpam-5705	51	76	∧	∧	PROPN
ejpam-5705	51	77	∂3	∂3	NUM
ejpam-5705	51	78	)	)	PUNCT
ejpam-5705	51	79	=	=	PUNCT
ejpam-5705	52	1	∂1	∂1	ADJ
ejpam-5705	52	2	∨	∨	NUM
ejpam-5705	52	3	(	(	PUNCT
ejpam-5705	52	4	∂3	∂3	NUM
ejpam-5705	52	5	∧	∧	PROPN
ejpam-5705	52	6	∂2	∂2	PROPN
ejpam-5705	52	7	)	)	PUNCT
ejpam-5705	52	8	,	,	PUNCT
ejpam-5705	52	9	(	(	PUNCT
ejpam-5705	52	10	6	6	X
ejpam-5705	52	11	)	)	PUNCT
ejpam-5705	52	12	the	the	DET
ejpam-5705	52	13	operation	operation	NOUN
ejpam-5705	52	14	∨	∨	NOUN
ejpam-5705	52	15	is	be	AUX
ejpam-5705	52	16	associative	associative	ADJ
ejpam-5705	52	17	in	in	ADP
ejpam-5705	52	18	v	v	NOUN
ejpam-5705	52	19	i.e.	i.e.	X
ejpam-5705	52	20	,	,	PUNCT
ejpam-5705	52	21	∂1	∂1	ADJ
ejpam-5705	52	22	∨	∨	NUM
ejpam-5705	52	23	(	(	PUNCT
ejpam-5705	52	24	∂2	∂2	PROPN
ejpam-5705	52	25	∨	∨	NUM
ejpam-5705	52	26	∂3	∂3	NUM
ejpam-5705	52	27	)	)	PUNCT
ejpam-5705	52	28	=	=	SYM
ejpam-5705	52	29	(	(	PUNCT
ejpam-5705	52	30	∂1	∂1	PROPN
ejpam-5705	52	31	∨	∨	NUM
ejpam-5705	52	32	∂2	∂2	NOUN
ejpam-5705	52	33	)	)	PUNCT
ejpam-5705	52	34	∨	∨	NUM
ejpam-5705	52	35	∂3	∂3	NOUN
ejpam-5705	52	36	,	,	PUNCT
ejpam-5705	52	37	(	(	PUNCT
ejpam-5705	52	38	7	7	X
ejpam-5705	52	39	)	)	PUNCT
ejpam-5705	52	40	the	the	DET
ejpam-5705	52	41	set	set	NOUN
ejpam-5705	52	42	vµ1	vµ1	NOUN
ejpam-5705	52	43	=	=	SYM
ejpam-5705	53	1	{	{	PUNCT
ejpam-5705	53	2	∂1	∂1	PROPN
ejpam-5705	53	3	∈	∈	PROPN
ejpam-5705	53	4	v	v	ADP
ejpam-5705	53	5	|	|	ADV
ejpam-5705	53	6	µ1	µ1	NOUN
ejpam-5705	53	7	≤	≤	NOUN
ejpam-5705	53	8	∂1	∂1	ADJ
ejpam-5705	53	9	}	}	PUNCT
ejpam-5705	53	10	=	=	SYM
ejpam-5705	53	11	{	{	PUNCT
ejpam-5705	53	12	µ1	µ1	PROPN
ejpam-5705	53	13	∨	∨	NOUN
ejpam-5705	53	14	∂1	∂1	NOUN
ejpam-5705	53	15	|	|	CCONJ
ejpam-5705	53	16	∂1	∂1	X
ejpam-5705	53	17	∈	∈	PROPN
ejpam-5705	53	18	v	v	NOUN
ejpam-5705	53	19	}	}	PUNCT
ejpam-5705	53	20	is	be	AUX
ejpam-5705	53	21	a	a	DET
ejpam-5705	53	22	distributive	distributive	ADJ
ejpam-5705	53	23	lattice	lattice	NOUN
ejpam-5705	53	24	under	under	ADP
ejpam-5705	53	25	induced	induced	ADJ
ejpam-5705	53	26	operations	operation	NOUN
ejpam-5705	53	27	∨	∨	NOUN
ejpam-5705	53	28	and	and	CCONJ
ejpam-5705	53	29	∧	∧	PROPN
ejpam-5705	53	30	with	with	ADP
ejpam-5705	53	31	µ1	µ1	PROPN
ejpam-5705	53	32	as	as	ADP
ejpam-5705	53	33	its	its	PRON
ejpam-5705	53	34	least	least	ADJ
ejpam-5705	53	35	element	element	NOUN
ejpam-5705	53	36	,	,	PUNCT
ejpam-5705	53	37	(	(	PUNCT
ejpam-5705	53	38	8)	8)	NUM
ejpam-5705	53	39	∂4	∂4	NOUN
ejpam-5705	53	40	∨	∨	NUM
ejpam-5705	53	41	{	{	PUNCT
ejpam-5705	53	42	∂1	∂1	PROPN
ejpam-5705	53	43	∧	∧	PROPN
ejpam-5705	53	44	(	(	PUNCT
ejpam-5705	53	45	∂2	∂2	PROPN
ejpam-5705	53	46	∧	∧	PROPN
ejpam-5705	53	47	∂3	∂3	NUM
ejpam-5705	53	48	)	)	PUNCT
ejpam-5705	53	49	}	}	PUNCT
ejpam-5705	54	1	=	=	NOUN
ejpam-5705	54	2	∂4	∂4	NOUN
ejpam-5705	54	3	∨	∨	NUM
ejpam-5705	54	4	{	{	PUNCT
ejpam-5705	54	5	(	(	PUNCT
ejpam-5705	54	6	∂1	∂1	X
ejpam-5705	54	7	∧	∧	PROPN
ejpam-5705	54	8	∂2	∂2	NOUN
ejpam-5705	54	9	)	)	PUNCT
ejpam-5705	54	10	∧	∧	NOUN
ejpam-5705	54	11	∂3	∂3	PROPN
ejpam-5705	54	12	}	}	PUNCT
ejpam-5705	54	13	,	,	PUNCT
ejpam-5705	54	14	(	(	PUNCT
ejpam-5705	54	15	9	9	X
ejpam-5705	54	16	)	)	PUNCT
ejpam-5705	54	17	∂1	∂1	ADJ
ejpam-5705	54	18	∨	∨	NOUN
ejpam-5705	54	19	(	(	PUNCT
ejpam-5705	54	20	∂2	∂2	PROPN
ejpam-5705	54	21	∨	∨	NUM
ejpam-5705	54	22	∂3	∂3	NUM
ejpam-5705	54	23	)	)	PUNCT
ejpam-5705	54	24	=	=	PUNCT
ejpam-5705	54	25	∂1	∂1	ADJ
ejpam-5705	54	26	∨	∨	NUM
ejpam-5705	54	27	(	(	PUNCT
ejpam-5705	54	28	∂3	∂3	PROPN
ejpam-5705	54	29	∨	∨	NUM
ejpam-5705	54	30	∂2	∂2	PROPN
ejpam-5705	54	31	)	)	PUNCT
ejpam-5705	54	32	,	,	PUNCT
ejpam-5705	54	33	(	(	PUNCT
ejpam-5705	54	34	10	10	NUM
ejpam-5705	54	35	)	)	PUNCT
ejpam-5705	54	36	∂1	∂1	ADJ
ejpam-5705	54	37	∨	∨	NOUN
ejpam-5705	54	38	∂2	∂2	NOUN
ejpam-5705	54	39	=	=	SYM
ejpam-5705	54	40	1	1	NUM
ejpam-5705	55	1	if	if	SCONJ
ejpam-5705	56	1	and	and	CCONJ
ejpam-5705	56	2	only	only	ADV
ejpam-5705	56	3	if	if	SCONJ
ejpam-5705	56	4	∂2	∂2	PROPN
ejpam-5705	56	5	∨	∨	NOUN
ejpam-5705	56	6	∂1	∂1	X
ejpam-5705	56	7	=	=	SYM
ejpam-5705	56	8	1	1	NUM
ejpam-5705	56	9	,	,	PUNCT
ejpam-5705	56	10	(	(	PUNCT
ejpam-5705	56	11	11	11	NUM
ejpam-5705	56	12	)	)	PUNCT
ejpam-5705	56	13	∂1	∂1	ADJ
ejpam-5705	56	14	∧	∧	PROPN
ejpam-5705	56	15	∂2	∂2	NOUN
ejpam-5705	56	16	=	=	SYM
ejpam-5705	56	17	∂2	∂2	NOUN
ejpam-5705	56	18	∧	∧	PROPN
ejpam-5705	56	19	∂1	∂1	ADJ
ejpam-5705	56	20	whenever	whenever	SCONJ
ejpam-5705	56	21	∂1	∂1	PRON
ejpam-5705	56	22	∨	∨	NOUN
ejpam-5705	56	23	∂2	∂2	NOUN
ejpam-5705	56	24	=	=	SYM
ejpam-5705	56	25	1	1	X
ejpam-5705	56	26	.	.	PUNCT
ejpam-5705	56	27	theorem	theorem	NOUN
ejpam-5705	56	28	1	1	NUM
ejpam-5705	56	29	(	(	PUNCT
ejpam-5705	56	30	[	[	X
ejpam-5705	56	31	6	6	NUM
ejpam-5705	56	32	]	]	NUM
ejpam-5705	56	33	)	)	PUNCT
ejpam-5705	56	34	.	.	PUNCT
ejpam-5705	57	1	an	an	DET
ejpam-5705	57	2	algebra	algebra	NOUN
ejpam-5705	57	3	(	(	PUNCT
ejpam-5705	57	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	57	5	,	,	PUNCT
ejpam-5705	57	6	1	1	NUM
ejpam-5705	57	7	)	)	PUNCT
ejpam-5705	57	8	of	of	ADP
ejpam-5705	57	9	type	type	NOUN
ejpam-5705	57	10	(	(	PUNCT
ejpam-5705	57	11	2	2	NUM
ejpam-5705	57	12	,	,	PUNCT
ejpam-5705	57	13	2	2	NUM
ejpam-5705	57	14	,	,	PUNCT
ejpam-5705	57	15	0	0	NUM
ejpam-5705	57	16	)	)	PUNCT
ejpam-5705	57	17	is	be	AUX
ejpam-5705	57	18	a	a	DET
ejpam-5705	57	19	pdl	pdl	NOUN
ejpam-5705	57	20	if	if	SCONJ
ejpam-5705	58	1	and	and	CCONJ
ejpam-5705	58	2	only	only	ADV
ejpam-5705	58	3	if	if	SCONJ
ejpam-5705	58	4	it	it	PRON
ejpam-5705	58	5	satisfies	satisfy	VERB
ejpam-5705	58	6	the	the	DET
ejpam-5705	58	7	following	following	NOUN
ejpam-5705	58	8	:	:	PUNCT
ejpam-5705	58	9	(	(	PUNCT
ejpam-5705	58	10	ld∨	ld∨	NOUN
ejpam-5705	58	11	)	)	PUNCT
ejpam-5705	58	12	∂1	∂1	ADV
ejpam-5705	58	13	∨	∨	NUM
ejpam-5705	58	14	(	(	PUNCT
ejpam-5705	58	15	∂2	∂2	PROPN
ejpam-5705	58	16	∧	∧	PROPN
ejpam-5705	58	17	∂3	∂3	NUM
ejpam-5705	58	18	)	)	PUNCT
ejpam-5705	59	1	=	=	SYM
ejpam-5705	59	2	(	(	PUNCT
ejpam-5705	59	3	∂1	∂1	PROPN
ejpam-5705	59	4	∨	∨	NUM
ejpam-5705	59	5	∂2	∂2	NOUN
ejpam-5705	59	6	)	)	PUNCT
ejpam-5705	59	7	∧	∧	NOUN
ejpam-5705	59	8	(	(	PUNCT
ejpam-5705	59	9	∂1	∂1	ADJ
ejpam-5705	59	10	∨	∨	NUM
ejpam-5705	59	11	∂3	∂3	NUM
ejpam-5705	59	12	)	)	PUNCT
ejpam-5705	59	13	,	,	PUNCT
ejpam-5705	59	14	(	(	PUNCT
ejpam-5705	59	15	rd∨	rd∨	X
ejpam-5705	59	16	)	)	PUNCT
ejpam-5705	59	17	(	(	PUNCT
ejpam-5705	59	18	∂1	∂1	X
ejpam-5705	59	19	∧	∧	PROPN
ejpam-5705	59	20	∂2	∂2	PROPN
ejpam-5705	59	21	)	)	PUNCT
ejpam-5705	59	22	∨	∨	NOUN
ejpam-5705	59	23	∂3	∂3	NOUN
ejpam-5705	59	24	=	=	PUNCT
ejpam-5705	59	25	(	(	PUNCT
ejpam-5705	59	26	∂1	∂1	ADJ
ejpam-5705	59	27	∨	∨	NUM
ejpam-5705	59	28	∂3	∂3	NOUN
ejpam-5705	59	29	)	)	PUNCT
ejpam-5705	60	1	∧	∧	NOUN
ejpam-5705	60	2	(	(	PUNCT
ejpam-5705	60	3	∂2	∂2	PROPN
ejpam-5705	60	4	∨	∨	NUM
ejpam-5705	60	5	∂3	∂3	NUM
ejpam-5705	60	6	)	)	PUNCT
ejpam-5705	60	7	,	,	PUNCT
ejpam-5705	60	8	(	(	PUNCT
ejpam-5705	60	9	rd∧	rd∧	PROPN
ejpam-5705	60	10	)	)	PUNCT
ejpam-5705	60	11	(	(	PUNCT
ejpam-5705	60	12	∂1	∂1	PROPN
ejpam-5705	60	13	∨	∨	NUM
ejpam-5705	60	14	∂2	∂2	NOUN
ejpam-5705	60	15	)	)	PUNCT
ejpam-5705	60	16	∧	∧	NOUN
ejpam-5705	60	17	∂3	∂3	NOUN
ejpam-5705	60	18	=	=	SYM
ejpam-5705	60	19	(	(	PUNCT
ejpam-5705	60	20	∂1	∂1	X
ejpam-5705	60	21	∧	∧	PROPN
ejpam-5705	60	22	∂3	∂3	NUM
ejpam-5705	60	23	)	)	PUNCT
ejpam-5705	60	24	∨	∨	PROPN
ejpam-5705	60	25	(	(	PUNCT
ejpam-5705	60	26	∂2	∂2	PROPN
ejpam-5705	60	27	∧	∧	PROPN
ejpam-5705	60	28	∂3	∂3	NUM
ejpam-5705	60	29	)	)	PUNCT
ejpam-5705	60	30	,	,	PUNCT
ejpam-5705	60	31	(	(	PUNCT
ejpam-5705	60	32	l1	l1	PROPN
ejpam-5705	60	33	)	)	PUNCT
ejpam-5705	60	34	(	(	PUNCT
ejpam-5705	60	35	∂1	∂1	PROPN
ejpam-5705	60	36	∨	∨	NUM
ejpam-5705	60	37	∂2	∂2	NOUN
ejpam-5705	60	38	)	)	PUNCT
ejpam-5705	60	39	∧	∧	NOUN
ejpam-5705	60	40	∂2	∂2	NOUN
ejpam-5705	60	41	=	=	SYM
ejpam-5705	60	42	∂2	∂2	PROPN
ejpam-5705	60	43	,	,	PUNCT
ejpam-5705	60	44	(	(	PUNCT
ejpam-5705	60	45	l3	l3	PROPN
ejpam-5705	60	46	)	)	PUNCT
ejpam-5705	60	47	∂1	∂1	NOUN
ejpam-5705	60	48	∨	∨	X
ejpam-5705	60	49	(	(	PUNCT
ejpam-5705	60	50	∂1	∂1	PROPN
ejpam-5705	60	51	∧	∧	PROPN
ejpam-5705	60	52	∂2	∂2	NOUN
ejpam-5705	60	53	)	)	PUNCT
ejpam-5705	60	54	=	=	SYM
ejpam-5705	61	1	∂1	∂1	ADJ
ejpam-5705	61	2	,	,	PUNCT
ejpam-5705	61	3	(	(	PUNCT
ejpam-5705	61	4	i1	i1	PROPN
ejpam-5705	61	5	)	)	PUNCT
ejpam-5705	61	6	∂1	∂1	PROPN
ejpam-5705	61	7	∨	∨	NUM
ejpam-5705	61	8	1	1	NUM
ejpam-5705	61	9	=	=	SYM
ejpam-5705	61	10	1	1	NUM
ejpam-5705	61	11	,	,	PUNCT
ejpam-5705	61	12	(	(	PUNCT
ejpam-5705	61	13	i2	i2	PROPN
ejpam-5705	61	14	)	)	PUNCT
ejpam-5705	61	15	1	1	NUM
ejpam-5705	61	16	∧	∧	PROPN
ejpam-5705	61	17	∂1	∂1	ADJ
ejpam-5705	61	18	=	=	SYM
ejpam-5705	61	19	∂1	∂1	ADJ
ejpam-5705	61	20	,	,	PUNCT
ejpam-5705	61	21	for	for	ADP
ejpam-5705	61	22	all	all	DET
ejpam-5705	61	23	∂1	∂1	ADJ
ejpam-5705	61	24	,	,	PUNCT
ejpam-5705	61	25	∂2	∂2	PROPN
ejpam-5705	61	26	,	,	PUNCT
ejpam-5705	61	27	∂3	∂3	NOUN
ejpam-5705	61	28	∈	∈	PROPN
ejpam-5705	61	29	v	v	NOUN
ejpam-5705	61	30	.	.	PUNCT
ejpam-5705	62	1	definition	definition	NOUN
ejpam-5705	62	2	2	2	NUM
ejpam-5705	62	3	(	(	PUNCT
ejpam-5705	62	4	[	[	X
ejpam-5705	62	5	6	6	NUM
ejpam-5705	62	6	]	]	NUM
ejpam-5705	62	7	)	)	PUNCT
ejpam-5705	62	8	.	.	PUNCT
ejpam-5705	63	1	a	a	DET
ejpam-5705	63	2	paradistributive	paradistributive	ADJ
ejpam-5705	63	3	latticoid	latticoid	NOUN
ejpam-5705	63	4	(	(	PUNCT
ejpam-5705	63	5	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	63	6	,	,	PUNCT
ejpam-5705	63	7	1	1	NUM
ejpam-5705	63	8	)	)	PUNCT
ejpam-5705	63	9	is	be	AUX
ejpam-5705	63	10	said	say	VERB
ejpam-5705	63	11	to	to	PART
ejpam-5705	63	12	be	be	AUX
ejpam-5705	63	13	associative	associative	ADJ
ejpam-5705	63	14	if	if	SCONJ
ejpam-5705	63	15	it	it	PRON
ejpam-5705	63	16	satisfies	satisfy	VERB
ejpam-5705	63	17	the	the	DET
ejpam-5705	63	18	following	follow	VERB
ejpam-5705	63	19	condition	condition	NOUN
ejpam-5705	63	20	∂1	∂1	ADP
ejpam-5705	63	21	∧	∧	PROPN
ejpam-5705	63	22	(	(	PUNCT
ejpam-5705	63	23	∂2	∂2	NOUN
ejpam-5705	63	24	∧	∧	PROPN
ejpam-5705	63	25	∂3	∂3	NUM
ejpam-5705	63	26	)	)	PUNCT
ejpam-5705	63	27	=	=	SYM
ejpam-5705	63	28	(	(	PUNCT
ejpam-5705	63	29	∂1	∂1	X
ejpam-5705	63	30	∧	∧	PROPN
ejpam-5705	63	31	∂2	∂2	NOUN
ejpam-5705	63	32	)	)	PUNCT
ejpam-5705	63	33	∧	∧	NOUN
ejpam-5705	63	34	∂3	∂3	NOUN
ejpam-5705	63	35	for	for	ADP
ejpam-5705	63	36	all	all	DET
ejpam-5705	63	37	∂1	∂1	ADJ
ejpam-5705	63	38	,	,	PUNCT
ejpam-5705	63	39	∂2	∂2	PROPN
ejpam-5705	63	40	,	,	PUNCT
ejpam-5705	63	41	∂3	∂3	NOUN
ejpam-5705	63	42	∈	∈	PROPN
ejpam-5705	63	43	v.	v.	PROPN
ejpam-5705	63	44	r.	r.	PROPN
ejpam-5705	63	45	bandaru	bandaru	PROPN
ejpam-5705	64	1	et	et	PROPN
ejpam-5705	64	2	al	al	PROPN
ejpam-5705	64	3	.	.	PUNCT
ejpam-5705	64	4	/	/	SYM
ejpam-5705	64	5	eur	eur	PROPN
ejpam-5705	64	6	.	.	PUNCT
ejpam-5705	65	1	j.	j.	PROPN
ejpam-5705	65	2	pure	pure	PROPN
ejpam-5705	65	3	appl	appl	PROPN
ejpam-5705	65	4	.	.	PROPN
ejpam-5705	65	5	math	math	PROPN
ejpam-5705	65	6	,	,	PUNCT
ejpam-5705	65	7	18	18	NUM
ejpam-5705	65	8	(	(	PUNCT
ejpam-5705	65	9	2	2	NUM
ejpam-5705	65	10	)	)	PUNCT
ejpam-5705	65	11	(	(	PUNCT
ejpam-5705	65	12	2025	2025	NUM
ejpam-5705	65	13	)	)	PUNCT
ejpam-5705	65	14	,	,	PUNCT
ejpam-5705	65	15	5705	5705	NUM
ejpam-5705	65	16	4	4	NUM
ejpam-5705	65	17	of	of	ADP
ejpam-5705	65	18	13	13	NUM
ejpam-5705	65	19	definition	definition	NOUN
ejpam-5705	65	20	3	3	NUM
ejpam-5705	65	21	(	(	PUNCT
ejpam-5705	65	22	[	[	X
ejpam-5705	65	23	6	6	NUM
ejpam-5705	65	24	]	]	PUNCT
ejpam-5705	65	25	)	)	PUNCT
ejpam-5705	65	26	.	.	PUNCT
ejpam-5705	66	1	let	let	VERB
ejpam-5705	66	2	v	v	PART
ejpam-5705	66	3	be	be	AUX
ejpam-5705	66	4	a	a	DET
ejpam-5705	66	5	pdl	pdl	NOUN
ejpam-5705	66	6	.	.	PUNCT
ejpam-5705	67	1	then	then	ADV
ejpam-5705	67	2	,	,	PUNCT
ejpam-5705	67	3	an	an	DET
ejpam-5705	67	4	element	element	NOUN
ejpam-5705	67	5	µ1	µ1	PROPN
ejpam-5705	67	6	∈	∈	NOUN
ejpam-5705	67	7	v	v	NOUN
ejpam-5705	67	8	is	be	AUX
ejpam-5705	67	9	said	say	VERB
ejpam-5705	67	10	to	to	PART
ejpam-5705	67	11	be	be	AUX
ejpam-5705	67	12	a	a	DET
ejpam-5705	67	13	minimal	minimal	ADJ
ejpam-5705	67	14	element	element	NOUN
ejpam-5705	67	15	if	if	SCONJ
ejpam-5705	67	16	for	for	ADP
ejpam-5705	67	17	any	any	DET
ejpam-5705	67	18	u	u	PROPN
ejpam-5705	67	19	∈	∈	PROPN
ejpam-5705	67	20	v	v	NOUN
ejpam-5705	67	21	,	,	PUNCT
ejpam-5705	67	22	u	u	NOUN
ejpam-5705	67	23	≤	≤	X
ejpam-5705	67	24	µ1	µ1	PROPN
ejpam-5705	67	25	⇒	⇒	NOUN
ejpam-5705	67	26	u	u	NOUN
ejpam-5705	67	27	=	=	PROPN
ejpam-5705	67	28	µ1	µ1	PROPN
ejpam-5705	67	29	.	.	PUNCT
ejpam-5705	68	1	lemma	lemma	PROPN
ejpam-5705	68	2	2	2	NUM
ejpam-5705	68	3	(	(	PUNCT
ejpam-5705	68	4	[	[	X
ejpam-5705	68	5	6	6	NUM
ejpam-5705	68	6	]	]	PUNCT
ejpam-5705	68	7	)	)	PUNCT
ejpam-5705	68	8	.	.	PUNCT
ejpam-5705	69	1	let	let	VERB
ejpam-5705	69	2	v	v	PART
ejpam-5705	69	3	be	be	AUX
ejpam-5705	69	4	a	a	DET
ejpam-5705	69	5	pdl	pdl	NOUN
ejpam-5705	69	6	.	.	PUNCT
ejpam-5705	70	1	then	then	ADV
ejpam-5705	70	2	,	,	PUNCT
ejpam-5705	70	3	for	for	ADP
ejpam-5705	70	4	any	any	DET
ejpam-5705	70	5	µ1	µ1	PROPN
ejpam-5705	70	6	∈	∈	PROPN
ejpam-5705	70	7	v	v	NOUN
ejpam-5705	70	8	,	,	PUNCT
ejpam-5705	70	9	the	the	DET
ejpam-5705	70	10	following	follow	VERB
ejpam-5705	70	11	are	be	AUX
ejpam-5705	70	12	equivalent	equivalent	ADJ
ejpam-5705	70	13	:	:	PUNCT
ejpam-5705	70	14	(	(	PUNCT
ejpam-5705	70	15	1	1	X
ejpam-5705	70	16	)	)	PUNCT
ejpam-5705	70	17	µ1	µ1	NOUN
ejpam-5705	70	18	is	be	AUX
ejpam-5705	70	19	minimal	minimal	ADJ
ejpam-5705	70	20	,	,	PUNCT
ejpam-5705	70	21	(	(	PUNCT
ejpam-5705	70	22	2	2	NUM
ejpam-5705	70	23	)	)	PUNCT
ejpam-5705	70	24	∂1	∂1	ADJ
ejpam-5705	70	25	∧	∧	PROPN
ejpam-5705	70	26	µ1	µ1	PROPN
ejpam-5705	70	27	=	=	PUNCT
ejpam-5705	70	28	µ1	µ1	NOUN
ejpam-5705	70	29	for	for	ADP
ejpam-5705	70	30	all	all	DET
ejpam-5705	70	31	∂1	∂1	ADJ
ejpam-5705	70	32	∈	∈	PROPN
ejpam-5705	70	33	v	v	NOUN
ejpam-5705	70	34	,	,	PUNCT
ejpam-5705	70	35	(	(	PUNCT
ejpam-5705	70	36	3	3	X
ejpam-5705	70	37	)	)	PUNCT
ejpam-5705	70	38	∂1	∂1	ADJ
ejpam-5705	70	39	∨	∨	NUM
ejpam-5705	70	40	µ1	µ1	NOUN
ejpam-5705	70	41	=	=	SYM
ejpam-5705	70	42	∂1	∂1	ADJ
ejpam-5705	70	43	for	for	ADP
ejpam-5705	70	44	all	all	DET
ejpam-5705	70	45	∂1	∂1	PRON
ejpam-5705	70	46	∈	∈	PROPN
ejpam-5705	70	47	v	v	NOUN
ejpam-5705	70	48	.	.	PUNCT
ejpam-5705	71	1	definition	definition	NOUN
ejpam-5705	71	2	4	4	NUM
ejpam-5705	71	3	(	(	PUNCT
ejpam-5705	71	4	[	[	X
ejpam-5705	71	5	6	6	NUM
ejpam-5705	71	6	]	]	NUM
ejpam-5705	71	7	)	)	PUNCT
ejpam-5705	71	8	.	.	PUNCT
ejpam-5705	72	1	a	a	DET
ejpam-5705	72	2	non	non	ADJ
ejpam-5705	72	3	-	-	ADJ
ejpam-5705	72	4	empty	empty	ADJ
ejpam-5705	72	5	subset	subset	NOUN
ejpam-5705	72	6	f	f	PROPN
ejpam-5705	72	7	of	of	ADP
ejpam-5705	72	8	a	a	DET
ejpam-5705	72	9	pdl	pdl	NOUN
ejpam-5705	72	10	v	v	NOUN
ejpam-5705	72	11	is	be	AUX
ejpam-5705	72	12	said	say	VERB
ejpam-5705	72	13	to	to	PART
ejpam-5705	72	14	be	be	AUX
ejpam-5705	72	15	a	a	DET
ejpam-5705	72	16	filter	filter	NOUN
ejpam-5705	72	17	if	if	SCONJ
ejpam-5705	72	18	it	it	PRON
ejpam-5705	72	19	satisfies	satisfy	VERB
ejpam-5705	72	20	the	the	DET
ejpam-5705	72	21	following	following	NOUN
ejpam-5705	72	22	:	:	PUNCT
ejpam-5705	72	23	∂1	∂1	ADJ
ejpam-5705	72	24	,	,	PUNCT
ejpam-5705	72	25	∂2	∂2	PROPN
ejpam-5705	72	26	∈	∈	PROPN
ejpam-5705	72	27	f	f	PROPN
ejpam-5705	72	28	⇒	⇒	VERB
ejpam-5705	72	29	∂1	∂1	NUM
ejpam-5705	72	30	∧	∧	PROPN
ejpam-5705	72	31	∂2	∂2	PROPN
ejpam-5705	72	32	∈	∈	PROPN
ejpam-5705	72	33	f	f	X
ejpam-5705	72	34	,	,	PUNCT
ejpam-5705	72	35	∂1	∂1	PROPN
ejpam-5705	72	36	∈	∈	PROPN
ejpam-5705	72	37	f	f	X
ejpam-5705	72	38	,	,	PUNCT
ejpam-5705	72	39	µ1	µ1	PROPN
ejpam-5705	72	40	∈	∈	PROPN
ejpam-5705	72	41	v	v	ADP
ejpam-5705	72	42	⇒	⇒	PROPN
ejpam-5705	72	43	µ1	µ1	PROPN
ejpam-5705	72	44	∨	∨	NUM
ejpam-5705	72	45	∂1	∂1	PROPN
ejpam-5705	72	46	∈	∈	PROPN
ejpam-5705	72	47	f.	f.	PROPN
ejpam-5705	72	48	theorem	theorem	VERB
ejpam-5705	72	49	2	2	NUM
ejpam-5705	72	50	(	(	PUNCT
ejpam-5705	72	51	[	[	X
ejpam-5705	72	52	6	6	NUM
ejpam-5705	72	53	]	]	PUNCT
ejpam-5705	72	54	)	)	PUNCT
ejpam-5705	72	55	.	.	PUNCT
ejpam-5705	73	1	let	let	VERB
ejpam-5705	73	2	s	s	PRON
ejpam-5705	73	3	be	be	AUX
ejpam-5705	73	4	a	a	DET
ejpam-5705	73	5	non	non	ADJ
ejpam-5705	73	6	-	-	ADJ
ejpam-5705	73	7	empty	empty	ADJ
ejpam-5705	73	8	subset	subset	NOUN
ejpam-5705	73	9	of	of	ADP
ejpam-5705	73	10	v	v	NOUN
ejpam-5705	73	11	.	.	PUNCT
ejpam-5705	74	1	then	then	ADV
ejpam-5705	74	2	[	[	X
ejpam-5705	74	3	s	s	X
ejpam-5705	74	4	)	)	PUNCT
ejpam-5705	74	5	=	=	SYM
ejpam-5705	74	6	{	{	PUNCT
ejpam-5705	74	7	∂1	∂1	PROPN
ejpam-5705	74	8	∨	∨	NOUN
ejpam-5705	74	9	(	(	PUNCT
ejpam-5705	74	10	n	n	CCONJ
ejpam-5705	74	11	∧	∧	PROPN
ejpam-5705	74	12	i=1	i=1	PROPN
ejpam-5705	74	13	si	si	NOUN
ejpam-5705	74	14	)	)	PUNCT
ejpam-5705	74	15	|	|	ADV
ejpam-5705	74	16	si	si	PROPN
ejpam-5705	74	17	∈	∈	PROPN
ejpam-5705	74	18	s	s	PROPN
ejpam-5705	74	19	,	,	PUNCT
ejpam-5705	74	20	∂1	∂1	PROPN
ejpam-5705	74	21	∈	∈	PROPN
ejpam-5705	74	22	v	v	NOUN
ejpam-5705	74	23	,	,	PUNCT
ejpam-5705	74	24	n	n	X
ejpam-5705	74	25	is	be	AUX
ejpam-5705	74	26	a	a	DET
ejpam-5705	74	27	positive	positive	ADJ
ejpam-5705	74	28	integer	integer	NOUN
ejpam-5705	74	29	}	}	PUNCT
ejpam-5705	74	30	is	be	AUX
ejpam-5705	74	31	the	the	DET
ejpam-5705	74	32	smallest	small	ADJ
ejpam-5705	74	33	filter	filter	NOUN
ejpam-5705	74	34	of	of	ADP
ejpam-5705	74	35	v	v	NOUN
ejpam-5705	74	36	containing	contain	VERB
ejpam-5705	74	37	s.	s.	PROPN
ejpam-5705	74	38	note	note	VERB
ejpam-5705	74	39	that	that	SCONJ
ejpam-5705	74	40	if	if	SCONJ
ejpam-5705	74	41	s	s	VERB
ejpam-5705	74	42	=	=	X
ejpam-5705	74	43	{	{	PUNCT
ejpam-5705	74	44	∂1	∂1	PROPN
ejpam-5705	74	45	}	}	PUNCT
ejpam-5705	74	46	,	,	PUNCT
ejpam-5705	74	47	then	then	ADV
ejpam-5705	74	48	we	we	PRON
ejpam-5705	74	49	write	write	VERB
ejpam-5705	74	50	[	[	X
ejpam-5705	74	51	s	s	X
ejpam-5705	74	52	)	)	PUNCT
ejpam-5705	74	53	=	=	PUNCT
ejpam-5705	75	1	[	[	X
ejpam-5705	75	2	∂1	∂1	X
ejpam-5705	75	3	)	)	PUNCT
ejpam-5705	75	4	,	,	PUNCT
ejpam-5705	75	5	the	the	DET
ejpam-5705	75	6	principal	principal	ADJ
ejpam-5705	75	7	ideal	ideal	NOUN
ejpam-5705	75	8	of	of	ADP
ejpam-5705	75	9	v	v	NUM
ejpam-5705	75	10	generated	generate	VERB
ejpam-5705	75	11	by	by	ADP
ejpam-5705	75	12	‘	'	PUNCT
ejpam-5705	75	13	∂1	∂1	ADJ
ejpam-5705	75	14	’	'	PUNCT
ejpam-5705	75	15	.	.	PUNCT
ejpam-5705	76	1	hence	hence	ADV
ejpam-5705	76	2	[	[	X
ejpam-5705	76	3	∂1	∂1	X
ejpam-5705	76	4	)	)	PUNCT
ejpam-5705	76	5	=	=	SYM
ejpam-5705	76	6	{	{	PUNCT
ejpam-5705	76	7	℘	℘	PROPN
ejpam-5705	76	8	∨	∨	NUM
ejpam-5705	76	9	∂1	∂1	NOUN
ejpam-5705	76	10	|	|	ADV
ejpam-5705	76	11	℘	℘	NOUN
ejpam-5705	76	12	∈	∈	NOUN
ejpam-5705	76	13	v	v	NOUN
ejpam-5705	76	14	}	}	PUNCT
ejpam-5705	76	15	.	.	PUNCT
ejpam-5705	77	1	according	accord	VERB
ejpam-5705	77	2	to	to	ADP
ejpam-5705	77	3	corollary	corollary	ADJ
ejpam-5705	77	4	8	8	NUM
ejpam-5705	77	5	and	and	CCONJ
ejpam-5705	77	6	lemma	lemma	PROPN
ejpam-5705	77	7	12	12	NUM
ejpam-5705	77	8	of	of	ADP
ejpam-5705	77	9	[	[	X
ejpam-5705	77	10	6	6	NUM
ejpam-5705	77	11	]	]	PUNCT
ejpam-5705	77	12	,	,	PUNCT
ejpam-5705	77	13	the	the	DET
ejpam-5705	77	14	following	follow	VERB
ejpam-5705	77	15	lemma	lemma	PROPN
ejpam-5705	77	16	holds	hold	VERB
ejpam-5705	77	17	.	.	PUNCT
ejpam-5705	78	1	lemma	lemma	PROPN
ejpam-5705	78	2	3	3	NUM
ejpam-5705	78	3	(	(	PUNCT
ejpam-5705	78	4	[	[	X
ejpam-5705	78	5	6	6	NUM
ejpam-5705	78	6	]	]	PUNCT
ejpam-5705	78	7	)	)	PUNCT
ejpam-5705	78	8	.	.	PUNCT
ejpam-5705	79	1	let	let	VERB
ejpam-5705	79	2	v	v	PART
ejpam-5705	79	3	be	be	AUX
ejpam-5705	79	4	a	a	DET
ejpam-5705	79	5	pdl	pdl	NOUN
ejpam-5705	79	6	and	and	CCONJ
ejpam-5705	79	7	f	f	PROPN
ejpam-5705	79	8	be	be	AUX
ejpam-5705	79	9	a	a	DET
ejpam-5705	79	10	filter	filter	NOUN
ejpam-5705	79	11	of	of	ADP
ejpam-5705	79	12	v	v	NOUN
ejpam-5705	79	13	.	.	PUNCT
ejpam-5705	80	1	then	then	ADV
ejpam-5705	80	2	for	for	ADP
ejpam-5705	80	3	any	any	DET
ejpam-5705	80	4	∂1	∂1	ADJ
ejpam-5705	80	5	,	,	PUNCT
ejpam-5705	80	6	∂2	∂2	PROPN
ejpam-5705	80	7	∈	∈	PROPN
ejpam-5705	80	8	v	v	NOUN
ejpam-5705	80	9	,	,	PUNCT
ejpam-5705	80	10	we	we	PRON
ejpam-5705	80	11	have	have	VERB
ejpam-5705	80	12	the	the	DET
ejpam-5705	80	13	following	following	NOUN
ejpam-5705	80	14	:	:	PUNCT
ejpam-5705	80	15	(	(	PUNCT
ejpam-5705	80	16	1	1	X
ejpam-5705	80	17	)	)	PUNCT
ejpam-5705	80	18	∂1	∂1	NOUN
ejpam-5705	80	19	∈	∈	PROPN
ejpam-5705	81	1	[	[	X
ejpam-5705	81	2	∂2	∂2	NOUN
ejpam-5705	81	3	)	)	PUNCT
ejpam-5705	82	1	if	if	SCONJ
ejpam-5705	82	2	and	and	CCONJ
ejpam-5705	82	3	only	only	ADV
ejpam-5705	83	1	if	if	SCONJ
ejpam-5705	83	2	∂1	∂1	ADJ
ejpam-5705	83	3	=	=	SYM
ejpam-5705	83	4	∂1	∂1	ADJ
ejpam-5705	83	5	∨	∨	NUM
ejpam-5705	83	6	∂2	∂2	NOUN
ejpam-5705	83	7	for	for	ADP
ejpam-5705	83	8	all	all	DET
ejpam-5705	83	9	∂1	∂1	ADJ
ejpam-5705	83	10	,	,	PUNCT
ejpam-5705	83	11	∂2	∂2	PROPN
ejpam-5705	83	12	∈	∈	PROPN
ejpam-5705	83	13	v	v	NOUN
ejpam-5705	83	14	,	,	PUNCT
ejpam-5705	83	15	(	(	PUNCT
ejpam-5705	83	16	2	2	X
ejpam-5705	83	17	)	)	PUNCT
ejpam-5705	83	18	∂1	∂1	ADJ
ejpam-5705	83	19	∨	∨	NUM
ejpam-5705	83	20	∂2	∂2	NOUN
ejpam-5705	83	21	∈	∈	PROPN
ejpam-5705	84	1	f	f	PROPN
ejpam-5705	85	1	if	if	SCONJ
ejpam-5705	85	2	and	and	CCONJ
ejpam-5705	85	3	only	only	ADV
ejpam-5705	85	4	if	if	SCONJ
ejpam-5705	85	5	∂2	∂2	PROPN
ejpam-5705	85	6	∨	∨	NUM
ejpam-5705	85	7	∂1	∂1	PROPN
ejpam-5705	85	8	∈	∈	PROPN
ejpam-5705	85	9	f	f	X
ejpam-5705	85	10	,	,	PUNCT
ejpam-5705	85	11	(	(	PUNCT
ejpam-5705	85	12	3	3	X
ejpam-5705	85	13	)	)	PUNCT
ejpam-5705	85	14	[	[	X
ejpam-5705	85	15	∂1	∂1	X
ejpam-5705	85	16	∨	∨	NUM
ejpam-5705	85	17	∂2	∂2	NOUN
ejpam-5705	85	18	)	)	PUNCT
ejpam-5705	85	19	=	=	PUNCT
ejpam-5705	86	1	[	[	X
ejpam-5705	86	2	∂2	∂2	NOUN
ejpam-5705	86	3	∨	∨	NUM
ejpam-5705	86	4	∂1	∂1	NUM
ejpam-5705	86	5	)	)	PUNCT
ejpam-5705	86	6	,	,	PUNCT
ejpam-5705	86	7	(	(	PUNCT
ejpam-5705	86	8	4	4	X
ejpam-5705	86	9	)	)	PUNCT
ejpam-5705	86	10	[	[	X
ejpam-5705	86	11	∂1	∂1	X
ejpam-5705	86	12	∧	∧	PROPN
ejpam-5705	86	13	∂2	∂2	NOUN
ejpam-5705	86	14	)	)	PUNCT
ejpam-5705	86	15	=	=	PUNCT
ejpam-5705	87	1	[	[	X
ejpam-5705	87	2	∂2	∂2	NOUN
ejpam-5705	87	3	∧	∧	NOUN
ejpam-5705	87	4	∂1	∂1	ADJ
ejpam-5705	87	5	)	)	PUNCT
ejpam-5705	87	6	=	=	PUNCT
ejpam-5705	88	1	[	[	X
ejpam-5705	88	2	∂1	∂1	X
ejpam-5705	88	3	)	)	PUNCT
ejpam-5705	88	4	∨	∨	NOUN
ejpam-5705	89	1	[	[	X
ejpam-5705	89	2	∂2	∂2	NOUN
ejpam-5705	89	3	)	)	PUNCT
ejpam-5705	89	4	.	.	PUNCT
ejpam-5705	90	1	theorem	theorem	VERB
ejpam-5705	90	2	3	3	NUM
ejpam-5705	90	3	(	(	PUNCT
ejpam-5705	90	4	[	[	X
ejpam-5705	90	5	6	6	NUM
ejpam-5705	90	6	]	]	NUM
ejpam-5705	90	7	)	)	PUNCT
ejpam-5705	90	8	.	.	PUNCT
ejpam-5705	91	1	the	the	DET
ejpam-5705	91	2	collection	collection	NOUN
ejpam-5705	91	3	f	f	X
ejpam-5705	91	4	(	(	PUNCT
ejpam-5705	91	5	v	v	NOUN
ejpam-5705	91	6	)	)	PUNCT
ejpam-5705	91	7	of	of	ADP
ejpam-5705	91	8	all	all	DET
ejpam-5705	91	9	filters	filter	NOUN
ejpam-5705	91	10	of	of	ADP
ejpam-5705	91	11	a	a	DET
ejpam-5705	91	12	pdl	pdl	NOUN
ejpam-5705	91	13	v	v	NOUN
ejpam-5705	91	14	forms	form	NOUN
ejpam-5705	91	15	a	a	DET
ejpam-5705	91	16	distributive	distributive	ADJ
ejpam-5705	91	17	lattice	lattice	NOUN
ejpam-5705	91	18	under	under	ADP
ejpam-5705	91	19	set	set	ADJ
ejpam-5705	91	20	inclusion	inclusion	NOUN
ejpam-5705	91	21	,	,	PUNCT
ejpam-5705	91	22	in	in	ADP
ejpam-5705	91	23	which	which	PRON
ejpam-5705	91	24	,	,	PUNCT
ejpam-5705	91	25	the	the	DET
ejpam-5705	91	26	glb	glb	NOUN
ejpam-5705	91	27	and	and	CCONJ
ejpam-5705	91	28	lub	lub	NOUN
ejpam-5705	91	29	of	of	ADP
ejpam-5705	91	30	any	any	DET
ejpam-5705	91	31	two	two	NUM
ejpam-5705	91	32	filters	filter	NOUN
ejpam-5705	91	33	f	f	PROPN
ejpam-5705	91	34	and	and	CCONJ
ejpam-5705	91	35	g	g	PROPN
ejpam-5705	91	36	are	be	AUX
ejpam-5705	91	37	given	give	VERB
ejpam-5705	91	38	by	by	ADP
ejpam-5705	91	39	f	f	PROPN
ejpam-5705	91	40	∧g	∧g	PROPN
ejpam-5705	91	41	=	=	SYM
ejpam-5705	91	42	f	f	PROPN
ejpam-5705	91	43	∩g	∩g	NOUN
ejpam-5705	91	44	and	and	CCONJ
ejpam-5705	91	45	f	f	PROPN
ejpam-5705	91	46	∨g	∨g	PROPN
ejpam-5705	91	47	=	=	SYM
ejpam-5705	91	48	{	{	PUNCT
ejpam-5705	91	49	∂1	∂1	X
ejpam-5705	91	50	∧	∧	PROPN
ejpam-5705	91	51	∂2	∂2	NOUN
ejpam-5705	91	52	|	|	ADV
ejpam-5705	91	53	∂1	∂1	X
ejpam-5705	91	54	∈	∈	PROPN
ejpam-5705	91	55	f	f	NOUN
ejpam-5705	91	56	and	and	CCONJ
ejpam-5705	91	57	∂2	∂2	PROPN
ejpam-5705	91	58	∈	∈	PROPN
ejpam-5705	91	59	g	g	NOUN
ejpam-5705	91	60	}	}	PUNCT
ejpam-5705	91	61	,	,	PUNCT
ejpam-5705	91	62	respectively	respectively	ADV
ejpam-5705	91	63	.	.	PUNCT
ejpam-5705	92	1	definition	definition	NOUN
ejpam-5705	92	2	5	5	NUM
ejpam-5705	92	3	(	(	PUNCT
ejpam-5705	92	4	[	[	X
ejpam-5705	92	5	6	6	NUM
ejpam-5705	92	6	]	]	NUM
ejpam-5705	92	7	)	)	PUNCT
ejpam-5705	92	8	.	.	PUNCT
ejpam-5705	93	1	a	a	DET
ejpam-5705	93	2	non	non	ADJ
ejpam-5705	93	3	-	-	ADJ
ejpam-5705	93	4	empty	empty	ADJ
ejpam-5705	93	5	subset	subset	NOUN
ejpam-5705	93	6	i	i	PRON
ejpam-5705	93	7	of	of	ADP
ejpam-5705	93	8	a	a	DET
ejpam-5705	93	9	pdl	pdl	NOUN
ejpam-5705	93	10	v	v	NOUN
ejpam-5705	93	11	is	be	AUX
ejpam-5705	93	12	said	say	VERB
ejpam-5705	93	13	to	to	PART
ejpam-5705	93	14	be	be	AUX
ejpam-5705	93	15	an	an	DET
ejpam-5705	93	16	ideal	ideal	NOUN
ejpam-5705	93	17	if	if	SCONJ
ejpam-5705	93	18	it	it	PRON
ejpam-5705	93	19	satisfies	satisfy	VERB
ejpam-5705	93	20	the	the	DET
ejpam-5705	93	21	following	following	NOUN
ejpam-5705	93	22	:	:	PUNCT
ejpam-5705	93	23	∂1	∂1	ADJ
ejpam-5705	93	24	,	,	PUNCT
ejpam-5705	93	25	∂2	∂2	PROPN
ejpam-5705	93	26	∈	∈	PROPN
ejpam-5705	93	27	i	i	PRON
ejpam-5705	93	28	⇒	⇒	VERB
ejpam-5705	93	29	∂1	∂1	NUM
ejpam-5705	93	30	∨	∨	NUM
ejpam-5705	93	31	∂2	∂2	NOUN
ejpam-5705	93	32	∈	∈	PROPN
ejpam-5705	94	1	i	i	PRON
ejpam-5705	94	2	,	,	PUNCT
ejpam-5705	94	3	∂1	∂1	PROPN
ejpam-5705	94	4	∈	∈	PROPN
ejpam-5705	94	5	i	i	PRON
ejpam-5705	94	6	,	,	PUNCT
ejpam-5705	94	7	µ1	µ1	PROPN
ejpam-5705	94	8	∈	∈	PROPN
ejpam-5705	94	9	v	v	ADP
ejpam-5705	94	10	⇒	⇒	NOUN
ejpam-5705	94	11	∂1	∂1	ADJ
ejpam-5705	94	12	∧	∧	PROPN
ejpam-5705	94	13	µ1	µ1	PROPN
ejpam-5705	94	14	∈	∈	PROPN
ejpam-5705	94	15	i.	i.	NOUN
ejpam-5705	94	16	theorem	theorem	VERB
ejpam-5705	94	17	4	4	NUM
ejpam-5705	94	18	(	(	PUNCT
ejpam-5705	94	19	[	[	X
ejpam-5705	94	20	6	6	NUM
ejpam-5705	94	21	]	]	PUNCT
ejpam-5705	94	22	)	)	PUNCT
ejpam-5705	94	23	.	.	PUNCT
ejpam-5705	95	1	let	let	VERB
ejpam-5705	95	2	s	s	PRON
ejpam-5705	95	3	be	be	AUX
ejpam-5705	95	4	a	a	DET
ejpam-5705	95	5	non	non	ADJ
ejpam-5705	95	6	-	-	ADJ
ejpam-5705	95	7	empty	empty	ADJ
ejpam-5705	95	8	subset	subset	NOUN
ejpam-5705	95	9	of	of	ADP
ejpam-5705	95	10	v	v	NOUN
ejpam-5705	95	11	.	.	PUNCT
ejpam-5705	96	1	then	then	ADV
ejpam-5705	96	2	(	(	PUNCT
ejpam-5705	96	3	s	s	X
ejpam-5705	96	4	]	]	X
ejpam-5705	96	5	=	=	X
ejpam-5705	96	6	{	{	PUNCT
ejpam-5705	96	7	(	(	PUNCT
ejpam-5705	96	8	n	n	NUM
ejpam-5705	96	9	∨	∨	NUM
ejpam-5705	96	10	i=1	i=1	PROPN
ejpam-5705	96	11	si	si	ADJ
ejpam-5705	96	12	)	)	PUNCT
ejpam-5705	96	13	∧	∧	NOUN
ejpam-5705	96	14	∂1	∂1	ADJ
ejpam-5705	97	1	|	|	ADV
ejpam-5705	97	2	si	si	PROPN
ejpam-5705	97	3	∈	∈	PROPN
ejpam-5705	97	4	s	s	PROPN
ejpam-5705	97	5	,	,	PUNCT
ejpam-5705	97	6	∂1	∂1	PROPN
ejpam-5705	97	7	∈	∈	PROPN
ejpam-5705	97	8	v	v	NOUN
ejpam-5705	97	9	,	,	PUNCT
ejpam-5705	97	10	n	n	X
ejpam-5705	97	11	is	be	AUX
ejpam-5705	97	12	a	a	DET
ejpam-5705	97	13	positive	positive	ADJ
ejpam-5705	97	14	integer	integer	NOUN
ejpam-5705	97	15	}	}	PUNCT
ejpam-5705	97	16	is	be	AUX
ejpam-5705	97	17	the	the	DET
ejpam-5705	97	18	smallest	small	ADJ
ejpam-5705	97	19	ideal	ideal	NOUN
ejpam-5705	97	20	of	of	ADP
ejpam-5705	97	21	v	v	NOUN
ejpam-5705	97	22	containing	contain	VERB
ejpam-5705	97	23	s.	s.	PROPN
ejpam-5705	97	24	note	note	VERB
ejpam-5705	97	25	that	that	SCONJ
ejpam-5705	97	26	if	if	SCONJ
ejpam-5705	97	27	s	s	VERB
ejpam-5705	97	28	=	=	X
ejpam-5705	97	29	{	{	PUNCT
ejpam-5705	97	30	∂1	∂1	PROPN
ejpam-5705	97	31	}	}	PUNCT
ejpam-5705	97	32	,	,	PUNCT
ejpam-5705	97	33	then	then	ADV
ejpam-5705	97	34	we	we	PRON
ejpam-5705	97	35	write	write	VERB
ejpam-5705	97	36	(	(	PUNCT
ejpam-5705	97	37	s	s	X
ejpam-5705	97	38	]	]	X
ejpam-5705	97	39	=	=	X
ejpam-5705	97	40	(	(	PUNCT
ejpam-5705	97	41	∂1	∂1	PROPN
ejpam-5705	97	42	]	]	X
ejpam-5705	97	43	,	,	PUNCT
ejpam-5705	97	44	the	the	DET
ejpam-5705	97	45	principal	principal	ADJ
ejpam-5705	97	46	ideal	ideal	NOUN
ejpam-5705	97	47	of	of	ADP
ejpam-5705	97	48	v	v	NUM
ejpam-5705	97	49	generated	generate	VERB
ejpam-5705	97	50	by	by	ADP
ejpam-5705	97	51	‘	'	PUNCT
ejpam-5705	97	52	∂1	∂1	ADJ
ejpam-5705	97	53	’	'	PUNCT
ejpam-5705	97	54	.	.	PUNCT
ejpam-5705	98	1	hence	hence	ADV
ejpam-5705	98	2	(	(	PUNCT
ejpam-5705	98	3	∂1	∂1	X
ejpam-5705	98	4	]	]	X
ejpam-5705	98	5	=	=	SYM
ejpam-5705	98	6	{	{	PUNCT
ejpam-5705	98	7	∂1	∂1	ADJ
ejpam-5705	98	8	∧	∧	PROPN
ejpam-5705	98	9	℘	℘	NOUN
ejpam-5705	98	10	|	|	ADV
ejpam-5705	98	11	℘	℘	VERB
ejpam-5705	98	12	∈	∈	NOUN
ejpam-5705	98	13	v	v	NOUN
ejpam-5705	98	14	}	}	PUNCT
ejpam-5705	98	15	.	.	PUNCT
ejpam-5705	99	1	according	accord	VERB
ejpam-5705	99	2	to	to	ADP
ejpam-5705	99	3	corollary	corollary	ADJ
ejpam-5705	99	4	5	5	NUM
ejpam-5705	99	5	,	,	PUNCT
ejpam-5705	99	6	lemma	lemma	PROPN
ejpam-5705	99	7	11	11	NUM
ejpam-5705	99	8	and	and	CCONJ
ejpam-5705	99	9	corollary	corollary	ADJ
ejpam-5705	99	10	6	6	NUM
ejpam-5705	99	11	of	of	ADP
ejpam-5705	99	12	[	[	X
ejpam-5705	99	13	6	6	NUM
ejpam-5705	99	14	]	]	PUNCT
ejpam-5705	99	15	,	,	PUNCT
ejpam-5705	99	16	the	the	DET
ejpam-5705	99	17	following	follow	VERB
ejpam-5705	99	18	lemma	lemma	PROPN
ejpam-5705	99	19	holds	hold	VERB
ejpam-5705	99	20	.	.	PUNCT
ejpam-5705	100	1	r.	r.	PROPN
ejpam-5705	100	2	bandaru	bandaru	PROPN
ejpam-5705	100	3	et	et	PROPN
ejpam-5705	100	4	al	al	PROPN
ejpam-5705	100	5	.	.	PUNCT
ejpam-5705	100	6	/	/	SYM
ejpam-5705	100	7	eur	eur	PROPN
ejpam-5705	100	8	.	.	PUNCT
ejpam-5705	101	1	j.	j.	PROPN
ejpam-5705	101	2	pure	pure	PROPN
ejpam-5705	101	3	appl	appl	PROPN
ejpam-5705	101	4	.	.	PROPN
ejpam-5705	101	5	math	math	PROPN
ejpam-5705	101	6	,	,	PUNCT
