id	sid	tid	token	lemma	pos
ejpam-2515	1	1	european	european	PROPN
ejpam-2515	1	2	journal	journal	PROPN
ejpam-2515	1	3	of	of	ADP
ejpam-2515	1	4	pure	pure	ADJ
ejpam-2515	1	5	and	and	CCONJ
ejpam-2515	1	6	applied	apply	VERB
ejpam-2515	1	7	mathematics	mathematic	NOUN
ejpam-2515	1	8	vol	vol	NOUN
ejpam-2515	1	9	.	.	PROPN
ejpam-2515	2	1	9	9	NUM
ejpam-2515	2	2	,	,	PUNCT
ejpam-2515	2	3	no	no	INTJ
ejpam-2515	2	4	.	.	NOUN
ejpam-2515	2	5	4	4	NUM
ejpam-2515	2	6	,	,	PUNCT
ejpam-2515	2	7	2016	2016	NUM
ejpam-2515	2	8	,	,	PUNCT
ejpam-2515	2	9	367	367	NUM
ejpam-2515	2	10	-	-	SYM
ejpam-2515	2	11	382	382	NUM
ejpam-2515	2	12	issn	issn	PROPN
ejpam-2515	2	13	1307	1307	NUM
ejpam-2515	2	14	-	-	SYM
ejpam-2515	2	15	5543	5543	NUM
ejpam-2515	2	16	–	–	PUNCT
ejpam-2515	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2515	2	18	hypergroups	hypergroup	NOUN
ejpam-2515	2	19	associated	associate	VERB
ejpam-2515	2	20	with	with	ADP
ejpam-2515	2	21	ternary	ternary	ADJ
ejpam-2515	2	22	relations	relation	NOUN
ejpam-2515	2	23	and	and	CCONJ
ejpam-2515	2	24	the	the	DET
ejpam-2515	2	25	associated	associated	ADJ
ejpam-2515	2	26	join	join	NOUN
ejpam-2515	2	27	space	space	NOUN
ejpam-2515	2	28	of	of	ADP
ejpam-2515	2	29	the	the	DET
ejpam-2515	2	30	spherical	spherical	ADJ
ejpam-2515	2	31	geometry	geometry	NOUN
ejpam-2515	2	32	sakarapani	sakarapani	PROPN
ejpam-2515	2	33	govindarajan	govindarajan	PROPN
ejpam-2515	2	34	pg	pg	PROPN
ejpam-2515	2	35	and	and	CCONJ
ejpam-2515	2	36	research	research	PROPN
ejpam-2515	2	37	department	department	PROPN
ejpam-2515	2	38	of	of	ADP
ejpam-2515	2	39	mathematics	mathematic	NOUN
ejpam-2515	2	40	,	,	PUNCT
ejpam-2515	2	41	a.v.c	a.v.c	PROPN
ejpam-2515	2	42	.	.	PUNCT
ejpam-2515	3	1	college	college	NOUN
ejpam-2515	3	2	(	(	PUNCT
ejpam-2515	3	3	autonomous	autonomous	ADJ
ejpam-2515	3	4	)	)	PUNCT
ejpam-2515	3	5	,	,	PUNCT
ejpam-2515	3	6	(	(	PUNCT
ejpam-2515	3	7	affiliated	affiliate	VERB
ejpam-2515	3	8	to	to	PART
ejpam-2515	3	9	bharathidasan	bharathidasan	VERB
ejpam-2515	3	10	university	university	NOUN
ejpam-2515	3	11	,	,	PUNCT
ejpam-2515	3	12	trichy	trichy	NOUN
ejpam-2515	3	13	)	)	PUNCT
ejpam-2515	3	14	mannampandal	mannampandal	NOUN
ejpam-2515	3	15	,	,	PUNCT
ejpam-2515	3	16	tamil	tamil	PROPN
ejpam-2515	3	17	nadu	nadu	PROPN
ejpam-2515	3	18	,	,	PUNCT
ejpam-2515	3	19	india	india	PROPN
ejpam-2515	3	20	abstract	abstract	NOUN
ejpam-2515	3	21	.	.	PUNCT
ejpam-2515	4	1	the	the	DET
ejpam-2515	4	2	paper	paper	NOUN
ejpam-2515	4	3	deals	deal	VERB
ejpam-2515	4	4	with	with	ADP
ejpam-2515	4	5	hypergroupoids	hypergroupoid	NOUN
ejpam-2515	4	6	obtained	obtain	VERB
ejpam-2515	4	7	from	from	ADP
ejpam-2515	4	8	ternary	ternary	ADJ
ejpam-2515	4	9	relations.the	relations.the	DET
ejpam-2515	4	10	correspondence	correspondence	NOUN
ejpam-2515	4	11	between	between	ADP
ejpam-2515	4	12	ternary	ternary	ADJ
ejpam-2515	4	13	relation	relation	NOUN
ejpam-2515	4	14	and	and	CCONJ
ejpam-2515	4	15	hypergroups	hypergroup	NOUN
ejpam-2515	4	16	,	,	PUNCT
ejpam-2515	4	17	studied	study	VERB
ejpam-2515	4	18	by	by	ADP
ejpam-2515	4	19	the	the	DET
ejpam-2515	4	20	author	author	NOUN
ejpam-2515	4	21	,	,	PUNCT
ejpam-2515	4	22	especially	especially	ADV
ejpam-2515	4	23	in	in	ADP
ejpam-2515	4	24	the	the	DET
ejpam-2515	4	25	case	case	NOUN
ejpam-2515	4	26	when	when	SCONJ
ejpam-2515	4	27	the	the	DET
ejpam-2515	4	28	relationρ	relationρ	NOUN
ejpam-2515	4	29	is	be	AUX
ejpam-2515	4	30	symmetric	symmetric	ADJ
ejpam-2515	4	31	and	and	CCONJ
ejpam-2515	4	32	reflexive	reflexive	ADJ
ejpam-2515	4	33	,	,	PUNCT
ejpam-2515	4	34	is	be	AUX
ejpam-2515	4	35	analyzed	analyze	VERB
ejpam-2515	4	36	here	here	ADV
ejpam-2515	4	37	in	in	ADP
ejpam-2515	4	38	the	the	DET
ejpam-2515	4	39	most	most	ADV
ejpam-2515	4	40	general	general	ADJ
ejpam-2515	4	41	context.a	context.a	NOUN
ejpam-2515	4	42	necessary	necessary	ADJ
ejpam-2515	4	43	and	and	CCONJ
ejpam-2515	4	44	sufficient	sufficient	ADJ
ejpam-2515	4	45	condition	condition	NOUN
ejpam-2515	4	46	on	on	ADP
ejpam-2515	4	47	a	a	DET
ejpam-2515	4	48	ternary	ternary	ADJ
ejpam-2515	4	49	relation	relation	NOUN
ejpam-2515	4	50	ρ	ρ	NOUN
ejpam-2515	4	51	is	be	AUX
ejpam-2515	4	52	obtained	obtain	VERB
ejpam-2515	4	53	for	for	ADP
ejpam-2515	4	54	the	the	DET
ejpam-2515	4	55	associated	associate	VERB
ejpam-2515	4	56	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	4	57	to	to	PART
ejpam-2515	4	58	be	be	AUX
ejpam-2515	4	59	a	a	DET
ejpam-2515	4	60	hypergroup	hypergroup	NOUN
ejpam-2515	4	61	or	or	CCONJ
ejpam-2515	4	62	a	a	DET
ejpam-2515	4	63	join	join	NOUN
ejpam-2515	4	64	space	space	NOUN
ejpam-2515	4	65	.	.	PUNCT
ejpam-2515	5	1	extension	extension	NOUN
ejpam-2515	5	2	of	of	ADP
ejpam-2515	5	3	a	a	DET
ejpam-2515	5	4	hyperoperation	hyperoperation	NOUN
ejpam-2515	5	5	associated	associate	VERB
ejpam-2515	5	6	with	with	ADP
ejpam-2515	5	7	a	a	DET
ejpam-2515	5	8	ternary	ternary	ADJ
ejpam-2515	5	9	relation	relation	NOUN
ejpam-2515	5	10	being	be	AUX
ejpam-2515	5	11	employed	employ	VERB
ejpam-2515	5	12	to	to	PART
ejpam-2515	5	13	obtain	obtain	VERB
ejpam-2515	5	14	a	a	DET
ejpam-2515	5	15	associated	associated	ADJ
ejpam-2515	5	16	join	join	NOUN
ejpam-2515	5	17	space	space	NOUN
ejpam-2515	5	18	of	of	ADP
ejpam-2515	5	19	the	the	DET
ejpam-2515	5	20	spherical	spherical	ADJ
ejpam-2515	5	21	geometry	geometry	NOUN
ejpam-2515	5	22	.	.	PUNCT
ejpam-2515	6	1	2010	2010	NUM
ejpam-2515	6	2	mathematics	mathematic	NOUN
ejpam-2515	6	3	subject	subject	NOUN
ejpam-2515	6	4	classifications	classification	NOUN
ejpam-2515	6	5	:	:	PUNCT
ejpam-2515	6	6	20n20	20n20	NUM
ejpam-2515	6	7	;	;	PUNCT
ejpam-2515	6	8	04a05	04a05	NUM
ejpam-2515	6	9	key	key	ADJ
ejpam-2515	6	10	words	word	NOUN
ejpam-2515	6	11	and	and	CCONJ
ejpam-2515	6	12	phrases	phrase	NOUN
ejpam-2515	6	13	:	:	PUNCT
ejpam-2515	6	14	ternary	ternary	ADJ
ejpam-2515	6	15	relation	relation	NOUN
ejpam-2515	6	16	,	,	PUNCT
ejpam-2515	6	17	hypergroups	hypergroup	NOUN
ejpam-2515	6	18	,	,	PUNCT
ejpam-2515	6	19	join	join	VERB
ejpam-2515	6	20	spaces	space	NOUN
ejpam-2515	6	21	,	,	PUNCT
ejpam-2515	6	22	spherical	spherical	ADJ
ejpam-2515	6	23	geometry	geometry	NOUN
ejpam-2515	6	24	,	,	PUNCT
ejpam-2515	6	25	associated	associate	VERB
ejpam-2515	6	26	join	join	NOUN
ejpam-2515	6	27	space	space	NOUN
ejpam-2515	6	28	1	1	NUM
ejpam-2515	6	29	.	.	PUNCT
ejpam-2515	7	1	introduction	introduction	NOUN
ejpam-2515	7	2	hyper	hyper	ADJ
ejpam-2515	7	3	structure	structure	NOUN
ejpam-2515	7	4	theory	theory	NOUN
ejpam-2515	7	5	was	be	AUX
ejpam-2515	7	6	born	bear	VERB
ejpam-2515	7	7	during	during	ADP
ejpam-2515	7	8	the	the	DET
ejpam-2515	7	9	8th	8th	ADJ
ejpam-2515	7	10	congress	congress	PROPN
ejpam-2515	7	11	of	of	ADP
ejpam-2515	7	12	scandinavian	scandinavian	ADJ
ejpam-2515	7	13	mathematicians	mathematician	NOUN
ejpam-2515	7	14	in	in	ADP
ejpam-2515	7	15	1934	1934	NUM
ejpam-2515	7	16	,	,	PUNCT
ejpam-2515	7	17	when	when	SCONJ
ejpam-2515	7	18	f.	f.	PROPN
ejpam-2515	7	19	marty	marty	PROPN
ejpam-2515	8	1	[	[	X
ejpam-2515	8	2	17	17	NUM
ejpam-2515	8	3	]	]	PUNCT
ejpam-2515	8	4	defined	define	VERB
ejpam-2515	8	5	hypergroups	hypergroup	NOUN
ejpam-2515	8	6	,	,	PUNCT
ejpam-2515	8	7	a	a	DET
ejpam-2515	8	8	natural	natural	ADJ
ejpam-2515	8	9	generalization	generalization	NOUN
ejpam-2515	8	10	of	of	ADP
ejpam-2515	8	11	the	the	DET
ejpam-2515	8	12	concept	concept	NOUN
ejpam-2515	8	13	of	of	ADP
ejpam-2515	8	14	group	group	NOUN
ejpam-2515	8	15	,	,	PUNCT
ejpam-2515	8	16	and	and	CCONJ
ejpam-2515	8	17	began	begin	VERB
ejpam-2515	8	18	to	to	PART
ejpam-2515	8	19	analyze	analyze	VERB
ejpam-2515	8	20	their	their	PRON
ejpam-2515	8	21	properties	property	NOUN
ejpam-2515	8	22	and	and	CCONJ
ejpam-2515	8	23	applied	apply	VERB
ejpam-2515	8	24	to	to	ADP
ejpam-2515	8	25	them	they	PRON
ejpam-2515	8	26	to	to	ADP
ejpam-2515	8	27	non	non	PRON
ejpam-2515	8	28	commutative	commutative	ADJ
ejpam-2515	8	29	groups	group	NOUN
ejpam-2515	8	30	,	,	PUNCT
ejpam-2515	8	31	rational	rational	ADJ
ejpam-2515	8	32	fractions	fraction	NOUN
ejpam-2515	8	33	and	and	CCONJ
ejpam-2515	8	34	algebraic	algebraic	ADJ
ejpam-2515	8	35	functions	function	NOUN
ejpam-2515	8	36	etc	etc	X
ejpam-2515	8	37	,	,	PUNCT
ejpam-2515	8	38	.	.	PUNCT
ejpam-2515	9	1	since	since	SCONJ
ejpam-2515	9	2	then	then	ADV
ejpam-2515	9	3	various	various	ADJ
ejpam-2515	9	4	connection	connection	NOUN
ejpam-2515	9	5	between	between	ADP
ejpam-2515	9	6	hypergroups	hypergroup	NOUN
ejpam-2515	9	7	and	and	CCONJ
ejpam-2515	9	8	other	other	ADJ
ejpam-2515	9	9	subjects	subject	NOUN
ejpam-2515	9	10	of	of	ADP
ejpam-2515	9	11	theoretical	theoretical	ADJ
ejpam-2515	9	12	and	and	CCONJ
ejpam-2515	9	13	applied	apply	VERB
ejpam-2515	9	14	mathematics	mathematic	NOUN
ejpam-2515	9	15	have	have	AUX
ejpam-2515	9	16	been	be	AUX
ejpam-2515	9	17	established	establish	VERB
ejpam-2515	9	18	.	.	PUNCT
ejpam-2515	10	1	the	the	DET
ejpam-2515	10	2	most	most	ADV
ejpam-2515	10	3	important	important	ADJ
ejpam-2515	10	4	applications	application	NOUN
ejpam-2515	10	5	to	to	ADP
ejpam-2515	10	6	geometry	geometry	NOUN
ejpam-2515	10	7	,	,	PUNCT
ejpam-2515	10	8	topology	topology	NOUN
ejpam-2515	10	9	,	,	PUNCT
ejpam-2515	10	10	cryptography	cryptography	NOUN
ejpam-2515	10	11	and	and	CCONJ
ejpam-2515	10	12	code	code	NOUN
ejpam-2515	10	13	theory	theory	NOUN
ejpam-2515	10	14	,	,	PUNCT
ejpam-2515	10	15	graphs	graph	NOUN
ejpam-2515	10	16	and	and	CCONJ
ejpam-2515	10	17	hypergraphs	hypergraph	NOUN
ejpam-2515	10	18	,	,	PUNCT
ejpam-2515	10	19	probability	probability	NOUN
ejpam-2515	10	20	theory	theory	NOUN
ejpam-2515	10	21	,	,	PUNCT
ejpam-2515	10	22	binary	binary	ADJ
ejpam-2515	10	23	relations	relation	NOUN
ejpam-2515	10	24	,	,	PUNCT
ejpam-2515	10	25	theory	theory	NOUN
ejpam-2515	10	26	of	of	ADP
ejpam-2515	10	27	fuzzy	fuzzy	ADJ
ejpam-2515	10	28	sets	set	NOUN
ejpam-2515	10	29	and	and	CCONJ
ejpam-2515	10	30	rough	rough	ADJ
ejpam-2515	10	31	sets	set	NOUN
ejpam-2515	10	32	,	,	PUNCT
ejpam-2515	10	33	automata	automata	NOUN
ejpam-2515	10	34	theory	theory	NOUN
ejpam-2515	10	35	are	be	AUX
ejpam-2515	10	36	found	find	VERB
ejpam-2515	10	37	in	in	ADP
ejpam-2515	10	38	[	[	X
ejpam-2515	10	39	8	8	NUM
ejpam-2515	10	40	]	]	PUNCT
ejpam-2515	10	41	.	.	PUNCT
ejpam-2515	11	1	the	the	DET
ejpam-2515	11	2	first	first	ADJ
ejpam-2515	11	3	association	association	NOUN
ejpam-2515	11	4	between	between	ADP
ejpam-2515	11	5	binary	binary	PROPN
ejpam-2515	11	6	relation	relation	PROPN
ejpam-2515	11	7	and	and	CCONJ
ejpam-2515	11	8	hyperstructures	hyperstructure	NOUN
ejpam-2515	11	9	appeared	appear	VERB
ejpam-2515	11	10	in	in	ADP
ejpam-2515	11	11	j.	j.	PROPN
ejpam-2515	11	12	nieminen	nieminen	PROPN
ejpam-2515	12	1	[	[	X
ejpam-2515	12	2	18	18	NUM
ejpam-2515	12	3	]	]	X
ejpam-2515	12	4	,	,	PUNCT
ejpam-2515	12	5	who	who	PRON
ejpam-2515	12	6	studied	study	VERB
ejpam-2515	12	7	hypergroups	hypergroup	NOUN
ejpam-2515	12	8	related	relate	VERB
ejpam-2515	12	9	to	to	ADP
ejpam-2515	12	10	connected	connect	VERB
ejpam-2515	12	11	simple	simple	ADJ
ejpam-2515	12	12	graphs	graph	NOUN
ejpam-2515	12	13	.	.	PUNCT
ejpam-2515	13	1	in	in	ADP
ejpam-2515	13	2	the	the	DET
ejpam-2515	13	3	same	same	ADJ
ejpam-2515	13	4	direction	direction	NOUN
ejpam-2515	13	5	p.	p.	NOUN
ejpam-2515	13	6	corsini	corsini	PROPN
ejpam-2515	14	1	[	[	X
ejpam-2515	14	2	3	3	NUM
ejpam-2515	14	3	]	]	PUNCT
ejpam-2515	14	4	worked	work	VERB
ejpam-2515	14	5	,	,	PUNCT
ejpam-2515	14	6	considering	consider	VERB
ejpam-2515	14	7	different	different	ADJ
ejpam-2515	14	8	hyperoperations	hyperoperation	NOUN
ejpam-2515	14	9	associated	associate	VERB
ejpam-2515	14	10	with	with	ADP
ejpam-2515	14	11	graphs	graph	NOUN
ejpam-2515	14	12	.	.	PUNCT
ejpam-2515	15	1	j.	j.	PROPN
ejpam-2515	15	2	chvalina	chvalina	PROPN
ejpam-2515	16	1	[	[	X
ejpam-2515	16	2	1	1	NUM
ejpam-2515	16	3	]	]	PUNCT
ejpam-2515	16	4	used	use	VERB
ejpam-2515	16	5	ordered	order	VERB
ejpam-2515	16	6	structures	structure	NOUN
ejpam-2515	16	7	for	for	ADP
ejpam-2515	16	8	the	the	DET
ejpam-2515	16	9	construction	construction	NOUN
ejpam-2515	16	10	of	of	ADP
ejpam-2515	16	11	semihypergroups	semihypergroup	NOUN
ejpam-2515	16	12	and	and	CCONJ
ejpam-2515	16	13	hypergroups	hypergroup	NOUN
ejpam-2515	16	14	.	.	PUNCT
ejpam-2515	17	1	later	later	ADV
ejpam-2515	17	2	on	on	ADV
ejpam-2515	17	3	,	,	PUNCT
ejpam-2515	17	4	i.	i.	PROPN
ejpam-2515	17	5	rosenberg	rosenberg	PROPN
ejpam-2515	18	1	[	[	X
ejpam-2515	18	2	20	20	NUM
ejpam-2515	18	3	]	]	PUNCT
ejpam-2515	18	4	introduced	introduce	VERB
ejpam-2515	18	5	a	a	DET
ejpam-2515	18	6	hyperoperation	hyperoperation	NOUN
ejpam-2515	18	7	obtained	obtain	VERB
ejpam-2515	18	8	by	by	ADP
ejpam-2515	18	9	a	a	DET
ejpam-2515	18	10	binary	binary	PROPN
ejpam-2515	18	11	relation	relation	NOUN
ejpam-2515	18	12	;	;	PUNCT
ejpam-2515	18	13	the	the	DET
ejpam-2515	18	14	new	new	ADJ
ejpam-2515	18	15	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	18	16	has	have	AUX
ejpam-2515	18	17	been	be	AUX
ejpam-2515	18	18	investigated	investigate	VERB
ejpam-2515	18	19	by	by	ADP
ejpam-2515	18	20	p.	p.	PROPN
ejpam-2515	18	21	corsini	corsini	PROPN
ejpam-2515	19	1	[	[	X
ejpam-2515	19	2	5	5	NUM
ejpam-2515	19	3	,	,	PUNCT
ejpam-2515	19	4	6	6	NUM
ejpam-2515	19	5	]	]	PUNCT
ejpam-2515	19	6	,	,	PUNCT
ejpam-2515	19	7	p.	p.	NOUN
ejpam-2515	19	8	corsini	corsini	PROPN
ejpam-2515	19	9	and	and	CCONJ
ejpam-2515	19	10	v.	v.	ADP
ejpam-2515	19	11	leoreanu	leoreanu	NOUN
ejpam-2515	19	12	[	[	X
ejpam-2515	19	13	7	7	NUM
ejpam-2515	19	14	]	]	PUNCT
ejpam-2515	19	15	email	email	NOUN
ejpam-2515	19	16	address	address	NOUN
ejpam-2515	19	17	:	:	PUNCT
ejpam-2515	19	18	govindavc@gmail.com	govindavc@gmail.com	X
ejpam-2515	19	19	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2515	20	1	367	367	NUM
ejpam-2515	20	2	c	c	NOUN
ejpam-2515	20	3	©	©	PROPN
ejpam-2515	20	4	2016	2016	NUM
ejpam-2515	20	5	ejpam	ejpam	VERB
ejpam-2515	20	6	all	all	DET
ejpam-2515	20	7	rights	right	NOUN
ejpam-2515	20	8	reserved	reserve	VERB
ejpam-2515	20	9	.	.	PUNCT
ejpam-2515	21	1	s.	s.	PROPN
ejpam-2515	21	2	govindarajan	govindarajan	PROPN
ejpam-2515	21	3	/	/	SYM
ejpam-2515	21	4	eur	eur	PROPN
ejpam-2515	21	5	.	.	PUNCT
ejpam-2515	22	1	j.	j.	PROPN
ejpam-2515	22	2	pure	pure	PROPN
ejpam-2515	22	3	appl	appl	PROPN
ejpam-2515	22	4	.	.	PROPN
ejpam-2515	22	5	math	math	PROPN
ejpam-2515	22	6	,	,	PUNCT
ejpam-2515	22	7	9	9	NUM
ejpam-2515	22	8	(	(	PUNCT
ejpam-2515	22	9	2016	2016	NUM
ejpam-2515	22	10	)	)	PUNCT
ejpam-2515	22	11	,	,	PUNCT
ejpam-2515	22	12	367	367	NUM
ejpam-2515	22	13	-	-	SYM
ejpam-2515	22	14	382	382	NUM
ejpam-2515	22	15	368	368	NUM
ejpam-2515	22	16	and	and	CCONJ
ejpam-2515	22	17	recently	recently	ADV
ejpam-2515	22	18	by	by	ADP
ejpam-2515	22	19	i.	i.	PROPN
ejpam-2515	22	20	cristea	cristea	PROPN
ejpam-2515	22	21	and	and	CCONJ
ejpam-2515	22	22	m.	m.	NOUN
ejpam-2515	22	23	ştefanescu	ştefanescu	PROPN
ejpam-2515	23	1	[	[	X
ejpam-2515	23	2	10	10	NUM
ejpam-2515	23	3	]	]	PUNCT
ejpam-2515	23	4	.	.	PUNCT
ejpam-2515	24	1	p.corsini	p.corsini	PUNCT
ejpam-2515	24	2	introduced	introduce	VERB
ejpam-2515	24	3	a	a	DET
ejpam-2515	24	4	new	new	ADJ
ejpam-2515	24	5	hyperoperation	hyperoperation	NOUN
ejpam-2515	24	6	obtained	obtain	VERB
ejpam-2515	24	7	by	by	ADP
ejpam-2515	24	8	a	a	DET
ejpam-2515	24	9	binary	binary	ADJ
ejpam-2515	24	10	relation	relation	NOUN
ejpam-2515	24	11	[	[	X
ejpam-2515	24	12	4	4	NUM
ejpam-2515	24	13	]	]	PUNCT
ejpam-2515	24	14	.	.	PUNCT
ejpam-2515	25	1	another	another	DET
ejpam-2515	25	2	approach	approach	NOUN
ejpam-2515	25	3	to	to	ADP
ejpam-2515	25	4	the	the	DET
ejpam-2515	25	5	connection	connection	NOUN
ejpam-2515	25	6	between	between	ADP
ejpam-2515	25	7	hypergroups	hypergroup	NOUN
ejpam-2515	25	8	and	and	CCONJ
ejpam-2515	25	9	ordered	order	VERB
ejpam-2515	25	10	set	set	NOUN
ejpam-2515	25	11	is	be	AUX
ejpam-2515	25	12	initiated	initiate	VERB
ejpam-2515	25	13	by	by	ADP
ejpam-2515	25	14	m.	m.	NOUN
ejpam-2515	25	15	ştefanescu	ştefanescu	PROPN
ejpam-2515	26	1	[	[	X
ejpam-2515	26	2	12	12	NUM
ejpam-2515	26	3	]	]	PUNCT
ejpam-2515	26	4	and	and	CCONJ
ejpam-2515	26	5	recently	recently	ADV
ejpam-2515	26	6	hypergroupoids	hypergroupoid	NOUN
ejpam-2515	26	7	associated	associate	VERB
ejpam-2515	26	8	with	with	ADP
ejpam-2515	26	9	n	n	X
ejpam-2515	26	10	-	-	PUNCT
ejpam-2515	26	11	ary	ary	PROPN
ejpam-2515	26	12	(	(	PUNCT
ejpam-2515	26	13	n	n	CCONJ
ejpam-2515	26	14	≥	≥	NOUN
ejpam-2515	26	15	3	3	NUM
ejpam-2515	26	16	)	)	PUNCT
ejpam-2515	26	17	relations	relation	NOUN
ejpam-2515	26	18	are	be	AUX
ejpam-2515	26	19	studied	study	VERB
ejpam-2515	26	20	by	by	ADP
ejpam-2515	26	21	i.	i.	PROPN
ejpam-2515	26	22	cristea	cristea	PROPN
ejpam-2515	26	23	and	and	CCONJ
ejpam-2515	26	24	m.	m.	NOUN
ejpam-2515	26	25	ştefanescu	ştefanescu	PROPN
ejpam-2515	27	1	[	[	X
ejpam-2515	27	2	11	11	NUM
ejpam-2515	27	3	]	]	PUNCT
ejpam-2515	27	4	and	and	CCONJ
ejpam-2515	27	5	i.	i.	PROPN
ejpam-2515	27	6	cristea	cristea	PROPN
ejpam-2515	28	1	[	[	X
ejpam-2515	28	2	9	9	NUM
ejpam-2515	28	3	]	]	PUNCT
ejpam-2515	28	4	alone	alone	ADV
ejpam-2515	28	5	.	.	PUNCT
ejpam-2515	29	1	b.	b.	PROPN
ejpam-2515	29	2	davvaz	davvaz	PROPN
ejpam-2515	29	3	and	and	CCONJ
ejpam-2515	29	4	t.	t.	PROPN
ejpam-2515	29	5	vougioklis[13	vougioklis[13	PROPN
ejpam-2515	29	6	]	]	PUNCT
ejpam-2515	29	7	introduced	introduce	VERB
ejpam-2515	29	8	the	the	DET
ejpam-2515	29	9	concept	concept	NOUN
ejpam-2515	29	10	of	of	ADP
ejpam-2515	29	11	n	n	CCONJ
ejpam-2515	29	12	-	-	PUNCT
ejpam-2515	29	13	ary	ary	PROPN
ejpam-2515	29	14	hypergroups	hypergroup	NOUN
ejpam-2515	29	15	as	as	ADP
ejpam-2515	29	16	a	a	DET
ejpam-2515	29	17	generalization	generalization	NOUN
ejpam-2515	29	18	of	of	ADP
ejpam-2515	29	19	hypergroups	hypergroup	NOUN
ejpam-2515	29	20	in	in	ADP
ejpam-2515	29	21	the	the	DET
ejpam-2515	29	22	sense	sense	NOUN
ejpam-2515	29	23	of	of	ADP
ejpam-2515	29	24	marty	marty	PROPN
ejpam-2515	29	25	.	.	PUNCT
ejpam-2515	30	1	i.	i.	PROPN
ejpam-2515	30	2	cristea	cristea	PROPN
ejpam-2515	31	1	[	[	X
ejpam-2515	31	2	9	9	X
ejpam-2515	31	3	]	]	PUNCT
ejpam-2515	31	4	introduced	introduce	VERB
ejpam-2515	31	5	a	a	DET
ejpam-2515	31	6	new	new	ADJ
ejpam-2515	31	7	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	31	8	associated	associate	VERB
ejpam-2515	31	9	with	with	ADP
ejpam-2515	31	10	n	n	CCONJ
ejpam-2515	31	11	-	-	PUNCT
ejpam-2515	31	12	ary	ary	NOUN
ejpam-2515	31	13	relations	relation	NOUN
ejpam-2515	31	14	and	and	CCONJ
ejpam-2515	31	15	obtained	obtain	VERB
ejpam-2515	31	16	necessary	necessary	ADJ
ejpam-2515	31	17	conditions	condition	NOUN
ejpam-2515	31	18	for	for	SCONJ
ejpam-2515	31	19	the	the	DET
ejpam-2515	31	20	new	new	ADJ
ejpam-2515	31	21	hypergropoid	hypergropoid	NOUN
ejpam-2515	31	22	to	to	PART
ejpam-2515	31	23	be	be	AUX
ejpam-2515	31	24	a	a	DET
ejpam-2515	31	25	hypergroup	hypergroup	NOUN
ejpam-2515	31	26	or	or	CCONJ
ejpam-2515	31	27	a	a	DET
ejpam-2515	31	28	join	join	NOUN
ejpam-2515	31	29	space	space	NOUN
ejpam-2515	31	30	;	;	PUNCT
ejpam-2515	31	31	the	the	DET
ejpam-2515	31	32	new	new	ADJ
ejpam-2515	31	33	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	31	34	has	have	AUX
ejpam-2515	31	35	been	be	AUX
ejpam-2515	31	36	investigated	investigate	VERB
ejpam-2515	31	37	by	by	ADP
ejpam-2515	31	38	s.	s.	PROPN
ejpam-2515	31	39	govindarajan	govindarajan	PROPN
ejpam-2515	31	40	(	(	PUNCT
ejpam-2515	31	41	the	the	DET
ejpam-2515	31	42	author	author	NOUN
ejpam-2515	31	43	)	)	PUNCT
ejpam-2515	31	44	and	and	CCONJ
ejpam-2515	31	45	g.	g.	PROPN
ejpam-2515	31	46	ramesh	ramesh	PROPN
ejpam-2515	32	1	[	[	X
ejpam-2515	32	2	14	14	NUM
ejpam-2515	32	3	]	]	PUNCT
ejpam-2515	32	4	to	to	PART
ejpam-2515	32	5	find	find	VERB
ejpam-2515	32	6	sufficient	sufficient	ADJ
ejpam-2515	32	7	condition	condition	NOUN
ejpam-2515	32	8	if	if	SCONJ
ejpam-2515	32	9	any	any	PRON
ejpam-2515	32	10	so	so	SCONJ
ejpam-2515	32	11	that	that	SCONJ
ejpam-2515	32	12	the	the	DET
ejpam-2515	32	13	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	32	14	introduced	introduce	VERB
ejpam-2515	32	15	by	by	ADP
ejpam-2515	32	16	i.	i.	PROPN
ejpam-2515	32	17	cristea	cristea	PROPN
ejpam-2515	32	18	to	to	PART
ejpam-2515	32	19	be	be	AUX
ejpam-2515	32	20	a	a	DET
ejpam-2515	32	21	hypergroup	hypergroup	NOUN
ejpam-2515	32	22	or	or	CCONJ
ejpam-2515	32	23	a	a	DET
ejpam-2515	32	24	join	join	NOUN
ejpam-2515	32	25	space	space	NOUN
ejpam-2515	32	26	.	.	PUNCT
ejpam-2515	33	1	in	in	ADP
ejpam-2515	33	2	the	the	DET
ejpam-2515	33	3	same	same	ADJ
ejpam-2515	33	4	direction	direction	NOUN
ejpam-2515	33	5	,	,	PUNCT
ejpam-2515	33	6	albeit	albeit	SCONJ
ejpam-2515	33	7	with	with	ADP
ejpam-2515	33	8	different	different	ADJ
ejpam-2515	33	9	hyperoperations	hyperoperation	NOUN
ejpam-2515	33	10	went	go	VERB
ejpam-2515	33	11	the	the	DET
ejpam-2515	33	12	paper	paper	NOUN
ejpam-2515	33	13	by	by	ADP
ejpam-2515	33	14	the	the	DET
ejpam-2515	33	15	author	author	NOUN
ejpam-2515	33	16	and	and	CCONJ
ejpam-2515	33	17	g.	g.	PROPN
ejpam-2515	33	18	ramesh	ramesh	PROPN
ejpam-2515	34	1	[	[	X
ejpam-2515	34	2	15	15	NUM
ejpam-2515	34	3	]	]	PUNCT
ejpam-2515	34	4	.	.	PUNCT
ejpam-2515	35	1	next	next	ADV
ejpam-2515	35	2	,	,	PUNCT
ejpam-2515	35	3	the	the	DET
ejpam-2515	35	4	author	author	NOUN
ejpam-2515	35	5	and	and	CCONJ
ejpam-2515	35	6	g.	g.	PROPN
ejpam-2515	35	7	ramesh	ramesh	PROPN
ejpam-2515	35	8	established	establish	VERB
ejpam-2515	35	9	a	a	DET
ejpam-2515	35	10	new	new	ADJ
ejpam-2515	35	11	correspondence	correspondence	NOUN
ejpam-2515	35	12	between	between	ADP
ejpam-2515	35	13	n	n	CCONJ
ejpam-2515	35	14	-	-	PUNCT
ejpam-2515	35	15	ary	ary	NOUN
ejpam-2515	35	16	relations	relation	NOUN
ejpam-2515	35	17	and	and	CCONJ
ejpam-2515	35	18	hypergroupoids	hypergroupoid	NOUN
ejpam-2515	35	19	and	and	CCONJ
ejpam-2515	35	20	found	find	VERB
ejpam-2515	35	21	conditions	condition	NOUN
ejpam-2515	35	22	on	on	ADP
ejpam-2515	35	23	a	a	DET
ejpam-2515	35	24	ternary	ternary	ADJ
ejpam-2515	35	25	relationρ	relationρ	NOUN
ejpam-2515	35	26	,	,	PUNCT
ejpam-2515	35	27	such	such	ADJ
ejpam-2515	35	28	that	that	SCONJ
ejpam-2515	35	29	hρ	hρ	PROPN
ejpam-2515	35	30	is	be	AUX
ejpam-2515	35	31	a	a	DET
ejpam-2515	35	32	hypergroup	hypergroup	NOUN
ejpam-2515	35	33	or	or	CCONJ
ejpam-2515	35	34	a	a	DET
ejpam-2515	35	35	join	join	NOUN
ejpam-2515	35	36	space	space	NOUN
ejpam-2515	35	37	[	[	X
ejpam-2515	35	38	16	16	NUM
ejpam-2515	35	39	]	]	PUNCT
ejpam-2515	35	40	.	.	PUNCT
ejpam-2515	36	1	in	in	ADP
ejpam-2515	36	2	the	the	DET
ejpam-2515	36	3	same	same	ADJ
ejpam-2515	36	4	paper	paper	NOUN
ejpam-2515	36	5	,	,	PUNCT
ejpam-2515	36	6	the	the	DET
ejpam-2515	36	7	author	author	NOUN
ejpam-2515	36	8	and	and	CCONJ
ejpam-2515	36	9	g.	g.	PROPN
ejpam-2515	36	10	ramesh	ramesh	PROPN
ejpam-2515	36	11	studied	study	VERB
ejpam-2515	36	12	these	these	DET
ejpam-2515	36	13	hypergroups	hypergroup	NOUN
ejpam-2515	36	14	under	under	ADP
ejpam-2515	36	15	the	the	DET
ejpam-2515	36	16	union	union	NOUN
ejpam-2515	36	17	and	and	CCONJ
ejpam-2515	36	18	intersection	intersection	NOUN
ejpam-2515	36	19	of	of	ADP
ejpam-2515	36	20	relations	relation	NOUN
ejpam-2515	36	21	.	.	PUNCT
ejpam-2515	37	1	in	in	ADP
ejpam-2515	37	2	the	the	DET
ejpam-2515	37	3	papers	paper	NOUN
ejpam-2515	37	4	[	[	X
ejpam-2515	37	5	14	14	NUM
ejpam-2515	37	6	]	]	PUNCT
ejpam-2515	37	7	and	and	CCONJ
ejpam-2515	37	8	[	[	X
ejpam-2515	37	9	16	16	NUM
ejpam-2515	37	10	]	]	PUNCT
ejpam-2515	37	11	,	,	PUNCT
ejpam-2515	37	12	we	we	PRON
ejpam-2515	37	13	obtained	obtain	VERB
ejpam-2515	37	14	a	a	DET
ejpam-2515	37	15	necessary	necessary	ADJ
ejpam-2515	37	16	and	and	CCONJ
ejpam-2515	37	17	sufficient	sufficient	ADJ
ejpam-2515	37	18	condition	condition	NOUN
ejpam-2515	37	19	on	on	ADP
ejpam-2515	37	20	the	the	DET
ejpam-2515	37	21	n(n	n(n	PROPN
ejpam-2515	37	22	≥	≥	NOUN
ejpam-2515	37	23	3)-ary	3)-ary	ADJ
ejpam-2515	37	24	relation	relation	NOUN
ejpam-2515	37	25	ρ	ρ	PROPN
ejpam-2515	37	26	for	for	SCONJ
ejpam-2515	37	27	hρ	hρ	NOUN
ejpam-2515	37	28	to	to	PART
ejpam-2515	37	29	be	be	AUX
ejpam-2515	37	30	a	a	DET
ejpam-2515	37	31	hypergroup	hypergroup	NOUN
ejpam-2515	37	32	,	,	PUNCT
ejpam-2515	37	33	especially	especially	ADV
ejpam-2515	37	34	in	in	ADP
ejpam-2515	37	35	the	the	DET
ejpam-2515	37	36	case	case	NOUN
ejpam-2515	37	37	when	when	SCONJ
ejpam-2515	37	38	ρ	ρ	PROPN
ejpam-2515	37	39	is	be	AUX
ejpam-2515	37	40	reflexive	reflexive	ADJ
ejpam-2515	37	41	and	and	CCONJ
ejpam-2515	37	42	symmetric	symmetric	ADJ
ejpam-2515	37	43	relation	relation	NOUN
ejpam-2515	37	44	.	.	PUNCT
ejpam-2515	38	1	in	in	ADP
ejpam-2515	38	2	this	this	DET
ejpam-2515	38	3	paper	paper	NOUN
ejpam-2515	38	4	,	,	PUNCT
ejpam-2515	38	5	the	the	DET
ejpam-2515	38	6	analysis	analysis	NOUN
ejpam-2515	38	7	of	of	ADP
ejpam-2515	38	8	connection	connection	NOUN
ejpam-2515	38	9	between	between	ADP
ejpam-2515	38	10	hyperpgroups	hyperpgroup	NOUN
ejpam-2515	38	11	and	and	CCONJ
ejpam-2515	38	12	the	the	DET
ejpam-2515	38	13	n(n=	n(n=	NOUN
ejpam-2515	38	14	3)-ary	3)-ary	ADJ
ejpam-2515	38	15	relations	relation	NOUN
ejpam-2515	38	16	is	be	AUX
ejpam-2515	38	17	continued	continue	VERB
ejpam-2515	38	18	.	.	PUNCT
ejpam-2515	39	1	we	we	PRON
ejpam-2515	39	2	confine	confine	VERB
ejpam-2515	39	3	with	with	ADP
ejpam-2515	39	4	ternary	ternary	ADJ
ejpam-2515	39	5	relations	relation	NOUN
ejpam-2515	39	6	,	,	PUNCT
ejpam-2515	39	7	by	by	ADP
ejpam-2515	39	8	remarking	remark	VERB
ejpam-2515	39	9	that	that	SCONJ
ejpam-2515	39	10	any	any	DET
ejpam-2515	39	11	results	result	NOUN
ejpam-2515	39	12	obtained	obtain	VERB
ejpam-2515	39	13	with	with	ADP
ejpam-2515	39	14	regards	regard	NOUN
ejpam-2515	39	15	to	to	ADP
ejpam-2515	39	16	n(n	n(n	PROPN
ejpam-2515	39	17	=	=	SYM
ejpam-2515	39	18	3)-ary	3)-ary	ADJ
ejpam-2515	39	19	relation	relation	NOUN
ejpam-2515	39	20	can	can	AUX
ejpam-2515	39	21	be	be	AUX
ejpam-2515	39	22	obtained	obtain	VERB
ejpam-2515	39	23	analogously	analogously	ADV
ejpam-2515	39	24	to	to	ADP
ejpam-2515	39	25	the	the	DET
ejpam-2515	39	26	case	case	NOUN
ejpam-2515	39	27	of	of	ADP
ejpam-2515	39	28	n(n	n(n	PROPN
ejpam-2515	39	29	≥	≥	NUM
ejpam-2515	39	30	4)-ary	4)-ary	ADJ
ejpam-2515	39	31	relation	relation	NOUN
ejpam-2515	39	32	.	.	PUNCT
ejpam-2515	40	1	here	here	ADV
ejpam-2515	40	2	,	,	PUNCT
ejpam-2515	40	3	we	we	PRON
ejpam-2515	40	4	consider	consider	VERB
ejpam-2515	40	5	the	the	DET
ejpam-2515	40	6	ternary	ternary	ADJ
ejpam-2515	40	7	relation	relation	NOUN
ejpam-2515	40	8	in	in	ADP
ejpam-2515	40	9	a	a	DET
ejpam-2515	40	10	most	most	ADV
ejpam-2515	40	11	general	general	ADJ
ejpam-2515	40	12	context	context	NOUN
ejpam-2515	40	13	and	and	CCONJ
ejpam-2515	40	14	,	,	PUNCT
ejpam-2515	40	15	we	we	PRON
ejpam-2515	40	16	find	find	VERB
ejpam-2515	40	17	a	a	DET
ejpam-2515	40	18	necessary	necessary	ADJ
ejpam-2515	40	19	and	and	CCONJ
ejpam-2515	40	20	sufficient	sufficient	ADJ
ejpam-2515	40	21	conditions	condition	NOUN
ejpam-2515	40	22	such	such	ADJ
ejpam-2515	40	23	that	that	SCONJ
ejpam-2515	40	24	hρ	hρ	PROPN
ejpam-2515	40	25	is	be	AUX
ejpam-2515	40	26	a	a	DET
ejpam-2515	40	27	hypergroup	hypergroup	NOUN
ejpam-2515	40	28	or	or	CCONJ
ejpam-2515	40	29	a	a	DET
ejpam-2515	40	30	join	join	NOUN
ejpam-2515	40	31	space	space	NOUN
ejpam-2515	40	32	.	.	PUNCT
ejpam-2515	41	1	several	several	ADJ
ejpam-2515	41	2	extensions	extension	NOUN
ejpam-2515	41	3	of	of	ADP
ejpam-2515	41	4	hyperoperations	hyperoperation	NOUN
ejpam-2515	41	5	being	be	AUX
ejpam-2515	41	6	employed	employ	VERB
ejpam-2515	41	7	,	,	PUNCT
ejpam-2515	41	8	among	among	ADP
ejpam-2515	41	9	them	they	PRON
ejpam-2515	41	10	,	,	PUNCT
ejpam-2515	41	11	one	one	NUM
ejpam-2515	41	12	for	for	ADP
ejpam-2515	41	13	which	which	PRON
ejpam-2515	41	14	coincides	coincide	VERB
ejpam-2515	41	15	with	with	ADP
ejpam-2515	41	16	w.	w.	PROPN
ejpam-2515	41	17	prenowitz	prenowitz	PROPN
ejpam-2515	41	18	[	[	X
ejpam-2515	41	19	19	19	NUM
ejpam-2515	41	20	]	]	PUNCT
ejpam-2515	41	21	extension	extension	NOUN
ejpam-2515	41	22	of	of	ADP
ejpam-2515	41	23	hyperoperation	hyperoperation	NOUN
ejpam-2515	41	24	associated	associate	VERB
ejpam-2515	41	25	with	with	ADP
ejpam-2515	41	26	spherical	spherical	ADJ
ejpam-2515	41	27	geometry	geometry	NOUN
ejpam-2515	41	28	is	be	AUX
ejpam-2515	41	29	remarkable	remarkable	ADJ
ejpam-2515	41	30	,	,	PUNCT
ejpam-2515	41	31	but	but	CCONJ
ejpam-2515	41	32	in	in	ADP
ejpam-2515	41	33	a	a	DET
ejpam-2515	41	34	little	little	ADJ
ejpam-2515	41	35	different	different	ADJ
ejpam-2515	41	36	form	form	NOUN
ejpam-2515	41	37	.	.	PUNCT
ejpam-2515	42	1	that	that	PRON
ejpam-2515	42	2	is	is	ADV
ejpam-2515	42	3	,	,	PUNCT
ejpam-2515	42	4	w.	w.	PROPN
ejpam-2515	42	5	prenowitz	prenowitz	PROPN
ejpam-2515	42	6	extended	extend	VERB
ejpam-2515	42	7	the	the	DET
ejpam-2515	42	8	hyperoperation	hyperoperation	NOUN
ejpam-2515	42	9	by	by	ADP
ejpam-2515	42	10	adjoining	adjoin	VERB
ejpam-2515	42	11	an	an	DET
ejpam-2515	42	12	ideal	ideal	ADJ
ejpam-2515	42	13	element	element	NOUN
ejpam-2515	42	14	e	e	NOUN
ejpam-2515	42	15	and	and	CCONJ
ejpam-2515	42	16	e	e	PROPN
ejpam-2515	42	17	6∈	6∈	PROPN
ejpam-2515	42	18	s	s	PART
ejpam-2515	42	19	,	,	PUNCT
ejpam-2515	42	20	but	but	CCONJ
ejpam-2515	42	21	we	we	PRON
ejpam-2515	42	22	set	set	VERB
ejpam-2515	42	23	e	e	PROPN
ejpam-2515	42	24	∈	∈	PROPN
ejpam-2515	42	25	s.	s.	PROPN
ejpam-2515	42	26	the	the	DET
ejpam-2515	42	27	n	n	NUM
ejpam-2515	42	28	-	-	PUNCT
ejpam-2515	42	29	ary	ary	PROPN
ejpam-2515	42	30	relations	relation	NOUN
ejpam-2515	42	31	were	be	AUX
ejpam-2515	42	32	studied	study	VERB
ejpam-2515	42	33	for	for	ADP
ejpam-2515	42	34	their	their	PRON
ejpam-2515	42	35	applications	application	NOUN
ejpam-2515	42	36	in	in	ADP
ejpam-2515	42	37	theory	theory	NOUN
ejpam-2515	42	38	of	of	ADP
ejpam-2515	42	39	dependence	dependence	NOUN
ejpam-2515	42	40	space	space	NOUN
ejpam-2515	42	41	.	.	PUNCT
ejpam-2515	43	1	moreover	moreover	ADV
ejpam-2515	43	2	,	,	PUNCT
ejpam-2515	43	3	they	they	PRON
ejpam-2515	43	4	are	be	AUX
ejpam-2515	43	5	used	use	VERB
ejpam-2515	43	6	in	in	ADP
ejpam-2515	43	7	database	database	NOUN
ejpam-2515	43	8	theory	theory	NOUN
ejpam-2515	43	9	,	,	PUNCT
ejpam-2515	43	10	providing	provide	VERB
ejpam-2515	43	11	a	a	DET
ejpam-2515	43	12	convenient	convenient	ADJ
ejpam-2515	43	13	tool	tool	NOUN
ejpam-2515	43	14	for	for	ADP
ejpam-2515	43	15	database	database	NOUN
ejpam-2515	43	16	modeling	modeling	NOUN
ejpam-2515	43	17	.	.	PUNCT
ejpam-2515	44	1	the	the	DET
ejpam-2515	44	2	operations	operation	NOUN
ejpam-2515	44	3	such	such	ADJ
ejpam-2515	44	4	as	as	ADP
ejpam-2515	44	5	union	union	NOUN
ejpam-2515	44	6	,	,	PUNCT
ejpam-2515	44	7	intersection	intersection	NOUN
ejpam-2515	44	8	,	,	PUNCT
ejpam-2515	44	9	difference	difference	NOUN
ejpam-2515	44	10	and	and	CCONJ
ejpam-2515	44	11	cartesian	cartesian	ADJ
ejpam-2515	44	12	product	product	NOUN
ejpam-2515	44	13	on	on	ADP
ejpam-2515	44	14	n	n	CCONJ
ejpam-2515	44	15	-	-	PUNCT
ejpam-2515	44	16	ary	ary	PROPN
ejpam-2515	44	17	relations	relation	NOUN
ejpam-2515	44	18	are	be	AUX
ejpam-2515	44	19	useful	useful	ADJ
ejpam-2515	44	20	to	to	PART
ejpam-2515	44	21	describe	describe	VERB
ejpam-2515	44	22	information	information	NOUN
ejpam-2515	44	23	manipulations	manipulation	NOUN
ejpam-2515	44	24	in	in	ADP
ejpam-2515	44	25	databases	database	NOUN
ejpam-2515	44	26	.	.	PUNCT
ejpam-2515	45	1	these	these	DET
ejpam-2515	45	2	operations	operation	NOUN
ejpam-2515	45	3	are	be	AUX
ejpam-2515	45	4	useful	useful	ADJ
ejpam-2515	45	5	in	in	ADP
ejpam-2515	45	6	the	the	DET
ejpam-2515	45	7	construction	construction	NOUN
ejpam-2515	45	8	of	of	ADP
ejpam-2515	45	9	new	new	ADJ
ejpam-2515	45	10	database	database	NOUN
ejpam-2515	45	11	.	.	PUNCT
ejpam-2515	46	1	first	first	ADV
ejpam-2515	46	2	we	we	PRON
ejpam-2515	46	3	recall	recall	VERB
ejpam-2515	46	4	some	some	DET
ejpam-2515	46	5	necessary	necessary	ADJ
ejpam-2515	46	6	definitions	definition	NOUN
ejpam-2515	46	7	:	:	PUNCT
ejpam-2515	46	8	for	for	ADP
ejpam-2515	46	9	a	a	DET
ejpam-2515	46	10	non	non	X
ejpam-2515	46	11	empty	empty	ADJ
ejpam-2515	46	12	set	set	ADJ
ejpam-2515	46	13	h	h	NOUN
ejpam-2515	46	14	,	,	PUNCT
ejpam-2515	46	15	we	we	PRON
ejpam-2515	46	16	denote	denote	VERB
ejpam-2515	46	17	by	by	ADP
ejpam-2515	46	18	p∗(h	p∗(h	PROPN
ejpam-2515	46	19	)	)	PUNCT
ejpam-2515	46	20	the	the	DET
ejpam-2515	46	21	set	set	NOUN
ejpam-2515	46	22	of	of	ADP
ejpam-2515	46	23	all	all	DET
ejpam-2515	46	24	non	non	PRON
ejpam-2515	46	25	empty	empty	ADJ
ejpam-2515	46	26	subsets	subset	NOUN
ejpam-2515	46	27	of	of	ADP
ejpam-2515	46	28	h.	h.	PROPN
ejpam-2515	46	29	•	•	PROPN
ejpam-2515	46	30	a	a	DET
ejpam-2515	46	31	non	non	X
ejpam-2515	46	32	empty	empty	ADJ
ejpam-2515	46	33	set	set	ADJ
ejpam-2515	46	34	h	h	NOUN
ejpam-2515	46	35	,	,	PUNCT
ejpam-2515	46	36	endowed	endow	VERB
ejpam-2515	46	37	with	with	ADP
ejpam-2515	46	38	a	a	DET
ejpam-2515	46	39	mapping	mapping	NOUN
ejpam-2515	46	40	,	,	PUNCT
ejpam-2515	46	41	called	call	VERB
ejpam-2515	46	42	hyperoperation	hyperoperation	NOUN
ejpam-2515	46	43	•	•	ADP
ejpam-2515	46	44	◦	◦	NOUN
ejpam-2515	46	45	:	:	PUNCT
ejpam-2515	46	46	h	h	NOUN
ejpam-2515	46	47	×h	×h	PROPN
ejpam-2515	46	48	−→	−→	ADJ
ejpam-2515	46	49	p∗(h	p∗(h	NOUN
ejpam-2515	46	50	)	)	PUNCT
ejpam-2515	46	51	is	be	AUX
ejpam-2515	46	52	called	call	VERB
ejpam-2515	46	53	a	a	DET
ejpam-2515	46	54	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	46	55	.	.	PUNCT
ejpam-2515	47	1	•	•	NUM
ejpam-2515	47	2	a	a	DET
ejpam-2515	47	3	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	47	4	which	which	PRON
ejpam-2515	47	5	verifies	verify	VERB
ejpam-2515	47	6	the	the	DET
ejpam-2515	47	7	following	following	ADJ
ejpam-2515	47	8	conditions	condition	NOUN
ejpam-2515	47	9	:	:	PUNCT
ejpam-2515	47	10	(	(	PUNCT
ejpam-2515	47	11	1	1	X
ejpam-2515	47	12	)	)	PUNCT
ejpam-2515	47	13	(	(	PUNCT
ejpam-2515	48	1	x	x	X
ejpam-2515	48	2	◦	◦	VERB
ejpam-2515	48	3	y	y	NOUN
ejpam-2515	48	4	)	)	PUNCT
ejpam-2515	48	5	◦	◦	NOUN
ejpam-2515	48	6	z	z	NOUN
ejpam-2515	49	1	=	=	SYM
ejpam-2515	49	2	x	x	PUNCT
ejpam-2515	49	3	◦	◦	NOUN
ejpam-2515	49	4	(	(	PUNCT
ejpam-2515	49	5	y	y	PROPN
ejpam-2515	49	6	◦	◦	PROPN
ejpam-2515	49	7	z	z	PROPN
ejpam-2515	49	8	)	)	PUNCT
ejpam-2515	49	9	,	,	PUNCT
ejpam-2515	49	10	for	for	ADP
ejpam-2515	49	11	all	all	DET
ejpam-2515	49	12	x	x	SYM
ejpam-2515	49	13	,	,	PUNCT
ejpam-2515	49	14	y	y	PROPN
ejpam-2515	49	15	,	,	PUNCT
ejpam-2515	49	16	z	z	PROPN
ejpam-2515	49	17	∈	∈	PROPN
ejpam-2515	49	18	h	h	NOUN
ejpam-2515	49	19	,	,	PUNCT
ejpam-2515	49	20	(	(	PUNCT
ejpam-2515	49	21	2	2	NUM
ejpam-2515	49	22	)	)	PUNCT
ejpam-2515	49	23	x	x	SYM
ejpam-2515	49	24	◦	◦	NOUN
ejpam-2515	49	25	h	h	NOUN
ejpam-2515	49	26	=	=	NOUN
ejpam-2515	49	27	h	h	NOUN
ejpam-2515	49	28	=	=	PUNCT
ejpam-2515	50	1	h	h	NOUN
ejpam-2515	50	2	◦	◦	NOUN
ejpam-2515	50	3	x	x	X
ejpam-2515	50	4	,	,	PUNCT
ejpam-2515	50	5	for	for	ADP
ejpam-2515	50	6	all	all	DET
ejpam-2515	50	7	x	x	SYM
ejpam-2515	50	8	∈	∈	PROPN
ejpam-2515	50	9	h	h	NOUN
ejpam-2515	50	10	,	,	PUNCT
ejpam-2515	50	11	(	(	PUNCT
ejpam-2515	50	12	reproduction	reproduction	NOUN
ejpam-2515	50	13	axiom	axiom	NOUN
ejpam-2515	50	14	)	)	PUNCT
ejpam-2515	50	15	is	be	AUX
ejpam-2515	50	16	called	call	VERB
ejpam-2515	50	17	a	a	DET
ejpam-2515	50	18	hypergroup	hypergroup	NOUN
ejpam-2515	50	19	.	.	PUNCT
ejpam-2515	51	1	s.	s.	PROPN
ejpam-2515	51	2	govindarajan	govindarajan	PROPN
ejpam-2515	51	3	/	/	SYM
ejpam-2515	51	4	eur	eur	PROPN
ejpam-2515	51	5	.	.	PUNCT
ejpam-2515	52	1	j.	j.	PROPN
ejpam-2515	52	2	pure	pure	PROPN
ejpam-2515	52	3	appl	appl	PROPN
ejpam-2515	52	4	.	.	PROPN
ejpam-2515	52	5	math	math	PROPN
ejpam-2515	52	6	,	,	PUNCT
ejpam-2515	52	7	9	9	NUM
ejpam-2515	52	8	(	(	PUNCT
ejpam-2515	52	9	2016	2016	NUM
ejpam-2515	52	10	)	)	PUNCT
ejpam-2515	52	11	,	,	PUNCT
ejpam-2515	52	12	367	367	NUM
ejpam-2515	52	13	-	-	SYM
ejpam-2515	52	14	382	382	NUM
ejpam-2515	52	15	369	369	NUM
ejpam-2515	52	16	•	•	NOUN
ejpam-2515	52	17	if	if	SCONJ
ejpam-2515	52	18	,	,	PUNCT
ejpam-2515	52	19	for	for	ADP
ejpam-2515	52	20	any	any	DET
ejpam-2515	52	21	x	x	SYM
ejpam-2515	52	22	,	,	PUNCT
ejpam-2515	52	23	y	y	PROPN
ejpam-2515	52	24	∈	∈	PROPN
ejpam-2515	52	25	h	h	NOUN
ejpam-2515	52	26	,	,	PUNCT
ejpam-2515	52	27	x	x	VERB
ejpam-2515	52	28	◦	◦	NOUN
ejpam-2515	52	29	y	y	NOUN
ejpam-2515	52	30	=	=	SYM
ejpam-2515	52	31	h	h	NOUN
ejpam-2515	52	32	,	,	PUNCT
ejpam-2515	52	33	then	then	ADV
ejpam-2515	52	34	(	(	PUNCT
ejpam-2515	52	35	h	h	NOUN
ejpam-2515	52	36	,	,	PUNCT
ejpam-2515	52	37	◦	◦	NOUN
ejpam-2515	52	38	)	)	PUNCT
ejpam-2515	52	39	is	be	AUX
ejpam-2515	52	40	called	call	VERB
ejpam-2515	52	41	the	the	DET
ejpam-2515	52	42	total	total	ADJ
ejpam-2515	52	43	hypergroup	hypergroup	NOUN
ejpam-2515	52	44	.	.	PUNCT
ejpam-2515	53	1	•	•	INTJ
ejpam-2515	53	2	if	if	SCONJ
ejpam-2515	53	3	a	a	PRON
ejpam-2515	53	4	and	and	CCONJ
ejpam-2515	53	5	b	b	NOUN
ejpam-2515	53	6	are	be	AUX
ejpam-2515	53	7	nonempty	nonempty	ADJ
ejpam-2515	53	8	subsets	subset	NOUN
ejpam-2515	53	9	of	of	ADP
ejpam-2515	53	10	h	h	NOUN
ejpam-2515	53	11	,	,	PUNCT
ejpam-2515	53	12	then	then	ADV
ejpam-2515	53	13	we	we	PRON
ejpam-2515	53	14	denote	denote	VERB
ejpam-2515	53	15	the	the	DET
ejpam-2515	53	16	set	set	NOUN
ejpam-2515	53	17	a	a	DET
ejpam-2515	53	18	◦	◦	NOUN
ejpam-2515	53	19	b	b	NOUN
ejpam-2515	54	1	=	=	PRON
ejpam-2515	54	2	⋃b∈b	⋃b∈b	PROPN
ejpam-2515	54	3	a∈a	a∈a	VERB
ejpam-2515	54	4	a	a	DET
ejpam-2515	54	5	◦	◦	NOUN
ejpam-2515	54	6	b.	b.	PROPN
ejpam-2515	54	7	•	•	NOUN
ejpam-2515	54	8	if	if	SCONJ
ejpam-2515	54	9	a	a	PRON
ejpam-2515	54	10	and	and	CCONJ
ejpam-2515	54	11	b	b	NOUN
ejpam-2515	54	12	are	be	AUX
ejpam-2515	54	13	nonempty	nonempty	ADJ
ejpam-2515	54	14	subsets	subset	NOUN
ejpam-2515	54	15	of	of	ADP
ejpam-2515	54	16	h	h	NOUN
ejpam-2515	54	17	,	,	PUNCT
ejpam-2515	54	18	then	then	ADV
ejpam-2515	54	19	we	we	PRON
ejpam-2515	54	20	denote	denote	VERB
ejpam-2515	54	21	a	a	DET
ejpam-2515	54	22	/	/	SYM
ejpam-2515	54	23	b	b	NOUN
ejpam-2515	54	24	=	=	SYM
ejpam-2515	54	25	⋃b∈b	⋃b∈b	PROPN
ejpam-2515	54	26	a∈a	a∈a	VERB
ejpam-2515	54	27	a	a	DET
ejpam-2515	54	28	/	/	SYM
ejpam-2515	54	29	b.	b.	PROPN
ejpam-2515	54	30	•	•	NOUN
ejpam-2515	54	31	a	a	DET
ejpam-2515	54	32	commutative	commutative	ADJ
ejpam-2515	54	33	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	54	34	(	(	PUNCT
ejpam-2515	54	35	h	h	NOUN
ejpam-2515	54	36	;	;	PUNCT
ejpam-2515	54	37	◦	◦	NOUN
ejpam-2515	54	38	)	)	PUNCT
ejpam-2515	54	39	is	be	AUX
ejpam-2515	54	40	called	call	VERB
ejpam-2515	54	41	a	a	DET
ejpam-2515	54	42	join	join	NOUN
ejpam-2515	54	43	space	space	NOUN
ejpam-2515	54	44	if	if	SCONJ
ejpam-2515	54	45	the	the	DET
ejpam-2515	54	46	following	follow	VERB
ejpam-2515	54	47	implication	implication	NOUN
ejpam-2515	54	48	holds	hold	VERB
ejpam-2515	54	49	:	:	PUNCT
ejpam-2515	54	50	for	for	ADP
ejpam-2515	54	51	any	any	DET
ejpam-2515	54	52	(	(	PUNCT
ejpam-2515	54	53	a	a	PRON
ejpam-2515	54	54	,	,	PUNCT
ejpam-2515	54	55	b	b	NOUN
ejpam-2515	54	56	,	,	PUNCT
ejpam-2515	54	57	c	c	NOUN
ejpam-2515	54	58	,	,	PUNCT
ejpam-2515	54	59	d	d	NOUN
ejpam-2515	54	60	)	)	PUNCT
ejpam-2515	54	61	∈	∈	PROPN
ejpam-2515	54	62	h4	h4	PROPN
ejpam-2515	54	63	,	,	PUNCT
ejpam-2515	54	64	a	a	PRON
ejpam-2515	54	65	/	/	SYM
ejpam-2515	54	66	b∩	b∩	NOUN
ejpam-2515	54	67	c	c	NOUN
ejpam-2515	54	68	/	/	SYM
ejpam-2515	54	69	d	d	NOUN
ejpam-2515	54	70	6=	6=	NUM
