id	sid	tid	token	lemma	pos
ejpam-5042	1	1	european	european	PROPN
ejpam-5042	1	2	journal	journal	PROPN
ejpam-5042	1	3	of	of	ADP
ejpam-5042	1	4	pure	pure	ADJ
ejpam-5042	1	5	and	and	CCONJ
ejpam-5042	1	6	applied	apply	VERB
ejpam-5042	1	7	mathematics	mathematic	NOUN
ejpam-5042	1	8	vol	vol	NOUN
ejpam-5042	1	9	.	.	PROPN
ejpam-5042	2	1	17	17	NUM
ejpam-5042	2	2	,	,	PUNCT
ejpam-5042	2	3	no	no	INTJ
ejpam-5042	2	4	.	.	NOUN
ejpam-5042	2	5	2	2	NUM
ejpam-5042	2	6	,	,	PUNCT
ejpam-5042	2	7	2024	2024	NUM
ejpam-5042	2	8	,	,	PUNCT
ejpam-5042	2	9	1129	1129	NUM
ejpam-5042	2	10	-	-	SYM
ejpam-5042	2	11	1145	1145	NUM
ejpam-5042	2	12	issn	issn	PROPN
ejpam-5042	2	13	1307	1307	NUM
ejpam-5042	2	14	-	-	SYM
ejpam-5042	2	15	5543	5543	NUM
ejpam-5042	2	16	–	–	PUNCT
ejpam-5042	3	1	ejpam.com	ejpam.com	X
ejpam-5042	3	2	published	publish	VERB
ejpam-5042	3	3	by	by	ADP
ejpam-5042	3	4	new	new	PROPN
ejpam-5042	3	5	york	york	PROPN
ejpam-5042	3	6	business	business	PROPN
ejpam-5042	3	7	global	global	ADJ
ejpam-5042	3	8	parapseudo	parapseudo	NOUN
ejpam-5042	3	9	-	-	NOUN
ejpam-5042	3	10	complementation	complementation	NOUN
ejpam-5042	3	11	on	on	ADP
ejpam-5042	3	12	paradistributive	paradistributive	ADJ
ejpam-5042	3	13	latticoids	latticoid	NOUN
ejpam-5042	3	14	suryavardhani	suryavardhani	ADJ
ejpam-5042	3	15	ajjarapu1	ajjarapu1	PROPN
ejpam-5042	3	16	,	,	PUNCT
ejpam-5042	3	17	ravikumar	ravikumar	PROPN
ejpam-5042	3	18	bandaru2	bandaru2	PROPN
ejpam-5042	3	19	,	,	PUNCT
ejpam-5042	3	20	rahul	rahul	PROPN
ejpam-5042	3	21	shukla3,∗	shukla3,∗	PROPN
ejpam-5042	3	22	,	,	PUNCT
ejpam-5042	3	23	young	young	ADJ
ejpam-5042	3	24	bae	bae	NOUN
ejpam-5042	3	25	jun4	jun4	PROPN
ejpam-5042	3	26	1	1	NUM
ejpam-5042	3	27	department	department	NOUN
ejpam-5042	3	28	of	of	ADP
ejpam-5042	3	29	mathematics	mathematic	NOUN
ejpam-5042	3	30	,	,	PUNCT
ejpam-5042	3	31	gitam	gitam	NOUN
ejpam-5042	3	32	deemed	deem	VERB
ejpam-5042	3	33	to	to	PART
ejpam-5042	3	34	be	be	AUX
ejpam-5042	3	35	university	university	NOUN
ejpam-5042	3	36	,	,	PUNCT
ejpam-5042	3	37	hyderabad	hyderabad	PROPN
ejpam-5042	3	38	campus	campus	NOUN
ejpam-5042	3	39	,	,	PUNCT
ejpam-5042	3	40	telangana-502329	telangana-502329	ADJ
ejpam-5042	3	41	,	,	PUNCT
ejpam-5042	3	42	india	india	PROPN
ejpam-5042	3	43	2	2	NUM
ejpam-5042	3	44	department	department	NOUN
ejpam-5042	3	45	of	of	ADP
ejpam-5042	3	46	mathematics	mathematic	NOUN
ejpam-5042	3	47	,	,	PUNCT
ejpam-5042	3	48	school	school	NOUN
ejpam-5042	3	49	of	of	ADP
ejpam-5042	3	50	advanced	advanced	ADJ
ejpam-5042	3	51	sciences	science	NOUN
ejpam-5042	3	52	,	,	PUNCT
ejpam-5042	3	53	vit	vit	PROPN
ejpam-5042	3	54	-	-	PUNCT
ejpam-5042	3	55	ap	ap	PROPN
ejpam-5042	3	56	university	university	PROPN
ejpam-5042	3	57	,	,	PUNCT
ejpam-5042	3	58	andhra	andhra	PROPN
ejpam-5042	3	59	pradesh-522237	pradesh-522237	NOUN
ejpam-5042	3	60	,	,	PUNCT
ejpam-5042	3	61	india	india	PROPN
ejpam-5042	3	62	3	3	NUM
ejpam-5042	3	63	department	department	PROPN
ejpam-5042	3	64	of	of	ADP
ejpam-5042	3	65	mathematical	mathematical	ADJ
ejpam-5042	3	66	sciences	sciences	PROPN
ejpam-5042	3	67	and	and	CCONJ
ejpam-5042	3	68	computing	computing	NOUN
ejpam-5042	3	69	,	,	PUNCT
ejpam-5042	3	70	walter	walter	PROPN
ejpam-5042	3	71	sisulu	sisulu	PROPN
ejpam-5042	3	72	university	university	PROPN
ejpam-5042	3	73	,	,	PUNCT
ejpam-5042	3	74	mthatha	mthatha	NOUN
ejpam-5042	3	75	5117	5117	NUM
ejpam-5042	3	76	,	,	PUNCT
ejpam-5042	3	77	south	south	PROPN
ejpam-5042	3	78	africa	africa	PROPN
ejpam-5042	3	79	4	4	NUM
ejpam-5042	3	80	department	department	NOUN
ejpam-5042	3	81	of	of	ADP
ejpam-5042	3	82	mathematics	mathematics	PROPN
ejpam-5042	3	83	education	education	NOUN
ejpam-5042	3	84	,	,	PUNCT
ejpam-5042	3	85	gyeongsang	gyeongsang	PROPN
ejpam-5042	3	86	national	national	PROPN
ejpam-5042	3	87	university	university	PROPN
ejpam-5042	3	88	,	,	PUNCT
ejpam-5042	3	89	jinju	jinju	NOUN
ejpam-5042	3	90	52828	52828	NUM
ejpam-5042	3	91	,	,	PUNCT
ejpam-5042	3	92	korea	korea	PROPN
ejpam-5042	3	93	abstract	abstract	NOUN
ejpam-5042	3	94	.	.	PUNCT
ejpam-5042	4	1	in	in	ADP
ejpam-5042	4	2	this	this	DET
ejpam-5042	4	3	paper	paper	NOUN
ejpam-5042	4	4	,	,	PUNCT
ejpam-5042	4	5	we	we	PRON
ejpam-5042	4	6	introduce	introduce	VERB
ejpam-5042	4	7	the	the	DET
ejpam-5042	4	8	concept	concept	NOUN
ejpam-5042	4	9	of	of	ADP
ejpam-5042	4	10	a	a	DET
ejpam-5042	4	11	parapseudo	parapseudo	NOUN
ejpam-5042	4	12	-	-	NOUN
ejpam-5042	4	13	complementation	complementation	NOUN
ejpam-5042	4	14	in	in	ADP
ejpam-5042	4	15	a	a	DET
ejpam-5042	4	16	paradistributive	paradistributive	ADJ
ejpam-5042	4	17	latticoid(pdl	latticoid(pdl	NOUN
ejpam-5042	4	18	)	)	PUNCT
ejpam-5042	4	19	and	and	CCONJ
ejpam-5042	4	20	investigate	investigate	VERB
ejpam-5042	4	21	its	its	PRON
ejpam-5042	4	22	elementary	elementary	ADJ
ejpam-5042	4	23	properties	property	NOUN
ejpam-5042	4	24	.	.	PUNCT
ejpam-5042	5	1	we	we	PRON
ejpam-5042	5	2	demonstrate	demonstrate	VERB
ejpam-5042	5	3	the	the	DET
ejpam-5042	5	4	independence	independence	NOUN
ejpam-5042	5	5	of	of	ADP
ejpam-5042	5	6	the	the	DET
ejpam-5042	5	7	axioms	axiom	NOUN
ejpam-5042	5	8	related	relate	VERB
ejpam-5042	5	9	to	to	ADP
ejpam-5042	5	10	its	its	PRON
ejpam-5042	5	11	definition	definition	NOUN
ejpam-5042	5	12	,	,	PUNCT
ejpam-5042	5	13	highlighting	highlight	VERB
ejpam-5042	5	14	the	the	DET
ejpam-5042	5	15	flexibility	flexibility	NOUN
ejpam-5042	5	16	of	of	ADP
ejpam-5042	5	17	this	this	DET
ejpam-5042	5	18	concept	concept	NOUN
ejpam-5042	5	19	.	.	PUNCT
ejpam-5042	6	1	additionally	additionally	ADV
ejpam-5042	6	2	,	,	PUNCT
ejpam-5042	6	3	we	we	PRON
ejpam-5042	6	4	establish	establish	VERB
ejpam-5042	6	5	necessary	necessary	ADJ
ejpam-5042	6	6	conditions	condition	NOUN
ejpam-5042	6	7	for	for	ADP
ejpam-5042	6	8	a	a	DET
ejpam-5042	6	9	pdl	pdl	NOUN
ejpam-5042	6	10	with	with	ADP
ejpam-5042	6	11	a	a	DET
ejpam-5042	6	12	minimal	minimal	ADJ
ejpam-5042	6	13	element	element	NOUN
ejpam-5042	6	14	to	to	PART
ejpam-5042	6	15	be	be	AUX
ejpam-5042	6	16	parapseudocomplemented	parapseudocomplemente	VERB
ejpam-5042	6	17	and	and	CCONJ
ejpam-5042	6	18	explore	explore	VERB
ejpam-5042	6	19	the	the	DET
ejpam-5042	6	20	properties	property	NOUN
ejpam-5042	6	21	required	require	VERB
ejpam-5042	6	22	for	for	ADP
ejpam-5042	6	23	parapseudo	parapseudo	NOUN
ejpam-5042	6	24	-	-	NOUN
ejpam-5042	6	25	complementation	complementation	NOUN
ejpam-5042	6	26	to	to	PART
ejpam-5042	6	27	be	be	AUX
ejpam-5042	6	28	equationally	equationally	ADV
ejpam-5042	6	29	definable	definable	ADJ
ejpam-5042	6	30	.	.	PUNCT
ejpam-5042	7	1	moreover	moreover	ADV
ejpam-5042	7	2	,	,	PUNCT
ejpam-5042	7	3	we	we	PRON
ejpam-5042	7	4	establish	establish	VERB
ejpam-5042	7	5	a	a	DET
ejpam-5042	7	6	one	one	NUM
ejpam-5042	7	7	-	-	PUNCT
ejpam-5042	7	8	to	to	ADP
ejpam-5042	7	9	-	-	PUNCT
ejpam-5042	7	10	one	one	NUM
ejpam-5042	7	11	correspondence	correspondence	NOUN
ejpam-5042	7	12	between	between	ADP
ejpam-5042	7	13	the	the	DET
ejpam-5042	7	14	set	set	NOUN
ejpam-5042	7	15	of	of	ADP
ejpam-5042	7	16	all	all	DET
ejpam-5042	7	17	minimal	minimal	ADJ
ejpam-5042	7	18	elements	element	NOUN
ejpam-5042	7	19	and	and	CCONJ
ejpam-5042	7	20	the	the	DET
ejpam-5042	7	21	set	set	NOUN
ejpam-5042	7	22	of	of	ADP
ejpam-5042	7	23	all	all	DET
ejpam-5042	7	24	parapseudo	parapseudo	NOUN
ejpam-5042	7	25	-	-	PUNCT
ejpam-5042	7	26	complementations	complementation	NOUN
ejpam-5042	7	27	.	.	PUNCT
ejpam-5042	8	1	2020	2020	NUM
ejpam-5042	8	2	mathematics	mathematic	NOUN
ejpam-5042	8	3	subject	subject	NOUN
ejpam-5042	8	4	classifications	classification	NOUN
ejpam-5042	8	5	:	:	PUNCT
ejpam-5042	8	6	06d99	06d99	NUM
ejpam-5042	8	7	key	key	ADJ
ejpam-5042	8	8	words	word	NOUN
ejpam-5042	8	9	and	and	CCONJ
ejpam-5042	8	10	phrases	phrase	NOUN
ejpam-5042	8	11	:	:	PUNCT
ejpam-5042	8	12	parapseudo	parapseudo	NOUN
ejpam-5042	8	13	-	-	NOUN
ejpam-5042	8	14	complementation	complementation	NOUN
ejpam-5042	8	15	,	,	PUNCT
ejpam-5042	8	16	paradistributive	paradistributive	ADJ
ejpam-5042	8	17	latticoid(pdl	latticoid(pdl	NOUN
ejpam-5042	8	18	)	)	PUNCT
ejpam-5042	8	19	,	,	PUNCT
ejpam-5042	8	20	minimal	minimal	ADJ
ejpam-5042	8	21	element	element	NOUN
ejpam-5042	8	22	,	,	PUNCT
ejpam-5042	8	23	filter	filter	NOUN
ejpam-5042	8	24	,	,	PUNCT
ejpam-5042	8	25	boolean	boolean	ADJ
ejpam-5042	8	26	algebra	algebra	NOUN
ejpam-5042	8	27	.	.	PUNCT
ejpam-5042	9	1	1	1	X
ejpam-5042	9	2	.	.	X
ejpam-5042	9	3	introduction	introduction	NOUN
ejpam-5042	9	4	in	in	ADP
ejpam-5042	9	5	the	the	DET
ejpam-5042	9	6	realm	realm	NOUN
ejpam-5042	9	7	of	of	ADP
ejpam-5042	9	8	algebraic	algebraic	ADJ
ejpam-5042	9	9	structures	structure	NOUN
ejpam-5042	9	10	,	,	PUNCT
ejpam-5042	9	11	a	a	DET
ejpam-5042	9	12	variety	variety	NOUN
ejpam-5042	9	13	of	of	ADP
ejpam-5042	9	14	algebras	algebra	NOUN
ejpam-5042	9	15	,	,	PUNCT
ejpam-5042	9	16	including	include	VERB
ejpam-5042	9	17	lattices	lattice	NOUN
ejpam-5042	9	18	and	and	CCONJ
ejpam-5042	9	19	boolean	boolean	ADJ
ejpam-5042	9	20	algebras	algebra	NOUN
ejpam-5042	9	21	,	,	PUNCT
ejpam-5042	9	22	provide	provide	VERB
ejpam-5042	9	23	generalizations	generalization	NOUN
ejpam-5042	9	24	of	of	ADP
ejpam-5042	9	25	the	the	DET
ejpam-5042	9	26	concept	concept	NOUN
ejpam-5042	9	27	of	of	ADP
ejpam-5042	9	28	complement	complement	NOUN
ejpam-5042	9	29	.	.	PUNCT
ejpam-5042	10	1	within	within	ADP
ejpam-5042	10	2	this	this	DET
ejpam-5042	10	3	context	context	NOUN
ejpam-5042	10	4	,	,	PUNCT
ejpam-5042	10	5	the	the	DET
ejpam-5042	10	6	notion	notion	NOUN
ejpam-5042	10	7	of	of	ADP
ejpam-5042	10	8	pseudo	pseudo	NOUN
ejpam-5042	10	9	-	-	NOUN
ejpam-5042	10	10	complementation	complementation	NOUN
ejpam-5042	10	11	has	have	AUX
ejpam-5042	10	12	been	be	AUX
ejpam-5042	10	13	extended	extend	VERB
ejpam-5042	10	14	to	to	PART
ejpam-5042	10	15	encompass	encompass	VERB
ejpam-5042	10	16	a	a	DET
ejpam-5042	10	17	wide	wide	ADJ
ejpam-5042	10	18	range	range	NOUN
ejpam-5042	10	19	of	of	ADP
ejpam-5042	10	20	semigroups	semigroup	NOUN
ejpam-5042	10	21	,	,	PUNCT
ejpam-5042	10	22	referred	refer	VERB
ejpam-5042	10	23	to	to	ADP
ejpam-5042	10	24	as	as	ADP
ejpam-5042	10	25	pseudo	pseudo	NOUN
ejpam-5042	10	26	-	-	ADJ
ejpam-5042	10	27	complemented	complement	VERB
ejpam-5042	10	28	semilattices	semilattice	NOUN
ejpam-5042	10	29	.	.	PUNCT
ejpam-5042	11	1	the	the	DET
ejpam-5042	11	2	study	study	NOUN
ejpam-5042	11	3	of	of	ADP
ejpam-5042	11	4	pseudocomplements	pseudocomplement	NOUN
ejpam-5042	11	5	in	in	ADP
ejpam-5042	11	6	distributive	distributive	ADJ
ejpam-5042	11	7	lattices	lattice	NOUN
ejpam-5042	11	8	was	be	AUX
ejpam-5042	11	9	first	first	ADV
ejpam-5042	11	10	introduced	introduce	VERB
ejpam-5042	11	11	and	and	CCONJ
ejpam-5042	11	12	extensively	extensively	ADV
ejpam-5042	11	13	researched	research	VERB
ejpam-5042	11	14	by	by	ADP
ejpam-5042	11	15	g.	g.	PROPN
ejpam-5042	11	16	birkhoff[2	birkhoff[2	PROPN
ejpam-5042	11	17	]	]	PUNCT
ejpam-5042	11	18	and	and	CCONJ
ejpam-5042	11	19	orrin	orrin	PROPN
ejpam-5042	11	20	frink[5	frink[5	PROPN
ejpam-5042	11	21	]	]	PUNCT
ejpam-5042	11	22	.	.	PUNCT
ejpam-5042	12	1	i.	i.	PROPN
ejpam-5042	12	2	chajda	chajda	PROPN
ejpam-5042	12	3	et	et	PROPN
ejpam-5042	12	4	al.[3	al.[3	PROPN
ejpam-5042	12	5	,	,	PUNCT
ejpam-5042	12	6	4	4	NUM
ejpam-5042	12	7	]	]	PUNCT
ejpam-5042	12	8	introduced	introduce	VERB
ejpam-5042	12	9	the	the	DET
ejpam-5042	12	10	so	so	ADV
ejpam-5042	12	11	-	-	PUNCT
ejpam-5042	12	12	called	call	VERB
ejpam-5042	12	13	sectionally	sectionally	ADV
ejpam-5042	12	14	∗corresponding	∗corresponde	VERB
ejpam-5042	12	15	author	author	NOUN
ejpam-5042	12	16	.	.	PUNCT
ejpam-5042	13	1	doi	doi	NOUN
ejpam-5042	13	2	:	:	PUNCT
ejpam-5042	13	3	https://doi.org/10.29020/nybg.ejpam.v17i2.5042	https://doi.org/10.29020/nybg.ejpam.v17i2.5042	NUM
ejpam-5042	13	4	email	email	NOUN
ejpam-5042	13	5	addresses	address	NOUN
ejpam-5042	13	6	:	:	PUNCT
ejpam-5042	13	7	syerrapr@gitam.in	syerrapr@gitam.in	PROPN
ejpam-5042	13	8	(	(	PUNCT
ejpam-5042	13	9	s.	s.	PROPN
ejpam-5042	13	10	ajjarapu	ajjarapu	PROPN
ejpam-5042	13	11	)	)	PUNCT
ejpam-5042	13	12	,	,	PUNCT
ejpam-5042	13	13	ravimaths83@gmail.com	ravimaths83@gmail.com	PROPN
ejpam-5042	13	14	(	(	PUNCT
ejpam-5042	13	15	r.	r.	PROPN
ejpam-5042	13	16	bandaru	bandaru	PROPN
ejpam-5042	13	17	)	)	PUNCT
ejpam-5042	13	18	,	,	PUNCT
ejpam-5042	13	19	rshukla@wsu.ac.za	rshukla@wsu.ac.za	NOUN
ejpam-5042	13	20	(	(	PUNCT
ejpam-5042	13	21	r.	r.	NOUN
ejpam-5042	13	22	shukla	shukla	PROPN
ejpam-5042	13	23	)	)	PUNCT
ejpam-5042	13	24	,	,	PUNCT
ejpam-5042	13	25	skywine@gmail.com	skywine@gmail.com	X
ejpam-5042	14	1	(	(	PUNCT
ejpam-5042	14	2	y.	y.	PROPN
ejpam-5042	14	3	b.	b.	PROPN
ejpam-5042	14	4	jun	jun	PROPN
ejpam-5042	14	5	)	)	PUNCT
ejpam-5042	14	6	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5042	14	7	1129	1129	NUM
ejpam-5042	15	1	©	©	PROPN
ejpam-5042	15	2	2024	2024	NUM
ejpam-5042	15	3	ejpam	ejpam	NOUN
ejpam-5042	15	4	all	all	DET
ejpam-5042	15	5	rights	right	NOUN
ejpam-5042	15	6	reserved	reserve	VERB
ejpam-5042	15	7	.	.	PUNCT
ejpam-5042	16	1	r.	r.	PROPN
ejpam-5042	16	2	shukla	shukla	PROPN
ejpam-5042	16	3	et	et	PROPN
ejpam-5042	16	4	al	al	PROPN
ejpam-5042	16	5	.	.	PUNCT
ejpam-5042	16	6	/	/	SYM
ejpam-5042	16	7	eur	eur	PROPN
ejpam-5042	16	8	.	.	PUNCT
ejpam-5042	17	1	j.	j.	PROPN
ejpam-5042	17	2	pure	pure	PROPN
ejpam-5042	17	3	appl	appl	PROPN
ejpam-5042	17	4	.	.	PROPN
ejpam-5042	17	5	math	math	PROPN
ejpam-5042	17	6	,	,	PUNCT
ejpam-5042	17	7	17	17	NUM
ejpam-5042	17	8	(	(	PUNCT
ejpam-5042	17	9	2	2	NUM
ejpam-5042	17	10	)	)	PUNCT
ejpam-5042	17	11	(	(	PUNCT
ejpam-5042	17	12	2024	2024	NUM
ejpam-5042	17	13	)	)	PUNCT
ejpam-5042	17	14	,	,	PUNCT
ejpam-5042	17	15	1129	1129	NUM
ejpam-5042	17	16	-	-	SYM
ejpam-5042	17	17	1145	1145	NUM
ejpam-5042	17	18	1130	1130	NUM
ejpam-5042	17	19	pseudocomplemented	pseudocomplemente	VERB
ejpam-5042	17	20	lattices	lattice	NOUN
ejpam-5042	17	21	and	and	CCONJ
ejpam-5042	17	22	posets	poset	NOUN
ejpam-5042	18	1	and	and	CCONJ
ejpam-5042	19	1	demonstrated	demonstrate	VERB
ejpam-5042	19	2	their	their	PRON
ejpam-5042	19	3	roles	role	NOUN
ejpam-5042	19	4	in	in	ADP
ejpam-5042	19	5	algebraic	algebraic	ADJ
ejpam-5042	19	6	structures	structure	NOUN
ejpam-5042	19	7	.	.	PUNCT
ejpam-5042	20	1	they	they	PRON
ejpam-5042	20	2	defined	define	VERB
ejpam-5042	20	3	congruences	congruence	NOUN
ejpam-5042	20	4	and	and	CCONJ
ejpam-5042	20	5	filters	filter	NOUN
ejpam-5042	20	6	in	in	ADP
ejpam-5042	20	7	their	their	PRON
ejpam-5042	20	8	structures	structure	NOUN
ejpam-5042	20	9	,	,	PUNCT
ejpam-5042	20	10	derived	derive	VERB
ejpam-5042	20	11	mutual	mutual	ADJ
ejpam-5042	20	12	relationship	relationship	NOUN
ejpam-5042	20	13	between	between	ADP
ejpam-5042	20	14	them	they	PRON
ejpam-5042	20	15	and	and	CCONJ
ejpam-5042	20	16	described	describe	VERB
ejpam-5042	20	17	basic	basic	ADJ
ejpam-5042	20	18	properties	property	NOUN
ejpam-5042	20	19	of	of	ADP
ejpam-5042	20	20	congruences	congruence	NOUN
ejpam-5042	20	21	in	in	ADP
ejpam-5042	20	22	strongly	strongly	ADV
ejpam-5042	20	23	sectionally	sectionally	ADV
ejpam-5042	20	24	pseudocomplemented	pseudocomplemente	VERB
ejpam-5042	20	25	posets	poset	NOUN
ejpam-5042	20	26	.	.	PUNCT
ejpam-5042	21	1	later	later	ADV
ejpam-5042	21	2	,	,	PUNCT
ejpam-5042	21	3	the	the	DET
ejpam-5042	21	4	concept	concept	NOUN
ejpam-5042	21	5	of	of	ADP
ejpam-5042	21	6	a	a	DET
ejpam-5042	21	7	relative	relative	ADJ
ejpam-5042	21	8	pseudocomplemented	pseudocomplemented	ADJ
ejpam-5042	21	9	lattice	lattice	NOUN
ejpam-5042	21	10	was	be	AUX
ejpam-5042	21	11	introduced	introduce	VERB
ejpam-5042	21	12	by	by	ADP
ejpam-5042	21	13	r.	r.	PROPN
ejpam-5042	21	14	p.	p.	PROPN
ejpam-5042	21	15	dilworth(dilworth	dilworth(dilworth	PROPN
ejpam-5042	21	16	1939	1939	NUM
ejpam-5042	21	17	)	)	PUNCT
ejpam-5042	21	18	where	where	SCONJ
ejpam-5042	21	19	he	he	PRON
ejpam-5042	21	20	interpreted	interpret	VERB
ejpam-5042	21	21	relative	relative	ADJ
ejpam-5042	21	22	pseudocomplement	pseudocomplement	NOUN
ejpam-5042	21	23	as	as	ADP
ejpam-5042	21	24	logical	logical	ADJ
ejpam-5042	21	25	connective	connective	ADJ
ejpam-5042	21	26	implication	implication	NOUN
ejpam-5042	21	27	.	.	PUNCT
ejpam-5042	22	1	m.	m.	NOUN
ejpam-5042	22	2	mandelker[6	mandelker[6	PROPN
ejpam-5042	22	3	]	]	PUNCT
ejpam-5042	22	4	expanded	expand	VERB
ejpam-5042	22	5	on	on	ADP
ejpam-5042	22	6	this	this	DET
ejpam-5042	22	7	concept	concept	NOUN
ejpam-5042	22	8	by	by	ADP
ejpam-5042	22	9	introducing	introduce	VERB
ejpam-5042	22	10	and	and	CCONJ
ejpam-5042	22	11	investigating	investigate	VERB
ejpam-5042	22	12	the	the	DET
ejpam-5042	22	13	notions	notion	NOUN
ejpam-5042	22	14	of	of	ADP
ejpam-5042	22	15	relative	relative	ADJ
ejpam-5042	22	16	annihilators	annihilator	NOUN
ejpam-5042	22	17	in	in	ADP
ejpam-5042	22	18	lattices	lattice	NOUN
ejpam-5042	22	19	and	and	CCONJ
ejpam-5042	22	20	relatively	relatively	ADV
ejpam-5042	22	21	pseudo	pseudo	NOUN
ejpam-5042	22	22	-	-	ADJ
ejpam-5042	22	23	complemented	complemented	ADJ
ejpam-5042	22	24	lattices	lattice	NOUN
ejpam-5042	22	25	.	.	PUNCT
ejpam-5042	23	1	mandelker	mandelker	PROPN
ejpam-5042	23	2	proposed	propose	VERB
ejpam-5042	23	3	the	the	DET
ejpam-5042	23	4	annihilator	annihilator	NOUN
ejpam-5042	23	5	(	(	PUNCT
ejpam-5042	23	6	a	a	DET
ejpam-5042	23	7	,	,	PUNCT
ejpam-5042	23	8	b	b	NOUN
ejpam-5042	23	9	)	)	PUNCT
ejpam-5042	23	10	of	of	ADP
ejpam-5042	23	11	element	element	NOUN
ejpam-5042	23	12	a	a	DET
ejpam-5042	23	13	relative	relative	NOUN
ejpam-5042	23	14	to	to	ADP
ejpam-5042	23	15	b	b	NOUN
ejpam-5042	23	16	as	as	ADP
ejpam-5042	23	17	a	a	DET
ejpam-5042	23	18	natural	natural	ADJ
ejpam-5042	23	19	generalization	generalization	NOUN
ejpam-5042	23	20	of	of	ADP
ejpam-5042	23	21	the	the	DET
ejpam-5042	23	22	pseudo	pseudo	NOUN
ejpam-5042	23	23	-	-	NOUN
ejpam-5042	23	24	complement	complement	VERB
ejpam-5042	23	25	a	a	DET
ejpam-5042	23	26	∗	∗	NOUN
ejpam-5042	23	27	b.	b.	NOUN
ejpam-5042	24	1	it	it	PRON
ejpam-5042	24	2	represents	represent	VERB
ejpam-5042	24	3	the	the	DET
ejpam-5042	24	4	set	set	NOUN
ejpam-5042	24	5	of	of	ADP
ejpam-5042	24	6	elements	element	NOUN
ejpam-5042	24	7	x	x	PUNCT
ejpam-5042	24	8	satisfying	satisfy	VERB
ejpam-5042	24	9	a	a	DET
ejpam-5042	24	10	∩	∩	NOUN
ejpam-5042	24	11	x	x	SYM
ejpam-5042	24	12	≤	≤	PROPN
ejpam-5042	24	13	b.	b.	X
ejpam-5042	24	14	the	the	DET
ejpam-5042	24	15	greatest	great	ADJ
ejpam-5042	24	16	element	element	NOUN
ejpam-5042	24	17	of	of	ADP
ejpam-5042	24	18	(	(	PUNCT
ejpam-5042	24	19	a	a	DET
ejpam-5042	24	20	,	,	PUNCT
ejpam-5042	24	21	b	b	NOUN
ejpam-5042	24	22	)	)	PUNCT
ejpam-5042	24	23	,	,	PUNCT
ejpam-5042	24	24	if	if	SCONJ
ejpam-5042	24	25	it	it	PRON
ejpam-5042	24	26	exists	exist	VERB
ejpam-5042	24	27	,	,	PUNCT
ejpam-5042	24	28	is	be	AUX
ejpam-5042	24	29	defined	define	VERB
ejpam-5042	24	30	as	as	ADP
ejpam-5042	24	31	the	the	DET
ejpam-5042	24	32	relative	relative	ADJ
ejpam-5042	24	33	pseudo	pseudo	NOUN
ejpam-5042	24	34	-	-	NOUN
ejpam-5042	24	35	complement	complement	VERB
ejpam-5042	24	36	a	a	DET
ejpam-5042	24	37	∗	∗	X
ejpam-5042	24	38	b.	b.	PROPN
ejpam-5042	25	1	thus	thus	ADV
ejpam-5042	25	2	,	,	PUNCT
ejpam-5042	25	3	a	a	DET
ejpam-5042	25	4	lattice	lattice	NOUN
ejpam-5042	25	5	is	be	AUX
ejpam-5042	25	6	considered	consider	VERB
ejpam-5042	25	7	relatively	relatively	ADV
ejpam-5042	25	8	pseudo	pseudo	NOUN
ejpam-5042	25	9	-	-	VERB
ejpam-5042	25	10	complemented	complemented	ADJ
ejpam-5042	25	11	if	if	SCONJ
ejpam-5042	25	12	each	each	DET
ejpam-5042	25	13	annihilator	annihilator	NOUN
ejpam-5042	25	14	has	have	VERB
ejpam-5042	25	15	a	a	DET
ejpam-5042	25	16	greatest	great	ADJ
ejpam-5042	25	17	element	element	NOUN
ejpam-5042	25	18	,	,	PUNCT
ejpam-5042	25	19	making	make	VERB
ejpam-5042	25	20	it	it	PRON
ejpam-5042	25	21	a	a	DET
ejpam-5042	25	22	principal	principal	ADJ
ejpam-5042	25	23	ideal	ideal	NOUN
ejpam-5042	25	24	.	.	PUNCT
ejpam-5042	26	1	a	a	DET
ejpam-5042	26	2	dual	dual	ADJ
ejpam-5042	26	3	weakly	weakly	ADJ
ejpam-5042	26	4	complemented	complemented	ADJ
ejpam-5042	26	5	lattice	lattice	NOUN
ejpam-5042	26	6	was	be	AUX
ejpam-5042	26	7	introduced	introduce	VERB
ejpam-5042	26	8	by	by	ADP
ejpam-5042	26	9	wille[15	wille[15	NOUN
ejpam-5042	26	10	]	]	X
ejpam-5042	26	11	and	and	CCONJ
ejpam-5042	26	12	kwuida[13	kwuida[13	NOUN
ejpam-5042	26	13	]	]	X
ejpam-5042	26	14	.	.	PUNCT
ejpam-5042	27	1	their	their	PRON
ejpam-5042	27	2	contributions	contribution	NOUN
ejpam-5042	27	3	connected	connect	VERB
ejpam-5042	27	4	to	to	ADP
ejpam-5042	27	5	the	the	DET
ejpam-5042	27	6	notion	notion	NOUN
ejpam-5042	27	7	of	of	ADP
ejpam-5042	27	8	annihilators	annihilator	NOUN
ejpam-5042	27	9	of	of	ADP
ejpam-5042	27	10	distributive	distributive	ADJ
ejpam-5042	27	11	dual	dual	ADJ
ejpam-5042	27	12	weakly	weakly	ADJ
ejpam-5042	27	13	complemented	complemented	ADJ
ejpam-5042	27	14	lattice	lattice	NOUN
ejpam-5042	27	15	with	with	ADP
ejpam-5042	27	16	a	a	DET
ejpam-5042	27	17	certain	certain	ADJ
ejpam-5042	27	18	type	type	NOUN
ejpam-5042	27	19	of	of	ADP
ejpam-5042	27	20	ideals	ideal	NOUN
ejpam-5042	27	21	called	call	VERB
ejpam-5042	27	22	as	as	ADP
ejpam-5042	27	23	closed	close	VERB
ejpam-5042	27	24	ideals	ideal	NOUN
ejpam-5042	27	25	and	and	CCONJ
ejpam-5042	27	26	later	later	ADV
ejpam-5042	27	27	proved	prove	VERB
ejpam-5042	27	28	that	that	SCONJ
ejpam-5042	27	29	closed	closed	ADJ
ejpam-5042	27	30	ideals	ideal	NOUN
ejpam-5042	27	31	depend	depend	VERB
ejpam-5042	27	32	on	on	ADP
ejpam-5042	27	33	the	the	DET
ejpam-5042	27	34	dual	dual	ADJ
ejpam-5042	27	35	weak	weak	ADJ
ejpam-5042	27	36	complementation	complementation	NOUN
ejpam-5042	27	37	operation	operation	NOUN
ejpam-5042	27	38	on	on	ADP
ejpam-5042	27	39	the	the	DET
ejpam-5042	27	40	lattice	lattice	NOUN
ejpam-5042	27	41	of	of	ADP
ejpam-5042	27	42	all	all	DET
ejpam-5042	27	43	ideals	ideal	NOUN
ejpam-5042	27	44	i(l	i(l	PROPN
ejpam-5042	27	45	)	)	PUNCT
ejpam-5042	27	46	of	of	ADP
ejpam-5042	27	47	l.	l.	PROPN
ejpam-5042	27	48	eman	eman	PROPN
ejpam-5042	27	49	ghareeb	ghareeb	PROPN
ejpam-5042	27	50	rezk[9	rezk[9	PROPN
ejpam-5042	27	51	]	]	PUNCT
ejpam-5042	27	52	introduced	introduce	VERB
ejpam-5042	27	53	the	the	DET
ejpam-5042	27	54	concept	concept	NOUN
ejpam-5042	27	55	of	of	ADP
ejpam-5042	27	56	closed	closed	ADJ
ejpam-5042	27	57	ideals	ideal	NOUN
ejpam-5042	27	58	and	and	CCONJ
ejpam-5042	27	59	annihilators	annihilator	NOUN
ejpam-5042	27	60	over	over	ADP
ejpam-5042	27	61	the	the	DET
ejpam-5042	27	62	class	class	NOUN
ejpam-5042	27	63	of	of	ADP
ejpam-5042	27	64	distributive	distributive	ADJ
ejpam-5042	27	65	dual	dual	ADJ
ejpam-5042	27	66	weakly	weakly	ADJ
ejpam-5042	27	67	complemented	complemented	ADJ
ejpam-5042	27	68	lattices	lattice	NOUN
ejpam-5042	27	69	.	.	PUNCT
ejpam-5042	28	1	the	the	DET
ejpam-5042	28	2	connection	connection	NOUN
ejpam-5042	28	3	between	between	ADP
ejpam-5042	28	4	closed	close	VERB
ejpam-5042	28	5	ideals	ideal	NOUN
ejpam-5042	28	6	and	and	CCONJ
ejpam-5042	28	7	annihilators	annihilator	NOUN
ejpam-5042	28	8	in	in	ADP
ejpam-5042	28	9	this	this	DET
ejpam-5042	28	10	class	class	NOUN
ejpam-5042	28	11	was	be	AUX
ejpam-5042	28	12	obtained	obtain	VERB
ejpam-5042	28	13	.	.	PUNCT
ejpam-5042	29	1	m.	m.	PROPN
ejpam-5042	29	2	s.	s.	PROPN
ejpam-5042	29	3	rao[7	rao[7	PROPN
ejpam-5042	29	4	]	]	PUNCT
ejpam-5042	29	5	introduced	introduce	VERB
ejpam-5042	29	6	the	the	DET
ejpam-5042	29	7	concept	concept	NOUN
ejpam-5042	29	8	of	of	ADP
ejpam-5042	29	9	δ	δ	NOUN
ejpam-5042	29	10	-	-	PUNCT
ejpam-5042	29	11	ideals	ideal	NOUN
ejpam-5042	29	12	in	in	ADP
ejpam-5042	29	13	pseudo	pseudo	NOUN
ejpam-5042	29	14	-	-	ADJ
ejpam-5042	29	15	complemented	complement	VERB
ejpam-5042	29	16	distributive	distributive	ADJ
ejpam-5042	29	17	lattices	lattice	NOUN
ejpam-5042	29	18	and	and	CCONJ
ejpam-5042	29	19	then	then	ADV
ejpam-5042	29	20	stone	stone	NOUN
ejpam-5042	29	21	lattices	lattice	NOUN
ejpam-5042	29	22	are	be	AUX
ejpam-5042	29	23	characterized	characterize	VERB
ejpam-5042	29	24	in	in	ADP
ejpam-5042	29	25	terms	term	NOUN
ejpam-5042	29	26	of	of	ADP
ejpam-5042	29	27	δ	δ	NOUN
ejpam-5042	29	28	-	-	NOUN
ejpam-5042	29	29	ideals	ideal	NOUN
ejpam-5042	29	30	.	.	PUNCT
ejpam-5042	30	1	further	far	ADV
ejpam-5042	30	2	the	the	DET
ejpam-5042	30	3	properties	property	NOUN
ejpam-5042	30	4	of	of	ADP
ejpam-5042	30	5	normal	normal	ADJ
ejpam-5042	30	6	ideals	ideal	NOUN
ejpam-5042	30	7	of	of	ADP
ejpam-5042	30	8	pseudo	pseudo	NOUN
ejpam-5042	30	9	-	-	ADJ
ejpam-5042	30	10	complemented	complement	VERB
ejpam-5042	30	11	distributive	distributive	ADJ
ejpam-5042	30	12	lattices	lattice	NOUN
ejpam-5042	30	13	and	and	CCONJ
ejpam-5042	30	14	the	the	DET
ejpam-5042	30	15	characterization	characterization	NOUN
ejpam-5042	30	16	of	of	ADP
ejpam-5042	30	17	disjunctive	disjunctive	ADJ
ejpam-5042	30	18	lattices	lattice	NOUN
ejpam-5042	30	19	with	with	ADP
ejpam-5042	30	20	the	the	DET
ejpam-5042	30	21	help	help	NOUN
ejpam-5042	30	22	of	of	ADP
ejpam-5042	30	23	normal	normal	ADJ
ejpam-5042	30	24	ideals	ideal	NOUN
ejpam-5042	30	25	was	be	AUX
ejpam-5042	30	26	studied	study	VERB
ejpam-5042	30	27	by	by	ADP
ejpam-5042	30	28	m.	m.	NOUN
ejpam-5042	30	29	s.	s.	PROPN
ejpam-5042	30	30	rao	rao	PROPN
ejpam-5042	30	31	et	et	PROPN
ejpam-5042	30	32	al.[8	al.[8	PROPN
ejpam-5042	30	33	]	]	PUNCT
ejpam-5042	30	34	the	the	DET
ejpam-5042	30	35	theory	theory	NOUN
ejpam-5042	30	36	of	of	ADP
ejpam-5042	30	37	pseudo	pseudo	NOUN
ejpam-5042	30	38	-	-	NOUN
ejpam-5042	30	39	complements	complement	NOUN
ejpam-5042	30	40	for	for	ADP
ejpam-5042	30	41	posets	poset	NOUN
ejpam-5042	30	42	was	be	AUX
ejpam-5042	30	43	developed	develop	VERB
ejpam-5042	30	44	by	by	ADP
ejpam-5042	30	45	p.	p.	PROPN
ejpam-5042	30	46	v.	v.	PROPN
ejpam-5042	31	1	venkatanarasimhan	venkatanarasimhan	PROPN
ejpam-5042	32	1	[	[	X
ejpam-5042	32	2	14	14	NUM
ejpam-5042	32	3	]	]	PUNCT
ejpam-5042	32	4	,	,	PUNCT
ejpam-5042	32	5	who	who	PRON
ejpam-5042	32	6	introduced	introduce	VERB
ejpam-5042	32	7	the	the	DET
ejpam-5042	32	8	concepts	concept	NOUN
ejpam-5042	32	9	of	of	ADP
ejpam-5042	32	10	ideals	ideal	NOUN
ejpam-5042	32	11	and	and	CCONJ
ejpam-5042	32	12	semi	semi	NOUN
ejpam-5042	32	13	-	-	NOUN
ejpam-5042	32	14	ideals	ideal	NOUN
ejpam-5042	32	15	and	and	CCONJ
ejpam-5042	32	16	derived	derive	VERB
ejpam-5042	32	17	several	several	ADJ
ejpam-5042	32	18	results	result	NOUN
ejpam-5042	32	19	that	that	PRON
ejpam-5042	32	20	paved	pave	VERB
ejpam-5042	32	21	the	the	DET
ejpam-5042	32	22	way	way	NOUN
ejpam-5042	32	23	for	for	ADP
ejpam-5042	32	24	research	research	NOUN
ejpam-5042	32	25	on	on	ADP
ejpam-5042	32	26	pseudo	pseudo	NOUN
ejpam-5042	32	27	-	-	NOUN
ejpam-5042	32	28	complements	complement	NOUN
ejpam-5042	32	29	in	in	ADP
ejpam-5042	32	30	distributive	distributive	ADJ
ejpam-5042	32	31	lattices	lattice	NOUN
ejpam-5042	32	32	.	.	PUNCT
ejpam-5042	33	1	these	these	DET
ejpam-5042	33	2	findings	finding	NOUN
ejpam-5042	33	3	revealed	reveal	VERB
ejpam-5042	33	4	that	that	SCONJ
ejpam-5042	33	5	if	if	SCONJ
ejpam-5042	33	6	every	every	DET
ejpam-5042	33	7	element	element	NOUN
ejpam-5042	33	8	in	in	ADP
ejpam-5042	33	9	a	a	DET
ejpam-5042	33	10	pseudo	pseudo	NOUN
ejpam-5042	33	11	-	-	ADJ
ejpam-5042	33	12	complemented	complement	VERB
ejpam-5042	33	13	semilattice	semilattice	NOUN
ejpam-5042	33	14	or	or	CCONJ
ejpam-5042	33	15	dual	dual	ADJ
ejpam-5042	33	16	semilattice	semilattice	NOUN
ejpam-5042	33	17	is	be	AUX
ejpam-5042	33	18	normal	normal	ADJ
ejpam-5042	33	19	,	,	PUNCT
ejpam-5042	33	20	the	the	DET
ejpam-5042	33	21	algebra	algebra	NOUN
ejpam-5042	33	22	can	can	AUX
ejpam-5042	33	23	be	be	AUX
ejpam-5042	33	24	classified	classify	VERB
ejpam-5042	33	25	as	as	ADP
ejpam-5042	33	26	a	a	DET
ejpam-5042	33	27	boolean	boolean	ADJ
ejpam-5042	33	28	algebra	algebra	NOUN
ejpam-5042	33	29	.	.	PUNCT
ejpam-5042	34	1	this	this	DET
ejpam-5042	34	2	conclusion	conclusion	NOUN
ejpam-5042	34	3	led	lead	VERB
ejpam-5042	34	4	to	to	ADP
ejpam-5042	34	5	new	new	ADJ
ejpam-5042	34	6	proofs	proof	NOUN
ejpam-5042	34	7	for	for	ADP
ejpam-5042	34	8	well	well	ADV
ejpam-5042	34	9	-	-	PUNCT
ejpam-5042	34	10	known	know	VERB
ejpam-5042	34	11	theorems	theorem	NOUN
ejpam-5042	34	12	,	,	PUNCT
ejpam-5042	34	13	such	such	ADJ
ejpam-5042	34	14	as	as	ADP
ejpam-5042	34	15	the	the	DET
ejpam-5042	34	16	existence	existence	NOUN
ejpam-5042	34	17	of	of	ADP
ejpam-5042	34	18	maximal	maximal	ADJ
ejpam-5042	34	19	ideals	ideal	NOUN
ejpam-5042	34	20	in	in	ADP
ejpam-5042	34	21	posets	poset	NOUN
ejpam-5042	34	22	and	and	CCONJ
ejpam-5042	34	23	the	the	DET
ejpam-5042	34	24	product	product	NOUN
ejpam-5042	34	25	of	of	ADP
ejpam-5042	34	26	all	all	DET
ejpam-5042	34	27	maximal	maximal	ADJ
ejpam-5042	34	28	dual	dual	ADJ
ejpam-5042	34	29	ideals	ideal	NOUN
ejpam-5042	34	30	being	be	AUX
ejpam-5042	34	31	the	the	DET
ejpam-5042	34	32	dual	dual	ADJ
ejpam-5042	34	33	ideal	ideal	NOUN
ejpam-5042	34	34	of	of	ADP
ejpam-5042	34	35	dense	dense	ADJ
ejpam-5042	34	36	components	component	NOUN
ejpam-5042	34	37	in	in	ADP
ejpam-5042	34	38	a	a	DET
ejpam-5042	34	39	poset	poset	NOUN
ejpam-5042	34	40	with	with	ADP
ejpam-5042	34	41	a	a	DET
ejpam-5042	34	42	zero	zero	NUM
ejpam-5042	34	43	element	element	NOUN
ejpam-5042	34	44	.	.	PUNCT
ejpam-5042	35	1	u.	u.	PROPN
ejpam-5042	35	2	m.	m.	PROPN
ejpam-5042	35	3	swamy	swamy	PROPN
ejpam-5042	35	4	and	and	CCONJ
ejpam-5042	35	5	g.	g.	PROPN
ejpam-5042	35	6	c.	c.	PROPN
ejpam-5042	35	7	rao[11	rao[11	PROPN
ejpam-5042	35	8	]	]	PUNCT
ejpam-5042	35	9	introduced	introduce	VERB
ejpam-5042	35	10	the	the	DET
ejpam-5042	35	11	concept	concept	NOUN
ejpam-5042	35	12	of	of	ADP
ejpam-5042	35	13	an	an	DET
ejpam-5042	35	14	almost	almost	ADV
ejpam-5042	35	15	distributive	distributive	ADJ
ejpam-5042	35	16	lattice	lattice	NOUN
ejpam-5042	35	17	(	(	PUNCT
ejpam-5042	35	18	adl	adl	PROPN
ejpam-5042	35	19	)	)	PUNCT
ejpam-5042	35	20	as	as	ADP
ejpam-5042	35	21	a	a	DET
ejpam-5042	35	22	unifying	unifying	ADJ
ejpam-5042	35	23	abstraction	abstraction	NOUN
ejpam-5042	35	24	for	for	ADP
ejpam-5042	35	25	various	various	ADJ
ejpam-5042	35	26	lattice	lattice	ADJ
ejpam-5042	35	27	-	-	PUNCT
ejpam-5042	35	28	theoretic	theoretic	NOUN
ejpam-5042	35	29	generalizations	generalization	NOUN
ejpam-5042	35	30	of	of	ADP
ejpam-5042	35	31	boolean	boolean	ADJ
ejpam-5042	35	32	algebras	algebra	NOUN
ejpam-5042	35	33	and	and	CCONJ
ejpam-5042	35	34	boolean	boolean	ADJ
ejpam-5042	35	35	rings	ring	NOUN
ejpam-5042	35	36	.	.	PUNCT
ejpam-5042	36	1	furthermore	furthermore	ADV
ejpam-5042	36	2	,	,	PUNCT
ejpam-5042	36	3	in	in	ADP
ejpam-5042	36	4	collaboration	collaboration	NOUN
ejpam-5042	36	5	with	with	ADP
ejpam-5042	36	6	g.	g.	PROPN
ejpam-5042	36	7	n.	n.	PROPN
ejpam-5042	36	8	rao[12	rao[12	PROPN
ejpam-5042	36	9	]	]	PUNCT
ejpam-5042	36	10	,	,	PUNCT
ejpam-5042	36	11	they	they	PRON
ejpam-5042	36	12	extended	extend	VERB
ejpam-5042	36	13	the	the	DET
ejpam-5042	36	14	concept	concept	NOUN
ejpam-5042	36	15	of	of	ADP
ejpam-5042	36	16	pseudo	pseudo	NOUN
ejpam-5042	36	17	-	-	NOUN
ejpam-5042	36	18	complementation	complementation	NOUN
ejpam-5042	36	19	to	to	ADP
ejpam-5042	36	20	almost	almost	ADV
ejpam-5042	36	21	distributive	distributive	ADJ
ejpam-5042	36	22	lattices	lattice	NOUN
ejpam-5042	36	23	and	and	CCONJ
ejpam-5042	36	24	demonstrated	demonstrate	VERB
ejpam-5042	36	25	that	that	SCONJ
ejpam-5042	36	26	the	the	DET
ejpam-5042	36	27	class	class	NOUN
ejpam-5042	36	28	of	of	ADP
ejpam-5042	36	29	pseudo	pseudo	NOUN
ejpam-5042	36	30	-	-	VERB
ejpam-5042	36	31	complemented	complement	VERB
ejpam-5042	36	32	adls	adls	NOUN
ejpam-5042	36	33	is	be	AUX
ejpam-5042	36	34	equationally	equationally	ADV
ejpam-5042	36	35	definable	definable	ADJ
ejpam-5042	36	36	.	.	PUNCT
ejpam-5042	37	1	they	they	PRON
ejpam-5042	37	2	also	also	ADV
ejpam-5042	37	3	explored	explore	VERB
ejpam-5042	37	4	the	the	DET
ejpam-5042	37	5	relationship	relationship	NOUN
ejpam-5042	37	6	between	between	ADP
ejpam-5042	37	7	annihilator	annihilator	PROPN
ejpam-5042	37	8	ideals	ideal	NOUN
ejpam-5042	37	9	and	and	CCONJ
ejpam-5042	37	10	pseudo	pseudo	NOUN
ejpam-5042	37	11	-	-	NOUN
ejpam-5042	37	12	complementations	complementation	NOUN
ejpam-5042	37	13	in	in	ADP
ejpam-5042	37	14	an	an	DET
ejpam-5042	37	15	adl	adl	NOUN
ejpam-5042	37	16	and	and	CCONJ
ejpam-5042	37	17	established	establish	VERB
ejpam-5042	37	18	a	a	DET
ejpam-5042	37	19	one	one	NUM
ejpam-5042	37	20	-	-	PUNCT
ejpam-5042	37	21	to	to	ADP
ejpam-5042	37	22	-	-	PUNCT
ejpam-5042	37	23	one	one	NUM
ejpam-5042	37	24	correspondence	correspondence	NOUN
ejpam-5042	37	25	between	between	ADP
ejpam-5042	37	26	pseudo	pseudo	NOUN
ejpam-5042	37	27	-	-	NOUN
ejpam-5042	37	28	complementations	complementation	NOUN
ejpam-5042	37	29	and	and	CCONJ
ejpam-5042	37	30	maximal	maximal	ADJ
ejpam-5042	37	31	elements	element	NOUN
ejpam-5042	37	32	in	in	ADP
ejpam-5042	37	33	an	an	DET
ejpam-5042	37	34	adl	adl	NOUN
ejpam-5042	37	35	assuming	assume	VERB
ejpam-5042	37	36	the	the	DET
ejpam-5042	37	37	existence	existence	NOUN
ejpam-5042	37	38	of	of	ADP
ejpam-5042	37	39	one	one	NUM
ejpam-5042	37	40	pseudo	pseudo	NOUN
ejpam-5042	37	41	-	-	NOUN
ejpam-5042	37	42	complementation	complementation	NOUN
ejpam-5042	37	43	.	.	PUNCT
ejpam-5042	38	1	recently	recently	ADV
ejpam-5042	38	2	,	,	PUNCT
ejpam-5042	38	3	r.	r.	PROPN
ejpam-5042	38	4	k.	k.	PROPN
ejpam-5042	38	5	bandaru	bandaru	PROPN
ejpam-5042	38	6	et	et	PROPN
ejpam-5042	38	7	al.[1	al.[1	PROPN
ejpam-5042	38	8	]	]	PUNCT
ejpam-5042	38	9	introduced	introduce	VERB
ejpam-5042	38	10	the	the	DET
ejpam-5042	38	11	concept	concept	NOUN
ejpam-5042	38	12	of	of	ADP
ejpam-5042	38	13	a	a	DET
ejpam-5042	38	14	paradistributive	paradistributive	ADJ
ejpam-5042	38	15	latticoid(pdl	latticoid(pdl	NOUN
ejpam-5042	38	16	)	)	PUNCT
ejpam-5042	38	17	as	as	ADP
ejpam-5042	38	18	a	a	DET
ejpam-5042	38	19	generalization	generalization	NOUN
ejpam-5042	38	20	of	of	ADP
ejpam-5042	38	21	distributive	distributive	ADJ
ejpam-5042	38	22	lattice	lattice	NOUN
ejpam-5042	38	23	and	and	CCONJ
ejpam-5042	38	24	investigated	investigate	VERB
ejpam-5042	38	25	its	its	PRON
ejpam-5042	38	26	properties	property	NOUN
ejpam-5042	38	27	.	.	PUNCT
ejpam-5042	39	1	they	they	PRON
ejpam-5042	39	2	introduced	introduce	VERB
ejpam-5042	39	3	the	the	DET
ejpam-5042	39	4	notions	notion	NOUN
ejpam-5042	39	5	of	of	ADP
ejpam-5042	39	6	an	an	DET
ejpam-5042	39	7	ideal	ideal	NOUN
ejpam-5042	39	8	and	and	CCONJ
ejpam-5042	39	9	a	a	DET
ejpam-5042	39	10	filter	filter	NOUN
ejpam-5042	39	11	in	in	ADP
ejpam-5042	39	12	a	a	DET
ejpam-5042	39	13	pdl	pdl	NOUN
ejpam-5042	39	14	and	and	CCONJ
ejpam-5042	39	15	studied	study	VERB
ejpam-5042	39	16	their	their	PRON
ejpam-5042	39	17	properties	property	NOUN
ejpam-5042	39	18	.	.	PUNCT
ejpam-5042	40	1	they	they	PRON
ejpam-5042	40	2	proved	prove	VERB
ejpam-5042	40	3	a	a	DET
ejpam-5042	40	4	subdirect	subdirect	NOUN
ejpam-5042	40	5	representation	representation	NOUN
ejpam-5042	40	6	theorem	theorem	NOUN
ejpam-5042	40	7	for	for	ADP
ejpam-5042	40	8	associative	associative	ADJ
ejpam-5042	40	9	pdls	pdl	NOUN
ejpam-5042	40	10	which	which	PRON
ejpam-5042	40	11	simplifies	simplify	VERB
ejpam-5042	40	12	r.	r.	PROPN
ejpam-5042	40	13	shukla	shukla	PROPN
ejpam-5042	40	14	et	et	PROPN
ejpam-5042	40	15	al	al	PROPN
ejpam-5042	40	16	.	.	PUNCT
ejpam-5042	40	17	/	/	SYM
ejpam-5042	40	18	eur	eur	PROPN
ejpam-5042	40	19	.	.	PUNCT
ejpam-5042	41	1	j.	j.	PROPN
ejpam-5042	41	2	pure	pure	PROPN
ejpam-5042	41	3	appl	appl	PROPN
ejpam-5042	41	4	.	.	PROPN
ejpam-5042	41	5	math	math	PROPN
ejpam-5042	41	6	,	,	PUNCT
ejpam-5042	41	7	17	17	NUM
ejpam-5042	41	8	(	(	PUNCT
ejpam-5042	41	9	2	2	NUM
ejpam-5042	41	10	)	)	PUNCT
ejpam-5042	41	11	(	(	PUNCT
ejpam-5042	41	12	2024	2024	NUM
ejpam-5042	41	13	)	)	PUNCT
ejpam-5042	41	14	,	,	PUNCT
ejpam-5042	41	15	1129	1129	NUM
ejpam-5042	41	16	-	-	SYM
ejpam-5042	41	17	1145	1145	NUM
ejpam-5042	41	18	1131	1131	NUM
ejpam-5042	41	19	many	many	ADJ
ejpam-5042	41	20	results	result	NOUN
ejpam-5042	41	21	in	in	ADP
ejpam-5042	41	22	pdls	pdl	NOUN
ejpam-5042	41	23	.	.	PUNCT
ejpam-5042	42	1	the	the	DET
ejpam-5042	42	2	main	main	ADJ
ejpam-5042	42	3	objective	objective	NOUN
ejpam-5042	42	4	of	of	ADP
ejpam-5042	42	5	this	this	DET
ejpam-5042	42	6	paper	paper	NOUN
ejpam-5042	42	7	is	be	AUX
ejpam-5042	42	8	to	to	PART
ejpam-5042	42	9	introduce	introduce	VERB
ejpam-5042	42	10	the	the	DET
ejpam-5042	42	11	concept	concept	NOUN
ejpam-5042	42	12	of	of	ADP
ejpam-5042	42	13	parapseudo	parapseudo	NOUN
ejpam-5042	42	14	-	-	NOUN
ejpam-5042	42	15	complementation	complementation	NOUN
ejpam-5042	42	16	in	in	ADP
ejpam-5042	42	17	a	a	DET
ejpam-5042	42	18	paradistributive	paradistributive	ADJ
ejpam-5042	42	19	latticoid	latticoid	NOUN
ejpam-5042	42	20	(	(	PUNCT
ejpam-5042	42	21	pdl	pdl	NOUN
ejpam-5042	42	22	)	)	PUNCT
ejpam-5042	42	23	and	and	CCONJ
ejpam-5042	42	24	investigate	investigate	VERB
ejpam-5042	42	25	its	its	PRON
ejpam-5042	42	26	properties	property	NOUN
ejpam-5042	42	27	.	.	PUNCT
ejpam-5042	43	1	we	we	PRON
ejpam-5042	43	2	provide	provide	VERB
ejpam-5042	43	3	examples	example	NOUN
ejpam-5042	43	4	to	to	PART
ejpam-5042	43	5	illustrate	illustrate	VERB
ejpam-5042	43	6	the	the	DET
ejpam-5042	43	7	independence	independence	NOUN
ejpam-5042	43	8	of	of	ADP
ejpam-5042	43	9	the	the	DET
ejpam-5042	43	10	axioms	axiom	NOUN
ejpam-5042	43	11	defined	define	VERB
ejpam-5042	43	12	for	for	ADP
ejpam-5042	43	13	parapseudo	parapseudo	NOUN
ejpam-5042	43	14	-	-	NOUN
ejpam-5042	43	15	complementation	complementation	NOUN
ejpam-5042	43	16	.	.	PUNCT
ejpam-5042	44	1	specifically	specifically	ADV
ejpam-5042	44	2	,	,	PUNCT
ejpam-5042	44	3	we	we	PRON
ejpam-5042	44	4	prove	prove	VERB
ejpam-5042	44	5	that	that	SCONJ
ejpam-5042	44	6	a	a	DET
ejpam-5042	44	7	pdl	pdl	NOUN
ejpam-5042	44	8	v	v	NOUN
ejpam-5042	44	9	is	be	AUX
ejpam-5042	44	10	parapseudo	parapseudo	NOUN
ejpam-5042	44	11	-	-	PUNCT
ejpam-5042	44	12	complemented	complemented	ADJ
ejpam-5042	44	13	if	if	SCONJ
ejpam-5042	45	1	and	and	CCONJ
ejpam-5042	45	2	only	only	ADV
ejpam-5042	45	3	if	if	SCONJ
ejpam-5042	45	4	the	the	DET
ejpam-5042	45	5	annihilator	annihilator	PROPN
ejpam-5042	45	6	filter	filter	NOUN
ejpam-5042	45	7	[	[	X
ejpam-5042	45	8	ρ]•	ρ]•	PROPN
ejpam-5042	45	9	is	be	AUX
ejpam-5042	45	10	a	a	DET
ejpam-5042	45	11	principal	principal	ADJ
ejpam-5042	45	12	filter	filter	NOUN
ejpam-5042	45	13	for	for	ADP
ejpam-5042	45	14	any	any	DET
ejpam-5042	45	15	ρ	ρ	PROPN
ejpam-5042	45	16	∈	∈	PROPN
ejpam-5042	45	17	v	v	NOUN
ejpam-5042	45	18	.	.	PUNCT
ejpam-5042	46	1	additionally	additionally	ADV
ejpam-5042	46	2	,	,	PUNCT
ejpam-5042	46	3	we	we	PRON
ejpam-5042	46	4	establish	establish	VERB
ejpam-5042	46	5	a	a	DET
ejpam-5042	46	6	one	one	NUM
ejpam-5042	46	7	-	-	PUNCT
ejpam-5042	46	8	to	to	ADP
ejpam-5042	46	9	-	-	PUNCT
ejpam-5042	46	10	one	one	NUM
ejpam-5042	46	11	correspondence	correspondence	NOUN
ejpam-5042	46	12	between	between	ADP
ejpam-5042	46	13	the	the	DET
ejpam-5042	46	14	set	set	NOUN
ejpam-5042	46	15	of	of	ADP
ejpam-5042	46	16	all	all	DET
ejpam-5042	46	17	minimal	minimal	ADJ
ejpam-5042	46	18	elements	element	NOUN
ejpam-5042	46	19	and	and	CCONJ
ejpam-5042	46	20	the	the	DET
ejpam-5042	46	21	set	set	NOUN
ejpam-5042	46	22	of	of	ADP
ejpam-5042	46	23	all	all	DET
ejpam-5042	46	24	parapseudocomplementations	parapseudocomplementation	NOUN
ejpam-5042	46	25	in	in	ADP
ejpam-5042	46	26	v	v	NOUN
ejpam-5042	46	27	.	.	PUNCT
ejpam-5042	47	1	finally	finally	ADV
ejpam-5042	47	2	,	,	PUNCT
ejpam-5042	47	3	we	we	PRON
ejpam-5042	47	4	demonstrate	demonstrate	VERB
ejpam-5042	47	5	that	that	SCONJ
ejpam-5042	47	6	the	the	DET
ejpam-5042	47	7	corresponding	corresponding	ADJ
ejpam-5042	47	8	boolean	boolean	ADJ
ejpam-5042	47	9	algebras	algebra	NOUN
ejpam-5042	47	10	v	v	ADP
ejpam-5042	47	11	♦	♦	PROPN
ejpam-5042	47	12	and	and	CCONJ
ejpam-5042	47	13	v	v	NOUN
ejpam-5042	47	14	♢	♢	PROPN
ejpam-5042	47	15	are	be	AUX
ejpam-5042	47	16	isomorphic	isomorphic	ADJ
ejpam-5042	47	17	.	.	PUNCT
ejpam-5042	48	1	the	the	DET
ejpam-5042	48	2	remainder	remainder	NOUN
ejpam-5042	48	3	of	of	ADP
ejpam-5042	48	4	this	this	DET
ejpam-5042	48	5	paper	paper	NOUN
ejpam-5042	48	6	is	be	AUX
ejpam-5042	48	7	structured	structure	VERB
ejpam-5042	48	8	as	as	SCONJ
ejpam-5042	48	9	follows	follow	VERB
ejpam-5042	48	10	:	:	PUNCT
ejpam-5042	48	11	section	section	NOUN
ejpam-5042	48	12	1	1	NUM
ejpam-5042	48	13	provides	provide	VERB
ejpam-5042	48	14	a	a	DET
ejpam-5042	48	15	brief	brief	ADJ
ejpam-5042	48	16	introduction	introduction	NOUN
ejpam-5042	48	17	to	to	ADP
ejpam-5042	48	18	the	the	DET
ejpam-5042	48	19	concept	concept	NOUN
ejpam-5042	48	20	of	of	ADP
ejpam-5042	48	21	pseudo	pseudo	NOUN
ejpam-5042	48	22	-	-	NOUN
ejpam-5042	48	23	complementation	complementation	NOUN
ejpam-5042	48	24	,	,	PUNCT
ejpam-5042	48	25	followed	follow	VERB
ejpam-5042	48	26	by	by	ADP
ejpam-5042	48	27	preliminaries	preliminary	NOUN
ejpam-5042	48	28	in	in	ADP
ejpam-5042	48	29	section	section	NOUN
ejpam-5042	48	30	2	2	NUM
ejpam-5042	48	31	.	.	PUNCT
ejpam-5042	48	32	section	section	NOUN
ejpam-5042	48	33	3	3	NUM
ejpam-5042	48	34	presents	present	VERB
ejpam-5042	48	35	the	the	DET
ejpam-5042	48	36	definition	definition	NOUN
ejpam-5042	48	37	of	of	ADP
ejpam-5042	48	38	parapseudo	parapseudo	NOUN
ejpam-5042	48	39	-	-	NOUN
ejpam-5042	48	40	complementation	complementation	NOUN
ejpam-5042	48	41	on	on	ADP
ejpam-5042	48	42	a	a	DET
ejpam-5042	48	43	pdl	pdl	NOUN
ejpam-5042	48	44	,	,	PUNCT
ejpam-5042	48	45	highlighting	highlight	VERB
ejpam-5042	48	46	the	the	DET
ejpam-5042	48	47	independence	independence	NOUN
ejpam-5042	48	48	of	of	ADP
ejpam-5042	48	49	the	the	DET
ejpam-5042	48	50	axioms	axiom	NOUN
ejpam-5042	48	51	through	through	ADP
ejpam-5042	48	52	illustrative	illustrative	ADJ
ejpam-5042	48	53	examples	example	NOUN
ejpam-5042	48	54	.	.	PUNCT
ejpam-5042	49	1	in	in	ADP
ejpam-5042	49	2	section	section	NOUN
ejpam-5042	49	3	4	4	NUM
ejpam-5042	49	4	,	,	PUNCT
ejpam-5042	49	5	we	we	PRON
ejpam-5042	49	6	delve	delve	VERB
ejpam-5042	49	7	into	into	ADP
ejpam-5042	49	8	the	the	DET
ejpam-5042	49	9	heart	heart	NOUN
ejpam-5042	49	10	of	of	ADP
ejpam-5042	49	11	our	our	PRON
ejpam-5042	49	12	investigation	investigation	NOUN
ejpam-5042	49	13	by	by	ADP
ejpam-5042	49	14	proving	prove	VERB
ejpam-5042	49	15	the	the	DET
ejpam-5042	49	16	necessary	necessary	ADJ
ejpam-5042	49	17	and	and	CCONJ
ejpam-5042	49	18	sufficient	sufficient	ADJ
ejpam-5042	49	19	conditions	condition	NOUN
ejpam-5042	49	20	for	for	ADP
ejpam-5042	49	21	a	a	DET
ejpam-5042	49	22	paradistributive	paradistributive	ADJ
ejpam-5042	49	23	latticoid	latticoid	NOUN
ejpam-5042	49	24	(	(	PUNCT
ejpam-5042	49	25	pdl	pdl	NOUN
ejpam-5042	49	26	)	)	PUNCT
ejpam-5042	49	27	with	with	ADP
ejpam-5042	49	28	a	a	DET
ejpam-5042	49	29	minimal	minimal	ADJ
ejpam-5042	49	30	element	element	NOUN
ejpam-5042	49	31	to	to	PART
ejpam-5042	49	32	be	be	AUX
ejpam-5042	49	33	parapseudo	parapseudo	NOUN
ejpam-5042	49	34	-	-	VERB
ejpam-5042	49	35	complemented	complement	VERB
ejpam-5042	49	36	.	.	PUNCT
ejpam-5042	50	1	additionally	additionally	ADV
ejpam-5042	50	2	,	,	PUNCT
ejpam-5042	50	3	we	we	PRON
ejpam-5042	50	4	establish	establish	VERB
ejpam-5042	50	5	that	that	SCONJ
ejpam-5042	50	6	the	the	DET
ejpam-5042	50	7	class	class	NOUN
ejpam-5042	50	8	of	of	ADP
ejpam-5042	50	9	parapseudo	parapseudo	NOUN
ejpam-5042	50	10	-	-	PUNCT
ejpam-5042	50	11	complemented	complement	VERB
ejpam-5042	50	12	pdls	pdl	NOUN
ejpam-5042	50	13	is	be	AUX
ejpam-5042	50	14	equationally	equationally	ADV
ejpam-5042	50	15	definable	definable	ADJ
ejpam-5042	50	16	,	,	PUNCT
ejpam-5042	50	17	providing	provide	VERB
ejpam-5042	50	18	a	a	DET
ejpam-5042	50	19	solid	solid	ADJ
ejpam-5042	50	20	foundation	foundation	NOUN
ejpam-5042	50	21	for	for	ADP
ejpam-5042	50	22	further	further	ADJ
ejpam-5042	50	23	exploration	exploration	NOUN
ejpam-5042	50	24	of	of	ADP
ejpam-5042	50	25	this	this	DET
ejpam-5042	50	26	concept	concept	NOUN
ejpam-5042	50	27	.	.	PUNCT
ejpam-5042	51	1	moving	move	VERB
ejpam-5042	51	2	forward	forward	ADV
ejpam-5042	51	3	to	to	ADP
ejpam-5042	51	4	section	section	NOUN