ejpam-5705	101	7	18	18	NUM
ejpam-5705	101	8	(	(	PUNCT
ejpam-5705	101	9	2	2	NUM
ejpam-5705	101	10	)	)	PUNCT
ejpam-5705	101	11	(	(	PUNCT
ejpam-5705	101	12	2025	2025	NUM
ejpam-5705	101	13	)	)	PUNCT
ejpam-5705	101	14	,	,	PUNCT
ejpam-5705	101	15	5705	5705	NUM
ejpam-5705	101	16	5	5	NUM
ejpam-5705	101	17	of	of	ADP
ejpam-5705	101	18	13	13	NUM
ejpam-5705	101	19	lemma	lemma	PROPN
ejpam-5705	101	20	4	4	NUM
ejpam-5705	101	21	(	(	PUNCT
ejpam-5705	101	22	[	[	X
ejpam-5705	101	23	6	6	NUM
ejpam-5705	101	24	]	]	PUNCT
ejpam-5705	101	25	)	)	PUNCT
ejpam-5705	101	26	.	.	PUNCT
ejpam-5705	102	1	let	let	VERB
ejpam-5705	102	2	v	v	PART
ejpam-5705	102	3	be	be	AUX
ejpam-5705	102	4	a	a	DET
ejpam-5705	102	5	pdl	pdl	NOUN
ejpam-5705	103	1	and	and	CCONJ
ejpam-5705	103	2	i	i	PRON
ejpam-5705	103	3	be	be	VERB
ejpam-5705	103	4	an	an	DET
ejpam-5705	103	5	ideal	ideal	NOUN
ejpam-5705	103	6	of	of	ADP
ejpam-5705	103	7	v	v	NOUN
ejpam-5705	103	8	.	.	PUNCT
ejpam-5705	104	1	then	then	ADV
ejpam-5705	104	2	,	,	PUNCT
ejpam-5705	104	3	for	for	ADP
ejpam-5705	104	4	any	any	DET
ejpam-5705	104	5	∂1	∂1	ADJ
ejpam-5705	104	6	,	,	PUNCT
ejpam-5705	104	7	∂2	∂2	PROPN
ejpam-5705	104	8	∈	∈	PROPN
ejpam-5705	104	9	v	v	NOUN
ejpam-5705	104	10	,	,	PUNCT
ejpam-5705	104	11	we	we	PRON
ejpam-5705	104	12	have	have	VERB
ejpam-5705	104	13	the	the	DET
ejpam-5705	104	14	following	following	NOUN
ejpam-5705	104	15	:	:	PUNCT
ejpam-5705	104	16	(	(	PUNCT
ejpam-5705	104	17	1	1	X
ejpam-5705	104	18	)	)	PUNCT
ejpam-5705	104	19	∂1	∂1	ADJ
ejpam-5705	104	20	∈	∈	NOUN
ejpam-5705	104	21	(	(	PUNCT
ejpam-5705	104	22	∂2	∂2	NOUN
ejpam-5705	104	23	]	]	X
ejpam-5705	104	24	if	if	SCONJ
ejpam-5705	105	1	and	and	CCONJ
ejpam-5705	105	2	only	only	ADV
ejpam-5705	105	3	if	if	SCONJ
ejpam-5705	105	4	∂1	∂1	ADJ
ejpam-5705	105	5	=	=	SYM
ejpam-5705	105	6	∂2	∂2	NOUN
ejpam-5705	105	7	∧	∧	PROPN
ejpam-5705	105	8	∂1	∂1	ADJ
ejpam-5705	105	9	,	,	PUNCT
ejpam-5705	105	10	(	(	PUNCT
ejpam-5705	105	11	2	2	X
ejpam-5705	105	12	)	)	PUNCT
ejpam-5705	105	13	∂1	∂1	NOUN
ejpam-5705	105	14	∧	∧	PROPN
ejpam-5705	105	15	∂2	∂2	NOUN
ejpam-5705	105	16	∈	∈	PROPN
ejpam-5705	106	1	i	i	PRON
ejpam-5705	106	2	if	if	SCONJ
ejpam-5705	106	3	and	and	CCONJ
ejpam-5705	106	4	only	only	ADV
ejpam-5705	106	5	if	if	SCONJ
ejpam-5705	106	6	∂2	∂2	PROPN
ejpam-5705	106	7	∧	∧	PROPN
ejpam-5705	106	8	∂1	∂1	X
ejpam-5705	106	9	∈	∈	X
ejpam-5705	106	10	i	i	PRON
ejpam-5705	106	11	,	,	PUNCT
ejpam-5705	106	12	(	(	PUNCT
ejpam-5705	106	13	3	3	X
ejpam-5705	106	14	)	)	PUNCT
ejpam-5705	106	15	(	(	PUNCT
ejpam-5705	106	16	∂1	∂1	X
ejpam-5705	106	17	∧	∧	PROPN
ejpam-5705	106	18	∂2	∂2	NOUN
ejpam-5705	106	19	]	]	X
ejpam-5705	106	20	=	=	SYM
ejpam-5705	106	21	(	(	PUNCT
ejpam-5705	106	22	∂2	∂2	PROPN
ejpam-5705	106	23	∧	∧	PROPN
ejpam-5705	106	24	∂1	∂1	ADJ
ejpam-5705	106	25	]	]	X
ejpam-5705	106	26	=	=	SYM
ejpam-5705	106	27	(	(	PUNCT
ejpam-5705	106	28	∂1	∂1	X
ejpam-5705	106	29	]	]	X
ejpam-5705	106	30	∧	∧	PROPN
ejpam-5705	106	31	(	(	PUNCT
ejpam-5705	106	32	∂2	∂2	PROPN
ejpam-5705	106	33	]	]	PUNCT
ejpam-5705	106	34	.	.	PUNCT
ejpam-5705	107	1	theorem	theorem	ADJ
ejpam-5705	107	2	5	5	NUM
ejpam-5705	107	3	(	(	PUNCT
ejpam-5705	107	4	[	[	X
ejpam-5705	107	5	6	6	NUM
ejpam-5705	107	6	]	]	NUM
ejpam-5705	107	7	)	)	PUNCT
ejpam-5705	107	8	.	.	PUNCT
ejpam-5705	108	1	the	the	DET
ejpam-5705	108	2	collection	collection	NOUN
ejpam-5705	108	3	i(v	i(v	NOUN
ejpam-5705	108	4	)	)	PUNCT
ejpam-5705	108	5	of	of	ADP
ejpam-5705	108	6	all	all	DET
ejpam-5705	108	7	ideals	ideal	NOUN
ejpam-5705	108	8	of	of	ADP
ejpam-5705	108	9	a	a	DET
ejpam-5705	108	10	pdl	pdl	NOUN
ejpam-5705	108	11	v	v	NOUN
ejpam-5705	108	12	forms	form	NOUN
ejpam-5705	108	13	a	a	DET
ejpam-5705	108	14	distributive	distributive	ADJ
ejpam-5705	108	15	lattice	lattice	NOUN
ejpam-5705	108	16	under	under	ADP
ejpam-5705	108	17	set	set	ADJ
ejpam-5705	108	18	inclusion	inclusion	NOUN
ejpam-5705	108	19	,	,	PUNCT
ejpam-5705	108	20	in	in	ADP
ejpam-5705	108	21	which	which	PRON
ejpam-5705	108	22	,	,	PUNCT
ejpam-5705	108	23	the	the	DET
ejpam-5705	108	24	glb	glb	NOUN
ejpam-5705	108	25	and	and	CCONJ
ejpam-5705	108	26	lub	lub	NOUN
ejpam-5705	108	27	of	of	ADP
ejpam-5705	108	28	any	any	DET
ejpam-5705	108	29	two	two	NUM
ejpam-5705	108	30	ideals	ideal	NOUN
ejpam-5705	108	31	i	i	PRON
ejpam-5705	108	32	and	and	CCONJ
ejpam-5705	108	33	j	j	PROPN
ejpam-5705	108	34	are	be	AUX
ejpam-5705	108	35	given	give	VERB
ejpam-5705	108	36	by	by	ADP
ejpam-5705	108	37	i	i	PROPN
ejpam-5705	108	38	∧	∧	PROPN
ejpam-5705	108	39	j	j	PROPN
ejpam-5705	109	1	=	=	SYM
ejpam-5705	109	2	i	i	PROPN
ejpam-5705	109	3	∩	∩	PROPN
ejpam-5705	109	4	j	j	PROPN
ejpam-5705	109	5	and	and	CCONJ
ejpam-5705	109	6	i	i	PROPN
ejpam-5705	109	7	∨	∨	PROPN
ejpam-5705	109	8	j	j	PROPN
ejpam-5705	110	1	=	=	PRON
ejpam-5705	110	2	{	{	PUNCT
ejpam-5705	110	3	∂1	∂1	PROPN
ejpam-5705	110	4	∨	∨	NUM
ejpam-5705	110	5	∂2	∂2	NOUN
ejpam-5705	110	6	|	|	ADV
ejpam-5705	110	7	∂1	∂1	X
ejpam-5705	110	8	∈	∈	X
ejpam-5705	111	1	i	i	PRON
ejpam-5705	111	2	and	and	CCONJ
ejpam-5705	111	3	∂2	∂2	PROPN
ejpam-5705	111	4	∈	∈	PROPN
ejpam-5705	111	5	j	j	PROPN
ejpam-5705	111	6	}	}	PUNCT
ejpam-5705	111	7	,	,	PUNCT
ejpam-5705	111	8	respectively	respectively	ADV
ejpam-5705	111	9	.	.	PUNCT
ejpam-5705	112	1	a	a	DET
ejpam-5705	112	2	proper	proper	ADJ
ejpam-5705	112	3	filter(ideal	filter(ideal	NOUN
ejpam-5705	112	4	)	)	PUNCT
ejpam-5705	113	1	p	p	NOUN
ejpam-5705	113	2	of	of	ADP
ejpam-5705	113	3	v	v	NOUN
ejpam-5705	113	4	is	be	AUX
ejpam-5705	113	5	said	say	VERB
ejpam-5705	113	6	to	to	PART
ejpam-5705	113	7	be	be	AUX
ejpam-5705	113	8	a	a	DET
ejpam-5705	113	9	prime	prime	ADJ
ejpam-5705	113	10	filter(ideal	filter(ideal	NOUN
ejpam-5705	113	11	)	)	PUNCT
ejpam-5705	113	12	if	if	SCONJ
ejpam-5705	113	13	for	for	ADP
ejpam-5705	113	14	any	any	DET
ejpam-5705	113	15	℘	℘	NOUN
ejpam-5705	113	16	,	,	PUNCT
ejpam-5705	113	17	ℏ	ℏ	PROPN
ejpam-5705	113	18	∈	∈	NOUN
ejpam-5705	113	19	v	v	NOUN
ejpam-5705	113	20	,	,	PUNCT
ejpam-5705	113	21	℘	℘	PROPN
ejpam-5705	113	22	∨	∨	NUM
ejpam-5705	113	23	ℏ	ℏ	PROPN
ejpam-5705	113	24	∈	∈	ADJ
ejpam-5705	113	25	p	p	NOUN
ejpam-5705	113	26	(	(	PUNCT
ejpam-5705	113	27	℘	℘	PROPN
ejpam-5705	113	28	∧	∧	PROPN
ejpam-5705	113	29	ℏ	ℏ	NOUN
ejpam-5705	113	30	∈	∈	PROPN
ejpam-5705	113	31	p	p	NOUN
ejpam-5705	113	32	)	)	PUNCT
ejpam-5705	113	33	⇒	⇒	VERB
ejpam-5705	113	34	℘	℘	PROPN
ejpam-5705	113	35	∈	∈	PROPN
ejpam-5705	113	36	p	p	NOUN
ejpam-5705	113	37	or	or	CCONJ
ejpam-5705	113	38	ℏ	ℏ	PRON
ejpam-5705	113	39	∈	∈	PROPN
ejpam-5705	113	40	p	p	NOUN
ejpam-5705	113	41	.	.	PUNCT
ejpam-5705	114	1	a	a	DET
ejpam-5705	114	2	proper	proper	ADJ
ejpam-5705	114	3	filter(ideal	filter(ideal	NOUN
ejpam-5705	114	4	)	)	PUNCT
ejpam-5705	114	5	m	m	PROPN
ejpam-5705	114	6	of	of	ADP
ejpam-5705	114	7	v	v	NOUN
ejpam-5705	114	8	is	be	AUX
ejpam-5705	114	9	said	say	VERB
ejpam-5705	114	10	to	to	PART
ejpam-5705	114	11	be	be	AUX
ejpam-5705	114	12	maximal	maximal	ADJ
ejpam-5705	114	13	if	if	SCONJ
ejpam-5705	114	14	it	it	PRON
ejpam-5705	114	15	is	be	AUX
ejpam-5705	114	16	not	not	PART
ejpam-5705	114	17	properly	properly	ADV
ejpam-5705	114	18	contained	contain	VERB
ejpam-5705	114	19	in	in	ADP
ejpam-5705	114	20	any	any	DET
ejpam-5705	114	21	proper	proper	ADJ
ejpam-5705	114	22	filter(ideal	filter(ideal	NOUN
ejpam-5705	114	23	)	)	PUNCT
ejpam-5705	114	24	of	of	ADP
ejpam-5705	114	25	v	v	NOUN
ejpam-5705	114	26	.	.	PUNCT
ejpam-5705	115	1	a	a	DET
ejpam-5705	115	2	prime	prime	ADJ
ejpam-5705	115	3	filter	filter	NOUN
ejpam-5705	115	4	p	p	NOUN
ejpam-5705	115	5	of	of	ADP
ejpam-5705	115	6	v	v	NOUN
ejpam-5705	115	7	is	be	AUX
ejpam-5705	115	8	said	say	VERB
ejpam-5705	115	9	to	to	PART
ejpam-5705	115	10	be	be	AUX
ejpam-5705	115	11	minimal	minimal	ADJ
ejpam-5705	115	12	,	,	PUNCT
ejpam-5705	115	13	if	if	SCONJ
ejpam-5705	115	14	it	it	PRON
ejpam-5705	115	15	is	be	AUX
ejpam-5705	115	16	minimal	minimal	ADJ
ejpam-5705	115	17	among	among	ADP
ejpam-5705	115	18	all	all	DET
ejpam-5705	115	19	the	the	DET
ejpam-5705	115	20	prime	prime	ADJ
ejpam-5705	115	21	filters	filter	NOUN
ejpam-5705	115	22	of	of	ADP
ejpam-5705	115	23	v	v	NOUN
ejpam-5705	115	24	.	.	PUNCT
ejpam-5705	116	1	a	a	DET
ejpam-5705	116	2	prime	prime	ADJ
ejpam-5705	116	3	filter	filter	NOUN
ejpam-5705	116	4	p	p	NOUN
ejpam-5705	116	5	is	be	AUX
ejpam-5705	116	6	said	say	VERB
ejpam-5705	116	7	to	to	PART
ejpam-5705	116	8	be	be	AUX
ejpam-5705	116	9	a	a	DET
ejpam-5705	116	10	minimal	minimal	ADJ
ejpam-5705	116	11	prime	prime	ADJ
ejpam-5705	116	12	filter	filter	NOUN
ejpam-5705	116	13	belonging	belong	VERB
ejpam-5705	116	14	to	to	ADP
ejpam-5705	116	15	a	a	DET
ejpam-5705	116	16	filter	filter	NOUN
ejpam-5705	117	1	i	i	PRON
ejpam-5705	117	2	,	,	PUNCT
ejpam-5705	117	3	if	if	SCONJ
ejpam-5705	117	4	it	it	PRON
ejpam-5705	117	5	is	be	AUX
ejpam-5705	117	6	minimal	minimal	ADJ
ejpam-5705	117	7	among	among	ADP
ejpam-5705	117	8	all	all	DET
ejpam-5705	117	9	the	the	DET
ejpam-5705	117	10	prime	prime	ADJ
ejpam-5705	117	11	filters	filter	NOUN
ejpam-5705	117	12	of	of	ADP
ejpam-5705	117	13	v	v	NOUN
ejpam-5705	117	14	containing	contain	VERB
ejpam-5705	117	15	i.	i.	NOUN
ejpam-5705	117	16	a	a	DET
ejpam-5705	117	17	prime	prime	ADJ
ejpam-5705	117	18	filer	filer	NOUN
ejpam-5705	117	19	p	p	PROPN
ejpam-5705	117	20	of	of	ADP
ejpam-5705	117	21	v	v	NOUN
ejpam-5705	117	22	is	be	AUX
ejpam-5705	117	23	a	a	DET
ejpam-5705	117	24	minimal	minimal	ADJ
ejpam-5705	117	25	prime	prime	ADJ
ejpam-5705	117	26	filter	filter	NOUN
ejpam-5705	117	27	if	if	SCONJ
ejpam-5705	117	28	and	and	CCONJ
ejpam-5705	117	29	only	only	ADV
ejpam-5705	117	30	if	if	SCONJ
ejpam-5705	117	31	for	for	ADP
ejpam-5705	117	32	each	each	DET
ejpam-5705	117	33	℘	℘	PROPN
ejpam-5705	117	34	∈	∈	PROPN
ejpam-5705	117	35	p	p	NOUN
ejpam-5705	117	36	,	,	PUNCT
ejpam-5705	117	37	there	there	PRON
ejpam-5705	117	38	exists	exist	VERB
ejpam-5705	117	39	ℏ	ℏ	PROPN
ejpam-5705	117	40	/∈	/∈	PUNCT
ejpam-5705	118	1	p	p	X
ejpam-5705	118	2	such	such	ADJ
ejpam-5705	118	3	that	that	SCONJ
ejpam-5705	118	4	℘	℘	PROPN
ejpam-5705	118	5	∨	∨	NUM
ejpam-5705	118	6	ℏ	ℏ	NOUN
ejpam-5705	118	7	=	=	SYM
ejpam-5705	118	8	1	1	X
ejpam-5705	118	9	.	.	PUNCT
ejpam-5705	119	1	lemma	lemma	PROPN
ejpam-5705	119	2	5	5	NUM
ejpam-5705	119	3	(	(	PUNCT
ejpam-5705	119	4	[	[	X
ejpam-5705	119	5	7	7	NUM
ejpam-5705	119	6	]	]	NUM
ejpam-5705	119	7	)	)	PUNCT
ejpam-5705	119	8	.	.	PUNCT
ejpam-5705	120	1	let	let	VERB
ejpam-5705	120	2	v	v	PART
ejpam-5705	120	3	be	be	AUX
ejpam-5705	120	4	a	a	DET
ejpam-5705	120	5	pdl	pdl	NOUN
ejpam-5705	120	6	and	and	CCONJ
ejpam-5705	120	7	a	a	DET
ejpam-5705	120	8	⊆	⊆	NUM
ejpam-5705	120	9	v	v	NOUN
ejpam-5705	120	10	.	.	PUNCT
ejpam-5705	121	1	then	then	ADV
ejpam-5705	121	2	(	(	PUNCT
ejpam-5705	121	3	1	1	NUM
ejpam-5705	121	4	)	)	PUNCT
ejpam-5705	121	5	.	.	PUNCT
ejpam-5705	122	1	a•	a•	PROPN
ejpam-5705	122	2	=	=	SYM
ejpam-5705	122	3	{	{	PUNCT
ejpam-5705	122	4	τ	τ	PROPN
ejpam-5705	122	5	∈	∈	PROPN
ejpam-5705	122	6	v	v	ADP
ejpam-5705	122	7	|	|	ADV
ejpam-5705	122	8	τ	τ	X
ejpam-5705	122	9	∨	∨	NOUN
ejpam-5705	122	10	℘	℘	PROPN
ejpam-5705	122	11	=	=	SYM
ejpam-5705	122	12	1	1	NUM
ejpam-5705	122	13	for	for	ADP
ejpam-5705	122	14	all	all	DET
ejpam-5705	122	15	℘	℘	PROPN
ejpam-5705	122	16	∈	∈	PRON
ejpam-5705	122	17	a	a	PRON
ejpam-5705	122	18	}	}	PUNCT
ejpam-5705	122	19	is	be	AUX
ejpam-5705	122	20	a	a	DET
ejpam-5705	122	21	filter	filter	NOUN
ejpam-5705	122	22	of	of	ADP
ejpam-5705	122	23	v	v	NOUN
ejpam-5705	122	24	.	.	PUNCT
ejpam-5705	123	1	(	(	PUNCT
ejpam-5705	123	2	2	2	NUM
ejpam-5705	123	3	)	)	PUNCT
ejpam-5705	123	4	.	.	PUNCT
ejpam-5705	124	1	for	for	ADP
ejpam-5705	124	2	any	any	DET
ejpam-5705	124	3	℘	℘	NOUN
ejpam-5705	124	4	,	,	PUNCT
ejpam-5705	124	5	ℏ	ℏ	PROPN
ejpam-5705	124	6	∈	∈	NOUN
ejpam-5705	124	7	v	v	NOUN
ejpam-5705	124	8	,	,	PUNCT
ejpam-5705	124	9	[	[	PUNCT
ejpam-5705	124	10	℘	℘	PROPN
ejpam-5705	124	11	∧	∧	PROPN
ejpam-5705	124	12	ℏ]•	ℏ]•	NOUN
ejpam-5705	124	13	=	=	PUNCT
ejpam-5705	125	1	[	[	X
ejpam-5705	125	2	℘]•	℘]•	PROPN
ejpam-5705	125	3	∩	∩	X
ejpam-5705	125	4	[	[	X
ejpam-5705	125	5	ℏ]•	ℏ]•	NOUN
ejpam-5705	125	6	,	,	PUNCT
ejpam-5705	125	7	where	where	SCONJ
ejpam-5705	125	8	[	[	PUNCT
ejpam-5705	125	9	℘	℘	PROPN
ejpam-5705	125	10	∧	∧	PROPN
ejpam-5705	125	11	ℏ]•	ℏ]•	NOUN
ejpam-5705	125	12	=	=	PUNCT
ejpam-5705	125	13	{	{	PUNCT
ejpam-5705	125	14	τ	τ	PROPN
ejpam-5705	125	15	∈	∈	PROPN
ejpam-5705	125	16	v	v	ADP
ejpam-5705	125	17	|	|	ADV
ejpam-5705	125	18	τ	τ	X
ejpam-5705	125	19	∨	∨	X
ejpam-5705	125	20	(	(	PUNCT
ejpam-5705	125	21	℘	℘	PROPN
ejpam-5705	125	22	∧	∧	PROPN
ejpam-5705	125	23	ℏ	ℏ	PROPN
ejpam-5705	125	24	)	)	PUNCT
ejpam-5705	125	25	=	=	PUNCT
ejpam-5705	125	26	1	1	NUM
ejpam-5705	125	27	}	}	PUNCT
ejpam-5705	125	28	.	.	PUNCT
ejpam-5705	126	1	(	(	PUNCT
ejpam-5705	126	2	3	3	NUM
ejpam-5705	126	3	)	)	PUNCT
ejpam-5705	126	4	.	.	PUNCT
ejpam-5705	127	1	for	for	ADP
ejpam-5705	127	2	any	any	DET
ejpam-5705	127	3	℘	℘	NOUN
ejpam-5705	127	4	,	,	PUNCT
ejpam-5705	127	5	ℏ	ℏ	PROPN
ejpam-5705	127	6	∈	∈	NOUN
ejpam-5705	127	7	v	v	NOUN
ejpam-5705	127	8	,	,	PUNCT
ejpam-5705	127	9	[	[	PUNCT
ejpam-5705	127	10	℘	℘	PROPN
ejpam-5705	127	11	∨	∨	NUM
ejpam-5705	127	12	ℏ]••	ℏ]••	NOUN
ejpam-5705	128	1	=	=	PUNCT
ejpam-5705	129	1	[	[	X
ejpam-5705	129	2	℘]•	℘]•	PROPN
ejpam-5705	129	3	•	•	NOUN
ejpam-5705	129	4	∩	∩	X
ejpam-5705	129	5	[	[	X
ejpam-5705	129	6	ℏ]••	ℏ]••	NOUN
ejpam-5705	129	7	,	,	PUNCT
ejpam-5705	129	8	where	where	SCONJ
ejpam-5705	129	9	[	[	PUNCT
ejpam-5705	129	10	℘	℘	PROPN
ejpam-5705	129	11	∧	∧	PROPN
ejpam-5705	129	12	ℏ]•	ℏ]•	NOUN
ejpam-5705	129	13	•	•	NOUN
ejpam-5705	129	14	=	=	SYM
ejpam-5705	129	15	{	{	PUNCT
ejpam-5705	129	16	τ	τ	PROPN
ejpam-5705	129	17	∈	∈	PROPN
ejpam-5705	129	18	v	v	ADP
ejpam-5705	129	19	|	|	ADV
ejpam-5705	129	20	τ	τ	PROPN
ejpam-5705	129	21	∨	∨	NUM
ejpam-5705	129	22	ȷ	ȷ	NOUN
ejpam-5705	129	23	=	=	SYM
ejpam-5705	129	24	1	1	NUM
ejpam-5705	129	25	for	for	ADP
ejpam-5705	129	26	all	all	DET
ejpam-5705	129	27	℘	℘	PROPN
ejpam-5705	129	28	∈	∈	PROPN
ejpam-5705	129	29	[	[	X
ejpam-5705	129	30	℘	℘	PROPN
ejpam-5705	129	31	∧	∧	PROPN
ejpam-5705	129	32	ℏ]•	ℏ]•	NOUN
ejpam-5705	129	33	}	}	PUNCT
ejpam-5705	129	34	.	.	PUNCT
ejpam-5705	130	1	definition	definition	NOUN
ejpam-5705	130	2	6	6	NUM
ejpam-5705	130	3	(	(	PUNCT
ejpam-5705	130	4	[	[	X
ejpam-5705	130	5	7	7	NUM
ejpam-5705	130	6	]	]	NUM
ejpam-5705	130	7	)	)	PUNCT
ejpam-5705	130	8	.	.	PUNCT
ejpam-5705	131	1	let	let	AUX
ejpam-5705	131	2	(	(	PUNCT
ejpam-5705	131	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	131	4	,	,	PUNCT
ejpam-5705	131	5	1	1	NUM
ejpam-5705	131	6	)	)	PUNCT
ejpam-5705	131	7	be	be	AUX
ejpam-5705	131	8	a	a	DET
ejpam-5705	131	9	paradistributive	paradistributive	ADJ
ejpam-5705	131	10	latticoid	latticoid	NOUN
ejpam-5705	131	11	(	(	PUNCT
ejpam-5705	131	12	pdl	pdl	NOUN
ejpam-5705	131	13	)	)	PUNCT
ejpam-5705	131	14	and	and	CCONJ
ejpam-5705	131	15	consider	consider	VERB
ejpam-5705	131	16	a	a	DET
ejpam-5705	131	17	unary	unary	ADJ
ejpam-5705	131	18	operation	operation	NOUN
ejpam-5705	131	19	denoted	denote	VERB
ejpam-5705	131	20	as	as	ADP
ejpam-5705	131	21	℘	℘	PROPN
ejpam-5705	131	22	7→	7→	NUM
ejpam-5705	131	23	℘	℘	NOUN
ejpam-5705	131	24	♦	♦	PROPN
ejpam-5705	131	25	on	on	ADP
ejpam-5705	131	26	v	v	NUM
ejpam-5705	131	27	.	.	PUNCT
ejpam-5705	132	1	this	this	DET
ejpam-5705	132	2	operation	operation	NOUN
ejpam-5705	132	3	is	be	AUX
ejpam-5705	132	4	called	call	VERB
ejpam-5705	132	5	a	a	DET
ejpam-5705	132	6	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5705	132	7	on	on	ADP
ejpam-5705	132	8	v	v	NOUN
ejpam-5705	132	9	if	if	SCONJ
ejpam-5705	132	10	it	it	PRON
ejpam-5705	132	11	satisfies	satisfy	VERB
ejpam-5705	132	12	the	the	DET
ejpam-5705	132	13	following	follow	VERB
ejpam-5705	132	14	conditions	condition	NOUN
ejpam-5705	132	15	:	:	PUNCT
ejpam-5705	132	16	(	(	PUNCT
ejpam-5705	132	17	ppc1	ppc1	PROPN
ejpam-5705	132	18	)	)	PUNCT
ejpam-5705	132	19	if	if	SCONJ
ejpam-5705	132	20	℘	℘	PROPN
ejpam-5705	132	21	∨	∨	NUM
ejpam-5705	132	22	ℏ	ℏ	NOUN
ejpam-5705	132	23	=	=	SYM
ejpam-5705	132	24	1	1	NUM
ejpam-5705	132	25	,	,	PUNCT
ejpam-5705	132	26	then	then	ADV
ejpam-5705	132	27	℘	℘	VERB
ejpam-5705	132	28	∨	∨	NUM
ejpam-5705	132	29	ℏ	ℏ	PROPN
ejpam-5705	132	30	♦	♦	PROPN
ejpam-5705	132	31	=	=	PROPN
ejpam-5705	132	32	℘.	℘.	PROPN
ejpam-5705	132	33	(	(	PUNCT
ejpam-5705	132	34	ppc2	ppc2	PROPN
ejpam-5705	132	35	)	)	PUNCT
ejpam-5705	132	36	℘	℘	PROPN
ejpam-5705	132	37	∨	∨	NUM
ejpam-5705	132	38	℘	℘	PROPN
ejpam-5705	132	39	♦	♦	NOUN
ejpam-5705	132	40	=	=	PROPN
ejpam-5705	132	41	1	1	PROPN
ejpam-5705	132	42	.	.	PUNCT
ejpam-5705	133	1	(	(	PUNCT
ejpam-5705	133	2	ppc3	ppc3	ADJ
ejpam-5705	133	3	)	)	PUNCT
ejpam-5705	133	4	(	(	PUNCT
ejpam-5705	133	5	℘	℘	X
ejpam-5705	133	6	∧	∧	PROPN
ejpam-5705	133	7	ℏ	ℏ	PROPN
ejpam-5705	133	8	)	)	PUNCT
ejpam-5705	133	9	♦	♦	PROPN
ejpam-5705	133	10	=	=	PUNCT
ejpam-5705	133	11	℘	℘	PROPN
ejpam-5705	133	12	♦	♦	PROPN
ejpam-5705	133	13	∨	∨	NUM
ejpam-5705	133	14	ℏ	ℏ	PROPN
ejpam-5705	133	15	♦	♦	PROPN
ejpam-5705	133	16	.	.	PUNCT
ejpam-5705	134	1	definition	definition	NOUN
ejpam-5705	134	2	7	7	NUM
ejpam-5705	134	3	(	(	PUNCT
ejpam-5705	134	4	[	[	X
ejpam-5705	134	5	7	7	NUM
ejpam-5705	134	6	]	]	NUM
ejpam-5705	134	7	)	)	PUNCT
ejpam-5705	134	8	.	.	PUNCT
ejpam-5705	135	1	by	by	ADP
ejpam-5705	135	2	a	a	DET
ejpam-5705	135	3	homomorphism	homomorphism	NOUN
ejpam-5705	135	4	of	of	ADP
ejpam-5705	135	5	a	a	DET
ejpam-5705	135	6	pdl	pdl	PROPN
ejpam-5705	135	7	(	(	PUNCT
ejpam-5705	135	8	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	135	9	,	,	PUNCT
ejpam-5705	135	10	1	1	NUM
ejpam-5705	135	11	)	)	PUNCT
ejpam-5705	135	12	into	into	ADP
ejpam-5705	135	13	a	a	DET
ejpam-5705	135	14	pdl	pdl	NOUN
ejpam-5705	135	15	(	(	PUNCT
ejpam-5705	135	16	v	v	NOUN
ejpam-5705	135	17	′,∨′,∧′	′,∨′,∧′	NOUN
ejpam-5705	135	18	,	,	PUNCT
ejpam-5705	135	19	1′	1′	NUM
ejpam-5705	135	20	)	)	PUNCT
ejpam-5705	135	21	,	,	PUNCT
ejpam-5705	135	22	we	we	PRON
ejpam-5705	135	23	mean	mean	VERB
ejpam-5705	135	24	,	,	PUNCT
ejpam-5705	135	25	a	a	DET
ejpam-5705	135	26	mapping	mapping	NOUN
ejpam-5705	135	27	f	f	NOUN
ejpam-5705	135	28	:	:	PUNCT
ejpam-5705	135	29	v	v	X
ejpam-5705	135	30	→	→	SYM
ejpam-5705	135	31	v	v	NOUN
ejpam-5705	135	32	′	′	NOUN
ejpam-5705	135	33	satisfying	satisfy	VERB
ejpam-5705	135	34	the	the	DET
ejpam-5705	135	35	following	following	NOUN
ejpam-5705	135	36	:	:	PUNCT
ejpam-5705	135	37	(	(	PUNCT
ejpam-5705	135	38	1	1	X
ejpam-5705	135	39	)	)	PUNCT
ejpam-5705	135	40	f(µ1	f(µ1	VERB
ejpam-5705	135	41	∨	∨	NUM
ejpam-5705	135	42	µ2	µ2	PROPN
ejpam-5705	135	43	)	)	PUNCT
ejpam-5705	135	44	=	=	SYM
ejpam-5705	135	45	f(µ1	f(µ1	NOUN
ejpam-5705	135	46	)	)	PUNCT
ejpam-5705	136	1	∨′	∨′	PRON
ejpam-5705	136	2	f(µ2	f(µ2	NOUN
ejpam-5705	136	3	)	)	PUNCT
ejpam-5705	136	4	,	,	PUNCT
ejpam-5705	136	5	(	(	PUNCT
ejpam-5705	136	6	2	2	X
ejpam-5705	136	7	)	)	PUNCT
ejpam-5705	136	8	f(µ1	f(µ1	VERB
ejpam-5705	136	9	∧	∧	PROPN
ejpam-5705	136	10	µ2	µ2	PROPN
ejpam-5705	136	11	)	)	PUNCT
ejpam-5705	136	12	=	=	SYM
ejpam-5705	136	13	f(µ1	f(µ1	NOUN
ejpam-5705	136	14	)	)	PUNCT
ejpam-5705	137	1	∧′	∧′	PROPN
ejpam-5705	137	2	f(µ2	f(µ2	NOUN
ejpam-5705	137	3	)	)	PUNCT
ejpam-5705	137	4	,	,	PUNCT
ejpam-5705	137	5	(	(	PUNCT
ejpam-5705	137	6	3	3	X
ejpam-5705	137	7	)	)	PUNCT
ejpam-5705	137	8	f(1	f(1	PROPN
ejpam-5705	137	9	)	)	PUNCT
ejpam-5705	137	10	=	=	SYM
ejpam-5705	137	11	f(1′	f(1′	PROPN
ejpam-5705	137	12	)	)	PUNCT
ejpam-5705	137	13	.	.	PUNCT
ejpam-5705	138	1	3	3	X
ejpam-5705	138	2	.	.	PUNCT
ejpam-5705	138	3	•-pdl	•-pdl	PUNCT
ejpam-5705	138	4	in	in	ADP
ejpam-5705	138	5	this	this	DET
ejpam-5705	138	6	section	section	NOUN
ejpam-5705	138	7	,	,	PUNCT
ejpam-5705	138	8	we	we	PRON
ejpam-5705	138	9	introduce	introduce	VERB
ejpam-5705	138	10	a	a	DET
ejpam-5705	138	11	new	new	ADJ
ejpam-5705	138	12	type	type	NOUN
ejpam-5705	138	13	of	of	ADP
ejpam-5705	138	14	pdls	pdl	NOUN
ejpam-5705	138	15	called	call	VERB
ejpam-5705	138	16	•-pdls	•-pdls	NOUN
ejpam-5705	138	17	and	and	CCONJ
ejpam-5705	138	18	demonstrate	demonstrate	VERB
ejpam-5705	138	19	that	that	SCONJ
ejpam-5705	138	20	if	if	SCONJ
ejpam-5705	138	21	v	v	NOUN
ejpam-5705	138	22	is	be	AUX
ejpam-5705	138	23	parapseudo	parapseudo	NOUN
ejpam-5705	138	24	-	-	PUNCT
ejpam-5705	138	25	complemented	complement	VERB
ejpam-5705	138	26	pdl	pdl	NOUN
ejpam-5705	138	27	,	,	PUNCT
ejpam-5705	138	28	then	then	ADV
ejpam-5705	138	29	for	for	ADP
ejpam-5705	138	30	any	any	DET
ejpam-5705	138	31	℘	℘	PROPN
ejpam-5705	138	32	∈	∈	NOUN
ejpam-5705	138	33	v	v	NOUN
ejpam-5705	138	34	,	,	PUNCT
ejpam-5705	138	35	[	[	X
ejpam-5705	138	36	℘]•	℘]•	PUNCT
ejpam-5705	138	37	=	=	PUNCT
ejpam-5705	138	38	[	[	PUNCT
ejpam-5705	138	39	℘	℘	X
ejpam-5705	138	40	♦	♦	PROPN
ejpam-5705	138	41	)	)	PUNCT
ejpam-5705	138	42	and	and	CCONJ
ejpam-5705	139	1	[	[	X
ejpam-5705	139	2	℘]•	℘]•	PROPN
ejpam-5705	139	3	•	•	NOUN
ejpam-5705	139	4	=	=	PUNCT
ejpam-5705	139	5	[	[	PUNCT
ejpam-5705	139	6	℘	℘	PROPN
ejpam-5705	139	7	♦	♦	PROPN
ejpam-5705	139	8	]•.	]•.	X
ejpam-5705	139	9	r.	r.	PROPN
ejpam-5705	139	10	bandaru	bandaru	PROPN
ejpam-5705	139	11	et	et	PROPN
ejpam-5705	139	12	al	al	PROPN
ejpam-5705	139	13	.	.	PUNCT
ejpam-5705	139	14	/	/	SYM
ejpam-5705	139	15	eur	eur	PROPN
ejpam-5705	139	16	.	.	PUNCT
ejpam-5705	140	1	j.	j.	PROPN
ejpam-5705	140	2	pure	pure	PROPN
ejpam-5705	140	3	appl	appl	PROPN
ejpam-5705	140	4	.	.	PROPN
ejpam-5705	140	5	math	math	PROPN
ejpam-5705	140	6	,	,	PUNCT
ejpam-5705	140	7	18	18	NUM
ejpam-5705	140	8	(	(	PUNCT
ejpam-5705	140	9	2	2	NUM
ejpam-5705	140	10	)	)	PUNCT
ejpam-5705	140	11	(	(	PUNCT
ejpam-5705	140	12	2025	2025	NUM
ejpam-5705	140	13	)	)	PUNCT
ejpam-5705	140	14	,	,	PUNCT
ejpam-5705	140	15	5705	5705	NUM
ejpam-5705	140	16	6	6	NUM
ejpam-5705	140	17	of	of	ADP
ejpam-5705	140	18	13	13	NUM
ejpam-5705	140	19	with	with	ADP
ejpam-5705	140	20	this	this	DET
ejpam-5705	140	21	motivation	motivation	NOUN
ejpam-5705	140	22	,	,	PUNCT
ejpam-5705	140	23	we	we	PRON
ejpam-5705	140	24	define	define	VERB
ejpam-5705	140	25	a	a	DET
ejpam-5705	140	26	•	•	ADJ
ejpam-5705	140	27	pdl	pdl	NOUN
ejpam-5705	140	28	to	to	PART
ejpam-5705	140	29	be	be	AUX
ejpam-5705	140	30	a	a	DET
ejpam-5705	140	31	pdl	pdl	NOUN
ejpam-5705	140	32	wherein	wherein	NOUN
ejpam-5705	140	33	for	for	ADP
ejpam-5705	140	34	any	any	DET
ejpam-5705	140	35	℘	℘	PROPN
ejpam-5705	140	36	∈	∈	NOUN
ejpam-5705	140	37	v	v	NOUN
ejpam-5705	140	38	,	,	PUNCT
ejpam-5705	140	39	[	[	X
ejpam-5705	140	40	℘]•	℘]•	PROPN
ejpam-5705	140	41	•	•	NOUN
ejpam-5705	140	42	=	=	PUNCT
ejpam-5705	141	1	[	[	PUNCT
ejpam-5705	141	2	℘	℘	NUM
ejpam-5705	141	3	′	′	NUM
ejpam-5705	141	4	]	]	PUNCT
ejpam-5705	141	5	•	•	NOUN
ejpam-5705	141	6	for	for	ADP
ejpam-5705	141	7	some	some	DET
ejpam-5705	141	8	℘	℘	NUM
ejpam-5705	141	9	′	′	NUM
ejpam-5705	141	10	∈	∈	NOUN
ejpam-5705	141	11	v	v	NOUN
ejpam-5705	141	12	.	.	PUNCT
ejpam-5705	142	1	this	this	DET
ejpam-5705	142	2	class	class	NOUN
ejpam-5705	142	3	of	of	ADP
ejpam-5705	142	4	•-pdls	•-pdls	NOUN
ejpam-5705	142	5	contains	contain	VERB
ejpam-5705	142	6	the	the	DET
ejpam-5705	142	7	class	class	NOUN
ejpam-5705	142	8	of	of	ADP
ejpam-5705	142	9	parapseudo	parapseudo	NOUN
ejpam-5705	142	10	-	-	PUNCT
ejpam-5705	142	11	complemented	complement	VERB
ejpam-5705	142	12	pdls	pdl	NOUN
ejpam-5705	142	13	.	.	PUNCT
ejpam-5705	143	1	further	far	ADV
ejpam-5705	143	2	,	,	PUNCT
ejpam-5705	143	3	we	we	PRON
ejpam-5705	143	4	define	define	VERB
ejpam-5705	143	5	a	a	DET
ejpam-5705	143	6	congruence	congruence	NOUN
ejpam-5705	143	7	relation	relation	NOUN
ejpam-5705	143	8	θ	θ	PROPN
ejpam-5705	144	1	=	=	SYM
ejpam-5705	144	2	{	{	PUNCT
ejpam-5705	144	3	(	(	PUNCT
ejpam-5705	144	4	℘	℘	NOUN
ejpam-5705	144	5	,	,	PUNCT
ejpam-5705	144	6	ℏ	ℏ	NOUN
ejpam-5705	144	7	)	)	PUNCT
ejpam-5705	144	8	|	|	ADV
ejpam-5705	145	1	[	[	X
ejpam-5705	145	2	℘]•	℘]•	PUNCT
ejpam-5705	145	3	=	=	PUNCT
ejpam-5705	145	4	[	[	X
ejpam-5705	145	5	ℏ]•	ℏ]•	NOUN
ejpam-5705	145	6	}	}	PUNCT
ejpam-5705	145	7	and	and	CCONJ
ejpam-5705	145	8	prove	prove	VERB
ejpam-5705	145	9	that	that	SCONJ
ejpam-5705	145	10	v	v	NOUN
ejpam-5705	145	11	is	be	AUX
ejpam-5705	145	12	a	a	DET
ejpam-5705	145	13	•-pdl	•-pdl	PUNCT
ejpam-5705	145	14	if	if	SCONJ
ejpam-5705	145	15	and	and	CCONJ
ejpam-5705	145	16	only	only	ADV
ejpam-5705	145	17	if	if	SCONJ
ejpam-5705	145	18	v	v	NOUN
ejpam-5705	145	19	/	/	SYM
ejpam-5705	145	20	θ	θ	PROPN
ejpam-5705	145	21	is	be	AUX
ejpam-5705	145	22	a	a	DET
ejpam-5705	145	23	boolean	boolean	ADJ
ejpam-5705	145	24	algebra	algebra	NOUN
ejpam-5705	145	25	.	.	PUNCT
ejpam-5705	146	1	throughout	throughout	ADP
ejpam-5705	146	2	this	this	DET
ejpam-5705	146	3	paper	paper	NOUN
ejpam-5705	146	4	,	,	PUNCT
ejpam-5705	146	5	v	v	NOUN
ejpam-5705	146	6	means	mean	NOUN
ejpam-5705	146	7	(	(	PUNCT
ejpam-5705	146	8	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	146	9	,	,	PUNCT
ejpam-5705	146	10	1	1	NUM
ejpam-5705	146	11	)	)	PUNCT
ejpam-5705	146	12	.	.	PUNCT
ejpam-5705	147	1	lemma	lemma	PROPN
ejpam-5705	147	2	6	6	NUM
ejpam-5705	147	3	.	.	PUNCT
ejpam-5705	148	1	if	if	SCONJ
ejpam-5705	148	2	v	v	NOUN
ejpam-5705	148	3	is	be	AUX
ejpam-5705	148	4	a	a	DET
ejpam-5705	148	5	parapseudo	parapseudo	NOUN
ejpam-5705	148	6	-	-	PUNCT
ejpam-5705	148	7	complemented	complement	VERB
ejpam-5705	148	8	pdl	pdl	NOUN
ejpam-5705	148	9	,	,	PUNCT
ejpam-5705	148	10	then	then	ADV
ejpam-5705	148	11	[	[	X
ejpam-5705	148	12	℘]•	℘]•	PUNCT
ejpam-5705	148	13	=	=	PUNCT
ejpam-5705	148	14	[	[	PUNCT
ejpam-5705	148	15	℘	℘	X
ejpam-5705	148	16	♦	♦	PROPN
ejpam-5705	148	17	)	)	PUNCT
ejpam-5705	148	18	and	and	CCONJ
ejpam-5705	149	1	[	[	X
ejpam-5705	149	2	℘]•	℘]•	PROPN
ejpam-5705	149	3	•	•	NOUN
ejpam-5705	149	4	=	=	PUNCT
ejpam-5705	149	5	[	[	PUNCT
ejpam-5705	149	6	℘	℘	X
ejpam-5705	149	7	♦	♦	NOUN
ejpam-5705	149	8	]•	]•	X
ejpam-5705	149	9	=	=	PUNCT
ejpam-5705	150	1	[	[	X
ejpam-5705	150	2	℘••	℘••	X
ejpam-5705	150	3	]	]	PUNCT
ejpam-5705	150	4	where	where	SCONJ
ejpam-5705	150	5	℘	℘	PROPN
ejpam-5705	150	6	∈	∈	NOUN
ejpam-5705	150	7	v	v	NOUN
ejpam-5705	150	8	.	.	PUNCT
ejpam-5705	151	1	proof	proof	NOUN
ejpam-5705	151	2	.	.	PUNCT
ejpam-5705	152	1	µ1	µ1	PROPN
ejpam-5705	152	2	∈	∈	PROPN
ejpam-5705	153	1	[	[	X
ejpam-5705	153	2	℘]•	℘]•	PROPN
ejpam-5705	153	3	⇔	⇔	PROPN
ejpam-5705	153	4	µ1	µ1	PROPN
ejpam-5705	153	5	∨	∨	NOUN
ejpam-5705	153	6	℘	℘	PROPN
ejpam-5705	153	7	=	=	SYM
ejpam-5705	153	8	1	1	NUM
ejpam-5705	153	9	⇔	⇔	PROPN
ejpam-5705	153	10	µ1	µ1	PROPN
ejpam-5705	153	11	∨	∨	NOUN
ejpam-5705	153	12	℘	℘	PROPN
ejpam-5705	153	13	♦	♦	PROPN
ejpam-5705	153	14	=	=	PUNCT
ejpam-5705	153	15	µ1	µ1	PROPN
ejpam-5705	153	16	⇔	⇔	PROPN
ejpam-5705	153	17	µ1	µ1	PROPN
ejpam-5705	153	18	∈	∈	PROPN
ejpam-5705	153	19	[	[	X
ejpam-5705	153	20	℘	℘	NOUN
ejpam-5705	153	21	♦	♦	NOUN
ejpam-5705	153	22	)	)	PUNCT
ejpam-5705	153	23	.	.	PUNCT
ejpam-5705	154	1	therefore	therefore	ADV
ejpam-5705	154	2	,	,	PUNCT
ejpam-5705	154	3	[	[	X
ejpam-5705	154	4	℘]•	℘]•	PROPN
ejpam-5705	154	5	=	=	PUNCT
ejpam-5705	154	6	[	[	PUNCT
ejpam-5705	154	7	℘	℘	PROPN
ejpam-5705	154	8	♦	♦	PROPN
ejpam-5705	154	9	)	)	PUNCT
ejpam-5705	154	10	.	.	PUNCT
ejpam-5705	155	1	let	let	VERB
ejpam-5705	155	2	µ1	µ1	NOUN
ejpam-5705	155	3	∈	∈	PROPN
ejpam-5705	155	4	[	[	X
ejpam-5705	155	5	℘]•	℘]•	PROPN
ejpam-5705	155	6	•	•	NUM
ejpam-5705	155	7	.	.	PUNCT
ejpam-5705	156	1	then	then	ADV
ejpam-5705	156	2	µ1	µ1	PROPN
ejpam-5705	156	3	∨	∨	PROPN
ejpam-5705	156	4	µ2	µ2	PROPN
ejpam-5705	156	5	=	=	PROPN
ejpam-5705	156	6	1	1	NUM
ejpam-5705	156	7	for	for	ADP
ejpam-5705	156	8	all	all	DET
ejpam-5705	156	9	µ2	µ2	PROPN
ejpam-5705	156	10	∈	∈	PROPN
ejpam-5705	156	11	[	[	X
ejpam-5705	156	12	℘]•.	℘]•.	ADJ
ejpam-5705	156	13	clearly	clearly	ADV
ejpam-5705	156	14	℘	℘	VERB
ejpam-5705	156	15	♦	♦	PROPN
ejpam-5705	156	16	∈	∈	PROPN
ejpam-5705	157	1	[	[	X
ejpam-5705	157	2	℘]•	℘]•	PROPN
ejpam-5705	157	3	(	(	PUNCT
ejpam-5705	157	4	since	since	SCONJ
ejpam-5705	157	5	℘	℘	PROPN
ejpam-5705	157	6	♦	♦	PROPN
ejpam-5705	157	7	∨	∨	NUM
ejpam-5705	157	8	℘	℘	PROPN
ejpam-5705	157	9	=	=	SYM
ejpam-5705	157	10	1	1	NUM
ejpam-5705	157	11	)	)	PUNCT
ejpam-5705	157	12	.	.	PUNCT
ejpam-5705	158	1	therefore	therefore	ADV
ejpam-5705	158	2	µ1	µ1	PROPN
ejpam-5705	158	3	∨	∨	NOUN
ejpam-5705	158	4	℘	℘	PROPN
ejpam-5705	158	5	♦	♦	NOUN
ejpam-5705	158	6	=	=	SYM
ejpam-5705	158	7	1	1	NUM
ejpam-5705	158	8	implies	imply	VERB
ejpam-5705	158	9	µ1	µ1	PROPN
ejpam-5705	158	10	∈	∈	PROPN
ejpam-5705	158	11	[	[	X
ejpam-5705	158	12	℘	℘	NOUN
ejpam-5705	158	13	♦	♦	PROPN
ejpam-5705	158	14	]•.	]•.	NOUN
ejpam-5705	158	15	conversely	conversely	ADV
ejpam-5705	158	16	,	,	PUNCT
ejpam-5705	158	17	let	let	VERB
ejpam-5705	158	18	µ1	µ1	NOUN
ejpam-5705	158	19	∈	∈	NOUN
ejpam-5705	158	20	[	[	X
ejpam-5705	158	21	℘	℘	PROPN
ejpam-5705	158	22	♦	♦	PROPN
ejpam-5705	158	23	]•.	]•.	PRON
ejpam-5705	158	24	then	then	ADV
ejpam-5705	158	25	µ1	µ1	PROPN
ejpam-5705	158	26	∨	∨	NOUN
ejpam-5705	158	27	℘	℘	PROPN
ejpam-5705	158	28	♦	♦	NOUN
ejpam-5705	158	29	=	=	SYM
ejpam-5705	158	30	1	1	X
ejpam-5705	158	31	.	.	PUNCT
ejpam-5705	159	1	let	let	VERB
ejpam-5705	159	2	µ2	µ2	PROPN
ejpam-5705	159	3	∈	∈	PROPN
ejpam-5705	160	1	[	[	X
ejpam-5705	160	2	℘]•.	℘]•.	ADJ
ejpam-5705	160	3	then	then	ADV
ejpam-5705	160	4	µ2	µ2	PROPN
ejpam-5705	160	5	∨	∨	NOUN
ejpam-5705	160	6	℘	℘	X
ejpam-5705	160	7	=	=	SYM
ejpam-5705	160	8	1	1	NUM
ejpam-5705	160	9	and	and	CCONJ
ejpam-5705	160	10	hence	hence	ADV
ejpam-5705	160	11	µ2	µ2	PROPN
ejpam-5705	160	12	∨	∨	NUM
ejpam-5705	160	13	℘	℘	PROPN
ejpam-5705	161	1	♦	♦	NOUN
ejpam-5705	161	2	=	=	PROPN
ejpam-5705	161	3	µ2	µ2	PROPN
ejpam-5705	161	4	.	.	PUNCT
ejpam-5705	162	1	µ1	µ1	PROPN
ejpam-5705	162	2	∨	∨	PROPN
ejpam-5705	162	3	µ2	µ2	PROPN
ejpam-5705	162	4	=	=	PUNCT
ejpam-5705	162	5	µ1	µ1	PROPN
ejpam-5705	162	6	∨	∨	NUM
ejpam-5705	162	7	µ2	µ2	PROPN
ejpam-5705	162	8	∨	∨	NUM
ejpam-5705	162	9	℘	℘	PROPN
ejpam-5705	162	10	♦	♦	PROPN
ejpam-5705	162	11	=	=	PUNCT
ejpam-5705	162	12	µ1	µ1	PROPN
ejpam-5705	163	1	∨	∨	NOUN
ejpam-5705	163	2	℘	℘	PROPN
ejpam-5705	163	3	♦	♦	PROPN