ejpam-2515	54	71	;	;	PUNCT
ejpam-2515	54	72	=	=	SYM
ejpam-2515	54	73	⇒	⇒	VERB
ejpam-2515	54	74	a	a	DET
ejpam-2515	54	75	◦	◦	NOUN
ejpam-2515	54	76	d∩	d∩	NOUN
ejpam-2515	54	77	b	b	NUM
ejpam-2515	54	78	◦	◦	NOUN
ejpam-2515	54	79	c	c	NOUN
ejpam-2515	54	80	6=	6=	NUM
ejpam-2515	54	81	;	;	PUNCT
ejpam-2515	54	82	(	(	PUNCT
ejpam-2515	54	83	transposition	transposition	NOUN
ejpam-2515	54	84	axiom	axiom	NOUN
ejpam-2515	54	85	)	)	PUNCT
ejpam-2515	54	86	.	.	PUNCT
ejpam-2515	55	1	for	for	ADP
ejpam-2515	55	2	more	more	ADJ
ejpam-2515	55	3	details	detail	NOUN
ejpam-2515	55	4	on	on	ADP
ejpam-2515	55	5	hypergroup	hypergroup	PROPN
ejpam-2515	55	6	theory	theory	NOUN
ejpam-2515	55	7	,	,	PUNCT
ejpam-2515	55	8	see	see	VERB
ejpam-2515	55	9	[	[	X
ejpam-2515	55	10	2	2	NUM
ejpam-2515	55	11	,	,	PUNCT
ejpam-2515	55	12	8	8	NUM
ejpam-2515	55	13	,	,	PUNCT
ejpam-2515	55	14	21	21	NUM
ejpam-2515	55	15	]	]	PUNCT
ejpam-2515	55	16	.	.	PUNCT
ejpam-2515	56	1	2	2	X
ejpam-2515	56	2	.	.	X
ejpam-2515	56	3	properties	property	NOUN
ejpam-2515	56	4	of	of	ADP
ejpam-2515	56	5	the	the	DET
ejpam-2515	56	6	n	n	CCONJ
ejpam-2515	56	7	-	-	PUNCT
ejpam-2515	56	8	ary	ary	PROPN
ejpam-2515	56	9	relations	relation	NOUN
ejpam-2515	56	10	in	in	ADP
ejpam-2515	56	11	this	this	DET
ejpam-2515	56	12	section	section	NOUN
ejpam-2515	56	13	we	we	PRON
ejpam-2515	56	14	present	present	VERB
ejpam-2515	56	15	some	some	DET
ejpam-2515	56	16	basic	basic	ADJ
ejpam-2515	56	17	notions	notion	NOUN
ejpam-2515	56	18	about	about	ADP
ejpam-2515	56	19	the	the	DET
ejpam-2515	56	20	n	n	NUM
ejpam-2515	56	21	-	-	PUNCT
ejpam-2515	56	22	ary	ary	PROPN
ejpam-2515	56	23	relations	relation	NOUN
ejpam-2515	56	24	defined	define	VERB
ejpam-2515	56	25	on	on	ADP
ejpam-2515	56	26	a	a	DET
ejpam-2515	56	27	nonempty	nonempty	ADV
ejpam-2515	56	28	set	set	VERB
ejpam-2515	56	29	h	h	NOUN
ejpam-2515	56	30	,	,	PUNCT
ejpam-2515	56	31	n	n	PROPN
ejpam-2515	56	32	∈	∈	PROPN
ejpam-2515	56	33	n	n	CCONJ
ejpam-2515	56	34	a	a	DET
ejpam-2515	56	35	natural	natural	ADJ
ejpam-2515	56	36	number	number	NOUN
ejpam-2515	56	37	such	such	ADJ
ejpam-2515	56	38	that	that	SCONJ
ejpam-2515	56	39	n	n	NUM
ejpam-2515	56	40	≥	≥	NOUN
ejpam-2515	56	41	3	3	NUM
ejpam-2515	56	42	,	,	PUNCT
ejpam-2515	56	43	and	and	CCONJ
ejpam-2515	56	44	ρ	ρ	NOUN
ejpam-2515	56	45	⊆	⊆	NUM
ejpam-2515	56	46	hn	hn	PROPN
ejpam-2515	56	47	is	be	AUX
ejpam-2515	56	48	an	an	DET
ejpam-2515	56	49	n	n	CCONJ
ejpam-2515	56	50	-	-	PUNCT
ejpam-2515	56	51	ary	ary	NOUN
ejpam-2515	56	52	relation	relation	NOUN
ejpam-2515	56	53	on	on	ADP
ejpam-2515	56	54	h.	h.	PROPN
ejpam-2515	56	55	definition	definition	NOUN
ejpam-2515	56	56	1	1	NUM
ejpam-2515	56	57	(	(	PUNCT
ejpam-2515	56	58	[	[	X
ejpam-2515	56	59	9	9	NUM
ejpam-2515	56	60	,	,	PUNCT
ejpam-2515	56	61	11	11	NUM
ejpam-2515	56	62	]	]	NUM
ejpam-2515	56	63	)	)	PUNCT
ejpam-2515	56	64	.	.	PUNCT
ejpam-2515	57	1	the	the	DET
ejpam-2515	57	2	relation	relation	NOUN
ejpam-2515	57	3	ρ	ρ	PROPN
ejpam-2515	57	4	is	be	AUX
ejpam-2515	57	5	said	say	VERB
ejpam-2515	57	6	to	to	PART
ejpam-2515	57	7	be	be	AUX
ejpam-2515	57	8	:	:	PUNCT
ejpam-2515	57	9	(	(	PUNCT
ejpam-2515	57	10	1	1	X
ejpam-2515	57	11	)	)	PUNCT
ejpam-2515	57	12	reflexive	reflexive	VERB
ejpam-2515	57	13	if	if	SCONJ
ejpam-2515	57	14	for	for	ADP
ejpam-2515	57	15	any	any	DET
ejpam-2515	57	16	x	x	SYM
ejpam-2515	57	17	∈	∈	PROPN
ejpam-2515	57	18	h	h	NOUN
ejpam-2515	57	19	,	,	PUNCT
ejpam-2515	57	20	the	the	DET
ejpam-2515	57	21	n	n	CCONJ
ejpam-2515	57	22	-	-	PUNCT
ejpam-2515	57	23	tuple	tuple	NOUN
ejpam-2515	57	24	(	(	PUNCT
ejpam-2515	57	25	x	x	X
ejpam-2515	57	26	,	,	PUNCT
ejpam-2515	57	27	x	x	INTJ
ejpam-2515	57	28	,	,	PUNCT
ejpam-2515	57	29	.	.	PUNCT
ejpam-2515	57	30	.	.	PUNCT
ejpam-2515	58	1	.	.	PUNCT
ejpam-2515	59	1	,	,	PUNCT
ejpam-2515	59	2	x	x	X
ejpam-2515	59	3	)	)	PUNCT
ejpam-2515	59	4	∈	∈	PROPN
ejpam-2515	59	5	ρ	ρ	NOUN
ejpam-2515	59	6	;	;	PUNCT
ejpam-2515	59	7	(	(	PUNCT
ejpam-2515	59	8	2	2	NUM
ejpam-2515	59	9	)	)	PUNCT
ejpam-2515	59	10	n	n	CCONJ
ejpam-2515	59	11	-	-	PUNCT
ejpam-2515	59	12	transitive	transitive	ADJ
ejpam-2515	59	13	if	if	SCONJ
ejpam-2515	59	14	it	it	PRON
ejpam-2515	59	15	has	have	VERB
ejpam-2515	59	16	the	the	DET
ejpam-2515	59	17	following	follow	VERB
ejpam-2515	59	18	property	property	NOUN
ejpam-2515	59	19	:	:	PUNCT
ejpam-2515	59	20	if	if	SCONJ
ejpam-2515	59	21	(	(	PUNCT
ejpam-2515	59	22	x	x	NOUN
ejpam-2515	59	23	1	1	NUM
ejpam-2515	59	24	,	,	PUNCT
ejpam-2515	59	25	.	.	PUNCT
ejpam-2515	59	26	.	.	PUNCT
ejpam-2515	59	27	.	.	PUNCT
ejpam-2515	60	1	,	,	PUNCT
ejpam-2515	60	2	x	x	X
ejpam-2515	60	3	n	n	X
ejpam-2515	60	4	)	)	PUNCT
ejpam-2515	60	5	∈	∈	PROPN
ejpam-2515	60	6	ρ	ρ	PROPN
ejpam-2515	60	7	,	,	PUNCT
ejpam-2515	60	8	(	(	PUNCT
ejpam-2515	60	9	y	y	PROPN
ejpam-2515	60	10	1	1	NUM
ejpam-2515	60	11	,	,	PUNCT
ejpam-2515	60	12	.	.	PUNCT
ejpam-2515	60	13	.	.	PUNCT
ejpam-2515	60	14	.	.	PUNCT
ejpam-2515	61	1	,	,	PUNCT
ejpam-2515	61	2	y	y	PROPN
ejpam-2515	61	3	n	n	ADJ
ejpam-2515	61	4	)	)	PUNCT
ejpam-2515	61	5	∈	∈	PROPN
ejpam-2515	61	6	ρ	ρ	PROPN
ejpam-2515	61	7	hold	hold	NOUN
ejpam-2515	61	8	and	and	CCONJ
ejpam-2515	61	9	if	if	SCONJ
ejpam-2515	61	10	there	there	PRON
ejpam-2515	61	11	exist	exist	VERB
ejpam-2515	61	12	natural	natural	ADJ
ejpam-2515	61	13	numbers	number	NOUN
ejpam-2515	61	14	i	i	PRON
ejpam-2515	61	15	0	0	PUNCT
ejpam-2515	61	16	>	>	X
ejpam-2515	61	17	j	j	PROPN
ejpam-2515	61	18	0	0	PUNCT
ejpam-2515	61	19	such	such	ADJ
ejpam-2515	61	20	that	that	SCONJ
ejpam-2515	61	21	1	1	NUM
ejpam-2515	61	22	<	<	X
ejpam-2515	61	23	i	i	PRON
ejpam-2515	61	24	0	0	NUM
ejpam-2515	61	25	≤	≤	NUM
ejpam-2515	61	26	n	n	CCONJ
ejpam-2515	61	27	,	,	PUNCT
ejpam-2515	61	28	1	1	NUM
ejpam-2515	61	29	≤	≤	NUM
ejpam-2515	61	30	j	j	NOUN
ejpam-2515	61	31	0	0	PUNCT
ejpam-2515	61	32	<	<	X
ejpam-2515	61	33	n	n	X
ejpam-2515	61	34	,	,	PUNCT
ejpam-2515	61	35	x	x	PROPN
ejpam-2515	61	36	i0	i0	PROPN
ejpam-2515	61	37	=	=	PUNCT
ejpam-2515	61	38	y	y	PROPN
ejpam-2515	61	39	j0	j0	PROPN
ejpam-2515	61	40	,	,	PUNCT
ejpam-2515	61	41	then	then	ADV
ejpam-2515	61	42	the	the	DET
ejpam-2515	61	43	n	n	CCONJ
ejpam-2515	61	44	-	-	PUNCT
ejpam-2515	61	45	tuple	tuple	NOUN
ejpam-2515	61	46	(	(	PUNCT
ejpam-2515	61	47	x	x	PROPN
ejpam-2515	61	48	i1	i1	PROPN
ejpam-2515	61	49	,	,	PUNCT
ejpam-2515	61	50	.	.	PUNCT
ejpam-2515	61	51	.	.	PUNCT
ejpam-2515	62	1	.	.	PUNCT
ejpam-2515	63	1	,	,	PUNCT
ejpam-2515	63	2	x	x	X
ejpam-2515	64	1	i	i	PRON
ejpam-2515	64	2	k	k	PROPN
ejpam-2515	64	3	,	,	PUNCT
ejpam-2515	64	4	y	y	PROPN
ejpam-2515	64	5	j	j	PROPN
ejpam-2515	64	6	k+1	k+1	X
ejpam-2515	64	7	,	,	PUNCT
ejpam-2515	64	8	.	.	PUNCT
ejpam-2515	64	9	.	.	PUNCT
ejpam-2515	64	10	.	.	PUNCT
ejpam-2515	65	1	,	,	PUNCT
ejpam-2515	65	2	y	y	PROPN
ejpam-2515	65	3	jn	jn	PROPN
ejpam-2515	65	4	)	)	PUNCT
ejpam-2515	66	1	∈	∈	PROPN
ejpam-2515	66	2	ρ	ρ	PROPN
ejpam-2515	66	3	for	for	ADP
ejpam-2515	66	4	any	any	DET
ejpam-2515	66	5	natural	natural	ADJ
ejpam-2515	66	6	number	number	NOUN
ejpam-2515	66	7	1	1	NUM
ejpam-2515	66	8	≤	≤	NOUN
ejpam-2515	67	1	k	k	NOUN
ejpam-2515	67	2	<	<	X
ejpam-2515	67	3	n	n	PROPN
ejpam-2515	68	1	and	and	CCONJ
ejpam-2515	68	2	i	i	PRON
ejpam-2515	68	3	1	1	NUM
ejpam-2515	68	4	,	,	PUNCT
ejpam-2515	68	5	.	.	PUNCT
ejpam-2515	68	6	.	.	PUNCT
ejpam-2515	69	1	.	.	PUNCT
ejpam-2515	70	1	,	,	PUNCT
ejpam-2515	70	2	i	i	PRON
ejpam-2515	70	3	k	k	PROPN
ejpam-2515	70	4	,	,	PUNCT
ejpam-2515	70	5	jk+1	jk+1	PROPN
ejpam-2515	70	6	,	,	PUNCT
ejpam-2515	70	7	.	.	PUNCT
ejpam-2515	70	8	.	.	PUNCT
ejpam-2515	70	9	.	.	PUNCT
ejpam-2515	71	1	,	,	PUNCT
ejpam-2515	71	2	j	j	PROPN
ejpam-2515	71	3	n	n	CCONJ
ejpam-2515	71	4	such	such	ADJ
ejpam-2515	71	5	that	that	SCONJ
ejpam-2515	71	6	1≤	1≤	NUM
ejpam-2515	71	7	i1	i1	PROPN
ejpam-2515	71	8	<	<	X
ejpam-2515	71	9	.	.	PUNCT
ejpam-2515	71	10	.	.	PUNCT
ejpam-2515	71	11	.	.	PUNCT
ejpam-2515	72	1	<	<	X
ejpam-2515	72	2	ik	ik	PROPN
ejpam-2515	72	3	<	<	X
ejpam-2515	72	4	i0	i0	PROPN
ejpam-2515	72	5	,	,	PUNCT
ejpam-2515	72	6	j0	j0	PROPN
ejpam-2515	72	7	<	<	X
ejpam-2515	72	8	jk+1	jk+1	X
ejpam-2515	72	9	<	<	X
ejpam-2515	72	10	.	.	PUNCT
ejpam-2515	72	11	.	.	PUNCT
ejpam-2515	72	12	.	.	PUNCT
ejpam-2515	73	1	<	<	X
ejpam-2515	73	2	jn	jn	PROPN
ejpam-2515	73	3	≤	≤	PROPN
ejpam-2515	73	4	n	n	CCONJ
ejpam-2515	73	5	;	;	PUNCT
ejpam-2515	73	6	(	(	PUNCT
ejpam-2515	73	7	3	3	X
ejpam-2515	73	8	)	)	PUNCT
ejpam-2515	73	9	symmetric	symmetric	NOUN
ejpam-2515	73	10	if	if	SCONJ
ejpam-2515	73	11	(	(	PUNCT
ejpam-2515	73	12	x1	x1	PROPN
ejpam-2515	73	13	,	,	PUNCT
ejpam-2515	73	14	x2	x2	PROPN
ejpam-2515	73	15	,	,	PUNCT
ejpam-2515	73	16	.	.	PUNCT
ejpam-2515	73	17	.	.	PUNCT
ejpam-2515	73	18	.	.	PUNCT
ejpam-2515	74	1	,	,	PUNCT
ejpam-2515	74	2	xn	xn	X
ejpam-2515	74	3	)	)	PUNCT
ejpam-2515	74	4	∈	∈	PROPN
ejpam-2515	74	5	ρ	ρ	NOUN
ejpam-2515	74	6	implies	imply	VERB
ejpam-2515	74	7	(	(	PUNCT
ejpam-2515	74	8	xn	xn	PROPN
ejpam-2515	74	9	,	,	PUNCT
ejpam-2515	74	10	xn−1	xn−1	PROPN
ejpam-2515	74	11	,	,	PUNCT
ejpam-2515	74	12	.	.	PUNCT
ejpam-2515	74	13	.	.	PUNCT
ejpam-2515	74	14	.	.	PUNCT
ejpam-2515	75	1	,	,	PUNCT
ejpam-2515	75	2	x1	x1	X
ejpam-2515	75	3	)	)	PUNCT
ejpam-2515	75	4	∈	∈	PROPN
ejpam-2515	75	5	nρ	nρ	PROPN
ejpam-2515	75	6	(	(	PUNCT
ejpam-2515	75	7	4	4	NOUN
ejpam-2515	75	8	)	)	PUNCT
ejpam-2515	75	9	strongly	strongly	ADV
ejpam-2515	75	10	symmetric	symmetric	ADJ
ejpam-2515	75	11	if	if	SCONJ
ejpam-2515	75	12	(	(	PUNCT
ejpam-2515	75	13	x1	x1	PROPN
ejpam-2515	75	14	,	,	PUNCT
ejpam-2515	75	15	.	.	PUNCT
ejpam-2515	75	16	.	.	PUNCT
ejpam-2515	75	17	.	.	PUNCT
ejpam-2515	76	1	,	,	PUNCT
ejpam-2515	76	2	xn	xn	X
ejpam-2515	76	3	)	)	PUNCT
ejpam-2515	76	4	∈	∈	PROPN
ejpam-2515	76	5	ρ	ρ	PROPN
ejpam-2515	76	6	implies	imply	VERB
ejpam-2515	76	7	(	(	PUNCT
ejpam-2515	76	8	xσ(1	xσ(1	PROPN
ejpam-2515	76	9	)	)	PUNCT
ejpam-2515	76	10	,	,	PUNCT
ejpam-2515	76	11	.	.	PUNCT
ejpam-2515	76	12	.	.	PUNCT
ejpam-2515	76	13	.	.	PUNCT
ejpam-2515	77	1	,	,	PUNCT
ejpam-2515	77	2	xσ(n	xσ(n	PROPN
ejpam-2515	77	3	)	)	PUNCT
ejpam-2515	77	4	)	)	PUNCT
ejpam-2515	78	1	∈	∈	PROPN
ejpam-2515	78	2	ρ	ρ	PROPN
ejpam-2515	78	3	for	for	ADP
ejpam-2515	78	4	any	any	DET
ejpam-2515	78	5	permutation	permutation	NOUN
ejpam-2515	78	6	σ	σ	NOUN
ejpam-2515	78	7	of	of	ADP
ejpam-2515	78	8	the	the	DET
ejpam-2515	78	9	set	set	NOUN
ejpam-2515	78	10	{	{	PUNCT
ejpam-2515	78	11	1	1	NUM
ejpam-2515	78	12	,	,	PUNCT
ejpam-2515	78	13	.	.	PUNCT
ejpam-2515	78	14	.	.	PUNCT
ejpam-2515	78	15	.	.	PUNCT
ejpam-2515	79	1	,	,	PUNCT
ejpam-2515	79	2	n	n	CCONJ
ejpam-2515	79	3	}	}	PUNCT
ejpam-2515	79	4	;	;	PUNCT
ejpam-2515	79	5	(	(	PUNCT
ejpam-2515	79	6	5	5	NUM
ejpam-2515	79	7	)	)	PUNCT
ejpam-2515	79	8	n	n	CCONJ
ejpam-2515	79	9	-	-	PUNCT
ejpam-2515	79	10	ary	ary	NOUN
ejpam-2515	79	11	preordering	preordering	NOUN
ejpam-2515	79	12	on	on	ADP
ejpam-2515	79	13	h	h	NOUN
ejpam-2515	79	14	if	if	SCONJ
ejpam-2515	79	15	it	it	PRON
ejpam-2515	79	16	is	be	AUX
ejpam-2515	79	17	reflexive	reflexive	ADJ
ejpam-2515	79	18	and	and	CCONJ
ejpam-2515	79	19	n	n	CCONJ
ejpam-2515	79	20	-	-	PUNCT
ejpam-2515	79	21	transitive	transitive	ADJ
ejpam-2515	79	22	;	;	PUNCT
ejpam-2515	79	23	(	(	PUNCT
ejpam-2515	79	24	6	6	X
ejpam-2515	79	25	)	)	PUNCT
ejpam-2515	79	26	an	an	DET
ejpam-2515	79	27	n	n	ADV
ejpam-2515	79	28	-equivalence	-equivalence	NOUN
ejpam-2515	79	29	on	on	ADP
ejpam-2515	79	30	h	h	NOUN
ejpam-2515	79	31	if	if	SCONJ
ejpam-2515	79	32	it	it	PRON
ejpam-2515	79	33	is	be	AUX
ejpam-2515	79	34	reflexive	reflexive	ADJ
ejpam-2515	79	35	,	,	PUNCT
ejpam-2515	79	36	strongly	strongly	ADV
ejpam-2515	79	37	symmetric	symmetric	ADJ
ejpam-2515	79	38	and	and	CCONJ
ejpam-2515	79	39	n	n	CCONJ
ejpam-2515	79	40	-	-	PUNCT
ejpam-2515	79	41	transitive	transitive	ADJ
ejpam-2515	79	42	;	;	PUNCT
ejpam-2515	79	43	(	(	PUNCT
ejpam-2515	79	44	7	7	X
ejpam-2515	79	45	)	)	PUNCT
ejpam-2515	79	46	diagonal	diagonal	ADJ
ejpam-2515	79	47	n	n	CCONJ
ejpam-2515	79	48	-	-	PUNCT
ejpam-2515	79	49	ary	ary	PROPN
ejpam-2515	79	50	relation	relation	NOUN
ejpam-2515	79	51	on	on	ADP
ejpam-2515	79	52	h	h	NOUN
ejpam-2515	79	53	if	if	SCONJ
ejpam-2515	79	54	ρ	ρ	PROPN
ejpam-2515	79	55	=	=	SYM
ejpam-2515	79	56	{	{	PUNCT
ejpam-2515	79	57	(	(	PUNCT
ejpam-2515	79	58	x	x	INTJ
ejpam-2515	79	59	,	,	PUNCT
ejpam-2515	79	60	x	x	INTJ
ejpam-2515	79	61	,	,	PUNCT
ejpam-2515	79	62	.	.	PUNCT
ejpam-2515	79	63	.	.	PUNCT
ejpam-2515	80	1	.	.	PUNCT
ejpam-2515	81	1	,	,	PUNCT
ejpam-2515	81	2	x	x	X
ejpam-2515	81	3	)	)	PUNCT
ejpam-2515	81	4	|	|	ADV
ejpam-2515	81	5	x	x	SYM
ejpam-2515	81	6	∈	∈	PROPN
ejpam-2515	81	7	h	h	NOUN
ejpam-2515	81	8	}	}	PUNCT
ejpam-2515	81	9	.	.	PUNCT
ejpam-2515	82	1	2.1	2.1	NUM
ejpam-2515	82	2	.	.	PUNCT
ejpam-2515	82	3	projections	projection	NOUN
ejpam-2515	82	4	and	and	CCONJ
ejpam-2515	82	5	join	join	VERB
ejpam-2515	82	6	relations	relation	NOUN
ejpam-2515	82	7	definition	definition	NOUN
ejpam-2515	82	8	2	2	NUM
ejpam-2515	82	9	(	(	PUNCT
ejpam-2515	82	10	[	[	X
ejpam-2515	82	11	9	9	NUM
ejpam-2515	82	12	]	]	PUNCT
ejpam-2515	82	13	)	)	PUNCT
ejpam-2515	82	14	.	.	PUNCT
ejpam-2515	83	1	let	let	VERB
ejpam-2515	83	2	ρ	ρ	NOUN
ejpam-2515	83	3	be	be	AUX
ejpam-2515	83	4	an	an	DET
ejpam-2515	83	5	n	n	CCONJ
ejpam-2515	83	6	-	-	PUNCT
ejpam-2515	83	7	ary	ary	NOUN
ejpam-2515	83	8	relation	relation	NOUN
ejpam-2515	83	9	on	on	ADP
ejpam-2515	83	10	a	a	DET
ejpam-2515	83	11	nonempty	nonempty	ADV
ejpam-2515	83	12	set	set	VERB
ejpam-2515	83	13	h	h	NOUN
ejpam-2515	83	14	and	and	CCONJ
ejpam-2515	83	15	k	k	NOUN
ejpam-2515	83	16	<	<	X
ejpam-2515	83	17	n.	n.	PROPN
ejpam-2515	83	18	the	the	DET
ejpam-2515	83	19	(	(	PUNCT
ejpam-2515	83	20	i1	i1	PROPN
ejpam-2515	83	21	,	,	PUNCT
ejpam-2515	83	22	.	.	PUNCT
ejpam-2515	83	23	.	.	PUNCT
ejpam-2515	84	1	.	.	PUNCT
ejpam-2515	85	1	,	,	PUNCT
ejpam-2515	85	2	ik)projection	ik)projection	NOUN
ejpam-2515	85	3	of	of	ADP
ejpam-2515	85	4	ρ	ρ	PROPN
ejpam-2515	85	5	,	,	PUNCT
ejpam-2515	85	6	denoted	denote	VERB
ejpam-2515	85	7	by	by	ADP
ejpam-2515	85	8	ρi1,ik	ρi1,ik	INTJ
ejpam-2515	85	9	,	,	PUNCT
ejpam-2515	85	10	is	be	AUX
ejpam-2515	85	11	a	a	DET
ejpam-2515	85	12	kary	kary	PROPN
ejpam-2515	85	13	relation	relation	NOUN
ejpam-2515	85	14	on	on	ADP
ejpam-2515	85	15	h	h	NOUN
ejpam-2515	85	16	defined	define	VERB
ejpam-2515	85	17	by	by	ADP
ejpam-2515	85	18	:	:	PUNCT
ejpam-2515	85	19	if	if	SCONJ
ejpam-2515	85	20	(	(	PUNCT
ejpam-2515	85	21	a1	a1	NOUN
ejpam-2515	85	22	,	,	PUNCT
ejpam-2515	85	23	a2	a2	PROPN
ejpam-2515	85	24	,	,	PUNCT
ejpam-2515	85	25	a3	a3	NOUN
ejpam-2515	85	26	,	,	PUNCT
ejpam-2515	85	27	an	an	PRON
ejpam-2515	85	28	)	)	PUNCT
ejpam-2515	85	29	∈	∈	PROPN
ejpam-2515	85	30	ρ	ρ	PROPN
ejpam-2515	85	31	,	,	PUNCT
ejpam-2515	85	32	then	then	ADV
ejpam-2515	85	33	(	(	PUNCT
ejpam-2515	85	34	ai1	ai1	X
ejpam-2515	85	35	,	,	PUNCT
ejpam-2515	85	36	.	.	PUNCT
ejpam-2515	85	37	.	.	PUNCT
ejpam-2515	86	1	.	.	PUNCT
ejpam-2515	87	1	,	,	PUNCT
ejpam-2515	87	2	aik	aik	NOUN
ejpam-2515	87	3	)	)	PUNCT
ejpam-2515	87	4	∈	∈	PROPN
ejpam-2515	87	5	ρi1,	ρi1,	NOUN
ejpam-2515	87	6	...	...	PUNCT
ejpam-2515	87	7	,ik	,ik	PUNCT
ejpam-2515	87	8	definition	definition	NOUN
ejpam-2515	87	9	3	3	NUM
ejpam-2515	87	10	(	(	PUNCT
ejpam-2515	87	11	[	[	X
ejpam-2515	87	12	9	9	NUM
ejpam-2515	87	13	]	]	PUNCT
ejpam-2515	87	14	)	)	PUNCT
ejpam-2515	87	15	.	.	PUNCT
ejpam-2515	88	1	let	let	VERB
ejpam-2515	88	2	ρ	ρ	NOUN
ejpam-2515	88	3	be	be	AUX
ejpam-2515	88	4	an	an	DET
ejpam-2515	88	5	n	n	CCONJ
ejpam-2515	88	6	-	-	PUNCT
ejpam-2515	88	7	ary	ary	NOUN
ejpam-2515	88	8	relation	relation	NOUN
ejpam-2515	88	9	on	on	ADP
ejpam-2515	88	10	a	a	DET
ejpam-2515	88	11	nonempty	nonempty	ADV
ejpam-2515	88	12	set	set	VERB
ejpam-2515	88	13	h	h	NOUN
ejpam-2515	88	14	λ	λ	PROPN
ejpam-2515	88	15	an	an	DET
ejpam-2515	88	16	m	m	PROPN
ejpam-2515	88	17	-	-	ADJ
ejpam-2515	88	18	ary	ary	PROPN
ejpam-2515	88	19	relation	relation	NOUN
ejpam-2515	88	20	on	on	ADP
ejpam-2515	88	21	the	the	DET
ejpam-2515	88	22	same	same	ADJ
ejpam-2515	88	23	set	set	NOUN
ejpam-2515	88	24	h.	h.	PROPN
ejpam-2515	88	25	the	the	DET
ejpam-2515	88	26	join	join	PROPN
ejpam-2515	88	27	relation	relation	NOUN
ejpam-2515	88	28	of	of	ADP
ejpam-2515	88	29	ρ	ρ	PROPN
ejpam-2515	88	30	and	and	CCONJ
ejpam-2515	88	31	λ	λ	PROPN
ejpam-2515	88	32	,	,	PUNCT
ejpam-2515	88	33	denoted	denote	VERB
ejpam-2515	88	34	by	by	ADP
ejpam-2515	88	35	jp(ρ	jp(ρ	PROPN
ejpam-2515	88	36	,	,	PUNCT
ejpam-2515	88	37	λ	λ	NOUN
ejpam-2515	88	38	)	)	PUNCT
ejpam-2515	88	39	where	where	SCONJ
ejpam-2515	88	40	1	1	NUM
ejpam-2515	88	41	<	<	X
ejpam-2515	88	42	p	p	X
ejpam-2515	88	43	<	<	X
ejpam-2515	88	44	n	n	X
ejpam-2515	88	45	,	,	PUNCT
ejpam-2515	88	46	1	1	NUM
ejpam-2515	88	47	<	<	X
ejpam-2515	88	48	p	p	X
ejpam-2515	88	49	<	<	X
ejpam-2515	88	50	m	m	NOUN
ejpam-2515	88	51	is	be	AUX
ejpam-2515	88	52	an	an	DET
ejpam-2515	88	53	m+n−p	m+n−p	PROPN
ejpam-2515	88	54	relation	relation	NOUN
ejpam-2515	88	55	on	on	ADP
ejpam-2515	88	56	h	h	NOUN
ejpam-2515	88	57	that	that	PRON
ejpam-2515	88	58	consists	consist	VERB
ejpam-2515	88	59	of	of	ADP
ejpam-2515	88	60	m+n−p	m+n−p	NOUN
ejpam-2515	88	61	-	-	PUNCT
ejpam-2515	88	62	tuples	tuple	NOUN
ejpam-2515	88	63	(	(	PUNCT
ejpam-2515	88	64	a1	a1	NOUN
ejpam-2515	88	65	,	,	PUNCT
ejpam-2515	88	66	.	.	PUNCT
ejpam-2515	88	67	.	.	PUNCT
ejpam-2515	89	1	.	.	PUNCT
ejpam-2515	90	1	,	,	PUNCT
ejpam-2515	90	2	am−p	am−p	NOUN
ejpam-2515	90	3	,	,	PUNCT
ejpam-2515	90	4	c1	c1	NOUN
ejpam-2515	90	5	,	,	PUNCT
ejpam-2515	90	6	.	.	PUNCT
ejpam-2515	90	7	.	.	PUNCT
ejpam-2515	91	1	.	.	PUNCT
ejpam-2515	92	1	,	,	PUNCT
ejpam-2515	92	2	cp	cp	X
ejpam-2515	92	3	,	,	PUNCT
ejpam-2515	92	4	b1	b1	NOUN
ejpam-2515	92	5	,	,	PUNCT
ejpam-2515	92	6	.	.	PUNCT
ejpam-2515	92	7	.	.	PUNCT
ejpam-2515	93	1	.	.	PUNCT
ejpam-2515	94	1	,	,	PUNCT
ejpam-2515	94	2	bn−p	bn−p	PROPN
ejpam-2515	94	3	)	)	PUNCT
ejpam-2515	94	4	∈	∈	PROPN
ejpam-2515	94	5	ρ	ρ	PROPN
ejpam-2515	94	6	and	and	CCONJ
ejpam-2515	94	7	(	(	PUNCT
ejpam-2515	94	8	c1	c1	PROPN
ejpam-2515	94	9	,	,	PUNCT
ejpam-2515	94	10	c2	c2	PROPN
ejpam-2515	94	11	,	,	PUNCT
ejpam-2515	94	12	.	.	PUNCT
ejpam-2515	94	13	.	.	PUNCT
ejpam-2515	94	14	.	.	PUNCT
ejpam-2515	95	1	,	,	PUNCT
ejpam-2515	95	2	cp	cp	X
ejpam-2515	95	3	,	,	PUNCT
ejpam-2515	95	4	b1	b1	NOUN
ejpam-2515	95	5	,	,	PUNCT
ejpam-2515	95	6	.	.	PUNCT
ejpam-2515	95	7	.	.	PUNCT
ejpam-2515	96	1	.	.	PUNCT
ejpam-2515	97	1	,	,	PUNCT
ejpam-2515	97	2	bn−p	bn−p	PROPN
ejpam-2515	97	3	)	)	PUNCT
ejpam-2515	97	4	∈	∈	PROPN
ejpam-2515	97	5	λ	λ	PROPN
ejpam-2515	97	6	.	.	PUNCT
ejpam-2515	98	1	s.	s.	PROPN
ejpam-2515	98	2	govindarajan	govindarajan	PROPN
ejpam-2515	98	3	/	/	SYM
ejpam-2515	98	4	eur	eur	PROPN
ejpam-2515	98	5	.	.	PUNCT
ejpam-2515	99	1	j.	j.	PROPN
ejpam-2515	99	2	pure	pure	PROPN
ejpam-2515	99	3	appl	appl	PROPN
ejpam-2515	99	4	.	.	PROPN
ejpam-2515	99	5	math	math	PROPN
ejpam-2515	99	6	,	,	PUNCT
ejpam-2515	99	7	9	9	NUM
ejpam-2515	99	8	(	(	PUNCT
ejpam-2515	99	9	2016	2016	NUM
ejpam-2515	99	10	)	)	PUNCT
ejpam-2515	99	11	,	,	PUNCT
ejpam-2515	99	12	367	367	NUM
ejpam-2515	99	13	-	-	SYM
ejpam-2515	99	14	382	382	NUM
ejpam-2515	99	15	370	370	NUM
ejpam-2515	99	16	let	let	VERB
ejpam-2515	99	17	ρ	ρ	NOUN
ejpam-2515	99	18	be	be	AUX
ejpam-2515	99	19	a	a	DET
ejpam-2515	99	20	ternary	ternary	ADJ
ejpam-2515	99	21	relation	relation	NOUN
ejpam-2515	99	22	on	on	ADP
ejpam-2515	99	23	h.	h.	PROPN
ejpam-2515	99	24	the	the	DET
ejpam-2515	99	25	join	join	PROPN
ejpam-2515	99	26	relation	relation	PROPN
ejpam-2515	99	27	j2(ρ	j2(ρ	PROPN
ejpam-2515	99	28	,	,	PUNCT
ejpam-2515	99	29	ρ	ρ	NOUN
ejpam-2515	99	30	)	)	PUNCT
ejpam-2515	99	31	denoted	denote	VERB
ejpam-2515	99	32	by	by	ADP
ejpam-2515	99	33	α	α	PROPN
ejpam-2515	99	34	is	be	AUX
ejpam-2515	99	35	a	a	DET
ejpam-2515	99	36	4	4	NUM
ejpam-2515	99	37	-	-	PUNCT
ejpam-2515	99	38	ary	ary	NOUN
ejpam-2515	99	39	relation	relation	NOUN
ejpam-2515	100	1	such	such	ADJ
ejpam-2515	100	2	that	that	SCONJ
ejpam-2515	100	3	(	(	PUNCT
ejpam-2515	100	4	x	x	X
ejpam-2515	100	5	,	,	PUNCT
ejpam-2515	100	6	y	y	PROPN
ejpam-2515	100	7	,	,	PUNCT
ejpam-2515	100	8	z	z	NOUN
ejpam-2515	100	9	)	)	PUNCT
ejpam-2515	100	10	∈	∈	PROPN
ejpam-2515	100	11	j2(ρ	j2(ρ	PROPN
ejpam-2515	100	12	,	,	PUNCT
ejpam-2515	100	13	ρ)	ρ)	NUM
ejpam-2515	100	14	⇐	⇐	ADJ
ejpam-2515	100	15	⇒	⇒	NOUN
ejpam-2515	100	16	(	(	PUNCT
ejpam-2515	100	17	x	x	X
ejpam-2515	100	18	,	,	PUNCT
ejpam-2515	100	19	y	y	PROPN
ejpam-2515	100	20	,	,	PUNCT
ejpam-2515	100	21	z	z	NOUN
ejpam-2515	100	22	)	)	PUNCT
ejpam-2515	100	23	,	,	PUNCT
ejpam-2515	100	24	(	(	PUNCT
ejpam-2515	100	25	y	y	NOUN
ejpam-2515	100	26	,	,	PUNCT
ejpam-2515	100	27	z	z	PROPN
ejpam-2515	100	28	,	,	PUNCT
ejpam-2515	100	29	t	t	PROPN
ejpam-2515	100	30	)	)	PUNCT
ejpam-2515	100	31	∈	∈	PROPN
ejpam-2515	100	32	ρ	ρ	NOUN
ejpam-2515	100	33	.	.	PUNCT
ejpam-2515	101	1	if	if	SCONJ
ejpam-2515	101	2	we	we	PRON
ejpam-2515	101	3	denote	denote	VERB
ejpam-2515	101	4	the	the	DET
ejpam-2515	101	5	join	join	PROPN
ejpam-2515	101	6	relation	relation	PROPN
ejpam-2515	101	7	j2(ρ	j2(ρ	PROPN
ejpam-2515	101	8	,	,	PUNCT
ejpam-2515	101	9	ρ	ρ	PROPN
ejpam-2515	101	10	)	)	PUNCT
ejpam-2515	101	11	by	by	ADP
ejpam-2515	101	12	the	the	DET
ejpam-2515	101	13	symbol	symbol	NOUN
ejpam-2515	101	14	α	α	NOUN
ejpam-2515	101	15	then	then	ADV
ejpam-2515	101	16	its	its	PRON
ejpam-2515	101	17	projection	projection	NOUN
ejpam-2515	101	18	relations	relation	NOUN
ejpam-2515	101	19	are	be	AUX
ejpam-2515	101	20	denoted	denote	VERB
ejpam-2515	101	21	by	by	ADP
ejpam-2515	101	22	α	α	PROPN
ejpam-2515	101	23	1,2,4	1,2,4	NUM
ejpam-2515	101	24	and	and	CCONJ
ejpam-2515	101	25	α	α	PROPN
ejpam-2515	101	26	1,3,4	1,3,4	NUM
ejpam-2515	101	27	.	.	PUNCT
ejpam-2515	102	1	2.2	2.2	NUM
ejpam-2515	102	2	.	.	PUNCT
ejpam-2515	103	1	some	some	DET
ejpam-2515	103	2	results	result	NOUN
ejpam-2515	103	3	on	on	ADP
ejpam-2515	103	4	hypergroupoids	hypergroupoid	NOUN
ejpam-2515	103	5	associated	associate	VERB
ejpam-2515	103	6	with	with	ADP
ejpam-2515	103	7	n	n	CCONJ
ejpam-2515	103	8	ary	ary	PROPN
ejpam-2515	103	9	relations	relation	NOUN
ejpam-2515	103	10	to	to	ADP
ejpam-2515	103	11	each	each	DET
ejpam-2515	103	12	ternary	ternary	ADJ
ejpam-2515	103	13	relation	relation	NOUN
ejpam-2515	103	14	ρ	ρ	PROPN
ejpam-2515	103	15	on	on	ADP
ejpam-2515	103	16	h	h	NOUN
ejpam-2515	103	17	,	,	PUNCT
ejpam-2515	103	18	the	the	DET
ejpam-2515	103	19	hyperproduct	hyperproduct	NOUN
ejpam-2515	103	20	is	be	AUX
ejpam-2515	103	21	defined	define	VERB
ejpam-2515	103	22	in	in	ADP
ejpam-2515	103	23	[	[	X
ejpam-2515	103	24	9	9	NUM
ejpam-2515	103	25	]	]	PUNCT
ejpam-2515	103	26	as	as	SCONJ
ejpam-2515	103	27	follows	follow	VERB
ejpam-2515	103	28	:	:	PUNCT
ejpam-2515	103	29	(	(	PUNCT
ejpam-2515	103	30	β	β	NOUN
ejpam-2515	103	31	)	)	PUNCT
ejpam-2515	103	32	for	for	ADP
ejpam-2515	103	33	any	any	DET
ejpam-2515	103	34	x	x	SYM
ejpam-2515	103	35	,	,	PUNCT
ejpam-2515	103	36	y	y	PROPN
ejpam-2515	103	37	∈	∈	PROPN
ejpam-2515	103	38	h	h	NOUN
ejpam-2515	103	39	,	,	PUNCT
ejpam-2515	103	40	x	x	VERB
ejpam-2515	103	41	⊗ρ	⊗ρ	ADJ
ejpam-2515	103	42	y	y	PROPN
ejpam-2515	103	43	=	=	PRON
ejpam-2515	103	44	{	{	PUNCT
ejpam-2515	103	45	z	z	NOUN
ejpam-2515	103	46	∈	∈	PROPN
ejpam-2515	103	47	h	h	NOUN
ejpam-2515	104	1	|	|	ADV
ejpam-2515	104	2	(	(	PUNCT
ejpam-2515	104	3	x	x	INTJ
ejpam-2515	104	4	,	,	PUNCT
ejpam-2515	104	5	z	z	PROPN
ejpam-2515	104	6	,	,	PUNCT
ejpam-2515	104	7	y	y	PROPN
ejpam-2515	104	8	)	)	PUNCT
ejpam-2515	104	9	∈	∈	PROPN
ejpam-2515	104	10	ρ	ρ	PROPN
ejpam-2515	104	11	}	}	PUNCT
ejpam-2515	104	12	.	.	PUNCT
ejpam-2515	105	1	the	the	DET
ejpam-2515	105	2	hyperproduct	hyperproduct	NOUN
ejpam-2515	105	3	defined	define	VERB
ejpam-2515	105	4	in	in	ADP
ejpam-2515	105	5	(	(	PUNCT
ejpam-2515	105	6	β	β	NOUN
ejpam-2515	105	7	)	)	PUNCT
ejpam-2515	105	8	associated	associate	VERB
ejpam-2515	105	9	to	to	ADP
ejpam-2515	105	10	ternary	ternary	ADJ
ejpam-2515	105	11	relation	relation	NOUN
ejpam-2515	105	12	ρ	ρ	NOUN
ejpam-2515	105	13	is	be	AUX
ejpam-2515	105	14	generalized	generalize	VERB
ejpam-2515	105	15	to	to	ADP
ejpam-2515	105	16	the	the	DET
ejpam-2515	105	17	case	case	NOUN
ejpam-2515	105	18	of	of	ADP
ejpam-2515	105	19	an	an	DET
ejpam-2515	105	20	n	n	CCONJ
ejpam-2515	105	21	-	-	PUNCT
ejpam-2515	105	22	ary	ary	NOUN
ejpam-2515	105	23	relation	relation	NOUN
ejpam-2515	105	24	ρ(n≥	ρ(n≥	NOUN
ejpam-2515	105	25	3	3	NUM
ejpam-2515	105	26	)	)	PUNCT
ejpam-2515	105	27	,	,	PUNCT
ejpam-2515	105	28	using	use	VERB
ejpam-2515	105	29	projection	projection	NOUN
ejpam-2515	105	30	as	as	ADP
ejpam-2515	105	31	in	in	ADP
ejpam-2515	105	32	the	the	DET
ejpam-2515	105	33	following	following	NOUN
ejpam-2515	105	34	:	:	PUNCT
ejpam-2515	105	35	(	(	PUNCT
ejpam-2515	105	36	δ1	δ1	NOUN
ejpam-2515	105	37	)	)	PUNCT
ejpam-2515	105	38	for	for	ADP
ejpam-2515	105	39	any	any	DET
ejpam-2515	105	40	i	i	PROPN
ejpam-2515	105	41	∈	∈	PROPN
ejpam-2515	105	42	{	{	PUNCT
ejpam-2515	105	43	2	2	NUM
ejpam-2515	105	44	,	,	PUNCT
ejpam-2515	105	45	.	.	PUNCT
ejpam-2515	105	46	.	.	PUNCT
ejpam-2515	106	1	.	.	PUNCT
ejpam-2515	107	1	,	,	PUNCT
ejpam-2515	107	2	n−	n−	NOUN
ejpam-2515	107	3	1	1	NUM
ejpam-2515	107	4	}	}	PUNCT
ejpam-2515	107	5	,	,	PUNCT
ejpam-2515	107	6	x	x	PROPN
ejpam-2515	107	7	⊗i	⊗i	PROPN
ejpam-2515	107	8	y	y	PROPN
ejpam-2515	107	9	=	=	PRON
ejpam-2515	107	10	{	{	PUNCT
ejpam-2515	107	11	z	z	NOUN
ejpam-2515	107	12	∈	∈	PROPN
ejpam-2515	107	13	h	h	NOUN
ejpam-2515	108	1	|	|	ADV
ejpam-2515	108	2	(	(	PUNCT
ejpam-2515	108	3	x	x	INTJ
ejpam-2515	108	4	,	,	PUNCT
ejpam-2515	108	5	z	z	PROPN
ejpam-2515	108	6	,	,	PUNCT
ejpam-2515	108	7	y	y	NOUN
ejpam-2515	108	8	)	)	PUNCT
ejpam-2515	108	9	∈	∈	PROPN
ejpam-2515	108	10	ρ	ρ	PROPN
ejpam-2515	108	11	1,i	1,i	NUM
ejpam-2515	108	12	,	,	PUNCT
ejpam-2515	108	13	n	n	CCONJ
ejpam-2515	108	14	}	}	PUNCT
ejpam-2515	108	15	(	(	PUNCT
ejpam-2515	108	16	δ2	δ2	PROPN
ejpam-2515	108	17	)	)	PUNCT
ejpam-2515	108	18	x	x	PUNCT
ejpam-2515	108	19	⊗ρ	⊗ρ	PROPN
ejpam-2515	108	20	y	y	PROPN
ejpam-2515	108	21	=	=	PRON
ejpam-2515	108	22	{	{	PUNCT
ejpam-2515	108	23	z	z	NOUN
ejpam-2515	108	24	∈	∈	PROPN
ejpam-2515	108	25	h	h	NOUN
ejpam-2515	109	1	|	|	ADV
ejpam-2515	109	2	(	(	PUNCT
ejpam-2515	109	3	x	x	INTJ
ejpam-2515	109	4	,	,	PUNCT
ejpam-2515	109	5	z	z	PROPN
ejpam-2515	109	6	,	,	PUNCT
ejpam-2515	109	7	y	y	NOUN
ejpam-2515	109	8	)	)	PUNCT
ejpam-2515	109	9	∈	∈	PROPN
ejpam-2515	109	10	⋃n−1	⋃n−1	NOUN
ejpam-2515	109	11	i=2	i=2	PROPN
ejpam-2515	109	12	ρ1,i	ρ1,i	PROPN
ejpam-2515	109	13	,	,	PUNCT
ejpam-2515	109	14	n	n	NOUN
ejpam-2515	109	15	}	}	PUNCT
ejpam-2515	109	16	=	=	NOUN
ejpam-2515	109	17	⋃n−1	⋃n−1	NOUN
ejpam-2515	109	18	i=2	i=2	PROPN
ejpam-2515	109	19	x	x	PUNCT
ejpam-2515	109	20	⊗i	⊗i	PROPN
ejpam-2515	109	21	y	y	PROPN
ejpam-2515	109	22	.	.	PUNCT
ejpam-2515	110	1	this	this	PRON
ejpam-2515	110	2	(	(	PUNCT
ejpam-2515	110	3	h,⊗ρ	h,⊗ρ	PROPN
ejpam-2515	110	4	)	)	PUNCT
ejpam-2515	110	5	is	be	AUX
ejpam-2515	110	6	a	a	DET
ejpam-2515	110	7	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	110	8	if	if	SCONJ
ejpam-2515	111	1	and	and	CCONJ
ejpam-2515	111	2	only	only	ADV
ejpam-2515	111	3	if	if	SCONJ
ejpam-2515	111	4	the	the	DET
ejpam-2515	111	5	projection	projection	NOUN
ejpam-2515	111	6	ρ1,n	ρ1,n	PROPN
ejpam-2515	111	7	is	be	AUX
ejpam-2515	111	8	the	the	DET
ejpam-2515	111	9	total	total	ADJ
ejpam-2515	111	10	relation	relation	NOUN
ejpam-2515	111	11	,	,	PUNCT
ejpam-2515	111	12	that	that	PRON
ejpam-2515	111	13	is	be	AUX
ejpam-2515	111	14	ρ1,n	ρ1,n	PROPN
ejpam-2515	111	15	=	=	SYM
ejpam-2515	111	16	h	h	PROPN
ejpam-2515	111	17	×	×	PROPN
ejpam-2515	111	18	h.	h.	NOUN
ejpam-2515	111	19	the	the	DET
ejpam-2515	111	20	necessary	necessary	ADJ
ejpam-2515	111	21	and	and	CCONJ
ejpam-2515	111	22	sufficient	sufficient	ADJ
ejpam-2515	111	23	condition	condition	NOUN
ejpam-2515	111	24	on	on	ADP
ejpam-2515	111	25	ρ	ρ	PROPN
ejpam-2515	111	26	for	for	ADP
ejpam-2515	111	27	the	the	DET
ejpam-2515	111	28	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	111	29	hρ	hρ	PROPN
ejpam-2515	111	30	to	to	PART
ejpam-2515	111	31	be	be	AUX
ejpam-2515	111	32	a	a	DET
ejpam-2515	111	33	quasi	quasi	ADJ
ejpam-2515	111	34	hypergroup	hypergroup	NOUN
ejpam-2515	111	35	and	and	CCONJ
ejpam-2515	111	36	necessary	necessary	ADJ
ejpam-2515	111	37	condition	condition	NOUN
ejpam-2515	111	38	on	on	ADP
ejpam-2515	111	39	ρ	ρ	PROPN
ejpam-2515	111	40	for	for	SCONJ
ejpam-2515	111	41	hρ	hρ	NOUN
ejpam-2515	111	42	to	to	PART
ejpam-2515	111	43	be	be	AUX
ejpam-2515	111	44	a	a	DET
ejpam-2515	111	45	semihypergroup	semihypergroup	NOUN
ejpam-2515	111	46	are	be	AUX
ejpam-2515	111	47	obtained	obtain	VERB
ejpam-2515	111	48	by	by	ADP
ejpam-2515	111	49	i.	i.	PROPN
ejpam-2515	111	50	cristea	cristea	PROPN
ejpam-2515	112	1	[	[	X
ejpam-2515	112	2	9	9	NUM
ejpam-2515	112	3	]	]	PUNCT
ejpam-2515	112	4	.	.	PUNCT
ejpam-2515	113	1	they	they	PRON
ejpam-2515	113	2	are	be	AUX
ejpam-2515	113	3	useful	useful	ADJ
ejpam-2515	113	4	in	in	ADP
ejpam-2515	113	5	the	the	DET
ejpam-2515	113	6	succeeding	succeed	VERB
ejpam-2515	113	7	sections	section	NOUN
ejpam-2515	113	8	and	and	CCONJ
ejpam-2515	113	9	so	so	ADV
ejpam-2515	113	10	stated	state	VERB
ejpam-2515	113	11	below	below	ADV
ejpam-2515	113	12	.	.	PUNCT
ejpam-2515	114	1	proposition	proposition	NOUN
ejpam-2515	114	2	1	1	NUM
ejpam-2515	114	3	(	(	PUNCT
ejpam-2515	114	4	[	[	X
ejpam-2515	114	5	9	9	NUM
ejpam-2515	114	6	,	,	PUNCT
ejpam-2515	114	7	proposition	proposition	NOUN
ejpam-2515	114	8	11	11	NUM
ejpam-2515	114	9	]	]	PUNCT
ejpam-2515	114	10	)	)	PUNCT
ejpam-2515	114	11	.	.	PUNCT
ejpam-2515	115	1	let	let	VERB
ejpam-2515	115	2	ρ	ρ	NOUN
ejpam-2515	115	3	be	be	AUX
ejpam-2515	115	4	an	an	DET
ejpam-2515	115	5	n	n	CCONJ
ejpam-2515	115	6	-	-	PUNCT
ejpam-2515	115	7	ary	ary	NOUN
ejpam-2515	115	8	relation	relation	NOUN
ejpam-2515	115	9	on	on	ADP
ejpam-2515	115	10	h.	h.	PROPN
ejpam-2515	115	11	then	then	ADV
ejpam-2515	115	12	(	(	PUNCT
ejpam-2515	115	13	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	115	14	)	)	PUNCT
ejpam-2515	115	15	is	be	AUX
ejpam-2515	115	16	a	a	DET
ejpam-2515	115	17	quasihypergroup	quasihypergroup	NOUN
ejpam-2515	116	1	if	if	SCONJ
ejpam-2515	116	2	and	and	CCONJ
ejpam-2515	116	3	only	only	ADV
ejpam-2515	116	4	if	if	SCONJ
ejpam-2515	116	5	ρ1,n	ρ1,n	PROPN
ejpam-2515	116	6	=	=	PUNCT
ejpam-2515	116	7	h	h	NUM
ejpam-2515	116	8	×	×	NOUN
ejpam-2515	116	9	h	h	NOUN
ejpam-2515	116	10	,	,	PUNCT
ejpam-2515	116	11	and	and	CCONJ
ejpam-2515	116	12	there	there	PRON
ejpam-2515	116	13	exists	exist	VERB
ejpam-2515	116	14	i	i	PRON
ejpam-2515	116	15	,	,	PUNCT
ejpam-2515	116	16	j	j	PROPN
ejpam-2515	116	17	with	with	ADP
ejpam-2515	116	18	2	2	NUM
ejpam-2515	116	19	≤	≤	NUM
ejpam-2515	116	20	i	i	PROPN
ejpam-2515	116	21	,	,	PUNCT
ejpam-2515	116	22	j	j	PROPN
ejpam-2515	116	23	≤	≤	PROPN
ejpam-2515	116	24	n	n	CCONJ
ejpam-2515	116	25	−	−	PROPN
ejpam-2515	116	26	1	1	NUM
ejpam-2515	116	27	,	,	PUNCT
ejpam-2515	116	28	such	such	ADJ
ejpam-2515	116	29	that	that	DET
ejpam-2515	116	30	ρ1,i	ρ1,i	PROPN
ejpam-2515	116	31	=	=	SYM
ejpam-2515	116	32	ρ	ρ	PROPN
ejpam-2515	116	33	j	j	PROPN
ejpam-2515	116	34	,	,	PUNCT
ejpam-2515	116	35	n	n	PROPN
ejpam-2515	116	36	=	=	NOUN
ejpam-2515	116	37	h	h	NOUN
ejpam-2515	116	38	×h	×h	NOUN
ejpam-2515	116	39	.	.	PUNCT
ejpam-2515	117	1	using	use	VERB
ejpam-2515	117	2	the	the	DET
ejpam-2515	117	3	projection	projection	NOUN
ejpam-2515	117	4	of	of	ADP
ejpam-2515	117	5	j2(ρ	j2(ρ	PROPN
ejpam-2515	117	6	,	,	PUNCT
ejpam-2515	117	7	ρ	ρ	PROPN
ejpam-2515	117	8	)	)	PUNCT
ejpam-2515	117	9	,	,	PUNCT
ejpam-2515	117	10	necessary	necessary	ADJ
ejpam-2515	117	11	condition	condition	NOUN
ejpam-2515	117	12	for	for	ADP
ejpam-2515	117	13	a	a	DET
ejpam-2515	117	14	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	117	15	(	(	PUNCT
ejpam-2515	117	16	h,⊗ρ	h,⊗ρ	PROPN
ejpam-2515	117	17	)	)	PUNCT
ejpam-2515	117	18	to	to	PART
ejpam-2515	117	19	be	be	AUX
ejpam-2515	117	20	a	a	DET
ejpam-2515	117	21	semihypergroup	semihypergroup	NOUN
ejpam-2515	117	22	is	be	AUX
ejpam-2515	117	23	obtained	obtain	VERB
ejpam-2515	117	24	in	in	ADP
ejpam-2515	117	25	[	[	X
ejpam-2515	117	26	9	9	NUM
ejpam-2515	117	27	]	]	PUNCT
ejpam-2515	117	28	as	as	SCONJ
ejpam-2515	117	29	follows	follow	VERB
ejpam-2515	117	30	:	:	PUNCT
ejpam-2515	117	31	proposition	proposition	NOUN
ejpam-2515	117	32	2	2	NUM
ejpam-2515	117	33	(	(	PUNCT
ejpam-2515	117	34	[	[	X
ejpam-2515	117	35	9	9	NUM
ejpam-2515	117	36	,	,	PUNCT
ejpam-2515	117	37	proposition	proposition	NOUN
ejpam-2515	117	38	16	16	NUM
ejpam-2515	117	39	]	]	PUNCT
ejpam-2515	117	40	)	)	PUNCT
ejpam-2515	117	41	.	.	PUNCT
ejpam-2515	118	1	let	let	VERB
ejpam-2515	118	2	ρ	ρ	NOUN
ejpam-2515	118	3	be	be	AUX
ejpam-2515	118	4	a	a	DET
ejpam-2515	118	5	reflexive	reflexive	ADJ
ejpam-2515	118	6	and	and	CCONJ
ejpam-2515	118	7	symmetric	symmetric	ADJ
ejpam-2515	118	8	ternary	ternary	PROPN
ejpam-2515	118	9	relation	relation	PROPN
ejpam-2515	118	10	h.	h.	PROPN
ejpam-2515	118	11	if	if	SCONJ
ejpam-2515	118	12	ρ	ρ	PROPN
ejpam-2515	118	13	6⊂	6⊂	NUM
ejpam-2515	118	14	α1,2,4	α1,2,4	PROPN
ejpam-2515	118	15	or	or	CCONJ
ejpam-2515	118	16	ρ	ρ	PROPN
ejpam-2515	118	17	6⊂	6⊂	NUM
ejpam-2515	118	18	α1,3,4	α1,3,4	PROPN
ejpam-2515	118	19	,	,	PUNCT
ejpam-2515	118	20	then	then	ADV
ejpam-2515	118	21	the	the	DET
ejpam-2515	118	22	hyperoperation	hyperoperation	NOUN
ejpam-2515	118	23	⊗ρ	⊗ρ	NOUN
ejpam-2515	118	24	is	be	AUX
ejpam-2515	118	25	not	not	PART
ejpam-2515	118	26	associative	associative	ADJ
ejpam-2515	118	27	.	.	PUNCT
ejpam-2515	119	1	corollary	corollary	ADJ
ejpam-2515	119	2	1	1	NUM
ejpam-2515	119	3	(	(	PUNCT
ejpam-2515	119	4	[	[	X
ejpam-2515	119	5	9	9	NUM
ejpam-2515	119	6	,	,	PUNCT
ejpam-2515	119	7	corollary	corollary	ADJ
ejpam-2515	119	8	17	17	NUM
ejpam-2515	119	9	]	]	PUNCT
ejpam-2515	119	10	)	)	PUNCT
ejpam-2515	119	11	.	.	PUNCT
ejpam-2515	120	1	let	let	VERB
ejpam-2515	120	2	ρ	ρ	NOUN
ejpam-2515	120	3	be	be	AUX
ejpam-2515	120	4	a	a	DET
ejpam-2515	120	5	reflexive	reflexive	ADJ
ejpam-2515	120	6	and	and	CCONJ
ejpam-2515	120	7	symmetric	symmetric	ADJ
ejpam-2515	120	8	ternary	ternary	PROPN
ejpam-2515	120	9	relation	relation	PROPN
ejpam-2515	120	10	h.	h.	PROPN
ejpam-2515	121	1	if	if	SCONJ
ejpam-2515	121	2	(	(	PUNCT
ejpam-2515	121	3	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	121	4	)	)	PUNCT
ejpam-2515	121	5	is	be	AUX
ejpam-2515	121	6	a	a	DET
ejpam-2515	121	7	semihypergroup	semihypergroup	NOUN
ejpam-2515	121	8	,	,	PUNCT
ejpam-2515	121	9	then	then	ADV
ejpam-2515	121	10	ρ	ρ	PROPN
ejpam-2515	121	11	⊂	⊂	PROPN
ejpam-2515	121	12	α1,2,4	α1,2,4	PROPN
ejpam-2515	121	13	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	121	14	.	.	PUNCT
ejpam-2515	122	1	proposition	proposition	NOUN
ejpam-2515	122	2	3	3	NUM
ejpam-2515	122	3	.	.	PUNCT
ejpam-2515	123	1	let	let	VERB
ejpam-2515	123	2	ρ	ρ	NOUN
ejpam-2515	123	3	be	be	AUX
ejpam-2515	123	4	a	a	DET
ejpam-2515	123	5	reflexive	reflexive	ADJ
ejpam-2515	123	6	and	and	CCONJ
ejpam-2515	123	7	symmetric	symmetric	ADJ
ejpam-2515	123	8	n	n	CCONJ
ejpam-2515	123	9	-	-	PUNCT
ejpam-2515	123	10	ary	ary	PROPN
ejpam-2515	123	11	relation	relation	NOUN
ejpam-2515	123	12	h	h	NOUN
ejpam-2515	123	13	which	which	PRON
ejpam-2515	123	14	satisfies	satisfy	VERB
ejpam-2515	123	15	the	the	DET
ejpam-2515	123	16	condition	condition	NOUN
ejpam-2515	123	17	(	(	PUNCT
ejpam-2515	123	18	s	s	NOUN
ejpam-2515	123	19	)	)	PUNCT
ejpam-2515	123	20	(	(	PUNCT
ejpam-2515	123	21	x	x	X
ejpam-2515	123	22	,	,	PUNCT
ejpam-2515	123	23	a1	a1	PROPN
ejpam-2515	123	24	,	,	PUNCT
ejpam-2515	123	25	.	.	PUNCT
ejpam-2515	123	26	.	.	PUNCT
ejpam-2515	123	27	.	.	PUNCT
ejpam-2515	124	1	an−2	an−2	PROPN
ejpam-2515	124	2	,	,	PUNCT
ejpam-2515	124	3	y	y	NOUN
ejpam-2515	124	4	)	)	PUNCT
ejpam-2515	124	5	∈	∈	PROPN
ejpam-2515	124	6	ρ	ρ	NUM
ejpam-2515	124	7	⇐	⇐	ADJ
ejpam-2515	124	8	⇒	⇒	PROPN
ejpam-2515	124	9	(	(	PUNCT
ejpam-2515	124	10	x	x	X
ejpam-2515	124	11	,	,	PUNCT
ejpam-2515	124	12	aσ(1	aσ(1	PROPN
ejpam-2515	124	13	)	)	PUNCT
ejpam-2515	124	14	,	,	PUNCT
ejpam-2515	124	15	.	.	PUNCT
ejpam-2515	124	16	.	.	PUNCT
ejpam-2515	124	17	.	.	PUNCT
ejpam-2515	125	1	aσ(n−2	aσ(n−2	PROPN
ejpam-2515	125	2	)	)	PUNCT
ejpam-2515	125	3	,	,	PUNCT
ejpam-2515	125	4	y	y	X
ejpam-2515	125	5	)	)	PUNCT
ejpam-2515	125	6	∈	∈	PROPN
ejpam-2515	125	7	ρ	ρ	NOUN
ejpam-2515	125	8	for	for	ADP
ejpam-2515	125	9	any	any	DET
ejpam-2515	125	10	permutation	permutation	NOUN
ejpam-2515	125	11	σ	σ	NOUN
ejpam-2515	125	12	of	of	ADP
ejpam-2515	125	13	the	the	DET
ejpam-2515	125	14	set	set	NOUN
ejpam-2515	125	15	{	{	PUNCT
ejpam-2515	125	16	1,2	1,2	NUM
ejpam-2515	125	17	,	,	PUNCT
ejpam-2515	125	18	.	.	PUNCT
ejpam-2515	125	19	.	.	PUNCT
ejpam-2515	125	20	.	.	PUNCT
ejpam-2515	126	1	,	,	PUNCT
ejpam-2515	126	2	n-1	n-1	PROPN
ejpam-2515	126	3	}	}	PUNCT
ejpam-2515	126	4	.	.	PUNCT
ejpam-2515	127	1	if	if	SCONJ
ejpam-2515	127	2	,	,	PUNCT
ejpam-2515	127	3	there	there	PRON
ejpam-2515	127	4	exists	exist	VERB
ejpam-2515	127	5	j	j	PROPN
ejpam-2515	127	6	∈	∈	PROPN
ejpam-2515	127	7	{	{	PUNCT
ejpam-2515	127	8	2	2	NUM
ejpam-2515	127	9	,	,	PUNCT
ejpam-2515	127	10	.	.	PUNCT
ejpam-2515	127	11	.	.	PUNCT
ejpam-2515	128	1	.	.	PUNCT
ejpam-2515	129	1	,	,	PUNCT
ejpam-2515	130	1	n	n	CCONJ
ejpam-2515	130	2	−	−	PROPN
ejpam-2515	130	3	1	1	NUM
ejpam-2515	130	4	}	}	PUNCT
ejpam-2515	130	5	such	such	ADJ
ejpam-2515	130	6	that	that	DET
ejpam-2515	130	7	ρ1	ρ1	NOUN
ejpam-2515	130	8	,	,	PUNCT
ejpam-2515	130	9	j	j	PROPN
ejpam-2515	130	10	,	,	PUNCT
ejpam-2515	130	11	n	n	PROPN
ejpam-2515	130	12	6⊂	6⊂	NUM
ejpam-2515	130	13	α1,n,2n−2	α1,n,2n−2	PROPN
ejpam-2515	130	14	or	or	CCONJ
ejpam-2515	130	15	ρ1	ρ1	PROPN
ejpam-2515	130	16	,	,	PUNCT
ejpam-2515	130	17	j	j	PROPN
ejpam-2515	130	18	,	,	PUNCT
ejpam-2515	130	19	n	n	PROPN
ejpam-2515	130	20	6⊂	6⊂	NUM
ejpam-2515	130	21	α1,n−1,2n−2	α1,n−1,2n−2	PROPN
ejpam-2515	130	22	,	,	PUNCT
ejpam-2515	130	23	then	then	ADV
ejpam-2515	130	24	the	the	DET
ejpam-2515	130	25	hyperoperation	hyperoperation	NOUN
ejpam-2515	130	26	⊗ρ	⊗ρ	NOUN
ejpam-2515	130	27	is	be	AUX
ejpam-2515	130	28	not	not	PART
ejpam-2515	130	29	associative	associative	ADJ
ejpam-2515	130	30	.	.	PUNCT
ejpam-2515	131	1	proposition	proposition	NOUN
ejpam-2515	131	2	4	4	NUM
ejpam-2515	131	3	(	(	PUNCT
ejpam-2515	131	4	[	[	X
ejpam-2515	131	5	9	9	NUM
ejpam-2515	131	6	,	,	PUNCT
ejpam-2515	131	7	proposition	proposition	NOUN
ejpam-2515	131	8	14	14	NUM
ejpam-2515	131	9	]	]	PUNCT
ejpam-2515	131	10	)	)	PUNCT
ejpam-2515	131	11	.	.	PUNCT
ejpam-2515	132	1	let	let	VERB
ejpam-2515	132	2	ρ	ρ	NOUN
ejpam-2515	132	3	be	be	AUX
ejpam-2515	132	4	a	a	DET
ejpam-2515	132	5	ternary	ternary	ADJ
ejpam-2515	132	6	relation	relation	NOUN
ejpam-2515	132	7	on	on	ADP
ejpam-2515	132	8	h	h	NOUN
ejpam-2515	132	9	such	such	ADJ
ejpam-2515	133	1	that	that	DET
ejpam-2515	133	2	ρ1,3	ρ1,3	PROPN
ejpam-2515	133	3	=	=	SYM
ejpam-2515	133	4	ρ1,2	ρ1,2	PROPN
ejpam-2515	134	1	=	=	PUNCT
ejpam-2515	135	1	h	h	NOUN
ejpam-2515	136	1	×h	×h	PROPN
ejpam-2515	137	1	or	or	CCONJ
ejpam-2515	137	2	ρ1,3	ρ1,3	PROPN
ejpam-2515	137	3	=	=	SYM
ejpam-2515	137	4	ρ2,3	ρ2,3	PROPN
ejpam-2515	137	5	if	if	SCONJ
ejpam-2515	137	6	ρ	ρ	PROPN
ejpam-2515	137	7	is	be	AUX
ejpam-2515	137	8	3	3	NUM
ejpam-2515	137	9	-	-	PUNCT
ejpam-2515	137	10	transitive	transitive	ADJ
ejpam-2515	137	11	,	,	PUNCT
ejpam-2515	137	12	then	then	ADV
ejpam-2515	137	13	(	(	PUNCT