ejpam-5042	51	5	5	5	NUM
ejpam-5042	51	6	,	,	PUNCT
ejpam-5042	51	7	we	we	PRON
ejpam-5042	51	8	focus	focus	VERB
ejpam-5042	51	9	on	on	ADP
ejpam-5042	51	10	the	the	DET
ejpam-5042	51	11	independence	independence	NOUN
ejpam-5042	51	12	of	of	ADP
ejpam-5042	51	13	the	the	DET
ejpam-5042	51	14	parapseudo	parapseudo	NOUN
ejpam-5042	51	15	-	-	PUNCT
ejpam-5042	51	16	complementation	complementation	NOUN
ejpam-5042	51	17	♦	♦	NOUN
ejpam-5042	51	18	within	within	ADP
ejpam-5042	51	19	the	the	DET
ejpam-5042	51	20	corresponding	corresponding	ADJ
ejpam-5042	51	21	boolean	boolean	ADJ
ejpam-5042	51	22	algebra	algebra	NOUN
ejpam-5042	51	23	v	v	ADP
ejpam-5042	51	24	♦	♦	PROPN
ejpam-5042	51	25	.	.	PUNCT
ejpam-5042	52	1	by	by	ADP
ejpam-5042	52	2	presenting	present	VERB
ejpam-5042	52	3	a	a	DET
ejpam-5042	52	4	rigorous	rigorous	ADJ
ejpam-5042	52	5	proof	proof	NOUN
ejpam-5042	52	6	,	,	PUNCT
ejpam-5042	52	7	we	we	PRON
ejpam-5042	52	8	demonstrate	demonstrate	VERB
ejpam-5042	52	9	that	that	SCONJ
ejpam-5042	52	10	the	the	DET
ejpam-5042	52	11	structure	structure	NOUN
ejpam-5042	52	12	and	and	CCONJ
ejpam-5042	52	13	properties	property	NOUN
ejpam-5042	52	14	of	of	ADP
ejpam-5042	52	15	v	v	NOUN
ejpam-5042	52	16	♦	♦	PROPN
ejpam-5042	52	17	are	be	AUX
ejpam-5042	52	18	not	not	PART
ejpam-5042	52	19	affected	affect	VERB
ejpam-5042	52	20	by	by	ADP
ejpam-5042	52	21	the	the	DET
ejpam-5042	52	22	specific	specific	ADJ
ejpam-5042	52	23	choice	choice	NOUN
ejpam-5042	52	24	of	of	ADP
ejpam-5042	52	25	parapseudo	parapseudo	NOUN
ejpam-5042	52	26	-	-	NOUN
ejpam-5042	52	27	complementation	complementation	NOUN
ejpam-5042	52	28	.	.	PUNCT
ejpam-5042	53	1	this	this	DET
ejpam-5042	53	2	insight	insight	NOUN
ejpam-5042	53	3	enhances	enhance	VERB
ejpam-5042	53	4	our	our	PRON
ejpam-5042	53	5	understanding	understanding	NOUN
ejpam-5042	53	6	of	of	ADP
ejpam-5042	53	7	the	the	DET
ejpam-5042	53	8	relationship	relationship	NOUN
ejpam-5042	53	9	between	between	ADP
ejpam-5042	53	10	parapseudo	parapseudo	NOUN
ejpam-5042	53	11	-	-	NOUN
ejpam-5042	53	12	complementation	complementation	NOUN
ejpam-5042	53	13	and	and	CCONJ
ejpam-5042	53	14	the	the	DET
ejpam-5042	53	15	underlying	underlying	ADJ
ejpam-5042	53	16	boolean	boolean	ADJ
ejpam-5042	53	17	algebra	algebra	NOUN
ejpam-5042	53	18	.	.	PUNCT
ejpam-5042	54	1	in	in	ADP
ejpam-5042	54	2	summary	summary	NOUN
ejpam-5042	54	3	,	,	PUNCT
ejpam-5042	54	4	through	through	ADP
ejpam-5042	54	5	our	our	PRON
ejpam-5042	54	6	research	research	NOUN
ejpam-5042	54	7	,	,	PUNCT
ejpam-5042	54	8	we	we	PRON
ejpam-5042	54	9	establish	establish	VERB
ejpam-5042	54	10	the	the	DET
ejpam-5042	54	11	necessary	necessary	ADJ
ejpam-5042	54	12	and	and	CCONJ
ejpam-5042	54	13	sufficient	sufficient	ADJ
ejpam-5042	54	14	conditions	condition	NOUN
ejpam-5042	54	15	for	for	ADP
ejpam-5042	54	16	parapseudo	parapseudo	NOUN
ejpam-5042	54	17	-	-	NOUN
ejpam-5042	54	18	complementation	complementation	NOUN
ejpam-5042	54	19	in	in	ADP
ejpam-5042	54	20	pdls	pdl	NOUN
ejpam-5042	54	21	,	,	PUNCT
ejpam-5042	54	22	highlight	highlight	VERB
ejpam-5042	54	23	the	the	DET
ejpam-5042	54	24	equationally	equationally	ADV
ejpam-5042	54	25	definable	definable	ADJ
ejpam-5042	54	26	nature	nature	NOUN
ejpam-5042	54	27	of	of	ADP
ejpam-5042	54	28	parapseudo	parapseudo	NOUN
ejpam-5042	54	29	-	-	PUNCT
ejpam-5042	54	30	complemented	complement	VERB
ejpam-5042	54	31	pdls	pdl	NOUN
ejpam-5042	54	32	,	,	PUNCT
ejpam-5042	54	33	and	and	CCONJ
ejpam-5042	54	34	demonstrate	demonstrate	VERB
ejpam-5042	54	35	the	the	DET
ejpam-5042	54	36	independence	independence	NOUN
ejpam-5042	54	37	of	of	ADP
ejpam-5042	54	38	the	the	DET
ejpam-5042	54	39	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5042	54	40	within	within	ADP
ejpam-5042	54	41	the	the	DET
ejpam-5042	54	42	associated	associated	ADJ
ejpam-5042	54	43	boolean	boolean	ADJ
ejpam-5042	54	44	algebra	algebra	NOUN
ejpam-5042	54	45	.	.	PUNCT
ejpam-5042	55	1	this	this	DET
ejpam-5042	55	2	study	study	NOUN
ejpam-5042	55	3	contributes	contribute	VERB
ejpam-5042	55	4	to	to	ADP
ejpam-5042	55	5	a	a	DET
ejpam-5042	55	6	deeper	deep	ADJ
ejpam-5042	55	7	understanding	understanding	NOUN
ejpam-5042	55	8	of	of	ADP
ejpam-5042	55	9	parapseudo	parapseudo	NOUN
ejpam-5042	55	10	-	-	NOUN
ejpam-5042	55	11	complementation	complementation	NOUN
ejpam-5042	55	12	and	and	CCONJ
ejpam-5042	55	13	its	its	PRON
ejpam-5042	55	14	implications	implication	NOUN
ejpam-5042	55	15	in	in	ADP
ejpam-5042	55	16	the	the	DET
ejpam-5042	55	17	context	context	NOUN
ejpam-5042	55	18	of	of	ADP
ejpam-5042	55	19	paradistributive	paradistributive	ADJ
ejpam-5042	55	20	latticoids	latticoid	NOUN
ejpam-5042	55	21	.	.	PUNCT
ejpam-5042	56	1	2	2	X
ejpam-5042	56	2	.	.	X
ejpam-5042	56	3	preliminaries	preliminary	NOUN
ejpam-5042	56	4	first	first	ADV
ejpam-5042	56	5	we	we	PRON
ejpam-5042	56	6	recall	recall	VERB
ejpam-5042	56	7	the	the	DET
ejpam-5042	56	8	necessary	necessary	ADJ
ejpam-5042	56	9	definitions	definition	NOUN
ejpam-5042	56	10	and	and	CCONJ
ejpam-5042	56	11	results	result	NOUN
ejpam-5042	56	12	from	from	ADP
ejpam-5042	56	13	[	[	X
ejpam-5042	56	14	1	1	NUM
ejpam-5042	56	15	]	]	PUNCT
ejpam-5042	56	16	.	.	PUNCT
ejpam-5042	57	1	definition	definition	NOUN
ejpam-5042	57	2	1	1	NUM
ejpam-5042	57	3	.	.	PUNCT
ejpam-5042	58	1	an	an	DET
ejpam-5042	58	2	algebra	algebra	NOUN
ejpam-5042	58	3	(	(	PUNCT
ejpam-5042	58	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	58	5	,	,	PUNCT
ejpam-5042	58	6	1	1	NUM
ejpam-5042	58	7	)	)	PUNCT
ejpam-5042	58	8	of	of	ADP
ejpam-5042	58	9	type	type	NOUN
ejpam-5042	58	10	(	(	PUNCT
ejpam-5042	58	11	2,2,0	2,2,0	NOUN
ejpam-5042	58	12	)	)	PUNCT
ejpam-5042	58	13	is	be	AUX
ejpam-5042	58	14	called	call	VERB
ejpam-5042	58	15	a	a	DET
ejpam-5042	58	16	paradistributive	paradistributive	ADJ
ejpam-5042	58	17	latticoid	latticoid	NOUN
ejpam-5042	58	18	,	,	PUNCT
ejpam-5042	58	19	abbreviated	abbreviate	VERB
ejpam-5042	58	20	as	as	ADP
ejpam-5042	58	21	pdl	pdl	NOUN
ejpam-5042	58	22	,	,	PUNCT
ejpam-5042	58	23	if	if	SCONJ
ejpam-5042	58	24	it	it	PRON
ejpam-5042	58	25	assures	assure	VERB
ejpam-5042	58	26	the	the	DET
ejpam-5042	58	27	subsequent	subsequent	ADJ
ejpam-5042	58	28	axioms	axiom	NOUN
ejpam-5042	58	29	:	:	PUNCT
ejpam-5042	58	30	(	(	PUNCT
ejpam-5042	58	31	ld∨	ld∨	NOUN
ejpam-5042	58	32	)	)	PUNCT
ejpam-5042	58	33	κ1	κ1	NOUN
ejpam-5042	58	34	∨	∨	PROPN
ejpam-5042	58	35	(	(	PUNCT
ejpam-5042	58	36	κ2	κ2	PROPN
ejpam-5042	58	37	∧	∧	PROPN
ejpam-5042	58	38	κ3	κ3	PROPN
ejpam-5042	58	39	)	)	PUNCT
ejpam-5042	58	40	=	=	PUNCT
ejpam-5042	58	41	(	(	PUNCT
ejpam-5042	58	42	κ1	κ1	PROPN
ejpam-5042	58	43	∨	∨	NUM
ejpam-5042	58	44	κ2	κ2	PROPN
ejpam-5042	58	45	)	)	PUNCT
ejpam-5042	58	46	∧	∧	PROPN
ejpam-5042	58	47	(	(	PUNCT
ejpam-5042	58	48	κ1	κ1	PROPN
ejpam-5042	58	49	∨	∨	NUM
ejpam-5042	58	50	κ3	κ3	PROPN
ejpam-5042	58	51	)	)	PUNCT
ejpam-5042	58	52	.	.	PUNCT
ejpam-5042	59	1	(	(	PUNCT
ejpam-5042	59	2	rd∨	rd∨	X
ejpam-5042	59	3	)	)	PUNCT
ejpam-5042	59	4	(	(	PUNCT
ejpam-5042	59	5	κ1	κ1	NOUN
ejpam-5042	59	6	∧	∧	PROPN
ejpam-5042	59	7	κ2	κ2	PROPN
ejpam-5042	59	8	)	)	PUNCT
ejpam-5042	59	9	∨	∨	NUM
ejpam-5042	59	10	κ3	κ3	PROPN
ejpam-5042	59	11	=	=	SYM
ejpam-5042	59	12	(	(	PUNCT
ejpam-5042	59	13	κ1	κ1	PROPN
ejpam-5042	59	14	∨	∨	NUM
ejpam-5042	59	15	κ3	κ3	PROPN
ejpam-5042	59	16	)	)	PUNCT
ejpam-5042	59	17	∧	∧	PROPN
ejpam-5042	59	18	(	(	PUNCT
ejpam-5042	59	19	κ2	κ2	PROPN
ejpam-5042	59	20	∨	∨	NUM
ejpam-5042	59	21	κ3	κ3	PROPN
ejpam-5042	59	22	)	)	PUNCT
ejpam-5042	59	23	.	.	PUNCT
ejpam-5042	60	1	(	(	PUNCT
ejpam-5042	60	2	l1	l1	PROPN
ejpam-5042	60	3	)	)	PUNCT
ejpam-5042	60	4	(	(	PUNCT
ejpam-5042	60	5	κ1	κ1	PROPN
ejpam-5042	60	6	∨	∨	NUM
ejpam-5042	60	7	κ2	κ2	PROPN
ejpam-5042	60	8	)	)	PUNCT
ejpam-5042	60	9	∧	∧	PROPN
ejpam-5042	60	10	κ2	κ2	NOUN
ejpam-5042	60	11	=	=	SYM
ejpam-5042	60	12	κ2	κ2	PROPN
ejpam-5042	60	13	.	.	PUNCT
ejpam-5042	61	1	(	(	PUNCT
ejpam-5042	61	2	l2	l2	NOUN
ejpam-5042	61	3	)	)	PUNCT
ejpam-5042	61	4	(	(	PUNCT
ejpam-5042	61	5	κ1	κ1	PROPN
ejpam-5042	61	6	∨	∨	NUM
ejpam-5042	61	7	κ2	κ2	PROPN
ejpam-5042	61	8	)	)	PUNCT
ejpam-5042	61	9	∧	∧	NOUN
ejpam-5042	61	10	κ1	κ1	NOUN
ejpam-5042	61	11	=	=	PUNCT
ejpam-5042	61	12	κ1	κ1	NOUN
ejpam-5042	61	13	.	.	PUNCT
ejpam-5042	62	1	(	(	PUNCT
ejpam-5042	62	2	l3	l3	PROPN
ejpam-5042	62	3	)	)	PUNCT
ejpam-5042	62	4	κ1	κ1	NOUN
ejpam-5042	62	5	∨	∨	PROPN
ejpam-5042	62	6	(	(	PUNCT
ejpam-5042	62	7	κ1	κ1	NOUN
ejpam-5042	62	8	∧	∧	PROPN
ejpam-5042	62	9	κ2	κ2	PROPN
ejpam-5042	62	10	)	)	PUNCT
ejpam-5042	62	11	=	=	SYM
ejpam-5042	62	12	κ1	κ1	NOUN
ejpam-5042	62	13	.	.	PUNCT
ejpam-5042	63	1	(	(	PUNCT
ejpam-5042	63	2	i1	i1	PROPN
ejpam-5042	63	3	)	)	PUNCT
ejpam-5042	63	4	κ1	κ1	NOUN
ejpam-5042	63	5	∨	∨	NUM
ejpam-5042	63	6	1	1	NUM
ejpam-5042	63	7	=	=	SYM
ejpam-5042	63	8	1	1	NUM
ejpam-5042	63	9	.	.	X
ejpam-5042	64	1	for	for	ADP
ejpam-5042	64	2	any	any	DET
ejpam-5042	64	3	κ1	κ1	NOUN
ejpam-5042	64	4	,	,	PUNCT
ejpam-5042	64	5	κ2	κ2	NOUN
ejpam-5042	64	6	,	,	PUNCT
ejpam-5042	64	7	κ3	κ3	PROPN
ejpam-5042	64	8	∈	∈	PROPN
ejpam-5042	64	9	v	v	NOUN
ejpam-5042	64	10	.	.	PUNCT
ejpam-5042	65	1	for	for	ADP
ejpam-5042	65	2	any	any	DET
ejpam-5042	65	3	κ1	κ1	NOUN
ejpam-5042	65	4	,	,	PUNCT
ejpam-5042	65	5	κ2	κ2	PROPN
ejpam-5042	65	6	∈	∈	PROPN
ejpam-5042	65	7	v	v	NOUN
ejpam-5042	65	8	,	,	PUNCT
ejpam-5042	65	9	we	we	PRON
ejpam-5042	65	10	say	say	VERB
ejpam-5042	65	11	that	that	SCONJ
ejpam-5042	65	12	κ1	κ1	NOUN
ejpam-5042	65	13	is	be	AUX
ejpam-5042	65	14	less	less	ADJ
ejpam-5042	65	15	than	than	ADP
ejpam-5042	65	16	or	or	CCONJ
ejpam-5042	65	17	equal	equal	ADJ
ejpam-5042	65	18	to	to	ADP
ejpam-5042	65	19	κ2	κ2	NOUN
ejpam-5042	65	20	and	and	CCONJ
ejpam-5042	65	21	write	write	VERB
ejpam-5042	65	22	κ1	κ1	NOUN
ejpam-5042	65	23	≤	≤	NOUN
ejpam-5042	65	24	κ2	κ2	NOUN
ejpam-5042	66	1	if	if	SCONJ
ejpam-5042	66	2	r.	r.	PROPN
ejpam-5042	66	3	shukla	shukla	PROPN
ejpam-5042	66	4	et	et	PROPN
ejpam-5042	66	5	al	al	PROPN
ejpam-5042	66	6	.	.	PUNCT
ejpam-5042	66	7	/	/	SYM
ejpam-5042	66	8	eur	eur	PROPN
ejpam-5042	66	9	.	.	PUNCT
ejpam-5042	67	1	j.	j.	PROPN
ejpam-5042	67	2	pure	pure	PROPN
ejpam-5042	67	3	appl	appl	PROPN
ejpam-5042	67	4	.	.	PROPN
ejpam-5042	67	5	math	math	PROPN
ejpam-5042	67	6	,	,	PUNCT
ejpam-5042	67	7	17	17	NUM
ejpam-5042	67	8	(	(	PUNCT
ejpam-5042	67	9	2	2	NUM
ejpam-5042	67	10	)	)	PUNCT
ejpam-5042	67	11	(	(	PUNCT
ejpam-5042	67	12	2024	2024	NUM
ejpam-5042	67	13	)	)	PUNCT
ejpam-5042	67	14	,	,	PUNCT
ejpam-5042	67	15	1129	1129	NUM
ejpam-5042	67	16	-	-	SYM
ejpam-5042	67	17	1145	1145	NUM
ejpam-5042	67	18	1132	1132	NUM
ejpam-5042	67	19	κ1	κ1	NOUN
ejpam-5042	67	20	∧	∧	PROPN
ejpam-5042	67	21	κ2	κ2	NOUN
ejpam-5042	67	22	=	=	SYM
ejpam-5042	67	23	κ1	κ1	NOUN
ejpam-5042	67	24	or	or	CCONJ
ejpam-5042	67	25	equivalently	equivalently	ADV
ejpam-5042	67	26	κ1	κ1	NOUN
ejpam-5042	67	27	∨	∨	NUM
ejpam-5042	67	28	κ2	κ2	PROPN
ejpam-5042	67	29	=	=	SYM
ejpam-5042	67	30	κ2	κ2	NOUN
ejpam-5042	67	31	and	and	CCONJ
ejpam-5042	67	32	it	it	PRON
ejpam-5042	67	33	can	can	AUX
ejpam-5042	67	34	be	be	AUX
ejpam-5042	67	35	easily	easily	ADV
ejpam-5042	67	36	observed	observe	VERB
ejpam-5042	67	37	that	that	SCONJ
ejpam-5042	67	38	≤	≤	NUM
ejpam-5042	67	39	is	be	AUX
ejpam-5042	67	40	a	a	DET
ejpam-5042	67	41	partial	partial	ADJ
ejpam-5042	67	42	order	order	NOUN
ejpam-5042	67	43	on	on	ADP
ejpam-5042	67	44	v	v	NOUN
ejpam-5042	67	45	.	.	PUNCT
ejpam-5042	68	1	the	the	DET
ejpam-5042	68	2	element	element	NOUN
ejpam-5042	68	3	1	1	NUM
ejpam-5042	68	4	,	,	PUNCT
ejpam-5042	68	5	in	in	ADP
ejpam-5042	68	6	definition	definition	NOUN
ejpam-5042	68	7	1	1	NUM
ejpam-5042	68	8	,	,	PUNCT
ejpam-5042	68	9	is	be	AUX
ejpam-5042	68	10	called	call	VERB
ejpam-5042	68	11	the	the	DET
ejpam-5042	68	12	greatest	great	ADJ
ejpam-5042	68	13	element	element	NOUN
ejpam-5042	68	14	.	.	PUNCT
ejpam-5042	68	15	example	example	NOUN
ejpam-5042	69	1	1	1	NUM
ejpam-5042	69	2	.	.	PUNCT
ejpam-5042	69	3	let	let	VERB
ejpam-5042	69	4	v	v	PART
ejpam-5042	69	5	be	be	AUX
ejpam-5042	69	6	a	a	DET
ejpam-5042	69	7	non	non	ADJ
ejpam-5042	69	8	-	-	ADJ
ejpam-5042	69	9	empty	empty	ADJ
ejpam-5042	69	10	set	set	NOUN
ejpam-5042	69	11	.	.	PUNCT
ejpam-5042	70	1	fix	fix	VERB
ejpam-5042	70	2	some	some	DET
ejpam-5042	70	3	element	element	NOUN
ejpam-5042	70	4	ϱ0	ϱ0	NOUN
ejpam-5042	70	5	∈	∈	PROPN
ejpam-5042	70	6	v	v	NOUN
ejpam-5042	70	7	.	.	PUNCT
ejpam-5042	71	1	then	then	ADV
ejpam-5042	71	2	,	,	PUNCT
ejpam-5042	71	3	for	for	ADP
ejpam-5042	71	4	any	any	DET
ejpam-5042	71	5	ρ	ρ	NOUN
ejpam-5042	71	6	,	,	PUNCT
ejpam-5042	71	7	ϱ	ϱ	PROPN
ejpam-5042	71	8	∈	∈	PROPN
ejpam-5042	71	9	v	v	PART
ejpam-5042	71	10	define	define	VERB
ejpam-5042	71	11	∨	∨	NOUN
ejpam-5042	71	12	and	and	CCONJ
ejpam-5042	71	13	∧	∧	NOUN
ejpam-5042	71	14	on	on	ADP
ejpam-5042	71	15	v	v	NUM
ejpam-5042	71	16	by	by	ADP
ejpam-5042	71	17	ρ	ρ	PROPN
ejpam-5042	71	18	∨	∨	NUM
ejpam-5042	71	19	ϱ	ϱ	X
ejpam-5042	71	20	=	=	PUNCT
ejpam-5042	71	21	{	{	PUNCT
ejpam-5042	71	22	ρ	ρ	NOUN
ejpam-5042	71	23	ϱ	ϱ	ADP
ejpam-5042	71	24	̸=	̸=	PROPN
ejpam-5042	71	25	ϱ0	ϱ0	NOUN
ejpam-5042	71	26	ϱ0	ϱ0	NOUN
ejpam-5042	71	27	ϱ	ϱ	NOUN
ejpam-5042	71	28	=	=	X
ejpam-5042	71	29	ϱ0	ϱ0	NOUN
ejpam-5042	71	30	and	and	CCONJ
ejpam-5042	71	31	ρ	ρ	NUM
ejpam-5042	71	32	∧	∧	PROPN
ejpam-5042	71	33	ϱ	ϱ	PROPN
ejpam-5042	71	34	=	=	PUNCT
ejpam-5042	71	35	{	{	PUNCT
ejpam-5042	71	36	ϱ	ϱ	PROPN
ejpam-5042	71	37	ϱ	ϱ	ADP
ejpam-5042	71	38	̸=	̸=	PROPN
ejpam-5042	71	39	ϱ0	ϱ0	NOUN
ejpam-5042	71	40	ρ	ρ	NOUN
ejpam-5042	71	41	ϱ	ϱ	ADP
ejpam-5042	71	42	=	=	X
ejpam-5042	71	43	ϱ0	ϱ0	NOUN
ejpam-5042	71	44	then	then	ADV
ejpam-5042	71	45	(	(	PUNCT
ejpam-5042	71	46	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	71	47	,	,	PUNCT
ejpam-5042	71	48	ϱ0	ϱ0	NOUN
ejpam-5042	71	49	)	)	PUNCT
ejpam-5042	71	50	is	be	AUX
ejpam-5042	71	51	a	a	DET
ejpam-5042	71	52	disconnected	disconnected	ADJ
ejpam-5042	71	53	pdl	pdl	NOUN
ejpam-5042	71	54	with	with	ADP
ejpam-5042	71	55	ϱ0	ϱ0	NOUN
ejpam-5042	71	56	as	as	ADP
ejpam-5042	71	57	its	its	PRON
ejpam-5042	71	58	greatest	great	ADJ
ejpam-5042	71	59	element	element	NOUN
ejpam-5042	71	60	.	.	PUNCT
ejpam-5042	72	1	lemma	lemma	PROPN
ejpam-5042	72	2	1	1	X
ejpam-5042	72	3	.	.	PUNCT
ejpam-5042	73	1	let	let	AUX
ejpam-5042	73	2	(	(	PUNCT
ejpam-5042	73	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	73	4	,	,	PUNCT
ejpam-5042	73	5	1	1	NUM
ejpam-5042	73	6	)	)	PUNCT
ejpam-5042	73	7	be	be	AUX
ejpam-5042	73	8	a	a	DET
ejpam-5042	73	9	pdl	pdl	NOUN
ejpam-5042	73	10	.	.	PUNCT
ejpam-5042	74	1	then	then	ADV
ejpam-5042	74	2	for	for	ADP
ejpam-5042	74	3	any	any	DET
ejpam-5042	74	4	κ1	κ1	NOUN
ejpam-5042	74	5	,	,	PUNCT
ejpam-5042	74	6	κ2	κ2	PROPN
ejpam-5042	74	7	,	,	PUNCT
ejpam-5042	74	8	κ3	κ3	PROPN
ejpam-5042	74	9	,	,	PUNCT
ejpam-5042	74	10	κ4	κ4	PROPN
ejpam-5042	74	11	∈	∈	PROPN
ejpam-5042	74	12	v	v	NOUN
ejpam-5042	74	13	,	,	PUNCT
ejpam-5042	74	14	we	we	PRON
ejpam-5042	74	15	have	have	VERB
ejpam-5042	74	16	the	the	DET
ejpam-5042	74	17	following	following	NOUN
ejpam-5042	74	18	:	:	PUNCT
ejpam-5042	74	19	(	(	PUNCT
ejpam-5042	74	20	1	1	X
ejpam-5042	74	21	)	)	SYM
ejpam-5042	74	22	1	1	NUM
ejpam-5042	74	23	∧	∧	PROPN
ejpam-5042	74	24	κ1	κ1	NOUN
ejpam-5042	74	25	=	=	PUNCT
ejpam-5042	74	26	κ1	κ1	NOUN
ejpam-5042	74	27	.	.	PUNCT
ejpam-5042	75	1	(	(	PUNCT
ejpam-5042	75	2	2	2	X
ejpam-5042	75	3	)	)	PUNCT
ejpam-5042	75	4	κ1	κ1	NOUN
ejpam-5042	75	5	∧	∧	PROPN
ejpam-5042	75	6	1	1	NUM
ejpam-5042	75	7	=	=	SYM
ejpam-5042	75	8	κ1	κ1	NOUN
ejpam-5042	75	9	.	.	PUNCT
ejpam-5042	76	1	(	(	PUNCT
ejpam-5042	76	2	3	3	NUM
ejpam-5042	76	3	)	)	PUNCT
ejpam-5042	76	4	1	1	NUM
ejpam-5042	76	5	∨	∨	NOUN
ejpam-5042	76	6	κ1	κ1	NOUN
ejpam-5042	76	7	=	=	SYM
ejpam-5042	76	8	1	1	NUM
ejpam-5042	76	9	.	.	PUNCT
ejpam-5042	77	1	(	(	PUNCT
ejpam-5042	77	2	4	4	NUM
ejpam-5042	77	3	)	)	PUNCT
ejpam-5042	77	4	(	(	PUNCT
ejpam-5042	77	5	κ1	κ1	PROPN
ejpam-5042	77	6	∨	∨	NUM
ejpam-5042	77	7	κ2	κ2	PROPN
ejpam-5042	77	8	)	)	PUNCT
ejpam-5042	77	9	∧	∧	PROPN
ejpam-5042	77	10	κ3	κ3	PROPN
ejpam-5042	77	11	=	=	SYM
ejpam-5042	77	12	(	(	PUNCT
ejpam-5042	77	13	κ1	κ1	NOUN
ejpam-5042	77	14	∧	∧	PROPN
ejpam-5042	77	15	κ3	κ3	PROPN
ejpam-5042	77	16	)	)	PUNCT
ejpam-5042	77	17	∨	∨	NUM
ejpam-5042	77	18	(	(	PUNCT
ejpam-5042	77	19	κ2	κ2	PROPN
ejpam-5042	77	20	∧	∧	PROPN
ejpam-5042	77	21	κ3	κ3	PROPN
ejpam-5042	77	22	)	)	PUNCT
ejpam-5042	77	23	.	.	PUNCT
ejpam-5042	78	1	(	(	PUNCT
ejpam-5042	78	2	5	5	X
ejpam-5042	78	3	)	)	PUNCT
ejpam-5042	78	4	κ1	κ1	NOUN
ejpam-5042	78	5	∨	∨	NOUN
ejpam-5042	78	6	(	(	PUNCT
ejpam-5042	78	7	κ2	κ2	PROPN
ejpam-5042	78	8	∧	∧	PROPN
ejpam-5042	78	9	κ3	κ3	PROPN
ejpam-5042	78	10	)	)	PUNCT
ejpam-5042	78	11	=	=	PROPN
ejpam-5042	78	12	κ1	κ1	PROPN
ejpam-5042	78	13	∨	∨	PROPN
ejpam-5042	78	14	(	(	PUNCT
ejpam-5042	78	15	κ3	κ3	PROPN
ejpam-5042	78	16	∧	∧	PROPN
ejpam-5042	78	17	κ2	κ2	PROPN
ejpam-5042	78	18	)	)	PUNCT
ejpam-5042	78	19	.	.	PUNCT
ejpam-5042	79	1	(	(	PUNCT
ejpam-5042	79	2	6	6	X
ejpam-5042	79	3	)	)	PUNCT
ejpam-5042	79	4	the	the	DET
ejpam-5042	79	5	operation	operation	NOUN
ejpam-5042	79	6	∨	∨	NOUN
ejpam-5042	79	7	is	be	AUX
ejpam-5042	79	8	associative	associative	ADJ
ejpam-5042	79	9	in	in	ADP
ejpam-5042	79	10	v	v	NOUN
ejpam-5042	79	11	i.e.	i.e.	X
ejpam-5042	79	12	,	,	PUNCT
ejpam-5042	79	13	κ1	κ1	NOUN
ejpam-5042	79	14	∨	∨	NOUN
ejpam-5042	79	15	(	(	PUNCT
ejpam-5042	79	16	κ2	κ2	PROPN
ejpam-5042	79	17	∨	∨	NUM
ejpam-5042	79	18	κ3	κ3	PROPN
ejpam-5042	79	19	)	)	PUNCT
ejpam-5042	79	20	=	=	PUNCT
ejpam-5042	80	1	(	(	PUNCT
ejpam-5042	80	2	κ1	κ1	PROPN
ejpam-5042	80	3	∨	∨	NUM
ejpam-5042	80	4	κ2	κ2	PROPN
ejpam-5042	80	5	)	)	PUNCT
ejpam-5042	80	6	∨	∨	NUM
ejpam-5042	80	7	κ3	κ3	PROPN
ejpam-5042	80	8	.	.	PUNCT
ejpam-5042	81	1	(	(	PUNCT
ejpam-5042	81	2	7	7	X
ejpam-5042	81	3	)	)	PUNCT
ejpam-5042	81	4	the	the	DET
ejpam-5042	81	5	set	set	NOUN
ejpam-5042	81	6	vµ1	vµ1	NOUN
ejpam-5042	81	7	=	=	SYM
ejpam-5042	81	8	{	{	PUNCT
ejpam-5042	81	9	κ1	κ1	NOUN
ejpam-5042	81	10	∈	∈	PROPN
ejpam-5042	81	11	v	v	ADP
ejpam-5042	81	12	|	|	ADV
ejpam-5042	81	13	µ1	µ1	NOUN
ejpam-5042	81	14	≤	≤	NOUN
ejpam-5042	81	15	κ1	κ1	NOUN
ejpam-5042	81	16	}	}	PUNCT
ejpam-5042	81	17	=	=	SYM
ejpam-5042	81	18	{	{	PUNCT
ejpam-5042	81	19	µ1	µ1	PROPN
ejpam-5042	81	20	∨	∨	NUM
ejpam-5042	81	21	κ1	κ1	NOUN
ejpam-5042	81	22	|	|	ADP
ejpam-5042	81	23	κ1	κ1	NOUN
ejpam-5042	81	24	∈	∈	PROPN
ejpam-5042	81	25	v	v	NOUN
ejpam-5042	81	26	}	}	PUNCT
ejpam-5042	81	27	is	be	AUX
ejpam-5042	81	28	a	a	DET
ejpam-5042	81	29	distributive	distributive	ADJ
ejpam-5042	81	30	lattice	lattice	NOUN
ejpam-5042	81	31	under	under	ADP
ejpam-5042	81	32	induced	induced	ADJ
ejpam-5042	81	33	operations	operation	NOUN
ejpam-5042	81	34	∨	∨	NOUN
ejpam-5042	81	35	and	and	CCONJ
ejpam-5042	81	36	∧	∧	PROPN
ejpam-5042	81	37	with	with	ADP
ejpam-5042	81	38	µ1	µ1	PROPN
ejpam-5042	81	39	as	as	ADP
ejpam-5042	81	40	its	its	PRON
ejpam-5042	81	41	least	least	ADJ
ejpam-5042	81	42	element	element	NOUN
ejpam-5042	81	43	.	.	PUNCT
ejpam-5042	82	1	(	(	PUNCT
ejpam-5042	82	2	8)	8)	NUM
ejpam-5042	82	3	κ4	κ4	NOUN
ejpam-5042	82	4	∨	∨	NOUN
ejpam-5042	82	5	{	{	PUNCT
ejpam-5042	82	6	κ1	κ1	NOUN
ejpam-5042	82	7	∧	∧	PROPN
ejpam-5042	82	8	(	(	PUNCT
ejpam-5042	82	9	κ2	κ2	PROPN
ejpam-5042	82	10	∧	∧	PROPN
ejpam-5042	82	11	κ3	κ3	PROPN
ejpam-5042	82	12	)	)	PUNCT
ejpam-5042	82	13	}	}	PUNCT
ejpam-5042	83	1	=	=	SYM
ejpam-5042	83	2	κ4	κ4	PROPN
ejpam-5042	83	3	∨	∨	NUM
ejpam-5042	83	4	{	{	PUNCT
ejpam-5042	83	5	(	(	PUNCT
ejpam-5042	83	6	κ1	κ1	NOUN
ejpam-5042	83	7	∧	∧	PROPN
ejpam-5042	83	8	κ2	κ2	PROPN
ejpam-5042	83	9	)	)	PUNCT
ejpam-5042	83	10	∧	∧	PROPN
ejpam-5042	83	11	κ3	κ3	PROPN
ejpam-5042	83	12	}	}	PUNCT
ejpam-5042	83	13	.	.	PUNCT
ejpam-5042	84	1	(	(	PUNCT
ejpam-5042	84	2	9	9	X
ejpam-5042	84	3	)	)	PUNCT
ejpam-5042	84	4	κ1	κ1	NOUN
ejpam-5042	84	5	∨	∨	NOUN
ejpam-5042	84	6	(	(	PUNCT
ejpam-5042	84	7	κ2	κ2	PROPN
ejpam-5042	84	8	∨	∨	NUM
ejpam-5042	84	9	κ3	κ3	PROPN
ejpam-5042	84	10	)	)	PUNCT
ejpam-5042	85	1	=	=	PROPN
ejpam-5042	85	2	κ1	κ1	PROPN
ejpam-5042	85	3	∨	∨	PROPN
ejpam-5042	85	4	(	(	PUNCT
ejpam-5042	85	5	κ3	κ3	PROPN
ejpam-5042	85	6	∨	∨	NUM
ejpam-5042	85	7	κ2	κ2	PROPN
ejpam-5042	85	8	)	)	PUNCT
ejpam-5042	85	9	.	.	PUNCT
ejpam-5042	86	1	(	(	PUNCT
ejpam-5042	86	2	10	10	NUM
ejpam-5042	86	3	)	)	PUNCT
ejpam-5042	86	4	κ1	κ1	NOUN
ejpam-5042	86	5	∨	∨	NUM
ejpam-5042	86	6	κ2	κ2	NOUN
ejpam-5042	86	7	=	=	PUNCT
ejpam-5042	86	8	1	1	NUM
ejpam-5042	86	9	if	if	SCONJ
ejpam-5042	86	10	and	and	CCONJ
ejpam-5042	86	11	only	only	ADV
ejpam-5042	86	12	if	if	SCONJ
ejpam-5042	86	13	κ2	κ2	NOUN
ejpam-5042	86	14	∨	∨	NOUN
ejpam-5042	86	15	κ1	κ1	NOUN
ejpam-5042	86	16	=	=	SYM
ejpam-5042	86	17	1	1	NUM
ejpam-5042	86	18	.	.	PUNCT
ejpam-5042	87	1	(	(	PUNCT
ejpam-5042	87	2	11	11	NUM
ejpam-5042	87	3	)	)	PUNCT
ejpam-5042	87	4	κ1	κ1	NOUN
ejpam-5042	87	5	∧	∧	PROPN
ejpam-5042	87	6	κ2	κ2	NOUN
ejpam-5042	87	7	=	=	SYM
ejpam-5042	87	8	κ2	κ2	NOUN
ejpam-5042	87	9	∧	∧	PROPN
ejpam-5042	87	10	κ1	κ1	NOUN
ejpam-5042	87	11	whenever	whenever	SCONJ
ejpam-5042	87	12	κ1	κ1	PROPN
ejpam-5042	87	13	∨	∨	PROPN
ejpam-5042	87	14	κ2	κ2	PROPN
ejpam-5042	87	15	=	=	SYM
ejpam-5042	87	16	1	1	X
ejpam-5042	87	17	.	.	PUNCT
ejpam-5042	87	18	theorem	theorem	NOUN
ejpam-5042	87	19	1	1	NUM
ejpam-5042	87	20	.	.	PUNCT
ejpam-5042	88	1	an	an	DET
ejpam-5042	88	2	algebra	algebra	NOUN
ejpam-5042	88	3	(	(	PUNCT
ejpam-5042	88	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	88	5	,	,	PUNCT
ejpam-5042	88	6	1	1	NUM
ejpam-5042	88	7	)	)	PUNCT
ejpam-5042	88	8	of	of	ADP
ejpam-5042	88	9	type	type	NOUN
ejpam-5042	88	10	(	(	PUNCT
ejpam-5042	88	11	2	2	NUM
ejpam-5042	88	12	,	,	PUNCT
ejpam-5042	88	13	2	2	NUM
ejpam-5042	88	14	,	,	PUNCT
ejpam-5042	88	15	0	0	NUM
ejpam-5042	88	16	)	)	PUNCT
ejpam-5042	88	17	is	be	AUX
ejpam-5042	88	18	a	a	DET
ejpam-5042	88	19	pdl	pdl	NOUN
ejpam-5042	88	20	if	if	SCONJ
ejpam-5042	89	1	and	and	CCONJ
ejpam-5042	89	2	only	only	ADV
ejpam-5042	89	3	if	if	SCONJ
ejpam-5042	89	4	it	it	PRON
ejpam-5042	89	5	satisfies	satisfy	VERB
ejpam-5042	89	6	the	the	DET
ejpam-5042	89	7	following	following	NOUN
ejpam-5042	89	8	:	:	PUNCT
ejpam-5042	89	9	(	(	PUNCT
ejpam-5042	89	10	ld∨	ld∨	NOUN
ejpam-5042	89	11	)	)	PUNCT
ejpam-5042	89	12	κ1	κ1	NOUN
ejpam-5042	89	13	∨	∨	PROPN
ejpam-5042	89	14	(	(	PUNCT
ejpam-5042	89	15	κ2	κ2	PROPN
ejpam-5042	89	16	∧	∧	PROPN
ejpam-5042	89	17	κ3	κ3	PROPN
ejpam-5042	89	18	)	)	PUNCT
ejpam-5042	89	19	=	=	PUNCT
ejpam-5042	89	20	(	(	PUNCT
ejpam-5042	89	21	κ1	κ1	PROPN
ejpam-5042	89	22	∨	∨	NUM
ejpam-5042	89	23	κ2	κ2	PROPN
ejpam-5042	89	24	)	)	PUNCT
ejpam-5042	90	1	∧	∧	PROPN
ejpam-5042	90	2	(	(	PUNCT
ejpam-5042	90	3	κ1	κ1	PROPN
ejpam-5042	90	4	∨	∨	NUM
ejpam-5042	90	5	κ3	κ3	PROPN
ejpam-5042	90	6	)	)	PUNCT
ejpam-5042	90	7	(	(	PUNCT
ejpam-5042	90	8	rd∨	rd∨	X
ejpam-5042	90	9	)	)	PUNCT
ejpam-5042	90	10	(	(	PUNCT
ejpam-5042	90	11	κ1	κ1	NOUN
ejpam-5042	90	12	∧	∧	PROPN
ejpam-5042	90	13	κ2	κ2	PROPN
ejpam-5042	90	14	)	)	PUNCT
ejpam-5042	90	15	∨	∨	NUM
ejpam-5042	90	16	κ3	κ3	PROPN
ejpam-5042	90	17	=	=	SYM
ejpam-5042	90	18	(	(	PUNCT
ejpam-5042	90	19	κ1	κ1	PROPN
ejpam-5042	90	20	∨	∨	NUM
ejpam-5042	90	21	κ3	κ3	PROPN
ejpam-5042	90	22	)	)	PUNCT
ejpam-5042	90	23	∧	∧	PROPN
ejpam-5042	90	24	(	(	PUNCT
ejpam-5042	90	25	κ2	κ2	PROPN
ejpam-5042	90	26	∨	∨	NUM
ejpam-5042	90	27	κ3	κ3	PROPN
ejpam-5042	90	28	)	)	PUNCT
ejpam-5042	90	29	(	(	PUNCT
ejpam-5042	90	30	rd∧	rd∧	PROPN
ejpam-5042	90	31	)	)	PUNCT
ejpam-5042	90	32	(	(	PUNCT
ejpam-5042	90	33	κ1	κ1	PROPN
ejpam-5042	90	34	∨	∨	NUM
ejpam-5042	90	35	κ2	κ2	PROPN
ejpam-5042	90	36	)	)	PUNCT
ejpam-5042	90	37	∧	∧	PROPN
ejpam-5042	90	38	κ3	κ3	PROPN
ejpam-5042	90	39	=	=	SYM
ejpam-5042	90	40	(	(	PUNCT
ejpam-5042	90	41	κ1	κ1	NOUN
ejpam-5042	90	42	∧	∧	PROPN
ejpam-5042	90	43	κ3	κ3	PROPN
ejpam-5042	90	44	)	)	PUNCT
ejpam-5042	90	45	∨	∨	NUM
ejpam-5042	90	46	(	(	PUNCT
ejpam-5042	90	47	κ2	κ2	PROPN
ejpam-5042	90	48	∧	∧	PROPN
ejpam-5042	90	49	κ3	κ3	PROPN
ejpam-5042	90	50	)	)	PUNCT
ejpam-5042	90	51	(	(	PUNCT
ejpam-5042	90	52	l1	l1	PROPN
ejpam-5042	90	53	)	)	PUNCT
ejpam-5042	90	54	(	(	PUNCT
ejpam-5042	90	55	κ1	κ1	PROPN
ejpam-5042	90	56	∨	∨	NUM
ejpam-5042	90	57	κ2	κ2	PROPN
ejpam-5042	90	58	)	)	PUNCT
ejpam-5042	90	59	∧	∧	PROPN
ejpam-5042	90	60	κ2	κ2	NOUN
ejpam-5042	90	61	=	=	SYM
ejpam-5042	90	62	κ2	κ2	PROPN
ejpam-5042	90	63	(	(	PUNCT
ejpam-5042	90	64	l3	l3	PROPN
ejpam-5042	90	65	)	)	PUNCT
ejpam-5042	90	66	κ1	κ1	NOUN
ejpam-5042	90	67	∨	∨	PROPN
ejpam-5042	90	68	(	(	PUNCT
ejpam-5042	90	69	κ1	κ1	NOUN
ejpam-5042	90	70	∧	∧	PROPN
ejpam-5042	90	71	κ2	κ2	NOUN
ejpam-5042	90	72	)	)	PUNCT
ejpam-5042	90	73	=	=	SYM
ejpam-5042	90	74	κ1	κ1	PROPN
ejpam-5042	90	75	(	(	PUNCT
ejpam-5042	90	76	i1	i1	PROPN
ejpam-5042	90	77	)	)	PUNCT
ejpam-5042	90	78	κ1	κ1	NOUN
ejpam-5042	90	79	∨	∨	NUM
ejpam-5042	90	80	1	1	NUM
ejpam-5042	90	81	=	=	SYM
ejpam-5042	90	82	1	1	NUM
ejpam-5042	90	83	(	(	PUNCT
ejpam-5042	90	84	i2	i2	PROPN
ejpam-5042	90	85	)	)	PUNCT
ejpam-5042	90	86	1	1	NUM
ejpam-5042	90	87	∧	∧	PROPN
ejpam-5042	90	88	κ1	κ1	NOUN
ejpam-5042	90	89	=	=	PUNCT
ejpam-5042	90	90	κ1	κ1	NOUN
ejpam-5042	90	91	.	.	PUNCT
ejpam-5042	91	1	for	for	ADP
ejpam-5042	91	2	all	all	DET
ejpam-5042	91	3	κ1	κ1	NOUN
ejpam-5042	91	4	,	,	PUNCT
ejpam-5042	91	5	κ2	κ2	NOUN
ejpam-5042	91	6	,	,	PUNCT
ejpam-5042	91	7	κ3	κ3	PROPN
ejpam-5042	91	8	∈	∈	PROPN
ejpam-5042	91	9	v	v	NOUN
ejpam-5042	91	10	.	.	PUNCT
ejpam-5042	92	1	definition	definition	NOUN
ejpam-5042	92	2	2	2	NUM
ejpam-5042	92	3	.	.	PUNCT
ejpam-5042	93	1	a	a	DET
ejpam-5042	93	2	paradistributive	paradistributive	ADJ
ejpam-5042	93	3	latticoid	latticoid	NOUN
ejpam-5042	93	4	(	(	PUNCT
ejpam-5042	93	5	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	93	6	,	,	PUNCT
ejpam-5042	93	7	1	1	NUM
ejpam-5042	93	8	)	)	PUNCT
ejpam-5042	93	9	is	be	AUX
ejpam-5042	93	10	said	say	VERB
ejpam-5042	93	11	to	to	PART
ejpam-5042	93	12	be	be	AUX
ejpam-5042	93	13	associative	associative	ADJ
ejpam-5042	93	14	if	if	SCONJ
ejpam-5042	93	15	it	it	PRON
ejpam-5042	93	16	satisfies	satisfy	VERB
ejpam-5042	93	17	the	the	DET
ejpam-5042	93	18	following	follow	VERB
ejpam-5042	93	19	condition	condition	NOUN
ejpam-5042	93	20	κ1	κ1	NOUN
ejpam-5042	93	21	∧	∧	PROPN
ejpam-5042	93	22	(	(	PUNCT
ejpam-5042	93	23	κ2	κ2	PROPN
ejpam-5042	93	24	∧	∧	PROPN
ejpam-5042	93	25	κ3	κ3	PROPN
ejpam-5042	93	26	)	)	PUNCT
ejpam-5042	93	27	=	=	PUNCT
ejpam-5042	94	1	(	(	PUNCT
ejpam-5042	94	2	κ1	κ1	NOUN
ejpam-5042	94	3	∧	∧	PROPN
ejpam-5042	94	4	κ2	κ2	PROPN
ejpam-5042	94	5	)	)	PUNCT
ejpam-5042	94	6	∧	∧	PROPN
ejpam-5042	94	7	κ3	κ3	PROPN
ejpam-5042	94	8	for	for	ADP
ejpam-5042	94	9	all	all	DET
ejpam-5042	94	10	κ1	κ1	NOUN
ejpam-5042	94	11	,	,	PUNCT
ejpam-5042	94	12	κ2	κ2	NOUN
ejpam-5042	94	13	,	,	PUNCT
ejpam-5042	94	14	κ3	κ3	PROPN
ejpam-5042	94	15	∈	∈	PROPN
ejpam-5042	94	16	v.	v.	PROPN
ejpam-5042	94	17	r.	r.	PROPN
ejpam-5042	94	18	shukla	shukla	PROPN
ejpam-5042	94	19	et	et	PROPN
ejpam-5042	94	20	al	al	PROPN
ejpam-5042	94	21	.	.	PUNCT
ejpam-5042	94	22	/	/	SYM
ejpam-5042	94	23	eur	eur	PROPN
ejpam-5042	94	24	.	.	PUNCT
ejpam-5042	95	1	j.	j.	PROPN
ejpam-5042	95	2	pure	pure	PROPN
ejpam-5042	95	3	appl	appl	PROPN
ejpam-5042	95	4	.	.	PROPN
ejpam-5042	95	5	math	math	PROPN
ejpam-5042	95	6	,	,	PUNCT
ejpam-5042	95	7	17	17	NUM
ejpam-5042	95	8	(	(	PUNCT
ejpam-5042	95	9	2	2	NUM
ejpam-5042	95	10	)	)	PUNCT
ejpam-5042	95	11	(	(	PUNCT
ejpam-5042	95	12	2024	2024	NUM
ejpam-5042	95	13	)	)	PUNCT
ejpam-5042	95	14	,	,	PUNCT
ejpam-5042	95	15	1129	1129	NUM
ejpam-5042	95	16	-	-	SYM
ejpam-5042	95	17	1145	1145	NUM
ejpam-5042	95	18	1133	1133	NUM
ejpam-5042	95	19	let	let	VERB
ejpam-5042	95	20	v	v	PART
ejpam-5042	95	21	be	be	AUX
ejpam-5042	95	22	a	a	DET
ejpam-5042	95	23	pdl	pdl	NOUN
ejpam-5042	95	24	.	.	PUNCT
ejpam-5042	96	1	then	then	ADV
ejpam-5042	96	2	,	,	PUNCT
ejpam-5042	96	3	an	an	DET
ejpam-5042	96	4	element	element	NOUN
ejpam-5042	96	5	µ1	µ1	PROPN
ejpam-5042	96	6	∈	∈	NOUN
ejpam-5042	96	7	v	v	NOUN
ejpam-5042	96	8	is	be	AUX
ejpam-5042	96	9	said	say	VERB
ejpam-5042	96	10	to	to	PART
ejpam-5042	96	11	be	be	AUX
ejpam-5042	96	12	a	a	DET
ejpam-5042	96	13	minimal	minimal	ADJ
ejpam-5042	96	14	element	element	NOUN
ejpam-5042	96	15	if	if	SCONJ
ejpam-5042	96	16	for	for	ADP
ejpam-5042	96	17	any	any	DET
ejpam-5042	96	18	u	u	PROPN
ejpam-5042	96	19	∈	∈	PROPN
ejpam-5042	96	20	v	v	NOUN
ejpam-5042	96	21	,	,	PUNCT
ejpam-5042	96	22	u	u	NOUN
ejpam-5042	96	23	≤	≤	X
ejpam-5042	96	24	µ1	µ1	PROPN
ejpam-5042	96	25	⇒	⇒	NOUN
ejpam-5042	96	26	u	u	NOUN
ejpam-5042	96	27	=	=	PROPN
ejpam-5042	96	28	µ1	µ1	PROPN
ejpam-5042	96	29	.	.	PUNCT
ejpam-5042	97	1	lemma	lemma	PROPN
ejpam-5042	97	2	2	2	X
ejpam-5042	97	3	.	.	PUNCT
ejpam-5042	98	1	let	let	VERB
ejpam-5042	98	2	v	v	PART
ejpam-5042	98	3	be	be	AUX
ejpam-5042	98	4	a	a	DET
ejpam-5042	98	5	pdl	pdl	NOUN
ejpam-5042	98	6	.	.	PUNCT
ejpam-5042	99	1	then	then	ADV
ejpam-5042	99	2	,	,	PUNCT
ejpam-5042	99	3	for	for	ADP
ejpam-5042	99	4	any	any	DET
ejpam-5042	99	5	µ1	µ1	PROPN
ejpam-5042	99	6	∈	∈	PROPN
ejpam-5042	99	7	v	v	NOUN
ejpam-5042	99	8	,	,	PUNCT
ejpam-5042	99	9	the	the	DET
ejpam-5042	99	10	following	follow	VERB
ejpam-5042	99	11	are	be	AUX
ejpam-5042	99	12	equivalent	equivalent	ADJ
ejpam-5042	99	13	:	:	PUNCT
ejpam-5042	99	14	(	(	PUNCT
ejpam-5042	99	15	1	1	NUM
ejpam-5042	99	16	)	)	PUNCT
ejpam-5042	99	17	.	.	PUNCT
ejpam-5042	100	1	µ1	µ1	PROPN
ejpam-5042	100	2	is	be	AUX
ejpam-5042	100	3	minimal	minimal	ADJ
ejpam-5042	100	4	(	(	PUNCT
ejpam-5042	100	5	2	2	NUM
ejpam-5042	100	6	)	)	PUNCT
ejpam-5042	100	7	.	.	PUNCT
ejpam-5042	101	1	κ1	κ1	PROPN
ejpam-5042	101	2	∧	∧	PROPN
ejpam-5042	101	3	µ1	µ1	PROPN
ejpam-5042	101	4	=	=	PUNCT
ejpam-5042	101	5	µ1	µ1	NOUN
ejpam-5042	101	6	for	for	ADP
ejpam-5042	101	7	all	all	DET
ejpam-5042	101	8	κ1	κ1	NOUN
ejpam-5042	101	9	∈	∈	PROPN
ejpam-5042	101	10	v	v	ADP
ejpam-5042	101	11	(	(	PUNCT
ejpam-5042	101	12	3	3	NUM
ejpam-5042	101	13	)	)	PUNCT
ejpam-5042	101	14	.	.	PUNCT
ejpam-5042	102	1	κ1	κ1	PROPN
ejpam-5042	102	2	∨	∨	NUM
ejpam-5042	102	3	µ1	µ1	PROPN
ejpam-5042	102	4	=	=	PROPN
ejpam-5042	102	5	κ1	κ1	NOUN
ejpam-5042	102	6	for	for	ADP
ejpam-5042	102	7	all	all	DET
ejpam-5042	102	8	κ1	κ1	NOUN
ejpam-5042	102	9	∈	∈	PROPN
ejpam-5042	102	10	v	v	NOUN
ejpam-5042	102	11	.	.	PUNCT
ejpam-5042	103	1	definition	definition	NOUN
ejpam-5042	103	2	3	3	NUM
ejpam-5042	103	3	.	.	PUNCT
ejpam-5042	104	1	a	a	DET
ejpam-5042	104	2	non	non	ADJ
ejpam-5042	104	3	-	-	ADJ
ejpam-5042	104	4	empty	empty	ADJ
ejpam-5042	104	5	subset	subset	NOUN
ejpam-5042	104	6	f	f	PROPN
ejpam-5042	104	7	of	of	ADP
ejpam-5042	104	8	a	a	DET
ejpam-5042	104	9	pdl	pdl	NOUN
ejpam-5042	104	10	v	v	NOUN
ejpam-5042	104	11	is	be	AUX
ejpam-5042	104	12	said	say	VERB
ejpam-5042	104	13	to	to	PART
ejpam-5042	104	14	be	be	AUX
ejpam-5042	104	15	a	a	DET
ejpam-5042	104	16	filter	filter	NOUN
ejpam-5042	104	17	if	if	SCONJ
ejpam-5042	104	18	it	it	PRON
ejpam-5042	104	19	satisfies	satisfy	VERB
ejpam-5042	104	20	the	the	DET
ejpam-5042	104	21	following	follow	VERB
ejpam-5042	104	22	:	:	PUNCT
ejpam-5042	104	23	κ1	κ1	NOUN
ejpam-5042	104	24	,	,	PUNCT
ejpam-5042	104	25	κ2	κ2	PROPN
ejpam-5042	104	26	∈	∈	PROPN
ejpam-5042	105	1	f	f	PROPN
ejpam-5042	105	2	⇒	⇒	VERB
ejpam-5042	105	3	κ1	κ1	PROPN
ejpam-5042	105	4	∧	∧	PROPN
ejpam-5042	105	5	κ2	κ2	PROPN
ejpam-5042	105	6	∈	∈	PROPN
ejpam-5042	105	7	f.	f.	PROPN
ejpam-5042	105	8	κ1	κ1	PROPN
ejpam-5042	105	9	∈	∈	PROPN
ejpam-5042	106	1	f	f	PROPN
ejpam-5042	106	2	,	,	PUNCT
ejpam-5042	106	3	µ1	µ1	PROPN
ejpam-5042	106	4	∈	∈	PROPN
ejpam-5042	106	5	v	v	ADP
ejpam-5042	106	6	⇒	⇒	PROPN
ejpam-5042	106	7	µ1	µ1	PROPN
ejpam-5042	106	8	∨	∨	PROPN
ejpam-5042	106	9	κ1	κ1	PROPN
ejpam-5042	106	10	∈	∈	PROPN
ejpam-5042	106	11	f.	f.	PROPN
ejpam-5042	106	12	theorem	theorem	PROPN
ejpam-5042	106	13	2	2	X
ejpam-5042	106	14	.	.	PUNCT
ejpam-5042	107	1	let	let	VERB
ejpam-5042	107	2	s	s	PRON
ejpam-5042	107	3	be	be	AUX
ejpam-5042	107	4	a	a	DET
ejpam-5042	107	5	non	non	ADJ
ejpam-5042	107	6	-	-	ADJ
ejpam-5042	107	7	empty	empty	ADJ
ejpam-5042	107	8	subset	subset	NOUN
ejpam-5042	107	9	of	of	ADP
ejpam-5042	107	10	v	v	NOUN
ejpam-5042	107	11	.	.	PUNCT
ejpam-5042	108	1	then	then	ADV
ejpam-5042	108	2	[	[	X
ejpam-5042	108	3	s	s	X
ejpam-5042	108	4	)	)	PUNCT
ejpam-5042	108	5	=	=	SYM
ejpam-5042	108	6	{	{	PUNCT
ejpam-5042	108	7	κ1	κ1	PROPN
ejpam-5042	108	8	∨	∨	PROPN
ejpam-5042	108	9	(	(	PUNCT
ejpam-5042	108	10	n	n	CCONJ
ejpam-5042	108	11	∧	∧	PROPN
ejpam-5042	108	12	i=1	i=1	PROPN
ejpam-5042	108	13	si	si	NOUN
ejpam-5042	108	14	)	)	PUNCT
ejpam-5042	108	15	|	|	ADV
ejpam-5042	108	16	si	si	PROPN
ejpam-5042	108	17	∈	∈	PROPN
ejpam-5042	108	18	s	s	PROPN
ejpam-5042	108	19	,	,	PUNCT
ejpam-5042	108	20	κ1	κ1	NOUN
ejpam-5042	108	21	∈	∈	PROPN
ejpam-5042	108	22	v	v	NOUN
ejpam-5042	108	23	,	,	PUNCT
ejpam-5042	108	24	1	1	NUM
ejpam-5042	108	25	≤	≤	NUM
ejpam-5042	108	26	i	i	PRON
ejpam-5042	108	27	≤	≤	ADJ
ejpam-5042	108	28	n	n	CCONJ
ejpam-5042	108	29	and	and	CCONJ
ejpam-5042	108	30	n	n	PROPN
ejpam-5042	108	31	is	be	AUX
ejpam-5042	108	32	a	a	DET
ejpam-5042	108	33	positive	positive	ADJ
ejpam-5042	108	34	integer	integer	NOUN
ejpam-5042	108	35	}	}	PUNCT
ejpam-5042	108	36	is	be	AUX
ejpam-5042	108	37	the	the	DET
ejpam-5042	108	38	smallest	small	ADJ
ejpam-5042	108	39	filter	filter	NOUN
ejpam-5042	108	40	of	of	ADP
ejpam-5042	108	41	v	v	NOUN
ejpam-5042	108	42	containing	contain	VERB
ejpam-5042	108	43	s.	s.	PROPN
ejpam-5042	108	44	lemma	lemma	PROPN
ejpam-5042	109	1	3	3	X
ejpam-5042	109	2	.	.	PUNCT
ejpam-5042	109	3	let	let	VERB
ejpam-5042	109	4	v	v	PART
ejpam-5042	109	5	be	be	AUX
ejpam-5042	109	6	a	a	DET
ejpam-5042	109	7	pdl	pdl	NOUN
ejpam-5042	109	8	and	and	CCONJ
ejpam-5042	109	9	f	f	PROPN
ejpam-5042	109	10	be	be	AUX
ejpam-5042	109	11	a	a	DET
ejpam-5042	109	12	filter	filter	NOUN
ejpam-5042	109	13	of	of	ADP
ejpam-5042	109	14	v	v	NOUN
ejpam-5042	109	15	.	.	PUNCT
ejpam-5042	110	1	then	then	ADV
ejpam-5042	110	2	for	for	ADP
ejpam-5042	110	3	any	any	DET
ejpam-5042	110	4	κ1	κ1	NOUN
ejpam-5042	110	5	,	,	PUNCT
ejpam-5042	110	6	κ2	κ2	PROPN
ejpam-5042	110	7	∈	∈	PROPN
ejpam-5042	110	8	v	v	NOUN
ejpam-5042	110	9	,	,	PUNCT
ejpam-5042	110	10	we	we	PRON
ejpam-5042	110	11	have	have	VERB
ejpam-5042	110	12	the	the	DET
ejpam-5042	110	13	following	following	NOUN
ejpam-5042	110	14	:	:	PUNCT
ejpam-5042	110	15	(	(	PUNCT
ejpam-5042	110	16	1	1	X
ejpam-5042	110	17	)	)	PUNCT
ejpam-5042	111	1	[	[	X
ejpam-5042	111	2	κ1	κ1	NOUN
ejpam-5042	111	3	)	)	PUNCT
ejpam-5042	111	4	=	=	SYM
ejpam-5042	111	5	{	{	PUNCT
ejpam-5042	111	6	ρ	ρ	PROPN
ejpam-5042	111	7	∨	∨	PROPN
ejpam-5042	111	8	κ1	κ1	NOUN
ejpam-5042	112	1	|	|	NOUN
ejpam-5042	112	2	ρ	ρ	PROPN
ejpam-5042	112	3	∈	∈	PROPN
ejpam-5042	112	4	v	v	ADP
ejpam-5042	112	5	}	}	PUNCT
ejpam-5042	112	6	.	.	PUNCT
ejpam-5042	113	1	(	(	PUNCT
ejpam-5042	113	2	2	2	X
ejpam-5042	113	3	)	)	PUNCT
ejpam-5042	113	4	κ1	κ1	NOUN
ejpam-5042	113	5	∈	∈	PROPN
ejpam-5042	113	6	[	[	X
ejpam-5042	113	7	κ2	κ2	NOUN
ejpam-5042	113	8	)	)	PUNCT
ejpam-5042	113	9	if	if	SCONJ
ejpam-5042	114	1	and	and	CCONJ
ejpam-5042	114	2	only	only	ADV
ejpam-5042	114	3	if	if	SCONJ
ejpam-5042	114	4	κ1	κ1	NOUN
ejpam-5042	114	5	=	=	SYM
ejpam-5042	114	6	κ1	κ1	PROPN
ejpam-5042	114	7	∨	∨	NUM
ejpam-5042	114	8	κ2	κ2	NOUN
ejpam-5042	114	9	for	for	ADP
ejpam-5042	114	10	all	all	DET
ejpam-5042	114	11	κ1	κ1	NOUN
ejpam-5042	114	12	,	,	PUNCT
ejpam-5042	114	13	κ2	κ2	PROPN
ejpam-5042	114	14	∈	∈	PROPN
ejpam-5042	114	15	v	v	NOUN
ejpam-5042	114	16	.	.	PUNCT
ejpam-5042	115	1	(	(	PUNCT
ejpam-5042	115	2	3	3	X
ejpam-5042	115	3	)	)	PUNCT
ejpam-5042	115	4	κ1	κ1	NOUN
ejpam-5042	115	5	∨	∨	NUM
ejpam-5042	115	6	κ2	κ2	PROPN
ejpam-5042	115	7	∈	∈	PROPN
ejpam-5042	115	8	f	f	PROPN
ejpam-5042	116	1	if	if	SCONJ
ejpam-5042	116	2	and	and	CCONJ
ejpam-5042	116	3	only	only	ADV
ejpam-5042	116	4	if	if	SCONJ
ejpam-5042	116	5	κ2	κ2	NOUN
ejpam-5042	116	6	∨	∨	NUM
ejpam-5042	116	7	κ1	κ1	PROPN
ejpam-5042	116	8	∈	∈	PROPN
ejpam-5042	116	9	f	f	X
ejpam-5042	116	10	.	.	PUNCT
ejpam-5042	117	1	(	(	PUNCT
ejpam-5042	117	2	4	4	X
ejpam-5042	117	3	)	)	PUNCT
ejpam-5042	118	1	[	[	X
ejpam-5042	118	2	κ1	κ1	PROPN
ejpam-5042	118	3	∨	∨	NUM
ejpam-5042	118	4	κ2	κ2	NOUN
ejpam-5042	118	5	)	)	PUNCT
ejpam-5042	118	6	=	=	PUNCT
ejpam-5042	119	1	[	[	X
ejpam-5042	119	2	κ2	κ2	PROPN
ejpam-5042	119	3	∨	∨	NUM
ejpam-5042	119	4	κ1	κ1	NOUN
ejpam-5042	119	5	)	)	PUNCT
ejpam-5042	119	6	.	.	PUNCT
ejpam-5042	120	1	(	(	PUNCT
ejpam-5042	120	2	5	5	X
ejpam-5042	120	3	)	)	PUNCT
ejpam-5042	120	4	[	[	X
ejpam-5042	120	5	κ1	κ1	NOUN
ejpam-5042	120	6	∧	∧	PROPN
ejpam-5042	120	7	κ2	κ2	NOUN
ejpam-5042	120	8	)	)	PUNCT
ejpam-5042	120	9	=	=	PUNCT
ejpam-5042	121	1	[	[	X
ejpam-5042	121	2	κ2	κ2	NOUN
ejpam-5042	121	3	∧	∧	PROPN
ejpam-5042	121	4	κ1	κ1	NOUN
ejpam-5042	121	5	)	)	PUNCT
ejpam-5042	121	6	=	=	PUNCT
ejpam-5042	122	1	[	[	X
ejpam-5042	122	2	κ1	κ1	NOUN
ejpam-5042	122	3	)	)	PUNCT
ejpam-5042	122	4	∨	∨	NUM
ejpam-5042	123	1	[	[	X
ejpam-5042	123	2	κ2	κ2	NOUN
ejpam-5042	123	3	)	)	PUNCT
ejpam-5042	123	4	.	.	PUNCT
ejpam-5042	124	1	theorem	theorem	NOUN
ejpam-5042	124	2	3	3	NUM
ejpam-5042	124	3	.	.	PUNCT
ejpam-5042	125	1	the	the	DET
ejpam-5042	125	2	collection	collection	NOUN
ejpam-5042	125	3	f	f	X
ejpam-5042	125	4	(	(	PUNCT
ejpam-5042	125	5	l	l	NOUN
ejpam-5042	125	6	)	)	PUNCT
ejpam-5042	125	7	of	of	ADP
ejpam-5042	125	8	all	all	DET
ejpam-5042	125	9	filters	filter	NOUN
ejpam-5042	125	10	of	of	ADP
ejpam-5042	125	11	a	a	DET
ejpam-5042	125	12	pdl	pdl	NOUN
ejpam-5042	125	13	v	v	NOUN
ejpam-5042	125	14	forms	form	NOUN
ejpam-5042	125	15	a	a	DET
ejpam-5042	125	16	distributive	distributive	ADJ
ejpam-5042	125	17	lattice	lattice	NOUN
ejpam-5042	125	18	under	under	ADP
ejpam-5042	125	19	set	set	ADJ
ejpam-5042	125	20	inclusion	inclusion	NOUN
ejpam-5042	125	21	,	,	PUNCT
ejpam-5042	125	22	in	in	ADP
ejpam-5042	125	23	which	which	PRON
ejpam-5042	125	24	,	,	PUNCT
ejpam-5042	125	25	the	the	DET
ejpam-5042	125	26	glb	glb	NOUN
ejpam-5042	125	27	and	and	CCONJ
ejpam-5042	125	28	lub	lub	NOUN
ejpam-5042	125	29	of	of	ADP
ejpam-5042	125	30	any	any	DET
ejpam-5042	125	31	f	f	PROPN
ejpam-5042	125	32	and	and	CCONJ
ejpam-5042	125	33	g	g	PROPN
ejpam-5042	125	34	are	be	AUX
ejpam-5042	125	35	given	give	VERB
ejpam-5042	125	36	respectively	respectively	ADV
ejpam-5042	125	37	by	by	ADP
ejpam-5042	125	38	f	f	PROPN
ejpam-5042	125	39	∧g	∧g	PROPN
ejpam-5042	125	40	=	=	SYM
ejpam-5042	125	41	f	f	PROPN
ejpam-5042	125	42	∩g	∩g	NOUN
ejpam-5042	125	43	and	and	CCONJ
ejpam-5042	125	44	f	f	PROPN
ejpam-5042	125	45	∨g	∨g	PROPN
ejpam-5042	125	46	=	=	SYM
ejpam-5042	125	47	{	{	PUNCT
ejpam-5042	125	48	κ1	κ1	NOUN
ejpam-5042	125	49	∧	∧	PROPN
ejpam-5042	125	50	κ2	κ2	NOUN
ejpam-5042	125	51	|	|	ADV
ejpam-5042	125	52	κ1	κ1	NOUN
ejpam-5042	125	53	∈	∈	PROPN
ejpam-5042	125	54	f	f	PROPN
ejpam-5042	125	55	and	and	CCONJ
ejpam-5042	125	56	κ2	κ2	PROPN
ejpam-5042	125	57	∈	∈	PROPN
ejpam-5042	125	58	g	g	NOUN
ejpam-5042	125	59	}	}	PUNCT
ejpam-5042	125	60	.	.	PUNCT
ejpam-5042	126	1	definition	definition	NOUN
ejpam-5042	126	2	4	4	NUM
ejpam-5042	126	3	.	.	PUNCT
ejpam-5042	126	4	by	by	ADP
ejpam-5042	126	5	a	a	DET
ejpam-5042	126	6	homomorphism	homomorphism	NOUN
ejpam-5042	126	7	of	of	ADP
ejpam-5042	126	8	a	a	DET
ejpam-5042	126	9	pdl	pdl	PROPN
ejpam-5042	126	10	(	(	PUNCT
ejpam-5042	126	11	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	126	12	,	,	PUNCT
ejpam-5042	126	13	1	1	NUM
ejpam-5042	126	14	)	)	PUNCT
ejpam-5042	126	15	into	into	ADP
ejpam-5042	126	16	a	a	DET
ejpam-5042	126	17	pdl	pdl	NOUN
ejpam-5042	126	18	(	(	PUNCT
ejpam-5042	126	19	v	v	NOUN
ejpam-5042	126	20	′,∨′,∧′	′,∨′,∧′	NOUN
ejpam-5042	126	21	,	,	PUNCT
ejpam-5042	126	22	1′	1′	NUM
ejpam-5042	126	23	)	)	PUNCT
ejpam-5042	126	24	,	,	PUNCT
ejpam-5042	126	25	we	we	PRON
ejpam-5042	126	26	mean	mean	VERB
ejpam-5042	126	27	,	,	PUNCT
ejpam-5042	126	28	a	a	DET
ejpam-5042	126	29	mapping	mapping	NOUN
ejpam-5042	126	30	f	f	NOUN
ejpam-5042	126	31	:	:	PUNCT
ejpam-5042	126	32	v	v	X
ejpam-5042	126	33	→	→	SYM
ejpam-5042	126	34	v	v	NOUN
ejpam-5042	126	35	′	′	NOUN
ejpam-5042	126	36	satisfying	satisfy	VERB
ejpam-5042	126	37	the	the	DET
ejpam-5042	126	38	following	following	NOUN
ejpam-5042	126	39	:	:	PUNCT
ejpam-5042	126	40	(	(	PUNCT
ejpam-5042	126	41	1	1	X
ejpam-5042	126	42	)	)	PUNCT
ejpam-5042	126	43	f(µ1	f(µ1	VERB
ejpam-5042	126	44	∨	∨	NUM
ejpam-5042	126	45	µ2	µ2	PROPN
ejpam-5042	126	46	)	)	PUNCT
ejpam-5042	126	47	=	=	SYM
ejpam-5042	126	48	f(µ1	f(µ1	NOUN
ejpam-5042	126	49	)	)	PUNCT
ejpam-5042	127	1	∨′	∨′	PRON
ejpam-5042	127	2	f(µ2	f(µ2	NOUN
ejpam-5042	127	3	)	)	PUNCT
ejpam-5042	127	4	(	(	PUNCT
ejpam-5042	127	5	2	2	X
ejpam-5042	127	6	)	)	PUNCT
ejpam-5042	127	7	f(µ1	f(µ1	VERB
ejpam-5042	127	8	∧	∧	PROPN
ejpam-5042	127	9	µ2	µ2	PROPN
ejpam-5042	127	10	)	)	PUNCT
ejpam-5042	127	11	=	=	SYM
ejpam-5042	127	12	f(µ1	f(µ1	NOUN
ejpam-5042	127	13	)	)	PUNCT
ejpam-5042	127	14	∧′	∧′	PROPN
ejpam-5042	127	15	f(µ2	f(µ2	NOUN
ejpam-5042	127	16	)	)	PUNCT
ejpam-5042	127	17	(	(	PUNCT
ejpam-5042	127	18	3	3	X
ejpam-5042	127	19	)	)	PUNCT
ejpam-5042	127	20	f(1	f(1	PROPN
ejpam-5042	127	21	)	)	PUNCT
ejpam-5042	127	22	=	=	SYM
ejpam-5042	127	23	f(1′	f(1′	PROPN
ejpam-5042	127	24	)	)	PUNCT
ejpam-5042	127	25	.	.	PUNCT
ejpam-5042	128	1	3	3	X
ejpam-5042	128	2	.	.	X
ejpam-5042	128	3	parapseudo	parapseudo	NOUN
ejpam-5042	128	4	-	-	NOUN
ejpam-5042	128	5	complementation	complementation	NOUN
ejpam-5042	128	6	on	on	ADP
ejpam-5042	128	7	paradistributive	paradistributive	ADJ
ejpam-5042	128	8	latticoids	latticoid	NOUN
ejpam-5042	128	9	in	in	ADP
ejpam-5042	128	10	this	this	DET
ejpam-5042	128	11	section	section	NOUN
ejpam-5042	128	12	,	,	PUNCT
ejpam-5042	128	13	we	we	PRON
ejpam-5042	128	14	define	define	VERB
ejpam-5042	128	15	a	a	DET
ejpam-5042	128	16	parapseudo	parapseudo	NOUN
ejpam-5042	128	17	-	-	NOUN
ejpam-5042	128	18	complementation	complementation	NOUN
ejpam-5042	128	19	on	on	ADP
ejpam-5042	128	20	a	a	DET
ejpam-5042	128	21	pdl	pdl	NOUN
ejpam-5042	128	22	and	and	CCONJ
ejpam-5042	128	23	present	present	VERB
ejpam-5042	128	24	some	some	DET
ejpam-5042	128	25	fundamental	fundamental	ADJ
ejpam-5042	128	26	findings	finding	NOUN
ejpam-5042	128	27	which	which	PRON
ejpam-5042	128	28	helps	help	VERB
ejpam-5042	128	29	in	in	ADP
ejpam-5042	128	30	verification	verification	NOUN
ejpam-5042	128	31	of	of	ADP
ejpam-5042	128	32	the	the	DET
ejpam-5042	128	33	axioms	axioms	ADJ
ejpam-5042	128	34	independency	independency	NOUN
ejpam-5042	128	35	.	.	PUNCT
ejpam-5042	129	1	definition	definition	NOUN
ejpam-5042	129	2	5	5	NUM
ejpam-5042	129	3	.	.	PUNCT
ejpam-5042	130	1	let	let	AUX
ejpam-5042	130	2	(	(	PUNCT
ejpam-5042	130	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	130	4	,	,	PUNCT
ejpam-5042	130	5	1	1	NUM
ejpam-5042	130	6	)	)	PUNCT
ejpam-5042	130	7	be	be	AUX
ejpam-5042	130	8	a	a	DET
ejpam-5042	130	9	paradistributive	paradistributive	ADJ
ejpam-5042	130	10	latticoid	latticoid	NOUN
ejpam-5042	130	11	(	(	PUNCT
ejpam-5042	130	12	pdl	pdl	NOUN
ejpam-5042	130	13	)	)	PUNCT
ejpam-5042	130	14	and	and	CCONJ
ejpam-5042	130	15	consider	consider	VERB
ejpam-5042	130	16	a	a	DET
ejpam-5042	130	17	unary	unary	ADJ
ejpam-5042	130	18	operation	operation	NOUN
ejpam-5042	130	19	denoted	denote	VERB
ejpam-5042	130	20	as	as	ADP
ejpam-5042	130	21	ρ	ρ	PROPN
ejpam-5042	130	22	7→	7→	PROPN
ejpam-5042	130	23	ρ	ρ	NUM
ejpam-5042	130	24	♦	♦	PROPN
ejpam-5042	130	25	on	on	ADP
ejpam-5042	130	26	v	v	NUM
ejpam-5042	130	27	.	.	PUNCT
ejpam-5042	131	1	this	this	DET
ejpam-5042	131	2	operation	operation	NOUN
ejpam-5042	131	3	is	be	AUX
ejpam-5042	131	4	called	call	VERB
ejpam-5042	131	5	a	a	DET
ejpam-5042	131	6	parapseudo	parapseudo	NOUN
ejpam-5042	131	7	-	-	NOUN
ejpam-5042	131	8	complementation	complementation	NOUN
ejpam-5042	131	9	on	on	ADP
ejpam-5042	131	10	v	v	PRON
ejpam-5042	131	11	if	if	SCONJ
ejpam-5042	131	12	it	it	PRON
ejpam-5042	131	13	satisfies	satisfy	VERB
ejpam-5042	131	14	the	the	DET
ejpam-5042	131	15	following	follow	VERB
ejpam-5042	131	16	conditions	condition	NOUN
ejpam-5042	131	17	:	:	PUNCT
ejpam-5042	131	18	(	(	PUNCT
ejpam-5042	131	19	ppc1	ppc1	PROPN
ejpam-5042	131	20	)	)	PUNCT
ejpam-5042	131	21	if	if	SCONJ
ejpam-5042	131	22	ρ	ρ	PROPN
ejpam-5042	131	23	∨	∨	NUM
ejpam-5042	131	24	ϱ	ϱ	ADP
ejpam-5042	131	25	=	=	SYM
ejpam-5042	131	26	1	1	NUM