ejpam-5705	163	4	∨	∨	NOUN
ejpam-5705	163	5	µ2	µ2	PROPN
ejpam-5705	163	6	=	=	PROPN
ejpam-5705	163	7	1	1	NUM
ejpam-5705	163	8	∨	∨	NUM
ejpam-5705	163	9	µ2	µ2	PROPN
ejpam-5705	163	10	=	=	NOUN
ejpam-5705	163	11	1	1	NUM
ejpam-5705	163	12	therefore	therefore	ADV
ejpam-5705	163	13	µ1	µ1	PROPN
ejpam-5705	163	14	∈	∈	PROPN
ejpam-5705	164	1	[	[	X
ejpam-5705	164	2	℘]•	℘]•	PROPN
ejpam-5705	164	3	•	•	NOUN
ejpam-5705	164	4	.	.	PUNCT
ejpam-5705	165	1	hence	hence	ADV
ejpam-5705	165	2	[	[	X
ejpam-5705	165	3	℘	℘	X
ejpam-5705	165	4	♦	♦	NOUN
ejpam-5705	165	5	]•	]•	X
ejpam-5705	165	6	=	=	PUNCT
ejpam-5705	166	1	[	[	X
ejpam-5705	166	2	℘]•	℘]•	PROPN
ejpam-5705	166	3	•	•	NOUN
ejpam-5705	166	4	=	=	PUNCT
ejpam-5705	166	5	[	[	PUNCT
ejpam-5705	166	6	℘	℘	PROPN
ejpam-5705	166	7	♦	♦	PROPN
ejpam-5705	166	8	♦	♦	PROPN
ejpam-5705	166	9	)	)	PUNCT
ejpam-5705	166	10	.	.	PUNCT
ejpam-5705	167	1	definition	definition	NOUN
ejpam-5705	167	2	8	8	NUM
ejpam-5705	167	3	.	.	PUNCT
ejpam-5705	168	1	a	a	DET
ejpam-5705	168	2	pdl	pdl	PROPN
ejpam-5705	168	3	(	(	PUNCT
ejpam-5705	168	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	168	5	,	,	PUNCT
ejpam-5705	168	6	1	1	NUM
ejpam-5705	168	7	)	)	PUNCT
ejpam-5705	168	8	is	be	AUX
ejpam-5705	168	9	called	call	VERB
ejpam-5705	168	10	a	a	PRON
ejpam-5705	168	11	•-pdl	•-pdl	PUNCT
ejpam-5705	168	12	if	if	SCONJ
ejpam-5705	168	13	,	,	PUNCT
ejpam-5705	168	14	for	for	ADP
ejpam-5705	168	15	each	each	DET
ejpam-5705	168	16	℘	℘	PROPN
ejpam-5705	168	17	∈	∈	PROPN
ejpam-5705	168	18	v	v	NOUN
ejpam-5705	168	19	,	,	PUNCT
ejpam-5705	168	20	[	[	X
ejpam-5705	168	21	℘]•	℘]•	PROPN
ejpam-5705	168	22	•	•	NOUN
ejpam-5705	168	23	=	=	PUNCT
ejpam-5705	169	1	[	[	PUNCT
ejpam-5705	169	2	℘	℘	NUM
ejpam-5705	169	3	′	′	NOUN
ejpam-5705	169	4	]	]	PUNCT
ejpam-5705	169	5	•	•	NUM
ejpam-5705	169	6	where	where	SCONJ
ejpam-5705	169	7	℘	℘	PROPN
ejpam-5705	169	8	′	′	NUM
ejpam-5705	169	9	∈	∈	PROPN
ejpam-5705	169	10	v	v	NOUN
ejpam-5705	169	11	.	.	PUNCT
ejpam-5705	170	1	note	note	VERB
ejpam-5705	170	2	that	that	SCONJ
ejpam-5705	170	3	every	every	DET
ejpam-5705	170	4	parapseudo	parapseudo	NOUN
ejpam-5705	170	5	-	-	PUNCT
ejpam-5705	170	6	complemented	complemented	ADJ
ejpam-5705	170	7	pdl	pdl	NOUN
ejpam-5705	170	8	is	be	AUX
ejpam-5705	170	9	a	a	DET
ejpam-5705	170	10	•-pdl	•-pdl	NOUN
ejpam-5705	170	11	.	.	PUNCT
ejpam-5705	171	1	in	in	ADP
ejpam-5705	171	2	the	the	DET
ejpam-5705	171	3	following	following	NOUN
ejpam-5705	171	4	we	we	PRON
ejpam-5705	171	5	give	give	VERB
ejpam-5705	171	6	an	an	DET
ejpam-5705	171	7	example	example	NOUN
ejpam-5705	171	8	of	of	ADP
ejpam-5705	171	9	a	a	DET
ejpam-5705	171	10	•-pdl	•-pdl	NOUN
ejpam-5705	171	11	.	.	NOUN
ejpam-5705	171	12	example	example	NOUN
ejpam-5705	172	1	2	2	NUM
ejpam-5705	172	2	.	.	PUNCT
ejpam-5705	172	3	let	let	VERB
ejpam-5705	172	4	a	a	DET
ejpam-5705	172	5	=	=	PUNCT
ejpam-5705	172	6	{	{	PUNCT
ejpam-5705	172	7	1	1	NUM
ejpam-5705	172	8	,	,	PUNCT
ejpam-5705	172	9	℘1	℘1	NOUN
ejpam-5705	172	10	,	,	PUNCT
ejpam-5705	172	11	℘2	℘2	NOUN
ejpam-5705	172	12	}	}	PUNCT
ejpam-5705	172	13	and	and	CCONJ
ejpam-5705	172	14	b	b	X
ejpam-5705	172	15	=	=	SYM
ejpam-5705	172	16	{	{	PUNCT
ejpam-5705	172	17	1	1	NUM
ejpam-5705	172	18	,	,	PUNCT
ejpam-5705	172	19	ℏ	ℏ	PROPN
ejpam-5705	172	20	}	}	PUNCT
ejpam-5705	172	21	are	be	AUX
ejpam-5705	172	22	two	two	NUM
ejpam-5705	172	23	disconnected	disconnected	ADJ
ejpam-5705	172	24	pdls	pdl	NOUN
ejpam-5705	172	25	.	.	PUNCT
ejpam-5705	173	1	let	let	VERB
ejpam-5705	173	2	v	v	VERB
ejpam-5705	173	3	=	=	PUNCT
ejpam-5705	173	4	a	a	DET
ejpam-5705	173	5	×	×	NOUN
ejpam-5705	173	6	b	b	X
ejpam-5705	173	7	=	=	PRON
ejpam-5705	173	8	{	{	PUNCT
ejpam-5705	173	9	(	(	PUNCT
ejpam-5705	173	10	1	1	NUM
ejpam-5705	173	11	,	,	PUNCT
ejpam-5705	173	12	1	1	NUM
ejpam-5705	173	13	)	)	PUNCT
ejpam-5705	173	14	,	,	PUNCT
ejpam-5705	173	15	(	(	PUNCT
ejpam-5705	173	16	1	1	NUM
ejpam-5705	173	17	,	,	PUNCT
ejpam-5705	173	18	ℏ	ℏ	PROPN
ejpam-5705	173	19	)	)	PUNCT
ejpam-5705	173	20	,	,	PUNCT
ejpam-5705	173	21	(	(	PUNCT
ejpam-5705	173	22	℘1	℘1	VERB
ejpam-5705	173	23	,	,	PUNCT
ejpam-5705	173	24	1	1	NUM
ejpam-5705	173	25	)	)	PUNCT
ejpam-5705	173	26	,	,	PUNCT
ejpam-5705	173	27	(	(	PUNCT
ejpam-5705	173	28	℘1	℘1	X
ejpam-5705	173	29	,	,	PUNCT
ejpam-5705	173	30	ℏ	ℏ	NOUN
ejpam-5705	173	31	)	)	PUNCT
ejpam-5705	173	32	,	,	PUNCT
ejpam-5705	173	33	(	(	PUNCT
ejpam-5705	173	34	℘2	℘2	PROPN
ejpam-5705	173	35	,	,	PUNCT
ejpam-5705	173	36	1	1	NUM
ejpam-5705	173	37	)	)	PUNCT
ejpam-5705	173	38	,	,	PUNCT
ejpam-5705	173	39	(	(	PUNCT
ejpam-5705	173	40	℘2	℘2	PROPN
ejpam-5705	173	41	,	,	PUNCT
ejpam-5705	173	42	ℏ	ℏ	PROPN
ejpam-5705	173	43	)	)	PUNCT
ejpam-5705	173	44	}	}	PUNCT
ejpam-5705	173	45	.	.	PUNCT
ejpam-5705	174	1	define	define	VERB
ejpam-5705	174	2	∨	∨	NOUN
ejpam-5705	174	3	and	and	CCONJ
ejpam-5705	174	4	∧	∧	NOUN
ejpam-5705	174	5	on	on	ADP
ejpam-5705	174	6	v	v	NOUN
ejpam-5705	174	7	under	under	ADP
ejpam-5705	174	8	point	point	NOUN
ejpam-5705	174	9	-	-	PUNCT
ejpam-5705	174	10	wise	wise	ADJ
ejpam-5705	174	11	:	:	PUNCT
ejpam-5705	174	12	∨	∨	NOUN
ejpam-5705	174	13	(	(	PUNCT
ejpam-5705	174	14	1	1	NUM
ejpam-5705	174	15	,	,	PUNCT
ejpam-5705	174	16	1	1	NUM
ejpam-5705	174	17	)	)	PUNCT
ejpam-5705	174	18	(	(	PUNCT
ejpam-5705	174	19	1	1	NUM
ejpam-5705	174	20	,	,	PUNCT
ejpam-5705	174	21	ℏ	ℏ	PROPN
ejpam-5705	174	22	)	)	PUNCT
ejpam-5705	174	23	(	(	PUNCT
ejpam-5705	174	24	℘1	℘1	VERB
ejpam-5705	174	25	,	,	PUNCT
ejpam-5705	174	26	1	1	NUM
ejpam-5705	174	27	)	)	PUNCT
ejpam-5705	174	28	(	(	PUNCT
ejpam-5705	174	29	℘1	℘1	PROPN
ejpam-5705	174	30	,	,	PUNCT
ejpam-5705	174	31	ℏ	ℏ	NOUN
ejpam-5705	174	32	)	)	PUNCT
ejpam-5705	174	33	(	(	PUNCT
ejpam-5705	174	34	℘2	℘2	PROPN
ejpam-5705	174	35	,	,	PUNCT
ejpam-5705	174	36	1	1	NUM
ejpam-5705	174	37	)	)	PUNCT
ejpam-5705	174	38	(	(	PUNCT
ejpam-5705	174	39	℘2	℘2	PROPN
ejpam-5705	174	40	,	,	PUNCT
ejpam-5705	174	41	ℏ	ℏ	PROPN
ejpam-5705	174	42	)	)	PUNCT
ejpam-5705	174	43	(	(	PUNCT
ejpam-5705	174	44	1	1	NUM
ejpam-5705	174	45	,	,	PUNCT
ejpam-5705	174	46	1	1	NUM
ejpam-5705	174	47	)	)	PUNCT
ejpam-5705	174	48	(	(	PUNCT
ejpam-5705	174	49	1	1	NUM
ejpam-5705	174	50	,	,	PUNCT
ejpam-5705	174	51	1	1	NUM
ejpam-5705	174	52	)	)	PUNCT
ejpam-5705	174	53	(	(	PUNCT
ejpam-5705	174	54	1	1	NUM
ejpam-5705	174	55	,	,	PUNCT
ejpam-5705	174	56	1	1	NUM
ejpam-5705	174	57	)	)	PUNCT
ejpam-5705	174	58	(	(	PUNCT
ejpam-5705	174	59	1	1	NUM
ejpam-5705	174	60	,	,	PUNCT
ejpam-5705	174	61	1	1	NUM
ejpam-5705	174	62	)	)	PUNCT
ejpam-5705	174	63	(	(	PUNCT
ejpam-5705	174	64	1	1	NUM
ejpam-5705	174	65	,	,	PUNCT
ejpam-5705	174	66	1	1	NUM
ejpam-5705	174	67	)	)	PUNCT
ejpam-5705	174	68	(	(	PUNCT
ejpam-5705	174	69	1	1	NUM
ejpam-5705	174	70	,	,	PUNCT
ejpam-5705	174	71	1	1	NUM
ejpam-5705	174	72	)	)	PUNCT
ejpam-5705	174	73	(	(	PUNCT
ejpam-5705	174	74	1	1	NUM
ejpam-5705	174	75	,	,	PUNCT
ejpam-5705	174	76	1	1	NUM
ejpam-5705	174	77	)	)	PUNCT
ejpam-5705	174	78	(	(	PUNCT
ejpam-5705	174	79	1	1	NUM
ejpam-5705	174	80	,	,	PUNCT
ejpam-5705	174	81	ℏ	ℏ	NOUN
ejpam-5705	174	82	)	)	PUNCT
ejpam-5705	174	83	(	(	PUNCT
ejpam-5705	174	84	1	1	NUM
ejpam-5705	174	85	,	,	PUNCT
ejpam-5705	174	86	1	1	NUM
ejpam-5705	174	87	)	)	PUNCT
ejpam-5705	174	88	(	(	PUNCT
ejpam-5705	174	89	1	1	NUM
ejpam-5705	174	90	,	,	PUNCT
ejpam-5705	174	91	ℏ	ℏ	NOUN
ejpam-5705	174	92	)	)	PUNCT
ejpam-5705	174	93	(	(	PUNCT
ejpam-5705	174	94	1	1	NUM
ejpam-5705	174	95	,	,	PUNCT
ejpam-5705	174	96	1	1	NUM
ejpam-5705	174	97	)	)	PUNCT
ejpam-5705	174	98	(	(	PUNCT
ejpam-5705	174	99	1	1	NUM
ejpam-5705	174	100	,	,	PUNCT
ejpam-5705	174	101	ℏ	ℏ	NOUN
ejpam-5705	174	102	)	)	PUNCT
ejpam-5705	174	103	(	(	PUNCT
ejpam-5705	174	104	1	1	NUM
ejpam-5705	174	105	,	,	PUNCT
ejpam-5705	174	106	1	1	NUM
ejpam-5705	174	107	)	)	PUNCT
ejpam-5705	174	108	(	(	PUNCT
ejpam-5705	174	109	1	1	NUM
ejpam-5705	174	110	,	,	PUNCT
ejpam-5705	174	111	ℏ	ℏ	PROPN
ejpam-5705	174	112	)	)	PUNCT
ejpam-5705	174	113	(	(	PUNCT
ejpam-5705	174	114	℘1	℘1	VERB
ejpam-5705	174	115	,	,	PUNCT
ejpam-5705	174	116	1	1	NUM
ejpam-5705	174	117	)	)	PUNCT
ejpam-5705	174	118	(	(	PUNCT
ejpam-5705	174	119	1	1	NUM
ejpam-5705	174	120	,	,	PUNCT
ejpam-5705	174	121	1	1	NUM
ejpam-5705	174	122	)	)	PUNCT
ejpam-5705	174	123	(	(	PUNCT
ejpam-5705	174	124	1	1	NUM
ejpam-5705	174	125	,	,	PUNCT
ejpam-5705	174	126	1	1	NUM
ejpam-5705	174	127	)	)	PUNCT
ejpam-5705	174	128	(	(	PUNCT
ejpam-5705	174	129	℘1	℘1	VERB
ejpam-5705	174	130	,	,	PUNCT
ejpam-5705	174	131	1	1	NUM
ejpam-5705	174	132	)	)	PUNCT
ejpam-5705	174	133	(	(	PUNCT
ejpam-5705	174	134	℘1	℘1	VERB
ejpam-5705	174	135	,	,	PUNCT
ejpam-5705	174	136	1	1	NUM
ejpam-5705	174	137	)	)	PUNCT
ejpam-5705	174	138	(	(	PUNCT
ejpam-5705	174	139	℘1	℘1	VERB
ejpam-5705	174	140	,	,	PUNCT
ejpam-5705	174	141	1	1	NUM
ejpam-5705	174	142	)	)	PUNCT
ejpam-5705	174	143	(	(	PUNCT
ejpam-5705	174	144	℘1	℘1	VERB
ejpam-5705	174	145	,	,	PUNCT
ejpam-5705	174	146	1	1	NUM
ejpam-5705	174	147	)	)	PUNCT
ejpam-5705	174	148	(	(	PUNCT
ejpam-5705	174	149	℘1	℘1	PROPN
ejpam-5705	174	150	,	,	PUNCT
ejpam-5705	174	151	ℏ	ℏ	NOUN
ejpam-5705	174	152	)	)	PUNCT
ejpam-5705	174	153	(	(	PUNCT
ejpam-5705	174	154	1	1	NUM
ejpam-5705	174	155	,	,	PUNCT
ejpam-5705	174	156	1	1	NUM
ejpam-5705	174	157	)	)	PUNCT
ejpam-5705	174	158	(	(	PUNCT
ejpam-5705	174	159	1	1	NUM
ejpam-5705	174	160	,	,	PUNCT
ejpam-5705	174	161	ℏ	ℏ	PROPN
ejpam-5705	174	162	)	)	PUNCT
ejpam-5705	174	163	(	(	PUNCT
ejpam-5705	174	164	℘1	℘1	VERB
ejpam-5705	174	165	,	,	PUNCT
ejpam-5705	174	166	1	1	NUM
ejpam-5705	174	167	)	)	PUNCT
ejpam-5705	174	168	(	(	PUNCT
ejpam-5705	174	169	℘1	℘1	PROPN
ejpam-5705	174	170	,	,	PUNCT
ejpam-5705	174	171	ℏ	ℏ	NOUN
ejpam-5705	174	172	)	)	PUNCT
ejpam-5705	174	173	(	(	PUNCT
ejpam-5705	174	174	℘1	℘1	VERB
ejpam-5705	174	175	,	,	PUNCT
ejpam-5705	174	176	1	1	NUM
ejpam-5705	174	177	)	)	PUNCT
ejpam-5705	174	178	(	(	PUNCT
ejpam-5705	174	179	℘1	℘1	PROPN
ejpam-5705	174	180	,	,	PUNCT
ejpam-5705	174	181	ℏ	ℏ	NOUN
ejpam-5705	174	182	)	)	PUNCT
ejpam-5705	174	183	(	(	PUNCT
ejpam-5705	174	184	℘2	℘2	PROPN
ejpam-5705	174	185	,	,	PUNCT
ejpam-5705	174	186	1	1	NUM
ejpam-5705	174	187	)	)	PUNCT
ejpam-5705	174	188	(	(	PUNCT
ejpam-5705	174	189	1	1	NUM
ejpam-5705	174	190	,	,	PUNCT
ejpam-5705	174	191	1	1	NUM
ejpam-5705	174	192	)	)	PUNCT
ejpam-5705	174	193	(	(	PUNCT
ejpam-5705	174	194	1	1	NUM
ejpam-5705	174	195	,	,	PUNCT
ejpam-5705	174	196	1	1	NUM
ejpam-5705	174	197	)	)	PUNCT
ejpam-5705	174	198	(	(	PUNCT
ejpam-5705	174	199	℘2	℘2	PROPN
ejpam-5705	174	200	,	,	PUNCT
ejpam-5705	174	201	1	1	NUM
ejpam-5705	174	202	)	)	PUNCT
ejpam-5705	174	203	(	(	PUNCT
ejpam-5705	174	204	℘2	℘2	PROPN
ejpam-5705	174	205	,	,	PUNCT
ejpam-5705	174	206	1	1	NUM
ejpam-5705	174	207	)	)	PUNCT
ejpam-5705	174	208	(	(	PUNCT
ejpam-5705	174	209	℘2	℘2	PROPN
ejpam-5705	174	210	,	,	PUNCT
ejpam-5705	174	211	1	1	NUM
ejpam-5705	174	212	)	)	PUNCT
ejpam-5705	174	213	(	(	PUNCT
ejpam-5705	174	214	℘2	℘2	PROPN
ejpam-5705	174	215	,	,	PUNCT
ejpam-5705	174	216	1	1	NUM
ejpam-5705	174	217	)	)	PUNCT
ejpam-5705	174	218	(	(	PUNCT
ejpam-5705	174	219	℘2	℘2	PROPN
ejpam-5705	174	220	,	,	PUNCT
ejpam-5705	174	221	ℏ	ℏ	PROPN
ejpam-5705	174	222	)	)	PUNCT
ejpam-5705	174	223	(	(	PUNCT
ejpam-5705	174	224	1	1	NUM
ejpam-5705	174	225	,	,	PUNCT
ejpam-5705	174	226	1	1	NUM
ejpam-5705	174	227	)	)	PUNCT
ejpam-5705	174	228	(	(	PUNCT
ejpam-5705	174	229	1	1	NUM
ejpam-5705	174	230	,	,	PUNCT
ejpam-5705	174	231	ℏ	ℏ	PROPN
ejpam-5705	174	232	)	)	PUNCT
ejpam-5705	174	233	(	(	PUNCT
ejpam-5705	174	234	℘2	℘2	PROPN
ejpam-5705	174	235	,	,	PUNCT
ejpam-5705	174	236	1	1	NUM
ejpam-5705	174	237	)	)	PUNCT
ejpam-5705	174	238	(	(	PUNCT
ejpam-5705	174	239	℘2	℘2	PROPN
ejpam-5705	174	240	,	,	PUNCT
ejpam-5705	174	241	ℏ	ℏ	PROPN
ejpam-5705	174	242	)	)	PUNCT
ejpam-5705	174	243	(	(	PUNCT
ejpam-5705	174	244	℘2	℘2	PROPN
ejpam-5705	174	245	,	,	PUNCT
ejpam-5705	174	246	1	1	NUM
ejpam-5705	174	247	)	)	PUNCT
ejpam-5705	174	248	(	(	PUNCT
ejpam-5705	174	249	℘2	℘2	PROPN
ejpam-5705	174	250	,	,	PUNCT
ejpam-5705	174	251	ℏ	ℏ	NOUN
ejpam-5705	174	252	)	)	PUNCT
ejpam-5705	174	253	∧	∧	NOUN
ejpam-5705	174	254	(	(	PUNCT
ejpam-5705	174	255	1	1	NUM
ejpam-5705	174	256	,	,	PUNCT
ejpam-5705	174	257	1	1	NUM
ejpam-5705	174	258	)	)	PUNCT
ejpam-5705	174	259	(	(	PUNCT
ejpam-5705	174	260	1	1	NUM
ejpam-5705	174	261	,	,	PUNCT
ejpam-5705	174	262	ℏ	ℏ	PROPN
ejpam-5705	174	263	)	)	PUNCT
ejpam-5705	174	264	(	(	PUNCT
ejpam-5705	174	265	℘1	℘1	VERB
ejpam-5705	174	266	,	,	PUNCT
ejpam-5705	174	267	1	1	NUM
ejpam-5705	174	268	)	)	PUNCT
ejpam-5705	174	269	(	(	PUNCT
ejpam-5705	174	270	℘1	℘1	PROPN
ejpam-5705	174	271	,	,	PUNCT
ejpam-5705	174	272	ℏ	ℏ	NOUN
ejpam-5705	174	273	)	)	PUNCT
ejpam-5705	174	274	(	(	PUNCT
ejpam-5705	174	275	℘2	℘2	PROPN
ejpam-5705	174	276	,	,	PUNCT
ejpam-5705	174	277	1	1	NUM
ejpam-5705	174	278	)	)	PUNCT
ejpam-5705	174	279	℘2	℘2	PROPN
ejpam-5705	174	280	,	,	PUNCT
ejpam-5705	174	281	ℏ	ℏ	PROPN
ejpam-5705	174	282	)	)	PUNCT
ejpam-5705	174	283	(	(	PUNCT
ejpam-5705	174	284	1	1	NUM
ejpam-5705	174	285	,	,	PUNCT
ejpam-5705	174	286	1	1	NUM
ejpam-5705	174	287	)	)	PUNCT
ejpam-5705	174	288	(	(	PUNCT
ejpam-5705	174	289	1	1	NUM
ejpam-5705	174	290	,	,	PUNCT
ejpam-5705	174	291	1	1	NUM
ejpam-5705	174	292	)	)	PUNCT
ejpam-5705	174	293	(	(	PUNCT
ejpam-5705	174	294	1	1	NUM
ejpam-5705	174	295	,	,	PUNCT
ejpam-5705	174	296	ℏ	ℏ	PROPN
ejpam-5705	174	297	)	)	PUNCT
ejpam-5705	174	298	(	(	PUNCT
ejpam-5705	174	299	℘1	℘1	VERB
ejpam-5705	174	300	,	,	PUNCT
ejpam-5705	174	301	1	1	NUM
ejpam-5705	174	302	)	)	PUNCT
ejpam-5705	174	303	(	(	PUNCT
ejpam-5705	174	304	℘2	℘2	PROPN
ejpam-5705	174	305	,	,	PUNCT
ejpam-5705	174	306	ℏ	ℏ	PROPN
ejpam-5705	174	307	)	)	PUNCT
ejpam-5705	174	308	(	(	PUNCT
ejpam-5705	174	309	℘2	℘2	PROPN
ejpam-5705	174	310	,	,	PUNCT
ejpam-5705	174	311	1	1	NUM
ejpam-5705	174	312	)	)	PUNCT
ejpam-5705	174	313	(	(	PUNCT
ejpam-5705	174	314	℘2	℘2	PROPN
ejpam-5705	174	315	,	,	PUNCT
ejpam-5705	174	316	ℏ	ℏ	PROPN
ejpam-5705	174	317	)	)	PUNCT
ejpam-5705	174	318	(	(	PUNCT
ejpam-5705	174	319	1	1	NUM
ejpam-5705	174	320	,	,	PUNCT
ejpam-5705	174	321	ℏ	ℏ	NOUN
ejpam-5705	174	322	)	)	PUNCT
ejpam-5705	174	323	(	(	PUNCT
ejpam-5705	174	324	1	1	NUM
ejpam-5705	174	325	,	,	PUNCT
ejpam-5705	174	326	ℏ	ℏ	NOUN
ejpam-5705	174	327	)	)	PUNCT
ejpam-5705	174	328	(	(	PUNCT
ejpam-5705	174	329	1	1	NUM
ejpam-5705	174	330	,	,	PUNCT
ejpam-5705	174	331	ℏ	ℏ	PROPN
ejpam-5705	174	332	)	)	PUNCT
ejpam-5705	174	333	(	(	PUNCT
ejpam-5705	174	334	℘1	℘1	PROPN
ejpam-5705	174	335	,	,	PUNCT
ejpam-5705	174	336	ℏ	ℏ	NOUN
ejpam-5705	174	337	)	)	PUNCT
ejpam-5705	174	338	(	(	PUNCT
ejpam-5705	174	339	℘1	℘1	PROPN
ejpam-5705	174	340	,	,	PUNCT
ejpam-5705	174	341	ℏ	ℏ	NOUN
ejpam-5705	174	342	)	)	PUNCT
ejpam-5705	174	343	(	(	PUNCT
ejpam-5705	174	344	℘2	℘2	PROPN
ejpam-5705	174	345	,	,	PUNCT
ejpam-5705	174	346	ℏ	ℏ	PROPN
ejpam-5705	174	347	)	)	PUNCT
ejpam-5705	174	348	(	(	PUNCT
ejpam-5705	174	349	℘2	℘2	PROPN
ejpam-5705	174	350	,	,	PUNCT
ejpam-5705	174	351	ℏ	ℏ	PROPN
ejpam-5705	174	352	)	)	PUNCT
ejpam-5705	174	353	(	(	PUNCT
ejpam-5705	174	354	℘1	℘1	VERB
ejpam-5705	174	355	,	,	PUNCT
ejpam-5705	174	356	1	1	NUM
ejpam-5705	174	357	)	)	PUNCT
ejpam-5705	174	358	(	(	PUNCT
ejpam-5705	174	359	℘1	℘1	VERB
ejpam-5705	174	360	,	,	PUNCT
ejpam-5705	174	361	1	1	NUM
ejpam-5705	174	362	)	)	PUNCT
ejpam-5705	174	363	(	(	PUNCT
ejpam-5705	174	364	℘1	℘1	PROPN
ejpam-5705	174	365	,	,	PUNCT
ejpam-5705	174	366	ℏ	ℏ	NOUN
ejpam-5705	174	367	)	)	PUNCT
ejpam-5705	174	368	(	(	PUNCT
ejpam-5705	174	369	℘1	℘1	VERB
ejpam-5705	174	370	,	,	PUNCT
ejpam-5705	174	371	1	1	NUM
ejpam-5705	174	372	)	)	PUNCT
ejpam-5705	174	373	(	(	PUNCT
ejpam-5705	174	374	℘1	℘1	PROPN
ejpam-5705	174	375	,	,	PUNCT
ejpam-5705	174	376	ℏ	ℏ	NOUN
ejpam-5705	174	377	)	)	PUNCT
ejpam-5705	174	378	(	(	PUNCT
ejpam-5705	174	379	℘2	℘2	PROPN
ejpam-5705	174	380	,	,	PUNCT
ejpam-5705	174	381	1	1	NUM
ejpam-5705	174	382	)	)	PUNCT
ejpam-5705	174	383	(	(	PUNCT
ejpam-5705	174	384	℘2	℘2	PROPN
ejpam-5705	174	385	,	,	PUNCT
ejpam-5705	174	386	ℏ	ℏ	PROPN
ejpam-5705	174	387	)	)	PUNCT
ejpam-5705	174	388	(	(	PUNCT
ejpam-5705	174	389	℘1	℘1	PROPN
ejpam-5705	174	390	,	,	PUNCT
ejpam-5705	174	391	ℏ	ℏ	NOUN
ejpam-5705	174	392	)	)	PUNCT
ejpam-5705	174	393	(	(	PUNCT
ejpam-5705	174	394	℘1	℘1	PROPN
ejpam-5705	174	395	,	,	PUNCT
ejpam-5705	174	396	ℏ	ℏ	NOUN
ejpam-5705	174	397	)	)	PUNCT
ejpam-5705	174	398	(	(	PUNCT
ejpam-5705	174	399	℘1	℘1	PROPN
ejpam-5705	174	400	,	,	PUNCT
ejpam-5705	174	401	ℏ	ℏ	NOUN
ejpam-5705	174	402	)	)	PUNCT
ejpam-5705	174	403	(	(	PUNCT
ejpam-5705	174	404	℘1	℘1	PROPN
ejpam-5705	174	405	,	,	PUNCT
ejpam-5705	174	406	ℏ	ℏ	NOUN
ejpam-5705	174	407	)	)	PUNCT
ejpam-5705	174	408	(	(	PUNCT
ejpam-5705	174	409	℘1	℘1	PROPN
ejpam-5705	174	410	,	,	PUNCT
ejpam-5705	174	411	ℏ	ℏ	NOUN
ejpam-5705	174	412	)	)	PUNCT
ejpam-5705	174	413	(	(	PUNCT
ejpam-5705	174	414	℘2	℘2	PROPN
ejpam-5705	174	415	,	,	PUNCT
ejpam-5705	174	416	ℏ	ℏ	PROPN
ejpam-5705	174	417	)	)	PUNCT
ejpam-5705	174	418	(	(	PUNCT
ejpam-5705	174	419	℘2	℘2	PROPN
ejpam-5705	174	420	,	,	PUNCT
ejpam-5705	174	421	ℏ	ℏ	PROPN
ejpam-5705	174	422	)	)	PUNCT
ejpam-5705	174	423	(	(	PUNCT
ejpam-5705	174	424	℘2	℘2	PROPN
ejpam-5705	174	425	,	,	PUNCT
ejpam-5705	174	426	1	1	NUM
ejpam-5705	174	427	)	)	PUNCT
ejpam-5705	174	428	(	(	PUNCT
ejpam-5705	174	429	℘2	℘2	PROPN
ejpam-5705	174	430	,	,	PUNCT
ejpam-5705	174	431	1	1	NUM
ejpam-5705	174	432	)	)	PUNCT
ejpam-5705	174	433	(	(	PUNCT
ejpam-5705	174	434	℘2	℘2	PROPN
ejpam-5705	174	435	,	,	PUNCT
ejpam-5705	174	436	ℏ	ℏ	PROPN
ejpam-5705	174	437	)	)	PUNCT
ejpam-5705	174	438	(	(	PUNCT
ejpam-5705	174	439	℘1	℘1	VERB
ejpam-5705	174	440	,	,	PUNCT
ejpam-5705	174	441	1	1	NUM
ejpam-5705	174	442	)	)	PUNCT
ejpam-5705	174	443	(	(	PUNCT
ejpam-5705	174	444	℘1	℘1	PROPN
ejpam-5705	174	445	,	,	PUNCT
ejpam-5705	174	446	ℏ	ℏ	NOUN
ejpam-5705	174	447	)	)	PUNCT
ejpam-5705	174	448	(	(	PUNCT
ejpam-5705	174	449	℘2	℘2	PROPN
ejpam-5705	174	450	,	,	PUNCT
ejpam-5705	174	451	1	1	NUM
ejpam-5705	174	452	)	)	PUNCT
ejpam-5705	174	453	(	(	PUNCT
ejpam-5705	174	454	℘2	℘2	PROPN
ejpam-5705	174	455	,	,	PUNCT
ejpam-5705	174	456	ℏ	ℏ	PROPN
ejpam-5705	174	457	)	)	PUNCT
ejpam-5705	174	458	(	(	PUNCT
ejpam-5705	174	459	℘2	℘2	PROPN
ejpam-5705	174	460	,	,	PUNCT
ejpam-5705	174	461	ℏ	ℏ	PROPN
ejpam-5705	174	462	)	)	PUNCT
ejpam-5705	174	463	(	(	PUNCT
ejpam-5705	174	464	℘2	℘2	PROPN
ejpam-5705	174	465	,	,	PUNCT
ejpam-5705	174	466	ℏ	ℏ	PROPN
ejpam-5705	174	467	)	)	PUNCT
ejpam-5705	174	468	(	(	PUNCT
ejpam-5705	174	469	℘2	℘2	PROPN
ejpam-5705	174	470	,	,	PUNCT
ejpam-5705	174	471	ℏ	ℏ	PROPN
ejpam-5705	174	472	)	)	PUNCT
ejpam-5705	174	473	(	(	PUNCT
ejpam-5705	174	474	℘1	℘1	PROPN
ejpam-5705	174	475	,	,	PUNCT
ejpam-5705	174	476	ℏ	ℏ	NOUN
ejpam-5705	174	477	)	)	PUNCT
ejpam-5705	174	478	(	(	PUNCT
ejpam-5705	174	479	℘1	℘1	PROPN
ejpam-5705	174	480	,	,	PUNCT
ejpam-5705	174	481	ℏ	ℏ	NOUN
ejpam-5705	174	482	)	)	PUNCT
ejpam-5705	174	483	(	(	PUNCT
ejpam-5705	174	484	℘2	℘2	PROPN
ejpam-5705	174	485	,	,	PUNCT
ejpam-5705	174	486	ℏ	ℏ	PROPN
ejpam-5705	174	487	)	)	PUNCT
ejpam-5705	174	488	(	(	PUNCT
ejpam-5705	174	489	℘2	℘2	PROPN
ejpam-5705	174	490	,	,	PUNCT
ejpam-5705	174	491	ℏ	ℏ	PROPN
ejpam-5705	174	492	)	)	PUNCT
ejpam-5705	174	493	r.	r.	PROPN
ejpam-5705	174	494	bandaru	bandaru	PROPN
ejpam-5705	174	495	et	et	PROPN
ejpam-5705	174	496	al	al	PROPN
ejpam-5705	174	497	.	.	PUNCT
ejpam-5705	174	498	/	/	SYM
ejpam-5705	174	499	eur	eur	PROPN
ejpam-5705	174	500	.	.	PUNCT
ejpam-5705	175	1	j.	j.	PROPN
ejpam-5705	175	2	pure	pure	PROPN
ejpam-5705	175	3	appl	appl	PROPN
ejpam-5705	175	4	.	.	PROPN
ejpam-5705	175	5	math	math	PROPN
ejpam-5705	175	6	,	,	PUNCT
ejpam-5705	175	7	18	18	NUM
ejpam-5705	175	8	(	(	PUNCT
ejpam-5705	175	9	2	2	NUM
ejpam-5705	175	10	)	)	PUNCT
ejpam-5705	175	11	(	(	PUNCT
ejpam-5705	175	12	2025	2025	NUM
ejpam-5705	175	13	)	)	PUNCT
ejpam-5705	175	14	,	,	PUNCT
ejpam-5705	175	15	5705	5705	NUM
ejpam-5705	175	16	7	7	NUM
ejpam-5705	175	17	of	of	ADP
ejpam-5705	175	18	13	13	NUM
ejpam-5705	175	19	then	then	ADV
ejpam-5705	175	20	(	(	PUNCT
ejpam-5705	175	21	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	175	22	,	,	PUNCT
ejpam-5705	175	23	1′	1′	NUM
ejpam-5705	175	24	)	)	PUNCT
ejpam-5705	175	25	is	be	AUX
ejpam-5705	175	26	a	a	DET
ejpam-5705	175	27	pdl	pdl	NOUN
ejpam-5705	175	28	where	where	SCONJ
ejpam-5705	175	29	(	(	PUNCT
ejpam-5705	175	30	1	1	NUM
ejpam-5705	175	31	,	,	PUNCT
ejpam-5705	175	32	1	1	NUM
ejpam-5705	175	33	)	)	PUNCT
ejpam-5705	175	34	=	=	SYM
ejpam-5705	175	35	1	1	NUM
ejpam-5705	175	36	′	′	NOUN
ejpam-5705	175	37	.	.	PUNCT
ejpam-5705	176	1	now	now	ADV
ejpam-5705	176	2	,	,	PUNCT
ejpam-5705	176	3	we	we	PRON
ejpam-5705	176	4	verify	verify	VERB
ejpam-5705	176	5	that	that	SCONJ
ejpam-5705	176	6	this	this	PRON
ejpam-5705	176	7	is	be	AUX
ejpam-5705	176	8	a	a	DET
ejpam-5705	176	9	•-pdl	•-pdl	NOUN
ejpam-5705	176	10	.	.	PUNCT
ejpam-5705	177	1	(	(	PUNCT
ejpam-5705	177	2	i	i	NOUN
ejpam-5705	177	3	)	)	PUNCT
ejpam-5705	178	1	[	[	X
ejpam-5705	178	2	(	(	PUNCT
ejpam-5705	178	3	1	1	NUM
ejpam-5705	178	4	,	,	PUNCT
ejpam-5705	178	5	1)]•	1)]•	NUM
ejpam-5705	178	6	=	=	SYM
ejpam-5705	178	7	v	v	ADJ
ejpam-5705	178	8	⇒	⇒	NOUN
ejpam-5705	178	9	[	[	X
ejpam-5705	178	10	(	(	PUNCT
ejpam-5705	178	11	1	1	NUM
ejpam-5705	178	12	,	,	PUNCT
ejpam-5705	178	13	1)]•	1)]•	NUM
ejpam-5705	178	14	•	•	NOUN
ejpam-5705	178	15	=	=	SYM
ejpam-5705	178	16	v	v	NOUN
ejpam-5705	178	17	•	•	NOUN
ejpam-5705	178	18	=	=	SYM
ejpam-5705	178	19	{	{	PUNCT
ejpam-5705	178	20	(	(	PUNCT
ejpam-5705	178	21	1	1	NUM
ejpam-5705	178	22	,	,	PUNCT
ejpam-5705	178	23	1	1	NUM
ejpam-5705	178	24	)	)	PUNCT
ejpam-5705	178	25	}	}	PUNCT
ejpam-5705	179	1	=	=	SYM
ejpam-5705	180	1	[	[	X
ejpam-5705	180	2	(	(	PUNCT
ejpam-5705	180	3	℘2	℘2	PROPN
ejpam-5705	180	4	,	,	PUNCT
ejpam-5705	180	5	ℏ)]•.	ℏ)]•.	PROPN
ejpam-5705	180	6	(	(	PUNCT
ejpam-5705	180	7	ii	ii	PROPN
ejpam-5705	180	8	)	)	PUNCT
ejpam-5705	181	1	[	[	X
ejpam-5705	181	2	(	(	PUNCT
ejpam-5705	181	3	1	1	NUM
ejpam-5705	181	4	,	,	PUNCT
ejpam-5705	181	5	ℏ)]•	ℏ)]•	NOUN
ejpam-5705	181	6	=	=	SYM
ejpam-5705	181	7	{	{	PUNCT
ejpam-5705	181	8	(	(	PUNCT
ejpam-5705	181	9	1	1	NUM
ejpam-5705	181	10	,	,	PUNCT
ejpam-5705	181	11	1	1	NUM
ejpam-5705	181	12	)	)	PUNCT
ejpam-5705	181	13	,	,	PUNCT
ejpam-5705	181	14	(	(	PUNCT
ejpam-5705	181	15	℘1	℘1	VERB
ejpam-5705	181	16	,	,	PUNCT
ejpam-5705	181	17	1	1	NUM
ejpam-5705	181	18	)	)	PUNCT
ejpam-5705	181	19	,	,	PUNCT
ejpam-5705	181	20	(	(	PUNCT
ejpam-5705	181	21	℘2	℘2	PROPN
ejpam-5705	181	22	,	,	PUNCT
ejpam-5705	181	23	1	1	NUM
ejpam-5705	181	24	)	)	PUNCT
ejpam-5705	181	25	}	}	PUNCT
ejpam-5705	181	26	⇒	⇒	VERB
ejpam-5705	181	27	[	[	X
ejpam-5705	181	28	(	(	PUNCT
ejpam-5705	181	29	1	1	NUM
ejpam-5705	181	30	,	,	PUNCT
ejpam-5705	181	31	ℏ)]••	ℏ)]••	NOUN
ejpam-5705	181	32	=	=	PUNCT
ejpam-5705	181	33	{	{	PUNCT
ejpam-5705	181	34	(	(	PUNCT
ejpam-5705	181	35	1	1	NUM
ejpam-5705	181	36	,	,	PUNCT
ejpam-5705	181	37	1	1	NUM
ejpam-5705	181	38	)	)	PUNCT
ejpam-5705	181	39	,	,	PUNCT
ejpam-5705	181	40	(	(	PUNCT
ejpam-5705	181	41	℘1	℘1	VERB
ejpam-5705	181	42	,	,	PUNCT
ejpam-5705	181	43	1	1	NUM
ejpam-5705	181	44	)	)	PUNCT
ejpam-5705	181	45	,	,	PUNCT
ejpam-5705	181	46	(	(	PUNCT
ejpam-5705	181	47	℘2	℘2	PROPN
ejpam-5705	181	48	,	,	PUNCT
ejpam-5705	181	49	1)}•	1)}•	NUM
ejpam-5705	181	50	=	=	SYM
ejpam-5705	181	51	{	{	PUNCT
ejpam-5705	181	52	(	(	PUNCT
ejpam-5705	181	53	1	1	NUM
ejpam-5705	181	54	,	,	PUNCT
ejpam-5705	181	55	1	1	NUM
ejpam-5705	181	56	)	)	PUNCT
ejpam-5705	181	57	,	,	PUNCT
ejpam-5705	181	58	(	(	PUNCT
ejpam-5705	181	59	1	1	NUM
ejpam-5705	181	60	,	,	PUNCT
ejpam-5705	181	61	ℏ	ℏ	NOUN
ejpam-5705	181	62	)	)	PUNCT
ejpam-5705	181	63	}	}	PUNCT
ejpam-5705	181	64	=	=	SYM
ejpam-5705	182	1	[	[	X
ejpam-5705	182	2	(	(	PUNCT
ejpam-5705	182	3	℘1	℘1	NOUN
ejpam-5705	182	4	,	,	PUNCT
ejpam-5705	182	5	1	1	NUM
ejpam-5705	182	6	)	)	PUNCT
ejpam-5705	182	7	]	]	PUNCT
ejpam-5705	182	8	•.	•.	NOUN
ejpam-5705	182	9	(	(	PUNCT
ejpam-5705	182	10	iii	iii	NOUN
ejpam-5705	182	11	)	)	PUNCT
ejpam-5705	183	1	[	[	X
ejpam-5705	183	2	(	(	PUNCT
ejpam-5705	183	3	℘1	℘1	NOUN
ejpam-5705	183	4	,	,	PUNCT
ejpam-5705	183	5	1	1	NUM
ejpam-5705	183	6	)	)	PUNCT
ejpam-5705	183	7	]	]	PUNCT
ejpam-5705	184	1	•	•	NOUN
ejpam-5705	184	2	=	=	SYM
ejpam-5705	184	3	{	{	PUNCT
ejpam-5705	184	4	(	(	PUNCT
ejpam-5705	184	5	1	1	NUM
ejpam-5705	184	6	,	,	PUNCT
ejpam-5705	184	7	1	1	NUM
ejpam-5705	184	8	)	)	PUNCT
ejpam-5705	184	9	,	,	PUNCT
ejpam-5705	184	10	(	(	PUNCT
ejpam-5705	184	11	1	1	NUM
ejpam-5705	184	12	,	,	PUNCT
ejpam-5705	184	13	ℏ	ℏ	NOUN
ejpam-5705	184	14	)	)	PUNCT
ejpam-5705	184	15	}	}	PUNCT
ejpam-5705	184	16	⇒	⇒	VERB
ejpam-5705	184	17	[	[	X
ejpam-5705	184	18	(	(	PUNCT
ejpam-5705	184	19	℘1	℘1	NOUN
ejpam-5705	184	20	,	,	PUNCT
ejpam-5705	184	21	1	1	NUM
ejpam-5705	184	22	)	)	PUNCT
ejpam-5705	184	23	]	]	PUNCT
ejpam-5705	184	24	••	••	NOUN
ejpam-5705	184	25	=	=	SYM
ejpam-5705	184	26	{	{	PUNCT
ejpam-5705	184	27	(	(	PUNCT
ejpam-5705	184	28	1	1	NUM
ejpam-5705	184	29	,	,	PUNCT
ejpam-5705	184	30	1	1	NUM
ejpam-5705	184	31	)	)	PUNCT
ejpam-5705	184	32	,	,	PUNCT
ejpam-5705	184	33	(	(	PUNCT
ejpam-5705	184	34	1	1	NUM
ejpam-5705	184	35	,	,	PUNCT
ejpam-5705	184	36	ℏ)}•	ℏ)}•	ADJ
ejpam-5705	185	1	=	=	X
ejpam-5705	185	2	{	{	PUNCT
ejpam-5705	185	3	(	(	PUNCT
ejpam-5705	185	4	1	1	NUM
ejpam-5705	185	5	,	,	PUNCT
ejpam-5705	185	6	1	1	NUM
ejpam-5705	185	7	)	)	PUNCT
ejpam-5705	185	8	,	,	PUNCT
ejpam-5705	185	9	(	(	PUNCT
ejpam-5705	185	10	℘1	℘1	VERB
ejpam-5705	185	11	,	,	PUNCT
ejpam-5705	185	12	1	1	NUM
ejpam-5705	185	13	)	)	PUNCT
ejpam-5705	185	14	,	,	PUNCT
ejpam-5705	185	15	(	(	PUNCT
ejpam-5705	185	16	℘2	℘2	PROPN
ejpam-5705	185	17	,	,	PUNCT
ejpam-5705	185	18	1	1	NUM
ejpam-5705	185	19	)	)	PUNCT
ejpam-5705	185	20	}	}	PUNCT
ejpam-5705	185	21	=	=	PUNCT
ejpam-5705	186	1	[	[	X
ejpam-5705	186	2	(	(	PUNCT
ejpam-5705	186	3	1	1	NUM
ejpam-5705	186	4	,	,	PUNCT
ejpam-5705	186	5	ℏ)]•.	ℏ)]•.	X
ejpam-5705	186	6	(	(	PUNCT
ejpam-5705	186	7	iv	iv	X
ejpam-5705	186	8	)	)	PUNCT
ejpam-5705	186	9	[	[	X
ejpam-5705	186	10	(	(	PUNCT
ejpam-5705	186	11	℘1	℘1	NOUN
ejpam-5705	186	12	,	,	PUNCT
ejpam-5705	186	13	ℏ)]•	ℏ)]•	NOUN
ejpam-5705	186	14	=	=	SYM
ejpam-5705	186	15	{	{	PUNCT
ejpam-5705	186	16	(	(	PUNCT
ejpam-5705	186	17	1	1	NUM
ejpam-5705	186	18	,	,	PUNCT
ejpam-5705	186	19	1	1	NUM
ejpam-5705	186	20	)	)	PUNCT
ejpam-5705	186	21	}	}	PUNCT
ejpam-5705	186	22	⇒	⇒	VERB
ejpam-5705	186	23	[	[	X
ejpam-5705	186	24	(	(	PUNCT
ejpam-5705	186	25	℘1	℘1	NOUN
ejpam-5705	186	26	,	,	PUNCT
ejpam-5705	186	27	ℏ)]•	ℏ)]•	NOUN
ejpam-5705	186	28	•	•	NOUN
ejpam-5705	186	29	=	=	SYM
ejpam-5705	186	30	v	v	NOUN
ejpam-5705	186	31	=	=	PUNCT
ejpam-5705	187	1	[	[	X
ejpam-5705	187	2	(	(	PUNCT
ejpam-5705	187	3	1	1	NUM
ejpam-5705	187	4	,	,	PUNCT
ejpam-5705	187	5	1)]•.	1)]•.	NUM
ejpam-5705	187	6	(	(	PUNCT
ejpam-5705	187	7	v	v	NOUN
ejpam-5705	187	8	)	)	PUNCT
ejpam-5705	188	1	[	[	X
ejpam-5705	188	2	(	(	PUNCT
ejpam-5705	188	3	℘2	℘2	NOUN
ejpam-5705	188	4	,	,	PUNCT
ejpam-5705	188	5	1	1	NUM
ejpam-5705	188	6	)	)	PUNCT
ejpam-5705	188	7	]	]	PUNCT
ejpam-5705	189	1	•	•	NOUN
ejpam-5705	189	2	=	=	SYM
ejpam-5705	189	3	{	{	PUNCT
ejpam-5705	189	4	(	(	PUNCT
ejpam-5705	189	5	1	1	NUM
ejpam-5705	189	6	,	,	PUNCT
ejpam-5705	189	7	1	1	NUM
ejpam-5705	189	8	)	)	PUNCT
ejpam-5705	189	9	,	,	PUNCT
ejpam-5705	189	10	(	(	PUNCT
ejpam-5705	189	11	1	1	NUM
ejpam-5705	189	12	,	,	PUNCT
ejpam-5705	189	13	ℏ	ℏ	NOUN
ejpam-5705	189	14	)	)	PUNCT
ejpam-5705	189	15	}	}	PUNCT
ejpam-5705	189	16	⇒	⇒	VERB
ejpam-5705	189	17	[	[	X
ejpam-5705	189	18	(	(	PUNCT
ejpam-5705	189	19	℘2	℘2	NOUN
ejpam-5705	189	20	,	,	PUNCT
ejpam-5705	189	21	1	1	NUM
ejpam-5705	189	22	)	)	PUNCT
ejpam-5705	189	23	]	]	PUNCT
ejpam-5705	189	24	••	••	NOUN
ejpam-5705	189	25	=	=	SYM
ejpam-5705	189	26	{	{	PUNCT
ejpam-5705	189	27	(	(	PUNCT
ejpam-5705	189	28	1	1	NUM
ejpam-5705	189	29	,	,	PUNCT
ejpam-5705	189	30	1	1	NUM
ejpam-5705	189	31	)	)	PUNCT
ejpam-5705	189	32	,	,	PUNCT
ejpam-5705	189	33	(	(	PUNCT
ejpam-5705	189	34	1	1	NUM
ejpam-5705	189	35	,	,	PUNCT
ejpam-5705	189	36	ℏ)}•	ℏ)}•	ADJ
ejpam-5705	190	1	=	=	X
ejpam-5705	190	2	{	{	PUNCT
ejpam-5705	190	3	(	(	PUNCT
ejpam-5705	190	4	1	1	NUM
ejpam-5705	190	5	,	,	PUNCT
ejpam-5705	190	6	1	1	NUM
ejpam-5705	190	7	)	)	PUNCT
ejpam-5705	190	8	,	,	PUNCT
ejpam-5705	190	9	(	(	PUNCT
ejpam-5705	190	10	℘1	℘1	VERB
ejpam-5705	190	11	,	,	PUNCT
ejpam-5705	190	12	1	1	NUM
ejpam-5705	190	13	)	)	PUNCT
ejpam-5705	190	14	,	,	PUNCT
ejpam-5705	190	15	(	(	PUNCT
ejpam-5705	190	16	℘2	℘2	PROPN
ejpam-5705	190	17	,	,	PUNCT
ejpam-5705	190	18	1	1	NUM
ejpam-5705	190	19	)	)	PUNCT
ejpam-5705	190	20	}	}	PUNCT
ejpam-5705	190	21	=	=	PUNCT
ejpam-5705	191	1	[	[	X
ejpam-5705	191	2	(	(	PUNCT
ejpam-5705	191	3	1	1	NUM
ejpam-5705	191	4	,	,	PUNCT
ejpam-5705	191	5	ℏ)]•.	ℏ)]•.	X
ejpam-5705	191	6	(	(	PUNCT
ejpam-5705	191	7	vi	vi	NOUN
ejpam-5705	191	8	)	)	PUNCT
ejpam-5705	191	9	[	[	X
ejpam-5705	191	10	(	(	PUNCT
ejpam-5705	191	11	℘2	℘2	NOUN
ejpam-5705	191	12	,	,	PUNCT
ejpam-5705	191	13	ℏ)]•	ℏ)]•	NOUN
ejpam-5705	191	14	=	=	SYM
ejpam-5705	191	15	{	{	PUNCT
ejpam-5705	191	16	(	(	PUNCT
ejpam-5705	191	17	1	1	NUM
ejpam-5705	191	18	,	,	PUNCT
ejpam-5705	191	19	1	1	NUM
ejpam-5705	191	20	)	)	PUNCT
ejpam-5705	191	21	}	}	PUNCT
ejpam-5705	191	22	⇒	⇒	VERB
ejpam-5705	191	23	[	[	X
ejpam-5705	191	24	(	(	PUNCT
ejpam-5705	191	25	℘2	℘2	NOUN
ejpam-5705	191	26	,	,	PUNCT
ejpam-5705	191	27	ℏ)]•	ℏ)]•	NOUN
ejpam-5705	191	28	•	•	NOUN
ejpam-5705	191	29	=	=	SYM
ejpam-5705	191	30	v	v	NOUN
ejpam-5705	191	31	=	=	PUNCT
ejpam-5705	192	1	[	[	X
ejpam-5705	192	2	(	(	PUNCT
ejpam-5705	192	3	1	1	NUM
ejpam-5705	192	4	,	,	PUNCT
ejpam-5705	192	5	1)]•.	1)]•.	NUM
ejpam-5705	192	6	thus	thus	ADV
ejpam-5705	192	7	(	(	PUNCT
ejpam-5705	192	8	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	192	9	,	,	PUNCT
ejpam-5705	192	10	1′	1′	NUM
ejpam-5705	192	11	)	)	PUNCT
ejpam-5705	192	12	is	be	AUX
ejpam-5705	192	13	a	a	DET
ejpam-5705	192	14	•-pdl	•-pdl	NOUN
ejpam-5705	192	15	.	.	PUNCT
ejpam-5705	193	1	lemma	lemma	PROPN
ejpam-5705	193	2	7	7	X