ejpam-2515	137	14	h;⊗ρ	h;⊗ρ	NOUN
ejpam-2515	137	15	)	)	PUNCT
ejpam-2515	137	16	is	be	AUX
ejpam-2515	137	17	the	the	DET
ejpam-2515	137	18	total	total	ADJ
ejpam-2515	137	19	hypergroup	hypergroup	NOUN
ejpam-2515	137	20	.	.	PUNCT
ejpam-2515	138	1	example	example	NOUN
ejpam-2515	139	1	1	1	NUM
ejpam-2515	139	2	.	.	PUNCT
ejpam-2515	139	3	a	a	DET
ejpam-2515	139	4	ternary	ternary	ADJ
ejpam-2515	139	5	relation	relation	NOUN
ejpam-2515	139	6	ρ	ρ	NOUN
ejpam-2515	139	7	is	be	AUX
ejpam-2515	139	8	3	3	NUM
ejpam-2515	139	9	-	-	PUNCT
ejpam-2515	139	10	transitive	transitive	ADJ
ejpam-2515	139	11	if	if	SCONJ
ejpam-2515	139	12	and	and	CCONJ
ejpam-2515	139	13	only	only	ADV
ejpam-2515	139	14	if	if	SCONJ
ejpam-2515	139	15	it	it	PRON
ejpam-2515	139	16	satisfies	satisfy	VERB
ejpam-2515	139	17	the	the	DET
ejpam-2515	139	18	following	follow	VERB
ejpam-2515	139	19	conditions	condition	NOUN
ejpam-2515	139	20	:	:	PUNCT
ejpam-2515	139	21	(	(	PUNCT
ejpam-2515	139	22	i	i	NOUN
ejpam-2515	139	23	)	)	PUNCT
ejpam-2515	139	24	if	if	SCONJ
ejpam-2515	139	25	(	(	PUNCT
ejpam-2515	139	26	x	x	X
ejpam-2515	139	27	,	,	PUNCT
ejpam-2515	139	28	y	y	PROPN
ejpam-2515	139	29	,	,	PUNCT
ejpam-2515	139	30	z	z	NOUN
ejpam-2515	139	31	)	)	PUNCT
ejpam-2515	139	32	∈	∈	PROPN
ejpam-2515	139	33	ρ	ρ	PROPN
ejpam-2515	139	34	,	,	PUNCT
ejpam-2515	139	35	(	(	PUNCT
ejpam-2515	139	36	y	y	PROPN
ejpam-2515	139	37	,	,	PUNCT
ejpam-2515	139	38	u	u	NOUN
ejpam-2515	139	39	,	,	PUNCT
ejpam-2515	139	40	v	v	NOUN
ejpam-2515	139	41	)	)	PUNCT
ejpam-2515	139	42	∈	∈	PROPN
ejpam-2515	139	43	ρ	ρ	PROPN
ejpam-2515	139	44	,	,	PUNCT
ejpam-2515	139	45	then	then	ADV
ejpam-2515	139	46	(	(	PUNCT
ejpam-2515	139	47	x	x	X
ejpam-2515	139	48	,	,	PUNCT
ejpam-2515	139	49	u	u	NOUN
ejpam-2515	139	50	,	,	PUNCT
ejpam-2515	139	51	v	v	NOUN
ejpam-2515	139	52	)	)	PUNCT
ejpam-2515	139	53	∈	∈	PROPN
ejpam-2515	139	54	ρ	ρ	PROPN
ejpam-2515	139	55	(	(	PUNCT
ejpam-2515	139	56	ii	ii	NOUN
ejpam-2515	139	57	)	)	PUNCT
ejpam-2515	140	1	if	if	SCONJ
ejpam-2515	140	2	(	(	PUNCT
ejpam-2515	140	3	x	x	X
ejpam-2515	140	4	,	,	PUNCT
ejpam-2515	140	5	y	y	PROPN
ejpam-2515	140	6	,	,	PUNCT
ejpam-2515	140	7	z	z	NOUN
ejpam-2515	140	8	)	)	PUNCT
ejpam-2515	140	9	∈	∈	PROPN
ejpam-2515	140	10	ρ	ρ	PROPN
ejpam-2515	140	11	,	,	PUNCT
ejpam-2515	140	12	(	(	PUNCT
ejpam-2515	140	13	z	z	NOUN
ejpam-2515	140	14	,	,	PUNCT
ejpam-2515	140	15	u	u	NOUN
ejpam-2515	140	16	,	,	PUNCT
ejpam-2515	140	17	v	v	NOUN
ejpam-2515	140	18	)	)	PUNCT
ejpam-2515	140	19	∈	∈	PROPN
ejpam-2515	140	20	ρ	ρ	PROPN
ejpam-2515	140	21	,	,	PUNCT
ejpam-2515	140	22	then	then	ADV
ejpam-2515	140	23	(	(	PUNCT
ejpam-2515	140	24	x	x	X
ejpam-2515	140	25	,	,	PUNCT
ejpam-2515	140	26	y	y	PROPN
ejpam-2515	140	27	,	,	PUNCT
ejpam-2515	140	28	u	u	NOUN
ejpam-2515	140	29	)	)	PUNCT
ejpam-2515	140	30	∈	∈	PROPN
ejpam-2515	140	31	ρ	ρ	PROPN
ejpam-2515	140	32	,	,	PUNCT
ejpam-2515	140	33	(	(	PUNCT
ejpam-2515	140	34	x	x	X
ejpam-2515	140	35	,	,	PUNCT
ejpam-2515	140	36	y	y	PROPN
ejpam-2515	140	37	,	,	PUNCT
ejpam-2515	140	38	v	v	NOUN
ejpam-2515	140	39	)	)	PUNCT
ejpam-2515	140	40	∈	∈	PROPN
ejpam-2515	140	41	ρ	ρ	PROPN
ejpam-2515	140	42	,	,	PUNCT
ejpam-2515	140	43	(	(	PUNCT
ejpam-2515	140	44	x	x	X
ejpam-2515	140	45	,	,	PUNCT
ejpam-2515	140	46	u	u	NOUN
ejpam-2515	140	47	,	,	PUNCT
ejpam-2515	140	48	v	v	NOUN
ejpam-2515	140	49	)	)	PUNCT
ejpam-2515	140	50	∈	∈	PROPN
ejpam-2515	140	51	ρ	ρ	PROPN
ejpam-2515	140	52	,	,	PUNCT
ejpam-2515	140	53	(	(	PUNCT
ejpam-2515	140	54	y	y	PROPN
ejpam-2515	140	55	,	,	PUNCT
ejpam-2515	140	56	u	u	NOUN
ejpam-2515	140	57	,	,	PUNCT
ejpam-2515	140	58	v	v	NOUN
ejpam-2515	140	59	)	)	PUNCT
ejpam-2515	140	60	∈	∈	PROPN
ejpam-2515	140	61	ρ	ρ	PROPN
ejpam-2515	140	62	(	(	PUNCT
ejpam-2515	140	63	iii	iii	NOUN
ejpam-2515	140	64	)	)	PUNCT
ejpam-2515	140	65	if	if	SCONJ
ejpam-2515	140	66	(	(	PUNCT
ejpam-2515	140	67	x	x	X
ejpam-2515	140	68	,	,	PUNCT
ejpam-2515	140	69	y	y	PROPN
ejpam-2515	140	70	,	,	PUNCT
ejpam-2515	140	71	z	z	NOUN
ejpam-2515	140	72	)	)	PUNCT
ejpam-2515	140	73	∈	∈	PROPN
ejpam-2515	140	74	ρ	ρ	PROPN
ejpam-2515	140	75	,	,	PUNCT
ejpam-2515	140	76	(	(	PUNCT
ejpam-2515	140	77	u	u	NOUN
ejpam-2515	140	78	,	,	PUNCT
ejpam-2515	140	79	z	z	PROPN
ejpam-2515	140	80	,	,	PUNCT
ejpam-2515	140	81	v	v	NOUN
ejpam-2515	140	82	)	)	PUNCT
ejpam-2515	140	83	∈	∈	PROPN
ejpam-2515	140	84	ρ	ρ	PROPN
ejpam-2515	140	85	,	,	PUNCT
ejpam-2515	140	86	then	then	ADV
ejpam-2515	140	87	(	(	PUNCT
ejpam-2515	140	88	x	x	X
ejpam-2515	140	89	,	,	PUNCT
ejpam-2515	140	90	y	y	PROPN
ejpam-2515	140	91	,	,	PUNCT
ejpam-2515	140	92	v	v	NOUN
ejpam-2515	140	93	)	)	PUNCT
ejpam-2515	140	94	∈	∈	PROPN
ejpam-2515	140	95	ρ	ρ	PROPN
ejpam-2515	140	96	.	.	PUNCT
ejpam-2515	141	1	s.	s.	PROPN
ejpam-2515	141	2	govindarajan	govindarajan	PROPN
ejpam-2515	141	3	/	/	SYM
ejpam-2515	141	4	eur	eur	PROPN
ejpam-2515	141	5	.	.	PUNCT
ejpam-2515	142	1	j.	j.	PROPN
ejpam-2515	142	2	pure	pure	PROPN
ejpam-2515	142	3	appl	appl	PROPN
ejpam-2515	142	4	.	.	PROPN
ejpam-2515	142	5	math	math	PROPN
ejpam-2515	142	6	,	,	PUNCT
ejpam-2515	142	7	9	9	NUM
ejpam-2515	142	8	(	(	PUNCT
ejpam-2515	142	9	2016	2016	NUM
ejpam-2515	142	10	)	)	PUNCT
ejpam-2515	142	11	,	,	PUNCT
ejpam-2515	142	12	367	367	NUM
ejpam-2515	142	13	-	-	SYM
ejpam-2515	142	14	382	382	NUM
ejpam-2515	142	15	371	371	NUM
ejpam-2515	142	16	3	3	NUM
ejpam-2515	142	17	.	.	PUNCT
ejpam-2515	143	1	hypergroups	hypergroup	NOUN
ejpam-2515	143	2	associated	associate	VERB
ejpam-2515	143	3	with	with	ADP
ejpam-2515	143	4	ternary	ternary	ADJ
ejpam-2515	143	5	relations	relation	NOUN
ejpam-2515	143	6	we	we	PRON
ejpam-2515	143	7	begin	begin	VERB
ejpam-2515	143	8	by	by	ADP
ejpam-2515	143	9	remarking	remark	VERB
ejpam-2515	143	10	that	that	SCONJ
ejpam-2515	143	11	the	the	DET
ejpam-2515	143	12	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	143	13	(	(	PUNCT
ejpam-2515	143	14	h,⊗ρ	h,⊗ρ	PROPN
ejpam-2515	143	15	)	)	PUNCT
ejpam-2515	143	16	is	be	AUX
ejpam-2515	143	17	a	a	DET
ejpam-2515	143	18	semihypergroup	semihypergroup	NOUN
ejpam-2515	143	19	if	if	SCONJ
ejpam-2515	143	20	and	and	CCONJ
ejpam-2515	143	21	only	only	ADV
ejpam-2515	143	22	if	if	SCONJ
ejpam-2515	143	23	:	:	PUNCT
ejpam-2515	143	24	the	the	DET
ejpam-2515	143	25	following	follow	VERB
ejpam-2515	143	26	bi	bi	NOUN
ejpam-2515	143	27	-	-	NOUN
ejpam-2515	143	28	implication	implication	NOUN
ejpam-2515	143	29	holds	hold	VERB
ejpam-2515	143	30	:	:	PUNCT
ejpam-2515	143	31	(	(	PUNCT
ejpam-2515	143	32	β1	β1	PROPN
ejpam-2515	143	33	)	)	PUNCT
ejpam-2515	143	34	¨	¨	NOUN
ejpam-2515	143	35	∀a	∀a	NOUN
ejpam-2515	143	36	,	,	PUNCT
ejpam-2515	143	37	b	b	X
ejpam-2515	143	38	,	,	PUNCT
ejpam-2515	143	39	c	c	X
ejpam-2515	143	40	,	,	PUNCT
ejpam-2515	143	41	z	z	PROPN
ejpam-2515	143	42	∈	∈	PROPN
ejpam-2515	143	43	h	h	NOUN
ejpam-2515	143	44	,	,	PUNCT
ejpam-2515	143	45	there	there	PRON
ejpam-2515	143	46	exists	exist	VERB
ejpam-2515	143	47	x	x	X
ejpam-2515	143	48	∈	∈	PROPN
ejpam-2515	143	49	h	h	NOUN
ejpam-2515	143	50	,	,	PUNCT
ejpam-2515	143	51	such	such	ADJ
ejpam-2515	143	52	that	that	SCONJ
ejpam-2515	143	53	(	(	PUNCT
ejpam-2515	143	54	a	a	PRON
ejpam-2515	143	55	,	,	PUNCT
ejpam-2515	143	56	x	x	NOUN
ejpam-2515	143	57	,	,	PUNCT
ejpam-2515	143	58	b	b	NOUN
ejpam-2515	143	59	)	)	PUNCT
ejpam-2515	143	60	,	,	PUNCT
ejpam-2515	143	61	(	(	PUNCT
ejpam-2515	143	62	x	x	X
ejpam-2515	143	63	,	,	PUNCT
ejpam-2515	143	64	z	z	PROPN
ejpam-2515	143	65	,	,	PUNCT
ejpam-2515	143	66	c	c	NOUN
ejpam-2515	143	67	)	)	PUNCT
ejpam-2515	143	68	∈	∈	NOUN
ejpam-2515	143	69	ρ	ρ	NUM
ejpam-2515	143	70	⇐	⇐	ADJ
ejpam-2515	143	71	⇒	⇒	NOUN
ejpam-2515	143	72	there	there	PRON
ejpam-2515	143	73	exits	exit	VERB
ejpam-2515	143	74	y	y	PROPN
ejpam-2515	143	75	∈	∈	PROPN
ejpam-2515	143	76	h	h	NOUN
ejpam-2515	143	77	,	,	PUNCT
ejpam-2515	143	78	such	such	ADJ
ejpam-2515	143	79	that	that	SCONJ
ejpam-2515	143	80	(	(	PUNCT
ejpam-2515	143	81	a	a	PRON
ejpam-2515	143	82	,	,	PUNCT
ejpam-2515	143	83	z	z	PROPN
ejpam-2515	143	84	,	,	PUNCT
ejpam-2515	143	85	y	y	PROPN
ejpam-2515	143	86	)	)	PUNCT
ejpam-2515	143	87	,	,	PUNCT
ejpam-2515	143	88	(	(	PUNCT
ejpam-2515	143	89	b	b	X
ejpam-2515	143	90	,	,	PUNCT
ejpam-2515	143	91	y	y	PROPN
ejpam-2515	143	92	,	,	PUNCT
ejpam-2515	143	93	c	c	NOUN
ejpam-2515	143	94	)	)	PUNCT
ejpam-2515	143	95	∈	∈	NOUN
ejpam-2515	143	96	ρ	ρ	NOUN
ejpam-2515	143	97	now	now	ADV
ejpam-2515	143	98	,	,	PUNCT
ejpam-2515	143	99	let	let	VERB
ejpam-2515	143	100	ρ	ρ	NOUN
ejpam-2515	143	101	be	be	AUX
ejpam-2515	143	102	a	a	DET
ejpam-2515	143	103	ternary	ternary	ADJ
ejpam-2515	143	104	relation	relation	NOUN
ejpam-2515	143	105	on	on	ADP
ejpam-2515	143	106	h	h	NOUN
ejpam-2515	143	107	such	such	ADJ
ejpam-2515	143	108	that	that	PRON
ejpam-2515	144	1	ρ1,3	ρ1,3	PROPN
ejpam-2515	144	2	=	=	SYM
ejpam-2515	144	3	ρ1,2	ρ1,2	PROPN
ejpam-2515	144	4	=	=	SYM
ejpam-2515	144	5	ρ2,3	ρ2,3	NOUN
ejpam-2515	144	6	=	=	SYM
ejpam-2515	144	7	h×h	h×h	NOUN
ejpam-2515	144	8	.	.	PUNCT
ejpam-2515	145	1	the	the	DET
ejpam-2515	145	2	expression	expression	NOUN
ejpam-2515	145	3	(	(	PUNCT
ejpam-2515	145	4	β1	β1	PROPN
ejpam-2515	145	5	)	)	PUNCT
ejpam-2515	145	6	together	together	ADV
ejpam-2515	145	7	with	with	ADP
ejpam-2515	145	8	ρ1,3	ρ1,3	PROPN
ejpam-2515	145	9	=	=	SYM
ejpam-2515	145	10	ρ1,2	ρ1,2	PROPN
ejpam-2515	145	11	=	=	SYM
ejpam-2515	145	12	ρ2,3	ρ2,3	PUNCT
ejpam-2515	145	13	=	=	NOUN
ejpam-2515	145	14	h	h	NOUN
ejpam-2515	145	15	×h	×h	PROPN
ejpam-2515	145	16	and	and	CCONJ
ejpam-2515	145	17	example	example	NOUN
ejpam-2515	145	18	1	1	NUM
ejpam-2515	145	19	shows	show	VERB
ejpam-2515	145	20	that	that	SCONJ
ejpam-2515	145	21	ρ	ρ	PROPN
ejpam-2515	145	22	is	be	AUX
ejpam-2515	145	23	3	3	NUM
ejpam-2515	145	24	-	-	PUNCT
ejpam-2515	145	25	transitive	transitive	ADJ
ejpam-2515	145	26	.	.	PUNCT
ejpam-2515	146	1	that	that	PRON
ejpam-2515	146	2	is	be	AUX
ejpam-2515	146	3	,	,	PUNCT
ejpam-2515	146	4	if	if	SCONJ
ejpam-2515	146	5	(	(	PUNCT
ejpam-2515	146	6	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	146	7	)	)	PUNCT
ejpam-2515	146	8	is	be	AUX
ejpam-2515	146	9	a	a	DET
ejpam-2515	146	10	quasi	quasi	ADJ
ejpam-2515	146	11	hypergroup	hypergroup	NOUN
ejpam-2515	146	12	and	and	CCONJ
ejpam-2515	146	13	⊗ρ	⊗ρ	NOUN
ejpam-2515	146	14	satisfies	satisfy	VERB
ejpam-2515	146	15	the	the	DET
ejpam-2515	146	16	associative	associative	ADJ
ejpam-2515	146	17	axiom	axiom	NOUN
ejpam-2515	146	18	,	,	PUNCT
ejpam-2515	146	19	then	then	ADV
ejpam-2515	146	20	ρ	ρ	PROPN
ejpam-2515	146	21	is	be	AUX
ejpam-2515	146	22	3	3	NUM
ejpam-2515	146	23	-	-	PUNCT
ejpam-2515	146	24	transitive	transitive	ADJ
ejpam-2515	146	25	.	.	PUNCT
ejpam-2515	147	1	therefore	therefore	ADV
ejpam-2515	147	2	,	,	PUNCT
ejpam-2515	147	3	from	from	ADP
ejpam-2515	147	4	proposition	proposition	NOUN
ejpam-2515	147	5	4	4	NUM
ejpam-2515	147	6	and	and	CCONJ
ejpam-2515	147	7	from	from	ADP
ejpam-2515	147	8	the	the	DET
ejpam-2515	147	9	above	above	ADJ
ejpam-2515	147	10	paragraph	paragraph	NOUN
ejpam-2515	147	11	it	it	PRON
ejpam-2515	147	12	derives	derive	VERB
ejpam-2515	147	13	that	that	SCONJ
ejpam-2515	147	14	:	:	PUNCT
ejpam-2515	147	15	theorem	theorem	NOUN
ejpam-2515	147	16	1	1	X
ejpam-2515	147	17	.	.	PUNCT
ejpam-2515	148	1	let	let	VERB
ejpam-2515	148	2	ρ	ρ	NOUN
ejpam-2515	148	3	be	be	AUX
ejpam-2515	148	4	a	a	DET
ejpam-2515	148	5	ternary	ternary	ADJ
ejpam-2515	148	6	relation	relation	NOUN
ejpam-2515	148	7	on	on	ADP
ejpam-2515	148	8	h	h	NOUN
ejpam-2515	148	9	such	such	ADJ
ejpam-2515	148	10	that	that	PRON
ejpam-2515	149	1	ρ1,3	ρ1,3	PROPN
ejpam-2515	149	2	=	=	SYM
ejpam-2515	149	3	ρ1,2	ρ1,2	PROPN
ejpam-2515	149	4	=	=	SYM
ejpam-2515	149	5	ρ2,3	ρ2,3	PUNCT
ejpam-2515	149	6	=	=	PUNCT
ejpam-2515	150	1	h	h	PROPN
ejpam-2515	150	2	×	×	PROPN
ejpam-2515	150	3	h.	h.	NOUN
ejpam-2515	150	4	if	if	SCONJ
ejpam-2515	150	5	(	(	PUNCT
ejpam-2515	150	6	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	150	7	)	)	PUNCT
ejpam-2515	150	8	is	be	AUX
ejpam-2515	150	9	a	a	DET
ejpam-2515	150	10	hypergroup	hypergroup	NOUN
ejpam-2515	150	11	,	,	PUNCT
ejpam-2515	150	12	then	then	ADV
ejpam-2515	150	13	it	it	PRON
ejpam-2515	150	14	is	be	AUX
ejpam-2515	150	15	the	the	DET
ejpam-2515	150	16	total	total	ADJ
ejpam-2515	150	17	hypergroup	hypergroup	NOUN
ejpam-2515	150	18	.	.	PUNCT
ejpam-2515	151	1	however	however	ADV
ejpam-2515	151	2	,	,	PUNCT
ejpam-2515	151	3	we	we	PRON
ejpam-2515	151	4	can	can	AUX
ejpam-2515	151	5	prove	prove	VERB
ejpam-2515	151	6	the	the	DET
ejpam-2515	151	7	existence	existence	NOUN
ejpam-2515	151	8	of	of	ADP
ejpam-2515	151	9	a	a	DET
ejpam-2515	151	10	hypergroup	hypergroup	NOUN
ejpam-2515	151	11	(	(	PUNCT
ejpam-2515	151	12	h,⊗ρ	h,⊗ρ	PROPN
ejpam-2515	151	13	)	)	PUNCT
ejpam-2515	151	14	which	which	PRON
ejpam-2515	151	15	is	be	AUX
ejpam-2515	151	16	different	different	ADJ
ejpam-2515	151	17	from	from	ADP
ejpam-2515	151	18	the	the	DET
ejpam-2515	151	19	total	total	ADJ
ejpam-2515	151	20	hypergroup	hypergroup	NOUN
ejpam-2515	151	21	by	by	ADP
ejpam-2515	151	22	restricting	restrict	VERB
ejpam-2515	151	23	elements	element	NOUN
ejpam-2515	151	24	of	of	ADP
ejpam-2515	151	25	ρ	ρ	PROPN
ejpam-2515	151	26	.	.	PUNCT
ejpam-2515	152	1	proposition	proposition	NOUN
ejpam-2515	152	2	5	5	NUM
ejpam-2515	152	3	.	.	PUNCT
ejpam-2515	153	1	let	let	VERB
ejpam-2515	153	2	ρ	ρ	NOUN
ejpam-2515	153	3	be	be	AUX
ejpam-2515	153	4	a	a	DET
ejpam-2515	153	5	ternary	ternary	ADJ
ejpam-2515	153	6	relation	relation	NOUN
ejpam-2515	153	7	on	on	ADP
ejpam-2515	153	8	h	h	NOUN
ejpam-2515	154	1	such	such	ADJ
ejpam-2515	154	2	that	that	SCONJ
ejpam-2515	154	3	ρ	ρ	PROPN
ejpam-2515	154	4	1,3	1,3	NUM
ejpam-2515	154	5	=	=	SYM
ejpam-2515	154	6	h	h	NOUN
ejpam-2515	154	7	×h	×h	PROPN
ejpam-2515	154	8	.	.	PUNCT
ejpam-2515	155	1	consider	consider	VERB
ejpam-2515	155	2	the	the	DET
ejpam-2515	155	3	following	follow	VERB
ejpam-2515	155	4	condition	condition	NOUN
ejpam-2515	155	5	:	:	PUNCT
ejpam-2515	155	6	(	(	PUNCT
ejpam-2515	155	7	τ1	τ1	NOUN
ejpam-2515	155	8	)	)	PUNCT
ejpam-2515	155	9			NOUN
ejpam-2515	155	10			VERB
ejpam-2515	155	11			PRON
ejpam-2515	155	12			ADJ
ejpam-2515	155	13			NOUN
ejpam-2515	155	14	(	(	PUNCT
ejpam-2515	155	15	x	x	X
ejpam-2515	155	16	,	,	PUNCT
ejpam-2515	155	17	x	x	SYM
ejpam-2515	155	18	,	,	PUNCT
ejpam-2515	155	19	y	y	PROPN
ejpam-2515	155	20	)	)	PUNCT
ejpam-2515	155	21	,	,	PUNCT
ejpam-2515	155	22	(	(	PUNCT
ejpam-2515	155	23	x	x	X
ejpam-2515	155	24	,	,	PUNCT
ejpam-2515	155	25	y	y	PROPN
ejpam-2515	155	26	,	,	PUNCT
ejpam-2515	155	27	y	y	NOUN
ejpam-2515	155	28	)	)	PUNCT
ejpam-2515	155	29	∈	∈	PROPN
ejpam-2515	155	30	ρ	ρ	NOUN
ejpam-2515	155	31	∀(x	∀(x	X
ejpam-2515	155	32	,	,	PUNCT
ejpam-2515	155	33	y	y	NOUN
ejpam-2515	155	34	)	)	PUNCT
ejpam-2515	155	35	∈	∈	PROPN
ejpam-2515	155	36	h2	h2	NOUN
ejpam-2515	155	37	(	(	PUNCT
ejpam-2515	155	38	x	x	INTJ
ejpam-2515	155	39	,	,	PUNCT
ejpam-2515	155	40	y	y	PROPN
ejpam-2515	155	41	,	,	PUNCT
ejpam-2515	155	42	z	z	NOUN
ejpam-2515	155	43	)	)	PUNCT
ejpam-2515	155	44	6∈	6∈	NOUN
ejpam-2515	155	45	ρ	ρ	NOUN
ejpam-2515	155	46	if	if	SCONJ
ejpam-2515	155	47	x	x	X
ejpam-2515	155	48	,	,	PUNCT
ejpam-2515	155	49	y	y	PROPN
ejpam-2515	155	50	,	,	PUNCT
ejpam-2515	155	51	z	z	PROPN
ejpam-2515	155	52	are	be	AUX
ejpam-2515	155	53	distinct	distinct	ADJ
ejpam-2515	155	54	(	(	PUNCT
ejpam-2515	155	55	x	x	X
ejpam-2515	155	56	,	,	PUNCT
ejpam-2515	155	57	y	y	PROPN
ejpam-2515	155	58	,	,	PUNCT
ejpam-2515	155	59	x	x	NOUN
ejpam-2515	155	60	)	)	PUNCT
ejpam-2515	155	61	6∈	6∈	PROPN
ejpam-2515	155	62	ρ	ρ	NOUN
ejpam-2515	155	63	if	if	SCONJ
ejpam-2515	155	64	x	x	PROPN
ejpam-2515	155	65	6=	6=	ADP
ejpam-2515	155	66	y	y	PROPN
ejpam-2515	155	67	(	(	PUNCT
ejpam-2515	155	68	τ2	τ2	PROPN
ejpam-2515	155	69	)	)	PUNCT
ejpam-2515	155	70	¨	¨	NOUN
ejpam-2515	155	71	if	if	SCONJ
ejpam-2515	155	72	a	a	DET
ejpam-2515	155	73	,	,	PUNCT
ejpam-2515	155	74	b	b	NOUN
ejpam-2515	155	75	,	,	PUNCT
ejpam-2515	155	76	c	c	NOUN
ejpam-2515	155	77	,	,	PUNCT
ejpam-2515	155	78	d	d	X
ejpam-2515	155	79	are	be	AUX
ejpam-2515	155	80	distinct	distinct	ADJ
ejpam-2515	155	81	,	,	PUNCT
ejpam-2515	155	82	then	then	ADV
ejpam-2515	155	83	(	(	PUNCT
ejpam-2515	155	84	a	a	PRON
ejpam-2515	155	85	,	,	PUNCT
ejpam-2515	155	86	b	b	NOUN
ejpam-2515	155	87	,	,	PUNCT
ejpam-2515	155	88	c	c	NOUN
ejpam-2515	155	89	)	)	PUNCT
ejpam-2515	155	90	∈	∈	PROPN
ejpam-2515	155	91	ρ	ρ	PROPN
ejpam-2515	155	92	,	,	PUNCT
ejpam-2515	155	93	(	(	PUNCT
ejpam-2515	155	94	b	b	X
ejpam-2515	155	95	,	,	PUNCT
ejpam-2515	155	96	c	c	NOUN
ejpam-2515	155	97	,	,	PUNCT
ejpam-2515	155	98	d	d	NOUN
ejpam-2515	155	99	)	)	PUNCT
ejpam-2515	155	100	∈	∈	NOUN
ejpam-2515	155	101	ρ	ρ	NUM
ejpam-2515	155	102	⇐	⇐	ADJ
ejpam-2515	155	103	⇒	⇒	PROPN
ejpam-2515	155	104	(	(	PUNCT
ejpam-2515	155	105	a	a	DET
ejpam-2515	155	106	,	,	PUNCT
ejpam-2515	155	107	b	b	NOUN
ejpam-2515	155	108	,	,	PUNCT
ejpam-2515	155	109	d	d	NOUN
ejpam-2515	155	110	)	)	PUNCT
ejpam-2515	155	111	∈	∈	PROPN
ejpam-2515	155	112	ρ	ρ	PROPN
ejpam-2515	155	113	,	,	PUNCT
ejpam-2515	155	114	(	(	PUNCT
ejpam-2515	155	115	a	a	PRON
ejpam-2515	155	116	,	,	PUNCT
ejpam-2515	155	117	c	c	NOUN
ejpam-2515	155	118	,	,	PUNCT
ejpam-2515	155	119	d	d	NOUN
ejpam-2515	155	120	)	)	PUNCT
ejpam-2515	155	121	∈	∈	PROPN
ejpam-2515	155	122	ρ	ρ	PROPN
ejpam-2515	155	123	.	.	PUNCT
ejpam-2515	156	1	then	then	ADV
ejpam-2515	156	2	(	(	PUNCT
ejpam-2515	156	3	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	156	4	)	)	PUNCT
ejpam-2515	156	5	is	be	AUX
ejpam-2515	156	6	a	a	DET
ejpam-2515	156	7	hypergroup	hypergroup	NOUN
ejpam-2515	156	8	if	if	SCONJ
ejpam-2515	157	1	and	and	CCONJ
ejpam-2515	157	2	only	only	ADV
ejpam-2515	157	3	if	if	SCONJ
ejpam-2515	157	4	:	:	PUNCT
ejpam-2515	157	5	either	either	CCONJ
ejpam-2515	157	6	(	(	PUNCT
ejpam-2515	157	7	τ1	τ1	NOUN
ejpam-2515	157	8	)	)	PUNCT
ejpam-2515	157	9	alone	alone	ADV
ejpam-2515	157	10	holds	hold	VERB
ejpam-2515	157	11	or	or	CCONJ
ejpam-2515	157	12	both	both	DET
ejpam-2515	157	13	(	(	PUNCT
ejpam-2515	157	14	τ1	τ1	NOUN
ejpam-2515	157	15	)	)	PUNCT
ejpam-2515	157	16	and	and	CCONJ
ejpam-2515	157	17	(	(	PUNCT
ejpam-2515	157	18	τ2	τ2	NOUN
ejpam-2515	157	19	)	)	PUNCT
ejpam-2515	157	20	are	be	AUX
ejpam-2515	157	21	simultaneously	simultaneously	ADV
ejpam-2515	157	22	holds	hold	NOUN
ejpam-2515	157	23	.	.	PUNCT
ejpam-2515	158	1	proof	proof	NOUN
ejpam-2515	158	2	.	.	PUNCT
ejpam-2515	159	1	case(1	case(1	NOUN
ejpam-2515	159	2	):	):	PUNCT
ejpam-2515	159	3	suppose	suppose	VERB
ejpam-2515	159	4	(	(	PUNCT
ejpam-2515	159	5	τ1	τ1	NOUN
ejpam-2515	159	6	)	)	PUNCT
ejpam-2515	159	7	alone	alone	ADV
ejpam-2515	159	8	holds	hold	VERB
ejpam-2515	159	9	.	.	PUNCT
ejpam-2515	160	1	then	then	ADV
ejpam-2515	160	2	,	,	PUNCT
ejpam-2515	160	3	∀(x	∀(x	PRON
ejpam-2515	160	4	,	,	PUNCT
ejpam-2515	160	5	y	y	NOUN
ejpam-2515	160	6	)	)	PUNCT
ejpam-2515	160	7	∈	∈	PROPN
ejpam-2515	160	8	h2	h2	NOUN
ejpam-2515	160	9	(	(	PUNCT
ejpam-2515	160	10	x	x	X
ejpam-2515	160	11	,	,	PUNCT
ejpam-2515	160	12	x	x	SYM
ejpam-2515	160	13	,	,	PUNCT
ejpam-2515	160	14	y	y	PROPN
ejpam-2515	160	15	)	)	PUNCT
ejpam-2515	160	16	,	,	PUNCT
ejpam-2515	160	17	(	(	PUNCT
ejpam-2515	160	18	x	x	X
ejpam-2515	160	19	,	,	PUNCT
ejpam-2515	160	20	y	y	PROPN
ejpam-2515	160	21	,	,	PUNCT
ejpam-2515	160	22	y	y	NOUN
ejpam-2515	160	23	)	)	PUNCT
ejpam-2515	160	24	∈	∈	PROPN
ejpam-2515	160	25	ρ	ρ	NOUN
ejpam-2515	160	26	.	.	PUNCT
ejpam-2515	161	1	hence	hence	ADV
ejpam-2515	161	2	,	,	PUNCT
ejpam-2515	161	3	∀(x	∀(x	PRON
ejpam-2515	161	4	,	,	PUNCT
ejpam-2515	161	5	y	y	NOUN
ejpam-2515	161	6	)	)	PUNCT
ejpam-2515	161	7	∈	∈	PROPN
ejpam-2515	161	8	h2	h2	NOUN
ejpam-2515	161	9	,	,	PUNCT
ejpam-2515	161	10	{	{	PUNCT
ejpam-2515	161	11	x	x	INTJ
ejpam-2515	161	12	,	,	PUNCT
ejpam-2515	161	13	y	y	PROPN
ejpam-2515	161	14	}	}	PUNCT
ejpam-2515	161	15	⊂	⊂	PROPN
ejpam-2515	161	16	x	x	PUNCT
ejpam-2515	161	17	⊗ρ	⊗ρ	ADJ
ejpam-2515	161	18	y	y	PROPN
ejpam-2515	161	19	.	.	PUNCT
ejpam-2515	162	1	therefore	therefore	ADV
ejpam-2515	162	2	,	,	PUNCT
ejpam-2515	162	3	(	(	PUNCT
ejpam-2515	162	4	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	162	5	)	)	PUNCT
ejpam-2515	162	6	is	be	AUX
ejpam-2515	162	7	a	a	DET
ejpam-2515	162	8	quasi	quasi	NOUN
ejpam-2515	162	9	-	-	NOUN
ejpam-2515	162	10	hypergroup	hypergroup	NOUN
ejpam-2515	162	11	.	.	PUNCT
ejpam-2515	163	1	we	we	PRON
ejpam-2515	163	2	clearly	clearly	ADV
ejpam-2515	163	3	have	have	VERB
ejpam-2515	163	4	∀(x	∀(x	PRON
ejpam-2515	163	5	,	,	PUNCT
ejpam-2515	163	6	y	y	PROPN
ejpam-2515	163	7	,	,	PUNCT
ejpam-2515	163	8	z	z	NOUN
ejpam-2515	163	9	)	)	PUNCT
ejpam-2515	163	10	∈	∈	PROPN
ejpam-2515	163	11	h3	h3	NOUN
ejpam-2515	163	12	,	,	PUNCT
ejpam-2515	163	13	x	x	PUNCT
ejpam-2515	163	14	⊗ρ	⊗ρ	ADJ
ejpam-2515	163	15	(	(	PUNCT
ejpam-2515	163	16	y	y	PROPN
ejpam-2515	163	17	⊗ρ	⊗ρ	PROPN
ejpam-2515	163	18	z	z	PROPN
ejpam-2515	163	19	)	)	PUNCT
ejpam-2515	163	20	=	=	PUNCT
ejpam-2515	163	21	⋃	⋃	NOUN
ejpam-2515	163	22	a∈y⊗ρz	a∈y⊗ρz	PROPN
ejpam-2515	163	23	x	x	SYM
ejpam-2515	163	24	⊗ρ	⊗ρ	ADV
ejpam-2515	163	25	a	a	DET
ejpam-2515	163	26	=	=	SYM
ejpam-2515	163	27	{	{	PUNCT
ejpam-2515	163	28	x	x	PROPN
ejpam-2515	163	29	,	,	PUNCT
ejpam-2515	163	30	y	y	PROPN
ejpam-2515	163	31	,	,	PUNCT
ejpam-2515	163	32	z}=	z}=	PROPN
ejpam-2515	163	33	(	(	PUNCT
ejpam-2515	163	34	x	x	SYM
ejpam-2515	163	35	⊗ρ	⊗ρ	PROPN
ejpam-2515	164	1	y)⊗ρ	y)⊗ρ	NOUN
ejpam-2515	164	2	z.	z.	PROPN
ejpam-2515	165	1	so	so	ADV
ejpam-2515	165	2	,	,	PUNCT
ejpam-2515	165	3	⊗ρ	⊗ρ	PROPN
ejpam-2515	165	4	is	be	AUX
ejpam-2515	165	5	associative	associative	ADJ
ejpam-2515	165	6	,	,	PUNCT
ejpam-2515	165	7	whence	whence	NOUN
ejpam-2515	165	8	.	.	PUNCT
ejpam-2515	166	1	(	(	PUNCT
ejpam-2515	166	2	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	166	3	)	)	PUNCT
ejpam-2515	166	4	is	be	AUX
ejpam-2515	166	5	a	a	DET
ejpam-2515	166	6	hypergroup	hypergroup	NOUN
ejpam-2515	166	7	.	.	PUNCT
ejpam-2515	167	1	case(2	case(2	NOUN
ejpam-2515	167	2	):	):	PUNCT
ejpam-2515	167	3	suppose	suppose	VERB
ejpam-2515	167	4	both	both	DET
ejpam-2515	167	5	(	(	PUNCT
ejpam-2515	167	6	τ1	τ1	NOUN
ejpam-2515	167	7	)	)	PUNCT
ejpam-2515	167	8	and	and	CCONJ
ejpam-2515	167	9	(	(	PUNCT
ejpam-2515	167	10	τ2	τ2	NOUN
ejpam-2515	167	11	)	)	PUNCT
ejpam-2515	167	12	simultaneously	simultaneously	ADV
ejpam-2515	167	13	hold	hold	VERB
ejpam-2515	167	14	.	.	PUNCT
ejpam-2515	168	1	it	it	PRON
ejpam-2515	168	2	follows	follow	VERB
ejpam-2515	168	3	from	from	ADP
ejpam-2515	168	4	case	case	NOUN
ejpam-2515	168	5	(	(	PUNCT
ejpam-2515	168	6	1	1	NUM
ejpam-2515	168	7	)	)	PUNCT
ejpam-2515	168	8	that	that	SCONJ
ejpam-2515	168	9	(	(	PUNCT
ejpam-2515	168	10	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	168	11	)	)	PUNCT
ejpam-2515	168	12	is	be	AUX
ejpam-2515	168	13	a	a	DET
ejpam-2515	168	14	quasi	quasi	NOUN
ejpam-2515	168	15	-	-	NOUN
ejpam-2515	168	16	hypergroup	hypergroup	NOUN
ejpam-2515	168	17	.	.	PUNCT
ejpam-2515	169	1	all	all	PRON
ejpam-2515	169	2	that	that	PRON
ejpam-2515	169	3	remains	remain	VERB
ejpam-2515	169	4	to	to	PART
ejpam-2515	169	5	be	be	AUX
ejpam-2515	169	6	proved	prove	VERB
ejpam-2515	169	7	is	be	AUX
ejpam-2515	169	8	that	that	SCONJ
ejpam-2515	169	9	⊗ρ	⊗ρ	PROPN
ejpam-2515	169	10	associative	associative	NOUN
ejpam-2515	169	11	,	,	PUNCT
ejpam-2515	169	12	and	and	CCONJ
ejpam-2515	169	13	we	we	PRON
ejpam-2515	169	14	dispose	dispose	VERB
ejpam-2515	169	15	of	of	ADP
ejpam-2515	169	16	this	this	PRON
ejpam-2515	169	17	by	by	ADP
ejpam-2515	169	18	showing	show	VERB
ejpam-2515	169	19	that	that	SCONJ
ejpam-2515	169	20	∀(x	∀(x	X
ejpam-2515	169	21	,	,	PUNCT
ejpam-2515	169	22	y	y	PROPN
ejpam-2515	169	23	,	,	PUNCT
ejpam-2515	169	24	z	z	NOUN
ejpam-2515	169	25	)	)	PUNCT
ejpam-2515	169	26	∈	∈	PROPN
ejpam-2515	169	27	h3	h3	NOUN
ejpam-2515	169	28	,	,	PUNCT
ejpam-2515	169	29	(	(	PUNCT
ejpam-2515	169	30	x	x	SYM
ejpam-2515	169	31	⊗ρ	⊗ρ	PROPN
ejpam-2515	169	32	y)⊗ρ	y)⊗ρ	ADJ
ejpam-2515	169	33	z	z	PROPN
ejpam-2515	170	1	⊂	⊂	PUNCT
ejpam-2515	170	2	x	x	PUNCT
ejpam-2515	170	3	⊗ρ	⊗ρ	ADV
ejpam-2515	170	4	(	(	PUNCT
ejpam-2515	170	5	y	y	PROPN
ejpam-2515	170	6	⊗ρ	⊗ρ	PROPN
ejpam-2515	170	7	z	z	PROPN
ejpam-2515	170	8	)	)	PUNCT
ejpam-2515	170	9	,	,	PUNCT
ejpam-2515	170	10	and	and	CCONJ
ejpam-2515	170	11	conversely	conversely	ADV
ejpam-2515	170	12	.	.	PUNCT
ejpam-2515	171	1	let	let	VERB
ejpam-2515	171	2	a	a	DET
ejpam-2515	171	3	∈	∈	NOUN
ejpam-2515	171	4	(	(	PUNCT
ejpam-2515	171	5	x	x	SYM
ejpam-2515	171	6	⊗ρ	⊗ρ	PROPN
ejpam-2515	172	1	y)⊗ρ	y)⊗ρ	ADJ
ejpam-2515	172	2	z.	z.	PROPN
ejpam-2515	173	1	thus	thus	ADV
ejpam-2515	173	2	=	=	VERB
ejpam-2515	173	3	⇒	⇒	NOUN
ejpam-2515	173	4	there	there	ADV
ejpam-2515	173	5	exists	exist	VERB
ejpam-2515	173	6	u	u	PROPN
ejpam-2515	173	7	∈	∈	PROPN
ejpam-2515	173	8	x	x	PUNCT
ejpam-2515	173	9	⊗ρ	⊗ρ	PROPN
ejpam-2515	173	10	y	y	PROPN
ejpam-2515	173	11	such	such	ADJ
ejpam-2515	173	12	that	that	SCONJ
ejpam-2515	173	13	a	a	DET
ejpam-2515	173	14	∈	∈	PROPN
ejpam-2515	173	15	u⊗ρ	u⊗ρ	PROPN
ejpam-2515	173	16	z.	z.	PROPN
ejpam-2515	173	17	hence	hence	ADV
ejpam-2515	173	18	,	,	PUNCT
ejpam-2515	173	19	for	for	ADP
ejpam-2515	173	20	any	any	DET
ejpam-2515	173	21	a	a	DET
ejpam-2515	173	22	∈	∈	NOUN
ejpam-2515	173	23	(	(	PUNCT
ejpam-2515	173	24	x	x	SYM
ejpam-2515	173	25	⊗ρ	⊗ρ	PROPN
ejpam-2515	173	26	y)⊗ρ	y)⊗ρ	ADJ
ejpam-2515	173	27	z	z	NOUN
ejpam-2515	173	28	,	,	PUNCT
ejpam-2515	173	29	we	we	PRON
ejpam-2515	173	30	have	have	VERB
ejpam-2515	173	31	(	(	PUNCT
ejpam-2515	173	32	x	x	X
ejpam-2515	173	33	,	,	PUNCT
ejpam-2515	173	34	u	u	NOUN
ejpam-2515	173	35	,	,	PUNCT
ejpam-2515	173	36	y	y	NOUN
ejpam-2515	173	37	)	)	PUNCT
ejpam-2515	173	38	∈	∈	PROPN
ejpam-2515	173	39	ρ	ρ	PROPN
ejpam-2515	173	40	and	and	CCONJ
ejpam-2515	173	41	(	(	PUNCT
ejpam-2515	173	42	u	u	NOUN
ejpam-2515	173	43	,	,	PUNCT
ejpam-2515	173	44	a	a	PRON
ejpam-2515	173	45	,	,	PUNCT
ejpam-2515	173	46	z	z	NOUN
ejpam-2515	173	47	)	)	PUNCT
ejpam-2515	173	48	∈	∈	PROPN
ejpam-2515	173	49	ρ	ρ	PROPN
ejpam-2515	173	50	(	(	PUNCT
ejpam-2515	173	51	η	η	NOUN
ejpam-2515	173	52	)	)	PUNCT
ejpam-2515	173	53	.	.	PUNCT
ejpam-2515	174	1	we	we	PRON
ejpam-2515	174	2	show	show	VERB
ejpam-2515	174	3	that	that	SCONJ
ejpam-2515	174	4	a	a	DET
ejpam-2515	174	5	∈	∈	PROPN
ejpam-2515	174	6	x	x	SYM
ejpam-2515	174	7	⊗ρ	⊗ρ	NOUN
ejpam-2515	174	8	(	(	PUNCT
ejpam-2515	174	9	y	y	PROPN
ejpam-2515	174	10	⊗ρ	⊗ρ	PROPN
ejpam-2515	174	11	z	z	PROPN
ejpam-2515	174	12	)	)	PUNCT
ejpam-2515	174	13	to	to	PART
ejpam-2515	174	14	get	get	VERB
ejpam-2515	174	15	that	that	PRON
ejpam-2515	174	16	(	(	PUNCT
ejpam-2515	174	17	x	x	SYM
ejpam-2515	174	18	⊗ρ	⊗ρ	ADV
ejpam-2515	174	19	y)⊗ρ	y)⊗ρ	ADJ
ejpam-2515	174	20	z	z	PROPN
ejpam-2515	175	1	⊂	⊂	PUNCT
ejpam-2515	175	2	x	x	PUNCT
ejpam-2515	175	3	⊗ρ	⊗ρ	ADV
ejpam-2515	175	4	(	(	PUNCT
ejpam-2515	175	5	y	y	PROPN
ejpam-2515	175	6	⊗ρ	⊗ρ	PROPN
ejpam-2515	175	7	z	z	PROPN
ejpam-2515	175	8	)	)	PUNCT
ejpam-2515	175	9	.	.	PUNCT
ejpam-2515	176	1	we	we	PRON
ejpam-2515	176	2	consider	consider	VERB
ejpam-2515	176	3	the	the	DET
ejpam-2515	176	4	following	follow	VERB
ejpam-2515	176	5	situations	situation	NOUN
ejpam-2515	176	6	:	:	PUNCT
ejpam-2515	176	7	s.	s.	PROPN
ejpam-2515	176	8	govindarajan	govindarajan	PROPN
ejpam-2515	176	9	/	/	SYM
ejpam-2515	176	10	eur	eur	PROPN
ejpam-2515	176	11	.	.	PUNCT
ejpam-2515	177	1	j.	j.	PROPN
ejpam-2515	177	2	pure	pure	PROPN
ejpam-2515	177	3	appl	appl	PROPN
ejpam-2515	177	4	.	.	PROPN
ejpam-2515	177	5	math	math	PROPN
ejpam-2515	177	6	,	,	PUNCT
ejpam-2515	177	7	9	9	NUM
ejpam-2515	177	8	(	(	PUNCT
ejpam-2515	177	9	2016	2016	NUM
ejpam-2515	177	10	)	)	PUNCT
ejpam-2515	177	11	,	,	PUNCT
ejpam-2515	177	12	367	367	NUM
ejpam-2515	177	13	-	-	SYM
ejpam-2515	177	14	382	382	NUM
ejpam-2515	177	15	372	372	NUM
ejpam-2515	177	16	(	(	PUNCT
ejpam-2515	177	17	i	i	NOUN
ejpam-2515	177	18	)	)	PUNCT
ejpam-2515	177	19	let	let	VERB
ejpam-2515	177	20	(	(	PUNCT
ejpam-2515	177	21	x	x	X
ejpam-2515	177	22	,	,	PUNCT
ejpam-2515	177	23	u	u	NOUN
ejpam-2515	177	24	,	,	PUNCT
ejpam-2515	177	25	y	y	NOUN
ejpam-2515	177	26	)	)	PUNCT
ejpam-2515	177	27	∈	∈	PROPN
ejpam-2515	177	28	ρ	ρ	PROPN
ejpam-2515	177	29	with	with	ADP
ejpam-2515	177	30	(	(	PUNCT
ejpam-2515	177	31	u	u	NOUN
ejpam-2515	177	32	,	,	PUNCT
ejpam-2515	177	33	a	a	PRON
ejpam-2515	177	34	,	,	PUNCT
ejpam-2515	177	35	z	z	NOUN
ejpam-2515	177	36	)	)	PUNCT
ejpam-2515	177	37	∈	∈	PROPN
ejpam-2515	177	38	ρ	ρ	NOUN
ejpam-2515	177	39	.	.	PUNCT
ejpam-2515	178	1	using	use	VERB
ejpam-2515	178	2	the	the	DET
ejpam-2515	178	3	(	(	PUNCT
ejpam-2515	178	4	u	u	NOUN
ejpam-2515	178	5	,	,	PUNCT
ejpam-2515	178	6	a	a	PRON
ejpam-2515	178	7	,	,	PUNCT
ejpam-2515	178	8	z	z	NOUN
ejpam-2515	178	9	)	)	PUNCT
ejpam-2515	178	10	∈	∈	PROPN
ejpam-2515	178	11	ρ	ρ	X
ejpam-2515	178	12	in	in	ADP
ejpam-2515	178	13	(	(	PUNCT
ejpam-2515	178	14	τ2	τ2	NOUN
ejpam-2515	178	15	)	)	PUNCT
ejpam-2515	178	16	,	,	PUNCT
ejpam-2515	178	17	we	we	PRON
ejpam-2515	178	18	obtain	obtain	VERB
ejpam-2515	178	19	that	that	DET
ejpam-2515	178	20	(	(	PUNCT
ejpam-2515	178	21	u	u	NOUN
ejpam-2515	178	22	,	,	PUNCT
ejpam-2515	178	23	y	y	PROPN
ejpam-2515	178	24	,	,	PUNCT
ejpam-2515	178	25	a	a	PRON
ejpam-2515	178	26	)	)	PUNCT
ejpam-2515	178	27	,	,	PUNCT
ejpam-2515	178	28	(	(	PUNCT
ejpam-2515	178	29	y	y	NOUN
ejpam-2515	178	30	,	,	PUNCT
ejpam-2515	178	31	a	a	PRON
ejpam-2515	178	32	,	,	PUNCT
ejpam-2515	178	33	z	z	NOUN
ejpam-2515	178	34	)	)	PUNCT
ejpam-2515	178	35	∈	∈	PROPN
ejpam-2515	178	36	ρ	ρ	NOUN
ejpam-2515	178	37	.	.	PUNCT
ejpam-2515	179	1	by	by	ADP
ejpam-2515	179	2	the	the	DET
ejpam-2515	179	3	(	(	PUNCT
ejpam-2515	179	4	τ1	τ1	NOUN
ejpam-2515	179	5	)	)	PUNCT
ejpam-2515	179	6	and	and	CCONJ
ejpam-2515	179	7	from	from	ADP
ejpam-2515	179	8	(	(	PUNCT
ejpam-2515	179	9	y	y	PROPN
ejpam-2515	179	10	,	,	PUNCT
ejpam-2515	179	11	a	a	DET
ejpam-2515	179	12	,	,	PUNCT
ejpam-2515	179	13	z	z	NOUN
ejpam-2515	179	14	)	)	PUNCT
ejpam-2515	179	15	∈	∈	PROPN
ejpam-2515	179	16	ρ	ρ	PROPN
ejpam-2515	179	17	,	,	PUNCT
ejpam-2515	179	18	it	it	PRON
ejpam-2515	179	19	follows	follow	VERB
ejpam-2515	179	20	that	that	SCONJ
ejpam-2515	179	21	(	(	PUNCT
ejpam-2515	179	22	x	x	X
ejpam-2515	179	23	,	,	PUNCT
ejpam-2515	179	24	a	a	DET
ejpam-2515	179	25	,	,	PUNCT
ejpam-2515	179	26	a	a	PRON
ejpam-2515	179	27	)	)	PUNCT
ejpam-2515	179	28	∈	∈	PROPN
ejpam-2515	179	29	ρ	ρ	NOUN
ejpam-2515	179	30	with	with	ADP
ejpam-2515	179	31	(	(	PUNCT
ejpam-2515	179	32	y	y	PROPN
ejpam-2515	179	33	,	,	PUNCT
ejpam-2515	179	34	a	a	PRON
ejpam-2515	179	35	,	,	PUNCT
ejpam-2515	179	36	z	z	NOUN
ejpam-2515	179	37	)	)	PUNCT
ejpam-2515	179	38	∈	∈	PROPN
ejpam-2515	179	39	ρ	ρ	PROPN
ejpam-2515	179	40	.	.	PUNCT
ejpam-2515	180	1	thus	thus	ADV
ejpam-2515	180	2	,	,	PUNCT
ejpam-2515	180	3	there	there	PRON
ejpam-2515	180	4	exist	exist	VERB
ejpam-2515	180	5	a	a	DET
ejpam-2515	180	6	=	=	SYM
ejpam-2515	180	7	v	v	ADP
ejpam-2515	180	8	∈	∈	PROPN
ejpam-2515	180	9	y	y	PROPN
ejpam-2515	180	10	⊗ρ	⊗ρ	PROPN
ejpam-2515	180	11	z	z	PROPN
ejpam-2515	180	12	with	with	ADP
ejpam-2515	180	13	a	a	DET
ejpam-2515	180	14	∈	∈	PROPN
ejpam-2515	180	15	x	x	SYM
ejpam-2515	180	16	⊗ρ	⊗ρ	NOUN
ejpam-2515	180	17	a.	a.	NOUN
ejpam-2515	181	1	so	so	ADV
ejpam-2515	181	2	,	,	PUNCT
ejpam-2515	181	3	in	in	ADP
ejpam-2515	181	4	this	this	DET
ejpam-2515	181	5	case	case	NOUN
ejpam-2515	181	6	a	a	DET
ejpam-2515	181	7	∈	∈	NOUN
ejpam-2515	181	8	x	x	X
ejpam-2515	181	9	⊗ρ	⊗ρ	NOUN
ejpam-2515	181	10	(	(	PUNCT
ejpam-2515	181	11	y	y	PROPN
ejpam-2515	181	12	⊗ρ	⊗ρ	PROPN
ejpam-2515	181	13	z	z	PROPN
ejpam-2515	181	14	)	)	PUNCT
ejpam-2515	181	15	.	.	PUNCT
ejpam-2515	182	1	(	(	PUNCT
ejpam-2515	182	2	ii	ii	NOUN
ejpam-2515	182	3	)	)	PUNCT
ejpam-2515	182	4	now	now	ADV
ejpam-2515	182	5	,	,	PUNCT
ejpam-2515	182	6	we	we	PRON
ejpam-2515	182	7	consider	consider	VERB
ejpam-2515	182	8	the	the	DET
ejpam-2515	182	9	(	(	PUNCT
ejpam-2515	182	10	η)with	η)with	ADP
ejpam-2515	182	11	x	x	SYM
ejpam-2515	182	12	=	=	SYM
ejpam-2515	182	13	y	y	PROPN
ejpam-2515	182	14	.	.	PUNCT
ejpam-2515	183	1	from	from	ADP
ejpam-2515	183	2	(	(	PUNCT
ejpam-2515	183	3	τ1	τ1	NOUN
ejpam-2515	183	4	)	)	PUNCT
ejpam-2515	183	5	,	,	PUNCT
ejpam-2515	183	6	we	we	PRON
ejpam-2515	183	7	obtain	obtain	VERB
ejpam-2515	183	8	,	,	PUNCT
ejpam-2515	183	9	for	for	ADP
ejpam-2515	183	10	any	any	DET
ejpam-2515	183	11	x	x	SYM
ejpam-2515	183	12	∈	∈	PROPN
ejpam-2515	183	13	h	h	NOUN
ejpam-2515	183	14	,	,	PUNCT
ejpam-2515	183	15	(	(	PUNCT
ejpam-2515	183	16	x	x	X
ejpam-2515	183	17	,	,	PUNCT
ejpam-2515	183	18	x	x	X
ejpam-2515	183	19	,	,	PUNCT
ejpam-2515	183	20	x	x	X
ejpam-2515	183	21	)	)	PUNCT
ejpam-2515	183	22	∈	∈	PROPN
ejpam-2515	183	23	ρ	ρ	PROPN
ejpam-2515	183	24	.	.	PUNCT
ejpam-2515	184	1	from	from	ADP
ejpam-2515	184	2	(	(	PUNCT
ejpam-2515	184	3	η	η	NOUN
ejpam-2515	184	4	)	)	PUNCT
ejpam-2515	184	5	,	,	PUNCT
ejpam-2515	184	6	we	we	PRON
ejpam-2515	184	7	obtain	obtain	VERB
ejpam-2515	184	8	that	that	DET
ejpam-2515	184	9	u	u	NOUN
ejpam-2515	184	10	=	=	NOUN
ejpam-2515	184	11	x	x	X
ejpam-2515	184	12	and	and	CCONJ
ejpam-2515	184	13	(	(	PUNCT
ejpam-2515	184	14	x	x	INTJ
ejpam-2515	184	15	,	,	PUNCT
ejpam-2515	184	16	a	a	DET
ejpam-2515	184	17	,	,	PUNCT
ejpam-2515	184	18	z	z	NOUN
ejpam-2515	184	19	)	)	PUNCT
ejpam-2515	184	20	∈	∈	PROPN
ejpam-2515	184	21	ρ	ρ	NOUN
ejpam-2515	184	22	it	it	PRON
ejpam-2515	184	23	follows	follow	VERB
ejpam-2515	184	24	a	a	DET
ejpam-2515	184	25	∈	∈	NOUN
ejpam-2515	184	26	(	(	PUNCT
ejpam-2515	184	27	x	x	PUNCT
ejpam-2515	184	28	⊗ρ	⊗ρ	ADJ
ejpam-2515	184	29	x	x	NOUN
ejpam-2515	184	30	)	)	PUNCT
ejpam-2515	184	31	⊗ρ	⊗ρ	PROPN
ejpam-2515	184	32	z.	z.	PROPN
ejpam-2515	185	1	thus	thus	ADV
ejpam-2515	185	2	a	a	DET
ejpam-2515	185	3	∈	∈	PROPN
ejpam-2515	185	4	x	x	X
ejpam-2515	185	5	⊗ρ	⊗ρ	NOUN
ejpam-2515	185	6	(	(	PUNCT
ejpam-2515	185	7	x	x	SYM
ejpam-2515	185	8	⊗ρ	⊗ρ	PROPN
ejpam-2515	185	9	z	z	NOUN
ejpam-2515	185	10	)	)	PUNCT
ejpam-2515	185	11	.	.	PUNCT
ejpam-2515	186	1	we	we	PRON
ejpam-2515	186	2	have	have	VERB
ejpam-2515	186	3	,	,	PUNCT
ejpam-2515	186	4	(	(	PUNCT
ejpam-2515	186	5	x	x	X
ejpam-2515	186	6	,	,	PUNCT
ejpam-2515	186	7	a	a	DET
ejpam-2515	186	8	,	,	PUNCT
ejpam-2515	186	9	z	z	NOUN
ejpam-2515	186	10	)	)	PUNCT
ejpam-2515	186	11	∈	∈	PROPN
ejpam-2515	186	12	ρ	ρ	PROPN
ejpam-2515	186	13	and	and	CCONJ
ejpam-2515	186	14	(	(	PUNCT
ejpam-2515	186	15	by	by	ADP
ejpam-2515	186	16	the	the	DET
ejpam-2515	186	17	(	(	PUNCT
ejpam-2515	186	18	τ1	τ1	NOUN
ejpam-2515	186	19	)	)	PUNCT
ejpam-2515	186	20	)	)	PUNCT
ejpam-2515	187	1	(	(	PUNCT
ejpam-2515	187	2	x	x	X
ejpam-2515	187	3	,	,	PUNCT
ejpam-2515	187	4	a	a	DET
ejpam-2515	187	5	,	,	PUNCT
ejpam-2515	187	6	a	a	PRON
ejpam-2515	187	7	)	)	PUNCT
ejpam-2515	187	8	∈	∈	PROPN
ejpam-2515	187	9	ρ	ρ	PROPN
ejpam-2515	187	10	.	.	PUNCT
ejpam-2515	188	1	thus	thus	ADV
ejpam-2515	188	2	,	,	PUNCT
ejpam-2515	188	3	there	there	PRON
ejpam-2515	188	4	exist	exist	VERB
ejpam-2515	188	5	v	v	NOUN
ejpam-2515	188	6	=	=	PUNCT
ejpam-2515	188	7	a	a	DET
ejpam-2515	188	8	∈	∈	ADJ
ejpam-2515	188	9	h	h	NOUN
ejpam-2515	188	10	such	such	ADJ
ejpam-2515	188	11	that	that	SCONJ
ejpam-2515	188	12	(	(	PUNCT
ejpam-2515	188	13	x	x	X
ejpam-2515	188	14	,	,	PUNCT
ejpam-2515	188	15	a	a	DET
ejpam-2515	188	16	,	,	PUNCT
ejpam-2515	188	17	z	z	NOUN
ejpam-2515	188	18	)	)	PUNCT
ejpam-2515	188	19	∈	∈	PROPN
ejpam-2515	188	20	ρ	ρ	PROPN
ejpam-2515	188	21	with	with	ADP
ejpam-2515	188	22	(	(	PUNCT
ejpam-2515	188	23	x	x	INTJ
ejpam-2515	188	24	,	,	PUNCT
ejpam-2515	188	25	a	a	DET
ejpam-2515	188	26	,	,	PUNCT
ejpam-2515	188	27	a	a	PRON
ejpam-2515	188	28	)	)	PUNCT
ejpam-2515	188	29	∈	∈	PROPN
ejpam-2515	188	30	ρ	ρ	PROPN
ejpam-2515	188	31	,	,	PUNCT
ejpam-2515	188	32	so	so	ADV
ejpam-2515	188	33	,	,	PUNCT
ejpam-2515	188	34	in	in	ADP
ejpam-2515	188	35	this	this	DET
ejpam-2515	188	36	case	case	NOUN
ejpam-2515	188	37	,	,	PUNCT
ejpam-2515	188	38	a	a	DET
ejpam-2515	188	39	∈	∈	PROPN
ejpam-2515	188	40	x	x	SYM
ejpam-2515	188	41	⊗ρ	⊗ρ	NOUN
ejpam-2515	188	42	(	(	PUNCT
ejpam-2515	188	43	x	x	SYM
ejpam-2515	188	44	⊗ρ	⊗ρ	PROPN
ejpam-2515	188	45	z	z	NOUN
ejpam-2515	188	46	)	)	PUNCT
ejpam-2515	188	47	.	.	PUNCT
ejpam-2515	189	1	(	(	PUNCT
ejpam-2515	189	2	iii	iii	NOUN
ejpam-2515	189	3	)	)	PUNCT
ejpam-2515	189	4	finally	finally	ADV
ejpam-2515	189	5	,	,	PUNCT
ejpam-2515	189	6	we	we	PRON
ejpam-2515	189	7	consider	consider	VERB
ejpam-2515	189	8	the	the	DET
ejpam-2515	189	9	(	(	PUNCT
ejpam-2515	189	10	η	η	NOUN
ejpam-2515	189	11	)	)	PUNCT
ejpam-2515	189	12	with	with	ADP
ejpam-2515	189	13	y	y	PROPN
ejpam-2515	189	14	=	=	PUNCT
ejpam-2515	189	15	z.	z.	PROPN
ejpam-2515	189	16	put	put	VERB
ejpam-2515	189	17	y	y	PROPN
ejpam-2515	190	1	=	=	PUNCT
ejpam-2515	190	2	z	z	NOUN
ejpam-2515	190	3	in	in	ADP
ejpam-2515	190	4	(	(	PUNCT
ejpam-2515	190	5	η	η	NOUN
ejpam-2515	190	6	)	)	PUNCT
ejpam-2515	190	7	.	.	PUNCT
ejpam-2515	191	1	then	then	ADV
ejpam-2515	191	2	,	,	PUNCT
ejpam-2515	191	3	it	it	PRON
ejpam-2515	191	4	follows	follow	VERB
ejpam-2515	191	5	that	that	SCONJ
ejpam-2515	191	6	(	(	PUNCT
ejpam-2515	191	7	x	x	X
ejpam-2515	191	8	,	,	PUNCT
ejpam-2515	191	9	u	u	NOUN
ejpam-2515	191	10	,	,	PUNCT
ejpam-2515	191	11	z	z	NOUN
ejpam-2515	191	12	)	)	PUNCT
ejpam-2515	191	13	∈	∈	PROPN
ejpam-2515	191	14	ρ	ρ	PROPN
ejpam-2515	191	15	and	and	CCONJ
ejpam-2515	191	16	(	(	PUNCT
ejpam-2515	191	17	u	u	NOUN
ejpam-2515	191	18	,	,	PUNCT
ejpam-2515	191	19	a	a	PRON
ejpam-2515	191	20	,	,	PUNCT
ejpam-2515	191	21	z	z	NOUN
ejpam-2515	191	22	)	)	PUNCT
ejpam-2515	191	23	∈	∈	PROPN
ejpam-2515	191	24	ρ	ρ	NOUN
ejpam-2515	191	25	.	.	PUNCT
ejpam-2515	192	1	by	by	ADP
ejpam-2515	192	2	the	the	DET
ejpam-2515	192	3	(	(	PUNCT
ejpam-2515	192	4	τ2	τ2	NOUN
ejpam-2515	192	5	)	)	PUNCT
ejpam-2515	192	6	,	,	PUNCT
ejpam-2515	192	7	we	we	PRON
ejpam-2515	192	8	obtain	obtain	VERB
ejpam-2515	192	9	that	that	PRON
ejpam-2515	192	10	(	(	PUNCT
ejpam-2515	192	11	x	x	X
ejpam-2515	192	12	,	,	PUNCT
ejpam-2515	192	13	u	u	NOUN
ejpam-2515	192	14	,	,	PUNCT
ejpam-2515	192	15	a	a	PRON
ejpam-2515	192	16	)	)	PUNCT
ejpam-2515	192	17	∈	∈	PROPN
ejpam-2515	192	18	ρ	ρ	NOUN
ejpam-2515	192	19	.	.	PUNCT
ejpam-2515	193	1	now	now	ADV
ejpam-2515	193	2	,	,	PUNCT
ejpam-2515	193	3	we	we	PRON
ejpam-2515	193	4	have	have	VERB
ejpam-2515	193	5	(	(	PUNCT
ejpam-2515	193	6	x	x	X
ejpam-2515	193	7	,	,	PUNCT
ejpam-2515	193	8	u	u	NOUN
ejpam-2515	193	9	,	,	PUNCT
ejpam-2515	193	10	a	a	PRON
ejpam-2515	193	11	)	)	PUNCT
ejpam-2515	193	12	∈	∈	PROPN
ejpam-2515	193	13	ρ	ρ	NOUN
ejpam-2515	193	14	and	and	CCONJ
ejpam-2515	193	15	(	(	PUNCT
ejpam-2515	193	16	u	u	NOUN
ejpam-2515	193	17	,	,	PUNCT
ejpam-2515	193	18	a	a	PRON
ejpam-2515	193	19	,	,	PUNCT
ejpam-2515	193	20	z	z	NOUN
ejpam-2515	193	21	)	)	PUNCT
ejpam-2515	193	22	∈	∈	PROPN
ejpam-2515	193	23	ρ	ρ	NOUN
ejpam-2515	193	24	.	.	PUNCT
ejpam-2515	194	1	using	use	VERB
ejpam-2515	194	2	(	(	PUNCT
ejpam-2515	194	3	x	x	INTJ
ejpam-2515	194	4	,	,	PUNCT
ejpam-2515	194	5	u	u	NOUN
ejpam-2515	194	6	,	,	PUNCT
ejpam-2515	194	7	a	a	PRON
ejpam-2515	194	8	)	)	PUNCT
ejpam-2515	194	9	∈	∈	PROPN
ejpam-2515	194	10	ρ	ρ	NOUN
ejpam-2515	194	11	and	and	CCONJ
ejpam-2515	194	12	(	(	PUNCT
ejpam-2515	194	13	u	u	NOUN
ejpam-2515	194	14	,	,	PUNCT
ejpam-2515	194	15	a	a	PRON
ejpam-2515	194	16	,	,	PUNCT
ejpam-2515	194	17	z	z	NOUN
ejpam-2515	194	18	)	)	PUNCT
ejpam-2515	194	19	∈	∈	PROPN
ejpam-2515	194	20	ρ	ρ	X
ejpam-2515	194	21	in	in	ADP