ejpam-5042	131	27	,	,	PUNCT
ejpam-5042	131	28	then	then	ADV
ejpam-5042	131	29	ρ	ρ	PROPN
ejpam-5042	131	30	∨	∨	NUM
ejpam-5042	131	31	ϱ	ϱ	PROPN
ejpam-5042	131	32	♦	♦	PROPN
ejpam-5042	131	33	=	=	PROPN
ejpam-5042	131	34	ρ	ρ	PROPN
ejpam-5042	131	35	.	.	PUNCT
ejpam-5042	132	1	(	(	PUNCT
ejpam-5042	132	2	ppc2	ppc2	PROPN
ejpam-5042	132	3	)	)	PUNCT
ejpam-5042	132	4	ρ	ρ	PROPN
ejpam-5042	132	5	∨	∨	PROPN
ejpam-5042	132	6	ρ	ρ	PROPN
ejpam-5042	132	7	♦	♦	PROPN
ejpam-5042	132	8	=	=	PROPN
ejpam-5042	132	9	1	1	PROPN
ejpam-5042	132	10	.	.	PUNCT
ejpam-5042	133	1	(	(	PUNCT
ejpam-5042	133	2	ppc3	ppc3	ADJ
ejpam-5042	133	3	)	)	PUNCT
ejpam-5042	133	4	(	(	PUNCT
ejpam-5042	133	5	ρ	ρ	PROPN
ejpam-5042	133	6	∧	∧	PROPN
ejpam-5042	133	7	ϱ	ϱ	NOUN
ejpam-5042	133	8	)	)	PUNCT
ejpam-5042	133	9	♦	♦	PROPN
ejpam-5042	133	10	=	=	PROPN
ejpam-5042	133	11	ρ	ρ	PROPN
ejpam-5042	133	12	♦	♦	PROPN
ejpam-5042	133	13	∨	∨	NUM
ejpam-5042	133	14	ϱ	ϱ	PROPN
ejpam-5042	133	15	♦	♦	PROPN
ejpam-5042	133	16	.	.	PUNCT
ejpam-5042	134	1	r.	r.	PROPN
ejpam-5042	134	2	shukla	shukla	PROPN
ejpam-5042	134	3	et	et	PROPN
ejpam-5042	134	4	al	al	PROPN
ejpam-5042	134	5	.	.	PUNCT
ejpam-5042	134	6	/	/	SYM
ejpam-5042	134	7	eur	eur	PROPN
ejpam-5042	134	8	.	.	PUNCT
ejpam-5042	135	1	j.	j.	PROPN
ejpam-5042	135	2	pure	pure	PROPN
ejpam-5042	135	3	appl	appl	PROPN
ejpam-5042	135	4	.	.	PROPN
ejpam-5042	135	5	math	math	PROPN
ejpam-5042	135	6	,	,	PUNCT
ejpam-5042	135	7	17	17	NUM
ejpam-5042	135	8	(	(	PUNCT
ejpam-5042	135	9	2	2	NUM
ejpam-5042	135	10	)	)	PUNCT
ejpam-5042	135	11	(	(	PUNCT
ejpam-5042	135	12	2024	2024	NUM
ejpam-5042	135	13	)	)	PUNCT
ejpam-5042	135	14	,	,	PUNCT
ejpam-5042	135	15	1129	1129	NUM
ejpam-5042	135	16	-	-	SYM
ejpam-5042	135	17	1145	1145	NUM
ejpam-5042	135	18	1134	1134	NUM
ejpam-5042	135	19	if	if	SCONJ
ejpam-5042	135	20	there	there	PRON
ejpam-5042	135	21	is	be	VERB
ejpam-5042	135	22	no	no	DET
ejpam-5042	135	23	ambiguity	ambiguity	NOUN
ejpam-5042	135	24	about	about	ADP
ejpam-5042	135	25	the	the	DET
ejpam-5042	135	26	parapseudo	parapseudo	NOUN
ejpam-5042	135	27	-	-	NOUN
ejpam-5042	135	28	complementation	complementation	NOUN
ejpam-5042	135	29	on	on	ADP
ejpam-5042	135	30	a	a	DET
ejpam-5042	135	31	pdl	pdl	NOUN
ejpam-5042	135	32	v	v	NOUN
ejpam-5042	135	33	,	,	PUNCT
ejpam-5042	135	34	we	we	PRON
ejpam-5042	135	35	can	can	AUX
ejpam-5042	135	36	say	say	VERB
ejpam-5042	135	37	that	that	SCONJ
ejpam-5042	135	38	v	v	NOUN
ejpam-5042	135	39	is	be	AUX
ejpam-5042	135	40	a	a	DET
ejpam-5042	135	41	parapseudo	parapseudo	NOUN
ejpam-5042	135	42	-	-	PUNCT
ejpam-5042	135	43	complemented	complemented	ADJ
ejpam-5042	135	44	pdl	pdl	NOUN
ejpam-5042	135	45	(	(	PUNCT
ejpam-5042	135	46	ppdl	ppdl	NOUN
ejpam-5042	135	47	)	)	PUNCT
ejpam-5042	135	48	.	.	PUNCT
ejpam-5042	136	1	in	in	ADP
ejpam-5042	136	2	the	the	DET
ejpam-5042	136	3	case	case	NOUN
ejpam-5042	136	4	of	of	ADP
ejpam-5042	136	5	a	a	DET
ejpam-5042	136	6	distributive	distributive	ADJ
ejpam-5042	136	7	lattice	lattice	NOUN
ejpam-5042	136	8	with	with	ADP
ejpam-5042	136	9	one	one	NUM
ejpam-5042	136	10	,	,	PUNCT
ejpam-5042	136	11	ppc3	ppc3	ADJ
ejpam-5042	136	12	becomes	become	VERB
ejpam-5042	136	13	a	a	DET
ejpam-5042	136	14	consequence	consequence	NOUN
ejpam-5042	136	15	of	of	ADP
ejpam-5042	136	16	ppc1	ppc1	NOUN
ejpam-5042	136	17	and	and	CCONJ
ejpam-5042	136	18	ppc2	ppc2	NOUN
ejpam-5042	136	19	.	.	PUNCT
ejpam-5042	137	1	however	however	ADV
ejpam-5042	137	2	,	,	PUNCT
ejpam-5042	137	3	in	in	ADP
ejpam-5042	137	4	the	the	DET
ejpam-5042	137	5	case	case	NOUN
ejpam-5042	137	6	of	of	ADP
ejpam-5042	137	7	pdls	pdl	NOUN
ejpam-5042	137	8	,	,	PUNCT
ejpam-5042	137	9	ppc1	ppc1	NOUN
ejpam-5042	137	10	,	,	PUNCT
ejpam-5042	137	11	ppc2	ppc2	NOUN
ejpam-5042	137	12	,	,	PUNCT
ejpam-5042	137	13	and	and	CCONJ
ejpam-5042	137	14	ppc3	ppc3	PROPN
ejpam-5042	137	15	are	be	AUX
ejpam-5042	137	16	independent	independent	ADJ
ejpam-5042	137	17	.	.	PUNCT
ejpam-5042	138	1	now	now	ADV
ejpam-5042	138	2	,	,	PUNCT
ejpam-5042	138	3	we	we	PRON
ejpam-5042	138	4	provide	provide	VERB
ejpam-5042	138	5	examples	example	NOUN
ejpam-5042	138	6	to	to	PART
ejpam-5042	138	7	demonstrate	demonstrate	VERB
ejpam-5042	138	8	the	the	DET
ejpam-5042	138	9	independence	independence	NOUN
ejpam-5042	138	10	of	of	ADP
ejpam-5042	138	11	these	these	DET
ejpam-5042	138	12	axioms	axiom	NOUN
ejpam-5042	138	13	.	.	PUNCT
ejpam-5042	139	1	example	example	NOUN
ejpam-5042	139	2	2	2	NUM
ejpam-5042	139	3	.	.	X
ejpam-5042	139	4	consider	consider	VERB
ejpam-5042	139	5	a	a	DET
ejpam-5042	139	6	pdl	pdl	NOUN
ejpam-5042	139	7	v	v	NOUN
ejpam-5042	139	8	with	with	ADP
ejpam-5042	139	9	at	at	ADV
ejpam-5042	139	10	least	least	ADV
ejpam-5042	139	11	two	two	NUM
ejpam-5042	139	12	elements	element	NOUN
ejpam-5042	139	13	.	.	PUNCT
ejpam-5042	140	1	let	let	VERB
ejpam-5042	140	2	’s	’s	PRON
ejpam-5042	140	3	define	define	VERB
ejpam-5042	140	4	the	the	DET
ejpam-5042	140	5	unary	unary	ADJ
ejpam-5042	140	6	operation	operation	NOUN
ejpam-5042	140	7	ρ	ρ	PROPN
ejpam-5042	140	8	♦	♦	PROPN
ejpam-5042	140	9	=	=	PROPN
ejpam-5042	140	10	1	1	NUM
ejpam-5042	140	11	for	for	ADP
ejpam-5042	140	12	all	all	DET
ejpam-5042	140	13	ρ	ρ	NOUN
ejpam-5042	140	14	∈	∈	PROPN
ejpam-5042	140	15	v	v	NOUN
ejpam-5042	140	16	.	.	PUNCT
ejpam-5042	141	1	we	we	PRON
ejpam-5042	141	2	will	will	AUX
ejpam-5042	141	3	show	show	VERB
ejpam-5042	141	4	that	that	SCONJ
ejpam-5042	141	5	v	v	ADJ
ejpam-5042	141	6	satisfies	satisfie	NOUN
ejpam-5042	141	7	(	(	PUNCT
ejpam-5042	141	8	ppc2	ppc2	PROPN
ejpam-5042	141	9	)	)	PUNCT
ejpam-5042	141	10	and	and	CCONJ
ejpam-5042	141	11	(	(	PUNCT
ejpam-5042	141	12	ppc3	ppc3	ADJ
ejpam-5042	141	13	)	)	PUNCT
ejpam-5042	141	14	but	but	CCONJ
ejpam-5042	141	15	fails	fail	VERB
ejpam-5042	141	16	to	to	PART
ejpam-5042	141	17	satisfy	satisfy	VERB
ejpam-5042	141	18	(	(	PUNCT
ejpam-5042	141	19	ppc1	ppc1	PROPN
ejpam-5042	141	20	)	)	PUNCT
ejpam-5042	141	21	.	.	PUNCT
ejpam-5042	142	1	(	(	PUNCT
ejpam-5042	142	2	ppc2	ppc2	NOUN
ejpam-5042	142	3	):	):	PUNCT
ejpam-5042	142	4	for	for	ADP
ejpam-5042	142	5	any	any	DET
ejpam-5042	142	6	ρ	ρ	PROPN
ejpam-5042	142	7	∈	∈	PROPN
ejpam-5042	142	8	v	v	NOUN
ejpam-5042	142	9	,	,	PUNCT
ejpam-5042	142	10	we	we	PRON
ejpam-5042	142	11	have	have	VERB
ejpam-5042	142	12	ρ	ρ	PROPN
ejpam-5042	142	13	∨	∨	NUM
ejpam-5042	142	14	ρ	ρ	PROPN
ejpam-5042	142	15	♦	♦	PROPN
ejpam-5042	142	16	=	=	PROPN
ejpam-5042	142	17	ρ	ρ	PROPN
ejpam-5042	142	18	∨	∨	NUM
ejpam-5042	142	19	1	1	NUM
ejpam-5042	142	20	=	=	SYM
ejpam-5042	142	21	1	1	NUM
ejpam-5042	142	22	.	.	PUNCT
ejpam-5042	143	1	hence	hence	ADV
ejpam-5042	143	2	,	,	PUNCT
ejpam-5042	143	3	(	(	PUNCT
ejpam-5042	143	4	ppc2	ppc2	PROPN
ejpam-5042	143	5	)	)	PUNCT
ejpam-5042	143	6	is	be	AUX
ejpam-5042	143	7	satisfied	satisfied	ADJ
ejpam-5042	143	8	.	.	PUNCT
ejpam-5042	144	1	(	(	PUNCT
ejpam-5042	144	2	ppc3	ppc3	ADJ
ejpam-5042	144	3	):	):	PUNCT
ejpam-5042	144	4	let	let	VERB
ejpam-5042	144	5	ρ	ρ	NOUN
ejpam-5042	144	6	,	,	PUNCT
ejpam-5042	144	7	ϱ	ϱ	PROPN
ejpam-5042	144	8	∈	∈	PROPN
ejpam-5042	144	9	v	v	NOUN
ejpam-5042	144	10	.	.	PUNCT
ejpam-5042	145	1	we	we	PRON
ejpam-5042	145	2	have	have	VERB
ejpam-5042	145	3	(	(	PUNCT
ejpam-5042	145	4	ρ	ρ	PROPN
ejpam-5042	145	5	∧	∧	PROPN
ejpam-5042	145	6	ϱ	ϱ	NOUN
ejpam-5042	145	7	)	)	PUNCT
ejpam-5042	145	8	♦	♦	PROPN
ejpam-5042	145	9	=	=	PROPN
ejpam-5042	145	10	1	1	NUM
ejpam-5042	145	11	and	and	CCONJ
ejpam-5042	145	12	ρ	ρ	PROPN
ejpam-5042	145	13	♦	♦	PROPN
ejpam-5042	145	14	∨	∨	NUM
ejpam-5042	145	15	ϱ	ϱ	PROPN
ejpam-5042	145	16	♦	♦	PROPN
ejpam-5042	145	17	=	=	PROPN
ejpam-5042	145	18	1	1	NUM
ejpam-5042	145	19	∨	∨	NUM
ejpam-5042	145	20	1	1	NUM
ejpam-5042	145	21	=	=	SYM
ejpam-5042	145	22	1	1	NUM
ejpam-5042	145	23	.	.	PUNCT
ejpam-5042	146	1	therefore	therefore	ADV
ejpam-5042	146	2	,	,	PUNCT
ejpam-5042	146	3	(	(	PUNCT
ejpam-5042	146	4	ppc3	ppc3	ADJ
ejpam-5042	146	5	)	)	PUNCT
ejpam-5042	146	6	is	be	AUX
ejpam-5042	146	7	satisfied	satisfied	ADJ
ejpam-5042	146	8	.	.	PUNCT
ejpam-5042	147	1	now	now	ADV
ejpam-5042	147	2	,	,	PUNCT
ejpam-5042	147	3	we	we	PRON
ejpam-5042	147	4	examine	examine	VERB
ejpam-5042	147	5	(	(	PUNCT
ejpam-5042	147	6	ppc1	ppc1	PROPN
ejpam-5042	147	7	)	)	PUNCT
ejpam-5042	147	8	.	.	PUNCT
ejpam-5042	148	1	suppose	suppose	VERB
ejpam-5042	148	2	there	there	PRON
ejpam-5042	148	3	exists	exist	VERB
ejpam-5042	148	4	ϱ	ϱ	ADP
ejpam-5042	148	5	∈	∈	PROPN
ejpam-5042	148	6	v	v	ADP
ejpam-5042	148	7	such	such	DET
ejpam-5042	148	8	that	that	SCONJ
ejpam-5042	148	9	ϱ	ϱ	ADP
ejpam-5042	148	10	̸=	̸=	PROPN
ejpam-5042	148	11	1	1	NUM
ejpam-5042	148	12	.	.	PUNCT
ejpam-5042	149	1	we	we	PRON
ejpam-5042	149	2	have	have	VERB
ejpam-5042	149	3	ϱ	ϱ	ADP
ejpam-5042	149	4	∨	∨	NUM
ejpam-5042	149	5	1	1	NUM
ejpam-5042	149	6	=	=	SYM
ejpam-5042	149	7	1	1	NUM
ejpam-5042	149	8	.	.	PUNCT
ejpam-5042	150	1	however	however	ADV
ejpam-5042	150	2	,	,	PUNCT
ejpam-5042	150	3	ϱ	ϱ	ADP
ejpam-5042	150	4	∨	∨	NUM
ejpam-5042	150	5	1	1	NUM
ejpam-5042	150	6	♦	♦	PROPN
ejpam-5042	150	7	=	=	PUNCT
ejpam-5042	150	8	ϱ	ϱ	ADP
ejpam-5042	150	9	∨	∨	NUM
ejpam-5042	150	10	1	1	NUM
ejpam-5042	150	11	=	=	SYM
ejpam-5042	150	12	1	1	NUM
ejpam-5042	150	13	̸=	̸=	PROPN
ejpam-5042	150	14	ϱ.	ϱ.	NOUN
ejpam-5042	150	15	therefore	therefore	ADV
ejpam-5042	150	16	,	,	PUNCT
ejpam-5042	150	17	(	(	PUNCT
ejpam-5042	150	18	ppc1	ppc1	PROPN
ejpam-5042	150	19	)	)	PUNCT
ejpam-5042	150	20	is	be	AUX
ejpam-5042	150	21	not	not	PART
ejpam-5042	150	22	satisfied	satisfied	ADJ
ejpam-5042	150	23	when	when	SCONJ
ejpam-5042	150	24	ϱ	ϱ	NOUN
ejpam-5042	150	25	is	be	AUX
ejpam-5042	150	26	not	not	PART
ejpam-5042	150	27	equal	equal	ADJ
ejpam-5042	150	28	to	to	ADP
ejpam-5042	150	29	1	1	NUM
ejpam-5042	150	30	.	.	PUNCT
ejpam-5042	151	1	in	in	ADP
ejpam-5042	151	2	conclusion	conclusion	NOUN
ejpam-5042	151	3	,	,	PUNCT
ejpam-5042	151	4	the	the	DET
ejpam-5042	151	5	pdl	pdl	PROPN
ejpam-5042	151	6	v	v	NOUN
ejpam-5042	151	7	with	with	ADP
ejpam-5042	151	8	the	the	DET
ejpam-5042	151	9	unary	unary	ADJ
ejpam-5042	151	10	operation	operation	NOUN
ejpam-5042	151	11	ρ	ρ	PROPN
ejpam-5042	151	12	♦	♦	PROPN
ejpam-5042	151	13	=	=	NOUN
ejpam-5042	151	14	1	1	NUM
ejpam-5042	151	15	satisfies	satisfie	NOUN
ejpam-5042	151	16	(	(	PUNCT
ejpam-5042	151	17	ppc2	ppc2	PROPN
ejpam-5042	151	18	)	)	PUNCT
ejpam-5042	151	19	and	and	CCONJ
ejpam-5042	151	20	(	(	PUNCT
ejpam-5042	151	21	ppc3	ppc3	ADJ
ejpam-5042	151	22	)	)	PUNCT
ejpam-5042	151	23	but	but	CCONJ
ejpam-5042	151	24	fails	fail	VERB
ejpam-5042	151	25	to	to	PART
ejpam-5042	151	26	satisfy	satisfy	VERB
ejpam-5042	151	27	(	(	PUNCT
ejpam-5042	151	28	ppc1	ppc1	PROPN
ejpam-5042	151	29	)	)	PUNCT
ejpam-5042	151	30	when	when	SCONJ
ejpam-5042	151	31	v	v	NOUN
ejpam-5042	151	32	has	have	VERB
ejpam-5042	151	33	at	at	ADV
ejpam-5042	151	34	least	least	ADV
ejpam-5042	151	35	two	two	NUM
ejpam-5042	151	36	elements	element	NOUN
ejpam-5042	151	37	.	.	PUNCT
ejpam-5042	152	1	example	example	NOUN
ejpam-5042	153	1	3	3	X
ejpam-5042	153	2	.	.	PUNCT
ejpam-5042	153	3	let	let	VERB
ejpam-5042	153	4	v	v	PART
ejpam-5042	153	5	be	be	AUX
ejpam-5042	153	6	a	a	DET
ejpam-5042	153	7	bounded	bounded	ADJ
ejpam-5042	153	8	distributive	distributive	ADJ
ejpam-5042	153	9	lattice	lattice	NOUN
ejpam-5042	153	10	with	with	ADP
ejpam-5042	153	11	bounds	bound	NOUN
ejpam-5042	153	12	0	0	PUNCT
ejpam-5042	153	13	̸=	̸=	PROPN
ejpam-5042	153	14	1	1	NUM
ejpam-5042	153	15	.	.	PUNCT
ejpam-5042	154	1	define	define	VERB
ejpam-5042	154	2	ρ	ρ	PROPN
ejpam-5042	154	3	♦	♦	PROPN
ejpam-5042	154	4	=	=	PROPN
ejpam-5042	154	5	0	0	PROPN
ejpam-5042	154	6	for	for	ADP
ejpam-5042	154	7	all	all	DET
ejpam-5042	154	8	ρ	ρ	NOUN
ejpam-5042	154	9	∈	∈	PROPN
ejpam-5042	154	10	v	v	NOUN
ejpam-5042	154	11	.	.	PUNCT
ejpam-5042	155	1	we	we	PRON
ejpam-5042	155	2	will	will	AUX
ejpam-5042	155	3	show	show	VERB
ejpam-5042	155	4	that	that	SCONJ
ejpam-5042	155	5	v	v	ADJ
ejpam-5042	155	6	satisfies	satisfie	NOUN
ejpam-5042	155	7	(	(	PUNCT
ejpam-5042	155	8	ppc1	ppc1	PROPN
ejpam-5042	155	9	)	)	PUNCT
ejpam-5042	155	10	and	and	CCONJ
ejpam-5042	155	11	(	(	PUNCT
ejpam-5042	155	12	ppc3	ppc3	ADJ
ejpam-5042	155	13	)	)	PUNCT
ejpam-5042	155	14	but	but	CCONJ
ejpam-5042	155	15	fails	fail	VERB
ejpam-5042	155	16	to	to	PART
ejpam-5042	155	17	satisfy	satisfy	VERB
ejpam-5042	155	18	(	(	PUNCT
ejpam-5042	155	19	ppc2	ppc2	PROPN
ejpam-5042	155	20	)	)	PUNCT
ejpam-5042	155	21	.	.	PUNCT
ejpam-5042	156	1	(	(	PUNCT
ejpam-5042	156	2	ppc1	ppc1	PROPN
ejpam-5042	156	3	):	):	PUNCT
ejpam-5042	156	4	suppose	suppose	VERB
ejpam-5042	156	5	ρ	ρ	PROPN
ejpam-5042	156	6	∨	∨	NUM
ejpam-5042	156	7	ϱ	ϱ	X
ejpam-5042	156	8	=	=	SYM
ejpam-5042	156	9	1	1	NUM
ejpam-5042	156	10	,	,	PUNCT
ejpam-5042	156	11	where	where	SCONJ
ejpam-5042	156	12	ρ	ρ	NOUN
ejpam-5042	156	13	,	,	PUNCT
ejpam-5042	156	14	ϱ	ϱ	PROPN
ejpam-5042	156	15	∈	∈	PROPN
ejpam-5042	156	16	v	v	NOUN
ejpam-5042	156	17	.	.	PUNCT
ejpam-5042	157	1	we	we	PRON
ejpam-5042	157	2	have	have	VERB
ejpam-5042	157	3	ρ	ρ	PROPN
ejpam-5042	157	4	∨	∨	NUM
ejpam-5042	157	5	ϱ	ϱ	PROPN
ejpam-5042	157	6	♦	♦	PROPN
ejpam-5042	157	7	=	=	PROPN
ejpam-5042	157	8	ρ	ρ	PROPN
ejpam-5042	157	9	∨	∨	NOUN
ejpam-5042	157	10	0	0	NUM
ejpam-5042	158	1	=	=	SYM
ejpam-5042	158	2	ρ	ρ	PROPN
ejpam-5042	158	3	.	.	PUNCT
ejpam-5042	159	1	therefore	therefore	ADV
ejpam-5042	159	2	,	,	PUNCT
ejpam-5042	159	3	(	(	PUNCT
ejpam-5042	159	4	ppc1	ppc1	PROPN
ejpam-5042	159	5	)	)	PUNCT
ejpam-5042	159	6	is	be	AUX
ejpam-5042	159	7	satisfied	satisfied	ADJ
ejpam-5042	159	8	.	.	PUNCT
ejpam-5042	160	1	(	(	PUNCT
ejpam-5042	160	2	ppc3	ppc3	ADJ
ejpam-5042	160	3	):	):	PUNCT
ejpam-5042	160	4	for	for	ADP
ejpam-5042	160	5	any	any	DET
ejpam-5042	160	6	ρ	ρ	NOUN
ejpam-5042	160	7	,	,	PUNCT
ejpam-5042	160	8	ϱ	ϱ	PROPN
ejpam-5042	160	9	∈	∈	PROPN
ejpam-5042	160	10	v	v	NOUN
ejpam-5042	160	11	,	,	PUNCT
ejpam-5042	160	12	we	we	PRON
ejpam-5042	160	13	have	have	VERB
ejpam-5042	160	14	(	(	PUNCT
ejpam-5042	160	15	ρ	ρ	PROPN
ejpam-5042	160	16	∧	∧	PROPN
ejpam-5042	160	17	ϱ	ϱ	NOUN
ejpam-5042	160	18	)	)	PUNCT
ejpam-5042	160	19	♦	♦	PROPN
ejpam-5042	160	20	=	=	PROPN
ejpam-5042	160	21	0	0	PROPN
ejpam-5042	160	22	and	and	CCONJ
ejpam-5042	160	23	ρ	ρ	PROPN
ejpam-5042	160	24	♦	♦	PROPN
ejpam-5042	160	25	∨	∨	NUM
ejpam-5042	160	26	ϱ	ϱ	PROPN
ejpam-5042	160	27	♦	♦	PROPN
ejpam-5042	160	28	=	=	PROPN
ejpam-5042	160	29	0	0	PROPN
ejpam-5042	161	1	∨	∨	NUM
ejpam-5042	161	2	0	0	NUM
ejpam-5042	162	1	=	=	SYM
ejpam-5042	162	2	0	0	NUM
ejpam-5042	162	3	.	.	PUNCT
ejpam-5042	163	1	thus	thus	ADV
ejpam-5042	163	2	,	,	PUNCT
ejpam-5042	163	3	(	(	PUNCT
ejpam-5042	163	4	ppc3	ppc3	ADJ
ejpam-5042	163	5	)	)	PUNCT
ejpam-5042	163	6	is	be	AUX
ejpam-5042	163	7	satisfied	satisfied	ADJ
ejpam-5042	163	8	.	.	PUNCT
ejpam-5042	164	1	now	now	ADV
ejpam-5042	164	2	we	we	PRON
ejpam-5042	164	3	examine	examine	VERB
ejpam-5042	164	4	(	(	PUNCT
ejpam-5042	164	5	ppc2	ppc2	PROPN
ejpam-5042	164	6	)	)	PUNCT
ejpam-5042	164	7	.	.	PUNCT
ejpam-5042	165	1	suppose	suppose	VERB
ejpam-5042	165	2	0	0	NUM
ejpam-5042	165	3	∈	∈	PROPN
ejpam-5042	165	4	v	v	NOUN
ejpam-5042	165	5	.	.	PUNCT
ejpam-5042	166	1	we	we	PRON
ejpam-5042	166	2	have	have	VERB
ejpam-5042	166	3	0∨	0∨	NUM
ejpam-5042	166	4	0	0	NUM
ejpam-5042	166	5	♦	♦	PROPN
ejpam-5042	166	6	=	=	PROPN
ejpam-5042	166	7	0∨	0∨	NUM
ejpam-5042	166	8	0	0	NUM
ejpam-5042	167	1	=	=	SYM
ejpam-5042	167	2	0	0	NUM
ejpam-5042	167	3	,	,	PUNCT
ejpam-5042	167	4	but	but	CCONJ
ejpam-5042	167	5	we	we	PRON
ejpam-5042	167	6	require	require	VERB
ejpam-5042	167	7	0	0	NUM
ejpam-5042	168	1	∨	∨	NUM
ejpam-5042	168	2	0	0	NUM
ejpam-5042	168	3	♦	♦	PROPN
ejpam-5042	168	4	=	=	PROPN
ejpam-5042	168	5	1	1	NUM
ejpam-5042	168	6	.	.	PUNCT
ejpam-5042	168	7	therefore	therefore	ADV
ejpam-5042	168	8	,	,	PUNCT
ejpam-5042	168	9	(	(	PUNCT
ejpam-5042	168	10	ppc2	ppc2	PROPN
ejpam-5042	168	11	)	)	PUNCT
ejpam-5042	168	12	is	be	AUX
ejpam-5042	168	13	not	not	PART
ejpam-5042	168	14	satisfied	satisfied	ADJ
ejpam-5042	168	15	in	in	ADP
ejpam-5042	168	16	this	this	DET
ejpam-5042	168	17	case	case	NOUN
ejpam-5042	168	18	.	.	PUNCT
ejpam-5042	169	1	in	in	ADP
ejpam-5042	169	2	conclusion	conclusion	NOUN
ejpam-5042	169	3	,	,	PUNCT
ejpam-5042	169	4	the	the	DET
ejpam-5042	169	5	bounded	bound	VERB
ejpam-5042	169	6	distributive	distributive	ADJ
ejpam-5042	169	7	lattice	lattice	NOUN
ejpam-5042	169	8	v	v	NOUN
ejpam-5042	169	9	with	with	ADP
ejpam-5042	169	10	the	the	DET
ejpam-5042	169	11	unary	unary	ADJ
ejpam-5042	169	12	operation	operation	NOUN
ejpam-5042	169	13	ρ	ρ	PROPN
ejpam-5042	169	14	♦	♦	PROPN
ejpam-5042	169	15	=	=	PROPN
ejpam-5042	169	16	0	0	NUM
ejpam-5042	169	17	satisfies	satisfie	NOUN
ejpam-5042	169	18	(	(	PUNCT
ejpam-5042	169	19	ppc1	ppc1	PROPN
ejpam-5042	169	20	)	)	PUNCT
ejpam-5042	169	21	and	and	CCONJ
ejpam-5042	169	22	(	(	PUNCT
ejpam-5042	169	23	ppc3	ppc3	ADJ
ejpam-5042	169	24	)	)	PUNCT
ejpam-5042	169	25	but	but	CCONJ
ejpam-5042	169	26	fails	fail	VERB
ejpam-5042	169	27	to	to	PART
ejpam-5042	169	28	satisfy	satisfy	VERB
ejpam-5042	169	29	(	(	PUNCT
ejpam-5042	169	30	ppc2	ppc2	PROPN
ejpam-5042	169	31	)	)	PUNCT
ejpam-5042	169	32	when	when	SCONJ
ejpam-5042	169	33	v	v	NOUN
ejpam-5042	169	34	contains	contain	VERB
ejpam-5042	169	35	0	0	PUNCT
ejpam-5042	169	36	as	as	ADP
ejpam-5042	169	37	an	an	DET
ejpam-5042	169	38	element	element	NOUN
ejpam-5042	169	39	.	.	PUNCT
ejpam-5042	170	1	example	example	NOUN
ejpam-5042	171	1	4	4	NUM
ejpam-5042	171	2	.	.	PUNCT
ejpam-5042	171	3	let	let	VERB
ejpam-5042	171	4	v	v	PART
ejpam-5042	171	5	be	be	AUX
ejpam-5042	171	6	a	a	DET
ejpam-5042	171	7	disconnected	disconnected	ADJ
ejpam-5042	171	8	pdl	pdl	NOUN
ejpam-5042	171	9	with	with	ADP
ejpam-5042	171	10	atleast	atleast	ADJ
ejpam-5042	171	11	two	two	NUM
ejpam-5042	171	12	elements	element	NOUN
ejpam-5042	171	13	other	other	ADJ
ejpam-5042	171	14	than	than	ADP
ejpam-5042	171	15	1	1	NUM
ejpam-5042	171	16	.	.	PUNCT
ejpam-5042	172	1	then	then	ADV
ejpam-5042	172	2	(	(	PUNCT
ejpam-5042	172	3	v	v	PROPN
ejpam-5042	172	4	3,∨,∧	3,∨,∧	PROPN
ejpam-5042	172	5	,	,	PUNCT
ejpam-5042	172	6	1	1	NUM
ejpam-5042	172	7	)	)	PUNCT
ejpam-5042	172	8	is	be	AUX
ejpam-5042	172	9	a	a	DET
ejpam-5042	172	10	pdl	pdl	NOUN
ejpam-5042	172	11	,	,	PUNCT
ejpam-5042	172	12	where	where	SCONJ
ejpam-5042	172	13	∨,∧	∨,∧	PROPN
ejpam-5042	172	14	are	be	AUX
ejpam-5042	172	15	defined	define	VERB
ejpam-5042	172	16	co	co	ADJ
ejpam-5042	172	17	-	-	ADJ
ejpam-5042	172	18	ordinate	ordinate	NOUN
ejpam-5042	172	19	wise	wise	ADJ
ejpam-5042	172	20	.	.	PUNCT
ejpam-5042	173	1	now	now	ADV
ejpam-5042	173	2	,	,	PUNCT
ejpam-5042	173	3	for	for	ADP
ejpam-5042	173	4	any	any	DET
ejpam-5042	173	5	ρ	ρ	PROPN
ejpam-5042	173	6	∈	∈	PROPN
ejpam-5042	173	7	v	v	ADP
ejpam-5042	173	8	3	3	NUM
ejpam-5042	173	9	,	,	PUNCT
ejpam-5042	173	10	we	we	PRON
ejpam-5042	173	11	write	write	VERB
ejpam-5042	173	12	|ρ|	|ρ|	NOUN
ejpam-5042	173	13	for	for	ADP
ejpam-5042	173	14	the	the	DET
ejpam-5042	173	15	number	number	NOUN
ejpam-5042	173	16	of	of	ADP
ejpam-5042	173	17	non	non	NOUN
ejpam-5042	173	18	-	-	NOUN
ejpam-5042	173	19	units	unit	NOUN
ejpam-5042	173	20	in	in	ADP
ejpam-5042	173	21	ρ	ρ	PROPN
ejpam-5042	173	22	.	.	PUNCT
ejpam-5042	174	1	define	define	VERB
ejpam-5042	174	2	♦	♦	PROPN
ejpam-5042	174	3	on	on	ADP
ejpam-5042	174	4	v	v	NUM
ejpam-5042	174	5	3	3	NUM
ejpam-5042	174	6	as	as	SCONJ
ejpam-5042	174	7	follows	follow	VERB
ejpam-5042	174	8	:	:	PUNCT
ejpam-5042	174	9	for	for	ADP
ejpam-5042	174	10	any	any	DET
ejpam-5042	174	11	ρ	ρ	PROPN
ejpam-5042	174	12	∈	∈	PROPN
ejpam-5042	174	13	v	v	ADP
ejpam-5042	174	14	3	3	NUM
ejpam-5042	174	15	,	,	PUNCT
ejpam-5042	174	16	define	define	VERB
ejpam-5042	174	17	ρ	ρ	PROPN
ejpam-5042	174	18	♦	♦	PROPN
ejpam-5042	174	19	=	=	PROPN
ejpam-5042	174	20	(	(	PUNCT
ejpam-5042	174	21	ρ	ρ	PROPN
ejpam-5042	174	22	♦	♦	PROPN
ejpam-5042	174	23	1	1	NUM
ejpam-5042	174	24	,	,	PUNCT
ejpam-5042	174	25	ρ	ρ	PROPN
ejpam-5042	174	26	♦	♦	PROPN
ejpam-5042	174	27	2	2	NUM
ejpam-5042	174	28	,	,	PUNCT
ejpam-5042	174	29	ρ	ρ	PROPN
ejpam-5042	174	30	♦	♦	PROPN
ejpam-5042	174	31	3	3	NUM
ejpam-5042	174	32	)	)	PUNCT
ejpam-5042	174	33	where	where	SCONJ
ejpam-5042	174	34	,	,	PUNCT
ejpam-5042	174	35	for	for	ADP
ejpam-5042	174	36	i	i	PROPN
ejpam-5042	174	37	=	=	SYM
ejpam-5042	174	38	1	1	NUM
ejpam-5042	174	39	,	,	PUNCT
ejpam-5042	174	40	2	2	NUM
ejpam-5042	174	41	,	,	PUNCT
ejpam-5042	174	42	3	3	NUM
ejpam-5042	174	43	ρ	ρ	NUM
ejpam-5042	174	44	♦	♦	PROPN
ejpam-5042	175	1	i	i	PROPN
ejpam-5042	175	2	=	=	SYM
ejpam-5042	176	1			NOUN
ejpam-5042	176	2	1	1	NUM
ejpam-5042	176	3	ρi	ρi	NOUN
ejpam-5042	176	4	̸=	̸=	PROPN
ejpam-5042	176	5	1	1	NUM
ejpam-5042	176	6	0	0	NUM
ejpam-5042	176	7	ρi	ρi	NOUN
ejpam-5042	176	8	=	=	SYM
ejpam-5042	176	9	1	1	NUM
ejpam-5042	176	10	|ρ|	|ρ|	NOUN
ejpam-5042	176	11	=	=	SYM
ejpam-5042	176	12	2	2	NUM
ejpam-5042	176	13	2	2	NUM
ejpam-5042	176	14	ρi	ρi	NOUN
ejpam-5042	176	15	=	=	SYM
ejpam-5042	176	16	1	1	NUM
ejpam-5042	176	17	|ρ|	|ρ|	NOUN
ejpam-5042	176	18	=	=	SYM
ejpam-5042	176	19	1	1	NUM
ejpam-5042	176	20	,	,	PUNCT
ejpam-5042	176	21	|ρ|	|ρ|	X
ejpam-5042	176	22	>	>	SYM
ejpam-5042	176	23	2	2	NUM
ejpam-5042	176	24	and	and	CCONJ
ejpam-5042	176	25	1	1	NUM
ejpam-5042	176	26	♦	♦	NOUN
ejpam-5042	176	27	=	=	PUNCT
ejpam-5042	176	28	(	(	PUNCT
ejpam-5042	176	29	2	2	NUM
ejpam-5042	176	30	,	,	PUNCT
ejpam-5042	176	31	2	2	NUM
ejpam-5042	176	32	,	,	PUNCT
ejpam-5042	176	33	2	2	NUM
ejpam-5042	176	34	)	)	PUNCT
ejpam-5042	176	35	.	.	PUNCT
ejpam-5042	177	1	then	then	ADV
ejpam-5042	177	2	(	(	PUNCT
ejpam-5042	177	3	v	v	PROPN
ejpam-5042	177	4	3,∨,∧	3,∨,∧	PROPN
ejpam-5042	177	5	,	,	PUNCT
ejpam-5042	177	6	1	1	NUM
ejpam-5042	177	7	)	)	PUNCT
ejpam-5042	177	8	is	be	AUX
ejpam-5042	177	9	a	a	DET
ejpam-5042	177	10	ppdl	ppdl	NOUN
ejpam-5042	177	11	which	which	PRON
ejpam-5042	177	12	satisfies	satisfy	VERB
ejpam-5042	177	13	(	(	PUNCT
ejpam-5042	177	14	ppc1	ppc1	PROPN
ejpam-5042	177	15	)	)	PUNCT
ejpam-5042	177	16	and	and	CCONJ
ejpam-5042	177	17	(	(	PUNCT
ejpam-5042	177	18	ppc2	ppc2	PROPN
ejpam-5042	177	19	)	)	PUNCT
ejpam-5042	177	20	but	but	CCONJ
ejpam-5042	177	21	fails	fail	VERB
ejpam-5042	177	22	to	to	PART
ejpam-5042	177	23	satisfy	satisfy	VERB
ejpam-5042	177	24	(	(	PUNCT
ejpam-5042	177	25	ppc3	ppc3	ADJ
ejpam-5042	177	26	)	)	PUNCT
ejpam-5042	177	27	.	.	PUNCT
ejpam-5042	178	1	for	for	ADP
ejpam-5042	178	2	,	,	PUNCT
ejpam-5042	178	3	if	if	SCONJ
ejpam-5042	178	4	ρ	ρ	PROPN
ejpam-5042	178	5	=	=	SYM
ejpam-5042	178	6	(	(	PUNCT
ejpam-5042	178	7	0	0	NUM
ejpam-5042	178	8	,	,	PUNCT
ejpam-5042	178	9	1	1	NUM
ejpam-5042	178	10	,	,	PUNCT
ejpam-5042	178	11	1	1	NUM
ejpam-5042	178	12	)	)	PUNCT
ejpam-5042	178	13	and	and	CCONJ
ejpam-5042	178	14	ϱ	ϱ	X
ejpam-5042	178	15	=	=	SYM
ejpam-5042	178	16	(	(	PUNCT
ejpam-5042	178	17	1	1	NUM
ejpam-5042	178	18	,	,	PUNCT
ejpam-5042	178	19	0	0	NUM
ejpam-5042	178	20	,	,	PUNCT
ejpam-5042	178	21	1	1	NUM
ejpam-5042	178	22	)	)	PUNCT
ejpam-5042	178	23	,	,	PUNCT
ejpam-5042	178	24	then	then	ADV
ejpam-5042	178	25	ρ	ρ	PROPN
ejpam-5042	178	26	♦	♦	PROPN
ejpam-5042	178	27	=	=	PROPN
ejpam-5042	178	28	(	(	PUNCT
ejpam-5042	178	29	1	1	NUM
ejpam-5042	178	30	,	,	PUNCT
ejpam-5042	178	31	2	2	NUM
ejpam-5042	178	32	,	,	PUNCT
ejpam-5042	178	33	2	2	NUM
ejpam-5042	178	34	)	)	PUNCT
ejpam-5042	178	35	and	and	CCONJ
ejpam-5042	178	36	ϱ	ϱ	VERB
ejpam-5042	178	37	♦	♦	PROPN
ejpam-5042	178	38	=	=	PUNCT
ejpam-5042	178	39	(	(	PUNCT
ejpam-5042	178	40	2	2	NUM
ejpam-5042	178	41	,	,	PUNCT
ejpam-5042	178	42	1	1	NUM
ejpam-5042	178	43	,	,	PUNCT
ejpam-5042	178	44	2	2	NUM
ejpam-5042	178	45	)	)	PUNCT
ejpam-5042	178	46	and	and	CCONJ
ejpam-5042	178	47	ρ	ρ	NUM
ejpam-5042	178	48	∧	∧	PROPN
ejpam-5042	178	49	ϱ	ϱ	PROPN
ejpam-5042	178	50	=	=	PUNCT
ejpam-5042	178	51	(	(	PUNCT
ejpam-5042	178	52	0	0	NUM
ejpam-5042	178	53	,	,	PUNCT
ejpam-5042	178	54	0	0	NUM
ejpam-5042	178	55	,	,	PUNCT
ejpam-5042	178	56	1	1	NUM
ejpam-5042	178	57	)	)	PUNCT
ejpam-5042	178	58	.	.	PUNCT
ejpam-5042	179	1	hence	hence	ADV
ejpam-5042	179	2	(	(	PUNCT
ejpam-5042	179	3	ρ	ρ	PROPN
ejpam-5042	179	4	∧	∧	PROPN
ejpam-5042	179	5	ϱ	ϱ	NOUN
ejpam-5042	179	6	)	)	PUNCT
ejpam-5042	179	7	♦	♦	PROPN
ejpam-5042	179	8	=	=	SYM
ejpam-5042	179	9	(	(	PUNCT
ejpam-5042	179	10	1	1	NUM
ejpam-5042	179	11	,	,	PUNCT
ejpam-5042	179	12	1	1	NUM
ejpam-5042	179	13	,	,	PUNCT
ejpam-5042	179	14	0	0	NUM
ejpam-5042	179	15	)	)	PUNCT
ejpam-5042	179	16	and	and	CCONJ
ejpam-5042	179	17	ρ	ρ	PROPN
ejpam-5042	179	18	♦	♦	PROPN
ejpam-5042	179	19	∨	∨	NUM
ejpam-5042	179	20	ϱ	ϱ	PROPN
ejpam-5042	179	21	♦	♦	PROPN
ejpam-5042	179	22	=	=	PUNCT
ejpam-5042	179	23	(	(	PUNCT
ejpam-5042	179	24	1	1	NUM
ejpam-5042	179	25	,	,	PUNCT
ejpam-5042	179	26	1	1	NUM
ejpam-5042	179	27	,	,	PUNCT
ejpam-5042	179	28	2	2	NUM
ejpam-5042	179	29	)	)	PUNCT
ejpam-5042	179	30	.	.	PUNCT
ejpam-5042	180	1	therefore	therefore	ADV
ejpam-5042	180	2	,	,	PUNCT
ejpam-5042	180	3	(	(	PUNCT
ejpam-5042	180	4	ρ	ρ	PROPN
ejpam-5042	180	5	∧	∧	PROPN
ejpam-5042	180	6	ϱ	ϱ	NOUN
ejpam-5042	180	7	)	)	PUNCT
ejpam-5042	180	8	♦	♦	PROPN
ejpam-5042	180	9	̸=	̸=	PROPN
ejpam-5042	180	10	ρ	ρ	PROPN
ejpam-5042	180	11	♦	♦	PROPN
ejpam-5042	180	12	∨	∨	NUM
ejpam-5042	180	13	ϱ	ϱ	PROPN
ejpam-5042	180	14	♦	♦	PROPN
ejpam-5042	180	15	.	.	PUNCT
ejpam-5042	181	1	r.	r.	PROPN
ejpam-5042	181	2	shukla	shukla	PROPN
ejpam-5042	181	3	et	et	PROPN
ejpam-5042	181	4	al	al	PROPN
ejpam-5042	181	5	.	.	PUNCT
ejpam-5042	181	6	/	/	SYM
ejpam-5042	181	7	eur	eur	PROPN
ejpam-5042	181	8	.	.	PUNCT
ejpam-5042	182	1	j.	j.	PROPN
ejpam-5042	182	2	pure	pure	PROPN
ejpam-5042	182	3	appl	appl	PROPN
ejpam-5042	182	4	.	.	PROPN
ejpam-5042	182	5	math	math	PROPN
ejpam-5042	182	6	,	,	PUNCT
ejpam-5042	182	7	17	17	NUM
ejpam-5042	182	8	(	(	PUNCT
ejpam-5042	182	9	2	2	NUM
ejpam-5042	182	10	)	)	PUNCT
ejpam-5042	182	11	(	(	PUNCT
ejpam-5042	182	12	2024	2024	NUM
ejpam-5042	182	13	)	)	PUNCT
ejpam-5042	182	14	,	,	PUNCT
ejpam-5042	182	15	1129	1129	NUM
ejpam-5042	182	16	-	-	SYM
ejpam-5042	182	17	1145	1145	NUM
ejpam-5042	182	18	1135	1135	NUM
ejpam-5042	182	19	lemma	lemma	PROPN
ejpam-5042	182	20	4	4	NUM
ejpam-5042	182	21	.	.	PUNCT
ejpam-5042	183	1	let	let	AUX
ejpam-5042	183	2	(	(	PUNCT
ejpam-5042	183	3	v,+	v,+	NUM
ejpam-5042	183	4	,	,	PUNCT
ejpam-5042	183	5	·	·	PUNCT
ejpam-5042	183	6	,	,	PUNCT
ejpam-5042	183	7	0	0	NUM
ejpam-5042	183	8	,	,	PUNCT
ejpam-5042	183	9	1	1	NUM
ejpam-5042	183	10	)	)	PUNCT
ejpam-5042	183	11	be	be	AUX
ejpam-5042	183	12	a	a	DET
ejpam-5042	183	13	commutative	commutative	ADJ
ejpam-5042	183	14	regular	regular	ADJ
ejpam-5042	183	15	ring	ring	NOUN
ejpam-5042	183	16	with	with	ADP
ejpam-5042	183	17	unity	unity	NOUN
ejpam-5042	183	18	and	and	CCONJ
ejpam-5042	183	19	let	let	VERB
ejpam-5042	183	20	ρ0	ρ0	PRON
ejpam-5042	183	21	be	be	AUX
ejpam-5042	183	22	the	the	DET
ejpam-5042	183	23	unique	unique	ADJ
ejpam-5042	183	24	idempotent	idempotent	ADJ
ejpam-5042	183	25	element	element	NOUN
ejpam-5042	183	26	in	in	ADP
ejpam-5042	183	27	v	v	NOUN
ejpam-5042	183	28	such	such	ADJ
ejpam-5042	183	29	that	that	PRON
ejpam-5042	183	30	ρv	ρv	NOUN
ejpam-5042	183	31	=	=	SYM
ejpam-5042	183	32	ρ0v	ρ0v	PROPN
ejpam-5042	183	33	.	.	PUNCT
ejpam-5042	184	1	now	now	ADV
ejpam-5042	184	2	,	,	PUNCT
ejpam-5042	184	3	for	for	ADP
ejpam-5042	184	4	any	any	DET
ejpam-5042	184	5	ρ	ρ	NOUN
ejpam-5042	184	6	,	,	PUNCT
ejpam-5042	184	7	ϱ	ϱ	PROPN
ejpam-5042	184	8	∈	∈	PROPN
ejpam-5042	184	9	v	v	NOUN
ejpam-5042	184	10	,	,	PUNCT
ejpam-5042	184	11	define	define	VERB
ejpam-5042	184	12	(	(	PUNCT
ejpam-5042	184	13	1	1	X
ejpam-5042	184	14	)	)	PUNCT
ejpam-5042	184	15	ρ	ρ	PROPN
ejpam-5042	184	16	∨	∨	NUM
ejpam-5042	184	17	ϱ	ϱ	PROPN
ejpam-5042	184	18	=	=	SYM
ejpam-5042	184	19	ϱ0ρ	ϱ0ρ	PROPN
ejpam-5042	184	20	(	(	PUNCT
ejpam-5042	184	21	2	2	NUM
ejpam-5042	184	22	)	)	PUNCT
ejpam-5042	184	23	ρ	ρ	NOUN
ejpam-5042	184	24	∧	∧	PROPN
ejpam-5042	184	25	ϱ	ϱ	PROPN
ejpam-5042	184	26	=	=	SYM
ejpam-5042	184	27	ρ+	ρ+	NOUN
ejpam-5042	184	28	ϱ−	ϱ−	CCONJ
ejpam-5042	184	29	ϱ0ρ	ϱ0ρ	PROPN
ejpam-5042	184	30	(	(	PUNCT
ejpam-5042	184	31	3	3	NUM
ejpam-5042	184	32	)	)	PUNCT
ejpam-5042	184	33	ρ	ρ	PROPN
ejpam-5042	184	34	♦	♦	PROPN
ejpam-5042	184	35	=	=	PROPN
ejpam-5042	184	36	1−	1−	NUM
ejpam-5042	184	37	ρ0	ρ0	PROPN
ejpam-5042	184	38	.	.	PUNCT
ejpam-5042	185	1	then	then	ADV
ejpam-5042	185	2	(	(	PUNCT
ejpam-5042	185	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	185	4	,	,	PUNCT
ejpam-5042	185	5	0	0	NUM
ejpam-5042	185	6	)	)	PUNCT
ejpam-5042	185	7	is	be	AUX
ejpam-5042	185	8	a	a	DET
ejpam-5042	185	9	pdl	pdl	NOUN
ejpam-5042	185	10	in	in	ADP
ejpam-5042	185	11	which	which	PRON
ejpam-5042	185	12	1	1	NUM
ejpam-5042	185	13	is	be	AUX
ejpam-5042	185	14	a	a	DET
ejpam-5042	185	15	minimal	minimal	ADJ
ejpam-5042	185	16	element	element	NOUN
ejpam-5042	185	17	and	and	CCONJ
ejpam-5042	185	18	♦	♦	PROPN
ejpam-5042	185	19	is	be	AUX
ejpam-5042	185	20	a	a	DET
ejpam-5042	185	21	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5042	185	22	on	on	ADP
ejpam-5042	185	23	v	v	NOUN
ejpam-5042	185	24	.	.	PUNCT
ejpam-5042	186	1	proof	proof	NOUN
ejpam-5042	186	2	.	.	PUNCT
ejpam-5042	187	1	it	it	PRON
ejpam-5042	187	2	is	be	AUX
ejpam-5042	187	3	clear	clear	ADJ
ejpam-5042	187	4	that	that	SCONJ
ejpam-5042	187	5	(	(	PUNCT
ejpam-5042	187	6	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	187	7	,	,	PUNCT
ejpam-5042	187	8	0	0	NUM
ejpam-5042	187	9	)	)	PUNCT
ejpam-5042	187	10	is	be	AUX
ejpam-5042	187	11	a	a	DET
ejpam-5042	187	12	pdl	pdl	PROPN
ejpam-5042	187	13	.	.	PUNCT
ejpam-5042	187	14	note	note	VERB
ejpam-5042	187	15	that	that	SCONJ
ejpam-5042	187	16	,	,	PUNCT
ejpam-5042	187	17	for	for	ADP
ejpam-5042	187	18	any	any	DET
ejpam-5042	187	19	ρ	ρ	NOUN
ejpam-5042	187	20	,	,	PUNCT
ejpam-5042	187	21	ϱ	ϱ	PROPN
ejpam-5042	187	22	∈	∈	PROPN
ejpam-5042	187	23	v	v	NOUN
ejpam-5042	187	24	,	,	PUNCT
ejpam-5042	187	25	(	(	PUNCT
ejpam-5042	187	26	ρϱ)0	ρϱ)0	NOUN
ejpam-5042	187	27	=	=	PUNCT
ejpam-5042	187	28	ρ0ϱ0	ρ0ϱ0	PUNCT
ejpam-5042	187	29	and	and	CCONJ
ejpam-5042	187	30	(	(	PUNCT
ejpam-5042	187	31	ρ+	ρ+	NOUN
ejpam-5042	187	32	ϱ−	ϱ−	X
ejpam-5042	188	1	ρ0ϱ)0	ρ0ϱ)0	NOUN
ejpam-5042	188	2	=	=	SYM
ejpam-5042	188	3	ρ0	ρ0	PROPN
ejpam-5042	188	4	+	+	NOUN
ejpam-5042	188	5	ϱ0	ϱ0	NOUN
ejpam-5042	188	6	−	−	NOUN
ejpam-5042	188	7	ρ0ϱ0	ρ0ϱ0	NOUN
ejpam-5042	188	8	.	.	PUNCT
ejpam-5042	189	1	also	also	ADV
ejpam-5042	189	2	,	,	PUNCT
ejpam-5042	189	3	00	00	PUNCT
ejpam-5042	190	1	=	=	SYM
ejpam-5042	190	2	0	0	NUM
ejpam-5042	190	3	and	and	CCONJ
ejpam-5042	190	4	10	10	NUM
ejpam-5042	190	5	=	=	SYM
ejpam-5042	190	6	1	1	NUM
ejpam-5042	190	7	.	.	PUNCT
ejpam-5042	191	1	now	now	ADV
ejpam-5042	191	2	,	,	PUNCT
ejpam-5042	191	3	we	we	PRON
ejpam-5042	191	4	prove	prove	VERB
ejpam-5042	191	5	that	that	SCONJ
ejpam-5042	191	6	♦	♦	PROPN
ejpam-5042	191	7	is	be	AUX
ejpam-5042	191	8	a	a	DET
ejpam-5042	191	9	parapseudo	parapseudo	NOUN
ejpam-5042	191	10	-	-	NOUN
ejpam-5042	191	11	complementation	complementation	NOUN
ejpam-5042	191	12	on	on	ADP
ejpam-5042	191	13	v	v	NOUN
ejpam-5042	191	14	.	.	PUNCT
ejpam-5042	192	1	let	let	VERB
ejpam-5042	192	2	ρ	ρ	NOUN
ejpam-5042	192	3	,	,	PUNCT
ejpam-5042	192	4	ϱ	ϱ	PROPN
ejpam-5042	192	5	∈	∈	PROPN
ejpam-5042	192	6	v	v	NOUN
ejpam-5042	192	7	and	and	CCONJ
ejpam-5042	192	8	ρ	ρ	NUM
ejpam-5042	192	9	∨	∨	NUM
ejpam-5042	192	10	ϱ	ϱ	ADP
ejpam-5042	192	11	=	=	SYM
ejpam-5042	192	12	0	0	PROPN
ejpam-5042	192	13	.	.	PUNCT
ejpam-5042	193	1	then	then	ADV
ejpam-5042	193	2	ϱ0ρ	ϱ0ρ	PROPN
ejpam-5042	193	3	=	=	SYM
ejpam-5042	193	4	0	0	NUM
ejpam-5042	193	5	and	and	CCONJ
ejpam-5042	193	6	ρ	ρ	NUM
ejpam-5042	193	7	∨	∨	NUM
ejpam-5042	193	8	ϱ	ϱ	PROPN
ejpam-5042	193	9	♦	♦	PROPN
ejpam-5042	193	10	=	=	PROPN
ejpam-5042	193	11	(	(	PUNCT
ejpam-5042	193	12	ϱ	ϱ	PROPN
ejpam-5042	193	13	♦	♦	PROPN
ejpam-5042	193	14	)0ρ	)0ρ	PUNCT
ejpam-5042	193	15	=	=	PUNCT
ejpam-5042	193	16	ϱ	ϱ	PROPN
ejpam-5042	193	17	♦	♦	PROPN
ejpam-5042	193	18	ρ	ρ	PROPN
ejpam-5042	193	19	=	=	SYM
ejpam-5042	193	20	(	(	PUNCT
ejpam-5042	193	21	1−	1−	NUM
ejpam-5042	193	22	ϱ0)ρ	ϱ0)ρ	NOUN
ejpam-5042	193	23	=	=	SYM
ejpam-5042	193	24	ρ	ρ	PROPN
ejpam-5042	193	25	also	also	ADV
ejpam-5042	193	26	,	,	PUNCT
ejpam-5042	193	27	ρ	ρ	PROPN
ejpam-5042	193	28	∨	∨	PROPN
ejpam-5042	193	29	ρ	ρ	PROPN
ejpam-5042	193	30	♦	♦	PROPN
ejpam-5042	193	31	=	=	PROPN
ejpam-5042	193	32	ρ	ρ	PROPN
ejpam-5042	193	33	∨	∨	X
ejpam-5042	193	34	(	(	PUNCT
ejpam-5042	193	35	1−	1−	NUM
ejpam-5042	193	36	ρ0	ρ0	PROPN
ejpam-5042	193	37	)	)	PUNCT
ejpam-5042	193	38	=	=	PUNCT
ejpam-5042	193	39	(	(	PUNCT
ejpam-5042	193	40	1−	1−	NUM
ejpam-5042	193	41	ρ0)0ρ	ρ0)0ρ	NOUN
ejpam-5042	193	42	=	=	SYM
ejpam-5042	193	43	(	(	PUNCT
ejpam-5042	193	44	1−	1−	NUM
ejpam-5042	193	45	ρ0)ρ	ρ0)ρ	NOUN
ejpam-5042	193	46	=	=	SYM
ejpam-5042	193	47	ρ−	ρ−	PROPN
ejpam-5042	193	48	ρ	ρ	PROPN
ejpam-5042	193	49	=	=	SYM
ejpam-5042	193	50	0	0	X
ejpam-5042	193	51	.	.	PUNCT
ejpam-5042	194	1	let	let	VERB
ejpam-5042	194	2	ρ	ρ	NOUN
ejpam-5042	194	3	,	,	PUNCT
ejpam-5042	194	4	ϱ	ϱ	PROPN
ejpam-5042	194	5	∈	∈	PROPN
ejpam-5042	194	6	v	v	NOUN
ejpam-5042	194	7	.	.	PUNCT
ejpam-5042	195	1	then	then	ADV
ejpam-5042	195	2	,	,	PUNCT
ejpam-5042	195	3	ρ	ρ	PROPN
ejpam-5042	195	4	♦	♦	PROPN
ejpam-5042	195	5	∨	∨	NUM
ejpam-5042	195	6	ϱ	ϱ	PROPN
ejpam-5042	195	7	♦	♦	PROPN
ejpam-5042	195	8	=	=	PUNCT
ejpam-5042	195	9	(	(	PUNCT
ejpam-5042	195	10	1−	1−	NUM
ejpam-5042	195	11	ρ0	ρ0	PROPN
ejpam-5042	195	12	)	)	PUNCT
ejpam-5042	195	13	∨	∨	PROPN
ejpam-5042	195	14	(	(	PUNCT
ejpam-5042	195	15	1−	1−	NUM
ejpam-5042	195	16	ϱ0	ϱ0	NOUN
ejpam-5042	195	17	)	)	PUNCT
ejpam-5042	195	18	=	=	PUNCT
ejpam-5042	195	19	(	(	PUNCT
ejpam-5042	195	20	1−	1−	NUM
ejpam-5042	195	21	ϱ0)0(1−	ϱ0)0(1−	NOUN
ejpam-5042	195	22	ρ0	ρ0	PROPN
ejpam-5042	195	23	)	)	PUNCT
ejpam-5042	196	1	=	=	PUNCT
ejpam-5042	196	2	(	(	PUNCT
ejpam-5042	196	3	10	10	NUM
ejpam-5042	196	4	−	−	NOUN
ejpam-5042	196	5	ϱ0)(1−	ϱ0)(1−	ADJ
ejpam-5042	196	6	ρ0	ρ0	PROPN
ejpam-5042	196	7	)	)	PUNCT
ejpam-5042	196	8	=	=	PUNCT
ejpam-5042	196	9	(	(	PUNCT
ejpam-5042	196	10	1−	1−	NUM
ejpam-5042	196	11	ϱ0)(1−	ϱ0)(1−	ADJ
ejpam-5042	196	12	ρ0	ρ0	PROPN
ejpam-5042	196	13	)	)	PUNCT
ejpam-5042	196	14	=	=	SYM
ejpam-5042	197	1	1−	1−	NUM
ejpam-5042	197	2	ρ0	ρ0	NOUN
ejpam-5042	197	3	−	−	PROPN
ejpam-5042	197	4	ϱ0	ϱ0	PROPN
ejpam-5042	197	5	+	+	CCONJ
ejpam-5042	197	6	ρ0ϱ0	ρ0ϱ0	PROPN
ejpam-5042	197	7	=	=	SYM
ejpam-5042	197	8	1−	1−	NUM
ejpam-5042	197	9	(	(	PUNCT
ejpam-5042	197	10	ρ0	ρ0	PROPN
ejpam-5042	197	11	+	+	NOUN
ejpam-5042	197	12	ϱ0	ϱ0	NOUN
ejpam-5042	197	13	−	−	NOUN
ejpam-5042	197	14	ρ0ϱ0	ρ0ϱ0	NOUN
ejpam-5042	197	15	)	)	PUNCT
ejpam-5042	197	16	=	=	SYM
ejpam-5042	197	17	1−	1−	NUM
ejpam-5042	197	18	(	(	PUNCT
ejpam-5042	197	19	ρ+	ρ+	NOUN
ejpam-5042	197	20	ϱ−	ϱ−	PUNCT
ejpam-5042	197	21	ϱ0ρ)0	ϱ0ρ)0	PROPN
ejpam-5042	197	22	=	=	SYM
ejpam-5042	197	23	1−	1−	NUM
ejpam-5042	197	24	(	(	PUNCT
ejpam-5042	197	25	ρ	ρ	NOUN
ejpam-5042	197	26	∧	∧	NOUN
ejpam-5042	197	27	ϱ)0	ϱ)0	NOUN
ejpam-5042	197	28	=	=	SYM
ejpam-5042	197	29	(	(	PUNCT
ejpam-5042	197	30	ρ	ρ	PROPN
ejpam-5042	197	31	∧	∧	PROPN
ejpam-5042	197	32	ϱ	ϱ	PROPN
ejpam-5042	197	33	)	)	PUNCT
ejpam-5042	197	34	♦	♦	PROPN
ejpam-5042	197	35	therefore	therefore	ADV
ejpam-5042	197	36	,	,	PUNCT
ejpam-5042	197	37	♦	♦	PROPN
ejpam-5042	197	38	is	be	AUX
ejpam-5042	197	39	a	a	DET
ejpam-5042	197	40	parapseudo	parapseudo	NOUN
ejpam-5042	197	41	-	-	NOUN
ejpam-5042	197	42	complementation	complementation	NOUN
ejpam-5042	197	43	on	on	ADP
ejpam-5042	197	44	v	v	NUM
ejpam-5042	197	45	.	.	PUNCT
ejpam-5042	197	46	example	example	NOUN
ejpam-5042	198	1	5	5	NUM
ejpam-5042	198	2	.	.	PUNCT
ejpam-5042	199	1	let	let	AUX
ejpam-5042	199	2	(	(	PUNCT
ejpam-5042	199	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	199	4	,	,	PUNCT
ejpam-5042	199	5	1	1	NUM
ejpam-5042	199	6	)	)	PUNCT
ejpam-5042	199	7	be	be	AUX
ejpam-5042	199	8	a	a	DET
ejpam-5042	199	9	disconnected	disconnected	ADJ
ejpam-5042	199	10	pdl	pdl	NOUN
ejpam-5042	199	11	.	.	PUNCT
ejpam-5042	200	1	fix	fix	NOUN
ejpam-5042	200	2	ρ1	ρ1	NOUN
ejpam-5042	200	3	̸=	̸=	PROPN
ejpam-5042	200	4	1	1	NUM
ejpam-5042	200	5	∈	∈	NOUN
ejpam-5042	200	6	v	v	NOUN
ejpam-5042	200	7	and	and	CCONJ
ejpam-5042	200	8	define	define	VERB
ejpam-5042	200	9	♦	♦	PROPN
ejpam-5042	200	10	on	on	ADP
ejpam-5042	200	11	v	v	NOUN
ejpam-5042	200	12	as	as	SCONJ
ejpam-5042	200	13	follows	follow	VERB
ejpam-5042	200	14	:	:	PUNCT
ejpam-5042	200	15	µ	µ	NUM
ejpam-5042	200	16	♦	♦	PROPN
ejpam-5042	200	17	1	1	NUM
ejpam-5042	200	18	=	=	NOUN
ejpam-5042	200	19	{	{	PUNCT
ejpam-5042	200	20	1	1	NUM
ejpam-5042	200	21	µ1	µ1	NOUN
ejpam-5042	200	22	̸=	̸=	PROPN
ejpam-5042	200	23	1	1	NUM
ejpam-5042	200	24	ρ1	ρ1	NOUN
ejpam-5042	200	25	µ1	µ1	NOUN
ejpam-5042	200	26	=	=	SYM
ejpam-5042	200	27	1	1	NUM
ejpam-5042	200	28	then	then	ADV
ejpam-5042	200	29	♦	♦	PROPN
ejpam-5042	200	30	is	be	AUX
ejpam-5042	200	31	a	a	DET
ejpam-5042	200	32	parapseudo	parapseudo	NOUN
ejpam-5042	200	33	-	-	NOUN
ejpam-5042	200	34	complementation	complementation	NOUN
ejpam-5042	200	35	on	on	ADP
ejpam-5042	200	36	v	v	NOUN
ejpam-5042	200	37	.	.	PUNCT
ejpam-5042	201	1	in	in	ADP
ejpam-5042	201	2	the	the	DET
ejpam-5042	201	3	case	case	NOUN
ejpam-5042	201	4	of	of	ADP
ejpam-5042	201	5	a	a	DET
ejpam-5042	201	6	distributive	distributive	ADJ
ejpam-5042	201	7	lattice	lattice	NOUN
ejpam-5042	201	8	the	the	DET
ejpam-5042	201	9	dual	dual	ADJ
ejpam-5042	201	10	pseudo	pseudo	NOUN
ejpam-5042	201	11	-	-	NOUN
ejpam-5042	201	12	complementation	complementation	NOUN
ejpam-5042	201	13	,	,	PUNCT
ejpam-5042	201	14	if	if	SCONJ
ejpam-5042	201	15	exists	exist	NOUN
ejpam-5042	201	16	,	,	PUNCT
ejpam-5042	201	17	is	be	AUX
ejpam-5042	201	18	unique	unique	ADJ
ejpam-5042	201	19	.	.	PUNCT
ejpam-5042	202	1	but	but	CCONJ
ejpam-5042	202	2	,	,	PUNCT
ejpam-5042	202	3	in	in	ADP
ejpam-5042	202	4	a	a	DET
ejpam-5042	202	5	pdl	pdl	NOUN
ejpam-5042	202	6	there	there	PRON
ejpam-5042	202	7	can	can	AUX
ejpam-5042	202	8	be	be	AUX
ejpam-5042	202	9	several	several	ADJ
ejpam-5042	202	10	parapseudo	parapseudo	NOUN
ejpam-5042	202	11	-	-	PUNCT
ejpam-5042	202	12	complementations	complementation	NOUN
ejpam-5042	202	13	.	.	PUNCT
ejpam-5042	203	1	for	for	ADP
ejpam-5042	203	2	,	,	PUNCT
ejpam-5042	203	3	in	in	ADP
ejpam-5042	203	4	example	example	NOUN
ejpam-5042	203	5	5	5	NUM
ejpam-5042	203	6	,	,	PUNCT
ejpam-5042	203	7	we	we	PRON
ejpam-5042	203	8	get	get	VERB
ejpam-5042	203	9	one	one	NUM
ejpam-5042	203	10	parapseudo	parapseudo	NOUN
ejpam-5042	203	11	-	-	NOUN
ejpam-5042	203	12	complementation	complementation	NOUN
ejpam-5042	203	13	on	on	ADP
ejpam-5042	203	14	v	v	ADP
ejpam-5042	203	15	corresponding	correspond	VERB
ejpam-5042	203	16	to	to	ADP
ejpam-5042	203	17	each	each	DET
ejpam-5042	203	18	ρ1(̸=	ρ1(̸=	ADJ
ejpam-5042	203	19	1	1	NUM
ejpam-5042	203	20	)	)	PUNCT
ejpam-5042	203	21	∈	∈	PROPN
ejpam-5042	203	22	v	v	NOUN
ejpam-5042	203	23	.	.	PUNCT
ejpam-5042	204	1	theorem	theorem	ADJ
ejpam-5042	204	2	4	4	NUM
ejpam-5042	204	3	.	.	PUNCT
ejpam-5042	205	1	every	every	DET
ejpam-5042	205	2	finite	finite	NOUN
ejpam-5042	205	3	pdl	pdl	PROPN
ejpam-5042	205	4	is	be	AUX
ejpam-5042	205	5	parapseudo	parapseudo	NOUN
ejpam-5042	205	6	-	-	PUNCT
ejpam-5042	205	7	complemented	complemented	ADJ
ejpam-5042	205	8	.	.	PUNCT
ejpam-5042	206	1	r.	r.	PROPN
ejpam-5042	206	2	shukla	shukla	PROPN
ejpam-5042	206	3	et	et	PROPN
ejpam-5042	206	4	al	al	PROPN
ejpam-5042	206	5	.	.	PUNCT
ejpam-5042	206	6	/	/	SYM
ejpam-5042	206	7	eur	eur	PROPN
ejpam-5042	206	8	.	.	PUNCT
ejpam-5042	207	1	j.	j.	PROPN
ejpam-5042	207	2	pure	pure	PROPN
ejpam-5042	207	3	appl	appl	PROPN
ejpam-5042	207	4	.	.	PROPN
ejpam-5042	207	5	math	math	PROPN
ejpam-5042	207	6	,	,	PUNCT
ejpam-5042	207	7	17	17	NUM
ejpam-5042	207	8	(	(	PUNCT
ejpam-5042	207	9	2	2	NUM
ejpam-5042	207	10	)	)	PUNCT
ejpam-5042	207	11	(	(	PUNCT
ejpam-5042	207	12	2024	2024	NUM
ejpam-5042	207	13	)	)	PUNCT
ejpam-5042	207	14	,	,	PUNCT
ejpam-5042	207	15	1129	1129	NUM
ejpam-5042	207	16	-	-	SYM
ejpam-5042	207	17	1145	1145	NUM
ejpam-5042	207	18	1136	1136	NUM
ejpam-5042	207	19	proof	proof	NOUN
ejpam-5042	207	20	.	.	PUNCT
ejpam-5042	208	1	let	let	VERB
ejpam-5042	208	2	v	v	PART
ejpam-5042	208	3	be	be	AUX
ejpam-5042	208	4	a	a	DET
ejpam-5042	208	5	finite	finite	ADJ
ejpam-5042	208	6	pdl	pdl	PROPN
ejpam-5042	208	7	.	.	PUNCT
ejpam-5042	209	1	then	then	ADV
ejpam-5042	209	2	v	v	X
ejpam-5042	209	3	has	have	VERB
ejpam-5042	209	4	a	a	DET
ejpam-5042	209	5	minimal	minimal	ADJ
ejpam-5042	209	6	element	element	NOUN
ejpam-5042	209	7	,	,	PUNCT
ejpam-5042	209	8	say	say	VERB
ejpam-5042	209	9	m.	m.	NOUN
ejpam-5042	209	10	now	now	ADV
ejpam-5042	209	11	,	,	PUNCT
ejpam-5042	209	12	we	we	PRON
ejpam-5042	209	13	prove	prove	VERB
ejpam-5042	209	14	that	that	SCONJ
ejpam-5042	209	15	v	v	NOUN
ejpam-5042	209	16	is	be	AUX
ejpam-5042	209	17	parapseudo	parapseudo	NOUN
ejpam-5042	209	18	-	-	PUNCT
ejpam-5042	209	19	complemented	complemented	ADJ
ejpam-5042	209	20	.	.	PUNCT
ejpam-5042	210	1	for	for	ADP
ejpam-5042	210	2	this	this	PRON
ejpam-5042	210	3	,	,	PUNCT
ejpam-5042	210	4	define	define	VERB
ejpam-5042	210	5	♢	♢	PROPN
ejpam-5042	210	6	on	on	ADP
ejpam-5042	210	7	v	v	NUM
ejpam-5042	210	8	by	by	ADP
ejpam-5042	210	9	ρ	ρ	PROPN
ejpam-5042	210	10	♢	♢	PROPN
ejpam-5042	210	11	=	=	SYM
ejpam-5042	210	12	(	(	PUNCT
ejpam-5042	210	13	m	m	PROPN
ejpam-5042	210	14	∨	∨	NOUN
ejpam-5042	210	15	ρ	ρ	NOUN
ejpam-5042	210	16	)	)	PUNCT
ejpam-5042	210	17	♦	♦	PROPN
ejpam-5042	210	18	,	,	PUNCT
ejpam-5042	210	19	where	where	SCONJ
ejpam-5042	210	20	(	(	PUNCT
ejpam-5042	210	21	m	m	PROPN
ejpam-5042	210	22	∨	∨	NOUN
ejpam-5042	210	23	ρ	ρ	NOUN
ejpam-5042	210	24	)	)	PUNCT
ejpam-5042	210	25	♦	♦	PROPN
ejpam-5042	210	26	is	be	AUX
ejpam-5042	210	27	the	the	DET
ejpam-5042	210	28	dual	dual	ADJ
ejpam-5042	210	29	pseudo	pseudo	NOUN
ejpam-5042	210	30	-	-	NOUN
ejpam-5042	210	31	complement	complement	NOUN
ejpam-5042	210	32	of	of	ADP
ejpam-5042	210	33	m	m	PROPN
ejpam-5042	210	34	∨	∨	NOUN
ejpam-5042	210	35	ρ	ρ	NOUN
ejpam-5042	210	36	in	in	ADP
ejpam-5042	210	37	the	the	DET
ejpam-5042	210	38	finite	finite	ADJ
ejpam-5042	210	39	distributive	distributive	ADJ
ejpam-5042	210	40	lattice	lattice	NOUN
ejpam-5042	211	1	[	[	X
ejpam-5042	211	2	m	m	NOUN
ejpam-5042	211	3	,	,	PUNCT
ejpam-5042	211	4	1	1	NUM
ejpam-5042	211	5	]	]	PUNCT
ejpam-5042	211	6	and	and	CCONJ
ejpam-5042	211	7	ρ	ρ	PROPN
ejpam-5042	211	8	∈	∈	PROPN
ejpam-5042	211	9	v	v	NOUN
ejpam-5042	211	10	.	.	PUNCT
ejpam-5042	212	1	we	we	PRON
ejpam-5042	212	2	prove	prove	VERB
ejpam-5042	212	3	♢	♢	PROPN
ejpam-5042	212	4	is	be	AUX
ejpam-5042	212	5	parapseudo	parapseudo	NOUN
ejpam-5042	212	6	-	-	NOUN
ejpam-5042	212	7	complementation	complementation	NOUN
ejpam-5042	212	8	on	on	ADP
ejpam-5042	212	9	v	v	NOUN
ejpam-5042	212	10	.	.	PUNCT
ejpam-5042	213	1	let	let	VERB
ejpam-5042	213	2	ρ	ρ	NOUN
ejpam-5042	213	3	,	,	PUNCT
ejpam-5042	213	4	ϱ	ϱ	PROPN
ejpam-5042	213	5	∈	∈	PROPN
ejpam-5042	213	6	v	v	NOUN
ejpam-5042	213	7	.	.	PUNCT
ejpam-5042	214	1	then	then	ADV
ejpam-5042	214	2	ρ	ρ	PROPN
ejpam-5042	214	3	♢	♢	PROPN
ejpam-5042	214	4	∨	∨	PROPN
ejpam-5042	214	5	ρ	ρ	NOUN
ejpam-5042	214	6	=	=	SYM
ejpam-5042	214	7	ρ	ρ	PROPN
ejpam-5042	214	8	♢	♢	PROPN
ejpam-5042	214	9	∨	∨	NUM
ejpam-5042	214	10	(	(	PUNCT
ejpam-5042	214	11	ρ	ρ	PROPN
ejpam-5042	214	12	∨	∨	PROPN
ejpam-5042	214	13	m	m	PROPN
ejpam-5042	214	14	)	)	PUNCT
ejpam-5042	215	1	=	=	PRON
ejpam-5042	215	2	(	(	PUNCT
ejpam-5042	215	3	m	m	PROPN
ejpam-5042	215	4	∨	∨	NOUN
ejpam-5042	215	5	ρ	ρ	NOUN
ejpam-5042	215	6	)	)	PUNCT
ejpam-5042	215	7	♦	♦	PROPN
ejpam-5042	215	8	∨	∨	PROPN
ejpam-5042	215	9	(	(	PUNCT
ejpam-5042	215	10	m	m	PROPN
ejpam-5042	215	11	∨	∨	NOUN
ejpam-5042	215	12	ρ	ρ	NOUN
ejpam-5042	215	13	)	)	PUNCT
ejpam-5042	215	14	=	=	SYM
ejpam-5042	215	15	1	1	X
ejpam-5042	215	16	.	.	PUNCT
ejpam-5042	215	17	suppose	suppose	VERB
ejpam-5042	215	18	ϱ	ϱ	ADP
ejpam-5042	215	19	∨	∨	NUM
ejpam-5042	215	20	ρ	ρ	NOUN
ejpam-5042	215	21	=	=	SYM
ejpam-5042	215	22	1	1	NUM
ejpam-5042	215	23	.	.	PUNCT
ejpam-5042	216	1	then	then	ADV
ejpam-5042	216	2	(	(	PUNCT
ejpam-5042	216	3	m	m	PROPN
ejpam-5042	216	4	∨	∨	NOUN
ejpam-5042	216	5	ρ	ρ	NOUN
ejpam-5042	216	6	)	)	PUNCT
ejpam-5042	216	7	∨	∨	NOUN
ejpam-5042	216	8	(	(	PUNCT
ejpam-5042	216	9	m	m	PROPN
ejpam-5042	216	10	∨	∨	NUM
ejpam-5042	216	11	ϱ	ϱ	ADP