ejpam-5705	193	3	.	.	PUNCT
ejpam-5705	194	1	let	let	VERB
ejpam-5705	194	2	v	v	PART
ejpam-5705	194	3	be	be	AUX
ejpam-5705	194	4	a	a	DET
ejpam-5705	194	5	•-pdl	•-pdl	PUNCT
ejpam-5705	194	6	and	and	CCONJ
ejpam-5705	194	7	℘	℘	PROPN
ejpam-5705	194	8	∈	∈	PROPN
ejpam-5705	194	9	v	v	NOUN
ejpam-5705	194	10	.	.	PUNCT
ejpam-5705	195	1	then	then	ADV
ejpam-5705	195	2	[	[	X
ejpam-5705	195	3	℘]•	℘]•	PROPN
ejpam-5705	195	4	∩	∩	NOUN
ejpam-5705	195	5	[	[	X
ejpam-5705	195	6	℘]•	℘]•	PROPN
ejpam-5705	195	7	•	•	NOUN
ejpam-5705	195	8	=	=	PUNCT
ejpam-5705	195	9	{	{	PUNCT
ejpam-5705	195	10	1	1	NUM
ejpam-5705	195	11	}	}	PUNCT
ejpam-5705	195	12	.	.	PUNCT
ejpam-5705	196	1	proof	proof	NOUN
ejpam-5705	196	2	.	.	PUNCT
ejpam-5705	197	1	let	let	VERB
ejpam-5705	197	2	℘	℘	PROPN
ejpam-5705	197	3	∈	∈	NOUN
ejpam-5705	197	4	v	v	NOUN
ejpam-5705	197	5	.	.	PUNCT
ejpam-5705	198	1	then	then	ADV
ejpam-5705	198	2	[	[	X
ejpam-5705	198	3	℘]•	℘]•	PROPN
ejpam-5705	198	4	•	•	NOUN
ejpam-5705	198	5	=	=	PUNCT
ejpam-5705	199	1	[	[	X
ejpam-5705	199	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	199	3	for	for	ADP
ejpam-5705	199	4	some	some	DET
ejpam-5705	199	5	ℏ	ℏ	PROPN
ejpam-5705	199	6	∈	∈	PROPN
ejpam-5705	199	7	v	v	NOUN
ejpam-5705	199	8	.	.	PUNCT
ejpam-5705	200	1	let	let	VERB
ejpam-5705	200	2	µ1	µ1	NOUN
ejpam-5705	200	3	∈	∈	PROPN
ejpam-5705	201	1	[	[	X
ejpam-5705	201	2	℘]•	℘]•	PROPN
ejpam-5705	201	3	and	and	CCONJ
ejpam-5705	201	4	µ1	µ1	PROPN
ejpam-5705	201	5	∈	∈	PROPN
ejpam-5705	202	1	[	[	X
ejpam-5705	202	2	℘]•	℘]•	PROPN
ejpam-5705	202	3	•	•	NOUN
ejpam-5705	202	4	.	.	PUNCT
ejpam-5705	203	1	since	since	SCONJ
ejpam-5705	203	2	µ1	µ1	PROPN
ejpam-5705	203	3	∨	∨	NUM
ejpam-5705	203	4	µ1	µ1	NOUN
ejpam-5705	203	5	=	=	SYM
ejpam-5705	203	6	1	1	NUM
ejpam-5705	203	7	,	,	PUNCT
ejpam-5705	203	8	we	we	PRON
ejpam-5705	203	9	have	have	VERB
ejpam-5705	203	10	µ1	µ1	NOUN
ejpam-5705	203	11	=	=	SYM
ejpam-5705	203	12	1	1	NUM
ejpam-5705	203	13	.	.	PUNCT
ejpam-5705	204	1	therefore	therefore	ADV
ejpam-5705	204	2	[	[	X
ejpam-5705	204	3	℘]•	℘]•	PROPN
ejpam-5705	204	4	∩	∩	NOUN
ejpam-5705	204	5	[	[	X
ejpam-5705	204	6	℘]•	℘]•	PROPN
ejpam-5705	204	7	•	•	NOUN
ejpam-5705	204	8	=	=	PUNCT
ejpam-5705	204	9	{	{	PUNCT
ejpam-5705	204	10	1	1	NUM
ejpam-5705	204	11	}	}	PUNCT
ejpam-5705	204	12	.	.	PUNCT
ejpam-5705	205	1	lemma	lemma	PROPN
ejpam-5705	205	2	8	8	NUM
ejpam-5705	205	3	.	.	PUNCT
ejpam-5705	206	1	let	let	VERB
ejpam-5705	206	2	v	v	PART
ejpam-5705	206	3	be	be	AUX
ejpam-5705	206	4	a	a	DET
ejpam-5705	206	5	pdl	pdl	NOUN
ejpam-5705	206	6	.	.	PUNCT
ejpam-5705	207	1	then	then	ADV
ejpam-5705	207	2	the	the	DET
ejpam-5705	207	3	relation	relation	NOUN
ejpam-5705	207	4	θ	θ	PROPN
ejpam-5705	207	5	=	=	SYM
ejpam-5705	207	6	{	{	PUNCT
ejpam-5705	207	7	(	(	PUNCT
ejpam-5705	207	8	℘	℘	NOUN
ejpam-5705	207	9	,	,	PUNCT
ejpam-5705	207	10	ℏ	ℏ	NOUN
ejpam-5705	207	11	)	)	PUNCT
ejpam-5705	207	12	∈	∈	PROPN
ejpam-5705	207	13	v	v	ADP
ejpam-5705	207	14	×	×	NOUN
ejpam-5705	207	15	v	v	INTJ
ejpam-5705	208	1	|	|	NOUN
ejpam-5705	209	1	[	[	X
ejpam-5705	209	2	℘]•	℘]•	PROPN
ejpam-5705	209	3	=	=	PUNCT
ejpam-5705	209	4	[	[	X
ejpam-5705	209	5	ℏ]•	ℏ]•	NOUN
ejpam-5705	209	6	}	}	PUNCT
ejpam-5705	209	7	is	be	AUX
ejpam-5705	209	8	a	a	DET
ejpam-5705	209	9	congruence	congruence	NOUN
ejpam-5705	209	10	relation	relation	NOUN
ejpam-5705	209	11	on	on	ADP
ejpam-5705	209	12	v	v	NUM
ejpam-5705	209	13	.	.	PUNCT
ejpam-5705	210	1	proof	proof	NOUN
ejpam-5705	210	2	.	.	PUNCT
ejpam-5705	211	1	clearly	clearly	ADV
ejpam-5705	211	2	θ	θ	PROPN
ejpam-5705	211	3	is	be	AUX
ejpam-5705	211	4	an	an	DET
ejpam-5705	211	5	equivalence	equivalence	NOUN
ejpam-5705	211	6	relation	relation	NOUN
ejpam-5705	211	7	on	on	ADP
ejpam-5705	211	8	v	v	NUM
ejpam-5705	211	9	.	.	PUNCT
ejpam-5705	212	1	let	let	VERB
ejpam-5705	212	2	(	(	PUNCT
ejpam-5705	212	3	℘	℘	NOUN
ejpam-5705	212	4	,	,	PUNCT
ejpam-5705	212	5	ℏ	ℏ	NOUN
ejpam-5705	212	6	)	)	PUNCT
ejpam-5705	212	7	∈	∈	PROPN
ejpam-5705	212	8	θ	θ	PROPN
ejpam-5705	212	9	and	and	CCONJ
ejpam-5705	212	10	µ1	µ1	PROPN
ejpam-5705	212	11	∈	∈	PROPN
ejpam-5705	212	12	v	v	NOUN
ejpam-5705	212	13	.	.	PUNCT
ejpam-5705	213	1	then	then	ADV
ejpam-5705	213	2	[	[	X
ejpam-5705	213	3	℘]•	℘]•	PUNCT
ejpam-5705	213	4	=	=	PUNCT
ejpam-5705	214	1	[	[	X
ejpam-5705	214	2	ℏ]•.	ℏ]•.	X
ejpam-5705	214	3	now	now	ADV
ejpam-5705	214	4	[	[	X
ejpam-5705	214	5	℘∧µ1	℘∧µ1	NOUN
ejpam-5705	214	6	]	]	X
ejpam-5705	214	7	•	•	NOUN
ejpam-5705	214	8	=	=	SYM
ejpam-5705	215	1	[	[	X
ejpam-5705	215	2	℘]•∩[µ1	℘]•∩[µ1	X
ejpam-5705	215	3	]	]	X
ejpam-5705	215	4	•	•	NOUN
ejpam-5705	215	5	=	=	SYM
ejpam-5705	216	1	[	[	X
ejpam-5705	216	2	ℏ]•∩[µ1	ℏ]•∩[µ1	X
ejpam-5705	216	3	]	]	X
ejpam-5705	216	4	•	•	NOUN
ejpam-5705	216	5	=	=	SYM
ejpam-5705	217	1	[	[	X
ejpam-5705	217	2	ℏ∧µ1	ℏ∧µ1	NOUN
ejpam-5705	217	3	]	]	X
ejpam-5705	217	4	•.	•.	NOUN
ejpam-5705	217	5	therefore	therefore	ADV
ejpam-5705	217	6	(	(	PUNCT
ejpam-5705	217	7	℘∧µ1	℘∧µ1	NOUN
ejpam-5705	217	8	,	,	PUNCT
ejpam-5705	217	9	ℏ∧µ1	ℏ∧µ1	ADJ
ejpam-5705	217	10	)	)	PUNCT
ejpam-5705	217	11	∈	∈	PROPN
ejpam-5705	217	12	θ	θ	PROPN
ejpam-5705	217	13	.	.	PUNCT
ejpam-5705	217	14	let	let	VERB
ejpam-5705	217	15	τ	τ	PROPN
ejpam-5705	217	16	∈	∈	PROPN
ejpam-5705	217	17	[	[	X
ejpam-5705	217	18	℘∨µ1	℘∨µ1	NOUN
ejpam-5705	217	19	]	]	PUNCT
ejpam-5705	217	20	•.	•.	NOUN
ejpam-5705	217	21	then	then	ADV
ejpam-5705	217	22	τ	τ	X
ejpam-5705	217	23	∨℘∨µ1	∨℘∨µ1	X
ejpam-5705	217	24	=	=	SYM
ejpam-5705	217	25	1	1	NUM
ejpam-5705	217	26	and	and	CCONJ
ejpam-5705	217	27	hence	hence	ADV
ejpam-5705	217	28	τ	τ	X
ejpam-5705	217	29	∨µ1∨℘	∨µ1∨℘	NOUN
ejpam-5705	217	30	=	=	NUM
ejpam-5705	217	31	1	1	X
ejpam-5705	217	32	.	.	PUNCT
ejpam-5705	217	33	therefore	therefore	ADV
ejpam-5705	217	34	τ	τ	PROPN
ejpam-5705	217	35	∨µ1	∨µ1	NOUN
ejpam-5705	217	36	∈	∈	PROPN
ejpam-5705	217	37	[	[	X
ejpam-5705	217	38	℘]•	℘]•	PROPN
ejpam-5705	217	39	and	and	CCONJ
ejpam-5705	217	40	hence	hence	ADV
ejpam-5705	217	41	τ	τ	PROPN
ejpam-5705	217	42	∨	∨	NUM
ejpam-5705	217	43	µ1	µ1	PROPN
ejpam-5705	217	44	∈	∈	PROPN
ejpam-5705	218	1	[	[	X
ejpam-5705	218	2	ℏ]•.	ℏ]•.	X
ejpam-5705	218	3	so	so	SCONJ
ejpam-5705	218	4	that	that	SCONJ
ejpam-5705	218	5	τ	τ	PROPN
ejpam-5705	218	6	∨	∨	NUM
ejpam-5705	218	7	µ1	µ1	PROPN
ejpam-5705	218	8	∨	∨	NOUN
ejpam-5705	218	9	ℏ	ℏ	NOUN
ejpam-5705	218	10	=	=	SYM
ejpam-5705	218	11	1	1	NUM
ejpam-5705	218	12	which	which	PRON
ejpam-5705	218	13	implies	imply	VERB
ejpam-5705	218	14	that	that	SCONJ
ejpam-5705	218	15	τ	τ	PROPN
ejpam-5705	218	16	∨	∨	NUM
ejpam-5705	218	17	ℏ	ℏ	PROPN
ejpam-5705	218	18	∨	∨	NUM
ejpam-5705	218	19	µ1	µ1	NOUN
ejpam-5705	218	20	=	=	SYM
ejpam-5705	218	21	1	1	NUM
ejpam-5705	218	22	.	.	PUNCT
ejpam-5705	219	1	hence	hence	ADV
ejpam-5705	219	2	τ	τ	X
ejpam-5705	219	3	∈	∈	PROPN
ejpam-5705	219	4	[	[	X
ejpam-5705	219	5	ℏ∨µ1	ℏ∨µ1	NOUN
ejpam-5705	219	6	]	]	X
ejpam-5705	219	7	•	•	X
ejpam-5705	219	8	,	,	PUNCT
ejpam-5705	219	9	we	we	PRON
ejpam-5705	219	10	get	get	VERB
ejpam-5705	219	11	[	[	X
ejpam-5705	219	12	℘∨µ1	℘∨µ1	NOUN
ejpam-5705	219	13	]	]	PUNCT
ejpam-5705	219	14	•	•	NUM
ejpam-5705	219	15	⊆	⊆	NUM
ejpam-5705	219	16	[	[	X
ejpam-5705	219	17	ℏ∨µ1	ℏ∨µ1	NOUN
ejpam-5705	219	18	]	]	PUNCT
ejpam-5705	219	19	•.	•.	NOUN
ejpam-5705	219	20	similarly	similarly	ADV
ejpam-5705	219	21	,	,	PUNCT
ejpam-5705	219	22	we	we	PRON
ejpam-5705	219	23	get	get	VERB
ejpam-5705	219	24	that	that	DET
ejpam-5705	219	25	[	[	X
ejpam-5705	219	26	ℏ∨µ1	ℏ∨µ1	NOUN
ejpam-5705	219	27	]	]	X
ejpam-5705	219	28	•	•	NUM
ejpam-5705	219	29	⊆	⊆	NUM
ejpam-5705	219	30	[	[	X
ejpam-5705	219	31	℘∨µ1	℘∨µ1	NOUN
ejpam-5705	219	32	]	]	PUNCT
ejpam-5705	219	33	•.	•.	NOUN
ejpam-5705	219	34	thus	thus	ADV
ejpam-5705	219	35	[	[	PUNCT
ejpam-5705	219	36	℘	℘	PROPN
ejpam-5705	219	37	∨	∨	NUM
ejpam-5705	219	38	µ1	µ1	PROPN
ejpam-5705	219	39	]	]	PUNCT
ejpam-5705	219	40	•	•	NOUN
ejpam-5705	220	1	=	=	PUNCT
ejpam-5705	221	1	[	[	X
ejpam-5705	221	2	ℏ	ℏ	PROPN
ejpam-5705	221	3	∨	∨	NUM
ejpam-5705	221	4	µ1	µ1	PROPN
ejpam-5705	221	5	]	]	PUNCT
ejpam-5705	221	6	•.	•.	NOUN
ejpam-5705	221	7	therefore	therefore	ADV
ejpam-5705	221	8	(	(	PUNCT
ejpam-5705	221	9	℘	℘	PROPN
ejpam-5705	221	10	∨	∨	NUM
ejpam-5705	221	11	µ1	µ1	PROPN
ejpam-5705	221	12	,	,	PUNCT
ejpam-5705	221	13	ℏ	ℏ	PROPN
ejpam-5705	221	14	∨	∨	NUM
ejpam-5705	221	15	µ1	µ1	PROPN
ejpam-5705	221	16	)	)	PUNCT
ejpam-5705	221	17	∈	∈	PROPN
ejpam-5705	221	18	θ	θ	PROPN
ejpam-5705	221	19	.	.	PUNCT
ejpam-5705	222	1	hence	hence	ADV
ejpam-5705	222	2	θ	θ	PROPN
ejpam-5705	222	3	is	be	AUX
ejpam-5705	222	4	a	a	DET
ejpam-5705	222	5	congruence	congruence	NOUN
ejpam-5705	222	6	relation	relation	NOUN
ejpam-5705	222	7	on	on	ADP
ejpam-5705	222	8	v	v	NUM
ejpam-5705	222	9	.	.	PUNCT
ejpam-5705	223	1	note	note	VERB
ejpam-5705	223	2	that	that	SCONJ
ejpam-5705	223	3	,	,	PUNCT
ejpam-5705	223	4	by	by	ADP
ejpam-5705	223	5	the	the	DET
ejpam-5705	223	6	above	above	ADJ
ejpam-5705	223	7	lemma	lemma	PROPN
ejpam-5705	223	8	8	8	NUM
ejpam-5705	223	9	,	,	PUNCT
ejpam-5705	223	10	v	v	NOUN
ejpam-5705	223	11	/	/	SYM
ejpam-5705	223	12	θ	θ	PROPN
ejpam-5705	223	13	is	be	AUX
ejpam-5705	223	14	pdl	pdl	NOUN
ejpam-5705	223	15	under	under	ADP
ejpam-5705	223	16	the	the	DET
ejpam-5705	223	17	induced	induced	ADJ
ejpam-5705	223	18	operations	operation	NOUN
ejpam-5705	223	19	∨	∨	NOUN
ejpam-5705	223	20	and	and	CCONJ
ejpam-5705	223	21	∧	∧	NOUN
ejpam-5705	223	22	in	in	ADP
ejpam-5705	223	23	v	v	NOUN
ejpam-5705	223	24	and	and	CCONJ
ejpam-5705	223	25	is	be	AUX
ejpam-5705	223	26	defined	define	VERB
ejpam-5705	223	27	as	as	SCONJ
ejpam-5705	223	28	follows	follow	VERB
ejpam-5705	223	29	:	:	PUNCT
ejpam-5705	223	30	for	for	ADP
ejpam-5705	223	31	any	any	DET
ejpam-5705	223	32	℘/θ	℘/θ	NOUN
ejpam-5705	223	33	,	,	PUNCT
ejpam-5705	223	34	ℏ/θ	ℏ/θ	ADP
ejpam-5705	223	35	∈	∈	PROPN
ejpam-5705	223	36	v	v	NOUN
ejpam-5705	223	37	/	/	SYM
ejpam-5705	223	38	θ	θ	NOUN
ejpam-5705	223	39	,	,	PUNCT
ejpam-5705	223	40	(	(	PUNCT
ejpam-5705	223	41	i	i	NOUN
ejpam-5705	223	42	)	)	PUNCT
ejpam-5705	223	43	℘/θ	℘/θ	NOUN
ejpam-5705	223	44	∨	∨	NOUN
ejpam-5705	223	45	ℏ/θ	ℏ/θ	ADV
ejpam-5705	223	46	=	=	PUNCT
ejpam-5705	223	47	(	(	PUNCT
ejpam-5705	223	48	℘	℘	PROPN
ejpam-5705	223	49	∨	∨	NUM
ejpam-5705	223	50	ℏ)/θ	ℏ)/θ	PROPN
ejpam-5705	223	51	.	.	PUNCT
ejpam-5705	224	1	(	(	PUNCT
ejpam-5705	224	2	ii	ii	NOUN
ejpam-5705	224	3	)	)	PUNCT
ejpam-5705	224	4	℘/θ	℘/θ	NOUN
ejpam-5705	224	5	∧	∧	PROPN
ejpam-5705	224	6	ℏ/θ	ℏ/θ	NOUN
ejpam-5705	224	7	=	=	PUNCT
ejpam-5705	224	8	(	(	PUNCT
ejpam-5705	224	9	℘	℘	X
ejpam-5705	224	10	∧	∧	PROPN
ejpam-5705	224	11	ℏ)/θ	ℏ)/θ	PROPN
ejpam-5705	224	12	.	.	PUNCT
ejpam-5705	225	1	theorem	theorem	VERB
ejpam-5705	225	2	6	6	NUM
ejpam-5705	225	3	.	.	PUNCT
ejpam-5705	226	1	let	let	VERB
ejpam-5705	226	2	v	v	PART
ejpam-5705	226	3	be	be	AUX
ejpam-5705	226	4	a	a	DET
ejpam-5705	226	5	pdl	pdl	NOUN
ejpam-5705	226	6	with	with	ADP
ejpam-5705	226	7	a	a	DET
ejpam-5705	226	8	minimal	minimal	ADJ
ejpam-5705	226	9	element	element	NOUN
ejpam-5705	226	10	m.	m.	NOUN
ejpam-5705	226	11	then	then	ADV
ejpam-5705	226	12	v	v	NOUN
ejpam-5705	226	13	/	/	SYM
ejpam-5705	226	14	θ	θ	PROPN
ejpam-5705	226	15	is	be	AUX
ejpam-5705	226	16	distributive	distributive	ADJ
ejpam-5705	226	17	lattice	lattice	NOUN
ejpam-5705	226	18	with	with	ADP
ejpam-5705	226	19	the	the	DET
ejpam-5705	226	20	greatest	great	ADJ
ejpam-5705	226	21	element	element	NOUN
ejpam-5705	226	22	as	as	ADP
ejpam-5705	226	23	1	1	NUM
ejpam-5705	226	24	/	/	SYM
ejpam-5705	226	25	θ	θ	NOUN
ejpam-5705	226	26	,	,	PUNCT
ejpam-5705	226	27	and	and	CCONJ
ejpam-5705	226	28	m	m	PROPN
ejpam-5705	226	29	/	/	SYM
ejpam-5705	226	30	θ	θ	PROPN
ejpam-5705	226	31	as	as	ADP
ejpam-5705	226	32	the	the	DET
ejpam-5705	226	33	least	least	ADJ
ejpam-5705	226	34	element	element	NOUN
ejpam-5705	226	35	.	.	PUNCT
ejpam-5705	227	1	proof	proof	NOUN
ejpam-5705	227	2	.	.	PUNCT
ejpam-5705	228	1	let	let	VERB
ejpam-5705	228	2	℘/θ	℘/θ	NOUN
ejpam-5705	228	3	,	,	PUNCT
ejpam-5705	228	4	ℏ/θ	ℏ/θ	ADP
ejpam-5705	228	5	∈	∈	PROPN
ejpam-5705	228	6	v	v	NOUN
ejpam-5705	228	7	/	/	SYM
ejpam-5705	228	8	θ	θ	NOUN
ejpam-5705	228	9	.	.	PUNCT
ejpam-5705	229	1	since	since	SCONJ
ejpam-5705	229	2	[	[	X
ejpam-5705	229	3	℘∨ℏ]•	℘∨ℏ]•	PROPN
ejpam-5705	229	4	=	=	PUNCT
ejpam-5705	230	1	[	[	X
ejpam-5705	230	2	ℏ∨℘]•	ℏ∨℘]•	PROPN
ejpam-5705	230	3	,	,	PUNCT
ejpam-5705	230	4	we	we	PRON
ejpam-5705	230	5	have	have	VERB
ejpam-5705	230	6	(	(	PUNCT
ejpam-5705	230	7	℘∨ℏ	℘∨ℏ	X
ejpam-5705	230	8	,	,	PUNCT
ejpam-5705	230	9	ℏ∨℘	ℏ∨℘	ADJ
ejpam-5705	230	10	)	)	PUNCT
ejpam-5705	230	11	∈	∈	PROPN
ejpam-5705	230	12	θ	θ	PROPN
ejpam-5705	230	13	.	.	PUNCT
ejpam-5705	231	1	therefore	therefore	ADV
ejpam-5705	231	2	(	(	PUNCT
ejpam-5705	231	3	℘∨ℏ)/θ	℘∨ℏ)/θ	NOUN
ejpam-5705	231	4	=	=	SYM
ejpam-5705	231	5	(	(	PUNCT
ejpam-5705	231	6	ℏ∨℘)/θ	ℏ∨℘)/θ	PROPN
ejpam-5705	231	7	and	and	CCONJ
ejpam-5705	231	8	hence	hence	ADV
ejpam-5705	231	9	℘/θ∨ℏ/θ	℘/θ∨ℏ/θ	ADV
ejpam-5705	231	10	=	=	SYM
ejpam-5705	231	11	ℏ/θ∨℘/θ	ℏ/θ∨℘/θ	ADJ
ejpam-5705	231	12	.	.	PUNCT
ejpam-5705	232	1	thus	thus	ADV
ejpam-5705	232	2	v	v	X
ejpam-5705	232	3	/	/	SYM
ejpam-5705	232	4	θ	θ	PROPN
ejpam-5705	232	5	is	be	AUX
ejpam-5705	232	6	a	a	DET
ejpam-5705	232	7	distributive	distributive	ADJ
ejpam-5705	232	8	lattice	lattice	NOUN
ejpam-5705	232	9	.	.	PUNCT
ejpam-5705	233	1	clearly	clearly	ADV
ejpam-5705	233	2	1	1	NUM
ejpam-5705	233	3	/	/	SYM
ejpam-5705	233	4	θ	θ	PROPN
ejpam-5705	233	5	is	be	AUX
ejpam-5705	233	6	a	a	DET
ejpam-5705	233	7	greatest	great	ADJ
ejpam-5705	233	8	element	element	NOUN
ejpam-5705	233	9	.	.	PUNCT
ejpam-5705	234	1	suppose	suppose	VERB
ejpam-5705	234	2	m	m	PRON
ejpam-5705	234	3	is	be	AUX
ejpam-5705	234	4	a	a	DET
ejpam-5705	234	5	minimal	minimal	ADJ
ejpam-5705	234	6	element	element	NOUN
ejpam-5705	234	7	of	of	ADP
ejpam-5705	234	8	v	v	NOUN
ejpam-5705	234	9	.	.	PUNCT
ejpam-5705	235	1	then	then	ADV
ejpam-5705	235	2	for	for	ADP
ejpam-5705	235	3	any	any	DET
ejpam-5705	235	4	℘	℘	PROPN
ejpam-5705	235	5	∈	∈	NOUN
ejpam-5705	235	6	v	v	NOUN
ejpam-5705	235	7	,	,	PUNCT
ejpam-5705	235	8	m	m	PROPN
ejpam-5705	235	9	/	/	SYM
ejpam-5705	235	10	θ	θ	PROPN
ejpam-5705	235	11	∧	∧	PROPN
ejpam-5705	235	12	℘/θ	℘/θ	NUM
ejpam-5705	235	13	=	=	SYM
ejpam-5705	235	14	℘/θ	℘/θ	NUM
ejpam-5705	235	15	∧m	∧m	PROPN
ejpam-5705	235	16	/	/	SYM
ejpam-5705	235	17	θ	θ	NOUN
ejpam-5705	235	18	=	=	PUNCT
ejpam-5705	235	19	(	(	PUNCT
ejpam-5705	235	20	℘	℘	X
ejpam-5705	235	21	∧m)/θ	∧m)/θ	AUX
ejpam-5705	235	22	=	=	SYM
ejpam-5705	235	23	m	m	NOUN
ejpam-5705	235	24	/	/	SYM
ejpam-5705	235	25	θ	θ	PROPN
ejpam-5705	235	26	.	.	PUNCT
ejpam-5705	236	1	therefore	therefore	ADV
ejpam-5705	236	2	m	m	PROPN
ejpam-5705	236	3	/	/	SYM
ejpam-5705	236	4	θ	θ	PROPN
ejpam-5705	236	5	is	be	AUX
ejpam-5705	236	6	the	the	DET
ejpam-5705	236	7	least	least	ADJ
ejpam-5705	236	8	element	element	NOUN
ejpam-5705	236	9	of	of	ADP
ejpam-5705	236	10	v	v	NOUN
ejpam-5705	236	11	/	/	SYM
ejpam-5705	236	12	θ	θ	NOUN
ejpam-5705	236	13	.	.	PUNCT
ejpam-5705	236	14	note	note	VERB
ejpam-5705	236	15	that	that	SCONJ
ejpam-5705	236	16	[	[	X
ejpam-5705	236	17	1]•	1]•	NUM
ejpam-5705	236	18	=	=	SYM
ejpam-5705	236	19	{	{	PUNCT
ejpam-5705	236	20	℘	℘	NOUN
ejpam-5705	236	21	∈	∈	NOUN
ejpam-5705	236	22	v	v	ADP
ejpam-5705	236	23	|	|	ADV
ejpam-5705	236	24	℘	℘	VERB
ejpam-5705	236	25	∨	∨	NUM
ejpam-5705	236	26	1	1	NUM
ejpam-5705	236	27	=	=	SYM
ejpam-5705	236	28	1	1	NUM
ejpam-5705	236	29	}	}	PUNCT
ejpam-5705	236	30	=	=	SYM
ejpam-5705	236	31	v	v	NOUN
ejpam-5705	236	32	.	.	PUNCT
ejpam-5705	237	1	r.	r.	PROPN
ejpam-5705	237	2	bandaru	bandaru	PROPN
ejpam-5705	237	3	et	et	PROPN
ejpam-5705	237	4	al	al	PROPN
ejpam-5705	237	5	.	.	PUNCT
ejpam-5705	237	6	/	/	SYM
ejpam-5705	237	7	eur	eur	PROPN
ejpam-5705	237	8	.	.	PUNCT
ejpam-5705	238	1	j.	j.	PROPN
ejpam-5705	238	2	pure	pure	PROPN
ejpam-5705	238	3	appl	appl	PROPN
ejpam-5705	238	4	.	.	PROPN
ejpam-5705	238	5	math	math	PROPN
ejpam-5705	238	6	,	,	PUNCT
ejpam-5705	238	7	18	18	NUM
ejpam-5705	238	8	(	(	PUNCT
ejpam-5705	238	9	2	2	NUM
ejpam-5705	238	10	)	)	PUNCT
ejpam-5705	238	11	(	(	PUNCT
ejpam-5705	238	12	2025	2025	NUM
ejpam-5705	238	13	)	)	PUNCT
ejpam-5705	238	14	,	,	PUNCT
ejpam-5705	238	15	5705	5705	NUM
ejpam-5705	238	16	8	8	NUM
ejpam-5705	238	17	of	of	ADP
ejpam-5705	238	18	13	13	NUM
ejpam-5705	238	19	lemma	lemma	PROPN
ejpam-5705	238	20	9	9	NUM
ejpam-5705	238	21	.	.	PUNCT
ejpam-5705	239	1	let	let	VERB
ejpam-5705	239	2	v	v	PART
ejpam-5705	239	3	be	be	AUX
ejpam-5705	239	4	a	a	DET
ejpam-5705	239	5	pdl	pdl	NOUN
ejpam-5705	239	6	.	.	PUNCT
ejpam-5705	240	1	then	then	ADV
ejpam-5705	240	2	[	[	X
ejpam-5705	240	3	℘]•	℘]•	PUNCT
ejpam-5705	240	4	=	=	PUNCT
ejpam-5705	241	1	[	[	X
ejpam-5705	241	2	1]•	1]•	NUM
ejpam-5705	241	3	⇔	⇔	X
ejpam-5705	241	4	℘	℘	PROPN
ejpam-5705	241	5	=	=	SYM
ejpam-5705	241	6	1	1	X
ejpam-5705	241	7	.	.	PUNCT
ejpam-5705	241	8	proof	proof	NOUN
ejpam-5705	241	9	.	.	PUNCT
ejpam-5705	242	1	suppose	suppose	VERB
ejpam-5705	242	2	℘	℘	PROPN
ejpam-5705	242	3	=	=	SYM
ejpam-5705	242	4	1	1	X
ejpam-5705	242	5	.	.	PUNCT
ejpam-5705	243	1	then	then	ADV
ejpam-5705	243	2	[	[	X
ejpam-5705	243	3	℘]•	℘]•	PROPN
ejpam-5705	243	4	=	=	PUNCT
ejpam-5705	244	1	[	[	X
ejpam-5705	244	2	1]•.	1]•.	NOUN
ejpam-5705	244	3	conversely	conversely	ADV
ejpam-5705	244	4	,	,	PUNCT
ejpam-5705	244	5	assume	assume	VERB
ejpam-5705	244	6	that	that	SCONJ
ejpam-5705	244	7	℘	℘	PROPN
ejpam-5705	244	8	∈	∈	PROPN
ejpam-5705	244	9	v	v	NOUN
ejpam-5705	244	10	and	and	CCONJ
ejpam-5705	244	11	[	[	X
ejpam-5705	244	12	℘]•	℘]•	PROPN
ejpam-5705	244	13	=	=	PUNCT
ejpam-5705	245	1	[	[	X
ejpam-5705	245	2	1]•.	1]•.	ADJ
ejpam-5705	245	3	then	then	ADV
ejpam-5705	245	4	℘	℘	PROPN
ejpam-5705	245	5	∨	∨	NUM
ejpam-5705	245	6	1	1	NUM
ejpam-5705	245	7	=	=	SYM
ejpam-5705	245	8	1	1	NUM
ejpam-5705	245	9	implies	imply	VERB
ejpam-5705	245	10	that	that	SCONJ
ejpam-5705	245	11	℘	℘	PROPN
ejpam-5705	245	12	∈	∈	PROPN
ejpam-5705	246	1	[	[	X
ejpam-5705	246	2	1]•	1]•	NUM
ejpam-5705	246	3	=	=	SYM
ejpam-5705	246	4	[	[	X
ejpam-5705	246	5	℘]•.	℘]•.	ADJ
ejpam-5705	246	6	hence	hence	ADV
ejpam-5705	246	7	℘	℘	NUM
ejpam-5705	246	8	=	=	SYM
ejpam-5705	246	9	℘	℘	PROPN
ejpam-5705	246	10	∨	∨	NUM
ejpam-5705	246	11	℘	℘	NOUN
ejpam-5705	246	12	=	=	SYM
ejpam-5705	246	13	1	1	X
ejpam-5705	246	14	.	.	PUNCT
ejpam-5705	247	1	now	now	ADV
ejpam-5705	247	2	we	we	PRON
ejpam-5705	247	3	prove	prove	VERB
ejpam-5705	247	4	the	the	DET
ejpam-5705	247	5	following	following	NOUN
ejpam-5705	247	6	:	:	PUNCT
ejpam-5705	247	7	theorem	theorem	NOUN
ejpam-5705	247	8	7	7	NUM
ejpam-5705	247	9	.	.	PUNCT
ejpam-5705	248	1	let	let	VERB
ejpam-5705	248	2	v	v	PART
ejpam-5705	248	3	be	be	AUX
ejpam-5705	248	4	a	a	DET
ejpam-5705	248	5	pdl	pdl	NOUN
ejpam-5705	248	6	.	.	PUNCT
ejpam-5705	249	1	if	if	SCONJ
ejpam-5705	249	2	v	v	NOUN
ejpam-5705	249	3	/	/	SYM
ejpam-5705	249	4	θ	θ	PROPN
ejpam-5705	249	5	is	be	AUX
ejpam-5705	249	6	a	a	DET
ejpam-5705	249	7	boolean	boolean	ADJ
ejpam-5705	249	8	algebra	algebra	NOUN
ejpam-5705	249	9	then	then	ADV
ejpam-5705	249	10	v	v	NOUN
ejpam-5705	249	11	is	be	AUX
ejpam-5705	249	12	a	a	DET
ejpam-5705	249	13	•-pdl	•-pdl	NOUN
ejpam-5705	249	14	.	.	PUNCT
ejpam-5705	249	15	proof	proof	NOUN
ejpam-5705	249	16	.	.	PUNCT
ejpam-5705	250	1	let	let	VERB
ejpam-5705	250	2	v	v	NOUN
ejpam-5705	250	3	/	/	SYM
ejpam-5705	250	4	θ	θ	NOUN
ejpam-5705	250	5	be	be	AUX
ejpam-5705	250	6	boolean	boolean	ADJ
ejpam-5705	250	7	algebra	algebra	NOUN
ejpam-5705	250	8	and	and	CCONJ
ejpam-5705	250	9	℘	℘	PROPN
ejpam-5705	250	10	∈	∈	PROPN
ejpam-5705	250	11	v	v	NOUN
ejpam-5705	250	12	.	.	PUNCT
ejpam-5705	251	1	then	then	ADV
ejpam-5705	251	2	℘/θ	℘/θ	ADJ
ejpam-5705	251	3	∈	∈	PROPN
ejpam-5705	251	4	v	v	NOUN
ejpam-5705	251	5	/	/	SYM
ejpam-5705	251	6	θ	θ	NOUN
ejpam-5705	251	7	.	.	PUNCT
ejpam-5705	252	1	hence	hence	ADV
ejpam-5705	252	2	,	,	PUNCT
ejpam-5705	252	3	there	there	PRON
ejpam-5705	252	4	exists	exist	VERB
ejpam-5705	252	5	ℏ/θ	ℏ/θ	ADP
ejpam-5705	252	6	∈	∈	NOUN
ejpam-5705	252	7	v	v	NOUN
ejpam-5705	252	8	/	/	SYM
ejpam-5705	252	9	θ	θ	NOUN
ejpam-5705	252	10	such	such	ADJ
ejpam-5705	252	11	that	that	SCONJ
ejpam-5705	252	12	℘/θ∨ℏ/θ	℘/θ∨ℏ/θ	NOUN
ejpam-5705	252	13	=	=	NOUN
ejpam-5705	252	14	1	1	NUM
ejpam-5705	252	15	/	/	SYM
ejpam-5705	252	16	θ	θ	PROPN
ejpam-5705	252	17	and	and	CCONJ
ejpam-5705	252	18	℘/θ∧ℏ/θ	℘/θ∧ℏ/θ	ADJ
ejpam-5705	252	19	=	=	PUNCT
ejpam-5705	252	20	m	m	PROPN
ejpam-5705	252	21	/	/	SYM
ejpam-5705	252	22	θ	θ	PROPN
ejpam-5705	252	23	wherem	wherem	PROPN
ejpam-5705	252	24	/	/	SYM
ejpam-5705	252	25	θ	θ	PROPN
ejpam-5705	252	26	and	and	CCONJ
ejpam-5705	252	27	1	1	NUM
ejpam-5705	252	28	/	/	SYM
ejpam-5705	252	29	θ	θ	NOUN
ejpam-5705	252	30	are	be	AUX
ejpam-5705	252	31	least	least	ADJ
ejpam-5705	252	32	and	and	CCONJ
ejpam-5705	252	33	greatest	great	ADJ
ejpam-5705	252	34	elements	element	NOUN
ejpam-5705	252	35	in	in	ADP
ejpam-5705	252	36	v	v	NOUN
ejpam-5705	252	37	/	/	SYM
ejpam-5705	252	38	θ	θ	NOUN
ejpam-5705	252	39	respectively	respectively	ADV
ejpam-5705	252	40	.	.	PUNCT
ejpam-5705	253	1	now	now	ADV
ejpam-5705	253	2	℘/θ∧ℏ/θ	℘/θ∧ℏ/θ	ADV
ejpam-5705	253	3	=	=	SYM
ejpam-5705	253	4	(	(	PUNCT
ejpam-5705	253	5	℘∧ℏ)/θ	℘∧ℏ)/θ	NOUN
ejpam-5705	253	6	=	=	SYM
ejpam-5705	253	7	m	m	PROPN
ejpam-5705	253	8	/	/	SYM
ejpam-5705	253	9	θ	θ	PROPN
ejpam-5705	253	10	⇒	⇒	NOUN
ejpam-5705	253	11	(	(	PUNCT
ejpam-5705	253	12	℘∧ℏ,m	℘∧ℏ,m	PROPN
ejpam-5705	253	13	)	)	PUNCT
ejpam-5705	253	14	∈	∈	PROPN
ejpam-5705	253	15	θ	θ	NOUN
ejpam-5705	254	1	so	so	SCONJ
ejpam-5705	254	2	that	that	SCONJ
ejpam-5705	254	3	[	[	PUNCT
ejpam-5705	254	4	℘	℘	PROPN
ejpam-5705	254	5	∧	∧	PROPN
ejpam-5705	254	6	ℏ]•	ℏ]•	NOUN
ejpam-5705	254	7	=	=	PUNCT
ejpam-5705	255	1	[	[	X
ejpam-5705	255	2	℘]•	℘]•	PROPN
ejpam-5705	255	3	∩	∩	NOUN
ejpam-5705	255	4	[	[	X
ejpam-5705	255	5	ℏ]•	ℏ]•	NOUN
ejpam-5705	255	6	=	=	PUNCT
ejpam-5705	256	1	[	[	X
ejpam-5705	256	2	m]•	m]•	NOUN
ejpam-5705	256	3	which	which	PRON
ejpam-5705	256	4	is	be	AUX
ejpam-5705	256	5	true	true	ADJ
ejpam-5705	256	6	for	for	ADP
ejpam-5705	256	7	all	all	DET
ejpam-5705	256	8	℘	℘	PROPN
ejpam-5705	256	9	∈	∈	PROPN
ejpam-5705	256	10	v	v	NOUN
ejpam-5705	256	11	.	.	PUNCT
ejpam-5705	257	1	hence	hence	ADV
ejpam-5705	257	2	[	[	X
ejpam-5705	257	3	m]•	m]•	NOUN
ejpam-5705	257	4	⊆	⊆	NUM
ejpam-5705	257	5	[	[	X
ejpam-5705	257	6	℘]•	℘]•	VERB
ejpam-5705	257	7	for	for	ADP
ejpam-5705	257	8	all	all	DET
ejpam-5705	257	9	℘	℘	PROPN
ejpam-5705	257	10	∈	∈	PROPN
ejpam-5705	257	11	v	v	NOUN
ejpam-5705	257	12	.	.	PUNCT
ejpam-5705	258	1	let	let	VERB
ejpam-5705	258	2	µ1	µ1	NOUN
ejpam-5705	258	3	∈	∈	PROPN
ejpam-5705	258	4	[	[	X
ejpam-5705	258	5	m]•.	m]•.	X
ejpam-5705	258	6	then	then	ADV
ejpam-5705	258	7	µ1	µ1	PROPN
ejpam-5705	258	8	∈	∈	PROPN
ejpam-5705	258	9	[	[	X
ejpam-5705	258	10	µ1	µ1	NOUN
ejpam-5705	258	11	]	]	PUNCT
ejpam-5705	258	12	•.	•.	NOUN
ejpam-5705	258	13	therefore	therefore	ADV
ejpam-5705	258	14	µ1	µ1	PROPN
ejpam-5705	258	15	=	=	SYM
ejpam-5705	258	16	1	1	NUM
ejpam-5705	258	17	.	.	PUNCT
ejpam-5705	259	1	hence	hence	ADV
ejpam-5705	259	2	[	[	X
ejpam-5705	259	3	m]•	m]•	X
ejpam-5705	259	4	=	=	SYM
ejpam-5705	259	5	{	{	PUNCT
ejpam-5705	259	6	1	1	NUM
ejpam-5705	259	7	}	}	PUNCT
ejpam-5705	259	8	.	.	PUNCT
ejpam-5705	260	1	we	we	PRON
ejpam-5705	260	2	get	get	VERB
ejpam-5705	260	3	[	[	X
ejpam-5705	260	4	℘]•	℘]•	PROPN
ejpam-5705	260	5	∩	∩	NOUN
ejpam-5705	260	6	[	[	X
ejpam-5705	260	7	ℏ]•	ℏ]•	X
ejpam-5705	260	8	=	=	PUNCT
ejpam-5705	260	9	{	{	PUNCT
ejpam-5705	260	10	1	1	NUM
ejpam-5705	260	11	}	}	PUNCT
ejpam-5705	260	12	.	.	PUNCT
ejpam-5705	261	1	also	also	ADV
ejpam-5705	261	2	,	,	PUNCT
ejpam-5705	261	3	℘/θ	℘/θ	ADV
ejpam-5705	261	4	∨	∨	NOUN
ejpam-5705	261	5	ℏ/θ	ℏ/θ	ADV
ejpam-5705	261	6	=	=	PUNCT
ejpam-5705	261	7	(	(	PUNCT
ejpam-5705	261	8	℘	℘	PROPN
ejpam-5705	261	9	∨	∨	NUM
ejpam-5705	261	10	ℏ)/θ	ℏ)/θ	PROPN
ejpam-5705	261	11	=	=	SYM
ejpam-5705	261	12	1	1	NUM
ejpam-5705	261	13	/	/	SYM
ejpam-5705	261	14	θ	θ	NOUN
ejpam-5705	261	15	.	.	PUNCT
ejpam-5705	262	1	so	so	SCONJ
ejpam-5705	262	2	that	that	SCONJ
ejpam-5705	262	3	[	[	PUNCT
ejpam-5705	262	4	℘	℘	PROPN
ejpam-5705	262	5	∨	∨	NUM
ejpam-5705	262	6	ℏ]•	ℏ]•	NOUN
ejpam-5705	262	7	=	=	PUNCT
ejpam-5705	263	1	[	[	X
ejpam-5705	263	2	1]•	1]•	NUM
ejpam-5705	263	3	=	=	SYM
ejpam-5705	263	4	v.	v.	ADP
ejpam-5705	263	5	therefore	therefore	ADV
ejpam-5705	263	6	℘	℘	PROPN
ejpam-5705	263	7	∨	∨	NUM
ejpam-5705	263	8	℘	℘	PROPN
ejpam-5705	263	9	∨	∨	NUM
ejpam-5705	263	10	ℏ	ℏ	NOUN
ejpam-5705	263	11	=	=	SYM
ejpam-5705	263	12	1	1	NUM
ejpam-5705	263	13	implies	imply	VERB
ejpam-5705	263	14	that	that	SCONJ
ejpam-5705	263	15	℘	℘	PROPN
ejpam-5705	263	16	∨	∨	NUM
ejpam-5705	263	17	ℏ	ℏ	NOUN
ejpam-5705	263	18	=	=	SYM
ejpam-5705	263	19	1	1	NUM
ejpam-5705	263	20	.	.	PUNCT
ejpam-5705	263	21	hence	hence	ADV
ejpam-5705	263	22	ℏ	ℏ	PROPN
ejpam-5705	263	23	∈	∈	PROPN
ejpam-5705	264	1	[	[	X
ejpam-5705	264	2	℘]•	℘]•	PROPN
ejpam-5705	264	3	,	,	PUNCT
ejpam-5705	264	4	we	we	PRON
ejpam-5705	264	5	get	get	VERB
ejpam-5705	264	6	[	[	X
ejpam-5705	264	7	℘]•	℘]•	PROPN
ejpam-5705	264	8	•	•	NUM
ejpam-5705	264	9	⊆	⊆	NUM
ejpam-5705	264	10	[	[	X
ejpam-5705	264	11	ℏ]•.	ℏ]•.	X
ejpam-5705	264	12	let	let	VERB
ejpam-5705	264	13	τ	τ	PROPN
ejpam-5705	264	14	∈	∈	PROPN
ejpam-5705	265	1	[	[	X
ejpam-5705	265	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	265	3	and	and	CCONJ
ejpam-5705	265	4	∂4	∂4	NOUN
ejpam-5705	265	5	∈	∈	PROPN
ejpam-5705	266	1	[	[	X
ejpam-5705	266	2	℘]•.	℘]•.	ADJ
ejpam-5705	266	3	then	then	ADV
ejpam-5705	266	4	τ	τ	X
ejpam-5705	266	5	∨ℏ	∨ℏ	NOUN
ejpam-5705	266	6	=	=	SYM
ejpam-5705	266	7	1	1	NUM
ejpam-5705	266	8	and	and	CCONJ
ejpam-5705	266	9	∂4∨℘	∂4∨℘	NOUN
ejpam-5705	266	10	=	=	NOUN
ejpam-5705	266	11	1	1	X
ejpam-5705	266	12	.	.	PUNCT
ejpam-5705	267	1	now	now	ADV
ejpam-5705	267	2	τ	τ	X
ejpam-5705	267	3	∨∂4	∨∂4	PROPN
ejpam-5705	267	4	∈	∈	PROPN
ejpam-5705	267	5	[	[	X
ejpam-5705	267	6	℘]•	℘]•	PROPN
ejpam-5705	267	7	and	and	CCONJ
ejpam-5705	267	8	τ	τ	NUM
ejpam-5705	267	9	∨∂4	∨∂4	PROPN
ejpam-5705	267	10	∈	∈	PROPN
ejpam-5705	267	11	[	[	X
ejpam-5705	267	12	ℏ]•.	ℏ]•.	X
ejpam-5705	267	13	therefore	therefore	ADV
ejpam-5705	267	14	τ	τ	PROPN
ejpam-5705	267	15	∨∂4	∨∂4	PROPN
ejpam-5705	267	16	∈	∈	PROPN
ejpam-5705	268	1	[	[	X
ejpam-5705	268	2	℘]•	℘]•	PROPN
ejpam-5705	268	3	∩	∩	NOUN
ejpam-5705	268	4	[	[	X
ejpam-5705	268	5	ℏ]•	ℏ]•	X
ejpam-5705	268	6	=	=	PUNCT
ejpam-5705	268	7	{	{	PUNCT
ejpam-5705	268	8	1	1	NUM
ejpam-5705	268	9	}	}	PUNCT
ejpam-5705	268	10	.	.	PUNCT
ejpam-5705	269	1	hence	hence	ADV
ejpam-5705	269	2	τ	τ	X
ejpam-5705	269	3	∨∂4	∨∂4	PROPN
ejpam-5705	269	4	=	=	SYM
ejpam-5705	269	5	1	1	NUM
ejpam-5705	269	6	.	.	PUNCT
ejpam-5705	270	1	thus	thus	ADV
ejpam-5705	270	2	τ	τ	X
ejpam-5705	270	3	∈	∈	PROPN
ejpam-5705	270	4	[	[	X
ejpam-5705	270	5	℘]•	℘]•	PROPN
ejpam-5705	270	6	•	•	VERB
ejpam-5705	270	7	,	,	PUNCT
ejpam-5705	270	8	we	we	PRON
ejpam-5705	270	9	get	get	VERB
ejpam-5705	270	10	[	[	X
ejpam-5705	270	11	ℏ]•	ℏ]•	NOUN
ejpam-5705	270	12	⊆	⊆	NUM
ejpam-5705	270	13	[	[	X
ejpam-5705	270	14	℘]•	℘]•	PROPN
ejpam-5705	270	15	•	•	NOUN
ejpam-5705	270	16	.	.	PUNCT
ejpam-5705	271	1	therefore	therefore	ADV
ejpam-5705	271	2	[	[	X
ejpam-5705	271	3	℘]•	℘]•	PROPN
ejpam-5705	271	4	•	•	NOUN
ejpam-5705	271	5	=	=	PUNCT
ejpam-5705	272	1	[	[	X
ejpam-5705	272	2	ℏ]•.	ℏ]•.	X
ejpam-5705	272	3	hence	hence	ADV
ejpam-5705	272	4	v	v	NOUN
ejpam-5705	272	5	is	be	AUX
ejpam-5705	272	6	a	a	DET
ejpam-5705	272	7	•-pdl	•-pdl	NOUN
ejpam-5705	272	8	.	.	NOUN
ejpam-5705	272	9	observe	observe	VERB
ejpam-5705	272	10	that	that	SCONJ
ejpam-5705	272	11	the	the	DET
ejpam-5705	272	12	converse	converse	NOUN
ejpam-5705	272	13	of	of	ADP
ejpam-5705	272	14	the	the	DET
ejpam-5705	272	15	above	above	ADJ
ejpam-5705	272	16	theorem	theorem	NOUN
ejpam-5705	272	17	is	be	AUX
ejpam-5705	272	18	true	true	ADJ
ejpam-5705	272	19	if	if	SCONJ
ejpam-5705	272	20	v	v	NOUN
ejpam-5705	272	21	has	have	VERB
ejpam-5705	272	22	a	a	DET
ejpam-5705	272	23	minimal	minimal	ADJ
ejpam-5705	272	24	element	element	NOUN
ejpam-5705	272	25	which	which	PRON
ejpam-5705	272	26	we	we	PRON
ejpam-5705	272	27	prove	prove	VERB
ejpam-5705	272	28	in	in	ADP
ejpam-5705	272	29	the	the	DET
ejpam-5705	272	30	following	following	NOUN
ejpam-5705	272	31	:	:	PUNCT
ejpam-5705	272	32	theorem	theorem	NOUN
ejpam-5705	272	33	8	8	NUM
ejpam-5705	272	34	.	.	PUNCT
ejpam-5705	273	1	let	let	VERB
ejpam-5705	273	2	v	v	PART
ejpam-5705	273	3	be	be	AUX
ejpam-5705	273	4	a	a	DET
ejpam-5705	273	5	pdl	pdl	NOUN
ejpam-5705	273	6	with	with	ADP
ejpam-5705	273	7	a	a	DET
ejpam-5705	273	8	minimal	minimal	ADJ
ejpam-5705	273	9	element	element	NOUN
ejpam-5705	273	10	m.	m.	NOUN
ejpam-5705	273	11	if	if	SCONJ
ejpam-5705	273	12	v	v	NOUN
ejpam-5705	273	13	is	be	AUX
ejpam-5705	273	14	a	a	DET
ejpam-5705	273	15	•-pdl	•-pdl	NOUN
ejpam-5705	273	16	,	,	PUNCT
ejpam-5705	273	17	then	then	ADV
ejpam-5705	273	18	v	v	NOUN
ejpam-5705	273	19	/	/	SYM
ejpam-5705	273	20	θ	θ	PROPN
ejpam-5705	273	21	is	be	AUX
ejpam-5705	273	22	a	a	DET
ejpam-5705	273	23	boolean	boolean	ADJ
ejpam-5705	273	24	algebra	algebra	NOUN
ejpam-5705	273	25	.	.	PUNCT
ejpam-5705	274	1	proof	proof	NOUN
ejpam-5705	274	2	.	.	PUNCT
ejpam-5705	275	1	clearly	clearly	ADV
ejpam-5705	275	2	(	(	PUNCT
ejpam-5705	275	3	v	v	NOUN
ejpam-5705	275	4	/	/	SYM
ejpam-5705	275	5	θ,∨,∧	θ,∨,∧	NOUN
ejpam-5705	275	6	)	)	PUNCT
ejpam-5705	275	7	is	be	AUX
ejpam-5705	275	8	a	a	DET
ejpam-5705	275	9	distributive	distributive	ADJ
ejpam-5705	275	10	lattice	lattice	NOUN
ejpam-5705	275	11	with	with	ADP
ejpam-5705	275	12	the	the	DET
ejpam-5705	275	13	least	least	ADJ
ejpam-5705	275	14	element	element	NOUN
ejpam-5705	275	15	m	m	PROPN
ejpam-5705	275	16	/	/	SYM
ejpam-5705	275	17	θ	θ	PROPN
ejpam-5705	275	18	and	and	CCONJ
ejpam-5705	275	19	the	the	DET
ejpam-5705	275	20	greatest	great	ADJ
ejpam-5705	275	21	element	element	NOUN
ejpam-5705	275	22	1	1	NUM
ejpam-5705	275	23	/	/	SYM
ejpam-5705	275	24	θ	θ	NOUN
ejpam-5705	275	25	.	.	PUNCT
ejpam-5705	276	1	now	now	ADV
ejpam-5705	276	2	,	,	PUNCT
ejpam-5705	276	3	we	we	PRON