ejpam-2515	194	22	(	(	PUNCT
ejpam-2515	194	23	τ2	τ2	NOUN
ejpam-2515	194	24	)	)	PUNCT
ejpam-2515	194	25	,	,	PUNCT
ejpam-2515	194	26	we	we	PRON
ejpam-2515	194	27	obtain	obtain	VERB
ejpam-2515	194	28	that	that	DET
ejpam-2515	194	29	(	(	PUNCT
ejpam-2515	194	30	x	x	X
ejpam-2515	194	31	,	,	PUNCT
ejpam-2515	194	32	a	a	PRON
ejpam-2515	194	33	,	,	PUNCT
ejpam-2515	194	34	z	z	NOUN
ejpam-2515	194	35	)	)	PUNCT
ejpam-2515	194	36	∈	∈	PROPN
ejpam-2515	194	37	ρ	ρ	NOUN
ejpam-2515	194	38	.	.	PUNCT
ejpam-2515	195	1	now	now	ADV
ejpam-2515	195	2	,	,	PUNCT
ejpam-2515	195	3	(	(	PUNCT
ejpam-2515	195	4	τ1	τ1	NOUN
ejpam-2515	195	5	)	)	PUNCT
ejpam-2515	195	6	yields	yield	NOUN
ejpam-2515	195	7	that	that	DET
ejpam-2515	195	8	(	(	PUNCT
ejpam-2515	195	9	z	z	X
ejpam-2515	195	10	,	,	PUNCT
ejpam-2515	195	11	z	z	PROPN
ejpam-2515	195	12	,	,	PUNCT
ejpam-2515	195	13	z	z	NOUN
ejpam-2515	195	14	)	)	PUNCT
ejpam-2515	195	15	∈	∈	PROPN
ejpam-2515	195	16	ρ	ρ	NOUN
ejpam-2515	195	17	.	.	PUNCT
ejpam-2515	196	1	hence	hence	ADV
ejpam-2515	196	2	,	,	PUNCT
ejpam-2515	196	3	(	(	PUNCT
ejpam-2515	196	4	x	x	X
ejpam-2515	196	5	,	,	PUNCT
ejpam-2515	196	6	a	a	DET
ejpam-2515	196	7	,	,	PUNCT
ejpam-2515	196	8	z	z	NOUN
ejpam-2515	196	9	)	)	PUNCT
ejpam-2515	196	10	∈	∈	PROPN
ejpam-2515	196	11	ρ	ρ	PROPN
ejpam-2515	196	12	with	with	ADP
ejpam-2515	196	13	(	(	PUNCT
ejpam-2515	196	14	z	z	NOUN
ejpam-2515	196	15	,	,	PUNCT
ejpam-2515	196	16	z	z	PROPN
ejpam-2515	196	17	,	,	PUNCT
ejpam-2515	196	18	z	z	NOUN
ejpam-2515	196	19	)	)	PUNCT
ejpam-2515	196	20	∈	∈	PROPN
ejpam-2515	196	21	ρ	ρ	NOUN
ejpam-2515	196	22	and	and	CCONJ
ejpam-2515	196	23	so	so	ADV
ejpam-2515	196	24	a	a	DET
ejpam-2515	196	25	∈	∈	PROPN
ejpam-2515	196	26	x	x	SYM
ejpam-2515	196	27	⊗ρ	⊗ρ	NOUN
ejpam-2515	196	28	(	(	PUNCT
ejpam-2515	196	29	z	z	NOUN
ejpam-2515	196	30	⊗ρ	⊗ρ	PROPN
ejpam-2515	196	31	z	z	PROPN
ejpam-2515	196	32	)	)	PUNCT
ejpam-2515	196	33	.	.	PUNCT
ejpam-2515	197	1	we	we	PRON
ejpam-2515	197	2	have	have	AUX
ejpam-2515	197	3	proved	prove	VERB
ejpam-2515	197	4	that	that	SCONJ
ejpam-2515	197	5	,	,	PUNCT
ejpam-2515	197	6	for	for	ADP
ejpam-2515	197	7	any	any	DET
ejpam-2515	197	8	x	x	SYM
ejpam-2515	197	9	,	,	PUNCT
ejpam-2515	197	10	y	y	PROPN
ejpam-2515	197	11	,	,	PUNCT
ejpam-2515	197	12	z	z	PROPN
ejpam-2515	197	13	,	,	PUNCT
ejpam-2515	197	14	a	a	DET
ejpam-2515	197	15	∈	∈	PROPN
ejpam-2515	197	16	h	h	NOUN
ejpam-2515	197	17	,	,	PUNCT
ejpam-2515	197	18	a	a	DET
ejpam-2515	197	19	∈	∈	NOUN
ejpam-2515	197	20	x	x	SYM
ejpam-2515	197	21	⊗ρ	⊗ρ	NOUN
ejpam-2515	197	22	(	(	PUNCT
ejpam-2515	197	23	y	y	PROPN
ejpam-2515	197	24	⊗ρ	⊗ρ	PROPN
ejpam-2515	197	25	z	z	NOUN
ejpam-2515	197	26	)	)	PUNCT
ejpam-2515	198	1	=	=	VERB
ejpam-2515	198	2	⇒	⇒	VERB
ejpam-2515	198	3	a	a	DET
ejpam-2515	198	4	∈	∈	PROPN
ejpam-2515	198	5	x	x	SYM
ejpam-2515	198	6	⊗ρ	⊗ρ	NOUN
ejpam-2515	198	7	(	(	PUNCT
ejpam-2515	198	8	y	y	PROPN
ejpam-2515	198	9	⊗ρ	⊗ρ	PROPN
ejpam-2515	198	10	z	z	PROPN
ejpam-2515	198	11	)	)	PUNCT
ejpam-2515	198	12	;	;	PUNCT
ejpam-2515	198	13	i.e.	i.e.	X
ejpam-2515	198	14	(	(	PUNCT
ejpam-2515	198	15	x	x	SYM
ejpam-2515	198	16	⊗ρ	⊗ρ	NOUN
ejpam-2515	198	17	y)⊗ρ	y)⊗ρ	ADJ
ejpam-2515	198	18	z	z	PROPN
ejpam-2515	198	19	⊂	⊂	PUNCT
ejpam-2515	199	1	x	x	PUNCT
ejpam-2515	199	2	⊗ρ	⊗ρ	ADV
ejpam-2515	199	3	(	(	PUNCT
ejpam-2515	199	4	y	y	PROPN
ejpam-2515	199	5	⊗ρ	⊗ρ	PROPN
ejpam-2515	199	6	z	z	PROPN
ejpam-2515	199	7	)	)	PUNCT
ejpam-2515	199	8	.	.	PUNCT
ejpam-2515	200	1	similar	similar	ADJ
ejpam-2515	200	2	argument	argument	NOUN
ejpam-2515	200	3	establishes	establish	VERB
ejpam-2515	200	4	the	the	DET
ejpam-2515	200	5	other	other	ADJ
ejpam-2515	200	6	inclusion	inclusion	NOUN
ejpam-2515	200	7	x	x	PUNCT
ejpam-2515	200	8	⊗ρ	⊗ρ	ADV
ejpam-2515	200	9	(	(	PUNCT
ejpam-2515	200	10	y	y	PROPN
ejpam-2515	200	11	⊗ρ	⊗ρ	PROPN
ejpam-2515	200	12	z	z	X
ejpam-2515	200	13	)	)	PUNCT
ejpam-2515	201	1	⊂	⊂	PROPN
ejpam-2515	201	2	(	(	PUNCT
ejpam-2515	201	3	x	x	SYM
ejpam-2515	201	4	⊗ρ	⊗ρ	PROPN
ejpam-2515	202	1	y)⊗ρ	y)⊗ρ	NOUN
ejpam-2515	202	2	z.	z.	PROPN
ejpam-2515	203	1	conversely	conversely	ADV
ejpam-2515	203	2	,	,	PUNCT
ejpam-2515	203	3	we	we	PRON
ejpam-2515	203	4	suppose	suppose	VERB
ejpam-2515	203	5	that	that	SCONJ
ejpam-2515	203	6	hρ	hρ	PROPN
ejpam-2515	203	7	is	be	AUX
ejpam-2515	203	8	a	a	DET
ejpam-2515	203	9	semihypergroup	semihypergroup	NOUN
ejpam-2515	203	10	and	and	CCONJ
ejpam-2515	203	11	(	(	PUNCT
ejpam-2515	203	12	x	x	X
ejpam-2515	203	13	,	,	PUNCT
ejpam-2515	203	14	y	y	PROPN
ejpam-2515	203	15	,	,	PUNCT
ejpam-2515	203	16	z	z	NOUN
ejpam-2515	203	17	)	)	PUNCT
ejpam-2515	203	18	6∈	6∈	PROPN
ejpam-2515	203	19	ρ	ρ	NOUN
ejpam-2515	203	20	with	with	ADP
ejpam-2515	203	21	x	x	PROPN
ejpam-2515	203	22	,	,	PUNCT
ejpam-2515	203	23	y	y	PROPN
ejpam-2515	203	24	,	,	PUNCT
ejpam-2515	203	25	z	z	PROPN
ejpam-2515	203	26	are	be	AUX
ejpam-2515	203	27	all	all	ADV
ejpam-2515	203	28	distinct	distinct	ADJ
ejpam-2515	203	29	.	.	PUNCT
ejpam-2515	204	1	assume	assume	VERB
ejpam-2515	204	2	to	to	ADP
ejpam-2515	204	3	the	the	DET
ejpam-2515	204	4	contrary	contrary	NOUN
ejpam-2515	204	5	that	that	SCONJ
ejpam-2515	204	6	(	(	PUNCT
ejpam-2515	204	7	x	x	X
ejpam-2515	204	8	,	,	PUNCT
ejpam-2515	204	9	x	x	X
ejpam-2515	204	10	,	,	PUNCT
ejpam-2515	204	11	z	z	NOUN
ejpam-2515	204	12	)	)	PUNCT
ejpam-2515	204	13	,	,	PUNCT
ejpam-2515	204	14	(	(	PUNCT
ejpam-2515	204	15	x	x	X
ejpam-2515	204	16	,	,	PUNCT
ejpam-2515	204	17	z	z	PROPN
ejpam-2515	204	18	,	,	PUNCT
ejpam-2515	204	19	z	z	PROPN
ejpam-2515	204	20	)	)	PUNCT
ejpam-2515	204	21	6∈	6∈	PROPN
ejpam-2515	204	22	ρ	ρ	PROPN
ejpam-2515	204	23	,	,	PUNCT
ejpam-2515	204	24	for	for	ADP
ejpam-2515	204	25	some	some	DET
ejpam-2515	204	26	x	x	SYM
ejpam-2515	204	27	,	,	PUNCT
ejpam-2515	204	28	z	z	PROPN
ejpam-2515	204	29	∈	∈	PROPN
ejpam-2515	204	30	h.	h.	NOUN
ejpam-2515	204	31	then	then	ADV
ejpam-2515	204	32	,	,	PUNCT
ejpam-2515	204	33	it	it	PRON
ejpam-2515	204	34	follows	follow	VERB
ejpam-2515	204	35	that	that	SCONJ
ejpam-2515	204	36	z	z	NOUN
ejpam-2515	204	37	6∈x	6∈x	VERB
ejpam-2515	204	38	⊗ρ	⊗ρ	ADV
ejpam-2515	204	39	(	(	PUNCT
ejpam-2515	204	40	y	y	PROPN
ejpam-2515	204	41	⊗ρ	⊗ρ	PROPN
ejpam-2515	204	42	z	z	PROPN
ejpam-2515	204	43	)	)	PUNCT
ejpam-2515	205	1	=	=	PUNCT
ejpam-2515	205	2	x	x	SYM
ejpam-2515	205	3	⊗ρ	⊗ρ	ADJ
ejpam-2515	205	4	{	{	PUNCT
ejpam-2515	205	5	y	y	PROPN
ejpam-2515	205	6	,	,	PUNCT
ejpam-2515	205	7	z}=	z}=	PROPN
ejpam-2515	205	8	{	{	PUNCT
ejpam-2515	205	9	x	x	PROPN
ejpam-2515	205	10	,	,	PUNCT
ejpam-2515	205	11	y	y	PROPN
ejpam-2515	205	12	}	}	PUNCT
ejpam-2515	205	13	∪	∪	X
ejpam-2515	205	14	x	x	SYM
ejpam-2515	205	15	⊗ρ	⊗ρ	PROPN
ejpam-2515	205	16	z	z	PROPN
ejpam-2515	205	17	z	z	NOUN
ejpam-2515	205	18	∈(x	∈(x	VERB
ejpam-2515	205	19	⊗ρ	⊗ρ	ADJ
ejpam-2515	205	20	y)⊗ρ	y)⊗ρ	ADJ
ejpam-2515	205	21	z	z	PROPN
ejpam-2515	206	1	=	=	PRON
ejpam-2515	206	2	{	{	PUNCT
ejpam-2515	206	3	x	x	INTJ
ejpam-2515	206	4	,	,	PUNCT
ejpam-2515	206	5	y	y	PROPN
ejpam-2515	206	6	}	}	PUNCT
ejpam-2515	206	7	⊗ρ	⊗ρ	NOUN
ejpam-2515	206	8	z	z	NOUN
ejpam-2515	206	9	=	=	SYM
ejpam-2515	206	10	{	{	PUNCT
ejpam-2515	206	11	y	y	PROPN
ejpam-2515	206	12	,	,	PUNCT
ejpam-2515	206	13	z	z	NOUN
ejpam-2515	206	14	}	}	PUNCT
ejpam-2515	206	15	∪	∪	X
ejpam-2515	206	16	x	x	SYM
ejpam-2515	206	17	⊗ρ	⊗ρ	PROPN
ejpam-2515	206	18	z	z	NOUN
ejpam-2515	206	19	which	which	PRON
ejpam-2515	206	20	is	be	AUX
ejpam-2515	206	21	a	a	DET
ejpam-2515	206	22	contradiction	contradiction	NOUN
ejpam-2515	206	23	to	to	ADP
ejpam-2515	206	24	that	that	PRON
ejpam-2515	206	25	hρ	hρ	PROPN
ejpam-2515	206	26	is	be	AUX
ejpam-2515	206	27	a	a	DET
ejpam-2515	206	28	semihypergroup	semihypergroup	NOUN
ejpam-2515	206	29	.	.	PUNCT
ejpam-2515	207	1	thus	thus	ADV
ejpam-2515	207	2	(	(	PUNCT
ejpam-2515	207	3	τ1	τ1	NOUN
ejpam-2515	207	4	)	)	PUNCT
ejpam-2515	207	5	holds	hold	VERB
ejpam-2515	207	6	.	.	PUNCT
ejpam-2515	208	1	next	next	ADV
ejpam-2515	208	2	,	,	PUNCT
ejpam-2515	208	3	we	we	PRON
ejpam-2515	208	4	prove	prove	VERB
ejpam-2515	208	5	that	that	SCONJ
ejpam-2515	208	6	(	(	PUNCT
ejpam-2515	208	7	τ2	τ2	NOUN
ejpam-2515	208	8	)	)	PUNCT
ejpam-2515	208	9	holds	hold	VERB
ejpam-2515	208	10	.	.	PUNCT
ejpam-2515	209	1	suppose	suppose	VERB
ejpam-2515	209	2	to	to	ADP
ejpam-2515	209	3	the	the	DET
ejpam-2515	209	4	contrary	contrary	NOUN
ejpam-2515	209	5	that	that	SCONJ
ejpam-2515	209	6	(	(	PUNCT
ejpam-2515	209	7	τ2	τ2	NOUN
ejpam-2515	209	8	)	)	PUNCT
ejpam-2515	209	9	does	do	AUX
ejpam-2515	209	10	not	not	PART
ejpam-2515	209	11	holds	hold	VERB
ejpam-2515	209	12	.	.	PUNCT
ejpam-2515	210	1	let	let	VERB
ejpam-2515	210	2	(	(	PUNCT
ejpam-2515	210	3	x	x	X
ejpam-2515	210	4	,	,	PUNCT
ejpam-2515	210	5	u	u	NOUN
ejpam-2515	210	6	,	,	PUNCT
ejpam-2515	210	7	y	y	PROPN
ejpam-2515	210	8	)	)	PUNCT
ejpam-2515	210	9	,	,	PUNCT
ejpam-2515	210	10	(	(	PUNCT
ejpam-2515	210	11	u	u	NOUN
ejpam-2515	210	12	,	,	PUNCT
ejpam-2515	210	13	y	y	PROPN
ejpam-2515	210	14	,	,	PUNCT
ejpam-2515	210	15	z	z	NOUN
ejpam-2515	210	16	)	)	PUNCT
ejpam-2515	210	17	∈	∈	PROPN
ejpam-2515	210	18	ρ	ρ	PROPN
ejpam-2515	210	19	with	with	ADP
ejpam-2515	210	20	x	x	PROPN
ejpam-2515	210	21	,	,	PUNCT
ejpam-2515	210	22	u	u	PROPN
ejpam-2515	210	23	,	,	PUNCT
ejpam-2515	210	24	y	y	PROPN
ejpam-2515	210	25	,	,	PUNCT
ejpam-2515	210	26	z	z	PROPN
ejpam-2515	210	27	are	be	AUX
ejpam-2515	210	28	all	all	ADV
ejpam-2515	210	29	distinct	distinct	ADJ
ejpam-2515	210	30	.	.	PUNCT
ejpam-2515	211	1	suppose	suppose	VERB
ejpam-2515	211	2	that	that	SCONJ
ejpam-2515	211	3	(	(	PUNCT
ejpam-2515	211	4	x	x	X
ejpam-2515	211	5	,	,	PUNCT
ejpam-2515	211	6	y	y	PROPN
ejpam-2515	211	7	,	,	PUNCT
ejpam-2515	211	8	z	z	PROPN
ejpam-2515	211	9	)	)	PUNCT
ejpam-2515	211	10	6∈	6∈	PROPN
ejpam-2515	211	11	ρ	ρ	NOUN
ejpam-2515	211	12	.	.	PUNCT
ejpam-2515	212	1	we	we	PRON
ejpam-2515	212	2	have	have	VERB
ejpam-2515	212	3	from	from	ADP
ejpam-2515	212	4	(	(	PUNCT
ejpam-2515	212	5	τ1	τ1	NOUN
ejpam-2515	212	6	)	)	PUNCT
ejpam-2515	212	7	that	that	SCONJ
ejpam-2515	212	8	(	(	PUNCT
ejpam-2515	212	9	z	z	X
ejpam-2515	212	10	,	,	PUNCT
ejpam-2515	212	11	z	z	PROPN
ejpam-2515	212	12	,	,	PUNCT
ejpam-2515	212	13	z	z	NOUN
ejpam-2515	212	14	)	)	PUNCT
ejpam-2515	212	15	∈	∈	PROPN
ejpam-2515	212	16	ρ	ρ	NOUN
ejpam-2515	212	17	as	as	ADP
ejpam-2515	212	18	(	(	PUNCT
ejpam-2515	212	19	z	z	NOUN
ejpam-2515	212	20	,	,	PUNCT
ejpam-2515	212	21	z	z	NOUN
ejpam-2515	212	22	)	)	PUNCT
ejpam-2515	212	23	∈	∈	PROPN
ejpam-2515	212	24	h2	h2	NOUN
ejpam-2515	212	25	.	.	PUNCT
ejpam-2515	213	1	it	it	PRON
ejpam-2515	213	2	follows	follow	VERB
ejpam-2515	213	3	that	that	SCONJ
ejpam-2515	213	4	y	y	PROPN
ejpam-2515	213	5	6∈	6∈	PROPN
ejpam-2515	213	6	x	x	SYM
ejpam-2515	213	7	⊗ρ	⊗ρ	PROPN
ejpam-2515	213	8	z	z	PROPN
ejpam-2515	213	9	⊂	⊂	PUNCT
ejpam-2515	214	1	x	x	PUNCT
ejpam-2515	214	2	⊗ρ	⊗ρ	ADV
ejpam-2515	214	3	(	(	PUNCT
ejpam-2515	214	4	z	z	NOUN
ejpam-2515	214	5	⊗ρ	⊗ρ	PROPN
ejpam-2515	214	6	z	z	PROPN
ejpam-2515	214	7	)	)	PUNCT
ejpam-2515	214	8	but	but	CCONJ
ejpam-2515	214	9	y	y	PROPN
ejpam-2515	214	10	∈	∈	PROPN
ejpam-2515	214	11	u⊗ρ	u⊗ρ	PROPN
ejpam-2515	215	1	z	z	PROPN
ejpam-2515	216	1	⊂	⊂	PROPN
ejpam-2515	217	1	(	(	PUNCT
ejpam-2515	217	2	x	x	SYM
ejpam-2515	217	3	⊗ρ	⊗ρ	PROPN
ejpam-2515	217	4	y)⊗ρ	y)⊗ρ	NOUN
ejpam-2515	217	5	z	z	NOUN
ejpam-2515	217	6	which	which	PRON
ejpam-2515	217	7	is	be	AUX
ejpam-2515	217	8	a	a	DET
ejpam-2515	217	9	contradiction	contradiction	NOUN
ejpam-2515	217	10	to	to	ADP
ejpam-2515	217	11	that	that	PRON
ejpam-2515	217	12	hρ	hρ	PROPN
ejpam-2515	217	13	is	be	AUX
ejpam-2515	217	14	a	a	DET
ejpam-2515	217	15	semihypergroup	semihypergroup	NOUN
ejpam-2515	217	16	.	.	PUNCT
ejpam-2515	218	1	thus	thus	ADV
ejpam-2515	218	2	(	(	PUNCT
ejpam-2515	218	3	τ2	τ2	NOUN
ejpam-2515	218	4	)	)	PUNCT
ejpam-2515	218	5	holds	hold	VERB
ejpam-2515	218	6	.	.	PUNCT
ejpam-2515	219	1	remark	remark	PROPN
ejpam-2515	219	2	1	1	NUM
ejpam-2515	219	3	.	.	PUNCT
ejpam-2515	220	1	if	if	SCONJ
ejpam-2515	220	2	hρ	hρ	PROPN
ejpam-2515	220	3	is	be	AUX
ejpam-2515	220	4	a	a	DET
ejpam-2515	220	5	hypergroup	hypergroup	NOUN
ejpam-2515	220	6	and	and	CCONJ
ejpam-2515	220	7	(	(	PUNCT
ejpam-2515	220	8	τ1	τ1	NOUN
ejpam-2515	220	9	)	)	PUNCT
ejpam-2515	220	10	alone	alone	ADV
ejpam-2515	220	11	holds	hold	VERB
ejpam-2515	220	12	,	,	PUNCT
ejpam-2515	220	13	then	then	ADV
ejpam-2515	220	14	ρ	ρ	PROPN
ejpam-2515	220	15	is	be	AUX
ejpam-2515	220	16	symmetric	symmetric	ADJ
ejpam-2515	220	17	ternary	ternary	ADJ
ejpam-2515	220	18	relation	relation	NOUN
ejpam-2515	220	19	on	on	ADP
ejpam-2515	220	20	h.	h.	PROPN
ejpam-2515	220	21	s.	s.	PROPN
ejpam-2515	220	22	govindarajan	govindarajan	PROPN
ejpam-2515	220	23	/	/	SYM
ejpam-2515	220	24	eur	eur	PROPN
ejpam-2515	220	25	.	.	PUNCT
ejpam-2515	221	1	j.	j.	PROPN
ejpam-2515	221	2	pure	pure	PROPN
ejpam-2515	221	3	appl	appl	PROPN
ejpam-2515	221	4	.	.	PROPN
ejpam-2515	221	5	math	math	PROPN
ejpam-2515	221	6	,	,	PUNCT
ejpam-2515	221	7	9	9	NUM
ejpam-2515	221	8	(	(	PUNCT
ejpam-2515	221	9	2016	2016	NUM
ejpam-2515	221	10	)	)	PUNCT
ejpam-2515	221	11	,	,	PUNCT
ejpam-2515	221	12	367	367	NUM
ejpam-2515	221	13	-	-	SYM
ejpam-2515	221	14	382	382	NUM
ejpam-2515	221	15	373	373	NUM
ejpam-2515	221	16	proof	proof	NOUN
ejpam-2515	221	17	.	.	PUNCT
ejpam-2515	222	1	it	it	PRON
ejpam-2515	222	2	follows	follow	VERB
ejpam-2515	222	3	by	by	ADP
ejpam-2515	222	4	(	(	PUNCT
ejpam-2515	222	5	τ1	τ1	NOUN
ejpam-2515	222	6	)	)	PUNCT
ejpam-2515	222	7	of	of	ADP
ejpam-2515	222	8	proposition	proposition	NOUN
ejpam-2515	222	9	5	5	NUM
ejpam-2515	222	10	.	.	PUNCT
ejpam-2515	222	11	remark	remark	NOUN
ejpam-2515	222	12	2	2	NUM
ejpam-2515	222	13	.	.	PUNCT
ejpam-2515	223	1	if	if	SCONJ
ejpam-2515	223	2	hρ	hρ	PROPN
ejpam-2515	223	3	is	be	AUX
ejpam-2515	223	4	a	a	DET
ejpam-2515	223	5	hypergroup	hypergroup	NOUN
ejpam-2515	223	6	,	,	PUNCT
ejpam-2515	223	7	then	then	ADV
ejpam-2515	223	8	ρ	ρ	PROPN
ejpam-2515	223	9	is	be	AUX
ejpam-2515	223	10	reflexive	reflexive	ADJ
ejpam-2515	223	11	relation	relation	NOUN
ejpam-2515	223	12	on	on	ADP
ejpam-2515	223	13	h.	h.	PROPN
ejpam-2515	223	14	proof	proof	PROPN
ejpam-2515	223	15	.	.	PUNCT
ejpam-2515	224	1	according	accord	VERB
ejpam-2515	224	2	to	to	ADP
ejpam-2515	224	3	proposition	proposition	NOUN
ejpam-2515	224	4	5	5	NUM
ejpam-2515	224	5	,	,	PUNCT
ejpam-2515	224	6	we	we	PRON
ejpam-2515	224	7	have	have	VERB
ejpam-2515	224	8	∀(x	∀(x	NUM
ejpam-2515	224	9	,	,	PUNCT
ejpam-2515	224	10	y	y	NOUN
ejpam-2515	224	11	)	)	PUNCT
ejpam-2515	224	12	∈	∈	PROPN
ejpam-2515	224	13	h2	h2	NOUN
ejpam-2515	224	14	,	,	PUNCT
ejpam-2515	224	15	(	(	PUNCT
ejpam-2515	224	16	x	x	X
ejpam-2515	224	17	,	,	PUNCT
ejpam-2515	224	18	x	x	SYM
ejpam-2515	224	19	,	,	PUNCT
ejpam-2515	224	20	y	y	PROPN
ejpam-2515	224	21	)	)	PUNCT
ejpam-2515	224	22	∈	∈	PROPN
ejpam-2515	224	23	ρ	ρ	PROPN
ejpam-2515	224	24	,	,	PUNCT
ejpam-2515	224	25	so	so	ADV
ejpam-2515	224	26	,	,	PUNCT
ejpam-2515	224	27	for	for	ADP
ejpam-2515	224	28	(	(	PUNCT
ejpam-2515	224	29	x	x	INTJ
ejpam-2515	224	30	,	,	PUNCT
ejpam-2515	224	31	x	x	X
ejpam-2515	224	32	)	)	PUNCT
ejpam-2515	224	33	∈	∈	PROPN
ejpam-2515	224	34	h2	h2	NOUN
ejpam-2515	224	35	,	,	PUNCT
ejpam-2515	224	36	(	(	PUNCT
ejpam-2515	224	37	x	x	X
ejpam-2515	224	38	,	,	PUNCT
ejpam-2515	224	39	x	x	X
ejpam-2515	224	40	,	,	PUNCT
ejpam-2515	224	41	x	x	X
ejpam-2515	224	42	)	)	PUNCT
ejpam-2515	224	43	∈	∈	PROPN
ejpam-2515	224	44	ρ	ρ	PROPN
ejpam-2515	224	45	,	,	PUNCT
ejpam-2515	224	46	whence	whence	PROPN
ejpam-2515	224	47	ρ	ρ	PROPN
ejpam-2515	224	48	is	be	AUX
ejpam-2515	224	49	reflexive	reflexive	ADJ
ejpam-2515	224	50	.	.	PUNCT
ejpam-2515	225	1	remark	remark	NOUN
ejpam-2515	225	2	3	3	NUM
ejpam-2515	225	3	.	.	PUNCT
ejpam-2515	226	1	(	(	PUNCT
ejpam-2515	226	2	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	226	3	)	)	PUNCT
ejpam-2515	226	4	is	be	AUX
ejpam-2515	226	5	a	a	DET
ejpam-2515	226	6	quasihypergroup	quasihypergroup	NOUN
ejpam-2515	226	7	does	do	AUX
ejpam-2515	226	8	not	not	PART
ejpam-2515	226	9	imply	imply	VERB
ejpam-2515	226	10	the	the	DET
ejpam-2515	226	11	condition	condition	NOUN
ejpam-2515	226	12	(	(	PUNCT
ejpam-2515	226	13	τ1	τ1	NOUN
ejpam-2515	226	14	)	)	PUNCT
ejpam-2515	226	15	of	of	ADP
ejpam-2515	226	16	proposition	proposition	NOUN
ejpam-2515	226	17	5	5	NUM
ejpam-2515	226	18	,	,	PUNCT
ejpam-2515	226	19	as	as	SCONJ
ejpam-2515	226	20	we	we	PRON
ejpam-2515	226	21	can	can	AUX
ejpam-2515	226	22	see	see	VERB
ejpam-2515	226	23	in	in	ADP
ejpam-2515	226	24	the	the	DET
ejpam-2515	226	25	following	follow	VERB
ejpam-2515	226	26	example	example	NOUN
ejpam-2515	226	27	.	.	PUNCT
ejpam-2515	227	1	example	example	NOUN
ejpam-2515	228	1	2	2	NUM
ejpam-2515	228	2	.	.	PUNCT
ejpam-2515	228	3	let	let	VERB
ejpam-2515	228	4	h	h	NOUN
ejpam-2515	228	5	=	=	PRON
ejpam-2515	228	6	{	{	PUNCT
ejpam-2515	228	7	x	x	X
ejpam-2515	228	8	,	,	PUNCT
ejpam-2515	228	9	y	y	PROPN
ejpam-2515	228	10	,	,	PUNCT
ejpam-2515	228	11	z	z	NOUN
ejpam-2515	228	12	}	}	PUNCT
ejpam-2515	228	13	and	and	CCONJ
ejpam-2515	228	14	ρ	ρ	PROPN
ejpam-2515	228	15	=	=	SYM
ejpam-2515	228	16	{	{	PUNCT
ejpam-2515	228	17	(	(	PUNCT
ejpam-2515	228	18	x	x	INTJ
ejpam-2515	228	19	,	,	PUNCT
ejpam-2515	228	20	x	x	X
ejpam-2515	228	21	,	,	PUNCT
ejpam-2515	228	22	x	x	NOUN
ejpam-2515	228	23	)	)	PUNCT
ejpam-2515	228	24	,	,	PUNCT
ejpam-2515	228	25	(	(	PUNCT
ejpam-2515	228	26	y	y	PROPN
ejpam-2515	228	27	,	,	PUNCT
ejpam-2515	228	28	y	y	PROPN
ejpam-2515	228	29	,	,	PUNCT
ejpam-2515	228	30	y	y	PROPN
ejpam-2515	228	31	)	)	PUNCT
ejpam-2515	228	32	,	,	PUNCT
ejpam-2515	228	33	(	(	PUNCT
ejpam-2515	228	34	z	z	X
ejpam-2515	228	35	,	,	PUNCT
ejpam-2515	228	36	z	z	PROPN
ejpam-2515	228	37	,	,	PUNCT
ejpam-2515	228	38	z	z	NOUN
ejpam-2515	228	39	)	)	PUNCT
ejpam-2515	228	40	,	,	PUNCT
ejpam-2515	228	41	(	(	PUNCT
ejpam-2515	228	42	x	x	X
ejpam-2515	228	43	,	,	PUNCT
ejpam-2515	228	44	y	y	PROPN
ejpam-2515	228	45	,	,	PUNCT
ejpam-2515	228	46	z	z	NOUN
ejpam-2515	228	47	)	)	PUNCT
ejpam-2515	228	48	,	,	PUNCT
ejpam-2515	228	49	(	(	PUNCT
ejpam-2515	228	50	z	z	X
ejpam-2515	228	51	,	,	PUNCT
ejpam-2515	228	52	y	y	PROPN
ejpam-2515	228	53	,	,	PUNCT
ejpam-2515	228	54	x	x	NOUN
ejpam-2515	228	55	)	)	PUNCT
ejpam-2515	228	56	,	,	PUNCT
ejpam-2515	228	57	(	(	PUNCT
ejpam-2515	228	58	x	x	X
ejpam-2515	228	59	,	,	PUNCT
ejpam-2515	228	60	x	x	SYM
ejpam-2515	228	61	,	,	PUNCT
ejpam-2515	228	62	y	y	PROPN
ejpam-2515	228	63	)	)	PUNCT
ejpam-2515	228	64	,	,	PUNCT
ejpam-2515	228	65	(	(	PUNCT
ejpam-2515	228	66	y	y	NOUN
ejpam-2515	228	67	,	,	PUNCT
ejpam-2515	228	68	x	x	X
ejpam-2515	228	69	,	,	PUNCT
ejpam-2515	228	70	x	x	NOUN
ejpam-2515	228	71	)	)	PUNCT
ejpam-2515	228	72	,	,	PUNCT
ejpam-2515	228	73	(	(	PUNCT
ejpam-2515	228	74	x	x	X
ejpam-2515	228	75	,	,	PUNCT
ejpam-2515	228	76	x	x	X
ejpam-2515	228	77	,	,	PUNCT
ejpam-2515	228	78	z	z	NOUN
ejpam-2515	228	79	)	)	PUNCT
ejpam-2515	228	80	,	,	PUNCT
ejpam-2515	228	81	(	(	PUNCT
ejpam-2515	228	82	x	x	X
ejpam-2515	228	83	,	,	PUNCT
ejpam-2515	228	84	z	z	PROPN
ejpam-2515	228	85	,	,	PUNCT
ejpam-2515	228	86	z	z	NOUN
ejpam-2515	228	87	)	)	PUNCT
ejpam-2515	228	88	,	,	PUNCT
ejpam-2515	228	89	(	(	PUNCT
ejpam-2515	228	90	y	y	NOUN
ejpam-2515	228	91	,	,	PUNCT
ejpam-2515	228	92	z	z	PROPN
ejpam-2515	228	93	,	,	PUNCT
ejpam-2515	228	94	z	z	NOUN
ejpam-2515	228	95	)	)	PUNCT
ejpam-2515	228	96	,	,	PUNCT
ejpam-2515	228	97	(	(	PUNCT
ejpam-2515	228	98	z	z	X
ejpam-2515	228	99	,	,	PUNCT
ejpam-2515	228	100	x	x	X
ejpam-2515	228	101	,	,	PUNCT
ejpam-2515	228	102	x	x	NOUN
ejpam-2515	228	103	)	)	PUNCT
ejpam-2515	228	104	,	,	PUNCT
ejpam-2515	228	105	(	(	PUNCT
ejpam-2515	228	106	z	z	X
ejpam-2515	228	107	,	,	PUNCT
ejpam-2515	228	108	z	z	PROPN
ejpam-2515	228	109	,	,	PUNCT
ejpam-2515	228	110	x	x	NOUN
ejpam-2515	228	111	)	)	PUNCT
ejpam-2515	228	112	,	,	PUNCT
ejpam-2515	228	113	(	(	PUNCT
ejpam-2515	228	114	z	z	X
ejpam-2515	228	115	,	,	PUNCT
ejpam-2515	228	116	z	z	PROPN
ejpam-2515	228	117	,	,	PUNCT
ejpam-2515	228	118	y	y	PROPN
ejpam-2515	228	119	)	)	PUNCT
ejpam-2515	228	120	}	}	PUNCT
ejpam-2515	228	121	.	.	PUNCT
ejpam-2515	229	1	we	we	PRON
ejpam-2515	229	2	have	have	VERB
ejpam-2515	229	3	clearly	clearly	ADV
ejpam-2515	229	4	,	,	PUNCT
ejpam-2515	229	5	∀x	∀x	VERB
ejpam-2515	229	6	∈	∈	PROPN
ejpam-2515	229	7	h	h	NOUN
ejpam-2515	229	8	,	,	PUNCT
ejpam-2515	229	9	x	x	X
ejpam-2515	229	10	⊗ρ	⊗ρ	ADV
ejpam-2515	229	11	x	x	PUNCT
ejpam-2515	229	12	=	=	PRON
ejpam-2515	229	13	{	{	PUNCT
ejpam-2515	229	14	x	x	NOUN
ejpam-2515	229	15	}	}	PUNCT
ejpam-2515	229	16	,	,	PUNCT
ejpam-2515	229	17	x	x	PUNCT
ejpam-2515	229	18	⊗ρ	⊗ρ	NOUN
ejpam-2515	229	19	y	y	PROPN
ejpam-2515	229	20	=	=	PUNCT
ejpam-2515	229	21	{	{	PUNCT
ejpam-2515	229	22	x}=	x}=	PROPN
ejpam-2515	229	23	y	y	PROPN
ejpam-2515	229	24	⊗ρ	⊗ρ	PROPN
ejpam-2515	229	25	x	x	SYM
ejpam-2515	229	26	,	,	PUNCT
ejpam-2515	229	27	x	x	PUNCT
ejpam-2515	229	28	⊗ρ	⊗ρ	NOUN
ejpam-2515	229	29	z	z	NOUN
ejpam-2515	229	30	=	=	SYM
ejpam-2515	229	31	{	{	PUNCT
ejpam-2515	229	32	x	x	X
ejpam-2515	229	33	,	,	PUNCT
ejpam-2515	229	34	y	y	PROPN
ejpam-2515	229	35	,	,	PUNCT
ejpam-2515	229	36	z}=	z}=	PROPN
ejpam-2515	229	37	z	z	NOUN
ejpam-2515	229	38	⊗ρ	⊗ρ	NOUN
ejpam-2515	229	39	x	x	SYM
ejpam-2515	229	40	,	,	PUNCT
ejpam-2515	229	41	y	y	PROPN
ejpam-2515	229	42	⊗ρ	⊗ρ	PROPN
ejpam-2515	229	43	z	z	PROPN
ejpam-2515	229	44	=	=	PRON
ejpam-2515	229	45	{	{	PUNCT
ejpam-2515	230	1	z}=	z}=	PROPN
ejpam-2515	230	2	z	z	NOUN
ejpam-2515	230	3	⊗ρ	⊗ρ	PROPN
ejpam-2515	231	1	y.	y.	PROPN
ejpam-2515	232	1	so	so	ADV
ejpam-2515	232	2	,	,	PUNCT
ejpam-2515	232	3	we	we	PRON
ejpam-2515	232	4	obtain	obtain	VERB
ejpam-2515	232	5	the	the	DET
ejpam-2515	232	6	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	232	7	:	:	PUNCT
ejpam-2515	232	8	table	table	NOUN
ejpam-2515	232	9	1	1	NUM
ejpam-2515	232	10	:	:	PUNCT
ejpam-2515	232	11	example	example	NOUN
ejpam-2515	232	12	2	2	NUM
ejpam-2515	232	13	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	232	14	⊗ρ	⊗ρ	PROPN
ejpam-2515	232	15	x	x	PUNCT
ejpam-2515	232	16	y	y	PROPN
ejpam-2515	232	17	z	z	NOUN
ejpam-2515	232	18	x	x	PUNCT
ejpam-2515	232	19	x	x	PUNCT
ejpam-2515	232	20	x	x	SYM
ejpam-2515	232	21	x	x	NOUN
ejpam-2515	232	22	,	,	PUNCT
ejpam-2515	232	23	y	y	PROPN
ejpam-2515	232	24	,	,	PUNCT
ejpam-2515	232	25	z	z	NOUN
ejpam-2515	232	26	y	y	PROPN
ejpam-2515	232	27	x	x	SYM
ejpam-2515	232	28	y	y	PROPN
ejpam-2515	232	29	z	z	PROPN
ejpam-2515	232	30	z	z	NOUN
ejpam-2515	232	31	x	x	PROPN
ejpam-2515	232	32	,	,	PUNCT
ejpam-2515	232	33	y	y	PROPN
ejpam-2515	232	34	,	,	PUNCT
ejpam-2515	232	35	z	z	PROPN
ejpam-2515	232	36	z	z	NOUN
ejpam-2515	232	37	z	z	NOUN
ejpam-2515	233	1	we	we	PRON
ejpam-2515	233	2	have	have	VERB
ejpam-2515	233	3	∀x	∀x	X
ejpam-2515	233	4	∈	∈	PROPN
ejpam-2515	233	5	h	h	NOUN
ejpam-2515	233	6	,	,	PUNCT
ejpam-2515	233	7	x	x	PUNCT
ejpam-2515	233	8	⊗ρ	⊗ρ	ADJ
ejpam-2515	233	9	h	h	NOUN
ejpam-2515	234	1	=	=	NOUN
ejpam-2515	234	2	h	h	NOUN
ejpam-2515	235	1	=	=	NOUN
ejpam-2515	235	2	h	h	NOUN
ejpam-2515	235	3	⊗ρ	⊗ρ	PROPN
ejpam-2515	235	4	x.	x.	PUNCT
ejpam-2515	236	1	so	so	ADV
ejpam-2515	236	2	,	,	PUNCT
ejpam-2515	236	3	(	(	PUNCT
ejpam-2515	236	4	h;⊗ρ	h;⊗ρ	NOUN
ejpam-2515	236	5	)	)	PUNCT
ejpam-2515	236	6	is	be	AUX
ejpam-2515	236	7	a	a	DET
ejpam-2515	236	8	quasi	quasi	NOUN
ejpam-2515	236	9	hypergroup	hypergroup	NOUN
ejpam-2515	236	10	,	,	PUNCT
ejpam-2515	236	11	but	but	CCONJ
ejpam-2515	236	12	we	we	PRON
ejpam-2515	236	13	find	find	VERB
ejpam-2515	236	14	also	also	ADV
ejpam-2515	236	15	(	(	PUNCT
ejpam-2515	236	16	x	x	X
ejpam-2515	236	17	,	,	PUNCT
ejpam-2515	236	18	y	y	PROPN
ejpam-2515	236	19	,	,	PUNCT
ejpam-2515	236	20	y	y	PROPN
ejpam-2515	236	21	)	)	PUNCT
ejpam-2515	236	22	,	,	PUNCT
ejpam-2515	236	23	(	(	PUNCT
ejpam-2515	236	24	y	y	PROPN
ejpam-2515	236	25	,	,	PUNCT
ejpam-2515	236	26	y	y	PROPN
ejpam-2515	236	27	,	,	PUNCT
ejpam-2515	236	28	x	x	NOUN
ejpam-2515	236	29	)	)	PUNCT
ejpam-2515	236	30	6∈	6∈	PROPN
ejpam-2515	236	31	ρ	ρ	PROPN
ejpam-2515	236	32	.	.	PUNCT
ejpam-2515	236	33	notice	notice	VERB
ejpam-2515	236	34	that	that	SCONJ
ejpam-2515	236	35	(	(	PUNCT
ejpam-2515	236	36	x	x	X
ejpam-2515	236	37	,	,	PUNCT
ejpam-2515	236	38	y	y	PROPN
ejpam-2515	236	39	,	,	PUNCT
ejpam-2515	236	40	z	z	NOUN
ejpam-2515	236	41	)	)	PUNCT
ejpam-2515	236	42	∈	∈	PROPN
ejpam-2515	236	43	ρ	ρ	NOUN
ejpam-2515	236	44	and	and	CCONJ
ejpam-2515	236	45	x	x	SYM
ejpam-2515	236	46	6=	6=	PROPN
ejpam-2515	236	47	y	y	PROPN
ejpam-2515	236	48	6=	6=	PROPN
ejpam-2515	236	49	z.	z.	PROPN
ejpam-2515	236	50	moreover	moreover	ADV
ejpam-2515	236	51	,	,	PUNCT
ejpam-2515	236	52	(	(	PUNCT
ejpam-2515	236	53	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	236	54	)	)	PUNCT
ejpam-2515	236	55	is	be	AUX
ejpam-2515	236	56	a	a	DET
ejpam-2515	236	57	hypergroup	hypergroup	NOUN
ejpam-2515	236	58	.	.	PUNCT
ejpam-2515	237	1	remark	remark	PROPN
ejpam-2515	237	2	4	4	NUM
ejpam-2515	237	3	.	.	PUNCT
ejpam-2515	238	1	if	if	SCONJ
ejpam-2515	238	2	(	(	PUNCT
ejpam-2515	238	3	x	x	X
ejpam-2515	238	4	,	,	PUNCT
ejpam-2515	238	5	y	y	PROPN
ejpam-2515	238	6	,	,	PUNCT
ejpam-2515	238	7	z	z	NOUN
ejpam-2515	238	8	)	)	PUNCT
ejpam-2515	238	9	6∈	6∈	PROPN
ejpam-2515	238	10	ρ	ρ	NOUN
ejpam-2515	238	11	with	with	ADP
ejpam-2515	238	12	x	x	PROPN
ejpam-2515	238	13	,	,	PUNCT
ejpam-2515	238	14	y	y	PROPN
ejpam-2515	238	15	,	,	PUNCT
ejpam-2515	238	16	z	z	PROPN
ejpam-2515	238	17	are	be	AUX
ejpam-2515	238	18	all	all	ADV
ejpam-2515	238	19	distinct	distinct	ADJ
ejpam-2515	238	20	,	,	PUNCT
ejpam-2515	238	21	then	then	ADV
ejpam-2515	238	22	the	the	DET
ejpam-2515	238	23	condition	condition	NOUN
ejpam-2515	238	24	(	(	PUNCT
ejpam-2515	238	25	τ2	τ2	NOUN
ejpam-2515	238	26	)	)	PUNCT
ejpam-2515	238	27	is	be	AUX
ejpam-2515	238	28	neither	neither	CCONJ
ejpam-2515	238	29	necessary	necessary	ADJ
ejpam-2515	238	30	nor	nor	CCONJ
ejpam-2515	238	31	sufficient	sufficient	ADJ
ejpam-2515	238	32	for	for	ADP
ejpam-2515	238	33	(	(	PUNCT
ejpam-2515	238	34	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	238	35	)	)	PUNCT
ejpam-2515	238	36	to	to	PART
ejpam-2515	238	37	be	be	AUX
ejpam-2515	238	38	a	a	DET
ejpam-2515	238	39	hypergroup	hypergroup	NOUN
ejpam-2515	238	40	as	as	SCONJ
ejpam-2515	238	41	we	we	PRON
ejpam-2515	238	42	see	see	VERB
ejpam-2515	238	43	in	in	ADP
ejpam-2515	238	44	the	the	DET
ejpam-2515	238	45	following	follow	VERB
ejpam-2515	238	46	example	example	NOUN
ejpam-2515	238	47	.	.	PUNCT
ejpam-2515	239	1	example	example	NOUN
ejpam-2515	240	1	3	3	X
ejpam-2515	240	2	.	.	PUNCT
ejpam-2515	240	3	let	let	VERB
ejpam-2515	240	4	us	we	PRON
ejpam-2515	240	5	consider	consider	VERB
ejpam-2515	240	6	the	the	DET
ejpam-2515	240	7	ternary	ternary	ADJ
ejpam-2515	240	8	relation	relation	NOUN
ejpam-2515	240	9	ρ	ρ	NOUN
ejpam-2515	240	10	on	on	ADP
ejpam-2515	240	11	a	a	DET
ejpam-2515	240	12	non	non	X
ejpam-2515	240	13	empty	empty	ADJ
ejpam-2515	240	14	set	set	ADJ
ejpam-2515	240	15	h	h	NOUN
ejpam-2515	240	16	defined	define	VERB
ejpam-2515	240	17	as	as	SCONJ
ejpam-2515	240	18	follows	follow	VERB
ejpam-2515	240	19	:	:	PUNCT
ejpam-2515	240	20	ρ	ρ	PROPN
ejpam-2515	240	21	=	=	SYM
ejpam-2515	240	22	{	{	PUNCT
ejpam-2515	240	23	(	(	PUNCT
ejpam-2515	240	24	x	x	INTJ
ejpam-2515	240	25	,	,	PUNCT
ejpam-2515	240	26	x	x	SYM
ejpam-2515	240	27	,	,	PUNCT
ejpam-2515	240	28	y	y	PROPN
ejpam-2515	240	29	)	)	PUNCT
ejpam-2515	240	30	,	,	PUNCT
ejpam-2515	240	31	(	(	PUNCT
ejpam-2515	240	32	x	x	X
ejpam-2515	240	33	,	,	PUNCT
ejpam-2515	240	34	y	y	PROPN
ejpam-2515	240	35	,	,	PUNCT
ejpam-2515	240	36	y	y	PROPN
ejpam-2515	240	37	)	)	PUNCT
ejpam-2515	241	1	|	|	ADV
ejpam-2515	241	2	(	(	PUNCT
ejpam-2515	241	3	x	x	X
ejpam-2515	241	4	,	,	PUNCT
ejpam-2515	241	5	y	y	PROPN
ejpam-2515	241	6	)	)	PUNCT
ejpam-2515	241	7	∈	∈	PROPN
ejpam-2515	241	8	h2	h2	NOUN
ejpam-2515	241	9	}	}	PUNCT
ejpam-2515	241	10	.	.	PUNCT
ejpam-2515	242	1	we	we	PRON
ejpam-2515	242	2	find	find	VERB
ejpam-2515	242	3	ρ1,3	ρ1,3	PROPN
ejpam-2515	242	4	=	=	SYM
ejpam-2515	242	5	ρ1,2	ρ1,2	PROPN
ejpam-2515	243	1	=	=	SYM
ejpam-2515	243	2	ρ2,3	ρ2,3	PUNCT
ejpam-2515	243	3	=	=	NOUN
ejpam-2515	243	4	h	h	NOUN
ejpam-2515	243	5	×h	×h	PROPN
ejpam-2515	243	6	and	and	CCONJ
ejpam-2515	243	7	∀(x	∀(x	PRON
ejpam-2515	243	8	,	,	PUNCT
ejpam-2515	243	9	y	y	NOUN
ejpam-2515	243	10	)	)	PUNCT
ejpam-2515	243	11	∈	∈	PROPN
ejpam-2515	243	12	h2	h2	NOUN
ejpam-2515	243	13	,	,	PUNCT
ejpam-2515	243	14	x	x	PUNCT
ejpam-2515	243	15	⊗ρ	⊗ρ	NOUN
ejpam-2515	243	16	y	y	PROPN
ejpam-2515	243	17	=	=	PUNCT
ejpam-2515	243	18	{	{	PUNCT
ejpam-2515	243	19	x	x	X
ejpam-2515	243	20	,	,	PUNCT
ejpam-2515	243	21	y}=	y}=	PROPN
ejpam-2515	243	22	x	x	SYM
ejpam-2515	243	23	⊗ρ	⊗ρ	PROPN
ejpam-2515	243	24	y.	y.	NOUN
ejpam-2515	244	1	we	we	PRON
ejpam-2515	244	2	clearly	clearly	ADV
ejpam-2515	244	3	have	have	VERB
ejpam-2515	244	4	∀(x	∀(x	PRON
ejpam-2515	244	5	,	,	PUNCT
ejpam-2515	244	6	y	y	PROPN
ejpam-2515	244	7	,	,	PUNCT
ejpam-2515	244	8	z	z	NOUN
ejpam-2515	244	9	)	)	PUNCT
ejpam-2515	244	10	∈	∈	PROPN
ejpam-2515	244	11	h3	h3	NOUN
ejpam-2515	244	12	,	,	PUNCT
ejpam-2515	244	13	x	x	PUNCT
ejpam-2515	244	14	⊗ρ	⊗ρ	ADJ
ejpam-2515	244	15	(	(	PUNCT
ejpam-2515	244	16	y	y	PROPN
ejpam-2515	244	17	⊗ρ	⊗ρ	PROPN
ejpam-2515	244	18	z	z	PROPN
ejpam-2515	244	19	)	)	PUNCT
ejpam-2515	244	20	=	=	PRON
ejpam-2515	244	21	{	{	PUNCT
ejpam-2515	244	22	x	x	X
ejpam-2515	244	23	,	,	PUNCT
ejpam-2515	244	24	y	y	PROPN
ejpam-2515	244	25	,	,	PUNCT
ejpam-2515	244	26	z}=	z}=	PROPN
ejpam-2515	244	27	(	(	PUNCT
ejpam-2515	244	28	x	x	SYM
ejpam-2515	244	29	⊗ρ	⊗ρ	PROPN
ejpam-2515	244	30	y)⊗rho	y)⊗rho	PROPN
ejpam-2515	244	31	z.	z.	PROPN
ejpam-2515	245	1	moreover	moreover	ADV
ejpam-2515	245	2	(	(	PUNCT
ejpam-2515	245	3	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	245	4	)	)	PUNCT
ejpam-2515	245	5	is	be	AUX
ejpam-2515	245	6	a	a	DET
ejpam-2515	245	7	quasi	quasi	NOUN
ejpam-2515	245	8	-	-	NOUN
ejpam-2515	245	9	hypergroup	hypergroup	ADJ
ejpam-2515	245	10	,	,	PUNCT
ejpam-2515	245	11	since	since	SCONJ
ejpam-2515	245	12	ρ1,2	ρ1,2	PROPN
ejpam-2515	245	13	=	=	SYM
ejpam-2515	245	14	ρ2,3	ρ2,3	PUNCT
ejpam-2515	245	15	=	=	NOUN
ejpam-2515	245	16	h	h	NOUN
ejpam-2515	245	17	×h	×h	NOUN
ejpam-2515	245	18	.	.	PUNCT
ejpam-2515	246	1	s.	s.	PROPN
ejpam-2515	246	2	govindarajan	govindarajan	PROPN
ejpam-2515	246	3	/	/	SYM
ejpam-2515	246	4	eur	eur	PROPN
ejpam-2515	246	5	.	.	PUNCT
ejpam-2515	247	1	j.	j.	PROPN
ejpam-2515	247	2	pure	pure	PROPN
ejpam-2515	247	3	appl	appl	PROPN
ejpam-2515	247	4	.	.	PROPN
ejpam-2515	247	5	math	math	PROPN
ejpam-2515	247	6	,	,	PUNCT
ejpam-2515	247	7	9	9	NUM
ejpam-2515	247	8	(	(	PUNCT
ejpam-2515	247	9	2016	2016	NUM
ejpam-2515	247	10	)	)	PUNCT
ejpam-2515	247	11	,	,	PUNCT
ejpam-2515	247	12	367	367	NUM
ejpam-2515	247	13	-	-	SYM
ejpam-2515	247	14	382	382	NUM
ejpam-2515	247	15	374	374	NUM
ejpam-2515	247	16	now	now	ADV
ejpam-2515	248	1	,	,	PUNCT
ejpam-2515	248	2	we	we	PRON
ejpam-2515	248	3	give	give	VERB
ejpam-2515	248	4	an	an	DET
ejpam-2515	248	5	example	example	NOUN
ejpam-2515	248	6	to	to	PART
ejpam-2515	248	7	show	show	VERB
ejpam-2515	248	8	that	that	SCONJ
ejpam-2515	248	9	(	(	PUNCT
ejpam-2515	248	10	τ2	τ2	NOUN
ejpam-2515	248	11	)	)	PUNCT
ejpam-2515	248	12	is	be	AUX
ejpam-2515	248	13	a	a	DET
ejpam-2515	248	14	sufficient	sufficient	ADJ
ejpam-2515	248	15	condition	condition	NOUN
ejpam-2515	248	16	for	for	ADP
ejpam-2515	248	17	(	(	PUNCT
ejpam-2515	248	18	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	248	19	)	)	PUNCT
ejpam-2515	248	20	to	to	PART
ejpam-2515	248	21	be	be	AUX
ejpam-2515	248	22	a	a	DET
ejpam-2515	248	23	semihypergroup	semihypergroup	NOUN
ejpam-2515	248	24	though	though	ADV
ejpam-2515	248	25	(	(	PUNCT
ejpam-2515	248	26	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	248	27	)	)	PUNCT
ejpam-2515	248	28	is	be	AUX
ejpam-2515	248	29	a	a	DET
ejpam-2515	248	30	quasi	quasi	NOUN
ejpam-2515	248	31	-	-	NOUN
ejpam-2515	248	32	hypergroup	hypergroup	NOUN
ejpam-2515	248	33	.	.	PUNCT
ejpam-2515	249	1	example	example	NOUN
ejpam-2515	250	1	4	4	NUM
ejpam-2515	250	2	.	.	PUNCT
ejpam-2515	250	3	on	on	ADP
ejpam-2515	250	4	the	the	DET
ejpam-2515	250	5	set	set	NOUN
ejpam-2515	250	6	h	h	NOUN
ejpam-2515	250	7	=	=	SYM
ejpam-2515	250	8	{	{	PUNCT
ejpam-2515	250	9	1	1	NUM
ejpam-2515	250	10	,	,	PUNCT
ejpam-2515	250	11	2,3	2,3	NUM
ejpam-2515	250	12	,	,	PUNCT
ejpam-2515	250	13	4	4	NUM
ejpam-2515	250	14	}	}	PUNCT
ejpam-2515	250	15	,	,	PUNCT
ejpam-2515	250	16	we	we	PRON
ejpam-2515	250	17	consider	consider	VERB
ejpam-2515	250	18	the	the	DET
ejpam-2515	250	19	ternary	ternary	ADJ
ejpam-2515	250	20	relation	relation	NOUN
ejpam-2515	250	21	ρ	ρ	NOUN
ejpam-2515	250	22	defined	define	VERB
ejpam-2515	250	23	as	as	SCONJ
ejpam-2515	250	24	follows	follow	VERB
ejpam-2515	250	25	:	:	PUNCT
ejpam-2515	250	26	ρ	ρ	PROPN
ejpam-2515	250	27	=	=	NOUN
ejpam-2515	250	28	{	{	PUNCT
ejpam-2515	250	29	(	(	PUNCT
ejpam-2515	250	30	x	x	INTJ
ejpam-2515	250	31	,	,	PUNCT
ejpam-2515	250	32	x	x	SYM
ejpam-2515	250	33	,	,	PUNCT
ejpam-2515	250	34	y	y	PROPN
ejpam-2515	250	35	)	)	PUNCT
ejpam-2515	250	36	,	,	PUNCT
ejpam-2515	250	37	(	(	PUNCT
ejpam-2515	250	38	x	x	X
ejpam-2515	250	39	,	,	PUNCT
ejpam-2515	250	40	y	y	PROPN
ejpam-2515	250	41	,	,	PUNCT
ejpam-2515	250	42	y	y	PROPN
ejpam-2515	250	43	)	)	PUNCT
ejpam-2515	251	1	|	|	ADV
ejpam-2515	251	2	(	(	PUNCT
ejpam-2515	251	3	x	x	X
ejpam-2515	251	4	,	,	PUNCT
ejpam-2515	251	5	y	y	PROPN
ejpam-2515	251	6	)	)	PUNCT
ejpam-2515	251	7	∈	∈	PROPN
ejpam-2515	251	8	h2	h2	PROPN
ejpam-2515	251	9	}	}	PUNCT
ejpam-2515	251	10	∪	∪	X
ejpam-2515	251	11	{	{	PUNCT
ejpam-2515	251	12	(	(	PUNCT
ejpam-2515	251	13	1	1	NUM
ejpam-2515	251	14	,	,	PUNCT
ejpam-2515	251	15	2,1	2,1	NUM
ejpam-2515	251	16	)	)	PUNCT
ejpam-2515	251	17	,	,	PUNCT
ejpam-2515	251	18	(	(	PUNCT
ejpam-2515	251	19	1,2	1,2	NUM
ejpam-2515	251	20	,	,	PUNCT
ejpam-2515	251	21	3	3	NUM
ejpam-2515	251	22	)	)	PUNCT
ejpam-2515	251	23	,	,	PUNCT
ejpam-2515	251	24	(	(	PUNCT
ejpam-2515	251	25	1,3	1,3	NUM
ejpam-2515	251	26	,	,	PUNCT
ejpam-2515	251	27	2	2	NUM
ejpam-2515	251	28	)	)	PUNCT
ejpam-2515	251	29	,	,	PUNCT
ejpam-2515	251	30	(	(	PUNCT
ejpam-2515	251	31	1,2	1,2	NUM
ejpam-2515	251	32	,	,	PUNCT
ejpam-2515	251	33	4	4	NUM
ejpam-2515	251	34	)	)	PUNCT
ejpam-2515	251	35	,	,	PUNCT
ejpam-2515	251	36	(	(	PUNCT
ejpam-2515	251	37	2	2	NUM
ejpam-2515	251	38	,	,	PUNCT
ejpam-2515	251	39	3,2	3,2	NUM
ejpam-2515	251	40	)	)	PUNCT
ejpam-2515	251	41	,	,	PUNCT
ejpam-2515	251	42	(	(	PUNCT
ejpam-2515	251	43	2,3	2,3	NUM
ejpam-2515	251	44	,	,	PUNCT
ejpam-2515	251	45	1	1	NUM
ejpam-2515	251	46	)	)	PUNCT
ejpam-2515	251	47	,	,	PUNCT
ejpam-2515	251	48	(	(	PUNCT
ejpam-2515	251	49	2	2	NUM
ejpam-2515	251	50	,	,	PUNCT
ejpam-2515	251	51	3,4	3,4	NUM
ejpam-2515	251	52	)	)	PUNCT
ejpam-2515	251	53	,	,	PUNCT
ejpam-2515	251	54	(	(	PUNCT
ejpam-2515	251	55	3	3	NUM
ejpam-2515	251	56	,	,	PUNCT
ejpam-2515	251	57	2,1	2,1	NUM
ejpam-2515	251	58	)	)	PUNCT
ejpam-2515	251	59	,	,	PUNCT
ejpam-2515	251	60	(	(	PUNCT
ejpam-2515	251	61	4,2	4,2	NUM
ejpam-2515	251	62	,	,	PUNCT
ejpam-2515	251	63	1	1	NUM
ejpam-2515	251	64	)	)	PUNCT
ejpam-2515	251	65	,	,	PUNCT
ejpam-2515	251	66	(	(	PUNCT
ejpam-2515	251	67	4,3	4,3	NUM
ejpam-2515	251	68	,	,	PUNCT
ejpam-2515	251	69	2	2	NUM
ejpam-2515	251	70	)	)	PUNCT
ejpam-2515	251	71	}	}	PUNCT
ejpam-2515	251	72	.	.	PUNCT
ejpam-2515	252	1	we	we	PRON
ejpam-2515	252	2	obtain	obtain	VERB
ejpam-2515	252	3	the	the	DET
ejpam-2515	252	4	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	252	5	:	:	PUNCT
ejpam-2515	252	6	table	table	NOUN
ejpam-2515	252	7	2	2	NUM
ejpam-2515	252	8	:	:	PUNCT
ejpam-2515	252	9	example	example	NOUN
ejpam-2515	252	10	4	4	NUM
ejpam-2515	252	11	hypergroupoid	hypergroupoid	ADV
ejpam-2515	252	12	⊗ρ	⊗ρ	PROPN
ejpam-2515	252	13	1	1	NUM
ejpam-2515	252	14	2	2	NUM
ejpam-2515	252	15	3	3	NUM
ejpam-2515	252	16	4	4	NUM
ejpam-2515	252	17	1	1	NUM
ejpam-2515	252	18	1,2	1,2	NUM
ejpam-2515	252	19	1,2,3	1,2,3	NUM
ejpam-2515	252	20	1,2,3	1,2,3	NUM
ejpam-2515	252	21	1,2,4	1,2,4	NUM
ejpam-2515	252	22	2	2	NUM
ejpam-2515	252	23	1,2,3	1,2,3	NUM
ejpam-2515	252	24	2,3	2,3	NUM
ejpam-2515	252	25	2,3	2,3	NUM
ejpam-2515	252	26	2,3,4	2,3,4	NUM
ejpam-2515	252	27	3	3	NUM
ejpam-2515	252	28	1,2,3	1,2,3	NUM
ejpam-2515	252	29	2	2	NUM
ejpam-2515	252	30	,	,	PUNCT
ejpam-2515	252	31	3	3	NUM
ejpam-2515	252	32	3	3	NUM
ejpam-2515	252	33	3,4	3,4	NUM
ejpam-2515	252	34	4	4	NUM
ejpam-2515	252	35	1,2,4	1,2,4	NUM
ejpam-2515	252	36	2,3,4	2,3,4	NUM
ejpam-2515	252	37	3,4	3,4	NUM
ejpam-2515	252	38	4	4	NUM
ejpam-2515	252	39	clearly	clearly	ADV
ejpam-2515	252	40	,	,	PUNCT
ejpam-2515	252	41	we	we	PRON
ejpam-2515	252	42	have	have	VERB
ejpam-2515	253	1	ρ1,3	ρ1,3	PROPN
ejpam-2515	253	2	=	=	SYM
ejpam-2515	253	3	ρ1,2	ρ1,2	PROPN
ejpam-2515	253	4	=	=	SYM
ejpam-2515	253	5	ρ2,3	ρ2,3	PUNCT
ejpam-2515	253	6	=	=	NOUN
ejpam-2515	253	7	h	h	NOUN
ejpam-2515	253	8	×h	×h	NOUN
ejpam-2515	253	9	.	.	PUNCT
ejpam-2515	254	1	so	so	ADV
ejpam-2515	254	2	,	,	PUNCT
ejpam-2515	254	3	(	(	PUNCT
ejpam-2515	254	4	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	254	5	)	)	PUNCT
ejpam-2515	254	6	is	be	AUX
ejpam-2515	254	7	a	a	DET
ejpam-2515	254	8	quasi	quasi	NOUN
ejpam-2515	254	9	-	-	NOUN
ejpam-2515	254	10	hypergroup	hypergroup	NOUN
ejpam-2515	254	11	,	,	PUNCT
ejpam-2515	254	12	but	but	CCONJ
ejpam-2515	254	13	⊗ρ	⊗ρ	NOUN
ejpam-2515	254	14	is	be	AUX
ejpam-2515	254	15	not	not	PART
ejpam-2515	254	16	associative	associative	ADJ
ejpam-2515	254	17	.	.	PUNCT
ejpam-2515	255	1	indeed	indeed	ADV
ejpam-2515	255	2	,	,	PUNCT
ejpam-2515	255	3	we	we	PRON
ejpam-2515	255	4	have	have	VERB
ejpam-2515	255	5	(	(	PUNCT
ejpam-2515	255	6	1,2	1,2	NUM
ejpam-2515	255	7	,	,	PUNCT
ejpam-2515	255	8	3	3	X
ejpam-2515	255	9	)	)	PUNCT
ejpam-2515	255	10	∈	∈	PROPN
ejpam-2515	255	11	ρ	ρ	NOUN
ejpam-2515	255	12	and	and	CCONJ
ejpam-2515	255	13	(	(	PUNCT
ejpam-2515	255	14	2,3	2,3	NUM
ejpam-2515	255	15	,	,	PUNCT
ejpam-2515	255	16	4	4	NUM
ejpam-2515	255	17	)	)	PUNCT
ejpam-2515	255	18	∈	∈	PROPN
ejpam-2515	255	19	ρ	ρ	PROPN
ejpam-2515	255	20	,	,	PUNCT
ejpam-2515	255	21	but	but	CCONJ
ejpam-2515	255	22	(	(	PUNCT
ejpam-2515	255	23	1,3	1,3	NUM
ejpam-2515	255	24	,	,	PUNCT
ejpam-2515	255	25	4	4	NUM
ejpam-2515	255	26	)	)	PUNCT
ejpam-2515	255	27	6∈	6∈	NOUN
ejpam-2515	255	28	ρ	ρ	PROPN
ejpam-2515	255	29	while	while	SCONJ
ejpam-2515	255	30	(	(	PUNCT
ejpam-2515	255	31	1	1	NUM
ejpam-2515	255	32	,	,	PUNCT
ejpam-2515	255	33	2,4	2,4	NUM
ejpam-2515	255	34	)	)	PUNCT
ejpam-2515	255	35	∈	∈	PROPN
ejpam-2515	255	36	ρ	ρ	PROPN
ejpam-2515	255	37	.	.	PUNCT
ejpam-2515	256	1	therefore	therefore	ADV
ejpam-2515	256	2	,	,	PUNCT
ejpam-2515	256	3	1⊗ρ	1⊗ρ	NUM
ejpam-2515	256	4	(	(	PUNCT
ejpam-2515	256	5	4⊗ρ	4⊗ρ	NOUN
ejpam-2515	256	6	4	4	NUM
ejpam-2515	256	7	)	)	PUNCT
ejpam-2515	256	8	=	=	PRON
ejpam-2515	256	9	{	{	PUNCT
ejpam-2515	256	10	1	1	NUM
ejpam-2515	256	11	,	,	PUNCT
ejpam-2515	256	12	2,4	2,4	NUM
ejpam-2515	256	13	}	}	PUNCT
ejpam-2515	256	14	6=	6=	NUM
ejpam-2515	256	15	{	{	PUNCT
ejpam-2515	256	16	1,2	1,2	NUM
ejpam-2515	256	17	,	,	PUNCT
ejpam-2515	256	18	3,4}=	3,4}=	NUM
ejpam-2515	256	19	(	(	PUNCT
ejpam-2515	256	20	1⊗ρ	1⊗ρ	NUM
ejpam-2515	256	21	4)⊗ρ	4)⊗ρ	NOUN
ejpam-2515	256	22	4	4	NUM
ejpam-2515	256	23	.	.	PUNCT
ejpam-2515	257	1	if	if	SCONJ
ejpam-2515	257	2	we	we	PRON
ejpam-2515	257	3	suppose	suppose	VERB
ejpam-2515	257	4	(	(	PUNCT
ejpam-2515	257	5	1,3	1,3	NUM