ejpam-5042	216	12	)	)	PUNCT
ejpam-5042	216	13	=	=	SYM
ejpam-5042	216	14	1	1	NUM
ejpam-5042	216	15	and	and	CCONJ
ejpam-5042	216	16	m	m	PROPN
ejpam-5042	216	17	∨	∨	NUM
ejpam-5042	216	18	ϱ	ϱ	ADP
ejpam-5042	216	19	∈	∈	PROPN
ejpam-5042	217	1	[	[	X
ejpam-5042	217	2	m	m	X
ejpam-5042	217	3	,	,	PUNCT
ejpam-5042	217	4	1	1	NUM
ejpam-5042	217	5	]	]	PUNCT
ejpam-5042	217	6	.	.	PUNCT
ejpam-5042	218	1	hence	hence	ADV
ejpam-5042	218	2	(	(	PUNCT
ejpam-5042	218	3	m	m	PROPN
ejpam-5042	218	4	∨	∨	NOUN
ejpam-5042	218	5	ρ	ρ	NOUN
ejpam-5042	218	6	)	)	PUNCT
ejpam-5042	218	7	♦	♦	PROPN
ejpam-5042	218	8	≤	≤	PROPN
ejpam-5042	218	9	(	(	PUNCT
ejpam-5042	218	10	m	m	PROPN
ejpam-5042	218	11	∨	∨	NUM
ejpam-5042	218	12	ϱ	ϱ	ADP
ejpam-5042	218	13	)	)	PUNCT
ejpam-5042	218	14	.	.	PUNCT
ejpam-5042	219	1	thus	thus	ADV
ejpam-5042	219	2	ρ	ρ	NUM
ejpam-5042	219	3	♢	♢	PROPN
ejpam-5042	219	4	≤	≤	PROPN
ejpam-5042	219	5	(	(	PUNCT
ejpam-5042	219	6	m	m	PROPN
ejpam-5042	219	7	∨	∨	NUM
ejpam-5042	219	8	ϱ	ϱ	ADP
ejpam-5042	219	9	)	)	PUNCT
ejpam-5042	219	10	.	.	PUNCT
ejpam-5042	220	1	now	now	ADV
ejpam-5042	220	2	,	,	PUNCT
ejpam-5042	220	3	ϱ	ϱ	ADP
ejpam-5042	220	4	≤	≤	NUM
ejpam-5042	220	5	ϱ	ϱ	ADP
ejpam-5042	220	6	∨	∨	NUM
ejpam-5042	220	7	ρ	ρ	PROPN
ejpam-5042	220	8	♢	♢	PROPN
ejpam-5042	220	9	≤	≤	PROPN
ejpam-5042	220	10	ϱ	ϱ	ADP
ejpam-5042	220	11	∨	∨	NUM
ejpam-5042	220	12	m	m	PROPN
ejpam-5042	220	13	∨	∨	NOUN
ejpam-5042	220	14	ϱ	ϱ	PROPN
ejpam-5042	220	15	=	=	X
ejpam-5042	220	16	ϱ.	ϱ.	NOUN
ejpam-5042	220	17	therefore	therefore	ADV
ejpam-5042	220	18	,	,	PUNCT
ejpam-5042	220	19	ϱ	ϱ	PROPN
ejpam-5042	220	20	∨	∨	NUM
ejpam-5042	220	21	ρ	ρ	PROPN
ejpam-5042	220	22	♢	♢	PROPN
ejpam-5042	220	23	=	=	X
ejpam-5042	220	24	ϱ.	ϱ.	PROPN
ejpam-5042	220	25	let	let	VERB
ejpam-5042	220	26	ρ	ρ	NOUN
ejpam-5042	220	27	,	,	PUNCT
ejpam-5042	220	28	ϱ	ϱ	PROPN
ejpam-5042	220	29	∈	∈	PROPN
ejpam-5042	220	30	v	v	NOUN
ejpam-5042	220	31	.	.	PUNCT
ejpam-5042	221	1	then	then	ADV
ejpam-5042	221	2	(	(	PUNCT
ejpam-5042	221	3	ρ	ρ	PROPN
ejpam-5042	221	4	∧	∧	PROPN
ejpam-5042	221	5	ϱ	ϱ	PROPN
ejpam-5042	221	6	)	)	PUNCT
ejpam-5042	221	7	♢	♢	PROPN
ejpam-5042	221	8	=	=	SYM
ejpam-5042	221	9	(	(	PUNCT
ejpam-5042	221	10	m	m	PROPN
ejpam-5042	221	11	∨	∨	NOUN
ejpam-5042	221	12	(	(	PUNCT
ejpam-5042	221	13	ρ	ρ	PROPN
ejpam-5042	221	14	∧	∧	PROPN
ejpam-5042	221	15	ϱ	ϱ	NOUN
ejpam-5042	221	16	)	)	PUNCT
ejpam-5042	221	17	)	)	PUNCT
ejpam-5042	222	1	♦	♦	PROPN
ejpam-5042	222	2	=	=	PRON
ejpam-5042	222	3	(	(	PUNCT
ejpam-5042	222	4	(	(	PUNCT
ejpam-5042	222	5	m	m	PROPN
ejpam-5042	222	6	∨	∨	NOUN
ejpam-5042	222	7	ρ	ρ	NOUN
ejpam-5042	222	8	)	)	PUNCT
ejpam-5042	222	9	∧	∧	PROPN
ejpam-5042	222	10	(	(	PUNCT
ejpam-5042	222	11	m	m	PROPN
ejpam-5042	222	12	∨	∨	NUM
ejpam-5042	222	13	ϱ	ϱ	PROPN
ejpam-5042	222	14	)	)	PUNCT
ejpam-5042	222	15	)	)	PUNCT
ejpam-5042	222	16	♦	♦	PROPN
ejpam-5042	222	17	=	=	PRON
ejpam-5042	222	18	(	(	PUNCT
ejpam-5042	222	19	m	m	PROPN
ejpam-5042	222	20	∨	∨	NOUN
ejpam-5042	222	21	ρ	ρ	NOUN
ejpam-5042	222	22	)	)	PUNCT
ejpam-5042	222	23	♦	♦	PROPN
ejpam-5042	222	24	∨	∨	PROPN
ejpam-5042	222	25	(	(	PUNCT
ejpam-5042	222	26	m	m	PROPN
ejpam-5042	222	27	∨	∨	NUM
ejpam-5042	222	28	ϱ	ϱ	PROPN
ejpam-5042	222	29	)	)	PUNCT
ejpam-5042	222	30	♦	♦	PROPN
ejpam-5042	222	31	=	=	PROPN
ejpam-5042	222	32	ρ	ρ	PROPN
ejpam-5042	222	33	♢	♢	PROPN
ejpam-5042	222	34	∨	∨	NUM
ejpam-5042	222	35	ϱ	ϱ	PROPN
ejpam-5042	222	36	♢	♢	PROPN
ejpam-5042	222	37	.	.	PUNCT
ejpam-5042	223	1	let	let	AUX
ejpam-5042	223	2	(	(	PUNCT
ejpam-5042	223	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	223	4	,	,	PUNCT
ejpam-5042	223	5	1	1	NUM
ejpam-5042	223	6	)	)	PUNCT
ejpam-5042	223	7	be	be	AUX
ejpam-5042	223	8	a	a	DET
ejpam-5042	223	9	pdl	pdl	NOUN
ejpam-5042	223	10	.	.	PUNCT
ejpam-5042	224	1	by	by	ADP
ejpam-5042	224	2	an	an	DET
ejpam-5042	224	3	interval	interval	NOUN
ejpam-5042	224	4	in	in	ADP
ejpam-5042	224	5	v	v	NUM
ejpam-5042	224	6	,	,	PUNCT
ejpam-5042	224	7	we	we	PRON
ejpam-5042	224	8	mean	mean	VERB
ejpam-5042	224	9	the	the	DET
ejpam-5042	224	10	set	set	NOUN
ejpam-5042	224	11	[	[	X
ejpam-5042	224	12	ρ	ρ	NOUN
ejpam-5042	224	13	,	,	PUNCT
ejpam-5042	224	14	ϱ	ϱ	ADP
ejpam-5042	224	15	]	]	PUNCT
ejpam-5042	224	16	=	=	SYM
ejpam-5042	224	17	{	{	PUNCT
ejpam-5042	224	18	µ1	µ1	NOUN
ejpam-5042	224	19	∈	∈	NOUN
ejpam-5042	224	20	v	v	NOUN
ejpam-5042	224	21	|ρ	|ρ	ADJ
ejpam-5042	224	22	≤	≤	NUM
ejpam-5042	224	23	µ1	µ1	PROPN
ejpam-5042	224	24	≤	≤	NOUN
ejpam-5042	224	25	ϱ	ϱ	ADP
ejpam-5042	224	26	}	}	PUNCT
ejpam-5042	224	27	for	for	ADP
ejpam-5042	224	28	some	some	DET
ejpam-5042	224	29	ρ	ρ	NOUN
ejpam-5042	224	30	,	,	PUNCT
ejpam-5042	224	31	ϱ	ϱ	PROPN
ejpam-5042	224	32	∈	∈	PROPN
ejpam-5042	224	33	v	v	ADP
ejpam-5042	224	34	such	such	ADJ
ejpam-5042	224	35	that	that	SCONJ
ejpam-5042	224	36	ρ	ρ	PROPN
ejpam-5042	224	37	≤	≤	PROPN
ejpam-5042	224	38	ϱ.	ϱ.	NOUN
ejpam-5042	224	39	clearly	clearly	ADV
ejpam-5042	224	40	,	,	PUNCT
ejpam-5042	224	41	[	[	X
ejpam-5042	224	42	ρ	ρ	X
ejpam-5042	224	43	,	,	PUNCT
ejpam-5042	224	44	ϱ	ϱ	NOUN
ejpam-5042	224	45	]	]	PUNCT
ejpam-5042	224	46	is	be	AUX
ejpam-5042	224	47	closed	close	VERB
ejpam-5042	224	48	under	under	ADP
ejpam-5042	224	49	∨,∧.	∨,∧.	NOUN
ejpam-5042	224	50	since	since	SCONJ
ejpam-5042	224	51	[	[	X
ejpam-5042	224	52	ρ	ρ	X
ejpam-5042	224	53	,	,	PUNCT
ejpam-5042	224	54	ϱ	ϱ	X
ejpam-5042	224	55	]	]	PUNCT
ejpam-5042	224	56	is	be	AUX
ejpam-5042	224	57	a	a	DET
ejpam-5042	224	58	pdl	pdl	NOUN
ejpam-5042	224	59	with	with	ADP
ejpam-5042	224	60	ρ	ρ	PROPN
ejpam-5042	224	61	as	as	ADP
ejpam-5042	224	62	its	its	PRON
ejpam-5042	224	63	zero	zero	NUM
ejpam-5042	224	64	element	element	NOUN
ejpam-5042	224	65	and	and	CCONJ
ejpam-5042	224	66	ϱ	ϱ	NOUN
ejpam-5042	224	67	as	as	ADP
ejpam-5042	224	68	its	its	PRON
ejpam-5042	224	69	greatest	great	ADJ
ejpam-5042	224	70	element	element	NOUN
ejpam-5042	224	71	,	,	PUNCT
ejpam-5042	224	72	every	every	DET
ejpam-5042	224	73	interval	interval	NOUN
ejpam-5042	224	74	[	[	X
ejpam-5042	224	75	ρ	ρ	X
ejpam-5042	224	76	,	,	PUNCT
ejpam-5042	224	77	ϱ	ϱ	X
ejpam-5042	224	78	]	]	PUNCT
ejpam-5042	224	79	is	be	AUX
ejpam-5042	224	80	a	a	DET
ejpam-5042	224	81	bounded	bounded	ADJ
ejpam-5042	224	82	distributive	distributive	ADJ
ejpam-5042	224	83	lattice	lattice	NOUN
ejpam-5042	224	84	.	.	PUNCT
ejpam-5042	225	1	definition	definition	NOUN
ejpam-5042	225	2	6	6	NUM
ejpam-5042	225	3	.	.	PUNCT
ejpam-5042	226	1	a	a	DET
ejpam-5042	226	2	pdl	pdl	PROPN
ejpam-5042	226	3	(	(	PUNCT
ejpam-5042	226	4	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	226	5	,	,	PUNCT
ejpam-5042	226	6	1	1	NUM
ejpam-5042	226	7	)	)	PUNCT
ejpam-5042	226	8	is	be	AUX
ejpam-5042	226	9	said	say	VERB
ejpam-5042	226	10	to	to	PART
ejpam-5042	226	11	be	be	AUX
ejpam-5042	226	12	relatively	relatively	ADV
ejpam-5042	226	13	complemented	complemented	ADJ
ejpam-5042	226	14	if	if	SCONJ
ejpam-5042	226	15	every	every	DET
ejpam-5042	226	16	interval	interval	NOUN
ejpam-5042	226	17	[	[	X
ejpam-5042	226	18	ρ	ρ	X
ejpam-5042	226	19	,	,	PUNCT
ejpam-5042	226	20	ϱ	ϱ	ADP
ejpam-5042	226	21	]	]	PUNCT
ejpam-5042	226	22	,	,	PUNCT
ejpam-5042	226	23	ρ	ρ	PROPN
ejpam-5042	226	24	≤	≤	NUM
ejpam-5042	226	25	ϱ	ϱ	ADP
ejpam-5042	226	26	in	in	ADP
ejpam-5042	226	27	v	v	NUM
ejpam-5042	226	28	is	be	AUX
ejpam-5042	226	29	a	a	DET
ejpam-5042	226	30	complemented	complemented	ADJ
ejpam-5042	226	31	lattice	lattice	NOUN
ejpam-5042	226	32	.	.	PUNCT
ejpam-5042	227	1	theorem	theorem	NOUN
ejpam-5042	227	2	5	5	NUM
ejpam-5042	227	3	.	.	PUNCT
ejpam-5042	228	1	let	let	AUX
ejpam-5042	228	2	(	(	PUNCT
ejpam-5042	228	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	228	4	,	,	PUNCT
ejpam-5042	228	5	1	1	NUM
ejpam-5042	228	6	)	)	PUNCT
ejpam-5042	228	7	be	be	AUX
ejpam-5042	228	8	a	a	DET
ejpam-5042	228	9	pdl	pdl	NOUN
ejpam-5042	228	10	with	with	ADP
ejpam-5042	228	11	1	1	NUM
ejpam-5042	228	12	.	.	PUNCT
ejpam-5042	229	1	then	then	ADV
ejpam-5042	229	2	the	the	DET
ejpam-5042	229	3	following	following	NOUN
ejpam-5042	229	4	are	be	AUX
ejpam-5042	229	5	equivalent	equivalent	ADJ
ejpam-5042	229	6	:	:	PUNCT
ejpam-5042	229	7	(	(	PUNCT
ejpam-5042	229	8	1	1	NUM
ejpam-5042	229	9	)	)	PUNCT
ejpam-5042	229	10	.	.	PUNCT
ejpam-5042	230	1	v	v	NOUN
ejpam-5042	230	2	is	be	AUX
ejpam-5042	230	3	relatively	relatively	ADV
ejpam-5042	230	4	complemented	complemented	ADJ
ejpam-5042	230	5	.	.	PUNCT
ejpam-5042	231	1	(	(	PUNCT
ejpam-5042	231	2	2	2	NUM
ejpam-5042	231	3	)	)	PUNCT
ejpam-5042	231	4	.	.	PUNCT
ejpam-5042	232	1	v	v	NOUN
ejpam-5042	232	2	is	be	AUX
ejpam-5042	232	3	sectionally	sectionally	ADV
ejpam-5042	232	4	complemented	complement	VERB
ejpam-5042	232	5	,	,	PUNCT
ejpam-5042	232	6	i.e	i.e	PRON
ejpam-5042	232	7	the	the	DET
ejpam-5042	232	8	interval	interval	NOUN
ejpam-5042	233	1	[	[	X
ejpam-5042	233	2	ρ	ρ	X
ejpam-5042	233	3	,	,	PUNCT
ejpam-5042	233	4	1	1	NUM
ejpam-5042	233	5	]	]	PUNCT
ejpam-5042	233	6	,	,	PUNCT
ejpam-5042	233	7	ρ	ρ	PROPN
ejpam-5042	233	8	∈	∈	PROPN
ejpam-5042	233	9	v	v	NOUN
ejpam-5042	233	10	is	be	AUX
ejpam-5042	233	11	a	a	DET
ejpam-5042	233	12	complemented	complemented	ADJ
ejpam-5042	233	13	lattice	lattice	NOUN
ejpam-5042	233	14	.	.	PUNCT
ejpam-5042	234	1	(	(	PUNCT
ejpam-5042	234	2	3	3	NUM
ejpam-5042	234	3	)	)	PUNCT
ejpam-5042	234	4	.	.	PUNCT
ejpam-5042	235	1	given	give	VERB
ejpam-5042	235	2	ρ	ρ	PROPN
ejpam-5042	235	3	,	,	PUNCT
ejpam-5042	235	4	ϱ	ϱ	PROPN
ejpam-5042	235	5	∈	∈	PROPN
ejpam-5042	235	6	v	v	NOUN
ejpam-5042	235	7	,	,	PUNCT
ejpam-5042	235	8	there	there	PRON
ejpam-5042	235	9	exists	exist	VERB
ejpam-5042	235	10	a	a	DET
ejpam-5042	235	11	unique	unique	ADJ
ejpam-5042	235	12	µ1	µ1	NOUN
ejpam-5042	235	13	∈	∈	NOUN
ejpam-5042	235	14	v	v	ADP
ejpam-5042	235	15	such	such	ADJ
ejpam-5042	235	16	that	that	PRON
ejpam-5042	235	17	µ1	µ1	PROPN
ejpam-5042	235	18	∨	∨	NOUN
ejpam-5042	235	19	ρ	ρ	NOUN
ejpam-5042	235	20	=	=	SYM
ejpam-5042	235	21	1	1	NUM
ejpam-5042	235	22	and	and	CCONJ
ejpam-5042	235	23	µ1	µ1	PROPN
ejpam-5042	235	24	∧	∧	PROPN
ejpam-5042	235	25	ρ	ρ	PROPN
ejpam-5042	235	26	=	=	PROPN
ejpam-5042	235	27	ϱ∧	ϱ∧	PROPN
ejpam-5042	235	28	ρ	ρ	PROPN
ejpam-5042	235	29	.	.	PUNCT
ejpam-5042	236	1	proof	proof	NOUN
ejpam-5042	236	2	.	.	PUNCT
ejpam-5042	237	1	(	(	PUNCT
ejpam-5042	237	2	1	1	X
ejpam-5042	237	3	)	)	PUNCT
ejpam-5042	237	4	⇒	⇒	NOUN
ejpam-5042	237	5	(	(	PUNCT
ejpam-5042	237	6	2	2	X
ejpam-5042	237	7	)	)	PUNCT
ejpam-5042	237	8	is	be	AUX
ejpam-5042	237	9	clear	clear	ADJ
ejpam-5042	237	10	.	.	PUNCT
ejpam-5042	238	1	(	(	PUNCT
ejpam-5042	238	2	2	2	X
ejpam-5042	238	3	)	)	PUNCT
ejpam-5042	238	4	⇒	⇒	NOUN
ejpam-5042	238	5	(	(	PUNCT
ejpam-5042	238	6	3	3	NUM
ejpam-5042	238	7	)	)	PUNCT
ejpam-5042	238	8	:	:	PUNCT
ejpam-5042	238	9	assume	assume	VERB
ejpam-5042	238	10	(	(	PUNCT
ejpam-5042	238	11	2	2	NUM
ejpam-5042	238	12	)	)	PUNCT
ejpam-5042	238	13	and	and	CCONJ
ejpam-5042	238	14	let	let	VERB
ejpam-5042	238	15	ρ	ρ	NOUN
ejpam-5042	238	16	,	,	PUNCT
ejpam-5042	238	17	ϱ	ϱ	PROPN
ejpam-5042	238	18	∈	∈	PROPN
ejpam-5042	238	19	v	v	NOUN
ejpam-5042	238	20	.	.	PUNCT
ejpam-5042	239	1	so	so	SCONJ
ejpam-5042	239	2	that	that	SCONJ
ejpam-5042	239	3	the	the	DET
ejpam-5042	239	4	interval	interval	NOUN
ejpam-5042	239	5	[	[	X
ejpam-5042	239	6	ϱ	ϱ	ADP
ejpam-5042	239	7	∧	∧	PROPN
ejpam-5042	239	8	ρ	ρ	PROPN
ejpam-5042	239	9	,	,	PUNCT
ejpam-5042	239	10	1	1	NUM
ejpam-5042	239	11	]	]	PUNCT
ejpam-5042	239	12	is	be	AUX
ejpam-5042	239	13	complemented	complement	VERB
ejpam-5042	239	14	and	and	CCONJ
ejpam-5042	239	15	ρ	ρ	NUM
ejpam-5042	239	16	∈	∈	PROPN
ejpam-5042	240	1	[	[	X
ejpam-5042	240	2	ϱ	ϱ	ADP
ejpam-5042	240	3	∧	∧	PROPN
ejpam-5042	240	4	ρ	ρ	PROPN
ejpam-5042	240	5	,	,	PUNCT
ejpam-5042	240	6	1	1	NUM
ejpam-5042	240	7	]	]	PUNCT
ejpam-5042	240	8	.	.	PUNCT
ejpam-5042	241	1	if	if	SCONJ
ejpam-5042	241	2	µ1	µ1	PROPN
ejpam-5042	241	3	is	be	AUX
ejpam-5042	241	4	the	the	DET
ejpam-5042	241	5	complement	complement	NOUN
ejpam-5042	241	6	of	of	ADP
ejpam-5042	241	7	ρ	ρ	NOUN
ejpam-5042	241	8	in	in	ADP
ejpam-5042	241	9	[	[	X
ejpam-5042	241	10	ϱ	ϱ	PROPN
ejpam-5042	241	11	∧	∧	PROPN
ejpam-5042	241	12	ρ	ρ	PROPN
ejpam-5042	241	13	,	,	PUNCT
ejpam-5042	241	14	1	1	NUM
ejpam-5042	241	15	]	]	PUNCT
ejpam-5042	241	16	,	,	PUNCT
ejpam-5042	241	17	then	then	ADV
ejpam-5042	241	18	µ1	µ1	VERB
ejpam-5042	241	19	∧	∧	PROPN
ejpam-5042	241	20	ρ	ρ	PROPN
ejpam-5042	241	21	=	=	SYM
ejpam-5042	241	22	ϱ	ϱ	PROPN
ejpam-5042	241	23	∧	∧	PROPN
ejpam-5042	241	24	ρ	ρ	PROPN
ejpam-5042	241	25	and	and	CCONJ
ejpam-5042	241	26	µ1	µ1	PROPN
ejpam-5042	241	27	∨	∨	NUM
ejpam-5042	241	28	ρ	ρ	NOUN
ejpam-5042	241	29	=	=	SYM
ejpam-5042	241	30	1	1	NUM
ejpam-5042	241	31	.	.	PUNCT
ejpam-5042	242	1	since	since	SCONJ
ejpam-5042	242	2	any	any	DET
ejpam-5042	242	3	µ2	µ2	PROPN
ejpam-5042	242	4	∈	∈	PROPN
ejpam-5042	242	5	v	v	ADP
ejpam-5042	242	6	satisfies	satisfie	NOUN
ejpam-5042	242	7	µ2	µ2	PROPN
ejpam-5042	242	8	∧	∧	PROPN
ejpam-5042	242	9	ρ	ρ	PROPN
ejpam-5042	242	10	=	=	SYM
ejpam-5042	242	11	ϱ	ϱ	PROPN
ejpam-5042	242	12	∧	∧	PROPN
ejpam-5042	242	13	ρ	ρ	PROPN
ejpam-5042	242	14	and	and	CCONJ
ejpam-5042	242	15	µ2	µ2	PROPN
ejpam-5042	242	16	∨	∨	PROPN
ejpam-5042	242	17	ρ	ρ	X
ejpam-5042	242	18	=	=	SYM
ejpam-5042	242	19	1	1	NUM
ejpam-5042	242	20	belongs	belong	VERB
ejpam-5042	242	21	to	to	ADP
ejpam-5042	242	22	[	[	X
ejpam-5042	242	23	ϱ	ϱ	ADP
ejpam-5042	242	24	∧	∧	PROPN
ejpam-5042	242	25	ρ	ρ	PROPN
ejpam-5042	242	26	,	,	PUNCT
ejpam-5042	242	27	1	1	NUM
ejpam-5042	242	28	]	]	PUNCT
ejpam-5042	242	29	.	.	PUNCT
ejpam-5042	243	1	therefore	therefore	ADV
ejpam-5042	243	2	,	,	PUNCT
ejpam-5042	243	3	[	[	X
ejpam-5042	243	4	ϱ	ϱ	ADP
ejpam-5042	243	5	∧	∧	PROPN
ejpam-5042	243	6	ρ	ρ	PROPN
ejpam-5042	243	7	,	,	PUNCT
ejpam-5042	243	8	1	1	NUM
ejpam-5042	243	9	]	]	PUNCT
ejpam-5042	243	10	is	be	AUX
ejpam-5042	243	11	a	a	DET
ejpam-5042	243	12	boolean	boolean	ADJ
ejpam-5042	243	13	algebra	algebra	NOUN
ejpam-5042	243	14	and	and	CCONJ
ejpam-5042	243	15	hence	hence	ADV
ejpam-5042	243	16	the	the	DET
ejpam-5042	243	17	uniqueness	uniqueness	NOUN
ejpam-5042	243	18	of	of	ADP
ejpam-5042	243	19	µ1	µ1	PROPN
ejpam-5042	243	20	follows	follow	VERB
ejpam-5042	243	21	.	.	PUNCT
ejpam-5042	244	1	(	(	PUNCT
ejpam-5042	244	2	3	3	X
ejpam-5042	244	3	)	)	PUNCT
ejpam-5042	244	4	⇒	⇒	NOUN
ejpam-5042	244	5	(	(	PUNCT
ejpam-5042	244	6	1	1	NUM
ejpam-5042	244	7	)	)	PUNCT
ejpam-5042	244	8	:	:	PUNCT
ejpam-5042	244	9	assume	assume	VERB
ejpam-5042	244	10	(	(	PUNCT
ejpam-5042	244	11	3	3	NUM
ejpam-5042	244	12	)	)	PUNCT
ejpam-5042	244	13	.	.	PUNCT
ejpam-5042	245	1	let	let	VERB
ejpam-5042	245	2	ρ	ρ	NOUN
ejpam-5042	245	3	,	,	PUNCT
ejpam-5042	245	4	ϱ	ϱ	PROPN
ejpam-5042	245	5	∈	∈	NOUN
ejpam-5042	245	6	v	v	ADP
ejpam-5042	245	7	such	such	DET
ejpam-5042	245	8	that	that	SCONJ
ejpam-5042	245	9	ϱ	ϱ	ADP
ejpam-5042	245	10	≤	≤	NOUN
ejpam-5042	245	11	ρ	ρ	NOUN
ejpam-5042	245	12	and	and	CCONJ
ejpam-5042	245	13	let	let	VERB
ejpam-5042	245	14	µ1	µ1	NOUN
ejpam-5042	245	15	∈	∈	PROPN
ejpam-5042	245	16	[	[	X
ejpam-5042	245	17	ϱ	ϱ	PROPN
ejpam-5042	245	18	,	,	PUNCT
ejpam-5042	245	19	ρ	ρ	NOUN
ejpam-5042	245	20	]	]	X
ejpam-5042	245	21	.	.	PUNCT
ejpam-5042	246	1	then	then	ADV
ejpam-5042	246	2	by	by	ADP
ejpam-5042	246	3	(	(	PUNCT
ejpam-5042	246	4	3	3	NUM
ejpam-5042	246	5	)	)	PUNCT
ejpam-5042	246	6	,	,	PUNCT
ejpam-5042	246	7	there	there	PRON
ejpam-5042	246	8	exists	exist	VERB
ejpam-5042	246	9	µ2	µ2	PROPN
ejpam-5042	246	10	∈	∈	PROPN
ejpam-5042	246	11	v	v	ADP
ejpam-5042	246	12	such	such	ADJ
ejpam-5042	246	13	that	that	DET
ejpam-5042	246	14	µ1	µ1	PROPN
ejpam-5042	246	15	∨	∨	NOUN
ejpam-5042	246	16	µ2	µ2	PROPN
ejpam-5042	246	17	=	=	NOUN
ejpam-5042	246	18	1	1	NUM
ejpam-5042	246	19	,	,	PUNCT
ejpam-5042	246	20	µ2	µ2	PROPN
ejpam-5042	246	21	∧	∧	PROPN
ejpam-5042	246	22	µ1	µ1	PROPN
ejpam-5042	246	23	=	=	SYM
ejpam-5042	246	24	ϱ	ϱ	PROPN
ejpam-5042	246	25	∧	∧	PROPN
ejpam-5042	246	26	µ1	µ1	PROPN
ejpam-5042	246	27	=	=	NOUN
ejpam-5042	246	28	ϱ.	ϱ.	NOUN
ejpam-5042	247	1	it	it	PRON
ejpam-5042	247	2	is	be	AUX
ejpam-5042	247	3	clear	clear	ADJ
ejpam-5042	247	4	that	that	SCONJ
ejpam-5042	247	5	ϱ	ϱ	ADP
ejpam-5042	247	6	=	=	SYM
ejpam-5042	247	7	µ2	µ2	PROPN
ejpam-5042	247	8	∧	∧	PROPN
ejpam-5042	247	9	µ1	µ1	PROPN
ejpam-5042	247	10	=	=	SYM
ejpam-5042	247	11	µ1	µ1	NOUN
ejpam-5042	247	12	∧	∧	PROPN
ejpam-5042	247	13	µ2	µ2	PROPN
ejpam-5042	247	14	≤	≤	PUNCT
ejpam-5042	247	15	µ2	µ2	PROPN
ejpam-5042	247	16	.	.	PUNCT
ejpam-5042	248	1	now	now	ADV
ejpam-5042	248	2	,	,	PUNCT
ejpam-5042	248	3	we	we	PRON
ejpam-5042	248	4	prove	prove	VERB
ejpam-5042	248	5	that	that	SCONJ
ejpam-5042	248	6	the	the	DET
ejpam-5042	248	7	element	element	NOUN
ejpam-5042	248	8	µ2	µ2	PROPN
ejpam-5042	248	9	∧	∧	PROPN
ejpam-5042	248	10	ρ	ρ	PROPN
ejpam-5042	248	11	∈	∈	PROPN
ejpam-5042	248	12	[	[	X
ejpam-5042	248	13	ϱ	ϱ	X
ejpam-5042	248	14	,	,	PUNCT
ejpam-5042	248	15	ρ	ρ	NOUN
ejpam-5042	248	16	]	]	PUNCT
ejpam-5042	248	17	and	and	CCONJ
ejpam-5042	248	18	µ2	µ2	PROPN
ejpam-5042	248	19	∧	∧	PROPN
ejpam-5042	248	20	ρ	ρ	PROPN
ejpam-5042	248	21	is	be	AUX
ejpam-5042	248	22	complement	complement	NOUN
ejpam-5042	248	23	of	of	ADP
ejpam-5042	248	24	µ1	µ1	PROPN
ejpam-5042	248	25	in	in	ADP
ejpam-5042	248	26	[	[	X
ejpam-5042	248	27	ϱ	ϱ	X
ejpam-5042	248	28	,	,	PUNCT
ejpam-5042	248	29	ρ	ρ	NOUN
ejpam-5042	248	30	]	]	X
ejpam-5042	248	31	.	.	PUNCT
ejpam-5042	249	1	clearly	clearly	ADV
ejpam-5042	249	2	µ2	µ2	VERB
ejpam-5042	249	3	∧	∧	PROPN
ejpam-5042	249	4	ρ	ρ	PROPN
ejpam-5042	249	5	≤	≤	PROPN
ejpam-5042	249	6	ρ	ρ	NOUN
ejpam-5042	249	7	.	.	PUNCT
ejpam-5042	250	1	now	now	ADV
ejpam-5042	250	2	,	,	PUNCT
ejpam-5042	250	3	ϱ	ϱ	ADP
ejpam-5042	250	4	∨	∨	NUM
ejpam-5042	250	5	(	(	PUNCT
ejpam-5042	250	6	µ2	µ2	PROPN
ejpam-5042	250	7	∧	∧	PROPN
ejpam-5042	250	8	ρ	ρ	PROPN
ejpam-5042	250	9	)	)	PUNCT
ejpam-5042	250	10	=	=	PUNCT
ejpam-5042	250	11	(	(	PUNCT
ejpam-5042	250	12	ϱ	ϱ	PROPN
ejpam-5042	250	13	∨	∨	NUM
ejpam-5042	250	14	µ2	µ2	PROPN
ejpam-5042	250	15	)	)	PUNCT
ejpam-5042	250	16	∧	∧	PROPN
ejpam-5042	250	17	(	(	PUNCT
ejpam-5042	250	18	ϱ	ϱ	PROPN
ejpam-5042	250	19	∨	∨	NUM
ejpam-5042	250	20	ρ	ρ	NOUN
ejpam-5042	250	21	)	)	PUNCT
ejpam-5042	250	22	=	=	VERB
ejpam-5042	251	1	µ2	µ2	PROPN
ejpam-5042	251	2	∧	∧	PROPN
ejpam-5042	251	3	ρ	ρ	PROPN
ejpam-5042	251	4	.	.	PUNCT
ejpam-5042	252	1	hence	hence	ADV
ejpam-5042	252	2	µ2	µ2	PROPN
ejpam-5042	252	3	∧	∧	PROPN
ejpam-5042	252	4	ρ	ρ	PROPN
ejpam-5042	252	5	∈	∈	PROPN
ejpam-5042	252	6	[	[	X
ejpam-5042	252	7	ϱ	ϱ	PROPN
ejpam-5042	252	8	,	,	PUNCT
ejpam-5042	252	9	ρ	ρ	NOUN
ejpam-5042	252	10	]	]	X
ejpam-5042	252	11	.	.	PUNCT
ejpam-5042	253	1	now	now	ADV
ejpam-5042	253	2	,	,	PUNCT
ejpam-5042	253	3	µ1	µ1	PROPN
ejpam-5042	253	4	∨	∨	NOUN
ejpam-5042	253	5	(	(	PUNCT
ejpam-5042	253	6	µ2	µ2	PROPN
ejpam-5042	253	7	∧	∧	PROPN
ejpam-5042	253	8	ρ	ρ	PROPN
ejpam-5042	253	9	)	)	PUNCT
ejpam-5042	253	10	=	=	SYM
ejpam-5042	253	11	(	(	PUNCT
ejpam-5042	253	12	µ1	µ1	PROPN
ejpam-5042	253	13	∨	∨	NUM
ejpam-5042	253	14	µ2	µ2	PROPN
ejpam-5042	253	15	)	)	PUNCT
ejpam-5042	253	16	∧	∧	PROPN
ejpam-5042	253	17	(	(	PUNCT
ejpam-5042	253	18	µ1	µ1	PROPN
ejpam-5042	253	19	∨	∨	NOUN
ejpam-5042	253	20	ρ	ρ	NOUN
ejpam-5042	253	21	)	)	PUNCT
ejpam-5042	253	22	=	=	SYM
ejpam-5042	253	23	1	1	NUM
ejpam-5042	253	24	∧	∧	PROPN
ejpam-5042	253	25	(	(	PUNCT
ejpam-5042	253	26	µ1	µ1	PROPN
ejpam-5042	253	27	∨	∨	NOUN
ejpam-5042	253	28	ρ	ρ	NOUN
ejpam-5042	253	29	)	)	PUNCT
ejpam-5042	253	30	=	=	SYM
ejpam-5042	253	31	ρ	ρ	PROPN
ejpam-5042	253	32	and	and	CCONJ
ejpam-5042	253	33	ϱ	ϱ	X
ejpam-5042	253	34	=	=	PUNCT
ejpam-5042	253	35	µ2	µ2	PROPN
ejpam-5042	253	36	∧	∧	PROPN
ejpam-5042	253	37	µ1	µ1	PROPN
ejpam-5042	253	38	=	=	PUNCT
ejpam-5042	254	1	[	[	X
ejpam-5042	254	2	µ2	µ2	PROPN
ejpam-5042	254	3	∨	∨	PROPN
ejpam-5042	254	4	(	(	PUNCT
ejpam-5042	254	5	µ2	µ2	PROPN
ejpam-5042	254	6	∧	∧	PROPN
ejpam-5042	254	7	ρ	ρ	PROPN
ejpam-5042	254	8	)	)	PUNCT
ejpam-5042	254	9	]	]	PUNCT
ejpam-5042	254	10	∧	∧	NOUN
ejpam-5042	254	11	µ1	µ1	PROPN
ejpam-5042	254	12	.	.	PUNCT
ejpam-5042	255	1	=	=	PUNCT
ejpam-5042	255	2	(	(	PUNCT
ejpam-5042	255	3	µ2	µ2	PROPN
ejpam-5042	255	4	∧	∧	PROPN
ejpam-5042	255	5	µ1	µ1	PROPN
ejpam-5042	255	6	)	)	PUNCT
ejpam-5042	255	7	∨	∨	NOUN
ejpam-5042	256	1	[	[	X
ejpam-5042	256	2	(	(	PUNCT
ejpam-5042	256	3	µ2	µ2	PROPN
ejpam-5042	256	4	∧	∧	PROPN
ejpam-5042	256	5	ρ	ρ	PROPN
ejpam-5042	256	6	)	)	PUNCT
ejpam-5042	256	7	∧	∧	PROPN
ejpam-5042	256	8	µ1	µ1	PROPN
ejpam-5042	256	9	]	]	PUNCT
ejpam-5042	256	10	.	.	PUNCT
ejpam-5042	257	1	=	=	PUNCT
ejpam-5042	257	2	(	(	PUNCT
ejpam-5042	257	3	µ2	µ2	PROPN
ejpam-5042	257	4	∧	∧	PROPN
ejpam-5042	257	5	µ1	µ1	PROPN
ejpam-5042	257	6	)	)	PUNCT
ejpam-5042	257	7	∨	∨	NOUN
ejpam-5042	258	1	[	[	X
ejpam-5042	258	2	µ1	µ1	X
ejpam-5042	258	3	∧	∧	PROPN
ejpam-5042	258	4	(	(	PUNCT
ejpam-5042	258	5	µ2	µ2	PROPN
ejpam-5042	258	6	∧	∧	PROPN
ejpam-5042	258	7	ρ	ρ	PROPN
ejpam-5042	258	8	)	)	PUNCT
ejpam-5042	258	9	]	]	PUNCT
ejpam-5042	258	10	.	.	PUNCT
ejpam-5042	259	1	=	=	PUNCT
ejpam-5042	260	1	[	[	X
ejpam-5042	260	2	(	(	PUNCT
ejpam-5042	260	3	µ2	µ2	PROPN
ejpam-5042	260	4	∧	∧	PROPN
ejpam-5042	260	5	µ1	µ1	PROPN
ejpam-5042	260	6	)	)	PUNCT
ejpam-5042	260	7	∨	∨	NUM
ejpam-5042	260	8	µ1	µ1	PROPN
ejpam-5042	260	9	]	]	X
ejpam-5042	260	10	∧	∧	PROPN
ejpam-5042	260	11	[	[	X
ejpam-5042	260	12	(	(	PUNCT
ejpam-5042	260	13	µ2	µ2	PROPN
ejpam-5042	260	14	∧	∧	PROPN
ejpam-5042	260	15	µ1	µ1	PROPN
ejpam-5042	260	16	)	)	PUNCT
ejpam-5042	260	17	∨	∨	NOUN
ejpam-5042	260	18	(	(	PUNCT
ejpam-5042	260	19	µ2	µ2	PROPN
ejpam-5042	260	20	∧	∧	PROPN
ejpam-5042	260	21	ρ	ρ	PROPN
ejpam-5042	260	22	)	)	PUNCT
ejpam-5042	260	23	]	]	PUNCT
ejpam-5042	260	24	.	.	PUNCT
ejpam-5042	261	1	=	=	SYM
ejpam-5042	261	2	µ1	µ1	PROPN
ejpam-5042	261	3	∧	∧	PROPN
ejpam-5042	261	4	[	[	X
ejpam-5042	261	5	ϱ	ϱ	ADP
ejpam-5042	261	6	∨	∨	NUM
ejpam-5042	261	7	(	(	PUNCT
ejpam-5042	261	8	µ2	µ2	PROPN
ejpam-5042	261	9	∧	∧	PROPN
ejpam-5042	261	10	ρ	ρ	PROPN
ejpam-5042	261	11	)	)	PUNCT
ejpam-5042	261	12	]	]	PUNCT
ejpam-5042	261	13	.	.	PUNCT
ejpam-5042	262	1	=	=	SYM
ejpam-5042	262	2	µ1	µ1	PROPN
ejpam-5042	262	3	∧	∧	PROPN
ejpam-5042	262	4	[	[	X
ejpam-5042	262	5	(	(	PUNCT
ejpam-5042	262	6	ϱ	ϱ	PROPN
ejpam-5042	262	7	∨	∨	NUM
ejpam-5042	262	8	µ2	µ2	PROPN
ejpam-5042	262	9	)	)	PUNCT
ejpam-5042	262	10	∧	∧	PROPN
ejpam-5042	262	11	(	(	PUNCT
ejpam-5042	262	12	ϱ	ϱ	PROPN
ejpam-5042	262	13	∨	∨	NUM
ejpam-5042	262	14	ρ	ρ	NOUN
ejpam-5042	262	15	)	)	PUNCT
ejpam-5042	262	16	]	]	PUNCT
ejpam-5042	262	17	.	.	PUNCT
ejpam-5042	263	1	=	=	SYM
ejpam-5042	263	2	µ1	µ1	PROPN
ejpam-5042	263	3	∧	∧	PROPN
ejpam-5042	263	4	(	(	PUNCT
ejpam-5042	263	5	µ2	µ2	PROPN
ejpam-5042	263	6	∧	∧	PROPN
ejpam-5042	263	7	ρ	ρ	PROPN
ejpam-5042	263	8	)	)	PUNCT
ejpam-5042	263	9	.	.	PUNCT
ejpam-5042	264	1	therefore	therefore	ADV
ejpam-5042	264	2	,	,	PUNCT
ejpam-5042	264	3	µ2	µ2	PROPN
ejpam-5042	264	4	∧	∧	PROPN
ejpam-5042	264	5	ρ	ρ	PROPN
ejpam-5042	264	6	is	be	AUX
ejpam-5042	264	7	the	the	DET
ejpam-5042	264	8	complement	complement	NOUN
ejpam-5042	264	9	of	of	ADP
ejpam-5042	264	10	µ1	µ1	PROPN
ejpam-5042	264	11	in	in	ADP
ejpam-5042	264	12	[	[	X
ejpam-5042	264	13	ϱ	ϱ	X
ejpam-5042	264	14	,	,	PUNCT
ejpam-5042	264	15	ρ	ρ	NOUN
ejpam-5042	264	16	]	]	X
ejpam-5042	264	17	.	.	PUNCT
ejpam-5042	265	1	hence	hence	ADV
ejpam-5042	265	2	v	v	NOUN
ejpam-5042	265	3	is	be	AUX
ejpam-5042	265	4	relatively	relatively	ADV
ejpam-5042	265	5	complemented	complemented	ADJ
ejpam-5042	265	6	.	.	PUNCT
ejpam-5042	266	1	note	note	VERB
ejpam-5042	266	2	that	that	SCONJ
ejpam-5042	266	3	every	every	DET
ejpam-5042	266	4	relatively	relatively	ADV
ejpam-5042	266	5	complemented	complemented	ADJ
ejpam-5042	266	6	pdl	pdl	NOUN
ejpam-5042	266	7	is	be	AUX
ejpam-5042	266	8	an	an	DET
ejpam-5042	266	9	associative	associative	ADJ
ejpam-5042	266	10	pdl	pdl	PROPN
ejpam-5042	266	11	.	.	PUNCT
ejpam-5042	266	12	r.	r.	PROPN
ejpam-5042	266	13	shukla	shukla	PROPN
ejpam-5042	266	14	et	et	PROPN
ejpam-5042	266	15	al	al	PROPN
ejpam-5042	266	16	.	.	PUNCT
ejpam-5042	266	17	/	/	SYM
ejpam-5042	266	18	eur	eur	PROPN
ejpam-5042	266	19	.	.	PUNCT
ejpam-5042	267	1	j.	j.	PROPN
ejpam-5042	267	2	pure	pure	PROPN
ejpam-5042	267	3	appl	appl	PROPN
ejpam-5042	267	4	.	.	PROPN
ejpam-5042	267	5	math	math	PROPN
ejpam-5042	267	6	,	,	PUNCT
ejpam-5042	267	7	17	17	NUM
ejpam-5042	267	8	(	(	PUNCT
ejpam-5042	267	9	2	2	NUM
ejpam-5042	267	10	)	)	PUNCT
ejpam-5042	267	11	(	(	PUNCT
ejpam-5042	267	12	2024	2024	NUM
ejpam-5042	267	13	)	)	PUNCT
ejpam-5042	267	14	,	,	PUNCT
ejpam-5042	267	15	1129	1129	NUM
ejpam-5042	267	16	-	-	SYM
ejpam-5042	267	17	1145	1145	NUM
ejpam-5042	267	18	1137	1137	NUM
ejpam-5042	267	19	theorem	theorem	VERB
ejpam-5042	267	20	6	6	NUM
ejpam-5042	267	21	.	.	PUNCT
ejpam-5042	268	1	let	let	VERB
ejpam-5042	268	2	v	v	PART
ejpam-5042	268	3	be	be	AUX
ejpam-5042	268	4	a	a	DET
ejpam-5042	268	5	relatively	relatively	ADV
ejpam-5042	268	6	complemented	complemented	ADJ
ejpam-5042	268	7	pdl	pdl	NOUN
ejpam-5042	268	8	with	with	ADP
ejpam-5042	268	9	a	a	DET
ejpam-5042	268	10	minimal	minimal	ADJ
ejpam-5042	268	11	element	element	NOUN
ejpam-5042	268	12	m1	m1	NOUN
ejpam-5042	268	13	.	.	PUNCT
ejpam-5042	269	1	then	then	ADV
ejpam-5042	269	2	v	v	NOUN
ejpam-5042	269	3	is	be	AUX
ejpam-5042	269	4	parapseudo	parapseudo	NOUN
ejpam-5042	269	5	-	-	PUNCT
ejpam-5042	269	6	complemented	complement	VERB
ejpam-5042	269	7	pdl	pdl	NOUN
ejpam-5042	269	8	.	.	PUNCT
ejpam-5042	269	9	proof	proof	NOUN
ejpam-5042	269	10	.	.	PUNCT
ejpam-5042	270	1	let	let	VERB
ejpam-5042	270	2	v	v	PART
ejpam-5042	270	3	be	be	AUX
ejpam-5042	270	4	a	a	DET
ejpam-5042	270	5	relatively	relatively	ADV
ejpam-5042	270	6	complemented	complemented	ADJ
ejpam-5042	270	7	pdl	pdl	NOUN
ejpam-5042	270	8	with	with	ADP
ejpam-5042	270	9	a	a	DET
ejpam-5042	270	10	minimal	minimal	ADJ
ejpam-5042	270	11	element	element	NOUN
ejpam-5042	270	12	m1	m1	NOUN
ejpam-5042	270	13	.	.	PUNCT
ejpam-5042	271	1	for	for	ADP
ejpam-5042	271	2	any	any	DET
ejpam-5042	271	3	ρ	ρ	PROPN
ejpam-5042	271	4	∈	∈	PROPN
ejpam-5042	271	5	v	v	NOUN
ejpam-5042	271	6	,	,	PUNCT
ejpam-5042	271	7	let	let	VERB
ejpam-5042	271	8	ρ	ρ	NUM
ejpam-5042	271	9	♦	♦	PROPN
ejpam-5042	271	10	be	be	AUX
ejpam-5042	271	11	the	the	DET
ejpam-5042	271	12	complement	complement	NOUN
ejpam-5042	271	13	of	of	ADP
ejpam-5042	271	14	ρ	ρ	PROPN
ejpam-5042	271	15	∈	∈	PROPN
ejpam-5042	272	1	[	[	X
ejpam-5042	272	2	m1	m1	PROPN
ejpam-5042	272	3	∧	∧	PROPN
ejpam-5042	272	4	ρ	ρ	PROPN
ejpam-5042	272	5	,	,	PUNCT
ejpam-5042	272	6	1	1	NUM
ejpam-5042	272	7	]	]	PUNCT
ejpam-5042	272	8	.	.	PUNCT
ejpam-5042	273	1	now	now	ADV
ejpam-5042	273	2	,	,	PUNCT
ejpam-5042	273	3	we	we	PRON
ejpam-5042	273	4	prove	prove	VERB
ejpam-5042	273	5	that	that	SCONJ
ejpam-5042	273	6	♦	♦	PROPN
ejpam-5042	273	7	is	be	AUX
ejpam-5042	273	8	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5042	273	9	on	on	ADP
ejpam-5042	273	10	v	v	NUM
ejpam-5042	273	11	.	.	PUNCT
ejpam-5042	274	1	clearly	clearly	ADV
ejpam-5042	274	2	,	,	PUNCT
ejpam-5042	274	3	for	for	ADP
ejpam-5042	274	4	any	any	DET
ejpam-5042	274	5	ρ	ρ	PROPN
ejpam-5042	274	6	∈	∈	PROPN
ejpam-5042	274	7	v	v	NOUN
ejpam-5042	274	8	,	,	PUNCT
ejpam-5042	274	9	we	we	PRON
ejpam-5042	274	10	have	have	VERB
ejpam-5042	274	11	ρ∨ρ	ρ∨ρ	PROPN
ejpam-5042	274	12	♦	♦	PROPN
ejpam-5042	274	13	=	=	PROPN
ejpam-5042	274	14	1	1	X
ejpam-5042	274	15	.	.	PUNCT
ejpam-5042	275	1	let	let	VERB
ejpam-5042	275	2	ϱ	ϱ	ADP
ejpam-5042	275	3	∈	∈	PROPN
ejpam-5042	275	4	v	v	PART
ejpam-5042	275	5	be	be	AUX
ejpam-5042	275	6	such	such	ADJ
ejpam-5042	275	7	that	that	DET
ejpam-5042	275	8	ϱ∨ρ	ϱ∨ρ	NOUN
ejpam-5042	276	1	=	=	SYM
ejpam-5042	276	2	1	1	X
ejpam-5042	276	3	.	.	PUNCT
ejpam-5042	277	1	then	then	ADV
ejpam-5042	277	2	,	,	PUNCT
ejpam-5042	277	3	ϱ∨ρ	ϱ∨ρ	PROPN
ejpam-5042	277	4	♦	♦	PROPN
ejpam-5042	277	5	=	=	PUNCT
ejpam-5042	277	6	ϱ∨	ϱ∨	PROPN
ejpam-5042	277	7	(	(	PUNCT
ejpam-5042	277	8	ρ	ρ	PROPN
ejpam-5042	277	9	♦	♦	PROPN
ejpam-5042	277	10	∧ρ	∧ρ	PROPN
ejpam-5042	277	11	)	)	PUNCT
ejpam-5042	278	1	=	=	SYM
ejpam-5042	278	2	ϱ∨	ϱ∨	PROPN
ejpam-5042	278	3	(	(	PUNCT
ejpam-5042	278	4	m1∧ρ	m1∧ρ	PROPN
ejpam-5042	278	5	)	)	PUNCT
ejpam-5042	278	6	=	=	SYM
ejpam-5042	278	7	ϱ∨m1	ϱ∨m1	NUM
ejpam-5042	278	8	=	=	SYM
ejpam-5042	278	9	ϱ.	ϱ.	ADV
ejpam-5042	279	1	now	now	ADV
ejpam-5042	279	2	,	,	PUNCT
ejpam-5042	279	3	we	we	PRON
ejpam-5042	279	4	prove	prove	VERB
ejpam-5042	279	5	that	that	SCONJ
ejpam-5042	279	6	,	,	PUNCT
ejpam-5042	279	7	for	for	ADP
ejpam-5042	279	8	any	any	DET
ejpam-5042	279	9	ρ	ρ	NOUN
ejpam-5042	279	10	,	,	PUNCT
ejpam-5042	279	11	ϱ	ϱ	PROPN
ejpam-5042	279	12	∈	∈	PROPN
ejpam-5042	279	13	v	v	NOUN
ejpam-5042	279	14	,	,	PUNCT
ejpam-5042	279	15	(	(	PUNCT
ejpam-5042	279	16	ρ∧	ρ∧	PROPN
ejpam-5042	279	17	ϱ	ϱ	PROPN
ejpam-5042	279	18	)	)	PUNCT
ejpam-5042	279	19	♦	♦	PROPN
ejpam-5042	279	20	=	=	PROPN
ejpam-5042	279	21	ρ	ρ	PROPN
ejpam-5042	279	22	♦	♦	PROPN
ejpam-5042	279	23	∨	∨	NUM
ejpam-5042	279	24	ϱ	ϱ	PROPN
ejpam-5042	279	25	♦	♦	PROPN
ejpam-5042	279	26	.	.	PUNCT
ejpam-5042	280	1	now	now	ADV
ejpam-5042	280	2	,	,	PUNCT
ejpam-5042	280	3	(	(	PUNCT
ejpam-5042	280	4	ρ	ρ	PROPN
ejpam-5042	280	5	♦	♦	PROPN
ejpam-5042	280	6	∨	∨	NUM
ejpam-5042	280	7	ϱ	ϱ	PROPN
ejpam-5042	280	8	♦	♦	PROPN
ejpam-5042	280	9	)∨	)∨	PRON
ejpam-5042	280	10	(	(	PUNCT
ejpam-5042	280	11	ρ∧	ρ∧	PROPN
ejpam-5042	280	12	ϱ	ϱ	PROPN
ejpam-5042	280	13	)	)	PUNCT
ejpam-5042	280	14	=	=	SYM
ejpam-5042	280	15	(	(	PUNCT
ejpam-5042	280	16	ρ	ρ	PROPN
ejpam-5042	280	17	♦	♦	PROPN
ejpam-5042	280	18	∨	∨	NUM
ejpam-5042	280	19	ϱ	ϱ	PROPN
ejpam-5042	280	20	♦	♦	PROPN
ejpam-5042	280	21	∨	∨	NUM
ejpam-5042	280	22	ρ)∧	ρ)∧	PROPN
ejpam-5042	280	23	(	(	PUNCT
ejpam-5042	280	24	ρ	ρ	PROPN
ejpam-5042	280	25	♦	♦	PROPN
ejpam-5042	280	26	∨	∨	NUM
ejpam-5042	280	27	ϱ	ϱ	PROPN
ejpam-5042	280	28	♦	♦	PROPN
ejpam-5042	280	29	∨	∨	NUM
ejpam-5042	280	30	ϱ	ϱ	PROPN
ejpam-5042	280	31	)	)	PUNCT
ejpam-5042	280	32	=	=	SYM
ejpam-5042	280	33	(	(	PUNCT
ejpam-5042	280	34	ρ	ρ	PROPN
ejpam-5042	280	35	♦	♦	PROPN
ejpam-5042	280	36	∨	∨	PROPN
ejpam-5042	280	37	ρ	ρ	PROPN
ejpam-5042	280	38	∨	∨	NUM
ejpam-5042	280	39	ϱ	ϱ	PROPN
ejpam-5042	280	40	♦	♦	PROPN
ejpam-5042	280	41	)	)	PUNCT
ejpam-5042	280	42	∧	∧	PROPN
ejpam-5042	280	43	1	1	NUM
ejpam-5042	280	44	=	=	SYM
ejpam-5042	280	45	1	1	NUM
ejpam-5042	280	46	∧	∧	PROPN
ejpam-5042	280	47	1	1	NUM
ejpam-5042	280	48	=	=	SYM
ejpam-5042	280	49	1	1	NUM
ejpam-5042	280	50	.	.	PUNCT
ejpam-5042	281	1	then	then	ADV
ejpam-5042	281	2	,	,	PUNCT
ejpam-5042	281	3	(	(	PUNCT
ejpam-5042	281	4	ρ	ρ	PROPN
ejpam-5042	281	5	♦	♦	PROPN
ejpam-5042	281	6	∨	∨	NUM
ejpam-5042	281	7	ϱ	ϱ	PROPN
ejpam-5042	281	8	♦	♦	PROPN
ejpam-5042	281	9	)	)	PUNCT
ejpam-5042	281	10	∧	∧	PROPN
ejpam-5042	281	11	(	(	PUNCT
ejpam-5042	281	12	ρ	ρ	PROPN
ejpam-5042	281	13	∧	∧	PROPN
ejpam-5042	281	14	ϱ	ϱ	NOUN
ejpam-5042	281	15	)	)	PUNCT
ejpam-5042	281	16	=	=	SYM
ejpam-5042	281	17	(	(	PUNCT
ejpam-5042	281	18	ρ	ρ	PROPN
ejpam-5042	281	19	♦	♦	PROPN
ejpam-5042	281	20	∧	∧	PROPN
ejpam-5042	281	21	ρ	ρ	PROPN
ejpam-5042	281	22	∧	∧	PROPN
ejpam-5042	281	23	ϱ	ϱ	PROPN
ejpam-5042	281	24	)	)	PUNCT
ejpam-5042	281	25	∨	∨	NOUN
ejpam-5042	281	26	(	(	PUNCT
ejpam-5042	281	27	ϱ	ϱ	PROPN
ejpam-5042	281	28	♦	♦	PROPN
ejpam-5042	281	29	∧	∧	PROPN
ejpam-5042	281	30	ρ	ρ	PROPN
ejpam-5042	281	31	∧	∧	PROPN
ejpam-5042	281	32	ϱ	ϱ	NOUN
ejpam-5042	281	33	)	)	PUNCT
ejpam-5042	281	34	=	=	SYM
ejpam-5042	281	35	(	(	PUNCT
ejpam-5042	281	36	m1∧ρ∧ϱ)∨(ϱ	m1∧ρ∧ϱ)∨(ϱ	PROPN
ejpam-5042	281	37	♦	♦	PROPN
ejpam-5042	281	38	∧ϱ∧ρ	∧ϱ∧ρ	NOUN
ejpam-5042	281	39	)	)	PUNCT
ejpam-5042	281	40	=	=	SYM
ejpam-5042	281	41	(	(	PUNCT
ejpam-5042	281	42	m1∧ρ∧ϱ)∨(m1∧ϱ∧ρ	m1∧ρ∧ϱ)∨(m1∧ϱ∧ρ	NOUN
ejpam-5042	281	43	)	)	PUNCT
ejpam-5042	281	44	=	=	SYM
ejpam-5042	281	45	(	(	PUNCT
ejpam-5042	281	46	m1∧ρ∧ϱ)∨(m1∧ρ∧ϱ	m1∧ρ∧ϱ)∨(m1∧ρ∧ϱ	NOUN
ejpam-5042	281	47	)	)	PUNCT
ejpam-5042	281	48	=	=	SYM
ejpam-5042	281	49	(	(	PUNCT
ejpam-5042	281	50	m1∧ρ∧ϱ	m1∧ρ∧ϱ	NOUN
ejpam-5042	281	51	)	)	PUNCT
ejpam-5042	281	52	.	.	PUNCT
ejpam-5042	282	1	4	4	X
ejpam-5042	282	2	.	.	X
ejpam-5042	282	3	properties	property	NOUN
ejpam-5042	282	4	we	we	PRON
ejpam-5042	282	5	present	present	VERB
ejpam-5042	282	6	here	here	ADV
ejpam-5042	282	7	some	some	DET
ejpam-5042	282	8	elementary	elementary	ADJ
ejpam-5042	282	9	properties	property	NOUN
ejpam-5042	282	10	of	of	ADP
ejpam-5042	282	11	parapseudo	parapseudo	NOUN
ejpam-5042	282	12	-	-	PUNCT
ejpam-5042	282	13	complemented	complemented	ADJ
ejpam-5042	282	14	pdl	pdl	NOUN
ejpam-5042	282	15	and	and	CCONJ
ejpam-5042	282	16	further	far	ADV
ejpam-5042	282	17	prove	prove	VERB
ejpam-5042	282	18	some	some	DET
ejpam-5042	282	19	essential	essential	ADJ
ejpam-5042	282	20	conditions	condition	NOUN
ejpam-5042	282	21	for	for	ADP
ejpam-5042	282	22	a	a	DET
ejpam-5042	282	23	pdl	pdl	NOUN
ejpam-5042	282	24	with	with	ADP
ejpam-5042	282	25	a	a	DET
ejpam-5042	282	26	minimal	minimal	ADJ
ejpam-5042	282	27	element	element	NOUN
ejpam-5042	282	28	to	to	PART
ejpam-5042	282	29	be	be	AUX
ejpam-5042	282	30	parapseudocomplemented	parapseudocomplemente	VERB
ejpam-5042	282	31	.	.	PUNCT
ejpam-5042	283	1	the	the	DET
ejpam-5042	283	2	following	follow	VERB
ejpam-5042	283	3	lemma	lemma	PROPN
ejpam-5042	283	4	can	can	AUX
ejpam-5042	283	5	be	be	AUX
ejpam-5042	283	6	proved	prove	VERB
ejpam-5042	283	7	easily	easily	ADV
ejpam-5042	283	8	.	.	PUNCT
ejpam-5042	284	1	lemma	lemma	PROPN
ejpam-5042	284	2	5	5	X
ejpam-5042	284	3	.	.	PUNCT
ejpam-5042	285	1	let	let	VERB
ejpam-5042	285	2	v	v	PART
ejpam-5042	285	3	be	be	AUX
ejpam-5042	285	4	a	a	DET
ejpam-5042	285	5	parapseudo	parapseudo	NOUN
ejpam-5042	285	6	-	-	PUNCT
ejpam-5042	285	7	complemented	complement	VERB
ejpam-5042	285	8	pdl	pdl	NOUN
ejpam-5042	285	9	.	.	PUNCT
ejpam-5042	286	1	then	then	ADV
ejpam-5042	286	2	,	,	PUNCT
ejpam-5042	286	3	for	for	ADP
ejpam-5042	286	4	any	any	DET
ejpam-5042	286	5	ρ	ρ	NOUN
ejpam-5042	286	6	,	,	PUNCT
ejpam-5042	286	7	ϱ	ϱ	PROPN
ejpam-5042	286	8	∈	∈	PROPN
ejpam-5042	286	9	v	v	NOUN
ejpam-5042	286	10	,	,	PUNCT
ejpam-5042	286	11	we	we	PRON
ejpam-5042	286	12	have	have	VERB
ejpam-5042	286	13	the	the	DET
ejpam-5042	286	14	following	following	NOUN
ejpam-5042	286	15	:	:	PUNCT
ejpam-5042	286	16	(	(	PUNCT
ejpam-5042	286	17	1	1	NUM
ejpam-5042	286	18	)	)	PUNCT
ejpam-5042	286	19	.	.	PUNCT
ejpam-5042	287	1	1	1	NUM
ejpam-5042	287	2	♦	♦	PROPN
ejpam-5042	287	3	is	be	AUX
ejpam-5042	287	4	a	a	DET
ejpam-5042	287	5	minimal	minimal	ADJ
ejpam-5042	287	6	element	element	NOUN
ejpam-5042	287	7	.	.	PUNCT
ejpam-5042	288	1	(	(	PUNCT
ejpam-5042	288	2	2	2	NUM
ejpam-5042	288	3	)	)	PUNCT
ejpam-5042	288	4	.	.	PUNCT
ejpam-5042	289	1	if	if	SCONJ
ejpam-5042	289	2	ρ	ρ	PROPN
ejpam-5042	289	3	is	be	AUX
ejpam-5042	289	4	a	a	DET
ejpam-5042	289	5	minimal	minimal	ADJ
ejpam-5042	289	6	element	element	NOUN
ejpam-5042	289	7	,	,	PUNCT
ejpam-5042	289	8	then	then	ADV
ejpam-5042	289	9	ρ	ρ	PROPN
ejpam-5042	289	10	♦	♦	PROPN
ejpam-5042	289	11	=	=	PROPN
ejpam-5042	289	12	1	1	PROPN
ejpam-5042	289	13	.	.	PUNCT
ejpam-5042	290	1	(	(	PUNCT
ejpam-5042	290	2	3	3	NUM
ejpam-5042	290	3	)	)	PUNCT
ejpam-5042	290	4	.	.	PUNCT
ejpam-5042	291	1	1	1	NUM
ejpam-5042	291	2	♦	♦	PROPN
ejpam-5042	291	3	♦	♦	PROPN
ejpam-5042	291	4	=	=	PROPN
ejpam-5042	291	5	1	1	PROPN
ejpam-5042	291	6	.	.	PUNCT
ejpam-5042	291	7	(	(	PUNCT
ejpam-5042	291	8	4	4	NUM
ejpam-5042	291	9	)	)	PUNCT
ejpam-5042	291	10	.	.	PUNCT
ejpam-5042	292	1	ρ	ρ	PROPN
ejpam-5042	292	2	♦	♦	PROPN
ejpam-5042	292	3	∨	∨	PROPN
ejpam-5042	292	4	ρ	ρ	PROPN
ejpam-5042	292	5	=	=	SYM
ejpam-5042	292	6	1	1	NUM
ejpam-5042	292	7	.	.	PUNCT
ejpam-5042	292	8	(	(	PUNCT
ejpam-5042	292	9	5	5	NUM
ejpam-5042	292	10	)	)	PUNCT
ejpam-5042	292	11	.	.	PUNCT
ejpam-5042	293	1	ρ	ρ	PROPN
ejpam-5042	293	2	∨	∨	NUM
ejpam-5042	293	3	ρ	ρ	PROPN
ejpam-5042	293	4	♦	♦	PROPN
ejpam-5042	293	5	♦	♦	PROPN
ejpam-5042	293	6	=	=	PROPN
ejpam-5042	293	7	ρ	ρ	PROPN
ejpam-5042	293	8	.	.	PUNCT
ejpam-5042	293	9	(	(	PUNCT
ejpam-5042	293	10	6	6	NUM
ejpam-5042	293	11	)	)	PUNCT
ejpam-5042	293	12	.	.	PUNCT
ejpam-5042	294	1	ρ	ρ	PROPN
ejpam-5042	294	2	♦	♦	PROPN
ejpam-5042	294	3	=	=	PROPN
ejpam-5042	294	4	ρ	ρ	PROPN
ejpam-5042	294	5	♦	♦	PROPN
ejpam-5042	294	6	♦	♦	PROPN
ejpam-5042	294	7	♦	♦	PROPN
ejpam-5042	294	8	.	.	PUNCT
ejpam-5042	295	1	(	(	PUNCT
ejpam-5042	295	2	7	7	NUM
ejpam-5042	295	3	)	)	PUNCT
ejpam-5042	295	4	.	.	PUNCT
ejpam-5042	296	1	ρ	ρ	PROPN
ejpam-5042	296	2	♦	♦	PROPN
ejpam-5042	296	3	=	=	PROPN
ejpam-5042	296	4	1	1	NUM
ejpam-5042	296	5	⇔	⇔	PROPN
ejpam-5042	296	6	ρ	ρ	PROPN
ejpam-5042	296	7	♦	♦	PROPN
ejpam-5042	296	8	♦	♦	PROPN
ejpam-5042	296	9	is	be	AUX
ejpam-5042	296	10	minimal	minimal	ADJ
ejpam-5042	296	11	element	element	NOUN
ejpam-5042	296	12	.	.	PUNCT
ejpam-5042	297	1	(	(	PUNCT
ejpam-5042	297	2	8)	8)	NUM
ejpam-5042	297	3	.	.	NOUN
ejpam-5042	297	4	1	1	NUM
ejpam-5042	297	5	♦	♦	PROPN
ejpam-5042	297	6	≤	≤	PROPN
ejpam-5042	297	7	ρ	ρ	PROPN
ejpam-5042	297	8	♦	♦	PROPN
ejpam-5042	297	9	.	.	PUNCT
ejpam-5042	298	1	(	(	PUNCT
ejpam-5042	298	2	9	9	NUM
ejpam-5042	298	3	)	)	PUNCT
ejpam-5042	298	4	.	.	PUNCT
ejpam-5042	299	1	ρ	ρ	PROPN
ejpam-5042	299	2	♦	♦	PROPN
ejpam-5042	299	3	∨	∨	NUM
ejpam-5042	299	4	ϱ	ϱ	PROPN
ejpam-5042	299	5	♦	♦	PROPN
ejpam-5042	299	6	=	=	PUNCT
ejpam-5042	299	7	ϱ	ϱ	PROPN
ejpam-5042	299	8	♦	♦	PROPN
ejpam-5042	299	9	∨	∨	PROPN
ejpam-5042	299	10	ρ	ρ	PROPN
ejpam-5042	299	11	♦	♦	PROPN
ejpam-5042	299	12	.	.	PUNCT
ejpam-5042	300	1	(	(	PUNCT
ejpam-5042	300	2	10	10	NUM
ejpam-5042	300	3	)	)	PUNCT
ejpam-5042	300	4	.	.	PUNCT
ejpam-5042	301	1	ρ	ρ	PROPN
ejpam-5042	301	2	≤	≤	NUM
ejpam-5042	301	3	ϱ	ϱ	ADP
ejpam-5042	301	4	⇒	⇒	NOUN
ejpam-5042	301	5	ϱ	ϱ	PROPN
ejpam-5042	301	6	♦	♦	PROPN
ejpam-5042	301	7	≤	≤	PROPN
ejpam-5042	301	8	ρ	ρ	PROPN
ejpam-5042	301	9	♦	♦	PROPN
ejpam-5042	301	10	.	.	PUNCT
ejpam-5042	302	1	(	(	PUNCT
ejpam-5042	302	2	11	11	NUM
ejpam-5042	302	3	)	)	PUNCT
ejpam-5042	302	4	.	.	PUNCT
ejpam-5042	303	1	(	(	PUNCT
ejpam-5042	303	2	ρ	ρ	PROPN
ejpam-5042	303	3	∨	∨	NUM
ejpam-5042	303	4	ϱ	ϱ	PROPN
ejpam-5042	303	5	)	)	PUNCT
ejpam-5042	303	6	♦	♦	PROPN
ejpam-5042	303	7	≤	≤	PROPN
ejpam-5042	303	8	ϱ	ϱ	PROPN
ejpam-5042	303	9	♦	♦	PROPN
ejpam-5042	303	10	,	,	PUNCT
ejpam-5042	303	11	(	(	PUNCT
ejpam-5042	303	12	ρ	ρ	PROPN
ejpam-5042	303	13	∨	∨	NUM
ejpam-5042	303	14	ϱ	ϱ	PROPN
ejpam-5042	303	15	)	)	PUNCT
ejpam-5042	303	16	♦	♦	PROPN
ejpam-5042	303	17	≤	≤	PROPN
ejpam-5042	303	18	ρ	ρ	PROPN
ejpam-5042	303	19	♦	♦	PROPN
ejpam-5042	303	20	.	.	PUNCT
ejpam-5042	304	1	(	(	PUNCT
ejpam-5042	304	2	12	12	NUM
ejpam-5042	304	3	)	)	PUNCT
ejpam-5042	304	4	.	.	PUNCT
ejpam-5042	305	1	ρ	ρ	PROPN
ejpam-5042	305	2	♦	♦	PROPN
ejpam-5042	305	3	≤	≤	PROPN
ejpam-5042	305	4	ϱ	ϱ	PROPN
ejpam-5042	305	5	♦	♦	PROPN
ejpam-5042	305	6	⇔	⇔	PROPN
ejpam-5042	305	7	ϱ	ϱ	PROPN
ejpam-5042	305	8	♦	♦	PROPN
ejpam-5042	305	9	♦	♦	PROPN
ejpam-5042	305	10	≤	≤	PROPN
ejpam-5042	305	11	ρ	ρ	PROPN
ejpam-5042	305	12	♦	♦	PROPN
ejpam-5042	305	13	♦	♦	PROPN
ejpam-5042	305	14	.	.	PUNCT
ejpam-5042	306	1	(	(	PUNCT
ejpam-5042	306	2	13	13	NUM
ejpam-5042	306	3	)	)	PUNCT
ejpam-5042	306	4	.	.	PUNCT
ejpam-5042	307	1	ρ	ρ	PROPN
ejpam-5042	307	2	=	=	SYM
ejpam-5042	307	3	1	1	NUM
ejpam-5042	307	4	⇔	⇔	PROPN
ejpam-5042	307	5	ρ	ρ	PROPN
ejpam-5042	307	6	♦	♦	PROPN
ejpam-5042	307	7	♦	♦	PROPN
ejpam-5042	307	8	=	=	PROPN
ejpam-5042	308	1	1	1	X
ejpam-5042	308	2	.	.	PUNCT
ejpam-5042	309	1	lemma	lemma	PROPN
ejpam-5042	309	2	6	6	NUM
ejpam-5042	309	3	.	.	PUNCT
ejpam-5042	310	1	let	let	VERB
ejpam-5042	310	2	v	v	PART
ejpam-5042	310	3	be	be	AUX
ejpam-5042	310	4	a	a	DET
ejpam-5042	310	5	pdl	pdl	NOUN
ejpam-5042	310	6	with	with	ADP
ejpam-5042	310	7	two	two	NUM
ejpam-5042	310	8	minimal	minimal	ADJ
ejpam-5042	310	9	elements	element	NOUN
ejpam-5042	310	10	m1	m1	PROPN
ejpam-5042	310	11	and	and	CCONJ
ejpam-5042	310	12	m2	m2	PROPN
ejpam-5042	310	13	.	.	PUNCT
ejpam-5042	311	1	then	then	ADV
ejpam-5042	311	2	the	the	DET
ejpam-5042	311	3	bounded	bounded	ADJ
ejpam-5042	311	4	distributive	distributive	ADJ
ejpam-5042	311	5	lattices	lattice	NOUN
ejpam-5042	311	6	[	[	X
ejpam-5042	311	7	m1	m1	NOUN
ejpam-5042	311	8	,	,	PUNCT
ejpam-5042	311	9	1	1	NUM
ejpam-5042	311	10	]	]	PUNCT
ejpam-5042	311	11	and	and	CCONJ
ejpam-5042	311	12	[	[	X
ejpam-5042	311	13	m2	m2	PROPN
ejpam-5042	311	14	,	,	PUNCT
ejpam-5042	311	15	1	1	NUM
ejpam-5042	311	16	]	]	PUNCT
ejpam-5042	311	17	are	be	AUX
ejpam-5042	311	18	isomorphic	isomorphic	ADJ
ejpam-5042	311	19	.	.	PUNCT
ejpam-5042	312	1	proof	proof	NOUN
ejpam-5042	312	2	.	.	PUNCT
ejpam-5042	313	1	let	let	VERB
ejpam-5042	313	2	v	v	PART
ejpam-5042	313	3	be	be	AUX
ejpam-5042	313	4	a	a	DET
ejpam-5042	313	5	pdl	pdl	NOUN
ejpam-5042	313	6	with	with	ADP
ejpam-5042	313	7	two	two	NUM
ejpam-5042	313	8	minimal	minimal	ADJ
ejpam-5042	313	9	elements	element	NOUN
ejpam-5042	313	10	,	,	PUNCT
ejpam-5042	313	11	m1	m1	PROPN
ejpam-5042	313	12	and	and	CCONJ
ejpam-5042	313	13	m2	m2	PROPN
ejpam-5042	313	14	.	.	PROPN
ejpam-5042	314	1	define	define	VERB
ejpam-5042	314	2	f	f	NOUN
ejpam-5042	315	1	:	:	PUNCT
ejpam-5042	315	2	[	[	X
ejpam-5042	315	3	m1	m1	NOUN
ejpam-5042	315	4	,	,	PUNCT
ejpam-5042	315	5	1	1	NUM
ejpam-5042	315	6	]	]	PUNCT
ejpam-5042	315	7	→	→	SYM
ejpam-5042	315	8	[	[	X
ejpam-5042	315	9	m2	m2	PROPN
ejpam-5042	315	10	,	,	PUNCT
ejpam-5042	315	11	1	1	NUM
ejpam-5042	315	12	]	]	PUNCT
ejpam-5042	315	13	by	by	ADP
ejpam-5042	315	14	f(ρ	f(ρ	NOUN
ejpam-5042	315	15	)	)	PUNCT
ejpam-5042	315	16	=	=	SYM
ejpam-5042	315	17	m2	m2	PROPN
ejpam-5042	315	18	∨	∨	PROPN
ejpam-5042	315	19	ρ	ρ	PROPN
ejpam-5042	315	20	.	.	PUNCT
ejpam-5042	316	1	now	now	ADV
ejpam-5042	316	2	,	,	PUNCT
ejpam-5042	316	3	we	we	PRON
ejpam-5042	316	4	prove	prove	VERB
ejpam-5042	316	5	that	that	SCONJ
ejpam-5042	316	6	f	f	PROPN
ejpam-5042	316	7	is	be	AUX
ejpam-5042	316	8	an	an	DET
ejpam-5042	316	9	isomorphism	isomorphism	NOUN
ejpam-5042	316	10	.	.	PUNCT
ejpam-5042	317	1	clearly	clearly	ADV
ejpam-5042	317	2	f	f	PROPN
ejpam-5042	317	3	is	be	AUX
ejpam-5042	317	4	well	well	ADV
ejpam-5042	317	5	defined	define	VERB
ejpam-5042	317	6	.	.	PUNCT
ejpam-5042	318	1	let	let	VERB
ejpam-5042	318	2	ρ	ρ	NOUN
ejpam-5042	318	3	,	,	PUNCT
ejpam-5042	318	4	ϱ	ϱ	PROPN
ejpam-5042	318	5	∈	∈	PROPN
ejpam-5042	319	1	[	[	X
ejpam-5042	319	2	m1	m1	NOUN
ejpam-5042	319	3	,	,	PUNCT
ejpam-5042	319	4	1	1	NUM
ejpam-5042	319	5	]	]	PUNCT
ejpam-5042	319	6	and	and	CCONJ
ejpam-5042	319	7	f(ρ	f(ρ	NOUN
ejpam-5042	319	8	)	)	PUNCT
ejpam-5042	319	9	=	=	NUM
ejpam-5042	319	10	f(ϱ	f(ϱ	NOUN
ejpam-5042	319	11	)	)	PUNCT
ejpam-5042	319	12	.	.	PUNCT
ejpam-5042	320	1	then	then	ADV
ejpam-5042	320	2	m2	m2	PROPN
ejpam-5042	320	3	∨	∨	PROPN
ejpam-5042	320	4	ρ	ρ	PROPN
ejpam-5042	320	5	=	=	PROPN
ejpam-5042	320	6	m2	m2	PROPN
ejpam-5042	320	7	∨	∨	PROPN
ejpam-5042	320	8	ϱ.	ϱ.	NOUN
ejpam-5042	320	9	now	now	ADV
ejpam-5042	320	10	ρ	ρ	PROPN
ejpam-5042	320	11	=	=	SYM
ejpam-5042	320	12	m1	m1	PROPN
ejpam-5042	320	13	∨	∨	NUM
ejpam-5042	320	14	ρ	ρ	PROPN
ejpam-5042	320	15	=	=	PROPN
ejpam-5042	320	16	m1	m1	PROPN
ejpam-5042	320	17	∨	∨	NUM
ejpam-5042	320	18	m2	m2	PROPN
ejpam-5042	320	19	∨	∨	PROPN
ejpam-5042	320	20	ρ	ρ	PROPN
ejpam-5042	320	21	=	=	PROPN
ejpam-5042	320	22	m1	m1	PROPN
ejpam-5042	320	23	∨	∨	NUM
ejpam-5042	320	24	m2	m2	PROPN
ejpam-5042	320	25	∨	∨	NUM
ejpam-5042	320	26	ϱ	ϱ	PROPN
ejpam-5042	320	27	=	=	PROPN
ejpam-5042	320	28	m1	m1	PROPN
ejpam-5042	320	29	∨	∨	NOUN
ejpam-5042	320	30	ϱ	ϱ	PROPN
ejpam-5042	320	31	=	=	X
ejpam-5042	320	32	ϱ.	ϱ.	NOUN
ejpam-5042	320	33	therefore	therefore	ADV
ejpam-5042	320	34	,	,	PUNCT
ejpam-5042	320	35	f	f	PROPN
ejpam-5042	320	36	is	be	AUX
ejpam-5042	320	37	one	one	NUM
ejpam-5042	320	38	-	-	PUNCT
ejpam-5042	320	39	one	one	NUM
ejpam-5042	320	40	.	.	PUNCT
ejpam-5042	321	1	let	let	VERB
ejpam-5042	321	2	t	t	PROPN
ejpam-5042	321	3	∈	∈	PROPN
ejpam-5042	322	1	[	[	X
ejpam-5042	322	2	m2	m2	PROPN
ejpam-5042	322	3	,	,	PUNCT
ejpam-5042	322	4	1	1	NUM
ejpam-5042	322	5	]	]	PUNCT
ejpam-5042	322	6	.	.	PUNCT
ejpam-5042	323	1	then	then	ADV
ejpam-5042	323	2	m1	m1	PROPN
ejpam-5042	323	3	∨	∨	NUM
ejpam-5042	323	4	t	t	PROPN
ejpam-5042	323	5	∈	∈	PROPN
ejpam-5042	324	1	[	[	X
ejpam-5042	324	2	m1	m1	NOUN
ejpam-5042	324	3	,	,	PUNCT
ejpam-5042	324	4	1	1	NUM
ejpam-5042	324	5	]	]	PUNCT
ejpam-5042	324	6	and	and	CCONJ
ejpam-5042	324	7	f(m1	f(m1	NOUN
ejpam-5042	324	8	∨	∨	NUM
ejpam-5042	324	9	t	t	PROPN