ejpam-5705	276	4	prove	prove	VERB
ejpam-5705	276	5	that	that	SCONJ
ejpam-5705	276	6	v	v	NOUN
ejpam-5705	276	7	/	/	SYM
ejpam-5705	276	8	θ	θ	PROPN
ejpam-5705	276	9	is	be	AUX
ejpam-5705	276	10	complemented	complement	VERB
ejpam-5705	276	11	.	.	PUNCT
ejpam-5705	277	1	let	let	VERB
ejpam-5705	277	2	℘/θ	℘/θ	ADJ
ejpam-5705	277	3	∈	∈	VERB
ejpam-5705	277	4	v	v	NOUN
ejpam-5705	277	5	/	/	SYM
ejpam-5705	277	6	θ	θ	NOUN
ejpam-5705	277	7	.	.	PUNCT
ejpam-5705	278	1	then	then	ADV
ejpam-5705	278	2	there	there	PRON
ejpam-5705	278	3	exists	exist	VERB
ejpam-5705	278	4	ℏ	ℏ	PROPN
ejpam-5705	278	5	∈	∈	PROPN
ejpam-5705	278	6	v	v	ADP
ejpam-5705	278	7	such	such	ADJ
ejpam-5705	278	8	that	that	SCONJ
ejpam-5705	279	1	[	[	X
ejpam-5705	279	2	℘]•	℘]•	PROPN
ejpam-5705	279	3	•	•	NOUN
ejpam-5705	279	4	=	=	PUNCT
ejpam-5705	280	1	[	[	X
ejpam-5705	280	2	ℏ]•.	ℏ]•.	X
ejpam-5705	280	3	now	now	ADV
ejpam-5705	280	4	,	,	PUNCT
ejpam-5705	280	5	[	[	X
ejpam-5705	280	6	℘∨ℏ]••	℘∨ℏ]••	PUNCT
ejpam-5705	280	7	=	=	PUNCT
ejpam-5705	281	1	[	[	X
ejpam-5705	281	2	℘]•	℘]•	PROPN
ejpam-5705	281	3	•	•	NOUN
ejpam-5705	281	4	∩	∩	X
ejpam-5705	281	5	[	[	X
ejpam-5705	281	6	ℏ]••	ℏ]••	X
ejpam-5705	281	7	=	=	PUNCT
ejpam-5705	282	1	[	[	X
ejpam-5705	282	2	ℏ]•∩	ℏ]•∩	NOUN
ejpam-5705	282	3	[	[	X
ejpam-5705	282	4	ℏ]••	ℏ]••	X
ejpam-5705	282	5	=	=	SYM
ejpam-5705	282	6	{	{	PUNCT
ejpam-5705	282	7	1	1	NUM
ejpam-5705	282	8	}	}	PUNCT
ejpam-5705	282	9	which	which	PRON
ejpam-5705	282	10	implies	imply	VERB
ejpam-5705	282	11	that	that	SCONJ
ejpam-5705	283	1	[	[	X
ejpam-5705	283	2	℘∨ℏ]•	℘∨ℏ]•	PROPN
ejpam-5705	283	3	=	=	PUNCT
ejpam-5705	284	1	[	[	X
ejpam-5705	284	2	1]•	1]•	NUM
ejpam-5705	284	3	and	and	CCONJ
ejpam-5705	284	4	hence	hence	ADV
ejpam-5705	284	5	℘/θ∨ℏ/θ	℘/θ∨ℏ/θ	ADJ
ejpam-5705	284	6	=	=	SYM
ejpam-5705	284	7	1	1	NUM
ejpam-5705	284	8	/	/	SYM
ejpam-5705	284	9	θ	θ	NOUN
ejpam-5705	284	10	.	.	PUNCT
ejpam-5705	285	1	also	also	ADV
ejpam-5705	285	2	,	,	PUNCT
ejpam-5705	285	3	[	[	X
ejpam-5705	285	4	℘∧ℏ]•	℘∧ℏ]•	X
ejpam-5705	285	5	=	=	PUNCT
ejpam-5705	286	1	[	[	X
ejpam-5705	286	2	℘]•∩	℘]•∩	X
ejpam-5705	286	3	[	[	X
ejpam-5705	286	4	ℏ]•	ℏ]•	NOUN
ejpam-5705	286	5	=	=	PUNCT
ejpam-5705	287	1	[	[	X
ejpam-5705	287	2	℘]•	℘]•	PROPN
ejpam-5705	287	3	∩	∩	NOUN
ejpam-5705	287	4	[	[	X
ejpam-5705	287	5	℘]•	℘]•	PROPN
ejpam-5705	287	6	•	•	NOUN
ejpam-5705	287	7	=	=	SYM
ejpam-5705	287	8	{	{	PUNCT
ejpam-5705	287	9	1	1	NUM
ejpam-5705	287	10	}	}	PUNCT
ejpam-5705	287	11	=	=	PUNCT
ejpam-5705	288	1	[	[	X
ejpam-5705	288	2	m]•.	m]•.	X
ejpam-5705	288	3	therefore	therefore	ADV
ejpam-5705	288	4	(	(	PUNCT
ejpam-5705	288	5	℘	℘	X
ejpam-5705	288	6	∧	∧	NOUN
ejpam-5705	288	7	ℏ)/θ	ℏ)/θ	PROPN
ejpam-5705	288	8	=	=	SYM
ejpam-5705	288	9	m	m	PROPN
ejpam-5705	288	10	/	/	SYM
ejpam-5705	288	11	θ	θ	PROPN
ejpam-5705	288	12	⇒	⇒	NOUN
ejpam-5705	288	13	℘/θ	℘/θ	NOUN
ejpam-5705	288	14	∧	∧	PROPN
ejpam-5705	288	15	ℏ/θ	ℏ/θ	NOUN
ejpam-5705	288	16	=	=	NOUN
ejpam-5705	288	17	m	m	PROPN
ejpam-5705	288	18	/	/	SYM
ejpam-5705	288	19	θ	θ	NOUN
ejpam-5705	288	20	.	.	PUNCT
ejpam-5705	288	21	hence	hence	ADV
ejpam-5705	288	22	v	v	NOUN
ejpam-5705	288	23	/	/	SYM
ejpam-5705	288	24	θ	θ	PROPN
ejpam-5705	288	25	is	be	AUX
ejpam-5705	288	26	a	a	DET
ejpam-5705	288	27	boolean	boolean	ADJ
ejpam-5705	288	28	algebra	algebra	NOUN
ejpam-5705	288	29	.	.	PUNCT
ejpam-5705	289	1	4	4	X
ejpam-5705	289	2	.	.	X
ejpam-5705	289	3	dense	dense	ADJ
ejpam-5705	289	4	elements	element	NOUN
ejpam-5705	289	5	in	in	ADP
ejpam-5705	289	6	a	a	DET
ejpam-5705	289	7	pdl	pdl	NOUN
ejpam-5705	289	8	in	in	ADP
ejpam-5705	289	9	this	this	DET
ejpam-5705	289	10	section	section	NOUN
ejpam-5705	289	11	,	,	PUNCT
ejpam-5705	289	12	we	we	PRON
ejpam-5705	289	13	state	state	VERB
ejpam-5705	289	14	the	the	DET
ejpam-5705	289	15	definition	definition	NOUN
ejpam-5705	289	16	of	of	ADP
ejpam-5705	289	17	a	a	DET
ejpam-5705	289	18	dense	dense	ADJ
ejpam-5705	289	19	element	element	NOUN
ejpam-5705	289	20	in	in	ADP
ejpam-5705	289	21	a	a	DET
ejpam-5705	289	22	pdl	pdl	NOUN
ejpam-5705	289	23	v	v	NOUN
ejpam-5705	289	24	and	and	CCONJ
ejpam-5705	289	25	prove	prove	VERB
ejpam-5705	289	26	that	that	SCONJ
ejpam-5705	289	27	the	the	DET
ejpam-5705	289	28	set	set	NOUN
ejpam-5705	289	29	of	of	ADP
ejpam-5705	289	30	all	all	DET
ejpam-5705	289	31	dense	dense	ADJ
ejpam-5705	289	32	elements	element	NOUN
ejpam-5705	289	33	is	be	AUX
ejpam-5705	289	34	an	an	DET
ejpam-5705	289	35	ideal	ideal	NOUN
ejpam-5705	289	36	of	of	ADP
ejpam-5705	289	37	v	v	NOUN
ejpam-5705	289	38	.	.	PUNCT
ejpam-5705	290	1	we	we	PRON
ejpam-5705	290	2	characterize	characterize	VERB
ejpam-5705	290	3	•-pdl	•-pdl	PUNCT
ejpam-5705	290	4	v	v	NOUN
ejpam-5705	290	5	in	in	ADP
ejpam-5705	290	6	terms	term	NOUN
ejpam-5705	290	7	of	of	ADP
ejpam-5705	290	8	dense	dense	ADJ
ejpam-5705	290	9	elements	element	NOUN
ejpam-5705	290	10	.	.	PUNCT
ejpam-5705	291	1	further	far	ADV
ejpam-5705	291	2	,	,	PUNCT
ejpam-5705	291	3	we	we	PRON
ejpam-5705	291	4	introduce	introduce	VERB
ejpam-5705	291	5	the	the	DET
ejpam-5705	291	6	concept	concept	NOUN
ejpam-5705	291	7	of	of	ADP
ejpam-5705	291	8	a	a	DET
ejpam-5705	291	9	disjunctive	disjunctive	ADJ
ejpam-5705	291	10	pdl	pdl	NOUN
ejpam-5705	291	11	as	as	ADP
ejpam-5705	291	12	a	a	DET
ejpam-5705	291	13	pdl	pdl	NOUN
ejpam-5705	291	14	v	v	NOUN
ejpam-5705	291	15	in	in	ADP
ejpam-5705	291	16	which	which	PRON
ejpam-5705	291	17	for	for	ADP
ejpam-5705	291	18	any	any	DET
ejpam-5705	291	19	℘	℘	NOUN
ejpam-5705	291	20	,	,	PUNCT
ejpam-5705	291	21	ℏ	ℏ	PROPN
ejpam-5705	291	22	∈	∈	NOUN
ejpam-5705	291	23	v	v	NOUN
ejpam-5705	291	24	,	,	PUNCT
ejpam-5705	291	25	[	[	X
ejpam-5705	291	26	℘]•	℘]•	PROPN
ejpam-5705	291	27	=	=	PUNCT
ejpam-5705	292	1	[	[	X
ejpam-5705	292	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	292	3	implies	imply	VERB
ejpam-5705	292	4	℘	℘	PROPN
ejpam-5705	292	5	=	=	SYM
ejpam-5705	292	6	ℏ	ℏ	PROPN
ejpam-5705	292	7	and	and	CCONJ
ejpam-5705	292	8	prove	prove	VERB
ejpam-5705	292	9	that	that	SCONJ
ejpam-5705	292	10	,	,	PUNCT
ejpam-5705	292	11	•-pdl	•-pdl	X
ejpam-5705	292	12	is	be	AUX
ejpam-5705	292	13	disjunctive	disjunctive	ADJ
ejpam-5705	292	14	if	if	SCONJ
ejpam-5705	292	15	and	and	CCONJ
ejpam-5705	292	16	only	only	ADV
ejpam-5705	292	17	if	if	SCONJ
ejpam-5705	292	18	v	v	NOUN
ejpam-5705	292	19	is	be	AUX
ejpam-5705	292	20	a	a	DET
ejpam-5705	292	21	boolean	boolean	ADJ
ejpam-5705	292	22	algebra	algebra	NOUN
ejpam-5705	292	23	.	.	PUNCT
ejpam-5705	293	1	definition	definition	NOUN
ejpam-5705	293	2	9	9	NUM
ejpam-5705	293	3	.	.	PUNCT
ejpam-5705	294	1	an	an	DET
ejpam-5705	294	2	element	element	NOUN
ejpam-5705	294	3	℘	℘	PROPN
ejpam-5705	294	4	of	of	ADP
ejpam-5705	294	5	a	a	DET
ejpam-5705	294	6	pdl	pdl	NOUN
ejpam-5705	294	7	v	v	NOUN
ejpam-5705	294	8	is	be	AUX
ejpam-5705	294	9	called	call	VERB
ejpam-5705	294	10	a	a	DET
ejpam-5705	294	11	dense	dense	ADJ
ejpam-5705	294	12	element	element	NOUN
ejpam-5705	294	13	if	if	SCONJ
ejpam-5705	294	14	,	,	PUNCT
ejpam-5705	294	15	[	[	X
ejpam-5705	294	16	℘]•	℘]•	PROPN
ejpam-5705	294	17	=	=	PUNCT
ejpam-5705	294	18	{	{	PUNCT
ejpam-5705	294	19	1	1	NUM
ejpam-5705	294	20	}	}	PUNCT
ejpam-5705	294	21	.	.	PUNCT
ejpam-5705	295	1	lemma	lemma	PROPN
ejpam-5705	295	2	10	10	NUM
ejpam-5705	295	3	.	.	PUNCT
ejpam-5705	296	1	every	every	DET
ejpam-5705	296	2	•-pdl	•-pdl	PUNCT
ejpam-5705	296	3	contains	contain	VERB
ejpam-5705	296	4	a	a	DET
ejpam-5705	296	5	dense	dense	ADJ
ejpam-5705	296	6	element	element	NOUN
ejpam-5705	296	7	.	.	PUNCT
ejpam-5705	297	1	proof	proof	NOUN
ejpam-5705	297	2	.	.	PUNCT
ejpam-5705	298	1	let	let	VERB
ejpam-5705	298	2	v	v	PART
ejpam-5705	298	3	be	be	AUX
ejpam-5705	298	4	a	a	DET
ejpam-5705	298	5	•-pdl	•-pdl	PUNCT
ejpam-5705	298	6	and	and	CCONJ
ejpam-5705	298	7	℘	℘	PROPN
ejpam-5705	298	8	∈	∈	PROPN
ejpam-5705	298	9	v	v	NOUN
ejpam-5705	298	10	.	.	PUNCT
ejpam-5705	299	1	then	then	ADV
ejpam-5705	299	2	there	there	PRON
ejpam-5705	299	3	exists	exist	VERB
ejpam-5705	299	4	ℏ	ℏ	PROPN
ejpam-5705	299	5	∈	∈	PROPN
ejpam-5705	299	6	v	v	ADP
ejpam-5705	299	7	such	such	ADJ
ejpam-5705	299	8	that	that	SCONJ
ejpam-5705	300	1	[	[	X
ejpam-5705	300	2	℘]•	℘]•	PROPN
ejpam-5705	300	3	•	•	NOUN
ejpam-5705	300	4	=	=	PUNCT
ejpam-5705	301	1	[	[	X
ejpam-5705	301	2	ℏ]•.	ℏ]•.	X
ejpam-5705	301	3	now	now	ADV
ejpam-5705	301	4	,	,	PUNCT
ejpam-5705	301	5	[	[	PUNCT
ejpam-5705	301	6	℘	℘	NUM
ejpam-5705	301	7	∧	∧	PROPN
ejpam-5705	301	8	ℏ]•	ℏ]•	NOUN
ejpam-5705	301	9	=	=	PUNCT
ejpam-5705	302	1	[	[	X
ejpam-5705	302	2	℘]•	℘]•	PROPN
ejpam-5705	302	3	∩	∩	NOUN
ejpam-5705	302	4	[	[	X
ejpam-5705	302	5	ℏ]•	ℏ]•	X
ejpam-5705	302	6	=	=	PUNCT
ejpam-5705	302	7	{	{	PUNCT
ejpam-5705	302	8	1	1	NUM
ejpam-5705	302	9	}	}	PUNCT
ejpam-5705	302	10	.	.	PUNCT
ejpam-5705	303	1	hence	hence	ADV
ejpam-5705	303	2	℘	℘	VERB
ejpam-5705	303	3	∧	∧	PROPN
ejpam-5705	303	4	ℏ	ℏ	PROPN
ejpam-5705	303	5	is	be	AUX
ejpam-5705	303	6	a	a	DET
ejpam-5705	303	7	dense	dense	ADJ
ejpam-5705	303	8	element	element	NOUN
ejpam-5705	303	9	.	.	PUNCT
ejpam-5705	304	1	r.	r.	PROPN
ejpam-5705	304	2	bandaru	bandaru	PROPN
ejpam-5705	304	3	et	et	PROPN
ejpam-5705	304	4	al	al	PROPN
ejpam-5705	304	5	.	.	PUNCT
ejpam-5705	304	6	/	/	SYM
ejpam-5705	304	7	eur	eur	PROPN
ejpam-5705	304	8	.	.	PUNCT
ejpam-5705	305	1	j.	j.	PROPN
ejpam-5705	305	2	pure	pure	PROPN
ejpam-5705	305	3	appl	appl	PROPN
ejpam-5705	305	4	.	.	PROPN
ejpam-5705	305	5	math	math	PROPN
ejpam-5705	305	6	,	,	PUNCT
ejpam-5705	305	7	18	18	NUM
ejpam-5705	305	8	(	(	PUNCT
ejpam-5705	305	9	2	2	NUM
ejpam-5705	305	10	)	)	PUNCT
ejpam-5705	305	11	(	(	PUNCT
ejpam-5705	305	12	2025	2025	NUM
ejpam-5705	305	13	)	)	PUNCT
ejpam-5705	305	14	,	,	PUNCT
ejpam-5705	305	15	5705	5705	NUM
ejpam-5705	305	16	9	9	NUM
ejpam-5705	305	17	of	of	ADP
ejpam-5705	305	18	13	13	NUM
ejpam-5705	305	19	corollary	corollary	ADJ
ejpam-5705	305	20	1	1	NUM
ejpam-5705	305	21	.	.	PUNCT
ejpam-5705	306	1	in	in	ADP
ejpam-5705	306	2	a	a	DET
ejpam-5705	306	3	•-pdl	•-pdl	NOUN
ejpam-5705	306	4	,	,	PUNCT
ejpam-5705	306	5	every	every	DET
ejpam-5705	306	6	element	element	NOUN
ejpam-5705	306	7	of	of	ADP
ejpam-5705	306	8	[	[	PUNCT
ejpam-5705	306	9	1]•	1]•	NUM
ejpam-5705	306	10	is	be	AUX
ejpam-5705	306	11	a	a	DET
ejpam-5705	306	12	dense	dense	ADJ
ejpam-5705	306	13	element	element	NOUN
ejpam-5705	306	14	.	.	PUNCT
ejpam-5705	307	1	lemma	lemma	PROPN
ejpam-5705	307	2	11	11	NUM
ejpam-5705	307	3	.	.	PUNCT
ejpam-5705	308	1	in	in	ADP
ejpam-5705	308	2	a	a	DET
ejpam-5705	308	3	pdl	pdl	NOUN
ejpam-5705	308	4	,	,	PUNCT
ejpam-5705	308	5	every	every	DET
ejpam-5705	308	6	minimal	minimal	ADJ
ejpam-5705	308	7	element	element	NOUN
ejpam-5705	308	8	is	be	AUX
ejpam-5705	308	9	dense	dense	ADJ
ejpam-5705	308	10	element	element	NOUN
ejpam-5705	308	11	.	.	PUNCT
ejpam-5705	309	1	proof	proof	NOUN
ejpam-5705	309	2	.	.	PUNCT
ejpam-5705	310	1	let	let	VERB
ejpam-5705	310	2	m	m	PRON
ejpam-5705	310	3	be	be	AUX
ejpam-5705	310	4	a	a	DET
ejpam-5705	310	5	minimal	minimal	ADJ
ejpam-5705	310	6	element	element	NOUN
ejpam-5705	310	7	in	in	ADP
ejpam-5705	310	8	v	v	NOUN
ejpam-5705	310	9	and	and	CCONJ
ejpam-5705	310	10	℘	℘	VERB
ejpam-5705	310	11	∈	∈	PROPN
ejpam-5705	311	1	[	[	X
ejpam-5705	311	2	m]•.	m]•.	X
ejpam-5705	311	3	then	then	ADV
ejpam-5705	311	4	℘	℘	PROPN
ejpam-5705	311	5	∨	∨	NUM
ejpam-5705	311	6	m	m	NOUN
ejpam-5705	311	7	=	=	SYM
ejpam-5705	311	8	1	1	NUM
ejpam-5705	311	9	and	and	CCONJ
ejpam-5705	311	10	hence	hence	ADV
ejpam-5705	311	11	℘	℘	NUM
ejpam-5705	311	12	=	=	SYM
ejpam-5705	311	13	1	1	X
ejpam-5705	311	14	.	.	PUNCT
ejpam-5705	312	1	therefore	therefore	ADV
ejpam-5705	312	2	[	[	X
ejpam-5705	312	3	m]•	m]•	X
ejpam-5705	312	4	=	=	SYM
ejpam-5705	312	5	{	{	PUNCT
ejpam-5705	312	6	1	1	NUM
ejpam-5705	312	7	}	}	PUNCT
ejpam-5705	312	8	.	.	PUNCT
ejpam-5705	313	1	thus	thus	ADV
ejpam-5705	313	2	m	m	NOUN
ejpam-5705	313	3	is	be	AUX
ejpam-5705	313	4	dense	dense	ADJ
ejpam-5705	313	5	element	element	NOUN
ejpam-5705	313	6	.	.	PUNCT
ejpam-5705	314	1	lemma	lemma	PROPN
ejpam-5705	314	2	12	12	NUM
ejpam-5705	314	3	.	.	PUNCT
ejpam-5705	315	1	let	let	VERB
ejpam-5705	315	2	v	v	PART
ejpam-5705	315	3	be	be	AUX
ejpam-5705	315	4	a	a	DET
ejpam-5705	315	5	pdl	pdl	NOUN
ejpam-5705	315	6	.	.	PUNCT
ejpam-5705	316	1	then	then	ADV
ejpam-5705	316	2	,	,	PUNCT
ejpam-5705	316	3	the	the	DET
ejpam-5705	316	4	set	set	NOUN
ejpam-5705	316	5	of	of	ADP
ejpam-5705	316	6	all	all	DET
ejpam-5705	316	7	dense	dense	ADJ
ejpam-5705	316	8	elements	element	NOUN
ejpam-5705	316	9	of	of	ADP
ejpam-5705	316	10	v	v	NOUN
ejpam-5705	316	11	is	be	AUX
ejpam-5705	316	12	an	an	DET
ejpam-5705	316	13	ideal	ideal	NOUN
ejpam-5705	316	14	of	of	ADP
ejpam-5705	316	15	v	v	NOUN
ejpam-5705	316	16	.	.	PUNCT
ejpam-5705	317	1	proof	proof	NOUN
ejpam-5705	317	2	.	.	PUNCT
ejpam-5705	318	1	let	let	VERB
ejpam-5705	318	2	d	d	NOUN
ejpam-5705	318	3	=	=	PRON
ejpam-5705	318	4	{	{	PUNCT
ejpam-5705	318	5	µ1	µ1	NOUN
ejpam-5705	318	6	∈	∈	PROPN
ejpam-5705	318	7	v	v	ADP
ejpam-5705	318	8	|	|	NOUN
ejpam-5705	318	9	[	[	X
ejpam-5705	318	10	µ1	µ1	X
ejpam-5705	318	11	]	]	X
ejpam-5705	318	12	•	•	NOUN
ejpam-5705	318	13	=	=	SYM
ejpam-5705	318	14	{	{	PUNCT
ejpam-5705	318	15	1	1	NUM
ejpam-5705	318	16	}	}	PUNCT
ejpam-5705	318	17	}	}	PUNCT
ejpam-5705	318	18	and	and	CCONJ
ejpam-5705	318	19	℘	℘	NOUN
ejpam-5705	318	20	,	,	PUNCT
ejpam-5705	318	21	ℏ	ℏ	PROPN
ejpam-5705	318	22	∈	∈	PROPN
ejpam-5705	318	23	d.	d.	NOUN
ejpam-5705	319	1	then	then	ADV
ejpam-5705	319	2	[	[	X
ejpam-5705	319	3	℘]•	℘]•	PUNCT
ejpam-5705	319	4	=	=	SYM
ejpam-5705	319	5	{	{	PUNCT
ejpam-5705	319	6	1	1	NUM
ejpam-5705	319	7	}	}	PUNCT
ejpam-5705	319	8	and	and	CCONJ
ejpam-5705	319	9	[	[	X
ejpam-5705	319	10	ℏ]•	ℏ]•	X
ejpam-5705	319	11	=	=	X
ejpam-5705	319	12	{	{	PUNCT
ejpam-5705	319	13	1	1	NUM
ejpam-5705	319	14	}	}	PUNCT
ejpam-5705	319	15	.	.	PUNCT
ejpam-5705	320	1	let	let	VERB
ejpam-5705	320	2	τ	τ	PROPN
ejpam-5705	320	3	∈	∈	PROPN
ejpam-5705	320	4	[	[	X
ejpam-5705	320	5	℘∨ℏ]•.	℘∨ℏ]•.	PROPN
ejpam-5705	320	6	then	then	ADV
ejpam-5705	320	7	τ	τ	X
ejpam-5705	320	8	∨℘∨ℏ	∨℘∨ℏ	X
ejpam-5705	320	9	=	=	SYM
ejpam-5705	320	10	1	1	NUM
ejpam-5705	320	11	⇒	⇒	NOUN
ejpam-5705	320	12	τ	τ	PROPN
ejpam-5705	320	13	∨℘	∨℘	NOUN
ejpam-5705	320	14	∈	∈	PROPN
ejpam-5705	321	1	[	[	X
ejpam-5705	321	2	ℏ]•	ℏ]•	X
ejpam-5705	321	3	=	=	PUNCT
ejpam-5705	321	4	{	{	PUNCT
ejpam-5705	321	5	1	1	NUM
ejpam-5705	321	6	}	}	PUNCT
ejpam-5705	321	7	⇒	⇒	NOUN
ejpam-5705	321	8	τ	τ	PROPN
ejpam-5705	321	9	∨℘	∨℘	NOUN
ejpam-5705	321	10	=	=	SYM
ejpam-5705	321	11	1	1	NUM
ejpam-5705	321	12	⇒	⇒	NOUN
ejpam-5705	321	13	τ	τ	X
ejpam-5705	321	14	∈	∈	PROPN
ejpam-5705	322	1	[	[	X
ejpam-5705	322	2	℘]•	℘]•	PROPN
ejpam-5705	322	3	=	=	SYM
ejpam-5705	322	4	{	{	PUNCT
ejpam-5705	322	5	1	1	NUM
ejpam-5705	322	6	}	}	PUNCT
ejpam-5705	322	7	⇒	⇒	NOUN
ejpam-5705	322	8	τ	τ	PROPN
ejpam-5705	322	9	=	=	SYM
ejpam-5705	322	10	1	1	X
ejpam-5705	322	11	.	.	PUNCT
ejpam-5705	322	12	therefore	therefore	ADV
ejpam-5705	322	13	,	,	PUNCT
ejpam-5705	322	14	[	[	PUNCT
ejpam-5705	322	15	℘	℘	PROPN
ejpam-5705	322	16	∨	∨	NUM
ejpam-5705	322	17	ℏ]•	ℏ]•	NOUN
ejpam-5705	322	18	=	=	PUNCT
ejpam-5705	322	19	{	{	PUNCT
ejpam-5705	322	20	1	1	NUM
ejpam-5705	322	21	}	}	PUNCT
ejpam-5705	322	22	.	.	PUNCT
ejpam-5705	323	1	so	so	ADV
ejpam-5705	323	2	that	that	SCONJ
ejpam-5705	323	3	℘	℘	VERB
ejpam-5705	323	4	∨	∨	NUM
ejpam-5705	323	5	ℏ	ℏ	PROPN
ejpam-5705	323	6	∈	∈	PROPN
ejpam-5705	323	7	d.	d.	NOUN
ejpam-5705	323	8	now	now	ADV
ejpam-5705	323	9	,	,	PUNCT
ejpam-5705	323	10	let	let	VERB
ejpam-5705	323	11	℘	℘	PROPN
ejpam-5705	323	12	∈	∈	PROPN
ejpam-5705	323	13	d	d	NOUN
ejpam-5705	323	14	and	and	CCONJ
ejpam-5705	323	15	µ1	µ1	PROPN
ejpam-5705	323	16	∈	∈	PROPN
ejpam-5705	323	17	v	v	NOUN
ejpam-5705	323	18	.	.	PUNCT
ejpam-5705	324	1	then	then	ADV
ejpam-5705	324	2	[	[	X
ejpam-5705	324	3	℘]•	℘]•	PUNCT
ejpam-5705	324	4	=	=	PUNCT
ejpam-5705	324	5	{	{	PUNCT
ejpam-5705	324	6	1	1	NUM
ejpam-5705	324	7	}	}	PUNCT
ejpam-5705	324	8	.	.	PUNCT
ejpam-5705	325	1	if	if	SCONJ
ejpam-5705	325	2	τ	τ	PROPN
ejpam-5705	325	3	∈	∈	PROPN
ejpam-5705	325	4	[	[	X
ejpam-5705	325	5	℘	℘	NUM
ejpam-5705	325	6	∧	∧	NOUN
ejpam-5705	325	7	µ1	µ1	NOUN
ejpam-5705	325	8	]	]	X
ejpam-5705	325	9	•	•	NUM
ejpam-5705	325	10	,	,	PUNCT
ejpam-5705	325	11	then	then	ADV
ejpam-5705	325	12	τ	τ	X
ejpam-5705	325	13	∨	∨	X
ejpam-5705	325	14	(	(	PUNCT
ejpam-5705	325	15	℘	℘	X
ejpam-5705	325	16	∧	∧	NOUN
ejpam-5705	325	17	µ1	µ1	NOUN
ejpam-5705	325	18	)	)	PUNCT
ejpam-5705	325	19	=	=	SYM
ejpam-5705	325	20	1	1	NUM
ejpam-5705	325	21	⇒	⇒	NOUN
ejpam-5705	325	22	(	(	PUNCT
ejpam-5705	325	23	τ	τ	PROPN
ejpam-5705	325	24	∨	∨	NUM
ejpam-5705	325	25	℘	℘	PROPN
ejpam-5705	325	26	)	)	PUNCT
ejpam-5705	325	27	∧	∧	PROPN
ejpam-5705	325	28	(	(	PUNCT
ejpam-5705	325	29	τ	τ	PROPN
ejpam-5705	325	30	∨	∨	NUM
ejpam-5705	325	31	µ1	µ1	PROPN
ejpam-5705	325	32	)	)	PUNCT
ejpam-5705	325	33	=	=	SYM
ejpam-5705	325	34	1	1	NUM
ejpam-5705	325	35	⇒	⇒	NOUN
ejpam-5705	325	36	τ	τ	PROPN
ejpam-5705	325	37	∨	∨	NUM
ejpam-5705	325	38	℘	℘	PROPN
ejpam-5705	325	39	=	=	SYM
ejpam-5705	325	40	1	1	NUM
ejpam-5705	325	41	and	and	CCONJ
ejpam-5705	325	42	τ	τ	PROPN
ejpam-5705	325	43	∨	∨	NUM
ejpam-5705	325	44	µ1	µ1	NOUN
ejpam-5705	325	45	=	=	SYM
ejpam-5705	325	46	1	1	NUM
ejpam-5705	325	47	⇒	⇒	NOUN
ejpam-5705	325	48	τ	τ	PROPN
ejpam-5705	325	49	=	=	SYM
ejpam-5705	325	50	1	1	X
ejpam-5705	325	51	.	.	PUNCT
ejpam-5705	326	1	therefore	therefore	ADV
ejpam-5705	326	2	[	[	X
ejpam-5705	326	3	℘	℘	NUM
ejpam-5705	326	4	∧	∧	NOUN
ejpam-5705	326	5	µ1	µ1	PROPN
ejpam-5705	326	6	]	]	X
ejpam-5705	326	7	•	•	NOUN
ejpam-5705	326	8	=	=	SYM
ejpam-5705	326	9	{	{	PUNCT
ejpam-5705	326	10	1	1	NUM
ejpam-5705	326	11	}	}	PUNCT
ejpam-5705	326	12	.	.	PUNCT
ejpam-5705	327	1	hence	hence	ADV
ejpam-5705	327	2	℘	℘	VERB
ejpam-5705	327	3	∧	∧	PROPN
ejpam-5705	327	4	µ1	µ1	PROPN
ejpam-5705	327	5	∈	∈	PROPN
ejpam-5705	327	6	d.	d.	NOUN
ejpam-5705	327	7	thus	thus	ADV
ejpam-5705	327	8	d	d	PROPN
ejpam-5705	327	9	is	be	AUX
ejpam-5705	327	10	an	an	DET
ejpam-5705	327	11	ideal	ideal	NOUN
ejpam-5705	327	12	of	of	ADP
ejpam-5705	327	13	v	v	NOUN
ejpam-5705	327	14	.	.	PUNCT
ejpam-5705	328	1	lemma	lemma	PROPN
ejpam-5705	328	2	13	13	NUM
ejpam-5705	328	3	.	.	PUNCT
ejpam-5705	329	1	let	let	VERB
ejpam-5705	329	2	v	v	PART
ejpam-5705	329	3	be	be	AUX
ejpam-5705	329	4	a	a	DET
ejpam-5705	329	5	pdl	pdl	NOUN
ejpam-5705	329	6	.	.	PUNCT
ejpam-5705	330	1	then	then	ADV
ejpam-5705	330	2	,	,	PUNCT
ejpam-5705	330	3	for	for	ADP
ejpam-5705	330	4	any	any	DET
ejpam-5705	330	5	℘	℘	NOUN
ejpam-5705	330	6	,	,	PUNCT
ejpam-5705	330	7	ℏ	ℏ	PROPN
ejpam-5705	330	8	∈	∈	NOUN
ejpam-5705	330	9	v	v	NOUN
ejpam-5705	330	10	,	,	PUNCT
ejpam-5705	330	11	(	(	PUNCT
ejpam-5705	330	12	1	1	NUM
ejpam-5705	330	13	)	)	PUNCT
ejpam-5705	330	14	.	.	PUNCT
ejpam-5705	331	1	℘	℘	PROPN
ejpam-5705	331	2	∨	∨	NUM
ejpam-5705	331	3	ℏ	ℏ	NOUN
ejpam-5705	331	4	∈	∈	NOUN
ejpam-5705	332	1	d	d	NOUN
ejpam-5705	332	2	if	if	SCONJ
ejpam-5705	332	3	and	and	CCONJ
ejpam-5705	332	4	only	only	ADV
ejpam-5705	332	5	if	if	SCONJ
ejpam-5705	332	6	ℏ	ℏ	PROPN
ejpam-5705	332	7	∨	∨	VERB
ejpam-5705	332	8	℘	℘	PROPN
ejpam-5705	332	9	∈	∈	PROPN
ejpam-5705	332	10	d.	d.	NOUN
ejpam-5705	332	11	(	(	PUNCT
ejpam-5705	332	12	2	2	NUM
ejpam-5705	332	13	)	)	PUNCT
ejpam-5705	332	14	.	.	PUNCT
ejpam-5705	333	1	℘	℘	PROPN
ejpam-5705	333	2	∧	∧	NOUN
ejpam-5705	333	3	ℏ	ℏ	NOUN
ejpam-5705	333	4	∈	∈	NOUN
ejpam-5705	334	1	d	d	NOUN
ejpam-5705	334	2	if	if	SCONJ
ejpam-5705	335	1	and	and	CCONJ
ejpam-5705	335	2	only	only	ADV
ejpam-5705	335	3	if	if	SCONJ
ejpam-5705	335	4	ℏ	ℏ	PROPN
ejpam-5705	335	5	∧	∧	NOUN
ejpam-5705	335	6	℘	℘	PROPN
ejpam-5705	335	7	∈	∈	PROPN
ejpam-5705	335	8	d.	d.	NOUN
ejpam-5705	335	9	proof	proof	NOUN
ejpam-5705	335	10	.	.	PUNCT
ejpam-5705	336	1	(	(	PUNCT
ejpam-5705	336	2	1	1	NUM
ejpam-5705	336	3	)	)	PUNCT
ejpam-5705	336	4	.	.	PUNCT
ejpam-5705	337	1	let	let	VERB
ejpam-5705	337	2	℘	℘	NOUN
ejpam-5705	337	3	,	,	PUNCT
ejpam-5705	337	4	ℏ	ℏ	PROPN
ejpam-5705	337	5	∈	∈	PROPN
ejpam-5705	337	6	v	v	NOUN
ejpam-5705	337	7	and	and	CCONJ
ejpam-5705	337	8	℘	℘	VERB
ejpam-5705	337	9	∨	∨	NUM
ejpam-5705	337	10	ℏ	ℏ	PROPN
ejpam-5705	337	11	∈	∈	PROPN
ejpam-5705	337	12	d.	d.	NOUN
ejpam-5705	338	1	then	then	ADV
ejpam-5705	338	2	[	[	X
ejpam-5705	338	3	ℏ	ℏ	PROPN
ejpam-5705	338	4	∨	∨	NUM
ejpam-5705	338	5	℘]•	℘]•	PROPN
ejpam-5705	338	6	=	=	PUNCT
ejpam-5705	339	1	[	[	PUNCT
ejpam-5705	339	2	℘	℘	PROPN
ejpam-5705	339	3	∨	∨	NUM
ejpam-5705	339	4	ℏ]•	ℏ]•	NOUN
ejpam-5705	339	5	=	=	PUNCT
ejpam-5705	339	6	{	{	PUNCT
ejpam-5705	339	7	1	1	NUM
ejpam-5705	339	8	}	}	PUNCT
ejpam-5705	339	9	and	and	CCONJ
ejpam-5705	339	10	hence	hence	ADV
ejpam-5705	339	11	ℏ	ℏ	PROPN
ejpam-5705	339	12	∨	∨	NOUN
ejpam-5705	339	13	℘	℘	PROPN
ejpam-5705	339	14	∈	∈	PROPN
ejpam-5705	339	15	d.	d.	NOUN
ejpam-5705	339	16	conversely	conversely	ADV
ejpam-5705	339	17	,	,	PUNCT
ejpam-5705	339	18	assume	assume	VERB
ejpam-5705	339	19	that	that	SCONJ
ejpam-5705	339	20	ℏ	ℏ	PROPN
ejpam-5705	339	21	∨	∨	NOUN
ejpam-5705	339	22	℘	℘	PROPN
ejpam-5705	339	23	∈	∈	PROPN
ejpam-5705	339	24	d.	d.	NOUN
ejpam-5705	339	25	then	then	ADV
ejpam-5705	339	26	[	[	X
ejpam-5705	339	27	℘	℘	PROPN
ejpam-5705	339	28	∨	∨	NUM
ejpam-5705	339	29	ℏ]•	ℏ]•	NOUN
ejpam-5705	339	30	=	=	PUNCT
ejpam-5705	340	1	[	[	X
ejpam-5705	340	2	ℏ	ℏ	PROPN
ejpam-5705	340	3	∨	∨	NUM
ejpam-5705	340	4	℘]•	℘]•	PROPN
ejpam-5705	340	5	=	=	PUNCT
ejpam-5705	340	6	{	{	PUNCT
ejpam-5705	340	7	1	1	NUM
ejpam-5705	340	8	}	}	PUNCT
ejpam-5705	340	9	and	and	CCONJ
ejpam-5705	340	10	hence	hence	ADV
ejpam-5705	340	11	℘	℘	VERB
ejpam-5705	340	12	∨	∨	NUM
ejpam-5705	340	13	ℏ	ℏ	PROPN
ejpam-5705	340	14	∈	∈	PROPN
ejpam-5705	340	15	d.	d.	NOUN
ejpam-5705	340	16	(	(	PUNCT
ejpam-5705	340	17	2	2	NUM
ejpam-5705	340	18	)	)	PUNCT
ejpam-5705	340	19	.	.	PUNCT
ejpam-5705	341	1	let	let	VERB
ejpam-5705	341	2	℘	℘	NOUN
ejpam-5705	341	3	,	,	PUNCT
ejpam-5705	341	4	ℏ	ℏ	PROPN
ejpam-5705	341	5	∈	∈	PROPN
ejpam-5705	341	6	v	v	NOUN
ejpam-5705	341	7	and	and	CCONJ
ejpam-5705	342	1	℘	℘	VERB
ejpam-5705	342	2	∧	∧	PROPN
ejpam-5705	342	3	ℏ	ℏ	PROPN
ejpam-5705	342	4	∈	∈	PROPN
ejpam-5705	342	5	d.	d.	NOUN
ejpam-5705	342	6	then	then	ADV
ejpam-5705	342	7	ℏ	ℏ	VERB
ejpam-5705	342	8	∧	∧	PROPN
ejpam-5705	342	9	℘	℘	NUM
ejpam-5705	342	10	=	=	SYM
ejpam-5705	342	11	(	(	PUNCT
ejpam-5705	342	12	℘	℘	X
ejpam-5705	342	13	∧	∧	PROPN
ejpam-5705	342	14	ℏ	ℏ	NOUN
ejpam-5705	342	15	)	)	PUNCT
ejpam-5705	342	16	∧	∧	PROPN
ejpam-5705	342	17	(	(	PUNCT
ejpam-5705	342	18	ℏ	ℏ	NOUN
ejpam-5705	342	19	∧	∧	PROPN
ejpam-5705	342	20	℘	℘	PROPN
ejpam-5705	342	21	)	)	PUNCT
ejpam-5705	342	22	∈	∈	PROPN
ejpam-5705	342	23	d	d	NOUN
ejpam-5705	342	24	since	since	SCONJ
ejpam-5705	342	25	℘	℘	NUM
ejpam-5705	342	26	∧	∧	PROPN
ejpam-5705	342	27	ℏ	ℏ	NOUN
ejpam-5705	342	28	=	=	PUNCT
ejpam-5705	342	29	(	(	PUNCT
ejpam-5705	342	30	℘	℘	X
ejpam-5705	342	31	∧	∧	PROPN
ejpam-5705	342	32	ℏ	ℏ	PROPN
ejpam-5705	342	33	)	)	PUNCT
ejpam-5705	342	34	∨	∨	NOUN
ejpam-5705	342	35	(	(	PUNCT
ejpam-5705	342	36	ℏ	ℏ	PROPN
ejpam-5705	342	37	∧	∧	NOUN
ejpam-5705	342	38	℘	℘	PROPN
ejpam-5705	342	39	)	)	PUNCT
ejpam-5705	342	40	and	and	CCONJ
ejpam-5705	342	41	d	d	PROPN
ejpam-5705	342	42	is	be	AUX
ejpam-5705	342	43	an	an	DET
ejpam-5705	342	44	ideal	ideal	NOUN
ejpam-5705	342	45	of	of	ADP
ejpam-5705	342	46	v	v	NOUN
ejpam-5705	342	47	.	.	PUNCT
ejpam-5705	343	1	conversely	conversely	ADV
ejpam-5705	343	2	,	,	PUNCT
ejpam-5705	343	3	assume	assume	VERB
ejpam-5705	343	4	that	that	SCONJ
ejpam-5705	343	5	ℏ	ℏ	PROPN
ejpam-5705	343	6	∧	∧	PROPN
ejpam-5705	343	7	℘	℘	PROPN
ejpam-5705	343	8	∈	∈	PROPN
ejpam-5705	343	9	d.	d.	NOUN
ejpam-5705	343	10	then	then	ADV
ejpam-5705	343	11	℘	℘	VERB
ejpam-5705	343	12	∧	∧	PROPN
ejpam-5705	343	13	ℏ	ℏ	NOUN
ejpam-5705	343	14	=	=	PUNCT
ejpam-5705	343	15	(	(	PUNCT
ejpam-5705	343	16	ℏ	ℏ	NOUN
ejpam-5705	343	17	∧	∧	NOUN
ejpam-5705	343	18	℘	℘	PROPN
ejpam-5705	343	19	)	)	PUNCT
ejpam-5705	343	20	∧	∧	NOUN
ejpam-5705	343	21	(	(	PUNCT
ejpam-5705	343	22	℘	℘	X
ejpam-5705	343	23	∧	∧	PROPN
ejpam-5705	343	24	ℏ	ℏ	PROPN
ejpam-5705	343	25	)	)	PUNCT
ejpam-5705	343	26	∈	∈	PROPN
ejpam-5705	343	27	d.	d.	PROPN
ejpam-5705	343	28	lemma	lemma	PROPN
ejpam-5705	343	29	14	14	NUM
ejpam-5705	343	30	.	.	PUNCT
ejpam-5705	344	1	let	let	VERB
ejpam-5705	344	2	v	v	PART
ejpam-5705	344	3	be	be	AUX
ejpam-5705	344	4	a	a	DET
ejpam-5705	344	5	pdl	pdl	NOUN
ejpam-5705	344	6	and	and	CCONJ
ejpam-5705	344	7	℘	℘	NOUN
ejpam-5705	344	8	,	,	PUNCT
ejpam-5705	344	9	ℏ	ℏ	PROPN
ejpam-5705	344	10	∈	∈	PROPN
ejpam-5705	344	11	v	v	NOUN
ejpam-5705	344	12	.	.	PUNCT
ejpam-5705	345	1	if	if	SCONJ
ejpam-5705	345	2	ℏ	ℏ	PROPN
ejpam-5705	345	3	∈	∈	PROPN
ejpam-5705	346	1	[	[	X
ejpam-5705	346	2	℘]•	℘]•	X
ejpam-5705	346	3	then	then	ADV
ejpam-5705	346	4	[	[	X
ejpam-5705	346	5	℘]•	℘]•	PROPN
ejpam-5705	346	6	•	•	NUM
ejpam-5705	346	7	⊆	⊆	NUM
ejpam-5705	346	8	[	[	X
ejpam-5705	346	9	ℏ]•.	ℏ]•.	NOUN
ejpam-5705	346	10	proof	proof	NOUN
ejpam-5705	346	11	.	.	PUNCT
ejpam-5705	347	1	assume	assume	VERB
ejpam-5705	347	2	that	that	SCONJ
ejpam-5705	347	3	ℏ	ℏ	PRON
ejpam-5705	347	4	∈	∈	PROPN
ejpam-5705	348	1	[	[	X
ejpam-5705	348	2	℘]•	℘]•	PROPN
ejpam-5705	348	3	and	and	CCONJ
ejpam-5705	348	4	µ1	µ1	PROPN
ejpam-5705	348	5	∈	∈	PROPN
ejpam-5705	348	6	[	[	X
ejpam-5705	348	7	℘]•	℘]•	PROPN
ejpam-5705	348	8	•	•	NUM
ejpam-5705	348	9	.	.	PUNCT
ejpam-5705	349	1	then	then	ADV
ejpam-5705	349	2	µ1	µ1	PROPN
ejpam-5705	349	3	∨	∨	PROPN
ejpam-5705	349	4	µ2	µ2	PROPN
ejpam-5705	349	5	=	=	PROPN
ejpam-5705	349	6	1	1	NUM
ejpam-5705	349	7	for	for	ADP
ejpam-5705	349	8	all	all	DET
ejpam-5705	349	9	µ2	µ2	PROPN
ejpam-5705	349	10	∈	∈	PROPN
ejpam-5705	349	11	[	[	X
ejpam-5705	349	12	℘]•.	℘]•.	ADJ
ejpam-5705	349	13	hence	hence	ADV
ejpam-5705	349	14	µ1	µ1	PROPN
ejpam-5705	349	15	∨	∨	NOUN
ejpam-5705	349	16	ℏ	ℏ	NOUN
ejpam-5705	349	17	=	=	SYM
ejpam-5705	349	18	1	1	X
ejpam-5705	349	19	.	.	PUNCT
ejpam-5705	350	1	so	so	ADV
ejpam-5705	350	2	that	that	PRON
ejpam-5705	350	3	µ1	µ1	PROPN
ejpam-5705	350	4	∈	∈	PROPN
ejpam-5705	351	1	[	[	X
ejpam-5705	351	2	ℏ]•.	ℏ]•.	X
ejpam-5705	351	3	therefore	therefore	ADV
ejpam-5705	351	4	[	[	X
ejpam-5705	351	5	℘]•	℘]•	PROPN
ejpam-5705	351	6	•	•	NUM
ejpam-5705	351	7	⊆	⊆	NUM
ejpam-5705	351	8	[	[	X
ejpam-5705	351	9	ℏ]•.	ℏ]•.	NOUN
ejpam-5705	351	10	theorem	theorem	VERB
ejpam-5705	351	11	9	9	NUM
ejpam-5705	351	12	.	.	PUNCT
ejpam-5705	352	1	let	let	VERB
ejpam-5705	352	2	v	v	PART
ejpam-5705	352	3	be	be	AUX
ejpam-5705	352	4	a	a	DET
ejpam-5705	352	5	pdl	pdl	NOUN
ejpam-5705	352	6	.	.	PUNCT
ejpam-5705	353	1	then	then	ADV
ejpam-5705	353	2	v	v	AUX
ejpam-5705	353	3	be	be	AUX
ejpam-5705	353	4	a	a	DET
ejpam-5705	353	5	•-pdl	•-pdl	PUNCT
ejpam-5705	353	6	if	if	SCONJ
ejpam-5705	353	7	and	and	CCONJ
ejpam-5705	353	8	only	only	ADV
ejpam-5705	353	9	if	if	SCONJ
ejpam-5705	353	10	for	for	ADP
ejpam-5705	353	11	any	any	DET
ejpam-5705	353	12	℘	℘	PROPN
ejpam-5705	353	13	∈	∈	NOUN
ejpam-5705	353	14	v	v	NOUN
ejpam-5705	353	15	,	,	PUNCT
ejpam-5705	353	16	there	there	PRON
ejpam-5705	353	17	exists	exist	VERB
ejpam-5705	353	18	ℏ	ℏ	PROPN
ejpam-5705	353	19	∈	∈	PROPN
ejpam-5705	353	20	v	v	ADP
ejpam-5705	353	21	such	such	ADJ
ejpam-5705	353	22	that	that	SCONJ
ejpam-5705	353	23	℘	℘	PROPN
ejpam-5705	353	24	∨	∨	NUM
ejpam-5705	353	25	ℏ	ℏ	NOUN
ejpam-5705	353	26	=	=	SYM
ejpam-5705	353	27	1	1	NUM
ejpam-5705	353	28	and	and	CCONJ
ejpam-5705	353	29	℘	℘	PROPN
ejpam-5705	353	30	∧	∧	PROPN
ejpam-5705	353	31	ℏ	ℏ	PROPN
ejpam-5705	353	32	is	be	AUX
ejpam-5705	353	33	dense	dense	ADJ
ejpam-5705	353	34	element	element	NOUN
ejpam-5705	353	35	.	.	PUNCT
ejpam-5705	354	1	proof	proof	NOUN
ejpam-5705	354	2	.	.	PUNCT
ejpam-5705	355	1	suppose	suppose	VERB
ejpam-5705	355	2	v	v	NOUN
ejpam-5705	355	3	is	be	AUX
ejpam-5705	355	4	a	a	DET
ejpam-5705	355	5	•-pdl	•-pdl	PUNCT
ejpam-5705	355	6	and	and	CCONJ
ejpam-5705	355	7	℘	℘	PROPN
ejpam-5705	355	8	∈	∈	PROPN
ejpam-5705	355	9	v	v	NOUN
ejpam-5705	355	10	.	.	PUNCT
ejpam-5705	356	1	then	then	ADV
ejpam-5705	356	2	there	there	PRON
ejpam-5705	356	3	exists	exist	VERB
ejpam-5705	356	4	ℏ	ℏ	PROPN
ejpam-5705	356	5	∈	∈	PROPN
ejpam-5705	356	6	v	v	ADP
ejpam-5705	356	7	such	such	ADJ
ejpam-5705	356	8	that	that	SCONJ
ejpam-5705	357	1	[	[	X
ejpam-5705	357	2	℘]•	℘]•	PROPN
ejpam-5705	357	3	•	•	NOUN
ejpam-5705	357	4	=	=	PUNCT
ejpam-5705	358	1	[	[	X
ejpam-5705	358	2	ℏ]•.	ℏ]•.	X
ejpam-5705	358	3	hence	hence	ADV
ejpam-5705	358	4	℘	℘	PROPN
ejpam-5705	358	5	∧	∧	PROPN
ejpam-5705	358	6	ℏ	ℏ	PROPN
ejpam-5705	358	7	is	be	AUX
ejpam-5705	358	8	a	a	DET
ejpam-5705	358	9	dense	dense	ADJ
ejpam-5705	358	10	element	element	NOUN
ejpam-5705	358	11	.	.	PUNCT
ejpam-5705	359	1	also	also	ADV
ejpam-5705	359	2	,	,	PUNCT
ejpam-5705	359	3	℘	℘	PROPN
ejpam-5705	359	4	∈	∈	PROPN
ejpam-5705	360	1	[	[	X
ejpam-5705	360	2	℘]•	℘]•	PROPN
ejpam-5705	360	3	•	•	NOUN
ejpam-5705	360	4	=	=	PUNCT
ejpam-5705	361	1	[	[	X
ejpam-5705	361	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	361	3	implies	imply	VERB
ejpam-5705	361	4	that	that	SCONJ
ejpam-5705	361	5	℘	℘	PROPN
ejpam-5705	361	6	∨	∨	NUM
ejpam-5705	361	7	ℏ	ℏ	NOUN
ejpam-5705	361	8	=	=	SYM
ejpam-5705	361	9	1	1	X
ejpam-5705	361	10	.	.	PUNCT
ejpam-5705	361	11	conversely	conversely	ADV
ejpam-5705	361	12	,	,	PUNCT
ejpam-5705	361	13	assume	assume	VERB
ejpam-5705	361	14	that	that	SCONJ
ejpam-5705	361	15	the	the	DET
ejpam-5705	361	16	condition	condition	NOUN
ejpam-5705	361	17	holds	hold	VERB
ejpam-5705	361	18	.	.	PUNCT
ejpam-5705	362	1	we	we	PRON
ejpam-5705	362	2	prove	prove	VERB
ejpam-5705	362	3	that	that	SCONJ
ejpam-5705	362	4	v	v	NOUN
ejpam-5705	362	5	is	be	AUX
ejpam-5705	362	6	a	a	DET
ejpam-5705	362	7	•-pdl	•-pdl	NOUN
ejpam-5705	362	8	.	.	PUNCT
ejpam-5705	362	9	let	let	VERB
ejpam-5705	362	10	℘	℘	PROPN
ejpam-5705	362	11	∈	∈	NOUN
ejpam-5705	362	12	v	v	NOUN
ejpam-5705	362	13	.	.	PUNCT
ejpam-5705	363	1	then	then	ADV
ejpam-5705	363	2	there	there	PRON
ejpam-5705	363	3	exists	exist	VERB
ejpam-5705	363	4	ℏ	ℏ	PROPN
ejpam-5705	363	5	∈	∈	PROPN
ejpam-5705	363	6	v	v	ADP
ejpam-5705	363	7	such	such	ADJ
ejpam-5705	363	8	that	that	DET