ejpam-2515	257	6	,	,	PUNCT
ejpam-2515	257	7	4	4	NUM
ejpam-2515	257	8	)	)	PUNCT
ejpam-2515	257	9	∈	∈	NOUN
ejpam-2515	257	10	ρ	ρ	NOUN
ejpam-2515	257	11	then	then	ADV
ejpam-2515	257	12	(	(	PUNCT
ejpam-2515	257	13	τ2	τ2	NOUN
ejpam-2515	257	14	)	)	PUNCT
ejpam-2515	257	15	is	be	AUX
ejpam-2515	257	16	satisfied	satisfied	ADJ
ejpam-2515	257	17	,	,	PUNCT
ejpam-2515	257	18	and	and	CCONJ
ejpam-2515	257	19	then	then	ADV
ejpam-2515	257	20	⊗ρ	⊗ρ	PROPN
ejpam-2515	257	21	is	be	AUX
ejpam-2515	257	22	associative	associative	ADJ
ejpam-2515	257	23	.	.	PUNCT
ejpam-2515	258	1	proposition	proposition	NOUN
ejpam-2515	258	2	6	6	NUM
ejpam-2515	258	3	.	.	PUNCT
ejpam-2515	259	1	let	let	VERB
ejpam-2515	259	2	ρ	ρ	NOUN
ejpam-2515	259	3	be	be	AUX
ejpam-2515	259	4	a	a	DET
ejpam-2515	259	5	reflexive	reflexive	ADJ
ejpam-2515	259	6	and	and	CCONJ
ejpam-2515	259	7	symmetric	symmetric	ADJ
ejpam-2515	259	8	ternary	ternary	ADJ
ejpam-2515	259	9	relation	relation	NOUN
ejpam-2515	259	10	h	h	NOUN
ejpam-2515	260	1	such	such	ADJ
ejpam-2515	260	2	that	that	SCONJ
ejpam-2515	260	3	ρ1,3	ρ1,3	PROPN
ejpam-2515	260	4	=	=	SYM
ejpam-2515	260	5	h	h	PROPN
ejpam-2515	260	6	×	×	PROPN
ejpam-2515	260	7	h.	h.	PROPN
ejpam-2515	260	8	then	then	ADV
ejpam-2515	260	9	(	(	PUNCT
ejpam-2515	260	10	h,⊗ρ	h,⊗ρ	NOUN
ejpam-2515	260	11	)	)	PUNCT
ejpam-2515	260	12	is	be	AUX
ejpam-2515	260	13	a	a	DET
ejpam-2515	260	14	hypergroup	hypergroup	NOUN
ejpam-2515	260	15	,	,	PUNCT
ejpam-2515	260	16	which	which	PRON
ejpam-2515	260	17	is	be	AUX
ejpam-2515	260	18	different	different	ADJ
ejpam-2515	260	19	from	from	ADP
ejpam-2515	260	20	the	the	DET
ejpam-2515	260	21	total	total	ADJ
ejpam-2515	260	22	hypergroup	hypergroup	NOUN
ejpam-2515	260	23	if	if	SCONJ
ejpam-2515	260	24	and	and	CCONJ
ejpam-2515	260	25	only	only	ADV
ejpam-2515	260	26	if	if	SCONJ
ejpam-2515	260	27	:	:	PUNCT
ejpam-2515	260	28	(	(	PUNCT
ejpam-2515	260	29	1	1	X
ejpam-2515	260	30	)	)	PUNCT
ejpam-2515	260	31	ρ1,2	ρ1,2	ADJ
ejpam-2515	260	32	=	=	SYM
ejpam-2515	260	33	ρ2,3	ρ2,3	PUNCT
ejpam-2515	260	34	=	=	NOUN
ejpam-2515	260	35	h	h	NOUN
ejpam-2515	260	36	×h	×h	PROPN
ejpam-2515	260	37	(	(	PUNCT
ejpam-2515	260	38	2	2	X
ejpam-2515	260	39	)	)	PUNCT
ejpam-2515	260	40	ρ	ρ	PROPN
ejpam-2515	260	41	⊂	⊂	PROPN
ejpam-2515	260	42	α1,2,4	α1,2,4	PROPN
ejpam-2515	260	43	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	260	44	(	(	PUNCT
ejpam-2515	260	45	3	3	X
ejpam-2515	260	46	)	)	PUNCT
ejpam-2515	260	47	either	either	CCONJ
ejpam-2515	260	48	(	(	PUNCT
ejpam-2515	260	49	τ1	τ1	NOUN
ejpam-2515	260	50	)	)	PUNCT
ejpam-2515	260	51	alone	alone	ADV
ejpam-2515	260	52	holds	hold	VERB
ejpam-2515	260	53	or	or	CCONJ
ejpam-2515	260	54	both	both	DET
ejpam-2515	260	55	(	(	PUNCT
ejpam-2515	260	56	τ1	τ1	NOUN
ejpam-2515	260	57	)	)	PUNCT
ejpam-2515	260	58	and	and	CCONJ
ejpam-2515	260	59	(	(	PUNCT
ejpam-2515	260	60	τ2	τ2	NOUN
ejpam-2515	260	61	)	)	PUNCT
ejpam-2515	260	62	are	be	AUX
ejpam-2515	260	63	simultaneously	simultaneously	ADV
ejpam-2515	260	64	holds	hold	NOUN
ejpam-2515	260	65	.	.	PUNCT
ejpam-2515	261	1	proof	proof	NOUN
ejpam-2515	261	2	.	.	PUNCT
ejpam-2515	262	1	(=	(=	X
ejpam-2515	262	2	⇒	⇒	NOUN
ejpam-2515	262	3	)	)	PUNCT
ejpam-2515	262	4	it	it	PRON
ejpam-2515	262	5	results	result	VERB
ejpam-2515	262	6	by	by	ADP
ejpam-2515	262	7	proposition	proposition	NOUN
ejpam-2515	262	8	5	5	NUM
ejpam-2515	262	9	and	and	CCONJ
ejpam-2515	262	10	corollary	corollary	ADJ
ejpam-2515	262	11	1	1	NUM
ejpam-2515	262	12	.	.	PUNCT
ejpam-2515	263	1	(	(	PUNCT
ejpam-2515	263	2	⇐	⇐	ADP
ejpam-2515	263	3	=)	=)	PROPN
ejpam-2515	263	4	the	the	DET
ejpam-2515	263	5	conditions	condition	NOUN
ejpam-2515	263	6	of	of	ADP
ejpam-2515	263	7	proposition	proposition	NOUN
ejpam-2515	263	8	5	5	NUM
ejpam-2515	263	9	are	be	AUX
ejpam-2515	263	10	verified	verify	VERB
ejpam-2515	263	11	.	.	PUNCT
ejpam-2515	264	1	further	far	ADV
ejpam-2515	264	2	,	,	PUNCT
ejpam-2515	264	3	(	(	PUNCT
ejpam-2515	264	4	3	3	X
ejpam-2515	264	5	)	)	PUNCT
ejpam-2515	264	6	=	=	NOUN
ejpam-2515	264	7	⇒	⇒	NOUN
ejpam-2515	264	8	(	(	PUNCT
ejpam-2515	264	9	2	2	NUM
ejpam-2515	264	10	)	)	PUNCT
ejpam-2515	264	11	.	.	PUNCT
ejpam-2515	265	1	3.1	3.1	NUM
ejpam-2515	265	2	.	.	PUNCT
ejpam-2515	265	3	hypergroups	hypergroup	NOUN
ejpam-2515	265	4	associated	associate	VERB
ejpam-2515	265	5	with	with	ADP
ejpam-2515	265	6	reflexive	reflexive	ADJ
ejpam-2515	265	7	symmetric	symmetric	ADJ
ejpam-2515	265	8	ternary	ternary	ADJ
ejpam-2515	265	9	relations	relation	NOUN
ejpam-2515	265	10	recall	recall	VERB
ejpam-2515	265	11	now	now	ADV
ejpam-2515	265	12	what	what	PRON
ejpam-2515	265	13	a	a	DET
ejpam-2515	265	14	spherical	spherical	ADJ
ejpam-2515	265	15	geometry	geometry	NOUN
ejpam-2515	265	16	is	be	AUX
ejpam-2515	265	17	(	(	PUNCT
ejpam-2515	265	18	see	see	VERB
ejpam-2515	265	19	[	[	X
ejpam-2515	265	20	19	19	NUM
ejpam-2515	265	21	]	]	PUNCT
ejpam-2515	265	22	,	,	PUNCT
ejpam-2515	265	23	[	[	X
ejpam-2515	265	24	8	8	NUM
ejpam-2515	265	25	,	,	PUNCT
ejpam-2515	265	26	defn	defn	PROPN
ejpam-2515	265	27	.	.	PROPN
ejpam-2515	265	28	25	25	NUM
ejpam-2515	265	29	,	,	PUNCT
ejpam-2515	265	30	p.37	p.37	VERB
ejpam-2515	265	31	in	in	ADP
ejpam-2515	265	32	]	]	PUNCT
ejpam-2515	265	33	)	)	PUNCT
ejpam-2515	265	34	.	.	PUNCT
ejpam-2515	266	1	this	this	DET
ejpam-2515	266	2	definition	definition	NOUN
ejpam-2515	266	3	is	be	AUX
ejpam-2515	266	4	useful	useful	ADJ
ejpam-2515	266	5	in	in	ADP
ejpam-2515	266	6	order	order	NOUN
ejpam-2515	266	7	to	to	PART
ejpam-2515	266	8	characterize	characterize	VERB
ejpam-2515	266	9	the	the	DET
ejpam-2515	266	10	hypergroup	hypergroup	NOUN
ejpam-2515	266	11	hρ	hρ	ADP
ejpam-2515	266	12	definition	definition	NOUN
ejpam-2515	266	13	4	4	NUM
ejpam-2515	266	14	.	.	PUNCT
ejpam-2515	267	1	an	an	DET
ejpam-2515	267	2	(	(	PUNCT
ejpam-2515	267	3	abstract	abstract	ADJ
ejpam-2515	267	4	)	)	PUNCT
ejpam-2515	267	5	spherical	spherical	ADJ
ejpam-2515	267	6	geometry	geometry	NOUN
ejpam-2515	267	7	is	be	AUX
ejpam-2515	267	8	a	a	DET
ejpam-2515	267	9	system	system	NOUN
ejpam-2515	267	10	(	(	PUNCT
ejpam-2515	267	11	s	s	X
ejpam-2515	267	12	,	,	PUNCT
ejpam-2515	267	13	r	r	NOUN
ejpam-2515	267	14	)	)	PUNCT
ejpam-2515	267	15	,	,	PUNCT
ejpam-2515	267	16	where	where	SCONJ
ejpam-2515	267	17	s	s	NOUN
ejpam-2515	267	18	is	be	AUX
ejpam-2515	267	19	a	a	DET
ejpam-2515	267	20	set	set	NOUN
ejpam-2515	267	21	of	of	ADP
ejpam-2515	267	22	elements	element	NOUN
ejpam-2515	267	23	called	call	VERB
ejpam-2515	267	24	points	point	NOUN
ejpam-2515	267	25	and	and	CCONJ
ejpam-2515	267	26	r	r	NOUN
ejpam-2515	267	27	is	be	AUX
ejpam-2515	267	28	a	a	DET
ejpam-2515	267	29	ternary	ternary	ADJ
ejpam-2515	267	30	relation	relation	NOUN
ejpam-2515	267	31	on	on	ADP
ejpam-2515	267	32	s	s	NOUN
ejpam-2515	267	33	called	call	VERB
ejpam-2515	267	34	betweenness	betweenness	NOUN
ejpam-2515	267	35	,	,	PUNCT
ejpam-2515	267	36	which	which	PRON
ejpam-2515	267	37	satisfies	satisfy	VERB
ejpam-2515	267	38	the	the	DET
ejpam-2515	267	39	following	follow	VERB
ejpam-2515	267	40	postulates	postulate	NOUN
ejpam-2515	267	41	:	:	PUNCT
ejpam-2515	267	42	s.	s.	PROPN
ejpam-2515	267	43	govindarajan	govindarajan	PROPN
ejpam-2515	267	44	/	/	SYM
ejpam-2515	267	45	eur	eur	PROPN
ejpam-2515	267	46	.	.	PUNCT
ejpam-2515	268	1	j.	j.	PROPN
ejpam-2515	268	2	pure	pure	PROPN
ejpam-2515	268	3	appl	appl	PROPN
ejpam-2515	268	4	.	.	PROPN
ejpam-2515	268	5	math	math	PROPN
ejpam-2515	268	6	,	,	PUNCT
ejpam-2515	268	7	9	9	NUM
ejpam-2515	268	8	(	(	PUNCT
ejpam-2515	268	9	2016	2016	NUM
ejpam-2515	268	10	)	)	PUNCT
ejpam-2515	268	11	,	,	PUNCT
ejpam-2515	268	12	367	367	NUM
ejpam-2515	268	13	-	-	SYM
ejpam-2515	268	14	382	382	NUM
ejpam-2515	268	15	375	375	NUM
ejpam-2515	268	16	(	(	PUNCT
ejpam-2515	268	17	i	i	NOUN
ejpam-2515	268	18	)	)	PUNCT
ejpam-2515	268	19	if	if	SCONJ
ejpam-2515	268	20	(	(	PUNCT
ejpam-2515	268	21	x	x	X
ejpam-2515	268	22	,	,	PUNCT
ejpam-2515	268	23	y	y	PROPN
ejpam-2515	268	24	,	,	PUNCT
ejpam-2515	268	25	z	z	NOUN
ejpam-2515	268	26	)	)	PUNCT
ejpam-2515	268	27	∈	∈	PROPN
ejpam-2515	268	28	r	r	NOUN
ejpam-2515	268	29	,	,	PUNCT
ejpam-2515	268	30	then	then	ADV
ejpam-2515	268	31	x	x	SYM
ejpam-2515	268	32	,	,	PUNCT
ejpam-2515	268	33	y	y	PROPN
ejpam-2515	268	34	,	,	PUNCT
ejpam-2515	268	35	z	z	PROPN
ejpam-2515	268	36	are	be	AUX
ejpam-2515	268	37	distinct	distinct	ADJ
ejpam-2515	268	38	;	;	PUNCT
ejpam-2515	268	39	(	(	PUNCT
ejpam-2515	268	40	ii	ii	NOUN
ejpam-2515	268	41	)	)	PUNCT
ejpam-2515	268	42	if	if	SCONJ
ejpam-2515	268	43	(	(	PUNCT
ejpam-2515	268	44	x	x	X
ejpam-2515	268	45	,	,	PUNCT
ejpam-2515	268	46	y	y	PROPN
ejpam-2515	268	47	,	,	PUNCT
ejpam-2515	268	48	z	z	NOUN
ejpam-2515	268	49	)	)	PUNCT
ejpam-2515	268	50	∈	∈	PROPN
ejpam-2515	268	51	r	r	NOUN
ejpam-2515	268	52	,	,	PUNCT
ejpam-2515	268	53	then	then	ADV
ejpam-2515	268	54	(	(	PUNCT
ejpam-2515	268	55	z	z	X
ejpam-2515	268	56	,	,	PUNCT
ejpam-2515	268	57	y	y	PROPN
ejpam-2515	268	58	,	,	PUNCT
ejpam-2515	268	59	x	x	NOUN
ejpam-2515	268	60	)	)	PUNCT
ejpam-2515	268	61	∈	∈	PROPN
ejpam-2515	268	62	r	r	NOUN
ejpam-2515	268	63	;	;	PUNCT
ejpam-2515	268	64	(	(	PUNCT
ejpam-2515	268	65	iii	iii	X
ejpam-2515	268	66	)	)	PUNCT
ejpam-2515	268	67	for	for	ADP
ejpam-2515	268	68	any	any	DET
ejpam-2515	268	69	x	x	NOUN
ejpam-2515	268	70	,	,	PUNCT
ejpam-2515	268	71	there	there	PRON
ejpam-2515	268	72	exists	exist	VERB
ejpam-2515	268	73	a	a	DET
ejpam-2515	268	74	unique	unique	ADJ
ejpam-2515	268	75	x	x	NOUN
ejpam-2515	268	76	′	′	NUM
ejpam-2515	268	77	such	such	ADJ
ejpam-2515	268	78	that	that	PRON
ejpam-2515	268	79	x	x	SYM
ejpam-2515	269	1	6=	6=	NUM
ejpam-2515	269	2	x	x	SYM
ejpam-2515	269	3	′	′	NOUN
ejpam-2515	269	4	and	and	CCONJ
ejpam-2515	269	5	the	the	DET
ejpam-2515	269	6	following	follow	VERB
ejpam-2515	269	7	implication	implication	NOUN
ejpam-2515	269	8	holds	hold	VERB
ejpam-2515	269	9	:	:	PUNCT
ejpam-2515	269	10	(	(	PUNCT
ejpam-2515	269	11	x	x	X
ejpam-2515	269	12	,	,	PUNCT
ejpam-2515	269	13	u	u	NOUN
ejpam-2515	269	14	,	,	PUNCT
ejpam-2515	269	15	v	v	NOUN
ejpam-2515	269	16	)	)	PUNCT
ejpam-2515	269	17	∈	∈	NOUN
ejpam-2515	269	18	r=⇒	r=⇒	NOUN
ejpam-2515	269	19	(	(	PUNCT
ejpam-2515	269	20	u	u	NOUN
ejpam-2515	269	21	,	,	PUNCT
ejpam-2515	269	22	v	v	NOUN
ejpam-2515	269	23	,	,	PUNCT
ejpam-2515	269	24	x	x	NOUN
ejpam-2515	269	25	′	′	X
ejpam-2515	269	26	)	)	PUNCT
ejpam-2515	269	27	∈	∈	PROPN
ejpam-2515	270	1	r	r	NOUN
ejpam-2515	270	2	;	;	PUNCT
ejpam-2515	270	3	(	(	PUNCT
ejpam-2515	270	4	iv	iv	X
ejpam-2515	270	5	)	)	PUNCT
ejpam-2515	270	6	if	if	SCONJ
ejpam-2515	270	7	y	y	PROPN
ejpam-2515	270	8	6=	6=	PROPN
ejpam-2515	270	9	x	x	PROPN
ejpam-2515	270	10	and	and	CCONJ
ejpam-2515	270	11	y	y	PROPN
ejpam-2515	270	12	6=	6=	PROPN
ejpam-2515	270	13	x	x	SYM
ejpam-2515	270	14	′	′	NUM
ejpam-2515	270	15	,	,	PUNCT
ejpam-2515	270	16	then	then	ADV
ejpam-2515	270	17	there	there	PRON
ejpam-2515	270	18	exists	exist	VERB
ejpam-2515	270	19	u	u	PRON
ejpam-2515	270	20	such	such	ADJ
ejpam-2515	270	21	that	that	SCONJ
ejpam-2515	270	22	(	(	PUNCT
ejpam-2515	270	23	x	x	X
ejpam-2515	270	24	,	,	PUNCT
ejpam-2515	270	25	u	u	NOUN
ejpam-2515	270	26	,	,	PUNCT
ejpam-2515	270	27	y	y	PROPN
ejpam-2515	270	28	)	)	PUNCT
ejpam-2515	270	29	∈	∈	PROPN
ejpam-2515	270	30	r.	r.	PROPN
ejpam-2515	270	31	w.	w.	PROPN
ejpam-2515	270	32	prenowitz	prenowitz	PROPN
ejpam-2515	271	1	[	[	X
ejpam-2515	271	2	19	19	NUM
ejpam-2515	271	3	]	]	PUNCT
ejpam-2515	271	4	defined	define	VERB
ejpam-2515	271	5	the	the	DET
ejpam-2515	271	6	following	follow	VERB
ejpam-2515	271	7	hyperoperation	hyperoperation	NOUN
ejpam-2515	271	8	on	on	ADP
ejpam-2515	271	9	s	s	NOUN
ejpam-2515	271	10	:	:	PUNCT
ejpam-2515	271	11	∀(x	∀(x	NUM
ejpam-2515	271	12	,	,	PUNCT
ejpam-2515	271	13	y	y	PROPN
ejpam-2515	271	14	)	)	PUNCT
ejpam-2515	271	15	∈	∈	PROPN
ejpam-2515	271	16	s2	s2	PROPN
ejpam-2515	271	17	,	,	PUNCT
ejpam-2515	271	18	y	y	PROPN
ejpam-2515	271	19	6=	6=	PROPN
ejpam-2515	271	20	x	x	SYM
ejpam-2515	271	21	,	,	PUNCT
ejpam-2515	271	22	y	y	PROPN
ejpam-2515	271	23	6=	6=	PROPN
ejpam-2515	271	24	x	x	SYM
ejpam-2515	271	25	′	′	NUM
ejpam-2515	271	26	,	,	PUNCT
ejpam-2515	271	27	x	x	VERB
ejpam-2515	272	1	◦	◦	NOUN
ejpam-2515	272	2	y	y	NOUN
ejpam-2515	272	3	=	=	PUNCT
ejpam-2515	272	4	{	{	PUNCT
ejpam-2515	272	5	t	t	NOUN
ejpam-2515	273	1	|	|	ADV
ejpam-2515	273	2	(	(	PUNCT
ejpam-2515	273	3	x	x	X
ejpam-2515	273	4	,	,	PUNCT
ejpam-2515	273	5	t	t	PROPN
ejpam-2515	273	6	,	,	PUNCT
ejpam-2515	273	7	y	y	NOUN
ejpam-2515	273	8	)	)	PUNCT
ejpam-2515	273	9	∈	∈	NOUN
ejpam-2515	273	10	r	r	NOUN
ejpam-2515	273	11	}	}	PUNCT
ejpam-2515	273	12	,	,	PUNCT
ejpam-2515	273	13	x	x	PUNCT
ejpam-2515	273	14	◦	◦	NOUN
ejpam-2515	273	15	x	x	SYM
ejpam-2515	273	16	=	=	PRON
ejpam-2515	273	17	{	{	PUNCT
ejpam-2515	273	18	x	x	NOUN
ejpam-2515	273	19	}	}	PUNCT
ejpam-2515	273	20	.	.	PUNCT
ejpam-2515	274	1	now	now	ADV
ejpam-2515	274	2	,	,	PUNCT
ejpam-2515	274	3	let	let	VERB
ejpam-2515	274	4	us	we	PRON
ejpam-2515	274	5	set	set	VERB
ejpam-2515	274	6	:	:	PUNCT
ejpam-2515	275	1	r	r	NOUN
ejpam-2515	275	2	=	=	SYM
ejpam-2515	275	3	ρ	ρ	PROPN
ejpam-2515	275	4	.	.	PUNCT
ejpam-2515	275	5	again	again	ADV
ejpam-2515	275	6	,	,	PUNCT
ejpam-2515	275	7	recall	recall	VERB
ejpam-2515	275	8	that	that	SCONJ
ejpam-2515	275	9	the	the	DET
ejpam-2515	275	10	join	join	PROPN
ejpam-2515	275	11	relation	relation	PROPN
ejpam-2515	275	12	j2(ρ	j2(ρ	PROPN
ejpam-2515	275	13	,	,	PUNCT
ejpam-2515	275	14	ρ	ρ	NOUN
ejpam-2515	275	15	)	)	PUNCT
ejpam-2515	275	16	denoted	denote	VERB
ejpam-2515	275	17	by	by	ADP
ejpam-2515	275	18	α	α	PROPN
ejpam-2515	275	19	is	be	AUX
ejpam-2515	275	20	a	a	DET
ejpam-2515	275	21	4	4	NUM
ejpam-2515	275	22	-	-	PUNCT
ejpam-2515	275	23	ary	ary	NOUN
ejpam-2515	275	24	relation	relation	NOUN
ejpam-2515	276	1	such	such	ADJ
ejpam-2515	276	2	that	that	SCONJ
ejpam-2515	276	3	(	(	PUNCT
ejpam-2515	276	4	x	x	X
ejpam-2515	276	5	,	,	PUNCT
ejpam-2515	276	6	y	y	PROPN
ejpam-2515	276	7	,	,	PUNCT
ejpam-2515	276	8	z	z	NOUN
ejpam-2515	276	9	)	)	PUNCT
ejpam-2515	276	10	∈	∈	PROPN
ejpam-2515	276	11	j2(ρ	j2(ρ	PROPN
ejpam-2515	276	12	,	,	PUNCT
ejpam-2515	276	13	ρ)	ρ)	NUM
ejpam-2515	276	14	⇐	⇐	ADJ
ejpam-2515	276	15	⇒	⇒	NOUN
ejpam-2515	276	16	(	(	PUNCT
ejpam-2515	276	17	x	x	X
ejpam-2515	276	18	,	,	PUNCT
ejpam-2515	276	19	y	y	PROPN
ejpam-2515	276	20	,	,	PUNCT
ejpam-2515	276	21	z	z	NOUN
ejpam-2515	276	22	)	)	PUNCT
ejpam-2515	276	23	,	,	PUNCT
ejpam-2515	276	24	(	(	PUNCT
ejpam-2515	276	25	y	y	NOUN
ejpam-2515	276	26	,	,	PUNCT
ejpam-2515	276	27	z	z	PROPN
ejpam-2515	276	28	,	,	PUNCT
ejpam-2515	276	29	t	t	PROPN
ejpam-2515	276	30	)	)	PUNCT
ejpam-2515	276	31	∈	∈	PROPN
ejpam-2515	276	32	ρ	ρ	PROPN
ejpam-2515	276	33	.	.	PUNCT
ejpam-2515	276	34	suppose	suppose	VERB
ejpam-2515	276	35	that	that	SCONJ
ejpam-2515	276	36	ρ	ρ	PROPN
ejpam-2515	276	37	is	be	AUX
ejpam-2515	276	38	betweenness	betweenness	NOUN
ejpam-2515	276	39	relation	relation	NOUN
ejpam-2515	276	40	.	.	PUNCT
ejpam-2515	277	1	then	then	ADV
ejpam-2515	277	2	the	the	DET
ejpam-2515	277	3	postulates	postulate	NOUN
ejpam-2515	277	4	(	(	PUNCT
ejpam-2515	277	5	iii	iii	NOUN
ejpam-2515	277	6	)	)	PUNCT
ejpam-2515	277	7	and	and	CCONJ
ejpam-2515	277	8	(	(	PUNCT
ejpam-2515	277	9	iv	iv	X
ejpam-2515	277	10	)	)	PUNCT
ejpam-2515	277	11	of	of	ADP
ejpam-2515	277	12	definition	definition	NOUN
ejpam-2515	277	13	4	4	NUM
ejpam-2515	277	14	together	together	ADV
ejpam-2515	277	15	with	with	ADP
ejpam-2515	277	16	the	the	DET
ejpam-2515	277	17	definition	definition	NOUN
ejpam-2515	277	18	of	of	ADP
ejpam-2515	277	19	join	join	NOUN
ejpam-2515	277	20	relation	relation	NOUN
ejpam-2515	277	21	and	and	CCONJ
ejpam-2515	277	22	projection	projection	NOUN
ejpam-2515	277	23	relations	relation	NOUN
ejpam-2515	277	24	shows	show	VERB
ejpam-2515	277	25	that	that	SCONJ
ejpam-2515	277	26	,	,	PUNCT
ejpam-2515	277	27	for	for	ADP
ejpam-2515	277	28	any	any	DET
ejpam-2515	277	29	(	(	PUNCT
ejpam-2515	277	30	x	x	NOUN
ejpam-2515	277	31	,	,	PUNCT
ejpam-2515	277	32	y	y	PROPN
ejpam-2515	277	33	,	,	PUNCT
ejpam-2515	277	34	z	z	NOUN
ejpam-2515	277	35	)	)	PUNCT
ejpam-2515	277	36	∈	∈	PROPN
ejpam-2515	277	37	ρ	ρ	NOUN
ejpam-2515	277	38	,	,	PUNCT
ejpam-2515	277	39	there	there	PRON
ejpam-2515	277	40	exists	exist	VERB
ejpam-2515	277	41	a	a	DET
ejpam-2515	277	42	unique	unique	ADJ
ejpam-2515	277	43	x	x	NOUN
ejpam-2515	277	44	′	′	NUM
ejpam-2515	277	45	such	such	ADJ
ejpam-2515	277	46	that	that	PRON
ejpam-2515	277	47	x	x	SYM
ejpam-2515	277	48	6=	6=	NUM
ejpam-2515	277	49	x	x	SYM
ejpam-2515	277	50	′	′	NUM
ejpam-2515	277	51	and	and	CCONJ
ejpam-2515	277	52	(	(	PUNCT
ejpam-2515	277	53	x	x	X
ejpam-2515	277	54	,	,	PUNCT
ejpam-2515	277	55	y	y	PROPN
ejpam-2515	277	56	,	,	PUNCT
ejpam-2515	277	57	x	x	NOUN
ejpam-2515	277	58	′	′	X
ejpam-2515	277	59	)	)	PUNCT
ejpam-2515	277	60	∈	∈	PROPN
ejpam-2515	277	61	α1,2,4	α1,2,4	PROPN
ejpam-2515	277	62	,	,	PUNCT
ejpam-2515	277	63	(	(	PUNCT
ejpam-2515	277	64	x	x	X
ejpam-2515	277	65	,	,	PUNCT
ejpam-2515	277	66	z	z	NOUN
ejpam-2515	277	67	,	,	PUNCT
ejpam-2515	277	68	x	x	NOUN
ejpam-2515	277	69	′	′	X
ejpam-2515	277	70	)	)	PUNCT
ejpam-2515	277	71	∈	∈	PROPN
ejpam-2515	277	72	α1,3,4	α1,3,4	PROPN
ejpam-2515	277	73	.	.	PUNCT
ejpam-2515	278	1	we	we	PRON
ejpam-2515	278	2	observe	observe	VERB
ejpam-2515	278	3	that	that	SCONJ
ejpam-2515	278	4	the	the	DET
ejpam-2515	278	5	product	product	NOUN
ejpam-2515	278	6	⊗	⊗	PROPN
ejpam-2515	278	7	ρ	ρ	PROPN
ejpam-2515	278	8	and	and	CCONJ
ejpam-2515	278	9	◦	◦	NOUN
ejpam-2515	278	10	are	be	AUX
ejpam-2515	278	11	identical	identical	ADJ
ejpam-2515	278	12	and	and	CCONJ
ejpam-2515	278	13	the	the	DET
ejpam-2515	278	14	relation	relation	NOUN
ejpam-2515	278	15	ρ	ρ	NOUN
ejpam-2515	279	1	=	=	PUNCT
ejpam-2515	279	2	r	r	NOUN
ejpam-2515	279	3	if	if	SCONJ
ejpam-2515	279	4	and	and	CCONJ
ejpam-2515	279	5	only	only	ADV
ejpam-2515	279	6	if	if	SCONJ
ejpam-2515	279	7	ρ	ρ	PROPN
ejpam-2515	279	8	is	be	AUX
ejpam-2515	279	9	reflexive	reflexive	ADJ
ejpam-2515	279	10	and	and	CCONJ
ejpam-2515	279	11	symmetric	symmetric	ADJ
ejpam-2515	279	12	ternary	ternary	ADJ
ejpam-2515	279	13	relation	relation	NOUN
ejpam-2515	279	14	on	on	ADP
ejpam-2515	279	15	h.	h.	PROPN
ejpam-2515	279	16	hence	hence	ADV
ejpam-2515	279	17	,	,	PUNCT
ejpam-2515	279	18	we	we	PRON
ejpam-2515	279	19	obtain	obtain	VERB
ejpam-2515	279	20	the	the	DET
ejpam-2515	279	21	following	follow	VERB
ejpam-2515	279	22	proposition	proposition	NOUN
ejpam-2515	279	23	:	:	PUNCT
ejpam-2515	279	24	proposition	proposition	NOUN
ejpam-2515	279	25	7	7	NUM
ejpam-2515	279	26	.	.	PUNCT
ejpam-2515	280	1	let	let	VERB
ejpam-2515	280	2	ρ	ρ	NOUN
ejpam-2515	280	3	be	be	AUX
ejpam-2515	280	4	a	a	DET
ejpam-2515	280	5	reflexive	reflexive	ADJ
ejpam-2515	280	6	and	and	CCONJ
ejpam-2515	280	7	symmetric	symmetric	ADJ
ejpam-2515	280	8	ternary	ternary	ADJ
ejpam-2515	280	9	relation	relation	NOUN
ejpam-2515	280	10	on	on	ADP
ejpam-2515	280	11	h	h	NOUN
ejpam-2515	280	12	with	with	ADP
ejpam-2515	280	13	|h|	|h|	PROPN
ejpam-2515	280	14	≥	≥	NUM
ejpam-2515	280	15	3	3	NUM
ejpam-2515	280	16	such	such	ADJ
ejpam-2515	281	1	that	that	PRON
ejpam-2515	281	2	ρ1,3	ρ1,3	PROPN
ejpam-2515	282	1	=	=	SYM
ejpam-2515	283	1	h	h	PROPN
ejpam-2515	284	1	×h	×h	NOUN
ejpam-2515	284	2	.	.	PUNCT
ejpam-2515	285	1	if	if	SCONJ
ejpam-2515	285	2	ρ	ρ	PROPN
ejpam-2515	285	3	satisfies	satisfy	VERB
ejpam-2515	285	4	the	the	DET
ejpam-2515	285	5	following	follow	VERB
ejpam-2515	285	6	the	the	DET
ejpam-2515	285	7	postulates	postulate	NOUN
ejpam-2515	285	8	,	,	PUNCT
ejpam-2515	285	9	then	then	ADV
ejpam-2515	285	10	⊗	⊗	PROPN
ejpam-2515	285	11	ρ	ρ	PROPN
ejpam-2515	285	12	is	be	AUX
ejpam-2515	285	13	not	not	PART
ejpam-2515	285	14	associative	associative	ADJ
ejpam-2515	285	15	(	(	PUNCT
ejpam-2515	285	16	i	i	NOUN
ejpam-2515	285	17	)	)	PUNCT
ejpam-2515	285	18	if	if	SCONJ
ejpam-2515	285	19	(	(	PUNCT
ejpam-2515	285	20	x	x	X
ejpam-2515	285	21	,	,	PUNCT
ejpam-2515	285	22	y	y	PROPN
ejpam-2515	285	23	,	,	PUNCT
ejpam-2515	285	24	z	z	NOUN
ejpam-2515	285	25	)	)	PUNCT
ejpam-2515	285	26	∈	∈	PROPN
ejpam-2515	285	27	ρ	ρ	PROPN
ejpam-2515	285	28	,	,	PUNCT
ejpam-2515	285	29	then	then	ADV
ejpam-2515	285	30	x	x	SYM
ejpam-2515	285	31	,	,	PUNCT
ejpam-2515	285	32	y	y	PROPN
ejpam-2515	285	33	,	,	PUNCT
ejpam-2515	285	34	z	z	PROPN
ejpam-2515	285	35	are	be	AUX
ejpam-2515	285	36	distinct	distinct	ADJ
ejpam-2515	285	37	;	;	PUNCT
ejpam-2515	285	38	(	(	PUNCT
ejpam-2515	285	39	ii	ii	NOUN
ejpam-2515	285	40	)	)	PUNCT
ejpam-2515	285	41	if	if	SCONJ
ejpam-2515	285	42	x	x	PROPN
ejpam-2515	285	43	6=	6=	NUM
ejpam-2515	285	44	y	y	PROPN
ejpam-2515	285	45	,	,	PUNCT
ejpam-2515	285	46	then	then	ADV
ejpam-2515	285	47	(	(	PUNCT
ejpam-2515	285	48	x	x	X
ejpam-2515	285	49	,	,	PUNCT
ejpam-2515	285	50	y	y	PROPN
ejpam-2515	285	51	,	,	PUNCT
ejpam-2515	285	52	x	x	NOUN
ejpam-2515	285	53	)	)	PUNCT
ejpam-2515	285	54	6∈	6∈	PROPN
ejpam-2515	285	55	ρ	ρ	PROPN
ejpam-2515	285	56	;	;	PUNCT
ejpam-2515	285	57	(	(	PUNCT
ejpam-2515	285	58	iii	iii	NOUN
ejpam-2515	285	59	)	)	PUNCT
ejpam-2515	285	60	for	for	ADP
ejpam-2515	285	61	any	any	DET
ejpam-2515	285	62	(	(	PUNCT
ejpam-2515	285	63	x	x	NOUN
ejpam-2515	285	64	,	,	PUNCT
ejpam-2515	285	65	y	y	PROPN
ejpam-2515	285	66	,	,	PUNCT
ejpam-2515	285	67	z	z	NOUN
ejpam-2515	285	68	)	)	PUNCT
ejpam-2515	285	69	∈	∈	PROPN
ejpam-2515	285	70	ρ	ρ	NOUN
ejpam-2515	285	71	,	,	PUNCT
ejpam-2515	285	72	there	there	PRON
ejpam-2515	285	73	exists	exist	VERB
ejpam-2515	285	74	a	a	DET
ejpam-2515	285	75	unique	unique	ADJ
ejpam-2515	285	76	x	x	NOUN
ejpam-2515	285	77	′	′	NUM
ejpam-2515	285	78	such	such	ADJ
ejpam-2515	285	79	that	that	PRON
ejpam-2515	285	80	x	x	SYM
ejpam-2515	285	81	6=	6=	NUM
ejpam-2515	285	82	x	x	SYM
ejpam-2515	285	83	′	′	NUM
ejpam-2515	285	84	and	and	CCONJ
ejpam-2515	285	85	(	(	PUNCT
ejpam-2515	285	86	x	x	X
ejpam-2515	285	87	,	,	PUNCT
ejpam-2515	285	88	y	y	PROPN
ejpam-2515	285	89	,	,	PUNCT
ejpam-2515	285	90	x	x	NOUN
ejpam-2515	285	91	′	′	X
ejpam-2515	285	92	)	)	PUNCT
ejpam-2515	285	93	∈	∈	PROPN
ejpam-2515	285	94	α1,2,4	α1,2,4	PROPN
ejpam-2515	285	95	,	,	PUNCT
ejpam-2515	285	96	(	(	PUNCT
ejpam-2515	285	97	x	x	X
ejpam-2515	285	98	,	,	PUNCT
ejpam-2515	285	99	z	z	NOUN
ejpam-2515	285	100	,	,	PUNCT
ejpam-2515	285	101	x	x	NOUN
ejpam-2515	285	102	′	′	X
ejpam-2515	285	103	)	)	PUNCT
ejpam-2515	285	104	∈	∈	PROPN
ejpam-2515	285	105	α1,3,4	α1,3,4	PROPN
ejpam-2515	285	106	.	.	PUNCT
ejpam-2515	286	1	proof	proof	NOUN
ejpam-2515	286	2	.	.	PUNCT
ejpam-2515	287	1	the	the	DET
ejpam-2515	287	2	ρ	ρ	PROPN
ejpam-2515	287	3	verifies	verifie	NOUN
ejpam-2515	287	4	the	the	DET
ejpam-2515	287	5	postulates	postulate	NOUN
ejpam-2515	287	6	of	of	ADP
ejpam-2515	287	7	the	the	DET
ejpam-2515	287	8	betweenness	betweenness	PROPN
ejpam-2515	287	9	relation	relation	NOUN
ejpam-2515	287	10	on	on	ADP
ejpam-2515	287	11	h.	h.	PROPN
ejpam-2515	287	12	now	now	ADV
ejpam-2515	287	13	,	,	PUNCT
ejpam-2515	287	14	the	the	DET
ejpam-2515	287	15	proof	proof	NOUN
ejpam-2515	287	16	follows	follow	VERB
ejpam-2515	287	17	from	from	ADP
ejpam-2515	287	18	[	[	X
ejpam-2515	287	19	8	8	NUM
ejpam-2515	287	20	,	,	PUNCT
ejpam-2515	287	21	theorem	theorem	VERB
ejpam-2515	287	22	27	27	NUM
ejpam-2515	287	23	,	,	PUNCT
ejpam-2515	287	24	p.39	p.39	X
ejpam-2515	287	25	]	]	PUNCT
ejpam-2515	287	26	.	.	PUNCT
ejpam-2515	288	1	let	let	VERB
ejpam-2515	288	2	ρ	ρ	NOUN
ejpam-2515	288	3	be	be	AUX
ejpam-2515	288	4	a	a	DET
ejpam-2515	288	5	reflexive	reflexive	ADJ
ejpam-2515	288	6	ternary	ternary	ADJ
ejpam-2515	288	7	relation	relation	NOUN
ejpam-2515	288	8	h	h	NOUN
ejpam-2515	288	9	such	such	ADJ
ejpam-2515	288	10	that	that	SCONJ
ejpam-2515	288	11	ρ1,3	ρ1,3	PROPN
ejpam-2515	288	12	=	=	SYM
ejpam-2515	288	13	h×h	h×h	PROPN
ejpam-2515	288	14	.	.	PUNCT
ejpam-2515	289	1	let	let	VERB
ejpam-2515	289	2	(	(	PUNCT
ejpam-2515	289	3	x	x	X
ejpam-2515	289	4	,	,	PUNCT
ejpam-2515	289	5	a	a	PRON
ejpam-2515	289	6	,	,	PUNCT
ejpam-2515	289	7	y	y	NOUN
ejpam-2515	289	8	)	)	PUNCT
ejpam-2515	289	9	∈	∈	PROPN
ejpam-2515	289	10	ρ	ρ	NOUN
ejpam-2515	289	11	be	be	AUX
ejpam-2515	289	12	arbitrary	arbitrary	ADJ
ejpam-2515	289	13	and	and	CCONJ
ejpam-2515	289	14	x	x	INTJ
ejpam-2515	289	15	,	,	PUNCT
ejpam-2515	289	16	a	a	X
ejpam-2515	289	17	,	,	PUNCT
ejpam-2515	289	18	y	y	PROPN
ejpam-2515	289	19	are	be	AUX
ejpam-2515	289	20	distinct	distinct	ADJ
ejpam-2515	289	21	.	.	PUNCT
ejpam-2515	290	1	let	let	AUX
ejpam-2515	290	2	(	(	PUNCT
ejpam-2515	290	3	h;	h;	NOUN
ejpam-2515	290	4	◦	◦	NOUN
ejpam-2515	290	5	ρ	ρ	NOUN
ejpam-2515	290	6	)	)	PUNCT
ejpam-2515	290	7	be	be	VERB
ejpam-2515	290	8	the	the	DET
ejpam-2515	290	9	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	290	10	defined	define	VERB
ejpam-2515	290	11	as	as	SCONJ
ejpam-2515	290	12	follows	follow	VERB
ejpam-2515	290	13	.	.	PUNCT
ejpam-2515	291	1	∀(x	∀(x	PRON
ejpam-2515	291	2	,	,	PUNCT
ejpam-2515	291	3	y	y	NOUN
ejpam-2515	291	4	)	)	PUNCT
ejpam-2515	291	5	∈h2	∈h2	NOUN
ejpam-2515	291	6	,	,	PUNCT
ejpam-2515	291	7	x	x	PROPN
ejpam-2515	291	8	6=	6=	PROPN
ejpam-2515	291	9	y	y	PROPN
ejpam-2515	291	10	,	,	PUNCT
ejpam-2515	291	11	x	x	PUNCT
ejpam-2515	291	12	◦	◦	NOUN
ejpam-2515	291	13	ρ	ρ	X
ejpam-2515	291	14	y	y	NOUN
ejpam-2515	291	15	=	=	PRON
ejpam-2515	291	16	{	{	PUNCT
ejpam-2515	291	17	a	a	DET
ejpam-2515	291	18	|	|	NOUN
ejpam-2515	291	19	(	(	PUNCT
ejpam-2515	291	20	x	x	INTJ
ejpam-2515	291	21	,	,	PUNCT
ejpam-2515	291	22	a	a	PRON
ejpam-2515	291	23	,	,	PUNCT
ejpam-2515	291	24	y	y	NOUN
ejpam-2515	291	25	)	)	PUNCT
ejpam-2515	291	26	∈	∈	PROPN
ejpam-2515	291	27	ρ	ρ	PROPN
ejpam-2515	291	28	}	}	PUNCT
ejpam-2515	291	29	∪	∪	NOUN
ejpam-2515	291	30	{	{	PUNCT
ejpam-2515	291	31	x	x	NOUN
ejpam-2515	291	32	,	,	PUNCT
ejpam-2515	291	33	y	y	PROPN
ejpam-2515	291	34	}	}	PUNCT
ejpam-2515	291	35	∀x	∀x	X
ejpam-2515	291	36	∈h	∈h	NOUN
ejpam-2515	291	37	,	,	PUNCT
ejpam-2515	291	38	x	x	PUNCT
ejpam-2515	291	39	◦	◦	NOUN
ejpam-2515	291	40	ρ	ρ	NOUN
ejpam-2515	291	41	a	a	PRON
ejpam-2515	291	42	=	=	X
ejpam-2515	291	43	{	{	PUNCT
ejpam-2515	291	44	x	x	NOUN
ejpam-2515	291	45	}	}	PUNCT
ejpam-2515	291	46	.	.	PUNCT
ejpam-2515	292	1	indeed	indeed	ADV
ejpam-2515	292	2	,	,	PUNCT
ejpam-2515	292	3	◦	◦	NOUN
ejpam-2515	292	4	ρ	ρ	NOUN
ejpam-2515	292	5	is	be	AUX
ejpam-2515	292	6	an	an	DET
ejpam-2515	292	7	extension	extension	NOUN
ejpam-2515	292	8	of	of	ADP
ejpam-2515	292	9	⊗ρ	⊗ρ	NOUN
ejpam-2515	292	10	.	.	PUNCT
ejpam-2515	293	1	if	if	SCONJ
ejpam-2515	293	2	we	we	PRON
ejpam-2515	293	3	suppose	suppose	VERB
ejpam-2515	293	4	,	,	PUNCT
ejpam-2515	293	5	∀	∀	X
ejpam-2515	293	6	(	(	PUNCT
ejpam-2515	293	7	x	x	X
ejpam-2515	293	8	,	,	PUNCT
ejpam-2515	293	9	y	y	PROPN
ejpam-2515	293	10	)	)	PUNCT
ejpam-2515	293	11	∈	∈	PROPN
ejpam-2515	293	12	h2	h2	NOUN
ejpam-2515	293	13	,	,	PUNCT
ejpam-2515	293	14	(	(	PUNCT
ejpam-2515	293	15	x	x	X
ejpam-2515	293	16	,	,	PUNCT
ejpam-2515	293	17	y	y	PROPN
ejpam-2515	293	18	,	,	PUNCT
ejpam-2515	293	19	x	x	NOUN
ejpam-2515	293	20	)	)	PUNCT
ejpam-2515	293	21	6∈	6∈	NOUN
ejpam-2515	293	22	ρ	ρ	NOUN
ejpam-2515	293	23	when	when	SCONJ
ejpam-2515	293	24	x	x	PROPN
ejpam-2515	293	25	6=	6=	PROPN
ejpam-2515	293	26	y	y	PROPN
ejpam-2515	293	27	;	;	PUNCT
ejpam-2515	293	28	(	(	PUNCT
ejpam-2515	293	29	1	1	X
ejpam-2515	293	30	)	)	PUNCT
ejpam-2515	293	31	then	then	ADV
ejpam-2515	293	32	,	,	PUNCT
ejpam-2515	293	33	we	we	PRON
ejpam-2515	293	34	have	have	VERB
ejpam-2515	293	35	clearly	clearly	ADV
ejpam-2515	293	36	:	:	PUNCT
ejpam-2515	293	37	∀x	∀x	NUM
ejpam-2515	293	38	∈	∈	PROPN
ejpam-2515	293	39	h	h	NOUN
ejpam-2515	293	40	,	,	PUNCT
ejpam-2515	293	41	x	x	PUNCT
ejpam-2515	293	42	◦	◦	NOUN
ejpam-2515	293	43	ρ	ρ	NOUN
ejpam-2515	293	44	x	x	SYM
ejpam-2515	293	45	=	=	PRON
ejpam-2515	293	46	{	{	PUNCT
ejpam-2515	293	47	x}=	x}=	PROPN
ejpam-2515	293	48	x	x	SYM
ejpam-2515	293	49	⊗	⊗	PROPN
ejpam-2515	293	50	ρ	ρ	PROPN
ejpam-2515	293	51	x	x	SYM
ejpam-2515	293	52	⇐	⇐	ADJ
ejpam-2515	293	53	⇒	⇒	NOUN
ejpam-2515	293	54	(	(	PUNCT
ejpam-2515	293	55	x	x	X
ejpam-2515	293	56	,	,	PUNCT
ejpam-2515	293	57	x	x	X
ejpam-2515	293	58	,	,	PUNCT
ejpam-2515	293	59	x	x	X
ejpam-2515	293	60	)	)	PUNCT
ejpam-2515	293	61	∈	∈	PROPN
ejpam-2515	293	62	ρ	ρ	PROPN
ejpam-2515	293	63	s.	s.	PROPN
ejpam-2515	293	64	govindarajan	govindarajan	PROPN
ejpam-2515	293	65	/	/	SYM
ejpam-2515	293	66	eur	eur	PROPN
ejpam-2515	293	67	.	.	PUNCT
ejpam-2515	294	1	j.	j.	PROPN
ejpam-2515	294	2	pure	pure	PROPN
ejpam-2515	294	3	appl	appl	PROPN
ejpam-2515	294	4	.	.	PROPN
ejpam-2515	294	5	math	math	PROPN
ejpam-2515	294	6	,	,	PUNCT
ejpam-2515	294	7	9	9	NUM
ejpam-2515	294	8	(	(	PUNCT
ejpam-2515	294	9	2016	2016	NUM
ejpam-2515	294	10	)	)	PUNCT
ejpam-2515	294	11	,	,	PUNCT
ejpam-2515	294	12	367	367	NUM
ejpam-2515	294	13	-	-	SYM
ejpam-2515	294	14	382	382	NUM
ejpam-2515	294	15	376	376	NUM
ejpam-2515	294	16	∀(x	∀(x	NOUN
ejpam-2515	294	17	,	,	PUNCT
ejpam-2515	294	18	y	y	NOUN
ejpam-2515	294	19	)	)	PUNCT
ejpam-2515	294	20	∈	∈	PROPN
ejpam-2515	294	21	h2	h2	NOUN
ejpam-2515	294	22	,	,	PUNCT
ejpam-2515	294	23	x	x	PROPN
ejpam-2515	295	1	6=	6=	PROPN
ejpam-2515	295	2	y	y	PROPN
ejpam-2515	295	3	,	,	PUNCT
ejpam-2515	295	4	x	x	PUNCT
ejpam-2515	295	5	◦	◦	NOUN
ejpam-2515	295	6	ρ	ρ	X
ejpam-2515	295	7	y	y	NOUN
ejpam-2515	295	8	=	=	PRON
ejpam-2515	295	9	{	{	PUNCT
ejpam-2515	295	10	x	x	X
ejpam-2515	295	11	,	,	PUNCT
ejpam-2515	295	12	a	a	PRON
ejpam-2515	295	13	,	,	PUNCT
ejpam-2515	295	14	y}=	y}=	PROPN
ejpam-2515	295	15	x	x	SYM
ejpam-2515	295	16	⊗	⊗	PROPN
ejpam-2515	295	17	ρ	ρ	PROPN
ejpam-2515	295	18	y	y	PROPN
ejpam-2515	295	19	∪	∪	X
ejpam-2515	295	20	{	{	PUNCT
ejpam-2515	295	21	x	x	INTJ
ejpam-2515	295	22	,	,	PUNCT
ejpam-2515	295	23	y	y	PROPN
ejpam-2515	295	24	}	}	PUNCT
ejpam-2515	295	25	⇐	⇐	ADJ
ejpam-2515	295	26	⇒	⇒	NOUN
ejpam-2515	295	27	∀x	∀x	NUM
ejpam-2515	295	28	6=	6=	ADP
ejpam-2515	295	29	y	y	PROPN
ejpam-2515	295	30	,	,	PUNCT
ejpam-2515	295	31	(	(	PUNCT
ejpam-2515	295	32	x	x	X
ejpam-2515	295	33	,	,	PUNCT
ejpam-2515	295	34	a	a	PRON
ejpam-2515	295	35	,	,	PUNCT
ejpam-2515	295	36	y	y	NOUN
ejpam-2515	295	37	)	)	PUNCT
ejpam-2515	295	38	∈	∈	NOUN
ejpam-2515	295	39	ρ	ρ	X
ejpam-2515	295	40	∀x	∀x	X
ejpam-2515	295	41	∈	∈	PROPN
ejpam-2515	295	42	h	h	NOUN
ejpam-2515	295	43	,	,	PUNCT
ejpam-2515	295	44	x	x	PUNCT
ejpam-2515	295	45	◦	◦	NOUN
ejpam-2515	295	46	ρ	ρ	NOUN
ejpam-2515	295	47	a	a	X
ejpam-2515	295	48	=	=	X
ejpam-2515	295	49	{	{	PUNCT
ejpam-2515	295	50	x}=	x}=	PROPN
ejpam-2515	295	51	x	x	SYM
ejpam-2515	295	52	⊗	⊗	PROPN
ejpam-2515	295	53	ρ	ρ	PROPN
ejpam-2515	295	54	a	a	DET
ejpam-2515	295	55	⇐	⇐	ADJ
ejpam-2515	295	56	⇒	⇒	NOUN
ejpam-2515	295	57	(	(	PUNCT
ejpam-2515	295	58	x	x	X
ejpam-2515	295	59	,	,	PUNCT
ejpam-2515	295	60	x	x	X
ejpam-2515	295	61	,	,	PUNCT
ejpam-2515	295	62	a	a	PRON
ejpam-2515	295	63	)	)	PUNCT
ejpam-2515	295	64	∈	∈	PROPN
ejpam-2515	295	65	ρ	ρ	NOUN
ejpam-2515	295	66	if	if	SCONJ
ejpam-2515	295	67	(	(	PUNCT
ejpam-2515	295	68	x	x	NOUN
ejpam-2515	295	69	′	′	NUM
ejpam-2515	295	70	,	,	PUNCT
ejpam-2515	295	71	a′	a′	PROPN
ejpam-2515	295	72	,	,	PUNCT
ejpam-2515	295	73	y	y	PROPN
ejpam-2515	295	74	′	′	NOUN
ejpam-2515	295	75	)	)	PUNCT
ejpam-2515	295	76	∈	∈	PROPN
ejpam-2515	295	77	ρ	ρ	PROPN
ejpam-2515	295	78	and	and	CCONJ
ejpam-2515	295	79	x	x	SYM
ejpam-2515	295	80	′	′	NUM
ejpam-2515	295	81	,	,	PUNCT
ejpam-2515	295	82	a′	a′	PROPN
ejpam-2515	295	83	,	,	PUNCT
ejpam-2515	295	84	z′	z′	PROPN
ejpam-2515	295	85	,	,	PUNCT
ejpam-2515	295	86	a	a	PRON
ejpam-2515	295	87	are	be	AUX
ejpam-2515	295	88	distinct	distinct	ADJ
ejpam-2515	295	89	,	,	PUNCT
ejpam-2515	295	90	then	then	ADV
ejpam-2515	295	91	we	we	PRON
ejpam-2515	295	92	extend	extend	VERB
ejpam-2515	295	93	the	the	DET
ejpam-2515	295	94	product	product	NOUN
ejpam-2515	295	95	as	as	SCONJ
ejpam-2515	295	96	follows	follow	VERB
ejpam-2515	295	97	:	:	PUNCT
ejpam-2515	295	98	a	a	DET
ejpam-2515	295	99	◦	◦	NOUN
ejpam-2515	295	100	ρ	ρ	NOUN
ejpam-2515	295	101	a′	a′	NOUN
ejpam-2515	295	102	=	=	SYM
ejpam-2515	295	103	{	{	PUNCT
ejpam-2515	295	104	a	a	X
ejpam-2515	295	105	,	,	PUNCT
ejpam-2515	295	106	a′	a′	ADJ
ejpam-2515	295	107	}	}	PUNCT
ejpam-2515	295	108	whenever	whenever	SCONJ
ejpam-2515	295	109	6	6	NUM
ejpam-2515	295	110	∃	∃	PROPN
ejpam-2515	295	111	u	u	NOUN
ejpam-2515	295	112	∈	∈	PROPN
ejpam-2515	295	113	h	h	NOUN
ejpam-2515	295	114	such	such	ADJ
ejpam-2515	295	115	that	that	SCONJ
ejpam-2515	295	116	(	(	PUNCT
ejpam-2515	295	117	a	a	PRON
ejpam-2515	295	118	,	,	PUNCT
ejpam-2515	295	119	u	u	NOUN
ejpam-2515	295	120	,	,	PUNCT
ejpam-2515	295	121	a′	a′	PROPN
ejpam-2515	295	122	)	)	PUNCT
ejpam-2515	295	123	∈	∈	PROPN
ejpam-2515	295	124	ρ	ρ	PROPN
ejpam-2515	295	125	.	.	PUNCT
ejpam-2515	296	1	again	again	ADV
ejpam-2515	296	2	,	,	PUNCT
ejpam-2515	296	3	if	if	SCONJ
ejpam-2515	296	4	(	(	PUNCT
ejpam-2515	296	5	a	a	DET
ejpam-2515	296	6	,	,	PUNCT
ejpam-2515	296	7	u	u	NOUN
ejpam-2515	296	8	,	,	PUNCT
ejpam-2515	296	9	a′	a′	PROPN
ejpam-2515	296	10	)	)	PUNCT
ejpam-2515	296	11	∈	∈	PROPN
ejpam-2515	296	12	ρ	ρ	PROPN
ejpam-2515	296	13	,	,	PUNCT
ejpam-2515	296	14	then	then	ADV
ejpam-2515	296	15	we	we	PRON
ejpam-2515	296	16	define	define	VERB
ejpam-2515	296	17	the	the	DET
ejpam-2515	296	18	product	product	NOUN
ejpam-2515	296	19	recursively	recursively	ADV
ejpam-2515	296	20	as	as	ADP
ejpam-2515	296	21	above	above	ADJ
ejpam-2515	296	22	.	.	PUNCT
ejpam-2515	297	1	proposition	proposition	NOUN
ejpam-2515	297	2	8	8	NUM
ejpam-2515	297	3	.	.	PUNCT
ejpam-2515	298	1	let	let	VERB
ejpam-2515	298	2	ρ	ρ	NOUN
ejpam-2515	298	3	be	be	AUX
ejpam-2515	298	4	a	a	DET
ejpam-2515	298	5	reflexive	reflexive	ADJ
ejpam-2515	298	6	and	and	CCONJ
ejpam-2515	298	7	symmetric	symmetric	ADJ
ejpam-2515	298	8	ternary	ternary	ADJ
ejpam-2515	298	9	relation	relation	NOUN
ejpam-2515	298	10	on	on	ADP
ejpam-2515	298	11	h	h	NOUN
ejpam-2515	298	12	with	with	ADP
ejpam-2515	298	13	|h|	|h|	PROPN
ejpam-2515	298	14	≥	≥	NUM
ejpam-2515	298	15	3	3	NUM
ejpam-2515	298	16	such	such	ADJ
ejpam-2515	299	1	that	that	PRON
ejpam-2515	299	2	ρ1,3	ρ1,3	PROPN
ejpam-2515	300	1	=	=	SYM
ejpam-2515	301	1	h	h	PROPN
ejpam-2515	302	1	×h	×h	NOUN
ejpam-2515	302	2	.	.	PUNCT
ejpam-2515	303	1	if	if	SCONJ
ejpam-2515	303	2	ρ	ρ	PROPN
ejpam-2515	303	3	satisfies	satisfy	VERB
ejpam-2515	303	4	the	the	DET
ejpam-2515	303	5	following	follow	VERB
ejpam-2515	303	6	conditions	condition	NOUN
ejpam-2515	303	7	:	:	PUNCT
ejpam-2515	303	8	(	(	PUNCT
ejpam-2515	303	9	i	i	NOUN
ejpam-2515	303	10	)	)	PUNCT
ejpam-2515	303	11	any	any	DET
ejpam-2515	303	12	(	(	PUNCT
ejpam-2515	303	13	a	a	PRON
ejpam-2515	303	14	,	,	PUNCT
ejpam-2515	303	15	b	b	NOUN
ejpam-2515	303	16	,	,	PUNCT
ejpam-2515	303	17	c	c	NOUN
ejpam-2515	303	18	)	)	PUNCT
ejpam-2515	303	19	∈	∈	PROPN
ejpam-2515	303	20	ρ	ρ	PROPN
ejpam-2515	303	21	with	with	ADP
ejpam-2515	303	22	a	a	DET
ejpam-2515	303	23	,	,	PUNCT
ejpam-2515	303	24	b	b	NOUN
ejpam-2515	303	25	,	,	PUNCT
ejpam-2515	303	26	c	c	X
ejpam-2515	303	27	distinct	distinct	ADJ
ejpam-2515	303	28	=	=	NOUN
ejpam-2515	303	29	⇒	⇒	NOUN
ejpam-2515	303	30	(	(	PUNCT
ejpam-2515	303	31	x	x	X
ejpam-2515	303	32	,	,	PUNCT
ejpam-2515	303	33	b	b	PROPN
ejpam-2515	303	34	,	,	PUNCT
ejpam-2515	303	35	y	y	NOUN
ejpam-2515	303	36	)	)	PUNCT
ejpam-2515	303	37	∈	∈	PROPN
ejpam-2515	303	38	ρ	ρ	PROPN
ejpam-2515	303	39	,	,	PUNCT
ejpam-2515	303	40	∀(x	∀(x	X
ejpam-2515	303	41	,	,	PUNCT
ejpam-2515	303	42	y	y	NOUN
ejpam-2515	303	43	)	)	PUNCT
ejpam-2515	303	44	∈	∈	PROPN
ejpam-2515	303	45	h2	h2	NOUN
ejpam-2515	303	46	and	and	CCONJ
ejpam-2515	303	47	x	x	SYM
ejpam-2515	303	48	6=	6=	PROPN
ejpam-2515	303	49	y	y	PROPN
ejpam-2515	303	50	(	(	PUNCT
ejpam-2515	303	51	ii	ii	PROPN
ejpam-2515	303	52	)	)	PUNCT
ejpam-2515	303	53	∀(x	∀(x	PROPN
ejpam-2515	303	54	,	,	PUNCT
ejpam-2515	303	55	y	y	NOUN
ejpam-2515	303	56	)	)	PUNCT
ejpam-2515	303	57	∈	∈	PROPN
ejpam-2515	303	58	h2	h2	NOUN
ejpam-2515	303	59	,	,	PUNCT
ejpam-2515	303	60	x	x	PROPN
ejpam-2515	303	61	6=	6=	PROPN
ejpam-2515	303	62	y	y	PROPN
ejpam-2515	303	63	,	,	PUNCT
ejpam-2515	303	64	(	(	PUNCT
ejpam-2515	303	65	x	x	X
ejpam-2515	303	66	,	,	PUNCT
ejpam-2515	303	67	y	y	PROPN
ejpam-2515	303	68	,	,	PUNCT
ejpam-2515	303	69	x	x	NOUN
ejpam-2515	303	70	)	)	PUNCT
ejpam-2515	303	71	6∈	6∈	PROPN
ejpam-2515	303	72	ρ	ρ	PROPN
ejpam-2515	303	73	(	(	PUNCT
ejpam-2515	303	74	iii	iii	NOUN
ejpam-2515	303	75	)	)	PUNCT
ejpam-2515	303	76	∀x	∀x	VERB
ejpam-2515	303	77	∈	∈	PROPN
ejpam-2515	303	78	h	h	NOUN
ejpam-2515	303	79	,	,	PUNCT
ejpam-2515	303	80	(	(	PUNCT
ejpam-2515	303	81	x	x	X
ejpam-2515	303	82	,	,	PUNCT
ejpam-2515	303	83	x	x	X
ejpam-2515	303	84	,	,	PUNCT
ejpam-2515	303	85	b	b	X
ejpam-2515	303	86	)	)	PUNCT
ejpam-2515	303	87	∈	∈	NOUN
ejpam-2515	303	88	ρ	ρ	NOUN
ejpam-2515	303	89	then	then	ADV
ejpam-2515	303	90	the	the	DET
ejpam-2515	303	91	extension	extension	NOUN
ejpam-2515	303	92	(	(	PUNCT
ejpam-2515	303	93	h;	h;	PROPN
ejpam-2515	303	94	◦	◦	NOUN
ejpam-2515	303	95	ρ	ρ	NOUN
ejpam-2515	303	96	)	)	PUNCT
ejpam-2515	303	97	of	of	ADP
ejpam-2515	303	98	(	(	PUNCT
ejpam-2515	303	99	h	h	NOUN
ejpam-2515	303	100	;	;	PUNCT
ejpam-2515	303	101	⊗	⊗	PROPN
ejpam-2515	303	102	ρ	ρ	PROPN
ejpam-2515	303	103	)	)	PUNCT
ejpam-2515	303	104	defined	define	VERB
ejpam-2515	303	105	by	by	ADP
ejpam-2515	303	106	setting	set	VERB
ejpam-2515	303	107	∀(x	∀(x	PRON
ejpam-2515	303	108	,	,	PUNCT
ejpam-2515	303	109	y	y	NOUN
ejpam-2515	303	110	)	)	PUNCT
ejpam-2515	303	111	∈	∈	PROPN
ejpam-2515	303	112	h2	h2	NOUN
ejpam-2515	303	113	,	,	PUNCT
ejpam-2515	303	114	x	x	PROPN
ejpam-2515	303	115	6=	6=	PROPN
ejpam-2515	303	116	y	y	PROPN
ejpam-2515	303	117	,	,	PUNCT
ejpam-2515	303	118	x	x	PUNCT
ejpam-2515	303	119	◦	◦	NOUN
ejpam-2515	303	120	ρ	ρ	X
ejpam-2515	303	121	y	y	NOUN
ejpam-2515	303	122	=	=	PRON
ejpam-2515	303	123	{	{	PUNCT
ejpam-2515	303	124	z	z	NOUN
ejpam-2515	303	125	|	|	NOUN
ejpam-2515	303	126	(	(	PUNCT
ejpam-2515	303	127	x	x	INTJ
ejpam-2515	303	128	,	,	PUNCT
ejpam-2515	303	129	z	z	PROPN
ejpam-2515	303	130	,	,	PUNCT
ejpam-2515	303	131	y	y	PROPN
ejpam-2515	303	132	)	)	PUNCT
ejpam-2515	303	133	∈	∈	PROPN
ejpam-2515	303	134	ρ	ρ	PROPN
ejpam-2515	303	135	}	}	PUNCT
ejpam-2515	303	136	∪	∪	NOUN
ejpam-2515	303	137	{	{	PUNCT
ejpam-2515	303	138	x	x	NOUN
ejpam-2515	303	139	,	,	PUNCT
ejpam-2515	303	140	y	y	PROPN
ejpam-2515	303	141	}	}	PUNCT
ejpam-2515	303	142	is	be	AUX
ejpam-2515	303	143	a	a	DET
ejpam-2515	303	144	join	join	NOUN
ejpam-2515	303	145	space	space	NOUN
ejpam-2515	303	146	.	.	PUNCT
ejpam-2515	304	1	proof	proof	NOUN
ejpam-2515	304	2	.	.	PUNCT
ejpam-2515	305	1	suppose	suppose	VERB
ejpam-2515	305	2	(	(	PUNCT
ejpam-2515	305	3	x	x	X
ejpam-2515	305	4	,	,	PUNCT
ejpam-2515	305	5	z	z	PROPN
ejpam-2515	305	6	,	,	PUNCT
ejpam-2515	305	7	y	y	PROPN
ejpam-2515	305	8	)	)	PUNCT
ejpam-2515	305	9	∈	∈	PROPN
ejpam-2515	305	10	ρ	ρ	PROPN
ejpam-2515	305	11	.	.	PUNCT
ejpam-2515	306	1	then	then	ADV
ejpam-2515	306	2	,	,	PUNCT
ejpam-2515	306	3	we	we	PRON
ejpam-2515	306	4	clearly	clearly	ADV
ejpam-2515	306	5	have	have	VERB
ejpam-2515	306	6	∀(x	∀(x	NUM
ejpam-2515	306	7	,	,	PUNCT
ejpam-2515	306	8	y	y	NOUN
ejpam-2515	306	9	)	)	PUNCT
ejpam-2515	306	10	∈	∈	PROPN
ejpam-2515	306	11	h2	h2	NOUN
ejpam-2515	306	12	,	,	PUNCT
ejpam-2515	306	13	x	x	PROPN
ejpam-2515	306	14	6=	6=	PROPN
ejpam-2515	306	15	y	y	PROPN
ejpam-2515	306	16	,	,	PUNCT
ejpam-2515	306	17	x	x	PUNCT
ejpam-2515	306	18	◦	◦	NOUN