ejpam-5042	324	10	)	)	PUNCT
ejpam-5042	324	11	=	=	SYM
ejpam-5042	324	12	m2	m2	PROPN
ejpam-5042	324	13	∨	∨	PROPN
ejpam-5042	324	14	m1	m1	PROPN
ejpam-5042	324	15	∨	∨	NUM
ejpam-5042	324	16	t	t	PROPN
ejpam-5042	324	17	=	=	SYM
ejpam-5042	324	18	m2	m2	PROPN
ejpam-5042	324	19	∨	∨	NUM
ejpam-5042	324	20	t	t	PROPN
ejpam-5042	324	21	=	=	PUNCT
ejpam-5042	324	22	t.	t.	NOUN
ejpam-5042	324	23	hence	hence	ADV
ejpam-5042	324	24	,	,	PUNCT
ejpam-5042	324	25	f	f	PROPN
ejpam-5042	324	26	is	be	AUX
ejpam-5042	324	27	onto	onto	ADP
ejpam-5042	324	28	.	.	PUNCT
ejpam-5042	325	1	let	let	VERB
ejpam-5042	325	2	ρ	ρ	NOUN
ejpam-5042	325	3	,	,	PUNCT
ejpam-5042	325	4	ϱ	ϱ	PROPN
ejpam-5042	325	5	∈	∈	PROPN
ejpam-5042	325	6	[	[	X
ejpam-5042	325	7	m1	m1	NOUN
ejpam-5042	325	8	,	,	PUNCT
ejpam-5042	325	9	1	1	NUM
ejpam-5042	325	10	]	]	PUNCT
ejpam-5042	325	11	.	.	PUNCT
ejpam-5042	326	1	then	then	ADV
ejpam-5042	326	2	f(ρ	f(ρ	NOUN
ejpam-5042	326	3	∨	∨	NUM
ejpam-5042	326	4	ϱ	ϱ	ADP
ejpam-5042	326	5	)	)	PUNCT
ejpam-5042	326	6	=	=	SYM
ejpam-5042	326	7	m2	m2	PROPN
ejpam-5042	326	8	∨	∨	PROPN
ejpam-5042	326	9	ρ	ρ	PROPN
ejpam-5042	326	10	∨	∨	NUM
ejpam-5042	326	11	ϱ	ϱ	X
ejpam-5042	326	12	=	=	PUNCT
ejpam-5042	326	13	(	(	PUNCT
ejpam-5042	326	14	m2	m2	PROPN
ejpam-5042	326	15	∨	∨	PROPN
ejpam-5042	326	16	ρ	ρ	PROPN
ejpam-5042	326	17	)	)	PUNCT
ejpam-5042	326	18	∨	∨	PROPN
ejpam-5042	326	19	(	(	PUNCT
ejpam-5042	326	20	m2	m2	PROPN
ejpam-5042	326	21	∨	∨	NUM
ejpam-5042	326	22	ϱ	ϱ	PROPN
ejpam-5042	326	23	)	)	PUNCT
ejpam-5042	326	24	=	=	SYM
ejpam-5042	326	25	f(ρ	f(ρ	NOUN
ejpam-5042	326	26	)	)	PUNCT
ejpam-5042	326	27	∨	∨	NUM
ejpam-5042	326	28	f(ϱ	f(ϱ	NOUN
ejpam-5042	326	29	)	)	PUNCT
ejpam-5042	326	30	and	and	CCONJ
ejpam-5042	326	31	f(ρ	f(ρ	NOUN
ejpam-5042	326	32	∧	∧	PROPN
ejpam-5042	326	33	ϱ	ϱ	NOUN
ejpam-5042	326	34	)	)	PUNCT
ejpam-5042	326	35	=	=	SYM
ejpam-5042	326	36	m2	m2	PROPN
ejpam-5042	326	37	∨	∨	PROPN
ejpam-5042	326	38	(	(	PUNCT
ejpam-5042	326	39	ρ	ρ	PROPN
ejpam-5042	326	40	∧	∧	PROPN
ejpam-5042	326	41	ϱ	ϱ	NOUN
ejpam-5042	326	42	)	)	PUNCT
ejpam-5042	326	43	=	=	SYM
ejpam-5042	326	44	(	(	PUNCT
ejpam-5042	326	45	m2	m2	PROPN
ejpam-5042	326	46	∨	∨	PROPN
ejpam-5042	326	47	ρ	ρ	PROPN
ejpam-5042	326	48	)	)	PUNCT
ejpam-5042	326	49	∧	∧	PROPN
ejpam-5042	326	50	(	(	PUNCT
ejpam-5042	326	51	m2	m2	PROPN
ejpam-5042	326	52	∨	∨	NUM
ejpam-5042	326	53	ϱ	ϱ	PROPN
ejpam-5042	326	54	)	)	PUNCT
ejpam-5042	326	55	=	=	SYM
ejpam-5042	326	56	f(ρ	f(ρ	NOUN
ejpam-5042	326	57	)	)	PUNCT
ejpam-5042	326	58	∧	∧	NOUN
ejpam-5042	326	59	f(ϱ	f(ϱ	NOUN
ejpam-5042	326	60	)	)	PUNCT
ejpam-5042	326	61	,	,	PUNCT
ejpam-5042	326	62	which	which	PRON
ejpam-5042	326	63	implies	imply	VERB
ejpam-5042	326	64	f	f	PROPN
ejpam-5042	326	65	satisfies	satisfy	VERB
ejpam-5042	326	66	homomorphism	homomorphism	PROPN
ejpam-5042	326	67	property	property	NOUN
ejpam-5042	326	68	.	.	PUNCT
ejpam-5042	327	1	also	also	ADV
ejpam-5042	327	2	,	,	PUNCT
ejpam-5042	327	3	f(1	f(1	PROPN
ejpam-5042	327	4	)	)	PUNCT
ejpam-5042	327	5	=	=	SYM
ejpam-5042	327	6	m2	m2	PROPN
ejpam-5042	327	7	∨	∨	NUM
ejpam-5042	327	8	1	1	NUM
ejpam-5042	327	9	=	=	SYM
ejpam-5042	327	10	1	1	NUM
ejpam-5042	327	11	.	.	PUNCT
ejpam-5042	328	1	therefore	therefore	ADV
ejpam-5042	328	2	,	,	PUNCT
ejpam-5042	328	3	f	f	PROPN
ejpam-5042	328	4	is	be	AUX
ejpam-5042	328	5	an	an	DET
ejpam-5042	328	6	isomorphism	isomorphism	NOUN
ejpam-5042	328	7	.	.	PUNCT
ejpam-5042	329	1	r.	r.	PROPN
ejpam-5042	329	2	shukla	shukla	PROPN
ejpam-5042	329	3	et	et	PROPN
ejpam-5042	329	4	al	al	PROPN
ejpam-5042	329	5	.	.	PUNCT
ejpam-5042	329	6	/	/	SYM
ejpam-5042	329	7	eur	eur	PROPN
ejpam-5042	329	8	.	.	PUNCT
ejpam-5042	330	1	j.	j.	PROPN
ejpam-5042	330	2	pure	pure	PROPN
ejpam-5042	330	3	appl	appl	PROPN
ejpam-5042	330	4	.	.	PROPN
ejpam-5042	330	5	math	math	PROPN
ejpam-5042	330	6	,	,	PUNCT
ejpam-5042	330	7	17	17	NUM
ejpam-5042	330	8	(	(	PUNCT
ejpam-5042	330	9	2	2	NUM
ejpam-5042	330	10	)	)	PUNCT
ejpam-5042	330	11	(	(	PUNCT
ejpam-5042	330	12	2024	2024	NUM
ejpam-5042	330	13	)	)	PUNCT
ejpam-5042	330	14	,	,	PUNCT
ejpam-5042	330	15	1129	1129	NUM
ejpam-5042	330	16	-	-	SYM
ejpam-5042	330	17	1145	1145	NUM
ejpam-5042	330	18	1138	1138	NUM
ejpam-5042	330	19	theorem	theorem	VERB
ejpam-5042	330	20	7	7	NUM
ejpam-5042	330	21	.	.	PUNCT
ejpam-5042	331	1	let	let	VERB
ejpam-5042	331	2	v	v	PART
ejpam-5042	331	3	be	be	AUX
ejpam-5042	331	4	a	a	DET
ejpam-5042	331	5	pdl	pdl	NOUN
ejpam-5042	331	6	with	with	ADP
ejpam-5042	331	7	a	a	DET
ejpam-5042	331	8	minimal	minimal	ADJ
ejpam-5042	331	9	element	element	NOUN
ejpam-5042	331	10	,	,	PUNCT
ejpam-5042	331	11	m.	m.	NOUN
ejpam-5042	331	12	then	then	ADV
ejpam-5042	331	13	the	the	DET
ejpam-5042	331	14	following	following	NOUN
ejpam-5042	331	15	are	be	AUX
ejpam-5042	331	16	equivalent	equivalent	ADJ
ejpam-5042	331	17	:	:	PUNCT
ejpam-5042	331	18	(	(	PUNCT
ejpam-5042	331	19	1	1	NUM
ejpam-5042	331	20	)	)	PUNCT
ejpam-5042	331	21	.	.	PUNCT
ejpam-5042	332	1	v	v	NOUN
ejpam-5042	332	2	is	be	AUX
ejpam-5042	332	3	a	a	DET
ejpam-5042	332	4	parapseudo	parapseudo	NOUN
ejpam-5042	332	5	-	-	PUNCT
ejpam-5042	332	6	complemented	complement	VERB
ejpam-5042	332	7	pdl	pdl	NOUN
ejpam-5042	332	8	.	.	PUNCT
ejpam-5042	333	1	(	(	PUNCT
ejpam-5042	333	2	2	2	NUM
ejpam-5042	333	3	)	)	PUNCT
ejpam-5042	333	4	.	.	PUNCT
ejpam-5042	334	1	[	[	X
ejpam-5042	334	2	m	m	X
ejpam-5042	334	3	,	,	PUNCT
ejpam-5042	334	4	1	1	NUM
ejpam-5042	334	5	]	]	PUNCT
ejpam-5042	334	6	is	be	AUX
ejpam-5042	334	7	a	a	DET
ejpam-5042	334	8	dual	dual	ADJ
ejpam-5042	334	9	pseudo	pseudo	NOUN
ejpam-5042	334	10	-	-	ADJ
ejpam-5042	334	11	complemented	complement	VERB
ejpam-5042	334	12	lattice	lattice	NOUN
ejpam-5042	334	13	.	.	PUNCT
ejpam-5042	335	1	(	(	PUNCT
ejpam-5042	335	2	3	3	NUM
ejpam-5042	335	3	)	)	PUNCT
ejpam-5042	335	4	.	.	PUNCT
ejpam-5042	336	1	[	[	X
ejpam-5042	336	2	m1	m1	NOUN
ejpam-5042	336	3	,	,	PUNCT
ejpam-5042	336	4	1	1	NUM
ejpam-5042	336	5	]	]	PUNCT
ejpam-5042	336	6	is	be	AUX
ejpam-5042	336	7	a	a	DET
ejpam-5042	336	8	dual	dual	ADJ
ejpam-5042	336	9	pseudo	pseudo	NOUN
ejpam-5042	336	10	-	-	ADJ
ejpam-5042	336	11	complemented	complemented	ADJ
ejpam-5042	336	12	lattice	lattice	NOUN
ejpam-5042	336	13	for	for	ADP
ejpam-5042	336	14	all	all	DET
ejpam-5042	336	15	minimal	minimal	ADJ
ejpam-5042	336	16	elements	element	NOUN
ejpam-5042	336	17	m1	m1	NOUN
ejpam-5042	336	18	in	in	ADP
ejpam-5042	336	19	v	v	NUM
ejpam-5042	336	20	.	.	PUNCT
ejpam-5042	337	1	proof	proof	NOUN
ejpam-5042	337	2	.	.	PUNCT
ejpam-5042	338	1	(	(	PUNCT
ejpam-5042	338	2	1	1	X
ejpam-5042	338	3	)	)	PUNCT
ejpam-5042	338	4	⇒	⇒	NOUN
ejpam-5042	338	5	(	(	PUNCT
ejpam-5042	338	6	2	2	NUM
ejpam-5042	338	7	)	)	PUNCT
ejpam-5042	338	8	:	:	PUNCT
ejpam-5042	338	9	let	let	VERB
ejpam-5042	338	10	♢	♢	PROPN
ejpam-5042	338	11	be	be	AUX
ejpam-5042	338	12	a	a	DET
ejpam-5042	338	13	parapseudo	parapseudo	NOUN
ejpam-5042	338	14	-	-	NOUN
ejpam-5042	338	15	complementation	complementation	NOUN
ejpam-5042	338	16	on	on	ADP
ejpam-5042	338	17	v	v	NUM
ejpam-5042	338	18	.	.	PUNCT
ejpam-5042	339	1	we	we	PRON
ejpam-5042	339	2	know	know	VERB
ejpam-5042	339	3	that	that	SCONJ
ejpam-5042	339	4	[	[	X
ejpam-5042	339	5	m	m	X
ejpam-5042	339	6	,	,	PUNCT
ejpam-5042	339	7	1	1	NUM
ejpam-5042	339	8	]	]	PUNCT
ejpam-5042	339	9	is	be	AUX
ejpam-5042	339	10	a	a	DET
ejpam-5042	339	11	bounded	bounded	ADJ
ejpam-5042	339	12	distributive	distributive	ADJ
ejpam-5042	339	13	lattice	lattice	NOUN
ejpam-5042	339	14	.	.	PUNCT
ejpam-5042	340	1	now	now	ADV
ejpam-5042	340	2	define	define	VERB
ejpam-5042	340	3	♦	♦	PROPN
ejpam-5042	340	4	on	on	ADP
ejpam-5042	340	5	[	[	X
ejpam-5042	340	6	m	m	NOUN
ejpam-5042	340	7	,	,	PUNCT
ejpam-5042	340	8	1	1	NUM
ejpam-5042	340	9	]	]	PUNCT
ejpam-5042	340	10	by	by	ADP
ejpam-5042	340	11	ρ	ρ	PROPN
ejpam-5042	340	12	♦	♦	PROPN
ejpam-5042	340	13	=	=	PROPN
ejpam-5042	340	14	m∨	m∨	PROPN
ejpam-5042	340	15	ρ	ρ	PROPN
ejpam-5042	340	16	♢	♢	PROPN
ejpam-5042	340	17	for	for	ADP
ejpam-5042	340	18	all	all	DET
ejpam-5042	340	19	ρ	ρ	NOUN
ejpam-5042	340	20	∈	∈	PROPN
ejpam-5042	341	1	[	[	X
ejpam-5042	341	2	m	m	X
ejpam-5042	341	3	,	,	PUNCT
ejpam-5042	341	4	1	1	NUM
ejpam-5042	341	5	]	]	PUNCT
ejpam-5042	341	6	.	.	PUNCT
ejpam-5042	342	1	then	then	ADV
ejpam-5042	342	2	ρ	ρ	PROPN
ejpam-5042	342	3	♦	♦	PROPN
ejpam-5042	342	4	∈	∈	PROPN
ejpam-5042	343	1	[	[	X
ejpam-5042	343	2	m	m	X
ejpam-5042	343	3	,	,	PUNCT
ejpam-5042	343	4	1	1	NUM
ejpam-5042	343	5	]	]	PUNCT
ejpam-5042	343	6	and	and	CCONJ
ejpam-5042	343	7	ρ	ρ	PROPN
ejpam-5042	343	8	∨	∨	PROPN
ejpam-5042	343	9	ρ	ρ	PROPN
ejpam-5042	343	10	♦	♦	PROPN
ejpam-5042	343	11	=	=	PROPN
ejpam-5042	343	12	ρ	ρ	PROPN
ejpam-5042	343	13	∨	∨	X
ejpam-5042	343	14	(	(	PUNCT
ejpam-5042	343	15	m	m	PROPN
ejpam-5042	343	16	∨	∨	PROPN
ejpam-5042	343	17	ρ	ρ	PROPN
ejpam-5042	343	18	♢	♢	PROPN
ejpam-5042	343	19	)	)	PUNCT
ejpam-5042	344	1	=	=	SYM
ejpam-5042	344	2	ρ	ρ	PROPN
ejpam-5042	344	3	∨	∨	PROPN
ejpam-5042	344	4	ρ	ρ	PROPN
ejpam-5042	344	5	♢	♢	PROPN
ejpam-5042	344	6	∨m	∨m	NOUN
ejpam-5042	344	7	=	=	NOUN
ejpam-5042	344	8	1	1	NUM
ejpam-5042	344	9	∨m	∨m	NOUN
ejpam-5042	344	10	=	=	SYM
ejpam-5042	344	11	1	1	X
ejpam-5042	344	12	.	.	PUNCT
ejpam-5042	345	1	let	let	VERB
ejpam-5042	345	2	ϱ	ϱ	ADP
ejpam-5042	345	3	∈	∈	PROPN
ejpam-5042	345	4	[	[	X
ejpam-5042	345	5	m	m	X
ejpam-5042	345	6	,	,	PUNCT
ejpam-5042	345	7	1	1	NUM
ejpam-5042	345	8	]	]	PUNCT
ejpam-5042	345	9	and	and	CCONJ
ejpam-5042	345	10	ρ∨	ρ∨	PROPN
ejpam-5042	345	11	ϱ	ϱ	PROPN
ejpam-5042	345	12	=	=	SYM
ejpam-5042	345	13	1	1	X
ejpam-5042	345	14	.	.	PUNCT
ejpam-5042	346	1	then	then	ADV
ejpam-5042	346	2	ϱ∨	ϱ∨	PROPN
ejpam-5042	346	3	ρ	ρ	PROPN
ejpam-5042	346	4	=	=	SYM
ejpam-5042	346	5	1	1	NUM
ejpam-5042	346	6	and	and	CCONJ
ejpam-5042	346	7	hence	hence	ADV
ejpam-5042	346	8	ϱ∨	ϱ∨	PROPN
ejpam-5042	346	9	ρ	ρ	PROPN
ejpam-5042	346	10	♢	♢	PROPN
ejpam-5042	346	11	=	=	X
ejpam-5042	346	12	ϱ.	ϱ.	PROPN
ejpam-5042	347	1	now	now	ADV
ejpam-5042	347	2	ρ	ρ	PROPN
ejpam-5042	347	3	♦	♦	PROPN
ejpam-5042	347	4	∨	∨	NUM
ejpam-5042	347	5	ϱ	ϱ	PROPN
ejpam-5042	347	6	=	=	PROPN
ejpam-5042	347	7	m∨	m∨	PROPN
ejpam-5042	347	8	ρ	ρ	PROPN
ejpam-5042	347	9	♢	♢	PROPN
ejpam-5042	347	10	∨	∨	NUM
ejpam-5042	347	11	ϱ	ϱ	ADP
ejpam-5042	347	12	=	=	PUNCT
ejpam-5042	347	13	m∨	m∨	PROPN
ejpam-5042	347	14	ϱ∨	ϱ∨	PROPN
ejpam-5042	347	15	ρ	ρ	PROPN
ejpam-5042	347	16	♢	♢	PROPN
ejpam-5042	347	17	=	=	PROPN
ejpam-5042	347	18	m	m	PROPN
ejpam-5042	347	19	∨	∨	NOUN
ejpam-5042	347	20	ϱ	ϱ	X
ejpam-5042	347	21	=	=	X
ejpam-5042	347	22	ϱ.	ϱ.	NOUN
ejpam-5042	347	23	therefore	therefore	ADV
ejpam-5042	347	24	,	,	PUNCT
ejpam-5042	347	25	ρ	ρ	PROPN
ejpam-5042	347	26	♦	♦	PROPN
ejpam-5042	347	27	≤	≤	PROPN
ejpam-5042	347	28	ϱ.	ϱ.	NOUN
ejpam-5042	347	29	hence	hence	ADV
ejpam-5042	347	30	,	,	PUNCT
ejpam-5042	347	31	♦	♦	PROPN
ejpam-5042	347	32	is	be	AUX
ejpam-5042	347	33	dual	dual	ADJ
ejpam-5042	347	34	pseudo	pseudo	NOUN
ejpam-5042	347	35	-	-	NOUN
ejpam-5042	347	36	complementation	complementation	NOUN
ejpam-5042	347	37	on	on	ADP
ejpam-5042	347	38	[	[	X
ejpam-5042	347	39	m	m	NOUN
ejpam-5042	347	40	,	,	PUNCT
ejpam-5042	347	41	1	1	NUM
ejpam-5042	347	42	]	]	PUNCT
ejpam-5042	347	43	.	.	PUNCT
ejpam-5042	348	1	(	(	PUNCT
ejpam-5042	348	2	2	2	X
ejpam-5042	348	3	)	)	PUNCT
ejpam-5042	348	4	⇒	⇒	NOUN
ejpam-5042	348	5	(	(	PUNCT
ejpam-5042	348	6	3	3	NUM
ejpam-5042	348	7	)	)	PUNCT
ejpam-5042	348	8	:	:	PUNCT
ejpam-5042	348	9	suppose	suppose	VERB
ejpam-5042	348	10	[	[	X
ejpam-5042	348	11	m	m	X
ejpam-5042	348	12	,	,	PUNCT
ejpam-5042	348	13	1	1	NUM
ejpam-5042	348	14	]	]	PUNCT
ejpam-5042	348	15	is	be	AUX
ejpam-5042	348	16	a	a	DET
ejpam-5042	348	17	dual	dual	ADJ
ejpam-5042	348	18	pseudo	pseudo	NOUN
ejpam-5042	348	19	-	-	ADJ
ejpam-5042	348	20	complemented	complemented	ADJ
ejpam-5042	348	21	lattice	lattice	NOUN
ejpam-5042	348	22	.	.	PUNCT
ejpam-5042	349	1	then	then	ADV
ejpam-5042	349	2	[	[	X
ejpam-5042	349	3	m1	m1	NOUN
ejpam-5042	349	4	,	,	PUNCT
ejpam-5042	349	5	1	1	NUM
ejpam-5042	349	6	]	]	PUNCT
ejpam-5042	349	7	is	be	AUX
ejpam-5042	349	8	a	a	DET
ejpam-5042	349	9	dual	dual	ADJ
ejpam-5042	349	10	pseudo	pseudo	NOUN
ejpam-5042	349	11	-	-	ADJ
ejpam-5042	349	12	complemented	complemented	ADJ
ejpam-5042	349	13	lattice	lattice	NOUN
ejpam-5042	349	14	for	for	ADP
ejpam-5042	349	15	all	all	DET
ejpam-5042	349	16	minimal	minimal	ADJ
ejpam-5042	349	17	elements	element	NOUN
ejpam-5042	349	18	m1	m1	NOUN
ejpam-5042	349	19	in	in	ADP
ejpam-5042	349	20	v	v	NUM
ejpam-5042	349	21	.	.	PUNCT
ejpam-5042	350	1	(	(	PUNCT
ejpam-5042	350	2	3	3	X
ejpam-5042	350	3	)	)	PUNCT
ejpam-5042	350	4	⇒	⇒	NOUN
ejpam-5042	350	5	(	(	PUNCT
ejpam-5042	350	6	1	1	NUM
ejpam-5042	350	7	)	)	PUNCT
ejpam-5042	350	8	:	:	PUNCT
ejpam-5042	350	9	suppose	suppose	VERB
ejpam-5042	350	10	[	[	X
ejpam-5042	350	11	m1	m1	NOUN
ejpam-5042	350	12	,	,	PUNCT
ejpam-5042	350	13	1	1	NUM
ejpam-5042	350	14	]	]	PUNCT
ejpam-5042	350	15	is	be	AUX
ejpam-5042	350	16	a	a	DET
ejpam-5042	350	17	dual	dual	ADJ
ejpam-5042	350	18	pseudo	pseudo	NOUN
ejpam-5042	350	19	-	-	ADJ
ejpam-5042	350	20	complemented	complemented	ADJ
ejpam-5042	350	21	lattice	lattice	NOUN
ejpam-5042	350	22	for	for	ADP
ejpam-5042	350	23	all	all	DET
ejpam-5042	350	24	minimal	minimal	ADJ
ejpam-5042	350	25	elements	element	NOUN
ejpam-5042	350	26	m1	m1	NOUN
ejpam-5042	350	27	in	in	ADP
ejpam-5042	350	28	v	v	NUM
ejpam-5042	350	29	.	.	PUNCT
ejpam-5042	351	1	for	for	ADP
ejpam-5042	351	2	any	any	DET
ejpam-5042	351	3	ρ	ρ	PROPN
ejpam-5042	351	4	∈	∈	PROPN
ejpam-5042	351	5	v	v	NOUN
ejpam-5042	351	6	,	,	PUNCT
ejpam-5042	351	7	we	we	PRON
ejpam-5042	351	8	have	have	AUX
ejpam-5042	351	9	m∧	m∧	NOUN
ejpam-5042	351	10	ρ	ρ	PROPN
ejpam-5042	351	11	is	be	AUX
ejpam-5042	351	12	a	a	DET
ejpam-5042	351	13	minimal	minimal	ADJ
ejpam-5042	351	14	element	element	NOUN
ejpam-5042	351	15	in	in	ADP
ejpam-5042	351	16	v	v	NOUN
ejpam-5042	351	17	and	and	CCONJ
ejpam-5042	351	18	[	[	X
ejpam-5042	351	19	m∧	m∧	NOUN
ejpam-5042	351	20	ρ	ρ	PROPN
ejpam-5042	351	21	,	,	PUNCT
ejpam-5042	351	22	1	1	NUM
ejpam-5042	351	23	]	]	PUNCT
ejpam-5042	351	24	is	be	AUX
ejpam-5042	351	25	a	a	DET
ejpam-5042	351	26	dual	dual	ADJ
ejpam-5042	351	27	pseudo	pseudo	NOUN
ejpam-5042	351	28	-	-	ADJ
ejpam-5042	351	29	complemented	complement	VERB
ejpam-5042	351	30	lattice	lattice	NOUN
ejpam-5042	351	31	.	.	PUNCT
ejpam-5042	352	1	let	let	VERB
ejpam-5042	352	2	ρ	ρ	PRON
ejpam-5042	352	3	♦	♦	PROPN
ejpam-5042	352	4	be	be	AUX
ejpam-5042	352	5	the	the	DET
ejpam-5042	352	6	dual	dual	ADJ
ejpam-5042	352	7	pseudo	pseudo	NOUN
ejpam-5042	352	8	-	-	NOUN
ejpam-5042	352	9	complement	complement	NOUN
ejpam-5042	352	10	of	of	ADP
ejpam-5042	352	11	ρ	ρ	NOUN
ejpam-5042	352	12	in	in	ADP
ejpam-5042	352	13	[	[	X
ejpam-5042	352	14	m	m	NOUN
ejpam-5042	352	15	∧	∧	PROPN
ejpam-5042	352	16	ρ	ρ	PROPN
ejpam-5042	352	17	,	,	PUNCT
ejpam-5042	352	18	1	1	NUM
ejpam-5042	352	19	]	]	PUNCT
ejpam-5042	352	20	.	.	PUNCT
ejpam-5042	353	1	we	we	PRON
ejpam-5042	353	2	prove	prove	VERB
ejpam-5042	353	3	that	that	SCONJ
ejpam-5042	353	4	ρ	ρ	PROPN
ejpam-5042	353	5	↣	↣	PROPN
ejpam-5042	353	6	ρ	ρ	PROPN
ejpam-5042	353	7	♦	♦	PROPN
ejpam-5042	353	8	is	be	AUX
ejpam-5042	353	9	a	a	DET
ejpam-5042	353	10	parapseudo	parapseudo	NOUN
ejpam-5042	353	11	-	-	NOUN
ejpam-5042	353	12	complementation	complementation	NOUN
ejpam-5042	353	13	on	on	ADP
ejpam-5042	353	14	v	v	NOUN
ejpam-5042	353	15	.	.	PUNCT
ejpam-5042	354	1	clearly	clearly	ADV
ejpam-5042	354	2	,	,	PUNCT
ejpam-5042	354	3	ρ	ρ	PROPN
ejpam-5042	354	4	∨	∨	PROPN
ejpam-5042	354	5	ρ	ρ	PROPN
ejpam-5042	354	6	♦	♦	PROPN
ejpam-5042	354	7	=	=	PROPN
ejpam-5042	354	8	1	1	X
ejpam-5042	354	9	.	.	PUNCT
ejpam-5042	354	10	let	let	VERB
ejpam-5042	354	11	ϱ	ϱ	ADP
ejpam-5042	354	12	∈	∈	PROPN
ejpam-5042	354	13	v	v	NOUN
ejpam-5042	354	14	and	and	CCONJ
ejpam-5042	354	15	ϱ∨	ϱ∨	PROPN
ejpam-5042	354	16	ρ	ρ	PROPN
ejpam-5042	354	17	=	=	SYM
ejpam-5042	354	18	1	1	X
ejpam-5042	354	19	.	.	PUNCT
ejpam-5042	354	20	put	put	VERB
ejpam-5042	354	21	τ	τ	X
ejpam-5042	354	22	=	=	PUNCT
ejpam-5042	354	23	(	(	PUNCT
ejpam-5042	354	24	m∧	m∧	PROPN
ejpam-5042	354	25	ρ)∨	ρ)∨	PROPN
ejpam-5042	354	26	ϱ	ϱ	PROPN
ejpam-5042	354	27	=	=	PUNCT
ejpam-5042	354	28	(	(	PUNCT
ejpam-5042	354	29	m∨	m∨	PROPN
ejpam-5042	354	30	ϱ)∧	ϱ)∧	PROPN
ejpam-5042	354	31	(	(	PUNCT
ejpam-5042	354	32	ρ∨	ρ∨	PROPN
ejpam-5042	354	33	ϱ	ϱ	PROPN
ejpam-5042	354	34	)	)	PUNCT
ejpam-5042	354	35	=	=	SYM
ejpam-5042	354	36	(	(	PUNCT
ejpam-5042	354	37	m∨	m∨	PROPN
ejpam-5042	354	38	ϱ)∧	ϱ)∧	PROPN
ejpam-5042	354	39	1	1	NUM
ejpam-5042	354	40	=	=	SYM
ejpam-5042	354	41	m∨	m∨	NOUN
ejpam-5042	354	42	ϱ.	ϱ.	NOUN
ejpam-5042	354	43	then	then	ADV
ejpam-5042	354	44	τ	τ	PROPN
ejpam-5042	354	45	∈	∈	PROPN
ejpam-5042	355	1	[	[	X
ejpam-5042	355	2	m∧	m∧	NOUN
ejpam-5042	355	3	ρ	ρ	PROPN
ejpam-5042	355	4	,	,	PUNCT
ejpam-5042	355	5	1	1	NUM
ejpam-5042	355	6	]	]	PUNCT
ejpam-5042	355	7	and	and	CCONJ
ejpam-5042	355	8	ρ∨	ρ∨	PROPN
ejpam-5042	355	9	τ	τ	X
ejpam-5042	356	1	=	=	PUNCT
ejpam-5042	356	2	ρ∨m∨	ρ∨m∨	X
ejpam-5042	356	3	ϱ	ϱ	ADP
ejpam-5042	356	4	=	=	X
ejpam-5042	356	5	ρ∨	ρ∨	PROPN
ejpam-5042	356	6	ϱ	ϱ	ADP
ejpam-5042	356	7	=	=	SYM
ejpam-5042	356	8	1	1	X
ejpam-5042	356	9	.	.	PUNCT
ejpam-5042	357	1	so	so	SCONJ
ejpam-5042	357	2	that	that	SCONJ
ejpam-5042	357	3	ρ	ρ	PROPN
ejpam-5042	357	4	♦	♦	PROPN
ejpam-5042	357	5	≤	≤	PROPN
ejpam-5042	357	6	τ	τ	PROPN
ejpam-5042	357	7	.	.	PUNCT
ejpam-5042	358	1	now	now	ADV
ejpam-5042	358	2	,	,	PUNCT
ejpam-5042	358	3	τ	τ	PROPN
ejpam-5042	358	4	=	=	SYM
ejpam-5042	358	5	ρ	ρ	PROPN
ejpam-5042	358	6	♦	♦	PROPN
ejpam-5042	358	7	∨	∨	PROPN
ejpam-5042	358	8	τ	τ	PROPN
ejpam-5042	358	9	implies	imply	VERB
ejpam-5042	358	10	that	that	SCONJ
ejpam-5042	358	11	m	m	PROPN
ejpam-5042	358	12	∨	∨	NUM
ejpam-5042	358	13	ϱ	ϱ	ADP
ejpam-5042	358	14	=	=	PUNCT
ejpam-5042	358	15	ρ	ρ	PROPN
ejpam-5042	358	16	♦	♦	PROPN
ejpam-5042	358	17	∨m	∨m	PROPN
ejpam-5042	358	18	∨	∨	NUM
ejpam-5042	358	19	ϱ	ϱ	ADP
ejpam-5042	358	20	and	and	CCONJ
ejpam-5042	358	21	hence	hence	ADV
ejpam-5042	358	22	ϱ	ϱ	ADP
ejpam-5042	358	23	∨m	∨m	NOUN
ejpam-5042	358	24	∨	∨	NUM
ejpam-5042	358	25	ϱ	ϱ	ADP
ejpam-5042	358	26	=	=	SYM
ejpam-5042	358	27	ϱ	ϱ	ADP
ejpam-5042	358	28	∨	∨	NUM
ejpam-5042	358	29	ρ	ρ	PROPN
ejpam-5042	358	30	♦	♦	PROPN
ejpam-5042	358	31	∨	∨	PROPN
ejpam-5042	358	32	ϱ.	ϱ.	PROPN
ejpam-5042	358	33	thus	thus	ADV
ejpam-5042	358	34	,	,	PUNCT
ejpam-5042	358	35	we	we	PRON
ejpam-5042	358	36	get	get	VERB
ejpam-5042	358	37	ϱ	ϱ	ADP
ejpam-5042	358	38	=	=	SYM
ejpam-5042	358	39	ϱ	ϱ	ADP
ejpam-5042	358	40	∨	∨	NUM
ejpam-5042	358	41	ρ	ρ	PROPN
ejpam-5042	358	42	♦	♦	PROPN
ejpam-5042	358	43	.	.	PUNCT
ejpam-5042	359	1	finally	finally	ADV
ejpam-5042	359	2	,	,	PUNCT
ejpam-5042	359	3	let	let	VERB
ejpam-5042	359	4	ρ	ρ	NOUN
ejpam-5042	359	5	,	,	PUNCT
ejpam-5042	359	6	ϱ	ϱ	PROPN
ejpam-5042	359	7	∈	∈	PROPN
ejpam-5042	359	8	v	v	NOUN
ejpam-5042	359	9	.	.	PUNCT
ejpam-5042	360	1	we	we	PRON
ejpam-5042	360	2	have	have	VERB
ejpam-5042	360	3	ρ	ρ	PRON
ejpam-5042	360	4	∈	∈	PROPN
ejpam-5042	361	1	[	[	X
ejpam-5042	361	2	m	m	NOUN
ejpam-5042	361	3	∧	∧	PROPN
ejpam-5042	361	4	ρ	ρ	PROPN
ejpam-5042	361	5	,	,	PUNCT
ejpam-5042	361	6	1	1	NUM
ejpam-5042	361	7	]	]	PUNCT
ejpam-5042	361	8	and	and	CCONJ
ejpam-5042	361	9	ϱ	ϱ	ADP
ejpam-5042	361	10	∈	∈	PROPN
ejpam-5042	362	1	[	[	X
ejpam-5042	362	2	m	m	X
ejpam-5042	362	3	∧	∧	NOUN
ejpam-5042	362	4	ϱ	ϱ	ADP
ejpam-5042	362	5	,	,	PUNCT
ejpam-5042	362	6	1	1	NUM
ejpam-5042	362	7	]	]	PUNCT
ejpam-5042	362	8	.	.	PUNCT
ejpam-5042	363	1	now	now	ADV
ejpam-5042	363	2	,	,	PUNCT
ejpam-5042	363	3	(	(	PUNCT
ejpam-5042	363	4	m	m	VERB
ejpam-5042	363	5	∧	∧	NOUN
ejpam-5042	363	6	(	(	PUNCT
ejpam-5042	363	7	ρ	ρ	PROPN
ejpam-5042	363	8	∧	∧	PROPN
ejpam-5042	363	9	ϱ	ϱ	NOUN
ejpam-5042	363	10	)	)	PUNCT
ejpam-5042	363	11	)	)	PUNCT
ejpam-5042	363	12	∨	∨	PROPN
ejpam-5042	363	13	(	(	PUNCT
ejpam-5042	363	14	ρ	ρ	PROPN
ejpam-5042	363	15	♦	♦	PROPN
ejpam-5042	363	16	∨	∨	NUM
ejpam-5042	363	17	ϱ	ϱ	PROPN
ejpam-5042	363	18	♦	♦	PROPN
ejpam-5042	363	19	)	)	PUNCT
ejpam-5042	363	20	=	=	PUNCT
ejpam-5042	363	21	(	(	PUNCT
ejpam-5042	363	22	m	m	PROPN
ejpam-5042	363	23	∨	∨	PROPN
ejpam-5042	363	24	ρ	ρ	PROPN
ejpam-5042	363	25	♦	♦	PROPN
ejpam-5042	363	26	∨	∨	NUM
ejpam-5042	363	27	ϱ	ϱ	PROPN
ejpam-5042	363	28	♦	♦	PROPN
ejpam-5042	363	29	)	)	PUNCT
ejpam-5042	363	30	∧	∧	PROPN
ejpam-5042	363	31	(	(	PUNCT
ejpam-5042	363	32	(	(	PUNCT
ejpam-5042	363	33	ρ	ρ	PROPN
ejpam-5042	363	34	∧	∧	PROPN
ejpam-5042	363	35	ϱ	ϱ	NOUN
ejpam-5042	363	36	)	)	PUNCT
ejpam-5042	363	37	∨	∨	PROPN
ejpam-5042	363	38	ρ	ρ	PROPN
ejpam-5042	363	39	♦	♦	PROPN
ejpam-5042	363	40	∨	∨	NUM
ejpam-5042	363	41	ϱ	ϱ	PROPN
ejpam-5042	363	42	♦	♦	PROPN
ejpam-5042	363	43	)	)	PUNCT
ejpam-5042	363	44	.	.	PUNCT
ejpam-5042	364	1	=	=	PUNCT
ejpam-5042	364	2	(	(	PUNCT
ejpam-5042	364	3	m	m	PROPN
ejpam-5042	364	4	∨	∨	NOUN
ejpam-5042	364	5	ρ	ρ	PROPN
ejpam-5042	364	6	♦	♦	PROPN
ejpam-5042	364	7	∨	∨	NUM
ejpam-5042	364	8	ϱ	ϱ	PROPN
ejpam-5042	364	9	♦	♦	PROPN
ejpam-5042	364	10	)	)	PUNCT
ejpam-5042	364	11	∧	∧	PROPN
ejpam-5042	364	12	(	(	PUNCT
ejpam-5042	364	13	ρ	ρ	PROPN
ejpam-5042	364	14	∨	∨	PROPN
ejpam-5042	364	15	ρ	ρ	PROPN
ejpam-5042	364	16	♦	♦	PROPN
ejpam-5042	364	17	∨	∨	NUM
ejpam-5042	364	18	ϱ	ϱ	PROPN
ejpam-5042	364	19	♦	♦	PROPN
ejpam-5042	364	20	)	)	PUNCT
ejpam-5042	364	21	∧	∧	PROPN
ejpam-5042	364	22	(	(	PUNCT
ejpam-5042	364	23	ϱ	ϱ	PROPN
ejpam-5042	364	24	∨	∨	NUM
ejpam-5042	364	25	ρ	ρ	PROPN
ejpam-5042	364	26	♦	♦	PROPN
ejpam-5042	364	27	∨	∨	NUM
ejpam-5042	364	28	ϱ	ϱ	PROPN
ejpam-5042	364	29	♦	♦	PROPN
ejpam-5042	364	30	)	)	PUNCT
ejpam-5042	365	1	=	=	PUNCT
ejpam-5042	365	2	(	(	PUNCT
ejpam-5042	365	3	m	m	PROPN
ejpam-5042	365	4	∨	∨	PROPN
ejpam-5042	365	5	ρ	ρ	PROPN
ejpam-5042	365	6	♦	♦	PROPN
ejpam-5042	365	7	∨	∨	NUM
ejpam-5042	365	8	ϱ	ϱ	PROPN
ejpam-5042	365	9	♦	♦	PROPN
ejpam-5042	365	10	)	)	PUNCT
ejpam-5042	365	11	.	.	PUNCT
ejpam-5042	366	1	=	=	PUNCT
ejpam-5042	366	2	ρ	ρ	PROPN
ejpam-5042	366	3	♦	♦	PROPN
ejpam-5042	366	4	∨	∨	NUM
ejpam-5042	366	5	ϱ	ϱ	PROPN
ejpam-5042	366	6	♦	♦	PROPN
ejpam-5042	366	7	(	(	PUNCT
ejpam-5042	366	8	since	since	SCONJ
ejpam-5042	366	9	ρ	ρ	PROPN
ejpam-5042	366	10	♦	♦	PROPN
ejpam-5042	366	11	∈	∈	PROPN
ejpam-5042	367	1	[	[	X
ejpam-5042	367	2	m	m	X
ejpam-5042	367	3	∧	∧	PROPN
ejpam-5042	367	4	ρ	ρ	PROPN
ejpam-5042	367	5	,	,	PUNCT
ejpam-5042	367	6	1	1	NUM
ejpam-5042	367	7	]	]	PUNCT
ejpam-5042	367	8	)	)	PUNCT
ejpam-5042	367	9	therefore	therefore	ADV
ejpam-5042	367	10	,	,	PUNCT
ejpam-5042	367	11	ρ	ρ	PROPN
ejpam-5042	367	12	♦	♦	PROPN
ejpam-5042	367	13	∨	∨	NUM
ejpam-5042	367	14	ϱ	ϱ	PROPN
ejpam-5042	367	15	♦	♦	PROPN
ejpam-5042	367	16	∈	∈	PROPN
ejpam-5042	368	1	[	[	X
ejpam-5042	368	2	m	m	VERB
ejpam-5042	368	3	∧	∧	PROPN
ejpam-5042	368	4	(	(	PUNCT
ejpam-5042	368	5	ρ	ρ	PROPN
ejpam-5042	368	6	∧	∧	PROPN
ejpam-5042	368	7	ϱ	ϱ	NOUN
ejpam-5042	368	8	)	)	PUNCT
ejpam-5042	368	9	,	,	PUNCT
ejpam-5042	368	10	1	1	NUM
ejpam-5042	368	11	]	]	PUNCT
ejpam-5042	368	12	.	.	PUNCT
ejpam-5042	369	1	now	now	ADV
ejpam-5042	369	2	,	,	PUNCT
ejpam-5042	369	3	(	(	PUNCT
ejpam-5042	369	4	ρ	ρ	PROPN
ejpam-5042	369	5	∧	∧	PROPN
ejpam-5042	369	6	ϱ	ϱ	NOUN
ejpam-5042	369	7	)	)	PUNCT
ejpam-5042	369	8	∨	∨	PROPN
ejpam-5042	369	9	(	(	PUNCT
ejpam-5042	369	10	ρ	ρ	PROPN
ejpam-5042	369	11	♦	♦	PROPN
ejpam-5042	369	12	∨	∨	NUM
ejpam-5042	369	13	ϱ	ϱ	PROPN
ejpam-5042	369	14	♦	♦	PROPN
ejpam-5042	369	15	)	)	PUNCT
ejpam-5042	370	1	=	=	PRON
ejpam-5042	370	2	(	(	PUNCT
ejpam-5042	370	3	ρ	ρ	PROPN
ejpam-5042	370	4	∨	∨	PROPN
ejpam-5042	370	5	ρ	ρ	PROPN
ejpam-5042	370	6	♦	♦	PROPN
ejpam-5042	370	7	∨	∨	NUM
ejpam-5042	370	8	ϱ	ϱ	PROPN
ejpam-5042	370	9	♦	♦	PROPN
ejpam-5042	370	10	)	)	PUNCT
ejpam-5042	370	11	∧	∧	PROPN
ejpam-5042	370	12	(	(	PUNCT
ejpam-5042	370	13	ϱ	ϱ	PROPN
ejpam-5042	370	14	∨	∨	NUM
ejpam-5042	370	15	ρ	ρ	PROPN
ejpam-5042	370	16	♦	♦	PROPN
ejpam-5042	370	17	∨	∨	NUM
ejpam-5042	370	18	ϱ	ϱ	PROPN
ejpam-5042	370	19	♦	♦	PROPN
ejpam-5042	370	20	)	)	PUNCT
ejpam-5042	370	21	=	=	SYM
ejpam-5042	371	1	1	1	X
ejpam-5042	371	2	.	.	PUNCT
ejpam-5042	371	3	let	let	VERB
ejpam-5042	371	4	τ	τ	PROPN
ejpam-5042	371	5	∈	∈	PROPN
ejpam-5042	372	1	[	[	X
ejpam-5042	372	2	m	m	X
ejpam-5042	372	3	∧	∧	PROPN
ejpam-5042	372	4	(	(	PUNCT
ejpam-5042	372	5	ρ	ρ	PROPN
ejpam-5042	372	6	∧	∧	PROPN
ejpam-5042	372	7	ϱ	ϱ	NOUN
ejpam-5042	372	8	)	)	PUNCT
ejpam-5042	372	9	,	,	PUNCT
ejpam-5042	372	10	1	1	X
ejpam-5042	372	11	]	]	PUNCT
ejpam-5042	372	12	and	and	CCONJ
ejpam-5042	372	13	(	(	PUNCT
ejpam-5042	372	14	ρ	ρ	PROPN
ejpam-5042	372	15	∧	∧	PROPN
ejpam-5042	372	16	ϱ	ϱ	NOUN
ejpam-5042	372	17	)	)	PUNCT
ejpam-5042	372	18	∨	∨	NUM
ejpam-5042	372	19	τ	τ	X
ejpam-5042	372	20	=	=	SYM
ejpam-5042	372	21	1	1	X
ejpam-5042	372	22	.	.	PUNCT
ejpam-5042	373	1	then	then	ADV
ejpam-5042	373	2	,	,	PUNCT
ejpam-5042	373	3	(	(	PUNCT
ejpam-5042	373	4	ρ	ρ	PROPN
ejpam-5042	373	5	∨	∨	NUM
ejpam-5042	373	6	τ	τ	NOUN
ejpam-5042	373	7	)	)	PUNCT
ejpam-5042	373	8	∧	∧	PROPN
ejpam-5042	373	9	(	(	PUNCT
ejpam-5042	373	10	ϱ	ϱ	PROPN
ejpam-5042	373	11	∨	∨	NUM
ejpam-5042	373	12	τ	τ	X
ejpam-5042	373	13	)	)	PUNCT
ejpam-5042	373	14	=	=	SYM
ejpam-5042	373	15	1	1	NUM
ejpam-5042	373	16	which	which	PRON
ejpam-5042	373	17	implies	imply	VERB
ejpam-5042	373	18	that	that	SCONJ
ejpam-5042	373	19	ρ	ρ	PROPN
ejpam-5042	373	20	∨	∨	PROPN
ejpam-5042	373	21	τ	τ	X
ejpam-5042	373	22	=	=	SYM
ejpam-5042	373	23	1	1	NUM
ejpam-5042	373	24	and	and	CCONJ
ejpam-5042	373	25	ϱ	ϱ	ADP
ejpam-5042	373	26	∨	∨	NUM
ejpam-5042	373	27	τ	τ	X
ejpam-5042	373	28	=	=	SYM
ejpam-5042	373	29	1	1	X
ejpam-5042	373	30	.	.	PUNCT
ejpam-5042	373	31	also	also	ADV
ejpam-5042	373	32	,	,	PUNCT
ejpam-5042	373	33	(	(	PUNCT
ejpam-5042	373	34	m∧	m∧	X
ejpam-5042	373	35	ρ)∨	ρ)∨	PROPN
ejpam-5042	373	36	τ	τ	X
ejpam-5042	373	37	∈	∈	PROPN
ejpam-5042	373	38	[	[	X
ejpam-5042	373	39	m∧	m∧	NOUN
ejpam-5042	373	40	ρ	ρ	PROPN
ejpam-5042	373	41	,	,	PUNCT
ejpam-5042	373	42	1	1	NUM
ejpam-5042	373	43	]	]	PUNCT
ejpam-5042	373	44	and	and	CCONJ
ejpam-5042	373	45	ρ∨	ρ∨	PROPN
ejpam-5042	373	46	(	(	PUNCT
ejpam-5042	373	47	(	(	PUNCT
ejpam-5042	373	48	m∧	m∧	PROPN
ejpam-5042	373	49	ρ)∨	ρ)∨	PROPN
ejpam-5042	373	50	τ	τ	X
ejpam-5042	373	51	)	)	PUNCT
ejpam-5042	373	52	=	=	SYM
ejpam-5042	373	53	ρ∨	ρ∨	PROPN
ejpam-5042	373	54	(	(	PUNCT
ejpam-5042	373	55	τ	τ	PROPN
ejpam-5042	373	56	∨	∨	X
ejpam-5042	373	57	(	(	PUNCT
ejpam-5042	373	58	m∧	m∧	NOUN
ejpam-5042	373	59	ρ	ρ	NOUN
ejpam-5042	373	60	)	)	PUNCT
ejpam-5042	373	61	)	)	PUNCT
ejpam-5042	373	62	=	=	SYM
ejpam-5042	374	1	1	1	X
ejpam-5042	374	2	.	.	PUNCT
ejpam-5042	375	1	hence	hence	ADV
ejpam-5042	375	2	,	,	PUNCT
ejpam-5042	375	3	we	we	PRON
ejpam-5042	375	4	get	get	VERB
ejpam-5042	375	5	ρ	ρ	NOUN
ejpam-5042	375	6	♦	♦	PROPN
ejpam-5042	375	7	≤	≤	PROPN
ejpam-5042	375	8	(	(	PUNCT
ejpam-5042	375	9	m∧ρ)∨τ	m∧ρ)∨τ	X
ejpam-5042	375	10	.	.	PUNCT
ejpam-5042	376	1	so	so	ADV
ejpam-5042	376	2	that	that	SCONJ
ejpam-5042	376	3	,	,	PUNCT
ejpam-5042	376	4	(	(	PUNCT
ejpam-5042	376	5	m∧ρ)∨τ	m∧ρ)∨τ	X
ejpam-5042	376	6	=	=	SYM
ejpam-5042	376	7	ρ	ρ	PROPN
ejpam-5042	376	8	♦	♦	PROPN
ejpam-5042	376	9	∨	∨	PROPN
ejpam-5042	376	10	(	(	PUNCT
ejpam-5042	376	11	m∧ρ)∨τ	m∧ρ)∨τ	X
ejpam-5042	376	12	=	=	SYM
ejpam-5042	377	1	[	[	X
ejpam-5042	377	2	(	(	PUNCT
ejpam-5042	377	3	ρ	ρ	PROPN
ejpam-5042	377	4	♦	♦	PROPN
ejpam-5042	377	5	∨m)∧	∨m)∧	X
ejpam-5042	377	6	(	(	PUNCT
ejpam-5042	377	7	ρ	ρ	PROPN
ejpam-5042	377	8	♦	♦	PROPN
ejpam-5042	377	9	∨ρ)]∨τ	∨ρ)]∨τ	PROPN
ejpam-5042	377	10	=	=	PROPN
ejpam-5042	377	11	ρ	ρ	PROPN
ejpam-5042	377	12	♦	♦	PROPN
ejpam-5042	377	13	∨τ	∨τ	NOUN
ejpam-5042	377	14	.	.	PUNCT
ejpam-5042	378	1	therefore	therefore	ADV
ejpam-5042	378	2	,	,	PUNCT
ejpam-5042	378	3	m	m	VERB
ejpam-5042	378	4	∨	∨	NOUN
ejpam-5042	378	5	τ	τ	X
ejpam-5042	378	6	=	=	SYM
ejpam-5042	378	7	ρ	ρ	PROPN
ejpam-5042	378	8	♦	♦	PROPN
ejpam-5042	378	9	∨	∨	PROPN
ejpam-5042	378	10	τ	τ	PROPN
ejpam-5042	378	11	.	.	PUNCT
ejpam-5042	379	1	now	now	ADV
ejpam-5042	379	2	,	,	PUNCT
ejpam-5042	380	1	[	[	X
ejpam-5042	380	2	m	m	VERB
ejpam-5042	380	3	∧	∧	NOUN
ejpam-5042	380	4	(	(	PUNCT
ejpam-5042	380	5	ρ	ρ	PROPN
ejpam-5042	380	6	∧	∧	PROPN
ejpam-5042	380	7	ϱ	ϱ	NOUN
ejpam-5042	380	8	)	)	PUNCT
ejpam-5042	380	9	]	]	PUNCT
ejpam-5042	381	1	≤	≤	NUM
ejpam-5042	381	2	τ	τ	PROPN
ejpam-5042	381	3	implies	imply	VERB
ejpam-5042	381	4	τ	τ	X
ejpam-5042	381	5	=	=	PUNCT
ejpam-5042	382	1	[	[	X
ejpam-5042	382	2	m	m	VERB
ejpam-5042	382	3	∧	∧	NOUN
ejpam-5042	382	4	(	(	PUNCT
ejpam-5042	382	5	ρ	ρ	PROPN
ejpam-5042	382	6	∧	∧	PROPN
ejpam-5042	382	7	ϱ	ϱ	NOUN
ejpam-5042	382	8	)	)	PUNCT
ejpam-5042	382	9	]	]	PUNCT
ejpam-5042	382	10	∨	∨	NUM
ejpam-5042	382	11	τ	τ	X
ejpam-5042	382	12	=	=	SYM
ejpam-5042	382	13	(	(	PUNCT
ejpam-5042	382	14	m	m	PROPN
ejpam-5042	382	15	∨	∨	NOUN
ejpam-5042	382	16	τ	τ	X
ejpam-5042	382	17	)	)	PUNCT
ejpam-5042	382	18	∧	∧	PROPN
ejpam-5042	382	19	[	[	X
ejpam-5042	382	20	(	(	PUNCT
ejpam-5042	382	21	ρ	ρ	PROPN
ejpam-5042	382	22	∨	∨	PROPN
ejpam-5042	382	23	τ	τ	NOUN
ejpam-5042	382	24	)	)	PUNCT
ejpam-5042	382	25	∧	∧	PROPN
ejpam-5042	382	26	(	(	PUNCT
ejpam-5042	382	27	ϱ	ϱ	PROPN
ejpam-5042	382	28	∨	∨	NUM
ejpam-5042	382	29	τ	τ	X
ejpam-5042	382	30	)	)	PUNCT
ejpam-5042	382	31	]	]	PUNCT
ejpam-5042	383	1	=	=	PUNCT
ejpam-5042	383	2	m	m	PROPN
ejpam-5042	383	3	∨	∨	NOUN
ejpam-5042	383	4	τ	τ	X
ejpam-5042	383	5	.	.	PUNCT
ejpam-5042	384	1	therefore	therefore	ADV
ejpam-5042	384	2	,	,	PUNCT
ejpam-5042	384	3	ρ	ρ	PROPN
ejpam-5042	384	4	♦	♦	PROPN
ejpam-5042	384	5	∨	∨	NUM
ejpam-5042	384	6	τ	τ	X
ejpam-5042	384	7	=	=	SYM
ejpam-5042	384	8	τ	τ	PROPN
ejpam-5042	384	9	implies	imply	VERB
ejpam-5042	384	10	ρ	ρ	PROPN
ejpam-5042	384	11	♦	♦	PROPN
ejpam-5042	384	12	≤	≤	PROPN
ejpam-5042	384	13	τ	τ	PROPN
ejpam-5042	384	14	.	.	PUNCT
ejpam-5042	385	1	similarly	similarly	ADV
ejpam-5042	385	2	,	,	PUNCT
ejpam-5042	385	3	we	we	PRON
ejpam-5042	385	4	get	get	VERB
ejpam-5042	385	5	ϱ	ϱ	ADP
ejpam-5042	385	6	♦	♦	PROPN
ejpam-5042	385	7	≤	≤	PROPN
ejpam-5042	385	8	τ	τ	PROPN
ejpam-5042	385	9	.	.	PUNCT
ejpam-5042	386	1	hence	hence	ADV
ejpam-5042	386	2	ρ	ρ	PROPN
ejpam-5042	386	3	♦	♦	PROPN
ejpam-5042	386	4	∨	∨	NUM
ejpam-5042	386	5	ϱ	ϱ	PROPN
ejpam-5042	386	6	♦	♦	PROPN
ejpam-5042	386	7	≤	≤	PROPN
ejpam-5042	386	8	τ	τ	PROPN
ejpam-5042	386	9	.	.	PUNCT
ejpam-5042	387	1	thus	thus	ADV
ejpam-5042	387	2	,	,	PUNCT
ejpam-5042	387	3	we	we	PRON
ejpam-5042	387	4	get	get	VERB
ejpam-5042	387	5	that	that	PRON
ejpam-5042	387	6	(	(	PUNCT
ejpam-5042	387	7	ρ	ρ	PROPN
ejpam-5042	387	8	∧	∧	PROPN
ejpam-5042	387	9	ϱ	ϱ	NOUN
ejpam-5042	387	10	)	)	PUNCT
ejpam-5042	387	11	♦	♦	PROPN
ejpam-5042	387	12	=	=	PROPN
ejpam-5042	387	13	ρ	ρ	PROPN
ejpam-5042	387	14	♦	♦	PROPN
ejpam-5042	387	15	∨	∨	NUM
ejpam-5042	387	16	ϱ	ϱ	PROPN
ejpam-5042	387	17	♦	♦	PROPN
ejpam-5042	387	18	.	.	PUNCT
ejpam-5042	388	1	therefore	therefore	ADV
ejpam-5042	388	2	,	,	PUNCT
ejpam-5042	388	3	♦	♦	PROPN
ejpam-5042	388	4	is	be	AUX
ejpam-5042	388	5	a	a	DET
ejpam-5042	388	6	parapseudo	parapseudo	NOUN
ejpam-5042	388	7	-	-	NOUN
ejpam-5042	388	8	complementation	complementation	NOUN
ejpam-5042	388	9	on	on	ADP
ejpam-5042	388	10	v	v	NUM
ejpam-5042	388	11	.	.	PUNCT
ejpam-5042	389	1	lemma	lemma	PROPN
ejpam-5042	389	2	7	7	X
ejpam-5042	389	3	.	.	PUNCT
ejpam-5042	390	1	let	let	VERB
ejpam-5042	390	2	v	v	PART
ejpam-5042	390	3	be	be	AUX
ejpam-5042	390	4	a	a	DET
ejpam-5042	390	5	pdl	pdl	NOUN
ejpam-5042	390	6	and	and	CCONJ
ejpam-5042	390	7	a	a	DET
ejpam-5042	390	8	⊆	⊆	NUM
ejpam-5042	390	9	v	v	NOUN
ejpam-5042	390	10	.	.	PUNCT
ejpam-5042	391	1	then	then	ADV
ejpam-5042	391	2	the	the	DET
ejpam-5042	391	3	set	set	NOUN
ejpam-5042	391	4	a•	a•	NOUN
ejpam-5042	391	5	=	=	SYM
ejpam-5042	391	6	{	{	PUNCT
ejpam-5042	391	7	t	t	NOUN
ejpam-5042	391	8	∈	∈	PROPN
ejpam-5042	391	9	v	v	ADP
ejpam-5042	391	10	|	|	ADV
ejpam-5042	391	11	t	t	PROPN
ejpam-5042	391	12	∨	∨	NUM
ejpam-5042	391	13	ρ	ρ	X
ejpam-5042	391	14	=	=	SYM
ejpam-5042	391	15	1	1	NUM
ejpam-5042	391	16	for	for	ADP
ejpam-5042	391	17	all	all	DET
ejpam-5042	391	18	ρ	ρ	NOUN
ejpam-5042	391	19	∈	∈	PROPN
ejpam-5042	391	20	a	a	PRON
ejpam-5042	391	21	}	}	PUNCT
ejpam-5042	391	22	is	be	AUX
ejpam-5042	391	23	a	a	DET
ejpam-5042	391	24	filter	filter	NOUN
ejpam-5042	391	25	of	of	ADP
ejpam-5042	391	26	v	v	NOUN
ejpam-5042	391	27	.	.	PUNCT
ejpam-5042	392	1	r.	r.	PROPN
ejpam-5042	392	2	shukla	shukla	PROPN
ejpam-5042	392	3	et	et	PROPN
ejpam-5042	392	4	al	al	PROPN
ejpam-5042	392	5	.	.	PUNCT
ejpam-5042	392	6	/	/	SYM
ejpam-5042	392	7	eur	eur	PROPN
ejpam-5042	392	8	.	.	PUNCT
ejpam-5042	393	1	j.	j.	PROPN
ejpam-5042	393	2	pure	pure	PROPN
ejpam-5042	393	3	appl	appl	PROPN
ejpam-5042	393	4	.	.	PROPN
ejpam-5042	393	5	math	math	PROPN
ejpam-5042	393	6	,	,	PUNCT
ejpam-5042	393	7	17	17	NUM
ejpam-5042	393	8	(	(	PUNCT
ejpam-5042	393	9	2	2	NUM
ejpam-5042	393	10	)	)	PUNCT
ejpam-5042	393	11	(	(	PUNCT
ejpam-5042	393	12	2024	2024	NUM
ejpam-5042	393	13	)	)	PUNCT
ejpam-5042	393	14	,	,	PUNCT
ejpam-5042	393	15	1129	1129	NUM
ejpam-5042	393	16	-	-	SYM
ejpam-5042	393	17	1145	1145	NUM
ejpam-5042	393	18	1139	1139	NUM
ejpam-5042	393	19	proof	proof	NOUN
ejpam-5042	393	20	.	.	PUNCT
ejpam-5042	394	1	let	let	VERB
ejpam-5042	394	2	t1	t1	NOUN
ejpam-5042	394	3	,	,	PUNCT
ejpam-5042	394	4	t2	t2	PROPN
ejpam-5042	394	5	∈	∈	PROPN
ejpam-5042	394	6	a•.	a•.	NOUN
ejpam-5042	394	7	then	then	ADV
ejpam-5042	394	8	t1	t1	PROPN
ejpam-5042	394	9	∨	∨	NUM
ejpam-5042	394	10	ρ	ρ	PROPN
ejpam-5042	394	11	=	=	SYM
ejpam-5042	394	12	1	1	NUM
ejpam-5042	394	13	,	,	PUNCT
ejpam-5042	394	14	t2	t2	NOUN
ejpam-5042	394	15	∨	∨	NUM
ejpam-5042	394	16	ρ	ρ	NOUN
ejpam-5042	394	17	=	=	SYM
ejpam-5042	394	18	1	1	NUM
ejpam-5042	394	19	for	for	ADP
ejpam-5042	394	20	all	all	DET
ejpam-5042	394	21	ρ	ρ	NOUN
ejpam-5042	394	22	∈	∈	PROPN
ejpam-5042	394	23	v	v	NOUN
ejpam-5042	394	24	.	.	PUNCT
ejpam-5042	395	1	hence	hence	ADV
ejpam-5042	395	2	(	(	PUNCT
ejpam-5042	395	3	t1	t1	NOUN
ejpam-5042	395	4	∧	∧	PROPN
ejpam-5042	395	5	t2	t2	PROPN
ejpam-5042	395	6	)	)	PUNCT
ejpam-5042	395	7	∨	∨	NUM
ejpam-5042	395	8	ρ	ρ	NOUN
ejpam-5042	395	9	=	=	SYM
ejpam-5042	395	10	(	(	PUNCT
ejpam-5042	395	11	t1	t1	PROPN
ejpam-5042	395	12	∨	∨	NUM
ejpam-5042	395	13	ρ)∧	ρ)∧	PROPN
ejpam-5042	395	14	(	(	PUNCT
ejpam-5042	395	15	t2	t2	PROPN
ejpam-5042	395	16	∨	∨	NUM
ejpam-5042	395	17	ρ	ρ	NOUN
ejpam-5042	395	18	)	)	PUNCT
ejpam-5042	395	19	=	=	PUNCT
ejpam-5042	396	1	1∧	1∧	NUM
ejpam-5042	396	2	1	1	NUM
ejpam-5042	396	3	=	=	SYM
ejpam-5042	396	4	1	1	NUM
ejpam-5042	396	5	.	.	PUNCT
ejpam-5042	397	1	therefore	therefore	ADV
ejpam-5042	397	2	,	,	PUNCT
ejpam-5042	397	3	t1	t1	PROPN
ejpam-5042	397	4	∧	∧	PROPN
ejpam-5042	397	5	t2	t2	PROPN
ejpam-5042	397	6	∈	∈	PROPN
ejpam-5042	397	7	a•.	a•.	NOUN
ejpam-5042	397	8	now	now	ADV
ejpam-5042	397	9	,	,	PUNCT
ejpam-5042	397	10	let	let	VERB
ejpam-5042	397	11	t1	t1	PROPN
ejpam-5042	397	12	∈	∈	PROPN
ejpam-5042	397	13	a•	a•	PROPN
ejpam-5042	397	14	and	and	CCONJ
ejpam-5042	397	15	κ1	κ1	NOUN
ejpam-5042	397	16	∈	∈	PROPN
ejpam-5042	397	17	v	v	NOUN
ejpam-5042	397	18	.	.	PUNCT
ejpam-5042	398	1	then	then	ADV
ejpam-5042	398	2	κ1	κ1	PROPN
ejpam-5042	398	3	∨	∨	PROPN
ejpam-5042	398	4	t1	t1	PROPN
ejpam-5042	398	5	∨	∨	NUM
ejpam-5042	398	6	ρ	ρ	PROPN
ejpam-5042	398	7	=	=	PROPN
ejpam-5042	398	8	κ1	κ1	PROPN
ejpam-5042	398	9	∨	∨	NUM
ejpam-5042	398	10	1	1	NUM
ejpam-5042	398	11	=	=	SYM
ejpam-5042	398	12	1	1	NUM
ejpam-5042	398	13	.	.	PUNCT
ejpam-5042	398	14	hence	hence	ADV
ejpam-5042	398	15	,	,	PUNCT
ejpam-5042	398	16	we	we	PRON
ejpam-5042	398	17	get	get	VERB
ejpam-5042	398	18	κ1	κ1	PROPN
ejpam-5042	398	19	∨	∨	NUM
ejpam-5042	398	20	t1	t1	PROPN
ejpam-5042	398	21	∈	∈	PROPN
ejpam-5042	398	22	a•.	a•.	ADV
ejpam-5042	398	23	thus	thus	ADV
ejpam-5042	398	24	,	,	PUNCT
ejpam-5042	398	25	a•	a•	PROPN
ejpam-5042	398	26	is	be	AUX
ejpam-5042	398	27	a	a	DET
ejpam-5042	398	28	filter	filter	NOUN
ejpam-5042	398	29	of	of	ADP
ejpam-5042	398	30	v	v	NOUN
ejpam-5042	398	31	.	.	PUNCT
ejpam-5042	399	1	the	the	DET
ejpam-5042	399	2	filter	filter	NOUN
ejpam-5042	399	3	a•	a•	PROPN
ejpam-5042	399	4	is	be	AUX
ejpam-5042	399	5	called	call	VERB
ejpam-5042	399	6	the	the	DET
ejpam-5042	399	7	annihilator	annihilator	PROPN
ejpam-5042	399	8	filter	filter	NOUN
ejpam-5042	399	9	corresponding	correspond	VERB
ejpam-5042	399	10	to	to	ADP
ejpam-5042	399	11	a.	a.	NOUN
ejpam-5042	399	12	if	if	SCONJ
ejpam-5042	399	13	a	a	PRON
ejpam-5042	399	14	=	=	X
ejpam-5042	399	15	{	{	PUNCT
ejpam-5042	399	16	ρ	ρ	NOUN
ejpam-5042	399	17	}	}	PUNCT
ejpam-5042	399	18	,	,	PUNCT
ejpam-5042	399	19	we	we	PRON
ejpam-5042	399	20	write	write	VERB
ejpam-5042	399	21	a•	a•	NOUN
ejpam-5042	399	22	=	=	PUNCT
ejpam-5042	400	1	[	[	X
ejpam-5042	400	2	ρ]•.	ρ]•.	X
ejpam-5042	400	3	lemma	lemma	PROPN
ejpam-5042	400	4	8	8	NUM
ejpam-5042	400	5	.	.	PUNCT
ejpam-5042	401	1	let	let	VERB
ejpam-5042	401	2	v	v	PART
ejpam-5042	401	3	be	be	AUX
ejpam-5042	401	4	a	a	DET
ejpam-5042	401	5	pdl	pdl	NOUN
ejpam-5042	401	6	.	.	PUNCT
ejpam-5042	402	1	then	then	ADV
ejpam-5042	402	2	for	for	ADP
ejpam-5042	402	3	any	any	DET
ejpam-5042	402	4	ρ	ρ	NOUN
ejpam-5042	402	5	,	,	PUNCT
ejpam-5042	402	6	ϱ	ϱ	PROPN
ejpam-5042	402	7	∈	∈	PROPN
ejpam-5042	402	8	v	v	NOUN
ejpam-5042	402	9	,	,	PUNCT
ejpam-5042	403	1	[	[	X
ejpam-5042	403	2	ρ	ρ	X
ejpam-5042	403	3	∧	∧	NOUN
ejpam-5042	403	4	ϱ]•	ϱ]•	ADP
ejpam-5042	403	5	=	=	PUNCT
ejpam-5042	404	1	[	[	X
ejpam-5042	404	2	ρ]•	ρ]•	NUM
ejpam-5042	404	3	∩	∩	NOUN
ejpam-5042	404	4	[	[	X
ejpam-5042	404	5	ϱ]•.	ϱ]•.	X
ejpam-5042	404	6	proof	proof	NOUN
ejpam-5042	404	7	.	.	PUNCT
ejpam-5042	405	1	let	let	VERB
ejpam-5042	405	2	κ1	κ1	PROPN
ejpam-5042	405	3	∈	∈	PROPN
ejpam-5042	405	4	v	v	NOUN
ejpam-5042	405	5	.	.	PUNCT
ejpam-5042	406	1	then	then	ADV
ejpam-5042	406	2	,	,	PUNCT
ejpam-5042	406	3	κ1	κ1	NOUN
ejpam-5042	406	4	∈	∈	PROPN
ejpam-5042	406	5	[	[	PUNCT
ejpam-5042	406	6	ρ∧	ρ∧	NOUN
ejpam-5042	406	7	ϱ]•	ϱ]•	ADP
ejpam-5042	406	8	⇔	⇔	PROPN
ejpam-5042	406	9	κ1	κ1	PROPN
ejpam-5042	406	10	∨	∨	PROPN
ejpam-5042	406	11	(	(	PUNCT
ejpam-5042	406	12	ρ∧	ρ∧	PROPN
ejpam-5042	406	13	ϱ	ϱ	PROPN
ejpam-5042	406	14	)	)	PUNCT
ejpam-5042	406	15	=	=	SYM
ejpam-5042	406	16	1	1	NUM
ejpam-5042	406	17	⇔	⇔	X
ejpam-5042	406	18	(	(	PUNCT
ejpam-5042	406	19	κ1	κ1	PROPN
ejpam-5042	406	20	∨	∨	NUM
ejpam-5042	406	21	ρ)∧	ρ)∧	PROPN
ejpam-5042	406	22	(	(	PUNCT
ejpam-5042	406	23	κ1	κ1	NOUN
ejpam-5042	406	24	∨	∨	NUM
ejpam-5042	406	25	ϱ	ϱ	PROPN
ejpam-5042	406	26	)	)	PUNCT
ejpam-5042	406	27	=	=	SYM
ejpam-5042	406	28	1	1	NUM
ejpam-5042	406	29	⇔	⇔	PROPN
ejpam-5042	406	30	κ1	κ1	PROPN
ejpam-5042	406	31	∨	∨	NUM
ejpam-5042	406	32	ρ	ρ	X
ejpam-5042	406	33	=	=	SYM
ejpam-5042	406	34	1	1	NUM
ejpam-5042	406	35	and	and	CCONJ
ejpam-5042	406	36	κ1	κ1	NOUN
ejpam-5042	406	37	∨	∨	NUM
ejpam-5042	406	38	ϱ	ϱ	PROPN
ejpam-5042	406	39	=	=	SYM
ejpam-5042	406	40	1	1	NUM
ejpam-5042	406	41	⇔	⇔	PROPN
ejpam-5042	406	42	κ1	κ1	PROPN
ejpam-5042	406	43	∈	∈	PROPN
ejpam-5042	407	1	[	[	X
ejpam-5042	407	2	ρ]•	ρ]•	NUM
ejpam-5042	407	3	and	and	CCONJ
ejpam-5042	407	4	κ1	κ1	NOUN
ejpam-5042	407	5	∈	∈	PROPN
ejpam-5042	407	6	[	[	X
ejpam-5042	407	7	ϱ]•	ϱ]•	ADP
ejpam-5042	407	8	⇔	⇔	PROPN
ejpam-5042	407	9	κ1	κ1	PROPN
ejpam-5042	407	10	∈	∈	PROPN
ejpam-5042	408	1	[	[	X
ejpam-5042	408	2	ρ]•	ρ]•	NUM
ejpam-5042	408	3	∩	∩	NOUN
ejpam-5042	408	4	[	[	X
ejpam-5042	408	5	ϱ]•.	ϱ]•.	X
ejpam-5042	408	6	lemma	lemma	PROPN
ejpam-5042	408	7	9	9	NUM
ejpam-5042	408	8	.	.	PUNCT
ejpam-5042	409	1	let	let	VERB
ejpam-5042	409	2	v	v	PART
ejpam-5042	409	3	be	be	AUX
ejpam-5042	409	4	a	a	DET
ejpam-5042	409	5	pdl	pdl	NOUN
ejpam-5042	409	6	and	and	CCONJ
ejpam-5042	409	7	ρ	ρ	NUM
ejpam-5042	409	8	∈	∈	PROPN
ejpam-5042	409	9	v	v	NOUN
ejpam-5042	409	10	.	.	PUNCT
ejpam-5042	410	1	then	then	ADV
ejpam-5042	410	2	[	[	X
ejpam-5042	410	3	ρ	ρ	X
ejpam-5042	410	4	)	)	PUNCT
ejpam-5042	410	5	=	=	NOUN
ejpam-5042	410	6	v	v	NOUN
ejpam-5042	410	7	if	if	SCONJ
ejpam-5042	411	1	and	and	CCONJ
ejpam-5042	411	2	only	only	ADV
ejpam-5042	411	3	if	if	SCONJ
ejpam-5042	411	4	ρ	ρ	PROPN
ejpam-5042	411	5	is	be	AUX
ejpam-5042	411	6	a	a	DET
ejpam-5042	411	7	minimal	minimal	ADJ
ejpam-5042	411	8	element	element	NOUN
ejpam-5042	411	9	.	.	PUNCT
ejpam-5042	412	1	proof	proof	NOUN
ejpam-5042	412	2	.	.	PUNCT
ejpam-5042	413	1	suppose	suppose	VERB
ejpam-5042	413	2	[	[	X
ejpam-5042	413	3	ρ	ρ	X
ejpam-5042	413	4	)	)	PUNCT
ejpam-5042	413	5	=	=	SYM
ejpam-5042	413	6	v	v	NOUN
ejpam-5042	413	7	.	.	PUNCT
ejpam-5042	414	1	then	then	ADV
ejpam-5042	414	2	,	,	PUNCT
ejpam-5042	414	3	for	for	ADP
ejpam-5042	414	4	any	any	DET
ejpam-5042	414	5	κ1	κ1	NOUN
ejpam-5042	414	6	∈	∈	PROPN
ejpam-5042	414	7	v	v	NOUN
ejpam-5042	414	8	,	,	PUNCT
ejpam-5042	414	9	we	we	PRON
ejpam-5042	414	10	have	have	VERB
ejpam-5042	414	11	κ1	κ1	PROPN
ejpam-5042	414	12	∈	∈	PROPN
ejpam-5042	415	1	[	[	X
ejpam-5042	415	2	ρ	ρ	NOUN
ejpam-5042	415	3	)	)	PUNCT
ejpam-5042	415	4	and	and	CCONJ
ejpam-5042	415	5	hence	hence	ADV
ejpam-5042	415	6	κ1∨ρ	κ1∨ρ	NUM
ejpam-5042	415	7	=	=	SYM
ejpam-5042	415	8	κ1	κ1	PROPN
ejpam-5042	415	9	.	.	PUNCT
ejpam-5042	416	1	therefore	therefore	ADV
ejpam-5042	416	2	,	,	PUNCT
ejpam-5042	416	3	ρ	ρ	PROPN
ejpam-5042	416	4	is	be	AUX
ejpam-5042	416	5	a	a	DET
ejpam-5042	416	6	minimal	minimal	ADJ
ejpam-5042	416	7	element	element	NOUN
ejpam-5042	416	8	.	.	PUNCT
ejpam-5042	417	1	conversely	conversely	ADV
ejpam-5042	417	2	,	,	PUNCT
ejpam-5042	417	3	suppose	suppose	VERB
ejpam-5042	417	4	that	that	SCONJ
ejpam-5042	417	5	ρ	ρ	PROPN
ejpam-5042	417	6	is	be	AUX
ejpam-5042	417	7	a	a	DET
ejpam-5042	417	8	minimal	minimal	ADJ
ejpam-5042	417	9	element	element	NOUN
ejpam-5042	417	10	.	.	PUNCT
ejpam-5042	418	1	we	we	PRON
ejpam-5042	418	2	have	have	VERB
ejpam-5042	418	3	[	[	X
ejpam-5042	418	4	ρ	ρ	NOUN
ejpam-5042	418	5	)	)	PUNCT
ejpam-5042	418	6	⊆	⊆	NUM
ejpam-5042	418	7	v	v	NOUN
ejpam-5042	418	8	.	.	PUNCT
ejpam-5042	419	1	let	let	VERB
ejpam-5042	419	2	κ1	κ1	PROPN
ejpam-5042	419	3	∈	∈	PROPN
ejpam-5042	419	4	v	v	NOUN
ejpam-5042	419	5	.	.	PUNCT
ejpam-5042	420	1	then	then	ADV
ejpam-5042	420	2	κ1	κ1	PROPN
ejpam-5042	420	3	∨	∨	NUM
ejpam-5042	420	4	ρ	ρ	PROPN
ejpam-5042	420	5	=	=	SYM
ejpam-5042	420	6	κ1	κ1	NOUN
ejpam-5042	420	7	.	.	PUNCT
ejpam-5042	421	1	therefore	therefore	ADV
ejpam-5042	421	2	κ1	κ1	PROPN
ejpam-5042	421	3	∈	∈	PROPN
ejpam-5042	422	1	[	[	X
ejpam-5042	422	2	ρ	ρ	NOUN
ejpam-5042	422	3	)	)	PUNCT
ejpam-5042	422	4	.	.	PUNCT
ejpam-5042	423	1	hence	hence	ADV
ejpam-5042	423	2	[	[	X
ejpam-5042	423	3	ρ	ρ	X
ejpam-5042	423	4	)	)	PUNCT
ejpam-5042	423	5	=	=	SYM
ejpam-5042	423	6	v	v	NOUN
ejpam-5042	423	7	.	.	PUNCT
ejpam-5042	424	1	now	now	ADV
ejpam-5042	424	2	,	,	PUNCT
ejpam-5042	424	3	we	we	PRON
ejpam-5042	424	4	prove	prove	VERB
ejpam-5042	424	5	the	the	DET
ejpam-5042	424	6	following	follow	VERB
ejpam-5042	424	7	theorem	theorem	NOUN
ejpam-5042	424	8	which	which	PRON
ejpam-5042	424	9	characterize	characterize	VERB
ejpam-5042	424	10	parapseudo	parapseudo	NOUN
ejpam-5042	424	11	-	-	NOUN
ejpam-5042	424	12	complementation	complementation	NOUN
ejpam-5042	424	13	on	on	ADP
ejpam-5042	424	14	pdl	pdl	PROPN
ejpam-5042	424	15	.	.	PUNCT
ejpam-5042	424	16	theorem	theorem	PROPN
ejpam-5042	424	17	8	8	NUM
ejpam-5042	424	18	.	.	PUNCT
ejpam-5042	425	1	let	let	VERB
ejpam-5042	425	2	v	v	PART
ejpam-5042	425	3	be	be	AUX
ejpam-5042	425	4	a	a	DET
ejpam-5042	425	5	pdl	pdl	NOUN
ejpam-5042	425	6	.	.	PUNCT
ejpam-5042	426	1	then	then	ADV
ejpam-5042	426	2	v	v	NOUN
ejpam-5042	426	3	is	be	AUX
ejpam-5042	426	4	a	a	DET
ejpam-5042	426	5	parapseudo	parapseudo	NOUN
ejpam-5042	426	6	-	-	PUNCT
ejpam-5042	426	7	complemented	complement	VERB
ejpam-5042	426	8	pdl	pdl	NOUN
ejpam-5042	426	9	if	if	SCONJ
ejpam-5042	426	10	and	and	CCONJ
ejpam-5042	426	11	only	only	ADV
ejpam-5042	426	12	if	if	SCONJ
ejpam-5042	426	13	for	for	ADP
ejpam-5042	426	14	any	any	DET
ejpam-5042	426	15	ρ	ρ	PROPN
ejpam-5042	426	16	∈	∈	PROPN
ejpam-5042	426	17	v	v	NOUN
ejpam-5042	426	18	,	,	PUNCT
ejpam-5042	426	19	the	the	DET
ejpam-5042	426	20	annihilator	annihilator	PROPN
ejpam-5042	426	21	filter	filter	NOUN
ejpam-5042	426	22	[	[	X
ejpam-5042	426	23	ρ]•	ρ]•	PROPN
ejpam-5042	426	24	is	be	AUX
ejpam-5042	426	25	a	a	DET
ejpam-5042	426	26	principal	principal	ADJ
ejpam-5042	426	27	filter	filter	NOUN
ejpam-5042	426	28	.	.	PUNCT
ejpam-5042	427	1	proof	proof	NOUN
ejpam-5042	427	2	.	.	PUNCT