ejpam-5705	363	9	℘∨ℏ	℘∨ℏ	NUM
ejpam-5705	363	10	=	=	SYM
ejpam-5705	363	11	1	1	NUM
ejpam-5705	363	12	and	and	CCONJ
ejpam-5705	363	13	℘∧ℏ	℘∧ℏ	NOUN
ejpam-5705	363	14	is	be	AUX
ejpam-5705	363	15	a	a	DET
ejpam-5705	363	16	dense	dense	ADJ
ejpam-5705	363	17	element	element	NOUN
ejpam-5705	363	18	.	.	PUNCT
ejpam-5705	364	1	since	since	SCONJ
ejpam-5705	364	2	℘∨ℏ	℘∨ℏ	NUM
ejpam-5705	364	3	=	=	SYM
ejpam-5705	364	4	1	1	NUM
ejpam-5705	364	5	,	,	PUNCT
ejpam-5705	364	6	we	we	PRON
ejpam-5705	364	7	have	have	VERB
ejpam-5705	364	8	ℏ	ℏ	PRON
ejpam-5705	364	9	∈	∈	NOUN
ejpam-5705	365	1	[	[	X
ejpam-5705	365	2	℘]•.	℘]•.	ADJ
ejpam-5705	365	3	therefore	therefore	ADV
ejpam-5705	365	4	[	[	X
ejpam-5705	365	5	℘]•	℘]•	PROPN
ejpam-5705	365	6	•	•	NUM
ejpam-5705	365	7	⊆	⊆	NUM
ejpam-5705	365	8	[	[	X
ejpam-5705	365	9	ℏ]•.	ℏ]•.	X
ejpam-5705	365	10	now	now	ADV
ejpam-5705	365	11	,	,	PUNCT
ejpam-5705	365	12	let	let	VERB
ejpam-5705	365	13	τ	τ	PROPN
ejpam-5705	365	14	∈	∈	PROPN
ejpam-5705	366	1	[	[	X
ejpam-5705	366	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	366	3	and	and	CCONJ
ejpam-5705	366	4	µ1	µ1	PROPN
ejpam-5705	366	5	∈	∈	PROPN
ejpam-5705	366	6	[	[	X
ejpam-5705	366	7	℘]•.	℘]•.	ADJ
ejpam-5705	366	8	then	then	ADV
ejpam-5705	366	9	τ	τ	PROPN
ejpam-5705	366	10	∨	∨	NUM
ejpam-5705	366	11	ℏ	ℏ	X
ejpam-5705	366	12	=	=	SYM
ejpam-5705	366	13	1	1	NUM
ejpam-5705	366	14	and	and	CCONJ
ejpam-5705	366	15	µ1	µ1	PROPN
ejpam-5705	366	16	∨	∨	NOUN
ejpam-5705	366	17	℘	℘	NOUN
ejpam-5705	366	18	=	=	SYM
ejpam-5705	366	19	1	1	X
ejpam-5705	366	20	.	.	PUNCT
ejpam-5705	367	1	now	now	ADV
ejpam-5705	367	2	(	(	PUNCT
ejpam-5705	367	3	τ	τ	PROPN
ejpam-5705	367	4	∨	∨	NUM
ejpam-5705	367	5	µ1	µ1	PROPN
ejpam-5705	367	6	)	)	PUNCT
ejpam-5705	367	7	∨	∨	NOUN
ejpam-5705	367	8	(	(	PUNCT
ejpam-5705	367	9	℘	℘	PROPN
ejpam-5705	367	10	∧	∧	PROPN
ejpam-5705	367	11	ℏ	ℏ	PROPN
ejpam-5705	367	12	)	)	PUNCT
ejpam-5705	367	13	=	=	SYM
ejpam-5705	367	14	(	(	PUNCT
ejpam-5705	367	15	τ	τ	PROPN
ejpam-5705	367	16	∨	∨	NUM
ejpam-5705	367	17	µ1	µ1	PROPN
ejpam-5705	367	18	∨	∨	NUM
ejpam-5705	367	19	℘	℘	PROPN
ejpam-5705	367	20	)	)	PUNCT
ejpam-5705	367	21	∧	∧	PROPN
ejpam-5705	367	22	(	(	PUNCT
ejpam-5705	367	23	τ	τ	PROPN
ejpam-5705	367	24	∨	∨	NUM
ejpam-5705	367	25	µ1	µ1	PROPN
ejpam-5705	367	26	∨	∨	NUM
ejpam-5705	367	27	ℏ	ℏ	PROPN
ejpam-5705	367	28	)	)	PUNCT
ejpam-5705	367	29	=	=	SYM
ejpam-5705	367	30	1	1	NUM
ejpam-5705	367	31	∧	∧	PROPN
ejpam-5705	367	32	1	1	NUM
ejpam-5705	367	33	=	=	SYM
ejpam-5705	367	34	1	1	NUM
ejpam-5705	367	35	.	.	PUNCT
ejpam-5705	368	1	hence	hence	ADV
ejpam-5705	368	2	τ	τ	PROPN
ejpam-5705	368	3	∨	∨	NUM
ejpam-5705	368	4	µ1	µ1	PROPN
ejpam-5705	368	5	∈	∈	PROPN
ejpam-5705	368	6	[	[	X
ejpam-5705	368	7	℘	℘	PROPN
ejpam-5705	368	8	∧	∧	PROPN
ejpam-5705	368	9	ℏ]•	ℏ]•	NOUN
ejpam-5705	368	10	=	=	PUNCT
ejpam-5705	368	11	{	{	PUNCT
ejpam-5705	368	12	1	1	NUM
ejpam-5705	368	13	}	}	PUNCT
ejpam-5705	368	14	.	.	PUNCT
ejpam-5705	369	1	thus	thus	ADV
ejpam-5705	369	2	τ	τ	PROPN
ejpam-5705	369	3	∨	∨	NUM
ejpam-5705	369	4	µ1	µ1	PROPN
ejpam-5705	369	5	=	=	SYM
ejpam-5705	369	6	1	1	NUM
ejpam-5705	369	7	,	,	PUNCT
ejpam-5705	369	8	this	this	PRON
ejpam-5705	369	9	is	be	AUX
ejpam-5705	369	10	true	true	ADJ
ejpam-5705	369	11	for	for	ADP
ejpam-5705	369	12	all	all	DET
ejpam-5705	369	13	µ1	µ1	PROPN
ejpam-5705	369	14	∈	∈	PROPN
ejpam-5705	369	15	[	[	X
ejpam-5705	369	16	℘]•.	℘]•.	ADJ
ejpam-5705	369	17	we	we	PRON
ejpam-5705	369	18	get	get	VERB
ejpam-5705	369	19	τ	τ	X
ejpam-5705	369	20	∈	∈	PROPN
ejpam-5705	370	1	[	[	X
ejpam-5705	370	2	℘]•	℘]•	PROPN
ejpam-5705	370	3	•	•	NOUN
ejpam-5705	370	4	.	.	PUNCT
ejpam-5705	371	1	hence	hence	ADV
ejpam-5705	371	2	[	[	X
ejpam-5705	371	3	ℏ]•	ℏ]•	X
ejpam-5705	371	4	⊆	⊆	NUM
ejpam-5705	371	5	[	[	X
ejpam-5705	371	6	℘]•	℘]•	PROPN
ejpam-5705	371	7	•	•	NOUN
ejpam-5705	371	8	.	.	PUNCT
ejpam-5705	372	1	therefore	therefore	ADV
ejpam-5705	372	2	[	[	X
ejpam-5705	372	3	℘]•	℘]•	PROPN
ejpam-5705	372	4	•	•	NOUN
ejpam-5705	372	5	=	=	PUNCT
ejpam-5705	373	1	[	[	X
ejpam-5705	373	2	ℏ]•.	ℏ]•.	ADP
ejpam-5705	373	3	thus	thus	ADV
ejpam-5705	373	4	v	v	NOUN
ejpam-5705	373	5	is	be	AUX
ejpam-5705	373	6	a	a	DET
ejpam-5705	373	7	•-pdl	•-pdl	NOUN
ejpam-5705	373	8	.	.	NOUN
ejpam-5705	373	9	corollary	corollary	ADJ
ejpam-5705	373	10	2	2	NUM
ejpam-5705	373	11	.	.	PUNCT
ejpam-5705	374	1	let	let	VERB
ejpam-5705	374	2	v	v	PART
ejpam-5705	374	3	be	be	AUX
ejpam-5705	374	4	a	a	DET
ejpam-5705	374	5	pdl	pdl	NOUN
ejpam-5705	374	6	.	.	PUNCT
ejpam-5705	375	1	if	if	SCONJ
ejpam-5705	375	2	for	for	ADP
ejpam-5705	375	3	each	each	DET
ejpam-5705	375	4	℘	℘	PROPN
ejpam-5705	375	5	∈	∈	PROPN
ejpam-5705	375	6	v	v	NOUN
ejpam-5705	375	7	,	,	PUNCT
ejpam-5705	375	8	there	there	PRON
ejpam-5705	375	9	is	be	VERB
ejpam-5705	375	10	an	an	DET
ejpam-5705	375	11	element	element	NOUN
ejpam-5705	375	12	ℏ	ℏ	NOUN
ejpam-5705	375	13	∈	∈	NOUN
ejpam-5705	375	14	v	v	ADP
ejpam-5705	375	15	such	such	ADJ
ejpam-5705	375	16	that	that	SCONJ
ejpam-5705	375	17	℘	℘	PROPN
ejpam-5705	375	18	∨	∨	NUM
ejpam-5705	375	19	ℏ	ℏ	NOUN
ejpam-5705	375	20	=	=	SYM
ejpam-5705	375	21	1	1	NUM
ejpam-5705	375	22	and	and	CCONJ
ejpam-5705	375	23	℘	℘	PROPN
ejpam-5705	375	24	∧	∧	PROPN
ejpam-5705	375	25	ℏ	ℏ	PROPN
ejpam-5705	375	26	is	be	AUX
ejpam-5705	375	27	a	a	DET
ejpam-5705	375	28	minimal	minimal	ADJ
ejpam-5705	375	29	element	element	NOUN
ejpam-5705	375	30	,	,	PUNCT
ejpam-5705	375	31	then	then	ADV
ejpam-5705	375	32	v	v	NOUN
ejpam-5705	375	33	is	be	AUX
ejpam-5705	375	34	a	a	DET
ejpam-5705	375	35	•-pdl	•-pdl	NOUN
ejpam-5705	375	36	.	.	PUNCT
ejpam-5705	375	37	r.	r.	PROPN
ejpam-5705	375	38	bandaru	bandaru	PROPN
ejpam-5705	375	39	et	et	PROPN
ejpam-5705	375	40	al	al	PROPN
ejpam-5705	375	41	.	.	PUNCT
ejpam-5705	375	42	/	/	SYM
ejpam-5705	375	43	eur	eur	PROPN
ejpam-5705	375	44	.	.	PUNCT
ejpam-5705	376	1	j.	j.	PROPN
ejpam-5705	376	2	pure	pure	PROPN
ejpam-5705	376	3	appl	appl	PROPN
ejpam-5705	376	4	.	.	PROPN
ejpam-5705	376	5	math	math	PROPN
ejpam-5705	376	6	,	,	PUNCT
ejpam-5705	376	7	18	18	NUM
ejpam-5705	376	8	(	(	PUNCT
ejpam-5705	376	9	2	2	NUM
ejpam-5705	376	10	)	)	PUNCT
ejpam-5705	376	11	(	(	PUNCT
ejpam-5705	376	12	2025	2025	NUM
ejpam-5705	376	13	)	)	PUNCT
ejpam-5705	376	14	,	,	PUNCT
ejpam-5705	376	15	5705	5705	NUM
ejpam-5705	376	16	10	10	NUM
ejpam-5705	376	17	of	of	ADP
ejpam-5705	376	18	13	13	NUM
ejpam-5705	376	19	theorem	theorem	VERB
ejpam-5705	376	20	10	10	NUM
ejpam-5705	376	21	.	.	PUNCT
ejpam-5705	377	1	let	let	VERB
ejpam-5705	377	2	v	v	PART
ejpam-5705	377	3	be	be	AUX
ejpam-5705	377	4	•-pdl	•-pdl	VERB
ejpam-5705	377	5	.	.	PUNCT
ejpam-5705	378	1	then	then	ADV
ejpam-5705	378	2	the	the	DET
ejpam-5705	378	3	following	follow	VERB
ejpam-5705	378	4	conditions	condition	NOUN
ejpam-5705	378	5	are	be	AUX
ejpam-5705	378	6	equivalent	equivalent	ADJ
ejpam-5705	378	7	:	:	PUNCT
ejpam-5705	378	8	(	(	PUNCT
ejpam-5705	378	9	1	1	NUM
ejpam-5705	378	10	)	)	PUNCT
ejpam-5705	378	11	.	.	PUNCT
ejpam-5705	379	1	for	for	ADP
ejpam-5705	379	2	each	each	DET
ejpam-5705	379	3	℘	℘	PROPN
ejpam-5705	379	4	∈	∈	PROPN
ejpam-5705	379	5	v	v	NOUN
ejpam-5705	379	6	,	,	PUNCT
ejpam-5705	379	7	there	there	PRON
ejpam-5705	379	8	is	be	VERB
ejpam-5705	379	9	ℏ	ℏ	PRON
ejpam-5705	379	10	∈	∈	NOUN
ejpam-5705	379	11	v	v	ADP
ejpam-5705	379	12	such	such	ADJ
ejpam-5705	379	13	that	that	SCONJ
ejpam-5705	379	14	℘	℘	PROPN
ejpam-5705	379	15	∨	∨	NUM
ejpam-5705	379	16	ℏ	ℏ	NOUN
ejpam-5705	379	17	=	=	SYM
ejpam-5705	379	18	1	1	NUM
ejpam-5705	379	19	and	and	CCONJ
ejpam-5705	379	20	℘	℘	PROPN
ejpam-5705	379	21	∧	∧	PROPN
ejpam-5705	379	22	ℏ	ℏ	PROPN
ejpam-5705	379	23	is	be	AUX
ejpam-5705	379	24	a	a	DET
ejpam-5705	379	25	minimal	minimal	ADJ
ejpam-5705	379	26	element	element	NOUN
ejpam-5705	379	27	.	.	PUNCT
ejpam-5705	380	1	(	(	PUNCT
ejpam-5705	380	2	2	2	NUM
ejpam-5705	380	3	)	)	PUNCT
ejpam-5705	380	4	.	.	PUNCT
ejpam-5705	381	1	every	every	DET
ejpam-5705	381	2	dense	dense	ADJ
ejpam-5705	381	3	element	element	NOUN
ejpam-5705	381	4	of	of	ADP
ejpam-5705	381	5	v	v	NOUN
ejpam-5705	381	6	is	be	AUX
ejpam-5705	381	7	a	a	DET
ejpam-5705	381	8	minimal	minimal	ADJ
ejpam-5705	381	9	element	element	NOUN
ejpam-5705	381	10	.	.	PUNCT
ejpam-5705	382	1	proof	proof	NOUN
ejpam-5705	382	2	.	.	PUNCT
ejpam-5705	383	1	(	(	PUNCT
ejpam-5705	383	2	1	1	X
ejpam-5705	383	3	)	)	PUNCT
ejpam-5705	383	4	⇒	⇒	NOUN
ejpam-5705	383	5	(	(	PUNCT
ejpam-5705	383	6	2	2	NUM
ejpam-5705	383	7	):	):	PUNCT
ejpam-5705	383	8	assume	assume	VERB
ejpam-5705	383	9	(	(	PUNCT
ejpam-5705	383	10	1	1	NUM
ejpam-5705	383	11	)	)	PUNCT
ejpam-5705	383	12	.	.	PUNCT
ejpam-5705	384	1	let	let	VERB
ejpam-5705	384	2	℘	℘	PROPN
ejpam-5705	384	3	∈	∈	NOUN
ejpam-5705	384	4	v	v	AUX
ejpam-5705	384	5	be	be	AUX
ejpam-5705	384	6	a	a	DET
ejpam-5705	384	7	dense	dense	ADJ
ejpam-5705	384	8	element	element	NOUN
ejpam-5705	384	9	.	.	PUNCT
ejpam-5705	385	1	then	then	ADV
ejpam-5705	385	2	by	by	ADP
ejpam-5705	385	3	the	the	DET
ejpam-5705	385	4	assumption	assumption	NOUN
ejpam-5705	385	5	,	,	PUNCT
ejpam-5705	385	6	there	there	PRON
ejpam-5705	385	7	exists	exist	VERB
ejpam-5705	385	8	ℏ	ℏ	PROPN
ejpam-5705	385	9	∈	∈	PROPN
ejpam-5705	385	10	v	v	ADP
ejpam-5705	385	11	such	such	ADJ
ejpam-5705	385	12	that	that	SCONJ
ejpam-5705	385	13	℘	℘	PROPN
ejpam-5705	385	14	∨	∨	NUM
ejpam-5705	385	15	ℏ	ℏ	NOUN
ejpam-5705	385	16	=	=	SYM
ejpam-5705	385	17	1	1	NUM
ejpam-5705	385	18	and	and	CCONJ
ejpam-5705	385	19	℘	℘	PROPN
ejpam-5705	385	20	∧	∧	PROPN
ejpam-5705	385	21	ℏ	ℏ	PROPN
ejpam-5705	385	22	is	be	AUX
ejpam-5705	385	23	a	a	DET
ejpam-5705	385	24	minimal	minimal	ADJ
ejpam-5705	385	25	element	element	NOUN
ejpam-5705	385	26	.	.	PUNCT
ejpam-5705	386	1	now	now	ADV
ejpam-5705	386	2	℘	℘	VERB
ejpam-5705	386	3	∨	∨	NUM
ejpam-5705	386	4	ℏ	ℏ	NOUN
ejpam-5705	386	5	=	=	SYM
ejpam-5705	386	6	1	1	NUM
ejpam-5705	386	7	implies	imply	VERB
ejpam-5705	386	8	that	that	SCONJ
ejpam-5705	386	9	ℏ	ℏ	PROPN
ejpam-5705	386	10	∈	∈	PROPN
ejpam-5705	387	1	[	[	X
ejpam-5705	387	2	℘]•	℘]•	PROPN
ejpam-5705	387	3	=	=	PUNCT
ejpam-5705	387	4	{	{	PUNCT
ejpam-5705	387	5	1	1	NUM
ejpam-5705	387	6	}	}	PUNCT
ejpam-5705	387	7	.	.	PUNCT
ejpam-5705	388	1	therefore	therefore	ADV
ejpam-5705	388	2	ℏ	ℏ	X
ejpam-5705	388	3	=	=	SYM
ejpam-5705	388	4	1	1	X
ejpam-5705	388	5	.	.	PUNCT
ejpam-5705	388	6	now	now	ADV
ejpam-5705	388	7	℘	℘	PROPN
ejpam-5705	388	8	=	=	SYM
ejpam-5705	388	9	℘∧1	℘∧1	VERB
ejpam-5705	388	10	=	=	PUNCT
ejpam-5705	388	11	℘∧ℏ	℘∧ℏ	NOUN
ejpam-5705	388	12	is	be	AUX
ejpam-5705	388	13	a	a	DET
ejpam-5705	388	14	minimal	minimal	ADJ
ejpam-5705	388	15	element	element	NOUN
ejpam-5705	388	16	in	in	ADP
ejpam-5705	388	17	v	v	NUM
ejpam-5705	388	18	.	.	PUNCT
ejpam-5705	389	1	(	(	PUNCT
ejpam-5705	389	2	2	2	X
ejpam-5705	389	3	)	)	PUNCT
ejpam-5705	389	4	⇒	⇒	NOUN
ejpam-5705	389	5	(	(	PUNCT
ejpam-5705	389	6	1	1	NUM
ejpam-5705	389	7	):	):	PUNCT
ejpam-5705	389	8	assume	assume	VERB
ejpam-5705	389	9	(	(	PUNCT
ejpam-5705	389	10	2	2	NUM
ejpam-5705	389	11	)	)	PUNCT
ejpam-5705	389	12	.	.	PUNCT
ejpam-5705	390	1	let	let	VERB
ejpam-5705	390	2	℘	℘	PROPN
ejpam-5705	390	3	∈	∈	NOUN
ejpam-5705	390	4	v	v	NOUN
ejpam-5705	390	5	.	.	PUNCT
ejpam-5705	391	1	then	then	ADV
ejpam-5705	391	2	there	there	PRON
ejpam-5705	391	3	exists	exist	VERB
ejpam-5705	391	4	ℏ	ℏ	PROPN
ejpam-5705	391	5	∈	∈	PROPN
ejpam-5705	391	6	v	v	ADP
ejpam-5705	391	7	such	such	ADJ
ejpam-5705	391	8	that	that	DET
ejpam-5705	391	9	℘∨ℏ	℘∨ℏ	NUM
ejpam-5705	391	10	=	=	SYM
ejpam-5705	391	11	1	1	NUM
ejpam-5705	391	12	and	and	CCONJ
ejpam-5705	391	13	℘∧ℏ	℘∧ℏ	NOUN
ejpam-5705	391	14	is	be	AUX
ejpam-5705	391	15	dense	dense	ADJ
ejpam-5705	391	16	element	element	NOUN
ejpam-5705	391	17	by	by	ADP
ejpam-5705	391	18	theorem	theorem	NOUN
ejpam-5705	391	19	9	9	NUM
ejpam-5705	391	20	.	.	PUNCT
ejpam-5705	392	1	then	then	ADV
ejpam-5705	392	2	,	,	PUNCT
ejpam-5705	392	3	by	by	ADP
ejpam-5705	392	4	assumption	assumption	NOUN
ejpam-5705	392	5	,	,	PUNCT
ejpam-5705	392	6	℘	℘	PROPN
ejpam-5705	392	7	∧	∧	PROPN
ejpam-5705	392	8	ℏ	ℏ	PROPN
ejpam-5705	392	9	is	be	AUX
ejpam-5705	392	10	minimal	minimal	ADJ
ejpam-5705	392	11	element	element	NOUN
ejpam-5705	392	12	.	.	PUNCT
ejpam-5705	393	1	theorem	theorem	NOUN
ejpam-5705	393	2	11	11	NUM
ejpam-5705	393	3	.	.	PUNCT
ejpam-5705	394	1	let	let	VERB
ejpam-5705	394	2	v	v	PART
ejpam-5705	394	3	be	be	AUX
ejpam-5705	394	4	a	a	DET
ejpam-5705	394	5	•-pdl	•-pdl	PUNCT
ejpam-5705	394	6	and	and	CCONJ
ejpam-5705	394	7	d	d	X
ejpam-5705	394	8	the	the	DET
ejpam-5705	394	9	set	set	NOUN
ejpam-5705	394	10	of	of	ADP
ejpam-5705	394	11	all	all	DET
ejpam-5705	394	12	dense	dense	ADJ
ejpam-5705	394	13	elements	element	NOUN
ejpam-5705	394	14	of	of	ADP
ejpam-5705	394	15	v	v	NOUN
ejpam-5705	394	16	.	.	PUNCT
ejpam-5705	395	1	then	then	ADV
ejpam-5705	395	2	[	[	X
ejpam-5705	395	3	µ4	µ4	PROPN
ejpam-5705	395	4	∨	∨	NUM
ejpam-5705	395	5	µ1	µ1	PROPN
ejpam-5705	395	6	]	]	PUNCT
ejpam-5705	395	7	•	•	NOUN
ejpam-5705	395	8	=	=	PUNCT
ejpam-5705	396	1	[	[	X
ejpam-5705	396	2	µ4	µ4	PROPN
ejpam-5705	396	3	∨	∨	NUM
ejpam-5705	396	4	µ2	µ2	PROPN
ejpam-5705	396	5	]	]	PUNCT
ejpam-5705	396	6	•	•	NOUN
ejpam-5705	396	7	for	for	ADP
ejpam-5705	396	8	some	some	DET
ejpam-5705	396	9	µ4	µ4	PROPN
ejpam-5705	396	10	∈	∈	PROPN
ejpam-5705	397	1	d	d	NOUN
ejpam-5705	397	2	if	if	SCONJ
ejpam-5705	397	3	and	and	CCONJ
ejpam-5705	397	4	only	only	ADV
ejpam-5705	397	5	if	if	SCONJ
ejpam-5705	397	6	[	[	X
ejpam-5705	397	7	µ1	µ1	X
ejpam-5705	397	8	]	]	X
ejpam-5705	397	9	•	•	NOUN
ejpam-5705	397	10	=	=	PUNCT
ejpam-5705	398	1	[	[	X
ejpam-5705	398	2	µ2	µ2	NOUN
ejpam-5705	398	3	]	]	PUNCT
ejpam-5705	398	4	•.	•.	NOUN
ejpam-5705	398	5	proof	proof	NOUN
ejpam-5705	398	6	.	.	PUNCT
ejpam-5705	399	1	suppose	suppose	VERB
ejpam-5705	400	1	[	[	X
ejpam-5705	400	2	µ4	µ4	PROPN
ejpam-5705	400	3	∨	∨	NUM
ejpam-5705	400	4	µ1	µ1	PROPN
ejpam-5705	400	5	]	]	PUNCT
ejpam-5705	400	6	•	•	NOUN
ejpam-5705	400	7	=	=	PUNCT
ejpam-5705	401	1	[	[	X
ejpam-5705	401	2	µ4	µ4	PROPN
ejpam-5705	401	3	∨	∨	NUM
ejpam-5705	401	4	µ2	µ2	PROPN
ejpam-5705	401	5	]	]	PUNCT
ejpam-5705	401	6	•	•	NOUN
ejpam-5705	401	7	for	for	ADP
ejpam-5705	401	8	some	some	DET
ejpam-5705	401	9	µ4	µ4	PROPN
ejpam-5705	401	10	∈	∈	PROPN
ejpam-5705	401	11	d.	d.	NOUN
ejpam-5705	401	12	then	then	ADV
ejpam-5705	401	13	[	[	X
ejpam-5705	401	14	µ4	µ4	X
ejpam-5705	401	15	]	]	X
ejpam-5705	401	16	•	•	NOUN
ejpam-5705	401	17	=	=	SYM
ejpam-5705	401	18	{	{	PUNCT
ejpam-5705	401	19	1	1	NUM
ejpam-5705	401	20	}	}	PUNCT
ejpam-5705	401	21	,	,	PUNCT
ejpam-5705	401	22	we	we	PRON
ejpam-5705	401	23	get	get	VERB
ejpam-5705	401	24	[	[	X
ejpam-5705	401	25	µ4	µ4	X
ejpam-5705	401	26	]	]	PUNCT
ejpam-5705	401	27	••	••	NOUN
ejpam-5705	401	28	=	=	SYM
ejpam-5705	401	29	{	{	PUNCT
ejpam-5705	401	30	1}•	1}•	NUM
ejpam-5705	401	31	=	=	SYM
ejpam-5705	401	32	v	v	NOUN
ejpam-5705	401	33	.	.	PUNCT
ejpam-5705	402	1	now	now	ADV
ejpam-5705	402	2	[	[	X
ejpam-5705	402	3	µ1	µ1	NOUN
ejpam-5705	402	4	]	]	PUNCT
ejpam-5705	402	5	••	••	NOUN
ejpam-5705	403	1	=	=	X
ejpam-5705	403	2	[	[	X
ejpam-5705	403	3	µ4	µ4	X
ejpam-5705	403	4	]	]	PUNCT
ejpam-5705	403	5	••	••	NOUN
ejpam-5705	403	6	∩	∩	NOUN
ejpam-5705	403	7	[	[	X
ejpam-5705	403	8	µ1	µ1	NOUN
ejpam-5705	403	9	]	]	PUNCT
ejpam-5705	403	10	••	••	NOUN
ejpam-5705	403	11	=	=	SYM
ejpam-5705	404	1	[	[	X
ejpam-5705	404	2	µ4	µ4	PROPN
ejpam-5705	404	3	∨	∨	NUM
ejpam-5705	404	4	µ1	µ1	PROPN
ejpam-5705	404	5	]	]	PUNCT
ejpam-5705	404	6	••	••	NOUN
ejpam-5705	404	7	=	=	SYM
ejpam-5705	405	1	[	[	X
ejpam-5705	405	2	µ4	µ4	PROPN
ejpam-5705	405	3	∨	∨	NUM
ejpam-5705	405	4	µ2	µ2	PROPN
ejpam-5705	405	5	]	]	PUNCT
ejpam-5705	405	6	••	••	NOUN
ejpam-5705	405	7	=	=	X
ejpam-5705	406	1	[	[	X
ejpam-5705	406	2	µ4	µ4	X
ejpam-5705	406	3	]	]	PUNCT
ejpam-5705	406	4	••	••	NOUN
ejpam-5705	406	5	∩	∩	NOUN
ejpam-5705	406	6	[	[	X
ejpam-5705	406	7	µ2	µ2	NOUN
ejpam-5705	406	8	]	]	PUNCT
ejpam-5705	406	9	••	••	NOUN
ejpam-5705	406	10	=	=	SYM
ejpam-5705	407	1	[	[	X
ejpam-5705	407	2	µ2	µ2	X
ejpam-5705	407	3	]	]	PUNCT
ejpam-5705	407	4	••	••	NOUN
ejpam-5705	407	5	.	.	PUNCT
ejpam-5705	408	1	therefore	therefore	ADV
ejpam-5705	408	2	[	[	X
ejpam-5705	408	3	µ1	µ1	NOUN
ejpam-5705	408	4	]	]	PUNCT
ejpam-5705	408	5	••	••	NOUN
ejpam-5705	409	1	=	=	SYM
ejpam-5705	410	1	[	[	X
ejpam-5705	410	2	µ2	µ2	X
ejpam-5705	410	3	]	]	PUNCT
ejpam-5705	410	4	••	••	NOUN
ejpam-5705	410	5	.	.	PUNCT
ejpam-5705	411	1	hence	hence	ADV
ejpam-5705	411	2	[	[	X
ejpam-5705	411	3	µ1	µ1	X
ejpam-5705	411	4	]	]	X
ejpam-5705	411	5	•	•	NOUN
ejpam-5705	411	6	=	=	PUNCT
ejpam-5705	412	1	[	[	X
ejpam-5705	412	2	µ2	µ2	NOUN
ejpam-5705	412	3	]	]	PUNCT
ejpam-5705	412	4	•.	•.	NOUN
ejpam-5705	412	5	conversely	conversely	ADV
ejpam-5705	412	6	assume	assume	VERB
ejpam-5705	412	7	that	that	SCONJ
ejpam-5705	412	8	[	[	X
ejpam-5705	412	9	µ1	µ1	X
ejpam-5705	412	10	]	]	X
ejpam-5705	412	11	•	•	NOUN
ejpam-5705	413	1	=	=	PUNCT
ejpam-5705	414	1	[	[	X
ejpam-5705	414	2	µ2	µ2	NOUN
ejpam-5705	414	3	]	]	PUNCT
ejpam-5705	414	4	•.	•.	NOUN
ejpam-5705	414	5	since	since	SCONJ
ejpam-5705	414	6	v	v	NOUN
ejpam-5705	414	7	is	be	AUX
ejpam-5705	414	8	a	a	DET
ejpam-5705	414	9	•-pdl	•-pdl	PUNCT
ejpam-5705	414	10	and	and	CCONJ
ejpam-5705	414	11	µ1	µ1	PROPN
ejpam-5705	414	12	∈	∈	PROPN
ejpam-5705	414	13	v	v	NOUN
ejpam-5705	414	14	,	,	PUNCT
ejpam-5705	414	15	there	there	PRON
ejpam-5705	414	16	exists	exist	VERB
ejpam-5705	414	17	µ	µ	PROPN
ejpam-5705	414	18	′	′	NUM
ejpam-5705	414	19	1	1	NUM
ejpam-5705	414	20	∈	∈	NOUN
ejpam-5705	414	21	v	v	ADP
ejpam-5705	414	22	such	such	ADJ
ejpam-5705	414	23	that	that	SCONJ
ejpam-5705	414	24	[	[	X
ejpam-5705	414	25	µ1	µ1	NOUN
ejpam-5705	414	26	]	]	PUNCT
ejpam-5705	414	27	••	••	NOUN
ejpam-5705	414	28	=	=	SYM
ejpam-5705	415	1	[	[	X
ejpam-5705	415	2	µ	µ	X
ejpam-5705	415	3	′	′	NUM
ejpam-5705	415	4	1	1	NUM
ejpam-5705	415	5	]	]	PUNCT
ejpam-5705	415	6	•.	•.	NOUN
ejpam-5705	415	7	also	also	ADV
ejpam-5705	415	8	[	[	X
ejpam-5705	415	9	µ1	µ1	X
ejpam-5705	415	10	]	]	X
ejpam-5705	415	11	•	•	NOUN
ejpam-5705	415	12	=	=	PUNCT
ejpam-5705	416	1	[	[	X
ejpam-5705	416	2	µ2	µ2	X
ejpam-5705	416	3	]	]	X
ejpam-5705	416	4	•	•	NUM
ejpam-5705	416	5	implies	imply	VERB
ejpam-5705	416	6	that	that	SCONJ
ejpam-5705	417	1	[	[	X
ejpam-5705	417	2	µ1	µ1	X
ejpam-5705	417	3	]	]	X
ejpam-5705	417	4	•	•	NOUN
ejpam-5705	417	5	=	=	PUNCT
ejpam-5705	418	1	[	[	X
ejpam-5705	418	2	µ1	µ1	NOUN
ejpam-5705	418	3	∧	∧	PROPN
ejpam-5705	418	4	µ2	µ2	NOUN
ejpam-5705	418	5	]	]	PUNCT
ejpam-5705	418	6	•.	•.	NOUN
ejpam-5705	418	7	now	now	ADV
ejpam-5705	418	8	if	if	SCONJ
ejpam-5705	418	9	we	we	PRON
ejpam-5705	418	10	write	write	VERB
ejpam-5705	418	11	µ4	µ4	PROPN
ejpam-5705	418	12	=	=	SYM
ejpam-5705	418	13	(	(	PUNCT
ejpam-5705	418	14	µ1	µ1	PROPN
ejpam-5705	418	15	∧	∧	PROPN
ejpam-5705	418	16	µ2	µ2	NOUN
ejpam-5705	418	17	)	)	PUNCT
ejpam-5705	418	18	∧	∧	PROPN
ejpam-5705	418	19	µ	µ	NOUN
ejpam-5705	418	20	′	′	NOUN
ejpam-5705	418	21	1	1	NUM
ejpam-5705	418	22	then	then	ADV
ejpam-5705	418	23	,	,	PUNCT
ejpam-5705	418	24	[	[	X
ejpam-5705	418	25	µ4	µ4	X
ejpam-5705	418	26	]	]	X
ejpam-5705	418	27	•	•	NOUN
ejpam-5705	418	28	=	=	SYM
ejpam-5705	419	1	[	[	X
ejpam-5705	419	2	(	(	PUNCT
ejpam-5705	419	3	µ1	µ1	PROPN
ejpam-5705	419	4	∧	∧	PROPN
ejpam-5705	419	5	µ2	µ2	PROPN
ejpam-5705	419	6	)	)	PUNCT
ejpam-5705	419	7	]	]	PUNCT
ejpam-5705	420	1	•	•	NUM
ejpam-5705	420	2	∩	∩	X
ejpam-5705	420	3	[	[	X
ejpam-5705	420	4	µ	µ	X
ejpam-5705	420	5	′	′	NUM
ejpam-5705	420	6	1	1	NUM
ejpam-5705	420	7	]	]	PUNCT
ejpam-5705	420	8	•	•	NOUN
ejpam-5705	420	9	=	=	PUNCT
ejpam-5705	421	1	[	[	X
ejpam-5705	421	2	µ1	µ1	X
ejpam-5705	421	3	]	]	X
ejpam-5705	421	4	•	•	NOUN
ejpam-5705	421	5	∩	∩	NOUN
ejpam-5705	421	6	[	[	X
ejpam-5705	421	7	µ	µ	X
ejpam-5705	421	8	′	′	NUM
ejpam-5705	421	9	1	1	NUM
ejpam-5705	421	10	]	]	PUNCT
ejpam-5705	421	11	•	•	NOUN
ejpam-5705	421	12	=	=	PUNCT
ejpam-5705	422	1	[	[	X
ejpam-5705	422	2	µ1	µ1	X
ejpam-5705	422	3	]	]	X
ejpam-5705	422	4	•	•	NOUN
ejpam-5705	422	5	∩	∩	NOUN
ejpam-5705	422	6	[	[	X
ejpam-5705	422	7	µ1	µ1	NOUN
ejpam-5705	422	8	]	]	PUNCT
ejpam-5705	422	9	••	••	NOUN
ejpam-5705	422	10	=	=	SYM
ejpam-5705	422	11	{	{	PUNCT
ejpam-5705	422	12	1	1	NUM
ejpam-5705	422	13	}	}	PUNCT
ejpam-5705	422	14	therefore	therefore	ADV
ejpam-5705	422	15	µ4	µ4	PROPN
ejpam-5705	422	16	∈	∈	PROPN
ejpam-5705	422	17	d.	d.	PROPN
ejpam-5705	422	18	now	now	ADV
ejpam-5705	422	19	µ1	µ1	PROPN
ejpam-5705	422	20	∨	∨	PROPN
ejpam-5705	422	21	µ4	µ4	PROPN
ejpam-5705	422	22	=	=	PUNCT
ejpam-5705	422	23	µ1	µ1	PROPN
ejpam-5705	422	24	∨	∨	NOUN
ejpam-5705	422	25	(	(	PUNCT
ejpam-5705	422	26	(	(	PUNCT
ejpam-5705	422	27	µ1	µ1	PROPN
ejpam-5705	422	28	∧	∧	PROPN
ejpam-5705	422	29	µ2	µ2	NOUN
ejpam-5705	422	30	)	)	PUNCT
ejpam-5705	422	31	∧	∧	PROPN
ejpam-5705	422	32	µ	µ	NOUN
ejpam-5705	422	33	′	′	NOUN
ejpam-5705	422	34	1	1	NUM
ejpam-5705	422	35	)	)	PUNCT
ejpam-5705	422	36	=	=	SYM
ejpam-5705	422	37	µ1	µ1	NOUN
ejpam-5705	422	38	∧	∧	PROPN
ejpam-5705	422	39	(	(	PUNCT
ejpam-5705	422	40	µ1	µ1	PROPN
ejpam-5705	422	41	∨	∨	PROPN
ejpam-5705	422	42	µ	µ	NOUN
ejpam-5705	422	43	′	′	NUM
ejpam-5705	422	44	1	1	NUM
ejpam-5705	422	45	)	)	PUNCT
ejpam-5705	422	46	=	=	SYM
ejpam-5705	422	47	µ1	µ1	PROPN
ejpam-5705	422	48	.	.	PUNCT
ejpam-5705	423	1	also	also	ADV
ejpam-5705	423	2	µ2	µ2	VERB
ejpam-5705	423	3	∨	∨	PROPN
ejpam-5705	423	4	µ4	µ4	PROPN
ejpam-5705	423	5	=	=	PROPN
ejpam-5705	423	6	µ2	µ2	PROPN
ejpam-5705	423	7	∨	∨	NUM
ejpam-5705	423	8	(	(	PUNCT
ejpam-5705	423	9	(	(	PUNCT
ejpam-5705	423	10	µ1	µ1	PROPN
ejpam-5705	423	11	∧	∧	PROPN
ejpam-5705	423	12	µ2	µ2	NOUN
ejpam-5705	423	13	)	)	PUNCT
ejpam-5705	423	14	∧	∧	PROPN
ejpam-5705	423	15	µ	µ	NOUN
ejpam-5705	423	16	′	′	NOUN
ejpam-5705	423	17	1	1	NUM
ejpam-5705	423	18	)	)	PUNCT
ejpam-5705	423	19	=	=	PUNCT
ejpam-5705	424	1	(	(	PUNCT
ejpam-5705	424	2	µ2	µ2	PROPN
ejpam-5705	424	3	∨	∨	NUM
ejpam-5705	424	4	(	(	PUNCT
ejpam-5705	424	5	µ1	µ1	PROPN
ejpam-5705	424	6	∧	∧	PROPN
ejpam-5705	424	7	µ2	µ2	NOUN
ejpam-5705	424	8	)	)	PUNCT
ejpam-5705	424	9	)	)	PUNCT
ejpam-5705	424	10	∧	∧	NOUN
ejpam-5705	424	11	(	(	PUNCT
ejpam-5705	424	12	µ2	µ2	PROPN
ejpam-5705	424	13	∨	∨	PROPN
ejpam-5705	424	14	µ	µ	NOUN
ejpam-5705	424	15	′	′	NUM
ejpam-5705	424	16	1	1	NUM
ejpam-5705	424	17	)	)	PUNCT
ejpam-5705	424	18	=	=	VERB
ejpam-5705	425	1	µ2	µ2	PROPN
ejpam-5705	425	2	∧	∧	PROPN
ejpam-5705	425	3	(	(	PUNCT
ejpam-5705	425	4	µ2	µ2	PROPN
ejpam-5705	425	5	∨	∨	PROPN
ejpam-5705	425	6	µ	µ	NOUN
ejpam-5705	425	7	′	′	NUM
ejpam-5705	425	8	1	1	NUM
ejpam-5705	425	9	)	)	PUNCT
ejpam-5705	425	10	=	=	VERB
ejpam-5705	425	11	µ2	µ2	PROPN
ejpam-5705	425	12	.	.	PUNCT
ejpam-5705	426	1	thus	thus	ADV
ejpam-5705	426	2	[	[	X
ejpam-5705	426	3	µ1	µ1	PROPN
ejpam-5705	426	4	∨	∨	NUM
ejpam-5705	426	5	µ4	µ4	PROPN
ejpam-5705	426	6	]	]	PUNCT
ejpam-5705	426	7	•	•	NOUN
ejpam-5705	427	1	=	=	PUNCT
ejpam-5705	428	1	[	[	X
ejpam-5705	428	2	µ2	µ2	PROPN
ejpam-5705	428	3	∨	∨	NUM
ejpam-5705	428	4	µ4	µ4	PROPN
ejpam-5705	428	5	]	]	PUNCT
ejpam-5705	428	6	•	•	NUM
ejpam-5705	428	7	which	which	PRON
ejpam-5705	428	8	implies	imply	VERB
ejpam-5705	428	9	[	[	PUNCT
ejpam-5705	428	10	µ4	µ4	PROPN
ejpam-5705	428	11	∨	∨	NUM
ejpam-5705	428	12	µ1	µ1	PROPN
ejpam-5705	428	13	]	]	PUNCT
ejpam-5705	428	14	•	•	NOUN
ejpam-5705	428	15	=	=	PUNCT
ejpam-5705	429	1	[	[	X
ejpam-5705	429	2	µ4	µ4	PROPN
ejpam-5705	429	3	∨	∨	NUM
ejpam-5705	429	4	µ2	µ2	PROPN
ejpam-5705	429	5	]	]	PUNCT
ejpam-5705	429	6	•.	•.	NOUN
ejpam-5705	429	7	lemma	lemma	PROPN
ejpam-5705	429	8	15	15	NUM
ejpam-5705	429	9	.	.	PUNCT
ejpam-5705	430	1	let	let	VERB
ejpam-5705	430	2	v	v	PART
ejpam-5705	430	3	be	be	AUX
ejpam-5705	430	4	a	a	DET
ejpam-5705	430	5	pdl	pdl	NOUN
ejpam-5705	430	6	.	.	PUNCT
ejpam-5705	431	1	for	for	ADP
ejpam-5705	431	2	any	any	DET
ejpam-5705	431	3	µ1	µ1	PROPN
ejpam-5705	431	4	∈	∈	PROPN
ejpam-5705	431	5	v	v	NOUN
ejpam-5705	431	6	,	,	PUNCT
ejpam-5705	431	7	(	(	PUNCT
ejpam-5705	431	8	µ1	µ1	NOUN
ejpam-5705	431	9	:	:	PUNCT
ejpam-5705	431	10	d	d	X
ejpam-5705	431	11	)	)	PUNCT
ejpam-5705	431	12	=	=	SYM
ejpam-5705	431	13	{	{	PUNCT
ejpam-5705	431	14	℘	℘	NOUN
ejpam-5705	431	15	∈	∈	NOUN
ejpam-5705	431	16	v	v	ADP
ejpam-5705	431	17	|	|	ADV
ejpam-5705	431	18	℘	℘	VERB
ejpam-5705	431	19	∧	∧	NOUN
ejpam-5705	431	20	µ1	µ1	NOUN
ejpam-5705	431	21	∈	∈	NOUN
ejpam-5705	431	22	d	d	NOUN
ejpam-5705	431	23	}	}	PUNCT
ejpam-5705	431	24	is	be	AUX
ejpam-5705	431	25	an	an	DET
ejpam-5705	431	26	ideal	ideal	NOUN
ejpam-5705	431	27	of	of	ADP
ejpam-5705	431	28	v	v	NOUN
ejpam-5705	431	29	.	.	PUNCT
ejpam-5705	432	1	proof	proof	NOUN
ejpam-5705	432	2	.	.	PUNCT
ejpam-5705	433	1	let	let	VERB
ejpam-5705	433	2	℘	℘	NOUN
ejpam-5705	433	3	,	,	PUNCT
ejpam-5705	433	4	ℏ	ℏ	PROPN
ejpam-5705	433	5	∈	∈	PROPN
ejpam-5705	433	6	(	(	PUNCT
ejpam-5705	433	7	µ1	µ1	NOUN
ejpam-5705	433	8	:	:	PUNCT
ejpam-5705	433	9	d	d	X
ejpam-5705	433	10	)	)	PUNCT
ejpam-5705	433	11	.	.	PUNCT
ejpam-5705	434	1	then	then	ADV
ejpam-5705	434	2	℘∧µ1	℘∧µ1	PROPN
ejpam-5705	434	3	∈	∈	PROPN
ejpam-5705	434	4	d	d	PROPN
ejpam-5705	434	5	,	,	PUNCT
ejpam-5705	434	6	ℏ∧µ1	ℏ∧µ1	PROPN
ejpam-5705	434	7	∈	∈	PROPN
ejpam-5705	434	8	d.	d.	NOUN
ejpam-5705	434	9	therefore	therefore	ADV
ejpam-5705	434	10	(	(	PUNCT
ejpam-5705	434	11	℘∧µ1)∨(ℏ∧µ1	℘∧µ1)∨(ℏ∧µ1	ADJ
ejpam-5705	434	12	)	)	PUNCT
ejpam-5705	434	13	∈	∈	PROPN
ejpam-5705	434	14	d.	d.	NOUN
ejpam-5705	434	15	so	so	SCONJ
ejpam-5705	434	16	that	that	SCONJ
ejpam-5705	434	17	(	(	PUNCT
ejpam-5705	434	18	℘	℘	PROPN
ejpam-5705	434	19	∨	∨	NUM
ejpam-5705	434	20	ℏ	ℏ	NOUN
ejpam-5705	434	21	)	)	PUNCT
ejpam-5705	434	22	∧	∧	PROPN
ejpam-5705	434	23	µ1	µ1	PROPN
ejpam-5705	434	24	∈	∈	PROPN
ejpam-5705	434	25	d.	d.	NOUN
ejpam-5705	434	26	hence	hence	ADV
ejpam-5705	434	27	℘	℘	VERB
ejpam-5705	434	28	∨	∨	NUM
ejpam-5705	434	29	ℏ	ℏ	PRON
ejpam-5705	434	30	∈	∈	PROPN
ejpam-5705	434	31	(	(	PUNCT
ejpam-5705	434	32	µ1	µ1	NOUN
ejpam-5705	434	33	:	:	PUNCT
ejpam-5705	434	34	d	d	X
ejpam-5705	434	35	)	)	PUNCT
ejpam-5705	434	36	.	.	PUNCT
ejpam-5705	435	1	now	now	ADV
ejpam-5705	435	2	,	,	PUNCT
ejpam-5705	435	3	let	let	VERB
ejpam-5705	435	4	℘	℘	PROPN
ejpam-5705	435	5	∈	∈	PROPN
ejpam-5705	435	6	(	(	PUNCT
ejpam-5705	435	7	µ1	µ1	NOUN
ejpam-5705	435	8	:	:	PUNCT
ejpam-5705	435	9	d	d	X
ejpam-5705	435	10	)	)	PUNCT
ejpam-5705	435	11	and	and	CCONJ
ejpam-5705	435	12	τ	τ	PROPN
ejpam-5705	435	13	∈	∈	PROPN
ejpam-5705	435	14	v	v	NOUN
ejpam-5705	435	15	.	.	PUNCT
ejpam-5705	436	1	then	then	ADV
ejpam-5705	436	2	,	,	PUNCT
ejpam-5705	436	3	℘	℘	VERB
ejpam-5705	436	4	∧	∧	NOUN
ejpam-5705	436	5	µ1	µ1	NOUN
ejpam-5705	436	6	∈	∈	PROPN
ejpam-5705	436	7	d	d	NOUN
ejpam-5705	436	8	and	and	CCONJ
ejpam-5705	436	9	[	[	PUNCT
ejpam-5705	436	10	℘	℘	NUM
ejpam-5705	436	11	∧	∧	NOUN
ejpam-5705	436	12	µ1	µ1	PROPN
ejpam-5705	436	13	]	]	X
ejpam-5705	436	14	•	•	NOUN
ejpam-5705	436	15	=	=	SYM
ejpam-5705	436	16	{	{	PUNCT
ejpam-5705	436	17	1	1	NUM
ejpam-5705	436	18	}	}	PUNCT
ejpam-5705	436	19	.	.	PUNCT
ejpam-5705	437	1	hence	hence	ADV
ejpam-5705	437	2	[	[	X
ejpam-5705	437	3	(	(	PUNCT
ejpam-5705	437	4	℘	℘	PROPN
ejpam-5705	437	5	∧	∧	PROPN
ejpam-5705	437	6	τ	τ	NOUN
ejpam-5705	437	7	)	)	PUNCT
ejpam-5705	437	8	∧	∧	PROPN
ejpam-5705	437	9	µ1	µ1	PROPN
ejpam-5705	437	10	]	]	PUNCT
ejpam-5705	437	11	•	•	NOUN
ejpam-5705	438	1	=	=	PUNCT
ejpam-5705	439	1	[	[	PUNCT
ejpam-5705	439	2	℘	℘	NUM
ejpam-5705	439	3	∧	∧	PROPN
ejpam-5705	439	4	τ	τ	X
ejpam-5705	439	5	]	]	X
ejpam-5705	439	6	•	•	NOUN
ejpam-5705	439	7	∩	∩	NOUN
ejpam-5705	439	8	[	[	X
ejpam-5705	439	9	µ1	µ1	X
ejpam-5705	439	10	]	]	X
ejpam-5705	439	11	•	•	NOUN
ejpam-5705	439	12	=	=	SYM
ejpam-5705	440	1	[	[	X
ejpam-5705	440	2	℘]•	℘]•	PROPN
ejpam-5705	440	3	∩	∩	X
ejpam-5705	440	4	[	[	X
ejpam-5705	440	5	τ	τ	X
ejpam-5705	440	6	]	]	X
ejpam-5705	440	7	•	•	NOUN
ejpam-5705	440	8	∩	∩	NOUN
ejpam-5705	440	9	[	[	X
ejpam-5705	440	10	µ1	µ1	X
ejpam-5705	440	11	]	]	X
ejpam-5705	440	12	•	•	NOUN
ejpam-5705	441	1	=	=	PUNCT
ejpam-5705	442	1	[	[	X
ejpam-5705	442	2	τ	τ	X
ejpam-5705	442	3	]	]	X
ejpam-5705	442	4	•	•	NOUN
ejpam-5705	442	5	∩	∩	NOUN
ejpam-5705	442	6	[	[	X
ejpam-5705	442	7	℘]•	℘]•	PROPN
ejpam-5705	442	8	∩	∩	NOUN
ejpam-5705	442	9	[	[	X
ejpam-5705	442	10	µ1	µ1	X
ejpam-5705	442	11	]	]	X
ejpam-5705	442	12	•	•	NOUN
ejpam-5705	442	13	=	=	PUNCT
ejpam-5705	443	1	[	[	X
ejpam-5705	443	2	τ	τ	X
ejpam-5705	443	3	]	]	X
ejpam-5705	443	4	•	•	NOUN
ejpam-5705	443	5	∩	∩	NOUN
ejpam-5705	443	6	[	[	PUNCT
ejpam-5705	443	7	℘	℘	NUM
ejpam-5705	443	8	∧	∧	NOUN
ejpam-5705	443	9	µ1	µ1	PROPN
ejpam-5705	443	10	]	]	X
ejpam-5705	443	11	•	•	NOUN
ejpam-5705	443	12	=	=	SYM
ejpam-5705	443	13	{	{	PUNCT
ejpam-5705	443	14	1	1	NUM
ejpam-5705	443	15	}	}	PUNCT
ejpam-5705	443	16	therefore	therefore	ADV
ejpam-5705	443	17	(	(	PUNCT
ejpam-5705	443	18	℘	℘	PROPN
ejpam-5705	443	19	∧	∧	PROPN
ejpam-5705	443	20	τ	τ	NOUN
ejpam-5705	443	21	)	)	PUNCT
ejpam-5705	443	22	∧	∧	PROPN
ejpam-5705	443	23	µ1	µ1	NOUN
ejpam-5705	443	24	∈	∈	PROPN
ejpam-5705	443	25	d	d	NOUN
ejpam-5705	443	26	⇒	⇒	NOUN
ejpam-5705	443	27	℘	℘	PROPN
ejpam-5705	443	28	∧	∧	PROPN
ejpam-5705	443	29	τ	τ	PROPN
ejpam-5705	443	30	∈	∈	PROPN
ejpam-5705	443	31	(	(	PUNCT
ejpam-5705	443	32	µ1	µ1	NOUN
ejpam-5705	443	33	:	:	PUNCT
ejpam-5705	443	34	d	d	X
ejpam-5705	443	35	)	)	PUNCT
ejpam-5705	443	36	.	.	PUNCT
ejpam-5705	444	1	thus	thus	ADV
ejpam-5705	444	2	(	(	PUNCT
ejpam-5705	444	3	µ1	µ1	NOUN
ejpam-5705	444	4	:	:	PUNCT
ejpam-5705	444	5	d	d	X
ejpam-5705	444	6	)	)	PUNCT
ejpam-5705	444	7	is	be	AUX
ejpam-5705	444	8	an	an	DET
ejpam-5705	444	9	ideal	ideal	NOUN
ejpam-5705	444	10	of	of	ADP
ejpam-5705	444	11	v	v	NOUN
ejpam-5705	444	12	.	.	PUNCT
ejpam-5705	445	1	r.	r.	PROPN
ejpam-5705	445	2	bandaru	bandaru	PROPN
ejpam-5705	445	3	et	et	PROPN
ejpam-5705	445	4	al	al	PROPN
ejpam-5705	445	5	.	.	PUNCT
ejpam-5705	445	6	/	/	SYM
ejpam-5705	445	7	eur	eur	PROPN
ejpam-5705	445	8	.	.	PUNCT
ejpam-5705	446	1	j.	j.	PROPN
ejpam-5705	446	2	pure	pure	PROPN
ejpam-5705	446	3	appl	appl	PROPN
ejpam-5705	446	4	.	.	PROPN
ejpam-5705	446	5	math	math	PROPN
ejpam-5705	446	6	,	,	PUNCT
ejpam-5705	446	7	18	18	NUM
ejpam-5705	446	8	(	(	PUNCT