ejpam-2515	306	19	ρ	ρ	X
ejpam-2515	306	20	y	y	NOUN
ejpam-2515	306	21	=	=	PRON
ejpam-2515	306	22	{	{	PUNCT
ejpam-2515	306	23	z	z	NOUN
ejpam-2515	307	1	|	|	NOUN
ejpam-2515	307	2	(	(	PUNCT
ejpam-2515	307	3	x	x	INTJ
ejpam-2515	307	4	,	,	PUNCT
ejpam-2515	307	5	z	z	PROPN
ejpam-2515	307	6	,	,	PUNCT
ejpam-2515	307	7	y	y	PROPN
ejpam-2515	307	8	)	)	PUNCT
ejpam-2515	307	9	∈	∈	PROPN
ejpam-2515	307	10	ρ	ρ	PROPN
ejpam-2515	307	11	}	}	PUNCT
ejpam-2515	307	12	∪	∪	NOUN
ejpam-2515	307	13	{	{	PUNCT
ejpam-2515	307	14	x	x	NOUN
ejpam-2515	307	15	,	,	PUNCT
ejpam-2515	307	16	y	y	PROPN
ejpam-2515	307	17	}	}	PUNCT
ejpam-2515	307	18	∀x	∀x	VERB
ejpam-2515	307	19	∈	∈	PROPN
ejpam-2515	307	20	h	h	NOUN
ejpam-2515	307	21	,	,	PUNCT
ejpam-2515	307	22	x	x	PUNCT
ejpam-2515	307	23	◦	◦	NOUN
ejpam-2515	307	24	ρ	ρ	NOUN
ejpam-2515	307	25	x	x	SYM
ejpam-2515	307	26	=	=	PRON
ejpam-2515	307	27	{	{	PUNCT
ejpam-2515	307	28	x	x	NOUN
ejpam-2515	307	29	}	}	PUNCT
ejpam-2515	307	30	∀x	∀x	VERB
ejpam-2515	307	31	∈	∈	PROPN
ejpam-2515	307	32	h	h	NOUN
ejpam-2515	307	33	,	,	PUNCT
ejpam-2515	307	34	x	x	PUNCT
ejpam-2515	307	35	◦	◦	NOUN
ejpam-2515	307	36	ρ	ρ	NOUN
ejpam-2515	307	37	z	z	NOUN
ejpam-2515	307	38	=	=	SYM
ejpam-2515	307	39	{	{	PUNCT
ejpam-2515	307	40	x	x	NOUN
ejpam-2515	307	41	}	}	PUNCT
ejpam-2515	307	42	since	since	SCONJ
ejpam-2515	307	43	,	,	PUNCT
ejpam-2515	307	44	for	for	ADP
ejpam-2515	307	45	any	any	DET
ejpam-2515	307	46	x	x	SYM
ejpam-2515	307	47	,	,	PUNCT
ejpam-2515	307	48	y	y	PROPN
ejpam-2515	307	49	∈	∈	PROPN
ejpam-2515	307	50	h	h	NOUN
ejpam-2515	307	51	,	,	PUNCT
ejpam-2515	307	52	{	{	PUNCT
ejpam-2515	307	53	x	x	INTJ
ejpam-2515	307	54	,	,	PUNCT
ejpam-2515	307	55	y	y	PROPN
ejpam-2515	307	56	}	}	PUNCT
ejpam-2515	307	57	⊂	⊂	PROPN
ejpam-2515	307	58	x	x	PUNCT
ejpam-2515	307	59	◦	◦	VERB
ejpam-2515	307	60	ρ	ρ	NUM
ejpam-2515	307	61	y	y	NOUN
ejpam-2515	307	62	;	;	PUNCT
ejpam-2515	307	63	it	it	PRON
ejpam-2515	307	64	follows	follow	VERB
ejpam-2515	307	65	that	that	SCONJ
ejpam-2515	307	66	(	(	PUNCT
ejpam-2515	307	67	h;	h;	NOUN
ejpam-2515	307	68	◦	◦	NOUN
ejpam-2515	307	69	ρ	ρ	NOUN
ejpam-2515	307	70	)	)	PUNCT
ejpam-2515	307	71	is	be	AUX
ejpam-2515	307	72	a	a	DET
ejpam-2515	307	73	quasihypergroup	quasihypergroup	NOUN
ejpam-2515	307	74	.	.	PUNCT
ejpam-2515	308	1	moreover	moreover	ADV
ejpam-2515	308	2	,	,	PUNCT
ejpam-2515	308	3	since	since	SCONJ
ejpam-2515	308	4	ρ	ρ	PROPN
ejpam-2515	308	5	is	be	AUX
ejpam-2515	308	6	symmetric	symmetric	ADJ
ejpam-2515	308	7	,	,	PUNCT
ejpam-2515	308	8	it	it	PRON
ejpam-2515	308	9	follows	follow	VERB
ejpam-2515	308	10	that	that	SCONJ
ejpam-2515	308	11	x	x	PUNCT
ejpam-2515	308	12	◦	◦	NOUN
ejpam-2515	308	13	ρ	ρ	NOUN
ejpam-2515	308	14	y	y	NOUN
ejpam-2515	308	15	=	=	SYM
ejpam-2515	308	16	y	y	PROPN
ejpam-2515	308	17	◦	◦	NOUN
ejpam-2515	308	18	ρ	ρ	PROPN
ejpam-2515	308	19	x	x	VERB
ejpam-2515	308	20	,	,	PUNCT
ejpam-2515	308	21	for	for	ADP
ejpam-2515	308	22	any	any	DET
ejpam-2515	308	23	x	x	SYM
ejpam-2515	308	24	,	,	PUNCT
ejpam-2515	308	25	y	y	PROPN
ejpam-2515	308	26	∈	∈	PROPN
ejpam-2515	308	27	h	h	NOUN
ejpam-2515	308	28	,	,	PUNCT
ejpam-2515	308	29	and	and	CCONJ
ejpam-2515	308	30	therefore	therefore	ADV
ejpam-2515	308	31	(	(	PUNCT
ejpam-2515	308	32	h;	h;	NOUN
ejpam-2515	308	33	◦	◦	NOUN
ejpam-2515	308	34	ρ	ρ	NOUN
ejpam-2515	308	35	)	)	PUNCT
ejpam-2515	308	36	is	be	AUX
ejpam-2515	308	37	commutative	commutative	ADJ
ejpam-2515	308	38	.	.	PUNCT
ejpam-2515	309	1	now	now	ADV
ejpam-2515	309	2	,	,	PUNCT
ejpam-2515	309	3	we	we	PRON
ejpam-2515	309	4	prove	prove	VERB
ejpam-2515	309	5	that	that	SCONJ
ejpam-2515	309	6	the	the	DET
ejpam-2515	309	7	hyper	hyper	ADJ
ejpam-2515	309	8	operation	operation	NOUN
ejpam-2515	309	9	<	<	X
ejpam-2515	309	10	◦	◦	NOUN
ejpam-2515	309	11	ρ	ρ	X
ejpam-2515	309	12	>	>	X
ejpam-2515	309	13	is	be	AUX
ejpam-2515	309	14	associative	associative	ADJ
ejpam-2515	309	15	.	.	PUNCT
ejpam-2515	310	1	we	we	PRON
ejpam-2515	310	2	have	have	VERB
ejpam-2515	310	3	clearly	clearly	ADV
ejpam-2515	310	4	,	,	PUNCT
ejpam-2515	310	5	x	x	PUNCT
ejpam-2515	310	6	◦	◦	NOUN
ejpam-2515	310	7	ρ	ρ	X
ejpam-2515	310	8	(	(	PUNCT
ejpam-2515	310	9	y	y	PROPN
ejpam-2515	310	10	◦	◦	PROPN
ejpam-2515	310	11	ρ	ρ	PROPN
ejpam-2515	310	12	z	z	NOUN
ejpam-2515	310	13	)	)	PUNCT
ejpam-2515	311	1	=	=	NOUN
ejpam-2515	311	2	x	x	SYM
ejpam-2515	311	3	◦	◦	NOUN
ejpam-2515	311	4	ρ	ρ	X
ejpam-2515	311	5	{	{	PUNCT
ejpam-2515	311	6	y	y	PROPN
ejpam-2515	311	7	,	,	PUNCT
ejpam-2515	311	8	z′	z′	PROPN
ejpam-2515	311	9	,	,	PUNCT
ejpam-2515	311	10	z	z	NOUN
ejpam-2515	312	1	|	|	NOUN
ejpam-2515	312	2	(	(	PUNCT
ejpam-2515	312	3	y	y	PROPN
ejpam-2515	312	4	,	,	PUNCT
ejpam-2515	312	5	z′	z′	PROPN
ejpam-2515	312	6	,	,	PUNCT
ejpam-2515	312	7	z	z	NOUN
ejpam-2515	312	8	)	)	PUNCT
ejpam-2515	312	9	∈	∈	PROPN
ejpam-2515	312	10	ρ	ρ	NOUN
ejpam-2515	312	11	}	}	PUNCT
ejpam-2515	312	12	=	=	NOUN
ejpam-2515	312	13	x	x	SYM
ejpam-2515	312	14	◦	◦	NOUN
ejpam-2515	312	15	ρ	ρ	X
ejpam-2515	312	16	y	y	PROPN
ejpam-2515	312	17	∪	∪	NOUN
ejpam-2515	312	18	x	x	PUNCT
ejpam-2515	312	19	◦	◦	NOUN
ejpam-2515	312	20	ρ	ρ	NOUN
ejpam-2515	312	21	z′	z′	NUM
ejpam-2515	312	22	∪	∪	X
ejpam-2515	312	23	x	x	SYM
ejpam-2515	312	24	◦	◦	NOUN
ejpam-2515	312	25	ρ	ρ	X
ejpam-2515	312	26	{	{	PUNCT
ejpam-2515	312	27	z′	z′	NUM
ejpam-2515	312	28	|	|	NOUN
ejpam-2515	312	29	(	(	PUNCT
ejpam-2515	312	30	y	y	PROPN
ejpam-2515	312	31	,	,	PUNCT
ejpam-2515	312	32	z′	z′	PROPN
ejpam-2515	312	33	,	,	PUNCT
ejpam-2515	312	34	z	z	NOUN
ejpam-2515	312	35	)	)	PUNCT
ejpam-2515	312	36	∈	∈	PROPN
ejpam-2515	312	37	ρ	ρ	NOUN
ejpam-2515	312	38	}	}	PUNCT
ejpam-2515	312	39	=	=	NOUN
ejpam-2515	312	40	x	x	SYM
ejpam-2515	312	41	◦	◦	NOUN
ejpam-2515	312	42	ρ	ρ	X
ejpam-2515	312	43	y	y	PROPN
ejpam-2515	312	44	∪	∪	NOUN
ejpam-2515	312	45	x	x	PUNCT
ejpam-2515	312	46	◦	◦	NOUN
ejpam-2515	312	47	ρ	ρ	PROPN
ejpam-2515	312	48	z	z	PROPN
ejpam-2515	312	49	,	,	PUNCT
ejpam-2515	312	50	since	since	SCONJ
ejpam-2515	312	51	x	x	ADP
ejpam-2515	312	52	◦	◦	NOUN
ejpam-2515	312	53	ρ	ρ	NOUN
ejpam-2515	312	54	z′	z′	NUM
ejpam-2515	312	55	=	=	SYM
ejpam-2515	312	56	{	{	PUNCT
ejpam-2515	312	57	x	x	NOUN
ejpam-2515	312	58	}	}	PUNCT
ejpam-2515	312	59	⊂	⊂	PROPN
ejpam-2515	312	60	x	x	PUNCT
ejpam-2515	312	61	◦	◦	NOUN
ejpam-2515	312	62	ρ	ρ	NUM
ejpam-2515	312	63	y	y	NOUN
ejpam-2515	312	64	=	=	ADJ
ejpam-2515	312	65	x	x	SYM
ejpam-2515	312	66	◦	◦	NOUN
ejpam-2515	312	67	ρ	ρ	X
ejpam-2515	312	68	y	y	PROPN
ejpam-2515	312	69	∪	∪	NOUN
ejpam-2515	312	70	x	x	VERB
ejpam-2515	312	71	◦	◦	NOUN
ejpam-2515	312	72	ρ	ρ	X
ejpam-2515	312	73	{	{	PUNCT
ejpam-2515	312	74	x	x	PROPN
ejpam-2515	312	75	,	,	PUNCT
ejpam-2515	312	76	z′′	z′′	NOUN
ejpam-2515	312	77	,	,	PUNCT
ejpam-2515	312	78	z	z	NOUN
ejpam-2515	312	79	|	|	NOUN
ejpam-2515	312	80	(	(	PUNCT
ejpam-2515	312	81	x	x	INTJ
ejpam-2515	312	82	,	,	PUNCT
ejpam-2515	312	83	z′′	z′′	NOUN
ejpam-2515	312	84	,	,	PUNCT
ejpam-2515	312	85	z	z	NOUN
ejpam-2515	312	86	)	)	PUNCT
ejpam-2515	312	87	∈	∈	PROPN
ejpam-2515	312	88	ρ	ρ	PROPN
ejpam-2515	312	89	}	}	PUNCT
ejpam-2515	312	90	,	,	PUNCT
ejpam-2515	312	91	since	since	SCONJ
ejpam-2515	312	92	x	x	ADP
ejpam-2515	312	93	◦	◦	NOUN
ejpam-2515	312	94	ρ	ρ	NOUN
ejpam-2515	312	95	z	z	NOUN
ejpam-2515	312	96	=	=	PUNCT
ejpam-2515	312	97	{	{	PUNCT
ejpam-2515	312	98	z′′	z′′	PROPN
ejpam-2515	312	99	|	|	ADV
ejpam-2515	312	100	{	{	PUNCT
ejpam-2515	312	101	x	x	INTJ
ejpam-2515	312	102	,	,	PUNCT
ejpam-2515	312	103	z′′	z′′	NOUN
ejpam-2515	312	104	,	,	PUNCT
ejpam-2515	312	105	z	z	NOUN
ejpam-2515	312	106	)	)	PUNCT
ejpam-2515	312	107	∈	∈	PROPN
ejpam-2515	312	108	ρ	ρ	PROPN
ejpam-2515	312	109	}	}	PUNCT
ejpam-2515	312	110	∪	∪	NOUN
ejpam-2515	312	111	{	{	PUNCT
ejpam-2515	312	112	x	x	NOUN
ejpam-2515	312	113	,	,	PUNCT
ejpam-2515	312	114	z	z	NOUN
ejpam-2515	312	115	}	}	PUNCT
ejpam-2515	312	116	=(	=(	NOUN
ejpam-2515	312	117	x	x	SYM
ejpam-2515	312	118	◦	◦	NOUN
ejpam-2515	312	119	ρ	ρ	NUM
ejpam-2515	312	120	y	y	NOUN
ejpam-2515	312	121	)	)	PUNCT
ejpam-2515	312	122	◦	◦	NOUN
ejpam-2515	312	123	ρ	ρ	PROPN
ejpam-2515	312	124	z	z	PROPN
ejpam-2515	312	125	,	,	PUNCT
ejpam-2515	312	126	since	since	SCONJ
ejpam-2515	312	127	{	{	PUNCT
ejpam-2515	312	128	x	x	INTJ
ejpam-2515	312	129	,	,	PUNCT
ejpam-2515	312	130	z′′	z′′	PROPN
ejpam-2515	312	131	}	}	PUNCT
ejpam-2515	312	132	⊂	⊂	PROPN
ejpam-2515	312	133	(	(	PUNCT
ejpam-2515	312	134	x	x	SYM
ejpam-2515	312	135	◦	◦	NOUN
ejpam-2515	312	136	ρ	ρ	NUM
ejpam-2515	312	137	y	y	NOUN
ejpam-2515	312	138	)	)	PUNCT
ejpam-2515	312	139	it	it	PRON
ejpam-2515	312	140	remains	remain	VERB
ejpam-2515	312	141	to	to	PART
ejpam-2515	312	142	check	check	VERB
ejpam-2515	312	143	the	the	DET
ejpam-2515	312	144	condition	condition	NOUN
ejpam-2515	312	145	of	of	ADP
ejpam-2515	312	146	the	the	DET
ejpam-2515	312	147	join	join	NOUN
ejpam-2515	312	148	space	space	NOUN
ejpam-2515	312	149	.	.	PUNCT
ejpam-2515	313	1	set	set	VERB
ejpam-2515	313	2	a	a	DET
ejpam-2515	313	3	,	,	PUNCT
ejpam-2515	313	4	b	b	NOUN
ejpam-2515	313	5	,	,	PUNCT
ejpam-2515	313	6	c	c	NOUN
ejpam-2515	313	7	,	,	PUNCT
ejpam-2515	313	8	d	d	PROPN
ejpam-2515	313	9	∈	∈	PROPN
ejpam-2515	313	10	h	h	NOUN
ejpam-2515	313	11	such	such	ADJ
ejpam-2515	313	12	that	that	SCONJ
ejpam-2515	313	13	a	a	DET
ejpam-2515	313	14	/	/	SYM
ejpam-2515	313	15	b	b	NOUN
ejpam-2515	313	16	∩	∩	ADJ
ejpam-2515	313	17	c	c	X
ejpam-2515	313	18	/	/	SYM
ejpam-2515	313	19	d	d	NOUN
ejpam-2515	313	20	6=	6=	NUM
ejpam-2515	313	21	;	;	PUNCT
ejpam-2515	313	22	;	;	PUNCT
ejpam-2515	313	23	then	then	ADV
ejpam-2515	313	24	there	there	PRON
ejpam-2515	313	25	exists	exist	VERB
ejpam-2515	313	26	x	x	X
ejpam-2515	313	27	∈	∈	PROPN
ejpam-2515	313	28	a	a	DET
ejpam-2515	313	29	/	/	SYM
ejpam-2515	313	30	b	b	NOUN
ejpam-2515	313	31	∩	∩	ADJ
ejpam-2515	313	32	c	c	X
ejpam-2515	313	33	/	/	SYM
ejpam-2515	313	34	d	d	NOUN
ejpam-2515	313	35	,	,	PUNCT
ejpam-2515	313	36	that	that	PRON
ejpam-2515	313	37	is	be	AUX
ejpam-2515	313	38	a	a	DET
ejpam-2515	313	39	∈	∈	PROPN
ejpam-2515	313	40	x	x	PUNCT
ejpam-2515	313	41	◦	◦	NOUN
ejpam-2515	313	42	ρ	ρ	X
ejpam-2515	313	43	b	b	NOUN
ejpam-2515	313	44	=	=	PRON
ejpam-2515	313	45	{	{	PUNCT
ejpam-2515	313	46	z	z	NOUN
ejpam-2515	313	47	|	|	NOUN
ejpam-2515	313	48	(	(	PUNCT
ejpam-2515	313	49	x	x	INTJ
ejpam-2515	313	50	,	,	PUNCT
ejpam-2515	313	51	z	z	PROPN
ejpam-2515	313	52	,	,	PUNCT
ejpam-2515	313	53	b	b	NOUN
ejpam-2515	313	54	)	)	PUNCT
ejpam-2515	313	55	∈	∈	PROPN
ejpam-2515	313	56	ρ	ρ	PROPN
ejpam-2515	313	57	}	}	PUNCT
ejpam-2515	313	58	∪	∪	NOUN
ejpam-2515	313	59	{	{	PUNCT
ejpam-2515	313	60	x	x	NOUN
ejpam-2515	313	61	,	,	PUNCT
ejpam-2515	313	62	b	b	NOUN
ejpam-2515	313	63	}	}	PUNCT
ejpam-2515	313	64	and	and	CCONJ
ejpam-2515	313	65	c	c	NOUN
ejpam-2515	313	66	∈	∈	PROPN
ejpam-2515	313	67	x	x	PUNCT
ejpam-2515	313	68	◦	◦	NOUN
ejpam-2515	313	69	ρ	ρ	X
ejpam-2515	314	1	d	d	NOUN
ejpam-2515	314	2	=	=	PRON
ejpam-2515	314	3	{	{	PUNCT
ejpam-2515	314	4	z	z	NOUN
ejpam-2515	314	5	|	|	NOUN
ejpam-2515	314	6	(	(	PUNCT
ejpam-2515	314	7	x	x	INTJ
ejpam-2515	314	8	,	,	PUNCT
ejpam-2515	314	9	z	z	NOUN
ejpam-2515	314	10	,	,	PUNCT
ejpam-2515	314	11	d	d	NOUN
ejpam-2515	314	12	)	)	PUNCT
ejpam-2515	314	13	∈	∈	PROPN
ejpam-2515	314	14	ρ	ρ	PROPN
ejpam-2515	314	15	}	}	PUNCT
ejpam-2515	314	16	∪	∪	NOUN
ejpam-2515	314	17	{	{	PUNCT
ejpam-2515	314	18	x	x	NOUN
ejpam-2515	314	19	,	,	PUNCT
ejpam-2515	314	20	d	d	NOUN
ejpam-2515	314	21	}	}	PUNCT
ejpam-2515	314	22	.	.	PUNCT
ejpam-2515	315	1	we	we	PRON
ejpam-2515	315	2	consider	consider	VERB
ejpam-2515	315	3	the	the	DET
ejpam-2515	315	4	following	follow	VERB
ejpam-2515	315	5	situations	situation	NOUN
ejpam-2515	315	6	:	:	PUNCT
ejpam-2515	315	7	s.	s.	PROPN
ejpam-2515	315	8	govindarajan	govindarajan	PROPN
ejpam-2515	315	9	/	/	SYM
ejpam-2515	315	10	eur	eur	PROPN
ejpam-2515	315	11	.	.	PUNCT
ejpam-2515	316	1	j.	j.	PROPN
ejpam-2515	316	2	pure	pure	PROPN
ejpam-2515	316	3	appl	appl	PROPN
ejpam-2515	316	4	.	.	PROPN
ejpam-2515	316	5	math	math	PROPN
ejpam-2515	316	6	,	,	PUNCT
ejpam-2515	316	7	9	9	NUM
ejpam-2515	316	8	(	(	PUNCT
ejpam-2515	316	9	2016	2016	NUM
ejpam-2515	316	10	)	)	PUNCT
ejpam-2515	316	11	,	,	PUNCT
ejpam-2515	316	12	367	367	NUM
ejpam-2515	316	13	-	-	SYM
ejpam-2515	316	14	382	382	NUM
ejpam-2515	316	15	377	377	NUM
ejpam-2515	316	16	(	(	PUNCT
ejpam-2515	316	17	i	i	NOUN
ejpam-2515	316	18	)	)	PUNCT
ejpam-2515	316	19	let	let	VERB
ejpam-2515	316	20	a	a	DET
ejpam-2515	316	21	,	,	PUNCT
ejpam-2515	316	22	b	b	NOUN
ejpam-2515	316	23	,	,	PUNCT
ejpam-2515	316	24	c	c	NOUN
ejpam-2515	316	25	,	,	PUNCT
ejpam-2515	316	26	d	d	NOUN
ejpam-2515	316	27	,	,	PUNCT
ejpam-2515	316	28	z	z	PROPN
ejpam-2515	316	29	are	be	AUX
ejpam-2515	316	30	distinct	distinct	ADJ
ejpam-2515	316	31	and	and	CCONJ
ejpam-2515	316	32	z	z	NOUN
ejpam-2515	316	33	∈	∈	PROPN
ejpam-2515	316	34	a	a	DET
ejpam-2515	316	35	◦	◦	NOUN
ejpam-2515	316	36	ρ	ρ	PROPN
ejpam-2515	316	37	d.	d.	PROPN
ejpam-2515	316	38	recall	recall	VERB
ejpam-2515	316	39	that	that	SCONJ
ejpam-2515	316	40	,	,	PUNCT
ejpam-2515	316	41	for	for	ADP
ejpam-2515	316	42	any	any	DET
ejpam-2515	316	43	x	x	SYM
ejpam-2515	316	44	6=	6=	PROPN
ejpam-2515	316	45	y	y	PROPN
ejpam-2515	316	46	6=	6=	PROPN
ejpam-2515	316	47	z	z	PROPN
ejpam-2515	316	48	,	,	PUNCT
ejpam-2515	316	49	(	(	PUNCT
ejpam-2515	316	50	x	x	X
ejpam-2515	316	51	,	,	PUNCT
ejpam-2515	316	52	z	z	PROPN
ejpam-2515	316	53	,	,	PUNCT
ejpam-2515	316	54	y	y	PROPN
ejpam-2515	316	55	)	)	PUNCT
ejpam-2515	316	56	∈	∈	PROPN
ejpam-2515	316	57	ρ	ρ	NOUN
ejpam-2515	316	58	=	=	NOUN
ejpam-2515	316	59	⇒	⇒	NOUN
ejpam-2515	316	60	(	(	PUNCT
ejpam-2515	316	61	x	x	SYM
ejpam-2515	316	62	′	′	NUM
ejpam-2515	316	63	,	,	PUNCT
ejpam-2515	316	64	z	z	PROPN
ejpam-2515	316	65	,	,	PUNCT
ejpam-2515	316	66	y	y	PROPN
ejpam-2515	316	67	′	′	NOUN
ejpam-2515	316	68	)	)	PUNCT
ejpam-2515	316	69	∈	∈	PROPN
ejpam-2515	316	70	ρ	ρ	PROPN
ejpam-2515	316	71	,	,	PUNCT
ejpam-2515	316	72	for	for	ADP
ejpam-2515	316	73	all	all	DET
ejpam-2515	316	74	x	x	NOUN
ejpam-2515	316	75	′	′	NUM
ejpam-2515	316	76	6=	6=	NUM
ejpam-2515	316	77	y	y	PROPN
ejpam-2515	316	78	′.	′.	NOUN
ejpam-2515	316	79	then	then	ADV
ejpam-2515	316	80	,	,	PUNCT
ejpam-2515	316	81	it	it	PRON
ejpam-2515	316	82	follows	follow	VERB
ejpam-2515	316	83	that	that	SCONJ
ejpam-2515	316	84	z	z	PROPN
ejpam-2515	316	85	∈	∈	PROPN
ejpam-2515	316	86	b	b	PROPN
ejpam-2515	316	87	◦	◦	NOUN
ejpam-2515	316	88	ρ	ρ	X
ejpam-2515	316	89	c	c	NOUN
ejpam-2515	316	90	and	and	CCONJ
ejpam-2515	316	91	therefore	therefore	ADV
ejpam-2515	316	92	z	z	PROPN
ejpam-2515	316	93	∈	∈	PROPN
ejpam-2515	316	94	a	a	DET
ejpam-2515	316	95	◦	◦	NOUN
ejpam-2515	316	96	ρ	ρ	NOUN
ejpam-2515	316	97	d	d	NOUN
ejpam-2515	316	98	∩	∩	X
ejpam-2515	316	99	b	b	X
ejpam-2515	316	100	◦	◦	PROPN
ejpam-2515	316	101	ρ	ρ	PROPN
ejpam-2515	316	102	c.	c.	NOUN
ejpam-2515	316	103	similarly	similarly	ADV
ejpam-2515	316	104	,	,	PUNCT
ejpam-2515	316	105	if	if	SCONJ
ejpam-2515	316	106	z	z	PROPN
ejpam-2515	316	107	∈	∈	PROPN
ejpam-2515	316	108	b	b	PROPN
ejpam-2515	316	109	◦	◦	NOUN
ejpam-2515	316	110	ρ	ρ	X
ejpam-2515	317	1	c	c	NOUN
ejpam-2515	318	1	then	then	ADV
ejpam-2515	318	2	z	z	PROPN
ejpam-2515	318	3	∈	∈	PROPN
ejpam-2515	318	4	a	a	DET
ejpam-2515	318	5	◦	◦	NOUN
ejpam-2515	318	6	ρ	ρ	NOUN
ejpam-2515	318	7	d	d	NOUN
ejpam-2515	318	8	∩	∩	X
ejpam-2515	318	9	b	b	X
ejpam-2515	318	10	◦	◦	NOUN
ejpam-2515	318	11	ρ	ρ	PROPN
ejpam-2515	318	12	c.	c.	PROPN
ejpam-2515	318	13	(	(	PUNCT
ejpam-2515	318	14	ii	ii	PROPN
ejpam-2515	318	15	)	)	PUNCT
ejpam-2515	318	16	if	if	SCONJ
ejpam-2515	318	17	a	a	DET
ejpam-2515	318	18	,	,	PUNCT
ejpam-2515	318	19	b	b	NOUN
ejpam-2515	318	20	,	,	PUNCT
ejpam-2515	318	21	c	c	NOUN
ejpam-2515	318	22	,	,	PUNCT
ejpam-2515	318	23	d	d	NOUN
ejpam-2515	318	24	,	,	PUNCT
ejpam-2515	318	25	z	z	PROPN
ejpam-2515	318	26	are	be	AUX
ejpam-2515	318	27	distinct	distinct	ADJ
ejpam-2515	318	28	and	and	CCONJ
ejpam-2515	318	29	a	a	DET
ejpam-2515	318	30	=	=	X
ejpam-2515	319	1	x	x	X
ejpam-2515	319	2	then	then	ADV
ejpam-2515	319	3	c	c	PROPN
ejpam-2515	319	4	∈	∈	PROPN
ejpam-2515	319	5	a	a	DET
ejpam-2515	319	6	◦	◦	NOUN
ejpam-2515	319	7	ρ	ρ	NOUN
ejpam-2515	319	8	d	d	PROPN
ejpam-2515	319	9	,	,	PUNCT
ejpam-2515	319	10	and	and	CCONJ
ejpam-2515	319	11	since	since	SCONJ
ejpam-2515	319	12	c	c	PROPN
ejpam-2515	319	13	∈	∈	PROPN
ejpam-2515	319	14	b	b	PROPN
ejpam-2515	319	15	◦	◦	NOUN
ejpam-2515	319	16	ρ	ρ	NOUN
ejpam-2515	319	17	c	c	NOUN
ejpam-2515	319	18	,	,	PUNCT
ejpam-2515	319	19	it	it	PRON
ejpam-2515	319	20	follows	follow	VERB
ejpam-2515	319	21	that	that	SCONJ
ejpam-2515	319	22	c	c	PROPN
ejpam-2515	319	23	∈	∈	PROPN
ejpam-2515	319	24	a	a	DET
ejpam-2515	319	25	◦	◦	NOUN
ejpam-2515	319	26	ρ	ρ	NOUN
ejpam-2515	319	27	d	d	NOUN
ejpam-2515	319	28	∩	∩	X
ejpam-2515	319	29	b	b	X
ejpam-2515	319	30	◦	◦	NOUN
ejpam-2515	319	31	ρ	ρ	PROPN
ejpam-2515	319	32	c.	c.	PROPN
ejpam-2515	319	33	(	(	PUNCT
ejpam-2515	319	34	iii	iii	PROPN
ejpam-2515	319	35	)	)	PUNCT
ejpam-2515	319	36	if	if	SCONJ
ejpam-2515	319	37	a	a	DET
ejpam-2515	319	38	,	,	PUNCT
ejpam-2515	319	39	b	b	NOUN
ejpam-2515	319	40	,	,	PUNCT
ejpam-2515	319	41	c	c	NOUN
ejpam-2515	319	42	,	,	PUNCT
ejpam-2515	319	43	d	d	NOUN
ejpam-2515	319	44	,	,	PUNCT
ejpam-2515	319	45	z	z	PROPN
ejpam-2515	319	46	are	be	AUX
ejpam-2515	319	47	distinct	distinct	ADJ
ejpam-2515	319	48	and	and	CCONJ
ejpam-2515	319	49	c	c	NOUN
ejpam-2515	319	50	=	=	PUNCT
ejpam-2515	320	1	x	x	X
ejpam-2515	320	2	then	then	ADV
ejpam-2515	320	3	a	a	DET
ejpam-2515	320	4	∈	∈	PROPN
ejpam-2515	320	5	c	c	PROPN
ejpam-2515	320	6	◦	◦	PROPN
ejpam-2515	320	7	ρ	ρ	PROPN
ejpam-2515	320	8	b.	b.	PROPN
ejpam-2515	320	9	by	by	ADP
ejpam-2515	320	10	the	the	DET
ejpam-2515	320	11	symmetry	symmetry	NOUN
ejpam-2515	320	12	of	of	ADP
ejpam-2515	320	13	ρ	ρ	PROPN
ejpam-2515	320	14	,	,	PUNCT
ejpam-2515	320	15	it	it	PRON
ejpam-2515	320	16	follows	follow	VERB
ejpam-2515	320	17	that	that	SCONJ
ejpam-2515	320	18	a	a	DET
ejpam-2515	320	19	∈	∈	PROPN
ejpam-2515	320	20	b	b	NOUN
ejpam-2515	320	21	◦	◦	NOUN
ejpam-2515	320	22	ρ	ρ	NOUN
ejpam-2515	320	23	c	c	NOUN
ejpam-2515	320	24	,	,	PUNCT
ejpam-2515	320	25	and	and	CCONJ
ejpam-2515	320	26	since	since	SCONJ
ejpam-2515	320	27	a	a	DET
ejpam-2515	320	28	∈	∈	PROPN
ejpam-2515	320	29	a	a	DET
ejpam-2515	320	30	◦	◦	NOUN
ejpam-2515	320	31	ρ	ρ	NOUN
ejpam-2515	320	32	d	d	PROPN
ejpam-2515	320	33	,	,	PUNCT
ejpam-2515	320	34	it	it	PRON
ejpam-2515	320	35	follows	follow	VERB
ejpam-2515	320	36	that	that	SCONJ
ejpam-2515	320	37	a	a	DET
ejpam-2515	320	38	∈	∈	PROPN
ejpam-2515	320	39	a	a	DET
ejpam-2515	320	40	◦	◦	NOUN
ejpam-2515	320	41	ρ	ρ	NOUN
ejpam-2515	320	42	d	d	NOUN
ejpam-2515	320	43	∩	∩	X
ejpam-2515	320	44	b	b	X
ejpam-2515	320	45	◦	◦	NOUN
ejpam-2515	320	46	ρ	ρ	PROPN
ejpam-2515	320	47	c.	c.	NOUN
ejpam-2515	320	48	by	by	ADP
ejpam-2515	320	49	the	the	DET
ejpam-2515	320	50	same	same	ADJ
ejpam-2515	320	51	way	way	NOUN
ejpam-2515	320	52	,	,	PUNCT
ejpam-2515	320	53	we	we	PRON
ejpam-2515	320	54	establish	establish	VERB
ejpam-2515	320	55	that	that	SCONJ
ejpam-2515	320	56	a	a	DET
ejpam-2515	320	57	∈	∈	PROPN
ejpam-2515	320	58	a	a	DET
ejpam-2515	320	59	◦	◦	NOUN
ejpam-2515	320	60	ρ	ρ	NOUN
ejpam-2515	320	61	d	d	NOUN
ejpam-2515	320	62	∩	∩	NOUN
ejpam-2515	320	63	a	a	DET
ejpam-2515	320	64	◦	◦	NOUN
ejpam-2515	320	65	ρ	ρ	NOUN
ejpam-2515	320	66	c	c	NOUN
ejpam-2515	320	67	and	and	CCONJ
ejpam-2515	320	68	c	c	NOUN
ejpam-2515	320	69	∈	∈	PROPN
ejpam-2515	320	70	a	a	DET
ejpam-2515	320	71	◦	◦	NOUN
ejpam-2515	320	72	ρ	ρ	NOUN
ejpam-2515	320	73	c	c	NOUN
ejpam-2515	320	74	∩	∩	NOUN
ejpam-2515	320	75	a	a	DET
ejpam-2515	320	76	◦	◦	NOUN
ejpam-2515	320	77	ρ	ρ	NOUN
ejpam-2515	320	78	c	c	NOUN
ejpam-2515	320	79	in	in	ADP
ejpam-2515	320	80	the	the	DET
ejpam-2515	320	81	case	case	NOUN
ejpam-2515	320	82	a	a	DET
ejpam-2515	320	83	=	=	SYM
ejpam-2515	320	84	b	b	NOUN
ejpam-2515	320	85	and	and	CCONJ
ejpam-2515	320	86	c	c	NOUN
ejpam-2515	320	87	=	=	SYM
ejpam-2515	320	88	d	d	NOUN
ejpam-2515	320	89	respectively	respectively	ADV
ejpam-2515	320	90	.	.	PUNCT
ejpam-2515	321	1	we	we	PRON
ejpam-2515	321	2	can	can	AUX
ejpam-2515	321	3	conclude	conclude	VERB
ejpam-2515	321	4	that	that	SCONJ
ejpam-2515	321	5	a	a	DET
ejpam-2515	321	6	◦	◦	NOUN
ejpam-2515	321	7	ρ	ρ	NOUN
ejpam-2515	321	8	d	d	NOUN
ejpam-2515	321	9	∩	∩	X
ejpam-2515	321	10	b	b	X
ejpam-2515	321	11	◦	◦	NOUN
ejpam-2515	321	12	ρ	ρ	X
ejpam-2515	321	13	c	c	NOUN
ejpam-2515	321	14	6=	6=	NUM
ejpam-2515	321	15	;	;	PUNCT
ejpam-2515	321	16	,	,	PUNCT
ejpam-2515	321	17	so	so	CCONJ
ejpam-2515	321	18	(	(	PUNCT
ejpam-2515	321	19	h;	h;	PROPN
ejpam-2515	321	20	◦	◦	NOUN
ejpam-2515	321	21	ρ	ρ	NOUN
ejpam-2515	321	22	)	)	PUNCT
ejpam-2515	321	23	is	be	AUX
ejpam-2515	321	24	a	a	DET
ejpam-2515	321	25	join	join	NOUN
ejpam-2515	321	26	space	space	NOUN
ejpam-2515	321	27	.	.	PUNCT
ejpam-2515	322	1	let	let	VERB
ejpam-2515	322	2	<	<	X
ejpam-2515	322	3	◦	◦	VERB
ejpam-2515	322	4	ρ	ρ	X
ejpam-2515	322	5	>	>	X
ejpam-2515	322	6	be	be	AUX
ejpam-2515	322	7	the	the	DET
ejpam-2515	322	8	extension	extension	NOUN
ejpam-2515	322	9	of	of	ADP
ejpam-2515	322	10	<	<	X
ejpam-2515	322	11	⊗	⊗	PROPN
ejpam-2515	322	12	ρ	ρ	PROPN
ejpam-2515	322	13	>	>	PUNCT
ejpam-2515	322	14	as	as	SCONJ
ejpam-2515	322	15	it	it	PRON
ejpam-2515	322	16	is	be	AUX
ejpam-2515	322	17	defined	define	VERB
ejpam-2515	322	18	in	in	ADP
ejpam-2515	322	19	proposition	proposition	NOUN
ejpam-2515	322	20	8	8	NUM
ejpam-2515	322	21	and	and	CCONJ
ejpam-2515	322	22	ρ	ρ	PROPN
ejpam-2515	322	23	be	be	AUX
ejpam-2515	322	24	a	a	DET
ejpam-2515	322	25	ternary	ternary	ADJ
ejpam-2515	322	26	relation	relation	NOUN
ejpam-2515	322	27	on	on	ADP
ejpam-2515	322	28	h.	h.	PROPN
ejpam-2515	322	29	let	let	VERB
ejpam-2515	322	30	α	α	PRON
ejpam-2515	322	31	be	be	AUX
ejpam-2515	322	32	the	the	DET
ejpam-2515	322	33	join	join	PROPN
ejpam-2515	322	34	relation	relation	PROPN
ejpam-2515	322	35	j2(ρ	j2(ρ	PROPN
ejpam-2515	322	36	,	,	PUNCT
ejpam-2515	322	37	ρ	ρ	PROPN
ejpam-2515	322	38	)	)	PUNCT
ejpam-2515	322	39	.	.	PUNCT
ejpam-2515	323	1	using	use	VERB
ejpam-2515	323	2	the	the	DET
ejpam-2515	323	3	projections	projection	NOUN
ejpam-2515	323	4	of	of	ADP
ejpam-2515	323	5	α	α	PRON
ejpam-2515	323	6	,	,	PUNCT
ejpam-2515	323	7	we	we	PRON
ejpam-2515	323	8	give	give	VERB
ejpam-2515	323	9	the	the	DET
ejpam-2515	323	10	following	follow	VERB
ejpam-2515	323	11	proposition	proposition	NOUN
ejpam-2515	323	12	.	.	PUNCT
ejpam-2515	324	1	proposition	proposition	NOUN
ejpam-2515	324	2	9	9	NUM
ejpam-2515	324	3	.	.	PUNCT
ejpam-2515	325	1	let	let	VERB
ejpam-2515	325	2	ρ	ρ	NOUN
ejpam-2515	325	3	be	be	AUX
ejpam-2515	325	4	a	a	DET
ejpam-2515	325	5	reflexive	reflexive	ADJ
ejpam-2515	325	6	and	and	CCONJ
ejpam-2515	325	7	symmetric	symmetric	ADJ
ejpam-2515	325	8	ternary	ternary	ADJ
ejpam-2515	325	9	relation	relation	NOUN
ejpam-2515	325	10	on	on	ADP
ejpam-2515	325	11	h	h	NOUN
ejpam-2515	325	12	with	with	ADP
ejpam-2515	325	13	|h|	|h|	PROPN
ejpam-2515	325	14	≥	≥	NUM
ejpam-2515	325	15	3	3	NUM
ejpam-2515	325	16	such	such	ADJ
ejpam-2515	325	17	that	that	PRON
ejpam-2515	326	1	ρ1,3	ρ1,3	PROPN
ejpam-2515	326	2	=	=	SYM
ejpam-2515	326	3	ρ1,2	ρ1,2	PROPN
ejpam-2515	326	4	=	=	SYM
ejpam-2515	326	5	ρ2,3	ρ2,3	PUNCT
ejpam-2515	326	6	=	=	NOUN
ejpam-2515	326	7	h	h	NOUN
ejpam-2515	326	8	×h	×h	NOUN
ejpam-2515	326	9	.	.	PUNCT
ejpam-2515	327	1	if	if	SCONJ
ejpam-2515	327	2	ρ	ρ	PROPN
ejpam-2515	327	3	satisfies	satisfy	VERB
ejpam-2515	327	4	the	the	DET
ejpam-2515	327	5	following	follow	VERB
ejpam-2515	327	6	condition	condition	NOUN
ejpam-2515	327	7	:	:	PUNCT
ejpam-2515	327	8	(	(	PUNCT
ejpam-2515	327	9	1	1	X
ejpam-2515	327	10	)	)	PUNCT
ejpam-2515	327	11	if	if	SCONJ
ejpam-2515	327	12	x	x	X
ejpam-2515	327	13	,	,	PUNCT
ejpam-2515	327	14	y	y	PROPN
ejpam-2515	327	15	,	,	PUNCT
ejpam-2515	327	16	z	z	PROPN
ejpam-2515	327	17	are	be	AUX
ejpam-2515	327	18	distinct	distinct	ADJ
ejpam-2515	327	19	and	and	CCONJ
ejpam-2515	327	20	(	(	PUNCT
ejpam-2515	327	21	x	x	X
ejpam-2515	327	22	,	,	PUNCT
ejpam-2515	327	23	y	y	PROPN
ejpam-2515	327	24	,	,	PUNCT
ejpam-2515	327	25	z	z	NOUN
ejpam-2515	327	26	)	)	PUNCT
ejpam-2515	327	27	∈	∈	PROPN
ejpam-2515	327	28	α1,2,4	α1,2,4	PROPN
ejpam-2515	327	29	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	327	30	,	,	PUNCT
ejpam-2515	327	31	then	then	ADV
ejpam-2515	327	32	(	(	PUNCT
ejpam-2515	327	33	x	x	X
ejpam-2515	327	34	,	,	PUNCT
ejpam-2515	327	35	y	y	PROPN
ejpam-2515	327	36	,	,	PUNCT
ejpam-2515	327	37	z	z	NOUN
ejpam-2515	327	38	)	)	PUNCT
ejpam-2515	327	39	∈	∈	PROPN
ejpam-2515	327	40	ρ	ρ	NOUN
ejpam-2515	327	41	and	and	CCONJ
ejpam-2515	327	42	conversely	conversely	ADV
ejpam-2515	327	43	;	;	PUNCT
ejpam-2515	327	44	then	then	ADV
ejpam-2515	327	45	(	(	PUNCT
ejpam-2515	327	46	h;	h;	PROPN
ejpam-2515	327	47	◦	◦	NOUN
ejpam-2515	327	48	ρ	ρ	NOUN
ejpam-2515	327	49	)	)	PUNCT
ejpam-2515	327	50	is	be	AUX
ejpam-2515	327	51	a	a	DET
ejpam-2515	327	52	hypergroup	hypergroup	NOUN
ejpam-2515	327	53	.	.	PUNCT
ejpam-2515	328	1	proof	proof	NOUN
ejpam-2515	328	2	.	.	PUNCT
ejpam-2515	329	1	since	since	SCONJ
ejpam-2515	329	2	ρ1,2	ρ1,2	PROPN
ejpam-2515	329	3	=	=	SYM
ejpam-2515	329	4	ρ2,3	ρ2,3	PUNCT
ejpam-2515	329	5	=	=	NOUN
ejpam-2515	329	6	h	h	NOUN
ejpam-2515	329	7	×h	×h	PROPN
ejpam-2515	329	8	,	,	PUNCT
ejpam-2515	329	9	it	it	PRON
ejpam-2515	329	10	follows	follow	VERB
ejpam-2515	329	11	,	,	PUNCT
ejpam-2515	329	12	by	by	ADP
ejpam-2515	329	13	proposition	proposition	NOUN
ejpam-2515	329	14	1	1	NUM
ejpam-2515	329	15	,	,	PUNCT
ejpam-2515	329	16	that	that	PRON
ejpam-2515	329	17	(	(	PUNCT
ejpam-2515	329	18	h;	h;	PROPN
ejpam-2515	329	19	◦	◦	NOUN
ejpam-2515	329	20	ρ	ρ	NOUN
ejpam-2515	329	21	)	)	PUNCT
ejpam-2515	329	22	is	be	AUX
ejpam-2515	329	23	a	a	DET
ejpam-2515	329	24	quasihypergroup	quasihypergroup	NOUN
ejpam-2515	329	25	.	.	PUNCT
ejpam-2515	330	1	it	it	PRON
ejpam-2515	330	2	remains	remain	VERB
ejpam-2515	330	3	to	to	PART
ejpam-2515	330	4	check	check	VERB
ejpam-2515	330	5	the	the	DET
ejpam-2515	330	6	associative	associative	ADJ
ejpam-2515	330	7	axiom	axiom	NOUN
ejpam-2515	330	8	.	.	PUNCT
ejpam-2515	331	1	first	first	ADV
ejpam-2515	331	2	of	of	ADP
ejpam-2515	331	3	all	all	PRON
ejpam-2515	331	4	,	,	PUNCT
ejpam-2515	331	5	we	we	PRON
ejpam-2515	331	6	shall	shall	AUX
ejpam-2515	331	7	check	check	VERB
ejpam-2515	331	8	the	the	DET
ejpam-2515	331	9	following	follow	VERB
ejpam-2515	331	10	equality	equality	NOUN
ejpam-2515	331	11	:	:	PUNCT
ejpam-2515	331	12	∀(x	∀(x	NUM
ejpam-2515	331	13	,	,	PUNCT
ejpam-2515	331	14	y	y	PROPN
ejpam-2515	331	15	,	,	PUNCT
ejpam-2515	331	16	z	z	NOUN
ejpam-2515	331	17	)	)	PUNCT
ejpam-2515	331	18	∈	∈	PROPN
ejpam-2515	331	19	h3	h3	NOUN
ejpam-2515	331	20	,	,	PUNCT
ejpam-2515	331	21	x	x	PUNCT
ejpam-2515	331	22	◦	◦	NOUN
ejpam-2515	331	23	ρ	ρ	X
ejpam-2515	331	24	(	(	PUNCT
ejpam-2515	331	25	y	y	PROPN
ejpam-2515	331	26	◦	◦	PROPN
ejpam-2515	331	27	ρ	ρ	PROPN
ejpam-2515	331	28	z	z	NOUN
ejpam-2515	331	29	)	)	PUNCT
ejpam-2515	331	30	=	=	SYM
ejpam-2515	332	1	x	x	PUNCT
ejpam-2515	332	2	◦	◦	NOUN
ejpam-2515	332	3	ρ	ρ	NUM
ejpam-2515	332	4	y	y	PROPN
ejpam-2515	332	5	∪	∪	PROPN
ejpam-2515	332	6	y	y	PROPN
ejpam-2515	332	7	◦	◦	NOUN
ejpam-2515	332	8	ρ	ρ	PROPN
ejpam-2515	332	9	y	y	PROPN
ejpam-2515	332	10	∪	∪	PROPN
ejpam-2515	332	11	y	y	PROPN
ejpam-2515	332	12	◦	◦	PROPN
ejpam-2515	332	13	ρ	ρ	PROPN
ejpam-2515	332	14	z.	z.	PROPN
ejpam-2515	332	15	(	(	PUNCT
ejpam-2515	332	16	2	2	X
ejpam-2515	332	17	)	)	PUNCT
ejpam-2515	332	18	we	we	PRON
ejpam-2515	332	19	suppose	suppose	VERB
ejpam-2515	332	20	that	that	SCONJ
ejpam-2515	332	21	(	(	PUNCT
ejpam-2515	332	22	x	x	X
ejpam-2515	332	23	,	,	PUNCT
ejpam-2515	332	24	y	y	PROPN
ejpam-2515	332	25	,	,	PUNCT
ejpam-2515	332	26	z	z	NOUN
ejpam-2515	332	27	)	)	PUNCT
ejpam-2515	332	28	∈	∈	PROPN
ejpam-2515	332	29	α1,2,4	α1,2,4	PROPN
ejpam-2515	332	30	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	332	31	and	and	CCONJ
ejpam-2515	332	32	x	x	INTJ
ejpam-2515	332	33	,	,	PUNCT
ejpam-2515	332	34	y	y	PROPN
ejpam-2515	332	35	,	,	PUNCT
ejpam-2515	332	36	z	z	PROPN
ejpam-2515	332	37	are	be	AUX
ejpam-2515	332	38	distinct	distinct	ADJ
ejpam-2515	332	39	,	,	PUNCT
ejpam-2515	332	40	then	then	ADV
ejpam-2515	332	41	(	(	PUNCT
ejpam-2515	332	42	x	x	X
ejpam-2515	332	43	,	,	PUNCT
ejpam-2515	332	44	y	y	PROPN
ejpam-2515	332	45	,	,	PUNCT
ejpam-2515	332	46	z	z	NOUN
ejpam-2515	332	47	)	)	PUNCT
ejpam-2515	332	48	∈	∈	PROPN
ejpam-2515	332	49	ρ	ρ	NOUN
ejpam-2515	332	50	and	and	CCONJ
ejpam-2515	332	51	x	x	NOUN
ejpam-2515	332	52	,	,	PUNCT
ejpam-2515	332	53	y	y	PROPN
ejpam-2515	332	54	,	,	PUNCT
ejpam-2515	332	55	z	z	PROPN
ejpam-2515	332	56	are	be	AUX
ejpam-2515	332	57	distinct	distinct	ADJ
ejpam-2515	332	58	.	.	PUNCT
ejpam-2515	333	1	then	then	ADV
ejpam-2515	333	2	(	(	PUNCT
ejpam-2515	333	3	1	1	X
ejpam-2515	333	4	)	)	PUNCT
ejpam-2515	333	5	=	=	NOUN
ejpam-2515	333	6	⇒	⇒	NOUN
ejpam-2515	333	7	(	(	PUNCT
ejpam-2515	333	8	x	x	X
ejpam-2515	333	9	,	,	PUNCT
ejpam-2515	333	10	y	y	PROPN
ejpam-2515	333	11	,	,	PUNCT
ejpam-2515	333	12	z	z	NOUN
ejpam-2515	333	13	)	)	PUNCT
ejpam-2515	333	14	∈	∈	PROPN
ejpam-2515	333	15	ρ	ρ	NOUN
ejpam-2515	333	16	and	and	CCONJ
ejpam-2515	333	17	x	x	NOUN
ejpam-2515	333	18	,	,	PUNCT
ejpam-2515	333	19	y	y	PROPN
ejpam-2515	333	20	,	,	PUNCT
ejpam-2515	333	21	z	z	PROPN
ejpam-2515	333	22	are	be	AUX
ejpam-2515	333	23	distinct	distinct	ADJ
ejpam-2515	333	24	.	.	PUNCT
ejpam-2515	334	1	now	now	ADV
ejpam-2515	334	2	,	,	PUNCT
ejpam-2515	334	3	we	we	PRON
ejpam-2515	334	4	verify	verify	VERB
ejpam-2515	334	5	:	:	PUNCT
ejpam-2515	334	6	u	u	PROPN
ejpam-2515	334	7	∈	∈	PROPN
ejpam-2515	334	8	x	x	PUNCT
ejpam-2515	334	9	◦	◦	NOUN
ejpam-2515	334	10	ρ	ρ	X
ejpam-2515	334	11	(	(	PUNCT
ejpam-2515	334	12	y	y	PROPN
ejpam-2515	334	13	◦	◦	PROPN
ejpam-2515	334	14	ρ	ρ	PROPN
ejpam-2515	334	15	z)	z)	NUM
ejpam-2515	334	16	⇐	⇐	ADJ
ejpam-2515	334	17	⇒	⇒	NOUN
ejpam-2515	334	18	u	u	X
ejpam-2515	334	19	∈	∈	PROPN
ejpam-2515	334	20	x	x	PUNCT
ejpam-2515	334	21	◦	◦	NOUN
ejpam-2515	334	22	ρ	ρ	X
ejpam-2515	334	23	y	y	PROPN
ejpam-2515	334	24	∪	∪	PROPN
ejpam-2515	334	25	y	y	PROPN
ejpam-2515	334	26	◦	◦	NOUN
ejpam-2515	334	27	ρ	ρ	PROPN
ejpam-2515	334	28	y	y	PROPN
ejpam-2515	334	29	∪	∪	PROPN
ejpam-2515	334	30	y	y	PROPN
ejpam-2515	334	31	◦	◦	PROPN
ejpam-2515	334	32	ρ	ρ	PROPN
ejpam-2515	334	33	z.	z.	NOUN
ejpam-2515	335	1	=	=	PRON
ejpam-2515	335	2	⇒	⇒	NOUN
ejpam-2515	335	3	there	there	PRON
ejpam-2515	335	4	exists	exist	VERB
ejpam-2515	335	5	v	v	ADP
ejpam-2515	335	6	∈	∈	PROPN
ejpam-2515	335	7	y	y	PROPN
ejpam-2515	335	8	◦	◦	NOUN
ejpam-2515	335	9	ρ	ρ	PROPN
ejpam-2515	335	10	z	z	NOUN
ejpam-2515	335	11	such	such	ADJ
ejpam-2515	335	12	that	that	SCONJ
ejpam-2515	335	13	u	u	PROPN
ejpam-2515	335	14	∈	∈	PROPN
ejpam-2515	335	15	x	x	SYM
ejpam-2515	335	16	◦	◦	NOUN
ejpam-2515	335	17	ρ	ρ	NOUN
ejpam-2515	335	18	v.	v.	ADP
ejpam-2515	335	19	hence	hence	ADV
ejpam-2515	335	20	(	(	PUNCT
ejpam-2515	335	21	x	x	X
ejpam-2515	335	22	,	,	PUNCT
ejpam-2515	335	23	u	u	NOUN
ejpam-2515	335	24	,	,	PUNCT
ejpam-2515	335	25	v	v	NOUN
ejpam-2515	335	26	)	)	PUNCT
ejpam-2515	335	27	∈	∈	PROPN
ejpam-2515	335	28	ρ	ρ	PROPN
ejpam-2515	335	29	with	with	ADP
ejpam-2515	335	30	(	(	PUNCT
ejpam-2515	335	31	y	y	PROPN
ejpam-2515	335	32	,	,	PUNCT
ejpam-2515	335	33	v	v	NOUN
ejpam-2515	335	34	,	,	PUNCT
ejpam-2515	335	35	z	z	NOUN
ejpam-2515	335	36	)	)	PUNCT
ejpam-2515	335	37	∈	∈	PROPN
ejpam-2515	335	38	ρ	ρ	PROPN
ejpam-2515	335	39	.	.	PUNCT
ejpam-2515	335	40	recall	recall	PROPN
ejpam-2515	335	41	that	that	PRON
ejpam-2515	335	42	,	,	PUNCT
ejpam-2515	335	43	(	(	PUNCT
ejpam-2515	335	44	x	x	X
ejpam-2515	335	45	,	,	PUNCT
ejpam-2515	335	46	y	y	PROPN
ejpam-2515	335	47	,	,	PUNCT
ejpam-2515	335	48	z	z	NOUN
ejpam-2515	335	49	)	)	PUNCT
ejpam-2515	335	50	∈	∈	PROPN
ejpam-2515	335	51	α1,2,4	α1,2,4	PROPN
ejpam-2515	335	52	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	335	53	⇐	⇐	PROPN
ejpam-2515	335	54	⇒	⇒	NOUN
ejpam-2515	335	55	(	(	PUNCT
ejpam-2515	335	56	x	x	X
ejpam-2515	335	57	,	,	PUNCT
ejpam-2515	335	58	y	y	PROPN
ejpam-2515	335	59	,	,	PUNCT
ejpam-2515	335	60	t	t	PROPN
ejpam-2515	335	61	,	,	PUNCT
ejpam-2515	335	62	z	z	NOUN
ejpam-2515	335	63	)	)	PUNCT
ejpam-2515	335	64	∈	∈	PROPN
ejpam-2515	335	65	j2(ρ	j2(ρ	PROPN
ejpam-2515	335	66	,	,	PUNCT
ejpam-2515	335	67	ρ)	ρ)	NUM
ejpam-2515	335	68	⇐	⇐	ADJ
ejpam-2515	335	69	⇒	⇒	NOUN
ejpam-2515	335	70	(	(	PUNCT
ejpam-2515	335	71	x	x	X
ejpam-2515	335	72	,	,	PUNCT
ejpam-2515	335	73	y	y	PROPN
ejpam-2515	335	74	,	,	PUNCT
ejpam-2515	335	75	t	t	PROPN
ejpam-2515	335	76	)	)	PUNCT
ejpam-2515	335	77	,	,	PUNCT
ejpam-2515	335	78	(	(	PUNCT
ejpam-2515	335	79	y	y	PROPN
ejpam-2515	335	80	,	,	PUNCT
ejpam-2515	335	81	t	t	PROPN
ejpam-2515	335	82	,	,	PUNCT
ejpam-2515	335	83	z	z	NOUN
ejpam-2515	335	84	)	)	PUNCT
ejpam-2515	335	85	∈	∈	PROPN
ejpam-2515	335	86	ρ	ρ	PROPN
ejpam-2515	335	87	.	.	PUNCT
ejpam-2515	336	1	(	(	PUNCT
ejpam-2515	336	2	3	3	X
ejpam-2515	336	3	)	)	PUNCT
ejpam-2515	336	4	set	set	VERB
ejpam-2515	336	5	t	t	NOUN
ejpam-2515	337	1	=	=	PUNCT
ejpam-2515	337	2	v.	v.	CCONJ
ejpam-2515	337	3	then	then	ADV
ejpam-2515	337	4	,	,	PUNCT
ejpam-2515	337	5	we	we	PRON
ejpam-2515	337	6	have	have	VERB
ejpam-2515	337	7	(	(	PUNCT
ejpam-2515	337	8	x	x	X
ejpam-2515	337	9	,	,	PUNCT
ejpam-2515	337	10	y	y	PROPN
ejpam-2515	337	11	,	,	PUNCT
ejpam-2515	337	12	v	v	NOUN
ejpam-2515	337	13	)	)	PUNCT
ejpam-2515	337	14	,	,	PUNCT
ejpam-2515	337	15	(	(	PUNCT
ejpam-2515	337	16	y	y	NOUN
ejpam-2515	337	17	,	,	PUNCT
ejpam-2515	337	18	v	v	NOUN
ejpam-2515	337	19	,	,	PUNCT
ejpam-2515	337	20	z	z	NOUN
ejpam-2515	337	21	)	)	PUNCT
ejpam-2515	337	22	∈	∈	PROPN
ejpam-2515	337	23	ρ	ρ	PROPN
ejpam-2515	337	24	,	,	PUNCT
ejpam-2515	337	25	whence	whence	NOUN
ejpam-2515	337	26	(	(	PUNCT
ejpam-2515	337	27	x	x	X
ejpam-2515	337	28	,	,	PUNCT
ejpam-2515	337	29	u	u	NOUN
ejpam-2515	337	30	,	,	PUNCT
ejpam-2515	337	31	v	v	NOUN
ejpam-2515	337	32	)	)	PUNCT
ejpam-2515	337	33	∈	∈	PROPN
ejpam-2515	337	34	ρ	ρ	NOUN
ejpam-2515	337	35	and	and	CCONJ
ejpam-2515	337	36	(	(	PUNCT
ejpam-2515	337	37	x	x	X
ejpam-2515	337	38	,	,	PUNCT
ejpam-2515	337	39	y	y	PROPN
ejpam-2515	337	40	,	,	PUNCT
ejpam-2515	337	41	v	v	NOUN
ejpam-2515	337	42	)	)	PUNCT
ejpam-2515	337	43	∈	∈	PROPN
ejpam-2515	337	44	ρ	ρ	NOUN
ejpam-2515	337	45	.	.	PUNCT
ejpam-2515	338	1	by	by	ADP
ejpam-2515	338	2	the	the	DET
ejpam-2515	338	3	condition	condition	NOUN
ejpam-2515	338	4	specified	specify	VERB
ejpam-2515	338	5	and	and	CCONJ
ejpam-2515	338	6	by	by	ADP
ejpam-2515	338	7	the	the	DET
ejpam-2515	338	8	(	(	PUNCT
ejpam-2515	338	9	3	3	NUM
ejpam-2515	338	10	)	)	PUNCT
ejpam-2515	338	11	,	,	PUNCT
ejpam-2515	338	12	if	if	SCONJ
ejpam-2515	338	13	(	(	PUNCT
ejpam-2515	338	14	a	a	PRON
ejpam-2515	338	15	,	,	PUNCT
ejpam-2515	338	16	t	t	PROPN
ejpam-2515	338	17	,	,	PUNCT
ejpam-2515	338	18	b	b	NOUN
ejpam-2515	338	19	)	)	PUNCT
ejpam-2515	338	20	∈	∈	PROPN
ejpam-2515	338	21	α1,2,4	α1,2,4	PROPN
ejpam-2515	338	22	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	338	23	and	and	CCONJ
ejpam-2515	338	24	(	(	PUNCT
ejpam-2515	338	25	a	a	PRON
ejpam-2515	338	26	,	,	PUNCT
ejpam-2515	338	27	s	s	PROPN
ejpam-2515	338	28	,	,	PUNCT
ejpam-2515	338	29	b	b	X
ejpam-2515	338	30	)	)	PUNCT
ejpam-2515	338	31	∈	∈	PROPN
ejpam-2515	338	32	α1,2,4	α1,2,4	PROPN
ejpam-2515	338	33	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	338	34	∈	∈	PROPN
ejpam-2515	338	35	ρ	ρ	PROPN
ejpam-2515	338	36	,	,	PUNCT
ejpam-2515	338	37	t	t	PROPN
ejpam-2515	338	38	6=	6=	PROPN
ejpam-2515	338	39	s	s	VERB
ejpam-2515	338	40	then	then	ADV
ejpam-2515	338	41	(	(	PUNCT
ejpam-2515	338	42	a	a	PRON
ejpam-2515	338	43	,	,	PUNCT
ejpam-2515	338	44	t	t	PROPN
ejpam-2515	338	45	,	,	PUNCT
ejpam-2515	338	46	b	b	NOUN
ejpam-2515	338	47	)	)	PUNCT
ejpam-2515	338	48	∈	∈	PROPN
ejpam-2515	338	49	ρ	ρ	NOUN
ejpam-2515	338	50	and	and	CCONJ
ejpam-2515	338	51	(	(	PUNCT
ejpam-2515	338	52	a	a	PRON
ejpam-2515	338	53	,	,	PUNCT
ejpam-2515	338	54	s	s	PROPN
ejpam-2515	338	55	,	,	PUNCT
ejpam-2515	338	56	b	b	NOUN
ejpam-2515	338	57	)	)	PUNCT
ejpam-2515	338	58	∈	∈	PROPN
ejpam-2515	338	59	ρ	ρ	PROPN
ejpam-2515	338	60	;	;	PUNCT
ejpam-2515	338	61	s.	s.	PROPN
ejpam-2515	338	62	govindarajan	govindarajan	PROPN
ejpam-2515	338	63	/	/	SYM
ejpam-2515	338	64	eur	eur	PROPN
ejpam-2515	338	65	.	.	PUNCT
ejpam-2515	339	1	j.	j.	PROPN
ejpam-2515	339	2	pure	pure	PROPN
ejpam-2515	339	3	appl	appl	PROPN
ejpam-2515	339	4	.	.	PROPN
ejpam-2515	339	5	math	math	PROPN
ejpam-2515	339	6	,	,	PUNCT
ejpam-2515	339	7	9	9	NUM
ejpam-2515	339	8	(	(	PUNCT
ejpam-2515	339	9	2016	2016	NUM
ejpam-2515	339	10	)	)	PUNCT
ejpam-2515	339	11	,	,	PUNCT
ejpam-2515	339	12	367	367	NUM
ejpam-2515	339	13	-	-	SYM
ejpam-2515	339	14	382	382	NUM
ejpam-2515	339	15	378	378	NUM
ejpam-2515	339	16	it	it	PRON
ejpam-2515	339	17	follows	follow	VERB
ejpam-2515	339	18	that	that	SCONJ
ejpam-2515	339	19	(	(	PUNCT
ejpam-2515	339	20	a	a	PRON
ejpam-2515	339	21	,	,	PUNCT
ejpam-2515	339	22	t	t	PROPN
ejpam-2515	339	23	,	,	PUNCT
ejpam-2515	339	24	s	s	PART
ejpam-2515	339	25	)	)	PUNCT
ejpam-2515	339	26	∈	∈	PROPN
ejpam-2515	339	27	ρ	ρ	NOUN
ejpam-2515	339	28	or	or	CCONJ
ejpam-2515	339	29	(	(	PUNCT
ejpam-2515	339	30	a	a	PRON
ejpam-2515	339	31	,	,	PUNCT
ejpam-2515	339	32	s	s	PROPN
ejpam-2515	339	33	,	,	PUNCT
ejpam-2515	340	1	t	t	PROPN
ejpam-2515	340	2	)	)	PUNCT
ejpam-2515	340	3	∈	∈	PROPN
ejpam-2515	340	4	ρ	ρ	PROPN
ejpam-2515	340	5	.	.	PUNCT
ejpam-2515	341	1	therefore	therefore	ADV
ejpam-2515	341	2	,	,	PUNCT
ejpam-2515	341	3	from	from	ADP
ejpam-2515	341	4	(	(	PUNCT
ejpam-2515	341	5	x	x	INTJ
ejpam-2515	341	6	,	,	PUNCT
ejpam-2515	341	7	u	u	NOUN
ejpam-2515	341	8	,	,	PUNCT
ejpam-2515	341	9	v	v	NOUN
ejpam-2515	341	10	)	)	PUNCT
ejpam-2515	341	11	∈	∈	PROPN
ejpam-2515	341	12	ρ	ρ	PROPN
ejpam-2515	341	13	,	,	PUNCT
ejpam-2515	341	14	(	(	PUNCT
ejpam-2515	341	15	x	x	X
ejpam-2515	341	16	,	,	PUNCT
ejpam-2515	341	17	y	y	PROPN
ejpam-2515	341	18	,	,	PUNCT
ejpam-2515	341	19	v	v	NOUN
ejpam-2515	341	20	)	)	PUNCT
ejpam-2515	341	21	∈	∈	PROPN
ejpam-2515	341	22	ρ	ρ	NOUN
ejpam-2515	341	23	and	and	CCONJ
ejpam-2515	341	24	u	u	PROPN
ejpam-2515	341	25	6=	6=	PROPN
ejpam-2515	341	26	y	y	PROPN
ejpam-2515	341	27	it	it	PRON
ejpam-2515	341	28	results	result	VERB
ejpam-2515	341	29	(	(	PUNCT
ejpam-2515	341	30	x	x	X
ejpam-2515	341	31	,	,	PUNCT
ejpam-2515	341	32	u	u	NOUN
ejpam-2515	341	33	,	,	PUNCT
ejpam-2515	341	34	y	y	NOUN
ejpam-2515	341	35	)	)	PUNCT
ejpam-2515	341	36	∈	∈	PROPN
ejpam-2515	341	37	ρ	ρ	NOUN
ejpam-2515	341	38	or	or	CCONJ
ejpam-2515	341	39	(	(	PUNCT
ejpam-2515	341	40	x	x	INTJ
ejpam-2515	341	41	,	,	PUNCT
ejpam-2515	341	42	y	y	PROPN
ejpam-2515	341	43	,	,	PUNCT
ejpam-2515	341	44	u	u	NOUN
ejpam-2515	341	45	)	)	PUNCT
ejpam-2515	341	46	∈	∈	PROPN
ejpam-2515	341	47	ρ	ρ	NOUN
ejpam-2515	341	48	.	.	PUNCT
ejpam-2515	342	1	if	if	SCONJ
ejpam-2515	342	2	(	(	PUNCT
ejpam-2515	342	3	x	x	X
ejpam-2515	342	4	,	,	PUNCT
ejpam-2515	342	5	u	u	NOUN
ejpam-2515	342	6	,	,	PUNCT
ejpam-2515	342	7	y	y	NOUN
ejpam-2515	342	8	)	)	PUNCT
ejpam-2515	342	9	∈	∈	PROPN
ejpam-2515	342	10	ρ	ρ	PROPN
ejpam-2515	342	11	,	,	PUNCT
ejpam-2515	342	12	then	then	ADV
ejpam-2515	342	13	u	u	PROPN
ejpam-2515	342	14	∈	∈	PROPN
ejpam-2515	342	15	x	x	PUNCT
ejpam-2515	342	16	◦	◦	NOUN
ejpam-2515	342	17	ρ	ρ	NUM
ejpam-2515	342	18	y	y	NOUN