ejpam-5042	428	1	let	let	VERB
ejpam-5042	428	2	ρ	ρ	PROPN
ejpam-5042	428	3	∈	∈	PROPN
ejpam-5042	428	4	v	v	AUX
ejpam-5042	428	5	be	be	AUX
ejpam-5042	428	6	such	such	ADJ
ejpam-5042	428	7	that	that	SCONJ
ejpam-5042	429	1	[	[	X
ejpam-5042	429	2	ρ]•	ρ]•	X
ejpam-5042	429	3	=	=	SYM
ejpam-5042	430	1	[	[	X
ejpam-5042	430	2	κ1	κ1	NOUN
ejpam-5042	430	3	)	)	PUNCT
ejpam-5042	430	4	for	for	ADP
ejpam-5042	430	5	some	some	DET
ejpam-5042	430	6	κ1	κ1	NOUN
ejpam-5042	430	7	∈	∈	PROPN
ejpam-5042	430	8	v	v	NOUN
ejpam-5042	430	9	.	.	PUNCT
ejpam-5042	431	1	since	since	SCONJ
ejpam-5042	431	2	1	1	NUM
ejpam-5042	431	3	∈	∈	NOUN
ejpam-5042	431	4	v	v	NOUN
ejpam-5042	431	5	,	,	PUNCT
ejpam-5042	431	6	we	we	PRON
ejpam-5042	431	7	have	have	VERB
ejpam-5042	431	8	v	v	NOUN
ejpam-5042	431	9	=	=	SYM
ejpam-5042	432	1	[	[	X
ejpam-5042	432	2	1]•	1]•	NUM
ejpam-5042	432	3	=	=	PUNCT
ejpam-5042	433	1	[	[	X
ejpam-5042	433	2	m	m	X
ejpam-5042	433	3	)	)	PUNCT
ejpam-5042	433	4	for	for	ADP
ejpam-5042	433	5	some	some	DET
ejpam-5042	433	6	m	m	NOUN
ejpam-5042	433	7	∈	∈	NOUN
ejpam-5042	433	8	v	v	NOUN
ejpam-5042	433	9	.	.	PUNCT
ejpam-5042	434	1	hence	hence	ADV
ejpam-5042	434	2	by	by	ADP
ejpam-5042	434	3	lemma	lemma	PROPN
ejpam-5042	434	4	9	9	NUM
ejpam-5042	434	5	,	,	PUNCT
ejpam-5042	434	6	m	m	VERB
ejpam-5042	434	7	is	be	AUX
ejpam-5042	434	8	a	a	DET
ejpam-5042	434	9	minimal	minimal	ADJ
ejpam-5042	434	10	element	element	NOUN
ejpam-5042	434	11	in	in	ADP
ejpam-5042	434	12	v	v	NUM
ejpam-5042	434	13	.	.	PUNCT
ejpam-5042	435	1	define	define	VERB
ejpam-5042	435	2	ρ	ρ	PROPN
ejpam-5042	435	3	♢	♢	PROPN
ejpam-5042	435	4	=	=	PROPN
ejpam-5042	435	5	m	m	PROPN
ejpam-5042	435	6	∨	∨	NOUN
ejpam-5042	435	7	κ1	κ1	NOUN
ejpam-5042	435	8	.	.	PUNCT
ejpam-5042	436	1	now	now	ADV
ejpam-5042	436	2	,	,	PUNCT
ejpam-5042	436	3	we	we	PRON
ejpam-5042	436	4	prove	prove	VERB
ejpam-5042	436	5	that	that	SCONJ
ejpam-5042	436	6	♢	♢	PROPN
ejpam-5042	436	7	is	be	AUX
ejpam-5042	436	8	a	a	DET
ejpam-5042	436	9	parapseudo	parapseudo	NOUN
ejpam-5042	436	10	-	-	NOUN
ejpam-5042	436	11	complementation	complementation	NOUN
ejpam-5042	436	12	on	on	ADP
ejpam-5042	436	13	v	v	NOUN
ejpam-5042	436	14	.	.	PUNCT
ejpam-5042	437	1	let	let	VERB
ejpam-5042	437	2	ρ	ρ	PROPN
ejpam-5042	437	3	∈	∈	PROPN
ejpam-5042	437	4	v	v	NOUN
ejpam-5042	437	5	and	and	CCONJ
ejpam-5042	437	6	suppose	suppose	VERB
ejpam-5042	438	1	[	[	X
ejpam-5042	438	2	ρ]•	ρ]•	X
ejpam-5042	438	3	=	=	SYM
ejpam-5042	438	4	[	[	X
ejpam-5042	438	5	κ1	κ1	NOUN
ejpam-5042	438	6	)	)	PUNCT
ejpam-5042	438	7	=	=	PUNCT
ejpam-5042	439	1	[	[	X
ejpam-5042	439	2	κ2	κ2	NOUN
ejpam-5042	439	3	)	)	PUNCT
ejpam-5042	439	4	for	for	ADP
ejpam-5042	439	5	some	some	DET
ejpam-5042	439	6	κ1	κ1	NOUN
ejpam-5042	439	7	,	,	PUNCT
ejpam-5042	439	8	κ2	κ2	PROPN
ejpam-5042	439	9	∈	∈	PROPN
ejpam-5042	439	10	v	v	NOUN
ejpam-5042	439	11	.	.	PUNCT
ejpam-5042	440	1	then	then	ADV
ejpam-5042	440	2	κ1	κ1	NOUN
ejpam-5042	440	3	=	=	PUNCT
ejpam-5042	440	4	κ1	κ1	PROPN
ejpam-5042	440	5	∨	∨	NUM
ejpam-5042	440	6	κ2	κ2	PROPN
ejpam-5042	440	7	and	and	CCONJ
ejpam-5042	440	8	κ2	κ2	NOUN
ejpam-5042	440	9	=	=	SYM
ejpam-5042	440	10	κ2	κ2	PROPN
ejpam-5042	440	11	∨	∨	NUM
ejpam-5042	440	12	κ1	κ1	NOUN
ejpam-5042	440	13	.	.	PUNCT
ejpam-5042	441	1	therefore	therefore	ADV
ejpam-5042	441	2	,	,	PUNCT
ejpam-5042	441	3	m∨κ1	m∨κ1	PROPN
ejpam-5042	441	4	=	=	PUNCT
ejpam-5042	441	5	m∨κ1∨κ2	m∨κ1∨κ2	PROPN
ejpam-5042	441	6	=	=	PUNCT
ejpam-5042	441	7	m∨κ2∨κ1	m∨κ2∨κ1	NOUN
ejpam-5042	441	8	=	=	PUNCT
ejpam-5042	441	9	m∨κ2	m∨κ2	NUM
ejpam-5042	441	10	which	which	PRON
ejpam-5042	441	11	implies	imply	VERB
ejpam-5042	441	12	♢	♢	PROPN
ejpam-5042	441	13	is	be	AUX
ejpam-5042	441	14	well	well	ADV
ejpam-5042	441	15	-	-	PUNCT
ejpam-5042	441	16	defined	define	VERB
ejpam-5042	441	17	.	.	PUNCT
ejpam-5042	442	1	let	let	VERB
ejpam-5042	442	2	ρ	ρ	PROPN
ejpam-5042	442	3	∈	∈	PROPN
ejpam-5042	442	4	v	v	NOUN
ejpam-5042	442	5	.	.	PUNCT
ejpam-5042	443	1	then	then	ADV
ejpam-5042	443	2	ρ∨ρ	ρ∨ρ	PROPN
ejpam-5042	443	3	♢	♢	PROPN
ejpam-5042	443	4	=	=	SYM
ejpam-5042	443	5	ρ∨m∨κ1	ρ∨m∨κ1	PROPN
ejpam-5042	443	6	=	=	SYM
ejpam-5042	443	7	ρ∨κ1	ρ∨κ1	PUNCT
ejpam-5042	443	8	=	=	SYM
ejpam-5042	444	1	1	1	X
ejpam-5042	444	2	.	.	PUNCT
ejpam-5042	444	3	let	let	VERB
ejpam-5042	444	4	ϱ	ϱ	ADP
ejpam-5042	444	5	∈	∈	PROPN
ejpam-5042	444	6	v	v	NOUN
ejpam-5042	444	7	and	and	CCONJ
ejpam-5042	444	8	ϱ∨ρ	ϱ∨ρ	NOUN
ejpam-5042	444	9	=	=	SYM
ejpam-5042	444	10	1	1	X
ejpam-5042	444	11	.	.	PUNCT
ejpam-5042	444	12	then	then	ADV
ejpam-5042	444	13	ϱ	ϱ	ADP
ejpam-5042	444	14	∈	∈	PROPN
ejpam-5042	445	1	[	[	X
ejpam-5042	445	2	ρ]•	ρ]•	X
ejpam-5042	445	3	=	=	SYM
ejpam-5042	446	1	[	[	X
ejpam-5042	446	2	κ1	κ1	NOUN
ejpam-5042	446	3	)	)	PUNCT
ejpam-5042	446	4	.	.	PUNCT
ejpam-5042	447	1	therefore	therefore	ADV
ejpam-5042	447	2	,	,	PUNCT
ejpam-5042	447	3	ϱ	ϱ	PROPN
ejpam-5042	447	4	=	=	SYM
ejpam-5042	447	5	ϱ	ϱ	ADP
ejpam-5042	447	6	∨	∨	NUM
ejpam-5042	447	7	κ1	κ1	NOUN
ejpam-5042	447	8	=	=	SYM
ejpam-5042	447	9	ϱ	ϱ	ADP
ejpam-5042	447	10	∨	∨	NUM
ejpam-5042	447	11	m	m	PROPN
ejpam-5042	447	12	∨	∨	NOUN
ejpam-5042	447	13	κ1	κ1	NOUN
ejpam-5042	447	14	=	=	SYM
ejpam-5042	447	15	ϱ	ϱ	ADP
ejpam-5042	447	16	∨	∨	NUM
ejpam-5042	447	17	ρ	ρ	PROPN
ejpam-5042	447	18	♢	♢	PROPN
ejpam-5042	447	19	.	.	PUNCT
ejpam-5042	448	1	finally	finally	ADV
ejpam-5042	448	2	,	,	PUNCT
ejpam-5042	448	3	let	let	VERB
ejpam-5042	448	4	ρ	ρ	NOUN
ejpam-5042	448	5	,	,	PUNCT
ejpam-5042	448	6	ϱ	ϱ	PROPN
ejpam-5042	448	7	∈	∈	PROPN
ejpam-5042	448	8	v	v	NOUN
ejpam-5042	448	9	and	and	CCONJ
ejpam-5042	448	10	[	[	X
ejpam-5042	448	11	ρ]•	ρ]•	X
ejpam-5042	448	12	=	=	SYM
ejpam-5042	449	1	[	[	X
ejpam-5042	449	2	κ1	κ1	NOUN
ejpam-5042	449	3	)	)	PUNCT
ejpam-5042	449	4	,	,	PUNCT
ejpam-5042	450	1	[	[	X
ejpam-5042	450	2	ϱ]•	ϱ]•	X
ejpam-5042	450	3	=	=	PUNCT
ejpam-5042	450	4	[	[	X
ejpam-5042	450	5	κ2	κ2	NOUN
ejpam-5042	450	6	)	)	PUNCT
ejpam-5042	450	7	for	for	ADP
ejpam-5042	450	8	some	some	DET
ejpam-5042	450	9	κ1	κ1	NOUN
ejpam-5042	450	10	,	,	PUNCT
ejpam-5042	450	11	κ2	κ2	PROPN
ejpam-5042	450	12	∈	∈	PROPN
ejpam-5042	450	13	v	v	NOUN
ejpam-5042	450	14	.	.	PUNCT
ejpam-5042	451	1	then	then	ADV
ejpam-5042	451	2	,	,	PUNCT
ejpam-5042	451	3	[	[	X
ejpam-5042	451	4	ρ	ρ	X
ejpam-5042	451	5	∧	∧	NOUN
ejpam-5042	451	6	ϱ]•	ϱ]•	ADP
ejpam-5042	451	7	=	=	PUNCT
ejpam-5042	452	1	[	[	X
ejpam-5042	452	2	ρ]•	ρ]•	NUM
ejpam-5042	452	3	∩	∩	NOUN
ejpam-5042	452	4	[	[	X
ejpam-5042	452	5	ϱ]•	ϱ]•	X
ejpam-5042	452	6	=	=	PUNCT
ejpam-5042	452	7	[	[	X
ejpam-5042	452	8	κ1	κ1	NOUN
ejpam-5042	452	9	)	)	PUNCT
ejpam-5042	452	10	∩	∩	NOUN
ejpam-5042	452	11	[	[	X
ejpam-5042	452	12	κ2	κ2	NOUN
ejpam-5042	452	13	)	)	PUNCT
ejpam-5042	452	14	=	=	PUNCT
ejpam-5042	453	1	[	[	X
ejpam-5042	453	2	κ1	κ1	PROPN
ejpam-5042	453	3	∨	∨	NUM
ejpam-5042	453	4	κ2	κ2	NOUN
ejpam-5042	453	5	)	)	PUNCT
ejpam-5042	453	6	.	.	PUNCT
ejpam-5042	454	1	therefore	therefore	ADV
ejpam-5042	454	2	(	(	PUNCT
ejpam-5042	454	3	ρ∧ϱ	ρ∧ϱ	NUM
ejpam-5042	454	4	)	)	PUNCT
ejpam-5042	454	5	♢	♢	PROPN
ejpam-5042	454	6	=	=	SYM
ejpam-5042	454	7	m∨	m∨	PROPN
ejpam-5042	454	8	(	(	PUNCT
ejpam-5042	454	9	κ1∨κ2	κ1∨κ2	PROPN
ejpam-5042	454	10	)	)	PUNCT
ejpam-5042	454	11	=	=	PRON
ejpam-5042	454	12	(	(	PUNCT
ejpam-5042	454	13	m∨κ1)∨	m∨κ1)∨	PROPN
ejpam-5042	454	14	(	(	PUNCT
ejpam-5042	454	15	m∨κ2	m∨κ2	NOUN
ejpam-5042	454	16	)	)	PUNCT
ejpam-5042	454	17	=	=	SYM
ejpam-5042	454	18	ρ	ρ	NUM
ejpam-5042	454	19	♢	♢	PROPN
ejpam-5042	454	20	∨ϱ	∨ϱ	PROPN
ejpam-5042	454	21	♢	♢	PROPN
ejpam-5042	454	22	.	.	PUNCT
ejpam-5042	455	1	thus	thus	ADV
ejpam-5042	455	2	♢	♢	PROPN
ejpam-5042	455	3	is	be	AUX
ejpam-5042	455	4	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5042	455	5	on	on	ADP
ejpam-5042	455	6	v	v	NUM
ejpam-5042	455	7	.	.	PUNCT
ejpam-5042	456	1	conversely	conversely	ADV
ejpam-5042	456	2	,	,	PUNCT
ejpam-5042	456	3	if	if	SCONJ
ejpam-5042	456	4	v	v	NOUN
ejpam-5042	456	5	is	be	AUX
ejpam-5042	456	6	parapseudo	parapseudo	NOUN
ejpam-5042	456	7	-	-	PUNCT
ejpam-5042	456	8	complemented	complement	VERB
ejpam-5042	456	9	pdl	pdl	NOUN
ejpam-5042	456	10	,	,	PUNCT
ejpam-5042	456	11	then	then	ADV
ejpam-5042	456	12	for	for	ADP
ejpam-5042	456	13	any	any	DET
ejpam-5042	456	14	ρ	ρ	PROPN
ejpam-5042	456	15	∈	∈	PROPN
ejpam-5042	456	16	v	v	NOUN
ejpam-5042	456	17	,	,	PUNCT
ejpam-5042	456	18	we	we	PRON
ejpam-5042	456	19	have	have	VERB
ejpam-5042	456	20	[	[	X
ejpam-5042	456	21	ρ]•	ρ]•	X
ejpam-5042	456	22	=	=	SYM
ejpam-5042	457	1	[	[	X
ejpam-5042	457	2	ρ	ρ	X
ejpam-5042	457	3	♦	♦	PROPN
ejpam-5042	457	4	)	)	PUNCT
ejpam-5042	457	5	.	.	PUNCT
ejpam-5042	458	1	hence	hence	ADV
ejpam-5042	458	2	,	,	PUNCT
ejpam-5042	458	3	every	every	DET
ejpam-5042	458	4	annihilator	annihilator	NOUN
ejpam-5042	458	5	filter	filter	NOUN
ejpam-5042	458	6	is	be	AUX
ejpam-5042	458	7	a	a	DET
ejpam-5042	458	8	principal	principal	ADJ
ejpam-5042	458	9	filter	filter	NOUN
ejpam-5042	458	10	.	.	PUNCT
ejpam-5042	459	1	theorem	theorem	NOUN
ejpam-5042	459	2	9	9	NUM
ejpam-5042	459	3	.	.	PUNCT
ejpam-5042	460	1	let	let	VERB
ejpam-5042	460	2	v	v	PART
ejpam-5042	460	3	be	be	AUX
ejpam-5042	460	4	a	a	DET
ejpam-5042	460	5	pdl	pdl	NOUN
ejpam-5042	460	6	with	with	ADP
ejpam-5042	460	7	a	a	DET
ejpam-5042	460	8	minimal	minimal	ADJ
ejpam-5042	460	9	element	element	NOUN
ejpam-5042	460	10	m.	m.	NOUN
ejpam-5042	460	11	then	then	ADV
ejpam-5042	460	12	v	v	NOUN
ejpam-5042	460	13	is	be	AUX
ejpam-5042	460	14	parapseudocomplemented	parapseudocomplemente	VERB
ejpam-5042	460	15	pdl	pdl	PROPN
ejpam-5042	460	16	if	if	SCONJ
ejpam-5042	460	17	and	and	CCONJ
ejpam-5042	460	18	only	only	ADV
ejpam-5042	460	19	if	if	SCONJ
ejpam-5042	460	20	the	the	DET
ejpam-5042	460	21	set	set	NOUN
ejpam-5042	460	22	pf(v	pf(v	NOUN
ejpam-5042	460	23	)	)	PUNCT
ejpam-5042	460	24	of	of	ADP
ejpam-5042	460	25	all	all	DET
ejpam-5042	460	26	principal	principal	ADJ
ejpam-5042	460	27	filters	filter	NOUN
ejpam-5042	460	28	of	of	ADP
ejpam-5042	460	29	v	v	NOUN
ejpam-5042	460	30	is	be	AUX
ejpam-5042	460	31	a	a	DET
ejpam-5042	460	32	pseudocomplemented	pseudocomplemented	ADJ
ejpam-5042	460	33	lattice	lattice	NOUN
ejpam-5042	460	34	.	.	PUNCT
ejpam-5042	461	1	proof	proof	NOUN
ejpam-5042	461	2	.	.	PUNCT
ejpam-5042	462	1	suppose	suppose	VERB
ejpam-5042	462	2	v	v	NOUN
ejpam-5042	462	3	is	be	AUX
ejpam-5042	462	4	a	a	DET
ejpam-5042	462	5	parapseudo	parapseudo	NOUN
ejpam-5042	462	6	-	-	PUNCT
ejpam-5042	462	7	complemented	complement	VERB
ejpam-5042	462	8	pdl	pdl	NOUN
ejpam-5042	462	9	.	.	PUNCT
ejpam-5042	463	1	then	then	ADV
ejpam-5042	463	2	the	the	DET
ejpam-5042	463	3	set	set	NOUN
ejpam-5042	463	4	pf(v	pf(v	NOUN
ejpam-5042	463	5	)	)	PUNCT
ejpam-5042	463	6	forms	form	VERB
ejpam-5042	463	7	a	a	DET
ejpam-5042	463	8	distributive	distributive	ADJ
ejpam-5042	463	9	lattice	lattice	NOUN
ejpam-5042	463	10	.	.	PUNCT
ejpam-5042	464	1	let	let	VERB
ejpam-5042	464	2	[	[	X
ejpam-5042	464	3	ρ	ρ	NOUN
ejpam-5042	464	4	)	)	PUNCT
ejpam-5042	464	5	∈	∈	PROPN
ejpam-5042	464	6	pf	pf	X
ejpam-5042	464	7	(	(	PUNCT
ejpam-5042	464	8	v	v	NOUN
ejpam-5042	464	9	)	)	PUNCT
ejpam-5042	464	10	.	.	PUNCT
ejpam-5042	465	1	define	define	VERB
ejpam-5042	465	2	[	[	X
ejpam-5042	465	3	ρ	ρ	NOUN
ejpam-5042	465	4	)	)	PUNCT
ejpam-5042	465	5	♢	♢	PROPN
ejpam-5042	465	6	=	=	PUNCT
ejpam-5042	466	1	[	[	X
ejpam-5042	466	2	ρ	ρ	PROPN
ejpam-5042	466	3	♦	♦	PROPN
ejpam-5042	466	4	)	)	PUNCT
ejpam-5042	466	5	where	where	SCONJ
ejpam-5042	466	6	ρ	ρ	PROPN
ejpam-5042	466	7	♦	♦	PROPN
ejpam-5042	466	8	is	be	AUX
ejpam-5042	466	9	the	the	DET
ejpam-5042	466	10	parapseudocomplement	parapseudocomplement	NOUN
ejpam-5042	466	11	of	of	ADP
ejpam-5042	466	12	ρ	ρ	PROPN
ejpam-5042	466	13	∈	∈	PROPN
ejpam-5042	466	14	v	v	NOUN
ejpam-5042	466	15	.	.	PUNCT
ejpam-5042	467	1	we	we	PRON
ejpam-5042	467	2	prove	prove	VERB
ejpam-5042	467	3	that	that	SCONJ
ejpam-5042	467	4	♢	♢	PROPN
ejpam-5042	467	5	is	be	AUX
ejpam-5042	467	6	a	a	DET
ejpam-5042	467	7	pseudo	pseudo	NOUN
ejpam-5042	467	8	-	-	NOUN
ejpam-5042	467	9	complementation	complementation	NOUN
ejpam-5042	467	10	on	on	ADP
ejpam-5042	467	11	pf(v	pf(v	NOUN
ejpam-5042	467	12	)	)	PUNCT
ejpam-5042	467	13	.	.	PUNCT
ejpam-5042	468	1	now	now	ADV
ejpam-5042	468	2	,	,	PUNCT
ejpam-5042	468	3	r.	r.	PROPN
ejpam-5042	468	4	shukla	shukla	PROPN
ejpam-5042	468	5	et	et	PROPN
ejpam-5042	468	6	al	al	PROPN
ejpam-5042	468	7	.	.	PUNCT
ejpam-5042	468	8	/	/	SYM
ejpam-5042	468	9	eur	eur	PROPN
ejpam-5042	468	10	.	.	PUNCT
ejpam-5042	469	1	j.	j.	PROPN
ejpam-5042	469	2	pure	pure	PROPN
ejpam-5042	469	3	appl	appl	PROPN
ejpam-5042	469	4	.	.	PROPN
ejpam-5042	469	5	math	math	PROPN
ejpam-5042	469	6	,	,	PUNCT
ejpam-5042	469	7	17	17	NUM
ejpam-5042	469	8	(	(	PUNCT
ejpam-5042	469	9	2	2	NUM
ejpam-5042	469	10	)	)	PUNCT
ejpam-5042	469	11	(	(	PUNCT
ejpam-5042	469	12	2024	2024	NUM
ejpam-5042	469	13	)	)	PUNCT
ejpam-5042	469	14	,	,	PUNCT
ejpam-5042	469	15	1129	1129	NUM
ejpam-5042	469	16	-	-	SYM
ejpam-5042	469	17	1145	1145	NUM
ejpam-5042	469	18	1140	1140	NUM
ejpam-5042	469	19	[	[	X
ejpam-5042	469	20	ρ	ρ	NOUN
ejpam-5042	469	21	)	)	PUNCT
ejpam-5042	469	22	∩	∩	NOUN
ejpam-5042	469	23	[	[	X
ejpam-5042	469	24	ρ	ρ	X
ejpam-5042	469	25	)	)	PUNCT
ejpam-5042	469	26	♢	♢	PROPN
ejpam-5042	470	1	=	=	X
ejpam-5042	471	1	[	[	X
ejpam-5042	471	2	ρ	ρ	NOUN
ejpam-5042	471	3	)	)	PUNCT
ejpam-5042	471	4	∩	∩	NOUN
ejpam-5042	471	5	[	[	X
ejpam-5042	471	6	ρ	ρ	X
ejpam-5042	471	7	♦	♦	PROPN
ejpam-5042	471	8	)	)	PUNCT
ejpam-5042	471	9	=	=	PUNCT
ejpam-5042	472	1	[	[	X
ejpam-5042	472	2	ρ	ρ	PROPN
ejpam-5042	472	3	∨	∨	PROPN
ejpam-5042	472	4	ρ	ρ	PROPN
ejpam-5042	472	5	♦	♦	PROPN
ejpam-5042	472	6	)	)	PUNCT
ejpam-5042	472	7	=	=	PUNCT
ejpam-5042	473	1	[	[	X
ejpam-5042	473	2	1	1	NUM
ejpam-5042	473	3	)	)	PUNCT
ejpam-5042	473	4	.	.	PUNCT
ejpam-5042	474	1	let	let	VERB
ejpam-5042	474	2	τ	τ	PROPN
ejpam-5042	474	3	∈	∈	PROPN
ejpam-5042	474	4	v	v	NOUN
ejpam-5042	474	5	and	and	CCONJ
ejpam-5042	474	6	[	[	X
ejpam-5042	474	7	ρ	ρ	NOUN
ejpam-5042	474	8	)	)	PUNCT
ejpam-5042	474	9	∩	∩	NOUN
ejpam-5042	474	10	[	[	X
ejpam-5042	474	11	τ	τ	X
ejpam-5042	474	12	)	)	PUNCT
ejpam-5042	474	13	=	=	PUNCT
ejpam-5042	475	1	[	[	X
ejpam-5042	475	2	1	1	NUM
ejpam-5042	475	3	)	)	PUNCT
ejpam-5042	475	4	.	.	PUNCT
ejpam-5042	476	1	then	then	ADV
ejpam-5042	476	2	[	[	X
ejpam-5042	476	3	ρ	ρ	PROPN
ejpam-5042	476	4	∨	∨	NUM
ejpam-5042	476	5	τ	τ	X
ejpam-5042	476	6	)	)	PUNCT
ejpam-5042	476	7	=	=	PUNCT
ejpam-5042	477	1	[	[	X
ejpam-5042	477	2	1	1	NUM
ejpam-5042	477	3	)	)	PUNCT
ejpam-5042	477	4	implies	imply	VERB
ejpam-5042	477	5	ρ	ρ	PROPN
ejpam-5042	477	6	∨	∨	NUM
ejpam-5042	477	7	τ	τ	X
ejpam-5042	477	8	=	=	SYM
ejpam-5042	477	9	1	1	X
ejpam-5042	477	10	.	.	PUNCT
ejpam-5042	478	1	hence	hence	ADV
ejpam-5042	478	2	τ	τ	PROPN
ejpam-5042	478	3	∨	∨	PROPN
ejpam-5042	478	4	ρ	ρ	PROPN
ejpam-5042	478	5	♦	♦	PROPN
ejpam-5042	478	6	=	=	PROPN
ejpam-5042	478	7	τ	τ	PROPN
ejpam-5042	478	8	.	.	PUNCT
ejpam-5042	479	1	therefore	therefore	ADV
ejpam-5042	479	2	,	,	PUNCT
ejpam-5042	479	3	[	[	X
ejpam-5042	479	4	τ	τ	X
ejpam-5042	479	5	)	)	PUNCT
ejpam-5042	479	6	∩	∩	NOUN
ejpam-5042	479	7	[	[	X
ejpam-5042	479	8	ρ	ρ	X
ejpam-5042	479	9	♦	♦	PROPN
ejpam-5042	479	10	)	)	PUNCT
ejpam-5042	479	11	=	=	PUNCT
ejpam-5042	480	1	[	[	X
ejpam-5042	480	2	τ	τ	PROPN
ejpam-5042	480	3	∨	∨	PROPN
ejpam-5042	480	4	ρ	ρ	PROPN
ejpam-5042	480	5	♦	♦	PROPN
ejpam-5042	480	6	)	)	PUNCT
ejpam-5042	480	7	=	=	PUNCT
ejpam-5042	481	1	[	[	X
ejpam-5042	481	2	τ	τ	X
ejpam-5042	481	3	)	)	PUNCT
ejpam-5042	481	4	so	so	SCONJ
ejpam-5042	481	5	that	that	SCONJ
ejpam-5042	482	1	[	[	X
ejpam-5042	482	2	τ	τ	X
ejpam-5042	482	3	)	)	PUNCT
ejpam-5042	482	4	⊆	⊆	NUM
ejpam-5042	482	5	[	[	X
ejpam-5042	482	6	ρ	ρ	X
ejpam-5042	482	7	♦	♦	PROPN
ejpam-5042	482	8	)	)	PUNCT
ejpam-5042	482	9	=	=	PUNCT
ejpam-5042	483	1	[	[	X
ejpam-5042	483	2	ρ)	ρ)	X
ejpam-5042	483	3	♢	♢	PROPN
ejpam-5042	483	4	.	.	PUNCT
ejpam-5042	484	1	thus	thus	ADV
ejpam-5042	484	2	[	[	X
ejpam-5042	484	3	ρ	ρ	X
ejpam-5042	484	4	)	)	PUNCT
ejpam-5042	484	5	♢	♢	PROPN
ejpam-5042	484	6	is	be	AUX
ejpam-5042	484	7	the	the	DET
ejpam-5042	484	8	pseudo	pseudo	NOUN
ejpam-5042	484	9	-	-	NOUN
ejpam-5042	484	10	complement	complement	NOUN
ejpam-5042	484	11	of	of	ADP
ejpam-5042	484	12	[	[	X
ejpam-5042	484	13	ρ	ρ	NOUN
ejpam-5042	484	14	)	)	PUNCT
ejpam-5042	484	15	in	in	ADP
ejpam-5042	484	16	pf(v	pf(v	NOUN
ejpam-5042	484	17	)	)	PUNCT
ejpam-5042	484	18	.	.	PUNCT
ejpam-5042	485	1	conversely	conversely	ADV
ejpam-5042	485	2	,	,	PUNCT
ejpam-5042	485	3	suppose	suppose	VERB
ejpam-5042	485	4	pf(v	pf(v	NOUN
ejpam-5042	485	5	)	)	PUNCT
ejpam-5042	485	6	is	be	AUX
ejpam-5042	485	7	a	a	DET
ejpam-5042	485	8	pseudo	pseudo	NOUN
ejpam-5042	485	9	-	-	ADJ
ejpam-5042	485	10	complemented	complement	VERB
ejpam-5042	485	11	lattice	lattice	NOUN
ejpam-5042	485	12	.	.	PUNCT
ejpam-5042	486	1	let	let	VERB
ejpam-5042	486	2	ρ	ρ	PROPN
ejpam-5042	486	3	∈	∈	PROPN
ejpam-5042	486	4	v	v	NOUN
ejpam-5042	486	5	.	.	PUNCT
ejpam-5042	487	1	then	then	ADV
ejpam-5042	487	2	[	[	X
ejpam-5042	487	3	ρ	ρ	X
ejpam-5042	487	4	)	)	PUNCT
ejpam-5042	487	5	∈	∈	PROPN
ejpam-5042	487	6	pf	pf	X
ejpam-5042	487	7	(	(	PUNCT
ejpam-5042	487	8	v	v	NOUN
ejpam-5042	487	9	)	)	PUNCT
ejpam-5042	487	10	.	.	PUNCT
ejpam-5042	488	1	write	write	VERB
ejpam-5042	488	2	[	[	X
ejpam-5042	488	3	ρ	ρ	NOUN
ejpam-5042	488	4	)	)	PUNCT
ejpam-5042	488	5	♦	♦	PROPN
ejpam-5042	488	6	=	=	PUNCT
ejpam-5042	489	1	[	[	X
ejpam-5042	489	2	ρ1	ρ1	NOUN
ejpam-5042	489	3	)	)	PUNCT
ejpam-5042	489	4	the	the	DET
ejpam-5042	489	5	pseudo	pseudo	NOUN
ejpam-5042	489	6	-	-	NOUN
ejpam-5042	489	7	complement	complement	NOUN
ejpam-5042	489	8	of	of	ADP
ejpam-5042	489	9	[	[	X
ejpam-5042	489	10	ρ	ρ	NOUN
ejpam-5042	489	11	)	)	PUNCT
ejpam-5042	489	12	∈	∈	PROPN
ejpam-5042	489	13	pf	pf	X
ejpam-5042	489	14	(	(	PUNCT
ejpam-5042	489	15	v	v	NOUN
ejpam-5042	489	16	)	)	PUNCT
ejpam-5042	489	17	.	.	PUNCT
ejpam-5042	490	1	now	now	ADV
ejpam-5042	490	2	,	,	PUNCT
ejpam-5042	490	3	define	define	VERB
ejpam-5042	490	4	ρ	ρ	PROPN
ejpam-5042	490	5	♢	♢	PROPN
ejpam-5042	490	6	=	=	PROPN
ejpam-5042	490	7	m	m	PROPN
ejpam-5042	490	8	∨	∨	NUM
ejpam-5042	490	9	ρ1	ρ1	NOUN
ejpam-5042	490	10	.	.	PUNCT
ejpam-5042	491	1	then	then	ADV
ejpam-5042	491	2	we	we	PRON
ejpam-5042	491	3	prove	prove	VERB
ejpam-5042	491	4	that	that	SCONJ
ejpam-5042	491	5	♢	♢	PROPN
ejpam-5042	491	6	is	be	AUX
ejpam-5042	491	7	a	a	DET
ejpam-5042	491	8	parapseudo	parapseudo	NOUN
ejpam-5042	491	9	-	-	NOUN
ejpam-5042	491	10	complementation	complementation	NOUN
ejpam-5042	491	11	on	on	ADP
ejpam-5042	491	12	v	v	NOUN
ejpam-5042	491	13	.	.	PUNCT
ejpam-5042	492	1	first	first	ADV
ejpam-5042	492	2	we	we	PRON
ejpam-5042	492	3	observe	observe	VERB
ejpam-5042	492	4	that	that	SCONJ
ejpam-5042	492	5	♢	♢	PROPN
ejpam-5042	492	6	is	be	AUX
ejpam-5042	492	7	well	well	ADV
ejpam-5042	492	8	defined	define	VERB
ejpam-5042	492	9	.	.	PUNCT
ejpam-5042	493	1	suppose	suppose	VERB
ejpam-5042	494	1	[	[	X
ejpam-5042	494	2	ρ	ρ	NOUN
ejpam-5042	494	3	)	)	PUNCT
ejpam-5042	494	4	♦	♦	PROPN
ejpam-5042	494	5	=	=	PUNCT
ejpam-5042	495	1	[	[	X
ejpam-5042	495	2	ρ1	ρ1	NOUN
ejpam-5042	495	3	)	)	PUNCT
ejpam-5042	495	4	=	=	PUNCT
ejpam-5042	496	1	[	[	X
ejpam-5042	496	2	ρ2	ρ2	NOUN
ejpam-5042	496	3	)	)	PUNCT
ejpam-5042	496	4	.	.	PUNCT
ejpam-5042	497	1	then	then	ADV
ejpam-5042	497	2	m	m	PROPN
ejpam-5042	497	3	∨	∨	NOUN
ejpam-5042	497	4	ρ1	ρ1	NOUN
ejpam-5042	497	5	=	=	SYM
ejpam-5042	497	6	m	m	NOUN
ejpam-5042	497	7	∨	∨	NOUN
ejpam-5042	497	8	ρ1	ρ1	PROPN
ejpam-5042	497	9	∨	∨	NUM
ejpam-5042	497	10	ρ2	ρ2	NOUN
ejpam-5042	497	11	=	=	SYM
ejpam-5042	497	12	m	m	NOUN
ejpam-5042	497	13	∨	∨	NUM
ejpam-5042	497	14	ρ2	ρ2	PROPN
ejpam-5042	497	15	∨	∨	NOUN
ejpam-5042	497	16	ρ1	ρ1	NOUN
ejpam-5042	497	17	=	=	SYM
ejpam-5042	497	18	m	m	NOUN
ejpam-5042	497	19	∨	∨	NUM
ejpam-5042	497	20	ρ2	ρ2	NOUN
ejpam-5042	497	21	.	.	PUNCT
ejpam-5042	498	1	hence	hence	ADV
ejpam-5042	498	2	♢	♢	PROPN
ejpam-5042	498	3	is	be	AUX
ejpam-5042	498	4	well	well	ADV
ejpam-5042	498	5	defined	define	VERB
ejpam-5042	498	6	.	.	PUNCT
ejpam-5042	499	1	now	now	ADV
ejpam-5042	499	2	,	,	PUNCT
ejpam-5042	499	3	ρ	ρ	PROPN
ejpam-5042	499	4	∨	∨	PROPN
ejpam-5042	499	5	ρ	ρ	PROPN
ejpam-5042	499	6	♢	♢	PROPN
ejpam-5042	499	7	=	=	SYM
ejpam-5042	499	8	ρ	ρ	PROPN
ejpam-5042	499	9	∨m	∨m	NOUN
ejpam-5042	499	10	∨	∨	NUM
ejpam-5042	499	11	ρ1	ρ1	NOUN
ejpam-5042	499	12	=	=	SYM
ejpam-5042	499	13	ρ	ρ	PROPN
ejpam-5042	499	14	∨	∨	NOUN
ejpam-5042	499	15	ρ1	ρ1	NOUN
ejpam-5042	499	16	=	=	SYM
ejpam-5042	499	17	1	1	NUM
ejpam-5042	499	18	,	,	PUNCT
ejpam-5042	499	19	since	since	SCONJ
ejpam-5042	499	20	[	[	X
ejpam-5042	499	21	ρ	ρ	PROPN
ejpam-5042	499	22	∨	∨	NUM
ejpam-5042	499	23	ρ1	ρ1	NOUN
ejpam-5042	499	24	)	)	PUNCT
ejpam-5042	499	25	=	=	PUNCT
ejpam-5042	500	1	[	[	X
ejpam-5042	500	2	ρ	ρ	NOUN
ejpam-5042	500	3	)	)	PUNCT
ejpam-5042	500	4	∩	∩	NOUN
ejpam-5042	500	5	[	[	X
ejpam-5042	500	6	ρ1	ρ1	NOUN
ejpam-5042	500	7	)	)	PUNCT
ejpam-5042	500	8	=	=	PUNCT
ejpam-5042	501	1	[	[	X
ejpam-5042	501	2	ρ	ρ	NOUN
ejpam-5042	501	3	)	)	PUNCT
ejpam-5042	501	4	∩	∩	NOUN
ejpam-5042	501	5	[	[	X
ejpam-5042	501	6	ρ	ρ	NOUN
ejpam-5042	501	7	)	)	PUNCT
ejpam-5042	501	8	♦	♦	PROPN
ejpam-5042	501	9	=	=	PUNCT
ejpam-5042	502	1	[	[	X
ejpam-5042	502	2	1	1	NUM
ejpam-5042	502	3	)	)	PUNCT
ejpam-5042	502	4	.	.	PUNCT
ejpam-5042	503	1	let	let	VERB
ejpam-5042	503	2	ϱ	ϱ	ADP
ejpam-5042	503	3	∈	∈	PROPN
ejpam-5042	503	4	v	v	NOUN
ejpam-5042	503	5	and	and	CCONJ
ejpam-5042	503	6	ϱ	ϱ	ADP
ejpam-5042	503	7	∨	∨	NUM
ejpam-5042	503	8	ρ	ρ	NOUN
ejpam-5042	503	9	=	=	SYM
ejpam-5042	503	10	1	1	NUM
ejpam-5042	503	11	.	.	PUNCT
ejpam-5042	504	1	then	then	ADV
ejpam-5042	504	2	,	,	PUNCT
ejpam-5042	504	3	[	[	X
ejpam-5042	504	4	ρ	ρ	NOUN
ejpam-5042	504	5	)	)	PUNCT
ejpam-5042	504	6	∩	∩	NOUN
ejpam-5042	504	7	[	[	X
ejpam-5042	504	8	ϱ	ϱ	NOUN
ejpam-5042	504	9	)	)	PUNCT
ejpam-5042	504	10	=	=	PUNCT
ejpam-5042	505	1	[	[	X
ejpam-5042	505	2	1	1	NUM
ejpam-5042	505	3	)	)	PUNCT
ejpam-5042	505	4	and	and	CCONJ
ejpam-5042	505	5	hence	hence	ADV
ejpam-5042	505	6	[	[	X
ejpam-5042	505	7	ϱ	ϱ	NOUN
ejpam-5042	505	8	)	)	PUNCT
ejpam-5042	505	9	∩	∩	NOUN
ejpam-5042	505	10	[	[	X
ejpam-5042	505	11	ρ	ρ	NOUN
ejpam-5042	505	12	)	)	PUNCT
ejpam-5042	505	13	♦	♦	PROPN
ejpam-5042	505	14	=	=	PUNCT
ejpam-5042	506	1	[	[	X
ejpam-5042	506	2	ϱ	ϱ	NOUN
ejpam-5042	506	3	)	)	PUNCT
ejpam-5042	506	4	.	.	PUNCT
ejpam-5042	507	1	therefore	therefore	ADV
ejpam-5042	507	2	[	[	X
ejpam-5042	507	3	ϱ	ϱ	NOUN
ejpam-5042	507	4	)	)	PUNCT
ejpam-5042	507	5	∩	∩	NOUN
ejpam-5042	507	6	[	[	X
ejpam-5042	507	7	ρ1	ρ1	NOUN
ejpam-5042	507	8	)	)	PUNCT
ejpam-5042	508	1	=	=	PUNCT
ejpam-5042	509	1	[	[	X
ejpam-5042	509	2	ϱ	ϱ	X
ejpam-5042	509	3	)	)	PUNCT
ejpam-5042	509	4	which	which	PRON
ejpam-5042	509	5	implies	imply	VERB
ejpam-5042	509	6	that	that	SCONJ
ejpam-5042	510	1	[	[	X
ejpam-5042	510	2	ϱ	ϱ	NOUN
ejpam-5042	510	3	)	)	PUNCT
ejpam-5042	510	4	⊆	⊆	NUM
ejpam-5042	510	5	[	[	SYM
ejpam-5042	510	6	ρ1	ρ1	NOUN
ejpam-5042	510	7	)	)	PUNCT
ejpam-5042	510	8	.	.	PUNCT
ejpam-5042	511	1	hence	hence	ADV
ejpam-5042	511	2	ϱ	ϱ	ADP
ejpam-5042	511	3	=	=	SYM
ejpam-5042	511	4	ϱ	ϱ	ADP
ejpam-5042	511	5	∨	∨	NUM
ejpam-5042	511	6	ρ1	ρ1	NOUN
ejpam-5042	511	7	=	=	PUNCT
ejpam-5042	511	8	ϱ	ϱ	ADP
ejpam-5042	511	9	∨	∨	NUM
ejpam-5042	511	10	ρ1	ρ1	PROPN
ejpam-5042	511	11	∨	∨	NUM
ejpam-5042	511	12	m	m	NOUN
ejpam-5042	511	13	=	=	SYM
ejpam-5042	511	14	ϱ	ϱ	ADP
ejpam-5042	511	15	∨	∨	NUM
ejpam-5042	511	16	ρ	ρ	PROPN
ejpam-5042	511	17	♢	♢	PROPN
ejpam-5042	511	18	.	.	PUNCT
ejpam-5042	512	1	finally	finally	ADV
ejpam-5042	512	2	,	,	PUNCT
ejpam-5042	512	3	let	let	VERB
ejpam-5042	512	4	ρ	ρ	NOUN
ejpam-5042	512	5	,	,	PUNCT
ejpam-5042	512	6	ϱ	ϱ	PROPN
ejpam-5042	512	7	∈	∈	PROPN
ejpam-5042	512	8	v	v	NOUN
ejpam-5042	512	9	and	and	CCONJ
ejpam-5042	512	10	suppose	suppose	VERB
ejpam-5042	513	1	[	[	X
ejpam-5042	513	2	ρ	ρ	NOUN
ejpam-5042	513	3	)	)	PUNCT
ejpam-5042	513	4	♦	♦	PROPN
ejpam-5042	513	5	=	=	PUNCT
ejpam-5042	514	1	[	[	X
ejpam-5042	514	2	ρ1	ρ1	NOUN
ejpam-5042	514	3	)	)	PUNCT
ejpam-5042	514	4	,	,	PUNCT
ejpam-5042	515	1	[	[	X
ejpam-5042	515	2	ϱ	ϱ	X
ejpam-5042	515	3	)	)	PUNCT
ejpam-5042	515	4	♦	♦	PROPN
ejpam-5042	515	5	=	=	PUNCT
ejpam-5042	516	1	[	[	X
ejpam-5042	516	2	ϱ1	ϱ1	NOUN
ejpam-5042	516	3	)	)	PUNCT
ejpam-5042	516	4	for	for	ADP
ejpam-5042	516	5	some	some	DET
ejpam-5042	516	6	ρ1	ρ1	NOUN
ejpam-5042	516	7	,	,	PUNCT
ejpam-5042	516	8	ϱ1	ϱ1	PROPN
ejpam-5042	516	9	∈	∈	PROPN
ejpam-5042	516	10	v	v	NOUN
ejpam-5042	516	11	.	.	PUNCT
ejpam-5042	517	1	now	now	ADV
ejpam-5042	517	2	,	,	PUNCT
ejpam-5042	517	3	[	[	X
ejpam-5042	517	4	ρ∧ϱ	ρ∧ϱ	X
ejpam-5042	517	5	)	)	PUNCT
ejpam-5042	517	6	♦	♦	PROPN
ejpam-5042	517	7	=	=	PUNCT
ejpam-5042	518	1	[	[	X
ejpam-5042	518	2	ρ)	ρ)	X
ejpam-5042	518	3	♦	♦	PROPN
ejpam-5042	518	4	∩	∩	NOUN
ejpam-5042	518	5	[	[	X
ejpam-5042	518	6	ϱ	ϱ	NOUN
ejpam-5042	518	7	)	)	PUNCT
ejpam-5042	518	8	♦	♦	PROPN
ejpam-5042	518	9	=	=	PUNCT
ejpam-5042	519	1	[	[	X
ejpam-5042	519	2	ρ1)∩	ρ1)∩	X
ejpam-5042	519	3	[	[	X
ejpam-5042	519	4	ϱ1	ϱ1	NOUN
ejpam-5042	519	5	)	)	PUNCT
ejpam-5042	519	6	=	=	PUNCT
ejpam-5042	520	1	[	[	X
ejpam-5042	520	2	ρ1∨ϱ1	ρ1∨ϱ1	NOUN
ejpam-5042	520	3	)	)	PUNCT
ejpam-5042	520	4	.	.	PUNCT
ejpam-5042	521	1	hence	hence	ADV
ejpam-5042	521	2	,	,	PUNCT
ejpam-5042	521	3	by	by	ADP
ejpam-5042	521	4	definition	definition	NOUN
ejpam-5042	521	5	,	,	PUNCT
ejpam-5042	521	6	(	(	PUNCT
ejpam-5042	521	7	ρ∧ϱ	ρ∧ϱ	NUM
ejpam-5042	521	8	)	)	PUNCT
ejpam-5042	521	9	♢	♢	PROPN
ejpam-5042	521	10	=	=	SYM
ejpam-5042	521	11	m∨ρ1∨ϱ1	m∨ρ1∨ϱ1	PROPN
ejpam-5042	521	12	=	=	PUNCT
ejpam-5042	521	13	m	m	PROPN
ejpam-5042	521	14	∨	∨	NOUN
ejpam-5042	521	15	ρ1	ρ1	PROPN
ejpam-5042	521	16	∨m	∨m	NOUN
ejpam-5042	521	17	∨	∨	NUM
ejpam-5042	521	18	ϱ1	ϱ1	PROPN
ejpam-5042	521	19	=	=	SYM
ejpam-5042	521	20	ρ	ρ	PROPN
ejpam-5042	521	21	♢	♢	PROPN
ejpam-5042	521	22	∨	∨	NUM
ejpam-5042	521	23	ϱ	ϱ	PROPN
ejpam-5042	521	24	♢	♢	PROPN
ejpam-5042	521	25	.	.	PUNCT
ejpam-5042	522	1	thus	thus	ADV
ejpam-5042	522	2	♢	♢	PROPN
ejpam-5042	522	3	is	be	AUX
ejpam-5042	522	4	a	a	DET
ejpam-5042	522	5	parapseudo	parapseudo	NOUN
ejpam-5042	522	6	-	-	NOUN
ejpam-5042	522	7	complementation	complementation	NOUN
ejpam-5042	522	8	on	on	ADP
ejpam-5042	522	9	v	v	NOUN
ejpam-5042	522	10	.	.	PUNCT
ejpam-5042	523	1	in	in	ADP
ejpam-5042	523	2	1949	1949	NUM
ejpam-5042	523	3	,	,	PUNCT
ejpam-5042	523	4	p.ribenboim[10	p.ribenboim[10	ADV
ejpam-5042	523	5	]	]	PUNCT
ejpam-5042	523	6	had	have	AUX
ejpam-5042	523	7	first	first	ADV
ejpam-5042	523	8	observed	observe	VERB
ejpam-5042	523	9	that	that	SCONJ
ejpam-5042	523	10	the	the	DET
ejpam-5042	523	11	class	class	NOUN
ejpam-5042	523	12	of	of	ADP
ejpam-5042	523	13	pseudo	pseudo	NOUN
ejpam-5042	523	14	-	-	ADJ
ejpam-5042	523	15	complemented	complement	VERB
ejpam-5042	523	16	distributive	distributive	ADJ
ejpam-5042	523	17	lattices	lattice	NOUN
ejpam-5042	523	18	is	be	AUX
ejpam-5042	523	19	equational	equational	ADJ
ejpam-5042	523	20	.	.	PUNCT
ejpam-5042	524	1	now	now	ADV
ejpam-5042	524	2	,	,	PUNCT
ejpam-5042	524	3	we	we	PRON
ejpam-5042	524	4	prove	prove	VERB
ejpam-5042	524	5	that	that	SCONJ
ejpam-5042	524	6	the	the	DET
ejpam-5042	524	7	parapseudo	parapseudo	NOUN
ejpam-5042	524	8	-	-	NOUN
ejpam-5042	524	9	complementation	complementation	NOUN
ejpam-5042	524	10	on	on	ADP
ejpam-5042	524	11	paradistributive	paradistributive	ADJ
ejpam-5042	524	12	latticoids	latticoid	NOUN
ejpam-5042	524	13	is	be	AUX
ejpam-5042	524	14	also	also	ADV
ejpam-5042	524	15	equationally	equationally	ADV
ejpam-5042	524	16	definable	definable	ADJ
ejpam-5042	524	17	.	.	PUNCT
ejpam-5042	525	1	we	we	PRON
ejpam-5042	525	2	give	give	VERB
ejpam-5042	525	3	certain	certain	ADJ
ejpam-5042	525	4	equivalent	equivalent	ADJ
ejpam-5042	525	5	sets	set	NOUN
ejpam-5042	525	6	of	of	ADP
ejpam-5042	525	7	identities	identity	NOUN
ejpam-5042	525	8	which	which	PRON
ejpam-5042	525	9	characterize	characterize	VERB
ejpam-5042	525	10	the	the	DET
ejpam-5042	525	11	parapseudo	parapseudo	NOUN
ejpam-5042	525	12	-	-	NOUN
ejpam-5042	525	13	complementation	complementation	NOUN
ejpam-5042	525	14	on	on	ADP
ejpam-5042	525	15	v	v	NUM
ejpam-5042	525	16	.	.	PUNCT
ejpam-5042	526	1	for	for	ADP
ejpam-5042	526	2	this	this	PRON
ejpam-5042	526	3	,	,	PUNCT
ejpam-5042	526	4	first	first	ADV
ejpam-5042	526	5	we	we	PRON
ejpam-5042	526	6	need	need	VERB
ejpam-5042	526	7	the	the	DET
ejpam-5042	526	8	following	follow	VERB
ejpam-5042	526	9	lemmas	lemmas	NOUN
ejpam-5042	526	10	.	.	PUNCT
ejpam-5042	527	1	as	as	SCONJ
ejpam-5042	527	2	there	there	PRON
ejpam-5042	527	3	are	be	VERB
ejpam-5042	527	4	no	no	DET
ejpam-5042	527	5	hidden	hidden	ADJ
ejpam-5042	527	6	difficulties	difficulty	NOUN
ejpam-5042	527	7	to	to	PART
ejpam-5042	527	8	prove	prove	VERB
ejpam-5042	527	9	the	the	DET
ejpam-5042	527	10	following	follow	VERB
ejpam-5042	527	11	two	two	NUM
ejpam-5042	527	12	lemmas	lemma	NOUN
ejpam-5042	527	13	,	,	PUNCT
ejpam-5042	527	14	we	we	PRON
ejpam-5042	527	15	omit	omit	VERB
ejpam-5042	527	16	their	their	PRON
ejpam-5042	527	17	proofs	proof	NOUN
ejpam-5042	527	18	.	.	PUNCT
ejpam-5042	528	1	lemma	lemma	PROPN
ejpam-5042	528	2	10	10	NUM
ejpam-5042	528	3	.	.	PUNCT
ejpam-5042	529	1	let	let	VERB
ejpam-5042	529	2	v	v	PART
ejpam-5042	529	3	be	be	AUX
ejpam-5042	529	4	a	a	DET
ejpam-5042	529	5	parapseudo	parapseudo	NOUN
ejpam-5042	529	6	-	-	PUNCT
ejpam-5042	529	7	complemented	complement	VERB
ejpam-5042	529	8	pdl	pdl	NOUN
ejpam-5042	529	9	.	.	PUNCT
ejpam-5042	530	1	then	then	ADV
ejpam-5042	530	2	for	for	ADP
ejpam-5042	530	3	any	any	DET
ejpam-5042	530	4	ρ	ρ	NOUN
ejpam-5042	530	5	,	,	PUNCT
ejpam-5042	530	6	ϱ	ϱ	PROPN
ejpam-5042	530	7	∈	∈	PROPN
ejpam-5042	530	8	v	v	NOUN
ejpam-5042	530	9	,	,	PUNCT
ejpam-5042	530	10	the	the	DET
ejpam-5042	530	11	following	follow	VERB
ejpam-5042	530	12	are	be	AUX
ejpam-5042	530	13	equivalent	equivalent	ADJ
ejpam-5042	530	14	:	:	PUNCT
ejpam-5042	530	15	(	(	PUNCT
ejpam-5042	530	16	1	1	NUM
ejpam-5042	530	17	)	)	PUNCT
ejpam-5042	530	18	.	.	PUNCT
ejpam-5042	531	1	ρ	ρ	PROPN
ejpam-5042	531	2	∨	∨	NUM
ejpam-5042	531	3	ϱ	ϱ	ADP
ejpam-5042	531	4	=	=	SYM
ejpam-5042	531	5	1	1	NUM
ejpam-5042	531	6	.	.	PUNCT
ejpam-5042	531	7	(	(	PUNCT
ejpam-5042	531	8	2	2	NUM
ejpam-5042	531	9	)	)	PUNCT
ejpam-5042	531	10	.	.	PUNCT
ejpam-5042	532	1	ρ	ρ	PROPN
ejpam-5042	532	2	∨	∨	NUM
ejpam-5042	532	3	ϱ	ϱ	PROPN
ejpam-5042	532	4	♦	♦	PROPN
ejpam-5042	532	5	♦	♦	PROPN
ejpam-5042	532	6	=	=	PROPN
ejpam-5042	533	1	1	1	PROPN
ejpam-5042	533	2	.	.	PUNCT
ejpam-5042	533	3	(	(	PUNCT
ejpam-5042	533	4	3	3	NUM
ejpam-5042	533	5	)	)	PUNCT
ejpam-5042	533	6	.	.	PUNCT
ejpam-5042	534	1	ρ	ρ	PROPN
ejpam-5042	534	2	♦	♦	PROPN
ejpam-5042	534	3	♦	♦	PROPN
ejpam-5042	534	4	∨	∨	NUM
ejpam-5042	534	5	ϱ	ϱ	PROPN
ejpam-5042	534	6	♦	♦	PROPN
ejpam-5042	534	7	♦	♦	PROPN
ejpam-5042	534	8	=	=	PROPN
ejpam-5042	534	9	1	1	PROPN
ejpam-5042	534	10	.	.	PUNCT
ejpam-5042	535	1	(	(	PUNCT
ejpam-5042	535	2	4	4	NUM
ejpam-5042	535	3	)	)	PUNCT
ejpam-5042	535	4	.	.	PUNCT
ejpam-5042	536	1	ρ	ρ	PROPN
ejpam-5042	536	2	∨	∨	NUM
ejpam-5042	536	3	ϱ	ϱ	PROPN
ejpam-5042	536	4	♦	♦	PROPN
ejpam-5042	536	5	♦	♦	PROPN
ejpam-5042	536	6	=	=	PROPN
ejpam-5042	537	1	1	1	X
ejpam-5042	537	2	.	.	PUNCT
ejpam-5042	537	3	lemma	lemma	PROPN
ejpam-5042	537	4	11	11	NUM
ejpam-5042	537	5	.	.	PUNCT
ejpam-5042	538	1	let	let	VERB
ejpam-5042	538	2	v	v	PART
ejpam-5042	538	3	be	be	AUX
ejpam-5042	538	4	a	a	DET
ejpam-5042	538	5	parapseudo	parapseudo	NOUN
ejpam-5042	538	6	-	-	PUNCT
ejpam-5042	538	7	complemented	complement	VERB
ejpam-5042	538	8	pdl	pdl	NOUN
ejpam-5042	538	9	.	.	PUNCT
ejpam-5042	539	1	then	then	ADV
ejpam-5042	539	2	for	for	ADP
ejpam-5042	539	3	any	any	DET
ejpam-5042	539	4	ρ	ρ	NOUN
ejpam-5042	539	5	,	,	PUNCT
ejpam-5042	539	6	ϱ	ϱ	PROPN
ejpam-5042	539	7	∈	∈	PROPN
ejpam-5042	539	8	v	v	NOUN
ejpam-5042	539	9	,	,	PUNCT
ejpam-5042	539	10	the	the	DET
ejpam-5042	539	11	following	follow	VERB
ejpam-5042	539	12	hold	hold	NOUN
ejpam-5042	539	13	:	:	PUNCT
ejpam-5042	539	14	(	(	PUNCT
ejpam-5042	539	15	1	1	NUM
ejpam-5042	539	16	)	)	PUNCT
ejpam-5042	539	17	.	.	PUNCT
ejpam-5042	540	1	(	(	PUNCT
ejpam-5042	540	2	ρ	ρ	PROPN
ejpam-5042	540	3	∨	∨	NUM
ejpam-5042	540	4	ϱ	ϱ	PROPN
ejpam-5042	540	5	)	)	PUNCT
ejpam-5042	540	6	♦	♦	PROPN
ejpam-5042	540	7	♦	♦	PROPN
ejpam-5042	540	8	=	=	PROPN
ejpam-5042	540	9	ρ	ρ	PROPN
ejpam-5042	540	10	♦	♦	PROPN
ejpam-5042	540	11	♦	♦	PROPN
ejpam-5042	540	12	∨	∨	NUM
ejpam-5042	540	13	ϱ	ϱ	PROPN
ejpam-5042	540	14	♦	♦	PROPN
ejpam-5042	540	15	♦	♦	PROPN
ejpam-5042	540	16	.	.	PUNCT
ejpam-5042	541	1	(	(	PUNCT
ejpam-5042	541	2	2	2	NUM
ejpam-5042	541	3	)	)	PUNCT
ejpam-5042	541	4	.	.	PUNCT
ejpam-5042	542	1	(	(	PUNCT
ejpam-5042	542	2	ρ	ρ	PROPN
ejpam-5042	542	3	∨	∨	NUM
ejpam-5042	542	4	ϱ	ϱ	PROPN
ejpam-5042	542	5	)	)	PUNCT
ejpam-5042	542	6	♦	♦	PROPN
ejpam-5042	542	7	=	=	PROPN
ejpam-5042	542	8	(	(	PUNCT
ejpam-5042	542	9	ϱ	ϱ	ADP
ejpam-5042	542	10	∨	∨	NUM
ejpam-5042	542	11	ρ)	ρ)	NUM
ejpam-5042	542	12	♦	♦	PROPN
ejpam-5042	542	13	.	.	PUNCT
ejpam-5042	543	1	(	(	PUNCT
ejpam-5042	543	2	3	3	NUM
ejpam-5042	543	3	)	)	PUNCT
ejpam-5042	543	4	.	.	PUNCT
ejpam-5042	544	1	(	(	PUNCT
ejpam-5042	544	2	ρ	ρ	PROPN
ejpam-5042	544	3	∧	∧	PROPN
ejpam-5042	544	4	ϱ	ϱ	NOUN
ejpam-5042	544	5	)	)	PUNCT
ejpam-5042	544	6	♦	♦	PROPN
ejpam-5042	544	7	=	=	PROPN
ejpam-5042	544	8	(	(	PUNCT
ejpam-5042	544	9	ϱ	ϱ	PROPN
ejpam-5042	544	10	∧	∧	PROPN
ejpam-5042	544	11	ρ)	ρ)	NUM
ejpam-5042	544	12	♦	♦	PROPN
ejpam-5042	544	13	.	.	PUNCT
ejpam-5042	545	1	now	now	ADV
ejpam-5042	545	2	,	,	PUNCT
ejpam-5042	545	3	we	we	PRON
ejpam-5042	545	4	prove	prove	VERB
ejpam-5042	545	5	that	that	SCONJ
ejpam-5042	545	6	the	the	DET
ejpam-5042	545	7	parapseudo	parapseudo	NOUN
ejpam-5042	545	8	-	-	PUNCT
ejpam-5042	545	9	complementation	complementation	NOUN
ejpam-5042	545	10	pdl	pdl	NOUN
ejpam-5042	545	11	is	be	AUX
ejpam-5042	545	12	equationally	equationally	ADV
ejpam-5042	545	13	definable	definable	ADJ
ejpam-5042	545	14	.	.	PUNCT
ejpam-5042	546	1	lemma	lemma	PROPN
ejpam-5042	546	2	12	12	NUM
ejpam-5042	546	3	.	.	PUNCT
ejpam-5042	547	1	a	a	DET
ejpam-5042	547	2	unary	unary	ADJ
ejpam-5042	547	3	operation	operation	NOUN
ejpam-5042	547	4	♦	♦	PROPN
ejpam-5042	547	5	on	on	ADP
ejpam-5042	547	6	pdl	pdl	PROPN
ejpam-5042	547	7	v	v	PROPN
ejpam-5042	547	8	is	be	AUX
ejpam-5042	547	9	a	a	DET
ejpam-5042	547	10	parapseudo	parapseudo	NOUN
ejpam-5042	547	11	-	-	NOUN
ejpam-5042	547	12	complementation	complementation	NOUN
ejpam-5042	547	13	on	on	ADP
ejpam-5042	547	14	v	v	PRON
ejpam-5042	547	15	if	if	SCONJ
ejpam-5042	548	1	and	and	CCONJ
ejpam-5042	548	2	only	only	ADV
ejpam-5042	548	3	if	if	SCONJ
ejpam-5042	548	4	it	it	PRON
ejpam-5042	548	5	satisfies	satisfy	VERB
ejpam-5042	548	6	the	the	DET
ejpam-5042	548	7	following	follow	VERB
ejpam-5042	548	8	equations	equation	NOUN
ejpam-5042	548	9	:	:	PUNCT
ejpam-5042	548	10	(	(	PUNCT
ejpam-5042	548	11	1	1	NUM
ejpam-5042	548	12	)	)	PUNCT
ejpam-5042	548	13	.	.	PUNCT
ejpam-5042	549	1	ρ	ρ	PROPN
ejpam-5042	549	2	∨	∨	NUM
ejpam-5042	549	3	ρ	ρ	PROPN
ejpam-5042	549	4	♦	♦	PROPN
ejpam-5042	549	5	=	=	PROPN
ejpam-5042	549	6	1	1	PROPN
ejpam-5042	549	7	.	.	PUNCT
ejpam-5042	549	8	(	(	PUNCT
ejpam-5042	549	9	2	2	NUM
ejpam-5042	549	10	)	)	PUNCT
ejpam-5042	549	11	.	.	PUNCT
ejpam-5042	550	1	ρ	ρ	PROPN
ejpam-5042	550	2	∧	∧	PROPN
ejpam-5042	550	3	ρ	ρ	PROPN
ejpam-5042	550	4	♦	♦	PROPN
ejpam-5042	550	5	♦	♦	PROPN
ejpam-5042	550	6	=	=	PROPN
ejpam-5042	550	7	ρ	ρ	PROPN
ejpam-5042	550	8	♦	♦	PROPN
ejpam-5042	550	9	♦	♦	PROPN
ejpam-5042	550	10	.	.	PUNCT
ejpam-5042	551	1	(	(	PUNCT
ejpam-5042	551	2	3	3	NUM
ejpam-5042	551	3	)	)	PUNCT
ejpam-5042	551	4	.	.	PUNCT
ejpam-5042	552	1	(	(	PUNCT
ejpam-5042	552	2	ρ	ρ	PROPN
ejpam-5042	552	3	∧	∧	PROPN
ejpam-5042	552	4	ϱ	ϱ	NOUN
ejpam-5042	552	5	)	)	PUNCT
ejpam-5042	552	6	♦	♦	PROPN
ejpam-5042	552	7	=	=	PROPN
ejpam-5042	552	8	ρ	ρ	PROPN
ejpam-5042	552	9	♦	♦	PROPN
ejpam-5042	552	10	∨	∨	NUM
ejpam-5042	552	11	ϱ	ϱ	PROPN
ejpam-5042	552	12	♦	♦	PROPN
ejpam-5042	552	13	.	.	PUNCT
ejpam-5042	553	1	(	(	PUNCT
ejpam-5042	553	2	4	4	NUM
ejpam-5042	553	3	)	)	PUNCT
ejpam-5042	553	4	.	.	PUNCT
ejpam-5042	554	1	(	(	PUNCT
ejpam-5042	554	2	ρ	ρ	PROPN
ejpam-5042	554	3	∨	∨	NUM
ejpam-5042	554	4	ϱ	ϱ	PROPN
ejpam-5042	554	5	)	)	PUNCT
ejpam-5042	554	6	♦	♦	PROPN
ejpam-5042	554	7	♦	♦	PROPN
ejpam-5042	554	8	=	=	PROPN
ejpam-5042	554	9	ρ	ρ	PROPN
ejpam-5042	554	10	♦	♦	PROPN
ejpam-5042	554	11	♦	♦	PROPN
ejpam-5042	554	12	∨	∨	NUM
ejpam-5042	554	13	ϱ	ϱ	PROPN
ejpam-5042	554	14	♦	♦	PROPN
ejpam-5042	554	15	♦	♦	PROPN
ejpam-5042	554	16	.	.	PUNCT
ejpam-5042	555	1	(	(	PUNCT
ejpam-5042	555	2	5	5	NUM
ejpam-5042	555	3	)	)	PUNCT
ejpam-5042	555	4	.	.	PUNCT
ejpam-5042	556	1	ρ	ρ	PROPN
ejpam-5042	556	2	∨	∨	NUM
ejpam-5042	556	3	1	1	NUM
ejpam-5042	556	4	♦	♦	PROPN
ejpam-5042	556	5	=	=	PROPN
ejpam-5042	556	6	ρ	ρ	PROPN
ejpam-5042	556	7	.	.	PUNCT
ejpam-5042	556	8	r.	r.	PROPN
ejpam-5042	556	9	shukla	shukla	PROPN
ejpam-5042	556	10	et	et	PROPN
ejpam-5042	556	11	al	al	PROPN
ejpam-5042	556	12	.	.	PUNCT
ejpam-5042	556	13	/	/	SYM
ejpam-5042	556	14	eur	eur	PROPN
ejpam-5042	556	15	.	.	PUNCT
ejpam-5042	557	1	j.	j.	PROPN
ejpam-5042	557	2	pure	pure	PROPN
ejpam-5042	557	3	appl	appl	PROPN
ejpam-5042	557	4	.	.	PROPN
ejpam-5042	557	5	math	math	PROPN
ejpam-5042	557	6	,	,	PUNCT
ejpam-5042	557	7	17	17	NUM
ejpam-5042	557	8	(	(	PUNCT
ejpam-5042	557	9	2	2	NUM
ejpam-5042	557	10	)	)	PUNCT
ejpam-5042	557	11	(	(	PUNCT
ejpam-5042	557	12	2024	2024	NUM
ejpam-5042	557	13	)	)	PUNCT
ejpam-5042	557	14	,	,	PUNCT
ejpam-5042	557	15	1129	1129	NUM
ejpam-5042	557	16	-	-	SYM
ejpam-5042	557	17	1145	1145	NUM
ejpam-5042	557	18	1141	1141	NUM
ejpam-5042	557	19	proof	proof	NOUN
ejpam-5042	557	20	.	.	PUNCT
ejpam-5042	558	1	let	let	VERB
ejpam-5042	558	2	v	v	PART
ejpam-5042	558	3	be	be	AUX
ejpam-5042	558	4	a	a	DET
ejpam-5042	558	5	pdl	pdl	NOUN
ejpam-5042	558	6	and	and	CCONJ
ejpam-5042	558	7	♦	♦	PROPN
ejpam-5042	558	8	be	be	AUX
ejpam-5042	558	9	a	a	DET
ejpam-5042	558	10	unary	unary	ADJ
ejpam-5042	558	11	operation	operation	NOUN
ejpam-5042	558	12	on	on	ADP
ejpam-5042	558	13	v	v	NUM
ejpam-5042	558	14	satisfying	satisfy	VERB
ejpam-5042	558	15	the	the	DET
ejpam-5042	558	16	given	give	VERB
ejpam-5042	558	17	conditions	condition	NOUN
ejpam-5042	558	18	.	.	PUNCT
ejpam-5042	559	1	we	we	PRON
ejpam-5042	559	2	prove	prove	VERB
ejpam-5042	559	3	that	that	SCONJ
ejpam-5042	559	4	♦	♦	PROPN
ejpam-5042	559	5	is	be	AUX
ejpam-5042	559	6	a	a	DET
ejpam-5042	559	7	parapseudo	parapseudo	NOUN
ejpam-5042	559	8	-	-	NOUN
ejpam-5042	559	9	complementation	complementation	NOUN
ejpam-5042	559	10	on	on	ADP
ejpam-5042	559	11	v	v	NOUN
ejpam-5042	559	12	.	.	PUNCT
ejpam-5042	560	1	let	let	VERB
ejpam-5042	560	2	ρ	ρ	NOUN
ejpam-5042	560	3	,	,	PUNCT
ejpam-5042	560	4	ϱ	ϱ	PROPN
ejpam-5042	560	5	∈	∈	PROPN
ejpam-5042	560	6	v	v	NOUN
ejpam-5042	560	7	and	and	CCONJ
ejpam-5042	560	8	ϱ∨ρ	ϱ∨ρ	NOUN
ejpam-5042	560	9	=	=	SYM
ejpam-5042	560	10	1	1	X
ejpam-5042	560	11	.	.	PUNCT
ejpam-5042	561	1	then	then	ADV
ejpam-5042	561	2	,	,	PUNCT
ejpam-5042	561	3	ϱ	ϱ	PROPN
ejpam-5042	561	4	=	=	SYM
ejpam-5042	561	5	ϱ	ϱ	ADP
ejpam-5042	561	6	∨	∨	NUM
ejpam-5042	561	7	ϱ	ϱ	PROPN
ejpam-5042	561	8	♦	♦	PROPN
ejpam-5042	561	9	♦	♦	PROPN
ejpam-5042	561	10	(	(	PUNCT
ejpam-5042	561	11	by	by	ADP
ejpam-5042	561	12	(	(	PUNCT
ejpam-5042	561	13	2	2	NUM
ejpam-5042	561	14	)	)	PUNCT
ejpam-5042	561	15	)	)	PUNCT
ejpam-5042	562	1	=	=	PUNCT
ejpam-5042	562	2	ϱ	ϱ	ADP
ejpam-5042	562	3	∨	∨	NUM
ejpam-5042	562	4	1	1	NUM
ejpam-5042	562	5	♦	♦	PROPN
ejpam-5042	562	6	∨	∨	NUM
ejpam-5042	562	7	ϱ	ϱ	PROPN
ejpam-5042	562	8	♦	♦	PROPN
ejpam-5042	562	9	♦	♦	PROPN
ejpam-5042	562	10	(	(	PUNCT
ejpam-5042	562	11	by	by	ADP
ejpam-5042	562	12	(	(	PUNCT
ejpam-5042	562	13	5	5	NUM
ejpam-5042	562	14	)	)	PUNCT
ejpam-5042	562	15	)	)	PUNCT
ejpam-5042	562	16	=	=	PUNCT
ejpam-5042	562	17	ϱ	ϱ	ADP
ejpam-5042	562	18	∨	∨	NUM
ejpam-5042	562	19	(	(	PUNCT
ejpam-5042	562	20	ρ	ρ	PROPN
ejpam-5042	562	21	♦	♦	PROPN
ejpam-5042	562	22	∨	∨	PROPN
ejpam-5042	562	23	ρ	ρ	PROPN
ejpam-5042	562	24	♦	♦	PROPN
ejpam-5042	562	25	♦	♦	PROPN
ejpam-5042	562	26	)	)	PUNCT
ejpam-5042	563	1	♦	♦	PROPN
ejpam-5042	563	2	∨	∨	NUM
ejpam-5042	563	3	ϱ	ϱ	PROPN
ejpam-5042	563	4	♦	♦	PROPN
ejpam-5042	563	5	♦	♦	PROPN
ejpam-5042	563	6	(	(	PUNCT
ejpam-5042	563	7	by	by	ADP
ejpam-5042	563	8	(	(	PUNCT
ejpam-5042	563	9	1	1	NUM
ejpam-5042	563	10	)	)	PUNCT
ejpam-5042	563	11	)	)	PUNCT
ejpam-5042	564	1	=	=	PUNCT
ejpam-5042	564	2	ϱ	ϱ	ADP
ejpam-5042	564	3	∨	∨	NUM
ejpam-5042	564	4	(	(	PUNCT
ejpam-5042	564	5	ρ	ρ	PROPN
ejpam-5042	564	6	∧	∧	PROPN
ejpam-5042	564	7	ρ	ρ	PROPN
ejpam-5042	564	8	♦	♦	PROPN
ejpam-5042	564	9	)	)	PUNCT
ejpam-5042	564	10	♦	♦	PROPN
ejpam-5042	564	11	♦	♦	PROPN
ejpam-5042	564	12	∨	∨	PROPN
ejpam-5042	564	13	ϱ	ϱ	PROPN
ejpam-5042	564	14	♦	♦	PROPN
ejpam-5042	564	15	♦	♦	PROPN
ejpam-5042	564	16	(	(	PUNCT
ejpam-5042	564	17	by	by	ADP
ejpam-5042	564	18	(	(	PUNCT
ejpam-5042	564	19	3	3	NUM
ejpam-5042	564	20	)	)	PUNCT
ejpam-5042	564	21	)	)	PUNCT
ejpam-5042	565	1	=	=	PUNCT
ejpam-5042	566	1	ϱ	ϱ	ADP
ejpam-5042	566	2	∨	∨	NUM
ejpam-5042	566	3	(	(	PUNCT
ejpam-5042	566	4	(	(	PUNCT
ejpam-5042	566	5	ρ	ρ	PROPN
ejpam-5042	566	6	∧	∧	PROPN
ejpam-5042	566	7	ρ	ρ	PROPN
ejpam-5042	566	8	♦	♦	PROPN
ejpam-5042	566	9	)	)	PUNCT
ejpam-5042	566	10	∨	∨	NUM
ejpam-5042	566	11	ϱ	ϱ	PROPN
ejpam-5042	566	12	)	)	PUNCT
ejpam-5042	566	13	♦	♦	PROPN
ejpam-5042	566	14	♦	♦	PROPN
ejpam-5042	566	15	(	(	PUNCT
ejpam-5042	566	16	by	by	ADP
ejpam-5042	566	17	(	(	PUNCT
ejpam-5042	566	18	4	4	NUM
ejpam-5042	566	19	)	)	PUNCT
ejpam-5042	566	20	)	)	PUNCT
ejpam-5042	566	21	=	=	PUNCT
ejpam-5042	566	22	ϱ	ϱ	ADP
ejpam-5042	566	23	∨	∨	NUM
ejpam-5042	566	24	(	(	PUNCT
ejpam-5042	566	25	(	(	PUNCT
ejpam-5042	566	26	ρ	ρ	PROPN
ejpam-5042	566	27	∨	∨	NUM
ejpam-5042	566	28	ϱ	ϱ	NOUN
ejpam-5042	566	29	)	)	PUNCT
ejpam-5042	566	30	∧	∧	PROPN
ejpam-5042	566	31	(	(	PUNCT
ejpam-5042	566	32	ρ	ρ	PROPN
ejpam-5042	566	33	♦	♦	PROPN
ejpam-5042	566	34	∨	∨	NUM
ejpam-5042	566	35	ϱ	ϱ	PROPN
ejpam-5042	566	36	)	)	PUNCT
ejpam-5042	566	37	)	)	PUNCT
ejpam-5042	566	38	♦	♦	PROPN
ejpam-5042	566	39	♦	♦	PROPN
ejpam-5042	566	40	=	=	PROPN
ejpam-5042	566	41	ϱ	ϱ	PROPN
ejpam-5042	566	42	∨	∨	NUM
ejpam-5042	566	43	(	(	PUNCT
ejpam-5042	566	44	ρ	ρ	PROPN
ejpam-5042	566	45	♦	♦	PROPN
ejpam-5042	566	46	∨	∨	NUM
ejpam-5042	566	47	ϱ	ϱ	PROPN
ejpam-5042	566	48	)	)	PUNCT
ejpam-5042	566	49	♦	♦	PROPN
ejpam-5042	566	50	♦	♦	PROPN
ejpam-5042	566	51	=	=	PROPN
ejpam-5042	566	52	ϱ	ϱ	PROPN
ejpam-5042	566	53	∨	∨	NUM
ejpam-5042	566	54	ρ	ρ	PROPN
ejpam-5042	566	55	♦	♦	PROPN
ejpam-5042	566	56	♦	♦	PROPN
ejpam-5042	566	57	♦	♦	PROPN
ejpam-5042	566	58	∨	∨	NUM
ejpam-5042	566	59	ϱ	ϱ	PROPN
ejpam-5042	566	60	♦	♦	PROPN
ejpam-5042	566	61	♦	♦	PROPN
ejpam-5042	566	62	(	(	PUNCT
ejpam-5042	566	63	by	by	ADP
ejpam-5042	566	64	(	(	PUNCT
ejpam-5042	566	65	4	4	NUM
ejpam-5042	566	66	)	)	PUNCT
ejpam-5042	566	67	)	)	PUNCT
ejpam-5042	566	68	=	=	PUNCT
ejpam-5042	566	69	ϱ	ϱ	ADP
ejpam-5042	566	70	∨	∨	NUM
ejpam-5042	566	71	ρ	ρ	PROPN
ejpam-5042	566	72	♦	♦	PROPN
ejpam-5042	566	73	∨	∨	NUM
ejpam-5042	566	74	ϱ	ϱ	PROPN
ejpam-5042	566	75	♦	♦	PROPN
ejpam-5042	566	76	♦	♦	PROPN
ejpam-5042	566	77	(	(	PUNCT
ejpam-5042	566	78	by	by	ADP
ejpam-5042	566	79	(	(	PUNCT
ejpam-5042	566	80	2	2	NUM
ejpam-5042	566	81	)	)	PUNCT
ejpam-5042	566	82	)	)	PUNCT
ejpam-5042	566	83	=	=	PUNCT
ejpam-5042	566	84	ϱ	ϱ	ADP
ejpam-5042	566	85	∨	∨	NUM
ejpam-5042	566	86	ϱ	ϱ	PROPN
ejpam-5042	566	87	♦	♦	PROPN
ejpam-5042	566	88	♦	♦	PROPN
ejpam-5042	566	89	∨	∨	PROPN
ejpam-5042	566	90	ρ	ρ	PROPN
ejpam-5042	566	91	♦	♦	PROPN
ejpam-5042	566	92	(	(	PUNCT
ejpam-5042	566	93	by	by	ADP
ejpam-5042	566	94	(	(	PUNCT
ejpam-5042	566	95	3	3	NUM
ejpam-5042	566	96	)	)	PUNCT
ejpam-5042	566	97	)	)	PUNCT
ejpam-5042	566	98	=	=	PUNCT
ejpam-5042	566	99	ϱ	ϱ	ADP
ejpam-5042	566	100	∨	∨	NUM
ejpam-5042	566	101	ρ	ρ	PROPN
ejpam-5042	566	102	♦	♦	PROPN
ejpam-5042	566	103	(	(	PUNCT
ejpam-5042	566	104	by	by	ADP
ejpam-5042	566	105	(	(	PUNCT
ejpam-5042	566	106	2	2	NUM
ejpam-5042	566	107	)	)	PUNCT
ejpam-5042	566	108	)	)	PUNCT
ejpam-5042	566	109	therefore	therefore	ADV
ejpam-5042	566	110	,	,	PUNCT
ejpam-5042	566	111	it	it	PRON
ejpam-5042	566	112	follows	follow	VERB
ejpam-5042	566	113	from	from	ADP