ejpam-5705	446	9	2	2	NUM
ejpam-5705	446	10	)	)	PUNCT
ejpam-5705	446	11	(	(	PUNCT
ejpam-5705	446	12	2025	2025	NUM
ejpam-5705	446	13	)	)	PUNCT
ejpam-5705	446	14	,	,	PUNCT
ejpam-5705	446	15	5705	5705	NUM
ejpam-5705	446	16	11	11	NUM
ejpam-5705	446	17	of	of	ADP
ejpam-5705	446	18	13	13	NUM
ejpam-5705	446	19	theorem	theorem	NOUN
ejpam-5705	446	20	12	12	NUM
ejpam-5705	446	21	.	.	PUNCT
ejpam-5705	447	1	let	let	VERB
ejpam-5705	447	2	v	v	PART
ejpam-5705	447	3	be	be	AUX
ejpam-5705	447	4	a	a	DET
ejpam-5705	447	5	•-pdl	•-pdl	NOUN
ejpam-5705	447	6	.	.	PUNCT
ejpam-5705	448	1	then	then	ADV
ejpam-5705	448	2	θ	θ	X
ejpam-5705	448	3	=	=	SYM
ejpam-5705	448	4	{	{	PUNCT
ejpam-5705	448	5	(	(	PUNCT
ejpam-5705	448	6	µ1	µ1	PROPN
ejpam-5705	448	7	,	,	PUNCT
ejpam-5705	448	8	µ2	µ2	ADJ
ejpam-5705	448	9	)	)	PUNCT
ejpam-5705	448	10	∈	∈	PROPN
ejpam-5705	449	1	v	v	ADP
ejpam-5705	449	2	×	×	NOUN
ejpam-5705	449	3	v	v	NOUN
ejpam-5705	449	4	|	|	NOUN
ejpam-5705	450	1	(	(	PUNCT
ejpam-5705	450	2	µ1	µ1	NOUN
ejpam-5705	450	3	:	:	PUNCT
ejpam-5705	450	4	d	d	X
ejpam-5705	450	5	)	)	PUNCT
ejpam-5705	450	6	=	=	SYM
ejpam-5705	451	1	(	(	PUNCT
ejpam-5705	451	2	µ2	µ2	NOUN
ejpam-5705	451	3	:	:	PUNCT
ejpam-5705	451	4	d	d	X
ejpam-5705	451	5	)	)	PUNCT
ejpam-5705	451	6	}	}	PUNCT
ejpam-5705	451	7	,	,	PUNCT
ejpam-5705	451	8	where	where	SCONJ
ejpam-5705	451	9	θ	θ	NOUN
ejpam-5705	451	10	=	=	SYM
ejpam-5705	451	11	{	{	PUNCT
ejpam-5705	451	12	(	(	PUNCT
ejpam-5705	451	13	℘	℘	NOUN
ejpam-5705	451	14	,	,	PUNCT
ejpam-5705	451	15	ℏ	ℏ	NOUN
ejpam-5705	451	16	)	)	PUNCT
ejpam-5705	451	17	∈	∈	PROPN
ejpam-5705	451	18	v	v	ADP
ejpam-5705	452	1	×	×	NOUN
ejpam-5705	452	2	v	v	INTJ
ejpam-5705	453	1	|	|	NOUN
ejpam-5705	454	1	[	[	X
ejpam-5705	454	2	℘]•	℘]•	PROPN
ejpam-5705	454	3	=	=	PUNCT
ejpam-5705	455	1	[	[	X
ejpam-5705	455	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	455	3	}	}	PUNCT
ejpam-5705	455	4	.	.	PUNCT
ejpam-5705	456	1	proof	proof	NOUN
ejpam-5705	456	2	.	.	PUNCT
ejpam-5705	457	1	let	let	VERB
ejpam-5705	457	2	(	(	PUNCT
ejpam-5705	457	3	µ1	µ1	ADJ
ejpam-5705	457	4	,	,	PUNCT
ejpam-5705	457	5	µ2	µ2	ADJ
ejpam-5705	457	6	)	)	PUNCT
ejpam-5705	457	7	∈	∈	PROPN
ejpam-5705	457	8	θ	θ	PROPN
ejpam-5705	457	9	.	.	PUNCT
ejpam-5705	458	1	then	then	ADV
ejpam-5705	458	2	[	[	X
ejpam-5705	458	3	µ1	µ1	X
ejpam-5705	458	4	]	]	X
ejpam-5705	458	5	•	•	NOUN
ejpam-5705	458	6	=	=	PUNCT
ejpam-5705	459	1	[	[	X
ejpam-5705	459	2	µ2	µ2	NOUN
ejpam-5705	459	3	]	]	PUNCT
ejpam-5705	459	4	•.	•.	NOUN
ejpam-5705	459	5	now	now	ADV
ejpam-5705	459	6	,	,	PUNCT
ejpam-5705	459	7	for	for	ADP
ejpam-5705	459	8	any	any	DET
ejpam-5705	459	9	℘	℘	PROPN
ejpam-5705	459	10	∈	∈	NOUN
ejpam-5705	459	11	v	v	ADP
ejpam-5705	459	12	℘	℘	PROPN
ejpam-5705	459	13	∈	∈	PROPN
ejpam-5705	459	14	(	(	PUNCT
ejpam-5705	459	15	µ1	µ1	NOUN
ejpam-5705	459	16	:	:	PUNCT
ejpam-5705	459	17	d	d	X
ejpam-5705	459	18	)	)	PUNCT
ejpam-5705	459	19	⇔	⇔	PROPN
ejpam-5705	459	20	℘	℘	PROPN
ejpam-5705	459	21	∧	∧	PROPN
ejpam-5705	459	22	µ1	µ1	NOUN
ejpam-5705	459	23	∈	∈	PROPN
ejpam-5705	459	24	d	d	X
ejpam-5705	459	25	⇔	⇔	X
ejpam-5705	459	26	[	[	PUNCT
ejpam-5705	459	27	℘	℘	NUM
ejpam-5705	459	28	∧	∧	NOUN
ejpam-5705	459	29	µ1	µ1	PROPN
ejpam-5705	459	30	]	]	X
ejpam-5705	459	31	•	•	NOUN
ejpam-5705	459	32	=	=	SYM
ejpam-5705	459	33	{	{	PUNCT
ejpam-5705	459	34	1	1	NUM
ejpam-5705	459	35	}	}	PUNCT
ejpam-5705	459	36	⇔	⇔	NOUN
ejpam-5705	459	37	[	[	X
ejpam-5705	459	38	℘]•	℘]•	PROPN
ejpam-5705	459	39	∩	∩	NOUN
ejpam-5705	459	40	[	[	X
ejpam-5705	459	41	µ1	µ1	X
ejpam-5705	459	42	]	]	X
ejpam-5705	459	43	•	•	NOUN
ejpam-5705	459	44	=	=	SYM
ejpam-5705	459	45	{	{	PUNCT
ejpam-5705	459	46	1	1	NUM
ejpam-5705	459	47	}	}	PUNCT
ejpam-5705	459	48	⇔	⇔	NOUN
ejpam-5705	459	49	[	[	X
ejpam-5705	459	50	℘]•	℘]•	PROPN
ejpam-5705	459	51	∩	∩	X
ejpam-5705	459	52	[	[	X
ejpam-5705	459	53	µ2	µ2	X
ejpam-5705	459	54	]	]	X
ejpam-5705	459	55	•	•	NOUN
ejpam-5705	459	56	=	=	SYM
ejpam-5705	459	57	{	{	PUNCT
ejpam-5705	459	58	1	1	NUM
ejpam-5705	459	59	}	}	PUNCT
ejpam-5705	459	60	⇔	⇔	NOUN
ejpam-5705	459	61	[	[	PUNCT
ejpam-5705	459	62	℘	℘	PROPN
ejpam-5705	459	63	∧	∧	PROPN
ejpam-5705	459	64	µ2	µ2	NOUN
ejpam-5705	459	65	]	]	PUNCT
ejpam-5705	459	66	•	•	NOUN
ejpam-5705	459	67	=	=	SYM
ejpam-5705	459	68	{	{	PUNCT
ejpam-5705	459	69	1	1	NUM
ejpam-5705	459	70	}	}	PUNCT
ejpam-5705	459	71	⇔	⇔	X
ejpam-5705	459	72	℘	℘	PROPN
ejpam-5705	459	73	∧	∧	PROPN
ejpam-5705	459	74	µ2	µ2	PROPN
ejpam-5705	459	75	∈	∈	PROPN
ejpam-5705	459	76	d	d	PROPN
ejpam-5705	459	77	⇔	⇔	X
ejpam-5705	459	78	℘	℘	PROPN
ejpam-5705	459	79	∈	∈	PROPN
ejpam-5705	459	80	(	(	PUNCT
ejpam-5705	459	81	µ2	µ2	NOUN
ejpam-5705	459	82	:	:	PUNCT
ejpam-5705	459	83	d	d	X
ejpam-5705	459	84	)	)	PUNCT
ejpam-5705	459	85	therefore	therefore	ADV
ejpam-5705	459	86	(	(	PUNCT
ejpam-5705	459	87	µ1	µ1	NOUN
ejpam-5705	459	88	:	:	PUNCT
ejpam-5705	459	89	d	d	X
ejpam-5705	459	90	)	)	PUNCT
ejpam-5705	459	91	=	=	SYM
ejpam-5705	460	1	(	(	PUNCT
ejpam-5705	460	2	µ2	µ2	NOUN
ejpam-5705	460	3	:	:	PUNCT
ejpam-5705	460	4	d	d	X
ejpam-5705	460	5	)	)	PUNCT
ejpam-5705	460	6	.	.	PUNCT
ejpam-5705	461	1	on	on	ADP
ejpam-5705	461	2	the	the	DET
ejpam-5705	461	3	other	other	ADJ
ejpam-5705	461	4	hand	hand	NOUN
ejpam-5705	461	5	,	,	PUNCT
ejpam-5705	461	6	let	let	VERB
ejpam-5705	461	7	µ1	µ1	PROPN
ejpam-5705	461	8	,	,	PUNCT
ejpam-5705	461	9	µ2	µ2	PROPN
ejpam-5705	461	10	∈	∈	PROPN
ejpam-5705	461	11	v	v	PROPN
ejpam-5705	461	12	and	and	CCONJ
ejpam-5705	461	13	(	(	PUNCT
ejpam-5705	461	14	µ1	µ1	PROPN
ejpam-5705	461	15	:	:	PUNCT
ejpam-5705	461	16	d	d	X
ejpam-5705	461	17	)	)	PUNCT
ejpam-5705	461	18	=	=	SYM
ejpam-5705	462	1	(	(	PUNCT
ejpam-5705	462	2	µ2	µ2	NOUN
ejpam-5705	462	3	:	:	PUNCT
ejpam-5705	462	4	d	d	X
ejpam-5705	462	5	)	)	PUNCT
ejpam-5705	462	6	.	.	PUNCT
ejpam-5705	463	1	since	since	SCONJ
ejpam-5705	463	2	v	v	NOUN
ejpam-5705	463	3	is	be	AUX
ejpam-5705	463	4	a	a	DET
ejpam-5705	463	5	•-pdl	•-pdl	PUNCT
ejpam-5705	463	6	and	and	CCONJ
ejpam-5705	463	7	µ1	µ1	PROPN
ejpam-5705	463	8	∈	∈	PROPN
ejpam-5705	463	9	v	v	NOUN
ejpam-5705	463	10	,	,	PUNCT
ejpam-5705	463	11	there	there	PRON
ejpam-5705	463	12	exists	exist	VERB
ejpam-5705	463	13	µ3	µ3	PROPN
ejpam-5705	463	14	∈	∈	PROPN
ejpam-5705	463	15	v	v	ADP
ejpam-5705	463	16	such	such	ADJ
ejpam-5705	463	17	that	that	SCONJ
ejpam-5705	463	18	[	[	X
ejpam-5705	463	19	µ1	µ1	NOUN
ejpam-5705	463	20	]	]	PUNCT
ejpam-5705	463	21	••	••	NOUN
ejpam-5705	464	1	=	=	SYM
ejpam-5705	464	2	[	[	X
ejpam-5705	464	3	µ3	µ3	X
ejpam-5705	464	4	]	]	PUNCT
ejpam-5705	464	5	•.	•.	NOUN
ejpam-5705	464	6	so	so	SCONJ
ejpam-5705	464	7	that	that	SCONJ
ejpam-5705	464	8	µ1	µ1	PROPN
ejpam-5705	464	9	∧	∧	PROPN
ejpam-5705	464	10	µ3	µ3	NOUN
ejpam-5705	464	11	∈	∈	PROPN
ejpam-5705	464	12	d	d	NOUN
ejpam-5705	464	13	and	and	CCONJ
ejpam-5705	464	14	hence	hence	ADV
ejpam-5705	464	15	µ3∧µ1	µ3∧µ1	PROPN
ejpam-5705	464	16	∈	∈	PROPN
ejpam-5705	464	17	d.	d.	NOUN
ejpam-5705	464	18	therefore	therefore	ADV
ejpam-5705	464	19	µ3	µ3	PROPN
ejpam-5705	464	20	∈	∈	PROPN
ejpam-5705	464	21	(	(	PUNCT
ejpam-5705	464	22	µ1	µ1	NOUN
ejpam-5705	464	23	:	:	PUNCT
ejpam-5705	464	24	d	d	X
ejpam-5705	464	25	)	)	PUNCT
ejpam-5705	464	26	.	.	PUNCT
ejpam-5705	465	1	hence	hence	ADV
ejpam-5705	465	2	µ3	µ3	PROPN
ejpam-5705	465	3	∈	∈	PROPN
ejpam-5705	465	4	(	(	PUNCT
ejpam-5705	465	5	µ2	µ2	NOUN
ejpam-5705	465	6	:	:	PUNCT
ejpam-5705	465	7	d	d	X
ejpam-5705	465	8	)	)	PUNCT
ejpam-5705	465	9	.	.	PUNCT
ejpam-5705	466	1	we	we	PRON
ejpam-5705	466	2	get	get	VERB
ejpam-5705	466	3	µ3∧µ2	µ3∧µ2	PROPN
ejpam-5705	466	4	∈	∈	PROPN
ejpam-5705	466	5	d.	d.	NOUN
ejpam-5705	466	6	therefore	therefore	ADV
ejpam-5705	467	1	[	[	X
ejpam-5705	467	2	µ3	µ3	NUM
ejpam-5705	467	3	∧µ2	∧µ2	X
ejpam-5705	467	4	]	]	X
ejpam-5705	467	5	•	•	NOUN
ejpam-5705	467	6	=	=	SYM
ejpam-5705	467	7	{	{	PUNCT
ejpam-5705	467	8	1	1	NUM
ejpam-5705	467	9	}	}	PUNCT
ejpam-5705	467	10	and	and	CCONJ
ejpam-5705	467	11	hence	hence	ADV
ejpam-5705	467	12	[	[	X
ejpam-5705	467	13	µ3	µ3	X
ejpam-5705	467	14	]	]	X
ejpam-5705	467	15	•	•	NOUN
ejpam-5705	467	16	∩	∩	NOUN
ejpam-5705	468	1	[	[	X
ejpam-5705	468	2	µ2	µ2	X
ejpam-5705	468	3	]	]	X
ejpam-5705	468	4	•	•	NOUN
ejpam-5705	468	5	=	=	SYM
ejpam-5705	468	6	{	{	PUNCT
ejpam-5705	468	7	1	1	NUM
ejpam-5705	468	8	}	}	PUNCT
ejpam-5705	468	9	.	.	PUNCT
ejpam-5705	469	1	thus	thus	ADV
ejpam-5705	469	2	[	[	X
ejpam-5705	469	3	µ1	µ1	X
ejpam-5705	469	4	]	]	PUNCT
ejpam-5705	469	5	••	••	NOUN
ejpam-5705	469	6	∩	∩	NOUN
ejpam-5705	469	7	[	[	X
ejpam-5705	469	8	µ2	µ2	X
ejpam-5705	469	9	]	]	X
ejpam-5705	469	10	•	•	NOUN
ejpam-5705	469	11	=	=	SYM
ejpam-5705	469	12	1	1	X
ejpam-5705	469	13	.	.	PUNCT
ejpam-5705	469	14	now	now	ADV
ejpam-5705	469	15	,	,	PUNCT
ejpam-5705	469	16	let	let	VERB
ejpam-5705	469	17	℘	℘	PROPN
ejpam-5705	469	18	∈	∈	PROPN
ejpam-5705	469	19	[	[	X
ejpam-5705	469	20	µ2	µ2	NOUN
ejpam-5705	469	21	]	]	PUNCT
ejpam-5705	469	22	•.	•.	NOUN
ejpam-5705	469	23	then	then	ADV
ejpam-5705	469	24	µ1	µ1	PROPN
ejpam-5705	469	25	∨	∨	NOUN
ejpam-5705	469	26	℘	℘	PROPN
ejpam-5705	469	27	∈	∈	PROPN
ejpam-5705	470	1	[	[	X
ejpam-5705	470	2	µ2	µ2	NOUN
ejpam-5705	470	3	]	]	PUNCT
ejpam-5705	470	4	•.	•.	NOUN
ejpam-5705	470	5	also	also	ADV
ejpam-5705	470	6	µ1	µ1	VERB
ejpam-5705	470	7	∈	∈	PROPN
ejpam-5705	471	1	[	[	X
ejpam-5705	471	2	µ1	µ1	NOUN
ejpam-5705	471	3	]	]	PUNCT
ejpam-5705	471	4	••	••	NOUN
ejpam-5705	471	5	and	and	CCONJ
ejpam-5705	471	6	hence	hence	ADV
ejpam-5705	471	7	µ1	µ1	PROPN
ejpam-5705	471	8	∨	∨	NUM
ejpam-5705	471	9	℘	℘	PROPN
ejpam-5705	471	10	∈	∈	PROPN
ejpam-5705	471	11	[	[	X
ejpam-5705	471	12	µ1	µ1	NOUN
ejpam-5705	471	13	]	]	PUNCT
ejpam-5705	471	14	••	••	NOUN
ejpam-5705	471	15	.	.	PUNCT
ejpam-5705	472	1	thus	thus	ADV
ejpam-5705	472	2	µ1	µ1	PROPN
ejpam-5705	472	3	∨	∨	NOUN
ejpam-5705	472	4	℘	℘	NUM
ejpam-5705	472	5	=	=	SYM
ejpam-5705	472	6	1	1	NUM
ejpam-5705	472	7	,	,	PUNCT
ejpam-5705	472	8	we	we	PRON
ejpam-5705	472	9	get	get	VERB
ejpam-5705	472	10	℘	℘	NUM
ejpam-5705	472	11	∈	∈	PROPN
ejpam-5705	472	12	[	[	X
ejpam-5705	472	13	µ1	µ1	NOUN
ejpam-5705	472	14	]	]	PUNCT
ejpam-5705	472	15	•.	•.	NOUN
ejpam-5705	472	16	thus	thus	ADV
ejpam-5705	472	17	[	[	X
ejpam-5705	472	18	µ2	µ2	X
ejpam-5705	472	19	]	]	X
ejpam-5705	472	20	•	•	NUM
ejpam-5705	472	21	⊆	⊆	NUM
ejpam-5705	472	22	[	[	X
ejpam-5705	472	23	µ1	µ1	NOUN
ejpam-5705	472	24	]	]	PUNCT
ejpam-5705	472	25	•.	•.	NOUN
ejpam-5705	472	26	similarly	similarly	ADV
ejpam-5705	472	27	,	,	PUNCT
ejpam-5705	472	28	we	we	PRON
ejpam-5705	472	29	get	get	VERB
ejpam-5705	472	30	[	[	X
ejpam-5705	472	31	µ1	µ1	X
ejpam-5705	472	32	]	]	X
ejpam-5705	472	33	•	•	NUM
ejpam-5705	472	34	⊆	⊆	NUM
ejpam-5705	472	35	[	[	X
ejpam-5705	472	36	µ2	µ2	NOUN
ejpam-5705	472	37	]	]	PUNCT
ejpam-5705	472	38	•.	•.	NOUN
ejpam-5705	472	39	hence	hence	ADV
ejpam-5705	472	40	[	[	X
ejpam-5705	472	41	µ1	µ1	X
ejpam-5705	472	42	]	]	X
ejpam-5705	472	43	•	•	NOUN
ejpam-5705	472	44	=	=	PUNCT
ejpam-5705	473	1	[	[	X
ejpam-5705	473	2	µ2	µ2	X
ejpam-5705	473	3	]	]	X
ejpam-5705	473	4	•	•	NUM
ejpam-5705	473	5	which	which	PRON
ejpam-5705	473	6	implies	imply	VERB
ejpam-5705	473	7	(	(	PUNCT
ejpam-5705	473	8	µ1	µ1	ADJ
ejpam-5705	473	9	,	,	PUNCT
ejpam-5705	473	10	µ2	µ2	ADJ
ejpam-5705	473	11	)	)	PUNCT
ejpam-5705	473	12	∈	∈	PROPN
ejpam-5705	473	13	θ	θ	PROPN
ejpam-5705	473	14	.	.	PUNCT
ejpam-5705	473	15	therefore	therefore	ADV
ejpam-5705	473	16	θ	θ	PROPN
ejpam-5705	473	17	=	=	SYM
ejpam-5705	473	18	{	{	PUNCT
ejpam-5705	473	19	(	(	PUNCT
ejpam-5705	473	20	µ1	µ1	PROPN
ejpam-5705	473	21	,	,	PUNCT
ejpam-5705	473	22	µ2	µ2	ADJ
ejpam-5705	473	23	)	)	PUNCT
ejpam-5705	473	24	∈	∈	PROPN
ejpam-5705	473	25	v	v	ADP
ejpam-5705	473	26	×	×	NOUN
ejpam-5705	473	27	v	v	NOUN
ejpam-5705	473	28	|	|	NOUN
ejpam-5705	473	29	(	(	PUNCT
ejpam-5705	473	30	µ1	µ1	NOUN
ejpam-5705	473	31	:	:	PUNCT
ejpam-5705	473	32	d	d	X
ejpam-5705	473	33	)	)	PUNCT
ejpam-5705	473	34	=	=	SYM
ejpam-5705	473	35	(	(	PUNCT
ejpam-5705	473	36	µ2	µ2	NOUN
ejpam-5705	473	37	:	:	PUNCT
ejpam-5705	473	38	d	d	X
ejpam-5705	473	39	)	)	PUNCT
ejpam-5705	473	40	}	}	PUNCT
ejpam-5705	473	41	.	.	PUNCT
ejpam-5705	474	1	lemma	lemma	PROPN
ejpam-5705	474	2	16	16	NUM
ejpam-5705	474	3	.	.	PUNCT
ejpam-5705	475	1	let	let	VERB
ejpam-5705	475	2	v	v	PART
ejpam-5705	475	3	be	be	AUX
ejpam-5705	475	4	a	a	DET
ejpam-5705	475	5	pdl	pdl	NOUN
ejpam-5705	475	6	.	.	PUNCT
ejpam-5705	476	1	if	if	SCONJ
ejpam-5705	476	2	µ1	µ1	PROPN
ejpam-5705	476	3	∨	∨	NOUN
ejpam-5705	476	4	µ3	µ3	NOUN
ejpam-5705	476	5	=	=	SYM
ejpam-5705	476	6	1	1	NUM
ejpam-5705	476	7	=	=	SYM
ejpam-5705	476	8	µ2	µ2	PROPN
ejpam-5705	476	9	∨	∨	NUM
ejpam-5705	476	10	µ3	µ3	PROPN
ejpam-5705	476	11	and	and	CCONJ
ejpam-5705	476	12	µ1	µ1	PROPN
ejpam-5705	476	13	∧	∧	PROPN
ejpam-5705	476	14	µ2	µ2	PROPN
ejpam-5705	476	15	is	be	AUX
ejpam-5705	476	16	a	a	DET
ejpam-5705	476	17	dense	dense	ADJ
ejpam-5705	476	18	element	element	NOUN
ejpam-5705	476	19	.	.	PUNCT
ejpam-5705	477	1	then	then	ADV
ejpam-5705	477	2	µ3	µ3	NOUN
ejpam-5705	477	3	=	=	NOUN
ejpam-5705	477	4	1	1	X
ejpam-5705	477	5	.	.	PUNCT
ejpam-5705	478	1	proof	proof	NOUN
ejpam-5705	478	2	.	.	PUNCT
ejpam-5705	479	1	let	let	VERB
ejpam-5705	479	2	µ1∨µ3	µ1∨µ3	ADJ
ejpam-5705	479	3	=	=	SYM
ejpam-5705	479	4	1	1	NUM
ejpam-5705	479	5	=	=	SYM
ejpam-5705	479	6	µ2∨µ3	µ2∨µ3	PROPN
ejpam-5705	479	7	.	.	PUNCT
ejpam-5705	480	1	then	then	ADV
ejpam-5705	480	2	(	(	PUNCT
ejpam-5705	480	3	µ1∧µ2)∨µ3	µ1∧µ2)∨µ3	X
ejpam-5705	480	4	=	=	SYM
ejpam-5705	481	1	1	1	X
ejpam-5705	481	2	.	.	X
ejpam-5705	482	1	therefore	therefore	ADV
ejpam-5705	482	2	µ3	µ3	VERB
ejpam-5705	482	3	∈	∈	PROPN
ejpam-5705	482	4	[	[	X
ejpam-5705	482	5	µ1∧µ2	µ1∧µ2	NOUN
ejpam-5705	482	6	]	]	X
ejpam-5705	482	7	•	•	NOUN
ejpam-5705	482	8	=	=	SYM
ejpam-5705	482	9	{	{	PUNCT
ejpam-5705	482	10	1	1	NUM
ejpam-5705	482	11	}	}	PUNCT
ejpam-5705	482	12	and	and	CCONJ
ejpam-5705	482	13	hence	hence	ADV
ejpam-5705	482	14	µ3	µ3	VERB
ejpam-5705	482	15	=	=	SYM
ejpam-5705	482	16	1	1	X
ejpam-5705	482	17	.	.	PUNCT
ejpam-5705	483	1	lemma	lemma	PROPN
ejpam-5705	483	2	17	17	NUM
ejpam-5705	483	3	.	.	PUNCT
ejpam-5705	484	1	let	let	VERB
ejpam-5705	484	2	v	v	PART
ejpam-5705	484	3	be	be	AUX
ejpam-5705	484	4	a	a	DET
ejpam-5705	484	5	pdl	pdl	NOUN
ejpam-5705	484	6	.	.	PUNCT
ejpam-5705	485	1	if	if	SCONJ
ejpam-5705	485	2	[	[	X
ejpam-5705	485	3	µ1	µ1	NOUN
ejpam-5705	485	4	]	]	PUNCT
ejpam-5705	485	5	••	••	NOUN
ejpam-5705	485	6	=	=	SYM
ejpam-5705	486	1	[	[	X
ejpam-5705	486	2	µ3	µ3	X
ejpam-5705	486	3	]	]	X
ejpam-5705	486	4	•	•	NOUN
ejpam-5705	486	5	and	and	CCONJ
ejpam-5705	486	6	[	[	X
ejpam-5705	486	7	µ2	µ2	X
ejpam-5705	486	8	]	]	PUNCT
ejpam-5705	486	9	••	••	NOUN
ejpam-5705	486	10	=	=	X
ejpam-5705	487	1	[	[	X
ejpam-5705	487	2	µ4	µ4	X
ejpam-5705	487	3	]	]	X
ejpam-5705	487	4	•	•	NOUN
ejpam-5705	487	5	for	for	ADP
ejpam-5705	487	6	some	some	DET
ejpam-5705	487	7	µ1	µ1	PROPN
ejpam-5705	487	8	,	,	PUNCT
ejpam-5705	487	9	µ2	µ2	PROPN
ejpam-5705	487	10	,	,	PUNCT
ejpam-5705	487	11	µ3	µ3	NOUN
ejpam-5705	487	12	,	,	PUNCT
ejpam-5705	487	13	µ4	µ4	PROPN
ejpam-5705	487	14	∈	∈	PROPN
ejpam-5705	487	15	v	v	NOUN
ejpam-5705	487	16	,	,	PUNCT
ejpam-5705	487	17	then	then	ADV
ejpam-5705	487	18	µ1	µ1	PROPN
ejpam-5705	487	19	∨	∨	NOUN
ejpam-5705	487	20	µ2	µ2	PROPN
ejpam-5705	487	21	=	=	NOUN
ejpam-5705	487	22	1	1	NUM
ejpam-5705	487	23	if	if	SCONJ
ejpam-5705	487	24	and	and	CCONJ
ejpam-5705	487	25	only	only	ADV
ejpam-5705	487	26	if	if	SCONJ
ejpam-5705	487	27	µ3	µ3	PROPN
ejpam-5705	487	28	∧	∧	PROPN
ejpam-5705	487	29	µ4	µ4	PROPN
ejpam-5705	487	30	is	be	AUX
ejpam-5705	487	31	dense	dense	ADJ
ejpam-5705	487	32	element	element	NOUN
ejpam-5705	487	33	.	.	PUNCT
ejpam-5705	488	1	proof	proof	NOUN
ejpam-5705	488	2	.	.	PUNCT
ejpam-5705	489	1	assume	assume	VERB
ejpam-5705	489	2	[	[	X
ejpam-5705	489	3	µ1	µ1	X
ejpam-5705	489	4	]	]	PUNCT
ejpam-5705	489	5	••	••	NOUN
ejpam-5705	490	1	=	=	SYM
ejpam-5705	491	1	[	[	X
ejpam-5705	491	2	µ3	µ3	X
ejpam-5705	491	3	]	]	X
ejpam-5705	491	4	•	•	NOUN
ejpam-5705	491	5	and	and	CCONJ
ejpam-5705	491	6	[	[	X
ejpam-5705	491	7	µ2	µ2	X
ejpam-5705	491	8	]	]	PUNCT
ejpam-5705	491	9	••	••	NOUN
ejpam-5705	491	10	=	=	X
ejpam-5705	492	1	[	[	X
ejpam-5705	492	2	µ4	µ4	X
ejpam-5705	492	3	]	]	X
ejpam-5705	492	4	•	•	NOUN
ejpam-5705	492	5	for	for	ADP
ejpam-5705	492	6	some	some	DET
ejpam-5705	492	7	µ1	µ1	PROPN
ejpam-5705	492	8	,	,	PUNCT
ejpam-5705	492	9	µ2	µ2	PROPN
ejpam-5705	492	10	,	,	PUNCT
ejpam-5705	492	11	µ3	µ3	NOUN
ejpam-5705	492	12	,	,	PUNCT
ejpam-5705	492	13	µ4	µ4	PROPN
ejpam-5705	492	14	∈	∈	PROPN
ejpam-5705	492	15	v	v	NOUN
ejpam-5705	492	16	.	.	PUNCT
ejpam-5705	493	1	suppose	suppose	VERB
ejpam-5705	493	2	µ1	µ1	PROPN
ejpam-5705	493	3	∨	∨	PROPN
ejpam-5705	493	4	µ2	µ2	PROPN
ejpam-5705	493	5	=	=	PROPN
ejpam-5705	493	6	1	1	X
ejpam-5705	493	7	.	.	PUNCT
ejpam-5705	494	1	then	then	ADV
ejpam-5705	494	2	[	[	X
ejpam-5705	494	3	µ3	µ3	NOUN
ejpam-5705	494	4	∧	∧	PROPN
ejpam-5705	494	5	µ4	µ4	PROPN
ejpam-5705	494	6	]	]	PUNCT
ejpam-5705	494	7	•	•	NOUN
ejpam-5705	495	1	=	=	PUNCT
ejpam-5705	496	1	[	[	X
ejpam-5705	496	2	µ3	µ3	X
ejpam-5705	496	3	]	]	X
ejpam-5705	496	4	•	•	NOUN
ejpam-5705	496	5	∩	∩	NOUN
ejpam-5705	496	6	[	[	X
ejpam-5705	496	7	µ4	µ4	X
ejpam-5705	496	8	]	]	X
ejpam-5705	496	9	•	•	NOUN
ejpam-5705	496	10	=	=	PUNCT
ejpam-5705	497	1	[	[	X
ejpam-5705	497	2	µ1	µ1	X
ejpam-5705	497	3	]	]	PUNCT
ejpam-5705	497	4	••	••	NOUN
ejpam-5705	497	5	∩	∩	NOUN
ejpam-5705	497	6	[	[	X
ejpam-5705	497	7	µ2	µ2	NOUN
ejpam-5705	497	8	]	]	PUNCT
ejpam-5705	497	9	••	••	NOUN
ejpam-5705	497	10	=	=	SYM
ejpam-5705	498	1	[	[	X
ejpam-5705	498	2	µ1	µ1	PROPN
ejpam-5705	498	3	∨	∨	NUM
ejpam-5705	498	4	µ2	µ2	NOUN
ejpam-5705	498	5	]	]	PUNCT
ejpam-5705	498	6	••	••	NOUN
ejpam-5705	498	7	=	=	SYM
ejpam-5705	499	1	[	[	X
ejpam-5705	499	2	1]•	1]•	NUM
ejpam-5705	499	3	•	•	NOUN
ejpam-5705	499	4	=	=	SYM
ejpam-5705	499	5	{	{	PUNCT
ejpam-5705	499	6	1	1	NUM
ejpam-5705	499	7	}	}	PUNCT
ejpam-5705	499	8	therefore	therefore	ADV
ejpam-5705	499	9	µ3	µ3	PROPN
ejpam-5705	499	10	∧	∧	PROPN
ejpam-5705	499	11	µ4	µ4	PROPN
ejpam-5705	499	12	is	be	AUX
ejpam-5705	499	13	dense	dense	ADJ
ejpam-5705	499	14	element	element	NOUN
ejpam-5705	499	15	.	.	PUNCT
ejpam-5705	500	1	conversely	conversely	ADV
ejpam-5705	500	2	,	,	PUNCT
ejpam-5705	500	3	assume	assume	VERB
ejpam-5705	500	4	that	that	SCONJ
ejpam-5705	500	5	µ3	µ3	PROPN
ejpam-5705	500	6	∧	∧	PROPN
ejpam-5705	500	7	µ4	µ4	PROPN
ejpam-5705	500	8	is	be	AUX
ejpam-5705	500	9	a	a	DET
ejpam-5705	500	10	dense	dense	ADJ
ejpam-5705	500	11	element	element	NOUN
ejpam-5705	500	12	.	.	PUNCT
ejpam-5705	501	1	then	then	ADV
ejpam-5705	501	2	,	,	PUNCT
ejpam-5705	501	3	[	[	X
ejpam-5705	501	4	µ3∧µ4	µ3∧µ4	X
ejpam-5705	501	5	]	]	X
ejpam-5705	501	6	•	•	NOUN
ejpam-5705	501	7	=	=	SYM
ejpam-5705	501	8	{	{	PUNCT
ejpam-5705	501	9	1	1	NUM
ejpam-5705	501	10	}	}	PUNCT
ejpam-5705	501	11	.	.	PUNCT
ejpam-5705	502	1	clearly	clearly	ADV
ejpam-5705	502	2	µ1	µ1	PROPN
ejpam-5705	502	3	∈	∈	PROPN
ejpam-5705	502	4	[	[	X
ejpam-5705	502	5	µ3	µ3	X
ejpam-5705	502	6	]	]	PUNCT
ejpam-5705	502	7	•	•	NOUN
ejpam-5705	503	1	and	and	CCONJ
ejpam-5705	503	2	µ2	µ2	PROPN
ejpam-5705	503	3	∈	∈	PROPN
ejpam-5705	503	4	[	[	X
ejpam-5705	503	5	µ4	µ4	X
ejpam-5705	503	6	]	]	PUNCT
ejpam-5705	503	7	•.	•.	NOUN
ejpam-5705	503	8	then	then	ADV
ejpam-5705	503	9	µ1∨µ3	µ1∨µ3	PROPN
ejpam-5705	503	10	=	=	SYM
ejpam-5705	503	11	1	1	NUM
ejpam-5705	503	12	and	and	CCONJ
ejpam-5705	503	13	µ2∨µ4	µ2∨µ4	NOUN
ejpam-5705	503	14	=	=	SYM
ejpam-5705	503	15	1	1	X
ejpam-5705	503	16	.	.	PUNCT
ejpam-5705	504	1	therefore	therefore	ADV
ejpam-5705	504	2	µ1∨µ2∨µ3	µ1∨µ2∨µ3	ADP
ejpam-5705	504	3	=	=	PUNCT
ejpam-5705	504	4	µ1∨µ3∨µ2	µ1∨µ3∨µ2	PUNCT
ejpam-5705	504	5	=	=	SYM
ejpam-5705	504	6	1∨µ2	1∨µ2	PROPN
ejpam-5705	504	7	=	=	SYM
ejpam-5705	504	8	1	1	NUM
ejpam-5705	504	9	,	,	PUNCT
ejpam-5705	504	10	also	also	ADV
ejpam-5705	504	11	µ1∨µ2∨µ4	µ1∨µ2∨µ4	X
ejpam-5705	504	12	=	=	PUNCT
ejpam-5705	504	13	µ1∨1	µ1∨1	ADJ
ejpam-5705	504	14	=	=	SYM
ejpam-5705	504	15	1	1	X
ejpam-5705	504	16	.	.	PUNCT
ejpam-5705	504	17	therefore	therefore	ADV
ejpam-5705	504	18	(	(	PUNCT
ejpam-5705	504	19	µ1	µ1	PROPN
ejpam-5705	504	20	∨	∨	NUM
ejpam-5705	504	21	µ2	µ2	PROPN
ejpam-5705	504	22	)	)	PUNCT
ejpam-5705	504	23	∨	∨	NUM
ejpam-5705	504	24	µ3	µ3	NOUN
ejpam-5705	504	25	=	=	SYM
ejpam-5705	504	26	(	(	PUNCT
ejpam-5705	504	27	µ1	µ1	PROPN
ejpam-5705	504	28	∨	∨	NUM
ejpam-5705	504	29	µ2	µ2	PROPN
ejpam-5705	504	30	)	)	PUNCT
ejpam-5705	504	31	∨	∨	NUM
ejpam-5705	504	32	µ4	µ4	PROPN
ejpam-5705	504	33	.	.	PUNCT
ejpam-5705	505	1	hence	hence	ADV
ejpam-5705	505	2	µ3	µ3	PROPN
ejpam-5705	505	3	∨	∨	NUM
ejpam-5705	505	4	(	(	PUNCT
ejpam-5705	505	5	µ1	µ1	PROPN
ejpam-5705	505	6	∨	∨	PROPN
ejpam-5705	505	7	µ2	µ2	PROPN
ejpam-5705	505	8	)	)	PUNCT
ejpam-5705	505	9	=	=	SYM
ejpam-5705	505	10	µ4	µ4	PROPN
ejpam-5705	505	11	∨	∨	PROPN
ejpam-5705	505	12	(	(	PUNCT
ejpam-5705	505	13	µ1	µ1	PROPN
ejpam-5705	505	14	∨	∨	NUM
ejpam-5705	505	15	µ2	µ2	PROPN
ejpam-5705	505	16	)	)	PUNCT
ejpam-5705	505	17	=	=	SYM
ejpam-5705	505	18	1	1	NUM
ejpam-5705	505	19	which	which	PRON
ejpam-5705	505	20	implies	imply	VERB
ejpam-5705	505	21	that	that	SCONJ
ejpam-5705	505	22	µ1	µ1	PROPN
ejpam-5705	505	23	∨	∨	VERB
ejpam-5705	505	24	µ2	µ2	PROPN
ejpam-5705	505	25	∈	∈	PROPN
ejpam-5705	506	1	[	[	X
ejpam-5705	506	2	µ3	µ3	X
ejpam-5705	506	3	]	]	X
ejpam-5705	506	4	•	•	NOUN
ejpam-5705	506	5	∩	∩	NOUN
ejpam-5705	506	6	[	[	X
ejpam-5705	506	7	µ4	µ4	X
ejpam-5705	506	8	]	]	X
ejpam-5705	506	9	•	•	NOUN
ejpam-5705	506	10	=	=	PUNCT
ejpam-5705	507	1	[	[	X
ejpam-5705	507	2	µ3	µ3	NOUN
ejpam-5705	507	3	∧	∧	PROPN
ejpam-5705	507	4	µ4	µ4	PROPN
ejpam-5705	507	5	]	]	PUNCT
ejpam-5705	507	6	•	•	NOUN
ejpam-5705	507	7	=	=	SYM
ejpam-5705	507	8	{	{	PUNCT
ejpam-5705	507	9	1	1	NUM
ejpam-5705	507	10	}	}	PUNCT
ejpam-5705	507	11	.	.	PUNCT
ejpam-5705	508	1	therefore	therefore	ADV
ejpam-5705	508	2	µ1	µ1	PROPN
ejpam-5705	508	3	∨	∨	NOUN
ejpam-5705	508	4	µ2	µ2	PROPN
ejpam-5705	508	5	=	=	PROPN
ejpam-5705	508	6	1	1	X
ejpam-5705	508	7	.	.	PUNCT
ejpam-5705	508	8	r.	r.	PROPN
ejpam-5705	508	9	bandaru	bandaru	PROPN
ejpam-5705	508	10	et	et	PROPN
ejpam-5705	508	11	al	al	PROPN
ejpam-5705	508	12	.	.	PUNCT
ejpam-5705	508	13	/	/	SYM
ejpam-5705	508	14	eur	eur	PROPN
ejpam-5705	508	15	.	.	PUNCT
ejpam-5705	509	1	j.	j.	PROPN
ejpam-5705	509	2	pure	pure	PROPN
ejpam-5705	509	3	appl	appl	PROPN
ejpam-5705	509	4	.	.	PROPN
ejpam-5705	509	5	math	math	PROPN
ejpam-5705	509	6	,	,	PUNCT
ejpam-5705	509	7	18	18	NUM
ejpam-5705	509	8	(	(	PUNCT
ejpam-5705	509	9	2	2	NUM
ejpam-5705	509	10	)	)	PUNCT
ejpam-5705	509	11	(	(	PUNCT
ejpam-5705	509	12	2025	2025	NUM
ejpam-5705	509	13	)	)	PUNCT
ejpam-5705	509	14	,	,	PUNCT
ejpam-5705	509	15	5705	5705	NUM
ejpam-5705	509	16	12	12	NUM
ejpam-5705	509	17	of	of	ADP
ejpam-5705	509	18	13	13	NUM
ejpam-5705	509	19	theorem	theorem	NOUN
ejpam-5705	509	20	13	13	NUM
ejpam-5705	509	21	.	.	PUNCT
ejpam-5705	510	1	let	let	VERB
ejpam-5705	510	2	v	v	PART
ejpam-5705	510	3	be	be	AUX
ejpam-5705	510	4	a	a	DET
ejpam-5705	510	5	•-pdl	•-pdl	PUNCT
ejpam-5705	510	6	and	and	CCONJ
ejpam-5705	510	7	℘	℘	NOUN
ejpam-5705	510	8	,	,	PUNCT
ejpam-5705	510	9	ℏ	ℏ	PROPN
ejpam-5705	510	10	∈	∈	PROPN
ejpam-5705	510	11	v	v	NOUN
ejpam-5705	510	12	.	.	PUNCT
ejpam-5705	511	1	then	then	ADV
ejpam-5705	511	2	the	the	DET
ejpam-5705	511	3	following	follow	VERB
ejpam-5705	511	4	conditions	condition	NOUN
ejpam-5705	511	5	are	be	AUX
ejpam-5705	511	6	equivalent	equivalent	ADJ
ejpam-5705	511	7	:	:	PUNCT
ejpam-5705	511	8	(	(	PUNCT
ejpam-5705	511	9	1	1	NUM
ejpam-5705	511	10	)	)	PUNCT
ejpam-5705	511	11	.	.	PUNCT
ejpam-5705	512	1	[	[	X
ejpam-5705	512	2	℘]•	℘]•	PUNCT
ejpam-5705	512	3	=	=	PUNCT
ejpam-5705	512	4	[	[	X
ejpam-5705	512	5	ℏ]•.	ℏ]•.	X
ejpam-5705	512	6	(	(	PUNCT
ejpam-5705	512	7	2	2	NUM
ejpam-5705	512	8	)	)	PUNCT
ejpam-5705	512	9	.	.	PUNCT
ejpam-5705	513	1	for	for	ADP
ejpam-5705	513	2	any	any	DET
ejpam-5705	513	3	τ	τ	PROPN
ejpam-5705	513	4	∈	∈	PROPN
ejpam-5705	513	5	v	v	NOUN
ejpam-5705	513	6	,	,	PUNCT
ejpam-5705	513	7	℘	℘	PROPN
ejpam-5705	513	8	∧	∧	PROPN
ejpam-5705	513	9	τ	τ	X
ejpam-5705	513	10	is	be	AUX
ejpam-5705	513	11	dense	dense	ADJ
ejpam-5705	513	12	if	if	SCONJ
ejpam-5705	513	13	and	and	CCONJ
ejpam-5705	513	14	only	only	ADV
ejpam-5705	513	15	if	if	SCONJ
ejpam-5705	513	16	ℏ	ℏ	PROPN
ejpam-5705	513	17	∧	∧	PROPN
ejpam-5705	513	18	τ	τ	X
ejpam-5705	513	19	is	be	AUX
ejpam-5705	513	20	dense	dense	ADJ
ejpam-5705	513	21	.	.	PUNCT
ejpam-5705	514	1	proof	proof	NOUN
ejpam-5705	514	2	.	.	PUNCT
ejpam-5705	515	1	(	(	PUNCT
ejpam-5705	515	2	1	1	X
ejpam-5705	515	3	)	)	PUNCT
ejpam-5705	515	4	⇒	⇒	NOUN
ejpam-5705	515	5	(	(	PUNCT
ejpam-5705	515	6	2	2	X
ejpam-5705	515	7	)	)	PUNCT
ejpam-5705	515	8	is	be	AUX
ejpam-5705	515	9	clear	clear	ADJ
ejpam-5705	515	10	.	.	PUNCT
ejpam-5705	516	1	(	(	PUNCT
ejpam-5705	516	2	2	2	X
ejpam-5705	516	3	)	)	PUNCT
ejpam-5705	516	4	⇒	⇒	NOUN
ejpam-5705	516	5	(	(	PUNCT
ejpam-5705	516	6	1	1	NUM
ejpam-5705	516	7	):	):	PUNCT
ejpam-5705	516	8	assume	assume	VERB
ejpam-5705	516	9	(	(	PUNCT
ejpam-5705	516	10	2	2	NUM
ejpam-5705	516	11	)	)	PUNCT
ejpam-5705	516	12	.	.	PUNCT
ejpam-5705	517	1	let	let	VERB
ejpam-5705	517	2	µ1	µ1	PROPN
ejpam-5705	517	3	∈	∈	PROPN
ejpam-5705	517	4	[	[	X
ejpam-5705	517	5	℘]•.	℘]•.	ADJ
ejpam-5705	517	6	then	then	ADV
ejpam-5705	517	7	µ1	µ1	PROPN
ejpam-5705	517	8	∨	∨	NOUN
ejpam-5705	517	9	℘	℘	NOUN
ejpam-5705	517	10	=	=	SYM
ejpam-5705	517	11	1	1	X
ejpam-5705	517	12	.	.	PUNCT
ejpam-5705	518	1	now	now	ADV
ejpam-5705	518	2	,	,	PUNCT
ejpam-5705	518	3	for	for	ADP
ejpam-5705	518	4	µ1	µ1	PROPN
ejpam-5705	518	5	,	,	PUNCT
ejpam-5705	518	6	℘	℘	PROPN
ejpam-5705	518	7	,	,	PUNCT
ejpam-5705	518	8	ℏ	ℏ	PROPN
ejpam-5705	518	9	∈	∈	NOUN
ejpam-5705	518	10	v	v	ADP
ejpam-5705	518	11	there	there	PRON
ejpam-5705	518	12	exists	exist	VERB
ejpam-5705	518	13	µ3	µ3	NUM
ejpam-5705	518	14	,	,	PUNCT
ejpam-5705	518	15	u	u	NOUN
ejpam-5705	518	16	,	,	PUNCT
ejpam-5705	518	17	v	v	PROPN
ejpam-5705	518	18	∈	∈	NOUN
ejpam-5705	518	19	v	v	ADP
ejpam-5705	518	20	such	such	ADJ
ejpam-5705	518	21	that	that	SCONJ
ejpam-5705	518	22	[	[	X
ejpam-5705	518	23	µ1	µ1	NOUN
ejpam-5705	518	24	]	]	PUNCT
ejpam-5705	518	25	••	••	NOUN
ejpam-5705	519	1	=	=	SYM
ejpam-5705	519	2	[	[	X
ejpam-5705	519	3	µ3	µ3	X
ejpam-5705	519	4	]	]	X
ejpam-5705	519	5	•	•	NOUN
ejpam-5705	519	6	,	,	PUNCT
ejpam-5705	519	7	[	[	X
ejpam-5705	519	8	℘]•	℘]•	VERB
ejpam-5705	519	9	•	•	NOUN
ejpam-5705	519	10	=	=	PUNCT
ejpam-5705	520	1	[	[	X
ejpam-5705	520	2	u]•	u]•	X
ejpam-5705	520	3	,	,	PUNCT
ejpam-5705	520	4	[	[	X
ejpam-5705	520	5	ℏ]••	ℏ]••	X
ejpam-5705	520	6	=	=	PUNCT
ejpam-5705	520	7	[	[	X
ejpam-5705	520	8	v]•.	v]•.	NOUN
ejpam-5705	520	9	since	since	SCONJ
ejpam-5705	520	10	µ1	µ1	PROPN
ejpam-5705	520	11	∨	∨	NUM
ejpam-5705	520	12	℘	℘	NOUN
ejpam-5705	520	13	=	=	SYM
ejpam-5705	520	14	1	1	NUM
ejpam-5705	520	15	,	,	PUNCT
ejpam-5705	520	16	we	we	PRON
ejpam-5705	520	17	have	have	VERB
ejpam-5705	520	18	µ3	µ3	VERB
ejpam-5705	520	19	∧	∧	PROPN
ejpam-5705	520	20	u	u	NOUN
ejpam-5705	520	21	is	be	AUX
ejpam-5705	520	22	dense	dense	ADJ
ejpam-5705	520	23	element	element	NOUN
ejpam-5705	520	24	.	.	PUNCT
ejpam-5705	521	1	also	also	ADV
ejpam-5705	521	2	ℏ	ℏ	VERB
ejpam-5705	521	3	∨	∨	NUM
ejpam-5705	521	4	v	v	NOUN
ejpam-5705	521	5	=	=	SYM
ejpam-5705	521	6	1	1	NUM
ejpam-5705	522	1	and	and	CCONJ
ejpam-5705	522	2	[	[	X
ejpam-5705	522	3	ℏ	ℏ	X
ejpam-5705	522	4	∧	∧	PROPN
ejpam-5705	522	5	v]•	v]•	PROPN
ejpam-5705	522	6	=	=	PUNCT
ejpam-5705	523	1	[	[	X
ejpam-5705	523	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	523	3	∩	∩	ADJ
ejpam-5705	523	4	[	[	X
ejpam-5705	523	5	ℏ]••	ℏ]••	X
ejpam-5705	523	6	=	=	SYM
ejpam-5705	523	7	{	{	PUNCT
ejpam-5705	523	8	1	1	NUM
ejpam-5705	523	9	}	}	PUNCT
ejpam-5705	523	10	.	.	PUNCT
ejpam-5705	524	1	hence	hence	ADV
ejpam-5705	524	2	ℏ	ℏ	PROPN
ejpam-5705	524	3	∧	∧	PROPN
ejpam-5705	524	4	v	v	NOUN
ejpam-5705	524	5	is	be	AUX
ejpam-5705	524	6	dense	dense	ADJ
ejpam-5705	524	7	element	element	NOUN
ejpam-5705	524	8	.	.	PUNCT
ejpam-5705	525	1	but	but	CCONJ
ejpam-5705	525	2	,	,	PUNCT
ejpam-5705	525	3	by	by	ADP
ejpam-5705	525	4	the	the	DET
ejpam-5705	525	5	assumption	assumption	NOUN
ejpam-5705	525	6	,	,	PUNCT
ejpam-5705	525	7	℘	℘	PROPN
ejpam-5705	525	8	∧	∧	PROPN
ejpam-5705	525	9	v	v	NOUN
ejpam-5705	525	10	is	be	AUX
ejpam-5705	525	11	dense	dense	ADJ
ejpam-5705	525	12	,	,	PUNCT
ejpam-5705	525	13	so	so	CCONJ
ejpam-5705	525	14	it	it	PRON
ejpam-5705	525	15	is	be	AUX
ejpam-5705	525	16	left	leave	VERB
ejpam-5705	525	17	to	to	PART
ejpam-5705	525	18	prove	prove	VERB
ejpam-5705	525	19	that	that	SCONJ
ejpam-5705	525	20	µ3	µ3	NOUN
ejpam-5705	525	21	∧	∧	PROPN
ejpam-5705	525	22	v	v	NOUN
ejpam-5705	525	23	is	be	AUX
ejpam-5705	525	24	a	a	DET
ejpam-5705	525	25	dense	dense	ADJ
ejpam-5705	525	26	element	element	NOUN
ejpam-5705	525	27	.	.	PUNCT
ejpam-5705	526	1	let	let	VERB
ejpam-5705	526	2	µ2	µ2	PROPN
ejpam-5705	526	3	∈	∈	PROPN
ejpam-5705	527	1	[	[	X
ejpam-5705	527	2	µ3	µ3	NOUN
ejpam-5705	527	3	∧	∧	PROPN
ejpam-5705	527	4	v]•	v]•	PROPN
ejpam-5705	527	5	=	=	PUNCT
ejpam-5705	528	1	[	[	X
ejpam-5705	528	2	µ3	µ3	X
ejpam-5705	528	3	]	]	X
ejpam-5705	528	4	•	•	NOUN
ejpam-5705	528	5	∩	∩	NOUN
ejpam-5705	528	6	[	[	X
ejpam-5705	528	7	v]•	v]•	PROPN
ejpam-5705	528	8	.	.	PUNCT
ejpam-5705	529	1	then	then	ADV
ejpam-5705	529	2	µ2	µ2	PROPN
ejpam-5705	529	3	∨	∨	NOUN
ejpam-5705	529	4	v	v	NOUN
ejpam-5705	529	5	=	=	SYM
ejpam-5705	529	6	1	1	NUM
ejpam-5705	529	7	.	.	PUNCT
ejpam-5705	529	8	now	now	ADV
ejpam-5705	529	9	,	,	PUNCT
ejpam-5705	529	10	℘	℘	PROPN
ejpam-5705	529	11	∨	∨	NUM
ejpam-5705	529	12	µ2	µ2	PROPN
ejpam-5705	529	13	∨	∨	NUM
ejpam-5705	529	14	u	u	NOUN
ejpam-5705	529	15	=	=	SYM
ejpam-5705	529	16	1	1	NUM
ejpam-5705	529	17	=	=	SYM
ejpam-5705	529	18	v	v	NUM
ejpam-5705	529	19	∨	∨	NUM
ejpam-5705	529	20	µ2	µ2	PROPN
ejpam-5705	529	21	∨	∨	NUM
ejpam-5705	529	22	u	u	NOUN
ejpam-5705	529	23	and	and	CCONJ
ejpam-5705	529	24	℘	℘	PROPN
ejpam-5705	529	25	∧	∧	PROPN
ejpam-5705	529	26	v	v	NOUN