ejpam-2515	342	19	.	.	PUNCT
ejpam-2515	343	1	if	if	SCONJ
ejpam-2515	343	2	(	(	PUNCT
ejpam-2515	343	3	x	x	X
ejpam-2515	343	4	,	,	PUNCT
ejpam-2515	343	5	y	y	PROPN
ejpam-2515	343	6	,	,	PUNCT
ejpam-2515	343	7	u	u	NOUN
ejpam-2515	343	8	)	)	PUNCT
ejpam-2515	343	9	∈	∈	PROPN
ejpam-2515	343	10	ρ	ρ	PROPN
ejpam-2515	343	11	,	,	PUNCT
ejpam-2515	343	12	then	then	ADV
ejpam-2515	343	13	(	(	PUNCT
ejpam-2515	343	14	x	x	X
ejpam-2515	343	15	,	,	PUNCT
ejpam-2515	343	16	y	y	PROPN
ejpam-2515	343	17	,	,	PUNCT
ejpam-2515	343	18	z	z	NOUN
ejpam-2515	343	19	)	)	PUNCT
ejpam-2515	343	20	∈	∈	PROPN
ejpam-2515	343	21	α1,2,4∩α1,3,4	α1,2,4∩α1,3,4	PROPN
ejpam-2515	343	22	=	=	SYM
ejpam-2515	343	23	⇒	⇒	PROPN
ejpam-2515	343	24	(	(	PUNCT
ejpam-2515	343	25	y	y	PROPN
ejpam-2515	343	26	,	,	PUNCT
ejpam-2515	343	27	u	u	NOUN
ejpam-2515	343	28	,	,	PUNCT
ejpam-2515	343	29	z	z	NOUN
ejpam-2515	343	30	)	)	PUNCT
ejpam-2515	343	31	∈	∈	PROPN
ejpam-2515	343	32	ρ	ρ	PROPN
ejpam-2515	343	33	,	,	PUNCT
ejpam-2515	343	34	whence	whence	ADP
ejpam-2515	343	35	u	u	PROPN
ejpam-2515	343	36	∈	∈	PROPN
ejpam-2515	343	37	y	y	PROPN
ejpam-2515	343	38	◦	◦	NOUN
ejpam-2515	343	39	ρ	ρ	PROPN
ejpam-2515	343	40	z.	z.	PROPN
ejpam-2515	344	1	if	if	SCONJ
ejpam-2515	344	2	u=	u=	PROPN
ejpam-2515	344	3	y	y	PROPN
ejpam-2515	344	4	,	,	PUNCT
ejpam-2515	344	5	then	then	ADV
ejpam-2515	344	6	u=	u=	VERB
ejpam-2515	344	7	y	y	PROPN
ejpam-2515	344	8	∈	∈	PROPN
ejpam-2515	344	9	y	y	PROPN
ejpam-2515	344	10	◦	◦	NOUN
ejpam-2515	344	11	ρ	ρ	PROPN
ejpam-2515	344	12	y	y	PROPN
ejpam-2515	344	13	(	(	PUNCT
ejpam-2515	344	14	by	by	ADP
ejpam-2515	344	15	the	the	DET
ejpam-2515	344	16	reflexivity	reflexivity	NOUN
ejpam-2515	344	17	of	of	ADP
ejpam-2515	344	18	ρ	ρ	PROPN
ejpam-2515	344	19	)	)	PUNCT
ejpam-2515	344	20	.	.	PUNCT
ejpam-2515	345	1	therefore	therefore	ADV
ejpam-2515	345	2	,	,	PUNCT
ejpam-2515	345	3	u	u	PROPN
ejpam-2515	345	4	∈	∈	PROPN
ejpam-2515	345	5	x	x	PUNCT
ejpam-2515	345	6	◦	◦	NOUN
ejpam-2515	345	7	ρ	ρ	X
ejpam-2515	345	8	y	y	PROPN
ejpam-2515	345	9	∪	∪	PROPN
ejpam-2515	345	10	y	y	PROPN
ejpam-2515	345	11	◦	◦	NOUN
ejpam-2515	345	12	ρ	ρ	PROPN
ejpam-2515	345	13	y	y	PROPN
ejpam-2515	345	14	∪	∪	PROPN
ejpam-2515	345	15	y	y	PROPN
ejpam-2515	345	16	◦	◦	PROPN
ejpam-2515	345	17	ρ	ρ	PROPN
ejpam-2515	345	18	z.	z.	PROPN
ejpam-2515	345	19	⇐	⇐	PROPN
ejpam-2515	345	20	=	=	PRON
ejpam-2515	345	21	suppose	suppose	VERB
ejpam-2515	345	22	u	u	PRON
ejpam-2515	345	23	∈	∈	PROPN
ejpam-2515	345	24	x	x	PUNCT
ejpam-2515	345	25	◦	◦	NOUN
ejpam-2515	345	26	ρ	ρ	X
ejpam-2515	345	27	y	y	PROPN
ejpam-2515	345	28	.	.	PUNCT
ejpam-2515	346	1	then	then	ADV
ejpam-2515	346	2	(	(	PUNCT
ejpam-2515	346	3	x	x	X
ejpam-2515	346	4	,	,	PUNCT
ejpam-2515	346	5	u	u	NOUN
ejpam-2515	346	6	,	,	PUNCT
ejpam-2515	346	7	y	y	NOUN
ejpam-2515	346	8	)	)	PUNCT
ejpam-2515	346	9	∈	∈	PROPN
ejpam-2515	346	10	ρ	ρ	PROPN
ejpam-2515	346	11	.	.	PUNCT
ejpam-2515	347	1	let	let	VERB
ejpam-2515	347	2	(	(	PUNCT
ejpam-2515	347	3	x	x	X
ejpam-2515	347	4	,	,	PUNCT
ejpam-2515	347	5	y	y	PROPN
ejpam-2515	347	6	,	,	PUNCT
ejpam-2515	347	7	z	z	NOUN
ejpam-2515	347	8	)	)	PUNCT
ejpam-2515	347	9	∈	∈	PROPN
ejpam-2515	347	10	ρ	ρ	PROPN
ejpam-2515	347	11	⊂	⊂	PROPN
ejpam-2515	347	12	α1,2,4	α1,2,4	PROPN
ejpam-2515	347	13	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	347	14	.	.	PUNCT
ejpam-2515	348	1	since	since	SCONJ
ejpam-2515	348	2	(	(	PUNCT
ejpam-2515	348	3	x	x	INTJ
ejpam-2515	348	4	,	,	PUNCT
ejpam-2515	348	5	u	u	NOUN
ejpam-2515	348	6	,	,	PUNCT
ejpam-2515	348	7	y	y	NOUN
ejpam-2515	348	8	)	)	PUNCT
ejpam-2515	348	9	∈	∈	PROPN
ejpam-2515	348	10	ρ	ρ	PROPN
ejpam-2515	348	11	⊂	⊂	PROPN
ejpam-2515	348	12	α1,2,4	α1,2,4	PROPN
ejpam-2515	348	13	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	348	14	,	,	PUNCT
ejpam-2515	348	15	it	it	PRON
ejpam-2515	348	16	follows	follow	VERB
ejpam-2515	348	17	that	that	SCONJ
ejpam-2515	348	18	there	there	PRON
ejpam-2515	348	19	exists	exist	VERB
ejpam-2515	348	20	a	a	DET
ejpam-2515	348	21	v	v	NOUN
ejpam-2515	348	22	∈	∈	NOUN
ejpam-2515	348	23	h	h	NOUN
ejpam-2515	348	24	such	such	ADJ
ejpam-2515	348	25	that	that	SCONJ
ejpam-2515	348	26	(	(	PUNCT
ejpam-2515	348	27	x	x	X
ejpam-2515	348	28	,	,	PUNCT
ejpam-2515	348	29	u	u	NOUN
ejpam-2515	348	30	,	,	PUNCT
ejpam-2515	348	31	v	v	NOUN
ejpam-2515	348	32	)	)	PUNCT
ejpam-2515	348	33	∈	∈	PROPN
ejpam-2515	348	34	ρ	ρ	PROPN
ejpam-2515	348	35	,	,	PUNCT
ejpam-2515	348	36	(	(	PUNCT
ejpam-2515	348	37	u	u	NOUN
ejpam-2515	348	38	,	,	PUNCT
ejpam-2515	348	39	v	v	NOUN
ejpam-2515	348	40	,	,	PUNCT
ejpam-2515	348	41	z	z	NOUN
ejpam-2515	348	42	)	)	PUNCT
ejpam-2515	348	43	∈	∈	PROPN
ejpam-2515	348	44	ρ	ρ	NOUN
ejpam-2515	348	45	.	.	PUNCT
ejpam-2515	349	1	thus	thus	ADV
ejpam-2515	349	2	u	u	X
ejpam-2515	349	3	∈	∈	PROPN
ejpam-2515	349	4	x	x	SYM
ejpam-2515	349	5	◦	◦	NOUN
ejpam-2515	349	6	ρ	ρ	X
ejpam-2515	349	7	v.	v.	CCONJ
ejpam-2515	349	8	again	again	ADV
ejpam-2515	349	9	,	,	PUNCT
ejpam-2515	349	10	(	(	PUNCT
ejpam-2515	349	11	x	x	X
ejpam-2515	349	12	,	,	PUNCT
ejpam-2515	349	13	y	y	PROPN
ejpam-2515	349	14	,	,	PUNCT
ejpam-2515	349	15	z	z	NOUN
ejpam-2515	349	16	)	)	PUNCT
ejpam-2515	349	17	∈	∈	PROPN
ejpam-2515	349	18	ρ	ρ	PROPN
ejpam-2515	349	19	⊂	⊂	PROPN
ejpam-2515	349	20	α1,2,4	α1,2,4	PROPN
ejpam-2515	349	21	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	349	22	=	=	NOUN
ejpam-2515	349	23	⇒	⇒	NOUN
ejpam-2515	349	24	(	(	PUNCT
ejpam-2515	349	25	y	y	PROPN
ejpam-2515	349	26	,	,	PUNCT
ejpam-2515	349	27	v	v	NOUN
ejpam-2515	349	28	,	,	PUNCT
ejpam-2515	349	29	z	z	NOUN
ejpam-2515	349	30	)	)	PUNCT
ejpam-2515	349	31	∈	∈	PROPN
ejpam-2515	349	32	ρ	ρ	NOUN
ejpam-2515	349	33	.	.	PUNCT
ejpam-2515	350	1	hence	hence	ADV
ejpam-2515	350	2	,	,	PUNCT
ejpam-2515	350	3	from	from	ADP
ejpam-2515	350	4	(	(	PUNCT
ejpam-2515	350	5	x	x	INTJ
ejpam-2515	350	6	,	,	PUNCT
ejpam-2515	350	7	u	u	NOUN
ejpam-2515	350	8	,	,	PUNCT
ejpam-2515	350	9	v	v	NOUN
ejpam-2515	350	10	)	)	PUNCT
ejpam-2515	350	11	∈	∈	PROPN
ejpam-2515	350	12	ρ	ρ	PROPN
ejpam-2515	350	13	and	and	CCONJ
ejpam-2515	350	14	(	(	PUNCT
ejpam-2515	350	15	y	y	PROPN
ejpam-2515	350	16	,	,	PUNCT
ejpam-2515	350	17	v	v	NOUN
ejpam-2515	350	18	,	,	PUNCT
ejpam-2515	350	19	z	z	NOUN
ejpam-2515	350	20	)	)	PUNCT
ejpam-2515	350	21	∈	∈	PROPN
ejpam-2515	350	22	ρ	ρ	PROPN
ejpam-2515	350	23	,	,	PUNCT
ejpam-2515	350	24	it	it	PRON
ejpam-2515	350	25	follows	follow	VERB
ejpam-2515	350	26	that	that	SCONJ
ejpam-2515	350	27	u	u	PROPN
ejpam-2515	350	28	∈	∈	PROPN
ejpam-2515	350	29	x	x	PUNCT
ejpam-2515	350	30	◦	◦	NOUN
ejpam-2515	350	31	ρ	ρ	NUM
ejpam-2515	350	32	v	v	NOUN
ejpam-2515	350	33	with	with	ADP
ejpam-2515	350	34	v	v	ADP
ejpam-2515	350	35	∈	∈	PROPN
ejpam-2515	350	36	y	y	PROPN
ejpam-2515	350	37	◦	◦	NOUN
ejpam-2515	350	38	ρ	ρ	PROPN
ejpam-2515	350	39	z.	z.	PROPN
ejpam-2515	350	40	therefore	therefore	ADV
ejpam-2515	350	41	u	u	PROPN
ejpam-2515	350	42	∈	∈	PROPN
ejpam-2515	350	43	x	x	PUNCT
ejpam-2515	350	44	◦	◦	NOUN
ejpam-2515	350	45	ρ	ρ	X
ejpam-2515	350	46	(	(	PUNCT
ejpam-2515	350	47	y	y	PROPN
ejpam-2515	350	48	◦	◦	PROPN
ejpam-2515	350	49	ρ	ρ	PROPN
ejpam-2515	350	50	z	z	NOUN
ejpam-2515	350	51	)	)	PUNCT
ejpam-2515	350	52	.	.	PUNCT
ejpam-2515	351	1	now	now	ADV
ejpam-2515	351	2	,	,	PUNCT
ejpam-2515	351	3	suppose	suppose	VERB
ejpam-2515	351	4	u	u	PROPN
ejpam-2515	351	5	=	=	PROPN
ejpam-2515	351	6	y	y	PROPN
ejpam-2515	351	7	.	.	PUNCT
ejpam-2515	352	1	then	then	ADV
ejpam-2515	352	2	we	we	PRON
ejpam-2515	352	3	obtain	obtain	VERB
ejpam-2515	352	4	(	(	PUNCT
ejpam-2515	352	5	x	x	X
ejpam-2515	352	6	,	,	PUNCT
ejpam-2515	352	7	y	y	PROPN
ejpam-2515	352	8	,	,	PUNCT
ejpam-2515	352	9	v	v	NOUN
ejpam-2515	352	10	)	)	PUNCT
ejpam-2515	352	11	,	,	PUNCT
ejpam-2515	352	12	(	(	PUNCT
ejpam-2515	352	13	y	y	NOUN
ejpam-2515	352	14	,	,	PUNCT
ejpam-2515	352	15	v	v	NOUN
ejpam-2515	352	16	,	,	PUNCT
ejpam-2515	352	17	z	z	NOUN
ejpam-2515	352	18	)	)	PUNCT
ejpam-2515	352	19	∈	∈	PROPN
ejpam-2515	352	20	ρ	ρ	PROPN
ejpam-2515	352	21	since	since	SCONJ
ejpam-2515	352	22	(	(	PUNCT
ejpam-2515	352	23	x	x	INTJ
ejpam-2515	352	24	,	,	PUNCT
ejpam-2515	352	25	y	y	PROPN
ejpam-2515	352	26	,	,	PUNCT
ejpam-2515	352	27	z	z	NOUN
ejpam-2515	352	28	)	)	PUNCT
ejpam-2515	352	29	∈	∈	PROPN
ejpam-2515	352	30	α1,2,4	α1,2,4	PROPN
ejpam-2515	352	31	∩α1,3,4	∩α1,3,4	ADJ
ejpam-2515	352	32	.	.	PUNCT
ejpam-2515	353	1	hence	hence	ADV
ejpam-2515	353	2	,	,	PUNCT
ejpam-2515	353	3	from	from	ADP
ejpam-2515	353	4	(	(	PUNCT
ejpam-2515	353	5	x	x	X
ejpam-2515	353	6	,	,	PUNCT
ejpam-2515	353	7	y	y	PROPN
ejpam-2515	353	8	=	=	SYM
ejpam-2515	353	9	u	u	PROPN
ejpam-2515	353	10	,	,	PUNCT
ejpam-2515	353	11	v	v	NOUN
ejpam-2515	353	12	)	)	PUNCT
ejpam-2515	353	13	∈	∈	PROPN
ejpam-2515	353	14	ρ	ρ	PROPN
ejpam-2515	353	15	and	and	CCONJ
ejpam-2515	353	16	(	(	PUNCT
ejpam-2515	353	17	y	y	PROPN
ejpam-2515	353	18	,	,	PUNCT
ejpam-2515	353	19	v	v	NOUN
ejpam-2515	353	20	,	,	PUNCT
ejpam-2515	353	21	z	z	NOUN
ejpam-2515	353	22	)	)	PUNCT
ejpam-2515	353	23	∈	∈	PROPN
ejpam-2515	353	24	ρ	ρ	PROPN
ejpam-2515	353	25	,	,	PUNCT
ejpam-2515	353	26	it	it	PRON
ejpam-2515	353	27	follows	follow	VERB
ejpam-2515	353	28	u	u	PRON
ejpam-2515	353	29	∈	∈	PROPN
ejpam-2515	353	30	x	x	SYM
ejpam-2515	353	31	◦	◦	NOUN
ejpam-2515	353	32	ρ	ρ	NUM
ejpam-2515	353	33	v	v	NOUN
ejpam-2515	353	34	with	with	ADP
ejpam-2515	353	35	v	v	ADP
ejpam-2515	353	36	∈	∈	PROPN
ejpam-2515	353	37	y	y	PROPN
ejpam-2515	353	38	◦	◦	NOUN
ejpam-2515	353	39	ρ	ρ	PROPN
ejpam-2515	353	40	z.	z.	PROPN
ejpam-2515	353	41	therefore	therefore	ADV
ejpam-2515	353	42	u	u	PROPN
ejpam-2515	353	43	∈	∈	PROPN
ejpam-2515	353	44	x	x	PUNCT
ejpam-2515	353	45	◦	◦	NOUN
ejpam-2515	353	46	ρ	ρ	X
ejpam-2515	353	47	(	(	PUNCT
ejpam-2515	353	48	y	y	PROPN
ejpam-2515	353	49	◦	◦	PROPN
ejpam-2515	353	50	ρ	ρ	PROPN
ejpam-2515	353	51	z	z	PROPN
ejpam-2515	353	52	)	)	PUNCT
ejpam-2515	353	53	.	.	PUNCT
ejpam-2515	354	1	finally	finally	ADV
ejpam-2515	354	2	,	,	PUNCT
ejpam-2515	354	3	suppose	suppose	VERB
ejpam-2515	354	4	u	u	PROPN
ejpam-2515	354	5	∈	∈	PROPN
ejpam-2515	354	6	y	y	PROPN
ejpam-2515	354	7	◦	◦	PROPN
ejpam-2515	354	8	ρ	ρ	PROPN
ejpam-2515	354	9	z.	z.	PROPN
ejpam-2515	354	10	by	by	ADP
ejpam-2515	354	11	the	the	DET
ejpam-2515	354	12	definition	definition	NOUN
ejpam-2515	354	13	of	of	ADP
ejpam-2515	354	14	the	the	DET
ejpam-2515	354	15	product	product	NOUN
ejpam-2515	354	16	◦	◦	NOUN
ejpam-2515	354	17	ρ	ρ	PROPN
ejpam-2515	354	18	,	,	PUNCT
ejpam-2515	354	19	u	u	PROPN
ejpam-2515	354	20	∈	∈	PROPN
ejpam-2515	354	21	x	x	PUNCT
ejpam-2515	354	22	◦	◦	NOUN
ejpam-2515	354	23	ρ	ρ	NUM
ejpam-2515	354	24	u	u	NOUN
ejpam-2515	354	25	,	,	PUNCT
ejpam-2515	354	26	whence	whence	NOUN
ejpam-2515	354	27	(	(	PUNCT
ejpam-2515	354	28	x	x	X
ejpam-2515	354	29	,	,	PUNCT
ejpam-2515	354	30	u	u	NOUN
ejpam-2515	354	31	,	,	PUNCT
ejpam-2515	354	32	u	u	NOUN
ejpam-2515	354	33	)	)	PUNCT
ejpam-2515	354	34	∈	∈	PROPN
ejpam-2515	354	35	ρ	ρ	NOUN
ejpam-2515	354	36	and	and	CCONJ
ejpam-2515	354	37	so	so	ADV
ejpam-2515	354	38	u	u	PROPN
ejpam-2515	354	39	∈	∈	PROPN
ejpam-2515	354	40	x	x	PUNCT
ejpam-2515	354	41	◦	◦	NOUN
ejpam-2515	354	42	ρ	ρ	X
ejpam-2515	354	43	(	(	PUNCT
ejpam-2515	354	44	y	y	PROPN
ejpam-2515	354	45	◦	◦	PROPN
ejpam-2515	354	46	ρ	ρ	PROPN
ejpam-2515	354	47	z	z	NOUN
ejpam-2515	354	48	)	)	PUNCT
ejpam-2515	354	49	.	.	PUNCT
ejpam-2515	355	1	thus	thus	ADV
ejpam-2515	355	2	,	,	PUNCT
ejpam-2515	355	3	we	we	PRON
ejpam-2515	355	4	have	have	AUX
ejpam-2515	355	5	established	establish	VERB
ejpam-2515	355	6	the	the	DET
ejpam-2515	355	7	following	follow	VERB
ejpam-2515	355	8	result	result	NOUN
ejpam-2515	355	9	:	:	PUNCT
ejpam-2515	355	10	u	u	NOUN
ejpam-2515	355	11	∈	∈	PROPN
ejpam-2515	355	12	x	x	PUNCT
ejpam-2515	355	13	◦	◦	NOUN
ejpam-2515	355	14	ρ	ρ	X
ejpam-2515	355	15	(	(	PUNCT
ejpam-2515	355	16	y	y	PROPN
ejpam-2515	355	17	◦	◦	PROPN
ejpam-2515	355	18	ρ	ρ	PROPN
ejpam-2515	355	19	z)	z)	NUM
ejpam-2515	355	20	⇐	⇐	ADJ
ejpam-2515	355	21	⇒	⇒	NOUN
ejpam-2515	355	22	u	u	X
ejpam-2515	355	23	∈	∈	PROPN
ejpam-2515	355	24	x	x	PUNCT
ejpam-2515	355	25	◦	◦	NOUN
ejpam-2515	355	26	ρ	ρ	X
ejpam-2515	355	27	y	y	PROPN
ejpam-2515	355	28	∪	∪	PROPN
ejpam-2515	355	29	y	y	PROPN
ejpam-2515	355	30	◦	◦	NOUN
ejpam-2515	355	31	ρ	ρ	PROPN
ejpam-2515	355	32	y	y	PROPN
ejpam-2515	355	33	∪	∪	PROPN
ejpam-2515	355	34	y	y	PROPN
ejpam-2515	355	35	◦	◦	PROPN
ejpam-2515	355	36	ρ	ρ	PROPN
ejpam-2515	355	37	z.	z.	PROPN
ejpam-2515	355	38	by	by	ADP
ejpam-2515	355	39	the	the	DET
ejpam-2515	355	40	same	same	ADJ
ejpam-2515	355	41	way	way	NOUN
ejpam-2515	355	42	,	,	PUNCT
ejpam-2515	355	43	we	we	PRON
ejpam-2515	355	44	prove	prove	VERB
ejpam-2515	355	45	the	the	DET
ejpam-2515	355	46	following	follow	VERB
ejpam-2515	355	47	result	result	NOUN
ejpam-2515	355	48	:	:	PUNCT
ejpam-2515	355	49	u	u	NOUN
ejpam-2515	355	50	∈	∈	PROPN
ejpam-2515	355	51	(	(	PUNCT
ejpam-2515	355	52	x	x	SYM
ejpam-2515	355	53	◦	◦	NOUN
ejpam-2515	355	54	ρ	ρ	NUM
ejpam-2515	355	55	y	y	NOUN
ejpam-2515	355	56	)	)	PUNCT
ejpam-2515	355	57	◦	◦	NOUN
ejpam-2515	355	58	ρ	ρ	PROPN
ejpam-2515	355	59	z	z	NOUN
ejpam-2515	355	60	⇐	⇐	ADJ
ejpam-2515	355	61	⇒	⇒	NOUN
ejpam-2515	355	62	u	u	X
ejpam-2515	355	63	∈	∈	PROPN
ejpam-2515	355	64	x	x	PUNCT
ejpam-2515	355	65	◦	◦	NOUN
ejpam-2515	355	66	ρ	ρ	X
ejpam-2515	355	67	y	y	PROPN
ejpam-2515	355	68	∪	∪	PROPN
ejpam-2515	355	69	y	y	PROPN
ejpam-2515	355	70	◦	◦	NOUN
ejpam-2515	355	71	ρ	ρ	PROPN
ejpam-2515	355	72	y	y	PROPN
ejpam-2515	355	73	∪	∪	PROPN
ejpam-2515	355	74	y	y	PROPN
ejpam-2515	355	75	◦	◦	NOUN
ejpam-2515	355	76	ρ	ρ	PROPN
ejpam-2515	355	77	z.	z.	PROPN
ejpam-2515	356	1	we	we	PRON
ejpam-2515	356	2	find	find	VERB
ejpam-2515	356	3	x	x	PUNCT
ejpam-2515	356	4	◦	◦	NOUN
ejpam-2515	356	5	ρ	ρ	X
ejpam-2515	356	6	(	(	PUNCT
ejpam-2515	356	7	y	y	PROPN
ejpam-2515	356	8	◦	◦	PROPN
ejpam-2515	356	9	ρ	ρ	PROPN
ejpam-2515	356	10	z	z	NOUN
ejpam-2515	356	11	)	)	PUNCT
ejpam-2515	356	12	=	=	SYM
ejpam-2515	357	1	(	(	PUNCT
ejpam-2515	357	2	x	x	SYM
ejpam-2515	357	3	◦	◦	NOUN
ejpam-2515	357	4	ρ	ρ	NUM
ejpam-2515	357	5	y	y	NOUN
ejpam-2515	357	6	)	)	PUNCT
ejpam-2515	357	7	◦	◦	NOUN
ejpam-2515	357	8	ρ	ρ	PROPN
ejpam-2515	357	9	z.	z.	PROPN
ejpam-2515	358	1	this	this	PRON
ejpam-2515	358	2	completes	complete	VERB
ejpam-2515	358	3	the	the	DET
ejpam-2515	358	4	proof	proof	NOUN
ejpam-2515	358	5	.	.	PUNCT
ejpam-2515	359	1	4	4	X
ejpam-2515	359	2	.	.	X
ejpam-2515	359	3	the	the	DET
ejpam-2515	359	4	associated	associated	ADJ
ejpam-2515	359	5	join	join	NOUN
ejpam-2515	359	6	space	space	NOUN
ejpam-2515	359	7	of	of	ADP
ejpam-2515	359	8	the	the	DET
ejpam-2515	359	9	spherical	spherical	ADJ
ejpam-2515	359	10	geometry	geometry	NOUN
ejpam-2515	359	11	proposition	proposition	NOUN
ejpam-2515	359	12	10	10	NUM
ejpam-2515	359	13	.	.	PUNCT
ejpam-2515	360	1	let	let	VERB
ejpam-2515	360	2	ρ	ρ	NOUN
ejpam-2515	360	3	be	be	AUX
ejpam-2515	360	4	a	a	DET
ejpam-2515	360	5	reflexive	reflexive	ADJ
ejpam-2515	360	6	and	and	CCONJ
ejpam-2515	360	7	symmetric	symmetric	ADJ
ejpam-2515	360	8	ternary	ternary	ADJ
ejpam-2515	360	9	relation	relation	NOUN
ejpam-2515	360	10	on	on	ADP
ejpam-2515	360	11	h	h	NOUN
ejpam-2515	360	12	with	with	ADP
ejpam-2515	360	13	|h|	|h|	PROPN
ejpam-2515	360	14	≥	≥	NUM
ejpam-2515	360	15	3	3	NUM
ejpam-2515	361	1	such	such	ADJ
ejpam-2515	361	2	that	that	DET
ejpam-2515	361	3	ρ1,2	ρ1,2	ADJ
ejpam-2515	361	4	=	=	SYM
ejpam-2515	361	5	ρ2,3	ρ2,3	PUNCT
ejpam-2515	361	6	=	=	SYM
ejpam-2515	361	7	ρ1,3	ρ1,3	PROPN
ejpam-2515	361	8	=	=	SYM
ejpam-2515	361	9	h	h	PROPN
ejpam-2515	361	10	×h	×h	PROPN
ejpam-2515	361	11	.	.	PUNCT
ejpam-2515	362	1	let	let	VERB
ejpam-2515	362	2	ρ	ρ	NOUN
ejpam-2515	362	3	satisfies	satisfie	NOUN
ejpam-2515	362	4	the	the	DET
ejpam-2515	362	5	following	follow	VERB
ejpam-2515	362	6	postulates	postulate	NOUN
ejpam-2515	362	7	:	:	PUNCT
ejpam-2515	362	8	(	(	PUNCT
ejpam-2515	362	9	i	i	NOUN
ejpam-2515	362	10	)	)	PUNCT
ejpam-2515	362	11	if	if	SCONJ
ejpam-2515	362	12	(	(	PUNCT
ejpam-2515	362	13	x	x	X
ejpam-2515	362	14	,	,	PUNCT
ejpam-2515	362	15	y	y	PROPN
ejpam-2515	362	16	,	,	PUNCT
ejpam-2515	362	17	z	z	NOUN
ejpam-2515	362	18	)	)	PUNCT
ejpam-2515	362	19	∈	∈	PROPN
ejpam-2515	362	20	ρ	ρ	PROPN
ejpam-2515	362	21	,	,	PUNCT
ejpam-2515	362	22	then	then	ADV
ejpam-2515	362	23	x	x	SYM
ejpam-2515	362	24	,	,	PUNCT
ejpam-2515	362	25	y	y	PROPN
ejpam-2515	362	26	,	,	PUNCT
ejpam-2515	362	27	z	z	PROPN
ejpam-2515	362	28	are	be	AUX
ejpam-2515	362	29	distinct	distinct	ADJ
ejpam-2515	362	30	;	;	PUNCT
ejpam-2515	362	31	(	(	PUNCT
ejpam-2515	362	32	ii	ii	NOUN
ejpam-2515	362	33	)	)	PUNCT
ejpam-2515	362	34	for	for	ADP
ejpam-2515	362	35	any	any	DET
ejpam-2515	362	36	x	x	NOUN
ejpam-2515	362	37	,	,	PUNCT
ejpam-2515	362	38	there	there	PRON
ejpam-2515	362	39	exists	exist	VERB
ejpam-2515	362	40	a	a	DET
ejpam-2515	362	41	unique	unique	ADJ
ejpam-2515	362	42	x	x	NOUN
ejpam-2515	362	43	′	′	NUM
ejpam-2515	362	44	such	such	ADJ
ejpam-2515	362	45	that	that	SCONJ
ejpam-2515	362	46	(	(	PUNCT
ejpam-2515	362	47	x	x	X
ejpam-2515	362	48	,	,	PUNCT
ejpam-2515	362	49	y	y	PROPN
ejpam-2515	362	50	,	,	PUNCT
ejpam-2515	362	51	x	x	NOUN
ejpam-2515	362	52	′	′	X
ejpam-2515	362	53	)	)	PUNCT
ejpam-2515	362	54	∈	∈	PROPN
ejpam-2515	362	55	α1,3,4	α1,3,4	PROPN
ejpam-2515	362	56	;	;	PUNCT
ejpam-2515	362	57	(	(	PUNCT
ejpam-2515	362	58	iii	iii	X
ejpam-2515	362	59	)	)	PUNCT
ejpam-2515	362	60	if	if	SCONJ
ejpam-2515	362	61	x	x	PROPN
ejpam-2515	362	62	6=	6=	NUM
ejpam-2515	362	63	y	y	PROPN
ejpam-2515	362	64	,	,	PUNCT
ejpam-2515	362	65	then	then	ADV
ejpam-2515	362	66	(	(	PUNCT
ejpam-2515	362	67	x	x	X
ejpam-2515	362	68	,	,	PUNCT
ejpam-2515	362	69	y	y	PROPN
ejpam-2515	362	70	,	,	PUNCT
ejpam-2515	362	71	x	x	NOUN
ejpam-2515	362	72	)	)	PUNCT
ejpam-2515	362	73	6∈	6∈	PROPN
ejpam-2515	362	74	ρ	ρ	PROPN
ejpam-2515	362	75	.	.	PUNCT
ejpam-2515	363	1	then	then	ADV
ejpam-2515	363	2	the	the	DET
ejpam-2515	363	3	extension	extension	NOUN
ejpam-2515	363	4	(	(	PUNCT
ejpam-2515	363	5	h;e	h;e	NOUN
ejpam-2515	363	6	◦	◦	NOUN
ejpam-2515	363	7	ρ	ρ	NOUN
ejpam-2515	363	8	)	)	PUNCT
ejpam-2515	363	9	of	of	ADP
ejpam-2515	363	10	(	(	PUNCT
ejpam-2515	363	11	h	h	NOUN
ejpam-2515	363	12	;	;	PUNCT
ejpam-2515	363	13	⊗	⊗	PROPN
ejpam-2515	363	14	ρ	ρ	PROPN
ejpam-2515	363	15	)	)	PUNCT
ejpam-2515	363	16	defined	define	VERB
ejpam-2515	363	17	by	by	ADP
ejpam-2515	363	18	the	the	DET
ejpam-2515	363	19	following	following	NOUN
ejpam-2515	363	20	setting	set	VERB
ejpam-2515	363	21	is	be	AUX
ejpam-2515	363	22	a	a	DET
ejpam-2515	363	23	join	join	NOUN
ejpam-2515	363	24	space	space	NOUN
ejpam-2515	363	25	.	.	PUNCT
ejpam-2515	364	1	∀x	∀x	X
ejpam-2515	364	2	6=	6=	ADP
ejpam-2515	364	3	y	y	PROPN
ejpam-2515	364	4	,	,	PUNCT
ejpam-2515	364	5	choose	choose	VERB
ejpam-2515	364	6	t	t	PROPN
ejpam-2515	364	7	∈	∈	PROPN
ejpam-2515	364	8	h	h	NOUN
ejpam-2515	364	9	such	such	ADJ
ejpam-2515	364	10	that	that	SCONJ
ejpam-2515	364	11	x	x	PROPN
ejpam-2515	364	12	6=	6=	ADP
ejpam-2515	364	13	t	t	PROPN
ejpam-2515	364	14	6=	6=	PROPN
ejpam-2515	364	15	x	x	SYM
ejpam-2515	364	16	′.	′.	NOUN
ejpam-2515	364	17	set	set	VERB
ejpam-2515	364	18	∀x	∀x	NUM
ejpam-2515	364	19	6=	6=	NUM
ejpam-2515	364	20	y	y	PROPN
ejpam-2515	364	21	,	,	PUNCT
ejpam-2515	364	22	xe	xe	PROPN
ejpam-2515	364	23	◦	◦	PROPN
ejpam-2515	364	24	ρ	ρ	NOUN
ejpam-2515	364	25	y	y	NOUN
ejpam-2515	364	26	=	=	PRON
ejpam-2515	364	27	{	{	PUNCT
ejpam-2515	364	28	x	x	PROPN
ejpam-2515	364	29	,	,	PUNCT
ejpam-2515	364	30	t	t	PROPN
ejpam-2515	364	31	,	,	PUNCT
ejpam-2515	364	32	y}∀x	y}∀x	NOUN
ejpam-2515	364	33	∈	∈	PROPN
ejpam-2515	364	34	h	h	PROPN
ejpam-2515	364	35	,	,	PUNCT
ejpam-2515	364	36	xe	xe	PROPN
ejpam-2515	364	37	◦	◦	PROPN
ejpam-2515	364	38	ρ	ρ	PROPN
ejpam-2515	364	39	t	t	NOUN
ejpam-2515	364	40	=	=	SYM
ejpam-2515	364	41	{	{	PUNCT
ejpam-2515	364	42	x	x	NOUN
ejpam-2515	364	43	}	}	PUNCT
ejpam-2515	364	44	=	=	SYM
ejpam-2515	364	45	xe	xe	PROPN
ejpam-2515	364	46	◦	◦	NOUN
ejpam-2515	364	47	ρe	ρe	NOUN
ejpam-2515	364	48	=	=	SYM
ejpam-2515	364	49	{	{	PUNCT
ejpam-2515	364	50	x	x	NOUN
ejpam-2515	364	51	}	}	PUNCT
ejpam-2515	364	52	and	and	CCONJ
ejpam-2515	364	53	for	for	ADP
ejpam-2515	364	54	any	any	DET
ejpam-2515	364	55	t	t	PROPN
ejpam-2515	364	56	,	,	PUNCT
ejpam-2515	364	57	t	t	PROPN
ejpam-2515	364	58	′	′	NUM
ejpam-2515	364	59	∈	∈	PROPN
ejpam-2515	364	60	xe	xe	PROPN
ejpam-2515	364	61	◦	◦	PROPN
ejpam-2515	364	62	ρ	ρ	PROPN
ejpam-2515	364	63	y	y	PROPN
ejpam-2515	364	64	,	,	PUNCT
ejpam-2515	364	65	set	set	VERB
ejpam-2515	364	66	te	te	ADP
ejpam-2515	364	67	◦	◦	NOUN
ejpam-2515	364	68	ρ	ρ	NOUN
ejpam-2515	364	69	t	t	NOUN
ejpam-2515	364	70	′	′	NUM
ejpam-2515	365	1	=	=	SYM
ejpam-2515	365	2	{	{	PUNCT
ejpam-2515	365	3	t	t	PROPN
ejpam-2515	365	4	,	,	PUNCT
ejpam-2515	365	5	t	t	PROPN
ejpam-2515	365	6	′	′	NUM
ejpam-2515	365	7	}	}	PUNCT
ejpam-2515	365	8	s.	s.	PROPN
ejpam-2515	365	9	govindarajan	govindarajan	PROPN
ejpam-2515	365	10	/	/	SYM
ejpam-2515	365	11	eur	eur	PROPN
ejpam-2515	365	12	.	.	PUNCT
ejpam-2515	366	1	j.	j.	PROPN
ejpam-2515	366	2	pure	pure	PROPN
ejpam-2515	366	3	appl	appl	PROPN
ejpam-2515	366	4	.	.	PROPN
ejpam-2515	366	5	math	math	PROPN
ejpam-2515	366	6	,	,	PUNCT
ejpam-2515	366	7	9	9	NUM
ejpam-2515	366	8	(	(	PUNCT
ejpam-2515	366	9	2016	2016	NUM
ejpam-2515	366	10	)	)	PUNCT
ejpam-2515	366	11	,	,	PUNCT
ejpam-2515	366	12	367	367	NUM
ejpam-2515	366	13	-	-	SYM
ejpam-2515	366	14	382	382	NUM
ejpam-2515	366	15	379	379	NUM
ejpam-2515	366	16	proof	proof	NOUN
ejpam-2515	366	17	.	.	PUNCT
ejpam-2515	367	1	suppose	suppose	VERB
ejpam-2515	367	2	ρ	ρ	NOUN
ejpam-2515	367	3	be	be	AUX
ejpam-2515	367	4	a	a	DET
ejpam-2515	367	5	reflexive	reflexive	ADJ
ejpam-2515	367	6	and	and	CCONJ
ejpam-2515	367	7	symmetric	symmetric	ADJ
ejpam-2515	367	8	ternary	ternary	ADJ
ejpam-2515	367	9	relation	relation	NOUN
ejpam-2515	367	10	on	on	ADP
ejpam-2515	367	11	h.	h.	PROPN
ejpam-2515	367	12	then	then	ADV
ejpam-2515	367	13	,	,	PUNCT
ejpam-2515	367	14	from	from	ADP
ejpam-2515	367	15	the	the	DET
ejpam-2515	367	16	hypothesis	hypothesis	NOUN
ejpam-2515	367	17	,	,	PUNCT
ejpam-2515	367	18	we	we	PRON
ejpam-2515	367	19	obtain	obtain	VERB
ejpam-2515	367	20	the	the	DET
ejpam-2515	367	21	following	following	ADJ
ejpam-2515	367	22	implications	implication	NOUN
ejpam-2515	367	23	:	:	PUNCT
ejpam-2515	367	24	(	(	PUNCT
ejpam-2515	367	25	i	i	NOUN
ejpam-2515	367	26	)	)	PUNCT
ejpam-2515	367	27	if	if	SCONJ
ejpam-2515	367	28	(	(	PUNCT
ejpam-2515	367	29	x	x	X
ejpam-2515	367	30	,	,	PUNCT
ejpam-2515	367	31	y	y	PROPN
ejpam-2515	367	32	,	,	PUNCT
ejpam-2515	367	33	z	z	NOUN
ejpam-2515	367	34	)	)	PUNCT
ejpam-2515	367	35	∈	∈	PROPN
ejpam-2515	367	36	ρ	ρ	PROPN
ejpam-2515	367	37	,	,	PUNCT
ejpam-2515	367	38	then	then	ADV
ejpam-2515	367	39	x	x	SYM
ejpam-2515	367	40	,	,	PUNCT
ejpam-2515	367	41	y	y	PROPN
ejpam-2515	367	42	,	,	PUNCT
ejpam-2515	367	43	z	z	PROPN
ejpam-2515	367	44	are	be	AUX
ejpam-2515	367	45	distinct	distinct	ADJ
ejpam-2515	367	46	;	;	PUNCT
ejpam-2515	367	47	(	(	PUNCT
ejpam-2515	367	48	ii	ii	NOUN
ejpam-2515	367	49	)	)	PUNCT
ejpam-2515	367	50	if	if	SCONJ
ejpam-2515	367	51	(	(	PUNCT
ejpam-2515	367	52	x	x	X
ejpam-2515	367	53	,	,	PUNCT
ejpam-2515	367	54	y	y	PROPN
ejpam-2515	367	55	,	,	PUNCT
ejpam-2515	367	56	z	z	NOUN
ejpam-2515	367	57	)	)	PUNCT
ejpam-2515	367	58	∈	∈	PROPN
ejpam-2515	367	59	ρ	ρ	PROPN
ejpam-2515	367	60	,	,	PUNCT
ejpam-2515	367	61	then	then	ADV
ejpam-2515	367	62	(	(	PUNCT
ejpam-2515	367	63	z	z	X
ejpam-2515	367	64	,	,	PUNCT
ejpam-2515	367	65	y	y	PROPN
ejpam-2515	367	66	,	,	PUNCT
ejpam-2515	367	67	x	x	X
ejpam-2515	367	68	)	)	PUNCT
ejpam-2515	367	69	∈	∈	NOUN
ejpam-2515	367	70	ρ	ρ	NOUN
ejpam-2515	367	71	are	be	AUX
ejpam-2515	367	72	distinct	distinct	ADJ
ejpam-2515	367	73	.	.	PUNCT
ejpam-2515	368	1	(	(	PUNCT
ejpam-2515	368	2	iii	iii	X
ejpam-2515	368	3	)	)	PUNCT
ejpam-2515	368	4	for	for	ADP
ejpam-2515	368	5	any	any	PRON
ejpam-2515	368	6	x	x	NOUN
ejpam-2515	368	7	,	,	PUNCT
ejpam-2515	368	8	there	there	PRON
ejpam-2515	368	9	exists	exist	VERB
ejpam-2515	368	10	a	a	DET
ejpam-2515	368	11	unique	unique	ADJ
ejpam-2515	368	12	x	x	NOUN
ejpam-2515	368	13	′	′	NUM
ejpam-2515	368	14	such	such	ADJ
ejpam-2515	368	15	that	that	SCONJ
ejpam-2515	368	16	(	(	PUNCT
ejpam-2515	368	17	x	x	X
ejpam-2515	368	18	,	,	PUNCT
ejpam-2515	368	19	y	y	PROPN
ejpam-2515	368	20	,	,	PUNCT
ejpam-2515	368	21	x	x	NOUN
ejpam-2515	368	22	′	′	X
ejpam-2515	368	23	)	)	PUNCT
ejpam-2515	368	24	∈	∈	NOUN
ejpam-2515	369	1	α1,3,4	α1,3,4	NUM
ejpam-2515	369	2	=	=	AUX
ejpam-2515	369	3	⇒	⇒	NOUN
ejpam-2515	369	4	for	for	ADP
ejpam-2515	369	5	any	any	DET
ejpam-2515	369	6	x	x	NOUN
ejpam-2515	369	7	,	,	PUNCT
ejpam-2515	369	8	there	there	PRON
ejpam-2515	369	9	exists	exist	VERB
ejpam-2515	369	10	a	a	DET
ejpam-2515	369	11	unique	unique	ADJ
ejpam-2515	369	12	x	x	NOUN
ejpam-2515	369	13	′	′	NOUN
ejpam-2515	369	14	and	and	CCONJ
ejpam-2515	369	15	an	an	DET
ejpam-2515	369	16	element	element	NOUN
ejpam-2515	369	17	u	u	NOUN
ejpam-2515	369	18	∈	∈	NOUN
ejpam-2515	369	19	h	h	NOUN
ejpam-2515	369	20	such	such	ADJ
ejpam-2515	369	21	that	that	SCONJ
ejpam-2515	369	22	(	(	PUNCT
ejpam-2515	369	23	x	x	X
ejpam-2515	369	24	,	,	PUNCT
ejpam-2515	369	25	u	u	NOUN
ejpam-2515	369	26	,	,	PUNCT
ejpam-2515	369	27	y	y	NOUN
ejpam-2515	369	28	)	)	PUNCT
ejpam-2515	369	29	∈	∈	PROPN
ejpam-2515	369	30	ρ	ρ	PROPN
ejpam-2515	369	31	and	and	CCONJ
ejpam-2515	369	32	(	(	PUNCT
ejpam-2515	369	33	u	u	NOUN
ejpam-2515	369	34	,	,	PUNCT
ejpam-2515	369	35	y	y	PROPN
ejpam-2515	369	36	,	,	PUNCT
ejpam-2515	369	37	x	x	NOUN
ejpam-2515	369	38	′	′	X
ejpam-2515	369	39	)	)	PUNCT
ejpam-2515	369	40	∈	∈	PROPN
ejpam-2515	369	41	ρ	ρ	PROPN
ejpam-2515	369	42	,	,	PUNCT
ejpam-2515	369	43	(	(	PUNCT
ejpam-2515	369	44	iv	iv	X
ejpam-2515	369	45	)	)	PUNCT
ejpam-2515	369	46	if	if	SCONJ
ejpam-2515	369	47	x	x	PROPN
ejpam-2515	369	48	6=	6=	NUM
ejpam-2515	369	49	y	y	PROPN
ejpam-2515	369	50	,	,	PUNCT
ejpam-2515	369	51	then	then	ADV
ejpam-2515	369	52	(	(	PUNCT
ejpam-2515	369	53	x	x	X
ejpam-2515	369	54	,	,	PUNCT
ejpam-2515	369	55	y	y	PROPN
ejpam-2515	369	56	,	,	PUNCT
ejpam-2515	369	57	x	x	NOUN
ejpam-2515	369	58	)	)	PUNCT
ejpam-2515	369	59	6∈	6∈	NOUN
ejpam-2515	369	60	ρ	ρ	NOUN
ejpam-2515	369	61	=	=	PUNCT
ejpam-2515	369	62	⇒∀x	⇒∀x	NOUN
ejpam-2515	369	63	∈	∈	PROPN
ejpam-2515	369	64	h	h	NOUN
ejpam-2515	369	65	,	,	PUNCT
ejpam-2515	369	66	x	x	X
ejpam-2515	369	67	e	e	X
ejpam-2515	369	68	◦	◦	NOUN
ejpam-2515	369	69	ρ	ρ	NOUN
ejpam-2515	369	70	x	x	SYM
ejpam-2515	369	71	=	=	PRON
ejpam-2515	369	72	{	{	PUNCT
ejpam-2515	369	73	x	x	NOUN
ejpam-2515	369	74	}	}	PUNCT
ejpam-2515	369	75	.	.	PUNCT
ejpam-2515	370	1	hence	hence	ADV
ejpam-2515	370	2	,	,	PUNCT
ejpam-2515	370	3	ρ	ρ	PROPN
ejpam-2515	370	4	is	be	AUX
ejpam-2515	370	5	the	the	DET
ejpam-2515	370	6	betweenness	betweenness	PROPN
ejpam-2515	370	7	relation	relation	NOUN
ejpam-2515	370	8	on	on	ADP
ejpam-2515	370	9	h.	h.	PROPN
ejpam-2515	370	10	since	since	SCONJ
ejpam-2515	370	11	ρ1,2	ρ1,2	PROPN
ejpam-2515	370	12	=	=	SYM
ejpam-2515	370	13	ρ2,3	ρ2,3	PUNCT
ejpam-2515	370	14	=	=	NOUN
ejpam-2515	371	1	h	h	NOUN
ejpam-2515	371	2	×h	×h	PROPN
ejpam-2515	371	3	,	,	PUNCT
ejpam-2515	371	4	it	it	PRON
ejpam-2515	371	5	follows	follow	VERB
ejpam-2515	371	6	,	,	PUNCT
ejpam-2515	371	7	by	by	ADP
ejpam-2515	371	8	proposition	proposition	NOUN
ejpam-2515	371	9	1	1	NUM
ejpam-2515	371	10	,	,	PUNCT
ejpam-2515	371	11	that	that	PRON
ejpam-2515	371	12	(	(	PUNCT
ejpam-2515	371	13	h;e	h;e	NOUN
ejpam-2515	371	14	◦	◦	NOUN
ejpam-2515	371	15	ρ	ρ	NOUN
ejpam-2515	371	16	)	)	PUNCT
ejpam-2515	371	17	is	be	AUX
ejpam-2515	371	18	a	a	DET
ejpam-2515	371	19	quasihypergroup	quasihypergroup	NOUN
ejpam-2515	371	20	.	.	PUNCT
ejpam-2515	372	1	moreover	moreover	ADV
ejpam-2515	372	2	,	,	PUNCT
ejpam-2515	372	3	since	since	SCONJ
ejpam-2515	372	4	ρ	ρ	PROPN
ejpam-2515	372	5	is	be	AUX
ejpam-2515	372	6	symmetric	symmetric	ADJ
ejpam-2515	372	7	,	,	PUNCT
ejpam-2515	372	8	it	it	PRON
ejpam-2515	372	9	follows	follow	VERB
ejpam-2515	372	10	that	that	SCONJ
ejpam-2515	372	11	x	x	PUNCT
ejpam-2515	372	12	e	e	X
ejpam-2515	372	13	◦	◦	NOUN
ejpam-2515	372	14	ρ	ρ	NOUN
ejpam-2515	372	15	y	y	NOUN
ejpam-2515	372	16	=	=	PUNCT
ejpam-2515	372	17	y	y	PROPN
ejpam-2515	372	18	e	e	X
ejpam-2515	372	19	◦	◦	NOUN
ejpam-2515	372	20	ρ	ρ	NOUN
ejpam-2515	372	21	x	x	SYM
ejpam-2515	372	22	,	,	PUNCT
ejpam-2515	372	23	for	for	ADP
ejpam-2515	372	24	any	any	DET
ejpam-2515	372	25	x	x	SYM
ejpam-2515	372	26	,	,	PUNCT
ejpam-2515	372	27	y	y	PROPN
ejpam-2515	372	28	∈	∈	PROPN
ejpam-2515	372	29	h	h	NOUN
ejpam-2515	372	30	,	,	PUNCT
ejpam-2515	372	31	and	and	CCONJ
ejpam-2515	372	32	therefore	therefore	ADV
ejpam-2515	372	33	(	(	PUNCT
ejpam-2515	372	34	h;e	h;e	NOUN
ejpam-2515	372	35	◦	◦	NOUN
ejpam-2515	372	36	ρ	ρ	NOUN
ejpam-2515	372	37	)	)	PUNCT
ejpam-2515	372	38	is	be	AUX
ejpam-2515	372	39	commutative	commutative	ADJ
ejpam-2515	372	40	.	.	PUNCT
ejpam-2515	373	1	now	now	ADV
ejpam-2515	373	2	,	,	PUNCT
ejpam-2515	373	3	we	we	PRON
ejpam-2515	373	4	prove	prove	VERB
ejpam-2515	373	5	that	that	SCONJ
ejpam-2515	373	6	the	the	DET
ejpam-2515	373	7	hyper	hyper	ADJ
ejpam-2515	373	8	operation	operation	NOUN
ejpam-2515	373	9	〈	〈	PROPN
ejpam-2515	373	10	e	e	PROPN
ejpam-2515	373	11	◦	◦	NOUN
ejpam-2515	373	12	ρ	ρ	NOUN
ejpam-2515	373	13	〉	〉	NOUN
ejpam-2515	373	14	is	be	AUX
ejpam-2515	373	15	associative	associative	ADJ
ejpam-2515	373	16	.	.	PUNCT
ejpam-2515	374	1	we	we	PRON
ejpam-2515	374	2	shall	shall	AUX
ejpam-2515	374	3	check	check	VERB
ejpam-2515	374	4	the	the	DET
ejpam-2515	374	5	following	follow	VERB
ejpam-2515	374	6	inclusion	inclusion	NOUN
ejpam-2515	374	7	:	:	PUNCT
ejpam-2515	374	8	∀(x	∀(x	NUM
ejpam-2515	374	9	,	,	PUNCT
ejpam-2515	374	10	y	y	PROPN
ejpam-2515	374	11	,	,	PUNCT
ejpam-2515	374	12	z	z	NOUN
ejpam-2515	374	13	)	)	PUNCT
ejpam-2515	374	14	∈	∈	PROPN
ejpam-2515	374	15	h3	h3	NOUN
ejpam-2515	374	16	,	,	PUNCT
ejpam-2515	374	17	(	(	PUNCT
ejpam-2515	374	18	x	x	PART
ejpam-2515	374	19	e	e	X
ejpam-2515	374	20	◦	◦	NOUN
ejpam-2515	374	21	ρ	ρ	NOUN
ejpam-2515	374	22	y	y	NOUN
ejpam-2515	374	23	)	)	PUNCT
ejpam-2515	374	24	e	e	X
ejpam-2515	374	25	◦	◦	NOUN
ejpam-2515	374	26	ρ	ρ	NOUN
ejpam-2515	374	27	z	z	NOUN
ejpam-2515	374	28	⊂	⊂	PUNCT
ejpam-2515	374	29	x	x	PUNCT
ejpam-2515	375	1	e	e	X
ejpam-2515	375	2	◦	◦	NOUN
ejpam-2515	375	3	ρ	ρ	PROPN
ejpam-2515	375	4	(	(	PUNCT
ejpam-2515	375	5	y	y	PROPN
ejpam-2515	375	6	e	e	PROPN
ejpam-2515	375	7	◦	◦	NOUN
ejpam-2515	375	8	ρ	ρ	PROPN
ejpam-2515	375	9	z	z	NOUN
ejpam-2515	375	10	)	)	PUNCT
ejpam-2515	375	11	.	.	PUNCT
ejpam-2515	376	1	(	(	PUNCT
ejpam-2515	376	2	4	4	X
ejpam-2515	376	3	)	)	PUNCT
ejpam-2515	376	4	let	let	VERB
ejpam-2515	376	5	u	u	PRON
ejpam-2515	376	6	∈	∈	PROPN
ejpam-2515	376	7	(	(	PUNCT
ejpam-2515	376	8	x	x	X
ejpam-2515	376	9	e	e	X
ejpam-2515	376	10	◦	◦	NOUN
ejpam-2515	376	11	ρ	ρ	NOUN
ejpam-2515	376	12	y	y	NOUN
ejpam-2515	376	13	)	)	PUNCT
ejpam-2515	376	14	e	e	X
ejpam-2515	376	15	◦	◦	NOUN
ejpam-2515	376	16	ρ	ρ	PROPN
ejpam-2515	376	17	z.	z.	PROPN
ejpam-2515	376	18	then	then	ADV
ejpam-2515	376	19	,	,	PUNCT
ejpam-2515	376	20	there	there	PRON
ejpam-2515	376	21	exists	exist	VERB
ejpam-2515	376	22	v	v	ADP
ejpam-2515	376	23	∈	∈	PROPN
ejpam-2515	376	24	x	x	PUNCT
ejpam-2515	376	25	e	e	X
ejpam-2515	376	26	◦	◦	NOUN
ejpam-2515	376	27	ρ	ρ	NOUN
ejpam-2515	376	28	y	y	NOUN
ejpam-2515	376	29	such	such	ADJ
ejpam-2515	376	30	that	that	SCONJ
ejpam-2515	376	31	u	u	PROPN
ejpam-2515	376	32	∈	∈	PROPN
ejpam-2515	376	33	x	x	PUNCT
ejpam-2515	377	1	e	e	X
ejpam-2515	377	2	◦	◦	NOUN
ejpam-2515	377	3	ρ	ρ	NOUN
ejpam-2515	377	4	v.	v.	ADP
ejpam-2515	377	5	hence	hence	ADV
ejpam-2515	377	6	,	,	PUNCT
ejpam-2515	377	7	(	(	PUNCT
ejpam-2515	377	8	x	x	X
ejpam-2515	377	9	,	,	PUNCT
ejpam-2515	377	10	v	v	NOUN
ejpam-2515	377	11	,	,	PUNCT
ejpam-2515	377	12	y	y	NOUN
ejpam-2515	377	13	)	)	PUNCT
ejpam-2515	377	14	∈	∈	PROPN
ejpam-2515	377	15	ρ	ρ	PROPN
ejpam-2515	377	16	with	with	ADP
ejpam-2515	377	17	(	(	PUNCT
ejpam-2515	377	18	v	v	NOUN
ejpam-2515	377	19	,	,	PUNCT
ejpam-2515	377	20	u	u	NOUN
ejpam-2515	377	21	,	,	PUNCT
ejpam-2515	377	22	z	z	NOUN
ejpam-2515	377	23	)	)	PUNCT
ejpam-2515	377	24	∈	∈	PROPN
ejpam-2515	377	25	ρ	ρ	NOUN
ejpam-2515	377	26	.	.	PUNCT
ejpam-2515	378	1	we	we	PRON
ejpam-2515	378	2	distinguish	distinguish	VERB
ejpam-2515	378	3	the	the	DET
ejpam-2515	378	4	following	follow	VERB
ejpam-2515	378	5	cases	case	NOUN
ejpam-2515	378	6	:	:	PUNCT
ejpam-2515	378	7	(	(	PUNCT
ejpam-2515	378	8	i	i	NOUN
ejpam-2515	378	9	)	)	PUNCT
ejpam-2515	378	10	if	if	SCONJ
ejpam-2515	378	11	x	x	PROPN
ejpam-2515	378	12	6=	6=	ADP
ejpam-2515	378	13	y	y	PROPN
ejpam-2515	378	14	and	and	CCONJ
ejpam-2515	378	15	y	y	PROPN
ejpam-2515	378	16	6=	6=	PROPN
ejpam-2515	378	17	x	x	SYM
ejpam-2515	378	18	′	′	NUM
ejpam-2515	378	19	then	then	ADV
ejpam-2515	378	20	(	(	PUNCT
ejpam-2515	378	21	v	v	NOUN
ejpam-2515	378	22	,	,	PUNCT
ejpam-2515	378	23	y	y	PROPN
ejpam-2515	378	24	,	,	PUNCT
ejpam-2515	378	25	x	x	NOUN
ejpam-2515	378	26	′	′	X
ejpam-2515	378	27	)	)	PUNCT
ejpam-2515	378	28	∈	∈	PROPN
ejpam-2515	378	29	ρ	ρ	NOUN
ejpam-2515	378	30	;	;	PUNCT
ejpam-2515	378	31	it	it	PRON
ejpam-2515	378	32	follows	follow	VERB
ejpam-2515	378	33	(	(	PUNCT
ejpam-2515	378	34	x	x	INTJ
ejpam-2515	378	35	,	,	PUNCT
ejpam-2515	378	36	y	y	PROPN
ejpam-2515	378	37	,	,	PUNCT
ejpam-2515	378	38	x	x	NOUN
ejpam-2515	378	39	′	′	X
ejpam-2515	378	40	)	)	PUNCT
ejpam-2515	378	41	∈	∈	PROPN
ejpam-2515	379	1	α1,3,4	α1,3,4	PROPN
ejpam-2515	379	2	⊂	⊂	PROPN
ejpam-2515	379	3	ρ	ρ	PROPN
ejpam-2515	379	4	.	.	PUNCT
ejpam-2515	380	1	set	set	NOUN
ejpam-2515	380	2	:	:	PUNCT
ejpam-2515	380	3	y	y	PROPN
ejpam-2515	380	4	=	=	PUNCT
ejpam-2515	380	5	e.	e.	PROPN
ejpam-2515	381	1	hence	hence	ADV
ejpam-2515	381	2	,	,	PUNCT
ejpam-2515	381	3	from	from	ADP
ejpam-2515	381	4	x	x	SYM
ejpam-2515	381	5	e	e	X
ejpam-2515	381	6	◦	◦	NOUN
ejpam-2515	381	7	ρ	ρ	NOUN
ejpam-2515	381	8	e	e	NOUN
ejpam-2515	381	9	=	=	PRON
ejpam-2515	381	10	{	{	PUNCT
ejpam-2515	381	11	x	x	NOUN
ejpam-2515	381	12	}	}	PUNCT
ejpam-2515	381	13	and	and	CCONJ
ejpam-2515	381	14	v	v	ADP
ejpam-2515	381	15	∈	∈	NOUN
ejpam-2515	381	16	x	x	PUNCT
ejpam-2515	381	17	e	e	X
ejpam-2515	381	18	◦	◦	NOUN
ejpam-2515	381	19	ρ	ρ	NOUN
ejpam-2515	381	20	y	y	PROPN
ejpam-2515	381	21	,	,	PUNCT
ejpam-2515	381	22	it	it	PRON
ejpam-2515	381	23	follows	follow	VERB
ejpam-2515	381	24	v	v	NOUN
ejpam-2515	381	25	=	=	SYM
ejpam-2515	381	26	x	x	X
ejpam-2515	381	27	.	.	PUNCT
ejpam-2515	382	1	thus	thus	ADV
ejpam-2515	382	2	,	,	PUNCT
ejpam-2515	382	3	(	(	PUNCT
ejpam-2515	382	4	x	x	X
ejpam-2515	382	5	,	,	PUNCT
ejpam-2515	382	6	u	u	NOUN
ejpam-2515	382	7	,	,	PUNCT
ejpam-2515	382	8	z	z	NOUN
ejpam-2515	382	9	)	)	PUNCT
ejpam-2515	382	10	∈	∈	PROPN
ejpam-2515	382	11	ρ	ρ	NOUN
ejpam-2515	382	12	.	.	PUNCT
ejpam-2515	383	1	on	on	ADP
ejpam-2515	383	2	the	the	DET
ejpam-2515	383	3	other	other	ADJ
ejpam-2515	383	4	hand	hand	NOUN
ejpam-2515	383	5	,	,	PUNCT
ejpam-2515	383	6	from	from	ADP
ejpam-2515	383	7	z	z	PROPN
ejpam-2515	383	8	e	e	NOUN
ejpam-2515	383	9	◦	◦	NOUN
ejpam-2515	383	10	ρ	ρ	NOUN
ejpam-2515	383	11	y	y	NOUN
ejpam-2515	383	12	=	=	SYM
ejpam-2515	383	13	z	z	PROPN
ejpam-2515	383	14	and	and	CCONJ
ejpam-2515	383	15	from	from	ADP
ejpam-2515	383	16	the	the	DET
ejpam-2515	383	17	symmetry	symmetry	NOUN
ejpam-2515	383	18	,	,	PUNCT
ejpam-2515	383	19	it	it	PRON
ejpam-2515	383	20	follows	follow	VERB
ejpam-2515	383	21	(	(	PUNCT
ejpam-2515	383	22	y	y	PROPN
ejpam-2515	383	23	,	,	PUNCT
ejpam-2515	383	24	z	z	PROPN
ejpam-2515	383	25	,	,	PUNCT
ejpam-2515	383	26	z	z	NOUN
ejpam-2515	383	27	)	)	PUNCT
ejpam-2515	383	28	∈	∈	PROPN
ejpam-2515	383	29	ρ	ρ	PROPN
ejpam-2515	383	30	.	.	PUNCT
ejpam-2515	384	1	therefore	therefore	ADV
ejpam-2515	384	2	,	,	PUNCT
ejpam-2515	384	3	u	u	PROPN
ejpam-2515	384	4	∈	∈	PROPN
ejpam-2515	384	5	x	x	PUNCT
ejpam-2515	385	1	e	e	X
ejpam-2515	385	2	◦	◦	NOUN
ejpam-2515	385	3	ρ	ρ	PROPN
ejpam-2515	385	4	(	(	PUNCT
ejpam-2515	385	5	y	y	PROPN
ejpam-2515	385	6	e	e	PROPN
ejpam-2515	385	7	◦	◦	NOUN
ejpam-2515	385	8	ρ	ρ	PROPN
ejpam-2515	385	9	z	z	NOUN
ejpam-2515	385	10	)	)	PUNCT
ejpam-2515	385	11	.	.	PUNCT
ejpam-2515	386	1	by	by	ADP
ejpam-2515	386	2	the	the	DET
ejpam-2515	386	3	same	same	ADJ
ejpam-2515	386	4	way	way	NOUN
ejpam-2515	386	5	,	,	PUNCT
ejpam-2515	386	6	we	we	PRON
ejpam-2515	386	7	check	check	VERB
ejpam-2515	386	8	the	the	DET
ejpam-2515	386	9	following	follow	VERB
ejpam-2515	386	10	other	other	ADJ
ejpam-2515	386	11	inclusion	inclusion	NOUN
ejpam-2515	386	12	:	:	PUNCT
ejpam-2515	386	13	∀(x	∀(x	NUM
ejpam-2515	386	14	,	,	PUNCT
ejpam-2515	386	15	y	y	PROPN
ejpam-2515	386	16	,	,	PUNCT
ejpam-2515	386	17	z	z	NOUN
ejpam-2515	386	18	)	)	PUNCT
ejpam-2515	386	19	∈	∈	PROPN
ejpam-2515	386	20	h3	h3	NOUN
ejpam-2515	386	21	,	,	PUNCT
ejpam-2515	386	22	(	(	PUNCT
ejpam-2515	386	23	x	x	PART
ejpam-2515	386	24	e	e	X
ejpam-2515	386	25	◦	◦	NOUN
ejpam-2515	386	26	ρ	ρ	NOUN
ejpam-2515	386	27	y	y	NOUN
ejpam-2515	386	28	)	)	PUNCT
ejpam-2515	386	29	e	e	AUX
ejpam-2515	386	30	◦	◦	NOUN
ejpam-2515	386	31	ρ	ρ	NOUN
ejpam-2515	386	32	z	z	NOUN
ejpam-2515	386	33	⊇	⊇	NOUN
ejpam-2515	386	34	x	x	PUNCT
ejpam-2515	386	35	e	e	X
ejpam-2515	386	36	◦	◦	NOUN
ejpam-2515	386	37	ρ	ρ	PROPN
ejpam-2515	386	38	(	(	PUNCT
ejpam-2515	386	39	y	y	PROPN
ejpam-2515	386	40	e	e	PROPN
ejpam-2515	386	41	◦	◦	NOUN
ejpam-2515	386	42	ρ	ρ	PROPN
ejpam-2515	386	43	z	z	NOUN
ejpam-2515	386	44	)	)	PUNCT
ejpam-2515	386	45	(	(	PUNCT
ejpam-2515	386	46	5	5	NUM
ejpam-2515	386	47	)	)	PUNCT
ejpam-2515	386	48	(	(	PUNCT
ejpam-2515	386	49	ii	ii	NOUN
ejpam-2515	386	50	)	)	PUNCT
ejpam-2515	386	51	if	if	SCONJ
ejpam-2515	386	52	y	y	PROPN
ejpam-2515	386	53	=	=	PUNCT
ejpam-2515	386	54	x	x	SYM
ejpam-2515	386	55	′	′	NUM
ejpam-2515	386	56	,	,	PUNCT
ejpam-2515	386	57	then	then	ADV
ejpam-2515	386	58	(	(	PUNCT
ejpam-2515	386	59	x	x	PUNCT
ejpam-2515	386	60	e	e	X
ejpam-2515	386	61	◦	◦	NOUN
ejpam-2515	386	62	ρ	ρ	NOUN
ejpam-2515	386	63	y	y	NOUN
ejpam-2515	386	64	)	)	PUNCT
ejpam-2515	386	65	e	e	AUX
ejpam-2515	386	66	◦	◦	NOUN
ejpam-2515	386	67	ρ	ρ	NOUN
ejpam-2515	386	68	z	z	NOUN
ejpam-2515	386	69	=	=	PRON
ejpam-2515	386	70	{	{	PUNCT
ejpam-2515	386	71	x	x	PROPN
ejpam-2515	386	72	,	,	PUNCT
ejpam-2515	386	73	t	t	PROPN
ejpam-2515	386	74	,	,	PUNCT
ejpam-2515	386	75	x	x	NOUN
ejpam-2515	386	76	′	′	NOUN
ejpam-2515	386	77	}	}	PUNCT
ejpam-2515	386	78	e	e	NOUN
ejpam-2515	386	79	◦	◦	NOUN
ejpam-2515	386	80	ρ	ρ	NOUN
ejpam-2515	386	81	z	z	NOUN
ejpam-2515	386	82	=	=	PRON
ejpam-2515	386	83	{	{	PUNCT
ejpam-2515	386	84	x	x	X
ejpam-2515	386	85	,	,	PUNCT
ejpam-2515	386	86	e	e	NOUN
ejpam-2515	386	87	,	,	PUNCT
ejpam-2515	386	88	x	x	NOUN
ejpam-2515	386	89	′	′	NOUN
ejpam-2515	386	90	}	}	PUNCT
ejpam-2515	386	91	e	e	NOUN
ejpam-2515	386	92	◦	◦	NOUN
ejpam-2515	386	93	ρ	ρ	NOUN
ejpam-2515	386	94	z	z	NOUN
ejpam-2515	386	95	=	=	NOUN
ejpam-2515	386	96	x	x	SYM
ejpam-2515	386	97	e	e	NOUN
ejpam-2515	386	98	◦	◦	NOUN
ejpam-2515	386	99	ρ	ρ	PROPN
ejpam-2515	386	100	z	z	NOUN
ejpam-2515	386	101	,	,	PUNCT
ejpam-2515	386	102	∪	∪	X
ejpam-2515	386	103	{	{	PUNCT
ejpam-2515	386	104	z	z	NOUN
ejpam-2515	386	105	}	}	PUNCT
ejpam-2515	386	106	∪	∪	ADJ
ejpam-2515	386	107	x	x	SYM
ejpam-2515	386	108	′	′	NUM
ejpam-2515	386	109	e	e	NOUN
ejpam-2515	386	110	◦	◦	NOUN
ejpam-2515	386	111	ρ	ρ	NOUN
ejpam-2515	386	112	z	z	NOUN
ejpam-2515	386	113	=	=	PRON