ejpam-5042	566	114	(	(	PUNCT
ejpam-5042	566	115	1	1	NUM
ejpam-5042	566	116	)	)	PUNCT
ejpam-5042	566	117	and	and	CCONJ
ejpam-5042	566	118	(	(	PUNCT
ejpam-5042	566	119	3	3	X
ejpam-5042	566	120	)	)	PUNCT
ejpam-5042	566	121	that	that	SCONJ
ejpam-5042	566	122	♦	♦	PROPN
ejpam-5042	566	123	is	be	AUX
ejpam-5042	566	124	a	a	DET
ejpam-5042	566	125	parapseudo	parapseudo	NOUN
ejpam-5042	566	126	-	-	NOUN
ejpam-5042	566	127	complementation	complementation	NOUN
ejpam-5042	566	128	on	on	ADP
ejpam-5042	566	129	v	v	NUM
ejpam-5042	566	130	.	.	PUNCT
ejpam-5042	567	1	converse	converse	NOUN
ejpam-5042	567	2	follows	follow	VERB
ejpam-5042	567	3	from	from	ADP
ejpam-5042	567	4	lemma	lemma	PROPN
ejpam-5042	567	5	10	10	NUM
ejpam-5042	567	6	and	and	CCONJ
ejpam-5042	567	7	lemma	lemma	PROPN
ejpam-5042	567	8	11	11	NUM
ejpam-5042	567	9	.	.	PUNCT
ejpam-5042	568	1	lemma	lemma	PROPN
ejpam-5042	568	2	13	13	NUM
ejpam-5042	568	3	.	.	PUNCT
ejpam-5042	569	1	a	a	DET
ejpam-5042	569	2	unary	unary	ADJ
ejpam-5042	569	3	operation	operation	NOUN
ejpam-5042	569	4	♦	♦	PROPN
ejpam-5042	569	5	on	on	ADP
ejpam-5042	569	6	pdl	pdl	PROPN
ejpam-5042	569	7	v	v	PROPN
ejpam-5042	569	8	is	be	AUX
ejpam-5042	569	9	a	a	DET
ejpam-5042	569	10	parapseudo	parapseudo	NOUN
ejpam-5042	569	11	-	-	NOUN
ejpam-5042	569	12	complementation	complementation	NOUN
ejpam-5042	569	13	on	on	ADP
ejpam-5042	569	14	v	v	PRON
ejpam-5042	569	15	if	if	SCONJ
ejpam-5042	570	1	and	and	CCONJ
ejpam-5042	570	2	only	only	ADV
ejpam-5042	570	3	if	if	SCONJ
ejpam-5042	570	4	it	it	PRON
ejpam-5042	570	5	satisfies	satisfy	VERB
ejpam-5042	570	6	the	the	DET
ejpam-5042	570	7	following	follow	VERB
ejpam-5042	570	8	equations	equation	NOUN
ejpam-5042	570	9	:	:	PUNCT
ejpam-5042	570	10	(	(	PUNCT
ejpam-5042	570	11	1	1	NUM
ejpam-5042	570	12	)	)	PUNCT
ejpam-5042	570	13	.	.	PUNCT
ejpam-5042	571	1	ϱ	ϱ	ADP
ejpam-5042	571	2	∨	∨	NUM
ejpam-5042	571	3	ρ	ρ	PROPN
ejpam-5042	571	4	♦	♦	PROPN
ejpam-5042	571	5	=	=	PROPN
ejpam-5042	571	6	ϱ	ϱ	ADP
ejpam-5042	571	7	∨	∨	NUM
ejpam-5042	571	8	(	(	PUNCT
ejpam-5042	571	9	ρ	ρ	PROPN
ejpam-5042	571	10	∨	∨	NUM
ejpam-5042	571	11	ϱ)	ϱ)	PROPN
ejpam-5042	571	12	♦	♦	PROPN
ejpam-5042	571	13	.	.	PUNCT
ejpam-5042	572	1	(	(	PUNCT
ejpam-5042	572	2	2	2	NUM
ejpam-5042	572	3	)	)	PUNCT
ejpam-5042	572	4	.	.	PUNCT
ejpam-5042	573	1	ρ	ρ	PROPN
ejpam-5042	573	2	∨	∨	NUM
ejpam-5042	573	3	1	1	NUM
ejpam-5042	573	4	♦	♦	PROPN
ejpam-5042	573	5	=	=	PROPN
ejpam-5042	573	6	ρ	ρ	PROPN
ejpam-5042	573	7	.	.	PUNCT
ejpam-5042	574	1	(	(	PUNCT
ejpam-5042	574	2	3	3	NUM
ejpam-5042	574	3	)	)	PUNCT
ejpam-5042	574	4	.	.	PUNCT
ejpam-5042	575	1	1	1	NUM
ejpam-5042	575	2	♦	♦	PROPN
ejpam-5042	575	3	♦	♦	PROPN
ejpam-5042	575	4	=	=	PROPN
ejpam-5042	575	5	1	1	PROPN
ejpam-5042	575	6	.	.	PUNCT
ejpam-5042	575	7	(	(	PUNCT
ejpam-5042	575	8	4	4	NUM
ejpam-5042	575	9	)	)	PUNCT
ejpam-5042	575	10	.	.	PUNCT
ejpam-5042	576	1	(	(	PUNCT
ejpam-5042	576	2	ρ	ρ	PROPN
ejpam-5042	576	3	∧	∧	PROPN
ejpam-5042	576	4	ϱ	ϱ	NOUN
ejpam-5042	576	5	)	)	PUNCT
ejpam-5042	576	6	♦	♦	PROPN
ejpam-5042	576	7	=	=	PROPN
ejpam-5042	576	8	ρ	ρ	PROPN
ejpam-5042	576	9	♦	♦	PROPN
ejpam-5042	576	10	∨	∨	NUM
ejpam-5042	576	11	ϱ	ϱ	PROPN
ejpam-5042	576	12	♦	♦	PROPN
ejpam-5042	576	13	.	.	PUNCT
ejpam-5042	577	1	proof	proof	NOUN
ejpam-5042	577	2	.	.	PUNCT
ejpam-5042	578	1	let	let	VERB
ejpam-5042	578	2	v	v	PART
ejpam-5042	578	3	be	be	AUX
ejpam-5042	578	4	a	a	DET
ejpam-5042	578	5	pdl	pdl	NOUN
ejpam-5042	578	6	and	and	CCONJ
ejpam-5042	578	7	♦	♦	PROPN
ejpam-5042	578	8	be	be	AUX
ejpam-5042	578	9	a	a	DET
ejpam-5042	578	10	unary	unary	ADJ
ejpam-5042	578	11	operation	operation	NOUN
ejpam-5042	578	12	on	on	ADP
ejpam-5042	578	13	v	v	NUM
ejpam-5042	578	14	satisfying	satisfy	VERB
ejpam-5042	578	15	the	the	DET
ejpam-5042	578	16	given	give	VERB
ejpam-5042	578	17	equations	equation	NOUN
ejpam-5042	578	18	.	.	PUNCT
ejpam-5042	579	1	we	we	PRON
ejpam-5042	579	2	prove	prove	VERB
ejpam-5042	579	3	♦	♦	PROPN
ejpam-5042	579	4	is	be	AUX
ejpam-5042	579	5	a	a	DET
ejpam-5042	579	6	parapseudo	parapseudo	NOUN
ejpam-5042	579	7	-	-	NOUN
ejpam-5042	579	8	complementation	complementation	NOUN
ejpam-5042	579	9	on	on	ADP
ejpam-5042	579	10	v	v	NOUN
ejpam-5042	579	11	.	.	PUNCT
ejpam-5042	580	1	let	let	VERB
ejpam-5042	580	2	ρ	ρ	NOUN
ejpam-5042	580	3	,	,	PUNCT
ejpam-5042	580	4	ϱ	ϱ	PROPN
ejpam-5042	580	5	∈	∈	PROPN
ejpam-5042	580	6	v	v	NOUN
ejpam-5042	580	7	and	and	CCONJ
ejpam-5042	580	8	ϱ	ϱ	ADP
ejpam-5042	580	9	∨	∨	NUM
ejpam-5042	580	10	ρ	ρ	NOUN
ejpam-5042	580	11	=	=	SYM
ejpam-5042	580	12	1	1	NUM
ejpam-5042	580	13	.	.	PUNCT
ejpam-5042	580	14	then	then	ADV
ejpam-5042	580	15	ϱ	ϱ	ADP
ejpam-5042	580	16	∨	∨	NUM
ejpam-5042	580	17	ρ	ρ	PROPN
ejpam-5042	580	18	♦	♦	PROPN
ejpam-5042	580	19	=	=	PROPN
ejpam-5042	580	20	ϱ	ϱ	ADP
ejpam-5042	580	21	∨	∨	NUM
ejpam-5042	580	22	(	(	PUNCT
ejpam-5042	580	23	ρ	ρ	PROPN
ejpam-5042	580	24	∨	∨	NUM
ejpam-5042	580	25	ϱ	ϱ	PROPN
ejpam-5042	580	26	)	)	PUNCT
ejpam-5042	580	27	♦	♦	PROPN
ejpam-5042	580	28	=	=	PROPN
ejpam-5042	580	29	ϱ	ϱ	ADP
ejpam-5042	580	30	∨	∨	NUM
ejpam-5042	580	31	1	1	NUM
ejpam-5042	580	32	♦	♦	PROPN
ejpam-5042	580	33	=	=	PROPN
ejpam-5042	581	1	ϱ.	ϱ.	PROPN
ejpam-5042	582	1	now	now	ADV
ejpam-5042	582	2	ρ	ρ	PROPN
ejpam-5042	582	3	∨	∨	NUM
ejpam-5042	582	4	ρ	ρ	PROPN
ejpam-5042	582	5	♦	♦	PROPN
ejpam-5042	582	6	=	=	PROPN
ejpam-5042	582	7	ρ	ρ	PROPN
ejpam-5042	582	8	∨	∨	X
ejpam-5042	582	9	(	(	PUNCT
ejpam-5042	582	10	ρ	ρ	PROPN
ejpam-5042	582	11	∨	∨	PROPN
ejpam-5042	582	12	1	1	NUM
ejpam-5042	582	13	♦	♦	PROPN
ejpam-5042	582	14	)	)	PUNCT
ejpam-5042	582	15	♦	♦	PROPN
ejpam-5042	582	16	=	=	PROPN
ejpam-5042	582	17	ρ	ρ	PROPN
ejpam-5042	582	18	∨	∨	X
ejpam-5042	582	19	(	(	PUNCT
ejpam-5042	582	20	1	1	NUM
ejpam-5042	582	21	♦	♦	PROPN
ejpam-5042	582	22	∨	∨	PROPN
ejpam-5042	582	23	ρ	ρ	PROPN
ejpam-5042	582	24	)	)	PUNCT
ejpam-5042	582	25	♦	♦	PROPN
ejpam-5042	582	26	=	=	PROPN
ejpam-5042	582	27	ρ	ρ	PROPN
ejpam-5042	582	28	∨	∨	PROPN
ejpam-5042	583	1	1	1	NUM
ejpam-5042	583	2	♦	♦	PROPN
ejpam-5042	583	3	♦	♦	PROPN
ejpam-5042	583	4	=	=	PROPN
ejpam-5042	583	5	ρ	ρ	PROPN
ejpam-5042	583	6	∨	∨	NUM
ejpam-5042	583	7	1	1	NUM
ejpam-5042	583	8	=	=	SYM
ejpam-5042	583	9	1	1	NUM
ejpam-5042	583	10	shows	show	VERB
ejpam-5042	583	11	that	that	SCONJ
ejpam-5042	583	12	♦	♦	PROPN
ejpam-5042	583	13	is	be	AUX
ejpam-5042	583	14	a	a	DET
ejpam-5042	583	15	parapseudo	parapseudo	NOUN
ejpam-5042	583	16	-	-	NOUN
ejpam-5042	583	17	complementation	complementation	NOUN
ejpam-5042	583	18	on	on	ADP
ejpam-5042	583	19	v	v	NUM
ejpam-5042	583	20	.	.	PUNCT
ejpam-5042	584	1	conversely	conversely	ADV
ejpam-5042	584	2	,	,	PUNCT
ejpam-5042	584	3	assume	assume	VERB
ejpam-5042	584	4	that	that	SCONJ
ejpam-5042	584	5	♦	♦	PROPN
ejpam-5042	584	6	is	be	AUX
ejpam-5042	584	7	a	a	DET
ejpam-5042	584	8	parapseudo	parapseudo	NOUN
ejpam-5042	584	9	-	-	NOUN
ejpam-5042	584	10	complementation	complementation	NOUN
ejpam-5042	584	11	on	on	ADP
ejpam-5042	584	12	v	v	NOUN
ejpam-5042	584	13	.	.	PUNCT
ejpam-5042	585	1	then	then	ADV
ejpam-5042	585	2	,	,	PUNCT
ejpam-5042	585	3	by	by	ADP
ejpam-5042	585	4	lemma	lemma	PROPN
ejpam-5042	585	5	5	5	NUM
ejpam-5042	585	6	and	and	CCONJ
ejpam-5042	585	7	by	by	ADP
ejpam-5042	585	8	definition	definition	NOUN
ejpam-5042	585	9	5	5	NUM
ejpam-5042	585	10	we	we	PRON
ejpam-5042	585	11	have	have	VERB
ejpam-5042	585	12	(	(	PUNCT
ejpam-5042	585	13	2	2	NUM
ejpam-5042	585	14	)	)	PUNCT
ejpam-5042	585	15	,	,	PUNCT
ejpam-5042	585	16	(	(	PUNCT
ejpam-5042	585	17	3	3	NUM
ejpam-5042	585	18	)	)	PUNCT
ejpam-5042	585	19	,	,	PUNCT
ejpam-5042	585	20	(	(	PUNCT
ejpam-5042	585	21	4	4	NUM
ejpam-5042	585	22	)	)	PUNCT
ejpam-5042	585	23	.	.	PUNCT
ejpam-5042	586	1	so	so	ADV
ejpam-5042	586	2	,	,	PUNCT
ejpam-5042	586	3	it	it	PRON
ejpam-5042	586	4	is	be	AUX
ejpam-5042	586	5	enough	enough	ADJ
ejpam-5042	586	6	if	if	SCONJ
ejpam-5042	586	7	we	we	PRON
ejpam-5042	586	8	prove	prove	VERB
ejpam-5042	586	9	(	(	PUNCT
ejpam-5042	586	10	1	1	NUM
ejpam-5042	586	11	)	)	PUNCT
ejpam-5042	586	12	.	.	PUNCT
ejpam-5042	587	1	for	for	ADP
ejpam-5042	587	2	this	this	PRON
ejpam-5042	587	3	,	,	PUNCT
ejpam-5042	587	4	let	let	VERB
ejpam-5042	587	5	ρ	ρ	NOUN
ejpam-5042	587	6	,	,	PUNCT
ejpam-5042	587	7	ϱ	ϱ	PROPN
ejpam-5042	587	8	∈	∈	PROPN
ejpam-5042	587	9	v	v	NOUN
ejpam-5042	587	10	.	.	PUNCT
ejpam-5042	588	1	then	then	ADV
ejpam-5042	588	2	ρ	ρ	PROPN
ejpam-5042	588	3	∨	∨	PROPN
ejpam-5042	588	4	ϱ	ϱ	ADP
ejpam-5042	588	5	∨	∨	NUM
ejpam-5042	588	6	(	(	PUNCT
ejpam-5042	588	7	ρ	ρ	PROPN
ejpam-5042	588	8	∨	∨	NUM
ejpam-5042	588	9	ϱ	ϱ	PROPN
ejpam-5042	588	10	)	)	PUNCT
ejpam-5042	588	11	♦	♦	PROPN
ejpam-5042	588	12	=	=	SYM
ejpam-5042	588	13	1	1	NUM
ejpam-5042	588	14	⇒	⇒	NOUN
ejpam-5042	588	15	ϱ	ϱ	ADP
ejpam-5042	588	16	∨	∨	PROPN
ejpam-5042	588	17	(	(	PUNCT
ejpam-5042	588	18	ρ	ρ	PROPN
ejpam-5042	588	19	∨	∨	NUM
ejpam-5042	588	20	ϱ	ϱ	NOUN
ejpam-5042	588	21	)	)	PUNCT
ejpam-5042	588	22	♦	♦	PROPN
ejpam-5042	588	23	∨	∨	PROPN
ejpam-5042	588	24	ρ	ρ	PROPN
ejpam-5042	588	25	♦	♦	PROPN
ejpam-5042	588	26	=	=	PROPN
ejpam-5042	588	27	ϱ	ϱ	ADP
ejpam-5042	588	28	∨	∨	NUM
ejpam-5042	588	29	(	(	PUNCT
ejpam-5042	588	30	ρ	ρ	PROPN
ejpam-5042	588	31	∨	∨	NUM
ejpam-5042	588	32	ϱ	ϱ	NOUN
ejpam-5042	588	33	)	)	PUNCT
ejpam-5042	588	34	♦	♦	PROPN
ejpam-5042	588	35	⇒	⇒	NOUN
ejpam-5042	588	36	ϱ	ϱ	PROPN
ejpam-5042	588	37	∨	∨	PROPN
ejpam-5042	588	38	ρ	ρ	PROPN
ejpam-5042	588	39	♦	♦	PROPN
ejpam-5042	588	40	∨	∨	PROPN
ejpam-5042	588	41	(	(	PUNCT
ejpam-5042	588	42	ρ	ρ	PROPN
ejpam-5042	588	43	∨	∨	NUM
ejpam-5042	588	44	ϱ	ϱ	PROPN
ejpam-5042	588	45	)	)	PUNCT
ejpam-5042	588	46	♦	♦	PROPN
ejpam-5042	588	47	=	=	PROPN
ejpam-5042	588	48	ϱ	ϱ	ADP
ejpam-5042	588	49	∨	∨	NUM
ejpam-5042	588	50	(	(	PUNCT
ejpam-5042	588	51	ρ	ρ	PROPN
ejpam-5042	588	52	∨	∨	NUM
ejpam-5042	588	53	ϱ	ϱ	NOUN
ejpam-5042	588	54	)	)	PUNCT
ejpam-5042	588	55	♦	♦	PROPN
ejpam-5042	588	56	⇒	⇒	NOUN
ejpam-5042	588	57	ϱ	ϱ	PROPN
ejpam-5042	588	58	∨	∨	NUM
ejpam-5042	588	59	ρ	ρ	PROPN
ejpam-5042	588	60	♦	♦	PROPN
ejpam-5042	588	61	=	=	PROPN
ejpam-5042	588	62	ϱ	ϱ	ADP
ejpam-5042	588	63	∨	∨	NUM
ejpam-5042	588	64	(	(	PUNCT
ejpam-5042	588	65	ρ	ρ	PROPN
ejpam-5042	588	66	∨	∨	NUM
ejpam-5042	588	67	ϱ	ϱ	PROPN
ejpam-5042	588	68	)	)	PUNCT
ejpam-5042	588	69	♦	♦	PROPN
ejpam-5042	588	70	r.	r.	PROPN
ejpam-5042	588	71	shukla	shukla	PROPN
ejpam-5042	588	72	et	et	PROPN
ejpam-5042	588	73	al	al	PROPN
ejpam-5042	588	74	.	.	PUNCT
ejpam-5042	588	75	/	/	SYM
ejpam-5042	588	76	eur	eur	PROPN
ejpam-5042	588	77	.	.	PUNCT
ejpam-5042	589	1	j.	j.	PROPN
ejpam-5042	589	2	pure	pure	PROPN
ejpam-5042	589	3	appl	appl	PROPN
ejpam-5042	589	4	.	.	PROPN
ejpam-5042	589	5	math	math	PROPN
ejpam-5042	589	6	,	,	PUNCT
ejpam-5042	589	7	17	17	NUM
ejpam-5042	589	8	(	(	PUNCT
ejpam-5042	589	9	2	2	NUM
ejpam-5042	589	10	)	)	PUNCT
ejpam-5042	589	11	(	(	PUNCT
ejpam-5042	589	12	2024	2024	NUM
ejpam-5042	589	13	)	)	PUNCT
ejpam-5042	589	14	,	,	PUNCT
ejpam-5042	589	15	1129	1129	NUM
ejpam-5042	589	16	-	-	SYM
ejpam-5042	589	17	1145	1145	NUM
ejpam-5042	589	18	1142	1142	NUM
ejpam-5042	589	19	5	5	NUM
ejpam-5042	589	20	.	.	PUNCT
ejpam-5042	590	1	one	one	NUM
ejpam-5042	590	2	to	to	ADP
ejpam-5042	590	3	one	one	NUM
ejpam-5042	590	4	correspondence	correspondence	NOUN
ejpam-5042	590	5	in	in	ADP
ejpam-5042	590	6	this	this	DET
ejpam-5042	590	7	section	section	NOUN
ejpam-5042	590	8	,	,	PUNCT
ejpam-5042	590	9	we	we	PRON
ejpam-5042	590	10	prove	prove	VERB
ejpam-5042	590	11	that	that	SCONJ
ejpam-5042	590	12	,	,	PUNCT
ejpam-5042	590	13	if	if	SCONJ
ejpam-5042	590	14	♦	♦	PROPN
ejpam-5042	590	15	is	be	AUX
ejpam-5042	590	16	a	a	DET
ejpam-5042	590	17	parapseudo	parapseudo	NOUN
ejpam-5042	590	18	-	-	NOUN
ejpam-5042	590	19	complementation	complementation	NOUN
ejpam-5042	590	20	on	on	ADP
ejpam-5042	590	21	v	v	NUM
ejpam-5042	590	22	,	,	PUNCT
ejpam-5042	590	23	then	then	ADV
ejpam-5042	590	24	the	the	DET
ejpam-5042	590	25	set	set	NOUN
ejpam-5042	590	26	v	v	ADP
ejpam-5042	590	27	♦	♦	PROPN
ejpam-5042	590	28	=	=	PROPN
ejpam-5042	590	29	{	{	PUNCT
ejpam-5042	590	30	ρ	ρ	PROPN
ejpam-5042	590	31	♦	♦	PROPN
ejpam-5042	590	32	|	|	PROPN
ejpam-5042	590	33	ρ	ρ	PROPN
ejpam-5042	590	34	∈	∈	PROPN
ejpam-5042	590	35	v	v	NOUN
ejpam-5042	590	36	}	}	PUNCT
ejpam-5042	590	37	is	be	AUX
ejpam-5042	590	38	a	a	DET
ejpam-5042	590	39	boolean	boolean	ADJ
ejpam-5042	590	40	algebra	algebra	NOUN
ejpam-5042	590	41	.	.	PUNCT
ejpam-5042	591	1	furthermore	furthermore	ADV
ejpam-5042	591	2	,	,	PUNCT
ejpam-5042	591	3	there	there	PRON
ejpam-5042	591	4	exists	exist	VERB
ejpam-5042	591	5	a	a	DET
ejpam-5042	591	6	one	one	NUM
ejpam-5042	591	7	-	-	PUNCT
ejpam-5042	591	8	to	to	ADP
ejpam-5042	591	9	-	-	PUNCT
ejpam-5042	591	10	one	one	NUM
ejpam-5042	591	11	correspondence	correspondence	NOUN
ejpam-5042	591	12	between	between	ADP
ejpam-5042	591	13	the	the	DET
ejpam-5042	591	14	set	set	NOUN
ejpam-5042	591	15	of	of	ADP
ejpam-5042	591	16	all	all	DET
ejpam-5042	591	17	minimal	minimal	ADJ
ejpam-5042	591	18	elements	element	NOUN
ejpam-5042	591	19	of	of	ADP
ejpam-5042	591	20	v	v	NOUN
ejpam-5042	591	21	and	and	CCONJ
ejpam-5042	591	22	the	the	DET
ejpam-5042	591	23	set	set	NOUN
ejpam-5042	591	24	of	of	ADP
ejpam-5042	591	25	all	all	DET
ejpam-5042	591	26	parapseudocomplementations	parapseudocomplementation	NOUN
ejpam-5042	591	27	on	on	ADP
ejpam-5042	591	28	v	v	NOUN
ejpam-5042	591	29	.	.	PUNCT
ejpam-5042	592	1	finally	finally	ADV
ejpam-5042	592	2	,	,	PUNCT
ejpam-5042	592	3	it	it	PRON
ejpam-5042	592	4	is	be	AUX
ejpam-5042	592	5	worth	worth	ADJ
ejpam-5042	592	6	noting	note	VERB
ejpam-5042	592	7	that	that	SCONJ
ejpam-5042	592	8	the	the	DET
ejpam-5042	592	9	boolean	boolean	ADJ
ejpam-5042	592	10	algebra	algebra	NOUN
ejpam-5042	592	11	v	v	ADP
ejpam-5042	592	12	♦	♦	PROPN
ejpam-5042	592	13	is	be	AUX
ejpam-5042	592	14	independent	independent	ADJ
ejpam-5042	592	15	of	of	ADP
ejpam-5042	592	16	the	the	DET
ejpam-5042	592	17	specific	specific	ADJ
ejpam-5042	592	18	choice	choice	NOUN
ejpam-5042	592	19	of	of	ADP
ejpam-5042	592	20	parapseudo	parapseudo	NOUN
ejpam-5042	592	21	-	-	PUNCT
ejpam-5042	592	22	complementation	complementation	NOUN
ejpam-5042	592	23	♦	♦	PROPN
ejpam-5042	592	24	.	.	PUNCT
ejpam-5042	593	1	theorem	theorem	VERB
ejpam-5042	593	2	10	10	NUM
ejpam-5042	593	3	.	.	PUNCT
ejpam-5042	594	1	let	let	VERB
ejpam-5042	594	2	v	v	PART
ejpam-5042	594	3	be	be	AUX
ejpam-5042	594	4	a	a	DET
ejpam-5042	594	5	pdl	pdl	NOUN
ejpam-5042	594	6	with	with	ADP
ejpam-5042	594	7	a	a	DET
ejpam-5042	594	8	parapseudo	parapseudo	NOUN
ejpam-5042	594	9	-	-	PUNCT
ejpam-5042	594	10	complementation	complementation	NOUN
ejpam-5042	594	11	♦	♦	PROPN
ejpam-5042	594	12	.	.	PUNCT
ejpam-5042	595	1	for	for	ADP
ejpam-5042	595	2	any	any	DET
ejpam-5042	595	3	ρ	ρ	PROPN
ejpam-5042	595	4	♦	♦	PROPN
ejpam-5042	595	5	,	,	PUNCT
ejpam-5042	595	6	ϱ	ϱ	PROPN
ejpam-5042	595	7	♦	♦	PROPN
ejpam-5042	595	8	∈	∈	PROPN
ejpam-5042	595	9	v	v	ADP
ejpam-5042	595	10	♦	♦	PROPN
ejpam-5042	595	11	,	,	PUNCT
ejpam-5042	595	12	define	define	VERB
ejpam-5042	595	13	ρ	ρ	PROPN
ejpam-5042	595	14	♦	♦	PROPN
ejpam-5042	595	15	≤	≤	PROPN
ejpam-5042	595	16	ϱ	ϱ	ADP
ejpam-5042	595	17	♦	♦	PROPN
ejpam-5042	595	18	if	if	SCONJ
ejpam-5042	595	19	and	and	CCONJ
ejpam-5042	595	20	only	only	ADV
ejpam-5042	595	21	if	if	SCONJ
ejpam-5042	595	22	ρ	ρ	PROPN
ejpam-5042	595	23	♦	♦	PROPN
ejpam-5042	595	24	∧	∧	PROPN
ejpam-5042	595	25	ϱ	ϱ	PROPN
ejpam-5042	595	26	♦	♦	PROPN
ejpam-5042	595	27	=	=	PROPN
ejpam-5042	595	28	ρ	ρ	PROPN
ejpam-5042	595	29	♦	♦	PROPN
ejpam-5042	595	30	.	.	PUNCT
ejpam-5042	596	1	then	then	ADV
ejpam-5042	596	2	(	(	PUNCT
ejpam-5042	596	3	v	v	PROPN
ejpam-5042	596	4	♦	♦	PROPN
ejpam-5042	596	5	,	,	PUNCT
ejpam-5042	596	6	≤	≤	NUM
ejpam-5042	596	7	)	)	PUNCT
ejpam-5042	596	8	is	be	AUX
ejpam-5042	596	9	a	a	DET
ejpam-5042	596	10	boolean	boolean	ADJ
ejpam-5042	596	11	algebra	algebra	NOUN
ejpam-5042	596	12	.	.	PUNCT
ejpam-5042	597	1	proof	proof	NOUN
ejpam-5042	597	2	.	.	PUNCT
ejpam-5042	598	1	let	let	VERB
ejpam-5042	598	2	v	v	PART
ejpam-5042	598	3	be	be	AUX
ejpam-5042	598	4	a	a	DET
ejpam-5042	598	5	pdl	pdl	NOUN
ejpam-5042	598	6	with	with	ADP
ejpam-5042	598	7	a	a	DET
ejpam-5042	598	8	parapseudo	parapseudo	NOUN
ejpam-5042	598	9	-	-	PUNCT
ejpam-5042	598	10	complementation	complementation	NOUN
ejpam-5042	598	11	♦	♦	NOUN
ejpam-5042	598	12	.	.	PUNCT
ejpam-5042	599	1	clearly	clearly	ADV
ejpam-5042	599	2	,	,	PUNCT
ejpam-5042	599	3	≤	≤	PROPN
ejpam-5042	599	4	is	be	AUX
ejpam-5042	599	5	reflexive	reflexive	ADJ
ejpam-5042	599	6	and	and	CCONJ
ejpam-5042	599	7	anti	anti	ADJ
ejpam-5042	599	8	-	-	ADJ
ejpam-5042	599	9	symmetric	symmetric	ADJ
ejpam-5042	599	10	.	.	PUNCT
ejpam-5042	600	1	now	now	ADV
ejpam-5042	600	2	,	,	PUNCT
ejpam-5042	600	3	for	for	ADP
ejpam-5042	600	4	ρ	ρ	PROPN
ejpam-5042	600	5	♦	♦	PROPN
ejpam-5042	600	6	≤	≤	PROPN
ejpam-5042	600	7	ϱ	ϱ	PROPN
ejpam-5042	600	8	♦	♦	PROPN
ejpam-5042	600	9	and	and	CCONJ
ejpam-5042	600	10	ϱ	ϱ	VERB
ejpam-5042	600	11	♦	♦	PROPN
ejpam-5042	600	12	≤	≤	PROPN
ejpam-5042	600	13	τ	τ	PROPN
ejpam-5042	601	1	♦	♦	PROPN
ejpam-5042	601	2	,	,	PUNCT
ejpam-5042	601	3	we	we	PRON
ejpam-5042	601	4	have	have	VERB
ejpam-5042	601	5	ρ	ρ	NUM
ejpam-5042	601	6	♦	♦	PROPN
ejpam-5042	601	7	∧	∧	PROPN
ejpam-5042	601	8	ϱ	ϱ	PROPN
ejpam-5042	601	9	♦	♦	PROPN
ejpam-5042	601	10	=	=	PROPN
ejpam-5042	601	11	ρ	ρ	PROPN
ejpam-5042	601	12	♦	♦	PROPN
ejpam-5042	601	13	,	,	PUNCT
ejpam-5042	601	14	ϱ	ϱ	PROPN
ejpam-5042	601	15	♦	♦	PROPN
ejpam-5042	601	16	∧	∧	PROPN
ejpam-5042	601	17	τ	τ	PROPN
ejpam-5042	601	18	♦	♦	PROPN
ejpam-5042	601	19	=	=	PROPN
ejpam-5042	601	20	ϱ	ϱ	PROPN
ejpam-5042	601	21	♦	♦	PROPN
ejpam-5042	601	22	.	.	PUNCT
ejpam-5042	602	1	therefore	therefore	ADV
ejpam-5042	602	2	,	,	PUNCT
ejpam-5042	602	3	ρ	ρ	PROPN
ejpam-5042	602	4	♦	♦	PROPN
ejpam-5042	602	5	∨τ	∨τ	VERB
ejpam-5042	602	6	♦	♦	PROPN
ejpam-5042	602	7	=	=	PROPN
ejpam-5042	602	8	ρ	ρ	PROPN
ejpam-5042	602	9	♦	♦	PROPN
ejpam-5042	602	10	∨ϱ	∨ϱ	PROPN
ejpam-5042	602	11	♦	♦	PROPN
ejpam-5042	602	12	∨τ	∨τ	NOUN
ejpam-5042	602	13	♦	♦	PROPN
ejpam-5042	602	14	=	=	PUNCT
ejpam-5042	602	15	ϱ	ϱ	PROPN
ejpam-5042	602	16	♦	♦	PROPN
ejpam-5042	602	17	∨τ	∨τ	NOUN
ejpam-5042	602	18	♦	♦	PROPN
ejpam-5042	602	19	=	=	SYM
ejpam-5042	602	20	τ	τ	PROPN
ejpam-5042	602	21	♦	♦	PROPN
ejpam-5042	602	22	which	which	PRON
ejpam-5042	602	23	implies	imply	VERB
ejpam-5042	602	24	ρ	ρ	PROPN
ejpam-5042	602	25	♦	♦	PROPN
ejpam-5042	602	26	∧τ	∧τ	PROPN
ejpam-5042	602	27	♦	♦	PROPN
ejpam-5042	602	28	=	=	PROPN
ejpam-5042	602	29	ρ	ρ	PROPN
ejpam-5042	602	30	♦	♦	PROPN
ejpam-5042	602	31	∧(ρ	∧(ρ	PROPN
ejpam-5042	602	32	♦	♦	PROPN
ejpam-5042	602	33	∨τ	∨τ	PROPN
ejpam-5042	602	34	♦	♦	PROPN
ejpam-5042	602	35	)	)	PUNCT
ejpam-5042	602	36	=	=	PROPN
ejpam-5042	603	1	ρ	ρ	PROPN
ejpam-5042	603	2	♦	♦	PROPN
ejpam-5042	603	3	,	,	PUNCT
ejpam-5042	603	4	hence	hence	ADV
ejpam-5042	603	5	≤	≤	NUM
ejpam-5042	603	6	is	be	AUX
ejpam-5042	603	7	transitive	transitive	ADJ
ejpam-5042	603	8	.	.	PUNCT
ejpam-5042	604	1	therefore	therefore	ADV
ejpam-5042	604	2	,	,	PUNCT
ejpam-5042	604	3	≤	≤	PROPN
ejpam-5042	604	4	is	be	AUX
ejpam-5042	604	5	a	a	DET
ejpam-5042	604	6	partial	partial	ADJ
ejpam-5042	604	7	ordering	ordering	NOUN
ejpam-5042	604	8	on	on	ADP
ejpam-5042	604	9	v	v	PROPN
ejpam-5042	604	10	♦	♦	PROPN
ejpam-5042	604	11	.	.	PUNCT
ejpam-5042	605	1	let	let	VERB
ejpam-5042	605	2	ρ	ρ	PROPN
ejpam-5042	605	3	♦	♦	PROPN
ejpam-5042	605	4	,	,	PUNCT
ejpam-5042	605	5	ϱ	ϱ	PROPN
ejpam-5042	605	6	♦	♦	PROPN
ejpam-5042	605	7	∈	∈	PROPN
ejpam-5042	605	8	v	v	ADP
ejpam-5042	605	9	♦	♦	PROPN
ejpam-5042	605	10	.	.	PUNCT
ejpam-5042	606	1	then	then	ADV
ejpam-5042	606	2	(	(	PUNCT
ejpam-5042	606	3	ρ	ρ	PROPN
ejpam-5042	606	4	∧	∧	PROPN
ejpam-5042	606	5	ϱ	ϱ	NOUN
ejpam-5042	606	6	)	)	PUNCT
ejpam-5042	606	7	♦	♦	PROPN
ejpam-5042	606	8	=	=	PROPN
ejpam-5042	606	9	ρ	ρ	PROPN
ejpam-5042	606	10	♦	♦	PROPN
ejpam-5042	606	11	∨	∨	NUM
ejpam-5042	606	12	ϱ	ϱ	PROPN
ejpam-5042	606	13	♦	♦	PROPN
ejpam-5042	606	14	.	.	PUNCT
ejpam-5042	607	1	hence	hence	PROPN
ejpam-5042	607	2	ρ	ρ	PROPN
ejpam-5042	607	3	♦	♦	PROPN
ejpam-5042	607	4	∨	∨	NUM
ejpam-5042	607	5	ϱ	ϱ	PROPN
ejpam-5042	607	6	♦	♦	PROPN
ejpam-5042	607	7	∈	∈	PROPN
ejpam-5042	607	8	v	v	ADP
ejpam-5042	607	9	♦	♦	PROPN
ejpam-5042	607	10	and	and	CCONJ
ejpam-5042	607	11	we	we	PRON
ejpam-5042	607	12	have	have	AUX
ejpam-5042	607	13	ρ	ρ	VERB
ejpam-5042	607	14	♦	♦	PROPN
ejpam-5042	607	15	∨	∨	NUM
ejpam-5042	607	16	ϱ	ϱ	PROPN
ejpam-5042	607	17	♦	♦	PROPN
ejpam-5042	607	18	=	=	PUNCT
ejpam-5042	607	19	ϱ	ϱ	PROPN
ejpam-5042	607	20	♦	♦	PROPN
ejpam-5042	607	21	∨	∨	PROPN
ejpam-5042	607	22	ρ	ρ	PROPN
ejpam-5042	607	23	♦	♦	PROPN
ejpam-5042	607	24	.	.	PUNCT
ejpam-5042	608	1	so	so	SCONJ
ejpam-5042	608	2	that	that	SCONJ
ejpam-5042	608	3	,	,	PUNCT
ejpam-5042	608	4	ρ	ρ	PROPN
ejpam-5042	608	5	♦	♦	PROPN
ejpam-5042	608	6	∨	∨	NUM
ejpam-5042	608	7	ϱ	ϱ	PROPN
ejpam-5042	608	8	♦	♦	PROPN
ejpam-5042	608	9	is	be	AUX
ejpam-5042	608	10	the	the	DET
ejpam-5042	608	11	least	least	ADJ
ejpam-5042	608	12	upper	upper	ADJ
ejpam-5042	608	13	bound	bind	VERB
ejpam-5042	608	14	of	of	ADP
ejpam-5042	608	15	ρ	ρ	PROPN
ejpam-5042	608	16	♦	♦	PROPN
ejpam-5042	608	17	,	,	PUNCT
ejpam-5042	608	18	ϱ	ϱ	PROPN
ejpam-5042	608	19	♦	♦	PROPN
ejpam-5042	608	20	∈	∈	PROPN
ejpam-5042	608	21	v	v	ADP
ejpam-5042	608	22	♦	♦	PROPN
ejpam-5042	608	23	.	.	PUNCT
ejpam-5042	609	1	we	we	PRON
ejpam-5042	609	2	have	have	VERB
ejpam-5042	609	3	ρ	ρ	VERB
ejpam-5042	609	4	♦	♦	PROPN
ejpam-5042	609	5	♦	♦	PROPN
ejpam-5042	609	6	≤	≤	PROPN
ejpam-5042	609	7	ρ	ρ	PROPN
ejpam-5042	609	8	♦	♦	PROPN
ejpam-5042	609	9	♦	♦	PROPN
ejpam-5042	609	10	∨	∨	NUM
ejpam-5042	609	11	ϱ	ϱ	PROPN
ejpam-5042	609	12	♦	♦	PROPN
ejpam-5042	609	13	♦	♦	PROPN
ejpam-5042	609	14	implies	imply	VERB
ejpam-5042	609	15	(	(	PUNCT
ejpam-5042	609	16	ρ	ρ	PROPN
ejpam-5042	609	17	♦	♦	PROPN
ejpam-5042	609	18	♦	♦	PROPN
ejpam-5042	609	19	∨	∨	NUM
ejpam-5042	609	20	ϱ	ϱ	PROPN
ejpam-5042	609	21	♦	♦	PROPN
ejpam-5042	609	22	♦	♦	PROPN
ejpam-5042	609	23	)	)	PUNCT
ejpam-5042	610	1	♦	♦	PROPN
ejpam-5042	610	2	≤	≤	PROPN
ejpam-5042	610	3	ρ	ρ	PROPN
ejpam-5042	610	4	♦	♦	PROPN
ejpam-5042	610	5	.	.	PUNCT
ejpam-5042	611	1	similarly	similarly	ADV
ejpam-5042	611	2	,	,	PUNCT
ejpam-5042	611	3	we	we	PRON
ejpam-5042	611	4	get	get	VERB
ejpam-5042	611	5	(	(	PUNCT
ejpam-5042	611	6	ρ	ρ	PROPN
ejpam-5042	611	7	♦	♦	PROPN
ejpam-5042	611	8	♦	♦	PROPN
ejpam-5042	611	9	∨	∨	NUM
ejpam-5042	611	10	ϱ	ϱ	PROPN
ejpam-5042	611	11	♦	♦	PROPN
ejpam-5042	611	12	♦	♦	PROPN
ejpam-5042	611	13	)	)	PUNCT
ejpam-5042	612	1	♦	♦	PROPN
ejpam-5042	612	2	≤	≤	PROPN
ejpam-5042	612	3	ϱ	ϱ	PROPN
ejpam-5042	612	4	♦	♦	PROPN
ejpam-5042	612	5	.	.	PUNCT
ejpam-5042	613	1	therefore	therefore	ADV
ejpam-5042	613	2	,	,	PUNCT
ejpam-5042	613	3	(	(	PUNCT
ejpam-5042	613	4	ρ	ρ	PROPN
ejpam-5042	613	5	♦	♦	PROPN
ejpam-5042	613	6	♦	♦	PROPN
ejpam-5042	613	7	∨	∨	NUM
ejpam-5042	613	8	ϱ	ϱ	PROPN
ejpam-5042	613	9	♦	♦	PROPN
ejpam-5042	613	10	♦	♦	PROPN
ejpam-5042	613	11	)	)	PUNCT
ejpam-5042	613	12	♦	♦	PROPN
ejpam-5042	613	13	is	be	AUX
ejpam-5042	613	14	a	a	DET
ejpam-5042	613	15	lower	low	ADJ
ejpam-5042	613	16	bound	bind	VERB
ejpam-5042	613	17	of	of	ADP
ejpam-5042	613	18	ρ	ρ	PROPN
ejpam-5042	613	19	♦	♦	PROPN
ejpam-5042	613	20	,	,	PUNCT
ejpam-5042	613	21	ϱ	ϱ	PROPN
ejpam-5042	613	22	♦	♦	PROPN
ejpam-5042	613	23	∈	∈	PROPN
ejpam-5042	613	24	v	v	ADP
ejpam-5042	613	25	♦	♦	PROPN
ejpam-5042	613	26	.	.	PUNCT
ejpam-5042	614	1	let	let	VERB
ejpam-5042	614	2	τ	τ	PROPN
ejpam-5042	614	3	♦	♦	PROPN
ejpam-5042	614	4	∈	∈	PROPN
ejpam-5042	614	5	v	v	ADP
ejpam-5042	614	6	♦	♦	PROPN
ejpam-5042	614	7	and	and	CCONJ
ejpam-5042	614	8	τ	τ	PROPN
ejpam-5042	614	9	♦	♦	PROPN
ejpam-5042	614	10	≤	≤	PROPN
ejpam-5042	614	11	ρ	ρ	PROPN
ejpam-5042	614	12	♦	♦	PROPN
ejpam-5042	614	13	,	,	PUNCT
ejpam-5042	614	14	τ	τ	PROPN
ejpam-5042	614	15	♦	♦	PROPN
ejpam-5042	614	16	≤	≤	PROPN
ejpam-5042	614	17	ϱ	ϱ	PROPN
ejpam-5042	614	18	♦	♦	PROPN
ejpam-5042	614	19	.	.	PUNCT
ejpam-5042	615	1	then	then	ADV
ejpam-5042	615	2	ρ	ρ	PROPN
ejpam-5042	615	3	♦	♦	PROPN
ejpam-5042	615	4	♦	♦	PROPN
ejpam-5042	615	5	≤	≤	PROPN
ejpam-5042	616	1	τ	τ	PROPN
ejpam-5042	617	1	♦	♦	PROPN
ejpam-5042	617	2	♦	♦	PROPN
ejpam-5042	617	3	,	,	PUNCT
ejpam-5042	617	4	ϱ	ϱ	PROPN
ejpam-5042	617	5	♦	♦	PROPN
ejpam-5042	617	6	♦	♦	PROPN
ejpam-5042	617	7	≤	≤	PROPN
ejpam-5042	618	1	τ	τ	PROPN
ejpam-5042	619	1	♦	♦	PROPN
ejpam-5042	619	2	♦	♦	PROPN
ejpam-5042	619	3	.	.	PUNCT
ejpam-5042	620	1	hence	hence	ADV
ejpam-5042	620	2	ρ	ρ	PROPN
ejpam-5042	620	3	♦	♦	PROPN
ejpam-5042	620	4	♦	♦	PROPN
ejpam-5042	620	5	∨ϱ	∨ϱ	VERB
ejpam-5042	620	6	♦	♦	PROPN
ejpam-5042	620	7	♦	♦	PROPN
ejpam-5042	620	8	≤	≤	PROPN
ejpam-5042	621	1	τ	τ	PROPN
ejpam-5042	621	2	♦	♦	PROPN
ejpam-5042	621	3	♦	♦	PROPN
ejpam-5042	621	4	.	.	PUNCT
ejpam-5042	622	1	therefore	therefore	ADV
ejpam-5042	622	2	,	,	PUNCT
ejpam-5042	622	3	τ	τ	PROPN
ejpam-5042	622	4	♦	♦	PROPN
ejpam-5042	622	5	≤	≤	PROPN
ejpam-5042	622	6	(	(	PUNCT
ejpam-5042	622	7	ρ	ρ	PROPN
ejpam-5042	622	8	♦	♦	PROPN
ejpam-5042	622	9	♦	♦	PROPN
ejpam-5042	622	10	∨ϱ	∨ϱ	VERB
ejpam-5042	622	11	♦	♦	PROPN
ejpam-5042	622	12	♦	♦	PROPN
ejpam-5042	622	13	)	)	PUNCT
ejpam-5042	622	14	♦	♦	PROPN
ejpam-5042	622	15	.	.	PUNCT
ejpam-5042	623	1	thus	thus	ADV
ejpam-5042	623	2	(	(	PUNCT
ejpam-5042	623	3	ρ	ρ	PROPN
ejpam-5042	623	4	♦	♦	PROPN
ejpam-5042	623	5	♦	♦	PROPN
ejpam-5042	623	6	∨ϱ	∨ϱ	VERB
ejpam-5042	623	7	♦	♦	PROPN
ejpam-5042	623	8	♦	♦	PROPN
ejpam-5042	623	9	)	)	PUNCT
ejpam-5042	624	1	♦	♦	PROPN
ejpam-5042	624	2	is	be	AUX
ejpam-5042	624	3	the	the	DET
ejpam-5042	624	4	greatest	greatest	ADV
ejpam-5042	624	5	lower	low	ADJ
ejpam-5042	624	6	bound	bind	VERB
ejpam-5042	624	7	of	of	ADP
ejpam-5042	624	8	ρ	ρ	PROPN
ejpam-5042	624	9	♦	♦	PROPN
ejpam-5042	624	10	,	,	PUNCT
ejpam-5042	624	11	ϱ	ϱ	PROPN
ejpam-5042	624	12	♦	♦	PROPN
ejpam-5042	624	13	∈	∈	PROPN
ejpam-5042	624	14	v	v	ADP
ejpam-5042	624	15	♦	♦	PROPN
ejpam-5042	624	16	.	.	PUNCT
ejpam-5042	625	1	hence	hence	ADV
ejpam-5042	625	2	(	(	PUNCT
ejpam-5042	625	3	v	v	PROPN
ejpam-5042	625	4	♦	♦	PROPN
ejpam-5042	625	5	,	,	PUNCT
ejpam-5042	625	6	≤	≤	NUM
ejpam-5042	625	7	)	)	PUNCT
ejpam-5042	625	8	is	be	AUX
ejpam-5042	625	9	a	a	DET
ejpam-5042	625	10	lattice	lattice	NOUN
ejpam-5042	625	11	.	.	PUNCT
ejpam-5042	626	1	from	from	ADP
ejpam-5042	626	2	now	now	ADV
ejpam-5042	626	3	,	,	PUNCT
ejpam-5042	626	4	we	we	PRON
ejpam-5042	626	5	represent	represent	VERB
ejpam-5042	626	6	(	(	PUNCT
ejpam-5042	626	7	ρ	ρ	PROPN
ejpam-5042	626	8	♦	♦	PROPN
ejpam-5042	626	9	♦	♦	PROPN
ejpam-5042	626	10	∨	∨	NUM
ejpam-5042	626	11	ϱ	ϱ	PROPN
ejpam-5042	626	12	♦	♦	PROPN
ejpam-5042	626	13	♦	♦	PROPN
ejpam-5042	626	14	)	)	PUNCT
ejpam-5042	627	1	♦	♦	PROPN
ejpam-5042	627	2	=(	=(	PROPN
ejpam-5042	627	3	ρ	ρ	PROPN
ejpam-5042	627	4	♦	♦	PROPN
ejpam-5042	627	5	∧ϱ	∧ϱ	PROPN
ejpam-5042	627	6	♦	♦	PROPN
ejpam-5042	627	7	)	)	PUNCT
ejpam-5042	627	8	.	.	PUNCT
ejpam-5042	628	1	now	now	ADV
ejpam-5042	628	2	,	,	PUNCT
ejpam-5042	628	3	by	by	ADP
ejpam-5042	628	4	lemma	lemma	PROPN
ejpam-5042	628	5	5(8	5(8	NUM
ejpam-5042	628	6	)	)	PUNCT
ejpam-5042	628	7	,	,	PUNCT
ejpam-5042	628	8	we	we	PRON
ejpam-5042	628	9	have	have	VERB
ejpam-5042	628	10	1	1	NUM
ejpam-5042	628	11	♦	♦	PROPN
ejpam-5042	628	12	≤	≤	PROPN
ejpam-5042	628	13	ρ	ρ	PROPN
ejpam-5042	628	14	♦	♦	PROPN
ejpam-5042	628	15	for	for	ADP
ejpam-5042	628	16	all	all	DET
ejpam-5042	628	17	ρ	ρ	NOUN
ejpam-5042	628	18	∈	∈	PROPN
ejpam-5042	628	19	v	v	NOUN
ejpam-5042	628	20	.	.	PUNCT
ejpam-5042	629	1	so	so	ADV
ejpam-5042	629	2	that	that	SCONJ
ejpam-5042	629	3	,	,	PUNCT
ejpam-5042	629	4	1	1	NUM
ejpam-5042	629	5	♦	♦	PROPN
ejpam-5042	629	6	is	be	AUX
ejpam-5042	629	7	the	the	DET
ejpam-5042	629	8	least	least	ADJ
ejpam-5042	629	9	element	element	NOUN
ejpam-5042	629	10	in	in	ADP
ejpam-5042	629	11	v	v	ADP
ejpam-5042	629	12	♦	♦	PROPN
ejpam-5042	629	13	and	and	CCONJ
ejpam-5042	629	14	since	since	SCONJ
ejpam-5042	629	15	1	1	NUM
ejpam-5042	629	16	♦	♦	PROPN
ejpam-5042	629	17	♦	♦	PROPN
ejpam-5042	629	18	=	=	PROPN
ejpam-5042	629	19	1	1	NUM
ejpam-5042	629	20	,	,	PUNCT
ejpam-5042	629	21	1	1	NUM
ejpam-5042	629	22	∈	∈	NOUN
ejpam-5042	629	23	v	v	ADP
ejpam-5042	629	24	♦	♦	PROPN
ejpam-5042	629	25	it	it	PRON
ejpam-5042	629	26	is	be	AUX
ejpam-5042	629	27	the	the	DET
ejpam-5042	629	28	greatest	great	ADJ
ejpam-5042	629	29	element	element	NOUN
ejpam-5042	629	30	in	in	ADP
ejpam-5042	629	31	v	v	PROPN
ejpam-5042	629	32	♦	♦	PROPN
ejpam-5042	629	33	.	.	PUNCT
ejpam-5042	630	1	therefore	therefore	ADV
ejpam-5042	630	2	,	,	PUNCT
ejpam-5042	630	3	(	(	PUNCT
ejpam-5042	630	4	v	v	PROPN
ejpam-5042	630	5	♦	♦	PROPN
ejpam-5042	630	6	,	,	PUNCT
ejpam-5042	630	7	≤	≤	NUM
ejpam-5042	630	8	)	)	PUNCT
ejpam-5042	630	9	is	be	AUX
ejpam-5042	630	10	a	a	DET
ejpam-5042	630	11	bounded	bounded	ADJ
ejpam-5042	630	12	lattice	lattice	NOUN
ejpam-5042	630	13	.	.	PUNCT
ejpam-5042	631	1	finally	finally	ADV
ejpam-5042	631	2	,	,	PUNCT
ejpam-5042	631	3	we	we	PRON
ejpam-5042	631	4	prove	prove	VERB
ejpam-5042	631	5	that	that	SCONJ
ejpam-5042	631	6	(	(	PUNCT
ejpam-5042	631	7	v	v	PROPN
ejpam-5042	631	8	♦	♦	PROPN
ejpam-5042	631	9	,	,	PUNCT
ejpam-5042	631	10	≤	≤	NUM
ejpam-5042	631	11	)	)	PUNCT
ejpam-5042	631	12	has	have	AUX
ejpam-5042	631	13	complement	complement	VERB
ejpam-5042	631	14	and	and	CCONJ
ejpam-5042	631	15	satisfies	satisfy	VERB
ejpam-5042	631	16	distributive	distributive	ADJ
ejpam-5042	631	17	property	property	NOUN
ejpam-5042	631	18	.	.	PUNCT
ejpam-5042	632	1	let	let	VERB
ejpam-5042	632	2	ρ	ρ	NUM
ejpam-5042	632	3	♦	♦	PROPN
ejpam-5042	632	4	∈	∈	PROPN
ejpam-5042	632	5	v	v	ADP
ejpam-5042	632	6	♦	♦	PROPN
ejpam-5042	632	7	.	.	PUNCT
ejpam-5042	633	1	then	then	ADV
ejpam-5042	633	2	ρ	ρ	PROPN
ejpam-5042	633	3	♦	♦	PROPN
ejpam-5042	633	4	♦	♦	PROPN
ejpam-5042	633	5	∈	∈	PROPN
ejpam-5042	633	6	v	v	ADP
ejpam-5042	633	7	♦	♦	PROPN
ejpam-5042	633	8	and	and	CCONJ
ejpam-5042	633	9	ρ	ρ	PROPN
ejpam-5042	633	10	♦	♦	PROPN
ejpam-5042	633	11	∨ρ	∨ρ	PROPN
ejpam-5042	633	12	♦	♦	PROPN
ejpam-5042	633	13	♦	♦	PROPN
ejpam-5042	633	14	=	=	PROPN
ejpam-5042	633	15	1	1	NUM
ejpam-5042	633	16	and	and	CCONJ
ejpam-5042	633	17	ρ	ρ	PROPN
ejpam-5042	633	18	♦	♦	PROPN
ejpam-5042	633	19	∧ρ	∧ρ	PROPN
ejpam-5042	633	20	♦	♦	PROPN
ejpam-5042	633	21	♦	♦	PROPN
ejpam-5042	633	22	=	=	PROPN
ejpam-5042	633	23	(	(	PUNCT
ejpam-5042	633	24	ρ	ρ	PROPN
ejpam-5042	633	25	♦	♦	PROPN
ejpam-5042	633	26	♦	♦	PROPN
ejpam-5042	633	27	∨ρ	∨ρ	PROPN
ejpam-5042	633	28	♦	♦	PROPN
ejpam-5042	633	29	♦	♦	PROPN
ejpam-5042	633	30	♦	♦	PROPN
ejpam-5042	633	31	)	)	PUNCT
ejpam-5042	634	1	♦	♦	PROPN
ejpam-5042	634	2	=	=	SYM
ejpam-5042	634	3	(	(	PUNCT
ejpam-5042	634	4	ρ	ρ	PROPN
ejpam-5042	634	5	♦	♦	PROPN
ejpam-5042	634	6	♦	♦	PROPN
ejpam-5042	634	7	∨ρ	∨ρ	PROPN
ejpam-5042	634	8	♦	♦	PROPN
ejpam-5042	634	9	)	)	PUNCT
ejpam-5042	634	10	♦	♦	PROPN
ejpam-5042	634	11	=	=	PROPN
ejpam-5042	634	12	1	1	NUM
ejpam-5042	634	13	♦	♦	PROPN
ejpam-5042	634	14	.	.	PUNCT
ejpam-5042	635	1	hence	hence	ADV
ejpam-5042	635	2	ρ	ρ	PROPN
ejpam-5042	635	3	♦	♦	PROPN
ejpam-5042	635	4	♦	♦	PROPN
ejpam-5042	635	5	is	be	AUX
ejpam-5042	635	6	the	the	DET
ejpam-5042	635	7	complement	complement	NOUN
ejpam-5042	635	8	of	of	ADP
ejpam-5042	635	9	ρ	ρ	PROPN
ejpam-5042	635	10	♦	♦	PROPN
ejpam-5042	635	11	∈	∈	PROPN
ejpam-5042	635	12	v	v	ADP
ejpam-5042	635	13	♦	♦	PROPN
ejpam-5042	635	14	.	.	PUNCT
ejpam-5042	636	1	now	now	ADV
ejpam-5042	636	2	,	,	PUNCT
ejpam-5042	636	3	let	let	VERB
ejpam-5042	636	4	ρ	ρ	PROPN
ejpam-5042	636	5	♦	♦	PROPN
ejpam-5042	636	6	,	,	PUNCT
ejpam-5042	636	7	ϱ	ϱ	PROPN
ejpam-5042	636	8	♦	♦	PROPN
ejpam-5042	636	9	,	,	PUNCT
ejpam-5042	636	10	τ	τ	PROPN
ejpam-5042	636	11	♦	♦	PROPN
ejpam-5042	636	12	∈	∈	PROPN
ejpam-5042	636	13	v	v	ADP
ejpam-5042	636	14	♦	♦	PROPN
ejpam-5042	636	15	.	.	PUNCT
ejpam-5042	637	1	then	then	ADV
ejpam-5042	637	2	,	,	PUNCT
ejpam-5042	637	3	(	(	PUNCT
ejpam-5042	637	4	ρ	ρ	PROPN
ejpam-5042	637	5	♦	♦	PROPN
ejpam-5042	637	6	∧ϱ	∧ϱ	PROPN
ejpam-5042	637	7	♦	♦	PROPN
ejpam-5042	637	8	)	)	PUNCT
ejpam-5042	637	9	∨	∨	PROPN
ejpam-5042	637	10	(	(	PUNCT
ejpam-5042	637	11	ρ	ρ	PROPN
ejpam-5042	637	12	♦	♦	PROPN
ejpam-5042	637	13	∧τ	∧τ	PROPN
ejpam-5042	637	14	♦	♦	PROPN
ejpam-5042	637	15	)	)	PUNCT
ejpam-5042	637	16	=	=	PRON
ejpam-5042	638	1	(	(	PUNCT
ejpam-5042	638	2	ρ	ρ	PROPN
ejpam-5042	638	3	♦	♦	PROPN
ejpam-5042	638	4	♦	♦	PROPN
ejpam-5042	638	5	∨	∨	NUM
ejpam-5042	638	6	ϱ	ϱ	PROPN
ejpam-5042	638	7	♦	♦	PROPN
ejpam-5042	638	8	♦	♦	PROPN
ejpam-5042	638	9	)	)	PUNCT
ejpam-5042	639	1	♦	♦	PROPN
ejpam-5042	639	2	∨	∨	PROPN
ejpam-5042	639	3	(	(	PUNCT
ejpam-5042	639	4	ρ	ρ	PROPN
ejpam-5042	639	5	♦	♦	PROPN
ejpam-5042	639	6	♦	♦	PROPN
ejpam-5042	639	7	∨	∨	PROPN
ejpam-5042	639	8	τ	τ	PROPN
ejpam-5042	639	9	♦	♦	PROPN
ejpam-5042	639	10	♦	♦	PROPN
ejpam-5042	639	11	)	)	PUNCT
ejpam-5042	639	12	♦	♦	PROPN
ejpam-5042	639	13	.	.	PUNCT
ejpam-5042	640	1	=	=	PUNCT
ejpam-5042	641	1	[	[	X
ejpam-5042	641	2	(	(	PUNCT
ejpam-5042	641	3	ρ	ρ	PROPN
ejpam-5042	641	4	♦	♦	PROPN
ejpam-5042	641	5	♦	♦	PROPN
ejpam-5042	641	6	∨	∨	NUM
ejpam-5042	641	7	ϱ	ϱ	PROPN
ejpam-5042	641	8	♦	♦	PROPN
ejpam-5042	641	9	♦	♦	PROPN
ejpam-5042	641	10	)	)	PUNCT
ejpam-5042	642	1	∧	∧	PROPN
ejpam-5042	642	2	(	(	PUNCT
ejpam-5042	642	3	ρ	ρ	PROPN
ejpam-5042	642	4	♦	♦	PROPN
ejpam-5042	642	5	♦	♦	PROPN
ejpam-5042	642	6	∨	∨	PROPN
ejpam-5042	642	7	τ	τ	PROPN
ejpam-5042	642	8	♦	♦	PROPN
ejpam-5042	642	9	♦	♦	PROPN
ejpam-5042	642	10	)	)	PUNCT
ejpam-5042	643	1	]	]	X
ejpam-5042	643	2	♦	♦	PROPN
ejpam-5042	643	3	.	.	PUNCT
ejpam-5042	644	1	=	=	PUNCT
ejpam-5042	645	1	[	[	X
ejpam-5042	645	2	ρ	ρ	PROPN
ejpam-5042	645	3	♦	♦	PROPN
ejpam-5042	645	4	♦	♦	PROPN
ejpam-5042	645	5	∨	∨	PROPN
ejpam-5042	645	6	(	(	PUNCT
ejpam-5042	645	7	ϱ	ϱ	PROPN
ejpam-5042	645	8	♦	♦	PROPN
ejpam-5042	645	9	♦	♦	PROPN
ejpam-5042	645	10	∧	∧	PROPN
ejpam-5042	645	11	τ	τ	PROPN
ejpam-5042	645	12	♦	♦	PROPN
ejpam-5042	645	13	♦	♦	PROPN
ejpam-5042	645	14	)	)	PUNCT
ejpam-5042	646	1	]	]	X
ejpam-5042	646	2	♦	♦	PROPN
ejpam-5042	646	3	.	.	PUNCT
ejpam-5042	647	1	=	=	PUNCT
ejpam-5042	648	1	[	[	X
ejpam-5042	648	2	ρ	ρ	PROPN
ejpam-5042	648	3	♦	♦	PROPN
ejpam-5042	648	4	♦	♦	PROPN
ejpam-5042	648	5	∨	∨	PROPN
ejpam-5042	648	6	(	(	PUNCT
ejpam-5042	648	7	ϱ	ϱ	PROPN
ejpam-5042	648	8	♦	♦	PROPN
ejpam-5042	648	9	♦	♦	PROPN
ejpam-5042	648	10	∧	∧	PROPN
ejpam-5042	648	11	τ	τ	PROPN
ejpam-5042	648	12	♦	♦	PROPN
ejpam-5042	648	13	♦	♦	PROPN
ejpam-5042	648	14	)	)	PUNCT
ejpam-5042	649	1	]	]	PUNCT
ejpam-5042	649	2	♦	♦	PROPN
ejpam-5042	649	3	♦	♦	PROPN
ejpam-5042	649	4	♦	♦	PROPN
ejpam-5042	649	5	.	.	PUNCT
ejpam-5042	650	1	=	=	PUNCT
ejpam-5042	651	1	[	[	X
ejpam-5042	651	2	ρ	ρ	PROPN
ejpam-5042	651	3	♦	♦	PROPN
ejpam-5042	651	4	♦	♦	PROPN
ejpam-5042	651	5	♦	♦	PROPN
ejpam-5042	651	6	♦	♦	PROPN
ejpam-5042	651	7	∨	∨	PROPN
ejpam-5042	651	8	(	(	PUNCT
ejpam-5042	651	9	ϱ	ϱ	PROPN
ejpam-5042	651	10	♦	♦	PROPN
ejpam-5042	651	11	♦	♦	PROPN
ejpam-5042	651	12	∧	∧	PROPN
ejpam-5042	651	13	τ	τ	PROPN
ejpam-5042	651	14	♦	♦	PROPN
ejpam-5042	651	15	♦	♦	PROPN
ejpam-5042	651	16	)	)	PUNCT
ejpam-5042	651	17	♦	♦	PROPN
ejpam-5042	651	18	♦	♦	PROPN
ejpam-5042	651	19	]	]	PUNCT
ejpam-5042	651	20	♦	♦	PROPN
ejpam-5042	651	21	.	.	PUNCT
ejpam-5042	652	1	=	=	PUNCT
ejpam-5042	653	1	[	[	X
ejpam-5042	653	2	ρ	ρ	PROPN
ejpam-5042	653	3	♦	♦	PROPN
ejpam-5042	653	4	♦	♦	PROPN
ejpam-5042	653	5	∨	∨	PROPN
ejpam-5042	653	6	(	(	PUNCT
ejpam-5042	653	7	ϱ	ϱ	PROPN
ejpam-5042	653	8	♦	♦	PROPN
ejpam-5042	653	9	♦	♦	PROPN
ejpam-5042	653	10	♦	♦	PROPN
ejpam-5042	653	11	∨	∨	PROPN
ejpam-5042	653	12	τ	τ	PROPN
ejpam-5042	653	13	♦	♦	PROPN
ejpam-5042	653	14	♦	♦	PROPN
ejpam-5042	653	15	♦	♦	PROPN
ejpam-5042	653	16	)	)	PUNCT
ejpam-5042	653	17	♦	♦	PROPN
ejpam-5042	653	18	]	]	PUNCT
ejpam-5042	653	19	♦	♦	PROPN
ejpam-5042	653	20	.	.	PUNCT
ejpam-5042	654	1	=	=	PUNCT
ejpam-5042	655	1	[	[	X
ejpam-5042	655	2	ρ	ρ	PROPN
ejpam-5042	655	3	♦	♦	PROPN
ejpam-5042	655	4	♦	♦	PROPN
ejpam-5042	655	5	∨	∨	PROPN
ejpam-5042	655	6	(	(	PUNCT
ejpam-5042	655	7	ϱ	ϱ	PROPN
ejpam-5042	655	8	♦	♦	PROPN
ejpam-5042	655	9	∨	∨	PROPN
ejpam-5042	655	10	τ	τ	PROPN
ejpam-5042	655	11	♦	♦	PROPN
ejpam-5042	655	12	)	)	PUNCT
ejpam-5042	655	13	♦	♦	PROPN
ejpam-5042	655	14	]	]	PUNCT
ejpam-5042	655	15	♦	♦	PROPN
ejpam-5042	655	16	.	.	PUNCT
ejpam-5042	656	1	=	=	PROPN
ejpam-5042	656	2	ρ	ρ	PROPN
ejpam-5042	656	3	♦	♦	PROPN
ejpam-5042	656	4	∧(ϱ	∧(ϱ	PROPN
ejpam-5042	656	5	♦	♦	PROPN
ejpam-5042	656	6	∨	∨	NUM
ejpam-5042	656	7	τ	τ	PROPN
ejpam-5042	656	8	♦	♦	PROPN
ejpam-5042	656	9	)	)	PUNCT
ejpam-5042	656	10	.	.	PUNCT
ejpam-5042	657	1	thus	thus	ADV
ejpam-5042	657	2	(	(	PUNCT
ejpam-5042	657	3	v	v	PROPN
ejpam-5042	657	4	♦	♦	PROPN
ejpam-5042	657	5	,	,	PUNCT
ejpam-5042	657	6	≤	≤	NUM
ejpam-5042	657	7	)	)	PUNCT
ejpam-5042	657	8	is	be	AUX
ejpam-5042	657	9	a	a	DET
ejpam-5042	657	10	boolean	boolean	ADJ
ejpam-5042	657	11	algebra	algebra	NOUN
ejpam-5042	657	12	.	.	PUNCT
ejpam-5042	658	1	corollary	corollary	ADJ
ejpam-5042	658	2	7	7	NUM
ejpam-5042	658	3	.	.	PUNCT
ejpam-5042	659	1	let	let	VERB
ejpam-5042	659	2	v	v	PART
ejpam-5042	659	3	be	be	AUX
ejpam-5042	659	4	a	a	DET
ejpam-5042	659	5	parapseudo	parapseudo	NOUN
ejpam-5042	659	6	-	-	PUNCT
ejpam-5042	659	7	complemented	complemented	ADJ
ejpam-5042	659	8	pdl	pdl	NOUN
ejpam-5042	659	9	with	with	ADP
ejpam-5042	659	10	parapseudo	parapseudo	NOUN
ejpam-5042	659	11	-	-	PUNCT
ejpam-5042	659	12	complemenation	complemenation	NOUN
ejpam-5042	659	13	♦	♦	PROPN
ejpam-5042	659	14	.	.	PUNCT
ejpam-5042	660	1	then	then	ADV
ejpam-5042	660	2	the	the	DET
ejpam-5042	660	3	map	map	NOUN
ejpam-5042	660	4	f	f	X
ejpam-5042	660	5	:	:	PUNCT
ejpam-5042	660	6	v	v	PROPN
ejpam-5042	660	7	→	→	SYM
ejpam-5042	660	8	v	v	NUM
ejpam-5042	660	9	♦	♦	PROPN
ejpam-5042	660	10	defined	define	VERB
ejpam-5042	660	11	by	by	ADP
ejpam-5042	660	12	f(ρ	f(ρ	NOUN
ejpam-5042	660	13	)	)	PUNCT
ejpam-5042	660	14	=	=	SYM
ejpam-5042	660	15	ρ	ρ	PROPN
ejpam-5042	660	16	♦	♦	PROPN
ejpam-5042	660	17	♦	♦	PROPN
ejpam-5042	660	18	is	be	AUX
ejpam-5042	660	19	an	an	DET
ejpam-5042	660	20	epimorphism	epimorphism	NOUN
ejpam-5042	660	21	.	.	PUNCT
ejpam-5042	661	1	r.	r.	PROPN
ejpam-5042	661	2	shukla	shukla	PROPN
ejpam-5042	661	3	et	et	PROPN
ejpam-5042	661	4	al	al	PROPN
ejpam-5042	661	5	.	.	PUNCT
ejpam-5042	661	6	/	/	SYM
ejpam-5042	661	7	eur	eur	PROPN
ejpam-5042	661	8	.	.	PUNCT
ejpam-5042	662	1	j.	j.	PROPN
ejpam-5042	662	2	pure	pure	PROPN
ejpam-5042	662	3	appl	appl	PROPN
ejpam-5042	662	4	.	.	PROPN
ejpam-5042	662	5	math	math	PROPN
ejpam-5042	662	6	,	,	PUNCT
ejpam-5042	662	7	17	17	NUM
ejpam-5042	662	8	(	(	PUNCT
ejpam-5042	662	9	2	2	NUM
ejpam-5042	662	10	)	)	PUNCT
ejpam-5042	662	11	(	(	PUNCT
ejpam-5042	662	12	2024	2024	NUM
ejpam-5042	662	13	)	)	PUNCT
ejpam-5042	662	14	,	,	PUNCT
ejpam-5042	662	15	1129	1129	NUM
ejpam-5042	662	16	-	-	SYM
ejpam-5042	662	17	1145	1145	NUM
ejpam-5042	662	18	1143	1143	NUM
ejpam-5042	662	19	in	in	ADP
ejpam-5042	662	20	the	the	DET
ejpam-5042	662	21	following	following	NOUN
ejpam-5042	662	22	theorem	theorem	NOUN
ejpam-5042	662	23	,	,	PUNCT
ejpam-5042	662	24	we	we	PRON
ejpam-5042	662	25	establish	establish	VERB
ejpam-5042	662	26	a	a	DET
ejpam-5042	662	27	one	one	NUM
ejpam-5042	662	28	-	-	PUNCT
ejpam-5042	662	29	to	to	ADP
ejpam-5042	662	30	-	-	PUNCT
ejpam-5042	662	31	one	one	NUM
ejpam-5042	662	32	correspondence	correspondence	NOUN
ejpam-5042	662	33	between	between	ADP
ejpam-5042	662	34	the	the	DET
ejpam-5042	662	35	set	set	NOUN
ejpam-5042	662	36	of	of	ADP
ejpam-5042	662	37	all	all	DET
ejpam-5042	662	38	minimal	minimal	ADJ
ejpam-5042	662	39	elements	element	NOUN
ejpam-5042	662	40	in	in	ADP
ejpam-5042	662	41	v	v	NOUN
ejpam-5042	662	42	and	and	CCONJ
ejpam-5042	662	43	the	the	DET
ejpam-5042	662	44	set	set	NOUN
ejpam-5042	662	45	of	of	ADP
ejpam-5042	662	46	all	all	DET
ejpam-5042	662	47	parapseudo	parapseudo	NOUN
ejpam-5042	662	48	-	-	PUNCT
ejpam-5042	662	49	complemenations	complemenation	NOUN
ejpam-5042	662	50	on	on	ADP
ejpam-5042	662	51	v	v	NOUN
ejpam-5042	662	52	.	.	PUNCT
ejpam-5042	663	1	first	first	ADV
ejpam-5042	663	2	we	we	PRON
ejpam-5042	663	3	prove	prove	VERB
ejpam-5042	663	4	the	the	DET
ejpam-5042	663	5	following	follow	VERB
ejpam-5042	663	6	lemma	lemma	PROPN
ejpam-5042	663	7	.	.	PUNCT
ejpam-5042	664	1	lemma	lemma	PROPN
ejpam-5042	664	2	14	14	NUM
ejpam-5042	664	3	.	.	PUNCT
ejpam-5042	665	1	let	let	VERB
ejpam-5042	665	2	v	v	PART
ejpam-5042	665	3	be	be	AUX
ejpam-5042	665	4	a	a	DET
ejpam-5042	665	5	pdl	pdl	NOUN
ejpam-5042	665	6	with	with	ADP
ejpam-5042	665	7	two	two	NUM
ejpam-5042	665	8	parapseudo	parapseudo	NOUN
ejpam-5042	665	9	-	-	PUNCT
ejpam-5042	665	10	complemenations	complemenation	NOUN
ejpam-5042	665	11	♦	♦	PROPN
ejpam-5042	665	12	and	and	CCONJ
ejpam-5042	665	13	♢	♢	PROPN
ejpam-5042	665	14	.	.	PUNCT
ejpam-5042	666	1	then	then	ADV
ejpam-5042	666	2	,	,	PUNCT
ejpam-5042	666	3	for	for	ADP
ejpam-5042	666	4	any	any	DET
ejpam-5042	666	5	ρ	ρ	NOUN
ejpam-5042	666	6	,	,	PUNCT
ejpam-5042	666	7	ϱ	ϱ	PROPN
ejpam-5042	666	8	∈	∈	PROPN
ejpam-5042	666	9	v	v	NOUN
ejpam-5042	666	10	,	,	PUNCT
ejpam-5042	666	11	we	we	PRON
ejpam-5042	666	12	have	have	VERB
ejpam-5042	666	13	the	the	DET
ejpam-5042	666	14	following	following	NOUN
ejpam-5042	666	15	:	:	PUNCT
ejpam-5042	666	16	(	(	PUNCT
ejpam-5042	666	17	1	1	NUM
ejpam-5042	666	18	)	)	PUNCT
ejpam-5042	666	19	.	.	PUNCT
ejpam-5042	667	1	ρ	ρ	PROPN
ejpam-5042	667	2	♢	♢	PROPN
ejpam-5042	667	3	∨	∨	PROPN
ejpam-5042	667	4	ρ	ρ	PROPN
ejpam-5042	667	5	♦	♦	PROPN
ejpam-5042	667	6	=	=	PROPN
ejpam-5042	667	7	ρ	ρ	PROPN
ejpam-5042	667	8	♢	♢	PROPN
ejpam-5042	667	9	and	and	CCONJ
ejpam-5042	667	10	ρ	ρ	PROPN
ejpam-5042	667	11	♢	♢	PROPN
ejpam-5042	667	12	∧	∧	PROPN
ejpam-5042	667	13	ρ	ρ	PROPN
ejpam-5042	667	14	♦	♦	PROPN
ejpam-5042	667	15	=	=	PROPN
ejpam-5042	667	16	ρ	ρ	PROPN
ejpam-5042	667	17	♦	♦	PROPN
ejpam-5042	667	18	.	.	PUNCT
ejpam-5042	668	1	(	(	PUNCT
ejpam-5042	668	2	2	2	NUM
ejpam-5042	668	3	)	)	PUNCT
ejpam-5042	668	4	.	.	PUNCT
ejpam-5042	669	1	ρ	ρ	PROPN
ejpam-5042	669	2	♦	♦	PROPN
ejpam-5042	669	3	♢	♢	PROPN
ejpam-5042	669	4	=	=	PROPN
ejpam-5042	669	5	ρ	ρ	PROPN
ejpam-5042	669	6	♢	♢	PROPN
ejpam-5042	669	7	♢	♢	PROPN
ejpam-5042	669	8	.	.	PUNCT
ejpam-5042	670	1	(	(	PUNCT
ejpam-5042	670	2	3	3	NUM
ejpam-5042	670	3	)	)	PUNCT
ejpam-5042	670	4	.	.	PUNCT
ejpam-5042	671	1	ρ	ρ	PROPN
ejpam-5042	671	2	♦	♦	PROPN
ejpam-5042	671	3	=	=	PROPN
ejpam-5042	671	4	ϱ	ϱ	PROPN
ejpam-5042	671	5	♦	♦	PROPN
ejpam-5042	671	6	⇔	⇔	PROPN
ejpam-5042	671	7	ρ	ρ	PROPN
ejpam-5042	671	8	♢	♢	PROPN
ejpam-5042	671	9	=	=	SYM
ejpam-5042	671	10	ϱ	ϱ	PROPN
ejpam-5042	671	11	♢	♢	PROPN
ejpam-5042	671	12	.	.	PUNCT
ejpam-5042	671	13	(	(	PUNCT
ejpam-5042	671	14	4	4	NUM
ejpam-5042	671	15	)	)	PUNCT
ejpam-5042	671	16	.	.	PUNCT
ejpam-5042	672	1	ρ	ρ	PROPN
ejpam-5042	672	2	♦	♦	PROPN
ejpam-5042	672	3	=	=	PROPN
ejpam-5042	672	4	1	1	NUM
ejpam-5042	672	5	⇔	⇔	PROPN
ejpam-5042	672	6	ρ	ρ	PROPN
ejpam-5042	672	7	♢	♢	PROPN
ejpam-5042	672	8	=	=	SYM
ejpam-5042	672	9	1	1	NUM
ejpam-5042	672	10	⇔	⇔	X
ejpam-5042	672	11	(	(	PUNCT
ejpam-5042	672	12	ρ	ρ	PROPN
ejpam-5042	672	13	∨	∨	PROPN
ejpam-5042	672	14	ϱ	ϱ	ADP
ejpam-5042	672	15	=	=	SYM
ejpam-5042	672	16	1	1	NUM
ejpam-5042	672	17	⇒	⇒	NOUN
ejpam-5042	672	18	ϱ	ϱ	ADP
ejpam-5042	672	19	=	=	SYM
ejpam-5042	672	20	1	1	NUM
ejpam-5042	672	21	)	)	PUNCT
ejpam-5042	672	22	.	.	PUNCT
ejpam-5042	673	1	(	(	PUNCT
ejpam-5042	673	2	5	5	NUM
ejpam-5042	673	3	)	)	PUNCT
ejpam-5042	673	4	.	.	PUNCT
ejpam-5042	674	1	ρ	ρ	PROPN
ejpam-5042	674	2	♢	♢	PROPN
ejpam-5042	674	3	=	=	SYM
ejpam-5042	674	4	1	1	NUM
ejpam-5042	674	5	♢	♢	PROPN
ejpam-5042	674	6	∨	∨	PROPN
ejpam-5042	674	7	ρ	ρ	PROPN
ejpam-5042	674	8	♦	♦	PROPN
ejpam-5042	674	9	.	.	PUNCT
ejpam-5042	675	1	(	(	PUNCT
ejpam-5042	675	2	6	6	NUM
ejpam-5042	675	3	)	)	PUNCT
ejpam-5042	675	4	.	.	PUNCT
ejpam-5042	676	1	ρ	ρ	PROPN
ejpam-5042	676	2	♦	♦	PROPN
ejpam-5042	676	3	∧	∧	PROPN
ejpam-5042	676	4	ρ	ρ	PROPN
ejpam-5042	676	5	♦	♦	PROPN
ejpam-5042	676	6	♦	♦	PROPN
ejpam-5042	676	7	=	=	PROPN
ejpam-5042	676	8	1	1	NUM
ejpam-5042	676	9	♦	♦	PROPN
ejpam-5042	676	10	⇔	⇔	PROPN
ejpam-5042	676	11	ρ	ρ	PROPN
ejpam-5042	676	12	♢	♢	PROPN
ejpam-5042	676	13	∧	∧	PROPN
ejpam-5042	676	14	ρ	ρ	PROPN
ejpam-5042	676	15	♢	♢	PROPN
ejpam-5042	676	16	♢	♢	PROPN
ejpam-5042	676	17	=	=	PROPN