ejpam-5705	529	27	is	be	AUX
ejpam-5705	529	28	dense	dense	ADJ
ejpam-5705	529	29	element	element	NOUN
ejpam-5705	529	30	implies	imply	VERB
ejpam-5705	529	31	that	that	SCONJ
ejpam-5705	529	32	µ2	µ2	PROPN
ejpam-5705	529	33	∨	∨	NUM
ejpam-5705	529	34	u	u	NOUN
ejpam-5705	529	35	=	=	NOUN
ejpam-5705	529	36	1	1	NUM
ejpam-5705	529	37	.	.	PUNCT
ejpam-5705	530	1	now	now	ADV
ejpam-5705	530	2	,	,	PUNCT
ejpam-5705	530	3	µ2	µ2	PROPN
ejpam-5705	530	4	∨	∨	NUM
ejpam-5705	530	5	u	u	NOUN
ejpam-5705	530	6	=	=	SYM
ejpam-5705	530	7	1	1	NUM
ejpam-5705	530	8	=	=	SYM
ejpam-5705	530	9	µ2	µ2	PROPN
ejpam-5705	530	10	∨	∨	NUM
ejpam-5705	530	11	µ3	µ3	PROPN
ejpam-5705	530	12	and	and	CCONJ
ejpam-5705	530	13	µ3	µ3	VERB
ejpam-5705	530	14	∧	∧	PROPN
ejpam-5705	530	15	u	u	NOUN
ejpam-5705	530	16	is	be	AUX
ejpam-5705	530	17	dense	dense	ADJ
ejpam-5705	530	18	element	element	NOUN
ejpam-5705	530	19	implies	imply	VERB
ejpam-5705	530	20	that	that	SCONJ
ejpam-5705	530	21	µ2	µ2	PROPN
ejpam-5705	530	22	=	=	NOUN
ejpam-5705	530	23	1	1	X
ejpam-5705	530	24	.	.	PUNCT
ejpam-5705	531	1	therefore	therefore	ADV
ejpam-5705	531	2	µ3	µ3	PROPN
ejpam-5705	531	3	∧	∧	PROPN
ejpam-5705	531	4	v	v	NOUN
ejpam-5705	531	5	is	be	AUX
ejpam-5705	531	6	dense	dense	ADJ
ejpam-5705	531	7	element	element	NOUN
ejpam-5705	531	8	.	.	PUNCT
ejpam-5705	532	1	again	again	ADV
ejpam-5705	532	2	[	[	X
ejpam-5705	532	3	µ1	µ1	X
ejpam-5705	532	4	]	]	PUNCT
ejpam-5705	532	5	••	••	NOUN
ejpam-5705	533	1	=	=	SYM
ejpam-5705	533	2	[	[	X
ejpam-5705	533	3	µ3	µ3	X
ejpam-5705	533	4	]	]	X
ejpam-5705	533	5	•	•	NOUN
ejpam-5705	533	6	and	and	CCONJ
ejpam-5705	533	7	[	[	X
ejpam-5705	533	8	ℏ]••	ℏ]••	X
ejpam-5705	534	1	=	=	PUNCT
ejpam-5705	534	2	[	[	X
ejpam-5705	534	3	v]•	v]•	PROPN
ejpam-5705	534	4	and	and	CCONJ
ejpam-5705	534	5	µ3	µ3	PROPN
ejpam-5705	534	6	∧	∧	PROPN
ejpam-5705	534	7	v	v	NOUN
ejpam-5705	534	8	is	be	AUX
ejpam-5705	534	9	dense	dense	ADJ
ejpam-5705	534	10	element	element	NOUN
ejpam-5705	534	11	implies	imply	VERB
ejpam-5705	535	1	that	that	SCONJ
ejpam-5705	535	2	µ1	µ1	PROPN
ejpam-5705	535	3	∨	∨	NOUN
ejpam-5705	535	4	ℏ	ℏ	NOUN
ejpam-5705	535	5	=	=	SYM
ejpam-5705	535	6	1	1	X
ejpam-5705	535	7	.	.	X
ejpam-5705	535	8	therefore	therefore	ADV
ejpam-5705	535	9	µ1	µ1	PROPN
ejpam-5705	535	10	∈	∈	PROPN
ejpam-5705	536	1	[	[	X
ejpam-5705	536	2	ℏ]••	ℏ]••	X
ejpam-5705	536	3	.	.	PUNCT
ejpam-5705	537	1	hence	hence	ADV
ejpam-5705	537	2	[	[	X
ejpam-5705	537	3	℘]•	℘]•	PROPN
ejpam-5705	537	4	⊆	⊆	NUM
ejpam-5705	537	5	[	[	X
ejpam-5705	537	6	ℏ]•.	ℏ]•.	PRON
ejpam-5705	537	7	similarly	similarly	ADV
ejpam-5705	537	8	,	,	PUNCT
ejpam-5705	537	9	it	it	PRON
ejpam-5705	537	10	can	can	AUX
ejpam-5705	537	11	be	be	AUX
ejpam-5705	537	12	proved	prove	VERB
ejpam-5705	537	13	that	that	SCONJ
ejpam-5705	537	14	[	[	X
ejpam-5705	537	15	ℏ]•	ℏ]•	NOUN
ejpam-5705	537	16	⊆	⊆	NUM
ejpam-5705	537	17	[	[	X
ejpam-5705	537	18	℘]•.	℘]•.	ADJ
ejpam-5705	537	19	thus	thus	ADV
ejpam-5705	537	20	[	[	X
ejpam-5705	537	21	℘]•	℘]•	PROPN
ejpam-5705	537	22	=	=	PUNCT
ejpam-5705	537	23	[	[	X
ejpam-5705	537	24	ℏ]•.	ℏ]•.	NUM
ejpam-5705	537	25	definition	definition	NOUN
ejpam-5705	537	26	10	10	NUM
ejpam-5705	537	27	.	.	PUNCT
ejpam-5705	538	1	a	a	DET
ejpam-5705	538	2	pdl	pdl	PROPN
ejpam-5705	538	3	(	(	PUNCT
ejpam-5705	538	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	538	5	,	,	PUNCT
ejpam-5705	538	6	1	1	NUM
ejpam-5705	538	7	)	)	PUNCT
ejpam-5705	538	8	is	be	AUX
ejpam-5705	538	9	called	call	VERB
ejpam-5705	538	10	a	a	DET
ejpam-5705	538	11	disjunctive	disjunctive	ADJ
ejpam-5705	538	12	pdl	pdl	NOUN
ejpam-5705	538	13	,	,	PUNCT
ejpam-5705	538	14	if	if	SCONJ
ejpam-5705	538	15	for	for	ADP
ejpam-5705	538	16	each	each	DET
ejpam-5705	538	17	℘	℘	NOUN
ejpam-5705	538	18	,	,	PUNCT
ejpam-5705	538	19	ℏ	ℏ	PROPN
ejpam-5705	538	20	∈	∈	NOUN
ejpam-5705	538	21	v	v	NOUN
ejpam-5705	538	22	,	,	PUNCT
ejpam-5705	538	23	[	[	X
ejpam-5705	538	24	℘]•	℘]•	PROPN
ejpam-5705	538	25	=	=	PUNCT
ejpam-5705	539	1	[	[	X
ejpam-5705	539	2	ℏ]•	ℏ]•	NOUN
ejpam-5705	539	3	⇒	⇒	VERB
ejpam-5705	539	4	℘	℘	PROPN
ejpam-5705	539	5	=	=	SYM
ejpam-5705	539	6	ℏ.	ℏ.	NOUN
ejpam-5705	539	7	theorem	theorem	NOUN
ejpam-5705	539	8	14	14	NUM
ejpam-5705	539	9	.	.	PUNCT
ejpam-5705	540	1	let	let	AUX
ejpam-5705	540	2	(	(	PUNCT
ejpam-5705	540	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	540	4	)	)	PUNCT
ejpam-5705	540	5	be	be	AUX
ejpam-5705	540	6	a	a	DET
ejpam-5705	540	7	•-pdl	•-pdl	NOUN
ejpam-5705	540	8	.	.	PUNCT
ejpam-5705	541	1	then	then	ADV
ejpam-5705	541	2	the	the	DET
ejpam-5705	541	3	following	follow	VERB
ejpam-5705	541	4	conditions	condition	NOUN
ejpam-5705	541	5	are	be	AUX
ejpam-5705	541	6	equivalent	equivalent	ADJ
ejpam-5705	541	7	:	:	PUNCT
ejpam-5705	541	8	(	(	PUNCT
ejpam-5705	541	9	1	1	NUM
ejpam-5705	541	10	)	)	PUNCT
ejpam-5705	541	11	.	.	PUNCT
ejpam-5705	542	1	(	(	PUNCT
ejpam-5705	542	2	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	542	3	,	,	PUNCT
ejpam-5705	542	4	1	1	NUM
ejpam-5705	542	5	)	)	PUNCT
ejpam-5705	542	6	is	be	AUX
ejpam-5705	542	7	a	a	DET
ejpam-5705	542	8	boolean	boolean	ADJ
ejpam-5705	542	9	algebra	algebra	NOUN
ejpam-5705	542	10	.	.	PUNCT
ejpam-5705	543	1	(	(	PUNCT
ejpam-5705	543	2	2	2	NUM
ejpam-5705	543	3	)	)	PUNCT
ejpam-5705	543	4	.	.	PUNCT
ejpam-5705	544	1	v	v	NOUN
ejpam-5705	544	2	is	be	AUX
ejpam-5705	544	3	a	a	DET
ejpam-5705	544	4	disjunctive	disjunctive	ADJ
ejpam-5705	544	5	pdl	pdl	NOUN
ejpam-5705	544	6	.	.	PUNCT
ejpam-5705	545	1	(	(	PUNCT
ejpam-5705	545	2	3	3	NUM
ejpam-5705	545	3	)	)	PUNCT
ejpam-5705	545	4	.	.	PUNCT
ejpam-5705	546	1	v	v	NOUN
ejpam-5705	546	2	has	have	VERB
ejpam-5705	546	3	exactly	exactly	ADV
ejpam-5705	546	4	one	one	NUM
ejpam-5705	546	5	dense	dense	ADJ
ejpam-5705	546	6	element	element	NOUN
ejpam-5705	546	7	.	.	PUNCT
ejpam-5705	547	1	proof	proof	NOUN
ejpam-5705	547	2	.	.	PUNCT
ejpam-5705	548	1	(	(	PUNCT
ejpam-5705	548	2	1	1	X
ejpam-5705	548	3	)	)	PUNCT
ejpam-5705	548	4	⇒	⇒	NOUN
ejpam-5705	548	5	(	(	PUNCT
ejpam-5705	548	6	2	2	NUM
ejpam-5705	548	7	)	)	PUNCT
ejpam-5705	548	8	.	.	PUNCT
ejpam-5705	549	1	assume	assume	VERB
ejpam-5705	549	2	(	(	PUNCT
ejpam-5705	549	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	549	4	,	,	PUNCT
ejpam-5705	549	5	1	1	NUM
ejpam-5705	549	6	)	)	PUNCT
ejpam-5705	549	7	is	be	AUX
ejpam-5705	549	8	a	a	DET
ejpam-5705	549	9	boolean	boolean	ADJ
ejpam-5705	549	10	algebra	algebra	NOUN
ejpam-5705	549	11	.	.	PUNCT
ejpam-5705	550	1	let	let	VERB
ejpam-5705	550	2	℘	℘	NOUN
ejpam-5705	550	3	,	,	PUNCT
ejpam-5705	550	4	ℏ	ℏ	PROPN
ejpam-5705	550	5	∈	∈	PROPN
ejpam-5705	550	6	v	v	NOUN
ejpam-5705	550	7	and	and	CCONJ
ejpam-5705	550	8	[	[	X
ejpam-5705	550	9	℘]•	℘]•	PROPN
ejpam-5705	550	10	=	=	PUNCT
ejpam-5705	551	1	[	[	X
ejpam-5705	551	2	ℏ]•.	ℏ]•.	X
ejpam-5705	551	3	then	then	ADV
ejpam-5705	551	4	there	there	PRON
ejpam-5705	551	5	exists	exist	VERB
ejpam-5705	551	6	℘	℘	NUM
ejpam-5705	551	7	′	′	NUM
ejpam-5705	551	8	∈	∈	NOUN
ejpam-5705	551	9	v	v	ADP
ejpam-5705	551	10	such	such	ADJ
ejpam-5705	551	11	that	that	DET
ejpam-5705	551	12	℘	℘	PROPN
ejpam-5705	551	13	′	′	NUM
ejpam-5705	551	14	∨	∨	NUM
ejpam-5705	551	15	℘	℘	X
ejpam-5705	551	16	=	=	SYM
ejpam-5705	551	17	1	1	NUM
ejpam-5705	551	18	and	and	CCONJ
ejpam-5705	551	19	hence	hence	ADV
ejpam-5705	551	20	℘	℘	VERB
ejpam-5705	551	21	′	′	NUM
ejpam-5705	551	22	∈	∈	PROPN
ejpam-5705	552	1	[	[	X
ejpam-5705	552	2	℘]•	℘]•	PUNCT
ejpam-5705	552	3	=	=	PUNCT
ejpam-5705	553	1	[	[	X
ejpam-5705	553	2	ℏ]•.	ℏ]•.	X
ejpam-5705	553	3	therefore	therefore	ADV
ejpam-5705	553	4	℘	℘	PROPN
ejpam-5705	553	5	′	′	NOUN
ejpam-5705	553	6	∨	∨	NUM
ejpam-5705	553	7	ℏ	ℏ	X
ejpam-5705	553	8	=	=	SYM
ejpam-5705	553	9	1	1	X
ejpam-5705	553	10	.	.	PUNCT
ejpam-5705	553	11	hence	hence	ADV
ejpam-5705	553	12	℘	℘	VERB
ejpam-5705	553	13	≤	≤	NUM
ejpam-5705	553	14	ℏ.	ℏ.	NOUN
ejpam-5705	553	15	by	by	ADP
ejpam-5705	553	16	symmetry	symmetry	NOUN
ejpam-5705	553	17	,	,	PUNCT
ejpam-5705	553	18	ℏ	ℏ	PROPN
ejpam-5705	553	19	≤	≤	PUNCT
ejpam-5705	553	20	℘.	℘.	PROPN
ejpam-5705	553	21	hence	hence	ADV
ejpam-5705	553	22	℘	℘	NUM
ejpam-5705	553	23	=	=	SYM
ejpam-5705	553	24	ℏ.	ℏ.	NOUN
ejpam-5705	553	25	therefore	therefore	ADV
ejpam-5705	553	26	v	v	NOUN
ejpam-5705	553	27	is	be	AUX
ejpam-5705	553	28	a	a	DET
ejpam-5705	553	29	disjunctive	disjunctive	ADJ
ejpam-5705	553	30	pdl	pdl	NOUN
ejpam-5705	553	31	.	.	PUNCT
ejpam-5705	554	1	(	(	PUNCT
ejpam-5705	554	2	2	2	X
ejpam-5705	554	3	)	)	PUNCT
ejpam-5705	554	4	⇒	⇒	NOUN
ejpam-5705	554	5	(	(	PUNCT
ejpam-5705	554	6	3	3	NUM
ejpam-5705	554	7	)	)	PUNCT
ejpam-5705	554	8	.	.	PUNCT
ejpam-5705	555	1	assume	assume	VERB
ejpam-5705	555	2	v	v	PRON
ejpam-5705	555	3	is	be	AUX
ejpam-5705	555	4	a	a	DET
ejpam-5705	555	5	disjunctive	disjunctive	ADJ
ejpam-5705	555	6	pdl	pdl	NOUN
ejpam-5705	555	7	.	.	PUNCT
ejpam-5705	556	1	since	since	SCONJ
ejpam-5705	556	2	v	v	NOUN
ejpam-5705	556	3	is	be	AUX
ejpam-5705	556	4	•-pdl	•-pdl	ADJ
ejpam-5705	556	5	,	,	PUNCT
ejpam-5705	556	6	v	v	X
ejpam-5705	556	7	has	have	VERB
ejpam-5705	556	8	a	a	DET
ejpam-5705	556	9	dense	dense	ADJ
ejpam-5705	556	10	element	element	NOUN
ejpam-5705	556	11	.	.	PUNCT
ejpam-5705	557	1	suppose	suppose	VERB
ejpam-5705	557	2	v	v	NOUN
ejpam-5705	557	3	has	have	VERB
ejpam-5705	557	4	two	two	NUM
ejpam-5705	557	5	dense	dense	ADJ
ejpam-5705	557	6	elements	element	NOUN
ejpam-5705	557	7	say	say	VERB
ejpam-5705	557	8	℘	℘	PROPN
ejpam-5705	557	9	and	and	CCONJ
ejpam-5705	557	10	ℏ.	ℏ.	VERB
ejpam-5705	557	11	then	then	ADV
ejpam-5705	558	1	[	[	X
ejpam-5705	558	2	℘]•	℘]•	PUNCT
ejpam-5705	558	3	=	=	SYM
ejpam-5705	558	4	{	{	PUNCT
ejpam-5705	558	5	1	1	NUM
ejpam-5705	558	6	}	}	PUNCT
ejpam-5705	558	7	=	=	NOUN
ejpam-5705	559	1	[	[	X
ejpam-5705	559	2	ℏ]•.	ℏ]•.	X
ejpam-5705	559	3	hence	hence	ADV
ejpam-5705	559	4	℘	℘	PROPN
ejpam-5705	559	5	=	=	SYM
ejpam-5705	559	6	ℏ.	ℏ.	NOUN
ejpam-5705	559	7	(	(	PUNCT
ejpam-5705	559	8	3	3	NUM
ejpam-5705	559	9	)	)	PUNCT
ejpam-5705	559	10	⇒	⇒	NOUN
ejpam-5705	559	11	(	(	PUNCT
ejpam-5705	559	12	1	1	NUM
ejpam-5705	559	13	)	)	PUNCT
ejpam-5705	559	14	.	.	PUNCT
ejpam-5705	560	1	assume	assume	VERB
ejpam-5705	560	2	v	v	PRON
ejpam-5705	560	3	has	have	VERB
ejpam-5705	560	4	exactly	exactly	ADV
ejpam-5705	560	5	one	one	NUM
ejpam-5705	560	6	dense	dense	ADJ
ejpam-5705	560	7	element	element	NOUN
ejpam-5705	560	8	.	.	PUNCT
ejpam-5705	561	1	since	since	SCONJ
ejpam-5705	561	2	v	v	NOUN
ejpam-5705	561	3	is	be	AUX
ejpam-5705	561	4	a	a	DET
ejpam-5705	561	5	•-pdl	•-pdl	PUNCT
ejpam-5705	561	6	,	,	PUNCT
ejpam-5705	561	7	choose	choose	VERB
ejpam-5705	561	8	1	1	NUM
ejpam-5705	561	9	′	′	NUM
ejpam-5705	561	10	∈	∈	NOUN
ejpam-5705	561	11	v	v	ADP
ejpam-5705	561	12	such	such	ADJ
ejpam-5705	561	13	that	that	SCONJ
ejpam-5705	561	14	[	[	X
ejpam-5705	561	15	1]•	1]•	NUM
ejpam-5705	561	16	•	•	NOUN
ejpam-5705	561	17	=	=	PUNCT
ejpam-5705	562	1	[	[	X
ejpam-5705	562	2	1	1	NUM
ejpam-5705	562	3	′	′	NUM
ejpam-5705	562	4	]	]	PUNCT
ejpam-5705	562	5	•.	•.	NOUN
ejpam-5705	562	6	that	that	PRON
ejpam-5705	562	7	is	be	AUX
ejpam-5705	562	8	[	[	X
ejpam-5705	562	9	1	1	NUM
ejpam-5705	562	10	′	′	NUM
ejpam-5705	562	11	]	]	PUNCT
ejpam-5705	562	12	•	•	NOUN
ejpam-5705	562	13	=	=	SYM
ejpam-5705	562	14	{	{	PUNCT
ejpam-5705	562	15	1	1	NUM
ejpam-5705	562	16	}	}	PUNCT
ejpam-5705	562	17	.	.	PUNCT
ejpam-5705	563	1	hence	hence	ADV
ejpam-5705	563	2	,	,	PUNCT
ejpam-5705	563	3	by	by	ADP
ejpam-5705	563	4	(	(	PUNCT
ejpam-5705	563	5	3	3	NUM
ejpam-5705	563	6	)	)	PUNCT
ejpam-5705	563	7	,	,	PUNCT
ejpam-5705	563	8	1	1	NUM
ejpam-5705	563	9	′	′	NOUN
ejpam-5705	563	10	is	be	AUX
ejpam-5705	563	11	the	the	DET
ejpam-5705	563	12	only	only	ADJ
ejpam-5705	563	13	dense	dense	ADJ
ejpam-5705	563	14	element	element	NOUN
ejpam-5705	563	15	in	in	ADP
ejpam-5705	563	16	v	v	NOUN
ejpam-5705	563	17	.	.	PUNCT
ejpam-5705	564	1	let	let	VERB
ejpam-5705	564	2	℘	℘	PROPN
ejpam-5705	564	3	∈	∈	NOUN
ejpam-5705	564	4	v	v	NOUN
ejpam-5705	564	5	.	.	PUNCT
ejpam-5705	565	1	then	then	ADV
ejpam-5705	565	2	there	there	PRON
ejpam-5705	565	3	exists	exist	VERB
ejpam-5705	565	4	℘	℘	NUM
ejpam-5705	565	5	′	′	VERB
ejpam-5705	565	6	in	in	ADP
ejpam-5705	565	7	v	v	NUM
ejpam-5705	565	8	such	such	ADJ
ejpam-5705	565	9	that	that	SCONJ
ejpam-5705	566	1	[	[	X
ejpam-5705	566	2	℘]•	℘]•	PROPN
ejpam-5705	566	3	•	•	NOUN
ejpam-5705	566	4	=	=	PUNCT
ejpam-5705	567	1	[	[	PUNCT
ejpam-5705	567	2	℘	℘	NUM
ejpam-5705	567	3	′	′	NOUN
ejpam-5705	567	4	]	]	PUNCT
ejpam-5705	567	5	•.	•.	NOUN
ejpam-5705	567	6	hence	hence	ADV
ejpam-5705	567	7	℘	℘	VERB
ejpam-5705	567	8	∨	∨	NUM
ejpam-5705	567	9	℘	℘	PROPN
ejpam-5705	567	10	′	′	NUM
ejpam-5705	567	11	=	=	SYM
ejpam-5705	567	12	1	1	NUM
ejpam-5705	567	13	and	and	CCONJ
ejpam-5705	567	14	℘	℘	VERB
ejpam-5705	567	15	∧	∧	NOUN
ejpam-5705	567	16	℘	℘	PROPN
ejpam-5705	567	17	′	′	NUM
ejpam-5705	567	18	is	be	AUX
ejpam-5705	567	19	dense	dense	ADJ
ejpam-5705	567	20	element	element	NOUN
ejpam-5705	567	21	by	by	ADP
ejpam-5705	567	22	lemma	lemma	PROPN
ejpam-5705	567	23	10	10	NUM
ejpam-5705	567	24	.	.	PUNCT
ejpam-5705	568	1	therefore	therefore	ADV
ejpam-5705	568	2	℘	℘	VERB
ejpam-5705	568	3	∧	∧	NOUN
ejpam-5705	568	4	℘	℘	NOUN
ejpam-5705	568	5	′	′	NUM
ejpam-5705	569	1	=	=	SYM
ejpam-5705	569	2	1	1	NUM
ejpam-5705	569	3	′	′	NUM
ejpam-5705	569	4	which	which	PRON
ejpam-5705	569	5	is	be	AUX
ejpam-5705	569	6	true	true	ADJ
ejpam-5705	569	7	for	for	ADP
ejpam-5705	569	8	all	all	DET
ejpam-5705	569	9	℘	℘	PROPN
ejpam-5705	569	10	∈	∈	PROPN
ejpam-5705	569	11	v	v	NOUN
ejpam-5705	570	1	and	and	CCONJ
ejpam-5705	570	2	we	we	PRON
ejpam-5705	570	3	have	have	VERB
ejpam-5705	570	4	℘	℘	NUM
ejpam-5705	570	5	′	′	NUM
ejpam-5705	570	6	∧	∧	NOUN
ejpam-5705	570	7	℘	℘	NOUN
ejpam-5705	570	8	=	=	SYM
ejpam-5705	570	9	1	1	NUM
ejpam-5705	570	10	′	′	NUM
ejpam-5705	570	11	≤	≤	NUM
ejpam-5705	570	12	℘	℘	PROPN
ejpam-5705	570	13	.	.	PUNCT
ejpam-5705	571	1	therefore	therefore	ADV
ejpam-5705	571	2	v	v	NOUN
ejpam-5705	571	3	is	be	AUX
ejpam-5705	571	4	a	a	DET
ejpam-5705	571	5	bounded	bounded	ADJ
ejpam-5705	571	6	distributive	distributive	ADJ
ejpam-5705	571	7	lattice	lattice	NOUN
ejpam-5705	571	8	in	in	ADP
ejpam-5705	571	9	which	which	PRON
ejpam-5705	571	10	every	every	DET
ejpam-5705	571	11	element	element	NOUN
ejpam-5705	571	12	has	have	VERB
ejpam-5705	571	13	a	a	DET
ejpam-5705	571	14	complement	complement	NOUN
ejpam-5705	571	15	.	.	PUNCT
ejpam-5705	572	1	thus	thus	ADV
ejpam-5705	572	2	(	(	PUNCT
ejpam-5705	572	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5705	572	4	,	,	PUNCT
ejpam-5705	572	5	1′	1′	NUM
ejpam-5705	572	6	,	,	PUNCT
ejpam-5705	572	7	1	1	NUM
ejpam-5705	572	8	)	)	PUNCT
ejpam-5705	572	9	is	be	AUX
ejpam-5705	572	10	a	a	DET
ejpam-5705	572	11	boolean	boolean	ADJ
ejpam-5705	572	12	algebra	algebra	NOUN
ejpam-5705	572	13	.	.	PUNCT
ejpam-5705	573	1	5	5	NUM
ejpam-5705	573	2	.	.	X
ejpam-5705	573	3	conclusions	conclusion	NOUN
ejpam-5705	573	4	in	in	ADP
ejpam-5705	573	5	conclusions	conclusion	NOUN
ejpam-5705	573	6	,	,	PUNCT
ejpam-5705	573	7	this	this	DET
ejpam-5705	573	8	paper	paper	NOUN
ejpam-5705	573	9	presents	present	VERB
ejpam-5705	573	10	the	the	DET
ejpam-5705	573	11	concept	concept	NOUN
ejpam-5705	573	12	of	of	ADP
ejpam-5705	573	13	•pdl	•pdl	NOUN
ejpam-5705	573	14	,	,	PUNCT
ejpam-5705	573	15	dense	dense	ADJ
ejpam-5705	573	16	elements	element	NOUN
ejpam-5705	573	17	on	on	ADP
ejpam-5705	573	18	a	a	DET
ejpam-5705	573	19	pdl	pdl	NOUN
ejpam-5705	573	20	.	.	PUNCT
ejpam-5705	573	21	by	by	ADP
ejpam-5705	573	22	establishing	establish	VERB
ejpam-5705	573	23	necessary	necessary	ADJ
ejpam-5705	573	24	conditions	condition	NOUN
ejpam-5705	573	25	,	,	PUNCT
ejpam-5705	573	26	we	we	PRON
ejpam-5705	573	27	introduced	introduce	VERB
ejpam-5705	573	28	various	various	ADJ
ejpam-5705	573	29	results	result	NOUN
ejpam-5705	573	30	related	relate	VERB
ejpam-5705	573	31	to	to	ADP
ejpam-5705	573	32	this	this	DET
ejpam-5705	573	33	structure	structure	NOUN
ejpam-5705	573	34	.	.	PUNCT
ejpam-5705	574	1	furthermore	furthermore	ADV
ejpam-5705	574	2	,	,	PUNCT
ejpam-5705	574	3	our	our	PRON
ejpam-5705	574	4	study	study	NOUN
ejpam-5705	574	5	focussed	focusse	VERB
ejpam-5705	574	6	on	on	ADP
ejpam-5705	574	7	providing	provide	VERB
ejpam-5705	574	8	certain	certain	ADJ
ejpam-5705	574	9	characterization	characterization	NOUN
ejpam-5705	574	10	theorems	theorem	NOUN
ejpam-5705	574	11	for	for	ADP
ejpam-5705	574	12	•pdl	•pdl	NOUN
ejpam-5705	574	13	and	and	CCONJ
ejpam-5705	574	14	proved	prove	VERB
ejpam-5705	574	15	equivalence	equivalence	NOUN
ejpam-5705	574	16	conditions	condition	NOUN
ejpam-5705	574	17	for	for	SCONJ
ejpam-5705	574	18	v	v	NOUN
ejpam-5705	574	19	to	to	PART
ejpam-5705	574	20	be	be	AUX
ejpam-5705	574	21	•pdl	•pdl	NOUN
ejpam-5705	574	22	if	if	SCONJ
ejpam-5705	574	23	and	and	CCONJ
ejpam-5705	574	24	only	only	ADV
ejpam-5705	574	25	if	if	SCONJ
ejpam-5705	574	26	every	every	DET
ejpam-5705	574	27	v	v	NOUN
ejpam-5705	574	28	/	/	SYM
ejpam-5705	574	29	θ	θ	PROPN
ejpam-5705	574	30	is	be	AUX
ejpam-5705	574	31	r.	r.	PROPN
ejpam-5705	574	32	bandaru	bandaru	PROPN
ejpam-5705	575	1	et	et	PROPN
ejpam-5705	575	2	al	al	PROPN
ejpam-5705	575	3	.	.	PUNCT
ejpam-5705	575	4	/	/	SYM
ejpam-5705	575	5	eur	eur	PROPN
ejpam-5705	575	6	.	.	PUNCT
ejpam-5705	576	1	j.	j.	PROPN
ejpam-5705	576	2	pure	pure	PROPN
ejpam-5705	576	3	appl	appl	PROPN
ejpam-5705	576	4	.	.	PROPN
ejpam-5705	576	5	math	math	PROPN
ejpam-5705	576	6	,	,	PUNCT
ejpam-5705	576	7	18	18	NUM
ejpam-5705	576	8	(	(	PUNCT
ejpam-5705	576	9	2	2	NUM
ejpam-5705	576	10	)	)	PUNCT
ejpam-5705	576	11	(	(	PUNCT
ejpam-5705	576	12	2025	2025	NUM
ejpam-5705	576	13	)	)	PUNCT
ejpam-5705	576	14	,	,	PUNCT
ejpam-5705	576	15	5705	5705	NUM
ejpam-5705	576	16	13	13	NUM
ejpam-5705	576	17	of	of	ADP
ejpam-5705	576	18	13	13	NUM
ejpam-5705	576	19	boolean	boolean	ADJ
ejpam-5705	576	20	algebra	algebra	NOUN
ejpam-5705	576	21	.	.	PUNCT
ejpam-5705	577	1	lastly	lastly	ADV
ejpam-5705	577	2	,	,	PUNCT
ejpam-5705	577	3	concluded	conclude	VERB
ejpam-5705	577	4	concepts	concept	NOUN
ejpam-5705	577	5	with	with	ADP
ejpam-5705	577	6	showing	show	VERB
ejpam-5705	577	7	that	that	SCONJ
ejpam-5705	577	8	the	the	DET
ejpam-5705	577	9	v	v	NOUN
ejpam-5705	577	10	is	be	AUX
ejpam-5705	577	11	disjunctive	disjunctive	ADJ
ejpam-5705	577	12	if	if	SCONJ
ejpam-5705	577	13	and	and	CCONJ
ejpam-5705	577	14	only	only	ADV
ejpam-5705	577	15	if	if	SCONJ
ejpam-5705	577	16	v	v	NOUN
ejpam-5705	577	17	is	be	AUX
ejpam-5705	577	18	boolean	boolean	ADJ
ejpam-5705	577	19	algebra	algebra	NOUN
ejpam-5705	577	20	.	.	PUNCT
ejpam-5705	578	1	acknowledgements	acknowledgement	NOUN
ejpam-5705	578	2	the	the	DET
ejpam-5705	578	3	authors	author	NOUN
ejpam-5705	578	4	wish	wish	VERB
ejpam-5705	578	5	to	to	PART
ejpam-5705	578	6	thank	thank	VERB
ejpam-5705	578	7	the	the	DET
ejpam-5705	578	8	anonymous	anonymous	ADJ
ejpam-5705	578	9	reviewers	reviewer	NOUN
ejpam-5705	578	10	for	for	ADP
ejpam-5705	578	11	their	their	PRON
ejpam-5705	578	12	valuable	valuable	ADJ
ejpam-5705	578	13	suggestions	suggestion	NOUN
ejpam-5705	578	14	.	.	PUNCT
ejpam-5705	579	1	funding	fund	VERB
ejpam-5705	579	2	information	information	NOUN
ejpam-5705	579	3	this	this	DET
ejpam-5705	579	4	work	work	NOUN
ejpam-5705	579	5	was	be	AUX
ejpam-5705	579	6	supported	support	VERB
ejpam-5705	579	7	by	by	ADP
ejpam-5705	579	8	directorate	directorate	NOUN
ejpam-5705	579	9	of	of	ADP
ejpam-5705	579	10	research	research	NOUN
ejpam-5705	579	11	and	and	CCONJ
ejpam-5705	579	12	innovation	innovation	NOUN
ejpam-5705	579	13	,	,	PUNCT
ejpam-5705	579	14	walter	walter	PROPN
ejpam-5705	579	15	sisulu	sisulu	PROPN
ejpam-5705	579	16	university	university	PROPN
ejpam-5705	579	17	,	,	PUNCT
ejpam-5705	579	18	south	south	PROPN
ejpam-5705	579	19	africa	africa	PROPN
ejpam-5705	579	20	.	.	PUNCT
ejpam-5705	580	1	conflicts	conflict	NOUN
ejpam-5705	580	2	of	of	ADP
ejpam-5705	580	3	interest	interest	NOUN
ejpam-5705	580	4	or	or	CCONJ
ejpam-5705	580	5	competing	compete	VERB
ejpam-5705	580	6	interests	interest	NOUN
ejpam-5705	580	7	the	the	DET
ejpam-5705	580	8	authors	author	NOUN
ejpam-5705	580	9	declare	declare	VERB
ejpam-5705	580	10	that	that	SCONJ
ejpam-5705	580	11	they	they	PRON
ejpam-5705	580	12	have	have	VERB
ejpam-5705	580	13	no	no	DET
ejpam-5705	580	14	conflicts	conflict	NOUN
ejpam-5705	580	15	of	of	ADP
ejpam-5705	580	16	interest	interest	NOUN
ejpam-5705	580	17	.	.	PUNCT
ejpam-5705	581	1	informed	inform	VERB
ejpam-5705	581	2	consent	consent	VERB
ejpam-5705	581	3	the	the	DET
ejpam-5705	581	4	authors	author	NOUN
ejpam-5705	581	5	are	be	AUX
ejpam-5705	581	6	fully	fully	ADV
ejpam-5705	581	7	aware	aware	ADJ
ejpam-5705	581	8	and	and	CCONJ
ejpam-5705	581	9	satisfied	satisfied	ADJ
ejpam-5705	581	10	with	with	ADP
ejpam-5705	581	11	the	the	DET
ejpam-5705	581	12	contents	content	NOUN
ejpam-5705	581	13	of	of	ADP
ejpam-5705	581	14	the	the	DET
ejpam-5705	581	15	article	article	NOUN
ejpam-5705	581	16	.	.	PUNCT
ejpam-5705	582	1	references	reference	NOUN
ejpam-5705	582	2	[	[	X
ejpam-5705	582	3	1	1	NUM
ejpam-5705	582	4	]	]	PUNCT
ejpam-5705	582	5	g	g	NOUN
ejpam-5705	582	6	birkhoff	birkhoff	NOUN
ejpam-5705	582	7	.	.	PUNCT
ejpam-5705	583	1	lattice	lattice	PROPN
ejpam-5705	583	2	theory	theory	NOUN
ejpam-5705	583	3	.	.	PUNCT
ejpam-5705	584	1	colloquium	colloquium	NOUN
ejpam-5705	584	2	publications	publication	NOUN
ejpam-5705	584	3	,	,	PUNCT
ejpam-5705	584	4	american	american	PROPN
ejpam-5705	584	5	mathematical	mathematical	PROPN
ejpam-5705	584	6	society	society	NOUN
ejpam-5705	584	7	,	,	PUNCT
ejpam-5705	584	8	new	new	PROPN
ejpam-5705	584	9	york	york	PROPN
ejpam-5705	584	10	,	,	PUNCT
ejpam-5705	584	11	1940	1940	NUM
ejpam-5705	584	12	.	.	PUNCT
ejpam-5705	585	1	[	[	X
ejpam-5705	585	2	2	2	NUM
ejpam-5705	585	3	]	]	X
ejpam-5705	585	4	u	u	NOUN
ejpam-5705	585	5	m	m	NOUN
ejpam-5705	585	6	swamy	swamy	NOUN
ejpam-5705	585	7	and	and	CCONJ
ejpam-5705	585	8	g	g	PROPN
ejpam-5705	585	9	c	c	PROPN
ejpam-5705	585	10	rao	rao	PROPN
ejpam-5705	585	11	.	.	PUNCT
ejpam-5705	586	1	almost	almost	ADV
ejpam-5705	586	2	distributive	distributive	ADJ
ejpam-5705	586	3	lattices	lattice	NOUN
ejpam-5705	586	4	.	.	PUNCT
ejpam-5705	587	1	journal	journal	NOUN
ejpam-5705	587	2	of	of	ADP
ejpam-5705	587	3	the	the	DET
ejpam-5705	587	4	australian	australian	ADJ
ejpam-5705	587	5	mathematical	mathematical	ADJ
ejpam-5705	587	6	society	society	NOUN
ejpam-5705	587	7	.	.	PUNCT
ejpam-5705	588	1	series	series	PROPN
ejpam-5705	588	2	a.	a.	PROPN
ejpam-5705	588	3	,	,	PUNCT
ejpam-5705	588	4	31:77–91	31:77–91	NUM
ejpam-5705	588	5	,	,	PUNCT
ejpam-5705	588	6	1981	1981	NUM
ejpam-5705	588	7	.	.	PUNCT
ejpam-5705	589	1	[	[	X
ejpam-5705	589	2	3	3	X
ejpam-5705	589	3	]	]	SYM
ejpam-5705	589	4	g	g	PROPN
ejpam-5705	589	5	n	n	PRON
ejpam-5705	589	6	rao	rao	NOUN
ejpam-5705	589	7	and	and	CCONJ
ejpam-5705	589	8	t	t	PROPN
ejpam-5705	589	9	a	a	DET
ejpam-5705	589	10	habtamu	habtamu	ADJ
ejpam-5705	589	11	.	.	PUNCT
ejpam-5705	590	1	almost	almost	ADV
ejpam-5705	590	2	lattices	lattice	NOUN
ejpam-5705	590	3	.	.	PUNCT
ejpam-5705	591	1	journal	journal	PROPN
ejpam-5705	591	2	of	of	ADP
ejpam-5705	591	3	international	international	ADJ
ejpam-5705	591	4	mathematics	mathematics	PROPN
ejpam-5705	591	5	virtual	virtual	PROPN
ejpam-5705	591	6	institute	institute	PROPN
ejpam-5705	591	7	,	,	PUNCT
ejpam-5705	591	8	9(1):155–171	9(1):155–171	NUM
ejpam-5705	591	9	,	,	PUNCT
ejpam-5705	591	10	2019	2019	NUM
ejpam-5705	591	11	.	.	PUNCT
ejpam-5705	592	1	[	[	X
ejpam-5705	592	2	4	4	X
ejpam-5705	592	3	]	]	SYM
ejpam-5705	592	4	g	g	PROPN
ejpam-5705	592	5	n	n	PRON
ejpam-5705	592	6	rao	rao	NOUN
ejpam-5705	592	7	and	and	CCONJ
ejpam-5705	592	8	t	t	PROPN
ejpam-5705	592	9	a	a	DET
ejpam-5705	592	10	habtamu	habtamu	ADJ
ejpam-5705	592	11	.	.	PUNCT
ejpam-5705	593	1	filters	filter	NOUN
ejpam-5705	593	2	in	in	ADP
ejpam-5705	593	3	almost	almost	ADV
ejpam-5705	593	4	lattices	lattice	NOUN
ejpam-5705	593	5	.	.	PUNCT
ejpam-5705	594	1	bulletin	bulletin	NOUN
ejpam-5705	594	2	of	of	ADP
ejpam-5705	594	3	the	the	DET
ejpam-5705	594	4	international	international	ADJ
ejpam-5705	594	5	mathematics	mathematics	PROPN
ejpam-5705	594	6	virtual	virtual	PROPN
ejpam-5705	594	7	institute	institute	NOUN
ejpam-5705	594	8	,	,	PUNCT
ejpam-5705	594	9	10(1):69–82	10(1):69–82	NUM
ejpam-5705	594	10	,	,	PUNCT
ejpam-5705	594	11	2020	2020	NUM
ejpam-5705	594	12	.	.	PUNCT
ejpam-5705	595	1	[	[	X
ejpam-5705	595	2	5	5	NUM
ejpam-5705	595	3	]	]	PUNCT
ejpam-5705	595	4	t	t	NOUN
ejpam-5705	595	5	p	p	NOUN
ejpam-5705	595	6	speed	speed	NOUN
ejpam-5705	595	7	.	.	PUNCT
ejpam-5705	596	1	some	some	DET
ejpam-5705	596	2	remarks	remark	NOUN
ejpam-5705	596	3	on	on	ADP
ejpam-5705	596	4	a	a	DET
ejpam-5705	596	5	class	class	NOUN
ejpam-5705	596	6	of	of	ADP
ejpam-5705	596	7	distributive	distributive	ADJ
ejpam-5705	596	8	lattices	lattice	NOUN
ejpam-5705	596	9	.	.	PUNCT
ejpam-5705	597	1	,	,	PUNCT
ejpam-5705	597	2	journal	journal	NOUN
ejpam-5705	597	3	of	of	ADP
ejpam-5705	597	4	australian	australian	ADJ
ejpam-5705	597	5	mathematical	mathematical	ADJ
ejpam-5705	597	6	society	society	NOUN
ejpam-5705	597	7	,	,	PUNCT
ejpam-5705	597	8	9:289–296	9:289–296	NOUN
ejpam-5705	597	9	,	,	PUNCT
ejpam-5705	597	10	1969	1969	NUM
ejpam-5705	597	11	.	.	PUNCT
ejpam-5705	598	1	[	[	X
ejpam-5705	598	2	6	6	NUM
ejpam-5705	598	3	]	]	SYM
ejpam-5705	598	4	r	r	NOUN
ejpam-5705	598	5	bandaru	bandaru	NOUN
ejpam-5705	598	6	and	and	CCONJ
ejpam-5705	598	7	s	s	NOUN
ejpam-5705	598	8	ajjarapu	ajjarapu	PROPN
ejpam-5705	598	9	.	.	PUNCT
ejpam-5705	599	1	paradistributive	paradistributive	ADJ
ejpam-5705	599	2	latticoids	latticoids	PROPN
ejpam-5705	599	3	.	.	PUNCT
ejpam-5705	600	1	european	european	PROPN
ejpam-5705	600	2	journal	journal	PROPN
ejpam-5705	600	3	of	of	ADP
ejpam-5705	600	4	pure	pure	ADJ
ejpam-5705	600	5	and	and	CCONJ
ejpam-5705	600	6	applied	applied	ADJ
ejpam-5705	600	7	mathematics	mathematic	NOUN
ejpam-5705	600	8	,	,	PUNCT
ejpam-5705	600	9	17(2):819–834	17(2):819–834	NUM
ejpam-5705	600	10	,	,	PUNCT
ejpam-5705	600	11	2024	2024	NUM
ejpam-5705	600	12	.	.	PUNCT
ejpam-5705	601	1	[	[	X
ejpam-5705	601	2	7	7	NUM
ejpam-5705	601	3	]	]	X
ejpam-5705	601	4	s	s	PART
ejpam-5705	601	5	ajjarapu	ajjarapu	PROPN
ejpam-5705	601	6	,	,	PUNCT
ejpam-5705	601	7	r	r	NOUN
ejpam-5705	601	8	bandaru	bandaru	NOUN
ejpam-5705	601	9	,	,	PUNCT
ejpam-5705	601	10	r	r	NOUN
ejpam-5705	601	11	shukla	shukla	NOUN
ejpam-5705	601	12	,	,	PUNCT
ejpam-5705	601	13	and	and	CCONJ
ejpam-5705	601	14	y	y	PROPN
ejpam-5705	601	15	b	b	PROPN
ejpam-5705	601	16	jun	jun	PROPN
ejpam-5705	601	17	.	.	PUNCT
ejpam-5705	601	18	parapseudo	parapseudo	NOUN
ejpam-5705	601	19	-	-	NOUN
ejpam-5705	601	20	complementation	complementation	NOUN
ejpam-5705	601	21	on	on	ADP
ejpam-5705	601	22	a	a	DET
ejpam-5705	601	23	paradistributive	paradistributive	ADJ
ejpam-5705	601	24	latticoids	latticoid	NOUN
ejpam-5705	601	25	.	.	PUNCT
ejpam-5705	602	1	european	european	PROPN
ejpam-5705	602	2	journal	journal	PROPN
ejpam-5705	602	3	of	of	ADP
ejpam-5705	602	4	pure	pure	ADJ
ejpam-5705	602	5	and	and	CCONJ
ejpam-5705	602	6	applied	applied	ADJ
ejpam-5705	602	7	mathematics	mathematic	NOUN
ejpam-5705	602	8	,	,	PUNCT
ejpam-5705	602	9	17(2):1129–1145	17(2):1129–1145	NUM
ejpam-5705	602	10	,	,	PUNCT
ejpam-5705	602	11	2024	2024	NUM
ejpam-5705	602	12	.	.	PUNCT
ejpam-5705	603	1	[	[	X
ejpam-5705	603	2	8	8	NUM
ejpam-5705	603	3	]	]	X
ejpam-5705	603	4	r	r	NOUN
ejpam-5705	603	5	bandaru	bandaru	NOUN
ejpam-5705	603	6	,	,	PUNCT
ejpam-5705	603	7	p	p	NOUN
ejpam-5705	603	8	patel	patel	NOUN
ejpam-5705	603	9	,	,	PUNCT
ejpam-5705	603	10	r	r	NOUN
ejpam-5705	603	11	noorbhasha	noorbhasha	PROPN
ejpam-5705	603	12	,	,	PUNCT
ejpam-5705	603	13	r	r	NOUN
ejpam-5705	603	14	shukla	shukla	NOUN
ejpam-5705	603	15	,	,	PUNCT
ejpam-5705	603	16	and	and	CCONJ
ejpam-5705	603	17	s	s	AUX
ejpam-5705	603	18	ajjarapu	ajjarapu	PROPN
ejpam-5705	603	19	.	.	PUNCT
ejpam-5705	604	1	normal	normal	ADJ
ejpam-5705	604	2	paradistributive	paradistributive	ADJ
ejpam-5705	604	3	latticoids	latticoid	NOUN
ejpam-5705	604	4	.	.	PUNCT
ejpam-5705	605	1	european	european	PROPN
ejpam-5705	605	2	journal	journal	PROPN
ejpam-5705	605	3	of	of	ADP
ejpam-5705	605	4	pure	pure	ADJ
ejpam-5705	605	5	and	and	CCONJ
ejpam-5705	605	6	applied	applied	ADJ
ejpam-5705	605	7	mathematics	mathematic	NOUN
ejpam-5705	605	8	,	,	PUNCT
ejpam-5705	605	9	17(2):1306–1320	17(2):1306–1320	NUM
ejpam-5705	605	10	,	,	PUNCT
ejpam-5705	605	11	2024	2024	NUM
ejpam-5705	605	12	.	.	PUNCT
ejpam-5705	606	1	[	[	X
ejpam-5705	606	2	9	9	NUM
ejpam-5705	606	3	]	]	X
ejpam-5705	606	4	s	s	PART
ejpam-5705	606	5	ajjarapu	ajjarapu	PROPN
ejpam-5705	606	6	,	,	PUNCT
ejpam-5705	606	7	r	r	NOUN
ejpam-5705	606	8	bandaru	bandaru	NOUN
ejpam-5705	606	9	,	,	PUNCT
ejpam-5705	606	10	r	r	NOUN
ejpam-5705	606	11	r	r	NOUN
ejpam-5705	606	12	kotha	kotha	NOUN
ejpam-5705	606	13	,	,	PUNCT
ejpam-5705	606	14	and	and	CCONJ
ejpam-5705	606	15	r	r	NOUN
ejpam-5705	606	16	shukla	shukla	NOUN
ejpam-5705	606	17	.	.	PUNCT
ejpam-5705	607	1	topological	topological	ADJ
ejpam-5705	607	2	properties	property	NOUN
ejpam-5705	607	3	of	of	ADP
ejpam-5705	607	4	prime	prime	ADJ
ejpam-5705	607	5	filters	filter	NOUN
ejpam-5705	607	6	and	and	CCONJ
ejpam-5705	607	7	minimal	minimal	ADJ
ejpam-5705	607	8	prime	prime	ADJ
ejpam-5705	607	9	filters	filter	NOUN
ejpam-5705	607	10	on	on	ADP
ejpam-5705	607	11	a	a	DET
ejpam-5705	607	12	paradistributive	paradistributive	ADJ
ejpam-5705	607	13	latticoid	latticoid	NOUN
ejpam-5705	607	14	.	.	PUNCT
ejpam-5705	608	1	international	international	ADJ
ejpam-5705	608	2	journal	journal	PROPN
ejpam-5705	608	3	of	of	ADP
ejpam-5705	608	4	mathematics	mathematics	PROPN
ejpam-5705	608	5	and	and	CCONJ
ejpam-5705	608	6	mathematical	mathematical	ADJ
ejpam-5705	608	7	sciences	science	NOUN
ejpam-5705	608	8	,	,	PUNCT
ejpam-5705	608	9	2024(1862245):12	2024(1862245):12	NUM
ejpam-5705	608	10	pages	page	NOUN
ejpam-5705	608	11	,	,	PUNCT
ejpam-5705	608	12	2024	2024	NUM
ejpam-5705	608	13	.	.	PUNCT