ejpam-2515	386	114	{	{	PUNCT
ejpam-2515	386	115	x	x	X
ejpam-2515	386	116	,	,	PUNCT
ejpam-2515	386	117	e	e	NOUN
ejpam-2515	386	118	,	,	PUNCT
ejpam-2515	386	119	z	z	NOUN
ejpam-2515	386	120	}	}	PUNCT
ejpam-2515	386	121	∪	∪	X
ejpam-2515	386	122	{	{	PUNCT
ejpam-2515	386	123	z	z	NOUN
ejpam-2515	386	124	}	}	PUNCT
ejpam-2515	386	125	∪	∪	ADJ
ejpam-2515	386	126	x	x	SYM
ejpam-2515	386	127	′	′	NUM
ejpam-2515	386	128	e	e	NOUN
ejpam-2515	386	129	◦	◦	NOUN
ejpam-2515	386	130	ρ	ρ	NOUN
ejpam-2515	386	131	z	z	NOUN
ejpam-2515	386	132	=	=	PRON
ejpam-2515	386	133	{	{	PUNCT
ejpam-2515	386	134	x	x	X
ejpam-2515	386	135	,	,	PUNCT
ejpam-2515	386	136	e	e	NOUN
ejpam-2515	386	137	,	,	PUNCT
ejpam-2515	386	138	z	z	NOUN
ejpam-2515	386	139	}	}	PUNCT
ejpam-2515	386	140	∪	∪	X
ejpam-2515	386	141	{	{	PUNCT
ejpam-2515	386	142	x	x	NOUN
ejpam-2515	386	143	′	′	NUM
ejpam-2515	386	144	,	,	PUNCT
ejpam-2515	386	145	e	e	NOUN
ejpam-2515	386	146	,	,	PUNCT
ejpam-2515	386	147	z	z	NOUN
ejpam-2515	386	148	,	,	PUNCT
ejpam-2515	386	149	}	}	PUNCT
ejpam-2515	386	150	=	=	SYM
ejpam-2515	386	151	{	{	PUNCT
ejpam-2515	386	152	x	x	X
ejpam-2515	386	153	,	,	PUNCT
ejpam-2515	386	154	e	e	NOUN
ejpam-2515	386	155	,	,	PUNCT
ejpam-2515	386	156	x	x	NOUN
ejpam-2515	386	157	′	′	NUM
ejpam-2515	386	158	,	,	PUNCT
ejpam-2515	386	159	z	z	NOUN
ejpam-2515	386	160	}	}	PUNCT
ejpam-2515	386	161	=	=	NOUN
ejpam-2515	386	162	x	x	SYM
ejpam-2515	386	163	e	e	NOUN
ejpam-2515	386	164	◦	◦	NOUN
ejpam-2515	386	165	ρ	ρ	NOUN
ejpam-2515	386	166	(	(	PUNCT
ejpam-2515	386	167	x	x	NOUN
ejpam-2515	386	168	′	′	NUM
ejpam-2515	386	169	e	e	X
ejpam-2515	386	170	◦	◦	NOUN
ejpam-2515	386	171	ρ	ρ	NOUN
ejpam-2515	386	172	z	z	NOUN
ejpam-2515	386	173	)	)	PUNCT
ejpam-2515	387	1	so	so	ADV
ejpam-2515	387	2	(	(	PUNCT
ejpam-2515	387	3	h;e	h;e	NOUN
ejpam-2515	387	4	◦	◦	NOUN
ejpam-2515	387	5	ρ	ρ	NOUN
ejpam-2515	387	6	)	)	PUNCT
ejpam-2515	387	7	is	be	AUX
ejpam-2515	387	8	a	a	DET
ejpam-2515	387	9	commutative	commutative	ADJ
ejpam-2515	387	10	hypergroup	hypergroup	NOUN
ejpam-2515	387	11	.	.	PUNCT
ejpam-2515	388	1	now	now	ADV
ejpam-2515	388	2	,	,	PUNCT
ejpam-2515	388	3	let	let	VERB
ejpam-2515	388	4	us	we	PRON
ejpam-2515	388	5	check	check	VERB
ejpam-2515	388	6	the	the	DET
ejpam-2515	388	7	following	following	ADJ
ejpam-2515	388	8	implication	implication	NOUN
ejpam-2515	388	9	:	:	PUNCT
ejpam-2515	388	10	a	a	DET
ejpam-2515	388	11	/	/	SYM
ejpam-2515	388	12	b	b	NOUN
ejpam-2515	388	13	∩	∩	ADJ
ejpam-2515	388	14	c	c	X
ejpam-2515	388	15	/	/	SYM
ejpam-2515	388	16	d	d	NOUN
ejpam-2515	388	17	6=	6=	NUM
ejpam-2515	388	18	;	;	PUNCT
ejpam-2515	388	19	=	=	SYM
ejpam-2515	388	20	⇒	⇒	VERB
ejpam-2515	388	21	a	a	DET
ejpam-2515	388	22	e	e	NOUN
ejpam-2515	388	23	◦	◦	NOUN
ejpam-2515	388	24	ρ	ρ	PROPN
ejpam-2515	388	25	d	d	NOUN
ejpam-2515	388	26	∩	∩	PROPN
ejpam-2515	388	27	b	b	X
ejpam-2515	388	28	e	e	NOUN
ejpam-2515	388	29	◦	◦	NOUN
ejpam-2515	388	30	ρ	ρ	NOUN
ejpam-2515	388	31	c	c	NOUN
ejpam-2515	388	32	6=	6=	NUM
ejpam-2515	388	33	;	;	PUNCT
ejpam-2515	388	34	.	.	PUNCT
ejpam-2515	389	1	notice	notice	VERB
ejpam-2515	389	2	that	that	SCONJ
ejpam-2515	389	3	∀a	∀a	VERB
ejpam-2515	389	4	∈	∈	PROPN
ejpam-2515	389	5	h	h	NOUN
ejpam-2515	389	6	,	,	PUNCT
ejpam-2515	389	7	a	a	PRON
ejpam-2515	389	8	has	have	VERB
ejpam-2515	389	9	a	a	DET
ejpam-2515	389	10	unique	unique	ADJ
ejpam-2515	389	11	inverse	inverse	NOUN
ejpam-2515	389	12	a′	a′	NOUN
ejpam-2515	389	13	and	and	CCONJ
ejpam-2515	389	14	∀(a	∀(a	NUM
ejpam-2515	389	15	,	,	PUNCT
ejpam-2515	389	16	b	b	NOUN
ejpam-2515	389	17	)	)	PUNCT
ejpam-2515	389	18	∈	∈	PROPN
ejpam-2515	389	19	h2	h2	NOUN
ejpam-2515	389	20	,	,	PUNCT
ejpam-2515	389	21	a	a	PRON
ejpam-2515	389	22	/	/	SYM
ejpam-2515	389	23	b	b	NOUN
ejpam-2515	389	24	=	=	PUNCT
ejpam-2515	389	25	a	a	DET
ejpam-2515	389	26	e	e	NOUN
ejpam-2515	389	27	◦	◦	NOUN
ejpam-2515	389	28	ρ	ρ	PROPN
ejpam-2515	389	29	b′.	b′.	PROPN
ejpam-2515	389	30	s.	s.	PROPN
ejpam-2515	389	31	govindarajan	govindarajan	PROPN
ejpam-2515	389	32	/	/	SYM
ejpam-2515	389	33	eur	eur	PROPN
ejpam-2515	389	34	.	.	PUNCT
ejpam-2515	390	1	j.	j.	PROPN
ejpam-2515	390	2	pure	pure	PROPN
ejpam-2515	390	3	appl	appl	PROPN
ejpam-2515	390	4	.	.	PROPN
ejpam-2515	390	5	math	math	PROPN
ejpam-2515	390	6	,	,	PUNCT
ejpam-2515	390	7	9	9	NUM
ejpam-2515	390	8	(	(	PUNCT
ejpam-2515	390	9	2016	2016	NUM
ejpam-2515	390	10	)	)	PUNCT
ejpam-2515	390	11	,	,	PUNCT
ejpam-2515	390	12	367	367	NUM
ejpam-2515	390	13	-	-	SYM
ejpam-2515	390	14	382	382	NUM
ejpam-2515	390	15	380	380	NUM
ejpam-2515	390	16	so	so	ADV
ejpam-2515	390	17	,	,	PUNCT
ejpam-2515	390	18	a	a	DET
ejpam-2515	390	19	/	/	SYM
ejpam-2515	390	20	b	b	NOUN
ejpam-2515	390	21	∩	∩	ADJ
ejpam-2515	390	22	c	c	X
ejpam-2515	390	23	/	/	SYM
ejpam-2515	390	24	d	d	NOUN
ejpam-2515	390	25	6=	6=	NUM
ejpam-2515	390	26	;	;	PUNCT
ejpam-2515	390	27	=	=	SYM
ejpam-2515	390	28	⇒	⇒	VERB
ejpam-2515	390	29	a	a	DET
ejpam-2515	390	30	e	e	NOUN
ejpam-2515	390	31	◦	◦	NOUN
ejpam-2515	390	32	ρ	ρ	NUM
ejpam-2515	390	33	b′	b′	NUM
ejpam-2515	390	34	∩	∩	NOUN
ejpam-2515	390	35	c	c	NOUN
ejpam-2515	390	36	e	e	NOUN
ejpam-2515	390	37	◦	◦	NOUN
ejpam-2515	390	38	ρ	ρ	NOUN
ejpam-2515	390	39	d	d	NOUN
ejpam-2515	390	40	′	′	NUM
ejpam-2515	390	41	6=	6=	NUM
ejpam-2515	390	42	;	;	PUNCT
ejpam-2515	390	43	whence	whence	X
ejpam-2515	390	44	{	{	PUNCT
ejpam-2515	390	45	a	a	PRON
ejpam-2515	390	46	}	}	PUNCT
ejpam-2515	390	47	∩	∩	ADJ
ejpam-2515	390	48	b	b	X
ejpam-2515	390	49	e	e	NOUN
ejpam-2515	390	50	◦	◦	NOUN
ejpam-2515	390	51	ρ	ρ	NOUN
ejpam-2515	390	52	(	(	PUNCT
ejpam-2515	390	53	c	c	NOUN
ejpam-2515	390	54	e	e	NOUN
ejpam-2515	390	55	◦	◦	NOUN
ejpam-2515	390	56	ρ	ρ	NOUN
ejpam-2515	390	57	d	d	NOUN
ejpam-2515	390	58	′	′	NOUN
ejpam-2515	390	59	)	)	PUNCT
ejpam-2515	390	60	6=	6=	NUM
ejpam-2515	390	61	;	;	PUNCT
ejpam-2515	390	62	,	,	PUNCT
ejpam-2515	390	63	hence	hence	ADV
ejpam-2515	390	64	a	a	X
ejpam-2515	390	65	/	/	SYM
ejpam-2515	390	66	d	d	NOUN
ejpam-2515	390	67	′	′	NUM
ejpam-2515	390	68	∩	∩	PROPN
ejpam-2515	390	69	b	b	X
ejpam-2515	390	70	e	e	NOUN
ejpam-2515	390	71	◦	◦	NOUN
ejpam-2515	390	72	ρ	ρ	NOUN
ejpam-2515	390	73	c	c	NOUN
ejpam-2515	390	74	6=	6=	NUM
ejpam-2515	390	75	;	;	PUNCT
ejpam-2515	390	76	,	,	PUNCT
ejpam-2515	390	77	that	that	ADV
ejpam-2515	390	78	is	is	ADV
ejpam-2515	390	79	,	,	PUNCT
ejpam-2515	390	80	a	a	DET
ejpam-2515	390	81	e	e	NOUN
ejpam-2515	390	82	◦	◦	NOUN
ejpam-2515	390	83	ρ	ρ	PROPN
ejpam-2515	390	84	d	d	NOUN
ejpam-2515	390	85	∩	∩	PROPN
ejpam-2515	390	86	b	b	X
ejpam-2515	390	87	e	e	NOUN
ejpam-2515	390	88	◦	◦	NOUN
ejpam-2515	390	89	ρ	ρ	NOUN
ejpam-2515	390	90	c	c	NOUN
ejpam-2515	390	91	6=	6=	NUM
ejpam-2515	390	92	;	;	PUNCT
ejpam-2515	390	93	(	(	PUNCT
ejpam-2515	390	94	by	by	ADP
ejpam-2515	390	95	[	[	X
ejpam-2515	390	96	8	8	NUM
ejpam-2515	390	97	,	,	PUNCT
ejpam-2515	390	98	theorem	theorem	ADJ
ejpam-2515	390	99	(	(	PUNCT
ejpam-2515	390	100	64	64	NUM
ejpam-2515	390	101	,	,	PUNCT
ejpam-2515	390	102	2	2	NUM
ejpam-2515	390	103	)	)	PUNCT
ejpam-2515	390	104	,	,	PUNCT
ejpam-2515	390	105	p.12	p.12	PROPN
ejpam-2515	390	106	]	]	X
ejpam-2515	390	107	)	)	PUNCT
ejpam-2515	390	108	.	.	PUNCT
ejpam-2515	391	1	therefore	therefore	ADV
ejpam-2515	391	2	,	,	PUNCT
ejpam-2515	391	3	(	(	PUNCT
ejpam-2515	391	4	h;e	h;e	NOUN
ejpam-2515	391	5	◦	◦	NOUN
ejpam-2515	391	6	ρ	ρ	NOUN
ejpam-2515	391	7	)	)	PUNCT
ejpam-2515	391	8	is	be	AUX
ejpam-2515	391	9	a	a	DET
ejpam-2515	391	10	join	join	NOUN
ejpam-2515	391	11	space	space	NOUN
ejpam-2515	391	12	.	.	PUNCT
ejpam-2515	392	1	thus	thus	ADV
ejpam-2515	392	2	,	,	PUNCT
ejpam-2515	392	3	we	we	PRON
ejpam-2515	392	4	obtain	obtain	VERB
ejpam-2515	392	5	a	a	DET
ejpam-2515	392	6	join	join	NOUN
ejpam-2515	392	7	space	space	NOUN
ejpam-2515	392	8	with	with	ADP
ejpam-2515	392	9	identity	identity	NOUN
ejpam-2515	392	10	e′	e′	VERB
ejpam-2515	392	11	in	in	ADP
ejpam-2515	392	12	h.	h.	PROPN
ejpam-2515	392	13	to	to	PART
ejpam-2515	392	14	illustrate	illustrate	VERB
ejpam-2515	392	15	the	the	DET
ejpam-2515	392	16	application	application	NOUN
ejpam-2515	392	17	of	of	ADP
ejpam-2515	392	18	this	this	DET
ejpam-2515	392	19	proposition	proposition	NOUN
ejpam-2515	392	20	,	,	PUNCT
ejpam-2515	392	21	let	let	VERB
ejpam-2515	392	22	us	we	PRON
ejpam-2515	392	23	consider	consider	VERB
ejpam-2515	392	24	a	a	DET
ejpam-2515	392	25	ternary	ternary	ADJ
ejpam-2515	392	26	relation	relation	NOUN
ejpam-2515	392	27	defined	define	VERB
ejpam-2515	392	28	on	on	ADP
ejpam-2515	392	29	the	the	DET
ejpam-2515	392	30	set	set	NOUN
ejpam-2515	392	31	h	h	NOUN
ejpam-2515	392	32	=	=	SYM
ejpam-2515	392	33	{	{	PUNCT
ejpam-2515	392	34	1	1	NUM
ejpam-2515	392	35	,	,	PUNCT
ejpam-2515	392	36	2,3	2,3	NUM
ejpam-2515	392	37	,	,	PUNCT
ejpam-2515	392	38	4	4	NUM
ejpam-2515	392	39	}	}	PUNCT
ejpam-2515	392	40	with	with	ADP
ejpam-2515	392	41	ρ	ρ	PROPN
ejpam-2515	392	42	⊃	⊃	X
ejpam-2515	392	43	{	{	PUNCT
ejpam-2515	392	44	(	(	PUNCT
ejpam-2515	392	45	1	1	NUM
ejpam-2515	392	46	,	,	PUNCT
ejpam-2515	392	47	2,3	2,3	NUM
ejpam-2515	392	48	)	)	PUNCT
ejpam-2515	392	49	,	,	PUNCT
ejpam-2515	392	50	(	(	PUNCT
ejpam-2515	392	51	2,3	2,3	NUM
ejpam-2515	392	52	,	,	PUNCT
ejpam-2515	392	53	4	4	NUM
ejpam-2515	392	54	)	)	PUNCT
ejpam-2515	392	55	,	,	PUNCT
ejpam-2515	392	56	(	(	PUNCT
ejpam-2515	392	57	1,3	1,3	NUM
ejpam-2515	392	58	,	,	PUNCT
ejpam-2515	392	59	2	2	NUM
ejpam-2515	392	60	)	)	PUNCT
ejpam-2515	392	61	,	,	PUNCT
ejpam-2515	392	62	(	(	PUNCT
ejpam-2515	392	63	3	3	NUM
ejpam-2515	392	64	,	,	PUNCT
ejpam-2515	392	65	2,4	2,4	NUM
ejpam-2515	392	66	)	)	PUNCT
ejpam-2515	392	67	,	,	PUNCT
ejpam-2515	392	68	(	(	PUNCT
ejpam-2515	392	69	3	3	NUM
ejpam-2515	392	70	,	,	PUNCT
ejpam-2515	392	71	2,1	2,1	NUM
ejpam-2515	392	72	)	)	PUNCT
ejpam-2515	392	73	,	,	PUNCT
ejpam-2515	392	74	(	(	PUNCT
ejpam-2515	392	75	4	4	NUM
ejpam-2515	392	76	,	,	PUNCT
ejpam-2515	392	77	3,2	3,2	NUM
ejpam-2515	392	78	)	)	PUNCT
ejpam-2515	392	79	,	,	PUNCT
ejpam-2515	392	80	(	(	PUNCT
ejpam-2515	392	81	2,3	2,3	NUM
ejpam-2515	392	82	,	,	PUNCT
ejpam-2515	392	83	1	1	NUM
ejpam-2515	392	84	)	)	PUNCT
ejpam-2515	392	85	,	,	PUNCT
ejpam-2515	392	86	(	(	PUNCT
ejpam-2515	392	87	4,2	4,2	NUM
ejpam-2515	392	88	,	,	PUNCT
ejpam-2515	392	89	3	3	NUM
ejpam-2515	392	90	)	)	PUNCT
ejpam-2515	392	91	}	}	PUNCT
ejpam-2515	392	92	and	and	CCONJ
ejpam-2515	392	93	ρ1,3	ρ1,3	PROPN
ejpam-2515	392	94	=	=	SYM
ejpam-2515	393	1	ρ1,2	ρ1,2	PROPN
ejpam-2515	393	2	=	=	SYM
ejpam-2515	393	3	ρ2,3	ρ2,3	PUNCT
ejpam-2515	393	4	=	=	NOUN
ejpam-2515	393	5	h	h	NOUN
ejpam-2515	393	6	×h	×h	PROPN
ejpam-2515	393	7	.	.	PUNCT
ejpam-2515	394	1	let	let	VERB
ejpam-2515	394	2	x	x	SYM
ejpam-2515	394	3	=	=	SYM
ejpam-2515	394	4	1	1	NUM
ejpam-2515	394	5	,	,	PUNCT
ejpam-2515	394	6	x	x	PUNCT
ejpam-2515	394	7	′	′	NOUN
ejpam-2515	395	1	=	=	VERB
ejpam-2515	395	2	4	4	X
ejpam-2515	395	3	.	.	X
ejpam-2515	395	4	choose	choose	VERB
ejpam-2515	395	5	t	t	NOUN
ejpam-2515	395	6	=	=	SYM
ejpam-2515	395	7	2	2	NUM
ejpam-2515	395	8	and	and	CCONJ
ejpam-2515	395	9	t	t	NOUN
ejpam-2515	395	10	′	′	NUM
ejpam-2515	396	1	=	=	SYM
ejpam-2515	396	2	3	3	NUM
ejpam-2515	396	3	and	and	CCONJ
ejpam-2515	396	4	set	set	VERB
ejpam-2515	396	5	:	:	PUNCT
ejpam-2515	396	6	∀x	∀x	NUM
ejpam-2515	396	7	∈	∈	PROPN
ejpam-2515	396	8	h	h	NOUN
ejpam-2515	396	9	,	,	PUNCT
ejpam-2515	396	10	x	x	PUNCT
ejpam-2515	396	11	◦	◦	NOUN
ejpam-2515	396	12	ρ	ρ	NOUN
ejpam-2515	396	13	x	x	SYM
ejpam-2515	396	14	=	=	PRON
ejpam-2515	396	15	{	{	PUNCT
ejpam-2515	396	16	x	x	NOUN
ejpam-2515	396	17	}	}	PUNCT
ejpam-2515	396	18	.	.	PUNCT
ejpam-2515	397	1	applying	apply	VERB
ejpam-2515	397	2	the	the	DET
ejpam-2515	397	3	hyperoperation	hyperoperation	NOUN
ejpam-2515	397	4	defined	define	VERB
ejpam-2515	397	5	in	in	ADP
ejpam-2515	397	6	the	the	DET
ejpam-2515	397	7	proposition	proposition	NOUN
ejpam-2515	397	8	,	,	PUNCT
ejpam-2515	397	9	we	we	PRON
ejpam-2515	397	10	obtain	obtain	VERB
ejpam-2515	397	11	the	the	DET
ejpam-2515	397	12	hypergroupoid	hypergroupoid	NOUN
ejpam-2515	397	13	:	:	PUNCT
ejpam-2515	397	14	table	table	NOUN
ejpam-2515	397	15	3	3	NUM
ejpam-2515	397	16	:	:	PUNCT
ejpam-2515	397	17	join	join	VERB
ejpam-2515	397	18	space	space	NOUN
ejpam-2515	397	19	associated	associate	VERB
ejpam-2515	397	20	with	with	ADP
ejpam-2515	397	21	spherical	spherical	ADJ
ejpam-2515	397	22	geometry	geometry	NOUN
ejpam-2515	397	23	⊗	⊗	PROPN
ejpam-2515	397	24	ρ	ρ	PROPN
ejpam-2515	397	25	1	1	NUM
ejpam-2515	397	26	2	2	NUM
ejpam-2515	397	27	3	3	NUM
ejpam-2515	397	28	4	4	NUM
ejpam-2515	397	29	1	1	NUM
ejpam-2515	397	30	1	1	NUM
ejpam-2515	397	31	1,2,3	1,2,3	NUM
ejpam-2515	397	32	1,2,3	1,2,3	NUM
ejpam-2515	397	33	1,2	1,2	NUM
ejpam-2515	397	34	,	,	PUNCT
ejpam-2515	397	35	3,4	3,4	NUM
ejpam-2515	397	36	2	2	NUM
ejpam-2515	397	37	1,2,3	1,2,3	NUM
ejpam-2515	397	38	2	2	NUM
ejpam-2515	397	39	2,3	2,3	NUM
ejpam-2515	397	40	2,3,4	2,3,4	NUM
ejpam-2515	397	41	3	3	NUM
ejpam-2515	397	42	1,2,3	1,2,3	NUM
ejpam-2515	397	43	2	2	NUM
ejpam-2515	397	44	,	,	PUNCT
ejpam-2515	397	45	3	3	NUM
ejpam-2515	397	46	3	3	NUM
ejpam-2515	397	47	2,3,4	2,3,4	NUM
ejpam-2515	397	48	4	4	NUM
ejpam-2515	397	49	1,2,3,4	1,2,3,4	NUM
ejpam-2515	397	50	2,3,4	2,3,4	NUM
ejpam-2515	397	51	2,3,4	2,3,4	NUM
ejpam-2515	397	52	4	4	NUM
ejpam-2515	397	53	clearly	clearly	ADV
ejpam-2515	397	54	,	,	PUNCT
ejpam-2515	397	55	we	we	PRON
ejpam-2515	397	56	have	have	VERB
ejpam-2515	397	57	(	(	PUNCT
ejpam-2515	397	58	h;	h;	PRON
ejpam-2515	397	59	◦	◦	NOUN
ejpam-2515	397	60	ρ	ρ	NOUN
ejpam-2515	397	61	)	)	PUNCT
ejpam-2515	397	62	a	a	DET
ejpam-2515	397	63	join	join	NOUN
ejpam-2515	397	64	space	space	NOUN
ejpam-2515	397	65	.	.	PUNCT
ejpam-2515	398	1	we	we	PRON
ejpam-2515	398	2	have	have	AUX
ejpam-2515	398	3	consider	consider	VERB
ejpam-2515	398	4	only	only	ADV
ejpam-2515	398	5	one	one	NUM
ejpam-2515	398	6	element	element	NOUN
ejpam-2515	398	7	x	x	NOUN
ejpam-2515	398	8	=	=	SYM
ejpam-2515	398	9	1	1	NUM
ejpam-2515	398	10	and	and	CCONJ
ejpam-2515	398	11	its	its	PRON
ejpam-2515	398	12	inverse	inverse	NOUN
ejpam-2515	398	13	x	x	NOUN
ejpam-2515	398	14	′	′	NUM
ejpam-2515	398	15	=	=	NOUN
ejpam-2515	398	16	4	4	X
ejpam-2515	398	17	.	.	X
ejpam-2515	398	18	for	for	ADP
ejpam-2515	398	19	the	the	DET
ejpam-2515	398	20	remaining	remain	VERB
ejpam-2515	398	21	elements	element	NOUN
ejpam-2515	398	22	2	2	NUM
ejpam-2515	398	23	,	,	PUNCT
ejpam-2515	398	24	3	3	NUM
ejpam-2515	398	25	,	,	PUNCT
ejpam-2515	398	26	we	we	PRON
ejpam-2515	398	27	can	can	AUX
ejpam-2515	398	28	easily	easily	ADV
ejpam-2515	398	29	find	find	VERB
ejpam-2515	398	30	their	their	PRON
ejpam-2515	398	31	inverses	inverse	NOUN
ejpam-2515	398	32	in	in	ADP
ejpam-2515	398	33	infinite	infinite	ADJ
ejpam-2515	398	34	case	case	NOUN
ejpam-2515	398	35	which	which	PRON
ejpam-2515	398	36	is	be	AUX
ejpam-2515	398	37	necessary	necessary	ADJ
ejpam-2515	398	38	for	for	ADP
ejpam-2515	398	39	the	the	DET
ejpam-2515	398	40	spherical	spherical	ADJ
ejpam-2515	398	41	geometry	geometry	NOUN
ejpam-2515	398	42	.	.	PUNCT
ejpam-2515	399	1	5	5	X
ejpam-2515	399	2	.	.	X
ejpam-2515	399	3	conclusion	conclusion	NOUN
ejpam-2515	399	4	we	we	PRON
ejpam-2515	399	5	have	have	AUX
ejpam-2515	399	6	characterized	characterize	VERB
ejpam-2515	399	7	all	all	DET
ejpam-2515	399	8	the	the	DET
ejpam-2515	399	9	ternary	ternary	ADJ
ejpam-2515	399	10	relation	relation	NOUN
ejpam-2515	399	11	ρ	ρ	NOUN
ejpam-2515	399	12	such	such	ADJ
ejpam-2515	399	13	that	that	SCONJ
ejpam-2515	399	14	the	the	DET
ejpam-2515	399	15	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	399	16	hρ	hρ	PROPN
ejpam-2515	399	17	is	be	AUX
ejpam-2515	399	18	a	a	DET
ejpam-2515	399	19	hypergroup	hypergroup	NOUN
ejpam-2515	399	20	or	or	CCONJ
ejpam-2515	399	21	a	a	DET
ejpam-2515	399	22	join	join	NOUN
ejpam-2515	399	23	space	space	NOUN
ejpam-2515	399	24	.	.	PUNCT
ejpam-2515	400	1	we	we	PRON
ejpam-2515	400	2	have	have	AUX
ejpam-2515	400	3	stated	state	VERB
ejpam-2515	400	4	some	some	DET
ejpam-2515	400	5	connections	connection	NOUN
ejpam-2515	400	6	between	between	ADP
ejpam-2515	400	7	a	a	DET
ejpam-2515	400	8	general	general	ADJ
ejpam-2515	400	9	ternary	ternary	ADJ
ejpam-2515	400	10	relation	relation	NOUN
ejpam-2515	400	11	ρ	ρ	PROPN
ejpam-2515	400	12	and	and	CCONJ
ejpam-2515	400	13	hypergroups	hypergroup	NOUN
ejpam-2515	400	14	and	and	CCONJ
ejpam-2515	400	15	then	then	ADV
ejpam-2515	400	16	proved	prove	VERB
ejpam-2515	400	17	them	they	PRON
ejpam-2515	400	18	.	.	PUNCT
ejpam-2515	401	1	moreover	moreover	ADV
ejpam-2515	401	2	,	,	PUNCT
ejpam-2515	401	3	a	a	DET
ejpam-2515	401	4	correspondence	correspondence	NOUN
ejpam-2515	401	5	between	between	ADP
ejpam-2515	401	6	this	this	DET
ejpam-2515	401	7	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	401	8	and	and	CCONJ
ejpam-2515	401	9	the	the	DET
ejpam-2515	401	10	join	join	NOUN
ejpam-2515	401	11	space	space	NOUN
ejpam-2515	401	12	obtained	obtain	VERB
ejpam-2515	401	13	by	by	ADP
ejpam-2515	401	14	w.	w.	PROPN
ejpam-2515	401	15	prenowitz	prenowitz	PROPN
ejpam-2515	401	16	from	from	ADP
ejpam-2515	401	17	betweenness	betweenness	PROPN
ejpam-2515	401	18	(	(	PUNCT
ejpam-2515	401	19	ternary	ternary	ADJ
ejpam-2515	401	20	)	)	PUNCT
ejpam-2515	401	21	relation	relation	NOUN
ejpam-2515	401	22	has	have	AUX
ejpam-2515	401	23	been	be	AUX
ejpam-2515	401	24	established	establish	VERB
ejpam-2515	401	25	.	.	PUNCT
ejpam-2515	402	1	in	in	ADP
ejpam-2515	402	2	future	future	ADJ
ejpam-2515	402	3	work	work	NOUN
ejpam-2515	402	4	we	we	PRON
ejpam-2515	402	5	intend	intend	VERB
ejpam-2515	402	6	to	to	PART
ejpam-2515	402	7	study	study	VERB
ejpam-2515	402	8	the	the	DET
ejpam-2515	402	9	properties	property	NOUN
ejpam-2515	402	10	of	of	ADP
ejpam-2515	402	11	hypergroupoid	hypergroupoid	PROPN
ejpam-2515	402	12	associated	associate	VERB
ejpam-2515	402	13	with	with	ADP
ejpam-2515	402	14	the	the	DET
ejpam-2515	402	15	cartesian	cartesian	ADJ
ejpam-2515	402	16	product	product	NOUN
ejpam-2515	402	17	and	and	CCONJ
ejpam-2515	402	18	join	join	NOUN
ejpam-2515	402	19	of	of	ADP
ejpam-2515	402	20	two	two	NUM
ejpam-2515	402	21	ternary	ternary	ADJ
ejpam-2515	402	22	relations	relation	NOUN
ejpam-2515	402	23	.	.	PUNCT
ejpam-2515	403	1	moreover	moreover	ADV
ejpam-2515	403	2	,	,	PUNCT
ejpam-2515	403	3	we	we	PRON
ejpam-2515	403	4	try	try	VERB
ejpam-2515	403	5	to	to	PART
ejpam-2515	403	6	associate	associate	VERB
ejpam-2515	403	7	a	a	DET
ejpam-2515	403	8	directed	direct	VERB
ejpam-2515	403	9	connected	connected	ADJ
ejpam-2515	403	10	graph	graph	NOUN
ejpam-2515	403	11	with	with	ADP
ejpam-2515	403	12	the	the	DET
ejpam-2515	403	13	hypergroupoids	hypergroupoid	NOUN
ejpam-2515	403	14	which	which	PRON
ejpam-2515	403	15	have	have	AUX
ejpam-2515	403	16	been	be	AUX
ejpam-2515	403	17	considered	consider	VERB
ejpam-2515	403	18	in	in	ADP
ejpam-2515	403	19	this	this	DET
ejpam-2515	403	20	paper	paper	NOUN
ejpam-2515	403	21	.	.	PUNCT
ejpam-2515	404	1	acknowledgements	acknowledgement	NOUN
ejpam-2515	404	2	the	the	DET
ejpam-2515	404	3	authors	author	NOUN
ejpam-2515	404	4	thank	thank	VERB
ejpam-2515	404	5	the	the	DET
ejpam-2515	404	6	readers	reader	NOUN
ejpam-2515	404	7	of	of	ADP
ejpam-2515	404	8	european	european	PROPN
ejpam-2515	404	9	journal	journal	PROPN
ejpam-2515	404	10	of	of	ADP
ejpam-2515	404	11	pure	pure	ADJ
ejpam-2515	404	12	and	and	CCONJ
ejpam-2515	404	13	applied	applied	ADJ
ejpam-2515	404	14	mathematics	mathematic	NOUN
ejpam-2515	404	15	,	,	PUNCT
ejpam-2515	404	16	for	for	ADP
ejpam-2515	404	17	making	make	VERB
ejpam-2515	404	18	our	our	PRON
ejpam-2515	404	19	journal	journal	NOUN
ejpam-2515	404	20	successful	successful	ADJ
ejpam-2515	404	21	.	.	PUNCT
ejpam-2515	405	1	references	reference	NOUN
ejpam-2515	405	2	381	381	NUM
ejpam-2515	405	3	references	reference	NOUN
ejpam-2515	405	4	[	[	X
ejpam-2515	405	5	1	1	NUM
ejpam-2515	405	6	]	]	PUNCT
ejpam-2515	405	7	j	j	PROPN
ejpam-2515	405	8	chavlina	chavlina	PROPN
ejpam-2515	405	9	.	.	PUNCT
ejpam-2515	406	1	commutative	commutative	ADJ
ejpam-2515	406	2	hypergroups	hypergroup	NOUN
ejpam-2515	406	3	in	in	ADP
ejpam-2515	406	4	the	the	DET
ejpam-2515	406	5	sense	sense	NOUN
ejpam-2515	406	6	of	of	ADP
ejpam-2515	406	7	marty	marty	PROPN
ejpam-2515	406	8	and	and	CCONJ
ejpam-2515	406	9	ordered	order	VERB
ejpam-2515	406	10	sets	set	NOUN
ejpam-2515	406	11	.	.	PUNCT
ejpam-2515	407	1	in	in	ADP
ejpam-2515	407	2	i	i	PROPN
ejpam-2515	407	3	chajada	chajada	PROPN
ejpam-2515	407	4	,	,	PUNCT
ejpam-2515	407	5	r	r	NOUN
ejpam-2515	407	6	halas	hala	NOUN
ejpam-2515	407	7	,	,	PUNCT
ejpam-2515	407	8	and	and	CCONJ
ejpam-2515	407	9	f	f	PROPN
ejpam-2515	407	10	krutsky	krutsky	NOUN
ejpam-2515	407	11	,	,	PUNCT
ejpam-2515	407	12	editors	editor	NOUN
ejpam-2515	407	13	,	,	PUNCT
ejpam-2515	407	14	proceedings	proceeding	NOUN
ejpam-2515	407	15	of	of	ADP
ejpam-2515	407	16	the	the	DET
ejpam-2515	407	17	summer	summer	NOUN
ejpam-2515	407	18	school	school	NOUN
ejpam-2515	407	19	on	on	ADP
ejpam-2515	407	20	general	general	ADJ
ejpam-2515	407	21	algebra	algebra	NOUN
ejpam-2515	407	22	and	and	CCONJ
ejpam-2515	407	23	ordered	order	VERB
ejpam-2515	407	24	sets	set	NOUN
ejpam-2515	407	25	,	,	PUNCT
ejpam-2515	407	26	pages	page	NOUN
ejpam-2515	407	27	19–30	19–30	NUM
ejpam-2515	407	28	,	,	PUNCT
ejpam-2515	407	29	olomouc	olomouc	PROPN
ejpam-2515	407	30	,	,	PUNCT
ejpam-2515	407	31	czech	czech	PROPN
ejpam-2515	407	32	republic	republic	NOUN
ejpam-2515	407	33	,	,	PUNCT
ejpam-2515	407	34	1994	1994	NUM
ejpam-2515	407	35	.	.	PUNCT
ejpam-2515	408	1	verlag	verlag	PROPN
ejpam-2515	408	2	johannes	johannes	PROPN
ejpam-2515	408	3	heyn	heyn	VERB
ejpam-2515	408	4	.	.	PUNCT
ejpam-2515	409	1	[	[	X
ejpam-2515	409	2	2	2	X
ejpam-2515	409	3	]	]	X
ejpam-2515	409	4	p	p	X
ejpam-2515	409	5	corsini	corsini	PROPN
ejpam-2515	409	6	.	.	PUNCT
ejpam-2515	410	1	prolegomena	prolegomenon	NOUN
ejpam-2515	410	2	of	of	ADP
ejpam-2515	410	3	hypergroup	hypergroup	PROPN
ejpam-2515	410	4	theory	theory	PROPN
ejpam-2515	410	5	.	.	PUNCT
ejpam-2515	411	1	aviani	aviani	PROPN
ejpam-2515	411	2	editore	editore	PROPN
ejpam-2515	411	3	,	,	PUNCT
ejpam-2515	411	4	aviani	aviani	PROPN
ejpam-2515	411	5	editore	editore	PROPN
ejpam-2515	411	6	,	,	PUNCT
ejpam-2515	411	7	udine	udine	PROPN
ejpam-2515	411	8	,	,	PUNCT
ejpam-2515	411	9	italy	italy	PROPN
ejpam-2515	411	10	,	,	PUNCT
ejpam-2515	411	11	1993	1993	NUM
ejpam-2515	411	12	.	.	PUNCT
ejpam-2515	412	1	[	[	X
ejpam-2515	412	2	3	3	X
ejpam-2515	412	3	]	]	X
ejpam-2515	412	4	p	p	X
ejpam-2515	412	5	corsini	corsini	PROPN
ejpam-2515	412	6	.	.	PUNCT
ejpam-2515	413	1	hypergraphs	hypergraph	NOUN
ejpam-2515	413	2	and	and	CCONJ
ejpam-2515	413	3	hypergroups	hypergroup	NOUN
ejpam-2515	413	4	.	.	PUNCT
ejpam-2515	414	1	algebra	algebra	PROPN
ejpam-2515	414	2	universalis	universali	VERB
ejpam-2515	414	3	,	,	PUNCT
ejpam-2515	414	4	35(4):548–555	35(4):548–555	NUM
ejpam-2515	414	5	,	,	PUNCT
ejpam-2515	414	6	1996	1996	NUM
ejpam-2515	414	7	.	.	PUNCT
ejpam-2515	415	1	[	[	X
ejpam-2515	415	2	4	4	X
ejpam-2515	415	3	]	]	X
ejpam-2515	415	4	p	p	X
ejpam-2515	415	5	corsini	corsini	PROPN
ejpam-2515	415	6	.	.	PUNCT
ejpam-2515	416	1	binary	binary	ADJ
ejpam-2515	416	2	relations	relation	NOUN
ejpam-2515	416	3	and	and	CCONJ
ejpam-2515	416	4	hypergroupoids	hypergroupoid	NOUN
ejpam-2515	416	5	.	.	PUNCT
ejpam-2515	417	1	italian	italian	ADJ
ejpam-2515	417	2	journal	journal	NOUN
ejpam-2515	417	3	of	of	ADP
ejpam-2515	417	4	pure	pure	ADJ
ejpam-2515	417	5	and	and	CCONJ
ejpam-2515	417	6	applied	applied	ADJ
ejpam-2515	417	7	mathematics	mathematic	NOUN
ejpam-2515	417	8	,	,	PUNCT
ejpam-2515	417	9	7:11–18	7:11–18	NUM
ejpam-2515	417	10	,	,	PUNCT
ejpam-2515	417	11	2000	2000	NUM
ejpam-2515	417	12	.	.	PUNCT
ejpam-2515	418	1	[	[	X
ejpam-2515	418	2	5	5	X
ejpam-2515	418	3	]	]	X
ejpam-2515	418	4	p	p	X
ejpam-2515	418	5	corsini	corsini	NOUN
ejpam-2515	418	6	.	.	PUNCT
ejpam-2515	419	1	on	on	ADP
ejpam-2515	419	2	the	the	DET
ejpam-2515	419	3	hypergroups	hypergroup	NOUN
ejpam-2515	419	4	associated	associate	VERB
ejpam-2515	419	5	with	with	ADP
ejpam-2515	419	6	binary	binary	PROPN
ejpam-2515	419	7	relation	relation	PROPN
ejpam-2515	419	8	.	.	PUNCT
ejpam-2515	420	1	multi	multi	PROPN
ejpam-2515	420	2	valued	value	VERB
ejpam-2515	420	3	logic	logic	NOUN
ejpam-2515	420	4	,	,	PUNCT
ejpam-2515	420	5	5:407	5:407	NUM
ejpam-2515	420	6	–	–	PUNCT
ejpam-2515	420	7	419	419	NUM
ejpam-2515	420	8	,	,	PUNCT
ejpam-2515	420	9	2000	2000	NUM
ejpam-2515	420	10	.	.	PUNCT
ejpam-2515	421	1	[	[	X
ejpam-2515	421	2	6	6	NUM
ejpam-2515	421	3	]	]	PUNCT
ejpam-2515	421	4	p	p	X
ejpam-2515	421	5	corsini	corsini	PROPN
ejpam-2515	421	6	.	.	PUNCT
ejpam-2515	422	1	binary	binary	ADJ
ejpam-2515	422	2	relations	relation	NOUN
ejpam-2515	422	3	,	,	PUNCT
ejpam-2515	422	4	interval	interval	NOUN
ejpam-2515	422	5	structures	structure	NOUN
ejpam-2515	422	6	and	and	CCONJ
ejpam-2515	422	7	join	join	VERB
ejpam-2515	422	8	spaces	space	NOUN
ejpam-2515	422	9	.	.	PUNCT
ejpam-2515	423	1	journal	journal	NOUN
ejpam-2515	423	2	of	of	ADP
ejpam-2515	423	3	applied	apply	VERB
ejpam-2515	423	4	mathematics	mathematic	NOUN
ejpam-2515	423	5	and	and	CCONJ
ejpam-2515	423	6	computing	computing	NOUN
ejpam-2515	423	7	,	,	PUNCT
ejpam-2515	423	8	10(1	10(1	NUM
ejpam-2515	423	9	-	-	SYM
ejpam-2515	423	10	2):209–216	2):209–216	NUM
ejpam-2515	423	11	,	,	PUNCT
ejpam-2515	423	12	2002	2002	NUM
ejpam-2515	423	13	.	.	PUNCT
ejpam-2515	424	1	[	[	X
ejpam-2515	424	2	7	7	X
ejpam-2515	424	3	]	]	X
ejpam-2515	424	4	p	p	X
ejpam-2515	424	5	corsini	corsini	NOUN
ejpam-2515	424	6	and	and	CCONJ
ejpam-2515	424	7	v	v	ADP
ejpam-2515	424	8	leoreanu	leoreanu	NOUN
ejpam-2515	424	9	.	.	PUNCT
ejpam-2515	425	1	hypergroups	hypergroup	NOUN
ejpam-2515	425	2	and	and	CCONJ
ejpam-2515	425	3	binary	binary	ADJ
ejpam-2515	425	4	relations	relation	NOUN
ejpam-2515	425	5	.	.	PUNCT
ejpam-2515	426	1	algebra	algebra	PROPN
ejpam-2515	426	2	universalis	universali	VERB
ejpam-2515	426	3	,	,	PUNCT
ejpam-2515	426	4	43(4):321–330	43(4):321–330	NOUN
ejpam-2515	426	5	,	,	PUNCT
ejpam-2515	426	6	2000	2000	NUM
ejpam-2515	426	7	.	.	PUNCT
ejpam-2515	427	1	[	[	X
ejpam-2515	427	2	8	8	X
ejpam-2515	427	3	]	]	X
ejpam-2515	427	4	p	p	X
ejpam-2515	427	5	corsini	corsini	NOUN
ejpam-2515	427	6	and	and	CCONJ
ejpam-2515	427	7	v	v	ADP
ejpam-2515	427	8	leoreanu	leoreanu	NOUN
ejpam-2515	427	9	.	.	PUNCT
ejpam-2515	428	1	applications	application	NOUN
ejpam-2515	428	2	of	of	ADP
ejpam-2515	428	3	hyperstructure	hyperstructure	NOUN
ejpam-2515	428	4	theory	theory	PROPN
ejpam-2515	428	5	.	.	PUNCT
ejpam-2515	429	1	in	in	ADP
ejpam-2515	429	2	jeno	jeno	PROPN
ejpam-2515	429	3	szep	szep	PROPN
ejpam-2515	429	4	,	,	PUNCT
ejpam-2515	429	5	editor	editor	NOUN
ejpam-2515	429	6	,	,	PUNCT
ejpam-2515	429	7	advances	advance	NOUN
ejpam-2515	429	8	in	in	ADP
ejpam-2515	429	9	mathematics	mathematic	NOUN
ejpam-2515	429	10	,	,	PUNCT
ejpam-2515	429	11	pages	page	NOUN
ejpam-2515	429	12	1–20	1–20	PROPN
ejpam-2515	429	13	.	.	PUNCT
ejpam-2515	430	1	kluwer	kluwer	PROPN
ejpam-2515	430	2	academic	academic	ADJ
ejpam-2515	430	3	publishers	publisher	NOUN
ejpam-2515	430	4	,	,	PUNCT
ejpam-2515	430	5	dordrecht	dordrecht	PROPN
ejpam-2515	430	6	,	,	PUNCT
ejpam-2515	430	7	2003	2003	NUM
ejpam-2515	430	8	.	.	PUNCT
ejpam-2515	431	1	[	[	X
ejpam-2515	431	2	9	9	NUM
ejpam-2515	431	3	]	]	X
ejpam-2515	431	4	i	i	PRON
ejpam-2515	431	5	cristea	cristea	NOUN
ejpam-2515	431	6	.	.	PUNCT
ejpam-2515	432	1	several	several	ADJ
ejpam-2515	432	2	aspects	aspect	NOUN
ejpam-2515	432	3	on	on	ADP
ejpam-2515	432	4	the	the	DET
ejpam-2515	432	5	hypergroups	hypergroup	NOUN
ejpam-2515	432	6	associated	associate	VERB
ejpam-2515	432	7	with	with	ADP
ejpam-2515	432	8	n	n	CCONJ
ejpam-2515	432	9	-	-	PUNCT
ejpam-2515	432	10	ary	ary	PROPN
ejpam-2515	432	11	relation	relation	NOUN
ejpam-2515	432	12	.	.	PUNCT
ejpam-2515	433	1	ovidius	ovidius	PROPN
ejpam-2515	433	2	constanta	constanta	PROPN
ejpam-2515	433	3	,	,	PUNCT
ejpam-2515	433	4	series	series	NOUN
ejpam-2515	433	5	maths	math	NOUN
ejpam-2515	433	6	,	,	PUNCT
ejpam-2515	433	7	7(3):90–110	7(3):90–110	NUM
ejpam-2515	433	8	,	,	PUNCT
ejpam-2515	433	9	2009	2009	NUM
ejpam-2515	433	10	.	.	PUNCT
ejpam-2515	434	1	[	[	X
ejpam-2515	434	2	10	10	NUM
ejpam-2515	434	3	]	]	X
ejpam-2515	434	4	i	i	PRON
ejpam-2515	434	5	cristea	cristea	VERB
ejpam-2515	434	6	and	and	CCONJ
ejpam-2515	434	7	m	m	PROPN
ejpam-2515	434	8	ştefanescu	ştefanescu	PROPN
ejpam-2515	434	9	.	.	PUNCT
ejpam-2515	435	1	binary	binary	ADJ
ejpam-2515	435	2	relations	relation	NOUN
ejpam-2515	435	3	and	and	CCONJ
ejpam-2515	435	4	reduced	reduced	ADJ
ejpam-2515	435	5	hypergroups	hypergroup	NOUN
ejpam-2515	435	6	.	.	PUNCT
ejpam-2515	436	1	discrete	discrete	ADJ
ejpam-2515	436	2	maths	math	NOUN
ejpam-2515	436	3	,	,	PUNCT
ejpam-2515	436	4	308(16):3537–3544	308(16):3537–3544	NUM
ejpam-2515	436	5	,	,	PUNCT
ejpam-2515	436	6	2008	2008	NUM
ejpam-2515	436	7	.	.	PUNCT
ejpam-2515	437	1	[	[	X
ejpam-2515	437	2	11	11	NUM
ejpam-2515	437	3	]	]	X
ejpam-2515	437	4	i	i	PRON
ejpam-2515	437	5	cristea	cristea	VERB
ejpam-2515	437	6	and	and	CCONJ
ejpam-2515	437	7	m	m	PROPN
ejpam-2515	437	8	ştefanescu	ştefanescu	NOUN
ejpam-2515	437	9	.	.	PUNCT
ejpam-2515	438	1	hypergroups	hypergroup	NOUN
ejpam-2515	438	2	and	and	CCONJ
ejpam-2515	438	3	n	n	CCONJ
ejpam-2515	438	4	-	-	PUNCT
ejpam-2515	438	5	ary	ary	PROPN
ejpam-2515	438	6	relations	relation	NOUN
ejpam-2515	438	7	.	.	PUNCT
ejpam-2515	439	1	european	european	PROPN
ejpam-2515	439	2	journal	journal	PROPN
ejpam-2515	439	3	of	of	ADP
ejpam-2515	439	4	combinatorics	combinatoric	NOUN
ejpam-2515	439	5	,	,	PUNCT
ejpam-2515	439	6	31(3):780	31(3):780	NUM
ejpam-2515	439	7	–	–	PUNCT
ejpam-2515	439	8	789	789	NUM
ejpam-2515	439	9	,	,	PUNCT
ejpam-2515	439	10	2010	2010	NUM
ejpam-2515	439	11	.	.	PUNCT
ejpam-2515	440	1	[	[	X
ejpam-2515	440	2	12	12	NUM
ejpam-2515	440	3	]	]	X
ejpam-2515	440	4	m	m	VERB
ejpam-2515	440	5	ştefanescu	ştefanescu	NOUN
ejpam-2515	440	6	.	.	PUNCT
ejpam-2515	441	1	some	some	DET
ejpam-2515	441	2	interpretations	interpretation	NOUN
ejpam-2515	441	3	of	of	ADP
ejpam-2515	441	4	hypergroups	hypergroup	NOUN
ejpam-2515	441	5	.	.	PUNCT
ejpam-2515	442	1	bulletin	bulletin	NOUN
ejpam-2515	442	2	of	of	ADP
ejpam-2515	442	3	mathematical	mathematical	ADJ
ejpam-2515	442	4	society	society	NOUN
ejpam-2515	442	5	:	:	PUNCT
ejpam-2515	442	6	science	science	NOUN
ejpam-2515	442	7	and	and	CCONJ
ejpam-2515	442	8	maths	maths	PROPN
ejpam-2515	442	9	roumanie	roumanie	PROPN
ejpam-2515	442	10	tome	tome	PROPN
ejpam-2515	442	11	,	,	PUNCT
ejpam-2515	442	12	1(97	1(97	NUM
ejpam-2515	442	13	no	no	NOUN
ejpam-2515	442	14	.	.	PUNCT
ejpam-2515	443	1	1):99–104	1):99–104	NUM
ejpam-2515	443	2	,	,	PUNCT
ejpam-2515	443	3	2006	2006	NUM
ejpam-2515	443	4	.	.	PUNCT
ejpam-2515	444	1	[	[	X
ejpam-2515	444	2	13	13	NUM
ejpam-2515	444	3	]	]	SYM
ejpam-2515	444	4	b	b	NOUN
ejpam-2515	444	5	davaaz	davaaz	NOUN
ejpam-2515	444	6	and	and	CCONJ
ejpam-2515	444	7	t	t	NOUN
ejpam-2515	444	8	vougiouklis	vougioukli	VERB
ejpam-2515	444	9	.	.	PUNCT
ejpam-2515	445	1	n	n	X
ejpam-2515	445	2	-	-	PUNCT
ejpam-2515	445	3	ary	ary	PROPN
ejpam-2515	445	4	hypergroups	hypergroup	NOUN
ejpam-2515	445	5	.	.	PUNCT
ejpam-2515	446	1	iranian	iranian	ADJ
ejpam-2515	446	2	journal	journal	PROPN
ejpam-2515	446	3	of	of	ADP
ejpam-2515	446	4	science	science	NOUN
ejpam-2515	446	5	and	and	CCONJ
ejpam-2515	446	6	technology	technology	NOUN
ejpam-2515	446	7	transaction	transaction	NOUN
ejpam-2515	446	8	,	,	PUNCT
ejpam-2515	446	9	30(2):165–174	30(2):165–174	PROPN
ejpam-2515	446	10	,	,	PUNCT
ejpam-2515	446	11	2006	2006	NUM
ejpam-2515	446	12	.	.	PUNCT
ejpam-2515	447	1	[	[	X
ejpam-2515	447	2	14	14	NUM
ejpam-2515	447	3	]	]	SYM
ejpam-2515	447	4	s	s	VERB
ejpam-2515	447	5	govindarajan	govindarajan	NOUN
ejpam-2515	447	6	and	and	CCONJ
ejpam-2515	447	7	g	g	PROPN
ejpam-2515	447	8	ramesh	ramesh	PROPN
ejpam-2515	447	9	.	.	PUNCT
ejpam-2515	448	1	on	on	ADP
ejpam-2515	448	2	the	the	DET
ejpam-2515	448	3	hypergroups	hypergroup	NOUN
ejpam-2515	448	4	associated	associate	VERB
ejpam-2515	448	5	with	with	ADP
ejpam-2515	448	6	n	n	CCONJ
ejpam-2515	448	7	-	-	PUNCT
ejpam-2515	448	8	ary	ary	PROPN
ejpam-2515	448	9	relations	relation	NOUN
ejpam-2515	448	10	.	.	PUNCT
ejpam-2515	449	1	journal	journal	PROPN
ejpam-2515	449	2	of	of	ADP
ejpam-2515	449	3	informatics	informatics	PROPN
ejpam-2515	449	4	and	and	CCONJ
ejpam-2515	449	5	mathematical	mathematical	ADJ
ejpam-2515	449	6	sciences	science	NOUN
ejpam-2515	449	7	,	,	PUNCT
ejpam-2515	449	8	6(2):61–76	6(2):61–76	NUM
ejpam-2515	449	9	,	,	PUNCT
ejpam-2515	449	10	2014	2014	NUM
ejpam-2515	449	11	.	.	PUNCT
ejpam-2515	450	1	[	[	X
ejpam-2515	450	2	15	15	NUM
ejpam-2515	450	3	]	]	X
ejpam-2515	450	4	s	s	VERB
ejpam-2515	450	5	govindarajan	govindarajan	NOUN
ejpam-2515	450	6	and	and	CCONJ
ejpam-2515	450	7	g	g	PROPN
ejpam-2515	450	8	ramesh	ramesh	PROPN
ejpam-2515	450	9	.	.	PUNCT
ejpam-2515	451	1	a	a	DET
ejpam-2515	451	2	generalization	generalization	NOUN
ejpam-2515	451	3	of	of	ADP
ejpam-2515	451	4	corsini	corsini	PROPN
ejpam-2515	451	5	’s	’s	PART
ejpam-2515	451	6	hyperoperation	hyperoperation	NOUN
ejpam-2515	451	7	to	to	ADP
ejpam-2515	451	8	the	the	DET
ejpam-2515	451	9	case	case	NOUN
ejpam-2515	451	10	of	of	ADP
ejpam-2515	451	11	n	n	CCONJ
ejpam-2515	451	12	-	-	PUNCT
ejpam-2515	451	13	ary	ary	PROPN
ejpam-2515	451	14	relation	relation	NOUN
ejpam-2515	451	15	.	.	PUNCT
ejpam-2515	452	1	mathematics	mathematic	NOUN
ejpam-2515	452	2	applied	apply	VERB
ejpam-2515	452	3	in	in	ADP
ejpam-2515	452	4	science	science	NOUN
ejpam-2515	452	5	and	and	CCONJ
ejpam-2515	452	6	technology	technology	NOUN
ejpam-2515	452	7	,	,	PUNCT
ejpam-2515	452	8	7(1):7–26	7(1):7–26	NUM
ejpam-2515	452	9	,	,	PUNCT
ejpam-2515	452	10	2015	2015	NUM
ejpam-2515	452	11	.	.	PUNCT
ejpam-2515	453	1	[	[	X
ejpam-2515	453	2	16	16	NUM
ejpam-2515	453	3	]	]	SYM
ejpam-2515	453	4	s	s	VERB
ejpam-2515	453	5	govindarajan	govindarajan	NOUN
ejpam-2515	453	6	and	and	CCONJ
ejpam-2515	453	7	g	g	PROPN
ejpam-2515	453	8	ramesh	ramesh	PROPN
ejpam-2515	453	9	.	.	PUNCT
ejpam-2515	454	1	hypergroups	hypergroup	NOUN
ejpam-2515	454	2	associated	associate	VERB
ejpam-2515	454	3	with	with	ADP
ejpam-2515	454	4	union	union	NOUN
ejpam-2515	454	5	and	and	CCONJ
ejpam-2515	454	6	intersection	intersection	NOUN
ejpam-2515	454	7	of	of	ADP
ejpam-2515	454	8	two	two	NUM
ejpam-2515	454	9	n	n	CCONJ
ejpam-2515	454	10	-	-	PUNCT
ejpam-2515	454	11	ary	ary	PROPN
ejpam-2515	454	12	relations	relation	NOUN
ejpam-2515	454	13	.	.	PUNCT
ejpam-2515	455	1	international	international	ADJ
ejpam-2515	455	2	journal	journal	PROPN
ejpam-2515	455	3	of	of	ADP
ejpam-2515	455	4	algebra	algebra	PROPN
ejpam-2515	455	5	and	and	CCONJ
ejpam-2515	455	6	statistics	statistic	NOUN
ejpam-2515	455	7	,	,	PUNCT
ejpam-2515	455	8	4(1):7–19	4(1):7–19	NUM
ejpam-2515	455	9	,	,	PUNCT
ejpam-2515	455	10	2015	2015	NUM
ejpam-2515	455	11	.	.	PUNCT
ejpam-2515	456	1	references	reference	NOUN
ejpam-2515	456	2	382	382	NUM
ejpam-2515	457	1	[	[	X
ejpam-2515	457	2	17	17	NUM
ejpam-2515	457	3	]	]	X
ejpam-2515	457	4	f	f	PROPN
ejpam-2515	457	5	marty	marty	PROPN
ejpam-2515	457	6	.	.	PUNCT
ejpam-2515	458	1	sur	sur	PROPN
ejpam-2515	458	2	une	une	PROPN
ejpam-2515	458	3	generalization	generalization	PROPN
ejpam-2515	458	4	de	de	X
ejpam-2515	458	5	la	la	PROPN
ejpam-2515	458	6	notion	notion	NOUN
ejpam-2515	458	7	de	de	PROPN
ejpam-2515	458	8	group	group	NOUN
ejpam-2515	458	9	.	.	PUNCT
ejpam-2515	459	1	in	in	ADP
ejpam-2515	459	2	f.	f.	PROPN
ejpam-2515	459	3	marty	marty	PROPN
ejpam-2515	459	4	,	,	PUNCT
ejpam-2515	459	5	editor	editor	NOUN
ejpam-2515	459	6	,	,	PUNCT
ejpam-2515	459	7	eight	eight	NUM
ejpam-2515	459	8	congress	congress	PROPN
ejpam-2515	459	9	mathematics	mathematic	NOUN
ejpam-2515	459	10	scandenaves	scandenave	NOUN
ejpam-2515	459	11	,	,	PUNCT
ejpam-2515	459	12	stockholm	stockholm	PROPN
ejpam-2515	459	13	,	,	PUNCT
ejpam-2515	459	14	pages	page	NOUN
ejpam-2515	459	15	45–49	45–49	PROPN
ejpam-2515	459	16	,	,	PUNCT
ejpam-2515	459	17	sweden	sweden	PROPN
ejpam-2515	459	18	,	,	PUNCT
ejpam-2515	459	19	1935	1935	NUM
ejpam-2515	459	20	.	.	PUNCT
ejpam-2515	460	1	lund	lund	PROPN
ejpam-2515	460	2	:	:	PUNCT
ejpam-2515	460	3	h	h	PROPN
ejpam-2515	460	4	.	.	PUNCT
ejpam-2515	461	1	ohlsson	ohlsson	ADJ
ejpam-2515	461	2	botryckeri	botryckeri	NOUN
ejpam-2515	461	3	.	.	PUNCT
ejpam-2515	462	1	[	[	X
ejpam-2515	462	2	18	18	NUM
ejpam-2515	462	3	]	]	X
ejpam-2515	462	4	j	j	PROPN
ejpam-2515	462	5	nieminen	nieminen	PROPN
ejpam-2515	462	6	.	.	PUNCT
ejpam-2515	463	1	join	join	VERB
ejpam-2515	463	2	space	space	NOUN
ejpam-2515	463	3	graphs	graph	NOUN
ejpam-2515	463	4	.	.	PUNCT
ejpam-2515	464	1	journal	journal	NOUN
ejpam-2515	464	2	of	of	ADP
ejpam-2515	464	3	geometry	geometry	NOUN
ejpam-2515	464	4	,	,	PUNCT
ejpam-2515	464	5	33(1):99–103	33(1):99–103	NUM
ejpam-2515	464	6	,	,	PUNCT
ejpam-2515	464	7	1988	1988	NUM
ejpam-2515	464	8	.	.	PUNCT
ejpam-2515	465	1	[	[	X
ejpam-2515	465	2	19	19	NUM
ejpam-2515	465	3	]	]	PUNCT
ejpam-2515	465	4	w	w	PROPN
ejpam-2515	465	5	prenowitz	prenowitz	PROPN
ejpam-2515	465	6	.	.	PUNCT
ejpam-2515	466	1	spherical	spherical	ADJ
ejpam-2515	466	2	geometries	geometry	NOUN
ejpam-2515	466	3	and	and	CCONJ
ejpam-2515	466	4	multigroups	multigroup	NOUN
ejpam-2515	466	5	.	.	PUNCT
ejpam-2515	467	1	canadian	canadian	ADJ
ejpam-2515	467	2	journal	journal	PROPN
ejpam-2515	467	3	of	of	ADP
ejpam-2515	467	4	mathematics	mathematic	NOUN
ejpam-2515	467	5	,	,	PUNCT
ejpam-2515	467	6	2:100–119	2:100–119	NUM
ejpam-2515	467	7	,	,	PUNCT
ejpam-2515	467	8	1950	1950	NUM
ejpam-2515	467	9	.	.	PUNCT
ejpam-2515	468	1	[	[	X
ejpam-2515	468	2	20	20	NUM
ejpam-2515	468	3	]	]	X
ejpam-2515	468	4	i	i	PRON
ejpam-2515	468	5	g	g	PROPN
ejpam-2515	468	6	rosenberg	rosenberg	PROPN
ejpam-2515	468	7	.	.	PUNCT
ejpam-2515	469	1	hypergroups	hypergroup	NOUN
ejpam-2515	469	2	and	and	CCONJ
ejpam-2515	469	3	join	join	VERB
ejpam-2515	469	4	spaces	space	NOUN
ejpam-2515	469	5	determined	determine	VERB
ejpam-2515	469	6	by	by	ADP
ejpam-2515	469	7	relations	relation	NOUN
ejpam-2515	469	8	.	.	PUNCT
ejpam-2515	470	1	italian	italian	ADJ
ejpam-2515	470	2	journal	journal	NOUN
ejpam-2515	470	3	of	of	ADP
ejpam-2515	470	4	pure	pure	ADJ
ejpam-2515	470	5	and	and	CCONJ
ejpam-2515	470	6	applied	applied	ADJ
ejpam-2515	470	7	mathematics	mathematic	NOUN
ejpam-2515	470	8	,	,	PUNCT
ejpam-2515	470	9	4(4):93–101	4(4):93–101	NOUN
ejpam-2515	470	10	,	,	PUNCT
ejpam-2515	470	11	1998	1998	NUM
ejpam-2515	470	12	.	.	PUNCT
ejpam-2515	471	1	[	[	X
ejpam-2515	471	2	21	21	NUM
ejpam-2515	471	3	]	]	X
ejpam-2515	471	4	t	t	PROPN
ejpam-2515	471	5	vougiouklis	vougioukli	VERB
ejpam-2515	471	6	.	.	PUNCT
ejpam-2515	472	1	hyperstructures	hyperstructure	NOUN
ejpam-2515	472	2	and	and	CCONJ
ejpam-2515	472	3	their	their	PRON
ejpam-2515	472	4	representations	representation	NOUN
ejpam-2515	472	5	.	.	PUNCT
ejpam-2515	473	1	hadronic	hadronic	ADJ
ejpam-2515	473	2	press	press	PROPN
ejpam-2515	473	3	,	,	PUNCT
ejpam-2515	473	4	inc	inc	PROPN
ejpam-2515	473	5	.	.	PROPN
ejpam-2515	473	6	,	,	PUNCT
ejpam-2515	473	7	palm	palm	NOUN
ejpam-2515	473	8	harbor	harbor	PROPN
ejpam-2515	473	9	,	,	PUNCT
ejpam-2515	473	10	fl	fl	PROPN
ejpam-2515	473	11	,	,	PUNCT
ejpam-2515	473	12	1994	1994	NUM
ejpam-2515	473	13	.	.	PUNCT