ejpam-5042	676	18	1	1	NUM
ejpam-5042	676	19	♢	♢	NOUN
ejpam-5042	676	20	.	.	PUNCT
ejpam-5042	676	21	proof	proof	NOUN
ejpam-5042	676	22	.	.	PUNCT
ejpam-5042	677	1	let	let	VERB
ejpam-5042	677	2	v	v	PART
ejpam-5042	677	3	be	be	AUX
ejpam-5042	677	4	a	a	DET
ejpam-5042	677	5	pdl	pdl	NOUN
ejpam-5042	677	6	with	with	ADP
ejpam-5042	677	7	two	two	NUM
ejpam-5042	677	8	parapseudo	parapseudo	NOUN
ejpam-5042	677	9	-	-	PUNCT
ejpam-5042	677	10	complemenations	complemenation	NOUN
ejpam-5042	677	11	♦	♦	PROPN
ejpam-5042	677	12	and	and	CCONJ
ejpam-5042	677	13	♢	♢	PROPN
ejpam-5042	677	14	and	and	CCONJ
ejpam-5042	677	15	ρ	ρ	PROPN
ejpam-5042	677	16	,	,	PUNCT
ejpam-5042	677	17	ϱ	ϱ	PROPN
ejpam-5042	677	18	∈	∈	PROPN
ejpam-5042	677	19	v	v	NOUN
ejpam-5042	677	20	.	.	PUNCT
ejpam-5042	678	1	(	(	PUNCT
ejpam-5042	678	2	1	1	NUM
ejpam-5042	678	3	)	)	PUNCT
ejpam-5042	678	4	.	.	PUNCT
ejpam-5042	679	1	since	since	SCONJ
ejpam-5042	679	2	ρ	ρ	PROPN
ejpam-5042	679	3	♢	♢	PROPN
ejpam-5042	679	4	∨	∨	PROPN
ejpam-5042	679	5	ρ	ρ	NOUN
ejpam-5042	679	6	=	=	SYM
ejpam-5042	679	7	1	1	NUM
ejpam-5042	679	8	,	,	PUNCT
ejpam-5042	679	9	we	we	PRON
ejpam-5042	679	10	get	get	VERB
ejpam-5042	679	11	that	that	SCONJ
ejpam-5042	679	12	ρ	ρ	PROPN
ejpam-5042	679	13	♢	♢	PROPN
ejpam-5042	679	14	∨	∨	PROPN
ejpam-5042	679	15	ρ	ρ	PROPN
ejpam-5042	679	16	♦	♦	PROPN
ejpam-5042	679	17	=	=	PROPN
ejpam-5042	679	18	ρ	ρ	PROPN
ejpam-5042	679	19	♢	♢	PROPN
ejpam-5042	679	20	.	.	PROPN
ejpam-5042	680	1	hence	hence	PROPN
ejpam-5042	680	2	ρ	ρ	PROPN
ejpam-5042	680	3	♢	♢	PROPN
ejpam-5042	680	4	∧	∧	PROPN
ejpam-5042	680	5	ρ	ρ	PROPN
ejpam-5042	680	6	♦	♦	PROPN
ejpam-5042	680	7	=	=	PROPN
ejpam-5042	680	8	ρ	ρ	PROPN
ejpam-5042	680	9	♦	♦	PROPN
ejpam-5042	680	10	.	.	PUNCT
ejpam-5042	681	1	(	(	PUNCT
ejpam-5042	681	2	2	2	NUM
ejpam-5042	681	3	)	)	PUNCT
ejpam-5042	681	4	.	.	PUNCT
ejpam-5042	682	1	ρ	ρ	PROPN
ejpam-5042	682	2	♦	♦	PROPN
ejpam-5042	682	3	♢	♢	PROPN
ejpam-5042	682	4	=	=	PROPN
ejpam-5042	682	5	(	(	PUNCT
ejpam-5042	682	6	ρ	ρ	PROPN
ejpam-5042	682	7	♢	♢	PROPN
ejpam-5042	682	8	∧	∧	PROPN
ejpam-5042	682	9	ρ	ρ	PROPN
ejpam-5042	682	10	♦	♦	PROPN
ejpam-5042	682	11	)	)	PUNCT
ejpam-5042	682	12	♢	♢	PROPN
ejpam-5042	682	13	=	=	SYM
ejpam-5042	682	14	(	(	PUNCT
ejpam-5042	682	15	ρ	ρ	PROPN
ejpam-5042	682	16	♦	♦	PROPN
ejpam-5042	682	17	∧	∧	PROPN
ejpam-5042	682	18	ρ	ρ	PROPN
ejpam-5042	682	19	♢	♢	PROPN
ejpam-5042	682	20	)	)	PUNCT
ejpam-5042	682	21	♢	♢	PROPN
ejpam-5042	682	22	=	=	PROPN
ejpam-5042	682	23	ρ	ρ	PROPN
ejpam-5042	682	24	♢	♢	PROPN
ejpam-5042	682	25	♢	♢	PROPN
ejpam-5042	682	26	.	.	PUNCT
ejpam-5042	683	1	(	(	PUNCT
ejpam-5042	683	2	3	3	NUM
ejpam-5042	683	3	)	)	PUNCT
ejpam-5042	683	4	.	.	PUNCT
ejpam-5042	684	1	let	let	VERB
ejpam-5042	684	2	ρ	ρ	PRON
ejpam-5042	684	3	♦	♦	PROPN
ejpam-5042	684	4	=	=	PROPN
ejpam-5042	684	5	ϱ	ϱ	PROPN
ejpam-5042	684	6	♦	♦	PROPN
ejpam-5042	684	7	.	.	PUNCT
ejpam-5042	685	1	then	then	ADV
ejpam-5042	685	2	ρ	ρ	PROPN
ejpam-5042	685	3	♢	♢	PROPN
ejpam-5042	685	4	=	=	PROPN
ejpam-5042	685	5	ρ	ρ	PROPN
ejpam-5042	685	6	♢	♢	PROPN
ejpam-5042	685	7	♢	♢	PROPN
ejpam-5042	685	8	♢	♢	PROPN
ejpam-5042	685	9	=	=	PROPN
ejpam-5042	685	10	ρ	ρ	PROPN
ejpam-5042	685	11	♦	♦	PROPN
ejpam-5042	685	12	♢	♢	PROPN
ejpam-5042	685	13	♢	♢	PROPN
ejpam-5042	685	14	=	=	PROPN
ejpam-5042	685	15	ϱ	ϱ	PROPN
ejpam-5042	685	16	♦	♦	PROPN
ejpam-5042	685	17	♢	♢	PROPN
ejpam-5042	685	18	♢	♢	PROPN
ejpam-5042	685	19	=	=	PROPN
ejpam-5042	685	20	ϱ	ϱ	PROPN
ejpam-5042	685	21	♢	♢	PROPN
ejpam-5042	685	22	♢	♢	PROPN
ejpam-5042	685	23	♢	♢	PROPN
ejpam-5042	685	24	=	=	SYM
ejpam-5042	685	25	ϱ	ϱ	PROPN
ejpam-5042	685	26	♢	♢	PROPN
ejpam-5042	685	27	.	.	PUNCT
ejpam-5042	686	1	(	(	PUNCT
ejpam-5042	686	2	4	4	NUM
ejpam-5042	686	3	)	)	PUNCT
ejpam-5042	686	4	.	.	PUNCT
ejpam-5042	687	1	let	let	VERB
ejpam-5042	687	2	ρ	ρ	PRON
ejpam-5042	687	3	♦	♦	PROPN
ejpam-5042	687	4	=	=	PROPN
ejpam-5042	687	5	1	1	X
ejpam-5042	687	6	.	.	PUNCT
ejpam-5042	688	1	then	then	ADV
ejpam-5042	688	2	,	,	PUNCT
ejpam-5042	688	3	we	we	PRON
ejpam-5042	688	4	have	have	VERB
ejpam-5042	688	5	ρ	ρ	PROPN
ejpam-5042	688	6	♢	♢	PROPN
ejpam-5042	688	7	=	=	SYM
ejpam-5042	688	8	ρ	ρ	PROPN
ejpam-5042	688	9	♢	♢	PROPN
ejpam-5042	688	10	∨	∨	PROPN
ejpam-5042	688	11	ρ	ρ	PROPN
ejpam-5042	688	12	♦	♦	PROPN
ejpam-5042	688	13	=	=	PROPN
ejpam-5042	688	14	ρ	ρ	PROPN
ejpam-5042	688	15	♢	♢	PROPN
ejpam-5042	688	16	∨	∨	NUM
ejpam-5042	688	17	1	1	NUM
ejpam-5042	688	18	=	=	SYM
ejpam-5042	688	19	1	1	X
ejpam-5042	688	20	.	.	PUNCT
ejpam-5042	689	1	let	let	VERB
ejpam-5042	689	2	ρ	ρ	PRON
ejpam-5042	689	3	♢	♢	PROPN
ejpam-5042	689	4	=	=	SYM
ejpam-5042	689	5	1	1	NUM
ejpam-5042	689	6	and	and	CCONJ
ejpam-5042	689	7	ρ	ρ	NUM
ejpam-5042	689	8	∨	∨	NUM
ejpam-5042	689	9	ϱ	ϱ	ADP
ejpam-5042	689	10	=	=	SYM
ejpam-5042	689	11	1	1	NUM
ejpam-5042	689	12	.	.	PUNCT
ejpam-5042	689	13	then	then	ADV
ejpam-5042	689	14	ϱ	ϱ	VERB
ejpam-5042	689	15	=	=	SYM
ejpam-5042	689	16	ϱ	ϱ	PROPN
ejpam-5042	689	17	∨	∨	NUM
ejpam-5042	689	18	ρ	ρ	PROPN
ejpam-5042	689	19	♢	♢	PROPN
ejpam-5042	689	20	=	=	SYM
ejpam-5042	689	21	ϱ	ϱ	PROPN
ejpam-5042	689	22	∨	∨	NUM
ejpam-5042	689	23	1	1	NUM
ejpam-5042	689	24	=	=	SYM
ejpam-5042	689	25	1	1	X
ejpam-5042	689	26	.	.	PUNCT
ejpam-5042	689	27	suppose	suppose	VERB
ejpam-5042	689	28	ϱ	ϱ	PROPN
ejpam-5042	689	29	=	=	SYM
ejpam-5042	689	30	1	1	NUM
ejpam-5042	689	31	whenever	whenever	SCONJ
ejpam-5042	689	32	ρ	ρ	PROPN
ejpam-5042	689	33	∨	∨	NUM
ejpam-5042	689	34	ϱ	ϱ	ADP
ejpam-5042	689	35	=	=	SYM
ejpam-5042	689	36	1	1	NUM
ejpam-5042	689	37	.	.	PUNCT
ejpam-5042	690	1	so	so	SCONJ
ejpam-5042	690	2	that	that	SCONJ
ejpam-5042	690	3	ρ	ρ	PROPN
ejpam-5042	690	4	♦	♦	PROPN
ejpam-5042	690	5	=	=	PROPN
ejpam-5042	690	6	1	1	NUM
ejpam-5042	690	7	since	since	SCONJ
ejpam-5042	690	8	ρ	ρ	PROPN
ejpam-5042	690	9	∨	∨	NUM
ejpam-5042	690	10	ρ	ρ	PROPN
ejpam-5042	690	11	♦	♦	PROPN
ejpam-5042	690	12	=	=	PROPN
ejpam-5042	690	13	1	1	PROPN
ejpam-5042	690	14	.	.	PUNCT
ejpam-5042	690	15	(	(	PUNCT
ejpam-5042	690	16	5	5	NUM
ejpam-5042	690	17	)	)	PUNCT
ejpam-5042	690	18	.	.	PUNCT
ejpam-5042	691	1	we	we	PRON
ejpam-5042	691	2	have	have	VERB
ejpam-5042	691	3	(	(	PUNCT
ejpam-5042	691	4	1	1	NUM
ejpam-5042	691	5	♢	♢	PROPN
ejpam-5042	691	6	∨	∨	NUM
ejpam-5042	691	7	ρ	ρ	PROPN
ejpam-5042	691	8	♦	♦	PROPN
ejpam-5042	691	9	)	)	PUNCT
ejpam-5042	691	10	∨	∨	PROPN
ejpam-5042	691	11	ρ	ρ	PROPN
ejpam-5042	691	12	♢	♢	PROPN
ejpam-5042	691	13	=	=	SYM
ejpam-5042	691	14	1	1	NUM
ejpam-5042	691	15	♢	♢	PROPN
ejpam-5042	691	16	∨	∨	PROPN
ejpam-5042	691	17	ρ	ρ	PROPN
ejpam-5042	691	18	♢	♢	PROPN
ejpam-5042	691	19	∨	∨	PROPN
ejpam-5042	691	20	ρ	ρ	PROPN
ejpam-5042	691	21	♦	♦	PROPN
ejpam-5042	691	22	=	=	PROPN
ejpam-5042	691	23	ρ	ρ	PROPN
ejpam-5042	691	24	♢	♢	PROPN
ejpam-5042	691	25	∨	∨	PROPN
ejpam-5042	691	26	ρ	ρ	PROPN
ejpam-5042	691	27	♦	♦	PROPN
ejpam-5042	691	28	=	=	PROPN
ejpam-5042	691	29	ρ	ρ	PROPN
ejpam-5042	691	30	♢	♢	PROPN
ejpam-5042	691	31	.	.	PUNCT
ejpam-5042	692	1	(	(	PUNCT
ejpam-5042	692	2	6	6	NUM
ejpam-5042	692	3	)	)	PUNCT
ejpam-5042	692	4	.	.	PUNCT
ejpam-5042	693	1	let	let	VERB
ejpam-5042	694	1	ρ	ρ	NUM
ejpam-5042	694	2	♦	♦	PROPN
ejpam-5042	694	3	∧ρ	∧ρ	PROPN
ejpam-5042	694	4	♦	♦	PROPN
ejpam-5042	694	5	♦	♦	PROPN
ejpam-5042	694	6	=	=	PROPN
ejpam-5042	694	7	1	1	NUM
ejpam-5042	694	8	♦	♦	PROPN
ejpam-5042	694	9	.	.	PUNCT
ejpam-5042	695	1	then	then	ADV
ejpam-5042	695	2	ρ	ρ	PROPN
ejpam-5042	695	3	♢	♢	PROPN
ejpam-5042	695	4	∧ρ	∧ρ	PROPN
ejpam-5042	695	5	♢	♢	PROPN
ejpam-5042	695	6	♢	♢	PROPN
ejpam-5042	695	7	=	=	PROPN
ejpam-5042	695	8	ρ	ρ	PROPN
ejpam-5042	695	9	♢	♢	PROPN
ejpam-5042	695	10	∧ρ	∧ρ	PROPN
ejpam-5042	695	11	♦	♦	PROPN
ejpam-5042	695	12	♢	♢	PROPN
ejpam-5042	695	13	=	=	PROPN
ejpam-5042	695	14	(	(	PUNCT
ejpam-5042	695	15	1	1	NUM
ejpam-5042	695	16	♢	♢	PROPN
ejpam-5042	695	17	∨ρ	∨ρ	PROPN
ejpam-5042	695	18	♦	♦	PROPN
ejpam-5042	695	19	)∧(1	)∧(1	PROPN
ejpam-5042	695	20	♢	♢	PROPN
ejpam-5042	695	21	∨ρ	∨ρ	PROPN
ejpam-5042	695	22	♦	♦	PROPN
ejpam-5042	695	23	♦	♦	PROPN
ejpam-5042	695	24	)	)	PUNCT
ejpam-5042	695	25	=	=	PROPN
ejpam-5042	696	1	1	1	NUM
ejpam-5042	696	2	♢	♢	PROPN
ejpam-5042	696	3	∨(ρ	∨(ρ	PROPN
ejpam-5042	696	4	♦	♦	PROPN
ejpam-5042	696	5	∧ρ	∧ρ	PROPN
ejpam-5042	696	6	♦	♦	PROPN
ejpam-5042	696	7	♦	♦	PROPN
ejpam-5042	696	8	)	)	PUNCT
ejpam-5042	696	9	=	=	PUNCT
ejpam-5042	697	1	1	1	NUM
ejpam-5042	697	2	♢	♢	PROPN
ejpam-5042	697	3	∨	∨	NUM
ejpam-5042	697	4	1	1	NUM
ejpam-5042	697	5	♦	♦	PROPN
ejpam-5042	697	6	=	=	PROPN
ejpam-5042	697	7	1	1	NUM
ejpam-5042	697	8	♢	♢	PROPN
ejpam-5042	697	9	.	.	PUNCT
ejpam-5042	698	1	let	let	AUX
ejpam-5042	698	2	(	(	PUNCT
ejpam-5042	698	3	v,∨,∧	v,∨,∧	NOUN
ejpam-5042	698	4	,	,	PUNCT
ejpam-5042	698	5	1	1	NUM
ejpam-5042	698	6	)	)	PUNCT
ejpam-5042	698	7	be	be	AUX
ejpam-5042	698	8	a	a	DET
ejpam-5042	698	9	pdl	pdl	NOUN
ejpam-5042	698	10	with	with	ADP
ejpam-5042	698	11	a	a	DET
ejpam-5042	698	12	parapseudo	parapseudo	NOUN
ejpam-5042	698	13	-	-	PUNCT
ejpam-5042	698	14	complementation	complementation	NOUN
ejpam-5042	698	15	♦	♦	NOUN
ejpam-5042	698	16	,	,	PUNCT
ejpam-5042	698	17	and	and	CCONJ
ejpam-5042	698	18	m	m	VERB
ejpam-5042	698	19	a	a	DET
ejpam-5042	698	20	minimal	minimal	ADJ
ejpam-5042	698	21	element	element	NOUN
ejpam-5042	698	22	in	in	ADP
ejpam-5042	698	23	v	v	NOUN
ejpam-5042	698	24	.	.	PUNCT
ejpam-5042	699	1	we	we	PRON
ejpam-5042	699	2	define	define	VERB
ejpam-5042	699	3	a	a	DET
ejpam-5042	699	4	new	new	ADJ
ejpam-5042	699	5	operation	operation	NOUN
ejpam-5042	699	6	♦	♦	PROPN
ejpam-5042	699	7	m	m	PROPN
ejpam-5042	699	8	:	:	PUNCT
ejpam-5042	699	9	v	v	X
ejpam-5042	699	10	→	→	SYM
ejpam-5042	699	11	v	v	NOUN
ejpam-5042	699	12	as	as	SCONJ
ejpam-5042	699	13	follows	follow	VERB
ejpam-5042	699	14	:	:	PUNCT
ejpam-5042	699	15	for	for	ADP
ejpam-5042	699	16	any	any	DET
ejpam-5042	699	17	ρ	ρ	PROPN
ejpam-5042	699	18	∈	∈	PROPN
ejpam-5042	699	19	v	v	NOUN
ejpam-5042	699	20	,	,	PUNCT
ejpam-5042	699	21	we	we	PRON
ejpam-5042	699	22	have	have	VERB
ejpam-5042	699	23	ρ	ρ	NUM
ejpam-5042	699	24	♦	♦	PROPN
ejpam-5042	699	25	m	m	PROPN
ejpam-5042	699	26	=	=	PROPN
ejpam-5042	699	27	m	m	PROPN
ejpam-5042	699	28	∨	∨	NOUN
ejpam-5042	699	29	ρ	ρ	PROPN
ejpam-5042	699	30	♦	♦	PROPN
ejpam-5042	699	31	.	.	PUNCT
ejpam-5042	700	1	then	then	ADV
ejpam-5042	700	2	♦	♦	PROPN
ejpam-5042	700	3	m	m	PROPN
ejpam-5042	700	4	is	be	AUX
ejpam-5042	700	5	also	also	ADV
ejpam-5042	700	6	a	a	DET
ejpam-5042	700	7	parapseudo	parapseudo	NOUN
ejpam-5042	700	8	-	-	NOUN
ejpam-5042	700	9	complementation	complementation	NOUN
ejpam-5042	700	10	on	on	ADP
ejpam-5042	700	11	v	v	NOUN
ejpam-5042	700	12	in	in	ADP
ejpam-5042	700	13	which	which	PRON
ejpam-5042	700	14	1	1	NUM
ejpam-5042	700	15	♦	♦	PROPN
ejpam-5042	700	16	m	m	PROPN
ejpam-5042	700	17	=	=	NOUN
ejpam-5042	700	18	m.	m.	NOUN
ejpam-5042	700	19	theorem	theorem	VERB
ejpam-5042	700	20	11	11	NUM
ejpam-5042	700	21	.	.	PUNCT
ejpam-5042	701	1	let	let	VERB
ejpam-5042	701	2	v	v	PART
ejpam-5042	701	3	be	be	AUX
ejpam-5042	701	4	a	a	DET
ejpam-5042	701	5	parapseudo	parapseudo	NOUN
ejpam-5042	701	6	-	-	PUNCT
ejpam-5042	701	7	complemented	complement	VERB
ejpam-5042	701	8	pdl	pdl	NOUN
ejpam-5042	701	9	.	.	PUNCT
ejpam-5042	702	1	let	let	VERB
ejpam-5042	702	2	m	m	PRON
ejpam-5042	702	3	be	be	AUX
ejpam-5042	702	4	the	the	DET
ejpam-5042	702	5	set	set	NOUN
ejpam-5042	702	6	of	of	ADP
ejpam-5042	702	7	all	all	DET
ejpam-5042	702	8	minimal	minimal	ADJ
ejpam-5042	702	9	elements	element	NOUN
ejpam-5042	702	10	in	in	ADP
ejpam-5042	702	11	v	v	NOUN
ejpam-5042	702	12	and	and	CCONJ
ejpam-5042	702	13	pc(v	pc(v	NUM
ejpam-5042	702	14	)	)	PUNCT
ejpam-5042	702	15	be	be	AUX
ejpam-5042	702	16	the	the	DET
ejpam-5042	702	17	set	set	NOUN
ejpam-5042	702	18	of	of	ADP
ejpam-5042	702	19	all	all	DET
ejpam-5042	702	20	parapseudo	parapseudo	NOUN
ejpam-5042	702	21	-complemenations	-complemenation	NOUN
ejpam-5042	702	22	on	on	ADP
ejpam-5042	702	23	v	v	NUM
ejpam-5042	702	24	.	.	PUNCT
ejpam-5042	703	1	for	for	ADP
ejpam-5042	703	2	any	any	DET
ejpam-5042	703	3	m	m	NOUN
ejpam-5042	703	4	∈	∈	NOUN
ejpam-5042	703	5	m	m	PRON
ejpam-5042	703	6	,	,	PUNCT
ejpam-5042	703	7	define	define	VERB
ejpam-5042	703	8	♦	♦	PROPN
ejpam-5042	703	9	m	m	PROPN
ejpam-5042	703	10	:	:	PUNCT
ejpam-5042	703	11	v	v	X
ejpam-5042	703	12	→	→	SYM
ejpam-5042	703	13	v	v	NOUN
ejpam-5042	703	14	by	by	ADP
ejpam-5042	703	15	ρ	ρ	PROPN
ejpam-5042	703	16	♦	♦	PROPN
ejpam-5042	703	17	m	m	PROPN
ejpam-5042	703	18	=	=	PROPN
ejpam-5042	703	19	m∨	m∨	PROPN
ejpam-5042	703	20	ρ	ρ	PROPN
ejpam-5042	703	21	♦	♦	PROPN
ejpam-5042	703	22	for	for	ADP
ejpam-5042	703	23	all	all	DET
ejpam-5042	703	24	ρ	ρ	NUM
ejpam-5042	703	25	∈	∈	PROPN
ejpam-5042	703	26	v	v	NOUN
ejpam-5042	703	27	.	.	PUNCT
ejpam-5042	704	1	then	then	ADV
ejpam-5042	704	2	m	m	VERB
ejpam-5042	704	3	↣	↣	PROPN
ejpam-5042	704	4	ρ	ρ	PROPN
ejpam-5042	704	5	♦	♦	PROPN
ejpam-5042	704	6	m	m	PROPN
ejpam-5042	704	7	is	be	AUX
ejpam-5042	704	8	a	a	DET
ejpam-5042	704	9	bijection	bijection	NOUN
ejpam-5042	704	10	of	of	ADP
ejpam-5042	704	11	m	m	PROPN
ejpam-5042	704	12	onto	onto	ADP
ejpam-5042	704	13	pc(v	pc(v	NUM
ejpam-5042	704	14	)	)	PUNCT
ejpam-5042	704	15	.	.	PUNCT
ejpam-5042	705	1	proof	proof	NOUN
ejpam-5042	705	2	.	.	PUNCT
ejpam-5042	706	1	let	let	VERB
ejpam-5042	706	2	m	m	PRON
ejpam-5042	706	3	,	,	PUNCT
ejpam-5042	706	4	n	n	PROPN
ejpam-5042	706	5	∈	∈	PROPN
ejpam-5042	706	6	v	v	NOUN
ejpam-5042	706	7	be	be	AUX
ejpam-5042	706	8	such	such	ADJ
ejpam-5042	706	9	that	that	SCONJ
ejpam-5042	706	10	♦	♦	PROPN
ejpam-5042	706	11	m	m	PROPN
ejpam-5042	706	12	=	=	PROPN
ejpam-5042	706	13	♦	♦	PROPN
ejpam-5042	706	14	n.	n.	PROPN
ejpam-5042	706	15	then	then	ADV
ejpam-5042	706	16	1	1	NUM
ejpam-5042	706	17	♦	♦	PROPN
ejpam-5042	706	18	m	m	PROPN
ejpam-5042	706	19	=	=	PROPN
ejpam-5042	706	20	1	1	NUM
ejpam-5042	706	21	♦	♦	PROPN
ejpam-5042	706	22	n	n	PROPN
ejpam-5042	706	23	so	so	SCONJ
ejpam-5042	706	24	that	that	SCONJ
ejpam-5042	706	25	m∨	m∨	PROPN
ejpam-5042	706	26	1	1	NUM
ejpam-5042	706	27	♦	♦	PROPN
ejpam-5042	706	28	=	=	PROPN
ejpam-5042	706	29	n∨	n∨	PROPN
ejpam-5042	706	30	1	1	NUM
ejpam-5042	706	31	♦	♦	PROPN
ejpam-5042	706	32	.	.	PUNCT
ejpam-5042	707	1	hence	hence	ADV
ejpam-5042	707	2	m	m	VERB
ejpam-5042	707	3	=	=	ADJ
ejpam-5042	707	4	n.	n.	PROPN
ejpam-5042	707	5	also	also	ADV
ejpam-5042	707	6	,	,	PUNCT
ejpam-5042	707	7	for	for	ADP
ejpam-5042	707	8	any	any	DET
ejpam-5042	707	9	♢	♢	PROPN
ejpam-5042	707	10	∈	∈	PROPN
ejpam-5042	707	11	pc(v	pc(v	NOUN
ejpam-5042	707	12	)	)	PUNCT
ejpam-5042	707	13	,	,	PUNCT
ejpam-5042	707	14	if	if	SCONJ
ejpam-5042	707	15	m	m	VERB
ejpam-5042	707	16	=	=	SYM
ejpam-5042	707	17	1	1	NUM
ejpam-5042	707	18	♢	♢	PROPN
ejpam-5042	707	19	,	,	PUNCT
ejpam-5042	707	20	then	then	ADV
ejpam-5042	707	21	ρ	ρ	PROPN
ejpam-5042	707	22	♦	♦	PROPN
ejpam-5042	707	23	m	m	PROPN
ejpam-5042	707	24	=	=	PROPN
ejpam-5042	707	25	m	m	PROPN
ejpam-5042	707	26	∨	∨	NOUN
ejpam-5042	707	27	ρ	ρ	PROPN
ejpam-5042	707	28	♦	♦	PROPN
ejpam-5042	707	29	=	=	PROPN
ejpam-5042	707	30	1	1	NUM
ejpam-5042	707	31	♢	♢	PROPN
ejpam-5042	707	32	∨	∨	NUM
ejpam-5042	707	33	ρ	ρ	PROPN
ejpam-5042	707	34	♦	♦	PROPN
ejpam-5042	707	35	=	=	PROPN
ejpam-5042	707	36	ρ	ρ	PROPN
ejpam-5042	707	37	♢	♢	PROPN
ejpam-5042	707	38	by	by	ADP
ejpam-5042	707	39	lemma	lemma	PROPN
ejpam-5042	707	40	14(5	14(5	PROPN
ejpam-5042	707	41	)	)	PUNCT
ejpam-5042	707	42	.	.	PUNCT
ejpam-5042	708	1	then	then	ADV
ejpam-5042	708	2	♢	♢	PROPN
ejpam-5042	708	3	is	be	AUX
ejpam-5042	708	4	same	same	ADJ
ejpam-5042	708	5	as	as	SCONJ
ejpam-5042	708	6	♦	♦	PROPN
ejpam-5042	708	7	m	m	PROPN
ejpam-5042	708	8	and	and	CCONJ
ejpam-5042	708	9	m	m	PROPN
ejpam-5042	708	10	is	be	AUX
ejpam-5042	708	11	a	a	DET
ejpam-5042	708	12	minimal	minimal	ADJ
ejpam-5042	708	13	element	element	NOUN
ejpam-5042	708	14	.	.	PUNCT
ejpam-5042	709	1	thus	thus	ADV
ejpam-5042	709	2	m	m	ADP
ejpam-5042	709	3	↣	↣	PROPN
ejpam-5042	709	4	ρ	ρ	PROPN
ejpam-5042	709	5	♦	♦	PROPN
ejpam-5042	709	6	m	m	PROPN
ejpam-5042	709	7	is	be	AUX
ejpam-5042	709	8	a	a	DET
ejpam-5042	709	9	bijection	bijection	NOUN
ejpam-5042	709	10	of	of	ADP
ejpam-5042	709	11	m	m	PROPN
ejpam-5042	709	12	onto	onto	ADP
ejpam-5042	709	13	pc(v	pc(v	NUM
ejpam-5042	709	14	)	)	PUNCT
ejpam-5042	709	15	.	.	PUNCT
ejpam-5042	710	1	theorem	theorem	NOUN
ejpam-5042	710	2	12	12	NUM
ejpam-5042	710	3	.	.	PUNCT
ejpam-5042	711	1	if	if	SCONJ
ejpam-5042	711	2	v	v	NOUN
ejpam-5042	711	3	is	be	AUX
ejpam-5042	711	4	a	a	DET
ejpam-5042	711	5	pdl	pdl	NOUN
ejpam-5042	711	6	with	with	ADP
ejpam-5042	711	7	two	two	NUM
ejpam-5042	711	8	parapseudo	parapseudo	NOUN
ejpam-5042	711	9	-	-	PUNCT
ejpam-5042	711	10	complementations	complementation	NOUN
ejpam-5042	711	11	♦	♦	PROPN
ejpam-5042	711	12	and	and	CCONJ
ejpam-5042	711	13	♢	♢	PROPN
ejpam-5042	711	14	,	,	PUNCT
ejpam-5042	711	15	then	then	ADV
ejpam-5042	711	16	the	the	DET
ejpam-5042	711	17	map	map	NOUN
ejpam-5042	711	18	f	f	X
ejpam-5042	711	19	:	:	PUNCT
ejpam-5042	711	20	v	v	PROPN
ejpam-5042	711	21	♦	♦	PROPN
ejpam-5042	711	22	→	→	PROPN
ejpam-5042	711	23	v	v	PROPN
ejpam-5042	711	24	♢	♢	PROPN
ejpam-5042	711	25	defined	define	VERB
ejpam-5042	711	26	by	by	ADP
ejpam-5042	711	27	f(ρ	f(ρ	NOUN
ejpam-5042	711	28	♦	♦	NOUN
ejpam-5042	711	29	)	)	PUNCT
ejpam-5042	711	30	=	=	PUNCT
ejpam-5042	712	1	ρ	ρ	PROPN
ejpam-5042	712	2	♢	♢	PROPN
ejpam-5042	712	3	is	be	AUX
ejpam-5042	712	4	an	an	DET
ejpam-5042	712	5	isomorphism	isomorphism	NOUN
ejpam-5042	712	6	of	of	ADP
ejpam-5042	712	7	boolean	boolean	ADJ
ejpam-5042	712	8	algebras	algebra	NOUN
ejpam-5042	712	9	.	.	PUNCT
ejpam-5042	713	1	proof	proof	NOUN
ejpam-5042	713	2	.	.	PUNCT
ejpam-5042	714	1	let	let	VERB
ejpam-5042	714	2	v	v	PART
ejpam-5042	714	3	be	be	AUX
ejpam-5042	714	4	a	a	DET
ejpam-5042	714	5	pdl	pdl	NOUN
ejpam-5042	714	6	with	with	ADP
ejpam-5042	714	7	two	two	NUM
ejpam-5042	714	8	parapseudo	parapseudo	NOUN
ejpam-5042	714	9	-	-	PUNCT
ejpam-5042	714	10	complementations	complementation	NOUN
ejpam-5042	714	11	♦	♦	PROPN
ejpam-5042	714	12	and	and	CCONJ
ejpam-5042	714	13	♢	♢	PROPN
ejpam-5042	714	14	.	.	PROPN
ejpam-5042	715	1	clearly	clearly	ADV
ejpam-5042	715	2	the	the	DET
ejpam-5042	715	3	map	map	NOUN
ejpam-5042	716	1	f	f	X
ejpam-5042	716	2	:	:	PUNCT
ejpam-5042	716	3	v	v	PROPN
ejpam-5042	716	4	♦	♦	PROPN
ejpam-5042	716	5	→	→	PROPN
ejpam-5042	716	6	v	v	PROPN
ejpam-5042	716	7	♢	♢	PROPN
ejpam-5042	716	8	defined	define	VERB
ejpam-5042	716	9	by	by	ADP
ejpam-5042	716	10	f(ρ	f(ρ	NOUN
ejpam-5042	716	11	♦	♦	NOUN
ejpam-5042	716	12	)	)	PUNCT
ejpam-5042	716	13	=	=	PUNCT
ejpam-5042	717	1	ρ	ρ	PROPN
ejpam-5042	717	2	♢	♢	PROPN
ejpam-5042	717	3	is	be	AUX
ejpam-5042	717	4	well	well	ADV
ejpam-5042	717	5	-defined	-defined	ADJ
ejpam-5042	717	6	and	and	CCONJ
ejpam-5042	717	7	one	one	NUM
ejpam-5042	717	8	-one	-one	NUM
ejpam-5042	717	9	by	by	ADP
ejpam-5042	717	10	lemma	lemma	PROPN
ejpam-5042	717	11	14	14	NUM
ejpam-5042	717	12	.	.	PUNCT
ejpam-5042	718	1	by	by	ADP
ejpam-5042	718	2	definition	definition	NOUN
ejpam-5042	718	3	,	,	PUNCT
ejpam-5042	718	4	f	f	PROPN
ejpam-5042	718	5	is	be	AUX
ejpam-5042	718	6	onto	onto	ADP
ejpam-5042	718	7	.	.	PUNCT
ejpam-5042	719	1	let	let	VERB
ejpam-5042	719	2	ρ	ρ	PROPN
ejpam-5042	719	3	♦	♦	PROPN
ejpam-5042	719	4	,	,	PUNCT
ejpam-5042	719	5	ϱ	ϱ	PROPN
ejpam-5042	719	6	♦	♦	PROPN
ejpam-5042	719	7	∈	∈	PROPN
ejpam-5042	719	8	v	v	NOUN
ejpam-5042	719	9	.	.	PUNCT
ejpam-5042	720	1	then	then	ADV
ejpam-5042	720	2	,	,	PUNCT
ejpam-5042	720	3	f(ρ	f(ρ	PROPN
ejpam-5042	720	4	♦	♦	PROPN
ejpam-5042	720	5	∧ϱ	∧ϱ	PROPN
ejpam-5042	720	6	♦	♦	PROPN
ejpam-5042	720	7	)	)	PUNCT
ejpam-5042	720	8	=	=	PUNCT
ejpam-5042	720	9	f((ρ	f((ρ	PROPN
ejpam-5042	720	10	♦	♦	PROPN
ejpam-5042	720	11	♦	♦	PROPN
ejpam-5042	720	12	∨	∨	VERB
ejpam-5042	720	13	ϱ	ϱ	PROPN
ejpam-5042	720	14	♦	♦	PROPN
ejpam-5042	720	15	♦	♦	PROPN
ejpam-5042	720	16	)	)	PUNCT
ejpam-5042	720	17	♦	♦	PROPN
ejpam-5042	720	18	)	)	PUNCT
ejpam-5042	721	1	=	=	PRON
ejpam-5042	721	2	references	reference	NOUN
ejpam-5042	721	3	1144	1144	NUM
ejpam-5042	721	4	(	(	PUNCT
ejpam-5042	721	5	ρ	ρ	PROPN
ejpam-5042	721	6	♦	♦	PROPN
ejpam-5042	721	7	♦	♦	PROPN
ejpam-5042	721	8	∨	∨	NUM
ejpam-5042	721	9	ϱ	ϱ	PROPN
ejpam-5042	721	10	♦	♦	PROPN
ejpam-5042	721	11	♦	♦	PROPN
ejpam-5042	721	12	)	)	PUNCT
ejpam-5042	722	1	♢	♢	PROPN
ejpam-5042	722	2	=	=	PRON
ejpam-5042	722	3	(	(	PUNCT
ejpam-5042	722	4	ρ	ρ	PROPN
ejpam-5042	722	5	∨	∨	NUM
ejpam-5042	722	6	ϱ	ϱ	PROPN
ejpam-5042	722	7	)	)	PUNCT
ejpam-5042	722	8	♦	♦	PROPN
ejpam-5042	722	9	♦	♦	PROPN
ejpam-5042	722	10	♢	♢	PROPN
ejpam-5042	722	11	=	=	PROPN
ejpam-5042	722	12	(	(	PUNCT
ejpam-5042	722	13	ρ	ρ	PROPN
ejpam-5042	722	14	∨	∨	NUM
ejpam-5042	722	15	ϱ	ϱ	PROPN
ejpam-5042	722	16	)	)	PUNCT
ejpam-5042	722	17	♢	♢	PROPN
ejpam-5042	722	18	♢	♢	PROPN
ejpam-5042	722	19	♢	♢	PROPN
ejpam-5042	722	20	=	=	SYM
ejpam-5042	722	21	(	(	PUNCT
ejpam-5042	722	22	ρ	ρ	PROPN
ejpam-5042	722	23	♢	♢	PROPN
ejpam-5042	722	24	♢	♢	PROPN
ejpam-5042	722	25	∨	∨	PROPN
ejpam-5042	722	26	ϱ	ϱ	PROPN
ejpam-5042	722	27	♢	♢	PROPN
ejpam-5042	722	28	♢	♢	PROPN
ejpam-5042	722	29	)	)	PUNCT
ejpam-5042	722	30	♢	♢	PROPN
ejpam-5042	722	31	=	=	PROPN
ejpam-5042	722	32	ρ	ρ	PROPN
ejpam-5042	722	33	♢	♢	PROPN
ejpam-5042	722	34	∧ϱ	∧ϱ	PROPN
ejpam-5042	722	35	♢	♢	PROPN
ejpam-5042	722	36	=	=	PUNCT
ejpam-5042	722	37	f(ρ	f(ρ	PROPN
ejpam-5042	722	38	♦	♦	PROPN
ejpam-5042	722	39	)∧f(ϱ	)∧f(ϱ	PROPN
ejpam-5042	722	40	♦	♦	PROPN
ejpam-5042	722	41	)	)	PUNCT
ejpam-5042	722	42	.	.	PUNCT
ejpam-5042	723	1	also	also	ADV
ejpam-5042	723	2	,	,	PUNCT
ejpam-5042	723	3	f(ρ	f(ρ	PROPN
ejpam-5042	723	4	♦	♦	PROPN
ejpam-5042	723	5	∨	∨	NUM
ejpam-5042	723	6	ϱ	ϱ	PROPN
ejpam-5042	723	7	♦	♦	PROPN
ejpam-5042	723	8	)	)	PUNCT
ejpam-5042	724	1	=	=	SYM
ejpam-5042	724	2	f((ρ	f((ρ	NOUN
ejpam-5042	724	3	∧	∧	PROPN
ejpam-5042	724	4	ϱ	ϱ	NOUN
ejpam-5042	724	5	)	)	PUNCT
ejpam-5042	724	6	♦	♦	PROPN
ejpam-5042	724	7	)	)	PUNCT
ejpam-5042	724	8	=	=	PRON
ejpam-5042	725	1	(	(	PUNCT
ejpam-5042	725	2	ρ	ρ	PROPN
ejpam-5042	725	3	∧	∧	PROPN
ejpam-5042	725	4	ϱ	ϱ	PROPN
ejpam-5042	725	5	)	)	PUNCT
ejpam-5042	725	6	♢	♢	PROPN
ejpam-5042	725	7	=	=	PROPN
ejpam-5042	725	8	ρ	ρ	PROPN
ejpam-5042	725	9	♢	♢	PROPN
ejpam-5042	725	10	∨	∨	NUM
ejpam-5042	725	11	ϱ	ϱ	PROPN
ejpam-5042	725	12	♢	♢	PROPN
ejpam-5042	725	13	=	=	SYM
ejpam-5042	725	14	f(ρ	f(ρ	PROPN
ejpam-5042	725	15	♦	♦	NOUN
ejpam-5042	725	16	)	)	PUNCT
ejpam-5042	725	17	∨	∨	NUM
ejpam-5042	725	18	f(ϱ	f(ϱ	ADJ
ejpam-5042	725	19	♦	♦	PROPN
ejpam-5042	725	20	)	)	PUNCT
ejpam-5042	725	21	.	.	PUNCT
ejpam-5042	726	1	therefore	therefore	ADV
ejpam-5042	726	2	f	f	PROPN
ejpam-5042	726	3	is	be	AUX
ejpam-5042	726	4	an	an	DET
ejpam-5042	726	5	isomorphism	isomorphism	NOUN
ejpam-5042	726	6	.	.	PUNCT
ejpam-5042	727	1	6	6	NUM
ejpam-5042	727	2	.	.	X
ejpam-5042	727	3	conclusions	conclusion	NOUN
ejpam-5042	727	4	in	in	ADP
ejpam-5042	727	5	this	this	DET
ejpam-5042	727	6	paper	paper	NOUN
ejpam-5042	727	7	,	,	PUNCT
ejpam-5042	727	8	we	we	PRON
ejpam-5042	727	9	have	have	AUX
ejpam-5042	727	10	introduced	introduce	VERB
ejpam-5042	727	11	the	the	DET
ejpam-5042	727	12	concept	concept	NOUN
ejpam-5042	727	13	of	of	ADP
ejpam-5042	727	14	a	a	DET
ejpam-5042	727	15	parapseudo	parapseudo	NOUN
ejpam-5042	727	16	-	-	NOUN
ejpam-5042	727	17	complementation	complementation	NOUN
ejpam-5042	727	18	on	on	ADP
ejpam-5042	727	19	a	a	DET
ejpam-5042	727	20	paradistributive	paradistributive	ADJ
ejpam-5042	727	21	lattiocoid	lattiocoid	NOUN
ejpam-5042	727	22	and	and	CCONJ
ejpam-5042	727	23	examined	examine	VERB
ejpam-5042	727	24	its	its	PRON
ejpam-5042	727	25	elementary	elementary	ADJ
ejpam-5042	727	26	properties	property	NOUN
ejpam-5042	727	27	.	.	PUNCT
ejpam-5042	728	1	by	by	ADP
ejpam-5042	728	2	establishing	establish	VERB
ejpam-5042	728	3	necessary	necessary	ADJ
ejpam-5042	728	4	conditions	condition	NOUN
ejpam-5042	728	5	,	,	PUNCT
ejpam-5042	728	6	we	we	PRON
ejpam-5042	728	7	have	have	AUX
ejpam-5042	728	8	provided	provide	VERB
ejpam-5042	728	9	insights	insight	NOUN
ejpam-5042	728	10	into	into	ADP
ejpam-5042	728	11	when	when	SCONJ
ejpam-5042	728	12	a	a	DET
ejpam-5042	728	13	pdl	pdl	NOUN
ejpam-5042	728	14	with	with	ADP
ejpam-5042	728	15	a	a	DET
ejpam-5042	728	16	minimal	minimal	ADJ
ejpam-5042	728	17	element	element	NOUN
ejpam-5042	728	18	can	can	AUX
ejpam-5042	728	19	be	be	AUX
ejpam-5042	728	20	parapseudo	parapseudo	NOUN
ejpam-5042	728	21	-	-	VERB
ejpam-5042	728	22	complemented	complemented	ADJ
ejpam-5042	728	23	.	.	PUNCT
ejpam-5042	729	1	furthermore	furthermore	ADV
ejpam-5042	729	2	,	,	PUNCT
ejpam-5042	729	3	our	our	PRON
ejpam-5042	729	4	investigation	investigation	NOUN
ejpam-5042	729	5	has	have	AUX
ejpam-5042	729	6	focused	focus	VERB
ejpam-5042	729	7	on	on	ADP
ejpam-5042	729	8	the	the	DET
ejpam-5042	729	9	equationally	equationally	ADV
ejpam-5042	729	10	definable	definable	ADJ
ejpam-5042	729	11	nature	nature	NOUN
ejpam-5042	729	12	of	of	ADP
ejpam-5042	729	13	parapseudo	parapseudo	NOUN
ejpam-5042	729	14	-	-	NOUN
ejpam-5042	729	15	complementation	complementation	NOUN
ejpam-5042	729	16	,	,	PUNCT
ejpam-5042	729	17	identifying	identify	VERB
ejpam-5042	729	18	the	the	DET
ejpam-5042	729	19	properties	property	NOUN
ejpam-5042	729	20	required	require	VERB
ejpam-5042	729	21	for	for	ADP
ejpam-5042	729	22	this	this	DET
ejpam-5042	729	23	concept	concept	NOUN
ejpam-5042	729	24	to	to	PART
ejpam-5042	729	25	be	be	AUX
ejpam-5042	729	26	equationally	equationally	ADV
ejpam-5042	729	27	definable	definable	ADJ
ejpam-5042	729	28	within	within	ADP
ejpam-5042	729	29	a	a	DET
ejpam-5042	729	30	pdl	pdl	NOUN
ejpam-5042	729	31	.	.	PUNCT
ejpam-5042	730	1	this	this	PRON
ejpam-5042	730	2	contributes	contribute	VERB
ejpam-5042	730	3	to	to	ADP
ejpam-5042	730	4	a	a	DET
ejpam-5042	730	5	deeper	deep	ADJ
ejpam-5042	730	6	understanding	understanding	NOUN
ejpam-5042	730	7	of	of	ADP
ejpam-5042	730	8	the	the	DET
ejpam-5042	730	9	formalization	formalization	NOUN
ejpam-5042	730	10	and	and	CCONJ
ejpam-5042	730	11	algebraic	algebraic	ADJ
ejpam-5042	730	12	implications	implication	NOUN
ejpam-5042	730	13	of	of	ADP
ejpam-5042	730	14	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5042	730	15	.	.	PUNCT
ejpam-5042	731	1	additionally	additionally	ADV
ejpam-5042	731	2	,	,	PUNCT
ejpam-5042	731	3	we	we	PRON
ejpam-5042	731	4	have	have	AUX
ejpam-5042	731	5	established	establish	VERB
ejpam-5042	731	6	a	a	DET
ejpam-5042	731	7	one	one	NUM
ejpam-5042	731	8	-	-	PUNCT
ejpam-5042	731	9	to	to	ADP
ejpam-5042	731	10	-	-	PUNCT
ejpam-5042	731	11	one	one	NUM
ejpam-5042	731	12	correspondence	correspondence	NOUN
ejpam-5042	731	13	between	between	ADP
ejpam-5042	731	14	the	the	DET
ejpam-5042	731	15	set	set	NOUN
ejpam-5042	731	16	of	of	ADP
ejpam-5042	731	17	all	all	DET
ejpam-5042	731	18	minimal	minimal	ADJ
ejpam-5042	731	19	elements	element	NOUN
ejpam-5042	731	20	and	and	CCONJ
ejpam-5042	731	21	the	the	DET
ejpam-5042	731	22	set	set	NOUN
ejpam-5042	731	23	of	of	ADP
ejpam-5042	731	24	all	all	DET
ejpam-5042	731	25	parapseudo	parapseudo	NOUN
ejpam-5042	731	26	-	-	PUNCT
ejpam-5042	731	27	complementations	complementation	NOUN
ejpam-5042	731	28	in	in	ADP
ejpam-5042	731	29	a	a	DET
ejpam-5042	731	30	pdl	pdl	NOUN
ejpam-5042	731	31	.	.	PUNCT
ejpam-5042	732	1	this	this	DET
ejpam-5042	732	2	correspondence	correspondence	NOUN
ejpam-5042	732	3	highlights	highlight	VERB
ejpam-5042	732	4	the	the	DET
ejpam-5042	732	5	interplay	interplay	NOUN
ejpam-5042	732	6	between	between	ADP
ejpam-5042	732	7	minimal	minimal	ADJ
ejpam-5042	732	8	elements	element	NOUN
ejpam-5042	732	9	and	and	CCONJ
ejpam-5042	732	10	parapseudocomplementation	parapseudocomplementation	NOUN
ejpam-5042	732	11	,	,	PUNCT
ejpam-5042	732	12	providing	provide	VERB
ejpam-5042	732	13	a	a	DET
ejpam-5042	732	14	valuable	valuable	ADJ
ejpam-5042	732	15	connection	connection	NOUN
ejpam-5042	732	16	between	between	ADP
ejpam-5042	732	17	the	the	DET
ejpam-5042	732	18	structural	structural	ADJ
ejpam-5042	732	19	elements	element	NOUN
ejpam-5042	732	20	of	of	ADP
ejpam-5042	732	21	a	a	DET
ejpam-5042	732	22	pdl	pdl	NOUN
ejpam-5042	732	23	and	and	CCONJ
ejpam-5042	732	24	the	the	DET
ejpam-5042	732	25	concept	concept	NOUN
ejpam-5042	732	26	under	under	ADP
ejpam-5042	732	27	study	study	NOUN
ejpam-5042	732	28	.	.	PUNCT
ejpam-5042	733	1	in	in	ADP
ejpam-5042	733	2	future	future	NOUN
ejpam-5042	733	3	,	,	PUNCT
ejpam-5042	733	4	our	our	PRON
ejpam-5042	733	5	work	work	NOUN
ejpam-5042	733	6	will	will	AUX
ejpam-5042	733	7	focus	focus	VERB
ejpam-5042	733	8	on	on	ADP
ejpam-5042	733	9	♦	♦	PROPN
ejpam-5042	733	10	-pdl	-pdl	PROPN
ejpam-5042	733	11	,	,	PUNCT
ejpam-5042	733	12	stone	stone	NOUN
ejpam-5042	733	13	pdl	pdl	PROPN
ejpam-5042	733	14	and	and	CCONJ
ejpam-5042	733	15	study	study	VERB
ejpam-5042	733	16	their	their	PRON
ejpam-5042	733	17	topological	topological	ADJ
ejpam-5042	733	18	properties	property	NOUN
ejpam-5042	733	19	.	.	PUNCT
ejpam-5042	734	1	conflicts	conflict	NOUN
ejpam-5042	734	2	of	of	ADP
ejpam-5042	734	3	interest	interest	NOUN
ejpam-5042	734	4	or	or	CCONJ
ejpam-5042	734	5	competing	compete	VERB
ejpam-5042	734	6	interests	interest	NOUN
ejpam-5042	734	7	the	the	DET
ejpam-5042	734	8	authors	author	NOUN
ejpam-5042	734	9	declare	declare	VERB
ejpam-5042	734	10	that	that	SCONJ
ejpam-5042	734	11	they	they	PRON
ejpam-5042	734	12	have	have	VERB
ejpam-5042	734	13	no	no	DET
ejpam-5042	734	14	conflicts	conflict	NOUN
ejpam-5042	734	15	of	of	ADP
ejpam-5042	734	16	interest	interest	NOUN
ejpam-5042	734	17	.	.	PUNCT
ejpam-5042	735	1	informed	inform	VERB
ejpam-5042	735	2	consent	consent	VERB
ejpam-5042	735	3	the	the	DET
ejpam-5042	735	4	authors	author	NOUN
ejpam-5042	735	5	are	be	AUX
ejpam-5042	735	6	fully	fully	ADV
ejpam-5042	735	7	aware	aware	ADJ
ejpam-5042	735	8	and	and	CCONJ
ejpam-5042	735	9	satisfied	satisfied	ADJ
ejpam-5042	735	10	with	with	ADP
ejpam-5042	735	11	the	the	DET
ejpam-5042	735	12	contents	content	NOUN
ejpam-5042	735	13	of	of	ADP
ejpam-5042	735	14	the	the	DET
ejpam-5042	735	15	article	article	NOUN
ejpam-5042	735	16	.	.	PUNCT
ejpam-5042	736	1	acknowledgements	acknowledgement	NOUN
ejpam-5042	736	2	the	the	DET
ejpam-5042	736	3	authors	author	NOUN
ejpam-5042	736	4	wish	wish	VERB
ejpam-5042	736	5	to	to	PART
ejpam-5042	736	6	thank	thank	VERB
ejpam-5042	736	7	the	the	DET
ejpam-5042	736	8	anonymous	anonymous	ADJ
ejpam-5042	736	9	reviewers	reviewer	NOUN
ejpam-5042	736	10	for	for	ADP
ejpam-5042	736	11	their	their	PRON
ejpam-5042	736	12	valuable	valuable	ADJ
ejpam-5042	736	13	suggestions	suggestion	NOUN
ejpam-5042	736	14	.	.	PUNCT
ejpam-5042	737	1	references	reference	NOUN
ejpam-5042	737	2	[	[	X
ejpam-5042	737	3	1	1	NUM
ejpam-5042	737	4	]	]	X
ejpam-5042	737	5	r	r	NOUN
ejpam-5042	737	6	bandaru	bandaru	NOUN
ejpam-5042	737	7	and	and	CCONJ
ejpam-5042	737	8	s	s	NOUN
ejpam-5042	737	9	ajjarapu	ajjarapu	PROPN
ejpam-5042	737	10	.	.	PUNCT
ejpam-5042	738	1	paradistributive	paradistributive	ADJ
ejpam-5042	738	2	latticoids	latticoids	PROPN
ejpam-5042	738	3	.	.	PUNCT
ejpam-5042	739	1	european	european	PROPN
ejpam-5042	739	2	journal	journal	PROPN
ejpam-5042	739	3	of	of	ADP
ejpam-5042	739	4	pure	pure	ADJ
ejpam-5042	739	5	and	and	CCONJ
ejpam-5042	739	6	applied	applied	ADJ
ejpam-5042	739	7	mathematics	mathematic	NOUN
ejpam-5042	739	8	,	,	PUNCT
ejpam-5042	739	9	in	in	ADP
ejpam-5042	739	10	press	press	NOUN
ejpam-5042	739	11	.	.	PUNCT
ejpam-5042	740	1	https://doi.org/10.29020/nybg.ejpam.v17i2.5042	https://doi.org/10.29020/nybg.ejpam.v17i2.5042	X
ejpam-5042	740	2	.	.	PUNCT
ejpam-5042	741	1	[	[	X
ejpam-5042	741	2	2	2	X
ejpam-5042	741	3	]	]	SYM
ejpam-5042	741	4	g	g	NOUN
ejpam-5042	741	5	birkhoff	birkhoff	NOUN
ejpam-5042	741	6	.	.	PUNCT
ejpam-5042	742	1	lattice	lattice	PROPN
ejpam-5042	742	2	theory	theory	NOUN
ejpam-5042	742	3	.	.	PUNCT
ejpam-5042	743	1	colloquium	colloquium	NOUN
ejpam-5042	743	2	publications	publication	NOUN
ejpam-5042	743	3	,	,	PUNCT
ejpam-5042	743	4	american	american	PROPN
ejpam-5042	743	5	mathematical	mathematical	PROPN
ejpam-5042	743	6	society	society	NOUN
ejpam-5042	743	7	,	,	PUNCT
ejpam-5042	743	8	new	new	PROPN
ejpam-5042	743	9	york	york	PROPN
ejpam-5042	743	10	,	,	PUNCT
ejpam-5042	743	11	1940	1940	NUM
ejpam-5042	743	12	.	.	PUNCT
ejpam-5042	744	1	[	[	X
ejpam-5042	744	2	3	3	X
ejpam-5042	744	3	]	]	X
ejpam-5042	744	4	i	i	PRON
ejpam-5042	744	5	chajda	chajda	NOUN
ejpam-5042	744	6	and	and	CCONJ
ejpam-5042	744	7	h	h	NOUN
ejpam-5042	744	8	langer	langer	NOUN
ejpam-5042	744	9	.	.	PUNCT
ejpam-5042	745	1	filters	filter	NOUN
ejpam-5042	745	2	and	and	CCONJ
ejpam-5042	745	3	congruences	congruence	NOUN
ejpam-5042	745	4	in	in	ADP
ejpam-5042	745	5	sectionally	sectionally	ADV
ejpam-5042	745	6	pseudocomplemented	pseudocomplemente	VERB
ejpam-5042	745	7	lattices	lattice	NOUN
ejpam-5042	745	8	and	and	CCONJ
ejpam-5042	745	9	posets	poset	NOUN
ejpam-5042	745	10	.	.	PUNCT
ejpam-5042	746	1	soft	soft	ADJ
ejpam-5042	746	2	computing	computing	NOUN
ejpam-5042	746	3	,	,	PUNCT
ejpam-5042	746	4	25:8827–8837	25:8827–8837	PROPN
ejpam-5042	746	5	,	,	PUNCT
ejpam-5042	746	6	2021	2021	NUM
ejpam-5042	746	7	.	.	PUNCT
ejpam-5042	747	1	references	reference	NOUN
ejpam-5042	747	2	1145	1145	NUM
ejpam-5042	747	3	[	[	X
ejpam-5042	747	4	4	4	X
ejpam-5042	747	5	]	]	PUNCT
ejpam-5042	747	6	i	i	PRON
ejpam-5042	747	7	chajda	chajda	NOUN
ejpam-5042	747	8	and	and	CCONJ
ejpam-5042	747	9	h	h	NOUN
ejpam-5042	747	10	langer	langer	PROPN
ejpam-5042	747	11	.	.	PUNCT
ejpam-5042	748	1	implication	implication	NOUN
ejpam-5042	748	2	in	in	ADP
ejpam-5042	748	3	finite	finite	ADJ
ejpam-5042	748	4	posets	poset	NOUN
ejpam-5042	748	5	with	with	ADP
ejpam-5042	748	6	pseudocomplemented	pseudocomplemented	ADJ
ejpam-5042	748	7	sections	section	NOUN
ejpam-5042	748	8	.	.	PUNCT
ejpam-5042	749	1	soft	soft	ADJ
ejpam-5042	749	2	computing	computing	NOUN
ejpam-5042	749	3	,	,	PUNCT
ejpam-5042	749	4	26:5945–5953	26:5945–5953	NUM
ejpam-5042	749	5	,	,	PUNCT
ejpam-5042	749	6	2022	2022	NUM
ejpam-5042	749	7	.	.	PUNCT
ejpam-5042	750	1	[	[	X
ejpam-5042	750	2	5	5	NUM
ejpam-5042	750	3	]	]	X
ejpam-5042	750	4	o	o	X
ejpam-5042	750	5	frink	frink	PROPN
ejpam-5042	750	6	.	.	PUNCT
ejpam-5042	751	1	pseudo	pseudo	NOUN
ejpam-5042	751	2	-	-	NOUN
ejpam-5042	751	3	complements	complement	NOUN
ejpam-5042	751	4	in	in	ADP
ejpam-5042	751	5	semi	semi	NOUN
ejpam-5042	751	6	-	-	NOUN
ejpam-5042	751	7	lattices	lattice	NOUN
ejpam-5042	751	8	.	.	PUNCT
ejpam-5042	752	1	duke	duke	PROPN
ejpam-5042	752	2	mathematical	mathematical	PROPN
ejpam-5042	752	3	journal	journal	PROPN
ejpam-5042	752	4	,	,	PUNCT
ejpam-5042	752	5	29:505	29:505	NUM
ejpam-5042	752	6	–	–	PUNCT
ejpam-5042	752	7	514	514	NUM
ejpam-5042	752	8	,	,	PUNCT
ejpam-5042	752	9	1962	1962	NUM
ejpam-5042	752	10	.	.	PUNCT
ejpam-5042	753	1	[	[	X
ejpam-5042	753	2	6	6	NUM
ejpam-5042	753	3	]	]	PUNCT
ejpam-5042	753	4	m	m	VERB
ejpam-5042	753	5	mandelker	mandelker	NOUN
ejpam-5042	753	6	.	.	PUNCT
ejpam-5042	754	1	relative	relative	ADJ
ejpam-5042	754	2	annhilators	annhilator	NOUN
ejpam-5042	754	3	in	in	ADP
ejpam-5042	754	4	lattices	lattice	NOUN
ejpam-5042	754	5	.	.	PUNCT
ejpam-5042	755	1	duke	duke	PROPN
ejpam-5042	755	2	mathematical	mathematical	PROPN
ejpam-5042	755	3	journal	journal	PROPN
ejpam-5042	755	4	,	,	PUNCT
ejpam-5042	755	5	37:377	37:377	NUM
ejpam-5042	755	6	–	–	PUNCT
ejpam-5042	755	7	386	386	NUM
ejpam-5042	755	8	,	,	PUNCT
ejpam-5042	755	9	1970	1970	NUM
ejpam-5042	755	10	.	.	PUNCT
ejpam-5042	756	1	[	[	X
ejpam-5042	756	2	7	7	X
ejpam-5042	756	3	]	]	X
ejpam-5042	756	4	m	m	PROPN
ejpam-5042	756	5	sambasiva	sambasiva	PROPN
ejpam-5042	756	6	rao	rao	PROPN
ejpam-5042	756	7	.	.	PUNCT
ejpam-5042	757	1	δ	δ	PROPN
ejpam-5042	757	2	-	-	PUNCT
ejpam-5042	757	3	ideals	ideal	NOUN
ejpam-5042	757	4	in	in	ADP
ejpam-5042	757	5	pseudo	pseudo	NOUN
ejpam-5042	757	6	-	-	ADJ
ejpam-5042	757	7	complemented	complement	VERB
ejpam-5042	757	8	distributive	distributive	ADJ
ejpam-5042	757	9	lattices	lattice	NOUN
ejpam-5042	757	10	.	.	PUNCT
ejpam-5042	758	1	archivum	archivum	PROPN
ejpam-5042	758	2	mathematicum	mathematicum	PROPN
ejpam-5042	758	3	,	,	PUNCT
ejpam-5042	758	4	48(2):97–105	48(2):97–105	NUM
ejpam-5042	758	5	,	,	PUNCT
ejpam-5042	758	6	2012	2012	NUM
ejpam-5042	758	7	.	.	PUNCT
ejpam-5042	759	1	[	[	X
ejpam-5042	759	2	8	8	NUM
ejpam-5042	759	3	]	]	X
ejpam-5042	759	4	m	m	VERB
ejpam-5042	759	5	sambasiva	sambasiva	NOUN
ejpam-5042	759	6	rao	rao	PROPN
ejpam-5042	759	7	and	and	CCONJ
ejpam-5042	759	8	a	a	DET
ejpam-5042	759	9	e	e	NOUN
ejpam-5042	759	10	badawy	badawy	NOUN
ejpam-5042	759	11	.	.	PUNCT
ejpam-5042	760	1	normal	normal	ADJ
ejpam-5042	760	2	ideals	ideal	NOUN
ejpam-5042	760	3	of	of	ADP
ejpam-5042	760	4	pseudo	pseudo	NOUN
ejpam-5042	760	5	-	-	ADJ
ejpam-5042	760	6	complemented	complement	VERB
ejpam-5042	760	7	distributive	distributive	ADJ
ejpam-5042	760	8	lattices	lattice	NOUN
ejpam-5042	760	9	.	.	PUNCT
ejpam-5042	761	1	chamchuri	chamchuri	PROPN
ejpam-5042	761	2	journal	journal	PROPN
ejpam-5042	761	3	of	of	ADP
ejpam-5042	761	4	mathematics	mathematic	NOUN
ejpam-5042	761	5	,	,	PUNCT
ejpam-5042	761	6	9:61–73	9:61–73	NUM
ejpam-5042	761	7	,	,	PUNCT
ejpam-5042	761	8	2017	2017	NUM
ejpam-5042	761	9	.	.	PUNCT
ejpam-5042	762	1	[	[	X
ejpam-5042	762	2	9	9	NUM
ejpam-5042	762	3	]	]	PUNCT
ejpam-5042	762	4	e	e	X
ejpam-5042	762	5	g	g	PROPN
ejpam-5042	762	6	rezk	rezk	PROPN
ejpam-5042	762	7	.	.	PUNCT
ejpam-5042	763	1	closed	close	VERB
ejpam-5042	763	2	ideals	ideal	NOUN
ejpam-5042	763	3	and	and	CCONJ
ejpam-5042	763	4	annihilators	annihilator	NOUN
ejpam-5042	763	5	of	of	ADP
ejpam-5042	763	6	distributive	distributive	ADJ
ejpam-5042	763	7	dual	dual	ADJ
ejpam-5042	763	8	weakly	weakly	ADJ
ejpam-5042	763	9	complemented	complemented	ADJ
ejpam-5042	763	10	lattice	lattice	NOUN
ejpam-5042	763	11	.	.	PUNCT
ejpam-5042	764	1	european	european	PROPN
ejpam-5042	764	2	journal	journal	PROPN
ejpam-5042	764	3	of	of	ADP
ejpam-5042	764	4	pure	pure	ADJ
ejpam-5042	764	5	and	and	CCONJ
ejpam-5042	764	6	applied	applied	ADJ
ejpam-5042	764	7	mathematics	mathematic	NOUN
ejpam-5042	764	8	,	,	PUNCT
ejpam-5042	764	9	15(2):486–495	15(2):486–495	NUM
ejpam-5042	764	10	,	,	PUNCT
ejpam-5042	764	11	2022	2022	NUM
ejpam-5042	764	12	.	.	PUNCT
ejpam-5042	765	1	[	[	X
ejpam-5042	765	2	10	10	NUM
ejpam-5042	765	3	]	]	X
ejpam-5042	765	4	p	p	PRON
ejpam-5042	765	5	ribenboim	ribenboim	NOUN
ejpam-5042	765	6	.	.	PUNCT
ejpam-5042	766	1	characterization	characterization	NOUN
ejpam-5042	766	2	of	of	ADP
ejpam-5042	766	3	the	the	DET
ejpam-5042	766	4	pseudo	pseudo	NOUN
ejpam-5042	766	5	-	-	NOUN
ejpam-5042	766	6	complement	complement	NOUN
ejpam-5042	766	7	in	in	ADP
ejpam-5042	766	8	a	a	DET
ejpam-5042	766	9	distributive	distributive	ADJ
ejpam-5042	766	10	lattice	lattice	NOUN
ejpam-5042	766	11	with	with	ADP
ejpam-5042	766	12	least	least	ADJ
ejpam-5042	766	13	element	element	ADJ
ejpam-5042	766	14	.	.	PUNCT
ejpam-5042	767	1	summa	summa	ADJ
ejpam-5042	767	2	brasiliensis	brasiliensis	NOUN
ejpam-5042	767	3	mathematicae	mathematicae	PROPN
ejpam-5042	767	4	,	,	PUNCT
ejpam-5042	767	5	2(4):43–49	2(4):43–49	NUM
ejpam-5042	767	6	,	,	PUNCT
ejpam-5042	767	7	1949	1949	NUM
ejpam-5042	767	8	.	.	PUNCT
ejpam-5042	768	1	[	[	X
ejpam-5042	768	2	11	11	NUM
ejpam-5042	768	3	]	]	X
ejpam-5042	768	4	u	u	PROPN
ejpam-5042	768	5	m	m	NOUN
ejpam-5042	768	6	swamy	swamy	NOUN
ejpam-5042	768	7	and	and	CCONJ
ejpam-5042	768	8	g	g	PROPN
ejpam-5042	768	9	c	c	PROPN
ejpam-5042	768	10	rao	rao	PROPN
ejpam-5042	768	11	.	.	PUNCT
ejpam-5042	769	1	almost	almost	ADV
ejpam-5042	769	2	distributive	distributive	ADJ
ejpam-5042	769	3	lattices	lattice	NOUN
ejpam-5042	769	4	.	.	PUNCT
ejpam-5042	770	1	journal	journal	NOUN
ejpam-5042	770	2	of	of	ADP
ejpam-5042	770	3	the	the	DET
ejpam-5042	770	4	australian	australian	ADJ
ejpam-5042	770	5	mathematical	mathematical	ADJ
ejpam-5042	770	6	society	society	NOUN
ejpam-5042	770	7	.	.	PUNCT
ejpam-5042	771	1	series	series	PROPN
ejpam-5042	771	2	a.	a.	PROPN
ejpam-5042	771	3	,	,	PUNCT
ejpam-5042	771	4	31:77–91	31:77–91	NUM
ejpam-5042	771	5	,	,	PUNCT
ejpam-5042	771	6	1981	1981	NUM
ejpam-5042	771	7	.	.	PUNCT
ejpam-5042	772	1	[	[	X
ejpam-5042	772	2	12	12	NUM
ejpam-5042	772	3	]	]	X
ejpam-5042	772	4	u	u	PROPN
ejpam-5042	772	5	m	m	NOUN
ejpam-5042	772	6	swamy	swamy	NOUN
ejpam-5042	772	7	,	,	PUNCT
ejpam-5042	772	8	g	g	PROPN
ejpam-5042	772	9	c	c	PROPN
ejpam-5042	772	10	rao	rao	PROPN
ejpam-5042	772	11	,	,	PUNCT
ejpam-5042	772	12	and	and	CCONJ
ejpam-5042	772	13	g	g	PROPN
ejpam-5042	772	14	n	n	PRON
ejpam-5042	772	15	rao	rao	PROPN
ejpam-5042	772	16	.	.	PUNCT
ejpam-5042	773	1	pseudo	pseudo	NOUN
ejpam-5042	773	2	-	-	NOUN
ejpam-5042	773	3	complementation	complementation	NOUN
ejpam-5042	773	4	on	on	ADP
ejpam-5042	773	5	almost	almost	ADV
ejpam-5042	773	6	distributive	distributive	ADJ
ejpam-5042	773	7	lattices	lattice	NOUN
ejpam-5042	773	8	.	.	PUNCT
ejpam-5042	774	1	southeast	southeast	ADJ
ejpam-5042	774	2	asian	asian	ADJ
ejpam-5042	774	3	bulletin	bulletin	NOUN
ejpam-5042	774	4	of	of	ADP
ejpam-5042	774	5	mathematics	mathematic	NOUN
ejpam-5042	774	6	,	,	PUNCT
ejpam-5042	774	7	24:95–104	24:95–104	NUM
ejpam-5042	774	8	,	,	PUNCT
ejpam-5042	774	9	2000	2000	NUM
ejpam-5042	774	10	.	.	PUNCT
ejpam-5042	775	1	[	[	X
ejpam-5042	775	2	13	13	NUM
ejpam-5042	775	3	]	]	SYM
ejpam-5042	775	4	c	c	PROPN
ejpam-5042	775	5	thomaz	thomaz	PROPN
ejpam-5042	775	6	.	.	PUNCT
ejpam-5042	776	1	dicomplemented	dicomplemente	VERB
ejpam-5042	776	2	lattices	lattice	NOUN
ejpam-5042	776	3	.	.	PUNCT
ejpam-5042	777	1	a	a	DET
ejpam-5042	777	2	contextual	contextual	ADJ
ejpam-5042	777	3	generalization	generalization	NOUN
ejpam-5042	777	4	of	of	ADP
ejpam-5042	777	5	boolean	boolean	ADJ
ejpam-5042	777	6	algebra	algebra	NOUN
ejpam-5042	777	7	.	.	PUNCT
ejpam-5042	778	1	phd	phd	NOUN
ejpam-5042	778	2	thesis	thesis	PROPN
ejpam-5042	778	3	,	,	PUNCT
ejpam-5042	778	4	tu	tu	PROPN
ejpam-5042	778	5	dresden	dresden	PROPN
ejpam-5042	778	6	,	,	PUNCT
ejpam-5042	778	7	2004	2004	NUM
ejpam-5042	778	8	.	.	PUNCT
ejpam-5042	779	1	[	[	X
ejpam-5042	779	2	14	14	NUM
ejpam-5042	779	3	]	]	X
ejpam-5042	779	4	p	p	X
ejpam-5042	779	5	v	v	X
ejpam-5042	779	6	venkatanarasimhan	venkatanarasimhan	ADJ
ejpam-5042	779	7	.	.	PUNCT
ejpam-5042	780	1	pseudo	pseudo	NOUN
ejpam-5042	780	2	-	-	NOUN
ejpam-5042	780	3	complements	complement	NOUN
ejpam-5042	780	4	in	in	ADP
ejpam-5042	780	5	posets	poset	NOUN
ejpam-5042	780	6	.	.	PUNCT
ejpam-5042	781	1	proceedings	proceeding	NOUN
ejpam-5042	781	2	of	of	ADP
ejpam-5042	781	3	the	the	DET
ejpam-5042	781	4	american	american	PROPN
ejpam-5042	781	5	mathematical	mathematical	PROPN
ejpam-5042	781	6	society	society	NOUN
ejpam-5042	781	7	,	,	PUNCT
ejpam-5042	781	8	28(1):9–17	28(1):9–17	NUM
ejpam-5042	781	9	,	,	PUNCT
ejpam-5042	781	10	1971	1971	NUM
ejpam-5042	781	11	.	.	PUNCT
ejpam-5042	782	1	[	[	X
ejpam-5042	782	2	15	15	NUM
ejpam-5042	782	3	]	]	X
ejpam-5042	782	4	r	r	NOUN
ejpam-5042	782	5	wille	wille	NOUN
ejpam-5042	782	6	.	.	PUNCT
ejpam-5042	783	1	boolean	boolean	ADJ
ejpam-5042	783	2	concept	concept	NOUN
ejpam-5042	783	3	logic	logic	NOUN
ejpam-5042	783	4	.	.	PUNCT
ejpam-5042	784	1	in	in	ADP
ejpam-5042	784	2	b.	b.	PROPN
ejpam-5042	784	3	ganter	ganter	NOUN
ejpam-5042	784	4	and	and	CCONJ
ejpam-5042	784	5	g.	g.	PROPN
ejpam-5042	784	6	w.	w.	PROPN
ejpam-5042	784	7	mineau	mineau	PROPN
ejpam-5042	784	8	,	,	PUNCT
ejpam-5042	784	9	editors	editor	NOUN
ejpam-5042	784	10	,	,	PUNCT
ejpam-5042	784	11	conceptual	conceptual	ADJ
ejpam-5042	784	12	structures	structure	NOUN
ejpam-5042	784	13	:	:	PUNCT
ejpam-5042	784	14	logical	logical	ADJ
ejpam-5042	784	15	,	,	PUNCT
ejpam-5042	784	16	linguistic	linguistic	ADJ
ejpam-5042	784	17	and	and	CCONJ
ejpam-5042	784	18	computational	computational	ADJ
ejpam-5042	784	19	issues	issue	NOUN
ejpam-5042	784	20	.	.	PUNCT
ejpam-5042	784	21	,	,	PUNCT
ejpam-5042	784	22	pages	page	NOUN
ejpam-5042	784	23	14–18	14–18	NUM
ejpam-5042	784	24	,	,	PUNCT
ejpam-5042	784	25	germany	germany	PROPN
ejpam-5042	784	26	,	,	PUNCT
ejpam-5042	784	27	2000	2000	NUM
ejpam-5042	784	28	.	.	PUNCT
ejpam-5042	784	29	iccs	iccs	PROPN
ejpam-5042	784	30	2000	2000	NUM
ejpam-5042	784	31	darmstadt	darmstadt	PROPN
ejpam-5042	784	32	.	.	PUNCT